Hannah made four withdrawals of $20 from her checking account. She also
wrote a check for $215. By how much did the amount in her checking account
change?
(Show answer )

21. Area as sum = 12x + 60

Area as Product = 12(x + 5)

22. Area as sum = 5x + 20

Area as Product = 5(x + 4)

As a product, we can multiply the height and the base of the rectangle.

As a sum, we can find the area finding the sum of the areas of each pieces of the rectangle.

The missing pieces of that will fill into the circles is shown in the diagram attached below. Therefore, we would have the following:

21. Area as sum = 12x + 60

Area as Product = 12(x + 5)

22. Area as sum = 5x + 20

Area as Product = 5(x + 4)

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Answer:

10 and 42

Step-by-step explanation:

The difficulty with word problems is translating them into math.

Let's do that

---------------------

The sum of a number and two times a smaller number is 62.

let's call the bigger number b, and the smaller number s

b + 2s = 62

Three times the bigger number exceeds the smaller number by 116

3b = s + 116

-----------------------

Now manipulate one of the equations to isolate the variable

3b = s + 116

Subtract 116 from both sides

3b - 116 = s

substitute for s = 3b - 116 in

b + 2s = 62

b + 2(3b - 116) = 62

Distribute

b + 6b - 232 = 62

combine like terms

7b = 294

Divide both sides by 7

b = 42

to find s plug in b = 42 into

b + 2s = 62

42 + 2s = 62

subtract 42 from both side

2s = 20

divide both sides by 2

s = 10

Answer:

d would be correct

Step-by-step explanation:

A pyramid is a polyhedron formed by connecting a polygonal base and an a a p e x. The basic formula for pyramid volume is the same as for a cone: volume = (1/3) times  base area times height, where height is the height from the base to the a p e x. That formula is working for any type of base polygon and oblique and right pyramids.

Answer:

43.96 for circumference

153.86 for area

Step-by-step explanation:

use the fomrulas

Answer:

d=1

Step-by-step explanation:

2x1=7 is 9 :D

Hope this helps!!

Answer:

D equals 1

Step-by-step explanation:

2d+7=9

minus 7 from both sides of the equation to get:

2d=2

divide 2 from both sides to get

d=1

(a) The presence of a confounding variable Z, such as the severity of the fire, could make the relationship between the number of firefighters (X) and property damage (Y) spurious.

(b) The presence of a confounding variable Z, such as the popularity of the incumbent member or the characteristics of the constituency, could make the relationship between campaign spending (X) and percentage of vote (Y) spurious.

(c) The presence of a confounding variable Z, such as the overall lifestyle or socioeconomic status of the women, could make the relationship between coffee consumption (X) and the risk of depression (Y) spurious.

(d) The presence of a confounding variable Z, such as the overall economic conditions or demand for rum in Havana, could make the relationship between Presbyterian ministers' salaries (X) and the price of rum (Y) spurious.

In each of the given examples, the reported pattern of covariation between X and Y may be influenced by a confounding variable Z. A confounding variable is a variable that is related to both the independent variable (X) and the dependent variable (Y), which can lead to a spurious relationship between X and Y.

The presence of a confounding variable can create the illusion of a direct relationship between X and Y when, in reality, the observed relationship is due to the influence of Z.

For example, in the case of firefighters and property damage, the severity of the fire (Z) could be the underlying factor driving both the number of firefighters and the extent of property damage.

Similarly, in the case of campaign spending and percentage of vote, factors such as the popularity of the incumbent member or the characteristics of the constituency (Z) could be influencing both variables.

In the case of coffee consumption and the risk of depression, other lifestyle or socioeconomic factors (Z) may be responsible for the observed relationship rather than coffee itself. And in the case of Presbyterian ministers' salaries and the price of rum, economic conditions or demand for rum (Z) in Havana could be driving both variables.

Identifying and controlling for confounding variables is crucial in research to ensure accurate interpretations of the relationship between X and Y. It allows researchers to isolate the true causal relationship between the variables of interest.

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For a student with a shoe size of 9, the student's height is equal to 65 inches.

For a student with a height of 60 inches, the student's shoe size is equal to 6.5.

From the information provided, an equation for the line of best fit that represents or models the heights x (in inches) and shoe sizes y of several student is given by this mathematical expression:

y = 0.50x - 23.5

Where:

For a student with a shoe size of 9, the student's height is given by:

y = 0.50x - 23.5

0.50x = y + 23.5

Student's height, x = (y + 23.5)/0.50

Student's height, x = (9 + 23.5)/0.50

Student's height, x = 32.5/0.5

Student's height, x = 65 inches.

For a student with a height of 60 inches, the student's shoe size is given by:

y = 0.50x - 23.5

y = 0.50(60) - 23.5

y = 30 - 23.5

y = 6.5

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Answer:

18

Step-by-step explanation:

6 friends times 5 cookies is 30 cookies in total

30 cookies minus 12 cookies already made is 18!

Answer: 18 cookies

Step-by-step explanation:

Tara invites 6 friends, each friend gets 5 cookies.

So, 6 x 5 to find how many cookies are for 6 friends.

6 x 5

= 30 cookies

Tara only has 12 cookies. How much more does she need?

Everyone should get 30 cookies, but there is only 12.

Subtract to find the difference!

30-12=18

If four numbers are selected from the first ten natural numbers. The probability that only two of them are even is \(\frac{10}{21}\).

The probability of an event is a number that indicates how likely the event is to occur.

\(Probability =\frac{favourable \ outcomes}{total \ number \ of \ outcomes}\)

If four numbers are selected out of first 10 natural numbers, the probability that two of the numbers are even implies that other two number are odd. Out of 5 odd natural number (1,3,5,7,9) two are selected and similarly out of the 5 even natural number(2,4,6,8,10) , two are selected.

\(Probability =\frac{favourable \ outcomes}{total \ number \ of \ outcomes}\)

P = \(\frac{^5C_2 \ ^5C_2}{^{10}C_4} = \frac{10}{21}\)

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The complete question is given below,

If four numbers are selected from the first ten natural numbers. What is the probability that only two of them are even?

Answer:

I think the answer is option c

Step-by-step explanation:

The given function, \(f(n) = 10n + 10^2\), represents the runtime efficiency of an algorithm. To determine the algorithm's time complexity, we need to consider the dominant term or the highest order term in the function.

In this case, the dominant term is 10n, which represents a linear growth rate. As n increases, the runtime of the algorithm grows linearly. Therefore, the correct statement would be that the algorithm is O(n), indicating that its runtime is bounded by a linear function.

The other options mentioned in the statements are incorrect. The function \(f(n) = 10n + 10^2\) does not have a logarithmic term (logn) or a growth rate that matches any of the mentioned complexities (O(nlogn), O(logn), θ(n), Ω(n), Ω(logn)).

Hence, the correct answer is that all the options above are false. The algorithm's time complexity can be described as O(n) based on the given function.

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Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

Answer:

0

Step-by-step explanation:

the value of the units is 0

The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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Answer:

5/10=50%

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

3/706 is 0.00424929178, but if you mean 706/3, then the answer is 235 and 1/3. Hope this helps! :)

The sampling distribution of sample means is a mean of 79 and a standard deviation of 3.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.

Given that,

Population mean,  \(\bar{x}\) = 79

Population standard deviation, σ = 18

Sample size, n = 36

We have to determine the mean and standard deviation of a sampling distribution of sample means.

Let X denotes a random variable distributed with a mean and standard deviation of 85 and 28 respectively.

Also, if a random sample of size n is drawn from the population, then the sample mean is denoted by \(\bar{x}\).

The sampling distribution of sample means \(\bar{x}\) is given by:

ц \(\bar{x}\) = ц

σ \(\bar{x}\)  = σ/√n

Therefore, for the sample size n = 36, the sampling distribution of sample means \(\bar{x}\) is obtained as:

ц \(\bar{x}\) = 79

σ \(\bar{x}\)  = 18/√36 = 3

Hence, the required sampling distribution of sample means is mean of 79 and a standard deviation of 3.

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Based on the information provided, it is not clear what type of study the sales director is conducting. To determine the type of study, we need more specific details about the methodology and purpose of the study.  A survey involves collecting data by asking individuals a set of predetermined questions.

If the sales director is collecting data by asking participants about their opinions, preferences, or experiences, then it could be a survey.An observational study involves observing and recording data without intervening or manipulating any variables. If the sales director is simply observing and recording the sales behaviors and patterns of the sales team without any intervention.

An experiment involves manipulating variables and studying the effects on the outcome. If the sales director is testing different sales techniques or strategies by manipulating variables and measuring the impact on sales performance, then it could be an experiment.

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The sales director is conducting a survey. The sales director is conducting a survey to gather information from customers or other individuals. A survey is a useful research method for collecting data and gaining insights that can inform business decisions.

A survey is a research method that involves gathering information from a sample of individuals through the use of questionnaires, interviews, or online forms. It is commonly used to collect data on people's opinions, attitudes, behaviors, or characteristics.

In this case, the sales director is likely using a survey to gather information about customers, sales strategies, or market trends. Surveys can provide valuable insights that help businesses make informed decisions and improve their sales performance.

For example, the sales director may distribute a survey to customers to gather feedback on their satisfaction with the company's products or services. The survey could include questions about their buying preferences, reasons for choosing the company, or suggestions for improvement. By analyzing the responses, the sales director can identify areas of strength and areas that need improvement, ultimately helping to drive sales growth.

It is important to note that a survey is different from an observational study or an experiment. In an observational study, researchers simply observe and record data without intervening or manipulating variables. On the other hand, an experiment involves intentionally manipulating variables to determine cause-and-effect relationships.

In summary, the sales director is conducting a survey to gather information from customers or other individuals. A survey is a useful research method for collecting data and gaining insights that can inform business decisions.

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the measure of the fourth interior angle of the quadrilateral is 68° (Option A)

To find the measure of the fourth interior angle of a quadrilateral, we need to use the fact that the sum of all interior angles of a quadrilateral equals 360°. Given that three interior angles measure 55°, 117°, and 120°, we can find the measure of the fourth angle by subtracting the sum of these three angles from 360°.
First, calculate the sum of the three given angles: 55° + 117° + 120° = 292°.
Next, subtract this sum from 360° to find the fourth angle: 360° - 292° = 68°

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Answer:

20%└|∵|┐♪└|∵|┐♪└|∵|┐♪└|∵|┐♪

Step-by-step explanation:

denada ┌(・。・)┘♪

Answer:

20%

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Solution:

Given the inequality:

To solve the inequality,

step 1: Subtract 0.04x from both sides of the inequality.

Thus, we have

step 2: Subtract 1.1 from both sides of the inequality.

Thus, we have

step 3: Divide both sides of the inequality by the coefficient of x.

The coefficient of x is 0.04.

Thus, we have

Hence, in interval notation, we have

The graph of the solution is thus:

The value of Standard Deviation is needed to calculate the minimum sample size accurately. If you have the value of Standard Deviation, you can substitute it into the equation to find the minimum sample size.

To determine the minimum number of CEOs that the journalist must survey to be within $50,000 of the true average annual salary, we need to consider the margin of error in the confidence interval.

The margin of error is determined by the z-value associated with the desired confidence level and the standard deviation of the population.

Given that the z-value associated with a 95% confidence interval is 1.96, we can use the following formula to calculate the margin of error:

Margin of Error = z-value * (Standard Deviation / sqrt(sample size))

To be within $50,000 of the true average annual salary, we can set up the equation:

$50,000 = 1.96 * (Standard Deviation / sqrt(sample size))

Solving for the sample size (number of CEOs):

sqrt(sample size) = (1.96 * Standard Deviation) / $50,000

sample size = (($50,000)^2 * (Standard Deviation)^2) / (1.96)^2

The value of Standard Deviation is needed to calculate the minimum sample size accurately. If you have the value of Standard Deviation, you can substitute it into the equation to find the minimum sample size.

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Answer: 7) No   8) No

Step-by-step explanation:

According to the Pythagoras theorem of the right triangle,

Square of largest side = Sum of square of other two sides.

8) Given sides: 5cm, 12cm, 14cm

Here, Largest sides = 14 cm

\(5^2+12^2=25+144=169\neq14^2 \ \ \ [14^2=196]\)

These sides do not represent a right triangle.

7) Given sides:  9m, 4m, 5m

Largest side = 9 m

\(4^2+5^2=16+25=49\neq 9^2 \ \ \ \ \ [9^2=81]\)

These sides do not represent a right triangle.

The answer is 1. The ΣX for a sample of n=12 scores with M=8 is 96, 2. The mean for combined samples of n=15 (mean=10) and n=10 (mean=8) is 9.33, 3a. The original mean before adding 6 points is 8, 3b. The original mean before multiplying scores by 4 is 8, 4. The new sample means after removing X=18 is 22.5, and 5. The score added to a population with μ=24 to achieve μ=34 is 34.

1. For any sample, we can find the sum of the scores (ΣX) by multiplying the mean by the number of scores. So in this case:ΣX = M * nΣX = 8 * 12ΣX = 96Therefore, the ΣX value for this sample is 96.

2. To find the mean of the combined samples, we can use the formula: Mean of combined samples = (n1 * mean1 + n2 * mean2) / (n1 + n2) = Mean of combined samples = (15 * 10 + 10 * 8) / (15 + 10) = Mean of combined samples = 9.33. Therefore, the mean for the combined samples is 9.33.

3. a: We can use the formula for shifting the mean to find the original mean: M1 = M2 - kM1 = 14 - 6M1 = 8. Therefore, the value for the mean before 3 points were added to each score is 8. b. The researcher then realizes that she instead needs to multiply each score by 4. Using the original scores, she multiplies each by 4 and finds the mean to be M=32. We can again use the formula for shifting the mean to find the original mean: M1 = M2 / kM1 = 32 / 4M1 = 8. Therefore, the value of the mean prior to multiplying each score by 4 points is 8.

4. To find the new sample mean, we need to remove the score and adjust the mean accordingly. We can use the formula: New mean = (ΣX - X) / (n - 1)New mean = (ΣX - 18) / 10. Given that the original mean is 22, we can solve for ΣX:22 = ΣX / 1122 * 11 = ΣX243 = ΣX. Now we can plug in to find the new mean: New mean = (243 - 18) / 10 = New mean = 22.5. Therefore, the value of the new sample mean is 22.5.

5. We can use the formula for adding a score to a population to find the value of the added score: N μ = ΣX / NN * μ = ΣX / N + 1. Given that N = 10 and μ = 24 for the original population, we can solve for ΣX:10 * 24 = ΣX240 = ΣX. Now we can use the new mean and the formula to solve for the added score:11 * 34 = 240 + X / 11274 = 240 + XX = 34. Therefore, the value of the score that was added is 34.

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The answer provides solutions to the various statistical maths problems that involve calculations of mean and sum of scores. These problems explore the understanding of the concept of mean, summation and basic operations.

To answer these questions, you'll need to understand basic concepts of statistics, specifically the calculation of means, and summation of scores (ΣX). So, let's break them down one by one:

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The cylinder that is similar has a radius of 2.8 inches and a height of 2.4 inches.

A cylinder is a three-dimensional geometric shape characterized by its radius and height. In this case, we are given a cylinder with a radius of 2.8 inches and a height of 2.4 inches. To identify a similar cylinder, we need to find another cylinder with the same ratio of radius to height.

To determine the similarity of cylinders, we can compare the ratios of their corresponding dimensions. The given cylinder has a radius-to-height ratio of 2.8:2.4, which simplifies to 7:6. Therefore, any cylinder with a radius-to-height ratio of 7:6 will be similar to the given cylinder.

Cylinders that share the same ratio of 7:6 between their radius and height will have proportional dimensions. This means that if we were to increase or decrease the dimensions of one cylinder while maintaining the 7:6 ratio, we would obtain a similar cylinder. It's important to note that the actual measurements of the cylinders may differ, but their relative proportions will remain the same.

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Answer:

This equation is Linear.

Step-by-step explanation: