The first step to determine the function is to find the total cost of the auction. This is done by adding all the prizes and the cost of the food.
[tex]\begin{gathered} \text{ cost}=320+150+30+400 \\ \text{ cost}=900 \end{gathered}[/tex]The total cost of the auction is $900. Since the cost of 50 tickets should be able to cover the cost, we need to divide the total cost by the number of tickets to determine the cost of each ticket.
[tex]\begin{gathered} x=\frac{900}{50} \\ x=18 \end{gathered}[/tex]Each ticket must be sold as $18. The whole function is:
[tex]f(x)=18\cdot x-900[/tex]help me, this is so confusing
the following set of numbers, find the mean, median, mode and midrange.
9, 9, 10, 11, 13, 13, 13, 14, 25
Question content area bottom
Part 1
The mean, x, is the sum of the data divided by the number of pieces of data. The formula for calculating the mean is x=
Σx
n, where Σx represents the sum of all the data and n represents the number of pieces of data.
Part 2
First find the sum of all the data, Σx.
Σx
=
9+9+10+11+13+13+13+14+25
=
117117
Part 3
Second, find the number of pieces of data, n.
The number of pieces of data listed is enter your response here.
The mean, median, mode and midrange are 13, 13, 13, 17 respectively.
Define mean, median, mode and midrange.An average is a mean. To calculate the sum, add together all the numbers. After that, divide the total by the quantity of numbers.
The median is a midpoint. The fact that the median is in the middle of the road makes it easy to recall. Put the numbers in ascending order, lowest to largest. If there are odd numbers, find the middle one. Add the middle two numbers together and divide by two if the numbers are even.
The most frequent number in a group of numbers is called the mode.
The midpoint is discovered by arranging the numbers from smallest to largest. To determine the sum, add the two smallest and greatest numbers together. By 2, divide the total.
Given data -
The following set of numbers is 9, 9, 10, 11, 13, 13, 13, 14, 25
Σx = 117
To calculate the mean, we use the formula as
Mean = Σx / n
where n is the number of pieces of data i.e. n=9
Therefore, Mean = 117 / 9
Mean = 13
To calculate the median, we use the formula as
Median = Value of [tex](\frac{n+1}{2})^{th}[/tex] th observation
when n is an odd number
So, Median = 10/2
Median = 5
Here the [tex]5^{th}[/tex] observation is 13
As 13 occurs maximum number of times in the given set of numbers and it has 3 times in the given set
Therefore the mode = 13
To calculate the midrange, we use the formula as,
Midrange = (greatest number + least number) / 2
Here the greatest number is 25 and least number is 9
Therefore midrange = (25+9)/2
midrange = 34/2
midrange = 17
The mean, median, mode and midrange are 13, 13, 13, 17 respectively.
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Use the standard deviation values of the two samples to find the standard deviation of the sample mean differences.Sample Standard Deviationred box 3.868blue box 2.933
Given:
The standard deviation are given as,
[tex]\begin{gathered} \sigma_{m_1}=\text{ 3.868} \\ \sigma_{m_2}\text{ = 2.933} \\ \end{gathered}[/tex]Required:
The standard deviation of the sample mean differences.
Explanation:
The formula for the deviation of the sample mean difference is given as,
[tex]\begin{gathered} \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}} \\ \end{gathered}[/tex]Substituting the values in the above formula,
[tex]\begin{gathered} \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{3.868^2}{n_1}+\frac{2.933^2}{n_2}} \\ \sigma_{m_1}-\text{ }\sigma_{m_2}\text{ = }\sqrt{\frac{14.9614}{n_1}+\frac{8.6025}{n_2}} \end{gathered}[/tex]Answer:
Thus the required answer is,
[tex]\sigma_{m_1}-\text{\sigma}_{m_2}=\sqrt{\frac{\text{14.9614}}{n_1}+\frac{\text{8.6025}}{n_2}}[/tex]
I need help with this question please (just question 10, not the one below)
Let the cost of each packet of cheese is $x
Let the cost of each burger $y
Calvin bought 5 packets of cheese and 3 burgers for $29.99
Mathematically we can write
[tex]5x+3y=29.99\text{ ..(1)}[/tex]Alex bought 3 packets of cheese and 7 burgers for $32.71
Mathematically we can write
[tex]3x+7y=32.71\text{ ..(2)}[/tex]Now we have to solve equations (1) and (2) for x and y
Now 7*(1)-3*(2) implies
[tex]7\times(1)-3\times(2)\Rightarrow35x+21y-9x-21x=209.93-98.13\Rightarrow26x=111.8\Rightarrow x=\frac{111.8}{26}\Rightarrow x=4.30[/tex]Hence the price of each packets of cheese is $4.30
Find the mode of each set of data.21, 12, 12, 30, 36, 34, 40, 22
The mode of a set of data is the value that appears the most number of times in the set.
So, checking this set, we have:
21: one time
12: two times
30: one time
36: one time
34: one time
40: one time
22: one time
So the mode of this set is 12.
Which value of the variable is the solution of the equation? a + $5.92 = $12.29 a = $5.37. $5.47. $6.37. $6.27 Enter your answer in the box. 9
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
a + $5.92 = $12.29
a = ?
Step 02:
a + $5.92 = $12.29
a = $12.29 - $5.92
a = $6.37
The answer is:
a = $6.37
Triangle TUV is congruent to Triangle GFE. Solve for x, y and z. What is the perimeter of triangle TUV?
Explanation
Step 1
Two triangles are said to be congruent if they are of the same size and same shape.
so, the measures are equivalent
[tex]\begin{gathered} UV=y=12 \\ TU=x=10 \\ TV=GE=z=15 \end{gathered}[/tex]hence, the perimeter of the triangle TUV is
[tex]\begin{gathered} \text{Perimeter}=\text{side}1+\text{side}2+\text{side}3 \\ \text{replace} \\ P=10+15+12 \\ P=37\text{ ft} \end{gathered}[/tex]so, the answer is 37 ft
I hope this helps you
A patient started with a 1 liter bag of IV solution. When the doctor checked in on the patient, the bag contained 0.24 liters of the solution. How much solution had been infused into the patient?
Given,
The quantity of solution intially is 1 litre.
The quantity of solution left after infusion is 0.24 litre.
The quantity of solution had been infused into the patient is,
[tex]\begin{gathered} \text{Solution infused tothe patient = total solution -left solution} \\ =1\text{ litre-0.24 litre} \\ =0.76\text{ litre} \end{gathered}[/tex]Hence, the quantity of solution had been infused into the patient is 0.74
Four gallons of gasoline cost $17.56. What is the price per gallon?
write a relationship between the cost and the amount of gasoline
[tex]\begin{gathered} 4gal\Rightarrow17.56 \\ 1gal\Rightarrow x \end{gathered}[/tex]solve for the x
[tex]\begin{gathered} x=\frac{1gal\cdot17.56}{4gal} \\ x=4.39 \end{gathered}[/tex]the price per gallon is $4.39
I understand the problem but I do need help with finding the angle measure
= O DATA ANALYSIS AND STATISTICS Mean and median of a data set A group of 8 students was asked, "How many hours did you watch television last week?" Here are their responses. 16, 16, 9, 9, 9, 7, 16, 10 Find the median and mean number of hours for these students. If necessary, round your answers to the nearest tenth. (a) Median: hours (b) Mean: hours X Ś ?
Solution:
Given:
[tex]16,16,9,9,9,7,16,10[/tex]The median is the middle term from the data rearranged in rank order.
Rearranging the data;
[tex]7,9,9,9,10,16,16,16[/tex]From the data set, the middle term is 9 and 10.
Since two terms fall in the middle, then the median is the mean of the two terms.
Hence,
[tex]\begin{gathered} Median=\frac{9+10}{2} \\ Median=\frac{19}{2} \\ Median=9.5hours \end{gathered}[/tex]Therefore, to the nearest tenth, the median is 9.5 hours.
The mean is the average of the set of data.
[tex]\begin{gathered} mean=\frac{16+16+9+9+9+7+16+10\:}{8} \\ mean=\frac{92}{8} \\ mean=11.5hours \end{gathered}[/tex]Therefore, to the nearest tenth, the mean is 11.5 hours
Which of the following statements are true for the image of a triangle after a dilation that has a scale factor of 5/6
EXPLANATION
Since we have a dilation with a scale factor of 5/6, the appropriate statement is the following:
1st) Each angle has the same measure as its corresponding angle in the preimage. This is true because the dilations don't change the shape.
II. Each has a measure 5/6 the length of its corresponding side in the pre-image.
Kim's bank gives your 9% simple interest on her college savings account. Ifshe deposits $700 and leaves it in the account for 6 years, howmuch interest will it earn?
Kodex, this is the solution:
Principal = $ 700
Interest rate = 9% = 0.09
Term = 6 years
Let's calculate the interest, using the simple interest formula, as follows:
Interest = Principal * (Interest rate * Term)
Replacing by the values given to us, we have:
Interest = 700 * (0.09 * 6)
Interest = 700 * 0.54
Interest = 378
After 6 years, Kim will earn $ 378 of interest.
Is position on an x or y axis
Usually, time is the independent variable, so it goes in the x-axis.
Position is similar to distance, and spedd is the rate of variation of position or distance. All of these three are usually graphed in the y-axis, as they depend on time.
aSuppose you want to buy a new car that costs $32,600. You have no cash-only your old car, which is worth $5000 as a trade-in. The dealer says theinterest rate is 5% add-on for 4 years. Find the monthly paymentThe monthly payment is $(Type an integer or decimal rounded to the nearest cent as needed.)
Given:
Cost of a new car = $32,600
Trade-in old car cost = $5,000
Rate, r = 5% or 0.05
Time, t = 4 years
Asked: Find the monthly payment.
Solution:
[tex]PMT=\frac{P_O(\frac{r}{n})}{(1-(1+\frac{r}{n})^{-nt})}[/tex]where:
PMT = Loan Payment
Po = Loan Amount
r = Annual Interest Rate
n = Number of Compounds per year
t = Length of the Loan in years
Now that we have the formula, we will substitute the values.
Po = $32,600 - $5,000 = $27,600
r = 5% or 0.05
n = 12 (There are 12 months in 1 year)
t = 4 years
[tex]\begin{gathered} PMT=\frac{P_O(\frac{r}{n})}{(1-(1+\frac{r}{n})^{-nt})} \\ PMT=\frac{27600(\frac{0.05}{12})}{(1-(1+\frac{0.05}{12})^{-12\cdot4})} \\ PMT=\frac{115}{(1-0.8190710169^{})} \\ PMT=\frac{115}{0.1809289831} \\ PMT=635.6085026 \end{gathered}[/tex]ANSWER:
The monthly payment is $636. (Rounded to the nearest cent.)
True or false: if the determinant is 0, then the system has no solution?
If the determinat of a matrix is 0, then the linear system of equations it represents has no solution.
Then, the statement is true.
In the diagram of ABCD shown below, 'BA is drawn from vertex B to point A on DC, such that BC & BA.Аa.b.What kind of triangle is AABD? Explain.hat kind of triangle is ADBC? Explain.
We have the following information from the picture:
mmWe have that:
m m m
m m
Therefore, the angles in triangle ABD are m < D = 30, m< DAB = 120, and m < B = 30.
We need now to find the angles of the triangle ABC to find the rest of the angles.
In triangle ABC, we need to find the
Then, we can draw this as follows:
According to the angles, the triangle ABC is an Obtuse Triangle because it has an obtuse angle (
The triangle DBC is a right triangle because it has a right angle (
1331166633×644÷8797×5
1. The first thing to do is to carry out the two respective multiplications;
[tex]\begin{gathered} 133116633\times644=85,727,111,652 \\ 8797\times5=43,985 \\ \end{gathered}[/tex]2.Now we divide both results, leaving the first result as a dividend and the shortest result as a divisor.
[tex]\begin{gathered} 85,727,111,652/\text{ 43,985} \\ =1,949,007.881141 \end{gathered}[/tex]Fiona is playing Fetch with her dog she is standing at the coordinate points (7, -5) when she throws the stick, it lands at the coordinate point (-1, 10). How far did Fiona throw the stick
Answer:
Fiona threw the stick 17 units far
Explanation:
To know how far Fiona threw the stick, we find the distance between the given coordinate points, (7, -5) and (-1, 10)
The formula for the distance between two coordinate points is:
[tex]D=\sqrt[\square]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Here,
[tex]\begin{gathered} x_1=7 \\ y_1=-5 \\ x_2=-1 \\ y_2=10 \end{gathered}[/tex]Now,
[tex]\begin{gathered} D=\sqrt[]{(-1-7)^2+(10-(-5))^2} \\ =\sqrt[\square]{(-8)^2+(15)^2} \\ =\sqrt[\square]{64+225} \\ =\sqrt[\square]{289} \\ =17 \end{gathered}[/tex]Therefore, Fiona threw the stick 17 units far
The prices of cell phone cases in a store are normally distributed.The mean of the prices is $22.90,and the standard deviation is $4.90.If you want to look at the bottom 45% of cases in terms of price,what is the cutoff price so that 45% of all cases are priced below that amount?
Given:
Mean = 22.90
Standard Deviation = 4.90
Find the cutoff price so that 45% of all cases are priced below that amount.
To solve this problem, the first thing we need to do is to find the z-score for 45% or 0.45.
The z-score for 0.45 is -0.126.
Now, to find the cutoff price or the "score", we will use the following equation
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where:
z = z-score
x = score
μ = mean
σ = standard deviation
We are looking for the "x"
Derive the formula and substitute the given data.
[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]\sigma z=x-\mu[/tex][tex]x=z\sigma+\mu[/tex][tex]x=(-0.126)(4.90)+22.90[/tex][tex]x=22.28[/tex]We got a value of 22.28 for our score, therefore, the cutoff price must be $22.28.
Write a formula for the function obtained when the graph is shifted as described. When typing exponents use the carrot key ^ by pressing SHIFT and 6. For example x squared can be typed as x^2. Do not put spaces between your characters and remember to use parentheses in the appropriate places!f(x)=x^3 is shifted up 3 unit and to the left 7 units.The new equations f(x)=Answer
Given the function
[tex]f(x)=x^3[/tex]We are asked to shift the function up 3 units and to the left 7 units.
Explanation
1) To shift upwards, we will add outside of the argument
2) To shift to the left, we will add inside of the argument
Therefore;
[tex]x^3\rightarrow(x+7)^3+3[/tex]Answer:
[tex]f(x)=(x+7)^3+3[/tex]Grayson needs to order some new supplies for the restaurant where he works. The restaurant needs at least 761 forks. There are currently 205 forks. If each set on sale contains 10 forks, which inequality can be used to determine x, the minimum number of sets of forks Grayson should buy?options are.1. 761 ≥ 10(205+x)2. 761 ≤ 10(205+x)3. 761 ≥ 10x+2054. 761 ≤ 10x+205
The restaurant needs at least 761 forks.
There are currently 205 forks
Each set on sale contains 10 forks,
The number of set taht have to buy are x
Number of forks in x set are = 10x
Since, we need at least 761
So 761 should be graeter than equal to the sum of reamining forks and the new forks
i.e. 761 ≥ 10x + 205
Answer : 3. 761 ≥ 10x + 205
Part II: Identify the domain and range of the following relations. For each graph, indicate if the relation is also a function or not. 1) 2) 3) ly Function? Domain: Function? Domain: Function? Domain: Range: Range: Range:
A function is a relationship between two variables that satsifes the condition that there is one and only one value of the image (the dependent variable) for each value of the domain (the set of values of the independent variable).
All the set of values of the image are what is called the range.
1) It is a function, as there is one and only one value of y for each value of x.
The domain, the set of values that x can take, is all the real numbers.
The range, instead, only takes values above y=-3.
Answer:
Function: Yes
Domain: All real numbers
Range: y>=-3.
2) It is a function, as there is one and only one value of y for each value of x.
The domain, the set of values that x can take, is all the real numbers.
The range is also all the real numbers, as the arrows indicate no limit for the values that the function can take.
Answer:
Function: Yes
Domain: All real numbers
Range: All real numbers
3) It is a function, as there is one and only one value of y for each value of x.
The function is defined for values of x that are bigger or equal than -3, so the domain is x>=-3.
The values that the function takes are equal or bigger than 0, so the range is y>=0.
Answer:
Function: Yes
Domain: x >= -3
Range: y >= 0
Desmond fabricates a tiny microchip it is square in shape measuring seven. 5 mm on each side draw Desmond’s chip to scale on the grid below
Explanation
To draw the square, we were given a scale
2 units represent 1 mm
Therefore, 7.5mm will be
[tex]2\times7.5\text{ units =15 units}[/tex]So that we will have 15 units on all sides
The red sketch above represents the square with a length of 7.5mm
a landscaper is hired to take care of the lawn and shrubs around the house. the landscaper claims that the relationship between the number of hours worked and the total work fee is proportional. the fee for 4 hours of work is $140.
which of the following combinations of values for the landscapers work hours and total work fee support the claim that the relationship between the two values is proportional?
A. 3 hours for $105 B. 3.5 hours for $120 C. 4.75 hours for $166.25 D. 5.5 hours for $190 E. 6.25 hours for $210.25 F. 7.5 hours for $262.50
The two combinations that shows that the landscapers work hours and total work fee are proportional are: 3 hours for $105 and 7.5 hours for $262.50(option A and F)
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. It is represented by the proportional symbol.
Direct proportion is given by y= kx, where k is the constant and y and x are the variables.
If x represents the landscapers work hours and y represents the total work fee.
y= kx
when y = $140 and x= 4hours
k= 140/4= 35
therefore when x= 3 then y= 3×35=105
similarly when x= 7.5, y= 35×7.5=262.50
Only option A and F obeys the proportional relationship.
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Keith is saving money for a car. He has saved the same amount each year for the past three years, and records how much he has at the end of each year in the table below. (a)What is Keith's unit rate of change of dollars with respect to time; that is, how much does Keith save in one year? The unit rate is dollars per year. (b)Graph the proportional relationship described above, with the x-coordinate representing years, and the y- coordinate representing amount saved in thousands of dollars.
Answer:
(a)$1500 per year.
Explanation:
(a)From the table:
3000-1500=$1500
4500-3000=$1500
This means that every year, Keith adds $1500 to his savings.
The unit rate is $1500 per year.
(b)
If x=number of years; and
y=Amount saved (in thousands of dollars.)
When x=1, y=$1.5
When x=2, y=$3.0=2x1.5
When x=3, y=$4.5=3x1.5
The equation of proportion is therefore:
[tex]y=1.5x[/tex]When x=0, y=0 (0,0)
When x=1, y=1.5 (1, 1.5)
We join the points (0,0) and (1,1.5)
The graph of the proportional relationship is attached below.
-2-3t=-4t how do i solve for t?
You have the following equation:
2- 3t = -4t
In order to solve the previous equation you proceed as follow:
2- 3t = -4t sum 3t both sides
2 = -4t + 3t simplify
2 = -t multiply by -1 both sides
-2 = t
t = -2
Hence, the dolution for t is t=-2
The measure of two angles are (2n+18) and (7n-11). If these are vertical angles, what is the value of n.
Answer:
The value of n is 29/5
Explanation:
Given that (2n + 18) and (7n - 11) are two vertical angles, by definition, they are congruent.
so
2n + 18 = 7n - 11
Subtract 2n from both sides of the equation
2n + 18 - 2n = 7n - 11 - 2n
18 = 5n - 11
Add 11 from both sides of the equation
18 + 11 = 5n - 11 + 11
29 = 5n
Divide both sides by 5
n = 29/5
Answer:
n = 29/5 or 5 4/5
I need the correct choice and the answer for the box
Given the exponential equation:
[tex]16e^t=98[/tex]A student solved it.
Let's describe and correct the error the student made in solving the exponential equation.
Let's solve the equation.
Apply the following steps:
Step 1.
Divide both sides by 16
[tex]\begin{gathered} \frac{16e^t}{16}=\frac{98}{16} \\ \\ e^t=6.125 \end{gathered}[/tex]Step 2.
Take the natural logarithm of both sides
[tex]\begin{gathered} t\text{ ln\lparen e\rparen=ln\lparen6.125\rparen} \\ \\ \end{gathered}[/tex]Where:
ln(e) = 1
Hence, we have:
[tex]t=1.812[/tex]The student did not convert to the logarithmic form correctly. The solution should be t = 1.812
ANSWER:
A. The student did not convert to the logarithmic form correctly. The solution should be
t = 1.812
In the accompanying diagram of a circle of O …..
the theorem says:
[tex]PA^2=PB\cdot PC[/tex]PB=2
PC=2+6=8
[tex]PA=\sqrt[]{2\cdot8}=\sqrt[]{16}=4[/tex]So the answer is
PA=4
The scale from a square park to a drawing of the park is 5 miles to 1 miles. The actual park has an area of 1,600 m×2 what is the area of the drawing
The user corrected that the scale of a drawing of a park reads: 5 miles to 1 cm , and we know that the park measures 1,600 square meters (user insisted that this measure is given in square meters and not square miles).
So we have to convert the 1600 square meters into miles, knowing that 1 meter is the same as: 0.000621371 miles
then meters square will be equivalents to:
1 m^2 = (0.000621371 mi)^2
then 1600 m^2 = 0.00061776 mi^2
now, since 5 miles are represented by 1 cm, then 25 square miles will be represented by 1 square cm
and therefore 0.00061776 square miles will be the equivalent to:
0.00061776 / 25 cm^2 = 0.000024710 cm^2
So and incredibly small number of square cm.
I still believe that some of the information you gave me are not in meters but in miles. (For example, the park may not be in square meters but in squared miles). The park seems to have the size of a house according to the info.