Answer:
Step-by-step explanation:
number of samples, n = 10
Mean = (48 + 51 + 46 + 52 + 47 + 48 + 47 + 50 + 51 + 59)/10 = 49.9
Standard deviation = √(summation(x - mean)/n
Summation(x - mean) = (48 - 49.9)^2 + (51 - 49.9)^2 + (46 - 49.9)^2+ (52 - 49.9)^2 + (47 - 49.9)^2 + (48 - 49.9)^2 + (47 - 49.9)^2 + (50 - 49.9)^2 + (51 - 49.9)^2 + (59- 49.9)^2 = 128.9
Standard deviation = √128.9/10 = 3.59
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 10 - 1 = 9
Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05
α/2 = 0.05/2 = 0.025
the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975
Looking at the t distribution table,
z = 2.262
Margin of error = 2.262 × 3.59/√10
= 2.57
the lower limit of this confidence interval is
49.9 - 2.57 = 47.33
the lower limit of this confidence interval is
49.9 + 2.57 = 52.47
So it is false
If I have 196 points and then loose 227 points how many points do I have in total
Answer:
You would have -31 points left. :)
196 - 227 = -31
Hope this helped!!
Answer:
-31
Step-by-step explanation:
196 - 227 = -31
Complete each equivalent rate.
20 miles
1 gallon
180 miles
gallons
Answer:
20 gallons per 180 miles
Step-by-step explanation:
i need the steps for 29
You ride your bicycle 40 meters. How many complete revolutions does the front wheel make?
The front wheel of the bicycle makes approximately 18 complete revolutions.
Explanation:To find the number of complete revolutions the front wheel makes, we need to know the circumference of the wheel. Let's assume the diameter of the wheel is 0.7 meters. The circumference of the wheel can be calculated using the formula C = πd, where C is the circumference and d is the diameter. Substituting the given values, C = 3.14 * 0.7 = 2.198 meters.
Since the bicycle travels 40 meters, we can divide the distance traveled by the circumference of the wheel to find the number of complete revolutions. 40 / 2.198 = 18.19.
So, the front wheel of the bicycle makes approximately 18 complete revolutions.
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Find the following product if possible. Explain if it is not possible.
(See picture)
Answer:
The answer to your question is the letter a
Step-by-step explanation:
| 1 4 -1 | | 2 -1 |
| 3 2 2 | | 0 3 | Product = 2 x 3 and 3 x 2 = 2 x 2
| 5 2 | It is possible to do this product,
the result will be a 2 x 2 matrix
Process
1.- Multiply first row by first column and second row by second column.
2.- Multiply the second row by the first column and second row by the second column.
= (1 x 2) + (4 x 0) + (-1 x 5) = 2 + 0 - 5 = -3
= (1 x -1) + (4 x 3) + (-1 x 2) = -1 + 12 - 2 = 9
= (3 x 2) + (2 x 0) + (2 x 5) = 6 + 0 + 10 = 16
= (3 x -1) + (2 x 3) + (2 x 2) = -3 + 6 + 4 = 7
Result
| 3 9 |
| 16 7 |
You deposit $1800 into a bank account that pays 5% annual interest. Find the balance after 7 years if the interest is compounded quarterly. Round to the nearest cent
Answer:
The balance after 7 years would be $2,548.79
Step-by-step explanation:
We are given the following in the question:
P = $1800
r = 5% = 0.05
t = 7 years
The compound interest is given by:
[tex]A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.
When compounded quarterly, n = 4
Putting values, we get,
[tex]A = 1800\bigg(1+\dfrac{0.05}{4}\bigg)^{28}\\\\A = \$2,548.79[/tex]
Thus, the balance after 7 years would be $2,548.79
A researcher wishes to estimate the proportion of adults who have high-speed internet access. what size sample should be obtained if she wishes the estimate to be within 0.050.05 with 9999% confidence if (a) she uses a previous estimate of 0.580.58? (b) she does not use any prior estimates?
Answer:
a) [tex]n=\frac{0.58(1-0.58)}{(\frac{0.05}{2.58})^2}=648.600[/tex]
And rounded up we have that n=649
b) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.58})^2}=665.64[/tex]
And rounded up we have that n=666
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]
Part a
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.58(1-0.58)}{(\frac{0.05}{2.58})^2}=648.600[/tex]
And rounded up we have that n=649
Part b
For this case we can use an estimator for p as [tex]\hat p=0.5[/tex]
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.58})^2}=665.64[/tex]
And rounded up we have that n=666
Which one is bigger 2.300 mg or 2 g
Answer:
2 grams is bigger than 2.300 mg.
Step-by-step explanation:
1 milligram is equal to 0.001 gram.
1 gram is equal to 1000 milligrams.
If this helped you, Brainliest is appreciated.
Answer:
2 grams is bigger
Step-by-step explanation:
Two grams is bigger than 2.3 milligram . This is because 1 gram is equivalent to 1000 milligrams. To work that out you would multiply 2 by 1000, which is 2000
1 gram=1000 milligram
1) Multiply 2 by 1000.
[tex]1000*2=2000 mg[/tex]
However if it was a misplaced decimal and it was meant to be 2300 milligrams, then 2300 milligrams would be bigger.
The Pew Research Center interviewed a random sample of 1,546 adult Americans to determine the average time they spent sleeping per night. The sample mean was found to be 7.2 hours of sleep, with a sample standard deviation of 1.4 hours. Construct a 95% confidence interval for the true mean. Interpret your confidence interval in words.
Answer:
CI=[ 7.1302,7.2698]
we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]
Step-by-step explanation:
-Given that the sample size, n=1546 the mean is 7.2 hrs and the standard deviation, [tex]\sigma=1.4[/tex]
-The 95% confidence interval can be calculated using the formula:
[tex]CI=\mu\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\\\=\mu\pm z_{0.025}\times \frac{\sigma}{\sqrt{n}}\\\\=7.2\pm1.96\times \frac{1.4}{\sqrt{1546}}\\\\=7.2\pm 0.0698\\\\CI=[7.1302, \ 7.2698][/tex]
The confidence intervals is therefore 7.1302,7.2698]
Hence, we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]
The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 2,000 people entered the park, and the admission fees that were collected totaled $4,750. How many children and how many adults were admitted
Answer:
In that day 1300 children and 700 adults were admitted.
Step-by-step explanation:
Since the people who enter the park are either adults or children, the sum of these two types of people must be equal to the total amount that entered the park. So we have:
children + adults = 2000
The total amount collected must be the sum of the people that entered the park multiplied by the ticket fee for each type. We have:
1.5*children + 4*adults = 4750
We now have two equations and two variables so we can solve the system.
children + adults = 2000 equation 1
1.5*children + 4*adults = 4750 equation 2
We can multiply the equation 1 by -1.5 and sum it with the equation 2 to solve for adults, we have:
-1.5*children - 1.5*adults = -3500
1.5*children + 4*adults = 4750
2.5*adults = 1750
adults = 1750/2.5 = 700
To solve for children we apply the found value for adults on the equation 1.
children + 700 = 2000
children = 2000 - 700 = 1300
In that day 1300 children and 700 adults were admitted.
Answer:
700 adults and 1300 children
Step-by-step explanation:
Let 'C' represent number of children
'A' represent number of adults
->If 2,000 people entered the park, the equation will be
C+A=2000
C=2000-A ->eq(1)
->$1.50 for children and $4.00 for adults.
$1.50C+$4.00A=$4,750
Substituting for C from above.
$1.50(2000-A)+$4.00A= $4,750
$3000-$1.50A+$4.00A=$4,750
$2.50A = $4,750 - $3000
$2.50A=$1750
A= 700
and for children:
eq(1)=>
C=2000-700
C= 1300
Thus, 700 adults and 1300 children were admitted.
I need help asap:):):):
Answer:
4
Step-by-step explanation:
As you only need the answer (•‿•)
Answer:
5 shirts
Step-by-step explanation:
First, subtract the shipping from her money. 45 - 2.50 = 42.50. Now divide this by the price of each shirt. 42.50 ÷ 8.50 = 5. The shipping fee only applies once because it is for the entire order.
I need electricity asap :):):):(:
Answer:
C
Step-by-step explanation:
You distribute the 11 with the numbers in the parenthesis
skylar has 1/2 of her sub left from lunch she wants to cut it into thirds find the length of each piece
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given:
Skylar has 1/2 of her sub left from lunch she wants to cut it into thirds
Question asked:
Find the length of each piece ?
Solution:
Sub left from lunch = [tex]\frac{1}{2}[/tex]
As she want to cut into third, we will divide [tex]\frac{1}{2}[/tex] into [tex]\frac{1}{3}[/tex]
[tex]=\frac{1}{2}\div\frac{1}{3}\\ \\ =\frac{1}{2}\times\frac{3}{1} \\ \\ =\frac{3}{2}[/tex]
Thus, length of each piece will be [tex]\frac{3}{2}[/tex]
People use water to cook, clean, and drink every day. An estimate of 26.5% of the water used each day is for cleaning. If a family uses 68.9 gallons of water a day for cleaning, how many gallons do they use every day?
Final answer:
To find the total daily water usage of the family, divide the amount of water they use for cleaning, 68.9 gallons, by the percentage of their total usage that goes to cleaning, which is 26.5%. The result is that the family uses about 260 gallons of water every day.
Explanation:
To calculate how many gallons of water the family uses every day, we need to establish the total daily water usage based on the percentage used for cleaning.
Since we know that 26.5% of their total water usage is allocated for cleaning, and they use 68.9 gallons for this purpose, we can find the total daily usage with a simple division:
Total daily water usage = Water used for cleaning / Percentage used for cleaning Total daily water usage = 68.9 gallons / 0.265 Total daily water usage = 260 gallons (rounded to the nearest whole number)
Thus, the family uses approximately 260 gallons of water per day for all their needs, including cooking, cleaning, and drinking.
Final answer:
To find out how many gallons a family uses every day, set up a proportion to find the total amount of water used for cleaning and solve for x. The family uses approximately 259.62 gallons of water every day.
Explanation:
To find out how many gallons a family uses every day, we need to determine the total amount of water used for cleaning. The question states that 26.5% of the water used each day is for cleaning, and the family uses 68.9 gallons for cleaning. We can set up a proportion to find the total amount of water used:
26.5% / 100% = 68.9 / x
Now we can solve for x by cross multiplying:
26.5x = 68.9 * 100
Dividing both sides of the equation by 26.5, we find that x is approximately 259.62.
Therefore, the family uses approximately 259.62 gallons of water every day.
Akira turns in a written lab report to his science teacher.
Answer:
communicating results
Step-by-step explanation:
hope this helps
ax + 3x = bx + 5
solve for x
Answer:
Step-by-step explanation:
hello :
Ax + 3x = bx + 5
Ax + 3x-bx = bx-bx + 5
x(A+3-b) =5
x= 5/(A+3-b)
3. George is making a triangle that is similar to the one below. The length of the longest side of the new
triangle is 9 inches.
15 inches
8 inches
10 inches
What is the length of the shortest side of the new triangle?
Final answer:
The shortest side of the new similar triangle, where the longest side is 9 inches, is found to be 4.8 inches. This is determined by using the scale factor 3/5, obtained from the original triangle with sides 15 inches, 8 inches, and 10 inches.
Explanation:
The student asks for the length of the shortest side of a new triangle similar to the one given, with the length of the longest side being 9 inches. To find this, we need to use the concept of similar triangles. Similar triangles have proportional corresponding sides.
The original triangle has sides of lengths 15 inches (longest side), 8 inches (shortest side), and 10 inches. Given that the longest side of the new triangle is 9 inches, we can find the scale factor by dividing the new longest side by the original longest side: 9 inches / 15 inches = 3/5.
Now, we use this scale factor to find the length of the shortest side in the new triangle: 8 inches (original shortest side) x 3/5 (scale factor) = 4.8 inches.
Therefore, the length of the shortest side of the new triangle is 4.8 inches.
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A grocery store clerk put only packages of purple grapes and packages of green grapes on a shelf. The ratio of the number of packages of green grapes to the total number of packages on the shelf was 9 to 14. Which number could be the number of packages of purple grapes the clerk put on the shelf?
Answer:
The answer is 5, 10, 15, 20 or any positive multiples of 5
Step-by-step explanation:
Since the ratio of green grapes to the total number of grapes is 9:14 and there are only purple and green grapes on the shelf. It implies the total number of purple grapes to overall grapes is 5:14.
Since this ratio is already at it's lowest form, it implies the possible number of purple grapes are 5, 10, 15, 20 or any positive multiple of 5.
(5w7)2
What is the simplified power of the product?
A. 5w9
B. 10w14
C. 25w9
D. 25w14
Answer:
Its D i did the question
Step-by-step explanation:
Add 6x+2y=-2 and 3x-2y=-5
Answer:
[tex]6x+2y=-2\\3x-2y=-5\\-------\\9x=-7[/tex]
Step 1: Subtract 3 from both sides of the inequality.
Step 2: __________
Step 3: Divide both sides of the inequality by the coefficient of x.
What is the missing step in solving the inequality 5 – 8x < 2x + 3?
Add 2x to both sides of the inequality.
Subtract 8x from both sides of the inequality.
Subtract 2x from both sides of the inequality.
Add 8x to both sides of the inequality.
Answer:
Add 8x to both sides of the inequality
Step-by-step explanation:
took the quiz
If an object is projected upward from ground level with an initial velocity of 96 ft per sec, then its height in feet after t seconds is given by s(t)equalsminus16tsquaredplus96t. Find the number of seconds it will take to reach its maximum height. What is this maximum height?
Answer:
Number of seconds to reach maximum height = 3 seconds
Maximum height = 144 ft
Step-by-step explanation:
We are given that;
s(t) = -16t² + 96t
Now, s(t) is a function whose graph is an upside-down parabola, so the maximum s value occurs at the vertex.
Thus, the applicable formula for coordinate of vertex is t = -b/(2a) where a is the coefficient -16 and b is 96
Thus,t = -96/(2 x - 16)
t = 96/32
t = 3
Thus maximum height will be at 3 seconds.
Thus;
Max height = s(3) = -16(3)² + 96(3)
Max height = -144 + 288 = 144 ft
The object will reach its maximum height of 144 feet in 3 seconds.
Given information:
An object is projected upward from ground level with an initial velocity of 96 ft per sec.
The height in feet after t seconds is given by [tex]s(t)=-16t^2+96t[/tex].
Now, it is required to find the time at which the object will reach its maximum height.
The object will reach maximum height when velocity of the object becomes zero.
So, the velocity of the object can be written as,
[tex]s(t)=-16t^2+96t\\v(t)=\dfrac{d(s(t))}{dt}=-32t+96[/tex]
So, the time at maximum height can be calculated as,
[tex]v(t)=-32t+96=0\\t=3[/tex]
So, after 3 seconds the object will reach its maximum height.
Now, the maximum height of the object will be,
[tex]s(t)=-16t^2+96t\\s(3)=-16\times 3^2+96\times 3\\s(3)=144\rm \; ft[/tex]
Therefore, the object will reach its maximum height of 144 feet in 3 seconds.
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The function f(x)= 9√x gives the speed in feet per second (ft/s) of a free-falling object after it has fallen x feet (ignoring air resistance). FInd the speed of the object after it has fallen 26 feet. If necessary, round your answer to the nearest tenth.
Answer:
45.9ft/s
Step-by-step explanation:
Simply plug your given value into the function
[tex]f(26)=9\sqrt{26} = 45.9 (1.d.p.)[/tex]
can someone please help me with these algebra questions? image attached.
Answer:
The x-intercepts would be where the line hits the x-axis, so the x-intercepts would be:
-3, 2, and 5.
Step-by-step explanation:
Answer:
q4 is -3,2,5
and for q3 is the start point
Special Triangles
Find the missing side lengths. Leave answers as radicals in the simplest form.
Answer:
see explanation
Step-by-step explanation:
Using the cosine and tangent trigonometric ratios and the exact values
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{m}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] × m = 12 ( divide both sides by [tex]\sqrt{3}[/tex] )
m = [tex]\frac{12}{\sqrt{3} }[/tex] ← rationalise by multiplying numerator/ denominator by [tex]\sqrt{3}[/tex] )
m = [tex]\frac{12}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{12\sqrt{3} }{3}[/tex] = 4[tex]\sqrt{3}[/tex]
-------------------------------------------------------------------------------
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{n}{6}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
[tex]\sqrt{3}[/tex] × n = 6 ( divide both sides by [tex]\sqrt{3}[/tex] )
n = [tex]\frac{6}{\sqrt{3} }[/tex] ← rationalise the denominator
n = [tex]\frac{6}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]
-----------------------------------------------------------------------------------
Simplify each expression.
ln e3 =
ln e2y =
eln 1 =
eln 5x =
Answer:
Step-by-step explanation:
the answers for "in e^3" is 3
"in e^2y" is 2y
"e^in 1" is 1
"e^in 5x" is 5x
Answer: 3, 2y, 1, 5x.
We have to simplify the given expressions.
We use the formula: [tex]ln(e^a)=a[/tex].
So, [tex]ln(e^3)=3[/tex], here a = 3.
[tex]lne^{2y}=2y[/tex], here a = 2y.
We will use that: ln(1) = 0 and [tex]e^{ln(b)}=b[/tex]
[tex]e^{ln(1)}=e^0=1[/tex]
[tex]e^{ln(5x)}=5x[/tex], here b = 5x.
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The population of a small town is given by the function p=35t+1450,where t is the number of years since 2015. What would the town's population be in 2020
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------------------
Answer: The population is 1,625.
So the equation is:
p = 35t + 1,450.
t = the number of years since 2015.
2020 - 2015 = 5.
So now we are in 2020, which is 5 years ahead from 2015.
So: t = 5.
Now we need to rewrite the equation, then evaluate.
35(5) + 1,450 =
175 + 1,450 =
1,625What is the slope of the line through the points (-4, 6) and (-3, -1)?
Answer:
m= -7
Step-by-step explanation:
using the slope formula, plug in the variables and solve
m=rise/run
m=y2-y1 / x2-x1
(x1, y1) = coordinates of first point in the line
(x2, y2) = coordinates of second point in the line
Answer:
[tex]slope=-7[/tex]
Step-by-step explanation:
Use the slope formula for when you have two points:
[tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
It is y over x because slope is rise over run : the change in the y-axis over the change in the x-axis. Plug in values:
(-4,6) (-3,-1)
[tex]\frac{-1-6}{-3-(-4)}[/tex]
Simplify
[tex]\frac{-1-6}{-3+4}=\frac{-7}{1}[/tex]
Simplify
[tex]\frac{-7}{1}=-7[/tex]
Done.
The volume of a cylinder is 480 cm. The height of the cylinder is 30 cm. What is the radius of the
cylinder?
The radius of the cylinder is cm. (Simplify your answer.)
Answer:
Step-by-step explanation:
Given
Volume of Cylinder (V)= 480 cm
height (h) = 30 cm
radius (r) = ?
WE KNOW THAT WE HAVE FORMULA
Volume (V) = [tex]\pi r^{2} h[/tex]
480 = 3.14 * r^2 *30
480 = 94.2 r^2
480/94.2 = r^2
r^2 = 5.1
r =[tex]\sqrt{5.1}[/tex]
Therefore r = 2.3 cm
PLEASE HELP!!!!
Ms. Calcutta, the owner of a business park is adding a recycling station for every three office buildings. To make it easier for the tenants, she is going to to use the circumcenter of the three office buildings to place the recycling stations. By doing this, it will be easier to get to the station, because it is equidistant from the three office buildings.
Complete Question:
Justify the rationale behind Ms Calcutta's decision to use the circumcenter
Answer:
Check below for the answer and explanations.
Step-by-step explanation:
Ms Calcutta wants every occupant of the three office buildings to have equal easy access to the recycling station. The circumcenter of the three three office buildings, where the recycling station is located, has equal distance from the three offices, this means that all of Ms. Calcutta's workers in the three buildings can have to the recycling station equally without causing unnecessary inconvenience for occupants of any of the buildings.