Given that ABC~DEF Solve for x
A. 10
B. 17
C. 7
D. 6​

Answer:

The answer is Multiplication.

Step-by-step explanation:

The coefficient of the x term in f(x) is 2, and the coefficient of the x term in g(x) is 2. When we add or subtract the two functions, the coefficient of the x term remains 2. However, when we multiply the two functions, the coefficient of the x term becomes 4. Therefore, multiplication results in the largest coefficient on the x term.

Here is the solution for each of the operations:

Addition: f(x) + g(x) = (2x −1) + (2x + 4) = 4x + 3

Subtraction: f(x) - g(x) = (2x −1) - (2x + 4) = -5

Multiplication: f(x) * g(x) = (2x −1) * (2x + 4) = 4x^2 + 6x - 4

As you can see, the coefficient of the x term in f(x) * g(x) is 4, which is larger than the coefficients of the x terms in f(x) + g(x) and f(x) - g(x). Therefore, multiplication results in the largest coefficient on the x term.

25% of the kids are older than Evie.

To find the percentage of kids older than Evie, we need to determine the total number of kids who are older than 9 and divide it by the total number of kids (20), then multiply by 100.

The number of kids older than 9 is the sum of the kids who are 10 and 12 years old: 4 + 1 = 5.

Now we can calculate the percentage:

Percentage = (Number of kids older than 9 / Total number of kids) * 100

Percentage = (5 / 20) × 100

Percentage = 25%

Therefore, 25% of the kids are older than Evie.

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Answer:

3r^6

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Answer:

f[g(1)]=6.

Explanation:

Given f(n) and g(n) defined below:

First, we evaluate g(1):

Therefore:

Therefore, f[g(1)]=6.

Answer:

it is ether b or c

Step-by-step explanation:

The statement " Rate of college enrollment immediately after completing high school was 67% by 1997" is an example of (a) Descriptive Statistics.

The Descriptive statistics involves the use of measures, such as averages, proportions, and frequencies, to summarize and describe the main features of a set of data.

In this statement, the rate of 67% is a summary statistic that describes the proportion of high school graduates who enrolled in college immediately after completing high school in 1997.

Whereas; the inferential statistics involves making inferences or predictions about a population based on a sample of data.

The statement provides a summary statistic for the rate of college enrollment for a specific year, 1997, but it does not provide any inferences or predictions about the rate of college enrollment for other years or other populations , so it denoted a Descriptive Statistics .

The given question is incomplete , the complete question is

What type of Statistics does the statement "the rate of college enrollment immediately after high school completion was 67" represents ?

(a) Descriptive

(b) Inferential

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Given the polynomial division:

Remainder: -4

To express the remainder of a polynomial, the remainder -4 will be divided by (x + 1).

Therefore, since the remainder is -4, and the polynomial is divided by x+1, the correct way to express the remainder is:

ANSWER:

The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.

Given that From the top of a tower 14m high

The angle of depression of a student is 32°

we can use trigonometry to find the distance from the foot of the tower to the student:

tan(32°) = opposite/adjacent = 14/distance

Rearranging this equation gives:

distance = 14/tan(32°)

= 25.63m

Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.

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Answer:

Daily pay= $18

5 days pay = $90

Step-by-step explanation:

Archer's daily pay =p

Pay for 5 days= 5p

Gas = 1/2 of 5p

= 1/2 × 5p

= 5p/2

Water = $5

Balance = $40

5p = 5/2p + 5 + 40

5p - 5/2p = 45

10p -5p /2 = 45

5/2p = 45

p= 45÷ 5/2

= 45 × 2/5

= 90/5

P= $18

5p= 5 × $18

=$90

The equation to determine Archer's daily pay is

5p = 5/2p + 5 + 40

Divide both sides by 5

p = 5/2p + 45 ÷ 5

= (5/2p + 45) / 5

p= (5/2p + 45) / 5

The rate at which the water level is rising when it is 5 meters high is approximately 0.477 m/min

The volume of a conical tank:
V = (1/3)πr^2h
where V is the volume of the tank, r is the radius, and h is the height.
Differentiating both sides with respect to time, we get:
dV/dt = (1/3)π(2rh dr/dt + r^2 dh/dt)
Where dV/dt is the rate at which the volume is changing (in m^3/min), and dr/dt and dh/dt are the rates at which the radius and height are changing, respectively.
We know that water is pouring into the tank at a rate of 6m^3/min, so we can substitute this value for dV/dt. We also know that the height of the water level is rising, so dh/dt is what we need to find. Finally, we know that when the water level is 5 meters high, the radius of the water surface can be found using similar triangles:
r/h = 4/10
r = (4/10)h = 0.4h
Now we can substitute all of these values into the formula and solve for dh/dt:
6 = (1/3)π(2(0.4h)(dh/dt) + (0.4h)^2 dh/dt)
6 = (1/3)π(0.8h + 0.16h^2) dh/dt
dh/dt = 6 / [(1/3)π(0.8h + 0.16h^2)]
When the water level is 5 meters high, h = 5, so:

dh/dt = 6 / [(1/3)π(0.8(5) + 0.16(5)^2)]

dh/dt = 0.477m/min

Therefore, the rate at which the water level rises when it is 5 meters high is approximately 0.477 m/min.

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Answer:

12.5

Step-by-step explanation:

Answer:

The vertex is located at (-2,-1)

Step-by-step explanation:

The degree of the polynomial y 52-5z +6-3zº is 52.

The polynomial is y⁵² - 5z + 6 - 3z°. Let's simplify the polynomial to identify the degree:

The degree of a polynomial is defined as the highest degree of the term in a polynomial. The degree of a term is defined as the sum of exponents of the variables in that term. Let's look at the given polynomial:y⁵² - 5z + 6 - 3z°There are 4 terms in the polynomial: y⁵², -5z, 6, -3z°

The degree of the first term is 52, the degree of the second term is 1, the degree of the third term is 0, and the degree of the fourth term is 0. So, the degree of the polynomial is 52.

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Answer:

Side known in ratio as 8: 32

Side known in ratio as 9: 36

Side known in ration as 10: 40

Step-by-step explanation:

We can add all the numbers in the ration to form the sum of all the sides, or also equal to perimeter. 8+9+10 equals 27.

So we can write 27x=108

x=4. Multiply 4 to 8, then 9, then 10. You get 32, 36, 40

Hope this helped, Have a Great Day!!

Answer:

x = 1

Step-by-step explanation:

Were trying to solve for x so we would say 3 1/2 - 2 1/2 and we would be left with 1. So x=1, which you then substitute into the problem to make sure it's correct so 2 1/2 + 1 = 3 1/2.

Hope this helped

The exact area of each hexagonal shape is 181.5sqrt(3) cm^2. Option B

To determine the exact area of each hexagonal shape formed by the equilateral triangles, we need to calculate the area of one equilateral triangle and then multiply it by the number of triangles that make up the hexagon.

The formula to calculate the area of an equilateral triangle is:

Area = (sqrt(3) / 4) * side^2

Given that the side of each tile measures 11 cm, we can substitute this value into the formula to find the area of one equilateral triangle:

Area = (sqrt(3) / 4) * (11 cm)^2

= (sqrt(3) / 4) * 121 cm^2

= 121sqrt(3) / 4 cm^2

Now, since the hexagon is formed by six equilateral triangles, we can multiply the area of one triangle by 6 to find the total area of the hexagon:

Hexagon Area = 6 * (121sqrt(3) / 4 cm^2)

= 726sqrt(3) / 4 cm^2

= 181.5sqrt(3) cm^2

Therefore, the exact area of each hexagonal shape is 181.5sqrt(3) cm^2.

The correct answer is B: 181.5√3 cm^2.

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Step-by-step explanation:

when a variable depends on the product or quotient of two or more variables, it is a joint variation like in our case here.

F (e.g. gravity) varies directly with the masses of 2 objects (like 2 planets) and varies inversely with the distance to or between these objects.

so, the gravity between 2 planets gets stronger the more mass the planets have, but gets weaker the more distance there is between them.

there is only one constant considered in a joint variation statement. in our case : k

Answer:

38

Step-by-step explanation:

Just substitute it. The equation becomes

70 - 4(8)

70 - 32 = 38

Answer:

38

Step-by-step explanation:

70 - 4a =

70 - 4*8=

70 - 32= 38

I agree with Patricia's reasoning because the equation A(x) = -2x^2 + 36 is not a perfect square

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you add up the side lengths to determine the area

The area equation is given as

A(x) = -2x^2 + 36

Taking the square root of the above equation A(x) = -2x^2 + 36 would not yield a usable result

This is so because the equation A(x) = -2x^2 + 36 is not a perfect square

However, the equation can be factorized as follows

A(x) = -2x^2 + 36

Factor out 2

So, we have

A(x) = 2(-x^2 + 18)

The above implies that the length and the width of the rectangle are 2 and (-x^2 + 18), respectively

This means that factoring would be a more efficient way to solve for the maximum area compared to taking square roots

Hence, I agree with Patricia's reasoning

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Answer:

292.5

Step-by-step explanation:

65 times 4.5 = 292.5

The square miles that was burned if one square mile is 640 acres is 840.625 square miles.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Square miles that was burned = 538,000 / 640 = 840.625 square miles

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There are 840.625 square miles did the fire burn.

Division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in maths.

The wallow fire of 2011 burned 538,000 acres in eastern Arizona.

The area of square miles did the fire burned is;

\(\rm Area =\dfrac{538,000}{640}\\\\Area =840.625 \ square \ miles\)

Hence, there are 840.625 square miles did the fire burn.

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Rounding up to the nearest whole number, you would need to survey approximately 753 randomly selected air passengers to be 90% confident that the sample percentage is within 3.5 percentage points of the true population percentage.

To determine the sample size needed for estimating a population percentage with a specified margin of error and confidence level, we can use the formula for sample size calculation for proportions. The formula is:

n = (Z^2 * p * (1-p)) / E^2

Where:

n is the required sample size,

Z is the Z-score corresponding to the desired confidence level (for a 90% confidence level, Z ≈ 1.645),

p is the estimated population proportion (since we don't have an estimate, we can use 0.5 for maximum sample size),

E is the desired margin of error (in decimal form).

In this case, the desired margin of error is 3.5 percentage points, which is 0.035 in decimal form.

Plugging in the values, we have:

n = (1.645^2 * 0.5 * (1-0.5)) / 0.035^2

Calculating this expression gives us:

n ≈ 752.93

Rounding up to the nearest whole number, you would need to survey approximately 753 randomly selected air passengers to be 90% confident that the sample percentage is within 3.5 percentage points of the true population percentage.

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The reliability function, denoted by R(t), represents the probability that the electric ignition on the gas stove will survive beyond time t. To find the reliability function, we need to integrate the probability density function (PDF) over the given interval.

For 0 <= t <= 2:

R(t) = ∫[0 to t] f(x) dx = ∫[0 to t] 0.375x^2 dx = 0.125x^3 evaluated from 0 to t

R(t) = 0.125t^3 - 0.1250^3 = 0.125*t^3

For t > 2:

Since the model indicates that all ignitions expire within 2,000 days, the reliability function beyond t = 2 is 0.

The graph of the reliability function would show a curve starting at R(0) = 1 and gradually decreasing until t = 2, where it drops to 0 and remains 0 for all t > 2.

The hazard function, denoted by h(t), represents the instantaneous failure rate at time t. It can be calculated as the ratio of the probability density function (PDF) to the reliability function.

For 0 <= t <= 2:

h(t) = f(t) / R(t) = (0.375t^2) / (0.125t^3) = 3/t

The hazard function for 0 <= t <= 2 is given by h(t) = 3/t.

For t > 2:

Since the reliability function becomes 0 for t > 2, the hazard function is undefined or infinite for t > 2. This implies that beyond t = 2, the hazard of the electric ignition failure is extremely high or instantaneous.

The graph of the hazard function would show a decreasing curve starting from a high value at t = 0 and approaching infinity as t approaches 2. For t > 2, the hazard function is undefined or infinite.

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Answer:I think CBD

Step-by-step explanation:

The names possible to describe the shape Mr Meyer drew are square and rhombus.

A square is a quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles).

A rhombus is a quadrilateral whose four sides are all the same length.

We know a square has 4 sides that are equal and 4 right angles.

And Its properties are acquired by the shape Rhombus with equal sides, and opposite sides that are parallel to each other and angles are of right angle (90 degrees).

And many Quadrilaterals have a right angle but not 4 equal sides.

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By using multiplication and division, it can be calculated that-

The multiple according to the number 3 = 162

The submultiple according to the number 7 = 7

What is multiplication and division?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

Division is the process in which a value of single unit can be calculated from the value of multiple unit.

The number to be divided is called dividend. The  number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.

This is a problem of multiplication and division.

One segment measures 161 cm

So, to find the multiple according to the number 3, we have to divide 161 by 3

161 \(\div\) 3 = 53.67

Nearest integer of 53.67 is 54

The multiple according to the number 3 = 54 \(\times\) 3 = 162

To find the submultiple according to the number 7, we have to divide 161 by 7

161 \(\div\) 7 = 23

Nearest integer of 23 is 23

The submultiple according to the number 7 = 161 \(\div\) 23 = 7

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So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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Answer:

9h² + 51h + 28

Step-by-step explanation:

(5h + 4)(4h + 7)

=> 9h² + 35h + 16h + 28

=> 9h² + 51h + 28

Therefore, 9h² + 51h + 28 is the simplified expression.

Hoped this helped.

Answer:

20h^2 + 51h+28

Step-by-step explanation:

We will apply the FOIL method (first, outer, inner, last)

(5h + 4)(4h + 7)

Multiply 5h by 4h, first values, to get 20h^2

Multiply 5h by 7, outer values, to get 35h

Multiply 4 by 4h, inner values, to get 16h

Multiply 4 by 7, last values, to get 28

Now we will add them all up to receive our answer

20h^2 + 35h + 16h + 28 = 20h^2 + 51h + 28

By eliminating the parameter θ, we can find a Cartesian equation of the curve defined by the parametric equations x = 8 cos θ and y = 9 sin θ. The Cartesian equation of the curve is 64 - \(64y^2/81 = x^2\).

To eliminate the parameter θ, we can use the trigonometric identity \(cos^2\) θ + \(sin^2\) θ = 1. Let's start by squaring both sides of the given equations:

\(x^{2}\) = \((8cos theta)^2\) = 64 \(cos^2\) θ

\(y^2\) = \((9sin theta)^2\) = 81 \(sin^2\) θ

Now, we can rewrite these equations using the trigonometric identity:

\(x^{2}\) = 64 \(cos^2\) θ = 64(1 - \(sin^2\) θ) = 64 - 64 \(sin^2\) θ

\(y^2\) = 81 \(sin^2\) θ

Next, let's rearrange the equations:

64 \(sin^2\) θ = \(y^2\)

64 - 64 \(sin^2\) θ = \(x^{2}\)

Finally, we can combine these equations to obtain the Cartesian equation:

64 - 64 \(sin^2\) θ = \(x^{2}\)

64 \(sin^2\) θ = \(y^2\)

Simplifying further, we have:

\(64 - 64y^2/81 = x^2\)

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