The measures of the exterior angles of an octagon are
�
°
x°,
2
�
°
2x°,
4
�
°
4x°,
5
�
°
5x°,
6
�
°
6x°,
8
�
°
8x°,
9
�
°
9x°, and
10
�
°
10x°. Solve for
�
x.

Answer:

  100°

Step-by-step explanation:

You want the missing arc measure in the geometry where two chords cross at 85° and they intercept one arc of measure 70°.

The angle where chords cross is the average of the two arcs that they intercept. Here, that means ...

  85° = (AE +BC)/2

Solving for BC, we get ...

  2(85°) = AE +BC

  BC = 170° -AE = 100°

The missing arc measure is 100°.

The zeros of the polynomial are -5i, √5i, -√5i.

The given polynomial is: f(x)=x⁴+16x²-225.

Zeros of a polynomial are the values of x that make the polynomial equal to zero. These will be the x-intercepts of the polynomial's graph. To find the zeros of a polynomial, use the factored form of the polynomial and set each factor equal to zero. The solutions of this equation are the zeros of the polynomial.

The given zero is: -5i

To find the remaining zeros of the polynomial, we need to factor the polynomial.

We can factorize the polynomial as:

f(x) = (x² + 5i)(x² - 5i)

Finding Zeros:

Therefore, the remaining zeros of the polynomial are:

x = ±√5i

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The number of lbs in 15. oz is 9 3/8 lb

A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.

lb and oz are both units of weight of a substance.

1 oz = 0.0625 lb

therefore 1 oz = 625/1000

= 25/40 lb

15 oz = 25/40 × 15

= 75/8 lb

= 9 3/8 lb

therefore the number of lbs in 15 oz is 9 3/8 lb

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The shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population is approximately Normal

If the amount of orange juice that can be obtained from a single orange is Normally distributed, then the distribution of the sample mean of orange juice obtained from a sample of size 5 from this population will also be Normally distributed.

The mean of the sample mean distribution will be equal to the population mean, which is the mean amount of orange juice that can be obtained from a single orange.

The standard deviation of the sample mean distribution, also known as the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size.

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The given question is incomplete, the complete question is:

The amount of orange juice that can be obtained from a single orange is Normally distributed. A manufacturing company selects an SRS of size n = 5 from the population of all oranges in their inventory and calculates the sample mean amount of orange juice that is obtained. What is the shape of the distribution of the sample mean for all possible simple random samples of size 5 from this population?

The future value of the investment after 6 years is $14,370.88; while the effective annual interest rate is 2.56%.

To calculate the future value of the investment, we can use the formula: FV = PV (1 + r/n)^(nt), where FV is the future value, PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, PV = $12,000, r = 0.025, n = 12 (compounded monthly), and t = 6.

Plugging these values into the formula, we get:

FV = $12,000 (1 + 0.025/12)^(12*6)

FV = $12,000 (1.002083333)^72

FV = $14,370.88

Therefore, the future value of the investment after 6 years is $14,370.88.

To calculate the effective annual interest rate, we can use the formula: EAR = (1 + r/n)^(n) - 1, where r is the annual interest rate and n is the number of times the interest is compounded per year.

In this case, r = 0.025 and n = 12 (compounded monthly).

Plugging these values into the formula, we get:

EAR = (1 + 0.025/12)^(12) - 1

EAR = (1.002083333)^12 - 1

EAR = 0.02568245

Therefore, the effective annual interest rate is 2.568245%.

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Answer:      a. 8.4 meters       b. 14 wreaths

Step-by-step explanation:

The following equation shows the problem, with x representing the number of wreaths made:

12 = 9(0.4) + 0.6x

To answer a, get 0.6x alone:

12 = 9(0.4) + 0.6x

12 = 3.6 + 0.6x

8.4 = 0.6x

There were 8.4 meters available to make wreaths

To answer b, get x alone

8.4 = 0.6x

14 = x

Diego could make 14 wreaths with the available ribbon

Hope this helps!

In linear equation, 2000 pupils are there in the school.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

= 540/27%

= 54000/27

= 2000

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Answer:

<HDG = 39°

Step-by-step explanation:

Red square is a right angle which mean its a 90°

Those two angle <CDG and <HDG are complementary angle which mean they both add up to 90°

<CDG + <HDG = 90°

51° + (3t+15)° = 90°

Solve for t.

3t + 51 + 15 = 90°

3t + 66 = 90°

3t = 24

t = 8

Plug t = 8 into <HDG to find the measurement.

<HDG = 3t + 15

<HDG = 3*8 + 15

<HDG = 24 + 15

<HDG = 39°

The annual interest rate.

To find the annual interest rate r that will allow your balance to reach $2000 in 10 years, we need to use the formula for continuously compounded interest: A = Pert, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

We are given that P = $1000, A = $2000, and t = 10 years. Plugging these values into the formula, we get:

$2000 = $1000e10r

Dividing both sides by $1000, we get:

2 = e10r

Taking the natural logarithm of both sides, we get:

ln(2) = 10r

Dividing both sides by 10, we get:

r = ln(2)/10 ≈ 0.0693

Therefore, the annual interest rate r that will allow your balance to reach $2000 in 10 years is approximately 6.93%.

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The vertical asymptote(s) for R(x) is x=1 and x=-2. The horizontal asymptote(s) is y=0.

To find the vertical asymptotes, we look at each factor and look for any x-values that would make the factor equal to zero.

The factors are (2x+6), (x-1), (4-x), and (x+2).

So, x=1 would make (x-1) equal to zero and x=-2 would make (x+2) equal to zero.

To find the horizontal asymptote, we look at the degree of the highest exponent and divide it into the coefficient of the term with the highest degree.

Since the highest exponent is 1 and there is no coefficient, the answer is y=0.

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The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3)

The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

The commutative property of addition states that the order of the numbers does not matter when adding them together.

In this equation, the numbers are rearranged but the result is still the same. This is because the commutative property of addition allows for the numbers to be added in any order and still have the same result.

Here is the step-by-step explanation:

Identify the commutative property of addition, which states that a+b=b+a.

Look at the given equations and see which one follows the commutative property of addition.

The equation (1+2)+3=1+(2+3) follows the commutative property of addition because the numbers are rearranged but the result is still the same.

Therefore, the equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

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cost = 3/√34,  csct = √34/5, sect =√34/3 , and cott = 3/5

explanation:-

The given equation is: tant = 5/3, so, cot t = 3/5 as cot t= 1/tan t

we know sec² t - tan² t = 1

or, sec²t= 1 + tan²t = 1+(25/9) = 34/9

or, sect = √(34/9) = √34/3

or, cos t=√(9/34) = 3/√34 as cos t= 1/sec t

now, also, csc²t - cot²t = 1

or, csc²t = 1+cot²t = 1+ 9/25 = 34/25

or, csc t= √34/5

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Based on the information, we can infer that the surface area of the pyramid is: 105 inches²

To find the surface area of the pyramids we must perform the following procedure:

We must find the surface of each of the faces and the base.

According to this procedure, each face of the pyramid measures 20 inches². Then we must multiply this value by the number of faces of the pyramid (4).

We must add the surfaces of the faces and the base.

According to the above, the surface area of the pyramid would be 105 inches².

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A package that weighs 5 pounds will cost $15 for both options.

The equation can be used to symbolize the price, y: Y is equal to 5 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $15, which is represented by the equation y = 15, in order to send the package.

We'll compare the equation as a whole.

In this case,

5 + 2x = 15

Compile similar terms,

2x = 15 - 5

2x = 10

x = 10 / 2

x = 5

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The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 are r = -8 and r = 3.

The two real roots of the polynomial function S(r) = r^(5) + 5r^(4) - 7r^(3) - 43r^(2) - 8r - 48 can be found by factoring the polynomial and finding the values of r that make the function equal to zero.

First, we can factor the polynomial using the Rational Root Theorem, which states that if a polynomial has rational roots, they must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

In this case, the constant term is -48 and the leading coefficient is 1, so the possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, and ±48.

We can use synthetic division to test these possible roots and find the ones that make the function equal to zero. After testing the possible roots, we find that the two real roots are r = -8 and r = 3.

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Answer:

To determine who has a greater mean, we need to calculate the mean (average) number of miles ridden by Liz and Sara and compare them.

Day Liz Sara

1 7 6

2 12 8

3 10 5

4 8 10

5 5 7

To find the mean for Liz, we add up the miles she rode and divide by the number of days:

Mean for Liz = (7 + 12 + 10 + 8 + 5) / 5 = 8.4 miles per day

To find the mean for Sara, we add up the miles she rode and divide by the number of days:

Mean for Sara = (6 + 8 + 5 + 10 + 7) / 5 = 7.2 miles per day

Therefore, Liz has a greater mean than Sara by 1.2 miles per day (8.4 - 7.2 = 1.2).

shirt by sza and fav singer ariana grande!

thanks so much!

Answer:

Love The Way You Lie - Eminem

Using dilation, the scale factor here is 2,

X' = (2,2)

Y' = (4,4)

Z' = (6,0)

A thing must be scaled down or altered during the dilation process. It is a transformation that reduces or enlarges the objects using the supplied scale factor. The pre-image is the original figure, while the image is the new figure that emerges via dilatation. Two types of dilation exist:

Expansion describes an increase in an object's size.

Reduction in size is referred to as contraction.

In the given question,

The scale factor here is 2.

So, the new dilated triangle will be:

X' = (2,2)

Y' = (4,4)

Z' = (6,0)

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Answer:

not a function

Step-by-step explanation:

Answer:

not a function

Step-by-step explanation:

Answer:

5.5, 6, and 7.25

Step-by-step explanation:

3 numbers equal 18.75 tells us:

a + b + c = 18.75, where a, b, and c are the 3 unknown numbers respectively.

Next, we know that the range is 1.75. Let us consider that c is the greatest value and a is the smallest value. Thus, we can write

c - a = 1.75

Lastly, we know that there is a median of 6. This tells us that the "middle" number (which in this case would be b if c is greatest and a is smallest) should be 6.

b = 6.

Substituting we can write,

a + c + 6 = 18.75

a + c = 12.75

Also,

c - a = 1.75

c = a + 1.75

Substituting back into the other equation we get,

a + ( a + 1.75) = 12.75

2a + 1.75 = 12.75

2a = 11

a = 5.5

Now, we can find the last number.

c = (5.5) + 1.75

c = 7.25

Plug all 3 numbers back into the original equation to verify if our numbers are correct:

5.5 + 6 + 7.25 = 18.75

Thus, we know we are correct.

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The response is A.

Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.

The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range may alternatively be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

from the question:

According to the information provided, the number of pupils in each class might range from 9+6 = 15 to 9+6 = 3. Because the maximum value exceeds 15, options C and D cannot accurately represent the number of students in the classes.

Option A's median value is 9, and its range is 13, therefore the smallest value is 9-6, which equals 3, and the greatest value is 9+6, which equals 15. This information is accurately represented by the box-and-whisker plot in option A.

Option B's median value is 9, but its range (from 9-5 = 4 to 9+5 = 14) is only 11, which is less than the range that could be achieved by the number of students. As a result, option B cannot accurately reflect the number of students enrolled in each class.

Thus, the response is A.

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Answer:

4√5

Step-by-step explanation:

To simplify √20+√45-√5, we need to look for factors that can be simplified under the square root. We can simplify 20 and 45 by factoring out perfect squares:

√20 + √45 - √5 = √(4×5) + √(9×5) - √5

= 2√5 + 3√5 - √5

= 4√5

Therefore, the simplest form of the expression is 4√5

Answer:

Proof:

Using the given information, we know that PQ is approximately equal to QS and QS is exactly equal to ST.

Since a value that is approximately equal to another value can be treated as equal in many cases, we can say that PQ is roughly equal to ST.

To prove that PQ is exactly equal to ST, we must use the transitive property of equality.

Transitive Property of Equality: If a = b and b = c, then a = c.

Using the transitive property, we can say:

PQ ≈ QS and QS = ST → PQ ≈ ST

Since PQ is approximately equal to ST and they have the same units of measurement, we can round the values to the same number of decimal places and say:

PQ ≈ ST ≈ rounded value

Therefore, PQ is exactly equal to ST because they have the same rounded value.

NO, the ordered pair (9,2) is not the solution to the system 8x-4y=64 3y=6x-47.

The given ordered pair is (9,2) and the system of equations is:

8x-4y=64
3y=6x-47

To determine whether the given ordered pair is a solution to the system, we can substitute the values of x and y into the equations and see if they are true.

For the first equation:

8(9)-4(2)=64
72-8=64
64=64

For the second equation:

3(2)=6(9)-47
6=54-47
6=7

The first equation is true, but the second equation is not true. Therefore, the given ordered pair is not a solution to the system.

The final answer is: No, the given ordered pair is not a solution to the system.

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The base and height of the parallelogram is B = 16 cm and H = 48 cm

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the area of the parallelogram be represented as A

Now , area of parallelogram A = bh

And , base of a parallelogram is one third its height

So , B = ( 1/3 )H

And , area of parallelogram is A = 768 cm²

On simplifying , we get

768 = ( 1/3 )H²

Multiply by 3 on both sides , we get

H² = 2304

Taking square roots on both sides , we get

H = 48 cm

So , the height of the parallelogram is 48 cm

And , the base of the parallelogram is 16 cm

Hence , the base and height of the parallelogram are 16 cm and 48 cm respectively

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The best forecast is the one with the lowest MSE level. In this case, the "3 Month Moving Average" has the lowest MSE level of 2.1, making it the best forecast. Therefore, the correct answer is B. 3 Month Moving Average.

One common metric used to compare forecasting methods is the Mean Squared Error (MSE). The MSE measures the average squared difference between the actual values and the forecasted values, so a lower MSE indicates a better fit.

In this case, we have four different forecasting methods and their respective MSE values. The 3 Month Moving Average has the lowest MSE of 2.1, which suggests it is the best forecasting method among the four options.

Thus, the answer is B. 3 Month Moving Average.

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The investment οf $1,000 will be wοrth $1,225.04 after 3 years.

Cοmpοund interest is interest οn the principal amοunt οr lοan which is calculated accοrding tο the number οf cοmpοunds in οne year.

In this, the interest earned in each periοd is based οn the tοtal amοunt, which includes bοth the principal and the accumulated interest.

The fοrmula used fοr cοmpοund interest is

Here we have

The principal amοunt is $ 1000

The annual interest rate here is 7.5%  

The interest is cοmpounded annually.

The time periοd is 3 years  

Using the fοrmula,

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

A = 1,000 (1 + 0.075/1)⁽¹⁽³⁾⁾

= 1,000 (1.075)³

= $1,225.04  

Therefοre,

The investment of $1,000 will be wοrth $1,225.04 after 3 years.

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The answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.

The given expressions are f(x) = 3√x and g(x) = 2x. We need to find the following expressions: (a) (fog)(4) (b) (gof)(2) (c) (f of)(1) (d) (gog)(0)

(a) (fog)(4) = f(g(4)) = f(2(4)) = f(8) = 3√8 = 3√(4*2) = 3√4 * √2 = 3*2*√2 = 6√2

(b) (gof)(2) = g(f(2)) = g(3√2) = 2(3√2) = 6√2

(c) (f of)(1) = f(f(1)) = f(3√1) = f(3) = 3√3

(d) (gog)(0) = g(g(0)) = g(2(0)) = g(0) = 2(0) = 0

Therefore, the answers are (a) (fog)(4) = 6√2, (b) (gof)(2) = 6√2, (c) (f of)(1) = 3√3, and (d) (gog)(0) = 0.

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Answer:

dddiejehehegeheheheh