I Think The Answer Is A. Can You Check If I Am Correct In My Thinking? Thanks! (2024)

Answer:

The y-intercept = (0, 12621)

Explanation:

The initial population, P₀ = 12,621

Rate of increase, r = 6% = 6/100

r = 0.06

The number of years after the first census = x

The population after x years is given as:

[tex]\begin{gathered} P=P_0(1+r)^x \\ P=12621(1+0.06)^x \\ P=12621(1.06)^x \end{gathered}[/tex]

The graph that represents the above illustration is shown below

The y-intercept is found by setting x = 0, and finding the corresponding value of P

[tex]\begin{gathered} P=12621(1.06)^x \\ P=12621(1.06)^0 \\ P=12621 \end{gathered}[/tex]

The y-intercept = (0, 12621)

To determine the sales tax, we have to compute the 5.2% of 272.26. To determine the x% of y, we use the following expression:

[tex]y*\frac{x}{100}.[/tex]

Therefore, the 5.2% of 272.26 is:

[tex]272.26*\frac{5.2}{100}.[/tex]

Simplifying the above result, we get:

[tex]sales\text{ tax}\approx14.16.[/tex]

Answer: $14.16

If the point (x, y) is rotated around the origin by 90 degrees counterclockwise, then its image will be (-y, x)

We just change the sign of y-coordinate and switch the 2 coordinates

From the given figure we can see

The coordinates of point P are (4, 2)

Since the triangle will rotate around the origin by 90 degrees counterclockwise

Then change the sign of the y-coordinate to be -2, and switch x and y coordinates

The image of P is P', then

P' = (-2, 4)

The answers are

P = (4, 2)

P' = (-2, 4)

If ABCD is a rectangle, each of its four angles at the vertex is a right angle.

Then the angle at D is a right angle (measure of 90 degrees).

The right angle is divided in two angles, <1 and <2, by the diagonal, so <1 and <2 are complementary.

Then, we can write:

[tex]\begin{gathered} m\angle D=m\angle1+m\angle2=90\degree \\ (5x)+(8x-1)=90 \\ 13x-1=90 \\ 13x=90+1 \\ 13x=91 \\ x=\frac{91}{13} \\ x=7 \end{gathered}[/tex]

Then, with the value of x we can calculate m<1 and m<2:

[tex]\begin{gathered} m\angle1=5x=5\cdot7=35\degree \\ m\angle2=8x-1=8\cdot7-1=56-1=55\degree \end{gathered}[/tex]

Answer:

x = 7

m<1 = 35º

m<2 = 55º

The derivative of a constant is zero

, the only condition to have a slope of zero is when the function is a constant and a constant function has no tangent.

Hence, the answer is Otherwise.

The right angle triangle representing this scenario is shown below

A represents the beacon light

AB is the ship'e horizontal distance from the lighthouse

Taking angle A which is the angle of elevation as the reference angle,

opposite side = BC = 132

adjacent side = AB

To find AB, we would apply the tangent trigonomeric ratio which is expressed as

Tan # = opposite side/adjacent side

Therefore,

Tan 5 = 132/AB

ABtan5 = 132

AB = 132/tan5

AB = 1508.8

The ship's horizontal distance from the lighthouse and the shore is 1508.8 feet

We are given the following information

Toby eats tacos every 5 days.

Toby also drinks horchata every 6 days.

If Toby has horchata and tacos today how many days will he have to wait to enjoy his favorite treats on the same day again?

We need to find the least common multiple (LCM) of 5 and 6 days.

Multiples of 5 = 5, 10, 15, 20, 25, 30

Multiples of 6 = 6, 12, 18, 24, 30

As you can see, the least common multiple (LCM) of 5 and 6 is 30

Therefore, Toby has to wait for 30 days to enjoy his favorite treats on the same day again.

First, we find the constant of proportionality

[tex]k=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]

Let's replace the points (8,12) and (10,15).

[tex]k=\frac{15-12}{10-8}=\frac{3}{2}=1.5[/tex]

This means that 1 star is equivalent to 1.5 total points.

So, observe that 2 stars get 3 total points. 16 stars get 24 points. And, 12 stars get 18 points.

Hence, A, C, and D are correct.

See graph and explanation below

Explanation:

[tex]\begin{gathered} f\mleft(x\mright)=2x-5 \\ g\mleft(x\mright)\text{ = }\frac{x\text{ - 5}}{2} \end{gathered}[/tex]

Plotting both graphs:

To prove the functions are inverse of each other:

At any coordinate, the value of x (input) of one function is the the value of y (output ) of the second function and vice versa. The value of x (input) of second function is the the value of y (output ) of the First function.

for f(x): when x = -2.5, y = 0

for g(x): when x = 0, y = -2.5

for f(x): when x = 0, y = 5

for g(x): when x = 5, y = 0

The standard form of equation of a line is expressed as y = mx+c where;

m is the slope of the line

c is the intercept

Given the equation of the line y = -3x - 4​

you can see that the equation given is already in its standard form with -3 as the slope and -4 a the intercept.

Hence the standard form of the equation is still y = -3x - 4

Given:

[tex]y=\sqrt[]{x+1}[/tex]

Let's determine the domain and the range of the function.

The domain is the set of all possible values of x. It is also called the input.

The range is the set of possible values of y. It is also called the output.

• To find the domain, set the values in the radicand greater than or equal to zero and solve for x:

x + 1 ≥ 0

Subtract both sides by 1:

x + 1 - 1 ≥ 0 - 1

x ≥ -1

Therefore, the domain is all possible values greater or equal to -1:

x ≥ -1

To find the range, input the lowest value of the domain which is -1 and evaluate for y:

[tex]\begin{gathered} y\ge\sqrt[]{-1+1} \\ \\ y\ge\sqrt[]{0} \\ \\ y\ge0 \end{gathered}[/tex]

Therefore, the range of the function is all integers positive interges including zero.

The graph is attached below:

ANSWER:

C) Domain: x ≥ -1

Range: y ≥ 0

[tex]\frac{268.75}{2.5}=107.5[/tex]

First, find the slope (m):

Apply the formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Given the points:

(x1,y1) = (-8,1)

(x2,y2)= (-2.4)

m= 4-1 / -2-(-8) = 3 / 6 = 1/2

Slope intercept form:

y=mx+b

Where:

m= slope = 1/2

b= y-intercept

So far:

y = 1/2x + b

Replace (x,y) with any point , for example (-8,1), and solve for b

1 = 1/2 (-8) + b

1 = -4 + b

1+4= b

b= 5

Slope intercept form:

y= 1/2x + 5

point slope form:

y-y1 = m ( x- x1 )

y- 1 = m ( x + 8 )

We have the following:

[tex]4x^2-3xy[/tex]

replacing, x=-3 and y=-2:

[tex]\begin{gathered} 4\cdot(-3)^2-3\cdot(-3)\cdot(-2) \\ 4\cdot9-18 \\ 36-18=18 \end{gathered}[/tex]

The answer is 18.

step 1

In the right triangle ADE

Apply Pythagorean Theorem

Find AE

AE^2=AD^2+DE^2

substitute the given values

AE^2=12^2+5^2

AE^2=169

AE=13 units

step 2

In this problem triangle ADE and triangle CBE are similar

that means ----> the ratio of its corresponding sides is proportional

so

AE/EC=DE/EB

substitute the given values

13/EC=5/1

EC=13/5

EC=2.6 units

step 3

Find AC

AC=AE+EC

AC=13+2.6=15.6 units

therefore'

AC=15.6 units

Answer:

1.4 $/pound

Explanation:

The rate of change of the cost of water melon is expressed as;

Rate of change = C2-C1/p2-p1

Using the coordinates (C, p)

(0,0) and (0.35, 0.25)

Rate of change = 0.35-0/0.25-0

Rate of change = 0.35/0.25

Rate of change = 1.4 $/pound

Hence the rate of change of watermelon is 1.4 $/pound

Let's draw a rough drawing of what's needed to be solved.

x is the pitch of the roof and we need to solve for x.

This is a right triangle so we can use the Pythgaorean Theorem to solve it.

It states that in a right triangle, the Sum of the Squares of its legs is equal to the square of its Hypotenuse.

The hypotenuse is x

The legs are 16 and 14

Thus, we can write:

[tex]\begin{gathered} x^2=14^2+16^2 \\ x^2=452 \\ x=\sqrt[]{452} \\ x=\sqrt[]{4}\sqrt[]{113} \\ x=2\sqrt[]{113} \end{gathered}[/tex]

To express a fraction as a percent, divide the numerator by the denominator, then multiply by 100.

7 / 11 = 0.636

0.636 x 100 = 63.6 %

Answer:

A) 63.6 %

Answer:

The area of the rectangle changes by the factor of

[tex]9^2[/tex]

Explanation:

Let l and w represent the length and width of the rectangle respectively.

The area is

A = lw

If these change by a factor of nine, then we have:

9l and 9w

The area, which is the product of the length and width becomes:

[tex]\begin{gathered} A=9l\times9w \\ =9^2lw \\ =9^2A \end{gathered}[/tex]

SOLUTION:

Step 1:

In this question, we are given the following:

Find the sale price when the original price is $64.00

and the discount rate is 12%.

Step 2:

Recall that the discount rate is 12% and the original price is $ 64.00

Then, we have that:

[tex]\begin{gathered} 12\text{ \% of \$ 64.00} \\ =\frac{12}{100}X\text{ \$ 64.00} \\ =\frac{768}{100} \\ Discount=\text{ \$ 7.68} \end{gathered}[/tex]

Next,

We need to find the sale price =

[tex]\begin{gathered} \text{Original price - Discount price} \\ =\text{ \$ 64.00 - \$ 7. 68} \\ =\text{ \$ 56.32} \end{gathered}[/tex]

Answer: 3.5

Step-by-step explanation:

3x+2y=13

4x+y=15.25

System of equations

I solved using elimination but there are other methods

3x+2y=13

-8x-2y=-30.5

The y cancels out

3x=13

-8x=-30.5

=

-5x= -17.5

Solve

x=3.5

Answer:

$3.50

Step-by-step explanation:

Explanation:

An arc measure is an angle the arc makes at the center of a circle

From the given question, we will have to apply the intersecting chord theorem

If two chords intersect in the interior of a circle, then the measure of each angle is one half the sum of the

measures of the arcs intercepted by the angle and its vertical angle.

[tex]\begin{gathered} In\text{ our case} \\ m

Thus

[tex]\begin{gathered} 71.4=\frac{1}{2}(65.6^0+mRA) \\ \\ mRA=2\times71.4-65.6^0 \\ mRA=77.2^0 \end{gathered}[/tex]

Thus, the answer is 77.2 degrees

The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.

We have that the videogame system and games cost $632. And the cost of the games is 3 times as much as the cost of the system. Then we have the following expressions:

[tex]\begin{gathered} VS+G=632 \\ G=3\cdot VS \end{gathered}[/tex]

Where, VS = Videogame system and G = games.

We plug in 3*VS in the first equation to get:

[tex]VS+3\cdot VS=632[/tex]

And we solve for VS, to find the cost of the videogame system:

[tex]4\cdot VS=632[/tex]

We use the multiplication property of equality here, and multiply both sides of the equation by 1/4:

[tex]\begin{gathered} 4\cdot VS\cdot\frac{1}{4}=632\cdot\frac{1}{4} \\ VS=158 \end{gathered}[/tex]

The cost of the videogame system is $158. Now we can find the cost of the games, replacing VS in the first equation:

[tex]\begin{gathered} VS+G=632 \\ 158+G=632 \\ G=632-158=474 \end{gathered}[/tex]

Games cost $474.

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

Sample size: 12

Median: 66

Minimum: 60

Maximum: 70

First quartile: 63.5

Third quartile: 67.5

Interquartile Range: 4

Outliers: none

Solution

Step 1:

Write the matrix:

[tex]\begin{gathered} X\text{ = }\begin{bmatrix}{6} & {a} \\ {-2} & {-5}\end{bmatrix} \\ I\text{ = }\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \end{gathered}[/tex]

Step 2:

Find the inverse of X.

[tex]X^{-1}\text{ = }\frac{Adjoint}{Determinant}[/tex]

Step 3:

Find the determinant

[tex]\begin{gathered} Determinant\text{ of X = }\begin{bmatrix}{6} & {a} \\ {-2} & {-5}\end{bmatrix} \\ Co-factor\text{ of X = }\begin{bmatrix}{-5} & {2} \\ {-a} & {6}\end{bmatrix} \\ Adjoint\text{ is the transpose of the co-factor of X} \\ Adj\text{oint = }\begin{bmatrix}{-5} & {-a} \\ {2} & {6}\end{bmatrix} \\ Deterninant\text{ = 2a - 30} \end{gathered}[/tex]

Step 4:

[tex]\begin{gathered} X\text{ - }X^{-1}\text{ = I} \\ \\ \begin{bmatrix}{6} & {a} \\ {-2} & {-5}\end{bmatrix}\text{ - }\frac{\begin{bmatrix}{-5} & {-a} \\ {2} & {6}\end{bmatrix}}{2a\text{ - 30}}\text{ = }\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \\ \begin{bmatrix}{6} & {a} \\ {-2} & {-5}\end{bmatrix}\text{ - }\begin{bmatrix}{\frac{-5}{2a-30}} & {\frac{-a}{2a-30}} \\ {\frac{2}{2a-30}} & {\frac{6}{2a-30}}\end{bmatrix}\text{= }\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \\ \begin{bmatrix}{6\text{ + }\frac{5}{2a-30}} & {a\text{ + }\frac{a}{2a\text{ - 30}}} \\ {-2\text{ -}\frac{2}{2a\text{ - 30}}} & {-5-\text{ }\frac{6}{2a\text{ - 30}}}\end{bmatrix}\text{ = }\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \end{gathered}[/tex]

Step 5;

Write equations

[tex]\begin{gathered} \text{ 6 + }\frac{5}{2a\text{ - 30 }}\text{ = 1} \\ \frac{6(2a\text{ - 30\rparen + 5}}{2a\text{ - 30}}\text{ = 1} \\ \frac{6(2a\text{ -30\rparen + 5}}{2a\text{ - 30}}\text{ = 1} \\ 12a\text{ - 180 + 5 = 2a - 30} \\ 12a\text{ - 2a = 175 - 30} \\ 10a\text{ = 145} \\ \text{a = }\frac{145}{10} \\ \text{a = }\frac{29}{2} \end{gathered}[/tex]

Final answer

[tex]\begin{gathered} i)\text{ }X^{-1}\text{ = }\frac{1}{2a\text{ - 30}}\begin{bmatrix}{-5} & {-a} \\ {2} & {6}\end{bmatrix} \\ ii)\text{ }a\text{ = }\frac{29}{2}\text{ or 14.5} \end{gathered}[/tex]

Robert will have $40,561.53 more than Sadie.

What is Compound Interest?

Compound interest, also called "compounding interest," is the interest on the initial investment as well as the accrued interest on that investment.

Given that Sadie and Robert invested $89000 on different rates 77/8% and 41/4% respectively.

Formula for CI = P( 1 + \dfrac{r}{n}^{nt} )

Using this, we get Sadie's total amount = $415,064.26 and Robert's total amount = $455,625.79

Hence, Robert will have $40,561.53 more than Sadie.

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Let x represent the number of minutes.

The guidelines state that the speech must be at least 7 minutes but not to exceed 12 minutes. This means that x must be greater than or equal to 7 minutes but x must be lesser than or equal to 12 minutes.

The representation would be

[tex]\begin{gathered} x\text{ }\ge7\text{ } \\ x\text{ }\leq12 \\ The\text{ compound inequatity would be} \\ 7\text{ }\leq x\leq12 \end{gathered}[/tex]

Answer:

A) 5.92 billion dollars

B) 1.184 billion dollars per year

Explanation:

Part A)

The change in annual sales between 2010 and 2015 is calculated as the difference between the sales of 2015 and 2010. So, taking into account the table, we get:

59.42 - 53.5 = 5.92 billions of dollars

Because 59.42 billion are sales in 2015 and 53.5 billion are sales in 2010.

Therefore, the answer is 5.92 billion dollars

Part B)

The average rate of changes in sales from 2010 to 2015 is equal to the change in the annual sales divided by the number of years, so it is calculated as

[tex]\frac{59.42-53.5}{2015-2010}=\frac{5.92}{5}=1.184[/tex]

Therefore, the average rate of change is 1.184 billion dollars per year.

5,000 toothpicks must be sold in order to break even.

How many toothpicks sell?

Numerous aspects of business and finance make use of break-even points. It is the production level where total production revenue and total production costs are equal in accounting terms. The break-even point in investing is the point at which the purchase price is equal to the market price.

Here, let's assume that m toothpicks must be sold to break even = m

So, for m toothpicks, Total cost = Total Earnings

Currently, the price to produce 1 toothpick is $0.03

So, cost of production of m toothpicks = m x ( cost of 1 toothpick)

= $(0.03 m)

Also, fixed month cost = $100

So, Total cost of production = $100 + $0.03 m .... (1)

Again, the selling cost of 1 toothpick = $0.05

So, selling cost of m toothpicks = m ( cost of 1 toothpick) = $(0.05 m) ..(2)

From (1) and (2)

100 + 0.03 m = (0.05 m)

⇒ 100 = 0.02 m

or, m = 100/0.02

⇒ m = 5000

Therefore 5,000 toothpicks must be sold in order to break even.

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