Anton bought a picnic cooler. His total bill, with tax, was $7. 95.

He paid 6 percent sales tax. How much did he pay for the cooler

alone without the tax?

5. Write and solve the arithmetic problem for each step.

• For the cost of the cooler, solve:

?% of cost of cooler = $7. 95

• To find the total bill in terms of the cost of the cooler :

?% of cooler price

+ 6% of cooler price (tax)

?% of cost ($7. 95)

Answer:

3 = 3/4

but 3/4= 0.75

3 = 0.75

x = 25

cross multiply

0.75x = 75

divide both sides by 0.75

x = 100

therefore 25miles represent 100inch on a map

Answer:

3.14159 and so on

Step-by-step explanation:

Answer:

y = (-4/3)x + 4  

Step-by-step explanation:

Let y = mx + b, be the equation of the line in slope intercept form where we need to find m and b.

Perpendicular to y = (3/4)x - 5, means that m = - (1 / (3/4) ) = - 4/3

So, at this point, y = (-4/3)x + b.

Crossing the x - axis at 3 means that (3, 0) is a point on the line, where we note that x=3 and y=0.

Thus, we plug in these values into the equation y = (-4/3)x + b, to get

0 = (-4/3)(3) + b

0 = -4 + b, so that

b = 4.

Hence, the answer is:

y = (-4/3)x + 4

Answer:

148

Step-by-step explanation:

Answer:

X = 18

Step-by-step explanation:

X - 7 = 11

Add 7 to both sides

X - 7 + 7 = 11+7

X = 18

The spring can be stretched up to 8 feet beyond its natural length with a force not exceeding 24 pounds.

Hooke's Law states that the force required to maintain a spring stretched x units beyond its natural length (F) is proportional to x. Mathematically, this can be expressed as:

F ∝ x     (Equation 1)

The work done on a spring can be calculated using the formula:

Work = (1/2) k x^2     (Equation 2)

where k is the spring constant.

Given that the work required to stretch the spring from 2 feet beyond its natural length to 4 feet beyond its natural length is 18 ft-lb, we can write the following equation using Equation 2:

(1/2) k (4^2 - 2^2) = 18

Simplifying the equation:

k (16 - 4) = 36

12k = 36

k = 36/12

k = 3 ft-lb/ft^2

Now, we can use Equation 1 and the given force limit of 24 pounds to determine the maximum stretch beyond the natural length (x_max). We know that the force (F) is proportional to x:

F = kx

Substituting the values:

24 = 3x_max

Solving for x_max:

x_max = 24/3

x_max = 8 feet

Therefore, the spring can be stretched up to 8 feet beyond its natural length with a force not exceeding 24 pounds.

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Answer:

height x=21.5cm

Step-by-step explanation:

Surface area = 2+ area of triangles + area of the 3 rectangles

SA = 204

204 = 4*3 + x*5 + 5*4 + x*3

204 = 12 +20 +8x

204 -12-20 = 8x

172/8 = x

21.5 = x

Answer:

Step-by-step explanation:

x=20(.75)+2+10 (or 12 if it says that)

Answer:

The linear equation that represent the situation is \(x=20-0.75(10+2)\)

The remaining balance on his gift card is $11

Step-by-step explanation:

Let x represent the remaining balance.

We know that the linear equation that represent the situation is equal to\(x=20-0.75(10+2)\)

Solve

\(x=20-0.75(12)\)

\(x=20-9\)

x=$11

Answer:

V = 588.4 ft³

Step-by-step explanation:

Radius = 4.9 ft

Height = 7.8 ft

Volume of cylinder = \(\pi r^2h\)

V = (3.14)(4.9)²(7.8)

V = (3.14)(24.01)(7.8)

V = 588.4 ft³

Answer:

The input of a algebraic equation

Step-by-step explanation:

You're welcome

The given function f(x) = 25e^(-2x) represent the exponential decay.

According to th egiven question.

We have an exponential function.

f(x) = 25e^(-2x)

As we know that

If \(P = P_{o} e^{-kt}\) be an exponential function, then it will represent

Where,

P is the final amount

\(P_{o}\) is the intial amount

t is the time interval

k is the constant of proportionality

For the given question if we compare the given exponential function with the standard exponentential function we get

\(P_{o}\) = 25

k = 2

and t = x

Now,

e^(-2) = 0.13

Since, e^(-2) < 1.

Hence, the given function f(x) = 25e^(-2x) represent the exponential decay.

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A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

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\(35x( \frac{3}{7} = \frac{1}{5} + \frac{1}{x} ) \\ = > 35x \times \frac{3}{7} = > 35x \times \frac{1}{5} + 35x \times \frac{1}{x} \\ = > 5x \times 3 = 7x + 35 \\ = > 15x = 7x + 35 \\ = > 15x - 7x = 35 \\ = > 8x = 35 \\ = > x = \frac{35}{8} \\ = > x = 4.375\)

x = 4.375

To test whether shoes cost less on average at Payless than at Famous Footwear, we can conduct a two-sample t-test for the difference in means.

The null hypothesis is that there is no difference in the mean prices between the two stores, and the alternative hypothesis is that the mean price at Payless is less than the mean price at Famous Footwear.

We can calculate the t-statistic using the formula:

t = \((x1 - x2 - 0) / sqrt(s1^2/n1 + s2^2/n2)\)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the values given in the table, we get:

t =\((21.39 - 45.66 - 0) / sqrt((7.47^2/30) + (16.54^2/30))\) = -10.78

The degrees of freedom for this test is (30-1) + (30-1) = 58.

Using a t-table or calculator, we find the p-value to be very small, much less than 0.05.

Therefore, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 significance level that shoes cost less on average at Payless than at Famous Footwear.

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The mean vector of p(w) is zero, and the covariance matrix is a diagonal matrix with the variances of each element of w along the diagonal.

a. The likelihood function py(y|r) describes the probability distribution of the observed variable y given the Gaussian random variable r. Since y = A + b*r + w, we can express the likelihood as:

py(y|r) = p(y|A, b, r, w)

Given that w is an independent Gaussian noise with zero mean and covariance matrix , we can write the likelihood as:

py(y|r) = p(y|A, b, r) * p(w)

Since r is a Gaussian random variable with mean and covariance matrix 2r, we can express the conditional probability p(y|A, b, r) as a Gaussian distribution:

p(y|A, b, r) = N(A + b*r, )

Therefore, the likelihood function can be written as:

py(y|r) = N(A + b*r, ) * p(w)

b. The distribution p(w) is given as the product of the individual probability densities of the elements of w. Since w is an independent Gaussian noise, each element follows a Gaussian distribution with zero mean and variance from the diagonal covariance matrix. Therefore, we can write:

p(w) = p(w1) * p(w2) * ... * p(wn)

where p(wi) is the probability density function of the ith element of w, which is a Gaussian distribution with zero mean and variance .

To compute the mean and covariance of p(w), we can simply take the means and variances of each individual element of w. Since each element has a mean of zero, the mean vector of p(w) will also be zero.

For the covariance matrix, we can construct a diagonal matrix using the variances of each element of w. Let's denote this diagonal covariance matrix as . Then, the covariance matrix of p(w) will be:

Cov(w) = diag(, , ..., )

Each diagonal element represents the variance of the corresponding element of w.

In summary, the mean vector of p(w) is zero, and the covariance matrix is a diagonal matrix with the variances of each element of w along the diagonal.

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A. Using the distance formula, we can state that the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are equal, AC = BD = √50 units.

C. Based on the slopes of each side, there are 4 right angles on the rectangle.

The distance formula is used to find the distance that exist between tow points that are on a coordinate plane. The formula is: d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

What is the Slope of a Line?

Slope = change in y / change in x.

A. The coordinates of each of the vertices of the rectangle are:

A(1, 2)

B(7, 4)

C(8, 1)

D(2, -1)

Use the distance formula to find AB, CD, BC, and AD.

AB = √[(7−1)² + (4−2)²]

AB = √40

CD = √[(2−8)² + (−1−1)²]

CD = √40

BC = √[(8−7)² + (1−4)²]

BC = √10

AD = √[(2−1)² + (−1−2)²]

AD = √10

Therefore, the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.

B. The diagonals are AC and BD. Find their lengths using the distance formula:

AC = √(8−1)² + (1−2)²]

AC = √50 units

BD = √[(2−7)² + (−1−4)²]

BD = √50 units

Therefore, the diagonals are equal, AC = BD = √50 units.

C. Find the slope of AB, CD, BC, and AD:

Slope of AB = change in y / change in x = rise/run = 2/6 = 1/3

Slope of CD = 2/6 = 1/3

Slope of BC = -3/1 = -3

Slope of AD = -3/1 = -3

-3 is the negative reciprocal to 1/3, this means that, if the two lines that meet at a corner have these two slope, then they will form a right angle because they are perpendicular to each other.

Therefore, there are 4 right angles on the rectangle.

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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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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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The date that Chris will have both training sessions again is May 9.

In mathematics, a multiple simply means the product of any quantity. It should be noted that a multiple illustrate to the product of a number given.

In this situation, since Christ has bowling training every 8 days and hockey training every 2 days. The lowest common multiple for 2 and 8 is 8.

Therefore, the next date will be the addition of the day of the training and the number of days that are needed when the lowest common multiple was calculated. This will be illustrated thus:

= May 1 + 8 days

= May 9

The next training is May 9.

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Answer:

0.36

Step-by-step explanation:

first number is who put no and safety which is 192 then the total of selected no which is 534

at least that what i got sorry if wrong

Answer:

y=9

Step-by-step explanation:

For the statement to happen, the number should be 2.

An algebraic expression is is defined as the combination of numbers and variables in solving a particular mathematical question. Variable, usually letters, are used to denote the unknown quantity.

Let x = number

Based on the information given, add the number to the numerator of 11/35 and add twice the number to the denominator of 11/35, and the result should be equal to 1/3.

Hence, (11 + x) / (35 + 2x) = 1/3.

Simplify and solve for the value of x.

3(11 + x) = (35 + 2x)

33 + 3x = 35 + 2x

3x - 2x = 35 - 33

x = 2

number = 2

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The function of the town's population is an exponential growth

From the question, we have the following parameters that can be used in our computation:

Initial population = 3800

Growth  rate = 2% every year

From the above, we understand that

There is a growth in the population by 2% every year

Using the above as a guide, we have the following:

This means that the function is an exponential growth

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Answer: i would say 280.

Step-by-step explanation: because if you add 180 plus another set of it it would make 280

Answer:

180

Step-by-step explanation:

Since they are vertical angles, they are congruent to each other

m<1 = m<2

The value of  Pw(w) and Fw(w) are (0, 0.4, 0.8, 1) for different random variable X. And E[W] = -E[X] = -0 = 0.

(a) To find Pw(w), we need to determine the probability that the transformed random variable W takes on a specific value w. In this case, W = -X.

Since W is the negative of X, the probability that W equals w is equal to the probability that X equals -w.

Pw(w) = P(X = -w)

Considering the CDF of X, we have the following intervals:

For -∞ < x < -3: Fx(x) = 0

For -3 < x < 5: Fx(x) = 0.4

For 5 < x < 7: Fx(x) = 0.8

For 7 < x < ∞: Fx(x) = 1

Since W = -X, we can rewrite the intervals as:

For ∞ < w < 3: Fw(w) = 0 (since X = -w is not within the range of X)

For -3 < w < -5: Fw(w) = 0.4

For -5 < w < -7: Fw(w) = 0.8

For -∞ < w < -7: Fw(w) = 1

(b) To find Fw(w), we need to determine the cumulative distribution function (CDF) of W. From the previous calculations:

For ∞ < w < 3: Fw(w) = 0

For -3 < w < -5: Fw(w) = 0.4

For -5 < w < -7: Fw(w) = 0.8

For -∞ < w < -7: Fw(w) = 1

(c) To find E[W], we need to calculate the expected value of W. Since W = -X, we can express E[W] as:

E[W] = E[-X] = -E[X]

We can use the CDF Fx(x) to find the expected value of X:

E[X] = ∫ x * f(x) dx

Using the intervals and probabilities from the CDF:

E[X] = (-3 * 0.4) + (0 * (0.8 - 0.4)) + (6 * (1 - 0.8))

E[X] = -1.2 + 0 + 1.2

E[X] = 0

Therefore, E[W] = -E[X] = -0 = 0.

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Answer:

4.86 people/sq.miles

Step-by-step explanation:

the area of the state of Wyoming =

360 × 280 = 100,800 sq. miles

so, the population density =

490,408 ÷ 100,800

= 4.86 people/sq.miles

Answer:

8.50x \(\geq\) 348.50

41 hours

Step-by-step explanation:

x= amount of hours

Answer:

6.63

Step-by-step explanation:

This is the answer because 26.54 - 75 %

=6.63

Verified by FaZe DoDo

Answer:

296°

Step-by-step explanation: