Problem
5. The video store has a basic charge for a 3 day rental and a different charge per day late fee. Nate returned his video one day late and paid $5.50, Gina was four days late and paid $10,00 for her rental. What is the basic fee and the per day late fee the store charges?
Solution
For this case we can use the following notation:
y = 3 day payment x = per-day late fee
And we can set up these equations:
x+y = 5.50
4x +y= 10.00
From the first equation we can solve for x and we got:
x= 5.50 -y
We can replace this into the second equation and we got:
4(5.50-y) +y= 10.00
If we distribute the terms we got:
22 - 4y + y= 10.00
And solving for y we got:
22-10 = 3y
y= 4
and then we can solve for x and we got:
x= 5.50-4= 1.50
So our final solution would be x =1.5 and y= 4.00
Monica volunteered to pick up more than 10 pounds of trash along a highway near her neighborhood. On Friday she picked up 2 pounds of trash, and on Saturday she picked up 3 1/2 pounds of trash. If she picks up N pounds of trash on Sunday, which inequality can be used to determine whether Monica reached her goal?A 5 1/2 + N > 10 B 5 1/2 - N < 10C 5 1/2 > 10 + N D 5 1/2 < 10 - N
First of all, we start writing the information of the problem:
Friday 2 pounds
Saturday 3 1/2 pounds
Sunday N pounds
She has to pick up more than 10 pounds of trash, then:
2 + 3 1/2 + N >10
5 1/2 + N > 10
Finally, the answer is the letter A
Consider this expression.a3 – 7 + 18When a2 and 6-4, the value of the expression isWhat
Answer:
the value of the expression is 5
Step-by-step explanation:
note that the absolute value function always gives a positive value , that is
| - a | = | a | = a
given
[tex]\sqrt{a^3-7}[/tex] + | b | ← substitute a = 2 and b = - 4
= [tex]\sqrt{2^3-7}[/tex] + | - 4 |
= [tex]\sqrt{8-7}[/tex] + | 4 |
= [tex]\sqrt{1}[/tex] + 4
= 1 + 4
= 5
Tammy is saving up to go on a trip. he already has $26 saved and is planning on leaving for the trip in 8 months. if the trip is going to cost Tammy $150, how much does Tammy need to save each month
The cost of the trip is $150
First, we need to subtract the money he already saved from the cost of the trip
150-26=124
so we need to save $124 in 8 months
[tex]\frac{124}{8}=15.5[/tex]She needs to save $15.5 each month
In an equation
26+8x=150
where x is the money that she needs to save each month
we need to clear x
[tex]\begin{gathered} 8x=150-26 \\ 8x=124 \\ x=\frac{124}{8} \\ x=15.5 \end{gathered}[/tex]what is the center and radius of the circle?(x - 6)² + (y + 8)² = 81
The general equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h,k) is the center and r is the radius.
In this case, we have the following:
[tex](x-6)^2+(y+8)^2=81[/tex]Notice that we can write the equation in the following way:
[tex]\begin{gathered} (x-6)^2+(y+8)^2=81 \\ \Rightarrow(x+6)^2+(y-(-8))^2=(9)^2 \end{gathered}[/tex]therefore, the center of the circle is (h,k)=(6,-8) and the radius is r=9
Write10^8/10^0with a single power of 10 using the appropriate exponent rule.
The given expression is:
[tex]\frac{10^8}{10^0}[/tex]Accoring to exponent rule,
[tex]\begin{gathered} \frac{x^m}{x^n}=x^{m-n} \\ \text{Here, m and n are constants} \end{gathered}[/tex]Applying the above exponent rule to the given expression,
[tex]\frac{10^8}{10^0}=10^{8-0}=10^8[/tex]Therefore, 10^8/10^0 expressed as a single power of 10 is,
[tex]10^8[/tex]Can anyone answer this calc question please
The solutions to the equation involving derivatives is given as follows:
Greater solution: x = -5.91.Lesser solution: x = -8.08.Quotient ruleSuppose we have a rational quotient function as follows:
f(x) = g(x)/h(x).
The derivative is calculated as follows:
f'(x) = [g'(x)h(x) - h'(x)g(x)]/(h(x))²
In the context of this problem, the function is:
f(x) = x/(x + 7).
Hence the parameters to calculate the derivative are as follows:
g(x) = x.g'(x) = 1.h(x) = x + 7.h'(x) = 1.Then the derivative is given as follows:
f'(x) = [x + 7 - x]/(x + 7)²
It is equals to 6 when:
7/(x + 7)² = 6
6(x + 7)² = 7
6(x² + 14x + 49) = 7
6x² + 84x + 294 = 7
6x² + 84x + 287 = 0.
Which is a quadratic equation with coefficients given as follows:
a = 6, b = 84, c = 287.
Then the solutions are as follows:
x = -8.08 (lesser).x = -5.91 (greater).More can be learned about derivatives at https://brainly.com/question/25081524
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What expression could be used to find the volume of a cone
We have that the volume of the cylinder with height h and area of the base A is:
[tex]V_c=A\cdot h[/tex]we know that the volume of the cone is one third of the volume of the cylinder, if their height and area are the same. Then, in this case we have the following:
[tex]V_{\text{cone}}=\frac{1}{3}V_c_{}[/tex]given the size of a rectangle are 6in and 5in find the perimeter and the area of the rectangle
lenght (L)= 6in
Height (H)= 5in
perimeter = 2L+2 h
Eva Truett had an open-end lease for a minivan for her homedecorating business. The lease cost $315 per month for60 months. She paid a deposit of $1,200, a title fee of $135,and a license fee of $85. At the end of the lease, she can buythe van for its residual value of $3,850.a. What is the total lease cost?b. What is the total cost if she buys the van?
Given the word problem, we can deduce the following information:
1. The lease cost $315 per month for 60 months. It means the number of payments is 60 while the amount of payment is $315 per month.
2. Eva Truett paid:
Deposit=$1,200
Title Fee= $135
License Fee = $85
3. Residual Value= $3,850
To determine the total lease cost, we use the formula:
Total Lease Cost = ((Number of Payments)(Amount of Payment))+Deposit+Title
Fee+License Fee
We plug in what we know:
[tex]\begin{gathered} \text{Total Lease Cost = ((}60)(315))+1200+135+85 \\ \text{Calculate} \\ \text{Total Least Cost = 20,320} \end{gathered}[/tex]So, the total lease cost is $20,320.
You spin the spinner twice. 9 8 7 5 4 6 What is the probability of landing on a number greater than 6 and then landing on a divisor of 18? Simplify your answer and write it as a fraction or whole number. Submit
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]Determine the transformations needed to get f(x)= 4+2x from f(x)=x
EXPLANATION:
Given;
We are given the equation of a graph which is;
[tex]f(x)=x[/tex]This is transformed to give us the equation;
[tex]f(x)=4+2x[/tex]Required;
We are required to determine the transformations needed to get
[tex]\begin{gathered} f(x)=4+2x \\ from \\ f(x)=x \end{gathered}[/tex]Solution;
Note that from the first graph, which is f(x) = x (or y = x), what we have is x equals y at every value of x. However, when we have y = 2x, then that means when x = 1, y = 2. That is, for every value of x, the value of y is doubled. The line is vertically stretched LEFT by 2 units.
Afterwards, the equation becomes;
[tex]f(x)=4+2x[/tex]This means you now move the line 4 units up along the y-axis.
Therefore,
ANSWER:
[tex]\begin{gathered} Vertically\text{ }stretch\text{ }f(x)=x\text{ }left\text{ }by\text{ }2\text{ }units \\ \\ Transform\text{ }f(x)=x\text{ }up\text{ }by\text{ }4\text{ }units \end{gathered}[/tex]We can now plot both graphs as follows:
Graph of
[tex]f(x)=x[/tex]Also, we would have;
Graph of
[tex]f(x)=4+2x[/tex]Observe that the graph after the transformation has now tilted to the left and has moved from the origin (where x = 0, y = 0) up to the point where y = 4 (that is, x = 0, y = 4)
A bag contains marbles of different colors. How many ways unique ways or orders can you select 3 marbles
The answer is 6.
Think about the different marbles as marble '1', marble '2', and marble '3'.
If you fix the marble '1' to be the first pick, you're going to have two distinct possibilities.
_1_ _2_ _3_ and _1_ _3_ _2_
If you fix marble '2' as the first the same idea applies. If you multiply the amount of possibilities for each fixated marble by the total amount of marbles, you're going to get 3x2 = 6.
Given the position of the particle, what the position(s) of the particle when it’s at rest
The position function of a particle is given by:
[tex]X\mleft(t\mright)=\frac{2}{3}t^3-\frac{9}{2}t^2-18t[/tex]The velocity function is the derivative of the position:
[tex]\begin{gathered} V(t)=\frac{2}{3}(3t^2)-\frac{9}{2}(2t)-18 \\ \text{Simplifying:} \\ V(t)=2t^2-9t-18 \end{gathered}[/tex]The particle will be at rest when the velocity is 0, thus we solve the equation:
[tex]2t^2-9t-18=0[/tex]The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
[tex]t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Substituting:
[tex]\begin{gathered} t=\frac{9\pm\sqrt[]{81-4(2)(-18)}}{2(2)} \\ t=\frac{9\pm\sqrt[]{81+144}}{4} \\ t=\frac{9\pm\sqrt[]{225}}{4} \\ t=\frac{9\pm15}{4} \end{gathered}[/tex]We have two possible answers:
[tex]\begin{gathered} t=\frac{9+15}{4}=6 \\ t=\frac{9-15}{4}=-\frac{3}{2} \end{gathered}[/tex]We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
[tex]undefined[/tex]Amy $55.50 earned dollars for babysitting for five hoursHow much would only make if she was paid at the same rate and work seven hours
Match the correct letter to each coordinate point.Dialte the figure by a scale factor of 3\2
You have the following points for the vertex of the triangle IJK:
I(0,4)
J(4,-2)
K(-4,-2)
if the figure is dilated by a scale factor of 3/2, the previous point become:
I'(0, 4(3/2)) = I'(0, 6)
J'(4(3/2) , -2(3/2)) = J'(6 , -3)
K'(-4(3/2) , -2(3/2)) = K'(-6 , -3)
(Quadratic Regressions) Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profitearned at that price, y. Write a quadratic regression equation for this set of data,rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 22 dollars.
The general quadratic equation is:
y = ax² + bx + c
where a, b and c are constants.
Substituting with x = 18.5 and y = 11397, we get:
11397 = a*18.5² + b*18.5 + c
11397 = 342.25a + 18.5b + c (eq. 1)
Substituting with x = 25.5 and y = 16256, we get:
16256 = a*25.5² + b*25.5 + c
16256 = 650.25a + 25.5b + c (eq. 2)
Substituting with x = 35 and y = 16109, we get:
16109 = a*35² + b*35 + c
16109 = 1225a + 35b + c (eq. 3)
Equations 1, 2 and 3 make a system of 3 equations and 3 variables (a, b, and c).
Isolating c from equation 1 and replacing into equations 2 and 3, we get:
11397 = 342.25a + 18.5b + c
11397 - 342.25a - 18.5b = c
16256 = 650.25a + 25.5b + 11397 - 342.25a - 18.5b
16256 - 11397 = 650.25a - 342.25a - 18.5b + 25.5b
4859 = 308a + 7b (eq. 4)
16109 = 1225a + 35b + 11397 - 342.25a - 18.5b
16109 - 11397 = 1225a - 342.25a - 18.5b + 35b
4712 = 882.75a + 16.5b (eq. 5)
Isolating b from equation 4 and replacing into equation 5, we get:
[tex]\begin{gathered} 4859=308a+7b \\ 4859-308a=7b \\ \frac{4859-308a}{7}=b \end{gathered}[/tex][tex]\begin{gathered} 4712=882.75a+16.5(\frac{4859-308a}{7}) \\ 4712=882.75a+16.5\cdot\frac{4859}{7}-16.5\cdot\frac{308}{7}a \\ 4712=882.75a+11453.36-726a \\ 4712-11453.36=156.75a \\ -\frac{6741.36}{156.75}=a \\ -43=a \end{gathered}[/tex]Then, the value of b is:
[tex]\begin{gathered} b=\frac{4859-308\cdot(-43)}{7} \\ b=\frac{4859+13244}{7} \\ b=\frac{18103}{7} \\ b=2586.14 \end{gathered}[/tex]And the value of c is:
c = 11397 - 342.25*(-43) - 18.5*2586.14
c = 11397 + 14716.75 - 47843.59
c = -21729.84
Therefore, the quadratic regression is:
y = -43x² + 2586.14x - 21729.84
If the price is $22, then x = 22, and the value of y (profit) is:
y = -43*22² + 2586.14*22 - 21729.84
y = -20812 + 56895.08 - 21729.84
y = 14353.24
what does mean mean
There are more than one mean. The most used mean is the arithmetic mean (generally referred just as mean), which is the average of a set of numerical values. Other commonly used mean is the geometric mean. The objective of the means is to indicate the central tendency or typical value of a set of numbers.
Simplify 3x+5+8X-16+7X
Answer:
3x + 5 + 8x - 16 + 7x = 18x - 11
Explanation:
Given the expression:
3x + 5 + 8x - 16 + 7x
To simplify this
Collect like terms
3x + 8x + 7x + 5 - 16
= 18x - 11
1st question: who's in what team?2nd question: the students on each team who drew the greatest number will be the captain. who will be the captain of the Tigers? Who will be the captain of the Lions?
The students on the team of Rational Numbers are:
The students on the team of Irrational numbers are:
Lydia
Mr. Aba builds a circular patio with a diameter of 12 feet. He covers the patio with paving stones. The cost of the paving stone is $10.50 a square foot. To the nearest dollar, how much do the paving stones cost.A. $126.00B. $378.00C. $1,187D. $4,748Jacob chose D as the correct answer. How might he have gotten that answer?
Firstly, we are going to obtain the area of the circular patio.
[tex]\begin{gathered} A=\frac{\pi d^2}{4} \\ d\colon\text{diameter} \end{gathered}[/tex][tex]\begin{gathered} A=\frac{3.142\times12^2}{4} \\ A=113.112ft^2 \end{gathered}[/tex]If a paving stone cost $10.50 per square foot, then the total cost of the paving stones will cost:
[tex]\begin{gathered} C=113.112\times10.50 \\ C=\text{\$1,187.67} \end{gathered}[/tex]Hence, the correct option is Option C
Jacob mistook the given diameter of 12feet to be the radius.
He used the formula of the circular patio to be:
[tex]\begin{gathered} A=\pi r^2 \\ A=3.142\times12^2 \\ A=452.448ft^2 \end{gathered}[/tex]He then multiplied this area by the cost of $10.50, which is equal to:
[tex]\begin{gathered} C=452.448\times10.50 \\ C=\text{ \$4,750} \end{gathered}[/tex]LBN is a 30°-60°-90° triangle and LB = 18 in. Find NB.
In order to calculate the length of NB, let's use the cosine relation of the angle 30°.
The cosine relation is the length of the adjacent side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \cos (30\degree)=\frac{NB}{BL} \\ \frac{\sqrt[]{3}}{2}=\frac{NB}{18} \\ 2\cdot NB=18\sqrt[]{3} \\ NB=9\sqrt[]{3} \end{gathered}[/tex]What is the distance between (-1, 8) and (-5, -6) to the nearest tenth?A15.215.2B14.6C4.54.5D6.3
The distance d between two points (x1, y1) and (x2,y2) is given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute x1 = -1, y1 = 8, x2 = -5, and y2 = -6:
[tex]\begin{gathered} d=\sqrt{(-5-(-1))^2+(-6-8)^2} \\ d=\sqrt{(-5+1)^2+(-14)^2} \\ d=\sqrt{16+196}=\sqrt{212}\approx14.5602 \\ d\approx14.6 \end{gathered}[/tex]Therefore, the correct answer is choice B:
14.6
Alex earns $3 per hour at work. If Alex earns $15 totally, how many hours did he work?
Alex worked 5 hours
Explanation:Amount Alex earns per hour = $3
let the number of hours worked = h
Total amount earned = $15
Total amount earned = Amount Alex earns per hour × number of hours worked
15 = 3(h)
15 = 3h
divide both sides by 3:
15/3 = 3h/3
h = 5
Hence, Alex worked 5 hours
In triangle QUW, Point T is the centroid,and VT=5 . find QT and VQ .
Centroid Theorem of a Triangle: states that the centroid of a triangle is at 2/3 of the distance from the vertex to the mid-point of the opposite side. Meaning:
[tex]QT=\frac{2}{3}VQ[/tex]As the whole segment VQ is 3/3, then we can use this theorem:
[tex]VT=\frac{1}{3}VQ[/tex]We could get a general rule which is:
[tex]\text{part of a segment=(either 1/3 \lbrack{}smaller part\rbrack{}or 2/3 \lbrack{}longer part\rbrack}\cdot wholesegment\text{)}[/tex]Based on that, we know that 1/3 of the segment VQ equals VT, which equals 5 units. Then, to get VQ we would have to do the following:
[tex]VQ=VT\cdot3[/tex]Then...
[tex]VQ=5\cdot3=15[/tex]Now, to get QT:
[tex]QT=\frac{2}{3}VQ[/tex][tex]QT=\frac{2}{3}\cdot15=2\cdot5=10[/tex]Answer:
• QT = 10
,• QV = 15
Show all work such as tables on finding the domain and range of:a) h(x)= 2x+2
ANSWER
• Domain: (-∞, ∞)
,• Range: (-∞, ∞)
EXPLANATION
The domain is the set of all the x-values for which the function exists. The range is the set of all the y-values the function can take in the domain.
This is a linear function,
[tex]h(x)=2x+2[/tex]As we can see, there are no restrictions for x - i.e. x can take any value. Therefore, the domain is all real values.
The range is usually restricted by horizontal asymptotes, but since this is a linear function, it has no asymptotes and, therefore, the range is also all real values.
Hence, the domain is the set (-∞, ∞) and the range is the set (-∞, ∞).
it's a picture of the problem if not you won't understand
ANSWER:
Domain and range
(2, -3), (5,0) and (-2,3)
STEP-BY-STEP EXPLANATION:
When a function is inverted, a switch occurs between domain and range.
So the points are reversed, just like this:
[tex]\begin{gathered} (-3,2)\rightarrow(2,-3) \\ (0,5)\rightarrow(5,0) \\ (3,-2)\rightarrow(-2,3) \end{gathered}[/tex]Therefore, the correct answer is:
The domain and range of a function and its inverse switch. The graph pf the inverse of this functions passes through the points (2, -3), (5,0) and (-2,3)
if mKH=234 degrees and mPF = 42 degrees , find m< KIH
SOLUTION:
Step 1:
In this question, we are given the following:
This is a good application of Intersecting secant theorem for example:
I would give you a few minutes to go through the solution. If you don’t have anymore questions, I would be ending the session.Please, note that the solution to this problem can also always be found at brainly.com. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a nice day.Step 2:
Now, from the question, we can see that:
[tex]\begin{gathered} m\text{ }\angle KIH\text{ = }\frac{1}{2}(\hat{mKH}\hat{+mPF}\text{ )} \\ where \\ \hat{\text{mKH }}=234^0 \\ \hat{\text{mPF}}=42^0 \end{gathered}[/tex]Then, we have that:
[tex]m\angle KIH\text{ = }\frac{1}{2}(234^0+42^0)\text{ = }\frac{1}{2}(276)=138^0[/tex]CONCLUSION:
The final answer is:
[tex]m\text{ }\angle KIH=138^0[/tex]Determine the best method to solve the following equation, then solve. 3t^2-5t+7=-3
The best method to solve the equation is employing the Quadratic formula method
which is,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The equation given is,
[tex]3t^2-5t+7=-3[/tex]Add both sides by 3
[tex]\begin{gathered} 3t^2-5t+7+3=-3+3 \\ 3t^2-5t+10=0 \end{gathered}[/tex]Then, solve with the quadratic formula
[tex]t_{1,\: 2}=\frac{-\left(-5\right)\pm\sqrt{\left(-5\right)^2-4\cdot\:3\cdot\:10}}{2\cdot\:3}[/tex]Simplify the formula above
[tex]t_{1,2}=\frac{5\pm\sqrt[]{25-120}}{6}=\frac{5\pm\sqrt[]{-95}}{6}[/tex]Note that
[tex]\sqrt[]{-95}=\sqrt[]{-1}\times\sqrt[]{95}=\sqrt[]{95}i[/tex]Therefore,
[tex]t_{1,\: 2}=\frac{5\pm\sqrt{95}i}{6}[/tex]Separate the solution
[tex]t_1=\frac{5+\sqrt{95}i}{6},\: t_2=\frac{5-\sqrt{95}i}{6}[/tex]Rewrite the solution in standard complex form
[tex]t_1=\frac{5}{6}+\frac{\sqrt{95}}{6}i,t_2=\frac{5}{6}-\frac{\sqrt{95}}{6}i[/tex]Hence, the solutions to the quadratic equation are
[tex]t_1=\frac{5}{6}+i\frac{\sqrt[]{95}}{6},t_2=\frac{5}{6}-i\frac{\sqrt[]{95}}{6}[/tex]HELP ME PLEASEEEEEEEEE
Answer: x > -24
Step-by-step explanation:
To solve for x, we will isolate the variable. To do this, we will use inverse operations.
Given:
[tex]\displaystyle \frac{-x}{12} +13 < 15[/tex]
Subtract 13 from both sides of the equation:
[tex]\displaystyle \frac{-x}{12} < 2[/tex]
Multiply both sides of the equation by 12:
[tex]-x < 24[/tex]
Divide both sides of the equation by -1:
Since we are dividing by a negative, we "flip" the direction of the sign.
[tex]x > -24[/tex]
The number of calories per day consumed by adults is normally distributed with a mean of 3350 and with a standard deviation of 122. Which of the following is closest to the percent of adults who eat more than 3500 calories per day?
Let us write out the given data,
[tex]\begin{gathered} \mu=\operatorname{mean}=3350 \\ \sigma=standard\text{ deviation=122} \\ x=3500 \\ z=z-\text{score} \end{gathered}[/tex]Let us now write the formula for Z-score,
[tex]z=\frac{x-\mu}{\sigma}[/tex]Let us solve for z-score,
[tex]\begin{gathered} z=\frac{3500-3350}{122} \\ =\frac{150}{122}=1.2295 \\ z=1.2295 \end{gathered}[/tex]The probablity that the percent of adult who eat more than 3500 will be
[tex]\begin{gathered} Pr(z>1.23)\Rightarrow Pr(0Hence,the percent of adults who eat more than 3500 calories per day is 11%