Answer:
Yes
Since the time taken t= 7.58 hours required to complete both buildings is less than the 8-hours shift then she can finish the two buildings.
Step-by-step explanation:
Given;
Building A = 3,000 square feet
Building B = 2,460 square feet
Total area of building A and B = 3,000+2460
= 5460 square feet
Rate = 5 seconds per square foot
Time taken to complete both buildings is;
Time t = Total area × rate per area.
t = 5460 × 5 seconds
t = 27300 seconds
t = 27300/60 minutes = 455 minutes
t = 455/60 hours
t = 7.583333333333 hours
t = 7.58 hours
Since the time taken t required to complete both buildings is less than the 8-hours shift then she can finish the two buildings.
What is the value of x in the equation 0.7 x - 1.4 = -3.5
Answer:
x=12.5
Step-by-step explanation:
0.7x times (-1.4)=-3.5
-0.28x=-3.5 (divide both sides)
Ans:12.5
What is 3 1/2 times 4?
Answer:
14
Step-by-step explanation:
3 1/2 × 4
Convert 3 1/2 to an improper fraction.
7/2 × 4
7/2 × 4/1
Multiply.
(7× 4) / (2 × 1)
28 / 2
= 14
Answer: 14
Step-by-step explanation: To multiply a mixed number times a whole number, first write each of them as an improper fraction.
So we can rewrite 3 and 1/2 as the improper fraction 7/2
and we can write 4 as the improper fraction 4/1.
If you've forgotten how to write a mixed number as an improper fraction, feel free to ask me below and I will review this with you.
So now we have 7/2 × 4/1.
When we're multiplying fractions, we want to
cross-cancel first whenever possible.
So here, notice that we can cross-cancel 2 and 4 to 1 and 2.
So we have 7/1 × 2/1.
Now we just multiply across the numerators and multiply across the denominators and we have our answer, 14/1 or just 14.
which figure has the same order of rotational symmetry as a rectangle
Answer:
rhombus
Step-by-step explanation:
on edge
The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 51 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables a. More than 61 pounds
Answer:
0.007
Step-by-step explanation:
We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage
Step 1
We would have to find the sample standard deviation.
We use the formula = σ/√n
σ = 12.2 pounds
n = number of house holds = 51
= 12.2/√51
Sample Standard deviation = 1.7083417025.
Step 2
We find the z score for when the sample mean is more than 61
z-score formula is z = (x-μ)/σ
where:
x = raw score = 61 pounds
μ = the population mean = 56.8 pounds
σ = the sample standard deviation = 1.7083417025
z = (x-μ)/σ
z = (61 - 56.8)/ 1.7083417025
z = 2.45852
Finding the Probability using the z score table
P(z = 2.45852) = 0.99302
P(x>61) = 1 - P(z = 2.45852) = 0.0069755
≈ 0.007
Therefore,the probability that the sample mean will be more than 61 pounds is 0.007
Find the length of KU
Answer:
KU = 8
Step-by-step explanation:
From the diagram
KU + UN = KN , that is
KU + 40 = 48 ( subtract 40 from both sides )
KU = 8
Answer:
KU = 8
Step-by-step explanation:
UN = 40
KN = 48
KU + UN = 48
KU + 40 = 48 {Subtract 40 from both sides}
KU = 48 -40
KU = 8
Please help don't understand this. The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g?
Explanation:
The graph shows that f(x) has the y intercept at -5. This is where the red line crosses the vertical y axis. More specifically, the y intercept is located at the point (0,-5)
We're told that g(x) has a y intercept at -1. So we must move f(x) 4 units up to go from y = -5 to y = -1. This is because -5+4 = -1.
Do this for every point on f(x) and you'll end up with g(x) = f(x)+4. Recall that y = f(x). So saying f(x)+4 is the same as y+4 to indicate "shift up 4 units".
f(x) and g(x) have the same slope, but different y intercepts. So they are parallel lines that never cross.
An automobile manufacturer has given its car a 46.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 46.5. Assume the population standard deviation is known to be 1.1. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
[tex]z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23[/tex]
The p value would be given by:
[tex]p_v =2*P(z<-2.23)=0.0257[/tex]
For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG
Step-by-step explanation:
Information given
[tex]\bar X=46.5[/tex] represent the mean
[tex]\sigma=1.1[/tex] represent the population standard deviation
[tex]n=150[/tex] sample size
[tex]\mu_o =46.7[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean for this case is 46.7, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 46.7[/tex]
Alternative hypothesis:[tex]\mu \neq 46.7[/tex]
Since we know the population deviation the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23[/tex]
The p value would be given by:
[tex]p_v =2*P(z<-2.23)=0.0257[/tex]
For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG
Please help! V^2 = 25/81
Answer:
C and D
Step-by-step explanation:
khan acedemy
An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the given equation v²=25/81 can be found as shown below.
v²=25/81
Taking the square root of both sides of the equation,
√(v²) = √(25/81)
v = √(25/81)
v = √(5² / 9²)
v = ± 5/9
Hence, the solutions of the given equation are A, B, and C.
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Irvin buys a car for $21 comma 804. It depreciates 25% each year that he owns it. What is the depreciated value of the car after 1 yr? after 2 yr? The depreciated value of the car after 1 yr is $? The depreciated value of the car after 2 yr is $?
Answer:
The depreciated value of the car after 1 yr is $16,353
The depreciated value of the car after 2 yr is $12,264.75
Step-by-step explanation:
Given
purchase amount P= $21,804
rate of depreciation R= 25%
applying the formula for the car deprecation we have
[tex]A= P*(1-\frac{R}{100} )^n[/tex]
Where,
A is the value of the car after n years,
P is the purchase amount,
R is the percentage rate of depreciation per annum,
n is the number of years after the purchase.
1. The depreciated value of the car after 1 yr is
n=1
[tex]A= 21,804*(1-\frac{25}{100} )^1\\\\A= 21,804*(1-0.25 )^1\\\\A= 21,804*0.75\\\\A= 16353[/tex]
The depreciated value of the car after 1 yr is $16,353
2. The depreciated value of the car after 2 yr is
n=2
[tex]A= 21,804*(1-\frac{25}{100} )^2\\\\A= 21,804*(1-0.25 )^2\\\\A= 21,804*0.75^2\\\\A= 21,804*0.5625\\\\A= 12264.75[/tex]
The depreciated value of the car after 2 yr is $12,264.75
The amount of time it takes a bat to eat a frog was recorded for each bat in a random sample of 12 bats. The resulting sample mean and standard deviation were 21.9 minutes and 7.7 minutes, respectively. Assuming it is reasonable to believe that the population distribution of bat mealtimes of frogs is approximately normal, a. Construct a 95% confidence interval for the mean time for a bat to eat a frog. b. Construct a 95% confidence interval for the variance of the time for a bat to eat a frog.
Answer: a. CI for the mean: 17.327 < μ < 26.473
b. CI for variance: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093
Step-by-step explanation:
a. To construct a 95% confidence interval for the mean:
The given data are:
mean = 21.9
s = 7.7
n = 12
df = 12 - 1 = 11
1 - α = 0.05
[tex]\frac{\alpha}{2}[/tex] = 0.025
t-score = [tex]t_{0.025,11}[/tex] = 2.2001
Note: since the sample population is less than 30, it is used a t-score.
The formula for interval:
mean ± [tex]t.\frac{s}{\sqrt{n} }[/tex]
Substituing values:
21.9 ± 2.200.[tex]\frac{7.7}{\sqrt{12} }[/tex]
21.9 ± 4.573
The interval is: 17.327 < μ < 26.473
b. A 95% confidence interval for the variance:
The given values are:
[tex]s^{2}[/tex] = [tex]7.7^{2}[/tex]
[tex]s^{2}[/tex] = 59.29
α = 0.05
[tex]\frac{\alpha}{2}[/tex] = 0.025
[tex]1-\frac{\alpha}{2}[/tex] = 0.975
[tex]\chi^{2}_{0.025,11}[/tex] = 21.92
[tex]\chi^{2}_{0.975,11}[/tex] = 3.816
Note: To find the values for [tex]\chi^{2}_{\alpha/2,n-1}[/tex] and [tex]\chi^{2}_{1-\alpha/2,n-1}[/tex], look for them at the chi-square table
The formula to calculate interval:
([tex]\frac{(n-1).s^{2}}{\chi^{2}_{\alpha/2,n-1}} , \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2,n-1}}[/tex])
are the lower and upper limits, respectively.
Substituing values:
([tex]\frac{11.59.29}{21.92} , \frac{11.59.29}{3.816}[/tex])
(29.7532, 170.9093)
The interval for variance is: 29.7532 ≤ [tex]\sigma^{2}[/tex] ≤ 170.9093
The length of a rectangular garden is 3 yards greater
than the width of the garden. If the garden measures
15 yards diagonally, what is its length?
Answer:
12
Step-by-step explanation:
Let's call the width x and the length x + 3. Using the Pythagorean Theorem we can write:
(x + 3)² + x² = 15²
x² + 6x + 9 + x² = 225
2x² + 6x - 216 = 0
2(x² + 3x - 108) = 0
2(x + 12)(x - 9) = 0
x + 12 = 0 or x - 9 = 0
x = -12 or x = 9
x cannot be -12 because length/width can't be negative so x = 9 which means that the length is 9 + 3 = 12.
Clara writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram:
Answer:
CPCTC
Step-by-step explanation:
Statements 3 and 4 show the top and bottom triangles are congruent, and the left and right triangles are congruent. Statement 5 is making use of these facts to claim that the alternate interior angles are congruent. This claim is valid because ...
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
Decide whether the sets are equivalent {d: d is a month of the year} and {g : g is a state in the United States}
Answer:
Non equivalentStep-by-step explanation:
The equivalent between sets is determined by the number of elements. If two sets have the same number of elements, then they are equivalent sets.
In this case, a year has 12 months, and the US has 50 states. So, one month is not equal to 1 state because they have different natures and they represent a different proportion. A month represents 1/12 of a year and a state represents 1/50 of the total number of states.
Find the area of a circle with a diameter of 8yards. Use 3.14. The area of the circle is approximate
Answer:
50.24 yd²
Step-by-step explanation:
pi r² = (3.14)(4)² = 50.24
Drag the tiles to the boxes to form correct pairs. In the diagram, transversal t cuts across the parallel lines a and b. Match the pairs of angles with the relationship that shows they are congruent. alternate exterior angles ∠2, ∠3 and ∠5, ∠8 alternate interior angles ∠1, ∠8 and ∠2, ∠7 corresponding angles ∠3, ∠6 and ∠4, ∠5 vertical angles ∠1, ∠5 and ∠2, ∠6 arrowBoth arrowBoth arrowBoth arrowBoth
Answer:
here
alternate exterior angles--∠1, ∠8 and ∠2, ∠7
alternate interior angles--∠3, ∠6 and ∠4, ∠5
corresponding angles--∠1, ∠5 and ∠2, ∠6
vertical angles--∠2, ∠3 and ∠5, ∠8
Step-by-step explanation:
Answer:
here
alternate exterior angles--∠1, ∠8 and ∠2, ∠7
alternate interior angles--∠3, ∠6 and ∠4, ∠5
corresponding angles--∠1, ∠5 and ∠2, ∠6
vertical angles--∠2, ∠3 and ∠5, ∠8
Step-by-step explanation:
What is the equation of a circle with center (−8, 3) and radius 8?
Answer:
(x + 8)² + (y - 3)² = 64
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (- 8, 3) and r = 8 , thus
(x - (- 8))² + (y - 3)² = 8² , that is
(x + 8)² + (y - 3)² = 64
Answer:
See below.
Step-by-step explanation:
The equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the center and r is the radius.
Plug in what we know. (-8,3) for (h,k) respectively and 8 for the radius:
[tex](x-(-8))^2+(y-(3))^2=(8)^2[/tex]
[tex](x+8)^2+(y-3)^2=64[/tex]
The Beer Institute reported that monthly consumption of beer in is 1.7 gallons per person. A random sample of 36 adults was selected. Using a population standard deviation of 0.5 gallons per month per person, what is the probability that the sample mean was between 1.6 and 1.8 gallons per month per person?
Answer:
.7698
Step-by-step explanation:
In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. The line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded below the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded below the line. The graph represents which system of inequalities? y ≤ −3x − 1 y ≤ −x − 4 y > −3x + 1 y ≤ −x − 4 y < 3x − 1 y ≤ −x + 4 y ≤ 3x − 1 y ≥ −x + 4
Answer:
y ≤ 3x − 1, y ≤ −x + 4
Step-by-step explanation:
The line f(x) is solid and goes through the points (0, 4) and (4, 0) and is shaded below the line.
The line that satisfies the point (0,4) and (4,0) is y=-x+4
Since it is shaded below the line, we have the inequality sign: [tex]\leq[/tex]
Therefore, one of the lines is: [tex]y\leq -x+4[/tex]
The line g(x) is solid and goes through the points (0, -1) and (2, 5) and is shaded below the line.
Slope, [tex]m=\frac{5-(-1)}{2-0}=3[/tex]
When x=0, y=-1
y=mx+b
y=3x+b
-1=3(0)+b
b=-1
Therefore, the equation of the line is: [tex]y=3x-1[/tex]
Since it is shaded below the line, we have the inequality sign: [tex]\leq[/tex]
Therefore, the other line is: [tex]y\leq 3x-1[/tex]
An inequality is a comparison between two expressions not based on equality
The graph represents the system of the inequalities; y ≤ 3·x - 1, y ≤ -x + 4
Reason:
The given parameters are;
Points on the line f(x) = (0, 4), (4, 0)
[tex]Slope \ of \ the \ line, \ m =\dfrac{4-0}{0-4} = -1[/tex]
Therefore;
The equation of the line is y - 0 = -1·(x - 4), which gives;
y = -x + 4
The inequality representing the line is y ≤ -x + 4
Points on the line g(x) = (0, -1), (2, 5)
[tex]Slope \ of \ the \ line, \ m =\dfrac{-1-5}{0-2} = \dfrac{-6}{-3} =3[/tex]
Equation of the line is y - (-1) = 3·(x - 0)
∴ y = 3·x - 1
The inequality is y ≤ 3·x - 1,
The graph which represent the system of inequalities are;
y ≤ 3·x - 1, y ≤ -x + 4
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Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.) P(x) = −0.004x2 + 6x − 5,000 Increasing: Decreasing:
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Step-by-step explanation:
Critical points:
The critical points of a function f(x) are the values of x for which:
[tex]f'(x) = 0[/tex]
For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.
The critical points help us find these intervals.
In this question:
[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]
So
[tex]P'(x) = -0.008x + 6[/tex]
Critical point:
[tex]P'(x) = 0[/tex]
[tex]-0.008x + 6 = 0[/tex]
[tex]0.008x = 6[/tex]
[tex]x = \frac{6}{0.008}[/tex]
[tex]x = 750[/tex]
We have two intervals:
(0, 750) and [tex](750, \infty)[/tex]
(0, 750)
Will find P'(x) when x = 1
[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]
Positive, so increasing.
Interval [tex](750, \infty)[/tex]
Will find P'(x) when x = 800
[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]
Negative, then decreasing.
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
write the equation of a circle with the center (6,4) that passes through the coordinate (2,1) in your final answer include all of your calculations
Step-by-step explanation:
define define equation we need the value of the radius and
By what percent will the fraction increase if its numerator is increased by 60% and denominator is decreased by 20% ?
Answer:
100%
Step-by-step explanation:
Start with x.
x = x/1
Increase the numerator by 60% to 1.6x.
Decrease the numerator by 20% to 0.8.
The new fraction is
1.6x/0.8
Do the division.
1.6x/0.8 = 2x
The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.
The increase is 100%.
Answer:
33%
Step-by-step explanation:
let fraction be x/y
numerator increased by 60%
=x+60%ofx
=8x
denominator increased by 20%
=y+20%of y
so the increased fraction is 4x/3y
let the fraction is increased by a%
then
x/y +a%of (x/y)=4x/3y
or, a%of(x/y)=x/3y
[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]
therefore a=33
anda%=33%
A fair die is rolled repeatedly. Calculate to at least two decimal places:__________
a) the chance that the first 6 appears before the tenth roll
b) the chance that the third 6 appears on the tenth roll
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
d) the expected number of rolls until six 6's appear
e) the expected number of rolls until all six faces appear
Answer:
a. 0.34885
b. 0.04651
c. 0.02404
d. 36
e. 14.7, say 15 trials
Step-by-step explanation:
Q17070205
Note:
1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.
2. use R to find the probability values from the respective distributions.
a) the chance that the first 6 appears before the tenth roll
This means that a six appears exactly once between the first and the nineth roll.
Using binomial distribution, p=1/6, n=9, x=1
dbinom(1,9,1/6) = 0.34885
b) the chance that the third 6 appears on the tenth roll
This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.
Again, we have a binomial distribution of p=1/6, n=9, x=2
p1 = dbinom(2,9,1/6) = 0.27908
The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.
Thus the probability of both happening, by the multiplication rule, assuming independence
P(third on the tenth roll) = p1*p2 = 0.04651
c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.
Again, using binomial distribution, probability of 3-6's in the first 10 rolls,
p1 = dbinom(3,10,1/6) = 0.15504
Probability of 3-6's in the NEXT 10 rolls
p1 = dbinom(3,10,1/6) = 0.15504
Probability of both happening (multiplication rule, assuming both events are independent)
= p1 * p1 = 0.02404
d) the expected number of rolls until six 6's appear
Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6
= n(1-p)/p
Total number of rolls by adding n
= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36
e) the expected number of rolls until all six faces appear
P1 = 6/6 because the firs trial (roll) can be any face with probability 1
P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials
P3 = 6/4 ...
P4 = 6/3
P5 = 6/2
P6 = 6/1
So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials
can someone help me with 8÷2 2/9 −2 11/15
Answer:
7/3 or 13/15
Step-by-step explanation:
So you told me that it will be
8/(20/9) -2 11/15 I put parenthesis to make it easier to understand for me
so you must know that a/(b/c)=ac/b si
72/20 -2 11/15 so we work with -2 11/15 which is equal to -30/15 + 11/15 and that will be -19/15 so we have
72/20 - 19/15 we simplify
18/5 - 19/15 so we multiply and divide by 3 in 18/5
54/15 - 19/15 and we add up
35/15 which is equal to
7/3
If this is wrong so we work with -2 11/15 which is equal to -30/15 + 11/15 well it should be so we work with -2 11/15 which is equal to -30/15 - 11/15 and that equals -41/15 and we get
54/15-41/15
13/15
Which set of numbers could represent the lengths of the sides of a triangle? A. {3,4,8} B. {8,11,19} C. {11,5,5} D. {19,16,20}
Answer:
19, 16, 20
Step-by-step explanation:
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
Aka the highest number - the next highest number = lowest possible number.
3+4 is not greater than 8.
8 + 11 is not greater than 19.
5 + 5 is not greater than 11.
16+19 is greater than 20.
19+20 is greater than 16.
16+ 20 is greater than 19.
the set of numbers that could represent the lengths of the sides of a triangle is D. {19, 16, 20}.
To determine if a set of numbers can represent the lengths of the sides of a triangle, we need to apply the triangle inequality theorem. According to the theorem, for a triangle with side lengths a, b, and c:
a + b > c
a + c > b
b + c > a
Let's evaluate each set of numbers:
A. {3, 4, 8}
3 + 4 > 8 (7 > 8) - Not true
4 + 8 > 3 (12 > 3) - True
3 + 8 > 4 (11 > 4) - True
Since the first inequality is not true, set A cannot represent the lengths of the sides of a triangle.
B. {8, 11, 19}
8 + 11 > 19 (19 > 19) - Not true
8 + 19 > 11 (27 > 11) - True
11 + 19 > 8 (30 > 8) - True
Since the first inequality is not true, set B cannot represent the lengths of the sides of a triangle.
C. {11, 5, 5}
11 + 5 > 5 (16 > 5) - True
11 + 5 > 5 (16 > 5) - True
5 + 5 > 11 (10 > 11) - Not true
Since the third inequality is not true, set C cannot represent the lengths of the sides of a triangle.
D. {19, 16, 20}
19 + 16 > 20 (35 > 20) - True
19 + 20 > 16 (39 > 16) - True
16 + 20 > 19 (36 > 19) - True
All three inequalities are true for set D, so it can represent the lengths of the sides of a triangle.
Therefore, the set of numbers that could represent the lengths of the sides of a triangle is D. {19, 16, 20}.
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Which expression is equivalent to -3(2m - 1) - n? 6m - n - 3 6m - n + 3 -6m - n - 3 -6m - n +3
Answer:
-6m+3
Step-by-step explanation:
Answer:
An equivalent value is -6m -n +3
Step-by-step explanation:
Given
-3(2m-1)-n expand
=-6m+3-n
(also equals -6m -n +3 by commutativity)
I'm having a hard time with this. A new housing development extends 4 miles in one direction, makes a right turn, and then con- tinues for 3 miles. A new road runs between the beginning and ending points of the development. What is the perimeter of the triangle formed by the homes and the road? What is the area of the housing development?
Answer:
perimeter = 12 miles
area = 6 square miles
Step-by-step explanation:
Since it makes a right triangle, use the Pythagorean Formula.
3^2+4^2=c^2
9+16=c^2
25=c^2
5=c, so the hypotenuse of the right triangle is 5.
Perimeter = 3+4+5 = 12 miles
area = 1/2bh (1/2 base times height)
=1/2x3x4
=6
Area = 6 square miles
Find the linear approximation of the function f(x) = 4 − x at a = 0. L(x) = $$ Incorrect: Your answer is incorrect. Use L(x) to approximate the numbers 3.9 and 3.99 . (Rou
Answer:
[tex]L(x)=4-x[/tex]
[tex]L(3.9)=0.1\\L(3.99)=0.01[/tex]
Step-by-step explanation:
The linear approximating polynomial is: [tex]L(x) = f(a) + f'(a)(x - a)[/tex]
Given: [tex]f(x) = 4 - x[/tex] at a=0
f(0)=4-0=4
f'(x)=-1, Therefore: f'(a)=-1
Therefore, the linear approximation of f(x) at a=0 is:
[tex]L(x) = f(0) + f'(a)(x - 0)\\L(x)=4-x[/tex]
We then use our result to approximate 3.9 and 3.99.
[tex]L(3.9)=4-3.9=0.1\\L(3.99)=4-3.99=0.01[/tex]
Perform a glide reflection over the x-axis and 6 units to the right. Write the new coordinates. Then complete the translation. Thanks.
Answer:
After reflection, the coordinates would be A(-6,-8) B(-2,-6) C(-4,-2) and D(-8,-4). After translation, the coordinates would be A(0,-8) B(4,-6) C(2,-2) and D(-2,-4).
Step-by-step explanation:
If the figure ABCD consists of 4 points and we want to reflect this across the x-axis, then the y coordinate values of A, B, C and D will be negated. So,
(-6,8) becomes (-6,-8)
(-2,6) becomes (-2,-6)
(-4,2) becomes (-4,-2)
and (-8,4) becomes (-8,-4).
Now that we know what the reflection is, we translate it 6 units to the right. Therefore, the x value of each coordinate is increased by 6.
(-6,-8) becomes (0,-8)
(-2,-6) becomes (4,-6)
(-4,-2) becomes (2,-2)
and (-8,-4) becomes (-2,-4)
Hope this helped!
Convert into the following unit into 30 cm into miter
Answer:
it we'll be 0.3
Step-by-step explanation:
trust me man I like to explain but it's long
Answer:
0.3 meter or 3/10 meter
Step-by-step explanation:
As there are 100cm in 1 meter and you want to find 30cm in terms of meters.
It will be as
100cm = 1 meter (rule/lax)
100/100 cm = 1/100 meter (divide both sides of equation with 100)
1 cm = 1/100 meter
1 *30 cm = (1/100)*30 meter (multiply both sides with 30)
30 cm = 30/100 meter
30/100 more shortly can be written as 3/10 meter or in decimals 0.3 meter.
Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t months, the average score S(t), as a percentage, was found to be given by the following equation, whereStudents in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t months, the average score S(t), as a percentage, was found to be given by the following equation, where t>=0.
Required:
a. What was the average score when they initially took the test, t=0?
b. What was the average score after 4 months?
c. What was the average score after 24 months?
d. What percentage of their original answers did the students retain after 2 years?
e. The maximum of the function is_____%.
Answer:
a. 73; b. 48.9; c. 2; d. 33.8; e. 73
Step-by-step explanation:
Assume the function was
S(t)= 73 - 15 ln(t + 1), t ≥ 0
a. Average score at t = 0
S(0) = 73 - 15 ln(0 + 1) = 73 - 15 ln(1) = 73 - 15(0) =73 - 0 = 73
b. Average score at t = 4
S(4) = 73 - 15 ln(4 + 1) = 73 - 15 ln(5) = 73 - 15(1.61) =73 - 24.14 = 48.9
c. Average score at t =24
S(24) = 73 - 15 ln(24 + 1) = 73 - 15 ln(25) = 73 - 15(3.22) =73 - 48.28 = 24.7
d. Percent of answers retained
At t = 0. the students retained 73 % of the answers.
At t = 24, they retained 24.7 % of the answers.
[tex]\text{Percent retention} = \dfrac{\text{24.7}}{\text{73}} \times 100 \, \% = \text{33.8 \%}\\\\\text{The students retained $\large \boxed{\mathbf{33.8 \, \%}}$ of their original knowledge after two years.}[/tex]
e. Maximum of the function
The maximum of the function is at t= 0.
Max = 73 %
The graph below shows your knowledge decay curve. Knowledge decays rapidly at first but slows as time goes on.