(SAT Prep) Find the value of x.

Answer:

[tex]\displaystyle \frac{dy}{dx} = 20x^3[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]  

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = 5x^4 + 4[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

1

Step-by-step explanation:

First, find the inverse of the original function.

x = 2y + 2

x-2/2

Second, substitute x with 4 and solve.

4-2/2

2/2

1

Best of Luck!

If f(x) = 2x + 2 is invertible, then its inverse is another function f ⁻¹(x) such that

f(f ⁻¹(x)) = 2 f ⁻¹(x) + 2 = x

Solve for f ⁻¹(x) :

2 f ⁻¹(x) + 2 = x

2 f ⁻¹(x) = x - 2

f ⁻¹(x) = (x - 2)/2 = x/2 - 1

Then when x = 4, we have f ⁻¹ (4) = 4/2 - 1 = 2 - 1 = 1.

Answer: When the addition of two or more equations leads to the elimination of one of the variables.

Step-by-step explanation:

When we have a system of equations, the addition method seems to be useful only when adding the equations will lead to the elimination of one of the variables:

An example of this can be, for the variables x and y:

3*x + x*y - 2*y = 3

x^2 + x*y - 2y = 42

now we can "add" (actually subtract) the equations and get (eq2 minus eq1)

(x^2 + x*y - 2y) - (3*x + x*y - 2*y ) = 42 - 3

x^2 - 3*x = 39

x^2 - 3*x - 39 = 0

And now we can solve it for x, and then find the value of y.

Answer:

No image I cannot tell you

Step-by-step explanation:

Answer:

(a) The mean of the weight of the mice is 50.26 grams.

(b) The standard deviation of the weight of the mice is 14.08 grams.

Step-by-step explanation:

(a)

The mean is given as follows:

[tex]\bar X=\frac{\sum f_{i}x_{i}}{\sum f_{i}}[/tex]

    [tex]=\frac{5026}{100}\\\\=50.26[/tex]

Thus, the mean of the weight of the mice is 50.26 grams.

(b)

Compute the standard deviation as follows:

[tex]s=\frac{1}{\sum f_{i}-1}[\sum f_{i}x_{i}^{2}-\frac{1}{\sum f_{i}}(\sum f_{i}x_{i})^{2}][/tex]

  [tex]=\frac{1}{100-1}[254001-\frac{1}{100}(5026)^{2}]\\\\=\frac{1}{99}\times 1394.24\\\\=14.08323\\\\\approx 14.08[/tex]

Thus, the standard deviation of the weight of the mice is 14.08 grams.

Answer:

But the answer is 42

I did I got 42 .

:(

9514 1404 393

Answer:

  10.7 years

Step-by-step explanation:

The formula for the balance in an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. We want to solve for t.

  5800 = 3500(1 +0.0475/4)^(4t)

  58/35 = 1.011875^(4t) . . .  divide by 3500 and simplify a bit

  log(58/35) = 4t·log(1.011875) . . . . take logs

  t = log(58/35)/(4·log(1.011875)) . . . . divide by the coefficient of t

  t ≈ 10.6966 ≈ 10.7

The person must leave the money n the bank for about 10.7 years for it to reach $5800.

Answer:

2 + 109 = 111

Step-by-step explanation:

.............

Answer:

x <-3

Step-by-step explanation:

15 <-5x

divide both sides by 5 but since the coefficient of x is negative after dividing the sign changes.

x <-3

Answer:

x < −3

I hope this helps!

Answer:

16.25

Step-by-step explanation:

first do 12 -5 = 7. then 7/4 = 1.75 then 9+1.75 = 10.75 and finally 27-10.75= 16.25

Answer:

1: Equal

2: Negation

3: Negation

4: Neither

Step-by-step explanation:

Sorry if I got any of them wrong

Answer:

3hours and 12.5 minutes

Step-by-step explanation:

45/6=7.5x25=187.5/60=3hours and 12.5 minutes

Step-by-step explanation:

This is a linear equation in slope intercept form which is

[tex]y = mx + b[/tex]

where m is the slope and b is the y intercept.

The equation

[tex]y = - \frac{1}{3} x + 2[/tex]

Has a slope of -1/3 so this means that the slope will be decreasing. A negative linear equation increases as we go left. and decreases as we go right. The y intercept is 2. So this means the graph must pass through (0,2) and when x=0, y must be 2.

In other words, look for a line that the y values increase as we go left and decrease we go right. Also look for a point (0,2) and make sure the graph pass through it.

Answer:

d)  t = -10.12

Step-by-step explanation:

Explanation:-

Given sample size 'n'=10

Given the differences of mean x⁻ -μ = -3.36

Standard deviation of the sample 'S' =1.05 inches

We will use t-statistic

                      [tex]t = \frac{x^{-}-Mean }{\frac{S}{\sqrt{n} } }[/tex]

                     [tex]t= \frac{-3.36}{\frac{1.05}{\sqrt{10} } }[/tex]

                    t = -10.12

Answer: D

Step-by-step explanation:

Answer: B) The linear speed is 4750 inches per second, so this car would qualify.

Step-by-step explanation: To determine linear speed using revolutions per second, i.e., angular speed (ω):

v = ω.r

where r is radius.

As ω is in revolutions per second, transform into rad/s:

ω = 36 revolutions/s

1 revolution = 2π rad

ω = 36.2π rad/s

ω = 72π rad/s

Radius is 21 inches, which can be written as

r = 21 inches/rad

Linear speed is

v = [tex]\frac{72.\pi rad}{s} .\frac{21 in}{rad}[/tex]

v ≈ 4750 inches per seconds

Converting to miles per hour:

v = [tex]4750.\frac{5}{88}[/tex]

v = 270mph

At linear speed of 4750 inches per second, a car with wheel of radius 21-inch can qualify.

Answer:

Above is correct

Step-by-step explanation:

Answer:

The probability is 0.31084

Step-by-step explanation:

We can calculate this probability using the z-score route.

Mathematically;

z = (x-mean)/SD/√n

Where the mean = 16, SD = 3 and n = 36

For 15.8, we have;

z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4

For 16.2, we have

z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4

So the probability we want to calculate is;

P(-0.4<z<0.4)

We can get this using the standard normal distribution table;

So we have;

P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)

= 0.31084

Answer:

D.

Step-by-step explanation:

First, simply the inequality.

[tex]11\leq 2x+5\leq 15\\6\leq 2x\leq 10\\3\leq x\leq 5[/tex]

Based on the simplified inequality, you are looking for a line with closed points on 3 and 5. Therefore, the answer is D.

9514 1404 393

Answer:

Step-by-step explanation:

The 1-year interest is simply the invested amount times the interest rate.

Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...

  1400r + 900(r +.02) = 202

  2300r +18 = 202 . . . . . . . . . .simplify

  2300r = 184 . . . . . . . . . .subtract 18

  r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r

$1400 was invested at 8%.

$900 was invested at 10%.

Answer:

Below

Step-by-step explanation:

The formula of the volule of a cone is:

● V= (1/3) × Pi × r^2 × h

h is the height and r is the radius.

■■■■■■■■■■■■■■■■■■■■■■■■■■

We are given that the volume is 30 Pi m^3

● V = 30 Pi

● 1/3 × Pi × r^2 × h = 30 Pi

If we multiply h by 6 we should do the same for 30 Pi since it's an equation

● 1/3 × Pi × r^2 × h = 30 × Pi × 6

Answer:

REVIEW: B is Correct    Exit

A right circular cone has a volume of 30π m. If the height of the cone is multiplied by 6 but the radius remains fixed, which expression represents the resulting volume of the larger cone?

A. 6 + 30π m

B. 6 x 30π m

C. 6 x 30π m

D. 6 x (30π) m

Step-by-step explanation:

The answer is be all i did was dig into what the other person was saying and got b it is correct:)

Answer:

123.1 pounds is vary long, and I don't want to repeat, so 55.8372207 repeat.

Step-by-step explanation:

If you have any questions regarding my answer, tell me them in the comments, and I will come answer them for you. Have a good day.

9514 1404 393

Answer:

  f, h, g

Step-by-step explanation:

You can look at the slope of the tangent lines to the graphs at any given x-value. At x=5, we see that g(x) is the flattest curve and f(x) is the steepest.

In order from greatest to least growth rate, the functions are ...

  f(x), h(x), g(x)

Answer:

Question for number 3 is -3

Question for number 4 is 6

Step-by-step explanation:

Brainless please

Answer:

  -4

Step-by-step explanation:

(f+g)(1) = f(1) +g(1)

In each case, you need to locate the ordered pair with 1 as the first element.

  (1, f(1)) = (1, -2) . . . . f(1) = -2

  (1, g(1)) = (1, -2) . . . . g(1) = -2

  f(1) +g(1) = (-2) +(-2) = -4

(f+g)(1) = -4

Answer:

Step-by-step explanation:

2024800 : 100 * 5 = 101240

2024800 + 101240 = 2126040

2126040 : 100 * 5 = 106302

2126040 + 106302 = 2232342

in the first year, it increases by 5% of the original number, making the population at the end of that year 2 126 040. Then, the second year, it will increase by 5% of  2 126 040. This means that the final product or population after 2 years would be 2232342.

Answer:

6x-3=21

6x=24

x=4

........

6x+27=39

6x=39-27

6x=12

x=2

........

8x-10=14

8x=24

x=3

.........

6+6x=22

6x=22-6

x=3

......

12x-2=28

12x=26

x=3

.....

8-4x=16

-4x=8

x=-2

.....

4x-24=3x-3

4x-3x=24-3

x=21

....

9x+6=6x+12

9x-6x=12-6

3x=6

x=2

Answer:

Step-by-step explanation:

1. 3(2x - 1) = 21

 = 6x - 3 = 21

 = 6x = 24

 = x = 24/6 = 4

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

2. 3(2x+9) = 39

   = 6x + 27 = 39

   = 6x = 39 - 27

   = 6x = 12

   = x = 12/6 = 2

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

3. 2(4x - 5) = 14

  = 8x - 10 = 14

  = 8x = 14+10

 = x = 3

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

A = 1 and 8

B = 2 and 4

C = 2 and 7

I’m pretty sure this is right? I’m still learning too :p

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

Explanations:

For the sake of simplicity, imagine that lines m and n are parallel. They don't necessarily need to be in order to answer this problem, but it might help with the terminology better.

When we use the term "interior" we basically mean the region between or inside the parallel lines. So "exterior" is everything but that, which is composed of two separate regions that don't overlap. Exterior angles shown in this diagram are

angle 1, angle 5, angle 4, angle 8

The "alternate" refers to the idea that we're on alternate sides of the transversal cutting line. One pair of alternate exterior angles is angle 1 and angle 8. We have angle 1 below the transversal while angle 8 is on the opposite side and above the transversal. For similar reasoning, angles 5 and 4 are alternate exterior angles as well.

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

Notice how each line crosses to form an X shape, producing 4 angles that share the same common vertex point. For instance, angles 1, 5, 6 and 2 are all around the same point.

Angle 1 and angle 3 are corresponding angles because they

So in short, they are both in the same corner of each four corner angle configuration. They are both in the bottom left corner. This is the full list of all corresponding angle pairs

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

As stated in the first section above, the interior region is between the parallel lines. Alternate interior angles alternate being above and below the transversal line.

So this applies to angle 2 and angle 7. It also works for angle 3 and angle 6.

Answer:

complementary angles 25