The weekly incomes of trainees at a local company are normally distributed with a mean of $1,100 and a standard deviation of $250. If a trainee is selected at random, what is the probability that he or she earns less than $1,000 a week?

Select one:
a. 0.8141
b. 0.1859
c. 0.6554
d. 0.3446

Answer

93 boxes

Step-by-step explanation:

Week one= 3 boxes

Week two= 2×3=6 boxes

Week three= 2×6=12 boxes

Week four= 2×12=24 boxes

Week five= 2×24=48 boxes

Total number of boxes sold is the sum for boxes sold in week 1,2,3,4 and 5

[tex]T=3+6+12+24+48=93[/tex]

Answer:

Step-by-step explanation:

Week one= 3 boxes

Week two= 2×3=6 boxes

Week three= 2×6=12 boxes

Week four= 2×12=24 boxes

Week five= 2×24=48 boxes

Total number of boxes sold is the sum for boxes sold in week 1,2,3,4 and 5

T=3+6+12+24+48=93

Answer:

A. AE, EC

Step-by-step explanation:

Because you know that the bottom two angles are congruent, you can conclude that this is an isosceles triangle. This means that the sides are congruent.

Answer:

[tex]\boxed{\text{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}[/tex]

Step-by-step explanation:

When you reflect a point (x, y) in the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign. Thus,

E (8,4) ⟶ E' (-8,4)

F (-16,-8) ⟶ F' (16,-8)

G (24,-16) ⟶ G' (-24,-16)

[tex]\text{The reflected figure has coordinates } \boxed{\textbf{E$'$(-8, 4), F$'$(16,-8), G$'$(-24,-16)}}[/tex]

The figure EFG and its reflection E'F'G' are shown in the diagram below.

Answer:

  247,605

Step-by-step explanation:

Each year, the population is multiplied by a factor of (1 -14.6%) = 0.854. Multiplying by that factor for 10 years gives the value ...

  1,200,000×0.854^10 ≈ 247,605

The population in 1990 is predicted to be 247,605.

The vertical asymptotes for the rational function f(x) = (x - 9)(x + 7) / (x² - 4) are at x = 2 and x = -2.

The rational function provided is f(x) = (x - 9)(x + 7) / (x² - 4). The denominator of this rational function is a difference of squares, which can be further factored into (x - 2)(x + 2). Therefore, the equation for the denominator becomes 0 when x = 2 or x = -2. These values of x are undefined for the original rational function and hence, they are vertical asymptotes. Thus, the vertical asymptotes for the given rational function are x = 2 and x = -2.

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The answer, I think, is (1, -5);(4,3).

Answer:

1, −5); (4, 3)

Step-by-step explanation:

The starting point coordinates and the changes in x or y of each movement are given.  

Draw the given information in the coordinate plane to better visualize it. The truck starting coordinates are (−3, −8).

To find the vector that gives the translation (−3, −8)→(1, −5), subtract the x and y coordinates of the starting point from the x and y coordinates of the end point. The vector is: ⟨1 − (−3), −5 − (−8)⟩ = ⟨4,3⟩.

Therefore, the truck’s final position is (1, −5) and ⟨4, 3⟩ is the single translation vector that moves the truck from its starting position to its final position.

Answer:

The percentage of the students scored an A in neither Math 101 nor English 101 is 55%

Step-by-step explanation:

* Lets study the meaning of or , and on probability

- The use of the word or means that you are calculating the probability

  that either event A or event B happened

- Both events do not have to happen

- The use the word and, means that both event A and B have to happen

* The addition rules are:

# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen

  at the same time)

# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they  

  have at least one outcome in common)

- The union is written as A∪B or “A or B”.  

- The Both is written as A∩B or “A and B”

* Lets solve the question

- There are 100 student enrolled in both math and English Exams

- 30% of them scored an A in Math

- 35% of them scored an A in English

- 20% of them scored an A in both

- To find the neither lets find either and then subtracted from the total

∵ P(A or B) = P(A) + P(B) - P(A and B)

∵ P(Math) = 30%

∵ P(English) = 35%

∵ P(Math ∩ English) = 20%

∴ P(Math ∪ English) = 30% + 35% - 20% = 45%

- To find the neither subtract either from the total

∵ The total of students who enrolled is 100

∴ The percentage of the students who enrolled is 100%

∴ The percentage of the students scored an A in neither Math nor

   English = 100% - 45% = 55%

* The percentage of the students scored an A in neither Math 101 nor

   English 101 is 55%

To find the percentage of students who scored an A in neither Math 101 nor English 101, subtract the percentage of students who scored an A in both subjects from the total percentage of students who scored an A in either subject.

To find the percentage of students who scored an A in neither Math 101 nor English 101, we need to subtract the percentage of students who scored an A in both subjects from the total percentage of students who scored an A in either Math 101 or English 101.

Given that 30% of the students scored an A in Math 101, 35% of the students scored an A in English 101, and 20% of the students scored an A in both subjects, we can calculate the percentage of students who scored an A in neither subject as follows:

Percentage of students who scored an A in neither subject = 100% - (Percentage of students who scored an A in Math 101 + Percentage of students who scored an A in English 101 - Percentage of students who scored an A in both subjects)

= 100% - (30% + 35% - 20%)

= 100% - 45%

= 55%

Answer:

[tex]0.000\,000\,067\,12[/tex]

Step-by-step explanation:

The exponent of -8 tells you the most significant digit (6) goes in the 8th position to the right of the decimal point.

With some spaces to help in counting decimal places, the number is written ...

[tex]0.000\,000\,067\,12[/tex]

Answer:

  x ≈ 0.290640965127

Step-by-step explanation:

By subtracting the right side of the equation, we get a function that is zero at a real solution for x. The only x-intercept is at approximately 0.290640965127.

___

The graph shows the x-intercept to be 0.2906. The value above was obtained by Newton's method iteration. The roots of this cubic will all be irrational.

Answer:  see graph

Step-by-step explanation:

I am assuming the question should read: y = |x + 1| - 4

You can graph this using transformations or by creating a table.

Transformations:

The parent function is y = |x|

The transformation is moving the graph 1 unit to the left and 4 units down - the vertex is moved from the origin to (-1, -4)

Table:

Choose x-values and solve for y

[tex]\begin{array}{c|c||c}\underline{\quad x\quad }&\underline{\quad y=|x+1|-4\quad }&\underline{Coordinate}\\-1&y=|-1+1|-4&(-1,-4)\\0&y=|0+1|-4&(0,-3)\\1&y=|1+1|-4&(1,-2)\end{array}[/tex]

Answer:

5

Step-by-step explanation:

if the ratio is 1:6, and its yellow to total, that means that you would need to subract 1 from 6 to get the number to blue counters needed to get the correct ratio

Answer:5

Step-by-step explanation:

Answer:

4^ (r-s)

Step-by-step explanation:

When the bases are the same, and we are dividing, we subtract the exponents

x^a ÷ x^b = x^ (a-b)

4^r ÷ 4^s = 4^ (r-s)

Answer:

720

Step-by-step explanation:

So there are 6 slots and 6 commercials so.

There are 6 outcomes which means.

we can use this formula

(p-1)(p-2)(p-3)..etc.

So

We have (6-1)(6-2)(6-3)(6-4)(6-5)(6-6)

6,5,4,3,2,1,0 and zero is 0!=1

So now we multiply

6*5*4*3*2*1*1=720

Hopefully this helps!

Answer:

143

Step-by-step explanation:

Let x = original price

20% of the original price is .2x

We get 20 % off so we subtract it from the original price

x- .2 x

That is equal to 114.40

x-.2x = 114.40

Simplify

.8x = 114.40

Divide each side by .8

.8x/.8 = 114.40/.8

x = 143

The original price is 143

Answer:

143

Step-by-step explanation:

i got it right

Answer:

  (0, 0) and (-4, -2)

Step-by-step explanation:

See the graph. Only two of the listed points are on the curve.

First down = 25 yards.

Ball moved 6 yards closer = 25 - 6 or 19 yards.

Then 10 yards away = 19 + 10 or 29 yards.

Then 8 yards closer = 29 - 8 or 21 yards.

The ball at the end of the third down will be 21 yard rom Captain's end zone .

Addition and subtraction are the simple mathematical operations, that are used for adding values to get total and reducing or removing value.

We have,

At first down the football = 25 yards

Now,

According to the question,

During three downs,

So,

For first down of three downs moves closer = 25 - 6 = 19 yards,

Now,

For second down of three downs moves farther = 19 + 20 = 29 yards

Now,

For third down of three downs moves closer = 29 - 8 = 21 yards

So,

21 yards away from the Captains' end zone.

Hence, we can say that the ball at the end of the third down will be 21 yard rom Captain's end zone .

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Answer: 140

Step-by-step explanation:

Begin by dividing 78 by 2 to go back to the original amount before the grandmother doubled them. Then multiply by 3 (each room). Finally, add the 23 that were thrown away at the beginning.

Initially, there were 140 legos. Each room had 39 legos before grandmother doubled them to 78, so multiplying 39 by the 3 rooms gives 117 legos, plus 23 removed cracked legos equals 140 original legos.

The student is trying to calculate the original number of legos Ms. Kiyama had before any were removed or added. We know that each room ended up with 78 legos, and this number was obtained after grandmother doubled the amount in each room. Therefore, before being doubled, there would have been 78 / 2 = 39 legos in each room. Since these legos were distributed equally among three rooms, we'll multiply 39 legos by 3 rooms to find the total number of legos before they were doubled, which is 39 * 3 = 117 legos.

However, we must not forget that Ms. Kiyama initially got rid of 23 cracked legos. To find the original number, we need to add those 23 legos back to our total. So we take the 117 legos and add the 23 that were removed, giving us 117 + 23 = 140 legos. Therefore, Ms. Kiyama started with 140 legos.

Answer:

8(x+10)

Step-by-step explanation:

8x + $80

We can factor out an 8 from each term

8(x+10)

Answer:

   A)  $257.83

Step-by-step explanation:

A spreadsheet or financial calculator will tell you the monthly payment on $11,000 at 5.9% annual rate for 4 years is ...

  $257.83

Step-by-step explanation:

In the x direction:

x = x₀ + v₀ₓ t + ½ at²

x = (0 m) + (60 m/s cos 10°) (0.9 s) + ½ (0 m/s²) (0.9 s)²

x ≈ 53 m

In the y direction:

y = y₀ + v₀ᵧ t + ½ gt²

y = (0 m) + (60 m/s sin 10°) (0.9 s) + ½ (-9.8 m/s²) (0.9 s)²

y ≈ 5.4 m

Answer:

53.2 m horizontally and 5.4 m vertically

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Let x be the original number.

x/2 +11=12

Now solve for x

x=2

Answer:

The number was 2

Step-by-step explanation:

To solve this you would just have to work backwards using the inverses of operations previously used

First you would subtract 11 from 12:

12-11=1

Then you would multiply by 2:

1 x 2=2

Answer:

D. y = one divided by eightx2

Step-by-step explanation:

The standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2 is y = one divided by eightx2.

Answer:

7%

Step-by-step explanation:

I = PRT

I = 787.50

P = 750

T = 15

now we sub and find R (the rate)

787.50 = (750)(r)(15)

787.50 = 11250r

787.50 / 11250 = r

0.07 = r

0.07 x 100 = 7% = R

answer is 7%

Answer:

Step-by-step explanation:

The crater shape can be modeled by an absolute value function with a slope of 0.25. The vertex of the function will not be at (0, 0) but will be at (1600, -400). The usual methods of translating functions apply. Horizontal displacement of the vertex is subtracted from the independent variable; vertical displacement is added to the function value.

  d(h) = 0.25×|h -1600| -400

We know the horizontal displacement is 1600 ft, because the depth changes at a rate of 1/4 foot for each horizontal foot. A depth change of 400 feet will require 1600 horizontal feet to accomplish.

__

At a depth of 250 ft, the distance from the west edge can be found from ...

  -250 = 0.25|h -1600| -400

  150 = 0.25|h -1600| . . . . . . . . add 400

  600 = |h -1600| . . . . . . . . . . . multiply by 4

This resolves to two equations:

The depth is 250 ft at distances of 1000 ft and 2200 ft from the west edge.

_____

Comment on the equation

We have chosen to make depths be negative numbers. If you want the equation to give positive numbers for depth, multiply it by -1:

  d = 400 -0.25×|h -1600|

Answer:

0.25|x-1,600|-400 / 1,000 / 2,200

Step-by-step explanation:

Answer:

  (7, 9)

Step-by-step explanation:

The lines cross at point (7, 9). This is the solution.

__

If we assume the variables being graphed are x and y, then the solution is ...

Answer:

3 miles per hour

Step-by-step explanation:

because he runs 3 mile per hour , for another one hour 3 miles therefore it will be 3 miles per hour

Answer:

D

Step-by-step explanation:

y = -0.2 x²

This has a negative sign, as opposed to y = x², so it will point in the opposite direction.

The leading coefficient (0.2) is less than 1.  This means the parabola is shrunk vertically, or stretched horizontally.  So the parabola is wider than y = x².

Final answer:

The graph of y = -0.2x² is wider than and opens in the opposite direction of the graph of y = x² due to the negative and smaller in absolute value coefficient.

Explanation:

The comparison of the graphs of y = -0.2x² and y = x² is affected by the coefficients of the x² term. In the case of y = x², the coefficient is positive (1), implying the graph is a parabola that opens upwards. On the other hand, the negative coefficient (-0.2) in y = -0.2x² indicates the graph is also a parabola but opens downwards.

Furthermore, the absolute value of the coefficient affects the width of the parabola. A coefficient smaller in absolute value than 1, such as -0.2, makes the parabola wider than the parabola of y = x², which is the standard case. Therefore, the graph of y = -0.2x² is wider than and opens in the opposite direction of the graph of y = x².

Answer:

X would be the unit of measure (weight) and Y would be the ammount. In a equation that would be, 2x = y.

Answer:

The values of both x and y will be greater than or equal to zero.

Step-by-step explanation:

We are given that

Cost of 1 pound of peaches=$2

If x represents the number of pounds of peaches bought.

Total cost of the peaches represented by y.

We have to find the the values of x and y which describes the best.

To find the total cost of peaches we will multiply the cost of one pound with total number of pounds of peaches.

If cost of  1 pound of peaches=$2

Cost of x pounds of peaches=[tex]2\times x=2x[/tex]

Therefore, the total cost of x pounds of peaches, [tex]y=2x[/tex]

Weight of a thing  is always greater than 0 or equal to .

The total cost of a thing   is always greater than or equal to zero.

Therefore,the values of both x and y will be greater than or equal to zero.

[tex]\displaystyle\\\sum_{n=3}^5(-2x-4n)=-2x-4\cdot3+(-2x)-4\cdot4+(-2x)-4\cdot5\\\sum_{n=3}^5(-2x-4n)=-6x-12-16-20\\\sum_{n=3}^5(-2x-4n)=-6x-48[/tex]

[tex]\bf 4~~,~~\stackrel{4+5}{9}~~,~~\stackrel{9+5}{14}~~,~~\stackrel{14+5}{19}~~,~~\stackrel{19+5}{24}\qquad \impliedby \stackrel{\textit{common difference}}{d=5} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=4\\ d=5 \end{cases} \\\\\\ a_n=4+(n-1)5\implies a_n=4+5n-5\implies a_n=5n-1[/tex]