the sum of two and a number is at least 16

Answer:

P = -4

Step-by-step explanation:

Assuming that x = 20 and y = 24, you have to plug in these numbers for x and y to get to this equation P = 20 - 24.  You should get -4 when you subtract 24 from 20 giving you a negative answer.

Answer:

D

Step-by-step explanation:

\({a}^{2} + {b}^{2} = {c}^{2} \)

\( {27}^{2} + {36}^{2} = 2025 \\ {45}^{2} = 2025\)

Answer:

12

Step-by-step explanation:

= 6:3(3+3)

= 6/3 x 6

= 12

Derivative of the function f'(0) is equal to 0.

To find f'(0), we need to take the derivative of the function f(x) = 2xtan(3x) and evaluate it at x = 0.

Using the product rule and the chain rule, we can find the derivative of f(x) as follows:

f'(x) = 2[tan(3x) + 3x \(sec^2(3x)\)]

Now, let's evaluate f'(0):

f'(0) = 2[tan(3(0)) + 3(0) \(sec^2(3(0))\)]

= 2[tan(0) + 0 \(sec^2(0)\)]

= 2[0 + 0]

= 0

Therefore, f'(0) is equal to 0.

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(a) The probability of getting a total of 10 is 1/18; (b) The probability of getting at most a total of 11 is 1.

The probability of getting a total of 10 when a pair of fair dice is tossed can be found by dividing the number of favorable outcomes by the total number of possible outcomes. The total number of possible outcomes when two dice are tossed is 6 x 6 = 36. The favorable outcomes for getting a total of 10 are (4, 6) and (6, 4), so there are 2 favorable outcomes. Therefore, the probability of getting a total of 10 is 2/36 = 1/18.

The probability of getting at most a total of 11 can be found by adding the probabilities of getting a total of 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. The favorable outcomes for each of these totals are:

2: (1, 1)
3: (1, 2), (2, 1)
4: (1, 3), (2, 2), (3, 1)
5: (1, 4), (2, 3), (3, 2), (4, 1)
6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
9: (3, 6), (4, 5), (5, 4), (6, 3)
10: (4, 6), (5, 5), (6, 4)
11: (5, 6), (6, 5)

The total number of favorable outcomes is 2 + 2 + 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 = 36. Therefore, the probability of getting at most a total of 11 is 36/36 = 1.

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Therefore, the expression \(t^{(-3/4)}\) in rational form is:

\(B. 1/^4 \sqrt {t^3}\)

What is the exponential function?

An exponential function is a mathematical function of the form:

f(x) = aˣ

where "a" is a constant called the base, and "x" is a variable. Exponential functions can be defined for any base "a", but the most common base is the mathematical constant "e" (approximately 2.71828), known as the natural exponential function.

To write the expression \(t^{(-3/4)}\) in rational form, we need to eliminate the negative exponent.

Recall that a negative exponent can be rewritten as the reciprocal of the positive exponent. In this case,  \(t^{(-3/4)}\) can be written as 1/ \(t^{(-3/4)}\).

Therefore, the expression \(t^{(-3/4)}\)in rational form is:

\(B. 1/^4 \sqrt {t^3}\)

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Answer:

Step-by-step explanation:

Plot the point (2,5)    See image

slope = rise/run = so rise 2 run 1

Equation for line:

Formula for point slope:

y - y₁ = m (x - x₁)       Where

m=slope = 2

point (x₁, y₁) = (2, 5)

Substitute

y-5 = 2(x-2)                         >Distribute

y-5 =  2x -4                         >add 5 to both sides

y = 2x + 1

The answer is:

below

Work/explanation:

First, let's write the line's equation in point slope form

\(\bf{y-y_1=m(x-x_1)}\)

where m is the line's slope.

Plug in the data:

\(\bf{y-5=2(x-2)}\)

Now, we can graph it.

I have used the Desmos graphing calculator.

The correct expression that represents a quadratic expression is: 12x² + 8x - 1.

A quadratic equation is an algebraic expression that involves numbers and variables choosing the second degree of x.

Therefore, we can conclude that the correct quadratic equation from the options is 12x² + 8x - 1.

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Answer:

12x² + 8x - 1.

Step-by-step explanation:

For each additional staff member available decreases wait time by about 1.62 minutes. The statement is TRUE

The statement that when the wait time is 0 minutes, 18 staff are available is FALSE

The standard equation of  a line is given as y = mx + b where:

The slope is also known as the rate of change of the function.

If a line that models the data is given by the equation y=−1.62x+18;

This shows that each additional staff member available decreases wait time by about 1.62 minutes. The statement is TRUE

The y-intercept is the point where the line cuts the y-axis. The y-intercept (0, 18) means that when the wait time is 18 minutes, 0 staff are available, hence the given statement is FALSE

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Given:

The function is

\(y=\tan x\)

To find:

The domain of the given function.

Solution:

We know that, domain is the set of x-values or input values.

We have,

\(y=\tan x\)

\(y=\dfrac{\sin x}{\cos x}\)

The functions sin x and cos x are defined for all real values of x. So, the function tan x is defined for all real values of x except those value for which cos x = 0.

So, domain is \(-\infty<x<\infty, x\neq \dfrac{\pi}{2}+n\pi\).

Note: All options are incorrect.

Answer:

C

Step-by-step explanation:

all x≠pi/2+pi n

The probability that the randomly selected student does not have a cat is 13/18.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, we know that is a total of 18 students.

5 have cats

9 have dogs

6 do not have a cat and a dog

Probability formula: P(E) = Favourable events/Total events

The probability that the student does not have a cat:

P(E) = Favourable events/Total events

P(E) = 18-5/18

P(E) = 13/18

Therefore, the probability that the randomly selected student does not have a cat is 13/18.

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Check the picture below.

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−2,3)

Equation Form:

x=−2,y=3

but

Solve for x

y=−4x3+13

y=−x+1

Step-by-step explanation:

The algebraic equation "0.40x = 400" represents the words: forty percent of Mrs. Garcia's score is 400 points. Mrs. Garcia's score is 1000.

Algebraic equation is an equation made up of variables and coefficients that can be used to solve mathematical problems or questions.

To formulate an algebraic equation, we designate a variable for unknown values.

Mrs. Garcia's score is unknown, and so

let x = Mrs. Garcia's score

Based on the information given on the problem, forty percent of Mrs. Garcia's score is 400 points. Forty percent can be written as 0.40.

40% of x is 400

0.40x = 400

Hence, the algebraic equation for that is 0.40x = 400.

Evaluating the value of x,

0.40x = 400

x = 400 / 0.40

x = 1000

Therefore, Mrs. Garcia's score is 1000.

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We can rewrite this as:`W(t) = (H - C/20)e^(-kt)/20`if `H - 3200 > 0` and as `W(t) = (H + C/20)e^(kt)/20` if `H - 3200 < 0`.(c) As `t → ∞`, `W(t) → H/20` if `H - 3200 > 0` and `W(t) → 0` if `H - 3200 < 0`.

The differential equation is `dy/dx = sqrt(x² - 16)`

The existence/uniqueness theorem guarantees that there is a solution to this equation through the point (x0, y0) if the function `f(x,y) = dy/dx = sqrt(x² - 16)` and its partial derivative with respect to y are continuous in a rectangular region that includes the point (x0, y0).

If f and `∂f/∂y` are both continuous in a region containing the point `(x_0, y_0)` then there is at least one unique solution of the initial value problem `(y'(x)=f(x,y(x)),y(x_0)=y_0)`.

Using the existence and uniqueness theorem, we can see if there exists a solution that passes through the given points.

(a) The differential equation is `dW/dt = k(H - 20W)`, where `k = 1/3500`.

Here, W(t) is the person's weight at time t and H is their constant caloric intake.

(b) First, rearrange the equation `dW/dt = k(H - 20W)` into a separable form:`(dW/dt)/(H - 20W) = k`.

Then integrate both sides:`∫(dW/(H - 20W)) = ∫k dt`.

Using the u-substitution, let `u = H - 20W` so that `du/dt = -20(dW/dt)`.

Then `dW/dt = (-1/20)(du/dt)`.

Substituting these, we get `∫(-1/u) du = k ∫dt`.

Solving the integrals, we get: `ln|H - 20W| = kt + C`

where C is the constant of integration.

Exponentiating both sides gives:`|H - 20W| = e^(kt+C)`.

Simplifying:`|H - 20W| = Ce^kt`

where C is a new constant of integration.

Using the initial condition `W(0) = 160`, we get `|H - 20(160)| = C`.

Simplifying:`|H - 3200| = C`

Substituting back into the solution, we get:`H - 20W = ± Ce^kt`

We can rewrite this as:`W(t) = (H - C/20)e^(-kt)/20`if `H - 3200 > 0` and as `W(t) = (H + C/20)e^(kt)/20` if `H - 3200 < 0`.(c) As `t → ∞`, `W(t) → H/20` if `H - 3200 > 0` and `W(t) → 0` if `H - 3200 < 0`.

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Answer:

18 ways

Step-by-step explanation:

Number of Meat choices = 3

Number of Vegetable choices = 3

Number of Desserts = 2

Number of ways dinner can be chosen :

Number of meat choices * Number of vegetable choices * number of desserts

3 * 3 * 2

= 18

Hence, dinner can be chosen in 18 different choices.

Answer:0.8

Step-by-step explanation:

Answer

1/2 : 1/3 = 3/

2

= 1 1/

2

= 1.5

Step-by-step explanation:

1.5 is your answer

Answer:

Jeremy's acceleration is about \(1\,\frac{m}{s^2}\)  at t =10 s

His average speed is about 44.5 m/s in this section of his jump approximating with points on the curve (under-estimate)

His average speed is about 46 m/s if using the tangent line (over estimate)

Step-by-step explanation:

Jeremy's acceleration can be estimated by the curve's derivative at that point. That is the slope of the tangent line to the velocity curve at x = 10 sec. Please see attached image where the tangent line is drawn in orange, and the points to use to calculate its slope are drawn in green.

These points are : (6, 42) and (14,50) which using the slope formula give:

\(slope=\frac{y_2-y_1}{x_2-x_1}= \frac{50-42}{14-6}=\frac{8}{8} \frac{m}{s^2} = 1\,\frac{m}{s^2}\)

So his acceleration at that point is about \(1\,\frac{m}{s^2}\)

Now, using about the same interval of x-values (from 6 to 14), the corresponding speeds are approximately: 40 (for time 6 seconds) and 49 (for time 14 seconds (look for the red dots on the attached image). Since  the average velocity is given by the integral of the function between those points divided by the length of the interval where it is calculated:

\(v_{average}=\frac{area}{interval\,\,length}\)

and we don't have the actual velocity function to estimate the integral, we can approximate this area by that of a trapezoid that connects the red dots with the bottom of the horizontal axis (see red trapezoid in the image). Clearly from the image, this approximation would give us an under-estimate of the actual average speed.

The area of this trapezoid is: approximately:

\(Trapezoid\,\, area=(49+40)\,8/2=356\)

Then the average velocity estimated from it is:

\(v_{average}=\frac{356}{8} \frac{m}{s} =44.5\,\frac{m}{s}\)

If the area is approximated instead with the trapezoid form by the green points we used to calculate the acceleration (this would give us an over-estimate):

\(Trapezoid\,\, area=(50+42)\,8/2=368\)

Then the average velocity estimated from it is:

\(v_{average}=\frac{368}{8} \frac{m}{s} =46\,\frac{m}{s}\)

while his actual instantaneous velocity seems to be about 46 m/s from the graph

Answer:

a) 1.0

b) s=45

Step-by-step explanation:

Answer: False

Step-by-step explanation:

Researchers typically report the adjusted R-squared value in addition to the regular R-squared value, not because they lack confidence in the actual R-squared, but because the adjusted R-squared provides additional information about the goodness of fit of a statistical model. The regular R-squared value measures the proportion of the variance in the dependent variable that is explained by the independent variables in the model. However, it can be biased and increase as more predictors are added to the model, even if the additional predictors do not contribute significantly to the prediction.

The adjusted R-squared, on the other hand, takes into account the number of predictors in the model and penalizes the addition of irrelevant predictors. It provides a more conservative measure of the goodness of fit by adjusting for the number of predictors and the sample size. Researchers often use the adjusted R-squared to evaluate and compare different models with varying numbers of predictors or to assess the overall explanatory power of a model while considering its complexity.

In summary, researchers report the adjusted R-squared value to address the limitations of the regular R-squared and to provide a more accurate assessment of the model's goodness of fit.

Answer:

The solution is (-6,2)

Step-by-step explanation:

Answer:

Fr

Step-by-step explanation:

Step-by-step explanation:

The goal is to isolate that given variable. The process is the same process that you use to solve linear equations; the only difference is that you will be working with a lot more letters, you also prob will not be able to simplfy as much as linear equations

Answer:

it is more than one step so it takes longer to solve

Step-by-step explanation:

the process of isolating a variable in these literal equations is similar to solving a one-step equation because after isolating a variable you solve the rest of the equation,it is different from solving a one-step equation because it is more than one step so it takes longer to solve

Answer:

R = a cos nθ

Step-by-step explanation:

The polar equation is in the form of a rose curve, r = a cos nθ. Since n is an even integer, the rose will have 2n petals.

The polar equations that represent a rose curve are r = 8sin(θ) and r = 3sin(8θ).

A rose curve is a type of polar equation that represents a symmetric and beautiful curve with "petals." The general form of a rose curve is:

r = a * cos(b * θ) or r = a * sin(b * θ)

where 'a' and 'b' are constants.

Let's analyze each of the given polar equations:

r = 3cos(θ) - This is not a rose curve because it only has one petal. A rose curve typically has multiple petals.

r = 8sin(θ) - This is a rose curve with 8 petals. It has the form r = a * sin(b * θ), where a = 8 and b = 1.

r = 3sin(8θ) - This is a rose curve with 8 petals. It has the form r = a * sin(b * θ), where a = 3 and b = 8.

r = 8 + 3cos(θ) - This is not a rose curve because it doesn't have a pure sine or cosine term in the equation. Rose curves are generated by pure sine or cosine terms.

So, the polar equations that represent a rose curve are:

r = 8sin(θ) and r = 3sin(8θ).

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Answer: 8

Step-by-step explanation: If we can define $ as k$, this would mean /frac32 would be K+($6). So, the answer is 8

The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.

By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.

The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.

First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.

Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.

Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.

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Answer: 32

Step-by-step explanation:

Let x + y = 5

x = 5 - y....................(1)

10x + y -9 = 10y + x..... . (2)

Substituting (1) in (2)

10(5-y) + y - 9 = 10y + (5-y)

50-10y + y - 9 = 10y + 5 - y

41 - 9y = 9y + 5

-9y - 9y = 5-41

-18y = - 36

y = 36/2 = 2

So, x = 5-2 = 3

Answer:

The answer is 6x² - 21x.

Step-by-step explanation:

You have to substitute the expressions inro the formula :

\(A = length \times width\)

\(let \: l = 2x - 7,w = 3x\)

\(A = (2x - 7) \times 3x\)

\(A = 3x(2x - 7)\)

\(A = 6 {x}^{2} - 21x\)

The area of the rectangular garden is 6x² - 21x.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know, The area of a rectangle is (length×width).

Given, The rectangular garden has a length of (2x - 7) and a width of 3x.

Therefore, The area of the garden is,

= (2x - 7)×3x.

= 6x² - 21x.

= x(6x - 21).

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Answer:

100

Step-by-step explanation:

(50-45)*20

=5*20

=100

PLEASE GIVE BRAINLIEST

Answer:

Renzi can type 100 more words than Samuel

Step-by-step explanation:

PLZ MARK BRAINLIEST!!!

Answer:

-10

Step-by-step explanation:

f(n)= f(n-2)+f(n-1)

• Put n = 3

=> f(3) = f(3-2) + f(3-2)

=> f(3) = f(1) + f(2)

=> f(3) = -6 + -4

=> f(3) = -10

Answer:

it in a file here

Step-by-step explanation:

xycba.com/file