Answer:
14 dogs
Step-by-step explanation:
Use the formula
_+a-5+ c+3=31
And now if you add 14 it will work perfectly
Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11
The expansion of (3x-4y)¹¹ using Pascal's Triangle is:
177147x¹¹ - 2598156x¹⁰y - 17321040x⁹y² - 69284160x⁸y³ - 184757760x⁷y⁴ - 344881152x⁶y⁵ - 458941536x⁵y⁶ - 437944320 x⁴y⁷ - 291962880x³y⁸ - 129761280x²y⁹ + 34603008xy¹⁰ - 4194304y¹¹.
What is Pascal's Triangle?The triangle-shaped array of integers known as Pascal's triangle has one at the top and one on each of its two sides. Every new number has a value equal to the sum of the two numbers above it and is located between two other numbers and underneath them. Pascal's triangle is a triangular array of binomial coefficients that appears in algebra, combinatorics, and probability theory.In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)ⁿ. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.So, the expression is:
(3x-4y)¹¹Now, use Pascal's Triangle to expand as follows:
(Refer table attached below for expansion)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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If f(x) is an exponential function where f(3) = 11 and f(5.5) =57, then find the value of f(10.4), to the nearest hundredth
Solving a system of equations we can find the exponential function, then we can evaluate it to get:
f(10.4)= 1,427.2
How to find the value of f(10.4)?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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Determine whether descriptive or inferential statistics were used in the statement. in 2008, the average credit card debt for college students was $3173. (source: newser)
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.
What is descriptive statistics?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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Solve the equation without using a calculator
\(\displaystyle\\3^\frac{x+2}{3x-4}-2\cdot3^\frac{5x-10}{3x-4}=7\)
Answer:
x = 2=========================
Rewrite(5x - 10)/(3x - 4) = (6x - 8 - x - 2)/(3x - 4) = 2 - (x + 2)/(3x - 4)Substitute\(3^{(x + 2)/(3x - 4)} = t\)New equationt - 2·9/t = 7t - 18/t = 7t² - 7t - 18 = 0t² - 9t + 2t - 18 = 0t(t - 9) + 2(t - 9) = 0(t - 9)(t + 2) = 0t - 9 = 0 and t + 2 = 0t = 9 and t = - 2 (excluded as the power of 3 can't be negative)Substitute back\(3^{(x + 2)/(3x - 4)} = 9\)\(3^{(x + 2)/(3x - 4)} = 3^2\)\((x + 2)/(3x - 4) = 2\)\(x + 2 = 6x - 8\)\(6x - x = 2 + 8\)\(5x = 10\)\(x = 2\)
A bag contains pennies and nickels. You are given the number of pennies in the bag
and the ratio of pennies to nickels. Find the number of nickels in the bag.
18 pennies: 6 to 1
You are baking chocolate chip cookies. The recipe asks for 3 3/4 cups of flour and you want to make 2 times the original recipe.
A. 1 1/2 cups
B. 30/4 cups
C. 7 2/4 cups
D. 7 1/2 cups
Quincy and Julie are in charge of making a banner for the basketball game this friday. how much paper will they need for a parallelogram-shaped banner with a height of 3.5 feet and a base of 5.25 feet?
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
you sailed 0.032 units to the left and found treasure at 0.248 units find where the ship started
Please help me thank you
Step-by-step explanation:
X= 2, y= -6
X= 0, y= 0
X= -2, y= 6
X= -4, y= 12
X= - 7, y= 21
Please help answer I’m having trouble
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)
Graph the line that passes through the points (0, -5) and (5, 1) and
determine the equation of the line.
y
10
9
00
7
6
5
4
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)
help?
what fraction of a dollar is 236 cents?
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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Urgent I’m so confused thank you all
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
Addition(same sign)
add the number and copy the sign(unlike sign)
subtract the number and copy the sign of the larger numberSubtraction Change the sign of the subtrahend and proceed to additionMultiplication(same sign)
multiply the number and the sign is +(positive)(unlike sign)
multiply the number and the sign is -(negative)Hope that helps ( ╹▽╹ )
1) If there are 12 eggs in a dozen, which expression represents how many eggs are in x dozens? 12x O x= 12 O x-12 O 12.x 12 + x 12 + x - X
The expression that represents how many eggs are in x dozens is 12x.
How to find the expressionThe 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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Roll one-8 sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by .
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:
C (n , k) represents the number of combinations of "n" things taken "k" at a time, and p is the probability of success in a single trial.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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What is 52.35 − 1.58 =
Answer: 52.35 − 1.58 = 50.77
Step-by-step explanation:
an innovative math project goal was to introduce innovative approaches to teaching mathematics and engage students in group investigations and mathematical modeling. after a field test in 36 high schools over a three-year period researchers compared the performance of students in this new curriculum with those in a traditional curriculum. scores for 320 students in this new curriculum were compared to scores in a control group (traditional program) of 273 students. a 95% confidence interval for the mean difference in scores was calculated to be [5.573, 11.427]. A. State the null and alternative hypothesis that the researchers most likely used to compare the performance between these two types of curriculums.
B. What is the margin of error of this confidence interval?
C. If a 98% confidence interval would have been created, would the margin of error be larger or smaller.
D. Based on the confidence interval can the researchers conclude that there is a difference between the means in performance scores for the two types of math curriculum? Explain how you reached this conclusion.
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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At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .51. Find the probability that in a sample of 10 customers, fewer than 8 will order a nonalcoholic beverage.
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
Point: (2,7)
Reflected across y-axis: (-2,7)
Reflected across x-axis: ????
My options for the answer is
(-7,-2)
(-2,7)
(2,-7) which answer is it I have already tried the first one and it said it was wrong.
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.
Find the slope of the line 11x - 4y = 21.
Answer: 11/4
Step-by-step explanation: no need :”)
Please help asap! The question is below!
Based on the information, the hedgehogs have made the better offer
How to know who made the better offerThe 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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What is the solution for this inequality?
8x<-32
Answer:
8x<-32
x<4
Step-by-step explanation:
divide both of these numbers by 8
Step-by-step explanation:
rhrufh38299917489xjqgs8cjrnjci
Name two segments that share an endpoint with JM
Answer:
b
Step-by-step explanation:
(q1) Find the length of the curve described by the function
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 student was asked to give the exact solution to the equation
22x+4-9(2) = 0
The student's attempt is shown below:
22x+49(2)=0
22x+24-9(2) = 0
Let 2* = y
y²-9y+8=0
(y-8)(y-1)=0
y = 8 or y=1
So x = 3 or x = 0
(a) Identify the two errors made by the student.
(b) Find the exact solution to the equation.
(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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solve simultaneously 2x - y = - 10 and 3x + 2y = - 1
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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Solve the equation and enter the value of x below
-9x-3 = 60
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
Using the digits 5, 6, 7, 8, 9 and repetition is allowed how many options are there to
Create a 4 digit even number?
[2]
Create a 4 digit odd number?
Answer:
250 options to create an even number
375 options to create an odd number
What’s the value for x? Enter your answer as a decimal to the nearest tenth in the box
Answer:
23.6
Step-by-step explanation:
I hope it's correct
I need help with these problems
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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