3. 07 Quiz: Combine Functions Nearpod i H George has opened a new store and he is monitoring its success closely. He has found that this store's revenue each month can be modeled by r(x) = x2 + 5x + 14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x) = x2 - 4x + 5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r - c)(5) mean about George's new store? -O The new store will sell 900 items in its fifth month in business.

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The curl of vector field F is -i - j and the divergence of the vector field F is 0.

We have to follow the below steps:

Step 1: Find curl.

Step 2: Find divergence.

Curl :

Curl is the vector operator that defines the cross product of two vectors. It is applied to a vector field to generate another vector field.

Step 1:

Find the curl of vector field

Curl of the vector field F is defined as ,F = (P, Q, R)

Curl F = (Ry - Qz)i + (Pz - Rx)j + (Qx - Py)k

Where, Ry denotes the partial derivative of R with respect to y. Qz denotes the partial derivative of Q with respect to z, Pz denotes the partial derivative of P with respect to z .Rx denotes the partial derivative of R with respect to x, Qx denotes the partial derivative of Q with respect to x. Py denotes the partial derivative of P with respect to y.

Here,P = -x, Q = y, and R = -2.Then

Ry = 0, Qz = 0, Pz = 0, Rx = 0, Qx = 0, and Py = 0

Therefore, the curl of F = (Ry - Qz)i + (Pz - Rx)j + (Qx - Py)k= -i - j + 0k= -i - j

Then, the curl of vector field F is -i - j.

Divergence:

Divergence is a vector operator that operates on a vector field to produce a scalar value. It measures the magnitude of the outward flux of the vector field from an infinitesimal region around a particular point. Divergence is given by,

Divergence of the vector field F = (P, Q, R)div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Here, P = -x, Q = y, and R = -2.Then, ∂P/∂x = -1, ∂Q/∂y = 1, and ∂R/∂z = 0

Therefore, the divergence of the vector field F is

div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z= -1 + 1 + 0= 0

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If there is no difference between the distributions of scores in two groups, your effect size will be equal to 0 20.

What is distribution and example?

Distribution is the process of selling and delivering products and services to customers. The term is associated with marketing channels that are used to reach customers in different ways and different regions.

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the probability of roommate A winning the game is nine

Let Ra = selecting a rock.

Rb = picking a rock

Pa = picking a paper

Pb = picking a paper

Sa = picking a pair of scissors

Choosing scissors is Sb.

The events that could occur are:

RaRb RaPb RaSb PaRb PaSb PaPb SaRb SapB SaSb

As a result, the sample space for this experiment has a probability of 9 outcomes.

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If the engineers are planning a car design in which only 25 of adults fit , then this sitting height is 38.68 inches .

To find the sitting height for the tallest 2% of adults, we first find z-score for upper 2% of standard Normal Distribution ;

we know ; that z = (x - μ)/σ ;

where z is = z core, x is = sitting height , μ is = mean sitting height, and

σ is = standard deviation of sitting heights.

From the normal table : Upper 2% of standard normal distribution have a z-score of approximately 2.05 ;

So , 2.05 = (x - 35.4)/1.6 ;

Multiplying both sides by 1.6, we get ;

⇒ 3.28 = x - 35.4

On adding 35.4 to both sides, we get:

⇒ x = 38.68 ;

Therefore, the sitting height for the tallest 2% of adults is 38.68 inches .

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Answer:

A

Step-by-step explanation:

I think its A.. correct me if im wrong

Answer:

B

Step-by-step explanation:

Answer:

3.66

Step-by-step explanation:

35÷9.55=3.66

No, L is not decidable. To prove that L is not decidable, it is necessary to use a proof by contradiction. It can be assumed that L is decidable and it needs to be shown that this assumption leads to a contradiction.

A decidable language has a Turing machine that accepts and rejects all strings in a finite amount of time. The property of L that makes it undecidable is that it has an infinite number of even length strings. The contradiction can be shown using the following procedure:

First, let M be a Turing machine that decides L. It can be constructed using the definition of L.

Second, construct a Turing machine S that takes as input the description of another Turing machine T and simulates M on T. If M accepts T, then S enters an infinite loop.

Otherwise, S halts. If S is run on itself, it will either enter an infinite loop or halt. If S halts, then M does not accept S, which means that L(S) does not have an infinite number of even length strings. This is a contradiction. If S enters an infinite loop, then M accepts S, which means that L(S) has an infinite number of even length strings. This is also a contradiction. Therefore, L is not decidable.

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Answer:

Step-by-step explanation:

so "b" here, represents the off-set,  or in electrical engineering we call it the DC value.  it just means how far off of zero is the line when x = 0 .

So the question is   what is "Y"  when x= 0.   and this is what "b" represents.  

There is a bunch of math that we could do to find  slope and the equation of the line.

But, we can do this by inspection.  I mean, just looking at the numbers.

Note that when x = -1,  Y = 10 ,  then also,  when x = 1 , Y= 4,  sooo zero is excatly between -1 and 1  or,  take the difference of 10-4  , the Y values, and find the middle.    10-4 = 6  and then take half of that to find the middle, or half of 6 is  3.   so we know that at zero,  Y = 4+3  or   10-3  ,  note that these are the same ,  7.  so know we know,  when x=0, Y=7.   So "b" = 7  

got it?  it's a lot of thinking, and understanding.  But  you can see that the math it self is not tough.   :)   any questions?

Answer:

b = 7

Step-by-step explanation:

find slope:

10-16/-1-(-3)

-6/2

= -3

input any coordinate and slope in y=mx+b to get b:

16=-3(-3)+b

16= 9+b

b= 16-9

b = 7

Answer:

First option is the correct answer

Step-by-step explanation:

Speed of car = 450/9 = 50 mph

Speed of Bus = 510/12 = 42.5 mph

Speed of train= 300/8 = 37.5 mph

So,

The car has the fastest speed at 50 miles per hour.

If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.

In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.

The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.

To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.

Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.

By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.

If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.

If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.

By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.

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9514 1404 393

Answer:

  at most 63

Step-by-step explanation:

The inequality Jody can use to determine the number of sheets (s) of paper she can buy will be ...

  18.25 + 0.34s ≤ 40

  0.34s ≤ 21.75

  s ≤ 21.75/0.34 ≈ 63.97

Jody can buy up to 63 sheets of paper.

The power consumed by the device at t=1s is approximately `.

To find the total charge in the device at t=1s, we need to integrate the current function from 0 to 1. Since the initial charge is given as q(0) = 0, the total charge q(t) at time t can be found using the equation:

q(t) = ∫[0 to t] i(t') dt'

Let's calculate the integral:

q(t) = ∫[0 to t] 10(1 - e^(-0.5t')) dt'

= 10∫[0 to t] (1 - e^(-0.5t')) dt'

∫[0 to t] (1 - e^(-0.5t')) dt' = ∫[0 to t] dt' - ∫[0 to t] e^(-0.5t') dt'

The first integral is simply the integral of dt' from 0 to t, which gives us t. For the second integral, we can use the property:

∫[0 to t] e^(-kt') dt' = -1/k * e^(-kt') | [0 to t]

Applying this property to our integral, where k = 0.5, we have:

∫[0 to t] e^(-0.5t') dt' = -2 * e^(-0.5t) + 2

Substituting the results back into the original equation:

q(t) = 10(t - (-2 * e^(-0.5t) + 2))

= 10t + 20e^(-0.5t) - 20

Now, we can calculate the total charge at t = 1s:

q(1) = 10(1) + 20e^(-0.5(1)) - 20

= 10 + 20e^(-0.5) - 20

≈ 6.07 Coulombs

Therefore, the total charge in the device at t=1s is approximately 6.07 Coulombs.

To calculate the power consumed by the device at t=1s, we can use the equation:

P(t) = v(t) * i(t)

Substituting the given voltage and current functions:

P(t) = 5cos(2t) * 10(1 - e^(-0.5t))

At t=1s, we have:

P(1) = 5cos(2(1)) * 10(1 - e^(-0.5(1)))

Evaluating the cosine function:

P(1) = 5cos(2) * 10(1 - e^(-0.5))

≈ -3.92 W

Therefore, the power consumed by the device at t=1s is approximately -3.92 Watts.

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The equation of the parabola graphed is given as follows:

y = a(x + 1)² - 4.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

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Answer:

The answer is 324

Step-by-step explanation:

I don't know if it's the correct answer but I hope it helps

pls mark me as brainliest

The appropriate critical value for constructing a confidence interval in this setting is 1.88.

To find the appropriate critical value for constructing a confidence interval at a 94% confidence level, we can use a standard normal distribution table or a calculator.

First, we need to find the value of alpha, which is the significance level, which is equal to 1 - the confidence level. In this case, alpha is equal to 1 - 0.94 = 0.06.

Next, we need to find the critical value z* from the standard normal distribution table or calculator, which corresponds to the area to the right of z* being equal to alpha/2 = 0.03.

Using a standard normal distribution table or calculator, we can find that the critical value z* is approximately 1.88.

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Answer:

+, x + y = 3 => x = 3-y

thay vào xy =2 => (3-y)y = 2 <=> y^2 - 3y +2 = 0

<=> y=1 hoặc y = 2

=> x =2 hoặc x=1

=> x^2 + y^2 =5

The expressions without hyperbolic functions are as follows:

(a) sinh(0) = 0,

(b) cosh(0) = 1,

(c) tanh(0) = 0,

(d) sinh(1) = \((e^{(1)} - e^{(-1)})/2\), and

(e) tanh(1) = \((e^{(1)} - e^{(-1)})/(e^{(1)} + e^{(-1)})\).

The hyperbolic functions sinh(x), cosh(x), and tanh(x) can be defined in terms of exponential functions. We can use these definitions to express the given expressions without hyperbolic functions.

(a) sinh(0) = \((e^{(0)} - e^{(-0)})/2\) = (1 - 1)/2 = 0

(b) cosh(0) = \((e^{(0)} + e^{(-0)})/2\) = (1 + 1)/2 = 1

(c) tanh(0) = \((e^{(0)} - e^{(-0)})/(e^{(0)} + e^{(-0)})\) = (1 - 1)/(1 + 1) = 0

(d) sinh(1) = \((e^{(1)} - e^{(-1)})/2\)

(e) tanh(1) = \((e^{(1)} - e^{(-1)})/(e^{(1)} + e^{(-1)})\)

For expressions (d) and (e), we can leave them in this form as the exact values involve exponential functions. If you want an approximate decimal value, you can use a calculator to evaluate the expression.

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Step-by-step explanation:

the slope of a line is always the factor of x.

here : 1/2

it is the ratio y/x indicating how many units y changes, when x changes a certain angina amount of units when going from one point to another.

a perpendicular slope puts x and y upside-down and flips the sign.

here : -2/1 = -2

so, the equation looks like

y = -2x + b

b is the y-intercept, and we get this by putting the x and y coordinates of the given point into this equation and solve for b :

-1 = -2×-2 + b

-1 = 4 + b

b = -5

the full equation is therefore

y = -2x - 5

The answer is 1.5(a -3)

The Total Fertility Rate (TFR) in country X is 1, which means on average, each woman in the population has one child during her reproductive years.

The correct answer is: a) 1.3

To calculate the Total Fertility Rate (TFR), we need to determine the average number of children born to women in a specific population during their reproductive years.

In country X, women bear one child at age 25, one child at age 28, and one child at age 35. Since we know the age at which women have children, we can calculate the TFR.

Let's calculate the TFR step by step:

Determine the probability of a woman surviving to each reproductive age.

The probability of surviving to age 25 is one-third (as one-third of females die in infancy).

The probability of surviving from age 25 to age 28 is one-third (as one-third of females die between age 25 and 30).

The probability of surviving from age 28 to age 35 is one-third (as one-third of females die between age 30 and 60).

Determine the number of children born at each reproductive age.

At age 25, women have one child.

At age 28, women have one child.

At age 35, women have one child.

Multiply the probability of surviving to each reproductive age by the number of children born at that age.

For age 25: (1/3) * 1 = 1/3

For age 28: (1/3) * 1 = 1/3

For age 35: (1/3) * 1 = 1/3

Sum up the number of children born at each reproductive age.

TFR = (1/3) + (1/3) + (1/3) = 1

Therefore, the Total Fertility Rate (TFR) in country X is 1, which means on average, each woman in the population has one child during her reproductive years.

The correct answer is:

a) 1.3

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x = 9 is not an extraneous solution of the equation.

√x=√(x-8) + 2

Squaring both the sides of the equation, we get

(√x)² = (√(x-8)+2)²

x = (✓(x - 8))² + 2² + 2(✓(x - 8))(2)

x = x - 8 + 4 + 2(✓(x - 8))(2)

Subtracting x on both the sides of the equation, we get

- 4 + 2(✓(x - 8))(2) = 0

Adding 4 on both the sides of the equation, we get

4(✓(x - 8)) = 4

Dividing both sides of the equation by 4, we get

(✓(x - 8)) = 1

Squaring again on both the sides of the equation

x - 8 = 1

x = 9

Check for extraneous solution by putting the value of x = 9 in the original equation, we get

✓9 = ✓(9 - 8) + 2

✓9 = ✓1 + 2

3 = 1 + 2

3 = 3

⇒ LHS = RHS

∴ x = 9 is not an extraneous solution of the equation.

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Answer:

67 degrees

Step-by-step explanation:

Answer: 67

Step-by-step explanation: there all parallel to one another right and y and z are right beside each other therefore the same distance from M

Answer:

Hello,

x=5

Step-by-step explanation:

\(Since\ \overrightarrow{AD}=\overrightarrow{BC}, ABCD\ is\ a\ parallelogramm\\\\12x+60=150-6x\\\\18x=90\\\\x=\frac{90}{18} \\\\\boxed{x=5}\\\)

Given that sample standard deviation is zero. This indicates that the variance of sample is also zero as square of sample standard deviation is sample Variance. Variance is average of the squared deviations from mean. As shown in below formula

Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In the case the variance and standard deviation will be zero.

Variance = Summation n to i = 1 \(\frac{(X_{1-X} )^2}{n-1}\)

        0 = Summation n to i = 1\(\frac{(X_{1-X} )^2}{n-1}\)

                Summation n to i \({(X_{1-X} )^2\) = 0

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Answer:

It was correct for plato!

Step-by-step explanation:

Answer: I have put picture in there

Step-by-step explanation:

The measure of angle m∠TUV is determined as  46⁰.

The measure of angle TUV is calculated by applying the following formula as shown below;

difference between exterior and interior arc SW and TV = 2 ( m∠TUV)

"the angle formed by the interception of two tangents outside a circle is half the positive difference of the measure of the intercepted arcs".

So we will have the following equation and determine the value of angle TUV.

145 - 53 = 2(∠TUV)

92 = 2(∠TUV)

∠TUV = 92/2

∠TUV = 46⁰

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Answer:

17.2 feet

Step-by-step explanation:

The length of the ladder is 20.4 feet.

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Given that, the angle of elevation of the ladder is 73° when the bottom of the ladder is 15 feet from the side of the house.

Let the height of side of a house be x.

Now, tan73°=x/15

x/15=0.9192

x=0.9192×15

x=13.8 feet

Let the length of the ladder be y.

y²=15²+13.8²

y²=415.44

y=√415.44

y=20.4 feet

Therefore, the length of the ladder is 20.4 feet.

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Answer: 8.33

Step-by-step explanation:

Answer:

c=8.33

Step-by-step explanation:

Hope this helps

Plz Branliesst Answer\

The absolute minimum value is -18 at the point (7, 0), and the absolute maximum value is 35 at the point (7, 9) within the given triangular region

To find the absolute minimum and absolute maximum of the function f(x, y) = 10 - 4x + 7y on the closed triangular region with vertices (0, 0), (7, 0), and (7, 9), we need to evaluate the function at the critical points inside the region and at the boundary points.

Critical points:

To find the critical points, we need to find the points where the gradient of f(x, y) is equal to zero.

∇f(x, y) = (-4, 7)

Setting -4 = 0 and 7 = 0, we see that there are no critical points in the interior of the triangular region.

Boundary points:

We need to evaluate the function f(x, y) at the vertices of the triangular region.

(a) f(0, 0) = 10 - 4(0) + 7(0) = 10

(b) f(7, 0) = 10 - 4(7) + 7(0) = -18

(c) f(7, 9) = 10 - 4(7) + 7(9) = 35

Therefore, the absolute minimum value is -18 at the point (7, 0), and the absolute maximum value is 35 at the point (7, 9) within the given triangular region.

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Answer:

d which implies m/3 + 5 = 9