What is the prime factorization of 252?; What is the prime factorization of 50?; How do you find the prime factorization on a calculator?; What are the prime numbers for 52?

Hence, [tex]x=16[/tex] when [tex]y=48[/tex].

What is the direct variation?

A direct variation, also called direct proportion is a relationship between two variables [tex]x[/tex] and [tex]y[/tex] that can be written as [tex]y = kx[/tex], [tex]k\neq 0[/tex].

Here given that,

The direct variation and [tex]y=75[/tex] when [tex]x=25[/tex],

As we know that,

[tex]y[/tex]α[tex]x[/tex]

[tex]y=kx[/tex]

[tex]75=k(25)\\\\k=\frac{75}{25}\\\\k=3[/tex]

So, when [tex]y=48[/tex]

[tex]y=kx\\\\48=3x\\\\x=\frac{48}{3}\\\\x=16[/tex]

Hence, [tex]x=16[/tex] when [tex]y=48[/tex].

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In linear equation, 11x  * f(x) + 7 * f(X)  is (fg)(x) in standard form .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                            Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

f(x) . g(x) = f(x) . ( 11x + 7 )

Multiplicative Distribution Law   = f(x) * 11x + f(x) * 7

                                 = 11 * f(x) *  x+ 7 * f(x)

                                 = 11x * f(X) + 7 * f(x)

                                = 11x  * f(x) + 7 * f(X)

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From the given information, we can that y = [tex]sin^{-1}x[/tex] function is represented in the graph.

The opposite of the sine function is the inverse sine function, commonly referred to as the arcsine function. Since the sine (or sine function) of an angle is equal to the ratio of the opposite side to the hypotenuse, the sine inverse of that ratio will provide the angle's measurement.

According to graph

Domain is [-1, 1]

Range = [tex][-\frac{\pi }{2} ,\frac{\pi }{2} ][/tex]

Set an interval to limit [tex][-\frac{\pi }{2} ,\frac{\pi }{2} ][/tex] the sine-scope function's so that it is one to one and not unlimited.

The limited function is one to one since it satisfies the horizontal line test.

[tex]Each range value (-1 to 1) is within the limited domain (-\frac{\pi }{2} \frac{\pi }{2})[/tex]

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Answer:

  See attached

Step-by-step explanation:

You want the graphed figure dilated by different scale factors around different center points.

To find the image of a dilated point, figure how far it is from the center of dilation, then multiply that distance by the scale factor. Plot the image point at that distance from the center of dilation in the same direction as the original point.

Dilation by a factor of 1/2 cuts all the distances in half. 2 grid squares become 1; 4 grid squares become 2.

Dilation by a factor of 2 multiplies all the distances by 2. 2 grid squares become 4; 4 grid squares become 8.

In the attached graph, the points are labeled with subscripts a, b, c according to the dilation they correspond to. Note that the center of dilation doesn't move, so Q and Q_a are the same point, and S and S_c are the same point.

Answer: 13 27 to 15 27 = 2 hours

15 27 to 16 00 = 33 mins

1600 to 16 12 = 12 mins

Total = 2hours + 33 mins + 12 mins = 2 hours 45 mins = 2.75 hours

Distance = Speed x time = 56 x 2.75 = 154 km

Answer: 154 km

Step-by-step explanation:

We can determine whether the rocket is ascending or descending by evaluating the derivative at that time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.

What is a derivative of a function?

The derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.

To determine whether the rocket is ascending or descending at a given time, we need to find the derivative of the function h(t) and determine whether it is positive or negative.

The derivative of h(t) is given by h'(t) = -t²+42t+43. This is the rate of change of the height of the rocket at any given time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.

At t = 1 second, h'(t) = -1 + 42 + 43 = 44. Since the derivative is positive at t = 1, we know that the rocket is ascending at this time.

Hence, we can determine whether the rocket is ascending or descending by evaluating the derivative at that time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.

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Step-by-step explanation:

???

(x + y) + 3

this is 3 more than the sum of x and y.

If the mean is 8.5 minutes and the variance is 9 minutes then the upper confidence limit is 9.3765  .

In the question ,

it is given that ,

the number of sales person in the random sample (n) = 45 ,

the mean = 8.5 minutes

the variance is = 9 minutes .

So , the standard deviation is = 3.

For the 95% confidence interval the level of significance (α) is 0.05 .

So , α/2 = 0.05/2 = 0.025 .

So , from Z table ;

the value of [tex]Z_{\frac{\alpha }{2} }[/tex] is = 1.96 .

The formula for the confidence interval is

= [ mean ±  [tex]Z_{\frac{\alpha }{2} }[/tex](SD/√n)]

Substituting the values from above ,

we get ,

= [8.5 - 1.96*0.4472 , 8.5 + 1.96*0.4472]

Simplifying further ,

we get ,

= [ 7.6235 , 9.3765 ]

Therefore , the upper limit of the 95% confidence interval is 9.3765  .

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In image.

In the Image is the anser and explanation.

Answer:

  (d)  P ≥ -40

Step-by-step explanation:

You want the solution to P/8 ≥ -5.

Multiply both sides of the inequality by 8.

  8(P/8) ≥ 8(-5)

  P ≥ -40

The addition property of equality states that if two values are equal to a third value, then they are also equal to each other. In this case, 4 is equal to 5+2, so 4 must also be equal to 2+5. However, Mark wrote the equation incorrectly, so the correct statement would be 4 = 5 + 2.

The addition property of equality is a key concept in mathematics, and it is important to understand and use it correctly. In this case, 4 is equal to 5+2, so the correct statement would be 4 = 5 + 2. This is because the addition property of equality states that if two values are equal to a third value, then they are also equal to each other. Therefore, Mark's statement of 4 = 2 + 5 was incorrect, and the correct statement was 4 = 5 + 2. Understanding and applying the addition property of equality is essential for success in math.

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Answer:

.35

Step-by-step explanation:

Just drop the zero     .350 is    350 thousandths  = 35 hundredths

Answer:

13/15×13/14

Step-by-step explanation:

13/15 are not independents and then 12/14 aren't independants

The expression P(A + B) = P(A) + P(B) - P(AB) is proved.

Proved is shown below.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, complements of sets.

We have,

Consider A = {1, 2, 3, 4, 5}

B = {2, 3, 4, 6, 7}

P (A + B) = P (A U B)

P (AB) = P (A ∩ B) (Common values}

P (AB) = {2, 3, 4}

P (A + B ) = {1, 2, 3, 4, 5, 6, 7}

Now,

P(A + B) = P(A) + P(B) - P(AB)

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5} + {2, 3, 4, 6, 7} - {2, 3, 4}

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 2, 3, 3, 4, 4,5, 6, 7} - {2, 3, 4}

{1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5, 6, 7}

Thus,

P{A + B) = P(A) + P(B) - P(AB) proved.

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Answer: The number line that you really want to move is the right side. Then, at that point, the right choice is C.

What is a number line?

A number line alludes to a straight line in science that has numbers organized at customary stretches or divides along its width. A number line is frequently shown on a level plane and can be delayed toward any path.

On the off chance that you are at - 15 on the number line and you needed to push toward the positive numbers

The number line that you need to move in the right side. Then the correct option is C.

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Step-by-step explanation:

The angle of inclination of the hill is 1.369 degrees .

Given :

a bulldozer exerts 1000 pounds of force to prevent a 5000 lb lboulder from rolling down a hil determine the angle of inclination of the hill .

Angle of inclination :

Inclination of a line is the angle between the line and the positive direction of x − axis. Value of this angle is between 0 and 180 degrees . It is measured in anti - clockwise direction from the positive direction of x − axis .

Angle of inclination cos x = 1000 / 5000

cos x = 100 / 500

= 10 / 50

= 1 / 5

x = cos^-1 ( 1/5 )

x = 1.369 degrees .

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After solving the given expression using exponents properties, the resultant answer is h²⁴.

Exponentiation is a mathematical process that involves the base b and the exponent or power n.

It is represented as bⁿ and is pronounced as "b to the n."

Positive, negative, zero, and rational exponents are the four different categories. Positive exponents indicate the number of times a base should be multiplied by itself.

So, we have:

(h¹²/h⁴)³

Now, solve as follows using properties:

(h¹²/h⁴)³

(h¹²)³/(h⁴)³

h³⁶/h¹²

h³⁶⁻¹²

h²⁴

Therefore, after solving the given expression using exponents properties, the resultant answer is h²⁴.

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Whole numbers range in size from 0 to infinity.

The collection of rational numbers is p/q, q ≠0.

Integers have no decimal portion and range from -infinity to infinity.

Given that,

We have to finding whole numbers, integers, and rational numbers is necessary.

the collection of whole numbers and their opposites,

The group of numbers that can be expressed as fractions is called ______.

The group of counting numbers and zero is known as ______.

We know that,

All of the numbers that are there can be defined or represented using a number system.

Complex numbers (a + ib)

Imaginary numbers

(0 + ib)

Real numbers                                                                

(a + i0)                                                                            

Rational numbers              

(perfect squares)      

Irrational numbers      

(non-perfects squares)

Fractions.  

(p/q, q ≠ 0)          

Integers

Negative integers is - ∞ to - 1

Positive integers is 1 to ∞

whole numbers is 0 to ∞

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Solving the equation x^2 + (y- 5)^2 = 30 for isolating x^2 is x^2 = - y^2 + 10y + 5. (Option D)

Equation is a mathematical statement that expresses values of two mathematical expressions as equal and is indicated by the sign =.

In order to isolate x^2 in the equation x^2 + (y- 5)^2 = 30, the remaining terms must be solved and simplified and collected on the other side.

Given equation is:

x^2 + (y- 5)^2 = 30

Expanding the (y- 5)^2 using formula for square of the difference between the two terms.

In general form: (a – b)^2 = a^2 – 2ab + b^2

Hence,

(y- 5)^2 = y^2 – 2(y)(5) + 5^2 = y^2 – 10y + 25

The original equation becomes,

x^2 + y^2 – 10y + 25 = 30

Subtract y^2 – 10y + 25 from both sides and simplifying:

x^2 + y^2 – 10y + 25 – (y^2 – 10y + 25) = 30 – (y^2 – 10y + 25)

x^2 = 30 – y^2 + 10y - 25

x^2 = - y^2 + 10y + 5

Note: The question is incomplete as it is missing options which are A. x^2 = y^2 + 10y+5 B. x^2 =-y^2 + 10y+25 C. x^2 = 30 - y^2 D. x^2 = - y^2 + 10y+5

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The Method of Cylindrical Shells will be used to assist.

As previously, we construct a region R that is enclosed on the top by the graph of the function y = f (x), on the bottom by the x axis, and on the left and right by the lines x = a and x = b, respectively (a).

As seen in Figure 1, we then rotate this region around the y-axis (b). Be aware that this is distinct from what we have previously done..

Previously, areas that were described in terms of x-functions were centered on the x-axis or a line that ran parallel to it.

Since the shell is a cylinder, its volume equals the cross-sectional area times the cylinder's height. The cross-sections are annuli, which are essentially circles with holes in the middle and are formed like rings.

According to our question-

V= 2π ∫025/2 x [ 5 - √(2x) ] d x = 625π/ 4 cubic units

USING THE WASHER METHOD

V = ∫05 π (1/4) y4 d y = 625π/ 4 cubic units

Hence, The Method of Cylindrical Shells will be used to assist.

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The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.

Given that,

36 local middle school kids were chosen at random to take part in a taste test to choose a new menu item for a cafeteria. The Cajun potato barrels or the macaroni and cheese were the options offered to each pupil. 20 pupils chose the macaroni and cheese from the sampling, while 16 selected the Cajun potato barrels. On a scale from 1 (very dislike) to 9 (very much like), each student was asked to rank the object they selected (extremely like).

We have to find which of the following keeps this study from being an experiment with a sound design.

Each student was given the option of choosing either the macaroni and cheese or the Cajun potato barrels. Because the students' treatments were not distributed at random, those who preferred their cuisine chose it and gave it high marks. As a result, the study has selection bias.

Therefore, The treatments (new menu item) were not randomly assigned to the students when 36 local middle school kids were chosen at random to take part.

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If John invests $200 into an account with a 2.7% interest rate that is compounded semiannually, after 10 years he will have a future value of $261.52.

The future value is the compounded present value at an interest rate into the future.

The future value can be worked out using the FV table or formula.  We can also use an online finance calculator to find the future value of present-day investment.

N (# of periods) = 20 semiannual periods (10 years x 2)

I/Y (Interest per year) = 2.7%

PV (Present Value) = $200

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $261.52

Total Interest = $61.52

Thus, if John invests the present value of $200 into the account, after 10 years, his investment would become $261.52.

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The dimensions of the rectangle of maximum area are the length of 12√3 units and width of 4 units

Given that the ellipse has the equation: x²/144 + y²/16 = 1

Make x the subject:

x²/144 + y²/16 = 1

(x²+9y²)/144 = 1

x² + 9y² =144

x² = 144-9y²

x = √(144-9y²)

The  rectangle vertices is at (x,y), (-x,y), (x,-y), (-x,-y). Thus, the rectangle has a length and width of 2x and 2y respectively

The area of a rectangle inscribed inside an ellipse is given by:

Area (A) = 4xy

A = 4(√(144-9y²))y

A = 4y√(144-9y²)

A = 4√(144y²-9y⁴)

The maximum area of the rectangle is at dA/dy = 0  

dA/dy = 4[144-18³y/ (√(144y²-9y⁴))]

4[144-18y³/ (√(144y²-9y⁴))] = 0

144-18y³= 0

18y³ = 144

y³ = 144/18

y³ = 8

y = ∛8

y = 2

x = √(144-9y²)

x = √(144 - 9(2)²)

x = √108

x = 6√3

Thus, the dimensions are the length = 2x = 2×(6√3) = 12√3 units, the width = 2y = 2×2 = 4 units

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[tex]2^{x}[/tex] + [tex]\frac{2}{3}[/tex],  [tex]2^{x}[/tex], [tex]2^{x}+2[/tex], [tex]2^{x}-3[/tex] are examples of exponential parent function.So all of the given options are true.

Parent function:  The most basic function in a family of functions is the parent function. A family of functions is a collection of functions that have similar graph shapes because they all have the same greatest degree.

Four graphs that illustrate the U-shaped graph, or parabola, are displayed in the graph above. We can classify them as belonging to the same family of functions since they all have the same highest degree of two and the same form.

Exponential parent function: Algebraic expressions appear in the exponent of exponential functions. The formula for its parent function is y = [tex]b^{x}[/tex], where b can be any non-zero constant.

For above definitions we can conclude that all options given to us are exponential parent function.

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If x and y have a common prime factor then y and x also have a common prime factor,so x and y are symmetric.

If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.

If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.

x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R

Step-by-step explanation:

Part a:  x and y have a common prime factor

If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.

Reflexive: x and y are not reflexive since {1,1}∉ R(1 has no prime factor)

Symmetric: If x and y have a common prime factor then y and x also have a common prime factor , so x and y are symmetric.

Irreflexive: refer point A(above)

Transitive: x and y are not transitive since {2,9}∉ R(has no common prime factor)

Anti symmetric: x and y are not anti symmetric [Refer point B(above)]

If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.

b) x - y is a multiple of 3

If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.

Symmetric: If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric.

Antisymmetric x-y is not anti symmetric (refer above)

Irreflexive refer point D

Reflexive : x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.

Transitive: if x-y,y-z is multiples of 3 then x-z is also multiples of 3.so it is also transitive.

(c) x and y are both prime

If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.

Transitive: If x,y and y,z are primes then x,z are also primes.So it is transitive.

irreflexive Refer It is not reflexive since {4,4}∉ R(4 is not a prime)

Symmetric:  If x,y are primes then y,x are also primes.So it is symmetric..

Reflexive:It is not reflexive since {4,4}∉ R(4 is not a prime)

Antisymmetric: Refer point C

(d) x and y are twin primes (they are primes and their distance is 2)

x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R

Symmetric: x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R

Irreflexive Refer point D

Antisymmetric Refer point A

Reflexive:  It is not reflexive since {4,4}∉ R

Transitive: It is not transitive because (3,5)∈R and (5,3)∈R but (3,7)∉ R

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Answer: She could make those two changes to save money for her trip. Also, she could save a little bit of her salary to have enough money to go.

Step-by-step explanation:

This is just a guess but PLEASE GIVE ME BRAINLIEST if you're pleased with my answer.

63:

2x3=6

3x5=15

6+15=21

x 3 =…

63

Step-by-step explanation:

Answer:

4 yellow tulips and 8 white lilies.

Step-by-step explanation:

Ratio is 1:2:3 for yellow tulips, white lilies and the total.

Set up a proportion

[tex]\frac{yellow}{total}[/tex] = [tex]\frac{yellow}{total}[/tex]  Three of these numbers you know, Solve for the unknown

[tex]\frac{1}{3}[/tex] = [tex]\frac{x}{12}[/tex]  Cross multiply and solve for x

3x = 12  Divide both sides by 3

x = 4  This is the number of yellow tulips

Set up another proportion:

[tex]\frac{white lilies}{total}[/tex] = [tex]\frac{white lilies}{todal}[/tex]

[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{12}[/tex]  I can see that 3 x 4 = 12 so I will multiply the top number to 2 by 4 to get 8.