Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.
What are linear pair and part of a vertical pair?If two angles is said to create a linear pair, the angles are then regarded as supplementary and it is said that their measures often add up to 180°.
Note that Vertical angles are said to be pair of nonadjacent angles created by the crossing or the intersection of any two straight lines.
Since vertical angles are seen if "X" created by two straight lines then when you look at the image attached, you can see that the angle that can from this is Angle EFA.
Therefore, Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.
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What is the area of the circle?
Answer:
A =50.24 in ^2
Step-by-step explanation:
The diameter is 8 inches
The radius is 1/2 diameter
r = d/2 = 8/2 = 4
The area of the circle is given by
A = pi r^2
A = 3.14 (4)^2
A =50.24 in ^2
Answer:
C. 50.24 in²
Step-by-step explanation:
d= 8 in
r= 8/2= 4 in
Area= πr²= 3.14×4²= 50.24 in²
Determine the magnitude of the resultant force by adding the rectangular components of the three forces.
a) R = 29.7 N
b) R = 54.2 N
c) R = 90.8 N
d) R = 24.0 N
A machine produces 576 units in 18 hours at this rate how many will it produce in 28 hours
Answer: 896
Step-by-step explanation:
Let's use a rule of three here.
[tex]\frac{576}{x}=\frac{18}{28}[/tex]
Solve for x;
[tex]x=\frac{576*28}{18}[/tex]
[tex]x=896[/tex]
PLEASE HELP
Which of the following is an arithmetic sequence?
A: -2, 4, -6, 8, ...
B: -8, -6, -4, -2, ...
C: 2, 4, 8, 16, ...
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69.3 bpm. For a random sample of 140 adult males, the mean pulse rate is 69.8 bpm and the standard deviation is 11.2 bpm. Complete parts (a) and (b) below.
a. Express the original claim in symbolic form.
_,_,bpm
Answer:
Part a
Null hypothesis: [tex] \mu = 69.3[/tex]
Alternative hypothesis: [tex]\mu \neq 69.3[/tex]
Part b
[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]
Step-by-step explanation:
For this case we have the following info given :
[tex] \bar X = 69.8[/tex] the sample mean
[tex] n= 140[/tex] represent the sample size
[tex] s = 11.2[/tex] represent the standard deviation
Part a
And we want to test if the true mean is equal to 69.3 so then the system of hypothesis:
Null hypothesis: [tex] \mu = 69.3[/tex]
Alternative hypothesis: [tex]\mu \neq 69.3[/tex]
Part b: Find the statistic
The statistic is given by:
[tex] z= \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing the info we got:
[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]
Leila runs each lap in 6 minutes. She will run less than 9 laps today. What are the possible numbers of minutes she will run today? Use t for the number of minutes she will run today. Write your answer as an inequality solved for t.
Answer:
I'm not sure if Leila is allowed to run 0 laps.
6 ≤ t ≤ 48
Step-by-step explanation:
To find the number of possible laps, you just find the smallest possible number and the largest.
1 = smallest
8 = largest
But, you have to multiply by 6 to find the time.
6 ≤ t ≤ 48
Square A"B"C"D" is the final image after the rule was applied to square ABCD. On a coordinate plane, a square A double-prime B double-prime C double-prime D double-prime has points (negative 5, negative 3), (negative 3, negative 1), (negative 1, negative 3), (negative 3, negative 5). What are the coordinates of vertex A of square ABCD? (–1, –6) (–1, –2) (–1, 6) (–2, 1)
Answer:
The answer is (-2 , 1 ) or D on Edge
Step-by-step explanation:
The coordinates of vertex A of square ABCD is (-1, -2).
What are coordinates?Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane.
Given:
A(-5, -3), B(-3, -1), C(-1, -3) and D(-3, -5)
By using the rule
T(-4, -1)
So, the coordinate of Vertex A will be
A( -5 + 4, -3 + 1)
=A(-1, -2)
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A research company desires to know the mean consumption of meat per week among people over age 27. A sample of 1179 people over age 27 was drawn and the mean meat consumption was 1.5 pounds. Assume that the population standard deviation is known to be 1.2 pounds. Construct the 99% confidence interval for the mean consumption of meat among people over age 27. Round your answers to one decimal place.
Answer:
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{1.2}{\sqrt{1179}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 1.5 - 0.1 = 1.4 pounds
The upper end of the interval is the sample mean added to M. So it is 1.5 + 0.1 = 1.6 pounds
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
Given that it was less then 80degrees on a given day, what is the probability that it also rained that day?
The probability that it also rained that day would be 0.30
Solve for x.
6(x - 2) = 4
Answer:
8/3
Step-by-step explanation:
6(x-2)=4
x-2=4/6
x= 8/3
Answer:
x = 8/3
Step-by-step explanation:
Use Distributive Property
6(x-2) = 4
6x -12 = 4
add 12 on both sides
6x = 16
Divide by 6
x = 8/3
In decimal form: 2.667
You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.35 with a standard deviation of 0.46. You sample 25 day students, and the sample mean GPA is 2.58 with a standard deviation of 0.47. Test the claim using a 5% level of significance. Assume the sample standard deviations are unequal and that GPAs are normally distributed. Give answer to exactly 4 decimal places.Hypotheses:sub(H,0):sub(μ,1) = sub(μ,2)sub(H,1):sub(μ,1) ≠ sub(μ,2)**I'm not sure how to calculate this in excel***Enter the test statistic - round to 4 decimal places.A=Enter the p-value - round to 4 decimal places.A=
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean GPA of night students and μ2 be the mean GPA of day students.
The random variable is μ1 - μ2 = difference in the mean GPA of night students and the mean GPA of day students.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test.
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
μ1 = 2.35
μ2 = 2.58
s1 = 0.46
s2 = 0.47
n1 = 30
n2 = 25
t = (2.35 - 2.58)/√(0.46²/30 + 0.47²/25)
t = - 1.8246
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [0.46²/30 + 0.47²/25]²/[(1/30 - 1)(0.46²/30)² + (1/25 - 1)(0.47²/25)²] = 0.00025247091/0.00000496862
df = 51
We would determine the probability value from the t test calculator. It becomes
p value = 0.0746
Since alpha, 0.05 < than the p value, 0.0746, then we would fail to reject the null hypothesis.
resuelve las siguientes ecuaciones tales que 0° ≤ x ≤ 360°
sen x=sen (π/2-x)
cos x + 2 sen x= 2
csc x = sec x
2 cos x * tan x -1 = 0
4 cos2 x = 3 - 4 cos x
Answer:
4cos=2X
X=3-4COS
X=-1
PEOPLE! THIS IS URGENT! PLEASE HELP ME!!!! If the product 3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9, what is the sum of a and b?
Answer:
35
Step-by-step explanation:
3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9
a+b=?
------
all numbers get cancelled apart from the first denominator and the last numerator:
1/2*a= 9
a= 18then
b= a-1= 18-1= 17a+b= 18+17= 35
You are rolling two dice. When the two numbers (1-6) come up, you multiply the numbers
together. What is the probability of getting a product that is NOT divisible by 2?*
Answer:
1/4 probability of getting a product that isn't divisible by 2.
Step-by-step explanation:
These are all the possible outcomes
1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6
1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12
1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18
1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20 6 x 4 = 24
1 x 5 = 5 2 x 5 = 10 3 x 5 = 15 4 x 5 = 20 5 x 5 = 25 6 x 5 = 30
1 x 6 = 6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36
All of the outcomes that aren't divisible by 2 are in bold
There are 9 out of 36 possible outcomes that aren't divisible by 2
9/36 = 1/4
Are the two terms on each tile like terms? Sort the tiles into the appropriate categories.
-7y^2and y^2
-4p and p^2
0.5kt and -10kt
6 and 9
5x and 5
3ad and 2bd
Answer:
LIKE TERMS: 6 and 9, 0.5kt and -10kt, and -7y2 and y2. UNLIKE TERMS: 3ad and 2bd, 5x and 5, and the last one is -4p and p2
Step-by-step explanation:
Answer: like terms: 6&9 , 0.5kt&-10kt , -7y^2&y^2
unlike terms 3ad&2bd, 5x&5, -4p&p^2
Step-by-step explanation:
passed
In football seasons, a team gets 3 points for a win, 1 point for a draw and 0 points for a
loss. In a particular season, a team played 34 games and lost 6 games. If the team had a
total of 70 points at the end of the season, what is the difference between games won and lost
Answer:
The difference between the games won and lost = 21 - 6 =15
Step-by-step explanation:
According to the question In a football season a team gets 3 points for a win, 1 point for a draw and 0 points for a loss.
A particular season a team played 34 games and lost 6 games . Finding the difference between game won and game lost simply means we have to know the number of game lost and game won.
The team played a total of 34 games.
Total games played = 34
Out of the 34 games played they lost 6 games. That means the remaining games is either win or draw. Therefore,
34 - 6 = 28 games was won or draw
Let
the number of games won = x
the number of game drew = y
3x + y = 70.............(i)
x + y = 28................(ii)
x = 28 - y
insert the value of x in equation(i)
3(28 - y) + y = 70
84 - 3y + y = 70
84 - 70 = 3y -y
14 = 2y
divide both sides by 2
y = 14/2
y = 7
insert the value of y in equation(ii)
x + y = 28
x = 28 - 7
x = 21
The team won 21 games , drew 7 games and lost 6 games.
The difference between the games won and lost = 21 - 6 =15
Please help me with this problem I'm lost
Answer:
24
Step-by-step explanation:
Multiple (4)(2)= 8
-3(8) =24
A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes. A random sample of twelve service calls is taken. What is the probability that exactly eight of them take more than 93.6 minutes
Answer:
The probability that exactly eight of them take more than 93.6 minutes is 5.6015 [tex]\times 10^{-6}[/tex] .
Step-by-step explanation:
We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.
A random sample of twelve service calls is taken.
So, firstly we will find the probability that service calls take more than 93.6 minutes.
Let X = times for service calls.
So, X ~ Normal([tex]\mu=75,\sigma^{2} =15^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 75 minutes
[tex]\sigma[/tex] = standard deviation = 15 minutes
Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)
P(X > 93.6 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{93.6-75}{15}[/tex] ) = P(Z > 1.24) = 1 - P(Z [tex]\leq[/tex] 1.24)
= 1 - 0.8925 = 0.1075
The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.
Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;
[tex]P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = 12 service calls
r = number of success = exactly 8
p = probability of success which in our question is probability that
it takes more than 93.6 minutes, i.e. p = 0.1075.
Let Y = Number of service calls which takes more than 93.6 minutes
So, Y ~ Binom(n = 12, p = 0.1075)
Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)
P(Y = 8) = [tex]\binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}[/tex]
= [tex]495 \times 0.1075^{8} \times 0.8925^{4}[/tex]
= 5.6015 [tex]\times 10^{-6}[/tex] .
Describe the solutions of the following system in parametric vector form,and provide a geometric comparison with the solution set .
x1 + 3x2- 5x3 = 4
x1+ 4x2 - 8x3 = 7
-3x1- 7x2 +9x3 =6
Answer:
The equations are linearly independent so there is no parametric vector form
Step-by-step explanation:
I attached the solution.
A supermarket is redesigning it’s checkout lanes. Design A has a sample size of 50, sample mean of 4.1 minutes, and sample standard deviation of 2.2 minutes. Design B has a sample size of 50, sample mean of 3.5 minutes, and sample standard deviation of 1.5 minutes. At the 0.05 level of significance, determine if their is evidence that the checkout times of the two systems differ.
Answer:
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
Null hypothesis is accepted at 5 % level of significance
There is no significance difference between Design A and Design B
Step-by-step explanation:
Given sample size of design A
n₁ = 50
sample mean of design A x⁻₁ = 4.1 minutes
Sample standard deviation S₁ = 2.2 minutes
Given sample size of design B
n₂ = 50
sample mean of design A x⁻₂ = 3.5 minutes
Sample standard deviation S₂ = 1.5 minutes
Null Hypothesis : H₀ : There is no significance difference between Design A and Design B
Alternative Hypothesis : H₁:There is significance difference between Design A and Design B
Level of significance ∝ = 0.05
Test statistic
[tex]t = \frac{x^{-} _{1}- x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} }) } }[/tex]
where
[tex]S^{2} = \frac{n_{1} S_{1} ^{2} +n_{2} S^2_{2} }{n_{1} +n_{2} -2}[/tex]
[tex]S^{2} = \frac{50 (2.2)^{2} +50(1.5)^2}{50+50-2}[/tex]
On calculation , we get
S² = 3.6173
Test statistic
[tex]t = \frac{4.1-3.5}{\sqrt{3.617(\frac{1}{50} +\frac{1}{50} }) }[/tex]
On calculation , we get
t = 1.57736
Degrees of freedom
ν = n₁ + n₂ -2 = 50 +50 -2 =98
t₀.₀₂₅ ,₉₈ = 1.9845
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
null hypothesis is accepted
4. Dean Pelton wants to perform calculations to impress the accreditation consultants, but upon asking for information about GPAs at Greendale Community College, Chang only tells Pelton that the GPAs are distributed with a probability density function f(x) = D(2 + e −x ), 2 ≤ x ≤ 4 where D was some unknown "Duncan" constant. How many student records have to be retrieved so that the probability that the average GPA is less than 2.3 is less than 4 percent?
Answer:
the minimum records to be retrieved by using Chebysher - one sided inequality is 17.
Step-by-step explanation:
Let assume that n should represent the number of the students
SO, [tex]\bar x[/tex] can now be the sample mean of number of students in GPA's
To obtain n such that [tex]P( \bar x \leq 2.3 ) \leq .04[/tex]
⇒ [tex]P( \bar x \geq 2.3 ) \geq .96[/tex]
However ;
[tex]E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D[/tex]
[tex]E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D[/tex]
Similarly;
[tex]D\int\limits^4_2(2+ e^{-x}) dx = 1[/tex]
⇒ [tex]D*(2x-e^{-x} ) |^4_2 = 1[/tex]
⇒ [tex]D*4.117 = 1[/tex]
⇒ [tex]D= \dfrac{1}{4.117}[/tex]
[tex]\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103[/tex]
∴ [tex]Var (x) = E(x^2) - E^2(x) \\ \\ = .3348711[/tex]
Now; [tex]P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega \geq .691013) \ \ \ \ \ \ \ \ \ \ (x = E(\bar x ) - \mu)[/tex]
Using Chebysher one sided inequality ; we have:
[tex]P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}[/tex]
So; [tex](\omega = \bar x - \mu)[/tex]
⇒ [tex]E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}[/tex]
∴ [tex]P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}[/tex]
To determine n; such that ;
[tex]\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}[/tex]
⇒ [tex]n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}[/tex]
[tex]n \geq 16.83125[/tex]
Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.
Quick Start Company makes a 12-volt car batteries. After many years of product testing, the company knows the average life of a Quick Start battery is normally distributed, with mean=45 months and a std. deviation = 8 months.
If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?
If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries (to the nearest month)
Answer:
The company will expect to replace 13.03% of batteries.
The company should guarantee the batteries for 35 months.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 45, \sigma = 8[/tex]
If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?
This is the pvalue of Z when X = 36. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 45}{8}[/tex]
[tex]Z = -1.125[/tex]
[tex]Z = -1.125[/tex] has a pvalue of 0.1303.
The company will expect to replace 13.03% of batteries.
If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries
They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 45}{8}[/tex]
[tex]X - 45 = -1.28*8[/tex]
[tex]X = 34.76[/tex]
Rounding to the nearest month
The company should guarantee the batteries for 35 months.
What is the center of a circle represented by the equation (x+9)2+(y−6)2=102? Please Help
Answer:
(-9, 6)
Step-by-step explanation:
edgenuity 2020
hope this helps!
Joana wants to buy a car. Her parents loan her $5,000 for 5 years at 5% simple interest. How much will Joana pay in interest?
Answer:
1250
Step-by-step explanation:
5% of $5000 is 250
250X5= 1250
Please answer this correctly
Answer:
Step-by-step explanation:
George Fox university = 10,000,000 + 10,000,000
= full bag + full bag
( click 2 full bag}
Rockhurst university = 10,000,000 +10,000,000 +10,000,000 + 5,000,000
= full bag + full bag + full bag + half bag
(click 3 full bag and 1 half bag}
Lebanon Valley college = 10,000,000 +10,000,000 +10,000,000 +10,000,000+5,000,000
( click 4 full bag and 1 half bag)
Grand view college = 10,000,000
(click 1 full bag}
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 32 inches, what diameter pizza will reward you with the largest slice
Answer:
A 16 inches diameter will reward you with the largest slice of pizza.
Step-by-step explanation:
Let r be the radius and [tex]\theta[/tex] be the angle of a circle.
According with the graph, the area of the sector is given by
[tex]A=\frac{1}{2}r^2\theta[/tex]
The arc length of a circle with radius r and angle [tex]\theta[/tex] is r [tex]\theta[/tex]
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
[tex]2r+r\theta=32 \:in[/tex]
We need to express the area as a function of one variable, to do this we use the above equation and we solve for [tex]\theta[/tex]
[tex]2r+r\theta=32\\\\r\theta=32-2r\\\\\theta=\frac{32-2r}{r}[/tex]
Next, we substitute this equation into the area equation
[tex]A=\frac{1}{2}r^2(\frac{32-2r}{r})\\\\A=\frac{1}{2}r(32-2r)\\\\A=16r-r^2[/tex]
The domain of the area is
[tex]0<r<12[/tex]
To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.
[tex]\frac{d}{dr} A=\frac{d}{dr}(16r-r^2)\\\\A'(r)=\frac{d}{dr}(16r)-\frac{d}{dr}(r^2)\\\\A'(r)=16-2r16-2r=0\\\\-2r=-16\\\\\frac{-2r}{-2}=\frac{-16}{-2}\\\\r=8[/tex]
To check if r=8 is a maximum we use the Second Derivative test
if [tex]f'(c)=0[/tex] and [tex]f''(c)<0[/tex] , then f(x) has a local maximum at x = c.
The second derivative is
[tex]\frac{d}{dr} A'(r)=\frac{d}{dr} (16-2r)\\\\A''(r)=-2[/tex]
Because [tex]A''(r)=-2 <0[/tex] the largest slice is when r = 8 in.
The diameter of the pizza is given by
[tex]D=2r=2\cdot 8=16 \:in[/tex]
A 16 inches diameter will reward you with the largest slice of pizza.
1. The mean of the data set{9,5,y,2,x} is twice the data set {8,x,4,1,3}. What is (y-x) squared.
2. How many alcohol must be added to480 grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?
Answer:
1. (y - x)² = 256
2. 128g needed to be added
Step-by-step explanation:
1.
9 + 5 + 2 + y + x = 2(8 + 4 + 1 + 3 + x)
16 + y + x = 32 + 2x
y - x = 16
∴ (y - x)² = 256
2.
x = mass of alcohol to add
480 × 0.24 = 115.2 ← current mass of alcohol
0.4(480 + x) = 115.2 + x (×5)
2(480 + x) = 576 + 5x
960 + 2x = 576 + 5x
3x = 384
x = 128g
Runners are always talking about minutes per mile. This is the inverse of distance divided by time. Like, on my morning jogs I shoot for 11 minutes per mile. Next month, I'm doing a 10k (that's 10 kilometer) run with my daughter. I'm going to average 11 minutes per mile. Calculate, in minutes how long it will take me to complete the run averaging 11 minutes per mile.
Answer:
around 68 minutes 31 seconds.
Step-by-step explanation:
10km = miles = 6.21x11 = 68.31
Bus A and Bus B leave the bus depot at 6 am.
Bus A takes 20 minutes to do its route and bus B takes 35 minutes to complete its route.
At what time are they both back at the bus depot together?
Give your answer as a 12-hour clock time
Answer:
8.20 am
Step-by-step explanation:
First, we have that Bus A will be back after 20 minutes, then after 40, then 60, 80, 100, 120, 140, 160 minutes, etc.
Then, we have that Bus B will be back after 35 minutes, then 70, then 105, then 140, 175....
From the list above we see that the first time they are both back at the station is after 140 minutes. (it's the MCM).
If we express this in terms of minutes, since one hour has 60 minutes, 2 hours have 120 minutes and thus, 140 minutes is 2 hours and 20 minutes.
Therefore, they will be both back at the station 2 hours and 20 minutes after they first departed at 6 am, so they will be back at the depot at 8.20 am
A and b are similar shapes. B is an enlargement of a with scale factor 1.5 Work out the value of x, h and w
Answer:
x = 54°
h = 7.5cm
w= 6cm
Step-by-step explanation:
Find attached the diagrams as found at Maths made easy.
Similar shapes have same shapes but different sizes.
When two shapes are similar, the ratios of the lengths of their corresponding sides are equal.
B is an enlargement of A with scale factor 1.5. That is, each of the sides of B = 1.5 of each side of A
To determine the value of x, h and w, let's look at the relationship of A and B.
h = 1.5 × 5cm
h = 7.5cm
9cm = 1.5 × w
w = 9cm/1.5
w= 6cm
Since the angles do not change when a shape is enlarged, the value of x = 54°
x = 54°
