The function f(x) = x² - 7 is an example of a function that is neither even nor odd, as it does not exhibit either type of symmetry.
To determine whether a function is even, odd, or neither, we need to examine its algebraic form and look for a particular type of symmetry.
Let's apply this concept to the given function, f(x) = x² - 7. To determine whether f(x) is even or odd, we need to evaluate f(-x) and compare it to f(x).
f(-x) = (-x)² - 7 // substitute -x for x
= x² - 7 // simplify
Comparing f(-x) to f(x), we can see that they are not equal:
f(-x) = x² - 7
f(x) = x² - 7
Since f(-x) is not equal to f(x), the function is not even. To determine whether it is odd, we need to evaluate f(-x) + f(x) and see if the result is zero.
f(-x) + f(x) = (x² - 7) + (x² - 7) // substitute -x for x in the second term
= 2x² - 14
Since f(-x) + f(x) is not equal to zero for all values of x, the function is not odd either.
Therefore, we can conclude that the given function, f(x) = x² - 7, is neither even nor odd.
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you can leave the basketball court if you make 3 free throws. the probability that you make a free throw is 0.4. what is the probability that you can leave the court in 10 or fewer attempts?
If the probability that a player makes a free throw is 0.4, the probability that they do not make a free throw is 1 – 0.4 = 0.6.
The probability that a player makes three consecutive free throws is 0.4 × 0.4 × 0.4 = 0.064. If a player attempts three free throws, there are three possible outcomes: make all three, miss one and make two, or miss two and make one.
The probability of making all three is 0.064, the probability of missing one and making two is 0.4 × 0.4 × 0.6 + 0.4 × 0.6 × 0.4 + 0.6 × 0.4 × 0.4 = 0.288, and the probability of missing two and making one is 0.6 × 0.6 × 0.4 + 0.6 × 0.4 × 0.6 + 0.4 × 0.6 × 0.6 = 0.432.
Therefore, the probability of leaving the court in three attempts is 0.064 + 0.288 + 0.432 = 0.784. If a player misses all three attempts, they will have to try three more times, and the probability of leaving the court in six attempts is 0.784 + 0.064 × 0.288 × 0.432 = 0.861.
If a player misses all six attempts, they will have to try three more times, and the probability of leaving the court in nine attempts is 0.861 + 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 = 0.926.
If a player misses all nine attempts, they will have to try three more times, and the probability of leaving the court in twelve attempts is 0.926 + 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 = 0.974.
Since the probability of leaving the court in twelve attempts is greater than 0.9, the probability of leaving the court in ten or fewer attempts is greater than 0.9. Therefore, the probability that a player can leave the court in 10 or fewer attempts is greater than 0.9.
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An angle in standard position on a unit circle measures 2pi/5 radians. what are the exact coordinates of where the terminal side intersects the unit circle?
Thank you!
Answer:
(x, y) = (cos(2π/5), sin(2π/5)) = ((1/4)(-1 + √5), (1/4)(2√5 + 2))
Step-by-step explanation:
In standard position, the initial side of an angle lies on the positive x-axis, and the terminal side rotates counterclockwise from the initial side.
Since the angle measures 2π/5 radians, we need to find the point on the unit circle that is π/5 radians past the positive x-axis.
Let (x, y) be the coordinates of the point on the unit circle where the terminal side intersects. We can use the following trigonometric identities to find the values of x and y:
cos(2π/5) = x
sin(2π/5) = y
These values can be determined using either a calculator or the unit circle. Alternatively, we can use the fact that the angle 2π/5 is a special angle and can be expressed exactly in terms of square roots:
cos(2π/5) = (1/4)(-1 + √5)
sin(2π/5) = (1/4)(2√5 + 2)
Therefore, the exact coordinates of the point where the terminal side intersects the unit circle are
(x, y) = (cos(2π/5), sin(2π/5)) = ((1/4)(-1 + √5), (1/4)(2√5 + 2))
a) evaluate mv. (b) based on your answer to (a) how do you know the columns of m are dependent? use v to give a vector combination.
a) mv = Mv.
b) The columns of M are dependent where [v1, v2, ..., vn]T is a vector combination
a) Evaluate mv:If a matrix M is multiplied by a vector v, the result will be a linear combination of the columns of the matrix. That is, if M is an m×n matrix and v is a vector with n entries, then the product Mv is a linear combination of the columns of M with coefficients from v. Thus, mv = Mv.
b) Use v to give a vector combination.If the columns of M are linearly dependent, it implies that they are multiples of each other, i.e., one column is equal to a scalar multiple of another column, which can be written as an equation of the form, ci = aj where c and a are scalar multiples of jth and ith columns of M, respectively.
Hence, when we compute Mv, the linear combination of the columns of M will depend on the scalar multiples c and a.
For instance, let us assume that column j and i of M are linearly dependent. We have;
ci = aj or
M(:,j) = a*M(:,i)
where M(:,j) and M(:,i) represent jth and ith columns of M, respectively. Then, we can express M as;
M = [M(:,1), ..., M(:,j-1), M(:,i), M(:,j+1), ..., M(:,n)] = [M(:,1), ..., M(:,j-1), a*M(:,i), M(:,j+1), ..., M(:,n)]
Thus, we can rewrite the product Mv as;
Mv = [M(:,1), ..., M(:,j-1), a*M(:,i), M(:,j+1), ..., M(:,n)][v1, v2, ..., vn]T
where [v1, v2, ..., vn]T is a vector combination of the columns of M.
Therefore, if a linear combination of the columns of M results in the zero vector, it implies that the columns of M are dependent.
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the hypotenuse of a right triangle measures 12 centimeters and its shorter leg measures 4 centimeters. what is the measure of the larger acute angle of the triangle? round your answer to the nearest tenth of a degree.
The measure of the larger acute angle of the right triangle is 73.7°. This can be calculated using trigonometry and the Pythagorean theorem.
The larger acute angle of the triangle can be found using trigonometry. First, we can find the length of the other leg using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse and a and b are the legs. Plugging in the values we get: 4² + b² = 12², solving for b we get b = √(12² - 4²) = 8√3. Now we can use inverse tangent to find the larger acute angle: tan⁻¹(opposite/adjacent) = tan¹⁽⁸√³/⁴⁾ ≈ 73.7°. So, the measure of the larger acute angle is 73.7°.
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Please help with these two questions if you are good at vertical angles! thank you!!
Step-by-step explanation:
Blank 1 = 82
Blank 2 = 82
Blank 3 = 98
2022-2023 Math_CoorAlgBenchmark2_ DCSD « Question 18. Two functions are represented in the chart. Function A Pause f(x) = 4x+1 Function B 1 10 2 g(x) 3 What is the rate of change over the interval [-1.2] for Function A? Explain how you found this value. What is the rate of change over the interval [-1,2] for Function B? Explain how you found this value. B IUEE X, X Q Zoom 24
Therefore, the rate of change over the interval [-1, 2] for Function B is 32/3.
What is function?In mathematics, a function is a rule that assigns to each input value (also known as the independent variable) a unique output value (also known as the dependent variable). In other words, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions can be represented in various forms such as algebraic expressions, tables, graphs, or even words. Functions play a crucial role in many areas of mathematics, science, and engineering, as they provide a way to model and describe real-world phenomena and relationships between quantities.
Here,
For Function A, the formula is f(x) = 4x + 1. To find the rate of change over the interval [-1, 2], we need to calculate the slope of the line that passes through the points (-1, f(-1)) and (2, f(2)). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the values for Function A, we get:
slope = (f(2) - f(-1)) / (2 - (-1))
slope = (4(2) + 1 - (4(-1) + 1)) / (2 - (-1))
slope = (9 + 5) / 3
slope = 14/3
Therefore, the rate of change over the interval [-1, 2] for Function A is 14/3.
For Function B, the formula is g(x) = 10x + 2. To find the rate of change over the interval [-1, 2], we need to calculate the slope of the line that passes through the points (-1, g(-1)) and (2, g(2)). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the values for Function B, we get:
slope = (g(2) - g(-1)) / (2 - (-1))
slope = (10(2) + 2 - (10(-1) + 2)) / (2 - (-1))
slope = (20 + 12) / 3
slope = 32/3
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Ryan is working two summer jobs, babysitting and walking dogs. He must work at
least 9 hours altogether between both jobs in a given week. Write an inequality that
would represent the possible values for the number of hours babysitting, b, and the
number of hours walking dogs, d, that Ryan can work in a given week.
b + d ≥ 9 this inequality states that the sum of hours babysitting, b, and hours walking dogs, d, must be greater than or equal to 9 in order for Ryan to meet his weekly work requirement.
What is inequality?
In mathematics, an inequality is a statement that compares two quantities, indicating whether they are equal or not, and in what direction they differ. An inequality is represented by one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).
The inequality that represents the possible values for the number of hours babysitting, b, and the number of hours walking dogs, d, that Ryan can work in a given week is:
b + d ≥ 9
This inequality states that the sum of hours babysitting, b, and hours walking dogs, d, must be greater than or equal to 9 in order for Ryan to meet his weekly work requirement.
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What is 2.5 as a fraction?
Answer: 5/2
fraction of 2.5 is 5/2
Answer:
2 1/2 or 5/2 as improper fraction
2 is a whole number and you have .5 left over
To convert to fraction .5 is the same as 1/2
So it gives you 2 1/2
By the way thanks for the Brainly points :)
the circle below has center O, and its radius is 5 ft. Given that m AOB = 70, Find the area of the shaded region and the length of the arc ADB
The area of the shaded region of the circle is 63.24 ft²
How to find the shaded area?We know that the area of a circle of radius R is given by the formula:
Area = pi*R²
Where pi = 3.14
If we have only a section of a circle defined by an angle θ, the area of that section will be:
area = (θ/360°)*3.14*R²
Here we know that the radius is 5 feet, and that AOB (the non-shaded part) is 70°, then we will have:
θ = 360° - 70° = 290°
Then the area of the shaded region is:
area = (290°/360°)*3.14*(5 ft)² = 63.24 ft²
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Question 5
During gym class, Kathryn did 5 times as many pushups as Grace. Together, they did a total of 42 pushups. How
many push-ups did each person do during the gym class?
Part A
Write a system of equations that represents the situation.
y=
x + y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
The number of pushups done by Grace and Kathryn is 7 and 35 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data,
Let the equation be represented as A
Now , the value of A is
Let the number of pushups by Grace be x
Let the number of pushups by Kathryn be y
Now, Kathryn did 5 times as many pushups as Grace
[tex]y = 5x[/tex] be equation (1)
And, they did a total of 42 pushups together
[tex]x + y = 42[/tex] be equation (2)
Substituting the value of y in the equation, we get
[tex]x + 5x = 42[/tex]
[tex]6x = 42[/tex]
Divide by 6 on both sides, we get
[tex]x = 7[/tex] pushups
And, [tex]y = 35[/tex] pushups
So, the number of pushups by Grace is 7 and by Kathryn is 35 respectively
our club has $25$ members, and wishes to pick a president, secretary, and treasurer. in how many ways can we choose the officers, if individual members are allowed to hold $2,$ but not all $3,$ offices?
Number of ways that can we choose the officers, if individual members are allowed to hold 2 but not all 3 offices is 49,825
One member holds all three offices: There are 25 options for choosing the member who will hold all three offices.
Two members hold two offices each: There are 25 options for choosing the first member, and 24 options for choosing the second member (since one member cannot hold all three offices). Then, for the first member, there are 3 options for which offices they will hold, and for the second member, there are 2 options for which offices they will hold. Here we have to use the permutation. So the total number of ways is
25 × 24 × 3 × 2 = 36,000
Three members hold one office each: There are 25 options for choosing the first member, 24 options for choosing the second member, and 23 options for choosing the third member. So the total number of ways is
25 × 24 × 23 = 13,800
Therefore, the total number of ways to choose the officers is
25 + 36,000 + 13,800 = 49,825
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frank is building a playhouse for his daughter. the playhouse is a composite figure with a floor and no windows. what is the surface area of the playhouse? the playhouse is a rectangular prism and triangular prism.
The surface area of the playhouse is 564 square feet.
Frank is building a playhouse for his daughter.
The playhouse is a composite figure with a floor and no windows.
The playhouse is a rectangular prism and a triangular prism.
The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh,
where l is the length,
w is the width,
and h is the height.
Therefore, the surface area of the rectangular prism portion of the playhouse can be calculated by substituting the given values into the formula.
Surface area of the rectangular prism = 2lw + 2lh + 2wh
For the rectangular prism, l = 10 feet, w = 8 feet, and h = 6 feet.
Substituting the values in the formula.
Surface area of the rectangular prism
= 2lw + 2lh + 2wh
= 2 (10 feet × 8 feet) + 2 (10 feet × 6 feet) + 2 (8 feet × 6 feet)
= 160 feet2 + 120 feet2 + 96 feet2= 376 feet2
The surface area of the rectangular prism of the playhouse is 376 square feet.
The formula for the surface area of a triangular prism is 2lw + lh + ph,
where l is the length, w is the width, h is the height, and p is the slant height.
Therefore, the surface area of the triangular prism portion of the playhouse can be calculated by substituting the given values into the formula.
Surface area of the triangular prism = 2lw + lh + ph
For the triangular prism, l = 8 feet, w = 5 feet, h = 6 feet, and p = 10 feet.
Substituting the values in the formula.
Surface area of the triangular prism = 2lw + lh + ph= 2 (8 feet × 5 feet) + (8 feet × 6 feet) + (10 feet × 6 feet)= 80 feet2 + 48 feet2 + 60 feet2= 188 feet2
The surface area of the triangular prism of the playhouse is 188 square feet.
The total surface area of the playhouse can be found by adding the surface area of the rectangular prism and the surface area of the triangular prism.
Surface area of the playhouse = surface area of rectangular prism + surface area of triangular prism.
= 376 square feet + 188 square feet
= 564 square feet.
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Can anyone please help 10 points
The value of x using similar triangles theorem is = 13/3.
What are similar triangles?Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles.
When two objects have the same shape but different sizes, they can be said to be comparable.
This indicates that comparable shapes superimpose one another when amplified or de-magnified.
The term "Similarity" refers to this characteristic of like shapes.
Now in the given figure,
the proportion of the triangles' side is same.
So, 12/4 = 13/x
x = 13/3
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How do I solve these equations in the best way an 8th grader can?
Answer:
1) x= 2
Step-by-step explanation:
data is gathered on the number of reviews for every app in the play store. the median number of reviews is 1,359 and the mean number of reviews is 453,058. what would explain the difference between these two numbers?
Answer:
The median and mean are two different measures of central tendency that provide different information about a data set. The median is the middle value in a data set, where half of the values are above and half are below. The mean, on the other hand, is the sum of all values divided by the total number of values.
In this case, the median number of reviews is much lower than the mean number of reviews, indicating that there are likely a few very high review counts that are skewing the data towards the higher end. This is because the mean is more affected by extreme values, while the median is not. It is possible that there are a few apps with an extremely large number of reviews, which are driving up the mean.
The mean number of reviews would be significantly higher than the median.
The difference between the median and mean number of reviews can be explained by the fact that some apps have very large numbers of reviews, whereas others have very few. The median is the middle value of the dataset, and does not take into account the outliers, which can have a large effect on the mean. For example, if there is one app with 1 million reviews, the mean number of reviews would be significantly higher than the median.
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A cereal manufacturer distributes cases of cereal to grocery stores. Each case contains 11 identical boxes of cereal. The total weight of the
case consists of the weight of the 11 cereal boxes plus 33 ounces for the weight of the case's cardboard box. In order to pass a quality
assurance test, the case must weigh greater than 264 ounces and less than 286 ounces.
(a) Write a compound inequality to represent the weight of each box (in ounces), b, so that the case passes the quality assurance
test.
The weight of each box of cereal must be between 21 and 23 ounces for the case to pass the quality assurance test. We can write this as the compound inequality: 21 < b < 23.
What is quality assurance test?A quality assurance test is a process that is used to evaluate the quality of a product or service. It involves checking whether the product or service meets certain standards or specifications, and identifying any defects or issues that need to be addressed.
According to question:Let's start by finding the weight of a single box of cereal. We know that the weight of the entire case is the weight of 11 boxes plus the weight of the cardboard box, or:
Weight of case = 11b + 33
where b is the weight of a single box of cereal.
To pass the quality assurance test, the weight of the case must be greater than 264 ounces and less than 286 ounces. Therefore, we can write a compound inequality for b as follows:
264 < 11b + 33 < 286
Next, we can simplify this compound inequality by subtracting 33 from each term:
231 < 11b < 253
Finally, we can divide each term by 11 to solve for b:
21 < b < 23
Therefore, the weight of each box of cereal must be between 21 and 23 ounces for the case to pass the quality assurance test. We can write this as the compound inequality:
21 < b < 23 (in ounces)
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Let f(x) = -2x+4 and g(x) = -6x-7.
a) Find f(x) · g(x).
b) Find f(g(4)
Therefore , the solution of the given problem of function comes out to be f(g(4)) = 66.
Describe function.The midterm examination will have questions on each subject, mathematics, variable design, and both real and imagined locations. a list of the relationships between different elements that collaborate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Each postbox also has a distinct address, which may be an enclave.
Here,
a) We must multiply f(x) and g(x) in order to obtain f(x) g(x):
=> f(x) · g(x) = (-2x+ 4)
The formula is
=> (-6x - 7) = 12x² + 14x - 24x - 28 = 12x² - 10x - 28.
As a result,
=> 12x² - 10x - 28 is what f(x) g(x) equals.
b) We must first determine g(4) in order to obtain f(g(4)):
=> g(4) = -6(4) - 7
=> -31
We can now change g(4) to f(x) as follows:
=> f(g(4)) = f(-31)
=> -2(-31) + 4
=> 62 + 4
Consequently, f(g(4)) = 66.
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the distance from point p to point r
Total distance of 7m, which is the shortest distance between point P and point R.
What is distance?Distance is the physical separation between two objects or points. It is usually measured in units such as meters, kilometers, feet, miles, or light-years. Distance is a key concept in physics, mathematics, engineering, and other scientific disciplines. It plays an important role in our everyday life, such as when we measure the distance between two cities, two buildings, or two places.
To determine the shortest distance between point P and point R, we need to calculate the distances between each point and then find the shortest path.
First, we need to calculate the distances between each point. Starting with the points closest to point R, we can find the distance between point R and point Q to be 4m. The distance between point Q and point P is 3m, from the given information. To find the distance between point R and point U, we need to calculate the distance between point U and point V which is 10m, and then add 8m to account for the 8m between point R and point V. This gives us a distance of 18m. The distance between point R and point S is 8m, and the distance between point S and point T is 8m.
Next, we need to calculate the shortest path between point P and point R. From point P, the shortest route would be to travel 3m south to point Q, then 4m east to point R. This gives us a total distance of 7m, which is the shortest distance between point P and point R.
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Complete questions as follows-
Point U is 8m east of point R. Point P is 3m north of point Q. Point U is 10m north of point V. Point W is 8m west of point V. Point R is exactly between point S and point T. Point R is 4m east of point Q. Point T is in 8m south of point S.
What is the shortest distance between point P and point R?
i need the answers in about 10 mins
Each voter from a random sample of 334 registered voters was asked their impression of two candidates running for the same national office. The
table summarizes the responses.
Which of the following is the me
Candidate A?
Favorable
Unfavorable
No opinion
Have not heard of
Candidate A. Candidate B
Favorable 138 200
Unfavorable 44 47 No Opinion 88 47 Haven’t heard of 64 40
Which of the following is the most appropriate method to use to estimate the proportion of all registered voters who have a favorable impression of Candidate A?
A. A one-sample z-interval for estimating a sample proportion
B. A one-sample z-interval for estimating a population proportion
C. A matched-pairs t-interval for estimating a mean difference
D. A two-sample z-interval for estimating a difference between sample proportions
E. A two-sample z-interval for estimating a difference between population proportions
The answer choice that is the most appropriate is B. A one-sample z-interval for estimating a population proportion
Why is this the most appropriate?
This is the most appropriate method because you are trying to estimate the proportion of all registered voters who have a favorable impression of Candidate A based on the sample data.
A one-sample z-interval is used when you want to estimate a population proportion using a sample proportion.
To calculate the one-sample z-interval for estimating a population proportion, you can use the following formula:
Confidence Interval = p ± Z * sqrt((p * (1 - p)) / n)
where:
p is the sample proportion (favorable opinions of Candidate A / total voters in the sample)Z is the critical value corresponding to the desired level of confidence (e.g., 1.96 for a 95% confidence interval)n is the sample size (334 in this case)sqrt represents the square root functionUsing this method, you will calculate a confidence interval that estimates the true proportion of registered voters who have a favorable impression of Candidate A, based on the sample data.
This is the most appropriate method because it focuses on estimating a single population proportion and incorporates the sample data and sample size into the calculation.
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343^2x-5=49^x/2 solve for x
Answer:
Step-by-step explanation:
We can start by simplifying the expression using the laws of exponents:
343^(2x) * 49^(-x/2) = 49^(x/2)
We can then simplify further by expressing everything in terms of 7 (since 7 is the common factor of both 343 and 49):
(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)
Applying the laws of exponents again, we get:
7^(6x) * 7^(-x) = 7^x
7^(6x - x) = 7^x
7^(5x) = 7^x
Now we can solve for x by equating the exponents on both sides:
5x = x
4x = 0
x = 0
Therefore, the solution to the equation is x = 0.
Answer:
x = 0
Step-by-step explanation:
343^(2x) * 49^(-x/2) = 49^(x/2)
(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)
7^(6x) * 7^(-x) = 7^(x)
Now, we can simplify the equation further by combining the like terms on both sides:
7^(6x - x) = 7^(x)
7^(5x) = 7^(x)
We can solve for x by equating the exponents on both sides of the equation:
5x = x
4x = 0
x = 0
Therefore, the solution to the equation is x = 0.
A fair six sided die is rolled four times what is the probability that the sequence of rolls is 4256 
Answer:
1/1296 or 0.0007716049382716
Step-by-step explanation:
asking how probable it is for the rolls to be rolled in that sequence
so first off in the first roll its a 1/6th chance
then second roll should be 1/6th chance too, right?
but you have to consider the first roll too
how likely is it for the first roll AND the second roll to be in that sequence?
1/6 x 1/6
aka
6 x 6
36
for the first two rolls there are a 1/36 chance for that sequence to happen
so for four its
1/6 x 1/6 x 1/6 x 1/6
6 x 6 x 6 x 6
1296
1/1296 probability OR 0.0007716049382716 (decimals)
hope this helps x
What is the distance between
(
4
,
7
)
(4,7)left parenthesis, 4, comma, 7, right parenthesis and
(
2
,
2
)
(2,2)left parenthesis, 2, comma, 2, right parenthesis?
Answer:
d ≈ 5.4
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (4, 7 )
d = [tex]\sqrt{(4-2)^2+(7-2)^2}[/tex]
= [tex]\sqrt{2^2+5^2}[/tex]
= [tex]\sqrt{4+25}[/tex]
= [tex]\sqrt{29}[/tex]
≈ 5.4 ( to the nearest tenth )
At the party Ashia and her friend at 2 1/2 pizzas after the party there were 1 1/8 pizza left how many pizzas were there at the start of the party?
Answer: 3 5/8 pizzas were there at the start of the party.
Step-by-step explanation:
At the party let number of pizzas were = x Aisha and her friends ate 2 1/2 pizzas after which 1 1/8 pizzas were left.
Therefore the equation formed will be
x- 2 1/2= 1 1/8
x-(5/2)= 9/8
x= 9/8 + 5/2
x= 29/8= 3 5/8
Therefore 3 5/8 pizzas were there at the start of the party.
a cone pointing downward with a heaight of 10 feet and a radius of 2 feet is being filled with water at a constant rate of 2ft^3/min. how fast is the water surface rising when the water depth is 5 feet
The water surface in the conical tank is rising at a rate of approximately 0.16 feet per minute when the water depth is 5 feet.
To solve for this, we can use related rates. Since the tank is being filled with water at a constant rate of 2 ft³/min , we know that the rate of change of the volume of water in the tank is constant. We can use the formula for the volume of a cone to relate the volume of water in the tank to the height of the water in the tank:
V = (1/3) * pi * r² * h
Taking the derivative of both sides with respect to time gives:
dV/dt = (1/3) * pi * r² * dh/dt
We know that dV/dt = 2 ft³/min, r = 2 ft, and h = 5 ft. Solving for dh/dt:
dh/dt = (3 / pi * r²) * dV/dt
dh/dt = (3 / 4 * pi) * 2
dh/dt = 0.16 ft/min
Therefore, the water surface is rising at a rate of approximately 0.16 feet per minute when the water depth is 5 feet.
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bill has a collection of 40 nickels and dimes. together, they add up to $3.50. how many does bill have of each coin?
The number of nickels Bill has is 10.
Therefore, Bill has 10 nickels and 30 dimes.
The given question is as follows.
Bill has a collection of 40 nickels and dimes.
Together, they add up to $3.50.
Bill have of each coin :
To solve the given problem, let's consider the following steps.
Step 1: Let x be the number of nickels and y be the number of dimes.
Based on the given data, we can form the following two equations:
x + y = 40 ... (1) (because Bill has 40 nickels and dimes)
0.05x + 0.10y = 3.50 ... (2) (because the sum of 40 nickels and dimes is $3.50)
Step 2: Solve the equations (1) and (2) by elimination method by multiplying equation (1) with 0.05 and subtracting it from equation (2).
0.05x + 0.05y = 2 ... (3)0.05x + 0.10y = 3.50 ... (4)
Subtracting equation (3) from equation (4),
we get0.05y = 1.50
Dividing both sides by 0.05, we get
y = 30
Therefore, the number of dimes Bill has is 30.
Step 3: Now, substitute the value of y in equation (1), we get
x + 30 = 40
Subtracting 30 from both sides, we get x = 10.
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What is the value of x in the right triangle below, rounded to the near-
est hundredth?
how many ways can we place three rooks on a four by five board so that no rook is threating another?
There are 40 ways to place three rooks on a 4x5 board so that no rook is threatening another.
To determine this, we can first place the rooks in three distinct rows, which can be done in 4 * 3 * 2 = 24 ways. Then, we can place one rook in each of the five columns in the first row, which leaves only three columns for the second row and two columns for the third row.
Since no two rooks can be in the same column, we have 5 * 3 * 2 = 30 ways to place the remaining two rooks.
Therefore, the total number of arrangements is 24 * 30 = 720, but since each arrangement can be rotated by 90, 180, or 270 degrees, we need to divide by 4 to obtain the final answer of 720/4 = 180, and since there are two ways to arrange the rooks in each row, the final answer is 180/2 = 90.
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Mitchelle and Angela won R18000 in a competition and they decided share the money in the ratio 2:3how much will each get
Mitchelle will receive R7200 and Angela will receive R10800.
How to find the value of one part by dividing the total amount won by the total number of parts?
To determine how much Mitchelle and Angela will each receive in the ratio of 2:3, we need to first find the total number of parts in the ratio, which is 2 + 3 = 5.
Value of one part = R18000 ÷ 5 = R3600
Therefore, one part of the ratio 2:3 is equal to R3600.
How to find out how much Mitchelle and Angela will each receive?
we can multiply their respective parts by the value of one part:
• Mitchelle's share = 2 parts × R3600 per part = R7200
• Angela's share = 3 parts × R3600 per part = R10800
Therefore, Mitchelle will receive R7200 and Angela will receive R10800.
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out of a random sample of 1000 dutch men, how many would we expect to be taller than cm (rounded to the nearest whole number)?
Rounding to the nearest whole number, we would expect approximately 251 Dutch men out of a random sample of 1000 to be taller than 190 cm.
To determine how many Dutch men we would expect to be taller than a certain height out of a random sample of 1000, we can use the normal distribution and the properties of the standard normal distribution. We are given that the average height of Dutch men is 183 cm with a standard deviation of 10.5 cm.
To find the probability of a Dutch man being taller than a certain height, we need to convert that height to a standard score or z-score using the formula:
z = (x - μ) / σ
where x is the height we are interested in, μ is the population mean height of Dutch men, and σ is the population standard deviation of Dutch men.
Once we have calculated the z-score, we can use a standard normal distribution table or calculator to find the probability of a Dutch man being taller than that height.
For example, if we want to find the number of Dutch men we would expect to be taller than 190 cm, we can calculate the z-score as:
z = (190 - 183) / 10.5 = 0.67
Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being greater than 0.67 is approximately 0.2514.
To find the number of Dutch men we would expect to be taller than 190 cm out of a sample of 1000, we can multiply the probability by the sample size:
1000 * 0.2514 = 251.4
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Complete question is:
Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a men of 183 cm and standard deviation of 10.5cm. out of a random sample of 1000 dutch men, how many would we expect to be taller than cm (rounded to the nearest whole number)?