You invest $3000 in an account at 3.5% per year simple interest. How much will you have in the account at the beginning of the 7th year? Round your answer to the nearest whole dollar.

Answer:

Part 1) The measure of the angle is 47°

Part 2) The measure of the angle is 52°

Step-by-step explanation:

Part 1)

we know that

The inscribed angle is half that of the arc it comprises.

we have that

(12y-1)°=(9y+11)° ----> because the arc that the inscribed angles comprise is the same

Solve for y

12y-9y=11+1

3y=12

y=4°

Find the measure of the angle

(12y-1)°=12(4)-1=47°

Part 2)

we know that

The inscribed angle is half that of the arc it comprises.

we have that

2(3m+2)°=(4m+20)° ----> because the arc that the inscribed angles comprise is the same

Solve for m

6m+4=4m+20

6m-4m=20-4

2m=16

m=8

Find the measure of the angle

(4m+20)°=4(8)+20=52°

Answer:

Choice C.

Step-by-step explanation:

You already have two sides and two angles. Now you need the other two sides that include the angle. Choice C is correct.

Answer: C. [tex]\overline{SU}\cong\overline{JL}[/tex]

Step-by-step explanation:

In the given picture , we have two triangles ΔSTU and Δ JKL , in which we have

[tex]\overline{ST}\cong\overline{JK}[/tex]

[tex]\angle{S}\cong\angle{J}[/tex]

To prove ΔSTU is congruent to Δ JKL, we need [tex]\overline{SU}\cong\overline{JL}[/tex] such that [tex]\angle{S}\text{ and }\angle{J}[/tex] becomes congruent the included angles between pair of  congruent sides.

Hence, C is the right option.

Answer:

3 hours and 30 minutes

Step-by-step explanation:

Since both of these times are in the P.M., each hour has 60 minutes and 2:30 is half, add 30 minutes to get 3:00 P.M. and then add 3 hours to get 6:00 P.M. . 3 hours and 30 minutes added to 2:30 P.M. equals 6:00 P.M. :)

Answer:

3 hours and 30 minutes

Step-by-step explanation:

Kylie started basketball practice at 2:30

Kylie finished basketball practice at 6:00

Time duration = 3 hours and 30 minutes

2 : 30 → 3 : 00

( 30 minutes )

3 : 00 → 6 : 00

( 3 hours )

3 hours + 30 minutes = 3 hours and 30 minutes

Answer:

Step-by-step explanation:

Use the sum of angle formula:

  cos(a+b) = cos(a)cos(b) -sin(a)sin(b)

This gives you ...

  cos(x)cos(-π/6) -sin(x)sin(-π/6) = 1 + cos(x)cos(π/6) -sin(x)sin(π/6)

Subtracting the right-side trig function terms and factoring, we have ...

  cos(x)(cos(-π/6) -cos(π/6)) -sin(x)(sin(-π/6) -sin(π/6)) = 1

Since the cosine is an even function, cos(-π/6) = cos(π/6). Since the sine is an odd function, sin(-π/6) = -sin(π/6). This gives us ...

  cos(x)·0 -sin(x)(-2sin(π/6)) = 1

  sin(x) = 1/(2·sin(π/6)) = 1/(2·1/2) = 1

  x = arcsin(1)

  x = π/2

_____

When solving these by using a graphing calculator, it is convenient to subtract one side of the equation so you have a function of x that you want to find the zeros of. Here, we subtracted the right side. The graph shows the result is zero for x=π/2, as we know.

Answer:

20°

Step-by-step explanation:

40=2x,x=20°

Answer:

3w + 52 ≥ 90

Step-by-step explanation:

If she volunteers 3 hours per week for w weeks, then the number of hours from tutoring is 3w.  Add the 52 hours from her summer volunteering, and her total hours is 3w + 52.  This needs to be at least 90 hours for her to graduate, so:

3w + 52 ≥ 90

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Remember:

[tex](\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2[/tex]

Given the equation [tex]\sqrt{17-x}=x+3[/tex], you need to solve for the variable "x" to find its value.

You need to square both sides of the equation:

[tex](\sqrt{17-x})^2=(x+3)^2[/tex]

[tex]17-x=(x+3)^2[/tex]

Simplifying, you get:

[tex]17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0[/tex]

Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:

[tex](x-1)(x+8)=0[/tex]

Then:

[tex]x_1=1\\x_2=-8[/tex]

Let's check if the first solution is correct:

[tex]\sqrt{17-(1)}=(1)+3[/tex]

[tex]4=4[/tex] (It checks)

Let's check if the second solution is correct:

[tex]\sqrt{17-(-8)}=(-8)+3[/tex]

[tex]5\neq-5[/tex] (It does not checks)

Therefore, the solution is:

[tex]x=1[/tex]

the only solution is x = 1.

To solve the equation sqrt(17-x) = x+3, we first eliminate the square root by squaring both sides of the equation. Doing so yields:

17 - x = (x + 3)2

17 - x = x2 + 6x + 9

Next, we rearrange the equation to set it equal to zero, thus forming a quadratic equation:

x2 + 6x + 9 + x - 17 = 0

x2 + 7x - 8 = 0

Now, we factor the quadratic:

(x + 8)(x - 1) = 0

Hence, the solutions are:

x = -8

x = 1

To verify that these solutions satisfy the original equation, we perform a check by substituting them back into the original equation. However, we notice that the solution x = -8 does not work because it would result in taking the square root of a negative number, which is not possible in real numbers. So the only solution is x = 1.

Explanation of experimental and theoretical probability of rolling a 3 on a six-sided number cube.

The experimental probability of rolling a 3:

Simulate 35 rolls of a six-sided number cube to get results.

Count the number of times a 3 is rolled and calculate the experimental probability by dividing the number of 3s rolled by 35.

The theoretical probability of rolling a 3:

Theoretical probability = Number of favorable outcomes / Total number of outcomes = 1/6 (since there is 1 favorable outcome out of 6 possible outcomes).

Differences between theoretical and experimental probabilities:

Theoretical probability is based on calculations and assumptions, while experimental probability is based on actual observations. Discrepancies between the two can occur due to sample size, random variations, or errors in the simulation.

Answer:  6 nickels and 9 dimes

Step-by-step explanation:

15 coins - 3 extra dimes = 12

12 / 2 = 6

6 nickels

6 + 3 = 9 dimes

Answer: $11,250

1850 + (4/100)x = 1850 + 0.04x.

1850 + 0.04x > 2300

0.04x > 2300 - 1850

0.04x > 450

x > 450 / 0.04

x > $11,250

Answer

x> 11,250

yyyyyyyyyyyyyyyyyeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answer:

First option

x = 9.1, AB  = 16.5, CD = 14.1

Step-by-step explanation:

5 * x = 13 * 3.5

5x = 45.5

x = 9.1

AB = 3.5 + 13 = 16.5

CD = 5 + 9.1 = 14.1

The value of x and the length of each chord is x = 9.1, AB  = 16.5, CD = 14.1. Thus first option is correct.

If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.

Or

|AC| = |CB|

Let x be the measure of the length of ED.

[tex]5 \times x = 13 \times3.5\\5x = 45.5\\x = 9.1[/tex]

Therefore,

AB = 3.5 + 13 = 16.5

CD = 5 + 9.1 = 14.1

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The answer is 8......

Answer:

The answer is 8

Step-by-step explanation:

Just add the rest of the numbers and then subtract from the answer

Answer:

  72

Step-by-step explanation:

Exhaustive search shows the numbers to be 12, 24, 36. The sum of these three numbers is 72.

1)when we know x+y=90* the sine of x is equal to cosine of y , so the solution of the first is 0.6 again!

Answer:

Left diagram cos(y) = 0.6

Right diagram x = 5 makes the equation true.

Step-by-step explanation:

Left diagram

Both the sin(x) and the Cos(y) use the same side as the non hypotenuse side.

Therefore they most be equal.

So if sin(x) = 0.6, then cos(y) = 0.6

=========================

Right diagram

You can factor this to get the answer.

From the first 2 terms, take out x^2. From terms 3 and 4 take out 2.

x^2(x - 5) + 2(x - 5) = 0

Take out the common factor of (x - 5)

(x^2 +2)(x - 5)

x^2 + 2 yields a complex answer (which doesn't matter for this question)

x - 5 = 0

x = 5

Final answer:

To find the probability of drawing a four and then a five from a standard deck with replacement, multiply the probabilities of the independent events: (1/13) × (1/13) = 1/169.

Explanation:

The question involves calculating the probability of two independent events when drawing cards from a standard deck. The first event (A) is drawing a card that is a four, and the second event (B) is drawing a card that is a five. The probability of each of these events is calculated separately since the card is replaced after each draw, making the draws independent of each other.

The probability of drawing a four (P(A)) from a standard deck is 1/13, as there are four fours in a 52-card deck. Similarly, the probability of drawing a five (P(B)) is also 1/13. Since the events are independent, the combined probability is the product of the two probabilities: P(A) × P(B) = (1/13) × (1/13) = 1/169.

Answer:

(x, y) = (-20, 7), (-5, -2), (0, 3), (15, -4), (30, 5)

Step-by-step explanation:

You want 1/5x to match the x-value in the given table. To make that happen, multiply the given x by 5.

Example: when (1/5x) = -4, f(1/5x) = 7, so x = -4·5 = -20 for y = 7.

The transformation f(1/5x) is a horizontal expansion by a factor of 5, so each point of f(x) is now 5 times farther from the y-axis than it was.

The completed table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] is as follows:

x

−4

−1

0

3

6

​y

3

−2

3

7

5

To complete the table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\),[/tex] we need to substitute the given \(x\) values into the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] and calculate the corresponding \(y\) values.

The function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex]implies that we are scaling the input \(x\) by a factor of 5. This means the \(x\) values in the original table need to be multiplied by 5 to find the corresponding values for the new function. Let's calculate the values step by step:

1. For [tex]\(x = -4\):[/tex]

  [tex]\[y = f\left(\frac{1}{5}(-4)\right) = f(-0.8)\][/tex]

  Looking at the original table, when [tex]\(x = -0.8\), \(y = 3\).[/tex]

2. For [tex]\(x = -1\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(-1)\right) = f(-0.2)\][/tex]

  When [tex]\(x = -0.2\), \(y = -2\).[/tex]

3. For [tex]\(x = 0\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(0)\right) = f(0)\][/tex]

  When [tex]\(x = 0\), \(y = 3\).[/tex]

4. For [tex]\(x = 3\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(3)\right) = f(0.6)\][/tex]

  When [tex]\(x = 0.6\), \(y = 7\).[/tex]

5. For [tex]\(x = 6\):[/tex]

[tex]\[y = f\left(\frac{1}{5}(6)\right) = f(1.2)\][/tex]

  When [tex]\(x = 1.2\), \(y = 5\).[/tex]

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[tex]\bf \textit{Product to Sum Identities} \\\\sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5\theta )cos(2\theta )\implies \cfrac{1}{2}[sin(5\theta +2\theta )+sin(5\theta -2\theta )]\implies \cfrac{sin(7\theta )+sin(3\theta )}{2}[/tex]

The required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.

The product-to-sum formulae are used to represent the sum of the sine and cosine functions. These are generated from trigonometry's sum and difference formulae.

sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]

The trigonometry expression is given in the question

sin (5θ) cos (2θ)

According to  the product to sum Identities

sin A cos B = (1/2) [ sin (A + B) + sin (A - B) ]

Here A = 5θ and B = 2θ

sin (5θ) cos (2θ) = (1/2) [sin(5θ + 2θ) + sin(5θ - 2θ)]

sin (5θ) cos (2θ) = (1/2) [sin(7θ) + sin(3θ)]

sin (5θ) cos (2θ) =  [sin(7θ) + sin(3θ)] / 2

Thus, the required value of trigonometry expression is the product as a sum [sin(7θ) + sin(3θ)] / 2.

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Answer:

A

Step-by-step explanation:

Diagonals of a parallelogram bisect each other.

3x = 3

x = 1

y = x

y = 1

In a parallelogram, the parts in which each diagonal cuts the other are congruent.

This means that we must have

[tex]\begin{cases}3=3x\\x=y\end{cases}[/tex]

From the first equation we can deduce x=1, and thus y=x=1.

Answer

[tex]\frac{121}{4} \pi mm^2[/tex]

Explanation

Find the radius

11/2 = 5.5

The formula to find the area of a circle is [tex]\pi r^2[/tex]

[tex]\pi 5.5^2[/tex] = [tex]30.25\pi[/tex]

Convert number into fraction.

[tex]30.25 \rightarrow \frac{121}{4} \pi[/tex]

Area = [tex]\frac{121}{4} \pi mm^2[/tex]

Answer:

30.25π mm²

Step-by-step explanation:

The area (A) of a circle is calculated using the formula

A = πr² ← r is the radius

here diameter = 11 and radius is half of the diameter. thus

r = 5.5

A = π × 5.5² = 30.25π mm²

Final answer:

To locate the person who moved from (0, 1) with a slope of -4, we need to know the specific horizontal distance they moved. Without this, we can only say they moved downward 4 units for every 1 unit they moved to the right.

Explanation:

The student's question involves determining the position of a person who has moved along a slope on a coordinate plane. Since the individual started at the point (0, 1) and moved to the right with a slope of -4, we can assume they are moving in the negative y-direction (downward), as the negative slope indicates a decrease in y for every increase in x. The specific horizontal distance isn't given, so we cannot provide an exact new coordinate without more information. However, if we had a specific horizontal distance the person moved, we could calculate the new position using the slope (-4), which means for every 1 unit moved horizontally to the right, the person would move 4 units down.

Answer:

210.06 feet

Step-by-step explanation:

This is a classic right triangle trig problem.  The distance from the launch pad is the measure of the base of the right triangle.  The angle of elevation, 35, is the base angle (not the right angle).  How high the fireworks go up is the height of the triangle.  You have the reference angle of 35, the side adjacent to it, 300, and you're looking for the side length across from it, y.  The trig ratio that relates a reference angle to the sides opposite it and adjacent to it is the tangent ratio.  Setting that up:

[tex]tan(35)=\frac{y}{300}[/tex]

Solving for y:

y = 300 tan(35)

On your calculator in degree mode find y to be 210.06 feet.

By using basic trigonometry, specifically the tangent of the viewing angle, we can determine that the height of the fireworks when they explode is approximately 210 feet.

You are asking how to use trigonometry to find the height of the fireworks when they explode. If we combine your conditions that the launch was vertical and the viewing angle was 35°, we can use the tangent of that angle to find the height of the fireworks. The tangent of an angle in a right triangle is the opposite side (height in this case) divided by the adjacent side (distance from the launch, 300 feet in this case). So setting up the equation, we have: tan(35°) = height / 300. Solving for 'height', we get: height = 300 * tan(35°). Using a calculator, we find that tan(35°) is roughly 0.70021. Multiplying that by 300, we find that the height of the fireworks when they explode is approximately 210 feet.

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Answer:

every point will be 4 tons lower than it was

Step-by-step explanation:

26 is 4 less than 30, so the new function g(x) is ...

g(x) = f(x) -4

It is shifted down 4 units (tons) from the original function.

I know that the answer is A, however I can not answer the rest

Answer:

[tex]\$5,828.28[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$4,900\\ r=0.035\\n=2[/tex]  

substitute in the formula above  

[tex]A=\$4,900(1+\frac{0.035}{2})^{2*5}[/tex]  

[tex]A=\$4,900(1.0175)^{10}=\$5,828.28[/tex]

Answer:

5,828.28

Step-by-step explanation:

There are 252 ways to divide the 10 players into two teams of 5 without any restriction.

To determine the number of ways you can divide 10 players into two teams of 5 without any restriction,

Using the formula, C(n, k) = [tex]\frac{n!}{k!(n-k)!}[/tex]

By finding the number of ways to choose 5 players out of 10, which is the same as choosing the other 5 players who are not on the first team.

Where n = 10

k = 5

C(10, 5) = [tex]\frac{10!}{5!(10-5)!}[/tex]

C(10, 5) = [tex]\frac{10!}{5!(5)!}[/tex]

C(10, 5) = 10*9*8*7*6*5*4*3*2*1/5*4*3*2*1(5*4*3*2*1)

C(10, 5) = 30240/5*4*3*2*1

C(10, 5) = 252 ways

Therefore, there are 252 ways to divide the 10 players into two teams of 5 without any restriction.

She should expect 250 green marbles.

She has a 25 out of 40 chance of selecting a green marble each time since she is putting it back in the bag each time. 25/40 reduces to 5/8. Multiply 5/8 by 400 and you get 2000/8. Reduce the fraction to 250/1 or 250.

Answer:

100π

Step-by-step explanation:

step 1

Find the circumference

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=10\ in[/tex]

substitute

[tex]C=2\pi (10)[/tex]

[tex]C=20\pi\ in[/tex]

step 2

we know that

An object moves along a circular path and makes 5 revolutions in 1 minute

Remember that

[tex]1\ rev=2\pi r[/tex] ----> circumference of the circle

therefore

[tex]5\ rev=5(20\pi)=100\pi\frac{in}{minute} [/tex]

15/17. The value (ratio) of cos A is 15/17.

The trigonometric ratios of an acute angle are, basically, the sine, the cosine and the tangent. They are defined from an acute angle, α, of a right triangle, whose elements are the hypotenuse, the leg contiguous to the angle,  and the leg opposite the angle.

-The sine of the angle is the opposite leg divided by the hypotenuse.

-The cosine of the angle is the adjacent leg divided by the hypotenuse.

-The tangent of the angle is the opposite leg divided by the adjacent leg or, which is the same, the sine of the angle divided by the cosine of the angle.

cos A = adjacent leg/hypothenuse = BC/AC = 15/17

ANSWER

[tex]y = \sin(x) [/tex]

EXPLANATION

The trigonometric function that is zero at integral values is the sine function.

That is;

[tex]y = \sin(x) [/tex]

has x-intercepts at

[tex] n\pi[/tex]

where n is an integer.

In other words, the solution to the equation:

[tex] \sin(x) = 0[/tex]

is

[tex]x = n\pi[/tex]

where n is an integer.

Answer:

y=sin x

y=tan x

these are correct....

The mean is the average. The outlier is a number way bigger or smaller than the rest of the data. The outlier here would be 17. If you remove 17 and then find the average again, it will be smaller because all the numbers left are around the same range.

Answer: It will decrease