A circle with radius \pink{10}10start color #ff00af, 10, end color #ff00af has a sector with a central angle of \purple{\dfrac{2}{5}\pi} 5 2 ​ πstart color #9d38bd, start fraction, 2, divided by, 5, end fraction, pi, end color #9d38bd radians . What is the area of the sector? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.

Answer:

Choice B, 90

Step-by-step explanation:

Answer:

  (B) 146 feet

Step-by-step explanation:

You want to know the maximum height of a pebble whose height is described by p(t) = -16t² + 48t + 110.

We can write the equation in vertex form as follows:

  p(t) = -16(t² -3t) +110

  p(t) = -16(t² -3t +2.25) +110 +16(2.25)

  p(t) = -16(t -1.5)² +146

This shows the vertex of the quadratic curve to be (1.5, 146).

The maximum height of the pebble is 146 feet.

This statement is false because if their truth tables don't match then the analyzed statement would be false, they have to match.

The image below shows an example.

As you can observe, their truth values have to be equivalent.

Answer: 3:4

Step-by-step explanation:

If you actually divide it’ll make since , so first you want to divide the 2 , then you want to multiply the third of the two when you do that you have your answer

The standard deviation of a sample distribution, according to the central limit theorem, is equal to the population standard deviation divided by the square root of the sample size.

The central limit theorem states that when independent random variables are added, their sum tends toward a normal distribution, regardless of the shape of the original variables' distribution. This holds true under certain conditions, such as a sufficiently large sample size.

To calculate the standard deviation of a sample distribution, we divide the population standard deviation by the square root of the sample size. This adjustment accounts for the fact that as the sample size increases, the variability of the sample means decreases.

In summary, the standard deviation of a sample distribution is obtained by dividing the population standard deviation by the square root of the sample size. This relationship is based on the central limit theorem, which allows us to make inferences about a population based on a sample.

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The positive integers c, with c<100, that make the quadratic \(3x^{2} +20x+C\)have rational roots are 12 and 25.

A quadratic has rational roots if and only if its discriminant is a perfect square. The discriminant of \(3x^{2} +20x+C\) is 400−36c. For c<100, the discriminant is a perfect square if and only if \(400=36c-m^{2}\) for some integer m. This equation simplifies to \(36c=400-m^{2}\)

For c<100, the only possible values of c that satisfy this equation are c=12 and c=25.

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If the average height of two boys is 145 cm and one of the boys has a height of 140 cm, then the height of the other boy is 150 cm.

Let's denote the height of the other boy as x cm. We are given that the average height of the two boys is 145 cm.

According to the concept of average, the sum of the heights of the two boys divided by 2 should equal the average height.

So we can write the equation:

(140 cm + x cm) / 2 = 145 cm

Now, let's solve for x by multiplying both sides of the equation by 2:

140 cm + x cm = 290 cm

Subtracting 140 cm from both sides, we get:

x cm = 150 cm

Therefore, the height of the other boy is 150 cm.

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The angle x of the geometric system has a measure of 295°.

In this problem we find the case of a geometric system formed by three angles, whose sum is equal to a complete revolution, that is, a complete measure of 360°. Then, the geometric system is represented by the following mathematical equation:

x + 20° + 45° = 360°

x + 65° = 360°

x = 295°

Thus, the measure of the angle x within the geometric system is equal to 295°.

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The distances between the points are given as follows:

As these two distances are equal, point A is equidistant from the endpoints of segment BC.

The distance between points with coordinates \((x_1,y_1)\) and \((x_2,y_2)\) is given by the equation presented as follows:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Hence the distance of point A to the endpoint B is calculated as follows:

\(D = \sqrt{(7 - (-7))^2 + (0 - 8)^2} = \sqrt{260}\)

The distance of point A to the endpoint C is calculated as follows:

\(D = \sqrt{(-5 - (-7))^2 + (-8 - 8)^2} = \sqrt{260}\)

As the distance from point A to point B is equals to the distance from point A to point C, the point A is equidistant from the endpoints of segment BC.

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Answer:

3.33

Step-by-step explanation:

10(4)/12

40/12

3.33 or 3 1/3

Answer: for the first it is not direct varition while for the second one it i s

Step-by-step explanation:

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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Answer:

Step-by-step explanation:

Assuming that your salary is $1, your savings after each year would be:

End of year 1: $1 x 1.015 = $1.015

End of year 2: $1.015 x 1.015 = $1.03023

End of year 3: $1.03023 x 1.015 = $1.04586

End of year 4: $1.04586 x 1.015 = $1.06186

Therefore, after 4 years of saving your entire salary with a 1.5% increase each year, you would have approximately $1.06.

Answer:

1 gallon of gas gives an average of 20 miles, so 5 should get you about 100 depending on how fast your driving and what car you're driving.

The price per share of BBQ Corp. after there has been a stock split, or post - split, is $24. 15

When there is a stock - split, then each of outstanding shares that a company has, is divided into a number of shares that is determined by the stock split ratio.

The price of the individual shares are also divided into the same ratio as the shares.

This means that the price per share for BBQ Corp. post - split is:

= Price per share before split / 3

= 72. 45 / 3

= $24. 15

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Answer:

slope is m= y_2-y_1/x_2-x_1 and the y-intercept is where the line crosses over the x-axis

Step-by-step explanation:

fill in the points and do the equation m= rise(y points)/ run(x points)

m=slope

(x_1, y_1) =coordinates of first point in the line

(x_2, y_2)=coordinates of second point in the line

Answer:

First find out area of circle and find the A B X angle then substract Total area by ABX

Answer:

68

Step-by-step explanation:

The intercepted arc (AB) is double the inscribed angle (34)

The monthly payment for the car loan is approximately 16,216.38 pesos. The outstanding balance after 2 years is approximately 650,577.85 pesos.

To find the monthly payment for the car loan, we can use the formula for the monthly payment on a loan:

P = (r * PV) / (1 - (1 + r)^(-n))

Where:

P is the monthly payment

r is the monthly interest rate

PV is the loan amount (present value)

n is the total number of payments

In this case, the loan amount PV is 800,000 pesos, the monthly interest rate r is 7% / 12 (since the interest is compounded monthly), and the total number of payments n is 5 years * 12 months/year = 60 months.

Substituting these values into the formula, we have:

P = (0.07/12 * 800,000) / (1 - (1 + 0.07/12)^(-60))

Calculating this expression, we find that P ≈ 16,216.38 pesos.

So, the monthly payment for the car loan is approximately 16,216.38 pesos.

To find the outstanding balance after 2 years, we need to calculate the remaining balance after making monthly payments for 2 years. We can use the formula for the remaining balance on a loan:

Remaining Balance = PV * (1 + r)^n - P * ((1 + r)^n - 1) / r

Where:

PV is the loan amount (present value)

r is the monthly interest rate

n is the number of payments made

Substituting the given values into the formula, we have:

Remaining Balance = 800,000 * (1 + 0.07/12)^24 - 16,216.38 * ((1 + 0.07/12)^24 - 1) / (0.07/12)

Calculating this expression, we find that the outstanding balance after 2 years is approximately 650,577.85 pesos.

So, the outstanding balance after 2 years is approximately 650,577.85 pesos.

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The value of x from the given diagram is -6

Line is defined as the distance between two points. Given the line RP with the following measures

RP = 17

RQ = x + 14

QP = x + 15

Using the expression

RP = RQ + QP

Substitute

17 = x + 14 + x + 15

17 = 2x + 29

Determine the value of x

2x = 17 - 29
2x= -12

x = -6

Hence the value of x from the given diagram is -6

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Answer:

answer 2)  24\(\sqrt{5}\)

Step-by-step explanation:

after the dilation pt D is (8,-32)

after the dilation pt E is (-16,16)

if you use the distance formula for these two points you get \(\sqrt{2880}\) which simplifies to 24\(\sqrt{5}\)

To find the value of K, we start by analyzing the given equations and the properties of the graph of the function f(x).

From the equation 2(α - 1)^3 + 3(α - 1)^2 + 6α = 0, we can simplify and solve for α:

2α^3 - 6α^2 + 6α - 2 + 3α^2 - 6α + 3 + 6α = 0

2α^3 - 3α^2 + 3 = 0

Similarly, from the equation 2(1 - ß)^3 + 3(1 - ß)^2 - 6ß + 12 = 0, we can simplify and solve for ß:

2 - 6ß + 6ß^2 - 2ß^3 + 3 - 6ß + 12 = 0

-2ß^3 + 6ß^2 - 12ß + 17 = 0

Since α ≠ ß, these equations represent two different values for α and ß.

Next, we are given that the graph of y = f(x) is symmetric about the point (1, 0). This means that if (x, y) is a point on the graph, then (2 - x, y) is also a point on the graph. In other words, the function f(x) satisfies the symmetry property:

f(2 - x) = f(x)

Now, let's consider the integral ∫α ß f(x) dx. Since the graph of f(x) is symmetric about (1, 0), we can rewrite the integral as:

∫α ß f(x) dx = ∫1 α f(x) dx + ∫1 ß f(x) dx

Using the symmetry property, we can rewrite the second integral as:

∫1 ß f(x) dx = ∫1 2-ß f(x) dx

Combining the two integrals, we have:

∫α ß f(x) dx = ∫1 α f(x) dx + ∫1 2-ß f(x) dx

Now, if we let K = ∫1 2 f(x) dx, we can rewrite the above equation as:

∫α ß f(x) dx = ∫1 α f(x) dx + ∫1 2 f(x) dx - ∫2-ß 1 f(x) dx

Since the graph of f(x) is symmetric about (1, 0), the integral ∫2-ß 1 f(x) dx is equal to ∫1 2 f(x) dx. Therefore, we can simplify the equation further:

∫α ß f(x) dx = ∫1 α f(x) dx + ∫1 2 f(x) dx - ∫2-ß 1 f(x) dx

∫α ß f(x) dx = ∫1 α f(x) dx + ∫1 2 f(x) dx - ∫1 2 f(x) dx

∫α ß f(x) dx = ∫1 α f(x) dx

Since ∫α ß f(x) dx = K(α + ß), we can equate it to ∫1 α f(x) dx:

K(α + ß) = ∫1 α f(x) dx

Now, to find the value of K, we need to solve this equation for K. It depends on the specific form of the function f(x) and the limits of integration α and 1.

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Sarah's charges per hour for working during the week will be $9.5.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.

Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be

45x + 5y = 902.5           ...1

50x + 10y = 1045

25x + 5y = 522.5          ...2

Subtract equation 2 from equation 1, then we have

45x - 25x = 902.5 - 522.5

20x = 380

x = 19

And the value of y will be

25 (19) + 5y = 522.5

475 + 5y = 522.5

5y = 47.5

y = 9.5

Sarah's charges per hour for working during the week will be $9.5.

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the magnitude of the resultant is \(\sqrt{2}\) times the magnitude of each individual vector, not one-third.

No, that is incorrect. The magnitude of the resultant of three vectors having equal magnitudes and making an angle of 120 degrees with each other is not one-third the magnitude of the component vectors.

The magnitude of the resultant of three vectors depends on the angle between them, as well as their magnitudes. In general, the magnitude of the resultant of three vectors can be calculated using the law of cosines, which states that the square of the magnitude of the resultant (R^2) is equal to the sum of the squares of the magnitudes of the individual vectors (\(A^2, B^2, and C^2\)), plus twice the product of the magnitudes of two of the vectors multiplied by the cosine of the angle between them.

For three vectors of equal magnitude (A = B = C = m), the magnitude of the resultant can be calculated as:

\(R^2 = 3m^2 + 2m^2 * cos(120) = 3m^2 - m^2 = 2m^2\)

\(R = \sqrt{2} * m\)

Therefore, the magnitude of the resultant is sqrt(2) times the magnitude of each individual vector, not one-third.

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Question: Three Vectors Have Equal Magnitudes And Make 120° With Each Other. We Can Say That The Magnitude Of The Resultant Is One-Third The Magnitude Of The Component Vectors. The Resultant Is Zero. The Magnitude Of The Resultant Is Equal To The Magnitude Of The Component Vectors. The Magnitude Of The Resultant Is More Than Three Times The Magnitude Of Each component Vector.

Answer

(2x⁵ – 3x⁴ + 7) - (-x⁵ - 3x⁴ - 3)​ = 3x⁵ + 10

Explanation

We are asked to simplify the equation

(2x⁵ – 3x⁴ + 7) - (-x⁵ - 3x⁴ - 3)​

To do this, we will first open the brackets, then we will simplify further by adding or subtracting like terms.

(2x⁵ – 3x⁴ + 7) - (-x⁵ - 3x⁴ - 3)​

= 2x⁵ – 3x⁴ + 7 + x⁵ + 3x⁴ + 3

​= 2x⁵ + x⁵ - 3x⁴ + 3x⁴ + 7 + 3

= 3x⁵ + 0x⁴ + 10

= 3x⁵ + 10

Hope this Helps!!!

(5/8) ÷ (15/16) + (1/2)

To do this, we will use the order of operation pnemonic, PEMDAS

And in that order of operations, division comes before the addition is done.

So, we solve the first part first

(5/8) ÷ (15/16)

= (5/8) × (16/15)

= (80/120)

= (2/3)

(5/8) ÷ (15/16) + (1/2)

= (2/3) + (1/2)

We take LCM of the denominators first

(2/3) + (1/2) = (7/6)

(5/8) ÷ (15/16) + (1/2) = (7/6)

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The T - Test is the appropriate test for a comparison a group of 10 dogs and group of 10 cats.

According to the statement

we have to explain and tell bout the those test which is appropriate for the comparison of the group of 10 dogs and group of 10 cats.

So, For this purpose, we know that the

The test used on this are the those test for the applicable on th etwo groups.

So, We know that the

A t-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.

here the t test is used for the two samples.

So, The T - Test is the appropriate test for a comparison a group of 10 dogs and group of 10 cats.

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