A rocket is launched in the air. Its height in feet is given by h(t)=−16t^2 +24t where
t represents the time in seconds after launch. How long is the rocket in the air?

Answer:

Without a visual or additional information, it is difficult to determine the best function that models the stock data shown in the scatter plot.

However, we can make some observations based on the answer choices:

A. Y=0.3(2.94) +56.5 is not a linear function and does not seem to fit the general trend of the data.

B. Y=442x+53 is a linear function with a positive slope, but it does not seem to fit the general trend of the data.

C. Y=0.92)+58 is not a linear function and appears to be missing a variable.

D. Y=7.7x+47.7 is a linear function with a positive slope that seems to fit the general trend of the data.

Therefore, the best function that models the stock data shown in the scatter plot is likely D) Y=7.7x+47.7.

Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.

Exponents, usually referred to as powers and indices, are a type of mathematical operation that requires increasing a base number to a specific exponent. You can multiply the minimum amount by itself a given number of times using the exponent. For instance, the number 2 raised toward the power of 3 (printed as 23) is equivalent to 2 x 2 x 2, which is 8. Exponents are frequently employed in scientific notation, algebra, and other areas of mathematics to express extremely big or extremely small integers.

given

The distributive property of multiplication is used to multiply out the expression when expanding (x+2y) in ascending powers of x.

[tex](x + 2y) = x + 2yx^0[/tex]

By remembering that every number raised to the power of zero equals 1, we may simplify the second term. We thus have:

(x + 2y) = x + 2y(1) (1)

When we multiply the expression, we get:

(x + 2y) = x + 2y

Hence, x + 2y is the expansion of (x+2y) in ascending powers of x as that every number raised to the power of zero equals 1.

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n(A ∪ B ∪ C) = 16

n(A u B u C) = 2.

To find the number of elements in the set ( A cup B cup C), we need to find the union of the sets A, B, and C. This can be done by combining all the elements in A, B, and C, and then removing any duplicates.

So, (A ∪ B ∪ C) = {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 20}

Therefore, n(A ∪ B ∪ C) = 16.

To find the number of elements in the set ( A ∩ B ∩ C), we need to find the intersection of the sets A, B, and C. This can be done by finding the elements that are common to all three sets.

So, (A ∩ B ∩ C) = {8, 20}

Therefore, n(A u B u C) = 2.

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The ratio of the number of sweets that Amber has to the number of sweets that Callum has is 16:9.

A quantitative comparison of two or more quantities that shows their relative sizes is called a ratio.

In terms of how many times one is greater or less than the other, it describes the relationship between the two quantities.

Let's assume that Amber and Bethan bought x number of sweets, then Callum and David also bought x number of sweets.

According to the problem, Amber and Bethan share the sweets in the ratio 2:1. Therefore, Amber has (2/3)(x) sweets and Bethan has (1/3)(x) sweets.

Also, Callum and David share the sweets in the ratio 3:5. Therefore, Callum has (3/8)(x) sweets and David has (5/8)(x) sweets.

Now, we can find the ratio of the number of sweets that Amber has to the number of sweets that Callum has as follows:

Amber/Callum = [(2/3)(x)]/[(3/8)(x)] = (16/9)

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Answer:

Step-by-step explanation:

Therefore, the height of the tower is approximately 121.4 meters.

Answer:

2.125 inches

Step-by-step explanation:

We Know

On Monday, 1 7/8 inches of rain fell. On Tuesday, it rained 1/4 inch.

1 7/8 = 15/8

What was the total rainfall for the two days?

We Take

15/8 + 1/4 = 15/8 + 2/8 = 17/8 inches of rainfall

17/8 = 2.125

So, the total rainfall for the two days is 2.125 inches.

Answer:

2 1/8 inches

Step-by-step explanation:

You need to add the two amounts of rainfall together to get your answer, which is 1 7/8 + 1/4. To add these fractions, make the fractions equivalent. To find equivalent fractions, we multiply the numerator and the denominator by the same number.

Since 1/4 can be 2/8, you can now add 1 7/8 + 2/8. This equals 2 1/8.

Therefore, the total rainfall for the two days was 2 and 1/8 inches.

IM SO SORRY IF THIS DID NOT MAKE SENSE!

The equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).

A linear equation has the formula y = mx + b, where x and y are variables, m is the angle of the line's slope, and b denotes the y-intercept (the location where the line crosses the y-axis). On a graph, this equation represents a straight line.

The y-intercept of a linear equation, which is determined by the value of b, is first plotted on a graph. The slope is then used to determine further points along the line. How much y changes for each unit of x is indicated by the slope. For instance, if the slope is 2, then y grows by 2 for every unit increase in x.

Given that, a certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute.

Let us suppose number of minutes = x.

Then,

Cost = 0.75 + 0.15(x - 3)

hence, the equation that represents the cost of the call in dollars is option d. 0.75 + 0.15(x - 3).

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The complete question is:

[tex]f''(x)=-2+24x-12x^2\hspace{5em}f'(0)=16\hspace{5em}f(0)=2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \displaystyle \int~(-2+24x-12x^2)dx\implies -2x+12x^2 - 4x^3 + C=f'(x) \\\\\\ \stackrel{\textit{since we know that}}{f'(0)=16}\hspace{5em}-2(0)+12(0)^2-4(0)^3+C=16 \\\\\\ C=16\hspace{5em}\stackrel{\textit{so then we know that}}{-2x+12x^2 - 4x^3 + 16=f'(x)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\displaystyle \int~(-2x+12x^2 - 4x^3 + 16)dx\implies -x^2+4x^3-x^4+16x+C=f(x) \\\\\\ \stackrel{\textit{since we know that}}{f(0)=2}\hspace{5em}-(0)^2+4(0)^3+16(0)+C=2 \\\\\\ C=2\hspace{5em}\boxed{-x^2+4x^3-x^4+16x+2=f(x)}[/tex]

To answer this question, we need to compare the ratios of miles traveled to gallons of gas used for car A and car B when they both use 1 gallon of gas.

For car A, we can see from the graph that 50 miles are traveled for every 2 gallons of gas used, or in other words, 25 miles are traveled for every 1 gallon of gas used. Therefore, car A can travel 25 times the distance for 1 gallon of gas.

For car B, we can see from the table that 40 miles are traveled for every 2 gallons of gas used, or in other words, 20 miles are traveled for every 1 gallon of gas used. Therefore, car B can travel 20 times the distance for 1 gallon of gas.

To compare the two ratios, we can divide the ratio of miles traveled to gallons of gas used for car A by the ratio for car B:

25/20 = 1.25

Therefore, car A can travel 1.25 times the distance car B can travel when both cars use 1 gallon of gas.

Answer:1

Step-by-step explanation:

The point (2, 7) belongs to the solution region of the system of inequalities.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The system of inequalities given is:

y > 1.5x + 4

y > -x + 6

One point that belongs to the solution region of this system of inequalities is (2, 7).

To check if this point satisfies the system of inequalities, we can substitute the values of x and y into each inequality:

For the first inequality, y > 1.5x + 4, we have:

7 > 1.5(2) + 4

7 > 7

This is true, so the point (2, 7) satisfies the first inequality.

For the second inequality, y > -x + 6, we have:

7 > -(2) + 6

7 > 4

This is also true, so point (2, 7) satisfies the second inequality.

Therefore, points (2, 7) belong to the solution region of the system of inequalities.

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Answer: 20,493

Step-by-step explanation:

%45 off of $37,260 is the same as (45 x 45) / 100 which equals to: 16,767

Then do: 37,260 - 16,767 = 20,493

And there you have it! Hope this helps!!

About 9.1% of people have a systolic blood pressure above 130.about 34.1% of people have a systolic blood pressure between 120 and 130.

A number can be expressed in fractions of 100 using a percentage. When expressing it, the notation %, which stands for "per hundred," is frequently used. 50%, for instance, equals 50/100, or the percentage 1/2.

a. To find the percentage of people with a systolic blood pressure above 130, we need to find the area under the normal curve to the right of 130. Using a standard normal distribution table or a calculator, we can find that this area is approximately 9.1%. Therefore, about 9.1% of people have a systolic blood pressure above 130.

b. To find the percentage of people with a systolic blood pressure between 120 and 130, we need to find the area under the normal curve between 120 and 130. Using a standard normal distribution table or a calculator, we can find that this area is approximately 34.1%. Therefore, about 34.1% of people have a systolic blood pressure between 120 and 130.

c. To find the range of systolic blood pressures for the middle 60% of the population, we need to find the two values of systolic blood pressure that separate the centre 60% of the normal curve's area under the curve. Using a standard normal distribution table or a calculator, we can find that these values are approximately 111.4 and 128.6. Therefore, the range of systolic blood pressures for the middle 60% of the population is approximately 111.4 to 128.6.

d. To find the systolic blood pressure that qualifies a person for additional monitoring if they are in the top 15% of the population, we need to find the value of systolic blood pressure that separates the top 15% of the area under the normal curve from the rest. Using a standard normal distribution table or a calculator, we can find that this value is approximately 131.4. Therefore, a systolic blood pressure of 131.4 or higher would qualify a person for additional monitoring.

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a. approximately 10.56% of people have a systolic blood pressure above 130.

b. approximately 39.44% of people have a systolic blood pressure between 120 and 130.

c.  a systolic blood pressure of 128.32 or higher would qualify a person for additional monitoring if they are in the top 15% of the population.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

a. To find the percentage of people with a systolic blood pressure above 130, we need to calculate the area under the standard normal curve to the right of the z-score corresponding to a systolic blood pressure of 130.

z = (130 - 120) / 8 = 1.25

Using a standard normal distribution table or calculator, we find that the area to the right of z = 1.25 is 0.1056 or 10.56%. Therefore, approximately 10.56% of people have a systolic blood pressure above 130.

b. To find the percentage of people with a systolic blood pressure between 120 and 130, we need to calculate the area under the standard normal curve between the z-scores corresponding to systolic blood pressures of 120 and 130.

z1 = (120 - 120) / 8 = 0

z2 = (130 - 120) / 8 = 1.25

Using a standard normal distribution table or calculator, we find that the area between z = 0 and z = 1.25 is 0.3944 or 39.44%. Therefore, approximately 39.44% of people have a systolic blood pressure between 120 and 130.

c. To find the range of systolic blood pressures for the middle 60% of the population, we need to find the z-scores corresponding to the 20th and 80th percentiles of the standard normal distribution, which are -0.84 and 0.84, respectively.

The corresponding systolic blood pressures are:

lower limit: z1 * 8 + 120 = 113.68

upper limit: z2 * 8 + 120 = 130

Therefore, the range of systolic blood pressures for the middle 60% of the population is approximately 113.68 to 130.

d. To find the systolic blood pressure that qualifies a person for additional monitoring if they are in the top 15% of the population, we need to find the z-score corresponding to the 85th percentile of the standard normal distribution.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 85th percentile is 1.04.

The corresponding systolic blood pressure is:

systolic blood pressure = z * 8 + 120 = 128.32

Therefore, a systolic blood pressure of 128.32 or higher would qualify a person for additional monitoring if they are in the top 15% of the population.

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Answer:

Step-by-step explanation:

Answer:

Please refer to the attachment

Step-by-step explanation:

Substitute x-values in g(x).

Eg. g(x) at x=0 is g(0)

=> -5(0) -5

= (-5)

Answer:

To determine the type of function that best models the data in the table, we can observe the differences or ratios between successive values of y.

Using differences:

The first differences between successive values of y are:

1.5 - 0 = 1.5

6 - 1.5 = 4.5

13.5 - 6 = 7.5

24 - 13.5 = 10.5

The second differences between successive values of y are:

4.5 - 1.5 = 3

7.5 - 4.5 = 3

10.5 - 7.5 = 3

Since the second differences are constant, the function that best models the data is a quadratic function.

Using ratios:

The ratios between successive values of y are:

1.5/0 = undefined

6/1.5 = 4

13.5/6 = 2.25

24/13.5 ≈ 1.78

Since the ratios are not constant, the function that best models the data is not an exponential function.

Therefore, the type of function that best models the data in the table is a quadratic function. We can try to find a quadratic function of the form y = ax^2 + bx + c that passes through the given points. Using the first three points, we get the system of equations:

a(0)^2 + b(0) + c = 0

a(1)^2 + b(1) + c = 1.5

a(2)^2 + b(2) + c = 6

Solving this system of equations, we get:

a = 3/2

b = 0

c = 0

Therefore, the quadratic function that best models the data is y = (3/2)x^2.

Answer:

$27.00

Step-by-step explanation:

6 × $4.50 = $27.00

Answer:27

Step-by-step explanation:

4.50 x 6 = 27

Answer:

Step-by-step explanation:

8 points

The solution to the word problems are:

1) ∠JML = 63°

2) The center of the circle is (4, -4) and Radius = 4

3) The required measurement of the table cloth should be:

48 in x 36 in

4) The correct option of the similar triangles is:

UY/UV = UZ/ZW

1) The angle subtended by an arc at the Centre is twice the angle subtended at the circumference . More simply, the angle at the centre is double the angle at the circumference. Thus:

∠JML = 126/2 = 63°

2) The general formula for equation of a circle is expressed as:

(x - h)² + (y - k)² = r²

where:

(h, k) is the coordinate of the center of the circle

r is the radius

We are given the circle equation as:

(x + 4)² + (y - 4)² = 16

This can be rewritten as:

(x + 4)² + (y - 4)² = 4²

Thus:

Coordinates of center = (4, -4)

Radius = 4

3) The required measurement of the table cloth should be:

48 in x 36 in

4) Since both triangles are similar, then it means ratio of corresponding sides will be equal and as such:

UY/UV = UZ/ZW

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Because automatic automobile frequency is different from the dealership, there will be an association.

A list of objects is contained in a frequency table together with the frequency of each item.

The quantity of times that an event or value occurs is its frequency.

A frequency table, then, is a table that contains some facts and their frequency.

Considering the dealership's frequency schedule for both manual and automatic.

We can see that whereas manual transmission dealerships all use the same frequencies, automatic transmission dealerships use distinct frequencies. Since there is a relationship between the two, there will be an association.

Because automatic automobile frequency is different from dealership frequency, there will therefore be a link.

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The complete question is:

Three car dealerships were surveyed about the percentage of vehicles on their lot with automatic or manual transmission. The results are displayed below.

Answer:

Let's call the average speed on the winding road "x". Then, the average speed on the level road is "x + 20".

We know that the bus traveled on the winding road for 2 hours, so the distance traveled on the winding road is:

distance = rate × time = x × 2 = 2x

We also know that the bus traveled on the level road for 3 hours at an average speed of "x + 20", so the distance traveled on the level road is:

distance = rate × time = (x + 20) × 3 = 3x + 60

The total distance traveled is 290 miles, so we can write:

2x + 3x + 60 = 290

Combining like terms and solving for x, we get:

5x + 60 = 290

5x = 230

x = 46

Therefore, the average speed on the winding road is 46 mph, and the average speed on the level road is:

x + 20 = 46 + 20 = 66 mph.

Student loans and credit cards are two kinds of loans that most often have c. Compounding interest.

It's vital to understand that compound interest charges interest not solely on the borrowing amount but also the accruing interest. Failure to make timely payments can cause a notable rise in the owed total over an extended period of time.

Late fees and penalties are common for student loans and credit cards; thus, comprehending the repayment responsibilities as described within the terms and conditions becomes paramount for borrowers.

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

∠I < ∠J <∠K is the increasing order of angle.

A skew greatest and smallest walls are located where the roads leading to its ends meet. A crossroads could be where two paths converge. Angle is another outcome of two things interacting. They mimic dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various ways between their endpoints.

Here,

Using the provided image, we can calculate the angle measures of the IJK in the following order, from smallest to largest:

∠I: This angle seems to be the smallest one in the IJK system.

∠J: This angle seems to be the following bigger angle in IJK.

∠K: This angle seems to be the biggest one in IJK, according to K.

Therefore , the solution of the given problem of angles comes out to be
∠I < ∠J <∠K is the increasing order of angle.

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Correct option is D. the combined expenses are $300,000 more than the combined income.

In business, economics, statistics, and science, bar charts are frequently used to display and compare data. When dealing with data that can be divided into discrete categories, like nominal or ordinal data, they are especially helpful.

According to the Income and expenses graph;

We can verify each options one by one.

A. Expenses have increased $200,000 each year over the last 5 years:

If we see the graph for expenses in each year that is increased by $100,000 not the $200,000 over the last 5 years.
So, the option is wrong.

B. The income in Year 5 was twice the income in Year 1:

Income in year 1 = $600,000
Income in year 5 = $900,000

We can see here, income is not just double.
So, the option is wrong.

C. The sum of all expenses in Years 1, 2, and 3 was the same as the sum of all income in those years:

combined income in Years 1, 2, and 3 = $600,000 + $600,000 + $400,000  =  $1600,000
combined expenses in Years 1, 2, and 3 = $400,000 + $500,000 + $600,000 = $1500,000

Both are not equal.
So, the option is wrong.

D. The total amount expenses in Years 3 and 4 were $300,000 more than the total amount income in Years 3 and 4:

combined expenses in Years 3 and 4 = $600,000 + $700,000 = $13,00,000

combined income in Years 3 and 4 = $400,000 + $600,000 = $10,00,000

We can see here the combined expenses are $300,000 more than the combined income.

So, the option is correct.

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Answer: x = 625.4

Step-by-step explanation:

5x – 2 = 3125

      +2       +2

5x = 3127

/5        /5

x = 625.4

Answer: x=3127

Step-by-step explanation:5x times 2 - (3125)=0

5x times -3127=0

5x=3127

x=3127/1

x=3127

Answer:

2520

Step-by-step explanation:

There are 7 letters in MCHNLRN and they can be arranged into 7 ways:

7! = 5040 ways in total

However, the letter 'N' is repeated so we have to divide it by 2.

5040 ÷ 2 = 2520 ways

Answer:

2,520 ways

Step-by-step explanation:

MCHNLRN has 7 letters with one repetition.

therefore, =7!/2!

=2,520 ways

[tex]\displaystyle \int_{0}^{\frac{\pi }{3}}~\sin(x)dx\implies \left.\cfrac{}{} -\cos(x)\right]_{0}^{\frac{\pi }{3}}\implies\left( -\cfrac{1}{2}\right) ~~ - ~~(-1)\implies \cfrac{1}{2}[/tex]

Answer:

FD = 3.16

Step-by-step explanation:

To determine the length of FD, we can use the property of similar triangles that corresponding sides are in proportion to each other. That is,

AB/DE = BC/EF = CA/FD

We are given the lengths of AB, CA, and BC in triangle ABC, and we know that triangle ABC is similar to triangle DEF. We can use the first two sides to find the third side of triangle DEF as follows:

AB/DE = 11/DE = 7.9/EF

=> EF = (DE * 7.9) / 11

Next, we can use the third proportionality to find FD:

CA/FD = 7.6/FD = 11/EF

=> FD = (11 * 7.6) / EF

=> FD = (11 * 7.6) / ((DE * 7.9) / 11)

=> FD = (11^2 * 7.6) / (DE * 7.9)

Now, we just need to substitute the given values and solve for FD:

FD = (11^2 * 7.6) / (4.4 * 7.9)

FD = 3.16

Therefore, the length of FD is 3.16.

Answer: -3x+y

Step-by-step explanation:

This is a subtraction problem and "from" means it's the 1st number so

(2x+7y) - (5x + 6y)       be careful to distribute negative

2x +7y - 5x -6y

-3x+y

To find the simplest expression when (5x + 6y) is subtracted from (2x + 7y), we subtract the coefficients of like terms. This gives us -3x + y as the final result.

The expression represents the difference when (5x + 6y) is subtracted from (2x + 7y) can be found using the properties of addition and subtraction for algebraic expressions. We will combine like terms to simplify.

So, Subtract (5x + 6y) from (2x + 7y), it's like saying (2x + 7y) - (5x + 6y) this will give us:

-3x + y is the final expression in the simplest form.

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The probability of selecting a Republican and then an Independent is 1/15

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

Political discussion group consisting of

If the people are replaced, then we have

P(Republicans) = 5/15

P(Independents) = 3/15

So, we have

The probability of selecting a Republican and then an Independent

P = 5/15 * 3/15

Evaluate

P = 1/15

Hence, the probability of selecting a Republican and then an Independent is 1/15

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