HELP i need this done ASAP!

Answer:

r = c / 2π

Step-by-step explanation:

c = 2πr is the formula for the circumference of a circle of radius r.

We can solve this for r:

r = c / (2pi)

or

r = c / 2π

Answer:

D. 22

Step-by-step explanation:

Because if the missing side is 22 cm, the other two sides' sum would have to be greater than 22, but 13 + 9 = 22.

Answer: 90,000

Step-by-step explanation:

From the question, we are informed that in a local town, 54,000 families have incomes less than $25,000 per year. We are further told that this number of families is 60% of the families that had this income level 12 years ago.

To calculate the number of families who had incomes less than 25,000 per year 12 years ago goes thus:

Let the the number of families who had incomes less than 25,000 per year 12 years ago be represented by x.

Since we are told that this number of families is 60% of the families that had this income level 12 years ago. This means that:

60% of x = 54,000

60/100 × x = 54,000

0.6 × x = 54,000

0.6x = 54,000

Divide by 0.6

0.6x/0.6 = 54000/0.6

x = 90,000

The number of families who had incomes less than 25,000 per year 12 years ago was 90,000.

The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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Answer:

2047.5 cubic inches

Step-by-step explanation:

Volume of the storage chest :

Length × Width × Height

============================================================

Given :

⇒ Length = 26 in.

⇒ Width = 7.5 in.

⇒ Height = 10.5 in.

===========================================================

Solving :

⇒ Volume = 26 × 7.5 × 10.5

⇒ Volume = 273 × 7.5

⇒ Volume = 2047.5 cubic inches

Step-by-step explanation:

Slope of the given line is 3, so slope of the perpendicular line is also 3.

using pt slope form,

y+3=3(x-6)

y+3=3x-18

y=3x-21

The maximum volume of the box that can be constructed from the square sheet of metal is V = (x/2)^2 * (x - 2(x/2)) = x^3/8.

Let's assume that the original square sheet of metal has a side length of 'x'. We will cut squares of length 'y' from each corner of the sheet to form the metal box.

The length of the base of the box will be (x-2y) and its width will also be (x-2y), as two squares of length 'y' have been removed from each side of the square sheet. The height of the box will be 'y', as this is the size of the square that was cut out from each corner.

Therefore, the volume of the box can be expressed as V = (x - 2y)^2 y.

Taking the derivative of V with respect to y

dV/dy = 4y(x - 3y)(x - 2y)

Setting dV/dy to zero, we get:

4y(x - 3y)(x - 2y) = 0

This equation has three solutions: y=0, y=x/3, and y=x/2.

The first solution, y=0, corresponds to not cutting any squares from the corners of the sheet and therefore does not result in a box. The second solution, y=x/3, gives a volume of V=(x/3)^2(x-2x/3)=x^3/27, and the third solution, y=x/2, gives a volume of V=(x/2)^2(x-x)=x^3/4.

Therefore, the maximum volume of the box is obtained when y = x/2. In this case, the dimensions of the box are:

length = width = x - 2y = x - x = 0

height = y = x/2

However, since the box cannot have zero length or width, this means that the maximum volume occurs when y=x/2 is at the edge of the feasible region. Therefore, we should choose y=x/2 as the size of the squares to be cut out and the dimensions of the resulting box are:

length = width = x - 2y = x - x = 0

height = y = x/2

So, the maximum volume of the box that can be constructed from the square sheet of metal is V = (x/2)^2 * (x - 2(x/2)) = x^3/8.

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Answer:

child: 74 adult: 117 student: 37

Step-by-step explanation:

x=2z

x+y+z=191

7.5x+9.75y+8z=1593.5

The number of tickets sold for child is 86.

The number of tickets sold for adults is 62.

The number of tickets sold for child students is 43.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Total tickets sold = $1593.50 _____(1)

Total number of tickets sold = 191 _____(2)

Let the number of tickets sold for child = P _____(3)

Let the number of tickets sold for adults = Q _______(4)

Let the number of tickets sold for students = R ______(5)

Cost of child ticket = $7.50 ______(6)

Cost of adult tickets = $9.75 ______(7)

Cost of student tickets = $8 _______(8)

We can make equations as:

From (2), (3), (4), and (5)

P + Q + R = 191 ____(9)

From (1), (6), (7), and (8)

7.50P + 9.75Q + 8R = 1593.50 _____(10)

We have,

P = 2R putting in (9) and (10)

2R + Q + R = 191

We get,

3R + Q = 191 _____(11)

15R + 9.75Q + 8R = 1593.50

23R + 9.75Q = 1593.50 _____(12)

From (11).

Q = 191 - 3R putting in (12)

23R + 9.75 (191 - 3R) = 1593.50

23R + 1862.25 - 29.25R = 1593.50

-6.25R = -268.75

R = 43 putting in Q = 191 - 3R

We get,

Q = 191 - 3 x 43 = 191 - 129 = 62

Putting R = 43 in P = 2R

We get,

P = 2x43 = 86

We have,

P = 86, Q = 62 and R = 43

Thus,

The number of tickets sold for child is 86.

The number of tickets sold for adults is 62.

The number of tickets sold for child students is 43.

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Let's denote the amount invested at 8% as x and the amount invested at 10% as y.

According to the given information, Karim wants to invest a total of $100,000, and the combined annual income from both investments should be $9,000.

Set up the equations based on the information:

The first equation represents the total amount invested:

x + y = 100,000

The second equation represents the total annual income from the investments:

0.08x + 0.1y = 9,000

Solve the equations:

We can use the substitution or elimination method to solve the system of equations. Let's use the elimination method:

Multiply the first equation by 0.08 to match the coefficients of x:

0.08x + 0.08y = 8,000

Now subtract this equation from the second equation to eliminate x:

(0.08x + 0.1y) - (0.08x + 0.08y) = 9,000 - 8,000

0.02y = 1,000

Divide both sides of the equation by 0.02:

y = 1,000 / 0.02

y = 50,000

Substitute the value of y back into the first equation to solve for x:

x + 50,000 = 100,000

x = 100,000 - 50,000

x = 50,000

Calculate the amounts to invest:

Karim should invest $50,000 at 8% and $50,000 at 10% in order to obtain an annual income of $9,000 from both investments.

Karim should invest $50,000 at 8% and $50,000 at 10% in order to obtain an annual income of $9,000 from his investments.

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Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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The value of the angle θ₁, located in Quadrant IV with sin(θ₁) = -13/85, is such that cosθ₁ = 84/85.

In the given scenario, the angle θ₁ is located in Quadrant IV and sin(θ₁) is given as -13/85. We can use the trigonometric identity to determine the value of cosθ₁.

Using the Pythagorean identity sin²θ + cos²θ = 1, we can substitute sin(θ₁) = -13/85:

(-13/85)² + cos²θ₁ = 1

Simplifying:

169/7225 + cos²θ₁ = 1

cos²θ₁ = 1 - 169/7225

cos²θ₁ = (7225 - 169)/7225

cos²θ₁ = 7056/7225

Taking the square root of both sides, we get:

cosθ₁ = √(7056/7225)

Since the angle θ₁ is located in Quadrant IV where cosθ₁ is positive, the value of cosθ₁ is:

cosθ₁ = √(7056/7225)

Simplifying the square root:

cosθ₁ = 84/85

Therefore, the value of the angle cosθ₁ is 84/85.

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The complete question is:

The angle θ₁ is located in Quadrant IV and  sin(θ₁) = -13/85. What is the value of the angle cosθ₁?

Answer:

7.845 Hope this helps! :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

The sample suggests that the school is not believable, as the null hypothesis is rejected.

At the null hypothesis, it is tested if the proportion is of 20%, hence:

\(H_0: p = 0.2\)

At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:

\(H_1: p \neq 0.2\)

We have a two-tailed test, as we are testing if the proportion is different of a value, hence the critical value is of:

|z| = 1.96.

The test statistic is defined by the equation presented as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

The parameters for this problem are given as follows:

\(p = 0.2, n = 210, \overline{p} = \frac{58}{210} = 0.2762\)

Hence the test statistic is of:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.2762 - 0.2}{\sqrt{\frac{0.2(0.8)}{210}}}\)

z = 2.76.

The test statistic is greater than the critical value for the two-tailed test, hence the sample suggests that the school is not believable.

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Answer:

10

Step-by-step explanation:

Answer:

OPTION 2

Step-by-step explanation:

The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular  x   value. The   y   value of a point where a vertical line intersects a graph represents an output for that input  x   value. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that   x   value has more than one output. A function has only one output value for each input value.

--------------------------------------------------------------------------

HOW TO: GIVEN A GRAPH, USE THE VERTICAL LINE TEST TO DETERMINE IF THE GRAPH REPRESENTS A FUNCTION.

1.Inspect the graph to see if any vertical line drawn would intersect the curve more than once.

2.If there is any such line, the graph does not represent a function.

3.If no vertical line can intersect the curve more than once, the graph does represent a function.

(The 2nd pic represents a graph that has a function)

Answer:

The first graph is correct.

Step-by-step explanation:

Note that the equation states x ≥ 2.  It includes the "equals" sign, so the graph line should include 2.  This is indicated by the solid line, as opposed to the 4th graph, which shows it as a dashed line.  The dashed line is correct for x>2, but not for x ≥ 2.

Answer:

if the inequality symbol is ≤ then the answer is x ≤ 6. If the inequality symbol is < then the answer is x < 6.

Step-by-step explanation:

Hope this helped

Answer:

v=pi.r^2.h

1728=3.14*22r^2

1728/69.08=r^2

r^2=25.0144

r=5

Equation of the line 'm' is 5x - 6y - 30 = 0.

According to graph,

A(6,0) and B(0,-5) lies on the line m.

Slope-intercept form -> y = mx + c

Putting B(0,-5) in slope-intercept form,

-5 = m(0) + c

 c = -5

Putting A(6,0) in slope-intercept form,

  0 = m(6) - 5

6m = 5

 m = 5/6

Putting the values of m and c in slope-intercept form,

 y = (5/6)x - 5

6y = 5x - 30

5x - 6y - 30 = 0

Hence, equation of the line is 5x - 6y - 30 = 0.

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The coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point on the directed line segment that partitions it into a ratio of 1 to 3, we can use the concept of section formula.

The section formula states that if we have two points A(x₁, y₁) and B(x₂, y₂) dividing a line segment in the ratio of m₁ : m₂, then the coordinates of the dividing point P are given by:

Px = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂)

Py = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)

In this case, the ratio is 1:3, which means m₁ = 1 and m₂ = 3. The given points are A(6, 2) and B(8, -10). Substituting these values into the formula, we can calculate the coordinates of the dividing point P:

Px = (1 * 8 + 3 * 6) / (1 + 3) = 7

Py = (1 * -10 + 3 * 2) / (1 + 3) = -2/2 = -1

Therefore, the coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point that divides the line segment between (6, 2) and (8, -10) in a 1:3 ratio, we can use the section formula. Applying the formula, where m₁ is 1 and m₂ is 3, the point P(x, y) can be determined.

By substituting the values into the formula, the x-coordinate is calculated as (1 * 8 + 3 * 6) / (1 + 3) = 7, and the y-coordinate is (1 * -10 + 3 * 2) / (1 + 3) = -1. Thus, the coordinates of the point that partitions the line segment into a ratio of 1 to 3 are (7, -1).

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c) It would be larger, because higher confidence requires a larger margin of error.

When increasing the confidence level from 95% to 99%, the margin of error of the confidence interval tends to increase. This is because a higher confidence level means we want to be more certain or have a higher level of confidence in capturing the true population parameter.

To achieve a higher confidence level, we need to widen the interval to account for more potential variability in the population. As a result, the margin of error increases, reflecting the increased uncertainty and the need for a larger range of values to capture the true population parameter with higher confidence.

Therefore, the margin of error of a 99% confidence interval, based on the same sample, would be larger compared to the 95% interval.

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Answer:

b= 8

Step-by-step explanation:

you use Pythagorean theorem to solve this problem

a² + b² = c²

since you already have a and c and you're missing b you rearrange the formula to:

\(c^{2}\)-\(a^{2}\) = b²

17² - 15² = b²

64² = b²

\(\sqrt{64}\) = b

8 = b

Step-by-step explanation:

To find side b use Pythagoras theorem:

Hypotenuse²=Base²+Height ²

17²=B²+15²

289-225=B²

64=B²

√8=B²

So,

8 yards is Side B

Now,

We can use Heron's Formula

√S(S-A) (S-B) (S-C)

Let's find semi perimeter

17+15+8/2

40/2=20

So, S=20

Let A=8,B=15,C=17

√20(20-8) (20-15) (20-17)

√20×12×5×3

√2×2×5×5×2×2×3×3 (Factorising the numbers)

2×5×2×2×3

120 yards Answer

hope it helps...

all values of x that satisfy the inequality f(x)>0 are x < 2 or x > 6.we can solve this by using parabola equation

what is parabola ?

A parabola is a type of conic section, which is a curve that is formed by the intersection of a plane and a cone. In particular, a parabola is the set of all points in a plane that are equidistant to a fixed point (called the focus) and a fixed line

In the given question,

Since the vertex of the parabola is (4,-8), the equation of the parabola can be written in vertex form as:

f(x) = a(x-4)² - 8

where 'a' is a constant that determines the shape and orientation of the parabola.

To find the value of 'a', we can use one of the given points on the x-axis, say (2,0). Substituting x=2 and y=0 in the equation of the parabola, we get:

0 = a(2-4)² - 8

8 = 4a

a = 2

So, the equation of the parabola is:

f(x) = 2(x-4)² - 8

To find all values of x for which f(x)>0, we need to solve the inequality:

2(x-4)² - 8 > 0

Adding 8 to both sides, we get:

2(x-4)² > 8

Dividing both sides by 2, we get:

(x-4)² > 4

Taking the square root of both sides, we get:

x-4 > 2 or x-4 < -2

Simplifying, we get:

x > 6 or x < 2

Therefore, all values of x that satisfy the inequality f(x)>0 are x < 2 or x > 6.

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Answer:

The answer is B

I hope help you

Answer:

the correct answer for this equaction is B i think hope this helps!..

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

7x+5 = 9x -15

5 = 2x -15

2x = 20

x = 10

Therefore, Finally, we factor out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)), which simplifies to 1/cos(t) or sec(t).

To simplify 1 + sec(t) / 1 + cos(t), we need to use the identity sec(t) = 1 / cos(t).
So, 1 + sec(t) / 1 + cos(t) becomes 1 + 1/cos(t) / 1 + cos(t).
Next, we'll simplify the expression by multiplying the numerator and denominator by cos(t), which gives us (cos(t) + 1) / (cos^2(t) + cos(t)).
Finally, we can simplify this expression further by factoring out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)).
The cos(t) + 1 in the numerator cancels with the cos(t) + 1 in the denominator, leaving us with 1/cos(t) or sec(t).
To simplify 1 + sec(t) / 1 + cos(t), we use the identity sec(t) = 1 / cos(t). Then, we multiply the numerator and denominator by cos(t), which gives us (cos(t) + 1) / (cos^2(t) + cos(t)).

Therefore, Finally, we factor out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)), which simplifies to 1/cos(t) or sec(t).

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