A 5-foot stick casts a shadow of 4 feet at the same time Elin casts a shadow of 4 feet 6 inches.
How tall is Elin?
a. 5 ft
b. 6 ft
C. 5 ft 7.5 inches
d. 5 ft 6 inches

Answer:

x=12

Step-by-step explanation:

since they are supplementary they will have a sum of 180 degrees

The equation should look like this- (5x+4)+(4x+80)=180

after solving the equation- you get x=12

in order to see if that is correct you would plug in 12 where x is in our equation (5x+4)+(4x+80). which does equal 180 when 12 is plugged in

Therefore, 12 is your answer

Answer:

$200

Step-by-step explanation:

To find the retail price, multiply the wholesale cost by 1.6

125(1.6)

= 200

So, the retail price will be $200

We have the next information

Parabola that opens to the left

Vertex a the origin (0,0)

Focus (-4,0)

then we will have the next form for the equation of the parabola

where p is -4

therefore if we isolate the x we obtain

This type of study is prospective cohort study.

Controls consist of individuals from the source population who do not have the outcome of interest. Case-base sampling (also known as "case-cohort" sampling): Controls are selected from the population at risk at the beginning of the follow-up period in the cohort study within which the case-control study was nested.

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Answer:

Yoko bought 5 pounds of coffee.

If you want the steps, let me know. Hope this helps!!

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

6 percent of 5000 is 300. 300x2=600.

Sorry if im wrong

Answer:

$13.5

Step-by-step explanation:

cost of 1 text message= $1.80÷12 =$0.15

cost of 90 messages = $0.15×90 = $13.5

Answer: $13.50 for 90 text messages

Step-by-step explanation:

$0.15×90 = $13.5

$0.15 is the unit rate for 1 text message cost.

The perimeter of the triangle is 21.1 cm

The perimeter of a triangle is the total length of its three sides. It is calculated by adding the lengths of the three sides of the triangle. The perimeter is expressed in the same unit as the length of the sides.

Note:

The Pythagorean formula is a mathematical equation that relates to the sides of a right triangle.

Here we have

The right-angled triangle ABC

From the figure,

Length of side BC = 7 units

Length of side AC = 6 units

Using the Pythagorean formula,

=> AB² = BC² + AC²

=> AB² = 7² + 6²

=> AB² = 49 + 36

=> AB² = 65

=> AB = 8.06 [ Approx ]    

Hence,

Perimeter of the triangle = AB + BC + AC

= 8.06 + 7 + 6

= 21.06

= 21.1   [ Rounded to nearest one ]

Therefore,

The perimeter of the triangle is 21.1 cm

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Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.

In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.

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We need to compare the marginal cost of mining (MC1) with the marginal cost of obtaining ore through recycling (MC2). If MC1 is lower than MC2, it means that mining is a more cost-effective method than recycling.

Given that

MC1 = 7q1 and MC2 = 35 + 3q2,

we can set them equal to each other and solve for q1 to find the quantity at which the costs are equal.

In this case, 7q1 = 35 + 3q2.

To find the corresponding value of X, we substitute the quantity q1 into the inverse demand curve equation P = X - 0.19Q and solve for X.

Rearranging the equation, we have X = P + 0.19Q.

By substituting the expression for P and the quantity q1 into X, we can obtain the maximum value of X for which recycling is not cost-effective.

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Answer:

(4x+5)(x-3)

Step-by-step explanation:

You factor this by grouping together the numbers you get from multiplying/subtracting the numbers in the equation.

There is a weak relationship between education and income. Education not only raises the level of income is TRUE.

Education is the process of facilitating learning, or gaining of knowledge, skills and personal development.

Education effect on also your future. It makes bright future. if you are study in continuation it develops inner skills of human beings.

The income effect describes that the income effect evaluates consumer spending habits based on a change in their income. This is reflected in microeconomics via an upward shift in the downward-sloping demand curve.

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The given question is incomplete, complete question is:

statistics show that there is a weak relationship between education and income. please select the best answer from the choices provided

1. True

2. False

Answer:

the dryer and the washer                                                                      

Step-by-step explanation:

Answer:

The dryer cost $413

The washer cost $450

The total value in cents of all coins in the any row would be 16 cents.

In the pattern you described, the coins are arranged in rows such that each subsequent row has one more coin than the previous row. Let's analyze the values of the coins to determine the total value in cents of all the coins in the th row.

Assuming the values of the coins are as follows:

Penny: 1 cent

Nickel: 5 cents

Dime: 10 cents

We can observe that the pattern repeats after every three coins. The first three coins in the pattern are penny, nickel, dime. These coins have a total value of 1 + 5 + 10 = 16 cents.

For the subsequent rows, the pattern repeats with an offset of 3. For example, in the fourth row, the coins are penny, nickel, dime, which have the same total value as the first row, i.e., 16 cents.

So, regardless of the value of "th" (the row number), the total value in cents of all the coins in that row will always be 16 cents.

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The absolute maximum value of f on d is 4, and it occurs when x = 2, y = 0. The absolute minimum value of f on d is -37, and it occurs when x = 1, y = 3.

To find the absolute maximum and minimum values of f on the set d, use the following steps:Step 1: Calculate the partial derivatives of f with respect to x and y. f(x, y) = x2 4y2 − 2x − 8y 1∂f/∂x = 2x - 2∂f/∂y = -8y - 8Step 2: Set the partial derivatives to zero and solve for x and y.∂f/∂x = 0 ⇒ 2x - 2 = 0 ⇒ x = 1∂f/∂y = 0 ⇒ -8y - 8 = 0 ⇒ y = -1Step 3: Check the critical point(s) in the given domain d. 0 ≤ x ≤ 2, 0 ≤ y ≤ 3Since y cannot be negative, (-1) is not in the domain d. Therefore, there is no critical point in d.Step 4: Check the boundary of the domain d. When x = 0, f(x, y) = -8y - 1When x = 2, f(x, y) = 4 - 8y - 2When y = 0, f(x, y) = x2 - 2x - 1When y = 3, f(x, y) = x2 - 2x - 37Therefore, the absolute maximum value of f on d is 4, and it occurs when x = 2, y = 0.The absolute minimum value of f on d is -37, and it occurs when x = 1, y = 3.

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function: $f(x,y) = \(x^2 - 4y^2 - 2x - 8y +1$\) , The given domain is \(x^2 - 4y^2 - 2x - 8y +1$\)

Now we have to find the absolute maximum and minimum values of the function on the given domain d.To find absolute maximum and minimum values of the function on the given domain d, we will follow these steps:

Step 1: First, we have to find the critical points of the given function f(x,y) within the given domain d.

Step 2: Next, we have to evaluate the function f(x,y) at each of these critical points, and at the endpoints of the boundary of the domain d.

Step 3: Finally, we have to compare all of these values to determine the absolute maximum and minimum values of f(x,y) on the domain d.

Now, let's find critical points of the given function f(x,y) within the given domain d.To find the critical points of the function \($f(x,y) =\(x^2 - 4y^2 - 2x - 8y + 1$\)\), we will find its partial derivatives with respect to x and y, and set them equal to zero, i.e.\(\($f(x,y) = x^2 - 4y^2 - 2x - 8y + 1$\)\)

Solving these equations, we get:\($x = 1$\) and \($y = -1$\)So, the critical point is \($(1,-1)$.\)

Now, we need to find the function value at the critical point and the endpoints of the boundary of the domain d. We will use these five points:\($(0,0),(0,3),(2,0),(2,3),(1,-1)$\).

Now, let's evaluate the function f(x,y) at each of these five points:\(\($f(x,y) = x^2 - 4y^2 - 2x - 8y + 1$\)\)

Therefore, the absolute maximum value of f(x,y) is 1, and the absolute minimum value of f(x,y) is -67 on the domain d.

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This problem involves finding the probability distribution for the number of sums of 7 in five rolls of two dice and graphing the distribution with a probability histogram.

The problem also involves finding the probability distribution for the number of bull's eyes in eight attempts in an archery competition where Paul hits the bull's eye with 45% probability, finding the expected number of bull's-eyes, and interpreting the meaning of P(8).

(a) The probability of rolling a sum of 7 with two dice is 6/36 = 1/6. Thus, the probability of rolling a sum of 7 in one roll is 1/6. Using the binomial distribution formula, we can find the probability of getting exactly k sums of 7 in five rolls:

P(X=k) = (5 choose k) * \((1/6)^k\) * \((5/6)^(5-k)\)

(b) The probability distribution can be graphed with a probability histogram where the x-axis represents the number of sums of 7 and the y-axis represents the probabilities.

(c) The formula E(X) = np can be verified by finding the expected value of the number of sums of 7 in five rolls:

E(X) = 5 * (1/6) = 5/6

(a) The probability of hitting the bull's eye in an attempt is 0.45. Thus, the probability of hitting k bull's-eyes in eight attempts can be found using the binomial distribution formula:

P(X=k) = (8 choose k) * \((0.45)^k\) * \((0.55)^(8-k)\)

(b) The expected number of bull's-eyes in eight attempts can be found using the formula E(X) = np:

E(X) = 8 * 0.45 = 3.6

(c) P(8) represents the probability of hitting 8 bull's-eyes in 8 attempts, which is given by:

P(X=8) = (8 choose 8) * \((0.45)^8\) * \((0.55)^0\) = 0.013

This tells us that the probability of hitting 8 bull's-eyes in 8 attempts is very low, but still possible.

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James has $37.67 now after all his expenses

James had $x, his brother had $y, and his sister had $z when the morning began.

By using algebra,

James's sibling had twice as much money as James.

Now, x =y/2..... (i)

James had $27 fewer dollars than his sister did.

So, x = z - 27 ........ (ii)

⇒  {From equation (1)}

⇒ y/2 = z -27

⇒ y = 2z - 54

⇒ 2z - y =54 ..........(3)

Now, James and his sister each received $12 from his brother.

James now has $(x + 12), his brother now has $(y -24), and his sister now has $(z + 12).

Given that James' sister has twice as much money as James' brother after payoff,

So, z+12/2 = y-24

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

The result of resolving equations (3) and (4) is

3y = 54 + 100 = 154

⇒ y =  51.33.

The result of equation (3) is now z = 52.67.

And from equation (1), x = 51.3/2= 25.67

So, now, James has (25.67 + 12) = $37.67

Hence, James has $37.67 now after all his expenses

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Answer:

square, rectangle, parallelogram

Answer:

squares, rectangle, parallelogram, rhombus

Step-by-step explanation:

The method can you ALWAYS use to solve the quadratic equation will be the Quadratic Formula method. Then the correct option is C.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

A math question If an equation is written in standard form.

The factorization method sometimes gets difficult from the big number and in the case of the complex root. So, in that case, we use other methods.

In the Isolate the Square, we can find the roots of the equation. But the formula is also derived by this method. So, we do not even prefer this, method.

In this Quadratic Formula method, the formula is derived from the above method which is to Isolate the Square. Then this can be used always.

The method can you ALWAYS use to solve the quadratic equation will be the Quadratic Formula method. Then the correct option is C.

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Answer:

20%

Step-by-step explanation:

240240 many different possible rankings are there.

What is combination?

In mathematics, a choice is made from a set of various elements whenever the order of a choices is unimportant (unlike permutations). For instance, there really are three possible combinations of the two fruits, an apple and a pear, if three fruits are provided, like an apple, a tangerine, and a pear. Formally speaking, a set S's k distinctive components make up a subset known as a k-combination. In other words, 2 combinations are identical only if all of their members are the same. (How the people are arranged in each set is irrelevant.) how many k-combinations there are for a set of n components

The formula below calculates how many ways there are to make an ordered list of "unique components chosen from a set of 'n' elements, in accordance with the arrangement principle:

P(N,R)=  \(\frac{n!}{n-r!}\)

p(14,5)= 14!/9!

=14*13*12*11*10

=240240

Hence, 240240  many different possible rankings are there.

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a) The variable x is the average distance of Venus from the sun.

b) The equation for the given condition,

⇒ ⇒ 57.9 = 3.8 + x/2

c) The average distance of Venus from the sun = 108.2 million kilometers.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The average distance of Mercury from the sun = 57.9 million kilometers

And, This distance is 3.8 million kilometers more than half the average distance of Venus from the sun.

Now,

Since, The average distance of Mercury from the sun = 57.9 million kilometers

And, This distance is 3.8 million kilometers more than half the average distance of Venus from the sun.

Let the average distance of Venus from the sun = x

So, We can formulate;

⇒ 57.9 = 3.8 + x/2

Solve for x as;

⇒ 57.9 = 3.8 + x/2

⇒ 57.9 - 3.8 = x/2

⇒ x/2 = 54.1

⇒ x = 54.1 × 2

⇒ x = 108.2

Thus, The average distance of Venus from the sun = 108.2 million kilometers.

Therefore, a) The variable x is the average distance of Venus from the sun.

b) The equation for the given condition,

⇒ ⇒ 57.9 = 3.8 + x/2

c) The average distance of Venus from the sun = 108.2 million kilometers.

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Answer:

It would be the points (0,80) and (15,10)

Step-by-step explanation:

Just did it :)

Answer:

(0,80), (15,10)

Step-by-step explanation:

the second one is -14/3

edge 2022

Answer:

∠ ABD = 20°

Step-by-step explanation:

since BD is the angle bisector of ∠ ABC , then

∠ ABD = ∠ CBD , so

∠ ABD = \(\frac{1}{2}\) × ∠ ABC = \(\frac{1}{2}\) × 40° = 20°

Answer:

A F B J C

Step-by-step explanation:

Negative bases are not often used in logarithms because they produce complex results. For example, if the base is negative and the exponent is positive, the result will be a complex number.

Logarithms are generally used to solve equations or simplify complex problems. Having a negative base would complicate this process, as it would introduce complex numbers or even imaginary numbers into the equation. Consequently, it is not feasible to use negative bases with logarithms. Furthermore, if both the base and the exponent are negative, the result is undefined. This means that it is not possible to evaluate the expression. Therefore, for these reasons, it is usually not practical to use negative bases when working with logarithms.

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Answer:

To solve this equation for the coefficient of the x term, we need to first simplify the equation by solving for x. 5x^2 + 3x - 2 = x/3 Multiplying both sides by 3 to eliminate the fraction, we get: 15x^2 + 9x - 6 = x Bringing all terms to one side: 15x^2 + 8x - 6 = 0 Now, we can use the quadratic formula to solve for x: x = [-b ± √(b^2 - 4ac)] / 2a where a = 15, b = 8, and c = -6 x = [-8 ± √(8^2 - 4(15)(-6))] / 2(15) x = [-8 ±

There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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The statistic that would not change if 50 points were added to each score in the SAT tests is the Standard Deviation.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance.

The bigger the deviation within the data collection, the further the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.

Since they are used to determine standard deviation, sample size, mean, and data values all have an impact on standard deviation. By removing outliers, the sample size, mean, and standard deviation may all change.

Because 50 points was added to each score, they are still the same distance from each other which means the standard deviation will not change.

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