For a given function f (x), the domain is -4 < x <7, the range is 2 < y < 9, and has the point (4,8) on the graph. If h (z) = f(x+4), then
the domain of h (z) would be
type your answer....
the range would be type your answer.....
and the corresponding point would be moved to (type your answer.....
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y< type your answer.....
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The present value of the sequence of annual payments of Rs 25000 each, the first being made at the end of the 5th year and the last being paid at the end of the 12th year, if money is worth 6% is Rs. 158620.39.

1: We can use the formula to calculate the present value of the annuity:

P = A x [1 - (1+i)^-n] / i

Where

P = Present Value

A = Annuity

i = Interest Raten = Number of payments

2: Calculate the present value of each payment using the formula:

P1 = 25000 / (1.06)⁵

P2 = 25000 / (1.06)⁶

P3 = 25000 / (1.06)⁷

P4 = 25000 / (1.06)⁸

P5 = 25000 / (1.06)⁹

P6 = 25000 / (1.06)¹⁰

P7 = 25000 / (1.06)¹¹

P8 = 25000 / (1.06)¹²

3: Substitute the values into the formula to find the present value:

P = P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8

P = (25000 / (1.06)⁵) + (25000 / (1.06)⁶) + (25000 / (1.06)⁷) + (25000 / (1.06)⁸) + (25000 / (1.06)⁹) + (25000 / (1.06)¹⁰) + (25000 / (1.06)¹¹) + (25000 / (1.06)¹²)

P = 158620.39

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Answer:y=3/4x+5

Step-by-step explanation:

Consider what you know about the sampling distribution of the sample proportion. this sampling distribution will have a centre equal to the population proportion, or p.

For determining the correct option, we will check one by one all the given options:

From the given statements, we can conclude that.

As the sample size of the data increases, the corresponding value of n also starts increasing.

The value on the denominator of the standard deviation equation is n.

Therefore, the standard deviation will decrease as the value of n increases.

A tiny variance is one with a low standard deviation.

As a result, the variance will be minor as the sample size increases.

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Actual questions should be:

Consider what you know about the sampling distribution of the sample proportion. This sampling distribution

(1) has a shape that is skewed to the right, regardless of sample size.

(2) is a collection of the parameters of all possible samples of a particular size taken from a particular population.

(3) Will become more variable as the sample size increases.

(4) will have a center equal to the population proportion, or p.

(5) will be Normal in shape only if the sample size is at least 100 .

Answer:

Step-by-step explanation:

As a result, with a discount rate of 7%, the present value of an item that will be worth $200 in four years is roughly $152.57.

We may use the present value calculation to discount an item that will be worth $200 in four years back to today at a 7% discount rate:

PV equals FV / (1 + r)n

where n is the number of periods, r is the discount rate, PV is the present value, and FV is the future value.

If we substitute the values provided, we get:

PV = 200 / (1 + 0.07), divided by four, results in PV of $152.57.

As a result, with a discount rate of 7%, the present value of an item that will be worth $200 in four years is roughly $152.57.

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Answer:

\(\huge\boxed{\sf 6(x + 2)}\)

Step-by-step explanation:

= 2(5x + 3) - 2(2x - 3)

Expand

= 10x + 6 - 4x + 6

Combine like terms

= 10x - 4x + 6 + 6

Add or subtract as indicated

= 6x + 12

Take 6 common

= 6(x + 2)

\(\rule[225]{225}{2}\)

Hope this helped!

A. The probability that exactly 5 adults meet the criteria for hypertension is approximately 0.0916 or 9.16%.

B. The probability that none of the adults meet the criteria for hypertension is approximately 0.0255 or 2.55%.

C.  The probability that less than or equal to 7 adults meet the criteria for hypertension is approximately 0.9999 or 99.99%.

To calculate the probabilities,

Use the binomial probability formula.

The binomial probability formula is,

P(X = k) = C (n ,k) × \(p^k\) × \((1 - p)^{(n - k)\)

Where,

P(X = k) is the probability of exactly k successes

n is the number of trials

k is the number of successes

p is the probability of success in a single trial

(1 - p) is the probability of failure in a single trial

C(n, k) represents the binomial coefficient,

which can be calculated as n! / (k! × (n - k)!)

A. To calculate the probability that exactly 5 adults meet the criteria for hypertension,

n = 15 (number of adults assessed)

k = 5 (number of adults meeting the criteria)

p = 0.30 (probability of meeting the criteria)

A. Probability that exactly 5 adults meet the criteria for hypertension,

n = 15

k = 5

p = 0.30

P(X = 5) = C( 15, 5) × 0.30⁵ × (1 - 0.30)¹⁵⁻⁵

Using the binomial coefficient formula C (n ,k) = n! / (k! × (n - k)!), we have,

(¹⁵C₅) = 15! / (5! × (15 - 5)!) = 3003

P(X = 5) = 3003 × 0.30⁵ × 0.70¹⁰

Calculating the probability,

P(X = 5) = 0.0916 (approximately)

B. Probability that none of the adults meet the criteria for hypertension,

n = 15

k = 0

p = 0.30

P(X = 0) = (¹⁵C₀) × 0.30⁰× (1 - 0.30)¹⁵⁻⁰

(¹⁵C₀) = 1 (since choosing 0 from any set results in 1)

P(X = 0) = 1 × 0.30⁰ × 0.70¹⁵

Calculating the probability,

P(X = 0) = 0.0255 (approximately)

C. Probability that less than or equal to 7 adults meet the criteria for hypertension,

n = 15

k = 0, 1, 2, 3, 4, 5, 6, 7

p = 0.30

P(X ≤7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

Calculate each individual probability using the binomial probability formula and sum them up.

P(X ≤7) = (¹⁵C₀) × 0.30⁰ × 0.70¹⁵ + ¹⁵C₁× 0.30¹× 0.70¹⁴+ (¹⁵C₂) × 0.30²× 0.70¹³ + (¹⁵C₃) × 0.30³ × 0.70¹² + (¹⁵C₄) ×0.30⁴ × 0.70¹¹ + (¹⁵C₅) × 0.30⁵× 0.70¹⁰ + (¹⁵C₆) × 0.30⁶× 0.70⁹ + (¹⁵C₇) × 0.30⁷ ×0.70⁸

Calculating the probability,

P(X ≤ 7) ≈ 0.9999

Therefore, the probabilities for different conditions are,

A. For exactly 5 adults is 0.0916 or 9.16%.

B. For none of the adults is 0.0255 or 2.55%.

C. less than or equal to 7 adults is 0.9999 or 99.99%.

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Answer:

a) 81-6

b) 10.4

Step-by-step explanation:

a) assuming that the VAT is 20% of the 68 pounds,

you calculate 120% of 68 (convert percentage to decimal)

= 1,20 * 68 = 81.6 pounds

or

calculate 20% of 68 pounds and add the answer to 68 pounds:

(0.2 * 68) + 68 = 81.6 pounds

b) 20% of 52

first convert the percentage to decimals:

0.2 * 52 = 10.4 pounds

The correct option is C. It is safe to apply the central limit theorem, even if the sample size for each sample is 15, if the sample population is normally distributed.

The central limit theorem states that, if you take repeated samples of a population and calculate the mean of each sample, the distribution of the means of those samples will tend to be normally distributed, provided that the sample size is large enough. This means that, even if the original population is not normally distributed, the distribution of the means of the samples will tend towards a normal distribution as the sample size increases.

However, if the original population is already normally distributed, then you can apply the central limit theorem with a smaller sample size and still expect the distribution of the means of the samples to be normally distributed. Therefore, in order for it to be safe to apply the central limit theorem with a sample size of 15, the sample population must be normally distributed.

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Answer:

Let's call the distance between the lighthouse and the first boat "x" and the distance between the lighthouse and the second boat "y". We want to find the distance between the two boats, which we can call "d".

From the information given, we can draw the following diagram:

      /|

                  / |

                 /  |y

                /   |

               /θ2 |

              /____|

           L /  x  /B2

              θ1

               /|

              / |

             /  |y-x

            /   |

           /θ3 |

          /____|

         A1    B1

Where L is the lighthouse, A1 and B1 are the positions of the first and second boats respectively, θ1 is the angle of depression to the first boat, θ2 is the angle of depression to the second boat, θ3 is the angle between the two boats, and x and y are as defined above.

From the diagram, we can see that:

tan(θ1) = 80 / x

tan(θ2) = 80 / y

tan(θ3) = (y - x) / 80

We also know that the two boats are in a straight line, so the sum of the distances to each boat is equal to the distance between the boats:

x + y = d

To solve for d, we need to eliminate x and y from these equations. We can start by solving for x and y in terms of θ1 and θ2:

x = 80 / tan(θ1)

y = 80 / tan(θ2)

Substituting these expressions into the equation for d, we get:

d = x + y

= 80 / tan(θ1) + 80 / tan(θ2)

Now we just need to plug in the values given in the problem:

θ1 = 55°

θ2 = 40°

d = 80 / tan(55°) + 80 / tan(40°)

≈ 196.8 feet

Therefore, the distance between the two boats is approximately 196.8 feet.

The mass of the solid is 7π/2 units.

The task is to calculate the mass of the solid.

Step-by-step solution: The solid occupies the region between the unit sphere at the origin and a sphere of radius 2 with the center at the origin. The spherical coordinates in 3D space are (r,θ,φ), where:r = radius, θ = polar angle, φ = azimuthal angle.

The equations of the given sphere are r=1 for the unit sphere and r=2 for the second sphere.

Using spherical coordinates, the solid can be defined as 1≤r≤2, 0≤θ≤2π, 0≤φ≤π.

The density is equal to the distance from the origin, i.e. ρ = r.

The mass of the solid is given by the triple integral ρ dV taken over the solid, where dV is the volume element in spherical coordinates.dV = r²sin φ dφdθdr

The limits for the triple integral are: 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π, and 1 ≤ r ≤ 2.M = ∭ρ dV = ∭r(r²sin φ) dφdθdr= ∫[0,2π]∫[0,π]∫[1,2] r³sin φ drdφdθ= ∫[0,2π]∫[0,π] -cos φ [r⁴/4]₁ ₂ drdφdθ= ∫[0,2π]∫[0,π] 7/4 cos φ dφdθ= ∫[0,2π] 7sin φ/4 ]₀  π dθ= 14π/4= 7π/2 units.

The mass of the solid is 7π/2 units.

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Answer:

Your answer is correct, (-6, -4, 0, 2, 6).

Explanation:

Take the equation 3/2x+8

Then take each number and plug it in for "x".

For example:

3/2(6) + 8 = -1

or you can change the fraction into a decimal to make it easier...

1.5(6)+8=-1

Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.

An isomorphism is a bijective linear transformation, that is both one-to-one and onto. The determinant of a linear transformation can help determine if it is an isomorphism. If the determinant is non-zero, the linear transformation is invertible, and therefore an isomorphism. A linear transformation is an isomorphism if and only if its determinant is nonzero.
Additionally, another way to check if a linear transformation is an isomorphism is to check if the kernel, which is the set of all vectors that get mapped to zero, is equal to only the zero vector. If the kernel is only the zero vector, then the linear transformation is one-to-one and therefore an isomorphism.

Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.

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The probability that a woman was wearing a belt given that she was also carrying a purse is 0.333 or 33.3%.

To find the probability that a woman was wearing a belt given that she was also carrying a purse, we need to use conditional probability.

We know that out of the 30 women observed, 18 were carrying purses and 6 were both carrying purses and wearing belts.

This means that the number of women carrying purses who were also wearing belts is 6.
Therefore, the probability that a woman was wearing a belt given that she was also carrying a purse is:
P(wearing a belt | carrying a purse) = number of women wearing a belt and carrying a purse / number of women carrying a purse
P(wearing a belt | carrying a purse) = 6 / 18
P(wearing a belt | carrying a purse) = 0.333
Given the information provided, we can determine the probability of a woman wearing a belt, given that she is also carrying a purse.

First, we need to find the number of women carrying a purse and wearing a belt, which is 6. There are 18 women carrying purses in total.
So, to find the probability, we will use the formula:
P(Belt | Purse) = (Number of women wearing belts and carrying purses) / (Number of women carrying purses)
P(Belt | Purse) = 6 / 18
P(Belt | Purse) = 1/3 or approximately 0.33
Therefore, the probability that a woman was wearing a belt, given that she was also carrying a purse, is 1/3 or approximately 0.33.

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Answer:

-3

Step-by-step explanation:

To make the equation have infinitely many solutions, we need to make both sides equal.

i will use variable y in place of blank

-x + 20 + yx = -4x + 20

-x + yx = -4x

yx = -3x

y = -3

now we can check the answer

-x + 20 - 3x = -4x + 20

-4x + 20 = -4x + 20

0 = 0

this means there are infinitely many solutions

Answer:  1.83

Step-by-step explanation: I did the math

Answer:

C

Step-by-step explanation:

So to do this problem, first find the area of the figure before you apply the scale factor, and then multiply that by 49. The reason you multiply it by 49 and not 7 is because you're multiplying both the length and the width of the figure by 7, so you have 7 * 7 = 49.

The area of the figure to start is 10 (you can find this by simply counting the blocks).

Then, 10 * 49 = C. 490 units squared.

hope that makes sense!

Answer:

Step-by-step explanation:

The range is the difference between maximum and minimum values of data set:

The range is:

Answer:

Range = 70%

Step-by-step explanation:

The range of this data is given by

= maximum value - minimum value

= 100% - 30%

= 70%

Answer:

To clear her driveway, Maya needs to shovel 593.75 cubic feet of snow. Since her shovel can hold 1.5 cubic feet of snow, she will need to fill her shovel 593.75 / 1.5 = <<593.75/1.5=395.83333>>395.83333 shovels full of snow.

Since shovels can't be filled partially, we need to round this number up to the nearest whole number. Therefore, Maya will need to fill 396 shovels full of snow to clear her driveway.

Step-by-step explanation:

The resultant function is: L(1.1) ≈ 16√2 + 0.4`.

Given the function `f(x)=√128x³ + 384`.

The first derivative of `f(x)` is `f′(x) = 96x²/√128x³ + 384`

Let `x = 1` in `f′(x)` to obtain the slope of the tangent line at `x = 1`f′(1)

= `96(1)²/√128(1³) + 384`

= `96/24`

= `4`

The point at `x = 1` is `(1,f(1))`.

To find `f(1)`, substitute `x = 1` into the original function.f(1) = `√128(1³) + 384` = `√512` = `16√2`

Using the point-slope form of the equation of a line with slope `m = 4` and passing through `(1,16√2)` yields:

L(x) = `4(x - 1) + 16√2`

L(x) = `4x - 4 + 16√2`

L(x) = `4x + 16√2 - 4`

The equation of the tangent line is `L(x) = 4x + 16√2 - 4`.

To approximate `f(1.1)` using `L(x)`, substitute `x = 1.1`.

L(1.1) = `4(1.1) + 16√2 - 4`

L(1.1) = `4.4 + 16√2 - 4`

L(1.1) = `16√2 + 0.4`

Thus, `L(1.1) ≈ 16√2 + 0.4`.

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Answer:

B. 71°

Step-by-step explanation:

∠1 and ∠2 are corresponding angles.

Corresponding angles are congruent.

m∠1=m∠2=71°

The answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

A combination of numbers, variables, and operators that represents a quantity or mathematical relationship is called an expression.

First, divide sextillion (10²¹) by nonmillion (10⁶) to get 10¹⁵.

Next, multiply 10¹⁵ by 10,000 to get 10¹⁹.

Subtract 200 million (2 x 10⁸) from 10¹⁹ to get 9.9998 x 10¹⁸.

Finally, add 5,000 to get the result of approximately 9.9998 x 10¹⁸ + 5,000 = 9.9998 x 10¹⁸ + 0.0005 x 10¹⁸ = 9.9998 x 10¹⁸.

Therefore, the answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

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Answer:

I think is

2

-2(x +20x-100)

Given:

The function is

\(f(x)=\left(\dfrac{1}{3}\right)^x\)

To find:

The missing values for a, b, and c in the given table.

Solution:

We have,

\(f(x)=\left(\dfrac{1}{3}\right)^x\)

At x=-2,

\(f(-2)=\left(\dfrac{1}{3}\right)^{-2}\)

\(a=\left(3\right)^{2}\)         \(\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]\)

\(a=9\)

At x=-1,

\(f(-1)=\left(\dfrac{1}{3}\right)^{-1}\)

\(b=\left(3\right)^{1}\)         \(\left[\because \left(\dfrac{a}{b}\right)^{-n}=\left(\dfrac{b}{a}\right)^{n}\right]\)

\(b=3\)

At x=0,

\(f(0)=\left(\dfrac{1}{3}\right)^{0}\)

\(c=1\)         \(\left[\because a^0=1, a\neq 0\right]\)

Therefore, the missing values of a,b and c are 9, 3, and 1 respectively.

Answer: below

Step-by-step explanation:

The degree measure of the exterior angle triangle is ∠D = 137°.

Having three vertices and three angles that add up to 180 degrees, a triangle is a three-sided polygon.

given this, the angles D, E, and F in the triangle DEF are (4x + 15), (5x + 32), and 70 respectively.

The sum of the angles of a triangle is now 180°.

Therefore, we may write:  m ∠D m∠ E m ∠F = 180

When all the numbers are substituted, we obtain the following results: (9x + 117 = 180) 9x

= 180 -117 (4x + 15) + (5x + 32) + 70

⇒ 9x = 63

⇒ x = 7

As a result, we obtain m∠ D = (4x + 15)°,

m∠ D = (4 x 7 + 15)°,

m ∠D = (28 + 15)°, and m∠ D = (43)°.

Furthermore, m∠ E = (5x + 32)°

m ∠E = (5 x 7 + 32)°

m ∠E = (35 + 32)°

m ∠E = 67°

Since, The measure of the exterior angle to ∠D = m ∠E + m ∠F

= 67° + 70

= 137°

Thus, The measure of the exterior angle  ∠D will be 137°.

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Answer:

Scientific Notation: 4.88 ×10^7

Standard Form: 4.88 ×10^7

Step-by-step explanation:

6.1×10^(-3) = 0.0061

8×10^9 = 8000000000

0.0061×8000000000 = 48800000

\( = 4.88 \times {10}^{7} \)

Answer

B. 500 pi

Step-by-step explanation:

Answer:

1/√2

Approximate numerical value

1/√2 = 0.707106781186548

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

Rationalize the denominator

(1/√2) * (√2 / √2) = √2 / 2

Your answer should come to:

y = -2/3x + 3