I bought a new shirt last night that costs 46$. Becasue there was a little stain on it they gave me an 8% discount. How much did i
pay for the shirt

The acceleration of the box is 0.4 m/s².

The magnitude of the force that Rory applies is 20.12 N.

(a)

The acceleration of the box can be calculated using the formula:

\(a = (v_f^2 - v_i^2) / (2d)\)

where vf is the final velocity, vi is the initial velocity, and d is the distance traveled.

Substituting the given values, we get:

a = (1.2² - 0²) / (2 x 1.8)

a = 0.4 m/s²

(b)

To find the magnitude of the force that Rory applies, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration:

F(net) = ma

The resistance force is acting in the opposite direction to the force applied by Rory.

F(applied) - F(resistance) = ma

Substituting the given values.

F(applied) - 19 = 2.8 x 0.4

F(applied) = 19 + 1.12 = 20.12 N

Therefore, the magnitude of the force that Rory applies is 20.12 N.

Thus,

The acceleration of the box is 0.4 m/s².

The magnitude of the force that Rory applies is 20.12 N.

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1) The regression output in equation form for the standard wage equation is:

log(wage) = β0 + β1educ + β2tenure + β3exper + β4female + β5married + β6nonwhite + u

Sample size: N

R-squared: R^2

Standard errors of coefficients: SE(β0), SE(β1), SE(β2), SE(β3), SE(β4), SE(β5), SE(β6)

2) The coefficient in front of "female" represents the average difference in log(wage) between females and males, holding other variables constant.

3) The coefficient in front of "married" represents the average difference in log(wage) between married and unmarried individuals, holding other variables constant.

4) The coefficient in front of "nonwhite" represents the average difference in log(wage) between nonwhite and white individuals, holding other variables constant.

5) To manually test the null hypothesis that one more year of education leads to a 7% increase in wage, we need to calculate the estimated coefficient for "educ" and compare it to 0.07.

6) To test the null hypothesis using Stata, the command would be:

```stata

test educ = 0.07

```

7) To manually test the null hypothesis that gender does not matter against the alternative that women are paid lower ceteris paribus, we need to examine the coefficient for "female" and its statistical significance.

8) To find the estimated wage difference between female nonwhite and male white, we need to look at the coefficients for "female" and "nonwhite" and their respective values.

9) The null hypothesis for testing the difference in wages between female nonwhite and male white is that the difference is zero (no wage difference). The alternative hypothesis is that there is a wage difference. Use the appropriate Stata command to obtain the p-value and compare it to the significance level of 0.05 to determine if the null hypothesis is rejected.

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Answer:

-9

Step-by-step explanation:

for linear equations, the show off the line is the coefficient of x.

in this case, the slope would be -9

The value of this bond, if it paid interest annually, would be $850.78.

In order to calculate the value of the bond, we need to use the present value formula for a bond. The present value of a bond is the sum of the present values of its future cash flows, which include both the periodic coupon payments and the final principal payment at maturity.

To calculate the present value of the annual coupon payments, we can use the formula:

PV = C × (1 - (1 + r)⁻ⁿ) / r,

where PV is the present value, C is the coupon payment, r is the required yield to maturity, and n is the number of periods.

In this case, the coupon payment is $120 ($1,000 par value × 12% coupon rate), the required yield to maturity is 14% (0.14), and the number of periods is 13. Plugging these values into the formula, we get:

PV = $120 × (1 - (1 + 0.14)⁻¹³) / 0.14

  ≈ $850.78.

Therefore, the value of this bond, if it paid interest annually, would be approximately $850.78.

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Answer:

\(5.5\)

Step-by-step explanation:

Mean:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is

\(\mu = \frac{{\sum}x}{N}\)

The formula for the mean of a sample is

\(\bar{x} = \frac{{\sum}x}{n}\)

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:

\(\frac{55}{10} = 5.5\)

A correlation is a statistical measure of the relationship between two variables and is expressed as a numerical value between -1 and 1.

A correlation is a measure of the relationship between two variables that is expressed as a numerical value between -1 and 1. To calculate a correlation, start by collecting data on the two variables. Then, calculate the covariance, which is the sum of the product of the differences between the two variables, divided by the number of data points. Finally, calculate the correlation by dividing the covariance by the product of the standard deviations of the two variables. The correlation can range from -1, which signifies a perfect negative correlation, to 1, which signifies a perfect positive correlation. A correlation of 0 indicates that there is no correlation between the two variables.

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To simplify the expression sin(t)sec(t) - cos(t)sin(t), we can use trigonometric identities to rewrite it in terms of a single trigonometric function. The simplified expression is tan(t).

We start by factoring out sin(t) from the expression:

sin(t)sec(t) - cos(t)sin(t) = sin(t)(sec(t) - cos(t))

Next, we can use the identity sec(t) = 1/cos(t) to simplify further:

sin(t)(1/cos(t) - cos(t))

To combine the terms, we need a common denominator, which is cos(t):

sin(t)(1 - cos²(t))/cos(t)

Using the Pythagorean Identity sin²(t) + cos²(t) = 1, we can substitute 1 - cos²(t) with sin²(t):

sin(t)(sin²(t)/cos(t))

Finally, we can simplify the expression by using the identity tan(t) = sin(t)/cos(t):

sin(t)(tan(t))

Hence, the simplified expression of sin(t)sec(t) - cos(t)sin(t) is tan(t).

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The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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Answer:

as lengths of tangents of a circle from an external point are equal so

5x+6 = 56

5x = 50

x = 50/5

D) x = 10

The 90% confidence interval for the population mean amount spent on lunch by college students is approximately $9.02 to $11.58.

To find the 90% confidence interval for the population mean amount spent on lunch by college students, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard deviation / square root of sample size)

In this case, the sample mean is $10.30, the standard deviation is $2.21, and the sample size is 10.

Step 1: Find the critical value for a 90% confidence level.
Since the sample size is small (n < 30), we need to use a t-distribution instead of a z-distribution. The degrees of freedom for a sample size of 10 is 10 - 1 = 9. By looking up the critical value in the t-distribution table with 9 degrees of freedom and a confidence level of 90%, we find the critical value to be approximately 1.833.

Step 2: Calculate the standard error.
The standard error is the standard deviation divided by the square root of the sample size.
Standard Error = $2.21 / √10 ≈ $0.699

Step 3: Calculate the margin of error.
The margin of error is the critical value multiplied by the standard error.
Margin of Error = 1.833 * $0.699 ≈ $1.28

Step 4: Calculate the confidence interval.
The confidence interval is the sample mean plus or minus the margin of error.
Confidence Interval = $10.30 ± $1.28

Putting it all together, the 90% confidence interval for the population mean amount spent on lunch by college students is approximately $9.02 to $11.58.

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P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

Step-by-step explanation:

Assuming you are asking for

85,000,000 + 2.9 x 10^5 =

8.5 x 10^7 + 2.9 x 10^5 =

10^5 ( 8.5 x10^2 + 2.9) =

10^5 ( 850+2.9) =

10^5 ( 852.9) =

10^5 x 8.529 x 10 ^2=

8.529 x 10^7

or

85,000,000 + 2.9 x 10^5 =

85,000,000 + 290,000 =

85290000 =

8.529 x 10 ^7 (because we moved 7 spots to the left)

Based on a differentiable function g'(x) = 5x, the value of g(2) is 1.329 (A).

To find the value of g(2), we need to use the formula for the derivative of a differentiable function, which is:

g'(x) = (g(x+h) - g(x))/h.

Since we know that g'(x) = 5e and g(10) = 2e, we can plug these values into the formula and solve for g(2):

5e = (g(2+8) - g(2))/8

5e = (g(10) - g(2))/8

5e = (2e - g(2))/8

40e = 2e - g(2)

g(2) = 2e - 40e

g(2) = -38e

g(2) = -38(2.71828)

g(2) = -103.29464

g(2) = 1.329

Therefore, the value of g(2) is 1.329.

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Answer:

For this one I think the answer would be A and E

Step-by-step explanation:

when seeing if the coordinates represent a function, make sure none of the inputs repeat and none of the outputs repeat.

hope this helps

Answer:

rational numbers are the number which can not expressed into simpler fraction

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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Answer:

76 quarters, 3 dimes

Step-by-step explanation:

if the whole number is 19, you would have to figure out how many quarters would be in 19$. 76 quarters are in 19$. then you would have to figure out how many dimes are in 30 cents, there are 3 dimes in 230 cents

Answer:

66 Quarters and 28 dimes

Step-by-step explanation:

.10d + .25Q = 19.3Q

d + Q = 94

so d = 94 - Q

Substitution method:

.10(94 - Q) + .25Q = 19.30

9.4 - .10Q + .25Q = 19.30

9.4 + .15Q = 19.30

.15Q = 9.9

Q = 66 so d = 94 - 66 = 28

The cubic function that has a local maximum value of 4 at 1 and a local minimum value of –1,184 at 7 is:

\(f(x) = (-28/15)x^3 + (59/15)x^2 - 23x - 149/3\)

We can start by writing the cubic function in the general form:

\(f(x) = ax^3 + bx^2 + cx + d\)

To find the coefficients of the function, we can use the given information about the local maximum and minimum values.

First, we know that the function has a local maximum value of 4 at x = 1. This means that the derivative of the function is equal to zero at x = 1, and the second derivative is negative at that point. So, we have:

f'(1) = 0

f''(1) < 0

Taking the derivative of the function, we get:

\(f'(x) = 3ax^2 + 2bx + c\)

Since f'(1) = 0, we have:

3a + 2b + c = 0 (Equation 1)

Taking the second derivative of the function, we get:

f''(x) = 6ax + 2b

Since f''(1) < 0, we have:

6a + 2b < 0 (Equation 2)

Next, we know that the function has a local minimum value of -1,184 at x = 7. This means that the derivative of the function is equal to zero at x = 7, and the second derivative is positive at that point. So, we have:

f'(7) = 0

f''(7) > 0

Using the same process as before, we can get two more equations:

21a + 14b + c = 0 (Equation 3)

42a + 2b > 0 (Equation 4)

Now we have four equations (Equations 1-4) with four unknowns (a, b, c, d), which we can solve simultaneously to get the values of the coefficients.

To solve the equations, we can eliminate c and d by subtracting Equation 3 from Equation 1 and Equation 4 from Equation 2. This gives us:

a = -28/15

b = 59/15

Substituting these values into Equation 1, we can solve for c:

c = -23

Finally, we can substitute all the values into the general form of the function to get:

\(f(x) = (-28/15)x^3 + (59/15)x^2 - 23x + d\)

To find the value of d, we can use the fact that the function has a local maximum value of 4 at x = 1. Substituting x = 1 and y = 4 into the function, we get:

4 = (-28/15) + (59/15) - 23 + d

Solving for d, we get:

d = -149/3

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The system of equations that could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum , g is:

5f + 3g = 5.70

2f + 10g = 3.60

Chase bought 5 pieces of fudge and 3 pieces of bubble gum for $5.70:

5f + 3g = 5.70

Sara bought 2 pieces of fudge and 10 pieces of bubble gum for $3.60:

2f + 10g = 3.60

System of equations:

5f + 3g = 5.70

2f + 10g = 3.60

From the first equation:

5f + 3g = 5.70

5f = 5.70 - 3g

f = 5.7/5 - 3/5g

f = 1.14 - 0.6g

Replacing "f" in the second equation:

2f + 10g = 3.60

2(1.14 - 0.6g) + 10g = 3.6

2.28 - 1.2g + 10g = 3.6

8.8g = 3.6 - 2.28

8.8g = 1.32

g = 0.15

Replacing "g" in the first equation:

5f + 3g = 5.70

5f + 3(0.15) = 5.7

5f + 0.45 = 5.7

5f = 5.7 - 0.45

5f = 5.25

f = 5.25 / 5

f = 1.05

Fudge cost $1.05 and Bubble Gum cost $0.15

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Answer:

Hill 1: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 3: F(x) = 4(x - 2)(x + 5)

Step-by-step explanation:

Hill 1

You must go up and down to make a peak, so your function must cross the x-axis six times. You need six zeros.

Also, the end behaviour must have F(x) ⟶ -∞ as x ⟶ -∞ and F(x) ⟶ -∞ as x⟶ ∞. You need a negative sign in front of the binomials.

One possibility is

F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2

Multiplying the polynomial by -½ makes the slopes shallower. You must multiply by -2 to make them steeper. Of course, flipping the hills converts them into valleys.

Adding 3 to a function shifts it up three units. To shift it three units to the right, you must subtract 3 from each value of x.

The transformed function should be

F(x)  = -2(x +1)(x)(x -2)(x -3)(x - 6)(x - 7)

Hill 3

To make a shallow parabola, you must divide it by a number. The factor should be ¼, not 4.

The zeroes of your picture run from -4 to +7.

One of the zeros of your parabola is +5 (2 less than 7).

Rather than put the other zero at ½, I would put it at (2 more than -4) to make the parabola cover the picture more evenly.

The function could be

F(x) = ¼(x - 2)(x + 5).

In the image below, Hill 1 is red, Hill 2 is blue, and Hill 3 is the shallow black parabola.

Answer:

unsolvable

Step-by-step explanation:

by elemination 14x+7y=-7 (1)

-14x-7y=7 (2)

x and y will be 0 then

Answer:

6

Step-by-step explanation:

To find the average rate of change, we must calculate the slope over the interval -3/2 to 0. We can use the formula below.

f(b) - f(a) / b - a

f(0) - f(-3/2) / 0 - -3/2

1 - -8 / 3/2

9 / 3/2

18/3

6

Brainliest, please!

Answer:

8.6 which is closes to c=8.5

Step-by-step explanation:

*See Photo*

The distance between Mr. Chew and Puppy is 8.54 miles. Therefore, option C is the correct answer.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, the puppy runs in straight lines 5 miles west of Mr. Chew and then 7 miles north.

Let the distance between Mr. Chew and Puppy be x

Using Pythagoras theorem, we get

x²=5²+7²

x²=74

x=√74

x= 8.54 miles

Therefore, option C is the correct answer.

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Answer:

Step-by-step explanation:

y + 8 = 4(x - 1)

y + 8 = 4x - 4

y = 4x - 12

The area of the regular pentagon is about 9 square units.

To find the area of a regular polygon, we need to know the length of the apothem and the perimeter of the polygon. The apothem is the distance from the center of the polygon to the midpoint of one of its sides, and the perimeter is the sum of the lengths of all the sides.

Since the polygon is regular, all of its sides have the same length. Let's call that length "s". We also know that the polygon has 5 sides, so it is a pentagon. To find the perimeter, we can simply multiply the length of one side by the number of sides:

Perimeter = 5s

Now, to find the apothem, we can use the formula:

Apothem = (s/2) x tan(180/n)

Where "n" is the number of sides. For our pentagon, n = 5, so we have:

Apothem = (s/2) x tan(36)

We can simplify this a bit by noting that tan(36) is equal to approximately 0.7265. So we have:

Apothem = (s/2) x 0.7265

Now we have everything we need to find the area. The formula for the area of a regular polygon is:

Area = (1/2) x Perimeter x Apothem

Substituting in the values we found earlier, we have:

Area = (1/2) x 5s x (s/2) x 0.7265

Simplifying this expression, we get:

Area = (s^2 x 1.8176)

Rounding to the nearest whole number of square units, we have:

Area = 9

So the area of the regular pentagon is about 9 square units.

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Answer:

36

Step-by-step explanation:

(3*2)^2

3*2=6

6^2=36

Answer:

36

Step-by-step explanation:

(3x2)^2
6^2

36

Hopes this helps please mark brainliest

The function f(x) = 4x/(x² + 1) in the interval [-4, 0] has absolute maximum at x = 1 and absolute minimum at x = -1.

Given the function is f(x) = 4x/(x² + 1)

Differentiating the function with respect to 'x' we get,

f'(x) = d/dx [4x/(x² + 1)] = ((x² + 1)d/dx [4x] - 4x d/dx [(x² + 1)])/((x² + 1)²) = (4(x² + 1) - 8x²)/((x² + 1)²) = (4 - 4x²)/((x² + 1)²)

f''(x) = ((x² + 1)²(-8x) - (4 - 4x²)(2(x² + 1)*2x))/(x² + 1)⁴ = (8x(x² + 1) [-x² - 1 - 2 + 2x²])/(x² + 1)⁴ = (8x[x² - 3])/(x² + 1)³

Now, f'(x) = 0 gives

(4 - 4x²) = 0

1 - x² = 0

x² = 1

x = -1, 1

So at x = -1, f''(-1) = (-8(1 - 3))/((1 + 1)³) = 2 > 0

at x = 1, f''(1) =  (8(1 - 3))/((1 + 1)³) = -2 < 0

So at x = -1 the function has absolute minimum and at x = 1 the function has absolute maximum.

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Symbolab is an online math tool that offers a wide range of math-related services, including a derivative calculator. The derivative calculator provided by Symbolab is a free tool that allows users to calculate the derivative of a given function with respect to a variable.

To use the Symbolab derivative calculator, you simply need to enter the function you want to differentiate and choose the variable with respect to which you want to differentiate the function. The calculator will then provide you with the derivative of the function in a step-by-step format, including the derivative rules used at each step.

The Symbolab derivative calculator supports a wide range of functions, including trigonometric functions, exponential functions, logarithmic functions, and more. It also supports partial derivatives and implicit differentiation.

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SOLUTION:

Step 1:

In this question, we are given the following:

Brian has reduced his cholesterol level by 6% by following a strict diet and regular exercise.

This means that the remaining level will be ( 100 - 6 ) % = 94%

Step 2:

If his original level was 280,

Then, the approximate cholesterol level now will be:

CONCLUSION:

The final answer is: