In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet
with a diameter of 8500 kilometers, what should be the diameter of the drawing of
the planet?
In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.
What is millimeters?A millimeter, abbreviated mm, is the smallest unit for length in the metric, or Standard International, system of measurement. It is used to measure small lengths and for precise measurements. Millimeters can be converted to either units within the metric system or the customary system of measurement.
Divide 8500 kilometers by which 500 km equals 17.5 millimeters.
Therefore, In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.
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Hiro painted his room. After 333 hours of painting at a rate of 888 square meters per hour, he had 282828 square meters left to paint.
The solution is, the situation can be modeled as y = 52 - 8x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
So, the total area to be painted is (28 + 3 × 8) = 52 square meters.
Let y represent the area (in square meters) left to paint after x hours of painting then the situation can be modeled as
y = 52 - 8x ................ (1) (Answer)
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can someone please help me(10 points will give brainliest!!!)
Answer:
$2.6015900 toysStep-by-step explanation:
You want to know the meaning of D(2.60) = 159 if D(p) tells you the number of toys demanded at price p in hundreds.
Pattern matchingCompare D(p) to D(2.60) and you see that p=2.60. The problem statement tells you p is the price. This means ...
the price is $2.60The problem statement tells you that D(p) is the number of toys in hundreds. When D(p) is 159, the demand is 159 hundred toys.
the demand is 15900 toys<95141404393>
n the manufacturing of a plastic material, it is be- lieved that the cooling time has an influence on the impact strength. therefore a study is carried out in which plastic material impact strength is determined for 4 different cooling times cooling time in second : 15 25 35 40 impact strength in kj/m2 : 42.1 36.0 31.8 28.7 a) find explanatory and response variable? b) find equation of linear model that describes re- lationship between predicted value of response and explanatory variable? c) based on r2, what you can say about response and explanatory variable?
Explanatory variable: Cooling time in seconds
Response variable: Impact strength in kj/m2
To find the equation of the linear model that describes the relationship between the predicted value of the response and the explanatory variable, we can use linear regression analysis. Using a statistical software or a calculator, we can find the slope and intercept of the line that best fits the data.
The equation of the linear model is:
Impact strength = -1.23 * Cooling time + 62.61
R-squared (R2) is a statistical measure that represents the proportion of the variance in the dependent variable (impact strength) that is explained by the independent variable (cooling time). It ranges from 0 to 1, with higher values indicating a better fit of the model.
Based on the value of R2, we can say how much of the variation in impact strength can be explained by cooling time. The closer R2 is to 1, the better the model fits the data, and the more likely it is that the impact strength is affected by cooling time. A value of 1 would indicate that all the variation in impact strength is explained by cooling time, while a value of 0 would indicate that cooling time has no effect on impact strength.
Without knowing the actual value of R2, we cannot say for sure what the relationship is between the explanatory and response variables. However, if the value of R2 is high (close to 1), we can conclude that cooling time has a significant effect on impact strength. If the value of R2 is low (close to 0), we cannot conclude that cooling time has a significant effect on impact strength.
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Unit 4: congruent triangles
Homework 7: Proofs review.
please help, i don’t know the answers to 1 or 4.
Answer:
1. SAS
2. Not congruent
Step-by-step explanation:
1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.
If you rotate the first triangle, you'll see that it is the same as the second.
4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.
The solution is,
1. SAS
2. AAS
3. SAS
4. Not congruent.
What is congruent triangle?Two triangles are congruent if all three pairs of corresponding sides are equal. Two pairs of corresponding sides and the corresponding angles between them are equal.
here, we have,
we know that,
To identify which triangles are congruent measure the angles and sides of each of the triangles and compare them.
Meaning of congruent:
In mathematics, the word congruent is used if two figures have the same size and shape, although their orientation can be different.
Two triangles are congruent:
In the case of triangles two factors should be considered:
1) Lengths of each side are equal.
2) Angles are equal.
This means that to determine if the triangles are congruent, we must measure each side and angle and make sure these are the same in each triangle.
now, we have,
1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.
If you rotate the first triangle, you'll see that it is the same as the second and, similar for 2 & 3 by AAS & SAS.
4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.
Hence, 1. SAS
2. AAS
3. SAS
4. Not congruent.
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A space dome theatre is composed of a cylindrical base and a hemispherical roof. The space dome theatre has a base radius of 20m and a cylindrical height of 20m. what is the total volume of the space dome theatre?
The total volume of the space dome theatre is 41867 m³.
What is a sphere?In geometry, a sphere is a three-dimensional solid figure, which is round in shape.
The surface area is 4πr².
The volume is (4/3)πr³.
The diameter is 2×radius of the sphere.
What is a cylindrical shape?A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, The space dome theatre has a base radius of 20m.
Therefore, The volume of the hemispherical dome is,
= (2/3)π(20)³.
= (2/3)π×8000.
= (16000/3)π m³.
And, As the dome base has a radius of 20 m the cylindrical shape will also have the same.
Therefore, The volume of the cylindrical shape is,
= π(20)²×20.
= 8000π m³.
And, The total volume is the sum of the volumes of two shapes,
= 8000π + (16000/3)π m³.
= [(24000 + 16000)/3]π m³.
= (40000/3)π m³.
= 41867 m³.
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Does the following table show a proportional relationship between the variables ggg and hhh?
ggg 333 666 999
hhh 999 363636 818181
Choose 1 answer:
There is No relation between the variables ggg and hhh.
To determine if the given table shows a proportional relationship between the variables ggg and hhh, we need to check if the ratio of hhh to ggg is constant for all values of ggg.
Let's calculate the ratios of hhh to ggg for each value of ggg:
For ggg = 333, hhh/ggg = 999/333 = 3.
For ggg = 666, hhh/ggg = 363636/666 = 546.
For ggg = 999, hhh/ggg = 818181/999 = 819.
Since the ratios of hhh to ggg are not constant, the given table does not show a proportional relationship between the variables ggg and hhh.
Therefore, the answer is "No, the table does not show a proportional relationship between the variables ggg and hhh."
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Passion wants a rent car to take a trip and has a budget of 75. There is a fixed and daily fee of 10 . Write an inequality that would be used to solve for maximum number of days for which pasion can rent the car rent the car on her budget.
The inequality showing the maximum number of days he can rent a car is 10d ≤ 75.
The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.
Given that Passion has a budget of $75 and wants to rent a car for a trip. A fixed daily fee of 10 is charged.
The product of the number of days and the rent per day should be less than the amount he has.
The inequality mathematically can be written as:-
10t ≤ $75
Therefore, the inequality 10d ≤75 shows how many days he can rent an automobile for the most.
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Translate the sentence into an equation.
Seven more than the quotient of a number and 5 is equal to 3.
Use the variable B for the unknown number
Answer: 7 + [tex]\frac{B}{5}[/tex] = 3
Step-by-step explanation:
Its pretty simple, just do as the words say. :) the only issue could be "of a number and 5", so you go in order, letting B be the number, it's B/5
Which linear inequality is graphed with y > -X - 2 to
create the given solution set?
© y>x+1
© y
O y>x-1
O y
The linear inequality that is graphed with y > –x – 2 to create the given solution set is D. y < x + 1
How to explain the inequalityOne of the line is having the y intercept -2 and slope -1 having the equation y=-x-2. The shaded region is having the inequality y>-x-2.
The other line is having the y intercept 1 and slope of 1. Hence equation of line is y=x+1.
The shaded part is above the line .The inequality region is represented by the inequality y <x+1.
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Which linear inequality is graphed with y > –x – 2 to create the given solution set?
A=y > x + 1
B=y < x – 1
C=y > x – 1
D=y < x + 1
i need help asap f(x) = -x - 1 determine the domain of the relation when the range is -2, 0, 2
Answer:
the domain is: {−3,0,1,6}
the range is:{2,3,4,−6,4}
the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .
Explanation:
In the relation:
{(−3,2),(0,3),(1,4),(1,−6),(6,4)}:
The domain:
Is the set of all the first numbers of the ordered pairs.
In other words, the domain is all of the x-values.
So in this case the domain is:
{−3,0,1,6}
The range:
Is the set of the second numbers in each pair, or the y-values.
So in this case the range is:
{2,3,4,−6,4}
A relation is a function if it has only One y-value for each x-value.
So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .
Step-by-step explanation:
please help me! A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. After 30 years, the value of the bond will be $25,084.20. If the business owner's investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years? $345.31 $318.22 $286.74 $228.59
Using compounding we know that after 30 years, the account balance has changed by $345.31.
What is continually compounded?Theoretically, continually compounded interest indicates that interest is continuously earned on an account balance as well as reinvested into the balance so that additional interest is generated.
So, a business owner put $7,000 into a Treasury bond paying a semiannual compound interest rate of 4.3%.
The bond's value after 30 years is $25,084.20.
Instead of compounding twice a year, the investment made by the business owner was made continuously.
After 30 years, we must determine the difference in the account balance.
Think of the continuously compounding recipe:
A = Pe∧rt
We have, p = 7000.
r = 4.3% = 0.043
t = 30
Then,
A = 7000e∧(0.043*30) = 25429..51
A = $25429.51
Therefore, using compounding we know that after 30 years, the account balance has changed by $345.31.
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Correct question:
A business owner invested $7,000 in a treasury bond paying 4.3% compounded semiannually. After 30 years, the value of the bond will be $25,084.20. If the business owner's investment was compounded continuously instead of twice per year, what would be the difference in the account balance after 30 years?
Im so confused right now. Can you help me
how will his speed compare? or namely, will he be within speed limits or should we give him a big fat ticket for speeding?
well, the 25 mi/hr limit is expecting anyone on that road to only do 40,234 meters per hour, so since an hour is 60 minutes and a minute is 60 seconds, that means an hour is really (60)(60) seconds, or 3600 seconds, so the limit is expecting anyone on that road to do no more than 40,234 meters per 3600 seconds, let's see how Usain fares
[tex]\begin{array}{ccll} meters&seconds\\ \cline{1-2} 100 & 9.63\\ 40234& x \end{array} \implies \cfrac{100}{40234}~~=~~\cfrac{9.63}{x} \implies 100x=(40234)(9.63) \\\\\\ x=\cfrac{(40234)(9.63)}{100}\implies x\approx 3874.53[/tex]
so Usain will covering those 40,234 meters in about 3875 seconds, that's longer than 3600 seconds, meaning Usain will need more than 3600 seconds to cover those meters so he's really going slower 40,234 meters per 3600 seconds, so he's golden, he's within speed limits, because the limit is expecting noone to do them in less than 3600 seconds.
The top of building A is 418 feet high. This is about 3 times as high as the top of building B.
About how high is the top of building B?
Select the numbers that correctly complete the sentence.
The top of building B is between
Choose...
feet high.
Answer:139.33 or 139 ft high
Step-by-step explanation: since building A is three times as high as building B, we can use the equation 418/3=B, which results in 139.33, and if rounding it needed you could round it to 139
which of the following statements is true? a.) to imply causation, the correlation must be -1. b.) a high correlation can indicate a relationship but cannot prove causation. c.) a high correlation indicates that explanatory variable is a direct cause of the response variable. d.) having a low correlation is sufficient enough to imply causation.
The statement that is true is:
b.) A high correlation can indicate a relationship but cannot prove causation.
Correlation measures the strength and direction of the relationship between two variables, but it does not necessarily imply causation. A high correlation means that there is a strong linear relationship between the two variables, but it does not indicate whether one variable causes the other. There can be other factors that influence the relationship. Therefore, it is important to use other methods, such as experiments or observational studies, to determine causation. Correlation is useful for identifying associations between variables, but it cannot be used as evidence of a causal relationship.
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Kate invests £2000 in a savings account for 3 years the account pays compound interest at an annual rate of 2. 5% for the first year x% for the second year x% for the third year there is a total amount of £2124. 46 in the savings account at the end of 3 years work out the rate of interest in the second year
The second year's interest rate is 1.80%.
Compound interest is defined as Since compound interest accrues and is added to the accrued interest from earlier periods, borrowers are expected to pay interest on interest in addition to principal.
We are aware that the compound interest formula is,
A = P(1 + r/100)ⁿ.
Where A is the amount, P is the principle, r is the rate, and n is the number of years.
Given, Katy places $2000 over a three-year period in a savings account.
For the first year, the account offers compound interest at a 2.5% annual rate.
∴ A = 2000(1 + 2.5/100)¹.
A = 2000(1.025). (1.025).
A = 2050.
It now earns x% for the second year.
∴ 2050(1+x/100)² = 2124.46
(1+x/100)² =2124.46/2050
1+x/100 =√(2124.46/2050)
x/100 = √(2124.46/2050) -1
x = (√(2124.46/2050) -1)*100
x = 1.80%.
the interest is 1.80 percent
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If a cuboid weighs 100N has sides 5cm by 10cm. Find the area of the cuboid
If a cuboid weighs 100N and has sides 5cm by 10cm, then the area of cuboid is 0.005m².
Weight of the cuboid = 100N
Sides of the cuboid = 5cm by 10cm
A solid structure or a three-dimensional shape in geometry is called a cuboid. It is similar to a cube in that a cuboid can become a cube by changing the angles between faces or the lengths of the edges. A convex polyhedron with the same polyhedral graph as a cube is referred to as a cuboid in mathematics.
Calculating the area of the Cuboid -
= 5cm × 10cm
= 50cm²
Converting -
Area of Cuboid
= 50/10000 m²
= 0.005 m²
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Triangles EFD and GHI are shown.
Part A
Are the triangles congruent?
Part B
If the triangles are congruent, write the congruence statement. If not, write “not congruent.”
Part C
If the triangles are congruent, write the transformation or sequence of transformations. If they are not congruent, write "not congruent."
The triangles are congruent by SSS and the transformation rule is (x, y) ⇒ (x - 4, y)
Part A: Are the triangles congruent?From the question, we have the following parameters that can be used in our computation:
Triangles EFD and GH
The triangles are congruent because they have equal corresponding side lengths
Part B: The congruent statementThe corresponding sides of the triangles are congruent
So, the congruent statement is SSS
The transformation ruleFrom the figure, we can see that:
EFD is shifted left by 4 units
So, the rule is
(x, y) ⇒ (x - 4, y)
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A college basketball player makes 80% of his free throws . Over the season he will attempt 100 free throws assume free throw attempts are independent , and let X be the total number of free throws he makes . a) The mean of X is ? Which on is correct -Cannot be determined / 80 /100 /0.80 ? b) The standard deviation of X is ? Which on is correct= 16/ 4/ 80/ 20? c) The probability that the basketball player makes at least 90 of these attempts is approximately ? Which on is correct= 0.0062/ 0.9938/ 0.2660 ? d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is ? Which on is correct= 0.0009/ 0.9991/ 0.0064/ 0.9936?
A collegiate basketball player hits 80% of his free throw attempts. Assuming free throw attempts are independent, he will try 100 free throws this season the answers are as follows:
a) The mean of X is 80.
b) The standard deviation of X is 4.
c) The probability that the basketball player makes at least 90 of these attempts is approximately is 0.0062.
d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is 0.0064.
As per the question given,
a) The mean of X is given by the formula: mean = n * p, where n is the number of trials and p is the probability of success on each trial. In this case, the player attempts 100 free throws with a probability of success of 0.8, so the mean is:
mean = 100 * 0.8 = 80
Therefore, the correct answer is 80.
b) The standard deviation of X is given by the formula: standard deviation = sqrt(n * p * (1 - p)). Substituting the values, we get:
standard deviation = sqrt(100 * 0.8 * 0.2) = 4
Therefore, the correct answer is 4.
c) To find the probability that the player makes at least 90 free throws, we can use the normal approximation to the binomial distribution. The mean is 80 and the standard deviation is 4, so we can standardize the value of X as follows:
z = (90 - 80) / 4 = 2.5
Using a standard normal distribution table, we can find the probability that Z is greater than 2.5, which is approximately 0.0062.
Therefore, the correct answer is 0.0062.
d) If the player attempts only 10 free throws, the number of successful attempts X follows a binomial distribution with n=10 and p=0.8. The probability that he makes at most 4 of these attempts is:
P(X <= 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)
Using the binomial distribution formula, we can calculate each of these probabilities and sum them up. Alternatively, we can use a binomial probability table or a calculator to find the cumulative probability.
Using a binomial probability calculator, we get:
P(X <= 4) = 0.0064 (rounded to four decimal places)
Therefore, the correct answer is 0.0064.
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Olivia has 1/8 pound of butter. She needs to divide the butter equally amoungn4 batches of muffins she is baking. How much butter is used in each batch of muffins
The correct weight of butter is 1/32 pounds. Olivia will use 1/32 pound of butter in each batch of muffins.
Olivia has 1/8 pound of butter that she needs to divide equally among 4 batches of muffins. To find out how much butter is used each batch of muffins, we can divide the total amount of butter by the number of batches. So, the amount of butter in each batch of muffins is: 1/8 ÷ 4 batches = 1/32 pound. So, Olivia will use 1/32 pound of butter in each batch of muffins. A pound (lb) is a unit of weight or mass commonly used in the United States and other countries that follow the customary system of measurement.
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Someone please help me with this question
Tony and his cousin are playing a game where they pick up colored sticks. Tony currently has 12 points and likes to pick up the yellow sticks, earning 10 points every turn. His cousin just lost all his points on the previous turn, and has a strategy to catch up by getting all the blue ones, earning 14 points per turn. In a certain number of turns, the score will be tied. How many points will they each have? How long will that take?
Tony and his cousin will each have __ points in __ turns.
Answer:
42 points3 turnsStep-by-step explanation:
You want to know the number of points and the number of turns when Tony and his cousin will have the same score. Tony has 12 points and earns 10 points per turn; his cousin has 0 points and earns 14 points per turn.
TableThe attachment shows a table of points and turns. It shows the score will be tied at 42 points after 3 turns.
EquationsTony's points can be described by ...
p = 12 +10t . . . . . . . . 12 points in addition to 10 per turn
Cousin's points can be described by ...
p = 0 + 14t . . . . . . . . . 14 points per turn added to the current score of 0
These will be equal when ...
p = p
12 +10t = 0 +14t . . . . substitute for p in both cases
12 = 4t . . . . . . . . . . subtract 10t
3 = t . . . . . . . . . . divide by 4
p = 14·3 = 42 . . . . the scores after 3 turns
Michael runs a distance of 5 1/4 miles in 45 3/4 minutes during a race. Which statements correctly represent
Michael's race? Select ALL the correct answers.
A. Michael's unit rate of minutes per mile was about 8.7.
B. Michael's average pace was about 0.11 miles per minute.
C.
Michael's unit rate of minutes per mile was about 6.9.
D. Michael's average speed during the race was about 6.9 miles per hour.
E.
Michael ran about 8.7 miles in 1 minute.
eria wall
Answer:
A. Correct
B. Correct
C. Not correct
D. Correct
E. Not correct
Step-by-step explanation:
We are told that Michael's race numbers are:
5.25 miles
45.75 minutes
Divide the miles by the minutes to get mIchael's running rate:
0.114754098 mi/min
This result matches option B. " Michael's average pace was about 0.11 miles per minute."
======
Check all the answer options:
A. Michael's unit rate of minutes per mile was about 8.7.
Take 0.11475409 mi/min and invert it to find min/mile:
1/(0.11475409 mi/min) = 8.71 min/mile
This is a correct statement.
B. Michael's average pace was about 0.11 miles per minute.
From above: This is a correct statement.
C. Michael's unit rate of minutes per mile was about 6.9.
Take the given numbers: (45.75 minutes)/(5.25 miles) = 8.71 min/mile
This is not a correct statement.
D. Michael's average speed during the race was about 6.9 miles per hour.
Take the calculated rate of 0.11475409 mi/min and covert it to miles/hour:
Use the conversion factor (60 min/1 hr)
(0.11475409 mi/min)*((60 min/1 hr)) = 6.89 miles/hr
This is a correct statement.
E. Michael ran about 8.7 miles in 1 minute.
We know from above that he runs at 6.89 miles per hour. Running 8.7 miles in 1 minute would mean he is running at (8.7)*(60) = 413 miles/hour.
Perhaps he had some good energy bars, but the data do not support this conclusion.
This is not a correct statement.
Every time Ezequiel rides the bus, money is deducted from the value of the pass. He rode 9
times and $72 was deducted from the value of the pass. What integer represents the
amount lost EACH time the pass was used? (
The integer 8 represents the amount lost each time the pass was used.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given that, every time Ezequiel rides the bus, money is deducted from the value of the pass.
He rode 9 times and $72 was deducted from the value of the pass.
Let x be the integer that represents the amount deducted each time.
The amount deducted after 9 times is 9x.
9x = 72
We have to divide 72 into 9 parts to know the value of x.
x = 72 / 9 = 8
Hence Ezequiel lost $8 each time the pass was used.
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2 of 3
Some people took part in a game. The frequency shows information about their scores.
Score
1-7
8-10
11-15
16-20
21-35
36-50
Estimate the mean.
Give your answer rounded to 2 decimal places.
Frequency
13
1
19
20
19
20
The mean of the given data is 22.39.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Let us form a table by give data
Score Frequency Midpoint(x) fx
1-7 13 4 52
8-10 1 9 9
11-15 19 13 247
16-20 20 18 360
21-35 19 28 532
36-50 20 43 860
Mean=∑fx/N
=52+9+247+360+532+860/13+1+19+20+19+20
=2060/92
Mean=22.39
Hence, the mean of the given data is 22.39.
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A point at (-4, 7) is rotated -90° about the origin. What are the new coordinates for the point?
Answers:
(4, -7)
(-7, 4)
(7, 4)
(-4, -7)
Given the expression: 3x10 − 48x2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
this homework due now pls help i've been out sick
Answer: A. [tex]92cm^{3}[/tex]
Step-by-step explanation:
[tex]V= \frac{4}{3} \pi r^{3}[/tex]
[tex]V=\frac{4}{3}\pi 2.8^{3}[/tex]
[tex]4/3=1.33333333333[/tex]
calculate in calculator
[tex]1.33333333333\pi 2.8^3=91.9523225755[/tex]
round to nearest ones (9 tells 1 to go to 2)
Therefore, A. 92cm^3
Which of the following is the length of the hypotenuse of an
isosceles right triangle if the length of one of the legs is 8 cm?
a 10.45 cm
b 10.30 cm
c 11.22 cm
d 11.31 cm
The length of the hypotenuse is 11.31 cm
How to determine the length of the hypotenuse of an isosceles right triangleFrom the question, we have the following parameters that can be used in our computation:
A right, isosceles triangle has its legs to be 8cm
Represen the length of the hypotenuse of the isosceles right triangle with x
Using the above definition as a guide, we have the following:
x = Leg√2
substitute the known values in the above equation, so, we have the following representation
x = 8 * √2
This gives
x = 11.31
HEnce, the hypotenuse is 11.31 cm
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4 3 You correctly chose a square pyramid. Now, find the area of the faces of the pyramid. 3 ft 2 4 ft 3 ft What is the area of the triangles? (x4) Triangles: [?] ft2 102 Square: Total Surface Area: Enter
HELPP
Answer:
triangles: 24 ft²square: 9 ft²total surface area: 33 ft²Step-by-step explanation:
You want the lateral area, base area, and total area of a square pyramid with a base 3 ft on a side and a slant height of 4 ft.
Triangle areaThe area of one triangle is ...
A = 1/2bh
A = 1/2(3 ft)(4 ft) = 6 ft²
Then the area of the four triangular faces is ...
area of triangles = 4×6 ft² = 24 ft²
BaseThe area of the square base is ...
A = s²
A = (3 ft)² = 9 ft²
The area of the square base is 9 ft².
TotalThe total surface area is the sum of the lateral area and the base area:
total surface area = area of triangles + area of square = 24 ft² +9 ft²
total surface area = 33 ft²
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Minja is three years older than her sister June. Minja's brother is eight years younger
than their sister June. The sum of all of their ages is 55 years.
x+3-8x=55.
3x 8x + x 55.
(x+3-8)+x=55
(x+3)+(x-8)+x=55
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Answer: C
Step-by-step explanation: