a triangle with an area of 8 in^2 is dilated by a factor of 3. the area of the dilated triangle is ___ in^2(no image included)

The store sells a total of 18 types of chairs (this is the sum of all the types of chairs in the two way frequency table). From this table we notice that only two of them are filled with beads and made from velvet. Then the probability of choosing this is:

Therefore the probability is 1/9

Given data:

The given graph of the line.

The slope of the line passing through (4, 0) and (12, 2) is,

Thus, the solpe of the line is 1/4.

Step-by-step explanation:

Given data:

The given graph of the line.

The slope of the line passing through (4, 0) and (12, 2) is,

\begin{gathered}\begin{gathered} m=\frac{2-0}{12-4} \\ =\frac{2}{8} \\ =\frac{1}{4} \end{gathered}\end{gathered}

m=

12−4

2−0

=

8

2

=

4

1

Thus, the solpe of the line is 1/4.

rectangular prism volume is ,

As all the options are the same equation

so, we need to know the type of the sign of the inequality

As shown in the graph

The line is shaded so, the sign is < or >

The shaded area which is the solution of the inequaity is below the line

So, the sign is <

So, the answer is option B) 14x + 7y < 21

Given the expression

Using product rule

Where

Hence, answer is 1/243

The numerator is 1

The denominator is 243

Answer:

A circle is a closed geometric figure without any sides or angles. The unit circle has all the properties of a circle, and its equation is also derived from the equation of a circle. Further, a unit circle is useful to derive the standard angle values of all the trigonometric ratios.

Step-by-step explanation:

DEFINITIONS

The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B.

The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.

Using a Venn Diagram, the union and intersection of two sets can be seen below:

GIVEN

The sets are given to be:

QUESTION

1) (A ∪ B): The terms of the two sets contained in either set or the two sets are

2) (A ∩ B): The elements that are in both sets are

The solution of the linear system of three simultaneous equations is presented as follows; x = 2, y = 1 and z = 4

Simultaneous system of equations consists of a finite set of equations for which a solution to the equation system is required.

The linear system of three equations can be presented as follows;

13•x - 17•y + 16•z = 73...(1)

-11•x + 15•y + 17•z = 61...(2)

46•x + 10•y - 30•z = -18...(3)

The above system of equations can be solved using common multiples of the coefficients as follows;

Multiply equation (2) by 2 and equation (3) by 3 to get;

2 × (-11•x + 15•y + 17•z) = 2 × 61 = 122

3 × (46•x + 10•y - 30•z) = 3 × (-18) = -54

Subtracting equation (4) from equation (5) gives;

138•x + 30•y - 90•z - (-22•x + 30•y + 34•z) = -54 - 122 = -176

138•x - (-22•x) + 30•y - 30•y - 90•z - 34•z = -176

160•x - 124•z = -176

40•x - 31•z = 44

[tex] \displaystyle {z = \frac{(44 + 40\cdot x)}{31}}[/tex]

Plugging in the value of z in equation (1) and (2) gives;

1043•x - 527•y + 704 = 73 × 31 = 2236...(6)

Which gives;

[tex] \displaystyle {y = \frac{(1043\cdot x - 1559)}{527}}[/tex]

339•x + 465•y + 748 = 61 × 31 = 1891...(7)

Which gives; [tex] \displaystyle {y = \frac{(381 - 113\cdot x )}{155}}[/tex] which gives;

[tex] \displaystyle { \frac{(1043\cdot x - 1559)}{527}= \frac{(381 - 113\cdot x )}{155}}[/tex]

Therefore; 221216•x - 442432 = 0

x = 442432 ÷ 221216 = 2

x = 2

y = (1043×2 - 1559)÷527 = 1

y = 1

z = (44 + 40×2) ÷ 31 = 4

z = 4

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Maisa,. let's recall the formula for calculating the reference angle when the angle is > 360 degrees:

Reference angle = Given angle - 360

Reference angle = 745 - 360

Reference angle = 385

It's still higher value than 360, therefore we subtract 360 again.

Reference angle = 385 - 360

Reference angle = 25 degrees

The required product of the given expression [tex]5\times727[/tex] is [tex]3635[/tex].

Distributive property is defined as sum of two or more addends is multiplied by a number gives the same result by multiplying each addends separately and add the products.

For example:

[tex]a\times (b+c)=a\times b + a\times c[/tex]

Partial product is defined as the product of each digit of a number is multiplied by each digit of other number separately.

Solving the expression using Distributive property and partial products:

[tex]5 \times 727 = 5 \times ( 700 + 27 )\\[/tex]                     {∵ [tex]727=700+27[/tex]}                  

Here, Applying the distributive property we get:

            [tex]= 5 \times700 + 5 \times27\\ = 3500 + 135\\ = 3635[/tex]

Hence, the required value of the expression [tex]5\times727[/tex] is [tex]3635[/tex].

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The product of the 5×727 is 3635.

The definition of a distributive property states that when the sum of two or more addends is multiplied by a number, the results are the same whether the addends are multiplied individually or all at once. Like a×(b+c) = a × b + a × c.

The definition of a partial product is the result of multiplying each digit of one integer by each digit of the other number separately.

Given in question, 5 × 727

Using distributive property and partial product,

5 × 727 = 5 × (700 + 27)

            = 5 × 700 + 5 × 27

            = 3500 + 135

            = 3635

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ANSWER:

$ 85.44

STEP-BY-STEP EXPLANATION:

We have the value after tax, we must calculate the sum between the original value and the value equivalent to the established percentage, therefore, we calculate it like this:

The final price is $ 85.44

hello

the question here is a word problem and we can either use alphabhets to represent the variables.

let lattes be represented by x and milk be represented by y

since the total ounce of liquid is equals to 30, we equate the whole sentence to 30.

To answer the question, we must simplify the following expression:

We expand the terms in the polynomial using the distributive property for the multiplication:

Simplifying the last expression we have:

We see that the simplified expression:

• is quartic,

• doesn't have a constant term,

• has four terms,

• is a polynomial,

• it is not a trinomial.

Answer

The correct answers are:

• The simplified expression has four terms.

• The simplified expression is a polynomial.

Answer:

1. Cube A, because it's volume is greater than the volume of cube B

Explanation:

Cube A

Volume = 125 cubic inches

Therefore:

Cube B

The edge length, s = 4.8 inches.

We see that Cube A is the larger group because it's volume is greater than the volume of cube B.

The value of the building would be $699,400 in 4 years.

Depreciation is the when the value of an asset reduces as a result of wear and tear. Straight line depreciation is a method used in depreciating the value of an asset linearly with the passage of time.

The equation that can be used to determine the value of the building with a straight line depreciation is:

Value of the asset = initial value of the asset - (number of months x deprecation rate)

y = 829,000 - 2700x

The first step is to determine the number of months it would take for the building to have a value of $699,400.

$699,400 =  829,000 - 2700x

829,000 - 699,400 = 2,700x

129,600 = 2,700x

x = 129,600 / 2,700

x = 48 months

Now convert, months to years

1 year = 12 months

48 / 12 = 4 years

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Answer:

Step-by-step explanation:

As per the distance formula, the rate of the canoe in still water is 5 mph; the rate of the current is 1 mph.

Distance formula:

Distance is defined as the total movement of an object without any regard to direction. So, it is defined as the distance that covers how much ground an object despite its starting or ending point.

Distance = Speed x time

Given,

The Jones family took a 12-mile canoe ride down the Indian River in 2 hours. After lunch, the return trip back up the river took 3 hours.

Here we need to find the  rate of the canoe in still water and the rate of the current.

According to the given question we know that,

Speed downriver = (12 mi)/(2 h) = 6 mph.

Speed upriver =  (12 mi)/(3 h) = 4 mph.

Now, we need to find the canoe's rate in still water is the average of these speeds:

=> (6+4)/2 = 5 miles per hour.

Then the current's rate is calculated as the difference between the actual rate and the canoe's rate:

=> 6 - 5 = 1 miles per hour.

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Given: A figure is given.

Required: to determine the expression for the area of the figure. Also, determine the area when x=2.

Explanation: The area of the figure can be determined by dividing the figure as shown below-

Now, DEFG and ABCG represent rectangles. The dimensions of the rectangle DEFG is (2x+4) by (7x+2), and of the rectangle, ABCG is (4x+2) by BC where BC is-

Hence, the expression for the area is-

Further solving-

Substituting x=2 as follows-

Final Answer: The expression for the area of the figure is-

The area when x=2 is 158 sq units.

The equivalent inequality with x isolated in the left side is x<(L-Ky)/J

A positive number divided by both sides of an inequality results in an equal inequality. And if the inequality symbol is reversed, division on both sides of an inequality with a negative value results in an analogous inequality.

Following step by step process-

Jx+Ky<L (Given)

Subtracting Ky on both the side

Jx<L-Ky

Now dividing by J both side

x<(L-Ky)/J

Therefore, equivalent inequality with x isolated in the left side is x<(L-Ky)/J.

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The complete question is:

"Jx+Ky<L assume J<0

The equivalent inequality with x isolated in the left side is"

Given:

a. The amount of flour that the bakery used this month was a 50% increase relative to last month.

So, we will draw a diagram that represents the situation

As shown, for last month, we have drawn a rectangle divided into two equal areas, each one represents 50%

this month was a 50% increase, so, we have drawn 3 areas which represent 50% increase

b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.

As shown, for last month, we have drawn a rectangle with four equal areas

75% decrease, so, we have to remove 3 areas to make the remaining = 25%

So, the difference will give a 75% decrease

The length of the first piece is 5 inches when a 43-inch piece of steel is cut into three pieces.

According to the question,

We have the following information:

A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piece.

Now, let's take the length of the first piece to be x inches (as shown in the figure).

Length of second piece = 2x inches

Length of third piece = (3+5x) inches

Now, we have the following expression for addition:

x + 2x + 3 + 5x = 43

8x+3 = 43

8x = 43-3

8x = 40

x = 40/8

x = 5 inches

Hence, the length of the first piece is 5 inches.

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Our required probability is 99.82% or a 100%

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.

Percentages. The use of percentages to express statistics is one of the most popular. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By dividing the whole or whole number by 100, one percent (or 1%) is equal to one hundredth of the total or whole.

Given that P(operational infection occurs at a 3% rate)

P(operational repair failures) = 17%

P(infection and failure happen simultaneously) = 2%

The first thing we'll discover is that P(infection or failure) is given by 0.03 + 0.17 - 0.02 = 0.18 = 0.18%.

Therefore, the probability that these procedures will be successful and infection-free is given by 100 - 0.18 = 99.82%.

Consequently, 99.82% of a probability is needed.

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We have the next functions

Function notation

Describe the transformation in words

we have 2 transformations, the 2 that multiplies the function f(x) means that we will have an expansion in the y axis by 2, the one means that we will have a shift up by one unit

we know that

the rule of the translation in this problem is 2 units at left and 3 units up

so

(x,y) ------> (x-2,y+3)

Apply the rule

(7,2) ------> (7-2,2+3)

The radius of the cylinder is r=3 cm.

The height of the cylinder is h=7 cm.

The expression for the volume of the cylinder is,

Substituting the given values in the above equation,

Thus, option (C) is the correct solution.

You have the following expression:

consider a1 = 6.

In order to determine the value of a2, consider that if an = a2, then an-1 = a1. Replace these values into the previous sequence formula:

Hence, a2 is equal to 75

In order to corroborate that the points belong to the equation, we must subtitute the points into the equation.

If we substitute the points from option A, we get

for (1,8), we have

then, option A is false.

Now, if we substitute the points in option B, for point (2,5), we have

which is correct. Now, for point (-1.8) we obtain

Since all the points fulfil the equation, then option B is an answer.

Lets continue with option C and D.

If we substitute point (1,8) from option C, we have

then, option C is false.

If we substite point (4,11) from option D, we get

then, option D is false.

Therefore, the answer is option B.

Answer: Perimeter = 1.962 x 10^8 cm

Explanation:

The first step is to calculate the width of the rectangle. Recall,

Area = length x width

width = Area /length

From the information given,

Area = 5.612 times 10^14 cm squared

Length = 9.2 times 10^7cm

Thus,

width = 5.612 times 10^14 /9.2 times 10^7

width = 6.1 x 10^6

The formula for calculating the perimeter is

Perimeter = 2(length + width)

Thus,

Perimeter = 2(9.2 x 10^7 + 6.1 x 10^6)

Perimeter = 1.962 x 10^8 cm

Consider all the different possible combinations of 4 members of the committee (b,b,b,b), (b,b,b,g),...(g,g,g,g). We need to use the binomial distribution given below

In our case

Then,

To perform this multiplication, first, we have to transform the mixed numbers into fractions as follows:

Substituting these values into the multiplication, we get:

This result can be expressed as a mixed number as follows: