Joshua drove 22 miles in 55 minutes. If he drove at a constant rate, how far did he travel in one hour?

On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, whole numbers, or decimals.

The sine function that matches the graph is given as follows:

y = sin(2πx/7) - 1.

The sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

The maximum value is of 0, while the minimum value is of -2, hence the amplitude A is obtained as follows:

2A = 2. (as the difference of the maximum value and the minimum value is of 2).

A = 1.

A sine function with amplitude 1 should oscillate between -1 and 1, while this one oscillates between -2 and 0, hence the vertical shift is given as follows:

C = -1.

The period of the function is of 7 units, hence:

2π/B = 7

7B = 2π

B = 2π/7.

Then the function is defined as follows:

y = sin(2πx/7) - 1.

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Answer:

length = 6 cm , breadth = 4 cm

Step-by-step explanation:

the area (A) of the large rectangle = length × breadth

here length = 12 cm and breadth = 4 + x , then

A = 12(4 + x) cm²

the area (A) of the smaller rectangle = x(x + 2)

given area of larger is 4 times area of smaller then

12(x + 4) = 4x(x + 2) ← distribute parenthesis on both sides

12x + 48 = 4x² + 8x , that is

4x² + 8x = 12x + 48 ( subtract 12x + 48 from both sides )

4x² - 4x - 48 = 0 ( divide through by 4 )

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 3 = 0 ⇒ x = - 3

but x must be greater than zero, so x = 4

dimensions of smaller rectangle are

length = x + 2 = 4 + 2 = 6 cm

breadth = x = 4 cm

Answer:

a) The function is growth.

b) The growth rate in % is 4%. This can be determined by taking the natural logarithm of the coefficient (1.04) and multiplying it by 100.

ln(1.04)*100 = 3.98% ≈ 4%.

Answer:

(a) The central 95% of IQ scores in a standardized test would be found in the interval from 85 to 115. This is because a normal distribution is symmetric around the mean, and 95% of the data falls within two standard deviations of the mean. So, the interval would be mean - 2standard deviation to mean + 2standard deviation i.e. 100 - 215 to 100 + 215 = 85 to 115

(b) About 2.5% of people should have IQ scores above 115. This is because the IQ scores follow a normal distribution and IQ scores above 115 are considered to be in the top 2.5% of the distribution.

(c) About 16% of people should have IQ scores between 70 and 85. This is because the IQ scores follow a normal distribution, and IQ scores between 70 and 85 fall within one standard deviation of the mean (85 is one standard deviation below the mean and 70 is one standard deviation below that)

(d) About 0.1% of people should have IQ scores above 130. This is because IQ scores above 130 are considered to be in the top 0.1% of the distribution.

Step-by-step explanation:

The length of the rectangle is [tex]x^{4}[/tex]- 7 units.

We know that,

                  Area of a rectangle = length* width

           So,                       Length = Area/width

According to the question,

                                    Area = [tex]7x^{5} - 49x[/tex]

                                   Width = [tex]7x[/tex]

             Length of the given rectangle = Area/width

                                                                = [tex]\frac{7x^{5}- 49x}{7x}[/tex]

                                                                = [tex]\frac{7x(x^{4}- 7)}{7x}[/tex]

                                                                = [tex]x^{4} - 7[/tex]

Hence, the length of the rectangle is [tex]x^{4} - 7[/tex] units.

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The complete question is:

A rectangle has an area of [tex]7x^{5}- 49x[/tex]. Its width is 7x units. What is its length?

Answer:

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

Use the compound interest formula:

Where A - future amount, P - invested amount, r- annual interest rate, n - number of compounds a year, t - number of years

Given:

Substitute known values and solve for P:

Answer: Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.

Step-by-step explanation:

Multiplying the first equation by 2 we get:

Now, once we have amplified the original equations, the sum of the first equation and the second equation leads to:

Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.

The quotient of these two expressions is not a finite value.

A quotient is a result obtained by dividing one quantity by another. It is the number that results from dividing one number by another.

Here,

Given : The quotient of

2-√√√8

and

4+√12

is not a finite value.

Explanation:

The square root of 8 is 2, so the first square root is 2, the second one is also 2, the third one is 2 again.

So the expression inside the first square root becomes 8, and the whole first square root becomes 2.

So the final expression would be:

2 - (2) = 0

On the other hand, √12 = √(223) = 2*√3

So the final expression would be:

4+2*√3

Hence, the quotient of these two expressions is not a finite value.

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Answer:

Step-by-step explanation:

Linear functions can be used in many real-world applications such as:

Economics: Linear functions can be used to model the relationship between the price of a product and the quantity of the product that will be sold.

Engineering: Linear functions can be used to model the relationship between force and displacement in elastic materials.

Sciences: Linear functions can be used to model the relationship between the concentration of a substance in a solution and the time it takes for that substance to be consumed or produced.

Business and Finance: Linear functions can be used to model the relationship between the cost of a product and the number of products produced.

Graphing: Linear functions can be used to graph the relationship between different variables.

Transportation: Linear functions can be used to model the relationship between the distance traveled and the time it takes to travel that distance at a constant speed.

Construction: Linear functions can be used to model the relationship between the height of a building and the number of floors in the building.

Weather forecasting: Linear functions can be used to model the relationship between temperature and time of the day.

I'm going to provide a real life case for this answer. I own and manage an online soccer jersey store and the process behind it is quite simple:

1. Receive order

2. Buy jerseys from supplier

3. Resell at an slighly higher price

4. Pay taxes + shipping

Now, say that "x" is the amount of jerseys my store sells in a month. I can use functions to create an expression that tells me what is the total net revenue I get from selling "x" amount of jerseys a month.

For example, say that the jerseys cost $50 and you sell them for 60$. You also need to pay the shipping for each jersey (say it is $5 per jersey). Then, we can form a function like this:

[tex]y=60x-50x-5x[/tex]

As you can tell, the money that comes back to the seller ($60 dollars per jersey) is expressed as a possitive coefficient for variable "x" (number of sold jerseys). And, all the other costs, which is money that you spend in order to sell the jerseys, are expressed with a negative coefficient meaning that they are not net revenue, it isn't profit. Now, to see how much money you can make by selling 2 jerseys, simplify the function and substitute variable "x" (number of sold jerseys) by 1:

[tex]y=60x-55x\\ \\y=5x[/tex]

Say "y" is the net revenue:

[tex]y=5(2)\\ \\y=10[/tex]

You can also use functions to determine things such as, how many jerseys do I need to sell in order to make $750 of net revenue? In that case you do the following:

[tex](750)=5x\\\\x=\frac{750}{5} \\ \\x=150[/tex]

From this analysis, you can conclude that you need to sell 150 jerseys ij order to amke a net revenue of $750.

In conclusion, linear functions can be used to see how a variable value (normally called "x") can affect in the results in multiple daily situations: how many miles can your car run with a full tank, how much time do I need to work so I can buy a product, how much money I can spend in something so I can have saving of "x" amount at the end of the year, etc...

Answer:

The faster cyclist is traveling at 72 miles per hour.

Step-by-step explanation:

We know that the two cyclists are 72 miles apart and meet 3 hours later. We also know that the faster cyclist is 3 times as fast as the slower cyclist.

Let's call the speed of the slower cyclist x miles per hour.

If the faster cyclist is 3 times as fast as the slower cyclist, then their speed is 3x miles per hour.

We can use the formula: distance = speed x time

The distance covered by the slower cyclist is:

x * 3 = 72 miles

The distance covered by the faster cyclist is:

3x * 3 = 72 miles

We can use the formula: distance = speed x time again

x * 3 = 72

x = 24 miles/h

So the slower cyclist is traveling at 24 miles per hour.

To find the speed of the faster cyclist, we know that the faster cyclist is 3 times as fast as the slower cyclist.

The speed of the faster cyclist is:

3 * 24 = 72 miles/h

Answer:

B)  4√2

Step-by-step explanation:

Given expression:

[tex]7 \sqrt{2}-3\sqrt{8}+\sqrt{18}[/tex]

Rewrite 8 as 4 · 2 and 18 as 9 · 2:

[tex]\implies 7 \sqrt{2}-3\sqrt{4 \cdot 2}+\sqrt{9 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 7 \sqrt{2}-3\sqrt{4} \sqrt{2}+\sqrt{9} \sqrt{2}[/tex]

Carry out √4 and √9:

[tex]\implies 7 \sqrt{2}-3\cdot 2 \sqrt{2}+3 \sqrt{2}[/tex]

Multiply -3 and 2:

[tex]\implies 7 \sqrt{2}-6 \sqrt{2}+3 \sqrt{2}[/tex]

Factor out √2:

[tex]\implies (7 -6+3) \sqrt{2}[/tex]

Carry out the operations inside the parentheses:

[tex]\implies 4\sqrt{2}[/tex]

Answer:

The quotient of two real numbers is not necessarily an integer. When dividing two real numbers, the result can be any real number, including a fraction or a decimal. It can be an integer only if the divisor is a factor of the dividend. In other words, if the remainder of the division is zero, the quotient is an integer.

Step-by-step explanation:

There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson. The road junction to Timpson is option B. 20.57 miles.

To find the distance between Timpson and the junction point, we can use the Pythagorean theorem. Let's call the distance "d".

d^2 = (60 - 22)^2 + 12^2

d^2 = 38^2 + 144

d^2 = 1444

d = √(1444) = 38.03

So the distance between Timpson and the junction point is 38.03 miles. The distance between the junction point and Ashburn is simply 22 miles, so the total distance from Timpson to Ashburn is 20.57 miles (38.03 + 22).

Therefore, the distance between the road junction to Timpson is option B. 20.57 miles

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The complete question goes thus:

There is a straight road leading from the town of Timpson to Ashburn 60 miles east and 12 miles north. Partway down the road, it junctions with a second road, perpendicular to the first, leading to the town of Garrison, which is located 22 miles directly east of the town of Timpson. How far is the road junction to Timpson

A. 21.57miles

B. 20.57miles

C. 10.57miles

D. 57.12 miles

Answer:

Step-by-step explanation:

Assuming that the area is a rectangle with no obstructions or furniture, and that the people are standing shoulder-to-shoulder, then the area can fit approximately 200,000 people. This is calculated by multiplying 250 feet by 250 feet to get the total square feet of the area, which is 62,500 (250 x 250 = 62,500). Then divide the total square feet by the amount of space taken up by one person, which is 2.5 square feet, to get the approximate number of people that can fit in the area. 62,500 / 2.5 = 25,000, so 25,000 x 8 = 200,000 people.

Answer:

An area that is 20 feet wide and 25 feet long will be 20*25 = 500 square feet large. Division tells us how many times one number is contained within a number, so to find how many 2.5 square feet large people fit in a 500 square feet large space, we do 500/2.5 = 200 people.

Step-by-step explanation:

The system of equations can be used to find the number of pounds, x, of dried fruits and the number of pounds y, of nuts is; 6x + 2y = 40

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution the power of the equation must be in one degree.

We are given that the dried fruits cost $6 per pound

The nuts cost $2 per pound. It costs Simon $40 to make 12 pounds of trail mix.

We need to find  the number of pounds, x, of dried fruits and the number of pounds, y, of nuts that Simon used to make 12 pounds of trail mix.

Therefore, the system of equation will be 6x + 2y = 40

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Answer: Here it is

Step-by-step explanation:

A.

Arithmetic Mean: 30.57

Median: 32

Mode: 41

Range: 41-23 = 18

B.

Upper Quartile: 39

Lower Quartile: 25

D7: 25

P50: 32

C.

Variance: In order to calculate the variance I would need the data set to be presented in a tabular form with the observations as rows and one column for the data.

Coefficient of Variation: Same as above.

D.

Pearson coefficient of skewness: I would need the data set to be presented in a tabular form with the observations as rows and one column for the data.

Kurtosis: Same as above.

Polar form of the given problem are expressed below

In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modelled as a union of argument and modulus.

Given, Some numbers that we need to write in polar form

General formula of polar form = r * [tex]e^{ia}[/tex]

For polar/rectangular conversion we use the following transformations

r² = x² + y²

x = r cosa

y = r sina

Where a is angle

For (a) 1/5

r = 1/5

a = 0

Since angle is 0

Polar form = 1/5

For  (b) 4 +4i

r = √4² + 4² = 4√2

a = tan(4/4) = tan (1) = pi/4

Polar form = 4√2 [tex]e^{ipi/4}[/tex]

For (c) -6 + 6 i

r = √-6² + 6² = 6√2

a = tan(-6 /6)

a = -pi/4

Polar form = 6√2[tex]e^{-ipi/4}[/tex]

Therefore, polar form of the given questions written above.

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Answer: We can write an inequality to show how many more inches Bobby needs to grow to reach his desired height by using the following information:

Bobby hopes that he will someday be more than 72 inches tall.

He is currently 59 inches tall.

We can use the inequality x + 59 > 72, where x is the number of inches Bobby needs to grow to reach his desired height.

This inequality represents the total height (x + 59) being greater than the desired height (72).

To solve this inequality, we can subtract 59 from both sides:

x > 72 - 59

x > 13

So, Bobby needs to grow 13 inches or more to reach his desired height.

Step-by-step explanation:

Explanation:

The points do not fall on the same line, but the points trend upward as we move to the right. This means that a straight line can get somewhat close to all of the points to represent the average trend of what's going on.

Answer:

linear :)

Step-by-step explanation:

ive already answered this question and got it right <3

Table F shows a proportional relationship and its points are plotted in the graph shown in the image attached below.

In Mathematics, the graph of any proportional relationship is represented by a straight line with the data points passing through the origin (0, 0) because as the values on the x-axis increases or decreases, the values on the y-axis increases or decreases simultaneously.

Mathematically, a proportional relationship can be represented or modeled by the following linear equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2 = 8/4 = 10/2

Constant of proportionality, k = 2.

Therefore, the linear equation for this proportional relationship can be correctly written as follows:

y = kx

y = 7.5x

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Area of figure 1 is 468 cm² and figure 2 is 45 cm².

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

In these given figure for calculating the area of them we need to divide them into two or more shape like rectangle, triangle or square. For example, I will take Figure 1 and 2

For figure 1

Length of base = 16 + 14 =  30 cm

Length of right rectangle whose side is 14 and 14(smaller one)

Thus, its area = 14 * 14 = 196

Area of left rectangle whose side is 16 and 17 = 16 * 17 = 272

Total area of the figure = 272 + 196 = 468 square cm

For figure 2

If we split them into two shape they will become a square and a triangle

Area of triangle = 1/2 base * height = 1/2 * 6 *3 = 9

Area of square = side * side = 6*6 = 36

Thus, total area = 9 + 36 = 45 square cm

Therefore, Area of these given figures(in unit square) are:

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Answer:

Step-by-step explanation:

a. The least square regression equation of Y on X is: Y = 3.08X - 127.82

b. To estimate the blood pressure of a woman whose age is 45 years, we can use the least square regression equation above. Substituting X = 45, we get: Y = 3.08(45) - 127.82 = 143.46. Therefore, the estimated blood pressure of a woman whose age is 45 years is 143.46.

If h(x) is equal to the composition between functions f(x) and g(x), then we must have:

f(x) = 1/x.

Here we have the function:

h(x) = 1/(x - 5)

And we know that we can write function h as a composition of other two functions:

h(x) = f( g(x) )

Where we know that:

g(x) =x - 5

Remember that the composition of two functions means that we are evaluating one in the other, in this case is rater easy to notice that we must have:

f(x) = 1/x

Then when we evaluate this in g(x) we will get:

f(g(x)) = 1/g(x)

Now we can replace g(x) by the actual function:

f(g(x)) = 1/g(x) = 1/(x - 5)

And that is h(x).

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The derivation of the function y = (4x+9x^2)(3x-7x^4) by the means of direct formulas is y = 12x^2 + 27x^3 - 28x^5 - 63x^6.

The direct formula method is a way to multiply two or more algebraic expressions together by applying the distributive property and combining like terms. It is also known as the "FOIL" method for multiplying binomials.

The direct formula method involves breaking down each expression into its individual terms and then using the distributive property to multiply each term in the first expression by each term in the second expression. After that, the resulting terms are combined according to the addition and subtraction rules of like terms.

To derive the function y = (4x+9x^2)(3x-7x^4) using the direct formulas method, we need to multiply the two expressions inside the parentheses:

y = (4x+9x^2)(3x-7x^4)

y = 4x3x + 4x-7x^4 + 9x^23x + 9x^2-7x^4

Using the distributive property, we can simplify the expression by combining like terms:

y = 12x^2 - 28x^5 + 27x^3 - 63x^6

y = (12x^2 + 27x^3) - (28x^5 + 63x^6)

So the final expression is y = 12x^2 + 27x^3 - 28x^5 - 63x^6

The direct formulas method uses the distributive property and the combination of like terms to derive the final expression of the function.

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The vertex form of the parabola is y + 1 = - 4 · (x + 1)².

Graphically speaking, parabolae can be generated by quadratic equations, whose forms are described below: (Please notice that the parabola described by statement is parallel to y-axis since axis of symmetry is a vertical line)

Standard form

y = a · x² + b · x + c

Vertex form

y - k = C · (x - h)²

Where:

If we know that h = - 1, k = - 1 and (x, y) = (0, - 5), then the equation of the parabola in vertex form is:

C = (y - k) / (x - h)²

C = (- 5 + 1) / (0 + 1)²

C = - 4 / 1²

C = - 4

The equation of the parabola in vertex form is equal to y + 1 = - 4 · (x + 1)².

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Answer: Here it is

Step-by-step explanation:

a) The perimeter of a shape is the sum of the lengths of all its sides. In this case, the shape has sides with lengths of 4, 5h, 7, and 2h. Therefore, the expression for the perimeter of the shape can be written as:

Perimeter = 4 + 5h + 7 + 2h

To simplify this expression, we can combine like terms:

Perimeter = 4 + 7 + (5h + 2h)

Perimeter = 11 + 7h

So, the simplified expression for the perimeter of the shape is 11 + 7h

b) The perimeter of the shape is 42.

We can use this information and the expression we found in part a) to find the value of h. We know that:

Perimeter = 11 + 7h = 42

We can subtract 11 from both sides to get:

7h = 42 - 11 = 31

Finally, we can divide both sides by 7 to find the value of h:

h = 31/7

h = 4.428 (approximately 4.43)

Answer: To find the batting average of a player, we need to find the ratio of hits to total attempts.

Jana's ratio is 12/15, and Tasha's ratio is 9/10.

To compare these ratios, we can simplify both of them to a common denominator. In this case, the common denominator is 15.

Jana's ratio can be simplified to 12/15, which is equal to 0.8

Tasha's ratio can be simplified to (9/15), which is equal to 0.6

So, Jana has a ratio that means she has a better batting average (0.8) compared to Tasha (0.6)

Alternatively, we can convert these ratio to percentage by multiplying them by 100.

Jana's batting average is 12/15 * 100 = 80%

Tasha's batting average is 9/10 * 100 = 90%

By this way also we can see that Tasha's batting average is higher than Jana's batting average.

Step-by-step explanation:

Inequality becomes 0.21t + 15,040 <= 100,000

Energy consumption remains a principal source of human caused greenhouse gas emissions the predominant cause of climate change.

After 7 a.m., the power usage on a college campus increases at a rate of 21% per hour.

t be the number of hours

the power usage increases at a rate of 21% per hour

21% = 0.21, constant rate = 0.21 . So slope = 0.21

Prior to 7 a.m., 15,040 kWh have been used.

At 7.am , power used = 15,040kWh. so our y intercept is 15,040

We use slope intercept form y= mx+b

slope m = 0.21  and b = 15040

power usage , y = 0.21 t + 15040

The university has a daily goal to keep their power usage less than or equal to 100,000 kWh

Power usage is less than or equal to 100,000

So inequality becomes 0.21t + 15,040 <= 100,000

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The top of the hill have an altitude of 1391 feet above sea level

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

From the table, checkpoint 3 is at 1327 feet above sea level. Since the top of a hill rises 64 feet above checkpoint 3, hence:

Altitude of hill = 1327 + 64 = 1391 feet

The top of the hill is 1391 feet

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