Answer:
Step-by-step explanation:
Percent Error = | Actual Yield-Theoretical/ Theoretical Yield | *100%
Error= |-1/7|*100%= 14.29%
The following data show the number of cars passing through a toll booth during a certain time period over 15 days. 18 19 17 17 24 18 21 18 19 15 22 19 23 17 21 Identify the corresponding dotplot.
Answer: third from the top
Step-by-step explanation:
The correct answer is third from the top.
Arranging numbers in ascending order:
15 17 17 17 18 18 18 19 19 19 21 21 22 23 24
Let's count how many times each number occurs in this series of numbers.
row of numbers
15 +
16 not
17 + + +
18 + + +
19 + + +
20 not
21 + +
22 +
23 +
24 +
25 not
A system of equations is said to be redundant if one of the equations in the system is a linear combination of the other equations. Show by using the pivot operation that the following system is redundant. Is this system equivalent to a system of equations in canonical form?
a) x1 +x2 −3x3 = 7
b) −2x1 +x2 +5x3 = 2
c) 3x2 −x3 = 16
Answer:
prove that The given system of equations is redundant is attached below
Step-by-step explanation:
System of equations
x1 +x2 −3x3 = 7
−2x1 +x2 +5x3 = 2
3x2 −x3 = 16
To prove that the system is redundant we will apply the Gaussian elimination ( pivot operation )
attached below is the solution
9. What is the value of x if the quadrilateral is a rhombus? 15 5x 4x+3
Suppose 243 subjects are treated with a drug that is used to treat pain and 52 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20% of users develop nausea.
Part A- correct answer is C.
Part B- The test statistic for this hypothesis test is ___? (Round to two decimal places as needed)
Answer:
20%?
Step-by-step explanation:
Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selection down to ten mysteries and twelve Nonfiction books. If she randomly chooses four books fro her selections, what’s the probability that they will all be nonfiction?
twelve nonfiction books. If she randomly chooses four books
answer to 4 decimal places, if necessary.
Answer
Answer:
0.0677 = 6.77% probability that they will all be nonfiction
Step-by-step explanation:
The books are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
10 + 12 = 22 books.
She chooses 4 books, which means that [tex]n = 4[/tex]
12 nonfiction, which meas that [tex]k = 12[/tex]
What’s the probability that they will all be nonfiction?
This is P(X = 4). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,22,4,12) = \frac{C_{12,4}*C_{10,0}}{C_{22,4}} = 0.0677[/tex]
0.0677 = 6.77% probability that they will all be nonfiction
Can you help please fellow people
Answer:
using 2 below points to draw:
(0, 7)
(3.5, 6)
Step-by-step explanation:
using
Help me on this please
Answer:
x = 3.5
Step-by-step explanation:
Triangle to the right:
4^2 + x^2 = 8^2
16 + x^2 = 64
y^2 = 48
Triangle to the left:
x^2 + 6^2 = 48
x^2 + 36 = 48
x^2 = 12
x = sqrt(12)
x = 3.5
what tearm means per hundred
a.base b.percent c.percentage d.rate
the term per hundred means percent
hope it helps
Answer:
C. Percent
Explanation:
per hundred means 1 in 100. percent is referring to the unit that is 1 in 100 of another value
1ex. 1% of 100 (1 percent of 100)
2ex. 49% of 235 (49 percent of 235)
Sam thinks of a 4 digit number. The digit in the one’s place is 3 less than the digit in the ten’s place and digit in thousand’s place is 5 less than the digit in hundred’s place. The value of the hundred’s place is 800. The digit in ten’s place is the greatest even number. What is the number Sam is thinking of?
9514 1404 393
Answer:
3885
Step-by-step explanation:
The hundreds digit is 8, and the thousands digit is 5 less, so is 3.
The tens digit is 8 (the largest even digit), and the ones digit is 3 less, so is 5.
The number is ...
3885
Find the equation of the line tangent to y = sin(x) going through х = pi/4
Answer:
[tex]\displaystyle y - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2} \bigg( x - \frac{\pi}{4} \bigg)[/tex]
General Formulas and Concepts:
Algebra I
Coordinates (x, y)
Functions
Function Notation
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopePre-Calculus
Unit CircleCalculus
Derivatives
The definition of a derivative is the slope of the tangent lineDerivative Notation
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[sin(u)] = u'cos(u)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = sin(x)[/tex]
[tex]\displaystyle x = \frac{\pi}{4}[/tex]
Step 2: Differentiate
Trig Derivative: [tex]\displaystyle y' = cos(x)[/tex]Step 3: Find Tangent Slope
Substitute in x [Derivative]: [tex]\displaystyle y' \bigg( \frac{\pi}{4} \bigg) = cos \bigg( \frac{\pi}{4} \bigg)[/tex]Evaluate [Unit Circle]: [tex]\displaystyle y' \bigg( \frac{\pi}{4} \bigg) = \frac{\sqrt{2}}{2}[/tex]Step 4: Find Tangent Equation
Substitute in x [Function y]: [tex]\displaystyle y \bigg( \frac{\pi}{4} \bigg) = sin \bigg( \frac{\pi}{4} \bigg)[/tex]Evaluate [Unit Circle]: [tex]\displaystyle y \bigg( \frac{\pi}{4} \bigg) = \frac{\sqrt{2}}{2}[/tex]Substitute in variables [Point-Slope Form]: [tex]\displaystyle y - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2} \bigg( x - \frac{\pi}{4} \bigg)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Select the correct answer. What is the range of the function shown on the graph above?
A. -8
B.-2y <-7
C. -7 Sy < -2
D. -9
Answer: The answer would be D
Step-by-step explanation:
Hattie had $3,000 to invest and wants to earn 10.6% interest per year. She will put some of the money into an account that earns 12% per year and the rest into an account that earns 10% per year. How much money should she put into each account?
Answer:
900 at 12%
2100 at 10%
Step-by-step explanation:
Let x= amount invested at 12%
let y= amount invested at 10%
with that being said we can write the two equation
Equation 1: x+y=3000
Equation 2: 3000*.106=.12x+.1y
isolte x from equation 1
x= 3000-y
plug this into equation 2
318=.12(3000-y)+.1y
318=360-.12y+.1y
-42= -.02y
y= 2100
Plug this into equation 1
x+2100=3000
x=900
she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.
How to determine How much money should she put into each accountLet's denote the amount of money Hattie invests at 12% as \(x\) dollars, and the amount she invests at 10% as \(\$3000 - x\) dollars.
The formula for calculating interest is: \(\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}\).
For the 12% account:
Interest_12% = \(x \times 0.12 \times 1\) (1 year)
For the 10% account:
Interest_10% = \((3000 - x) \times 0.10 \times 1\) (1 year)
Hattie wants to earn 10.6% interest on the total investment, so we can set up the equation:
\(\text{Total Interest} = \text{Interest}_12% + \text{Interest}_10%\)
\(3000 \times 0.106 = x \times 0.12 + (3000 - x) \times 0.10\)
Now, solve for \(x\):
\(318 = 0.12x + 300 - 0.10x\)
\(318 = 0.02x + 300\)
\(18 = 0.02x\)
\(x = 900\)
Hattie should invest $900 at 12% and \(3000 - 900 = 2100\) at 10%.
Therefore, she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.
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Solve, then check algebraically and graphically. 9x-3=78
Answer:
[tex]9x - 3 = 78 \\ 9x - 3 + 3 = 78 + 3 \\ 9x = 81 \\ \frac{9x}{9} = \frac{81}{9} \\ x = 9[/tex]
Answer:
[tex]9x - 3 = 78 \\9 x = 78 + 3 \\ 9x = 81 \\ x = \frac{81}{9} \\ x = 9[/tex]
For the diagram below, which equation is the correct use of the distance
formula?
9514 1404 393
Answer:
D
Step-by-step explanation:
Any equation that does not have y2 as the first term in the second set of parentheses will be incorrect.
The correct usage is shown in equation D.
2. If 5 mg in 2 ml of liquid medication, how many mg is in 4 ml of medication?
Answer:
10mg
Step-by-step explanation:
We have a proportional relationship.
We know that there are 5mg in 2ml of liquid medication.
Now we want to know how many mg there are in 4 ml of medication.
First, we can rewrite it as:
4ml = 2ml + 2ml
And we know that, in every 2 ml of medicine, there are 5mg.
Then if we have two times 2ml of medicine, we have two times 5mg.
This is:
2*5mg = 10mg
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.
Required:
a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b. Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
c. What is the 95% confidence interval estimate of the difference between the two population proportions?
d. What is your conclusion?
Answer:
b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2
c)CI 95 % = ( 0.00002 ; 0.09998)
Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.
Recent Sample
Sample size n₁ = 1000
Number of events of people with financial fitness more than fair
x₁ = 410
p₁ = 410/ 1000 = 0.4 then q₁ = 1 - p₁ q₁ = 1 - 0.4 q₁ = 0.6
Sample a year ago
Sample size n₂ = 1200
Number of events of people with financial fitness more than fair
x₂ = 420
p₂ = 420/1200 p₂ = 0.35 q₂ = 1 - p₂ q₂ = 1 - 0.35 q₂ = 0.65
Test Hypothesis
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
CI 95 % then significance level α = 5% α = 0.05 α/2 = 0.025
To calculate p-value:
SE = √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂
SE = √ 0.4*0.6/1000 + 0.65*0.35/1200
SE = √ 0.00024 + 0.000189
SE = 0.021
z(s) = ( p₁ - p₂ ) / SE
z(s) = ( 0.4 - 0.35 )/0.021
z(s) = 0.05/ 0.021
z(s) = 2.38
We find p-value from z-table to be p-value = 0.00842
Comparing
p-value with α/2 = 0.025
α/2 > p-value
Then z(s) is in the rejection region for H₀. We reject H₀
CI 95 % = ( p₁ - p₂ ) ± 2.38*SE
CI 95 % = ( 0.05 ± 2.38*0.021 )
CI 95 % = ( 0.05 ± 0.04998)
CI 95 % = ( 0.00002 ; 0.09998)
CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate
$66.25 divided among 4 people
try more
complete the statement
1. Volume of pyramid= ________× volume of rectangular prism, V= l×w×h
So for pyramid, V= 1/3 (l×w×h) = (l×w×h) ÷ ________.
2. The volume of the cylinder is three times the volume of the cone or the volume of the is _________ that of the cylinder.
3. Volume of the cone = ________ volume of the cylinder.
4. Sphere's volume is 2/3 of the _________ volume.
please answer this questions because this is need to pass tomorrow!!
1. Volume of pyramid= One third× volume of rectangular prism, V= l×w×h
So for pyramid, V= 1/3 (l×w×h) = (l×w×h) ÷ 3.
2. The volume of the cylinder is three times the volume of the cone or the volume of the cone is one third that of the cylinder.
3. Volume of the cone = One third of volume of the cylinder.
4. Sphere's volume is 2/3 of the Cylinder's volume.
Answered by GAUTHMATH
Researchers study the relationship between interpersonal violence and health in college age women. The selected an alpha of 0.05. The researchers examined the average score on a psychological distress scale and compared the score for abused versus non abused women. A p value of 0.016 is reported. Based on this information, you know:
Answer:
There exists a relationship between interpersonal violence and health.
Step-by-step explanation:
The relationship between interpersonal violence and health :
The null hypothesis will be ; the is no relationship between interpersonal violence and health while the alternative will negate the Null ;
If no relationship exists, correlation Coefficient = 0 and if a relationship exists, then correlation Coefficient is not = 0
H0 : ρ = 0
H1 : ρ ≠ 0
α = 0.05
Reported Pvalue = 0.016
Decison region :
Reject H0 ; If Pvalue < α
Therefore, Since Pvalue < α ; we reject H0 and conclude that there exists a relationship between interpersonal violence and health.
Yellowstone National Park is a popular held trip destination. This year the senior class at
High School A and the senior class at High School B both planned trips there. The senior
class at High School A rented and filed 2 vans and 3 buses with 153 students. High
School Brented and nited il vans and 10 buses with 534 students. Every van had the
same number of students in it as did the buses. Find the number of students in each van
and in each bus.
Van: 39
Bus: 18
Van: 21
Bus: 21
o
Van: 27
Bus: 19
.
Van: 18
Bus: 39
Answer:
Who was the first president of United States?
Circle Theorems 1! need help
Answer:
45°
Step-by-step explanation:
<lmk=90°
angles in a triangle add up to 180
45+90+<o=180
<o=180-135
<o=45
Answer:
∠ O = 45°
Step-by-step explanation:
The angle between the tangent and the radius at the point of contact is 90°
The sum of the 3 angles in Δ OML is 180° , then
∠ O = 180° - (90 + 45)° = 180° - 135° = 45°
A bank records deposits as positive numbers and withdrawals as negative numbers.
Mike withdrew \$60$60dollar sign, 60 from his bank account 333 times.
What is the change in Mike's account balance after all 333 withdrawals?
\$$dollar sign
Answer:
i think that $19980 is the answer
Step-by-step explanation:
i hope it will help u
PLZ PLZ HELP
Mark is investing $47,000 in an account paying 5.26% interest compounded continuously.
What will Mark's account balance be in 17 years?
O $114,932.80
$114,925.39
$114,921.47
$114.925.46
===============================================
Work Shown:
A = P*e^(r*t)
A = 47000*e^(0.0526*17)
A = 114,932.799077198
A = 114,932.80
Notes:
P = 47,000 is the principal or amount depositedr = 0.0526 is the decimal form of 5.26%The "e" refers to the special constant e = 2.718... which is similar to pi = 3.14... I would let your calculator handle this constant. There should be a button labeled "e".Mark's account balance after 17 years would be $114,932.8
What is the formula for the continuous compounding?[tex]A=Pe^{rt}[/tex]
where,
A = Accrued amount
P = Principal amount
r = interest rate as a decimal
R = interest rate as a percent
r = R/100
t = time in years
For given question,
P = $47000, t = 17 years
R = 5.26%
[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]
Using the Continuous Compounding Formula,
[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]
Therefore, Mark's account balance after 17 years would be $114,932.8
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Which function represents the graph below?
Answer:
The answer is the third one below
Which list shows the following numbers in order from least to greatest: -15, 8, 4, -3, -7,
4, 8, -15, -7, -3
-15, 8, 4, -3, -7.
-15.-7.-3, 4.8
-15.-3, 4, -7.8
A rectangle has dimensions of 7 in. by 5 in. Consider the solid of revolution formed when the rectangle is rotated about its 7 in. side. What is the solid formed by the revolution?
cone cylinder What is the radius (in inches) of the base of the solid of revolution?
in What is the height (in inches) of the solid of revolution?
in Find the exact volume (in cubic inches) of the solid of revolution.
Answer:
(a) Cylinder, R = 5 in, H = 7 in
(b) Volume = 549.5 cubic inches
Step-by-step explanation:
length, L= 7 in
width, W = 5 in
(a) The solid is cylinder.
Radius, R = 5 in
(b) Height = 7 in
Volume of the cylinder
[tex]V = \pi r^2 h\\\\V = 3.14 \times 5 \times 5\times 7\\\\V = 549.5 in^3[/tex]
Where does the graph of f(x)=2√-x+2 start?
A. (−2,0)
B. (2,0)
C. (0,2)
D. (0,−2)
An important factor in selling a residential property is the number of times real estate agents show a home. A sample of 15 homes recently sold in the Buffalo, New York, area revealed the mean number of times a home was shown was 24 and the standard deviation of the sample was 5 people.
a. What is the margin of error for a 98% confidence interval? (Round your answer to 3 decimal places.)
b. What is the 98% confidence interval for the population mean? (Use Student's t Distribution Table.) (Round your answers to 2 decimal places.)
Answer:
a) The margin of error for a 98% confidence interval is of 3.388 people.
b) The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the hypergeometric distribution is used 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 = 15 - 1 = 14
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.624
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{5}{\sqrt{15}} = 3.388[/tex]
In which s is the standard deviation of the sample and n is the size of the sample. This means that the answer to question a is of 3.388.
Question b:
The lower end of the interval is the sample mean subtracted by M. So it is 24 - 3.39 = 20.61 people
The upper end of the interval is the sample mean added to M. So it is 24 + 3.39 = 27.39 people.
The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.
In 1999, a company had a profit of $173,000. In 2005, the profit was
$206,000. If the profit increased by the same amount each year, find the
rate of change of the company's profit in dollars per year. *
$5,500
$4,004
$379,000
$33,000
O $102.74
Answer:
A. $5500Step-by-step explanation:
The difference of years:
2005 - 1999 = 6The difference in profit over 6 years:
206000 - 173000 = 33000Average rate of change:
33000/6 = 5500It has been 6 years,
The main difference in profit over 6 years between 1999 and 2005 is,
→ 206000 - 173000
→ 33000
Then the average rate of change is,
→ 33000/6
→ 5500
Hence, $ 5500 is the correct option.
Which of the following slopes of a line pass through points (3, 1) and (0, 1)?