Two lines intersect at the point (1, 3).
The y-intercepts of the lines are 1 and 2.
What are the equations of the lines?

The volume of cylinders [tex]x^2 + y^2 = 4r^2[/tex] and [tex]y^2 + z^2 = 4r^2[/tex] is 88[tex]r^3[/tex]/3.

The volume of cylinders can be calculated using integrals from the top curve subtract the bottom curve. For expression above we can convert to find the dimensions of cylinders using Fubini's Theorem. So,

x^2 + y^2 = 4r^2 to x^2 = 4r^2 - y^2

y^2 + z^2 = 4r^2 to z^2 = 4r^2 - y^2

Thus, the volume of the given solid is,

v = [tex]\int r-r\int\sqrt{4r^2-y^2}-\sqrt{4r^2-y^2}\times 2\sqrt{4r^2-y^2} dx dy[/tex]

= [tex]2\int r-r(x\sqrt{4r^2-y^2})(\sqrt{4r^2-y^2})-\sqrt{4r^2-y^2}dy[/tex]

= [tex]2\int r - r[(4r^2-y^2)+(4r^2-y^2)]dy[/tex]

= [tex]2\int r - r[2(4r^2-y^2)]dy[/tex]

= [tex]4\int r - r(4r^2-y^2)dy[/tex]

= [tex]4(4r^2y-y^3/3)r-r[/tex]

= [tex]4(4r^2(r+r)-(r^3+r^3)/3)[/tex]

= [tex]4((4r^2)(2r)-2r^3/3)[/tex]

= [tex]8(4r^3-r^3/3)[/tex]

= [tex](8)(12r^3-r^3)/3[/tex]

= 88[tex]r^3[/tex]/3

Thus, the volume of cylinders is (88r^3)/3.

You question is incomplete, but most probably your full question was

find the volume of the given solid. bounded by the cylinders [tex]x^2 + y^2 = 4r^2[/tex], [tex]y^2 + z^2 = 4r^2[/tex]

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The closest volume of ball would be 321.4

What is Volume of sphere?

The volume of a sphere is a measure of the space occupied by the sphere, and can be calculated by the formula V = 4/3πr³, where r is the radius of the sphere. In other words, the volume can be found by multiplying 4/3 by π (3.14) by the cube of the radius of the sphere. For example, if the radius is 5, the volume of the sphere would be 4/3π x 5³, or approximately 523.60.

Solution:

Given that:

diameter = 8.5 in

hence, radius would be 4.25 in

                    [tex]Volume\ of \ ball = \frac{4}{3} \pi r^{3} \\\\Volume\ of \ ball = \frac{4}{3} \pi (4.25)^{3}\\\\Volume\ of \ ball = 321.4[/tex]

Hence, The closest volume of ball would be 321.4

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Answer:

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

Find prime factors of 1265.

We see it is divisible by 5 since ends with 5:

253 is not divisible by 3 or 9 since the sum of digits is not divisible by 3 or 9. It is not divisible by 7 (since 25 - 3*2 = 19 is not divisible by 7) but divisible by 11, since the sum of digits in odd places is same as the digit in the even place (recall divisibility by 11):

23 is a prime number so no more factors.

Hence the prime factorization of 1265 is:

Using 1 balls and bins, n balls are thrown into m bins; m and n are positive numbers. the probability of any given bin containing one ball is n/m n * (1 - (1 - 1/m)^n) / m^2

Given that n is the number of balls and m is the number of bins, the probability of any given bin containing one ball is n/m. Therefore, the variance of x is equal to the variance of a binomial random variable with n trials and probability of success p = n/m.

By the formula for the variance of a binomial random variable, the variance of x is equal to n * (1 - (1 - 1/m)^n) / m^2.

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Answer:

(18, -15)

Step-by-step explanation:

The vector AB is defined by its starting and endpoints. Usually, B would be at the end, but in this case A is. Since we are given its midpoint, that is, the point equidistant from both the coordinates A and B, we can find coordinate B by simply calculating the distance between A and the midpoint and reapplying this distance to the midpoint.

1. Finding the distance between the midpoint and A:

The distance between two coordinates, from what I can recall, is simply the final coordinate value minus the initial coordinate value, following the form (x2-x1, y2-y1). We know that A comes after the midpoint, because it is the endpoint (so it will be the final coordinate value). Applying this to the context of the question, (2-10, 13+1) = (-8,14).

2. Finding B using the distance between midpoint and A:

B will be the initial coordinate value because it comes before the midpoint. Therefore, giving B the values (x,y):   (10-x, -1-y) = (-8, 14). Separating into two equations (respective to each axis):

10-x=-8

-x=-18

x=18

-1-y=14

-y=15

y=-15

Therefore, the coordinate of B is (18, -15).

The linear equation on the table is the one in option D.

y = 25*x + 45

A general linear function is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know two points on the line, (x₁, y₁) and (x₂, y₂), the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Using the first two points, (0, 45) and (1, 70) we can get the slope:

a = (70 - 45)/(1 - 0) = 25

And because of the point (0, 45) we know that the y-intercept is b = 45, then the linear equation is:

y = 25*x + 45

So the correct option is D.

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After a transformation of each coordinate point, the correct code are as follows;

A. (-4, -2).

I. (0, 1).

C. (5, 0).

E. (0, 0).

In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

Next, we would apply a translation to each of the points as follows;

Point 1 (1, 2) →  (x - 5, y - 4) = (1 - 5, 2 - 4) = Point 1' (-4, -2).

Point 2 (2, 4) →  (x - 2, y - 3) = (2 - 2, 4 - 3) = Point 2' (0, 1).

Point 3 (4, 4) →  (x + 1, y - 4) = (4 + 1, 4 - 4) = Point 3' (5, 0).

Point 4 (3, 2) →  (x - 3, y - 2) = (3 - 3, 2 - 2) = Point 4' (0, 0).

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The fraction of the people surveyed that said that they buy neither product p nor product q is 1/6.

It is given to us that -

A survey is conducted with the number of people buying products p and q

We have to find out the fraction of the people surveyed said that they buy neither product p nor product q.

From the given information, the total number of products can be represented as -

[Total products bought] = [p products bought] + [q products bought] - [both p and q bought] + [neither p and q bought] ---- (1)

We have to find out -

[neither p and q bought]/[Total products bought]

Let us assume that the total products bought = 6

It is known that 1/3 of the people surveyed said that they buy product p but not product q.

=> [p products bought] - [both p and q bought] = 1/3 * 6

=> [p products bought] - [both p and q bought] = 2 ------ (2)

From equation (1), we can say that -

[Total products bought] = [p products bought] + [q products bought] - [both p and q bought] + [neither p and q bought]

=> 6 = ([p products bought] - [both p and q bought]) + [q products bought] + [neither p and q bought]

From equation (2), we can write the above equation as -

=> 6 = 2 + [q products bought] + [neither p and q bought]

=> [q products bought] + [neither p and q bought] = 4  ------ (3)

Again, it is also known that 1/2 of the people surveyed said that they buy product q.

=> [q products bought] = 1/2 *6

=> [q products bought] = 3 ---- (4)

From equation (3) and equation (4), we can say that -

[q products bought] + [neither p and q bought] = 4

=> 3 + [neither p and q bought] = 4

=> [neither p and q bought] = 1  ------ (5)

From equation (5) and the total number of products bought, we can say that -

[neither p and q bought]/[Total products bought] = 1/6

(Since, the total number of products bought = 6)

Therefore, the fraction of the people surveyed that said that they buy neither product p nor product q is 1/6.

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Answer:

She has carved 4 times as many bird figures

The z-score of the blood pressure readings are:

a = 1.4

b = 0.6

c = 1.2

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Mean = 121

Standard deviation = 15

The z-score is given as,

z = (x - mean) / Standard deviation

x = 142

z = (142 - 121) / 15

z = 21/15

z = 7/5

z = 1.4

x = 130

z = (130 - 121) / 15

z = 9/15

z = 3/5

z = 0.6

x = 103

z = (103 - 121) / 15

z = 18/15

z = 6/5

z = 1.2

Thus,

The readings are:

a = 1.4

b = 0.6

c = 1.2

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After solving the two digit number is 45.

In the given question,

The 2 digit number which become 5 by 6th of itself when it digit are revered.

The difference in the digit of the number being 1, then we have to find the two digit number.

Let the two digit number = 10y+x

When we reversed the number then the number is 10x+y

As given that;

10y+x = 5/6(10x+y)

Multiply by 6 on both side, we get

60y+6x = 50x+5y

Subtract 5y on both side, we get

55y+6x = 50x

Subtract 50x on both side, we get

55y-44x = 0

Divide by 11 on both side, we get

5y-4x = 0

4x-5y = 0......................(1)

It is given that the difference between the number is 1.

x-y = 1..................(2)

Multiply by 4 in equation 2

4x-4y = 4.........................(3)

Now subtract equation 3 and 1, we get

y = 4

Now putting the value of y in equation 2

x-4 = 1

Add 4 on both side, we get

x = 5

Since the number is 10y+x. So

10y+x = 10(4)+5

10y+x = 45

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Answer:

A. 276 miles apart

Step-by-step explanation:

We have the information that if two cities are 1 inch apart then the distance between them is 24 miles.

If it is 11.5 inches apart, then we should multiply the 24 miles per inch by 11.5

24 miles / 1 inch

(24 miles / 1 inch) * 11.5 inches

Inches cancel so you are left with

24 * 11.5 = 276 miles

Inequality can be used to find the domain of f(x)  is  [tex]$\quad x \geq 20$[/tex]

Interval Notation: [tex]$[20, \infty)$[/tex]

What is Domain definition?

The domain of a function is the set of input or argument values for which the function is real and defined.

Find non - negative values for radicals: [tex]$x \geq 20$[/tex]

The function domain

[tex]$$x \geq 20$$[/tex]

Range of[tex]$\sqrt{\frac{1}{2} x-10}+3:\left[\begin{array}{cc}\text { Solution: } & f(x) \geq 3 \\ \text { Interval Notation: } & {[3, \infty)}\end{array}\right]$[/tex]

Function range definition

The set of values of the dependent variable for which a function is defined

The range of an radical function of the form [tex]$c \sqrt{a x+b}+k$[/tex] is [tex]$f(x) \geq k$[/tex][tex]$k=3$[/tex]

[tex]$f(x) \geq 3$[/tex]

Axis interception points of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None

x - axis interception points of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None

y - axis interception point of [tex]$\sqrt{\frac{1}{2} x-10}+3$[/tex] : None

None

Extreme Points of [tex]$\sqrt{\frac{1}{2} x-10}+3: \quad$[/tex]Minimum (20,3)

First Derivative Test definition

Suppose that [tex]$x=c$[/tex] is a critical point of f(x) then, If [tex]$f^{\prime}(x) > 0$[/tex] to the left of [tex]$x=c$[/tex]and [tex]$f^{\prime}(x) < 0$[/tex] to the right of x=c then x=c is a local maximum. If [tex]$f^{\prime}(x) < 0$[/tex] to the left of [tex]$x=c$[/tex] and [tex]$f^{\prime}(x) > 0$[/tex] to the right of [tex]$x=c$[/tex] then [tex]$x=c$[/tex] is a local minimum. If [tex]$f^{\prime}(x)$[/tex] is the same sign on both sides of [tex]$x=c$[/tex] then [tex]$x=c$[/tex] is neither a local maximum nor a local minimum.

[tex]$$f^{\prime}(x)=\frac{1}{2 \sqrt{2} \sqrt{x-20}}$$[/tex]

Find intervals: Increasing:20 [tex]$ < x < \infty$[/tex]

Plug [tex]$x=20$[/tex] into [tex]$\sqrt{\frac{1}{2} x-10}+3: \quad 3$[/tex]

Minimum (20,3)

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Answer:

7

Step-by-step explanation:

4+3=7

7-4=3

7-3=4

By using the property of division, it can be calculated that M = -21 divided by 0 is not possible

What is division?

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

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

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

Anything divided by 0 is not possible.

M = -21 divided by 0 is not possible

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The equilibrium price is; $12

The quantity for the two equations is; 400

The equilibrium price formula is based on the demand and supply quantities; you will set quantity demanded (Qd) equal to quantity supplied.

The equilibrium price definition above is one that tells us that there is a price point that meets the needs of both supply and demand. In order to understand when those needs are met, we need to know how to find equilibrium price.

We are given;

Quantity supplied; S(p) = -200 + 50p

Quantity demanded; D(p) = 1060 - 55p

Thus, equilibrium price is p when;

S(p) = D(p)

-200 + 50p = 1060 - 55p

1060 + 200 = 55p + 50p

1260 = 105p

p = 1260/105

p = $12

S(p) = -200 + 50(12)

S(p) = 400

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Answer: This means that the range of values of k is k ∈ [-1/3, 1/3].

Step-by-step explanation: The quadratic equation (x+2)² +3k-1=0 can be written as (x+2)² = 1-3k. For the equation to have two real and distinct roots, the expression under the square root must be nonnegative. Therefore, we have the inequality 1-3k ≥ 0. Solving this inequality gives us -1/3 ≤ k ≤ 1/3. This means that the range of values of k is k ∈ [-1/3, 1/3].

Answer:

the angle would be 40 degrees

Step-by-step explanation:

using the alternative angle property the angle is 40

Answer: x = 14

Step-by-step explanation:

3x+9x-5=163

12x-5=163

12x=163+5

12x=168

x=14

The probability that exactly two of thirteen fireworks are blue ones out of total 4 selections is 63/143.

The stated data;

You want 2 of the 7 items she selects to be blue, leaving 2 to be red.

Selecting 2 blue out of 7 blues is ⁷C₂ = 7!/(5!.2!)  =  21

Selecting 2 red out of 6 red = ⁶C₂ = 6!/(4!2!) = 15

Selecting total of 4 out of 13 ; ¹³C₄ = 13! / (9!.4!) = 715

Thus, probability that exactly two of them are blue ones;

P(2 blue) = 21 x 15 / 715

P(2 blue) = 63/143

Thus, probability that exactly two of them are blue ones out of total 4 selections is 63/143.

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The linear function models the given situation will be equal to f(x) = $3600 - $400(x).

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Original price of Machine = $3600

Price lost by the machine each year = $400

Then, the equation will be,

f(x) = $3600 - $400(x)

Here, x represents the number of years.

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Answer:

f(x) = −400x + 3600

A lurking variable is an explanatory variable that was not examined in a study but has an effect on the value of the study's response variable.

A concealed variable affects both the dependent and independent variables, resulting in an incorrect connection. Confounding is a causal concept that cannot be expressed using correlations or linkages. Confounders have a significant quantitative role in explaining why correlation does not imply causation.

In the case of risk assessments assessing the degree and form of threat to human health, it is critical to account for confounding in order to isolate the impact of a specific hazard such as a food additive, pesticide, or new drug. It is difficult to recruit and screen volunteers with the same background (age, diet, education, geography, etc.) for prospective studies, and historical investigations can have similar variability.

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16π/5 is the area enclosed by the curve r= 8sin(5θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex]

where a and b is the boundary at which r=0

so after equation r=0

8sin(5θ) =0

=> sin(5θ) =0

=> 5θ = 0,π

=> θ = 0, π/5

so a=0 , b= π/5

now  

   A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex]    ------(i)

 so   [tex]r^2[/tex] = (8sin(5θ))^2

=> 64 [tex]sin^2[/tex] ( 5θ )

ans we know that

cos(2α) = 1 -  2[tex]sin^2[/tex] α

so   [tex]r^2[/tex]  =32 (1- cos(10θ) )

putting the value of r in the equation (i) we get :-

A = [tex]\int\limits^a_b {\frac{1}{2} *32(1-cos(10\alpha ) } \, d\alpha[/tex]

=> 16 * [tex]\int\limits^a_b {(1-cos(10\alpha ) } \, d\alpha[/tex]

here a=0 and b=π/5

after putting the value and solving the integral

A = 16π/5

so A is the area enclosed by r=8sin(5θ) is 16π/5

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At the rate of 135 containers per minute, it will take approximately 7.4 minutes to fill 1000 containers.

To determine the time it takes to fill 1000 containers, we need to divide the number of containers by the rate at which they are filled. In this case, we have 1000 containers and a filling rate of 135 containers per minute, so we divide 1000 by 135 to find the time it takes to fill the containers:

1000 containers / 135 containers/minute = 7.40740740740741 minutes

Since a minute cannot be divided into fractions, we must round the result to the nearest whole number. This means that it will take approximately 7.4 minutes to fill 1000 containers at a rate of 135 containers per minute.

The machine will take 7.41 minutes (approx) to fill 1000 Containers.

Time taken to fill 135 Containers= 1 minute ...............(Given)

Time taken to fill 1 Container= 1/135 minute

Time taken to fill 1000 Containers = 1000 × 1/135 minutes

                                                         = 1000/135 minutes

                                                         = 200/27 minutes

                                                         ≈ 7.41 minutes​.

Thus, The machine will take 7.41 minutes (approx) to fill 1000 Containers.

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Answer:

x = [tex]\frac{15-4y}{3}[/tex]

Step-by-step explanation:

3x + 4y = 15 ( subtract 4y from both sides )

3x = 15 - 4y ( isolate x by dividing both sides by 3 )

x = [tex]\frac{15-4y}{3}[/tex]

Answer:

d = 21

Step-by-step explanation:

Given equation:

[tex]5^d \div 5^3=5^{18}[/tex]

Multiply both sides by 5³:

[tex]\implies 5^d=5^{18} \times 5^3[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 5^d=5^{18+3}[/tex]

[tex]\implies 5^d=5^{21}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies d=21[/tex]

Answer:

Step-by-step explanation:

This is a trick question,  about the red marks again.   those marks are important b/c they tell you that the lengths are the same, so that the angles MUST also be the same.  That is  ,  D and E are equal

so set up your equations with that info

180 = 84 +2p

now use your algebra skillz to solve

180-84 / 2 = p

96/2 = p

48 = p

see??

Answer:15x3 /=divide 5 = 9

Step-by-step explanation:

because if you do 15x3 it is 45 then you divide it by 5 and get 9 as your answer!