Therefore, the correct answer is: The range is the best measure of variability, and it equals 78.
What is range?Range is a measure of variability that represents the difference between the maximum and minimum values in a dataset. It gives an indication of how spread out the data is. To find the range of a dataset, you simply subtract the minimum value from the maximum value. Range is often used as a quick and simple measure of variability, but it can be sensitive to outliers and extreme values.
Here,
1. For question 5, the appropriate measure of variability for the given data set is the range, which is the difference between the maximum value and the minimum value in the data set.
To find the maximum and minimum values from the given stem-and-leaf plot, we can look at the highest and lowest digits in each row. The highest value is 83 and the lowest value is 5, so the range is:
Range = 83 - 5 = 78
2. For question 6, the appropriate measure of center to represent the data in the given line plot is the median, because the data is skewed to the right and there are outliers present. The median is less sensitive to outliers than the mean.
Therefore, the correct answer is: The median is the best measure of center because there are outliers present.
To know more about range,
https://brainly.com/question/16664109
#SPJ1
Triangle ABC has vertices at A(−4, 3), B(0, 5), and C(−2, 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down.
A′(−4, −1), B′(0, 1), C′(−2, −4)
A′(−4, 7), B′(0, 9), C′(−2, 4)
A′(0, 3), B′(4, 4), C′(3, 0)
A′(−8, 7), B′(−4, 9), C′(−6, 4)
The coordinates of the vertices for the image if the preimage is translated 4 units down are A′(-4, -1), B′(0, 1), C′(-2, -4).
What is meant by preimage?
In geometry, a preimage is the original figure or shape before any transformation is applied. It is the initial configuration of the object that is being transformed. For example, if we have a square and we rotate it by 90 degrees, the original square is the preimage and the resulting figure after the rotation is the image.
To translate the preimage 4 units down, we need to subtract 4 from the y-coordinates of all vertices. Therefore, the coordinates of the image vertices are:
A′(-4, 3-4) = (-4, -1)
B′(0, 5-4) = (0, 1)
C′(-2, 0-4) = (-2, -4)
Therefore, the vertices of the image triangle are A′(-4, -1), B′(0, 1), and C′(-2, -4).
So, the correct option is: A′(-4, -1), B′(0, 1), C′(-2, -4).
To learn more about preimage visit:
https://brainly.com/question/30093252
#SPJ1
Rita started the day with R apps. then she deleted 5 apps and still had twice the amount of Cora (36). write an equation that represents the number of apps both girls have
Answer:
Step-by-step explanation:lllllLet's start by using "R" to represent the number of apps that Rita started with, and "C" to represent the number of apps that Cora started with.
We know that Rita deleted 5 apps, so she would have (R-5) apps remaining. And we know that she still had twice the amount of Cora, which is 36.
So we can write the equation:
R-5 = 2C
And we also know that Cora had 36 apps, so we can substitute that value in for C:
R-5 = 2(36)
Simplifying the right side:
R-5 = 72
Finally, we can solve for R by adding 5 to both sides:
R = 77
So Rita started with 77 apps, and Cora started with 36 apps. We can check that Rita deleted 5 and had twice as many as Cora by plugging our values into the original equation:
77 - 5 = 72
2(36) = 72
Both sides are equal, so our solution is correct.
a high school baseball player has a 0.253 batting average. in one game, he gets 8 at bats. what is the probability he will get at least 6 hits in the game?
The probability of a high school baseball player getting at least 6 hits in one game, given a 0.253 batting average, when he gets 8 at-bats, is 0.0197 or approximately 2%.
Given, the high school baseball player's batting average is 0.253, which means in 100 times he hits the ball, he will make 25.3 hits on average. We need to find the probability of getting at least 6 hits in a game when he gets 8 at-bats.
We will calculate the probability using the Binomial Probability formula. Here, the number of trials is 8, and the probability of success is 0.253. We need to find the probability of getting at least 6 hits.
P(X≥6) = 1 - P(X<6)
P(X<6) = ∑P(X=i), i=0 to 5
We can use the Binomial Probability Table to find these probabilities or use the Binomial Probability formula.
P(X<6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)
= C(8,0) (0.253)^0 (1 - 0.253)^8 + C(8,1) (0.253)^1 (1 - 0.253)^7 + C(8,2) (0.253)^2 (1 - 0.253)^6 + C(8,3) (0.253)^3 (1 - 0.253)^5 + C(8,4) (0.253)^4 (1 - 0.253)^4 + C(8,5) (0.253)^5 (1 - 0.253)^3
≈ 0.9799
Therefore, P(X≥6) = 1 - 0.9799
= 0.0201 or approximately 2%.
Hence, approximately 0.0197 or 1.97% is the probability of a high school baseball player, who has a batting average of 0.253, obtaining at least 6 hits when given 8 at-bats during a single game.
To know more about probability refer here:
https://brainly.com/question/1596693#
#SPJ11
Find the x-intercept of 3 tan(3x) over the interval (pi/6,3pi/6)
Express your answer in terms of pi.
The x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:
x = π/3 and x = 2π/3
What is function ?
A function is a mathematical object that takes one or more inputs, called the arguments or variables, and produces a unique output. The output is determined by a set of rules that specify how the function operates on the inputs. In other words, a function is a relationship between inputs and outputs.
Functions are typically denoted by a symbol or a name, such as f(x) or g(t). The input is usually represented by a variable, such as x or t, while the output is represented by the function value, such as f(x) or g(t).
Functions are used extensively in mathematics, science, engineering, and many other fields. They provide a way to model and analyze real-world phenomena, and they are essential tools for solving many problems in these fields. Examples of functions include polynomial functions, exponential functions, trigonometric functions, and logarithmic functions.
To find the x-intercept of the function 3 tan(3x) over the given interval, we need to find the values of x where the function equals zero.
Let's first simplify the function:
3 tan(3x) = 0
tan(3x) = 0
We know that tan(π/2) is undefined and that tan(π) = 0. Since the period of the tangent function is π, we can say that:
tan(3x) = 0 --> 3x = nπ for n ∈ ℤ
Now we solve for x:
3x = nπ
x = nπ/3
Since the interval is (π/6, 3π/6), we need to find the values of x that satisfy:
π/6 < x < 3π/6
π/6 < nπ/3 < 3π/6
1/2 < n < 3/2
So the values of x that satisfy the given condition are:
x = π/3 and x = 2π/3
Therefore, the x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:
x = π/3 and x = 2π/3
Expressed in terms of π, the x-intercepts are:
π/3π and 2π/3π, which simplify to:
x = 1/3 and x = 2/3.
To know more about Trigonometry visit :-
https://brainly.com/question/13729598
#SPJ1
A. ASA
B. SAS
C. HL
D. none of the above
Therefore , the solution of the given problem of congruence comes out to be the response is option A. ASA.
Congruence: What is it?Two angles are spoken to be congruent when their respective shapes have the same dimensions. Similar to that, if the sides of one form are now exactly the same length as the edges of another figure, the edges are congruent.
Here,
We can identify the sort of congruence between the two triangles based on the provided figure.
We can see that segment AC and segment DF are the only pair of congruent sides shared by the two rectangles.
Additionally, angle A and angle D as well as angle C and angle F are two sets of congruent angles.
In light of this,
we can use the Angle-Side-Angle (ASA)
congruence criterion, which says that two triangles are congruent if they have two pairs of congruent angles and a congruent side between them.
Therefore, the response is A. ASA.
To know more about congruence , visit:
https://brainly.com/question/7888063
#SPJ1
130.25.122.63mario's pizzeria bakes olive pieces in the outer crust of its 20-inch (diameter) pizza. there is at least one olive piece per inch of crust. how many olive pieces will you get in one slice of pizza? assume the pizza is cut into eight slices.
By using circumference of circle, we find that In one slice of pizza you will get about 8 olive pieces from Mario's Pizzeria.
The circumference of circle of a 20-inch diameter pizza can be calculated as follows:
Circumference = π × diameter
Circumference = 3.14 × 20
Circumference = 62.8 inches
If there is at least one olive piece per inch of crust, then there will be 62.8 olive pieces on the outer crust of the entire pizza.
If the pizza is cut into eight slices, each slice will have 1/8th of the total circumference of the pizza. Therefore, each slice will have:
62.8 inches ÷ 8 slices = 7.85 inches of outer crust
Since there is at least one olive piece per inch of crust, each slice will have approximately 8 olive pieces on the outer crust.
Therefore, you can expect to get about 8 olive pieces in one slice of pizza from Mario's Pizzeria.
To know more about circumference of circle:
https://brainly.com/question/26605972
#SPJ4
a 3 didget whole number thats divisBle by 6,9,4
gtrgrghtrhthjAnswer:
Step-by-step explanation:
g
Answer:
36
Step-by-step explanation:
4*9=36
9*4=36
6*5=36
Help meee plssssss!!!!!!11
Write an explicit formula that can be used to find the number of bacteria cells after each generation. Then use the formula to find how many cells there are after 10 generations.
Answer:
N = N0 x 2^n
Step-by-step explanation:
The formula for calculating the number of bacteria cells after n generations is N = N0 x 2^n, where N is the total number of cells after n generations, N0 is the initial number of cells, and 2^n represents the number of times the population doubles after n generations. Assuming an initial population of 100 cells, there will be approximately 102,400 cells after 10 generations.
Answer:
The explicit formula for the number of bacteria cells after each generation can be written as:
N = N0 * r^n
Where:
N is the number of bacteria cells after n generations
N0 is the initial number of bacteria cells (at n=0)
r is the growth rate (how many new cells are produced per existing cell)
Assuming that each bacteria cell doubles in number with each generation (i.e. r=2), the formula can be simplified to:
N = N0 * 2^n
To find the number of cells after 10 generations, we can substitute n=10 into the formula:
N = N0 * 2^10
Since we don't have a specific value for N0, we can't find the exact number of cells after 10 generations. However, we can make some assumptions. For example, if we assume that there are initially 100 bacteria cells (N0=100), we can calculate:
N = 100 * 2^10 = 102,400
So, if each bacteria cell doubles in number with each generation and there were initially 100 cells, there will be 102,400 cells after 10 generations.
please thank me by marking my answer as brainlest!
a random sample is normally distributed. if all values in the sample and all values in the population are multiplied by 2, what is the impact on cohen's d?
Multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d.
The impact of multiplying all values in a normally distributed random sample and population by 2 on Cohen's d is an increase in effect size. Cohen's d measures the degree of difference between two sets of scores, calculated by dividing the difference between the two means by the pooled standard deviation. Therefore, when values are multiplied by 2, the means increase, leading to an increase in effect size as measured by Cohen's d.
In addition, multiplying values by 2 also increases the magnitude of the standard deviation, which is a measure of spread. When the standard deviation is larger, it requires a larger mean difference for Cohen's d to register a significant effect. Therefore, by increasing the standard deviation, the effect size measure will increase.
To summarize, multiplying values by 2 in a normally distributed random sample and population increases the effect size as measured by Cohen's d. This is because multiplying values by 2 increases both the mean and the standard deviation, which results in a larger mean difference and a larger standard deviation, respectively. Consequently, the effect size measure increases.
See more about normally distributed at: https://brainly.com/question/2579706
#SPJ11
a sample of 116 motels is selected from a large urban area and the price for a night of lodging for a single room was determined for each motel. the mean rate is computed to be $91 and the standard deviation is $14 . one motel charged $55 per night which is the 15th percentile. another motel charged $118 per night which is the 75th percentile. step 2 of 5: how many motels charged $118 or less per night? round your answer to the nearest integer.
By standard deviation, The required number of motels that charged 118 or less per night is 87 (approx).
We are to determine how many motels charged 118 or less per night. We can use the normal distribution table to find out the z-score for the 75th percentile. We can then use this z-score to find out the price of lodging per night for the 118th percentile.
The formula to calculate the z-score is:[tex]z=\frac{X-\mu}{\sigma}[/tex], where X is the price of lodging per night, [tex]$\mu$[/tex]is the mean rate, [tex]$\sigma$[/tex] is the standard deviation.
The z-score for the 75th percentile is found using the normal distribution table as: z = 0.67 (approx). For the 75th percentile, the motel charged $118 per night. Therefore, we can write the formula as:[tex]0.67 = \frac{118 - 91}{14}[/tex] Simplifying, we get: [tex]0.67 = \frac{27}{14}[/tex]
Therefore, we can conclude that:118 = 91 + 14 [tex]\times[/tex] 0.67 Or, X = [tex]\mu[/tex] + z[tex]\sigma[/tex]= 91 + 0.67 [tex]\times[/tex] 14 = 100.38. Thus, motels that charged 118 or less per night can be found as follows: [tex]$$P(X \leq 118)[/tex]=[tex]P(Z \leq z)$$$$[/tex] = [tex]P(Z \leq 0.67)$$$$[/tex]= 0.7486.
Hence, the number of motels that charged 118 or less per night is:
0.7486 [tex]\times[/tex]116 = 87.06. Rounding it to the nearest integer, we get: 87 (approx). Therefore, the required number of motels that charged 118 or less per night is 87 (approx).
To know more about standard deviation refer here:
https://brainly.com/question/29088233
#SPJ11
WHAT IS THE ANSWER
I NEED HELP ASAP
Answer: yes, yes, no
Explanation: In order for a figure to be a triangle, the two smallest sides must add up to be larger than the biggest side. The reason why the last one isn't a triangle is because 6+8 EQUALS 14 and is not greater than 14.
Mitchell orders a plain turkey sandwich and a drink for lunch. The drink is $2.95
. Instead he is served the super sandwich with lettuce, tomato, and mayonnaise. The restaurant manager takes 15%
off the price of the sandwich.
Write an equation to determine the original price of Mitchell’s sandwich, x
, if his new bill is $8.86
.
Enter the correct equation in the box.
Answer:
7$
Step-by-step explanation:
✅
A gamer is observing her score, y, as she plays a video game. She currently has 3,200 points and is gaining 200 points for every minute, x, she plays.
Which of the following equations can be used to describe this linear relationship?
A. y = 3,200x − 200
B.y = 3,200x + 200
C. y = 200x − 3,200
D. y = 200x + 3,200
Answer: d
Step-by-step explanation:
the slope is positive 200 because she is gaining 200 points for every minute which is x. 200x or 200 multiplied by x is her slope and her y intercept is 3200
I will give brainliest to whoever gets it right first along with 20 points. ONLY ANSWER IF YOU KNOW IT!!!!
Ms. Leon will have a total of $840 in her savings account by the end of 4 years.
To calculate the total amount that Ms. Leon will have in her account at the end of 4 years with simple interest, we can use the following formula:
A = P(1 + rt)
where:
A = the total amount in the account at the end of the time period
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
t = the time period (in years)
Putting in the given values, we get:
A = 750(1 + 0.03 × 4)
A = 750(1.12)
A = $840
Therefore, at the end of 4 years, Ms. Leon will have a total of $840 in her savings account.
To know more about the simple interest visit:
https://brainly.com/question/25845758?
#SPJ1
jonathan is making chili for a get-together. his recipe calls for 1 1/2 cups of diced tomatoes for every 4 cups of chili. he wants to make 9 cups of chili. how many cups of diced tomatoes should he put in the chili?
2 3/4 cups of diced tomatoes should he put in the chili.
How many glasses should there be?
Simply said, a fraction is a portion of a whole. Mathematically, the number is expressed as a quotient with split numerator and denominator. The numerator and denominator of a simple fraction are both integers.
Tomatoes in cups expressed as a fraction higher than 1.
A mixed fraction is 2 3/4. Because it combines a full number with a fraction, it is known as that.
We must change the mixed fraction into an improper fraction in order to calculate the quantity of cups of tomatoes stated as a fraction greater than 1.
A fraction that has a larger numerator than denominator is said to be improper.
2 3/4 ⇒ ((2*4)+3)/4 ⇒ (8+3)/4 ⇒ 11/4
A fraction that is bigger than one is 11/4.
A fraction with the value 1 is 4/4. Hence, any fraction that has a numerator larger than one and less than four is a fraction. It is 11/4 in this instance.
To know more about denominator, click the below link
https://brainly.com/question/7067665
#SPJ4
what is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?
The probability of having exactly 10 pedestrians crossing from left to right during a 2-minute period is extremely low, at approximately 0.00118%.
We can approach this problem by using the Poisson distribution, which describes the probability of a certain number of events occurring within a given time period, given a known rate of occurrence.
Let X be the number of pedestrians crossing from left to right during a 2-minute period. Since the arrival processes from the left and right sides are independent Poisson processes with rates λL and λR, respectively, we can model X as a Poisson random variable with rate λ = λL + λR = 6.
Therefore, the probability of having exactly k pedestrians crossing from left to right during a 2-minute period is given by the Poisson distribution:
P(X = k) = (e^(-λ) * λ^k) / k!
Now we want to find the probability that in a particular crossing, there are a total of 10 pedestrians crossing from left to right. Let Y be the total number of pedestrians crossing in both directions during a 2-minute period.
Since the arrival processes from the left and right sides are independent, we can model Y as a Poisson random variable with rate 2λ = 12.
Since we know that there are 10 pedestrians crossing from left to right, there must be a total of 10 pedestrians crossing in both directions. Therefore, we want to find the probability that out of the 10 pedestrians, exactly 10 of them are crossing from left to right.
We can use the binomial distribution to calculate this probability. Let Z be the number of pedestrians crossing from left to right out of the 10 pedestrians. Since each pedestrian has an independent probability of crossing from left to right of 1/2, we have:
P(Z = 10) = (10 choose 10) * (1/2)^10
= 1/1024
Therefore, the probability that in a particular crossing, there are a total of 10 pedestrians and they are all crossing from left to right is:
P(X = 10, Y = 10) = P(X = 10) * P(Z = 10)
= (e^(-6) * 6^10 / 10!) * (1/1024)
≈ 0.0000118
Writing this probability in percentage gives = 0.0000118 x 100% = 0.00118%
To learn more about probability click on,
https://brainly.com/question/14937880
#SPJ4
Complete question is:
Pedestrians approach a crossing from the left and right sides following independent Poisson processes with average arrival rates of λL = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a light is flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right or from right to left). Assume that the left and right arrival processes are independent, that the light flashes every T = 2 minutes, and that crossing takes zero time – it is instantaneous.
1. What is the probability that in a particular crossing, there are total 10 pedestrian and they are all crossing from left to right?
Divide. Write the answer in simplest form.
6 and 3/5÷ 3/4
Answer:
44/5
Step-by-step explanation:
6 3/5 ÷ 3/4
6 3/5 = 33/5
33/5 ÷ 3/4 = 33/5 × 4/3 = 132/15 = 44/5
So, the answer is 44/5
Answer:
Step-by-step explanation:
1) Write the equation
[tex]\frac{3}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex] = ?
2) Multiply by the reciprocal of [tex]\frac{3}{4}[/tex]
[tex]\frac{3}{5}[/tex] × [tex]\frac{4}{3}[/tex] =?
3) Cancel out the GCF 3
[tex]\frac{1}{5}[/tex] × 4 =?
4) Solve
[tex]\frac{4}{5}[/tex] or 0.8
solve for x and find it
[tex]\frac{65x-14x+49-4}{14} = 36[/tex]The value of x is 9.
What is inquality?Inequality refers to a situation where there is a significant difference in the distribution of resources, opportunities, and power among individuals or groups in a society. It is a complex social and economic phenomenon that can manifest in various forms such as income inequality, wealth inequality, gender inequality, racial inequality, educational inequality, and healthcare inequality, among others.
Given by the question.
[tex]\frac{9x+7}{2} - \frac{7x-x+2}{7} = 36[/tex]
[tex]\frac{63x+44-14x+2x+4}{14} = 36[/tex]
[tex]\frac{65x-14x+49-4}{14} = 36[/tex]
[tex]51x+45=504\\51x= 459\\x=9[/tex]
To learn more about inquality:
https://brainly.com/question/29072717
#SPJ1
Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails. To the nearest percent, what is the experimental probability of Project A?
Answer:
Step-by-step explanation:
Ms. Sanchez is planning two projects for her student’s final assignment. Each student will have an equal chance of selecting Project A or Project B. Ms. Sanchez flips a coin to represent each student’s choice, with heads representing Project A and tails representing Project B. After 110 trials, there are 58 heads and 52 tails.
To the nearest percent, what is the experimental probability of Project B?
The experimental probability of Project A is 0.53.
What is Probability?A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.
As per the given data:
We are given that there are two projects, Project A and Project B.
A student has to choose one out of the two projects and, the student's choice is represented by the flip of a coin where heads representing Project A and tails representing Project B.
Head's = Project A
Tail's = Project B
Total number of trials = 110
Number of heads in the trials = 58 heads
Number of tails in the trials = 52 tails
For finding out the experimental probability of Project A:
= Number of favorable outcomes / Total number of trials
Number of favorable outcomes = Number of heads
= Number of heads / Total number of trials
= 58 / 110
= 0.53 (approx)
The experimental probability of Project A is 0.53.
Hence, The experimental probability of Project A is 0.53.
To learn more on Probability, click:
brainly.com/question/30034780
#SPJ2
Find the distance traveled by a particle with position ( x, y ) as t varies in the given time interval. Compare with the length of the curve.
x=sin^2(theta) , y=cos^2(theta) 0
The distance traveled is equal to sin^2(θ), as seen before.
To find the distance traveled by a particle with position (x, y) as t varies in the given time interval, we need to first find the parametric equations for x and y in terms of t, and then compute the arc length of the curve.
Given x = sin^2(t) and y = cos^2(t), we first find the derivatives of x and y with respect to t:
dx/dt = 2 * sin(t) * cos(t)
dy/dt = -2 * sin(t) * cos(t)
Next, we compute the square root of the sum of the squares of the derivatives:
sqrt((dx/dt)^2 + (dy/dt)^2) = sqrt((2 * sin(t) * cos(t))^2 + (-2 * sin(t) * cos(t))^2) = sqrt(4 * sin^2(t) * cos^2(t) + 4 * sin^2(t) * cos^2(t)) = 2 * sin(t) * cos(t)
Now, we can find the distance traveled by integrating the above expression with respect to t over the given time interval (0, θ):
Distance traveled = ∫(2 * sin(t) * cos(t) dt) from 0 to θ
Using the substitution u = sin(t), du = cos(t) dt, we get:
Distance traveled = ∫(2 * u du) from 0 to sin(θ)
Now, integrating with respect to u, we get:
Distance traveled = u^2 | from 0 to sin(θ) = (sin^2(θ)) - (0^2) = sin^2(θ)
The length of the curve can be computed as the arc length:
Length of the curve = ∫(2 * sin(t) * cos(t) dt) from 0 to θ
As we computed earlier, the distance traveled is equal to sin^2(θ). Therefore, the distance traveled by the particle is the same as the length of the curve.
To know more about distance, visit:
https://brainly.com/question/29055485#
#SPJ11
What is the standard form of the equation of the circle with the center and a radius of square 2 divided by 4
The standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.
The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
To use this formula, we first need to find the values of h, k, and r for the given circle with center and radius of square 2 divided by 4.
We know that the center of the circle is (h, k) = (2/4, -2/4) = (1/2, -1/2).
This means that h = 1/2 and k = -1/2.
The radius of the circle is r = square 2 divided by 4.
We can write this as r² = (square 2 divided by 4)² = 2/16 = 1/8.
Now we can substitute these values into the standard form equation to get:
(x - 1/2)² + (y + 1/2)² = 1/8
So the standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.
for such more question on standard form
https://brainly.com/question/19169731
#SPJ11
during a one-month promotional campaign, tiger films gave either a free dvd rental or a 12-serving box of microwave popcorn to new members. it cost the store $1 for each free rental and $2 for each box of popcorn. a total of 89 new members were signed up and the store's cost for the incentives was $135. how many of each incentive were given away?
By using system of equations, there are 43 free DVD rentals and 46 boxes of microwave popcorn were given away during the promotional campaign.
Let's use the following variables
x: the number of free DVD rentals given away
y: the number of boxes of microwave popcorn given away
We can set up a system of equations to represent the given information:
x + y = 89 (total number of new members signed up)
1x + 2y = 135 (total cost of the incentives)
We can solve for x or y in the first equation and substitute into the second equation
x = 89 - y
1(89 - y) + 2y = 135
89 - y + 2y = 135
y = 46
Substituting y = 46 into the first equation:
x + 46 = 89
x = 43
Therefore, 43 free DVD rentals and 46 boxes of microwave popcorn.
To know more about System of equations:
https://brainly.com/question/12895249
#SPJ4
The graph of a quadratic function with vertex (-3, - 1)
Find the range and the domain.
Therefore the range of the quadratic function with vertex (-3, -1) is y ≥ -1 and the domain is all real number and the Domain is real numbers .
How to the range ?A quadratic function's vertex form is given by:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the parabola's vertex. In this instance, we have:
[tex]h = -3, k = -1[/tex]
So the quadratic function's equation is:
[tex]y = a(x + 3)^2 - 1[/tex]
To determine the function's range, we must first determine the minimum value of y. Because the squared term's coefficient is positive, the parabola opens upwards and the vertex is a minimum point. As a result, the range is:
Range: y ≥ -1
To determine the function's domain, we must first determine the set of all x-values for which the function is defined. Due to the fact that a quadratic function is defined for all real numbers, the domain is:
Domain: All real numbers
So the domain of the quadratic function with vertex (-3, -1) is all real numbers, and its range is y -1.
To know more about quadratic function visit:-
https://brainly.com/question/29775037
#SPJ9
suppose the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. based on this information, what interval of prices would we expect at least 95% of new car prices to fall within?
New car prices to fall within is $18,300 - $41,900
Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.
Learn more about Standard deviation
brainly.com/question/23907081
#SPJ11
Which function results after applying the sequence of transformations to
f(x) = x5?
• stretch vertically by 3
• translate up 1 unit
• translate left 2 units
Answer:
[tex]3(x + 2)^5 + 1[/tex]
Step-by-step explanation:
we have,
[tex]y = x^5[/tex]
1. stretch vertically up by 3
[tex]y = 3x^5[/tex]
2. translate up 1 unit (Y = y + 1)
[tex]y = 3x^5 + 1[/tex]
3. translate left 2 units (X = x + 2)
[tex]y = 3(x + 2)^5 + 1[/tex]
Hopefully this answer helped you!!!
a counseling service records the number of calls to their hotline for the last year. what is the forecast for august if the forecast for june was 164 and the service uses exponential smoothing with an alpha of 0.7?
Forecast for August with an alpha of 0.7 and forecast of June 164 are to be calculated using exponential smoothing.
Exponential smoothing is a forecasting method that uses a weighted average of past time-series values to forecast future values. In a time-series, data values are obtained over time, such as over months or years, and then plotted in sequence.
The weights decrease exponentially as the observations get older. The EWMA formula used in exponential smoothing is as follows:
St=α × Yt-1+(1-α) × St-1
where,St is the smoothed statistic for the current period tYt is the original observation for the current period tSt-1 is the smoothed statistic for the previous period t-1α is the smoothing parameter 0≤α≤1, and usually close to 0.1.The smoothed statistic is also called the exponentially weighted moving average (EWMA).Calculating the forecast for August with alpha=0.7 and forecast of June 164 as follows:
St=α × Yt-1+(1-α) × St-1St =0.7 × 164+(1-0.7) × 164St=164
for such more question on exponential smoothing
https://brainly.com/question/15061467
#SPJ11
If f(1) = 10, and f(n) = f(n-1) + 4, then find the value of
ƒ (4).
The value of f(4) using recursive formula f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2 is 22
Finding the Value of f(4) Using Recursive FormulaGiven that f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2.
To find the value of f(4), we can use the recursive formula to work our way up from f(1) to f(4):
Using the above as a guide, we have the following:
f(2) = f(1) + 4 = 10 + 4 = 14
Next, we have
f(3) = f(2) + 4 = 14 + 4 = 18
Next, we have
f(4) = f(3) + 4 = 18 + 4 = 22
Therefore, the value of f(4) is 22.
Read more about sequence at
https://brainly.com/question/29431864
#SPJ1
how do these histograms demonstrate what the central limit theorem says about the sampling distribution model for sample means.
The histograms demonstrate that as sample size increases, the distribution of sample means becomes more normal, which is in line with the central limit theorem.
Histograms can be used to graphically represent a probability distribution, which is a measure of how likely it is that a random variable will take on a particular value.
The central limit theorem states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the population distribution.
The histograms demonstrate this by showing the distribution of sample means for different sample sizes. As the sample size increases, the shape of the histogram becomes more normal, with a narrower and taller distribution.
Therefore, this demonstrates that the central limit theorem holds true, as the distribution of sample means becomes more normal as sample size increases, regardless of the shape of the population distribution.
To know more about population distribution refer here:
https://brainly.com/question/1539005?
#SPJ11
Can you help me. I have 10 minutes to do this. Thanks!
Answer:
To find the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures, we first need to convert both temperatures to Celsius or Fahrenheit. Since Oklahoma's temperature is given in Fahrenheit and New Jersey's temperature is given in Celsius, we'll convert Oklahoma's temperature to Celsius.
Using the formula F = 1.8C + 32, we can solve for C:
-31°F = -35°C
(To see how we arrived at this conversion: first, we use the formula to convert Fahrenheit to Celsius: F = 1.8C + 32. Rearranging the equation, we can solve for C: (F - 32) / 1.8 = C. Plugging in -31°F for F, we get (-31 - 32) / 1.8 = -35°C)
Now we can find the difference in Celsius between the two temperatures:
|-35°C| - |-37°C| = |-2| = 2°C
So the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures is 2°C.
Given f(x)=5x+7 and g(x)=2x+2, find g(g(1-3w))
Enter as the final value or expression without parentheses
As a result, the final number or expression is g(g(1-3w)) ≈ -12w + 10 (without parenthesis).
Which of these are they known as?When adding extraneous information or perhaps an afterthought to a sentence, parentheses, a pair or punctuation marks, are most frequently utilized. Two curving vertical lines can be seen in parentheses: ( ).
We must first evaluate g(1-3w) and then re-insert that result into g(x) in order to determine g(g(1-3w)).
We must first determine g(1-3w):
Substitute x with 1-3w to get g(x) ≈ 2x + 2 and g(1-3w) ≈ 2(1-3w) + 2.
g(1-3w) ≈ 2 - 6w + 2 (distribute the 2)
g(1-3w) ≈ -6w + 4 (combine similar terms) (combine like terms)
We can again again enter the result of g(1-3w) into g(x):
If you substitute g(1-3w) for x, then g(x) ≈ 2x + 2 g(g(1-3w)) ≈ 2(-6w Plus 4) + 2
g(g(1-3w)) ≈ -12w + 8 + 2 (allocate the 2) (distribute the 2)
g(g(1-3w)) ≈ -12w + 10 (combine comparable terms) (combine like terms)
To know more about parentheses visit:
https://brainly.com/question/28146414
#SPJ1