As an avid cookies fan, you strive to only buy cookie brands that have a high number of chocolate chips in each cookie. Your minimum standard is to have cookies with more than 10 chocolate chips per cookie. After stocking up on cookies for the current Covid-related self-isolation, you want to test if a new brand of cookies holds up to this challenge. You take a sample of 15 cookies to test the claim that each cookie contains more than 10 chocolate chips. The average number of chocolate chips per cookie in the sample was 11.16 with a sample standard deviation of 1.04. You assume the distribution of the population is not highly skewed. Alternatively, you're interested in the actual p value for the hypothesis test. Using the previously calculated test statistic, what can you say about the range of the p value?

Answer:

g(-1)=4 ,f(g(-1))=18

Step-by-step explanation:

g(-1):

1-3(-1)=4

f(g(-1)):

sub in g(-1) as x

(4)^2+2=18

Where the above is given, the required angle m∠BAC = 45°.

In triangle ABC. AC represents the foreman’s line of sight to the top of the landfill. Landfill height is BC

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

According to conditions angle b = 90°

The sum of angles of a triangle= 180°

That is a + b + c = 180

Therefore, c = a

       a = (180 - b)/2

          = (180 - 90) / 2

          = 90 / 2

          = 45°

Hence, the required angle m∠BAC = 45°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Question 1 Create Triangle ABC by drawing AC. Segment AC represents the foreman’s line of sight to the top of the landfill. What is Angle m BAC?

To minimize the total weekly cost, the company should produce 23 units in Miami and 135 units in Baltimore.

To minimize the total weekly cost function C(x, y) = x^2 + (1/5)y^2 + 46x + 54y + 800, we need to find the values of x and y that minimize this function.

We can solve this problem using calculus. First, we calculate the partial derivatives of C(x, y) with respect to x and y:

∂C/∂x = 2x + 46

∂C/∂y = (2/5)y + 54

Next, we set these partial derivatives equal to zero and solve for x and y:

2x + 46 = 0 (equation 1)

(2/5)y + 54 = 0 (equation 2)

Solving equation 1 for x:

2x = -46

x = -23

Solving equation 2 for y:

(2/5)y = -54

y = -135

So, according to the partial derivatives, the critical point occurs at (x, y) = (-23, -135).

To determine if this critical point corresponds to a minimum, we need to calculate the second partial derivatives of C(x, y):

∂^2C/∂x^2 = 2

∂^2C/∂y^2 = 2/5

The determinant of the Hessian matrix is:

D = (∂^2C/∂x^2)(∂^2C/∂y^2) - (∂^2C/∂x∂y)^2 = (2)(2/5) - 0 = 4/5 > 0

Since the determinant is positive, we can conclude that the critical point (x, y) = (-23, -135) corresponds to a minimum.

Therefore, 23 units in Miami and 135 units in Baltimore should be produced to minimize the total weekly cost.

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Answer:

1) -4<x<-2

2) x<-7 or x75

3) 2<x<7

4) x<-5 or x<6

5) x<-8 or x74

Step-by-step explanation:

Answer:

27/64m^12 n^6

Step-by-step explanation:

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

5x + 15 = 15 + 5x

5x = 5x

x = x

?

Answer:

sample answer for edmentum

Step-by-step explanation:

The condition that z ′ (t) never vanishes is necessary to ensure that smooth curves have no cusps because if z ′ (t) does vanish at a point, then the curve is not smooth at that point.

The condition that z'(t) never vanishes is necessary to ensure that smooth curves have no cusps.
1. First, let's define the terms:
  - "Never vanishes": A function or its derivative doesn't equal zero at any point in its domain.
  - "Smooth curves": Curves with continuous derivatives at every point.
  - "No cusps": Points where the curve has an abrupt change in direction, leading to an undefined tangent.
2. The condition z'(t) never vanishes means that the derivative of the curve with respect to the parameter t always exists and is never zero. This implies that the tangent vector at every point on the curve is well-defined and non-zero.
3. Smooth curves have continuous derivatives, which ensures that there is a gradual change in the tangent vector along the curve. This gradual change helps to prevent any abrupt changes in the curve's direction.
4. The presence of a cusp in a curve would imply that the tangent at that point is undefined or infinite. However, if z'(t) never vanishes, the tangent vector is always well-defined and non-zero, thus eliminating the possibility of a cusp.
In conclusion, the condition that z'(t) never vanishes is necessary to ensure that smooth curves have no cusps, as it guarantees well-defined, non-zero tangent vectors at every point on the curve, preventing abrupt changes in direction that would cause a cusp.

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Given:

Type 41 words per min.

Find-:

How many min. take you to type 615 words

Explanation-:

1 min words type = 41

For 615 words,

41 words typed in 1 min.

For 1 words type it take min is:

For 615 words:

For type 615 words take time is 15 min.

Answer:

15 minutes.

Step-by-step explanation:

615 / 41

= 15

Answer:

\(\huge\boxed{\sf y=-\frac{3}{8} x+\frac{1}{2} }\)

Step-by-step explanation:

\(y=mx+b\)

Where m is slope and b is y-intercept

\(\displaystyle m=-\frac{3}{8} , \ b =\frac{1}{2}\)

Put in the above general equation!

So, the equation becomes:

\(\displaystyle y=-\frac{3}{8} x+\frac{1}{2}\)

Answer: y= (-3/8)x+(1/2)

Step-by-step explanation: Since you're given the slope (-3/8) and the y-intercept (1/2) it is easy to write the equation of the line. The equation of a line is defined as y=mx+b; where m is the slope (-3/8) and b is y-intercept (1/2). Therefore, the equation you are looking for is y=(-3/8)x+(1/2)

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

NO

Step-by-step explanation:

b/c when u say (5x)³ u will multiple 5x 3 times by itself . but when we say 5x³ you will multiple x 3 time . so they are d/t and you can't write 5x³ instade of (5x)³ .

Answer:

The number is 4.

The step describe to solve the problem is: add five and then multiply by

Step-by-step explanation:

Let the number be x.

As per the given condition as:

The difference of twice a number and five is three.

"Twice a number" means

"difference of twice a number and five" means

therefore, the translation of the given word problem to an equation is:

Now, solve the equation :

Addition Property of equality states that you add the same number to both sides of an equation.

Add 5 to both sides of an equation we get;

2x-5+5=3+5

Simplify:

2x = 8

Multiplication property of equality states that you multiply the same number to both sides of an equation.

Multiply by  both sides we get;

Simplify:

x = 4

The steps which describe to solve the problem is: add five and then multiply by

Therefore, the number x = 4

4 the answer is four as 4×2=8 and 8-5=3

Answer:

2p is the answer

Step-by-step explanation:

There would be a 2p unit gap

Answer:

4

Step-by-step explanation:

1/2x + 8 ≤10 / ×2

x + 16 ≤ 20

x ≤ 20 - 16

x ≤ 4

\(\dfrac{1}{2} x+8\leq 10\)

Subtract 8 from both sides:

\(\dfrac{1}{2} x+8-8\leq 10-8\)

\(\dfrac{1}{2} x\leq 2\)

Multiply both sides by 2:

\(2\times(\dfrac{1}{2} x)\leq 2\times(2)\)

\(\boxed{x\leq 4}\)

Answer:

Step-by-step explanation:

Using Law of Cosine

Suppose Angle A is 60 degrees which is between sides b and c.

we need to find the length of side a

a^2 = b^ + c^ - 2bcCos60

a^2 = 4 + 25 - 20Cos60

a^2 = 29 - 20Cos60

a = 4.3588

Step-by-step explanation:

the other answer is correct but missed a few steps in the explanation. so, just to be sure :

yes, we use the law of cosine (or I call it the general Pythagoras for non-right-angled triangles) :

c is the side opposite of the given angle. a, b are the other 2 sides.

c² = a² + b² - 2ab×cos(angle)

in our case

c² = 2² + 5² - 2×2×5×cos(60°) =

= 4 + 25 - 20×0.5 = 29 - 10 = 19

c (the third side) = sqrt(19) = 4.358898944... units

you see how this is connected to the regular Pythagoras in right-angled triangles ?

c² = a² + b² - 2ab×cos(90°)

cos(90°) = 0

and so all that is left is

c² = a² + b²

Step-by-step explanation:

Let distance travelled by Nichol =x

\({:}\longrightarrow\)\(\sf {\dfrac {3}{5}}\times x={\dfrac {3}{8}}\)

\({:}\longrightarrow\)\(\sf {\dfrac {3x}{5}}={\dfrac {3}{8}}\)

\({:}\longrightarrow\)\(\sf 8 (3x)=5×3 \)

\({:}\longrightarrow\)\(\sf 24x=15\)

\({:}\longrightarrow\)\(\sf x={\dfrac{24}{15}}\)

\({:}\longrightarrow\)\(\sf x=1.6\)

\(\therefore\) Nichol runs 1.6miles .

Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.

To complete the basic step of the proof, we need to show that the statement p(n) is true for the smallest positive integer n, which is 1.

Let's plug n = 1 into the statement p(n):\(1^3 = (\frac{1(1 + 1))}{2})^2\)

Simplifying the equation, we get:
\(1^3 = (1(2)/2)^2\\1^3 = (1^2)^2\\1 = 1\)

Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.

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The statement is true for n=1, and we have completed the basis step of the proof.

To complete the basis step of the proof for the statement p(n), we need to show that it is true for the smallest positive

integer n, which is 1.

Our statement is:

\(1^3 + 2^3 + 3^3 + ... + n^3 = (n(n+1)/2)^2.\)

For the basis step, let n = 1:

Left side: \(1^3 = 1\)

Right side:\((1(1+1)/2)^2 = (1(2)/2)^2 = (1)^2 = 1\)

Since the left side and the right side are equal, we have successfully completed the basis step of the proof for the statement p(n).

Therefore, the statement is true for n=1, and we have completed the basis step of the proof.

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The equation of the parabola used for the reflector is y = (1/6)x^2. The filament of the lightbulb is located at a distance of 1 inch from the vertex of the reflector.

To find the equation of the parabola used for the reflector, we need to determine the focal length (f) of the parabola. Since the filament of the light bulb is located at the focus, we can use the formula for the focal length of a parabola, which is f = d/4, where d is the depth of the reflector. In this case, the depth of the reflector is 6 inches, so the focal length is f = 6/4 = 1.5 inches.

The general equation of a parabola with its vertex at the origin is y = ax^2, where a is a constant. To find the specific equation for this reflector, we need to determine the value of a. Since the reflector has a width of 7 inches from rim to rim, the distance from the vertex to one side of the parabola is 7/2 = 3.5 inches. This distance corresponds to x in the equation. Plugging in these values, we have 3.5 = a(1.5)^2. Solving for a, we get a = 3.5 / (1.5)^2 = 1.55.

Therefore, the equation of the parabola used for the reflector is y = (1.55)x^2. Since the filament of the lightbulb is located at the focus, which is a distance equal to the focal length from the vertex, we know that the filament is located 1.5 inches from the vertex of the reflector.

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Answer: 1.29

Step-by-step explanation: y=1.29x+2

1.29 is the coefficient of X, slope, and the rate of change.

============================================================

Explanation:

Let's consider the tank's full capacity is 240 gallons. I'm picking this number because 12*20 = 240.

If the tank is 240 gallons, then the inlet pipe can fill it at a rate of 240/12 = 20 gallons per hour. Note after 12 hours, we have 12*20 = 240 gallons filled assuming the outlet pipe is sealed shut.

At the same time, the outlet pipe is draining at a rate of 240/20 = 12 gallons per hour. After 20 hours, the outlet pipe would drain out 12*20 = 240 gallons assuming the inlet pipe is not adding any water.

With the two pipes playing this tug-of-war battle, the inlet pipe ultimately wins because it's adding more gallons of water each hour, compared to the amount drained per hour. The net change is +20-12 = 8 gallons per hour.

This means it will take 240/8 = 30 hours to fill the tank with both pipes open.

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

Another approach:

The inlet pipe can fill the tank in 12 hours, so it gets 1/12 of the job done per hour. The outlet pipe drains the tank in 20 hours, so it gets 1/20 of the job done in one hour.

The net change is 1/12 - 1/20 = 5/60 - 3/60 = 2/60 = 1/30

This means that when both pipes are open, 1/30 of the job is done per hour. By "job", I mean "filling the tank".

If x is the number of hours needed to do one full job, then we can multiply that by the unit rate (1/30) and set the result equal to 1

(rate)*(time) = 1 job

(1/30)*x = 1

x = 30*1

x = 30

It takes 30 hours to do the job with both pipes open.

Answer:

10

Step-by-step explanation:

Answer:

1. WEA and and TSE

2.WES

3.50

Step-by-step explanation:

the inscribed angles are AWE, AWS, EST

As W is the center, ES is the Diameter

arc AE = 180-AWS

= 180-100

=80 degrees

Answer:

y = x + 2

Step-by-step explanation:

You can find the slant asymptote using polynomial long division because the numerator is one degree higher than the denominator.

(x^2+x+4)/(x-1)

I'm not sure how to show long division but you should get:

x+2 with remainder 6

Then your slant asymptote is y = x + 2

You can graph it on Desmos to verify

Answer:

mixed

36 3/5

proper

366/10

Step-by-step explanation:

the Answer is: (2,1)

Step-by-step explanation:

For the 3×3 matrices having  det(A)=−3 det(A)=−3, det(B)=7 the det(AB) is -21 ,det(3A) is -81 ,det(Aᵀ) is -3 , det(B-¹) is 1/7 and

To find the det(B²) is 49. values of det(AB), det(3A), det(Aᵀ), det(B-¹),

and det(B²) given that A and B are 3x3 matrices, det(A) = -3, and det(B) = 7.

1. det(AB):
Using the property of determinants, det(AB) = det(A) * det(B).

So, det(AB) = (-3) * (7) = -21.

2. det(3A):
For a 3x3 matrix, det(kA) = k³ * det(A) where k is a scalar. In this case, k = 3.

So, det(3A) = 3³ * (-3) = 27 * (-3) = -81.

3. det(Aᵀ):
The determinant of the transpose of a matrix is equal to the determinant of the original matrix.

So, det(Aᵀ) = det(A) = -3.

4. det(B-¹):
For the inverse of a matrix, det(B-¹) = 1 / det(B).

So, det(B-¹) = 1 / 7.

5. det(B²):
Using the property of determinants for powers, det(B²) = det(B) * det(B) = 7 * 7 = 49.

So, det(AB) = -21, det(3A) = -81, det(Aᵀ) = -3, det(B-¹) = 1/7, and det(B²) = 49.

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The measure represents the standard deviation of the sample means and is used in place of the population standard deviation when the population parameters are unknown is; t-test.

A hypothesis test for a population mean when In the case that the population standard deviation, σ, is unknown, carrying out a hypothesis test for the population mean is done in similarly like the population standard deviation is known. A major distinctive property is that unlike the standard normal distribution, the t-test is invoked.

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Answer:

standard error of the mean

Step-by-step explanation:

Plato/Edmentum