When the store had sold 29 of the boots that were on display, they brought out another 34 pairs from the stock room. If that gave them 174 pairs of boots out, how many pairs were on display originally?

Answer:

Step-by-step explanation:

We know, for square

\((side)^2=(Area)\\=>X^2=8\\\)

∴\(X=2\sqrt{2}\) unit

\(Now, Side=3X\)

\(Then,Area=(3X)^2=(3*2\sqrt{2} )^2=(6\sqrt{2} )^2=72 sq. unit\)

hope you have understood this...

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The area of square of side 3X is 72 square unit.

The square is a 4 sided figure, each side of the square is equal and make a right angle.

The area of square having sided a unit can be given by a² square unit.

Given that,

Area of square having side X is 8.

Since, formula for area of square having side X is X².

Implies that,

X² = 8

X = 2√2

The area of square having side 3X
side =3 × 2√2

side = 6√2

The area of square = (6√2)²

                                = 36 x 2

                                = 72

The area of square is 72 square unit.

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Answer:

x = 60

Step-by-step explanation:

80/ 4+x = 16

(4 + x) * 80/ 4+x = 16 = 16 (4 + x)

80 = 16 + 4 + x

80 = 20 + x

60 = x or x = 60

Answer:

To find the area of a parallelogram, you need to multiply the base of the parallelogram by its height. The formula is:

Area = base × height

Answer:

A = base × height

Step-by-step explanation:

Parallelogram, which is a shape containing 2 pairs of equal sides.

The equation of line that is perpendicular to given line is (y-y1) = m(x - x1)

A perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the pre-requisite to finding out the perpendicular line.

Consider the equation of the line is ax + by + c = 0 and coordinates are (x1, y1), the slope m1 = − a/b.

If one line is perpendicular to this line, the product of slopes should be -1. Let m1 and m2 be the slopes of two lines, and if they are perpendicular to each other, then their product will be -1.

So , the slope of line will be given that is m1

To find out the slope of perpendicular line ,

m1 . m2 = -1

=> m2 = -1 / m1

=> m2 = -b/a is slope of perpendicular line

So, the equation of perpendicular line is :

(y - y1 ) = m2 (x - x1)

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Answer:

Length + Width = 8 ft

Step-by-step explanation:

"The perimeter of a rectangle is 16 ft."

A perimeter is the sum of four sides of a rectangle.

OR...

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

A rectangle has "matching sides", so...

Length: Side 1 = Side 3

Width: Side 2 = Side 4

Therefore we can just say that:

Perimeter = (Length * 2) + (Width * 2)

We can pull the 2 out:

Perimeter = 2 * (Length + Width)

Since Perimeter = 18

16 = 2 * (Length + Width)

Divide both sides by 2

8 = Length + Width

Length + Width = 8 ft

The midsegment is equal to the average of the lengths of the bases, so:

Where:

and

Therefore:

Answer:

7 x -7 = -49

Step-by-step explanation:

To solve 7 to the power of -2 we multiply 7 by -7.

(っ◔◡◔)っ ♥ Hope It Helps ♥

The value of 7 with an exponent of -2 is 1/49 .

Given,

7 with an exponent of -2.

Now,

Let us simplify the given statement.

\(7^{-2}\) = 1/7²

Value of 7² is 49.

Thus the value of 7 with an exponent of -2  is 1/49 .

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The simple interest rate on the account is 7.5%.

The simple interest rate can be calculated by dividing the interest earned by the principal balance and the time period. In this case, the interest earned is $56.25, the principal balance is $300, and the time period is two and one-half years.

To find the interest rate, we use the formula:

Simple Interest = Principal × Rate × Time

Substituting the given values:

$56.25 = $300 × Rate × 2.5

To solve for the interest rate, divide both sides of the equation by $750:

Rate = $56.25 / ($300 × 2.5)

Simplifying the calculation:

Rate = $56.25 / $750

Rate = 0.075

Therefore, the simple interest rate on the account is 7.5%.

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To find the eigenvalues of A, we calculate the roots of the characteristic equation. The eigenvalues of A are -4, 1, and 10.

To find the eigenvalues of the matrix A, we start by calculating the characteristic equation. The characteristic equation is obtained by subtracting λ (the eigenvalue) times the identity matrix I from matrix A, and then taking the determinant of the resulting matrix. The characteristic equation is given by |A - λI| = 0.

For matrix A, we have A = [8, 4, -6; 0, -4, 5; 0, 0, 1]. By subtracting λI and taking the determinant, we get the equation:

|8-λ, 4, -6; 0, -4-λ, 5; 0, 0, 1-λ| = 0.

Simplifying and expanding the determinant, we obtain the characteristic equation:

(8-λ)(-4-λ)(1-λ) + 4(5)(1-λ) = 0.

Solving this equation, we find the eigenvalues:

λ₁ = -4, λ₂ = 1, λ₃ = 10.

To find the eigenvectors associated with each eigenvalue, we solve the equation (A - λI)v = 0, where v is the eigenvector. Substituting each eigenvalue into the equation, we solve for the corresponding eigenvector.

For λ₁ = -4, we have the equation (A + 4I)v = 0. By solving this system of equations, we find the eigenvector v₁ = [1, 1, 0].

For λ₂ = 1, we have the equation (A - I)v = 0. Solving this system of equations, we find the eigenvector v₂ = [1, 0, 0].

For λ₃ = 10, we have the equation (A - 10I)v = 0. Solving this system of equations, we find the eigenvector v₃ = [0, 0, 1].

Therefore, the eigenvalues of matrix A are -4, 1, and 10, and the corresponding eigenvectors are [1, 1, 0], [1, 0, 0], and [0, 0, 1], respectively.

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Use numerals instead of words, the value of k is equal to \(p^3\).

Let p and k be two integers. Since p - 1 is a factor of p^4 + p^2 + p - k, then we can express the equation as follows:

\((p - 1)(x) = p^4 + p^2 + p - k\)

By expanding the left side of the equation, we can write:

\(p^4 - p^3 + p^2 - p + x = p^4 + p^2 + p - k\)

Simplifying the equation, we get:

\(-p^3 + x = -k\)

Therefore, the value of k is equal to p^3.

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If p - 1 is a factor of polynomial p^4 + p^2 + p - k, the value of k is: 3

In this question we have been given a polynomial p^4 + p^2 + p - k .

We need to determine the value of k if p - 1 is a factor of p^4 + p^2 + p - k

Since  p - 1 is factor of p^4 + p^2 + p - k, p - 1 = 0

Consider p - 1 = 0

p = 1

This means p = 1 is root of given polynomial.

For p - 1 to be a factor the polynomial , on p = 1 submitting should equate to 0

i.e.,  p^4 + p^2 + p - k = 0

1^4 + 1^2 + 1 - k = 0

1 + 1 + 1 - k = 0

3 - k = 0

3 - k + k = 0 + k

k = 3

Therefore,  the value of k is: 3

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5

9x⁵=5

5y³=3

so 5>3=5

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(a)  Total urine volume is excreted during this time period is 442.34 mL.

(b) Equations for the velocity of urine is v = (-3 x \(V_t\) + 7.35) / 2.46 x \(10^{-5}\)

(a) To determine the total urine volume excreted during this time period, we need to integrate the flow rate function over the given time period. However, we are given two different equations for the flow rate for different ranges of time:

For t < 12 seconds, V = -0.306 x  \((t-7)^2\)  + 15

For 12 ≤ t < 26.7 seconds, V = -3 x \(V_t\)  + 7.35

To find the total urine volume, we need to first determine the time at which the flow rate changes from the first equation to the second.

We can do this by setting the two equations equal to each other and solving for t:

-0.306 x  \((t-7)^2\)  + 15 = -3 x \(V_t\) + 7.35

0.306 x  \((t-7)^2\) + 3 x \(V_t\)  = 7.65

0.306 x \((t-7)^2\) = 7.65 - 3 x \(V_t\)

\((t-7)^2\) = (7.65 - 3 x \(V_t\) ) / 0.306

t = 7 +/- \(\sqrt{((7.65 - 3 \times Vt) / 0.306)}\)

Since t < 12 for the first equation, we can ignore the negative root and use the positive root to find the time at which the flow rate changes:

t = 7 + \(\sqrt{((7.65 - 3 \times 12) / 0.306)}\)= 10.76 seconds

Now we can integrate each equation separately over their respective time ranges:

For 0 ≤ t < 10.76 seconds:

∫ V dt = ∫ (-0.306 x \((t-7)^2\) + 15) dt

= [-0.102 x \((t-7)^3\) + 15t] from t=0 to t=10.76

= 121.86 mL

For 10.76 ≤ t < 26.7 seconds:

∫ V dt = ∫ (-3 x \(V_t\) + 7.35) dt

= [-1.5 x \(V_t^2\) + 7.35t] from t=10.76 to t=26.7

= 320.48 mL

Therefore, the total urine volume excreted during this time period is:

121.86 mL + 320.48 mL = 442.34 mL

(b) To develop equations for the velocity of urine as it exits the body, we need to use the continuity equation, which states that the flow rate (V) is equal to the cross-sectional area (A) multiplied by the velocity (v):

V = A x v

We are given that the urethra has a diameter of 5.6 mm, which means the radius is 2.8 mm (or 0.0028 m).

The cross-sectional area can be calculated using the formula for the area of a circle:

A = π x \(r^2\)

A = 3.14 x \((0.0028)^2\)

A = 2.46 x   \(10^{-5}\) \(m^2\)

Now we can rearrange the continuity equation to solve for the velocity:

v = V / A

Substituting the given equations for V, we get:

For t < 12 seconds:

v = (-0.306 x \((t-7)^2\) + 15) / 2.46 x  \(10^{-5}\)

For 12 ≤ t < 26.7 seconds:

v = (-3 x  \(V_t\) + 7.35) / 2.46 x \(10^{-5}\)

Note that the velocity will be in units

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Question:-

The flow of urine from the bladder, through the urethra, and out of the body, is induced by increased pressure in the bladder resulting from muscle contractions around the bladder with simultaneous relaxation of the muscles in the urethra. The mean pressure in the bladder can be estimated using the velocity of urine as it exits the body. Assume that the bladder is about 5 cm above the external urethral orifice. (This height is different for males and females.) The flow rate of urine from the bladder can be approximately described with the following equations, where t is time in seconds, and V is flow rate in mL/s:

V = -0.306 X (t – 7)2 + 15 Osts 12

V = -3 X Vt 12 + 7.35 12 st < 26.7

(a) How much total urine volume is excreted during this time period?

(b) Develop equations for the velocity of as it exits the body. Assume that the urethra is 5.6 mm in diameter.

The recursive formula for the given problem is W(n) = W(n-1) + 2 * W(n-1), with the base case W(0) = 1. This formula calculates the number of n-letter "words" that can be created from an unlimited supply of 'a's, 'b's, and 'c's,

To derive the recursive formula, we consider two cases for the first letter of the word: either it is an 'a' or it is not. If the first letter is 'a', we need to ensure that the remaining (n-1) letters form a word with an even number of 'a's. Therefore, the number of words in this case is equal to W(n-1), as we are recursively solving for the remaining letters.

If the first letter is not 'a', we have the freedom to ch

oose from 'b' or 'c'. In this case, we have two options for each of the remaining (n-1) letters, resulting in 2 * W(n-1) possibilities. By summing these two cases, we obtain the recursive formula W(n) = W(n-1) + 2 * W(n-1), which calculates the total number of n-letter words satisfying the given criteria.

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The length of each of the wires is 206.16 ft

The length talks about how long the wires are from the top of the phone tower.

The given parameters are

height of the phone tower = 200 feet

The distance from the base to where it is pinned = 50 feet

Recall, each of them forms a right angled triangle

To find the lengths we use the Pythagoras rule

a²=b²+c²

Where a, b, c are the sides of each of the right angled triangles

a²=200²+50²

a²= 40,000+ 2500

Add together to have

a²=42,500

Taking the squares of both sides we have

a=√42500

a=206.16 feet

In conclusion each of the wires is 206.16 feet long

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Answer:

4 and 5

Step-by-step explanation:

n + 1 > 4

n > 4 - 1

n > 3

For the set { 1, 2 , 3 , 4, 5 }, 4 and 5 are greater than 3.

Hence, 4 and 5 makes the inequality n + 1 > 4 true.

Answer:

Jake can use 19.70 ccf to not exceed $ 64.00 in water bill.

Step-by-step explanation:

The cost function of water bill is:

\(C = C_{f}+C_{v}\)

Where:

\(C_{f}\) - Fix costs, measured in USD.

\(C_{v}\) - Variable costs, measured in USD.

The fix and variable costs are, respectively:

\(C_{f} = 24.60\)

\(C_{v} =2\cdot \left(\frac{Q}{100} \right)\)

Where \(Q\) is the water capacity consumed within a month, measured in cubic feet. Therefore, first formula is expanded:

\(C = 24.60+2\cdot \left(\frac{Q}{100} \right)\)

If \(C = 64\,USD\), the maximum water capacity is:

\(64 = 24.60+2\cdot \left(\frac{Q}{100} \right)\)

\(39.40 = 2\cdot \left(\frac{Q}{100} \right)\)

\(Q = 1970\,ft^{3}\)

Which is equivalent to 19.70 ccf.

When planning to do statistical inference, the term "1-ß" is commonly known as the power of a statistical test. The correct option is a. power

Power is the probability of correctly rejecting a null hypothesis when it is false. In other words, it represents the ability of a statistical test to detect a true effect or relationship between variables.

Statistical inference involves making decisions based on sample data to draw conclusions about a population. One of the key aspects of statistical inference is hypothesis testing, where we formulate null and alternative hypotheses and assess the evidence from the data to either reject or fail to reject the null hypothesis.

Type 2 error, denoted by β (beta), occurs when we fail to reject a null hypothesis that is actually false. It is the probability of not detecting a true effect or relationship in the data. Hence, the complement of β, which is 1-ß, represents the probability of correctly detecting a true effect.

Power is influenced by several factors, including the sample size, the effect size, the chosen significance level (α), and the variability of the data. A larger sample size, a larger effect size, a higher significance level, and lower variability all contribute to increased power.

It is important to consider power when designing a study or planning a statistical analysis. A low power implies a high risk of failing to detect true effects, leading to missed opportunities for meaningful conclusions. Researchers typically aim for higher power to ensure they have a good chance of detecting effects if they exist in the population.

In summary, when planning for statistical inference, 1-ß represents the power of a statistical test. It quantifies the probability of correctly detecting a true effect and is crucial for ensuring the validity and reliability of statistical analyses.

Therefore, option (a) "power" is the correct answer.

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A rhombus is a quadrilateral that has four sides of equal length. A rhombus also has two diagonals, which are perpendicular bisectors of each other. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

To find the perimeter of a rhombus using diagonals, follow these steps:

Step 1: Obtain the length of each diagonal of the rhombus.

Step 2: Use the length of the diagonals to find the length of each side.

Step 3: Add the length of each side to find the perimeter of the rhombus.

The perimeter is the sum of all the sides of a figure. To get the perimeter of a rhombus using diagonals, the length of each diagonal has to be found first. The formula for finding the length of each side of a rhombus is:  where the diagonal is the measure of the diagonal of the rhombus.

To find the perimeter of a rhombus, add the length of all the sides of the rhombus. This formula is given as follows: Perimeter = 4 × a, where a is the length of each side of the rhombus.

Therefore, the perimeter of a rhombus using diagonals can be found by following the above procedure and then using the formula to add all the sides of the rhombus.

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Solid, is there an actual question?

The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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This macroeconomic model illustrates how changes in different factors (consumption, investment, government spending, exports, and imports) and their relationships with income can impact the equilibrium level of national income.

Based on the given equations, Y represents the equilibrium level of national income, which is determined by the levels of consumption (C), investment (I), government spending (G), exports (X), and imports (M).

The consumption equation, C, is dependent on disposable income (Y-T), where a represents the marginal propensity to consume (MPC) and b represents autonomous consumption. This means that as disposable income increases, consumption will increase, but at a decreasing rate due to the MPC. Autonomous consumption, on the other hand, is independent of income and reflects the amount of consumption that would still occur even if income were zero.

The tax equation, T, shows that taxes are a function of income (Y), where t represents the tax rate. As income increases, taxes will also increase proportionally.

Overall, this macroeconomic model illustrates how changes in different factors (consumption, investment, government spending, exports, and imports) and their relationships with income can impact the equilibrium level of national income.

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The rate of interest per annum when he invested £6,500 and got £6,838 will be 5.2%.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The amount after one year is £6838 if he invested £6,500. Then the rate of interest is given as,

£6,838 = £6,500 × (1 + r)¹

1 + r = 1.052

r = 0.052 or 5.2%

The rate of interest per annum when he invested £6,500 and got £6,838 will be 5.2%.

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Answer:

BC = 6

Step-by-step explanation:

Look at two corresponding sides that have both lengths given.

They are AB = 4 and XY = 3.

We need BC, and its corresponding side YZ = 4.5.

We can use a proportion.

BC/YZ = AB/XY

a/4.5 = 4/3

3a = 4.5 * 4

a = 1.5 * 4

a = 6

Answer: BC = 6

Multiplication operation is the inverse of the one in the given equation which is 9 = p/8.

What is an inverse?

The opposite of another operation is referred to as the "inverse" in mathematics. The operations that cancel out or are the opposite of one another are referred to as inverse operations. The work of a pair is reversed by an inverse operation.

We are given an equation as 9 = p/8.

In this equation,  we can see that the operation used is division.

We know that inverse of division is multiplication.

Hence, multiplication operation is the inverse of the one in the given equation.

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Step-by-step explanation:

1. (1/10 × 1/10 × 1/10 × 1/10)^2

(10^-4)^2

10^-8

2. (1/10 × 1/10 × 1/10)^3

(10^-3)^3

10^-6

3. (10 × 10 × 10)^-2

(10^3)^-2

10^-6

Question

Write as a single exponent.

1. ( 1/10 x 1/10 x 1/10 x 1/10 )^2

2. ( 1/10 x 1/10 x 1/10 )^3

3. ( 10 x 10 x 10 )^-2

The frequency of a class is the number of data points that fall within the class is 1.

To determine the frequency of each class in the table shown, we must first divide the data points into the respective classes. The classes are 1003, 1062, 1063, 1122, 1123, 1182, 1183, 1242, 1243, 1302, 1303, and 1362.

For the class 1003, the frequency is 1, since there is only one data point (1003) in this class.

For the class 1062, the frequency is also 1 since there is only one data point (1062) in this class.

For the class 1063, the frequency is also 1 since there is only one data point (1063) in this class.

For the class 1122, the frequency is 1 since there is only one data point (1122) in this class.

For the class 1123, the frequency is 1 since there is only one data point (1123) in this class.

For the class 1182, the frequency is 1 since there is only one data point (1182) in this class.

For the class 1183, the frequency is 1 since there is only one data point (1183) in this class.

For the class 1242, the frequency is 1 since there is only one data point (1242) in this class.

For the class 1243, the frequency is 1 since there is only one data point (1243) in this class.

For the class 1302, the frequency is 1 since there is only one data point (1302) in this class.

For the class 1303, the frequency is 1 since there is only one data point (1303) in this class.

For the class 1362, the frequency is 1 since there is only one data point (1362) in this class.

Therefore, the frequency of each class in the table shown is 1.

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