Answers
ANSWER ; On average, Bailey reads 5/7 books per week
EXPLANATION;
Here, we want to get the average number of books per week Bailey reads
To get this, we simply have to divide the number of books she read by the number of weeks it took her to read them
Mathematically, we proceed as follows;
[tex]2\frac{1}{2}\text{ }\div\text{ 3}\frac{1}{2}[/tex]Now, to proceed with the division, we have to turn each of the mixed fractions to improper fraction ( a fraction that has its numerator greater than its denoinator)
To do this, we multiply the denominator by the stand alone number, then add the numerator; after which we place the sum over the denominator
We have an example as follows;
[tex]a\text{ }\frac{b}{c}\text{ = }\frac{(a\times c)+b}{c}[/tex]Applying this to the fractions, we have;
[tex]2\frac{1}{2}\text{ = }\frac{5}{2}\text{ and 3}\frac{1}{2}\text{ = }\frac{7}{2}[/tex]Finally, we proceed with the division;
[tex]\frac{5}{2}\text{ }\div\text{ }\frac{7}{2}\text{ = }\frac{5}{2}\times\frac{2}{7}\text{ = }\frac{5}{7}[/tex]Related Questions
what value of M makes the triangles similar? A. 1.5B. 5C. 6D. 9
Answers
Answer:
C. 6
Explanation:
If the two triangles are similar, then the ratio of corresponding sides are:
[tex]\frac{m}{3}=\frac{4}{2}[/tex]We solve for m.
[tex]\begin{gathered} \frac{m}{3}=2 \\ \implies m=3\times2 \\ m=6 \end{gathered}[/tex]The value of m is 6.
I really don’t get this one please i’ve been stuck forvever
Answers
Answer:
AAS
Step-by-step explanation:
2021/2022-YoryyQuestion 105 ptsHomeAnnouncementsConsider the following two systems of linear equations:GradesModulesdALEKSTwo Systems of Linear EquationsSystem ASystem B2x + 4y = 6 [A1]2x + 4y = 6 [31]x + y = 8 (A2)2y = - 10 [B2]How do we transform System A into System B?O Multiply equation [A2] by 2 and add it to equation [A1]. This results in equation[B2]Add equations [A1] and [A2). This results in equation [B2]• Multiply equation [A2] by -2 and add it to equation [A1]. This results inequation [B2]O Multiply equation [A1] by - 1 and add it to equation [A2]. This results in equation[B2]
Answers
2x + 4y = 6 [A1]
x + y = 8 (A2)
Multiply equation A2 by -2
-2x -2y = -16
Add this to A1
2x +4y = 6
-2x -2y = -16
---------------------
2y = -10
Multiply equation [A2] by -2 and add it to equation [A1]. This results in equation [B2]
On average Jane earns $189.75 every two weeks if Jane is early $8.25 an hour how many hours does chain work during this period
Answers
On average Jane earns $189.75 every two weeks.
Jane is earns $8.25 an hour,
thus, she worked 23 hours for the period for which she got the amount of $
Evelyn has a nickels and y pennies. She has a maximum of 20 coins worth aminimum of $0.40 combined. Solve this system of inequalities graphically anddetermine one possible solution.
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Let be "x" the number of nickels Evelyn has and "y" the number of pennies she has.
According to the information given in the exercise, she has a maximum of 20 coins. Then, you can set up the following inequality to represent it:
[tex]x+y\le20[/tex]Because "a maximum of 20 coins" indicates that the total number of coins is less than or equal to 20.
You also know that that money is worth a minimum of $0.40. Then, you can set up this inequality:
[tex]0.05x+0.01y\ge0.40[/tex]Since the first inequality is:
[tex]x+y\le20[/tex]You need to solve for "y" in order to rewrite it:
[tex]y\le-x+20[/tex]Knowing that the second inequality is:
[tex]0.05x+0.01y\ge0.40[/tex]You can solve for "y" in order to rewrite it:
[tex]\begin{gathered} 0.01y\ge-0.05x+0.40 \\ \\ y\ge\frac{-0.05x}{0.01}+\frac{0.40}{0.01} \\ \\ y\ge-5x+40 \end{gathered}[/tex]Therefore, the System of Inequalities is:
[tex]\begin{cases}y\le-x+20 \\ y\ge-5x+40\end{cases}[/tex]The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
- Notice that the first line of the system is:
[tex]y=-x+20[/tex]You can identify that:
[tex]b_1=20[/tex]You can find the x-intercept by substituting the following value of "y" into the equation and solving for "x":
[tex]y=0[/tex]Then, you get:
[tex]\begin{gathered} 0=-x+20 \\ x=20 \end{gathered}[/tex]Therefore, you know that the first line passes through these points:
[tex](20,0);(0,20)[/tex]- Since the second line is:
[tex]y=-5x+40[/tex]You can determine that:
[tex]b_2=40[/tex]To find the x-intercept, apply the same procedure used for the first line:
[tex]\begin{gathered} 0=-5x+40 \\ -40=-5x \\ \\ \frac{-40}{-5}=x \\ \\ x=8 \end{gathered}[/tex]Then, the line passes through these points:
[tex](8,0);(0,40)[/tex]- Notice that the symbol of the first inequality is:
[tex]\le[/tex]That indicates that the first line is solid and the shaded region must be below the line.
- The symbol of the second inequality is:
[tex]\ge[/tex]This indicates that the line is solid and the shaded region must be above the line.
Knowing the explained above, you can graph the System of Inequalities:
By definition, the solution of the System of Inequalities is the intersection region.
Then, in order to determine one possible solution, you can choose a point in the intersection region. This can be (the solution contains this point):
[tex](10,8)[/tex]Therefore, answers are:
-Inequality 1:
[tex]y\le-x+20[/tex]- Inequality 2:
[tex]y\ge-5x+40[/tex]- Graph:
- The solution contains this point:
[tex](10,8)[/tex]i’m doing a pre-test and do not know this answer. please help!
Answers
ANSWER
[tex]f(2)\ne0[/tex]The binomial is not a factor of the polynomial
EXPLANATION
Given;
Substitute the value of x;
[tex]\begin{gathered} f\left(x\right)=2x^3+x^2-5x+2 \\ x-2=0 \\ x=2 \end{gathered}[/tex]Now, find f(2);
[tex]\begin{gathered} f(2)=2\times2^3+2^2-5\times\:2+2 \\ =16+4-10+2 \\ =12 \end{gathered}[/tex]Hence, since;
[tex]f(2)\ne0[/tex]The binomial is not a factor of the polynomial.
evaluate(if possible) the six trigonometric function of the real number.
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We will evaluate the value given of t in the six trigonometric functions
[tex]\begin{gathered} \sin (t)=\sin (\frac{\pi}{2})=1 \\ \cos (t)=\cos (\frac{\pi}{2})=0 \\ \tan (t)=\tan (\frac{\pi}{2})=\text{not defined } \end{gathered}[/tex][tex]\begin{gathered} \csc (t)=\csc (\frac{\pi}{2})=1 \\ \sec (t)=\sec (\frac{\pi}{2})=\text{ not defined} \\ \cot (t)=\cot (\frac{\pi}{2})=0 \end{gathered}[/tex]In your lab, a substance's temperature has been observed to follow the function T()- (x- 2)3 +8. The turning point of the graph is where the substance changes from asolid to a liquid. Using complete sentences in your written answer, explain to yourfellow scientists how to find the turning point of this function. Hint: The turningpoint of the graph is similar to the vertex of a quadratic function. (10 points)
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We have the function:
[tex]T(x)=(x-2)^3+8[/tex]A turning point happens when the function reaches a maximum or a minimum.
In that points the value of the first derivative of the function is equal to 0.
So we can find the turning points by finding the first derivative and equal to zero:
[tex]undefined[/tex]Are the expressions : 140 + 8) + 3c - 2 and 4c + 2(0.5c + 1) equivalent? Show your work
Answers
We have the following:
To be equivalent they have to be equal, therefore we set both expressions equal
[tex]\frac{1}{2}\cdot(4c+8)+3c-2=4c+2\cdot(0.5c+1)[/tex]we simplify on both sides, and we are left
[tex]\begin{gathered} 2c+4+3c-2=4c+1c+2 \\ 5c+2=5c+2 \end{gathered}[/tex]When they are equal, it means that if they are equivalent
What value of x would make 4/x equal to 10/25
Answers
Kenny, this is the solution:
Let's solve for x:
4/x = 10/25
4 * 25 = x * 10
100 = 10x
Dividing by 10 at both sides:
10x/10 = 100/10
x = 10
The value for x is 10.
what is 0.5×10 ????????
Answers
In order to calculate the product of 0.5 and 10, there are different methods that can be used.
One of them is converting 0.5 into a fraction, and then multiplying the fraction by 10.
So we have:
[tex]\begin{gathered} 0.5=\frac{5}{10}=\frac{1}{2} \\ \\ \frac{1}{2}\cdot10=\frac{10}{2}=5 \end{gathered}[/tex]Therefore the product of 0.5 and 10 is equal to 5.
Hello, I know the mean of these numbers is 12, but what is the mean absolute deviation? How do I solve this?
Answers
Given:
Sample of 10 students is as below
[tex]12,15,8,9,14,8,17,14,8,15[/tex]Required:
We want to find the mean absolute deviation for the given sample
Explanation:
For this,
first we need to find the mean of given sample
[tex]\frac{12+15+8+9+14+8+17+14+8+15}{10}=\frac{120}{10}=12[/tex]Now
[tex]\begin{gathered} \text{l12-12l=0} \\ \text{l12-15l=3} \\ \text{l12-8l=4} \\ \text{l12-9l=3} \\ \text{l12-14l=2} \\ \text{l12-8l=4} \\ \text{l12-17l=5} \\ \text{l12-14l=2} \\ \text{l12-8l=4} \\ \text{l12-15l=3} \end{gathered}[/tex]now find the mean of new sample for mean absolute deviation
[tex]\frac{0+3+4+3+2+4+5+2+4+3}{10}=\frac{30}{10}=3[/tex]Final answer:
3
Given f(x) = 5x²- 2, what isf(2) =
Answers
f(x) = 5x²- 2
To calculate f(2) replace the value of x by 2:
f(2)= 5(2)^2-2
f(2)= 5(4)-2
f(2)= 20-2
f(2)= 18
find the probability of obtaining exactly three heads when flipping three coins.express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
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The probablity of getting one head on tossing one coin = 1/2
Sample space on tossing three coins are;
HHH TTT
HHT TTH
HTH THT
THH HTT
Total number of sample space = 8
Favorable outcome is getting head three
Number of situation when we get three head = 1
Probaility = 1/8
1/8 = 0.125
Probability of obtaining exactly three heads when flipping three coins is 0.125
How do I solve this problem? Prove Identities or simplify using sum and difference formula.
Answers
One of the trigonometric identities is :
[tex]\sin (A+B)=\sin A\cos B+\cos A\sin B[/tex]From the problem, we have :
[tex]\sin (\frac{3\pi}{2}+x)[/tex]Applying the identity above,
[tex]\sin (\frac{3\pi}{2}+x)=\sin \frac{3\pi}{2}\cos x+\cos \frac{3\pi}{2}\sin x[/tex]Note that :
[tex]\begin{gathered} \sin \frac{3\pi}{2}=-1 \\ \text{and} \\ \cos \frac{3\pi}{2}=0 \end{gathered}[/tex]The identity will be :
[tex]\begin{gathered} \sin \frac{3\pi}{2}\cos x+\cos \frac{3\pi}{2}\sin x \\ \Rightarrow(-1)(\cos x)+(0)(\sin x) \\ \Rightarrow-\cos x \end{gathered}[/tex]The answer is -cos x
What transformations have been made from the parent graph f(x)=logx to get f(x)=log(x−2)?
Answers
Given:
There are given the function:
[tex]f(x)=log(x-2)[/tex]Explanation:
According to the question:
We need to find the transformation of the given function.
So,
From the function:
[tex]f(x)=log(x-2)[/tex]Then,
The transformation is:
Horizontal shift right 2 units.
Final answer:
Hence, the correct option is B.
Triangle ABC was transformed to create triangle A'B'C'. Which rule best describes this transformation? (Look at the image for the answer options)
Answers
Letter F is the correct choice because the triangle is moved 7 units down, there is no change in x.
The VMS math department includes the following teachers: Ruhland, Boyer, Tisor and Tuholsky. The team is ordering pizza to eat during their afternoon meeting with Mrs. Welch. They split one pizza and 5 large drinks. The pizza cost $15.00. They spend a total of $26.75. Write and solve the equation to find the cost of one large drink.
Answers
They ordered one pizza and 5 large drinks, the pizza cost $15 and the total cost was $26.75, so the cost of one large drink is:
[tex]\begin{gathered} W\text{e call x the cost of one large drink:} \\ total\text{ cost = cost of one pizza + 5 }\cdot\text{ cost of one large drink} \\ 26.75=15+5\cdot x \\ 5\cdot x=26.75-15 \\ 5\cdot x=11.75 \\ x=\frac{11.75}{5}=2.35 \end{gathered}[/tex]So, one large drink cost $2.35
4000x4÷36500×30x6x6x6
Answers
the given expression is,
[tex]4000\times4\div36500\times30\times6\times6\times6[/tex]To the nearest tenth what is the value of x . Assuming that the hypothenuse is equal to 53.
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For this problem, we are given a right triangle with known angles and a known hypothenuse. We need to find the value of one of the sides.
To solve this problem, we need to use trigonometric relations. We can use the cosine or sine, if we use the sine we need to choose the 50º angle, if we use the csine we need to choose the 40º angle. Therefore we have:
[tex]\begin{gathered} \sin(50º)=\frac{x}{53}\\ \\ x=53\cdot\sin(50\degree)=53\cdot0.766=40.6 \end{gathered}[/tex]The value of x is approximately equal to 40.6.
2 5/2 – 2 3/2 =Please help me with this question.
Answers
We need to convert the mixed fractions to improper fractions.
First:
[tex]2\frac{5}{2}[/tex]We multiply the integer on top and bottom by 2 ( the denominator of the fractional part)
[tex]\frac{2\cdot2}{2}=\frac{4}{2}[/tex]And now we add it to the fractional part:
[tex]\frac{4}{2}+\frac{5}{2}=\frac{9}{2}[/tex]We repeat the same process with:
[tex]2\frac{3}{2}[/tex]Multiply the integer top and bottom by the denominator of the fractional part:
[tex]\frac{2\cdot2}{2}=\frac{4}{2}[/tex]And add:
[tex]\frac{4}{2}+\frac{3}{2}=\frac{7}{2}[/tex]Now, we can do the rest:
[tex]2\frac{5}{2}-2\frac{3}{2}=\frac{9}{2}-\frac{7}{2}=\frac{9-7}{2}=\frac{2}{2}=1[/tex]The answer is 1
Equivalent Ratios 6 : 12 = 20 : ?
Answers
We have to find the equivalent ratio for 6 : 12 = 20 : x.
We can write it as fractions and rearrange with a cross product like this:
[tex]\begin{gathered} \frac{6}{12}=\frac{20}{x} \\ 6\cdot x=20\cdot12 \\ 6x=240 \\ x=\frac{240}{6} \\ x=40 \end{gathered}[/tex]Answer: the ratio is 6 : 12 = 20 : 40
The graph below shows the relationship between the number of calories and the total amount of fat in different types of sandwiches. Which trend BEST describes the relationship in the graph? A. The points have a positive trend and are nonlinear B. The points have a negative trend and are nonlinear. C. The points have a positive trend and are mostly linear. D. The points have a negative trend and are mostly linear.
Answers
Given:
The graph shows the relationship between the number of calories and the total amount of fat in different types of sandwiches.
To find:
The trend that best describes the relationship in the graph
Explanation:
We know that,
When the points on a scatterplot graph produce a lower left to upper right pattern, then we say that there is a positive correlation.
Comparing we get,
The given graph represents a positive correlation.
Moreover, a linear relationship creates a straight line when plotted on a graph, a nonlinear relationship does not create a straight line but instead creates a curve.
Since it creates a straight line, therefore it has a linear relationship.
Final answer: Option C
The points have a positive trend and are mostly linear.
Solve for each of the variables.
Answers
The given figure is of a hexagon. So the sum of the interior angles is 720.
[tex]130+85+165+2x+3+x+8=720[/tex]So on solving,
3x=329
x=109.66
Hello, I need some help with this precalculus question for my homework, please HW Q11
Answers
ANSWER:
A. the solution set is:
[tex]x=\frac{\operatorname{\ln}(\frac{8}{7})}{12\operatorname{\ln}(3)}[/tex]A. The solution set is 0.010
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]7\left(9^{6x}\right)=8[/tex]We solve for x:
[tex]\begin{gathered} 9^{6x}=\frac{8}{7} \\ \\ 6x\cdot\ln(9)=\ln\left(\frac{8}{7}\right) \\ \\ x=\frac{\ln\left(\frac{8}{7}\right)}{6\cdot\ln(9)}=\frac{\ln\left(\frac{8}{7}\right)}{6\ln\left(3^2\right)}=\frac{\ln\left(\frac{8}{7}\right)}{6\cdot2\ln\left(3\right)} \\ \\ x=\frac{\ln\left(\frac{8}{7}\right)}{12\ln\left(3\right)} \\ \\ x\approx0.010 \end{gathered}[/tex]582 x 7 its multiplying multi digit numbers by the way it's not getting graded.
Answers
The expression is
582 x 7
By using a calculator,
582 x 7 = 4074
use the multiplication equality to solve for the unknown. A video game system and several games are sold for 632.dollar . The cost of the games is 3 times as much as the cost of the system. Find the cost of the system and the cost of the game
Answers
The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.
We have that the videogame system and games cost $632. And the cost of the games is 3 times as much as the cost of the system. Then we have the following expressions:
[tex]\begin{gathered} VS+G=632 \\ G=3\cdot VS \end{gathered}[/tex]Where, VS = Videogame system and G = games.
We plug in 3*VS in the first equation to get:
[tex]VS+3\cdot VS=632[/tex]And we solve for VS, to find the cost of the videogame system:
[tex]4\cdot VS=632[/tex]We use the multiplication property of equality here, and multiply both sides of the equation by 1/4:
[tex]\begin{gathered} 4\cdot VS\cdot\frac{1}{4}=632\cdot\frac{1}{4} \\ VS=158 \end{gathered}[/tex]The cost of the videogame system is $158. Now we can find the cost of the games, replacing VS in the first equation:
[tex]\begin{gathered} VS+G=632 \\ 158+G=632 \\ G=632-158=474 \end{gathered}[/tex]Games cost $474.
PRECALC./TRIG QUESTION: The shaft on the pedal of a bicycle is 7 inches long and attaches to the bicycle 11 inches off of the ground. If the pedal starts in the standard (3.00) position, and rotates counterclockwise, write an equation that can model the height of the pedal off of the ground based on the number of radians that it has been rotated
Answers
The height of the pedal off the ground can be modeled by a cosine function
[tex]h(\theta)=\text{ 18 - 7}\cos (\theta+\frac{\pi}{2})[/tex]Let, us try some scenarios, if the pedal is at the 3 oclock position, the angle = 0
h= 18-7cos90 = 18 - 0 = 18 inches.
If the pedal is at 12 oclock, the angle is pi/2 or 90 degrees, and
h= 18 - 7cos180 = 18+7 = 25 inches.
Find value of 2x+2y if x+2y = 6 and x+y = 10
Answers
Step-by-step explanation:
[tex]x + 2y = 6 \: \: equ1 \\ x + y = 10 \: \: equ2[/tex]
From equ2,
[tex]x = 10 - y[/tex]
Substituting the value of x in equ1,
[tex](10 - y) + 2y = 6[/tex]
Collect like terms
y=6-10
y = - 4
Substituting the value if y in equ2,
x+y=10
x+(-4)=10
x-4=10
x=10+4
x=14
Therefore, 2x+2y
2(14) + 2(-4)
28 - 8
=20
find the zero of the linear function by graphing. verify your answer algebraically f(x)= 2x + 3
Answers
f(x) = 2x + 3
f is a linear function, with a slope of 2 and a y intercept of 3
first step would be to draw a point at (0,3)
next go up 2 right 1 to (1,5) and draw a point
and just go like that
it should look like that
the zero is -1.5
algebraically
y = 2x + 3
0 = 2x + 3
-3 = 2x
-1.5 = x