Answers
In mathematical notation, ∑ means summation. So wherever you see the symbol, you have to sum over all elements in the set. Let's solve the question.
a. ∑m means, to sum all elements in the set m: ∑m = 12 + 15 + 20 + 30 = 77
b. ∑\(f^{2}\) means to sum all elements in the set f as the square of the elements f = \(5^{2} + 9^{2} + 10^{2} + 16^{2} = 25 + 81 + 100 + 256 = 462\)
c. ∑mf means to sum all elements as the product of the elements of m and f = (12×5) + (15×9) + (20\((12^{2}(5)) + (15^{2}(9)) + (20^{2}(10)) + (30^{2}(16)) = 21145\)10) + (30×16) = 875
d. ∑\(m^{2}f\) means to sum all elements as the product of the square of m and f = \(((12*12)(5)) + ((15*15)(9)) + ((20*20)(10)) + ((30*30)(16)) = 21145\)
Related Questions
PLEASE HELP 15 POINTS
Answers
Answer:
so you will put the point above the zero across from 6
the slope is rise/run
Step-by-step explanation:
If P = 42 when
x = 14, find P when
x= 2
Answers
Answer:
P= 6
42/14=3
Therefore, the ratio must be 3
Step-by-step explanation:
In trapezoid ABCD below, angles B and C are right angles.
(a) Circle the two sides from the four choices below that are parallel.
AB
BC
CD
DA
b) Find the area of the right trapezoid by breaking it
into a rectangle and right triangle and summing
their areas.
Rectangle:
Sum of areas:
Right Triangle:
D
24 cm
A
6 cm B
16 cm
C
Answers
The parallel sides are AB and CD while the area of the Trapezium is 240cm²
A.)
Parallel sides are directly opposite one another and their lines never meet. lines AB and CD.
Therefore, the two parallel sides are AB and CD
B.)
Area of Trapezium = Area of Rectangle + Area of Triangle
Area of rectangle = Length * width
Area of rectangle = 6 * 16 = 96 cm²
Area of Triangle = 1/2*base*height
Area of Triangle= 1/2 * 18 * 16
Area of Triangle = 144 cm²
Hence, area of Trapezium is 240 cm²
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Angle A and angle B are supplementary angles. If
angle B is 30° more than four times angle A, find
angle A and angle B.
Answers
Answer:
Angle A is 30
Angle B is 150
Step-by-step explanation:
So we have the supplementary angles A and B. In other words:
\(A+B=180\)
We are also told that Angle B is 30 more than four times Angle A. In an equation, this is:
\(B=30+4A\)
We now have a system of equations. Solve by substitution of B into the first equation:
\(A+B=180\)
\(A+(30+4A)=180\)
Combine like terms:
\(5A+30=180\)
Subtract 30:
\(5A=150\)
Divide by 5:
\(A=30\)
So, Angle A is 30 degrees.
And since the angles are supplementary, this means that Angle B is 180 minus 30 or 150 degrees.
Solve the equation. If the equation is an identity, choose identity. If it has no solution, choose no solution.
−12x+1=7x−14
A. 2
B. −2
C. identity
D. no solution
Answers
Answer:
There is one solution x = 15/19
Step-by-step explanation:
−12x+1=7x−14
Add 12x to each side
−12x+12x+1=7x+12x−14
1 = 19x-14
Add 14 to each side
1+14 = 19x-14+14
15 = 19x
Divide by 19
15/19 = 19x/19
15/19 =x
There is one solution x = 15/19
whats the answer? with the workout please
Answers
Answer:
reduction, scale factor of 1/2
Step-by-step explanation:
because the rectangle is getting smaller, it is a reduction. the length got shorter by 1/2 (2.5/5) so the scale factor is 1/2
(3x+5)(4x-2)=-2x(-6x+3)
Answers
Step-by-step explanation:
(3x+5)(4x-2)=-2x (-6x+3)
3x+5×4x-2=-12x+6x
3x-4x+12x-6x=-5-4
7x=9
7x/7=9/7
x=9/7
Please someone help I really need it and please answer if you can give me the answer I will give brainleast just please help me with this
Answers
Answer: I tried to use the step by step explanation of your exercise, I hope Otis helping you and have a nice rest of your day :)
1
Solve the inequality. Graph the solution.
(a)
2 < y/5
Answers
Answer:
Inequality form: y > 10
Interval Notation: (10, ∞)
The points earned by each choir team during the All-State Competition are as follows:
Choir Choir A Choir B Choir C Choir D
Points 129.5 130.1 130.8 129.8
If points are reported by rounding to the nearest whole number, which team has a different score? (5 points)
Choir A
Choir B
Choir C
Choir D
Answers
Answer:
d
Step-by-step explanation:
A population of beetles is growing according to a linear growth model. Initially, there were 20 beetles, and 6 weeks later, there were 25 beetles.(a) Write a linear model to describe the number of beetles over time, using weeks as the unit of time.Pt= (b) How many beetles are there expected to be 17 weeks after the initial point? beetles(c) When do you expect the number of beetles to reach 85? Round your answer to the nearest week.After weeks
Answers
Answer:
a) P(t) = 5/6t + 20
b) 34.2 beetles
c) After 78 weeks.
Step-by-step explanation:
a) A general linear growth model can be expressed as P(t) = at + b, where P is the number of beetles in time t and t is the time in weeks.
It is known that:
P(0) = 20
P(6) = 25
These values can be substituted in the general equation to find a and b:
P(t) = at + b
P(0) = 20:
20 = a*0 + b
20 = 0 + b
20 = b
So,
P(t) = at + 20
Using P(6) = 25:
25 = a*6 + 20
25 - 20 = a*6
5 = a*6
5/6 = a
So, the linear growth model can the represented as:
P(t) = 5/6t + 20
b)
The number of beetles after 17 weeks is P(17):
P(17) = 5/6*17 + 20
P(17) = 14.1 + 20
P(17) = 34.2
34.2 beetles.
c)
P(t) = 85
85 = 5/6t + 20
85 - 20 = 5/6t
65 = 5/6t
t = 65*6/5
t = 78
After 78 weeks.
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 3000 grams and astandard deviation of 1000 grams while babies born after a gestation period of 40 weeks have a mean weight of3400 grams and a standard deviation of 515 grams. If a 35-week gestation period baby weighs 3425 gramsand a 40-week gestation period baby weighs 3825 grams, find the corresponding Z-scores. Which babyweighs more relative to the gestation period?
Answers
Answer:
D. The baby born in 40 weeks weighs more relatively since its z-score, 0.83 is larger than the z-score of 0.43 for a baby born in week 35.
Explanation:
The z-score is calculated using the formula:
\(z=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}X=\text{Raw Score} \\ \mu=\text{Mean} \\ \sigma=\text{Standard Deviation}\end{cases}\)For the baby born after a 35-week gestation period.
• Weight = 3425 grams
,• Mean = 3000 grams
,• Standard Deviation = 1000 grams
The z-score is calculated below:
\(z=\frac{3425-3000}{1000}=\frac{425}{1000}=0.425\approx0.43\)The z-score is 0.43 correct to 2 decimal places.
For the baby born after a 40-week gestation period.
• Weight = 3825 grams
,• Mean = 3400 grams
,• Standard Deviation = 515 grams
The z-score is calculated below:
\(z=\frac{3825-3400}{515}=\frac{425}{515}\approx0.83\)The z-score is 0.83 correct to 2 decimal places.
Thus, we conclude that:
The baby born in 40 weeks weighs more relatively since its z-score, 0.83 is larger than the z-score of 0.43 for a baby born in week 35.
Option D is correct.
Mr. Hoffman has three red frisbees and five yellow frisbees. Select all the answers that represent a ratio relationship for Mr. Hoffman's frisbees.
Question 1 options:
A.11 to 5
B. 8 to 3
C. 5:11
D. 3:5
E. 5/3
Answers
As there are 3 and 5 frisbees, we can say that there is a relation between red and yellow
To make a jug of plant fertilizer, Malaika uses 6 cups of water and 3 scoops of fertilizer. Bart uses 8 cups of water and 5 scoops of fertilizer. Will Malaika's and Bart's plant fertilizer have the same strength? Explain.
Answers
Answer:
No they will no have the same strength. So what I did was find a common number between them so between 8 and 6 they both can be multiplied to 24. So 6 goes into 24 4 times so I multiplied 3 times 6 and then 8 goes into 24 3 times so I multiplied 3 and 5 and so the final answer is that bart has more strong fertilizer
Step-by-step explanation:
6*4=24 4*3=12
8*3=24 5*3=15
A company selling licenses for new e-commerce computer software advertises that firms using this software obtain, on average during the first year, a minimum yield of 10% on their initial investments. A random sample of 10 of these franchises produced the following yields for the first year of operation:
6. 1, 9. 2, 11. 5, 8. 6, 12. 1, 3. 9, 8. 4, 10. 1, 9. 4, 8. 9
Assuming that population yields are normally distributed, test the company's claim with a significance level of 5% (. 05).
I already calculated the sample mean and sample standard deviation, which are 8. 92 and 2. 4257 respectively
Answers
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. There is not enough evidence to conclude that the average yield on the initial investment is less than 10%.
To test the company's claim that the average yield on the initial investment is at least 10%, we can use a one-sample t-test. The null hypothesis is that the true mean yield is equal to 10%, while the alternative hypothesis is that it is less than 10%. We will use a significance level of 0.05.
The test statistic for a one-sample t-test is calculated as:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
In this case, the sample mean is 8.92, the hypothesized population mean is 10%, the sample standard deviation is 2.4257, and the sample size is 10. Plugging these values into the formula, we get:
t = (8.92 - 10) / (2.4257 / √10) = -1.699
The degrees of freedom for this test are n - 1 = 9.
Using a t-distribution table or calculator, we can find that the p-value for this test is 0.0647. This means that if the true mean yield is 10%, there is a 6.47% chance of obtaining a sample with a mean yield of 8.92 or lower.
In other words, based on the given sample, we cannot conclude that the company's claim is false. However, we also cannot say with certainty that the claim is true. Further testing with a larger sample size may be necessary to make a more conclusive determination.
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Is the quadrilateral shown a parallelogram? Justify
Answers
Which is equivalent to 216 Superscript one-third?
3
6
36
72
Answers
Answer:
I think is 6
hope this answer be right
Answer:
6
Step-by-step explanation:
If Al can paint a house in 15 hours and bill can paint the same house in 20 hours. How long will it take them if they work together?
Answers
Answer:
See below.
Step-by-step explanation:
Al can paint a house in 15 hours, which means in one hour, he can paint 1/15.
Using the same logic, bill can paint 1/20.
Together in one hour, they paint 1/15 + 1/20 = 7/60
Total hours: 60/7 = 8.57 hours. (8 hours and 34 minutes)
a canoe is 24 inches wide and 12 feet long write the ratio of its width to its length
Answers
The dimensions given are
\(\begin{gathered} \text{width}=24in \\ \text{length}=12ft \\ To\text{ convert the width to the same unit as the length,} \\ 12in=1ft,\text{ therefore} \\ 24in=2ft \\ \text{The ratio of the width to the length is therefore;} \\ 2ft\colon12ft \\ =\frac{2}{12} \\ =\frac{1}{6} \\ \text{The ratio of the width to the length is } \\ \text{Ratio}=1\colon6 \end{gathered}\)Type the correct answer in the box. use numerals instead of words. the pyramid of the sun in mexico is a square pyramid. the base edge is approximately 220 meters, and the height is approximately 70 meters. what is the approximate surface area of the sides of the pyramid to the nearest thousand square meters? the lateral surface area is about .
Answers
The approximate surface area of the sides of the pyramid to the nearest thousand square meters is A ≈ 1.06 × 10⁵ meters.
What is a square pyramid?A square pyramid is a pyramid with a square base in geometry. Every pyramid is called for its base. As a result, a square pyramid has a square base, four triangular sides, five vertices, and eight edges.To find the approximate surface area of the sides of the pyramid:
Formula:
A = a² + 2a √a²/4 + h²The given base is 220 meters and the height is 70 meters.
Insert values as follow:
A = a² + 2a √a²/4 + h² = 220² + 2 · 220 · √220²/4 + 70²≈ 1.05769 × 10⁵That is A ≈ 1.06 × 10⁵.Therefore, the approximate surface area of the sides of the pyramid to the nearest thousand square meters is A ≈ 1.06 × 10⁵ meters.
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Answer: 106000
Step-by-step explanation:
for those of you who don't know scientific notation
What is the critical value z* for constructing an 80% confidence interval?
Answers
Answer:khan is 1.282 or c
Step-by-step explanation:
Help ASAP 15 Points
No spam answers please
Answers
Not really sure what the second part is asking but maybe 5=7=9
a report says that the average amount of time a 10-year-old american child spends playing outdoors per day is between 20.02 and 25.36 minutes. what is the margin of error in this report?
Answers
The actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.
The margin of error in the report stating that a 10-year-old American child spends an average of 20.02 to 25.36 minutes playing outdoors per day can be calculated by subtracting the lower value from the higher value and dividing by 2. In this case, the margin of error is :
To find the margin of error, we need to calculate the halfway point between these two values.
(25.36 - 20.02) / 2 = 2.67
Therefore, the margin of error is approximately 2.67 minutes. This means that the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.
Thus, the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.
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Automatic Transmissions, Inc., has the following estimates for its new gear assembly project: price = $940 per unit; variable cost = $340 per unit; fixed costs = $3.4 million; quantity = 53,000 units. Suppose the company believes all of its estimates are accurate only to within ±15 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?
Answers
In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.
In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.
On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.
Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units
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Simplify the expression. (n^7)^2
Answers
Answer:
n^14
Step-by-step explanation:
Simplify. Note that when you have a power on top of a power, you multiply the two powers.
(n^7)^2 = n^(7 * 2) = n^14
n^14 is your answer.
~
Use power rule: (a^b)^c = a^b*c
Solve.
= (n^7)^2
= n^7*2
= n^14
Best of Luck!
When identifying and labeling angles. Why
do you have to be careful when using just
one letter to name an angle?
Answers
Answer:
There is a difference between A and a
Step-by-step explanation:
When you are labeling angles, capitol letter means the angle degree while a lowercase letter means a side length.
f(x) = 3x^2+1
1. f(-2) =
Answers
Answer:
Step-by-step explanation:
\(f(x) = 3x^{2} +1\\f(-2) = 3(-2)^{2} +1 = 12 + 1 =13\\\)
The answer is 13.
Hope that helps!
Answer:
\(f(-2) =13\)
Step-by-step explanation:
\(f(x) = 3x^2+1\), f(-2)
\(f(x) = 3x^2+1\)
\(f(-2) = 3(-2^2)+1\)
\(f(-2) = 3(4)+1\)
\(f(-2) = 12+1\)
\(f(-2) =13\)
Hope this helps!
You have just got paid and your planning to invest in the Nike Kobe 6. Though they currently cost
$320.00, they will be worth $500 in six months. There is an ad at the local Nike store, Buy one pair for
$320 and your receive a 25% discount on a second pair and a $50.00 discount on a third pair. You
decide to buy the three pairs. How much will you pay? How much will you make in six months if you
sell all 3 pairs?
Answers
The total cost of buying 3 pairs is $830 and in six months we will make $1,500.
What are mathematical operations?(Calculation is just another word for operation, examples of operations include addition, subtraction, multiplication, and division.)The importance of the order of operations stems from the fact that it ensures everyone can understand and approach a problem in the same way.So, the money we pay when we buy 3 pairs of Nike Kobe 3:
Cots of 1st pair: $320Cots of 2nd pair: 320/100 × 25 = 80 ⇒ 320 - 80 (25% discount) = $240Cots of 3rd pair: 320 - 50 ($50 discount) = $270The total cost of buying 3 pairs: 320+240+270 = $830
The money we will make in six months:
In six months: 3 × $500 = $1,500Therefore, the total cost of buying 3 pairs is $830 and in six months we will make $1,500.
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The diameter of a small pizza is 16 centimeters this is 2 centimeters more than two fiths of the diameter of a large pizza find the diameter of the large pizza
Answers
Answer:
35 cm
Step-by-step explanation:
Diameter of small pizza = 16
Let Diameter of large pizza = x
Diameter of small pizza = 2/5(x) + 2
2/5(x) + 2 = 16
(2x / 5) + 2 = 16
2x / 5 = 16 - 2
2x / 5 = 14
multiply both sides by 5
2x = 14 * 5
2x = 70
Divide both sides by 2
x = 70/2
x = 35
Diameter of large pizza = 35 mm
Please help me answer my homework in the image
Answers
Using distance formula, the triangle ABC is a scalene triangle
What is triangle ABCTo classify the triangle, we need to determine whether its sides are equal in length (in which case it's equilateral or isosceles), or whether they are all different lengths (in which case it's scalene). We can use the distance formula to calculate the length of each side of the triangle, as follows:
The distance formula gives us the distance between two points (x1, y1) and (x2, y2) in the coordinate plane:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Using this formula, we can find the length of each side of triangle ABC:
AB = √[(4-1)^2 + (4-0)^2] = √(9 + 16) = √25 = 5
BC = √[(6-4)^2 + (2-4)^2] = √(4 + 4) = 2√2
AC = √[(6-1)^2 + (2-0)^2] = √(25 + 4) = √29
We can see that AB = 5, BC = 2√2, and AC = √29. Since all three sides have different lengths, the triangle is scalene.
Note that the midpoints of the sides AB and BC are not relevant for determining the type of triangle. Also, it's not accurate to say that the midpoint of AB is (4/3, 2), as the coordinates of the midpoint are actually ((1+4)/2, (0+4)/2) = (2.5, 2), and similarly for the midpoint of BC.
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