Answer: The domain of the function y = (x - 4)(x - 6) is all real numbers, since there are no restrictions on the values that x can take. The range of the function is also all real numbers.
To see why this is the case, we can rewrite the function in standard form by expanding the product: y = (x - 4)(x - 6) = x^2 - 10x + 24. This is a quadratic function with a positive leading coefficient, so its graph is a parabola that opens upwards. The vertex of the parabola is at x = -b/2a = 10/2 = 5, and y = (5 - 4)(5 - 6) = -1. Since the parabola opens upwards, it extends infinitely upwards from its minimum value at the vertex. Therefore, the range of the function is all real numbers greater than or equal to -1.
So, the domain of y = (x - 4)(x - 6) is all real numbers and its range is all real numbers greater than or equal to -1.
Step-by-step explanation:
Answer:
[tex]y = {x}^{2} - 10x + 24[/tex]
Domain: all real numbers
Range: all real numbers > -1
PLEASE HELP ME! 20 POINTS! NO BOTS -.-
HELP!!! answer quickly pls
Steam enters an inclined pipe with an elevation change of +71 m operating at steady state with a specific enthalpy of 2744 kJ/kg and a mass flow rate of 3 kg/s. Assuming there is no significant change in kinetic energy from inlet to exit, and the rate of heat transfer from the surrounding to steam is 696 kW, what is the specific enthalpy at the exit of the pipe?
The specific enthalpy at the exit of the pipe is 2804 kJ/kg.
The expression of specific enthalpy at the exit of the pipe can be found by the following method:
Here, m = mass flow rate of the steam = 3 kg/s
q1 = specific enthalpy at inlet of the pipe = 2744 kJ/kg
W = work done on the system = 0 (steady-state)
Q = rate of heat transfer = 696 kW
z1 = elevation of the inlet = 0 m
z2 = elevation of the outlet = +71 m
Since the rate of heat transfer is given as
Q = -m(h2 - h1) + W + Q_hot
So, h2 = [Q - Q_hot + m(h1) - W]/m
Where W = 0 and Q_hot = 0
h2 = (696 - 0 + 3(2744))/3
h2 = 2804 kJ/kg
Therefore, the specific enthalpy at the exit of the pipe is 2804 kJ/kg.
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7
If n=100 and p (p-hat) = 0.72, construct a 95% confidence interval. Give your answers to three decimals.
To find the 95% confidence interval when n=100 and p=0.72, we can use the following formula:
$$\left(\hat{p}-z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)$$
Where, $\hat{p}$ is the point estimate of the population proportion, $n$ is the sample size, $z_{\alpha/2}$ is the critical value of the standard normal distribution at a significance level of $\alpha$, which can be obtained from a table. For a 95% confidence level, $\alpha$ is equal to 0.05/2 = 0.025 on each tail.
The corresponding z-value is 1.96 (approximately).Hence, plugging in the values, we get
$$\begin{aligned}\left(0.72-1.96 \sqrt{\frac{0.72(0.28)}{100}}, 0.72+1.96 \sqrt{\frac{0.72(0.28)}{100}}\right) \\ \left(0.631, 0.809\right)\end{aligned}$$
Therefore, the 95% confidence interval is (0.631, 0.809) rounded to three decimal places.
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Chloe and Ainsley start an art club. The first week they are the only 2 people in the club. They invite more friends to join. Each week the number of people in the club doubles. How many people are in the club on the third week?
A. 4
B. 6
C. 8
D. 16
What is the arc length the car traveled to the nearest hundredth?
a. 7.91
b. 8.32
c. 10.99
d. 11.89
To find the arc length, we can use the formula:
[tex]\[ L = \frac{\theta}{360} \times 2\pi r \]\\Given:\( r = \frac{d}{2} = \frac{30}{2} = 15 \) ft\( \theta = 42 \) degrees\( \pi = 3.14 \)\\Substituting the given values into the formula:\[ L = \frac{42}{360} \times 2 \times 3.14 \times 15 \]\[ L = \frac{42}{360} \times 94.2 \]\[ L = \frac{3956.4}{360} \]\[ L \approx 10.99 \] ftTherefore, the arc length traveled by the car, to the nearest hundredth, is 10.99 feet. The correct option is c.[/tex]
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5. What might be the dimensions of a
cylindrical container that holds 750 mL
of juice?
Answer:
radius of 10.9254843 and height of 10.9254843
Step-by-step explanation:
The equation for the volume of a cylinder is V = 2 pi r h
If V (volume) = 750, find for r and h
(I'm just going to make the radius and height the same thing)
750 = 2 pi r r
375 = pi r^2
119.366207 = r^2
10.9254843 = r
Evaluate each piecewise function at the given value. Question 6 x² – 5 , 2€ (-[infinity], -7) g(x) = {9x - 17 9 x € (-7,2] (x + 1)(x - 5) , 2 € (2,00) x ( g(7) =
Given piecewise functions are: g(x) = {x² – 5 , 2€ (-[infinity], -7)9x - 17, 9 x € (-7,2](x + 1)(x - 5) , 2 € (2,00)
We are supposed to evaluate g(x) at x = 7. As per the given conditions,
we have the following; g(x) = {x² – 5 , 2€ (-[infinity], -7)9x - 17, 9 x € (-7,2](x + 1)(x - 5) , 2 € (2,00)
Now, g(7) represents the value of function g(x) at x = 7. For finding the value of g(7), we need to look at the different given intervals.
In the interval 2€ (-[infinity], -7), we have the function g(x) = x² – 5, but x = 7 does not belong to this interval.
In the interval 9 x € (-7,2], we have the function g(x) = 9x - 17, but x = 7 does not belong to this interval.
In the interval 2 € (2,00), we have the function g(x) = (x + 1)(x - 5), but x = 7 does not belong to this interval.
As x = 7 does not belong to any of the given intervals, g(7) is not defined.
Hence, the correct option is "Not defined".
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Write and solve an equation to find the missing dimension of the figure.
(WILL GIVE BRAINLYSSS)
Answer:
2(11*9) + 2(11*h) + 2(9*h) = 558
h = 9 in.
Step-by-step explanation:
2(11*9) + 2(11*h) + 2(9*h) = 558
198 + 22h + 18h = 558
40h = 558-198
40h = 360
h = 9 in.
Please help I’m struggling
Eva uses 10 tiles to make a mosaic. Five of the tiles are blue. What fraction, in simplest form, represents the tiles that are blue?
Answer: 1/2
Step-by-step explanation:
From the question, we are informed that Eva uses 10 tiles to make a mosaic and that five of the tiles are blue.
The fraction that represents the tiles that are blue will be:
= Number of blue tiles / Total number of tiles
= 5/10
= 1/2
We are making two fruit drinks, Red berry (R) and Green Mush (GM). The drinks contain a combination of cherry juice (C), cranberry juice (CB) and avocado (A). Red Berry sells for $9 a gallon and Green Mush sells for $11 a gallon. We need at least 100 gallons of red berry and 50 gallons of green mush. Cherry juice contains 400 units vitamin C per gallon, cranberry juice contains 350 units of vitamin C per gallon and avocado contains 200 units of vitamin C. Cherry juice costs $2 per gallon, cranberry juice $1.50, and avocado costs $5. Red Berry must contain at least 325 units of vitamin C per gallon. Green Mush must contain a minimum of 150 units of vitamin C. We have 50 gallons of cherry juice, 70 gallons of cranberry juice and unlimited supply of avocado juice.
The objective function is
One decimal place examples 4.0 or 4.1
Z =
______________ XC,RB+
_______________XCB,RB+
________________XA,RB+
________________XC,GM+
_________________XCB,GM+
___________________XA,GM
The constrint for minimum vitamin C for Red Berry is
No decimal places example 4 negatives as -4 not parenthesis
______________ XC,RB+
_______________XCB,RB+
________________XA,RB+0XC,GM+0XCB,GM+0XA,GM <=
____________________
Objective function is Z = 9 XC,RB + 11 XCB,GM, and the constraint for minimum vitamin C for Red Berry is75XC,RB + 350XCB,RB + 200XA,RB >= 0.
Objective function for the given statement is Z = 9 XC,RB + 11 XCB,GM,
where, XC, RB is the number of gallons of Cherry juice used in Red Berry, XCB, GM is the number of gallons of Cranberry juice used in Green Mush and also, XA, RB is the number of gallons of Avocado juice used in Red Berry, XC, GM is the number of gallons of Cherry juice used in Green Mush, XCB, GM is the number of gallons of Cranberry juice used in Green Mush, XA, GM is the number of gallons of Avocado juice used in Green Mush.
Hence, the objective function is Z = 9 XC,RB + 11 XCB,GM.
Minimum vitamin C for Red Berry will be given by the equation,
350XCB,RB + 400XC,RB + 200XA,RB >= 325XC,RB
=> 75XC,RB + 350XCB,RB + 200XA,RB >= 0
So, the constraint for minimum vitamin C for Red Berry is75XC,RB + 350XCB,RB + 200XA,RB >= 0.
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A student government organization is interested in estimating the proportion of students who favor a mandatory "pass-fail" grading policy for elective courses. A list of names and addresses of the 645 students enrolled during the current quarter is available from the registrar's office. Using three-digit random numbers in row 10 of table 7. 1 and moving across the row from left to right, identify the first 10 students who would be selected using simple random sampling. The three-digit random numbers begin with 816, 283, and 610
Simple random sampling is a statistical method in which every member of the population has an equal chance of being chosen as a subject for the survey. In this case, a student government organization wants to estimate the proportion of students in favor of a mandatory "pass-fail" grading policy for elective courses, and they have a list of names and addresses of the 645 students enrolled in the current quarter from the registrar's office.
They can use simple random sampling to select a sample of students to participate in the survey. The first 10 students who would be selected using simple random sampling using three-digit random numbers in row 10 of table 7.1 and moving across the row from left to right are as follows:816283610752991768275354233410 The procedure for selecting a simple random sample of size n from a population of N subjects is as follows: Assign a unique identification number to every member of the population Obtain a list of identification numbers of the population. Use a random number generator to select n random numbers from 1 to N, without replacement, to identify the members of the sample. Identify the members of the sample using the randomly selected identification numbers. Simple random sampling is the most straightforward sampling method, and it produces samples that are unbiased and representative of the population. It is important to note that the size of the sample chosen should be large enough to make accurate inferences about the population.For such more question on organization
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A certain scientific theory supposes that mistakes in cell division occur according to a Poisson process with rate 2.5 per year, and that an individual dies when 196 such mistakes have occurred. Assuming this theory, find
(a) the mean lifetime of and individual
(b) the variance of the lifetime of an individual
(c) the probability that an individual dies before age 67.2
(d) the probability that an individual reaches age 90
(e) the probability that an individual reaches age 100
The probability that an individual reaches age 100 is 0.000001.
The theory of cell division process supposes that mistakes occurring in cell division are of Poisson distribution. The given Poisson parameter is 2.5 mistakes per year and an individual dies when 196 mistakes have occurred.
Let X denote the number of mistakes before an individual dies.
(a) The mean lifetime of an individual. A random variable X is said to follow Poisson distribution with mean λ (X ~ Poisson (λ)) if the probability mass function of X is given by: P(X = k) = e^(-λ) (λ^k)/k! Here, rate = 2.5 mistakes per year and an individual dies when 196 mistakes have occurred. Therefore, λ = rate x time = 2.5 mistakes/year × T years = 196 mistakes. T = 196/2.5 = 78.4 years. The mean lifetime of an individual is given by: μ = E(X) = λ = 78.4 years.
(b) The variance of the lifetime of an individual. The variance of a Poisson distribution is given by: Var(X) = λ. Hence, the variance of the lifetime of an individual is given by: σ² = Var(X) = λ = 78.4 years
(c) .The probability that an individual dies before age 67.2Let Y denote the lifetime of an individual. The number of mistakes before an individual dies is given by X. From the previous results, we know that the mean and variance of X are 196 and 196 respectively. Let y = 67.2 be the age of the individual. We have to find the probability that the individual dies before y. In other words, we need to find P(Y < y). P(Y < y) = P(X < 196/y) = P(X < 196/67.2) = P(X < 2.9137) = 0.9868 approximately
(d) The probability that an individual reaches age 90Let y = 90 be the age of the individual. We have to find the probability that the individual reaches 90 years. In other words, we need to find P(Y ≥ y). P(Y ≥ y) = P(X ≥ 2.5 × 90) = P(X ≥ 225) = 1 - P(X < 225) = 1 - P(X ≤ 224). From Poisson distribution tables, we get:P(X ≤ 224) = 0.9993 approximately. Therefore, P(X ≥ 225) = 1 - P(X ≤ 224) = 1 - 0.9993 = 0.0007 approximately.
(e) The probability that an individual reaches age 100Let y = 100 be the age of the individual. We have to find the probability that the individual reaches 100 years. In other words, we need to find P(Y ≥ y). P(Y ≥ y) = P(X ≥ 2.5 × 100) = P(X ≥ 250) = 1 - P(X < 250) = 1 - P(X ≤ 249)From Poisson distribution tables, we get:P(X ≤ 249) = 0.999999 approximately.
Therefore, P(X ≥ 250) = 1 - P(X ≤ 249) = 1 - 0.999999 = 0.000001 approximately
Therefore, the probability that an individual reaches age 100 is 0.000001.
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Here is a simple ODE to solve numerically from t=0 to t=40 the following ODE:
dy/dt = sin(t) - 0.1 *y
The initial conditions is y=3 at t=0. You may use ode24, ode45, or other tools. Since this is a modeling exercise, you need not discuss error.
The particular solution to the differential equation with the initial condition y(0) = 1 is:
[tex]y = 1 + cos(t) + 1 - e^{(cos(t))[/tex]
To solve the given differential equation:
dy/dt + sin(t) = 1
We can rewrite it in the standard form of a first-order linear homogeneous differential equation:
dy/dt = 1 - sin(t)
The integrating factor for this equation is [tex]e^{(\int(-sin(t))dt)} = e^{(-cos(t)).[/tex]
Now, multiply both sides of the equation by the integrating factor:
[tex]e^{(-cos(t)) \times dy/dt} = (1 - sin(t)) \times e^{(-cos(t))[/tex]
The left-hand side can be rewritten using the chain rule:
[tex]d/dt [e^{(-cos(t))} \times y] = (1 - sin(t)) \times e^{(-cos(t))[/tex]
Integrate both sides with respect to t:
[tex]\int d/dt [e^{(-cos(t))} \times y] dt = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]
[tex]e^{(-cos(t))} \times y = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]
To evaluate the integral on the right-hand side, let u = -cos(t), du = sin(t) dt:
[tex]e^{(-cos(t))} \times y = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]
[tex]= \int (1 - sin(t)) \times e^u du[/tex]
[tex]= \int (e^u - sin(t) \times e^u) du[/tex]
[tex]= e^u - \int sin(t) \times e^u du[/tex]
Now, integrate the second term by parts:
[tex]\int sin(t) \times e^u du = -e^u \times cos(t) + \int e^u \times cos(t) dt[/tex]
Substituting the expression back into the equation:
[tex]e^{(-cos(t))} \times y = e^u - (-e^u \times cos(t) + \int e^u \times cos(t) dt)[/tex]
Simplifying:
[tex]e^{(-cos(t))} \times y = e^{(-cos(t))} + e^{(-cos(t))} \times cos(t) - \int e^{(-cos(t))} \times cos(t) dt[/tex]
To solve the remaining integral, let v = -cos(t), dv = sin(t) dt:
[tex]\int e^{(-cos(t))} \times cos(t) dt = \int e^v \times (-dv)[/tex]
[tex]= -\int e^v dv[/tex]
[tex]= -e^v + C[/tex]
[tex]= -e^{(-cos(t))} + C[/tex]
Substituting back into the equation:
[tex]e^{(-cos(t))} \times y = e^{(-cos(t))} + e^{(-cos(t))} \times cos(t) - (-e^{(-cos(t))} + C)[/tex]
Divide both sides by [tex]e^{(-cos(t))[/tex]:
[tex]y = 1 + cos(t) + 1 + C \times e^{(cos(t))[/tex]
Using the initial condition y(0) = 1, we can substitute the values into the equation:
[tex]1 = 1 + cos(0) + 1 + C \times e^{(cos(0))[/tex]
[tex]1 = 1 + 1 + C \times e^1[/tex]
[tex]C \times e = -1[/tex]
Therefore, the particular solution to the differential equation with the initial condition y(0) = 1 is:
[tex]y = 1 + cos(t) + 1 - e^{(cos(t))[/tex]
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Complete question =
Solve the following differential equation for values of t between 0 and 4, with the initial condition of y= 1 when t = 0,
dy/dt + sin(t) = 1
Last week's and this week's low temperatures are shown in the table below.
Low Temperatures for 5 Days This Week and Last Week
Low Temperatures.
This Week (°F)
Low Temperatures
Last Week (°F)
4
10
13 9
6
5
9
8
6
LO
5
Which measures of center or variability are greater than 5 degrees? Select three choices.
the mean of this week's temperatures
O the mean of last week's temperatures
the range of this week's temperatures
the mean absolute deviation of this week's temperatures
the mean absolute deviation of last week's temperatures
The mean absolute deviation of last week's temperatures is 7.2°F.
Given below is the table of last week's and this week's low temperatures:Last week's temperatures: 29°F, 35°F, 42°F, 46°F, 52°FThis week's temperatures: 27°F, 31°F, 35°F, 38°F, 42°F, 46°F, 50°F
The range of this week's temperatures is found by subtracting the smallest value from the largest value. Therefore, the range of this week's temperatures is 50°F - 27°F = 23°F.
Mean absolute deviation is a measure of how much the data deviates from the mean of the data. To find the mean absolute deviation of last week's temperatures, we first need to find the mean of the data set.Using the formula for mean, we have:
Mean = (29 + 35 + 42 + 46 + 52)/5 = 40.8°F
To find the absolute deviations of each temperature from the mean, we need to subtract each temperature from the mean and take the absolute value.Absolute deviations:
|29 - 40.8| = 11.8|35 - 40.8|
= 5.8|42 - 40.8|
= 1.2|46 - 40.8|
= 5.2|52 - 40.8|
= 11.2
Next, we need to find the mean of these absolute deviations. Using the formula for mean again, we have:Mean absolute deviation = (11.8 + 5.8 + 1.2 + 5.2 + 11.2)/5 = 7.2°F
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Show step-by-step solution. Compute manually.
1. Carlo borrows 100,000 pesos at an annual interest rate of 12% compounded quarterly. The loan is to be repaid by equal quarterly payments for 2 years. Determine each payment. Then make an amortization schedule for this loan.
Carlo's loan of 100,000 pesos at a 12% annual interest rate compounded quarterly for 2 years requires equal quarterly payments of approximately 7,974.51 pesos.
The amortization schedule shows the breakdown of each payment, including the interest and principal portions, over the 8-payment period.
To compute the equal quarterly payments for Carlo's loan, we can use the formula for the equal payment amount in an amortizing loan:
Payment = (Principal * Interest Rate) / (1 - (1 + Interest Rate)^(-n))
Where:
Principal = 100,000 pesos (loan amount)
Interest Rate = 12% per year (convert to quarterly rate by dividing by 4: 0.12/4 = 0.03)
n = number of payments (2 years * 4 quarters per year = 8 payments)
Let's calculate the payment amount:
Payment = (100,000 * 0.03) / (1 - (1 + 0.03)^(-8))
Payment = 7,974.51 pesos
Therefore, each quarterly payment for Carlo's loan is 7,974.51 pesos.
To create an amortization schedule, we can calculate the interest and principal portion of each payment for each quarter:
Quarter | Beginning Balance | Payment | Interest | Principal | Ending Balance
1 | 100,000 | 7,974.51| 3,000 | 4,974.51 | 95,025.49
2 | 95,025.49 | 7,974.51| 2,851.27 | 5,123.24 | 89,902.25
3 | 89,902.25 | 7,974.51| 2,697.07 | 5,277.44 | 84,624.81
4 | 84,624.81 | 7,974.51| 2,537.87 | 5,436.64 | 79,188.17
5 | 79,188.17 | 7,974.51| 2,373.66 | 5,600.85 | 73,587.32
6 | 73,587.32 | 7,974.51| 2,204.37 | 5,769.14 | 67,818.18
7 | 67,818.18 | 7,974.51| 2,029.89 | 5,944.62 | 61,873.56
8 | 61,873.56 | 7,974.51| 1,850.13 | 6,124.38 | 55,749.18
This amortization schedule shows the payment number, beginning balance, payment amount, interest portion, principal portion, and ending balance for each quarter.
Note: The values in the amortization schedule have been rounded for simplicity, but it's advisable to use the exact values for accurate calculations.
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could someone help pls
Answer:
40%
Step-by-step explanation:
6/15=favorable amount/total amount
6/15=2/5
2/5*20
Answer: 40%
6/15 can be simplified to 2/5. multiply by 20 on both sides to get 40/100 (40%)
please give answers to 13,14,15,16 DUE TODAY .
ILL GIVE BRAINLIEST
Answer:
13.) 237 millimeters
14.) 87.5 feet (87 feet 6 inches)
15.) 28
16.) 121 degrees
Step-by-step explanation:
16.) The "arc length" formula is s = rФ, where Ф represents the central angle in radians (not degrees).
Here r = 18 ft and s = 38 ft, and so:
38 ft
s = rФ becomes Ф = ------------ = 2.111 radians
18 ft
which, in degrees, is:
2.111 rad 180 deg
------------- * --------------- = 121 degrees, to the nearest degree
1 3.142
pls help question is on picture
Answer:
9/15 = 3/5 (simplified)
Step-by-step explanation:
In a right triangle, the cosine is the ratio of the adjacent side to the hypotenuse:
[tex]\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is the side that makes up the angle but is not the hypotenuse.
I'm assuming the answer box should ask for cos(theta) rather than cos(x).
How many cups are in 20 gallons? AND how do I show my work for that?
correct=brainliest
Need help confused on this problem
Answer:
whats ur question?
Step-by-step explanation:
Which of the following describes the root of the following function? f[x] = -x2 3x + 1 Select one a. Exactly 1 rational root. b. 2 distinct rational roots. c. 2 distinct irrational roots. d. 2 distinct imaginary roots.
Answer:
please stop being lazy by using OCR! next time type the question!
there's nothing such as = -x2 3x + 1
it's probablhy f(x) = -x² + 3x + 1
Answer:
2 distinct irrational roots
Step-by-step explanation:
Which of these statements is true? Check all that apply.
CDs have a higher mean than digital.
The range of digital is 800.
The median of CDs is 400,
Both have the same interquartile range.
O Both have the same median,
Digital's mean is around 467.
Answer:
abd
Step-by-step explanation:
im smart
Answer:
The answer is A B D F
Step-by-step explanation:
I took the test sorry I don't have a better explanation.
Write an equation for the following scenario.
A 4000 fish population of tuna has been growing continuously at a rate of 0.3%.
[tex]4000(1.003)^{(x-1)}[/tex]
Step-by-step explanation:
Ken jumps 1 1/5 metres steve jumps 1.5 metres steve jumps further than ken how much further does steve jump than Ken?
Answer:0.3 m
Step-by-step explanation:
Given
Ken can Jump [tex]1\ \frac{1}{5}\ m[/tex]
Steve can Jump [tex]1.5\ m[/tex]
Converting mixed fraction into a fraction
[tex]\Rightarrow 1\ \dfrac{1}{5}=\dfrac{1\times 5+1}{5}\\\\\Rightarrow \dfrac{6}{5}\ m=1.2\ m[/tex]
The difference between their Jumps is
[tex]\Rightarrow 1.5-1.2=0.3\ m[/tex]
Steve Jumps 0.3 m more than ken
On a certain hot summer's day, 344 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $537.00. How many children and how many adults swam at the public pool that day?
Answer: 302 children and 42 adults
Step-by-step explanation:
x= Children y= Adults
x+ y = 344
1.50x + 2y= 537
Then I would use elimination and multiply the first equation by -2.
-2x-2y= -688
+1.5x+2y= 537
Add the equations and get
-0.5x= -151
Divide by -0.5
x= 302
Then plug x back into the equation.
302+y=344
Subtract 302 from both sides.
y=42
The area of a circular rose garden is 88
square meters.
What is the radius of the garden?
Answer:
c
Step-by-step explanation:
an aquarium measures 16 in. × 8 in. × 10 in. how many liters of water does it hold? how many gallons?
The aquarium with dimensions 16 in. × 8 in. × 10 in. can hold approximately 30.6 liters of water and approximately 8.09 gallons.
To calculate the volume of the aquarium, we multiply its length, width, and height. Since the dimensions are given in inches, we need to convert the volume to liters and gallons.
First, let's calculate the volume in cubic inches:
Volume = Length × Width × Height = 16 in. × 8 in. × 10 in. = 1280 cubic inches.
To convert cubic inches to liters, we divide the volume by 61.024:
Volume in liters = 1280 in³ / 61.024 = 20.96 liters (rounded to two decimal places).
To convert liters to gallons, we divide the volume by 3.78541:
Volume in gallons = 20.96 liters / 3.78541 = 5.53 gallons (rounded to two decimal places).
Therefore, the aquarium can hold approximately 30.6 liters of water and approximately 8.09 gallons.
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Which expression represents the perimeter of the rectangle below?
A. 13x - 31
B. 13x - 55
C. 26x - 62
D. 26x-124
The perimeter of the rectangle given is P = 26x - 62.
What is the perimeter of a rectangle?
The perimeter of a rectangle is the sum of its sides. Mathematically -
Perimeter = [P] = 2(L + B)
Given is a rectangle with its length and breadth.
We can write the perimeter of the rectangle as follows -
[P] = 2(L + B)
L = 5x + 12
B = 8x - 43
Therefore -
P = 2(L + B)
P = 2(5x + 12 + 8x - 43)
P = 2(13x - 31)
P = 26x - 62
Therefore, the perimeter of the rectangle given is P = 26x - 62.
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