The data can be modeled by the following system of linear equations.
-3x+10y = 160
x+2y=164
Equation 1
Equation 2
Equation 1 is modeled for the percentage of never-married American adults, y, x years after 1970 and Equation 2 is modeled for the percentage of married
American adults, y, x years after 1970. Use these models to complete parts a and b.
a. Determine the year, rounded to the nearest year, when the percentage of never-married adults will be the same as the percentage of married adults. For
that year, approximately what percentage of Americans, rounded to the nearest percent, will belong to each group?
In year
the percentage of never-married adults will be the same as the percentage of married adults. For that year, approximately % percentage of
Americans will belong to each group.

For this type of question, we should draw a graph and find the area of the common solutions

Now we can draw the graphs of them

The red line represents the first inequality

The blue line represents the second inequality

The area of the two colors represents the area of the solutions,

Let us check the given points which one lies in this area

Point (5, -2) lies on the area of the solutions

∴ (5, -2) is a solution

Point (-3, -4) lies in the blue area only

∴ (-3, -4) not a solution

Point (0, -3) lies in the red line and the red line is solid, which means any point on it will be on the area of the solutions

∴ (0, -3) is a solution

Point (0, 1) lies in the blue line and the blue line is dashed, which means any point that lies on it not belong to the area of the solutions

∴ (0, 1) is not a solution

Point (-4, 1) lies on the area of the solutions

∴ (-4, 1) is a solution

The solutions are (5, -2), (0, -3), and (-4, 1)

step 1

Find out the value of cosθ

cosθ=8/17 ------> by CAH

step 2

Find out the value of secθ

secθ=1/cosθ

secθ=17/8

step 3

Find out the length of the vertical leg in the given right triangle

Applying the Pythagorean Theorem

17^2=8^2+y^2

y^2=17^2-8^2

y^2=225

y=15

step 4

Find out the value f cotθ

cotθ=8/15 -----> adjacent side divided by the opposite side

therefore

Solution

Part a

The axis of symmetry

Part b

The vertex

Vertex (2,3)

Part c

The graph opens downward

Part D

The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.

The y-intercept

Another

The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x=0.

x=0 y=-5

Answer:

x = 13 [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

j(x)   =  [tex]\frac{-4}{3}[/tex] x + 7  Substitute -5 for x

j(-5) = [tex]\frac{-4}{3 }[/tex] ( -5) + 7  

or

j(-5) =[tex](\frac{-4}{3})[/tex] [tex](\frac{-5}{1})[/tex] + 7  A negative times a negative is a positive

j(-5) = [tex]\frac{20}{3}[/tex] + 7

j(-5) = [tex]\frac{20}{3}[/tex] + [tex]\frac{21}{3}[/tex]     [tex]\frac{21}{3}[/tex] means the same thing as 7

j(-5) = [tex]\frac{41}{3}[/tex] = 13 [tex]\frac{2}{3}[/tex]

Given a modelled account balance for the period of d days as shown below:

Given that the account balance is $38, we would calculate the number of days by substituting for f(d) = 38 in the modelled equation as shown below:

Since all coefficients of the variable d from degree 3 to 1 are integers, we would apply apply the Rational Zeros Theorem.

The trailing coefficient (coefficient of the constant term) is −35.

Find its factors (with plus and minus): ±1,±5,±7,±35. These are the possible values for dthat would give the zeros of the equation

Lets input x= 5

Since, x= 5 is a zero, then x-5 is a factor.

It can be observed that the roots of the equation would give one real root and two complex roots

Therefore,

Since number of days cannot a complex number, hence, the number of days that would give a balance of $38 is 5 days

Explanation

Since the given shapes are similar, which implies that they are proportional,

Therefore; we will have

Answer:

Okey, here we have the following:

Capital: 10000

Interest: 2%

Time: 7 Years= 7*4=28 quarters of year

Using the compound interest formula, we get:

Working we get:

She will have aproximately $11,498.73 in her account after 7 years.

As the scale factor is 4:1 it means that for each 4inches in scale drawing correspond to 1 inch in the object.

Then, to find the side lengths in the object you multiply the measure of each side in the scale drawing by 1/4:

Answer:

x = 5

m∠QRT = 44

Step-by-step explanation:

8x + 4 = 10x - 6

-10x       -10x

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

-2x + 4 = -6

      -4      -4

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

-2x = -10

÷-2    ÷-2

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

x = 5

m∠QRT

8x + 4

8(5) + 4

40 + 4 = 44

I hope this helps!

From the image, [tex](8x + 4 )° = (10x - 6)°[/tex]

Reason: Vertically opposite angles are equal.

Now, we solve for x

[tex]8x + 4 = 10x - 6[/tex]

collect like terms

[tex] 4 + 6 = 10x - 8x[/tex]

[tex]→ 10 = 2x[/tex]

Divide both sides by the coefficient of x to find the value of x

[tex] x = 5[/tex]

Now, substitute for the value of x in the expression for m∠QRT to find the degree

[tex](8x + 4 )° → (8(5) + 4)°[/tex]

Therefore: m∠QRT = 44°

Answer:

250 cubic inches

Explanation:

Given that:

Radius of the cylinder, = 3 in.

Height of the cylinder = 3r

= 3(3)

=9 in.

The formula to find the volume of a cylinder is

Plug the given values into the formula.

Rounding to nearest tenth gives 250 cubic inches, which is the required volume of the cylinder.

Explanation

In the bag of tokens, we are told 55​ red, 44​ green, and 55​ blue tokens. Therefore, the total number of tokens in the bag is

Hence to find the probability that a randomly selected token is not red becomes;

Answer: 9/14

Given:

There are given the statement about the elimination method and substitution method.

Explanation:

According to the concept:

One equation cannot be easily solved for a single variable.

Final answer:

Hence, the correct option is D.

The scatter plot is given and objective is to find the best line of fit for given scatter plot.

Let's take the few points of scatter plot,

(0,8) ,( -1,8) , (-4,10) ,( -8,12),(-10,14) (-12,14)

Take the line and check which graph contains most of the points of scatter plot.

The graph is ,

now take ,

The graph is,

This graph contains only one point of scatter plot.

Take,

Now the take the last equation,

this graph contains no point of the scatter plot.

From all the four graph of the lines it is observed that option 1) is the best line of fit for given scatter plot. because it contains 3 points of scatter plotes . which is more than the other graph of line.

Answer: Option 1)

Given:

Credit to rent earned for

Amount of total rent = $10,000

Amount unearned = amount of total rent ( 3 month / 8 month)

Unearned rent is : $3750

Given the function:

Let's find the amplitude and period of the function.

Apply the general cosine function:

Where A is the amplitude.

Comparing both functions, we have:

A = 1

b = 4

Hence, we have:

Amplitude, A = 1

To find the period, we have:

Therefore, the period is = π/2

The graph of the function is shown below:

The parent function of the given function is:

Let's describe the transformation..

Apply the transformation rules for function.

We have:

The transformation that occured from f(x) = cosx to g(x) = cos4x using the rules of transformation can be said to be a horizontal compression.

ANSWER:

Amplitude = 1

Period = π/2

Transformation = horizontal compression.

The Solution:

Given:

We are required to simplify the above expression in a+bi form.

Simplify by expanding:

Collecting the like terms, we get:

Therefore, the correct answer is [option 3]

The probability of getting exactly 1 blue marble from a bag which is  filled with 5 blue and 4 red marbles is 40/81.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A bag is filled with 5 blue and 4 red marbles.

The total number of marble in the bag are,

5+4=9

One marble is taken at random from the bag, the color is noted and then it is replaced. The probability of getting blue marble is,

P(B)=5/9

probability of getting red marble is,

P(R)=4/9

The Probability of getting red marble in first pick and  probability of getting blue marble in second pick

P1=5/9×4/9=20/81

The Probability of getting blue marble in first pick and probability of getting red marble in second pick is,

p2=4/9×5/9=20/81

The exactly 1 blue is taken out, when first marble is red and second is blue or the first one is blue and second one is red. Thus, the probability of getting exactly 1 blue is,

P=p1+p2

=20/81+20/81

40/81

Hence the probability of getting exactly 1 blue marble from a bag which is  filled with 5 blue and 4 red marbles is 40/81.

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we are asked about the claim that the fraction -12 / 8 is equivalent to the decimal expression -0.125... (repeating)

Without evaluating the expression, we can say that the clain is INCORRECT, since just the quotient 12/8 should give a number LARGER than "1" (one) in magnitude (the number 12 is larger than the number 8 in the denominator. We can also say that such division cannot ever give a repeating decimal at infinity, since divisions of integer numbers by 8 or 4 never render a repeating decimal, but a finite number of decimals.

First, lets note that the given functions are polynomials of degree 2. Since the domain of a polynomial is the entire set of real numbers, the domain for all cases is:

Now, lets find the range for all cases. In this regard, we will use the first derivative criteria in order to obtain the minimum (or maximim) point.

case 1)

In the first case, we have

which corresponds to the point (-1,-8). Then the minimum y-value is -8 because the leading coefficient is positive, which means that the curve opens upwards. So the range is

On the other hand, the horizontal intercept (or x-intercept) is the value of the variable x when the function value is zero, that is,

which gives

Case 2)

In this case, the first derivative criteria give us

Since the leading coefficient is positive, the curve opens upwards so the point (-1,5) is the minimum values. Then, the range is

and the horizontal intercepts do not exists.

Case 3)

In this case, the first derivative criteris gives

Since the leading coeffcient is negative the curve opens downwards and the maximum point is (0,9). So the range is

and the horizontal intercepts occur at

Case 4)

In this case, the first derivative yields

since the leading coefficient is postive the curve opens upwards and the point (2,-12) is the minimum point. Then the range is

and the horizontal intercetps ocurr when

Case 5)

In this case, the leading coefficient is positive so the curve opens upwards and the minimum point ocurrs at x=0. Therefore, the range is

and thehorizontal intercept is ('0,0).

In summary, by rounding to the nearest tenth, the answers are:

Since the slope of the line y=x+5 is m=1, then if the other line is parallel to y=x+5, then it must have the same slope, this is, m'=1.

Now we can use the point-slope formula to get the equation of the line:

therefore, the equation of the line in slope intercept form that goes through (-5,-3) and is parallel to the line y=x+5 is y=x+2

This is the equation for the line.

Here the given equation is,

We can calculate x intercept by substituting 0 for y, as there is no value of y,

the x intercept is none here. The graph is as follows,

The equation of line passing through two points (x_1,y_1) and (x_2,y_2) is,

Substitute the points in the equation to obtain the equation of line.

So equation of line is 3y+5x+21=0.

Answer: 45,000 ÷ 900=50

Step-by-step explanation:

By completing squares, we wll get that the solutions of the quadratic equation are:

x = 6 ± √35

Here we have the quadratic equation:

x² - 12x + 1 = 0

We can rewrite this as:

x² - 2*6x + 1 = 0

So we can add and subtract 6² to get:

x² - 2*6x + 1 + 6² - 6²  = 0

Now we rearrange the terms:

(x² - 2*6x + 6²) + 1 - 6² = 0

Now we can complete squares.

(x - 6)² + 1 - 36 = 0

(x - 6)² = 35

Now we solve for x:

x = 6 ± √35

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6.62% is annual interest rate must they earn to reach their goal.

What exactly does "interest rate" mean?

N = 25

PV = - $230,000

FV =  $1,850,000

PMT = 0

CPT Rate

Applying excel formula:

=RATE(25,0,-230,000,1,850,000)

=  6.62%

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Given

The total frequency is 15 respondents

The responses were: 0,0,0,0,0, 2, 3, 3, 4, 5, 6, 7, 10, 40 and 70

Solution

The population mean is the sum of all the values divided by the total frequency .

Remember that

A regular hexagon can be divided into 6 equilateral triangles

the measure of each interior angle in a regular hexagon is 120 degrees

so

see the attached figure to better undesrtand the problem

each equilateral triangle has three equal sides

the length of each side is given and is 12 units

Part A) Perimeter

the perimeter is equal to

P=6(12)=72 units

Part B

Find the area

Find the height of each equilateral triangle

we have

tan(60)=h/6

Remember that

therefore

the area of the polygon is

applying Pythagorean Theorem

12^2=6^2+h^2

h^2=12^2-6^2

h^2=108

h=6√3 units

Answer:

  we can use two ways to write 180° along with the inscribed angle theorem to obtain the desired relation

Step-by-step explanation:

Given ∆ABC inscribed in a circle O where E is the midpoint of arc BC and ED is a diameter, you want to prove ∠DEA = 1/2(∠B -∠C).

We can add add arcs to make 180° in two different ways, then equate the sums.

  arc EB +arc BA +arc AD = 180°

  arc EC +arc CA -arc AD = 180°

Equating these expressions for 180°, we have ...

  arc EB +arc BA +arc AD = arc EC +arc CA -arc AD

Recognizing that arc EB = arc EC, we can subtract (arc EB +arc BA -arc AD) from both sides to get ...

  2·arc AD = arc CA -arc BA

The inscribed angle theorem tells us ...

Making these substitutions into the above equation, we have ...

  4∠DEA = 2∠B -2∠C

Dividing by 4 gives the relation we're trying to prove:

  ∠DEA = 1/2(∠B -∠C)

Given,

The diagram of the triangle ABC and A'B'C' is shown in the question.

Required:

The translation of triangle from ABC to A'B'C'.

Here,

The coordinates of the point A is (2,5).

The coordinates of the point A' is (5,7)

The translation of the triangle is,

Hence, shifted 3 units right and 2 units up.

we have the equation

Solve for t

step 1

Multiply both sides by 2t(t-2) to remove fractions

simplify

Solve the quadratic equation

Using the formula

a=9

b=-78

c=48

substitute

The solutions for t are

t=8 and t=2/3

therefore

the answer is

t=2/3,8