Answer:
The solution:
X = 16 and Y = -6
Step-by-step explanation:
The equations to be solved are:
x+y = 10 ------- equation 1
x+2y = 4 ----------- equation 2
we can multiply equation 1 by -1 to make the value of x and y negative.
This will give us
-x- y = - 10 ------- equation 3
x+2y = 4 ----------- equation 2
We will now add equations 3 and 2 together so that x will cancel itself out.
this will give us
y = -10 +4 = -6
hence, we have the value of y as -6.
To get the value of x, we can put this value of y into any of the equations above. (I will use equation 1)
x - 6 = 10
from this, we have that x = 4
Therefore, we have our answer as
X = 16 and Y = -6
Help with one integral problem?
Answer: [tex]2\sqrt{1+tant}+C[/tex]
Step-by-step explanation:
To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.
[tex]\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } } \[/tex]
Let's first use our identities to rewrite the function. Since [tex]\frac{1}{cosx} =secx[/tex], we can use this identity.
[tex]\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,[/tex]
[tex]u=\sqrt{1+tant}[/tex]
[tex]du=\frac{sec^2t}{2\sqrt{1+tant} } dt[/tex]
Now that we have u and du, we can plug them back in.
[tex]\int\limits {2} \, du[/tex]
[tex]\int\limits{2} \, du=2u[/tex]
Since we know u, we can plug that in.
[tex]2\sqrt{1+tant}[/tex]
This may seem like the correct answer, but we forgot to add the constant.
[tex]2\sqrt{1+tant}+C[/tex]
Write the equation of a line that goes through point (0, -8) and has a slope of 0
Answer:
Step-by-step explanation:
y + 8 = 0(x - 0)
y + 8 = 0
y = -8
Ava's bacteria population is modeled by an equation. Chase models his bacteria
population with a graph. Ava says that on day 14, she will have more bacteria than Chase
Is she right? Why or why not?
Answer:
P(Chase) > P(Ava)
700 > 587
Therefore, Ava's claim is wrong!
On day 14, Chase's bacteria population will be greater than Ava's bacteria population.
Step-by-step explanation:
Please refer to the attached image.
Ava's bacteria population is modeled by the following equation.
[tex]$ b(t) = 200(1+0.08)^t $[/tex]
Where t is time in days and b(t) is the population of the bacteria after t days.
The graph represents the population of Chase's bacteria.
Ava claims that on day 14, she will have more bacteria than Chase.
Let us compare the population of both bacteria.
Chase bacteria population when t = 14 days:
From the graph, the population is approximately 700 at t = 14 days
P(Chase) ≈ 700
Ava bacteria population when t = 14 days:
at t = 14 days
[tex]b(t) = 200(1+0.08)^t \\\\ b(14) = 200(1.08)^{14} \\\\ b(14) = 200 (2.93719)\\\\ b(14) = 587.44[/tex]
So, the population is approximately 587 at t = 14 days
P(Ava) ≈ 587
P(Chase) > P(Ava)
700 > 587
Therefore, Ava's claim is wrong!
On day 14, Chase's bacteria population will be greater than Ava's bacteria population.
Answer:
D
Step-by-step explanation:
Trust
16. Find m<2.
a. 86°
b. 43°
C. 94°
d. 133
Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor air pollution. The article "Domestic Fuels, Indoor Air Pollution, and Children's Health" (Annals of the N.Y. Academy of Sciences, 2008: 209-217) pm-tented information on various pulmonary characteristics in samples of children whose households in India used either biomass fuel or liquefied petroleum gas (LPG). For the 755 children in biomass households, the sample mean peak expiratory flow (a person's maximum speed of expiration) was 3.30 Us, and the sample standard deviation was 1.20. For the 750 children whose households used liquefied petroleum gas, the sample mean PEF was 4.25 and the sample standard deviation was 1.75.
a. Calculate a confidence interval at the 95% confidence level for the population mean PEF for children in biomass households and then do likewise for children in LPG households. What is the simultaneous confidence level for the two intervals?
b. Carry out a test of hypotheses at significance level .01 to decide whether true average PEF is lower for children in biomass households than it is for children in LPG households (the cited article included a P-value for this test).
c. FEV1, the forced expiratory volume in 1 second, is another measure of pulmonary function. The cited article reported that for the biomass households the sample mean FEY, was 2.3 L/s and the sample standard deviation was .5 L/s. If this information is used to compute a 95% CI for population mean FEV1, would the simultaneous confidence level for this interval and the first interval calculated in (a) be the same as the simultaneous confidence level deter-mined there? Explain.
Answer:
A) 95% confidence interval for the population mean PEF for children in biomass households = (3.214, 3.386)
95% confidence interval for the population mean PEF for children in LPG households
= (4.125, 4.375)
Simultaneous confidence interval for both = (3.214, 4.375)
B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.
C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.375)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Step-by-step explanation:
A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.
Finding the critical value from the z-tables,
Significance level for 95% confidence interval
= (100% - 95%)/2 = 2.5% = 0.025
z (0.025) = 1.960 (from the z-tables)
For the children in the biomass households
Sample mean = 3.30
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.20
N = sample size = 755
σₓ = (1.20/√755) = 0.0436724715 = 0.04367
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 3.30 ± (1.960 × 0.04367)
CI = 3.30 ± 0.085598
95% CI = (3.214402, 3.385598)
95% Confidence interval = (3.214, 3.386)
For the children in the LPG households
Sample mean = 4.25
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.75
N = sample size = 750
σₓ = (1.75/√750) = 0.063900965 = 0.063901
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 4.25 ± (1.960 × 0.063901)
CI = 4.25 ± 0.125246
95% CI = (4.12475404, 4.37524596)
95% Confidence interval = (4.125, 4.375)
Simultaneous confidence interval for both = (3.214, 4.375)
B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.
The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.
Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂
The null hypothesis is
H₀: μ ≥ 0 or μ₁ ≥ μ₂
The alternative hypothesis is
Hₐ: μ < 0 or μ₁ < μ₂
Test statistic for 2 sample mean data is given as
Test statistic = (μ₂ - μ₁)/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = 3.30
n₁ = 755
s₁ = 1.20
μ₂ = 4.25
n₂ = 750
s₂ = 1.75
σ = √[(1.20²/755) + (1.75²/750)] = 0.07740
z = (3.30 - 4.25) ÷ 0.07740 = -12.27
checking the tables for the p-value of this z-statistic
Significance level = 0.01
The hypothesis test uses a one-tailed condition because we're testing in only one direction.
p-value (for z = -12.27, at 0.01 significance level, with a one tailed condition) = < 0.000000001
The interpretation of p-values is that
When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.
Significance level = 0.01
p-value = 0.000000001
0.000000001 < 0.01
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.
C) For FEY for biomass households,
Sample mean = 2.3 L/s
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation = 0.5
N = sample size = 755
σₓ = (0.5/√755) = 0.0182
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 2.30 ± (1.960 × 0.0182)
CI = 2.30 ± 0.03567
95% CI = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.375)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Hope this Helps!!!
Bill and Ben each have three cards numbered 4,5,6 they each take one of their own cards then they add the two numbers on the cards what is the probability that their answer is an odd number. What is the probability that their answer is a number less than 11.
Answer:
P(odd) = 4/9P(<11) = 2/3Step-by-step explanation:
There are 9 possible outcomes for (Bill, Ben)'s cards:
(4, 4) total 8; (4, 5) total 9; (4, 6) total 10;
(5, 4) total 9; (5, 5) total 10; (5, 6) total 11;
(6, 4) total 10; (6, 5) total 11; (6, 6) total 12.
Of these 9 outcomes, 4 have an odd total; 6 are less than 11.
P(odd) = 4/9
P(sum < 11) = 2/3
There are 3 times as many novels as comic books in a bookstore.If there are 2480 books altogether, how many comic books are there in the bookstore.
Answer:
620 comic books
2480 / 4 is 620.
620 x 3 is 1860.
1860 + 620 is 2480.
Done!
When would you need to arrange polynomials
what is the slope of the line given by the equation?
Answer:
the slope is 8
Step-by-step explanation:
The coefficient of x, "m" is the slope in the slope-intercept form:
y = mx + b
Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices. So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Indicate which of the following is the null hypothesis, and which is the alternate hypothesis.
There food preferences among vole species are independent of one another. _____
There is a relationship between voles and food preference. ______
To test for independence, we need to calculate the Chi-square statistic.
These are the data that Dr. Pagels collected:
meadow voles common voles
apple slices 26 32
peanut butter-oatmeal 35 25
When transferring your answers, make sure you carry them out to AT LEAST SIX SIGNIFICANT FIGURES unless otherwise stated.
_____= expected meadow vole/apple slices
_____= expected common vole/apple slices
_____= expected meadow vole/peanut butter-oatmeal
_____= expected common vole/peanut butter-oatmeal
_____= chi-square value
_____= degrees of freedom (whole number only)
_____= using Statistical Table A (pg 704 of your textbook), what is the chi-square critical value with significance level of alpha=0.05?
_____= will you reject or fail to reject the null hypothesis? (answer either reject or fail to reject)
Answer:
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 28.983051
Chi-square value = χ² = 2.154239
Degree of freedom = 1
Critical value = 3.841
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
Step-by-step explanation:
He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.
So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Data collected by Dr. Pagels:
meadow voles common voles Row Total
apple slices 26 32 58
peanut butter-oatmeal 35 25 60
Column Total 61 57 118
Where 118 is the grand total.
The expected number is given by
Expected = (row total)×(column total)/grand total
Expected meadow vole/apple slices = 58×61/118
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 58×57/118
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 60×61/118
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 60×57/118
Expected common vole/peanut butter-oatmeal = 28.983051
The chi-square statistic value is given by
χ² = Σ(Observed - Expected)²/Expected
χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051
χ² = 2.154239
The degrees of freedom is given by
DoF = (row - 1)×(col - 1)
For the given case, we have 2 rows and 2 columns
DoF = (2 - 1)×(2 - 1)
DoF = 1
The given level of significance = 0.05
The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be
Critical value = 3.841
Conclusion:
Reject H₀ If χ² > Critical value
We reject the Null hypothesis If the calculated chi-square value is more than the critical value.
For the given case,
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
How do you write 89,700,000,000 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]89.7 \times {10}^{9} [/tex]
Or
[tex]8.97 \times {10}^{10} [/tex]
Hope this helps you
Answer:
8.97 * 10 ^10
Step-by-step explanation:
We want one nonzero digit to the left of the decimal
8.97
We moved the decimal 10 places to the left
The exponent is positive 10 since we moved 10 places to the left
8.97 * 10 ^10
is this right one more i think lol
Answer:
Yup P is the right one having 62.26%
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
We can set it up as
P = 33/53
Q = 20/48
R = 54/90
S = 44/83
This is because we are calculating the percent of yellow birds in the total amt. of birds in a specified park.
Now we calculate =>
P = 33/53 = around 0.62
Q = 20/48 = around 0.416
R = 54/90 = 0.6
S = 44/83 = around 0.53
We find that Park P has the greatest percentage and -->
Thus, Park P is our answer and yes, you are correct.
write 26 as repeated multiplication
Answer:
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
2¹³
13 x 13
Step-by-step explanation:
We simply find numbers that can multiply to 26 and write out the multiplication to get our answer.
Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ticket prices were set at $12, the average attendance was 30,000. When the ticket prices were on sale for $10, the average attendance was 35,000.
(a) Let D(x) represent the number of people that will buy tickets when they are priced at x dollars per ticket. If D(x) is a linear function, use the information above to find a formula for D(x). Show your work!
(b) The revenue generated by selling tickets for a baseball game at x dollars per ticket is given by R(x) = x-D(x). Write down a formula for R(x).
(c) Next, locate any critical values for R(x). Show your work!
(d) If the possible range of ticket prices (in dollars) is given by the interval [1,24], use the Closed Interval Method from Section 4.1 to determine the ticket price that will maximize revenue. Show your work!
Optimal ticket price:__________ Maximum Revenue:___________
Answer:
(a)[tex]D(x)=-2,500x+60,000[/tex]
(b)[tex]R(x)=60,000x-2500x^2[/tex]
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
[tex]\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500[/tex]
Therefore, we have:
[tex]y=-2500x+b[/tex]
At point (12,30000)
[tex]30000=-2500(12)+b\\b=30000+30000\\b=60000[/tex]
Therefore:
[tex]D(x)=-2,500x+60,000[/tex]
(b)Revenue
[tex]R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2[/tex]
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
[tex]R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12[/tex]
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
[tex]R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0[/tex]
Therefore:
Optimal ticket price:$12Maximum Revenue:$360,000There are (7^13)^3 x 7^0 strawberries in a field . What is the total number of strawberries in the field
Answer:
Step-by-step explanation:
[tex]7^{0}=1[/tex]
[tex](7^{13})^{3}*7^{0}=7^{13*3}*1\\\\=7^{39}[/tex]
Una persona se dirige a un edificio y observa lo alto del mismo con un ángulo de elevación “x”, después de caminar 10m observa al mismo punto anterior con ángulo de elevación “y”, si la altura del edificio es de 30m. Calcule: "3Tgx.Ctgy + Tgx"
Answer:
3
Step-by-step explanation:
To begin with notice that
[tex]\displaymode{ \tan(x) = \frac{30}{10 + 30\cot(y)} }[/tex]
From that equation you get that
10 tan(x) + 30tan(x) cot(x) = 30
therefore
tan(x) + 3 tan(x) cot(x) = 3
what is -34/15 in decimal form
Answer:
2.26 repeating
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
hope this helpes
be sure to give brainliest
The tread life of a particular brand of tire is normally distributed with mean 60,000 miles and standard deviation 3800 miles. Suppose 35 tires are randomly selected for a quality assurance test. Find the probability that the mean tread life from this sample of 35 tires is greater than 59,000 miles. You may use your calculator, but show what you entered to find your answer. Round decimals to the nearest ten-thousandth (four decimal places).
Answer:
P [ x > 59000} = 0,6057
Step-by-step explanation:
We assume Normal Distribution
P [ x > 59000} = (x - μ₀ ) /σ/√n
P [ x > 59000} = (59000 - 60000)/ 3800
P [ x > 59000} = - 1000/3800/√35
P [ x > 59000} = - 1000*5,916 /3800
P [ x > 59000} = - 5916/3800
P [ x > 59000} = - 1,55
We look for p value for that z score n z-table and find
P [ x > 59000} = 0,6057
Jacqueline and Maria set up bug barns to catch lady bugs. Jacqueline caught ten more than three times the number of lady bugs that Maria caught. If c represents the number of lady bugs Maria caught, write an expression for the number of lady bugs that Jacqueline caught.
Answer:
(CX3)+10
Step-by-step explanation:
Answer:
c×3+10= j
Step-by-step explanation:
Find the hypotenuse of a right triangle (in cm) if one leg measures 7 cm and the other leg measures 11 cm. Round to the nearest thousandth. ____________ cm
Using the Pythagorean theorem
Hypotenuse = sqrt( 11^2 + 7^2)
= sqrt( 121 + 39)
= sqrt( 160)
= 12.694
11. What's the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? round to the nearest whole number.
O A. 746 67 m2
O B. 74 6 m2
O C.85 4 m2
O D. 8 54 m2
Answer:
85.4
Step-by-step explanation:
first you have to find the radius before you find the area. so given the height, the radius is 11.3 meters. then, you need to find the area behind the arc, which is 85.4 meters/
If Q(x) = x2 – X – 2, find Q(-3).
Answer:
10
Step-by-step explanation:
for this you need to sub the value of -3 for x
Q(-3)=(-3)^2-(-3)-2
=9+3-2
=10
Answer:
Q= x - X/x - 2/x
Step-by-step explanation:
hope this helps !
Given the following diagram, are OC and OE opposite rays ?
Answer:
No
Step-by-step explanation:
If they were opposite, they would be equal.
But they are not, (on one of the spaces in between them is smaller and one is larger.)
Hope I have helped you, since it seems I haven't helped "other people" the last time :/
Answer:
No
Step-by-step explanation:
Use synthetic division to solve What is the quotient?
Answer:
[tex]3{x}^{3} + 2x + 5[/tex]
Step-by-step explanation:
Sorry if my notes weren't very clear.
Answer:B
Step-by-step explanation: got it right
What is the greatest common factor of the polynomial below?
20x^3 - 14x
Answer:
the correct answer is 2x
Answer:
D. 2x
Step-by-step explanation:
20x² : 1, 2, 4, 5, 10, 20, x
14x : 1, 2, 7, 14, x
The greatest common factor of the polynomial is 2x.
2x(10x² - 7)
8÷2 2/9 −2 11/15 I need help and this is a whole equation I need this ASAP
Answer: (1 and 22/45)
Step-by-step explanation:
I guess that we are working with mixed numbers here, and we have the equation:
(8÷2 2/9) − (2 11/15)
first we solve: 8÷2 = 4.
Now, we can write this as:
(4 + 2/9) - (2 + 11/15)
(4 - 2) + (2/9 - 11/15)
now, 9*5 = 45
15*3 = 45
then we can write the right side as: 2/9 - 11/5 = 10/45 - 33/45 = -23/45
2 - 23/45
But in mixed numbers we also need to work with a positive rational, then we have:
2 - 23/45 = 1 + 1 -23/45 = 1 + 45/45 - 23/45 = 1 + 22/45
then the solution is:
(1 and 22/45)
Solve by completing the square. x2−12x=−27 Select each correct answer. −9 −3 3 9 15
Answer:
x=9,3
Step-by-step explanation:
x²-12x=-27
x²-12x+(12/2)²=-27+(12/2)²
x²-12x+6²=-27+36
(x-6)²=9
x-6=[tex] \frac{ + }{ - } \sqrt{9} [/tex]
x-6=+3 and x-6=-3
x=9 and 3
The table shows three unique functions. (TABLE IN PIC) Which statements comparing the functions are true? Select three options. Only f(x) and h(x) have y-intercepts. Only f(x) and h(x) have x-intercepts. The minimum of h(x) is less than the other minimums. The range of h(x) has more values than the other ranges. The maximum of g(x) is greater than the other maximums.
Answer:
(A)Only f(x) and h(x) have y-intercepts.
(C)The minimum of h(x) is less than the other minimums.
(E)The maximum of g(x) is greater than the other maximums.
Step-by-step explanation:
From the table
f(0)=0 and h(0)=0, therefore, Only f(x) and h(x) have y-intercepts. (Option A)
Minimum of f(x)=-14Minimum of g(x)=1/49Minimum of h(x)=-28Therefore, the minimum of h(x) is less than the other minimums. (Option C).
Maximum of f(x)=14
Maximum of g(x)=49
Maximum of h(x)=0
Therefore, the maximum of g(x) is greater than the other maximums. (Option E)
Answer: It's B,C, and E
Step-by-step explanation:
Lisa drew three circles to form a figure. The areas of the circles were in the
ratio 1:4:16. She then shaded some parts of the figure as shown.
What fraction of the figure was shaded?
Answer:
Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]
Step-by-step explanation:
Ratio of the areas of the given circles are 1 : 4 : 16
Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]
= 1 : 2 : 4
If the radius of the smallest circle = x units
Then the radius of the middle circle = 2x units
and the radius of the largest circle = 4x units
Area of the smallest circle = πx²
Area of the middle circle = π(2x)² = 4πx²
Area of the largest circle = π(4x)²= 16πx²
Area of the region which is not shaded in the middle circle = πx²(4 - 1)
= 3πx²
Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded
= 16πx² - 3πx²
= 13πx²
Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]
= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]
= [tex]\frac{13}{16}[/tex]
A square has a perimeter of 12x+52 units. Which expression represents the side leagth of the square in units
Answer:
12x/2 or 52/2
Step-by-step explanation:
Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.