Answer:
16 minutes
Step-by-step explanation:
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of Integral b a f(x) dx. Which one of the following statements is true?
Lower sum < Trapezoidal rule Value < Upper sum
Lower sum < Upper sum < Trapezoidal rule value
Trapezoidal rule < Lower sum < Upper sum
Cannot be determined without the x-values for the partitions
The left sum would be f0+f1+f2+f3
The right sum would be f1+f2+f3+f4
The trapezoidal rule value is:
(f0+f1)/2 + (f1+f2)/2+(f2+f3)/2 +(f3+f4)/2
This would put the trapezoidal rule in the middle , which makes the answer:
Lower sum < Trapezoidal rule Value < Upper sum
Answer:
Step-by-step explanation:
Given function f(x) is positive, increasing and concave up on the closed interval [a, b],
it means f(x1) < f(x2) if x1 < x2
So Lower sum < Upper sum
As Trapezoidal is average of f(x1) and f(x2) = [f(x1) + f(x2)] / 2
it is average of the Lower and Upper sum.
The answer is Lower sum < Trapezoidal rule Value < Upper sum
A researcher wants to prove that there is a difference in the average life spans between men and women in Japan. Let mu1 = average life span of Japanese women and mu2 = average life span of Japanese men. A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years. A random sample of 10 men showed an average lifespan of 77 years, with a sample standard deviation of 6.4 years. Assume that life spans are normally distributed and that the population variances are equal. If alpha = .05 and the null hypothesis is mu1 – mu2 = 0, what is (are) the critical value(s) for the hypothesis test?
Answer:
t < -2.101, and t > 2.101
Step-by-step explanation:
We are running a hypothesis for the difference of 2 sample means, assuming normality, and assuming that population variances are equal. This determines which test we run.
We have:
Sample 1: (women)
n = 10
x = 83
s = 7
Sample 2: (men)
n = 10
x = 77
s = 6.4
The hypothesis for the test are:
H0: µ1 - µ2 = 0
Ha: µ1 - µ2 ≠ 0
The significance level is 5%. The degrees of freedom is 2 less than the sum of the sample size, in this case, 18. Our t-value is: 2.101
Our critical values for the test statistic are: t < -2.101, and t > 2.101
The critical value(s) for the hypothesis test if A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years is t < -2.101, and t > 2.101.
What is average?The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
In Sample 1: (women)
n = 10
x = 83
s = 7
In Sample 2: (men)
n = 10
x = 77
s = 6.4
The hypothesis for the test are:
H₀: µ1 - µ2 = 0
Hₐ: µ1 - µ2 ≠ 0
The significance level is 5%. The degrees of freedom is 2 less than the sum of the sample size, in this case, 18. Our t-value is: 2.101
Our critical values for the test statistic are: t < -2.101, and t > 2.101
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The following table gives the percentage of music downloaded from the United States and other countries by U.S. users: Country U.S. Germany Canada Italy U.K. France Japan Other Percent 45.2 16.4 6.5 6.3 4.2 3.7 2.1 15.6 (a) Verify that the table does give a probability distribution for the experiment. The sum of the percents is %, so this does give a probability distribution. (b) What is the probability that a U.S. user who downloads music, selected at random, obtained it from either the United States or Canada? (Enter your answer to three decimal places.) (c) What is the probability that a U.S. user who downloads music, selected at random, does not obtain it from Italy, the United Kingdom (U.K.), or France? (Enter your answer to three decimal places.)
Answer:
A) 100%; B) 0.517; C) 0.858
Step-by-step explanation:
For part A,
We find the sum of the probabilities:
45.2+16.4+6.5+6.3+4.2+3.7+2.1+15.6 = 100
Since they sum to 100%, this is a probability distribution.
For part B,
We add together the probabilities for the US and Canada:
45.2+6.5 = 51.7% = 51.7/100 = 0.517
For part C,
We first add together the probabilities for Italy, the UK and France:
6.3+4.2+3.7 = 14.2%
Next we subtract this from 100%:
100-14.2 = 85.8% = 85.8/100 = 0.858
Final answer:
The table gives a probability distribution. The probability that a U.S. user obtained music from the United States or Canada is 51.7%. The probability that a U.S. user does not obtain music from Italy, the U.K., or France is 85.8%.
Explanation:
To verify that the table gives a probability distribution, we need to show that the sum of the percentages is equal to 100%. Summing the percentages from the table, we get:
45.2 + 16.4 + 6.5 + 6.3 + 4.2 + 3.7 + 2.1 + 15.6 = 100%
This confirms that the table does give a probability distribution for the experiment.
To find the probability that a U.S. user obtained music from either the United States or Canada, we add the percentages for these two countries:
45.2 + 6.5 = 51.7%
Therefore, the probability is 0.517 or 51.7%.
To find the probability that a U.S. user does not obtain music from Italy, the United Kingdom (U.K.), or France, we subtract the percentages for these three countries from 100%:
100% - (6.3 + 4.2 + 3.7) = 100% - 14.2% = 85.8%
Therefore, the probability is 0.858 or 85.8%.
Mr. Lubec put her 28 students into four equal groups she gave each group 35 sheets of paper how many sheets of paper to each student get
Answer:
5 sheets.
Step-by-step explanation:
There are 28 / 4 = 7 students in one group.
Each group was given 35 sheets of paper so each student got 35/7
= 5 sheets.
Each student will get 5 sheets of paper. This is found by dividing the total number of sheets per group (35) by the number of students in each group (7).
Explanation:To solve the problem, we first need to understand that Mr. Lubec's 28 students are divided into four equal groups. We divide 28 by 4 to determine how many students are in each group, which is 7 students. Mr. Lubec gave each group 35 sheets of paper. To find out how many sheets of paper each student receives, we divide the total number of sheets per group by the number of students in each group.
So, we calculate 35 sheets ÷ 7 students, which equals 5 sheets of paper per student. Therefore, each student will get 5 sheets of paper.
(10CQ) Find the length of c
Answer:
The length of c = 18.7 units ⇒ answer (d)
Step-by-step explanation:
In triangle ABC:
∵ measure of angle B = 17° 55'
∵ measure of angle C = 98° 15'
∵ The sum of measures of the interior angles of a triangle is 180°
∴ The measure of angle A = 180 - (17° 55' + 98° 15') = 63° 50'
∵ The length of a = 17 units
* To find the length of c use the sin Rule
- a/sin(A) = b/sin(B) = c/sin(C)
- a is the side opposite to angle A, b is the side opposite
to angle B and c is the side opposite to angle C
∴ 17/sin(63° 50') = c/sin(98° 15')
* By using cross-multiplication
∴ c = (17 × sin(98° 15')) ÷ sin(63° 50')
∴ c = 18.7 units
∴ The length of c = 18.7 units ⇒ answer (d)
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation.
2x − 7y = 4
3x + y = −17
A) 2(3x − 17) − 7y = 4
B) 2(−3x − 17) − 7y = 4
C) 2x − 7(3x − 17) = 4
D) 2x − 7(−3x − 17) = 4
Answer:
option D
2x − 7(−3x − 17) = 4
Step-by-step explanation:
Given in the question two equations
Equation 12x - 7y = 4
Equation 23x + y = -17
Rearranging equation 2 in terms of y
3x + y = -17
y = -17 - 3x
Put this value of y in Equation 1
2x - 7y = 4
2x - 7(-17 - 3x) = 4
So,
If you use the substitution method to solve the following system, new equation will be
2x - 7(- 3x - 17) = 4Answer:
The correct answer is D.
Step-by-step explanation:
I got it correct on the test. I hope this helps!
1. Solve for the variable in the following proportion.
n : 1/2 as 6 : 1 n=
2. Solve for the variable in the following proportion.
1/4 is to 1 1/4 as 2 is to b b=
3. In a group of students, the ratio of girls to boys is 3 to 2.
If there are 15 girls, how many total students are there?
A) 10
B) 20
C) 25
D) 30
4. On a field trip, there are 12 adults and 14 students.
What is the ratio of the number of adults to the total number of people on the field trip?
A) 6 to 13
B) 12 to 14
C) 26 to 12
D) 6 to 7
5. If 2d = 5c, then all of the following are true except _____.
A) 2/5= c/d
B) 5/2= d/c
C) 2/c= 5/d
D) 2/d= c/5
Please help and hurry. I need the answer as soon as possible.
The solutions to the given problems involve setting up and solving proportions, as well as understanding and applying ratios.
Explanation:1. To solve for the variable n in the proportion n : 1/2 as 6 : 1, we set up the equation n/0.5 = 6/1.
By cross-multiplying, we get n = 3.
2. To find the variable b in the proportion 1/4 is to 1 1/4 as 2 is to b, we write it as 1/4 : 5/4 = 2/b.
Cross-multiplying gives us b = 10.
3. To find out how many total students are there given the ratio of girls to boys is 3 to 2 and there are 15 girls, we use the ratio to find the number of boys 15 girls * (2 boys/3 girls) = 10 boys.
Adding the number of girls to the number of boys (15 + 10) gives us a total of 25 students, which is option (C).
4. For the field trip with 12 adults and 14 students, the ratio of the number of adults to the total number of people is 12/(12+14) = 12/26, which simplifies to 6/13, giving us option (A).
5. If 2d = 5c, the statement that is not true is D) 2/d = c/5, because when dividing both sides by the respective variables, it should be d/2 = c/5.
Final answer:
1. n = 3
2. b = 10
3. Option C: 25
4. Option A: 6 to 13
5. Option D: 2/d = c/5.
Explanation:
To solve for the variable n in the proportion n : 1/2 = 6 : 1,
you cross-multiply to get n * 1 = 6 * (1/2), which simplifies to n = 3.
Therefore, n=3.
To find the value of b in the proportion 1/4 : 1 1/4 = 2 : b,
we cross-multiply again, which gives us (1/4) * b = 2 * (5/4), after simplifying this, we get b = 10/1.
Therefore, b=10.
For the ratio of girls to boys, which is 3 to 2, if there are 15 girls, then for every 3 girls, there are 2 boys.
So, 15 girls represent 5 groups of 3 (because 15/3=5).
If there are 5 groups, then there must be 5 * 2 = 10 boys.
Therefore, adding the girls and boys gives us 15 + 10 = 25 total students, selecting Answer C) 25.
To determine the ratio of the number of adults to the total number of people on the field trip, we have 12 adults and 14 students, therefore the total number of people is 12 + 14 = 26.
The ratio of adults to the total number of people is 12:26, which simplifies to 6:13 after dividing both numbers by 2.
So, Answer A) 6 to 13 is correct.
If 2d = 5c, then dividing both sides by 2c gives us d/c = 5/2 or 2.5.
We can also divide by 2d to get c/d = 2/5.
The incorrect statement would be D) 2/d = c/5, as this doesn't match the original equation when cross-multiplied.
Find the missing side length. Round your answer to the nearest tenth.
A) 4.7
B) 5.5
C) 30.8
D) 43.2
Answer:
Option B. [tex]5.5[/tex]
Step-by-step explanation:
we know that
Applying the law of cosines
Let
c------> the missing side length
[tex]c^{2}=9^{2}+6^{2} -2(9)(6)cos(37)[/tex]
[tex]c^{2}=30.747[/tex]
[tex]c=5.5[/tex]
Answer to question #2
Answer:
see the attachment
Step-by-step explanation:
There are 16 ounces in 1 pound, so 96 ounces is 6 pounds. You solve this problem by making up the difference between the given amount and 6 pounds—basically, you subtract it from 6.
6 - 3 1/2 = 2 1/2 . . . . for example
Joes, who is the youngest member of the wrestling team at Northwood High school, is 5 years less than one-half the age of the coach. If the coach is n years old, which expression describes joe's age
1/2 n - 5 or (n/2) - 5
The correct expression which describes joe's age is,
⇒ 1/2n - 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Joes, who is the youngest member of the wrestling team at Northwood High school, is 5 years less than one-half the age of the coach.
Now, Let the coach is n years old.
Hence, We can formulate;
The correct expression which describes joe's age is,
⇒ 1/2n - 5
Thus, the expression which describes joe's age is,
⇒ 1/2n - 5
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Which of the following is a horizontal stretch of the parent function?
Answer:
C.
Step-by-step explanation:
Answer:
The correct option is 3.
Step-by-step explanation:
The parent function is
[tex]f(x)=|x|[/tex]
The horizontal stretch and compression is defined as
[tex]g(x)=|bx|[/tex]
If 0<b<1, then it is horizontal stretch and if b>1, then it is horizontal compression.
Graph 1 passing thought the point (1,-1).
[tex]-1=|b(1)|[/tex]
This statement is false for any value of b, because the value of modulus can not be negative.
Graph 2 passing thought the point (1,2).
[tex]2=|b(1)|[/tex]
[tex]2=b[/tex]
Since b>1, therefore this graph represent the horizontal compression.
Graph 3 passing thought the point (2,1).
[tex]1=|b(2)|[/tex]
[tex]\frac{1}{2}=b[/tex]
Since 0<b<1, therefore this graph represent the horizontal stretch.
Thus, the correct option is 3.
Suppose that in the town of Springfield, RI, the number of days per year with no measurable precipitation is approximately normally distributed with a mean of 85.1 days and a standard deviation of 7.5 days. Ms. Johnson, who lives on a farm just outside of Springfield, wonders if the mean number of days with no measurable precipitation on her farm is different from in town. Her grandfather maintained meticulous weather records. She obtains a simple random sample of eight years from her grandfather's records, and determines that the mean number of days with no measurable precipitation in those years was 82.3 days. She plans to conduct a one-sample ????z ‑test, assuming that the standard deviation of days with no measurable precipitation is the same at the farm as in town. Choose the appropriate null and alternative hypotheses for such a test.
Answer:
H0: µ = 85.1
Ha: µ ≠ 85.1
Step-by-step explanation:
She wants to see if the number of days is different. It could be higher or lower, so the alternate hypothesis uses the "not equal to" sign. If she wanted to see if it rained more on the farm, her alternate hypothesis would be
Ha: µ > 85.1
If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1
The solution for the null hypothesis is given below,
H0: µ = 85.1
Ha: µ ≠ 85.1
What is the null hypothesis?When there are two possibilities then we calculate the null hypothesis if the hypothesis is true hypothesis is accepted if it is To conduct a hypothesis test for the above situation. We define the null hypothesis and the alternative hypothesis.
She is checking to see if the number of days has changed. The alternative hypothesis utilizes the "not equal to" marker since it might be either higher or lower. Her alternate hypothesis, if she wanted to determine whether it rained more frequently on the farm, is
Ha: µ > 85.1
If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1.
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What is the probability that the roll of a six-sided die will be either even or odd? A) 1 6 B) 1 4 C) 1 2 D) 1
Answer:
D) 1
Step-by-step explanation:
Every whole number (including the ones on a die) are either even or odd, nothing else. So it is guaranteed for the number to be even or odd.
WILL GIVE BRAINLYEST
The Problem:
Ms. Chen is planning to take her camp group on a field trip to Pottery Bayou where each person will create her own piece of art pottery. The regular cost is $32 per person. There is a group special that costs $20 per person with an additional $84 fee for a private room. Ms. Chen is trying to decide if she should use the regular price or the group special.
Write an equation to show the total cost of the regular price with x people (8 points)
Write an equation to show the total cost of the group special with x people (8 points)
1) regular cost for one person is: 32 ×1 = $32
for X people it would be 32X as you should times by the number of people.
= 32x
2)1 person is (20×1) + 84
20 + 84 = $104
for X people it would be 20x + 84
= 20x + 84
Find the length of side a. Round to the nearest tenth.
A) 12
B) 378.4
C) 18.3
D) 19.5
Answer:
D) 19.5
Step-by-step explanation:
The law of cosines gives you the relation ...
a² = b² + c² - 2bc·cos(A)
Substituting the given values, you have ...
a² = 13² + 11² - 2·13·11·cos(108°) ≈ 378.379
a ≈ √378.379 ≈ 19.452 . . . . take the square root
a ≈ 19.5
What is the solution to the system of equations below use elimination 2x+5y=20 6x-5y=12 (X,Y)
Answer:
(4, 2.4)
Step-by-step explanation:
(2x+5y=20)3
-
6x-5y=12
----------------------
then....
6x+15y=60
-
6x-5y=12
--------------------
0 + 20y = 48
y=2.4
plug in 2.4 into one of the equations and you get that x= 4
What is the greatest common factor (GCF) of 80 and 50?
Answer: Choice B
Step-by-step explanation: The correct answer is 10, because 10 is the largest number that can you can divide both of these numbers by evenly.
1 4 of a pizza is split equally between 3 sisters. How much of a whole pizza will each sister get? A) 1 12 B) 1 3 C) 1 6 D) 1 7
Answer:
A. 1 12
Step-by-step explanation:
The friendly sausage factory (fsf) can produce hot dogs at a rate of 5,000 per day. fsf supplies hot dogs to local restaurants at a steady rate of 260 per day. the cost to prepare the equipment for producing hot dogs is $66. annual holding costs are 45 cents per hot dog. the factory operates 294 days a year.
a. find the optimal run size. (do not round intermediate calculations. round your answer to the nearest whole number.) optimal run size
b. find the number of runs per year. (round your answer to the nearest whole number.) number of runs
c. find the length (in days) of a run. (round your answer to the nearest whole number.)
Answer:
a. 21 327 hot dogs/run
b. 70 runs/yr
c. 4 da/run
Step-by-step explanation:
Data:
Production rate (p) = 5000/da
Usage rate (u) = 260/da
Setup cost (S) = $66
Annual carrying cost (H) = $0.45/hot dog
Production days (d) = 294 da
Calculations:
a. Optimal run size
(i) Annual demand (D) = pd = (5000 hot dogs/1 day) × (294 days/1 yr)
= 1 470 000 hot dogs/yr
(ii) Economic run size
[tex]Q_{0}= \sqrt{\frac{2DS }{ h}\times\frac{ p}{p-u }}[/tex]
[tex]= \sqrt{\frac{2\times1470000\times66 }{ 0.45}\times\frac{ 5000}{5000-260 }}[/tex]
[tex]= \sqrt{431200000\times\frac{ 5000}{4740 }}[/tex]
[tex]= \sqrt{454852321}[/tex]
= 21 327 hot dogs/run
b. Number of runs per year
Runs = D/Q₀ = (1 470 000 hot dogs/1yr) × (1 run/21 327 hotdogs)
= 70 runs/yr
c. Length of a run
Length = Q₀/p = (21 327 hot dogs/1 run) × (1 da/5000 hot dogs)
= 4 da/run
To find the optimal run size, use the EOQ formula and calculate the square root. Divide the annual demand by the optimal run size to find the number of runs per year. Finally, calculate the length of a run by dividing the days in a year by the number of runs per year.
Explanation:The optimal run size can be found using the Economic Order Quantity (EOQ) formula. EOQ = sqrt((2DS)/(H)) where D is the annual demand, S is the setup cost per order, and H is the holding cost per unit per year.
Using the given values:
D = 260 per day * 294 days = 76,440
S = $66
H = $0.45
EOQ = sqrt((2 * 76,440 * 66) / (0.45)) ≈ 6868
The optimal run size is approximately 6868 hot dogs.
The number of runs per year can be calculated by dividing the annual demand by the optimal run size:
Number of runs = 76,440 / 6868 ≈ 11.15
Since the factory operates 294 days a year, the number of runs per year is approximately 11.
The length of a run can be calculated by dividing the days in a year by the number of runs per year:
Length of a run = 294 / 11 ≈ 26.73
The length of a run is approximately 27 days.
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Which of the tables would show inverse variation?
Answer:
C
Step-by-step explanation:
An inverse variation is where the product of inputs and outputs is constant. This means x*y is always the same number.
A is not a solution since it has 3*-4 = -12 and -2*4 = -8. It's not the same.
B is not a solution since it has 2*8 = 16 and 3*12 = 36. It's not the same.
C is a solution since 12*4 = 48 and 8*6 = 48 and 4*12 = 48 and 3*16 = 48. It's the same.
D is not a solution since it has 1*6 = 6 and 2*4 = 8. It's not the same.
Identify the area of the figure. PLEASE HELP!!
Answer:
92m²
Step-by-step explanation:
The height of the triangle is the height of the square plus the height above the square, or 4+8=12 m.
The length of the hypotenuse is 15 m. The length of the known leg is 12 m.
Substitute 12 for b, 15 for c, and solve for a.
a=√15²-12²= √225−144 = √81 = 9
The bottom leg of the right triangle is 9 m.
To find the length of the base of the large triangle multiply the length of the bottom leg of the right triangle by 2.
The length of the base of the large triangle is (9)(2)=18 m.
Use a formula for the area of a triangle, A=12bh, to find the area of the triangle.
18 is base and 12 is height
A=(1/2)(18)(12)= 108
to find the area of the square:
A= 4²=16
A=108-16= 92m²
Fine the measure of the angle formed by the radius and the side of a regular dodecagon.
A.15
B.30
C.60
D.75
Answer:
Option D.75°
Step-by-step explanation:
we know that
The sum of the interior angles of a regular dodecagon is equal to
[tex]S=(n-2)*180[/tex]
where
n is the number of sides
In this problem
n=12 sides
substitute
[tex]S=(12-2)*180[/tex]
[tex]S=1,800\°[/tex]
Find the measure of each interior angle
Divide the sum of the interior angles by the number of sides
[tex]1,800\°/12=150\°[/tex]
The measure of the angle formed by the radius and the side of a regular dodecagon is half the measure of the interior angle
therefore
[tex]150\°/2=75\°[/tex]
Which of the following is not an inequality?
A.) p ≥ 5
B.) m > 16
C.) 3y = 15
D.) k < 9
C.) 3y=15 is not an inequality.
An inequality compares the magnitude of two numbers (greater than, less than, etc.). Choice C uses an equals sign.
Hope this helps!!
What is the simplest form of the expression below? 2x2 ? 10x ? 28 6x × 6 x ? 7
Final answer:
To simplify the expression, factorize the numerator and then cancel out any common terms with the denominator, resulting in the expression 1 / 3 + 2 / (3x).
Explanation:
To simplify the given expression 2x2 - 10x - 28 over 6x × (6x - 7), we need to factorize the numerator and see if any terms cancel out with the denominator. The factored form of the numerator is (2x + 4)(x - 7). The denominator can be written as 6x(6x - 7).
When we place the numerator over the denominator, we see that (x - 7) cancels out, simplifying our expression to (2x + 4) / 6x. This can further be simplified to 1 / 3 + 2 / (3x) by dividing both terms in the numerator by 6x
How many 5-letter combinations can be created from the letters in the word "friendly"?
Answer:
1). infer 2). fired 3). filed 4). filer 5). elfin 6). nerdy 7). felid 8). finer 9). liner 10). lined 11). fiery 12). fiend 13). ferly 14). ferny 15). lindy 16). fined 17). lifer 18). field 19). redly 20). riley 21). riled 22). liney 23). rifle 24). drily 25). fried 26). diner 27). flier 28). flied 29). idler 30). deify 31). reify 32). yield 33). refly 34). dynel 35). edify 36). flyer
hope this helps :)
Which of the following is the general solution of the differential equation dy/dx equals the quotient of 8 times x / y ?
A.)y^2 = x^2 + C
B.)x^2 - y^2 = C
C.)x^2 = 4x^2 + C
D.)y^2 = 8x^2 + C
I believe the answer is D
The general solution of the differential equation [tex]\frac{dy}{dx} = \frac{8x}{y}[/tex] using variable separable method is [tex]y^{2}= 8 x^{2} +C[/tex].
What is variable separable method?If it is possible to write a differential equation by the transportation of terms, in the form f(x) dx = g(y) dy where f(x) is the function of x and g(y) is the function of y, then we say that variables are separable.
The solution is given by:
[tex]\int\ {f(x)} \, dx = \int\ {g(y)} \, dy + c[/tex]
where c is the arbitrary constant.
[tex]\frac{dy}{dx} = \frac{8x}{y} \\\\y\, dy = 8x \,dx\\\\\int\ {y} \, dy = \int\ {8x} \, dx\\\\\frac{y^{2} }{2} = \frac{8x^{2} }{2} + C \\\\y^{2}= 8 x^{2} +C[/tex]
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f(x)=8x-7 find f(-6)
Robbie, a structural engineer, will earn $64,000 his first year working for a commercial construction company with annual raises of 8%. What are his total earnings at the end of 5 years?
Answer:
Total earnings at the end of 5 years
= $87071.293
Step-by-step explanation:
First year
$64,000
Second year
$64,000 + 8% of previous year
= $64,000 + 0.08*$64,000
= $69120
Third year
$69120 + 8% of previous year
= $69120 + 0.08*$69120
= $74649.6
Fourth year
$74649.6 + 8% of previous year
= $74649.6 + 0.08*$74649.6
= $80621.568
Fifth year
$80621.568 + 8% of previous year
= $80621.568 + 0.08*$80621.568
= $87071.293
Answer:
375.462.46
Step-by-step explanation:
Took the test and the other answer 87071.29 was wrong
Use the spinner to find each theoretical probability
P (a number no more than 5)
P (an even number)
P (a number less than 3)
A kite is designed on a rectangular grid with squares that measure 1cm by 1 cm. A hexagonal piece within the kite will be reserved for the company logo. Use the grid to identify the perimeter and area of the space reserved for the logo.
Answer:
The answer is the first answer
P = 8 + 4√13 cm
A = 36 cm²
Step-by-step explanation:
* Lets study the figure
- Its a kite with two diagonals
- The shortest one is 12 cm
- The longest one is 26 ⇒ axis of symmetry of the kite
- the shortest diagonal divides the longest into two parts
- The smallest part is 8 cm and the largest one is 18 cm
* To find the area reserved for the logo divide
the hexagonal piece into two congruent trapezium
- The length of the two parallel bases are 4 cm and 8 cm and
its height is 3 cm
- The length of non-parallel bases can calculated by Pythagoras rule
∵ The lengths of the two perpendicular sides are 2 cm and 3 cm
- 3 cm is the height of the trapezium
- 2 cm its the difference between the 2 parallel bases ÷ 2
(8 - 4)/2 = 4/2 = 2 cm
∴ The length of the non-parallel base = √(2² + 3²) = √13
* Now we can find the area of the space reserved for the logo
- The area of the trapezium = (1/2)(b1 + b2) × h
∴ The area = (1/2)(4 + 8) × 3 = (1/2)(12)(3) = 18 cm²
∵ The space reserved for the logo are 2 trapezium
∴ The area reserved for the logo = 2 × 18 = 36 cm²
* The area of the reserved space for the logo = 36 cm²
* The perimeter of the reserved space for the logo is the
perimeter of the hexagon
∵ The lengths of the sides of the hexagon are:
4 cm , 4 cm , √13 cm , √13 cm , √13 cm , √13 cm
∴ The perimeter = 2(4) + 4(√13) = 8 + 4√13 cm
* The perimeter of the reserved space for the logo = 8 + 4√13 cm