\( \frac{3 {a}^{2} - 9a}{ {a}^{2} - 9} = \frac{3a(a - 3)}{(a + 3)(a - 3)} = \frac{3a}{a + 3} \)
c)\( \frac{ {y}^{2} - 3yz -4 {z}^{2} }{3 {y}^{2} - 12yz } = \frac{(y + z)(y - 4z)}{3y(y - 4z)} = \frac{y + z}{3y} \)
d)\( \frac{ {d}^{2} + 4d + 4}{ {d}^{2} + 2d} = \frac{(d + 2)(d + 2)}{d(d + 2)} = \frac{d + 2}{d} \)
e)\( \frac{5f - 15}{3 {f}^{2} - 13f + 12} = \frac{5(f - 3)}{(3f - 4)(f - 3)} = \frac{5}{3f - 4} \)
I hope I helped you^_^
A elementary school art class teacher plans to display artwork next to the door of each of the classrooms in the school. Each classroom door will only have one piece of artwork displayed, and the school has 20 such doors. If the teacher has 10 sculptures, 11 sketches, and 9 oil paintings, what is the probability that 4 sculptures, 10 sketches, and 6 oil paintings are chosen to be displayed?
Answer:
56/8671
Explanation:
First, determine the total number of artworks.
• Sculptures = 10
,• Sketches = 11
,• Oil paintings = 9
Total = 10+11+9 = 30
20 artworks can be selected out of 30 in 30C20 ways.
Next:
• 4 sculptures can be selected out of 10 in 10C4 ways.
,• 10 sketches can be selected out of 11 in 11C10 ways.
,• 6 oil paintings can be selected out of 9 in 9C6 ways.
The combination formula is:
\(^nC_x=\frac{n!}{(n-x)!x!}\)Therefore:
\(\begin{gathered} ^{10}C_4=\frac{10!}{(10-4)!4!}=\frac{10!}{6!4!}=210 \\ ^{11}C_{10}=\frac{11!}{(11-10)!10!}=\frac{11!}{1!10!}=11 \\ ^9C_6=\frac{9!}{(9-6)!6!}=\frac{9!}{3!6!}=84 \\ ^{30}C_{20}=\frac{30!}{(30-20)!20!}=\frac{30!}{10!20!}=30045015 \end{gathered}\)Thus, the probability that 4 sculptures, 10 sketches, and 6 oil paintings are chosen to be displayed is:
\(\begin{gathered} \frac{^{10}C_4\times^{11}C_{10}\times^9C_6}{^{30}C_{20}} \\ =\frac{210\times11\times84}{30045015} \\ =\frac{194040}{30045015} \\ =\frac{56}{8671} \end{gathered}\)The probability is 56/8671.
a town had 2120 acres of pine trees a few years ago. only 15% of the acres of trees are left. how many acres of pine trees remain?
Answer:
318
Step-by-step explanation:
just to 2120 x .15
write an equation of the line that passes through each pair of points (0,1),(5,3)
The perimeter of a rectangle is 64cm. Its shortest side has a length of 3cm. State the length of the longest side.
Answer:
29
Step-by-step explanation:
P = 2l + 2w
64 = 6 + 2w
58/2 = w
=29
a9=35 d=4
write the value for the 9th term of the sequence
Given:
\(a_9=35\)
\(d=4\)
To find:
The value for the 9th term of the sequence.
Solution:
We have,
\(a_9=35\)
\(d=4\)
Here, d is the common difference. It means the given sequence is an arithmetic sequence.
We know that the nth term of an arithmetic sequence is:
\(a_n=a_1+(n-1)d\)
Where, \(a_1\) is the first term and d is the common difference.
If nth term is \(a_n\), then the 9th term is \(a_9\) and the value of \(a_9\) is given.
\(a_9=35\)
Therefore, the value for the 9th term of the sequence is 35.
Which transformation can NOT be used to prove that ABC is congruent to DEF?
Answer: it is dilation
Step-by-step explanation: i took the exam
Answer:dialation
Step-by-step explanation:
What is the area of this rectangle?
11 1/4
Step-by-step explanation:
Count up each individual square
true or false correlation between y and x has the same number but opposite sign as the correlation between x and y.
Answer:
true
Step-by-step explanation:
A correlation is symmetrical;x is as correlated with y as y is with x. The Pearson product-moment correlation can be understood within a regression context,however.
Please help me
\( \sf{with \: explanation \: again}\)
Answer:
50,000 joulesStep-by-step explanation:
total mass of people = 50× 5 = 250kg
height = 20m
force = mass × g = 250× 10 ( taking g= 10m/s²)
f= 2500Nwork done = force × distance
= 2500× 20
= 50000 joulesIn a deck, there are cards numbered 1 to 39 such that the number of cards of a particular number in the deck is same as 1 point the number on the card. Which of the following statement(s) is/are true about the mean and mode of the numbers on this deck of card? Mode is 39. Mean is 39 Mean is 26.33. Mode is 38. Mean is 20.0. Mode is not defined for this data.
The statement "Mean is 26.33" is true about the mean of the numbers on this deck of cards. The mode is not defined for this data.
To calculate the mean, we need to find the sum of all the numbers on the cards and divide it by the total number of cards. In this case, the sum of the numbers from 1 to 39 is 780. Dividing this sum by the total number of cards (39) gives us a mean of approximately 26.33.
However, the mode refers to the most frequently occurring number in a dataset. In this deck of cards, each number appears only once, so there is no number that occurs more frequently than others. Therefore, the mode is not defined for this data.
In summary, the mean of the numbers on the deck of cards is 26.33, and the mode is not defined.
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7 identical toys weigh 1.4 kg.
a) Convert 1.4 kg to grams.
b) What is the weight of one toy?
Give your answer in grams.
c) How much would 3 toys weigh?
Give your answer in grams.
Answer:
a] 1400 grams
b] 200 grams
c]600 grams
Step-by-step explanation:
1.4 x 1000=1400 grams
1.4 divide by 7 is 0.2 kg
0.2 x 3 = 0.6 x 1000=600 grams
Consider the vector v=(8,8,10). Find u such that the following is true. (a) The vector u has the same direction as v and one-half its length. u= (b) The vector u has the direction opposite that of v and one-fourth its length. u= (c) The vector u has the direction opposite that of v and twice its length. u=
(a) The vector u such that it has the same direction as v and one-half its length is u = (4, 4, 5)
(b) The vector u such that it has the direction opposite that of v and one-fourth its length is u = (-2, -2, -2.5)
(c) The vector u such that it has the direction opposite that of v and twice its length is u = (-16, -16, -20)
To obtain vector u with specific conditions, we can manipulate the components of vector v accordingly:
(a) The vector u has the same direction as v and one-half its length.
To achieve this, we need to scale down the magnitude of vector v by multiplying it by 1/2 while keeping the same direction. Therefore:
u = (1/2) * v
= (1/2) * (8, 8, 10)
= (4, 4, 5)
So, vector u has the same direction as v and one-half its length.
(b) The vector u has the direction opposite that of v and one-fourth its length.
To obtain a vector with the opposite direction, we change the sign of each component of vector v. Then, we scale down its magnitude by multiplying it by 1/4. Thus:
u = (-1/4) * v
= (-1/4) * (8, 8, 10)
= (-2, -2, -2.5)
Therefore, vector u has the direction opposite to that of v and one-fourth its length.
(c) The vector u has the direction opposite that of v and twice its length.
We change the sign of each component of vector v to obtain a vector with the opposite direction. Then, we scale up its magnitude by multiplying it by 2. Hence:
u = 2 * (-v)
= 2 * (-1) * v
= -2 * v
= -2 * (8, 8, 10)
= (-16, -16, -20)
Thus, vector u has the direction opposite to that of v and twice its length.
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5. Solve the system of equations
7x-4y+8z=37
3x+2y-4z=1 (note: the last equation represents a sphere with centre (0,0,0), radius √14)
x²+y²+z²=14
Answer:
Step-by-step explanation:
as
Respond these question please
The percentile rank of the score 71 on the test is 26.7.
What is a percentile?The value that a specific percentage falls under is known as the percentile. Ben, for instance, is the fourth-tallest child in a group of 20, and eighty percent of the kids are shorter than you.
Given:
58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
Calculate the percentile of score 71 as shown below,
\(Percentile = n / N \times 100\)
Here, n is the number of scores below 71 and N is the total number of scores,
Percentile = 4 / 15 × 100
Percentile = 0.267 × 100
Percentile = 26.7 percentile
Therefore, the percentile rank of the score 71 on the test is 26.7
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Mom said Joe and Jane could equally share the change in her purse. They found 2X 50c pieces and 2X 20c pieces and a 10c pieces. How much did they get each?
Hello
total = 2 x 50c + 2 x 20c + 10c = 150c
150c/2 = 75c
they get each 75c.
 What is the equation of the line pictured in slope intercept form?
Answer:
y=1/3x+4
Step-by-step explanation:
A high school physics teacher was conducting an experiment with his class on the length of time it will take a marble to roll down a sloped chute. The class ran repeated trials in order to determine the relationship between the length, in centimeters, of the chute and the time, in seconds, for the marble to roll down the chute. A linear relationship was observed and the correlation coefficient was 0.964. After discussing their results, the teacher instructed the students to convert all of the length measurements to meters but leave the time in seconds. What effect will this have on the correlation of the two variables
Answer:
Step-by-step explanation:
Because changing from centimeters to meters does not affect the value of the correlation, the correlation will remain 0.964.
The effect does have on the correlation of the two variables should be that it remain the same i.e. 0.964.
Impact on the correlation of the two variables:Since there is the changing from centimeters to meters so this does not impact the correlation value due to which it remain the constant i.e. 0.964.
Also, the correlation coefficient should be unit -less and the value should always ranged between -1 to 1.
Therefore, it remains the constant.
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What is the formula to find P(A) for a series of simple events (ex: tossing a coin and selecting a number at the same time)
The probability of event A is P(A) = 1/4 or 0.25.
The formula to find P(A) for a series of simple events is:
P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)
For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:
- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.
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For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees 927 companies paying for a larger portion of health care benefits. A recent Mercer survey showed that of U.S. employers were likely to require higher employee contributions for health care coverage in the upcoming year. Suppose the survey was based on a sample of companies. Compute the margin of error and a confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in the upcoming year.
We need to know the percentage of companies in the sample that are likely to require higher employee contributions in order to calculate the confidence interval.
Based on the information provided, we can calculate the margin of error and confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in the upcoming year. First, we need to know the sample size and the percentage of companies in the sample that are likely to require higher employee contributions. Unfortunately, this information is not given in the question. Without this information, it is impossible to calculate the margin of error and confidence interval. We need to know the sample size to determine the standard error of the proportion, which is necessary for calculating the margin of error. Additionally, we need to know the percentage of companies in the sample that are likely to require higher employee contributions in order to calculate the confidence interval.
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Hello! I need some help figuring out what 12 x 6,012 is. Ty!
Answer:
12 times 6012 u can type in calculator is 72144
Answer:
72144 is the answer.
Hope this helps
Select the correct answer from each drop-down menu.
Samuel received $250 as prize money for winning the St. Peterson High School Badminton Tournament. The money was deposited in a special scholarship account that offered an annual interest of 1.8% compounded semiannually. The amount he will have in the account after t years can be calculated using the expression below.
Use the given expression to complete the statements below.
The expression is the of the amount initially deposited and the of one and the rate of increase raised to the number of.
The choices are for 1 are sum, quotient, square, product. Choices for 2 is quotient, sum, product, difference. Choices for 3 are compounding periods, months, years.
Complete Question:
sierrac3000
06/28/2019
Select the correct answer from each drop-down menu.
Samuel received $250 as prize money for winning the St. Peterson High School Badminton Tournament. The money was deposited in a special scholarship account that offered an annual interest of 1.8% compounded semiannually. The amount he will have in the account after t years can be calculated using the expression below.
250(1+0.018/2)^2t
Use the given expression to complete the statements below.
The expression is the *blank* of the amount initially deposited and the *blank* of one and the rate of increase raised to the number of *blank*
1st Blank:
Product
Sum
Quotient
Square
2nd Blank:
Quotient
Product
Difference
Sum
3rd Blank:
Compounding Periods
Years
Months
Answer:
1st blank = product
2nd blank = sum
3rd blank = years
Step-by-step explanation:
The expression given above is :
250(1+0.018/2)^2t
The expression can thus be explained as:
The *product* of the amount initially deposited and the *sum* of one and the rate of increase raised to the number of *years*
Solve this equation: –2(x + 16) = –20 *
Answer:
\({\huge\purple{\fbox{{࿐αɴѕωєя࿐}}}}\)
\( - 2(x + 16) = - 20 \\ - 2x + 16 \times - 2 = - 20 \\ - 2x - 32 = - 20 \\ - 2x = - 20 + 32 \\ - 2x = 12 \\ x = \frac{12}{ - 2} \\ x = \frac{ - 12}{2} \\ x = - 6\)
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
\( \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}\)
Answer:
"solve this equation: - 2 (x+16)= - 20
Step-by-step explanation:
- 2x 16 + - 2 = - 20
- 2x - 32 = - 20
- 2x = - 20 + 32
x = - 12 :2
x = - 6
The mass of a bar of chocolate is 1800g
The density of the chocolate is 9g/cm
Find the mass of the ball in kg
The mass of the bar of chocolate in kilogram, kg is calculated to be 1.8kg
How to find the mass of the bar in kgGiven data
mass of a bar of chocolate is 1800g
density of the chocolate is 9g/cm
density is defined the ratio of mass and volume. therefore the density of the chocolate will be the ratio of the mass of the chocolate bar to the volume of the chocolate. this represented mathematically as:
The mass of the bar of chocolate is given in grams as 1800g
converting the unit to kg is done as follows
if 1kg is equal to 1000g, then how many kg is 1800g
= 1800 / 1000
= 1.8 kg
hence the mass of the chocolate bar in kg is 1.8 kg
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What is 5,239x713+10,963-563=
Answer:
3745807
Step-by-step explanation:
3745807 i hope i didn't calculate it wrong.
For EF in triangle EFG, what is the corresponding segment in similar triangle HFG?
Answer:
HF
Step-by-step explanation:
Answer: Side HF.
Step-by-step explanation: The corresponding segment to EF in similar triangle HFG is HF, you can confirm it by folding the triangle.
8 Ryan is 5½ feet tall. John is,5½ feet tall.
a Who is taller?
b
How much taller?
John is taller then Ryan, John is 0.08 feet taller then Ryan when John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
Given that,
John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
We have to find who is tall and how much is tall.
A fraction that has the numerator higher than or equal to the denominator is said to be improper.
Take the Ryan,
5 1/4 feet
21/4 feet
5.25 feet tall Ryan.
Take the John,
5 1/3 feet
16/3 feet
5.33 feet tall John.
We can see that John is taller then Ryan.
John is 0.08 feet taller then Ryan.
Therefore, John is taller then Ryan, John is 0.08 feet taller then Ryan when John is 5 1/3 feet tall, whereas Ryan is 5 1/4 feet.
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A traffic cone has a volume of 150 cubic inches. The height of the cone is 18 inches. What is the diameter of the traffic cone?
A.
3 inches
B.
5 inches
C.
10 inches
D.
50 inches
WILL GIVE BRAINLIEST!!
How do you solve for x in a logarithmic property?
The logarithmic form is written as logₐ(X)=b. It is a rearrangement of the exponential form, aᵇ=X.
What is Logarithmic Form?
The logarithmic form is written as logₐ(X)=b. It is generally the rearrangement of the exponential form, aᵇ=X. Any exponential equation can be written as a logarithm. The logarithmic form is mostly used to calculate an exponent of an equation. The logₐ(X)=b. is read as “log base a of X equals b“.
The logarithmic form is simply a rearrangement of an equation written in exponential form. The same numbers are used but they are written in a different order. The word log is written which implies that the logarithm function is being used.
Therefore, If the logarithmic form is logₐ(X)=b. then it is a rearranged as the exponential form as aᵇ=X.
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2. using calculations based on a perpetual inventory system, determine the inventory balance altira would report in its august 31, 2021, balance sheet and the cost of goods sold it would report in its august 2021 income statement using the average cost method. (round "average cost per unit" to 2 decimal places.)
As per the given income, the inventory balance on August 31,2021 is $98,002
The term income is referred as the money that a person or entity receives in exchange for their labor or products.
Here we have given that balance sheet and the cost of goods sold it would report in its august 2021 income statement using the average cost method.
And here we also know that on August 2021 Ending Inventory and the Cost of Goods Sold is calculated as,
=> Ending Inventory = 9,000 units at $5.88 per unit
Then the value of ending inventory is written as,
=> 9000 x 5.88 = $52,920
Then the Cost of goods sold is calculated as
=> 9,600 x $5.87 = $56,352
=> 7,000 x $5.95 = $41,650
Therefore, the cost of total goods sold is written as
=> 16,600 units = $98,002
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2+100=? ...it isnt hard u guys can do it
Answer:
102
Step-by-step explanation:
100 plus 2 equals 102
Hopefully this helps you :)
pls mark brainlest ;)