if a space shuttle is made using a scale of 1 inch 12 feet, if the model has high of 5.5 inches, then what is the height of the actual space rocket? shuttle

we can conclude that the statement "if a, b, and d are integers with d > 0, then (a b) div d = a div d b div d" is false.

We can prove that if a, b, and d are integers with d > 0, then (a + b) div d = a div d + b div d or disprove it by finding a counterexample.

Let's choose some specific values for a, b, and d to see if the equation holds. Let a = 8, b = 5, and d = 3.

(a + b) div d = (8 + 5) div 3 = 13 div 3 = 4

a div d + b div d = 8 div 3 + 5 div 3 = 2 + 1 = 3

Since (a + b) div d ≠ a div d + b div d for our chosen values of a, b, and d, we have found a counterexample that disproves the equation.

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Answer: 67

explanation:

47 x 13 = 611    -- so this is how many tickets he has total

611 / 9 = 67.9

So he can get 67 prizes.

a way you can check if this is right is by multiplying 67 by 9 and you see that is 603, and he has 611 tickets so he will even have a few tickets left over. but he can not get 68 prizes because if you see what 68 x 9 is, it is 612 which is one ticket more than what he has so he cant get it. So the max he can get is 67

Answer:

67

Step-by-step explanation:

We know that, in total, he made 47 baskets, and each basket is 13 tickets.

So in total, he made 611 tickets:

47·13

=611

Next, he wanted to get [a] prize(s), but each prize costs 9 tickets, we divide the total number of tickets he has by the prize cost.

611/9

=67.88...

You obviously can't get 0.88 of a prize, so the max amount of prizes that Arthur can get is 67.

Hope this helps! :)

The z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.

The determination of the z-coordinate of the mass center of the homogeneous paraboloid of revolution requires a long answer.

Firstly, we need to define the mass density of the paraboloid. Since it is a homogeneous object, its mass density is constant throughout its volume.

Let us denote this density as ρ.

Next, we need to find the volume of the paraboloid.

The volume of a paraboloid of revolution with a height h and a base radius r is given by V = (π/2) * r^2 * h/3.

In this case, the height of the paraboloid is 4 units and the radius of the base is 2 units. Thus, the volume of the paraboloid is:
V = (π/2) * (2)^2 * 4/3 = (8π/3) units^3

Now, we can find the mass of the paraboloid by multiplying its volume by its density:
M = ρ * V = ρ * (8π/3) units^3

The next step is to find the x and y coordinates of the mass center of the paraboloid.

We can do this by using double integrals:
x = (1/M) * ∬(paraboloid) x * ρ * dV
y = (1/M) * ∬(paraboloid) y * ρ * dV

Since the paraboloid is symmetric about the z-axis, we know that its mass center will lie on this axis, and thus, its x and y coordinates will be zero.

Finally, we need to find the z-coordinate of the mass center. We can do this by using the same double integral, but this time we integrate over the z-axis:
z = (1/M) * ∬(paraboloid) z * ρ * dV

To set up the double integral, we can use cylindrical coordinates, with ρ ranging from 0 to 2 and θ ranging from 0 to 2π.

The z-coordinate of any point on the paraboloid is given by z = (1/16) * (x^2 + y^2), so we can substitute this into the double integral:
z = (1/M) * ∫(0 to 2π) ∫(0 to 2) ∫(0 to (1/16)*(ρ^2)) ρ * z * ρ * ρ * dρ dθ dz

After evaluating this integral, we get:
z = (3/5) * h = (12/5) units

Therefore, the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.

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The given manufacturing process has a CpK value of 0.4, which indicates that it is not capable of meeting the requirement of producing protein bars with a weight of 17.5 ounces.

Explanation:

The CpK (Process Capability Index) value is a measure of how well a process is capable of meeting the specifications or requirements. It takes into account both the process mean and the variability of the process. A CpK value of 1 indicates that the process is capable of meeting the requirement, while a CpK value less than 1 indicates that the process is not capable of meeting the requirement.

In this case, the process mean is 18 ounces and the standard deviation is 2.5 ounces. To find the CpK value, we need to calculate the upper and lower specification limits. Since the requirement is to produce protein bars with a weight of 17.5 ounces, and the requirement is at -2.5 from the process mean, the lower specification limit would be 18 - 2.5 = 15.5 ounces. The upper specification limit would be 18 + 2.5 = 20.5 ounces.

The CpK value can be calculated using the formula:

CpK = min((USL - mean)/3σ, (mean - LSL)/3σ)

where USL is the upper specification limit, LSL is the lower specification limit, σ is the standard deviation, and mean is the process mean.

Substituting the values, we get:

CpK = min((20.5 - 18)/(3 × 2.5), (18 - 15.5)/(3 × 2.5))

= min(0.4, 0.4)

= 0.4

Since the CpK value is less than 1, the process is not capable of meeting the requirement of producing protein bars with a weight of 17.5 ounces. Therefore, the company needs to improve its manufacturing process to meet the requirements.

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(x, y) is an element of the set c × d, since x is an element of c and y is an element of d.

Since (x, y) was an arbitrary element in a × b, we can conclude that every element in a × b is also in c × d. Thus, we have shown that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d.

To show that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d, follow these steps:

Step 1: Understand the notation.
a ⊆ c means that every element in set a is also in set c.
b ⊆ d means that every element in set b is also in set d.

Step 2: Consider the Cartesian products.
a × b is the set of all ordered pairs (x, y) where x ∈ a and y ∈ b.
c × d is the set of all ordered pairs (x, y) where x ∈ c and y ∈ d.

Step 3: Show that a × b ⊆ c × d.
To prove this, we need to show that any ordered pair (x, y) in a × b is also in c × d.

Let (x, y) be an arbitrary ordered pair in a × b. This means that x ∈ a and y ∈ b.

Since a ⊆ c, we know that x ∈ c because every element in set a is also in set c.
Similarly, since b ⊆ d, we know that y ∈ d because every element in set b is also in set d.

Now, we have x ∈ c and y ∈ d, so the ordered pair (x, y) belongs to c × d.

Step 4: Conclusion
Since any arbitrary ordered pair (x, y) in a × b also belongs to c × d, we can conclude that a × b ⊆ c × d.

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Answer:

8x + 8y + 16

Step-by-step explanation:

It is simple perimeter is the sum of all side of the polygon (figure) so

P = (4X+5) + (2Y) + (X+5) + (2Y+3) + (3X) + (4Y+3)

I write

so

P = (4X+5) + (2Y) + (X+5) + (2Y+3) + (3X) + (4Y+3)

P = 8x + 8y + 16

so the perimeter of the figere is 8x + 8y + 16

Answer:

Step-by-step explanation:

Given,

Two positive number whose squares have a sum of 74 and a difference of 24

To Find:

The two positive number.

Explanation

Let the two positive numbers be x and y.

Then according to the question, we have two equations:

[tex]x^2 + y^2 = 74[/tex]                   (equation 1)

[tex]x^2 - y^2 = 24[/tex]                   (equation 2)

Now, use equation 2 to solve for one of the variables in terms of the other.

Adding [tex]y^2[/tex] to both sides gives:

[tex]x^2 = y^2 + 24[/tex]

Taking the square root of both sides gives:

[tex]x = \sqrt{(y^2 + 24)}[/tex]

Now substitute this expression for x into equation 1 and solve for y:

[tex](y^2 + 24) + y^2 = 74[/tex]

[tex]2y^2 + 24 = 74[/tex]

[tex]2y^2 = 50[/tex]

[tex]y^2 = 25[/tex]

[tex]y = 5[/tex]        (since we're looking for a positive number)

Now we can use the expression we found for x to get:

[tex]x = \sqrt{(y^2 + 24)} = \sqrt{25 + 24} = \sqrt{49} = 7[/tex]

So the two positive numbers are x = 7 and y = 5.

Therefore, the solution is x = 7 and y = 5.

Answer:

7 and 5

Step-by-step explanation:

Let x and y be the two unknown positive numbers.

Set up a system of equations using the defined variables and the given information:

[tex]\begin{cases}x^2 + y^2 = 74\\x^2 - y^2 = 24 \end{cases}[/tex]

Solve the system of equations by the method of elimination.

Add the two equations to eliminate the terms in y:

[tex]\begin{array}{crcccc}&x^2&+&y^2&=&74\\\vphantom{\dfrac12}+&x^2&-&y^2&=&24\\\cline{2-6}\vphantom{\dfrac12}&2x^2&&&=&98\end{array}[/tex]

Solve for x:

[tex]\begin{aligned}2x^2&=98\\2x^2 \div 2&=98 \div 2\\x^2&=49\\\sqrt{x^2}&=\sqrt{49}\\x&=\pm7\end{aligned}[/tex]

As x is positive, x = 7 only.

To find the value of y, substitute x = 7 into one of the equations:

[tex]\begin{aligned}x^2+y^2&=74\\(7)^2+y^2&=74\\49+y^2&=74\\49+y^2-49&=74-49\\y^2&=25\\\sqrt{y^2}&=\sqrt{25}\\y&=\pm 5\end{aligned}[/tex]

As y is positive, y = 5 only.

Therefore, the two positive numbers whose squares have a sum of 74 and a difference of 24 are 7 and 5.

(a) We have shown that there exists an element b ∈ B that is an upper bound for A.

(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.

(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.

Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).

Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.

(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.

Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.

This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.

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Most large companies rely on one person to evaluate system time requests instead of relying on a systems review committee.​ The above statement is true.

Most large companies do not rely on just one person to evaluate system requests. They typically rely on a systems review committee, which consists of multiple individuals with diverse expertise, to make more informed and balanced decisions regarding their systems.

Many small companies rely on a single person rather than a group of people to evaluate demand. The request is reasonable if possible. Attaching a report required by new federal law is an example of a blank check project. Limitations may include hardware, software, time, authorization, rights or cost.

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Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

If X1,…,Xn be an independent trials process, and S∗n be their standardized sum then,

limn→[infinity]P(S∗n > -0.28) = 0.6103

To answer this question, we need to use the central limit theorem. The central limit theorem states that if we have a large enough sample size, the distribution of the standardized sum (S∗n) approaches a normal distribution.

In this case, we want to find the limit of the probability that S∗n is greater than -0.28 as n approaches infinity.

Let Z be a standard normal random variable, then:

P(S∗n > -0.28) = P((S∗n - E[S∗n]) / sqrt(Var[S∗n]) > (-0.28 - E[S∗n]) / sqrt(Var[S∗n]))
= P(Z > (-0.28 - 0) / 1)
= P(Z > -0.28)

Using a standard normal distribution table, we can find that P(Z > -0.28) is approximately 0.6103.

Therefore, limn→[infinity]P(S∗n > -0.28) = 0.6103, since as n approaches infinity, S∗n approaches a standard normal distribution.

The correct question should be :

Let X1,…,Xn be an independent trials process, and S∗n be their standardized sum. What is limn→[infinity]P(S∗n > -0.28)?

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Answer:

Factor 5 out of 5x+35 deg.

5 (x+7 deg)

Step-by-step explanation:

Let's assume that the length of the rectangular kitchen is L and the width is W. We know that the area of the kitchen is 91 square meters, so we can write:

L x W = 91

We also know that the perimeter of the kitchen is 40 meters, which means:

2L + 2W = 40

We can simplify this equation by dividing both sides by 2:

L + W = 20

Now we have two equations:

L x W = 91

L + W = 20

We can use substitution to solve for one of the variables. Let's solve for L:

L = 20 - W

Now we can substitute this expression for L in the first equation:

(20 - W) x W = 91

Expanding this equation gives us a quadratic equation:

W^2 - 20W + 91 = 0

We can solve for W using the quadratic formula:

W = (20 ± √(20^2 - 4 x 1 x 91)) / (2 x 1)

W = (20 ± 3) / 2

W = 11 or W = 9

If W is 11, then L is 9. If W is 9, then L is 11. Therefore, the dimensions of the kitchen are either 9 meters by 11 meters or 11 meters by 9 meters.

In summary, we can use the area and perimeter of a rectangular shape to find its dimensions by setting up equations and solving for the variables. In this case, we used substitution and the quadratic formula to find the possible dimensions of a rectangular kitchen with an area of 91 square meters and a perimeter of 40 metres.

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The solution is: A score of approximately 38.2 separates the top 53% from the bottom 47% on this English test.

Here, we have,

We can use the inverse normal distribution function to find the z-score corresponding to the desired percentile, and then use the formula for standardizing a normal variable to find the corresponding raw score.

The score that separates the top 53% from the bottom 47% on an English test with a normal distribution, mean of 37.6, and standard deviation of 7.6 can be found using the inverse normal distribution function.

We need to find the z-score that corresponds to the 53rd percentile. We can do this using a standard normal distribution table or a calculator. The z-score corresponding to the 53rd percentile is approximately 0.07.

We can use the formula for standardizing a normal variable to find the corresponding raw score: z = (X - mean) / standard deviation Rearranging this formula, we get: X = z * standard deviation + mean

Plugging in the values we have: X = 0.07 * 7.6 + 37.6 X ≈ 38.2

A score of approximately 38.2 separates the top 53% from the bottom 47% on this English test.

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complete question:

scores on an english test are normally distributed with a mean of 37.6 and a standard deviation of 7.6. find the score that separates the top 53% from the bottom 47%

It is important to carefully consider the given information and the specific equation being used in order to determine the appropriate method for solving for a specific side of a shape.
Without knowing the specific equation mentioned in the question, it is difficult to determine whether Andre or Mai's approach is correct. However, in general, the equation used to solve for a specific side of a shape depends on the information given about the other sides and angles of the shape.

If the equation involves the known values of angles and/or sides that are not the one being solved for, then either Andre or Mai's approach may be valid, depending on which side or angle is known.

However, if the equation only involves the unknown side and no other information about the shape is given, then neither approach would be correct. In such a case, additional information or equations would be needed to solve for the unknown side.

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Therefore, The probability that the device will work is 0.634 or 63.4%.

This problem can be solved using the complement rule. The complement of the device working is all the parts failing. Therefore, the probability of the device not working is (1 - 0.216)^7 = 0.366. To find the probability of the device working, we subtract this from 1:
1 - 0.366 = 0.634.
To find the probability that the device will work, we'll use the complementary probability. This means we'll first find the probability that all parts fail and then subtract it from 1. Let's denote the probability of a part failing as q, which is equal to 1 - p.
Step 1: Calculate q.
q = 1 - p = 1 - 0.216 = 0.784
Step 2: Calculate the probability of all parts failing.
P(all parts fail) = q^7 = 0.784^7 ≈ 0.1278
Step 3: Calculate the probability that the device will work.
P(device works) = 1 - P(all parts fail) = 1 - 0.1278 ≈ 0.8722
In conclusion, the probability that the device will work is approximately 0.8722.

Therefore, The probability that the device will work is 0.634 or 63.4%.

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The maximum height of the ball is 9.29 feet.

The given function is h(t) = -161t²+32t+9

To find the maximum height of the ball, we need to find the vertex of the quadratic function.

The vertex of the parabola with equation h = ax² + bx + c is given by the point (-b/2a, f(-b/2a)).

In this case, a = -161, b = 32, and c = 9

so the vertex is located at t = -b/2a

= -32/2(-161)

= 0.1 seconds.

Plugging this value into the equation, we get the height

h = -161(0.1)² + 32(0.1) + 9

= 9.29 feet

Therefore, the maximum height of the ball is 9.29 feet.

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A photo of a beetle in a science book is increased to 555​% as large as the actual size. If the beetle is 14 ​millimeters. The size of the beetle in the photo is 77.7 millimeters.

To determine the size of the beetle in the photo, we can multiply its actual size by the percentage increase in size. 555% can also be expressed as a decimal, 5.55. Therefore, to find the size of the beetle in the photo, we multiply 14 millimeters by 5.55, which gives us 77.7 millimeters. This means that the beetle appears to be almost six times larger in the photo than its actual size. It's important to note that the size of the beetle in the photo may vary depending on the size of the book it's printed in or the resolution of the image.

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Answer is Speed of boat = 4 * 3.75 = 15 feet per second

To find the speed of the boat when 15 feet of rope is out, we can use the formula:

Speed of boat = rate of rope being pulled * time

We know that the rate of rope being pulled is 4 feet per second, and the amount of rope out is 15 feet. So, we can calculate the time it takes for 15 feet of rope to be pulled out, the equation is:

Time = distance / rate = 15 / 4 = 3.75 seconds

Now that we have the time, we can use the formula above to find the speed of the boat:

Speed of boat = 4 * 3.75 = 15 feet per second

As the boat gets closer and closer to the dock, the speed of the boat will decrease. This is because the angle of the rope pulling the boat towards the dock becomes sharper and sharper, causing more and more of the pulling force to be directed upwards instead of forwards. Additionally, the winch itself will be pulling at a sharper angle, reducing its effective force. This means that the boat will slow down as it approaches the dock, eventually coming to a stop when the pulling force is no longer sufficient to overcome the resistance of the water.

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In an analysis of variance, you reject the null hypothesis when the F ratio is:
b. much larger than 1.

Here's a step-by-step explanation:
1. The null hypothesis states that there are no significant differences among the groups being compared.
2. Variance is the measure of how much the individual data points in a dataset vary from the mean.
3. The F ratio is the ratio of two variances, specifically, the variance between group means and the variance within groups.
4. When the F ratio is much larger than 1, it indicates that the variance between group means is much larger than the variance within groups.
5. This suggests that there is a significant difference among the group means, leading to the rejection of the null hypothesis.

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To verify that f = ∇f, we need to find the gradient of f and compare it to f.

The line integral of f over the given path = 0

The gradient of f is given by:

∇f = (∂f/∂x) i + (∂f/∂y) j + (∂f/∂z) k

= (z/x) i j + 0 j k + (x ln(x)) k

Now, we can see that f = ∇f, since the corresponding components match:

f(x, y, z) = z x i j ln(x)k

= (z/x) i j x ln(x)k

= (z/x) i j + 0 j k + (x ln(x)) k

= (∂f/∂x) i + (∂f/∂y) j + (∂f/∂z) k

= ∇f

To evaluate the line integral of f over the given path, we need to parameterize the path and then compute the integral. The given path is a circle with center (6,0) and radius 1, so we can parameterize it as:

r(t) = <6 + cos(t), sin(t), 0>, 0 ≤ t ≤ 2π

Using this parameterization, we can compute the line integral as:

∫f(r(t)) ⋅ r'(t) dt from 0 to 2π

where r'(t) is the derivative of r(t) with respect to t.

We have:

r'(t) = <-sin(t), cos(t), 0>

f(r(t)) = y z ln(x) = sin(t) ⋅ 0 ⋅ ln(6 + cos(t)) = 0

So the line integral simplifies to:

∫0 dt from 0 to 2π

The integral of 0 over any interval is 0, so the final result is:

0

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The teacher asked the first 5 students on her class seating chart to write down where the class should go on a field trip is yes

Clara surveyed more than half the teachers at her school and then, without looking, selected the responses for her sample is no

To get a random sampling of every student in her school, Cheryl surveyed all the students in her math class is no

A company sent e-mails to its customers asking them to e-mail back their opinion of the company’s products. Only 10 of them e-mailed back is no

1) Yes, this is an example of random sampling.

The teacher used a systematic method of selecting the first 5 students on her seating chart to ensure that the sample is representative of the class.

2) No, this is not an example of random sampling.

Clara did not use a random selection method to choose the responses for her sample, which can result in a biased sample.

3) No, this is not an example of random sampling.

Cheryl only surveyed the students in her math class, which is not a representative sample of the entire school population.

4) No, this is not an example of random sampling.

The sample is not representative of the entire customer population since only 10 customers responded.

This may lead to biased results if the 10 customers who responded have different opinions than those who did not respond.

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Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

The upper class limits are- 29, 39, 49, 59, 69, 79, 89

The lower class limits are- 20, 30, 40, 50, 60, 70, 80

The class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5

The class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5

And the number of individuals included in the summary is 84.

Here, we are given the following dataset-

Age (yr) when          Frequency

award was won

20-29                       27

30-39                       32

40-49                       15

50-59                       3

60-69                       5

70-79                        1

80-89                       1

Upper class limit is the largest data value that can go in a class.

Thus, the upper class limits are- 29, 39, 49, 59, 69, 79, 89

Lower class limit is the smallest data value that can go in a class.

Thus, the lower class limits are- 20, 30, 40, 50, 60, 70, 80

The class midpoint is the average of the upper and lower limits of a class. Class midpoint = (upper limit + lower limit)/ 2

Thus, the class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5

Class boundary is the midpoint of the upper class limit of a class and the lower class limit of the previous class.

Thus, the  class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5

Frequency gives us the number of individuals/ objects belonging to a particular class.

Thus, the number of individuals included in the summary = 27 + 32 + 15 + 3 + 5 + 1 + 1 = 84

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complete question:

Identify the lower class limits, upper class limits,

class width, class midpoints, and class boundaries for

the given frequency distribution. Also identify the

number of individuals included in the summary.

Age (yr) when

award was won

20-29

30-39

40-49

50-59

60-69

70-79

80-89

Frequency

27

32

15

3

5

1

1

the lower class limit represents the smallest data value that can be included in the classThe statement is true.

The lower class limit is the smallest value that can be included in a class interval.

Therefore, the statement is correct.

The lower class limit represents the smallest data value that can be included in a particular class. In a frequency distribution table, data values are grouped into classes, and each class has a lower and upper class limit. The lower class limit denotes the lowest value within that class, and any data value equal to or greater than the lower limit but less than the upper limit falls into that class.

The statement is true, as the lower-class limit indeed represents the smallest data value that can be included in the class.

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Answer:

is it 193

Step-by-step explanation:

i added -1 and 192

Over 10.144 years of age are found in 75% of firm employees' autos.

We need to identify the z-score that corresponds to the age of the cars driven by firm employees that are 75% older than the other cars of 75th percentile of the normal distribution.

A normal distribution calculator or statistical software programme can be used to find this z-score. As an alternative, we can look for the value using a z-distribution table.

The formula for the z-score is:

z = (x - μ) / σ

If x is the value we are looking for, is the distribution's mean, and is its standard deviation.

We can use the common normal distribution table or a calculator with a built-in function to determine the z-score corresponding to the 75th percentile  to a cumulative probability of 0.75. The table value is 0.67.

As a result, we can determine the age of the company vehicles that are approximately 75% older than the others as follows:

x = μ + zσ

= 8 + (0.67)(3.2)

= 10.144

As a result, more than 75% of the cars that firm employees drive are older than 10.144 years.

For such more questions on Car Ages: 75th Percentile

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Answer: [tex]-3x^{2} +6x+9[/tex]

Step-by-step explanation: