The volume of the cone is 56.52 cubic inches.
What is a cone?Having a flat base and a smooth tapering tip or vertex, a cone is a three-dimensional geometric object.
Given, the radius of the cone is 3 inches and the height of the cone is 6 inches.
The volume of a cone is given by,
V=(1/3)πr²h
V = (1/3) × 3.14 × 3² ×6
V = 56.52 cubic inches
Hence, the volume of the cone is 56.52 cubic inches.
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Find the product of (x − 2i)^2.
The product of (x-2i)²=x²-4+i4x
What is the process of multiplication of complex numbers?The product or multiplication of two complex numbers is also a complex number. The formula for multiplying complex numbers is: (a + ib) (c + id) = (ac - bd) + i(ad + bc).
Given here (x-2i)² =(x-2i) (x-2i)
=x²-4+i4x
Hence, the product is x²-4+i4x
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Tablets are on sale for 15% off the original price (t), which can be expressed with the function p(t) = 0.85t. Local taxes are an additional 8% of the discounted price (p), which can be expressed with the function c(p) = 1.08p. Using this information, which of the following represents the final price of a tablet with the discount and taxes applied based on its original price? (2 points) c[p(t)] = 0.918t c(p) + p(t) = 1.93t c(p) ⋅ p(t) = 0.918pt t[c(p)] = 1.93p
The final price of the tablet is c(t) = 0.918.
What is sale price?
A sale price is the discounted price at which goods or services are being sold.
According to the given question
Tablets are on sale for 15% off the original price(t), which can be expressed with the function:
p(t) = 0.85t
The additional taxes of 8% of the discounted price(p), which can be expressed as a function:
c(p) = 1.08p
Therefore,
The final price of a tablet with the discount and taxes applied based on its original price is given by
c(p(t)) = 1.08 ×p(t)
c(p(t)) = 1.08×(0.85t)
c(p(t)) = 0.918t
⇒ c(t) =0.918t
Hence, the final price of the tablet is c(t) = 0.918.
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type the slope-intercept equation of the line that passes through the points (0,2) and (2,0) y={?]x+{ }
The number of significant figures in 0.01500 is
The number of significant figures in 0.01500 is 4.
What are significant figures?Significant figures (or significant digits) are the number of digits in a given value or a measurement, necessary to decide the accuracy and precision of measurement.
The given decimal number is 0.01500.
Certain rules help us determine the number of significant figures. These rules are as follows:
(1) All non-zero digits are significant.
(2) All zeros in between non-zero digits are significant.
(3) Zeros on the right of a decimal point and before (or to the left of) the first non-zero digit are not significant. They only represent the position of the decimal point.
(4) Zeros on the right of a decimal point are significant, provided there is no non-zero digit after them.
(5) Zeros on the right of the last non-zero digit after a decimal point are significant. So, final zeros or trailing zeros in the decimal part are significant.
(6) In a measurement value, zeros that occur on the right of the last non-zero digit are significant.
In the given decimal 0.01500, two non zero digits and two leading zeros are significant
So, number of significant figures are 4
Therefore, the number of significant figures in 0.01500 is 4.
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can someone help me please
What is the median of 36, 14, 21, 56, and 10?
Rationalize the denominator. write it in simplest terms.
1
- ------------
√18x
yes it is a negative
Which is relatively better: a score of 79on a psychology test or a score of 48on an economics test? scores on the psychology test have a mean of 85and a standard deviation of 5.scores on the economics test have a mean of 52and a standard deviation of 3?
The correct option is that a score of 79 on a psychology test is relatively better than a score of 48 on an economics test.
To determine which score is relatively better, we can calculate the z-scores for each test score. The z-score tells us how many standard deviations away from the mean a particular score is.
For the psychology test, the mean is 85 and the standard deviation is 5. The score is 79. The z-score can be calculated using the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where [tex]\( X \)[/tex] is the score,[tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.
For the psychology test:
[tex]\[ z_{psychology} = \frac{79 - 85}{5} = \frac{-6}{5} = -1.2 \][/tex]
For the economics test, the mean is 52 and the standard deviation is 3. The score is 48. Using the same formula:
[tex]\[ z_{economics} = \frac{48 - 52}{3} = \frac{-4}{3} \approx -1.33 \][/tex]
Now, comparing the z-scores:
- The z-score for the psychology test is -1.2, which means the score is 1.2 standard deviations below the mean.
- The z-score for the economics test is approximately -1.33, which means the score is about 1.33 standard deviations below the mean.
Since a lower (more negative) z-score indicates a worse relative performance, the score of 79 on the psychology test is relatively better than the score of 48 on the economics test, because -1.2 is greater than -1.33. This means that the psychology test score is closer to its mean relative to its standard deviation than the economics test score is to its mean relative to its standard deviation.
A cold front moved in last weekend. In 8 hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour?
I need the answer as quick as I can and I put it at max points!
Answer:
Step-by-step explanation:
The difference between 14 and 0 is 14, and the difference between 0 and -10 is 10. 14+10=24 for total change. For the average over 8 hours, we have 24/8=3 degrees
Perform the operation(s) and write the answer in simplest form.
( 1/2 + 1/3) / 15/4
A.) 3 1/8
B.) 53/90
C.) 2/9
D.) 8/75
What is the correct name for this circle?
Which point satisfies both f(x)=2^x and g(x)=3^x (0,1) (0,-1) (1,0) (-1,0)
Write the sum using summation notation
729 + 1000 + 1331 + 1728 + ... + n^3
1. Which of the following statements is true? A. 15 ÷ 0 = 0 B. 15 − 0 = 0 C. 0 ÷ 15 = 0 D. 15 + 0 = 0
How many sixteenth notes would be needed to have the same duration as 3 quarter notes? Represent this as a fraction
Explain how you would use a number line to find the absolute value of –12.
Find all values of $x$ such that $6= \dfrac{35}{x} -\dfrac{49}{x^2}$. If you find more than one value, then list your solutions in increasing order, separated by commas.
Answer:
[tex]x=\frac{7}{3} , \frac{7}{2}[/tex]
Step-by-step explanation:
[tex]6= \frac{35}{x} - \frac{49}{x^2}[/tex]
Now we need to solve for x
To get 'x' alone we make the denominators same
LCD = x^2
WE multiply the whole equation by x^2
[tex]6x^2 = 35x - 49[/tex]
Now we the equation =0, move all the terms to left hand side
[tex]6x^2-35x + 49=0[/tex]
Now we apply quadratic formula to solve for x
a= 6, b= -35 , c= 49
[tex]x= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x= \frac{-(-35)+-\sqrt{(-35)^2-4(6)(49)}}{2*6}[/tex]
[tex]x= \frac{35+-\sqrt{49}}{12}[/tex]
[tex]x= \frac{35+-7}{12}[/tex]
Now frame two equations , one with + and another with -
[tex]x= \frac{35+7}{12}[/tex] [tex]x= \frac{35-7}{12}[/tex]
[tex]x= \frac{42}{12}[/tex] [tex]x= \frac{28}{12}[/tex]
[tex]x= \frac{7}{2}[/tex] [tex]x= \frac{7}{3}[/tex]
So value of x= {7/3, 7/2}
Five students visiting the student health center for a free dental examination during national dental hygiene month were asked how many months had passed since their last visit to a dentist. their responses were as follows. 5 18 12 24 28 assuming that these five students can be considered a random sample of all students participating in the free checkup program, construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program. (give the answer to two decimal places.)
To find for the value of the confidence interval, let us first calculate for the values of x and s, the mean and standard deviation respectively.
x = (5 + 18 + 12 + 24 + 28) / 5
x = 17.4 months
s = sqrt{[(5 – 17.4)^2 + (18 – 17.4)^2 + (12 – 17.4)^2 + (24 – 17.4)^2 + (28 – 17.4)^2]/(5-1)}
s = 9.21
The formula for the confidence interval is given as:
Confidence Interval = x ± t s / sqrt(n)
Where t can be taken from standard distribution tables at 95% level at degrees of freedom = n – 1 = 4, t = 2.132. Therefore:
Confidence Interval = 17.4 ± 2.132 * 9.21 / sqrt(5)
Confidence Interval = 17.4 ± 8.78
Confidence Interval = 8.62 months, 26.18 months
Final answer:
To construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist, use the sample mean and sample standard deviation. Calculate the confidence interval using the formula and given data.
Explanation:
In order to construct a confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program, we can use the sample mean and sample standard deviation. The formula for constructing a confidence interval for the mean is:
Confidence Interval = sample mean ± (critical value) × (sample standard deviation / √sample size)
Using the given data, the sample mean is 17.4 months and the sample standard deviation is 9.18 months. With a confidence level of 95%, the critical value is 2.776. Plugging these values into the formula, we get:
Confidence Interval = 17.4 ± (2.776) × (9.18 / √5)
Calculating this, we find that the 95% confidence interval for the mean number of months elapsed since the last visit to a dentist is approximately 4.81 to 29.99 months.
bacterial colonies can triple in size every 4 days. if you start with 150 bacteria microorganisms, how large would the colony be after 16 days?
In the following triangle, find the values of the angles B and B', which are the best approximations to the solutions of this ambiguous case.
Answer:
Option B. B = 70.05° B' = 109.95°
Step-by-step explanation:
By the sine rule in a given triangle
sin 45°/16.5 = sinB/22
1/(1.414×16.5) = sinB/22
sinB = 22/(1.414×16.5) = 0.94
[tex]B = sin^{-1}(0.94)[/tex]
B = 70.05°
Now we know B' = 180 - Supplementary angle of B'
and B = B' ( opposite angles of equal sides are equal)
B' = 180 - B = 180 - 70.05 = 109.95°
Therefore option B is the answer.
(6.3 × 1011) ÷ (7 × 105)
how much would $500 invested at 6% interest compounded annually be worth after 4 years
a bell tolls every 10 minutes. another bell tolls every 15 minutes. both bells toll at 6:00pm. they will toll together at what time
Both the bells will ring after 30 minutes at 6:30 pm.
What is the lowest common multiple?The smallest common positive number that is a multiple of two or more numbers.
Given that, a bell tolls every 10 minutes. another bell tolls every 15 minutes. both bells toll at 6:00pm.
To find the time for which both will ring together, we will find LCM of 10and 15
10 = 5x2
15 = 5x3
LCM = 5x2x3 = 30
The LCM of 15 and 10 is 30
So, both will ring after 30 minutes.
Right now the time is 6:00 pm, so after 30 minutes it will be 6:30 pm
Hence, Both the bells will ring after 30 minutes at 6:30 pm.
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Mr. calloway is an algebra teacher. every class period he draws a piece of paper out of a hat without looking to determine the number of homework problems he will assign. each different color of paper represents a different number of homework problems. the hat contains 2 blue, 6 red, 10 yellow, and 7 purple pieces of paper.what is the probability that mr. calloway draws a purple piece of paper during the first class period and a blue piece of paper during the second class period if he replaces all pieces of paper before each drawing?
The probability that Mr. Calloway will draw a purple piece of paper during the first class period and a blue piece during the second class period with replacement is [tex]\frac{14}{25}[/tex].
The question involves calculating the probability of drawing a purple piece of paper during the first class period and a blue piece of paper during the second class period with replacement. To find this probability, we first calculate the probability of each event separately since the events are independent. Mr. Calloway's hat contains a total of 25 pieces of paper (2 blue, 6 red, 10 yellow, and 7 purple).
The probability of drawing a purple piece of paper in the first class period is the number of purple papers divided by the total number of papers:
P(purple) = Number of purple pieces / Total pieces = [tex]\frac{7}{25}[/tex]
Since the pieces are replaced, the probabilities in the second class period are the same as in the first. Thus, the probability of drawing a blue piece of paper in the second class is:
P(blue) = Number of blue pieces / Total pieces = [tex]\frac{2}{25}[/tex]
Because these events are independent, we multiply the probabilities of each event happening:
Total probability = P(purple) times P(blue) = ([tex]\frac{7}{25}[/tex]) times ([tex]\frac{2}{25}[/tex]) = [tex]\frac{14}{25}[/tex].
Therefore, the probability that Mr. Calloway draws a purple piece of paper during the first class period and a blue piece of paper during the second class period with replacement is [tex]\frac{14}{25}[/tex].
Julio just bought a $267,900 house. He had a 20 year mortgage with a fixed rate of 5.875%. Julio's monthly payments are $1558.09. What percent of the purchase price was Julio's down payment?
Answer: c
Step-by-step explanation:
The party store has a special on greetings cards. It charges $14 for 4 greeting cards and $1.50 for each additional card. Write an equation for the total cost of greeting cards in terms of the number of cards. Define your variables. What is the total cost of 9 greeting cards?
C=14 +1.5(x-4)
c= total cost
x = number of cards
cost for 9 cards:
x=9
c=14+1.5(9-4)
14+1.5(5) = 21.50
total cost = $21.50
Use ABC to find the value of sin A. See picture below. Thanks!
∠EFG and ∠GFH are a linear pair, m∠EFG=3n+19, and m∠GFH=55+33 What are m∠EFG and m∠GFH?
Which Graph correctly represents x+2y≤4?
Answer with Step-by-step explanation:
We are given an inequality:
x+2y≤4
We have to determine its correct graph
In graph A and graph C (0,4) lies in shaded region but (0,4) does not satisfy the inequality(since, 0+2×4=8 which is not less than or equal to 4)
Hence, A and C are not the graph of this inequality
In graph D (0,2) does not lie in shaded area but it satisfies the inequalityHence, D is also not the graph of this inequality
Hence, correct graph of x+2y≤4 is:
Graph B
Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.
(Picture one)
A. 126 cm3
B. 907.5 cm3
C. 605 cm3
D. 55 cm3
Find the surface area of the cylinder in terms of pi.
(Picture 2)
A) 396 pi in^2
B) 522 pi in^2
C) 360 pi in^2
D) 1008 pi in^2
The solution is, the volume of the square pyramid is 605 cm^3.
and, the surface area of the cylinder in terms of pi is 522 pi in^2.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
we know that,
volume of pyramid is:
V = 1/3 B h
here, we have,
B = 11*11
= 121
h = 15
so, we get,
V = 605 cm^3
again, we have,
surface area of the cylinder :
s = 2πr( r + h)
here, we have,
r = 9
h = 20
so, we get,
s = 522 pi in^2
Hence, The solution is, the volume of the square pyramid is 605 cm^3.
and, the surface area of the cylinder in terms of pi is 522 pi in^2.
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The volume of the square pyramid is A) 126 cm³ and the surface area of the cylinder is B) 522π in².
The volume of a square pyramid is expressed as:
Volume = l² × h/3
The surface area of a cylinder is expressed as:
Surface area = 2πrh + 2πr²
From the diagram:
For the square pyramid:
Length l = cm
Height h = 15cm
Volume =?
Volume = l² × h/3
Plug in the values:
Volume = 11² × 15/3
Volume = 121 × 5
Volume = 605 cm³
Option C) 605 cm³ is the correct answer.
Next, we find the surface area of the cylinder:
Radius r = 9 in
Height h = 20 in
Surface area = 2πrh + 2πr²
Plug in the values:
Surface area = (2π × 9 × 20) + (2π × 9²)
Surface area = 522π in²
Therefore, the surface of the cylinder is 522π in².
Option B) 522π in² is the correct answer.