PENSION FUNDS The managers of a pension fund have invested $1. 5 million in U. S. Government certificates of deposit (CDs) that pay interest at the rate of 2. 5%∕year compounded semiannually over a period of 10 years. At the end of this period, how much will the investment be worth?

A)  Rotate by 90° counterclockwise.

B) Reflection transformation about the line y = 5.

C) Parallel Lines are C₂D₂ and A₂B₂; EF and E₁F₁.

D) Perpendicular lines are;  D₁F₁ and  E₁F₁; DF and EF; DC and AB.

E) Line segments with slope of 0 are; AB, C₂D₂, A₂B₂, EF and E₁F₁

F) Line segments on the boat that have an undefined slope are; Lines A₁B₁, DF and DC.

G) Slope of Line ED = 1

A) The blue segment CD is seen on the graph as a perpendicular line with 2 units while the line segment C₂D₂ is seen as a horizontal line. Thus, to match CD with C₂D₂, we will rotate by 90° counterclockwise.

B) The transformations that would be used on the blue triangle to get it to match with the red triangle is a reflection transformation about the line y = 5.

C) The line segments that are parallel to each other are; C₂D₂ and A₂B₂; EF and E₁F₁.

D) The line segments that are perpendicular are;  D₁F₁ and  E₁F₁; DF and EF; DC and AB.

E) Horizontal lines that are parallel to the x-axis have zero slope. Thus, AB, C₂D₂, A₂B₂, EF and E₁F₁ all have zero slopes.

F) Undefined slope is the slope of a vertical line. Thus, Lines A₁B₁, DF and DC have undefined slopes.

G) Slope of ED = (5 - 4)/(-10 - (-11))

Slope of ED = 1/1

Slope = 1

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The two cars lying on one side of the plane are 50 meters apart.

An equation is an expression that shows the relationship between two or more numbers and variables.

let us assume that the height is 100 m. Let d represent the horizontal distance. For depression of 38°, Ф = 90 - 38 = 52°, hence:

tan(52°) = d / 100

d = 128 m

For depression of 52°, Ф = 90 - 52 = 38°, hence:

tan(38°) = d / 100

d = 78 m

Distance apart = 128 - 78 = 50 m.

The two cars lying on one side of the plane are 50 meters apart.

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Answer:

[tex]\huge\boxed{\sf x = 55\°}[/tex]

Step-by-step explanation:

Given that,

x° + 35° = 90° (complementary angles)

Subtract 35 to  both sides

x = 90 - 35

x = 55°

[tex]\rule[225]{225}{2}[/tex]

the actual height of the backboard is 8.18 feet.

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

Given

We have been given that Derek places  a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.

We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.

[tex]\frac{Actual height of ruler}{Shadow of ruler} = \frac{Actual height of black board}{Shadow of black board} \\\\\frac{12}{11} =\frac{Actual height of black board}{7.5} \\\\Actual height of black board = \frac{12}{11} * 7.5 = 8.18\\[/tex]

Therefore, the actual height of the back-board is 8.18 feet.

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Answer:

center (2, 9); radius 6

Step-by-step explanation:

Standard equation of a circle:

(x - h)² + (y - k)² = r²

where the center is (h, k), and r is the radius.

You have

(x - 2)² + (y - 9)² = 36

(x - 2)² + (y - 9)² = 6²

Compare this last form to

(x - h)² + (y - k)² = r²

h = 2; k = 9; r = 9

Answer: center (2, 9); radius 6

Answer:

centre = (2, 9 ) , radius = 6

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

(x - 2)² + (y = 9)² = 36 ← is in standard form

with centre (2, 9 ) and r² = 36 ⇒ r = [tex]\sqrt{36}[/tex] = 6

Answer:

r = -1.5

Step-by-step explanation:

recall that ,the recursive formula for a geometric sequence [tex]a_n[/tex] is :

[tex]a_{n} = r \times a_{n-1} \ \ \text{where r is the common ratio }[/tex]

therefore

The common ratio of the sequence:

[tex]a_{n} = -1.5 \times a_{n-1}[/tex]

is r = -1.5

Answer:

160 m³

Step-by-step explanation:

the volume of a rectangular prism is equal to :

= Base × height

= length × width × height

………………………………………

= 8 × 4 × 5

= 160

Note : the length can be 8 or 5

and the width can be 4 or 5

Answer: B

The main word that gives the answer away is product, which means to multiply.

The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)

Herein we have an equation that models the height of the ball as function of time, we need to evaluate the expression for t = 3 s to find the required height:

s(3) = - 4.9 · (3 s)² + 19.6 · (3 s) + 58.8

s(3) = 73.5 m

The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)

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The net force acting on the crate is the sum of all the forces acting in the different directions on the crate, which is 176 N to the left.

The net force is defined as the sum of all the forces acting on an object.

From the figure given that,

Upward force = 440 N

Downward force = - 440 N

Rightward force = 176 N

Leftward Force = - 352 N

The net vertical force acting on the crate = Upward force + Downward force

                                                                       =  440 N + (-440 N)

                                                                       = 0 N

The net horizontal force acting on the crate = Rightward force + Leftward force

                                                                       =176 N + (- 352 N)

                                                                       = - 176 N

Hence, the net force acting on the crate is - 176 N, which is 176 N to the left.

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Answer:

175N to the left

Step-by-step explanation:

Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at  B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C  which is at D(1, 5).

An equation is an expression that shows the relationship between two or more variables and numbers.

Point A is at A(2, 3) while point B is 4 right and 5 up from point A. Point B is at  B(6, 8). Also, point C is at C(9, 7). Point D is 8 left and 2 down from point C  which is at D(1, 5).

The location of point A, B, C and D is located on the graph.

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Using it's concept, the probabilities are given as follows:

a) 0.5455 = 54.55%.

b) 0.5909 = 59.09%.

c) 0.4615 = 46.15%.

d) 0.5556 = 55.56%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Item a:

Out of 110 people, 60 prefer sprite, hence the probability is:

p = 60/110 = 0.5455 = 54.55%.

Item b:

Out of 110 people, 65 are between 21 and 40, hence the probability is:

p = 65/110 = 0.5909 = 59.09%.

Item c:

65 people are between 21 and 40, and of those, 30 drink lemonade, hence the probability is:

p = 30/65 = 0.4615 = 46.15%.

Item d:

45 people are under 21 years of age, and of those, 25 drink sprite, hence the probability is:

p = 25/45 = 0.5556 = 55.56%.

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The expected value of a roll of this weighted die is; 13/3 or 4.33

We are given that;

A $6 sided die is weighted.

Probability of any number being rolled is proportional to the value of the roll.

Probability of a $2 being rolled is twice that of a $1 being rolled.

Thus, the expected Value is;

E(x) =  (1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*6)/(1 + 2 + 3 + 4 + 5 + 6)

E(x) = 13/3 = 4.33

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Answer:  0.6

Explanation:   You need to divide 3 by 5 and it will give you the answer of 0.6

The different ratios are 2 : 7, 2 : 9 and 7 : 9

The statement is given as:

8 out of 36 squares unfilled

This means that:

The part-to-part ratio is represented as:

Ratio = Unfilled : Filled

This gives

Unfilled : Filled = 8 : 28

Simplify

Unfilled : Filled = 2 : 7

The part-to-whole ratios are represented as:

Ratio = Unfilled : Total

Ratio = Filled : Total

So, we have:

Unfilled : Total = 8 : 36

Filled : Total = 28 : 36

Simplify

Unfilled : Total = 2 : 9

Filled : Total = 7 : 9

Hence, the different ratios are 2 : 7, 2 : 9 and 7 : 9

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Answer:

343

Step-by-step explanation:

7 cubed = 7 x 7 x 7 = 343

so, 343 is a perfect cube.

Answer:

C

Step-by-step explanation:

Answer:

2.5 pounds

Step-by-step explanation:

Answer:

  f(2) = -13

Step-by-step explanation:

Evaluate the given formula with the given value of the variable.

  f(1) = -16 . . . . . . . . . . given

  f(n) = -29 -f(n-1) . . . . given

For n = 2, we have ...

  f(2) = -29 -f(2-1) = -29 -f(1) = -29 -(-16) . . . . put 2 in place of n and evaluate

  f(2) = -13

The complete table is

                Dog         Not Dog         Total

Cat            31              10                     41

Not cat     24              7                       31

Total         55              17                      72

Given a venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet as shown in figure which is attached below.

In the figure cat and dog are overlapping which means 31 people like both.

The people that like only dog but not cat are 24 and the people that like only car but not dog is 10.

The people that like not cat not dog is 31-24=7.

The total people that like cats are 31+10=41 and the total people that dont like cat is 24+7=31

The total people that like dogs are 31+24=55 and the people that didn't like dogs are 31+10-24=17 and the total people that like both dog and not dog and also like cat and not cat is 55+17=41+31=72.

Hence, the complete table is shown in attached figure for the given venn diagram.

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Answer:

A

Step-by-step explanation:

As angles in a triangle add to 180 degrees, angle C measures 35 degrees.

Therefore, the answer is A, since thr triangles will be similar by AA.

There were 4 number of treatment conditions compared in this experiment for the given degree of freedom.

We have,

df = 3, 36

Now,

We know that,

Degree of freedom (df) = Number of treatments (t) - 1

i.e.

df = t - 1

So,

We have,

df = 3

Now,

Substituting the values,

We get,

3 = t - 1,

i.e.

t = 4

So, number of treatments conditions = 4

Hence we can say that there were 4 number of treatment conditions compared in this experiment for the given degree of freedom.

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The graph that shows the minimum amount due for a credit amount of x given that the credit limit is $2,000 is graph B.

Let x represent the credit amount  and y represent the minimum amount due.

For a bill of less than $100, the entire amount is due. That is for 0 ≤ x < $100, y = x

For a bill of at least $100 but less than $500, the minimum due is $100. That is for $100 ≤ x < $500, y = 100

For a bill of at least $500 but less than $1,000, the minimum due is $300. That is for $500 ≤ x < $1000, y = $300

For a bill of $1,000 or more, the minimum due is $500. But the credit limit is $2000. That is For $1000 ≤ x < $2000, y = $500

The graph that shows the minimum amount due for a credit amount of x  is graph B.

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The function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)

In this problem we have two functions related to each other because of the existence of rigid transformations. Rigid transformations are transformations applied to geometric loci such that Euclidean distance is conserved at every point of the geometric locus.

Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of horizontal translation 4 units in the + x direction:

f'(x) = - 2 · cos (x - 1 + 4) + 3

f'(x) = - 2 · cos (x + 3) + 3     (1)

Now we apply a reflection over the x-axis:

g(x) = - [- 2 · cos (x + 3) + 3]

g(x) = 2 · cos (x + 3) - 3

Therefore, the function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)

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The systems of linear equations have been matched with their respective solutions as shown in the image attached below.

A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

In this exercise, you're required to match the systems of linear equations with their respective solutions as shown in the image attached below.

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Option (A) - 4 is the correct answer.

The value of x for linear equation -6x + 4x = 8 is - 4.

If a variable's maximum power constantly equals 1, the equation is considered linear equation. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. Here, A is a coefficient, B is a constant, and x is a variable.

The given equation is -6x + 4x = 8.
Simplifying the above equation.
-2x = 8
Now, dividing both sides by -2.

x = -4
Therefore the value of x in equation -6x + 4x = 8 is -4.

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I understand that the question you are looking for is " Jorge wrote the equation -6x + 4x = 8. What is the value of x?

(A) –4

(B) –2

(C) 2

(D) 4  "

Answer: (A): -4            

Step-by-step explanation:

It's the correct option.

Answer:

[tex]\textsf{1.} \quad C^{-1}(F)=\dfrac{9}{5}F+32[/tex]

2.   [-273.15, ∞)

Step-by-step explanation:

Given:

[tex]C=\dfrac{5}{9}(F-32), \quad \text{where }F \geq -459.67[/tex]

To find the inverse of the given function, make F the subject:

[tex]\begin{aligned}C & =\dfrac{5}{9}(F-32)\\\implies \dfrac{9}{5}C & =F-32\\\implies F & = \dfrac{9}{5}C+32 \end{aligned}[/tex]

[tex]\textsf{Replace the } F \textsf{ with }C^{-1}(F)\textsf{ and the }C \textsf{ with } F:[/tex] :

[tex]\implies C^{-1}(F)=\dfrac{9}{5}F+32[/tex]

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

The given domain of the function C(F) is F ≥ -459.67

Therefore, the minimum value of the function is:

[tex]\implies C(-459.67)=\dffrac{5}{9}(-459.67-32)=-273.15[/tex]

This means the range of the function C(F) is C(F) ≥ -273.15

The domain of the inverse function is the range of the function.

Therefore, the domain of the inverse function in interval notation is:  [-273.15, ∞)

Answer: -273.15

Step-by-step explanation:

Since we are dealing with a proportion, it is determined by using the z-distribution that there is insufficient evidence to draw the conclusion that the proportion of all kochia plants that are resistant to glyphosate has increased because the test statistic is less than the critical value for the right-tailed test.

In this problem, we consider that:

[tex]$H_{0}: p_{2}-p_{1}=0$[/tex]

[tex]$H_{1}: p_{2}-p_{1} \neq 0$[/tex]

The proportions and standard errors are given by:

[tex]p_{1}=0.197, s_{1}=\sqrt{\frac{0.197(0.803)}{61}}=0.0509\\p_{2}=0.385, s_{2}=\sqrt{\frac{0.385(0.615)}{52}}=0.0675[/tex]

Hence, the distribution has mean and standard error given by:

[tex]\bar{p}=p_{2}-p_{1}=0.0675-0.0509=0.0166\\s=\sqrt{s_{1}^{2}+s_{2}^{2}}=\sqrt{0.0509^{2}+0.0675^{2}}=0.0845[/tex]

It is given by:

[tex]$z=\frac{\bar{p}-p}{s}$[/tex]

In which p = 0 is the value tested at the null hypothesis, hence:

[tex]z=\frac{0.0166}{0.0845}\\$z=0.2$[/tex]

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From the given graph, we can see by tracing that f(4) is -3.5

The given graph is a graph of a quadratic function with a parabola opening upwards.

According to the question, we are to find the value of y where the value of x is 4. From the given graph, we can see by tracing that f(4) is -3.5

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Using proportions, it is found that the angular velocity at the tip of the blade is of 753.98 radians per minute.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each revolution has [tex]2\pi[/tex] radians, hence in one minute, the 120 revolutions will have a measure in radians of:

M = 120 x 2pi = 240pi = 753.98

Hence the angular velocity is of 753.98 radians per minute.

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Answer:

A.

Step-by-step explanation:

36/12 = 3

3*2 = 6 cm

48/12 = 4

4*2 = 8 cm