A linear equation in one variable can have solution(s).
a. only 1
b. 2
c. 3
d. any number of

The statement that describes the conversion is To find the weight in pounds, multiply the number of ounce by the unit rate 16 ounces per pound

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

The double number line

On the double number line, we have:

16 ounces = 1 pound

This means that

To find the weight in pounds, multiply the number of ounce by the unit rate 16 ounces per pound

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Answer:Mr. Jacob purchased 7 adult tickets at $7.50 each, and 4 child tickets at $5.00 each, for a total of 11 tickets at a cost of $65.

Step-by-step explanation:

Answer:

Step-by-step explanation:x=28

The value of the unknown side length, BC, in given diagram is 28.3 ft

From the question, we are to determine the value of the unknown side length in the given diagram

By similar triangles theorem, we can write that

AX/XY = AB/BC

From the given information,

AX = 12ft

XY = 17 ft

AB = AX + XB

= 12 ft + 8 ft

= 20 ft

BC = ?

Then, we can write that

12/17 = 20/BC

Cross multiply

12 × BC = 17 × 20

12 × BC = 340

BC = 340/12

BC = 28.3

Hence, the value of BC is 28.3 ft

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The next two days when Alicia would be allowed to eat junk foods are Thursday and Tuesday.

The first day after Saturday when Alicia would have junk food can be determined by counting the fifth day after Saturday.

Sunday - first day

Monday - second day

Tuesday - third day

Wednesday - fourth day

Thursday - fifth day

The next day after Thursday when Alicia would have junk food is the fifth day after Thursday.

Friday - first day

Saturday - second day

Sunday - third day

Monday - fourth day

Tuesday - fifth day

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Answer: 27

Step-by-step explanation:

The commission amount the salesperson earn is $29.7.

The percentage formula is dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Selling price = $495

Commission = 6%

Now,

The amount of commission.

= 6% of 495

= 6/100 x 495

= 29.7

Thus,

The commission the salesperson earn is $29.7.

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a. The oldest grandchild got the most ice cream.

b. The remaining ice cream will be represented by a fraction of 59/100 of the original amount.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

a. The oldest grandchild got the most ice cream.

b. Let's first calculate the fraction of the ice cream that was left after serving the youngest and middle grandchild.

The youngest grandchild received 1/5 of the ice cream, which means 4/5 was left.

Then the middle grandchild got 1/4 of the remaining 4/5, which is 1/5. So 4/5 - 1/5 = 3/5 of the ice cream is left.

Now, if Grandpa Mick serves himself the same amount as the second grandchild (1/4 of the original amount), he will be taking 1/4 of 1/5 of the original amount, which is 1/20.

So the remaining ice cream will be 3/5 - 1/20 = 59/100 of the original amount.

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The question seems incomplete, the missing part would be as:

Grandpa Mick opened a pint of ice cream. He gave his youngest grandchild 1/5 of the ice cream and his middle grandchild 1/4 of the remaining ice cream. Then, he gave his oldest grandchild 1/3 of the ice cream that was left after serving the other. a. Who got the most ice cream?  b. What fraction of the pint of ice cream will be left if Grandpa Mick serves himself the same amount as the second grandchild?

Answer: rs>4

Step-by-step explanation: The product of r and s just means rs. Then, when it says more than, you know its going to be a greater than sign: >. So your inequality would be rs>4

I agree with Kofi that the circumference of a circle equals pi times the diameter. This is because the formula for the circumference of a circle is given by:

C = 2πr

Where C is the circumference, π is pi, and r is the radius of the circle. To find the diameter, we can double the radius, so we can write:

C = 2π(r) = π(2r) = πd

Where d is the diameter of the circle.

So, the formula for the circumference of a circle is indeed pi times the diameter, not just pi times the radius.

The number of students attended the play are 400 in number.

Two or more expressions with an Equal sign is called as Equation.

At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000

5x+10y=3000

The total number of tickets are 500

x+y=500

y=500-x

Now plug this in above equation

5x+10(500-x)=3000

5x+5000-10x=3000

5000-5x=3000

Add 5x on both sides

5000-3000=5x

2000=5x

Divide both sides by 5

400=x

Hence, the number of students attended the play are 400 in number.

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The posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.

With your positive test result from Test 2, we must apply Bayes' theorem to get Doctor B's posterior probability that you have cogscitis, which is:

P(A|B) = P(B|A) * P(A) / P(B)

The following probabilities are known:

P(A) = 0.001 (the population prevalence and previous likelihood of getting cogscitis)

P(B|A) = 0.95 (the possibility of receiving a positive Test 2 result while having cogscitis)

P(B|not A) = 0.10 (the possibility of receiving a positive test result from Test 2 even if you do not have  cogscitis)

The law of total probability, which asserts the following, can be used to determine the marginal probability of a positive test result (P(B)):

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where:

P(not A) = 1 - P(A) = 0.999 (the multiplier of the previous probability of contracting cogscitis)

Substituting the values, we get:

P(B) = 0.95 * 0.001 + 0.10 * 0.999 = 0.1008

The posterior probability of developing cogscitis can now be determined, given a positive test result from Test 2:

P(A|B) = P(B|A) * P(A) / P(B)

= 0.95 * 0.001 / 0.1008

= 0.0094

Therefore, the posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.

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Answer:

-7.5 OR -7 1/2

Step-by-step explanation:

20.5 - 28 = -7.5

OR

20 1/2 - 28 = -7 1/2

Answer:

$1350.68 to nearest cent.

Step-by-step explanation:

At the beginning $500 is deposited and this accumulates interest for 3 years At the end of first year it increases to 500( 1 + r) dollars

Then at the end of the 2 years its value is

500(1+ r)(1 + r)(

and at the end of 3 years value =

500(1 + r)(1 + r)(1 + r)

= 500(1 + r)^3 dollars

and as 1 + r = x we have:

500x^3 dollars

In the same way 200 for 2 years = 200x^2

and 600 for 1 year = 600x dollars.

Total = 500x^3 + 200x^2 + 600x.

b.

So, if the interest r = 2 % (= 0.02)

and x = 1.02

Total value after 3 years

= 500(1.02)^3 + 200(1.02)^2 + 600(1.02)

= 530.604 + 208.08 + 612

= $1350.684

The slope-intercept form of a line is y=2/3x + 2, the line is perpendicular and shifted down 8 is y = -3/2x - 6.

The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept. In the given equation, y = 2/3x + 2, the slope is 2/3 and the y-intercept is 2.

To find a line that is perpendicular to this line, we need to find a line that has a slope that is the negative reciprocal of the slope of the given line. The negative reciprocal of 2/3 is -3/2, so the slope of the new line will be -3/2.

Now we need to find the equation of the new line in slope-intercept form. We know the slope of the line (-3/2), so we can substitute this value for m in the slope-intercept form and get:

y = -3/2x + b

To find the value of b, which is the y-intercept of the new line, we need to use the fact that the line is shifted down 8 units. We can do this by subtracting 8 from the y-intercept of the given line (which is 2), to get:

b = 2 - 8 = -6

So the equation of the line that is perpendicular to y = 2/3x + 2 and shifted down 8 units is:

y = -3/2x - 6

This line has a slope of -3/2, which is the negative reciprocal of the slope of the given line, and a y-intercept of -6, which is 8 units lower than the y-intercept of the given line.

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Answer:

a recipe uses y cups of flour and x cups of sugar the amount of flour is 4 times  the amount of sugar

my proof I took the quiz

The expression that represents all the possible widths of the rectangle is given as follows:

0 < x < 5.

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:

A = lw.

For this problem, the length is 5 meters more than five times the width, hence:

l = 5 + 5w.

Hence the area is given as follows:

A = w(5 + 5w)

A = 5w² + 5w.

The area is less than 100m², hence the inequality is given as follows:

5w² + 5w < 100

5w² + 5w - 100 < 0.

w² + w - 20 < 0.

(w + 5)(w - 4) < 0.

Hence the solutions are:

The width cannot be negative, hence the interval is:

0 < x < 5.

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The dot product between u and v is 150.35 units²

In the problem given;

u = 10cos5

v = 16cos25

To find the dot product of two vectors, we need to find the product of the magnitude of the vectors and the cosine of the angle between them. Let's call the angle between the vectors θ.

The dot product of u and v is given by:

u•v = |u| * |v| * cos(θ)

where |u| and |v| are the magnitudes of vectors u and v. We are given the magnitudes of the vectors, which are |u| = 10 and |v| = 16.

To find cos(θ), we need to use the dot product formula with the given angle values:

cos(θ) = (u•v) / (|u| * |v|) = (|u| * |v| * cos(θ)) / (|u| * |v|)

Since u and v are both vectors in 2-dimensional space, we can use the law of cosines to find the angle between them:

cos(θ) = (u•v) / (|u| * |v|) = (u1 * v1 + u2 * v2) / (|u| * |v|)

where u1 and u2 are the components of vector u and v1 and v2 are the components of vector v.

To find the components of the vectors, we need to use the given angle values and the magnitudes of the vectors:

u1 = |u| * cos(5°) = 10 * cos(5°)

u2 = |u| * sin(5°) = 10 * sin(5°)

v1 = |v| * cos(25°) = 16 * cos(25°)

v2 = |v| * sin(25°) = 16 * sin(25°)

Substituting these values into the formula for cos(θ), we get:

cos(θ) = (u1 * v1 + u2 * v2) / (|u| * |v|) = (10 * cos(5°) * 16 * cos(25°) + 10 * sin(5°) * 16 * sin(25°)) / (10 * 16)

θ = 20°

u.v = 10 * 16 * cos 20

u.v = 150.35

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The correct answer to the given question about all of the diagonals drawn from a vertex of an n-gon is option b) n-1

If all of the diagonals are drawn from a vertex of an n-gon, the number of triangles formed is equal to the number of non-diagonal sides of the n-gon. To see why, imagine selecting a vertex of the n-gon and drawing all of the diagonals from that vertex. Each diagonal connects that vertex to a non-adjacent vertex of the n-gon, which splits the n-gon into a series of triangles. The total number of triangles formed is equal to the number of non-diagonal sides of the n-gon, because each non-diagonal side forms one triangle with the selected vertex and one of its adjacent vertices. An n-gon has n sides, so the number of non-diagonal sides is equal to n - 3. This is because each vertex is connected to two adjacent vertices, so there are n - 2 diagonal sides emanating from the selected vertex, and the remaining n - 2 sides are non-diagonal. In addition, there are three sides at the selected vertex that are not counted as non-diagonal sides, so we subtract 3 from n - 2 to get n - 3. Therefore, the answer is (B) n - 1.

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Daniella and her friends collected a total of 44 shells.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given ,

Daniella and her 10 friends are collecting shells on the beach to make crafts.

After they have collected the shells and put them in a pile, they split them evenly among the group. Each person gets 4 shells.

The correct equation for this problem is:

s = 11 x 4

where s is the total number of shells collected.

Simplifying this equation, we have:

s = 44

Therefore, they collected a total of 44 shells.

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The company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.

To predict the number of T-shirts with problems in a shipment of 3,000 short-sleeved and 3,000 long-sleeved T-shirts, we can use the proportion of T-shirts with problems in the random sample as an estimate of the proportion of T-shirts with problems in the population.

For short-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 4/60 = 0.067. For long-sleeved T-shirts, the proportion of T-shirts with problems in the sample is 1/60 = 0.017.

To estimate the number of short-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of short-sleeved T-shirts in the shipment:

Estimated number of short-sleeved T-shirts with problems = 0.067 x 3,000 = 201

Similarly, to estimate the number of long-sleeved T-shirts with problems in a shipment of 3,000, we can multiply the proportion by the total number of long-sleeved T-shirts in the shipment:

Estimated number of long-sleeved T-shirts with problems = 0.017 x 3,000 = 51

Therefore, the company should predict that there will be an estimated 201 short-sleeved T-shirts and 51 long-sleeved T-shirts with problems in a shipment of 3,000 shirts of each type.

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Answer:

1.) -12

2.) 28

3.) 40

Step-by-step explanation:

The elevation of an object is the height or depth of the object relative to the sea level. If the object is above sea level, its elevation will be positive. However, if the object is below sea level, its elevation will be negative. Therefore, we can conclude that the elevation of the fish is -12 m because it is below sea level.

By using unitary methods, the amount of rope is needed for both sites is 350 meters.

Unitary method is a mathematical problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units.

Let's start by looking at Site A, which is a rectangular area with a length of 60 meters and a width of 40 meters. To surround this area with rope, we need to measure the perimeter, which is the distance around the site.

=> Perimeter = 2 (length + width)

=>  2(60 + 40)

=> 2 x 100

=> 200 meters

Therefore, we need 200 meters of rope to surround Site A.

Now let's move on to Site B, which is also rectangular but has a length of 45 meters. To find the width of Site B, we can use the fact that it is similar in shape to Site A. Similar shapes have the same angles and proportional sides, so we can use a unitary method to find the missing dimension.

The length ratio of Site B to Site A is

=> 45/60 = 3/4

Since the shapes are similar, the width of Site B must also be 3/4 of the width of Site A.

Width of Site B = 3/4 x 40 = 30 meters

Now we can use the same formula as before to find the perimeter of Site B:

Perimeter = 2 (length + width)

=> 2(45 + 30)

=> 2 x 75

=> 150 meters

Therefore, we need 150 meters of rope to surround Site B.

To find the total amount of rope needed for both sites, we simply add the two perimeters:

Total rope needed = 200 + 150 = 350 meters

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Answe[tex]3\sqrt{2)[/tex]

Step-by-step explanation:

The probability that the line pressure will surpass 13.0 bars during any measurement is P [Z > 13] = 0,1587, or 15.87%.

If the line pressure exceeds 13.0 bars, there is a chance that:

P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [Z 13] will be located in the z table when z (score) =

Z (score) equals (Z - 0) /

Z = (13 - 12)/1 (score).

the z-table, we then discover

P [ Z ≤ 13] = 0,8413

Finally . P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [ Z > 13 ] = 1 - 0,8413

P [Z > 13] = 0,1587, which is equal to 15,87%.One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprovable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it.

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The domain and the range of the piecewise function for this problem are given as follows:

For this problem, the piecewise function is defined for all values of x, hence the domain is all real values.

The range is obtained as follows:

Hence the range is given as follows:

[-2, ∞).

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Answer:  His average is 85 now.

Step-by-step explanation:

Average is the sum of all his math tests divided by the number of the math tests he took, so we get:

[tex]\frac{sum }{11}=80[/tex]

sum = 11 x 80

sum = 880

880 - 30, we get 850, which becomes the new sum of the 10 math test scores, because he eliminated one test score.

[tex]\frac{850}{10} =85[/tex]

His average is 85 now.

A graph giving us a idea about relationship between the number of days and total amount of sunglasses is mentioned in the image attached below.

In this case, using Microsoft Excel, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot and the total number of sunglasses would be plotted on the y-axis (y-coordinate).

From the scatter plot (attached image) which shows the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 62

Hence, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and total amount of sunglasses.

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Answer:C

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

If the ratio is 7: 5 (oranges to apples) we can use this equation to solve the problem:

We multiply by 0.714285714 because we can see that 7 is being multiplied by 0.714285714 to get 5.

Therefore, if the ratio stays proportional, you will need 120 litres of apple juice for every 168 litres of orange juice.