According to the statement given in Part a, there is one table for 10 people and many tables for 4 and in total there are tables for 200 people. Taking x as the number of tables for 4 people, the inequality that represents this situation is:
[tex]\begin{gathered} 4x+10\leq200 \\ 4x\leq190 \\ x\leq47.5 \end{gathered}[/tex]It means that there must be less than or 47.5 tables in the cafeteria.
According to the statement given in Part b, there are 4 barrels that are the same size, and one that is 10 liters, in total they can hold 200 liters. Taking x as the volume hold by the 4 barrels , the inequality that represents this situation is:
[tex]\begin{gathered} 4x+10\leq200 \\ 4x\leq190 \\ x\leq47.5 \end{gathered}[/tex]It means that each barrel must hold less than or 47.5 liters of water.
These problems are similar because of the inequality used to find the solution is the same, they are different because of the variable that is found is completely different, the first one is the number of tables and the second one is the volume that can be hold by the barrels.
A skating rink manager finds that revenue R based on an hourly fee F
for skating is represented by the function R = -480F² + 3120F.
What hourly fee will produce maximum revenues?
The hourly fees of $3.25 will produce the maximum value of revenue in the Skating rink.
Given function of the form:
R = -480F² + 3120F
Here R is the revenue and F is the hourly fees.
Now we will differentiate with respect to F
Hence.
[tex]\frac{dR}{dF} = -960F + 3120[/tex]
Now to find the maximum value we have to find the value of F for which [tex]\frac{dR}{dF}[/tex] is zero.
hence :
-960F+3120 = 0
or, F=3.25
Hence the value of F is 3.25 for which the revenue will be maximum.
Maxima and minima, the corresponding plurals of lower and upper bound of a function, are used in mathematical analysis to refer to the highest and lowest value of such a function, whether it be within or a defined range, the local the relative extrema, or throughout the entire domain.
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Figure T is the result of a transformation on Figure S. Which transformation would accomplish this? 6 -4 -3 2 3 Figure S Figure T -3 -4 -5
Let:
[tex]\begin{gathered} A=(1,-1) \\ A^{\prime}=(3,-2) \\ A\to(x+a,y+b)\to A^{\prime} \\ so\colon \\ 1+a=3 \\ a=3-1=2 \\ ---- \\ -1+b=-2 \\ b=-2+1=-1 \\ so\colon \\ A\to(x+2,y-1)\to A^{\prime} \end{gathered}[/tex]Therefore, the transformation T is:
A translation 2 units right and 1 unit down
cost: $41.80
rate of tip: 20%
Answer:
50.16 if you add 20 %
if you need the original price and this is with the 20% included then 33.44
Step-by-step explanation:
Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets p left after
t minutes of printing is given by the function p(t) = -8t + 100.
Part A
How long would it take the printer to use all 100 sheets of paper? Explain how you found your answer.
It will take 12.5 minutes by the printer to use all 100 sheets of paper as the function is p(t) = -8t + 100 where p is the number of sheets left after t minutes of printing.
What is function?A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
Here,
p(t)=-8t+100
Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function .When all the 100 sheets printed , then the number of sheets will left to print =0.
Substitute p(t)=0 in the given function, to find the value of t,
0=-8t+100
8t=100
t=12.5 minutes
The function is p(t) = -8t + 100, where p is the number of sheets left after t minutes of printing, and it will take the printer 12.5 minutes to use all 100 sheets of paper.
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a student says that the solution of 375=x-28 is 347 explain the students error and find the correct answer
The given equation is:
375 = x - 28
To solve the equation:
Collect like terms
The -28 crosses the equality sign to the left and becomes 28
The equation then becomes:
375 + 28 = x
x = 403 (correct answer)
The students error is that when he collected like terms, he did not change the "-" sign in -28 to +
He did 375 - 28 = x
x = 347 (wrong)
A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made in the unit cost is given by the function C(x)=x^2-520x+79,797. What is the minimum unit cost? Do not round your answer.
Answer:
The minimum unit cost is $12,197.
Explanation:
The cost function is given below:
[tex]C\mleft(x\mright)=x^2-520x+79,797[/tex]To find the minimum unit cost, first, find the derivative of C(x).
[tex]C^{\prime}(x)=2x-520[/tex]Next, set the derivative equal to 0 and solve for x.
[tex]\begin{gathered} 2x-520=0 \\ 2x=520 \\ x=520\div2 \\ x=260 \end{gathered}[/tex]Finally, substitute x=260 into C(x) to find the minimum cost.
[tex]\begin{gathered} C\mleft(x\mright)=x^2-520x+79,797 \\ \implies C(260)=(260)^2-520(260)+79,797 \\ =67600-135,200+79,797 \\ =12,197 \end{gathered}[/tex]The minimum unit cost is $12,197.
9. Use the figure shown to identify each.
a. Vertical angles
b. Adjacent angles
c. Linear pairs
d. Supplementary angles
e. Complementary angles
The angles in the given figure are:
a. Vertical angles: angle 3 and angle 5.
b. Adjacent angles: angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs: angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles: angle 4 and angle 5.
e. Complementary angles: angle 1 and angle 2.
We are given a figure and we need to identify the angle.
Let us identify the angle:
a. Vertical angles:
Each of the pairs of opposite angles is made by two intersecting lines.
In the given figure,
angle 3 and angle 5 are vertical angles.
b. Adjacent angles:
In the given figure,
angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs:
The sum of the two angles should be 180 degrees.
In the given figure,
angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles:
The sum of the two angles should be 180 degrees.
In the given figure,
angle 4 and angle 5.
e. Complementary angles:
The sum of the two angles should be 90 degrees.
In the given figure,
angle 1 and angle 2.
Thus, the angles in the given figure are:
a. Vertical angles: angle 3 and angle 5.
b. Adjacent angles: angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs: angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles: angle 4 and angle 5.
e. Complementary angles: angle 1 and angle 2.
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you are planning a survey of starting salaries for recent business majors. in the 2018 survey by the national association of colleges and employers, the average starting salary was reported to be $56,720. if you assume that the standard deviation is $11,500, what sample size do you need to have a margin of error equal to $1,000 with 95% confidence?
The sample size you need to have a margin of error equal to $1,000 with 95% confidence is; 508
How to find the sample size?Formula for margin of error is given by the formula;
E = z(σ/√n)
where;
z is z-score at significance level
σ is standard deviation
n is sample size
We are given;
σ = $11500
z at significance level of 0.05 is 1.96
margin of error; E = $1000
Thus;
1000 = 1.96(11500/√n)
√n = (1.96 * 11500/1000)
√n = 22.54
n = 22.54²
n ≈ 508
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The first two steps to solve the equation 3x2−7=47+7xare shown below:Step 1: 3x2−7x−7−47=0Step 2: 21x2−49x−49−4=0Which property is applied in step 1 to obtain step 2?Adivision property of equalitydivision property of equalityBaddition property of equalityaddition property of equalityCmultiplication property of equalitymultiplication property of equalityDsubtraction property of equality
Which of these pieces of data about a package delivered by the post office is considered categorical data?A. Surface areaB. WeightC. Volume D. Dropoff location
Answer
D. Dropoff location
Step-by-step explanation
Quantitative variables are any variables where the data represent amounts (e.g. surface area, weight, or volume of a package). Categorical variables are any variables where the data represent groups (for example classifications like cities or brands).
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Two-thirds of the gross of 144 plates was used at the wedding reception. How many plates were not used?
Answer:
47 ? (might b wrong_?
Step-by-step explanation:
2/3 divided by 144= 0.00462962963, if you round its 47.
Answer:48
Step-by-step explanation: because two third of 144 plates is 96 so you subtract 96 from 144.
how long will it take for the population to reach 5656 fish, according to this model?
Question:
Solution:
The population growth is given by the following equation:
[tex]P(t)=(707)2^{\frac{t}{3}}[/tex]where P represents the number of individuals and t represents the number of years from the time of introduction. Now, if we have a population of 5656 fish, then the above equation becomes:
[tex]5656=(707)2^{\frac{t}{3}}[/tex]this is equivalent to:
[tex]2^{\frac{t}{3}}\text{ = }\frac{5656}{707}[/tex]this is equivalent to:
[tex]2^{\frac{t}{3}}\text{ = }8[/tex]this is equivalent to:
[tex](2^t)^{\frac{1}{3}}\text{ = }8[/tex]now, the inverse function of the root function is the exponential function. So that, we can apply the exponential function to the previous equation:
[tex]((2^t)^{\frac{1}{3}})^3\text{ = }8^3[/tex]this is equivalent to:
[tex](2^t)^{\frac{3}{3}}^{}\text{ = }512[/tex]this is equivalent to:
[tex]2^t\text{ = }512[/tex]now, we can apply the properties of the logarithms to the previous equation:
[tex]\log _2(2^t)\text{ = }log_2(512)[/tex]this is equivalent to:
[tex]t=log_2(512)\text{ = 9}[/tex]we can conclude that the correct answer is:
9 years
Find (f + g)(x), if f(x) = - 5x2 + 6 and g(x) = x2 - 6.4x2- 6x2 + 12- 4x2- 6x2 - 12
Given the functions:
[tex]\begin{gathered} f(x)=-5x^2+6 \\ g(x)=x^2-6 \end{gathered}[/tex][tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(-5x^2+6)+(x^2-6)=-5x^2+x^2+6-6 \\ (f+g)(x)=-4x^2+0=-4x^2 \end{gathered}[/tex]The answer is: C. -4x^2.
points (-2,1) and (3,y) have a slope of -3. find the y coordinate of the point
y coordinate of the point is -14
Explanation:Slope = change in y/change in x
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = -3} \end{gathered}[/tex]Since m is negative, it means the slope is negative.
[tex]\begin{gathered} It\text{ also means the 2nd y value will be smaller than the 1st y value to get negative slope} \\ x_1=-2,y_1=1,x_2=3,y_2\text{ = y} \\ m\text{ = }\frac{y-1}{3-(-2)} \end{gathered}[/tex][tex]\begin{gathered} -3\text{ = }\frac{y-1}{3+2} \\ -3\text{ = }\frac{y-1}{5} \\ -3(5)\text{ = y - 1} \\ -15\text{ = y - 1} \\ \end{gathered}[/tex][tex]\begin{gathered} -15\text{ + 1 = y} \\ y\text{ = -14} \\ y\text{ coordinate of the point is -14} \end{gathered}[/tex]Create and solve a story problem that would use this equation: y=5x+3 Be sure to define x, y, the constant, and the variable.
Answer:
A group of 3 teenagers wants to go out to a movie each ticket is 5 dollars, they all decide to share popcorn wich costs 3 dollars
Step-by-step explanation:
X=3 of the teenagers Y=18 the total cost
The constant is 5 because all the tickets cost and stay 5 dollars
And the variable is x because the amount of teenagers can change
Answer:
A Group Of 3 Family members wants to go out But the Table for 3 People cost 5 Dollars, So they just all decide to just Eat Icecream
Step-by-step explanation:
Which is $3. X=3 of the Family Members Y=18 The Total Cost The Constant is 5 because all of the tickets cost & stay $5 dollars & The variable is X because of the amount of money The Family Members have.
3 A of ch 75 -5 A study of traffic patterns in a large city shows that if the weather is rainy, there is a 50% chance of an automobile accident occurring during the morning commute. If the weather is clear, the chance of an accident is reduced to 25%. Suppose the weather forecast for tomorrow predicts a 75% chance of rain. Draw a tree diagram based on the information in the work space. (Level 4) Show Your Work US be A of ch
Solution
We can create the solution with the following tree diagram:
Part 2
For this case we want this probability:
P(rain and accident)
And we can do this operation:
P(rain and accident) = 0.75 *0.5 = 0.375
Part 3
For this case we want this probability:
P( no rain and accident)
And we can do this operation:
P(no rain and accident) = 0.25 *0.25 = 0.0625
Part 4
P(Accident) = 0.5*0.75 + 0.25*0.25= 0.4375
Solve for x in x^3 = 64/27.
ANSWER
[tex]x\text{ = }\frac{4}{3}[/tex]EXPLANATION
We have that:
[tex]x^3\text{ = }\frac{64}{27}[/tex]64 and 27 are perfect cubes. This is because they are integers that can be gotten when another integer is raised to the third power or multiplies itself three times.
So, to get x, we can find the cube root of both sides:
[tex]\begin{gathered} \sqrt[3]{x^3}\text{ = }\sqrt[3]{\frac{64}{27}} \\ \Rightarrow\text{ x = }\sqrt[3]{\frac{4\cdot4\cdot4}{3\cdot3\cdot3}} \\ x\text{ = }\frac{4}{3} \end{gathered}[/tex]That is the value of x.
Solve for x:
2.50+1.50x=3.25+1.25x
Answer:
x = 3
Step-by-step explanation:
Multiply both sides by 100
2.5 · 100 + 1.5x · 100 = 3.25 · 100 + 1.25x · 100
Refine:
250 + 150x - 250 = 325 + 125x - 250
Simplify:
150x = 125x + 75
Subtract 125x from both sides:
150x - 125x = 125x + 75 - 125x
simplify:
25x = 75
Now all you have to do is Divide both sides by 25:
[tex]\frac{25x}{25}[/tex] = [tex]\frac{75}{25}[/tex]
Now Finally the last part Now just Simplify so therefore the answer is
x = 3
Aaliyah is trying to solve (2 – -3)? lbut is stuck on the first step. Finish solving the equationusing the Complete the Square Method and select the correct value of x below.O2=3 -OD=3+Oc=i - 3O2=334567891011 12NE
Given:
[tex](x-3)^2=-1[/tex]To solve for x:
Taking square root on both sides we get,
[tex]\begin{gathered} x-3=\sqrt[]{-1} \\ x-3=i \\ x=3+i \end{gathered}[/tex]Hence, the correct option is, B.
What is the solution to the equation 7x−4=3x−8 , given the replacement set {−3, −1, 1} ?
A. -3
B. -1
C. 1
D. I don't know
Please answer fast!
I will give 85 points to whoever answers this question first, and I will also give whoever answers first brainliest.
Answer: B
Step-by-step explanation:
7x-4=3x-8
Combine like terms
7x-3x=4-8
Simplify
4x=-4
Divide
x=-1
The probability that an employee will be late to work at a large corporation is 0.21. What is the probability on a given day that in a department of 5 employees at least 3 are late ?
Given:
Number of employees are 5.
Probability that an employee will be late to work at a large corporation is 0.21.
The given data follows binomial distribution,
[tex]\begin{gathered} X\text{ \textasciitilde{}B(n,p,q)} \\ n=5 \\ p=0.21 \\ q=1-p=1-0.21=0.79 \\ P(X=x)=^nC_xp^xq^{n-x} \end{gathered}[/tex]The probability that at least 3 employees are late is given as,
[tex]\begin{gathered} P(X\ge3)=P(X=3)+P(X=4_{})+P(X=5) \\ P(X\ge3)=^5C_3(0.21)^3(0.79)^{5-3}+^5C_4(0.21)^4(0.79)^{5-4}+^5C_5(0.21)^5(0.79)^{5-5} \\ P(X\ge3)=0.0578+0.0077+0.0004 \\ P(X\ge3)=0.0659 \end{gathered}[/tex]Answer: The probability that in a department of 5 employees at least 3 are late is 0.0659.
x + 6=13 show the steps
5#Consider the following random sample of diameter measurements (in inches) of 12 softballs.4.72, 4.74, 4.83, 4.75, 4.73, 4.87, 4.69, 4.7, 4.76, 4.7, 4.79, 4.76Send data to calculatorIf we assume that the diameter measurements are normally distributed, find a 90% confidence interval for the mean diameter of a softball. Give the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.)Lower limit:??Upper limit:??
ANSWER:
Lower limit: 4.73
Upper limit: 4.78
STEP-BY-STEP EXPLANATION:
Given the following data set:
[tex]4.72,4.74,4.83,4.75,4.73,4.87,4.69,4.7,4.76,4.7,4.79,4.76[/tex]We calculate the mean and standard deviation:
[tex]\begin{gathered} \mu=\frac{4.72+4.74+4.83+4.75+4.73+4.87+4.69+4.7+4.76+4.7+4.79+4.76}{12}=\frac{57.04}{12}=4.753 \\ \\ \sigma=\sqrt{\frac{\lparen4.72-4.753^2+\left(4.74-4.753\right)^2+\lparen4.83-4.753)^2+\left(4.75-4.753\right)^2+\left(4.73-4.753\right)^2+\lparen4.87-4.753)^2+\left(4.69-4.753\right)^2+\lparen4.7-4.753)^2+\left(4.76-4.753\right)^2+\left(4.7-4.753\right)^2+\left(4.79-4.753\right)^2+\left(4.76-4.753\right)^2}{12-1}} \\ \\ \sigma=0.054 \end{gathered}[/tex]The critical limit of 90% confidence interval is 1.645
We can determine the limits as follows:
[tex]\begin{gathered} \text{ Lower limit: }\mu-Z\cdot\frac{\sigma}{\sqrt{n}}=4.753-1.645\cdot\frac{0.054}{\sqrt{12}}=4.727\cong4.73 \\ \\ \text{ Upper limit:: }\mu+Z\cdot\frac{\sigma}{\sqrt{n}}=4.753+1.645\cdot\frac{0.054}{\sqrt{12}}=4.778\cong4.78 \end{gathered}[/tex]What is the solution to the equation below? Round your answer to twodecimal places.eX = 7.9
Solution
For this case we have the following equation:
[tex]e^x=7.9[/tex]For this case we can apply natural log in both sides and we got:
[tex]\ln (x)=\ln (7.9)=2.07[/tex]and then the solution would be:
D. x =2.07
Beginning with the equation 27x=54, write the new equation produced by dividing both sides by 9
Answer:
3x=6
Step-by-step explanation:
27/9=3, 54/9=6 so answer is 3x = 6
Solve the quadratic equation by using the quadratic formula. 3x^2-5x+1=4 Enter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth.
Answer:
x = -0.47, x = 2.14
Step-by-step explanation:
Quadratic formula is my favorite!!
Let's first take that four over to the other side
Subtract 4 from both sides
3x^2-5x-3
a = 3
b = -5
c = -3
Remember quadratic formula: [tex]x=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex]
IGNORE THE A BEFORE THE ±
Plug in our a, b, and c values: [tex]x=\frac{-(-5)±\sqrt{5^2-4(3)(-3)} }{2(3)}[/tex]
Simplify: [tex]x=\frac{5±\sqrt{25+36} }{6}[/tex]
Simplify some more: [tex]x=\frac{5±\sqrt{61} }{6}[/tex]
Solve:
x ≈ -0.47
x ≈ 2.14
How do I figure out what graph(s) is linear or exponential? can someone explain how to do this for me?
Answer:
Linear functions are graphed as straight lines while exponential functions are curved. Linear functions are typically in the form y = mx + b, which is used to discover the slope, or simply the change in y divided by the change in x, while exponential functions are typically in the form y = (1 + r) x.
Step-by-step explanation:
Janice buys a stuffed animal for $16.20. There was a 8% tax on the toy. What was the cost of the stuffed animal before tax?
Answer:
$15
Step-by-step explanation:
After tax cost is $16.20
Since 8% tax this is 108% of before tax cost
16.20/1.08 = 15
THESE IS DUE TODAY PLEASE IM IN A RUSH
Answer:
3/8 gal
Step-by-step explanation:
[tex]5\frac{1}{4} \times \frac{1}{6} = \frac{21}{4} \times \frac{1}{6} = \frac{21}{24} = \frac{3}{8} [/tex]