One number is 5 more than twice another and their sum is 23.
Which of the following system of equations represents the word problem?
y= 2( x + 5) and x + y= 23
x + y = 23 and y= 2 x + 5
y=x+ 5 and y + 2(x+5) = 23
Answers
Answer:
x + y = 23 and y= 2 x + 5
Step-by-step explanation:
The number is 5 more than twice another so 2x + 5 = y
The two numbers have a sum of 23 so x + y = 23.
Related Questions
Numerical Integration • The function f(x)=e* can be used to generate the following table of unequally spaced data = x O 0.1 0.3 0.5 0.7 0.95 1.2 f(x) 1 0.9048 0.7408 0.6065 0.4966 0.3867 0.3012 . =
Answers
Numerical integration is a numerical analysis technique for calculating the approximate numerical value of a definite integral.
In general, integrals can be either indefinite integrals or definite integrals. A definite integral is an integral with limits of integration, while an indefinite integral is an integral without limits of integration.A numerical integration formula is an algorithm that calculates the approximate numerical value of a definite integral. Numerical integration is based on the approximation of the integrand using a numerical quadrature formula.
The numerical quadrature formula is used to approximate the value of the integral by breaking it up into small parts and summing the parts together.Equations for the calculation of integration by trapezoidal rule (1/2)h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h= Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes. The basic principle is to replace the integral by a simple sum that can be calculated numerically. This is done by partitioning the interval of integration into subintervals, approximating the integrand on each subinterval by an interpolating polynomial, and then evaluating the integral of each polynomial.
Based on the given table of unequally spaced data, we are to calculate the approximate numerical value of the definite integral. To do this, we will use the integration formula as given by the trapezoidal rule which is 1/2 h[f(x0)+2(f(x1)+...+f(xn-1))+f(xn)] where h = Δx [the space between the values], and x0, x1, x2...xn are the coordinates of the abscissas of the nodes. The table can be represented as follows:x 0.1 0.3 0.5 0.7 0.95 1.2f(x) 1 0.9048 0.7408 0.6065 0.4966 0.3867 0.3012Let Δx = 0.1 + 0.2 + 0.2 + 0.25 + 0.25 = 1, and n = 5Substituting into the integration formula, we have; 1/2[1(1)+2(0.9048+0.7408+0.6065+0.4966)+0.3867]1/2[1 + 2.3037+ 1.5136+ 1.1932 + 0.3867]1/2[6.3972]= 3.1986 (to 4 decimal places)
Therefore, the approximate numerical value of the definite integral is 3.1986.
The approximate numerical value of a definite integral can be calculated using numerical integration formulas such as the trapezoidal rule. The trapezoidal rule can be used to calculate the approximate numerical value of a definite integral of an unequally spaced table of data.
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Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function and interval. Enter the values in increasing order and enter N in any blanks you don't need to use. 7sin(2pix)
Answers
The value of c in increasing order which satisfy the Rolle's theorem for a given function is equal to c = 1/4 and c = 3/4.
Function f(x) = 7sin(2πx) ,
Interval = [0, 1]
To apply Rolle's Theorem, check the following conditions,
f(x) must be continuous on the closed interval [a, b].
Here, the interval is [0,1].
f(x) must be differentiable on the open interval (a, b).
f(a) = f(b)
Function f(x) = 7sin(2πx).
f(x) is continuous on the interval [0, 1].
f(x) is differentiable on the interval (0, 1), and its derivative is,
f'(x) = 14π cos(2πx)
The derivative is continuous on the interval (0, 1).
f(0) = 7sin(0)
= 0
f(1) = 7sin(2π)
= 0
Since f(0) = f(1) = 0,
⇒ As per Rolle's Theorem there exists at least one number c in the interval (0, 1) .
Such that f'(c) = 0.
Values of c that satisfy this conclusion,
Solve the equation
f'(c) = 14π cos(2πc)
⇒14π cos(2πc) = 0
⇒ cos(2πc) = 0
This equation has solutions at c = 1/4 and c = 3/4,
As
cos(2π(1/4))
= cos(π/2)
= 0
and
cos(2π(3/4))
= cos(3π/2)
= 0.
Therefore, the values of c that satisfy the conclusion of Rolle's Theorem for the given function are c = 1/4 and c = 3/4, and they are already in increasing order.
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The above question is incomplete, the complete question is:
Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function 7sin(2pix) and interval [0, 1 ]. Enter the values in increasing order and enter N in any blanks you don't need to use.
1.39 to 1 decimal point
Answers
Answer: 1.4 or just 1
Step-by-step explanation:
But we are going to a decimal point then go to 1.4, cause the 9 makes the 3 round-up. :)
Answer: 1.4
Step-by-step explanation:
I believe you're asking what 1.39 rounded to the nearest tenths place is, in that case it is 1.4
I need help ASAP!! Can someone please help me?
Answers
Answer:
See picture attachment.
Hope this helps :)
In a sample of 16 mini-golf balls, 6 are yellow and 10 are pink. If 2 balls are selected at random from the sample, one at a time without replacement, what is the probability that both balls are not pink?
Answers
Answer:
The probability is 1/8 that you'll pick 2 yellow balls.
Step-by-step explanation:
P(Both balls not pink) = P(Both balls yellow) = 6/16 * 5/15 = 1/8
If G( x ) = 3 x + 1, then G -1 (1) is...
-1/3
-4
-0
Answers
Answer:
-4
Step-by-step explanation:
3+1 = 4 so just put a dash at the start and you ger -4
Although a football field appears to be flat, some are actually shaped like a parabola so that rain runs off to both sides. The cross section of a field can be modeled by y = -0.000234x (20 160), where x and y are measured in feet. What is the width of the field? What is the maximum height of the surface of the field? Round your answers to the nearest tenth, if necessary.
The width of the field is feet. The maximum height of the field is about fleet.
Answers
Answer:
The ends of the field are at the zeros (x-intercept) of the function.
0 = -0.000234(x - 80)2 + 1.5 subtract 1.5 from both sides
-1.5 = -0.000234(x - 80)2 divide both sides by right coefficient
6410.25641 = (x - 80)2 take square root of both sides
80.064 = x - 80 add 8-0 to both sides
160.064 = x
The field is 160.064 feet wide.
The maximum is at the vertex, y = 1.5 feet
Step-by-step explanation:
Smallest to largest: 15/25 16/30 9/27
Answers
Answer:
Smallest: 9/27
Second: 16/30
Largest: 15/25
Step-by-step explanation:
15/25= 0.6
16/30= 0.53
9/27= 0.33
Easiest way to do this is to do this is to make them have the same digits.
0.60 or 0.6
0.53 or 0.5
0.33 or 0.3
now, you just find the order of these smallest to largest...
3, 5, 6
0.33, 0.53, 0.60
0.3, 0.5, 0.6
9/27, 16/30, 15/25
Hope this helps, Brainliest is appreciated :)
Have a Great day! cx
~Mitsuna
Lucy recently asked the servers at her restaurant to only give straws to customers who request them. She thinks that about half of the customers will ask for straws but hopes that the rate will be less than half. She randomly selects 100 customers and finds that 43 of them ask for a straw. To determine if these data provide convincing evidence that the proportion of customers who will ask for a straw is less than 50%, 150 trials of a simulation are conducted. Lucy is testing the hypotheses: H0: p = 50% and Ha: p < 50%, where p = the true proportion of customers who will ask for a straw. Based on the results of the simulation, the estimated P-value is 0.0733. Using a = 0.10, what conclusion should Lucy reach?
Because the P-value of 0.0733 < a, Lucy should reject H0. There is convincing evidence that the proportion of customers who will ask for a straw is less than 50%.
Because the P-value of 0.0733 < a, Lucy should reject Ha. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.
Because the P-value of 0.0733 < a, Lucy should fail to reject Ha. There is convincing evidence that the proportion of customers who will ask for a straw is less than 50%.
Because the P-value of 0.0733 < a, Lucy should fail to reject H0. There is not convincing evidence that the proportion of customers who will ask for a straw is less than 50%.
Answers
Based on the simulation results and using a significance level of 0.10, Lucy should fail to reject the alternative hypothesis, Ha: p < 50%.
This means that there is convincing evidence to support Lucy's claim that the proportion of customers who will ask for a straw is less than 50%.
The P-value of 0.0733 is less than the significance level of 0.10, which indicates that the probability of obtaining the observed result or one more extreme assuming the null hypothesis is true is low. Therefore, Lucy can reject the null hypothesis, H0: p = 50%, and conclude that there is evidence to support her belief that less than half of the customers will ask for a straw.
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Describe the translation of the graph of y = x2 that results in the graph of y = (x - 3)2.
up 3 units
down 3 units
right 3 units
left 3 units
Answers
Answer:
The translation of the graph of y = 2x that results in the graph of y =2(x-3) is 3 units to the right (right 3 units).
Find the break-even point for the given cost and revenue equations. round to the nearest whole unit. c = 15n 269,000 r = 95n a. 80 c. 3363 b. 2445 d. 110
Answers
The break-even point for the given equation c = 15n + 269,000 , r = 95n representing cost and revenue is equal to Option c. 3363units ( round up to nearest whole unit ).
As given in the question,
Cost equation is represented by :
c = 15n + 269,000
Revenue equation is given by ;
r = 95n
For the break-even point the cost is always equal to the revenue as there is no profit no loss.
c = r
15n + 269,000 = 95n
⇒ 95n - 15n = 269,000
⇒ 80n = 269,000
⇒ n = 269,000 / 80
⇒ n = 3362.5
⇒ n = 3363 units ( round up to nearest whole unit )
Therefore, the break-even point for the given cost and revenue is equal to Option c. 3363units ( round up to nearest whole unit ).
The above question is incomplete , the complete question is:
Find the break-even point for the given cost and revenue equations. round to the nearest whole unit. c = 15n + 269,000 , r = 95n
a. 80 c. 3363
b. 2445 d. 110
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Help a brother out grades go in tomorrow
Answers
Answer:
a. 3/8
Step-by-step explanation:
Answer:
A. Have a wonderful day! o(^▽^)o
Step-by-step explanation:
describe the error made in subtracting the two rational expressions shown 1/x-2-1/x 1
Answers
The error made in subtracting the two rational expressions 1/(x - 2) - 1/x is that the common denominator is not correctly identified and applied.
To subtract rational expressions, we need to find a common denominator and then subtract the numerators. In this case, the common denominator should be (x - 2) * x. However, the error lies in neglecting the parentheses in the first expression, leading to a miscalculation of the common denominator.
The correct subtraction of the given expressions should be: (x - 2)/(x - 2) - 1/(x * (x - 2)). Simplifying this expression further would result in (x - 2 - 1)/(x * (x - 2)), which can be simplified as (x - 3)/(x * (x - 2)).
Therefore, the error made in the subtraction lies in incorrectly identifying and applying the common denominator, which resulted in an inaccurate calculation of the expression.
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Robert has two packs of stickers.
In pack A, there are 6 white stickers and 4
purple stickers.
In pack B, there are 9 white stickers and 3
purple stickers.
Robert is going to take one sticker at
random from each pack.
What is the probability that he takes one
white and one purple sticker?
Give your answer as a fraction in its
simplest form.
Answers
The probability that Robert takes one white and one purple sticker is 3/40.
We have,
To calculate the probability of Robert taking one white and one purple sticker, we can use the multiplication rule of probability.
The probability of taking a white sticker from pack A = 6/10.
The probability of taking a purple sticker from pack B = 3/12.
Since the two events are independent, we can multiply these probabilities to get:
P(white from A and purple from B) = (6/10) x (3/12) = 9/120
Simplifying this fraction gives:
P(white and purple) = 3/40
Therefore,
The probability that Robert takes one white and one purple sticker is 3/40.
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a _______________ is a graph showing the differences in frequencies or percentages among categories of a nominal or an ordinal variable.
Answers
A bar chart is a graph that shows the differences in frequencies or percentages among categories of a nominal or an ordinal variable.
A bar chart is a commonly used graphical representation to display the distribution of data in different categories. It is particularly useful when working with nominal or ordinal variables, where the categories are distinct and unordered or have a specific order.
In a bar chart, each category is represented by a rectangular bar whose length corresponds to the frequency or percentage associated with that category. The height of the bar represents the magnitude or count of the variable in each category, allowing for easy visual comparison between the categories.
The bars in a bar chart can be arranged horizontally or vertically, depending on the preference or nature of the data. The chart may also include labels or annotations to indicate the category names or additional information.
By examining the lengths or heights of the bars in a bar chart, it becomes easy to identify the categories with the highest or lowest frequencies or percentages, as well as to compare the relative magnitudes among the different categories. This graphical representation aids in visualizing and interpreting the distribution of a nominal or an ordinal variable effectively.
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ten drill bits are randomly selected from a process. the times to failure (i.e., loss of acceptable sharpness) for the bits are recorded as 37, 39, 42, 43, 49, 50, 54, 55, 59, and 63 hours. assuming the failure times have a weibull distribution, analyze the data using probability plotting. estimate the shape and scale parameters. plot the original data versus the cdf model corresponding to your parameter estimates. add confidence limits.
Answers
In probability plotting, a graph of the cumulative distribution function (CDF) is plotted against a transformed version of the data to determine if the data come from a particular distribution.
The distance between the two lines is equal to the product of the critical value of the t-distribution and the standard error estimate.
This can be used to analyze the times to failure (i.e., loss of acceptable sharpness) for a random selection of ten drill bits from a process that follows a Weibull distribution.
To estimate the shape and scale parameters
follow these steps:
Step 1: Rank the data from smallest to largest
Step 2: Calculate the failure probability of each data point using the formula: i/(n+1), where i is the rank of the data point and n is the number of data points.
Step 3: Transform the failure probabilities using the inverse Weibull distribution function: F^(-1)(p) = (−ln(1−p))^β for a given shape parameter β and scale parameter η.
Step 4: Plot the transformed data against the theoretical distribution, which is a straight line for the Weibull distribution.
Step 5: Find the best-fitting line by eye, or by using regression analysis.
The slope of the line is equal to the shape parameter β, and the intercept is equal to the logarithm of the scale parameter ln(η).
The Weibull distribution can be represented as:\(F(x) = 1 − e^(-(x/η)^β)\), where β is the shape parameter and η is the scale parameter. The CDF model corresponding to your parameter estimates can be plotted by using the formula . This can be done by calculating the standard deviation of the residuals, and then calculating the upper and lower limits of the confidence interval using the t-distribution.
The confidence interval can be calculated as:β ± t(n−2,α/2) x SE(β)ln(η) ± t(n−2,α/2) x SE(ln(η))where SE(β) is the standard error estimate for the shape parameter, SE(ln(η)) is the standard error estimate for the logarithm of the scale parameter, and t(n−2,α/2) is the critical value of the t-distribution with n−2 degrees of freedom and a significance level of α/2.The confidence limits can be plotted as two parallel lines around the best-fitting line. The distance between the two lines is equal to the product of the critical value of the t-distribution and the standard error estimate.
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(b) suppose you want to estimate the average age of all boeing 727 airplanes now in active domestic u.s. service. you want to be 95% confident and you want a margin of error of 2 years. suppose the population standard deviation is 6.24 years. how large a sample should you take?
Answers
37.40 is large a sample should you take in confidence interval.
What does confidence interval mean?
Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval. If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty. In statistics, confidence is another word for probability.For the 95% confident interval of population mean , the margin of error (ME)
ME = Z 1 - 0.05/2 5/√n
2 = 1.96 * 6.24/√n
n = ( 1.94 * 6.24/2)²
n = 37.40
the required sample size (n) is 38 .
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what is the square root of 6
Answers
Answer:
2.449
Step-by-step explanation:
the square root of 6 is about 2.449
You have a cup of lemonade. Each ice cube has a length of 2 cm, a width of 1 1/4 cm and a height of 3 cm. What is the volume of one of the ice cubes? Show your steps and Explain how you used math to come to your decision.
Answers
volume : 7.5 cm²
volume of cube : length * width * height\(\hookrightarrow \sf Length \ * Width \ * \ Height\)
\(\hookrightarrow \sf 2 \ * 1\dfrac{1}{4} \ * \ 3\)
\(\hookrightarrow \sf 2 \ * \dfrac{5}{4} \ * \ 3\)
\(\hookrightarrow \sf \dfrac{15}{2}\)
\(\hookrightarrow \sf 7.5 \ cm^2\)
Answer:
\(\sf volume=7 \frac12 \ cm^3\)
Step-by-step explanation:
Formula
volume of cuboid = length × width × height
Given dimensions of the ice cube:
length = 2 cmwidth = 1 1/4 cmheight = 3cmSubstituting the given values into the formula:
\(\sf \implies volume=2\times 1 \frac14 \times 3\)
Converting to improper fractions:
\(\sf \implies volume=\dfrac21\times \dfrac54 \times \dfrac31\)
\(\sf =\dfrac{ 2\times 5 \times 3}{1 \times 4 \times 1}\)
\(\sf =\dfrac{30}{4}\)
Dividing the numerator and denominator by the highest common factor:
\(\sf \implies volume=\dfrac{30 \div 2}{4 \div 2}\)
\(\sf =\dfrac{15}{2}\)
Converting the improper fraction into a mixed number:
\(\sf \implies volume=7 \frac12 \ cm^3\)
4. The number of questions Tyler answers correctly is within 2 of the number of Benjamin's correct answers. Part A Write and solve an absolute value inequality to determine the number of questions Tyler answers correctly. T-B22 or B-T ≤2 Part B Based on your answer to Part A, what prizes will Tyler win? Explain.
Answers
Part A) Tyler answers within 2 questions of Benjamin if he answers B+2, B+1, B, B-1, or B-2 questions correctly.
Part B) Based on the solution from Part A, Tyler will win prizes for correctly answering the corresponding number of questions.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Part A:
Since we want to find the possible values of T, we can isolate T on one side of the inequality:
T - B ≤ 2
T ≤ B + 2
or
T - B ≥ -2
T ≥ B - 2
Therefore, Tyler answers within 2 questions of Benjamin if he answers B+2, B+1, B, B-1, or B-2 questions correctly.
Part B:
Based on the solution from Part A, Tyler will win prizes for correctly answering the corresponding number of questions.
This is because Tyler's score is within 2 questions of Benjamin's score. Therefore, he will receive the same prizes as Benjamin for answering the same number of questions, as well as additional prizes for answering 1 or 2 fewer questions than Benjamin.
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i need help!! can anybody help me?
Answers
x=67 is your answer
What is the measure of angle K, L and M?
HELP PLEASE
Answers
*
1. Find the value of the discriminant.
3x2 - 6x + 3 = 0
O 29
0 -18
OO
O 23
Answers
0 -18 is the answer to your question
Can an irrational number be represented on a number line?
Answers
Answer:
An irrational number can be represented approximately on a number line.
The weight of one serving of trail mix is 2.5 ounces. How many servings are there in 25 ounces of trail mix?
Answers
Explanation: 25/2.5 = 10
can you guys help me again lol-
Answers
Answer:
$93 per hour ?
125-405 = 280
280÷3= 93 per hour
How do you write a linear function from a data table?
Answers
The constant average rate of change is the slope of the line which can be used to write the linear function.
What is a Data Table ?
A table of data is linear if there is a constant average rate of change between all pairs of points.
Testing for Linearity
to test if a table of data is linear, calculate the average rate of change between each consecutive pair of pointsif the rate of change is constant, the data represents a linear functionif not, then it is not a linear functionFinding a Function from a Table that is Linear
the constant average rate of change found when determining that the table is linear is the slope of the line.use this slope and any one point from the table, write the equation using the point slope form, then solve for “y” to get the function equation.Learn more about linear functions at:
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Work out total charge that Cheryl will play if she uses her credit card to buy the tickets
Please can I have help asap
Answers
Answer:
£100.98
Step-by-step explanation:
Step 1: find total price of tickets
Total price of tickets = 6 adults (£12) + 3 child (£6) = 6(12) + 3(6)
= 72 + 18
Total of tickets = £90
Step 2: Find the extra added 10% booking fee
Booking fee added = 10% of £90
= 10/100 × 90
= 0.1 × 90
Adding booking fee = £9
Step 3: Calculate the added 2% that would be added for using credit card
Cheryl would be paying £99 with her credit card (price of tickets + added booking fee = £90 + £9)
2% of £99 = 2/100 × 99
Added credit card charges = 0.02 × 99 = £1.98
Step 4: Calculate the total charge to be paid by Cheryl if she uses her credit card for the payment
Total charge = cost of tickets + added booking fee + credit card charges
= £90 + £9 + £1.98
= £100.98
Answer:
100.98
Step-by-step explanation:
-2 ≤2x-4 <4 solve inequality
Answers
-8 < 4
hope it helps
Answer: -2≤-8<4
Step-by-step explanation:
the dot plot below shows the number of songs carly downloaded over 15 successive weekends. what is the greatest number of songs downloaded?
Answers
The greatest number of songs downloaded is 10."
How we find the greatest number of songs downloaded?"What is the greatest number of songs downloaded?" is:
Identify the highest point on the dot plot.Read the number of songs downloaded at that highest point.A dot plot is a graphical representation of data using dots. In this case, the dot plot shows the number of songs Carly downloaded over 15 successive weekends. Each dot represents the number of songs downloaded during a particular weekend
To find the greatest number of songs downloaded, we need to identify the highest point on the dot plot. This can be done by visually examining the dot plot and looking for the highest dot.
Once we identify the highest dot, we can see the number of songs downloaded during that particular weekend, which is the greatest number of songs downloaded over the 15 successive weekends.
if the highest dot on the dot plot represents 10 songs downloaded, then the answer to the question would be "The greatest number of songs downloaded is 10."
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