2x + 6
What is the value of this expression if x = 4?
A) 2
B) 8
C) 14
D) 20

To qualify for the special summer camp for accelerated students, a student must score at least approximately 978 on the standardized test, considering a score within the top 16% of all scores, given a mean score of 800 and a standard deviation of 120.

In a bell-shaped or normal distribution, the mean [tex]\(\mu\)[/tex] represents the central tendency of the data, and the standard deviation [tex]\(\sigma\)[/tex] measures the dispersion or spread of the scores. To find the score required to qualify for the top 16%, we use the z-score formula: [tex]\(z = \frac{X - \mu}{\sigma}\)[/tex], where X is the score, [tex]\(\mu\)[/tex] is the mean, and [tex]\(\sigma\)[/tex] is the standard deviation.

Given the mean score [tex]\(\mu = 800\)[/tex] and standard deviation [tex]\(\sigma = 120\)[/tex], the z-score corresponding to the top 16% is found using a standard normal distribution table or statistical software. The z-score associated with the top 16% is approximately z = 1.04.

Next, use the z-score formula to solve for the score X required to be in the top 16%: [tex]\(z = \frac{X - \mu}{\sigma}\)\\[/tex]. Rearranging the formula to solve for X gives us [tex]\(X = z \cdot \sigma + \mu\)[/tex]. Substituting the z-score value and the given mean and standard deviation into the equation yields [tex]\(X = 1.04 \cdot 120 + 800 = 978\)[/tex]. Hence, a student needs to score at least approximately 978 to qualify for the special summer camp for accelerated students, given the distribution of scores on the standardized test.

Answer:

the tank can hold 12.5 gallons when it is full

Step-by-step explanation:

Let's assume

tank can hold 'x' gallons when it is full

we are given

The gas gauge in a car shows it has 40% of a tank of gas

So, gas in car is

[tex]=\frac{40}{100}\times x[/tex]

and we have

the car has about 5 gallons

so, we can set it equal

and then we can solve for x

[tex]5=\frac{40}{100}\times x[/tex]

[tex]5=\frac{4}{10}\times x[/tex]

[tex]5=\frac{2}{5}\times x[/tex]

Multiply both sides 5

[tex]5\times 5=5\times \frac{2}{5}\times x[/tex]

[tex]5\times 5=2x[/tex]

[tex]25=2x[/tex]

we get

[tex]x=12.5[/tex]

So, the tank can hold 12.5 gallons when it is full

Answer:

B

Step-by-step explanation:

Answer:

600kW

Step-by-step explanation:

Referring to the fact that 10m/s of wind is 500kW so divide 500 by 10.

500/10=50

So there is 50 kW is 1m/s of wind. Now multiply 12 by 50

12x50=600

So for 12m/s of wind there is 600kW

At 12 m/s, the turbine generates 864 kW.

We can express the given relationship as P = k * v^3, where k is a constant of proportionality.

Given that a turbine generates 500 kW at a wind speed of 10 m/s, we can find k using the equation:

500 = k * 10^3

k = 500 / 1000

k = 0.5.

Now, to find out how much power the turbine would generate at 12 m/s. The calculation is :

P = 0.5 * 12^3

P = 0.5 * 1728

P = 864 kW.

The wind turbine generates 864 kW in a 12 m/s wind.

Final answer:

To find the scaled length of a line representing 5 feet on a scale drawing with a scale of 0.5 inches = 2 feet, set up a proportion and solve for x. The answer is 1.25 inches.

Explanation:

To calculate the length of a line on a scale drawing, you must use the scale provided and set up a proportion based on that scale. In this case, the scale is 0.5 inches = 2 feet. To find out what 5 feet would be on the drawing, we can set up a proportion where 0.5 inches/2 feet equals x inches/5 feet. Solving for x gives us:

0.5 inches / 2 feet = x inches / 5 feet

To keep the units consistent, we use cross-multiplication:

(0.5 inches) * 5 feet = 2 feet * x inches

2.5 inches = 2 feet * x inches

Now, divide both sides by 2 feet to solve for x:

x = 2.5 inches / 2 feet

x = 1.25 inches

Therefore, a line that represents an actual length of 5 feet would be 1.25 inches long on the scale drawing.

Answer:

9.00

Step-by-step explanation:

Use proportion:-

20% is equivalent to 1.80

1%  is equivalent to 1.80 / 20

100% is equivalent to (1.80 / 20 ) * 100

= 180 / 20

= 9

=  9.00

Answer:

Same side: 4, 1.5, 5/3, 0.2

Opposite side: -5, -1/4

Step-by-step explanation:

We know that dilation caused by a positive factor leads to the object being on the same side and dilation caused by a negative factor leads to the object being on the opposite side. Therefore, the dilation caused by positive numbers 4, 1.5, 5/3, 0.2 will lead to object being on the same side. And dilation caused by a negative numbers -5 and -1/4 will lead to object being reflected to the opposite side

Answer:

The cannonball will hit the ground after about 5.926 seconds.

Step-by-step explanation:

h(t) = -4.9t² + 27.5t + 9.1

If you graphed the function on a graph, the cannonball would be hitting the ground when the function crossed the x-axis at 0. So, to solve this arithmetically, you just need to set h(t) equal to 0.

-4.9t² + 27.5t + 9.1 = 0   Plug this into a calculator if you have one, if not solve with the quadratic formula.

[tex]\frac{-27.5 \pm \sqrt{(27.5^2) - 4(-4.9)(9.1)} }{2(-4.9)}[/tex]

t = -.0313

t = 5.9256

Since time can't be negative, you know your answer will be 5.926 seconds.

Answer:

t =5.93 seconds

Step-by-step explanation:

h(t) represents the height of the cannon ball.  Zero is when the ball will hit the ground.    Substitute zero for h(t).

0 = -4.9t² + 27.5t + 9.1

This is a complicated quadratics, so we will need to use the quadratic formula to solve

-b ± sqrt(b^2 -4ac)

-----------------------------

  2a

where a = -4.9   b = 27.5   and c = 9.1

-27.5  ± sqrt(27.5 ^2 -4 (-4.9) 9.1)

-----------------------------------------------

  2(-4.9)

-27.5  ± sqrt(756.25 +178.36)

-----------------------------------------------

  -9.8

-27.5  ± sqrt(943.61)

-----------------------------------------------

  -9.8

-27.5  ± 30.57139186

-----------------------------------------------

  -9.8

3.071391856/-9.8   or  -58.07139186/-9.8

-.313407332  or  5.925652231

But time cannot be negative,  the ball cannot land before it takes off,

so t= 5.925652231 seconds

Rounding to the nearest hundredth

t =5.93 seconds

Answers:

Mean = 13.55

Median = 13

Mode = 13

====================================================

Explanations

Mean:

To get the mean, multiply the ages with their corresponding frequencies. Then add up the results. I show this in the attached image below. The highlighted yellow cell is the sum of the x*y column (x = age, y = frequency). This value is 718.

Once you get to 718, you divide this over the total frequency which is 7+9+11+10+9+4+3 = 53 (so there is 53 people).

The mean is therefore 718/53 = 13.5471698113208 which rounds to 13.55

----------------------

Median:

The median is the middle most value. There are 53 values here (add up the frequencies), so the midpoint is at slot 53/2 = 26.5 = 27. The first 26 values are below the median, and the last 26 values are above the median leaving 53-26-26 = 53 - 52 = 1 value in the very exact center.

Add up the frequencies starting from 7 then to 9, etc until you get to 27. So we have

7+9 = 16 which isn't 27

7+9+11 = 16+11 = 27 perfect, we landed on 27

This means that the last copy of 13 is in slot 27. This is because the last frequency added (11) corresponds to the age 13.

That is why the median is 13

----------------------

Mode:

The mode is the most frequent value. Simply record the age that has the highest frequency. In this case, the highest frequency is 11 which corresponds to age 13, pointing to the mode being 13.

Answer:

Let B represents the number of basil plants and F represents the number of fennel plants,

As per the given condition: Michelle has a maximum of 4500 milliliters  of water for her plants today. Each basil plant requires 350 of water, and each fennel plant requires 525  of water.

Each basil plant require 350 of water

⇒ total number of basil plant require water = 350B

Each Fennel plant require 525 of water.

⇒ total number of fennel plant require water = 525F

Since, Michelle has a maximum of 4500 milliliters of water;

then;

[tex]350B+525F \leq 4500[/tex]

Therefore, an inequality that represents the number of basil plants(B) and fennel plants can water today is; [tex]350B+525F \leq 4500[/tex]

Answer:

D)

Step-by-step explanation:

sec(x) = 1/cos(x)

You know cos(x) = 1 for x=0, so sec(0) = 1.

You also know that sec(x) has vertical asymptotes where cos(x) = 0, at odd multiples of π/2. Only selection D matchest these characteristics.

Answer:

(3, 7)

Step-by-step explanation:

The midpoint of a line joining the points  (x1, y1) and (x2, y2) has midpoint

[(x1 + x2)/ 2]. (y1 + y2)/2 ]

Substituting the given points:-

Midpoint of MN =  (-2 + 8)/2 ,  (4 + 10)/2

= 6/2 , 14/2

= (3, 7)   (answer)

Answer:

see explanation

Step-by-step explanation:

the result 0 = 0

means the equation has an infinite number of solutions

Answer:

All values of x make the equation true... THIS  IS THE CORRECT ANSWER!

Step-by-step explanation:

Answer: 2x^3 - 7x^2 + 6x - 9 which is choice D

=========================================

Work Shown:

One way is to use the distribution rule two times

(x-3)(2x^2-x+3) = y(2x^2-x+3) ........... replace (x-3) with y

(x-3)(2x^2-x+3) = y(2x^2)+y(-x)+y(3) .... distribution rule

(x-3)(2x^2-x+3) = 2x^2*(y) - x(y) + 3(y)

(x-3)(2x^2-x+3) = 2x^2*(x-3) - x(x-3) + 3(x-3) .... replace y with x-3

(x-3)(2x^2-x+3) = 2x^3-6x^2 - x^2 + 3x + 3x - 9 ... distribution rule

(x-3)(2x^2-x+3) = 2x^3 - 7x^2 + 6x - 9

----------------------------

Or we can use the box method (see the attached image below). This is a visual way to organize the terms. You'll probably notice that the box method is basically the distribution rule. Each row is one distribution being applied. In row 1, we have x distributed to (2x^2-x+3). In row 2, we have -3 distributed to (2x^2-x+3). I color coded the table cells to highlight the like terms. Those like terms combine to -6x^2-x^2 = -7x^2 and 3x+3x = 6x as shown in the steps for the distribution above.

Each interior cell in the box is found by multiplying the corresponding outer terms. For example, in the first row, first column we have x^3 which is the result of multiplying the outer x and x^2 terms.

The correct choice is D) [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex].

To find the product[tex]\((x - 3)(2x^2 - x + 3)\)[/tex], we can use the distributive property:

[tex]\((x - 3)(2x^2 - x + 3) = x(2x^2 - x + 3) - 3(2x^2 - x + 3)\)[/tex]

Now, distribute the terms:

[tex]\[= x \cdot 2x^2 - x^2 + 3x - 3 \cdot 2x^2 + 3x - 9\][/tex]

Combine like terms:

[tex]\[= 2x^3 - x^2 + 6x - 6x^2 + 6x - 9\][/tex]

Combine the x terms:

[tex]\[= 2x^3 - 7x^2 + 6x - 9\][/tex]

Therefore, the expression [tex]\((x - 3)(2x^2 - x + 3)\)[/tex]  is equal to \[tex](2x^3 - 7x^2 + 6x - 9\)[/tex].

So, the correct choice is D) [tex]\(2x^3 - 7x^2 + 6x - 9\)[/tex].

Answer:

answer is 8

8+14x+6x+12=180

Step-by-step explanation:

Answer:

65,1,5.5

Step-by-step explanation:

Replace with 1 and simplify.

Answer:

6

Step-by-step explanation:

f(x) = 3x - 1

f(2) means evaluate  f(x) when x=2

f(2) = 3(2) -1

f(2) = 6-1=5

g(5) means evaluate g(x) when x=5

g(5) = -5+6

g(5) =1

f(-2) + g(5)

5+1

6

Answer:

6

Step-by-step explanation:

Answer: Negative infinity

note: if your teacher won't allow negative infinity, then try DNE for "does not exist"

=======================================================

Explanation:

As x gets closer to x = 4 from the left side of this value, then x starts at something like x = 3 and moves to x = 3.5, then to x = 3.9, then to x = 3.99, then to x = 3.999, etc

We get closer to x = 4 but never actually get there. If you look at the table attached, then f(x) = 1/(x-4) will keep getting more negative with larger and larger negative values. This growth goes on forever without any bound. So the limit is equal to negative infinity.

As you can see on the graph below, the curve heads downward as you approach x = 4 from the left hand side. Imagine you are a point on the curve, or this point is on a rollercoaster (the curve being the track itself). As you get closer to 4 from the left side, you go downhill. There is on limit to how far downhill you can go.

note: the graph and table in the attachment below were made by the free graphing calculator program GeoGebra

Answer with explanation:

The given rational function is

      [tex]y= \lim_{x \to 4^{-}} \frac{1}{x-4}[/tex]

To find the vertical Asymptotes , put

→  Denominator =0

→ x-4=0

→x=4, is the Vertical Asymptote.

Answer:

(-4,1)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

18/12=  [tex]1\frac{1}{2}[/tex] and  [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option,  [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of  [tex]1\frac{7}{8}[/tex].

A fraction represents a part of a whole.

If a fraction has a numerator that is less than the denominator then the fraction is proper.

An improper fraction has a numerator that is greater than the denominator.

A mixed number is an integer written with a fraction.

18/12 is a improper fraction, let us simplify it by dividing numerator and denominator by 6

18/12 is 3/2.

The mixed fraction of 3/2 is [tex]1\frac{1}{2}[/tex]

Now the given mixed fraction is [tex]1\frac{7}{8}[/tex]

When we convert to improper we get (8×1)+7/8 , which is 15/8

Hence, 18/12=  [tex]1\frac{1}{2}[/tex] and  [tex]1\frac{7}{8}[/tex] = 15/8 is the correct option,  [tex]1\frac{1}{2}[/tex] is mixed fraction of 18/12 and 15/8 is improper fraction of  [tex]1\frac{7}{8}[/tex].

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Answer:

R=6%

Step-by-step explanation:

Given:

Total money deposited = $ 520

Total years = 5

Total earned = $156

Simple interest

To Find:

interest rate=R=?

Solution:

We know the formula for calculating total amount earned by a simple interest rate and formula for it is

I = P(rT)                     ..................(i)

where I is total amount earned

P is total money invested

r is rate

and t is time

putting the values gives us

156 = 520 (r)(5)

156 = 2600 r

dividing both sides by 2600

r = [tex]\frac{156}{2600}[/tex]

r= 0.06

We have to find R

Now from simple rules of

we know that

R = r* 100 %

so putting the value of r

R = 0.06 * 100 %

R = 6%

which is the rate at which money was invested

Final answer:

78,045 rounded to the nearest thousand is 78,000. You round down because the hundreds digit (0) is less than 5. This approach to rounding applies in various arithmetic contexts.

Explanation:

To round 78,045 to the nearest thousand, we need to consider the hundreds digit, which is 0. In rounding, if the hundreds digit is 5 or greater, we would round up. However, because it is 0, we keep the thousands digit the same and replace all subsequent digits with zeros. Thus, 78,045 rounded to the nearest thousand is 78,000.

When dealing with whole numbers and rounding to a certain place value, it is crucial to look at the number to the immediate right of the place value you are rounding to. If this number is 5 or higher, you round up. Otherwise, you round down. This principle is true regardless of whether you are serving a subtraction operation, like 78,500 m - 362 m which rounds to 78,100 m, or if you're dealing with large numbers in scientific notation, such as 79,345 which can be represented as 7.9345 × 104.

The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is that x = 19 is the solution because 3 * 19 - 15 = 57 - 15 = 42.

The choice that describes whether x = 19 is the solution of the equation 42 = 3x - 15 is the option: x = 19 is not the solution because 3 * 19 - 15 = 3 * 4 = 12, not 42.

To check if a value is the solution to an equation, we substitute the value into the equation and perform the necessary calculations. In this case, substituting x = 19 into the equation 42 = 3x - 15 gives us 42 = 3 * 19 - 15 = 57 - 15 = 42. Since both sides of the equation are equal, x = 19 is indeed the solution.

The question is asking to determine if x = 19 is the solution for the equation 42 = 3x – 15. To verify this, we need to substitute x = 19 into the equation. So, we have 42 = 3(19) - 15 which simplifies to 42 = 57 - 15. After subtraction on the right side, we get 42 = 42, which is a true statement. Hence, x = 19 is indeed the solution to the equation 42 = 3x – 15.

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Answer:

Prefix Symbol Multiplier

deci d 0.1

centi c 0.01

milli m 0.001

micro µ 0.000001

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

The slope of a line passing through two points (a,b) and (c,d) is given by :-

[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]

In the given graph , the line is passing through (0,0) and (1,3) .\

Then the slope of line  passing through (0,0) and (1,3) will be :-

[tex]\text{Slope}=\dfrac{3-0}{1-0}\\\\\Rightarrow\ \text{Slope}=3[/tex]

Hence, the slope of the given line= 3

Answer:

sec theta = r/v

Step-by-step explanation:

sec theta  = 1 /  sin theta

We know that sin theta = opp/ hypotenuse

1 / sin theta = hypotenuse /  opp

sec theta = hypotenuse /  opp

sec theta = r/v

Answer:

10 ways, 6th row

Step-by-step explanation:

You will flip a coin five times and get three heads and two tails. You can get it in

[tex]C_5^3=\dfrac{5!}{3!(5-3)!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot1\cdot 2}=10[/tex]

different ways.

6th row tells her the number of favorable outcomes for this event.

Answer:

C = 81.6 degrees

Step-by-step explanation:

The formula for law of sines

sin A       sin B          sin C

--------  = -----------  = -------------

a                  b               c

Looking at the diagram,  we know A = 54, b = 7.4 and c = 15.8

not enough to use the law of sines

We will need to use the law of cosines

a^2 = b^2 + c^2 - 2ac cos A

Using the law of cosines, we can calculate the length of a

a^2 = 7.4^2 + 15.8^ -2*7.4*15.8 cos 54

a^2 = 54.6+249.64-233.84cos54

a^2 =166.7922966

a = 12.921

Now we can use the law of sines to find C

sin 54      sin C

--------  =  -------------

12.921           15.8

Using cross products

15.8 * sin 54 = 12.921 * sin C

Divide each side by 12.921

15.8 /12.921 * sin 54  = sin C

Take the arcsin of each side

arcsin (15.8 /12.921 * sin 54)  = arcsin (sin C)

arcsin (15.8 /12.921 * sin 54)  = C

C = 81.6 degrees

Answer:

The answer is 63/10, 63/100, 63/1000

Answer:

it would be SSS...

Step-by-step explanation:

Its meaning is "side side side''... so you see how the triangle, ABD has the dashed (same number of lines) through the lines of the triangle, it means the sides are all congruent meaning that the sides are the same

Answer:

The triangles are not congruent.

Step-by-step explanation:

The triangle ABD is an equilateral triangle, then all their sides are equal and all the angles are equal to 60º. Then x=60º and y=30º (because the sum of the internal angles of a triangle have to be 180º)

Then we can conclude that the triangles are not congruent because they share two sides, but does no have any angle in common, as we can see in the next list of the angles.

angle ADB= angle ABD= angle DAB=60º

angle BDC=30º

angle DCB=30º

angle CBD=120º