Answer:
The team scored a total of 90 goals.Step-by-step explanation:
The given question is
A futsal team scored 60 goals, corresponding to four-sixths of the league's total goals. How many goals were scored in the league?
If 60 goals represents four-sixths of the total goals, then how many goals were scored?
Here we need to use the rule of three, where the given equivalence is
[tex]60 \ goals = \frac{4}{6}[/tex]
And the total number of goals is represents by 1, which is the 100% of goals.
[tex]x=1\frac{60 \ goals}{\frac{4}{6} }=\frac{360}{4} \ goals\\ x=90[/tex]
Therefore, the team scored a total of 90 goals.
O total de gols marcados no campeonato foi de 90, como calculado por meio de uma equação proporcional representada pela fração de gols marcados pelo time de futsal.
Explanation:A questão relata que o time de futsal marcou 60 gols, o que equivale a quatro sextos do total de gols do campeonato. Para identificar o total de gols do campeonato, podemos configurar uma equação proporcional.
Se 4/6 corresponde a 60 gols, então 1/6 corresponde a 60 dividido por 4, que resulta em 15 gols. Uma vez que temos o valor representando 1/6, para obter o total de gols (ou seja, 6/6), simplesmente multiplicamos 15 por 6. Isso nos dá 90 gols.
Portanto, o total de gols marcados no campeonato foi de 90.
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What must be true regarding the distribution of the population? A. The population must be normally distributed and the sample size must be large. B. There are no requirements on the shape of the distribution of the population. C. The population must be normally distributed. nothing Your answer is correct.D. Since the sample size is large enough comma the population distribution does not nbsp need to be normal.
Answer:
C. The population must be normally distributed.
Step-by-step explanation:
Population distribution have to do with the classification of people living in a particular geographical area into different segment such as Age, Occupation, Sex, Geographical location.
For instance
If Age distribution is use, the total number of people living in say New york will classified into 0-10 11-19years 20-29years and so on
Sex distribution involves distribution into the male and Female Category
Occupation distribution of Population involves classification of occupant of an area according to their Job.. I.e.Drives-15 people, Lawyer =2 people and so on.
Geographical location distribution of population involves the classification of people living in a particular country according to their geographical names. I.e. Abuja=3.5million people etc.
The requirements on the distribution of the population can vary depending on the analytical methods being used. Some methods require the population to be normally distributed, while others, such as those based on the Central Limit Theorem, can work reliably with large sample sizes regardless of whether the population is normally distributed.
Explanation:In the field of statistics, when you are drawing conclusions or inferences from a dataset (sample), there are different requirements depending on the method used. Generally speaking, the assumption about the distribution of the population can vary.
For instance, if you are using methods based on the Central Limit Theorem (CLT), you might not require the population to be normal if your sample size is sufficiently large, as per option D. This is because the CLT states that if the sample size is large enough, the distribution of the sample means will approximate a normal distribution, regardless of the shape of the population distribution.
However, some analytical methods might require the population to be normally distributed for the method to produce reliable results. So, although there is not a one-size-fits-all answer, the requirements on the distribution of the population depend largely on the analytical methods being used.
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Complete the square for the expression
x
2
+8x
x2+8x
. Then factor the trinomial.
Answer:
x^2+8x+16
(x+4)^2
Step-by-step explanation:
x^2 +8x
Take the coefficient of the x term
8
Divide by 2
8/2 =4
Square it
4^2 =16
x^2+8x+16
We can factor it into
(x+8/2) ^2
(x+4)^2
Final answer:
Completing the square for the expression x² + 8x involves adding and subtracting 16 to form the perfect square trinomial (x + 4)² and then subtracting 16. The factored form of the resulting trinomial is (x + 4)² - 16.
Explanation:
To complete the square for the expression x² + 8x, we need to find a number that, when added to 8x, will make the expression a perfect square trinomial. The number we're looking for is ²⁄8², which is 16. So, we add and subtract 16 within the expression to maintain equality.
The expression becomes x² + 8x + 16 - 16. Now the first three terms form a perfect square trinomial (x + 4)², and we still have -16. The expression is (x + 4)² - 16.
To factor the trinomial, we write it as the square of a binomial: (x + 4)². Hence, the expression x² + 8x can be written as (x + 4)² - 16, which is the factored form of the trinomial resulting from the completion of the square.
Find all nth roots. Write your answers in polar form.
−√2+i√2, n=5
Answer:
help me and I will help you
17 24 26 13 what's the mean
Answer:
20
Step-by-step explanation:
Mean is the average of the numbers. You get the average by adding all the numbers and then dividing by the amount of numbers there are.
Example: 17+24+26+13=80 divided by 4 is 20
In one school, a half of all students who like math like science as well. Also, in that school, a third of all students who like science also like math.
b
In that school, what is the ratio of the number of students who like math to the number of students who like science?
Answer: 2/3
Step-by-step explanation:
N is the total number of students
M is the number of students thta like math
S is the number of students that like science.
We know that half of the elements in M also are elements from S
And a third of the elements of S also are elements of M
And because those elements are common elements for both sets, we should have that:
M/2 = S/3
then we have that:
M = (2/3)*S
The ratio is 2/3
this means that the number of students that like math is 2/3 times the number of students that like science.
The ratio of the number of students who like math to the number of students who like science is 2/3
What is ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
For the given case, we can assume the real quantities by variables.
Let we have:
M = Number of students who like mathsS = Number of students who like science.By given information, we have:
M/2 students like science too.S/3 students like maths too.Since the statement "M/2 students like science too" and "S/3 students like maths too" are same thing, so they're taking about same students who like math and science both, thus:
[tex]\dfrac{M}{2} = \dfrac{S}{3}\\\\\text{Multiplying both the sides by 2/S}\\\\\dfrac{M}{S} = \dfrac{2}{3}[/tex]
Thus, the ratio needed (ratio of number of students liking math to the number of students liking science) is M/N = 2/3
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An inventor has developed a new, energy-efficient lawn mower engine. He claims that the engine will run continuously for 5 hours (300 minutes) on a single gallon of regular gasoline. Suppose a simple random sample of 45 engines is tested. The engines run for an average of 290 minutes, assume the population standard deviation is 20 minutes. Test the null hypothesis that the mean run time is at least 300 minutes. Use a left sided test. Use a 0.025 level of significance.
a) Find the critical value for this test.
b) Find the test statistic
c) Find the p-value for this test.
d) My conclusion is :
e) Is the test statistically significant?
f) Could I use a symmetric confidence interval to solve this problem and if so what is it?
Answer:
b,c
Step-by-step explanation:
Using the equation y=x-5, describe how to create a
system of linear equations with an infinite number of
solutions.
Answer:
You would create another equations that have same form as given equation.
For example, given y = (2/3)x - 5
=> Other one could be y = 2[(1/3)x - 5/2]
...
Hope this helps!
:)
Answer:
Sample Response/Explanation: To have an infinite number of solutions, the equations must graph the same line. That means the equations must be equivalent. To form an equivalent equation, use the properties of equality to rewrite the given equation in a different form. Add, subtract, multiply, or divide both sides of the equation by the same amount.
Step-by-step explanation:
2 x + 5 = 10
what is x =?
Answer:
x=[tex]\frac{5}{2}[/tex]
Step-by-step explanation:
First, subtract 5 on both sides since when you subtract 5 from 5, it will give you 0.
Basically we are trying to get rid of the +5.
2x+5-5=10-5
2x=5
Divide by 2 to get rid of the 2 that is combined with the x.
2x/2=5/2
x=[tex]\frac{5}{2}[/tex]
Answer:x=5/2
Step-by-step explanation:
2x+5=10
Subtract 5 from both sides
2x+5-5=10-5
2x=5
Divide both sides by 2
2x/2=5/2
x=5/2
An aquarium manager wants to study gift shop browsing. She randomly observes 120 couples that visit the aquarium with children and finds that 107 enter the gift shop at the end of their visit. She randomly observes 76 couples that visit the aquarium with no children and finds that 59 enter the gift shop at the end of their visit. Find the lower bound of the 95% confidence interval for the difference in population proportions of couples with children that enter the gift sho
Answer:
95% confidence interval for the difference in population proportions of couples with children and with no children is [0.00134 , 0.219].
Step-by-step explanation:
We are given that an aquarium manager wants to study gift shop browsing.
She randomly observes 120 couples that visit the aquarium with children and finds that 107 enter the gift shop at the end of their visit. She randomly observes 76 couples that visit the aquarium with no children and finds that 59 enter the gift shop at the end of their visit.
Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportions is given by;
P.Q. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of couples that visit the aquarium with children who enters the gift shop at the end of their visit = [tex]\frac{107}{120}[/tex] = 0.89
[tex]\hat p_2[/tex] = sample proportion of couples that visit the aquarium with no children who enters the gift shop at the end of their visit = [tex]\frac{59}{76}[/tex] = 0.78
[tex]n_1[/tex] = sample of couples that visit the aquarium with children = 120
[tex]n_2[/tex] = sample of couples that visit the aquarium with no children = 76
Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.
So, 95% confidence interval for the difference between population proportions, is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < [tex]{(\hat p_1-\hat p_2)-(p_1-p_2)}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95
P( [tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < [tex](p_1-p_2)}[/tex] < [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95
95% confidence interval for [tex](p_1-p_2)}[/tex] =
[[tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex],[tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex]]
= [ [tex](0.89-0.78)-1.96 \times {\sqrt{\frac{0.89(1-0.89)}{120}+ \frac{0.78(1-0.78)}{76}} }[/tex] , [tex](0.89-0.78)+1.96 \times {\sqrt{\frac{0.89(1-0.89)}{120}+ \frac{0.78(1-0.78)}{76}} }[/tex] ]
= [0.00134 , 0.219]
Therefore, 95% confidence interval for the difference in population proportions of couples with children and with no children is [0.00134 , 0.219].
Jesse has 252 inches of string how many yards of string does he have
Answer:
7 yards
Step-by-step explanation:
252/12=21 21/3=7
Help anyone can somebody explain the answer please
Answer:
D
Step-by-step explanation:
8^2+x^2=16^2
PLEASE HELP ME I WILL MARK BRAINLIEST!!!
Answer:
v= 205.3
Step-by-step explanation:
The formula to solve a pyramid is v=(l*h*w)/3.
11*7*8=616
616/3=205.333.... (repeating 3)
about 205.3
~sorry I couldn't draw it out~
The National Assessment of Educational Progress (NAEP) gives a math assessment every year to 12th graders in the U.S. On the math test, a score above 275 indicates that a student has the skills to balance a checkbook. For a random sample of 500 young men, the mean NAEP math score is 272 with a standard deviation of 78. Do we have evidence to support the claim that young men nationwide have a mean score below 275? The null and alternative hypotheses are H 0: μ = 275, H a: μ < 275. The level of significance is 5%. The t-test statistic is −0.86 with a P-value of 0.20. What is the correct conclusion? Group of answer choices The evidence suggests that young men nationwide have a mean score less than 275. We do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide. The evidence suggests that young men nationwide have a mean score equal to 275. It is likely that these 500 young men have a mean score less than 275.
We do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide.
Explanation:The null hypothesis (H0) is that the mean NAEP math score for young men nationwide is 275. The alternative hypothesis (Ha) is that the mean score is less than 275. The level of significance is 5%.
The t-test statistic is -0.86 and the p-value is 0.20. Since the p-value is greater than the significance level (0.20 > 0.05), we fail to reject the null hypothesis. This means we do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide.
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Senior management of a consulting services firm is concerned about a growing decline in the firm’s weekly number of billable hours. The firm expects each professional employee to spend at least 40 hours per week on work. In an effort to understand this problem better, management would like to estimate the standard deviation of the number of hours their employees spend on work-related activities in a typical week. Rather than reviewing the records of all the firm’s full-time employees, the management randomly selected a sample of size 50 from the available frame. The sample mean and sample standard deviations were 46.4 and 7.2 hours, respectively. Construct a 97% confidence interval for the standard deviation of the number of hours this firm’s employees spend on work-related activities in a typical week
With 97% confidence, we estimate that the true standard deviation of the firm's employees' work hours lies within the range of approximately 5.832 to 7.950 hours per week.
To construct a 97% confidence interval for the standard deviation [tex](\(\sigma\))[/tex], we use the chi-square distribution. The formula for the confidence interval is given by:
[tex]\[ \left( \sqrt{\frac{(n-1)s^2}{\chi_{\alpha/2}^2}}, \sqrt{\frac{(n-1)s^2}{\chi_{1-\alpha/2}^2}} \right) \][/tex]
where [tex]\(n\)[/tex] is the sample size, [tex]\(s\)[/tex] is the sample standard deviation, [tex]\(\alpha\)[/tex]is the significance level, and [tex]\(\chi_{\alpha/2}^2\)[/tex] and [tex]\(\chi_{1-\alpha/2}^2\)[/tex] are the chi-square critical values.
Given that [tex]\(n = 50\)[/tex] , [tex]\(s = 7.2\)[/tex] , and [tex]\(\alpha = 0.03\)[/tex] (97% confidence level corresponds to [tex]\(\alpha/2 = 0.015\))[/tex] , we look up the critical values from the chi-square distribution table. For 49 degrees of freedom (50-1), the critical values are approximately 31.449 and 71.420.
Substitute these values into the formula:
[tex]\[ \left( \sqrt{\frac{49 \times 7.2^2}{31.449}}, \sqrt{\frac{49 \times 7.2^2}{71.420}} \right) \][/tex]
The formula for the confidence interval is:
[tex]\[ \left( \sqrt{\frac{(n-1)s^2}{\chi_{\alpha/2}^2}}, \sqrt{\frac{(n-1)s^2}{\chi_{1-\alpha/2}^2}} \right) \][/tex]
Given:
[tex]\[ n = 50, \ s = 7.2, \ \alpha = 0.03 \][/tex]
For 49 degrees of freedom (50-1), the chi-square critical values are approximately 31.449 [tex](\(\chi_{\alpha/2}^2\))[/tex] and 71.420 [tex](\(\chi_{1-\alpha/2}^2\))[/tex] .
Now, substitute these values into the formula:
[tex]\[ \left( \sqrt{\frac{49 \times 7.2^2}{31.449}}, \sqrt{\frac{49 \times 7.2^2}{71.420}} \right) \][/tex]
Calculating this yields approximately (5.832, 7.950).
Therefore, the 97% confidence interval for the standard deviation of the weekly work hours is approximately (5.832, 7.950).
In summary, with 97% confidence, we estimate that the true standard deviation of the firm's employees' work hours lies within the range of approximately 5.832 to 7.950 hours per week.
Order the numbers from least to greatest typical number of hours of sleep per employee
Answer:What?
Step-by-step explanation:
The vertex of the graph of a quadratic function is in the second quadrant. The related equation has no real solutions. Which statement is true?
a) The graph opens up.
b) The graph opens down.
c) The y-intercept is 0.
d) The axis of symmetry is x = 0.
Answer: a) The graph opens up.
Step-by-step explanation:
The vertex is the minimum/maximum of a parabola.
We know that the vertex is in the second quadrant (so it is in the quadrant of positive y values and negative x values)
We also know that it has no real roots, so the graph never touches the x-axis, and knowing that the vertex is above the x-axis, then the graph must open upwards.
Then the correct option is:
a) The graph opens up.
When the vertex of the graph of a quadratic function is in the second quadrant and has no real solutions, this means that the graph opens down. The other statements provided are not necessarily true in this specific context.
Explanation:In the context of this problem related to quadratic functions, if the vertex of the graph is in the second quadrant and there are no real solutions, the correct statement is (b) the graph opens down. Quadratic functions in the second quadrant that have no real solutions indeed point downwards. This is due to the fact that the function cannot touch or cross the x-axis (indicating that there are no real solutions).
As for option (c), the y-intercept could be any real number, so it does not have to be 0. Concerning option (d), the axis of symmetry can't be x = 0 as the vertex is in the second quadrant and x = 0 is the y-axis. Lastly, option (a) is false because if the graph opened up it would pass through the x-axis, providing real solutions, contrary to what is given in the problem.
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8 people share 1 pizza. How much each person receive ?
Answer:
1
Step-by-step explanation:
because one pizza is cut into 8 so
1 piece would be even
=1
The amount of pizza received by each person is 0.125.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The number of pizza is 1.
And, the total number of people is 8.
Now, the share of each people can be obtained as follows,
Consider that each people get the equal share.
The arithmetic operation used in this case is division.
Then, the problem can be solved by dividing 1 by 8 as follows,
⇒ 1 ÷ 8 = 1/8 = 0.125
The result of the division is a decimal number which shows that the amount of pizza for each people is the smallest part less than the whole.
Hence, the share of pizza received by each person is 0.125.
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What is the growth or decay and the percentage rate of Y=23(0.292)^x
Answer:
So the decay percentage rate is of 70.8%
Step-by-step explanation:
An exponentil function has the following format:
[tex]y = ca^{x}[/tex]
In which c is a constant.
If a>1, we have that a = 1 + r and r is the growth rate.
If a<1, we have that a = 1 - r and r is the decay rate.
In this problem:
a = 0.292
A is lesser than 1, so r is the decay rate.
1 - r = 0.292
r = 1 - 0.292
r = 0.708
So the decay percentage rate is of 70.8%
We randomly place 200 balls independently in 100 boxes in the most natural uniform way. That is, each ball is placed independently from the rest of the balls in such a way that the probability to put it into the ith box is one-percent (1 ≤ i ≤ 100). Let X denote the number of empty boxes at the end. What is the expected value of X? I also want the numerical value.
Answer:
The expected value of X is 13.4.
Step-by-step explanation:
For each boox any time a ball is placed, there are only two possible outcomes. Either the ball is put into the box, or it is not. The boxes are independent. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
200 balls placed in boxes:
This means that [tex]n = 200[/tex]
For each box, the ball has 1/100 probability of being put there:
This means that [tex]p = \frac{1}{100} = 0.01[/tex]
The probability of a box being empty:
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.01)^{0}.(0.99)^{200} = 0.1340[/tex]
Let X denote the number of empty boxes at the end. What is the expected value of X?
Each box has a 0.1340 probability of being empty at the end.
There are 100 boxes.
So
0.1340*100 = 13.4
The expected value of X is 13.4.
Distance from (3,5) and (-2,-2)
Answer:5,7
Step-by-step explanation:
5.62 (6.2+6.2) divided by 2
Look at the attached picture z
⤴
Hope it will help u...
30 points!!!!!!! EASY MATH!!!!!!!!!! PLZ HELP!!!!
f(x)=(x+1)^2
What is the domain of f?
Answer:
Domain: all real values
Step-by-step explanation:
f(x)=(x+1)^2
The domain is the values for x
We can use any value for x in the equation
Domain: all real values
Answer:
All real values of x
Step-by-step explanation:
f(x) = (x + 1)² is defined for all x
Hence the domain includes all real values of x
ow much fencing is required to enclose a circular gardan whose radius is 14m used 22 / 7 for pi
To enclose a circular garden with a radius of 14m, you would need 88 meters of fencing.
Explanation:To find the amount of fencing required to enclose a circular garden, you need to calculate the circumference of the garden. The formula for circumference is given by C = 2πr, where r is the radius of the garden.
Given that the radius is 14m, you can use the value of π as 22/7. So, the circumference is C = 2 * (22/7) * 14 = 88m.
Therefore, you would need 88 meters of fencing to enclose the circular garden.
Solve for v.
7(v-3)+7v = 21
Simplify your answer as much as possible.
Answer:
v = 3
Step-by-step explanation:
7(v - 3) + 7v = 21
distribute the 7 into the parentheses
7v -21 +7v = 21
combine like terms
14v - 21 = 21
add 21 on both sides
14v + 21 - 21 = 21 + 21 which equals 14v = 42
divide both sides by 14 to isolate v
14v/14 = 42/14
v = 3
hope this helps :)
It takes 15 hours for 4 men to paint a room.
How many men would be needed to paint the room in 10 hours?
Answer:
6
Step-by-step explanation:
If there was one man, he would have taken 15×4= 60 hours
To complete the job in 10 hours, 60÷10 = 6 men will be needed
To paint the room in 10 hours instead of 15, the calculation shows that 6 men would be needed. This is determined through the concept of work rate and inverse proportions, calculating the total man-hours and then dividing by the desired hours.
The question involves determining the number of men needed to paint a room in 10 hours, given it takes 15 hours for 4 men to paint the same room. This problem can be solved using the concept of work rate and inverse proportions, which is a common method in Mathematics to deal with time and work problems. First, we calculate the work rate of the 4 men together and then find how many men would be needed to complete the job in 10 hours at a proportional rate.
Calculation steps:
Identify the original work rate: 4 men take 15 hours.Compute the total man-hours required for the job: 4 men × 15 hours = 60 man-hours.To find the time it would take for an unknown number of men to complete the same task in 10 hours, set up the equation: x men × 10 hours = 60 man-hours.Solving for x gives x = 60 man-hours / 10 hours = 6 men.Therefore, 6 men would be needed to paint the room in 10 hours.
Mr. Ramirez purchased 20 concert tickets for a total of $225. The concert tickets costs $15 for adults and $10 for children under the age of 12. Write the system of equations and solve algebraically.
Answer:
C = 15
Step-by-step explanation:
Let A = # of adults and C = # of children.
A + C = 20
15A + 10C = 225
There are several ways to solve this system; here is one of them.
From the first equation: C = 20 - A
Substitute into the second equation: 15A + 10(20 - A) = 225
Multiply, collect terms, and subtract 200 from each side: 5A = 25 => A = 5
Since C = 20 - A, C = 15
The number of children's ticket bought is 15 and the number of adult tickets bought is 5.
The system of equations that can be derived from the question are:
a + b = 20 equation 1
15a + 10b = 225 equation 2
Where:
a = number of children's ticket bought
b = number of adult tickets bought
In order to determine the value of b, multiply equation 1 by 15.
15a + 15b = 300 equation 3
Subtract equation 2 from 3
5b = 75
b = 15
In order to determine the value of a, substitute for b in equation 1
a + 15 = 20
a = 20 - 15
a = 5
To learn more, please check: brainly.com/question/23589883?referrer=searchResults
Find the value of x
Answer:
x = 66
Step-by-step explanation:
The sum of the angles of a quadrilateral is 360 degrees
103+133+58+x = 360
Combine like terms
294+x = 360
Subtract 294 from each side
294+x-294 = 360-294
x = 66
The table shows data representing the total surface area
of a square pyramid with a slant height of 5 centimeters.
Answer:
B and C
Step-by-step explanation:
Answer:
parabola and quadratic
Step-by-step explanation:
just answered it
Reading 183 pages in 61 minutes is a pace of how many pages a minute
Answer: 3 pages per minute
Step-by-step explanation:
61x=183
x= the amount of pages
183/61= 3 pages
You can check this by multiplying 3 by 61 which = 183.
Answer:
3
Step-by-step explanation:
183 x
----- = -----
61 1
Cross Multiply
183= 61x
Divide
3=x
Probability. Help! I'll give you Brainliest if correct as well as quite a bit of points.
A card is chosen at random from a standard deck of 52 cards, and then it is replaced and another card is chosen. What is the probability that at least one of the cards is a diamond or an ace?
Answer:
17/52
Step-by-step explanation:
there are 13 diamonds in a standard deck of 52 cards.
the probability of getting a diamond will therefore be 13/52 = 1/4
there are 4 aces in a standard deck of 52 cards.
the probability of getting an ace will therefore be 4/52 = 1/13
the probability of getting a diamond or an ace will be 1/4 + 1/13
= 17/52