Solve this inequality and write the solution using interval notation:

The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.

According to the statement

we have given that the 3 integers are in an arithmetic progression and their product is prime.

And we have to find the sum of their squares.

So, let the three integers which is A, B, C.

And according to the arithmetic progression the

A = x and B = x-d, C = x-2d. here d is the common difference and x is a 1st term.

So, there product is prime

then

(x) (x-d) (x-2d) = c -(1)

And

their sum of square is

(x)^2 + (x-d)^2 + (x-2d)^2 - (2)

So, The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.

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The volume of the quarter-sized tank is 14034 cubic feet and  the volume of the holding tanks is 84857 cubic feet

The radius is given as;

r = 95 feet

For a quarter-sized tank, we divide the radius by 4.

So, we have

r = 95/4 feet

r = 23.75 feet

The volume is

V = 1/3 πr³

This gives

V = 1/3 * 22/7 * 23.75³

Evaluate

V = 14034

Hence, the volume of the quarter-sized tank is 14034 cubic feet

Here, we have

Radius, r = 15 feet

Height, h = 120 feet

The volume is

V = πr²h

This gives

V = 22/7 * 15² * 120

Evaluate

V = 84857

Hence, the volume of the holding tanks is 84857 cubic feet

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[tex]3x + y = - 4 \\ 3x + 0 = - 4 \\ 3x = - 4 \\ x = \frac{ - 4}{3} = - 1.333[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \bm{Last \: option \: (D.)}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Write the equation in slope-intercept form. Then solve y.

▪ [tex]\small\longrightarrow \sf{3x-3x + y = −3x -4}[/tex]

▪ [tex]\small\longrightarrow \sf{y= -3x-4}[/tex]

Identify the x-intercept,

[tex]\small \sf \longrightarrow{3x + 0 = - 4}[/tex]

[tex]\small\longrightarrow \sf{3x=-4}[/tex]

[tex]\small\longrightarrow \sf{x = - \dfrac{4}{3} }[/tex]

[tex]\small\longrightarrow \sf{x = -1.33}[/tex]

The graph has the next properties:

[tex]\small\longrightarrow \sf{Slope: \: 3}[/tex]

[tex]\small\longrightarrow \sf{x-intercept: \: (-1.33,0)}[/tex]

[tex]\small\longrightarrow \sf{y-intercept: \: (0,4) }[/tex]

The first series uses a linear function with - 1 as first element and 1 as common difference, then the rule corresponding to the series is y = |- 1 + x|.

The second series uses a linear function with - 3 as second element as 2 as common difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.

In this problem we have two cases of arithmetic series, which are sets of elements generated by a condition in the form of linear function and inside absolute power. Linear functions used in these series are of the form:

y = a + r · x      (1)

Where:

The first series uses a linear function with - 1 as first element and 1 as common difference, then the rule corresponding to the series is y = |- 1 + x|.

The second series uses a linear function with - 3 as second element as 2 as common difference, then the rule corresponding to the series is y = |- 3 + 2 · x|.

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the volume of the oblique pyramid is 16 cubic units

The formula for finding the volume of a oblique pyramid is given as;

Volume = [tex]\frac{1}{3}[/tex] × base area/ height

Where

base area = area of a right triangle

From the lengths of the triangle given, we can deduce that the opposite side is 24unit and the adjacent side or the base is 10 unit

let's put in the values to the formula

Base area = 10 × 24

Base area = 240 units

height = 5 units

Since we have both the height and the base area, let's find the volume

Volume = [tex]\frac{1}{3}[/tex] × [tex]\frac{240}{5}[/tex]

Volume = [tex]\frac{1}{3}[/tex] × [tex]48[/tex]

Find the division

Volume = 16 cubic units

Thus, the volume of the oblique pyramid is 16 cubic units

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The power series representation for the function, so the interval of convergence is (-9,9).

The definition of convergence refers to 2 or more matters coming together, joining collectively, or evolving into one. An example of convergence is when a crowd of people all move collectively into a unified organization.

Convergence is when two or extra matters come collectively to shape a brand new whole, like the convergence of plum and apricot genes within the plucot. Convergence comes from the prefix con-, meaning collectively, and the verb verge, because of this to show closer to.

The simple concept of convergence permits multiple responsibilities to be accomplished on a single device, which efficiently conserves space and power. for example, as opposed to wearing separate devices – like a cell cellphone, digital camera, and virtual organizer – each era converges on a single tool or telephone.

We have given f(x)=1/(9+x)

f(x)=(1/9)*(1/(1-(-x/9))

f(x)=summation of (n=0 to infinity) [1/9*(-x/9)n]

=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]

f(x)=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]

Let an=(-1)n*(xn/9n+1)

using the Ratio Test

L=lim n-->infinity|an+1/anL=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]/[(-1)n*(xn/9n+1)]|

=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]*[9n+1/(-1)n*(xn)]|

=lim n-->infinity|(-1)*(x)/9)|

=|-x/9|<1

x/9<1 and x>9>-1

x<9  and x>-9

x is -9<x<9

for x=9 the series ,summation of (n=0 to infinity) [(-1)n*(9n/9n+1)] =summation of (n=0 to infinity) [(-1)n*(/9)]

=1/9*summation of (n=0 to infinity) [(-1)n]

By the geometric series this summation of (n=0 to infinity) [(-1)n] diverges

=1/9*diverges

the series diverges for x=9

for x=-9 the series ,summation of (n=0 to infinity) [(-1)n*(-9)n/9n+1)] =summation of (n=0 to infinity) [(-1)2n*(/9)]

=1/9*summation of (n=0 to infinity) [(-1)2n]

which is diverges

so the interval of convergence is (-9,9)

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Answer:

TRUE

Since , Angle ABD is congruent or equal to Angle CBD

we know that sides opposite to equal angles are also equal.

i.e AD and CD are opposite sides to angles ABD and CBD respectively.

So, AD = CD

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

[tex]\longrightarrow \sf{2(1 + b) = 260}[/tex]

[tex]\longrightarrow \sf{2(x+30+x) = 260}[/tex]

[tex]\longrightarrow \sf{ 2x+30 = \dfrac{260}{20} }[/tex]

[tex]\longrightarrow \sf{2x + 30 =130}[/tex]

[tex]\longrightarrow \sf{2x = 130 - 30}[/tex]

[tex]\longrightarrow \sf{2x = 100}[/tex]

[tex]\longrightarrow \sf{x= \dfrac{100}{2} }[/tex]

• [tex]\longrightarrow \sf{b= \underline{50cm}}[/tex]

[tex]\longrightarrow \sf{= x + 30}[/tex]

[tex]\longrightarrow \sf{= 50 + 30}[/tex]

• [tex]\longrightarrow \sf{ \underline{80cm}}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large\bm{Breadth= \: 50cm}[/tex]

[tex]\large\bm{Length= \: 80cm}[/tex]

The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

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The correct option is C no, both 3.61^2 and 3,62^2 are greater than 13.

To check this, we can just square both of the bounds that he found, and see if it makes sense.

Walter says hat:

3.61 < √13 < 3.62

Then we must have:

(3.61)^2 < 13 < (3.62)^2

The lower bound is 3.61, if we square it we get:

3.61*3.61 = (3 + 0.61)*(3 + 0.61) = 9 + 6*0.61 + 0.61*0.61 = 13.0321

Now, this is larger than 13, so the above inequality is false, which means that Walter is incorrect, because both 3.61 and 3.62 are larger than √13 , then the correct option is C.

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Answer:

c

Step-by-step explanation:

c

Answer:

Define the variables.

Step-by-step explanation:

Define the variables, then set up the equations, and finally solve the system using graphing, substitution, or elimination method.

To set up or model a linear equation to fit a real-world application, First, we have to determine the known amounts or quantities before defining the unknown quantity as a variable.

A linear equation is defined as an equation in which the highest power of the variable is always one.

To set up a model linear equation to fit real-world applications

In the first step determine known amounts or quantities.

Then, assign the unknown amount to a variable.

Now, find a method or approach to express the second unknown in terms of the first if there are many unknown quantities.

Create an equation that translates the words into mathematical functions.

Complete the equation. Make certain that the solution, including the system of measurement, can be expressed in words.

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The improper fraction is 25 / 6 hours

The mixed fraction is  [tex]4\frac{1}{6}[/tex] hours.

The time is written as a decimal. A decimal is a number that is made up of integers and non-integers. The integers are separated from the non-integers by a decimal point.

A mixed number is a fraction that is made up of a whole number and a proper fraction. A proper fraction is a fraction whose numerator is less than the denominator. An improper fraction is a fraction whose numerator is greater than the denominator.

In order to convert 4.6 hours to a mixed fraction, the proper fraction has to be determined. To determine this value, multiply 0.6 by the minutes in an hour

0.6 x 60 minutes = 10 minutes

The decimal becomes : [tex]4\frac{10}{60}[/tex] hours

[tex]4\frac{1}{6}[/tex] hours

To convert the mixed fraction to an improper fraction, multiply the denominator by the whole number and add the numerator, then divide by the denominator

The improper fraction is : 25 / 6 hours

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∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.

Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².

∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find

[tex]\sin(30^\circ) = \dfrac{h}{4\,\rm cm} \implies h= 2\,\rm cm[/tex]

where [tex]h[/tex] is the length of the altitude originating from vertex O, and so

[tex]\left(\dfrac b2\right)^2 + h^2 = (4\,\mathrm{cm})^2 \implies b = 4\sqrt3 \,\rm cm[/tex]

where [tex]b[/tex] is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².

So, the total area of the shaded region is

(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²

Answer:

a. 9m

Step-by-step explanation:

Pi = 3.14 = 22/7

formula :

Area of a Sector of a Circle = (central angle)/360 * πr² =

(central angle)/360 * πr² = Area of a Sector of a Circle

43/360 * Pi * r^2 = 30.39

r^2 = (30.39 * 360) / (Pi * 43)

r^2 = (30.39 * 360) / (22/7 * 43)

r = √ (30.39 * 360 * 7) / (22 * 43)

r = √76582.8/946

r = √80.9543340381

8.99746264444 which is roughly

9

The radius of the sector will be 9m. The correct option is A.

The distance between two places along a segment of a curve is known as the arc length. Curve rectification is the process of measuring the length of an irregular arc segment by simulating it as a network of connected line segments.

The radius will be calculated as below:-

Area of a Sector of a Circle = (central angle)/360 * πr² =

(Ф)/360 * πr² = Area of a Sector of a Circle

43/360 * Pi * r²= 30.39

r² = (30.39 * 360) / (Pi x 43)

r²= (30.39 x 360) / (22/7 x 43)

r = √ (30.39 x 360 x 7) / (22 x 43)

r = √76582.8/946

r = √80.9543340381

r = 9

Therefore, the radius of the sector will be 9m. The correct option is A.

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The expression which represents Daria's total cost is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05

Total cost = x + (5% of x)

= x + (0.05 × x)

= x + (0.05x)

Total cost = 1.05x

Therefore, the correct answer is; 1.05x because adding 5% to the cost of the shoes is the same as multiplying the cost by 1.05

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The average of the values from that average of 6 is 0

We have the numbers to be

0 2 4 10 14 and have an average of 6

To find their distances, we should substract each from the given average

We have;

6 - 0 =6

6 -2 = 4

6 -4 = 2

6 - 10 = -4

6 - 14 = -8

The average of this distances is

= pro

= [tex]\frac{0}{6}[/tex]

= 0

Thus, the average of the values from that average of 6 is 0

The complete question is

These values have an average of 6. What is the average distance of those values from that average of 6?

0 2 4 10 14

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The answer is 1.

Here, we need to know the trigonometric values of sin 30° and cos 60°, which are :

Hence, sin 30° and cos 60° :

Answer:

c

Step-by-step explanation:

if you take the triangle off of the left side and attach it to the left side then you would have a 6 by 4 rectangle that has an area of 24 units squared.

68 is the wrong number in the sequence 808, 408, 208,108, 68

A number system is defined as a system of writing to express numbers.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The given sequence is 808, 408, 208,108, 68

Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.

808, 408, 208,108, 68

Let us find the difference between the consecutive numbers

400, 200, 100, 40

As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.

Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68

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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Take note that there is a vertical asymptote at x = -4. This means that our function has the form:

▪ [tex]\longrightarrow \sf{F (x)=\dfrac{A}{x + 4} }[/tex]

[tex]\leadsto[/tex] By comparing it with the given options, the correct option is A.

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

◉ [tex] \bm{A. \: \: F(x)= \dfrac{1}{x + 4} }[/tex]

Answer:

s = 55 degrees

t  = 35 degrees

Step-by-step explanation:

I am not sure what the question is, but I am assuming that you are trying to find the value for s and t

S and 125 are supplemental.  That means that they add to 180.  180 - 125 = 55.

The two angles opposite of s together add up to 125.  I know that one angle is 90, so t is 125 -90 or 35

Answer:

That would be a model.

Step-by-step explanation:

Like climate scientists use a model of the Earth's processes to make predictions of climate change.

Based on the given parameters, the volume of the cylinder is 62.5/3 π cubic units

From the question, the given parameters are:

Shape = Sphere

Volume = 62.5/3π

Radius = 2.5

Height of cylinder = 0.208

The volume of a cylinder is calculated using the following formula:

V = 4/3πr^3

Substitute the known values in the above equation

V = 4/3 * π * (2.5)^3

Evaluate the exponent

V = 4/3 * π * 15.625

Evaluate the product of 15.625 and 4

V = 1/3 * π * 62.5

Evaluate the product of 62.5 and 1/3

V = 62.5/3 π

This means that the volume of the cylinder is 62.5/3 π cubic units

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Answer:

14 children

Step-by-step explanation:

Half the children like pets and a quarter of the children do not, so another quarter does not have preference. Let x = total number of children, and we would have this equation.

0.25x = 7

x = 28

Since we are asked to give the number of children who like pets, 28/2 = 14 is the answer.

Answer:

See attached image

Step-by-step explanation:

Every step holds except for step 5

In mathematics, it deals with numbers of operations according to the statements.

Here,
Step 1 is the result of the distribution of -5 while opening the parenthesis, So, Step 1 holds the distributive property.

Step 2, states adding like terms across each side, so combining as terms hold,

Step 3, Addition over the equal sign. So it also holds

Step 4, subtraction of 12 over the equal sign. So subtraction of the terms also holds.

Step 5, does not hold because the number 12 gets divided by 8 it is not an associative property.

Thus, Every step holds except for step 5.

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Answer:

sub -2 into 12x^3 - 15

h(-2) = 12(-2)^3 -15

        = -111

hope this helps!!!! If it's incorrect I'm sorry :(

Answer:

[tex]h(-2) =\boxed{ \bf -111}[/tex]

Step-by-step explanation:

The function [tex]h(x)[/tex] is defined as:

[tex]h(x) = 12x^3 - 15[/tex]

To calculate the value of [tex]h(-2)[/tex], we have to replace the [tex]x[/tex] in the definition of [tex]h(x)[/tex] with -2:

[tex]h(-2)[/tex] = [tex]12(-2)^3 - 15[/tex]

       ⇒ [tex]12(-8) -15[/tex]

       ⇒ -96 - 15

       ⇒ -111

Answer:

2.5 feet

Step-by-step explanation:

Since circumference is just pi(we're using 3.14 in this case) * diameter, which is our answer, we need to divide the circumference(which is 7.58) BY 3.14, which is pi. This leaves us with the diameter, which is 2.5. The unit is already feet, so we needn't do anything about that.

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

Suppose an infinity sequence defined by:

[tex]\sum_{k = 0}^{\infty} f(k)[/tex]

Then we have to calculate the following limit:

[tex]\lim_{k \rightarrow \infty} f(k)[/tex]

If the limit goes to infinity, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

[tex]f(k) = \frac{k^3}{k^4 + 10}[/tex]

Hence the limit is:

[tex]\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0[/tex]

Hence, the infinite sequence converges, as the limit does not go to infinity.

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The series diverges by the comparison test.

We have for large enough [tex]k[/tex],

[tex]\displaystyle \frac{k^3}{k^4+10} \approx \frac{k^3}{k^4} = \frac1k[/tex]

so that

[tex]\displaystyle \sum_{k=0}^\infty \frac{k^3}{k^4+10} = \frac1{10} + \sum_{k=1}^\infty \frac{k^3}{k^4+10} \approx \frac1{10} + \sum_{k=1}^\infty \frac1k[/tex]

and the latter sum is the divergent harmonic series.

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

According to the given information ,there still 4 pockets to check .

Then

the possibility that the money will be in the next pocket :

[tex]=\frac{1}{4}[/tex]

Answer: Answer above me is correct