Answer:
\(2^3 (3 x 5^2 + 2^2) = 600x+32 \) is the correct equation
Step-by-step explanation:
\(2^3 (3 x 5^2 + 2^2) = 600x+32\\ 2^4 (3 x 5^5 +2^2)= 150000x+64\\ 2^3 (3 x 5^2 +2^5) = 600x+256\\ 2^4 (3 x 5^5 +2^1^6)= 150000x+1048576\)
Hope this helps! Brainliest would be much appreciated!
Have a great day! : )
I WILL MARK BRAINLIEST IF ANSWER IN LESS THAN 5 MINUTES!!!!!!! tory is buying bananas. she has 15 dollars and bananas are 2.45 each. how many bananas can she buy?
Answer:
6 bananas
Step-by-step explanation:
Divide the dollars by the price for bananas
15/2.45
6.12244898
Round down because she cannot buy part of a banana
6 bananas
Guys can you please help. I dont understand. Thank you. :))))
Lines AB and CD intersect at E. If the measure of angle AEC=5x-20 and the measure of angle BED=x+50, find, in degrees, the measure of angle CEB.
Answer: 112.5
Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.
Which of the following are solutions to the inequality
below?
t>7
t = 6
t = 7
t = 8
t = -7
A. t= 6
B. t= 7
C. t=8
D. t= -7
Answer:
t > 7 or t is greater than 7, so the answer is C. t = 8 because 8 is greater than 7. :)
f the current population size is x individuals, what fraction of the resources are they using collectively?
The fraction of resources used collectively by X individuals can be represented as X/R, where R represents the total resources available. The fraction of resources not being used is represented as (R-X)/R. The per-capita growth rate can be represented as dX/dt = kX, where k is the proportionality constant. The differential equation for the population's size is dX/dt = kX.
A detailed explanation:
a) If the current population size is X individuals, then the fraction of resources they are using collectively can be calculated as X/R, where R represents the total resources available. This calculation gives us the proportion of resources used by X individuals relative to the total resources available.
b) To calculate the fraction of resources not being used, we subtract the fraction of resources used by X individuals from 1. So, the fraction of resources not being used is (R-X)/R.
c) The per-capita rate of change of X can be represented as dX/dt = kX, where k is the proportionality constant. This equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k.
d) To convert the equation into a differential equation for the population's size, we simply make X' stand alone on the left-hand side of the equation. So, the differential equation for the population's size becomes dX/dt = kX.
e) This differential equation states that the rate of change of X (dX/dt) is proportional to X and the constant of proportionality is k. This equation can be used to model the growth of a population over time and to understand the relationship between the population size and the rate of change of the population.
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Complete questin:
If the current population size is X individuals, what fraction of the resources are they using collectively? c) In the same situation, what fraction of the resources are not being used? d) The per-capita rate of change of X can be written as 7%. The key assumption mentioned above says that this quantity is pro- portional to the expression you wrote down in part (c). Call the proportionality constant 1', and write an equation for the per-capita growth rate. e) Convert this equation into a differential equation (change equa- tion) for the population's size. (Just make X' stand alone on the left-hand side of the equation.)
Aluminum can have a capacity of 2.32 L. How many milliliters of soup can it hold? Helpfull tip (1 L = 1,000 mL)
Answer:
2320 mLStep-by-step explanation:
Convert the volume from L to mL according to capacity of the can.
2.32 L = 2.32 * 1000 mL = 2320 mLAnswer:
2320 milliliters
Step-by-step explanation:
1 liter = 1000 milliliters
If the can has a capacity of 2.32 liters, then to calculate how many milliliters it can hold, we need to multiply it by 1000:
⇒ 2.32 liters = 2.32 × 1000
= 2320 milliliters
**To multiply a number by 1000, simply move the decimal point 3 places to the right**
An exponential function is represented in the table below.
Which equation best represents the function?
A. f(x)=3(2⁻ˣ)
B. f(x)=3(2ˣ)
C. f(x)=2⁻ˣ+3
D. f(x)=2ˣ+3
The equation that best represents the exponential function in the table is B. f(x) = 3(2ˣ).
To determine the equation that represents the exponential function in the table, we need to analyze the relationship between the input values (x) and the corresponding output values (f(x)).
Looking at the table, we observe that as the value of x increases, the corresponding value of f(x) also increases. This indicates exponential growth. Additionally, we can see that when x increases by 1, f(x) multiplies by a constant factor of 2.
In option B, the equation f(x) = 3(2ˣ) represents exponential growth with a base of 2. The coefficient 3 represents a vertical scaling factor that stretches or compresses the graph vertically. This equation aligns with the given table, where the output values are three times the corresponding values of 2ˣ.
Options A, C, and D do not accurately represent the given table. Option A, f(x) = 3(2⁻ˣ), represents exponential decay, not growth. Option C, f(x) = 2⁻ˣ + 3, represents an exponential term with a negative exponent, which is not observed in the table. Option D, f(x) = 2ˣ + 3, represents exponential growth with a base of 2, but the absence of the coefficient 3 does not match the given table.
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what is (fxg)(x)
f(x)=x^3-4x+2
g(x)=x^2+2
Answer: x^6+6x^4+8x^2+2
Step-by-step explanation:
Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in
(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2
help please!!!!!!!!!!!!!!!!!
The solution of the equation, (x + 5)² = 9 is x = -2 or x - 8.
How to solve an equation?The equation (x + 5)² = 9 can be solved as follows:
Therefore, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore, let's solve for the variable x in the equation. A variable is a number represented by a letter in an equation.
Hence,
(x + 5)² = 9
(x + 5)(x + 5) = 9
x² + 5x + 5x + 25 = 9
x² + 10x + 25 = 9
x² + 10x + 25 - 9 = 0
x² + 10x + 16 = 0
x² + 2x + 8x + 16 = 0
x(x + 2) + 8(x + 2) = 0
(x + 2)(x + 8) = 0
Therefore,
x = - 2 or x = -8
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Each boldface number is the value of either a parameter or a statistic. In each case, state which it is. In an experiment to test the effectiveness of single -sex classrooms, girls assigned at random to a coeducational chemistry class gained an average of 12.2 points from a pretest to a posttest. Girls assigned randomly to a single-sex chemistry class taught by the same teacher gained 15.1 points.
We are comparing the average gain in test scores for two different groups of girls - those assigned to coeducational chemistry classes and those assigned to single-sex chemistry classes. Since these gains are calculated from the data obtained from these specific groups of girls, they represent statistics rather than parameters.
In the given scenario:
The boldface number "12.2" represents a statistic.
The boldface number "15.1" represents a statistic.
A statistic is a numerical value that summarizes a sample of data, while a parameter is a numerical value that summarizes a population.
In this case, we are comparing the average gain in test scores for two different groups of girls - those assigned to coeducational chemistry classes and those assigned to single-sex chemistry classes. Since these gains are calculated from the data obtained from these specific groups of girls, they represent statistics rather than parameters.
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At the football game they sold $4 pizzas and $2 sodas which made the school$260 the number of Sodas sold was five more than three times a number of pizzas sold determine the amount of pizza and sodad sold
\(\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}\)
\(\Huge \textsf{Step-by-step explanation}\)
\(\LARGE \bold{\textsf{Step 1: Assign Variables}}\)
\(\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}\)
\(\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}\)
\(\large \bold{ \textsf{From the problem, we know that:}}\)
\(\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}\)
\(\large \bold{ \textsf{We can use this information to write two equations:}}\)
\(\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}\)
\(\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}\)
\(\LARGE \bold{\textsf{Step 3: Solve the system of equations}}\)
\(\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}\)
\(\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}\)
\(\large \textsf{Simplifying this expression gives us:}\)
\(\textsf{10\textit{p} + 10 = 260}\)
\(\large \textsf{Subtracting 10 from both sides:}\)
\(\textsf{10\textit{p} = 250}\)
\(\large \textsf{Dividing both sides by 10}\)
\(\textsf{\textit{p} = 25}\)
\(\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}\)
\(\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}\)
\(\large \textsf{So, 25 pizzas and 80 sodas were sold.}\)
----------------------------------------------------------------------------------------------------------
in the eai sampling problem, the population mean is 51800 and the population standard deviation is 4000 . when the sample size is 64 , what is the probability of obtaining a sample mean within 500 of the population mean.
the probability of obtaining a sample mean within 500 of the population mean is approximately 0.6827.
To solve this problem, we need to use the central limit theorem which states that the distribution of the sample means will be approximately normal with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
Given that the population mean is 51800 and the population standard deviation is 4000, we can calculate the standard error of the mean as follows:
Standard error of the mean = 4000 / sqrt(64) = 500
We want to find the probability of obtaining a sample mean within 500 of the population mean. This can be written as:
P(51800 - 500 < X < 51800 + 500)
where X is the sample mean.
We can standardize this interval using the standard error of the mean:
P(-1 < Z < 1)
where Z is a standard normal variable.
Using a standard normal table, we find that the probability of Z being between -1 and 1 is approximately 0.6827.
Therefore, the probability of obtaining a sample mean within 500 of the population mean is approximately 0.6827.
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What is the capital of California? explain where this city is located and when it was founded
Answer:
The capital of California is Sacramento (I cannot really give a paragraph for you but I can provide information.
- Located in the north-central part of the state
- Found on 9 September 1850
Step-by-step explanation:
25 added to the difference between Y and 7
Answer:
(y-7) +25
Step-by-step explanation:
( y-7 ) +25
25 is added after the difference. so that's only the answer.
Find out the relation between faces,edges and vertices.form an equation using the variables as faces,edges and vertices.
solve the equation manually and by using artificial inteligence tool and check whether equation is satisfying in all solids or not.
The relation between faces, edges, and vertices can be determined by Euler’s Formula which is F + V - E = 2
Also, the equation is satisfying for the solid Octagonal prism
Faces: It is denoted by 'F'
A face of a figure can be defined as the individual flat surfaces of a solid object.
Vertices: It is denoted by 'V'
A point where two or more line segments meet is known as a vertex.
The plural of vertex is vertices. In simpler words, we can say that a vertex is a corner.
Edges: It is denoted by 'E'
An edge in a shape can be defined as a point where two faces meet.
The line segments that form the skeleton of the 3D shapes are known as edges.
Relation between faces, edges, and vertices can be determined by using Euler’s Formula.
Euler’s Formula for faces, edges, and vertices is F + V - E = 2
Let's consider the solid shape of an Octagonal prism.
The number of faces in an Octagonal prism is 10
The number of edges in an Octagonal prism is 24
Number of vertices in an Octagonal prism is 16
Euler’s Formula: F + V - E = 2
10 + 16 - 24 = 2
26 - 24 = 2
2 = 2
The equation is satisfying for the solid Octagonal prism.
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a number s is at least -2 or less than -6
Answer:
-6<x<-2
Step-by-step explanation:
. If Ya/n and Y2/n are the respective independent relative frequencies of success associated with the two binomial distributions b(n, P1) and b(n, P2), compute n such that the approximate probability that the random
interval (Y1/n - Y2/n) ‡ 0.05 covers pi - p2 is at least 0.80. HINT: Take p* = P° = 1/2 to provide an upper bound
for n.
we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.
To compute n, we can use the formula:
n = ((zα/2)^2 * 2p*(1-p*)) / (ε^2)
Where zα/2 is the z-score associated with a confidence level of 1-α, p* is the probability of success for a binomial distribution, and ε is the margin of error.
Since we are given that the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 is at least 0.80, we can set α = 0.20 to find the corresponding z-score of 1.28.
Using p* = 1/2 as an upper bound for both P1 and P2, we can calculate the margin of error as:
ε = zα/2 * sqrt((p*(1-p*)) / n)
Plugging in the values, we get:
0.05 = 1.28 * sqrt((0.25) / n)
Solving for n, we get:
n = 501.76
Therefore, we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.
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An amusement park sold 42 discount tickets and 18 full-price tickets. What percentage of the tickets sold were discount tickets?
Answer:
43%
Step-by-step explanation:
18/42 ≈ 43%
The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list. 9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58 one of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1. 5×iqr rule for outliers, is there evidence to support the student’s claim?.
Based on the 1.5 × IQR rule for outliers, there is no evidence to support the student's claim because there is only one outlier at 58 minutes.
What is an interquartile range of the data?The interquartile range is the difference between upper and lower quartiles. The semi-interquartile range is half the interquartile range. When the data set is small, it is simple to identify the values of quartiles.
Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):
IQR = Q₃ - Q₁
The following interquartile ranges was calculated by using Excel:
Q₃ = 31.5
Q₁ = 20.5
Now, the interquartile range (IQR) is given by:
IQR = Q₃ - Q₁
IQR = 31.5 - 20.5
IQR = 11
Based on the 1.5 × IQR rule for outliers, we have:
1.5 × IQR = 1.5 × 11 = 16.5
Therefore, our fences will be 16.5 points below Q₁ and 16.5 points above Q₃:
Lower fence = 20.5 - 16.5 = 4.5
Upper fence = 4.5 + 31.5 = 36.
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at is the volume of this triangular prism? 7m, 24m, 22m
Answer:
3,696
Step-by-step explanation:
7x24x22 equals 3,696
24x7=168
168x22=3,696
10. Multiply the following numbers using scientific notation. show the steps. (See Ex. 5)
(2 x 103)(3 x 104).
11. Divide the following numbers using scientific notation. Show the steps as they are done in the lesson. (See Ex. 6)
-42 x 102
14 x 103
Answer:
10) 6 × 10⁷
11) -3 × 10⁻¹
Step-by-step explanation:
Assuming that (2 x 103)(3 x 104) =
(2 × 10³)(3 × 10⁴) =
(2 × 10³) × (3 × 10⁴)
And the division of
(-42 x 102) and (14 x 103) =
(-4.2 × 10²) ÷ (1.4 × 10³)
__________________
It is hard to know without an image, assumptions can vary.
Determine if the following infinite series converge or diverge using the indicated test. If a certain test is inconclusive, please state it as such. (a) ∑ n=1
[infinity]
n 2
+1
7n 2
+8
(Use the divergence test) (b) ∑ n=1
[infinity]
n+2
1
(Use the integral test) (c) ∑ n=2
[infinity]
n 2
−n
1
(Use the limit comparison test) (d) ∑ n=1
[infinity]
n!
2 n
(Use the ratio test)
(a) The series diverges.
(b) The series diverges.
(c) The test is inconclusive.
(d) The series diverges.
We have,
(a)
To determine if the series ∑ (n² + 1)/(7n² + 8) converges or diverges, we can use the divergence test.
Divergence Test:
If the limit of the terms of a series is not zero, then the series diverges.
Let's apply the divergence test to the given series:
lim (n → ∞) [(n² + 1)/(7n² + 8)]
As n approaches infinity, the dominant terms in the numerator and denominator are n² and 7n², respectively.
Taking the limit:
lim (n → ∞) [(n² + 1)/(7n² + 8)] = 1/7
Since the limit of the terms is not zero, the series diverges by the divergence test.
(b)
To determine if the series ∑ (n+2)/n converges or diverges, we can use the integral test.
Integral Test:
If the integral of the function f(x) from 1 to infinity converges or diverges, then the series ∑ f(n) converges or diverges, respectively.
Let's apply the integral test to the given series:
∫[1, ∞] (x+2)/x dx
Evaluating the integral:
∫[1, ∞] (x+2)/x dx = ∫[1, ∞] (1 + 2/x) dx = [x + 2ln|x|] [1, ∞]
Taking the limit as x approaches infinity:
lim (x → ∞) [x + 2ln|x|] = ∞
Since the integral diverges, the series ∑ (n+2)/n also diverges by the integral test.
(c)
To determine if the series ∑ (n² - n)/n converges or diverges, we can use the limit comparison test.
Limit Comparison Test:
If the limit of the ratio between the terms of a given series and a known convergent or divergent series is a nonzero finite value, then both series have the same nature of convergence or divergence.
Let's compare the given series to the series ∑ 1/n:
lim (n → ∞) [(n² - n)/n] / (1/n)
= lim (n → ∞) (n² - n) / n
= lim (n → ∞) (n - 1)
= ∞
Since the limit is infinity, the limit comparison test is inconclusive.
We cannot determine the convergence or divergence of the given series using this test.
(d)
To determine if the series ∑ n! / (\(2^n\)) converges or diverges, we can use the ratio test.
Ratio Test:
If the limit of the ratio between consecutive terms of a series is less than 1, then the series converges.
If the limit is greater than 1 or infinite, the series diverges.
Let's apply the ratio test to the given series:
lim (n → ∞)\([(n+1)! / (2^{n+1})] / [n! / (2^n)]\)
= lim (n → ∞)\((n+1)! / n! * (2^n / 2^{n+1})\)
= lim (n → ∞) (n+1) / 2
Taking the limit:
lim (n → ∞) (n+1) / 2 = ∞
Since the limit is infinite, the series ∑ n! / (2^n) diverges by the ratio test.
Thus,
(a) The series diverges.
(b) The series diverges.
(c) The test is inconclusive.
(d) The series diverges.
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Use the original price and the markup to find the retail price.
Original price: $70; Markup: 25%
Answer:
$87.50
Step-by-step explanation:
(70*0.25)+70=87.50
Hope this helps!
Answer:
$87.50
Step-by-step explanation:
The original price of the product is $70. To find the markup price multiply 70 by 0.25 which equals 17.50. Add 70 and 17.50 to get your final answer of $87.50.
Select the scenario which is an example of simple random sampling.
a.An international airline wants to study the demand for its services. They group their destinations into regions, randomly select 20
of these regions, and study every destination in each of the selected regions.
b.A newspaper article focuses on local public health initiatives. At the end of the article, the author asks readers to send in their opinion on smoking in public areas.
c.A supermarket wants to study the buying habits of its customers. They choose every 20th customer entering the supermarket to fill out the survey.
d.College administration wants to conduct a survey to determine the demand for an insurance program at the college. Students are selected randomly from the college and mailed a questionnaire.
The scenario that is an example of simple random sampling is option C: "A supermarket wants to study the buying habits of its customers. They choose every 20th customer entering the supermarket to fill out the survey."
Simple random sampling is a method of selecting a sample from a population in which every member of the population has an equal chance of being chosen.
In option C, the supermarket chooses every 20th customer entering the store, which ensures that each customer has an equal chance of being selected. Therefore, this is an example of simple random sampling.
Options A, B, and D do not meet the criteria for simple random sampling, as they involve selecting specific regions, asking for opinions from readers, or mailing questionnaires to students, which does not ensure that every member of the population has an equal chance of being selected.
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What is the volume of the following cylinder? Do not round your answer. (Use 3.14 for π.)
volume = ____yd3
Answer: 1962.5
Step-by-step explanation: Just did this question it's right hope this helps
The square root of the difference of X and five as an algebraic expression
Answer:
we
Step-by-step explanation:
we
at what rate is the angle between a clock's minute and hour hands changing at 10 o'clock in the evening
Answer:
Step-by-step explanation:
I guess 6%?
3(5y + 1) = 18y
Step by step (show work)
Right answers
Answer:
please make me brain least
Step-by-step explanation:
=3×5y+1
=15y+1
=16y
The solution to the equation 3(5y + 1) = 18y is y = 1.
Here, we have,
To solve the equation 3(5y + 1) = 18y step by step, we will distribute the 3 to the terms inside the parentheses, simplify the equation, and then solve for y.
Here's how:
Distribute the 3 to the terms inside the parentheses:
3 * 5y + 3 * 1 = 18y
Simplifying:
15y + 3 = 18y
Now, we want to isolate the variable y.
Let's begin by moving all terms with y to one side of the equation.
We can do this by subtracting 15y from both sides:
15y + 3 - 15y = 18y - 15y
Simplifying:
3 = 3y
We now have the equation 3 = 3y.
To solve for y, we need to get rid of the coefficient 3 that is multiplied by y.
We can achieve this by dividing both sides of the equation by 3:
(3/3) = (3y/3)
Simplifying further:
1 = y
We have found the solution for the variable y.
Therefore, the solution to the equation 3(5y + 1) = 18y is y = 1.
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solve by quadratic formula:
3x^2+6x+1
Answer:x=0.183 x=-1.816
Step-by-step explanation:
Use Quadratic Formula
Mark Brainliest
Translate this sentence into an equation. 40 is the sum of 21 and ricks age? use the variable are to represent ricks age.
Answer:
40=21+x
Explanation:
x= Rick's age
a. Find m
b. you write the measures of