A triangular brace has an angle measure of 30 degrees with a side opposite this angle measuring 8 inches. The base of the triangular brace, which is adjacent to the given measure, is 6 inches in length. Which of the following statements is correct ?

Answer:

x^5/x^2 = 2^5/2^2

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 5 to get 3.

23

Calculate 2 to the power of 3 and get 8.

8

hopefully i helped :)

Explanation:

I think that what you need to do is make the x 2? which makes it 2^5/2^2

2x2x2x2x2=32

2x2=4

so I think the answer is 32/4 which is 8

Answer:8

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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Step-by-step explanation:

6n-2n=4n

4n+7=5

5-7= -2

4n=-2

-2/4= -0.5

therefore,

n= -0.5

Answer:

9.3. your ans. nabsbss

To solve the initial value problem (IVP) given by Jy' = y tan(x) + x sin(2x) with the initial condition y(0) = 1, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

Jy' - y tan(x) = x sin(2x)

The integrating factor for this equation is given by the exponential of the integral of -tan(x) dx:

IF = exp(-∫ tan(x) dx)

Using the trigonometric identity tan(x) = sin(x)/cos(x), we have:

IF = exp(-∫ sin(x)/cos(x) dx)

Now, we can integrate the above expression by applying a substitution. Let u = cos(x), then du = -sin(x) dx:

IF = exp(-∫ (1/u) du)

IF = exp(-ln|u|) = 1/u

Substituting u back in terms of x, we have:

IF = 1/cos(x)

Now, we can multiply the integrating factor with both sides of the equation:

1/cos(x) * (Jy' - y tan(x)) = 1/cos(x) * x sin(2x)

Simplifying the left side using the product rule, we have:

(1/cos(x)) Jy' - y sin(x) = x sin(2x)/cos(x)

Now, we can integrate both sides of the equation with respect to x:

∫ [(1/cos(x)) Jy' - y sin(x)] dx = ∫ (x sin(2x)/cos(x)) dx

Integrating the left side, we get:

(1/J) ∫ J dy = ∫ (x sin(2x)/cos(x)) dx

This simplifies to:

y = J^(-1) ∫ (x sin(2x)/cos(x)) dx + C

where C is the constant of integration.

To find the particular solution, we need to evaluate the integral on the right side. However, the integral does not have a simple closed-form solution, so we would need to approximate it numerically using numerical methods or software.

Once we have the particular solution, we can substitute the initial condition y(0) = 1 to determine the value of the constant C and obtain the complete solution to the IVP.

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the p-value (0.208) is greater than the significance level (0.01), we fail to reject the null hypothesis

To determine if there is evidence to suggest that the proportion of voters who believe pharmaceutical companies invent diseases to make money is different for Democrats and Republicans, we can perform a hypothesis test. Let p1 be the proportion of Democrats who believe in the conspiracy theory, and p2 be the proportion of Republicans who believe in the conspiracy theory.

Let's set up the hypotheses:

Null hypothesis (H0): p1 - p2 = 0 (There is no difference in the proportions of Democrats and Republicans who believe in the conspiracy theory)

Alternative hypothesis (Ha): p1 - p2 ≠ 0 (There is a difference in the proportions of Democrats and Republicans who believe in the conspiracy theory)

We will use a two-sample proportion test to test these hypotheses. The test statistic for this test is given by:

\(\[ Z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}} \]\)

where:

- \(\( \hat{p}_1 \)\) and \(\( \hat{p}_2 \)\) are the sample proportions of Democrats and Republicans who believe in the conspiracy theory, respectively.

- n₁ and n₂ are the sample sizes of Democrats and Republicans, respectively.

- \(\( \hat{p} \)\) is the overall proportion of belief in the conspiracy theory, calculated as the total number of believers divided by the total sample size.

The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true.

Given the sample data:

Democrats: n₁ = 788 and \(\( \hat{p}_1 = \frac{137}{788} \)\)

Republicans: n₂ = 866 and \(\( \hat{p}_2 = \frac{105}{866} \)\)

Let's calculate the test statistic and the p-value:

Step 1: Calculate \(\( \hat{p} \)\):

Total number of believers = 137 + 105 = 242

Total sample size = 788 + 866 = 1654

\(\( \hat{p} = \frac{242}{1654} \)\)

Step 2: Calculate the test statistic (Z):

\(\[ Z = \frac{\frac{137}{788} - \frac{105}{866}}{\sqrt{\frac{242}{1654} \cdot \left(1 - \frac{242}{1654}\right) \cdot \left(\frac{1}{788} + \frac{1}{866}\right)}} \]\)

≈ -1.258

Step 3: Calculate the p-value using the standard normal distribution table for a two-tailed test.

To calculate the p-value, we need to find the probability that a standard normal distribution is less than or greater than the absolute value of the test statistic. Since the alternative hypothesis is two-sided (p1 ≠ p2), we will calculate the p-value as twice the probability of the test statistic being greater than the absolute value of the calculated z-value.

Using a standard normal distribution table or a statistical software, we find that the p-value is approximately 0.208.

Conclusion:

Since the p-value (0.208) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is insufficient evidence to suggest that the proportion of voters who believe pharmaceutical companies invent diseases to make money is different for Democrats and Republicans.

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The z score for the number 7 is -0.92.

The standard deviation is 4.32

X is the score that is 7 given.

We have to calculate the z score for doing so we need the mean also.

Mean is obtained by dividing the sum of numbers / total frequency.

Mean = Summation of numbers / total numbers

= 5, 7, 9, 11, 13, 15, 17 / 7

= 77/7

= 11

Formula of z-score, Z= x - mean /S.D.

x is the number that is 7.

S D is the standard deviation.

Z= 7-11 / 4.32

= -4/4.32

Z score = -0.92

In data, the standard deviation is a degree of the quantity of version or dispersion of a fixed of values. A low fashionable deviation suggests that the values have a tendency to be near the suggest of the set, while a high widespread deviation shows that the values are spread out over a much broader range.

Standard deviation is vital because it is able to assist users check chance. Bear in mind a funding option with a median annual return of 10% in line with the year. However, this average changed into derived from the past three-year returns of 50%, -15%, and -5%. with the aid of calculating the same old deviation and understanding your low likelihood of really averaging 10% in any single given 12 months, you're better armed to make knowledgeable decisions and apprehend underlying risk.

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Answer:

The ends of the field are at the zeros (x-intercept) of the function.

0 = -0.000234(x - 80)2 + 1.5      subtract 1.5 from both sides

-1.5 = -0.000234(x - 80)2           divide both sides by right coefficient

6410.25641 = (x - 80)2              take square root of both sides

80.064 = x - 80                         add 8-0 to both sides

160.064 = x

The field is 160.064 feet wide.  

The maximum is at the vertex, y = 1.5 feet

Step-by-step explanation:

The factors of the polynomial f (x) = x^5 - 7x - 22x³ + 44x² - 104x + 288 that is true for f (9) = 0 are (x - 9) and (x⁴ + 2x³ - 4x² + 8x - 32).

The factor theorem states that: if p(x) is divisible by x - a if and only if p(a)=0.

The polynomial expression x^5 - 7x - 22x³ + 44x² - 104x + 288 and f (9) = 0, then x - 9 = 0 is a factor. Applying long division as follows;

x^5 divided by x equals x⁴

x - 9 multiplied by x⁴ equals x^5 - 9x⁴

subtract x^5 - 9x⁴ from x^5 - 7x - 22x³ + 44x² - 104x + 288 will result to 2x⁴ - 22x³ + 44x² - 104x + 288

2x⁴ divided by x equals 2x³

x - 9 multiplied by 2x³ equals 2x⁴ - 18x³

subtract 2x⁴ - 18x³ from 2x⁴ - 22x³ + 44x² - 104x + 288 will result to -4x³ + 44x² - 104x + 288

-4x³ divided by x equals -4x²

x - 9 multiplied by -4x² equals -4x³ + 36x²

subtract -4x³ + 36x² from -4x³ + 44x² - 104x + 288 will result to 8x² - 104x + 288

8x² divided by x equals 8x

x - 9 multiplied by 8x equals 8x - 72x

subtract 8x - 72x from 8x² - 104x + 288 will result to - 32x + 288.

-32x divided by x equals -32

x - 9 multiplied by -32 equals -32x + 288

subtract -32x + 288 from- 32x + 288 will result to a remainder 0(zero).

We can then conclude the factors (x - 9) and (x⁴ + 2x³ - 4x² + 8x - 32) are the product of linear factors for the polynomial f (x) = x^5 - 7x - 22x³ + 44x² - 104x + 288 that makes it zero.

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Answer:

i DONT KNOW THIS BECAUSE I HAVEN'T GONE OVER THIS IN SCHOOL

Step-by-step explanation:

Answer:

Therefore, [(-7) × (-6)] × 4 equals 168.

Step-by-step explanation:

To solve the expression [(-7) × (-6)] × 4, we can follow the order of operations, which is parentheses, multiplication, and then addition or subtraction.

First, let's simplify the expression inside the parentheses:

(-7) × (-6) = 42

Now, we substitute this value back into the original expression:

[(-7) × (-6)] × 4 = 42 × 4

Next, we perform the multiplication:

42 × 4 = 168

Therefore, [(-7) × (-6)] × 4 equals 168.

the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

To form a third-degree polynomial function with real coefficients such that the complex number 6 + i and the real number 7 are zeros, we can use the fact that complex zeros come in conjugate pairs.

Given that 6 + i is a zero, its conjugate 6 - i will also be a zero. Thus, the zeros of the polynomial are 6 + i, 6 - i, and 7.

To find the polynomial function, we start by forming the factors corresponding to each zero:

(x - (6 + i))   --> This corresponds to the zero 6 + i

(x - (6 - i))   --> This corresponds to the zero 6 - i

(x - 7)        --> This corresponds to the zero 7

To simplify the factors, we multiply them out:

(x - (6 + i))(x - (6 - i))(x - 7)

= ((x - 6) - i)((x - 6) + i)(x - 7)

= ((x - 6)² - i²)(x - 7)

= ((x - 6)² + 1)(x - 7)

Expanding the squared term:

= (x² - 12x + 36 + 1)(x - 7)

= (x² - 12x + 37)(x - 7)

Therefore, the third-degree polynomial function with real coefficients, having the zeros 6 + i, 6 - i, and 7, is:

f(x) = (x² - 12x + 37)(x - 7)

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Answer:

a

Step-by-step explanation:

The mass of the isotope after 45 hours is 2.5 grams.

Given, from the table we can find that when time is 10 hours,

the mass is 12.6 grams;

when time is 25 hours the mass is 6.3 grams .

And 12.6 × 1/2 = 6.3

Also we can find when time is 15 hours the mass is 10 grams,

when time is 30 hours, the mass is 5 grams as:

10 × 1/2 = 5

so we know that half life period is:

25 - 10 = 30 - 15 = 15 hours.

When time is 45 hours,

45 = 15+115

= 3 half life periods, so the mass is :

20 × 1/2 × 1/2 × 1/2

= 2.5 grams.

Hence the mass of the isotope after 45 hours is 2.5 grams.

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Answer:

Step-by-step explanation:

The tangent function relates an angle to the measures of its adjacent and opposite sides. The inverse tangent (arctan) function can be used to find the angle from its tangent value.

  Tan = Opposite/Adjacent

   angle = arctan(opposite/adjacent)

A = arctan(3/4) ≈ 37°

B = arctan(2/1) ≈ 63°

C = arctan(2/7) ≈ 16°

Answer:

-(m-9.6)/5=-0.9

-m+9.6=-0.9x5

-m+9.6=4.5

-m=4.5-9.6

-m=-5.1

m=5.1

Given :

Let sin(45°)=0.7071.

To Find :

The angle measure (μ), in degrees for cos(μ)=−0.7071 and value equivalent to 360n + , where n is an integer .

Solution :

We know , value of sin x and cos x is same at x = 45° .

Now , cos (-x) = cos(90°+x)

Therefore , μ in given question is :

μ =90°+45°

μ=135°

So , for angle of type 360°n + :

μ = 360°n + 135° .

Hence , this is the required solution .

Answer:

A

Step-by-step explanation:

Age and you can also use weight too

you can easily group people by their age and weight but not by eye color

example

age people

5 - 10 14

10 - 15 5

the table above shows that we have 14 people within the range of 5 to 10 years

and likewise the weight of the people can serve the same purpose

Therefore, the admission for each child is $12.50 and for each adult is $0.36.

A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are commonly used to represent linear transformations, systems of linear equations, and vectors in linear algebra.

A matrix can be represented by enclosing its entries in brackets, like this:

\([ 1 2 3]\)

\([ 4 5 6]\)

\([ 7 8 9]\)

In this example, the matrix has 3 rows and 3 columns, and its entries are the numbers from 1 to 9. Matrices can be added, subtracted, multiplied, and transformed using various operations, making them a powerful tool in mathematics and computer science.

Let's use matrices to solve this problem.

Let x be the cost of admission for children and y be the cost of admission for adults. Then we can set up two equations based on the information given:

\(12x + 33y = 162\)

\(8x + 33y = 122\)

We can represent this system of equations as an augmented matrix:

| 12 33 | 162 |

| 8 33 | 122 |

To solve for x and y, we need to perform row operations to reduce the matrix to row echelon form. Let's start by subtracting 3 times the second row from the first row:

| 0 12 | 24 |

| 8 33 | 122 |

Next, we can divide the first row by 12 to get a leading 1:

\(| 0 1 | 2 |\)

\(| 8 33 | 122 |\)

Now we can subtract 8 times the second row from the first row:

| 0 1 | 2 |

| 8 33 | 122 |

| -8 -33 | -16 |

We can divide the second and third rows by 33 and -33, respectively, to get leading 1s:

| 0 1 | 2 |

| 0 1 | 4/11 |

| 1 1 | 16/33 |

Finally, we can subtract the second row from the first row:

| 0 0 | 10/11 |

| 0 1 | 4/11 |

| 1 1 | 16/33 |

This is the row echelon form of the augmented matrix. We can now solve for y by substituting the value of y into the second equation:

\(0x + y = 4/11\)

\(y = 4/11\)

So, the cost of admission for adults is $4/11, or approximately $0.36.

To solve for x, we can substitute the values of x and y into either of the original equations. Let's use the first equation:

\(12x + 33y = 162\)

\(12x + 33(4/11) = 162\)

\(12x = 162 - 12\)

\(x = 150/12\)

\(x = 25/2\)

So, the cost of admission for children is $25/2, or $12.50.

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\(3\sqrt{2} - 4 * (\sqrt{2})^2 = 3\sqrt{2} - 8\)

Answer = \(3\sqrt{2} - 8\)

Answer:

A and B

Step-by-step explanation:

Because 223, and 319 are both greater than 220, which means it would burn all the calories.

As per the BMI, the dependent variable is outcome

In this study, the researcher wants to compare the effectiveness of two different exercise programs in reducing BMI in individuals with diabetes. The participants will be randomly assigned to either the aerobic dancing group or the walking group, and their BMI will be measured before and after the six-month exercise program.

The changes in BMI between the two groups will be compared to determine which exercise program is more effective in reducing BMI in this population. The dependent variable in this study is the change in BMI, as it is the outcome that is being measured and compared between the two groups.

Overall, this study will provide valuable insights into the effectiveness of different exercise programs in reducing BMI in older adults with diabetes, which can have important implications for their overall health and wellbeing.

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Step-by-step explanation:

Total money = 15.40 × 5 = 77

Ethan gets 5 boxes for 77

Answer:

£72

Step-by-step explanation:

To get all the marks on the question you have to say 6.5/100*£77=£5 and then put the answer £72

Hope this helps

Answer:

Reflection. Hope this helps you :)

To calculate the covariance and correlation coefficient of U and V, we need to first find the expected value and variance of U and V.

The covariance of two variables is a gauge of their relationship. In other words, it is a measure of how much the values of two variables tend to fluctuate together. Positive covariance shows that the values of the two variables tend to rise or decrease together, whereas negative covariance indicates that the values of one variable tend to increase when the values of the other variable drop. In probability theory and statistics, covariance is frequently employed to determine the association between two variables. It is determined by multiplying the variances of the two variables from their respective means and dividing the result by the total number of observations. This metric can be helpful for seeing trends and patterns in data and aiding analysts in forecasting.

How to solve?

The expected value of U is $E[U] = E[2 - X_1 - 2X_2] = 2 - m - 2m = -2m. Similarly, the expected value of V is $E[V] = E[3 + 3X_2 - X_3] = 3 + 3m - m = 4m.

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To calculate the value of covariance and correlation coefficient of U and V, we have to find their expected value along with variance.

A measure of the link between two random variables and how much they fluctuate together is called covariance. Alternately, we may say that it establishes the relationship between the two variables' changes, i.e., that a change in one variable is equivalent to a change in the other.

When one variable changes, covariance shows the link between the other two variables. Both variables are said to have positive covariance if a rise in one causes an increase in the other. Reduced values of one variable also result in reduced values of the other.

for expected value of U ;

= $E[U]

= E[2 - X_1 - 2X_2]

= 2 - m - 2m = -2m.

Similarly, the expected value of V;

= $E[V]

= E[3 + 3X_2 - X_3]

= 3 + 3m - m

= 4m.

now we can easily calculate the covariance and correlation coefficient of U,V.

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The minimum value of the average cost over the interval (1, 10).To find the minimum value of the average cost, we first need to find the average cost function.

AC(x) = C(x) / x
Substituting the given cost function, we get:
AC(x) = (x^3 + 36x + 432) / x
Simplifying this expression, we get:
AC(x) = x^2 + 36 + 432/x
Now, we need to find the minimum value of this function on the given intervals. To do this, we take the derivative of the function and set it equal to zero:
AC'(x) = \(2x - 432/x^2\) = 0
Solving for x, we get:
x = \((216)^{(1/3)\) ≈ 6.89
This critical point lies within the interval (1, 10), so we need to check the endpoints as well as this critical point to determine the minimum value of the average cost.

Calculating the values of the average cost at these three points, we get:
AC(1) = 469
AC(6.89) ≈ 51.9
AC(10) = 78.4
Therefore, the minimum value of the average cost over the interval (1, 10) is approximately $51.9. Note that this value is rounded to the nearest tenth as requested.

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9514 1404 393

Answer:

Step-by-step explanation:

Solve for y. The slope (m) is the coefficient of x. The y-intercept (b) is the constant.

1. 3y = -2x +5

  y = -2/3x +5/3 . . . . . m = -2/3, b = 5/3

__

2. y = 2.4x -8 . . . . . . . m = 2.4, b = -8