Which histogram correctly displays the information above

9514 1404 393

Answer:

  x = (8/9)(4 +√7) ≈ 5.9073

Step-by-step explanation:

Maybe you want to know the value of x.

The Pythagorean theorem can be used to find the length of the bottom side of the right triangle. It is ...

  bottom = √((5x)² -(3x)²) = √(16x²) = 4x

Then the cosine of the angle at lower left is ...

  cos(α) = Adjacent/Hypotenuse

  cos(α) = 4x/5x = 4/5

Now, the law of cosines can be used to find x. Using the angle whose cosine we just found, we have ...

  (4x)² = (5x)² +8² -2(5x)(8)cos(α)

  16x² = 25x² +64 -80x(4/5)

  9x² -64x +64 = 0 . . . . . put in standard form

The quadratic formula can be used to find the solutions.

  x = (-(-64) ±√((-64)² -4(9)(64)))/(2(9))

  x = (64 ±√1792)/18 = (32 ±8√7)/9 ≈ {1.204, 5.907}

In this context, only the larger solution makes sense.

  x = (8/9)(4 +√7) ≈ 5.9073

_____

Formulas used

Law of Cosines

For sides a, b, c and angle C opposite side c, ...

  [tex]c^2=a^2+b^2-2ab\cdot\cos(C)[/tex]

Quadratic formula

For quadratic ax²+bx+c=0, the solutions are ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Pythagorean theorem

For legs a, b, and hypotenuse c of a right triangle, ...

  c² = a² + b²

_____

Alternate solution

As an alternative to using the Law of Cosines, you can define "y" to be the length of the dashed bottom leg of the triangle whose hypotenuse is 4x. Two equations can be written using y and the Pythagorean theorem for the right triangles in which y is all or part of a leg. This set of equations can be solved for x to get the same result as the one shown above.

Complete question is;

The attached chart shows the (approximate) total number of subprime home mortgages in a state in November 2008, broken down into four categories.

What is the probability that a randomly selected subprime mortgage in the state during November 2008 was not current? (Round your answer to two decimal places.)

Answer:

Probability that the one randomly selected was not current = 0.36

Step-by-step explanation:

From the attached image, we can see that the four mortgage categories are mutually exclusive. This means that none of the 4 status depends on any other.

From the image attached;

Total number of subprime mortgages = 196,280

Number of current mortgages = 126,330

Thus;

Probability of a randomly selected subprime mortgage being current = 126330/196280 = 0.64

Then;

Probability that the one randomly selected was not current = 1 - 0.64

Probability that the one randomly selected was not current = 0.36

Answer:

x = 140   y = 105                x · y = 14700 m²

Step-by-step explanation:

good question

it looks like 3 sides of length x

and 4 sides of length y

area 1 = area 2

and the length of all the sides sum to 840

  3x + 4y = 840      find the maximum area = 2· x · y

This is a calculus problem that I can't remember how solve

 if x = 0   y = 210

           if   y = 0   x = 280       280 / 2 = 140   the mid-point  the logical answer

if x = 140   y = 105                x · y = 14700 m²         this appears to be the max

if x = 135   y = 108.75            x · y = 14681.25 m²      smaller area

if x = 145   y = 101.25             x · y = 14681.25 m²      smaller area

I need an eqaution with a quadratic and take the first derivative

 y = (840 - 3x) / 4      xy = max area     y = max area/x

(max area) / x = (840 - 3x) / 4      solve for x

    max area  = x(840 - 3x) / 4

    max area  = [840x/4 - 3x²/4] '        

    max area  = 210x  -  3x²/4            take the first derivative  

    max area  = 210  -  6x/4               maximum occurs when slope = 0

           0   =  210 - 3x/2    

        3x/2 = 210

           x  = 210·2/3

           x  = 420 / 3

          x  = 140   y = 105

3(140) + 4(105) =   420 + 420  = 840    checks

Answer:

RS 36

12%

Step-by-step explanation:

Profit = total selling price - cost price

(28 - 25) x 12 = 36

Percentage profit = (profit / cost price) x 100

Cost price = 25 x 12 = 300

(36/300) x 100 = 12%

Answer:

Range=2

Step-by-step explanation:

Range=Highest number-Lowest number

          =5-3=2

Hope it Help

Mark Me Brillainest

Answer:

X=35 Y=73

Step-by-step explanation:

use the opposite angle theorem for x. X would equal 35.

we know that x is 35. So 2y+35=180

180-35=2y

y=72.5 or 73

srry I can’t help with question 2. I don’t know how

Answer:

that's confusing.. is there a picture?

Answer:

A down payment of $5,388.50  to get the principle to $19611.50  for a monthly payment of $400 for 60 months at 8.25%

Step-by-step explanation:

I used a payment calculator

I don't know how else to solve the problem.  I thought I could find the equation, but I don't think this is it, since P didn't equal 19611.50

A = P[r(1+r)n] / [(1+r)n - 1]    

if you have the correct formula follow this process

A = 400        P principle ???    r = i%/12 = 0.0825/12 =  0.006875    n= 5×12 = 60

     solve for P      then    down payment = 25000 - P

 P = A / [r(1+r)n] / [(1+r)n - 1]    

    = A [(1+r)n - 1]  /  [r(1+r)n]

    =  400 [(1 +.006875)60 -1]  /  [0.006875( 1 +0.006875)60]

Answer:

32600

Step-by-step explanation:

b

x is 10 times greater then y 3+n 5

Answer:

a) 375 = 3 × 3 × 3× 3 × 5

in index form it is 3 × 5³.

prime factor of,

150 = 2 × 3 × 5 × 5.

To find the HCF, multiply all the prime factors common to both numbers: Therefore, HCF = 3 × 5 × 5.

ANS : 75

hope this helps you☺️☺️

Answer:92.7

Step-by-step explanation:

Use the compound interst formula: A= P(1+r)^n

750(1+.06)^2=842.7

Now substract the principal to find the compound interest : 842.7-750= 92.7

Hope it helps

Answer:

1. 12x-5y = -20 Answer: 2(picture)

2. y =x+4 Answer: 1(picture)

Step-by-step explanation: Hope this help :D

Answer:

58m^2

Step-by-step explanation:

2x9 = 18

8x5 = 40

18+40 = 58

Answer:

20[tex]\pi[/tex]

Step-by-step explanation:

Circumference formula: [tex]2\pi r[/tex]

Since the diameter is 20, the radius will be half of the diameter

r=d/2, where d=20

r=20/2=10

C=[tex]2\pi r[/tex]

C=2(10)[tex]\pi[/tex]

C=20[tex]\pi[/tex]

Answer:

answer:

answe:

answ:

ans:

an:

as:

a:

:

Step-by-step explanation:

what is the ability that the children will have green eyes collar

Answer:

512

16 · 4 = 64

64 · 8 = 512

Answer:

ok

Step-by-step explanation:

Answer:

post the whole problem it's cut off

Let a (n) denote the n-th term of the sequence. Since the terms form an arithmetic sequence, you have

a (n) = a (n - 1) + d

for some fixed constant d. You can write any term in the sequence as a function of the first term:

a (n) = [a (n - 2) + d] + d = a (n - 2) + 2d

a (n) = [a (n - 3) + d] + 2d = a (n - 3) + 3d

and so on, down to

a (n) = a (1) + (n - 1) d

so given that a (11) = 57 (so that n = 11), you have

a (1) + 10d = 57 … … … [1]

The sum of the first and fourth terms is 29:

a (1) + a (4) = 29

but we can write a (4) in terms of a (1) :

a (1) + [a (1) + 3d] = 29

which gives us another equation in a (1) and d :

2 a (1) + 3d = 29 … … … [2]

Now solve [1] and [2] :

-2 (a (1) + 10d) + (2 a (1) + 3d) = -2 (57) + 29

-17d = -85

d = 5

a (1) + 10d = a (1) + 50 = 57

a (1) = 7

Then the n-th term of the sequence is given by

a (n) = 7 + 5 (n - 1) = 5n + 2

The actual area of the apartment will be 960 square feet.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

A blueprint shows an apartment with an area of 15 square inches.

If the blueprint's scale is 1 inch : 8 feet.

Then the scale factor will be 8/1 feet per inch.

Then the actual area square footage of the apartment will be

Actual area = 15 x (scale factor)²

Then the actual area of the footage will be

Actual area = 15 x (8/1)²

Actual area = 15 x 64

Actual area = 960 square feet

Thus, the actual area of the apartment will be 960 square feet.

More about the dilation link is given below.

https://brainly.com/question/2856466

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Answer:

angle=63°

I hope it's helps you

Answer:

1hr: $9

2hr: $18

3hr: $27

4hr: $36

5hr: $45

6hr: $54

Step-by-step explanation:

You can use Desmos, the graphing calculator (online tool)  

Answer:

D. 32.3

Step-by-step explanation:

Length-a  

Width-b

A=ab=6.8×4.75=32.3

Answer:

The equation of line is

[tex]\text{yield}=1.15\times \text{fertilizer}+10.1[/tex]

Step-by-step explanation:

The general equation of line is given as

[tex]y=mx+b[/tex]

where

y is the dependent variable which is yield in this case.

x is the independent variable which is fertilizer in this case

m is the coefficient of the fertilizer whose value is 1.150 from the given values.

b is the constant whole value is 10.100 from the given values.

Thus the equation becomes.

[tex]\text{yield}=1.15\times \text{fertilizer}+10.1[/tex]

Answer:

Step-by-step explanation:

The answer is TRUE

True

Answer: (7,3)

Step-by-step explanation:

Find the midpoint of the diameter to find the center

mid-point formula

[tex](\frac{(x_{1} +x_{2)} }{2} ,\frac{(y_{1} +y_{2} )}{2} )[/tex]

Using points (4,5) and (10,1)

[tex](\frac{4+10}{2} , (\frac{5+1}{2} )\\(\frac{14}{2},\frac{6}{2}) \\\\(7,3)[/tex]

The coordinates of the center of the circle are (7, 3).

Given that, in a circle, the coordinates of the endpoints of a diameter are (4,5) and (10,1).

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

The formula to find the midpoint of line segment is (x, y) = [(x1+x2)/2, (y1+y2)/2]

The center of the circle is midpoint of a diameter

Here, (x, y) = ((4+10)/2, (5+1)/2)

= (14/2, 6/2)

= (7, 3)

Therefore, the coordinates of the center of the circle are (7, 3).

To learn more about the formula of midpoint visit:

https://brainly.com/question/4728902.

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Answer:

I might be in highschool, but I'm sure I can still help.

Step-by-step explanation:

See the 45 degree angles? that means they're equal sides. So 4v2 = 5.65, right? so if you take 180 - 5.65, and then divide by two, you should have the length to each of those sides. They're equal, remember. So, the answer would be 180 - 5.65 = 174.35. 174.35 / 2 = 87.175. In this case, k = 87.175 :)