a)0.2407 is the point estimate of the proportion.
b) The 95% confidence interval for the proportion that beat estimates is (0.4858, 0.6746).
c) A sample size of 754 is needed to achieve a desired margin of error of 0.05.
(a) What is the point estimate of the proportion?
The point estimate of the proportion that fell short of estimates is 39/162 = 0.2407. Rounded to four decimal places, this is pshort = 0.2407.
(b) How to determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates?
To determine the margin of error and provide a 95% confidence interval for the proportion that beat estimates, we need to first find the point estimate and standard error of the proportion that beat estimates.
The point estimate of the proportion that beat estimates is 94/162 = 0.5802.
The standard error can be calculated as:
SE = √(p×(1-p)/n)
where p is the point estimate of the proportion that beat estimates and n is the sample size. Substituting the values we get:
SE = √(0.5802×(1-0.5802)/162) = 0.0482
To calculate the margin of error, we use the formula:
ME = zSE
where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, z* = 1.96 (from the standard normal distribution table).
Substituting the values we get:
ME = 1.96×0.0482 = 0.0944
Therefore, the margin of error is 0.0944. To find the 95% confidence interval, we add and subtract the margin of error from the point estimate of the proportion that beat estimates:
CI = 0.5802 ± 0.0944
CI = (0.4858, 0.6746)
Therefore, the 95% confidence interval for the proportion that beat estimates is (0.4858, 0.6746).
(c) How large a sample is needed if the desired margin of error is 0.05?
To find the sample size needed for a desired margin of error of 0.05, we use the formula:
n* = (z*/ME)² × p×(1-p)
where z* is the z-score corresponding to the desired confidence level (we use 1.96 for a 95% confidence level), ME is the desired margin of error (0.05), and p is an estimate of the proportion (we use the point estimate of 0.5802 for the proportion that beat estimates).
Substituting the values we get:
n* = (1.96/0.05)² × 0.5802×(1-0.5802) = 753.16
Rounding up to the next integer, we get n* = 754. Therefore, a sample size of 754 is needed to achieve a desired margin of error of 0.05.
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HELP PLEASE
Solve by graphing g(x)=lx-4l+3
Please refer to the attachment
,Kofi, Adoma and Esenam are three siblings, Kofi is x years older than Adoma and Adoma is y years older than Esenam. a. How much older than Esenam is Kofi ? b. If Esenam is 5 years old, how old is (i) Adoma (ii)Kofi
a. K = E + (x + y). This implies that Kofi is (x + y) older than Esenam.
b. (i) Adoma = (5 + y) years
(ii) Kofi = (5 + (x+y)) years
What is a word problem?Word problem is a topic that requires the transformation of a mathematical statement into an equation, such that the variable is to be determined.
In the given question, we have;
Let the age of Kofi, Adoma, and Esenam be represented by K, A and E respectively. So that;
K = A + x ...... i
A = E + y........ ii
substitute i into ii
K = (E + y) + x
= E + (x + y)
K = E + (x + y) ........ iii
Thus,
a. From equation iii, we can deduce that Kofi is (x + y) years older than Esenam.
b. The age of Adoma = 5 + y years
ii. The age of Kofi = 5 + (x + y) years
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Suppose that you borrow $10,000 for four years at 8% toward the purchase of a car. Use PMT=
find the monthly payments and the total interest for the loan.
The monthly payment is
(Do not round until the final answer. Then round to the nearest cent as needed.)
ample
Get more help
Clear all
-|C
Check answer
Answer:
To find the monthly payments, we can use the PMT function in Excel or a financial calculator. The formula is:
PMT(rate, nper, pv)
where rate is the interest rate per period, nper is the total number of periods, and pv is the present value (i.e. loan amount).
For this problem, the interest rate is 8%/12 = 0.0066667 per month, the number of periods is 4 years * 12 months/year = 48 months, and the present value is $10,000. Therefore, the formula becomes:
PMT(0.0066667, 48, 10000)
Evaluating this formula gives a monthly payment of $242.42.
To find the total interest for the loan, we can multiply the monthly payment by the number of periods (i.e. 48) and subtract the loan amount. This gives:
total interest = monthly payment * number of periods - loan amount
total interest = $242.42 * 48 - $10,000
total interest = $2,678.16
Therefore, the monthly payments are $242.42 and the total interest for the loan is $2,678.16.
Step-by-step explanation:
According to the association of public and land grant universities (aplu) graduate students represents only 15% of post secondary students, but account for approximately 40% of the current student loan balances if the nations current studen loan balance is at 1.5 trillion estimate the amount of student debt held by graduate students by converting 1.5 trillion and 40% (0.4 as a decimal) to scientific notation then multiplying, give your answer in scientific notation.
A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long. Find the perimeter and the area
Answer:
Parameter= 98ft
Area=180ft^2
Step-by-step explanation:
Parameter= Length times 2 plus width times 2 or
L2+W2=P 4(2)+45(2)=8+90=98
Area= LxW=A^2
4x45=180^2
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
The y-intercept represents Adam's base salary
Step-by-step explanation:
Since it's y = 0.28x + 38,000, when x is 0, the salary is 38,000 without commission.
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PLEASE HELP ME!!! Unit 10 Circles Homework Inscribed Angles questions 15 and 17
Applying the inscribed angle theorem, we have the missing measures as: 15. m<DEF = 127° 16. m(PL) = 62°
How to Apply the Inscribed Angle Theorem?15. Angle DEF is an inscribed angle while arc FGD is the intercepted arc. Thus, according to the inscribed angle theorem, we have:
m<DEF = 1/2(m(FGD)
Plug in the values:
6x + 37 = 1/2(19x - 31)
2(6x + 37) = 19x - 31
12x + 74 = 19x - 31
12x - 19x = -74 - 31
-7x = -105
x = 15
m<DEF = 6x + 37 = 6(15) + 37 = 127°
16. m<LMP = m<LNP
Plug in the values:
5x - 19 = 2x + 11
5x - 2x = 19 + 11
3x = 30
x = 10
m(PL) = 2(LMP) [based on the inscribed angle theorem]
Plug in the values:
m(PL) = 2(5x - 19)
Plug in the value of x:
m(PL) = 2(5(10) - 19)
m(PL) = 62°
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The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.
a(t) = 2t + 2, v(0) = −15, 0 ≤ t ≤ 5
Find the distance traveled during the given time interval.
I keep getting 25/3 but that is not correct :(
Answer:
[tex]\dfrac{137}{3}\approx 45.7\; \sf m[/tex]
Step-by-step explanation:
To find the velocity function, integrate the acceleration function (and add a constant of integration).
[tex]\begin{aligned}\displaystyle v(t)=\int a(t) &= \int (2t + 2)\; \text{d}t\\\\&=\int 2t \; \text{d}t+\int 2\; \text{d}t\\\\&=\dfrac{1}{2} \cdot 2t^{(1+1)}+2t+\text{C}\\\\&=t^2+2t+\text{C}\end{aligned}[/tex]
To find the constant of integration, C, substitute v(0) = -15 into the velocity function and solve for C:
[tex]\begin{aligned}v(0)=(0)^2+2(0)+\text{C}&=-15\\0+0+\text{C}&=-15\\\text{C}&=-15\end{aligned}[/tex]
Therefore, the velocity function (in m/s) is:
[tex]v(t)=t^2+2t-15[/tex]
As we want to find the distance travelled during the given time interval 0 ≤ t ≤ 5, we first need to determine if the particle momentarily stops at any point in the given interval (and therefore changes direction). The particle will stop when its velocity is zero, so when v(t) = 0:
[tex]\begin{aligned}v(t)&=0\\\implies t^2+2t-15&=0\\t^2+5t-3t-15&=0\\t(t+5)-3(t+5)&=0\\(t-3)(t+5)&=0\\\\\implies t&=3, -5\end{aligned}[/tex]
As time is positive only, the velocity is zero at t = 3 seconds.
Therefore, at t = 3, the particle changes direction and begins to move in the opposite direction. Therefore, the displacement between 0 ≤ t ≤ 5 consists of two parts: 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5.
To find the distance travelled, first find the displacement function by integrating the velocity function:
[tex]\begin{aligned}\displaystyle s(t)=\int v(t) &= \int (t^2+2t-15)\; \text{d}t\\\\&= \int t^2\; \text{d}t+\int 2t\; \text{d}t-\int 15\; \text{d}t\\\\&=\dfrac{1}{3}t^3+t^2-15t\left(+\text{C}\right) \end{aligned}[/tex]
Distance is the absolute value of displacement.
As we want to find the distance travelled for the intervals 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5, we need to add the absolute values of displacement for these intervals. So, the absolute values of the definite integrals for these intervals:
[tex]\begin{aligned}\textsf{Distance}&=\left|\int^3_0 v(t)\right|+\left|\int^5_3 v(t)\right|\\\\&=\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^3_0\right|+\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^5_3\right|\\\\&=\left|\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)-\left(\dfrac{1}{3}(0)^3+(0)^2-15(0)\right)\right|+\\&\left|\left(\dfrac{1}{3}(5)^3+(5)^2-15(5)\right)-\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)\right|\\\\&=\left|(-27-0)\right|+\left|\left(-\dfrac{25}{3}-(-27)\right)\right|\end{aligned}[/tex]
[tex]\begin{aligned}&=27+\dfrac{56}{3}\\\\&=\dfrac{137}{3}\end{aligned}[/tex]
Therefore, the total distance travelled during the given time interval is 137/3 ≈ 45.7 meters.
Richard is saving money for a down payment on a car. He opens a savings account at his local bank and deposits $500. He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate. What does the y-intercept of linear model represent?
Question 8 options:
The date the savings account was started.
The starting amount in his savings account.
The date when he will have enough money.
The largest amount that he can save.
In a case whereby Richard is saving money for a down payment on a car He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate y-intercept of linear model represent B. The starting amount in his savings account.
How can the linear model be interpreted?It should be noted that in a linear equation the y intercept can be seen as one that is starting point whereby x is zero, which implkies that starting balance he had is 1000 in the bank.
Therefore, from the equation y = 200x + 500, the y-intercept of linear model serves as the starting amount in his savings account.
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Graph the equation y=-x^2+12x−35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Answer:
To graph the equation y=-x^2+12x-35, we need to find the vertex and the roots of the equation.
The equation can be written in vertex form as y=-(x-6)^2+1, where the vertex is (6,1).
To find the roots, we need to set y=0 and solve for x:
0=-x^2+12x-35
x^2-12x+35=0
(x-5)(x-7)=0
x=5 or x=7
So the roots are (5,0) and (7,0).
The vertex is at (6,1) and the roots are at (5,0) and (7,0). The curve is a downward-facing parabola.
During one week an overnight delivery company found that the weight of its parcels were normally distributed with a mean of 32 ounces and a standard deviation of 8 ounces.
What percent of the parcels weighed between 16 ounces and 40 ounces? Round your answer to one decimal place.
The percent of the parcels weighed between 16 ounces and 40 ounces is 81.9%.
What is z-score?To solve this problem, first, find the z-scores for the weights of 16 ounces and 40 ounces using the given mean and standard deviation:
z1 = (16 - 32) / 8 = -2
z2 = (40 - 32) / 8 = 1
Next, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we get:
P(-2 < Z < 1) = 0.8186
So, approximately 81.9% of the parcels weighed between 16 ounces and 40 ounces.
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A class plants 20 seeds. Only 60% of the seeds grow into plants. How many plants does the class have?
Answer:
If only 60% of the seeds planted by the class grow into plants, we can find the number of plants by multiplying the total number of seeds planted by the percentage of seeds that grow, expressed as a decimal.
To do this, we can start with the total number of seeds planted, which is 20, and multiply by 0.6:
20 x 0.6 = 12
Therefore, the class has 12 plants.
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During 2022, Sam Reed purchased 350 shares of common stock issued by New Generation Electronics for $7800 including commission. Later in the same year, Sam sold the shares for $8400 after commission. Calculate the following. (Round all answers to two decimal places.)
1. Profit on this stock transaction: $
2. Percentage return on investment: %
This stock trade generated a profit of $600 and a 7.69% return on investment.
The total amount received from selling the shares, after commission.
The total cost of purchasing the shares = $7800
Total amount received from selling the shares = $8400
The commission paid for purchasing the shares and for selling the shares will cancel out since they will both be subtracted, so we do not need to consider them.
Profit on this stock transaction = Total amount received - Total cost of purchasing
= $8400 - $7800
= $600
To calculate the percentage return on investment, we need to divide the profit by the total cost of purchasing the shares, and then multiply by 100 to express it as a percentage.
Percentage return on investment = (Profit / Total cost of purchasing) x 100%
= ($600 / $7800) x 100%
= 7.69%
Therefore, the profit on this stock transaction was $600 and the percentage return on investment was 7.69%.
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Tickets numbered 1−10 are drawn at random and placed back in the pile. Find the probability that at least one ticket numbered with a 6 is drawn if there are 4 drawings that occur. Round your answer to two decimal places.
Answer:
The probability that atleast one ticket labeled 2-6 is drawn is 0.94
Numbered ticket = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Number of draws = 4
Required picks = {2, 3, 4, 5, 6}
Recall :
Probability = required outcome / Total possible outcomes
Probability of choosing a required ticket :
5/10 = 1/2
Therefore, the probability that none of the required tickets is chosen :
(1/2 × 1/2 × 1/2 × 1/2) = 1/16
The probability that atleasr one ticket labeled 2-6 is drawn is :
1 - P(none is chosen) = 1 - 1/16 = 15/16 = 0.9375
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What is the midpoint of the line segment graphed below?
The midpoint of the line joining the endpoints (-1, 5) and (-8, -4) will be (-4.5, 0.5).
Given that:
Endpoints, (-1, 5) and (-8, -4)
The coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The midpoint is calculated as,
(x, y) = [(-1 - 8) / 2, (5 - 4) / 2]
(x, y) = (-9 / 2, 1 / 2)
(x, y) = (-4.5, 0.5)
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Write an equation in the form y = mx +b of the line that is described.
The line rises from left to right. It passes through the origin and a second point with equal x and y
coordinates.
The equation of the line is y Write your response here...
Answer:
I have my answer in the picture i will upload
please check the below pictures.
A square fence has a perimeter of (24x + 36) units. What is the length of one side of the fence?
Answer:
The perimeter of a square is four times the length of one side, so we can write:
4s = 24x + 36
Dividing both sides by 4, we get:
s = 6x + 9
Therefore, the length of one side of the fence is 6x + 9 units.
Step-by-step explanation:
What is the value of cos(15°)?
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 2 EndFraction
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 4 EndFraction
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 2 EndFraction
we know that,
[tex] \sf \dashrightarrow \: cos(a - b) = cos a \times cos b + sin a \times sin b[/tex]
Therefore,
[tex] \sf \leadsto \: cos \: 15 \degree[/tex]
[tex] \sf \leadsto \: cos \: (45 \degree - 30 \degree)[/tex]
[tex] \sf \leadsto \: cos \: 45 \degree . \: cos \: 30 \degree + \: sin \: 45 \degree . \: sin \: 30 \degree[/tex]
[tex] \sf \leadsto \: \frac{1}{ \sqrt{2} } \: . \: \frac{ \sqrt{3} }{2} + \: \frac{1}{ \sqrt{2} } \: . \: \: \frac{1}{2} \\ [/tex]
[tex] \sf \leadsto \: \frac{1. \: \sqrt{3} }{ \sqrt{2} \: . \: 2} \: + \: \frac{1 \: .\: 1}{ \sqrt{2} \: .\: 2} \\ [/tex]
[tex] \sf \leadsto \: \frac{ \: \sqrt{3} }{ 2\sqrt{2} \: } \: + \: \frac{1}{ 2\sqrt{2} \: } \\ [/tex]
[tex] \sf \leadsto \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: \\ [/tex]
Therefore Value of cos 15° is [tex] \sf \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: [/tex]
Horatio has $230 to be used only on his car. He
wishes to save $160 of this money and spend $24.95 on
an oil change. Horatio knows that gas costs $3.81 per
gallon. Which of the following show how many gallons
of gas (g) he could buy? Select all that apply.
A g≤11.82
B g≤60.37
C 3.81g ≤45.05
D 3.81g ≤ 230 +160+24.95
E 160 + 24.95 +3.81g ≤ 230
184.95 +3.81g ≤ 45.05
F 184.95 + 3.81g < 45.05
The statement that shows the quantity of gallons of gas that he can buy would be =g≤11.82. That is option A.
How to calculate the quantity of gallons Horatio is able to buy?The total number of money he has to spend on his vehicle = $230
The amount of money he wishes to save = $160
The remaining amount he can spend = 230+160 = $70
The amount he wishes to spend on oil change = $24.95
The remaining amount = 70-24.95
= $40.05
The cost per gallon of gas = $3.81 per gallon.
The quantity of gallons of gas he can purchase = 40.05/3.81 = 10.51 gallons.
Therefore the quantity of gallons of gas he can purchase would be g≤11.82
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Diane is a camp counselor she did signs in new obstacle course and tested course with three friends the Doppler shows the time it takes to complete the obstacle course. What is the mean absolute deviation(MAD)of the times.
Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.
What is mean absolute deviation?Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean or median of that dataset. It measures the dispersion or variability of the data points in relation to the central tendency of the dataset.
To calculate the MAD, you first find the mean or median of the dataset, and then you calculate the absolute difference between each data point and the mean or median. The absolute differences are then averaged to give the mean absolute deviation.
MAD is expressed in the same units as the original data and is commonly used in finance, economics, and other fields to measure the variability of financial returns, economic indicators, or other datasets. MAD is a robust measure of dispersion that is less sensitive to extreme values or outliers compared to other measures of dispersion such as standard deviation.
Let's say the times taken by the four people are:
Diane: 2 minutes
Friend 1: 1.5 minutes
Friend 2: 2.5 minutes
Friend 3: 1.75 minutes
The mean of these times is:
Mean = (2 + 1.5 + 2.5 + 1.75) / 4 = 1.9375 minutes
Next, we need to find the absolute deviations of each time from the mean. To do this, we subtract the mean from each time and take the absolute value of the result:
|2 - 1.9375| = 0.0625
|1.5 - 1.9375| = 0.4375
|2.5 - 1.9375| = 0.5625
|1.75 - 1.9375| = 0.1875
Then, we find the mean of these absolute deviations:
MAD = (0.0625 + 0.4375 + 0.5625 + 0.1875) / 4 = 0.3125 minutes
Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.
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For what values of x and y are the triangles to the right congruent by HL?
The values of x and y that make the triangles congruent by HL are:
x = 3 and y = 1
Congruent triangles: Calculating the values of x and yFrom the question, we are to determine the values of x and y that make the triangles congruent by HL.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Thus,
For the triangles to be right congruent by HL
x = y + 2
and
x + 1 = 4y
Solve the equations simultaneously
Substitute x = y + 2 in the second equation
x + 1 = 4y
y + 2 + 1 = 4y
y + 3 = 4y
3 = 4y - y
3 = 3y
Divide both sides by 3
3/3 = 3y/3
1 = y
Therefore,
y = 1
Substitute the value of y into the first equation
x = y + 2
x = 1 + 2
x = 3
Hence,
The values are:
x = 3 and y = 1
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Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d= 163t
D. d= 81.50t
Answer:
b but I'm not exactly sureb
which average is the most representative of the data
The median is the average that is most representative of the data.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
In this problem, we have that smaller values have a higher number of observations, meaning that the data-set is not symmetric.
As the data-set is not symmetric, it means that the median is the average that is most representative of the data.
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It is possible to select 3 restraunts in how many different ways?
There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.
In mathematics, what are a permutation and combination?Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.
n C r = r! * (n-r)!
where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).
By replacing these values, we obtain:
20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
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Consider a rectangle with width of x units and an area of 10 square units. The length l of the rectangle can be modeled by the function f (x) = 10\x. Suppose the width of the rectangle increases 1 unit, while the area remains constant. Which graph models the length of the new rectangle?
please explain the answer step by step and explain why you chose the option you chose.
In linear equation, The graph in option 3 models the length of the new rectangle.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
According to the problem,
width of the rectangle is x units
Area of the rectangle is 10 square units
Length of the rectangle is given by f(x) = 10/x
Now if width becomes (x+1) units
∴ Length will be represented as 10/(x+1)
Now from the given options we need to find the exact graph of f(x) = 10/(x +1)
Here if x = 4 , y =2
So the point (4 , 2) is satisfied which is only happening in the graph of option 3
Option 3 represents the correct graph.
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Need Help fast please
A graph of the transformed function [tex]y=\frac{1}{(x+2)^2} +5[/tex] is shown in the image attached below.
What is a translation?In Mathematics and Geometry, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image;
g(x) = f(x + N)
On the other hand, the translation a geometric figure upward simply means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image;
g(x) = f(x) + N
Since the parent function is [tex]y = \frac{1}{x^{2} }[/tex], it ultimately implies that the transformed function would be created by translating the parent function to the left by 1 units and 5 units upward as shown below.
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The one-to-one functions g and h are defined as follows.
Fro the one to one functions g and h defined, the value of :
g⁻¹(6) = 2
h⁻¹(x) = 7x + 8
(h⁻¹ o h)(1) = 1
Given one to one functions h and g.
We have that,
g(2) = 6
So, g⁻¹(6) = 2
We have,
y = (x - 8) / 7
Switch x and y.
x = (y - 8) / 7
7x = y - 8
y = 7x + 8
So, h⁻¹(x) = 7x + 8
(h⁻¹ o h) (x) = h⁻¹ (h(x))
= h⁻¹ ((x - 8) / 7)
= 7 ((x - 8) / 7)) + 8
= x - 8 + 8
= x
(h⁻¹ o h) (1) = 1
Hence the functions are found.
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PLEASE HELP - A triangle with side lengths a, b, and c is shown below. Which statement about the side lengths must be true?
Answer:
A
Step-by-step explanation:
You want to know which inequality must be true regarding the side lengths of a triangle.
Triangle inequalityThe triangle inequality requires the sum of any two side lengths be greater than the length of the third side:
a + b > c . . . . . choice A
__
Additional comment
This means it must also be true that ...
a + c > b
b + c > a
Of course, this means the sum of the two shortest sides must be more than the longest side. It also means any side length must lie between the sum and difference of the other two side lengths:
|a - b| < c < a + b
The version of this inequality most often seen uses the > or < symbol. Some authors use the ≥ or ≤ symbol instead. This allows triangles that look like a line segment and have zero area.
an aquarium is 3 feet wide, 1.5 feet tall, and 5 feet long. The bottom is covered with gravel to a height of 3 inches. the tank will be filled with water to 3 inches below the top. what is the volume of the tank that will be filled with water in ft cubed
The volume of the tank that will be filled with water through which the given relation is satisfied is [tex]22.5ft^{3}[/tex]
What about volume of cuboid?
The volume of a cuboid is the amount of space occupied by the three-dimensional solid figure known as a cuboid. A cuboid is a box-shaped object with six rectangular faces, where each face has a pair of parallel sides, and opposite faces are equal in size and shape.
The formula for calculating the volume of a cuboid is:
Volume = length x width x height
where length, width, and height are the three dimensions of the cuboid.
The unit of measurement for the volume of a cuboid will depend on the unit of measurement used for each dimension. For example, if the length, width, and height are measured in centimeters, then the volume of the cuboid will be expressed in cubic centimeters (cm³). Similarly, if the dimensions are measured in meters, the volume will be expressed in cubic meters (m³).
According to the given information:
As, we know that volume of cuboid is = length x breath x height
Here, length = 5 feet, breath = 3 feet and height = 1.5 feet
Volume of the aquarium = 5 x 3 x 1.5 = [tex]22.5ft^{3}[/tex]
So, the given result is [tex]22.5ft^{3}[/tex]
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The solids are similar.
Find the surface area of
solid B to the nearest
hundredth.
Cylinder A
24 mm
S = 594 mm²
Cylinder B
16 mm
The surface area of solid B is
square millimeters.
Answer:
264π
Step-by-step explanation: