Michael Started with 30 baseball cards and gave away X number of cards John you started with 40 baseball cards and gave away twice as many as Michael did how many baseball cards did Michael giveaway if they had the same number of cards left?
Answers
Answer:
He gave 20
Step-by-step explanation:
30 minus 10 equals 20 and if John gave times that he would have 20 (40-20) which will give him the same answer.
Related Questions
if sat scores are normally distributed with a mean of 500 and standard deviation of 100, what is minimum score is needed to ensure that you are ni the top 7
Answers
To determine the minimum score needed to ensure that you are in the top 7%, we need to find the z-score associated with the top 7% and then convert it back to the raw score.
The top 7% corresponds to an area of 0.07 under the standard normal distribution curve. To find the z-score associated with this area, we can use a standard normal distribution table or a calculator.
Using a standard normal distribution table or calculator, we find that the z-score corresponding to an area of 0.07 is approximately 1.4051.
To convert this z-score back to the raw score, we can use the formula:
x = z * standard deviation + mean
Substituting the values into the formula, we get:
x = 1.4051 * 100 + 500
x ≈ 140.51 + 500
x ≈ 640.51
Therefore, the minimum score needed to ensure that you are in the top 7% is approximately 640.51.
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Which of the following is equivalent to 67?
Answers
Answer:
efefe
Step-by-step explanation:
fef greht jy7i8
4 x 5-10 - 2 (1-2) + 5=
Answers
Answer:
\(17\)
Step-by-step explanation:
\(4\cdot \:5-10-2\left(1-2\right)+5\)
\(\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\)
\(=4\cdot \:5-10-2\left(-1\right)+5\)
\(=20-10-2\left(-1\right)+5\)
\(=20-10-\left(-2\right)+5\)
\(20-10=10\)
\(=10-\left(-2\right)+5\)
\(-\left(-2\right)=+2\)
\(=10+2+5\)
\(10+2=12\)
\(=12+5\)
\(12+5=17\)
\(=17\)
graph one is linear so incorrect prolly but help ty ty
Answers
The function given is:
\(f(x)=x^3+3\)It is required to find the graph of f(5x).
Recall that the graph of f(kx) for k>1 is the horizontal compression or shrink of the graph of f(x) by k units. The graph is compressed horizontally towards the y-axis.
Graph the given function f(x)=x³+3:
Compress the graph horizontally by k=5 units as shown below:
The required graph is:
The graph that best fits this is graph 4.
The answer is gra
Most engaged couples expect or at least hope that they will have high levels of marital satisfaction. However, because 54% of first marriages end in divorce, social scientists have begun investigating influences on marital satisfaction. (Data Source: These data were obtained from the National Center for Health Statistics. ) Suppose a counseling psychologist sets out to look at the role of having children in relationship longevity. A sample of 78 couples with children score an average of 51. 1 with a sample standard deviation of 4. 7 on the Marital Satisfaction Inventory. A sample of 94 childless couples score an average of 45. 2 with a sample standard deviation of 12. 1. Higher scores on the Marital Satisfaction Inventory indicate greater satisfaction.
Suppose you intend to conduct a hypothesis test on the difference in population means. In preparation, you identify the sample of couples with children as sample 1 and the sample of childless couples as sample 2. Organize the provided data by completing the following table:
Answers
To organize the provided data, we can create a table comparing the samples of couples with children (sample 1) and childless couples (sample 2) as follows:
Sample Sample Size Sample Mean Sample Standard Deviation
1 78 51.1 4.7
2 94 45.2 12.1
In this table, we have listed the sample number (1 and 2), the sample size (number of couples in each group), the sample mean (average Marital Satisfaction Inventory score), and the sample standard deviation (measure of variability in the scores) for each group. This organization allows us to compare the data and proceed with hypothesis testing on the difference in population means between the two groups.
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Amir operates a large lobster boat. The operating cost for the boat is $2.250 each day. At the end of each day, he sells all his freshly caught lobster to either the local restaurant or the local grocery store with the following conditions:
• The price per pound that the restaurant is willing to pay follows a triangular distribution with minimum value $1.50, maximum value $5.50, and likeliest value $3.50.
• The price per pound that the grocery store is willing to pay is decreasing with more lobsters: $3.85 - 50.0005 * y, where y is the total lobster amount sold in pounds.
• The amount of lobster that Amir catches in a single day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.
Amir decides to sell a fixed percentage of lobster to the local restaurant and the rest to local grocery stores. Using either math or simulation, can you help Amir determine what percentage he should choose in order to maximize his expected profit in the long run?
Previous question
Answers
The expected profit in the long run can be determined by calculating the expected value of the total revenue from selling the lobsters. The expected total revenue is the sum of the expected revenue from selling the lobsters to the restaurant and the from selling the lobsters to the grocery store.
The expected value of the revenue from selling the lobsters to the restaurant can be calculated by multiplying the expected price per pound from the restaurant by the expected amount of lobsters caught in a day. The expected price per pound from the restaurant follows a triangular distribution with minimum value $1.50, maximum value $5.50, and likeliest value $3.50. The expected amount of lobsters caught in a day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.
The expected value of the revenue from selling the lobsters to the grocery store can be calculated by multiplying the expected price per pound from the grocery store by the expected amount of lobsters caught in a day. The expected price per pound from the grocery store is decreasing with more lobsters: $3.85 - 50.0005 * y, where y is the total lobster amount sold in pounds. The expected amount of lobsters caught in a day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.
Given the expected values of the total revenue from selling the lobsters to the restaurant and the grocery store, Amir can use simulation to determine the optimal percentage of lobsters to sell to the restaurant in order to maximize his expected profit in the long run. He can run several simulations with different percentages of lobsters to be sold to the restaurant and compare the expected profits for each simulation. The percentage that produces the highest expected profit is the optimal percentage for Amir to maximize his expected profit in the long run.
Amir can use simulation to determine the optimal percentage of lobsters to sell to the restaurant in order to maximize his expected profit in the long run. He can calculate the expected value of the total revenue from selling the lobsters to the restaurant and the grocery store, and then run several simulations with different percentages of lobsters to be sold to the restaurant to compare the expected profits for each simulation. The percentage that produces the highest expected profit is the optimal percentage for Amir to maximize his expected profit in the long run.
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Let U = {(x, y, z) € R^3 | x + 2y – 3z =0}. a) (2pt) Show directly (by verifying the conditions for a subspace) that U is a subspace of R^3. You may not invoke results learned in class or from the notes. b) (2pts) Find a basis for U. You must explain your method. c) (1pt) Using your answer from part b) determine Dim(U).
Answers
a) U is subspace of R^3.
b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.
c) 2.
a) To show that U is a subspace of R^3, we need to verify the following three conditions:
i) The zero vector (0, 0, 0) is in U.
ii) U is closed under addition.
iii) U is closed under scalar multiplication.
i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.
ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:
x1 + 2y1 - 3z1 = 0 (by definition of U)
x2 + 2y2 - 3z2 = 0 (by definition of U)
Adding these two equations, we get:
(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0
which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.
iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:
x + 2y - 3z = 0 (by definition of U)
Multiplying both sides of this equation by c, we get:
cx + 2cy - 3cz = 0
which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.
Since U satisfies all three conditions, it is a subspace of R^3.
b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:
x = 3z - 2y
y = (x - 3z)/2
Substituting z = t into these equations, we get:
x = 3t - 2y
y = (x - 3t)/2
Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:
(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)
Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.
c) Since the basis for U has two elements, the dimension of U is 2.
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Solve the following problems using Elimination.
NO LINKS PLS-
8x - 5y =-18
2x + 5y = 58
Answers
9514 1404 393
Answer:
(x, y) = (4, 10)
Step-by-step explanation:
The coefficients of y are opposites, so the y-terms can be eliminated by adding the equations.
(8x -5y) +(2x +5y) = (-18) +(58)
10x = 40 . . . . . . simplify
x = 4 . . . . . . . . . divide by 10
Substituting this into the second equation gives ...
2(4) +5y = 58
5y = 50 . . . . . . . . subtract 8
y = 10 . . . . . . . . . .divide by 5
The solution is (x, y) = (4, 10).
A developmental psychologist studies moral awareness in male and female adolescents. Casual observation suggests that girls develop moral awareness earlier than boys, though most published research contains only male participants. A standard measure of moral awareness, on validated using only a male sample, has a mu = 72 and sigma = 18. The psychologist administers the measure to 58 13-year-old girls, whose mean scores was M = 76. Test the hypothesis that the moral awareness of girls is different from males. Conduct a complete hypothesis test using alpha =. 1
Answers
To test the hypothesis that the moral awareness of girls is different from males, we need to conduct a two-tailed hypothesis test with a significance level of alpha = .1.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
Null hypothesis: The population mean of moral awareness scores for girls is equal to the population mean of moral awareness scores for boys (μg = μb).
Alternative hypothesis: The population mean of moral awareness scores for girls is different from the population mean of moral awareness scores for boys (μg ≠ μb).
We will use a one-sample t-test to test this hypothesis since we have a sample mean and standard deviation and want to compare it to a known population mean.
First, we need to calculate the t-statistic:
t = (M - μ) / (s / √(n))
where M = 76 (sample mean), μ = 72 (population mean for males), s = 18 (population standard deviation for males), and n = 58 (sample size).
t = (76 - 72) / (18 / √(58)) = 1.59
Next, we need to determine the critical t-value using a t-distribution table with degrees of freedom (df) = n - 1 = 57 and a two-tailed test with
alpha = 1. The critical t-value is ±1.984.
Since our calculated t-value (1.59) falls within the range of -1.984 to 1.984, we fail to reject the null hypothesis.
Therefore, we do not have sufficient evidence to conclude that the moral awareness of girls is different from boys at a significance level of
alpha = .1.
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The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Answers
The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data
How to explain the informationThe answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.
In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.
Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.
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pope john paul ii's 1979 visit to this eastern bloc nation, his homeland, drew millions of followers and helped spark a decade-long underground movement against the communist government.
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In June 1979, the Pope travelled to Poland for the second time.
The foundation of the Solidarity trade union, which was a crucial force in the overthrow of Communism in eastern Europe, was reportedly set in motion as a result of this journey, which some historians claim was the most important of all his travels.
John Paul paid visits to Warsaw, Gniezno, Kraków, Nowy Targ, Auschwitz, and Jasna Gora while in Poland. Millions of fans attended the nine-day tour.
His visit to his homeland drew millions of followers and helped spark a decade-long underground movement against the communist government.
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What is the arc length S what is shown below?
The angle in the image is a central angle în radians.
Answers
Answer:
14 cm
Step-by-step explanation:
The applicable formula is ...
s = rθ
s = (7 cm)(2) = 14 cm
there is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others.
Answers
There is not one particular frequency distribution that is correct, but there are frequency distributions that are less desirable than others. This statement is TRUE.
Definition of Frequency DistributionIf interpreted linguistically, frequency distribution is the process of distributing frequencies. In statistics, frequency is the number of times a variable is represented by numbers or numbers. Conditions that are carried out repeatedly in the number series, frequency is also defined as frequency, frequent to rare.
Frequency distribution is a condition that describes the presence of frequency starting from symptoms that appear in the form of numbers, then distributed, divided to radiated. Presentation of numbers in this frequency designation can be in the form of tables, graphs and pictures. Until then the most frequently mentioned term appeared, namely the frequency distribution table.
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Tickets A Girl Scout troop sells 62 tickets to their mother-and-daughter dinner, for a total of $216. If the tickets cost $4.00 for mothers and $3.00 for daughters, how many of each ticket did they sell?
Answers
Answer:
mothers: 30
daughters: 32
Step-by-step explanation:
A Girl Scout troop sells 62 tickets to their mother-and-daughter dinner, for a total of $216. If the tickets cost $4.00 for mothers and $3.00 for daughters, how many of each ticket did they sell?
This is represented by the algebraic equations:
m + d = 62
4m + 3d = 216
Solve the first equation for d:
m + d = 62
d = 62 - m
Substitute d = 62 - m into second equation:
4m + 3d = 216
4m + 3(62 - m) = 216
4m + 186 - 3m = 216
subtract 186 from both sides:
4m + 186 - 3m - 186 = 216 - 186
4m - 3m = 30
combine left side:
m = 30
SO: there were 30 tickets sold to mothers.
Take the first equation and let m = 30:
m + d = 62
30 + d = 62
subtract 30 from both sides:
30 + d - 30 = 62 - 30
d = 32
_______________________
check: when m = 30 and d = 32
m + d = 62
30 + 32 = 62, CORRECT
4m + 3d = 216
4(30) + 3(32) = 216
120 + 96 = 216, CORRECT
The troop sold 30 mother tickets and 32 daughter tickets.
Let's start by using a system of equations to solve this problem. Let x be the number of mother tickets sold and y be the number of daughter tickets sold. We can write the following equations:
x + y = 62 (the total number of tickets sold)
4x + 3y = 216 (the total amount of money earned from ticket sales)
Now we can use the first equation to solve for one of the variables in terms of the other. For example, let's solve for x in terms of y:
x = 62 - y
Now we can substitute this value of x into the second equation:
4(62 - y) + 3y = 216
Simplifying this equation gives us:
248 - 4y + 3y = 216
Simplifying further gives us:
-y = -32
And finally, solving for y gives us:
y = 32
Now we can plug this value of y back into the first equation to solve for x:
x + 32 = 62
x = 30
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Help me pls, Write the equation of the line in fully simplified slope-intercept form.
Answers
An equation of the line in fully simplified slope-intercept form include the following: y = -3x/2 + 8.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (2 - 5)/(4 - 2)
Slope (m) = -3/2
At data point (2, 5) and a slope of -3/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -3/2(x - 2)
y = -3x/2 + 3 + 5
y = -3x/2 + 8
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3)If a prism has 5 sides for its base how many faces should the prism have?
0
1
5
10
Answers
Write the prime factorization of 21. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
Answers
The prime factorization of the number 21 is:
21 = 3*7
How to write the prime factorization?We want to write the prime factorization of 21.
To do so, we just need to divide the number by prime numbers.
The first prime number we can try is 2, if we divide by 2 we get:
21/2 = 10.5
This is not an integer, so 2 is not a factor.
The next one is 3:
21/3 = 7
Now we can rewrite:
21 = 3*7
Where 3 and 7 are prime numbers, so that is the prime factorization.
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what percentage of 340 is 425?
Answers
Answer:
125%
Step-by-step explanation:
1. Set up the equation
425/340 = x/100
(percentages are out of 100 so this equation means 425 out of 340 is equal to a number out of 100)
2. Cross multiply
340x = 42500
3. Solve for x
x = 125
Answer:
125%
Step-by-step explanation:
425-340 is 85.
85 of 340 is 0.25, which means it is 25% of 240.
Since 425 is greater than 340, add 100% to the 25% you found with 85.
425 = 300 + 85
y = 100% + 25%
125%
1. You get a student loan from the New Mexico Educational Assistance Foundation to pay for your educational expenses this year. Find the interest on the loan if you borrowed ₱2 000 at 8% for 1 year.
Answers
Answer:
$160
Step-by-step explanation:
Step one:
given data
Principal = $2000
rate= 8%
time t= 1 year
Required
The Simple interest paid after 1 year
Step two:
Simple interest = PRT/100
Simple interest = 2000*8*1/100
Simple interest = 16000/100
Simple interest =$160
The simple interest paid after 1 year is $160
"please answer all parts
Suppose that the position of a body moving along a coordinate line at simet is given by each function below, where a, b, and k are constants. Show in both cases that the acceleration proportional to s"
Answers
In both cases, case 1 and case 2 the given position functions demonstrate that the acceleration is proportional to the position.
To show that the acceleration is proportional to the position in both cases, we need to differentiate the given position functions twice with respect to time.
Case 1: Position function \(\(s(t) = ae^{kt}\)\)
Taking the first derivative with respect to time:
\(\(\frac{ds}{dt} = ake^{kt}\)\)
Taking the second derivative:
\(\(\frac{d^2s}{dt^2} = ak^2e^{kt}\)\)
Since the acceleration \(\(\frac{d^2s}{dt^2}\)\) is proportional to the position \(\(s(t)\)\) in this case, we can see that the acceleration is indeed proportional to the position.
Case 2: Position function \(\(s(t) = a\sin(bt)\)\)
Taking the first derivative with respect to time:
\(\(\frac{ds}{dt} = ab\cos(bt)\)\)
Taking the second derivative:
\(\(\frac{d^2s}{dt^2} = -ab^2\sin(bt)\)\)
In this case as well, the acceleration \(\(\frac{d^2s}{dt^2}\)\) is proportional to the position \(\(s(t)\),\) confirming that the acceleration is proportional to the position.
Therefore, in both cases, the given position functions demonstrate that the acceleration is proportional to the position.
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which point of concurrency is determined by the three altitudes of any triangle?
Answers
The point of concurrency that is determined by the three altitudes of any triangle is called orthocenter.
In geometry, an orthocenter is the intersection of the altitudes of a triangle. An altitude of a triangle is a line through a vertex of the triangle, perpendicular to the opposite side.
In other words, if you were to draw three lines from the vertices of a triangle down to the opposite sides, and these lines were all perpendicular to their respective sides, the point at which all three lines intersect would be the orthocenter of the triangle.
The orthocenter is one of the four points of concurrency that can be determined in a triangle, along with the circumcenter, the centroid, and the incenter. The circumcenter is the center of the circumcircle of the triangle, the centroid is the center of the triangle's mass, and the incenter is the center of the circle inscribed in the triangle.
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Robinson and Friday are the only people on Despair, a small island. They both produce grain and meat. Let G denote the quantity of grain, and M denote the quantity of meat. The following equations summarize their production possibility curves (PPCS) per week. Robinson: G=21−7M Friday: G=146−8M Suppose Despair is a closed economy. If Robinson and Friday would like to jointly consume 16 units of meat per week, they would be able to jointly consume a maximum of [Answer] units of grain per week. (In decimal numbers, with two decimal places, please.) Continue with the previous question. In this closed economy, any admissible terms of trade between Robinson and Friday have to smaller than [Answer] units of grain per unit of meat. (In decimal numbers, with two decimal places, please.) Answer: Question 19 Not complete Marked out of 1.00 P Flag question Continue with the previous question. Suppose Despair is now opened up to trade with the rest of the world, and can trade at world terms of trade of 11.8 units of grain per unit of meat. If Robinson and Friday would like to jointly consume 16 units of meat per week, they would be able to jointly consume a maximum of [Answer] units of grain per week. (In decimal numbers, with two decimal places, please.) Answer:
Answers
The Robinson and Friday jointly consume a maximum of 0 units of grain per week when they produce 16 units of meat.
The second part of the question is 8 units of grain per unit of meat.
To find the maximum units of grain that Robinson and Friday can jointly consume per week when they produce 16 units of meat, to find the intersection point of their production possibility curves (PPCs).
Robinson's PPC: G = 21 - 7M
Friday's PPC: G = 146 - 8M
Setting both equations equal to each other:
21 - 7M = 146 - 8M
Simplifying the equation:
M = 125
Substituting the value of M back into either equation, let's use Robinson's PPC:
G = 21 - 7(125)
G = 21 - 875
G = -854
Since negative quantities are not meaningful in this context, disregard the negative solution.
To find the admissible terms of trade, to find the slope of their production possibility curves at the point where they consume 16 units of meat.
Taking the derivative of Robinson's production possibility curve equation with respect to M:
dG/dM = -7
Taking the derivative of Friday's production possibility curve equation with respect to M:
dG/dM = -8
The absolute values of these slopes represent the opportunity cost of meat in terms of grain for each person. Therefore, the admissible terms of trade between Robinson and Friday have to be smaller than the absolute value of the steepest slope, which is 8 units of grain per unit of meat.
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Kayla rode her bike 75 miles home from college one weekend and then rode the bus back to college. It took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike, and the average speed of the bus was 10 miles per hour faster than kayla’s biking speed. Find kayla’s biking speed
Answers
When Kayla rode her bike home from college one weekend, her biking speed is 15 miles per hour
Speed is defined as the ratio between the distance and the amount of time an object traveled.
speed = distance/time
If the average speed of the bus was 10 miles per hour faster than Kayla’s biking speed, we have:
average speed of the bus = 10 mph + biking speed
let x = biking speed
y = average speed of the bus
y = 10 + x
Covering the same distance of 75 miles, calculate the time it took her riding the bus and the bike.
time = distance/speed
time riding the bus = 75 miles/(10 + x)
time riding the bike = 75 miles/x
If it took her 2 hours less to ride back to college on the bus than it took her to ride home on her bike
time riding the bus = time riding the bike - 2
75 miles/(10 + x) = (75 miles/x) - 2
75/(10 + x) = (75 - 2x)/x
Multiplying both sides by x(10 + x),
x(10 + x)[75/(10 + x)] = x(10 + x)[(75 - 2x)/x]
75x = 750 - 20x + 75x - 2x^2
2x^2 + 20x - 750 = 0
x^2 + 10x - 375 = 0
(x - 15)(x + 25) = 0
x = 15 ; x = -25
Since we cannot have negative amount of time, choose x = 15.
Hence, Kayla's biking speed is 15 miles per hour.
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Please helppp me outtttt
Answers
Answer:
i believe the answer to your question is aas
Answer:
AAS
Step-by-step explanation:
i dont know (i asked my brother)
Solve the equation shown:
2.5x + 18 = 3.5x - 4
X=
Answers
Answer:
X=22
Step-by-step explanation:
Step 1: Subtract 3.5x from both sides.
2.5x+18−3.5x=3.5x−4−3.5x
−x+18=−4
Step 2: Subtract 18 from both sides.
−x+18−18=−4−18
−x=−22
Step 3: Divide both sides by -1.
−x/-2 = -22/-1
x=22
The value of x in the given equation is 22
The given equation;
2.5x + 18 = 3.5x - 4
To find:
the value of xThe equation is simplified as follows;
2.5x + 18 = 3.5x - 4
collect similar terms together
2.5x - 3.5x = - 4 - 18
- x = - 22
x = 22
Thus, the value of x in the given equation is 22
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Julie had 2730 cards and Kim had 3570 cards at first.
Julie gave some of her cards to Kim. In the end, Kim had thrice as many cards as Julie.
How many cards did Julie give Kim.
Answers
Answer:
1155
Step-by-step explanation:
Total number of cards is 2730+3570=6300
Since Kim now has 3 times the card of Julie so Julie must have 6300/4=1575.
So, Julie gave 2730-1575=1155
Answer:
1155 cards
Step-by-step explanation:
3(2730-x)=3570+x
8190 - 3x = 3570 + x
4620 - 3x = x
4620 = 4x
1155 = x
You polled 2805 Americans and asked them if they drink tea daily. 724 said yes. With a 95% confidence level, construct a confidence interval of the proportion of Americans who drink tea daily. Specify the margin of error and the confidence interval in your answer.
Answers
According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766). The margin of error is approximately 0.0140.
How to construct a confidence interval?To construct a confidence interval for the proportion of Americans who drink tea daily, we can use the formula:
Confidence Interval = p ± Z * \(\sqrt\)((p * (1 - p)) / n)Where,
p = the sample proportion
Z = the critical value corresponding to the desired confidence level
n = the sample size
Given:
Sample size (n) = 2805Number of Americans who drink tea daily (p) = 724/2805 ≈ 0.2580 (rounded to four decimal places)Z-value for a 95% confidence level ≈ 1.96Now, let's calculate the confidence interval and margin of error:
Confidence Interval = 0.2580 ± 1.96 * \(\sqrt\)((0.2580 * (1 - 0.2580)) / 2805)Confidence Interval ≈ (0.2485, 0.2766)Margin of Error = 1.96 * \(\sqrt\)((0.2580 * (1 - 0.2580)) / 2805)Margin of Error ≈ 0.0140According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766), with a margin of error of approximately 0.0140.
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earnings. 2. A minibus had 23 passengers at the beginning of a journey. Twelve passengers alighted at the hrst stop while 9 boarded. Six of those who boarded at the first stop alighted at the second stop and 12 got in. the minibus should not stop again up to the final destination. The charges from the starting point were sh.50 up to the first stop sh. 70 up to the second stop and sh.85 up to the first destination. a) How many passengers alighted at the final destination? b) How many passengers were ferried by the minibus through the journey? c) How much money was collected during the trip?
Answers
. A minibus had 23 passengers at the beginning of a journey. The passengers alighted at the final destination, passengers were ferried by the minibus through the journey, and money collected during the trip are
20 passengers alighted. 24 passengers 2820 shillings. How many passengers alighted at the final destination?Generally, a) The minibus had
23 - 12 + 9 = 20 passengers at the first stop.
After the second stop, it had
20 - 6 + 12 = 26, passengers.
At the final destination, 26 - 6 = 20 passengers alighted.
b) The minibus ferried a total of
23 + 12 + 9 - 6 - 12 = 24 passengers through the journey.
c) The charges for the first stop were
50 * 12 = 600 shillings.
The charges for the second stop were
70 * 6 = 420 shillings.
The charges for the final destination were
85 * 20 = 1700 shillings.
The total amount of money collected during the trip was
600 + 420 + 1700 = 2820 shillings.
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Jenny has 2 dogs. One dog had a litter of 6 puppies last week. Her other dog just had a litter of 10 puppies yesterday. How many dogs does Jenny have now?
Answers
Answer:
18 dogs.
Step-by-step explanation:
Including the 2 she started with would start her off with 2 dogs. Then she had 6 more dogs which gives you
2+6 = 8 dogs
Then she had 10 more dogs which gives you
8+10 = 18 dogs.
Therefore, she has 18 dogs now.
Answer:
18
Step-by-step explanation:
2 + 6 + 10 = 18
I feel like this is much more difficult than expected.
Consider the function p(x)= x-4/(-4x^2+4) . what are the critical points?
Answers
The critical points for the rational function defined as \(p(x) = \frac{ x - 4}{-4x² + 4}\) are equal to the \(x =\ frac{ -4 ± \sqrt {13}}{ 3} \).
A critical point of a function y = f(x) is a point say (c, f(c)) on graph of f(x) where either the derivative is 0 (or) the derivative is not defined. Steps to determine the critical point(s) of a function y = f(x):
calculate the derivative f '(x).Set f '(x) = 0 and solve it to determine all the values of x (if any) satisfying it.determine all the values of x (if any) where f '(x) is NOT defined. All the values of x (only which are in the domain of f(x)) from above steps the x-coordinates of the critical points. Then determine the corresponding y-coordinates by substitute each of them.Writing all such pairs (x, y) represents the critical points.\(p(x) = \frac{ x - 4}{-4x² + 4}\)
We have to determine the critical points for function. Using the above steps, p'(x) = 0
=> \(p'(x) = \frac{(-4x² + 4) -( x - 4)(-8x)}{(-4x² + 4)²}\)
\( = \frac{(-4x² + 4) - 8x² - 32x)}{(-4x² + 4)²}\)
\( = \frac{(-12x² - 32x + 4)}{(-4x² + 4)²}\)
so, \(\frac{(-12x² - 32x + 4)}{(-4x² + 4)²} = 0\)
=> - 12x² - 32x + 4 = 0
=> 3x² + 8x + 1 = 0
solve the Quadratic equation by quadratic formula,
=> \(x = \frac{ -8 ± \sqrt { 64 - 12}}{ 6} \)
\(x = \frac{ -4 ± \sqrt {13}}{ 3} \).
Hence, required value are \(x = \frac{ -4 ± \sqrt {13}}{ 3} \).
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