A couple quick algebra 1 questions for 50 points!

Only answer if you know the answer, quick shout-out to Subtomex0, tysm for the help!

The area of the patio is 192 [tex]m^{2}[/tex]

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Length of swimming pool=18 m

Width of swimming pool=8 m

Area of swimming pool= 18*8 = 144[tex]m^{2}[/tex]

Width of patio=3m

Total length of swimming pool=18+2(3)=24 m

Total width of swimming pool=8+2(3)=14 m

Total area=24*14=336 [tex]m^{2}[/tex]

Area of patio= total area - Area of swimming pool

                     =336-144

                     =192 [tex]m^{2}[/tex]

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Answer:

Sum is

Step-by-step explanation:

Using compound interest, it is found that they must deposit $9,143.47 in order to have the desired amount.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For this problem, the parameters are:

A(15) = 30000, r = 0.08, n = 4

Then we solve for P to find the initial deposit:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]30000 = P\left(1 + \frac{0.08}{4}\right)^{4 \times 15}[/tex]

[tex]P = \frac{30000}{(1.02)^{60}}[/tex]

P = $9,143.47.

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Answer:

265

Step-by-step explanation:

You subtract 275 minus 10

$247.5 was the original amount on the credit card

Lets simplify the problem,

Total amount after late fee = $275

Late fee deduction = 10%

Original amount = 275 - 10% of 275

= 275 - 27.5

= $247.5

So $247.5 was the original amount on the credit card before the late fee.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

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Answer:

B. (5,12,13)

Step-by-step explanation:

The only answer with two side lengths that are greater than the largest side length.

Answer: B

[tex]x + 2y \leq 4 \textrm{ and } 3x + y \leq 4[/tex]

Step-by-step explanation:

Insert the values of x and y for any point in the heavily shaded region and see if it satisfies both inequalities

We can see that the origin (0,0) is inside the shaded region so use these values because they are the easiest to compute

Plug in x = 0 and y = 0 into the first inequality
0 + 2.0 = 0 which is greater than 5.

So we can eliminate both A and D since they both contain incorrect inequalities

Now, test the second inequality with x = 0 and y = 0

For B we get

3.0 + 0 = 0 which is indeed less than 4

C is not applicable since 0 is not greater-than-equal to 4

Hence B is the correct solution

This can be verified using a graphing tool (see image)

The value of the expression 6/5 * 240 is 288

The expression is given as:

6/5 * 240

Divide 240 by 5

6 * 48

Multiply 6 and 48

288

Hence, the value of the expression 6/5 * 240 is 288

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The number of ways we can select 3 cracked and 2 good is 1200 ways.

Given there are 5 eggs in which 3 eggs are cracked and 2 eggs which are good.

We have to find the number of ways we can select 3 cracked and 2 good eggs from 5 eggs.

Number of ways can be found through permutations.

The factorial of n  equals the product of n with the smaller factorial..

Permutations is the technique of calculating  various ways in which objects from a set may be selected, generally without replacement, to form subsets.

n[tex]P_{r}[/tex]=n!/(n-r)!

So the number of ways will be 5[tex]P_{3}[/tex]*5[tex]P_{2}[/tex]

([tex]5P_{3}[/tex] for cracked eggs and [tex]5C_{2}[/tex] for good eggs)

=5!/(5-3)!*51/(5-2)!

=5*4*3*2!/2!*5*4*3!/3!

=5*4*3*5*4

=1200

Hence there are 1200 ways through which 3 cracked and 2 good eggs can be selected from 5 eggs.

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The perimeter of the triangle whose coordinates are A (2, 2), B (3, 3), and C (4, 2) is 4.828

We can determine the perimeter of a triangle with vertices by utilizing the distance formula.

Given that, we have the vertices (x₁,y₁), (x₂, y₂), (x₃, y₃). Then the length of each sides can be expressed as follows:

SIde AB = [tex]\mathbf{\sqrt{(x_1 -x_2)^2 +(y_1 -y_2)^2}}[/tex]

Side AC = [tex]\mathbf{\sqrt{(x_1 -x_3)^2 +(y_1 -y_3)^2}}[/tex]

Side BC = [tex]\mathbf{\sqrt{(x_2 -x_3)^2 +(y_2 -y_3)^2}}[/tex]

Replacing the values of the coordinates into the given formula above the perimeter of the triangle is 4.828

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The expression that represents well the geometric sequence is [tex]f(n) = 8 \cdot 2^{n-1}[/tex] and the value of the fourth term is 64. (Correct choice: B)

Geometric sequences are exponential expressions with discrete domain, whose form is presented and explained below:

[tex]f(n) = a \cdot r^{n-1}[/tex], where a, r are real numbers and n is a natural number.     (1)

Where:

According to the statement, we know that the first term of the geometric sequence is 8 and between any two consecutive terms there is a common ratio of 2. If we know that a = 8, r = 2 and n = 4, then the fourth term of the series by means of (1) is:

[tex]f(4) = 8 \cdot 2^{4-1}[/tex]

f(4) = 8 · 8

f(4) = 64

The expression that represents the geometric sequence is [tex]f(n) = 8 \cdot 2^{n-1}[/tex] and the value of the fourth term is 64.

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The slope of given data is a -3.

According to the statement

we have given a some data and we have to find the slope of the data.

So, data given is:

x, has the entries, negative 2, negative 1, 0, 1, 2.

y, has the entries, negative 2, 1, 4, 7, 10.

and we have to find the slope of the data

So, we know that it is a data represent in the graph then

We know that a there is a graphical representation of data.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

And when we observe this data then we see that the there is some increase the y axis value as compare to the x axis values.

So,

For each unit of run in the x-values, there is an increase of 3 in the y-values. The slope is rising over Run so 3/1 = 3

So, The slope of given data is a -3.

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Answer: the answer is a -3

Step-by-step explanation:

The measure of angle BC (m ∠BC) is 90°

From the question, we are to determine the measure of angle BC

From the given information, we have that

B P ⊥ P C

This means line BP is perpendicular to line PC

The angle between two perpendicular lines is 90°

Hence, the measure of angle BC (m ∠BC) is 90°.

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The interquartile range of the data set is 8

To do this we have to arrange in ascending order

= 8,9,9,9,10,11,13,15,17,18,22

Q2 = The median of the data is 11.

We have to find the median of the half before 11 and the median of the half after 11.

We would have

8,9,9,9,10

Q1 = 9

And 13,15,17,18,22

Q3 = 17

The interquartile range is

Q3 - Q1

= 17 - 9

= 8

The interquartile range of the data set is 8

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Correct question

Study the following data set.

{8,15,9,18,9,17,22,10,11,9,13}

What is the interquartile range of the data set?

The total surface area of a regular square pyramid having slant height of 10units and base length of 6 units is 168 square inches which is fifth option.

Given that slant height is 10 units and base lengths of 6 units.

We are required to calculate total surface area of regular square pyramid.

We know that total surface area of regular square based pyramid is equal to [tex]s^{2} +s\sqrt{s^{2} +4h^{2} }[/tex] in which s is side of base length and h is slant height of regular square pyramid.

Total surface area=[tex]6^{2} +6\sqrt{6^{2} +4*10^{2} }[/tex]

=36+6[tex]\sqrt{36+400}[/tex]

=36+6[tex]\sqrt{436}[/tex]

=36+6*20.88

=36+125.28

=161.28

Nearest option is 168 square inches.

Hence the total surface are of regular square based pyramid is option 5 which is 168 square inches.

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The expanded form of the given expression is 2 × w × z × z

From the question, we are to determine the expanded form of the given expression

The given expression is

2wz²

To write an expression in an expanded form, we will write the expression as a repeated multiplication in the simplest way possible.

To do this, we will first expand the index in the given expression.

The index in the given expression is z²

Thus, we get

z² = z × z

Now, we will include the remaining individual terms in the expression and write them as product.

That is,

2wz² = 2 × w × z × z

Hence, the expanded form of the given expression is 2 × w × z × z

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The figure that is not equivalent to 2¾ is 2¼ × 2½. That is option B.

Simplification is a process that is used to make a fraction appear in its simplest forms.

The fraction given is = 2¾

The simplification of the fraction= 2^3/4 = 2

But simplification of 2¼ × 2½ is equal to;

2¼= 0.5

2½= 1

Therefore 2¾ is not equivalent to 2¼ × 2½ when simplified.

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like the place where you are applying TURNED TRIANGLE.

coz literrally it means that if the trianlge has for example angle a on its right side then we turn the triangle as a whole and make the turn such that angle a is anywhere else but not on our right side....

I believe the explanation is clear, if not do contact me

The measure of angle E is (b) 50°

The given parameters are:

The similarity of the triangles implies that:

From the figure, we have:

angle A = 50

Substitute angle A = 50 in angle A = angle E

angle E = 50

Hence, the measure of angle E is (b) 50°

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The  appropriate display to show the spread of 150 test scores for Mrs. Hansen's last science test is: b.  box and whisker plot.

Box and whisker plot which is also called box plot can be defined as the plot that show a graphical presentation of data set by helping to display the data set or data score .

Hence a graphical presentation display to show the spread of 150 test scores for Mrs. Hansen's last science test is option B which is Box and whisker plot .

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The percentage of population has a resting heart rate is 15.7%.

Given that the mean of the data is 70 beats per minute and standard deviation is 4 beats per minute.

A probability distribution is a mathematical function that describes the probability of several possible values ​​of a variable.

Mean, μ=70

Standard deviation, σ=4

Given that the heart rate is resting between 74 and 82.

Now, we will use the standard normal formula

P(x₁<x<x₂)=P((x₁-μ)/σ<x<(x₂-μ)/σ)

Here x₁=74 and x₂=82.

Substitute these values in the formula, we get

P(74<x<82)=P((74-70)/4<x<(82-70)/4)

P(74<x<82)=P(4/4<x<12/4)

P(74<x<82)=P(1<x<3)

P(74<x<82)=P(x<3)-P(x<1)

Now, we will find the values by using the z-table, we get

P(74<x<82)=0.998-0.841

P(74<x<82)=0.157

P(74<x<82)=15.7%

Hence, the percentage of the population has a resting rate between 74 and 82 with the mean data is 70 beats per minute and the standard deviation data is 4 beats per minute is 15.7%.

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The weight of a 36-inch piece of PVC pipe is 0.20 pounds

The given parameters about the 36-inch piece of PVC pipe are

Height, h = 36 inches

Outside diameter, D = 0.82 inches

Inside diameter, d= 0.75 inches

The volume of the PVC pipe is then calculated as:

V = πh(D/2)^2 - πh(d/2)^2

Substitute the known parameters in the above equation

V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2

Evaluate the quotients

V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2

Evaluate the exponents

V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625

Evaluate the products

V = 19.002024 - 15.89625

Evaluate the difference

V = 3.105774 cubic inches

From the question, we have:

Weight =  0.063 pounds per cubic inch

So, the total weight is

Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch

Evaluate the product

Total weight = 0.195663762 pounds

Approximate

Total weight = 0.20 pounds

Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds

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Using the normal distribution, we have that:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given, respectively, by:

[tex]\mu = 5.34, \sigma = 0.03[/tex]

The 8th percentile separates the bottom 8%, that is, X when Z = -1.405, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.405 = \frac{X - 5.34}{0.03}[/tex]

X - 5.34 = -1.405 x 0.03

X = 5.30.

The 92th percentile separates the top 8%, that is, X when Z = 1.405, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.405 = \frac{X - 5.34}{0.03}[/tex]

X - 5.34 = 1.405 x 0.03

X = 5.38.

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Answer:

For every x value, the y value would be double of the x value. (ex, x=2, y=4)

Step-by-step explanation:

If you look closely at every x value and see their y-values for the ordered pair, you will see that the x-value in question was doubled in order to find the y-value. This will result in the linear equation: [tex]y=2x[/tex].

Answer:

6288388288288828ffjfjjrjir

The concept of factoring quadratic equations simply is one of the ways to solve for the zeroes of the quadratic equation.

The concept of factoring quadratics is a technique which is characterized by expressing the quadratic equation ax2 + bx + c = 0 as a product of its associated linear factors as (x - f)(x - g), in which case, f and g are the roots of the quadratic equation ax2 + bx + c = 0.

Factoring is an important concept that helps express equations of any type in simpler forms The mode of operation of the factoring works such that, the polynomial is rewritten in a simpler form and consequently, expressed as a product of it's linear factors.

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Answer:

Step-by-step explanation:

Reflection over any line is a rigid transformation that does not change angles or lengths. Dilation is a transformation that changes lengths by the same scale factor, but has no effect on angles. Dilated figures are similar to the original.

When ΔXYZ is reflected over a vertical line, no lengths or angles are changed. When the reflected triangle is dilated by half, we get ...

  Y'X' = (1/2)YX . . . . . . . makes option 3 false

  X'Z' = (1/2)XZ . . . . . . . makes option 4 true

Since no angles are changed, we have ...

  Angle XZY ≅ Angle Y'Z'X'   (another name for angle X'Z'Y')

  ... makes option 2 true

Of course, the resulting triangle is similar to the original, so ...

  △XYZ ~ △X'Y'Z' . . . . . option 1 is true

Answer:

C

Step-by-step explanation:

Example
Find 55% of 200.

200 times 0.55 = 110

Answer: the answer is B

Step-by-step explanation:

if we want to find the percent of 700 people out of 4400 people, we would do 700/4400, which is equal to 0.16, or 16 percent.

The values that are included in the random variable of the experiment that include rolling one 6-sided die and one 10-sided die are 10, 14 and 16

The experiment elements are given as:

The sample spaces of both dice are:

6-sided = {1, 2, 3...., 6}

10-sided = {1, 2, 3...., 10}

When the outcomes of both dice are added, we have:

Sample space = {2, 3, 4, 5, 6, 7, 8, 9, .............. 16}

Minimum = 2

Maximum = 16

This means that the values that are included in the random variable are in the range 2 - 16 i.e. starting from 2 and ending in 16

Hence, the values that are included in the random variable of using one 6-sided die and one 10-sided die and rolling them together are 10, 14 and 16

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A margin of sampling "error" is a statistical calculation for how accurate a poll's results are.

A population parameter's sampling error is the discrepancy between the sample statistic used to estimate it and the parameter itself. For instance, sampling error is the variance between a population mean and a sample mean.

The sampling errors can be placed into four categories:

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