The sum of two numbers is 26. One number is
9 more than the other one. Find the numbers.

Answer:

y = x + 1

Step-by-step explanation:

(3, 4); m = 1

Slope-intercept:

y - y1 = m(x - x1)

y - 4 = 1(x - 3)

y - 4 = x - 3

y = x - 3 + 4

y = x + 1

The cup will hold more ice cream than cone since volume of cup is 169.6 cubic inches which is greater than volume of 25.1 cubic inches.

The volume of a cone is given by the formula:

V= 1/3.π\(r^{2}\)h

where r is the radius of the circular base and h is the height.

The volume of a cylinder is given by the formula:

V= π\(r^{2}\)h

where r is the radius of the circular base and h is the height.

Assuming that the height of both the cone and the cup is the same, we can compare their volumes by comparing their radii.

For the cone, the radius r is equal to half the diameter of the circular base, which is equal to w/2 = 2 in.

The height of the cone is equal to y, which is 6 in.

V= 1/3.π\(r^{2}\)h= 1/3.π\(2^{2}\)6

For the cup, the radius r is equal to x/2 = 3

The height of the cup is equal to y, which is also 6 in.

Using these values, we can calculate the volume of the cup as:

\(V_cup\)= π\(r^{2}\)h=π\(3^{2}\)6

Therefore, the cup will hold more ice cream than the cone.

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Answer:

oi 5. 16

Step-by-step explanation:

Answer:

5. 6a^2 + 10a

6. 21h^2 - 9h

Step-by-step explanation:

(2a*3a) + (2a*5) = 6a^2 + 10a

(-3h)*(-7h) + (-3h)*3 = 21h^2 - 9h

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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Answer:

\((x-7)(x-7)\)

Step-by-step explanation:

We begin with the given quadratic expression:

\(49-14x+x^2\)

Just for my own ease, I will rewrite this in descending order of powers

\(x^2-14x+49\)

In order to factor this expression, we need to look for two numbers that meet the following criteria.

When they are added together, you get \(-14\)

When they are multiplied together, you get \(49\)

A simple way to find our answer is to begin with the product of multiplication and list each of the numbers that can be multiplied together to get us our given result

To get 49, we could multiply

1 and 49

-1 and -49

7 and 7

-7 and -7

Now, we can just add both of these terms together to see while one gives us our desired result

\(1+49=50\\-1-49=-50\\7+7=14\\-7-7=-14\)

As you can see, -7 and -7 were the two values that gave us -14.

This means that they are the terms within our factor.

Therefore, our factored form would be \((x-7)(x-7)\)

Answer:

(7 - x) (7 - x)

Step-by-step explanation:

First, I'm multiplying 49 by the co-efficient of x(1) to get 49. Then I'm going to see what factors of 49 add up to -14. Those are -7 and -7.

Next, I'm going to rewrite this polynomial:

49 - 7x - 7x + x^2

Then, I group them into two groups:

49 - 7x

&

-7x + x^2

Then, I factor them out:

49 - 7x = 7 (7 - x)

-7x + x^2 = -x (7 - x)

After that, I take the outer coefficients and put them in parenthesis:

7 (7 - x)

&

-x (7 - x)

= (7 - x)

Finally, I put both of our grouped parenthesis together:

(7 - x) (7 - x)

In the Stackelberg case, Firm 1 has a higher profit (562.5 > 277.78) and Firm 2 has a lower profit (156.25 < 277.78) than in the simultaneous-move case.

1. In the Stackelberg case, let Firm 1 choose output y1 first, and then Firm 2 decides y2 after observing y1. Firm 1 is the leader and Firm 2 is the follower. Thus, the optimization problem for Firm 2 is as follows:

Max p(y1 + y2) * y2 - c2(y2), where y1 is chosen by Firm 1.

Thus, the profit function of Firm 2 is Π2(y1, y2) = (100 − 2(y1 + y2))y2 − 4y2

                                                                              = (100 − 2y1 − 2y2)y2

Differentiating with respect to y2, we obtain:

∂Π2(y1, y2) / ∂y2 = 100 − 2y1 − 4y2

Setting this equal to zero, we obtain:

50 − y1 = 2y2

Thus, Firm 2's best response function is: yˆ2(y1) = (50 − y1)/2

Now, Firm 1 knows that Firm 2 will choose yˆ2 given that it already chose y1.

Firm 1 chooses y1 to maximize its own profit, which is:

Π1(y1) = (100 − 2(y1 + yˆ2(y1)))y1 − 2y1

= (100 − 2y1 − 25 + 0.5y1)y1

= (75 − 1.5y1)y1

Differentiating with respect to y1, we obtain:

∂Π1(y1) / ∂y1 = 75 − 3y1

Setting this equal to zero, we obtain:

y1 = 25

Thus, yˆ1 = 25, and yˆ2 = (50 − y1)/2 = 12.5.

The profit of Firm 1 is Π1(y1) = (75 − 1.5y1)y1 = 562.5, and the profit of Firm 2 is

= Π2(y1, y2)

= (100 − 2y1 − 2y2)y2

= 156.25.2.

In the simultaneous-move case, the optimization problem for Firm 1 is as follows:

Max p(y1 + y2) * y1 - c1(y1) - c2(y2)

Similarly, the optimization problem for Firm 2 is: Max p(y1 + y2) * y2 - c1(y1) - c2(y2)

These two problems can be combined into a single problem by substituting

p(y1 + y2) = 100 − 2(y1 + y2) and

c1(y1) = 2y1 and c2(y2) = 4y2.

Thus, the profit function of each firm is:

Π1(y1, y2) = (50 − y1 − y2)y1Π2(y1, y2) = (50 − y1 − y2)y2

The first-order conditions for maximizing these profit functions are:

= ∂Π1(y1, y2) / ∂y1

= 50 − 2y1 − y2

= 0

∂Π2(y1, y2) / ∂y2 = 50 − y1 − 2y2 = 0

Solving these equations simultaneously, we obtain:

y1 = 16.67, y2 = 16.67, and Π1(y1, y2) = Π2(y1, y2) = 277.78.

Comparing this to the Stackelberg case, we see that both firms are worse off in the simultaneous-move case. In the Stackelberg case, Firm 1 has a higher profit (562.5 > 277.78), and Firm 2 has a lower profit (156.25 < 277.78) than in the simultaneous-move case. Thus, Firm 1 is better off in the Stackelberg case, and Firm 2 is worse off.

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Answer:

f(x)=x²-4x+2

f(-1)= (-1)²-4(-1)+2

= 1+4+2

=7

The time taken to reach the bottom when the person skies down will be 22.5 seconds.

It should be noted that the person is skiing down a 1,350 meter ski slope at 60 meters per second.

There, t represent your skiing time in seconds.

The appropriate expression to illustrate the scenario will be:

1350 - 60t = 0

Therefore, 60t = 1350

t = 1350/60

t = 22.5

The time taken to each the bottom will be 22.5 seconds.

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The extraneous roots occur when x-1=0, resulting in x=1, but this leads to a division by zero, making it extraneous. Hence, no valid solutions exist.The extraneous roots of the equation x/x-1-2x=1/x-1 are the values of x that make the denominators equal to zero.


1. To find the extraneous roots, set the denominators x-1 and x-1 equal to zero.
2. Solving x-1=0, we find x=1 as a potential extraneous root.
3. However, substituting x=1 back into the original equation shows that it leads to a division by zero, making it extraneous.
4. Therefore, there are no valid solutions for this equation.

The extraneous roots occur when x-1=0, resulting in x=1, but this leads to a division by zero, making it extraneous. Hence, no valid solutions exist.

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Answer:

£46.20

Step-by-step explanation:

9514 1404 393

Answer:

  \(f^{-1}(x)=\dfrac{\sqrt[3]{3x+12}}{3}\)

Step-by-step explanation:

For function ...

  \(y=f(x)\)

sometimes we know y, but we want to find the corresponding value x. That is, we would like to have an inverse function:

  \(x=f^{-1}(y)\)

Here, I have said the input to the inverse function is the value of y for which we want the corresponding value of x.

__

Normally, we write the inverse function basically the same way we write the function. The input is named x, and the output is named y. We can swap the variable names for input and output either before or after we find the equation that relates them.

Perhaps you can see that finding the inverse function

  \(x=f^{-1}(y)\)

amounts to solving the function relation y = f(x) for x. If we interchange variables first, it is the same as solving x = f(y) for y.

__

To find the inverse, we can interchange the variables and solve for y.

  \(x=f(y)=9y^3-4\\\\x+4=9y^3\qquad\text{add 4}\\\\\dfrac{x+4}{9}=y^3\qquad\text{divide by 9}\\\\\dfrac{3x+12}{27}=y^3\qquad\text{make the denominator a cube; multiply by 3}\\\\y=\dfrac{\sqrt[3]{3x+12}}{3}\qquad\text{take the cube root}\\\\\boxed{f^{-1}(x)=\dfrac{\sqrt[3]{3x+12}}{3}}\)

_____

The graph of the inverse of a function is the reflection of the graph of the function across the line y=x. The given function and the inverse we found are graphed in the attachment. The dashed line is y=x.

Answer:

55

Step-by-step explanation:

Hope it helps! :D

the probability of at least two person have same birthday would be: 100%-99.72%= 0.28%

In this question, you are asked the probability for any of the 2 person to have the same birthday. To answer this it will be easier to calculate how much the probability for no one has same birthday. Let say the first person birthday is 1. Then the next person birthday should be other than 1, which mean 364 possible days out of 365 days.

Then the calculation for 2 people would be:  

(365!/365-2!)/(365^(2)= (365!/363!)/ 365^2=  0.9972=99.72%

Then the probability of at least two person have same birthday would be: 100%-99.72%= 0.28%

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13) The electron configuration [Kr]5s²4d¹5p³ corresponds to the element iodine (I).

14) The electron configuration [Xe]6s²4f¹⁴5d¹⁰6p⁶ corresponds to the element lead (Pb).

15) The electron configuration [Rn]7s²5f¹⁴ corresponds to the element lawrencium (Lr).

16) The electron configuration 1s²2s²2p¹3s²3p⁵4s²4d¹⁰4p⁹ is valid.

17) The electron configuration 1s²2s²2p¹3s²3d³ is not valid as it violates the Aufbau principle.

18) The electron configuration [Ra]7s²5f is not valid as it is incomplete.

19) The electron configuration [Kr]5s²4d¹⁰5p³ is valid.

20) The electron configuration [X] is not a valid electron configuration as it does not specify the specific subshells and electrons present.

13) The electron configuration [Kr]5s²4d¹5p³ corresponds to iodine (I) because it has 53 electrons. The [Kr] represents the electron configuration of the noble gas krypton, and the subsequent orbitals represent the additional electrons in the iodine atom.

14) The electron configuration [Xe]6s²4f¹⁴5d¹⁰6p⁶ corresponds to lead (Pb) because it has 82 electrons. The [Xe] represents the electron configuration of the noble gas xenon, and the subsequent orbitals represent the additional electrons in the lead atom.

15) The electron configuration [Rn]7s²5f¹⁴ corresponds to lawrencium (Lr) because it has 103 electrons. The [Rn] represents the electron configuration of the noble gas radon, and the subsequent orbitals represent the additional electrons in the lawrencium atom.

16) The electron configuration 1s²2s²2p¹3s²3p⁵4s²4d¹⁰4p⁹ is a valid electron configuration because it follows the Aufbau principle, filling the orbitals in increasing order of energy.

17) The electron configuration 1s²2s²2p¹3s²3d³ is not valid because it violates the Aufbau principle. According to the Aufbau principle, electrons should fill the orbitals in increasing order of energy.

18) The electron configuration [Ra]7s²5f is not valid because it is incomplete. It should specify the specific subshells and electrons present in the atom.

19) The electron configuration [Kr]5s²4d¹⁰5p³ is a valid electron configuration for an element, following the Aufbau principle.

20) [X] is not a valid electron configuration as it does not specify the specific subshells and electrons present. It is incomplete and does not provide information about any element.

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Answer:

I dont no the answer

Step-by-step explanation:

but maybe try the app socratic

Answer:

A turtle travels about 90 feet

Because if a turtle can travel 450 feet within 25 minutes, then dividing 25 by 450 is 18 feet per minute, but if you multiply 5 minute x 18 feet, you get 90 feet in all.

So, a turtle can travel 450 feet per 25 minutes,

18 feet per minute, and

90 feet per 5 minutes

Hope this helps and I hope it is right, I used my skill thinking to solve this. So, please let me know if it did help and you do get it.

SRRC is a pulse shaping filter used in digital communications to minimize intersymbol interference and improve the signal-to-noise ratio.

The square root raised cosine (SRRC) is a famous heartbeat molding channel utilized in computerized correspondences, especially in applications like advanced tweak and demodulation. It is intended to limit intersymbol obstruction (ISI) by restricting the data transmission of the sent sign while keeping a consistent envelope.

The SRRC channel is described by a reaction that is like the raised cosine channel, yet with a square root capability applied to the recurrence reaction. This outcomes in a smoother change between the passband and stopband, which assists with decreasing ISI and work on the sign to-clamor proportion.

The SRRC channel is usually utilized in correspondence frameworks that utilization quadrature sufficiency regulation (QAM) or stage shift keying (PSK) tweak plans, as it gives great ghastly control and heartbeat molding properties that are appropriate to these kinds of signs.

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Answer:

x = 9

Step-by-step explanation:

6x + 4x = 90   They are complementary angles, meaning they add up to 90

10x = 90

x = 90/10 = 9

x = 9

Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

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Let's break down the expression for Tony's combined total earnings step by step.

First, we consider Tony's earnings as a tutor. He earns $11 per hour as a tutor, so the amount he earns from tutoring is given by the product of his hourly rate ($11) and the number of hours he worked as a tutor (t). This can be represented as $11t.

Next, we consider Tony's earnings as a waiter. He earns $13 per hour as a waiter, so the amount he earns from waiting tables is given by the product of his hourly rate ($13) and the number of hours he worked as a waiter. Since Tony worked a total of 106 hours this month and spent t hours as a tutor, he must have worked (106 - t) hours as a waiter. This can be represented as $13(106 - t).

To calculate Tony's combined total earnings for the month, we add the amount he earned as a tutor ($11t) to the amount he earned as a waiter ($13(106 - t)). This yields the expression:

Earnings = $11t + $13(106 - t)

This expression represents the total dollar amount Tony earned this month, considering the number of hours he worked as a tutor (t) and waiter (106 - t).

Answer:

1/2 1/4 1/8 1/10

Step-by-step explanation:

Answer:

D. The relationship is linear; y + 9= -4/5(x + 2).

Step-by-step explanation:

yes its linear because the x values increase by a constant value 4 and the y values by a constant value -5.

one general form for a linear equation is

y - y1 = m(x - x1)      m = slope and (x1,y1) is a point on the line

from the data the slope iis  (-7-(-2)) /  (-5-(-9)  =  -5 / 4

so using the point (3, -17):-

y - (-17) = (-5/4) ( x - 3)

y + 17 = -5x/4 + 15/4

4y + 68 = -5x + 15

4y = -5x - 53  

thats the equation of the line

Answer:

any number equal to or less than -4

Step-by-step explanation:

x - 1 < -4

< represents that -4 is a larger number than x - 1. we know that -4 is a negative number, so anything below -4 would be less. x = -4 would be a good solution, but the reality is that any number equal to or less than -4 is the correct answer. I hope this helps!

Answer:

(a)V=36πh

Explanation:

• Radius = 6 meters

Part A

An equation that represents the volume V as a function of the height h is:

Part B

Using 3.14 as an approximation for π

The graph of the function is attached below: (V is on the y-axis and h is on the x-axis).

Part C

The initial equation for volume is:

When h=1

If you double the height of a cylinder, h=2:

We observe that when the height is doubled, the volume of the cylinder is also doubled.

Part D

The initial equation for volume is:

If the height of the cylinder is multiplied by 1/3, we have:

The volume of the cylinder will be divided by 3.

Using the graph, we observe a horizontal stretch of the graph by 1/3.

9514 1404 393

Answer:

  15

Step-by-step explanation:

We are given that the relation f can be represented by the ordered pair ...

  (15, -3)

and we are told that g is the inverse relation. That means the ordered pair ...

  (-3, 15)

is part of g. In short, g(-3) = 15.

Answer:

A

Step-by-step explanation:

After 1.8 years, the value equals the amount she paid for the car.

The value will be $ 22,131.10.

To solve the problem, find both the expense equation and depreciation equation.

The exponential depreciation equation will be:

\(y=25,900(1-0.082)^x\)

Where x represents time in years.

The expense equation will be: y=550 x+10,000

Where x represents the number of months that have passed

If x represents time in years in the expense equation, then it determines the yearly payment rather than the monthly payment.

Over the course of the year, Nina will have paid 550(12) or $ 6,600 in car payments.

The new yearly expense equation will be: y=6,600 x+10,000

Where x is time in years.

Use the two equations to find the point of intersection which will give the time she paid for the car and the value paid by her.

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