Craig hired 3 high school students to work for his dog walking business. This week, they walked a total of 31 dogs.
Allyson walked 5 less dogs than Brooke.
Carlos walked 3 more dogs than Brooke.
How many dogs did Carlos walk this week?

The expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

So, the expression is:

Now, use Pascal's Triangle to expand as follows:

Therefore, the expansion of (3x-4y)¹¹ using Pascal's Triangle is:

177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ -  344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.

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Solving a system of equations we can find the exponential function, then we can evaluate it to get:

f(10.4)= 1,427.2

We know that f(x) is a exponential function, then we can write it as:

f(x) = A*b^x

First, we know that:

f(3) = 11

f(5.5) = 57

Then we can write a system of equations:

11 = A*b^3

57 = A*b^5.5

Taking the quotient between the two equations we will get:

57/11 = (A*b^5.5)/(A*b^3)

5.18 = b^(5.5 - 3)

5.18 = b^2.5

Solving for b we will get:

(5.18)^(1/2.5) = b

1.93 = b

with that, we can get the value of b.

11 = A*(1.93)^3

A = 11/(1.93)^3

A = 1.53

So the function is:

f(x)= 1.53*(1.93)^x

Then:

f(10.4) = 1.53*(1.93)^10.4 = 1,427.2

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The collection, description, analysis, and drawing of conclusions from quantitative data are all included in the area of statistics, which is a branch of applied mathematics. Probability theory, linear algebra, and calculus of differential and integrals are some of the core mathematical concepts in statistics.

Descriptive statistics were used in the statement.

Descriptive statistics is a branch of statistics that deals with the collection, presentation, and summary of data. It is used to describe and summarize the main features of a data set, such as measures of central tendency (e.g., mean, median, mode) and measures of dispersion (e.g., range, variance, standard deviation).

In this case, the statement is simply reporting a single value, the average credit card debt for college students in 2008. This is an example of a descriptive statistic because it is a summary measure that describes a characteristic of the population or sample under study.

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Descriptive statistics were used in the statement.

Descriptive statistics is a branch οf statistics that deals with the analysis, descriptiοn, and summarizatiοn οf data. It invοlves the use οf variοus statistical measures, such as measures οf central tendency (mean, median, and mοde), measures οf dispersiοn (standard deviatiοn, variance, range), and graphical representatiοns (histοgrams, bοx plοts, scatter plοts, etc.) tο describe the features οf a dataset.

Descriptive statistics were used in the statement. The statement is simply describing the average credit card debt fοr cοllege students in 2008. Descriptive statistics are used tο describe οr summarize a dataset οr pοpulatiοn, while inferential statistics are used tο draw cοnclusiοns οr make predictiοns abοut a larger pοpulatiοn based οn a sample οf data. Since the statement οnly prοvides infοrmatiοn abοut a specific grοup οf cοllege students in 2008, it dοes nοt invοlve making any inferences οr predictiοns beyοnd this grοup.

Hence, Descriptive statistics were used in the statement.

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Answer:

=========================

Answer:

18.375 ft²

Step-by-step explanation:

Given that,

Quincy and Julie want to make a banner of size 3 1/2 feet by 5 1/4 feet for the game this week.

To find, poster paper needed to make a banner

Formula to be used is the surface area of a parallelogram

                                                (base * height)

                                                =  (21/4) * (7/2)

                                                =  18.375 ft²

So poster paper required to make a banner for the game this Friday = 18.375 ft²

Step-by-step explanation:

X= 2, y= -6

X= 0, y= 0

X= -2, y= 6

X= -4, y= 12

X= - 7, y= 21

Answer:

(1, 0.5)

Step-by-step explanation:

i just used order of operations calculator

Solving the equation with elimination method, I got x=1, y= 1/2

Pair (1.00, 0.50)

Answer:

y = 10/1x - 5

Step-by-step explanation:

y=mx+b

m=slope  b=y-intercept

therefore

y=10/1x -5

(10/1 is a fractions just too lazy to make it a fraction on here)

236/100, 59/25, or 2 9/25

Step-by-step explanation:

There are 100 cents in a dollar, so 236/100 is your starting fraction. The simplest improper fraction would be 59/25. But if you're looking for a mixed number, you get 2 9/25.

236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.

To solve this problem,

We need to convert 236 cents into dollars.

Since there are 100 cents in one dollar,

we can divide 236 by 100 to get the equivalent dollar value.

⇒ 236 cents ÷ 100 cents per dollar = 2.36 dollars

Now that we know that 236 cents is equivalent to 2.36 dollars,

we can express it as a fraction of a dollar.

To do this, we'll use the fact that one dollar is equivalent to 100 cents, which means that one dollar can be expressed as the fraction 100/100.

To find the fraction of a dollar that 2.36 dollars represents,

we'll divide 2.36 by 1.

⇒ 2.36 ÷ 1 = 2.36/1

To express this as a fraction of a dollar,

Multiply both the numerator and denominator by 100 to get,

⇒ (2.36 x 100) / (1 x 100) = 236/100

Simplifying this fraction, we get,

⇒ 236/100 = 118/50

Therefore,

236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.

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Answer:

12v⁴ + 11v⁷

Step-by-step explanation:

1. Combine like terms

(-3v⁴ + 2v⁷) + (9v⁷ + 15v⁴)

=

-3v⁴ + 2v⁷ + 9v⁷ + 15v⁴

2. Group the like terms

(-3v⁴ + 15v⁴) + (2v⁷ + 9v⁷)

=

12v⁴ + 11v⁷

Final answer:

12v⁴ + 11v⁷

\({\boxed{\boxed{\sf{\red\ANSWER:}}}}

\)

\(7u {}^{7} + 18u {}^{4} \)

arrange it to standard form

if there is a same degree copy it

must understand this

(same sign)

(unlike sign)

(same sign)

(unlike sign)

Hope that helps (⁠ ⁠╹⁠▽⁠╹⁠ ⁠)

The expression that represents how many eggs are in x dozens is 12x.

The expression that represents how many eggs are in x dozens is 12x.

breaking it down further

There are 12 eggs in a dozen.

If you have x dozens, you want to find out how many eggs there are in x times that amount.

So, the number of eggs in x dozens is represented by 12x. Multiplying the number of dozens (x) by the number of eggs in one dozen (12) gives you the total number of eggs.

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The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = \(C(n , k) * p^k * (1 - p)^{(n - k)}\)

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = \(C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}\)

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

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Answer: 52.35 − 1.58 = 50.77

Step-by-step explanation:

The 95% confidence interval for the mean difference of scores [5.573,11.427].

A) Null and Alternative hypothesis are

H₀ : μ₁ - μ₂ =0

Hₐ : μ₁ - μ₂ ≠ 0

B) Margin of Error of 95% confidence interval is 2.927

C) Margin of error increase with increasing the confidence interval. So, the margin of error large at 98% confidence interval.

D) Because zero is not included in the confidence interval, and all values in the confidence interval [5.573, 11.427] are positive.

A sample of scores for 320 students in this new curriculum were compared to scores in a control group (traditional program) of 273 students.

(A) Null and Alternative hypothesis are

H₀ : μ₁ - μ₂ =0 ( There is no difference between the means in performance scores for the two types of math curriculum )

Hₐ : μ₁ - μ₂ ≠ 0 ( There is a difference between the means in performance scores for the two types of math curriculum ) (Claim)

(B)We have given data that ,

Confidence Interval : [5.573, 11.427]

Sample mean (X-bar) is given by:

X-bar =( 5.573 + 11.427)/2 =17/2 = 8.5

Using margin of error formula,

MOE = mean - lower bound of confidence interval

Margin of Error = 8.5 - 5.573= 2.927

=> Margin of Error = 2.927

(C)If a 98% confidence interval would have been created, the margin of error would be larger because the margin of error increases as the confidence level increases from 95% to 98%

(D)Based on the confidence interval the researchers can conclude that there is a difference between the means in performance scores for the two types of math curriculum because 0 is not included in the confidence interval, [5.573, 11.427] and all values in the confidence interval [5.573, 11.427] are positive.

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Answer:

1-0.7584=0.2416

Step-by-step explanation:

The probability nobody will order a non-A beverage is .56^8=0.0097

all 8 will order a non-A beverage is 0.44^8=0.0014

fewer than 6:

look at 6,7,8

Those add to 0.0794 and the answer is 1- that or 0.9206. Also 2nd VARS (.44,8,5)

b. at least 5 is 5,6,7,8

that is 1-P(0-4)

=1-0.7584=0.2416

Answer:

(2,-7)

Step-by-step explanation:

Reflection rule for across the x-axis: \((x,y)\rightarrow (x,-y)\)

Using the rule and point (2,7):

\((2,7)\rightarrow(2,-7)\)

(2,-7) should be the correct answer.

Brainilest Appreciated.

Answer: 11/4

Step-by-step explanation: no need :”)

Based on the information, the hedgehogs have made the better offer

The Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:

PV = S(t) * e^(-rt)

The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:

PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt

= 736,918.63

Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:

PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt

= 753,472.49

Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.

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Answer:

8x<-32

x<4

Step-by-step explanation:

divide both of these numbers by 8

Step-by-step explanation:

rhrufh38299917489xjqgs8cjrnjci

Answer:

b

Step-by-step explanation:

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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Answer:

-7

Step-by-step explanation:

-9x-3=60

add 3 to each side to cancel -3

-9x-3+3=60+3

simplify

-9x=63

divide by -9 to cancel the -9

-9x/-9=63/-9

simplify

x=-7

Answer:

250 options to create an even number

375 options to create an odd number

Answer:

23.6

Step-by-step explanation:

I hope it's correct

Measure of ∠C = 77°

And,  Sides of triangles are;

a = 0.95

b = 0.566

c = 0.99

What is Sine rule of triangle?

By the definition of sine rule,

sin A / a = sin B / b = sin C / c

Where, a, b, c are sides of a triangle.

Given that;

Measure of ∠A = 27°

Measure of ∠B = 76°

Since, Sum of all angles of triangle = 180°

Hence,

∠A +  ∠B +  ∠C = 180°

27° + 76° + ∠C = 180°

∠C = 180° - 103°

∠C = 77°

So, Measure of ∠C = 77°

Since, By the definition of sine rule,

sin A / a = sin B / b = sin C / c

Since, sin A = sin 27° = 0.95

sin B = sin 76° = 0.566

sin C = sin 77° = 0.99

Hence,

0.95 / a = 0.566 / b = 0.99 / c = 1 / k

Taking terms as;

0.95 / a = 1 / k

a = 0.95 k

And, 0.566 / b = 1 / k

b = 0.566 k

And, 0.99 / c = 1 / k

c = 0.99 k

Hence, Sides of triangles are;

a : b : c = 0.95 k : 0.566 k : 0.99 k

a : b : c = 0.95 : 0.566 : 0.99

Thus, Measure of ∠C = 77°

And,  Sides of triangles are;

a = 0.95

b = 0.566

c = 0.99

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