if f(x) = -5x +5 and g(x) +3x +8, find g(f(x))

There are 7290 4-digit positive integers that satisfy the given conditions.

We have,

To determine the number of 4-digit positive integers that satisfy the given conditions, we need to count the possibilities for each condition and then find their intersection.

Condition (A):

Each of the first two digits must be 1, 4, or 5.

Since there are 3 choices for each of the first two digits, there are

3 x 3 = 9 possibilities for condition (A).

Condition (B):

The last two digits cannot be the same digit.

There are 10 choices for the first digit, and for each of these choices, there are 9 choices for the second digit (excluding the chosen digit). Therefore, there are 10 x 9 = 90 possibilities for condition (B).

Condition (C): Each of the last two digits must be 5, 7, or 8.

There are 3 choices for each of the last two digits, resulting in 3 x 3 = 9 possibilities for condition (C).

To find the total number of 4-digit positive integers satisfying all three conditions, we multiply the possibilities for each condition together:

9 x 90 x 9 = 7290

Therefore,

There are 7290 4-digit positive integers that satisfy the given conditions.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ4

If Pamela has registered for the first time, it will remain on the Do Not Call list permanently. If she has re-registered, it will remain on the list for an additional five years from the date of re-registration.

The length of time that Pamela's phone number will remain on the National Do Not Call Registry depends on whether she registered her number on the Do Not Call Registry for the first time or if she has re-registered her number after it has already been on the list for a while.

If Pamela registered her phone number for the first time, it will be added to the Do Not Call Registry within 31 days of her registration date. Her phone number will remain on the list permanently, unless she requests to remove it or the number is disconnected.

If Pamela has re-registered her phone number after it has already been on the list for a while, her number's registration will be extended for another five years from the date she re-registered it.

Therefore, if Pamela registered her phone number for the first time, it will remain on the list permanently. If she has re-registered her number, it will remain on the list for an additional five years from the date of re-registration.

Learn more about do not call registry

brainly.com/question/30780624

#SPJ11

The number of years that the deposit was held for is 3 years.

From the information, Mr. Johnson deposited $2000 in an account that earns simple interest at an annual interest rate of 6%. and he received $360 as interest at the end of the tenure.

It should be noted that simple interest is Illustrated as:

I = PRT

Therefore, T = Interest / Principal × Rate

Time = 360 / (2000 × 6%)

Time = 360 / 120

Time = 3 years

Learn more about interest on:

brainly.com/question/25793394

#SPJ1

Answer:

B

Step-by-step explanation:

In 45 45 90 triangles the ratio is a:a:a root 2 so the answer would be 3root 2/2 or c because when multiplied again by root 2 it will get you 3.

A characteristic or measure obtained by using all the data values for a specific population is called a parameter.

A parameter in statistics is a number that identifies a population trait. The average height of all adult males in the population, for instance, may be a criterion if we were interested in researching the heights of all adult men in the United States. The standard deviation, variance, median, mode, and range of a population are other examples of parameters.

In most cases, parameters must be calculated using statistical techniques from a sample of the population. Statistics are the values derived from the sample and are used to predict the values of the related parameters.

Learn more about data population here:

https://brainly.com/question/24846692

#SPJ1

Answer:

p/8

Step-by-step explanation:

Answer:

\(\frac{2}{15}\)

Step-by-step explanation:

1. There are 9 balls in total in the first box, and 6 red balls in there so we would represent this as \(\frac{6}{9}\) and that can be simplified to \(\frac{1}{3}\) .

2. There are 5 balls in total in the second box, and 2 blue balls in there, so we would represent this as \(\frac{2}{5}\) . This can't be simplified, so we leave it like that.

3. Because it's a consecutive event we multiply the probabilities, which gives us \(\frac{2}{15}\) . This can't be simplified, and that gives us our answer.

The rate that would result in a single investment doubling in 3 years with annual compound interest can be calculated using the rule of 72.

The rule of 72 states that if you divide 72 by the annual interest rate (as a percentage), you get the approximate number of years it takes for an investment to double in value.

So, to find the annual interest rate that would result in a single investment doubling in 3 years, we need to solve the equation: 72 / r = 3 where the r is the annual interest rate (as a percentage).

Simplifying the equation, we get:

r = 24

Therefore, the annual interest rate that would result in a single investment doubling in 3 years is 24%.

Read more about rule of 72

brainly.com/question/30197467

#SPJ1

Answer:

The distance between points C and D is 5.83

Step-by-step explanation:

We need to find distance between points C and D

Looking at the graph we can find coordinates (x,y) of points C and D

Coordinates of point C are: (-4,3)

Coordinates of point D are: (1,0)

The formula used to calculate Distance is:

\(Distance=\sqrt{(x_2-x_1)^+(y_2-y_1)^2}\)

Putting values and finding distance between points C and D

\(x_1=-4, y_1=3, x_2=1, y_2=0\)

\(Distance=\sqrt{(x_2-x_1)^+(y_2-y_1)^2}\\Distance=\sqrt{(1-(-4))^2+(0-3)^2} \\Distance=\sqrt{(1+4)^2+(-3)^2} \\Distance=\sqrt{(5)^2+(-3)^2} \\Distance=\sqrt{25+9}\\Distance=\sqrt{34}\\ Distance=5.83\)

So, the distance between points C and D is 5.83

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

To know more about marginal utility related question visit:

https://brainly.com/question/30841513

#SPJ11

Answer:

STEP 3

Step-by-step explanation:

Francesca drew point (–2, –10) on the terminal ray of angle , which is in standard position. She found values for the six trigonometric functions using the steps below.

A unit circle is shown. A ray intersects point (negative 2, negative 10) in quadrant 3. Theta is the angle formed by the ray and the x-axis in quadrant 1.

Francesca made her first error in step 3 because the sine, cosine, and tangent ratios are incorrect, which also resulted in incorrect cosecant, secant, and tangent functions.

please mark me brainlyest <i cant spell it >

The probability of getting the specific sequence t, h, h, h, h, t, t, t, t, t, t when tossing a coin 11 times is 1/2048.

To find the probability of this specific sequence occurring, we need to use the formula for the probability of a specific sequence of independent events:

P(A and B and C and D and E and F and G and H and I and J and K) = P(A) * P(B) * P(C) * P(D) * P(E) * P(F) * P(G) * P(H) * P(I) * P(J) * P(K)

In this case, A represents the first toss being a tails (t), B represents the second toss being a heads (h), and so on until K represents the eleventh toss being a tails (t).

Using the given sequence, we can calculate the individual probabilities for each toss:

P(A) = 1/2 (since there is a 50/50 chance of getting either heads or tails on the first toss)

P(B) = 1/2 (since there is a 50/50 chance of getting heads on the second toss after getting tails on the first toss)

P(C) = 1/2 (since there is a 50/50 chance of getting heads on the third toss after getting heads on the second toss)

P(D) = 1/2 (since there is a 50/50 chance of getting heads on the fourth toss after getting heads on the third toss)

P(E) = 1/2 (since there is a 50/50 chance of getting heads on the fifth toss after getting heads on the fourth toss)

P(F) = 1/2 (since there is a 50/50 chance of getting tails on the sixth toss after getting heads on the fifth toss)

P(G) = 1/2 (since there is a 50/50 chance of getting tails on the seventh toss after getting tails on the sixth toss)

P(H) = 1/2 (since there is a 50/50 chance of getting tails on the eighth toss after getting tails on the seventh toss)

P(I) = 1/2 (since there is a 50/50 chance of getting tails on the ninth toss after getting tails on the eighth toss)

P(J) = 1/2 (since there is a 50/50 chance of getting tails on the tenth toss after getting tails on the ninth toss)

P(K) = 1/2 (since there is a 50/50 chance of getting tails on the eleventh toss after getting tails on the tenth toss)

Multiplying these probabilities together gives us the probability of getting the sequence t, h, h, h, h, t, t, t, t, t, t:

P(t, h, h, h, h, t, t, t, t, t, t) = (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/2048

Learn more about probability:

https://brainly.com/question/13604758

#SPJ11

The expression that most accurately describes the change in the patient's temperature is -2° (3).

Option 3 is the correct answer.

We have,

The expression that most accurately describes the change in the patient's temperature would be:

-2° + (-2°) + (-2°)

This expression represents the successive temperature drops of 2° each time.

By adding the negative values, we account for the decrease in temperature.

This can be written as,

= -2° x 3

= -2° (3)

Thus,

The expression that most accurately describes the change in the patient's temperature is -2° (3).

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer:

30

Step-by-step explanation:

A)  IF = e⁰∫.dx

B) e⁰∫.dx = -1/3 x⁻³ + c, where c is the arbitrary constant.

C) e⁰∫.dx = -1/3 x⁻³ + e⁰∫.dx


A) The given equation is:

∫.dx = x⁻¹

The integrating factor (IF) is:

IF = e⁰∫.dx

B) Substituting the IF, we have:

e⁰∫.dx x⁻¹ = x⁻¹

Rearranging the equation, we obtain:

∫e⁰∫.dx dx = ∫x⁻¹ dx

Integrating both sides, we get:

e⁰∫.dx = -1/3 x⁻³ + c, where c is the arbitrary constant.

C) To solve the initial value problem, we need to find the value of c. To do this, substitute x = 0 in the equation and solve for c. We obtain:

e⁰∫.dx = -1/3 x⁻³ + c

e⁰∫.dx = -1/3 (0)⁻³ + c

e⁰∫.dx = c

Thus, the value of c is e⁰∫.dx.

Therefore, the general solution is:

e⁰∫.dx = -1/3 x⁻³ + e⁰∫.dx

This is the solution to the initial value problem.

In summary, the equation ∫.dx = x⁻¹ was solved by finding the integrating factor (IF) of e⁰∫.dx, and then using it to find the general solution of -1/3 x⁻³ + e⁰∫.dx.

The value of the arbitrary constant was found by substituting x = 0 and solving for c. Thus, the general solution of the initial value problem was obtained.


Learn more about arbitrary constant here:

https://brainly.com/question/29093928#


#SPJ11

The relationship between 3x+4y=1 and 6x+8y=2 is that they are parallel lines.

Any linear equation has the form of y=mx+b

m is the slope of the equation

b is the y-intercept

The easiest way to see the relationship between the two lines is to transform them both into slope-intercept form, which is y=mx+b.

Equation 1 can be rewritten as

3x+4y=1

4y=1-3x

y= \(\frac{1-3x}{4}\)

Equation 2 can be rewritten as:

6x+8y=2

8y=2-6x

y = \(\frac{2-6x}{8}\)

Y= \(\frac{1-3x}{4}\)

In this form, we can easily identify that both lines have a slope of \(-\frac{3}{4}\), but that they have different y-intercepts. Lines will equal slopes but different y-intercepts are parallel.

Therefore, the lines are parallel.

To know more about slope-intercept form and parallel lines, visit: https://brainly.com/question/1612114?referrer=searchResults

#SPJ4

Answer:

Ohh

Step-by-step explanation:

The answer is already there

Answer:

The fraction of its drop height after the fourth bounce is

\(\displaystyle \frac{16}{625}\)

Step-by-step explanation:

Let's suppose the rubber ball is dropped from a height H0. Every time the ball bounces back it reaches 8/10 of the initial drop height.

The ball's height H(x) after bounce number x is:

\(\displaystyle H(x)=H_o\left(\frac{8}{20}\right)^x\)

Simplifying:

\(\displaystyle H(x)=H_o\left(\frac{2}{5}\right)^x\)

After the fourth bounce, the height is:

\(\displaystyle H(4)=H_o\left(\frac{2}{5}\right)^4\)

\(\displaystyle H(4)=H_o\frac{2^4}{5^4}\)

\(\displaystyle H(4)=H_o\frac{16}{625}\)

The fraction of its drop height after the fourth bounce is

\(\mathbf{\displaystyle \frac{16}{625}}\)

The CDF of Z is:

F_Z(z) = { 0 for z < 0

{ 1/2 - z/2 for 0 ≤ z < 1

{ 1 for z ≥ 1

(a) Let Z = X - Y. We will find the CDF and PDF of Z.

The CDF of Z is given by:

F_Z(z) = P(Z <= z)

= P(X - Y <= z)

= ∫∫[x-y <= z] f_X(x) f_Y(y) dx dy (by the definition of joint PDF)

= ∫∫[y <= x-z] f_X(x) f_Y(y) dx dy (since x - y <= z is equivalent to y <= x - z)

= ∫_0^1 ∫_y+z^1 f_X(x) f_Y(y) dx dy (using the limits of y and x)

= ∫_0^1 (1-y-z) dy (since X and Y are uniformly distributed over [0,1], their PDF is constant at 1)

= 1/2 - z/2

Hence, the CDF of Z is:

F_Z(z) = { 0 for z < 0

{ 1/2 - z/2 for 0 ≤ z < 1

{ 1 for z ≥ 1

To know more about random variables refer here:

https://brainly.com/question/17238189

#SPJ11

The curve y = x^(-2) represents a hyperbola that is symmetric about the y-axis. Let's examine the two given points on the curve, (-4, 1/16) and (-1/2, 4), within the interval -4 to -1/2.

The point (-4, 1/16) means that when x is -4, y (or f(x)) is 1/16. This indicates that at x = -4, the corresponding y-value is 1/16. Similarly, the point (-1/2, 4) signifies that when x is -1/2, y is 4.

By plotting these two points on a graph, we can visualize the curve and its behavior within the given interval.

The point (-4, 1/16) is located in the fourth quadrant, close to the x-axis. The point (-1/2, 4) is in the second quadrant, closer to the y-axis. Since the curve y = x^(-2) is symmetric about the y-axis, we can infer that it extends further into the first and third quadrants.

As x approaches -4 from the interval (-4, -1/2), the values of y decrease rapidly. As x approaches -1/2, y approaches positive infinity. This behavior is consistent with the shape of the hyperbola y = x^(-2), where y becomes increasingly large as x approaches zero.

It's worth noting that the given interval (-4, -1/2) does not include x = 0, as x^(-2) is undefined at x = 0 due to division by zero. Therefore, we do not have information about the behavior of the curve at x = 0 within this interval.

To summarize, the given points (-4, 1/16) and (-1/2, 4) lie on the curve y = x^(-2) within the interval -4 to -1/2. Plotting these points reveals the shape and behavior of the hyperbola, showing a rapid decrease in y as x approaches -4 and an increase in y as x approaches -1/2.

Learn more about hyperbola here

https://brainly.com/question/26250569

#SPJ11

Consider the curve y=x^-2 on the interval -4 -1/2, recall that the two given points on the curve y = x^(-2) on the interval -4 to -1/2 are (-4, 1/16) and (-1/2, 4).

Answer:

the answer is m=5/3, hope this really helps.

Answer:

slope: \(\frac{5}{3}\)

slope-intercept form: y=\(\frac{5}{3}\)x+\(\frac{10}{3}\)

Step-by-step explanation:

Hope this helps!

Answer:

13 stamps : 17 stickers

Step-by-step explanation:

52 stamps : 68 stickers can be simplified down to 13 stamps : 17 stickers because their greatest common factor is 4

Answer:

3/5

Step-by-step explanation:

6x  - 10y = -100

Write this equation in slope-intercept form: y = mx +b

-10y = -6x - 100

Divide the entire equation by (-10)

\(\dfrac{-10}{-10}y=\dfrac{-6}{-10}x-\dfrac{100}{-10}\\\\y =\dfrac{3}{5}x+10\)

Slope = 3/5

Parallel lines have same slope.

Slope of the parallle line = 3/5

Answer:

The median for the students is 2 and the median for the teachers is 3.

Step-by-step explanation:

We can find the median by writing the numbers represented in each dot plot in order.

For the students,

0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

The middle value is between 2 and 2; this makes it 2.

For the teachers,

0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 8

The middle value is between 3 and 3; this makes it 3.

This means the second choice is correct.

I CANT HELP :(

Step-by-step explanation:

:(

On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

To learn more about postsynaptic membrane visit:

brainly.com/question/14969022

#SPJ11

Answer:

Fair

Step-by-step explanation:

Based on the description provided in the question it is safe to say that the survey that Paula conducted is completely Fair. This is mainly due to the fact that her pool of participants are completely random. Paula does not control who will walk through the schools doors first. Therefore she cannot be biased since she is surveying whoever walks through the doors first regardless of her personal opinions or feelings.

column four 8, 15, 40, 45, 52.

Answer:

It's C. With more trials, the frequency of heads up will equal the frequency of tails up.

Step-by-step explanation:

edge

Answer:

Step-by-step explanation:

2y+6+y+8=20

3y+14=20

3y=6

y=2