14. The drawing shows a concrete walkway around a pool. What is the total area of the concrete?
A. 150 ft²
B. 165 ft²
C. 50 ft²
D. 65 ft²

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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The maximum number of interior angles of a convex n-gon that can have measure 131° is equals to the seven.

A polygon is said to be convex n-gon when no line segments between the points, goes inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°. Sum of interior angles of n sided polygon

= 180(n- 2) degrees

We have, Alex assume that one of interior angle of convex n-gon is 131° . Let total maximum number of interior angles of a convex n-gon or polygon that can have measure 131° be "x".

Total measures of all remaining interior angles, (n - x) of this polygon

= 180(n- 2) - 131x

But for a convex n-gon, interior angles of a convex polygon are less than 180°. So,

180(n- 2) - 131x < (n - x) 180

Now, solve this Inequality,

=> 180n - 360 - 131x < 180n - 180x

=> -360 + 180x - 131x < - 180x + 180x

=> - 360 + 49x < 0

=> 49x < 360

=> x < 360/49

=> x < 7.34 ~ 7

So, the required value of x is 7 .

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The amount of orange that Manny and Josh have leftover after eating lunch is 1.

A fraction is a non-integer. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below

Oranges Manny has left = 1 - 4/9 = 5/9

Oranges Josh has left = 1 - 5/9 = 4/9

Oranges they both have left = 5/9 + 4/9 = 1

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Answer:

x=10.8

Step-by-step explanation:

the image is the working out. hope this helps.

Answer:

wheres the question

Step-by-step explanation:

value of a2+a4+a6+……+a98 IS EQUAL TO 93.

Given, the common difference (d) =1

Let a1=a Given, a1+a2+……+a98=137

⇒(98/2)(2a+97)=137    [Sn=n/2[2a+(n−1)d]

⇒2a+97=137/49…eq.(1)

a2+a4+…+a98    (n=49 terms)

a2+a4+…+a98=49/2(a2+a98)

a2+a4+…+a98=49/2[(a+1)+a+97]

a2+a4+…+a98=49/2[2a+97+1]

a2+a4+…+a98=49/2[(137/49)+1] [using eq. 1]

a2+a4+…+a98=137/2+49/2

a2+a4+…+a98=186/2 =93

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The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).

In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).

"A number": This is represented by the variable x, which can take any value.

"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.

"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).

In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.

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Answer:16x^2+6x

Step-by-step explanation:

The probability that a senior graduated owing more than $16,000 in student loan debt is approximately 0.1056 or 10.56%.

To find the probability that a senior graduated owing more than $16,000 in student loan debt, we can use the standard normal distribution and z-scores.

Let's denote X as the student loan debt of a senior. Given that the debt is normally distributed with a mean (μ) of $12,000 and a standard deviation (σ) of $3,200, we want to calculate P(X > $16,000).

First, we need to calculate the z-score, which measures the number of standard deviations that $16,000 is away from the mean:

z = (X - μ) / σ

Plugging in the values:

z = ($16,000 - $12,000) / $3,200

z ≈ 1.25

Next, we find the area under the standard normal curve to the right of the z-score of 1.25. This represents the probability of a senior having a debt of $16,000 or less.

P(X ≤ $16,000) = 0.8944

To find P(X > $16,000), we subtract this probability from 1:

P(X > $16,000) = 1 - P(X ≤ $16,000)

P(X > $16,000) ≈ 1 - 0.8944

P(X > $16,000) ≈ 0.1056

Therefore, the probability that a senior graduated owing more than $16,000 in student loan debt is approximately 0.1056 or 10.56%.

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Answer:

Solve the equation for  x  by finding  a ,  b , and  c

of the quadratic then applying the quadratic formula.

x = − 2  Double roots

Answer:

The second graph

Step-by-step explanation:

hope it help

Answer:

9.4

Step-by-step explanation:

a2+b2=c2

8^2 + 5^2 = c2

64 + 25 = 89

square root of 89 = 9.4

Answer: -2

Step-by-step explanation:

Answer:

I hope it is correct....

Answer:

An exponential function has the form `f(x) = ab^x`, where `a` and `b` are constants. To find the exponential function that passes through the points `(-2,1)` and `(-1,2)`, we can use these points to set up a system of equations to solve for the values of `a` and `b`.

Substituting the coordinates of the first point into the equation for an exponential function gives us:

`1 = ab^(-2)`

Substituting the coordinates of the second point into the equation for an exponential function gives us:

`2 = ab^(-1)`

Dividing these two equations gives us:

`(2)/(1) = (ab^(-1))/(ab^(-2))`

`2 = b`

Now that we know that `b=2`, we can substitute this value back into either equation to solve for `a`. Substituting into the first equation gives us:

`1 = a(2)^(-2)`

`1 = a(1/4)`

`a = 4`

So, the exponential function that passes through the points `(-2, 1)` and `(-1, 2)` is given by:

`f(x) = 4 * 2^x`.

To find the exponential function for the graph passing through (-2,1) and (-1,2), we need to use the general form of an exponential function, which is:

y = a * b^x

where:

a is the initial value or the y-intercept of the function

b is the base of the exponential function

x is the variable or the exponent

To determine the values of a and b, we need to use the two given points and solve for the corresponding equations. Substituting the first point (-2,1), we get:

1 = a * b^(-2)

Substituting the second point (-1,2), we get:

2 = a * b^(-1)

Now, we can solve for a and b by eliminating one variable. Dividing the second equation by the first equation, we get:

2/1 = a * b^(-1) / (a * b^(-2))

2 = b

Substituting this value of b into the first equation, we get:

1 = a * 2^(-2)

a = 4

Therefore, the exponential function that passes through (-2,1) and (-1,2) is:

y = 4 * 2^x

or

f(x) = 4 * 2^x

Answer

Find out the  m∠p .

To prove

As in ΔDAB is a right triangle

Apply pythagorean theorem

Hypotenuse ² = Perpendicular ² + Base²

DB² = AB² + AD²

AB = 5 units

AD = 6 units

Put in the above formula

DB² = 5² + 6²

     = 25 + 36

    = 61

          = 7.8 units (approx)

Now in  ΔDCB is a right triangle .

By using the trignometric identity .

As DC = 4 units

DB = 7.8 units  (approx)

Put all the values in the trignometric identity .

∠p = 59.15 ° (approx)

20.44% of Container A is full after the pumping is complete.

Given that two containers hold water are side by side, both in the shape of a cylinder.

Container A has a radius of 13 feet and a height of 18 feet.

Container B has a radius of 11 feet and a height of 20 feet:

Container A is full of water and the water is pumped into Container B until Container B is completely full.

We need to find what is the percent of Container A that is full after the pumping is complete?

Volume of cylinder = π × r² × h

Volume of container A = 3042π ft³

Volume of container B = 2420π ft³

After the pumping is complete,

The volume in container B will be of 2420π ft³

In container A, it will be of 3042π ft³ - 2420π ft³, out of a total of 622π ft³.

Therefore, the percentage is:

622π / 3042π x 100% = 20.44%

Hence, 20.44% of Container A is full after the pumping is complete.

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Answer:

Step-by-step explanation:

48[3+15÷{4+10÷(3-13)}]

=48[ 3+15%{4+10%(-10)}]

=48[3+15%{4-1}]

=48[3+15%3]

=48[3+5]

=48*8

=384

Answer:

18

Step-by-step explanation:

This is actually pretty easy. Keep this in mind.

There are 34 total students. 16 of them like bananas and the rest like apples. All you really need to do is count up from 16 to 34 to find the answer.

The simple equation for this is: 34-16

Thus, the answer is 18.

a) The test statistic is t = -2.46, with 23 degrees of freedom, and a p-value of .021. Since the p-value is less than .05, we reject the null hypothesis and conclude that there is a significant difference in aggression between the two groups.

b) The negative sign indicates that the drug that lowers brain levels of serotonin has a negative effect on aggression. Cohen's d of -1.42 indicates a large effect size, which means that the difference in means between the two groups is significant.

a) Test for a significant difference in aggression between the two groups using the independent samples t-test: A t-test is used to determine whether the means of two groups are significantly different from each other. To conduct an independent samples t-test, the following conditions must be met:

The two groups are independent of one another.
The data are normally distributed (or close to it).
The variances of the two groups are approximately equal.

The first condition is met since the two groups of rats are independent samples. The second condition cannot be assessed without more information, so we will assume it is met. The third condition can be tested using the Levene's test for equality of variances.

The null hypothesis for the Levene's test is that the variances of the two groups are equal. We will use an alpha level of .05.

The test statistic is F = 3.406, with 1 and 23 degrees of freedom, and a p-value of .079. Since the p-value is greater than .05, we fail to reject the null hypothesis and conclude that the variances of the two groups are approximately equal.

Now we can conduct the independent samples t-test. The null hypothesis is that there is no significant difference in aggression between the two groups. The alternative hypothesis is that there is a significant difference in aggression between the two groups.

The test statistic is t = -2.46, with 23 degrees of freedom, and a p-value of .021. Since the p-value is less than .05, we reject the null hypothesis and conclude that there is a significant difference in aggression between the two groups.

b) Compute Cohen's d: Cohen's d is a measure of effect size that describes the standardized difference between two means. It is calculated by subtracting the mean of one group from the mean of the other group, and then dividing by the pooled standard deviation. The formula for Cohen's d is:

d = (M1 - M2) / Spooled

where M1 is the mean of group 1, M2 is the mean of group 2, and Spooled is the pooled standard deviation. The pooled standard deviation is calculated using the following formula:

Spooled = √(((n1 - 1) * S1^2 + (n2 - 1) * S2^2) / (n1 + n2 - 2))

where n1 and n2 are the sample sizes of group 1 and group 2, and S1 and S2 are the standard deviations of group 1 and group 2.

Using the values from the study:

M1 = 14
M2 = 19
S1 = √(180.5 / 9) = 4.26
S2 = √(130 / 14) = 2.93
n1 = 10
n2 = 15

Spooled = √(((10 - 1) * 4.26^2 + (15 - 1) * 2.93^2) / (10 + 15 - 2)) = 3.53

d = (14 - 19) / 3.53 = -1.42

The negative sign indicates that the drug that lowers brain levels of serotonin has a negative effect on aggression. Cohen's d of -1.42 indicates a large effect size, which means that the difference in means between the two groups is significant.

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The value of b in the function f(x) = 5x² - bx + 8 when (2, 8) is on the graph is 10

From the question, we have the following parameters that can be used in our computation:

The function f(x) = 5x² - bx + 8

Also, we have the point

(2, 8)

This means that x = 2 and f(x) = 8

Substitute the known values in the above equation, so, we have the following representation

5(2)² - b(2) + 8 = 8

So, we have

5(2)² - b(2) = 0

Divide through by 2

5(2) - b = 0

This means that

b = 5(2)

Evaluate

b = 10

Hence, the value of b is 10

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Complete question

In the xy-plane, the point (2, 8) lies on the graph of the function f(x) = 5x² - bx+8. What is the value of b ?

Answer:

ai) n(E⋂C) = ∅ = null

n(E⋂G) = 4

aii) see attachment

bi) n(C⋂G) = x = 1

bii) n(G) only = 3

Step-by-step explanation:

Let chemistry = C

Economic = E

Government = G

n(E) = 12

n(G) = 8

n(C) = 7

ai) number of pupils for economics and chemistry = 0

number of pupils for economics and government = 4

The set notation for both:

n(E⋂C) = ∅ = null

n(E⋂G) = 4

aii) find attached the Venn diagram

bi) n(C⋂G) = ?

Let number of n(C⋂G) = x

From the Venn diagram

n(C) only = 12-4 = 8

n(G) only = 8-(4+x) = 4-x

n(E) only = 7-x

n(E⋂C⋂G) = 0

n(E⋂C) = 0

n(E⋂G) = 4

Total: 8+ 4-x + 7-x + x + 0+0+4 = 22

23 -x = 22

23-22 = x

x = 1

n(C⋂G) = x = 1

Number of pupils that take both chemistry and government = 1

(bii) government only = n(G) only = 4-x

n(G) only = 4-1 = 3

Number of students that take government only = 3

The concept of "equally likely outcomes" refers to the idea that every possible outcome in a given sample space has an equal chance of occurring. In other words, if we were to conduct the experiment multiple times, each possible outcome would have an equal probability of being observed.

In the case of rolling a fair die, the sample space consists of the numbers 1 through 6, and each of these outcomes has an equal probability of occurring. This is because the die is assumed to be fair, meaning that each side has an equal chance of landing face-up.

However, in the case of a loaded die, the sample space does not have equally likely outcomes. This is because the probabilities of each outcome are not equal. A loaded die is one that has been manipulated in some way so that certain outcomes are more likely than others. For example, if the loaded die has been weighted to favor the number 6, then the probability of rolling a 6 would be higher than the probability of rolling any of the other numbers.

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Answer:

Q5

∠3 = ∠4

Q6.

∠S + ∠T = 90°

Q7.

∠X + ∠Y = 180°

Q8.

∠1 = ∠4

Q9.

∠K = ∠L

Answer:

Q5

∠3 = ∠4

Q6.

∠S + ∠T = 90°

Q7.

∠X + ∠Y = 180°

Q8.

∠1 = ∠4

Q9.

∠K = ∠L

Step-by-step explanation:

Answer: Parallelogram Opposite Sides Converse

Step-by-step explanation:

There are 2 pairs of opposite congruent sides.

Answer: 8/7

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 56 and 49 is 7

Divide both the numerator and denominator by the GCD

56 ÷ 7

49 ÷ 7

Reduced fraction:

8

7

Therefore, 56/49 simplified to lowest terms is 8/7.