Place parentheses and brackets in the expression below so that it equals 18
2³ x 4/2 +2

Answer: 5/3a + 4/2b

Step-by-step explanation:

[tex]\dfrac{4}{3} a-\dfrac{1}{2} b+\dfrac{1}{3} a+\dfrac{5}{2} b[/tex]

Rearrange:

[tex]\dfrac{4}{3} a+\dfrac{1}{3} a-\dfrac{1}{2} b+\dfrac{5}{2} b[/tex]

Combine Like Terms:

[tex]\dfrac{4}{3} a+\dfrac{1}{3} a=\dfrac{5}{3} a\\-\dfrac{1}{2}b+\dfrac{5}{2} b=\dfrac{4}{2} b[/tex]

[tex]\fbox{$\dfrac{5}{3}$a + $\dfrac{4}{2}$b}[/tex]

Answer:

33<35; 3 cans for 0.98

Step-by-step explanation:

0.98÷3=0.326... rounds to 33 cents

4.14÷12=0.345 rounds to 35 cents

so correlation coefficient = σ^XY/σ^Xσ^Y = 1.225 / 1.36 = 0.9

Step-by-step explanation:                                                                          

a) We need to find the conditional p m f of X when Y = 1.

So, when Y = 1, there are only two X values: X =1 and X =2.

X can have any of the following values: 0, 1, 2, or 3                                                                                                        

so P(0) = 0/ 0.2 = 0          

P(1) = 0.1/(0.1+0.1) = 0.5

P(2) = 0.1/( 0.1+ 0.1) = 0.5

P(3) = 0/ 0.2 = 0

b)  The correlation coefficient of X and Y isρXY              

ρ^XY=(X,Y)=(X,Y)/σ^Xσ^Y=σ^XY/σ^Xσ^Y

We will calculate σ^X first by μ^x

f x(x) = 0.2; x = 0

= 0.2; x =1

= 0.2 ; x = 2

= 0.4 ; x = 3

μ^x = 0.2 * 0 + 0.2 * 1 + 0.2 * 2 + 0.4 * 3 = 1.8

σ^X^ 2 = 0.2 * 1.82 + 0.2 * 0.82 + 0.2 * 0.22 + 0.4 * 1.22 = 1.36

σ^X = 1.166

We will calculate σ^y first by μ^y

f^ x (X) = 0.2; y = 0

= 0.2; y =1

= 0.2 ; y= 2

= 0.4 ; y = 3

μ^y = 0.2 * 0 + 0.2 * 1 + 0.2 * 2 + 0.4 * 3 = 1.8

σ^y^ 2 = 0.2 * 1.82 + 0.2 * 0.82 + 0.2 * 0.22 + 0.4 * 1.22 = 1.36

σ^y = 1.166

Now we will calculate σ^XY

σ^2^XY = 0.4 * ( 3 - 1.8)* ( 3-1.8) + 0.2 *( 0 -1.8) * ( 0 - 1.8) + 0.1 * ( 1- 1.8) * ( 1- 1.8) + 0.1 * ( 2 -1.8) * ( 1 -1.8) + 0.1 * ( 1 - 1.8) * ( 2 - 1.8) + 0.1 * ( 2 - 1.8) * ( 2 - 1.8) = 1.26

σ^XY = 1.225        

so correlation coefficient = σ^XY/σ^Xσ^Y = 1.225 / 1.36 = 0.9

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Answer: b i think

Step-by-step explanation:

Answer:

if x is -6,

4(-6) + 8y = -40

-24 + 8y = -40

-24 +(-40) = 8y

-24 -40 =8y

-64 = 8y

-64 ÷ 8 =8y ÷ 8

-8 = y

Answer:

-2

Step-by-step explanation:

4x + 8y = -40

since X= -6

then 4(-6) + 8y = -40

-24 + 8y = -40

8y = -40 +24

since the -24 crossed the equal to sign it becomes +24

8y = -16

8y/8 = -16/8

y = -2

Answer:  18

Step-by-step explanation: Here's how I got my answer:

24.75 + 54.79

I added it because both the jersey AND the shorts make up a full uniform.

=79.54

Now, we need to divide the 79.54 (total cost for 1 jersey) by 1500, to find out how many/about how many jersey's she can afford. If you divide correctly, you should get 18.85843600704048. So, we need to round DOWN, because we need to see how many jerseys we can afford WITHOUT GOING OVER the budget. So, rounding down I got 18. 18 would be your answer, though you would have some money left over.

The probability that the same students who passed the first quiz also passed the second quiz given that 19 students passed the first quiz is 0.63

What is probability ?

Probability can be defined as the ratio of number of favourable outcomes and total number of outcomes.

This is a case of conditional probability. The conditional probability of an event, A given that B has occurred is is written as P(AIB). We would calculate the probability as

P(AIB) = Probability of A and B/Probability of B

Looking at the given question, Probability of S and F is 12/21 (12 of the students in the class passed both quizzes)

Probability of S = 19/21

Therefore,

P(SIF) = (12/21) / (19/21)

(PSIF) = 12/21 * 21/19

(PSIF) = 12/19 = 0.63

Therefore, The probability that the same students who passed the first quiz also passed the second quiz given that 19 students passed the first quiz is 0.63

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Books about rainforests that are on the shelves are 48

The distributive property states that an expression of the form A(B + C) can be solved by a multiplication over addition operation that is

A(B + C) = AB + AC

This property is known by distributive law and applies to subtraction also.

Given;

Poetry section of the library has 6 bookcases.

Number of shelves in each bookcase = 3

Total shelves =  (Number of shelves in each bookcase) x (Number of bookcases in each poetry section)

= 3 x 16

= 48

Therefore, number of total books in the poetry section= 180

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Answer:

0 :/

Step-by-step explanation:

S(48) = (48/2)(2a+47d),

S(36) = (36/2)(2a+35d).

Now S(48) = 4S(36)

24(2a+47d) = 4*18(2a+35d) = 72(2a+35d).

Then 2a+47d = 3(2a+35d) and

6a +105d -2a -47d = 0,

4a +58d = 0,

2a+29d = 0.

Now S(30) = (30/2)(2a+29d) = (15)(2a+29d)=0

Answer:

Below

Step-by-step explanation:

Large rectangle - smaller inside rectangle = shaded area

(200 x 300) - ( 100 x 160) = 44 000 in^2

-46x = -64x

-2 × 11 = -22

-2 × -12x = -24x

-22 -24x = -46x

-4 × 16x = -64x

I'm soooooo sorry if this is not correct but this is the way i know how to do it

The hypotenuse of this triangle is equal to 16√5 cm.

In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

Note: c = 4a

Substituting the given parameters into the Pythagorean's theorem formula, we have the following;

a² + b² = c²

a² + (4√15)² = 4a²

4a² - a² = (4√15)²

3a² = 240

a² = 80

a = 4√5 cm.

For the hypotenuse, we have:

Hypotenuse, c = 4a

Hypotenuse, c = 4(4√5)

Hypotenuse, c = 16√5 cm.

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Answer:

Hypotenuse : 16cm

Shorter leg of triangle: 4cm

Step-by-step explanation:

So, we are told [tex]4\sqrt{15}[/tex]  is the longer leg, let's say this is a.

[tex]4\sqrt{15} = \sqrt{240}[/tex], the Pythagorean is [tex]a^2+b^2=c^2[/tex], we'll say b = shortest leg, which is what we're solving for.

Since the hypotenuse (c), is 4 times b I changed it to 4b in my equation.

[tex]\sqrt{240} + b = 4b[/tex], square this to get [tex]240 + b^2 = 16b^2[/tex], -b^2 on both sides

[tex]240=15b^2[/tex], then divide by 15. [tex]16=b^2[/tex], use square root and you get [tex]4 = b[/tex]

hope this helps. btw since hypotenuse is 4 times b, just do 16cm, but your answer is 4 cm

Answer:

Step-by-step explanation:

250 divided by 50 = 5

50 goes into 250 5 times

Answer:

2

Step-by-step explanation:

4-2=2 take four cows,then sell two of them you will remain with two

Answer:

D. [tex]10^{\circ}[/tex]

Step-by-step explanation:

Let the measure of minor arc [tex]AE[/tex] be [tex]\alpha[/tex] and the measure of minor arc [tex]BD[/tex] be [tex]\beta[/tex].

Using the secant-secant theorem, [tex]\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}[/tex].

By the inscribed angle theorem, [tex]\alpha=84^{\circ}[/tex].

Thus, [tex]\beta=20^{\circ}[/tex].

By the inscribed angle theorem, [tex]x=10^{\circ}[/tex].

1/3 - inch cubes across the bottom layer = 30

the number of layers is 9

Total number of 1/3-inch cubes 270 cubes

The small cube inside has a dimension of 1/3

The area of the cube is 1/3 * 1/3 = 1/9

the area of the bottom layer is 2 * 1 2/3 = 10/3

the number of small cubes across the bottom is

=  10/3 / 1/9

= 30

The number of layers is calculated by division

= total height of layers / 1/3-inch side of the cube

= 3 / 1/3

= 9 layers

Total number of 1/3-inch cube

= 30 * 9

= 270 cubes

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Answer:

625

5 is multiplied 4 times, that is, 5 × 5 × 5 × 5 = 625

The taxes paid for each taxable income is given as follows:

a. $400,000: $113,775.

b. $10,954: $1,095.4.

c. $108,962: $18,904.88.

d. $209,850: $47,222.5.

The amount of taxes is obtained identifying the correct interval in the table and then applying the proportions.

For a taxable income of $400,000, the tax is of $45,210 plus 35% of the income ​over $204,100, hence:

45210 + 0.35(400000 - 204100) = $113,775.

For a taxable income of $10,954, the tax is a simple 10%, hence:

0.1 x 10954 = $1,095.4.

For a taxable income of $108,962, the tax is of 12962 plus 24% over 84,200, hence:

12962 + 0.24 x (108962 - 84200) = $18,904.88.

For a taxable income of $209,850, the tax is of $45,210 plus 35% of the income ​over $204,100, hence:

45210 + 0.35(209850 - 204100) = $47,222.5.

Recapping, we identify between which two values the taxable income is located, and then apply the tax rule defined by the table for the range in which the income is located.

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Answer:

Step-by-step explanation:

The trick is to think of these as fractions and multiplying them instead of dividing them.

Since dividing things is the same as multiplying by it's reciprocal, so something like

[tex]\frac{4}{y+2}[/tex]

turns into

[tex]\frac{4}{1} *\frac{1}{y+2}[/tex]

Following this concept,

[tex]\frac{4}{1} *\frac{1}{y+2-3}*\frac{1}{y-2+12}*\frac{1 }{y^{2} -4}[/tex]

and then

[tex]\frac{4}{1} *\frac{1}{y-1}*\frac{1}{y+10}*\frac{1 }{y^{2} -4}\\[/tex]

Now we'll have to multiply out everything like this

[tex]\frac{4}{(y-1)(y+10)(y^2-4)}[/tex]

so it becomes

[tex]\frac{4}{(y^2-9y-10)(y^2-4)}[/tex]

which turns into

[tex]\frac{4}{y^4-9y^3+22y^2+40}[/tex]

And there you have it as a single fraction.

The perimeter of the triangle is 7x + y -4 feet. The correct option is B.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given:

The sides of the triangles are 4x+5 feet, y-7 feet and 3x-2 feet.

To find the perimeter:

The perimeter of the triangle is the sum of all the sides of the triangle.

So, the perimeter = (4x+5) + (y-7) + (3x-2)

The perimeter = 4x+5 + y-7 + 3x-2

The perimeter = 4x + 3x + y +5 -7 -2

The perimeter = 4x + 3x + y +5 -9

The perimeter = 7x + y -4 feet.

Therefore, 7x + y -4 feet is the perimeter.

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The equation of the line that passed through the points, can be found to be y = -4 x + 1

The equation of a line takes the form:

y = mx + b

m = slope

b = y - intercept

The slope is:

= ( Y2 - Y1 ) / ( X 2 - X 1 )

Given the points, (-1,5) and (2,-7), the slope is:

= ( - 7 - 5 ) / ( 2 - ( - 1 ))

= - 12 / 3

= - 4

The y - intercept can be found by plugging in the slope and the value of a point into the equation:

- 7 = -4 ( 2 ) + b

b = -7 + 8

b = 1

The equation is therefore:

y = -4 x + 1

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The function to represent the given scenario is y=25+0.15x and the number of miles travelled is 240 miles.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Given that, Bang-up Motors will rent-a-car for $25 plus $0.15 per mile traveled.

a) Let the number of hours be x and the total number of hours be y.

Now, y=25+0.15x

b) If your bill was $61, then the number of miles are

61=25+0.15x

0.15x=36

x=36/0.15

x= 240 miles

Therefore, the number of miles travelled is 240 miles.

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Answer: 8

Step-by-step explanation:

10/2=5

6/2=d=3

c/2=4

c=8

Answer:

C = 8

Step-by-step explanation:

If the triangles are similar, then the sides are proportional. And if the hyptenuse BA is 2 times larger than the hypotenuse PR (10:5), then the long leg "C" is 2 times larger than the long leg QP. That is, its length is 4 x 2 = 8

The slope of the taxi fare is a positive slope.

Distance is a measure of the space between two points. It is the length of a physical path between two points, usually measured in units of meters or kilometers. Distance can also refer to the amount of time or energy it takes to travel between two points. Distance is a fundamental concept in physics, mathematics, and other scientific fields. Distance can also be used to measure relationships between people, such as the distance between two people's homes.

The x-axis would represent the distance, while the y-axis would represent the fare. As the distance increases, the fare increases at a rate of 2 dollars for every additional 1 km.

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The pattern represented by the scatter plot in Graph A are as follows;

1. a) The pattern of the graph with a scale factor of 1 unit equivalent to 1 y-value is the y-value at a point is 1 + the x-value at the specified point

b) When the scale factor is changed to 0.1 y-value unit to each unit of the graph, the pattern is each y-value is 0.1 × the x-value at the point plus 0.1

A scatter plot is the plot of variable pairs along the two axis of a coordinate plane such that the pattern formed indicates the correlation between the values.

1. a. The values of the coordinate points of the Graph A using a scale of 1 to 1 unit of the graph are; (1, 2), (2, 3), (3, 4), (4, 5), (5, 6)

A pattern of the graph can be obtained by finding the value of the x and y values as follows;

The first difference in the y-values that is constant indicates, that the relationship is a linear relationship

The slope of the graph is; (3 - 2)/(2 - 1) = 1

The equation of the graph is therefore; y - 2 = 1 × (x - 1) = x - 1

y = x - 1 + 2 = x + 1

y = x + 1

The pattern is therefore, each value of y is equivalent to the value of x + 1

(b) Changing the scale of 1 unit on the graph to 0.1 unit of the y-value, we get; (1, 0.2), (2, 0.3), (3, 0.4), (4, 0.5), (5, 0.6)

Therefore, the slope of the graph is; (0.3 - 0.2)/(2 - 1) = 0.1

The equation of the graph is therefore; y - 0.2 = 0.1 × (x - 1)

y - 0.2 = 0.1 × (x - 1)

y - 0.2 = 0.1·x - 0.1

y = 0.1·x - 0.1 + 0.2 = 0.1·x + 0.1

y = 0.1·x + 0.1
The pattern represented by the graph after the scale is changed to a decimal value of 0.1 y-value to 1 unit of the graph is; y = 0.1·x + 0.1

Which is each y-value is 0.1 + the product of the x-value and 0.1

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Considering the expression of a line, the equation of the line that passes through the points (-1,5) and (2,-7) is y= -4x +1.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in  y = mx + b, the value of the ordinate to the origin can be obtained.

In this case, being (x₁, y₁)= (-1, 5) and (x₂, y₂)= (2, -7), the slope m can be calculated as:

m= (-7 - 5)÷ (2 - (-1))

m= (-7 - 5)÷ (2 + 1)

m= (-12)÷ 3

m= -4

Considering point 1 and the slope m, you obtain:

5= (-4)× (-1) + b

5= 4+b

5 -4= b

1= b

Finally, the equation of the line is y= -4x +1.

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Answer:

The y-intercept is -2.

Step-by-step explanation:

The line intersects at the y-axis on the point (0, -2).