Manny, this is the solution to the arithmetic sequence:
Sum = 1 + 3 + 5 + 7 + 9........+ 59
d = 2 (Common difference)
An = 2n - 1
A1 = 1
n = 59 + 1 /2 (Last number of the sequence plus 1 and the result divided by 2)
n = 30
Therefore, we use the arithmetic sequence sum formula:
n (A1 + d (n - 1)/2)
Replacing by the values we know:
30 (1 + 2 (30 - 1)/2)
30 * 30
900
The sum of this arithmetic sequence is 900
the product of two consecutive integers is 90 find the two integers then check your answer?
Let n be the integer. Then, we can write the following equation
[tex]n(n+1)=90[/tex]which is equal to
[tex]n^2+n-90=0[/tex]We can solve this quadratic function by applying the quadratic formula:
[tex]n=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where in our case a=1, b=1 and c= -90. By substituting these values into the last formula, we get
[tex]n=\frac{-1\pm\sqrt[]{1^2-4(1)(-90)}}{2(1)}[/tex]then, we have
[tex]\begin{gathered} n=\frac{-1\pm\sqrt[]{1+360}}{2} \\ n=\frac{-1\pm\sqrt[]{361}}{2} \\ n=\frac{-1\pm19}{2} \end{gathered}[/tex]Then, the first solution is
[tex]\begin{gathered} n=\frac{-1+19}{2} \\ n=\frac{18}{2} \\ n=9 \end{gathered}[/tex]and the second solution is
[tex]\begin{gathered} n=\frac{-1-19}{2} \\ n=-\frac{20}{2} \\ n=-10 \end{gathered}[/tex]Then, we have the following solutions:
- Negative integer: n= - 10
- Positive integer: n=9
help me pleaseee!!!
thank you
The equation of line passing through the point (-2 , 11) and (1, -4) will be;
⇒ y = - 5x + 1
What is Equation of line?
The equation of line in slope - intercept form is defined as;
⇒ y = mx + b
Where, m is slope
And, b is y - intercept.
Given that;
Two points on the line are (-2 , 11) and (1, -4).
Now, Equation of line is calculated as;
Slope of the line (m) = (- 4 - 11) / (1 - (-2))
= - 15/ 3
= - 5
The equation of line is;
⇒ y - y₁ = m (x - x₁)
Substitute all the values we get;
⇒ y - 11 = - 5 (x - (-2))
⇒ y - 11 = - 5 (x + 2)
⇒ y - 11 = -5x - 10
⇒ y = - 5x - 10 + 11
⇒ y = - 5x + 1
Thus, The equation of line passing through the point (-2 , 11) and (1, -4) will be;
⇒ y = - 5x + 1
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How does the graph of the transformed function g(x) = log7(3x-9) compare to the graph of its parent function f(x) = log7x
The correct option is A
The graph has been horizontally stretched, 9 units to the right.
Explanation:Given the function:
[tex]f(x)=\log _7x[/tex]The function:
[tex]f(x)=\log _7(3x-9)[/tex]is a horizontally stretched transformation, 9 units to the right.
4.An object of mass 480 kg is in free fall in a vacuum where there is no air resistance. Determine the acceleration of the object.
The only force is free fall. Mass is not relevant and there is no air resistance
It is estimated that approximately 8.23% Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation for diabetes will correctly diagnose 98% of all adults over with diabetes as having the disease and incorrectly diagnoses 3.5% of all adults over without diabetes as having the disease.
a) Find the probability that a randomly selected adult over does not have diabetes, and is diagnosed as having diabetes (such diagnoses are called "false positives").
b) Find the probability that a randomly selected adult of is diagnosed as not having diabetes.
c) Find the probability that a randomly selected adult over actually has diabetes, given that he/she is diagnosed as not having diabetes
The probabilities in this problem are given as follows:
a) False positive: 0.0321 = 3.21%.
b) Diagnosed as not having diabetes: 0.8872 = 88.72%.
c) Actually has diabetes, if diagnosed as not having: 0.0019 = 0.19%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is given as follows:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which the parameters are described as follows:
P(B|A) is the probability of event B happening, given that event A happened.[tex]P(A \cap B)[/tex] is the probability of both events A and B happening.P(A) is the probability of event A happening.For item a, we have that:
100 - 8.23 = 91.77% of the people do not have diabetes.Of those, 3.5% are diagnosed with diabetes.Hence the probability of a false positive is given as follows:
p = 0.9177 x 0.035 = 0.0321 = 3.21%.
For item b, the percentage of people who is not diagnosed as having diabetes is divided as:
96.5% of 91.77% (do not have diabetes).2% of 8.23% (have diabetes).Hence the probability is:
P(A) = 0.965 x 0.9177 + 0.02 x 0.0823 = 0.8872 = 88.72%.
For item c, we find the conditional probability, as follows:
[tex]P(A \cap B) = 0.02 \times 0.0823 = 0.001646[/tex]
Then:
P(B|A) = 0.001646/0.8872 = 0.0019 = 0.19%.
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What is the slope-intercept form of the equation of the line that passes through (2, -3) and (4, 3)?
A. y = - 3x + 6
B. y= 3x - 12
C. y= 1/3x - 9
D. y= 3x - 9
The equation of line is D. y = 3x - 9
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The m is a common symbol for slope.
The equation of a straight line is given by y=mx+c where m is the slope, c is the intercept, and x and y are variables.
Formula to be used :
[tex]m=\frac{y_{1}-y_{2} }{x_{1} -x_{2} }[/tex] where( y1,x1) and (y2 ,x2) are the coordinates of the points passing through the line.
Calculating Slope, [tex]m=\frac{3-(-3)}{4-2} =\frac{6}{2} =3[/tex]
Now, writing the equation of line is
[tex]y -y_{1} =m(x-x_{1} )\\y -3 =3(x-4)\\y-3 =3x - 12\\y =3x -12+3\\y =3x -9[/tex]
Thus, the slope-intercept form of the equation is y =3x -9.
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- If triangle TIE is reflected over the y-axis, what are thenew points, (T', '', and E'), in the image? T(-5,-1) 1(-5,-3)E(-1,-1).
Answer
T' = (5, -1)
I' = (5, -3)
E' = (1, -1)
Explanation
Given the below triangle
T = ( -5, -1)
I = (-5, -3)
E = (-1, -1)
When reflected over y -axis, the x - cordinate is negated while the y - coordinate remains unchanged
Mathematically,
(x , y ) ------------------------ (-x , y)
T = ( -5, 1)
T' = [-(-5) , -1)]
T' = (5, -1)
I = (-5, -3)
I' = [-(-5) , -3)
I' = (5, -3)
E = (-1, -1)
E' = [-(-1), -1)]
E' = (1, -1)
Therefore, the reflected triangle over y - axis has the following points
T' = (5, -1)
I' = (5, -3)
E' = (1, -1)
Find the scale factor that was used to changethe Original (O) to the Scaled Image (S).o10"S
QUESTION
Find the scale factor that was used to change (o) to the scale image (s)
[o]10 [s] 4
solution
To find the scale factor, you will simply use the formula:
Scale factor = scaled image / original
Scale factor = 4/10 = 0.4
Answer:
Find the scale factor that was used to change the Original (O) to the Scaled Image (S).o'10"S
The basic formula that is used for calculating the scale factor is, Scale factor = Dimension of the new shape ÷ Dimension of the original shape. In case, if the original figure is scaled up, the formula is written as, Scale factor = Larger figure dimensions ÷ Smaller figure dimensions.
Step-by-step explanation:
Find the x-intercept and y-intercept of the graph of 2x+6y=6 . Then graph.x-intercept = (,0)y-intercept = (0,)12345-1-2-3-4-512345-1-2-3-4-5Clear All Draw: LineParabolaAbsolute valueCircleDotQuestion HelpQuestion 2: Video1
SOLUTION:
Step 1:
In this question, we are meant to find the x-intercept and y-intercept of the graph of :
[tex]\text{2x + 6y = 6}[/tex]First, we are meant to graph it
Second, we are meant to find:
a) x-intercept
b) y - intercept
Step 2:
The graph of :
[tex]\text{2 x + 6y = 6}[/tex]is as follows:
Step 3:
Given the equation:
[tex]\begin{gathered} 2x\text{ + 6y = 6} \\ For\text{ the x-intercept, we have that:} \\ \text{when y = 0, we have that:} \\ 2x\text{ + 6 (0 ) = 6} \\ 2\text{ x+ 0 = 6} \\ 2x\text{ = 6} \\ \text{Divide both sides by 2 , we have that:} \\ \text{x = }\frac{6}{2} \\ \text{x = 3} \\ \text{Then , the x - intercept = ( 3, 0 )} \end{gathered}[/tex]Next, given the equation:
[tex]\begin{gathered} 2x\text{ + 6 y = 6} \\ For\text{ the y - intercept, we have that:} \\ \text{when x = 0 , we have that:} \\ 2\text{ ( 0 ) + 6 y = 6} \\ 0\text{ + 6y = 6} \\ 6y\text{ = 6} \\ \text{Divide both sides by 6, we have that:} \\ y\text{ = }\frac{6}{6} \\ y\text{ = 1} \\ \text{Then , the y -intercept = ( 0 , 1 )} \end{gathered}[/tex]Can someone help me, please and thanks!
Answer:
wait do you need all the answers to it
robin invests $55 at 10% compounded annually for 3 years. How much will her investment be worth in 3 years?
the investment after 3 years will be worth $73.21
Explanation:Amount invested = Principal
P = $55
n = number of time scompounded = annually
n = 1
rate = r = 10% = 0.1
FV = future value after 3 years
Using compound interest formula:
[tex]FV\text{ = P(1 +}\frac{r}{n})^{nt}[/tex]substituting the values in the formula:
[tex]\begin{gathered} FV\text{ = }55(1\text{ + }\frac{0.1}{1})^{1\times3} \\ FV\text{ = }55(1\text{ + }0.1)^3 \\ FV\text{ = }55(1.1)^3 \\ FV\text{ = 55(}1.331) \\ FV\text{ = 73.205 approx i}mately\text{ to nearest cents is }73.21 \end{gathered}[/tex]Hence, the investment after 3 years will be worth $73.21
Write an integer for this situation.12°C above zero
12°C above zero -----> means
0°C+12°C=12°C
answer is
the integer is +12The stingray population in a particular reef is decreasing at a rate of 1.4% per year. The population was 3800 in the year 2008. What is the best prediction of the population in the year 2013? Round to the nearest whole number, Show all work for full credit.
We have a initial population P(0) of 3800.
We know that the population is decreasing by 1.4% each year, so the population at year 1 (2009) we will have a population of:
[tex]\begin{gathered} P(1)=P(0)-0.014\cdot P(0) \\ P(1)=(1-0.014)\cdot P(0) \\ P(1)=0.986\cdot P(0) \end{gathered}[/tex]We can generalize this for P(n), where n is the number of years from 2008.
[tex]\begin{gathered} P(2)=0.986\cdot P(1)=0.986\cdot(0.986\cdot P(0))=0.986^2\cdot P(0) \\ \Rightarrow \\ P(n)=0.986^n\cdot P(0)=0.986^n\cdot3800=3800\cdot0.986^n \end{gathered}[/tex]From 2008 to 2013 we have 2013-2008=5 years, so for the year 2013, the value of n is n=5.
Then, the population for 2013 will be P(5) and can be calculated as:
[tex]P(5)=3800\cdot0.986^5\approx3800\cdot0.932\approx3541[/tex]Answer: the predicted population for the year 2013 is 3541.
If u(x) = −2x² +3 and v(x)=1/x, what is the range of (uv)(x)?
Given:
[tex]\begin{gathered} u(x)=-2x^2+3 \\ v(x)=\frac{1}{x} \end{gathered}[/tex]Required:
To find the range of the function (uv)(x).
Explanation:
We know that
[tex]\begin{gathered} (uv)(x)=u(v(x)) \\ \\ =u(\frac{1}{x}) \\ \\ =-2(\frac{1}{x^2})+3 \\ \\ =-\frac{2}{x^2}+3 \end{gathered}[/tex]The horizontal asymptote of this function is at y=3.
So, the range of this function is from
[tex](-\infty,3)[/tex]Final Answer:
The range of (uv)(x) is
[tex](-\infty,3)[/tex]A restaurant bill for four people is 122 route leave the $8018 tip what percentage tip is that A restaurant beer for four people is 120 the group me is a tip of $18 what percent of tip is that
The total tip for a four-person meal at a restaurant is $122, people $8018. The percentage of the tip is 22%.
Given that,
The total tip for a four-person meal at a restaurant is $122, people $8018. What proportion of a tip is that? Four restaurant beers cost 120 each, and the group tip is $180.
We have to calculate the how much percentage of a tip is there.
In a variety of situations, such as restaurants, hotels, salons, and other establishments in the service sector, leaving a tip is common. Knowing how to compute a tip and knowing how much to tip is crucial for a variety of reasons, including the fact that many service sector personnel, like waiters, rely heavily on gratuities for the majority of their income. This means that these experts might not be able to support themselves and their families without tips.
Percentage= tip/amount
Percentage= $180/$8018
Percentage= 22%
Therefore, the percentage of the tip is 22%
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It takes bbb minutes for Sylvia's bathtub to fill with water.
How many minutes will it take to fill 333 same-size bathtubs?
Write your answer as an expression.
Time taken to fill 3 same-size bathtubs is 3b minutes.
Its given in the question that it takes b minutes to fill Sylvia's bathtub with water.
Time taken to fill same-size bathtub as an expression = 3*b
= 3b minutes.
Hence, time takes to fill 3 bathtubs of the same size as of Sylvia's bathtub to fill with water is 3b minutes.
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Tell whether the data represents a linear, an exponential, or a quadratic function. Then, write the function. Picture is attached. I need help!
SOLUTION:
Case: Equations
Method:
The table:
Plotting the points
Studying the points, could either be quadratic or exponential.
We will proceed to test the points but because the increase of the y values as x increases from left to right is not a fine pattern, it will most likely not be exponential.
Next, we test a quadratic model on the graph
[tex]y=ax^2+bx+c[/tex]Final answer:
Quadratic function
[tex]y=x^2+4x-12[/tex]To be linear, you'd need a fixed increase in the y-values for a constant increase in the x-values. As x increases by 1 in each new point, your y-values increase by 1, 3, 5, and 7 respectively. That is not the same increase each time. This is not linear.
To be exponential, you need a fixed percent increase in the y-values between the points. From (-2,-16) to (-1,-15), your increase is 1/16 or 6.25%. From (-1,-15) to (0,-12), your increase is 3/15 or 20%. That is not a constant percent increase.
The only option left is quadratic.
To find the function, start with c = -12, based on the point (0,-12).
This gives you f(x) = ax^2 + bx -12
Next plug in (2,0) into f(x): 0 = 4a + 2b - 12
And plug in (1,-7) into f(x): -7 = a + b -12
You now have two equations with two unknowns.
Solve equation 2 for a:
5-b = a
Substitute that into equation 1
0 = 4(5-b) + 2b - 12
0 = 20 -4b + 2b - 12
-8 = -2b
4 = b
Substitute that b-value into 5-b=a
5 - 4 = a
1 = a
You have your three values and have your function:
f(x) = 1x^2 + 4x - 12 or f(x) = x^2 + 4x - 12
You can confirm that the other points also fit with this function.
Apply the Pythagorean theorem to find the distance between two points in a coordinator system
Using pythagoras theorem to find the distance between two points in a coordinate:
[tex]\begin{gathered} A=(-5,5) \\ B=(-1,1) \end{gathered}[/tex][tex]\begin{gathered} A=(-5,5)\longrightarrow x_1=-5,y_1=5 \\ B=(-1,1)\longrightarrow x_2=-1,y_2=1 \\ \text{vertical line = opposite =5-1=4} \\ \text{horizontal line = adjacent = -5--1=-5+1=-4} \end{gathered}[/tex]To calculate the distance between the points AB = hypotenuse
[tex]\begin{gathered} \text{Hypotenuse}^2=opposite^2+adjacent^2 \\ AB^2=4^2+(-4)^2 \\ AB^2=16+16 \\ AB^2=32 \\ AB=\sqrt[]{32} \\ AB=4\sqrt[]{2} \end{gathered}[/tex]Therefore the distance between the points in the coordinate system = 4√2
To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for each hour of labor.
How much would the painting company charge to paint a house that needs 20 hours of labor? A house that needs 50 hours?
Draw a line representing the relationship between x, the number of hours it takes the painting company to finish the house, and y, the total cost of painting the house. Label the two points from the earlier question on your graph.
Answers:
20hr=100$
50hr=2500$
Step-by-step explanation:
you are standing on a cliff that is 400 feet tall. You throw your Geometry book off the cliff and it lands 300 feet from the base of the cliff. What is the angle of depression that you are looking down at your book (round to the nearest tenth)
From the question,
Let H be the height of the Cliff
Let Y be the distance of the geometry book from the base of the cliff.
[tex]\begin{gathered} \text{The Height of the Cliff, H=400} \\ \text{The distance at the base, Y = 300} \\ \emptyset\text{ = The angle of depression} \end{gathered}[/tex]Note that the angle of depression is alternate to the angle of elevation'
[tex]undefined[/tex]Angie is working on solving an exponential equation 23^x=6; however, she’s not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation using the change of base formula.
we have the equation
[tex]23^x=6[/tex]Remember the definition of logarithm
[tex]\begin{gathered} If \\ a^x=b \\ then \\ x=\log_ab \end{gathered}[/tex]Applying the definition of a logarithm to this problem
we have that
[tex]x=\log_{23}6[/tex]Apply change of base formula
Remember that
[tex]\log_bM=\frac{\log_{10}M}{\log_{10}b}=\frac{logM}{logb}[/tex]so
[tex]\log_{23}6=\frac{log6}{log23}[/tex]therefore
The answer is
[tex]x=\frac{log6}{log23}[/tex]A die was rolled 60 times. It landed on one—11 times, two—9 times, four—12 times, five—12 times, and six—8 times. How many times was three rolled in these 60 times?
If a die is rolled 60 times, then it will land on number three 8 times.
When a die was rolled 60 times.
The die landed on one 11 times, two on 9 times, on four 12 times, on five 12 times, and on six 8 times.
Now, we know a die has six sides with numbers 1,2,3,4,5, and 6 marked on it.
Let x be the number of times the die landed on 3.
The total number of times the die rolled = the sum of the number of times each number landed when rolled.
number times 1 landed + number times 2 landed + number times 3 landed + number times 4 landed + number times 5 landed + number times 6 landed = 60
11 + 9 + x + 12 + 12 + 8 = 60
52 + x = 60
Subtracting 52 from each side of the equation,
52 + x - 52 = 60 - 52
x = 8
Hence, the number of times that three rolled is 8.
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Calculate the five-number summary of the given data. Use the approximation method.
6, 5, 3, 3, 25, 22, 3, 23, 7, 3, 20, 19, 23, 18, 5
The five number summary is:
Minimum = 3
First quartile(Q1) =3
Median =7
Third quartile(Q3) = 22
Maximum = 25
What is five number summary?A five-number summary is especially useful in descriptive analyses or when investigating a large data set for the first time. A summary is made up of five values: the data set's most extreme values (the maximum and minimum values), the lower and upper quartiles, and the median.Given data, 6, 5, 3, 3, 25, 22, 3, 23, 7, 3, 20, 19, 23, 18, 5.
we have to arrange in ascending order ,
3, 3, 3, 3, 5, 5,6, 7, 18, 19, 20, 22, 23, 23, 25
Minimum value = 3
Maximum value = 25
since , number of data = 15
So , Median = middle term = 7
Median of first half = First quartile
here first half = { 3, 3, 3, 3, 5, 5, 6}
median of first half terms = 3 (middle term)
Q1 = 3
Third quartile = Median of second half terms
( 18, 19, 20, 22, 23, 23, 25)
median of second half terms = 22
Q3 = 22
Hence, the five-number summary for the given data set :
min = 3, Q1 =3, median =7 , Q3 = 22, max = 25 .
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1. Do you recommend this person open a credit card account? Why or why not?
2. If they do open the new credit card account, what's one thing this individual should monitor or use caution?
Crystal-
Took time off after high school and during the first year, worked full-time and moved out of her parents house
Is responsible for her own expenses
Took out a large car loan which she quickly fell behind on in payments
Overdrew her checking account numerous times, spending money she didn't have to live a fun, carefree lifestyle
In year two, traded in the car for a much cheaper one, settled her outstanding debt on the car loan, and put herself on a much stricter budget
Now moved back in with her parents and enrolled in community college
Considering applying for her first credit card
1. Crystal can open a new credit card account.
2. If Crystal opens a credit card account, she should keep track of her spending and pay monthly bills on time.
Since Crystal has paid off her debts from the car loan, moved to her parent's home, and enrolled in community college, the chances of her getting into debt are quite low, so she can get a credit card to take care of her expenses as long as she works full time and keeps track of her monthly bills.
If Crystal opens a credit card account, she should keep a spending track and pay her monthly bills on time. She should work full-time and make sure that she pays it off.
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You are mixing up a recipe that requires 7:3:2:1 flour, water, sugar, butter. When you are done, you should have 39 cups of batter. How many cups of each ingredient do you need?¶ Please show your work. Hint: this is really a total proportion problem and you will want to set up 3 to 4 proportions to find the result. 1 Flour = Water = Sugar = Butter= cups. cups. cups. cups.
The proportion of flour, water, sugar and butter required in the batter are 21, 9, 6 and 3 cups respectively
What is RatioIn mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
In this given question, we can find the value of each ingredient;
The cups of flour required is
[tex]7:3:2:1 = 7 + 3 + 2 + 1 = 13\\\frac{7}{13} * 39 = 21 cups[/tex]
The cups of water required is
[tex]\frac{3}{13}*39 = 9 cups[/tex]
The cups of sugar required is
[tex]\frac{2}{13}* 39 = 6 cups\\[/tex]
The cups of butter required is
[tex]\frac{1}{13}*39 = 3 cups[/tex]
The number of cups of flour, water, sugar and butter required are 21, 9, 6 and 3 cups respectively.
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Use Sine to find the value of C. B #1-2 39° C a w A А 6 in. C Show your work for full credit.
Sarah has 3 candy bars. She wants to share the candy bars with her friends that everyone gets a serving that is equivalent to 2/5 of a candy bar. To determine how many servings Sarah can make, she dividends 3 divided by 2/5 and get gets 7 1/2
Sarah is unsure this is correct. Use the diagram below and the dropdown menus to help explain if Sarah is correct or not.
Claire drew a model of five tenths explain how Claire could change her model to show how many hundredths are in five tenths
Let x be the number of hundredths in 5/10. Then 100 times x gives 5/10.
[tex]100x=\frac{5}{10}[/tex]Solve for x.
[tex]\begin{gathered} x=\frac{\frac{5}{10}}{100} \\ =0.005 \end{gathered}[/tex]So, there are 0.005 hundredths in 5/10.
8. Maya and Angelo go to Marge's Donut Shop every Friday on the way to school. The shop sells donuts, muffins and coffee. A cup of
coffee costs $0.75 more than a donut. Maya buys 12 donuts and 2 cups of coffee which costs $19.
a. How much does 1 cup of coffee cost?
b. Angelo buys 6 donuts and 2 muffins which costs $12.50 total. How much does 1 muffin cost?
a) The cost of 1 cup coffee will be $2
b) The cost of 1 muffin will be $1.67
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The cost of a cup of coffee is $0.75 more than a donut.
Maya buys 12 donuts and 2 cups of coffee which costs $19.
Now,
Let the cost of coffee = x
And, The cost of donut = y
The cost of muffins = z
Since, The cost of a cup of coffee is $0.75 more than a donut.
So, we can formulate;
⇒ x = y + 0.75 .... (i)
And, Maya buys 12 donuts and 2 cups of coffee which costs $19.
So, We can formulate;
⇒ 12y + 2x = $19
Substitute the value of first equation in above equation we get;
⇒ 12y + 2x = $19
⇒ 12y + 2 (y + 0.75 ) = $19
⇒ 12y + 2y + 1.5 = $19
⇒ 14y + 1.5 = $19
⇒ 14y = $19 - 1.5
⇒ 14y = 17.5
⇒ y = 17.5 / 14
⇒ y = 1.25
Hence,
⇒ x = y + 0.75
⇒ x = 1.25 + 0.75
⇒ x = 2
Thus, The cost of 1 cup of coffee = $2
Since, Angelo buys 6 donuts and 2 muffins which costs $12.50 total.
So, we can formulate;
6z + 2y = $12.50
Substitute y = 1.25 in above equation, we get;
6z + 2 × 1.25 = $12.50
6z + 2.50 = 12.50
6z = 12.50 - 2.50
6z = 10.00
z = 10.00 / 6
z = 1.67
Thus, The cost of 1 muffin will be $1.67.
Therefore,
a) The cost of 1 cup coffee will be $2
b) The cost of 1 muffin will be $1.67
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Pitts bought pots for5 dollars each and joe bought buckets for 7dollars each if they spent140 dollars for 192 items how many of each type did they bought
Explanations;
Let the number of pots be "x"
Let the number of buckets be "y"
Since we have 192 items, hence;
x + y = 192 ............................... 1
If Pitts bought pots for 5 dollars each and joe bought buckets for 7dollars each and spent 140 dollars, this can be expressed as:
5x + 7y = 140 ............................ 2
Solve the equations simultaneously to get the value of x and y:
x + y = 192 ............................... 1 * 7
5x + 7y = 140 ............................ 2 * 1
_________________________________________________
7x + 7y = 1344
5x + 7y = 140
Subtract
7x - 5x = 1344 - 140
2x = 1204
x = 1204/2
x = 602
This shows that 602 pots were bought.
Substitute x = 602 into the equation 1 to get y:
602 + y = 192
y = 192 - 602
y = -410
Since the y value cannot be negative, we can say that 602 pots were bought but the solution to the system of equation is (602, -410)
