Evaluate the following polynomial when x = 4

3x³x²+2x - 7

5x = 7x - 8

7x - 5x = 8

2x = 8

x = 8 ÷ 2

x = 4

Answer:

Step-by-step explanation:

The recursive form is a(n + 1) = a(n) + 2, with a(1) = 8.

The next term is a(6) = a(5) + 2, which heere is a(6) = 16 + 2 = 18

Answer:

3

Step-by-step explanation:

-(-5) -2

5 - 2

3

Answer:

-7

Step-by-step explanation:

Hope this helps

Answer:

Function 1 has the greatest rate of change.

Step-by-step explanation:

The rate of change is also known as the slope.

Slope is rise over run: change in y over change in x.

Function 1's slope: 3 / 2

Function 2's slope: (0 - (-4)) / (5 - (-5)) = 4/10 = 2/5

3/2 > 2/5

Function 1 has the greatest rate of change.

I + J is an ideal of R because it satisfies closure under addition and absorption of elements from R.

To show that I + J is an ideal of R, we need to verify two conditions: closure under addition and absorption of elements from R.

Let x, y ∈ I + J. This means that x = a + b and y = c + d, where a ∈ I, b ∈ J, c ∈ I, and d ∈ J. We have:

  x + y = (a + b) + (c + d) = (a + c) + (b + d)

  Since a + c ∈ I and b + d ∈ J (as I and J are ideals), (a + c) + (b + d) ∈ I + J. Therefore, I + J is closed under addition.

Let r ∈ R and x ∈ I + J. This means that x = a + b, where a ∈ I and b ∈ J. We have:

  rx = r(a + b) = ra + rb

  Since ra ∈ I (as I is an ideal) and rb ∈ J (as J is an ideal), ra + rb ∈ I + J. Therefore, I + J absorbs elements from R.

Hence, we have shown that I + J satisfies the conditions of being an ideal of R.

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Answer:

Length of window = 9 inch

Width of window = 7 inch

Step-by-step explanation:

Given;

Area of window and frame = 195 inch²

Frame width = 3 inch

Length of window = x + 2

Width of window = x

Find:

Value of x

Computation:

Length of window and frame = x + 2 + 3 + 3

Length of window and frame = x + 8

Width of window and frame = x + 3 + 3

Width of window and frame = x + 6

Area of window and frame = (l)(b)

(x + 8)(x + 6) = 195

x² + 6x + 8x + (8)(6) = 195

x² + 14x + 48 = 195

x² + 14x - 147 = 0

x² + 21x - 7x - 147 = 0

x(x + 21) - 7(x + 21) = 0

So,

x + 21 = 0 and x - 7 = 0

So,

X = 7

Value of x = 7

Length of window = 9 inch

Width of window = 7 inch

Answer:

the answer is 4

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Answer:

I don't know

Step-by-step explanation:

I don't know

To determine whether the boxplot represents the information given in the histogram, we need to examine the characteristics of both the boxplot and the histogram.

The boxplot provides a visual representation of the distribution of a dataset, showing the minimum, first quartile, median, third quartile, and maximum values. It also displays any outliers that may be present. On the other hand, a histogram provides a graphical representation of the frequency or count of data values within specified intervals or bins.

Without specific information or visuals of the boxplot and histogram in question, it is not possible to directly compare them and determine their compatibility. Therefore, it is not possible to answer the question based on the information provided.

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Hey there!

ASSUMING

2(3r + 4) - 3 (r + 1) = 11

IF SO

2(3r + 4) - 3 (r + 1) = 11

2(3r + 4) - 3 (1r + 1) = 11

DISTRIBUTE

2(3r) + 2(4) - 3(1r) - 1(1) = 11

6r + 8 - 3r - 1 = 11

COMBINE the LIKE TERMS

(6r - 3r) + (8 - 3) = 11

6r - 3r + 8 - 3 = 11

3r + 5 = 11

SUBTRACT 5 to BOTH SIDES

3r + 5 - 5 = 11 - 5

SIMPLIFY!

3r = 11 - 5

3r = 6

DIVIDE 3 to BOTH SIDES
3r/3 = 6/3

SIMPLIFY!

r = 6/3

r = 2

Therefore, the answer should be: r = 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

A child who is 44.39 inches tall is one standard deviation above the mean. Approximately 50.58% of children are between 41.25 and 44.29 inches tall.

To find the percentage of children between 41.25 and 44.29 inches tall, we need to calculate the area under the normal distribution curve within this range.

Given that the child's height of 44.39 inches is one standard deviation above the mean, we can infer that the mean height is 44.39 - 1 = 43.39 inches.

Next, we need to determine the standard deviation. Since the child's height of 44.39 inches is one standard deviation above the mean, we know that the difference between the mean and 41.25 inches is also one standard deviation.

Let's denote the standard deviation as σ. We have:

43.39 - 41.25 = σ

Simplifying the equation:

σ = 2.14

Now, we can calculate the percentage of children between 41.25 and 44.29 inches tall using the z-scores.

The z-score formula is given by:

z = (x - μ) / σ

For the lower bound, x = 41.25 inches:

z₁ = (41.25 - 43.39) / 2.14 = -0.997

For the upper bound, x = 44.29 inches:

z₂ = (44.29 - 43.39) / 2.14 = 0.421

We need to find the area under the normal distribution curve between z₁ and z₂. Using a standard normal distribution table or a calculator, we can find the corresponding probabilities.

Let P₁ be the probability associated with z₁, and P₂ be the probability associated with z₂. Then, the percentage of children between 41.25 and 44.29 inches tall is given by:

Percentage = (P₂ - P₁) * 100

Using the z-score table or a calculator, we find that P₁ ≈ 0.1587 and P₂ ≈ 0.6645.

Substituting these values into the formula:

Percentage = (0.6645 - 0.1587) * 100 ≈ 50.58%

Therefore, approximately 50.58% of children are between 41.25 and 44.29 inches tall.

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Increasingly, developers are using tools that can quickly create screen mockups, referred to as element Wireframes

Wireframes is a type of tool which is allow designers to quickly and effectively mock up an outline of a design as easily as possible. Designers easily drag the images and drop to placeholder images , header and content also.

There are three types of wireframes, which is very useful :

Wireframes generally is used for visual designer, developer, business analysts, user experience designers and information architecture and user research.

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2(19-7) im pretty sure

Answer:

f(x) was translated to the left by 5 units to form g(x)

Step-by-step explanation:

Given the function f(x) = x to g(x)=x-5, if you look at the g(x) function, you will see that 5 was subtracted from the abscissa x that is;

g(x) = f(x) - 5

This shows' that the function f(x) was translated to the left by 5 units to form g(x). This described the required translation

Answer:

3

Step-by-step explanation:

(4+y+9+5+2+7)/6=5

(27+y)/6=5

Y=3

Answer:

5x+3=23

Step-by-step explanation:

Answer:

$4 per smoothie

Step-by-step explanation:

5x+4=23

Answer:

-3, -4, -4, 0, 16, 64, 192.

Step-by-step explanation:

I don't know for sure if this is correct, but when i did it theses are the answers i got. You do y=8*2^x. Meaning you substitute the x for the x values such as -3, -2, and -1.  

Also if you have one there's a setting you can go to on an actual calculator and type in this on a Y/X chart. I didn't use one this time because i don't have one, but thought you'd find that information useful.

Answer: Observational study

Step-by-step explanation:

The study illustrated in the question is an observational study. It is referred to as an observational study, because in this case, the price of the individual cereals us not being controlled by the students. They've no control over it.

If it was an experiment, there'll have been a control group and the students will have control over the price. Also, the sampling methods used here is a systematic random sampling.

Answer:

Distance= 15.3

Step-by-step explanation:

By plugging in the values of x and y obtained from the linear programming solution, we can calculate the unused amounts of sugar, flour, and time.

To determine the number of grape and apple pies that will maximize revenues, we can use linear programming. Let's set up the problem:

Let x be the number of apple pies produced.

Let y be the number of grape pies produced.

Objective function:

Maximize Revenue = 4.50x + 3.60y

Constraints:

1.5x + 2y ≤ 2100 (sugar constraint)

3x + 3y ≤ 3000 (flour constraint)

6x + 3y ≤ 60*60 (time constraint, converting hours to minutes)

The problem can be solved using linear programming software or a graphing calculator. The optimal values for x and y will provide the number of apple and grape pies that maximize revenue.

Regarding part b, to determine the amounts of sugar, flour, and time that will be unused, we can compare the amount used with the amount available.

Unused Sugar = 2100 - (1.5x + 2y)

Unused Flour = 3000 - (3x + 3y)

Unused Time = (60*60) - (6x + 3y)

By plugging in the values of x and y obtained from the linear programming solution, we can calculate the unused amounts of sugar, flour, and time. Remember to round the final answers to the nearest whole number.

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Answer:

-2.15

Step-by-step explanation:

Plug it into the calculator and it should give you the same answer.

Answer:

The answer is -2.15.

Step-by-step explanation:

Hope this helped Mark BRAINLIEST!!!

Answer: 27 gallons

Step-by-step explanation:

Since the car can go 35½ miles in 1½ miles gallons, we need to first calculate the number of miles that the car can go in 1 gallon. This will be:

= 35½ / 1½

= 71/2 / 3/2

= 71/2 × 2/3

= 23⅔ miles per gallon.

Therefore, the amount of gallons that the car need to go 639 miles will be:

= 639 / 23⅔

= 639 ÷ 71/3

= 639 × 3/71

= 27

The car will need 27 gallons.

The homogeneous equation corresponding to W = Span(2, 1, -3) is 0.

To discover a set of one or more homogeneous equations for which the corresponding answer set is W = Span(2, 1, -three), we will use the idea of linear independence.

The set of vectors v1, v2, ..., vn is linearly unbiased if the only strategy to the equation a1v1 + a2v2 + ... + anvn = 0 (wherein a1, a2, ..., an are scalars) is a1 = a2 = ... = an = 0.

Since W = Span(2, 1, -3), any vector in W may be represented as a linear aggregate of (2, 1, -three). Let's name this vector v.

Now, to find a homogeneous equation corresponding to W, we need to discover a vector u such that u • v = 0, in which • represents the dot product.

Let's bear in mind the vector u = (1, -1, 2). To check if u • v = 0, we compute the dot product:

(1)(2) + (-1)(1) + (2)(-3) = 2 - 1 - 6 = -5.

Since u • v = -five ≠ zero, the vector u = (1, -1, 2) is not orthogonal to v = (2, 1, -3).

To discover a vector that is orthogonal to v, we can take the go product of v with any other vector. Let's pick the vector u = (1, -2, 1).

Calculating the cross product u × v, we get:

(1)(-3) - (-2)(1), (-1)(-3) - (1)(2), (2)(1) - (1)(1) = -3 + 2, 3 - 2, 2 - 1 = -1, 1, 1.

So, the vector u = (-1, 1, 1) is orthogonal to v = (2, 1, -3).

Therefore, the homogeneous equation corresponding to W = Span(2, 1, -3) is:

(-1)x + y + z = 0.

Note that this equation represents an entire answer set, now not only an unmarried solution. Any scalar more than one of the vectors (-1, 1, 1) will satisfy the equation and belong to W.

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The correct question is:

All entire functions f where f(0) = 7, f'(2) = 4, and |ƒ"(2)| ≤ π for all z € C are given by f(z) = 2z + 7.

Given that f is an entire function, which means that it is holomorphic on the entire complex plane C. Let us write the Taylor series for f(z) centered at z = 0. Since f is an entire function, its Taylor series has an infinite radius of convergence. Thus, we can write:
f(z) = a0 + a1z + a2z² + · · ·
Differentiating both sides of the above equation with respect to z, we get:
f′(z) = a1 + 2a2z + · · ·
Given that f(0) = 7 and f'(2) = 4, we get the following equations:
a0 = 7
a1 + 4 = f′(2)
Subtracting the second equation from the first, we get:
a1 = −3
Differentiating both sides of the above equation with respect to z, we get:
f″(z) = 2a2 + · · ·
Using the inequality |ƒ"(2)| ≤ π, we get the following inequality:
|2a2| ≤ π
Thus, we get the inequality:
|a2| ≤ π/2
Therefore, the Taylor series for f(z) is given by:
f(z) = 7 − 3z + a2z² + · · ·
where |a2| ≤ π/2.

However, we can further simplify the expression by observing that f(z) = 2z + 7 is an entire function that satisfies the given conditions. Therefore, by the identity theorem for holomorphic functions, we conclude that f(z) = 2z + 7 is the unique entire function that satisfies the given conditions.

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The properties of the Fourier transform stated in (1) and (2) are incorrect.

The properties of the Fourier transform stated in (1) and (2) are incorrect.

Let's examine each property:

(1) (Fu)(E) = 27 (F-\u) (-):

The expression on the left side, (Fu)(E), represents the Fourier transform of a function u evaluated at frequency E.

However, the expression on the right side, 27 (F-\u) (-), is not a valid representation of the Fourier transform.

The notation (F-\u) (-) is unclear and does not align with the standard conventions of the Fourier transform.

(2) (F(t,0))(E) - (FU)(8 + a):

Similarly, the expression on the left side, (F(t,0))(E), suggests the Fourier transform of a function F evaluated at time t and frequency E.

However, the subtraction of (FU)(8 + a) is not a well-defined operation in the context of the Fourier transform. The relationship between F(t,0) and FU is not clear, and the addition of 8 + a lacks proper justification.

Therefore, both properties (1) and (2) provided for the Fourier transform are inaccurate.

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The surface area of the right prism cone is,

⇒ 1960 units²

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A right prism shown in image.

Now, We get;

Base area of cone = 14 x 10

                            = 140

And, Height of cone = 6

And, Perimeter of the base = 2 (10 + 14)

                                           = 280

Thus, WE know that;

The surface area of the right prism cone is,

⇒ 2B + hP

⇒ 2 × 140 + 6 × 280

⇒ 280 + 6 × 280

⇒ 280 + 1680

⇒ 1960 units²

Thus, The surface area of the right prism cone is,

⇒ 1960 units²

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The probability of getting at least 7 non-defective units is 0.1718 and the probability of getting at most 6 defective units is 0.8282.In a simultaneous inspection of 10 units, the probabilities of getting a defective unit and non-defective unit are equal.

(a) Probability of getting a defective unit = P(D)Probability of getting a non-defective unit = P(N)P(D)

= P(N) (equal probabilities)P(D)

= 1/2P(N)

= 1/2Total number of units inspected

= 10(a)

Find the probability of getting at least 7 non-defective units

P(X = x) = nCx * P^x * q^(n-x)

Where nCx is the binomial coefficient

P is the probability of successq is the probability of failuren is the total number of trialsx is the number of successes

(a) The probability of getting at least 7 non-defective units

= P(X ≥ 7)P(X ≥ 7)

= P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)P(X = x)

[tex]= nCx * P^x * q^{(n-x)}P(X = 7)[/tex]

= 10C7 * (1/2)^7 * (1/2)^3 = 0.1172P(X = 8)

= 10C8 * (1/2)^8 * (1/2)^2 = 0.0439P(X = 9)

= 10C9 * (1/2)^9 * (1/2)^1 = 0.0098P(X = 10)

= 10C10 * (1/2)^10 * (1/2)^0 = 0.00098P(X ≥ 7)

= 0.1172 + 0.0439 + 0.0098 + 0.00098

= 0.1718

(b) Find the probability of getting at most 6 defective units

P(X = x) = [tex]nCx * P^x * q^{(n-x)}[/tex]

Where nCx is the binomial coefficient P is the probability of success

q is the probability of failuren is the total number of trialsx is the number of successes

(b) The probability of getting at most 6 defective units

= P(X ≤ 6)P(X ≤ 6)

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

= [tex]nCx * P^x * q^{(n-x) }\times P(X = 0)[/tex]

= 10C0 * (1/2)^0 * (1/2)^10

= 0.00098P(X = 1)

= 10C1 * (1/2)^1 * (1/2)^9 = 0.0098P(X = 2) = 10C2 * (1/2)^2 * (1/2)^8 = 0.044P(X = 3)

= 10C3 * (1/2)^3 * (1/2)^7 = 0.1172P(X = 4)

= 10C4 * (1/2)^4 * (1/2)^6 = 0.2051P(X = 5)

= 10C5 * (1/2)^5 * (1/2)^5 = 0.2461P(X = 6)

= 10C6 * (1/2)^6 * (1/2)^4 = 0.2051P(X ≤ 6)

= 0.00098 + 0.0098 + 0.044 + 0.1172 + 0.2051 + 0.2461 + 0.2051

= 1- P(X ≥ 7) = 1 - 0.1718= 0.8282

The probability of getting at least 7 non-defective units is 0.1718 and the probability of getting at most 6 defective units is 0.8282.

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The value of ∭E (x² + y²) dv over the region E between the given spheres.

To evaluate the integral ∭E (x² + y²) dv using spherical coordinates, we first need to express the volume element dv in terms of spherical coordinates.

In spherical coordinates, the volume element is given by dv = r² sin(φ) dr dφ dθ, where r represents the radial distance, φ represents the polar angle, and θ represents the azimuthal angle.

Since we are integrating over the region E between the spheres x² + y² + z² = 9 and x² + y² + z² = 16, the limits of integration for r, φ, and θ will be as follows:

r: from the lower sphere to the upper sphere, which corresponds to r = 3 to r = 4

φ: from 0 to π (since we are considering the entire range of polar angle)

θ: from 0 to 2π (since we are considering the entire range of azimuthal angle)

Now, let's substitute these values and evaluate the integral:

∭E (x² + y²) dv = ∭E (r² sin(φ) cos²(θ) + r² sin(φ) sin²(θ)) dr dφ dθ

Integrating over θ from 0 to 2π, and integrating over φ from 0 to π, we have:

∭E (x² + y²) dv = ∫[0,2π] ∫[0,π] ∫[3,4] (r² sin(φ) cos²(θ) + r² sin(φ) sin²(θ)) dr dφ dθ

Now, we can evaluate the integral by performing the integration step by step, starting from the innermost integral.

After evaluating the integral, the final result will give us the value of ∭E (x² + y²) dv over the region E between the given spheres.

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Answer:

=8x+4

Step-by-step explanation:

=2(4x+2)

a=2,b=4x,c=2

=2 x 4x + 2 x 2

Simplify- 2 x 4x + 2 x 2: 8x + 4