121 as a product of primes

Answer:

4x+5x+6x and 15x

is the only answer

Step-by-step explanation:

For the minimum value, the first derivative of function is equate to zero and value of second derivative is posiive.

Determine the first derivative of cost function.

For maximum and minimu value,

Determie the second derivative of the cost function.

The second derivative of cost function is positive for all value of x. So x = 90 machines corresponds to the minimum value of function.

Answer: 90 machines

Answer:

P(Red) = 26/52, P(Black) = 26/51

Step-by-step explanation:

There are 26 red cards and 26 black cards in a standard deck of 52 cards.

This means the probability of picking a red card from the deck is 26/52.

Now, since we are taking out the red card after drawing from the deck, we only have 51 cards. Therefore, the probability of picking a black card from the deck is 26/51.

5 "Always." Consecutive angles of a rectangle are always congruent.

6 "Never." A parallelogram is not always a square.

7 "Sometimes." In a rhombus, the diagonals are always perpendicular bisectors of each other, but they are not always congruent.

8 "Always." A rectangle has congruent sides, but not necessarily all four sides.

9 Given: ABCD is a parallelogram

To prove: AABC = ACDA

Proof:

AB || DC (definition of parallelogram)

AD || BC (definition of parallelogram)

∠ABC = ∠CDA (alternate interior angles)

AC = AC (reflexive property)

∠BCA = ∠DAC (alternate interior angles)

Therefore, AABC = ACDA (ASA congruence theorem)

10 Given: TRAP is an isosceles trapezoid

To prove: AAPR ARTA

TR = AP (definition of isosceles trapezoid)

∠APT = ∠ATR (alternate interior angles)

∠PAR = ∠RTA (alternate interior angles)

∠PAR = ∠APT (angles at a point)

Therefore, AAPR ARTA (AA congruence theorem)

Consecutive angles of a rectangle are always congruent. This is a property of rectangles that is true for every rectangle.

A square is a specific type of parallelogram that has all four sides congruent and all four angles right angles.

A rectangle has two pairs of opposite sides that are congruent, but the adjacent sides may have different lengths. This is a defining characteristic of rectangles, and it is always true for every rectangle.

The ASA congruence theorem states that two triangles are congruent if two angles and the included side of one triangle are congruent to the two angles and the included side of the other triangle. In this case, ∠ABC and ∠CDA are congruent by (3), AC is congruent by (4), and ∠BCA and ∠DAC are congruent by (5). Therefore, AABC = ACDA by the ASA congruence theorem.

The AA congruence theorem states that two triangles are congruent if two angles of one triangle are congruent to two angles of the other triangle, and the side between those angles is congruent in both triangles

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Answer:

Step-by-step explanation:

Degree means highest exponent.  got it?

Answer:

Step-by-step explanation:

Answer:

We need to add 400 ml of pure water to obtain the solution at 55%

Step-by-step explanation:

Concentration

The concentration of a solution measures the amount of solute that has been dissolved in a given amount of solution. The question states the alcohol is the solute and water is the solvent to produce the mix or solution.

The concentration can be calculated with the formula:

\(\displaystyle c=\frac{solute}{solute+solvent}*100\%\)

Originally, the mixture was 95% concentrated.

Substituting in the formula:

\(\displaystyle 95\%=\frac{solute}{solute+solvent}*100\%\)

We know there were 550 ml of solution (solute+solvent), thus

\(solution*0.95=solute=522.5\ ml\)

Now we know there were 522.5 ml of alcohol.

We now need to add x ml of water to have a 55% concentrated solution. Recall that water is solvent, the solute keeps its original value, thus:

\(\displaystyle 55\%=\frac{solute}{550+x}*100\%\)

Operating:

\(0.55(550+x)=522.5\)

Dividing by 0.55

\(550+x=950\)

Thus \(x=950-550=400\)

We need to add 400 ml of pure water to obtain the solution at 55%

Answer:

Step-by-step explanation:

Given the number of liver transplants performed in a particular country in year x approximated by f (x) = -239.7+ 2390lnx where x≥5. If x = 5 corresponds to year 1995. x will be equivalent to 23 in the year 2013.

a) Number of transplant in 2013 can be gotten by substituting x = 18 into the equation above.

f (x) = -239.7+ 2390lnx

f (23) = -239.7+ 2390ln 23

f (23) = -239.7+ 2390(3.14)

f(23) = 7264.9

The number of liver transplant in 2013 is approximately 7265

b) If f (x) = -239.7+ 2390lnx

f'(x) = 2390 * 1/x

f'(23) = 2390/23

f'(23) = 103.913

Matching the name of the sampling method:

1. Situations surveying every 3rd driver coming through a tollbooth: Systematic

2. Separating all students by grade level, and selecting 10 students from each grade:  Stratified

3. Number every name on a list and use a random number generator to select the first 50 numbers: Simple Random

4. Asking people on the street:  Convenience

5. Randomly select two tables in the cafeteria and survey all the people at those two tables: Cluster

With basic random sampling, we choose components of the population at random. Simple random sampling involves numbering each name in a list and choosing the top 50 numbers using a random number generator.

In cluster sampling, we divide the population into various clusters that are suitable for representing the population. We then randomly select the clusters, and sample each of their components.

Cluster sampling is the practice of choosing two tables at random and surveying everyone at those tables. Researchers sample people based on convenience when they use convenience sampling.

Convenient sampling includes things like asking random strangers on the street. Sampling in systematic sampling is done using a system (rule).

The third driver who passes through a toll booth is surveyed as an example of systematic sampling. According to a trait or condition, such as grade level, the population is divided in stratified sampling.

Hence, stratified sampling would include dividing all students into grade levels and choosing 10 from each grade.

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The complete question is:

Match the name of the sampling method descriptions given.

1. Situations surveying every 3rd driver coming through a tollbooth

2. Separating all students by grade level, and selecting 10 students from each grade

3. Number every name on a list and use a random number generator to select the first 50 numbers

4. Asking people on the street

5. Randomly select two tables in the cafeteria and survey all the people at those two tables

Sampling Method

a. Simple Random

b. Cluster C

c. Convenience

d. Systematic

e. Stratified

24. 1st one

Step-by-step explanation:

the X cancals out the x leaving the z so it is the 1st one

Answer:

24. \(-\frac{3}{2} z\)

25. 6

Step-by-step explanation:

For number 24:

To simplify this down, we can break it up into this:

\(\frac{3}{-2} \cdot \frac{x}{x} \cdot \frac{z}{1}\)

3 divided by -2 is \(-\frac{3}{2}\), x over x is just 1, and z over 1 is z.

So \(-\frac{3}{2} z\).

For number 25:

If we know the value of y and z we can just substitute inside the equation.

\(\frac{-18}{-3}\)

A negative divided by a negative is the same as a positive over a positive.

\(18\div3=6\)

Hope this helped!

Answer:

0.07

Step-by-step explanation:

The total bill amount including sales tax of 6.5% will be $74.54.

To calculate the total bill amount including sales tax, we need to add the tax amount to the original cost.

First, we need to calculate the amount of sales tax on the service plan:

Sales tax amount = 6.5% of $69.99

Sales tax amount = 0.065 x $69.99

Sales tax amount = $4.55 (rounded to two decimal places)

Next, we add the sales tax amount to the original cost of the service plan:

Total bill amount = $69.99 + $4.55

Total bill amount = $74.54

Therefore, the total bill amount including sales tax will be $74.54.

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The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

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Answer:

Larger number = 32

Step-by-step explanation:

Smaller number = x

Larger number = y

y - x = 8    -----------(I)

3y = 4x  ---------------(II)

3y/4 = x

Plug in x = 3y/4 in equation (I)

\(y - \frac{3}{4}y = 8\\\\\frac{4}{4}y - \frac{3}{4}y = 8\\\\\frac{1}{4}y = 8\\\)

 y = 8*4

  y = 32

Plug in y = 32 in equation (II)

3y = 4x

3*32 = 4x

4x = 3*32

x = \(\frac{3*32}{4}\)

x = 3 *8

x = 24

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

Area = 2826 cm^2

Circumference = 188.4 cm

Step-by-step explanation:

Area of a circle = πr^2 3.14 X (30^2) = 2826

Circumference = 2πr or πd 2 X 3.14 X 30 = 188.4

\( \mathbb\red{ANSWER} \)

Area Formula :

\( \green{\pi {r}^{2} }\)

\( \pink{ \pi \times {30cm}^{2} }\)

\( \orange{ 3.14 \times 900 {cm}^{2} }\)

\( \red{2826 {cm}^{2} }\)

Circumference Formula:

\( \green{\pi \times d}\)

\( \pink{3.14 \times 60cm}\)

\( \orange{188.4cm}\)

\( \mathbb\blue{HOPE \:IT\: HELPS} \)

The volume of the pyramid is determined as 433.33 mm³.

The volume of the right square pyramid is calculated by applying the following formula.

V = ¹/₃a²h

where;

The volume of the pyramid is calculated as follows;

V = ¹/₃ (10 mm)² x ( 13 mm )

V = 433.33 mm³

Thus, the volume of the pyramid is calculated from the formula stated.

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Answer: 2nd from the botttom

Step-by-step explanation:

Solving the inequality, we get \(m \geq 7\), which matches with the third graph.

Answer:

x= c-3m/m+3-b

Step-by-step explanation:

use Math   way

Step-by-step explanation:

(b-m-3)x-3m+c =0

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hope u got it!!

Answer:

Linearly Dependent for not all scalars are null.

Step-by-step explanation:

Hi there!

1)When we have vectors like \(v_{1},v_{2},v_{3}, ...\) we call them linearly dependent if we have scalars \(a_{1},a_{2},a_{3},...\) as scalar coefficients of those vectors, and not all are null and their sum is equal to zero.

\(a_{1}\vec{v_{1}}+a_{2}\vec{v_{2}}+a_{3}\vec{v_{3}}+...a_{m}\vec{v_{m}}=0\)  

When all scalar coefficients are equal to zero, we can call them linearly independent

2)  Now let's examine the Matrix given:

\(\begin{bmatrix}1 &-2 &2 &3 \\ -2 & 4 & -4 &3 \\ 0&1 &-1 & 4\end{bmatrix}\)

So each column of this Matrix is a vector. So we can write them as:

\(\vec{v_{1}}=\left \langle 1,-2,1 \right \rangle,\vec{v_{2}}=\left \langle -2,4,-1 \right \rangle,\vec{v_{3}}=\left \langle 2,-4,4 \right \rangle\vec{v_{4}}=\left \langle 3,3,4 \right \rangle\) Or

Now let's rewrite it as a system of equations:

\(a_{1}\begin{bmatrix}1\\ -2\\ 0\end{bmatrix}+a_{2}\begin{bmatrix}-2\\ 4\\ 1\end{bmatrix}+a_{3}\begin{bmatrix}2\\ -4\\ -1\end{bmatrix}+a_{4}\begin{bmatrix}3\\ 3\\ 4\end{bmatrix}=\begin{bmatrix}0\\ 0\\ 0\end{bmatrix}\)

2.1) Since we want to try whether they are linearly independent, or dependent we'll rewrite as a Linear system so that we can find their scalar coefficients, whether all or not all are null.

Using the Gaussian Elimination Method, augmenting the matrix, then proceeding the calculations, we can see that not all scalars are equal to zero. Then it is Linearly Dependent.

 \(\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ -2 &4 &-4 &3 \\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )R_{1}\times2 +R_{2}\rightarrow R_{2}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &0 &9 &0\\ 0 & 1 &-1 &4 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )\ R_{2}\Leftrightarrow R_{3}\left ( \left.\begin{matrix}1 &-2 &2 &3 \\ 0 &1 &-1 &4 \\ 0 &0 &9 &0 \\ \end{matrix}\right|\begin{matrix}0\\ 0\\ 0\end{matrix} \right )\)\(\left\{\begin{matrix}1a_{1} &-2a_{2} &+2a_{3} &+3a_{4} &=0 \\ &1a_{2} &-1a_{3} &+4a_{4} &=0 \\ & & &9a_{4} &=0 \end{matrix}\right.\Rightarrow a_{1}=0, a_{2}=a_{3},a_{4}=0\)

\(S=\begin{bmatrix}0\\ a_{3}\\ a_{3}\\ 0\end{bmatrix}\)

The recursive rule is f(n) = f(n - 1) * 2; f(1) = 9 and the explicit rule is f(n) = 9(2)^n-1

The recursive rule

From the question, we have the following parameters that can be used in our computation:

The table

The table definitions imply that we simply multiply 2 to the previous term to get the current term

This means that

f(n) = f(n - 1) * 2

Where

f(1) = 9

The explicit rule

The table definitions imply that we simply multiply 2 to the previous term to get the current term

a = 9

r = 2

So we have

f(n) = a * r^n-1

This gives

f(n) = 9(2)^n-1

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The range of the function is {1,-1,10} for function f(x)=2x³−3x .

A relation is a function if it has only One y-value for each x-value.

In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.

The given function is f(x)=2x³−3x

The domain is {-1,1,2}

Now f(-1)=2(-1)³-3(-1)

=-2+3=1

f(1)=2(1)³-3(1)=2-3=-1

f(2)=2(2)³-3(2)=16-6=10

Hence, the range of the function is {1,-1,10} for  f(x)=2x³−3x .

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The expression of 602.16 dam in decimeters can be written as 60216 decimeter.

The concept that will be used in the calculation is conversion. to perform this conversion, it is important to note that 1 Decimeter (dm) is equal to 0.01 dekameter (dam).

Then, if 1dm = 0.01 dam

               Xdm     = 602.16 dam

Where x is the value in decimeter.

Then we can cross multiply as :

X= (602.16 dam * 1dm)/ 0.01 dam

= 60216 decimeter.

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Answer:

Choice B is the closest

Step-by-step explanation:

A-lateral = 2πrh

r = D/2 = 16.5/2 = 8.25

h = 14

A = 2π(8.25)(14) = 725.7 in²

All 3 angles add up to 180 degrees.

so 40 + 2x + 3x = 180

40 + 5x = 180

5x = 140

x = 28

So angle A = 2x = 2(28) = 56 degrees.

Answer: 56°

Step-by-step explanation:

We know that a triangle's angles add up to 180 degrees. We will create an equation to help us solve for x using this information.

     Given:

           2x + 3x + 40 = 180

     Combine like terms:

           5x + 40 = 180

     Subtract 40 from both sides of the equation:

           5x = 140

     Divide both sides of the equation by 5:

           x = 28

Next, we will substitute this value of x into the expression for ∠A.

     ∠A = 2x = 2(28) = 56°

After 8 canisters is the total cost the same for the members as it is for non-members.

Mathematical operations come in various types, with division being one. The expressions or numbers are divided into the same number of components during this operation.

Given, membership of program costs $52.

And a canister of powder costs $42.50 for members.

Non-members pay $49 for a canister of protein powder.

That means difference of cost of a canister of protein powder between members and non-members:

$49 - $42.50 = $6.50

To find the number of canister:

Divide $52 by $6.50.

52/6.50

= 8 canister.

Cost of 8 canisters :

For non-members, 8 x $49 = $392

For members, 8 x $42.50 + $52 = $392

Therefore, total cost the same for the members as it is for non-members is after 8 canisters.

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