Answers
Answer:
b
Step-by-step explanation:
Related Questions
In a class of 42 students, the number of boys is 2/5 of the girls. Find the number of boys and girls in the class.
Answers
Answer:
BOYS = 30.
GIRLS = 12.
Step-by-step explanation:
Boys: B
Girls: G
B = (2/5)G
B + G = 42.
(2/5)G + G = 42
2G + 5G = 210
7G = 210
G = 210/7
G = 30.
B = (2/5)G
B = (2/5)(30)
B = 60/5
B = 12.
Answer:
\(\Huge \boxed{\bold{\text{12 Boys}}}\)
\(\Huge \boxed{\bold{\text{30 Girls}}}\)
Step-by-step explanation:
Let the number of girls be \(g\) and the number of boys be \(b\).
According to the problem: \(b = \frac{2}{5} \times g\)
We also know that the total number of students is 42, so \(b + g = 42\).
Now, we have two equations with two variables:
\(b = \frac{2}{5} \times g\) \(b + g = 42\)We can solve these equations to find the values of \(b\) and \(g\).
Step 1: Solve for \(\bold{b}\) in terms of \(\bold{g}\)
From the first equation, we have\(b = \frac{2}{5} \times g\)
Step 2: Substitute the expression for \(\bold{b}\) into the second equation
Replace \(b\) in the second equation with the expression we found in step 1.
\(\frac{2}{5} \times g + g = 42\)
Step 3: Solve for \(\bold{g}\)
Now, we have an equation with only one variable, \(g\):
\(\frac{2}{5} \times g + g = 42\)
To solve for \(g\), first find a common denominator for the fractions:
\(\frac{2}{5} \times g + \frac{5}{5} \times g = 42\)
Combine the fractions:
\(\frac{7}{5} \times g = 42\)
Now, multiply both sides of the equation by \(\frac{5}{7}\) to isolate \(g\):
\(g = 42 \times \frac{5}{7}\)\(g = 30\)Step 4: Find the value of \(\bold{b}\)
Now that we have the value of \(g\), we can find the value of \(b\) using the first equation:
\(b = \frac{2}{5} \times g\)\(b = \frac{2}{5} \times 30\)\(b = 12\)So, there are 12 boys and 30 girls in the class.
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2-6² +4 2
please help it's review for my finals
Answers
Answer: I don’t know :(
Step-by-step explanation:
Answer:
8
Have an amazing day!
Find the value of x in this figure.
MN and MP are tangent to circle O
Answers
Answer:
P and N are 90 because the tangent drawn from a external point is perpendicular to the circle
90+90+60+x=360
x=360-240
x= 120
(Please help, due by midnight PST in 2hours) Find x and y.
Answers
I hope it helped. Give Brainly if it help
What is the following product? Assume x>0
3√x^2 * 4√x^3
Answers
Answer: its c. x(12root x power 5)
Step-by-step explanation:
What is the resulting integral?
Answers
Answer:
\(\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx = \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Exponential Rule [Root Rewrite]: \(\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}\)Exponential Rule [Rewrite]: \(\displaystyle b^{-m} = \frac{1}{b^m}\)Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Antiderivatives - Integrals
Integration Constant C
U-Substitution
U-SolveIntegration Rule [Reverse Power Rule]: \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)
Integration Property [Multiplied Constant]: \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)
Integration Property [Addition/Subtraction]: \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)
Step-by-step explanation:
Step 1: Define
\(\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx\)
Step 2: Identify Variables
Find the variables u-solve using u-substitution.
U-Substitution
\(\displaystyle u = 1 + \sqrt{x}\)
\(\displaystyle du = \frac{1}{2\sqrt{x}}dx\)
U-Solve
\(\displaystyle x = (u - 1)^2\)
\(\displaystyle dx = 2\sqrt{x}du\)
Step 3: Integration
[Integral] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle 2\int {\frac{1}{(1 + \sqrt{x})^5}} \, dx\)[Integral] U-Solve: \(\displaystyle 2\int {\frac{1}{(1 + \sqrt{(u - 1)^2})^5}} \, 2\sqrt{x}du\)[Integral] Simplify: \(\displaystyle 2\int {\frac{2\sqrt{x}}{u^5}} \, du\)[Integral] Rewrite [Integration Property - Multiplied Constant]: \(\displaystyle 4\int {\frac{\sqrt{x}}{u^5}} \, du\)[Integral] U-Solve: \(\displaystyle 4\int {\frac{\sqrt{(u - 1)^2}}{u^5}} \, du\)[Integral] Simplify: \(\displaystyle 4\int {\frac{u - 1}{u^5}} \, du\)[Integral] Rewrite [Integration Property - Subtraction]: \(\displaystyle 4[\int {\frac{u}{u^5}} \, du - \int {\frac{1}{u^5}} \, du]\)[Integrals] Simplify: \(\displaystyle 4[\int {\frac{1}{u^4}} \, du - \int {\frac{1}{u^5}} \, du]\)[Integrals] Rewrite [Exponential Rule - Rewrite]: \(\displaystyle 4[\int {u^{-4}} \, du - \int {u^{-5}} \, du]\)[Integrals] Reverse Power Rule: \(\displaystyle 4[\frac{u^{-3}}{-3} - \frac{u^{-4}}{-4}] + C\)Rewrite [Exponential Rule - Rewrite]: \(\displaystyle 4[\frac{-1}{3u^3} + \frac{1}{4u^4}] + C\)[Brackets] Multiply: \(\displaystyle \frac{-4}{3u^3} + \frac{4}{4u^4} + C\)Back-Substitute: \(\displaystyle \frac{-4}{3(1 + \sqrt{x})^3} + \frac{4}{4(1 + \sqrt{x})^4} + C\)Combine: \(\displaystyle \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C\)Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-
axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?
4
3
1
3-2-11
99 +4
1 234
4
A
$65
A B and B C
A A, B B, C C
Fach trianola ie a rinht triannla
Answers
The reason why Figure A is congruent to Figure C is that they undergo the same sequence of transformations: a translation followed by a reflection.
The statement "Figure A is translated 3 units right and 2 units up. The translated figure is labeled Figure B. Figure B is reflected over the x-axis. The reflected figure is labeled Figure C" describes a sequence of transformations applied to Figure A to obtain Figure C.
When Figure A is translated 3 units right and 2 units up, it undergoes a rigid transformation known as a translation. This transformation preserves the shape and size of the figure. The translated figure, Figure B, will have the same dimensions and orientation as Figure A but will be shifted to the right and up.
When Figure B is reflected over the x-axis, it undergoes a reflection. This transformation flips the figure vertically, changing the sign of the y-coordinates of its vertices while keeping the x-coordinates the same. The reflected figure, Figure C, will have the same shape and size as Figure B, but it will be oriented in the opposite direction.
Since translations and reflections are both rigid transformations, they preserve congruence. Therefore, Figure A and Figure C are congruent because they undergo the same sequence of transformations (translation followed by reflection) from Figure A.
In conclusion, Figures A and C go through the same set of transformations, a translation and a reflection, which explains why they are congruent.
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whats 1girl + 1 girl=
Answers
Answer:
(whats 1girl + 1 girl=) uhh ima go with 2girl ;)
Step-by-step explanation:
whats 1girl + 1 girl=?
well 1+1=2 so 1girl + 1 girl= 2girl
WHAT IS 1% OF 75??? !!!!!
HELPPPP!!!!
Answers
Answer:
the answer is 0.75
Step-by-step explanation:
you divide by 100
Answer: 0.75
Just divide 75 by 100. Hope this helps
Draw an abacus and illustrate this expression 4×8⁴+2×8²+4×8⁰ on it
Answers
According to the information, this number on an abacus would look like this: tens of a thousand = 10,000, units of a thousand = 6,000, hundreds = 500, tens = 10, and units = 6.
How to illustrate this value on an abacus?To illustrate this value on an abacus we must find the number of this operation as shown below:
4 * 8⁴ + 2 * 8² + 4 * 8⁰4*4,096 + 2*64 + 4*116,384 + 128 + 416,516Now we must express it in an abacus, then we must separate each number by classifying it in the type of units to which it corresponds as shown below:
ten thousand = 10,000thousand units = 6,000hundreds = 500tens = 10units = 6Learn more about abacus in: https://brainly.com/question/13385199
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What are the coordinates of the point on the directed line segment from ( − 7 , 9 ) (−7,9) to ( 3 , − 1 ) (3,−1) that partitions the segment into a ratio of 2 to 3?
Answers
The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).
To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.
Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:
x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3
Similarly, the y-coordinate of the point is given by:
y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5
Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).
To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).
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Which expression represents "3 times the quantity 1 plus p"?
Answers
Answer: 3(1p)
Step-by-step explanation:
Answer: 3+3p or 3p+3
Step-by-step explanation:First write the information given. You will need to multiply the quantity 3 by each of the terms one and p. It should look something like this 3(1+p). Multiply three to both quantities and the answer yields 3+3p or 3p+3.
Multiply. (2.1 X 10/2) X (3.5 X 10/5)
Answers
we first solve each bracket
we can write 2.1 as 21/10 and 3.5 as 35/10
(21/10x10/2)x(35/10x10/5)
the 10's simplify
21/2x35/5=21/2x7=147/2=73.5
A large company event was held in a park on a hot day. Afterward, many of the employees got sick. Some blamed the potato salad. To investigate, a random sample of 20 sick employees and a random sample of 20 non-sick employees are selected. Each selected individual is asked if they ate the potato salad. The results are displayed in the table.
Management would like to know if there is convincing evidence that the distribution of responses about eating the potato salad differs for all employees who are sick versus those who are not sick. What are the appropriate hypotheses for this test?
H0: There is no difference in the distribution of responses among those who are and are not sick.
Ha: There is a difference in the distribution of responses among those who are and are not sick.
H0: There is a difference in the distribution of responses among those who are and are not sick.
Ha: There is no difference in the distribution of responses among those who are and are not sick.
H0: There is no difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Ha: There is a difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
H0: There is a difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Ha: There is no difference in the distribution of responses for the 20 employees who are sick and the 20 employees who are not sick.
Answers
The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.
The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.
The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.
On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.
By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.
Therefore, the correct answer is:
H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.
Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.
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The number of homeless people in a city decreased from 1800 to 1500. Find the percentdecrease in homelessness.
Answers
= (1800-1500)/1800 x 100%
=300/1800 x 100%
= 16.67 %
Percentage decrease
= 16.67 %
Best answer gets brain ly
Answers
The new coordinates of the image of the shape are
(3, -2) (2, -2) (2, -4)The picture of the graph showing the image is attached
How to make a 90 degrees clockwise rotationThe rule for 90 degrees clockwise rotation is
(x, y) becomes (y, -x)
The rule involves interchanging the coordinates of the ordered pair such that x takes the place of y and y tales the place of x and a change of sign
performing the rotation we have the new coordinates as below
(2, 3) becomes (3, -2)
(2, 2) becomes (2, -2)
(4, 2) becomes (2, -4)
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Which of the following is the product of the rational expressions shown below ? (x + 3)/(x + 2) * (x - 3)/(x - 2)
Answers
Answer:
Option D : \(\frac{x^2-9}{x^2-4}\) is the correct answer.
Step-by-step explanation:
Given rational expression is:
\(\frac{x+3}{x+2}*\frac{x-3}{x-2}\)
In the first step of solving the rational expression, we will multiply the nominators and denominators.
\(\frac{(x+3)(x-3)}{(x+2)(x-2)}\)
\(\frac{x^2-3x+3x-9}{x^2-2x+2x-4}\)
Now we will solve the alike terms.
\(\frac{x^2-9}{x^2-4}\)
The product of rational expression is \(\frac{x^2-9}{x^2-4}\)
Hence,
Option D : \(\frac{x^2-9}{x^2-4}\) is the correct answer.
Answer:
option D
Step-by-step explanation:
Ap3x
Hallie used a birthday check her mother gave hero to start a savings account. She plans to save $25 per month as well. After 9 months Hallie has 300. Write and solve a linear equation to find original check from Hallie's mother.
Answers
Answer:
$75
Step-by-step explanation:
x+(25×9)=300
x+225=300
x=300-225
x=$75
A computer training institute has 625 students that are paying a course fee of $400. Their research shows that for every $20 reduction in the fee, they will attract another 50 students. Which equation could be used to represent this situation, where x is the course fee and R(x) is the total revenue?
R(x) = −2.5x2 + 1625x
R(x) = −3x2 + 1650x
R(x) = 3x2 − 1650x
R(x) = 2.5x2 − 1625x
Answers
The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²
What is an Equations?Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
N(x) = 625 + 2.5x
The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:
R(x) = (625 + 2.5x)(400 - x)
Simplifying the expression, we get:
R(x) = 250000 + 375x - 2.5x²
Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:
R(x) = 250000 + 375x - 2.5x²
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Help solving this problem
Answers
Answer:
A=0.50
B=0.477
C=0.423<p<0.531
Step-by-step explanation:
sample size N :333
number of success X: 159
sample part of success x/n = 159/333
x=0.477 B
0.50 A Half a chance to flip a tail or head
part C:
\(0.477 plusminus 1.96 * \sqrt{ \frac{0.477 (1 - 0.477)}{333} } \)
simplify
\(0.477 plusminus 1.96 * 0.0536\)
expand
\(0.477 + 1.96 * 0.0536\)
\(0.531\)
expand minus
\(0.477 - 1.96 * 0.0536\)
\(0.423\)
finally answer part c
\(0.423 < p < 0.531\)
an employee at a factory is paid $9.25 per hour plus a $8.00 bonus for every 20 transformers assemble.
Answers
Answer:
Step-by-step explanation
Answer:
$13.47 per hour
Step-by-step explanation:
Total earnings = 9.25 (h) + 8 (t/20)
Where h is the number of hours and t is the number of transformers.
Since he worked for 36 hours and assembled 380 transformers:
Total earnings = 9.25 (36) + 8 (380/20)
Total earnings = 333+152 = $485
Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):
485/36 = $13.47 per hour.
2x² + 5x, what will it a Perfect Square? make
Answers
Answer:
2x² + 5x + c = 0
For this quadratic equation to have one double root, the discriminant must equal 0.
5² - 4(2)(c) = 0
25 - 8c = 0
c = 25/8
2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.
Explanation:2x² + 5x is not a perfect square.
A perfect square is an expression that can be factored into the square of a binomial. To determine if an expression is a perfect square, we can look at the coefficient of x². In this case, the coefficient is 2, which is not a perfect square.Learn more about Perfect Square here:https://brainly.com/question/34063927
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-2(x + 2) =?x - 4
Pleeeaseee answer
Answers
X= 0
What is the slope of the line
Answers
Step-by-step explanation:
Look at the points (0,-3) and ( 3,0)
slope, m = rise / run = 3 / 3 = 1
Answer:
1
Step-by-step explanation:
y=x+3
Mrs. Daiz has 9 eggs. She cooks 5 how mich left
Answers
Answer:
You have for uncooked eggs left.
Step-by-step explanation:
9 (total amount of eggs) - 5 (eggs left after she cooks) = 4 eggs cooked.
Please help me solve this Question 1)Y=x^6/5 , y=4x^1/5
Find the area between the curves
…The answer they want looks similar to this (ex. 123/455 • 12^11/10)
Thank you so much I really appreciate it
Answers
Answer:
\(\frac{200}{33} \cdot 4^{\frac{1}{5} }\)
Step-by-step explanation:
We have :
\(y = x^{\frac{6}{5} } \,\,\, and \,\,\, y = 4x^{\frac{1}{5} }\)
\(y = x^{\frac{6}{5} } = 4x^{\frac{1}{5} }\\\\\implies x^{\frac{6}{5} } = 4x^{\frac{1}{5} }\\\\\implies 4x^{\frac{1}{5} } - x^{\frac{6}{5} } = 0\\\\\implies x^{\frac{1}{5} }[4 - x] = 0\\\\\implies x^{\frac{1}{5} } = 0 \;\;\;or\;\;\;4-x=0\\\\\implies x = 0 \;\;\;or\;\;\; x = 4\)
Area between the curves:
\(\int\limits^4_0 {4x^{\frac{1}{5} }} \, dx -\int\limits^4_0 {x^{\frac{6}{5} }} \, dx \\\\=4\int\limits^4_0 {x^{\frac{1}{5} }} \, dx -\int\limits^4_0 {x^{\frac{6}{5} }} \, dx \\\\=4[\frac{x^{^{\frac{1}{5} +1}}}{\frac{1}{5} +1} ]_{_0}^{^4}-[\frac{x^{^{\frac{6}{5} +1}}}{\frac{6}{5} +1} ]_{_0}^{^4}\\\\=4[\frac{x^{^{\frac{6}{5}}}}{\frac{6}{5}} ]_{_0}^{^4} - [\frac{x^{^{\frac{11}{5}}}}{\frac{11}{5}} ]_{_0}^{^4}\\\\\)
\(= 4(\frac{5}{6})[x^{^{\frac{6}{5}}}]_{_0}^{^4} - \frac{5}{11} [x^{^{\frac{11}{5}}}]_{_0}^{^4}\\\\=\frac{10}{3}[4^{^{\frac{6}{5}}}-0^{^{\frac{6}{5}}}] -\frac{5}{11}[4^{^{\frac{11}{5}}}-0^{^{\frac{11}{5}}}] \\\\=\frac{10}{3} [4^{^{\frac{5}{5}}} * 4^{^{\frac{1}{5}}}] - \frac{5}{11} [4^{^{\frac{10}{5}}} * 4^{^{\frac{1}{5}}}]\\\\=\frac{10}{3} [4 * 4^{^{\frac{1}{5}}}] - \frac{5}{11} [4^{^{2}} * 4^{^{\frac{1}{5}}}]\\\\\)
\(= 4^{^{\frac{1}{5}}}[\frac{10*4}{3} - \frac{5*4^2}{11} ]\\\\= 4^{^{\frac{1}{5}}}[\frac{40}{3} - \frac{80}{11} ]\\\\= 4^{^{\frac{1}{5}}}[\frac{40(11) - 80(3)}{3(11)} ]\\\\= 4^{^{\frac{1}{5}}}[\frac{440 - 240}{33} ]\\\\= 4^{^{\frac{1}{5}}}[\frac{200}{33} ]\)
A right triangular prism is shown.
6 in.
11 in.
8 in.
What is the volume in cubic inches of the prism? Enter only the number.
Answers
The volume in cubic inches of the prism is 528 cubic inches.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of the Cuboid.
The volume is calculated as:-
V = L x W x H
V = 6 x 11 x 8
V = 528 cubic inches
Therefore the volume in cubic inches of the prism is 528 cubic inches.
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Many people use scanners to read documents and store them into pdf file. To help determine which brand of scanner to buy, a student conducts an experiment in which 8 different documents were scanned by each of the two scanners that he is interested in. He records the number of errors made by each. Can he infer that Brand A (the more expensive scanner) is better than Brand B
Answers
The data is missing in the question. The data is provided below :
Document : 1 2 3 4 5 6 7 8
Brand A 17 29 18 14 21 25 22 29
Brand B 21 38 15 19 22 30 31 37
Solution :
State of the hypothesis of the null hypothesis and alternate hypothesis.
Null hypothesis : \($h_A = h_B$\)
Alternate hypothesis : \($h_A > h_B$\)
These hypothesis is a one tailed test. The null hypothesis will get rejected when the mean difference between the sample means is very small.
Significance level = 0.05
Therefore the standard error is : \($SE = \sqrt{(\frac{s^2_1}{n_1})+(\frac{s^2_2}{n_2})}$\)
= 3.602
And the degree of freedom, DF = 14
\($t=\frac{(x_1-x_2)-d}{SE}$\)
= -1.319
Here, \($s_1$\) = standard deviation of the sample 1
\($s_2$\) = standard deviation of the sample 2
\($n_1$\) = size of the sample 1
\($n_2$\) = size of the sample 2
\($x_1$\) = mean of the sample 1
\($x_2$\) = mean of the sample 2
d = the hypothesis difference between the population mean
The observed difference in a sample means t static of -1.32. From t distribution calculator to determine P(\($t \leq -1.32$\)) = 0.1042
Since the P value of 0.1042 is greater than significance level o 0.05, we therefore cannot reject the null hypothesis.
But from the test, we have no sufficient evidence that supports that Brand A is better than Brand B.
A family bought a total of 13 tickets to a magic show, some adult and some child. The family paid a total of $85
Adult tickets are $15 each and child tickets are $5 each.
Let x represent adult tickets and y represent child tickets.
Write an equation to model the total amount of money that they spent.
Answers
Answer:
250 $3 tickets and 100 $2 tickets were sold.
Step-by-step explanation:
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?
Solution:
Step 1: Set up a table with quantity and value.
quantityvaluetotal$3 tickets$2 ticketstogether
Step 2: Fill in the table with information from the question.
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?
Let x = number of $3 tickets
Let y = number of $2 tickets
Total = quantity × value
quantityvaluetotal$3 ticketsx33x$2 ticketsy22ytogether350950
Step 3: Add down each column to get the equations
x + y = 350 (equation 1)
3x + 2y = 950 (equation 2)
Use Substitution Method
Isolate variable x in equation 1
x = 350 – y (equation 3)
Substitute equation 3 into equation 2
3(350 – y) + 2y = 950
1050 – 3y + 2y = 950
3y – 2y = 1050 – 950
y = 100
Substitute y = 100 into equation 1
x + 100 = 350
x = 250
A farmer, Mrs. Many, grows and sells two popular varieties of tomatoes: Better Boy tomatoes and Big Beef tomatoes. Both varieties of tomato take about 75 days to mature. She is designing a study to test the effectiveness of a new soil additive to increase tomato growth. She has 40 Better Boy tomatoes and 60 Big Beef tomatoes for her experiment.
Required:
a. Preliminary research suggests that Better Boy tomatoes and Big Beef tomatoes respond differently to the additive. What sort of experimental design would you choose for this study, and why?
b. Explain why an experiment involving 40 Better Boy tomatoes and 60 Big Beef tomatoes is preferable to one involving 4 Better Boy tomatoes and 6 Big Beef tomatoes.
c. Describe a design for this experiment. Be sure to include a description of how you assign individuals to the treatment groups.
Answers
Answer:
I believe the answer is B tell me if I'm correct please