A pair of shoes originally costs $60. They are on sale for 25 percent off and sales tax is 7%. Cost is calculated by first applying the discount, then sales tax.

what is the total cost of the shoes including tax?​

Answer:

No (The linear model did a very bad job of approximating the data.)

I am so sorry if this in incorrect.

The percentage illumination of the moon's surface is not a linear function of day

From the complete question, the dataset can be represented using the following table:

Days   Percentage Illumination

1           2%

2          6%

3          50%

4          100%

Notice that as the number of days increase by 1, the percentage illumination of the moon increase at different intervals

This means that the percentage illumination is not a linear function of day

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The coefficient of x⁴y⁴ is 70 when the expression is (x+y)⁸ by binomial coefficient expansion.

Given that,

We have a equation that is (x+y)⁸.

We have to find what is coefficient of x⁴y⁴ when we expand the coefficients with number.

We know that,

Take the expression

(x+y)⁸

By using binomial coefficient expansion visit:  

(x+y)⁸= ⁸C₀x⁰y⁸⁻⁰+ ⁸C₁x¹y⁸⁻¹+ ⁸C₂x²y⁸⁻²+ ⁸C₃x³y⁸⁻³+ ⁸C₄x⁴y⁸⁻⁴+ ⁸C₅x⁵y⁸⁻⁵+ ⁸C₆x⁶y⁸⁻⁶+ ⁸C₇x⁷y⁸⁻⁷ +⁸C₈x⁸y⁸⁻⁸

(x+y)⁸= ⁸C₀x⁰y⁸+ ⁸C₁x¹y⁷+ ⁸C₂x²y⁶+ ⁸C₃x³y⁵+ ⁸C₄x⁴y⁴+ ⁸C₅x⁵y³+ ⁸C₆x⁶y²+ ⁸C₇x⁷y¹ +⁸C₈x⁸y⁰

So the coefficient of x⁴y⁴ is ⁸C₄.

⁸C₄= 8!/(4!(8-4)!)

⁸C₄= 8!/4!4!

⁸C₄=70.

Therefore, The coefficient of x⁴y⁴ is 70 when the expression is (x+y)⁸ by binomial coefficient expansion.

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Step-by-step explanation:

Given: Radius , r =21 cm

The angle at the center of the circle, n° =140°

Length of an arc =?

W.K.T Formula, Length of an arc = 2πr( n°÷360°) units

= 2*(22/7)*21*(140°/360°)

= 154/3

= 51.33cm

Answer:

2*(22/7)*21*(140°/360°)

= 154/3

= 51.33cm

Step-by-step explanation:

y-(-9) = -6(x-(-4)), y = -6x-33

Answer:

x = -20.5

Step-by-step explanation:

Simplifying

4(3x + -5) = 7(2x + 3)

Reorder the terms:

4(-5 + 3x) = 7(2x + 3)

(-5 * 4 + 3x * 4) = 7(2x + 3)

(-20 + 12x) = 7(2x + 3)

Reorder the terms:

-20 + 12x = 7(3 + 2x)

-20 + 12x = (3 * 7 + 2x * 7)

-20 + 12x = (21 + 14x)

Solving

-20 + 12x = 21 + 14x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-14x' to each side of the equation.

-20 + 12x + -14x = 21 + 14x + -14x

Combine like terms: 12x + -14x = -2x

-20 + -2x = 21 + 14x + -14x

Combine like terms: 14x + -14x = 0

-20 + -2x = 21 + 0

-20 + -2x = 21

Add '20' to each side of the equation.

-20 + 20 + -2x = 21 + 20

Combine like terms: -20 + 20 = 0

0 + -2x = 21 + 20

-2x = 21 + 20

Combine like terms: 21 + 20 = 41

-2x = 41

Divide each side by '-2'.

x = -20.5

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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Answer:

R = ∞

I = (-∞, ∞)

Step-by-step explanation:

Use the ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] / [xⁿ⁺⁵ / (2n!]│

lim(n→∞)│[xⁿ⁺⁶ / (2(n+1)!)] × (2n! / xⁿ⁺⁵)│

lim(n→∞)│x 2n! / (2(n+1)!)│

lim(n→∞)│n! / (n+1)!││x│

lim(n→∞) (1 / (n+1))│x│

0

The series converges if the limit is less than 1.

The limit is always less than 1, so the radius of convergence is infinite.

So the interval of convergence is (-∞, ∞).

In order to find an equation of the line shown in the graph, we'll use the two points given: (0,5) and (-1,0). First of all, let's find the slope of the line:

So, the slope is m=5.

The equation of the line will be:

y-y0 = m(x-x0)

y-0 = 5(x+1)

y = 5x+5

The answer of the following are; A. 16 yellow marbles were chosen

B. 24 marbles were chosen

C. Not enough information.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are obtained data from the question. This include the following:

marble = 40

Black marble =..?

A. From the question given, 3/5 of the 40 marbles were chosen. It therefore means that 2/5 were not chosen and 16 of these were black.

yellow marble chosen = 2/5 x 40 = 16.

Therefore, 16 yellow marbles were chosen.

B. From the question given, 3/5 of the 40 marbles were chosen.

marble chosen = 3/5 x 40 = 24.

Therefore, 24 marbles were chosen.

C. Not enough information because the number of black marbles in the bag was not given, we can not obtain the total number of marbles that were not chosen.

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Answer:

− 8 a ^7

Step-by-step explanation:

See picture for steps :)

Answer:

Answer is option a,b and d.

Step-by-step explanation:

Property of exponents:

\( \frac{ {a}^{m} }{ {b}^{n} } = {a}^{m - n} \)

Answer:

(2,6)

Step-by-step explanation:

Option:B

The triangle is rotated 90 degree clockwise around the point (0,0). The point is (-6,2) is made to rotate. The image so formed is at the point (2,6).

Large sample significance tests for a single proportion are based on the  statistic binomial. the correct option is A

Significance test can be defined as tests for statistical significance indicate whether observed differences between assessment results occur because of sampling error. Significance tests give a formal process for using sample data to evaluate the likelihood of some claim about a population value.

Therefore a Large sample significance tests for a single proportion are based on the  statistic binomial.

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9514 1404 393

Answer:

Step-by-step explanation:

The above-listed answer choices are the only ones that are self-consistent.

The quotient choices all have a leading coefficient of 3, and the result of dividing by <some number> is a leading coefficient of 1. Obviously, the <some number> must be 3 (first choice on the second menu).

Looking only at the constant term, we see that after division by 3, we have 3. So the original quotient constant term must be 3×3 = 9 (first choice on the first menu). Note that we have chosen the correct answer simply by looking at coefficients, not even bothering with actual division of variables.

The probability that a defective component will be detected only by the first inspector is 0.19

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

The probability that all three defective components in a batch escape detection by both inspectors is 0.

It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.

Therefore P(A)=P(B)=81%=0.81

At least one inspector does not detect a defect on 38% of all defective components.

Therefore, bar P(A∩B)=0.38

As we know:

bar P(A∩B)=1-P(A∩B)=0.38

P(A∩B)=1-0.38=0.62

A defective component will be detected only by the first inspector.

P(A∩barB)=P(A)-P(A∩B)

=0.81-0.62

P(A∩barB)=0.19

The probability that a defective component will be detected only by the first inspector is 0.19

Part (B) A defective component will be detected by exactly one of the two inspectors.

This can be written as: P(A∩barB)+P(barA∩B)

As we know:

P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)

Substitute the respective values we get:

P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)

=0.81+0.81-2(0.62)

=1.62-1.24

P(A∩ barB)+P(bar A∩B)=0.38

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

Part (C) All three defective components in a batch escape detection by both inspectors

This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)

As we know bar P(A∩B)=P(bar A∪ bar B)=0.38

From part (B): P(bar A∩B)+P(A∩bar B)=0.38

This can be written as:

P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0

The probability that all three defective components in a batch escape detection by both inspectors is 0

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The difference in speed between Explorer B and Explorer A is 600 miles per hour.

In order to determine how fast the satellites are travelling, the average speed of the satellites have to be calculated. Average speed is the total distance covered per time.

Average speed = total distance / total time

Average speed of Space Explorer B = 74,400 / 12 = 6,200 miles per hour

Average speed of Space Explorer A = 72,800 / 13 = 5,600 miles per hour

Difference in speed = 6,200 miles per hour - 5,600 miles per hour = 600 miles per hour.

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Answer:

70 m and 60 m

Step-by-step explanation:

The formula for the area of a rectangle is length ⋅ width.

The area of the pasture of 4200 meters.

70 ⋅ 60 = 4200.

The formula for the perimeter of a rectangle is side + side + side + side.

The perimeter of the rectangle is 260 meters.

70 + 60 + 70 + 60 = 260.

Therefore, the length and width of this pasture are 70 meters and 60 meters.

4² is simplified expression for  \(\frac{4^{4} 4^{3} }{4^{5} }\).

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

Here, Given expression = \(\frac{4^{4} 4^{3} }{4^{5} }\)

\(\frac{4^{4} 4^{3} }{4^{5} }\) = \(\frac{4^{4+3} }{4^{5} }\)

      = 4⁷/4⁵

      = 4⁷⁻⁵

      = 4²

Thus, 4² is simplified expression for \(\frac{4^{4} 4^{3} }{4^{5} }\).

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Answer:

54

Step-by-step explanation:

63 * 2 = m of arc DF

arc DF = 126

180 - 126 = 54

Arc FE = 54

Answer:

arc FE = 54°

Step-by-step explanation:

Because DE is a diagonal, ∠DFE is 90°.

∠FDE = 180° - 90° - 63° = 27°

arc FE = 2(∠FDE) = 2(27°) = 54°

To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

Answer: $12.96

Given:

1305 bags of carrots purchased

Total cost = $16,910

Step-by-step explanation:

To find the unit cost, divide 16910 by 1305 to find the cost of one bag of carrots:

\(\frac{16910}{1305} = 12.96\)  (rounded to nearest hundredth)

Answer:

t(c)  =  3.355

Step-by-step explanation:

We assume a normal distribution, and with sample size n = 9 we should follow a t -student test on both tails since the FDA is interested in determining if the amount of drug absorbed is different from 3.5 micrograms.

Therefore if α  = 0,01    that means that confidence interval is 99 % or 0,99

Finally with   α/2 = 0,005   and 8 degrees of freedom we find in t-student table  t(c)  =  3.355

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

\(SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}\)

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

\(SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))\)

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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Answer:

cos(G)= 0.66667

Then value of angle G is

= 48.12°

Step-by-step explanation:

Right triangle EFG has its right angle at F.

EG=6, and FG=4.

What is the value of Cos(G)?

The value of cos(g)

= adjacent/hypotenuse

Where FG = adjacent

EG =  hypotenuse

.cos(G) = 4/6

cos(G)= 0.66667

G = 48.12°

Answer:

f(x) \(\leq\) 3x + 4

g(x)  ≥ -1/2x - 5

Step-by-step explanation:

Point D is below f(x)  and above g(x)

Helping in the name of Jesus.

Answer:

393.5$

Step-by-step explanation:

$18,000 -- car price

Total sum (105%) = \(\frac{18000}{100}\)* 105%

Hence

\(\frac{18000/100*105}{48}\) = 393.5$

Step-by-step explanation:

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