Simplify. Show your work. Last one

Answer:

[tex]\boxed{\tt y=48}[/tex]

Step-by-step explanation:

[tex]\tt \cfrac{3}{16}=\cfrac{9}{y}[/tex]

Cross multiply:-

[tex]\tt 3 \times y=(9)\times (16)[/tex]

[tex]\tt 3y=144[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3y}{3}=\cfrac{144}{3}[/tex]

Simplify:-

[tex]\tt y=48[/tex]

_________________

Hope this helps!

Answer:y=48 I hope this is helpful good luck have a good day

Step-by-step explanation:

3/16 = 9/y

Determine the defined range

3/16=9/y y=0 cross out the equal sign y=0

Simplify the equation using cross-multiplication

3y=144

Divide both sides of the equation by 3

y=48

Check if the solution is in the defined range

The probability of selecting 25 data values with a mean less than 190 is 0.6%.

What is probability?

What is mean?

Why do you use the word deviation?

Population mean = 20

Standard deviation = 20

Sample size= 25

Sample mean= 190

z = 190-200/20/5

Square root of 25 -10/4 = 2.

Corresponding term is 0.4938 P(X<190) = 0.500-0.4938

P(X<190) = 0.0062 or 0.62

P(X<190) = 0.6%

Hence, the probability of selecting 25 data values with a mean less than 190 is 0.6%.

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The power series cos(i)  [tex]= \sum^\infty_{n = 0} (-1)^n {\frac{i^{2n}}{(2n)!}}[/tex] and it converges to a real number 1.5308

The power series expansion of cosine function

cos(x) =>

[tex]= \sum^\infty_{n = 0} (-1)^n {\frac{x^{2n}}{(2n)!}}\\= 1 - \frac{x^2}{2!} +\frac{ x^4}{4!} - ....[/tex]

Given in the question that,

i = √(-1)

Using the power series for cos(x) , the power series for cos(i) =>

cos(i) =[tex]1 - \frac{i^2}{2!} +\frac{ i^4}{4!} - ....[/tex]

As we know ,

i² = -1 and i⁴ = 1

So, cos(i) = 1 -(-1)/2 + (1/24) - (-1 / 720) + . . .

=> 1 + 1/2 + 1/24 + 1/270+  . . .

Power series = >

cos(i) = [tex]= \sum^\infty_{n = 0} (-1)^n {\frac{i^{2n}}{(2n)!}}[/tex]

The series is convergent to the value 1.5308 which is a average of e and 1/e

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The area under the curve r²=50sin2Θ is (15.71)unit square

A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.

The given parabola is r²=50sin2∅,

where r=5

Where r=radius of the circle of the parabola

Substitute r=5 in the parabola

5²=50sin2∅

Simplifying the equation to find the value of ∅25=50sin2∅[tex]\frac{25}{50}[/tex]=sin2∅

Finding the sine inverse, we havesin[tex]^{-1} 0.5=2[/tex]∅30⁰=2∅∅=15⁰

The angle made by the parabola is 15⁰

note r=5

Area = 22/7 × 5

Area = 15.71 unit²

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The value   of   x≥2  are: 2,4,5,6

Inequality—the state of not being equal, particularly in status, rights, and opportunities1—is central to social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.

An inequality compares two values to determine whether one is less than, greater than, or simply not equal to the other. a b indicates that a is not equal to b.

Given ,

2x - 4≥1

State the values of x within 1 and 6

2x - 4≥1

2x ≥ 1 +4

2x ≥ 5

Divide both sides by 2

2x/2 ≥  5/2

x = 2

(1,6) is an open interval which means that 1 and 6are not inclusive of the values of x.

So:

therefore the values of   x≥2  are: 2,4,5,6

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The side of the hexagonal prism is 8.77 cm

What is a hexagonal prism?

A hexagonal prism has 8 faces, 18 edges, and 12 vertices. Out of the 8 faces, 6 are parallelograms, and 2 are hexagons, and that's why it is called a hexagonal prism. These hexagons are at the base and the top as the opposite faces of a prism are the same.

Given data ,

Let the volume V of the hexagonal prism be V = 2800 cm³

Let the height of the hexagonal prism be H = 14 cm

Now , let the side of the hexagonal prism be = A cm

The volume of the hexagonal prism be V = ( ( 3 √3 / 2 ) ) a²h

where a is the side of the hexagonal base

h is the height of the hexagonal prism

Substituting the values in the equation , we get

The volume of the cube be V = ( ( 3 √3 / 2 ) ) a²h

V = ( ( 3 √3 / 2 ) ) a²h

2800 = ( 3 √3 / 2 ) x a² x 14

200 = ( 3 √3 / 2 ) x a²

Multiply by 2 on both sides of the equation , we get

400 = 3√3 x a²

Divide by 3√3 on both sides of the equation , we get

a² = 76.98

Taking square roots on both sides of the equation , we get

a = 8.77 cm

Therefore , the value of a is 8.77 cm

Hence , The side of the hexagonal prism is 8.77 cm

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Answer:

Step-by-step explanation:

A line that is perpendicular to another will have the opposite slope.

y = [tex]-\frac{1}{3}[/tex]a + b

To find b, substitute y and a with the given values

6 =  [tex]-\frac{1}{3}[/tex](-6) + b

6 = 2 + b

-2  -2

4 = b

thus

y = [tex]-\frac{1}{3}[/tex]a + 4

The length of OB' after dilation 3 units.

What is dilation of triangle?

Dilation is a method for producing similar figures. By increasing distances by the scale factor, each point is extended outwards from the center point.

Dimensions of the new shape = Dimensions of the original shape × Scale factor.

in a given triangle,

Dilation is using the rule d o,4, it means is that triangle was enlarged by a scale factor of 4 with point O as the center of dilation.

[tex]ob = \frac{3}{4}[/tex]

[tex]o'b' = 4 * \frac{3}{4}[/tex]

[tex]o'b' = 3 units[/tex]

The length of OB' after dilation 3 units.

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Tamar raise $15

What is division ?

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

A group is divided into equal portions when it is divided. For a game or activity, division can be used to divide a class into equal groups. It can also be used to divide a pizza among friends in equal pieces. Divided into partitive and quotative, there are two forms of division.

There are 2 ways one by writing equation and the other by using logic

1. by using equation

3*x=45

x=45/3

 = 15

2. Logically

If Jack has $45 which is 3 times Tamara's we can reverse the statement:

45/3

=15

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The value of car after 2 years is $17,008.8, as percent it is 28.2% and depreciation is 27.75%

Value of car after two years will be calculated by calculating the depreciation each year.

Depreciation after first year = 60,320 - 15%×60,320

Depreciation after first year = 60,320 - 9,048

Depreciation after first year = $51,272

Depreciation after second year = 51,272 - 15%×51,272

Depreciation after second year = 51,272 - 7690.8

Depreciation after second year = $43,311.2

Value after depreciation = 60,320 - 43,311.2

Value after depreciation = $17,008.8

Value of car as percentage = 17008.8/60320×100

Value of car as percentage = 28.2%

Depreciation after two years period = 9048 + 7690.8

Depreciation after two years period = 16,738.8

Depreciation as percentage = 16738.8/60320×100

Depreciation as percentage = 27.75%

The correct answers are a) $17008.8, b) 28.2% and c) 27.75%.

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Answer: the space shuttle

Step-by-step explanation:

Answer:

1/2 x 1/10^-9

Step-by-step explanation:

(1.5x10^-5)/(3.0x10^4)

=> 1.5/3 x 10^-5/10^4

=> 1/2 x 10^-9

Answer:

= 5

Step-by-step explanation:

(1.5*10⁵) / (3.0*10⁴)

1.5*10⁵ = 15*10⁴

Then:

(1.5*10⁵) / (3.0*10⁴) = (15*10⁴) / (3*10⁴) = 15/3

= 5

The evaluation of the trendline in line graph of the trendline displaying the value of a 2000 Toyota Camry since the year 2000 are as follows;

a. Independent variable; Time

Dependent variable; Value

b. The equation is; V = 22,500 - 1,166.[tex]\overline 6[/tex]·t

c. The y-intercept is at the point (0, 22,500), which indicates that the value of the 2000 Toyota Camry in the year 2,000 is $22,500

d. The slope of the trendline is -1,166.[tex]\overline {6}[/tex], which indicates that the annual reduction in the price of the 2000 Toyota Camry is $1,166.[tex]\overline 6[/tex]

e. The value of the car in 2017 based on the trendline is $2,666.[tex]\overline{6}[/tex]

A trendline is a line drawn through a scatterplot, minimizing the distances between the points in the chart and the line itself, and shows the trend of the scatterplot.

a. The independent variable is the variable that is the input variable of the function, which the researcher can vary or the value that is controlled.

Therefor;

The dependent variable is the value under study, therefore;

b. The points on the line graph are; (0, 22,500), and (15, 5,000), the slope is therefore;

m = (5,000 - 22,500)/(15 - 0) = -3,500/3

The equation is therefore;

V - 22,500 = -3,500/3·t

V = -3,500/3·t + 22,500

c. The y-intercept of the trend line is (0, 22,500), which indicates that in the year 2,000, the price of the 2,000 Toyota Camry was $22,500

d. The slope of the trend line is -3,500/3 = -1,166.[tex]\overline 6[/tex], which indicates that the value of the Toyota Camry, 2000, reduces at a rate of $1,166.[tex]\overline 6[/tex], each year.

e. In the year 2017, t = 17, therefore;

V = 22,500 - (3,500/3) × 17 = 2,666.[tex]\overline {6}[/tex]

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Answer:6

Step-by-step explanation:

Answer:

look below

Step-by-step explanation:

Step 1: Determine the amount of pure solvent needed.

100 gallons x 0.5 (50%) = 50 gallons of pure solvent

Step 2: Determine the amount of each solution to use.

30% solution: 50 gallons of pure solvent / 0.3 = 166.67 gallons of 30% solution

80% solution: 50 gallons of pure solvent / 0.8 = 62.5 gallons of 80% solution

Step 3: Total the amount of solution used.

166.67 gallons of 30% solution + 62.5 gallons of 80% solution = 229.17 gallons total

Answer:

r = d(x-e)

or r = dx - de

Step-by-step explanation:

x = e + [tex]\frac{r}{d}[/tex]  subtract e from both sides.

x - e = [tex]\frac{r}{d}[/tex]  Multiply both sides by d

d(x -e) = r

or

dx -de = r

Answer/Step-by-step explanation:

Zeros are x-intercepts. (Solutions are zeros are x-intercepts!)

If you are allowed to use technology, such as a graphing calculator or an online graphing tool, input the function and look for the x-intercepts. Graphing calculators have menus to find them for you. It is a legit way to "verify the zeros" Also, since this is a third degree function (highest exponent is a 3rd power) but the leading coefficient is negative, the end behavior acts the same as:

y = -x^3

a much simpler version. Actually, even simpler:

y = -x

All of these, go up to the left and down to the right. Or some teachers/classes/books/programs want you to say:

as x goes to negative infinity, y goes to infinity (up to the left) and as x goes to infinity, y goes to negative infinity (down to the right)

SO, if you cannot use technology, put the given x-intercept into the function. And check that it gives you a value of 0. Like this:

f(x) =

-x^3-7x^2-7x+15

check by substituting -5 for x

f(-5) =

-(-5)^3-7(-5)^2-7(-5)+15

= 125 -7(25) +35+15

= 125- 175 + 35 + 15

= 0

When you use x =-5 you get y = 0. This verifies that -5 is a zero.

Check -3.

f(-3)=-(-3)^3-7(-3)^2-7(-3)+15

= 27 -7(9) +21 +15

= 27 - 63 +21 +15

= 0

Verified!

Lastly, check 1:

f(1)=-(1)^3-7(1)^2-7(1)+15

= -1 - 7 - 7 + 15

= 0

Verified!

The given expressions are equivalent.

What is equivalent expression?

Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).

Consider the given expressions,

-(-3m + 6 - 12 + 15m) and 2(1 - 2m)

First simplify the expression -(-3m + 6 - 12 + 15m)

= 3m - 6 + 12 - 15m

= -12m + 6

Divide the expression by 3,

= -4m + 2

= 2 + 4m            ..(1)

Now, consider the expression,  2(1 - 2m)

Simplifying this,

2(1 - 2m) = 2 - 4m         ..(2)

From (1) and (2) we can see that the expressions are equivalent.

Hence, the given expressions are equivalent.

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The most petunias Ying Ying will ever purchase is 28.

Given data;

Using x as the total amount of money in her wallet and m as the price per petunia

The money remaining in the wallet after buying 2 petunias equals $6.50 according to the provided table.

Now,

6.50 = x - 2m ⇒ (I)

In addition, $5 was left in the wallet after the purchase of 8 petunias,

5 = x - 8m ⇒ (II)

Here, (I) - (II);

6.50 - 5 = x - 2m - x + 8m

1.50 = 6m

m = 0.25

One petunia costs $0.25.

Therefore, the total number of petunias Ying Ying buys at most is,

When 14 petunias brought money left in the wallet is $3.50.

Now,

→ 3.50/0.25 = 14

The total number of petunias Ying Ying buys at most is 14 + 14 = 28

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The given statement exists true. A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization).

A matrix can be expressed as the union of two distinct matrices, Q and R, using the QR matrix decomposition. R is a square upper/right triangular matrix and Q is an orthogonal matrix. R is also invertible because it is square and doesn't have zeros in its diagonal entries.

A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization). Finding eigenvalues and solving linear least squares problems both use QR factorization.

A = QR. Be aware that the QR-factorization of a rectangular matrix A is sometimes understood with Q square and R rectangular rather than Q rectangular and R square, as with the MATLAB command qr.

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The probability that a point chosen at random lies in the shaded region is 0.28

From the question, we are to find the probability that a point chosen at random lies in the shaded region.

The shaded region is a triangle.

The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle

First, we will calculate the unknown side of the triangle

Let the unknown side be x.

Then, from the Pythagorean theorem, we can write that

12² = 6² + x²

144 = 36 + x²

x² = 144 - 36

x² = 108

x = √108

x = 6√3

From formula,

Area of a triangle = 1/2 × base × height

Area of the triangle = 1/2 × 6 × 6√3

Area of the triangle = 18√3 square units

Now, we will determine the area of the circle

Area of a circle = πr²

Where r is the radius

From the given information,

Diameter of the circle = 12

But,

Radius = Diameter / 2

Therefore,

r = 12/2

r = 6

Thus,

Area of the circle = 3.14 × 6²

Area of the circle = 113.04 square units

Now,

The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04

The probability that a point chosen at random lies in the shaded region = 0.2758

The probability that a point chosen at random lies in the shaded region ≈ 0.28

Hence, the probability is 0.28

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The amount of pizza ate by Simon, Eira and Martin is

Simon eats 3/8 of a pizza = 3/8

The amount of pizza left after Simon ate

= 1 - 3/8

= 5/8

Eira and Martin eat an equal share of the pizza that is left

that is the amount left was shared into 2

= 5/8 ÷ 2

= 5/16 each for both of them

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The half of the number is 4.5 .

Given in question as  14 is subtracted from 6 times a number.

Let us suppose a number is x.

First find 6 times of a number = 6*x.

6 times can be defined as x + x + x + x + x + x = 6*x.

We have to subtract from 6 times a number.

14 is subtracted from 6 times a number means 6x - 14.

After subtracting 14 is left.

So 6x - 14 = 40.

Add 14 both side of equal sign.

6x-14+14 = 40+14.

6x = 54.

x = 54/6.

x = 9.

Half of the number x is 9/2 = 4.5.

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For a student with a shoe size of 9, the student's height is equal to 65 inches.

For a student with a height of 60 inches, the student's shoe size is equal to 6.5.

From the information provided, an equation for the line of best fit that represents or models the heights x (in inches) and shoe sizes y of several student is given by this mathematical expression:

y = 0.50x - 23.5

Where:

For a student with a shoe size of 9, the student's height is given by:

y = 0.50x - 23.5

0.50x = y + 23.5

Student's height, x = (y + 23.5)/0.50

Student's height, x = (9 + 23.5)/0.50

Student's height, x = 32.5/0.5

Student's height, x = 65 inches.

For a student with a height of 60 inches, the student's shoe size is given by:

y = 0.50x - 23.5

y = 0.50(60) - 23.5

y = 30 - 23.5

y = 6.5

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A table of values and an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the internet cafe are as follows:

C                         t

$10.60                1

$11.20                 2

$11.80                 3

C = 0.60t + 10.

In order to write an equation for the total cost, we would assign variables to the amount of time used and the total cost of using a computer, and then translate the word problem into algebraic equation as follows:

Since the cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use, an equation for the total cost is given by:

C = 0.60t + 10

When t = 1, we have:

Total cost, C = 0.60(1) + 10

Total cost, C = $10.60.

When t = 2, we have:

Total cost, C = 0.60(2) + 10

Total cost, C = $11.20.

When t = 3, we have:

Total cost, C = 0.60(3) + 10

Total cost, C = $11.80.

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      idddddddddddddddkkkkkkkkkkkkkkkkkkkkkkkk annnnthinggggggg            

Answer:(2x+1)(3x-4)

Step-by-step explanation:Factor the expression out first by getting 6x^2+3x-8x-4. From there, factor again to 3x(2x+1)-4(2x+1) to get the answer (2x+1)(3x-4)

Answer:

(3x - 4)(2x - 1)

Step-by-step explanation:

6x^2 - 5x - 4

When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)

x^2 - 5x - 24

Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)

24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.

As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.

One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.

Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.

(6x - 8)(6x - 3)

We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.

(6x - 8)/2 and (6x - 3)/3.   3*2 = 6

(3x - 4)(2x - 1)

Answer:

see explanation

Step-by-step explanation:

(a)

given y is directly proportional to x³ then the equation relating them is

y = kx³ ← k is the constant of proportion

to find k use the condition y = 20h when x = h

20h = kh³ ( divide both sides by h³ )

[tex]\frac{20h}{h^3}[/tex] = k , then

k = [tex]\frac{20}{h^2}[/tex]

y = [tex]\frac{20}{h^2}[/tex] x³ = [tex]\frac{20x^3}{h^2}[/tex]

(b)

when y = 67.5h , then

67.5h = [tex]\frac{20x^3}{h^2}[/tex] ( multiply both sides by h² to clear the fraction )

67.5h³ = 20x³ ( divide both sides by 20 )

3.375h³ = x³ ( take cube root of both sides )

[tex]\sqrt[3]{3.375h^3}[/tex] = x , that is

x = 1.5h

The formula for y in terms of x and h will be y = (20 / h²)x³ and y = 20h. The x in terms of then y = 67.5 h will be x = 1.5h.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

y is directly proportional to the cube of x. Then we have

y ∝ x³

y = kx³

We have y = 20h when x = h, then

20h = k(h)³

k = 20 / h²

The formula for y in terms of x and h is given as,

y = (20 / h²)x³

y = (20 / h²)  (h³)

y = 20h

If y = 67.5 h, then we have

67.5 h = (20 / h²)x³

3.375 h³ = x³

x = 1.5h

The formula for y in terms of x and h will be y = (20 / h²)x³ and y = 20h. The x in terms of then y = 67.5 h will be x = 1.5h.

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The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Suppose the current age of Angela is A while Khali is K.

In 5 years,

A + 5 = K

In 3 years,

K + 3 = 2(A + 3)

K + 3 = 2A + 6

K + 3 = 2(K - 5) + 6

K + 3 = 2K - 10 + 6

2K - K = 3 + 4

K = 7 years old,

A = 7 - 5 = 2 years old.

Hence "The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old".

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The image with line segment AB is dilated from (6, 3) and (3, 3) with scale factor of 1.8

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor.

In this case, the image with endpoints of line segments AB which are (9, 4) and (5, -4) and dilated to become (6, 3) and (3, 3) would have a scale factor of;

scale factor = 9 * x = 5

x = 9 / 5 = 1.8

The scale factor is 1.8

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