Answer:
[tex]K \approx 51.2^\circ[/tex]
[tex]K \approx 128.8^\circ[/tex]
Step-by-step explanation:
Given
[tex]k = 480[/tex]
[tex]j = 420[/tex]
[tex]\angle J = 43^\circ[/tex]
Required
Find the measure of K
The value of K ranges from: [tex]0^\circ \le K \le 180^\circ[/tex]
To do this, we apply sine rule;
[tex]\frac{j}{\sin J} = \frac{k}{\sin K}[/tex]
So, we have:
[tex]\frac{420}{\sin 43} = \frac{480}{\sin K}[/tex]
Cross multiply
[tex]\sin K * 420 = \sin 43 * 480[/tex]
Make sin K the subject
[tex]\sin K= \frac{\sin 43 * 480}{420}[/tex]
[tex]\sin K= \frac{0.6820 * 480}{420}[/tex]
[tex]\sin K= 0.7794[/tex]
Take arc sin of both sides
[tex]K = sin^{-1}(0.7794)[/tex]
[tex]K \approx 51.2^\circ[/tex]
Recall that: [tex]0^\circ \le K \le 180^\circ[/tex]
The other possible value of K is:
[tex]K \approx 180 - 51.2[/tex]
[tex]K \approx 128.8^\circ[/tex]
Please help please please ASAP please please help please
Answer:
true
Step-by-step explanation:
the total surface area of a solid is the sum of all faces both the bottom (base) and the top
Trend lines
The scatterplot below shows several data
points and an approximate trend line for
the data.
у
350
300
250
200
150
100
SO
D 200 400 600
1.
Which is the best estimate of the value
of x that corresponds to the y value of
325? (8.18, 8.1C, 8.1E, 8.1F)
A 175
B 700
C 625
D 125
Can someone pls help me?
Answer:
26
Step-by-step explanation:
a complementary angle measures 90 degrees. minus the 64 would be 26
The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the Quality of Management and the Reputation of the Company for over 250 world-wide corporations. Both the Quality of Management and the Reputation of the Company were rated on an Excellent, Good, and Fair categorical scale. Assume the sample data for 200 respondents below applies to this study.
Reputation of Company
Quality of management Excellent Good Fair
Excellent 40 25 5
Good 35 35 10
Fair 25 10 15
Required:
a. Use α = 0.05 level of significance and test for independence of the quality of management and the reputation of the company. What is the p-value and what is your conculsion??
b. If there is a dependence or association between the two ratings, discuss and use the probabilities to justify your answer.
Answer:
The calculated χ² = 17.0281 falls in the critical region χ² ≥ 9.49 so we reject the null hypothesis that the quality of management and the reputation of the company are independent and conclude quality of management and the reputation of the company are dependent
The p-value is 0 .001909. The result is significant at p < 0.05
Part b:
40 > 8.5
35> 7.5
25> 4
Step-by-step explanation:
1) Let the null and alternative hypothesis as
H0: the quality of management and the reputation of the company are independent
against the claim
Ha: the quality of management and the reputation of the company are dependent
2) The significance level alpha is set at 0.05
3) The test statistic under H0 is
χ²= ∑ (o - e)²/ e where O is the observed and e is the expected frequency
which has an approximate chi square distribution with ( 3-1) (3-1)= 4 d.f
4) Computations:
Under H0 ,
Observed Expected E χ²= ∑(O-e)²/e
40 35.00 0.71
25 24.50 0.01
5 10.50 2.88
35 40.00 0.62
35 28.0 1.75
10 12.00 0.33
25 25.00 0.00
10 17.50 3.21
15 7.50 7.50
∑ 17.0281
Column Totals 100 70 30 200 (Grand Total)
5) The critical region is χ² ≥ χ² (0.05)2 = 9.49
6) Conclusion:
The calculated χ² = 17.0281 falls in the critical region χ² ≥ 9.49 so we reject the null hypothesis that the quality of management and the reputation of the company are independent and conclude quality of management and the reputation of the company are dependent.
7) The p-value is 0 .001909. The result is significant at p < 0.05
The p- values tells that the variables are dependent.
Part b:
If we take the excellent row total = 70 and compare it with the excellent column total= 100
If we take the good row total = 70 and compare it with the good column total= 80
If we take the fair row total = 50 and compare it with the fair column total= 30
The two attributes are said to be associated if
Thus we see that ( where (A)(B) are row and columns totals and AB are the cell contents)
AB> (A)(B)/N
40 > 1700/200
40 > 8.5
35> 1500/200
35> 7.5
25> 800/200
25> 4
and so on.
Hence they are positively associated
A bag contains 3 red balls and 1 blue ball. A second bag contains 1 red ball and 1 blue ball. A ball is randomly picked from each bag and is then placed in the other bag. What is the expected number of red balls in the first bag? (mean or expected value)
Answer:
"2.82" seems to be the correct solution.
Step-by-step explanation:
As we know,
A bag (Bag A) contains,
Red balls = 3
Blue ball = 1
A second bag (Bag B) contains,
Red balls = 1
Blue ball = 1
Now,
⇒ P(Bag A, red ball) = [tex]P(A)\times P(r)\times P(r)[/tex]
On substituting the values, we get
⇒ = [tex]\frac{1}{2}\times \frac{3}{4}\times \frac{2}{3}[/tex]
⇒ = [tex]\frac{1}{4}[/tex]
Similarly,
Probability of second bag will be:
⇒ P(Bag B) = [tex]\frac{1}{2}[/tex]
hence,
In the first bag (Bag A), the expected number of red balls will be:
⇒ [tex]E(n)=\Sigma P(n)\times n[/tex]
On substituting the values, we get
⇒ [tex]=3 (\frac{1}{4})+2(\frac{1}{8} )+4(\frac{1}{24} )+3(\frac{1}{12} )+3(\frac{4}{20} )+4(\frac{1}{20} )+2(\frac{3}{20} )+\frac{2}{20}[/tex]
⇒ [tex]= \frac{169}{60}[/tex]
⇒ [tex]=2.82[/tex]
Education reform is one of the most hotly debated subjects on both state and national policymakers’ list of socioeconomic topics. Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given to 10th graders. Four predictor variables are used: (1) STR is the student-to-teacher ratio in %, (2) TSAL is the average teacher’s salary in $1,000s, (3) INC is the median household income in $1,000s, and (4) SGL is the percentage of single-parent households. A portion of the data is shown in the accompanying table.
Score STR(%) TSAL(in $1000) INC(in $1000) SGL(%)
227.0 19.00 44.01 48.89 4.70
230.67 17.90 40.17 43.91 4.60
. . . . .
. . . . .
230.67 19.20 44.79 47.64 5.10
Required:
a. For each explanatory variable, discuss whether it is likely to have a positive or negative causal effect on Score.
b. Find the sample regression equation. Are the signs of the slope coefficients as expected?
c. What is the predicted score if STR = 18, TSAL = 50, INC = 60, SGL = 5?
d. What is the predicted score if everything else is the same as in part(c) except INC = 80?
Answer:
A:
STR= -
TSAL= +
INC=+
SGL=-
B:
231.89 - .50 - .02 + .29 -.88
B2:
STR=Y
TSAL=N
INC=Y
SGL=Y
C:
234.89
D:
240.69
Step-by-step explanation:
In a classroom of 24 students, five-eighths of the students brought their lunch to school. How many of the students in the classroom does this represent?
(Explain how you got your answer please)
(1) 3
(2) 5
(3) 10
(4) 15
(5) 20
Answer:In my opinion 10 is the answer
hope it helps you
Find the measure of arc HJ.
Answer:
98 degrees
Step-by-step explanation:
HJ = (5x - 7)
Because it's a full circle:
61 + 34 + (5x - 7) + (9x - 22) = 360
95 + (14x - 29) = 360
14x = 360 - 95 + 29 = 294
x = 21
HJ = 5x - 7 = 5 * 21 - 7 = 105 - 7 = 98
I will give Brainiest
Jim, Dan, and David share some sweets in the ratio 6:2:1. Jim gets 25 more sweets than David. How many sweets are there altogether
Answer:
45 sweets.
Step-by-step explanation:
6:2:1
To solve how many Jim and Dan has I did 6 x n and 1 x n until the difference of the two numbers equaled 25.
6 x 5 = 30
1 x 5 = 5
30 - 5 = 25.
So, Jim as 30 candy and Dan has 1. How much does David have?
Just do the same thing but with 2 x n:
2 x 5 = 10.
Now add them together:
30 + 10 + 5 = 45.
Therefore, 45 sweets!
Rectangle QRST is dilated with the origin as the center of dilation to create rectangle Q'R'S'T'.
Which rule represents the dial toon applied to rectangle QRST to create triangle QRST
Answer:
Rule: dilation about the origin by a scale factor of 2
Step-by-step explanation:
Given
See attachment for QRST and Q'R'S'T
Required
The dilation rule
First, we calculate the scale factor (k)
From the attachment, we have:
[tex]QR = 4[/tex]
[tex]Q'R' = 8[/tex]
k, is then calculated as:
[tex]k = \frac{Q'R'}{QR}[/tex]
[tex]k = \frac{8}{4}[/tex]
[tex]k =2[/tex]
Hence, QRST is dilated by a factor of 2
Your cousin is building a sand box for his daughter
How much sand will he need to fill the box
how much paint does he need for the box
Answer:
volume of box(v)=l×b×h
=1×6×4
=24ft^3
so it required 24volume sand to fill the box
How much interest would $1,000 earn in one year at a rate of 6%, compounded annually? What would be the new balance?
Please, help me!
Answer:
The investment will generate $ 60 in interest, with which the new balance will be $ 1060.
Step-by-step explanation:
To determine how much interest would $ 1,000 earn in one year at a rate of 6%, compounded annually, and what would be the new balance, the following calculations must be performed:
1000 x (1 + 0.06 / 1) ^ 1x1 = X
1000 x 1.06 ^ 1 = X
1000 x 1.06 = X
1060 = X
Therefore, the investment will generate $ 60 in interest, with which the new balance will be $ 1060.
Help me !!!
Please I really need it
Answer:
i don't know
Step-by-step explanation:
5. Simplify
(7x2+ 8) - (x2 - 2)
Answer:
[tex](7 \times 2 + 8) - ( {x}^{2} - 2) \\ (14 + 8) - ( {x}^{2} - 2) \\ 14 + 8 - {x}^{2} + 2 \\ 22 + {x}^{2} + 2 \\ 24 + {x}^{2} [/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
what factors determine the amount of interest earned on a fixed principal
Answer:
The interest rate and the number of compounding periods best describe the factors that determine the amount of interest because they encompass the ideas of time and yield.
Step-by-step explanation:
Hope this helps!!!
. You want to buy a new pair of shoes. You have a coupon for $15 off. Once you get to the store, you realize your shoes are on sale for 20% off, but you can't use both the sale price and the coupon. Which discount would offer a better deal if the original price of the shoes is $150? Explain your decision.
Answer:
I would use the sale price.
Step-by-step explanation:
20% of 150 is 30. So, you get $30 off if you use the sale price rather then the $15 coupon.
how to calculate tax rebate
JUST THE SECOND ONE EASY PLS ASAP
Answer:
51
Step-by-step explanation:
Use an online calculator
Two dice are tossed. Find the probability of getting the sum of the
dice equal to 16. (Hint: Draw a tree diagram of the possibilities of
two tosses of a die, and then find the sum of the numbers on
each branch.)
Answer:
Step-by-step explanation:
If you are talking about a die with 6 faces, then 16 isn't possible. 12 is the highest possible number.
If you are talking about some other kind of die, you have to specify it.
I'm going to assume you made a mistake and meant 6.
There are 5 ways to get six
3 - 3
4 - 2
2 - 4
5 - 1
1 - 5
There are 36 ways of throwing 2 dice.
So the probability = 5/36 = 0.1389
If you really did mean 16 then the probability = 0
The origin is a point anywhere along the x-axis. True or False
Answer:
False
Step-by-step explanation:
The origin is at 0 on the x-axis, and 0 on the y-axis. Hence, (0,0) lies on both the axis.
hope this helps and is right. p.s. i really need brainliest :)
if my answer is wrong then i am incredibly sorry!
The statement "The origin is a point anywhere along the x-axis" is False.
What is Origin?Origin is referred to as the first point or the starting point from which we begin our calculations or measurements in mathematics, particularly in the subject of coordinate geometry. The 0 on a ruler is the point at which we begin taking measurements; as a result, it is referred regarded as the scale's origin.
As, The intersection of the x and y axes in a coordinate plane is where the origin is located.
Coordinates can be used to name any point on the coordinate plane.
The coordinates are where the origin is ( 0, 0 ).
So, the x- coordinate is 0 and y- coordinates is 0.
Hence, the given statement is False.
Learn more about Origin here:
https://brainly.com/question/30135643
#SPJ2
Fine the volume please
Answer:
212 m²
Step-by-step explanation:
4 x 4 x 5 = 80
6+6+50+30+40
The relationship below is proportional true or false
Answer:
false.........
Step-by-step explanation:
......
I need help solve this !! Pls help pls not links ;)
Answer:
A / D / E
Step-by-step explanation:
f (1) = 1
f(2) = 5
f(3) = 9
Pencils 6 18 Erasers 2 will mark brainlest
Answer:
this is your answer as it lies in a same ratio..
Help help help help help
Find m∠D
m∠D=
greatly appreciate if done asap:)
Whatever answer this question first gets a thanks and 14 points Please answer quickly ✌
Answer:
5) x = 25
6) x = 48
Step-by-step explanation:
5)
65 + x = 90
65 - 65 + x = 90 - 65
x = 25
--------------------------------------
6)
A complementary angle is 90 degrees.
42 + x = 90
42 - 42 + x = 90 - 42
x = 48
please answer fast!!
Answer:
x=70
Step-by-step explanation:
[tex]2x + 1 = 141 \\ 2x = 140 \\ x = 70[/tex]
Answer:
x=70
Step-by-step explanation:
I hope i was right have a good day!!
A random sample of 30 males with online dating profiles are recruited for a study about lying in online dating profiles. Each male's actual height is measured and compared to the height posted in their online profile. The difference between the online profile height and the actual height (profile- actual) for each male is computed. The mean difference in height is determined to be 0.57 inches with a standard deviation of 0.81 inches. Determine a 95% confidence interval for the difference in mean profile height and mean actual height of online daters.
Answer:
The 95% confidence interval for the difference in mean profile height and mean actual height of online daters is between 0.27 and 0.87 inches.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 30 - 1 = 29
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 29 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0452
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.0452\frac{0.81}{\sqrt{30}} = 0.3[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 0.57 - 0.3 = 0.27 inches.
The upper end of the interval is the sample mean added to M. So it is 0.57 + 0.3 = 0.87 inches.
The 95% confidence interval for the difference in mean profile height and mean actual height of online daters is between 0.27 and 0.87 inches.