Step-by-step explanation:
N6000×5=N30000
1)N30000-N25000=N5000
2)N5000÷N25000×100℅=20℅
the length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58 degree to 36 degree calculate correct to three significant figure the height of the pole
Step-by-step explanation:
(A) Let a triangle be formed with height of pole h, length of base b and angle of elevation 58°. (Due to lack of a figure).
Tan 58° = h / b = 1.6
(B) Let another triangle be formed with height of pole h, length of base (b + 90) and angle of elevation 36°. (Due to lack of a figure).
Tan 36° = h / (b + 90) = 0.72
(C) Simplifying the two equations :
1.6b = 0.72b + 64.8
b = 64.8 / 0.88 = 73.6 m
h (height of pole) = 1.6 * 73.6 = 117.76 m
lisa goes to school for 7 hours per day works 3 hours per day and sleeps 8 hours per day. what is the ratio of hours lisa works to hours lisa sleeps?
Answer:
ratio of hours lisa works to hours lisa sleeps= 3:8
Step-by-step explanation:
lisa goes to school for 7 hours per day lisa works 3 hours per day
Lisa sleeps 8 hours per day.
For the ratio of hours lisa works to hours lisa sleeps
ratio of hours lisa works to hours lisa sleeps= hours Lisa works/hours Lisa sleeps
ratio of hours lisa works to hours lisa sleeps= 3/8
ratio of hours lisa works to hours lisa sleeps= 3:8
Randomly selected 110 student cars have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 75 faculty cars have ages with a mean of 5.3 years and a standard deviation of 3.7 years.
1. Use a 0.02 significance level to test the claim that student cars are older than faculty cars.
Is there sufficient evidence to support the claim that student cars are older than faculty cars?
A. Yes.
B. No.
2. Construct a 98% confidence interval estimate of the difference μ1âμ2, where μ1 is the mean age of student cars and μ is the mean age of faculty cars.
Answer:
1. Yes, there is sufficient evidence to support the claim that student cars are older than faculty cars.
2. The 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].
Step-by-step explanation:
We are given that randomly selected 110 student cars to have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 75 faculty cars to have ages with a mean of 5.3 years and a standard deviation of 3.7 years.
Let [tex]\mu_1[/tex] = mean age of student cars.
[tex]\mu_2[/tex] = mean age of faculty cars.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \leq \mu_2[/tex] {means that the student cars are younger than or equal to faculty cars}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1>\mu_2[/tex] {means that the student cars are older than faculty cars}
(1) The test statistics that will be used here is Two-sample t-test statistics because we don't know about the 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 age of student cars = 8 years
[tex]\bar X_2[/tex] = sample mean age of faculty cars = 5.3 years
[tex]s_1[/tex] = sample standard deviation of student cars = 3.6 years
[tex]s_2[/tex] = sample standard deviation of student cars = 3.7 years
[tex]n_1[/tex] = sample of student cars = 110
[tex]n_2[/tex] = sample of faculty cars = 75
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]\sqrt{\frac{(110-1)\times 3.6^{2}+(75-1)\times 3.7^{2} }{110+75-2} }[/tex] = 3.641
So, the test statistics = [tex]\frac{(8-5.3)-(0)} {3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} } }[/tex] ~ [tex]t_1_8_3[/tex]
= 4.952
The value of t-test statistics is 4.952.
Since the value of our test statistics is more than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we support the claim that student cars are older than faculty cars.
(2) The 98% confidence interval for the difference between the two population means ([tex]\mu_1-\mu_2[/tex]) is given by;
98% C.I. for ([tex]\mu_1-\mu_2[/tex]) = [tex](\bar X_1-\bar X_2) \pm (t_(_\frac{\alpha}{2}_) \times s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} })[/tex]
= [tex](8-5.3) \pm (2.326 \times 3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} })[/tex]
= [tex][2.7 \pm 1.268][/tex]
= [1.432, 3.968]
Here, the critical value of t at a 1% level of significance is 2.326.
Hence, the 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].
On-the-Go Phone Company has two monthly plans for their customers. The EZ Pay Plan costs $0.15 per minute. The 40 to Go Plan costs $40 per month plus $0.05 per minute.
Write an expression that represents that monthly bill for x minutes on the EZ Pay Plan.
Answer:
Ok, the EZ plan can be written as:
C1(x) = $0.15*x
where x is the number of minutes used in the whole Month.
The 40 to Go Plan can be written as:
C2(x) = $0.05*x + $40.
So we have two linear relationships.
The Ez plan has a larger slope, but has no y-intercept.
So we now can find the number of minutes needed to have the exact monthly cost in each plan:
C1(x) = C2(x)
$0.15*x = $0.05*x + $40
($0.15 - $0.05)*x = $40
$0.10*x = $40
x = $40/$0.10 = 400.
So if in one month, you use exactly 400 minutes, you will pay exactly the same wich each plan.
Now, if you speak less than 400 minutes, is better to use the EZ Pay Plan, because it has o y-intercept, and is more efficient for lower values of x.
If you will use more than 400 minutes per month, then the 40 to Go Plan is better, because the slope is smaller.
A quality control manager is concerned about variability of the net weight of his company’s individual yogurt cups. To check the consistency, he takes a random sample of sixteen 6-ounce yogurt cups and finds the mean of the sampled weights to be 5.85 ounces and the sample standard deviation to be 0.2 ounce. Test the hypotheses H0: µ ≥ 6 Ha: µ < 6 at the 5% level of significance. Assume the population of yogurt-cup net weights is approximately normally distributed. Based on the results of the test, will the manager be satisfied that the company is not under-filling its cups? State the decision rule, the test statistic, and the manager’s decision.
Answer:
Decision rule : The p-value < [tex]\alpha[/tex] so the null hypothesis is rejected
The test statistics is [tex]t = -2.8[/tex]
The manger will not be manager be satisfied that the company is not under-filling since the company is under-filling its cups
Step-by-step explanation:
From the question we are told that
The sample size is n = 16
The sample mean is [tex]\= x = 5.85[/tex]
The standard deviation is [tex]\sigma = 0.2[/tex]
The null hypothesis is [tex]H_o : \mu \ge 6[/tex]
The alternative hypothesis is [tex]H_a : \mu < 6[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 5.86 - 6 }{ \frac{ 0.2}{ \sqrt{ 16} } }[/tex]
=> [tex]t = -2.8[/tex]
The p-value is obtained from the z-table the value is
[tex]p-value = P(Z < -2.8 ) = 0.0025551[/tex]
[tex]p-value = 0.0025551[/tex]
Given that the [tex]p-value < \alpha[/tex] we reject the null hypothesis
Hence there is sufficient evidence to support the concern of the quality control manager. and the manger will not be satisfied that since the test proof that the company is under-filling its cups
Delilah drew 3 points on her paper. When she connects these points,must they form a triangle? Why or why not?
If the three points all fall on the same straight line, then a triangle will not form. Instead, a line will. We call these points to be collinear.
If the points aren't collinear, then a triangle forms.
Answer:
No.
Step-by-step explanation:
The points may be in a straight line, and that doesn't form a triangle.
Estimate the cost of painting a homecoming float if the area to be painted is 9 feet by 16 feet and a quart of paint that covers 53 square feet costs $11.99
Answer:
$32.58
Step-by-step explanation:
The area needed to be painted = 9 feet × 16 feet = 144 ft². The cost of painting a 53 ft² room is a quart of paint which costs $11.99, therefore the quart needed to paint 144 ft² area is:
[tex]Number\ of \ quart=\frac{144\ ft^2}{53\ ft^2} =2.717\ quart\\[/tex]
Since one quart cost $11.99, therefore the cost of 2.717 quart is:
Cost = 2.717 × $11.99 = $32.58
It would cost $32.58 to paint a 9 feet by 16 feet
help please !
m∠1=25°, m∠4=34°, m∠6=146°. Find m∠9
.
Answer:
Option (B)
Step-by-step explanation:
Since all the four rays A, E, D and F are diverging from a point C in the different directions.
Therefore, sum of all the angles formed at a point C will be equal to 360°
m∠1 + m∠4 + m∠6 + m∠9 = 360°
25° + 34° + 146° + m∠9 = 360°
m∠9 = 360° - 205°
= 155°
Therefore, measure of angle 9 is 155°.
Option (B) will be the correct option.
The distance round a rectangular cafe 35m,the ratio of the length of the cafe to it's width is 3:2 calculate the dimension of the cafe
Hey there! I'm happy to help!
Let's create a basic rectangle with this length to width ratio.
Two sides are 3 and two of them have a length of 2. This would give us a perimeter (distance around) of 10.
We want to find a rectangle with a perimeter of 35 meters with this same ratio. What we can do is multiply all of the dimensions of our first rectangle by 3.5 (to get our perimeter of 10 to 35, we multiply by 3.5).
3×3.5=10.5
2×3.5=7
If we simplify 10.5:7, we have 3:2, and the perimeter of a rectangle with a length of 10.5 and a width of 7 would equal 35 meters.
Have a wonderful day! :D
A building company claims that 70% of all new houses they build are finished within 3 weeks. A study show that, over 45 new houses, only 20 have been done in 3 weeks. Does the company claim valid at a level of significance of 0.05 and 0.01
Answer:
Calculated z= 3.515
The Z∝/2 = ±1.96 for ∝= 0.05
The Z∝/2 = ± 2.58 for ∝= 0.01
Yes the company claims valid at a level of significance of 0.05 and 0.01
Step-by-step explanation:
Here p1= 70% = 0.7
p2= 20/45= 0.444 q= 1-p= 1-.444= 0.56
The level of significance is 0.05 and 0.01
The null and alternative hypotheses are
H0; p1= p2 Ha: p1≠p2
The test statistic used here is
Z= p1-p2/ √pq/n
Z= 0.7-0.44/ √ 0.44*0.56/45
z= 0.26/ √0.2464/45
z= 3.515
The Z∝/2 = ±1.96 for ∝= 0.05
The Z∝/2 = ± 2.58 for ∝= 0.01
For the significance level 0.05 reject null hypothesis
For the significance level 0.01 reject null hypothesis
Yes the company claims valid at a level of significance of 0.05 and 0.01
It the ratio of boys to girls in 2:5 in the class, how many girls would there be if there are 10 boys?
First set up the ratio 2/5 = 10/x where x is the number of girls.
Now, we can use cross-products to find the missing value.
So we have (2)(x) = (5)(10).
Simplifying, we have 2x = 50.
Dividing both sides by 2, we find that x = 25.
So there are 25 girls in the class if there are 10 boys.
Point Mis the midpoint of AB. AM = 3x + 3, and AB= 83 – 6.
What is the length of AM?
Enter your answer in the box.
units
Answer:
AM= Half of AB
or, 3x+3=(8x-6)/2
or, 6x+6=8x-6
or, 2x=12
Therefore,x=6
so,AM=3*6+3=21
So the units is 21
Answer:
[tex]\Huge \boxed{21}[/tex]
Step-by-step explanation:
AM = 3x + 3
AB = 8x - 6
Point M is the midpoint of AB.
So, AM = AB/2
3x + 3 = (8x - 6)/2
Multiplying both sides by 2.
2(3x + 3) = 8x - 6
Expanding brackets.
6x + 6 = 8x - 6
Subtracting 6x from both sides.
6 = 2x - 6
Adding 6 to both sides.
12 = 2x
Dividing both sides by 2.
6 = x
Let x = 6 for the length of AM.
3(6) + 3
18 + 3
21
What's the value of x in the figure? A) 78° B) 57° C) 76° D) 33°
A)78°
135°+a° =180°
a°=45°
57°+x°+a°=180°
57°+x°+45°=180°
102°+x°=180°
x°=180°-102°
x°=78°
Which statement is true? Step by step.
Answer:
I believe the answer is A.
Step-by-step explanation:
If there are 13 daises per bouquet, that means one bouquet is all daises. The other bouquet has 30 flowers. 30-13 is 17 which means there are 17 other flowers rather than daises. 17 is greater than 13 by 4 which is not that much. Therefore I think the answer is letter A.
Answer:
The correct answer is A. The probability of randomly selecting a daisy from Bouquet S is less than the probability of randomly selecting a daisy from bouquet T.
Step-by-step explanation:
We are told that Bouquet S contains 30 flowers and 13 of those flowers are daisies. Therefore, the probability of selecting a daisy from Bouquet S can be modeled by:
13/30, which is greater than 1/3 but less than 1/2
We are also told that Bouquet T contains 13 flowers and 13 daises. From this information, we can conclude that all of the flowers in Bouquet T are daises, or the probability can be modeled by:
13/13 = 1
Therefore, because the probability of selecting a daisy from Bouquet S is 13/30 and the probability of selecting a daisy from Bouquet T is 1, we can conclude that, as option A states, the probability of selecting a daisy from Bouquet S is less than the probability of selecting a daisy from Bouquet T.
Hope this helps!
Original population
500
Current population
2,000
Find the percent of increase,
[?]%
Answer: 300%
Step-by-step explanation:
percent of increase: new/old×100%-100%
Since it is percent of increase, you need to subtract the original percent (100%) from the current percent.
------------------
new (current)=2000
old (original)=500
new/old×100%-100%
=2000/500×100%-100%
=4×100%-100%
=400%-100%
=300%
Hope this helps!! :)
Please let me know if you have any question or need further explanation
anyone know this answer −4y−4+(−3)
Answer:
− 4 y − 7
Step-by-step explanation:
Remove parentheses.
− 4 y − 4 − 3
Subtract 3 from − 4
− 4 y − 7
.
Find an equation of the vertical line passing through the point (-4, 2). x=
Answer:
x = -4
Step-by-step explanation:
This vertical line is x = -4. That's all we need here.
Which of the following is the y-intercept of:
2 y = x-8 ?
(0.4)
(-4.0)
(4,0)
(0,4)
PLZ HELP I NEED THE ANSWER QUICK
[tex](0,-4)[/tex] fits the linear equation perfectly.
Hope this helps.
Answer:
the y-intercept is the point (0, -4) on the plane
Step-by-step explanation:
In order to find the y-intercept, write the equation in "slope intercept form" solving for "y":
[tex]2\,y=x-8\\y=\frac{x-8}{2} \\y=\frac{x}{2} -\frac{8}{2} \\y=\frac{x}{2} -4[/tex]
Recall now that the y-intercept is the value at which the line crosses the y-axis (when x = 0), therefore:
[tex]y=\frac{x}{2} -4\\y=\frac{0}{2} -4\\y=-4[/tex]
So the y-intercept is the point (0, -4) on the plane.
The conjugate of 2+5 i (is) -2 -5 i
True or false
Answer:
False the conjugate of 2+5i is 2-5i .
Step-by-step explanation:
Hope it will help you :)
Convert 9 days into weeks
Answer:
1 week= 7 days
number of days= 9
number of weeks= 1 week and 2 days
hope it helps :)
please mark it the brainliest!
Answer:
1 week and 2 days
Step-by-step explanation:
Select the fraction with the largest value, 1/5, 1/8, or 3/4
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why JOY = LIM
Answer:
Option B
Option E
Step-by-step explanation:
By the use of following postulates we can prove the two right triangles to be congruent.
1). HA - [Equal hypotenuse and an cute angles]
2). LL - [Two legs should be equal]
3). LA - [One leg and one angle must be equal]
4). ASA - [Two angles and the side containing these angles should be equal]
In the given right triangles,
1). OJ ≅ IL
2). ∠O ≅ ∠I
3). ∠J ≅ ∠L
Therefore, two postulates HA, ASA will be applicable for the congruence of the two triangles given.
Options A and E will be the answer.
Answer:
asa, ha, aas
Step-by-step explanation:
part 9: I need help. please help me
Answer: A) a² = b² - w² + 2wx
Step-by-step explanation:
b² - (w - x)² = a² - x²
b² - (w² - 2wx + x²) = a² - x²
b² - w² + 2wx - x² = a² - x²
b² - w² + 2wx = a²
What is the value of 30-2(7+2)-1
Answer: 11
Step-by-step explanation:
30 - 2(7+2)- 1 Distribute or solve parentheses
30 - 14 -4 - 1
30 - 19 = 11
Explain how to identify if the graph of a relation is a function or not
Answer:
[see below]
Step-by-step explanation:
A function is a relation where one domain value is assigned to exactly one range.
An x-value in a function must not repeat.
One way to see if a graph is a function is to use a vertical line test. If the line passes trough the line twice, then it is not a function. On a table, check the x-value column or row. If any of the numbers repeat, then it is not a function. On a mathematical map, check to see if the arrows from a domain number points to one range value on the other side. If it points to two range numbers, then it is not a function.Hope this helps.
What is the value of x that makes the given equation true? x−3x=2(4+x)
Answer:
x = -2
Step-by-step explanation:
x−3x=2(4+x)
Distribute
x - 3x = 8 +2x
Combine like terms
-2x = 8+2x
Subtract 2x from each side
-2x-2x = 8+2x-2x
-4x = 8
Divide by -4
-4x/-4 = 8/-4
x = -2
Answer:
x-3x=2(4+x)
-2x=8+2x
-2x-2x=8
-4x=8
x=8/-4
x=-2
hope it helps budy x=2
mark me brainliest
which symbol will make |-8|?|-10|
>
<
=
which property is shown by 4+(5+6)=(4+5)+6?
commutative property of addition
distributive property
additive Indentity
associative property of addition
Answer:
[tex]|-8|<|-10| \Longleftrightarrow 8 < 10[/tex]
[tex]\text{Which property is shown by } 4+(5+6)=(4+5)+6?[/tex]
[tex]\text{It is the associative property of addition}[/tex]
You can group the addends in any combination and it won't change the result.
a. Is the a discrete random variable, a continuous random variable, or not a random variable? amount of rain in City B during April A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
Answer:
The correct answer is:
It is a continuous random variable. (B)
Step-by-step explanation:
Continuous random variables are variables that take on infinite possibility of values, hence the number of possible outcomes of a random variable cannot be counted. For instance, in this example, the amount of rainfall measured using a rain guage or a pluviometer has infinite possibilities of outcomes. it can either be 22.3 Liters, 20.1 Liters etc, up to infinity, in fact between 20 and 21 litres, there is an infinite possibility of outcomes.
Discrete random variables are variables that have a finite possibility of outcomes. the possibilities of occurrences can be counted. For example, if a coin is tossed, the coin can either land on its head or tail, hence there are two possibilities, making the variables discrete
The correct answer is:
It is a continuous random variable (B)
Step-by-step explanation:
Continuous Random Variables are variables that take on a number of possibilities of values that cannot be counted. The values have infinite possibilities. In this example, the height of a Giraffe measured in meters can be an unlimited possibility if values say, 10.5m, 15.22m 12.0m etc. The possibilities are endless.
Discrete Random variables are variables that take on a number of possibility of occurrences that can be counted. For instance, if a dice is rolled, the possibilities can either be a 1, 2, 3, 4, 5 or 6. There are six values that can be gotten, nothing in-between.
THANKS
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-3=9(5-2k)/5 Show your work
Answer:
K=3.333
Step-by-step explanation:
-3=9(5-2k)/5
-3=45-18k/5
-15=45-18k
18k=60
K=60/18
K=3.3333
10. Which relation is a function?
la A (8, -4), (8, 4), (6, -3), (6, 3).
(0,0)
B (4,7), (8,5), (6,4), (5, 3), (4, 2)
C (0,0), (1, 1), (2, 2), (3, 3), (4,7)
D (0,0), (1,0), (1, 1), (2, 1), (1, 2)
Answer:
C. Why? No repeating x values.