Mrs. Smith spent $67.40 on groceries. The tax rate is 2%. What is the amount of sales tax?

Answer: 9

Step-by-step explanation:

Formula : Mean = \(\dfrac{\text{Sum of observations}}{\text{Number of observaions}}\)

Given: 5 students participated in a push-up competition.

The amount of push-ups each student completed is listed: 12, 7, 10, 11,5.

Mean = \(\dfrac{12+7+10+77+5}{5}\)

\(=\dfrac{45}{5}=9\)

Hence, the mean number of push-ups = 9

Formula is

#1

\(\\ \sf\longmapsto (54-2)180\)

\(\\ \sf\longmapsto 52(180)\)

\(\\ \sf\longmapsto 9360°\)

#2

\(\\ \sf\longmapsto (19-2)180\)

\(\\ \sf\longmapsto 17(180)\)

\(\\ \sf\longmapsto 3060\)

#3

\(\\ \sf\longmapsto 292-2(180)\)

\(\\ \sf\longmapsto 290(180)\)

\(\\ \sf\longmapsto 52200\)

#4

\(\\ \sf\longmapsto (5-2)180\)

\(\\ \sf\longmapsto 3(180)\)

\(\\ \sf\longmapsto 540\)

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

At least 75% of the flights (or 15 out of the 20 flights) will last between 3 days and 11 days, according to Chebyshev's Theorem.

Chebyshev's Theorem states that for any given number k greater than 1, at least (\(1-\frac{1}{k^2}\)) of the data values in any data set will fall within k standard deviations of the mean.

In this case, we can use Chebyshev's Theorem to determine the minimum number of flights that lasted between 3 and 11 days.

Given:

Mean (μ) = 7 days

Standard Deviation (σ) = 2 days

To find the number of flights within the range of 3 to 11 days, we need to calculate how many standard deviations away from the mean these values are.

Lower Bound:

Value = 3 days

Number of standard deviations away from the

\(mean = \frac{(Value - Mean)}{ Standard Deviation}\)

\(mean =\frac{(3 - 7) }{2}\)

\(mean =\frac{-4}{2}\)

\(mean = -2\)

Upper Bound:

Value = 11 days

Number of standard deviations away from the

\(mean = \frac{(Value - Mean)}{Standard Deviation}\)

\(mean = \frac{(11 - 7)}{2}\)

\(mean = \frac{4}{2}\)

\(mean = 2\)

According to Chebyshev's Theorem, the minimum proportion of data values within k standard deviations of the mean is given by \((1- \frac{1}{k^2} )\).

So, we need to determine the proportion of data within 2 standard deviations, which is k = 2.

Proportion within 2 standard deviations = \(1-\frac{1}{2^2}\)

\(=1-\frac{1}{4}\)

\(= 1 - 0.25\)

\(= 0.75\)

Now, we can find the percentage of \(0.75\):

\(= 0.75\times 100\)

\(= 75\%\)

Therefore, at least 75% of the flights (or 15 out of the 20 flights) will last between 3 days and 11 days, according to Chebyshev's Theorem.

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The correct answer is, P(X > 18) is the same as P(X < 18). Option b is correct. The probability P(X > 18) is related to P(X < 18) in such a way that: P(X > 18) is the same as 1 − P(X < 18).

Explanation:

The mean length of a certain product X is μ = 18 inches.

As we know that the length of a certain product X is normally distributed.

So, we can conclude that: Z = (X - μ) / σ, where Z is the standard normal random variable.

Let's find the probability of X > 18 using the standard normal distribution table:

P(X > 18) = P(Z > (18 - μ) / σ)P(Z > (18 - 18) / σ) = P(Z > 0) = 0.5

Therefore, P(X > 18) = 0.5

Using the complement rule, the probability of X < 18 can be obtained:

P(X < 18) = 1 - P(X > 18)P(X < 18) = 1 - 0.5P(X < 18) = 0.5

Therefore, the probability P(X > 18) is the same as P(X < 18).

Hence, the correct answer is, P(X > 18) is the same as P(X < 18). Option b is correct.

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Answer:

\(x = 3\)

Step-by-step explanation:

\( \frac{5}{6} - \frac{x}{6} = \frac{1}{3} \\ \\ \frac{5 - x}{6} = \frac{1}{3} \\ \\ 3(5 - x) = 6 \\ \\ 15 - 3x = 6 \\ \\ 3x = 15 - 6 \\ \\ 3x = 9 \\ \\ x = \frac{9}{3} \\ \\ x = 3\)

I hope I helped you^_^

What I do understand of the quesetion, it should be "The change from Thursday to Friday represents a bigger  change in temperature."

The margin of error is Margin of Error = z * σ /√n = 1 * 0.8 / √14 = 0.213Pounding to one decimal place,Margin of Error ≈ 0.2Thus, the margin of error is 0.2 (Pound to one decimal place as needed).

Given: c

= 0.95, z

= 1, n

= 14 To find: Margin of Error Formula to be used:Margin of Error

= z * σ /√n where z

= z-value of the standard normal distributionσ

= Standard deviation of the population n

= Sample size Given n < 30, we can use t-distribution to find margin of error.We know,σ

= e / z where e

= margin of error Substituting the given values in the above formula, we getσ

= 3 + 2.8 / 6

= 0.8Using the t-distribution table, for 0.95 and 13 degrees of freedom (n-1), we get the t-value as 2.160.The margin of error is Margin of Error

= z * σ /√n

= 1 * 0.8 / √14

= 0.213Pounding to one decimal place,Margin of Error ≈ 0.2Thus, the margin of error is 0.2 (Pound to one decimal place as needed).

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Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

The three numbers which are in the ratio 1:2:3 and whose sum of the cubes is 4500 are 5, 10, and 15.

As given in the question,

Let us consider three number which are in the ratio 1: 2 : 3 be,

y, 2y , and 3y.

As per given condition:

Sum of their cubes = 4500

⇒x³ + (2x)³ + (3x)³ = 4500

⇒ x³ ( 1 + 8 + 27 ) = 4500

⇒36x³ = 4500

⇒ x³ = 4500/36

⇒x³ = 125

⇒ x = ∛125

⇒ x = 5

⇒2x = 10

⇒3x = 15

Therefore, three numbers which are in the given ratio are given by 5, 10, 15.

The above question is incomplete, the complete question is :

Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. Find the numbers.

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Answer:

Y = 1

Step-by-step explanation:

Proportional

Answer:

y=1

Step-by-step explanation:

Because they are proportional, the two points have to be equal if they were like a fraction. This means (15,3) would be 15/3 which is equal to 5. The other point is (5,?), so that means that the point will have to be 1. This is because then the point will be equal to 5.

Hope this helps

A sample size of 753 would be required to create the desired 98% confidence interval with an accuracy of within 3.0%.

To determine the sample size needed to create a 98% confidence interval with an accuracy of 3.0%, we can use the formula:

n = (z^2 * p * (1-p)) / E^2

where:

n = sample size
z = z-score for the desired confidence level (98% = 2.33)
p = estimated population proportion (0.40)
E = desired margin of error (0.03)

Plugging in the values, we get:

n = (2.33^2 * 0.40 * (1-0.40)) / 0.03^2
n = 623.22

Rounding up to the nearest whole number, we get a sample size of 624. Therefore, the person would need to use a sample size of 624 in order to create a 98% confidence interval with an accuracy of 3.0% for the unknown population proportion.
To create a 98% confidence interval for an unknown population proportion with an accuracy of within 3.0% and an estimated population proportion of 0.40, you'll need to determine the required sample size. You can use the following formula for sample size calculation:

n = (Z^2 * p * (1-p)) / E^2

where n is the sample size, Z is the Z-score associated with the desired confidence level (98% in this case), p is the estimated population proportion (0.40), and E is the margin of error (3.0% or 0.03).

For a 98% confidence level, the Z-score is approximately 2.33. Plugging the values into the formula:

n = (2.33^2 * 0.40 * (1-0.40)) / 0.03^2

n ≈ 752.07

Since a sample size of 753 would be required to create the desired 98% confidence interval with an accuracy of within 3.0%.

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The volume of the rectangular piece with sides of lengths of 7.08 × 10–3 m, 2.18 × 10–2 m, and 4.51 × 10–3m is 6. 96 × 10^ -7 m

Volume is defined as the amount of space or capacity occupied by a three-dimensional shape.

It is represented in cubic units.

Formula:

Volume, V = length × breadth × height

Given the values;

7. 08 × 10 ^-3m , 2.18 × 10^ -2m and 4. 51 × 10^-3m

Multiply all the lengths

Volume = 7. 08 × 10 ^-3 × 2.18 × 10^ -2 × 4. 51 × 10^-3

= 69.6 × 10^-8

= 6. 96 × 10^ -7 m

Therefore, the volume of the rectangular piece is 6. 96 × 10^ -7 m

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Answer:

A

Step-by-step explanation:

trust

Answer:

10:17 (girls to total students)

7:17 (boys to total students)

10:7 (girls to boys)

7:10 (boys to girls)

Step-by-step explanation:

Answer:

I got this question too! I'm not sure

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Because you are looking at the parallel lines not the strait cuz if it asked for the strait you would be adding.

Solution:

Find the Highest Common Factor of 12, 24, and 36.

Highest Common Factor = 12

Divide.

\(12\div12=1\)

\(24\div12=2\)

\(36\div12=3\)

12 symbolizes the amount of baskets there are.

---------------------------------------------

Answer:

1 lemon per basket.

2 apple's per basket.

3 banana's per basket.

---------------------------------------------

There is no possible way that there can be the same amount of fruit in each basket.

---------------------------------------------

To find the greatest number of pieces of fruit that can be put in each plastic container, we need to find the greatest common divisor (GCD) of the given numbers. The GCD is the highest number that divides all the numbers evenly. In this case, the GCD is 12.

To find the greatest number of pieces of fruit that can be put in each plastic container, we need to find the greatest common divisor (GCD) of the given numbers. The GCD is the highest number that divides all the numbers evenly. In this case, we want to find the GCD of 24, 36, and 12.

The prime factorization of 24 is 2 * 2 * 2 * 3. The prime factorization of 36 is 2 * 2 * 3 * 3. The prime factorization of 12 is 2 * 2 * 3.  

The GCD is found by taking the common factors with the lowest exponent. So the GCD of 24, 36, and 12 is 2 * 2 * 3 = 12. Therefore, Carina can put 12 pieces of fruit in each plastic container.

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Answer:

5. y=-3x-3

6.y=5/3x+5

Step-by-step explanation:

you take the slope of the line and substitute it for x and take the y-intercept and sub it in for b

I hope this is right

To find the joint PDF/PDF of X and Y, we'll use the conditional probability formula. The joint PDF/PDF of X and Y is denoted as fX,Y(x, y).

Given that X follows a Beta(a, b) distribution, the PDF of X is:

fX(x) =\((1/Beta(a, b)) * (x^_(a-1))\)\(* ((1-x)^_(b-1))\)

Now, for a fixed constant y, the conditional PDF of Y given X = x is defined as:

fY|X(y|x) = 1  

if y = constant

0   otherwise

Since the value of Y is constant given X = x, we have:

fX,Y(x, y) = fX(x) * fY|X(y|x)

For y = constant, the joint PDF of X and Y is:

fX,Y(x, y) = fX(x) * fY|X(y|x)

          =\((1/Beta(a, b)) * (x^_(a-1))\)\(* ((1-x)^_(b-1))\)\(* 1\)  if y = constant

          = 0   otherwise

Therefore, the joint PDF/PDF of X and Y is fX,Y(x, y)

= (1/Beta(a, b)) * (x^(a-1)) * ((1-x)^(b-1))

if y = constant, and 0 otherwise.

(b) To find E[Y] and V(Y), we'll use the properties of conditional expectation.

E[Y] = E[E[Y|X]]

     = E[constant]  

(since Y|X = x is constant)

     = constant

Therefore, E[Y] is equal to the fixed constant.

V(Y) = E[V(Y|X)] + V[E[Y|X]]

Since Y|X is constant for any given value of X, the variance of Y|X is 0. Therefore:

V(Y) = E[0] + V[constant]

     = 0 + 0

     = 0

Thus, V(Y) is equal to 0.

(c) To find E[X|Y = y], we'll use the definition of conditional expectation.

E[X|Y = y] = ∫[0,1] x * fX|Y(x|y) dx

Given that Y|X is a constant, fX|Y(x|y) = fX(x), as the value of X does not depend on the value of Y.

Therefore, E[X|Y = y] = ∫[0,1] x * fX(x) dx

Using the PDF of X, we substitute it into the expression:

E[X|Y = y]

= ∫[0,1] x * [(1/Beta(a, b)) \(* (x^_(a-1))\)\(* ((1-x)^_(b-1))]\)\(dx\)

We can then integrate this expression over the range [0,1] to obtain the result.

Unfortunately, the integral does not have a closed-form solution, so it cannot be expressed in terms of elementary functions. Therefore, we can only compute the expected value of X given Y = y numerically using numerical integration techniques or approximation methods.

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Answer:

there y= -x - 3 is correct

Step-by-step explanation:

(-4,1) ; (-3,0)

y= -x - 3

with (-4,1)

1 = -(-4) - 3 = 4 - 3 = 1. left = right

with (-3,0)

0 = -(-3) - 3 = 3 - 3 = 0. left = right

so the line y = -x - 3 is passes through points (-4,1) and (-3,0)

There will be 2216 square cm of the painted surface on the box, which is completely covered with paint.

For the calculate of the area of rectangles:

Area = length * breadth

So, Outer area.

A1 = 2*16*10 + 2*24*10 + 1*16*24

A1 = 1184 sq.cm

Inner area:

A2 = 2*14*9 + 2*22*9 + 1*14*22

A2 = 956 sq. cm

Top area:

A3 = 16*24 - 14*22

A3 = 76 sq. cm

Complete area A = 1184 + 956 + 76

A = 2216 sq. cm

Thus, there will be 2216 square cm of the painted surface on the box, which is completely covered with paint.

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The equation 9x − 3x + 1 = k has two distinct real solutions precisely when k < −49​. Therefore, the equation 9x − 3x + 1 = k has two distinct real solutions precisely when k < −49/36.

Given equation is 9x − 3x + 1 = kLet us simplify the given equation9x − 3x + 1 = k⇒ 6x + 1 = k⇒ 6x = k − 1⇒ x = (k − 1) / 6

Now, the discriminant of the given quadratic equation isD = b² - 4ac= (-3)² - 4(9)(1-k)= 9-36(1-k)= - 27-36k

Let us analyze the given equation for different values of k

(i) k < −49/36,  When k < −49/36, D > 0, the roots are real and distinct 9x − 3x + 1 = k⇒ 6x + 1 = k⇒ 6x = k − 1⇒ x = (k − 1) / 6

(ii) k = −49/36,  When k = −49/36, D = 0, the roots are real and equal 9x − 3x + 1 = k⇒ 6x + 1 = k⇒ 6x = k − 1⇒ x = (k − 1) / 6

(iii) k > −49/36,When k > −49/36, D < 0, the roots are complex 9x − 3x + 1 = k⇒ 6x + 1 = k⇒ 6x = k − 1⇒ x = (k − 1) / 6

Thus, we can conclude that the equation 9x − 3x + 1 = k has two distinct real solutions precisely when k < −49/36.

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Answer:

hope this answer helps you dear....take care!

Answer:

\(total \: angleof \: a \: triangle = 180 \\ then \\ x + 3x - 1 + x - 19 = 180 \\ 5x - 20 = 180 \\ 5x = 180 + 20 \\ 5x = 200 \\ x = \frac{200}{5} \\ x = 40 \\ thank \: you\)

Answer:

7.68

Step-by-step explanation:

Answer: PRIME NUMBERS BETWEEN 30 AND 45 ARE 31, 37, 41, and 43.

Answer:

37

Step-by-step explanation:

Reverse the steps

-144/-6 = 24

24 + 13 = 37