Brooke is buying a tent that is in the shape of a rectangular pyramid. The base is 6 feet by 8 feet. If the tent holds 88 cubic feet of air, how tall is the tent's center pole?

The supplied roots' polynomial equation is x³-7x²+20x-24=0.

A polynomial equation is one in which a polynomial is set to zero. It is an equation composed of variables, non-negative integer exponents, and coefficients, as well as operations and an equal sign. It has various exponents. The highest one represents the equation's degree. To be a polynomial equation, the variable in the equation must contain only non-negative integer exponents. Specifically, variable exponents should be non-negative and neither negative nor fractional.

Given that, solution polynomial equation of the least degree has roots of 3, 2+2i, and 2-2i.

Now, x=3, x=2+2i and x=2-2i

x-3, x-2-2i and x-2+2i

So, the polynomial equation is (x-3)(x-2-2i)(x-2+2i)=0

=(x-3)(x(x-2-2i)-2(x-2-2i)+2i(x-2-2i))=0

=(x-3)(x²-2x-2xi-2x+4+4i+2xi-4i-4i²)=0

=(x-3)(x²-2x-2x+4-4i²)=0

=(x-3)(x²-4x+4+4)=0 (∵i²=-1)

=(x-3)(x²-4x+8)=0

=x(x²-4x+8)-3(x²-4x+8)=0

=x³-4x²+8x-3x²+12x-24=0

= x³-7x²+20x-24=0

The supplied roots' polynomial equation is x³-7x²+20x-24=0.

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From the numeric value of the formula, the tuition and fees for the school year ending in 2010 was of $26,270.

The numeric value of a function is found replacing each instance of x by the value that we want to find.

For this problem, the cost function is given by:

T(x) = 26x² + 806x + 15610.

In which x is the number of years after 2000.

Hence the cost in 2010 will be given by:

T(10) = 26(10)² + 806(10) + 15610 = $26,270.

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Answer:

y=120

z=20

Step-by-step explanation:

angle below y is 60° because of corresponding angles

y=180-60=120

y+(4z-20)=180(angles in a straight line)

120+4z-20=180

100+4z=180

4z=180-100

4z=80

z=80/4

z=20°

(1) Frames covered with shade cloth mean = 1.71 and standard deviation = 0.401

(2) control pvc frames only mean = 19.26 and standard deviation = 0.536

(3) warmer (pvc frames covered with plastic) mean = 2.08 and standard deviation = 0.774.

(1) Using the cooler mean and SD:

The calculations are shown in the table below:

[tex]\begin{array}{lll} & \mathrm{X} & (\mathrm{X} \text {-mean })^{2} \\& 1.59 & 0.0144 \\& 1.43 & 0.0784 \\& 1.88 & 0.0289 \\& 1.26 & 0.2025 \\& 1.91 & 0.04 \\& 1.86 & 0.0225 \\& 1.9 & 0.0361 \\& 1.57 & 0.0196 \\& 1.79 & 0.0064 \\& 1.72 & 0.0001 \\& 2.41 & 0.49 \\& 2.34 & 0.3969 \\& 0.83 & 0.7744 \\& 1.34 & 0.1369 \\& 1.76 & 0.0025 \\\text { Total } & 25.59 & 2.2496\end{array}[/tex]

Sample size

[tex]$$n=15$$[/tex]

Sample sum:

[tex]$$\sum x=25.59$$[/tex]

Sample mean:

[tex]$$\begin{aligned}\bar{x}=\frac{\sum x}{n} &=25.59 / 15 \\&=1.71\end{aligned}$$[/tex]

Sample standard deviation:

[tex]\begin{aligned}s=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} &=\sqrt(2.2496 /(15-1)) \\&=0.401\end{aligned}[/tex]

(2) Using the control mean and SD:

The calculations are shown in the table below:

[tex]\begin{array}{lll} & \mathrm{X} & (\mathrm{X}-\text { mean })^{2} \\& 1.92 & 0.0289 \\& 2 & 0.0625 \\& 2.19 & 0.1936 \\& 1.12 & 0.3969 \\& 1.78 & 0.0009 \\& 1.84 & 0.0081 \\& 2.45 & 0.49 \\& 2.03 & 0.0784 \\& 1.52 & 0.0529 \\& 0.51 & 1.5376 \\& 1.9 & 0.0225 \\\text { Total } & 19.26 & 2.8723\end{array}[/tex]

Sample size:

[tex]$$n=11$$[/tex]

Sample sum:

[tex]$$\sum x=19.26$$[/tex]

Sample mean:

[tex]\begin{aligned}s=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} &=\sqrt(2.8723 /(11-1)) \\&=0.536\end{aligned}[/tex]

(3) Assuming a warmer mean and SD:

The calculations are shown in the table below:

[tex]$\begin{array}{lll} & \mathrm{X} & (\text { X-mean })^{2} \\ & 2.57 & 0.3969 \\ & 2.6 & 0.4356 \\ & 1.93 & 0.0001 \\ & 1.58 & 0.1296 \\ & 2.3 & 0.1296 \\ & 0.84 & 1.21 \\ & 2.65 & 0.5041 \\ & 0.14 & 3.24 \\ & 2.74 & 0.64 \\ & 2.53 & 0.3481 \\ & 2.13 & 0.0361 \\ & 2.86 & 0.8464 \\ & 2.31 & 0.1369 \\ & 1.91 & 0.0009 \\ \text { Total } & 29.09 & 8.0543\end{array}$[/tex]

Sample size:

[tex]$n=14$[/tex]

Sample sum:

[tex]$$\sum x=29.09$$[/tex]

Sample mean:

[tex]$$\begin{aligned}\bar{x}=\frac{\sum x}{n} &=29.09 / 14 \\&=2.08\end{aligned}$$[/tex]

Sample standard deviation:

[tex]s=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}} &=\sqrt(7.7883 /(14-1)) \\&[/tex]

  [tex]=0.774[/tex]

Hence, these are the different samples of mean and standard deviation.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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Based on the fact that there are 8 sports drinks and 6 peach flavored drinks, the probability that all 4 drinks picked by Malia would be peach flavored is 0.2143.

The probability that all 4 drinks will be peach flavored can be found as:

= Probability of first drink being peach x Probability of second drink being peach + Probability of third drink being peach + Probability of fourth drink being peach

The probability of the drinks being peach flavored is:

= 6/8 x 5/7 x 4/6 x 3/5

= 0.2143

In conclusion, the probability that all the drinks are peach flavored is 0.2143.

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Answer:

BC = 13

Step-by-step explanation:

x + 10 + x + 14 = 22

2x + 24 = 22

2x = -2

x = -1

BC = x + 14 = -1 + 14 = 13

Answer:

35:14

Step-by-step explanation:

On calculator 5/2 =2.5

Try this choice to get the same percentage

Answer:

B = 10 : 4 & D = 35 : 14

Step-by-step explanation:

Hope this helps :)

Answer:

(-3,3/2)

Step-by-step explanation:

It's easy just add the abscissa and ordinate individually and divide the obtained abscissa and ordinate by 2

Answer: The answer is the third option. Bosnian Serbs were the aggressors in the war that is discussed in Zlata’s Diary. This diary is a book by  Zlata Filipović. It was written from 1991 to 1993 during the Bosnian war.

Step-by-step explanation: hope this helps!!!!

the image (new coordinate) after the translation is (-2.5, 9.8)

Here we have a rule (also called a transformation or an operator) that works as:

T(x, y) = (x - 7.5, y + 6.8)

So we decrease the x-value by 7.5 and increase the y-value by 6.8. This is a translation of 7.5 units to the left and 6.8 units upwards.

Now, our point is (5, 3), if we apply that transformation we will get:

T(5, 3) = (5 - 7.5, 3 + 6.8) = (-2.5, 9.8)

That is the image after the translation.

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Part A: The equation of least squares regression line is

ŷ = 0.4684X + 64.69888

Part B: The residual that we have here is - 1.382

Part C: Residual refers to the difference between the observed value and the predicted value

Sum of X = 102.5

Sum of Y = 695

Mean X = 10.25

Mean Y = 69.5

Sum of squares (SSX) = 33.625

Sum of products (SP) = 15.75

Regression Equation = ŷ = bX + a

b = SP/SSX = 15.75/33.63 = 0.4684

a = MY - bMX = 69.5 - (0.47*10.25) = 64.69888

ŷ = 0.4684X + 64.69888

Residual = observed - predicted

The observed = 68

The predicted = 0.4684 x 10 + 64.69888

= 4.684 + 64.69888

= 69.382

residual = 68 - 69.382

= -1.38

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Answer: 15

Step-by-step explanation:

The algebraic expression for the phrase "the quotient of y and 6" is y / 6

The difference of -3 - 4 is -7.

The algebraic expression of the following phrase "the quotient of y and 6" is as follows:

Quotient is a quantity produced by the division of two numbers.

Therefore, the algebraic expression for the phrase "the quotient of y and 6" is y / 6

The difference of -3 - 4 can be calculated as follows:

The difference of -3 - 4 is -7.

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Answer:D

Step-by-step explanation:

Answer:

qw1

Step-by-step explanation:

C ) If your bank goes out of business, you lose your money is a false statement .

Since banks are insured by FDIC . So if a bank becomes dissolves or becomes bankrupt FDIC covers the loss of customers of bank upto a certain limit .

A ) Banks are insured by the government.

This is a true statement .

B ) Money can be stolen or lost if you keep it at home . Even this is a true statement .

D ) Your money can grow if you keep it in a bank account . This is also a true statement .

Hence , C ) If your bank goes out of business, you lose your money is a false statement .

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without further Ado, let's pick two points off the table, check the picture below, and let's roll on.

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{-3}{2 +1} \implies \cfrac{ -3 }{ 3 }\implies -1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-1}(x-\stackrel{x_1}{(-1)}) \implies y -3= -1 (x +1) \\\\\\ y-3=-x-1\implies {\LARGE \begin{array}{llll} y = -x+2 \end{array}} \qquad \impliedby \stackrel{y-intercept}{(0~~,~~2)}[/tex]

Answer:

ain't no way you need help my bou

Answer:if they choose the family tickets its 15% off the regular ticketts individually

Step-by-step explanation:

Answer:

e foot

Step-by-step explanation:

Answer:

How far down the wall did

the ladder

Step-by-step explanation:

Answer: b=7.5

Step-by-step explanation:

b+5=20-b

b+b+5=20-b+b     ==> add b on both sides to put b on only one side of the equation

2b+5=20

2b=15

b=7.5

-10

By BODMAS Method

8 + 3*4 ÷ -2*3

8 + 3* [tex]\frac{4}{-2}[/tex] *3

8 + 3*-2*3

8 +(-18)

-10

The order of operations (BODMAS) in mathematics and computer programming refers to a set of rules that represent standards for which operations to carry out first in order to evaluate a specific mathematical expression.

For instance, since the advent of contemporary algebraic notation, multiplication has been given a higher priority than addition in mathematics and most computer languages.

As a result, 1 + (2 × 3) = 7, rather than (1 + 2) × 3 = 9. is the value assigned to the expression 1 + 2 × 3. BODMAS was first used in the 16th and 17th centuries when addition and multiplication were given priority. BODMAS could only is used as a superscript to the right of their base.

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The length of DNA in Scientific notation (standard form) = 34[tex]e^{-8}[/tex] meters

Also, the significant figure in the measurement = 1

In this question, we have been given the length of human DNA.

The genetic information of almost every living thing is stored in a tiny strand called DNA.

Human DNA is 3.4 x 10-8 meter long.

We need to write the length in standard form.

3.4 x 10-8 meter

= 3.4 x 10 ^ (-8)

= 3.4 x 0.00000001

= 0.000000034

= 0.00000003

Here Significant Figures = 1

Decimals = 8

And the length in Scientific Notation = 34[tex]e^{-8}[/tex] meters

Therefore, the length of DNA in Scientific notation (standard form) = 34[tex]e^{-8}[/tex] meters

Also, the significant figure in the measurement = 1

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The distance from point X to line p is 2√17 units.

We are given the point X as:

X = ( - 2 , 5 )

We need to find the distance of X from the line p.

We will do this by using the distance formula:

Distance = √ (y₂ - y₁)² + (x₂ - x₁)²

Distance = √ (- 2 - 0) ² - (5 - ( - 3))  ²

= √ ( - 2) ² - (5 + 3) ²

= √ ( - 2) ² - (8) ²

= √ 4 + 64

= √ 68

= 2 √17 units

Therefore, the distance from point X to line p is 2√17 units.

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Your question was incomplete. Please find the content below:

Find the distance from point X to line p. An image of a point X, a line p, and three segments joining the point and the line. Question 12 options:

A. 2 √34 units

B. √85 units

C. 2 √17 units

D. √17 units

Using a system of equations, the expression, in terms of x, for the total number of students at the college is:

T = 11x.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem

For this problem, considering the Venn diagram, we have that:

Thus the total number of students in the college is given by:

T = A + B + x.

1/2 of the students who learn the piano also learn the guitar, hence:

A = x.

Thus the number of students who play the piano is:

A + x = x + x = 2x.

5 times as many students learn the guitar as learn the piano, hence:

B + x = 5(2x)

B + x = 10x

B = 9x.

Hence:

T = A + B + x

T = x + 9x + x

T = 11x.

The expression, in terms of x, for the total number of students at the college is:

T = 11x.

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The correct statements regarding the given bar graph are as follows:

A bar graph shows the number of times that each observation appears in the data-set.

The first correct statement is:

Mickton had more rainy days in July than in January, November, and December combined in 2012 and 2013.

As:

30 + 29 > 8 + 5 + 11 + 7 + 10 + 4

The second correct statement is:

There were 13 rainy days in February 2013.

Due to the blue bar in Feb.

The third correct statement is:

The month with the greatest difference in the number of rainy days between 2012 and 2013 was December.

Difference of 10 - 4 = 6 days, which is the biggest.

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Answer:

5

Step-by-step explanation:

Given expression:

when k = 12

substituting k = 12 in equation

⇒ (4(12) + 2) ÷ 10

⇒ (48 + 2) ÷ 10

⇒ 50 ÷ 10

⇒ 5

The following illustrate the examples of Qualitative data: (1) the eye color of children participating in after-school activities and (2) the traits of various bird species.

Data that cannot be quantified or expressed in numbers are referred to as qualitative data.

Now,

(1) The time, in minutes, it took students to finish their exams: It is quantifiable data since the number of minutes it took pupils to complete their tests can be measured.

(2) The eye color of students involved in after-school activities: Since the eye color of students participating in after-school activities cannot be quantified, the information is qualitative.

(3) The characteristics of different types of birds: The characteristics of many bird species can never be quantified quantitatively; therefore, the information is qualitative.

(4) The scores on the last exam: It is quantitative data since the results of the last exam may be quantified and expressed in numbers.

(5) The weights of different books: It is quantifiable data because it is possible to measure the weights of various books.

Hence, the eye color of children participating in after-school activities and the traits of various bird species are examples of qualitative data.

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Answer:

that is the answer

you cant simplify the equation further

3x ^ 2 + 56x - 7 is the answer

Step-by-step explanation:

Answer:

hdshsjjkksjsjskskwiisiw