please simplify this equation
Answer:
The answer is -24√35
Step-by-step explanation:
-6√7 × 4√5
Using the rules of surds multiply the numbers outside the square root and the ones inside
That's
(-6×4)(√ 7 × √5)
= - 24√7×5
= -24√35
Hope this helps you
Answer:
-24√35
Step-by-step explanation:
-6√7 × 4√5
-6 × √7 × 4 √5
-6 × 4 × √7 × √5
-24 × √(7 × 5)
-24√35
Answer quick! EASY! WILL GIVE YALL BRAINLIESTTT
Answer:
7
Step-by-step explanation:
:)
QUICK HELP HURRY! Simplify the expression. [tex]10^{-2} +10^{-1}[/tex]
Answer:
11/100 or 0.11
Step-by-step explanation:
10^-2 is also equal to 1/100
10^-1 is also equal to 1/10
Simply add them now:
1/100+1/10
= 1/100+ 10/100
= 11/100=0.11
Hope this helped!
Obtain the number 175 in two steps, using the numbers 3, 10 and 25 exactly once. You may use addition, subtraction, or multiplication.
Answer: (10 - 3) x 25 = 175
Step-by-step explanation:
10 - 3 = 7
7 x 25 = 175
Tony used a photocopier to dilate the design for a monorail track system. The figure below shows the design and its photocopy
A
10 m
B
F
E
8 m
D
D
С
G
Design
Photocopy
The ratio of CD:GH is 2:3. What is the length, in meters, of side EH on the photocopied image? (5 points)
Answer:
12 m
Step-by-step explanation:
Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.
Thus, we are given the ratio, CD:GH = 2:3.
This means, any of the corresponding lengths of both figures would be in that same ratio.
Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.
The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔
[tex] \frac{AD}{EH} = \frac{2}{3} [/tex]
[tex] \frac{8}{EH} = \frac{2}{3} [/tex]
Cross multiply
[tex] 3*8 = 2*EH [/tex]
[tex] 24 = 2*EH [/tex]
Divide both sides by 2 to make EH the subject of formula
[tex] \frac{24}{2} = \frac{2*EH}{2} [/tex]
[tex] 12 = EH [/tex]
The length of side EH = 12 m
Which is the best description for the graph?
The graph is increasing everywhere
The graph is decreasing everywhere
The graph is increasing then decreasing
The graph is decreasing then increasing
Answer:
D
Step-by-step explanation:
It's decreasing then once it hits the origin, it starts to increase again. I hope this helps you:)
Answer:
D
Step-by-step explanation:
What is the volume of this aquarium?
Answer:
9,000 inches^3
Step-by-step explanation:
The first part is 20 x 20 x 20, which equals 8,000
The second part is 10 x 10 x 10, which is 1,000
1,000 + 8,000 = 9,000
of the following fractions which is 50% greater than 3/7
Answer:
9/14
Step-by-step explanation:
3/7 + 50%×3/7 =
= 3/7 + 1/2×3/7
= 3/7 + 3/14
= 6/14 + 3/14
= 9/14
The required fraction which 50% grater than 3/7 is 9/14.
Fraction to determine that 50% grater than 3/7.
Fraction of the values is number represent in form of Numerator and denominator.
Here, fraction = 50% grater than 3/7
= 1.5 x 3/7
= 4.5/7
= 45/70
= 9/14
Thus, The required fraction which 50% grater than 3/7 is 9/14.
Learn more about fraction here:
https://brainly.com/question/10354322
#SPJ5
Which of the following equations represents a line that is perpendicular to
y = -2x+4 and passes through the point, (4, 2)?
A. y=-3x +2
B. y - x
O C. y - 3x+4
O D. y = -2x
Answer: B) y = 1/2x
Step-by-step explanation:
In a perpendicular line, the slope is the opposite reciprocal. Thus, the equation can be simplified into y = 1/2x+b. Then, to get b, simply plug in 4 for x and 2 for y
2=1/2(4)+b
2=2+b
0=b
Thus, the equation of the line is y = 1/2x + 0, or y = 1/2x
Hope it helps <3
An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.Beverage Sample Sample Sample Size Mean SDStrawberry Drink 10 537 22Cola 10 559 17Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value.State the relevant hypotheses. (Use \mu1 for the strawberry drink and \mu2 for the cola.)H0: \mu1 - \mu2 = 0 Ha: \mu1 - \mu2 > 0H0: \mu1 - \mu2 = 0 Ha: \mu1 - \mu2 < 0 H0: \mu1 - \mu2 = 0 Ha: \mu1 - \mu2\geq 0H0: \mu1 - \mu2 = 0 Ha: \mu1 - \mu2\neq 0Compute the test statistic value and find the P-value. (Round your test statistic to three decimal places and your P-value to four decimal places.)t = ___P-value = ___State the conclusion in the problem context. (Use \alpha = 0.05.)Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H0. The data does not suggest that cola has a higher average compression strength than the strawberry drink. Fail to reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Fail to reject H0. The data does not suggest that cola has a higher average compression strength than the strawberry drink.What assumptions are necessary for your analysis?The distributions of compression strengths are approximately normal.The distributions of compression strengths have equal means. The distributions of compression strengths are the same.The distributions of compression strengths have equal variances.
Answer:
A) Option B is correct.
H₀: μ₁ = μ₂
Hₐ: μ₁ - μ₂ < 0
B) t = -2.502
p-value = 0.0112
C) Option A is correct.
Reject H₀. The data suggests that cola has a higher average compression strength than the strawberry drink.
D) Option A is correct.
The distributions of compression strengths are approximately normal.
Step-by-step explanation:
The complete Question is presented in the two attached images to this answer.
A) To perform this test we first define the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, we want to test if the extra carbonation of cola results in a higher average compression strength. That is, that cola has a higher average compression strength than the strawberry drink.
Hence, the null hypothesis would be that there isn't significant evidence to suggest that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.
The alternative hypothesis is that there is significant evidence to suggest that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.
Mathematically, if the average compression strength of strawberry drink is μ₁, the average compression strength of cola is μ₂ and the difference in compression strengths is μ = μ₁ - μ₂
The null hypothesis is represented as
H₀: μ = 0 or μ₁ = μ₂
The alternative hypothesis is represented as
Hₐ: μ < 0 or μ₁ - μ₂ < 0
B) So, to perform this test, we need to compute the test statistic
Test statistic for 2 sample mean data is given as
Test statistic = (μ₁ - μ₂))/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = average compression strength of strawberry drink = 537
n₁ = sample size of the sample of strawberry drink in cans surveyed = 10
s₁ = standard deviation of the compression strength of strawberry drink in cans surveyed= 22
μ₂ = average compression strength of cola = 559
n₂ = sample size of the sample of cola in cans surveyed = 10
s₂ = standard deviation of the compression strength of strawberry drink in cans surveyed = 17
σ = [(17²/10) + (22²/10)] = 77.5903160379 = 8.792
We will use the t-distribution as no information on population standard deviation is provided
t = (537 - 559) ÷ 8.792
= -2.502 = -2.50
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n₁ + n₂ - 2 = 10 + 10- 2 = 18
Significance level = 0.05
The hypothesis test uses a one-tailed condition because we're testing in only one direction (whether compression strength of cola in can is greater).
p-value (for t = -2.50, at 0.05 significance level, df = 18, with a one tailed condition) = 0.011154 = 0.0112 to 4 d.p.
C) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.0112
0.0112 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis accept the alternative hypothesis & say that the extra carbonation of cola results in a higher average compression strength, that is, cola has a higher average compression strength than the strawberry drink.
D) The necessary conditions required before a t-test is deemed valid include.
- The samples used must be a random sample of the population distribution with each variable in the sample independent of other one.
- The distribution of the population where the samples were extracted from must be normal or approximately normal to ensure some degree of normality for the samples.
Hence, the necessary assumption for this t-test among the options is that the distributions of compression strengths are approximately normal.
Hope this Helps!!!
A 12 sided die is rolled the set of equally likely outcomes is 123 456-789-10 11 and 12 find the probability of rolling a number greater than three
Answer:
6
Step-by-step explanation:
nerd physics
what is 3x3x4/45 does anyone know the answer
Answer:
4/5 or 0.8
Step-by-step explanation:
3*3*4/45
3*3=9
9*4=32
32/45=4/5
Hope it helps ;)
━━━━━━━☆☆━━━━━━━
▹ Answer
0.8 (4/5 or 8 × 10⁻¹)
▹ Step-by-Step Explanation
3 × 3 × 4 ÷ 45
3² × 4 ÷ 45
9 × 4 ÷ 45
36 ÷ 45
= 0.8 (4/5 or 8 × 10⁻¹)
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
The expression 3 × 7 – 4 × 8 + 2 is equivalent to which of the following?
Answer:
-9
Step-by-step explanation:
3 time 7
minus
4 times 8
21 - 32
-11+2= -9
What is the range of the graph of the equation y= k/x?
Answer:
all real number except 0
Step-by-step explanation:
Please answer this correctly
Answer:
3/20s
Step-by-step explanation:
Please Help!! And Fast!! Will give Brainliest to the Best Answers (75 points) --- The historical society hired an artist to restore a stained glass window panel. After studying the original drawings, the artist knows that panel ABCD is square. He also knows that FG is a perpendicular bisector of BC and BC ≅ BE. However, in order to restore the panel to match its original specifications, he needs to know the measure of ∠BED. Given: ABCD is a square FG ⊥ BC BC ≅ BE Step 1: Draw EC on the diagram. Use the given information to explain how you know △EGC ≅ △EGB. Add the appropriate notation to the diagram. (5 points) Step 2: Building on the information from Step 1, use the spaces below to prove that m∠BEC = 60°. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Statements Reasons 1. △EGC ≅ △EGB 1. Given 2. EB ≅ EC 3. Given 4. EB ≅ EC ≅ BC 5. m∠BEC = 60° Step 3: Next, use the spaces below to prove the measure of ∠ECD = 30°. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Given: ABCD is a square FG ⊥ BC BC ≅ BE △ECG ≅ △EBG △BEC is equilateral m∠BEC = 60° Prove: m∠ECD = 30° Statements Reasons 1. △BEC is equilateral 2. m∠GCE = 60° 3. ABCD is a square 4. Substitution Step 4: Find m∠BED. Show your work and explain your reasoning. Add the appropriate notation to the diagram. (6 points; 4 points for showing work and explaining reasoning; 1 point for final answer; 1 point for diagram) Given: ABCD is a square FG ⊥ BC BC ≅ BE △ECG ≅ △EBG △BEC is equilateral m∠BEC = 60° △ECD is isosceles Find: m∠BED
Answer: I had the same assingment and came here looking for answers myself. When I saw the only anwser was 20 (Which is wrong) I decided I would try my best and If I got it right come back here and share the correct answers for future students.
Just look at the PDF attached below, I somehow got a 50/50.
Step-by-step explanation:
Statements Reasons
1. △EGC ≅ △EGB 1. Given
2. EB ≅ EC Supposition
3. <EGC ≅ <EGB Given
4. Equilateral Triangle EB ≅ EC ≅ BC
5. Equilateral Triangle m∠BEC = 60°
Statements Reasons
1. △BEC is equilateral AAS≅AAS postulate (angle angle side)
2. m∠ GCE = 60° m∠ BEC = 60° Equilateral Triangles
3. FG ⊥ BC & FG ⊥ AD ABCD is a square
4. m∠ECD + m∠ BEC = 30°+60° Substitution (right angles)
m∠DCG = 90° right angles of a square
m∠BED= 135°
Statements Reasons
1. △ECG ≅ △EBG Given
2. ABCD is a square Given
3. BC ≅ BE Given
4. AB ≅ DC ABCD is a square
5. m∠ABE ≅ m∠DCE Outside angles of congruent
triangles △EGB≅ △EGC
5. △AEB≅ △DEC S.S.A ≅ S.S.A. ( side side angle) Postulate
△BEC is equilateral m∠BEC = 60°
△ECD is isosceles m CD= mCE
∠ECD = 30° m∠BEC = 60°
As m∠BEC +∠ECD = 30°+ 60° right angle of the square ABCD
The equal sides of the isosceles triangles are called the legs and the unequal third side is called the base.
Angles opposite to the equal sides of the isosceles triangle must also be equal.
As the third angle is 30° so the other two angles must be 75° each to make a total of 180°.
m∠BED= m∠BEC + m∠CED
= 60° + 75°= 135°
https://brainly.com/question/22140109
Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can get at least 25% of the student population to sign a petition. So far, 82 students have signed the petition. Jose used the following steps to write an inequality that can be used to determine the number of student signatures still needed: Step 1. Declare the variable: Let x = the number of student signatures still needed. Step 2. Create a ratio equivalent to StartFraction total number of signatures needed over total number of students in the school EndFraction : StartFraction x + 82 over 426 EndFraction. Step 3. Convert 25% to a decimal: 25% = 0.25. Step 4. Write the inequality: StartFraction x + 82 over 426 EndFraction less-than-or-equal-to 0.25. What is Jose’s error? In Step 1, x should be equal to the total number of students in the school. In Step 2, the ratio should be StartFraction x over 426 EndFraction. In Step 3, the decimal should be 0.025. In Step 4, the inequality should be StartFraction x + 82 over 426 EndFraction greater-than-or-equal-to 0.25.
Answer:
Step 4
Step-by-step explanation:
Jose's Steps are:
Step 1: Declare the variable:
Let x = the number of student signatures still needed.
Step 2: Create a ratio equivalent to:
[tex]\dfrac{\text{Total number of signatures needed}}{\text{Total number of students in the school}} =\dfrac{x + 82}{426}.[/tex]
Step 3: Convert 25% to a decimal:
25% = 0.25.
Step 4: Write the inequality:
[tex]\dfrac{x + 82}{426}\leq 0.25[/tex]
Since they need at least 25% of the student population to sign a petition, In Step 4, the inequality should be:
[tex]\dfrac{x + 82}{426}\geq 0.25[/tex]
Answer:
(D).Step 4
Step-by-step explanation:
I got it right on edge
I NEED HELP PLEASE, THANKS! :)
Find the angle θ between u = <7, –2> and v = <–1, 2>.
47.5°
42.5°
132.5°
137.5°
Answer:
Step-by-step explanation:
Cos θ = u*v
IuI *IvI
u * v = 7*(-1) + (-2)*2
= -7 - 4
= -11
IuI = [tex]\sqrt{7^{2}+(-2)^{2}}\\[/tex]
= [tex]\sqrt{49+4}\\\\[/tex]
= [tex]\sqrt{53}[/tex]
I vI = [tex]\sqrt{(-1)^{2}+2^{2}}\\[/tex]
= [tex]\sqrt{1+4}\\\\[/tex]
= [tex]\sqrt{5}\\[/tex]
Cos θ = [tex]\frac{-11}{\sqrt{53}*\sqrt{5} } \\\\[/tex]
= [tex]\frac{-11}{16.28}\\\\[/tex]
Cos θ = -0.68
θ = 132.5°
An unevenly heated metal plate has temperature T(x,y) in degrees Celsius at a point (x,y). If T(2,1) = 107, Tx(2,1) = 9, and Ty(2,1) = −8, estimate the temperature at the point (2.03,0.95).
Answer: 107.67°C
Step-by-step explanation:
I guess that we could do a Taylor expansion around the point (2, 1)
Remember that a Taylor expansion around the point (a, b) is:
[tex]T(x,y) = T(a, b) + \frac{dT(a,b)}{dx}(x - a) + \frac{dT(a,b)}{dy}(y - b) + .....[/tex]
Where the latter terms need higher orders of the derivates of T, so we can not find them, regardless of that, this expansion will be accurate near the point (a, b),
Then, using this, we can write our expanssion as:
T(x,y) = 107 + 9*(x - 2) - 8*(y - 1)
Now we evaluate this in x = 2.03 and y = 0.95
T(2.03, 0.95) = 107 + 9(2.03 - 2) - 8*(0.95 - 1) = 107.67
Then a good estimation of the temperature at the point (2.03,0.95) is 107.67°C
The estimate of the temperature of the unevenly heated metal plate at temperature at the point (2.03,0.95) is;
T(2.03, 0.95) = 107.67 °C
Formula for taylor expansion around a point (a, b) is given as;
T(x, y) = T(a,b) + [tex]\frac{dT(a,b)}{dx}[/tex](x - a) + [tex]\frac{dT(a,b)}{dy}[/tex](y - b) + ....
We are given;
T(2,1) = 107
T'x(2,1) = [tex]\frac{dT(a,b)}{dx}[/tex] = 9
T'y(2,1) = [tex]\frac{dT(a,b)}{dy}[/tex] = −8
Plugging in the relevant values into our taylor expansion above gives;
T(x, y) = 107 + 9(x - 2) - 8(y - 1)
Now, we want to estimate the temperature at the point (2.03, 0.95).
Thus, we will plug in x = 2.03 and y = 0.95 to get;
T(2.03, 0.95) = 107 + 9(2.03 - 2) - 8(0.95 - 1)
T(2.03, 0.95) = 107 + 0.27 + 0.4
T(2.03, 0.95) = 107.67 °C
Read more at; https://brainly.com/question/9211177
A certain shampoo is available in two sizes. A 13.5 ounces bottle cost $2.98. A 29.2 ounce bottle cost $6.12. Find the Unit price for each size. Then state which size is the better buy based on the unit price. Round your answer to the nearest cent
Answer:
9.2 ounce bottle cost $6.12 is better buy with unit price of $0.22
Step-by-step explanation:
Unit price of any product is given by
unit price = weight of product/ price of product
Given sizes
A
13.5 ounces bottle cost $2.98
cost of 1 ounce of shampoo for this size = cost price/weight of shampoo
cost of 1 ounce of shampoo for this size =2.98/13.5 = $0.22
Unit price for this size is $.022
B
9.2 ounce bottle cost $6.12
cost of 1 ounce of shampoo for this size = cost price/weight of shampoo
cost of 1 ounce of shampoo for this size =6.12/9.2 = 0.66
Unit price for this size is $0.66
As $0.22 is less than $0.66 thus,
9.2 ounce bottle cost $6.12 is better buy.
College students spend $183 more each year on textbooks and course materials than on computer equipment. They spend a total of $819 on textbook and course materials and equipment each year. How much is spent each year on textbooks and course materials and computer equipment?
Answer:
Textbooks: $506Course Materials and Electronics: $323Step-by-step explanation:
First, we need to divide the amount into 2 equal parts:
$819/2 = $414.50
Now, because they spent $183 more on textbooks, we add half of that to $414.50.
$414.50 + $91.50 = $506
$414.50 - $91.50 = $323
To make sure that the amount spent on textbooks is $183 more than the amount spent on course materials and computers, we need to add $183 to $323. If we get $506, our answer is correct.
$323 + $183 = $506 ✅
Textbooks: $506Course Materials and Electronics: $323I'm always happy to helpA man bought a pair of jeans for $23.00 a shirt for $14.00 and two ties for $7.98 each. What was the total cost of his clothing ?
Answer:
$52.96
Step-by-step explanation:
To find the total cost of his clothing, add up the prices of everything he bought.
Jeans: $23.00
Shirt: $14
Ties: 2 ties for $7.98 each.
Each tie costs $7.98, and the man bought two ties. Therefore, multiply 2 and $7.98
2*$7.98 = $15.96
Add all the prices together.
jeans + shirt + ties
$23 + $14 + $15.96
$37 + $15.96
$52.96
The total cost of his clothing is $52.96
Answer:
total cost=52.96
Step-by-step explanation:
Things he bought:
jeans for $23.00
a shirt for $14.00
two ties for $7.98 each
the total const would be the sum of all his clothes
which is
jeans for $23.00
+shirt for $14.00
+one tie for $7.98
+one tie for $7.98
_______________
total cost=52.96
HOPE IT HELPS :0
PLEASE MARK IT THE BRAINLIEST!
if 2 X degree is the exterior angle of triangle and x degree and 45 degree are opposite interior angle find the value of x degree
Answer:
x = 45 degrees
Step-by-step explanation:
The measure of exterior angles is equal to the sum of non-adjacent interior angles
=> 2x = x+45
=> 2x-x = 45
=> x = 45 degrees
Answer:
45 degrees.
Step-by-step explanation:
The exterior angle = sum of the 2 opposite interior angles.
2x = x + 45
2x - x = 45
x = 45.
Evaluate the following definite integral.
10
∫ 13y/ y^2-9y-22 .dy
-1
Answer:
[tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -9 \ln (12)[/tex]
General Formulas and Concepts:
Pre-Calculus
Partial Fraction DecompositionCalculus
Differentiation
DerivativesDerivative NotationDerivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
U-Substitution
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy[/tex]
Step 2: Integrate Pt. 1
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\frac{y}{y^2 - 9y - 22}} \, dy[/tex][Integrand] Factor: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\frac{y}{(y - 11)(y + 2)}} \, dy[/tex]Step 3: integrate Pt. 2
[Integrand] Split [Partial Fraction Decomp]: [tex]\displaystyle \frac{y}{(y - 11)(y + 2)} = \frac{A}{y - 11} + \frac{B}{y + 2}[/tex][Decomp] Rewrite: [tex]\displaystyle y = A(y + 2) + B(y - 11)[/tex][Decomp] Substitute in y = -2: [tex]\displaystyle -2 = A(-2 + 2) + B(-2 - 11)[/tex]Simplify: [tex]\displaystyle -2 = -13B[/tex]Solve: [tex]\displaystyle B = \frac{2}{13}[/tex][Decomp] Substitute in y = 11: [tex]\displaystyle 11 = A(11 + 2) + B(11 - 11)[/tex]Simplify: [tex]\displaystyle 11 = 13A[/tex]Solve: [tex]\displaystyle A = \frac{11}{13}[/tex][Split Integrand] Substitute in variables: [tex]\displaystyle \frac{y}{(y - 11)(y + 2)} = \frac{\frac{11}{13}}{y - 11} + \frac{\frac{2}{13}}{y + 2}[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Split Integrand]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13\int\limits^{10}_{-1} {\bigg( \frac{\frac{11}{13}}{y - 11} + \frac{\frac{2}{13}}{y + 2} \bigg)} \, dy[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \int\limits^{10}_{-1} {\frac{\frac{11}{13}}{y - 11}} \, dy + \int\limits^{10}_{-1} {\frac{\frac{2}{13}}{y + 2}} \, dy \bigg][/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}\int\limits^{10}_{-1} {\frac{1}{y - 11}} \, dy + \frac{2}{13}\int\limits^{10}_{-1} {\frac{1}{y + 2}} \, dy \bigg][/tex]Step 5: Integrate Pt. 4
Identify variables for u-substitution.
Integral 1
Set u: [tex]\displaystyle u = y - 11[/tex][u] Differentiation [Basic Power Rule, Derivative Properties]: [tex]\displaystyle du = dy[/tex][Bounds] Switch: [tex]\displaystyle \left \{ {{y = 10 ,\ u = 10 - 11 = -1} \atop {y = -1 ,\ u = -1 - 11 = -12}} \right.[/tex]Integral 2
Set v: [tex]\displaystyle v = y + 2[/tex][v] Differentiate [Basic Power Rule, Derivative Properties]: [tex]\displaystyle dv = dy[/tex][Bounds] Switch: [tex]\displaystyle \left \{ {{y = 10 ,\ v = 10 + 2 = 12} \atop {y = -1 ,\ v = -1 + 2 = 1}} \right.[/tex]Step 6: Integrate Pt. 5
[Integrals] U-Substitution: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}\int\limits^{-1}_{-12} {\frac{1}{u}} \, du + \frac{2}{13}\int\limits^{12}_{1} {\frac{1}{v}} \, dv \bigg][/tex][Integrals] Logarithmic Integration: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}(\ln |u|) \bigg| \limits^{-1}_{-12} + \frac{2}{13}(\ln |v|) \bigg| \limits^{12}_{1} \bigg][/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 13 \bigg[ \frac{11}{13}[-\ln (12)] + \frac{2}{13}[\ln (12)] \bigg][/tex]Simplify: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = 11[-\ln (12)] + 2[\ln (12)][/tex]Simplify: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -11\ln (12)] + 2\ln (12)[/tex]Simplify: [tex]\displaystyle \int\limits^{10}_{-1} {\frac{13y}{y^2 - 9y - 22}} \, dy = -9 \ln (12)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
How much dirt is in a hole that is 3 in by 3 in by 1 ft? Please give a detailed explanation for Brainliest.
Answer:
Well the best answer would be 1 0.75 cubic feet bag of dirt
Step-by-step explanation:
helpppppppp with this please will give bralienst
Answer:
n = 600
Step-by-step explanation:
To solve this equation:
1. Simplify all like terms: 5400/9 = 600 = n
2. The n cannot be simplified.
3. The answer is n = 600 because 5400/9 is 600 which is equal to n
The variance in drug weights is critical in the pharmaceutical industry. For a specific drug, with weights measured in grams, a sample of 18 units provided a sample variance of 0.36. a. Construct a 90% confidence interval estimate of the population variance for the weight of this drug. Show your work. b. Construct a 90% confidence interval estimate of the population standard deviation.
Answer:
a) 0.2218 to 0.7057
b) 0.4710 to 0.8401
Step-by-step explanation:
Given:
sample = n = 18
sample variance = s² = 0.36
To find:
a) 90% confidence interval estimate of the population variance.
b) 90% confidence interval estimate of the population standard deviation.
a)
Compute degree of freedom
degree of freedom = df = n - 1 = 18 - 1 = 17
Compute value of α for a 90% confidence interval
The confidence level for 90% is:
c = 0.90
So
α = 1 - c = 1 - 0.90 = 0.1
α = 0.1
Now use the table of critical values of the chi-square distribution in order to find critical values. Search for the 17th row of table using df = 17 and find the column corresponding to 1 - α/2 i.e. 0.95 of table for upper tail critical values and column corresponding to α /2 i.e. 0.05 of table for lower tail critical values.
Using the table:
[tex]X^{2}_{0.95}[/tex] = 8.672
[tex]X^{2}_{0.05}[/tex] = 27.587
90% Confidence interval estimate of the population variance
The boundaries of CI are computed using formula:
(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] ≤ σ² ≤ (n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex]
(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] = (18-1) 0.36 / 27.587
= (17) 0.36 / 27.587
= 6.12 / 27.587
(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] = 0.2218
(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex] = (18-1) 0.36 / 8.672
= (17) 0.36 / 8.672
= 6.12 / 8.672
= 0.7057
This results in inequalities 0.2218 ≤ σ² ≤ 0.7057 for the variance
b)
90% Confidence interval estimate of the population standard deviation
The boundaries of CI are computed using formula:
√(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] ≤ σ ≤ √(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex]
√(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] = √((18-1) 0.36 / 27.587)
= √((17) 0.36 / 27.587)
= √(6.12 / 27.587)
= √0.2218
= 0.4709
= 0.4710
√(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex] = √((18-1) 0.36 / 8.672)
= √((17) 0.36 / 8.672)
= √ (6.12 / 8.672)
= √0.7057
= 0.8401
0.4710 ≤ σ ≤ 0.8401 for the standard deviation.
Find the value of z such that 0.11 of the area lies to the right of z. Round your answer to two decimal places.
Answer:
1.23?
Step-by-step explanation:
In a random sample of high school seniors, the proportion who used text messaging was 0.88. In a random sample of high school freshmen, this proportion was 0.68. Researchers found the difference in proportions to be statistically significant and obtained one of the following numbers for the p-value. Which is it?
a. 1.5
b. 0.02
c. 0.78
d. 0.30
Answer:
Option B - 0.02
Step-by-step explanation:
In this question, the p-value is used to tell us the probability that a difference of (0.88 – 0.68) which is 0.2 or greater would occur in the distribution of simulated differences. This is created done with the assumption that there is no true difference in the two populations.
Due to the fact that the researchers found the difference in proportions to be statistically significant, hence these results would rarely occur due to just the sampling variability and thus the p-value must be small.
Looking at the options, the p-value in Option (B) will be the correct response,l as it indicates that a difference of 0.2 or more would only occur about 2% of the time by chance alone provided the proportion who text were the same in the population of seniors and the population of freshmen. This resonates well with the claim that the difference in proportions is statistically significant.
Thus, Option B is the correct answer.
(06.01 MC) What is the value of the expression shown below? 8 + (7 + 1) 2 ÷ 4 ⋅ (5 points) Select one: a. 7 b. 9 c. 21
Answer:
b. 9
Just use PEMDAS