The cost of K-12 education per student was $2200 in 1978 and increased to $10,300 in 2008. (Source: Department of Education). (a) Find a linear equation that models these data. Let C represent the cost per student and x represent the number of years after 1978.

Answer:

[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]

Step-by-step explanation:

Given

[tex]\cos(x - y)[/tex]

Required

State the formula

From trigonometry identity, the formula of [tex]\cos(x - y)[/tex] is:

[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]

Answer:

x=1; y=2; z=3

Step-by-step explanation:

Rearrange for convince:

2y-4z+6x = -2

-4y+2z-3x=-5

-6y+3z+4x=1

Now we take to pairs and eliminate the same var.:

2y-4z+6x = -2 *2

-4y+2z-3x=-5

and

-4y+2z-3x=-5 *-3

-6y+3z+4x=1. *2

We get:

4y-8z+12y=-4

-4y+2z-3x=-5

= -6z+9x=-9

and

12y-6x+9x=15

-12y+6x+8x=2

= 17x=17

We now know x = 1, so z is:

-6z+9=-9

-6z=-18

z=3

Let’s grab the first formula and find y:

6+2y-12=-2

6+2y=10

2y=4

y = 2

Answer:

it is b

Step-by-step explanation:

Answer:

B. [tex]x=24[/tex]

Step-by-step explanation:

We can start by isolating the square root by adding one to both sides:

[tex]-1+\sqrt{3x-8} =7\\\sqrt{3x-8}=8[/tex]

Now, we can square both sides and solve:

[tex]3x-8=64\\3x=72\\x=24[/tex]

Answer:

0.28 = 28% probability that a randomly selected driver will come to complete stop

Step-by-step explanation:

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

In this question:

Recording of 75 drivers.

Of those, 21 came to a complete stop.

Then

21/75 = 0.28

0.28 = 28% probability that a randomly selected driver will come to complete stop

Solution :

Given :

mean weight of the dogs, [tex]$\overline x$[/tex] = 69

Number of dogs, n = 37

Standard deviation, σ = 9.2

Confidence interval = 90%

At 90% confidence interval for the true population mean dog weight is given by :

[tex]$= \overline x \pm \frac{\sigma}{\sqrt n} \times z_{0.05}$[/tex]

[tex]$= 69\pm \frac{9.2}{\sqrt_{37}}} \times 1.64485$[/tex]

[tex]$=69 \pm 2.487799$[/tex]

= (66.5122, 71.4878)

Answer:

82 is what r equals

Step-by-step explanation:

So, lets go over what we know:

D equals rt, or r * t:

D=r*t

The table shows:

t=2 - d=164

t=3 - d=246

These are the only 2 values we need to look at.

We know that D= r*t, and we can just plug in the values found in the table for t and d to solve for r. So:

164= r * 2

Divide both sides by 2 to iscolate r:

82=r

So it seems like r is equal to 82, however this might be exponential or inaccurate, so lets double check witht the nexty values on the table:

246=r*3

Divide by 3 to iscolate the r:

82=r

So we know that r must equal 82.

Hope this helps!

Answer:

Step-by-step explanation:

Have a good grades and study well sweetie

Answer:

(x-3) * (x-2

Step-by-step explanation:

Answer:

x = 52.0

Step-by-step explanation:

Reference angle = 68°

Length of side Opposite to reference angle = x

Adjacent length = 21

Apply the trigonometric function, TOA, which is given as:

Tan 68° = Opp/Adj

Substitute

Tan 68° = x/21

21 × Tan 68° = x

51.9768238 = x

x = 51.9768238 ≈ 52.0 (approximated to nearest tenth)

Answer:

0.6328 = 63.28% probability that he obtains at most one correct answer

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he obtains the correct answer, or he does not. The probability of obtaining the correct answer on a question is independent of any other questions, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Five-question

This means that [tex]n = 5[/tex]

Each question has exact four choices for the answer, but only one of which is correct.

This means that [tex]p = \frac{1}{4} = 0.25[/tex]

Find the probability that he obtains at most one correct answer

This is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.25)^{0}.(0.75)^{5} = 0.2373[/tex]

[tex]P(X = 1) = C_{5,1}.(0.25)^{1}.(0.75)^{4} = 0.3955[/tex]

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2373 + 0.3955 = 0.6328[/tex]

0.6328 = 63.28% probability that he obtains at most one correct answer

Answer:

$3437.5

Step-by-step explanation:

Given data

Unit cost= $2.75

qty demanded= 1250

To get to the total, we have to multiply the quantity by the unity cost

=2.75*1250

=$3437.5

Hence the total cost is

$3437.5

Answer:

look at the domain, where the line is on the x-axis

Step-by-step explanation:

C. a translation and a dilation

Step-by-step explanation:

the other person isn't wrong they just put it in the wrong order

Answer:c

Step-by-step explanation:took the test

Answer:

Step-by-step explanation:

Answer:

The average rate of change is 22

Step-by-step explanation:

Given

[tex]f(x) = x^4 - 5x[/tex]

Required

Average rate of change over [0,3]

This is calculated as:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

So, we have:

[tex]Rate = \frac{f(3) - f(0)}{3 - 0}[/tex]

[tex]Rate = \frac{f(3) - f(0)}{3}[/tex]

Calculate f(3) and f(0)

[tex]f(x) = x^4 - 5x[/tex]

[tex]f(3) = 3^4 - 5 * 3 =66[/tex]

[tex]f(0) = 0^4 - 5 * 0 = 0[/tex]

So, we have:

[tex]Rate = \frac{f(3) - f(0)}{3}[/tex]

[tex]Rate = \frac{66-0}{3}[/tex]

[tex]Rate = \frac{66}{3}[/tex]

[tex]Rate = 22[/tex]

Answer:

32

Step-by-step explanation:

40 = 100%

how many are 80% ?

well, 80% = 80× 1%

1% = 100% / 100

so, in our case

80% = 80×40/100 = 8×4 = 32

as a shortcut you consider a percentage x as a ratio factor of x/100 you multiply the 100% number with.

in our case

80% = 40 × 80/100 = 32

Answer:

(a) The slope of f(x) is greater than the slope of g(x)

(b) f(x) has a greater y intercept

Step-by-step explanation:

Given

[tex]\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}[/tex]

[tex]g(x) = 3x - 2[/tex]

Solving (a): Compare the slopes

The slope (m) of f(x) is calculated as;

[tex]m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]

This gives:

[tex]m = \frac{f(0) - f(1)}{0 - 1}[/tex]

[tex]m = \frac{f(0) - f(1)}{- 1}[/tex]

Substitute values for f(0) and f(1)

[tex]m = \frac{-1 - 7}{- 1}[/tex]

[tex]m = \frac{-8}{- 1}[/tex]

[tex]m = 8[/tex]

The slope of g(x) can be gotten using the following comparison

[tex]g(x) = mx + b[/tex]

[tex]m \to slope[/tex]

So:

[tex]g(x) = 3x -2[/tex]

[tex]m = 3[/tex]

[tex]m_{f(x)} > m_{g(x)}[/tex]

Solving (b): Compare the y intercept

y intercept is when [tex]x = 0[/tex]

From the table of f(x)

[tex]f(0) = -1[/tex]

From the equation of g(x)

[tex]g(x) = 3x -2[/tex]

[tex]g(0) = 3*0-2[/tex]

[tex]g(0) =-2[/tex]

[tex]f(0) > g(0)[/tex]

Answer:

9notebooks

Step-by-step explanation:

5×y≤45( where y is number of notebooks)

$5=1notebook

$45=$45/$5x1

=9

therefore, you'll be able to buy nine notebooks with$45

Answer:

$5n = $45

n = 9

Step-by-step explanation:

Let n represent the amount of notebooks

$5n = $45

Divide each side by 5

$5n/5 = $45/5

n = 9

so the maximum number of notebooks you can buy is 9

Answer: 21 days overdue

Explanation: Since her fine was same as the amount on the following day. 21 will be closest to the number of day overdue so it is 21 days.

Answer:

22

Explanation:

 They are saying that it has to be the closest number to the number of days overdue, cannot be neither 10 nor 14, and it cannot be 18 because that's one day from the days it's been overdue, and the question is saying: Her fine was the same as the amount on the following day. The graph shows us that it is about 1 more day than 18, so the only reasonable answer here is 22.

Also, I got it correct on edg =)

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{3 = \dfrac{k +8}{3}}[/tex]

[tex]\rightarrow\mathsf{\dfrac{k+8}{3}=3}[/tex]

[tex]\large\textsf{MULTIPLY by 3 to BOTH SIDES}[/tex]

[tex]\mathsf{3\times3=\dfrac{k+8}{3}\times3}[/tex]

[tex]\large\textsf{Work out the equation above to get to the next step}[/tex]

[tex]\large\textsf{We get: }\mathsf{k + 8 = 9}[/tex]

[tex]\large\textsf{SUBTRACT 8 to BOTH SIDES}[/tex]

[tex]\mathsf{k +8-8=9-8}[/tex]

[tex]\large\textsf{CANCEL out: 8 - 8 because that gives you 0}\\\\\\\\\large\textsf{KEEP: 9 - 8 because that gives you the value of k.}[/tex]

[tex]\mathsf{k = 9 -8}[/tex]

[tex]\mathsf{9-8=\boxed{k}}[/tex]

[tex]\mathsf{9-8=\boxed{\large\textsf{\bf 1}}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge k = \bf 1}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

The efficiency of this line is 0.85 = 85%.

Step-by-step explanation:

Efficiency:

The efficiency is given by the following formula:

[tex]E = \frac{T_t}{tn}[/tex]

In which [tex]T_t[/tex] is the total task time, [tex]t[/tex] is the largest assigned cycle time and n is the number of workstations.

5 workstations

This means that [tex]n = 5[/tex]

The sum of the 21 task times is 85 minutes.

This means that [tex]T_t = 85[/tex]

The largest assigned cycle time is 20 minutes.

This means that [tex]n = 20[/tex]

What is the efficiency of this line?

[tex]E = \frac{T_t}{tn} = \frac{85}{20*5} = \frac{85}{100} = 0.85[/tex]

The efficiency of this line is 0.85 = 85%.

Answer:

17

Step-by-step explanation:

_____________ Hair color

Eye color ___ Brown ___ Black ___ total

Green _____ 22 ________ 15 ____ 37

Blue _______ 18 ________ 19 ____ 37

Total _______40 ________34 ____ 74

Calculate the expected frequency of Blue Eyes and Black Hair?

The expected frequency Count ;

(row total * column total) / total number of observations

Expected frequency ;

Blue eye n black hair = (37 * 34) / 74

Expected frequency count = 1258 / 74 = 17

Expected count = 17

Answer:

The row total of blue eyes is 18 + 19 = 37.

The column total of black hair is 15 + 19 = 34.

The total of the whole table is 22 + 15 + 18 +19 = 74.

Step-by-step explanation:

E=(37)(34)/74=1258/74=17

Answer:

B) The function has a maximum value of (1)

Step-by-step explanation:

The given function has a maximum value, as its curve is inverted. The maximum value is the largest (y) value that a function can attain. As one can see, this value is (1), because the (y-coordinate) of the highest point on its curve is (1). This function has no minimum value, its endpoints go on infinitely in a negative direction.

Answer:

C. 90√3

Step-by-step explanation:

5√2 . 9√6 = 45√12 = 45×2√3

= 90√3

The simplified form is 90√3.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Given expression is, 5√2×9√6

                               =5×9×√(2×6)

                               =45×√12

                               =45×2√3

                               =90√3

Hence, the simplified form is 90√3 .

To learn more on multiplication click:

https://brainly.com/question/5992872

#SPJ2

Answer:

[tex]m =-4[/tex]

Step-by-step explanation:

Given

[tex]p(m-3 , -6) = p(-7 , -6)[/tex]

Required

Find m

[tex]p(m-3 , -6) = p(-7 , -6)[/tex]

By comparison:

[tex]m-3 = -7[/tex]

Add 3 to both sides

[tex]m = -7+3[/tex]

[tex]m =-4[/tex]

Answer:

$19.25

Step-by-step explanation:

11 ÷ 4 = $2.75  this is the cost per gallon of milk

2.75 * 7 = $19.25  this is the cost for 7 gallons of milk

Hope this helps

Answer:

$ 19.25

Step-by-step explanation:

 Milk(gallons)         Cost

        4                    11

        7                     x

  [tex]\frac{4}{7} = \frac{11}{x}\\\\4 \times x = 11 \times 7\\\\4x = 77\\\\x = \frac{77}{4} = \$ 19.25[/tex]

9514 1404 393

Answer:

  {e, m, o, r}

Step-by-step explanation:

Perhaps most straightforward is the simple list in order of appearance.

  {m, o, r, e}

Often, we prefer rostered sets to be in lexicographical order:

  {e, m, o, r}