write your answer as a mixed number in simplest from
3 9/10 + 4 9/10

The dimensions that need to be used so that the enclosed area of the two adjacent rectangular corrals will be maximum is 90 by 120 feet.

What do you mean by adjacent?

Adjacent refers to something that is close to or nearby. Your next-door neighbor is the person who lives in the home or apartment that is next to yours, even though you may consider the individuals who live up and down your street to be your neighbor.

Two things can be considered adjacent if they contact each other or share a wall or border. If two angles in geometry share a side and a vertex, they are said to be adjacent. In other words, neighbor angles do not overlap and are adjacent to each other immediately.

Solution Explained:

So according to the question, we get the equation

Perimeter is 4x + 3y = 720

⇒ x = 180 - [tex]\frac{3}{4}y[/tex]

Taking Area = 2xy

= 2(180 - [tex]\frac{3}{4} y[/tex])y

= 360y - [tex]\frac{3}{2} y^{2}[/tex]

Differentiating the function w.r.t y

A'(y) = 360-3y

Setting to 0

0 = 360 - 3y

⇒ y = 360 / 3 ⇒ 120

Now putting the value of y in

x =  [tex]180- \frac{3}{4} X 120[/tex]

x = 180 - 90 = 90

So, the dimensions are 90 by 120 feet.

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Answer:

f(-2)=-12

f(3)= -2

Step-by-step explanation:

f(x) is original form

So for f(-2) we find where x is -2 and in this case f(x) is -12

And for f(3) we do similar but since x=3 isn’t on the table we see a pattern that whne x goes up one f(x) adds 2 so 3 is -2

Hopes this helps

There were a total of 625 customers who bought at a gas station on Wednesday

From the question, we have the following parameters that can be used in our computation:

Number of customers that purchase doughnuts = 225

Proportion of customers who made additional purchase = 36%

The above parameters mean that:

Proportion of customers who made additional purchase = 36% of The total number of customers

Using the above as a guide, we have the following equation

36% * The total number of customers = 225

Divide both sides by 36%

The total number of customers = 625

Hence, the total number of customers is 625

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To calculate the slope of the line, we have that its points are A(x₁, y₁) and B(x₂,y₂), we apply the following formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{\Delta y}{\Delta x} \iff m=\frac{y_2-y_1}{x_2-x_1} } \end{gathered}$}}[/tex]

To solve, we have that the points are:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{A(x_1=\underbrace{2} \ \ , \ \ y_1=\overbrace{7} \ ) \ and \ B(x_2=\underbrace{-4} \ \ , \ \ y_2=\overbrace{19} } \end{gathered}$}}[/tex]

What we do to solve is that we substitute this data in the formula provided above.

 [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\dfrac{y_2-y_1}{x_2-x_1} } \end{gathered}$}}[/tex]

 [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{19-7}{-4-2} } \end{gathered}$}}[/tex]

 [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{12}{-6}=-2 } \end{gathered}$}}[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

true

The width of the rectangle, x is 2.76 cm

Given,

The area of a rectangle = 17.6 square centimeters

Length of the rectangle = 2.3x

Width of the rectangle = x

We have to find the value of x.

Here,

Area of rectangle = length × width

Then,

17.6 = 2.3x × x

17.6 = 2.3x²

x² = 17.6/2.3

x² = 7.65

x = √7.65

x = 2.76

Now,

Width of the rectangle =  2.76 cm

Length of the rectangle = 2.76 × 2.3 = 6.35 cm

Therefore,

The value of x, that is the width of the rectangle is 2.76 cm

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The p-value when the test statistic is equal to 2.30 is 0.033.

A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data.

A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct.

The statistical significance of the difference that was found increases with decreasing p-value.

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.

So, the p-value will be:

The t-value for (n-1 = 20-1 = 19) degrees of freedom serves as the test statistic in this experiment.

Using the formula: T.DIST.2T(2.3,19)

The p-value will be 0.033.

Therefore, the p-value when the test statistic is equal to 2.30 is 0.033.

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Complete question:

A restaurant decides to test their oven's thermostat to see if it is working properly, that is if the actual temperature inside the oven is the same as the temperature to which the thermostat was set. Twenty times, the oven was set to 350 degrees and then the temperature was measured with a thermometer.

H o: μ=350 and Ha: μ≠350

The test statistic is equal to 2.30. What is the p-value _____?

The account, will reach $5500 in 33.33 years. if Victoria deposits $5000 into a savings account.

The direct crediting of cash flows associated to an investment or deposit is referred to as simple interest. Simple interest is a quick and straightforward way to calculate the interest amount on a loan. Simple interest is calculated by multiplying the daily interest rate by the principle by the number of days between payments.

The written formula is "Simple Interest = Principal x Interest Rate x Time." This is the most fundamental method of calculating interest.

Victoria deposited $5000 into a savings account with an annual basic interest rate of 0.3%.

Simple Interest Formula

A = P(1 + rt)

5500 = 5000(1 + 0.003t)

5500 = 5000 + 15t

15t = 500

The account will reach $5500 in 33.33 years.

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Part a: The volume of such base would appear to be larger than it was if the bubble was already let go before the titration's equivalence point.

Part b: There would be no impact if the bubble had already been let go after the equivalent point.

For the stated condition-

An air bubble was present in the buret tip as the student started his part II titration. Unnoticed bubble release occurred at some point in the titration.

The inaccuracy in his titration findings that the bubble would've have made if:

Part a: If the bubble had burst before the titration's equivalence point, the base's volume would have appeared larger than it originally was, having the base seem stronger than it is, and changing calculations.

Part b: There would be no impact if the bubble had already been let go after the equivalent point.

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The solution to the system of equation y = - 2x - 7 and 9x - 10y = 12 is,

x = - 2 and y = - 3.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.

Given, Are two linear equations y = - 2x - 7 and 9x - 10y = 12.

Therefore,

9x - 10y = 12.

9x - 10(- 2x - 7) = 12.

9x + 20x + 70 = 12.

29x = - 58.

x = - 2 and hence y = - 2(-2) - 7 ⇒ y = - 3.

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The statement which is true about the two equilateral triangles is b)The two triangles are the same shape but not the same size. So, correct option is b.

In calculation, a symmetrical triangle is a triangle where every one of the three sides have a similar length. In the natural Euclidean calculation, a symmetrical triangle is likewise equiangular; that is, every one of the three inward points are additionally compatible to one another and are each 60°. It is likewise an ordinary polygon, so it is additionally alluded to as a normal triangle.

Some of hypotheses which are made sense of utilizing symmetrical triangle:

The side length of the primary symmetrical triangle is 3 inches.The side-length of the second symmetrical triangle is 4 inches.Since both the triangles are symmetrical triangles, in this way they have same shape.

Be that as it may, the two triangles have different side lengths in this way they have different size.

Hence, option b is correct.

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(Complete question) is:

on a piece of paper, use a protractor and a ruler to construct two equilateral triangles: one with a side length of 3 inches and one with a side length of 4 inches. which statement is true about the two triangles?

a. The two triangles are the same size but not the same shape.

b. The two triangles are the same shape but not the same size.

c. The two triangles are the same size and same shape.

d. It is impossible to construct equilateral triangles with these side lengths.

Answer:

15

Step-by-step explanation:

Given functions:

[tex]g(x)=14-\dfrac{2}{3}x[/tex]

[tex]h(x)=-x-7[/tex]

g(9) means to substitute x = 9 into function g(x):

[tex]\begin{aligned}\implies g(9)&=14-\dfrac{2}{3}(9)\\&=14-\dfrac{18}{3}\\&=14-6=8\end{aligned}[/tex]

h(-14) means to substitute x = -14 into function h(x).

[tex]\begin{aligned}\implies h(-14)&=-(-14)-7\\&=14-7\\&=7\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies g(9)+h(-14)&=8+7\\&=15\end{aligned}[/tex]

As one calculation:

[tex]\begin{aligned}\implies g(9) + h(-14)&=\left(14-\dfrac{2}{3}(9)\right)+\left(-(-14)-7\right)\\&=\left(14-\dfrac{18}{3}\right)+\left(14-7\right)\\&=\left(14-6\right)+\left(14-7\right)\\&=8+7\\&=15\end{aligned}[/tex]

For given situation, the probability that a house belongs to the second county, knowing that it has a garage attached to it = 0.8

Assume event a: a house belongs to the first county;

event b: a house belongs to the second;

event c: a house belongs to the third;

event g: a house has an attached garage.

20% of the houses in the first county,

⇒ P(a) = 20%

30%  of the houses in the second county

⇒ P(b) = 30%

50%  of the houses in the first county.

⇒ P(c) = 50%

a garage is attached to 70% of the houses in the first county,

⇒ P(a ∩ g) = 70%

a garage is attached to 80% of the houses in the second county

⇒ P(b ∩ g) = 80%

and a garage is attached to 90% of the houses in the third county.

⇒ P(c ∩ g) = 90%

We need to find the probability that a house belongs to the second county, knowing that it has a garage attached to it.

i.e., P(b ∩ g) which is 80% = 0.8

Therefore, the probability that a house belongs to the second county, knowing that it has a garage attached to it is 0.8

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The time that the car will travel when the average speed is 55mph is 11 hours.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

From the information, the car has an average speed of 55 mph and it's travelling at 605 miles.

It should be noted that time will be calculated as the distance divided by the speed that given and this will be:

Time = Distance / Speed

Time = 605 / 55

Time = 11

The time is 11 hours.

This simply illustrates the time.

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Answer:

Help guys can you help me

Following 60 minutes of calls, the credit balance is $22.33 on a phone card.

For the stated equation-

It's necessary to use the credit that remains after 60 minutes of calls.

Credit balance is $26. 23 - 29 minutes later.

Credit balance is $22. 85 - 59 minutes later.

Take the minutes as 'x' they are and the remaining credit as 'y' it is;

(29, 26. 23)

(59, 22. 85)

The equation will be because it is a linear function:

Y - y1 = m(x - x1)

Slope m = (y2 - y1)/(x2 - x1)

m = (22.85 - 26.23)/(55 - 29)

m = -3.38/30

m = - 0.13

Put the values in equation of the line.

y - 26. 23 = -0.13 (x - 29)

y = -0.13x + 30

For x = 59 minutes, remaining credit;;

y = -0.13(59) + 30

y = 22.33

Thus, following 60 minutes of calls, the credit balance is $22.33 on a phone card.

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The critical value that corresponds to a confidence level of 90 % [1.34503037 , ∞ ).

Given:

you intend to estimate a population mean with a confidence interval. you believe the population to have a normal distribution. your sample size is 15. find the critical value that corresponds to a confidence level of 90%.

sample size n = 15

confidence interval ci = 90

we know that,

Degrees of freedom df = n - 1

here n = 15

df = n - 1

= 15 - 1

= 14

Using the graphical t value calculator:

with df = 14 significance level = 1 - 0.90 = 0.10

so t = [1.34503037 , ∞ )

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Selena got the greater fraction of the questions correctly as 5/6 > 4/6.

For the stated data in the question.

Correctly answered by Selena in science quiz = 5/6

In decimal form.

5/6 = 0.833

Correctly answered by Ana in science quiz = 4/6 .

In decimal form;

4/6 = 0.666

Now,

0.666 > 0.8333

Thus,

5/6  > 4/6

Therefore, Selena got the greater fraction of the questions correctly as 5/6 > 4/6.

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Answer:

a) 12 · y = x

b) If the points show equivalent fractions and the line goes through (0,0)

Step-by-step explanation:

a1) divide any numbers from the x and y line (for example, 2 ÷ 24 would give us 12)

a2) This equation makes sense because any number from the x line (for example, 2) multiplied by 12 would give us the number from the y line (in this example, 24).

The integers when product of two consecutive odd integers is 21 more than twice the larger

integer are 5 and 7.

Let the integers be x and x + 2. Since the product of two consecutive odd integers is 21 more than twice the larger integer. This will be:

x(x + 2) = 2(x + 2) + 21

x² + 2x = 2x + 4 + 21

x² + 2x = 2x + 25

Collect like terms.

x² + 2x - 2x - 25

x² - 25

x² - 5²

= (x - 5)(x + 5)

x - 5 = 0

x = 0 + 5

x = 5

The higher number will be:

= x + 2

= 5 + 2

= 7

The numbers are 5 and 7

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It's better to use adjusted R-squared than simple R because the adjusted R-squared is adjusted for the number of variables and sample size whereas simple R has different values for each size.

Adjusted R-squared considers and tests different independent variables against the model and R-squared does not.

Many investors prefer adjusted R-squared because adjusted R-squared can provide a more precise view of the correlation by also taking into account how many independent variables are added to a particular model against which the stock index is measured.

The unadjusted R-squared increases or stays the same as more variables are included, whereas the adjusted R-squared is adjusted for the number of variables and large sample size.

Adjusted R-squared is calculated for multiple explanatory variables and R-squared value is calculated for only one explanatory variable.

That's why It is better to use values of adjusted R instead of simply values of R

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Answer:

898.88

Step-by-step explanation:

if you multiply 800 by 1.06, then multiply that answer by 1.06, you get 898.88

The probability that  at least 6% of those in the sample believe the thing about reptilian people controlling our world is 0.0567

What is binomial probability distribution?

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

According to the given question:

n = 100 random sample

p = 0.6 probability of success

P(X = x) = n to x pˣ(1-p)ⁿ⁻ˣ

P(X = 30) = 100 to 30 (0.6)³⁰(0.4)⁷⁰

               = 0.0567

Hence the probability that  at least 6% of those in the sample believe the thing about reptilian people controlling our world is 0.0567

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Answer:

  4) ∠J = ∠L = 88°; ∠K = 92°

  5) ∠P = ∠R = 34°; ∠S = 146°

  6) ∠T = 54°; ∠U = ∠W = 126°

Step-by-step explanation:

You want the remaining angles in each rhombus where one angle is specified.

In a rhombus, as in any parallelogram, opposite angles are congruent, and adjacent angles are supplementary.

In each of the rhombi, the adjacent angle is supplementary:

  4) 180° -92° = 88°

  5) 180° -146° = 34°

  6) 180° -54° = 126°

Then the angle measures of interest are ...

  4) ∠J = ∠L = 88°; ∠K = 92°

  5) ∠P = ∠R = 34°; ∠S = 146°

  6) ∠T = 54°; ∠U = ∠W = 126°

If a scatterplot of standardized, bivariate data displays data that are mostly lying in the upper left and lower right-hand quadrants, then the Pearson correlation is typically going to be negative. The above statement is false.

Bivariate data involves studying and comparing two separate variables. For example, a researcher may record how long it takes people to complete a crossword puzzle while measuring the stress levels of the participants. In this example, the two variables that the researcher is examining are time and stress.

Scatterplots display these bivariate data sets and provide a visual representation of the relationship between variables. In a scatterplot, each point represents a paired measurement of two variables for a specific subject, and each subject is represented by one point on the scatterplot.

When the points on a scatterplot graph produce a lower-left-to-upper-right pattern, we say that there is a positive correlation between the two variables. This pattern means that when the score of one observation is high, we expect the score of the other observation to be high as well, and vice versa.

When the points on a scatterplot graph produce a upper-left-to-lower-right pattern, we say that there is a negative correlation between the two variables. This pattern means that when the score of one observation is high, we expect the score of the other observation to be low, and vice versa.

In statistics, the Pearson correlation coefficient ― also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), the bivariate correlation or colloquially simply as the correlation coefficient ― is a measure of linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation).

The Pearson correlation method is the most common method to use for numerical variables; it assigns a value between − 1 and 1, where 0 is no correlation, 1 is total positive correlation, and − 1 is total negative correlation. This is interpreted as follows: a correlation value of 0.7 between two variables would indicate that a significant and positive relationship exists between the two. A positive correlation signifies that if variable A goes up, then B will also go up, whereas if the value of the correlation is negative, then if A increases, B decreases.

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The test statistic results for that scenario is -1.5.

Simplified the calculation by eliminating thousands of dollars.

[tex]\bar x[/tex] = sample mean = 18.5

s = sample standard deviation = 5

n = sample size = 25

[tex]\mu_{0}[/tex] = population mean for the null hypothesis = 20

Since the question provide us a test statistic formula. So,

[tex]t_{0}[/tex] = [tex]\frac{\bar x - \mu_0}{\frac{s}{\sqrt{n}}}[/tex]

= [tex]\frac{18.5 - 20}{\frac{5}{\sqrt{25}}}[/tex]

= [tex]\frac{-1.5}{\frac{5}{5}}[/tex]

= -1.5 / 1

= -1.5

Thus, the result for test statistic in that scenario is -1.5.

Your question is incomplete, but most probably your full question was (image attached)

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Answer:

56 in^2

Step-by-step explanation:

The formula for calculating area of a triangle is:

The height is 7t and base is 4t:

the value of t = 4 so replace x with 4:

The rectangle's measurements are 13.2 feet wide by 19.2 feet long, giving it a total area of 253 square feet.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Here,

length of rectangle=l

width=w

l=w+6

area=l*w

253=(w+6)*w

w²+6w-253=0

w=13.2 feet

l=19.2 feet

The dimensions for the rectangle that have area as 253 sq-feet will be 13.2 feet as width and 19.2 feet as length.

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By using the principle of counting, it can be calculated that

Total number of ways to arrange the four face cards in a 52-card deck =  11880

What is principle of counting?

Principle of counting states that if there are m ways to do one job and m ways to do another job after that job, there are m [tex]\times[/tex] n ways to do both the jobs together.

There are three face cards of hearts, three face cards of diamonds, three face card of clubs and three face cards of spade

Total number of face cards = 3 + 3 + 3 + 3 = 12

We can arrange the four face card in  [tex]{12 \choose 4}[/tex] ways = 495 ways

The four cards should be arranged in a row.

Number of choices for the first card = 4

Number of choices for the second card = 3

Number of choices for the third card = 2

Number of choices for the fourth card = 1

Total number of ways  to arrange the four cards in a row = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1 = 24

Total number of ways to arrange the four face cards in a 52-card deck =

495 [tex]\times[/tex] 24 = 11880

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