Teachers' salaries in north dakota the average teacher's salary in north dakota is $35,441. assume a normal distribution with s $5100.

a. what is the probability that a randomly selected teacher's salary is greater than $45,000?

b. for a sample of 75 teachers, what is the probability that the sample mean is greater than $38,000?

50

These numbers are double those of the (7, 24, 25) triple. 2×25 = 50.

You can also figure it out from ...

... x = √(14² +48²) = √(196 +2304) = √2500 = 50

A. 1/7

The slope of the given line is the coefficient of x, -7. The slope of a perpendicular line will be the opposite reciprocal of that:

... -1/(-7) = 1/7 . . . . . seems to match selection A

_____

Comment on the answer choices

We assume this question suffers from a problem seen often on Brainly where questions and/or answers are copied and pasted without any follow-up editing to make sure the copy is faithful. Often, math symbols are special characters that get filtered out in the process.

The fraction bar commonly comes up missing. Here, that makes 1/7 look like 17, which makes the correct answer look like "none of the above."

A. 28

We assume m is the measure of the marked unknown angles: ∠BZY ≅ ∠BZA

(5x +3)° = (2x +18)°

Divide by ° and subtract 2x+3:

... 3x = 15

... x = 5

Then ∠BZA = (2·5 +18)° = m = 28°

Answer:

80 adult tickets were sold

Step-by-step explanation:

If you subtract the extra 20 adult tickets from ticket numbers and revenue, you get ...

equal numbers of $4 and $8 tickets were sold for a total of $720 collected

Since that is some number of ticket pairs worth $12 per pair, there must have been ...

$720/12 = 60 pairs of $4 and $8 tickets

The number of adult tickets is 20 more than this, so is

60 + 20 = 80 . . . . adult tickets sold

_____

If you feel better with an equation, rather than numerical reasoning, you can let n represent the number of adult tickets. Then n-20 is the number of student tickets and total revenue is ...

8n +4(n-20) = 880

12n -80 = 880 . . . . . simplify

12n = 960 . . . . . . . . . add 80

n = 80 . . . . . . . . . . . . divide by 12

_____

Comment on the different solutions

Using n for the number of adult tickets, we effectively chose a scenario where we added 20 student tickets to bring the total to $960 for some number of $12 pairs of tickets. That number is 80, the number of adult tickets.

In the "word solution" given at first, we effectively solved for the number of student tickets, then added 20 to get the number of adult tickets. The corresponding equation would be ...

4s +8(s+20) = 880 . . . s = number of student tickets sold

12s = 720 . . . . . . . . . subtract 160, the price of the 20 extra adult tickets

Answer:

hundreds

Step-by-step explanation:

The quotient of 3216/8 is 402. 4 is the first digit, and is in the hundreds place.

Answer:

D  2n+2

Step-by-step explanation:

We can check the slope of the function

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

   = (10-8)/(4-3)

   = 2/1

The slope is 2

We can use the point slope form of a line to calculate the equation for a line

y-y1 = m(x-x1)

y-2 = 2(x-2)

Distribute

y-6=2x-4

Add 6 to each side

y-6+6  = 2x-4+6

y = 2x+2

7.65%

There are 200 times $100 in $20,000, so the interest amount per $100 is ...

... $3,279/200 = $16.395 per hundred

In the row of the given table corresponding to 48 months, the smallest amount of interest listed is $23.48 per $100. The APR on the loan of concern is clearly less than 10.75%.

A financial calculator says the interest rate on a loan of $20,000 with 48 monthly payments of ($20,000 +3,279)/48 = $484.98 is about 7.65%.

Answer:

2.3x + 1.23y = 23

Step-by-step explanation:

The bag of chips is x because it is getting multiplied by 2.3.

The candy is y because it is getting multiplied by 1.23.

The reason they equal 23 is to figure out the maximum amount of each snack you can get without going over the money limit.

Answer:

107

Step-by-step explanation:

These are easier to do if you simplify them first.

... = x^6(5 -2 -3) +x^2(-3 +4) +7

... = x^2 +7

For x = -10, this is

... (-10)^2 +7 = 100 +7 = 107

Answer:

$6

Step-by-step explanation:

The graph shows you that 4 pounds of apples (and no cranberries) can be purchased for $24. Thus each pound costs ...

... $24/(4 pounds) = $6/pound

Answer:

-5(x² -2x +3)

Step-by-step explanation:

5 is a factor common to all of the coefficients. It is convenient to have the x² coefficient be positive in the factored form, so the result of factoring out -5 is ...

... -5((-5x²/-5) +(10x/-5) +(-15/-5)) = -5(x² -2x +3)

Answer:

-5(x² -2x +3) your welcome

Step-by-step explanation:

[tex]a_n=3a_{n-1}-4[/tex]

Try the answers

You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.

a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works

b) -7 -2 = -9 . . . . ≠ -25

c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25

d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25

The formula that works is the first one.

_____

Derive it

All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...

[tex]a_n=p\cdot a_{n-1}+q[/tex]

Then, to get the second term from the first, we have

... 1·p +q = -1

And to get the third term from the second, we have

... -1·p +q = -7

Subtracting the second equation from the first gives ...

... 2p = 6

... p = 3 . . . . . . . this is sufficient to identify the first answer as correct

We can find q from the first equation.

... q = -1 -p = -1 -3 = -4

So, our recursion relation is ...

[tex]a_n=3a_{n-1}-4[/tex]

Answer:

c ∈ {-7, -3, 2, 5}

Step-by-step explanation:

"Illegal" values are those values that make the expression undefined—that is, they make the denominator zero.

The denominator of the product factors as (c+7)(c-2)(c-5)(c+3), so the values of c that will make this product zero are ones that make the factors zero:

... c = -7, +2, +5, -3

_____

Comment on factoring

Each of the quadratics is factored by finding two factors of the constant whose sum is the coefficient of the linear term. You want ...

... factors of -14 = -1·14 = -2·7 . . . . that add to give +5. They are -2 and 7, so the quadratic factors as (c-2)(c+7)

... factors of -15 = 1·(-15) = 3·(-5) . . . . that add to give -2. They are 3 and -5, so the quadratic factors as (c+3)(c-5).

Answer:

55,900 cm²

Step-by-step explanation:

The area of a triangle is half the product of its base and height.

... A = (1/2)·b·h

... = (1/2)(430 cm)(260 cm)

... = 55,900 cm²

Answer:

# of granola bars and it's cost.

Step-by-step explanation:

It is asking for the meaning of 2B. Note that inside the question, it states that:

"The price of a granola bar is B dollars".

It also states that:

"Donovan eats 2 granola bars".

This means that to solve for the total spent on granola bars, you multiply the price (B) with the amount gotten (2 in this case).

~

Answer:

2B

Step-by-step explanation:

Means the amount Donovan spends on granola bars each day. Since he has 2 granola bars and the price is B dollars.

Answer:

[tex]3GR=27[/tex]

Step-by-step explanation:

Since area of rectangle BCND is given as 90 and one of its side is 10, the other side MUST be 9.

[tex]CN*BC=90\\CN*10=90\\CN=9[/tex]

In Rhombus CGNR, CN and GR are congruent (property of Rhombus). Hence GR = 9 as well.

Thus 3GR = 3(9) = 27

First answer choice is right.

Try this option. Answer: 72+18π

Step-by-step explanation:

Formula is:

Area= 2*Area_of_two_squares + 1/2 *Area_of_the_circle, where

Area_of_1_square=6*6=36 cm²;

Area_of_the_circle=π*6²=36π cm²;

finally, according to the formula above Area=2*36+0.5*36π=72+18π

Answer:

Step-by-step explanation:

72+18pi

Answer:

x = −4 and x = 4

Step-by-step explanation:

4x² = 64

Lets get x² on its own. To do this we divide each sides by 4:

x² = 16

Now to get just x, we need to square root this answer:

√x² = √16

x = √16

x = 4

But this can be ±4 as it -4 and 4 squared both give 16.

So your answer is x = −4 and x = 4

Answer:

x = −4 and x = 4

Step-by-step explanation:

c on edg

78%

The percentage change is calculated from ...

... percent change = ((new amount) -(old amount))/(old amount) × 100%

... = (64 -36)/36 × 100%

... = 28/36 × 100%

... ≈ 0.78 × 100%

... ≈ 78%

1,094 bacteria

There are 6 periods of 4 hours in 24 hours, so the population will be multiplied by 1/2 6 times. That is, it will be multiplied by (1/2)^6 = 1/64.

The population then will be ...

... 70,000/64 ≈ 1094

Answer:

(-3/2, -5/2)

Step-by-step explanation:

When a point is dilated about the origin, each coordinate value is multiplied by the dilation factor. You seem to have ...

... -2x = 3 ⇒ x = -3/2

... -2y = 5 ⇒ y = -5/2

_____

In each case, you solve the linear equation by dividing by the coefficient of the variable.

The exercise is asking you to compute the volume of five different spheres and cylinders, choosing 5 different random values.

Remember the formulas for the volumes: given a radius [tex] r [/tex], the volume of the sphere is

[tex] \dfrac{4}{3}\pi r^3 [/tex]

Whereas the volume of the cylinder is

[tex] \pi h r^2[/tex]

In this specific case, you're told that the height of the cylinder is the same as the diameter of the sphere (i.e. twice the radius). So, the formula of the cylinder updates to

[tex] \pi (2r) r^2 = 2\pi r^3 [/tex]

So, all you need to do is to pick 5 random numbers, use them as the radius [tex] r [/tex], and for each of them compute the volume and cylinder sphere as indicated above.

For example, if you choose a radius [tex] r=5 [/tex], you will have

[tex] \text{Sphere: } V = \dfrac{4}{3}\pi 5^3 = \dfrac{500\pi}{3} [/tex]

[tex] \text{Cylinder: } V = 2\pi 5^3 = 250\pi [/tex]

Now choose your 5 random values and do the same!

C = 2.00r +20

The coefficient is the multiplier of r, the cost of each ride. If it has gone down by $0.50, then its new value is ...

... 2.50 -0.50 = 2.00

The constant in the equation is the initial cost of the wristband. It is the value of C when r=0. If it has gone up by $5, its new value is ...

... 15 + 5 = 20

Answer: 6x - 18 (choice C)

Angle TSR is the same as angle RST. The order of the letters doesn't matter as long as the middle letter is the same (known as the vertex point).

Segment SQ bisects angle RST, so that means the two smaller pieces (angle TSQ and angle RSQ) are exactly half in measure compared to angle RST. Put another way, angle RST is twice that of angle RSQ

So,

angle RST = 2*(angle RSQ)

angle RST = 2*(3x - 9)

angle RST = 2*(3x) + 2*(-9)

angle RST = 6x - 18

The correct answer to the subtraction problem is 246 yards of Joshua's fishing line remaining in the water after reeling in 113 yards out of 359 yards. Joshua's initial answer of 489 yards is incorrect.

The student is asking for verification of Joshua’s solution to a subtraction problem that involves determining how much fishing line remains in the water after some has been reeled in. Joshua initially had 359 yards of line in the water and reeled in 113 yards. To find the remaining length of the line in the water, we subtract the length of the line reeled in from the initial length.

Step-by-Step Explanation

Start with the initial length of the fishing line in the water: 359 yards.

Subtract the length of the line that was reeled in: 113 yards.

Perform the subtraction: 359 yards - 113 yards = 246 yards.

So, the length of the fishing line that remained in the water was 246 yards.

Joshua’s answer of 489 yards is not reasonable because it does not reflect the correct subtraction (359 - 113 = 246). The correct answer is 246 yards still in the water.

Let x be the certain number of inches mentioned in the problem. So, three less than this quantity is [tex] x-3 [/tex]

This means that you have to sketch a rectangle labelling the short side with 2, and the long sides with [tex] x-3 [/tex]

Answer:

-2

Step-by-step explanation:

From the given graph, the point A(1, -4) and B(-1, 0)

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

x1 = 1, y1 = -4, x2 = -1 and y2 = 0

Slope (m) = (0 - (-4))/(-1 - 1)

= 4/-2

Slope = -2

Thank you.

Answer:

see below

Step-by-step explanation:

a)  w <= 40 lbs

b)  Do you have any bag that weigh 0 lbs or negative lbs?

We need to rewrite the inequality so that these are not there

0<= w <= 40 lbs

49°

∠DEF = ∠1 +∠2 = 50° +48° = 98°

∠ABC = ∠DEF because they are alternate exterior angles, hence congruent.

∠3 = ∠4 because they are vertical angles.

∠3 = (1/2)∠ABC = (1/2)·98° . . . . . ∠4 is half of ∠ABC

∠3 = 49°