Evelyn is thinking of constructing a swimming pool in the plot next to her house such that it is surrounded by grass as given in the figure below. The dimensions of the plot is 50 ft x 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.

A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence.

In case the 95 % confidence interval would be given by

[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]

A confidence interval exists "a range of values that's likely to contain a population value with a certain degree of confidence. It exists often denoted a % whereby a population means lies between an upper and lower interval".

The margin of error exists the range of values below and above the sample statistic in a confidence interval.

Normal distribution, exists a "probability distribution that exist symmetric about the mean, showing that data near the mean exists more frequent in occurrence than data far from the mean".

[tex]$\bar{X}_1=5.84$[/tex] represent the sample mean 1

[tex]$\bar{X}_2=3.96$[/tex] represent the sample mean 2

n 1 = 25 represent the sample 1 size

n 2 = 25 represent the sample 2 size

[tex]$s_1=2.211334$[/tex] sample standard deviation for sample 1

[tex]$s_2=2.35372$[/tex] sample standard deviation for sample 2

[tex]$\mu_1-\mu_2$[/tex] parameter of interest.

The confidence interval for the difference of means exists given by the following formula:

[tex]$\left(\bar{X}_1-\bar{X}_2\right) \pm t_{\alpha / 2} \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} \text \dots{ (1) }$$[/tex]

The point of estimate for [tex]$\mu_1-\mu_2$[/tex] exists just given by:

[tex]$\bar{X}_1-\bar{X}_2=5.84-3.96=1.88$$[/tex]

In order to estimate the critical value [tex]$t_{\alpha / 2}$[/tex] we require to estimate first the degrees of freedom, given by:

[tex]$d f=n_1+n_2-1=25+25-2=48$$[/tex]

Since the Confidence is 0.95 or 95 %, the value of [tex]$\alpha=0.05$[/tex]and α 2 = 0.025, and we can utilize excel, a calculator or a table to estimate the critical value. The excel command would be: " = -T.INV (0.025, 48) ". And we see that [tex]$t_{\alpha / 2}=2.01$[/tex]

In order to replace into formula (1), we get

[tex]$1.88-2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=0.582$[/tex]

[tex]$1.88+2.01 \sqrt{\frac{2.211334^2}{25}+\frac{2.35372^2}{25}}=3.178$[/tex]

In case the 95 % confidence interval would be given by

[tex]$0.582 \leq \mu_1-\mu_2 \leq 3.178$[/tex]

Because all the values for the confidence interval are higher than 0, we may infer that there are significant differences between the means of the two groups in this case, with the mean for group 1 (Medicine) being considerably higher than the mean for group 2 (Placebo) at 5% of significance.

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Answer:

1) trinomial

2) binomial

3) binomial

4) trinomial

5) monomial

Step-by-step explanation:

Monomial: 1 term

Binomial: 2 terms

Trinomial: 3 terms

Terms are separated by plus and minus signs.

1) trinomial

2) binomial

3) binomial

4) trinomial

5) monomial

Answer:

x = ±√7  and   x=±i√2

Step-by-step explanation:

x^4-5x^2-14=0

Factor

(x^2 - 7) ( x^2 +2) =0

Using the zero product property

x^2 -7 =0     x^2 + 2 =0

x^2 =7            x^2 = -2

Taking the square root of each side

(x^2)^1/2 =7^1/2           ( x^2)^1/2 = (-2)^1/2

x = ±√7                              x=±i√2

Answer:

3

Step-by-step explanation:

1 + 2 = 3

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Answer:

3

Step-by-step explanation:

1 + 2 = 3

Let break it down.

Lets say you have 1 apple

Your friend has 2 apples

All together you have 1 + 1 + 1 = 3 apples

Since the school district will allow parents to decide whether they want their children to be in the tracked or non-tracked group, the type of design that the school district has implemented is  a. matched design.

A matched group design is an experimental layout where the study subjects are selected because their variables match.

Therefore, In a matched pairs design, study participants are matched according to important variables or shared traits that are pertinent to the study's subject. The second step involves assigning one member of each pair to the control group and the other to the experimental group.

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See full question below

Parents have raised major concerns over a school district's proposed experiment to examine the effectiveness of removing math tracks and instead placing all students into one open math class. In response, the school district has decided not to randomly assign students to be placed in tracked or non-tracked math classes. Instead, the school district will allow parents to decide whether they want their children to be in the tracked or non-tracked group.

which methodological problem is very likely under this scenario

Select one:

a. matched design

b. pre-post design

c. nonequivalent comparison design

d. multiple time-series design

Fabric bought by Paul and Rita to make a shirt was 1 7/8 m and 1 3/4 m respectively , Paul bought 1/8 m more than Rita.

As given in the question,

Length of fabric bought by Paul to make his shirt = 1 7/8 m

Length of fabric bought by Rita to make his shirt = 1 3/4 m

Convert length of fabric into proper fraction

Paul fabric = 1 7/8 m

                 = 15 /8 m

Rita fabric = 1 3/4 m

                = 7 /4 m

Length of Paul fabric more than Rita

Length of more fabric bought by Paul than Rita = (15 /8) - ( 7/4)

                                                                          = (15/8) - (14/8)

                                                                          = 1/8 m

Therefore, fabric bought by Paul and Rita to make a shirt was 1 7/8 m and 1 3/4 m respectively , Paul bought 1/8 m more than Rita.

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Answer: D

Step-by-step explanation:

as when 3746 is rounded to the nearest hundred t is 4000

whereas when 3746 is rounded to the nearest ten it is 3800.

4000 is larger than 3800 so the answer is D.

it's 27/8 .........................

The first transformation is the hardest to write using algebraic notation.

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

Notice the first figure, the graph is translated 4 units to the left.

But, the second figure shows a vertical stretch of 2 times.

Let the function be y=f(x).

Then, the translation 4 units to the left using algebraic notation is written as:

y = f(x+4)

And, the vertical stretch of two times is:

y = 2f(x)

Clearly, the first transformation is the hardest to write using algebraic notation.

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When rolling two dice the possible outcomes are:

Probability is calculated as follows:

There is a total of 6x6 = 36 possible outcomes. From the table, we can see that 5 of them are a 6 and 3 of them are a 10. Then, the number of favorable outcomes is 5 + 3 = 8. Therefore, the probability of winning on your next turn is:

Answer:

BD = 56

Step-by-step explanation:

x + 21 = 4x

3x = 21

x = 7

x + 4x + 21

5x + 21

35 + 21

56

Answer: 1.6 or 2

Step-by-step explanation:

If you are rounding it to the nearest tenths then the answer is 1.6 but if you are rounding to the nearest whole number then its 2.

Answer:

Angle YVX = 59°

Angle Y = 85°

x = 3

Step-by-step explanation:

You got the first two correct.

The last bit, use the fact that the shape is a parallelogram, the opposite sides are equal.

2x = 6

x = 3

Answer

Graph 1 = 1/3 slope

Graph 2 = -1/3 slope

Graph 3 = 3 slope

Graph 4 = -3 slope

I found these by counting rise over run,

or y/x to points on the line that cross the x or y axis.

The graphs that have a line that go up from left to right are positive slopes

The graphs that have a line that go down from left to right are negative slopes

Problems solved!

Answer:

100000000000000000000000000000

Step-by-step explanation:

The reason that can be used to show that the lines are parallel is: alternate exterior angles converse.

The alternate exterior angles converse can be defined as rule that states that if two exterior angles that lie on each of the lines that is crossed by a transversal are congruent, then the lines can be said to be parallel lines.

The diagram below shows two lines that are intersected by a transversal. It also shows two pairs of alternate exterior angles, a and d, and b and c.

If angles a and d are congruent or angles b and c are congruent, then both lines can be proven to be parallel to each other by the alternate exterior angles converse.

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Step 1: Distributive property:

Step 2: Subtraction Property of Equality

Step 3: Simplifying

Step 4: Division property of equality

Step 5: Simplifying

Given the expression

9(u + 2) = -45

Step 1: Expand using the Distributive property:

9u + 9(2) = -45

9u + 18 = -45

Step 2: Subtract 18 from both sides (Subtraction property of equality)

9u + 18 - 18 = -45 - 18

Step 3: Simplifying

9u = -63

Step 4: Divide both sides by 9 (Division property of equality)

9u/9 = -63/9

Step 5: Simplifying

u = -7

Answer:

The answer is 43

Step-by-step explanation:

Remember that the sum of the angles of all triangles is 180 degrees.

80+57+x=180

137+x=180

x=43

Answer:

See below

Step-by-step explanation:

3 / (6i)    =   3 / (6 * sqrt(-1) )

To rationalize the denominator , multiply both top and bottom of the fraction by   ( 6i)

=  18i / ( 6i * 6i)   = 18i / (36 i^2 ) = 18 i / (-36 ) = - i/2

Answer:

6.39 and 100.8

Step-by-step explanation:

To find a certain percent of a number, convert the percent to a decimal and multiply them together

0.09 * 71 = 6.39

1.26 * 80 = 100.8

ANSWER:

No solution

STEP-BY-STEP EXPLANATION:

We have the following inequality:

The value of 7 is not less than -2, so this is false.

Which means that the set has no solution

corresponding (option D)

Since the lines are parallel and a tranversal line cuts the two lines:

The angle 2 at the top of the first line correspods to angle 6 at the top of the second line.

Angle 2 and angle 6 are equal.

Hence. we say angle 2 and angle 6 are corresponding angles (option D)

Answer:

78

Step-by-step explanation:

80-2+78 soo,

78+2 +80 with means 102+78 =180

Answer:

102 + 78 = 180

Step-by-step explanation:

Answer: x=-3(-y+3)

Step-by-step explanation:

We get that the expected temperature is

In a bar graph the length of the bar need not be in proportion to the information being False.

Bar graph. A bar chart is frequently used to compare values of different things at a specific time. It presents information visually using rectangles (bars). It generally serves as a visual aid for proportions, patterns, comparisons, and contrasts.

To represent value, it makes use of bars that stretch to various heights. Vertical bars, horizontal bars, grouped bars (several bars that compare values in a category), and stacked bars can all be used to construct bar graphs (bars containing multiple types of information).

A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.

comparisons of several variables that are simple. clarity in the presentation of data trends. Simple value determination.

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