$2,870 per month. He pays $574 a month for rent. What percent of his monthly pay goes to rent?

Step-by-step explanation:

I= 74810

II=66733

III=71392

iv=239904

Answer:

x = 48°

Step-by-step explanation:

Complementary angles

Angles that sum to 90°.

Vertical Angle Theorem

When two straight lines intersect, the vertical angles are congruent (equal).

Therefore, angle x is equal to the angle that is complementary to 42°.

To find x, subtract 42° from 90°:

⇒ x = 90° - 42°

⇒ x = 48°

Answer:

  c > 5

Step-by-step explanation:

The properties of equality can be used to solve inequalities. Attention needs to be paid to ordering.

We can subtract 3 from both sides to solve this.

  c +3 > 8 . . . . . . given

  c +3 -3 > 8 -3 . . . . subtract 3 from both sides

  c > 5 . . . . . . . . . simplify

The solution is c > 5.

__

Additional comment

Adding or subtracting a value to a number on a number line is equivalent to shifting it right or left. It does not change ordering.

Multiplying or dividing by a positive number is equivalent to expanding or compressing the distance from zero. It does not change ordering.

Multiplying or dividing by a negative number reflects the value across the origin, in addition to expanding or compressing the distance from zero. This reflection reverses the left-right ordering. For example, -2 < -1, but 2 > 1. (Both numbers multiplied by -1.)

As long as you're aware of the effect on ordering, you can use any of the properties of equality to solve inequalities.

Answer:

Options 1 and 2

Step-by-step explanation:

Question 13

Part (a)

[tex]\frac{3840-3905}{110}=\boxed{0.5\overline{90}}[/tex]

By similar logic, the other answers are

(b) 2.6818181....

(c) 3.5909090...

(d) 1.1363636...

Question 14

Part (a)

[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]

Part (b)

[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]

Answer:

answer

x= 40°

Step-by-step explanation:

x= 40° [ base angle of isocles triangle]

Answer:

W = (P -2L)/2

Step-by-step explanation:

P = 2(L + W)  Distribute the 2

P = 2L + 2W   Subtract 2L from both sides

P - 2L = 2W  Divide both sides by 2

(P-2L)/2 = W  

Answer:

The area of the figure is C. 48.5 cm²

If you fix a point on the curve in the given interval, and revolve that point about the [tex]x[/tex]-axis, it will trace out a circle with radius given by the function value [tex]y[/tex] for that point [tex]x[/tex]. The perimeter of this circle is then [tex]2\pi(8\sqrt x) = 16\pi \sqrt x[/tex].

The surface in question is essentially what you get by joining infinitely many of these circles at every point in the interval [0, 9].

So, the surface area is given by the definite integral

[tex]\displaystyle \int_0^9 16\pi \sqrt x \, dx = 16\pi\times\frac23 x^{3/2}\bigg|_{x=0}^{x=9} = \frac{32\pi}3 \left(9^{3/2} - 0^{3/2}\right) = \boxed{288\pi}[/tex]

Answer:

[tex]\frac{5}{100}\times35[/tex]

[tex]0.05\times35[/tex]

Step-by-step explanation:

Given:

Which of the following options have the same value as 5% 35, percent of 35?

Following Options:

[tex]5 \times 35[/tex]

[tex]\frac{5}{100}\times35[/tex]

[tex]0.5\times0.35[/tex]

[tex]0.05\times35[/tex]

[tex]\frac{5}{10}\times35[/tex]

Solve:

[tex]5[/tex] % [tex]= 0.05=\frac{5}{100}[/tex]

Thus the following options:

[tex]5 \times 35[/tex]           [ False x ]

5 does not equal 5%

[tex]\frac{5}{100}\times35[/tex]         [True √ ]

[tex]5[/tex]% [tex]=\frac{5}{100}[/tex]

[tex]0.5\times0.35[/tex]      [ False x ]

[tex]0.5 = 0.50[/tex]

[tex]0.05\times35[/tex]       [True √ ]

[tex]5[/tex]% [tex]= 0.05=\frac{5}{100}[/tex]

[tex]\frac{5}{10}\times35[/tex]          [ False x ]

[tex]\frac{5}{10}=0.50[/tex]

Therefore, the options [B] [tex]\frac{5}{100}\times35[/tex] and [D] [tex]0.05\times35[/tex] is True.

Kavinsky

The answers to the given addition operations are

7) 6 Hundredths add to 4 tenths add to 6 ones is equal to 6.46

8) 82 Hundredths add to 9 tenths add to 4 tens is equal to 41.72

From the question, we are to add the given numbers

7. 6 Hundredths add to 4 tenths add to 6 ones is equal to

6 Hundredths = 0.06

4 tenths = 0.4

6 ones = 6

Thus, we get

0.06 + 0.4 + 6 = 6.46

8. 82 Hundredths add to 9 tenths add to 4 tens is equal to

82 Hundredths = 0.82

9 tenths = 0.9

4 tens = 40

Thus, we get

0.82 + 0.9 + 40 = 41.72

Hence, the answers to the given addition operations are

7) 6 Hundredths add to 4 tenths add to 6 ones is equal to 6.46

8) 82 Hundredths add to 9 tenths add to 4 tens is equal to 41.72

Learn more on Addition operation here: https://brainly.com/question/4248979

#SPJ1

sinE is 0.5

What are similar triangles?

Two triangles will be similar if the angles are equal (corresponding angles), and sides are in the same ratio or proportion (corresponding sides). Similar triangles may have different individual lengths of the sides of triangles, but their angles must be equal and their corresponding ratio of the length of the sides must be the same.

Clearly, given triangle AFB and triangle DFE are similar.

We know that Similar Triangles have the same corresponding angle

We can find sinE as show below:

From diagram clearly

∠A=∠E

and ∠B=∠D

Since, ∠A=∠E

Taking sin on both sides

sinA=sinE

Give, sinA=0.5

sinA=sinE=0.5

⇒ sinE=0.5

Hence, sinE is 0.5

Learn more about Similar triangles here:

https://brainly.com/question/11920446

#SPJ1

The proportion of the population exists less than 30 then

(x< 30) = 0.986.

To estimate the z-score using the formula, z = (x - µ)/σ

Where, x be the randomly chosen values = 30

µ be the mean = 31

σ be the standard deviation = 10

Proportion of the population that exists less than 18 = P(x < 30)

Plug in the values into z = (x - µ)/σ, to get z-score.

Substitute the values in the above equation, we get

z = (30 - 31)/10

z = -1/10 = -0.1

Therefore, the value of z = - 0.1.

To learn more about proportion of the population refer to:

https://brainly.com/question/18403865

#SPJ9

Answer:

Step-by-step explanation:

cosA×cos 2A-sin4A×sinA

=cosAcos2A-2sin2Acos2A sin A

=cos 2A(cosA-2sin2AsinA)

=cos 2A(cosA-2×2sinAcosAsin A)

=cos2A×cosA(1-4sin²A)

=cos 2AcosA(1-4(1-cos²A))

=cos2A×cosA(1-4+4cos²A)

=cos 2A(-3cosA+4cos³A)

=cos 2A(4cos³A-3cosA)

=cos 2A×cos3A

Answer:

9

Step-by-step explanation:

To find the rate of change we use the formula

f(x2) - f(x1)

------------------

x2 -x1

f(x) = 9x

x2 = 9  and x1 = 0

f(x2) = 9( 8) = 72

f(x1) = 9(0) =0

The rate of change is

72 - 0

------------

8-0

72

----

8

9

The rate of change is 9

Answer:

9

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given:

Therefore:

Substitute the given values into the average rate of change formula:

[tex]\begin{aligned}\implies \dfrac{f(8)-f(0)}{8-0} & = \dfrac{9(8)-9(0)}{8-0}\\\\& = \dfrac{72-0}{8-0}\\\\& = \dfrac{72}{8}\\\\& = 9\end{aligned}[/tex]

Therefore, the average rate of change of the function f(x) over the interval 0 ≤ x ≤ 8 is 9.

Learn more about average rates of change here:

https://brainly.com/question/27986470

https://brainly.com/question/27794689

Step-by-step explanation:

1/4×48

=12

So if 12people are out of state

48-12=36,is the number of people living in the state

If we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex]

Given an expression 8v(v+3)(v+3).

We are required to rewrite the given expression.

Expression is a combination of numbers, symbols, fraction , determinants,indeterminants, coefficients. They are not mostly found in equal to form. It expresses a relationship of a line or something else.

The expression is 8v(v+3)(v+3). There are three terms in which variable is v.

To rewrite the expression we have to multiply all the three terms with each other which can be done as under:

=8v(v+3)(v+3)

=[tex](8v^{2}+24v)(v+3)[/tex]

=[tex]8v^{3}+24v^{2}+24v^{2}+72v[/tex]

=[tex]8v^{3}+48v^{2} +72v[/tex]

Now divide it by 8.

=[tex]v^{3}+6v^{2} +9v[/tex]

Hence if we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex] .

Learn more about expressions at https://brainly.com/question/723406

#SPJ1

radius -15

Surface Area of a sphere =4πr^2

=4x22/7x15x15

=19800/7

=2828.57

Answer:

(3+3) x (3+1)

Step-by-step explanation:

nice

We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

The expression can be used to find the area, in square units, of the Shaded triangle in the Square is  1/2 ( 4 · 4 ) .

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = side x side

where s = side length.

If a diagonal is drawn to create 2 halves, then area of each half is 8.

So, The area of a square = 1/2 ( 4 · 4 ) = 16.

If a square has a side length of 4, then the area of the square is 16.

The expression can be used to find the area, in square units, of the Shaded triangle in the Square is  1/2 ( 4 · 4 ) .

Learn more about the area;

https://brainly.com/question/1658516

#SPJ1

Answer:

The Co-ordinate of C is (4/3, -1/2)

Step-by-step explanation:

We have two equation one is of straight line equation which is:

                                              y=2x-3           (i)

Other equation is of quadratic function which is:

                                         y=-3x^2+5         (ii)

Put the value of y from equation (i) in equation (ii)

So, we have:

                                     2x-3=-3x^2+5

                                      3x^2+2x-8=0

By factorization:

                                    3x^2+6x-4x-8=0

                                   3x(x+2)-4x(x+2)=0

                                        (x+2)(3x-4)=0

              x+2=0                             ;                      3x-4=0

              x=-2                                ;                       x=4/3

Put first x=-2 in equation (i)

                                                y=2(-2)-3

                                                  y=-4-3

                                                    y=-7

Now Put x=4/3 in equation (i)

                                             y=2(4/3)-3

                                                 y=8/3-3

                                                   y=-1/2

So, we have two Order pair One is (-2 , -7) and Second one is (4/3 , -1/2)

Hence the Co-ordinate of C is:

                                               C=(4/3 , -1/2)

Answer:

Point C:  (3, 3)

Point D:  (3, -22)

Step-by-step explanation:

If the distance between points C and D is 25 units, the y-value of point D will be 25 less than the y-value of point C.  The x-values of the two points are the same.

Therefore:

[tex]\textsf{Equation 1}: \quad y=2x-3[/tex]

[tex]\textsf{Equation 2}: \quad y-25=-3x^2+5[/tex]

As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:

[tex]\implies 2x-3-25=-3x^2+5[/tex]

[tex]\implies 3x^2+2x-33=0[/tex]

[tex]\implies 3x^2-9x+11x-33=0[/tex]

[tex]\implies 3x(x-3)+11(x-3)=0[/tex]

[tex]\implies (x-3)(3x+11)=0[/tex]

[tex]\implies x=3, -\dfrac{11}{3}[/tex]

From inspection of the given graph, the x-value of points C and D is positive, therefore x = 3.

To find the y-value of points C and D, substitute the found value of x into the two original equations of the lines:

[tex]\begin{aligned} \textsf{Point C}: \quad 2x-3 & =y\\2(3)-3 & =3\\ \implies & (3, 3)\end{aligned}[/tex]

[tex]\begin{aligned} \textsf{Point D}: \quad -3x^2+5 & = y \\ -3(3)^2+5 & =-22\\ \implies & (3, -22)\end{aligned}[/tex]

Therefore, point C is (3, 3) and point D is (3, -22).

Answer:

the function is an exponential funtion.

Step-by-step explanation:

learned it

Answer: 250:1

Step-by-step explanation:

Divide the measurement of appearance by the actual measurement.

[tex]100,000/400=250[/tex]

The magnification scale is 250:1. The scale is used by a 250X magnifying lense.

The exponential function is illustrated below.

An exponential function has a growth factor or 3.76. What is the percentage growth rate?

The growth factor (b) is given as:

b = 3.76

So, the percentage growth rate (r) is calculated as:

r = b - 1

Substitute known values

r = 3.76 - 1

Evaluate the difference

r = 276%

The way to solve Financial Problems using Sequences & Series will be:

The first salary that Mr James earn is 10000 and there is a yearly increase of 2000. Find his salary in the 5th year. This will be:

= a + (n - 1)d

= 1000 + (5 - 1)2000

= 10000 + (4 × 2000)

= 10000 + 8000.

= 18000

Learn more about exponential growth on:

https://brainly.com/question/4172151

#SPJ1

The vertex form of the equation f(x) = x^2 - 3x, is f(x) = (x - 3/2)^2 - 9/5

The quadratic function is given as:

f(x) = x^2 - 3x

Differentiate the function

f'(x) = 2x - 3

Set the function to 0

2x - 3 = 0

Add 3 to both sides

2x = 3

Divide by 2

x = 3/2

Set x = 3/2 in f(x) = x^2 - 3x

f(x) = 3/2^2 - 3 * 3/2

Evaluate

f(x) = -9/5

So, we have:

(x, f(x)) = (3/2, -9/5)

The above represents the vertex of the quadratic function.

This is properly written as:

(h, k) = (3/2, -9/5)

The vertex form of a quadratic function is

f(x) = a(x - h)^2 + k

So, we have:

f(x) = a(x - 3/2)^2 - 9/5

In f(x) = x^2 - 3x,

a = 1

So, we have:

f(x) = (x - 3/2)^2 - 9/5

Hence, the vertex form of the equation f(x) = x^2 - 3x, is f(x) = (x - 3/2)^2 - 9/5

Read more about vertex form at

https://brainly.com/question/24850937

#SPJ1

Answer: (5,3)

Step-by-step explanation:

Substituting into point-slope form, the equation of the line is

[tex]y-5=-2(x-4)[/tex]

Which rearranges as follows:

[tex]y-5=-2x+8\\\\y=-2x+13[/tex]

To determine if a point lies on a line, you can see if its coordinates satisfy the equation.

Of all the options, only (5,3) works.

a) The monthly payment for each loan is as follows:

30-year $1,954.93

15-year $3,053.25

b) The savings in interest by using the 15-year loan is $154,189,20 ($286,774.20 - $132,585).

c) No. the monthly payment for the 15-year loan is not twice that of the 30-year loan as the loan term.

d) The interest savings for the 15-year loan are more than one-half of the interest paid on the 30-year loan.

The calculations for the monthly payments, including interests can be carried out using an online finance calculator, as follows:

N (# of periods) = 360 months (12 x 30 years)

I/Y (Interest per year) = 3.85%

PV (Present Value) = $417000

FV (Future Value) = $0

Results:

PMT = $1,954.93

Sum of all periodic payments = $703,774.80 ($1,954.93 x 360)

Total Interest = $286,774.20 ($703,774.80 - $417,000)

N (# of periods) = 180 months (12 x 15 years)

I/Y (Interest per year) = 3.85%

PV (Present Value) = $417000

FV (Future Value) = $0

Results:

PMT = $3,053.25

Sum of all periodic payments = $549,585 ($3,053.25 x 180)

Total Interest = $132,585 ($549,585 - $417,000)

Learn more about periodic payments at https://brainly.com/question/13098072

#SPJ1

The solution to the question is mathematically given as

1)

H0: M [tex]\geqslant[/tex] 300

H0: M [tex]\geqslant[/tex] 300

2)

Z distribution.

3)

z=-2.4

4)

P=0.0082

5)

"H0" is rejected as a hypothesis with a level of significance of 0.05.

Generally, the equation for is mathematically given as

Solutions

we have, [tex]$u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}[/tex]

(1):

H0: M [tex]\geqslant[/tex] 300 dollars;  customers save at least 300 dollars per year by switching to them.

H0: M [tex]\geqslant[/tex] 300 dollars:

(This is a left-tailed test)

(2):

when [tex]\sigma[/tex] is known, we use the Z test. we use Z distribution.

(3):

[tex]\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}[/tex]

(4):

[tex]Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082[/tex]

(5):

In conclusion, Since p-value = 0·0082 <0.05

This is statistically significant at the 0.05 level.

We thus "Refect H0" using a threshold of significance of 0.05.

"H0" is rejected as a hypothesis with a level of significance of 0.05.

There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.

Therefore, we would not consider making the transition to this firm.

Read more about probability

https://brainly.com/question/795909

#SPJ1

The length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³. This can be obtained using the formula of finding the volume of the pyramid with base as square.

The formula of finding the volume of the pyramid with base as square is,

⇒ V = s²h/3

where V is the volume of the square pyramid, s is the side length of the base and h is the height of the square pyramid.

Here in the question it is given that,

that is, s = 11 ft, V = 400 ft³

By using the formula of finding the volume of the pyramid with base as square we get,

V = s²h/3

400 = (11)²h/3

By rearranging the equation we get,

h = 400 × 3/11²

h = 9.92 ft

Hence the length of the missing side is 9.92 ft given that the base of the following pyramid is a square, base side length(s) is 11 ft and the volume of the square pyramid is 400 ft³.

Learn more about square pyramid here:

brainly.com/question/17615619

#SPJ1

Answer:

yes yes yes yes yes Yes Yes you are cute