Solve using substitution.
y = 5x - 9
y = -2x + 5

Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

Answer: 48 cups

Step-by-step explanation: The way to scale a recipe by number of servings is to multiply the original amount by the desired serving size and then divide by the original serving size.

The correct statement is Option B: I and III are true, II is false. Amy and Bob will continue to specialize and trade to mutual advantage, and Bob is better off than before.

I. Amy and Bob will continue to specialize and trade to mutual advantage: This statement is true. Since Amy can pick three baskets of either apples or grapes in an hour, she has a comparative advantage in picking both fruits compared to Bob. Bob, on the other hand, can only pick two baskets of either fruit in an hour. By specializing in their respective areas of comparative advantage and trading with each other, both Amy and Bob can benefit from increased productivity and efficiency.

II. Amy is better off than she was before: This statement is false. Although Amy has become more efficient in picking both apples and grapes, she is not better off compared to before because her productivity remains the same. She can still pick three baskets in an hour, whether it's apples or grapes.

III. Bob is better off than he was before: This statement is true. Bob has improved his productivity in both apple and grape picking. Previously, he could only pick one basket of either fruit, but now he can pick two baskets in an hour. This increase in productivity makes Bob better off than he was before.

Therefore, the correct statement is Option B: I and III are true, II is false.

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Answer:

Approximately 1.0% of the remaining water leaked out in the second hour.

Step-by-step explanation:

If 20% of the water leaked out in the first hour, then 80% of the water remained in the barrel at the end of the first hour.

To find out what percent of the remaining water leaked out in the second hour, we need to first calculate the fraction of the original amount of water that remains after the first hour. If we let W be the original amount of water in the barrel, then the amount of water that remains after the first hour is:

W1 = W(1 - 0.20) = 0.8W

where W1 is the amount of water remaining after the first hour.

The amount of water that leaks out in the second hour is not given, so let's call it x. Then, the amount of water remaining in the barrel after the second hour is:

W2 = W1(1 - x)

Substituting the expression for W1 we found above, we get:

W2 = 0.8W(1 - x)

We want to find the percent of the remaining water that leaked out in the second hour, which is equal to the fraction (x/W2) multiplied by 100%. So we have:

(x/W2) x 100% = (x / (0.8W(1 - x))) x 100%

We're given that this percentage is equal to some value, say P. So we can write:

P = (x / (0.8W(1 - x))) x 100%

Solving for x:

x = (0.8W(1 - x) / 100%) x P

x = 0.008W(1 - x)P

Expanding and simplifying:

x = 0.008WP - 0.008xP

1.008xP = 0.008WP

x = (0.008WP) / 1.008P

x = 0.00794W

Therefore, the percent of the remaining water that leaked out in the second hour is:

(x/W2) x 100% = (0.00794W / (0.8W(1 - 0.00794))) x 100% ≈ 1.0%

So approximately 1.0% of the remaining water leaked out in the second hour.

To determine the value of the rate constant (k) and the half-life for a first-order reaction, we can use the integrated rate law and the given information. The value of [A]₀/[A] will be determined when the reaction is 44.0% complete.

For a first-order reaction, the integrated rate law is given by the equation: ln([A]₀/[A]) = -kt, where [A]₀ is the initial concentration of the reactant, [A] is the concentration at a given time, k is the rate constant, and t is the time.

Since the reaction is 44.0% complete, the remaining concentration of the reactant is 56.0% ([A] = 0.56[A]₀).

Plugging in the values into the integrated rate law equation, we have: ln([A]₀/0.56[A]₀) = -k(4.0 minutes).

Simplifying the equation, we get: ln(1/0.56) = -4.0k.

Using a calculator, we find that ln(1/0.56) is approximately -0.5878.

Now we can solve for k: -0.5878 = -4.0k.

Dividing both sides by -4.0, we find that k is approximately 0.1469 min⁻¹

To determine the half-life (t₁/₂), we can use the equation t₁/₂ = ln(2)/k. Plugging in the value of k, we have: t₁/₂ = ln(2)/0.1469 ≈ 4.72 minutes.

Therefore, the value of [A]₀/[A] when the reaction is 44.0% complete is approximately 1/0.56, the rate constant (k) is approximately 0.1469 min⁻¹, and the half-life (t₁/₂) is approximately 4.72 minutes.

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Answer:

-350ft

Step-by-step explanation:

so basically 605 is negative and 255 is a negative then you add those two then it would be -860 then you subtract the positive 475 and that will equal -350

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).

The point-slope form of an equation of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line

m is the slope of the line.

We can use the given point (−5,−2) as (x1,y1)

Choose any value for the slope m to write the equation of the line in point-slope form.

For example:

Option 1:

Let's choose the slope m to be 2.

Then the equation of the line becomes:

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

Simplifying the equation:

y + 2 = 2(x + 5)

Option 2:

Let's choose the slope m to be -3.

Then the equation of the line becomes:

y - (-2) = -3(x - (-5))

Simplifying the equation:

y + 2 = -3(x + 5)

Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).

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Answer:

It's the third option.

Step-by-step explanation:

the answer is b and c

sorry if im wrong

Answer:  see below

Step-by-step explanation: Initial velocity = terminal velocity. At the top of travel, the velocity is 0 as the ball is motionless. Then it travels 3 seconds (due to gravity). Grav is 9.8m/sec squared. So 1st second = 9.8m. 2nd second is 2x9.8m. 3rd second is 3x9.8m = 29.4 m/sec.

Answer:

Step-by-step explanation:

Given points

Midpoint formula

Midpoint is (2, 2)

Answer:

8, 6, 4, 2

Step-by-step explanation:

f(n)=-2(n-1)+8

Plug n =1

f(1)=-2(1-1)+8 = - 2*0+8 = 0+ 8 = 8

Plug n =2

f(1)=-2(2-1)+8 = - 2*1+8 = - 2+ 8 = 6

Plug n =3

f(1)=-2(3-1)+8 = -2*2+8 = -4+ 8 = 4

Plug n =4

f(1)=-2(4-1)+8 = -2*3+8 = -6+ 8 = 2

Answer:

x = 9

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

50° is an exterior angle of the triangle, thus

38 + 4x - 24 = 50 , that is

14 + 4x = 50 ( subtract 14 from both sides )

4x = 36 ( divide both sides by 4 )

x = 9

Answer:

\(\huge\boxed{\sf x = 9}\)

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of non-adjacent interior angles.

So,

50 = 38 + 4x - 24

50 = 4x + 14

Subtract 14 to both sides

50 - 14 = 4x

36 = 4x

Divide 4 to both sides

36 / 4 = x

x = 9

\(\rule[225]{225}{2}\)

Hope this helped!

We started by finding the area of the two respective circles, then we found the area of the path, after which we estimated the number of sand bags needed to be 51.8 bags

Ans 51.8 bags

Given data

Area of path = Area of outer edge - area of garden

Area of path = πD^2/4 - πd^2/4

Area of path = 3.142*36^2/4 - 3.142*30^2/4

Area of path = 3.142*1296/4 - 3.142*900/4

Area of path = 4072.032/4 - 2827.8/4

Area of path = 1018.008 - 706.95

Area of path = 311.058 square yd

1 bag of sand will cover 6yd^2

x bags of sand will cover 311.058 yd^2

cross multiply we have

x = 311.058/6

x = 51.843 bags of sand

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Answer:

Explained below.

Step-by-step explanation:

(1)

Sample space is a set of all possible outcomes of an experiment.

The sample space in this case is:

S = {HF, HW, MF, MW}

(a)

Compute the value of P (W) as follows:

P (F) + P (W) = 1

P (W) = 1 - P (F)

P (W) = 1 - 0.50

P (W) = 0.50

(b)

Compute the value of P (MF) as follows:

P (HF) + P (MF) = P (F)

P (MF) = P (F) - P (HF)

P (MF) = 0.50 - 0.20

P (MF) = 0.30

(c)

Compute the value of P (M) as follows:

P (M) = P (MF) + P (MW)

P (M) = 0.30 + 0.10

P (M) = 0.40

Compute the value of P (H) as follows:

P (H) + P (M) = 1

P (H) = 1 - P (M)

P (H) = 1 - 0.40

P (H) = 0.60

Answer:

1. $19.91

Step-by-step explanation:

a. D. magna is an effective grazer of the G. semen alga. b. a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

a. The scatterplot of the data shows a clear negative correlation between the number of D. magna grazers and the net growth rate of G. semen. As the number of grazers increases, the net growth rate of G. semen decreases. This suggests that D. magna is an effective grazer of the G. semen alga.

b. The correlation coefficient between the number of grazers and the net growth rate is -0.996. This indicates a strong negative correlation between the two variables, which supports the interpretation that D. magna is an effective grazer of G. semen. The closer the correlation coefficient is to -1, the stronger the negative correlation between the two variables. In this case, the correlation coefficient is very close to -1, which indicates a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

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Bro you in my math class you cheatin yo I’m crying

A translation down 3 units and a rotation of 90° counterclockwise about the origin.

What is transformation?

In mathematics, a transformation is a function that maps points from one coordinate system to another. Transformations are used to describe the movement or changes of objects in a space, such as points, lines, or shapes.

The series of transformations that map △ABC to △A'B'C' is:

A translation down 3 units and a rotation of 90° counterclockwise about the origin.

To see why, we can apply each transformation in sequence:

Translation down 3 units: This moves point A from (1,3) to (-2,0), point B from (4,4) to (1,1), and point C from (3,0) to (0,-3).

Rotation of 90° counterclockwise about the origin: This rotates point A' from (-2,0) to (0,-2), point B' from (1,1) to (-1,1), and point C' from (0,-3) to (3,0).

Therefore, the final image △A'B'C' is obtained by translating △ABC down 3 units and rotating it 90° counterclockwise about the origin. Option A, "Translation down 3 units and a rotation of 90° counterclockwise about the origin," is the correct answer.

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Answer:

-1.3705187977

Answer:

\(\frac{28}{27}\)

Step-by-step explanation:

\(\frac{2(4+\frac{2}{3} )}{9}\\ \\\frac{2}{9} * \frac{14}{3} \\ \\\frac{28}{27}\)

The sample size should be selected as 100 in order to be 99% confident that the sample mean differs from the population mean by ±0.5 km (or within a range of 0.5 km).

To determine the sample size needed to estimate the distance students travel to school with a 99% confidence level and a margin of error of ±0.5 km, we can use the formula for sample size calculation:

n = (Z * σ / E)^2

where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence level, which corresponds to Z = 2.576)

σ = population standard deviation

E = margin of error

Plugging in the given values:

n = (2.576 * 2.25 / 0.5)^2

Calculating this equation gives us the required sample size:

n ≈ 99.98

Since we cannot have a fractional sample size, we round up to the nearest whole number.

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Answer:

0.236

Step-by-step explanation:

First put it in order

0.199, 0.211, 0.225, 0.236, 0.257, 0.264, and 0.283

Then find the middle number

0.236

Answer:

C

Step-by-step explanation:

put them in order, median is the middle number

Answer:

X would equal 5

Step-by-step explanation:

You isolate the variable by dividing each side by factors that don't contain the variable

The proper reason if this statement is provided as a fact at the beginning of a proof is: C. given.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Since the statement (<1 and <4 are vertical angles) is provided as a fact at the beginning of this proof, this ultimately implies that the statement is given.

Additionally, postulates are generally used to prove that some angles, two triangles are similar, or geometric shapes are congruent, etc.

In conclusion, truth is typically never used in a proof.

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Answer:

5, 25

Step-by-step explanation:

Answer:

y=-1/2x-9/2

Step-by-step explanation:

check picture

The equation of the line perpendicular to y = 2x - 3 that passes through the point (-3, -3) is y = (-1/2)x - 9/2 in slope-intercept form.

To find the equation of a line perpendicular to y = 2x - 3, we need to determine the slope of the original line and then find the negative reciprocal of that slope.

The original line has a slope of 2. The negative reciprocal of 2 is -1/2.

Now, we have the slope (-1/2) and the point (-3, -3) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Substituting the values:

y - (-3) = (-1/2)(x - (-3))

y + 3 = (-1/2)(x + 3)

Expanding and simplifying:

y + 3 = (-1/2)x - 3/2

y = (-1/2)x - 3/2 - 3

y = (-1/2)x - 3/2 - 6/2

y = (-1/2)x - 9/2

Therefore, the equation of the line perpendicular to y = 2x - 3 that passes through the point (-3, -3) is y = (-1/2)x - 9/2 in slope-intercept form.

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The solution of the equation is M = 21.

What is the solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given equation is

M/M + 4 +4/4 - M = M²/M² - 16

Cancel out common terms:

1 + 4 + 1 - M = 1 - 16

Now add the like terms of the left side expressions:

6 - M = 1 - 16

Now add the like terms of the right side expressions:

6 - M =- 15

Subtract 6 from both sides:

-M = -15 -6

-M = -21

Multiply -1 on both sides:

M = 21

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