Students in a Statistics course claimed that doing homework had not helped prepare them for the mid- term exam. The exam score (y) and homework score (x) averaged up to the time of the midterm for the

the probability of randomly selecting a red marble from the urn is 9/43. This means that if you were to randomly select a marble from the urn, the chances of selecting a red marble would be 9/43. This is because there are 9 red marbles in the urn out of a total of 43 marbles in the urn.

An urn contains 43 marbles consisting of 9 red marbles, 30 blue marbles, and 4 yellow marbles. To find out the probability of randomly selecting a red marble from the urn, we first need to find the total number of marbles in the urn. The total number of marbles in the urn is obtained by adding up the number of red marbles, blue marbles, and yellow marbles in the urn. Thus, the total number of marbles in the urn is:
9 + 30 + 4 = 43
Therefore, there are a total of 43 marbles in the urn. The probability of randomly selecting a red marble from the urn is obtained by dividing the number of red marbles in the urn by the total number of marbles in the urn. Thus, the probability of randomly selecting a red marble from the urn is:
9/43
Therefore, the probability of randomly selecting a red marble from the urn is 9/43. This means that if you were to randomly select a marble from the urn, the chances of selecting a red marble would be 9/43. This is because there are 9 red marbles in the urn out of a total of 43 marbles in the urn.

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Given:

1st graph suits the equation.

Above graph is the final answer.

The rate at which air is being pumped in when the radius of the sphere is 10 cm and increasing at a rate of 2 cm/s is 400π/3 cm³/s.

The volume V of a sphere with radius r is given by V = (4/3)πr³. Taking the derivative of this expression with respect to time t, we get dV/dt = 4πr²(dr/dt). This equation relates the rate of change of volume to the rate of change of the radius. We are given that the radius is increasing at a rate of 2 cm/s, so dr/dt = 2 cm/s.

At the instant when the radius is 10 cm, we can find the rate at which air is being pumped in by substituting r = 10 cm and dr/dt = 2 cm/s into the equation for dV/dt. Thus, we have dV/dt = 4π(10)²(2) = 800π cm³/s.

Therefore, when the radius of the spherical balloon is 10 cm and is increasing at a rate of 2 cm/s, the rate at which air is being pumped in is 400π/3 cubic centimeters per second.

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CM is the perpendicular bisector of AB at M, it means that CM is perpendicular to AB, and AM=BM. Therefore, we have two right triangles, triangle AMC and triangle BMC, with a shared side CM, and AM=BM.

By the Pythagorean theorem, we know that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Applying this to triangles AMC and BMC, we have:

AC² = AM² + CM²

BC² = BM² + CM²

Since AM=BM, we can substitute AM for BM in the second equation, giving:

BC² = AM² + CM²

Since the left-hand sides of these two equations are equal (by the given that CM is the perpendicular bisector of AB), we can set their right-hand sides equal to each other and simplify:

AC² = BC²

Taking the square root of both sides gives us:

AC = BC

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Step-by-step explanation:

They were quite antiquated.B) 5x + 52

The pair of equations whose lines are perpendicular is (d) y = 1/6x + 3; y = -6x - 3

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

The pair of equations

By definition;

The slopes of perpendicular lines are opposite reciporcals

So, we have

(a) -1/3 and -3 false

(b) -3 and -6 false

(c) 3 and 3 false

(d) 1/6 and -6 true

Hence, the equations are (d) y = 1/6x + 3; y = -6x - 3

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Answer:

5.7 gal / hour

5.7 gal / 60 min

5.7(16) c / 60 min

Answer:

13.12%

Step-by-step explanation:

The population mean is greater than 30.To determine the sample mean that would result in a p-value of 0.05, we need to work backwards from the given significance level.

First, we need to find the test statistic. Since the alternative hypothesis is one-sided (μ>30), we will use a one-sample z-test. The test statistic is calculated as:

z = (xbar - μ) / (s / sqrt(n))

where xbar is the sample mean, μ is the hypothesized population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

Since we want the p-value to be equal to 0.05, we need to find the z-score that corresponds to a one-tailed area of 0.05. Using a standard normal distribution table or calculator, we find that this z-score is 1.645.

Substituting this value into the formula for the test statistic, we get:

1.645 = (xbar - 30) / (10 / sqrt(70))

Solving for xbar, we get:

xbar = 30 + 1.645 * (10 / sqrt(70))

xbar = 31.77

Therefore, the sample mean that would result in a p-value of 0.05 is 31.77. This means that if we were to obtain a sample mean of 31.77 or higher, we would reject the null hypothesis at a significance level of 0.05 in favor of the alternative hypothesis that the population mean is greater than 30.

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P:-

\(\\ \sf\longmapsto (x+y)^2-4x^2y^2\)

\(\\ \sf\longmapsto x^2+2xy+y^2-4x^2y^2\)

\(\\ \sf\longmapsto x^2+y^2-4x^2y^2+2xy\)

Q:-

\(\\ \sf\longmapsto x^2-2(x+y)-y^2\)

\(\\ \sf\longmapsto x^2-2x-2y-y^2\)

\(\\ \sf\longmapsto x^2-y^2-2x-2y\)

S:-

\(\\ \sf\longmapsto x^2-4x-21+10y-y^2\)

\(\\ \sf\longmapsto x^2-y^2-4x+10y-21\)

T:-

\(\\ \sf\longmapsto a^2-10a+24+6b-9b^2\)

\(\\ \sf\longmapsto a^2-9b^2-10a+6b+24\)

Answer:

One segment is 8.89 long and the other one is: 11.11 long

Step-by-step explanation:

Recall that the bisector of a triangle divides the opposite side it intersects into two segments that are proportional to the other two sides of the triangle.

In our case the bisector is generated on the angle opposite to the size 20 side (it is the smallest angle in the triangle since it is opposite to the smallest side). This bisector divides the side of length 20 into a segment of length x and a segment of length 20-x.

The proportionality indicated by the bisector theorem gives;

\(\frac{20-x}{x} =\frac{30}{24}\)

and we can solve for "x":

\(\frac{20-x}{x} =\frac{30}{24}\\24\,(20-x)=30\,x\\480-24\,x=30\,x\\480=54\,x\\x=480/54\\x\approx8.89\)

Then the other segment is:  20 - 8.89 = 11.11

Answer:

see attached

Step-by-step explanation:

(i) F' shown in red = Rotation 180° about point (2, 1)

(ii) F'' show in blue = Reflection of F' in x-axis

Answer:

i think it is b but I can be wrong

Answer:

Its B sorry if im wrong im 75% sure its b tho

Step-by-step explanation:

<3

The correct answer is A. If a given resource has not been fully used in a linear programming problem, it indicates that the resource constraint is not binding. In other words, the optimal solution does not require the full utilization of that resource.

Therefore, the shadow price associated with that constraint will have a positive value, indicating the increase in objective function value with a unit increase in the availability of that resource. For a linear programming problem, if a given resource has not been fully used, we can conclude that the shadow price associated with that constraint will have a value of zero.

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Answer:q = 6+43r/9

Step-by-step explanation:

Assuming R=9q-43r-6 is what you meant
R+6 = 9q - 43r
R + 6 + 43r = 9q
q = 6+43r/9

Answer:

it 2,5

Step-by-step explanation:

Answer: y is 40 x is 60

Step-by-step explanation:

Answer:

x=40 and y =5

Step-by-step explanation:

Answer:

1 solution

Step-by-step explanation:

A system of linear equations has no solution when the graphs are parallel.

Answer:

g = At/60

Step-by-step explanation:

A = 60(g/t)

To solve for 'g'

Open the bracket

A = 60g/t

Multiply both sides by t

At = 60g

Divide both sides by 60

At/60 = 60g/60

At/60 = g

Answer:

Step-by-step explanation:

-2 <= x + 3

x >= -5

x+3 <= 7

x <= 4

Answer:

x ∈[-5,4]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step one:

we are told that the expression for profit is

\(p = 1.25n - 475\)-----------------1

the above equation represents the situation

given

profit is  $950

Required

n=number of bars

950=1.25n-475

collect like terms

950-475=1.25n

475=1.25n

divide both sides by 1.25

n=475/1.25

n= 380candy bars

George's dog is approximately 32.41 meters away from its crate, if it ran 22 meters, turned and ran 11 meters, and then turned 120° to face its crate.

To determine the distance from George's dog to its crate after the described movements, we can use the concept of a triangle and trigonometry.

The dog initially runs 22 meters, then turns and runs 11 meters, forming the two sides of a triangle. The third side of the triangle represents the distance from the dog's final position to the crate.

To find this distance, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c and angle C opposite side c, the equation is c² = a² + b² - 2abcos(C).

In this case, a = 22 meters, b = 11 meters, and C = 120°. Plugging these values into the equation, we have

c² = 22² + 11² - 2(22)(11)cos(120°).

Evaluating the expression, we get

c ≈ 32.41 meters.

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Answer:

The answer is A: 9/11

Answer: 4.8lbs, This claim is false

Step-by-step explanation:

Leo weighs 192 pounds. Then Leo's heart weight will be 76.258 ounces. So, its claim is false.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Hummingbirds have abnormally huge hearts for their body size. In the event that an individual's heart was essentially as large as a hummingbird's, their heart would weigh as much as an enormous canine's. A typical hummingbird weighs 0.3524 ounces and has a heart that weighs 0.00875 ounces.

The ratio of heart to weight is given as,

Ratio = 0.00875 / 0.3524

Ratio = 0.024829

The average weight of a large dog is usually more than 80 pounds. Leo weighs 192 pounds. Then Leo's heart weight is calculated as,

⇒ 0.024829 x 192 x 16

⇒ 76.28 ounces

Their heart weight of Leo is less than the weight of the dog. So, its claim is false.

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A proof competition is held annually by Contradiction Club, with special prizes awarded for first, second, third, and fourth place. If 16 students participate in the competition this year, the awards can be allocated among the students in 120 different ways.

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I understand that algebraic operations can be confusing at first, but I'll do my best to explain them step by step. Let's start with addition and subtraction in algebra, and then move on to multiplication and division.

Addition in Algebra:

Start with two or more algebraic expressions or terms that you need to add together.

Identify like terms, which are terms that have the same variables raised to the same powers. For example, 3x and 5x are like terms because they both have the variable x raised to the power of 1.

Combine the coefficients (the numbers in front of the variables) of the like terms. For example, if you have 3x + 5x, you add the coefficients 3 and 5 to get 8.

Write the sum of the coefficients next to the common variable. In this case, it would be 8x.

If there are any remaining terms without a like term, simply write them as they are. For example, if you have 8x + 2y, you cannot combine them because x and y are different variables.

Subtraction in Algebra:

Subtraction is similar to addition, but instead of adding terms, we subtract them.

Start with two algebraic expressions or terms.

Identify like terms, as we did in addition.

Instead of adding the coefficients, subtract the coefficients of the like terms.

Write the difference of the coefficients next to the common variable.

Handle any remaining terms without a like term in the same way as in addition.

Multiplication in Algebra:

Multiply the coefficients of the terms together. For example, if you have 2x * 3y, multiply 2 by 3 to get 6.

Multiply the variables together. In this case, multiply x by y to get xy.

Write the product of the coefficients and variables together. So, 2x * 3y becomes 6xy.

Division in Algebra:

Divide the coefficients of the terms. For example, if you have 12x / 4, divide 12 by 4 to get 3.

Divide the variables. If you have x / y, you cannot simplify it further because x and y are different variables. So, you leave it as x / y.

Remember, these steps are general guidelines, and there might be additional rules and concepts specific to certain algebraic expressions.

It's important to practice and familiarize yourself with these operations to gain confidence and improve your understanding.

Percentage for each enantiomer is 95%, 5%. Option (d) is Correct.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages. %, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

% ee = % enantiomer A - % ensarstomer B

wheee ee is enantiomeric excess.

ee = 90%.

In the provided options, 90%. the difference is given by subtracting 95%, 5%

95% - 5% = 90%

4th option is 5%, 90% correct.

Percentage of each enantiomer is 95%, 5%.

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Answer:

ehhhh probably C cuz it makes more sense

If the total amount of money gathered by Diego in the jar is $7.05. The link between the number of nickels n and the quantity of money in dollars is expressed by the equation 0.05 + n = 7.05.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Let $7.05 exists the total amount of money collected by Diego in the jar.

Where d is the number of dimes

n is the number of nickels

A) Let the equation be 0.05 + n = 7.05

Subtract 0.05 from both sides of the equation, we get

0.05 + n - 0.05 = 7.05 - 0.05

simplifying the above equation, we get

n = 7

B) Let the equation be 0.05 n = 7.05

Divide the equation by 0.05, we get

0.05 n / 0.05 = 7.05 / 0.05

n = 141

C) Let the equation be 7.05 + n = 0.05

Subtract 7.05 from both sides of the equation, we get

7.05 + n - 7.05 = 0.05 - 7.05

simplifying the above equation, we get

n = - 7

D) Let the equation be 7.05n = 0.05

Divide the equation by 7.05, we get

7.05 n / 7.05 = 7.05 / 0.05

n = 1 / 141.

If the total amount of money gathered by Diego in the jar is $7.05. The link between the number of nickels n and the quantity of money in dollars is expressed by the equation 0.05 + n = 7.05.

Therefore, the correct answer is option A) 0.05 + n = 7.05.

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