The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips.

(a) What is the probability that a randomly selected bag contains betesen 1000 and 1400 chocolate chips?

(b) What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips?

(c) What proportion of bags contains more than 1175 chocolate chips?

(d) What is the percentile rank of a bag that contains 1425 chocolate chips?

Answer:

5 3/7

Step-by-step explanation:

Answer:

let's see what to do

Step-by-step explanation:

\( \frac{38}{7} = \frac{35 + 3}{7} = \frac{35}{7} + \frac{3}{7} = 5 + \frac{3}{7} \\ \)

End....

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Answer:

b

Step-by-step explanation:

4 to -1 is 5 units

Answer:

slope = 2

Step-by-step explanation:

will make it so simple and short

slope = rise / run

slope = 6 / 3

slope = 2

Answer:

B

Step-by-step explanation:

The formula for slope is (y2-y1)/(x2-x1)

In this case it is (1+5)/(3-0)

6/3

2

Step-by-step explanation:

this will be the answer of the question where quotient is 3 and the remainder is 35x + 210

Answer:

\(\frac{6x - 1}{2(x - 6)}\)

Step-by-step explanation:

\(6x^2 + 35x - 6 \ \div \ 2x^2 - 7 2\\\\6x^2 + 36x - x - 6 \ \div \ 2(x^2 - 36)\\\\6x(x + 6) - 1(x + 6) \ \div \ 2(x^2 - 6^2)\\\\(6x - 1)(x + 6) \ \div \ 2(x- 6)(x+ 6) \ \ \ \ \ \ \ \ \ \ [ \ x^2 -a^2 = (x-a)(x+a) \ ]\\\\\frac{(6x - 1)(x + 6) }{2(x- 6)(x+ 6)} = \frac{6x - 1}{2(x-6)}\)

The amount paid by the store is given as follows:

$111.54.

The amount paid by the store is obtained applying the proportions in the context of the problem.

The original price is symbolized as follows:

x.

The markup price was of 30%, hence the decimal multiplier is given as follows:

130% = 1.3.

The selling price is of $145, hence the original price is obtained as follows:

1.3x = 145

x = 145/1.3

x = $111.54.

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The equation solved for the variable are;

h = S- 2B/p

b = S - hp/2

To determine the equation, we need to know that the subject of formula for  an equation is described as the variable that is made to stand on one end of the equality sign.

It is the variable that is being worked out.

From the information given, we have that;

S= hp + 2B.

To make the height with the variable 'h' the subject, we have;

collect the terms

hp = S - 2B

Divide by the coefficient

h = S- 2B/p

For b, we have;

S - hp = 2b

divide by the coefficient

b = S - hp/2

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Answer:

Pita, by 44 cm

Step-by-step explanation:

1,35 m = 135 cm

179 cm > 135 cm, so Pita is taller than Rachael

The difference is:

179 cm - 135 cm = 44 cm

Answer:

x = 25°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°

The given triangle is a right triangle which means one of its angle has a measure of 90°

since thd other angle is given as 65 to calculate x we just add the given measures and subtract it from 180

90° + 65 + x = 180

155 + x = 180 subtract 155 from both sides

x = 25°

The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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Answer:

x = 15

Step-by-step explanation:

the segment inside the triangle is an angle bisector and divides the side opposite the bisected angle into segments that are proportional to the other two sides, that is

\(\frac{x}{21-x}\) = \(\frac{25}{10}\) ( cross- multiply )

10x = 25(21 - x)

10x = 525 - 25x ( add 25x to both sides )

35x = 525 ( divide both sides by 35 )

x = 15

Answer:

length = 4 feet

width = 9 feet

Step-by-step explanation:

Perimeter of a rectangle = 2W + 2L,  where W is the width and L is the length

If the perimeter is 26 feet, then:   26 = 2W + 2L

If the width is 5 feet more than the length, then:  W = L + 5  

Substitute  W = L + 5  into  26 = 2W + 2L and solve for L:

26 = 2(L + 5) + 2L

26 = 2L + 10 + 2L

26 = 4L + 10

16 = 4L

L = 4

Now substitute L = 4 into W = L + 5 to find W:

W = 4 + 5 = 9

Therefore, length = 4 feet and width = 9 feet

Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, the length of the window is 4 feet and the width of the window is 9 feet.

Answer:

b) - 10

Step-by-step explanation:

To find the average rate of change, we have divide the change in y of f(x) , by the change in x(input).

   \(\sf \boxed{\text{\bf Average rate of change = $\dfrac{f(b)-f(a)}{b-a}$}}\)

 a = 4 ; f(a) = -17

b = 6 ;   f(b) = -37

     \(\sf Average \ rate \ of \ change = \dfrac{-37-[-17]}{6-4}\)

                                         \(\sf =\dfrac{-37+17}{2}\\\\=\dfrac{-20}{2}\\\\=-10\)

Answer:

Step-by-step explanation:

no          x                y                   xy                               x²

1           2300         74             170200                      5290000

2          1800          73             131400                      3240000

3          2500         70             175000                     6250000

4          2700         66             178200                     7290000

5          2000         63             126000                     4000000

6          1700          62             105400                     2890000

7           1500         52              78000                      2250000

8           2700        68              183600                    7290000

Total   17200         528           1147800                   38500000

Mean of x is

\(\bar x = \frac{17200}{8} =2150\)

Mean of y is

\(\bar y = \frac{528}{8} =66\)

From the table above

we find \(\hat B_1\)

\(\hat B_1=\frac{\sum xy- \bar x \sum y}{\sum x^2- n \barx^2} \\\\=\frac{1147800-2150(528)}{38500000-8(2150)^2} \\\\=\frac{1147800-1135200}{38500000-36980000} \\\\=\frac{12600}{1520000} \\\\=0.008289\)

so \(\hat b_0\) is

\(\hat b_0=\bar y-\bar B_1 x\\\\=66-0.008289(2150)\\\\=66-17.82135\\\\=48.17865\)

The line of regression is

The price x is 1900

\(\hat y =\hat B_0+\hat B_1x\\\\=48.17865+0.008289\times1900\\\\=48.17865+15.7491\\\\=63.928\)

The line of regression is 63.928

Answer:

y=48.2+0.00829x;64

Step-by-step explanation:

The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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Let "x" represent the age of Brian.

Andrew is elder than Brian by 2 years, we can symbolize his age as "x+2"

Frank is twice as old as Andrew, we can symbolize his age as "2(x+2)"

Sarah has half the age of Brian's, we can symbolize her age as "x/2"

Frank ans Sarah's ages differ by 40 years, we can symbolize this as:

Solve the term is parenthesis

x=24 years

Andrew's age is

Andrew is 26 years old

Answer: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Step-by-step explanation:

Hope this is right!!!!

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Answer:

A.

Step-by-step explanation:

In the attached file

Answer:

b that is the corect answer

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

f(-4) means to find the y-value where x is -4. The blue graph passes through the point (-4,-1), so y=-1 when x=-4.

Based on the assumption mentioned above, the dimensions of the open box would be:

Length: 5 units

Width: 3.75 units

Height: 2.5 units.

To create an open box as a prop for the school play, Jackson will need three dimensions: length, width, and height. The given dimensions provided are 5, 3.75, and 2.5, but it is not specified which dimension corresponds to which measurement.

To determine which dimension represents which measurement (length, width, or height), we need additional information or clarification. Typically, the length refers to the longest side of the box, the width is the shorter side, and the height is the vertical dimension.

If we assume that 5 represents the length, 3.75 represents the width, and 2.5 represents the height, we can proceed with those dimensions. However, it's important to note that without confirmation or further context, this assumption may not be accurate.

Therefore, based on the assumption mentioned above, the dimensions of the open box would be:

Length: 5 units

Width: 3.75 units

Height: 2.5 units.

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Answer:

what passes through those points and what do yoy need to know about them?

The difference in speed between Explorer B and Explorer A is 600 miles per hour.

In order to determine how fast the satellites are travelling, the average speed of the satellites have to be calculated. Average speed is the total distance covered per time.

Average speed = total distance / total time

Average speed of Space Explorer B = 74,400 / 12 = 6,200 miles per hour

Average speed of Space Explorer A = 72,800 / 13 = 5,600 miles per hour

Difference in speed = 6,200 miles per hour - 5,600 miles per hour = 600 miles per hour.

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Answer:

critical value is considered part of the rejection region.

Step-by-step explanation:

hope this helps!

Linear is a straight line. You might have heard of Linear Function.

\(y = mx + b\)

The equation above is slope-intercept form.

Exponential is both increasing graph and decreasing graph depending on the coefficient.

Exponential Equation

\(y = {a}^{x} \: \: \: (a > 0) \: \: (a \neq1)\)

Exponential Graph increases when a-term is greater or equal to 1.

Exponential Graph decreases when a-term is greater than 0 but less than 1.

From the equation, it is exponential of x-term as an exponent. The equation matches with exponential form.

The question is missing some parts. Here is the complete question.

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost in type II ovens. A samplle of 61 type I ovens has a mean repair cost of $79.60, with a standard deviation of $23.47. A sample of 45 type II ovens has a mean repair cost of $75.25, with standar deviation of $15.07. Conduct a hypothesis test of the technician's claim at the 0.05 level of significance. Let \(\mu_{1}\) be the true mean repair cost for type I ovens and \(\mu_{2}\) be the true mean repair cost for type II ovens.

Step 1 of 4: State null and alternative hypothesis for the test.

Step 2 of 4: Compute the value of test statistics. Round your answer to 2 decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to 3 decimal places.

Step 4 of 4: Make the decision for the hypothesis test. (Reject or fail to reject Null Hypothesis)

Answer and Step-by-step explanation:

First, state null and alternative hypothesis:

\(H_{0}: \mu_{1}=\mu_{2}\)

\(H_{a}: \mu_{1}>\mu_{2}\)

Use z-statistics:

\(z = \frac{x_{1}-x_{2}}{y}\)

where x₁ and x₂ are the means and:

\(y=\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}} }\)

Calculating value of test stattistic:

\(y=\sqrt{\frac{(23.47)^{2}}{61}+\frac{75.25^{2}}{45} }\)

\(y = \sqrt{9.030+5.046}\)

\(y = \sqrt{14.076}\)

y = 3.752

\(z = \frac{79.6-75.25}{3.752}\)

z = 1.16

The test statistics is z = 1.16

The decision rule for rejecting null hypothesis is: \(\alpha\) ≤ test statistics

Using z-score table, it is possible to determine p-value, which is:

p-value = 0.877

Comparing p-value with level of significance (α = 0.05):

0.877 > 0.05

Therefore, we fail to reject the null hypothesis.

Differentiate both sides of

\(6x f(x)^4 + 9x^3 f(x) = 78\)

with respect to x :

\(\left(6x f(x)^4 + 9x^3 f(x)\right)' = (78)' \\\\ 6\left(xf(x)^4\right)' + 9\left(x^3f(x)\right)' = 0\)

Use the product and chain rules for the left side:

\(\left(xf(x)^4\right)' = (x)'f(x)^4 + x\left(f(x)^4\right)' = f(x)^4 + 4xf(x)^3f'(x)\)

\(\left(x^3f(x)\right)' = \left(x^3\right)'f(x) + x^3f'(x) = 3x^2f(x)+x^3f'(x)\)

Solve for f '(x) :

\(6\left(f(x)^4+4xf(x)^3f'(x)\right) + 9\left(3x^2f(x)+x^3f'(x)\right) = 0 \\\\ 6f(x)^4+27x^2f(x) + \left(24xf(x)^3+9x^3\right)f'(x) = 0 \\\\ f'(x) = -\dfrac{6f(x)^4+27x^2f(x)}{24xf(x)^3+9x^3}\)

Then

\(f'(1) = \boxed{\dfrac{14}{61}}\)

Answer:

163,665

Step-by-step explanation:

To calculate the amount of fruit flies that will be there in 20 weeks, you can use the following formula:

FV= PV*(1+r)^n

FV= Future value

PV= Present value= 10,000

r= rate= 15%

n= number of periods= 20

FV=10,000*(1,15)^20

FV=163,665

According to this, the answer is that there will be 163,665 fruit flies in 20 weeks.