Answer:
The answer is True.
Step-by-step explanation:
Sales variance is computed in same manner as cost variance that is computing both price and volume variance. However interpretation of end result will not be same. For example in material price variance if
A = actual purchase price = $ 4, B = standard purchase price= $ 5 and Qt= quantity purchased = 500 units then
Material price varaince = 500 (5-4) = 500,
This gives us favourable price variance of 500 dollars. However in sales price variance if
A = actual sales price = $ 4, B = standard sale price= $ 5 and Qt= quantity sold = 500 units then
Sale price varaince = 500 (5-4) = (500)
This gives us unfavourable sales price variance of 500 dollars.
This show that formulas to compute variances are same but sale price decrease give us un favorable variance and cost price decrease gives us favorable price variance and vice versa.
How many possible 4-digit combinations are there with the numbers 2, 3, 4, 5, 6, 7, 8, and 9 if none of the numbers appear more than once (i.E. 2343, 2333, 2323, etc.)?
Answer:
[tex]1680[/tex]
Step-by-step explanation:
we need a 4-digit number from the numbers [tex]2,3,4,5,6,7,8\ and\ 9[/tex] (without repetition ).
possible number at thousand place [tex]=8[/tex]
Possible numbers at hundred place[tex]=8-1=7[/tex]
Possible numbers at [tex]10^{th}[/tex] place [tex]=7-1=6[/tex]
possible number at unit place [tex]=6-1=5[/tex]
So total possible numbers
[tex]=8\times7\times6\times5\\=1680[/tex]
Other method :
We are taking [tex]4[/tex] numbers out of [tex]8[/tex] and here order matters so we will use permutation.
Total possible numbers [tex]=^8P_{4}[/tex]
[tex]\frac{8!}{(8-4)!}\\ =\frac{8!}{4!}\\ =8\times7\times6\times5\\=1680[/tex]
Determine whether the following statement regarding the hypothesistest for two population proportions is true or false.
However small the difference between two population proportion ,for sufficiently large sample size, the null hypothesis of equalpopulation proportions is likely to be rejected.
The statement is true; as sample size increases, even small differences between two population proportions can lead to the rejection of the null hypothesis. The decreasing standard error with larger samples increases the test statistic, leading to smaller p-values. However, practical significance should also be considered alongside statistical significance.
Explanation:The statement regarding the hypothesis test for two population proportions is true. As the sample size increases, even a very small difference between the two population proportions becomes significant. This is because with larger sample sizes, the standard error of the difference between the two proportions decreases, which increases the test statistic used in hypothesis testing. As a result, we are more likely to reject the null hypothesis of equal population proportions if the sample size is sufficiently large, assuming there is indeed a small actual difference.
The null hypothesis typically states that there is no effect or no difference, and in the case of two population proportions, it states that the proportions are equal. When we conduct a hypothesis test, we calculate the probability of observing our sample data, or something more extreme, given that the null hypothesis is true. This probability is known as the p-value. A small p-value indicates that the observed data is unlikely under the null hypothesis, leading to its rejection.
However, it's important to note that the ability to detect small differences with large samples does not imply that those differences are practically significant, only statistically so. Therefore, in addition to hypothesis testing, it's essential to consider effect size and practical significance when interpreting results.
.
What is the twentieth term of the arithmetic sequence 21, 18, 15, 12, ... ?
78
-39
-36
1
Answer:
-36.
Step-by-step explanation:
First term a1 = 21.
Common difference d = 18 - 21 = -3 (15-18 = -3)
nth term an = a1 + (n - 1)d
So 20th term = 21 + (20-1) -3
= 21 - 3 * 19
= 21 - 57
= -36.
The 20th term of the arithmetic sequence will be -36.
The nth teem of an arithmetic sequence is calculated by using the formula: a + (n - 1) d.
The 20th term will be:
= a + (n - 1) d.
= a + (20 - 1)d
= a + 19d
where,
a = first term = 21
d = common difference = 2nd term - 1st term = 18 - 21 = -3
Therefore, 20th term will be:
= a + 19d
= 21 + 19(-3)
= 21 - 57
= -36
Therefore, the 20th term is -36
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What is the Common difference in the sequence 10,20,30,40,50...?
Answer:
10
Step-by-step explanation:
divide the last number by the previous number
Answer:
10
Step-by-step explanation:
If you calculate it correctly, every number in front of that number it 10 above.
Assuming that the roots of the given qudratic equation are a,b find the sum and product of the roots.
Answer: Sum of root a+b = -c/d
Product of root ab= e/d
Step-by-step explanation:
Let the general quadratic equation be dx² + cx + e = 0
And the root of the equation be
'a' and 'b'
Using the general formula to find the solution to the quadratic equation
a = -c+√c²- 4de/2d
b = -c-√c²- 4de/2d
Taking the sum of the roots
a+b = (-c+√c²- 4de/2d) + (-c-√c²- 4de/2d)
a+b = (-c-c+√c²- 4de/2d - √c²- 4de/2d)/2d
a+b = -2c/2d
a+b = -c/d
The sum of the root of the quadratic equation will be -c/d
Product of roots
ab = (-c+√c²- 4de/2d)(-c-√c²- 4de/2d)
= {c² +(c√c²- 4de)- (c√c²- 4de) -(c²-4de)}/4d²
= {c²-c²+4de}/4d²
= 4de/4d²
= e/d
The product of the above quadratic equation will be e/d
Evaluate the expression \dfrac{x^5}{x^2} x 2 x 5 start fraction, x, start superscript, 5, end superscript, divided by, x, squared, end fraction for x=2x=2x, equals, 2.
Answer:
8
Step-by-step explanation:
Fill in the variable value and do the arithmetic.
[tex]\dfrac{2^5}{2^2}=\dfrac{32}{4}=8[/tex]
___
Of course, the fraction can be simplified first:
[tex]\dfrac{x^5}{x^2}=x^{5-2}=x^3\\\\2^3=8[/tex]
To evaluate the expression, substitute x with 2, simplify the exponents, and perform the multiplication
Explanation:To evaluate the expression \dfrac{x^5}{x^2} \times 2 \times 5
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PLZZ HELPP!!! WILL GIVE BRAINLIEST!!!
Let f(x) = 8x^3 + 18x^2 − 10 and g(x) = 4x + 1. Find f(x)/g(x).
A. 2x^2 + 4x - 1 + 9/4x + 1
B. 2x^2 + 4x - 1 - 9/4x + 1
C. 2x^2 + 4x + 1 + 9/4x + 1
D. 2x^2 + 4x + 1 - 9/4x + 1
Answer:B. 2x^2 + 4x - 1 - 9/4x + 1
Step-by-step explanation:
f(x) = 8x^3 + 18x^2 − 10
g(x) = 4x + 1
We want to determine f(x)/g(x). We would apply the long division method. The steps are shown in the attached photo.
The correct answer is
2x^2 + 4x - 1 - 9/4x + 1
Answer:
[tex]\text{B. }2x^{2} - 4x - 1 - \dfrac{9}{4x + 1}[/tex]
Step-by-step explanation:
One way is to use long division.
2x² + 4x - 1
4x + 1) 8x³ + 18x² - 10
8x³ + 2x²
16x²
16x² + 4x
-4x - 10
-4x - 1
- 9
[tex]\dfrac{8x^{3} + 18x^{2} - 10} {4x+1} = 2x^{2} - 4x - 1 - \dfrac{9}{4x + 1}[/tex]
You begin with $90 in your savings account and your friend begins with $35 in her savings account. You deposite $10 in savings each week, and your friend deposites $15 in savings each week
Answer:
Part a) The graph in the attached figure (see the explanation)
Part b) The friend is not correct
Step-by-step explanation:
The questions are
a. Write and graph a system of linear equations that represent the amounts in each of your savings accounts
b. Your friend says that in 10 weeks you will both have the same amount of money in your savings accounts. Is your friend correct? Use the graph from part (a) to explain your answer.
Part a)
Let
x ----> the number of weeks
y ---> the amount in the saving account
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept or initial value of the linear equation
In this problem we have
Your saving accounts
The slope is equal to [tex]m=\$10\ each\ week[/tex]
The y-intercept is equal to [tex]b=\$90[/tex]
substitute
[tex]y=10x+90[/tex] ----> equation A
Your friend saving accounts
The slope is equal to [tex]m=\$15\ each\ week[/tex]
The y-intercept is equal to [tex]b=\$35[/tex]
substitute
[tex]y=15x+35[/tex] ----> equation B
using a graphing tool
the graph in the attached figure
Part b) Your friend says that in 10 weeks you will both have the same amount of money in your savings accounts. Is your friend correct? Use the graph from part (a) to explain your answer
we know that
When solving a system of equations by graphing, the solution of the system is the intersection point both graphs
In this problem, the intersection point is (11,200)
That means ----> In 11 weeks, both you and your friend have the same amount of money saved up, $200
Therefore
The friend is not correct
Decide which trigonometric ratio to use. Solve for x in the triangle below. Round your answer to the hundredths place.
4.59
0.07
6.55
5.60
(I have more questions in my recently asked too that I could really use help with as soon as possible.) Thank you.
Answer:
4.59
Step-by-step explanation:
sin(angle) = opposite / hypotenus
Write the equation of the line that has a slope of 2 and passes through the point (-3,4).
A) y = 2x - 2
B) y = 2x + 2
C) y = 2x + 7
D) y = 2x + 10
Answer:
The answer to your question is letter D
Step-by-step explanation:
Data
slope = m = 2
Point (-3, 4)
Process
1.- Substitute the data in the line equation
y - y1 = m(x - x1)
y - 4 = 2 (x + 3)
2.- Expand
y - 4 = 2x + 6
3.- Solve for y and simplify
y = 2x + 6 + 4
y = 2x + 10
Answer:
y=2x+10
Step-by-step explanation:
John weighs three times as much as Karen. Two times John's weight plus Karen's weight is 875 pounds. How much does John weigh? How much does Karen weigh?
Answer:
John- 375
Karen- 125
Step-by-step explanation:
Answer 1...
j =3k
2j + k = 875
substituting the first eqn into the 2nd
2(3k) + k = 875
6k+ k =875
7k = 875
k =875/7 =125
thus j = 3(125) =375
Answer:john weighs 375 pounds.
Karen weighs 125 pounds
Step-by-step explanation:
Let x represent the weight of John.
Let y represent the weight of Karen.
John weighs three times as much as Karen. This means that
x = 3y
Two times John's weight plus Karen's weight is 875 pounds. This means that
2x + y = 875 - - - - - - - -1
Substituting x = 3y into equation 1, it becomes
2 × 3y + y = 875
6y + y = 875
7y = 875
y = 875/7 = 125
Substituting y = 125 into x = 3y. It becomes
x = 3 × 125 = 375
Your mother takes you to your grandparents house for dinner. She drives 60 minutes at a constant speed of 40 miles per hour. She reaches the highway, quickly speeds up, and drives another 30 minutes at constant speed for 70 miles per hour. How far did you and your mother travel altogether? How long did the trip take?
Answer:
Step-by-step explanation:
We will separate our trips as "slow" and "fast". Filling in a motion table:
d = r x t
slow
fast
We know that the slow rate is 40 mph and the time is, in hours (because the time has to match the rate. We can't say "40 mph" and then state the time in minutes), 1 hour.
We know that the fast rate is 70 mph and the time in hours is .5 hours.
If distance = rate times time, then the distance traveled at the slow speed is 40 * 1 = 40 miles
The distance traveled at the fast speed is 70 * .5 = 35 miles.
The trip was 40 + 35 = 75 miles total, and the time it took was 1 + .5 = 1.5 hours.
The length of the top of a computer desk is 2 1/4 feet longer than it's width. If it's width measures y feet, express its length as an algebraic expression in y
Answer:
Step-by-step explanation:
The top of the computer desk is rectangular in shape.
Let y represent the width of the rectangle.
The length of the top of the computer desk is 2 1/4 feet longer than its width. Converting 2 1/4 feet to improper fraction, it becomes 9/4 feet. Therefore, the algebraic expression of the length of the of the top of the computer desk in terms of y would be
Length = y + 9/4
In a pot worth $2.35, there are 6 quarters, 5 dimes, 5 pennies, and the rest of the coins are nickels. What is the ratio of nickels to dimes?
Answer:
6:5
Step-by-step explanation:
It is given that a pot worth $2.35 and there are 6 quarters, 5 dimes, 5 pennies, the rest of the coins are nickels.
We know that
$1 = 100 cents
1 penny = 1 cent = $0.01
1 nickel = 5 cents. = $0.05
1 dime = 10 cents. = $0.10
1 quarter = 25 cents = $0.25
The value of 6 quarters is
[tex]6\times 0.25=1.50[/tex]
The value of 5 dimes is
[tex]5\times 0.10=0.50[/tex]
The value of 5 pennies is
[tex]5\times 0.01=0.05[/tex]
Let x be the number of nickels. So, the value of x nickels is
[tex]x\times 0.05=0.05x[/tex]
Total value of 6 quarters, 5 dimes, 5 pennies, and x nickels is
[tex]Total =1.50+0.50+0.05+0.05x[/tex]
[tex]Total =2.05+0.05x[/tex]
It is given that the pot worth is $2.35.
[tex]2.05+0.05x=2.35[/tex]
Subtract 2.05 from both sides.
[tex]0.05x=0.30[/tex]
Divide both sides by 0.05.
[tex]x=6[/tex]
The number of nickels is 5.
[tex]\dfrac{Nickel}{Dimes}=\dfrac{6}{5}=6:5[/tex]
Therefore, the ratio of nickels to dimes is 6:5.
In a pot worth $2.35 containing 6 quarters, 5 dimes, 5 pennies, and some nickels, the ratio of nickels to dimes is 6:5.
To find the ratio of nickels to dimes, we need to determine the number of nickels and dimes in the pot. We know that there are 6 quarters, 5 dimes, and 5 pennies in the pot, which is a total of 16 coins. Therefore, the number of nickels should be the difference between the total number of coins and the sum of quarters, dimes, and pennies.
The total value of the coins in the pot is $2.35. Since 6 quarters are worth $1.50, 5 dimes are worth $0.50, and 5 pennies are worth $0.05, the remaining value should come from the nickels.
Thus, the value of the nickels is $2.35 - $1.50 - $0.50 - $0.05 = $0.30. Since each nickel is worth $0.05, the number of nickels is $0.30 ÷ $0.05 = 6.
The ratio of nickels to dimes is therefore 6:5, which means that for every 6 nickels, there are 5 dimes.
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Diane loves coasters that dip into tunnels during the ride.Her favorite coaster is modeled by h(t)=2t +23t-59t+24. Using rational route theorem, what are the possible rational zeros for the function
Answer:
The possible rational zeros for the function are
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±3/2
Step-by-step explanation:
I believe that there is an error in the function with the exponents, it must be:
[tex]h(t) = 2t^{3} + 23t^{2}+59t+24[/tex]
If this is the function that you need, then we must use the rational zero theorem. It says that if a polynomial function, written in descending order of the exponents, has integer coefficients, then any rational zero must be of the form ± p/ q, where p is a factor of the constant term and q is a factor of the leading coefficient.
Thus
In this case the constant term is 24 and then
p = ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
The factor of the leading coefficient is 2, thus
q = ±1, ±2
The possible rational zeros for the function are
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24, ±1/2, ±3/2
Please answer with how you did it
Answer:
B) 0.11
Step-by-step explanation:
Use the conditional probability formula.
P(transfer | never graduated) = P(transfer & never graduated) / P(never graduated)
__
Denominator
But the P(never graduated) is made of two parts:
P(never graduated) = P(transfer & never graduated) + P(freshman & never graduated)
= (1 -0.80)×(1 -0.85) + (0.80)×(1 -0.70)
= (0.20)(0.15) + (0.80)(0.30)
= 0.0300 +0.2400 = 0.2700
__
Numerator
The numerator of our fraction is one of the components we just calculated:
P(transfer & never graduated) = (1 -0.80)×(1 -0.85) = 0.0300
__
Conditional Probability
So ...
P(transfer | never graduated) = 0.0300/0.2700 = 1/9 ≈ 0.11
Percent and Percent Change - Item 884404Question 4 of 6 Martina makes $8 as a regular employee. If she becomes a manager, she will increase her hourly rate by 30%. Use the drop-down menus to build an equation that could be used to find a manager's hourly pay rate, x
Answer:
10.4
Step-by-step explanation:
8+8*0.3
= 10.4
Hope that helps
Answer:
10.4
Step-by-step explanation:
8+8*0.3
= 10.4
Hope that helps
A group of friends decided to rent a house in Aspen, Colorado for a week of skiing. They each had to chip in $70 for the week’s lodging. If they had been able to convince three more people to go, the cost per person would have been reduced by $14. What was the rent for the week?
Answer:
70/5
Step-by-step explanation:
70/3 and then try 70/4 and then 70/5
The total rent for the week was $840, based on the given conditions of per person cost and the price decrease with additional participants.
Explanation:The subject of this question is Mathematics, and this is a problem ideally pitched at high school level. It involves constructing equations from the given information to solve the problem.
Let's begin by determining the amount of people who went on the trip initially. We'll call them 'n'. The cost per person on the trip was $70, so that the total cost of the trip is $70n.
Now, if they had persuaded three more people to go (n + 3), the cost per person would've dropped by $14 to $56 which, multiplied by the new total of attendees would still be equal to the total cost of the trip ($56(n + 3)).
As such, we build the equation $70n = $56(n + 3). Here's the breakdown and solving of the equation: $70n = $56n + $168.
Subtracting $56n from both sides gives $14n = $168. Dividing both sides by 14 finally gives n = 12.
To find the total cost of the rent, substitute n = 12 into the equation $70n, yielding $70(12) = $840.
So, the rent for the week was $840.
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After sales tax your brand new car is $17,300. What is the total price of the car with DMV fees of 1.25% of the purchase price of the car?
A. $261.25
B. $17,516.25
C. $216.25
D. $17,561.25
The right answer is Option B.
Step-by-step explanation:
Given,
Purchase price of car = $17,300
DMV fees = 1.25% of purchase price
DMV fees = [tex]\frac{1.25}{100}*17300=\frac{21625}{100}[/tex]
DMV fees = $216.25
Total price of car = Purchase price + DMV fees
Total price of car = 17300 + 216.25 = $17516.25
The total price of car is $17,516.25
The right answer is Option B.
Keywords: percentage, division
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Write an equation of the line containing the given point and perpendicular to the given line:
(7,- 4); 9x+7y=4
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
9x+7y=4
7y = - 9x + 4
y = -9x/7 + 4/7
Comparing with the slope intercept form, slope = - 9/7
If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (7,-4) is 7/9
To determine the intercept, we would substitute m = 7/9, x = 7 and y = -4 into y = mx + c. It becomes
- 4 = 7/9×7 + c = 49/9 + c
c = - 4 - 49/9 = -85/9
The equation becomes
y = 7x/9 - 85/9
Answer:
Step-by-step explanation:
any eq. of line perpendicular to 9x+7y=4 is
7x-9y=a
it passes through (7,-4)
7(7)-9(-4)=a
49+36=a
a=85
reqd. eq. is 7x-9y=85
A line passes through the points
(P,a) and (P,-a) where p and a are real numbers and p=/0.
Describe each of the following and explain your reasoning please.
1. slope of the line
2. equation of the line
3. Y-intercept
4. slope of a line perpendicular to the given line
Answer:
Step-by-step explanation:
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the information given,
y2 = - a
y1 = a
x2 = 0
x1 = 0
Slope = (- a - a)/0-0 = -2a/0 = 0
2) equation of the line is represented in the slope intercept form as y = mx + c
Where
m = slope
c = intercept.
To determine c, we would substitute y = a, x = p and m = 0 into y= mx + c. It becomes
a = 0×p + c
c = a
The equation becomes
y = a
3) y intercept,c = a
4) the slope of a line perpendicular to the given line is a negative reciprocal of the slope of the given line. Therefore,
Slope = - 0 = 0
to prove that triangle age and triangle old are congruent by sas what other information is needed
Answer:
Congruency of triangle by SAS rule.
Step-by-step explanation:
We have to prove that [tex]\triangle AGE \text{ and } \triangle OLD[/tex] are congruent to each other by SAS congruency rule.
Thus, we need the following information to do so:
A pair of equal corresponding side.An equal pair of equal corresponding angle.A second pair of equal corresponding side.Corresponding sides are:
AG and OLGE and LDAE and ADCorresponding angles are:
[tex]\angle AGE \text{ and } \angle OLD\\\angle GEA \text{ and } \angle LDO\\\angle GAE \text{ and } \angle LOD[/tex]
12) Oliver is not allowed to watch more than 4 hours of television a week. He watched his favorite show on Monday which was 1 hour long and his favorite Tuesday show which was 1.5 hours long. How many more hours of television can he watch? Set up an equation and solve. A) 2.5x = 4; Oliver can watch 1.6 more hours this week. B) x + 1 + 1.5 = 4; Oliver can watch 1.5 more hours this week. C) x + 4 = 1 + 1.5; Oliver can watch 1.5 more hours this week.
Answer:
B. Oliver can watch TV for 1.5 hours more this week.
Step-by-step explanation:
Oliver is not allowed to watch more than 4 hours of television a week. He watched his favorite show on Monday which was 1 hour long and his favorite Tuesday show which was 1.5 hours long.
So he has already finished 2.5 hours of watching . He can watch only for 4 hours for the total week.
Let x be the number of more hours for which he can watch television.
Then ,
x + 1 + 1.5 = 4
x + 2.5 = 4
x = 4 - 2.5
x = 1.5 hours.
So Oliver can watch television for at most 1.5 hours for the rest of the week.
Then the correct option is B.
When analyzing related data variables, how can one tell which one is the independent variable and which one is the dependent variable?
Answer:
Dependent and independent Variable.
Step-by-step explanation:
Dependent and independent Variable.
The two variables in an experiment are independent and dependent variable. Usually, the dependent variable is denoted by y and the independent variable a re denoted by [tex]x_i[/tex]The dependent variable depends on independent variable in an experiment and thus cannot be controlled.On the other hand we can change or control the independent variables to test effect on dependent variable.As the independent variable are changed, we observe corresponding changes in the dependent variable.Example: Let money spend be the dependent variable. It depends on an independent variable of shopping. We may control or change or shopping habits to see the changes in the money spent. Money spent totally depends in the amount f shopping done.The width of a rectangle is 4 more than half the length.
If the perimeter of the rectangle is 74, what is the width?
Perimeter of rectangle: P = 2l + 2w
Width= ? Length= ?
Answer:
The answer to your question is L = 22; w = 15
Step-by-step explanation:
Data
length = L
width = w
Perimeter = 74
Condition
w = L/2 + 4
Formula
P = 2L + 2w
Substitution
74 = 2L + 2(L/2 + 4)
Simplification
74 = 2L + L + 8
74 = 3L + 8
74 - 8 = 3L
3L = 66
L = 66/3
L = 22
w = 22/2 + 4
w = 11 + 4
w = 15
Use the information to answer the questions.
In triangle ABC, a = 11 in., measure angle B=70 deg and
c = 9 in.
Which information about the triangle is given?
Answer:
Part 1) The length of two sides and the measure of the included angle (Side-Angle-Side)
Part 2) [tex]b^2=a^2+c^2-2(a)(c)cos(B)[/tex]
Part 3) [tex]b=11.6\ in[/tex]
Step-by-step explanation:
we have
In the triangle ABC
[tex]a=11\ in\\c=9\ in\\B=70^o[/tex]
Part 1) Which information about the triangle is given?
In this problem we have the length of two sides and the measure of the included angle (Side-Angle-Side)
see the attached figure to better understand the problem
Part 2) Which formula can you use ti find b?
I can use the law of cosines
[tex]b^2=a^2+c^2-2(a)(c)cos(B)[/tex]
we have
[tex]a=11\ in\\c=9\ in\\B=70^o[/tex]
substitute the given values
[tex]b^2=11^2+9^2-2(11)(9)cos(70^o)[/tex]
[tex]b^2=202-67.72[/tex]
[tex]b=11.59\ in[/tex]
Part 3) What is b, rounded to the nearest tenth?
Remember that
To Round a number
a) Decide which is the last digit to keep
b) Leave it the same if the next digit is less than [tex]5[/tex] (this is called rounding down)
c) But increase it by [tex]1[/tex] if the next digit is [tex]5[/tex] or more (this is called rounding up)
In this problem we have
[tex]11.59\ in[/tex]
We want to keep the digit [tex]5[/tex]
The next digit is [tex]9[/tex] which is 5 or more, so increase the "5" by 1 to "6"
therefore
[tex]b=11.6\ in[/tex]
Andre rents a bike for a day. The rental changes can be determined by the equation: R = $0.5d, where R is rental changes and d is number of days she rents the bike. Calculate the unit rate.
Answer:the unit rate is $0.5
Step-by-step explanation:
Andre rents a bike for a day. The rental changes can be determined by the equation: R = $0.5d, where R is rental changes and d is number of days she rents the bike.
The unit rate multiplied by the number of days for which the bike was rented would give the total rental charge. From the given equation, the unit rate would be $0.5
A student wanted to estimate the number of chocolate chips in a commercial brand of cookie. He sampled 100 cookies and found an average of 10.5 chips per cookie. If we assume the standard deviation is 8, what is a 99% confidence interval for the average number of chips per cookie?A. (8.4,12.6)B. (8.9,12.1)C. (5.3,10.7)
Answer:
The 99% confidence interval is given by (8.4;12.6)
A. (8.4,12.6)
Step-by-step explanation:
1) Notation and definitions
n=100 represent the sample size
[tex]\bar X= 10.5[/tex] represent the sample mean
[tex]\sigma=8[/tex] represent the population standard deviation assumed
m represent the margin of error
Confidence =99% or 0.99
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
2) Calculate the critical value zc
On this case we can to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=NORM.INV(0.005,0,1)" for [tex]z_{\alpha/2}=-2.58[/tex]
"=NORM.INV(1-0.005,0,1)" for [tex]z_{1-\alpha/2}=2.58[/tex]
The critical value [tex]zc=\pm 2.74[/tex]
3) Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
[tex]m=z_c \frac{\sigma}{\sqrt{n}}[/tex]
[tex]m=2.58 \frac{8}{\sqrt{100}}=2.064[/tex]
4) Calculate the confidence interval
The interval for the mean is given by this formula:
[tex]\bar X \pm z_{c} \frac{\sigma}{\sqrt{n}}[/tex]
And calculating the limits we got:
[tex]10.5 - 2.58 \frac{8}{\sqrt{100}}=8.4[/tex]
[tex]10.5 + 2.58 \frac{8}{\sqrt{100}}=12.6[/tex]
The 99% confidence interval is given by (8.4;12.6)
A. (8.4,12.6)
An airline has six flights from New York to California and seven flights from California to Hawaii per day. If the flights are to be made on separate days, how many different flight arrangements can the airline offer from New York to Hawaii?
a) 6*7=42
b) 6+7=13
c) 67 = 279936
d) 76 = 117649
Answer: Option 'a' is correct.
Step-by-step explanation:
Since we have given that
Number of flights from New York to California = 6
Number of flights from California to New York = 7
Since if the flights are to be made on separate days,
So, they are independent events.
So, the number of different flight arrangements that can be made offer from New York to Hawaii would be
[tex]6\times 7\\\\=42[/tex]
Hence, Option 'a' is correct.
This is a Mathematics problem about combinations, specifically calculating the total number of possible flight arrangements from New York to Hawaii, given the number of flights per day on two separate routes. The answer is found by multiplying the number of flights from New York to California (6) by the number of flights from California to Hawaii (7), which equals 42 arrangements.
Explanation:The subject of this question is Mathematics, specifically involving the concept of combinations and arrangements. The total number of flight arrangements from New York to Hawaii can be calculated by simply multiplying the number of flights from New York to California by the number of flights from California to Hawaii. Therefore, the correct answer would be a) 6*7=42.
Conceptually, this is because for each of the 6 flights from New York to California, there are 7 possible continuing flights to Hawaii. To find all possible combinations, you would multiply the two numbers together. Through visualization, this could be seen as having 6 'branches' from New York to California, then 7 'branches' from California to Hawaii for each initial branch, giving a total of 42 possible routes.
Learn more about Combinations here:https://brainly.com/question/24703398
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Logan borrowed some money from his friend in order to help buy a new video game system and agreed to pay the friend back a constant amount each week. Logan originally borrowed $40 from his friend and after 7 weeks, he still owed his friend $26. Write an equation for the function L(t),L(t),representing the amount Logan owes his friend after tt weeks.
Answer:L(t) = 40 - 2t
Step-by-step explanation:
Total amount of money that Logan borrowed from his friend to buy the video game system is $40
Let x represent the constant amount that he agreed to pay the friend back each week.
After 7 weeks, he still owed his friend $26. This means that the amount that he paid in 7 weeks is 7×x = $7x
He still owed his friend $26.
This means that amount paid in 7 weeks would be 40 - 26 = $14
Therefore
7x = 14
x = 14/7 = 2
He pays $2 each week.
Let t represent the number of weeks, the equation for the function L(t),representing the amount Logan owes his friend after t weeks would be
L(t) = 40 - 2t