according to the question the volume of the right rectangular prism is 67.5 cubic inches.
what is volume?Volume is characterized as the space involved inside the limits of an article in three-layered space. The capacity of the object is another name for it.
A right rectangular prism's volume can be calculated by multiplying its lengths, width, and height. The prism's measurements are 3, 3/4, 5, & 4 1/2 inches.
First, we need to convert 4 1/2 to an improper fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2
Now, we can multiply the dimensions together to find the volume:
Volume = length x width x height
Volume = 3 x 3/4 x 5 x 9/2
Volume = 67.5 cubic inches
Hence, the bottom rectangular prism has a 67.5 cubic inch volume.
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Tom and John are engaged in buying and selling certain products A and B. Tom BUYS 5 of product A but
SELLS twice as much of product B. John on the other hand SELLS three times what Tom BOUGHT of
product A and BUYS 13 of product B. At the end of the business day, John banks Ksh 110,000/- while
Tom banks Ksh 230,000.
Under the assumption that the sale prices for product A and B are the same for the two men, and the costs prices for the products A and B are also the same for the two men, obtain the following:
The price for product A which was determined as Ksh 42,727.27 and the price for product B as 44,363.63
Question: If there was a mark up of 25% on the cost price and a discount of 15% on the sale price, how
much would each of the partners have banked at the end of the business day?
Product A is priced at Ksh 55,000, while Product B is priced at Ksh 32,000.
How to calculate Product A and B?Assume that the selling price for both the two items A and B is "S" and the cost price for both is "C". Using this knowledge, we can create two equations that relate the costs and revenues of the two items, one for Tom and one for John:
Tom: 5C - 2(5S) = [tex]P_1[/tex]
John: 3(5C) - 13C = [tex]P_2[/tex]
where [tex]P_1[/tex] and [tex]P_2[/tex] represent Tom's and John's respective profits.
We are aware that John deposits Ksh. 110,000 while Tom deposits Ksh. 230,000 at the end of the business day. Thus, we can say:
[tex]P_1[/tex] = 230,000 - 5C
[tex]P_2[/tex] = 110,000 - 18C
These values are what we obtain when we enter them into the equations for Tom and John:
5C - 2(5S) = 230.000 - 5C
When we simplify these equations, we obtain:
10C - 10S = 230,000
2C = 110,000
Solving for C, we get:
C = 55,000
We may determine S by adding this value back into the original equation:
10(55,000) - 10S = 230,000
Simplifying this equation, we get:
S = 32,000
Therefore, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.
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Jacob drove from Nicktown to Binghamton at
an average speed of 70 mph. If it took him 4
hours to get there, how far is Binghamton from
Nicktown?
A. 17.5 miles
B. 210 miles
C. 280 miles
D. 300 miles
- w/5 + 9 = 13 what w
Answer:
w = -20
"The beautiful thing about learning is that no one can take it away from you." :)
Explain how to simplify this expression: (7a + 9) + (4a - 7).
The simplified expression would be 11a + 2.
Simplifying an expressionIn order to simplify the given expression, we first need to combine like terms.
The terms can be combined by adding their coefficients:
(7a + 4a) = 11a(9 - 7) = 2Now we can substitute these combined terms back into the original expression:
(7a + 9) + (4a - 7) = 7a + 4a + 9 - 7
And then simplify further:
= 11a + 2
Therefore, the simplified form of the expression (7a + 9) + (4a - 7) is 11a + 2.
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PLEASE ANSWER AND DONT PUT RANDOM SUTFF.
1. Which linear equation is being represented by the graph?
(A)y = -3/4x + 4
(B)y = 3/4x - 3
(C)y = 3/4x + 4
(D)y = -3/4x - 3
2. Which equation best represents the relationship between x and y in the graph?
(A)y = 3x - 2
(B)y = 2x + 3/2
(C)y = -1/2x + 3
(D)y = -2x + 3
Please help with the question below
please write the answer in a decimal
Answer
15.71 cm
Explanation
A school bus has 22 rows of seats, and 4 students can be seated in each row. Students riding in the bus have filled 19 rows of seats, and 1/2 of the remaing seats. How many seats on the bus are empty?
Thus, remaining seats on the school bus that are empty is found as: 6 seats.
Explain about the fraction of number:The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts by which the whole has already been divided is shown by the denominator. It is positioned in the fraction's lower portion, just below fractional bar.How several sections of both the fraction are displayed or chosen is shown in the numerator. It is positioned well above fractional bar in the upper portion of the fraction.Given data:
Total rows of seats = 22Number of seats in each row = 4Filled rows = 191/2 of the remaining.Total seats in bus = Total rows of seats * Number of seats in each row
Total seats in bus = 22 * 4
Total seats in bus = 88
Filled seats = 19 * 4 = 76
Left seats = 88 - 76 = 12
Now, 1/2 of the 12 seats is filled = 6 seats.
remaining seats = 6
Thus, remaining seats on the school bus that are empty is found as: 6 seats.
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Pls help with this problem in the attached photo
There is a 1.8% probability that a customer will buy clothes, shoes, AND jewelry.
This statement is false. The probability that a customer buys clothes, shoes, and jewelry is not given
How to solve the problem ?
Let's denote the event that a customer buys clothes by C, the event that a customer buys jewelry by J, and the event that a customer buys shoes by S. We are given that the probabilities of these events are independent. Therefore, the probability of a customer buying clothes and shoes, denoted by C and S, is simply the product of the probabilities of buying clothes and buying shoes, which is 0.6 × 0.3 = 0.18. Similarly, the probability of a customer not buying shoes and buying jewelry, denoted by S' and J, is simply the product of the probabilities of not buying shoes and buying jewelry, which is 0.7 × 0.1 = 0.07.
Using these probabilities, we can now check the statements:
There is a 15% probability that a customer buys NO clothes, NO shoes, and NO jewelry.
This statement is true. The probability that a customer buys none of these items is simply the complement of the probability that the customer buys at least one of them. Using the inclusion-exclusion principle, we have:
P(C ∪ J ∪ S) = P(C) + P(J) + P(S) - P(C ∩ J) - P(C ∩ S) - P(J ∩ S) + P(C ∩ J ∩ S)
P(C ∪ J ∪ S) = 0.6 + 0.1 + 0.3 - 0 - 0.18 - 0 + P(C ∩ J ∩ S)
P(C ∪ J ∪ S) = 0.52 + P(C ∩ J ∩ S)
Therefore, the probability that a customer buys none of these items is:
P((C ∪ J ∪ S)') = 1 - P(C ∪ J ∪ S) = 0.48 - P(C ∩ J ∩ S)
We are not given the value of P(C ∩ J ∩ S), but we know that it cannot be negative. Therefore, the maximum value of P((C ∪ J ∪ S)') is 0.48, which corresponds to the case where P(C ∩ J ∩ S) = 0. In this case, the probability that a customer buys none of these items is 0.48, which is 15% of 1.
There is a 70% probability that a customer does NOT buy shoes.
This statement is true. The probability that a customer does not buy shoes is simply the complement of the probability that the customer buys shoes, which is 0.3. Therefore, the probability that a customer does not buy shoes is 1 - 0.3 = 0.7, which is 70% of 1.
There is an 8.5% chance that a customer buys jewelry.
This statement is false. The probability that a customer buys jewelry is not given directly. However, we can use the information about the probability of not buying shoes and buying jewelry to find it. We have:
P(S' ∩ J) = P(S') × P(J) = 0.7 × 0.1 = 0.07
Therefore, the probability that a customer buys jewelry is:
P(J) = P(S' ∩ J) + P(S ∩ J) = 0.07 + 0 = 0.07
This is 7% of 1, not 8.5%.
There is a 1.8% probability that a customer will buy clothes, shoes, AND jewelry.
This statement is false. The probability that a customer buys clothes, shoes, and jewelry is not given
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Given the following functions find and simplify (f-g)(1) f(x)=-x^2-x-3 g(x)=-1
To find (f-g)(1), we first need to find f(1) and g(1): f(1) = -(1)^2 - 1 - 3 = -5 g(1) = -1 Now we can substitute these values into (f-g)(x) = f(x) - g(x) and simplify: (f-g)(1) = f(1) - g(1) = (-5) - (-1) = -4 Therefore, (f-g)(1) = -4.
Ling bought d donuts to share with coworkers. There were 6 donuts in each box. Write an expression that shows how many boxes of donuts Ling bought.
the expression would be used as follows:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
Ling bought 108 boxes of donuts.
This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought.
What is mathematical equation?Equations are used to solve problems involving unknowns, such as how much a person owes for groceries or how many people are required to complete a certain task.
The expression that would show how many boxes of donuts Ling bought is:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
In this expression, N represents the number of boxes of donuts Ling bought and D represents the number of donuts. This expression can be used to calculate the number of boxes of donuts Ling bought when the number of donuts is known.
For example, if Ling bought 18 donuts, the expression would be used as follows:
Number of boxes of donuts (N) = 6 x Number of donuts (D)
N = 6 x 18
N = 108
Therefore, Ling bought 108 boxes of donuts.
This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought. The expression can be used whenever the number of donuts is known and can be used to calculate the number of boxes of donuts Ling bought.
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Find the maximum value of = √ subject to the cost constraint K + 4L = 16.
Estimate the change in the optimal value of Q if the cost constraint is changes to K +
4L = 17
Answer:
This problem can be solved using the method of Lagrange multipliers. Let's define the Lagrangian function as: L(K, L, λ) = Q - λ(K + 4L - 16) Taking partial derivatives with respect to K, L, and λ, we get: dL/dK = 0 => 1 - λ = 0 => λ = 1 dL/dL = 0 => 1 - 4λ = 0 => λ = 1/4 dL/dλ = K + 4L - 16 = 0 Solving the last equation for K, we get: K = 16 - 4L Substituting this into the Lagrangian function, we get: L = Q - λ(16 - 4L + 4
Given the polynomial 3x3 − 4x2 + 9x − 12, rewrite the polynomial as a product of binomials.
(x2 + 3)(3x + 4)
(x2 + 3)(3x − 4)
(x2 − 3)(3x + 4)
(x2 − 3)(3x − 4)
Answer:
(x^2+3)(3x-4)
Step-by-step explanation:
To answer this question we can employ a technique called factor by grouping. This strategy has us factor out values from the first two numbers and last two numbers to simplify the expression.
3x^3-4x^2+9x-12
x^2(3x-4)+3(3x-4)
(x^2+3)(3x-4)
Therefore, the answer is the second option.
Let f(x) = IxI and g(x) = x^2
Find all values of x for which f(x) > g(x)
write your answer in interval notation
PLS HELP I WILL GIVE 50 POINTS
The interval in which the inequality is true is:
-1 < x < 1
For which values of x we have f(x) > g(x)?
Here we know that:
f(x) = |x|
g(x) = x²
Now, remember that in a product:
a*A
we have:
|a*A | > a if A > 1.
|a*A| < a if A < 1.
So, in a square like in g(x) = x²
if -1 < x < 1
Then the outcome will be smaller than the input, because we are multiplying by a numer smaller than 1.
Then:
f(x) > g(x)
|x| > x²
In the interval -1 < x < 1
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Compare the following box plots below. Which of the following statements is NOT true?
Class B has a higher median
Class A has greater variability
Both A and B have students who are only children
Over half of the students in class A have two or more siblings
Comparing the box plots, the statements which are not true are Class A has greater variability and over half of the students in Class A have two or more siblings.
Based on the given box plots, we can make the following observations:
a) Class B has a higher median: True. We can see from the plot that the median line for Class B (represented by the orange line inside the box) is higher than the median line for Class A (represented by the blue line inside the box).
b) Class A has greater variability: False. We can see from the plot that the boxes for both classes have similar lengths, indicating similar variability. However, Class A has a few more outliers compared to Class B, which indicates some extreme values that are far from the median.
c) Both A and B have students who are only children: True. We can see from the plot that both classes have a box plot labelled "0" indicating that some students in each class are only children.
d) Over half of the students in class A have two or more siblings: False. We can see from the plot that the box labelled "2+" in Class A only covers about a third of the box, indicating that less than a third of the students have two or more siblings. Therefore, the statement is not true.
Therefore, the answer is b) Class A has greater variability and d) Over half of the students in Class A have two or more siblings.
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(3, -3) and (8, 12)
Step-by-step explanation:
what did you ask the question? ask it clearly please?? if you ask clearly the question. we also give answer
The period of the sinusoidal graph shown is:
3 п
2
A П
В
2п
C
-2п -п
-3
-3
-6
у
TT
2п х
The period of a sinusoidal graph is the distance between two consecutive peaks or troughs of the graph. From the given graph, we can see that the graph completes one full cycle from x = 0 to x = 2π. Therefore, the period of the graph is 2π.
How can we determine the period of a sinusoidal graph?The period of a sinusoidal graph is the distance between two consecutive peaks or troughs of the graph. It can be determined by calculating the length of one complete cycle of the graph.
What does the period of a sinusoidal graph tell us about the function?The period of a sinusoidal graph tells us how often the function repeats itself. It is an important characteristic of the function that can help us analyze its behavior and make predictions about its future values.
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A trapezoid has an
area of 35 mm².
What is the height
of the trapezoid?
8 mm
6 mm
The height of the trapezoid is 7 mm.
A quadrilateral with one set of parallel opposite sides is referred to as a trapezium.
To find the height of a trapezoid when the area and the lengths of the parallel bases are given, we can use the formula:
h = 2A / ([tex]b_1 + b_2[/tex])
where
h is the height,
A is the area,
[tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of the parallel bases.
As per given information in the question.
Using the given area of 35 mm² and the lengths of the parallel bases,
For [tex]b_1[/tex] = 8 mm and [tex]b_2[/tex] = 6 mm
we get:
h = 2 x 35 / (8 + 6) = 7 mm
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How do you solve this?
Below 10 in.*6 in.*14 in., the triangular prism's volume is 420 cubic inches.
The area of the base must be multiplied by the prism's height in order to determine the volume of a triangular prism.
The base of this triangular prism is a triangle with a base of 6 inches and a height of 10 inches, so its area is:
Area of base = (1/2) × base × height = (1/2) × 6 in × 10 in = 30 in²
The height of the triangular prism is given as 14 inches.
Hence, the triangular prism's volume is:
Volume = Area of base × height = 30 in² × 14 in = 420 cubic inches.
So, the volume of the triangular prism is 420 cubic inches.
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Convert 3
2
3
years to months.
1 year = 12 months
Answer:
3878.65
Step-by-step explanation:
Answer: 3876
Step-by-step explanation:
If you are asking how many months are in 323 years, then the answer is 3,876 months
323(12)
3x + y = 3
x + y = 2
Solve the system of equations.
3x + y = 3
x + y = 2
Solve the system of equations.
A x = 12
, y = 3x = 1 2 , y = 3
B x = 32
, y = 12
x = 3 2 , y = 1 2
C x = 3, y = 12
x = 3, y = 1 2
D x = 12
, y = 32
x = 1 2 , y = 3 2
E x = 52
, y = -92
Answer: x = [tex]\frac{1}{2}[/tex] , y= [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
8x÷4=100 What is the value of x in the equation?
Answer:
Solving 8x ÷ 4 = 100, we have:
2x = 100
x = 50
So the value of x is 50.
Answer:
x = 50
Step-by-step explanation:
To answer this question, we have to isolate the x. To do this, we have to get rid of any other numbers around it by doing the inverse of the operation.
1)
÷ 4 = ×4 to both sides8x ÷ 4 × 4 = 8x100 × 4 = 4008x = 4002)
8x = ÷ 8 to both sides8x ÷ 8 = x400 ÷ 8 = 50x = 50This means that x is 50!
To check our answer is correct we can substitute 50 to x in the question...
(8 × 50) ÷ 4 = 100It is correct!
Hope this helps, have a lovely day! :)
Complete the square to solve the quadratic below. 1=2x^2+7x
the solutions to the quadratic equation 1 = 2x^2 + 7x are:
[tex]x= \frac{(-7+\sqrt{51} )}{4}[/tex] and [tex]x= \frac{(-7-\sqrt{51})}{4}[/tex]
ToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToTo solve this quadratic equation by completing the square, we need to rewrite the equation in the form of (x + p)^2 + q = 0, where p and q are constants. This will allow us to solve for x.
First, we can factor out the coefficient of the x^2 term, which is 2:
[tex]2x^2 + 7x - 1 = 0[/tex]
Next, we can isolate the x^2 and x terms on one side of the equation by subtracting 1 from both sides:
[tex]2x^2 + 7x = 1[/tex]
Now, we need to add and subtract a constant term inside the parentheses to create a perfect square trinomial. To determine this constant term, we take half of the coefficient of the x term (which is 7/2) and square it:
[tex](\frac{7}{2} )^{2} = \frac{49}{4}[/tex]
So we add and subtract 49/4 inside the parentheses:
[tex]2x^2 + 7x + \frac{49}{4} - \frac{49}{4} = 1[/tex]
We can simplify the left side by factoring the perfect square trinomial:
[tex]2(x + \frac{7}{4} )^2 - \frac{51}{8} = 0[/tex]
Now, we can solve for x by isolating the perfect square term and taking the square root of both sides:
[tex]2(x + \frac{7}{4} )^2 = \frac{51}{8}[/tex]
[tex](x + \frac{7}{4} )^2 = \frac{51}{16}[/tex]
[tex]x + \frac{7}{4}=±\sqrt{\frac{51}{16} }[/tex]
[tex]x = -\frac{7}{4} ± \sqrt{\frac{51}{16} } /2[/tex]
Simplifying this expression, we get:
[tex]x = (-7 ±\sqrt{51} )/4[/tex]
Therefore, the solutions to the quadratic equation 1 = 2x^2 + 7x are:
[tex]x = (-7 + \sqrt{51} )/4 and x = (-7 -\sqrt{51} )/4.[/tex]
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Sneeze: According to a study done by Nick Wilson of Otago University Wellington, the probability a
randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on
a bench in a mall and observe 300 randomly selected individuals’ habits as they sneeze.
Task 1: What is and what is ?
Task 2: What are the mean and standard deviation?
Task 3: What are the conditions that must be met to use the normal approximation to the binomial
distribution? Are they met?
Thus, the mean and standard deviation for the randomly selected individuals is found as: mean = 80.1 and standard derivation = 7.66.
Explain about the standard deviation:The standard deviation is a measurement of how widely spaced out a set of data is from the mean. The bigger the dispersion or variability, the higher the standard deviation and the greater the magnitude of the value's divergence from its mean. It represents the absolute variability of a distribution.
Given data:
Number of population n = 300
probability p = 0.267
Mean is given as np:
np = 300*0.267
np = 80.1
standard derivation: √np(1 - p)
√np(1 - p) = √80.1(1 - 0.267)
√np(1 - p) = √58.7133
√np(1 - p) = 7.66
Thus, the mean and standard deviation for the randomly selected individuals is found as: mean = 80.1 and standard derivation = 7.66.
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Correct question:
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe 300 randomly selected individuals’ habits as they sneeze.
What are the mean and standard deviation?
simplify -2(2x - 5) -4x
Answer: -8x +10
Step-by-step explanation:
-2(2x -5) -4x
1. simplify parthentheses
-4x +10 -4x
add like terms
-8x +10
Write a matrix equation for the given systems of equations.
2x-6y-2z = 1
3y-2z=-5
2y + 2z = -3
Now, we can write the matrix equation as:
AX = B
| 2 -6 -2 | | x | | 1 |
| 0 3 -2 | | y | = | -5 |
| 0 2 2 | | z | | -3 |
How to solve the matricesTo write the given system of equations as a matrix equation, we will represent it in the form AX = B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants.
Given a system of equations:
2x - 6y - 2z = 13y - 2z = -52y + 2z = -3We can represent the matrices as follows:
A = | 2 -6 -2 |
| 0 3 -2 |
| 0 2 2 |
X = | x |
| y |
| z |
B = | 1 |
| -5 |
| -3 |
Now, we can write the matrix equation as:
AX = B
| 2 -6 -2 | | x | | 1 |
| 0 3 -2 | | y | = | -5 |
| 0 2 2 | | z | | -3 |
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you can make one of the following investments:
Option 1: $50 initial investment with an average annual growth rate of 9% starting at age 30
Option 2: $50 initial investment with an average annual growth rate of 8% starting at age 20
Option 3: $100 initial investment with an average annual growth rate of 7% starting at age 25
Based on these calculations, Option 3 yields the highest future value at age 35.
How to solveTo compare the investment options at different ages, we can use the future value formula:
FV = PV * (1 + r)^t
where:
FV = future value of the investment
PV = present value or initial investment
r = annual growth rate (as a decimal)
t = number of years the investment grows
Here are the general equations for each option:
Option 1: FV1 = 50 * (1 + 0.09)^(t - 10)Option 2: FV2 = 50 * (1 + 0.08)^tOption 3: FV3 = 100 * (1 + 0.07)^(t - 5)To compare the options at ages 20, 25, 30, and 35, calculate the future value for each option at those ages by plugging in the corresponding value of t.
Age 20:
FV1 = N/A (Option 1 hasn't started yet)
FV2 = 50 * (1 + 0.08)^0 = $50
FV3 = N/A (Option 3 hasn't started yet)
Age 25:
FV1 = N/A (Option 1 hasn't started yet)
FV2 = 50 * (1 + 0.08)^5 ≈ $73.86
FV3 = 100 * (1 + 0.07)^0 = $100
Age 30:
FV1 = 50 * (1 + 0.09)^0 = $50
FV2 = 50 * (1 + 0.08)^10 ≈ $107.95
FV3 = 100 * (1 + 0.07)^5 ≈ $140.26
Age 35:
FV1 = 50 * (1 + 0.09)^5 ≈ $77.16
FV2 = 50 * (1 + 0.08)^15 ≈ $157.46
FV3 = 100 * (1 + 0.07)^10 ≈ $196.72
Based on these calculations, Option 3 yields the highest future value at age 35.
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Solve the systems by elimination.
10x + 10y = 40
5x + 3y = 8
Answer:
x = -2, y = 6
Step-by-step explanation:
First, find the opposite of 10 by multiplying 5x+3y=8 by -2 to eliminate 10x.
10x+10y=40
-2(5x+3y=8)
10x+10y=40
-10x-6y=-16 (Subtract 10y - 6y) (Subtract 40 - 16)
4y = 24 (Divide by 4 on both sides)
y = 6
Substitute 6 in the y value in any of the equations.
10x+10(6)=40 (Replaced 10y with 10(6) )
10x+60=40
-60 = -60 (Subtract 60 from both sides)
10x = -20 (Divide by 10 on both sides)
10 10
x = -2
Janct was driving home from work at a speed of 40 mph. Realizing she forgot her documents as she arrived home, she then drove back to work at a speed of 60 mph. What is her average speed for the entire trip?
A. 48 mph
B.49 mph
C. 50 mph
D. 52 mph
Answer: 50 mph
Step-by-step explanation:
HELP ASAP 25 PONITS
The percent markdown rounded to the nearest percent is 13%.
What is percent markdown?Markdown represents the difference between the original or full price of an item and the current price that's reduced. It's typically expressed as a percentage.
Equation:To find the percent markdown, we first need to calculate the amount of markdown, which is the difference between the original price and the sale price:
Markdown = $175.90 - $153.77 = $22.13
Next, we need to find the percent markdown by dividing the markdown by the original price and multiplying by 100:
Percent Markdown = (Markdown / Original Price) x 100
Percent Markdown = ($22.13 / $175.90) x 100
Percent Markdown = 0.1258 x 100
Percent Markdown = 12.58%
Rounded to the nearest percent, the percent markdown is 13%.
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Are conditional probabilities always dependent?
Answer:
Two events are said to be independent if one event occurring does not affect the probability that the other event will occur. However, if one event occurring or not does, in fact, affect the probability that the other event will occur, the two events are said to be dependent.
If one event occurs or not, it does, in fact, affect the probability that the other event will occur, and then the two events are said to be dependent.