Step-by-step explanation:
here,
C={ a,b,x,y}
D ={ m,n,o,p}
now,
C union D ={a,b,x,y} union {m,n,o,p}
= {a,b,x,y,m,n,o,p}
therefore C union D ={ a,b,x,y,m,n,o,p}
hope u get it...
Please help I don’t understand And I need an explanation
Hey there! :)
Answer:
56 m².
Step-by-step explanation:
To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:
Solve for the rectangle: (A = l × w)
A = 8 × 5
A = 40 m²
Solve for the triangle: (A = 1/2 (bh))
A = 1/2(4 · 8)
A = 1/2(32)
A = 16 m².
Add up the two areas:
40 + 16 = 56 m².
Answer:
Area of triangle+ the area of rectangle
Step-by-step explanation:
Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²
Area of rectangle is length × breadth= 5×8: 40 m²
Area of the shape is 40m²+16m²= 56m²
Julie has three boxes of pens. The diagram shows expressions for the number of pens in each box. Look at these equations.
Equals B +12
B equals C +4
Write an equation to show the relationship between a + c
Answer:
a=c+16here,
a=b+12
b=a-12----> equation (i)
b= c+4
putting the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
hope this helps...
Good luck on your assignment...
The value of a + c is 16.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
a=b+12
So, b=a-12 ---- equation (i)
and, b= c+4
Substitute the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
Hence, the value of a+ c is 16.
Learn more about Algebra here:
https://brainly.com/question/24875240
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Two identical decks of 52 cards are mixed together, yielding a stack of 104 cards. How many different ways are there to order this stack of 104 cards?
Answer:
here the order will be 104! =[tex]1.029e^{166}[/tex]
Step-by-step explanation:
since the cards are to arranged in no particular order that is why we used combination to find the result.
Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.
Diane's bank is offering 5% interest, compounded monthly. If Diane invests $10,500 and wants $20,000 when she withdrawals, how long should she keep her money in for? Round to the nearest tenth of a year.
Answer:
The time period is 13 years.
Step-by-step explanation:
Interest rate (r )= 5% or 5%/12 = 0.42% per months
The investment amount (Present value) = $10500
Final expected amount (future value) = $20000
Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.
Use the below formula to find the time period.
Future value = present value (1 + r )^n
20000 = 10500(1+0.0042)^n
1.9047619 = (1+0.0042)^n
1.9047619 = 1.0042^n
n = 153.74 months.
Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)
The mayor of a town has proposed a plan for the construction of an adjoining community. A political study took a sample of 900 voters in the town and found that 45% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 42%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
P-value = 0.0367
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the percentage of residents who favor construction is significantly over 42%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.42\\\\H_a:\pi>0.42[/tex]
The sample has a size n=900.
The sample proportion is p=0.45.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.42*0.58}{900}}\\\\\\ \sigma_p=\sqrt{0.000271}=0.016[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.45-0.42-0.5/900}{0.016}=\dfrac{0.029}{0.016}=1.79[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>1.79)=0.0367[/tex]
The slope of a line is 1, and the y-intercept is -1. What is the equation of the line written in slope-intercept form?
Answer:
y=x-1
Step-by-step explanation:
since the slope is just one up and one over and it's positive it would just be x
and since the intercept is just -1 it would be y=x-1
The hourly rate of substitute teachers for 12 local school districts is given below. Assuming that the data are normally distributed, use a TI-83, or TI-84 calculator to find the 90% confidence interval for the mean hourly rate of substitute teachers in the region.20 13 21 18 19 2219 15 12 12 18 21
Answer:
[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]
[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]
Step-by-step explanation:
Data given
20 13 21 18 19 22 19 15 12 12 18 21
We can calculate the sample mean and deviation with the following formulas:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And we got:
[tex]\bar X = 17.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.61 represent the sample standard deviation
n=12 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=12-1=11[/tex]
Since the Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be given by [tex]t_{\alpha/2}=[/tex]
Now we have everything in order to replace into formula (1):
[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]
[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]
Calculate
(14x5x4) / (28 x 2)
Answer:
5
Step-by-step explanation:
(14 × 5 × 4) ÷ (28 × 2)
Solve brackets.
280 ÷ 56
Divide.
= 5
How do you solve 36 times [tex]\sqrt{3}[/tex]
Answer:
62.3538
Step-by-step explanation:
There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.
Could someone explain how to find square roots please?
Answer: graphing calculator!
Step-by-step explanation: if you’re looking for the square root of a # that isn’t a perfect square (ie. sqrt4, sqrt 36) then you have to use a calculator for that. however the idea behind square roots is just a # multiplied by itself to give the original #. just ask yourself “what can i multiply by itself to get the original number”. hope that helped !
Answer:
By multiplying the number by its power 2.
E.g= 4^2
A random sample of 13 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 950 and the sample standard deviation is s = 10. Use Appendix D to find the values of Student’s t.
1. Construct an interval estimate of mu with 99% confidence. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
2. Construct an interval estimate of mu with 99% confidence, assuming that s = 20. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
3. Construct an interval estimate of mu with 99% confidence, assuming that s = 40. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
Answer:
1. The 99% confidence interval is from 941.527 to 958.473
2. The 99% confidence interval is from 933.054 to 966.946
3. The 99% confidence interval is from 916.108 to 983.892
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sample size,
s is the sample standard deviation,
[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level
The t-score corresponding to 99% confidence level is
Significance level = α = 1 - 0.99 = 0.01/2 = 0.005
Degree of freedom = n - 1 = 13 - 1 = 12
From the t-table at α = 0.005 and DoF = 12
t-score = 3.055
1. 99% Confidence Interval when s = 10
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]
The 99% confidence interval is from 941.527 to 958.473
2. 99% Confidence Interval when s = 20
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]
The 99% confidence interval is from 933.054 to 966.946
3. 99% Confidence Interval when s = 40
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]
The 99% confidence interval is from 916.108 to 983.892
As the sample standard deviation increases, the range of confidence interval also increases.
what does r equal? 1/13r=-8/15
Answer:
[tex]\boxed{\sf \ \ \ -\dfrac{15}{104} \ \ \ }[/tex]
Step-by-step explanation:
hello,
first of all let's assume that r is different from 0 as this is not allowed to divide by 0
[tex]\dfrac{1}{13r}=\dfrac{-8}{15}[/tex]
multiply by 13r it comes
[tex]\dfrac{13r}{13r}=1=\dfrac{-8*13r}{15}[/tex]
now multiply by 15
[tex]-8*13r=15\\<=> r = \dfrac{-15}{8*13}=-\dfrac{15}{104}[/tex]
hope this helps
Answer:[tex]r=-\frac{104}{15}[/tex] or -6.93333....
Step-by-step explanation:
[tex]\mathrm{Multiply\:both\:sides\:by\:}13[/tex]
[tex]13\cdot \frac{1}{13}r=13\left(-\frac{8}{15}\right)[/tex] =-104/15
simplify
[tex]r=-\frac{104}{15}[/tex]
MARK BRAINLIEST PLEASE
The y-intercept of a parabola is 1, and its vertex is at (1,0). What function does the graph represent?
OA. Rx) = (x - 1)2
OB. Rx) = (x + 1)2
OC. Rx) = -1(x - 1)
OD. Rx) = -1(x + 1)2
Reset
Next
Answer:
A
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, 0) , thus
y = a(x - 1)² + 0
To find a substitute the coordinates of the y- intercept (0, 1) into the equation
1 = a(- 1)² = a , thus
a = 1
y = (x - 1)² → A
Considering it's y-intercept and vertex, the equation of the parabola is given by:
[tex]y = (x - 1)^2[/tex]
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient.
In this problem, the vertex is (1,0), hence h = 1, k = 0 and:
[tex]y = a(x - 1)^2[/tex]
The y-intercept is of 1, hence, when x = 0, y = 1, so:
[tex]y = a(x - 1)^2[/tex]
[tex]1 = a(0 - 1)^2[/tex]
[tex]a = 1[/tex]
Hence, the equation is:
[tex]y = (x - 1)^2[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answer:
1140 ways.
Step-by-step explanation:
The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).
The 17 identical candies, can be distributed among the 4 children in :
=(17 + 4 - 1)C(4–1) = 20C3 ways.
= 20!/((20–3)!*3!) ways.
= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways
= 20*19*3 ways.
=1140 ways.
5(2x - 3) = 5
What does x equal?
Answer:
x=2
Step-by-step explanation:
5(2x - 3) = 5
Divide by 5
5/5(2x - 3) = 5/5
2x-3 = 1
Add 3 to each side
2x-3 +3 = 1+3
2x = 4
Divide by 2
2x/2 = 4/2
x =2
Answer:
x = 2
Step-by-step explain:
5(2x-3) = 5
Divide both sides by 5
2x-3 = 1
Add 3 to both sides
2x = 4
Divide both sides by 2
x = 2
Melvin has game and education apps on his tablet. He noticed that he has 3 game apps for every 2 education apps. Which of the following is another way to write this ratio? 1:2 2:1 2:3 3:2
3:3
Answer:
3: 2
Step-by-step explanation:
game Apps: education apps:
3: 2
In this activity, you will use equations to represent this proportional relationship: Olivia is making bead bracelets for her friends. She can make 3 bracelets in 15 minutes.
Part A
Find the constant of proportionality in terms of minutes per bracelet.
Part B
What does the proportionality constant represent in this situation?
Part C
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part A. Be sure to assign a variable for each quantity.
Part D
Now find the constant of proportionality in terms of number of bracelets per minute.
Part E
What does the proportionality constant represent in this situation?
Part F
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part D. Be sure to assign a variable for each quantity.
Part G
How are the constants of proportionality you found in parts A and D related?
Part H
Are the two equations you developed in parts C and F equivalent? Explain.
Answer:
Step-by-step explanation:
A) The constant of proportionality in terms of minutes per bracelet is
15/3 = 5 minutes per bracelet
B) The constant of proportionality represents man hour rate
C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
t = kb
D) the constant of proportionality in terms of number of bracelets per minute is
3/15 = 1/5
E) The constant of proportionality represents production rate
F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
b = kt
G) The constants of proportionality are reciprocals
H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.
Answer:the sample answers, change them up so you dont get in trouble
A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality=15 MINUTES/3 BRACELETS=5 minutes per bracelet.
B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.
C Here’s one way to set up the equation:
time = constant of proportionality × number of bracelets
Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.
thats all ik srry
Step-by-step explanation:
Two random samples are taken from private and public universities
(out-of-state tuition) around the nation. The yearly tuition is recorded from each sample and the results can be found below. Test to see if the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions. Assume unequal variances. Use a 1% level of significance.
Private Institutions (Group 1 )
43,120
28,190
34,490
20,893
42,984
34,750
44,897
32,198
18,432
33,981
29,498
31,980
22,764
54,190
37,756
30,129
33,980
47,909
32,200
38,120
Public Institutions (Group 2)
25,469
19,450
18,347
28,560
32,592
21,871
24,120
27,450
29,100
21,870
22,650
29,143
25,379
23,450
23,871
28,745
30,120
21,190
21,540
26,346
Hypotheses:
H0: μ1 (?) μ2
H1: μ1 (?) μ2
What are the correct hypotheses for this problem?
-A. H0: μ1 = μ2 ; H1: μ1 ≠ μ2
-B. H0: μ1 = μ2 ; H1: μ1 > μ2
-C. H0: μ1 ≤ μ2 ; H1: μ1 ≥ μ2
-D. H0: μ1 < μ2 ; H1: μ1 = μ2
-E. H0: μ1 ≠ μ2 ; H1: μ1 = μ2
-F. H0: μ1 ≥ μ2 ; H1: μ1 ≤ μ2
Answer:
Step-by-step explanation:
For private Institutions,
n = 20
Mean, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05
Standard deviation = √(summation(x - mean)²/n
Summation(x - mean)² = (43120 - 34623.05)^2+ (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95
Standard deviation = √(1527829234.95/20
s1 = 8740.22
For public Institutions,
n = 20
Mean, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15
Summation(x - mean)² = (25469 - 25063.15)^2+ (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95
Standard deviation = √(283738188.55/20
s2 = 3766.55
This is a test of 2 independent groups. Let μ1 be the mean out-of-state tuition for private institutions and μ2 be the mean out-of-state tuition for public institutions.
The random variable is μ1 - μ2 = difference in the mean out-of-state tuition for private institutions and the mean out-of-state tuition for public institutions.
We would set up the hypothesis. The correct option is
-B. H0: μ1 = μ2 ; H1: μ1 > μ2
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)
t = 9559.9/2128.12528473889
t = 4.49
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114
df = 26
We would determine the probability value from the t test calculator. It becomes
p value = 0.000065
Since alpha, 0.01 > than the p value, 0.000065, then we would reject the null hypothesis. Therefore, at 1% significance level, the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions.
Please answer this correctly
Answer:
1/9
Step-by-step explanation:
first, u need 9 ---> 1/3
then u need 8 ---> 1/3 also
Multiply them and get...1/9
To pass a certain marksmanship test, an individual is required to shoot at a target until he hits it six times. He is judged on the number of trials that are necessary to achieve this. If the probability of his hitting a target on any trial is 0.25, what is the probability that he requires 18 shots?
Answer:
The probability that he requires 18 shots is 0.04785
Step-by-step explanation:
To answer this, we shall be using the negative binomial distribution
From the question;
P = 0.25 , r = 6
q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial
P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)
P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785
Which two equations are the equations of vertical asymptotes of the function y = 5∕3 tan(3∕4x)?
A) x-2pi/3 and x=-2pi/3
B) x=0 and x=2pi/3
C) x=4pi/3 and x =4pi/3
D) x=0 and x=4pi/3
I did not know how to paste the pi symbol so I used the letters (pi)
Answer:
A)x=2pi/3 and x=-2pi/3
Step-by-step explanation:
The function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values where the tan(a) has vertical asymptotes.
we know that tan(a) has vertical asymptotes in [tex]a=\frac{\pi }{2}[/tex] and [tex]a=\frac{-\pi }{2}[/tex], if we made [tex]a=\frac{3x}{4}[/tex] and solve for x, we get:
for [tex]a=\frac{\pi }{2}[/tex]
[tex]\frac{\pi }{2} =\frac{3x}{4}\\x = \frac{2\pi }{3}[/tex]
for [tex]a=\frac{-\pi }{2}[/tex]
[tex]\frac{-\pi }{2} =\frac{3x}{4}\\x = \frac{-2\pi }{3}[/tex]
Finally, the function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values x=2pi/3 and x=-2pi/3
Answer:
A
Step-by-step explanation:
Quadrilaterals WXYZ and BADC are congruent. In addition, WX ≅ DC and XY ≅ BC.
If AD = 4 cm and AB = 6 cm, what is the perimeter of WXYZ?
18 cm
20 cm
22 cm
24 cm
Answer: 20 cm
If quadrilaterals WXYZ and BADC are congruent, then their corresponding sides are congruent.
Given that
WX≅DC,
XY≅BC,
you can state that
YZ≅AB,
WZ≅AD.
If AD = 4 cm and AB = 6 cm, then WZ = 4 cm and YZ = 6 cm. Opposite rectangle sides are congruent, then XY = 4 cm and WX = 6 cm.
The perimeter of WXYZ is
P = WX + XY + YZ + WZ = 6 + 4 + 6 + 4 = 20 cm.
You are graphing Square ABCDABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the square: A(4, -7), B(8, -7),A(4,−7),B(8,−7),A, left parenthesis, 4, comma, minus, 7, right parenthesis, comma, B, left parenthesis, 8, comma, minus, 7, right parenthesis, comma and C(8, -3)C(8,−3)C, left parenthesis, 8, comma, minus, 3, right parenthesis. What are the coordinates of point DDD? \large((left parenthesis , \large))right parenthesis
Answer:
D(4,-3)
Step-by-step explanation:
Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)
Let the coordinate of the fourth vertex be D(x,y).
We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.
The diagonals are BD and AC
Midpoint of BD = Midpoint of AC
[tex]\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3[/tex]
The coordinates of the fourth vertex is D(4,-3)
Answer:
(4,-3)
Step-by-step explanation:
Q‒1. [5×4 marks] a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? (150) b) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? c) How many odd numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? d) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? e) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once?
Answer:
a) 294
b) 180
c) 75
d) 174
e) 105
Step-by-step explanation:
I assume that for each problem, the first digit can't be 0.
a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.
6×7×7 = 294
b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.
6×6×5 = 180
c) Again, each digit can only be used once, but this time, the last digit must be odd.
If only the last digit is odd, there are 3×3×3 = 27 possible numbers.
If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.
If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.
If all three digits are odd, there are 3×2×1 = 6 possible numbers.
The total is 27 + 24 + 18 + 6 = 75.
d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.
If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.
If the first digit is greater than 3, there are 3×7×7 = 147 numbers.
The total is 6 + 21 + 147 = 174.
e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.
If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.
The total is 15 + 90 = 105.
What is the measure of angle S?
480
56°
930
101°
Answer:
m∠s = 93°
Step-by-step explanation:
We know that any quadrilateral's sum of angles adds up to 360°. In that case,
360 - (56 + 132 + 79) = m∠s
m∠s = 93°
Answer:
S° = 93 °
Step-by-step explanation:
[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]
In the morning, Marco sold 12 cups of lemonade for $3. By the end of the day, he had earned $9. How many cups of lemonade did he sell in all? Kaycee wrote the proportion 12/3=9/c for this situation identifly the error and give tow ways to write the proportion correctly
Answer:
36 cups
3/12 = 9/c
Step-by-step explanation
3 ÷ 12 = .25
each cup = 25 cents
9 ÷ .25 = 36
Marco sold 36 cups of lemonade.
3/12 = 9/c
Answer:
36 cups
Step-by-step explanation:
We can set up a proportion:
12/3=c/9
Cross multiply.
12*9=3*c
108=3c
Divide both sides by 3.
c=36
The error that the proportion Kaycee set up was
cups/price=price/cups
This is not proportionate.
Possible proportions include:
cups/price=cups/price
price/cups=price/cups
cups/cups=price/price
price/price=cups/cups
I NEED HELP PLEASE, THANKS! :)
Answer:
Option B
Step-by-step explanation:
Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -
[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]
Convert this to slope - intercept form -
[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]
Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -
( 0, 10 ),
( 15, 9 ),
( 17, 0 )
When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -
Option B
How do I calculate velocity?
Answer:
v = Δs/Δt
Step-by-step explanation:
Velocity is equal to the displacement/distance (delta symbol s) over the change of time (delta symbol t).
Kurtis is a statistician who claims that the average salary of an employee in the city of Yarmouth is no more than $55,000 per year. Gina, his colleague, believes this to be incorrect, so she randomly selects 61 employees who work in Yarmouth and records their annual salaries. Gina calculates the sample mean income to be $56,500 per year with a sample standard deviation of 3,750. Using the alternative hypothesis Ha:μ>55,000, find the test statistic t and the p-value for the appropriate hypothesis test. Round the test statistic to two decimal places and the p-value to three decimal places.
Degrees of Freedom
0.0004 0.0014 0.0024 0.0034 0.0044 0.0054 0.0064
54 3.562 3.135 2.943 2.816 2.719 2.641 2.576
55 3.558 3.132 2.941 2.814 2.717 2.640 2.574
56 3.554 3.130 2.939 2.812 2.716 2.638 2.572
57 3.550 3.127 2.937 2.810 2.714 2.636 2.571
58 3.547 3.125 2.935 2.808 2.712 2.635 2.569
59 3.544 3.122 2.933 2.806 2.711 2.633 2.568
60 3.540 3.120 2.931 2.805 2.709 2.632 2.567
Answer:
Test statistic t = 3.12
P-value = 0.001
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year (Gina's claim).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=55000\\\\H_a:\mu> 55000[/tex]
The significance level is 0.05.
The sample has a size n=61.
The sample mean is M=56500.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3750.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3750}{\sqrt{61}}=480.138[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{56500-55000}{480.138}=\dfrac{1500}{480.138}=3.12[/tex]
The degrees of freedom for this sample size are:
df=n-1=61-1=60
This test is a right-tailed test, with 60 degrees of freedom and t=3.12, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.12)=0.001[/tex]
As the P-value (0.001) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average salary of an employee in the city of Yarmouth is is significantly greater than $55,000 per year.
How fast was the battery charged? _______ percent per minute. How long did it take the battery to be fully charged? ________ minutes.
Answer:
Q1 is: 2.2 percent per minute
Q2 is: 35 minutes
Step-by-step explanation:
For the first question, take 89 percent, and subtract 23 from it, then divide by 30 minutes for the rate per minute.
For the second question take 23 percent, find out how much is left until 100 percent (77 percent) and use the rate from the last question (2.2 percent per minute), to find out how much time charging 77 percent takes. (You get 35 by using: 77 divided by 2.2)