Blake is going to invest in an account paying an interest rate of 3% compounded annually. How much would Blake need to invest, to the nearest ten dollars, for the value of the account to reach $83,000 in 16 years?

\( \sqrt{147} \\ = \sqrt{3 \times 7 \times 7} \\ = 7 \sqrt{3} \)

Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

The trigonometric expression sin x = 3/5 can be used to find the value of x, and a = 0.6 for the expression x = sin⁻¹(a).

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We use the trigonometric ratio of sine of the angle x, so that we make x the subject by finding the sine inverse of the fraction of the opposite side and the hypotenuse as follows:

sin x = 3/5

x = sin⁻¹(0.6)

x = 36.8699

Therefore, the trigonometric expression sin x = 3/5 can be used to find the value of x, and a = 0.6 for the expression x = sin⁻¹(a).

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The required function y = 7 cos (2π * 0.1 * x) and period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

he cosine function can be used to model periodic motion, and its general form is:

y = A cos (Bx + C) + D

where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

In this case, we know that a 14 in. wave occurs every 10 s, so we can use this information to find the frequency, which is the reciprocal of the period. The period is the time it takes for one complete cycle of the wave, which in this case is 10 s.

Therefore, the frequency is:

\(f = \frac{1}{T}=\frac{1}{10} = 0.1 Hz\)

We can also see that the amplitude of the wave is 7 inches, since the wave has a height of 14 inches from its highest point to its lowest point.

Now we can write the function that models the height of the particle in inches y as it moves in seconds x:

y = 7 cos (2π * 0.1 * x)

Here, the frequency is expressed in radians per second (2π * 0.1 = 0.2π), since the cosine function takes radians as its argument. The phase shift and vertical shift are both zero in this case, since the wave starts at its highest point and has no vertical shift.

Therefore, the period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

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Answer:

A.

Step-by-step explanation:

Give the data set: 2, 4, 6, 8, 10, 12.

Find the following:

Min, Q1, Median, Q3, and Max.

Min. = 2

Q1 = 4

Median = (6+8)/2 = 7

Q3 = 10

Max = 12

Check the box plot to see which one represents these values above.

Thus:

The correct box plot would have the whisker to your left at 2, representing the min value.

The Q1 would be at represented by the beginning box the edge of the rectangular box that starts at 4.

The median would be represented by the vertical line that divides the box which would be on 7.

The Q3 would be on the end of the box which is at 10.

The max would be represented by the other whisker that goes to our right, representing 12.

The box plot is that represents this data is the box plot given in option A.

Answer:

0.66 melones por niño o 2/3

Step-by-step explanation:

10/15=2/3=0.66

Answer:

X is the midpoint of the line wxy

The length of XY is 17 units.

Used the concept;

A mid-point of a line segment;

Since, X is the mid-point of WY

Hence, WX = XY

And, WX =  WY and XY =  WY

Here, we have;

WX = 3x - 1

WY = 10x - 26

So, By using the rule WX =  WY

3x - 1 =  (10x - 26)

Simplify the right-hand side

3x - 1 = 5x - 13

Add 1 to both sides

3x = 5x - 12

Subtract 5x from both sides

- 2x = -12

Divide both sides by -2

x = 6

Since, XY = WX

And, WX = 3x - 1

So, XY = 3x - 1

Substitute the value of x in the expression of XY

XY = 3(6) - 1

XY = 18 - 1

XY = 17 units

So, The length of XY is 17 units

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The correct and complete question is,

If X is the midpoint of WY, WX = 3x - 1 and WY = 10x – 26, find XY.

Answer:

8/19

Step-by-step explanation:

The probability that a student is chosen randomly from the class passed the test and completed the homework will be 0.1637.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

In a math class with 19 students, a test was given the same day that an assignment was due.

There were 10 students who passed the test and 11 students who completed the assignment.

There were 6 students who failed the test and also did not complete the assignment.

Then the probability that a student is chosen randomly from the class passed the test and completed the homework will be

The number of the student who has done at least one assignment or passed the test is 19 - 6 = 13

n(A) = passes student

n(B) = given assignment

Then we have

\(\rm n(A \cap B) = n(A) + n(B) - n(A \cup B) \\\\n(A \cap B) = 10 + 11 - 13\\\\n(A \cap B) = 8\)

Then the probability will be

\(\rm P = \dfrac{^8C_2}{^{19}C_2}\\\\P = \dfrac{28}{171}\\\\P = 0.1637\)

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The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

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If circle with center N with m∠MNP=124 ∘ and MN=13,  the area of sector MNP is approximately equal to 194.86 square units.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360°) x πr²

Where r is the radius of the circle.

In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:

Area of sector = (124/360) x π(13)²

Area of sector ≈ 194.86

Therefore, the area of sector MNP is approximately equal to 194.86 square units.

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The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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Answer:

jjjjjiii

5

Step-by-step explanation:

2.5x+1.5 × 4 = 36

so the area = 36

which means that (2.5x + 1.5) X 4 = 36

so then you need to cancel out things on the left, by that I mean, to get rid of the x4 you must ÷4 on each side

2.5x + 1.5= 9

2.5x= 7.5

x= 3

Hope that helps

Answer:

The price of a fruit bowl at the cafe is $3

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Got it right

Given

no. of coins = 42

worth of coins = $5.90

Find

number of nickels

Explanation

The number of quaters is 42 - x

0.05x + 0.25(42 - x) = 5.9

-0.2x + 10.5 = 5.9

-0.2x = -4.6

x = 23

Final Answer

Number of Nickels, x = 23

[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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The area of the region inside the inner loop is 4.5π

Using the formula A = 1/2 ∫[a,b] r^2(θ) dθ. In the case of the limaçon's inner loop, a has been set as 0, b is equal to π, and r equals 3 - 6 cosθ. Together, these values give us the following equation expression for the area:

A = 1/2 ∫[0,π] (3 - 6 cosθ)^2 dθ

= 1/2 ∫[0,π] (9 - 36 cosθ + 36 cos^2θ) dθ

= 1/2 [9θ - 36 sinθ + 12 sin(2θ)]|[0,π]

= 1/2 [9π]

= 45π

Therefore, the area of the inner loop in this instance is calculated as 4.5π.

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I Hope This Helps!

Answer

= 4.5π

ANSWER: 480 out of 1200 were taken at the Honolulu Zoo.

Answer:15/2+3=15/5=3

Step-by-step explanation:

the answer is 3 since (2+3) equals to 5 and 15 divided by 5 equals 3

Answer:

In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.

To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.

Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.

Answer:

its the first one or the last one

Step-by-step explanation:

i got the same thing on the graph sry

Answer:

Step-by-step explanation:

Answer:4.8

Step-by-step explanation:

30/3 x 1.6

Answer:

The first picture/20 cans = 1 dollar

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

The time taken to reaches its maximum height is 3s.

In the question,

It is given that,

Height, h(t) = \(96t - 16t^{2}\)

The maximum value of the function is obtained if the first derivative of the function h (t) = 0.

\(\frac{dh(t)}{dt} = 96 - 32t = 0\)

⇒ \(t = 3\)

So, time taken to reach its max height is 3 seconds.

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Answer:

40x+24y-56=

8(5x+2y-7)

Step-by-step explanation:

what does it read????

i want to answer the question but i dont have any information

C.) The independence of the two ice machines means that knowing how much one machine fills does not help us predict how much the other fills.