Which function best fits the following points?
A.=-12.84032+0.0225x
O B. y=65.0778-772.9605*
O C. y=-197.0571x2+ 245.6243x + 6.0321
O D. None of the above

The angles and length of the triangle area as follows:

The sum of angles in a triangle is 180 degree.

Therefore,

∠DBC = 180 - 29 - 90 = 61°

Hence,

∠A = 180 - 29 - 61 - 55 = 35°

∠CBD = 61°

Using trigonometric ratios,

sin 55 = opposite / hypotenuse

sin 55 = AD / 40

AD = 40 sin 55

AD = 32.7660817716

AD = 32.77 units

cos 55 = adjacent / hypotenuse

cos 55 = BD / 40

BD = 40 cos 55

BD = 22.943057454

BD = 22.94 units

sin 29 = 22.94 / BC

BC = 22.94 sin 29

BC = 11.1215326885

BC = 11.12 units

cos 29 = CD / 11.12

CD = 11.12 cos 29

CD = 9.72577114339

CD = 9.73 units

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Usando la distribución hipergeométrica,  la probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es: 0.2 = 20%.

La fórmula es:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

Los valores de los parámetros son:

N = 6, k = 3, n = 2.

La probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es P(X = 2), por eso:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,6,2,3) = \frac{C_{3,2}C_{3,0}}{C_{6,2}} = 0.2[/tex]

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Tthe inequality that describes this graph is y ≤ 1/3x - 4/3

The graph that completes the question is added as an attachment

From the attached graph, we have the following points

(0, -1.3) and (3, -0.3)

The slope is calculated as:

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

Substitute the known values in the above equation

m = (-0.3 + 1.3)/(3 - 0)

Evaluate

m = 1/3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = 1/3(x - 0) - 1.3

Evaluate

y = 1/3x - 4/3

From the graph, we have the following highlights:

The first highlight above implies, the inequality can be any of ≥ and ≤

While the second highlight above implies, the inequality is ≤

Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3

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Using translation concepts, the transformations are described as follows:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is:

[tex]f(x) = 2^x[/tex]

The transformed function is:

[tex]g(x) = -2^x + 4[/tex]

We have that the transformations in this problem can be described as follows:

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The number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is  924, 000 ways

Note that the formula for combination is given as;

Combination = [tex]\frac{n!}{r!(n-r)!}[/tex]

From the information we have that;

There are 28 questions in the pool

The test should have a total of 10 questions;

6 difficult , 10 average and 12 easy questions

We are asked to determine the combination of;

3 difficult questions

4 average questions

3 easy questions

6C3 = [tex]\frac{6!}{3!(6-3)!}[/tex]

6C3 = [tex]\frac{720}{36}[/tex]

6C3 = 20

10C4 = [tex]\frac{10!}{4!(10-4)!}[/tex]

10C4 = [tex]\frac{3628800}{17280}[/tex]

10C4 = 210

12C4 = [tex]\frac{12!}{4!(12-4)!}[/tex]

12C4 = 220

The number of ways of constructing the questions is

= 20 × 210 × 220

= 924, 000 ways

Thus, the number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is  924, 000 ways

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Answer:

[tex]y=\frac{-3}{4}x-3[/tex]

Step-by-step explanation:

This is a linear graph so the equation will be in the format of y=mx+b.

b, the y-intercept, will be -3, as that is where the line crosses the y-axis.

m, the slope, is [tex]\frac{-3}{4}[/tex], calculated from the change in y over the change in x from points (-4,0) to (0,-3).

Now substitute the values in our equation:

[tex]y=\frac{-3}{4}x-3[/tex]

Answer:

y= -3/4+[-3]

Step-by-step explanation:

Answer:

your question is not correct i can not find the answer

Using the probability concept, we have that:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 35 people, out of which 17 are female and 5 are male that prefer mint chocolate chip, hence:

p = (17 + 5)/35 = 22/35 = 0.6286.

There is a 0.6286 = 62.86% probability that a randomly selected person is female or prefers mint chocolate chip.

Out of the same 35 people, 11 people prefer cookie and cream and 2 people prefer vanilla, hence:

p = (11 + 2)/35 = 13/35 = 0.3714

There is a 0.3714 = 37.14% probability that a randomly selected person prefers cookie and cream or vanilla.

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Answer:

sorry i thought i knew it

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

using the rules of exponents

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] : nm > n

[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] : n > m

[tex]\frac{6a^2b^{-2} }{8a^{-3b^3} }[/tex] ← separate the variables

= [tex]\frac{6}{8}[/tex] × [tex]\frac{a^2}{a^{-3} }[/tex] × [tex]\frac{b^{-2} }{b^3}[/tex]

= [tex]\frac{3}{4}[/tex] × [tex]a^{2-(-3)}[/tex] × [tex]\frac{1}{b^{3-(-2)} }[/tex]

= [tex]\frac{3}{4}[/tex] × [tex]a^{2+3}[/tex] × [tex]\frac{1}{b^{3+2} }[/tex]

= [tex]\frac{3}{4}[/tex] × [tex]a^{5}[/tex] × [tex]\frac{1}{b^{5} }[/tex]

= [tex]\frac{3a^{5} }{4b^{5} }[/tex]

Answer:

250 - 6 - 3n

Step-by-step explanation:

Let n equal the number of students.

Answer:

16

Step-by-step explanation:

18,903

The set of natural numbers greater than or equal to 6 will be 6, 7, 8, 9, 10, ....

It should be noted that the first information is about the set of natural numbers greater than or equal to 6. Therefore, they will be 6 and above.

It should be noted that the descriptive form simply states in words the elements that are in a set. It is the verbal description of the elements in the set. It is the determination of the elements that belong to a set and those that doesn't.

Also, the way that a set is described is known as the roster form. In this case, the contents of a set can be described by listing the elements that are in the set which are separated by a comma inside the bracket.

Also, the roster form: (5, 7, 9, 11) indicates odd natural numbers. The numbers that are given are odd.

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Answer:

2y - 100

Step-by-step explanation:

Last year's income = y

2y-100

well, keeping in mind that a year has 365 years, so let's see

[tex]\stackrel{Oct}{10}~~ + ~~\stackrel{Nov}{30}~~ + ~~\stackrel{Dec}{31}~~ + ~~\stackrel{Jan}{31}~~ + ~~\stackrel{Feb}{21}\implies 123~days[/tex]

so the 3600 were borrowed for only 123 days of a year, that'd be 123/365 of a year, thus

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3694.63\\ P=\textit{original amount deposited}\dotfill & \$3600\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{123}{365} \end{cases}[/tex]

[tex]3694.63=3600[1+(\frac{r}{100})(\frac{123}{365})]\implies \cfrac{3694.63}{3600}=1+\cfrac{123r}{36500} \\\\\\ \cfrac{3694.63}{3600}-1=\cfrac{123r}{36500}\implies \left( \cfrac{36500}{123} \right)\left( \cfrac{3694.63}{3600}-1 \right)=r\implies \stackrel{\%}{7.8}\approx r[/tex]

7.8% is the simple interest rate was charged if Robin repaid $3,694.63.

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

A=P(1+rt)

A is final amount, P is principle amount, r is rate of interest and t is time.

We know that in a year we have 365 days.

But the time here is from oct 21 to feb 21, which has 123 days.

so the 3600 were borrowed for only 123 days of a year, that'd be 123/365 of a year, thus

Apply these values in formula

A=P(1+rt)

3694.63=3600(1+r/100(123/365))

3694.63=3600(1+123r/36500)

3694.63/3600=1+123r/36500

3694.63/3600-1=123r/36500

(3694.63-3600)/3600=123r/36500

94.63/3600=123r/36500

Apply cross multiplication

3453995=442800r

7.80=r

Hence 7.8% is the simple interest rate was charged if Robin repaid $3,694.63.

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Answer:

12 and 14

Step-by-step explanation:

12 * 14 = 168

Answer:

12 & 14

Step-by-step explanation:

the work: x = first even number, (x+2) = second even number

The equation

[tex]x(x+2)=168[/tex]

[tex]x^{2} +2x=168[/tex]

[tex]x^{2} +2x-168=0[/tex]

Factoring

[tex](x-12)(x+14)=0[/tex]

first factor

[tex]x-12=0\\x=12[/tex]

Second factor

[tex]x+14=0\\x=-14[/tex]

The solution is the positive number

x = 12     is the first even number

x + 2 = 12 + 2 = 14    is the second even number

Hope this helps

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

From the question, we have the following ordered pairs

x intercepts = (6,0) and (18, 0)

Vertex = (12, -36)

Points (21, 41.25)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is the calculated using

m = [f(21) - f(18)]/[21 - 18]

This becomes

m = [f(21) - f(18)]/3

Substitute the known values in the above equation

m = [41.25 - 0]/3

Evaluate the difference

m = 41.25/3

Evaluate the quotient

m = 13.75

Approximate

m=14

Hence, the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

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Complete question

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

See attachment for graph

The decision is to fail to reject the null given that p value is not ≤ 0.05.

The hypothesis

H0 = p = 0.63

H1 = p < 0.63

α = 0.05

sample proportion = 71/125 = 0.568

x = 71

n = 125

standard error of the proportion

√0.63(1-0.63)/125

= 0.0431

The null hypothesis follows a standard normal distribution. This is a left tailed test.

We are to reject the null if the p value is less than 0.05

p < 0.05

This probability test is a z probability test.

Z test = 0.568 - 0.63 / 0.0431

test statistic = -1.436

-Z0.05 =

Critical value =  -1.645

p(z < -1.436)

p value = 0.0755

The decision would be to fail to reject the null hypothesis. The reason would be due to the fact that p value is greater than significance.

P-value is not ≤ α 0.05

0.0755 > 0.05

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Answer:

d - 7

Step-by-step explanation:

The word "difference" tells us that we will be using subtraction. Also, subtraction is not the same if you reverse the terms like, x - 2 and 2 - x are not the same. In your question it say "d and 7" so that's the order we use in the algebraic expression.

Answer:

(x-5)(x+1)

Step-by-step explanation:

x² - 4x + 5 = (x-5)(x+1)

Converting the portions to decimal, the grade that has the greatest portion of students is: 3rd grade.

The bigger the digit that is close to the decimal point, the bigger the number given.

Also, percentage can be converted to decimal by dividing the given percent by 100. Percent means over 100.

Fractions can also be converted to decimals by simply dividing the numerator by the denominator.

To compare the portion of students interested in playing an instrument in each grade, let all the portions be in decimals.

Converting 25/36 to decimal, we have: 0.694 (3rd grade)

Converting 61.24% to decimal, we have: 61.24/100 = 0.6124 (4th grade)

From the rest of the portions given, 0.694 is greater than the others.

Therefore, the grade that has the greatest portion of students is: 3rd grade.

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Answer:

3 hours

Step-by-step explanation:

When the ships meet each other, that means the the distance travelled for both ships are the same, that is where the 2nd ship will overtake the ship.

Distance = Speed * Time

So, given information from the question, and letting x be the time in hours (from when the 1st ship departs), we can deduce:

Distance travelled of 1st ship = Distance travelled of 2nd ship

30x = 40(x-1)

30x = 40x - 40

-10x = - 40

x = [tex]\frac{-40}{-10}[/tex]

= 4

Since we are calculating based on the 2nd ship,

Time taken for 2nd ship to overtake first ship = x - 1 = 4 - 1 = 3 hours.

Answer: (0,6)

Step-by-step explanation:

The solution is where the graphs intersect.

The best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.

It should be noted that conjecture simply means a conclusion that's proffered on a tentative basis without any proof.

From the information, Charlie used construction paper, scissors and a ruler to construct an isosceles triangle with a pair of sides each 3 inches long and an acute angle on top.

Here, the best conjecture for Charlie to develop is that an altitude drawn to the base of the isosceles triangle creates the smaller congruent triangles by the HL postulate.

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Answer:

328,233

Step-by-step explanation:

Use the algorithm method.

4 8 9 9

×     6 7

3 6 6 6

3 4 2 9 3

2 5 5 5  

2 9 3 9 4 0

1  1 1  

3 2 8 2 3 3

⇒ 328,233

The speed ratio of the two trains is 4:3, that is, for every 4 hours that one train is delayed, the other is delayed 3.

To find the speed ratio of the trains we must do the following operation:

Note: This question is incomplete because there is some information missing. Here is the complete information in:

A train started from Howrah for Allahabad another train started from Allahabad for Howrah at the same time. The two trains reached their destinations in 9hours and 16 hours respectively after they meet each other. Find the ratio of speed of the two trains.​

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Rewriting the left-hand side as follows,

[tex](2\cos\theta-6\sin \theta)^2 +(6\cos \theta+2\sin \theta)^2\\\\=4\cos^2 \theta-24\cos \theta \sin \theta+36 \sin^2 \theta+36 \cos^2 \theta+24 \cos \theta \sin \theta+4 \sin^2 \theta\\\\=40\cos^2 \theta+40 \sin^2 \theta\\\\=40(\cos^2 \theta+\sin^2 \theta)\\\\=40[/tex]

Answer:

A)

Step-by-step explanation:

3+3=6 6>5

3+5=8 3<8

A)

Answer:

Step-by-step explanation:

y=x²+(3+1)x-3

y=x²+3x+1x-3

y=x(x+3)-1(x+3)

y=(x-1)(x+3)