Total cost per day = $23.5
Money customer can spend = $70
Remaining money with the customer after he paid $23.5 = 70 - 23.5 = $46.5
Cost of mile per hour = $0.30
Number of miles = 46.5/0.3
= 155 miles
Final answer
155 miles
Martha Invests $7700 in a new savings account which earns 5.2 % annual interest, compounded continuously. What will be the value of her
Investment after 4 years?
The value of Martha's investment after 4 years will be $32,443.80.
What is the value of the investment?When an amount earns an interest that is compounded continuously, it means that the investment grows at an exponential rate continuously over the investment period. The investment period in this question is 4 years.
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateFuture value of the investment = $7,700 x (2.718^0.052) x 4 = $32,443.80
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A company's stock begins the week with a price of $43.85 per share. THe price changes by +$2.70 each day for the first two days, by - $1.10 each day for the next two days, and, and by - $4.45 on the last day. At the end of the last day, what is the price per share of the company`s stock, in dollars?
Given:
Initial price of the stock=$43.85
Change for the first two days=+$2.70
Change for next two days=-$1.10
Last day=-$4.45
The objective is to find the price at the last day.
Let's take the price at final day as x.
[tex]\begin{gathered} x=43.85+2.70+2.70-1.10-1.10-4.45 \\ x=42.6 \end{gathered}[/tex]Hence, the price of the stock at the last day is $42.6
1. In a class of 22 students, 9 have a cat and 5 have a dog. There are 3 students who have a cat and a dog. What is the probability that a student chosen randomly from class has a cat or a dog? 2. In a class of 29 students, 15 are female and 8 have an A in the class. There are 11 students who are male and do not have an A in the class. What is the probability that a student chosen randomly from the class is a female who has an A?3. In a class of 18 students, 11 have a cat and 12 have a dog. There are 4 students who do not have a cat or a dog. What is the probability that a student chosen randomly from the class has a cat or a dog?4. In a class of 22 students, 5 are a female and 11 have an A in the class. There are 3 students who are female and have an A in the class. What is the probability that a student chosen randomly from the class is a male?5. In a math class with 28 students, a test was given the same day that an assingment was due. There were 19 students who passed the test and 18 students who completed the assingment. There were 6 students who failed the test and also did not complete the assingment . What is the probability that a student who did not complete the homework passed the test?6. In a class of 21 students, 7 have a brother and 6 have a sister. There are 4 students who have a brother and a sister. What is the probability that a student who has a brother also has a sister?
1. Let's make a diagram:
In the class, 6+3+2= 11 students have a pet, either a cat or a dog
Therefore, the probability that a student chosen randomly from class has a cat or a dog is:
[tex]\frac{11}{22}\rightarrow\frac{1}{2}=0.5[/tex]2. Let's take a look at the diagram of the situation:
Out of 29 students, 5 are female and have an A.
Therefore, the probability that a student chosen randomly from the class is a female who has an A is:
[tex]\frac{5}{29}\rightarrow0.17[/tex]3. Let's take a look at the diagram of the situation:
There are 18-4= 14 students with a pet, either a cat or a dog. Therefore, the probability that a student chosen randomly from the class has a cat or a dog is:
[tex]\frac{14}{18}\rightarrow\frac{7}{9}=0.78[/tex]4. Let's take a look at the diagram of the situation:
There are 9+8= 17 males in the class. Therefore, the probability that a student chosen randomly from the class is a male is:
[tex]\frac{17}{22}=0.77[/tex]5. Let's take a look at the diagram of the situation:
Notice that out of 28-18= 10 students that didn't complete the homework, 4 students passed the test.
Therefore, the probability that a student who did not complete the homework passed the test is:
[tex]\frac{4}{10}=0.4[/tex]6. Let's take a look at the diagram of the situation:
Slope -2/3 points (1,-5)Graph.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
slope = -2/3
point (1 , - 5)
Step 02:
graph:
equation of the line:
Point-slope form of the line
(y - y1) = m (x - x1)
x1 = 1
y1 = -5
(y - (-5)) = -2/3 (x - 1)
[tex]y\text{ + 5 = }\frac{-2}{3}x\text{ +}\frac{2}{3}[/tex][tex]\text{y = }\frac{-2}{3}x+\frac{2}{3}-5=\frac{-2}{3}x-\frac{13}{3}[/tex]Step 03:
Graph:
y = -2/3 x - 13/3
point 1 (1 , -5)
point 2:
if x = 0, y:
y = -2/3 (0) - 13/3
y = - 13/3
point 2 (0 , -13/3)
graph:
That is the full solution
A line passing through the point (4,2) with a slope of m = 2 also passes through what other points?1. The line passes through the point 2. The line also passes through the point
The 2 point can be 6 and 6 (6, 6)
Write the equation of the line in slope intercept form that is parallel to the given line and goes through the given point.y=3×+1; (-3,-2)
Explanation
Step 1
remember the slope intercep form
[tex]y=mx+b[/tex]where m is the slope, and b is the y-intercept
so, we have
[tex]y=3x+1\rightarrow y=mx+b[/tex]hence,for the given line
slope=3
b=1
Step 2
2 lines are parallel if the slope is the same, so the slope of the line we are looking for is 3 too.
[tex]\begin{gathered} \text{if line 1}\parallel Line2 \\ \text{then} \\ \text{slope}_1=slope_2 \end{gathered}[/tex]therefore, we need a line that has
slope=3
and passes through (-3,-2)
we can use
[tex]\begin{gathered} y-y_1=slope(x-x_1) \\ \text{where} \\ \text{the point is(x}_{1,}y_1) \end{gathered}[/tex]replace
[tex]\begin{gathered} y-y_1=slope(x-x_1) \\ y-(-2)=3(x-(-3)) \\ y+2=3(x+3) \\ y+2=3x+9 \\ \text{subtract 2 in both sides} \\ y+2-2=3x+9-2 \\ y=3x+7 \end{gathered}[/tex]I hope this helps you
23. In the figure below,PNbisects ZMPR IfmXMPN= 3r + 12 and mZNPR = 4r - 2. what isMAMPR?MNPR
hello
to solve this question, we need to find msince line PN bisects mmmm[tex]\begin{gathered} m<\text{MPR}=(3r+12)+(4r-2) \\ m<\text{MPR}=3r+12+4r-2 \\ m<\text{MPR}=7r-10 \end{gathered}[/tex]therefore, m
Write the proportional equation for the table that represents a proportional relationship. Use the variable that is provided in parenthesis beside each label.
The proportional relationship can be express as y = kx, where x is the independent variable and y is the dependent variable.
For table 1, T is the independent variable and C is the dependent variable, so the relationship that we are looking for is C = kT
Using the table, C = 30 when T = 2.
Substitute this to find k.
[tex]\begin{gathered} C=kT \\ 30=2k \\ k=\frac{30}{2}=15 \end{gathered}[/tex]Therefore, the equation is C = 15T
For table 2, G is the independent variable and C is the dependent variable. So the equation is C = kG
Using the table, C = 10.60 when G = 4.
Substitute this to find k.
[tex]\begin{gathered} C=kG \\ 10.60=4k \\ k=\frac{10.60}{4}=2.65 \end{gathered}[/tex]The equation is C = 2.65G
Question is in the photo. Disregard checked answer I just guessed don’t know if it’s right or wrong
Answer:
0, 3, and 6
Explanation:
Given the second derivative of the function, f(x) below:
[tex]f^{\prime}^{\prime}(x)=x^2(x-3)(x-6)[/tex]To find the x-coordinate of the point of inflection, set the second derivative of the function equal to zeroand solve for x:
[tex]\begin{gathered} x^2(x-3)(x-6)=0 \\ \implies x^2=0,x-3=0,x-6=0 \\ \implies x=0,3,6 \end{gathered}[/tex]The x-coordinates of the point of inflection are 0, 3, and 6.
identify the end of a sample period for the function
Solution
[tex]f(x)=2\text{ csc \lparen t+}\frac{\pi}{4})-1[/tex][tex]undefined[/tex]The final answer
Option D
[tex]x=\frac{5\pi}{4}[/tex]Order these numbers from least to greatest. -16,-18,-15,-12
Answer:
-18,-16,-15,-12
Step-by-step explanation:
The larger the negative number, the smaller it is, Reorganize accordingly.
59 volunteers at the research and rescue center will be participating in a rescue mission. There will be one team leader assigned to each group of 6 volunteers . How many team leaders will be needed so that every volunteer can participate in the rescue mission?
10 team leaders will be needed so that every volunteer can participate in the rescue mission.
Given:
59 volunteers at the research and rescue center will be participating in a rescue mission.
There will be one team leader assigned to each group of 6 volunteers .
Number of team leaders = number of volunteers / 6
= 59/6
= 9.83 ≈ 10.
we cannot assign 0.83 team leader so it is will be taken 1.
Hence the 10 team leaders will be needed so that every volunteer can participate in the rescue mission.
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Differentiate: f(x) = e^2x
Given:
[tex]f(x)=e^{2x}[/tex]Aim:
We need to differentiate the function f(x).
Explanation:
Differentiate the function f(x).
[tex]\frac{df\mleft(x\mright)}{dx}=\frac{de^{2x}}{dx}[/tex][tex]\text{Use chain rule }\frac{de^{2x}}{dx}=^{}e^{2x}\frac{d(2x)^{}}{dx}\text{.}[/tex][tex]f^{\prime}(x)=e^{2x}\cdot\frac{d(2x)}{dx}[/tex][tex]\text{Use chain rule }\frac{d(2x)^{}}{dx}=2.[/tex][tex]f^{\prime}(x)=e^{2x}\cdot2[/tex][tex]f^{\prime}(x)=2e^{2x}[/tex]Final answer:
[tex]f^{\prime}(x)=2e^{2x}[/tex]Complete the equation for the piece wise function graphed below.
Answer:
[tex]f(x)=\mleft\{\begin{aligned}-0.5x+3,if-6\le x\le-2 \\ -3,if-2Explanation:For the value of x such that: -6≤x≤-2
We have the endpoints (-6,0) and (-2, -2).
We determine the equation in the slope-intercept form, y=mx+b.
[tex]\begin{gathered} \text{Slope,m}=\frac{0-(-2)}{-6-(-2)} \\ =\frac{2}{-6+2} \\ =\frac{2}{-4} \\ m=-0.5 \end{gathered}[/tex]The equation then becomes:
[tex]y=-0.5x+b[/tex]Using the point (-6,0)
[tex]\begin{gathered} 0=-0.5(6)+b \\ b=3 \end{gathered}[/tex]Therefore: f(x)=-0.5x+3, -6≤x≤-2
Next, f(x)=-3 for -2
Finally, for 1The endpoints are (1,-4) and (6,1)
[tex]\text{Slope,m}=\frac{-4-1}{1-6}=\frac{-5}{-5}=1[/tex]Using the point (1,-4)
[tex]\begin{gathered} y=mx+b \\ -4=1(1)+b \\ b=-4-1=-5 \end{gathered}[/tex]Therefore, f(x)=x-5, for 1
The completed function will now be:
[tex]f(x)=\mleft\{\begin{aligned}-0.5x+3,-6\le x\le-2 \\ -3,-2Gretchen's gross annual salary is $34,788. What is the maximum amount of rent shecan afford to pay per month? Round answer to the nearest whole number.
Given:
Grethen's gross annual salary = $34, 788
The maximum amount of rent she can afford to pay per month can be found using the formula:
[tex]\text{Max amount of rent she can pay = }\frac{Gross\text{ annual salary}}{Number\text{ of months in a year}}[/tex]Applying the formula:
[tex]\begin{gathered} \text{Max amount of rent she can pay= }\frac{34788}{12} \\ =\text{ \$2899} \end{gathered}[/tex]Hence, the maximum amount of rent she can afford to pay per month is $2899
Answer: $2899
Answer the questions by drawing on the coordinate plane below. You may need to print the test and graphthe images by hand.
From the figure, we have the following coordinates of the vertices :
[tex]\begin{gathered} Q(-4,2) \\ R(-1,1) \\ S(-2,4) \end{gathered}[/tex]a. Rotation of 180 degrees about the origin has a rule of :
[tex](x,y)\rightarrow(-x,-y)[/tex]The sign of the coordinates will change from positive to negative or negative to positive.
The new coordinates will be :
[tex]\begin{gathered} Q(-4,2)\rightarrow Q^{\prime}(4,-2) \\ R(-1,1)\rightarrow R^{\prime}(1,-1) \\ S(-2,4)\rightarrow S^{\prime}(2,-4) \end{gathered}[/tex]The graph will be :
b. Reflection across the x-axis has a rule of :
[tex](x,y)\rightarrow(x,-y)[/tex]Only the y coordinate will change its sign.
So from the coordinates we got in a.
[tex]\begin{gathered} Q^{\prime}(4,-2)\rightarrow Q^{\doubleprime}(4,2) \\ R^{\prime}(1,-1)\rightarrow R^{\doubleprime}^{\prime}(1,1) \\ S^{\prime}(2,-4)\rightarrow S^{\doubleprime}(2,4) \end{gathered}[/tex]The graph will be :
if a=b, then b=a A Commutative property of equality B Reflexive Property of Equality C Symmetric Property of congruence D Symmetric Property of Equality
The given statement is:
[tex]a=b\to b=a[/tex]The symmetric property of equalities states:
This can be described as: if a is equal to b, then b is equal to a, so if a=b, then b=a.
The answer is d. Symmetric Property of Equality
The Moore's are purchasing a new upright freezer. The inner dimensions of the freezer are 0.5 meter by 0.6 meter by 1.5 meters. (a) What is the volume of the freezer in cubic meters? (b) What is the volume of the freezer in cubic centimeters? (Hint 1 cubic meter = 100 x 100 x 100 cubic 1.5 m centimeters.) 0.6 m 0.5 m T = lwh Response
Explanation:
a)
The volume of a rectangular prism - which is the shape this freezer has - is:
[tex]V=\text{width x length x height}[/tex]These measures are all in meters, so the volume of the freezer in meters is:
[tex]V=0.5m\times0.6m\times1.5m=0.45m^3[/tex]b) If 1 m³ = 100 x 100 x 100 cm³ this is the same as 1 m³ = 1,000,000 cm³. To find the volume in cubic centimeters we have to use this equality to transform the volume found in item (a) from cubic meters to cubic centimeters:
[tex]\frac{0.45m^3}{1m^3}\times1,000,000\operatorname{cm}=450,000\operatorname{cm}^3[/tex]Answers:
• a) ,V = 0.45 m³
,• b) ,V = 450,000 cm³
Sofia earned a score of 29 on Exam A that had a mean of 23 and a standarddeviation of 5. She is about to take Exam B that has a mean of 350 and astandard deviation of 20. How well must Sofia score on Exam B in order to doequivalently well as she did on Exam A? Assume that scores on each exam arenormally distributed.
Step 1: Write out the formula for finding the z-score of a number
[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]\begin{gathered} z=\text{ the z-score} \\ x=\text{ the number whose z-score we are looking for} \\ \mu=\text{ the mean of the distribution} \\ \sigma=the\text{ standard deviation of the distribution} \end{gathered}[/tex]Step 2: Find the z-score of 29
[tex]\begin{gathered} In\text{ this case,} \\ \mu=23,\sigma=5,x=29 \end{gathered}[/tex]Therefore,
[tex]z=\frac{29-23}{5}=\frac{6}{5}[/tex]Step 3: Find a score on Exam B that has a z-score 6/5
[tex]\begin{gathered} In\text{ this case,} \\ \mu=350,\sigma=20,x=\text{?} \end{gathered}[/tex]Therefore,
[tex]\frac{6}{5}=\frac{x-350}{20}[/tex]Cross-multiplying we have
[tex]\begin{gathered} 6\times20=5(x-350) \\ 120=5x-1750 \\ 120+1750=5x \\ 5x=1870 \\ x=\frac{1870}{5} \\ x=374 \end{gathered}[/tex]Hence, Sofia must score 374 marks in Exam B in order to do equivalently well as she did on Exam A
X+5y+10z=84
X+2=z
X+y+z=15
In the given system of equations the value of x is 19, the value of y is -21 and the value of z is 17.
System of equations:
System of equations also known as set of simultaneous or an equation system, is a finite set of equations for which are used to find the common solutions.
Given,
Here we have the system of equation,
X+5y+10z=84
X+2=z
X+y+z=15
And we need to find the value of x, y and z.
The given equation are arrange in order to solve it easily,
x + 5y + 10z = 84 ------------(1)
x - z = 2 -----------------(2)
x + y + z = 15 -------------(3)
Multiply first equation by -1 and add the result to the second equation. The result is:
-5y -11z = -82 -------------(4)
Multiply first equation by -1 and add the result to the third equation. The result is:
-4y - 9y = -69 -------------(5)
Multiply second equation by -4/5 and add the result to the fifth equation. The result is:
-1/5z = -17/5
z = -17/5 x -5
z = 17
Apply the value of z on the equation (5), then we get,
-4y - 9(17) = -69
-4y - 153 = -69
-4y = -69 + 153
-4y = 84
y = 84/-4
y = -21
Apply the value of z on the equation (2), then we get,
x - z = 2
x - 17 = 2
x = 19.
Therefore, the value of x = 19, y = -21 and the value of z = 17.
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Find the equation of the linear function represented by the table in slope intercept form:Answer: y =
Answer:
y=5x-3
Explanation:
The slope-intercept form of the equation of a straight line is:
[tex]y=mx+b\text{ where }\begin{cases}m=\text{slope} \\ b=y-\text{intercept}\end{cases}[/tex]First, determine the slope using any two pair of points: (0,-3) and (1,2)
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{2-(-3)}{1-0} \\ m=\frac{5}{1} \\ m=5 \end{gathered}[/tex]Next, determine the y-intercept:
The y-intercept is the point where x=0.
• From the table, b=-3.
Thus, the required equation is:
[tex]y=5x-3[/tex]Select the correct answer. Which system of equations has a solution of (-2,0,1); QA I ty = -2 y – 2 = 1 + - 2 = -1 B. -31 + 2y = 6 y + z = 2 - Y - 2 = -1 OC. 3r - y = -6
SOLUTION:
We are to find the system of equation that has a solution of (-2,0,1).
From the above statement, x = -2, y = 0 and z = 1.
In order to now find the appropriate system for the solution, we need to substitute these values into all the four given options.
After careful substitutions, I was able to find the correct one as follows;
Recall that x = -2, y = 0 and z = 1.
[tex]\begin{gathered} 3x\text{ - y = -6} \\ 3(-2)\text{ - 0 = -6} \end{gathered}[/tex][tex]\begin{gathered} 2y\text{ - 5z = }-5 \\ 2(0)\text{ - 5(1) = 0 - 5 = -5} \end{gathered}[/tex][tex]undefined[/tex]Find the inverse of the function Which of the four options is it?
Answer
Option D is correct
f⁻¹(x) = (x - 6)/(-3)
Explanation
First of, the inverse of a function is a function that reverses the actions of the function. That is, for the inverse function, if we are given f(x), we would be able to obtain x.
The step to finding a function's inverse is to write y instead of f(x). We then rewrite by replacing the y by x and then make y the subject of formula, the y which is a subject of formula now, represents the inverse function, f⁻¹(x).
f(x) = -3x + 6
write y instead of f(x)
y = -3x + 6
rewrite by replacing the y by x
x = -3y + 6
We can rewrite this as
-3y + 6 = x
make y the subject of formula
-3y = x - 6
Divide both sides by -3
(-3y/-3) = (x - 6)/(-3)
y = (x - 6)/(-3)
f⁻¹(x) = (x - 6)/(-3)
Hope this Helps!!!
Which of the following does not show a range? Question 3 options:90-1000-1005080-90
third option(50) because a range is a group of data from one point to another
What is the length of the hypotenuse of a 45° -45° -90° triangle with leg length 5√3?
Let's begin by listing out the given information:
The figure of the question is attached below
This is a right triangle. As such, we will solve using Trigonometric Ratio (SOHCAHTOA). In this case, we will use SOH
[tex]undefined[/tex]Write an equation of the line perpendicularto the given line that contains P.P (4, 4): y = -2x-8
For this problem we want to find the equation of a line perpendicular to the line y=-2x-8 and passing through the point (4,4). We can see that the slope for the line given is m1=-2 and since we want a perpendicular line we need to satisfy the following:
[tex]m_1\cdot m_2=-1[/tex]And solving for m2 we got:
[tex]m_2=-\frac{1}{m_1}=-\frac{1}{-2}=\frac{1}{2}[/tex]And then with the point given we can find the intercept:
[tex]4=\frac{1}{2}(4)+b[/tex][tex]b=4-2=2[/tex]And the equation for the line would be:
[tex]y=\frac{1}{2}x+2[/tex]Dilate the figure by the scale factor. Then enterthe new coordinates.A(2,4)K=4C(-4,1)A'([?],[ 1)8121) B'([],[ ]C'([],[1.
Answers:
A'(8, 16)
B'(8, -4)
C'(-16, 4)
Explanation:
The new coordinates of the figure can be calculated as:
[tex](x,y)\to(k\cdot x,k\cdot y)[/tex]Where k is the scale factor. So, the new coordinates are:
[tex]A(2,4)\to(4\cdot2,4\cdot4)=A^{\prime}(8,16)[/tex][tex]B(2,-1)\to(4\cdot2,4\cdot-1)=B^{\prime}(8,-4)[/tex][tex]C(-4,1)\to(4\cdot-4,4\cdot1)=C^{\prime}(-16,4)[/tex]Therefore, the answers are:
A'(8, 16)
B'(8, -4)
C'(-16, 4)
If log2 5=x and log2 3=y, determine log2 20 can you help me learn how to do this?
Answer:
2+x
Explanation:
Given the following:
[tex]\begin{gathered} \log _25=x \\ \log _23=y \end{gathered}[/tex]The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).
[tex]\begin{gathered} \log _220=\log _2(4\times5) \\ =\log _2(2^2\times5) \end{gathered}[/tex]Next, since we have the multiplication sign, we use the addition law:
[tex]=\log _22^2+\log _25[/tex]The power of the number becomes the product of the log, so we have:
[tex]=2\log _22+\log _25[/tex]When you have the same base and number, the result is always 1.
[tex]\begin{gathered} \log _22=1 \\ \implies2\log _22+\log _25=2(1)+\log _25 \\ =2+x \end{gathered}[/tex]Therefore:
[tex]\text{log}_220=2+x[/tex]Ineed help with a math question. i linked it below
EXPLANATION:
We are given the measure of central tendency of two different sets of data.
For the first data set, the mean is 13.4g, while for the second the mean is 19.7g.
The Mean Absolute Deviation for both data sets is 3g.
We need to understand the MAD (mean absolute deviation). This measures how far off each data point is from the mean, either to the left, or to the right.
For set 1, the each data is 3 units away from the mean. Also for set 2, each data is 3 units away from the mean.
We can conclude then that;
ANSWER:
(1) There is no significant difference between the distributions
(2) The difference in mean mass between data set 1 and data set 2 is very small.
(3) The MAD means that both sets of marbles have similar distribution.
A spinner is divided into a red section and a blue section. In a game, the spinner is spun twice. If the spinner lands on red at least once, then Kim wins the game; otherwise, Natalie wins the game. What fraction of the spinner must be red for the game to be fair? A. 1/4B. 1 - square root 2/2C. 1/2D. square root 2/2
A: the spinner lands on red
If you spin the spinner twice, the results are independent, then the probability of getting two reds is P(A)*P(A)
We need this probability equal to 1/2 in order to get a fair game. Since there are 2 possible outcomes (red or blue), then P(A) = x/2. Now we can write the next equation:
[tex]\begin{gathered} \frac{x}{2}\cdot\frac{x}{2}=\frac{1}{2} \\ \frac{x^2}{4}=\frac{1}{2} \\ x^2=\frac{4}{2} \\ x=\sqrt[]{2} \end{gathered}[/tex]This means that √2/2 of the spinner must be red