6 A survey was given to 12th-grade students of West High School to
determine the location for the senior class trip. The results are shown
in the table below.
To the nearest percent, what percent of the boys chose Niagara Falls?

Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:

[tex]n = 39, \pi = \frac{8}{39} = 0.2051[/tex]

Hence the bounds of the interval are:

As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

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a) The target cost for Model J20, assuming that the historical markup on product cost and selling price is maintained, is $200 per unit.

b) The required cost reduction per unit is $30 per unit ($230 - $200).

c) An evaluation of the three engineering improvements together to determine if the required cost reduction (drift) can be achieved as follows:

While the calculated cost reduction, including direct materials, is $25, the required reduction to achieve the target markup cost is $30.

Thus, the expected target cost reduction does not add up with the calculated cost reduction, envisaged by the engineers.

Model J20 Selling price per unit = $460

Direct materials $175

Direct labor 40

Factory overhead 15

Total $230

Direct labor rate = $30 per hour

Direct labor rate per minute = $0.50 ($30/60)

Direct labor hours per unit = 1¹/₃ hours ($40/$30) or 80 minutes

Normal direct labor time = 80 minutes

Plastic printer cover =        -15 minutes

Total new direct labor time = 65 minutes

Direct labor rate per unit = $32.50 ($0.5 x 65)

Additional inspection time = 6 minutes

Injection molding machine = 1 minute

Direct materials cost = $155 ($175 - $20)

Historical markup = 200% ($460/$230 x 100)

Target cost based on historical markup = $200 ($400 x 100/200)

Required cost reduction per unit is $30 per unit ($230 - $200)

1. Direct labor reduction of $7.50 per unit ($40 - $32.50)

2. Additional inspection $3 per unit (6 x $0.50)

3. Injection molding productivity improvement $0.50 per unit

4. Material cost reduction = $20

Total savings are $25 per unit ($7.50 - $3 + $0.50 + $20).

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Answer: 148 degrees

Step-by-step explanation:

The total measure of all exterior angles of a convex pentagon is 360 degrees.

If four of them equal 53 degrees then all those together is 212 degrees

53 times 4 = 212

Then you would just subtract 212 from 360 to see the measure of the last exterior angle. Which is 148 degrees!

Hope this helps :)

Answer:

80 in.²

Step-by-step explanation:

The total surface area of the pyramid is the sum of the area of the base and the areas of the 4 triangular sides.

Square: area = s²

Square: side = 4 in.

Triangular side: area = bh/2

Triangular side: base = 4 in.; height = 8 in.

Area of the base: s² = (4 in.)² = 16 in.²

Total area of the 4 triangular sides: 4 × bh/2 = 2bh = 2 × 4 in. × 8 in. = 64 in.²

Surface area = 16 in.² + 64 in.² = 80 in.²

Answer:

(9/3) * 4 * 2

Step-by-step explanation:

:DDDD

Answer:

2(9 / 3) * 4

Step-by-step explanation:

this is one of the many ways to solve this

9/3 is 3

2 times 3 is 6

6 times 4 is 24

therefore 2(9 / 3) * 4 is 24

Answer:

16 batches

Step-by-step explanation:

we can divide 12 by 3/4 or 0.75: 12/0.75 = 16

The percentage when Potiphar woke up late is 14.4%.

From the information, it was stated that Potiphar takes a horse and buggy to work everyday. In order to come on time, he must wake up promptly at 6.30am and then hop on the buggy and that anytime he wakes up late or the horse was in traffic, he will be late.

It was further illustrated based on the information given in the question that he was late 24.4% of the time and the horse was in traffic for 10% of the time.

Therefore, the percentage when he woke up late will be gotten by simply subtracting the percentages that we have above. This will be illustrated below:

= 24.4% - 10%

= 14.4%

Therefore, the percentage when Potiphar woke up late is 14.4%.

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The value of b as described in the task content by means of solving the two equations simultaneously is; b= -10.

The given simultaneous equations as indicated have been manipulated to determine the value of a which is; 0.5 in the task content.

Hence, by substituting a= 0.5 into the equation; 5 = 30a + b; we have;

5 = 30(0.5) + b

b = 5- 15 = -10.

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The volume of the cone illustrated will be 117.2 unit³.

From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.

It should be noted that the volume of a cone is calculated as:

= 1/3 πr²h.

where,

π = 3.142

r = radius = 4cm

h = height = 7cm

In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:

= 1/3πr²h

= 1/3 × 3.14 × 4² × 7

= 117.2 unit³

Therefore, the volume of the shape is 117.2 unit³.

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Complete question:

A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.

The correct option is B) 67.4%

A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.

Given here, P(probability that a worker is a college graduate) = 32%

                                                                                                      = 0.32

q (probability that a worker is not a college graduate) is 1-0.32 = 0.68  

now μ(mean) = n×p

                      = 50×0.32

                      = 16

Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]

                                           σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]

                                           σ = 3.2985

now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)

                      = P(z<0.45)  

                      = 0.674 [using z table]

                      = 67.4%

Hence option 2 is the correct answer

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Answer: A

Step-by-step explanation:

[tex]\sin \theta[/tex] is equal to the y-coordinate.

Answer: square root 3/2

Step-by-step explanation:

The equation 7x + 28 = 7(x + 4) has infinite many solutions

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation is given as

7x + 28 = 7(x + 4)

Open the bracket

7x + 28 = 7x + 28

Subtract 7x from both sides of the equation

28 = 28

Subtract 28 from both sides of the equation

0 = 0

The above equation is true, because both sides of the equation are the same

This means that the equation has infinite many solutions

Hence, the equation 7x + 28 = 7(x + 4) has infinite many solutions

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Answer:

500 rocks

Step-by-step explanation:

25*20 = 500

[tex]\huge\purple{Hi!}[/tex]

The area of a regular polygon is one-half the product of its apothem and its perimeter.

Separate the variables.

[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]

Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].

[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]

[tex]\ln|y| = \frac12 \ln|u| + C[/tex]

[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]

[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]

[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]

Using separation of variables, the solution to the differential equation is:

y = ksqrt(x² + 11)

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is:

(x² + 11)y' = xy

Applying separation of variables, we have that:

y'/y = x/(x² + 11)

[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]

[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]

[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]

[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]

Hence the solution is:

y = ksqrt(x² + 11)

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The answers are :

a)

b)

Let's find point A by using g(x). A is clearly the y-intercept so take x = 0.

Points B and C can be found using f(x). As they are the x-intercepts, take y = 0.

As B lies to the left of the y-axis, its x-coordinate is negative.

As C lies to the right of the y-axis, its x-coordinate is positive.

Point D can be found using g(x). D is clearly the x-intercept so take y = 0.

Point E lies at the intersection of f(x) and g(x). So they have to be equated.

Answer:

see explanation

Step-by-step explanation:

(a)

A lies on the y- axis with x- coordinate of zero

substitute x = 0 into either of f(x) or g(x) for y- coordinate

g(0) = 2(0) + 1 = 0 + 1 = 1

then A (0, 1 )

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

B and C lie on the x- axis with y- coordinate of zero

let f(x) = 0 and solve for x , that is

1 - x² = 0 , then

x² = 1 ( take square root of both sides )

x = ± [tex]\sqrt{1}[/tex] = ± 1

then B (- 1, 0 ) and C (1, 0 )

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

D is the point on the x- axis where g(x) crosses

let g(x) = 0 and solve for x

2x + 1 = 0 ( subtract 1 from both sides )

2x = - 1 ( divide both sides by 2 )

x = - [tex]\frac{1}{2}[/tex]

then D (- [tex]\frac{1}{2}[/tex] , 0 )

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

(b)

E is the point of intersection of f(x) and g(x) so equate them, that is

2x + 1 = 1 - x² ( subtract 1 - x² from both sides )

x² + 2x = 0 ← factor out x from each term

x(x + 2) = 0

equate each factor to zero and solve for x

x = 0 ← x- coordinate of A

x + 2 = 0 ⇒ x = - 2 ← x- coordinate of E

substitute x = - 2 into g(x) for corresponding y- coordinate

g(- 2) = 2(- 2) + 1 = - 4 + 1 = - 3

then E (- 2, - 3 )

Tthe inequality that describes this graph is y ≤ 1/3x - 4/3

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(0, -1.3) and (3, -0.3)

The slope is calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (-0.3 + 1.3)/(3 - 0)

Evaluate

m = 1/3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1/3(x - 0) - 1.3

Evaluate

y = 1/3x - 4/3

From the graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≤

Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3

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Answer:

angle <B = 76

Step-by-step explanation:

The measure of an exterior angle is equal to sum of two interior angles that is not adjacent to the exterior angle.

We can write the following equation with this information to find the value of angle <B

<B + 71 = 147 subtract 71 from both sides

<B = 76

Answer:

y = 20x + 200

Step-by-step explanation:

The 200 is the constant.  It is only added once, but the monthly deposits are added at 20 every month.  

After 1 month:

y = 20x + 200

y = 20(1) + 200

y = 20 + 200

y =220       money deposited.

After 2 months:

y = 20x + 200

y = 20(2) + 200

y = 40 + 200

y =240 money deposited.

After 3 months:

y = 20x + 200

y = 20(3) + 200

y = 60 + 200

y = 260  money deposited

And so on, and so on, and so on...

The statements that are true are angle MNL is complementary to angle KNL and angle GNM is supplementary to angle JNK. Option B and E

Ray NL creates two angles in the lower right quadrant.

The two angles created form a total of  90°, so the two angles formed are complementary. The relation is given as;

∠MNL + ∠KNL = ∠MNK = 90°

Hence ∠MNL and ∠KNL are complementary

∠GNM and ∠JNK are both right angles (and also vertical angles). They sum up to180°. They can be said to be supplementary.

∠GNM and ∠JNK are supplementary

Thus, the statements that are true are angle MNL is complementary to angle KNL and angle GNM is supplementary to angle JNK

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The amount of the loss exists 1350.

Amount of Loss means an amount equivalent to the outstanding balance of the principal amount, less any amounts recognized by perfecting rights under a security agreement, together with such interest as the executive director shall permit, to a maximum of such interest as may be permitted by rule.

Given: Mr. Black purchased a television set for $450.00. He subsequently sold the television set at a defeat of 30%.

From the given information, we get

[tex]$4500\cdot \frac{30}{100}[/tex]

simplifying, we get

[tex]$4500\cdot \frac{30}{100}[/tex]

= 1350

Therefore, the amount of the loss exists 1350.

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Answer:

6%

Step-by-step explanation:

Got it right on the test.

we just need to reflect the graph of g(x) around the y-axis, and then shift the whole graph 5 units upwards.

Here we have two functions:

[tex]g(x) = ln(x)\\\\f(x) = ln(-x) + 5[/tex]

Ok, let's start with g(x), which graph we know. If we reflect it around the y-axis, then the new function will be:

f(x) = g(-x)

If now we shift it up 5 units, then we get:

f(x) = g(-x) + 5

Replacing g(x):

f(x) = ln(-x) + 5

Which is our function

So we just need to reflect the graph of g(x) around the y-axis, and then move the whole graph 5 units upwards.

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a) 88 degrees

b) 44 degrees

The focal length of the given ellipse is given as (±6, 0)

An ellipse is defined as a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant or when a cone is cut by an oblique plane which does not intersect the base.

The standard equation of an ellipse is expressed as;

x^2/a^2 + y^2/b^2 = 1

The formula for calculating the focus of the ellipse is given as:

c^2 = b^2 - a^2

Given the equation of an ellipse

(x-7)^2/64 + (y-5)^2/100 = 1

This can also be expressed as:

(x-7)^2/8^2 + (y-5)^2/10^2 = 1

Comparing with the general equation

a = 8 and b = 10

Substitute

c^2 = 10^2 - 8^2

c^2 = 100 - 64

c^2 = 36

c = 6

Hence the focal length of the given ellipse is given as (±6, 0)

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Answer:

11/12

Step-by-step explanation:

no of sample space=12

number of 7 to occur is 1/12

number of not 7:

since the total probability is 1

so 1-1/12=11/12

it is that wich is klweijxmpx

Answer:

l = 2.25 cm

Step-by-step explanation:

given l is inversely proportional to w² then the equation relating them is

l = [tex]\frac{k}{w^2}[/tex] ← k is the constant of proportion

(i)

to find k use the condition w = 1.5 , l = 16 , then

16 = [tex]\frac{k}{1.5^2}[/tex] = [tex]\frac{k}{2.25}[/tex] ( multiply both sides by 2.25 )

36 = k

l = [tex]\frac{36}{w^2}[/tex] ← equation of proportion

(ii)

when w = 4 , then

l = [tex]\frac{36}{4^2}[/tex] = [tex]\frac{36}{16}[/tex] = 2.25 cm

The cheaper price among this set of orange sales is the one done by trader B, who sells 8 for N120.

The cheaper price can be computed by finding out the price per unit.

                               Price of Set     Unit Price

Sale of 6 oranges        N100           N16.67 (N100/6)

Sale of 8 oranges        N120           N15.00 (N120/8)

Thus, selling 8 oranges for N120 is cheaper than selling 6 oranges for N100, and N1.67.

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