If mDH =(11x + 7) degrees , mGF = (5x + 9) degrees , and mEF = (10x - 22) degrees, find mDH

After 10 years, the car will be worth 0.54 of the price when Rob purchases it. The result is obtained using the exponential depreciation equation.

The depreciation can be calculated by the exponential depreciation equation.

y = P (1 - r)ˣ

Where

If given

How much will the car be worth after 10 years?

The depreciation rate would be

r = 6%

r = 6/100

r = 0.06

So, after 10 years, the car would be worth

y = P (1 - r)ˣ

y = P (1 - 0.06)¹⁰

y = P (0.94)¹⁰

y = P (0.54)

y = 0.54P

Hence, after 10 years, the car will be worth 0.54 of its original price.

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Answer:

9 inches

Step-by-step explanation:

Set it up like a fraction ratio and solve for x.  as the price (denominator) and amount (numerator) have a set ratio, you can cross-multiply for your answer.

[tex]\frac{13}{52} =\frac{x}{36\\}\\[/tex]

13*36 = 468

468/52 = 9

Another way would be to divide 13 by 52 and multiply by 36, but then you end up with decimals and cross multiplication will be easier in the long run.

The mean and the standard deviation of the following numbers 20, 33, 44, 53, 69, 75, 89, 90 are 59.125 and 22.461 respectively

The mean is the average value in a collection and a standard deviation is the average amount of variability in a data.

mean= sum of data in the collection/ number of data

= (20+33+44+53+69+75+89+90)/8 = 473/8 = 59.125( nearest thousandth)

standard deviation= sum of √(x- mean)^2/ number of data while x is each number in the data

finding (x- mean)^2 for each value of x

(20-59.125)^2=848.266

(33-59.125)^2=682.516

(44-59.125)^2=228.766

(53-59.125)^2=37.516

(69-59.125)^2=102.516

(75-59.125)^2= 260.016

(89-59.125)^2= 907.516

(90-59.125)^2= 968.766

S.D= √(848.266+682.516+228.766+37.516+102.516+260.016+907.516+968.766)/8 =

√504.484

Therefore S.D =22.461 ( to the nearest thousandth)

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For the standardized dataset , the value of median = mean , which is equal to 7

The mean of the close friends people have = 7

The variance = 100

Standard deviation can be found using the formula

                   v = σ²

where  v is the variance and

            σ is the standard deviation

Then ,                  σ² = 100

                            σ  = √100

                            σ  = 10

Therefore , the standard deviation for the close friends have is 10

The standard score for these vales can be found using the formula

                         Z = (X - μ) / σ

where Z is the standard score

           X is the raw score

           μ is the mean

           σ is the standard deviation

Using this formula, the standard score of any raw score can be calculated.

For, the standardized dataset , the value of median will be equal to value of median.

                           Median = mean

                           Median = 7

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The probability P(5 ≤ x ≤ 9) is 0.6847

Assume that x has a normal distribution

We have been the mean and standard deviation μ = 6; σ = 2.

To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.

z = (5 - 6)/2

  = -0.5

and z = (9 - 6)/2

         = 1.5

Then the probability is calculated as:

P(x ≤ 5) = 0.3085

P(x ≤ 9) = 0.9932

P(5 ≤ x ≤ 9) = 0.9932 - 0.3085

P(5 ≤ x ≤ 9) = 0.6847

Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847

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At x=0

at x=1

at x=2

a=1/2

So correct option is (c).

I will ask my question here

is p(x)

bye :)

ANSWER:

Therefore there are about 234 grams

STEP-BY-STEP EXPLANATION:

We have that the density is given by this formula

We have the value of the density and the volume, therefore we can calculate the number of grams as follows:

we have the quadratic equation

we have that

a=1

b=-1

c=-12

Applying the formula to solve a quadratic equation

The values of u are

u=4 and u=-3

therefore

The answer is

The value of sin 2x=0.8304 ,cos 2x=0.557,tan 2x=1.498 when the value of tan x is 8/15 and using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and abbreviations (csc).

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

sin 2x=2 tan x/(1+(tan x)²)

cos 2x=(1-(tan x)²)/(1+(tan x)²)

tan 2x=sin 2x/cos 2x=2 tan x/(1-(tan x)²)

Here,

tan x=8/15

sin 2x=2 tan x/(1+(tan x)²)

= 2*8/15/(1+(8/15)²)

=(16/15)/(289/225)

=(16*15)/(289)

≈0.8304

cos 2x=(1-(tan x)²)/(1+(tan x)²)

=(1-(8/15)²)/(1+(8/15)²)

=(225-64)/(225+64)

≈0.557

tan 2x=sin 2x/cos 2x

tan 2x= 0.8304/0.557

=1.498

≈1.5

When the value of tan x is 8/15, the values of sin 2x=0.8304, cos 2x=0.557, and tan 2x=1.498 using the trigonometry identities as tan x as the formula in sin 2x, cos 2x, tan 2x.

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A line's equation written using a single point on the line and the line's slope is referred to as the point-slope form. The slope is the rise over run, or the ratio of the change in the y values over the change in the x values, and the point form is denoted as (x,y).

y= 3 / 10x + 8

y=mx+b, where

y=mx+b

y=3/ 10x+8

m=3/10  b=8

Slope: 3/ 10, and the y-intercept is at (0, 8).

x           y

0         8

10        11.

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Answer:

x<-2, x>-7

Step-by-step explanation:

1st one

add 7 to 3 =10

-5 divide by 10 = -2

2nd one

add 7 to -42 = -35

-35 divided by 5 = -7

Using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.

So, more pink sand is available to each girl:

Sand available to each girl:

Pink sand more to each girl:

Therefore, using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.

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The equation of a line through the origin and (-5,6) is y =  -1.2x

It is important to note that the equation of a line is expressed as;

y = mx + c

Where;

From the information given, we have the points;

(0, 0) and ( -5, 6)

The formula for slope is given as;

slope, m = y₂ - y₁/ x₂ -x₁

slope, m = 6 - 0/ -5 - 0

slope, m = 6/ -5

slope, m = - 1. 2

To determine the intercept, we have;

6 = -1. 2(-5) + c

expand the bracket

c = 6 - 6

c = 0

The equation is given as;

y = -1.2x

Hence, the equation is y = -1.2x

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The movies for the movie marathon can be chosen in 120  different ways .

In the question ,

it is given that

total number of movies = 10 movies

number of movies that need to be played in specific order = 7 movies .

we have to find how many different ways can the movies be selected for the movie marathon .

we can solve this with Combination ,

where n = 10  and r = 7

So C(n,r) =  C (10,7)

= 10! / (3! * 7! )

= (10*9*8*7!)/(3! * 7! )

= ( 10*9*8) / (3*2 )

= 10 * 3 * 4

= 120 ways .

Therefore , The movies for the movie marathon can be chosen in 120  different ways .

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The amount to be paid after paying interest of 7% for 10 years is 10,2000

The amount to be borrowed from the bank = 6000

Interest rate for the amount per year = 7%

The total time period of the loan = 10 years

Thus , the final amount can be calculated by using the formula

                    A = P(1 + rt)

where A is the final amount

          P is the principal amount to be borrowed

          r is the rate of interest

          t is the time period

Now, let us substitute the known values in the above equation , we get

             A = 6000 ( 1 + 0.07 x 10)

                 = 6000 (1 + 0.7)

                 = 6000 (1.7)

             A = 10,200

Therefore , the final amount to be paid is 10,200

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Answer:

2^9

Step-by-step explanation:

8 is [tex]2^3\\[/tex], so we can replace [tex]8^3[/tex] for [tex](2^3)^3[/tex]

Exponents separated by parenthesis, multiply.

So [tex](2^3)^3=2^9[/tex]

28-6x = 2x -84

Add 6x to both sides:

28 = 8x -84

Add 84 to both sides

112 = 8x

Divide both sides by 8

X = 112/8

X = 14

m∠F = 140º

1) Since that trapezoid is a quadrilateral, then we can affirm that the Sum of their interior angles is:

Note that "n" refers to the number of sides:

Notice also that angle H is a right angle since this is not an Isosceles Trapezoid

So we can write out the following

9x +14x +4x + 90 = 360º

27x = 360 -90

27x = 270

x =10

Alternatively, angles between parallel lines are supplementary

2) To find out the measure of angle ∠F We'll need to plug x=10 into that expression:

m∠F = 14x

m∠F = 140º

The blue graph is represented by the equation g(x) = (x - 5)²

The possible graph that completes the question is added as an attachment

From the attached graph, we have the following parameters

Also from the graph, we have the equation of the function f(x) to be

f(x) = x²

Solving further, we can see that:

The only difference is that, f(x) is shifted to the right by 5 units

This means that

g(x) = f(x - 5)

So, we have

g(x) = (x - 5)²

Hence, the blue graph equation is g(x) = (x - 5)²

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Answer:

f(x)=x+2 Passes through

x-y=2 DOES NOT pass through

Step-by-step explanation:

Method- plug in x and see if the y matches the points. (1,3) (7,9)

f(x)=x+2

f(1)=1+2=3

f(7)=7+2=9

Matches!

x-y=2

1-y=2 --> y=-1

Does not match

The basket of pennies will be 1/4 full on the 13th day

From the question, the given parameters are:

The above parameters illustrate an exponential function

An exponential function is represented as

A(n) = A * (r)ⁿ⁻¹

Where

A represents the initial value

It is full on the 15th day

So, we have

1 = A *(2)¹⁵⁻¹

Evaluate

1 = A *(2)¹⁴

Divide by (2)¹⁴

A = (2)⁻¹⁴

Substitute A = (2)⁻¹⁴ in A(n) = A * (r)ⁿ⁻¹

A(n) = (2)⁻¹⁴ * (2)ⁿ⁻¹

When it is one-quarter full, we have

1/4 = (2)⁻¹⁴ * (2)ⁿ⁻¹

Multiply by (2)¹⁴

(2)¹² = (2)ⁿ⁻¹

By comparison, we have

n - 1 = 12

Add 1 to both sides

n = 13

Hence, the basket will be one-quarter full on the 13th day

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The value of x in the triangle is 17 degrees.

A triangle is a polygon with three sides and angles.

The sum of angles in a triangle is 180 degrees.

Therefore, ABC is a triangle and CDE is a also a triangle.

Let's find the angle x in the triangle CDE.

Hence,

∠ACB = 180 - 4x - 49 (sum of angles in a triangle is 180 degrees)

∠ACB =  180 - 49 - 4x

∠ACB = 131 - 4x

Therefore,

180 = ∠DCE  + ∠DEC  + ∠CDE  

∠CDE   = 100°

∠DEC = x

∠DCE = ∠ACB = 131 - 4x

Hence,

180 = 131 - 4x + x + 100

180 = 231 - 4x + x

180 - 231 = -3x

-51 = -3x

divide both sides by -3

x = -51 / -3

x = 17

Therefore,

x = 17

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Answer:

The answer would be 1.3, and the three is repeating.

Step-by-step explanation:

First, make 4 2/15 into a improper fraction.

4 2/15= 62/15

Now, when we divide fraction, use the rule Keep, Change, Flip.

Keep the 62/15.

Change the division sign into a multiplication sign.

To make the 3.1 into a fraction, put a one over it.

3.1/1

Now, flip the fraction.

3.1/1= 1/3.1

Your equation will look like this:

62/15x1/3.1

Multiply across.

62/46.5

Now simplify.

The answer would be 1.3, and the three is repeating.

The graph given in the problem is the function of cosine that is;

y = -cos x

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it. If the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

Suppose that we've got:

f(x) = a cos (bx - c) + d

Then, this function has the Amplitude (the maximum distance of the graph from the middle line) = a

Period = [tex]\dfrac{2\pi}{b}[/tex]

Phase shift = [tex]\dfrac{c}{b}[/tex]

Maximum value: a + d

Minimum value: -a + d

Here we can see that the graph is the function of cosine that is;

y = -cos x

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Using the Central Limit Theorem, the formulas are given as follows:

The Central Limit Theorem states that a random variable X with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] can have the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

A distribution of proportions, with a  proportion p in a sample of size n, also respects the Central Limit Theorem, as the the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation given as follows:

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The result of 34+(12+14)2.2 in the mixed fraction is  [tex]91\frac{1}{5}[/tex]

The expression is

34+(12+14)2.2

The mixed fraction is defined as the fraction that consist of one whole number part and a simple fraction part. simple fraction is the fraction that consist of numerator and denominator as whole numbers. The top term of  the simple fraction is called numerator and bottom term of the simple fraction is called denominator.

The expression is

=34+(12+14)2.2

First do the arithmetic operation in the bracket

= 34 + 26×2.2

Do the Multiplication

= 34+57.2

= 91.2

Convert the decimal form to simple fraction

91.2 = 456/5

Convert the simple fraction to the mixed fraction

456/5 = [tex]91\frac{1}{5}[/tex]

Hence, The result of 34+(12+14)2.2 in the mixed fraction is  [tex]91\frac{1}{5}[/tex]

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Step 1: Speed is defined as the rate of covering a distance, mathematically it is given by

Step 2: Make the time (t) of the subject in the above speed formula

Step 3: Given the distance covered and the average speed used during the trip as

Step 4: Substitute the values for distance and speed in the time formula in step 2

Hence, Santa's trip will take up to 21 hours

Answer:

To find out the time required to travel the distance of 1260 miles we need to divide the total distance travelled by the distance travelled in one hour.

[tex]1260/60=21[/tex]

So, it tool 21 hours for Santa to complete the trip

Answer:

9.  [tex]256u^8 v^{16}[/tex]

10.  [tex]-32x^{10} y^{35}[/tex]

11.  [tex]-x^{12}y^{20}[/tex]

12.  1

13.  [tex]\frac{2}{3xy^3}[/tex]

14.  [tex]\frac{h^8}{3j^6k^6}[/tex]

15.  [tex]\frac{1}{4z}[/tex]

Answer:

9.  256u^8 v^16

10.  -32x^10 y^35

11.  x^12 y^21

12.  1

Step-by-step explanation:

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