Answer:
The volume of the cone is 63.3m³
Step-by-step explanation:
First of all to solve this problem we need to know the formula to calculate the volume of a cone
v = volume
r = radius = 2.2m
h = height = 12.5m
π = 3.14
v = 1/3 * π * r² * h
we replace with the known values
v = 1/3 * 3.14 * (2.2m)² * 12.5m
v = 1/3 * 3.14 * 4.84m² * 12.5m
v = 63.32m³
rount to the neares tenth
v = 63.32m³ = 63.3m³
The volume of the cone is 63.3m³
Answer: 63.4
Step-by-step explanation:
You round to the tenths giving you 63.4
Suppose the students construct a 95% confidence interval for the true weight of their rocks. Whose interval do you expect to be more precise (narrower)? (i) The student who weighed the rock 20 times. (ii) The student who weighed the rock 5 times. (iii) Both intervals would be equally precise.
Answer:
(i) The student who weighed the rock 20 times.
Step-by-step explanation:
The margin of error of a confidence interval is:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
From the equation above, the larger the size of the sample, the lower the margin is, that is, the narrower the interval is.
In this question:
A student weighed the rock 20 times and other the 5. From above, the one who weighed the rock 20 times will have the more precise interval.
So the correct answer is:
(i) The student who weighed the rock 20 times.
Sarah enjoys reading books as a hobby. Complete the rate chart below to find how many pages Sarah reads in a certain number of hours. Time (in hours) 3 6 9 12 15 Number of Pages Read 120 240 360 480 ? A. 780 B. 520 C. 600 D. 578
Answer: C. 600
Step-by-step explanation:
Sarah reads at a pace of 120 pages per 3 hours.
All we have to do is add 120 pages to the 480 pages.
480+120=600
A movie complex is showing the same movie in three theatres. In theatre A, 112 of the 160 seats are filled. In theatre B, 84 seats are filled and 56 are empty. In theatre C, 63 of the 180 seats are empty. Which theatre has the greatest percent of seats filled?
Answer:
a
Step-by-step explanation:
bc it does. and it has the highest percentage of it
Evaluate -8 -3+8+ (-3).
Answer:-6
Step-by-step explanation:
-8-3+8+(-3)
-8-3+8-3
Rearranging we get
8-8-3-3
0-6=-6
The correct answer is:
[tex]-8 - 3 + 8 + (-3) = -6.[/tex]
1. Start with -8.
2. Subtract 3: [tex]-8 - 3 = -11[/tex].
3. Add 8: [tex]-11 + 8 = -3.[/tex]
4. Subtract 3: [tex]-3 - 3 = -6[/tex].
Complete correct question:
Evaluate [tex]-8 -3+8+ (-3)[/tex].
What is the slope, m, and y-intercept for the line that is plotted on the grid below? On a coordinate plane, a line goes through points (0, 4) and (negative 2, 0). m = One-half, (0, –2) m = One-half, (0, 4) m = 2, (0, –2) m = 2, (0, 4)
Answer:
D. m = 2, (0, 4)
Step-by-step explanation:
the answer is D
I got it write on the quiz
Answer:
yes it is D :D
Step-by-step explanation:
How do you know that the right triangles are the bases of the prism
Answer:
if the triangular faces are equilateral, the prism is regular, in which case the rectangular faces are congruent. The rectangular faces are said to be lateral, while the triangular faces are bases. If the bases are horizontal, they are sometimes called the top and the bottom (faces).
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Step-by-step explanation:
Find the distance between (3, 24) and (7,
56).
Answer:
Square root of 1040.
Or decimal form - 32.249
Step-by-step explanation:
Suppose that prices of a certain model of a new home are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.
Answer:
68% of buyers paid between $147,700 and $152,300.
Step-by-step explanation:
We are given that prices of a certain model of a new home are normally distributed with a mean of $150,000.
Use the 68-95-99.7 rule to find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.
Let X = prices of a certain model of a new home
SO, X ~ Normal([tex]\mu=150,000 ,\sigma=2,300[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean price = $150,000
[tex]\sigma[/tex] = standard deviation = $2,300
Now, according to 68-95-99.7 rule;
Around 68% of the values in a normal distribution lies between [tex]\mu-\sigma[/tex] and [tex]\mu-\sigma[/tex].
Around 95% of the values occur between [tex]\mu-2\sigma[/tex] and [tex]\mu+2\sigma[/tex] .
Around 99.7% of the values occur between [tex]\mu-3\sigma[/tex] and [tex]\mu+3\sigma[/tex].
So, firstly we will find the z scores for both the values given;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{147,700-150,000}{2,300}[/tex] = -1
Z = [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{152,300-150,000}{2,300}[/tex] = 1
This indicates that we are in the category of between [tex]\mu-\sigma[/tex] and [tex]\mu-\sigma[/tex].
SO, this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.
Approximately 95% of the buyers paid between $147,700 and $152,300.
Explanation:To find the percentage of buyers who paid between $147,700 and $152,300, we can use the 68-95-99.7 rule for normal distributions. According to this rule, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
The mean of the prices is $150,000 and the standard deviation is $2,300. The difference between $147,700 and $152,300 is $4,600, which is 2 standard deviations away from the mean. Therefore, we can expect approximately 95% of buyers to have paid between $147,700 and $152,300.
So, approximately 95% of the buyers paid between $147,700 and $152,300.
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How much larger is a pizza in 18-in square pizza pan than a pizza made in a 18-in diameter circular pan? Use 3.14 for pi
The 18-inch square pizza is 69.66 square inches larger than the 18-inch diameter circular pizza. This calculation is done by finding the areas of both the square and the circle and then subtracting the circular area from the square one.
Explanation:The subject of this question is Mathematics, specifically dealing with the comparison of areas of geometric shapes, and the problem seems to be aimed at a middle school level. To find out how much larger a square pizza is compared to a circular pizza, we will calculate the area of both shapes and then compare the two.
The area of the square pizza is straightforward since the length of a side is given as 18 inches. The formula for the area of a square is A = a², so:
Area of square pizza = 18 in × 18 in = 324 in².
Next, let's calculate the area of the circular pizza using the formula: A = πr², where r is the radius. The diameter is given as 18 inches, so the radius (r) is half of the diameter, which is 9 inches. Using 3.14 for π, we find:
Area of circular pizza = 3.14 × 9 in × 9 in = 3.14 × 81 in² = 254.34 in².
To find the difference in areas, we subtract the area of the circular pizza from the area of the square pizza:
Difference in areas = 324 in² - 254.34 in² = 69.66 in².
Therefore, an 18-inch square pizza is 69.66 square inches larger than an 18-inch diameter circular pizza.
Q1: A group of 50 biomedical students recorded their pulses rates by counting the number of beats for 60 seconds. (15)
80
48
88
70
84
82
66
84
82
64
44
72
90
70
86
104
58
84
72
60
90
108
62
52
72
86
66
104
78
82
96
54
68
76
72
88
102
74
68
74
78
66
72
90
62
100
92
84
76
72
(a) Construct frequency distribution.
(b) Compute mode, median and mean of the frequency distribution.
(c) The lower and upper quartile of the frequency distribution.
Answer:
The answers are in the explanation.
Step-by-step explanation:
a)
X1 -Absolute frecuency -cumulative absolute frequency -Relative frecuency
44 1 1 0.021
48 1 2 0.021
52 1 3 0.021
54 1 4 0.021
58 1 5 0.021
60 1 6 0.021
62 2 7 0.042
64 1 8 0.021
66 3 12 0.063
68 2 14 0.042
70 2 16 0.042
72 6 22 0.126
74 2 24 0.042
76 2 26 0.042
78 2 28 0.042
80 1 29 0.021
82 3 32 0.063
84 4 36 0.084
86 2 38 0.042
88 2 40 0.042
90 3 43 0.063
92 1 44 0.021
96 1 45 0.021
100 1 46 0.021
102 1 47 0.021
104 2 49 0.042
108 1 50 0.021
Total: 50 50 1
b) Mean: is the number average = 3806/48 = 78.12 Median: is the number or average number of half = 76 Mode: Is the number that appears most frequently = 72c) Lower quartile: 67Upper quartile: 84Removing which point from the coordinate plane would make the graph a function of X?
What is the approximate difference in tenths between StartRoot 12 EndRoot and StartRoot 15 EndRoot? 0.2 0.4 1.5 1.7
Final answer:
The approximate difference in tenths between the square roots of 12 and 15 is 0.4. This is found by approximating the square roots (3.46 and 3.87, respectively) and subtracting the smaller from the larger.
Explanation:
The student asks for the approximate difference in tenths between StartRoot 12 EndRoot and StartRoot 15 EndRoot. To find the square roots we can use a calculator or estimate:
Square root of 12 is approximately 3.46.
Square root of 15 is approximately 3.87.
Now find the difference:
3.87 - 3.46 = 0.41
0.4 is the approximate difference in tenths between the square roots of 12 and 15. The options given are 0.2, 0.4, 1.5, and 1.7. Therefore, the closest value to our calculation is 0.4.
Luther takes 45 bottles of water on a camping trip. If he drinks 80 % of them how many does he have left?
Answer:
9
Step-by-step explanation:
80% of 45 is 36
45-36=9
The last day we were in school was March 13. There are 180 days in a school year.
1. How many total days of school have we missed as of today?
2. What percentage of days were we in school this year?
Is this qusioun as of today may 18?
Based on the dates given, you missed approximately 90 days of school. If your school year usually starts around August 25, you were in school for about 170 days out of a 180-day school year. That means you were in school for approximately 94.44% of the year.
Explanation:To solve this question, first, we need to find the number of days missed. You mentioned your last day in school was March 13. Assuming today's date is June 13, that is approximately 3 months. As each month has about 30 days, then 3 months would total about 90 days missed from school. To summarize:
Last school day: March 13Today's date: June 13Total days missed: Approximately 90The second part of the question requires us to find the percentage of days you were in school. You mentioned that there are 180 school days in a year. If the last day was on March 13 and the school year usually begins around August 25, that would make approximately 170 days in school before the school closures. So, the calculation would be (170/180)*100% = approximately 94.44%. Hence, you were in school for approximately 94.44% of the year.
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Paul works out with 3 weights that are each 2.5 kilograms each. What is the total mass of the 2.5 kilogram weights in grams
Answer:
750000
Step-by-step explanation:
3 times 2.5 = 7.5 then to convert to grams times by 1000 which is 750000
The sum of 2ab^2 and (-5ab^2) is the same as the sum of (-6ab^2) and
Answer:
? = 3ab^2
for the sum of (-6ab^2) and 3ab^2
Step-by-step explanation:
2ab^2 +(-5ab^2) =(-6ab^2) + ?
-3ab^2 = -6ab^2 + ?
? = 6ab^2 - 3ab^2
? = 3ab^2
what are the properties of parallelogram
Answer:
The properties of the parallelogram are simply those things that are true about it. These properties concern its sides, angles, and diagonals.
Step-by-step explanation:
The parallelogram has the following properties:
Opposite sides are parallel by definition.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
The diagonals bisect each other.
If you just look at a parallelogram, the things that look true (namely, the things on this list) are true and are thus properties, and the things that don’t look like they’re true aren’t properties.
If you draw a picture to help you
when I was six my brother was half my age. next year if I turn 40 how old will my brother be?
Answer:
37
Step-by-step explanation:
You were 6 and he was half which made him 3
So you’re gonna turn 40 he’s gonna be three years younger than you which is 37
Hope I helped
On a coordinate plane, a line goes through (negative 8, 10), (0, 0), and (8, negative 10). What is the equation of the line that is perpendicular to the given line and passes through the point (5, 3)? 4x – 5y = 5 5x + 4y = 37 4x + 5y = 5 5x – 4y = 8
Answer:
4x-5y =5
Step-by-step explanation:
First we need to find the slope of the line
m = (y2-y1)/(x2-x1)
= (0-10)/(0- -8)
= -10/(0+8)
-10/8
-5/4
We want a line with a perpendicular slope
That line will have a negative reciprocal slope
-1 (-5/4)
4/5
We have the slope and a point
y= mx+b is the slope intercept form of a line
y = 4/5x+b
Substitute the point into the equation
3 = 4/5(5)+b
3 =4+b
b = -1
The equation of the line is y = 4/5x-1
Multiply each side by 5 to get rid of the fractions
5y = 4x -5
Subtract 4x from each side
-4x+5y = -5
Multiply each side by -1
4x-5y =5
Answer:
4x - 5y = 5
Step-by-step explanation:
Slope of the given line:
(-10-0)/(8-0)
-10/8
-5/4
Slope of the Perpendicular line
4/5
y = ⅘x + c
3 = (4/5)(5) + c
3 = 4 + c
c = -1
y = (4/5)x - 1
5y = 4x - 5
4x - 5y = 5
Help me pleassseeeeeeee
What is the point-slope form of a line with slope 2/5 that contains the point (-3, 6)?
O A. y-6= -2/5(x+3)
O B. y+6 = 2/5(x+3)
O C. y-6 = 2/5(x+3)
O D.y-3 = 2/5(x+3)
Answer:
y -6 = 2/5(x+3)
Step-by-step explanation:
The point slope form of an equation is
y -y1 = m(x-x1)
where m is the slope and (x1,y1) is the point
y -6 = 2/5(x- -3)
y -6 = 2/5(x+3)
C.) y - 6 = 2/5(x + 3)
The original point slope equation is the following
[tex]y - y_1 = m(x-x_1)[/tex]
When you plug in negative point values into this equation, the sign changes from '-' to '+'. This is how you can determine which equation accurately represents the line.
Write 2 ones and 5 hundredths as a decimal
Answer:
2.05
Step-by-step explanation:
Look at this chart
2 ones and 5 hundredths can be written as 2.05 in decimal form.
What are decimals?Decimals are values that utilize a dot known as the decimal point to distinguish between the whole number portion and the fractional portion. This dot acts as a separator marking the boundary, between these two parts of a number. The fractional section of a decimal can be expressed in units such as tenths, hundredths, thousandths and forth.
In this case the digit 2 signifies the number element of the value while 0.05 represents its fractional component. The presence of the point ensures a division, between these two segments, one being whole and the other being fractional.
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What are the dimensions of the cross section formed by
a plane intersecting this rectangular prism parallel to its
base?
The cross section is a
The length of the cross section is
The width of the cross section is
cm.
cm.
ith = 4 cm
Answer:
rectangle, 5,4
Step-by-step explanation:
i just did the assignment and got it right
Will the sugar, the sand, or both dissolve in the water?
Answer:
sugar
Step-by-step explanation:
Answer:
Sugar will dissolve
Step-by-step explanation:
Sand does not dissolve in water, but it absorbs water to some extent
A well-known battery manufacturer claims its product lasts at least 5000 hours, on average. If a sample of 81 batteries has an average lifetime of 4917.5 hours with a standard deviation of 450 hours, use the critical value approach to determine whether you reject or not reject the null hypothesis at a 5% level of significance. What does this mean in terms of the manufacturer's claim
Answer:
[tex]t=\frac{4917.5-5000}{\frac{450}{\sqrt{81}}}=-1.65[/tex]
The degrees of freedom for this case are:
[tex]df=n-1=81-1=80[/tex]
We need to find a critical value in the t distribution with 80 degrees of freedom who accumulates 0.05 of the area in the left and we got:
[tex] t_{cric}= -1.664[/tex]
Since the calculated value is not less than the critical value we don't have enough evidence to conlcude that the true mean is significantly lower than 5000 hours. Then the claim by the manufacturer (product lasts at least 5000 hours) makes sense.
Step-by-step explanation:
Information given
[tex]\bar X=4917.5[/tex] represent the sample mean
[tex]s=450[/tex] represent the sample standard deviation
[tex]n=81[/tex] sample size
[tex]\mu_o =5000[/tex] represent the value to check
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic (variable of interest)
System of hypothesis
We want to determine if product lasts at least 5000 hours, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 5000[/tex]
Alternative hypothesis:[tex]\mu < 5000[/tex]
The statistic for a one sample t testo for the true mean is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{4917.5-5000}{\frac{450}{\sqrt{81}}}=-1.65[/tex]
The degrees of freedom for this case are:
[tex]df=n-1=81-1=80[/tex]
We need to find a critical value in the t distribution with 80 degrees of freedom who accumulates 0.05 of the area in the left and we got:
[tex] t_{cric}= -1.664[/tex]
Since the calculated value is not less than the critical value we don't have enough evidence to conlcude that the true mean is significantly lower than 5000 hours. Then the claim by the manufacturer (product lasts at least 5000 hours) makes sense.
Multiply 71 by 8 and then add 379
Answer: 947
Step-by-step explanation:
71 x 8 = 568
568 + 379 = 947
Answer = 947
Answer:
947
Step-by-step explanation
multiply 71 and 8 then add 379
In a science fair project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left hand, and then she asked the therapists to identify the selected hand by placing their hand just under Emily's hand without seeing it and without touching it. Among 296 trials, the touch therapists were correct 143 times.
Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?
Answer:
a 0.5
b 0.4831
c 0.4354 < P < 0.53008
Step-by-step explanation:
Given that :
Probability (P) of a head or a tail when a coin is being tossed or flipped = 1/2 = 0.5
Sample size (n) = 296
Selected sample (X) = 143
a) Given that Emily used a coin toss to select either her right hand or her left hand, what proportion of correct responses would be expected if the touch therapists made random guesses?
The proportion of correct responses that would be expected if the touch therapists made random guesses is 0.5
b) Using Emily's sample results, what is the best point estimate of the therapists' success rate?
Point estimate [tex](p') = \frac{X}{n}[/tex]
= [tex](p') = \frac{143}{296}[/tex]
= 0.4831
c) Using Emily's sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.
The [tex]Z_c[/tex] for 90% is 1.645
Using the formula P" -E < P < P" + E
where E = margin of error : [tex]Z_c * \sqrt{\frac{P(1-P)}{n} }[/tex]
[tex]=1.645 * \sqrt{\frac{0.4831(0.5169)}{296} }[/tex]
[tex]=1.645 * \sqrt{\frac{0.2497}{296} }[/tex]
[tex]=1.645*0.029[/tex]
= 0.0477
∴ P" -E < P < P" + E
= 0.4831 - 0.0477 < P < 0.4831 + 0.0477
= 0.4354 < P < 0.53008
Answer:
The proportion of correct responses would be in between [tex](0.4345)<P<(0.53008)[/tex]
Step-by-step explanation:
Given information:
Sample size [tex](n)=296[/tex]
Selected sample [tex](x) =143[/tex]
Probability of head or tail will be 0.5 because a coin is tossed.
So the proportion of correct responses if the therapist made random decision will be 0.5.
Now with the help of sample result:
Point estimate:
[tex](p)'=x/n\\(p')=143/296\\(p')=0.4831[/tex]
Now, if we take confidence level of 90%
Then, [tex]Z=1.645[/tex]
As,
[tex](P"-E)<(P)<(P"+E)[/tex]
Where , E is the margin of error.
[tex]E=Z \times \sqrt \frac{P(1-P)}{n} \\E=1.654 \times \sqrt \frac{(0.4831 \times0.5169}{296} \\E=1.645\times 0.029\\E=0.0477[/tex]
Therefore:
[tex](P"-E)<(P)<(P"+E)[/tex]
[tex](0.4831-0.0477)<P<(0.4831+0.0477)\\(0.4345)<P<(0.53008)[/tex]
Hence, the proportion of correct responses would be in between [tex](0.4345)<P<(0.53008)[/tex].
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I’m so confused! Please help! :)
Answer:
The answer is 18.84
Step-by-step explanation:
The diameter is 6.
Circumference = d[tex]\pi[/tex]
6 * 3.14 = 18.84
SOMEONE PLEASE HELP
The table lists the types of blocks found in a box of toys. Find P
Answer: P= 0.174
Step-by-step explanation:
Using the principle of probability, the probability of obtaining a green and round block from the toy box would be 0.174
P(green and round) can be interpreted as P(GREEN n ROUND)
From the table given :
P(green and round) = 4Total number of blocks in the toy = 23Recall :
Probability = required outcome / Total possible outcomesHence, P(green and round) = 4/23 = 0.1739 = 0.174
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The picture below is of a Little League Baseball field. The distance from Home Plate to First Base is 60 feet, and from Home Plate to the center of the Pitcher’s Mound is 46 feet. The baseball "diamond" is actually a square (distance between each base is 60 feet), so the angle made by each base is 90°. So, if a line were connecting Home Plate with the Pitcher’s mound, it would create a 45° angle. So, approximately how far is First Base from the center of the Pitcher’s Mound? (HINT: The pitcher’s mound is not in the middle of the field, so there are NO right angles in this problem.) (
Answer:
42.58 FT
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Answer:
While chalking the lines on a little league baseball field, Tory determined that the distance between each of the bases is 45 feet. What would be the approximate distance from home plate to second base be if measured through the pitchers mound?
Step-by-step explanation:
42.58