On average a clothing store gets 120 customers per day. What is the probability of getting 35 customers in the first four hours? Assume the store is open 12 hours each day.

The specified scale factor of the dilation from S to M is 3/2 therefore, the scale factor of the dilation transformation from M to S is 2/3

A dilation is a transformation in which the lengths of the sides of the image are increased or decreased in the proportion, specified by a scale factor to the dimensions of the pre-image.

The specified scale factor from triangle S to triangle M = 3/2

3/2 = 1.5

Therefore, the length of the sides of triangle M are 1.5 times the lengths of the sides of triangle S

Let L represent the length of a side of triangle S, we get;

The length of the corresponding side on triangle M = 1.5 × L

The scale factor from triangle M to triangle S is found by taking the ratio of the corresponding sides of triangle S and M as follows;

Scale factor, SF, from M to S  = Length of a side on triangle S ÷ Length of the corresponding side on triangle

Therefore;

\(SF = \dfrac{L}{1.5\cdot L} = \dfrac{1}{1.5}\)

1.5 = 3/2, therefore;

\(SF = \dfrac{1}{1.5} = \dfrac{1}{\frac{3}{2} } =\dfrac{2}{3}\)

Therefore, the scale factor from M to S is 2/3

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If the cafeteria ordered 400 paper plates. They used 226 at breakfast. They bought 100 more. Then, they used some plates for lunch. Now there are 78 plates. The number of  plates that was used at lunch is 196.

Given :

Paper plates ordered = 400 plates

Plates used for breakfast = 226

Additional plate bought = 100

Plate used for lunch = ?

Hence,

Let calculate the plate left after breakfast

Number of plates = Paper plates ordered - Plates used for breakfast

Number of plates = 400 plates - 226 plates

Number of plates = 174 plates

Now let determine the plates that were used for lunch

Pates used for lunch :

Pates used for lunch = (174 + 100) -78

Pates used for lunch = 274 -78

Pates used for lunch = 196 plates

Therefore we can conclude that the number of  plates that was used at lunch is 196 plates .

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Answer:

It can be used to figure it out because you will multiply the 10% by 4 and you'll get 40 percent.

Step-by-step explanation:

Please mark brainliest

Answer:

You can determine by adding the percentage up. See down below.

Step-by-step explanation:

64 x 10% = 6.4

40% will mean 6.4 x 4 which equals 25.6

40% = 25.6

10% = 6.4

10% of 46 would be 4.6.

Answer: 2:3

Step-by-step explanation:

12/6=2

18/6=3

Answer:

Option A.

Step-by-step explanation:

Options:

A. 3 to 4

B. 4 to 3

C. 4 to 7

D. 7 to 4

In order to simplify a fraction the numerator and the denominator have to have common factors that they can be divided by.

\(\frac{12}{16}\)

Divide

\(CF=4\)

\(12\div4=3\)

\(16\div4=4\)

\(=\frac{3}{4}\)

Hope this helps.

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Bob had 50 pencils in the beginning.

A fractional number is expressed in the form -

x/y    {where y ≠ 0)

Given is that Bob gave four - fifths of his pencils to Barbara, then he gave two - thirds of the remaining pencils to bonnie.

Assume that he had {x} pencils in the beginning. We can write -

4x/5 + 2/3(x - 4x/5) = 10

4x/5 + 2x/3 - 8x/15 = 10

x(4/5 + 2/3 - 8/15) = 10

x = 10/0.93

x = 50

Therefore, Bob had 50 pencils in the beginning.

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{QUESTION IN ENGLISH -

Bob gave four fifths of his pencils to Barbara, then he gave two thirds of the remaining pencils to bonnie, if he ended up with 10 pencils for himself... how many pencils did bob have at the beginning?}

Answer:

y= -6

Step-by-step explanation:

For part a, you can use a chi-squared test to determine whether the variance in the sample exceeds the maximum acceptable variance in the population.

The null hypothesis for this test is that the variance in the sample is equal to or less than the maximum acceptable variance, and the alternative hypothesis is that the variance in the sample is greater than the maximum acceptable variance.

To perform the test, you need to first calculate the chi-squared statistic, which is given by:

X² = (n-1) * s² / σ²

where n is the sample size (in this case, 15), s is the sample standard deviation (in this case, 0.014 inches), and σ is the maximum acceptable variance (in this case, 0.0001 inches).

Plugging in the values, you get:

X² = (15-1) * .014² / .0001² = 27.44

Next, you need to determine the degrees of freedom for the test. In this case, the degrees of freedom is equal to the sample size minus 1, so the degrees of freedom is 14.

With the chi-squared statistic and the degrees of freedom, you can look up the p-value in a chi-squared table or use a chi-squared calculator to determine the p-value. The p-value is the probability of observing a chi-squared statistic as large or larger than the one you calculated, assuming the null hypothesis is true.

If the p-value is less than the significance level (in this case, .10), then you can reject the null hypothesis and conclude that the variance in the sample exceeds the maximum acceptable variance. In this case, the p-value is between 0.01 and 0.025, so you can reject the null hypothesis and conclude that the variance in the sample exceeds the maximum acceptable variance.

For part b, you can use a t-test to construct a 90% confidence interval estimate of the variance in the population. The confidence interval is an interval estimate of the true variance in the population, and the 90% confidence level means that there is a 90% probability that the true variance in the population falls within the confidence interval.

To construct the confidence interval, you first need to calculate the standard error of the variance, which is given by:

SE = s / √(n-1)

where s is the sample standard deviation and n is the sample size. Plugging in the values, you get:

SE = 0.014 / √(15-1) = 0.0041

Next, you need to determine the t-value for the confidence interval. The t-value is based on the degrees of freedom and the confidence level. With 14 degrees of freedom and a 90% confidence level, the t-value is 1.76.

With the standard error and the t-value, you can construct the confidence interval as follows:

Lower bound = s² - t * SE = .014² - 1.76 * 0.0041 = 0.00012 inches

Upper bound = s² + t * SE = .014² + 1.76 * 0.0041 = 0.00042 inches

Therefore, the 90% confidence interval estimate of the variance of the ball bearings in the population is .00012 to .00042 inches.

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Answer:

13

Step-by-step explanation:

because...math

The main limiting issue with the domain this function is potentially picking an x-value that makes that denominator equal 0, because dividing by 0 is bad.

So, the domain will be all real numbers, except for those that make g(x)=0.

g(-1) = 0, g(-2)=0, and g(2) = 0, so -1, -2, and 2 must be excluded from the domain.

Your answer is {x ∈ ℝ| x ≠ −1, −2, 2}.

Answer:

\(\textsf{Domain}: \quad \{ x \in \mathbb{R}\;|\;x \neq -1, -2, 2\}\)

Step-by-step explanation:

Given functions:

\(\begin{cases} f(x)=x^2+6x+5\\g(x)=x^3+x^2-4x-4\end{cases}\)

Factor function f(x):

\(\begin{aligned}\implies f(x)&= x^2+6x+5\\&=x^2+x+5x+5\\&=x(x+1)+5(x+1)\\&=(x+5)(x+1)\end{aligned}\)

Factor function g(x):

\(\begin{aligned}\implies g(x)&=x^3+x^2-4x-4\\&=(x+1)(x^2-4)\\&=(x+1)(x+2)(x-2)\end{aligned}\)

Therefore the composite function is:

\(\implies \dfrac{f(x)}{g(x)}=\dfrac{(x+5)(x+1)}{(x+1)(x+2)(x-2)}\)

A rational function is undefined when the denominator equals zero.

Therefore, the given composite function is undefined when (x+1)(x+2)(x-2)=0:

The domain of a function is the set of all possible input values (x-values).

Therefore, as the composite function is undefined when x = -1, x = -2 and x = 2, the domain is:

Answer:

\(S_{45}\) = 9000

Step-by-step explanation:

there is a common difference between consecutive terms , that is

11 - 2 = 20 - 11 = 9

this indicates the sequence is arithmetic with nth term

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 2 and d = 9 , then

\(S_{45}\) = \(\frac{45}{2}\) [ (2 × 2) + (44 × 9) ]

    = 22.5(4 + 396)

    = 22.5 × 400

    = 9000

The distance is 41.

The distance between two points of a line is given as:

Distance =  =  \(\sqrt{(c - a)^2 + (d - b)^2}\)

Where (a, b) and (c, d) are the two points.

We have,

Two points are (-18, 9) and (22, 0).

We can consider the points as:

(-18, 9) = (a, b)

(22, 0) = (c, d).

Now,

Substituting the values in the distance formula.

Distance =  =  \(\sqrt{(c - a)^2 + (d - b)^2}\)

=  \(\sqrt{(c - a)^2 + (d - b)^2}\)

= \(\sqrt{(22 + 18)^2 + (0 - 9)^2}\)

[ 22 + 18 = 40 ]

[ 40 x 40 = 1600 ]

[ 9 x 9 = 81 ]

So,

= \(\sqrt{1600 + 81 }\)

= \(\sqrt{1681}\)

[ 41 x 41 = 1681 ]

= 41

Thus,

The distance between (-18, 9) and (22, 0) is 41.

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Answer:

x = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

8 = 2x + 4

Step 2: Solve for x

Answer:

3

Step-by-step explanation:

9514 1404 393

Answer:

  neither parallel nor perpendicular

Step-by-step explanation:

Putting both in slope-intercept form, we can compare the slopes.

  y = -x -2

  y = -2/5x +6

The different slopes have a product of 2/5, not -1, so the lines are neither parallel (same slope) nor perpendicular (product is -1).

__

A graph of the lines confirms this.

Answer:

\( \cos(x) = - \frac{5}{ \sqrt{41} } \)

\( \csc(x) = \frac{ \sqrt{41} }{4} \)

\( \tan(x) = - \frac{4}{5} \)

Step-by-step explanation:

We know that (-5,4) is the terminal side. This means out legs will measure 5 and 4 if we graph it on a triangle.

We need to find the cos, csc, and tan measure of this point.

We can find cos by using the formula of

\( \cos(x) = \frac{adj}{hyp} \)

The adjacent side is -5 and we can find the hypotenuse by doing pythagorean theorem.

\( { - 5}^{2} + {4}^{2} = \sqrt{41} \)

So using the info the answer is

\( \cos(x) = \frac{ - 5}{ \sqrt{41} } \)

We can find tan but first me must find sin x.

\( \sin(x) = \frac{opp}{hyp} \)

\( \sin(x) = \frac{4}{ \sqrt{41} } \)

So now we just use this identity,

\( \tan(x) = \sin(x) \div \cos(x) \)

\( \tan(x) = \frac{ \frac{4}{ \sqrt{41} } }{ \frac{ - 5}{ \sqrt{41} } } = - \frac{4}{5} \)

So tan x=

\( - \frac{ 4}{5} \)

We can find csc by taking the reciprocal of sin so the answer is easy which is

\( \frac{ \sqrt{41} }{4} \)

Answer:

bro!! I'm on the same question on ap3x!!

lol

Step-by-step explanation:

Sorry this is so late.

The answer is "Add the left side of equation 2 to the left side of equation 1"

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The slope and the intercept for this problem are given as follows:

Hence the functions that models the cost for x tons with each company are given as follows:

The costs will be the same when:

C2(x) = C1(x)

300.75x = 5005 + 50.5x

x = 5005/(300.75 - 50.5)

x = 20 tons.

The cost will be of:

C2(20) = 300.75 x 20 = $6,015.

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Answer:

The correct answer would be the purple graph

Step-by-step explanation:

I hope this helps!

The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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Answer:

Step-by-step explanation:

Given that:

t          0           1              2          3            4            5           6            7

A'(t)    0.91       0.83       0.76     0.69       0.62      0.58      0.48      0.44

a)  \(\Delta x = \dfrac{5-0}{5}\)

\(\Delta x = 1\)

\(L_ 5= \Delta x ( (A'(0)+A'(1)+A'(2)+A'(3)+A'(4)) \\ \\ = 1 (0.91 + 0.83+ 0.76 +0.69 + 0.62 ) \\\\ L_5 =1( 3.81) \\ \\ \mathbf{L_5 = 3.81}\)

\(R_ 5= \Delta x ( (A'(1)+A'(2)+A'(3)+A'(4)+A'(5)) \\ \\ = 1 ( 0.83+ 0.76 +0.69 + 0.62 +0.58) \\\\ R_5 =1( 3.48) \\ \\ \mathbf{R_5 = 3.48}\)

The true statement:

\(Since, R_5 = 3.48 \ and \ L_5 = 3.81; \\ \\ Then : R_5 \le \int \limits ^5_0 A'(t) dt \le L_5\)

From the given number line, the variable "m" could take the values of -2, -3.5, 0, and -5

To determine which values the variable "m" could take from the given number line, we need to identify the points or intervals on the number line that correspond to the possible values of "m".

Looking at the number line, we can see the following values:

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

From this list, the values that "m" could take are:

-2, -3.5, 0, -5

These values are present on the number line, indicating that they are possible values for "m".

Therefore, the variable "m" could take the values -2, -3.5, 0, and -5 from the given number line.

It's important to note that the values -7 and 4 are not present on the number line, so they are not possible values for "m" based on the information provided.

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The area of the given figure is 27.5 square centimeter which has a rectangle and triangles

The given figure has a rectangle and triangles

The area of rectangle is length times width

Area of rectangle =5×4

=20 square centimeter

Area of triangle =1/2×base×height

=1/2×2.5×3

=7.5/2

=3.75 square centimeter

As there are two triangle = 2(3.75)

=7.5 square centimeter

Total area = 7.5+ 20

=27.5 square centimeter

Hence, the area of the given figure is 27.5 square centimeter

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Answer:

Step-by-step explanation:

Use the slope formula.

\(\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1} }\)

Use the distance formula.

\(: \Longrightarrow \sf{\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}}\)

\(\sf{x_2=8}\\\\\\\sf{x_1=3}\\\\\\\sf{y_2=2}\\\\\\\sf{y_1=2}\)

Rewrite the problem down.

\(\sf{\sqrt{\left(8-3\right)^2+\left(2-2\right)^2}}\)

Solve.

Use the order of operations.

PEMDAS stands for:

Solve parentheses, first.

⇒ (8-3)²

⇒ 8-3=5

⇒ 5²+(2-2)²

⇒ (2-2)=0

⇒ 0²

Rewrite the problem down.

⇒ 5²+0²

Do exponents next.

⇒ 5²=5*5=25

⇒ 0²=0*0=0

⇒ 25+0

Add.

⇒ 25+0=25

You can also divide the numbers from left to right.

→ 25/5=5

I hope this helps. Let me know if you have any questions.

Answer:

-14x-7

Step-by-step explanation:

\((-8x+2)-(6x+9)\)

\(=-8x-6x+2-9\)

\(=-14x-7\)

Answer:

2x - 7

Step-by-step explanation:

Rewrite this expression without parentheses.  Distribute that -1 across 6x and 9:

-8x + 2 - 6x - 9 = 2x - 7

Answer:

The wife IQ is 103 when the husband IQ is 100.

Step-by-step explanation:

The given equation of the regression line is y = -11 + 1.14x, where x represents the IQ score of the husband.

If the husband IQ is 100 the the wife IQ is

y = -11 + 1.14x,

y = -11 + 1.14(100)

y = -11 + 114

y = 103

Answer: D

Step-by-step explanation:

To determine which ordered pair is a solution to the inequality, we can substitute the values of x and y into the inequality and check if it is true.

Let's start with ordered pair A (80, 6):

1/4x ≤ 7/3y + 2

1/4(80) ≤ 7/3(6) + 2

20 ≤ 14 + 2

20 ≤ 16

This is not true, so ordered pair A is not a solution to the inequality.

Now let's try ordered pair B (48, 9):

1/4x ≤ 7/3y + 2

1/4(48) ≤ 7/3(9) + 2

12 ≤ 21 + 2

12 ≤ 23

This is also not true, so ordered pair B is not a solution to the inequality.

Next, let's try ordered pair C (40, 3):

1/4x ≤ 7/3y + 2

1/4(40) ≤ 7/3(3) + 2

10 ≤ 7 + 2

10 ≤ 9

This is false, so option C is not a solution to the inequality.

Finally, we have option D: (2, -6)

1/4(2) ≤ 7/3(-6) + 2

1/2 ≤ -14 + 2

1/2 ≤ -12

This is true, so option D is a solution to the inequality.

Therefore, the answer is D: (2, -6).

Answer:

x + 2y - 5 = 0

Step-by-step explanation:

We can see that , the graph passes through (0,2.5) and (5,0) . Therefore the ,

We can use the intercept form of equation as ,

=> x/a + y/b = 1

=> x/5 + y/2.5 = 1

=> x + 2y/5 = 1

=> x + 2y = 5

=> x + 2y -5 = 0 .

This equation can be verified by plotting the graph .[ Refer to attachment ]