An architect needs to consider the pitch, or steepness, of a roof in order to ensure precipitation runoff. The graph below shows
the vertical height, y, versus the horizontal distance, x, as measured from the roof peak's support beam.
Roof Steepness
y
14
12
10
8
Vertical Height (feet)
4
2
+X
10 12 14
0
2
4
6
8
Horizontal Distance (feet)
Determine the equation that could be used to represent this situation.

Answer:

7 is the answer

Step-by-step explanation:

if we put 1/4 or 2 then the statement will wrong so 7 is the right answer

Answer:

A

Step-by-step explanation:

If 4A (7) is greater than 10, then 4x7=28. 28 is greater than 10.

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Hope this helps you...

Answer:

Quantity (lbs) of type 1 candy  x = 8

Quantity (lbs) of type 2 candy  y = 17,5

Step-by-step explanation:

Let´s call  "x" quantity (in pounds) of candy type 1 in the mixture, and "y" quantity (in pounds ) of candy type 2, then according to the problem statement.

x  +  y  =  25,5

2,20*x  +  7,30*y = 5,70 * 25,5   ⇒  2,20*x  +  7,30*y = 145,35

Then we have a two equation system

x  +  y  =  25,5                                   ⇒   y = 25,5 - x

2,20*x  +  7,30*y = 145,35               ⇒ 2,20*x + 7,30* (25,5 - x ) = 145,35

2,20*x + 186,15 - 7,30*x = 145,35

5,1*x  = 40,8

x = 40,8/5,1

x = 8 lbs

And   y  =  25,5 - 8

y = 17,5 lbs

Answer:

83.0

Step-by-step explanation:

We have all three sides and the only thing we're missing is the X angle. And that's okay!

All you have to do is plug in the numbers into each variable. In this case if you are going to solve for X, you should use this equation.

[tex]x^2=y^2+z^2-2yzcosX[/tex]

x = 17ft

y = 8ft

x = 16fi

Then you can algebraically solve for cosX, and then use the inverse of cosx to get the angle.

Answer:

The center is (1,4)

Step-by-step explanation:

The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.

Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:

[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]

So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:

[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]

75 meters

Step-by-step explanation:

5 x 30/2

= 5 x 15

= 75 meters

Full Question

Of the cartons produced by a​ company, 10​% have a​ puncture, 6​% have a smashed​ corner, and 0.4​% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing​ ____%. ​(Type an integer or a decimal. Do not​ round.)

Answer:

[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]

Step-by-step explanation:

Given

[tex]Puncture\ Corner = 10\%[/tex]

[tex]Smashed\ Corner = 6\%[/tex]

[tex]Punctured\ and\ Smashed\ Corner = 0.4\%[/tex]

Required

[tex]P(Punctured\ or\ Smashed\ Corner)[/tex]

For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;

[tex]P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)[/tex]

Substitute:

10% for P(Puncture Corner),

6% for P(Smashed Corner) and

0.4% for P(Punctured and Smashed Corner)

[tex]P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%[/tex]

[tex]P(Punctured\ or\ Smashed\ Corner) = 15.6\%[/tex]

Convert % to fraction

[tex]P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}[/tex]

Convert to decimal

[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]

Using Venn probabilities, it is found that:

In this problem, the events are:

The "or" probability is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Then:

[tex]P(A \cup B) = 0.1 + 0.06 - 0.004 = 0.156[/tex]

The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.

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Answer:

The expression that fits into the box is x¹⁵⁸

Step-by-step explanation:

Let the empty box be y

(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵

Here, we will apply the laws of indices.

The laws of indices gives the answer for the expressions

1) xᵏ × xˢ = xᵏ⁺ˢ

2) xᵏ ÷ xˢ = xᵏ⁻ˢ

3) (xᵏ)ˢ = xᵏ•ˢ

So,

(x¹²)⁵ = x⁶⁰

(x⁻²)⁹ = x⁻¹⁸

(x⁴⁰)⁵ = x²⁰⁰

(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵

Becomes

x⁶⁰ × x⁻¹⁸ × y = x²⁰⁰

x⁶⁰⁻¹⁸ × y = x²⁰⁰

x⁴² × y = x²⁰⁰

y = x²⁰⁰ ÷ x⁴²

y = x²⁰⁰⁻⁴² = x¹⁵⁸

Hope this Helps!!!

Explanation:

f(x) and y are often used interchangeably. We are asked to find the x value(s) when y = 7.

Circle the rows where 7 shows up in the y column. You should find that x = -1 and x = 1 are circled as well.

So f(x) = 7 leads to x = -1 or x = 1. In other words, f(-1) = 7 and f(1) = 7 also.

For the function given the value of x can be two, one is 1 and the other one is -1 if the f(x)=7

A function relates an input to an output means it is a kind of relationship between the variable y and x. It is denoted through f(x).

A variable is defined as a quantity that may assume any one of a set of values.

How to find the value of x in a function?

In the question the function is given as:

Function is denoted through f(x) and f(x) shows the value of x. We know that the value of f(x)=7 which is given in the question. So we will take the value of x in the front of 7 which is written in the y column. We have got two values in this which are 1 and -1. So they both will be the values of x.

Hence the value of x for the function given in the question are -1 and 1

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Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830

Step-by-step explanation:

(a)

To find P(Z>-1.13):

Since Z is negative, it lies on left hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.3708

So,

P(Z>-1.13) = 0.5 + 0.3708 = 0.8708

(b)

To find P(Z<0.18):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.0714

So,

P(Z<0.18) = 0.5 + 0.0714 = 0.5714

(c)

To find P(Z>8):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.5 nearly

So,

P(Z>8) = 0.5 - 0.5 nearly = 0.0000  

(d)

To find P(| Z | < 0.5)

that is

To find P(-0.5 < Z < 0.5):

Case 1: For Z from - 0.5 to mid value:

Table of Area Under the Standard Normal Curve gives area = 0.1915

Case 2: For Z from mid value to 0.5:

Table of Area Under the Standard Normal Curve gives area = 0.1915

So,

P(| Z | < 0.5) = 2 * 0.1915 = 0.3830

The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

(a) The value of [tex]P(z>-1.13)=0.8708[/tex].

(b) The value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c) The value of [tex]P(Z > 8) = 0.0000[/tex].

(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Given:

The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]

(a)

Find the value for [tex]P(Z > -1.13)[/tex].

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.3708[/tex].

Now,

[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]

Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].

(b)

Find the value for [tex]P(Z < 0.18)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.0714[/tex].

Now,

[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]

Thus, the value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c)

Find the value for [tex]P(Z >8)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area \approx 0.5[/tex].

Now,

[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]

Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].

(d)

Find the value for [tex]P(|Z| <0.05)[/tex].

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Now,

[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]

Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].

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Answer:

The new car travels 247.5 miles more than the old one on 30 gallons of gas.

Step-by-step explanation:

The fuel consumption of the old car was:

[tex]car_{old} = 18 + \frac{1}{4} = \frac{73}{4} \text{ miles per gallon}[/tex]

The new one can travel a distance of 390 7/8 miles by using 14 3/4 gallons of fuel, therefore the consumption is:

[tex]car_{new} = \frac{390.875}{14.75} = 26.5 \text{ miles per gallon}[/tex]

If the tank holds 30 gallons, on the old car the distance would be:

[tex]distance_{old} = 18.25*30 = 547.5 \text{ miles}[/tex]

On the new one it will be:

[tex]distance_{new} = 26.5*30 = 795 \text{ miles}[/tex]

So the new car is able to travel 247.5 miles more than the old one on 30 gallons of gas.

Answer:

A. x = 4.

Step-by-step explanation:

An extreme is the highest or lowest value of the function. In this case, the extreme of the parabola is the lowest point, or the vertex.

We can see that point is at about A. x = 4.

Hope this helps!

Answer:

4

Step-by-step explanation:

Answer:

1/8 < 1/6

Step-by-step explanation:

The top is divided into 8 and 1 part is shaded so 1/8

The bottom is divided into 6 and 1 part is shaded so 1/6

Comparing

1/8 < 1/6

Answer: $34.18

Step-by-step explanation:

Let the cost of the Jacket = $x and

The cost of the sweater. = $y

Now total price. = $71.55.

So, $x + $y. = $71.55 -- 1

From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation

y = ( x - $3.19 )

Now substitute for y in the equation (1) above.

x + ( x - 3.19 ) = 71.55

Now solve the equation

x + x - 3.19 = 71.55

2x - 3.19. = 71.55

2x = 71.55 + 3.19

2x. = 74.74

x = 74.74/2

= $37.37. cost of the jacket

Now to determine the cost of the sweater,

$71.55 - $37.37 = $34.18

The cost of the sweater = $34.18.

Work Shown:

A = P*(1+r/n)^(n*t) .... compound interest formula

A = 200(1+0.07/1)^(1*5) .... plug in given info

A = 200*(1.07)^5

A = 200*1.4025517307

A = 280.51034614

A = 280.51

Answer: The length of the line B'C" is 1 unit.

Step-by-step explanation:

Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.

If A (2,2), B= (4,3) and C=(6,3).

Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]

Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]

[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]

Length of image = scale factor x length in original figure

B'C' = 0.5 × BC

= 0.5 × 2

= 1 unit

Hence, the length of the line B'C" is 1 unit.

Answer:

16076.8

Step-by-step explanation:

Volume of Cylinder=πr²h

h= 20 m

r = 32/2 = 16

=πr²h

=  (3.14)(16^2)(20)

=16076.8 m^2

HOPE IT HELPS :)

PLEASE MARK IT THE BRAINLIEST!

Answer:

7 cm

Step-by-step explanation:

14 / 2 = 7 cm

7cm is the distance Harry needs to walk on the map?

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.

Given that,

Harry is trying to complete his hill walking scouts badge.

He is using a map with a scale of 1 cm : 2 km.

To earn the badge he needs to walk 14 km.

Let the distance he needs to walk on the map is x.

By given data we write an equation

1/2=x/14

Apply Cross Multiplication

14/2=x

7=x

Hence, 7cm is the distance he needs to walk on the map.

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Answer:

  see below

Step-by-step explanation:

The rotated location of D' is (-2, 1). The "arrow" points to the left. The attached figure is the best I could do with your distorted image.

You have to rotate the figure 90 counterclockwise about the origin.

Answer:

The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15

Step-by-step explanation:

Eight less than four times a number is less than 56 . The expression can be written below

let

the number  = a

4a - 8 < 56

add 8 to both sides

4a - 8 + 8 < 56 + 8

4a < 64

divide both sides by 4

a < 64/4

a < 16

The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15

Answer:

0.40517 is the probability

Step-by-step explanation:

The first thing to do here is to calculate the corresponding z-score

Mathematically;

z-score = x-mean/SD

from the question,

x = 78, mean = 75 and SD = 12.5

Plugging these values in the z-score equation, we have;

z-score = (78-75)/12.5 = 3/12.5 = 0.24

So the probability we want to calculate is that;

P(z < 0.24)

we can get this by using the standard normal distribution table,

The value according to the table is;

0.40517

Answer:

D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Step-by-step explanation:

Correct answer is in bold. Incorrect answer have the mistakes put between stars ***   ***.

50 POINTS!!!! I ALSO GIVE BRAINLIEST, BUT YOU HAVE TO ANSWER QUICK Choose the correct graph of the given system of equations. A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically?

A. On a graph, plot the line y = −x + 1, which has y-intercept = ***−1*** and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.

B. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = ***1***, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.

C. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = ***−2*** and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

A.) 7.2 x 10^-5 = 0.000000072

B.) 6.3 x 10^-9 = 0.0000000063

C.) 4.54 x 10^-5 = 0.0000454

D.) 7.041 x 10^-10 = 0.0000000007041

Hope this helped!!  ٩(◕‿◕｡)۶

The numbers can be written as;

A.) 7.2 x 10^{-5} = 0.000000072

B.) 6.3 x 10^{-9} = 0.0000000063

C.) 4.54 x 10^{-5} = 0.0000454

D.) 7.041 x 10^{-10} = 0.0000000007041

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given the parameters

We need to Write these as normal numbers

A.) 7.2 x 10^{-5} = 0.000000072

B.) 6.3 x 10^{-9} = 0.0000000063

C.) 4.54 x 10^{-5} = 0.0000454

D.) 7.041 x 10^{-10} = 0.0000000007041

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*check attachment for the correct figure given in this question with the right labelled angles

Answer:

[tex] x = 86, y = 67, z = 94 [/tex]

Step-by-step explanation:

From the given figure attached below, values of x, y, and z can be found as follow:

Value of x:

[tex] x = 180 - (38 + 56) [/tex] => sum of angles in a triangle

[tex] x = 180 - 94 [/tex]

[tex]x = 86[/tex]

Value of z:

[tex] z = 180 - 86 [/tex] => angles on a straight line

[tex]z = 94[/tex]

Value of y:

[tex] y = 180 - (19 + 94) [/tex] => sum of angles in a triangle.

[tex] y = 180 - 113 [/tex]

[tex]y = 67[/tex]

[tex] x = 86, y = 67, z = 94 [/tex]

Answer:

9x9= 81

3x3x3x3=81

81 to the first power.

Step-by-step explanation:

I hope this helps in any way:)

The question in part c is not clear, nevertheless, part a and part b would be solved.

Answer:

a. The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

b. The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Step-by-step explanation:

a. Given

an + 2 = an + an + 1

where a1 = 1 and a2 = 1.

a3 = a1 + a2

= 2

a4 = a2 + a3

= 3

a5 = a3 + a4

= 5

a6 = a5 + a4

= 8

a7 = a6 + a5

= 13

a8 = a7 + a6

= 21

a9 = a8 + a7

= 34

a10 = a9 + a8

= 55

a11 = a10 + a9

= 89

a12 = a11 + a10

= 144

The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

(b)

Given

bn = an+1/an

b1 = a2/a1

= 1/1 = 1.000

b2 = a3/a2

= 2/1 = 1.000

b3 = a4/a3

= 3/2 = 1.500

b4 = a5/a4

= 5/3 = 1.667

b5 = a6/a5

= 8/5 = 1.600

b6 = a7/a6

= 13/8 = 1.625

b7 = a8/a7

= 21/13 = 1.615

b8 = a9/a8

= 34/21 = 1.619

b9 = a10/a9

= 55/34 = 1.618

b10 = a11/a10

= 89/55 = 1.618

The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Answer:

.9375 days

Step-by-step explanation:

1.25 / 4 = 0.3125

0.3125 x 3 - 0.9375

Answer:

[tex]\boxed{9}[/tex]

Step-by-step explanation:

The two angles are complementary to each other.

That means they add up to 90 degrees.

[tex]5x+15+30=90[/tex]

[tex]5x+45=90[/tex]

[tex]5x=45[/tex]

[tex]x=9[/tex]

Answer:

x = 9

Step-by-step explanation:

So you know that the total is 90 degrees.

What you need to do is create an equation.

5x + 15 + 30 = 90

Then, solve the equation like this.

5x + 15 + 30 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 45 ÷ 5

x = 9

Hope this helps! :)

Answer:

Step-by-step explanation:

Given the half like of a material to be 8.3 hours and the amount of iron-52 left after t hours is modeled by the equation [tex]A(t) = A_0 a^{t}[/tex], we can get A(t) as shown;

At t = 8.3 hours, A(8.3) = 1/2

Initially at t = 0; A(0) = 1

Substituting this values into the function we will have;

[tex]\frac{1}{2} = 1 * a^{8.3}\\\\Taking \ the \ log \ of\ both \ sides;\\\\log(\frac{1}{2} ) = log(a^{8.3} )\\\\log(\frac{1}{2} ) = 8.3 log(a)\\\\\fr-0.30103 = 8.3 log(a)\\\Dividing\ both\ sides\ by \ 8.3\\\\\frac{-0.30103}{8.3} = log(a)\\\\log(a) = - 0.03627\\\\a =10^{-0.03627} \\\\a = 0.919878 (to\ 6dp)[/tex]

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that:

the standardized test scores of the students in a school are normally distributed with:

mean = 85 points

standard deviation = 3 points

Using the empirical rule:

=85 - (3 × 3)

= 85 - 9

= 76

The given value of 76 points is 3 standard deviations below mean

Therefore;

the percent score between the given value of 76 points and the  mean 85 points is:

99.7/2 = 49.85%   ( since 99.7 data value lies within 3 standard deviation)

Also ; the percent of value above the mean score = 50%

Therefore, the probability that a student's score is greater than 76 points is

= (49.85 + 50 )%

 = 99.85%

Answer:

mean=85

sd=3

85-3*3=76

its between 76 and 85=99.7/2=49.85%

50% mean above.

49.85+50=99.85%

Step-by-step explanation: