4. A Space Z engineer is testing the design of a new heat shield for its Komodo spacecraft. The design is meant to prevent
the interior of the shield from reaching a temperature of 200◦C. Over the course of 24 trials, the average temperature
of the shield was 194.37◦C with a standard deviation of 4.29◦C. Assume all temperature measurements follow a normal
distribution.

(a) Test at the 1% level of significance if the shield’s average temperature is less than 200◦C.

(b) Explain a Type I error in the context of the data.

The pressure of the gas is 7kg/cm^2.

Joint Variation is a situation in which the value of one variable depends on two, or more, other variables when the other variables are held constant

Given that: The volume V of a fixed amount of a gas varies directly as the temperature T and inversely as the pressure P. This can be written as:

VαT and Vα 1/P

Combining the two relations gives:

Thus Vα T/P  

V = kT/P        (where k is a constant)

PV=kT

k = PV/T

P =kT/V

Given: V = 70 cm^3

when T = 420 kelvin

P = 18 kg/cm^2

k = 18×70 / 420

k = 1260/420

k = 3

Given: T = 140 kelvin and

V = 60 cm^3.

Find the pressure

P = kT/V

P = 3×140/60

= 420/60

= 7kg/cm^2

Therefore, the pressure when T = 140 kelvin and V = 60 cm^3 is 7kg/cm^2.

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Regarding the hypothesis tested in this problem, it is found that:

a) The test statistic is: t = 0.49.

b) The p-value is: 0.6297..

c) The null hypothesis is not rejected, as the p-value is greater than the significance level.

d) It appears that the students are legitimately good at estimating one minute, as the sample does not give enough evidence to reject the null hypothesis.

The test statistic of the t-distribution is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which the variables of the equation are given as follows:

The value tested at the hypothesis is:

[tex]\mu = 60[/tex]

From the sample, using a calculator, the other parameters are given as follows:

[tex]\overline{x} = 62.47, s = 19.2, n = 15[/tex]

Hence the test statistic is obtained as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{62.47 - 60}{\frac{19.2}{\sqrt{15}}}[/tex]

t = 0.49.

The p-value is obtained using a t-distribution calculator, with a two-tailed test, as we are testing if the mean is different a value, in this case 60, with:

Hence the p-value is of 0.6297.

Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected, attesting to the ability of the students to estimate one minute.

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The area of two lawns will be 4000 square meters.

According to the question,

We have the following information:

Craig mows two lawns. The first lawn is 40 meters long and 20 meters wide. The second lawn has the same length, and a width that is 4 times as much as the first one.

So, the width of the second lawn = 4*20

Width of second lawn = 80 m

Now, formula to find area of rectangle:

Length*width

Area of first lawn:

40*20

800 square meters

Area of second lawn:

40*80

3200 square meters

Now, the area of two lawns = area of first lawn+ area of second lawn

Area = 800+3200

Area = 4000 square meters

Hence, the total area of two lawns is 4000 square meters.

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Answer:

8%

Step-by-step explanation:

The solution to x in the  equation is 1/3x + 2/9x =10 is 18

To solve for x we follow the step;

Step 1: Combine the equation multiple into single fraction

1/3x + 2/9x =10

[tex]\frac{x}{3}[/tex] +[tex]\frac{2x}{9}[/tex] =10

Step 2: Find the common denominator

[tex]\frac{3x}{9}[/tex] + [tex]\frac{2x}{9}[/tex] =10

Step 3: Add the fraction with common denominator

[tex]\frac{3x +2x}{9}[/tex]= 10

[tex]\frac{5x}{9}[/tex] =10

Step 4: Cross multiply

5x = 9(10)

5x = 90

Step 4: Divide both 5

[tex]\frac{5x}{5}[/tex] =[tex]\frac{90}{5}[/tex]

x= 18

Therefore, the solution for x in the equation is 18

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Answer:

I believe the first one is log8(5/3), the second is log5(3), and the third is -2log2(5)

Step-by-step explanation:

I got this by applying the properties of logarithms which are:

logₐ mn = logₐ m + logₐ n (product property)

logₐ m/n = logₐ m - logₐ n (quotient property)

logₐ mn = n logₐ m (power property)

logb = (log꜀ a) / (log꜀ b) (change of base property)

The constant of proportionality of the equation y =−7.48​x is - 7.48.

Proportional relationships are relationships between two variables where their ratios are equivalent

In other words, two variables have a proportional relationship if the ratios of the variables are equivalent.

Therefore, a proportional relationship is one in which two quantities vary directly with each other.

Hence, in mathematical form,

y ∝ x

y = kx

where

y varies directly as the variable x.

In the equation,

k = - 7.48

Therefore, the constant of proportionality  is - 7.48.

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It would take 8 months of membership for the total money paid of $321.91.

An equation is an expression that shows the relationship between two or more numbers and variables. A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

Let x be the number of months subscribed. Hence,

For Fitness :

Total payment = 33.99 x + 49.99

if you paid a total of $321.91 then the number of months subscribed will be;

321.91  = 33.99 x + 49.99

33.99 x = 321.91  - 49.99

33.99 x = 271.92

x = 271.92/33.99

x = 8

It would take 8 months of membership for the total money paid of $321.91.

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The first mechanic worked for 10 hours and second mechanic worked for 5 hours.

Given,

Price of first mechanic service =$85/hr

Price of second mechanic service=$45/hr

Total time they worked together=15 hours

Total combined price charged=$1075

Let

Time spend by first mechanic on work =x

Time spend by second mechanic on work =y

Price charged by first mechanic on total work =85x

Price charged by second mechanic on total work=45y

Equation for total time spend by them together on work can be written as,

[tex]x+y=15.....i\\\\y=15-x[/tex]

Equation for total price charged by them can be written as,

[tex]85x+45y=1075\\[/tex]

Substituting y,

[tex]85x+45(15-x)=1075\\\\85x+675-45x=1075\\\\40x+675=1075\\\\40x=1075-675\\\\40x=400\\\\x=10\\[/tex]

Substituting x in eq.[tex]i[/tex],

[tex]10+y=15\\\\y=15-10\\\\y=5[/tex]

Hence, the first mechanic worked for 10 hours and second mechanic worked for 5 hours.

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The x value we get is 10 when the sides are 8x-13 and 5x+17 in a congruent triangle.

Given that,

The sides as 8x-13 and 5x+17

We have to find the x value.

If two or more triangles are congruent, it depends on how big their sides and angles are. The three sides and three angles of a triangle determine its size and shape, accordingly. Two triangles are said to be congruent if the pairings of respective sides and corresponding angles are equal.

We say now,

8x-13 = 5x+17

8x-5x=17+13

3x=30

x=30/3

x=10

Therefore, The x value we get is 10 when the sides are 8x-13 and 5x+17 in a congruent triangle.

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Since the function is not one-to-one, the inverse function of f(x) = x³ + 3x² - 4 is not defined at x = -4.

An original function is composed by a set of points in the following format:

(x,y).

On the graph of the function, we have that:

On the inverse function, the input and the output are exchanged, hence the format of the point is:

(y,x).

To find the numeric value of the inverse function at x = -4, we need to identify the value of x on the original function where y = -4.

However, looking at the graph of the function given at the end of the answer, the function is not one-to-one at y = -4, since f(-3) = f(0) = 4, thus the inverse function is not defined at x = -4.

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The equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.

According to the question,

We have the following information:

The difference of ten times a number and six is fourteen.

Now, let's take the number to be x.

So, we have the following expression:

10x-6 = 14

Now, moving 6 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

10x = 14+6

10x = 20

x = 20/10

x = 2

Hence, the equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.

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The solution for the function f(x) is x = 9/4 or -1.

Function is a combination of different types of variable and constants.

A function is denoted by f(x).

The given function is,

f(x) = x²+11x²-15x-27

⇒f(x) = 12x²-15x-27

To find solution of this function, find factor,

f(x) = 12x²-27x+12x-27

f(x) = 3x(4x-9) + 3(4x-9)

f(x) = (4x-9)(3x+3)

To find solutions substitute f(x)=0,

⇒(4x-9)(3x+3) =0

x=9/4 or -1

So the possible value of x is 9/4 or -1.

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The fraction of the students taking the test exceeded your score will be 47 / 250.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

Assume that a public testing administration gives a test in which the outcomes are regularly dispersed with a mean of 550 and a standard deviation of 85. On the off chance that you score a 625 on the test.

Then the fraction of the students taking the test exceeded your score will be given as,

z = (625 - 550) / 85

z = 75 / 85

z = 0.8824

Then the fraction is given as,

P(x > 625) = P(z > 0.8824)

P(x > 625) = 0.188

P(x > 625) = 47 / 250

The fraction of the students taking the test exceeded your score will be 47 / 250.

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Answer:

5 hours 15 minutes

Step-by-step explanation:

using the relationship

time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{273}{52}[/tex] = 5.25 hours = 5 hours 15 minutes

The next three terms in the sequence are  -1/16, 1/32, -1/64

The correct option is option C)

What is a sequence?

A sequence is an set of values separated by commas Referring to a generalized rule. They have a relation among them. One of the common sequences are arithmetic progression

We are given a sequence of -1, 1/2, -1/4, 1/8,

We have to describe the next three terms of the sequence

If we notice closely the given sequence is an geometric sequence

Hence they have a common factor known as common ratio

in it we divide a term by its previous term

Hence

Ratio= (1/2)/-1

Ratio = -1/2

Now to find the next terms we multiply this with the last term we get

1/8*-1/2= -1/16

Now Hence the next three terms are -1/16, 1/32, -1/64

The correct option is option c)

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Given equation 2x + 4y = 4 has infinitely many solutions.

We have been given an equation 2x + 4y = 4

We need to find the number of solutions.

Above equation is a linear equation with two variables.

We know that, a linear equation in two variables has infinitely many solutions.

For any value real value of x we can find corresponding value of y.

Since x can takes infinitely many inputs the output would be infinitely many.

Therefore, given equation 2x + 4y = 4 has infinitely many solutions.

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The probability expression when converted from odd's expression is 8/17

From the question, we have the following odd parameters

Odd = 8 to 9

To start with, we need to express the odd as ratio

So, we have the following representation

Odds ratio = 8 : 9

Solving further, we need to express the ratio as fraction

So, we have the following representation

Odds fraction = 8/9

To convert the above odd's expression to probability expression, we make use of the following equation

This is represented as

P = Odds/(Odds + 1)

Substitute the known values in the above equation

So, we have the following equation

P = (8/9)/(8/9 + 1)

Evaluate the sum

This gives

P = (8/9)/(17/9)

Express the quotient as product

P = (8/9) * (9/17)

Evaluate

P = 8/17

Hence, the probability is 8/17

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Answer:

x = 15

Step-by-step explanation:

A segment joining the midpoints of two sides of a triangle is half the length of the third side , then

x + 3 = [tex]\frac{1}{2}[/tex] × 36 = 18 ( subtract 3 from both sides )

x = 15

The numeric value of the expression -b + 8x when b = 5 and x = -6 is given as follows:

-53.

To find the numeric value of a function or of an expression, we replace each instance of the variable/variables in the function or in the expression by the value/values at which we want to find the numeric value.

In this problem, the expression is given as follows:

-b + 8x.

The values at which the numeric value is to be found are:

b = 5, x = -6.

Hence:

Thus the numeric value of the expression is obtained as follows:

-5 + 8(-6) = -5 - 48 = -53.

The problem is given by the image at the end of the answer.

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Answer:

[tex]\frac{3}{40}=0.075[/tex]

Step-by-step explanation:

The probability of a person selected at random from this group having type AB blood is 15 out of 200 total people. Therefore:

[tex]\frac{15}{200}=\frac{3}{40}=0.075=7.5\%[/tex]

The z-score of a person who scored 128 on the exam is equal to 2.9

A z-score is also referred to as a z-value or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

Mathematically, the z-score of a given sample score in a normal distribution can be calculated by using this formula:

[tex]z=\frac{x\;-\;u}{\sigma}[/tex]

Where:

Substituting the given parameters into the formula, we have;

Z-score, z = (128 - 70)/(20)

Z-score, z = 58/20

Z-score, z = 2.9

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Answer:

The slope would be undefined

Step-by-step explanation:

If the slope is perpendicular to the x-axis that means it is vertical, all vertical lines have undefined slopes therefore the slope is undefined.

Answer: 32

Step-by-step explanation:

If you multiply 2 1/5 by 35 you would get 70.4, .4 is equivalent to 2/5, so 70.4 = 70 2/5.

Answer:

2.6

Step-by-step explanation:

2 7/12

12x2=24

24+7=31

31/12=2.583333

Answer:

its 262.5%

Step-by-step explanation:

A total of 2587 students attended the collage

From the question, the given parameters are:

The above parameters implies that

Number of students that attended = 56% x Total number of students

Represent the total number of students with x

So, we have the following representation

Number of students that attended = 56% * x

Where

x = 4620

So, we have

Number of students that attended = 56% x 4620

Evaluate the products

Number of students that attended  = 2587.2

Approximate

Number of students that attended = 2587

Hence, 2587 of the students attended the collage

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The correct option regarding which option represents a polynomial is given as follows:

b. ii only.

Polynomials are expressions that are given in the following format:

[tex]p(x) = a_nx^n + a_{n-1}x^{n - 1} + \cdots + a_1x + a_0[/tex]

In which n is the degree of the polynomial.

The exponents n have to be all whole numbers for the expression to represent a polynomial, meaning that they cannot be negative neither fractions or decimal values.

Thus the only expression that represents a polynomial is:

ii. 5x³ + 3x² + x + 2.

The reasons for the expressions that do not represent a polynomial are given as follows:

Hence the correct option is given by option b.

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There were 500 times more views were on Saturday than Sunday

In this question, we have been given a website got 4 × 10^9 views on Saturday and 8 × 10^6 views on Sunday.

We need to find the number of times more views were on Saturday than Sunday.

We need to divide 4 × 10^9 by 8 × 10^6

( 4 × 10^9) / (8 × 10^6)

= (4/8) * 10^(9 - 6)                   ..............(rule of exponents)

= 0.5 * 10^3

= 500      

Therefore, there were 500 times more views were on Saturday than Sunday.

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Answer:

No

Step-by-step explanation:

A right angle triangle will have a 90° angle. If you don't know what that looks like. Check the rectangle above triangle C. All of the angles in it are 90°.

Bonus:

If you wanted check the length is of the third side of triangle c. It is 17 in, this is because you look at the top of the rectangle and the top of the triangle and they are both the same length.

Answer:

I feel like it is it depends on the way you are leaning and if these sides are rounded or not

If they are rounded then yes this is a right triangle is not then no but it is close

Step-by-step explanation:

it might just be if the third side is rounded

We find out using the Pythagorean theorem

12^2+12^2=c^2

144+144

288=c^2

Square root both sides

16.97=c

Hopes this helps please mark brainliest