Denisha has already read 42 pages
novel for her English class. For the rest of
the month, she plans to read 24 pages
every 3 days. What is the constant rate of
change in this situation?
A.
page per day
B. 6 pages per day
C. 8 pages per day
D. 24 pages per day

Answer:

If the store marks up the price of the diving board by 45%, the selling price will be 100% + 45% = 145% of the cost price.

Let's calculate the selling price:

Selling price = Cost price + Mark-up

Mark-up = Selling price - Cost price

Mark-up = (145% of cost price) - cost price

Mark-up = 0.45 * cost price

We know that the store paid $261 for the diving board, so:

Mark-up = 0.45 * $261 = $117.45

Therefore, the amount of the mark-up is $117.45.

well, what's 45% of 261?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{45\% of 261}}{\left( \cfrac{45}{100} \right)261}\implies \text{\LARGE 117.45}[/tex]

Answer:

Step-by-step explanation:

100 students all together.

50+70=120....so 20 must like both.

The probability that a person chosen at random at age 40 or older has only completed high school is 0.2912.

Probability is the chance or likelihood that something will occur. It is quantified using numbers, ranging from 0 (no chance) to 1 (certainty). It also helps us to draw conclusions about the chances of something happening based on the available data.

The total number of people who have only completed high school

=(5394)

the total number of people in the age group 40 and over =(18521)

By dividing both the data, we get

5394/18521= 0.2912

From the given data in the table, we can calculate the probability that a person chosen at random at age 40 or older has only completed high school.

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The dimensions of the triangle with maximum area are a base of 11 cm and a height of 11 cm.

We are given that the sum of the base and height of a triangle is 22 cm. Let's call the base of the triangle "b" and the height "h". Then we have the equation:

b + h = 22

We want to find the dimensions of the triangle that will give us the maximum area.

The formula for the area of a triangle is A = (1/2)bh.

We can use the equation b + h = 22 to solve for one of the variables in terms of the other.

we can solve for h:

h = 22 - b

Substituting this into the formula for the area, we get:

A = (1/2)b(22 - b)

The equation 0 = 11b - (1/2)b² can be rearranged to:

(1/2)b² - 11b = 0

We can then use the quadratic formula to solve for "b"

b = 11 ± 11

So the value of b that gives us the maximum area is b = 11 cm. Substituting this back into the equation h = 22 - b, we get:

h = 22 - 11 = 11 cm

Triangle has a base of 11 cm and a height of 11 cm.

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The relationship between distance and travel time. It is not excessively strong or weak. In other words, the rate of change in journey time is moderate and constant with respect to distance.

positive negative moderate weak linear nonlinear relationship between distance and travel time can be described as follows:•

           Positive• Linear• Moderate

   Explain as we move from point A to point B, the distance covered and the travel time it takes to get there are positively correlated. As the distance increases, the travel time required to reach the destination also increases, resulting in a positive correlation.

          The relationship between distance and travel time is linear because the rate at which distance is covered remains constant, resulting in a straight-line relationship on a graph. It means that if distance doubles, the travel time will also double, indicating a linear relationship.

Hence, the linear relationship is also referred to as a direct relationship. On a graph, the line that represents the relationship between distance and travel time is moderate. This implies that the slope of the line is neither too steep nor too gentle.

               Thus, it is neither too strong nor too weak. In other words, the rate of change in travel time is consistent as distance changes, making it moderate.

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the original number after simplification is 5600.

A fraction is a numerical quantity representing a part of a whole or a ratio between two numbers. It is expressed as one integer, called the numerator, written above a horizontal line, and another integer, called the denominator, written below the line.  For example, the fraction 2/5 represents two out of five equal parts or 2 divided by 5,

We can start by using the fact that 14.5% can be written as a decimal fraction 0.145.

Let X be the original number we want to find.

Then we can set up the following equation:

0.145 ×X = 812

To solve for X, we can divide both sides by 0.145:

X = 812 / 0.145 = 5600

Therefore, the original number is 5600.

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Answer:

When x = 0, y = 2^0 + 6 = 7. So the first point is (0, 7).

When x = 1, y = 2^1 + 6 = 8. So the second point is (1, 8).

When x = 2, y = 2^2 + 6 = 10. So the third point is (2, 10).

When x = -1, y = 2^-1 + 6 = 6.5. So the fourth point is (-1, 6.5).

When x = -2, y = 2^-2 + 6 = 6.25. So the fifth point is (-2, 6.25)

Answer:

the value of x is approximately 0.382 cm.

Step-by-step explanation:

Answer:

I got 162?

Step-by-step explanation:

I broke down each individual shape (7 rectangles and 2 triangles) and used each shapes surface area formula.

triangle surface area formula is 1/2*b*h, and there are 2 of the same triangles of the exact same size and 7 rectangles. 3 are same size rectangles, 2 are same size rectangles and the other 2 are different sized rectangles. Then add altogether.

Answer:

15/x * 100 %

Step-by-step explanation:

Since we don't know the total, we have 15/x * 100 % as the percent of how many people passed the test. (x is amount of people, 15 or greater.)

The sugar concentration would be approximately 62.5%.

To find the concentration of sugar in the solution, we need to use the formula:

In this case, the solute is sugar and the solvent is water. We are given that the mass of sugar is 50 grams and the mass of water is 30 grams. However, we need to convert the mass of water to volume since we need the volume of the entire solution to calculate the concentration.

We can assume that the density of water is 1 g/mL, so the volume of water is 30 mL. The total volume of the solution is therefore 50 mL + 30 mL = 80 mL.

Now we can use the formula to find the concentration of sugar:

So the concentration of sugar in the solution is approximately 0.625 grams per milliliter.

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The principal sum is Rs. 1640 if the difference in simple interest between 3 years and 4 years is Rs. 82 at a rate of 5% per annum.

Let x be the principal sum. According to the problem, the difference in simple interest between 3 years and 4 years is Rs. 82. This means that the interest earned in the fourth year is Rs. 82 more than the interest earned in the third year.

Using the formula for simple interest, we can calculate the interest earned in each year:

Simple interest for 3 years = (x * 5% * 3) = 0.15x

Simple interest for 4 years = (x * 5% * 4) = 0.2x

The difference between the two is:

0.2x - 0.15x = 0.05x

We are given that this difference is equal to Rs. 82, so:

0.05x = 82

Solving for x, we get:

x = 82 / 0.05 = 1640

Therefore, the principal sum is Rs. 1640.

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The last two rows of the table should be completed as follows:

Input   Output

8       22.80

10      28.50

An algebraic expression is a mathematical phrase that contains numbers, variables, and operations. It is used to represent a single quantity or value, and can be written in terms of one or more variables.

The rule given is an algebraic expression, x, which is the input, multiplied by 2.85, which is the output. Using this information, we can determine the cost of 10 muffins.

To find the cost of 10 muffins, we can use the algebraic expression given. First, we will multiply 10, the number of muffins, by 2.85, the cost of one muffin. This gives us a total of 28.50. Therefore, the cost of 10 muffins is 28.50.

Using this same rule and process, we can also determine the cost of any number of muffins. For example, if we want to know the cost of 15 muffins, we can simply multiply 15 by 2.85, giving us a total of 42.75.

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Answer:

The correct order to draw 65 agle would be:

C

A

B

D

The radius of the given circle is x = 3 and x = 3/11.

A polynomial equation of degree two is a quadratic equation, indicating that the variable's maximum exponent is 2. There are various ways to solve a quadratic equation, including factoring, completing the square, and applying the quadratic formula. Finding two quadratic expression factors that multiply to produce the constant term c and add to produce the linear term b's coefficient is known as factoring. The quadratic expression is completed by adding and removing a constant component to create a perfect square trinomial that can be factored or solved by calculating the square root.

In the given figure connect the points QF and QG using a line segment, thus forming two right angled triangle.

The perpendicular segment QA divides the base into two equal parts. Thus, the base of the triangle is 8.

Using the Pythagorean theorem we have:

(QF)² = (8)² + (4x + 3)²

QG² = 8² + (7x - 6)²

In the figure QF = QG = r thus:

(8)² + (4x + 3)² = 8² + (7x - 6)²

Expanding using the algebraic identity:

16x² + 24x + 9 = 49x² - 84x + 36

33x² - 108x + 27 = 0

3(11x² - 36x + 9) = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substitute the values a = 11, b = -36, and c = 9:

x = (-(-36) ± √((-36)² - 4(11)(9))) / 2(11)

x = (36 ± √(1296 - 396)) / 22

x = (36 ± √900) / 22

x = (36 ± 30) / 22

x = (36 + 30) / 22 = 3

x = (36 - 30) / 22 = 3/11

x = 3 and x = 3/11.

Thus, the radius of the given circle is x = 3 and x = 3/11.

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Answer:

x = - 2

Step-by-step explanation:

the equation of a vertical line parallel to the y- axis is

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through all points with an x- coordinate of - 2 , then

x = - 2 ← equation of line

A skater has a mean score of 7. 25 points. An equation to determine the skaters total scores received from eight judges is equals to the x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.

Mean is called the average of the values and is calculated by dividing the addition of values by the total number of values. It is denoted by [tex]\bar X[/tex]. That is bar above X represents mean of x number of values. Mathematically, Mean = (Sum of all the values/Total number of values).We have in a skating compotion where each skater receives score from eight judges. Now, Mean or average of score points obtained by a skater = 7.25 points. Let the skater's received score from eight judges be equals to x₁,x₂,x₃,x₄,x₅,x₆,x₇, x₈. Total score received by skater = x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ and we have to write the equation to determine the skaters total scores. Now, in this case mean of scores means the sum of scores received by skaters from eight judges divided by eight (judges).

=> 7.25 = (x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈)/8

=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈

= 8× 7.25

=> x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈

= 58

which is equation of 8 variables for total score. Therefore, the required equation is x₁ + x₂ + x₃ + x₄ + x₅ + x₆ + x₇ + x₈ = 58.

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When the function d(x) = -x +(-3), then the value of d(0) is -3

In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.

In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.

To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:

d(0) = -(0) - 3

The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as

d(0) = -3

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Answer: Yes Sofia will have enough money

=======================================================

Explanation:

Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.

The area of the rectangle is 16*7 = 112 square meters.

The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be

sum of the exterior sides = perimeter

6+7+16+7+6+x = 54

42+x = 54

x = 54-42

x = 12

The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.

area of the trapezoid = 0.5*height*(base1+base2)

area = 0.5*5.66*(16+12)

area = 79.24 square meters

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

Recap so far

The total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.

Let's convert that to square decimeters.

Recall that 1 decimeter = 10 centimeters

Multiply both sides by 10

1 decimeter = 10 centimeters

10*(1 decimeter) = 10*(10 centimeters)

10 decimeters = 100 centimeters

10 decimeters = 1 meter

Then,

[tex]191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\[/tex]

The entire lawn is 19124 square decimeters.

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

We have one final block of calculations to determine the total price.

x = number of rolls

1 roll covers 90 square decimeters

x rolls cover 90x square decimeters

90x = 19124

x = 19124/90

x = 212.489 approximately

Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).

In short, Sofia needs 213 rolls.

1 roll costs $4.50

213 rolls will cost 213*4.50 = 958.50 dollars.

This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).

Sofia will have enough money to pay for all of the grass.

Answer:

42x-27

Step-by-step explanation:

Each pair of numbers (m, h) which meet the inequality is the answer to the inequality. m < h plus 2.

A factor pair is a collection of two factors that, when multiplied together, produce a certain result in mathematics. In those other words, it's a pair of integers that we multiply to produce a result. For instance, the factor pair that yields the result in the multiplication formula 6 7 = 42 is composed of the numbers 6 and 7. 42

By adding 14 to both sides, starting with -14 + 7m 7h, we may simplify the left side:

-14 + 7m plus 14 < 7h plus 14

Even more condensed, we get at:

7m < 7h plus 14

The inequality can then be divided by 7 on both sides: m h + 2.

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The total surface area of the remaining portion is approximately 23.14 in.

To find the total surface area of the remaining portion of a wooden sphere after two equal caps have been removed, use the formula SA = 4πr2. A sphere is symmetrical, and thus, the diameter of the wooden sphere is equal to the diameter of the remaining portion. The radius of the remaining portion is equal to half the diameter of the sphere minus the radius of the cap.

The diameter of the wooden sphere is 11.8 in. As such, the radius of the sphere is 5.9 in. If two equal caps are removed, the diameter of the remaining portion is equal to 11.8 in - 2x R_cap, where R_cap is the radius of the cap. Since the caps are equal, we can simplify the formula to

D = 11.8 - 2R_cap. R_cap is equal to the radius of a circle with area equal to the surface area of one cap. As such, we can use the formula SA = 2πrh + πr2 to find the surface area of the cap. We know the diameter of the sphere is 11.8 in. Thus, the radius of the sphere is 5.9 in. We also know that the height of the cap is 5.9 in. Since the caps are equal, we can use the formula to find the surface area of one cap and multiply by 2 to get the total surface area of both caps.

SA_cap = 2π(5.9 in)(5.9 in) + π(5.9 in)

2SA_cap = 2π(34.84 in2) + π(34.84 in2)

SA_cap = 2π(34.84 in2) + 109.45 in2SA_cap ≈ 219.74 in

Since the surface area of the cap is equal to 219.74 in, we can use the formula to find the radius of the cap.

219.74 in = 2πrh + πr22(219.74 in2)

= 2π(5.9 in)h + π(5.9 in)22(219.74 in2)

= 37.699 in2 + 109.45 in23r2

= 72.533 in2r ≈ 4.545 in

Using the formula D = 11.8 - 2R_cap, we can find the diameter of the remaining portion of the wooden sphere.

D = 11.8 - 2(4.545 in)D ≈ 2.71 in

The radius of the remaining portion of the wooden sphere is equal to 5.9 in - 4.545 in. Thus, the radius of the remaining portion of the sphere is 1.355 in. Finally, we can find the total surface area of the remaining portion of the sphere.

SA = 4πr2SA = 4π(1.355 in)2SA ≈ 23.14 in

Therefore, the total surface area of the remaining portion is approximately 23.14 in.

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Answer:

For WXYZ to be a parallelogram, both pairs of opposite sides must be parallel.

So, we have 7m + 4 = 9m and 5y + 13 - (2n - 1) = 6y - 8 - (n + 6).

Solving the first equation, we get m = 2.

Solving the second equation, we get y - n = 4.

Thus, for WXYZ to be a parallelogram, m = 2 and y - n = 4, so option B is correct.

Answer:

<b> <i>

Step-by-step explanation:

The cost of one small crate of apples is $12 and the cost of one large crate of peaches is $8. The cost of 7 small cates of apples and 5 large containers of peach is $126.

The system of equations that describe the question is:

3s + 10l = 116 equation 1

11s + 20l = 292 equation 2

Where:

s = cost of one small crate of apples

l = cost of one large crate of peaches

The elimination method would be used to determine the values of s and l.

Multiply equation 1 by 2

6s + 20l = 232 equation 3

Subtract equation 3 from equation 2:

5s = 60

Divide both sides of the equation by 5

s = 60 / 5

s = $12

Substitute for s in equation 1:

3(12) + 10l = 116

36 + 10l = 116

10l = 116 - 36

10l = 80

l = 80 / 10

l = 8

Cost of 7 small crates of apples and 5 large containers of peaches = (7 x 12) + (8 x 5) = $124

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Answer:

Elise's average pay per hour for the year 2017 was £11.88.

Step-by-step explanation:

First, we need to calculate Elise's monthly salary in 2017 after the 3% increase:

3% of £2100 = 0.03 x £2100 = £63

Elise's new monthly salary in 2017 = £2100 + £63 = £2163

Next, we need to calculate her total earnings in 2017:

Total earnings = monthly salary x number of months worked

Elise worked for 45 weeks in 2017, which is approximately 10.4 months:

Total earnings = £2163 x 10.4 = £22,477.20

Finally, we can calculate her average pay per hour for the year:

Total number of hours worked = 42 hours/week x 45 weeks = 1890 hours

Average pay per hour = total earnings / total number of hours worked

Average pay per hour = £22,477.20 / 1890 hours = £11.88 per hour

Answer:

I got $13.73 per hour

Step-by-step explanation:

If you multiply 2100 by 12 months you get $25200 for an annual salary before percent increase.

Then you include the 3% salary increase each month 25200 x .03 = 756 then add the two 25200 + 756 = 25956 OR you can calculate the longer way by doing each individual month, either way it will be the same answer. 2100 x .03 = 63 then 2100 + 63 = 2163 then 2163 x 12 = 25956

Then you divide 25956 by the number of weeks worked in the year. 25956/45 = 576.8

So, each week $576.8 was earned.

Then to get an hourly rate, you divide this by the number of hours worked in each week. 576.8/42 = 13.73

So, the hourly rate is $13.73.

I hope this helped :)

P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).

0.5333

A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly

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Answer:

You didn't give any options, but I'm guessing one of them has a 3 in the tens digits, which should be the right answer

Step-by-step explanation:

300?

The true statement is, Parameter values can be used within the method code block. (option e).

In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.

Parameter values can be used within the method code block.

This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.

In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.

Hence the option (e) is correct.

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To solve the question asked, you can say:  So the other side of the triangle will be as [tex]A = \sqrt73[/tex].

A triangle is a closed two-dimensional geometric object consisting of three line segments, called edges, that intersect at three places called vertices. Triangles are distinguished by their sides and angles. A triangle can be equilateral (all sides equal), isosceles, or odd, depending on the sides. Triangles are classified as acute (any angle less than 90 degrees), right (angles equal to 90 degrees), or obtuse (any angle greater than 90 degrees). The area of ​​a triangle can be calculated using the formula A =​​ (1/2)bh. where A is the area, b is the base of the triangle, and h is the height of the triangle.  

here in the triangle we have sides that are 3 and 8

we can use

[tex]A^2 = B^2 + C^2\\A^2 = 3^2 + 8^2\\A^2 = 9+64\\A^2 = 73\\A = \sqrt73[/tex]

So the other side of the triangle will be as [tex]A = \sqrt73[/tex].

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