Answer:
14
Step-by-step explanation:
all you have to do is multiply 15x3 which is 45 and subtract 3 or 1 which is 14 she has 14 friends.
Hometown Grocery, Inc. has 50 comma 000 shares of common stock outstanding and 4 comma 000 shares of preferred stock outstanding. The common stock is $ 4.00 par value; the preferred stock is 9% noncumulative with a $ 100.00 par value. On October 15, 2018, the company declares a total dividend payment of $ 54 comma 000. What is the amount of dividend that will be paid for each share of common stock? (Round your answer to the nearest cent.)
Answer:
$0.36 per share
Step-by-step explanation:
The data provided in the question are as follows
Common stock outstanding = 50,000 shares
Preferred stock outstanding = 4,000 shares
Par value of common stock = $4
Interest rate and par value of preferred stock = 9% and $100
Total dividend payment declared = $54,000
So, the amount of dividend for each share of common stock is
= (Total dividend payment declared - Preferred stock outstanding × interest rate × par value) ÷ (common stock outstanding)
= ($54,000 - 4,000 × $100 × 9%) ÷ (50,000 shares)
= ($54,000 - $36,000) ÷ (50,000 shares)
= $18,000 ÷ 50,000 shares
= $0.36 per share
Triangles LMN and XYZ are congruent. Write congruence statements comparing the corresponding parts. Then determine which transformation(s) map LMN onto XYZ
Answer:
180 degrees rotation
Step-by-step explanation:
Solution:
- The congruency statements are as follows:
Angles: L ≅ X
M ≅ Y
N ≅ Z
Sides: LM ≅ XY
MN ≅ YZ
LN ≅ XZ
Transformation:
L ( -4 , 1 ) ------- > X ( 4 , - 1 )
( x , y ) -----------> ( -x , -y )
180 degrees rotation
The congruence can be expressed as ∆LMN ≅ ∆XYZ. To map LMN onto XYZ, a transformation like translation, rotation, reflection, or a combination thereof can be used.
If triangles LMN and XYZ are congruent to each other, the corresponding parts must be equal in both measure and shape. The congruence statement for these triangles would be ∆LMN ≅ ∆XYZ, which implies that angle L is congruent to angle X, angle M to angle Y, and angle N to angle Z. Additionally, side LM is congruent to side XY, side MN to side YZ, and side NL to side XZ.
Regarding the transformation that maps triangle LMN onto XYZ, if they are congruent, any of the following rigid motions (also known as isometries) could be used: a translation, a rotation, a reflection, or a combination of these. Since these transformations preserve distance and angle measures, the size and shape of triangle LMN will remain unchanged, and it will match exactly onto triangle XYZ.
Please show your work. Thank you for taking the time of day to help me!
At Best Burgers, Jack collected sales data on the type of side order served with each type of burger purchased for a week.
Jack serves a half pound of onion rings or french fries with every kind of burger.
If Jack sells 120 bacon cheeseburgers total, about how many pounds of onion rings will he serve with them? (round to nearest whole number)
A) 15 pounds
B) 18 pounds
C) 30 pounds
D) 54 pounds
Answer:
30
Step-by-step explanation:
Look at the bottom line of the chart.
He sold 41 sides of French fries and 40 sides of onion rings.
41 + 40 = 81
Since he sold a total of 81 sides with bacon cheeseburgers, that means he sold a total of 81 bacon cheeseburgers.
We have a ratio:
81 bacon cheeseburgers to 40 sides of onion rings
Now he sold 120 bacon cheeseburgers, so we set up a proportion to find the number of sides of onion rings. Let the unknown number be x.
81 burgers is to 40 sides as 120 burgers is to x sides
81/40 = 120/x
We solve for x by cross multiplying.
81x = 40 * 120
81x = 4800
x = 4800/81 = 59.3
That means he serves 59 sides of onion rings.
Each serving of onion rings is half pound.
59 * 0.5 = 29.5
For 120 bacon cheeseburgers, he serves approximately 29.5 lb of onion rings.
Answer: 30
Answer:
30 pounds
Bacon cheeseburger with onion rings:
40
(41 + 40)
=
40
81
= 0.4938
then,
120 x 0.4938 = 59.256
then,
59.256 x .50 = 29.628
Maria received 55% of the vote in a student council election. What decimal and fraction, written in its simplest form, are equivalent to the percentage of the vote maria received
Answer:
The decimal and fraction equivalent to the percentage of the vote maria received is 0.55 and [tex]\frac{11}{20}[/tex] .
Step-by-step explanation:
Given:
Maria received 55% of the vote in a student council election.
Now, to find the decimal and fraction of the percentage of the vote maria received.
Percentage of vote Maria received = 55%.
So, the fraction and decimal of the percentage in its simplest form:
[tex]\frac{55}{100}[/tex]
On simplifying it:
[tex]=\frac{11}{20}[/tex].
Thus, the fraction is [tex]\frac{11}{20} .[/tex]
[tex]\frac{11}{20}[/tex]
[tex]=0.55.[/tex]
Hence in the decimal is [tex]0.55.[/tex]
Therefore, the decimal and fraction equivalent to the percentage of the vote maria received is 0.55 and [tex]\frac{11}{20}[/tex] .
Jerry says I've got my money in a great account that compounds interest monthly. The equation y=388 (1.008) represents how much money I have at the end of the month. What is Jerry 's monthly interest rate? What is his annual interest rate? Write an equation to represent your total money if you invest $500 in an account with the same rate of return .Let m represent the number of months the money has been invested
Answer:
(a)His monthly Interest Rate=0.8%
(b)Annual Interest Rate = 9.6%
(c)[tex]500(1.008)^m[/tex]
Step-by-step explanation:
For a Principal P invested at a yearly rate r, compounded m times in t years
Amount at Compound Interest= [tex]P(1+\frac{r}{m})^{mt}[/tex]
Comparing with Jerry's equation y=388 (1.008)
(a)His monthly Interest Rate= 0.008=0.8%
(b)Annual Interest Rate= Monthly Interest Rate X 12 =0.8 X 12 = 9.6%
(c)If I invest $500 at the same rate of return,
Total Money after m months
= [tex]P(1+\frac{r}{m})^{mt}[/tex][tex]=500(1+0.008)^{m}[/tex][tex]=500(1.008)^m[/tex]
Final answer:
Jerry's monthly interest rate is 0.8%, and his annual interest rate is approximately 9.96%. An investment of $500 in the same account would grow according to the equation [tex]y = 500(1.008)^{m}[/tex], where m represents the months invested.
Explanation:
Jerry says he's got his money in a great account that compounds interest monthly. The equation [tex]y=388(1.008)^{m}[/tex] represents how much money he has at the end of the month. The monthly interest rate is found in the equation inside the parentheses, 1.008, which means the monthly interest rate is 0.8% (since 1.008 is equal to 1 plus 0.008 or 1 + 0.8/100). To find the annual interest rate, we need to use the compounding formula, which for monthly compounding can be simplified to [tex](1 + monthly interest rate)^{12} - 1[/tex]. so, [tex](1.008)^{12}- 1[/tex] gives an annual rate of approximately 9.96%.
To write an equation representing your total money if you invest $500 in an account with the same rate of return, we use the formula [tex]y = P(1 + r)^{m}[/tex], where P is the principal amount ($500), r is the monthly interest rate (0.008), and m represents the number of months the money has been invested. Therefore, the equation is [tex]y = 500(1.008)^{m}[/tex].
To estimate the average annual expenses of students on books and class materials a sample of size 36 is taken. The sample mean is $850 and the sample standard deviation is $54. A 99% confidence interval for the population mean is:_______.A) $823.72 to $876.28.
B) $832.36 to $867.64.
C) $826.82 to $873.18.
D) $825.48 to $874.52.
Answer:
its C i think
Step-by-step explanation:
Biking at 10 mph, it takes Kristen 1/2 hour to reach the train station to go to work. Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 28 mph. How far does Kristen travel to work
Answer: 38 mph
Step-by-step explanation:
Add. 10 plis 28 is 38.
Answer: 19 miles
Step-by-step explanation:
Distance = speed × time
Biking at 10 mph, it takes Kristen 1/2 hour to reach the train station to go to work. This means that the distance covered on her way to the train station is
0.5 × 10 = 5 miles
Kristen then takes the train to work, and it takes another 1/2 hour for her to get to work when the train travels 28 mph. Distance covered by the train is
0.5 × 28 = 14 miles
Therefore, the distance that Kristen travels to work is
14 + 5 = 19 miles
Please help me with this!
Answer:
-540
Step-by-step explanation:
The coefficient of the k-th term of (a+b)^n is nCk. (k = 0, 1, 2, ..., n)
Here, we want the coefficient of a^3b^3 for n=6, so k=3 and the coefficient is ...
6C3 = 6!/(3!(6-3)!) = 5·4 = 20
So for a=3x and b=-y, we want ...
20a^3b^3 = 20(3x)^3(-y)^3 = -540x^3y^2
The coefficient you're looking for is -540.
In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 5.3 and a standard deviation of 2.5. Answer parts (a)dash(d) below. (a) Find the probability that a randomly selected study participant's response was less than 4. The probability that a randomly selected study participant's response was less than 4 is nothing. (Round to four decimal places as needed.)
Answer:
P ( X < 4 ) = 0.3015
Step-by-step explanation:
Given:
- The ratings for current lives on a scale 0 - 10 were normally distributed with parameters mean (u) and standard deviation (s).
u = 5.3
s = 2.5
Find:
Find the probability that a randomly selected study participant's response was less than 4.
Solution:
- Declare a random variable X that follows a normally distribution with parameters u and s, mean and standard deviation respectively.
X~N( 5.3 , 2.5 )
- To determine the probability of the rating to be less than 4 for a randomly selected study participant's response we have:
P ( X < 4 )
- Compute the Z-score value for the limit given:
P ( Z < (4 - 5.3) / 2.5 )
P ( Z < -0.52 )
- Use the Z-Table to calculate the above probability as follows:
P ( Z < -0.52 ) = 0.3015
- Hence, the required probability is equivalent to Z-score value probability:
P ( X < 4 ) = P ( Z < -0.52 ) = 0.3015
The probability that a randomly selected study participant's response was less than 4 is 0.3015.
To find the probability that a randomly selected study participant's response was less than 4, we can use the properties of the normal distribution. Given that the mean is 5.3 and the standard deviation is 2.5, we can standardize the value 4 using the z-score formula: z = (X - µ) / σ, where X is the value of interest, µ is the mean, and σ is the standard deviation. Once we find the z-score, we look up this value in the standard normal distribution table (Z-table) or use a calculator to find the probability.
Step-by-step calculation:Calculate the z-score for X = 4: z = (4 - 5.3) / 2.5 = -0.52.Look up the z-score in the Z-table or use a calculator to find the probability that Z < -0.52.For a z-score of -0.52, the probability is approximately 0.3015 (found from Z-table or through calculator).The probability that a randomly selected study participant's response was less than 4 is therefore 0.3015, or 30.15% when converted into percentage form.
A palindrome is a string whose reverse is identical to the original string. Give examples of bit strings of length 5 and 6 that are palindromes. How many bit string palindromes of length n are there? How many ternary string palindromes of length n are there?
Answer:
The answers to the question are as follows
a). Please see the examples of bit strings of length 5 and 6 that are palindromes in the following explanation.
b). The number of even length palindromes is [tex]26^{\frac{n}{2} }[/tex]
The number of odd length palindromes is [tex]26^{\frac{n+1}{2} }[/tex]
c). The number of ternary string palindromes of length n is 702.
Step-by-step explanation:
a). Examples of bit strings of length 5 and 6 that are palindromes are
Bit strings of length 5 Bit strings of length 6
Kayak Hannah
Level Redder
Civic Terret
Madam Kakkak
Solos degged
Tenet
Rotor
Minim
Radar
Refer
Terret
b). When n is even, we have a choice of any of the 26 characters for the first letter, similarly, we can choose any character for the second, and so on up till the n/2 th position after which subsequent letters depend on the letter chosen before the half point following the definition of a palindrome.
Therefore we have n/2 independent choices with repetition therefore we have [tex]26^{\frac{n}{2} }[/tex] palindromes of even length with or without meaning in the alphabet
On the other hand, when n is odd, we are free to chose any letter up to the middle letter as before this means we have [tex]\frac{n-1}{2} +1 = \frac{n+1}{2}[/tex] free choices
Therefore the number of odd length palindromes are [tex]26^{\frac{n+1}{2} }[/tex]
c). For a ternary string palindrome, we have 26 letters for the first position, and also 26 for the second, while the third is the same as the first which is one option.
Where n = 2 we have 26 ways of selecting the first and second letters which are equal
Therefore the number of ternary string palindromes of length n are 26×26 + 26 = 702
Bit string palindromes of length 5 and 6 are strings that are the same forward and backward, like '10101' or '100001'. The number of palindromic bit strings of length n is 2 raised to the floor of n/2, and the number of ternary string palindromes of length n is 3 raised to the floor of n/2.
Explanation:A palindrome is a string that remains the same when reversed. Examples of bit string palindromes of length 5 include '10001', '01110', '10101', '01010'. For length 6, examples could be '100001', '011110', '101101', '010010'.
In general, to calculate the number of palindromic bit strings for any given length, the first half of the string can be anything (2 ⌊n/2⌋ possibilities), and the second half must mirror the first. Thus there are 2 ⌊n/2⌋ bit string palindromes of length n.
For ternary palindromes (strings composed of the digits 0, 1, and 2), use the same logic but switch the base to 3. Thus there are 3 ⌊n/2⌋ ternary string palindromes of length n.
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The equation Upper A left parenthesis t right parenthesis equals 2000 e Superscript 0.055 t gives the balance after t years of an initial investment of 2000 dollars which pays 5.50% compounded continuously. a. Find a formula for StartFraction dA Over dt EndFraction b. Find and interpret Upper A prime left parenthesis 8 right parenthesis. Include appropriate units. c. Compare the approximation of $171 to the actual change. Report your answer to two decimal places.
Answer:
a) Rate of change of amount
[tex]A'(t) =110e^{0.055t}[/tex]
b) &170.79
c) 0.21
Step-by-step explanation:
We are given the following in the question:
The balance is given by the equation:
[tex]A(t) =- 2000e^{0.055t}[/tex]
where t is the time in years and the initial investment is $2000 when compounded continuously.
a) Rate of change of amount
[tex]\dfrac{d(A(t))}{dt} = \dfrac{d}{dt}(2000e^{0.055t})\\\\\dfrac{d(A(t))}{dt} = 2000e^{0.055t}\times 0.055\\\\\dfrac{d(A(t))}{dt} =110e^{0.055t}[/tex]
b) We have to find the value of A'(8)
[tex]A'(t) =110e^{0.055t}\\A'(8) = 110e^{0.055(8)} = 170.79[/tex]
Interpretation:
The future value of 9 year investment of $2000 will be $170.79 more than the future value of 8 year investment.
c) Comparison
Approximation = $171
Actual change = $170.79
Difference =
[tex]\text{Approximation - Actual change}\\=171 - 170.79\\=0.21[/tex]
Thus, the error is 0.21
The formula for dA/dt is 2000(0.055)e^(0.055t). A'(8) is found by substituting t=8 into dA/dt. To compare the approximation of $171 to the actual change, subtract the initial investment from the new balance after 8 years.
Explanation:a. To find the formula for dA/dt, we differentiate the equation A(t) = 2000e^(0.055t) with respect to t. Using the chain rule, we have dA/dt = 2000(0.055)e^(0.055t).
b. To find A'(8), we substitute t = 8 into the expression for dA/dt. Plugging in the values, we get A'(8) = 2000(0.055)e^(0.055(8)). This will give us the rate of change of the balance after 8 years.
c. To compare the approximation of $171 to the actual change, we subtract the initial investment of $2000 from the new balance after 8 years. The approximation is $171, so the actual change is A(8) - 2000. Plugging in the values, we get A(8) - 2000 = 2000e^(0.055(8)) - 2000.
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Demont made one fourth pound of rock candy.He will separate the candy into four stacks.If he puts an equal amount of candy in each sack,what fraction of a pound of candy will be in each sack.
To determine the amount of candy per sack, divide the total one fourth pound of rock candy by four, resulting in 1/16 pound of candy in each sack.
Explanation:Demont has made one fourth pound of rock candy and needs to divide this equally into four sacks. To find the amount of candy in each sack, we divide the total amount of rock candy by the number of sacks.
Here's the calculation:
Total rock candy = 1/4 pound
Number of sacks = 4
Amount of candy per sack = 1/4 pound ÷ 4 = 1/16 pound per sack
Therefore, each sack will contain 1/16 pound of rock candy.
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75.percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ?
Answer:
33%
Step-by-step explanation:
Assuming the weight of the mixture to be 100g**, then the weight of ryegrass in the mixture would be 30g.
Also, assume the weight mixture X used in the mixture is Xg, then the weight of mixture Y used in the mixture would be (100-X)g.
So we can now equate the parts of the ryegrass in the mixture as:
0.4X + 0.25(100-X) = 30
<=> 0.4X + 25 - 0.25X = 30
<=> 0.15X = 5
<=> X = 5/0.15 = 500/15 = 100/3
So the weight of mixture X as a percentage of the weight of the mixture
= (weight of X/weight of mixture) * 100%
= (100/3)/100 * 100%
= 33%
You invest $3,200 in an account that pays an interest rate of 8.5%, compounded continuously.
Calculate the balance of your account after 6 years. Round your answer to the nearest hundredth.
Answer: the balance is $5328.95
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 3200
r = 8.5% = 8.5/100 = 0.085
t = 6 years
Therefore,
A = 3200 x 2.7183^(0.085 x 6)
A = 3200 x 2.7183^(0.51)
A = $5328.95 to the nearest hundredth
Answer:
FOR PLATO/EDMENTUM USER THE right answer is: 5328.93
Step-by-step explanation:
In a standard normal distribution, the a. mean and the standard deviation are both 1 b. mean is 0 and the standard deviation is 1 c. mean is 1 and the standard deviation is 0 d. mean and the standard deviation can have any value
The mean and standard deviation for the Standard normal distribution is 0 and 1 respectively. Option b is correct.
What is a standard normal distribution?The standard normal distribution is a type of normal distribution that has a mean of 0 and a standard deviation of 1. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centered at zero.
Since the standard normal distribution is a normal distribution curve in which the values of the mean is 0 and the value of The standard normal distribution is a normal distribution curve where the values of the mean and standard deviation is 1.
Thus, the correct option for the given question is Option B.
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In a standard normal distribution, the mean is 0 and the standard deviation is 1. This defines a distribution where data is symmetrically spread around the mean, and a z-score can be used to determine how many standard deviations a value is from the mean.
In a standard normal distribution, the correct answer to the student's question is that the mean is 0 and the standard deviation is 1. This is represented by option b. In a standard normal distribution, often denoted as Z ~ N(0, 1), the mean (μ) equals 0, which signifies that the distribution is centered on the zero point on a number line.
The standard deviation (σ) equals 1, indicating that the values within the distribution are spread out in such a way that one standard deviation away from the mean encompasses approximately 68% of the data in a symmetrical fashion on both sides of the mean.
The concept of z-scores in the context of the standard normal distribution allows for the comparison of different values within different populations. A z-score represents how many standard deviations away a value is from the population mean.
It is crucial to note that the standard deviation cannot be negative; it represents the dispersion of the dataset around the mean, and therefore can only be positive or zero.
A sports survey taken at THS shows that 48% of the respondents liked soccer, 66% liked basketball and 38% liked hockey. Also,30% liked soccer and basketball, 22% liked basketball and hockey, 28% liked soccer and hockey. finally, 12% liked all three sports. A. Draw a. venn diagram to represent the given information. B. What is the probability that a randomly selected student likes basketball or hockey? Solve this by also using an appropriate formula. C. What is the probability that a randomly selected student does not like any of these sports?
Answer:
a) The Venn diagram is presented in the attached image to this answer.
b) 0.82
c) 0.16
Step-by-step explanation:
a) The Venn diagram is presented in the attached image to this answer.
n(U) = 100%
n(S) = 48%
n(B) = 66%
n(H) = 38%
n(S n B) = 30%
n(B n H) = 22%
n(S n H) = 28%
n(S n B n H) = 12%
The specific breakdowns for each subgroup is calculated on the Venn diagram attached.
b) The probability that a randomly selected student likes basketball or hockey.
P(B U H)
From the Venn diagram,
n(B U H) = n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) = 26 + 10 + 18 + 12 + 16 + 0 = 82%
P(B U H) = 82/100 = 0.82
c) The probability that a randomly selected student does not like any of these sports.
P(S' n B' n H')
n(S' n B' n H') = n(U) - [n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) + n(S n B' n H')]
n(S' n B' n H') = 100 - (26 + 10 + 18 + 12 + 16 + 0 + 2) = 100 - 84 = 16%
P(S' n B' n H') = 16/100 = 0.16
Write the quadratic function in standard form.
y=2(x - 3)² +9
Answer:
y = 2x^2 - 12x + 27
Step-by-step explanation:
Step 1: Distribute the power
y = 2(x - 3)² + 9
y = 2(x^2 - 6x + 9) + 9
y = 2x^2 - 12x + 18 + 9
y = 2x^2 - 12x + 27
Answer: y = 2x^2 - 12x + 27
need help fast, please help
Yo sup??
by Pythagoras theorem we can say
38²=34²+b²
b²=1444-1156
=288
b=17
Hope this helps
Answer:
D = 17
Step-by-step explanation:
Hope this helps
Compute the amount of interest earned in the following simple interest problem A deposit of $1,295 at 7% for 180 days
Answer: the amount of interest earned is $44.7
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount deposited.
P represents the principal or amount deposited.
R represents interest rate
T represents the duration in years.
From the information given,
P = $1295
R = 7%
T = 180 day. Assuming there are 365 days in a year. Converting 180 days to years, it becomes
180/365 = 0.49315 year
Therefore,
I = (1295 × 7 × 0.49315)/100 = $840,
I = $44.7
Angle x is a third quadrant angle such that cos x= −2/5 .
What is the exact value of cos(x/2) ?
Enter your answer, in simplest radical form, in the box.
cos(x/2) =
Answer:
-√(3/10)
Step-by-step explanation:
cos(x) = 2[cos(x/2)]² - 1
-2/5 = 2[cos(x/2)]² - 1
3/5 = 2[cos(x/2)]²
3/10 = [cos(x/2)]²
cos(x/2) = +/- sqrt(3/10)
Since x is in the 3rd quadrant, x/2 would be in the second quadrant.. so cos(x/2) is negative
[tex]x[/tex] is in quadrant III, so [tex]\pi<x<\frac{3\pi}2[/tex].
This makes [tex]\frac\pi2<\frac x2<\frac{3\pi}4[/tex], which means [tex]\frac x2[/tex] lies in quadrant II, for which we expect [tex]\cos\frac x2<0[/tex].
Recall the double-angle identity:
[tex]\cos^2\dfrac x2=\dfrac{1+\cos x}2[/tex]
[tex]\implies\cos\dfrac x2=-\sqrt{\dfrac{1-\frac25}2}=-\sqrt{\dfrac3{10}}[/tex]
Find the value of each variable in the parallelogram
pls help:)
Answer:
Step-by-step explanation:
In a parallelogram, the opposite sides are equal and parallel.
Also, consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.
Angle 2m and angle n are supplementary angles. Therefore,
2m + n = 180 - - - - - - - - - - - -1
Also, the opposite angle in a parallelogram are equal. This means that
2m = 70
m = 70/2
m = 35 degrees
Substituting m = 35 into equation 1, it becomes
2 × 35 + n = 180
70 + n = 180
n = 180 - 70
n = 110 degrees
The value of m and n are 35 and 110 respectively.
We are given that one of the angles of the parallelogram is [tex]70^\circ[/tex].
Since opposite angles in a parallelogram are supplementary, the angle directly opposite the 70° angle must be [tex]180^\circ -70^\circ = 110^\circ[/tex].
We are also given that one of the non-consecutive interior angles has a measure of 2m°.
Since consecutive interior angles in a parallelogram add up to 180°, the angle next to the 2m° angle must have a measure of 180°- 2m°.
The opposite sides of a parallelogram are congruent.
This means that n° must be congruent to 110°. So, n = 110.
We can now solve for 'm'.
Since the angle next to the 2m° angle must have a measure of 180°−2m° and this angle is also congruent to 110°.
We have the equation: [tex]110^\circ = 180^\circ - 2m^\circ[/tex]
[tex]2m^\circ = 70^\circ[/tex]
[tex]m=35[/tex]
please help me with this question
Answer:
Step-by-step explanation:
Haven't seen a related rates problem in a while! These are fun! Not too bad when you keep your stuff organized. First, label what you've been given. If the radius is decreasing, then we have
[tex]\frac{dr}{dt}=-.2[/tex]
We are told to find [tex]\frac{dV}{dt}[/tex] when r = 9.
Now we have to find the derivative of the volume of a sphere using implicit differentiation. The derivative is
[tex]\frac{dV}{dt}=\frac{4}{3}\pi3r^2\frac{dr}{dt}[/tex]
It looks like we have everything we need to solve for the unknown. The derivative is even already set up to solve for the change in volume. All we have to do now is plug in the values.
[tex]\frac{dV}{dt}=\frac{4}{3}\pi3(81)(-.2)[/tex]
This does give us a negative number, -203.575 to be exact, but if you answer it without the negative, you say that the volume is decreasing at the rate of 203.575 cm/min cubed
Mr. Burk traveled 240 miles last weekend. His average rate of speed for the trip was 70 miles per hour. Since he did not stop, about how many hours long was his trip?
Answer:
about 3 1/2 hours long
Step-by-step explanation:
70 goes into 240 evenly 3 times, and 70×3 equals 210. that leaves 30 miles remaining. since he is moving at an average rate of 70mph, 3/7 would be the remaining time. to decimal that equals a total of about 3 hours and 25 minutes, which, rounded up, equals 3 and 1 half hours.
Linda Johnson, a broker, sold a home for $85,000. The home had been listed with another real estate firm for a 7% commission. The commission split between Johnson's principal broker and the other principal broker was 50/50. The commission split between Johnson and her principal broker was 65% to the broker, 35% to the principal broker. What was Johnson's commission from the sale of the home
Answer:
Linda's share was $ 1933.75
Step-by-step explanation:
We first need to calculate the comission that was paid to the other real state firm wich is 7% of the sales price, so we can use the following equation:
Comission = 85000 * (7/100) = 85000*0.07 = 5950 $
Since this comission was split in half between Johnson's broker and the other broker we have 5950/2 = 2975 for each of them. From that value 65% should stay with the broker wich is Linda in this case so:
Linda's share = 2975*(65/100) = 2975*(0.65) = 1933.75 $.
Given Information:
Sale Amount = $85,000
Commission rate = 7%
Linda Johnson commission rate = 65% of 50% of commission amount
Required Information:
Linda Johnson share in the sale = ?
Answer:
Linda Johnson share in the sale = $1933.75
Step-by-step explanation:
Linda Johnson share in the sale is
Linda's share = 65% of 50% of commission amount
Where commission amount is
commission amount = 7% of sale amount
commission amount = 0.07*85,000
commission amount = $5,950
Linda's share = 0.65*0.50*5,950
Linda's share = $1933.75
Twin brothers, Billy and Bobby, kid mother grandparents lawn together for 60 minutes. Billy could mow the lawn by himself in 20 minutes less time then it would take Bobby. How long will it take Bobby to mow the lawn by himself
Answer:
Bobby around 131 minutes and Billy around 111 minutes
Step-by-step explanation:
To solve the problem it is important to raise equations regarding what happens.
They tell us that Billy (Bi) and Bobby (Bo) can mow the lawn in 60 minutes. That is to say that what they prune in a minute is giving as follows:
1 / Bo + 1 / Bi = 1/60 (1)
They say Billy could mow the lawn only in 20 minutes less than it would take Bobby, therefore
1 / Bi = 1 / (Bo-20) (2)
Replacing (2) in (1) we have:
1 / Bo + 1 / (Bo-20) = 1/60
Resolving
(Bo - 20 + B0) / (Bo * (Bo-20) = 1/60
120 * Bo - 1200 = Bo ^ 2 - 20Bo
Rearranging:
Bo ^ 2 - 140Bo -1200 = 0
Now applying the general equation
Bo = 130.82 or Bo = 9.17, this last value cannot be because Billy took 20 minutes less and neither can he prune faster than the two together, therefore Bobby only takes around 131 minutes and Billy around 111 minutes
Checking with equation 1:
1/131 +1/111 = ~ 1/60
Final answer:
Bobby would take 120 minutes to mow the lawn by himself.
Explanation:
The question asks us to calculate how long it will take Bobby to mow the lawn by himself if it takes his twin brother Billy 20 minutes less to do the job on his own, and they can mow the lawn together in 60 minutes. To solve this, we can use the concept of work rate and the idea that the combined work rate of Billy and Bobby equals the reciprocal of the time they take to work together.
Let's assume Bobby takes x minutes to mow the lawn by himself. Thus, Billy would take x - 20 minutes. We can express their work rates as:
Bobby's work rate: 1/x lawn/minuteBilly's work rate: 1/(x - 20) lawn/minuteThe combined work rate when they mow together is the sum of their individual work rates, which is equal to 1/60 since they take 60 minutes together. So, we have:
1/x + 1/(x - 20) = 1/60
By solving this equation for x, we find the time it takes Bobby to mow the lawn by himself.
Multiply through by 60x(x - 20) to clear the denominators:60(x - 20) + 60x = x(x - 20)60x - 1200 + 60x = x^2 - 20xCombine like terms:x^2 - 140x + 1200 = 0Solve for x using the quadratic formula or by factoring:(x - 120)(x - 10) = 0Therefore, x = 120 or x = 10. Since x has to be greater than 20, x = 120 is the correct solution.Hence, Bobby will take 120 minutes to mow the lawn by himself.
Sin * (x - y) , if sin x = 8/17 cos y = 12/37
Answer:
-429/629
Step-by-step explanation:
Use angle difference formula:
sin(x − y) = sin x cos y − sin y cos x
Assuming x and y are in the first quadrant:
sin(x − y) = sin x cos y − √(1 − cos²y)√(1 − sin²x)
Plugging in values:
sin(x − y) = (8/17) (12/37) − √(1 − (12/37)²)√(1 − (8/17)²)
sin(x − y) = (8/17) (12/37) − (35/37)(15/17)
sin(x − y) = -429/629
Faculty members at Lowell Place High School want to determine whether there are enough students to have a Valentine's Day Formal. Eighty-eight of the 200 students said they would attend the Valentine's Day Formal. Construct and interpret a 90% confidence interval for p.
Answer:
The 90% confidence interval is (0.383,0.497)
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 200
Number of children that would attend Valentine's Day Forma, x = 88
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{88}{200} = 0.44[/tex]
90% Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = \pm 1.64[/tex]
Putting the values, we get:
[tex]0.44\pm 1.64(\sqrt{\dfrac{0.44(1-0.44)}{200}}) = 0.44\pm 0.057\\\\=(0.383,0.497)[/tex]
Interpretation:
The 90% confidence interval is (0.383,0.497). We are 90% confident that the proportion of children attending Valentine's Day Formal is between 38.3% and 49.7%
The sum of the differences must be zero for any distribution consisting of n observations.
A. True
B. False
Answer:
false
Step-by-step explanation:
Suppose parametric equations for the line segment between (6,9) and (0,0) have the form: x = a+bt y = c+dt If the parametric curve starts at (6,9) when t=0 and ends at (0,0) at t=1, then find: a = b = c = d =
What is 0.05 Equal to 0.5.
Please help I dont know where to start
the standard deviation of a simple random sample of 40 calling times on a payphone is found to be 2.6 minutes. find the test statistic to test a claim that the standard deviation of all phone calls on a payphone is less than 2.9 minutes. use a 0.05 significance level
32.152
31.348
48.519
34.966
Answer:
Option B) 31.348
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 49
Sample standard deviation, s = 2.6 minutes
Population standard deviation, [tex]\sigma[/tex] = 2.9 minutes
Significance level, [tex]\alpha[/tex] = 0.05
We have o find the test statistic.
Formula:
[tex]\chi^2 = \dfrac{(n-1)s^2}{\sigma^2}\\\\\chi^2 =\displaystyle\frac{(40-1)(2.6)^2}{(2.9)^2}\\\\\chi^2=31.348[/tex]
Thus, the test statistic is
Option B) 31.348