Answer:
Step-by-step explanation:The fraction is equal to one because numerator and denominator are the same
Answer:
43 + / + 43 is equal to 1
Step-by-step explanation:
Hope this helps!
Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1
The area bounded by region between the curve [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] is
[tex]0[/tex] square units.
To find the Area,
Integrate the difference between the two curves over the interval of intersection.
Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .
The point of Intersection is the common point between the two curve.
Value of [tex]x[/tex] and [tex]y[/tex] coordinate will be equal for both curve at point of intersection
In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].
[tex]1 = x^2-24[/tex]
Rearrange, like and unlike terms:
[tex]25 = x^2[/tex]
[tex]x =[/tex] ±5
The point of intersection for two curves are:
[tex]x = +5[/tex] and [tex]x = -5[/tex]
Integrate the difference between the two curve over the interval [-5,5] to calculate the area.
Area = [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]
Simplify,
[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]
Integrate,
[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]
Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.
[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]
= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]
[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]
[tex]= 0[/tex]
The Area between the two curves is [tex]0[/tex] square units.
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help with this I don't know how to solve please and thanks
Answer:
6.5 ft
Step-by-step explanation:
When we draw out our picture of our triangle and label our givens, we should see that we need to use cos∅:
cos57° = x/12
12cos57° = x
x = 6.53567 ft
HELP I KEEP GETTING WRONG ANSWERS!!!!!
Answer:
B) 65
Step-by-step explanation:
Plug in the corresponding numbers to the corresponding variables:
w = -4 ; v = 5 ; u = 2
4w² - v + 3u
4(-4²) - (5) + 3(2)
Remember to follow PEMDAS.
PEMDAS =
Parenthesis
Exponents
Multiplications
Division
Addition
Subtraction
& is the order of operation.
First, solve the power:
4(-4²) - (5) + 3(2)
(-4²) = (-4)(-4) = 16
Next, multiply:
4(16) - 5 + 3(2)
64 - 5 + 6
Finally, combine the terms:
(64 + 6) - 5
70 - 5
65
B) 65 is your answer.
~
g A CD player with an original price of $380.00 is on sale at 35% off. What is the discount amount and the CD player sale price?
Answer:
Cost: $247
Discount: $133
Step-by-step explanation:
Simply multiply 380 and 35% off together to get your answer:
380(1 - 0.35)
380(0.65)
247
To find the discount amount, simply subtract the 2 numbers to get your answer:
380 - 247 = 133
Use matrix operations to solve the following systems of linear equations. Use comments to explain which value is x1, x2, etc
3x1-10 x2- 5x3+30x4 = -1
4x1+7x2+ 5x3- 3x4=0
x2+ x3-3x4 =1
x1-2x2-10x3+6x4 = -1
Answer:
x⁴ = -0.955939
x³ = 0.206897
x² = -2.07471
x = 2.65517
Step-by-step explanation:
Step 1: Rewrite equations in standard form
30x⁴ - 5x³ - 10x² + 3x = -1
-3x⁴ + 5x³ + 7x² + 4x = 0
-3x⁴ + x³ + x² = 1
6x⁴ - 10x³ - 2x² + x = -1
Step 2: Write in matrix form
Top Row: [30 -5 -10 3 | -1]
2nd Row: [-3 5 7 4 | 0]
3rd Row: [-3 1 1 0 0 | 1]
Bottom Row: [6 -10 -2 1 | -1]
Step 3: Plug in calc with RREF function
Top Row: [1 0 0 0 | -499/522]
2nd Row: [0 1 0 0 | 6/29]
3rd Row: [0 0 1 0 | -361/174]
4th Row: [0 0 0 1 | 77/29]
In a large city, the city supervisor wants to find the average number of aluminum cans that each family recycles per month. So, she surveys 18 families and finds that these 18 families recycle an average of 140 cans per month with a standard deviation of 26 cans per month. Find the 90 % confidence interval for the mean number of cans that all of the families in the city recycle per month.
Answer:
The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 18 - 1 = 17
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.74
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.74\frac{26}{\sqrt{18}} = 10.66[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 140 - 10.66 = 129.34 cans per month
The upper end of the interval is the sample mean added to M. So it is 140 + 10.66 = 150.66 cans per month.
The 90% onfidence interval for the mean number of cans that all of the families in the city recycle per month is between 129.34 and 150.66 cans per month
The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.
Requried:
a. What is the probabilty that a random sample of n = 40 oil changes results in a sample mean time less than 15 minutes?
b. Suppose the manager agrees to pay each employee a $50 bonus if they meet a certain goal. On a typical Saturday, the oil-change facility will perform 40 oil changes between 10 A.M. and 12 P.M. Treating this as a random sample, there
would be a 10% chance of the mean oil-change time being at or below what value? This will be the goal established by the manager.
Answer:
(a) Probability that a random sample of n = 45 oil changes results in a sample mean time < 10 minutes i=0.0001.
(b) The mean oil-change time is 15.55 minutes.
Step-by-step explanation:
Let us denote the sample mean time as x
From the Then x = mean time = 16.2 minutes
The given standard deviation = 3.4 minutes
The value of n sample size = 45
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.
Answer:
45
Step-by-step explanation:
I really don't but it seems right
Answer:
b
Step-by-step explanation:
just did it on edge
F(x)+6x+11 inverse function
Answer:
y = x/6 − 11/6
Step-by-step explanation:
y = 6x + 11
To find the inverse, switch x and y, then solve for y.
x = 6y + 11
x − 11 = 6y
y = x/6 − 11/6
!!HELP WILL GIVE BRAIN LIST!! Examine the diagram and information to answer the question. A circle in the coordinate plane has a radius of 6 and a center at the point (3,2). Point (x,y) lies on the circle. The triangle formed by points (3,2), (x,2) and (x,y) is a right triangle. What is the equation of the circle? Match the expression or equation to the steps used to find the equation of the circle. answers TO fill IN the match |x−3| (x−2)2+(y−3)2=62 |x−2| |y−3| (x−3)2+(y−2)2=62 |y−2|
Answer:
|y-2||x-3|(x-3)²+(y-2)² = 36Step-by-step explanation:
1. The length of the vertical leg of the triangle is the magnitude of the difference between the y-coordinate of the point on the circle and the y-coordinate of the center:
|y -2|
2. The length of the horizontal leg of the triangle is the magnitude of the difference between the x-coordinate of the point on the circle and the x-coordinate of the center:
|x -3|
3. The Pythagorean theorem tells you the sum of the squares of the leg length is equal to the square of the hypotenuse length. The hypotenuse is given as 6, so the equation is ...
[tex]|y-2|^2 +|x-3|^2=6^2[/tex]
Since the square of a number is the same as the square of its magnitude, we can write this as ...
[tex](x-3)^2+(y-2)^2=36[/tex]
You must estimate the mean temperature (in degrees Fahrenheit) with the following sample temperatures: 44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7 Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 98% C.I.
Answer:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
Step-by-step explanation:
For this problem we have the following dataset given:
44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7
We can find the mean and sample deviation with the following formulas:
[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex] s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex]\bar X= 51.278[/tex]
[tex] s= 22.979[/tex]
The confidence interval for the mean is given by:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The degrees of freedom are:
[tex] df=n-1= 9-1=8[/tex]
The confidence would be 0.98 and the significance [tex]\alpha=0.02[/tex] then the critical value would be:
[tex] t_{\alpha/2}= 2.896[/tex]
Ad replacing we got:
[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]
[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]
And the interval would be:
[tex] (29.10 \leq \mu \leq 73.46)[/tex]
Would this be correct even though I didn’t use the chain rule to solve?
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
32 percent of the customers of a fast food chain order the Whopper, French fries and a drink. A random sample of 10 cash register receipts is selected. What is the probability that eight receipts will show that the above three food items were ordered?
Answer: 0.0023
Step-by-step explanation:
Let X be the binomial variable that represents the number of receipts will show that the above three food items were ordered.
probability of success p = 32% = 0.32
Sample size : n= 10
Binomial probability function :
[tex]P(X=x)= \ ^nC_xp^x(1-p)^{n-x}[/tex]
Now, the probability that eight receipts will show that the above three food items were ordered :
[tex]P(X=8)=\ ^{10}C_8(0.32)^8(1-0.32)^2\\\\=\dfrac{10!}{8!2!}(0.32)^8(0.68)^2\\\\=5\times9(0.0000508414176684)\\\\=0.00228786379508\approx0.0023[/tex]
hence, the required probability = 0.0023
Identify whether the given value is a discrete random variable, a continuous random variable, or if it is not a random variable:
1) A college basketball player's height that is reported in the game-day program
2) The color of a student's car
3) The exact weight of an airline passenger's carry-on bag
Answer:
1. continuous random variable
2. not a random variable
3. a continuous random variable
Step-by-step explanation:
The classifications are as follow
a) The height of the player reported in the game day program is treated as a continuous random variable as these values could be determined through measuring them
b) The color of student car is not a random variable as it does not contain any quantitative data or we can say numerical data
c) The exact weight of the bag is a continuous variable as it is lie between the range
Question
Gabrielle is
7
years older than Mikhail. The sum of their ages is
91
. What is Mikhail's age?
Answer:
42
Step-by-step explanation:
Since Gabrielle is 7 years older than Mikhail, we subtract 7 from 91. Then we divide it by 2. So 84/2=42. Since Gabrielle is 7 years older we add 7 to 42. She is 49 and Mikhail is 42 years old. To double check our answer we should add both of the ages we got to make sure they add up to 91, so 42+49 is 91.
A farmer wants to take 4 of his animals to a city. He has to select the animals from 5 cows and 5 goats. (a) How many possible selections can he make? (b) In how many of these selections will there be more cows than goats?
Answer:
(a) 210
(b) 55
Step-by-step explanation:
(a) I'm assuming the animals are considered to be unique rather than identical. The order of the animals isn't important, so the number of ways he can choose 4 animals from 10 is:
₁₀C₄ = 210
(b) If there are more cows than goats, then there are either 3 cows and 1 goat:
₅C₃ ₅C₁ = 50
Or there are 4 cows:
₅C₄ = 5
The total number of combinations is 55.
What is the solution to this sysiem of inear equacions?
3x-2= 14
5x+y=32
• (3,5)
• (6,2)
• (8,-1)
• (14,-18)
Answer:
the answer i got was (16/3,16/3)
Step-by-step explanation:
The ratio of the areas of two circles is 121/100. What is the ratio of the radii of the two circles
Answer:
11/10
Step-by-step explanation:
The area ratio is the square of the radius ratio (k):
(121/100) = k²
k = √(121/100) = 11/10
The ratio of radii is 11/10.
A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the standard deviation to be 1.8. She thinks the mean is 5.7 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.12 at the 85% level of confidence? Round your answer up to the next integer.
Answer:
The sample size 'n' = 242
Step-by-step explanation:
Step(i):-
Given mean of the sample = 5.7
Given standard deviation of the sample (σ) = 1.8
The Margin of error (M.E) = 0.12
Level of significance = 0.85 or 85%
Step(ii):-
The margin of error is determined by
[tex]M.E = \frac{Z_{\alpha }S.D }{\sqrt{n} }[/tex]
The critical value Z₀.₁₅ = 1.036
[tex]0.12 = \frac{1.036 X 1.8 }{\sqrt{n} }[/tex]
Cross multiplication , we get
[tex]\sqrt{n} = \frac{1.036 X 1.8}{0.12}[/tex]
√n = 15.54
Squaring on both sides, we get
n = 241.49≅ 241.5≅242
Conclusion:-
The sample size 'n' = 242
find the least common denominator for these two rational expressions. x/x^2-25, c/x^2-3x-10
Answer:
Step-by-step explanation:
Hello,
Let 's notice that
[tex]x^2-25=x^2-5^2=(x-5)(x+5) \ \ and \\\\x^2-3x-10=(x-5)(x+2) \ \text{as sum of the zeroes is 3 and the product is -10}[/tex]
So the least common denominator is
[tex](x-5)(x+5)(x+2)[/tex]
hope this helps
A takeaway sells 10-inch pizzas and 12-inch pizzas.
The profit made in week 1 is 0.69 and week 2 is 0.71.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
A takeaway sells 10-inch pizzas and 12-inch pizzas.
From the table
For week 1:
Proportion= 509/ 736 = 0.69
and, week 2:
Proportion= 765/ 1076 = 0.71
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What is the area of this composite shape? Enter your answer in the box. in²
Answer:
Area = 53 in²
Step-by-step explanation:
area of a box = 8 * 6 = 48 in²
area of a triangle = 1/2 * b * h
b = 6 - 4 = 2 in
h = 13 - 8 = 5 in
area of a triangle = 1/2 * 2 * 5 = 5 in²
total area = area of a triangle + area of a box
total area = 5 in² + 48 in²
total area = 53 in²
Can someone teach me how to solve this problem please:)
Answer:
x= -3, y= -5
or x= 5, y=3
Step-by-step explanation:
① Label the 2 equations
x² +y²= 34 -----(1)
3x -3y= 6 -----(2)
From (2):
x -y= 2 -----(3)
Notice that (x-y)²= x² -2xy +y²
Thus, (equation 3)²= (equation 1) -2xy
Squaring (3):
(x -y)²= 2²
(x -y)²= 4
Expand terms in bracket:
x² -2xy +y²= 4
x² +y² -2xy= 4 -----(4)
subst. (1) into (4):
34 -2xy= 4
2xy= 34 -4 (bring constant to 1 side)
2xy= 30 (simplify)
xy= 30 ÷2 (÷2 throughout)
xy= 15 -----(5)
From (3):
x= y +2 -----(6)
I'll rewrite 2 of the equations.
x= y +2 -----(6)
xy= 15 -----(5)
Subst. (6) into (5):
y(y+2)= 15
y² +2y= 15
y² +2y -15= 0
(y +5)(y -3)=0
y+5= 0 or y-3=0
y= -5 or y= 3
Subst. into (6):
x= -5 +2 or x= 3 +2
x= -3 or x= 5
Answer:
y=-5, y=3
x=-3., x=5
Step-by-step explanation:
x^2+y^2=34
3x-3y=6
isolate x in te equation
3x-3y=6
x=3/3 y+6/3
x=y+2
plug the y+2 in the equation:
x^2+y^2=34
(y+2)^2+y^2=34
y^2+4y+4+y^2=34
2y^2+4y=34-4
2y^2+4y=30 divide by 2
y^2+2x-15=0 factorize
(y+5)(y-3)=0 eiter y+5=0 ten y=-5 or y-3=0 then y=3
now plug the solution in the equation
3x-3y=6
3x-3(-5)=6
3x=6-15
x=-9/3=-3
for y=3
3x-3y=6
3x-9=6
3x=15
x=5
A manufacturing company measures the weight of boxes before shipping them to the customers. Assume that the weights of boxes are normally distributed with mean 90 lbs and standard deviation 24 lbs. a) Find the probability that a randomly selected box will exceed 94 lbs. b) If a sample of 36 boxes is randomly selected, find the probability that the average of the boxes exceeds 94 lbs.
Answer:
24
Step-by-step explanation:
whats the answer ?? ill mark brainliest
Answer:
[tex]\boxed{Option A ,D}[/tex]
Step-by-step explanation:
The remote (non-adjacent) interior angles of the exterior angle 1 are <4 and <6
At the farm, corn costs $2.50 per pound. How much would 3 1/2 pounds of corn cost? Write your answer in dollars and cents.
Multiply price per pound by total pounds:
2.50 x 3.5 = 8.75
Total cost = $8.75
Answer:
The cost is $8.75 for 3.5 lbs
Step-by-step explanation:
The rate is 2.50 per pound
Multiply the number of pounds by the rate
3.5 * 2.50 =8.75
The cost is $8.75 for 3.5 lbs
On average, the printer uses 500 sheets of paper each day with a standard deviation of 10 sheets. What is the probability that the printer uses more than 508 sheets?
Answer:
P [ x > 508 ] = 0,2
Step-by-step explanation:
P [ x > 508 ] = 1 - P [ x ≤ 508]
P [ x ≤ 508 ] = ( 508 - 500 ) / 10
P [ x ≤ 508 ] = 8/10
P [ x ≤ 508 ] = 0,8
Then
P [ x > 508 ] = 1 - P [ x ≤ 508]
P [ x > 508 ] = 1 - 0,8
P [ x > 508 ] = 0,2
Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.)
Answer:
85.932 cm³
Step-by-step explanation:
The volume of rectangular prism is obtained as the product of its length (l) by its width (w) and by its height (h):
[tex]V=l*w*h[/tex]
The volume of a prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm is:
[tex]V=4.4*3.1*6.3\\V=85.932\ cm^3[/tex]
The volume of this prism is 85.932 cm³.
Consider rolling dice and getting a total of 8. Find the probability if two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places.)
Answer:
13.89%
Step-by-step explanation:
The probability when two dices are rolled and their sum is 8 is shown below:
But before that we need to see the probabilities of the sum i.e 8
2 + 6 = 8
3 + 5 = 8
4 + 4 = 8
5 + 3 = 8
6 + 2 = 8
There are 5 outcomes
And, the two dice is 36 i.e square of 6
So, the probability of two dices are rolled and their sum is 8 is
= [tex]\frac{5}{36}[/tex]
= 13.89%
You obtain a simple interest loan from National city for $2500 at 7.6% for 5 years. Find the amount of interest on the loan
Answer:
950
Step-by-step explanation:
2500(0.076)(5) = 950