Mrs.Vernon paid $72 interest for a 2-year loan at 9% annual interest. How much money did she borrow?​

Answer:

h= 33mm

volume of square pyramid =1/3 Sh

5 x 5=25 /3 =8.3

275/8.3 =33

The equation that describes this situation is:

105 = 7l

Let's break down the given information:

Mu walks laps to raise money for charity.

For each lap Mu walks, her sponsors will donate $7.

Mu has walked l laps.

The total amount raised by Mu is $105.

To write an equation to describe this situation, let's use the variables:

l represents the number of laps Mu has walked.

$7 represents the amount donated for each lap.

The equation can be written as follows:

Total amount raised = Amount donated per lap × Number of laps

$105 = $7 × l

Therefore, the equation that describes this situation is:

105 = 7l

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Answer:

\(16\)

Step-by-step explanation:

\( {x}^{2} - 8x + c\)

\( {x}^{2} + c - 8x\)

To find the c value \(c = ( \frac{b}{2})^{2} \) , divide the coefficient of x by 2 and square the result.

\(( - 1 \times 4 {)}^{2} \)

\(( - 4 {)}^{2} \)

\(16\)

So on solving the provided question, we can say that Volume of cone is \(\pi r^2\frac{h}{3}\) = 10561.39 cm cubic and  surface area  of cone = \(\pi r( r + \sqrt{ h^2 + r^2 } )\) = 37.2338688 cm sq.

A cone is a three-dimensional geometric object with a flat base and a smooth tapering apex or vertex. In a plane without vertices, a cone is created by connecting a series of line segments, half-lines, or lines that are common to all points on the base. A cone is a three-dimensional structure with a seamless transition from a flat base, which is typically circular, to the vertex or apex, which serves as the axis to the base's center. An obvious three-dimensional geometric shape with an upwardly flattened curved surface is called a cone.

Volume of cone is \(\pi r^2\frac{h}{3}\)

V = 3.14*15.5*15.5*42/3 = 10561.39 cm cubic.

surface area  of cone = \(\pi r( r + \sqrt{ h^2 + r^2 } )\)

SA = \(3.14*15.5 * \sqrt{1764 + 240.25} \\3.14*15.5 * \sqrt{2004.25}\)

SA = 3.14*15.44.768

SA = 37.2338688 cm sq.

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Answer:

22/a

Step-by-step explanation:

The quotient of 22 and a number = 22/a

Answer:

$34.29, Gavin spent $34.29.

Step-by-step explanation:

12 ÷ 0.35 = 34.2857142857

Round to nearest hundreth: 34.29

Answer:

$4.20

Step-by-step explanation:

dozen = 12 flowers

0.35x12=4.20

Answer:

the answer is A. you use the vertical line test

Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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Answer:

Infinite Solutions

Step-by-step explanation:

We have a system of equation and are asked to determine how many solutions there are.

y + 2x = 4

2y + 4x = 8

To solve, we can first get y by itself in the first equation.

y + 2x = 4

Subtract 2x from both sides :

y = 4 - 2x

Now that y is alone, we can plug it into the second equation :

2(4 - 2x) + 2x = 8

Distribute :

(2(4) - 2(2x)) + 2x = 8

8 - 4x + 2x = 8

Add like terms :

-4x + 2x

8 - 2x = 8

Subtract 8 from both sides :

-2x = 0

Therefore this set of equations has Infinite Solutions.

This can also be determined by graphing.

Start by adding the whole part of the numbers

then add the fractions

since the fraction also gave a mixed number it can be added to the whole part we already had

The correct answer option is the fourth one.

To stretch a spring 1 ft. from its natural length, a 15 ft-lb work is needed. To stretch a spring 6 in. from its natural length, the required work is 3.75 ft-lb

The work done on a spring is given by the formula:

W = 1/2 . kx²

Where:

k = spring constant

x = spring displacement

From the formula, we know that the work is directly proportional to the square of displacement, or mathematically:

                W ∝ x²

Therefore,

W₁ : W₂ = x₁² : x₂²

Data from the problem

W₁ = 15 ft-lb

x₁ = 1 ft

x₂ = 6 in. = 0.5 ft

Hence,

15 : W₂ = 1² : 0.5²

W₂ = 0.25 x 15 = 3.75 ft-lb

Hence, the required work to stretch the spring 6 in beyond its natural length is 3.75 ft-lb

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Answer:

13

Step-by-step explanation:

a²+b²=c²

(12)²+(5)²=c²

√12²+5²=√c²

13=c

Answer:

5^2+12^2=c^2

25+144=c^2

169=c^2

c=√169

c=13

The length and width are 18 meters and 6 meters respectively.

Given that

We know that

The perimeter of the rectangle be

48 = 2 (length + breadth)

48 = 2(3x + x)

48 = 6x + 2x

48 = 8x

x = 6

So, the width is 6 meters.

And, the length be 18 meters.

Therefore we can conclude that The length and width are 18 meters and 6 meters respectively.

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The Ways to use coordinates to prove quadrilaterals are parallelograms, rectangles, rhombi, or squares are listed below:

Here are some ways to use coordinates to prove quadrilaterals are parallelograms, rectangles, rhombi, or squares:

Parallelogram: To prove that a quadrilateral is a parallelogram using coordinates, you need to show that both pairs of opposite sides are parallel.

Rectangle: To prove that a quadrilateral is a rectangle using coordinates, you need to show that it is both a parallelogram and that it has four right angles.

Rhombus: To prove that a quadrilateral is a rhombus using coordinates, you need to show that it is both a parallelogram and that it has four congruent sides.

Square: To prove that a quadrilateral is a square using coordinates, you need to show that it is both a rectangle and a rhombus.

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There are many assumption that must be met for independent samples t-tests and anovas, but not for single sample z or t tests

The assumption that must be met for testing independent samples from t-test or anovas are :

1. Takes into account the normal distribution of the dependent variable.

2. Makes the supposition that the variance of the two groups is equal to that of the dependent variable.

3. Pretends that the two samples are unrelated to one another.

4. Random selection is used to select samples from the population.

5. All observations in a t-test with an independent sample must be unrelated to one another.

6. To use the independent sample t-test, dependent variables must be measured on an interval or ratio scale.

Where For single Sample t-test ,

Data should be randomly selected and normally distributed

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The mistake is that it is 1/16 not 16. The person probably did the reciprocal or incorrectly used the fraction

Answer:

The exponent for the answer should be -2. Therefore, the answer will be 4⁻² or 1/16.

Step-by-step explanation:

When dividing fractions, you subtract the exponents as long as they have the same base.

Since the exponents both have the base of 4, subtract 9 - 11.

9 - 11 = -2

The exponent would be -2 and the answer would be 4⁻².

When an exponent is negative, you take the inverse of the base raised to the positive exponent.

Since 4² = 16 or 16/1, 4⁻² would be 1/16.

The answer would be 4⁻² or 1/16.

Hope that helps.

The allowance time, if the standard time is 234.15 minutes and the basic time is 233.4 minutes is 0.75 minute

To calculate the allowance time, we can use the following formula:

Allowance time = Standard time - Basic time

Thus, Allowance time = 234.15 minutes - 233.4 minute = 0.75 minutes

Therefore, the allowance time is 0.75 minutes.

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Answer:

Perpendicular: \(y=-\frac{1}{3}x+\frac{19}{3}\)

Parallel: \(y=3x-7\)

Step-by-step explanation:

So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: \(\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}\). In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: \(-\frac{1}{3}\). Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: \(y=-\frac{1}{3}x+b\). We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: \(5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b\). This gives you the complete equation: \(y=-\frac{1}{3}x+\frac{19}{3}\)

So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: \(y=3x+b\text{ where b}\ne-3\). The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: \(5=3(4)+b\implies5=12+b\implies-7=b\). This gives you the complete equation: \(y=3x-7\)

Answer:

D

Step-by-step explanation:

the definition of \(\left[\begin{array}{ccc}n\\k\\\end{array}\right]\)

= \(\frac{n!}{k!(n-k)!}\)

The probability that the mean lifetime of 25 randomly selected tires of this type will exceed than 42,000 miles is 25.14.

To break this problem, we need to use the standard normal distribution, assuming that the distribution of tire continuances is roughly normal. We can regularize the value of 42,000 using the formula

z = ( x- μ)/ σ

where x is the value of interest( 42,000 long hauls), μ is the mean tire continuance( 40,000 long hauls), and σ is the standard deviation( 3,000 miles). Plugging in the values, we get

z = ( 42,000- 40,000)/ 3,000 = 0.67

Using a standard normal distribution table or calculator, we can find the probability that an aimlessly named tire will last further than 42,000 long miles by looking up the area to the right of z = 0.67 under the standard average wind. This probability is roughly 25.14.

thus, the probability that a tire named arbitrarily from this brand will last more than 42,000 miles is roughly 25.14.

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The correct question is given below-

A particular brand of tires lasts an average of 40,000 miles with a standard deviation of 3,000 miles. What is the probability a tire selected at random lasts more than 42,000 miles?

\( \large \bf\implies\frac{12}{61} \)

\( \tt \frac{8}{101} , \frac{9}{91} , \frac{10}{81} , \frac{11}{71} ...\)

We have to add 1 in numerator and -10 in denominator because

\( \tt \frac{8}{101} , \frac{9}{91} , \frac{10}{81} , \frac{11}{71} ...[Given]\)

\( \frac{8 \: + \: 1}{101 \: - \: 10} = \frac{9}{91} \\\\ \frac{9 + 1}{91 - 10} = \frac{10}{81} \\ \\ \frac{10 + 1}{81 - 10} = \frac{11}{71} \\ \\ \frac{11 + 1}{71 - 10} = \frac{12}{61} ...\)

The difference is 1 in numerator so we add 1 and the difference is -10 in denominator so we subtract -10.

Answer:

The mathematical sentence that describes the inequality 5n - 10 > 26 is: Ten subtracted from 5 times n is greater than 26. I hope this mathematical sentence is what you are looking for,

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

n

>

36

/5

Interval Notation:

(

36

/5

,

∞

)

Answer:

The Answer is, (A) Ten less than five times a number is greater than twenty-six.

Step-by-step explanation:

Answer:

\( - \frac{58}{20} < - \sqrt{8} < \frac{17}{22} < 0.78\)

Step-by-step explanation:

There you go, have a good day

The impact propensity can be interpreted as the slope coefficient for the tax personal exemption (pe) or its first lag in

the regression equation.

To determine the impact propensity in the regression of the general fertility rate (GFR) on the tax personal exemption

(PE) and its first lag, you should follow these steps:

Estimate the regression model using the available data. The model should look like this:

GFR = β0 + β1 × PE + β2 × PE_lag + ε

Where GFR is the general fertility rate, PE is the tax personal exemption, PE_lag is the tax personal exemption's first

lag, and ε is the error term.

Obtain the estimated coefficients (β0, β1, and β2) from the fitted regression model.

These coefficients will help you determine the impact propensity.

Calculate the impact propensity. The impact propensity in this context refers to the change in the general fertility rate

resulting from a one-unit increase in the tax personal exemption, taking into account both its current and lagged

effects.

To find the impact propensity, sum the coefficients for the tax personal exemption and its first lag:

Impact propensity = β1 + β2

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To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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The inequality that best describes the width of the garden is

Width ≤ 6 yards

Area ≤ Length* Width

Length = 5 yards

Width = ??

Area = 30 square yards

From the formula of the area of rectangle we have

Area = Length * Width

Let the width be x

Substitute

30 = 5 * x

30 = 5x

Divide both sides by 5

x = 30/5

x = 6 yards

Hence the with should be less than or equal to 6 yards

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The optima of the Lagrangian objective function is minimized at z = 54,000. Also the Lagrange multiplier solution corresponds to a minimum.

The optimal values for the Lagrangian objective function can be determined by solving the given optimization problem using Lagrange multipliers. We have the objective function z = 6x₁² + 12x₂² and the constraint g(x₁, x₂) = 90 = x₁ + x₂.

To find the optimal values, we form the Lagrangian function L(x₁, x₂, λ) = f(x₁, x₂) - λ(g(x₁, x₂) - 90). Here, λ is the Lagrange multiplier.

Taking the partial derivatives with respect to x₁, x₂, and λ, and setting them to zero, we obtain the following equations:

∂L/∂x₁ = 12x₁ - λ = 0

∂L/∂x₂ = 24x₂ - λ = 0

∂L/∂λ = x₁ + x₂ - 90 = 0

Solving these equations simultaneously, we find x₁ = 30, x₂ = 60, and λ = 360. Substituting these values back into the objective function, we get z = 6(30)² + 12(60)² = 54,000.

To determine whether this is a maximum or minimum, we can examine the second partial derivatives of the Lagrangian. Calculating the second partial derivatives, we have:

∂²L/∂x₁² = 12

∂²L/∂x₂² = 24

Since both second partial derivatives are positive, we can conclude that the Lagrange multiplier solution corresponds to a minimum. Therefore, the optima of the Lagrangian objective function is minimized at z = 54,000.

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Answer:

6 is the answer

Step-by-step explanation:

MARK ME AS BRAINLIEST

Answer:

6+[12÷(4+2)]-2

6+[12÷6]-2

6+4-2

10-2

8