Identify the indicated sum for the geometric series.
S7 for 162 − 54 + 18 − 6 + .....

If a=4, b=6, and sina=3/5 in triangle abc, then sin b equals: 9/10

To find sin(b) in triangle ABC, we can use the sine function in a right angle and the given information.

Given:

a = 4

b = 6

sin(a) = 3/5

We know that the sine of an angle in a right triangle is equal to the ratio of the length of the side opposite the angle to the length of the hypotenuse.

In triangle ABC, let's label the side opposite angle a as side c and the hypotenuse as side h.

sin(a) = c / h

Substituting the given values:

3/5 = 4 / h

To solve for h, we can cross-multiply:

3h = 5 * 4

3h = 20

h = 20 / 3

Now, we can use the sine function to find sin(b):

sin(b) = side opposite angle b / hypotenuse

sin(b) = 6 / (20 / 3)

sin(b) = 6 * (3 / 20)

sin(b) = 18 / 20

sin(b) = 9 / 10

Therefore, sin(b) equals 9/10.

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Answer:

D. subtract 31 from both sides

you cant combine cuz theyre not like terms and you have to undo the constant number before you undo the second term in the equation so you will end up needing to do letter choice D first.

Step-by-step explanation:

hope this helped a little bit :)

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Explanation:

The expression 31-12t is the same as 31+(-12t). Adding a negative is the same as subtracting a positive.

Then we can flip the two terms getting -12t+31. This is because we can add two numbers in any order.

So we're effectively solving -12t+31 = 211

The first step is to subtract 31 from both sides to undo the +31. We follow PEMDAS in reverse to isolate the variable.

We do not have sufficient evidence to conclude that the mean number of alcoholic drinks consumed by students at the liberal arts college is significantly different from the mean number consumed by college students in general.

We need to conduct a hypothesis test to determine whether the mean number of alcoholic drinks consumed by students at the liberal arts college is significantly different from the mean number consumed by college students in general.

To conduct the hypothesis test, we need to set up the null and alternative hypotheses.

Null Hypothesis: The mean number of alcoholic drinks consumed by students at the liberal arts college is equal to the mean number consumed by college students in general (μ = 4.73).

Alternative Hypothesis: The mean number of alcoholic drinks consumed by students at the liberal arts college is not equal to the mean number consumed by college students in general (μ ≠ 4.73).

We would then need to calculate the test statistic, which would be a t-score. This can be calculated using the formula:

t = (x bar - μ) / (s / √n)

where x bar is the sample mean (5), μ is the hypothesized population mean (4.73), s is the sample standard deviation, and n is the sample size (54).

Assuming that the sample standard deviation is unknown, we would need to estimate it using the sample data. This gives us:

s = √[Σ(xi - x bar)² / (n - 1)] = 3.05

Plugging in the values, we get:

t = (5 - 4.73) / (3.05 / √54) = 1.67

To determine the p-value, we would need to consult a t-distribution table with 53 degrees of freedom (n - 1). The p-value corresponding to a t-score of 1.67 with 53 degrees of freedom is approximately 0.102.

Since the p-value is greater than the level of significance (α) typically chosen (0.05), we fail to reject the null hypothesis. This means we do not have sufficient evidence to conclude that the mean number of alcoholic drinks consumed by students at the liberal arts college is significantly different from the mean number consumed by college students in general.

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From the picture, we can see that we have a right triangle. The hypontenuse (the side opposite to the right angle) is the side whose length of 14, where the side whise length is 11, and the one whose length is x, are the two hicks. We can establish the relationship of the Pythagoras theorem for this triangle:

We can solve for x:

To find the square root of 75, we can decompose it:

75/5 = 15

15/5 = 3

3/3 = 1.

Then, 75 can be expressed the following way:

Then:

Since the square root of a product is the product of the square roots:

The value of x is approximately 8.66,

If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.

This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.

The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.

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Answer:

\(\frac{1}{-35}\)

Step-by-step explanation:

\(\frac{1}{-35}\) * -35 = 1

The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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Answer:

17

Step-by-step explanation:

The exponential function of the form y=ab^x that has the given points is y = (25/7)(7/5)^x

We can use the given points to set up a system of equations and solve for the values of a and b in the exponential function y = ab^x.

Using the point (1,5), we get:

5 = ab^1

Using the point (2,7), we get:

7 = ab^2

Now, we can solve for a and b by dividing the second equation by the first:

7/5 = (ab^2)/(ab^1

Simplifying this expression, we get:

7/5 = b

Substituting this value of b back into one of the original equations, we can solve for a:

5 = a(b^1) = a(b) = a(7/5)

Simplifying this expression, we get:

a = 25/7

So, the exponential function that passes through the points (1,5) and (2,7) is:

y = (25/7)(7/5)^x

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Step-by-step explanation:

Let x be the size of 1 of the 2 congruent angles.

The size of the other congruent angle is also x.

Since sum of angles in a triangle = 180°,

Measure of 3rd angle in the triangle

= 180° - 1st angle - 2nd angle

= (180 - 2x)°.

Answer:

The Isosceles Triangle Theorem, All interior angles of a triangle add up to 180 degrees. Basically the equation would be (angle 1) + (angle 2) + (angle 3) = 180. whichever angle you dont have you replace with x and solve for it. For example if you had a triangle with two congruent angles of 36 then it would be 36+36+x=180 and you would solve it like any other equation eventually showing you that x = 108. it also works backwards if you are trying to solve for the 2 missing congruent angles.

Step-by-step explanation:

Answer: 00.10

Step-by-step explanation: Add 00.10 to 79.90 and you get 80. Brainliest please?

The second-order partial derivatives of \(\(f(x, y) = x^2 + y - e^x + y^2\)\)are:

\(\(\frac{{\partial^2 f}}{{\partial x^2}} = 2 - e^x\), \(\frac{{\partial^2 f}}{{\partial y^2}} = 2\),\(\frac{{\partial^2 f}}{{\partial x \partial y}} = 0\),\(\frac{{\partial^2 f}}{{\partial y \partial x}} = 0\)\) . The value of \(\(w(x, y) = x^2 - y^2 + 10x\)\) at \(\(t = \frac{1}{2}\pi\)\) is -1. The value of \(\(\frac{{dw}}{{dt}}\)\)at \(\(t = \frac{1}{2}\pi\)\) is -10.

The second-order partial derivatives of the function f(x, y) = x² + y - eˣ+ y² are as follows:

The second partial derivative with respect to x, denoted by (∂²f)/(∂x²), evaluates to 2 - eˣ. This derivative represents the rate of change of the rate of change of f with respect to x.

The second partial derivative with respect to y, (∂²f)/(∂y²), simplifies to 2. It represents the rate of change of the rate of change of f with respect to y. The mixed partial derivatives, (∂²f)/(∂x∂y) and (∂²f)/(∂y∂x), both evaluate to 0. This indicates that the order of differentiation does not affect the result, implying symmetry in the mixed partial derivatives.

To evaluate the function \(w(x, y) = x^2 - y^2 + 10x\) at t = 1/2π, we substitute x = cos(t) and y = sin(t). Substituting these values into the expression for w yields w(cos(t), \(sin(t)) = cos^2(t) - sin^2(t) + 10cos(t)\). Plugging in t = 1/2π, we find w(0, 1) = -1.

Finally, to find dw/dt at t = 1/2π, we differentiate w with respect to t and substitute t = 1/2π. By taking the derivative, we obtain dw/dt = -2sin(t)cos(t) - 2sin(t)cos(t) - 10sin(t). Substituting t = 1/2π gives dw/dt|t=1/2π = -10.

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Answer:

It is the first graph

Step-by-step explanation:

The line under the > and < sign means that it must include the 3 and the 0.  The closed circle is showing that the 3 and 0 or included.

Answer:

(d)

Step-by-step explanation:

1) He multiplied both sides by 2.

2) He combined like terms.

3) He added 4 to both sides.

4) He divided both sides by 8.

Answer:

1)D 2)C 3)A 4)B 5) A

Step-by-step explanation:

1) The area rectangle is 36x^2 -1

We know ,

A= l*b

=36x^2 -1

=(6x)^2 -1

=(6x+1) (6x-2)

This the value of l,b respectively.

So, Perimeter of rectangle is 2(l+b)

P=2(6x+1) + 2(6x-1)

=24x

2)The area of square is 4(x+5)^2

We know,

A=l^2

=4(x+5)^2

=4(x^2 + 10x + 25)

=(2x+10)^2

This is the value of l=2x+10.

So, Perimeter of square is 4l

P=4(2x+10)

=8x+40

3)The fully factorized form is

= -2x^2 + 10x +12

= -2x^2 + 12x -2x +12

= -2x(x-6) -2(x-6)

= -2(x-6) (x+1)

4)The fully factorized form is

=x^4 -81

=(x^2)^2 -9^2

=(x^2 + 9) (x^2 - 9)

=(x^2 + 9) (x^2 - 3^2)

=(x^2 + 9) (x + 3) (x - 3)

5)The fully factorized form is

= 5x^4 - 320

= 5(x^4 - 64)

= 5((x^2)^2 - 8^2)

= 5(x^2 + 8) (x^2-8)

(-8,-2)

Reflecting across the x-axis means leaving the x value the same but negating the y value

Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

Answer:

Step-by-step explanation:

We know a complete revolution happens in 360 degrees so let set up a proportion.

1.25/5=  x/360

1/4= x/360

x=90

So this angle was 90 degrees.

Notice that the circumference of a circle is 2pi radians.

So a full revolution takes 2pi radians to occur.

1/4 of that will be pi/2 radians.

So, the radians is pi/2

Yes, there is evidence to support the claim that there is a difference in the mean performance of the two methods. To test this, we can perform a two-sample t-test. The p-value for the test is 0.034. This means that there is a 3.4% chance of obtaining this difference in performance if the two methods are actually the same. Since this is lower than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant difference in the mean performance of the two methods.

To construct a 95% confidence interval for the difference in mean ratio of predicted to observed load, we can use the following formula:

95% confidence interval for the difference in mean ratio of predicted to observed load = (mean Lehigh Method - mean Karlsruhe Method) ± (t-score * standard error)

Where t-score is the critical value of t from the t-table with (degrees of freedom = n1 + n2 - 2) and confidence level 95%, and standard error is the standard error of the difference in sample means.

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Answer:

\(2 - \frac{y}{4}\)

Step-by-step explanation:

Given equation:

                          \(\frac{40 - 5y}{20}\)

Problem;

Simplify the equation;

Solution:

         \(\frac{40 - 5y}{20}\) can be expressed as;

  = \(\frac{40}{20}\)  - \(\frac{5y}{20}\)

       dividing by 20 gives;

 = 2 - \(\frac{y}{4}\)

The equation simplified is;

  = \(2 - \frac{y}{4}\)

The angle of rotation for a figure reflected in two lines that intersect to form a 72-degree angle is 144 degrees. The correct option is (c).

To find the angle of rotation for a figure reflected in two lines that intersect to form a 72-degree angle, follow these steps:

1: Identify the angle formed by the intersection of the two lines. In this case, it's 72 degrees.

2: The angle of rotation for a reflection in two lines is twice the angle between those lines.

3: Multiply the angle by 2. So, 72 degrees * 2 = 144 degrees.

Therefore, the angle of rotation for a figure reflected in two lines that intersect to form a 72-degree angle is (c) 144 degrees.

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Answer:

6

Step-by-step explanation:

A painter mixes 2 1/2 pints (2.5 pints) of yellow paint with 4 pints of red paint to make a certain shade of orange paint. The ratio of yellow paint to red paint is 2.5:4. In order to find the pints of yellow paint needed to be mixed with 10 pints of red paint, we will use conversion fractions.

10 red pints × (2.5 yellow pints/ 4 red pints) ≈ 6 pints (we round off to 1 significant figure)

Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

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Answer:

- (27n^3 - 12n - 1) over 3n

Step-by-step explanation:

Answer:

The Great Western Trail = 4,455 miles

Step-by-step explanation:

The Iditarod Trail = 1,025 miles long

The Great Western Trail is 355 miles longer than 4 times the length of the Iditarod Trail.

The Great Western Trail = (4 × 1,025) miles + 355 miles

= 4,100 miles + 355 miles

= 4,455 miles

The Great Western Trail = 4,455 miles

The probability distribution of random variable x is

a) 1.78 is the anticipated value of x;

b) The variance of x is 0.6484.

(a) The expected value of x can be found using the formula:

\(E(x) = Σ[x * f(x)]\)

where x's potential values are all added up.

Using the given probability distribution, we have:

\(E(x) = (0 * 0.27) + (1 * 0.35) + (2 * 0.05) + (3 * 0.25) + (4 * 0.08)\)

\(E(x) = 1.78\)

As a result, 1.78 is the expected value of x.

(b) The variance of x can be found using the formula:

\(Var(x) = E(x^2) - [E(x)]^2\)

where E(x) represents the anticipated value of x and E(x2) represents the expected value of x2.

To find E(x^2), we can use the formula:

\(E(x^2) = Σ[x^2 * f(x)]\)

Using the given probability distribution, we have:

\(E(x^2) = (0^2 * 0.27) + (1^2 * 0.35) + (2^2 * 0.05) + (3^2 * 0.25) + (4^2 * 0.08)\)

\(E(x^2) = 3.33\)

Consequently, the variation of x is:

\(Var(x) = E(x^2) - [E(x)]^2\)

\(var(x) = 3.33 - (1.78)^2\)

\(var(x) = 0.6484\) (rounded to four decimal places)

x's variance is 0.6484

As a result, x's variance is 0.6484.

1.78 is the anticipated value of x

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Answer:

78

Step-by-step explanation:

because I know everything

Answer:

8 batches

Step-by-step explanation:

A recipe for cookies calls for 2/3 of a cup of sugar. Elena used 5 1/3 cups of sugar to make multiple batches of cookies. How many batches did she make?

From the above question, 1 recipe = 1 batch of cookies

Hence:

2/3 cup of sugar = 1 batch of cookies

5 1/3 cups of sugar = x batches of cookies

Cross Multiply

2/3 cup × x batches = 5 1/3 cup × 1 batch

x batches = 5 1/3 cup × 1 batch/2/3 cup

x batches = 16/3 ÷ 2/3

x batches = 16/3 × 3/2

= 8 batches

Therefore she made 8 batches