These data are the number of on campus burglaries reported in a given year for nine western Pennsylvania universities.15 11 4 15 9 7 12 5 15For the data find the mean median mid range in the mall round to one decimal place if necessary.
Answers
Recall how to find the mean, the median, the midrange and the mode of a data set.
To find the mean, add all the values and divide the result over the amount of values:
[tex]\frac{15+11+4+15+9+7+12+5+15}{9}=\frac{93}{9}=10.333...\approx10.3[/tex]To find the median, list the data from smallest to largest and identify the number that is placed at the middle of the list. If the number of data points is even, the median is the average of the two middle data points in the list:
[tex]4,5,7,9,11,12,15,15,15[/tex]In this case, the median is 11 because there are 4 numbers before it and 4 numbers after it.
To find the midrange, calculate the mean between the minimum and maximum numbers of the data set:
[tex]\frac{4+15}{2}=9.5[/tex]The mode is the value that appears most frequently in the data set. In this case, the number 15 appears three times and the rest just 1. Then, the mode is 15.
Therefore, the answers are:
Mean: 10.3
Median: 11
Midrange: 9.5
Mode: 15
Related Questions
Cam decided to rent a storage unit to store his sailboat. The mast of the boat is 20 feet long. The storage unit is 4ft by 8ft by 19ft. Will the mast fit in the storage unit?A. YesB. No
Answers
Step 1
Find the volume of the storage
[tex]Length\times width\times height[/tex]From the data given the storage could have a height of 4ft or 8ft or 19ft. The mast of the sailboat is 20 feet long. This means that no matter which of the measurements is the height of the store, the mast of the sailboat will not fit in because it is longer than all those heights.
Therefore, the answer will be;
No the storage unit is too small to fit the mast of the sailboat
Cual es la coordenada-y del punto C ? What is the y-coordinate of pint C ?
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The y co-ordinate of the point C is 13.
Given, the points are :
A (2,4) = (x₁,y₁)
B (10,10) = (x₂,y₂)
Ratio of the length AC to CB is 3:1.
⇒ 3:1 = m:n
⇒ section formula C = (mx₂-nx₁/m-n) , my₂-ny₁/m-n)
substitute the values.
⇒ C = (3(10)-1(2)/3-1 , 3(10)-1(4)/3-1)
⇒ C = (30-2/2 , 30-4/2)
⇒ C = (28/2 , 26/2)
⇒ C = (14 , 13)
Hence the y coordinate of C is 13.
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A randomly generated list of numbers from 0 to 4 is being used to simulatean event, with the number 4 representing a success. What is the estimatedprobability of a success?A. 20%B. 75%C. 25%D. 80%
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Given:
A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing success.
Required:
What is the estimated probability of success.
Explanation:
The probability is
[tex]=\frac{\text{ Number of favorable cases}}{\text{ Total number of cases}}[/tex]0, 1, 2, 3, 4, 5 are choices.
Favorable case is number 4.
So, probability
[tex]\begin{gathered} =\frac{1}{5} \\ =0.2 \\ =20\% \end{gathered}[/tex]Answer:
Option A is correct.
You deposit $400 in an account that earns simple interest at an annual rate of 5%.
a. Write and graph a function that represents the amount (in dollars) of interest
earned after t years. Interpret the slope of the graph.
b. Is there enough money in the account after 4 years to buy a drum set that costs
$500?
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The answer of the given question based on simple interest is (a) The graph of this function is a straight line with a slope of 20. (b) There is not enough money in the account after 4 years to buy the drum set.
What is Simple interest?Simple interest is type of interest that is calculated on the principal amount (initial amount) of loan or investment. It is fixed percentage of principal, and does not take into account any interest earned or accrued over time.
a. The formula for simple interest is I = Prt, In this case, P = 400 and r = 0.05, so the function for the amount of interest earned after t years is:
I(t) = 400 * 0.05 * t = 20t
To graph this function, we can plot points for different values of t and connect them with a line. For example:
When t = 0, I(t) = 0
When t = 1, I(t) = 20
When t = 2, I(t) = 40
When t = 3, I(t) = 60
When t = 4, I(t) = 80
The graph of this function is a straight line with a slope of 20. The slope represents the rate of change of the interest earned per year. In this case, the slope is positive, which means that the interest earned increases linearly with time.
b. After 4 years, the interest earned is:
I(4) = 20 * 4 = 80
The total amount in account after 4 years will be:
A = P + I = 400 + 80 = 480
Since the cost of the drum set is $500, there is not enough money in the account after 4 years to buy the drum set.
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AABC is isosceles.mZA = 3x + 40 and mZC = x + 50BAmZA= [ ? 1°
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ANSWER:
The value of the angle A is 55°
STEP-BY-STEP EXPLANATION:
Angles opposite equal sides are angles that are also equal.
Therefore, in this case A and C are equal angles, therefore we can do the following equation:
[tex]\begin{gathered} A=C \\ 3x+40=x+50 \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 3x-x=50-40 \\ 2x=10 \\ x=\frac{10}{2} \\ x=5 \end{gathered}[/tex]Now we replace the value of x, in A and we are left with:
[tex]\begin{gathered} A=3\cdot5+40 \\ A=15+40 \\ A=55 \end{gathered}[/tex]QuestionThe lid of a water bottle is a circle with a radius of 0.5 inches. Find a. The circumference of the lid. b. The area of the lid. Use 3.14 for pi.
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Given in the question:
a.) The lid of a water bottle is a circle with a radius of 0.5 inches.
A.) The circumference of the lid.
Step 1: Since the lid is a circle, let's recall the formula for finding the circumference at a given radius.
[tex]\text{ C= 2}\pi r[/tex]Step 2: Let's plug in the r = 0.5 inches in the formula to get the circumference.
[tex]\text{ C= 2}\pi r[/tex][tex]\text{ C= 2(3.14)}(0.5)[/tex][tex]\text{ C= 3}.14\text{ inches}[/tex]Therefore, the Circumference of the lid is 3.14 inches.
B.) The area of the lid.
Step 1: Let's recall the formula for finding the area of a circle at a given radius.
[tex]\text{ A = }\pi r^2[/tex]Step 2: Let's plug in the r = 0.5 inches in the formula to get the area.
[tex]\text{ A = }\pi r^2[/tex][tex]A=(3.14)(0.5)^2[/tex][tex]\text{ A = 0.785 in.}^2[/tex]Therefore, the Area of the lid is 0.785 in.².
A purse sells for $325. What was the original price of the purse if it is being sold at a 1625% markup?
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You have that the price of a purse is $325 with a 16.25% markup.
In order to determine what was the original price of the purse, you consider that the original price minus 16.25% of the unknown original price x is equal to 325.
Consider that the 16.25% of a quantity is simply the multiplication of (16.25/100) for such a quanity.
Then, you have:
x - (16.25/100)x = 325 "original price minus 16.25% of the original price"
calculate the quotient left side:
x - 0.1625x = 325
simplify like terms left side:
0.8375x = 325
divide by 0.8375 both sides:
x = 325/0.8375
x = 388.05
Hence, the original price of the purse was $388.05
The regulation height of a basketball hoop is 10 feet. Let the location of thebasket be represented in the coordinate plane by the point (0, 10). Let the ballbe thrown at a 45° angle with the ground.1. Suppose Nancy is standing a horizontal distance of 10 feet from thebasket at the point (-10, 0), and she shoots a basket from 6 feet in theair with an initial velocity of 22 ft/s.Question 1)C. Will Nancy make the basket? Defend your reasoning.D. Use appropriate tools strategically. Experiment on yourcalculator with different direction angles until the player makes abasket. What angle did you use?
Answers
Answer:
(A): Using the equations of motion, we can determine the answer as follows:
[tex]\begin{gathered} x(t)=x_{\circ}+v_{\circ}cos(\theta)t\rightarrow(1) \\ \\ y(t)=y_{\circ}+v_{\circ}sin(\theta)-\frac{1}{2}gt^2\rightarrow(2) \\ \\ y(x)=xtan(\theta)-\frac{g}{2(v_{\circ})^2cos^2(\theta)}x^2\rightarrow(3) \end{gathered}[/tex]formula (3) is obtained from (1) and (2), using equation (3) the answer is determined as below:
[tex]\begin{gathered} y(x)=xtan(\theta)-\frac{g}{2(v_{\circ})^2cos^2(\theta)}x^2 \\ \\ v_{\circ}=22\text{ f/s} \\ \\ \theta=45 \\ \\ g=32.1522\text{ f/s} \\ \\ y(x)=xtan(45)-\frac{32.1522}{2\times22^2cos^2(45)}x^2 \\ \\ y(x)=x-\frac{32.1522}{2\times22^2cos^2(45)}x^2 \\ \\ y(x)=x-\frac{32.152,2}{484}x^2 \\ \\ y(x)=x-0.06643x^2 \\ \\ (x,y)\rightarrow\text{ Adjusting the position for the shift gives:} \\ \\ y(x)=[(x+10)-0.06643(x+10)^2]+6\rightarrow(4) \end{gathered}[/tex]The plot of the (4) reveals the following:
Therefore the answer is no.
(D) Trying a new angle theta = 60 degrees gives the following new answer:
Therefore the answer is:
[tex]\theta=60^{\circ}[/tex]I'm kinda confused on this question. here it is "if a= 8, b = 4, and c=10 what is (b+c) the answers given to me are22112320and 2560.
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Given the graph of a function f. A) Graph f(x) -3B) Graph f(x+4)C) Graph -f(x)See picture of the graph of function f attached
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From the given problem, the figure shows the graph of f(x).
Note that translating the graph in a manner of :
[tex]f(x)+c[/tex]will shift the graph c units upward if the sign is positive or c units downward if the sign is negative.
We are looking for the graph of f(x) - 3
Since the sign is negative, we will shift the grahp 3 units downward, the graph will be like this.
As you can see, the orginal graph intersects at the origin (0, 0). The new graph intersects at (0, -3) since we moved or shifted the graph 3 units downward.
Additional :
If f(x) is translated in a manner of f(x+c), the graph will be shifted c units to the left if c is positive and will be shifted c units to the right if c is negative.
If f(x) is transformed in a manner of -f(x), the graph will reflect over the x-axis.
If the original point is (x, y). It will become (x, -y)
Find X and y intercepts 7x+10y=40
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To find the intercept of the function on the x-axis, replace y = 0 and solve for x:
[tex]\begin{gathered} y=0 \\ 7x+10y=40 \\ 7x+10(0)=40 \\ 7x+0=40 \\ 7x=40 \\ \text{ Divide by 7 from both sides of the equation} \\ \frac{7x}{7}=\frac{40}{7} \\ x=\frac{40}{7} \end{gathered}[/tex]Therefore, the x-intercept of the function is in the ordered pair:
[tex](\frac{40}{7},0)[/tex]To find the intercept of the function on the y-axis, replace x = 0 and solve for y:
[tex]\begin{gathered} x=0 \\ 7(0)+10y=40 \\ 0+10y=40 \\ 10y=40 \\ \text{ Divide by 10 from both sides of the equation} \\ \frac{10y}{10}=\frac{40}{10} \\ y=4 \end{gathered}[/tex]Therefore, the y-intercept of the function is in the ordered pair:
[tex](0,4)[/tex]This is a 4 part question as u can see in directions please help I’m stuck on this question on my homework
Answers
Given the function:
[tex]f\left(x\right)=3x-8[/tex]a) the inverse function is:
[tex]f^{-1}\left(x\right)=\frac{1}{3}(x+8)[/tex]So, we have two linear functions, which are one-to-one (every element of the function's codomain is the image of at most one element of its domain).
b) In order to graph both functions, keep in mind that f is a line with slope 3 and y-intercept at y = -8. As for f^{-1} it is a line with slope 1/3 and y-intercept at y = 8/3. You can simply graph both function on the same axes by calculating the values of f and f^{-1} given some values of x, for instance:
x = ..., -2 , -1, 0, 1, 2,...
f(x) =
f^{-1} =
As can be seen in the following graph: purple line represents f and pink line represents f^{-1}:
c) The domain and range of f(x) and f^{-1} is the same:
[tex]f:\text{ }\Re\rightarrow\operatorname{\Re}[/tex][tex]f^{-1}^:\text{ }\Re\rightarrow\Re[/tex]What is the perimeter of a triangle with coordinates A (-1, 5), B (-1, 1), and C (2, 1)?
A. 12 units
B. 6 units
C. 24 units
D. 20 units
Helppp
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Centroid: CG[0; 2.333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0; 1]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 143.13° = 143°7'48″ = 0.644 rad
∠ B' = β' = 90° = 1.571 rad
∠ C' = γ' = 126.87° = 126°52'12″ = 0.927 rad
Circle all systems of equations that have NO solutions. A. y = 5 – 3x y = -3x + 4 B. y = 4x – 1 4y = 16x – 4 C. 5x – 2y = 3 10x – 4y = 6 D. 3x + 7y = 42 6x + 14 y = 50 E. y = 5 + 2x y = 5x + 2
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To determine if a system of equation have solution you have to determine if the slope (m) is equal or diferent.
If the slope is the same it has NO solution
If the slope is different has a solution
If the equations are equivalents have infinite solutions
To determine the slope the equation must be is the form:
[tex]y=mx+b[/tex]Then
A.
y = 5 – 3x
In this equation the slope is m = -3
y = -3x + 4
In this equation the slope is m= - 3
The system has NO solution
B.
y = 4x – 1
m= 4
4y = 16x – 4
You need to simplify the equation, as follow:
[tex]\frac{4}{4}y=\frac{16}{4}x-\frac{4}{4}[/tex][tex]y=4x-1[/tex]Then the equation are the same it means the system has infinited solutions.
C.
5x – 2y = 3
[tex]-2y=3-5x[/tex][tex]y=-\frac{3}{2}+\frac{5}{2}x[/tex]m= 5/2
10x – 4y = 6
[tex]-4y=6-10x[/tex][tex]y=-\frac{6}{4}+\frac{10}{4}x[/tex]Simplify:
[tex]y=-\frac{3}{2}+\frac{5}{2}x[/tex]Then the equation are the same it means the system has infinited solutions.
D.
3x + 7y = 42
[tex]7y=42-3x[/tex][tex]y=\frac{42}{7}-\frac{3}{7}x[/tex][tex]y=6-\frac{3}{7}x[/tex]m= -3/7
6x + 14 y = 50
[tex]14y=50-6x[/tex][tex]y=\frac{50}{14}-\frac{6}{14}x[/tex][tex]y=\frac{25}{7}-\frac{3}{7}x[/tex]m= -3/7
The system has NO solution
E.
y = 5 + 2x
m= 2
y = 5x + 2
m= 5
The system has one solution
Then the systems that have NO solution are: A and D
Can you please help me answer this question thank you if it’s A, B C or D
Answers
Concept
In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
Given:
period of record = 5 years
mean daily revenue = $5400
Standard deviation = $54
We want to identify which of the options perfectly describes the sampling distribution of the sample mean supposing that 36 days are randomly selected.
Using the central limit theorem, we know that regardless of the distribution one samples from if the population mean and standard deviation are:
[tex]\begin{gathered} population\text{ mean (}\mu) \\ \text{Standard devaition (}\sigma) \end{gathered}[/tex]then, the mean is approximately normally distributed and has a value equal to the population mean, while the standard deviation of the sample means is:
[tex]\frac{\sigma}{\sqrt[]{n}}[/tex]Hence the standard deviation of the sample means is:
[tex]\begin{gathered} =\text{ }\frac{54}{\sqrt[]{36}} \\ =\text{ \$9} \end{gathered}[/tex]We can conclude that the distribution is normal with a mean of $5400 and a standard deviation of $9
Answer: Option B
Linear function ху 60 10-8 The values in the table represent a linear function. How does the value of y change in relation to a change in the value of x? A) for every change in x by-2, y changes by 4 B) for every change in x by 2, y changes by-4 C) for every change in x by -4, y changes by -2 D) for every change in x by -2, y changes by -4
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Here, we want to get how the value of y change relative to a change in value of x
There are 28 students in a homeroom. How may différent ways can they be chosen tobe elected President, Vice President, Treasurer, and Secretary?
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There are 28 students in a homeroom. How many différent ways can they be chosen to be elected President, Vice President, Treasurer, and Secretary?
In this problem, we have a permutation
so
Find out 28P4
[tex]28P4=\frac{28!}{(28-4)!}[/tex]28P4=491,400
therefore
the answer is 491,400Click on ,begin emphasis,all,end emphasis, the factors of the polynomial.
Answers
Let's assume that we have a polynomial p(x) with a leading coefficient a and zeros are labelled with letters r. Then its factors have the form:
[tex](x-r)[/tex]Remember that the zeros of a function are the x-values of its x-intercepts i.e. the points where it meets with the x-axis. By looking at the picture you'll notice that the graph of the function intercepts the x-axis at three x values: -3, -1 and 3. Then the factors of this polynomial are:
[tex]\begin{gathered} (x-(-3))=(x+3) \\ (x-(-1))=(x+1) \\ (x-3) \end{gathered}[/tex]AnswerThen the correct options are (x+3), (x-3) and (x+1).
Multiply the following polynomials. Once simplified, name the resulting polynomial. (3x^2 - 4) (5x - 6)name:
Answers
Cubic
Explanation:(3x² - 4) (5x - 6)
= 3x²(5x - 6) - 4(5x - 6)
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
= 15x³ - 18x² - 20x + 24
Naming polynomial base on the number of terms:
There are 4 terms in the polynomial above
4 terms is named polynomial of 4 terms
Naming by degree:
The highest degree (exponent) = 3
Polynomial with degree 3 is called cubic
So we can name the polynomial as cubic
Took a pic for better quality, Can you answer as quick as possible, this is due at 9:00, Thanks
Answers
The scatter plot represents a group of points that is clearly decreasing at a steady rate, this means that the equation that represents them is a linear equation with negative inclination. A linear equation is given by the following formulla:
[tex]y=m\cdot x+b[/tex]Where m is the inclination and b is the y-intercept. Since the inclination must be negative, the only possible option is A.
What is the value of x? ? 21 21 Drawing not to scale 78 156 D787
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We can find the value of x, by using the property of issoceles triangle:
A isosceles triangle is a triangle that has two sides of equal length.
In the given figure, triangle have two sides of equal length 21, thus the given triangle is issoceles.
Since, the angle opposite to the equal sides are equal,
so, the third angle of the given triangle is x
The sum of all angles in a triangle is equal to 180 degrees.
In the given figure : x, x & 34
[tex]\begin{gathered} x\text{ + x +34=180} \\ 2x+34=180 \\ 2x=180-34 \\ 2x=146 \\ x=\frac{146}{2} \\ x=73 \end{gathered}[/tex]So, x = 73º
Answer: D) 73º
Question 8 of 10The diagonal of a TV is 30 inches long. Assuming that this diagonal forms apair of 30-60-90 right triangles, what are the exact length and width of the TV?A. 60 inches by 60/3 inchesB. 15 inches by 15/5 inchesC. 60/2 inches by 600/2 inchesO D. 15.2 inches by 15.2 inches
Answers
The diagram of the triangle formed is shown below
The length is BC and the width is AB
To find BC, we would apply the cosine trigonometric ratio which is expressed as
Cos# = adjacent side /hypotenuse
hypotenuse = AC = 30
adjacent side = BC
# = 30
Thus, we have
[tex]\begin{gathered} \text{Cos}30\text{ = }\frac{BC}{30} \\ \text{Note, Cos30 = }\frac{\sqrt[]{3}}{2} \\ We\text{ have} \\ \frac{\sqrt[]{3}}{2}=\text{ }\frac{BC}{30} \\ 2BC\text{ = 30}\sqrt[]{3} \\ BC\text{ = }\frac{30\sqrt[]{3}}{2} \\ BC\text{ = 15}\sqrt[]{3} \end{gathered}[/tex]To find AB, we would apply the sine trigonometric ratio which is expressed as
Sin# = opposite side /hypotenuse
hypotenuse = AC = 30
opposite side = AB
# = 30
Thus, we have
Sin30 = AB/30
Recall, sin30 = 0.5
Thus,
0.5 = AB/30
AB = 30 * 0,5
AB = 15
Thus, the correct option is B
I need the work and the right answer and explain what the mistake he made was
Answers
The mistake was the inequalities sign that was changed .The inequality sign is not suppose to be greater than or equal to but it should be less than or equal to.
Create a box and whisker plot (Label everything!!)
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Solution
We have the following data:
11,16,11,15,9,10,11,13,15,17,10,14,17,10,13,15,11,12,12,11,12,14,15,15,13,10,15,12,11
We can calculate the median and the respective quartiles so we need to sort the data and we have:
9 10 10 10 10 11 11 11 11 11 11 12 12 12 12 13 13 13 14 14 15 15 15 15 15 15 16 17 17
Then we have:
Min = 9
Q1 = 11
Median = 12
Q3= 15
Max = 17
And then we can create the boxplot and we got:
Use the rules of exponents to evaluate and simplify the expression. Type all without negative exponents. Make sure “a”and “b” are both in parentheses
Answers
We are given the following expression:
[tex](ab)^{-2}[/tex]First, we will use the following property of exponentials:
[tex](xy)^{-c}=x{}^{-c}y^{-c}[/tex]Applying the property we get:
[tex](ab)^{-2}=(a^{-2})(b^{-2})[/tex]Now, we use the following property of exponentials:
[tex]x^{-c}=\frac{1}{x^c}[/tex]Applying the property we get:
[tex](a^{-2})(b^{-2})=\frac{1}{(a^2)(b^2)}=\frac{1}{(ab)^2}[/tex]Since we can't simplify any further this is the final answer.
In parallelogram DEFG, DE=6 Inches and DF= 6.4 Inches. Diagonals GE and DF Intersect at point H. If GH=4 inches, what is the length of GE?
Answers
SOLUTION
Consider the figure below:
It is given that the diagonals DF and GE intersects at H
Recall that the daigonals of parallelogram bisect each other
It follows:
[tex]GH=HE[/tex]Since it is given that GH=4, it follows:
[tex]HE=4[/tex]Using segment addition postulate, it follows:
[tex]\begin{gathered} GE=GH+HE \\ GE=4+4 \\ GE=8 \end{gathered}[/tex]Therefore the required answer is GE=8 inches
Let f(x)=x^2 and g(x)=x-3. Find (f o g)(-5)
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Solution
Given that
[tex]\begin{gathered} f(x)=x^2 \\ \\ g(x)=x-3 \\ \\ \Rightarrow(f\circ g)(-5)=f(g(-5)) \\ \\ g(-5)=-5-3=-8 \\ \\ \Rightarrow f(g(-5))=f(-8) \\ \\ f(-8)=(-8)^2=64 \\ \\ \Rightarrow(f\circ g)(-5)=64 \end{gathered}[/tex]Victor normally sells roadside cashews for $12 per pound and his roadside stands today is discounting the price 25% if Carla buys 2 3/4 pounds of roasted cashews at the Discounted price how much will she pay
Answers
Victor sells roadside cashews for $12 per pound.
Today, the price is discounted by 25%. The discount is
25% of $12 = 25/100*$12 = $3
Thus the discounted price is $12 - $3 = $9 per pound
Carla buys 2 3/4 pounds of roasted cashews at that discounted price, thus she will pay:
$9 * 2 3/4
Expressing 2 3/4 as a single fraction:
2 3/4 = 2 + 3/4 = (8+3)/4 = 11/4
Carla will pay:
$9 * 11/4 = $24.75
Carla will pay $24.75
-5x+2=-9x+38 am crying
Answers
The given equation is
[tex]-5x+2=-9x+38[/tex]First, we add 9x on each side.
[tex]\begin{gathered} -5x+9x+2=-9x+9x+38 \\ 4x+2=38 \end{gathered}[/tex]Then, we subtract 2 from each side.
[tex]\begin{gathered} 4x+2-2=38-2 \\ 4x=36 \end{gathered}[/tex]At last, we divide the equation by 4.
[tex]\begin{gathered} \frac{4x}{4}=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Hence, the solution is x = 9.Algebra1B CP identify a nonviable solution and explain why it is nonviable within the context of the problem
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SOLUTION
Step 1 : Attached is the graph that shows the solutions of the two equations:
Step 2: We need the get the values of x and y in the two sets of the equations.
[tex]\begin{gathered} x\text{ + 2y }\leq\text{ 500 --equ 1 multiplied by 3 = 3 x + 6y }\leq\text{ 1500 ---equ 3} \\ 3x\text{ + 4y }\leq\text{ 1200 ---- equ 2} \\ \text{equ 3 minus equ 2, we have that :} \\ 6y\text{ - 4y }\leq\text{ }1500\text{ - 1200} \\ 2y\text{ }\leq\text{ 300} \\ \text{Divide both sides by 2 , we have that:} \\ y\text{ }\leq150 \\ \text{put y }\leq\text{ 150 in equ 1, } \\ x\text{ + 2y }\leq\text{ 500} \\ x\text{ + 2 (150 ) }\leq\text{ 500} \\ x\text{ + 300 }\leq\text{ 150} \\ x\text{ }\leq\text{ 500 - 300} \\ x\text{ }\leq\text{ 200} \end{gathered}[/tex]CONCLUSION: It means that the number of shirts, x = 200
while the number of pyjamas , y = 150