Shoes and hats are on sale. The expression 1/4(s + 24. 80) can be used to determine the discount when you buy shoes with a retail price of s dollars and hats with a total retail price of $24. 80. Write another expression that can be used to determine the discount

The distance of the boat is 191.2 miles, 12.8° and N12.8E from the original location.

To calculate the distance, direction angle, and bearing of the boat from its original location, we will need to use trigonometry to determine the final position of the boat.

a) The distance traveled in the eastward direction is 130 miles. Then, using the bearing of N38E, we can calculate the northward and eastward distances traveled in the second leg of the journey. The bearing of N38E can be thought of as an angle of 38 degrees measured clockwise from due east.

Using trigonometry to calculate the northward distance traveled, we have,

(72 miles) * (sin 38°)

= 36 miles

And the eastward distance traveled is (72 miles) * (cos 38°)

= 59.04 miles.

The final position of the boat is at a distance can be calculated by:

130 miles east + 59.04 miles east

= 189.04 miles east and 36 miles north from the original location.

b) To find the distance from the original location, we use the Pythagorean theorem,

d =  [tex]\sqrt{189.04^{2} +36^{2} }[/tex]

d = 191.2 miles

To find the direction angle, we use arctan(north/east) = arctan(36/189.04) = 12.8°

Bearing is the direction angle measured clockwise from north. So, bearing = 12.8°

Hence, the final position of the boat is 191.2 miles, 12.8°, and N12.8E from the original location.

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NA (There is not enough information given to determine the value of MZ)

In this question, we are given that WY is 4.6 for us to find the value of MZ We need more information to be in a position to answer this. More information includes maybe we know the value of M or at least having some relationship between WY and MZ for us to draw a conclusion and come up with the value of MZ. If at all we had a common value in WY and MZ say M then it could be easier to come to a conclusion and finally get the value of MZ.

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The height of the person is approximately 0.426 meters or 42.6 cm.

We can use the concept of similar triangles to solve this problem. The height of the building and the length of its shadow form a right triangle, with the height as the opposite side and the shadow as the hypotenuse. The person and their shadow also form a similar right triangle, with the height of the person as the opposite side and the shadow as the hypotenuse.

We can set up the following proportion:

(Height of building)/(length of shadow) = (height of person)/(length of shadow)

48/30 = h/0.8

Solving for h, we get:

h = (48/30) * 0.8 = 0.533 * 0.8 = 0.426

Therefore, the height of the person is approximately 0.426 meters or 42.6 cm.

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The inequality that shows the maximum number of hours Penelope can rent is 35 + 4x ≤ 75

An equation shows how two or more numbers and variables are related to each other.

Let x represent the number of hours to rent

There is a fixed $35 fee and an hourly fee of $4. Hence:

Total cost = 4x + 35

Penelope has a budget of $75. hence:

35 + 4x ≤ 75

The inequality is 35 + 4x ≤ 75

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Answer: -120

6 less than is 6 - and 3 times a number 42 is 3 x 42 so...

6 - (3 x 42) = -120

Answer:

[tex]x = \frac{9}{5} [/tex]

Step-by-step explanation:

[tex] - 7( - 7 \times ( - x - 1)) = 6 (- \times ( - 2x - 3))[/tex]

[tex] - 7 + 7x + 7 = 6 + 2x + 3[/tex]

[tex]7x - 2x = 6 + 3 + 7 - 7[/tex]

[tex]5x = 9[/tex]

[tex] \frac{5x}{5} = \frac{9}{5} [/tex]

[tex]x = \frac{9}{5} [/tex]

The statement whether each data set is likely to be distributed nor not:

Number of minutes required to complete a marathon - Yes.

Number of miles in a marathon: - No.

Average age of a person who runs a marathon: No.

The distribution of values in a field is described by a statistical distribution, often known as a probability distribution. In other words, the statistical distribution identifies the typical and unusual values. The bell-shaped normal distribution is one of many varieties of statistical distributions.

Let n miles in marathon.

To normally distribute, number of minutes required to complete a marathon:

The number of minutes required to complete a marathon is likely to be normally distributed with small amounts in tails (very slow, very fast) and large amount in middle.

So, yes.

To normally distribute,  number of miles in a marathon:

The number of miles is a fixed number, not normally distributed.

So, no.

To normally distribute, average age of a person who runs a marathon:

The average age is a fixed number

Average age is not likely to be normally distributed.

So, no.

Therefore, the first one is yes, and the other two are no.

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The table with values for x or y that make this equation true : 3x + y = 15 are

x       2     4      6      0      3      5      7/3

y       9     3     -3     15      6     0       8      

What is solving an equation?

One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side.

Consider, the given equation: 3x + y = 15

We have to complete the given table for the values of x and y.

Plug x = 2 in the given equation.

⇒  3(2) + y = 15

        6 + y = 16

              y = 9

Plug y = 3  in the given equation.

3x + 3 = 15

     3x = 12

       x = 4

Plug x = 6  in the given equation.

3(6) + y = 15

 18 + y = 15

        y = -3

Plug x = 0  in the given equation.

3(0) + y = 15

         y = 15

Plug x = 3  in the given equation.

3(3) + y = 15

  9 + y = 15

        y = 6

Plug y = 0  in the given equation.

3x + 0 = 15

     3x = 15

       x = 5

Plug y = 8  in the given equation.

3x + 8 = 15

3x = 7

x = 7/3

Hence, the table with values for x or y that make this equation true : 3x+y=15 are

x       2     4      6      0      3      5      7/3

y       9     3     -3     15      6     0       8      

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Therefore , the solution of the given problem of trigonometry  comes out to be surface x² + y² + z² = p².

Trigonometry is the discipline of mathematics that studies correlations between angles and sides of triangles. Trigonometry is present in all of geometry because every straight-sided shape may be reduced to a set of triangles. Remarkably intricate connections exist between trigonometry and other areas of mathematics, particularly calculus, real or complicated, exponentials, logarithms, and infinite series.

Here,

Given:

p = sinθ sin∅

To Locate:

the equation's surface

Solution:

adding p to both sides of the equation

p sinθ sin∅ = p²

p sinθ sin∅ = p²

p sinθ sin∅ =y

x²+y²+z²=y

x² + y² - y+ z² = 0

x²+ (y - 1/2)²+ z² = 1/4

r² =1/4, r= √1/4,

The surface of the sphere having a radius of 1/2 and a center at (0, 1/2, 0) is designated as 1/4.

Sphere-centered coordinates

x = sin p sin

y = sin(p), sin(p),

z = p cos∅

x² + y² + z² = p²

Therefore , the solution of the given problem comes out to be surface

x² + y² + z² = p².

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Answer:

Y-intercept: (0, -7)

X-intercept: (-14,0)

Step-by-step explanation:

To find the y-intercept, we need to put 0 in for x

0 + 2y = -14

2y = -14

y = -7

So, the y-intercept is located at (0, -7)

To find the x-intercept, we need to put 0 in for y

x + 2(0) = -14

x = -14

So, the x-intercept is located at (-14,0)

Step-by-step explanation:

To find the y-intercep, we need to put 0 in for x

0 + 2y= -14

2y = -14

y = - 7

So, the y - intercept is located at ( 0, - 7)

Answer:

Step-by-step explanation: 2.922

Answer: 2.922

Step-by-step explanation: (Look at the attachment for the best experience, or idea) So, as you can see in the attachment below, we first need to line up the decimal points with one another. They subtract in line with the other decimals and borrow. As we know, our answer is 2.922.

It will take Emily 12.1 hours to mow 5 acres

Variation is the relation between a set of values of one variable and a set of values of other variables

Let T and A represent the time and area respectively

Since the time it takes Emily to mow a lawn is proportional to its area. We can write:

T α A

T = kA (where k is constant of proportionality)

It takes her about 30 minutes to mow 1,000 square yards. That is:

T = 30 and A = 1,000

T = kA

30 = 1000k

k = 30/1000

k = 0.03

Time for 5 acres:

5 acres = 5 × 4840 = 24200 square yards   (1 acre = 4840 square yards)

T = kA

T = 0.03 × 24200

T = 726 minutes     (divide by 60 to get time in hours)

T = 12.1 hours

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Difference between coldest and hottest temperature was greater in march than July.

The range is the difference between the highest and lowest values within a set of numbers. To calculate range, subtract the smallest number from the largest number in the set.

Given,

Range of temperature in march = 32°

⇒ difference in temperature in march ΔT = 32°

Range of temperature in July = 8°

⇒ difference in temperature in July Δt  = 8°

By the above observation

ΔT > Δt .

difference in temperature in march > difference in temperature in July.

Hence, In month of march, there was greater difference between the hottest and coldest temperature than in month of July.

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Answer:

4y / x-y

Step-by-step explanation:

First change 1 to y/y. This allows us to rewrite the first term as a single fraction.

We can also factor the denominator of the second term.

x^2 - y^2 factors into (x - y)(x + y)

The y cancels and also the term x+y cancels. See image.

The short explanation of the effects of the above operations will not affect the inequality.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9, then we have

4 x 3 x 2 x 4 x 9 < 7 x 3 x 2 x 4 x 9

864 < 1512

2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)

11 + 3 + (-4) > - 2 + 3 + (-4)

10 > - 3

3. -2 ≤ -2 Subtract 6 from both sides, then 8, and then 2

-2 - 6 - 8 - 2 ≤ -2 - 6 - 8 - 2

- 18 ≤ - 18

4. -4 < 8 Divide both sides by -4, then by -2

- 4 / (-4) > 8 / (-4)

1 / (-2) > - 2 / (-2)

- 1/2 < 1

The short explanation of the effects of the above operations will not affect the inequality.

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Answer:

C

Step-by-step explanation:

Answer:

- 7√10

Step-by-step explanation:

Step 1 : Take √10 common

2√10 - 5√10 - 4√10

= √10 ( 2 - 5 - 4 )

Step 2 : Subtract the numbers separately.

2 - 5 - 4

= 2 - 9

= - 7

Step 3 : Multiply √10 and - 7

√10 * - 7 = - 7√10

Answer in explanation:

although there's an addition sign, you subtract the two because a

(+) + (-) = (-) subtract

[This is a general rule, writing down the "rules" for reference is a good way to help if your having trouble]

subtract to find your answer (you keep the sign of 1.8 because it's the larger number.)

1.3 + (-1.8) =

-0.5

-0.5 is your answer

Hope this is clear!

For two numbers to be proportional, they need to be directly increasing or decreasing in a constant ratio.

If Donny makes $9.75 per lawn, we can make a table that looks like this:

1 Lawn = $9.95

2 Lawns = $19.90

3 Lawns = $29.85...

And so on.

You can see this is proportional because it has a constant ratio between both elements.

(1 to 9.95)

So, it is proportional.

Therefore , the solution to the given question of percentage comes out to be 7.89.

A% is a number that represents the percentage of 100 that it is, and it can also be stated as a decimal or a fraction. To convert a percentage to a fraction, place 100 in the denominator and the percentage number in the numerator.

Here,

Given : 40% of the money, a Trainer is given

30% of the money ,a student lead

Find the discount

40 * .15 = 6

Take this from the original price

0.30* 6.3 =1.89

The sale price is 6 + 1.89 =7.89

Therefore , the solution to the given question of percentage comes out to be 7.89.

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The number of pounds each package would have to weigh for the total cost of shipping the packages to be the same will be 7.50 pounds.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The cost to transport an item varies between two shipping providers. The price charged by Company A is $6.50 plus $0.35 per pound. Charges from Company B are $7.25 plus $0.25 per pound.

Let 'p' be the number of pounds and 'T' be the total cost of shipping. Then the equations are given as,

T = 0.35p + 6.50

T = 0.25p + 7.25

If the total cost of shipping the packages is to be the same. Then the number of pounds is given as,

0.35p + 6.50 = 0.25p + 7.25

0.35p - 0.25p = 7.25 - 6.50

0.10p = 0.75

p = 7.50 pounds

The number of pounds each package would have to weigh for the total cost of shipping the packages to be the same will be 7.50 pounds.

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Answer:

[tex] \sf \: \frac{75}{12} \: (or) \: 6.25[/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: 15 \times \frac{5}{12} [/tex]

[tex] \sf \rightarrow \: \frac{(15 \times 5)}{12} [/tex]

[tex] \sf \rightarrow \: \frac{75}{12} = 6.25[/tex]

Hence, the product is 6.25.

(x+5) is not a factor of f(x) because x = -5 does not satisfy the given equation f(x) = x³ - 4x² + 3x + 7.

Step 1. First we solve the equation x +5 = 0, we get

x = -5

Step 2. By putting the value of x = -5 in f(x) check whether we get a zero or a number other than zero.

If we get zero then x+5 is a factor of f(x) and if we get a number other than zero then x+5 is not a factor of f(x)

f(-5) =  (-5)³ − 4(-5)² + 3(-5) + 7 = - 233

Since we got -233 and not 0. Therefore, (x+5) is not a factor of f(x).

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The whole section is 9/4 unit.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Mr.Parrillo’s class has adopted a section of a highway to keep clean.

1/3 of the section is 3/4.

To find the length of the whole section:

Multiply by 3.

So,

The length of the whole section = 3 (3/4)

The length of the whole section = 9/4

Therefore, 9/4 unit is the length.

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Answer:

m = 2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

We see the y increase by 4 and the x increase by 2, so the slope is

m = 4/2 = 2

So, m = 2

This probability does not support the Trump/Farage claim that 60% of all immigrants are male.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes, and how likely they are.

The probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found using the binomial probability formula, which calculates the probability of a specific number of successes (male immigrants) in a fixed number of trials (sample size) with a fixed probability of success (p = 0.60).

Using the binomial formula, the probability of obtaining 257 or fewer males in a sample of 583 immigrants can be found by summing the probabilities of obtaining 257 males, 256 males, 255 males, etc. up to 0 males.

Using a binomial calculator, we can find that the probability of obtaining 257 or fewer males in a sample of 583 immigrants is about 0.04.

This probability is quite low, which suggests that it is unlikely to obtain 257 or fewer males in a sample of 583 immigrants if the proportion of male immigrants is actually 60%.

Therefore, this probability does not support the Trump/Farage claim that 60% of all immigrants are male.

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Linear refers to a straight line when plotted on a graph, while logarithmic refers to a curve that follows the logarithmic function. Linear relationships are those where the rate of change is constant. Logarithmic relationships are those where the rate of change increases or decreases as the value of the independent variable increases.

Linear relationships are those where the rate of change is constant no matter how the independent variable changes. In this type of relationship, the y-value increases or decreases at a constant rate as the x-value increases. For example, if a graph shows a linear relationship, the data points will form a straight line when plotted on a graph. Logarithmic relationships are those where the rate of change increases or decreases as the independent variable increases. In this type of relationship, the y-value increases or decreases more quickly as the x-value increases. This can be seen when plotting the data on a graph as a curved line. An example of this type of relationship is the exponential growth of a population as the population increases.

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The process of the faces of a three-dimensional figure determine two-dimensional shapes created by slicing the figure is explained below.

The term three dimensional figure is defined as solid shapes or figures that have three dimensions.

Basically these kind of shapes has length, width and height are the dimensions of 3D shapes and the common names of these shapes are cube, cuboid, cone, cylinder and sphere.

Where as the two dimensional figure is defined as  horizontal and vertical axes that is x-axis and y-axis) and it is also known as 2d shapes are flat figures that have only length and width. And thus shapes do not have thickness or height.

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The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979

What is Probability ?

probability can be defined as the ratio of the number of favourable outcomes and the total number of outcomes.

We are given with an exponential distribution with

λ=0.01386.

The probability distribution function is:

F(x)=λ * e power (−λx)

Cumulative distribution function is

F(x) = 1- e power (−λx)

The mean of the exponential distribution function

E(X) = 1 / λ

= 1/0.01386

= 72.15

Hence, E(X) = 72.15

The variance of the exponential distribution function

V(X) = 1 / λ ^{2}

= 1/0.01386*0.01386

= 5205.63

V(X) = 5205.63

Probability that the distance is at most 100m

P(X <= 100 ) = F (100)

= 1- e power (−λx)

= 1 - e power (-0.01386*100)

= 1- e power (-1.386)

= 1-0.25007

= 0.749926

Therefore, P(X<=100) = 0.749926

probability that the distance is at most 200m

P ( X<= 200) = F(200)

=1-e power (−λx)

=1-e power (-0.01386*200)

= 1 - e power (-2.772)

= 1-0.06253

= 0.9375

P(X<= 200) = 0.9375

Probability that the distance is between 100 and 200m

P(100<= X <= 200) = F(200) - F(100)

= 0.9375-0.7499

=01876

P(100 <= X <= 200) = 0.1876

Probability that the distance exceeds the mean distance by more than 2 standard deviation.

P( X + P>μ+2σ) = P(X>72.15+2√5205.63)

= P(X > 72.15 +144.3)

P(X>216.45)

= 1-P(X<= 216.45)

1 - (1- e power (-0.01386*216.45)

=  e power (-2.9999)

= 0.04979

P( X + P>μ+2σ) = 0.04979

Hence , The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979

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Yes, because as x increases, y increases and because all of the pairs represent the same ratio.

When two sets of provided numbers change in proportion, the ratios are said to be directly proportional if they do so in the same direction.

If two ratios or fractions are equivalent, it may be shown using the proportion formula. By dividing the supplied numbers, we may determine the value that is missing. You may write the percentage formula as a: A and d are the extreme terms, and b and c are the middle terms, according to the formula b::c: d = a/b = c/d.

Yes, because as x increases, y increases.

Yes, because all of the pairs represent the same ratio.

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