Suppose f(x) and g(x) are differentiable functions satisfying f(1) = f′(1) = 2. Let
h(x) = g(f(x)) − g(2x). Determine whether h′(1) > 1

The probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.

When a random variable X is normally distributed, with the mean as μ, and standard deviation as σ, then the probability P(X < x) is calculated using the Z-score table, as the probability P(Z < z), where z is calculated using the formula, z = (x - μ)/σ.

In the question, we are asked to find the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12.

We calculate as follows:

P(X < 105)

= P(Z < (105-90)/12)

= P(Z < 1.25)

Now we check the z-score table for the value of z as 1.25.

On the left column we choose the value 1.2.

On the top row, we choose the value .05.

The intersection of these, gives us the value,

P(Z < 1.25) = 0.8944.

Thus, the probability P(X < 105), assuming that the random variable X is normally distributed, with mean μ = 90 and standard deviation σ = 12 is calculated to be 0.8944.

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Answer:  

- 2/3

Step-by-step explanation:

Answer:

Any equation that has the same slope as the line y = -2/3x + 1 but a different y-intercept will be parallel because the lines will never intersect. For example, y = -2/3x + 2 or y = -2/3x + 3.

Brainliest, please :)

The domain of a function is the range of its inverse, and vice versa.

So, the domain is [tex]x > 1[/tex] and the range is [tex]y > 3[/tex].

Answer:

24 F

Step-by-step explanation:

Temp increases by 4F per hour.

-8F - 6F = 12F / 3hours

Answer:

40

Step-by-step explanation:

Set up a proportion

Inch/ threads = inch to threads

.1/4 = 1/x  Cross multiple

.1x = 4  Divide both sides by .1

x = 40

The value of the circumference (C) of a circle, having a radius (r) = 0.8695 mm, using the formula C = 2πr, is calculated to be 5.4632296245926504416865368435231‬ mm.

A circle is a shape formed by all points in a plane that are at a particular distance from the center.

The linear distance around a circle is defined as its circumference. In other words, if a circle is opened to produce a straight line, the length of that line equals the circumference of the circle.

The formula for the circumference of a circle is given:

C = 2πr,

where C is the circumference of the circle, r is its radius, and π is a constant.

We are asked to find the circumference of the circle (C), given its radius (r) = 0.8695 mm.

Using the formula of the circumference C = 2πr, we can find the circumference as:

C = 2*π*(0.8695) mm,

or, C = 5.4632296245926504416865368435231‬ mm.

Thus, the value of the circumference (C) of a circle, having a radius (r) = 0.8695 mm, using the formula C = 2πr, is calculated to be 5.4632296245926504416865368435231‬ mm.

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The probability of selecting from the platter a chocolate cupcake and then a yellow cupcake is  0.10.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of selecting a chocolate cupcake and then a yellow cupcake = (number of chocolate cupcake / total number of cupcakes) x (number of yellow cupcakes / total number of cupcakes - 1)

(13 / 38) x (11 / 37) = 0.10

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The equation that shows the proportional relationship between his defense and offense cards is y = 2x

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the defense cards and x represent the offense cards.

For every 2 offense cards, he owns 4 defense cards. Hence:

4 = 2m

m = 2

y = 2x

The equation that shows the proportional relationship between his defense and offense cards is y = 2x

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Answer: Point of intersection (0, -2)

Step-by-step explanation:

Answer:

S =  (0, -2)

Step-by-step explanation:

Convert both standard form equations to slope-intercept form.

-5x+2y=-4 ⇒ y = 5/2(Decimal form: 2.5)x - 2

2x-y=2 ⇒ y = 2x - 2

Given:

⇒ L1 = y = 5/2x - 2

⇒ L2 = y = 2x - 2

The intersection is point:

⇒ S = (0, -2)

Steps:

To find intersection point we need to solve the following system of equations.

STEP 1: Solve for x

5/2x - 2 = 2x - 2

5/2x - 2x = -2 + 2

1/2x = 0

x = 0

STEP 2:  Solve for y by substituting x = 0 into  first equation.

y = 5/2 * 0 - 2 = 0 - 2 = -2

Answer:

6.2%, 0.6, 5/8, 2/3

Step-by-step explanation:

For some reason, you have written the same numbers over and over.  It looks like there are only really 4 numbers.

I changed each number into a decimal and then compared them.

6.2% to change a percent to a decimal, move the decimal 2 places to the left so 6.2% equals 0.062.

0.6 is already in decimal form

5/8 you divide 5 by 8.  Put in your calculator 5 the division symbol and then  8 to get  0.625.

2/3 is 0.6 repeating or 0.66666 forever.

Now compare:

62% = 0.62

0.6

5/8 = 0.625

2/3 = 0.66666...

Induced pluripotent stem cells can be a valuable tool in science and medicine because: A. induced pluripotent stem cells can become any cell type in the body, but are from adults, avoiding the controversies associated with embryonic stem cells.

A cell can be defined as the fundamental functional, structural and smallest unit of life, which is typically found in all living organisms.  

In Science, all living organisms are broadly grouped into two (2) main categories according to cell type and these include the following;

Basically, the reason why induced pluripotent stem cells can be a valuable tool in science and medicine is simply because they can become any cell type within the body of a living organism, but are usually derived from adults that are avoiding the controversies associated with embryonic stem cells.

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Complete Question:

Induced pluripotent stem cells are cells from adults that have been reprogrammed to imitate embryonic stem cells. Why might induced pluripotent stem cells be a valuable tool in science and medicine?

A. Induced pluripotent stem cells can become any cell type in the body, but are from adults, avoiding the controversies associated with embryonic stem cells

B. Induced pluripotent stem cells are the only type of stem cell that's truly pluripotent.

C. Induced pluripotent stem cells may become any cell type in the body, but are fraught with ethical questions over their use.

D. Induced pluripotent stem cells are derived from adult cells and therefore may have DNA abnormalities, allowing scientists to understand the effects of sun exposure or toxins on DNA

Answer:

53 times per second

Step-by-step explanation:

There are 60 seconds in 1 minute, so divide the 3180 flaps per minute into 60 equal parts.

3180 / 60 = 53

Answer:

(0, -2) and (2, 0)

Step-by-step explanation:

The solution to a systems of equations is when the x and y values are equal for two equations. This can also been seen as when the two equations intersect. So by looking at the graph you see the line and the circle intersect at the point (2, 0) and (0, -2) which are going to be the two solutions to the systems of equations.

The value of (p*q)(5) and (q*p)(5) is 288

The functions are given as:

p(x)=x+1

q(x)=2x^2-2

Calculate p(5) and q(5)

p(5)=5+1 = 6

q(5)=2(5)^2-2 = 48

The functions are then calculated as:

(p*q)(5) = p(5) * q(5)

(p*q)(5) = 6 * 48

(p*q)(5) = 288

Also, we have:

(q*p)(5) = (p*q)(5)

(q*p)(5) = 288

Hence, the value of (p*q)(5) and (q*p)(5) is 288

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Complete question

Suppose that the functions p and q are defined as follows. p(x)=-x-1 q(x)=-2x^2-2 Find the following. (p*q)(5) (q*p)(5)

Answer:

7.26

Step-by-step explanation:

Here

Diameter=2m

Length =2.6m

Breadth=4m

Now

Area of circle=(22*2*2*4)/7

=22/7

=3.14m^2

again

Area of rectangle= lb

=2.6m*4m

=10.4m^2

So

Area of the shaded region is 10.4m^2-3.14m^2

=7.26m^2

The answer is 7.26 m².

To find the shaded area, subtract the area of the circle from the area of the rectangle.

Answer:

The constant of variation is 4

Step-by-step explanation:

We are looking for the constant of variation when t varies directly as the square of s

t = k s^2  where k is the constant of variation

t = 64 and s = 4

64 = k  4^2

64 = k * 16

Divide each side by 16

64/16 = k * 16/16

4 = k

The constant of variation is 4

Answer: 14.8

Step-by-step explanation: If the number in the hundredths place is less than 5, you must round down. On the contrary, if that number is 5 or greater, you must round up. This applies for rounding to any place not just the tenths place. For example, if you were to round it to the ones place, the answer would be 15.

Answer:

14.8

Step-by-step explanation:

The hundredth is smaller than 5, therefore you have to round down.

hope it helps

The lateral area of the cone is calculated as: B. 47 in.².

Lateral area = πrl

Given the following:

Slant height (l) = 5 inches

Radius (r) = 3 inches.

π = 3.14

Plug in the values

Lateral area = (3.14)(3)(5)

Lateral area ≈ 47 in.²

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The vertices of the feasible region are as follows,

(-14, -11), (9, -11) and (6, 4)

What is a Feasible Region?

The area of the graph where all constraints are satisfied is the feasible solution zone or feasible region. It might also be thought of as the point where each constraint line's valid regions intersect. Any decision in this region would lead to a workable resolution for our objective function.

Vertices of the Feasible Region

As it can be seen in the graph, the vertices of the feasible region surrounded by the given constraints are:

(-14, -11), (9, -11) and (6, 4)

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Answer:

1.6 < x < 9.6

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

5.6 - 4 < x < 5.6 + 4

1.6 < x < 9.6

Answer:

The Probability of both happening is 0.304.

Step-by-step explanation:

P(A) × P(B)

=  0.76 × 0.4

=  0.304

Let [tex]x[/tex] and [tex]y[/tex] be the amounts of available alloy (AA) and pure magic steel that are used, so we also have

[tex]x + y = 2.7[/tex]

DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of

[tex]0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}[/tex]

[tex]0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}[/tex]

[tex]0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}[/tex]

For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; [tex]x[/tex] kg of it will contain [tex]0.21x[/tex] kg of gold, [tex]0.09x[/tex] kg of silver, and [tex]0.70x[/tex] kg of steel. Each kg of magic steel of course contributes 1 kg of steel; [tex]y[/tex] kg of it will contribute [tex]y[/tex] kg of steel.

Then the dwarves need

• total gold: [tex]0.21x = 0.189[/tex]

• total silver: [tex]0.09x = 0.081[/tex]

• total steel: [tex]0.70x + y = 2.43[/tex]

Solve for [tex]x[/tex] and [tex]y[/tex]. The first two equations are consistent and give [tex]x = 0.90[/tex], and substituting this into the third we find [tex]y = 1.80[/tex]. So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.

The probability of that exactly 8 of them favor the building of the health center is 0. 399

From the information given, we have that 70% of the community favors the building of the health center

Number of citizens chosen = 14

P(8) = [tex]\frac{8}{14}[/tex] × [tex]\frac{70}{100}[/tex]

P(8)  = [tex]0. 57[/tex] × [tex]0. 7[/tex]

P(8) = [tex]0. 399[/tex]

Thus, the probability of that exactly 8 of them favor the building of the health center is 0. 399

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Answer:

(4, 7/2)

Step-by-step explanation:

midpoint = x values/2, y values/2

Answer: 2.25 inches

Step-by-step explanation:

The radius of a circle is half the diameter.

Answer: The initial population is 18 and 1 year(t=1) later it is 38

Step-by-step explanation:

38 = 18 * e^(1*k), where k is the growth rate

e^(1*k) = 38/18

Take the natural log(ln) of both sides of the = k = ln(38/18) = 0.747

P(t) = 18 * e^(0.747*t), where P(t) is the population affected at time t(years since 1996)

Answer:

y = 0.8425   or   y = -0.8425

Step-by-step explanation:

All points in the Cartesian coordinate system have an x and y coordinate, defined by two perpendicular measurements.

If the point is on the unit circle, then the radius of the circle is defined to be 1 unit, and the corresponding right triangle follows the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

For a unit circle:

[tex]x^2+y^2=1^2[/tex]

Substituting the known value for x, and simplifying...

[tex](-0.5387)^2+y^2=(1)^2[/tex]

[tex]0.29019769+y^2=1[/tex]

Subtracting 0.29019769 from both sides to begin to isolate "y"...

[tex]y^2=1-0.29019769[/tex]

[tex]y^2=0.70980231[/tex]

Applying the square root property...

[tex]\sqrt{y^2}=\pm \sqrt{0.70980231}[/tex]

[tex]y=\pm 0.8424976171...[/tex]

So, (to 4 decimal places), the y coordinate could be either 0.8425 or -0.8425.

With only the given information, either result is a valid answer.

the probability of getting heads on a two-face coin is simply 1/2.

now, what is the probability of getting 1/2 AND 1/2 AND 1/2 AND 1/2 AND 1/2?   well, AND means "times", namely

[tex]\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\implies \cfrac{1}{32}[/tex]

well, and since it's a two-face coin, the probability for each face is equal, 1/2, so Heads has a chance of 1/2 each time, or we can also say that Tails has a chance of 1/2 each time, so if Tails has the same probability over 5 times as Head does.