The coach recorded the time it took 14 students to run a mile. The times are as follows: 9:23, 8:15, 9:23, 9:01, 6:55, 7:20, 9:14, 6:21, 7:12, 7:34, 6:10, 9:15, 9:18. Use the data set to complete the frequency table. Then use the table to make a histogram

Answer:

150

Step-by-step explanation:

1:30=5:x

5*30=150

5:150=1:30

In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

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Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

fractions with the same denominator added together

You must add the numerators and keep the same denominator when adding fractions with the same denominator. Since the denominators of the two fractions are the same, we must add the numerators while maintaining the same denominator, which is 4.

What are the parts of fraction?

A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.

The number below the bar is called the denominator . It tells the number of equal parts into which the whole has been divided. The number above the bar is called the numerator. It tells how many of the equal parts are being considered.

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Answer:

Step-by-step explanation:

\(6x + 7 - 10 = 12(3x - 4)\)

Expand the terms in the bracket

That's

\(6x - 3 = 36x - 48\)

Subtract 36x from both sides of the equation

\(6x - 36x - 3 = 36x - 36x - 48 \\ - 30x - 3 = - 48\)

Add 3 to both sides of the equation

\( - 30x + 3 - 3 = - 48 + 3 \\ - 30x - 45\)

Divide both sides by - 30

\( \frac{ - 30x}{ - 30} = \frac{ - 45}{ - 30} \)

We have the final answer as

\(x = \frac{3}{2} \)

Hope this helps you

Marc's current marginal tax rate can be determined by referring to the U.S. tax rate schedule for the year 2021 based on his taxable income.

To calculate Marc's current marginal tax rate, we need to look at the U.S. tax rate schedule for the year 2021. The tax rate schedule consists of several tax brackets, each with its corresponding tax rate. As taxable income increases, individuals move into higher tax brackets and are subject to higher tax rates. Based on Marc's taxable income of $260,000, we would need to refer to the tax rate schedule to determine his marginal tax rate. As the exact tax rates within the brackets can vary, it's important to consult the specific tax rate schedule for the given year.

By locating the corresponding tax bracket for $260,000 in taxable income, we can identify the applicable tax rate. Marc's current marginal tax rate would be the tax rate associated with the bracket that includes his interest.

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Answer:

7 17/99

Step-by-step explanation:

Answer:

y=-x-2

Step-by-step explanation:

Parallel lines have the same slope. In the equation of a line in the form y=mx+b, m is the slope. The equation of line q is 5x+5y=-9 → 5y=-5x-9 → y=-x-(9/5), so the slope (m) is -1.

y=mx+b

y=-x+b

Now sub in the point (-1,-1) to find b:

-1=-(-1)+b

-1=1+b

b=-2

So our equation for r is y=-x-2

Answer:

y = -x - 2

Step-by-step explanation:

put line q into slope-intercept form:

y = -x - 9/5

Now you know the slope that line r must have, -1 (parallel lines have equal slopes)

use the point (-1, -1) to find 'b', or the y-intercept of line r

y = mx + b

-1 = -1(-1) + b

-1 = 1 + b

b = -1+(-1)

b = -2

7) The given distribution of data is:

19, 17, 18, 21, 14, 17, 16, 22, 14, 22, 16

This can be rearranged as:

14, 14, 16, 16, 17, 17, 18, 19, 21, 22, 22

The frequency distribution table is drawn below

The dot plot is drawn right after the frequency table

Answer:

see below

Step-by-step explanation:

2: letter at the vertex,  placing a letter or number inside .... , or by using 3 letters

3:

WXY

WXZ

YXZ

4: X

Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

Answer:

We have this equation: y = 4x + 6 and we need to solve it for x, so x should be at one side of the equation without any otehr number.

y = 4x + 6

Now, we pass the 4x at the left substracting:

y - 4x = 6

And the y summing at the other side:

4x = 6 + y

And now, we can pass the 4 which is multiplying x dividing to the other side

x = \(\frac{6+y}{4}\)

Therefore , the solution to this problem of unitary method comes out to be he should use 4 teaspoons of chocolate syrup instead of 5.

A single or distinct variable is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

Here,

Given :This recipe was doubled by Kiran. He used 4 cups of crushed ice, 6 tablespoons of chocolate syrup, 6 tablespoons of peanut butter, and 2 cups of yogurt.

1. Kiran's smoothie would be more chocolatey than Clare's. All ingredients are doubled, but there is an extra teaspoon of chocolate syrup in his smoothie.

2. Answers vary. Sample response: he should use 4 teaspoons of chocolate syrup instead of 5.

Therefore , the solution to this problem of unitary method comes out to be  he should use 4 teaspoons of chocolate syrup instead of 5.

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To set up this confidence interval, first identify the population parameter of interest, next select the appropriate estimator, then check the conditions for constructing the confidence interval that are: Randomization, Sample size and Distribution shape.

State:
Zachary wants to estimate the mean number of daily texts he sent over the past four years using a 90% confidence interval. He has an SRS of 50 days, with a daily average of 22.5 messages. The data is strongly skewed to the right with many outliers.

Plan:
1. Identify the population parameter of interest: The mean number of daily texts sent by Zachary over the past four years (µ).
2. Select the appropriate estimator: In this case, it's the sample mean = 22.5 messages.
3. Check the conditions for constructing the confidence interval:
  a. Randomization: Zachary used a simple random sample (SRS) of 50 days, which satisfies the randomization condition.
  b. Sample size: The sample size is n = 50, which is typically considered large enough for constructing a confidence interval.
  c. Distribution shape: Since the data is strongly skewed to the right with many outliers, the normality condition might not be satisfied. In this case, the Central Limit Theorem (CLT) may not apply, and the confidence interval might not be accurate.

Given the potential issue with the distribution shape, Zachary should consider either transforming the data to approximate normality or using a nonparametric method.

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Answer: P(7)=P(5)=12

Step-by-step explanation:

The probability of choosing milk and not milk will be 0.5833 and 0.4167, respectively.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A sack contains 7 milk and 5 dim chocolates. A sweet is chosen indiscriminately.

The total number of the sweets will be given as,

Total events = 7 + 5 = 12

The probability of choosing milk will be given as,

P = (7/12)

P = 0.5833

The probability of choosing not to milk will be given as,

P = (5/12)

P = 0.4167

The probability of choosing milk and not milk will be 0.5833 and 0.4167, respectively.

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Answer:

189.36 metres

Step-by-step explanation:

We can use trigonometry to solve this problem.

Let's draw a diagram to help visualize the situation:

```

          |

          |

          |90m

          |

          |

          |

-----------|--------------------

          x

```

We can see that the angle of depression is the angle formed by a horizontal line from the top of the cliff to the boat, and a line of sight from the top of the cliff to the boat. We can also see that the height of the cliff is 90 meters.

Using trigonometry, we can find the distance x between the boat and the foot of the cliff:

tan(26.2°) = opposite / adjacent

tan(26.2°) = 90 / x

To solve for x, we can rearrange the equation:

x = 90 / tan(26.2°)

x ≈ 189.36 meters

Therefore, the boat is approximately 189.36 meters from the foot of the cliff.

Answer:

x=0

Step-by-step explanation:

simplify: 15(x-3) over 15 ( srry i dont know how to make that a fraction.)

3(2x-3)= 3x-9

3x-9=6x-9

move all terms containing x to the left side of the equation

-3x-9=-9

move all terms not containing x to the right side of the equation

-3x=0

divide both sides by -3 and simplify if needed

x=0

( hope this helped.)

The difference in the maximum values of the function g(x) and f(x) is  11 .

In the question ,

it is given that

the function f(x) is = -(x-5)² + 4

So,  f(-3) = -(-3-5)² + 4 = -60

f(-2) = -45

f(-1) = -32

f(0) = -21

f(1) = -12

f(2) = -5

So , from the above  data we can see that the maximum value of f(x) is -5

and form the table , we can see that the maximum value of g(x) is 6 .

So , the difference between the maximum value of f(x) and g(x) is

= 6 - (-5)

= 6 + 5

= 11

Therefore , the difference in the maximum values of g(x) and f(x) is  11 .

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Answer:

17 obtuse triangle

Step-by-step explanation:

hope it helps

Answer:

11. corresponding

12. consecutive interior

13. alternate exterior

14. alternate interior

15. corresponding

16. consecutive interior

17. alternate interior

Hello.

First, find the cost of 1 orange by dividing 75 by 15:

75÷15=Rs 5

So that's the cost of 1 orange.

Now, multiply that by 12:

5×12=Rs 60

Therefore, the cost of 12 oranges is Rs 60

I hope it helps.

Have a nice day.

\(\boxed{imperturbability}\)

Answer:

C. (1,6)

Step-by-step explanation:

y=5x+1

y=x+5

x+5 = 5x+1

4x = 4

x = 1

y = 1 + 5 = 6

(x,y) = (1,6)

If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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Answer:

A= 1/2 (8)(5)

Step-by-step explanation:

I just Did The Quiz and got 100%

The area of a triangle is 1/2 × base × height so it will be 1/2 × (8) × (5) so none of the given options is correct.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

Given a triangle,

The area of any triangle is given as ;

A = 1/2 × base × height

Base = 5 inches

Height = 8 inches

So,

A = 1/2 × (8) × (5) will be the correct formula for finding the area of this triangle.

Hence "The area of a triangle is 1/2 × base × height so it will be 1/2 × (8) × (5)".

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-0.22 as  a repeating fraction is -22/99

The decimal is given as:

-0.22

Express as fraction

-22/100

Subtract 1 from the denominator to rewrite it as a repeating number

-22/99

Hence, -0.22 as  a repeating fraction is -22/99

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Given : number -3/4 - and  number line​

To Find :  represent -3/4 - on number line​

Solution:

Numbers with a negative sign are less than zero

Right of zero represented by ‘+’ sign and to the left of zero represented by ‘–’ sign.

+ sign numbers can be denoted as simply numbers  

On a number line the number increases as we move to the right and decreases as we move to the left.  

1 : Draw a line and mark some points at equal distance on it

Mark a point as zero on it. Points to the right of zero are positive integers and are marked simply 1, 2, 3  and so on , while points to the left of zero are negative integers and are marked – 1, – 2, – 3 and so on

- 3/4

Divide number line between -1 & 0  in  4 Equal parts and go 3 part left of 0 to show - 3/4 on number line

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Given that there are s sides of a regular polygon, the change in length of each side if the are is increased by a factor of x is (x/s) m .

Let the number of sides of the regular polygon be s.

Given area of polygon = 144 \(m^2\)

The area of a regular polygon is the length of its side * number of sides.

Area of polygon = Number of sides * length of side

Length of side =  Area of polygon/Number of sides = 144/s m

If the area of polygon increases by x \(m^2\\\), the new area becomes (144+x)\(m^2\).

The new length of side = (144+x)/s

The change in length of side = new length - old length = \(\frac{144+x}{s} - \frac{144}{s} = \frac{x}{s}\)

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Answer:

d

Step-by-step explanation:

(x+3)/6 = 5/4

butterfly method

4(x+3) = 5×6

4x+12 = 30

4x = 30-12

4x = 18

x = 18/4

x = 9/2

There are 6 different ways to select a cone if it matters which flavor is on top, which is in the middle and which is on the bottom by permutation.

Permutation is the arrangement of objects when the order of arrangement matters.

Here the arrangement is done in 3! ways.

The formula used is

nPr= n!/(n-r)!

Here n=3, r=3

Therefore 3P3= 3!/ (3-3)!= 3!/ 0! =3!= 6 ways( since 0!=1 )

Alternatively,

When selecting a cone, there are six distinct possibilities if it matters which flavor is on top, which is in the middle, and which is on the bottom.

There are three options for the flavor that will be on top, followed by two options for the middle flavor, and then the remaining flavor for the bottom cone.

This gives you 3*2*1=6 possible cone arrangements.

Suppose we have three flavors: vanilla, chocolate, and strawberry.

If it is important which flavor is on top, which is in the middle, and which is on the bottom, there are only six distinct options that can be chosen for the cone. The six choices are:

v a n i l l a, c h o c o l a t e, s t r a w b e r r y

v a n i l l a, s t r a w b e r r y, c h o c o l a t e

s t r a w b e r r y, c h o c o l a t e, v a n i l l a

s t r a w b e r r y, v a n i l l a, c h o c o l a t e

v a n i l l a, c h o c o l a t e, s t r a w b e r r y

c h o c o l a t e, s t r a w b e r r y, vanilla

Therefore, there are 6 different ways to select a cone if it matters which flavor is on top, which is in the middle and which is on the bottom.

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Answer:

y = 1/2 x - 6

Step-by-step explanation:

y = mx + b

y = (1/2)x + b

-4 = (1/2) × 4 + b

-4 = 2 + b

b = -6

y = 1/2 x - 6

The answer is:

\(\rm{y=\dfrac{1}{2} x-6}\)

Work/explanation:

Given the slope and a point on the line, we can write the equation in point slope form, which is:

\(\rm{y-y_1=m(x-x_1)}\)

Where m is the slope and (x₁, y₁).

Plug the data in the formula:

\(\rm{y-(-4)=\dfrac{1}{2}(x-4)}\)

Simplify:

\(\rm{y+4=\dfrac{1}{2} (x-4)}\)

Now focus on the right side & simplify it :

\(\rm{y+4=\dfrac{1}{2}x-2}\)

Finally, subtract 4 on each side:

\(\rm{y=\dfrac{1}{2} x-2-4}\)

Simplify:

\(\rm{y=\dfrac{1}{2} x-6}\)

This is our equation in slope intercept form.

a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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