letry. 14 Chapter 9: Chapter 9 rest Chapter Test
A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height of the roof.
Round your answer to the nearest tenth.
15 ft
h
8 ft
17 ft

Answer:

2(x^2 + 8x -55)

Step-by-step explanation:

Well to do the box method we first need to simplify the given equation further to,

[tex]2x^2 + 16x - 110\\[/tex],

For this quadratic the box method doesn't work so we can divide everything by 2 make make it

2(x^2 + 8x -55)

Thus,

[tex]2x^2 + 16x - 110\\[/tex] factored is 2(x^2 + 8x -55).

Hope this helps :)

Answer:

The highest number on a die is 6. when we roll out two die the total sum cannot be more that 12. and each sum having the same probability of showing up.

The outcome of our experiment can be 2,3,4,5,6,7,9,10,11 or 12.

Step-by-step explanation:

Statistical experiment can be simply stated as the likelihood of an an event to occur or not.

hii

Step-by-step explanation:

length-10x

width-x

perimeter-2(l+b)

66=2(10x+x)

66-2=10x+x

64=11x

x=11/64

lenght-11

width-64

Answer:

[tex]\boxed{7.955>7.95}[/tex]

Step-by-step explanation:

7.95 can also be written as 7.950 .

So, we'll compare 7.955 and 7.950.

All the digits in ones, tenths, hundredths place are equal so we'll look at the thousandths place.

5 is in the thousandths place of 7.955 and 0 is in the thousandths place of 7.950. Since 5 is greater than 0 so 7.955 is greater than 7.95. It can also be written as:

7.955 > 7.950

Answer:

d) The t-distribution with 5 degrees of freedom must be used

Step-by-step explanation:

For cases of Normal Distribution where the variance is unknown and the sample size n is smaller than 30, we must use the t-student distribution.

The shape of the curve for t-student is bell-shape (flatter and with wider tails than the bell shape of normal distribution.

Actually, when we deal with t-student distribution we are dealing with a family of curves that will become closer and closer to the bell shape of the normal distribution as the degree of freedom increases. From values of n =30( and bigger),  we can assume that the curve of t-student is the same as for normal distribution

Answer:

3 or -3

Step-by-step explanation:

sqrt(9)

What number multiplied by itself will give you 9

3*3 =9

-3 * -3 =9

The square root of 9 is 3 or -3

Answer: A. [tex]d=\sqrt{(190-7t)^2+(130-4t)^2}[/tex]

B. Minimum distance between them  = 18.61 feet.

C. After 28.76 seconds Sven and Rudyard are closest.

Step-by-step explanation:

A) Let (0,0) be the intersection point.

Then, Initial Location of Sven (0,190).

Speed of Sven = 7 feet per second

Then, position of Sven after t seconds = (0,190-7t)  [speed = distance x time]

Similarly, Initial position of Rudyard= (130,0)

Speed of Rudyard = 4 feet per second

Position after t seconds = (130-4t,0)

Distance d between Sven and Rudyard t seconds after they start walking:

[tex]d=\sqrt{(190-7t)^2+(130-4t)^2}[/tex]

B) Let [tex]d(t)=\sqrt{(190-7t)^2+(130-4t)^2}\\[/tex]

[tex]d'(t)=2(190-7t)(-7)+(2)(130-4t)(-4)\\\\=130t-3700[/tex]

Put d'(t)=0

[tex]130t-3700=0\\\\\Rightarrow\ t=\dfrac{3700}{130}\approx28.46\ sec[/tex]

Minimum distance :

[tex]d(28.46)=\sqrt{(190-7(28.46))^2+(130-4(28.46))^2}\\\\=\sqrt{346.154}\approx18.61\ feet[/tex]

Hence, the minimum distance between them  = 18.61 feet.

c) After 28.76 seconds Sven and Rudyard are closest.

Answer:

Percentage volume of the Grand Canyon filled by the snow = 0.911 %

Step-by-step explanation:

This question is incomplete; please find the complete question in the attachment.

Given :

Area of the snow cover = 72150 square miles

Depth of the snow = 8 inches

Volume of the Grand Canyon = 4.166 × 101² m³

Solution:

Area of the snow cover = 72150 square miles

≈ 72150 × 2589988 square meter

≈ 1.868 × 10¹¹ square meter

Depth of the snow = 8 inches ≈ 0.2032 m

Volume of the snow on this area = Area × depth of the snow

                                                       = 1.868 × 10¹¹ × 0.2032

                                                       = 3.796 × 10¹⁰ m³

Volume of the Grand Canyon = 4.166 × 10¹² m³

Percentage volume of the Grand Canyon filled by the snow

= [tex]\frac{\text{Volume of the snow}}{\text{Volume of the Grand Canyon}}\times 100[/tex]

= [tex]\frac{3.796\times 10^{10} }{4.166\times 10^{12} }\times 100[/tex]

= 0.911%

Answer:

replicating

Step-by-step explanation:

Answer:

Largest integer in the interval [−∞, 31] is 31.

Step-by-step explanation:

Given the interval: [−∞, 31]

To find: The largest integer in this interval.

Solution:

First of all, let us learn about the representation of intervals.

Two kind of brackets can be used to represent the intervals. i.e. () and [].

Round bracket means not included in the interval and square bracket means included in the interval.

Also, any combination can also be used.

Let us discuss one by one.

1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.

Smallest p

Largest q

2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.

Smallest value just greater than p.

Largest value just smaller than q.

3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.

Smallest value p.

Largest value just smaller than q.

4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.

Smallest value just greater than p.

Largest value q.

As per above explanation, we can clearly observe that:

The largest integer which belongs to the following interval: [−∞, 31] is 31.

Answer:

length=16 feet and width=12 feet

Answer:

Length = 16ft, width = 12ft

Step-by-step explanation:

4:2 or 2:1

so you need to mulitply everything by 2

length =  8*2 = 16ft

width = 6*2 = 12ft

Answer:

Null hypothesis: u = 8.8 liters

Alternative hypothesis: u < 8.8 liters

Step-by-step explanation:

The null hypothesis is always opposite to Tue alternative hypothesis and is the default hypothesis.

In this case study, the null hypothesis is that the average American consumes 8.8 liters of alcohol per year: u = 8.8

The alternative hypothesis is that does the average American consumes less than 8.8 liters of alcohol per year: u < 8.8 liters

Answer:

c

Step-by-step explanation:

Answer:

A. x <= 2

Step-by-step explanation:

The domain of a real function should be all real numbers. In

f(x) = sqrt(2-x)

we need 2-x to be non-negative, therefore

2-x >= 0

which implies

x <= 2

Answer:

[tex]\Huge \boxed{{x\leq 2}}[/tex]

Step-by-step explanation:

The function is given,

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

The domain of a function are all possible values of x.

There are restrictions for the value of x.

2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.

[tex]2-x\geq 0[/tex]

[tex]-x\geq -2[/tex]

[tex]x\leq 2[/tex]

The domain of the function is x ≤ 2.

Answer:

y = 19/14 and x = 25/42

Step-by-step explanation:

Answer:

(5/2, 4/3)

Step-by-step explanation:

the solution is the point (2.41,1.36)

x=5/2  

y=4/3

Answer:

The value of e is approximately 2.71828.

Step-by-step explanation:

An exponential function is of the form:

[tex]y=a^{x}[/tex]

Here a is any value that is more than 0.

The natural form of an exponential function is:

[tex]y=e^{x}[/tex]

Here e is known as the Euler's number.

The value of e is approximately 2.71828.

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

Answer:

The answer above is correct B

Step-by-step explanation:

Took the Unit Test Review on edg 2020 correct

Answer:

D. (0, 7).

Step-by-step explanation:

Moving from (4,3) to (2, 5) we move 2 to the left; 2 - 4 = 2 then 2 up 3 + 5 = +2.

So the point C is 2-2, 5+2 = (0, 7).

Answer:

105.6

Step-by-step explanation:

If the mean is 8.8, than that means that in total the sum must be (8.8 * 12) which equals 105.6.

This is because the sum of all the numbers in a list divided by the amount of numbers in a list equals the mean.

Answer:

Step-by-step explanation:

The perimeter of a rectangle is expressed as 2(L+B) where;

L is the length and B is the breadth of the triangle.

P = 2(L+B)

68 = 2(L+B)

L+B = 68/2

L+B = 34

L = 34 - B ... 1

Area of the rectangle A = LB... 2

Substituting equation 1 into 2 will give;

A = (34-B)B

A = 34B-B²

To maximize the area of the triangle, dA/dB must be equal to zero i.e

dA/dB = 0

dA/dB = 34 - 2B = 0

34-2B = 0

2B = 34

Dividing both sides of the equation by 2 we will have;

B = 34/2

B = 17

Substituting B = 17 into equation 1 to get the length L

L = 34-17

L = 17m

This shows that the rectangle with maximum area is a square since L = B = 17m

The dimension of the rectangle is Length = 17m and Breadth = 17m

The dimensions are 17m and 17m.

The perimeter of a rectangle is given as:

= 2(length + width)

Since in their case, the lengths have same values, this will be:

Perimeter = 2(l + l)

Perimeter = 4l

4l = 68

L = 68/4

L = 17m

Therefore, the dimensions are 17m and 17m.

Read related link on:

https://brainly.com/question/15366172

Answer:

500 pounds

Step-by-step explanation:

Let the pressure applied to the leverage bar be represented by p

Let the distance from the object be represented by d.

The pressure applied to a leverage bar varies inversely as the distance from the object.

Written mathematically, we have:

[tex]p \propto \dfrac{1}{d}[/tex]

Introducing the constant of proportionality

[tex]p = \dfrac{k}{d}[/tex]

If 150 pounds is required for a distance of 10 inches from the object

[tex]150 = \dfrac{k}{10}\\\\k=1500[/tex]

Therefore, the relationship between p and d is:

[tex]p = \dfrac{1500}{d}[/tex]

When d=3 Inches

[tex]p = \dfrac{1500}{3}\\\implies p=500$ pounds[/tex]

The pressure applied when the distance is 3 inches is 500 pounds.

Answer:

Step-by-step explanation:

y= 3x

x            y

0           0

1             3

2            6

3             9

-1            -3

-2             -6

Answer:

126

Step-by-step explanation:

Total volume of sand = pi/3*(6^2)*(15) + pi*(6)^2*(30) = 1260*pi mm^3

So it will therefore take 1260*pi/10*pi = 126 seconds for all of the sand from the top hourglass to drip down to the bottom hourglass.

Answer:

Inventory turnover ratio is 3.74

explanation:

Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.

Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold

= $35,500 / $9500

= 3.74

Answer: x < 7, and x > -7

Step-by-step explanation:

Simply square root both sides of the equation.  The square root of x^2 is x and the square root of 49 can be 7 or -7.

Hope it helps <3

Answer:

x < 7      and x > -7

Step-by-step explanation:

x^2 < 49

Take the square root of each side, remembering to flip the inequality when we take the negative

sqrt( x^2) < + sqrt(49)     and  sqrt( x^2)> - sqrt(49)

x < 7      and x > -7

Answer:

a) h(x; 7, 5, 12) = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)

b) 2.92

Step-by-step explanation:

a)

Here

Number of interviewees = N = 12

Number of job openings = M = 5

Interviews schedules for the first day =  n = 7

N − M = 12 - 5 = 7

Using hypergeometric distribution:

Let X be the no. top four candidates interviewed on first day.

The probability mass function of X:

P(X = x) = [tex](^{M} C_{x})[/tex]   [tex](^{N-M} C_{n-x})[/tex] /  [tex](^{N} C_{n})[/tex]

It can be written as:

h(x; n, M, N)  =  [tex](^{M} C_{x})[/tex]   [tex](^{N-M} C_{n-x})[/tex] /  [tex](^{N} C_{n})[/tex]    

                    = (5Cx) (7C7-x) / (12C7)

                    = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)

h(x; 7, 5, 12) = (⁵Cₓ)( ⁷C₇₋ₓ) / (¹²C₇)

b)

The expectation is: E(X) = np

E(X) = n * M/N

              = 7 * 5/12

              = 7 * 0.41667

              = 2.9167

Answer:

C. surface area of 5 rectangular prisms.

Step-by-step explanation:

The table in the given figure as shown above has a rectangular flat top that has a solid shape of rectangular prism.

It also has 4 legs that are also rectangular in shape. The legs are rectangular prisms.

To determine the quantity of paint Kimberly would need, she needs to make use of the surface area of the table.

The surface area of the table = surface area of the top + surface area of the 4 legs = surface area of 5 rectangular prisms.

Answer:

C

Step-by-step explanation:

Mensuration:

Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.

Plane Figure: A figure which lies in a plane is called a plane figure.

For e.g:  a rectangle, square, a rhombus, a parallelogram, a trapezium.

Perimeter:

The perimeter of a closed plane figure is the total length of its boundary.

In case of a triangle or a polygon the perimeter is  the sum of the length of its sides.

Unit of perimeter is a centimetre  (cm), metre(m) kilometre(km) e.t.c

Area: The area of the plane figure is the measure of the surface enclose by its boundary.

The area of a triangle are a polygon is the measure of the surface enclosed by its sides.

A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.

Circumference of a circle is the perimeter of a circle.

In a circle the radius is half of the diameter.

The approximate value of π( Pi) is= 22/7 

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Answer:

The answer is below

Step-by-step explanation:

Given that:

Mean (μ) = 3 ounces. standard deviation (σ) = 0.15, sample size (n) = 13 and confidence (C) = 98%

α = 1 - C = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01.

The z score of 0.01 (α/2) corresponds to the z score of 0.49 (0.5 - 0.01) which from the normal distribution table is 2.33.

The margin of error (E) is:

[tex]E=z_{0.01}*\frac{\sigma}{\sqrt{n} } = 2.33*\frac{0.15}{\sqrt{13} }=0.1\\[/tex]

The confidence interval = μ ± E = 3 ± 0.1 = (2.9, 3.1)

The confidence interval is between 2.9 ounce and 3.1 ounce

Answer:

± (1 ÷ 9)

Step-by-step explanation:

Data provided in the question

Since  3 is added to the absolute value and -9

The result is 4

Now this information should be transformed in a mathematical equation

Let us assume be x so the product of the number and -9 be -9x

Fo rthe absolute value we use the mode. Thus the required expression is:

3 + |-9x|

Given that the result is 4

So, it would be

3 + |-9x| = 4

Now Solving the above equation which is given below:

|-9x| = 4-3

|-9x| = 1

here we will remove the mode by introducing ± sign which is shown below:

-9x = ± 1

-9x = 1 or -9x = -1

x = -1/9

or

x = [tex]\frac{1}{9}[/tex]

Therefore, the value of x is ± (1 ÷ 9).