Answer:
Length = 36cm
Width = 12 cm
Step-by-step explanation:
Perimeter = all the sides added up.
Perimeter of a rectangle = L + L + W + W OR 2L + 2W
We are given that the length = 3 times the width. So L = 3W
P = 2L + 2W
96 = 2 (3W) + 2W
96 = 6W +2W
96 = 8W (divide both sides by 8)
W = 12 cm
To find the length- we know the length is 3 times the width.
So L = 3 x 12 = 36 cm
A worker in the USA is paid $22,000 per year as a gross salary. The worker is asked to reduce her salary to $19,000 per annum. What is the percentage decrease? Round you answer to the nearest whole percent.
a plane flying at a certian altitude is observed from two points that are 3 miles apart. the Angles of elevation made by the two points are 55deg and 72deg
The altitude of the plane is 8 miles
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
we know that in the right triangle ABC
tan function is ratio of opposite side and adjacent side
tan(72°)=h/x
h=xtan(72°) ....... equation 1
In the right triangle ABD
tan(55°)=h/(x+3)
h=(x+3)tan(55°) ..... equation 2
From equation 1 and 2
xtan(72°)=(x+3)tan(55°)
xtan(72°)-xtan(55°)=3tan(55°)
x[tan(72°)-tan(55°)]=3tan(55°)
x=3tan(55°)/[tan(72°)-tan(55°)]
We have to find the value of h
h=xtan(72°)
h=[3tan(55°)*tan(72°)]/[tan(72°)-tan(55°)]
h=8 miles
Hence, the height is 8 miles of the plane.
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A news organization interested in chronicling winter holiday travel trends conducted a survey. Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays. Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays. Construct a 99% confidence interval for the difference in population proportions of people in the eastern half of a country who fly to visit family members for the winter holidays and people in the western half of a country who fly to visit family members for the winter holidays. Assume that random samples are obtained and the samples are independent. (Round your answers to three decimal places.) z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576
Answer:
(-0.481 , -0.144)
Step-by-step explanation:
Confidence Interval for difference is proportion formula is given as:
p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]
For p1
Of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays.
n1 = 96 people
p1 = x/n
x = 42 people
p1 = 42/96
= 0.4375
1 - p1 = 0.5625
For p2
Of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays.
n2 = 108 people
p2 = x/n
x = 81 people
p2 = 81/108
= 0.75
1 - p2 = 0.25
99% confidence interval = 2.576
p1 - p2 ± z ×√[p1(1 - p1)/n1 +p2 (1 - p2)/n2]
= 0.4375 - 0.75 ± 2.576 ×√[0.4375(1 -0.4375)/96 +0.75 (1 - 0.75)/108]
= -0.3125 ± 2.576 × √0.4375× 0.5625/96 + 0.75 × 0.25 /108
= -0.3125 ± 2.576 × √0.0025634766 + 0.0017361111
= -0.3125 ± 2.576 × √0.0042995877
= -0.3125 ±2.576 × 0.0655712414
= -0.3125 ± 0.1689115178464
Confidence Interval
-0.3125 - 0.1689115178464
= -0.4814115178
Approximately to 3 decimal places = -0.481
= -0.3125 + 0.1689115178464
= -0.1435884822
Approximately to 3 decimal places = -0.144
Therefore, the 99% confidence interval for difference in proportion = (-0.481 , -0.144)
Find the interest on 2180 for one year at simple interest 4%
please mark me as brainlest
Please click on this picture and explain why I got this answer wrong
Answer: $79.12
Step-by-step explanation:
We have to find total amount that was paid for dinner
5 people each order was worth $12.80
Therefore, total bill = 12.80*5
= $64
Tax: 7.5%
Therefore, the bill after tax was:
[tex]=64(\frac{100+7.5}{100})\\= 64(1.075)\\[/tex]
Bill with tax = $68.8
Gratuity = 15.0% of bill with tax
Therefore, gratuity = 0.15 * 68.8
= $10.32
Ended up paying in total = Gratuity + Bill with tax
= $68.8 + $10.32
= $79.12
Help ! What do we know about the slopes of two lines if we are told that the lines are parallel?
Answer:
they have the same slope
Step-by-step explanation:
because if they are parallel they have the same slope
What would Y be equal to in the problem 0.5x + 0.6y = 5.4
Answer:
y = -[tex]\frac{5}{6}[/tex]x + 9
Step-by-step explanation:
0.5x + 0.6y = 5.4
0.6y = -0.5x + 5.4
Multiply 10 on all sides.
6y = -5x + 54
Divide 6 on all sides.
y = -[tex]\frac{5}{6}[/tex]x + 9
PLEASE HELP IM BEGGING YOU!!!
Find the value of x. Round angle measures to the nearest degree.
Answer:
61°Step-by-step explanation:
sin x = 29/33sin x =0.8787x = arcsin(0.8787)arcsin (0.8787) = 61.5°Correct choice is 61°
If the probability of an event is
23
96
, what is the probability of the event not happening?
Answer:
73/96
Step-by-step explanation:
I hope you meant 23/96
the probability of not happening would be 1-23/96
73/96
y – 3(2y – 7) = 76
solve for Y!!
Answer:
y=-11
Step-by-step explanation:
Answer:
y = -11
Step-by-step explanation:
y – 3(2y – 7) = 76
y - 6y + 21 = 76
-5y + 21 = 76
-5y = 55
y = -11
What is the measure of BAC. Degree of 53
Answer:
37
Step-by-step explanation:
-2w - 5w =
Please help me it’s due tomorrow
Answer:
-7w
Step-by-step explanation:
-2w - 5w = -7wI hope this helps!
Answer:
-7w
Step-by-step explanation:
Since they are like terms, think about it as the w not being there at all and just doing -2 - 5.
Jackson weighed all of his pet guinea pigs and found the average weight to be 2.4 pounds. If the standard error of the sample mean was 0.2227 and the sample standard deviation was 0.63 pounds, how many guinea pigs does Jackson have
Using the Central Limit Theorem, it is found that Jackson has 8 guinea pigs.
What does the Central Limit Theorem state?It states that the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], in which [tex]\sigma[/tex] is the standard deviation of the population.
In this problem, we have that [tex]s = 0.2227, \sigma = 0.63[/tex], hence we solve for n to find the number of guinea pigs that he has.
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.2227 = \frac{0.63}{\sqrt{n}}[/tex]
[tex]0.2227\sqrt{n} = 0.63[/tex]
[tex]\sqrt{n} = \frac{0.63}{0.2227}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{0.63}{0.2227}\right)^2[/tex]
[tex]n = 8[/tex]
Jackson has 8 guinea pigs.
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Let f be the continuous function defined on [-6,6]. Let g be the function given by g(x) = [tex]\int\limits^x_{-1} {f(t)} \, dt[/tex] . Write an equation for the tangent to the graph of g at x=4
Answer:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle g(x) = \int_{-1}^x f(t)\, dt[/tex]
And we want to write the equation for the tangent to the graph of g at x = 4.
First, determine g(4):
[tex]\displaystyle \begin{aligned} g(4) & = \int_{-1}^{(4)} f(t)\, dt \end{aligned}[/tex]
This is equivalent to the area of f from -1 to 4:
[tex]\displaystyle \begin{aligned} g(4) & = \frac{1}{2}(2)(3) + \frac{1}{2}(2)(-3)+\frac{1}{2}(-3+(-2))(1) \\ \\ & = \frac{1}{2}(6-6-5) \\ \\ & = -\frac{5}{2}\end{aligned}[/tex]
Note that areas under the x-axis are negative.
Find g'(4):
[tex]\displaystyle \begin{aligned} g'(x) = \frac{d}{dx}\left[ \int_{-1}^x f(t)\, dt\right]\end{aligned}[/tex]
By the Fundamental Theorem of Calculus:
[tex]\displaystyle \begin{aligned} g'(x) & = f'(x) \\ \\ g'(4) & = f'(4) \\ \\ & =1 \end{aligned}[/tex]
Note f is a line for 3 < x < 6 with a slope of 1.
Therefore:
[tex]\displaystyle \begin{aligned} h(x) -g(x_1) & = g'(x_1)(x-x_1) \\ \\ h(x) - \left(-\frac{5}{2}\right) & = (1)(x-(4)) \\ \\ h(x)& = (x-4) - \frac{5}{2} \\ \\ & = x - \frac{13}{2}\end{aligned}[/tex]
In conclusion, the equation of the tangent line is:
[tex]\displaystyle h(x) = x-\frac{13}{2}[/tex]
What is the quotient of 534÷112
Answer:
4.76785714286
1. The full Renegade dance Jalaiah created is 56 seconds long. For a 15-second-long TikTok, what percent of Renegade is used?
Answer:
3.7
Step-by-step explanation:
You have to divide
Answer:
i do not know tbh .
Step-by-step explanation:
A study was conducted investigating the long-term prognosis of children who have suffered an acute episode of bacterial meningitis, an inflammation of the membranes enclosing the brain and spinal cord. Listed below are the times to the onset of seizure for 13 children who took part in the study [10]. In months, the measurements are: 0.10 0.25 0.50 4 12 12 24 24 31 36 42 55 96 60 Chapter 3 Numerical Summary Measures
(a) Find the following numerical summary measures of the data.
i. mean
ii. range
iii. median
iv. interquartile range
v. mode
vi. standard deviation
(b) Show that L.~,: 1 (x;- X) is equal to 0.
Answer:
I'll help you
Step-by-step explanation:
In the given set of data, mean is 0.352, range is 0.86, median is 0.31, interquartile range is 0.28, mode is 0.12 and 0.24, and standard deviation is 0.81.
What is a data set?A data set is a certain number of data given in any order.
Given, the measurements for 13 children are: 0.10, 0.25, 0.50, 0.4, 0.12, 0.12, 0.24, 0.24, 0.31, 0.36, 0.42, 0.55, 0.96.
By rearranging the data set in ascending order we get:
(0.10, 0.12, 0.12, 0.24, 0.24, 0.25, 0.31, 0.36, 0.4, 0.42, 0.50, 0.55, 0.96.)
1. Therefore, mean
= (0.10 + 0.25 + 0.50 + 0.4 + 0.12 + 0.12 + 0.24 + 0.24 + 0.31 + 0.36 + 0.42 + 0.55 + 0.96)/13
= 4.57/13
= 0.352
2. Therefore, range
= (0.96 - 0.10)
= 0.86
3. Therefore, median = 0.31
4. Here, median of the first half of the data set is
= Q₁
= (0.12 + 0.24)/2
= 0.18
Again, median of the second half of the data set is
= Q₃
= (0.42 + 0.50)/2
= 0.46
Therefore, the interquartile range
= (Q₃ - Q₁)
= (0.46 - 0.18)
= 0.28
5. Therefore, mode = 0.12, 0.24
6. Therefore, standard deviation is
= √[(x₁ - X)² + (x₂ - X)² + (x₃ - X)² + (x₄ - X)² + (x₅ - X)² + (x₆ - X)² + (x₇ - X)² + (x₈ - X)² + (x₉ - X)² + (x₁₀ - X)² + (x₁₁ - X)² + (x₁₂ - X)² + (x₁₃ - X)²]
Here, x₁, x₂,......, x₁₃ are given data set in ascending order.
X = mean of the given data set.
Therefore, standard deviation is
= √[(0.10 - 0.352)² + (0.12 - 0.352)² + (0.12 - 0.352)² + (0.24 - 0.352)² + (0.24 - 0.352)² + (0.25 - 0.352)² + (0.31 - 0.352)² + (0.36 - 0.352)² + (0.40 - 0.352)² + (0.42 - 0.352)² + (0.50 - 0.352)² + (0.55 - 0.352)² + (0.96 - 0.352)²]
= √[.064 + 0.054 + 0.054 + 0.013 + 0.013 + 0.01 + 0.0018 + 0.00006 + 0.0023 + 0.0046 + 0.023 + 0.039 + 0.37]
= √(.6488)
= 0.81
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Describe how the graph of y = -2(x-4)3 + 1 can be obtained from the graph of y = x3.
I am guessing you meant y=-2(x-4)^3+1 from x^3
From the parent cubic function x^3,
a(x-k)^3+h is its transformation and it would be vertical stretch by a, followed by a horizontal translation by k and vertical translation by h
Your equation follows the same format it has a negative sign at the front before the ( ) which means a reflection over the x axis at the beginning
SO your graph is a
1.reflection over the x axis
2.followed by a vertical stretch by 2
3.followed by a horizonal translation to the right 4
4.followed by a vertical translation up 1
from x^3
I hope this helped, please ask if you have any questions!
A box is 36 inches long
18 inches wide
And 6 inches deep
How many cubic feet are in the box
3,888 ft³
Step-by-step explanation:
Multiply the dimensions together.
Therefore, the box is 3,888 ft³.
a container holds 24 pints of lemonade. how much is this in gallons?
Answer:
The answer is 3 gallons.
8. An adult male elephant can weigh up to 15,000 pounds. How many tons is this?
show your work.
Answer:
this is 7.5 tons.
Step-by-step explanation:
Simply divide 15,000lbs by 2,000lbs (how many lbs in a ton), and you get 7.5!
What is the measure of DE ? Would the correct answer be 5in
Answer:
I think it would be 5 I'm honestly not 100% sure though!
(The following information applies to the questions displayed below.
term
ns li
Saskatewan Can Company manufactures recyclable soft-drink cans. A
unit of production is a case of 12 dozen cans. The following standards
have been set by the production-engineering staff and the controller.
ook
Len
en W
rint
Direct Labor:
Quantity, 0.16 hour
Rate, $8.00 per hour
Direct Material:
Quantity, 9 kilograms
Price $0.42 per kilogram
erences
du. C
owth
sines
Actual material purchases amounted to 233,200 kilograms at $0.475
per kilogram. Actual costs incurred in the production of 22,000 units
were as follows:
arkets
pwth
Direct Labor:
Direct material:
$33,264 for 3,960 hours
$98,230 for 206,800 kilograms
onge
innov
sign,
Required:
The direct material price variance of Saskatewan Can Company will be $6552.
How to calculate the direct material price variance?From the information given, it should be noted that the direct material price variance will be calculated thus.
Firstly, the actual materials cost will be:
= Actual quantity × Actual price
= 218400 × $0.65
= $141960
The projected materials cost will be:
= 218400 × $0.62
= $135408
Therefore, the price variance will be:
= $141960 - $135408
= $6552
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Given the parent function f(x)= ???
in red, write the equation for the transformed function g(x)
in green in terms of f(x)
.
by name and label all inputs. 1: Saving for Retirement Devon is young and has just graduated college with her associate's degree. She plans to start saving money for retirement as soon as she starts her new job. By taking 10% of her monthly gross income, Devon is able to contribute (a) $ $587 each month to a retirement plan. The account is expected to earn interest with an APR of 5.25% compounded monthly. Round answers to two decimal places. a. How much money will be in Devon's retirement account if she continues to make the same monthly investment for 40 years? (3 pt) I b. Overall, Devon contributed how much of her own money into the retirement account? (4 pt)
The amount of money in Devon's retirement account if she saves $587 each month for 40 years is $956,488.14.
The total amount of her money contributed is $956,488.14.
What is the value of th retirement account?The formula that can be used to determine the future value of the retirement account is:
Future value = monthly contribution x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 5.25% / 12 = 0.4375%n = number of years = 40 x 12 = 480{[(1.004375^480) - 1] / 0.004375} x $587 = $956,488.14
Total contributions = $587 x 12 x 40 = $281,760
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help is needed here please and thank you!
How do I find the value of x??
Answer:
85
Step-by-step explanation:
The sum of the angles inside a triangle is 180 degrees.
A circle is 360 degrees, making half of it be 180 as well.
Since there are 121 degrees already marked, subtract it from 180 and you will get 59 degrees.
36 + 59 = 95
180 - 95 = 85 degrees.
Answer:
x = 85
Step-by-step explanation:
angles of a triangle = 180 degrees (all angles must equal 180)
if you minus 121 from 180, it will give the interior angle which is 59 degrees
therefore 59 + 36 + x = 180
to find x plus 59 and 36 = 95 degrees
180 - 95 = 85
x = 85 degrees
what is -5½×2¾ ????
Answer:
Mixed fraction: -15 1/8
Improper fraction: 121/8
Please help with the attached file! Thank you
9514 1404 393
Answer:
see attached
Step-by-step explanation:
There is no 'y'. Your problem statement has a typo.
Pick any values of x you like. I find small integers are usually convenient. I also find a spreadsheet does repetitive evaluation very nicely. See the attached for an appropriate table.
three notebooks and 4 binders are $9.00. two notebooks and 4 binders cost $8.00. how much does a binder cost?