Zia is building a plastic model rocket that has the combined shape of a cone and a cylinder as shown. additionally, the cylinder has a hemisphere hollowed out of its bottom. the plastic for the cone weighs 1.4 grams per cubic centimeter and the plastic for the cylinder weights only 0.8 grams per cubic centimeter.
(a) the volume of plastic that remains in the cylinder after it has been hollowed out to the nearest cubic centimeter.
(b) what has a greater total weight, the plastic that makes up the cone or the plastic that makes up the cylinder after it has been hollowed out?

Answers

Answer 1

Answer:

226 cm^3

The mass of plastic used to make cylinder is greater

Step-by-step explanation:

Given:-

- The density of cone material, ρc = 1.4 g / cm^3

- The density of cylinder material, ρl = 0.8 g / cm^3

Solution:-

- To determine the volume of plastic that remains in the cylinder after gouging out a hemispherical amount of material.

- We will first consider a solid cylinder with length ( L = 10 cm ) and diameter ( d = 6 cm ). The volume of a cylinder is expressed as follows:

                                  [tex]V_L =\pi \frac{d^2}{4} * L[/tex]

- Determine the volume of complete cylindrical body as follows:

   

                                 [tex]V_L = \pi \frac{(6)^2}{4} * 10\\\\V_L = 90\pi cm^3\\[/tex]

- Where the volume of hemisphere with diameter ( d = 6 cm ) is given by:

                                 [tex]V_h = \frac{\pi }{12}*d^3[/tex]

- Determine the volume of hemisphere gouged out as follows:

                                 [tex]V_h = \frac{\pi }{12}*6^3\\\\V_h = 18\pi cm^3[/tex]

- Apply the principle of super-position and subtract the volume of hemisphere from the cylinder as follows to the nearest ( cm^3 ):

                               [tex]V = V_L - V_h\\\\V = 90\pi - 18\pi \\\\V = 226 cm^3[/tex]

Answer: The amount of volume that remains in the cylinder is 226 cm^3

- The volume of cone with base diameter ( d = 6 cm ) and height ( h = 5 cm ) is expressed as follows:

   

                               [tex]V_c = \frac{\pi }{12} *d^2 * h[/tex]

- Determine the volume of cone:

                              [tex]V_c = \frac{\pi }{12} *6^2 * 5\\\\V_c = 15\pi cm^3[/tex]

- The mass of plastic for the cylinder and the cone can be evaluated using their respective densities and volumes as follows:

                             [tex]m_i = p_i * V_i[/tex]

- The mass of plastic used to make the cylinder ( after removing hemispherical amount ) is:

                           [tex]m_L = p_L * V\\\\m_L = 0.8 * 226\\\\m_L = 180.8 g[/tex]

- Similarly the mass of plastic used to make the cone would be:

                           [tex]m_c = p_c * V_c\\\\m_c = 1.4 * 15\pi \\\\m_c = 65.973 g[/tex]

Answer: The total weight of the cylinder ( m_l = 180.8 g ) is greater than the total weight of the cone ( m_c = 66 g ).

                             

Answer 2

The volume of the remaining plastic in the cylinder is large, which

makes the weight much larger than the weight of the cone.

Responses:

(a) Volume of the remaining plastic in the cylinder is 226 cm³(b) The weight of the cylinder is greater than the weight of the cone.

How can the weight and volume be evaluated?

Density of the plastic for the cone = 1.4 g/cm³

Density of the plastic used for the cylinder = 0.8 g/cm³

From a similar question, we have;

Height of the cylinder = 10 cm

Diameter of the cylinder = 6 cm

Height of the cone = 5 cm

(a) Radius of the cylinder, r = 6 cm ÷ 2 = 3 cm

Volume of a cylinder = π·r²·h

Volume of a hemisphere = [tex]\mathbf{\frac{2}{3}}[/tex] × π×  r³

Volume of the cylinder after it has been hollowed out, V, is therefore;

[tex]V = \mathbf{\pi \times r^2 \times h - \frac{2}{3} \times \pi \times r^3}[/tex]

Which gives;

[tex]V = \pi \times 3^2 \times 10 - \frac{2}{3} \times \pi \times 3^3 \approx \mathbf{ 226}[/tex]

Volume of the cylinder after it has been hollowed out, V ≈ 226 cm³

(b) Volume of the cone = [tex]\mathbf{\frac{1}{3}}[/tex] × π × 3² × 5 47.1

Mass of the cone = 47.1 cm³ × 1.4 g/cm³ ≈ 66 g

Mass of the hollowed cylinder ≈ 226 cm³ × 0.8 g/cm³ = 180.8 g

The mass and therefore, the weight of the plastic that makes up the hollowed cylinder is greater than the weight of the plastic that makes up the cone.

Learn more about volume and density of solids here:

https://brainly.com/question/4773953


Related Questions

Which of the following measurements is more precise?
4.69 m or 8.99 m

Answers

Answer:

The measures represent the same precision

When we talk about precision in measurements, we need to mention the significant figures, because that determines the precision.

Specifically, the more significant figures there are, more precise will be the number.

In this case, you can observe that both numbers have the same number of significant figures, which is 3, which means both numbers are equal in precision.

A florist currently makes a profit of $20 on each of her celebration bouquets and sells a average of 30 bouquets every week

Answers

Answer:

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW;

A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.

CHECK THE ATTACHMENT FOR THE GRAPH

EXPLANATION;

FIRST QUESTION:

From the graph maximum profit is the value gotten where p(X) has maximum value, and the maximum value is observed at y- axis at P(X)to be 675.

Thefore, maximum profit the florist will earn from celebration bouquet is $675.

SECOND QUESTION:

Break even is the exact point that profit p(x) is observed as zero.

Checking the given g graph the point where there is zero value of p(X) is observed at x=20 and x= -10 but we can only pick the positive value which is x=20

Therefore, the florist will break even after 20 one- dollar decreases

THIRD QUESTION;

The interval of number of one dollar decreases can be observed at the point where we have the value of P(x) been more than zero, looking at the given graph, the P(x) has its value greater than zero at the interval 0 to 20.Therefore, it can be concluded that the interval of number of one dollar decreases for which the florist makes a profit from celebration bouquet is (0, 20)

Answer:

Step-by-step explanation:

You have also been asked to set up the basket ball court what is the circumference of the circle

Answers

Answer: circumference of the circle is 11.31 meters

C=\pi d\\C=\pi (2r)\\C=2\pi r

Where radius (r) is half of diameter (d)

Since radius of the circle shown in 1.8m, we plug it in the formula and get:

C=2\pi r\\C=2\pi (1.8)\\C=11.31

So C = 11.31 meters

Sorry but I need the points

Please help I'm Timed Will Name Brainliest if Correct.

Answers

Answer:

A

Step-by-step explanation:

We can see that Function A's y coordinate doubles every time. The function A = f(x) = 5(2)^x. It is an exponential growth function, and therefore y can never be 0. This means that A does not have an x-intercept.

Function B is a rational function. x cannot be 0, since that would result in an undefined number. This also means that B does not have an x-intercept.

2. A manufacturer produces light bulbs at a Poisson rate of 300 per hour. The probability that a light bulb is defective is 0.012. During production, the light bulbs are tested, one by one, and the defective ones are put in a special can that holds up to a maximum of 50 light bulbs. On average, how long does it take until the can is lled

Answers

Answer:

On average it will take 13 hrs 53 minutes before the van is filled

Step-by-step explanation:

The first thing we need to do here is to find find the number of defective light bulbs

Using the poisson process, that would be;

λ * p

where λ is the poisson rate of production which is 300 per hour

and p is the probability that the produced bulb is defective = 0.012

So the number of defective bulbs produced within the hour = 0.012 * 300 = 3.6 light bulbs per hour

Now, let X be the time until 50 light bulbs are produced. Then X is a random variable with the parameter (r, λ) = (50, 3.6)

What we need to find however is E(X)

Thus, the expected value of a gamma random variable X with the parameter (x, λ) is;

E(X) = r/λ = 50/3.6 = 13.89

Thus the amount of time it will take before the Can will be filled is 13 hrs 53 minutes

A, B, and C are collinear points C is the midpoint of AB AC = 5x - 6 CB = 2x Find AB

Answers

Answer:

  AB = 8

Step-by-step explanation:

Since C is the midpoint, ...

  AC = CB

  5x -6 = 2x

  3x = 6 . . . . . . . add 6-2x

  x = 2

Then the length of AB is ...

  AB = 2(CB) = 2(2x) = 4(2)

  AB = 8

If one angle equals 34”, then the measure of its complement angle is 56°.
True
OO
False
I need help

Answers

Answer:

True

Step-by-step explanation:

Complementary means they should sum to 90 degrees

34+56=90

Answer:

True

Step-by-step explanation:

Complementary angles are angles that add to 90 degrees, or a right angle.

If the two angles are complementary, then they will add to 90 degrees.

One angle is 34°, and it's complement is 56°.

Add the angles.

34°+56°

90°

Since they add to 90 degrees, they are complementary angles. Therefore, the statement is true.

work out the length of the container. Giver your answer to the nearest whole centimetre.
Dennis is making a container for tomato plant. The container will be in the shape of a cuboid.

missing length ? 40cm by 55cm.
The capacity of the container will be 180 litres.
1 Litre =1000cm cuboid.

Answers

Answer:

Length of the container = 82 cm

Step-by-step explanation:

Given:

Breadth of the container is 40 cm and height of the container is 55 cm

Volume of the container is 180 litres

To find: length of the container

Solution:

A container is in the shape of the cuboid.

Volume of cuboid = length × breadth × height

Put breadth = 40 cm , height = 55 cm and volume = 180 litres = 180000 [tex]cm^3[/tex]

(as 1 litre = 1000 [tex]cm^3[/tex] )

Therefore,

[tex]180000=length\,\times \,40\times 55\\length = \frac{180000}{40\times 55}=81.82\approx 82\,\,cm[/tex]

In the diagram below, AB is parallel to CD. What is the value of x?
А. 150
В. 60
С. 120
D. 30

Answers

The value of x is 150. I subtracted 180-30 to get 150.

Answer:

x=150 because these are supplementary angles

The probability that a can of paint contains contamination is 3.23%, and the probability of a mixing error is 2.4%. The probability of both is 1.03%. What is the probability that a randomly selected can has contamination or a mixing error?

Answers

Answer:

4.6%.

Step-by-step explanation:

The probability that a can of paint contains contamination(C) is 3.23%

P(C)=3.23%

The probability of a mixing(M) error is 2.4%.

P(M)=2.4%

The probability of both is 1.03%.

[tex]P(C \cap M)=1.03\%[/tex]

We want to determine the probability that a randomly selected can has contamination or a mixing error. i.e. [tex]P(C \cup M)[/tex]

In probability theory:

[tex]P(C \cup M) = P(C)+P(M)-P(C \cap M)\\P(C \cup M)=3.23+2.4-1.03\\P(C \cup M)=4.6\%[/tex]

The probability that a randomly selected can has contamination or a mixing error is 4.6%.

Please answer this correctly

Answers

Answer:

20-39 => 2

40-59 => 1

60-79 => 1

80-99 => 6

100-119 => 5

Answer: 2, 1, 1, 6, 5

Step-by-step explanation:

20-39

2 | 3

3 | 9

40-59

5 | 0

60-79

7 | 5

80-99

8 | 1 2 4

9 | 3 9 9

100-119

10 | 1 1 5 6

11 | 1

Use the following equation to answer the questions below:

y − 2 = 1 /3 (x + 4)

Find the equation of the line that is passing through (8, 2) and is perpendicular to the given line.

Answers

Answer:

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped you plz don't forget to thank me...

Pythagorean theorem please help

Answers

Answer:

4√73

Step-by-step explanation:

x^2= 12^2 + 32^2

x^2= 144+ 1024

x^2=1168

x= 4√73

Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢ 580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of GH¢2,358.60, how much was his total investment?

Answers

Answer:

  GH¢2082.12

Step-by-step explanation:

Let "a" represent the amount invested at 12%. Then (a+580) is the amount invested at 14%. The total amount invested (t) is ...

  t = (a) +(a +580) = 2a+580

Solving for a, we get

  a = (t -580)/2

__

The accumulated amount from the investment at 12% is 1.12a. And the accumulated amount from the investment at 14% is 1.14(a+580). Together, these accumulated amounts total GH¢2358.60.

  1.12(t -580)/2 +1.14((t -580/2 +580) = 2358.60

  0.56t -0.56(580) +0.57t -0.57(580) +1.14(580) = 2358.60 . . . remove parens

  1.13t + 5.8 = 2358.60 . . . . . . . . . simplify

  1.13t = 2352.80 . . . . . . . . . . . . . . subtract 5.8

  t = 2352.80/1.13 = 2082.12 . . . . divide by the coefficient of t

Mr. Azu's total investment was GH¢2082.12.

NFL player Gerald Sensabaugh recorded a 46 inch standing vertical jump at the 2005 NFL Combine, at that time the highest for any NFL player in the history of the Combine. Sensabaugh weighed about 200 lb when he set the record. Part A What was his speed as he left the floor

Answers

Answer:

His speed as he left the floor is 4.83 m/s.

Step-by-step explanation:

Given: 46 inches = 1.1684 m and mass = 200 lb = 90.7185 Kg.

From the third equation of motion under free fall,

  [tex]V^{2}[/tex] = [tex]U^{2}[/tex] - 2gs

Where; V is the final velocity (0), U is the initial velocity (unknown), g is the value of gravity - 10 m/[tex]s^{2}[/tex] and s is the distance = 1.1684 m.

Then;

0 = [tex]U^{2}[/tex] - 2gs

[tex]U^{2}[/tex] = 2gs

   = 2 × 10 × 1.1684

  = 23.368

⇒ U = [tex]\sqrt{23.368}[/tex]

       = 4.8340 m/s

The initial velocity, U = 4.83 m/s.

Therefore, his speed as he left the floor is 4.83 m/s.

Answer:

His speed as he left the floor is 4.83 m/s.

Step-by-step explanation:

The top tree broke and fell over.the remaining tree teunk is 3 feet tall.the tip of the tree rests on the ground 14 feet from the base of the trunk.what is the lenght of the broken part of the tree to the nearest tenth of a foot

Answers

Answer:

14.3 feet.

14.3 feet

Step-by-step explanation:

The problem forms a right triangle in which:

The Vertical Leg of the Right Triangle = 3 feet

The Horizontal Leg of the Right Triangle =14 feet

We are to determine the length of the broken part of the tree. This is the Hypotenuse of the Right Triangle,

Using Pythagoras Theorem

[tex]Hypotenuse^2=Opposite^2+Adjacent^2\\Hypotenuse^2=14^2+3^2\\Hypotenuse^2=205\\Hypotenuse=\sqrt{205}\\Hypotenuse=14.32\\ \approx 14.3 feet $(to the nearest tenth of a foot).\\Therefore, the lenght of the broken part of the tree to the nearest tenth of a foot is 14.3 feet.[/tex]

What’s the correct answer for this?

Answers

Answer:

B and C

Step-by-step explanation:

The correct option are

B) a cross section of rectangular pyramid perpendicular to the base

C) a cross section of a rectangular prism that is parallel to it's base

The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 5 in, what is the length of the chalkboard? A. 6.67 in B. 9.33 in C. 12 in D. 14 in

Answers

Answer:

  A.  6.67 in

Step-by-step explanation:

  length/width = 4/3 = x/5

Multiply by 5:

  5(4/3) = x = 20/3 = 6 2/3

The length of the chalkboard is 6.67 inches.

What is the slope-intercept equation of the line below?

Answers

Let’s start with the y intercept
When x is 0 look at the y, the y is the blue dot which means it’s -2

For the slope you calculate rise over run basically count up then left and see how many would hit the line at an exact point

Your slope is y= 4/5x -2

Hope this helps!

Answer:D

Step-by-step explanation:

-2=4/5(0)-2

-2=0-2

-2=-2

-6/5=4/5(1)-2

-6/5=4/5-10/5

-6/5=4/5-10/5

-6/5=-6/5

The length of the sides of a square are initially 0 cm and increase at a constant rate of 8 cm per second. Write a formula that expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing. s

Answers

Answer:

s(t)=8t

Step-by-step explanation:

The length of the sides of a square are initially 0 cm and increase at a constant rate of 8 cm per second.

Let the length of the Square = s

[tex]\dfrac{ds}{dt}=8 $cm/seconds, s_0=0 cm[/tex]

We solve the differential equation above subject to the given initial condition.

[tex]\dfrac{ds}{dt}=8\\ds=8$ dt\\Take the integral of both sides\\\int ds=\int 8$ dt\\s(t)=8t+C, where C is the constant of integration\\When t=0, s=0cm\\s(0)=0=8(0)+C\\C=0\\Therefore, s(t)=8t[/tex]

The formula that expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing is:

s(t)=8t (in cm)

A sample of 1100 computer chips revealed that 77% of the chips fail in the first 1000 hours of their use. The company's promotional literature states that 76% of the chips fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that fail is different from the stated percentage. Find the value of the test statistic. Round your answer to two decimal places.

Answers

Answer:

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.77 -0.76}{\sqrt{\frac{0.76(1-0.76)}{1100}}}=0.778[/tex]  

Step-by-step explanation:

Information given

n=1100 represent the random sample taken

[tex]\hat p=0.77[/tex] estimated proportion of chips that fall in the first 1000 hours of their use

[tex]p_o=0.76[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Solution

We need to conduct a hypothesis in order to check if the true proportion is equal to 0.76.:  

Null hypothesis:[tex]p=0.76[/tex]  

Alternative hypothesis:[tex]p \neq 0.76[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.77 -0.76}{\sqrt{\frac{0.76(1-0.76)}{1100}}}=0.778[/tex]  

2 number cubes are rolled
what is the probability that the first lands on an odd number and the second lands on an even number? ​

Answers

Answer:

1/4

Step-by-step explanation:

1/2 times 1/2

1/2 because there is 3 odds and 3 evens

the total is 6

3/6 equals to 1/2

so 1/2 times 1/2 is 1/4

WILL GIVE BRAINLIEST! HURRY

Answers

Answer:

-1/2 =x

Step-by-step explanation:

4x - 6 = 10x -3

Subtract 4x from each side

4x-4x - 6 = 10x-4x -3

-6 = 6x-3

Add 3 to each side

-6+3 = 6x

-3 = 6x

Divide each side by 6

-3/6 = 6x/6

-1/2 =x

[tex]answer \\ - \frac{1}{2} \\ solution \\ 4x - 6 = 10x - 3 \\ or \: 4x - 10x = - 3 + 6 \\ or \: - 6x = 3 \\ or \: x = \frac{3}{ - 6} \\ x = - \frac{1}{2} \\ hope \: it \: helps[/tex]

Find values of a. b. and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
X + y = 6
y + z = 6
x + z = 6
ax + by + cz = 0
a) a unique solution (a. b .c)=([])
b) no solution (a. b .c)=([])
c) infinitely many solutions (a. b, c) = ([])

Answers

Answer:

Step-by-step explanation:

The given equations are

x + y = 6- - - - - - - - -1

y + z = 6- - - - - - - -2

x + z = 6- - - - - - - - - 3

From equation 2, y = 6 - z

Substituting y = 6 - z into equation 1, it becomes

x + 6 - z = 6

x - z = 6 - 6

x - z = 0

x = z

Substituting x = z into equation 3, it becomes

z + z = 6

2z = 6

z = 6/2

z = 3

x = 3

Substituting x = 3 into equation 1, it becomes

3 + y = 6

y = 6 - 3

y = 3

ax + by + cz = 0

3a + 3b + 3c = 0

3(a + b + c) = 0

Therefore, it is impossible

A company sells eggs whose individual weights are normally distributed with a mean of 70\,\text{g}70g70, start text, g, end text and a standard deviation of 2\,\text{g}2g2, start text, g, end text. Suppose that these eggs are sold in packages that each contain 444 eggs that represent an SRS from the population. What is the probability that the mean weight of 444 eggs in a package \bar x x ˉ x, with, \bar, on top is less than 68.5\,\text{g}68.5g68, point, 5, start text, g, end text?

Answers

Answer:

6.68% probability that the mean weight is below 68.5g.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]

Probability that the mean weight is below 68.5g:

This is 1 subtracted by the pvalue of Z when X = 68.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{68.5 - 70}{1}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a pvalue of 0.0668

6.68% probability that the mean weight is below 68.5g.

Answer:

P(x ∠ 68.5) = 0.07

Step-by-step explanation:

Got it right on khan.

What is the inverse of f(x)-x/x+2, where x ≠ -2

Answers

Step-by-step explanation:

You can take the inverse of a function by replacing all x-values in the equation with y-values and vice versa and subsequently solving for y:

Equation given:

[tex]f(x) = \frac{-x}{x+2}[/tex]

Replace all x-values with y and all y-values with x:

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

Solve for y:

[tex]x(y+2) = -y\\\\xy + 2x = -y\\\\2x = -y - xy\\\\2x = y(-1+-x)\\\\-\frac{2x}{x+1} =y[/tex]

This is the inverse of f(x), where x ≠ 2..

If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles

Answers

Answer:

The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.

Step-by-step explanation:

The question is incomplete:

Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.

                           18–24 25–34 35–55 55 and over Total

Liked Crunchicles   4       9       3 23                  39

Disliked Crunchicles 5        27      28 64              124

No Preference         7        27          10 93                 137

Total                        16        63      41 180            300

One consumer from the survey is selected at random. If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles .

If the consumer is 70 years old is included in the category "55 and over" from this survey. There are 180 subjects in that category.

The number that likes Crunchicles and are 55 and over is 23.

If we calculate the probability as the relative frequency, we have:

[tex]P(\text{L }|\text{ 55+})=\dfrac{P(\text{L \& 55+})}{P(5\text{5+})}=\dfrac{23}{180}=0.1278[/tex]

L: Likes Crunchicles.

The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.

For many years "working full-time" was 40 hours per week. A business researcher gathers data on the hours that corporate employees work each week. She wants to determine if corporations now require a longer work week. Group of answer choices Testing a claim about a single population proportion. Testing a claim about a single population mean. Testing a claim about two population proportions. Testing a claim about two population means.

Answers

Answer:

Correct option is: Testing a claim about two population means.

Step-by-step explanation:

In this provided scenario, a researchers wants to determine if corporations require a longer work week for the employees "working full-time".

It is given that for many years "working full-time" was 40 hours per week.

The researchers researcher gathers data on the hours that corporate employees work each week.

It is quite clear that the researcher wants to determine whether the number of hours worked per week must be increased from 40 hours or not.

A test for the difference between two population means would help the researcher to reach the conclusion.

Thus, the correct option is: Testing a claim about two population means.

What’s the correct answer for this? Select all that apply

Answers

Answer:

B and C

Step-by-step explanation:

The correct options are :

A cross-section that is perpendicular to the base of a cube.

A cross-section that is perpendicular to the base of a cylinder whose base diameter and height are the same.  

In both the cases the length and the width of the section are equal

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18. Using the diagram below as reference, write a paragraph proof to prove that the symmetric property of congruence exists for any two angles. (IMAGE BELOW)

Given: ∠A is congruent to ∠B
Prove: ∠B is congruent to ∠A
Plan: Show that ∠A and ∠B have the same measure, thus ∠B and ∠A have the same measure under symmetry for equality. Conclude with ∠B being congruent to ∠A.


Answers

Answer:

Below.

Step-by-step explanation:

Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.

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