Write an equation to find the necessary score on the final exam for a student to earn an A (90%) in the class.
Answers
For the given table:
We will find the necessary score on the final exam for a student to earn an A (90%) in the class.
so,
The equation will be:
[tex]92\cdot(0.2)+95\cdot(0.3)+88\cdot(0.2)+x\cdot(0.3)=90[/tex]now, solve the equation to find x:
[tex]\begin{gathered} 64.5+0.3x=90 \\ 0.3x=90-64.5 \\ 0.3x=25.5 \\ x=\frac{25.5}{0.3} \\ \\ x=85 \end{gathered}[/tex]So, the answer will be:
The student needs a score of 85% on the final exam to earn a 90%
Related Questions
Eugenia rolls a six-sided number cube. What is the probability that she gets anumber greater than 4?
Answers
A cube is six sided. The numbers which are greater than 4 in a cube are 5 and 6. So, there are two sides on the cube which has numbers greater than 4.
Hence, the number of desired outcomes, N=2.
Since the cube is six sided, the total number of outcomes, T=6.
So, the probability of getting a number greater than 4 while rolling a cube is,
[tex]P=\frac{N}{T}=\frac{2}{6}=\frac{1}{3}[/tex]Therefore, the probability of getting a number greater than 4 is 1/3.
Option B is correct.
Nolan just drove at a constant rate for 5 hours here is now 340 miles from where he started. A. At what rate was he driving? B. Nolan has another 204 miles to go. If he continues to drive at the same rate, how long will it take him?
Answers
A) 68 mph. B) 3h
1) Gathering the data
time: 5 hours
Space= 340 miles
A) To find the rate, we can calculate it by simply writing a quotient between the Space and the time, (since Nolan is constantly moving
[tex]V=\frac{340}{5}=68\text{ mph}[/tex]So Nolan was at 68 mph
B) We can find out by setting a proportion since it's been said that the speed is constant. 340 miles have already been driven there are 204 miles to go.
340------5 hours
204 ---- x
340x = 204 *5 Divide both sides by 340
x=3
So it will take more 3 hours so that Nolan can finish his trip.
1. This is a two part question. If you are going 65 kilometers per hour how many meters per second are you traveling? a) What conversions will you use to solve this problem? b) Complete the conversion. Show your work. Make sure to include units
Answers
The value of 65 km/hr in meter/second will be 18.05 m/sec by the method of "To convert km/hr to m/s ,multiply the quantity by 5/18."
What is kilometer per hour?A derived unit for both speed and velocity, kilometers per hour is a measurement that takes length in kilometers and time in hours. Although kph or kmph are also occasionally used, km/h is the correct abbreviation for this unit.
a. 65 KM/hour to metre/second
=65*5/18
=18.05 m/second
b. To convert km/hr to m/s ,multiply the quantity by 5/18.
as 1 KM=1000 m
1 hour=3600 seconds
x* 1000/3600
x*5/18
According to the formula "To convert km/hr to m/s, multiply the quantity by 5/18," 65 km/hr will equal 18.05 m/s.
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The perpendicular bisectors of a triangle are congruent. Their common point is the:
Answers
Given
The perpendicular bisector of the triangle are concurrent. Their common point is the .........
Find
Complete the statement
Explanation
The three angle bisector of triangel are concurrent in a point equidistant from the sides of the triangle.
The point of concurrency of the angle bisectors of a triangle is known as
circumcenter.
Final Answer
Hence , the correct option is C
Express the number in scientific notation 6,340,000,000
Answers
Solution:
The number is given below as
[tex]6,340,000,000[/tex]Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form
Concept:
count the number from the last number and then stop in front of the first number 6 and then multiply in powers of 10
The general form of a scientific notation is given below as
By applying the concept, we will have
[tex]\begin{gathered} 6,340,000,000=6.34\times1,000,000,000 \\ 6,340,000,000=6.34\times10^9 \end{gathered}[/tex]Hence,
The final answer is
[tex]6.34\times10^9[/tex]3. Factor 3x from 12x2 + 15x 3
Answers
SOLUTION
In this question, we are meant to factor
[tex]\begin{gathered} 3xfrom12x^2+15x^3 \\ \text{Next, we factor in this manner,} \\ 3\text{ x ( }4x+5x^2\text{ )} \\ \text{CONCLUSION : The correct solution is 3 x ( 4 x + 5 x }^2\text{ )} \end{gathered}[/tex]what is 1 + 1 and two times 15
Answers
Solution
1 + 1= 2
2* 15= 30
A function whose values repeat based on positions of a point that moves around a circle is called a sinusoid.
Answers
Given
A function moves around a circle
Find
Is the function sinusoidal
Explanation
Final Answer
Yes, the function is sinusoidal
ZA and ZB are supplementary angles. If mZAZB = (7x – 26)°, then find the measure of ZA.
Answers
the sum of two supplementary angles is 180 degrees
[tex]m\angle A+m\angle B=180[/tex]7x+10+7x-26 = 180
14x = 180 + 16
x = 196/14
x = 14
so the value of m7x+10
= 7(14) + 10
= 98 + 10
= 108
m
(10) When using substitution to solve this system of equations, what is the result of the first step? Eq#1 y = 6x + 3 Eq#2 x + 2y = 5
Answers
Given data:
The first equation given is y = 6x + 3.
The second equation given is x + 2y = 5.
Subsitute (6x+3) for y in second equation.
[tex]x+2(6x+3)=5[/tex]Thus, the first option is correct.
The Fighting Irish won 7 games, lost 2 and tied 1. What percent of their games did they win?
Answers
N = Total number of games = 7
W = games won = 7 + 2 + 1 = 10
% games they won = W/N = 7/10 = 0.7 = 70%
which represents the inverse of the fuction f(x)=4x?a. h(x) = x + 4xb. h(x) = x - 4c. h(x) = 3/4xd. h(x) = 1/4x
Answers
If we want to calculate the inverse, we have to solve for x the following equation
[tex]\begin{gathered} y=4x \\ x=\frac{y}{4} \end{gathered}[/tex]Therefore the inverse function is
[tex]h(x)=\frac{1}{4}x[/tex]Find three odd consecutive integers whose sum is 531
Answers
The number = 531
There are no three consecutive odd integers whose sum is 531
Because the difference between consecutive integer is 1
Which ordered pair does not lie on the graph of Y=x/4+5?A (-8,3)B (-4,6)C (12,8)D (20,10)
Answers
Answer
B (-4, 6)
Step-by-step explanation
Given the expression:
[tex]y=\frac{x}{4}+5[/tex]Substituting x = -8, we get:
[tex]\begin{gathered} y=\frac{-8}{4}+5 \\ y=-2+5 \\ y=3 \end{gathered}[/tex]Then, the point (-8, 3) lies on the line.
Substituting x = -4, we get:
[tex]\begin{gathered} y=\frac{-4}{4}+5 \\ y=-1+5 \\ y=4 \end{gathered}[/tex]Then, the point (-4, 6) does not lie on the line, the point (-4, 4) does.
1. Given that f(x)=x²-4 and that g(x)=√√x-1:
A. State (f-g)(x) and (fog)(x).
B. State
and determine its domain.
C. Determine whether each of the following functions is odd, even, or neither odd nor
even: f(x)=x²-4, g(x)=√√x-1.
D. State (g/f)(x) and find all vertical asymptotes.
Please show work! Thank you so much!
Answers
Given the functions are,
[tex]f(x)=x^2-4\\g(x)=\sqrt[3]{x-1}[/tex]
Then the subtraction of functions is given by,
[tex](f-g)(x)=f(x)-g(x)=x^2-4-\sqrt[3]{x-1}[/tex]
Again,
[tex](f\circ g)(x)=f(g(x))=f(\sqrt[3]{x-1})=(x-1)^{2/3}-4[/tex]
And,
[tex]\left(\frac{f}g{}\right)(x)=\frac{f(x)}{g(x)}=\frac{x^2-4}{\sqrt[3]{x-1}}[/tex], it exists when x not equals to 1.
So domain of the function is all real number except 1.
Since, [tex]f(-x)=(-x)^2-4=x^2-4=f(x)[/tex], then the function is an even function.
Since [tex]g(-x)=\sqrt[3]{-x-1}[/tex], so it is neither odd function nor even function.
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RewritingInstructions: Rewrite the equation in Slope-Intercept Form.y-2=-5(x- 2)Check
Answers
In general, the slope-intercept form of a linear equation is
[tex]\begin{gathered} y=mx+b \\ m,b\rightarrow\text{ constants} \end{gathered}[/tex]Thus, in our case,
[tex]\begin{gathered} y-2=-5(x-2) \\ \Rightarrow y-2=-5x+10 \\ \Rightarrow y=-5x+12 \end{gathered}[/tex]The answer is y=-5x+12Solve 7sin(pi/6 * x) = 2 for the four smallest positive solutions
Answers
Answer:
x =0.55, 5.45, 12.55, 17.45
Explanation:
First, we divide both sides by 7. This gives
[tex]\sin(\frac{\pi}{6}x)=\frac{2}{7}[/tex]then taking the inverse sine of both sides gives
[tex]\frac{\pi}{6}x=2\pi n\pm\sin^{-1}[\frac{2}{7}][/tex]since
[tex]\sin^{-1}[\frac{2}{7}]=16.60[/tex]Therefore,
[tex]\frac{\pi}{6}x=2\pi n\pm16.60[/tex]Multpilying both sides by 6/π
[tex][/tex]Arithmetic and Geometric Sequences. The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
Answers
From the information provided, observe that the three terms are connected by a common ratio.
The first term is multiplied by a value denoted as letter r (common ratio) to derive the second term. The second term is also multiplied by r to derive the third term, and so on.
Therefore;
[tex]\begin{gathered} 5\times r=4 \\ r=\frac{4}{5} \\ 4\times r=\frac{16}{5} \\ r=\frac{16}{5}\text{ / }\frac{4}{1} \\ r=\frac{16}{5}\times\frac{1}{4} \\ r=\frac{4}{5} \end{gathered}[/tex]From the above calculation, the common ratio is 4/5. Therefore, the 10th term in the sequence shall be;
[tex]\begin{gathered} T_n=a\times r^{n-1} \\ \text{Where;} \\ a=5,r=\frac{4}{5},n=\text{nth term} \\ T_{10}=5\times(\frac{4}{5})^{10-1} \\ T_{10}=5\times(\frac{4}{5})^9 \\ T_{10}=5\times\frac{262144}{1953125} \\ T_{10}=\frac{262144}{390625} \end{gathered}[/tex]The 10th term is as shown above. To round this figure to the nearest thousandth, we need to convert this fraction into a decimal.
Hence we would have;
[tex]\begin{gathered} T_{10}=\frac{262144}{390625} \\ T_{10}=0.67108864 \\ T_{10}\approx0.671\text{ (to the nearest thousandth)} \end{gathered}[/tex]What is the probability that a student would randomly choose a school uniform outfit with a plaid skirt and black sneakers ?
Answers
Notice that as for the type of shoes, there are two possibilities either loafers or black sneakers.
Therefore, the probability of choosing black sneakers is 0.5.
On the other hand, after picking the black sneakers, there are 4 possibilities as to the sort of skirt/pants to use, and the probability of choosing a plaid skirt is 1/4=0.25.
Thus, the probability of randomly choosing a plaid skirt and black sneakers is
[tex]P(sneakers\cap plaid)=0.5*0.25=0.125[/tex]Therefore, the answer is 0.125 or 1/8 (both are correct).The perimeter of a rectangular picture frame can be represented by the expression 6x,where x is one of the side lengths. Rewrite the expression as the sum of the four side lengths.
Answers
Perimeter is formed by 4 side lengths.
Divide perimeter in 4 parts
x= side length
P = 6x = x + x + 4x
then length of the other sides lengths is= 2x
So then ANSWER IS
P= x + x + 2x + 2x
Question 3: 11 ptsArating for the school bus, Bruce records the colors of all cars passing through an intersection. The tablethe results. Estimate the probability that the next car through the intersection will be black. Express youras a percent. If necessary, round your answer to the nearest tenth.
Answers
To find the probability that the next car through the intersection will be black divide the number of black car by the total number of cars.
The total number of cars is the sum of the number of cars of each color, which is 58.
[tex]P=\frac{9}{58}=0.155[/tex]Expressed as a percent it is 15.5%.
It means that the correct answer is the last choice.
(b) A company has 39 salespeople. A boardmember at the company asks for a list of the topsalespeople, ranked in order of effectiveness. How many such rankings are possible?0ExplanationCheck
Answers
Since 1 person cannot be in the top 4 salespeople more than once, then, we use combinations instead of permutations.
[tex]39C4=\frac{39!}{4!(39-4)!}[/tex]Simplify the expression,
[tex]39C4=\frac{39!}{4!35!}[/tex][tex]\begin{gathered} 39C4=\frac{39\ast38\ast37\ast36}{4\ast3\ast2\ast1} \\ 39C4=\frac{1974024}{24} \\ 39C4=82251 \end{gathered}[/tex]answer:
The 4 top list can be arranged in 82251 ways
I need help with this practice problem Having a tough time completing step by step
Answers
we have the expression
[tex]\frac{cos(sin^{-1}(\frac{1}{2}))}{tan(cos^{-1}(-\frac{1}{2}))}[/tex]step 1
Find out the value of sin^-1 (1/2) and cos^-1(-1/2)
[tex]\begin{gathered} sin^{-1}(\frac{1}{2})=30^o \\ cos^{-1}(-\frac{1}{2})=120^0 \end{gathered}[/tex]substitute in the original expression
[tex]\frac{cos(30^o)}{tan(120^o)}=-\frac{1}{2}[/tex]Therefore
The answer is -1/25. What is the sum of 3 5/24, 6 7/24, and 9 9/24?,A. 14²/3B. 14 1/8C. 18 7/8D. 13 1/2
Answers
To answer this question, we can realize that we have mixed fractions. Then we need to add integers and fractions separately as follows:
1. We have:
[tex]3\frac{5}{24}+6\frac{7}{24}+9\frac{9}{24}[/tex]2. And this expression is equivalent to:
[tex]3+\frac{5}{24}+6+\frac{7}{24}+9+\frac{9}{24}[/tex]3. Now, we can add the integer parts, and the fractional parts separately as follows:
[tex](3+6+9)+(\frac{5}{24}+\frac{7}{24}+\frac{9}{24})[/tex]4. Therefore:
[tex]18+\frac{5+7+9}{24}=18+\frac{21}{24}[/tex]5. We finally need to simplify the fraction, and then we will have:
[tex]\begin{gathered} \frac{21}{24}=\frac{\frac{21}{3}}{\frac{24}{3}}=\frac{7}{8} \\ 18+\frac{7}{8}=18\frac{7}{8} \end{gathered}[/tex]In summary, therefore, we have that the sum of the above fractions is:
[tex]18\frac{7}{8}[/tex][Option C.]
find the probability of obtaining five heads when flipping five coins. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
Answers
1/32
Explanation:In an experiment, we can only get head or tail:
Probability of getting a head = 1/2
Probability of obtaining five heads when flipping five coins:
[tex]\begin{gathered} \text{Probability = (1/2)}^{number\text{ of flips}} \\ \text{Probability = (1/2)}^5 \\ \end{gathered}[/tex][tex]\text{Probability = 1/32}[/tex]Complete the table and answer the questions below.a) without graphing, which equation from above has the steepest line? How do you know?b) without graphing, which equation describes a decreasing line? How do you know?
Answers
The values on the table are:
[tex]\begin{gathered} y=x-3 \\ \Rightarrow slope\colon m=1 \\ \Rightarrow y-axis\colon b=-3 \\ y=\frac{1}{5}x+2 \\ \Rightarrow slope\colon m=\frac{1}{5} \\ \Rightarrow y-axis\colon b=2 \\ y=-2x \\ \Rightarrow slope\colon m=-2 \\ \Rightarrow y-axis\colon b=0 \end{gathered}[/tex]a) the steepest slope is m=-2 (from the third option). We can see this because in the first option, the rate of change is 1 and in the second option is 1/5. Then for each increase of x, the value of y will be modified but not as much as in the equation y=-2x.
b)the equation y=-2x represents a decreasing line, since the slope is negative.
Which statement best explains the relationship betweenlines AB and CD?
Answers
GIven:-
An graph with two parallel lines.
To find:-
The given condition which sutis it.
Now we find two points form the line.
The points from the line AB is,
[tex](-4,-2),(4,4)[/tex]The points from the line CD is,
[tex](0,-3),(4,0)[/tex]Now the slope of AB is,
[tex]\frac{4+2}{4+4}=\frac{6}{8}=\frac{3}{4}[/tex]Now the slope of CD is,
[tex]\frac{0+3}{4}=\frac{3}{4}[/tex]The both slopes are equal so we have,
They are parallel because the slopes are equal.
1) Compare the following numbers. Choose the correct inequality symbol 10 pointsto go in the circle. *Remember the inequality symbol “eats” the biggernumber!√8 + 3 ? 8 + √3
Answers
√8 + 3 ? 8 + √3
√8 is between √4 (= 2) and √9 (= 3), then
√8 + 3 < 3 + 3 = 6
Therefore,
√8 + 3 < 8 + √3
write the equation of the line using the given slope and pointm=4 (2,6)
Answers
1) We can write the equation of the line, using this point (2,6) and the slope m=4.
2) So, let's plug into the slope-intercept form the point and the slope to find the y-intercept
[tex]\begin{gathered} y=mx+b \\ 6=4(2)+b \\ 6=8+b \\ 6-8=b \\ b=-2 \end{gathered}[/tex]3) Thus, we can write out the following equation:
[tex]y=4x-2[/tex]f(x) = -x^2 + x + 13Find f(9)
Answers
To answer this question, we need to substitute the value of 9 into the quadratic function as follows:
[tex]f(9)=-(9)^2+9+13=-81+22\Rightarrow f(9)=-59[/tex]Therefore, the answer is f(9) = -59.