find the area of a circle with a circumfrence with 12.56 units.

Based on the inscribed quadrilateral conjecture: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

The inscribed quadrilateral conjecture states that the opposite angle of any inscribed quadrilateral are supplementary to each other. That is, they have a sum of 180 degrees.

From the diagram given, the opposite angles in the trapezoid, 115 + 65 = 180 degrees.

Therefore, we can conclude that: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

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Answer:

y=1x-4

Step-by-step explanation:

Point Slope Formula: y=m(x-x1)+y

y=1(x-5)+1

1x-5+1

y=1x-4 (y=mx+b)

A linear equation in slope intercept form is: \(y = mx+ c\).

The slope intercept form of \(3x + 3y = 24\) is \(y = -x + 8\)

Given

\(3x + 3y = 24\)

Subtract 3x from both sides

\(3x - 3x + 3y = -3x + 24\)

\(3y = -3x + 24\)

Divide both sides by 3

\(\frac{3y}3 = \frac{-3x}3 + \frac{24}3\)

\(y = -x + 8\)

By comparing \(y = -x + 8\) and \(y =mx + c\);

We can conclude that: \(y = -x + 8\) is the slope intercept form of \(3x + 3y = 24\)

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The p-value associated with this test statistic is p<0.05

The p-value for this particular test is the probability of observing a sample mean as extreme as 40.5 or more extreme, assuming that the null hypothesis is true.

Using a significance level of 0.05, we reject the null hypothesis if the p-value is less than 0.05.

The test statistic is calculated as follows:

z = (χ - μ) / (σ / √(n)),

where χ is the sample mean, μ is the hypothesized population mean (40 hours), σ is the population standard deviation (1.25 hours), and n is the sample size (10).

Substituting these values gives:

z = (40.5 - 40) / (1.25 /√10) = 2.83

Using a z-table or calculator, we find that the p-value associated with this test statistic is less than 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to support the claim that battery life exceeds 40 hours at a significance level of 0.05.

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The complete question is given as:

The life in hours of a battery is known to be approximately normally distributed with standard deviation σ = 1.25 hours. A random sample of 10 batteries has a mean life of x = 40.5 hours. a. Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0.05. b. What is the P-value for the test in part (a)?

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Answer:

23

Step-by-step explanation:

Given in the picture below (BODMAS rule is applied)

I hope my answer helps you

Answer:

Step-by-step explanation:

5 + 2 x 3² =                         (remember PEMDAS)

5 + 2 x 9 =

5 + 18 =

23

Answer:

45%

Step-by-step explanation:

1,450 - 1,000 = 450

the 450 becomes 0.45

to make 0.45 a percent, we multiply it by 100

0.45 x 100 = 45

45%

The given equation is in point slope form, which means that follows this structure:

Where x1 and y1 are the coordinates of one point on the line. According to this, the point that is on the graph is (-2/3, 17).

Answer:

The formula for the slope is:

\(\frac{y_2-y_1}{x_2-x_1}\)

Assign each given point to a variable:

Substitute in the values into the formula:

\(\frac{y_2-y_1}{x_2-x_1}=\frac{11-7}{5-(-3)}=\frac{4}{8} =\frac{1}{2}\)

Therefore, the slope is 1/2.

Answer:

1/2

Step-by-step explanation:

The formula for slope: \(\frac{y^2-y^1}{x^2-x^1}\)

Plug in:

\(\frac{11-7}{5-(-3)}\)

11 - 7 = 4

5-(-3)

5 + 3 = 8

4/8 = 1/2

The slope is 1/2.

Hope this helped.

We evaluate S_n by substituting x = 0.4 into the nth partial sum and obtain our approximation for the integral.

To approximate the definite integral ∫(0 to 0.4)

\( {e}^{-x^3} \)

dx with an error less than

\( {10}^{ - 4} \)

we can use a Taylor series expansion for

\({e}^{-x^3} \)

The Taylor series expansion of

\({e}^{-x^3} \)

centered at x = 0 is:

\( {e}^{-x^3} = 1 - x^3 + (x^3)^2/2! - (x^3)^3/3! + ...\)

By integrating this series term by term, we can approximate the integral. Let's denote the nth partial sum of the series as S_n.

To estimate the number of terms needed for the desired accuracy, we can use the error estimate formula for alternating series:

|Error| ≤ |a_(n+1)|, where a_(n+1) is the absolute value of the first omitted term.

In this case, |a_(n+1)| =

\(|(x^3)^{n+1} /(n+1)!| ≤ {0.4}^{(3(n+1)} /(n+1)!

\)

By setting

\({0.4}^{(3(n+1))} /(n+1)! < 10^(-4)\)

and solving for n, we can determine the number of terms required.

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Answer:

D

Step-by-step explanation:

Do rise/run (1/3), so D.

Answer:

whaaaaat are u talking about

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Here, we want to select the graph of the given exponential function values

Let us take a look at the y-intercept

At the y-intercept, the value of x is 0

The y-intercept for this particular equation is 1

This mean that the y-intercept value is 1

hence, the graph will touch the y-axis at the point y = 1

looking at the graphs , only the graph D provides this, and that should be our answer

a) The probability that the murder was committed with a knife: 0.55

b) The probability that the cook did it, given that the murder was committed with a knife: 0.275

To determine the probability that the murder was committed with a knife, we first need to find the total number of weapons.

The butler has four poison tipped pens, two crowbars and four knives and the cook has three rolling pins and seven knives.

So, the total knives: 4 + 7 = 11

crowbars: 2

poison tipped pens: 4

and rolling pins: 3

So, the total number of weapons: 11 + 2 + 4+ 3 = 20

The probability that the murder was committed with a knife:

p = 11/20

p = 0.55

Now we need to find the probability that the cook did it, given that the murder was committed with a knife.

P = 0.55 × 0.5

P = 0.275

The required probability is 0.275

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Answer: 48 pupils get the bus to the cinema and 36 pupils walk to the cinema.

Step-by-step explanation:

Let's suppose that there are a total of N pupils.

We know that N/4 walk to the cinema.

We know that N/3 get the bus to the cinema.

And the remainder is equal to 60 people.

Then:

N - N/4 - N/3 = 60

N*(1 - 1/4 - 1/3) = 60

N( 12/12 - 3/12 - 4/12) = 60

N*( 5/12) = 60

N = (12/5)*60 = 144

Then the number of pupils that walk to the cinema is N/4, or:

144/4 = 36

And the number of pupils that get the bus is N/3, or:

144/3 = 48.

Interpreting a correlation requires careful consideration of factors such as causation, confounding variables, nonlinearity, outliers, and sample characteristics.

Interpreting a correlation between two variables can be difficult for several reasons:

Causation vs. correlation: Correlation measures the strength and direction of the relationship between two variables but does not imply causation. Just because two variables are correlated does not mean that one variable causes the other. It is essential to avoid making causal claims based solely on correlation.

Confounding variables: Correlations can be influenced by the presence of confounding variables that affect both variables being studied. Without accounting for these confounding factors, it can be challenging to determine the true nature of the relationship between the variables of interest.

Nonlinear relationships: Correlation coefficients, such as Pearson's correlation coefficient, measure linear relationships between variables. If the relationship is nonlinear, the correlation may not accurately capture the association. It is crucial to consider other types of analysis or transformations to capture more complex relationships.

Outliers and influential observations: Extreme values or outliers in the data can have a significant impact on correlation coefficients. These outliers may distort the correlation and lead to incorrect interpretations. It is important to examine the data for influential observations that may unduly influence the correlation results.

Sample size and representativeness: The size and representativeness of the sample can affect the reliability and generalizability of correlation results. Small or biased samples may not provide a representative picture of the population, leading to misleading interpretations.

Overall, it is important to use correlations as part of a broader analysis and consider additional evidence before drawing definitive conclusions about the relationship between variables.

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Investment X earns the greater amount of interest over a period of 2 years.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let's consider that Ian invests in X, then:

Principle amount, P = $6,000
Time, T = 2 Years

Rate of Interest, R = 4.5% at simple Interest = 0.045

The interest earned is:

Interest = PRT = $6,000 × 0.045 × 2 = $540

Now, consider that Ian invests in Y, then:

Principle amount, P = $6,000
Time, n = 2 Years

Rate of Interest, R = 4% at Compound Interest = 0.04

The interest earned is:

Interest = P(1+R)ⁿ - P

            = $6,000(1+0.04)² - $6,000

            = $489.6

Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.

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Answer:

Answer below

Step-by-step explanation:

First you line up the digits

3.60

*

2.05

then you do regular multiplication

Answer:

The second vendor because when you purchase 6 liters, it costs less to get it from the second vednor.

Step-by-step explanation:

Compare the price at 6 liters.

3.80(3)= $11.40

$2.70(4)= $10.80

Answer: 25%

Step-by-step explanation:

To find the percentage, you divide 6 by 24. That equals 0.25, which is a decimal. You need to make it a percent, so multiply 0.25 by 100 which is equal to 25%.

Answer:

0.07

Step-by-step explanation:

The length of the protein molecule, in meters, is 208 × 10⁻⁹m.

To find the length of the protein molecule:

Diameter of hydrogen atom = 104 × 10⁻¹⁰m

We are given that A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom.

Therefore, the length of the protein molecule, in meters, is 208 × 10⁻⁹m.

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The correct question is given below:

The diameter of a hydrogen atom is about 1.04 cross times 10 to the power of negative 10 end exponent meters. A protein molecule has an overall length of 2000 times (or 2 cross times 10 cubed times) the diameter of a hydrogen atom. What is the length of the protein molecule, in meters, if it were written in scientific notation?

The probability of selecting exactly three clubs from a standard deck is 0.088. Where n = 5; p = 0.25; q = 0.75; and x = 3 . It is calculated by using binomial probability.

The binomial probability formula is

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾ = \(\frac{n!}{(n-x)!x!} p^xq^{(n-x)}\)

Where n is the number of trials, p i is the probability of success, and q is the probability of failure.

And q = 1 - p

It is given that, a card is selected from a standard deck and replaced.

This experiment has repeated a total of five times. i.e., trials n = 5

So, the probability of success is p = 1/4 = 0.25

(Since one card is to be selected from the five trials where each time the card is replaced)

Then, the probability of failure is q = 1 - 0.25 = 0.75

And it is given that we need to find the probability of selecting exactly three clubs. So, the required random variable is x = 3.

Then, using the binomial probability formula, we get

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

⇒ P(X = 3) = ⁵C₃ p³q⁽⁵⁻³⁾ = ⁵C₃(0.25)³(0.75)² = 0.0878

On rounding off, we get the required probability as 0.088.

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The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.

a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.

b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.

c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.

d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.

Therefore, the number of different spanning trees for each graph is:

a) K3: 1

b) K4: 4

c) K2,2: 2

d) C5: 5  

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The sequence is an arithmetic progression. The common difference is 1 while the first term is 43 .

d = common difference

a = first term

Since we were given last term we use the following formula

But we need to find number of term which is n

Answer:

Decreasing linear

Step-by-step explanation:

An arithmetic sequence decreases by a set amount every time through subtraction, so that means it's linear

Answer:

\(\textsf{A.} \quad g(x)=\sqrt{4x}-2\)

Step-by-step explanation:

Transformations

For a > 0

\(f(x)+a \implies f(x) \: \textsf{translated $a$ units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated $a$ units down}\)

\(a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}\)

\(f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}\)

Given parent function:

\(f(x) = \sqrt{x}\)

1.  Horizontal stretch by a factor of 4:

f(4x) is a horizontal stretch by a factor of 1/4.

So f(1/4x) is a horizontal stretch by a factor of 4.

\(f\left(\frac{1}{4}x\right)\implies g(x)=\sqrt{\frac{1}{4}x}\)

2. Vertical shift by 2 units down:

\(f\left(\frac{1}{4}x\right)-2\implies g(x)=\sqrt{\frac{1}{4}x}-2\)

For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

The first point is the p-value is the probability of obtaining a value for the test statistic at least as extreme as that provided by the sample

Second point is here

Confidence level = 0.95

So level of significance = 0.05

and the p-value = 0.09

Since the p-value is higher than the level of significance we do not reject the null hypothesis.

Hence the answer should not be rejected

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Answer:

the slope is 5. 5/1

Step-by-step explanation:

Use rise over run to find slope. It is the easiest way to find slope

You rise 5 and 1 to the right

Answer:

The slope is 5

Step-by-step explanation:

So you're just trying to find the slop. We're going to choose 2 points to use which are already marked on the graph.

(0, 2) and (-1, -3)

So to find the slope, we have to find (the difference in y) / (the difference in x)

So we're going to do

-3-2/-1-0

Which is

-5/-1

So since there are two negatives, it become positive, and it'll simplify into 5.

So the slope of the line is 5

Answer: 26

Step-by-step explanation:

Two Angles are Complementary when they add up to 90 degrees (a Right Angle). Then

∠A + ∠B = 90

∠A =90- ∠B

∠A  = 26

Answer:

The measure of \(\angle A\):

\(\angle A = 26\textdegree\)

Step-by-step explanation:

Since both \(\angle A\) and \(\angle B\) are complementary (Which they both add up to 90°), and you want to find the measure of

Measure of \(\angle A\): unknown

Measure of \(\angle B\): 64°

Finding the measure of \(\angle A\):

\(90 - 64 = 26\)

\(\angle A = 26\textdegree\)

So, the measure for \(\angle A\) is \(26\textdegree\).