Find the exact value of cos A in simplest radical form.

Answer:

The answer is A.

Step-by-step explanation:

First, you look at the longest time which is 7/8. Next, you look at the shortest time which is 1/8. You take 1/8 from 7/8 which is 6/8 which is A.

Answer:

6 6 6 6 11

Step-by-step explanation:

The median is the middle number

the mode is the number of items, usually the number that are the same.

the mean is the average

the range is the number between the smallest and the largest.

So the information you have makes 4 of the 5 numbers the same.

The middle number is 6. This is an interesting fact because it means that 4 of the five numbers are 6

x 6 6 6 6  or  6 6 6 6 x  is what you know so far.

The range is a bit of a devil. And so is the mean. We need the mean to be related to  5*7 = 35. So the sum of the five numbers equals 35. The range would have to be 5, I think. (35 - 4*6) = 11

The difference between 11 and 6 = 5

So 11 works for everything but the range.

If the range must be ten, then x = 16 but then the mean = 8 and 7  is incorrect

So I can get 3 out of 4, but not them all.

Answer:

A

Step-by-step explanation:

Think about it.

y = (0)x + b

this gives

y = b

therefore Y equals a single number regardless of the x value.

This behavior is shown in table A.

Joan went to the store and bought A watermelon for $3 some grapes. Grapes coughed $5.25 per pound if jamba X pounds for grapes which equation best represents y the total Amount joan has to pay before text

a) the series converges when |x| < 1, the interval of convergence is (-1, 1) in interval notation.
b) the series converges for all x, the interval of convergence is (-∞, ∞) in interval notation.

c) both the Ratio Test and the Root Test yield the same result for the radius of convergence, but the Root Test is simpler to use

What does convergence mean?

The ability to go closer to a limit as a function's argument changes or grows or as the number of terms in the series does is a property (exhibited by some infinite series and functions).

(a) Using the Ratio Test:

We have the series\(∑(k=0)^{\infty} x^k / (4k(k+7)).\)

Let's apply the Ratio Test:

\(lim(k - > \infty) |(x^{(k+1)} / (4(k+1)((k+1)+7))) / (x^k / (4k(k+7)))|\)

Simplifying the expression, we get:

\(lim(k - > \infty) |x^{(k+1)} / (4(k+1)(k+8))| * |4k(k+7) / x^k|\)

The absolute values and constants cancel out, resulting in:

\(lim(k- > \infty) |x / ((k+1)(k+8))|\)

As k approaches infinity, both (k+1) and (k+8) approach infinity, and the expression becomes:

\(lim(k - > \infty) |x / (k^2 + 9k + 8)|\)

To find the limit, we can focus on the highest power term in the denominator, which is k². Dividing both the numerator and denominator by k², we get:

lim(k→∞) |x / (1 + 9/k + 8/k²)|

As k approaches infinity, the terms 9/k and 8/k² both approach zero, and the expression becomes:

lim(k→∞) |x / 1| = |x|

For the series to converge, |x| must be less than 1. Therefore, the radius of convergence, R, is 1.

To find the interval of convergence, we consider the values of x for which the series converges.

Since the series converges when |x| < 1, the interval of convergence is (-1, 1) in interval notation.

(b) Using the Root Test:

We have the series ∑(k=0)^(∞) x^k / (4k(k+7)).

Let's apply the Root Test:

lim(k→∞) (|x^k / (4k(k+7))|)^(1/k)

Simplifying the expression, we get:

lim(k→∞) (|x / (4k(k+7))|)^(1/k) * |x / (4k(k+7))|^(1/k)

The limit of (1/k) as k approaches infinity is 0, so the expression becomes:

lim(k→∞) (|x / (4k(k+7))|)^(0) * |x / (4k(k+7))|

Simplifying further:

lim(k→∞) |x / (4k(k+7))|

As k approaches infinity, the denominator becomes large, and the expression approaches zero. Thus, the limit is:

lim(k→∞) |x / (4k(k+7))| = 0

For the series to converge, the limit must be less than 1. However, the limit is always 0, which is less than 1 for all values of x. Therefore, according to the Root Test, the radius of convergence, R, is infinite (∞).

Since the series converges for all x, the interval of convergence is (-∞, ∞) in interval notation.

(c) In this case, both the Ratio Test and the Root Test yield the same result for the radius of convergence, but the Root Test is simpler to use.

The Root Test only involves taking the limit of the absolute value of the terms raised to the power of 1/k, whereas the Ratio Test requires taking the ratio of consecutive terms and evaluating a limit involving

hence, a) the series converges when |x| < 1, the interval of convergence is (-1, 1) in interval notation.
b) the series converges for all x, the interval of convergence is (-∞, ∞) in interval notation.

c) both the Ratio Test and the Root Test yield the same result for the radius of convergence, but the Root Test is simpler to use

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The probability that a chosen point, in the figure lies in the shaded region is 3.18.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

The probability of the point chosen in the shaded region is calculated by the formulae

Probability = \(\frac{Area of shaded region}{Total area}\)

To find the total area we need to find the area of a triangle and the area of a semicircle.

Area of triangle = 1/2 * Base * Height

                          = 1/2 * 15 * 6

                          = 45

Area of semicircle =  \(\frac{\pi r^{2} }{2}\)

                              = \(\frac{\pi (3)^{2} }{2}\)

                              =14.13

Therefore the probability that chosen point = \(\frac{45}{14.13}\) = 3.18

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The area of the region bounded by the curves area is 52

First, we need to determine the limits of integration. From the given equations, we know that the curves intersect at (-1,24) and (1,22). Since x=2 is a vertical line, we can integrate from x=-1 to x=2.
Area = \(∫[a,b] (f(x) - g(x)) dx\)
where f(x) is the upper curve and g(x) is the lower curve.
In this case, the upper curve is y=23+x and the lower curve is y=1-x. Substituting y=23+x into the equation for the lower curve, we get:
\(23+x=1-x\)
Solving for x, we get x=-11/2.

However, this value is outside of our limits of integration, so we can ignore it.
Now we can set up the integral:
Area =\( ∫[-1,2] (23+x - (1-x)) dx\)
Simplifying, we get:
Area =\( ∫[-1,2] (24+2x) dx\)
Integrating, we get:
Area = \([12x^2 + 24x]_(-1)^2\)
Area = \((12(2)^2 + 24(2)) - (12(-1)^2 + 24(-1))\)
\(Area = 52\)
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Answer:

1/3

Step-by-step explanation:

Given equation is

3x - 9y = 4

⇒ 3x - 4 = 9y

⇒ y = 3/9 x - 4/9

⇒ y = 1/3 x - 4/9

y = 1/3 x - 4/9 is of the form y = mx + c.

m = slope and c is the y-intercept.

Comparing this, we get m = 1/3 and c = (0,-4/9)

Therefore, the slope m = 1/3

Answer:

(3,1)

Step-by-step explanation:

When a point is reflected across the y axis, the sign of its x coordinate flips. Since point A is at (-3,-5), when it is reflected across the y axis its new position will be (3,-5). Now, point A is 3 units from the line y=-2, meaning that when it is reflected across it will be 3 units away from the other direction. (-2+(3))=1, meaning that the final coordinates of point A are (3,1). Hope this helps!

Answer:

it could be 2x=5

Step-by-step explanation:

i said it could be

To find the expected number of times Joan rolls a 3, we use the formula for mean of a binomial distribution.

The correct option is, option (C) 6.

The probability of rolling a number 3 on any given roll is 1/4

If Joan rolls the die 20 times, the number of times she rolls a 3 will follow a binomial distribution with n = 20 (number of trials) and p = 1/4 (probability of success).

The formula for the probability mass function of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (the number of times Joan rolls a 3), k is the number of successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can calculate the probability of rolling a 3 exactly k times out of 20 rolls:

P(X=k) = (20 choose k) * (1/4)^k * (3/4)^(20-k)

To find the expected number of times Joan rolls a 3, we can use the formula for the mean of a binomial distribution:

E(X) = n * p

In this case, E(X) = 20 * 1/4 = 5

Therefore, the expected number of times Joan rolls a 3 is 5.

Since the possible answers are integers, the closest answer to 5 is 6. Therefore, the answer is (C) 6.

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For given line segments RS = TR

In this question, we have been given two line segments QS and TU intersected at point R.

Also, we have been given QS = TU, QR = RU

We need to prove, RS = TR

We can observe that,

QS = QR + RS

and UT = UR + RT

QS = TU                               ................(Given)

QR + RS = UR + RT

QR + RS = QR + RT              .............(Given QR = RU )

QR + RS - QR = QR + RT - QR     .............(subtraction property of equality)

RS = TR

Hence proved.

Therefore, for given line segments RS = TR

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Answer:

41.57 in²

Step-by-step explanation:

Answer:

41.57 in² round it up and it's 42

Step-by-step explanation:

I just did it

Brainliest pls

Answer:

A

Step-by-step explanation:

Given

8 - 2x + 6x = 24 , that is

8 + 4x = 24 ( subtract 8 from both sides )

4x = 16 ( divide both sides by 4 )

x = 4 → A

The standard form equation of a circle, where (0,0) is the center and 3 is the radius.

A co-vertex is one of the endpoints of the minor axis of an ellipse, not a circle. However, assuming you meant to say that the circle has a radius of 3 and its center is at the origin (0,0), we can answer your question.

The equation of a circle with center (0,0) and radius 3 is given by:

x^2 + y^2 = 3^2

which simplifies to:

x^2 + y^2 = 9

This is the standard form equation of a circle, where (0,0) is the center and 3 is the radius.

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Answer:

y = 5/2 x - 13

Step-by-step explanation:

A line perpendicular to y=-2/5x-1 has a slope equal to the negative reciprocal of -2/5. The slope of the line passing through (2,-8) can be calculated as follows:

m = -(-5/2) = 5/2

The equation of the line in point-slope form is:

y - (-8) = (5/2)(x - 2)

Expanding the equation gives:

y + 8 = 5/2 x - 5

Solving for y:

y = 5/2 x - 5 - 8

y = 5/2 x - 13

The equation of the line is:

y = 5/2 x - 13

Answer:

8.33

Step-by-step explanation:

1hr=60 minutes

?hr = 500 minutes

To find how many hours, divide 500 by 60

500/60 = 8.33

500 minutes = 8.33 hours

Answer:

Largest whole number that divides evenly into both numbers.

Step-by-step explanation:

GCF is greatest common factor. It is also known as LCM of lowest common multiple.

It is the set of whole numbers that divides evenly into all numbers with zero remainder.

For example, three numbers are 8,12 and 20.

The factors of 8 are: 1, 2, 4, 8

The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 20 are: 1, 2, 4, 5, 10, 20

The GCF of these three numbers is 4. 4 divides evenly into all numbers.

Hence, the correct option is (B).

Answer:

A and E

Step-by-step explanation:

hope yall have a great day!

Answer:

The answer is A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer: one hundred + fourteen point six hundred + seventy four

Step-by-step explanation:

Answer:

One hundred and fourteen point six seven four

The equation, when stated to be either direct or inverse variation, and the possible constants of variation, are:

To determine whether 7x + 8y = -1 represents a direct or inverse variation, we need to rewrite it in the form y = kx or y = k/x.

y = (-7/8)x - 1/8

Since the equation is in the form y = (-7/8)x - 1/8, it has a constant term (-1/8), which means it does not represent a direct variation (y = kx). Since the equation is not in the form y = k/x or xy = k, it does not represent an inverse variation either.

The equation 5x = 25/y:

First, multiply both sides by y:

5xy = 25

Now, divide both sides by 5:

xy = 5

Since the equation is in the form xy = 5, it represents an inverse variation. The constant of variation, k, is 5.

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Using factorization, the factors of 2 x²+x-28 are x = - 4 and x = 7/2

The factorization approach simplifies any algebraic or quadratic equation by using the fundamental factorization formula, which represents the equations as the product of factors rather than extending the brackets. Any equation may have an integer, a variable, or the algebraic expression itself as a component.

Given equation is -

2 x²+x-28

we will use the method of factorization.

⇒ 2x² + 8x -7x -28

⇒ 2x(x+4) - 7(x+4)

⇒ (x+4) (2x - 7)

⇒ x = -4 and x = 7/2

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

It is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques.

Multicollinearity is a statistical phenomenon where two or more independent variables in a regression model are highly correlated with each other. This can cause problems in the regression model as it becomes difficult to distinguish the individual effects of the independent variables on the dependent variable.
When multicollinearity is present in a regression model, the p-values of the slopes of the independent variables are affected. The p-value measures the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. The null hypothesis in a regression model is that the slope of the independent variable is zero, meaning that there is no relationship between the independent variable and the dependent variable.
Multicollinearity can cause the standard errors of the slopes to increase, leading to inflated p-values. In other words, the significance of the relationship between the independent variable and the dependent variable may be underestimated. This is because the highly correlated independent variables are both trying to explain the same variation in the dependent variable, leading to an unreliable estimate of the effect of each independent variable on the dependent variable.
Therefore, it is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques. This can help to ensure that the regression model produces reliable estimates of the effects of the independent variables on the dependent variable.

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Step-by-step explanation:

Factors of 2015   are  5   13   31   65  155   403  

 so I expect the ages are   65  and  31  

    65 - 31 = 34      

P = 2 * (6x - 5) + 2 * (1/4x + 2)

  = 12x - 10 + 1/2x + 4

  = 12 1/2x - 6   => A

If 40% of adults questioned reported that their health was excellent, then the probability that when 13 adults are randomly selected, 3 or fewer are in excellent-health is (b) 0.169.

The number of adults randomly selected is = 13 adults,

We need to find probability of getting 3 or fewer people reporting excellent health which is considered as success , in 13 trials

The probability of success = 0.4     ...because proportion of adults reporting excellent health in general population.

We use "binomial-probability" formula to calculate probability:

⇒ P(X ≤ 3) = ΣP(X = k), for k = 0, 1, 2, 3

where X = number of successes = people reporting excellent health and P(X = k) = probability of getting exactly k successes;

⇒ P(X = k) = C(n,k) × p^k × (1-p)^(n-k),

where n = number of trials, p = probability of success, and

substituting values,

We get,

⇒ P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3),

⇒ C(13,0) × (0.4)⁰ × (0.6)¹³ + C(13,1) × (0.4)¹ × (0.6)¹² + C(13,2) × (0.4)² × (0.6)¹¹ + C(13,3) × (0.4)³ × (0.6)¹⁰,

≈ 0.1686 ≈ 0.169.

Therefore, the required probability is approximately 0.169, the correct option is (b).

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