Answer:
16
Step-by-step explanation:
Let x and y be two numbers other than 12.
We have been given that the average (arithmetic mean) of three positive numbers is 10. We can represent this information in an equation as:
[tex]\frac{x+y+12}{3}=10[/tex]
We are also told that the product of the other two numbers is 32. We can represent this information in an equation as:
[tex]x\cdot y=32...(2)[/tex]
[tex]x=\frac{32}{y}[/tex]
Upon substituting this value in above equation, we will get:
[tex]\frac{\frac{32}{y}+y+12}{3}=10[/tex]
[tex]\frac{\frac{32}{y}\cdot y+y\cdot y+12\cdot y}{3}=10\cdot y[/tex]
[tex]\frac{32+y^2+12y}{3}=10y[/tex]
[tex]\frac{32+y^2+12y}{3}\cdot 3=10y\cdot 3[/tex]
[tex]32+y^2+12y=30y[/tex]
[tex]y^2+12y-30y+32=30y-30y[/tex]
[tex]y^2-18y+32=0[/tex]
[tex]y^2-16y+2y+32=0[/tex]
[tex]y(y-16)-2(y-16)=0[/tex]
[tex](y-16)(y-2)=0[/tex]
[tex]y=2, 16[/tex]
Since product of 2 and 16 is 32, therefore, the greatest of the three numbers would be 16.
Answer:
The greatest of the three number is 16.
Step-by-step explanation:
We are given the following in the question:
Let x and y be the two numbers.
[tex]\text{Mean} = \dfrac{12+x+y}{3} = 10\\\\12 + x + y = 30\\x + y = 18[/tex]
Also
[tex]xy = 32[/tex]
Puting values, we get,
[tex]x(18-x) = 32\\-x^2 + 18x - 32 = 0\\x^2 - 18x + 32 = 0\\(x-16)(x-2) = 0\\x = 16, x = 2[/tex]
When x = 16, y = 2
When x = 2, y = 16
Thus, the greatest of the three number is 16.
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.
Learn more about Continuous Compounding here:https://brainly.com/question/36501885
#SPJ3
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
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.
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
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.
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.
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.
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.
Use the following information to complete parts I, II, and III. 1 hour=3600 seconds
1 year = 31556952 secondsI. Use scientific notation to estimate the number of hours in one year. II. Use scientific notation to calculate the exact number of hours in one year. III. In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.
Answer:
I) There are [tex]8.760\times 10^3[/tex] hours in 1 year.
II) The exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.
Step-by-step explanation:
Given : 1 hour=3600 seconds
1 year = 31556952 seconds.
To find :
I) Use scientific notation to estimate the number of hours in one year.
1 day = 24 hours
1 year = 365 days
So, number of hours in one year is given by,
[tex]n=24\times 365[/tex]
[tex]n=8760[/tex]
In scientific notation,
[tex]8760=8.760\times 10^3[/tex]
So, there are [tex]8.760\times 10^3[/tex] hours in 1 year.
II) 1 year = 31556952 seconds.
1 hour = 3600 seconds
In one year the number of hour is given by,
[tex]n=\frac{31556952}{3600}[/tex]
[tex]n=8765.82[/tex]
In scientific notation,
[tex]8765.82=8.76582\times 10^3[/tex]
So, the exact number of hours in one year is [tex]8.76582\times 10^3[/tex] hours.
III) In two or more complete sentences, compare your answers to parts I and II. In your comparison, discuss similarities and differences.
The exact numbers of hours using 365 days is 8760 which is written as [tex]8.760\times 10^3[/tex] in scientific notation but using the given data we get [tex]8.76582\times 10^3[/tex] hours.Comparing these answers the first one has only 3 significant figures and the second answer has six significant figures.If we round these we get [tex]8.8\times 10^3[/tex] hours which has two significant numbers.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%
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
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 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
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
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:
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:
The internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0. How many different numbers can be assigned in this system?
Answer:
This system have 9000 different numbers.
Step-by-step explanation:
We know that the internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0.
We have total 10 digits.
In the first place we have 9 possibilities, because from the conditions of the task in the first place there cannot be 0.
In second, third and fourth place we have 10 possibilities.
Therefore, we get
[tex]N=9\cdot 10\cdot10 \cdot 10=9000[/tex]
This system have 9000 different numbers.
In this phone system, there are 9,000 different internal telephone numbers that can be assigned.
Explanation:The internal telephone numbers in the phone system on a campus consists of 4 digits, with the 1st not equal to 0. To find the number of different numbers that can be assigned in this system, we need to consider the possibilities for each digit position. Since the first digit cannot be 0, there are 9 choices (1 through 9) for the first digit. For the remaining three digits, each digit can be any number from 0 to 9, resulting in 10 choices for each of the three remaining digits. Therefore, the total number of different numbers that can be assigned in this system is
9 * 10 * 10 * 10 = 9,000.
Learn more about internal telephone numbers here:https://brainly.com/question/14986306
#SPJ12
PLEASE HELP ASAP!!!! WILL MARK BRAINLIEST
Answer:
Boi
Step-by-step ex:
Answer:
Option 4
Step-by-step explanation:
x - 4 is negative for x < 4
Mod makes it positive,
-(x - 4) = 4 - x
4 - x for x < 4,
x - 4 for other x values (which are greater than/equal to 4)
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.
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ5
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.
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:
A fruit drink company tested a new flavor .In a test 46% of the people talking part liked the new flavor.If 69 people liked the new flavor, how many people took the test
Answer:
150 people took the test.
Step-by-step explanation:
Given:
Number of people liked the new flavor = 69
Percentage of people liked the new flavor = 46%
We need to find the number of people who took the test.
Solution:
Let the number of people who took the test be 'x'.
So we can say that;
Percentage of people liked the new flavor multiplied by the number of people who took the test is equal to Number of people liked the new flavor.
framing in equation form we get;
[tex]46\%\times x =69\\\\\frac{46}{100}x=69\\\\0.46x =69[/tex]
Dividing both side by 0.46 we get;
[tex]\frac{0.46x}{0.46}=\frac{69}{0.46}\\\\x= 150[/tex]
Hence 150 people took the test.
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%
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]
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 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
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
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]
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
The height of a rectangular prism is 20cm. It has a surface area of 2400 square centimeters. What are two possible sets of lengths and widths? Find one set of dimensions with l and w equal in length as well as a set dimensions that are not equal
Step-by-step explanation:
Below is an attachment containing the solution.
Final answer:
The dimensions are 24cm x 15cm x 20cm.
Explanation:
To find two possible sets of lengths and widths for the rectangular prism with a height of 20cm and a surface area of 2400cm2, we need to understand the formula for the surface area of a rectangular prism: SA = 2(lw + lh + wh). Here, l = length, w = width, and h = height.
Since we know the height (h = 20cm) and the surface area (SA = 2400cm2), we can set up the equation:
2(lw + 20l + 20w) = 2400
We will consider two cases: one where the length and width are equal (since that is a specific request), and another where they are not.
Case 1: Length and width are equal (l = w). We simplify the equation to:
2(l2 + 40l) = 2400
Solving for l gives us l = w = 20cm. Therefore, the dimensions are 20cm x 20cm x 20cm.
Case 2: Length and width are not equal. To find a possible set, we can assume a width and solve for the length:
Let's assume w = 15cm. Plugging this into the equation gives us:
2(l15 + 20l + 20 x 15) = 2400
Solving for l gives us l = 24cm.
Therefore, the dimensions are 24cm x 15cm x 20cm.
Which polygons are congruent?Select each correct answer. Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark. a rhombus with all sides marked 15 units long. a square with two sides marked 15 units and four right angles. Two rectangles labeled B M D J and K Z Y A. Sides B M and D J are each labeled twelve, and sides D M and J B are each labeled six. Side K Z and side Y A are each labeled four. Side Y Z and side K A are each labeled three. All angles in both rectangles are right angles.
Answer:
Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark.
Answer:
b m d j and k z y a
Step-by-step explanation: