Question f(1)= ?
Please explain

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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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°

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

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

Step-by-step explanation:

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:3x7

Step-by-step explanation:Area is width x length. So 3x7.

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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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:

4680°/28 = 167.14°

Step-by-step explanation:

So, for a polygon with 28 sides, the sum of the measures of the interior angles is 26(180°) = 4680°. Since the polygon is regular, each interior angle has the same measure. So, the measure of each interior angle = 4680°/28 = 167.14°

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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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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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:

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

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: 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 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:

ain't no way you need help my bou

Answer:

hdshsjjkksjsjskskwiisiw

Answer:

that is the answer

you cant simplify the equation further

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

Step-by-step explanation:

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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Answer:

3,321

Step-by-step explanation:

1-0.19=0.81

4100*0.81=3,321

3,321 students went on the trip.

Hope this helps!

Please mark as brainliest if correct!

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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Answer: 15

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

Answer:

first option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 4 ) and (x₂, y₂ ) = (3, - 4 )

m = [tex]\frac{-4-4}{3-1}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4 , then

y = - 4x + c ← is the partial equation

to find substitute either of the 2 points into the partial equation

using (1, 4 ) , then

4 = - 4 + c ⇒ c = 4 + 4 = 8

y = - 4x + 8 ← equation of line

Answer:

A

Step-by-step explanation:

Substitute in the equation remove each x and put 1 if the result is 4 that's mean it's the true equation

Answer:

x=29

z=13

<RIG= 59°

<ZIM=31°

(vertically opposite angles)

<ZIA=<MIG

3x-56=x+2

group like terms

3x-x=56+2

2x=58

divide both side by the coefficient of x

2x/2=58/2

x=29

<RIG+<GIM=90°

4z+7+x+2=90°

where x=29

4z+7+29+2=90°

4z+38=90°

make for 4z the subject

4z=90°-38°

4z=52°

let z stand alone

4z/4=52/4

z=13

<RIG=4z+7

where z=13

4(13)+7

52°=RIGZ

<ZIM=x+2

where x =39+2

x=31°

Answer:

x = 29

z = 13

Angle RIG = 59 deg.

Angle ZIM = 41 deg.

Step-by-step explanation:

So we know that angle ZIA = angle MIG

3x - 56 = x + 2

We can solve this equation

2x = 58

x = 29

Next, angle RIG + GIM = 90 degrees.

So if we do 4z + 7 + x + 2 = 90 degrees when x = 29, we can plug x in.

4z + 7 + 29 + 2 = 90 degrees

4z + 38 = 90 degrees

4z = 90 - 38

4z = 52

z = 13

Angle RIG = 4z + 7

We know that z = 13

4 * 13 + 7 = 52

Therefore RIGZ = 52 degrees.

Angle ZIM = x + 2

x = 39 + 2

x = 41

Answer:D

Step-by-step explanation:

(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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