Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product by first multiplying the coefficients...then adding your "like term" angles...for instance, cos (2pi/5) + cos (-pi/2) = cos (2pi/5 + -pi/2)...then use the calculator in RADIAN mode to evaluate." Doing those steps, I got the correct constant but a coefficient that was completely off. For the second one, I was told "Good effort...express the quotient by first dividing the coefficients...then subtract your "like term" angles...for instance, cos (2pi/5) - cos (-pi/2) = cos (pi/6 - pi/3)...Finally, use the calculator (in radian MODE) to evaluate."
Answers
Answer:
Solution ( Second Attachment ) : - 2.017 + 0.656i
Solution ( First Attachment ) : 16.140 - 5.244i
Step-by-step explanation:
Second Attachment : The quotient of the two expressions would be the following,
[tex]6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,
( 1 ) cos(x) = sin(π / 2 - x)
( 2 ) sin(x) = cos(π / 2 - x)
If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,
( 1 ) [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]
( 2 ) [tex]\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}[/tex]
These two identities makes sin(π / 10) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and cos(π / 10) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex].
Therefore cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]. Substitute,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex]
And now simplify this expression to receive our answer,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex] = [tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i[/tex],
[tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}[/tex] = [tex]-2.01749\dots[/tex] and [tex]\:\frac{3\sqrt{3-\sqrt{5}}}{4}[/tex] = [tex]0.65552\dots[/tex]
= [tex]-2.01749+0.65552i[/tex]
As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.
________________________________________
First Attachment : We know from the previous problem that cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex], cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,
[tex]6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}[/tex]
We know that [tex]6\sqrt{5+\sqrt{5}} = 16.13996\dots[/tex] and [tex]-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots[/tex] . Therefore,
Solution : [tex]16.13996 - 5.24419i[/tex]
Which rounds to about option b.
Related Questions
Given the function f ( x ) = 2 x + 8 , evaluate and simplify the expressions below. See special instructions on how to enter your answers.
Answers
Answer:
[tex]f(a) = 2a + 8[/tex]
[tex]f(x + h) = 2x + 2h + 8[/tex]
[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x + 8[/tex]
Required
[tex]f(a)[/tex]
[tex]f(x + h)[/tex]
[tex]\frac{f(x + h) - f(x)}{h}[/tex]
Solving for f(a)
Substitute a for x in the given parameter
[tex]f(x) = 2x + 8[/tex] becomes
[tex]f(a) = 2a + 8[/tex]
Solving for f(x+h)
Substitute x + h for x in the given parameter
[tex]f(x + h) = 2(x + h) + 8[/tex]
Open Bracket
[tex]f(x + h) = 2x + 2h + 8[/tex]
Solving for [tex]\frac{f(x + h) - f(x)}{h}[/tex]
Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)
[tex]\frac{f(x + h) - f(x)}{h}[/tex] becomes
[tex]\frac{2x + 2h + 8 - (2x + 8)}{h}[/tex]
Open Bracket
[tex]\frac{2x + 2h + 8 - 2x - 8}{h}[/tex]
Collect Like Terms
[tex]\frac{2x - 2x+ 2h + 8 - 8}{h}[/tex]
Evaluate the numerator
[tex]\frac{2h}{h}[/tex]
[tex]2[/tex]
Hence;
[tex]\frac{f(x + h) - f(x)}{h} = 2[/tex]
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?
Answers
Complete Question
Two samples from the same population both have M = 84 and s2 = 20, but one sample has n = 10 and the other has n = 20 scores. Both samples are used to evaluate a hypothesis stating that μ = 80 and to compute Cohen’s d. How will the outcomes for the two samples compare?
a.
The larger sample is more likely to reject the hypothesis and will produce a larger value for Cohen’s d.
b.
The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.
c.
The larger sample is less likely to reject the hypothesis and will produce a larger value for Cohen’s d.
d.
The larger sample is less likely to reject the hypothesis, but the two samples will have the same value for Cohen’s d.
Answer:
The Cohen's d value is [tex]d = 0.895[/tex]
The correct option is b
Step-by-step explanation:
From the question we are told that
The sample mean of each population is [tex]M = 84[/tex]
The variance of each population is [tex]s^2 = 20[/tex]
The first sample size is [tex]n_1 = 10[/tex]
The second sample size is [tex]n_2 = 20[/tex]
The null hypothesis is [tex]H_o : \mu = 80[/tex]
Generally the standard deviation is mathematically evaluated as
[tex]s = \sqrt{20 }[/tex]
=> [tex]s = 4.47[/tex]
The first test statistics is evaluated as
[tex]t_1 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_1} } }[/tex]
=> [tex]t_1 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{10} } }[/tex]
=> [tex]t_1 = 2.8298[/tex]
The second test statistics is evaluated as
[tex]t_2 = \frac{M - \mu }{ \frac{\sigma }{ \sqrt{n_2} } }[/tex]
=> [tex]t_2 = \frac{84 - 80 }{ \frac{4.47 }{ \sqrt{20} } }[/tex]
=> [tex]t_2 = 4.0[/tex]
The sample with the larger test statistics (sample size) will more likely reject the null hypothesis
Generally the Cohen's d value is mathematically evaluated as
[tex]d = \frac{M - \mu }{s }[/tex]
=> [tex]d = \frac{ 84 - 80 }{4.47 }[/tex]
=> [tex]d = 0.895[/tex]
Given that the the sample mean and sample size are the same for both sample the Cohen's d value will be the same
Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order both a square pizza and a soft drink.
Required:
Is ordering a soft drink independent of ordering a square pizza? Explain
Answers
Answer:
Ordering a soft drink is independent of ordering a square pizza.
Step-by-step explanation:
20% more customers order a soft drink than pizza, therefore they cannot be intertwined.
Given: P(A)=0.5 & P(B)=.7
P(A∩B) = P(A) × P(B)
= 0.5 × .7
= 0.35
P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.5 + .7 - 0.35
= 0.85
P(AΔB) = P(A) + P(B) - 2P(A∩B)
= 0.5 + .7 - 2×0.35
= 0.5
P(A') = 1 - P(A)
= 1 - 0.5
= 0.5
P(B') = 1 - P(B)
= 1 - .7
= 0.3
P((A∪B)') = 1 - P(A∪B)
= 1 - 0.85
= 0.15
Yes ordering a soft drink is independent of ordering a square pizza.
We have given 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order both a square pizza and a soft drink.
Let A: denote pizza
B: Soft drink
Then,
P(A)=0.5 and P(B)=0.7
And P(A∩B) = P(A) × P(B)
= 0.5 × 0.7
= 0.35
We know P(A∪B) = P(A) + P(B) - P(A∩B)
= 0.5 + 0.7 - 0.35
= 0.85
P(AΔB) = P(A) + P(B) - 2P(A∩B)
= 0.5 + 0.7 - 2×0.35
= 0.5
Also we know P(A') = 1 - P(A)
= 1 - 0.5
= 0.5
And P(B') = 1 - P(B)
= 1 -0.7
= 0.3
And P((A∪B)') = 1 - P(A∪B)
= 1 - 0.85
= 0.15
Learn more:https://brainly.in/question/16017018
Find the indicated complement. A certain group of women has a 0.12% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
Answers
Answer:
the probability will be 0.
Step-by-step explanation:
0.12%= 0.0012= 3/2500.
Ted has to gift wrap a box of chocolates that is shaped like a triangular prism. What is the minimum amount of wrapping paper he needs?
Answers
Answer:
69.48 square inches
Step-by-step explanation:
The amount of wrapping paper needed = surface area of the triangular prism
Surface area of triangular prism is given as, area = Perimeter of triangular base*height of prism + 2(base area)
Perimeter of triangular base = sum of the 3 sides of the prism
Perimeter of base = 3.5 + 3.5 + 3 = 10 inches
Height of prism = 6 inches
Base area = ½*base of triangle * height of triangle = ½*3*3.16 = 4.74 in²
Surface area of triangular prism = [tex] 10*6 + 2(4.74) [/tex]
[tex] S.A = 60 + 9.48 = 69.48 in^2[/tex]
Amount of wrapping paper needed is 69.48 square inches .
An opinion poll asked a random sample of adults whether they believe flu shots are ineffective in the United States. A commentator believes less than 35% of all adults believe they are ineffective. Which null and alternative hypotheses should be used to test this claim? H0: p ≠ 0.35, Ha: p 0.35
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
The second option is the correct option
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\r p = 0.35[/tex]
The Null Hypothesis is [tex]H_o : \r p = 0.35[/tex]
The reason for this is that the this original claim when represented mathematically does not contain an equality sign ([tex]i.e \ it \ is \ mathematically \ represented \ as \ \r p < 0.35[/tex]) so the null hypothesis is the compliment of it ( i.e [tex]\r p = 0.35[/tex])
The Alternative hypothesis is [tex]H_a : \r p < 0.35[/tex]
Suppose your weekly local lottery has a winning chance of 1/106. You buy lottery from them for x weeks in a row. What is the probability that you never win?
Answers
Answer:
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]
Step-by-step explanation:
Given that;
the winning chance of a weekly local lottery = [tex]\dfrac{1}{10^6}[/tex]
= [tex]\dfrac{1}{1000000}[/tex]
The probability of losing = 1 - probability of winning (winning chance)
The probability of losing = [tex]1- \dfrac{1}{1000000}[/tex]
The probability of losing =[tex]\dfrac{999999}{1000000}[/tex]
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{1}{10^6} )^0 ( \dfrac{999999}{1000000})^x[/tex]
The probability mass function that you never win [tex]^xC_o[/tex] = [tex](\dfrac{999999}{1000000})^x[/tex]
if pentagon OPQRS is dilated by a scale factor or ?
from the origin to create O'P'Q'R'S: what is the ordered pair of point S'?
Answers
Answer:
Option (D) : (3.5, 8.75)
A researcher wishes to see if the average weights of newborn male infants are higher than the
average weights of newborn female infants. She selects a random sample of 12 male infants and
finds the mean weight is 7.70 pounds. She selects a random sample of 9 female infants and finds
that the mean Leight is 7.80 pounds. Assume that the variables are normally distributed and the
population standard deviation is 0.5 for each group.
Using alpha=0.05 to test if the mean weight of the males is higher than the mean weight of the
females, the pvalue of the test is:
Answers
Answer:
The p-value is [tex]p-value = 0.62578[/tex]
Step-by-step explanation:
From the question we are told that
The sample size of male infant is [tex]n_1 = 12[/tex]
The sample size of female infant is [tex]n_2= 9[/tex]
The sample mean of male infant is [tex]\= x_1 = 7.70 \ lb[/tex]
The sample mean of female infant is [tex]\= x_2 = 7.80 \ lb[/tex]
The population standard deviation is [tex]\sigma = 0.5[/tex]
The significance level is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu_ 1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_1 : \mu_1 > \mu_2[/tex]
The test statistics is mathematically represented as
[tex]t =\frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma }{n_1} } + \frac{\sigma }{n_2} } }[/tex]
=> [tex]t = \frac{7.70 -7.80}{\sqrt{\frac{0.5 }{12} } + \frac{0.5 }{9} } }[/tex]
=> [tex]t = -0.3207[/tex]
From the z-table the p-value is obtained, the value is
[tex]p-value = P(Z > -0.3207) = 0.62578[/tex]
[tex]p-value = 0.62578[/tex]
HELPP PLEASEE ��2222 is the diameter of a circle. The coordinates are �(−2, −3) and �(−12, −5). At what coordinate is the center of the circle located? A. (5, 1) B. (−5, −1) C. (−4, −7) D. (−7, −4)
Answers
Answer:
(-7, -4) which is your answer D in the list of options
Step-by-step explanation:
The center of the circle should be located half way in between the given points on the plane.
Then the center ahs to be located half way for the x coordinates of both points:
half way between -12 and -2 (notice that there is a difference of 10 units between them), therefore half way would be at 5 units to the right from the furthest point, that is -12 + 5 = -7
Similarly, for the y coordinate, we see that the difference is between -5 and -3 (a difference of two units) therefore the center point will be located half way (that is one unit) up from the lowest y coordinate: -5 + 1 = -4
Then the center of the circle is located at (-7, -4)
A truck carries 360 crates of avocados to a grocery distribution center. If there are 8640 avocados total, how many avocados are in each crate?
Answers
Answer:
There are 24 avocados in each crate.
Step-by-step explanation:
This is a division problem.
8640/360 = 24
There are 24 avocados in each crate.
The Masim family’s monthly budget is shown in the circle graph provided in the image. The family has a current monthly income of $5,000. How much money do they spend on food each month? A. $250 B. $500 C. $750 D. 1,100 Please show ALL work! <3
Answers
Answer:
C. $750
Step-by-step explanation:
The amount of money to be spent monthly on food = percentage covered by food in the circle ÷ 100% × total monthly income
= [tex] \frac{15}{100}*5000 [/tex]
[tex] = \frac{15}{1}*50 [/tex]
[tex] 15*50 = 750 [/tex]
Amount of money spent each month by the Masims is $750.
If x represents the rate that Joy traveled at for the first half of the trip, write an
expression that represents the amount of time it takes Joy to complete the second half of the
trip at the slower rate.
Answers
Answer:
time taken for trip 2nd half > time taken for trip 1st half
Step-by-step explanation:
Let the total distance of Joy's trip be = D
Then, the first half distance travelled = D/2
The rate (speed) at which Joy travels during first half = x
So, time taken to travel first half = Distance / Speed
= (D/2) / x = D / 2x
Second half of trip distance travelled = remaining D/2Let the rate (speed) at which Joy travels during second half = x'
As given, x' (second half speed) < x (first half speed)
So, time taken to travel first half = Distance / Speed
(D/2) / x' = D / 2x'
As x' < x : D / 2x' > D / 2x .
Trip 1st half Time taken trip < 2nd half ; or trip 2nd half time taken > 1st half
A market survey shows that 50% of the population used Brand Z computers last year, 4% of the population quit their jobs last year, and 2% of the population used Brand Z computers and then quit their jobs. Are the events of using Brand Z computers and quitting your job independent
Answers
Answer:
the events of using Brand Z computers and quitting your job are independent.
Step-by-step explanation:
Let A be the event that the population used Brand Z computers and let B be the event that the population quit their jobs.
We are told that 50% of the population used Brand Z computers last year. Thus, the probability of event A is;
P(A) = 50% = 0.5
Also, we are told that 4% of the population quit their jobs last year. Thus the probability of event B is;
P(B) = 4% = 0.04
Since 2% of the population used Brand Z computers and then quit their jobs. Then the probability of the population used Brand Z computers and then quit their jobs is;
P(A ∩ B) = 2% = 0.02
From the law of independent events, if A and B are to be independent events, then;
P(A ∩ B) = P(A) × P(B)
Thus;
P(A ∩ B) = 0.5 × 0.04 = 0.02
This is same value as what was given in the question, thus the events of using Brand Z computers and quitting your job are independent.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Years in which U.S. presidents were inaugurated
Answers
Answer:
Interval Level of Measurement
Step-by-step explanation:
The Interval level of measurement highlights the distances between two measurements. These distances are meaningful and could be rated as low intervals or high intervals. Intervals also indicate class and order between measurements. The inauguration of the United States President is an event that occurs 72 to 78 days after the presidential election. It is usually done as a private and public oath-taking ceremony on January 20, four years after the last presidential election. So, even if the president is on a second term, this event must be held.
The last U.S presidential election occurred on January 20, 2017, and the next one will be held on January 21, 2021. So there is an interval of four years between the last and next U.S presidential inauguration ceremony.
CD is the perpendicular bisector of XY Determine the value of x. Question 8 options: A) –2 B) –1∕2 C) 4 D) 1.25
Answers
Answer:
Step-by-step explanation:
12x - 9 = 8x + 7
4x - 9 = 7
4x = 16
x = 4
solution is C
The solution is Option C.
The value of x is given from the equation x = 4
What is perpendicular bisector?A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.
The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn
Given data ,
Let the first line be represented as CD
Let the second line be represented as XY
Now , CD is the perpendicular bisector of XY
So , the point F is the midpoint of the line segment XY
The measure of line segment XF = 12x - 9
The measure of line segment FY = 8x + 7
From the perpendicular bisector theorem ,
The measure of line segment XF = The measure of line segment FY
Substituting the values in the equation , we get
12x - 9 = 8x + 7
Subtracting 8x on both sides of the equation , we get
4x - 9 = 7
Adding 9 on both sides of the equation , we get
4x = 16
Divide by 4 on both sides of the equation , we get
x = 4
Therefore , the value of x = 4
Hence , the value of the equation is x = 4
To learn more about perpendicular bisectors click :
https://brainly.com/question/4137998
#SPJ2
Use the probability distribution table to answer the question.
What is P(1 < X < 5)?
Enter your answer, as a decimal, in the box.
Answers
Add up the P(x) values that correspond to x = 2 through x = 4
0.07+0.22+0.22
So we have a 51% chance of getting an x value such that 1 < x < 5
By using the probability distribution table, the value of P(1<x<5) is 0.51
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true
What is Probability distribution?A probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events
Given,
We have to find the value of P(1<x<5)
P(1<x<5) = P(2)+P(3)+P(4)
P(2)=0.07
P(3)=0.22
P(4)=0.22
P(1<x<5) = 0.07+0.22+0.22 =0.51
Hence, the value of P(1<x<4)= 0.51
Learn more about Probability and Probability distribution here
https://brainly.com/question/14210034
#SPJ2
Which polynomial function has zeros when ? A: B: C: D:
Answers
Which equation demonstrates the additive identity property?
Answers
Answer:
See Explanation
Step-by-step explanation:
The options are not given; however, you can take a clue from my explanation to answer your question
Let x be a real number;
Additive identity property implies that; adding x to 0 or 0 to x gives x;
In other words;
[tex]x + 0 = x[/tex]
[tex]0 + x = x[/tex]
Note that x can be replaced with any real number; Take for instance
[tex]1 + 0 = 1[/tex]
[tex]0 + 2.5 = 2.5[/tex]
[tex]3 + 0 = 3[/tex]
There are uncountable number of examples;
However, take note that adding 0 to a given digit results in the exact digit and that's the implication of addition identity property
Answer:
(7+4i)+0=7+4i
Step-by-step explanation:
I don't understand word problems can someone please answer it for me and I need it ASAP.
Answers
Answer:
Inequality: 3 + 1.2c
What you'd put on graph: 1 ≥ 13.50
PLEASE HELP WILL GIVE BRAINLIEST AND THX Which ratios have a unit rate of 3? Choose all that apply. 15/2 cups: 2 1/2 cups 1 cup: 1/4 cups 2/3 cups: 1 cup 3 3/4 cups: 2 cups 2 cups: 2/3 cups 2 1/2 cups: 5/6 cups
Answers
Answer:
15/2 cups: 2 1/2 cups
2 cups: 2/3 cups
2 1/2 cups: 5/6 cups
Step-by-step explanation:
Take and divide each by the smaller number
15/2 cups: 2 1/2 cups
First put in improper fraction form
15/2 : 5/2
Divide each by 5/2
15/2 ÷ 5/2 : 5/2 ÷5/2
15/2 * 2/5 : 1
3 :1 yes
1 cup: 1/4 cups
Divide each by 1/4 ( which is the same as multiplying by 4)
1*4 : 1/4 *1
4 : 1 no
2/3 cups: 1 cup
Divide each by 2/3 ( which is the same as multiplying by 3/2)
2/3 * 3/2 : 1 * 3/2
1 : 3/2 no
3 3/4 cups: 2 cups
Change to improper fraction
( 4*3+3)/4 : 2
15/4 : 2
Divide each side by 2
15/8 : 2/2
15/8 : 1 no
2 cups: 2/3 cups
Divide each side by 2/3 ( which is the same as multiplying by 3/2)
2 * 3/2 : 2/3 *3/2
3 : 1 yes
2 1/2 cups: 5/6 cups
Change to an improper fraction
( 2*2+1)/2 : 5/6
5/2 : 5/6
Divide each side by 5/6( which is the same as multiplying by 6/5)
5/2 * 6/5 : 5/6 * 6/5
3 : 1 yes
The 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3
What is the ratio?It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.
For checking: 15/2 cups: 2 1/2 cups
= (15/2)/(5/2) [2(1/2) = 5/2]
= 3
For checking: 1 cup: 1/4 cups
= 1/(1/4)
= 4
For checking: 2/3 cups: 1 cup
=(2/3)/1
= 2/3
For checking: 3 3/4 cups: 2 cups
= (15/4)(2)
= 15/8
For checking: 2 cups: 2/3 cups
= (2)/(2/3)
= 3
For checking: 2 1/2 cups: 5/6 cups
= (5/2)/(5/6)
= 3
Thus, the 15/2 cups: 2 1/2 cups, 2 cups: 2/3 cups, and 2 1/2 cups: 5/6 cups have a unit rate of 3
Learn more about the ratio here:
brainly.com/question/13419413
#SPJ2
Quadrilateral ABCD is similiar to quadrilateral EFGH. The lengths of the three longest sides in quadrilateral ABCD are 60 feet, 40 feet, and 30 feet long. If the two shortest sides of quadrilateral EFGH are 6 feet long and 12 feet long, how long is the 2nd longest side on quadrilateral EFGH?
Answers
Answer:
24
Step-by-step explanation:
For ABCD the three longest are:
60,40,30
60 to 40 is 20
40 to 30 is 10
so each time it's decreasing by 1/2
For EFGH the two shortest are:
6 and 12
12 to 6 is 1/2
Assuming there is a pattern
it logically would be 24
as 12(2)=24
jeff buys 44 watermelons, he gets into a car accident and loses 31, how many does jeff have left
Answers
Answer:
Jeff has 3 watermelons left
Step-by-step explanation:
44-31=13 watermelons
Answer:
13
Step-by-step explanation:
44
-31
13
i will give brainliest and 5 stars if you help ASAP
Answers
Explanation:
Triangle XYZ is an isosceles triangle with XY = ZY and Angle YXZ = XZY
And YXZ = a = 32 degree
Which mean XZY also = 32 degrees
Find XYZ:
XYZ + YXZ + YZX = 180
XYZ + 32 + 32 = 180
XYZ + 64 = 180
XYZ = 180 - 64
XYZ = 116
coefficient of 8x+7y
Answers
Answer:
8
Step-by-step explanation:
Identify the exponents on the variables in each term, and add them together to find the degree of each term.
8x→1
7y→1
The largest exponent is the degree of the polynomial.
1
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient of a polynomial is the coefficient of the leading term.
____________________________________________________________
The leading term in a polynomial is the term with the highest degree.
8x
The leading coefficient in a polynomial is the coefficient of the leading term.
8
List the results.
Polynomial Degree: 1
Leading Term: 8x
Leading Coefficient: 8
Hope This Helps!!!
Which represents a measure of volume?
O 5 cm
O 5 square cm
05 cm
05 cm
Answers
Answer:
5 cm³
Step-by-step explanation:
The correct options to the given question will be:
5 cm³ 5 square cm 5 cm 5 cm²The volume of a solid is referred to as the space that the figure occupies. The three dimensions are covered and recorded to measure the volume. It is measured by multiplying the length, breadth, and the height of the solid. Since three units are multiplies, therefore the unit of the volume becomes a cubic unit. Usually, the volume is measured in cubic meter or cubic centimetre.
Find the value of the variable(s) in each figure. Explain your reasoning. Thank you in advance
Answers
Answer:
1. x 55
2. y 117
x 51
3.x39
y116
4.x 18
5.x 48
y 14
for the last one I'm not sure. please give 5 start
Assume that thermometer readings are normally distributed with a mean of 0C and a standard deviation of 1.00C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.) Between and
Answers
Answer: 0.0546 and 0.9829
Step-by-step explanation:
solution:
= P( 1.50< Z <2.25 )
= P(Z <2.25 ) - P(Z <1.50 )
Using z table,
= 0.9878-0.9332
=0.0546
b.
= P( -2.12< Z <3.73 )
= P(Z <3.73) - P(Z <-2.12 )
Using z table,
= 0.9999-0.0170
=0.9829
A random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6. A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.02 for the test. Assume that the population variances are not equal and that the two populations are norm
Answers
Answer:
We conclude that there is no difference in potential mean sales per market in Region 1 and 2.
Step-by-step explanation:
We are given that a random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6.
A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5.
Let [tex]\mu_1[/tex] = mean sales per market in Region 1.
[tex]\mu_2[/tex] = mean sales per market in Region 2.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1-\mu_2[/tex] = 0 {means that there is no difference in potential mean sales per market in Region 1 and 2}
Alternate Hypothesis, [tex]H_A[/tex] : > [tex]\mu_1-\mu_2\neq[/tex] 0 {means that there is a difference in potential mean sales per market in Region 1 and 2}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+ {\frac{1}{n_2}}} }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean sales in Region 1 = 84
[tex]\bar X_2[/tex] = sample mean sales in Region 2 = 78.3
[tex]s_1[/tex] = sample standard deviation of sales in Region 1 = 6.6
[tex]s_2[/tex] = sample standard deviation of sales in Region 2 = 8.5
[tex]n_1[/tex] = sample of supermarkets from Region 1 = 12
[tex]n_2[/tex] = sample of supermarkets from Region 2 = 17
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]s_p=\sqrt{\frac{(12-1)\times 6.6^{2}+(17-1)\times 8.5^{2} }{12+17-2} }[/tex] = 7.782
So, the test statistics = [tex]\frac{(84-78.3)-(0)}{7.782 \times \sqrt{\frac{1}{12}+ {\frac{1}{17}}} }[/tex] ~ [tex]t_2_7[/tex]
= 1.943
The value of t-test statistics is 1.943.
Now, at a 0.02 level of significance, the t table gives a critical value of -2.472 and 2.473 at 27 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that there is no difference in potential mean sales per market in Region 1 and 2.
7 students in a class,3/4 th pound of a cake .divide cake each student?
Answers
Answer:
9 1/3
Step-by-step explanation:
1. Set up the equation and solve
7 ÷ 3/4 = 9 1/3
Answer:
3/28 pounds or approximately 0.107 pounds
Step-by-step explanation:
To find out the amount of cake that each of the 7 students would get, we simply need to split the 3/4th pounds of cake amongst the 7 students.
Simply write the equation as follows:
(3/4)/7 = 3/28
So each student would get 3/28 of a pound of cake which is approximately 0.107 pounds of cake.
Cheers.
