Write an equation, in slope-intercept form of the line through these two points. (2, 9) and (0, 2)

Answer:

2/5

Step-by-step explanation:

subtract 130,35,and 74 from 400 you will have 160/400 left then you find the greatest common and divide! and get 2/5

Answer: 2/5

Step-by-step explanation:

Ben gives 35 to Sonia, 130 to Phill, 75 to Lance, in total he gives away 240 counters. the fraction of the counters left in his bag would be 400-240 which is 160 and so his fraction would be 160/400 and this in simplest form would be 8/20 if you divide by 20 and then to simplify that you can divide by 4 to get 2/5

Answer:

it’s years

Step-by-step explanation:

Answer:

the value for k is 7 please do you get it

The tennis ball will hit the ground \(5\) seconds after being dropped from an initial height of  \(400\)feet.

To determine when the tennis ball hits the ground, we need to find the value of t when h becomes 0, since at that time the height of the ball is zero, which means it has hit the ground.

So, we can set  \(h = 0\) and solve for t:

\(0 = -16t^2 + 400\)

Adding 16t^2 to both sides:

\(16t^2 = 400\)

Dividing both sides by 16:

\(t^2 = 25\)

Taking the square root of both sides:

\(t = \pm5\)

Since we cannot have a negative time, we can disregard the negative solution.

Therefore, the tennis ball will hit the ground  \(5\) seconds after being dropped from an initial height of  \(400\) feet.

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First we need to know what a bisector is. A bisector is a line that divides an object into equal parts. So, If we know that line L is a bisector line, we know that PA = PB.

Hope this Helps!!! :)

To find the expected number of sixes appearing on three die rolls, we can calculate the probability of rolling a six on each individual roll and then multiply it by the number of rolls.

The probability of rolling a six on a single roll of a fair die is 1/6, since there are six equally likely outcomes (numbers 1 to 6) and only one of them is a six.

Since the rolls are independent events, we can multiply the probabilities together to find the probability of rolling a six on all three rolls:

(1/6) * (1/6) * (1/6) = 1/216

Therefore, the probability of rolling a six on all three rolls is 1/216.

To find the expected number of sixes, we multiply the probability by the number of rolls:

Expected number of sixes = (1/216) * 3 = 1/72

So, the expected number of sixes appearing on three die rolls is 1/72.

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Answer:

n=2

Step-by-step explanation:

Answer:

the value of n is 2 llalala

Answer:

maybe the answer ris 36×4 and then 30×4 and subtract the result?!?!

Answer: D

Step-by-step explanation:

3+30 is 33

33-15 is 18

So the answer is D.

Step-by-step explanation:

use the formula given

a is the first term

d is the differences between adjacent numbers

and then you substitute the value

Step-by-step explanation:

= 1/2 ÷ 2/5

= 1/2 × 5/2

= 5/4

Answer:

\( \sf 1 \frac{1}{4} \)

Step-by-step explanation:

\( \sf = \frac{1}{2} \div \frac{2}{5} \)

\( \sf = \frac{1}{2} \times \frac{5}{2} \)

\( \sf = \frac{1 \times 5}{2 \times 2} \)

\( \sf = \frac{5}{4} \)

\( \sf = 1 \frac{1}{4} \)

Based on the given information, a sample of 140 patients found that 35 were uninsured. To determine if there is enough evidence to support the director's claim, we need to conduct a hypothesis test.

The null hypothesis (H0) is that the proportion of uninsured patients is equal to the director's claim. The alternative hypothesis (Ha) is that the proportion of uninsured patients is not equal to the director's claim.
To test this, we calculate the test statistic and compare it to the critical value at the 0.02 significance level. If the test statistic falls in the rejection region, we reject the null hypothesis.
Using the formula for proportions, the test statistic is calculated as (35/140) - (director's claim).

Then, we compare the test statistic to the critical value from the standard normal distribution.
If the test statistic falls in the rejection region (critical value > test statistic), we reject the null hypothesis and conclude that there is enough evidence to support the director's claim.

If not, we fail to reject the null hypothesis and do not have enough evidence to support the claim.
In order to provide a more accurate answer, please provide the director's claim and the critical value at the 0.02 level.

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six squared plus x squared equal to nineteen squared is 18.02

Or, 6² + x² = 19² , this implies 18.02

Square value:

A square is the result of multiplying a number by itself. The verb "to square" is used to express this operation. A square is the same as a power of 2 and is denoted by an exponent 2; for example, the square of 3 can be written as 32, which is the number 9. In some cases where the exponent is not available, such as in programming languages ​​or plain text files, the notation x²  or x* *2 can be used instead of x2. The adjective corresponding to square is quadratic.

According to the Question:

6² + x² = 19²

⇒ x² = 19² - 6²

⇒ x² = 361 - 36

⇒ x² = 325

⇒ x = √325

⇒x = 18.02

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The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

From the information provided above, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius (r) = 3

Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

Step-by-step explanation:

Divide both sides by 1/3, which is equivalent to mulitplying by 3

x - 10 = -12

Add 10 to both sides

x = -2

let's say for a second that that angle is θ, so we can say that

\(sin^{-1}\left(\cfrac{\sqrt{7}}{7} \right)=\theta \qquad therefore\qquad tan\left[ sin^{-1}\left(\cfrac{\sqrt{7}}{7} \right) \right]\implies tan(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{this really means}}{sin^{-1}\left(\cfrac{\sqrt{7}}{7} \right)=\theta}\implies \cfrac{\stackrel{opposite}{\sqrt{7}}}{\underset{hypotenuse}{7}}=sin(\theta )\)

let us notice something, the opposite side is positive, that means either the I or II Quadrant, however the sin⁻¹ function has a range constrained to π/2 to -π/2, which excludes the II Quadrant, so that means that θ must be on the I Quadrant, where the adjacent side or cosine or "x" is positive too.

now, let's use the pythagorean theorem to get the adjacent side for θ

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{7}\\ a=adjacent\\ b=\stackrel{opposite}{\sqrt{7}}\\ \end{cases} \\\\\\ \pm\sqrt{7^2-(\sqrt{7})^2}=a\implies \pm\sqrt{42}=a\implies \stackrel{I~Quadrant}{+\sqrt{42}=a} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(tan(\theta )\implies \cfrac{\stackrel{opposite}{\sqrt{7}}}{\underset{adjacent}{\sqrt{42}}}\implies \cfrac{\sqrt{7}\cdot \sqrt{42}}{\sqrt{42}\cdot \sqrt{42}}\implies \cfrac{\sqrt{294}}{42}\implies \cfrac{7\sqrt{6}}{42}\implies \cfrac{\sqrt{6}}{6}\)

When a figure is dilated with a scale factor of 1, there is no change in size or shape. The figure remains unchanged, with every point retaining its original position. This is because a scale factor of 1 indicates that there is no stretching or shrinking occurring.

When a figure is dilated with a scale factor of 1, it means that the size and shape of the figure remains unchanged. The word "dilate" means to stretch or expand, but in this case, a scale factor of 1 implies that there is no stretching or shrinking occurring.

To understand this concept better, let's consider an example. Imagine we have a square with side length 5 units. If we dilate this square with a scale factor of 1, the resulting figure will have the same side length of 5 units as the original square. The shape and proportions of the figure will be identical to the original square.

This happens because a scale factor of 1 means that every point in the figure remains in the same position. There is no change in size or shape. The figure is essentially a copy of the original, overlapping perfectly.

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Answer: the answer is 700

Answer:

its 700.

Step-by-step explanation:

700.

According to the liquidity preference hypothesis, the expected forward rate in the third year when ∆ is 1% is 12.18%, and the yield to maturity on a three-year zero-coupon bond is 10.35%.

According to the liquidity preference hypothesis, the interest rate for a long-term investment is expected to be equal to the average short-term interest rate over the investment period. In this case, the expected forward rate for the third year is stated as 4.28%.

To calculate the expected forward rate for the third year, we first need to calculate the prices of zero-coupon bonds for each year. Let's start by calculating the price of a four-year zero-coupon bond, which is determined to be $731.74.

The rate of return on a four-year zero-coupon bond is then calculated as follows:

Rate of return = (1000 - 731.74) / 731.74 = 0.3661 = 36.61%.

Next, we use the yield of the four-year zero-coupon bond to calculate the price of a three-year zero-coupon bond, which is found to be $526.64.

The expected rate in the third year can be calculated using the formula:

Expected forward rate for year 3 = (Price of 1-year bond) / (Price of 2-year bond) - 1

By substituting the values, we find:

Expected forward rate for year 3 = ($959.63 / $865.20) - 1 = 0.1088 or 10.88%

If ∆ (delta) is 1%, we can calculate the expected forward rate in the third year as follows:

Expected forward rate for year 3 = (1 + 0.1088) × (1 + 0.01) - 1 = 0.1218 or 12.18%

Therefore, according to the liquidity preference hypothesis, the expected forward rate in the third year, when ∆ is 1%, is 12.18%.

Additionally, the yield to maturity on a three-year zero-coupon bond can be calculated using the formula:

Yield to maturity = (1000 / Price of bond)^(1/n) - 1

Substituting the values, we find:

Yield to maturity = (1000 / $526.64)^(1/3) - 1 = 0.1035 or 10.35%

Hence, the yield to maturity on a three-year zero-coupon bond is 10.35%.

In conclusion, according to the liquidity preference hypothesis, the expected forward rate in the third year when ∆ is 1% is 12.18%, and the yield to maturity on a three-year zero-coupon bond is 10.35%.

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Mark should use the volume formula to determine the number of cubic feet of soil needed to fill the planter half-full. To fill the planter half-full, he would require 18 cubic feet of soil.

In order to determine the amount of soil needed to fill the planter half-full, Mark should use the volume formula. The volume of a rectangular box is calculated by multiplying its length, width, and height. In this case, the length of the planter is 12 feet, the width is 6 feet, and the height is 3 feet. By multiplying these dimensions together (12 x 6 x 3), Mark can find the total volume of the planter, which is 216 cubic feet.

However, the question specifies that Mark needs to fill the planter only half-full. Therefore, he would require half of the calculated volume, which is 216 cubic feet divided by 2, resulting in 108 cubic feet. Therefore, Mark needs 108 cubic feet of soil to fill the planter half-full.

It's worth noting that the trick detail mentioned in the question is the requirement for the planter to be half-full. This means Mark needs to consider only half of the total volume when calculating the amount of soil required.

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The probability that a randomly selected american enjoys both activities is 23 % .

Given :

14 % of americans like to only cook and 48 % of americans like to only shop, while 85 % enjoy either cooking or shopping .

14 % = 0.14

48 % = 0.48

overlapping is 85 % = 0.85

P ( A ) = 0.14

P ( B ) = 0.48

P ( A and B ) = 0.85

we know that,

P ( A or B ) = P ( A ) + P ( B ) - P ( A and B )

= 0.14 + 0.48 - 0.85

= 0.62 - 0.85

= -0.23

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Answer:

120

Step-by-step explanation:

5!, called 5 factorial is the product of all positive intergers from 5 down though 1. by definition, 0! is 0.

Factorials are basically the number times itself-1 the 2 the 3 until it times it by itself-(itself-1). n!=n*(n-1)*n(n-2).....*n-(n-1).

For example 2!=2*1=2 and 6!=6*5*4*3*2*1=720

keep in mind that I am not an expert so the blanks I filled in might be wrong and the explanation might have errors

5!, called "5 factorial," is the product of all positive integers from 5 down through 1. By definition, 0! is equal to 1.

Factorial is a mathematical operation denoted by an exclamation mark (!). It represents the product of all positive integers from a given number down to 1. In the case of 5!, it is calculated as 5 × 4 × 3 × 2 × 1, resulting in the value of 120.

The exclamation mark notation allows us to represent the factorial of a number concisely. For example, 5! represents the factorial of 5. It is important to note that 0! is defined to be equal to 1. This is a special case in factorial calculations. While it may seem counterintuitive, it is defined this way to maintain consistency and enable certain mathematical calculations and formulas.

Therefore, 5! is the product of all positive integers from 5 down through 1, equaling 120, and 0! is defined to be 1.

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To find the vertical, horizontal, and oblique asymptotes of the function f(x) = (x²-1)/(x-3), we can analyze the behavior of the function as x approaches certain values.

1. Vertical Asymptotes: Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a specific value. To find vertical asymptotes, we look for values of x that make the denominator of the function equal to zero, excluding any corresponding factors in the numerator that cancel out. In this case, we set x-3 = 0 and solve for x:

x - 3 = 0

x = 3

Therefore, there is a vertical asymptote at x = 3.

2. Horizontal Asymptote: To determine the horizontal asymptote, we examine the behavior of the function as x approaches positive or negative infinity. We can find the horizontal asymptote by comparing the degrees of the numerator and denominator. In this case, the degree of the numerator is 2 and the degree of the denominator is 1. Since the degree of the numerator is greater, there is no horizontal asymptote.

3. Oblique Asymptote: To find the oblique asymptote, we divide the numerator by the denominator using long division or synthetic division. The quotient represents the equation of the oblique asymptote if the degree of the numerator is exactly one greater than the degree of the denominator.

Performing long division, we have:

       x - 2

    -------------

x - 3 | x² - 1

       - (x² - 3x)

       ------------

                3x - 1

               - (3x - 9)

               ----------

                         8

The quotient is x - 2, which represents the equation of the oblique asymptote.

In summary:

- The function has a vertical asymptote at x = 3.

- There is no horizontal asymptote.

- The oblique asymptote is given by the equation y = x - 2.

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A circle is a curve sketched out by a point moving in a plane. Except for the first statement both the second and the third statement is true.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

The complete question is mentioned in the below image.

For the given circle,

The area of the sector is,

Area of sector = π(4)²×[2π/(3×2π)] = 16π/3

The area of the circle is,

Area of the circle = π×(4)² = 16π

The length of the Arc is,

Length of the arc = 2π×(4)×[2π/(3×2π)] = 8π/3

Hence, Except for the first statement both the second and the third statement is true.

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Answer:

yehhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

42°

Step-by-step explanation:

These traingles are refelctions, A≅D   B≅C

Answer:

I got 3x^2 -3x-60

but you might wanna check again.

Answer:

52 because in 1 cup equivalent to 8 ounces.. if she drinks 6 cups that is 48 ounces plus the half cups 4 ounces so 52 ounces all in all

Answer:

52

Step-by-step explanation: