Express in the form 1: n.
Give n as a decimal.
18:9
Answer:
n = 0.5
Step-by-step explanation:
In order to compare the performance of students in large enrollment and small enrollment sections, 35 students from large sections and 35 students from small sections of a freshman mathematics course were randomly selected. The mean and sample standard deviation of grades on the common final exam for the students from large sections were 72.8 and 7.4; for the students from small sections, the mean and standard deviation were 75.3 and 6.8. A 90% confidence interval for the difference in the mean common final exam scores between students in the two types of sections is about:
Answer:
The 90% confidence interval for the difference in the mean common final exam scores between students in the two types of sections is about (-5.3, 0.3).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
35 students from large sections. The mean and sample standard deviation of grades on the common final exam for the students from large sections were 72.8 and 7.4;
This means that:
[tex]\mu_L = 72.8, s_L = \frac{7.4}{\sqrt{35}} = 1.25[/tex]
35 students from small sections. For the students from small sections, the mean and standard deviation were 75.3 and 6.8.
This means that:
[tex]\mu_S = 75.3, s_S = \frac{6.8}{\sqrt{35}} = 1.15[/tex]
Distribution of the difference in the mean common final exam scores between students in the two types of sections:
Has mean and standard error given by:
[tex]\mu = \mu_L - \mu_S = 72.8 - 75.3 = -2.5[/tex]
[tex]s = \sqrt{s_L^2+s_S^2} = \sqrt{1.25^2 + 1.15^2} = 1.7[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs = 1.645*1.7 = 2.8[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is -2.5 - 2.8 = -5.3
The upper end of the interval is the sample mean added to M. So it is -2.5 + 2.8 = 0.3
The 90% confidence interval for the difference in the mean common final exam scores between students in the two types of sections is about (-5.3, 0.3).
A. 2 in
B. 4 in
C. 8 in
D. 16 in
The perimeter of a rectangular mat is 16 feet. It is 6 feet long. How wide is it?
A 2 ft
B 1 ft
C3ft
D4ft
Answer:
2ft
Step-by-step explanation:
because perimeter of a rectangle formula is p=2(l+w)
A store pay $120 for a bicycle. The store has a 60% markup policy. What is the selling price of the bicycle? (answer $192)
Use your answer from the above question to help answer this question!! The store is now going out of business and is selling all of the bicycles at a 30% discount. What is the sale price of the bicycle?
Three years ago, the annual tuition at a university was $3,000. The following year, the tuition was $3,300, and last year, the tuition was $3,630. If the tuition has continued to grow in the same manner, what is the tuition this year? What do you expect it to be the next year?
Answer:
$3990
Step-by-step explanation:
First, if the tuition increased by 300 the first year, and 330 the next year, I can infer that the tuition increases by $30 a year. This year, the the tuition will cost 360, because 330 + 30 = 360. So, this year the tuition will be 3990, because 3630 + 360 = 3990.
Hope this helps
Someone please help
Answer:
Step-by-step explanation:
Exponential function representing final amount with compound interest compounded continuously,
[tex]A=Pe^{rt}[/tex]
Here, A = Final amount
P = principal amount
r = Rate of interest
t = Duration of investment
For P = $9600
r = 6%
A = 2 × 9600 = $19200
By substituting these values in the formula,
[tex]19200=9600(e)^{0.06\times t}[/tex]
[tex]2=e^{0.06t}[/tex]
[tex]ln(2)=ln(e^{0.06t})[/tex]
ln(2) = 0.06t
t = [tex]\frac{0.693147}{0.06}[/tex]
t = 11.55245
t ≈ 11.5525 years
Any amount will get doubled (with the same rate of interest and duration of investment) in the same time.
Therefore, $960000 will get doubled in 11.5525 years.
6 x [(6 x 2.3) + 3.9]
Answer:
106.2
Step-by-step explanation:
First, Multiply 6 and 2.3
6x2.3= 13.8
Once you found your product, add 13.8 and 3.9
13.8+3.9= 17.7
6 x 17.7= 106.2One positive number is 9 more than twice another. If their product is 731, find the numbers.
Answer:
361
Step-by-step explanation:
The table shows the number of apples and the total weight of the apples estimate the weight of 6 apples
Answer:
6 apples will weigh about 1,533 grams
Step-by-step explanation:
Set up an equation:
2
Variable x = weight of 6 apples
2/511 = 6/x
Cross multiply
2 × x = 511 × 6
2x = 3066
Divide both sides by 2
x = 1533
Check your work
2/511 = 6/1533
2 × 1533 = 511 × 6
3066 = 3066
Correct
Please help! Will give brainliest!
Don't give a like.
9514 1404 393
Answer:
fractiondenominatorproductnumeratorStep-by-step explanation:
When you multiply a fraction by a whole number, the denominator in the product is the same as the denominator of the fraction. The numerator in the product is the product of the whole number and the numerator of the fraction.
__
That's the rule. It is derived from the fact that multiplication indicates repeated addition.
[tex]\dfrac{2}{7}\times3=\dfrac{2}{7}+\dfrac{2}{7}+\dfrac{2}{7}=\dfrac{2+2+2}{7}=\dfrac{2\times3}{7}\qquad\text{for example}[/tex]
Need ASAP I’ll mark brainliest if right
Answer:
616 in²
Step-by-step explanation:
14 × 14 × 22/7
=> 616
Answer:
616 inches squared
Step-by-step explanation:
14 × 14 × 22/7
=> 616
pls answer me this all question
Answer:
a. [tex]5 \frac{21}{40} [/tex]
b. [tex] \frac{1}{42} [/tex]
Step-by-step explanation:
[tex]a. \: 12 \frac{2}{5} - 6 \frac{7}{8} [/tex]
[tex] \frac{62}{5} - \frac{55}{8} [/tex]
[tex] \frac{62}{8} \times \frac{8}{8} - \frac{55}{8} \times \frac{5}{5} [/tex]
[tex] \frac{62 \times 8 - 55 \times 5}{40} [/tex]
[tex] \frac{221}{40} [/tex]
[tex]5 \frac{21}{40} [/tex]
[tex]b. \: \frac{3}{14} - \frac{4}{21} [/tex]
[tex] \frac{3}{14} \times \frac{3}{3} - \frac{4}{21} \times \frac{2}{2} [/tex]
[tex] \frac{3 \times 3}{42} - \frac{4 \times 2}{42} [/tex]
[tex] \frac{1}{42} [/tex]
Hope it is helpful....
HELP ME PLEASEEEEEEEEE
0/25 is 0. 5/10 is 0.5 3/4 is 0.75 2/3 is 0.66666
Line A contains the points (– 6, – 3) and (– 2, – 1). Line B contains the points (8, 2) and (12, 4).
How many solutions does the system of equations have?
Answer:
One Answer
Step-by-step explanation:
Take two points like (8,2) and (12,4) and do y2-y1/x2-x1.
4-2/12-8 = 4/2 = 2.
Then that another point and plug it in to the equation, y = 2x + b.
i will use (8,2). 2 = 2(8)+b. solve this and you get b= -14.
now you found your answer. y=2x + -14.
What is the value of the second quartile
Answer:
the value is 20 out of 100
Step-by-step explanation:
The following prism has a base area of 20\pi20π20, pi square units and a volume of 120\pi120π120, pi cubic units. The cylinder has the same base area and height. What is the volume of the cylinder?
Given:
A prism has a base area of [tex]20\pi [/tex] square units and a volume of [tex]120\pi[/tex] cubic units.
To find:
The volume of the cylinder if the cylinder has the same base area and height.
Solution:
Volume of a prism is:
[tex]V=Bh[/tex]
Where, B is the base area and h is the height of the prism.
The volume of cylinder is:
[tex]V=\pi r^2h[/tex]
[tex]V=Bh[/tex]
Where, r is the radius, h is the height of the cylinder and [tex]B=\pi r^2[/tex] is the base area.
Since base area and height of the cylinder are same as the prism, therefore, there volumes are equal.
Hence the volume of the cylinder is [tex]120\pi[/tex] cubic units.
Answer:
120 pi cubic units
Step-by-step explanation:
What is the volume of the rectangular solid below?
Answer:
16 cubic units
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
A right triangle has a hypotenuse of 18 feet and a side length opposite ∠A of 12 feet. What is the measure of ∠A to the nearest degree?
Answer:
∠A = 42°
Step-by-step explanation:
sin ∠A = 12/18 = 0.6667
∠A = 41.81°
Answer:
42 degrees
Step-by-step explanation:
The dimensions of a figure are 5(2x+3). Which figure below represents the same figure and its area? F H 12x 36 5x 8 10x 15 2x 15
Answer:
The correct answer is G(1, 4).so go through it.
Solve for x
6-6x = -24
Answer:
=
5
Step-by-step explanation:
Answer:
X = 5
Step-by-step explanation:
The sum of the measures of three
angles is 90°
The measure of angle M is 2x
The measure of angle N is 3x + 8
The measure of angle Q is 7x - 2
What is the value of x?
FOR BRAINLIST!!
Answer:
A
Step-by-step explanation:
Equation
2x + 3x + 8 + 7x - 2 = 90
Solution
Combine like terms on the left
12x + 6 = 90 Subtract 6 on both sides
12x = 90 - 6
12x = 84 Divide by 12
x = 84/12
x = 7
what steps can be taken to find the product of 8.31 and 1,000
8300 is the product of 8.31 and 1,000
What is Multiplication?Multiplication is a method of finding the product of two or more numbers
We need to find the product of 8.31 and 1,000.
product of Eight point three one and thousand.
In the given numbers 8.31 is a decimal number and 1000 is a whole number.
To multiply both let us make thousand as a whole number by placing two zeros on right side of 1000 with a point.
1000.00
× 8.31
_________
8310
Hence, 8300 is the product of 8.31 and 1,000
To learn more on Multiplication click:
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find the asymptotes, domain, range and end behavior and sketch the parent graph with the translated graph
Answer:
27) x = 2^(y) – 5.
Asymptote: x = -5.
D: x > -5; (-5, infinity).
R: -infinity < f(x) < infinity; ARN;
(-infinity, infinity).
x → -infinity, f(x) → -infinity.
x → +infinity, f(x) → +infinity.
________________________
28) x = 2^-(y–3).
Asymptote: x = 0.
D: x > 0; (0, infinity).
R: -infinity < f(x) < infinity; ARN;
(-infinity, infinity).
x → -infinity, f(x) → +infinity.
x → +infinity, f(x) → -infinity.
________________________
29) x = 4^(y–2) + 1.
Asymptote: x = 1.
D: x > 1; (1, infinity).
R: -infinity < f(x) < infinity; ARN;
(-infinity, infinity).
x → -infinity, f(x) → -infinity.
x → +infinity, f(x) → +infinity.
________________________
An auditorium has 40 rows of seats. There are 20
seats in the first row. Each row has 2 more seats
than the row before.
Identify the number of seats in the first 4 rows:
Answer:
140 seats
Step-by-step explanation:
40 rows
1ˢᵗ row = 20 seats
39 next rows = 2×20 = 40 seats
First 4 rows = 20 seats + 3(40) seats = 140 seats
➪the 2ⁿᵈ, 3ʳᵈ and 4ᵗʰ rows have equal number of seats = 40 seats
Answer:
98
Step-by-step explanation:
X
A regular heptagon has a side of approximately 4.3 ft and an apothem of approximately 4.5 ft.
Find the area of the heptagon.
X
1+1
2.
X
4.5 ft
4.3 ft
Any know the answe
Answer: 67.7ft²
Step-by-step explanation:
Note that a heptagon has 7 sides.
The area of a heptagon is given as:
= 1/2 × nsr
where,
n = number of sides = 7
s = length of side = 4.3ft
r = apothem= 4.5ft
Area of the heptagon = ½nsr
= ½ × 7 × 4.3 × 4.5
= 135.45/2
= 67.7ft²
Therefore, the area of the heptagon is 67.7ft²
what is the difference between
7z
and z to the power of 7
Answer:
7z is the sum of seven 'z's while z to the power of z is the multiplication of z to itself z times.
Step-by-step explanation:
7z is 7 times of z.
7z= z +z +z +z +z +z +z
z⁷ (z to the power of 7) is multiplying z by itself 7 times.
z⁷= z ×z ×z ×z ×z ×z ×z
Use a+= then find the perimeter
A rectangle with a length of 15 feet has a
diagonal that measures 17 feet. Find the
perimeter of the rectangle.
A. 46 feet
B. 32 feet
C. 58 feet
D. 64 feet
ОА
Answer:
The answer is 46
Step-by-step explanation:
Since there is a diagonal, you can't assume that it is the width because if it was the width, it would say so. Since 17 was the measure of the diagonal, I did pythagorean theorem: 15^2 + x^2 = 17^2 --> 225 + x^2 = 289 --> x^2 = 64 --> x = 8. So now we have figured out the width of the rectangle and it's 8. Now we can add: 8 + 8 + 15 + 15 = 46. That is why the answer is 46.
The perimeter of the rectangle 46 feet.
The correct option is (A).
What is perimeter?Perimeter is the distance around the edge of a shape.
Learn how to find the perimeter by adding up the side lengths of various shapes.
Given : length= 15 feet and diagonal= 17 feet
Since there is a diagonal.
So, using Pythagorean theorem:
H² = P²+B²
15²+ x² = 17²
or, 225 + x² = 289
or, x² = 64
x = ± 8 feet.
Thus, width = 8 feet
Perimeter of rectangle= 2*(l+b)
= 2*(15+8)
= 2*23
=46 feet
Learn more about perimeter here:
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Please help fast !!!!
2. 1/3
3.
a) 40
b)30 or 40
c) 110
Answer:
2. [tex]\frac{1}{3} = 33%[/tex]
3. A. [tex]\frac{1}{4} = 25[/tex]
B. [tex]\frac{1}{2} = 50[/tex]
C. [tex]\frac{4}{5} = 80[/tex]
Step-by-step explanation:
Hope this helps
Which of the following is a biconditional statement?
Question 4 options:
A)
A shape has four sides if and only if it's a quadrilateral.
B)
If a shape has four sides, then it's a quadrilateral.
C)
If a shape is a quadrilateral, then it has four sides.
D)
If a shape doesn't have four sides, then it isn't a quadrilateral.
Answer:A)
A shape has four sides if and only if it's a quadrilateral.
Step-by-step explanation:
If a conditional statement and its converse are both true, then the statement is a biconditional statement. Biconditional statements can be written using the phrase “if and only if.” For example, a polygon is a hexagon if and only if it has six sides.