Data
• $4.55 per hour
,• Earns an average of 19 tips (assuming that the tips are in dollars).
Procedure
To identify the algebraic expression, we have to identify the variable earn (the quantity that depends on something) and the fixed (the one that is mostly constant).
Based on the information given, we can assume that the variable quantity is $4.55, as it depends on the time, and the fixed is $19. Thus, the algebraic expression can be written as follows:
[tex]E=4.55t+19[/tex]where E represents the earnings and t represents the time.
Answer:
[tex]E=4.55t+19[/tex]Assume the radius of a certain planet is 2460 km and the planet is a sphere. What is its surface area?
Answer:
Explanation:
The surface area of a sphere is calculated using the formula:
[tex]A=4\pi r^2[/tex]Given that the radius of a certain spherical planet, r = 2460 km
[tex]undefined[/tex]which of the following graphs represents the equation Y -4 equals 3(x-1)?
Answer:
Explanation:
Given the equation:
[tex]y-4=3(x-1)[/tex]To determine its graph, check the graph that corresponds to the x and y-intercepts of this line.
When x=0
[tex]undefined[/tex]A card is selected from a standard deck of cards. What is the probability of selecting a King or an even card?
Given:
A card is selected from a standard deck of cards.
Required:
We need to find the probability of selecting a King or an even card.
Explanation:
The sample space =the total number of cards = 52.
[tex]n(S)=52[/tex]Let A be an event of selection a king.
The number of cards that is king = 4.
The favourable outcomes =The number of the card king
[tex]n(A)=4[/tex]The probability of selecting a king
[tex]P(A)=\frac{n(A)}{n(S)}=\frac{4}{52}[/tex]Let B be an event of selection an even card.
There are 5 even values (2,4,6,8,10) and 4 of each in the deck.
The number of cards that is even card=20.
The favourable outcomes =The number of the even card
[tex]n(B)=20[/tex]The probability of selecting an even card
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{20}{52}[/tex]
The probability of selecting a King or an even card is
[tex]=P(A)+P(B)[/tex][tex]=\frac{4}{52}+\frac{20}{52}=\frac{24}{52}[/tex][tex]=\frac{6}{13}[/tex]Final answer:
The probability of selecting a King or an even card 6/13.
1. If ∠2 measures 120°, what is the measure of ∠1? Explain how you found the measure of ∠1.2. Think of the top and middle shelves as two lines cut by a transversal. What type of angles are ∠1 and ∠5?3. Use the relationship between ∠1 and ∠5 to decide whether the top and middle shelves are parallel.(Needs exterior angles)4. Is the bottom shelf parallel to the top shelf? Explain.5. Is the bottom shelf parallel to the middle shelf? Explain.
1.
The shelves can be assumed to be straight lines, and as straight lines have a 180° angle, then:
[tex]m\angle2+m\angle1=180\degree[/tex]We know the value of m∠2. Thus, we can replace it and solve for m∠1:
[tex]120\degree+m\angle1=180\degree[/tex][tex]m\angle1=180\degree-120\degree[/tex][tex]m\angle1=60\degree[/tex]2.
If we can suppose that the top and middle shelves are cut by a transversal, then ∠1 and ∠5 are corresponding angles.
3.
When two parallel lines are cut by a transversal, they form corresponding angles, and these are equal in measure. Therefore, as:
[tex]m\angle1=m\angle5=60\degree[/tex]Then we can say that the top and middle shelves are parallel.
4.
As m∠11 = m∠2, we can say that they are alternate exterior angles, which are formed when parallel lines are cut by a transversal. Therefore, the bottom shelf is parallel to the top shelf.
5.
Finally, we can see that as m∠11 = 120°, we are in the same situation as in question 1, for which we conclude that m∠9 = 60°. Now, we have the same situation as in question 2, in which m∠5 and m∠9 are corresponding. Thus the bottom shelf is parallel to the middle shelf.
We want to solve the following system of equations.x^2 + y^2 = 1y = 2x + 2One of the solutions to this system is (-1,0).Find the other solution.
Answer:
(-3/5, 4/5)
Explanation:
Given the system of equations:
[tex]\begin{gathered} x^2+y^2=1 \\ y=2x+2 \end{gathered}[/tex]First, we substitute y=2x+2 into the first equation to obtain:
[tex]\begin{gathered} x^2+(2x+2)^2=1 \\ x^2+(2x+2)(2x+2)=1 \\ x^2+4x^2+4x+4x+4=1 \\ 5x^2+8x+4-1=0 \\ 5x^2+8x+3=0 \end{gathered}[/tex]We solve the derived quadratic equation for x,
[tex]\begin{gathered} 5x^2+8x+3=0 \\ 5x^2+5x+3x+3=0 \\ 5x(x+1)+3(x+1)=0 \\ (5x+3)(x+1)=0 \\ 5x+3=0\text{ or }x+1=0 \\ x=-\frac{3}{5}\text{ or -1} \end{gathered}[/tex]We then solve for the corresponding values of y using any of the equations.
[tex]\begin{gathered} \text{When x=-1} \\ y=2x+2 \\ y=2(-1)+2 \\ y=0 \\ When\text{ }x=-\frac{3}{5} \\ y=2(-\frac{3}{5})+2 \\ =\frac{4}{5} \end{gathered}[/tex]Therefore, the solutions o this system are:
(-1,0) and (-3/5, 4/5).
The other solution is (-3/5, 4/5).
The board of directors of a company must have select a president, a secretary and a treasurer in how many possible ways can this be accomplished if there are 22 members on the board
Given
Total number of members = 22
Find
Possible ways of selection of president, a secretary and a treasurer
Explanation
As we know , the number of possible ways of selection is given by
[tex]N=^nP_r[/tex]there are three members required so , r = 3
now , substitute the values in above equation
[tex]\begin{gathered} N=^{22}P_3 \\ N=\frac{22!}{(22-3)!} \\ \\ N=\frac{22!}{19!} \\ \\ N=22\times21\times20 \\ N=9240 \end{gathered}[/tex]Final Answer
Possible ways of selection of president, a secretary and a treasurer = 9240
f(x) = 5x2 – 7(4x + 3). What is the value of f(3)?
Given the function:
[tex]f(x)=5x^2-7(4x+3)[/tex]we can find f(3) by making x = 3 and solving for the term f. In this case, we have the following:
[tex]\begin{gathered} f(3)=5(3)^2-7(4(3)+3) \\ =5(9)-7(12+3)=45-7(15)=45-105=-60 \\ \Rightarrow f(3)=-60 \end{gathered}[/tex]therefore, f(3) = -60
From the table above what is the probability that the respondent chosen at random answers something other than somewhat likely
Find the probability that the respondent will choose "somewhat likely". Divide the number of respondents who chose the option by the total number of respondents.
[tex]\begin{gathered} P(SL)=\frac{290}{\~likely)=\frac{290}{210+290+340+80+80}} \\ =\frac{290}{1000} \\ =0.29 \end{gathered}[/tex]Since we need to find the probability of the complement of "somewhat likely", subtract the obtained probability from 1.
[tex]\begin{gathered} P(notSL)_{}=1-0.29 \\ =0.71 \end{gathered}[/tex]Question 2You buy a house for $299,000. If you make a 20% down payment, how much will your principal and interest payment be per month if you take out a 30 year loan with an interest rate of 4.25%.
The price of the house is $29900
At first you paid 20% of that price, to calculate how much the down payment was you have to do as follows:
[tex]299000\cdot0.2=59800[/tex]The down payment was $59800 and there are $299000-$59800=$239200 left to pay.
From this $239200 you have to calculate the interest rate:
$239200*0.0425= $10166 → this represents the total interest rate you'll pay
This is a 30 year loan, which means you'll pay
30*12=360
for 360 months
Divide the principal payment $239200 by 360 to calculate the monthly fee:
[tex]\frac{239200}{360}=664.44[/tex]Do the same with the total interest rate:
[tex]\frac{10166}{360}=28.24[/tex]Monthly you'll pay $664.44 plus $28.24 of interest, that adds up for a total of $692.68
P= rt , Solve for t in this literal equation
t = P/r
Explanations:The given equation is:
P = rt
To solve for t by dividing both sides by r
[tex]\begin{gathered} \frac{P}{r}=\frac{rt}{r} \\ \frac{P}{r}=t \end{gathered}[/tex]Therefore:
[tex]t\text{ = }\frac{P}{r}[/tex]hello, i was wondering how to solve this? i am having trouble to solve this.
see the attached figure to better understand the problem
the angle between the two vectors is x and the vertex is R
What is the measurement of DC? How do you know ?
The vertices B, C and D form a right triangle.
Knowing 2 sides of the tright triangle, like BD and BC, we can find the length ofthe third side, DC, using the Pythagorean theorem: the sum of the squares of the length of the legs, DC and BC, is equal to the square of the length of the hypotenuse BD.
[tex]DC^2+BC^2=BD^2[/tex]Replacing with the values, we can calculate DC:
[tex]\begin{gathered} DC^2+60^2=100^2 \\ DC^2+3600=10000 \\ DC^2=10000-3600 \\ DC^2=6400 \\ DC=\sqrt[]{6400} \\ DC=80 \end{gathered}[/tex]Answer:
The correct options are
A: 80
B: Pythagorean theorem
Don'te is sitting on the bus on the way home from school and is thinking about the fact that he has three homeworkassignments to do tonight. The table below shows his estimated probabilities of completing 0, 1, 2, or all 3 of theassignments.Number of Homework Assignments Completed0123Probability162951813What is the probability he will not do exactly 1 assignment?2/9Ob 7/9Ос 7/18Od 1
SOLUTION
Don'te is sitting on the bus on the way home from school and is thinking about the fact that he has three homework assignments to do tonight.
The table below shows his estimated probabilities of completing 0, 1, 2, or all 3 of the
assignments.
Number of Homework
Assignments Completed Probability
0 1/ 6
1 2/ 9
2 5/18
3 1/ 3
What is the probability he will NOT do exactly 1 assignment?
1/ 6 + 5 / 18 + 1/ 3 = 7 / 9 ................. OPTION B
write the equation of the line, with the given properties, in slope-intercept form.Slope=-6, through (-8,8)
The given slope is:
[tex]m=-6[/tex]And the point:
[tex](-8,8)[/tex]we label the coordinates as follows:
[tex]\begin{gathered} x_1=-8 \\ y_1=8 \end{gathered}[/tex]And now, we use the slope-point formula, which is:
[tex]y-y_1=m(x-x_1)[/tex]substituting the known values of slope m and the point:
[tex]y-8=-6(x-(-8))[/tex]We need to solve this for y to find the slope intercept form (which is y=mx+b):
[tex]\begin{gathered} y-8=-6(x+8) \\ y-8=-6x-48 \\ y=-6x-48+8 \\ y=-6x-40 \end{gathered}[/tex]The slope-intercept form is:
y = -6x - 40
Leah's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 5 coffees in all, 20% of which were regular. How many regular coffees did the cafe serve? regular coffees
Let regular coffee be x and decaffeinated be y. If they served 5 coffees in all, and
Construct a 95% confidence interval of the population proportion using the given information x=180, n = 300 the lower bound is the upper bound isRound to three decimal places as needed
Given;
[tex]x=180,n=300[/tex]Then, we can find the point estimation as;
[tex]\begin{gathered} \hat{p}=\frac{x}{n} \\ \hat{p}=\frac{180}{360}=0.60 \end{gathered}[/tex][tex]Z_{\frac{\alpha}{2}}=Z_{0.05}=1.96[/tex]Thus, the margin of error E is;
[tex]\begin{gathered} E=Z_{\frac{\alpha}{2}}\sqrt[]{\frac{\hat{p}(1-\hat{p})}{n}} \\ E=1.96\sqrt[]{\frac{0.60(0.40)}{300}} \\ E=1.96\sqrt[]{0.0008} \\ E=0.055 \end{gathered}[/tex]A 95% confidence interval for population proportion p is;
[tex]\hat{p}\pm E=0.60\pm0.055[/tex]The lower bound is;
[tex]0.60-0.055=0.545[/tex]The upper bound is;
[tex]0.60+0.055=0.655[/tex]4(−5x − 6) = 4(9x + 4)
Answer: X= -5/7
Step-by-step explanation:
4(-5x-6)=4(9x+4)
-20x-24=4(9x+4)
-20x-24=4(9x+4)
-20x-24=36x+16
Then add 24 to both sides:
Use inductive reasoning to find the next number in the pattern: 1 / 3 , 2 / 4, 3 / 5, ____.
..
SOLUTION
[tex]\frac{1}{3},\frac{2}{4},\frac{3}{5},...[/tex]The sequence progresses by the addition of 1 to both numberator and denominator.
[tex]\frac{3+1}{5+1}=\frac{4}{6}[/tex]The next number is 4/6.
The cost of a pound of nails increased from $2.03 to $2.19. What is the percent of increase to the nearest whole-number percent?(Type an integer
Hello there. To solve this question, we'll have to remember some properties about percents.
We start with percent of increase: it is the difference between how much a thing is from another and 100%.
Now, to calculate this amount, we take the ratio of the numbers. In this case, the cost of a pound of nails.
Knowing it increased from $2.03 to $2.19, we calculate:
2.19/2.03 = 1.079
Multiply by 100% to find its amount in percent
1.079 * 100% = 107.9%
Now, we simply take the difference:
107.9% - 100% = 7.9%
Rounding this percent to the nearest whole-number percent, we get:
8%
A data set consists of these points: (2, 4), (4, 7), (5, 12). Malinda found theregression equation to be ŷ = -2.5x - 1.5. Is she correct?A. No. The value for b is incorrect.B. Yes. This is the correct equation.OC. No. Both a and b are incorrect.D. No. The value for a is incorrect.
From the given cooridnate values, we can see that the linear regression model is given by:
the line
[tex]y=2.5x-1.5[/tex]If a and b denote the slope and y-intercept then , by comparing with the given solution, we can note that the slope (a) is incorrect. It must be 2.5 instead of -2.5. Therefore, the answer is option D
a cube has 6 faces that are red, yellow, or blue. maggie rolls the cube 20 times and records the color facing up.
From the information given, the number of outcomes from 20 trials are
Red = 7
Yellow = 6
Blue = 7
From the outcomes, since the number of outcomes for red and blue are equal, it means that the number of red and blue faces would be the same. The only option where they are the same is the last option. Since the total number of faces is 6, the remaining face which is yellow is possibly 2. Thus, the correct option is
The cube has 2 red faces, 2 blue faces and 2 yellow faces
Find -7/8 - 2 1/6. Write your answer as a mixed number in simplest form.
Answer:
3 1/24
Step-by-step explanation:
For what value of x does f(x) = 1?
Answer Choices:
A. x = 0
B. x= 1
C. x = 5
D. x = -5
Points EGNK or midpoints explain how you know figure EGHK is a parallelogram
Solution
Given a triangle FDH with E, G and H the midpoints of the sides of the triangle
Considering the figure EGHK,
Line EG is parallel and equal to line KH
Line, EK is parallel and equal to line GH
This is a feature of a parallelogram i.e two pair of opposite sides of a parallelogram are parallel and equal
∠GEK is equal to ∠GHK and ∠EGH is equal to ∠EKH
This is a feature of a parallelogram i.e
What is the sum of 7/8 and 11/8
In NOP, PNOP and m2O = 32. Find m P.
Solving Angle Problems.
[tex]PN\cong\text{ OP implies congruency, that is, length PN is the same as length OP.}[/tex]It follows therefore that
[tex]\begin{gathered} \angle NPO=\angle NOP=32^o\ldots.(\operatorname{Re}ason\colon\text{ Base angles of the isosceles triangle)} \\ \text{Hence}, \\ m\angle P=32^o \end{gathered}[/tex]The correct answer is the measure of angle P is 32 degrees
Suppose you ride your bicycle to the library traveling at .50 km/min. It takes you 25minutes to get to the library. How far did you travel
Answer:
50km
Step-by-step explanation:
We know that every minute we travel .5 km....
[tex]\frac{1 min}{.50 km}[/tex]
But we want to know how far we traveled in 25 mins
[tex]\frac{25 mins}{? km}[/tex]
So we go and do....
[tex]\frac{1 min}{.50 km} * \frac{25 mins}{? km}[/tex]
Then we have to divide 25 by .50
[tex]\frac{25 mins}{.50 km}[/tex]
Which Gives us
50 so he traveled 50km
Answer:
12.5km
Step-by-step explanation:
Hey! Let's help you with your question here!
We can begin by figuring out what we know!
Known InformationBicycle traveling at .50km/min (0.50km/min)It takes 25 minutes to get to the library.What we don't know and solving for itWhat we don't know is the distance traveled based on the given time. Now, what do we do? Well, we already know that the bicycle is traveling at a distance of .50km per minute and it takes us 25 minutes to get to the library. All we need to do here is take the distance per minute and multiply it by the total amount of minutes it takes to reach the destination. It would look something like this:
[tex]=(0.50km/s)*25[/tex]
[tex]=0.50*25[/tex]
[tex]=12.5[/tex]
Therefore, we can see that if we travel at a distance of .50km/min for 25 total minutes, we get a final distance of 12.5km.
Martina created this box plot to represent the number of inches of snow that fell during the winter in several different cities. Snowfall Summary 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Number of inches (a) What was the least amount of snowfall in any of the cities? (b) In which quarter is the data most concentrated? Explain how you know. (c) In which quarter is the data most spread out? Explain how you know.
a)
The minimum happens at the end of the left whisker of the box plot, from the graph we notice that his happens at five. Therefore, the minium amount of snow in any of the cities was 5.
b)
The data is more concenrtated in the second quarter (from the median to the third quartile) this comes from the fact that the length of this part of the block is smaller compared to the second quarter.
c)
The data is more spread out in the second quarter (from the second quartile to the median); this comes from the fact that the length of that part of the box is larger than any other part of the plot
QuestionThe following is a data set of the average weekly number of cups of coffee consumed by employees in an office. Find the mean and median and determine if the mean or median is the better measure of central tendency.5,0,5,2,0,10,7,8,10,21,5,8,2,5,3,5Select the correct answer below:Mean = 5, Median = 6The median is the better measure of central tendency.Mean = 5, Median = 6The mean is the better measure of central tendency.Mean = 6, Median = 5The median is the better measure of central tendency.Mean = 6, Median = 5The mean is the better measure of central tendency.
Explanation
we will begin by finding the mean and median of the data set
The mean is simply the average of the set, which will be
[tex]mean=\frac{5+0+5+2+0+10+7+8+10+21+5+8+2+5+3+5}{16}=\frac{96}{16}=6[/tex]The median is
[tex]\begin{gathered} \mathrm{The\:median\:is\:the\:value\:separating\:the\:higher\:half\:of\:the\:data\:set,\:from\:the\:lower\:half.} \\ \mathrm{If\:the\:number\:of\:terms\:is\:odd,\:then\:the\:median\:is\:the\:middle\:element\:of\:the\:sorted\:set} \\ If\:the\:number\:of\:terms\:\:is\:even,\:then\:the\:median\:is\:the\:arithmetic\:mean\:of\:the\:two\:middle\:elements\:of\:the\:sorted\:set \end{gathered}[/tex]Thus, we have the median as 5
To check which is a better measure, we will have to check the skewness
The skew value is 1.51
This means it is positively skewed
Thus
If the distribution is positively skewed then the mean is greater than the median which is in turn greater than the mode.
Therefore, the answer is
Jalen measured a bookcase to be 8.4 ft the actual measurement is 5.6 ft what is Gary percent error
We start by calculating the difference between the expected measured value and the value measured by Gary:
8.4 ft - 5.6 ft = 2.8 ft
Now we estimate what 2.8 ft is of the actual measurement 8.4 ft. That is:
2.8 / 8.4 = 0.33333... this is written in percent form as: 33.33%
This is the percent error.