2. Find the length of the arc shown in red. Leave
your answer in terms of pi.

A) 1.5 pi cm
B) 2.5 pi cm
C) 3.5 pi cm
D) 4.5 pi cm

Answer:

3

Step-by-step explanation:

3 is not a factor of 16.

Is that a valid answer? lol

Hi there!

First of all, let's determine the factors of 16.

Remember, a factor is a number that a number can be evenly divided by.

Example: 5 is a factor of 10, because 10 can be evenly divided by 5.

So, the factors of 16 are:

1, 2, 4, 8, and 16.

Now, there's an infinite amount of numbers that are not factors of 16. Here are some of them:

3, 5,7,9, 10,11, 12, 13, 14, 15...

Hope it helps.

Feel free to ask if you have any doubts.

\(\bf{-MistySparkles^**^*\)

Answer:

y=x^2 +10x+6 should be the answer

Step-by-step explanation:

Answer:

7. 32

8. 68

9. 16

10. 29

Step-by-step explanation:

7. =90°-58

=32

8. =68°

9. = (1 + 5x)°

= (1 + 5(16)°

=81

10. = (2x + 3)°

= (2(29) + 3)°

= 61°

Answer:

4401.05

Step-by-step explanation:

simplified 4400+210/200

The P-value is greater than the level of significance of 0.05, we fail to reject the null hypothesis and conclude that there is: not enough evidence to suggest that the population mean of tree-ring dates is different from 1284 A.D. at the 5% level of significance.

(a) The sample mean is x = 1271.8 A.D. and the sample standard deviation is s = 35.8 yr.

(b) To test whether the population mean of tree-ring dates is different from 1284 A.D., we can use a one-sample t-test with the null hypothesis H0: μ = 1284 and the alternative hypothesis Ha: μ ≠ 1284, where μ is the population mean of tree-ring dates. Using a calculator or a t-table, the sample test statistic is calculated as:

t = (x - μ) / (s / √n) = (1271.8 - 1284) / (35.8 / √10) = -1.263

(c) The P-value for this test is the probability of obtaining a sample mean as extreme or more extreme than 1271.8 if the null hypothesis is true. Since this is a two-tailed test and the calculated t-value is negative, we need to find the area in the left tail and right tail of the t-distribution with 9 degrees of freedom.

From a t-table or using a calculator, we find the area in the left tail to be 0.1295 and the area in the right tail to be 0.1295. Therefore, the P-value is the sum of the two tail probabilities, which is P = 2 × 0.1295 = 0.259.

Since the P-value is greater than the level of significance of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the population mean of tree-ring dates is different from 1284 A.D. at the 5% level of significance.

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Complete question:

Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of prehistoric Indian ruins in the southwestern United States. Suppose it is thought that a certain pueblo was occupied around 1284 A.D. (based on evidence from potsherds and stone tools). The following data give tree-ring dates (A.D.) from adjacent archaeological sites:

1189 1267 1268 1275 1275 1271 1272 1316 1317 1230

(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to one decimal place.)

x = A.D.

s = yr

(ii) Assuming the tree-ring dates in this excavation area follow a distribution that is approximately normal, does this information indicate that the population mean of tree-ring dates in the area is different from (either higher or lower than) 1284 A.D.? Use a 5% level of significance.

(a) What is the level of significance?

(b) What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find the P-value. (Round your answer to four decimal places.)

(a)i. Evaluating the constant:

\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)

Therefore, the probability density function is:

\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:

From the graph, it is observed that the density function is skewed to the left.

(b)i. The mean:

\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)

ii. The second moment about the origin:

\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)

Therefore, the variance is:

\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)

iii. The standard deviation:

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)

i. The cumulative distribution function:

\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)

ii. The probability density function can be obtained by differentiating the cumulative distribution function:

\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)

iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)

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Answer:

4

Step-by-step explanation:

Let the number = x

Added to 11 = 11+x

Multiply result by 3 = 3(11+x)

Final result = 45

Solving

3(11 + x) =45

33 +3x = 45

3x= 45-33

3x=12

X=4 by dividing both side by 3

Step-by-step explanation:

1.

2.

3.

4.

5.

6.  This seems a typo... 460 is likely $60

Answer:

Step-by-step explanation:

150/50 using rise over run for the slope

The slope is 3 meaning for every pound the handling fee goes up in 3 dollars

In 1320 ways can a president, vice-president, and secretary be chosen from a club with 12 members. Number of ways can be calculated by using permutation.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

A permutation is a mathematical procedure that counts all possible arrangements of a given set in which the arrangement's order matters.

President can be choose in 12 ways

Vice-president can be choose in 11 ways

Secretary can be choose in 10 ways

Total number of ways = 12 ×11×10=1320

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It should be noted that mathematics is multicultural. This implies that mathematics applies to different cultures.

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Answer:

a² + 5a - 8

Step-by-step explanation:

If the construction paper has a length of a² + 7a - 3, and Katelyn cut a piece 2a + 5 long, the amount of construction paper that would be left is,

a² + 7a - 3 - (2a + 5)

= a² + 7a - 3 - 2a - 5

collecting like terms, we have

= a² + 7a - 2a - 3 - 5

simplifying, we have

= a² + 5a - 8

You cannot compare two marginal distributions to see if the corresponding two are related . So, the statement is false .

The answer to the stated question is false . No , you cannot compare two marginal distributions to see if the corresponding two variables are related.

The given question is related to probability and statistics.

Coming to probability distribution , it is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events.

The marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables.

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The total output of 15 workers will be 105 units per day.Work and time are correlated so using this we could solve the question.

What is work and time?

Time is the duration of any activity or work that occurs or continues.

Work is a task or set of activities designed to achieve a specific result.

Main Body:

This can be done by simply multiplying both number of days and total work in one day.Hence the equation become:

total output = total workers*total work done by one person.

Total output = 7*15

hence,total output = 105 units

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Answer:

77

Step-by-step explanation:

We Know

30% of r = 33

Find 1% by taking

33 / 30 = 1.1

What is 70% of R?

We take

1.1 x 70 = 77

So, 70% of R is 77

The question requires to first find the value of R by solving the equation (0.30*R = 33). Then, calculate 70% of R by multiplying the found R value with 0.70.

The question tells us that 30% of R equals 33. To find the value of R, we can set up an equation where 0.30 (which is 30% in decimal form) times R equals 33. Dividing both sides of the equation by 0.30 will give us the value for R. Once we have found R, we can then find 70% of R by multiplying R by 0.70 (70% in decimal form).

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The value of x corresponds to option B: 10.5 as the figure provided has two congruent figures inside it.

From the given image, we can consider that that the two triangles- one for which side x is given, and another for which measurements of both sides are given- are congruent. This is because they both have one common side and one angle equal to another at a vertex (refer image).

Thus, we have:

(x / 19.3) = (3.9 / 7.2)

Then, attempting to find the value of x we have:

x = (3.9 / 7.2) × (19.3)

= 10.5

Therefore, option B gives the measure of the side x of the given triangle, where x = 10.5.

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Answer:

Step-by-step explanation:

we will use ratio

magazines : cost

4 : $15

16 : $60

we will multiply 4 by 4 and 15 also by 4 so 16 magazines will cost $60

The cost of 16 magazines is $22.5.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Isabel bought 4 magazines for a total of $15.

The unit rate of the magazines,

= 15/4 = $3.75.

The cost of 16 magazines,

= 6 x 3.75

= $22.5

Therefore, the cost is $22.5.

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The ratio of charge magnitude \(\frac{q_1}{q_2}\) is : 0.206

If a ring of radius R carry a charge Q, then electric field at a point P at a distance x is given by

\(E=\frac{kQx}{(R^2+x^{2} )^\frac{3}{2} }\)

Let us recap important information from the question

Electric field at point P due to ring 1

\(E_1=\frac{kq_1R}{(R^2+R^{2} )^\frac{3}{2} }=\frac{kq_1}{R^2}\)

Electric field at point P due to ring 2

\(E_2=\frac{kq_22R}{(R^2+(2R)^{2} )^\frac{3}{2} }=\frac{2kq_1}{11.2R^2}\)

Now,

\(1.15=\frac{11.2q_1}{2q_2}\\ \\\frac{q_1}{q_2} =\frac{2}{11.2}(1.15)=0.206\)

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Answer:

combine like terms

Step-by-step explanation:

plz mark my answer as brainlist plzzzz.

hope this will be helpful to you.

Answer:

two different ways of theoretical and experimental explanation

both are correct

hope they helped you

Dale invested $900 at a simple interest rate of 6%. To find the worth of his investment after two years, we can use the formula for simple interest:

I = P * r * t

where I is the interest, P is the principal amount, r is the rate of interest, and t is the time period.

Substituting the given values, we have:

I = $900 * 6% * 2 years = $108

The worth of Dale's investment after 2 years is equal to the sum of the principal amount and the simple interest.

Worth of investment after 2 years = Principal + Simple interest = $900 + $108 = $1008

Therefore, the worth of Dale's investment after two years is $1008.

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Answer:

5.4

Step-by-step explanation:

using pythagoras theorem

a²+b²=c²

5²+2²=c²

c²= 25+4

c²=29

\( \sqrt{c ^{2} } = \sqrt{29} \)

c=5.4

Answer:

The initial cost of Elizabeth's books is $345. After one year, the cost of her books increased by 7%, which is an increase of $345 x 7/100 = $24.15

So, the cost of her books after one year is $345 + $24.15 = $369.15

To find the price of her books after five years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the initial principal (or starting amount), r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $345, r = 7/100, n = 1, and t = 5

So, A = $345 (1 + 7/100)^5 = $345 * 1.07^5 = $475.14

Rounding this to the nearest dollar, we get $475.

Therefore, the price of Elizabeth's books after five years is $475.

Answer:

The probability of rolling an odd number or a two on a six-sided die is 1/2 + 1/6 = 2/3. This means that if you roll a six-sided die 300 times, you can expect to roll an odd number or a two approximately 200 times

Step-by-step explanation:

Answer: 400 TIMES

Step-by-step explanation:

1/6 +1/2

4/6

2/3

The equation of the tangent line to the graph of y = ln(x^2) at the point (5, ln(25)) is y = (2/5)x - (2/5)ln(25) + ln(25). This line passes through the point (5, ln(25)) and has a slope of 2/5.

To find the equation of the tangent line to the graph of y = ln(x^2) at the point (5, ln(25)), we need to use the formula for the equation of a tangent line:
y - y1 = m(x - x1)
where (x1, y1) is the point of tangency and m is the slope of the tangent line. To find the slope, we need to take the derivative of y = ln(x^2):
y' = 2x/x^2 = 2/x
At x = 5, the slope of the tangent line is:
m = 2/5
So the equation of the tangent line is:
y - ln(25) = (2/5)(x - 5)
Simplifying this equation, we get:
y = (2/5)x - (2/5)ln(25) + ln(25)
Thus, the equation of the tangent line to the graph of y = ln(x^2) at the point (5, ln(25)) is y = (2/5)x - (2/5)ln(25) + ln(25). This line passes through the point (5, ln(25)) and has a slope of 2/5.
To find the equation of the tangent line to the graph of y = ln(x^2) at the point (5, ln(25)), we first need to determine the derivative of the function. The derivative represents the slope of the tangent line at any point on the graph.
The function is y = ln(x^2). Using the chain rule, the derivative is:
dy/dx = (1/x^2) * (2x) = 2/x
Now, we will find the slope of the tangent line at the point (5, ln(25)) by substituting x = 5 into the derivative:
m = 2/5
So, the slope of the tangent line at the point (5, ln(25)) is 2/5. To find the equation of the tangent line, we use the point-slope form:
y - y1 = m(x - x1)
Substitute the point (5, ln(25)) and the slope 2/5 into the equation:
y - ln(25) = (2/5)(x - 5)
This is the equation of the tangent line to the graph of y = ln(x^2) at the point (5, ln(25)).

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Answer:

see explanation

Step-by-step explanation:

The sum of the angles around D = 360° , then

x = 360 - (114 + 90) ← equation to find x

  = 360 - 156

  = 204

Answer:

it s A

Step-by-step explanation:

if the two to the power of ten is on the outside, you will always need to add that to the other powers of ten

Brianliest plz thanks

Answer:

Shaheem paid $76 as his total.

Step-by-step explanation:

He paid $20 to get in, Emily paid $40 for 5 rides, and if you divide that to get the payment for one ride which is $8. So you multiply 8 by 7 because 7 is how many rides he rode which equals to 56, plus 20(his enter fee) would be $76.