Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: 15x + 10y ≥ 1100
Explain how to graph the solution set.
Answers
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot points (73.33,0) and (0,110). Since the equality symbol is ≥, which has an equal sign to it, connect the points using a solid line.
Next, let's find a point on the graph. Suppose it is the origin at (0,0). Use this points to the equation.
15x + 10y ≥ 1,100
15(0) + 10(0) ? 1,100
0 ? 1,100
0 < 1,100
It makes the symbol ≥ false. Therefore, it means that the other region bounded by the line is the solution. So, you shade this area. The final graph is shown in the picture attached.
To graph the solution set of the inequality 15x + 10y ≥ 1100, find the intercepts of the graph and draw a line passing through them. Then, test a point not on the line to determine which side represents the solution set. The solution set of the inequality is the region below the line on the graph.
Explanation:To graph the solution set of the inequality 15x + 10y ≥ 1100, we can start by identifying the intercepts of the graph. An intercept is a point where the graph intersects either the x-axis or the y-axis. To find the x-intercept, we set y = 0 in the inequality: 15x + 10(0) ≥ 1100. Simplifying this equation, we have 15x ≥ 1100. Dividing both sides by 15, we get x ≥ 73.33. Therefore, the x-intercept is (73.33, 0).
To find the y-intercept, we set x = 0 in the inequality: 15(0) + 10y ≥ 1100. Simplifying this equation, we have 10y ≥ 1100. Dividing both sides by 10, we get y ≥ 110. Therefore, the y-intercept is (0, 110).
After finding the intercepts, we can draw a line passing through these two points. Since the inequality is ≥, the line will be solid (including the points on the line). Finally, we determine which side of the line represents the solution set. We can choose a test point not on the line, such as (0, 0), and substitute its coordinates into the inequality. If the inequality is true, the shaded region representing the solution set should be below the line.
If the inequality is false, the shaded region should be above the line. In this case, substituting (0, 0) into the inequality gives 15(0) + 10(0) = 0, which is less than 1100. Therefore, the shaded region should be below the line. The solution set of the inequality 15x + 10y ≥ 1100 is the region below the line on the graph.
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Related Questions
Please Help!!! "What is the area of trapezoid ABCD? Enter your answer as a decimal or whole number in the box. Do not round at any steps."
Answers
AB = (-3,2) and (1,5)
BC = (1,5) and (7,-3)
CD = (7, -3) and (0, -2)
AD or DA = (0,-2) and (-3,2)
Now, just use the distance formula for each line. Doing so gives us:
AB = 5
BC = 10
CD = 7.071107...
DA or AD = 5
The height is AB, the first base is BC and the second base is CD. We can plug the values for these sides into the trapezoid area formula, which is A = base 1 + base 2 all over 2 times the height. Doing so gives us 37.5 units². Therefore, the answer to your query is 37.5 units². Hope this helps and have a nice day!
Answer:
The Answer is 37.5
Step-by-step explanation:
Ellen garcia earns $23.68 an hour as an assistant aircraft mechanic at a local airport. she must work _____ hours a week to earn $850 a week. (enter only the number and round to the nearest whole hour.)
Answers
divide the amount she wants to make ( 850) by her hourly pay (23.68)
850 / 23.68 = 35.895
rounded to the nearest whole hour is 36 hours
LaTonya has 16 photos on her phone , and Luis has p photos in his wallet.
Which algebraic expression represents the total number of photos that LaTonya and Luis have ?
Answers
Answer:
The expression is 16 + p
Step-by-step explanation:
Algebraic expression is a mathematical phrase that contains numbers and variables with an operation ( addition or subtraction etc. )
Given,
The number of photos Latonya has on her phone = 16,
While p represents the number of photos Luis has in his wallet,
Where p is a variable,
So, the total number of photos = Latonya's photos + Luis's photos
= 16 + p
Hence, the required expression is '16 +p'
henry is following the recipe card to make a cake. he had 95 cups of flour. how many cakes can henry make?
flour needed for each cake
2 2/9 cups of batter
1/2 cup for topping
Answers
total flour needed = flour need for batter + flour needed for topping
Substituting,
total flour needed = 2 2/9 cups + 1/2 cup = 49/18 cups
Then, we divide the total amount of flour by the answer obtained above to determine the number of cakes that can be made.
number of cakes = total amount of flour / total flour needed per cake
number of cakes = 95 cups / (49/18) = 34.89 cakes
Hence, the number of cakes that can be produced is only 34.
Answer:
the number of cakes that can be produced is only 34.
Step-by-step explanation:
total flour needed = flour need for batter + flour needed for topping
,
total flour needed = 2 2/9 cups + 1/2 cup = 49/18 cups
after, we divide the total amount of flour by the answer obtained above to determine the number of cakes that can be made.
number of cakes is the total amount of flour needed per cake
number of cakes is 95 cups / (49/18) = 34.89 cakes
the number of cakes that can be produced is only 34.
Which pair of angles shares ray A-F as a common side?
Answers
Given : FA is a ray.
Find out the pair of angles share the common side FA.
To proof
As shown in the diagram
∠ BAF and ∠DAF are th.e pair of angles shares FA as a common side
REASON
Adjacent Angles are those angles that share a common side, a common vertex, and no common interior points.
as ∠ BAF and ∠DAF shares common vertex A and common side FA.
Therefore
∠ BAF and ∠DAF are th.e pair of angles shares FA as a common side
The ratio of the number of cookies to the number of cupcakes in a box is 5:4. Which table shows the possible amounts of cookies and cupcakes in a box, given the ratio?
#1
Cookies: Cupcakes:
5 4
10 8
20 16
40 32
#2
Cookies: Cupcakes:
5 4
10 9
20 19
40 39
#3
Cookies: Cupcakes:
5 4
6 5
7 6
8 7
#4
Cookies: Cupcake:
5 4
7 6
9 8
11 10
Answers
Table 1 shows the possible amounts of cookies and cupcakes in a box, given the ratio of 5 : 4.
What is Ratio?
A ratio indicates how many times one number contain in another number.
Given that;
The ratio of the number of cookies to the number of cupcakes in a box is 5 : 4.
Now, In the table 1;
The ratio are given as,
5 : 4
10 : 8
20 : 16
40 : 32
Since, The ratio are 5 : 4.
Simplify all the ratio as;
10 : 8 = 10/8
= 5/4
= 5 : 4
And, 20 : 16 = 20/16
= 10/8
= 5/4
= 5 : 4
And, 40 : 32 = 40/32
= 20/16
= 10/8
= 5/4
= 5 : 4
Thus, Table 1 shows the possible amounts of cookies and cupcakes in a box, given the ratio of 5 : 4.
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Your parents win the lottery and offer you an incredible deal. They will pay you money each day for 30 days for doing your chores. You can choose to be paid one million dollars on the 30th day, or you can pay be paid one cent the first day, and each day the amount you get paid is doubled from the previous day. Which is deal would you choose and why?
Answers
Solve x2 + 6x + 7 = 0.
Answers
Answer:
[tex]x=-3+\sqrt{3}[/tex] , [tex]x=-3-\sqrt{3}[/tex]
Step-by-step explanation:
x2 + 6x + 7 = 0
Solve the equation for x
To solve this we apply quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
a= 1 , b= 6 , c= 7
Plug in all the values in the formula
[tex]x=\frac{-6+-\sqrt{6^2-4(1)(7)} }{2(1)}[/tex]
[tex]x=\frac{-6+-\sqrt{36-28} }{2(1)}[/tex]
[tex]x=\frac{-6+-\sqrt{8} }{2(1)}[/tex]
[tex]x=\frac{-6+-2\sqrt{2} }{2}[/tex]
Divide each term by 2
[tex]x=-3+- \sqrt{3}[/tex]
so we got two value for x
[tex]x=-3+\sqrt{3}[/tex] , [tex]x=-3-\sqrt{3}[/tex]
there are 45 cans of mixed nuts if each can has 338 nuts what is the total number of nuts,n, in all of the cans
Answers
The total number of nuts in all the cans is found by multiplying the number of cans (45) by the number of nuts in each can (338). Hence, the total number of nuts, n, in all of the cans is 15210.
Explanation:This problem is related to simple multiplication. Here, you have 45 cans of nuts and each can contains 338 nuts. So if you want to find the total number of nuts in all the cans, you need to multiply 45 (total number of cans) by 338 (number of nuts in each can).
The multiplication is as follows:
45 * 338 = 15210
So, the total number of nuts, n, in all of the cans is 15210.
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Felicia installed a new pool for $17,190 using a 12-month deferred payment plan with an interest rate of 18.67%. What is the balance after the deferment period if payments of $589 are made each month?
a. $10,122.00
b. $20,688.76
c. $13,620.76
d. $17,190.00
Answers
Answer:
a. $10,122.00
Step-by-step explanation:
By definition the deferment period is a time during which a borrower does not have to pay interest or repay the principal on a loan.
In this case the balance should be the initial value $17,190, but Felicia made 12 payments of $589 each one.
So, $589 x 12 = $ 7,068.
$17,190- $ 7,068 = $10,122
At a grocery store, blueberries come packaged in 8-ounce containers for $2.80. At a farmer's market, blueberries cost $4.20 for 14 ounces. There are 16 ounces in one pound. Which statement accurately compares the cost of blueberries?
Answers
In the grocery, the prices per product is represented by:
$2.80/8 ounce
$0.35/ounce
Converted to pounds...
$5.6/lb
In the farmer's market, the prices per product is represented by:
$4.2/ 14 ounces
$0.30/ounce
Converted to pounds...
$4.8/lb
The farmer's market blueberries is cheaper than the grocery's by $0.80 per pound.
Answer:
$0.80
Step-by-step explanation:
Problem: Find the value of $x$ that maximizes $$f(x) = \log (-20x + 12\sqrt{x}).$$ If there is no maximum value, write "NONE".
Answers
Answer:
The value of x is 0.09
Step-by-step explanation:
Here, the given function is,
[tex]f(x)=\log(-20x+12\sqrt{x})[/tex]
Differentiating with respect to x,
[tex]f'(x)=\frac{1}{-20x+12\sqrt{x}}(-20+\frac{12}{2\sqrt{x}})[/tex]
[tex]=\frac{-20+\frac{6}{\sqrt{x}}}{-20x+12\sqrt{x}}[/tex]
[tex]=\frac{-10+\frac{3}{\sqrt{x}}}{-10x+6\sqrt{x}}[/tex]
[tex]=\frac{-10\sqrt{x}+3}{2\sqrt{x}(-5x+3\sqrt{x})}[/tex]
Again differentiating with respect to x,
[tex]f''(x)=-\frac{(-10\sqrt{3}+3)(-15x+3\sqrt{3})}{4x\sqrt{x}(-5x+3\sqrt{x})}[/tex]
For maxima or minima,
[tex]f'(x) = 0[/tex]
[tex]\implies \frac{-10\sqrt{3}+3}{2\sqrt{x}(-5x+3\sqrt{3})}=0[/tex]
[tex]\implies x \approx 0.09[/tex]
At x = 0.09,
f''(x) = negative,
Hence, for x = 0.09, f(x) is maximum.
The ratio of the number of Mimi’s Eminem CD’s to the number of Rita’s Eminem CD’s is 5:8. Rita has 18 more Eminem CD’s than Mimi. If Rita gives 22 CD’s to Mimi, what will be the new ratio of the number of Mimi’s Eminem CD’s to Rita’s?
Answers
M/R=5/8 and R=18+m =>M/(18+M)=5/8
5(18+M)=8M =>M=30, and R=18+30=48
Next, Rita gives 22 CD to Mimi, so Rita has now 48-22=26, and Mimi has 30+22=52
M/R=52/26=2/1
2:1 is the answer
Which phrase accurately describes a distribution that's bell shaped but not symmetric
Answers
Answer:
The distribution is skewed (either to the left or to the right).
Step-by-step explanation:
Skewness is the measure of how symmetric the distribution of the data is around its mean. It can be skewed either to the left or to the right (meaning that one of the "tails" of the distribution is longer than the other). This means that the mass your data set's observations tends to accumulate more around one extreme of the distribution than around the other.
A strictly symmetric, normal distribution would have a skewness measure of 0.
What is m∠AEB?
Enter your answer in the box.
Answers
5x-10=3x+40
Subtract 3x to both sides
2x-10=40
Add 10 to both sides
2x=50
Divide both sides by 2
x=25
After we have gotten the value of x we can plug it in into the equation of angle AEB:
5x-10
Substitute x by 25
5(25)-10
Distribute
125-10
Substract
115
The measurement of angle AEB is 115
Hope it helped!, have a great day.
Answer: It's 115 I took the k12 test
Step-by-step explanation:
A sofa is on sale for 357 which is 32 percent less than the original price how much is the original price
Answers
x - 357 / x = 32 / 100
(cross multiply)
100(x - 357) = 32x
100x - 35700 = 32x
(subtract 100x from both sides)
-35700 = -68x
525 = x
so the sofa was originally $525
The sofa's original price is calculated by using the formula: original price = sale price/percentage in decimal format. In this case, the percentage is 68%, and hence the original price would be 357 / 0.68 which is equal to $525.
Explanation:This is a percentage problem. If the sale price of $357 represents 68% of the original price (because 100% - 32% is 68%), we can find the original price of the sofa using the formula: original price = sale price/percentage in decimal format.
Therefore, the original price would be 357 / 0.68 = $525
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List two advantages of buying and two advantages of renting
Answers
Answer:
advantages of buying:
-you own your own property
-the value of your property may increase over time
-you can improve or decorate your house as you wish
advantages of renting:
-your landlord is responsible for repairs
-you need to pay fewer up-front cost
-paying rent on time helps you build a good credit history
-renting is better if you dont plan to stay long
-you can have roomates to share costs
A box contains 3 items that are labeled a, b, and
c. two items are selected at random (without replacement) from this box. list all the possible outcomes for this experiment.
Answers
you could pick:
A & B
A & C
B & C
B & A
C & A
C & B
The total number of possible outcomes is 6 and this can be determined by using the given data.
Given :
A box contains 3 items that are labeled a, b, and c.Two items are selected at random (without replacement) from this box.The following steps can be used in order to determine all the possible outcomes for this experiment:
Step 1 - According to the given data, the total number of items in the box is 3.
Step 2 - The total number of outcomes for this experiment is given by:
Total outcomes = 3!
Step 3 - Simplify the above expression.
Total outcomes = 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1
= 6
Step 4 - Now, the list of all the outcomes for this experiment:
A and B
A and C
B and C
B and A
C and A
C and B
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A marble is drawn at random from the bag shown below. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink marbles.What is the probability that the marble drawn is a green or blue?
Answers
probability that the marble drawn is a green or blue is 8/20 = 2/5
3 + 4+ 5+8 = 20 total marbles
3 green +5 blue = 8 marbles
probability = 8/20 reduces to 2/5
The Frostburg-Truth bus travels on a straight road from Frostburg Mall to Sojourner Truth Park. The mall is 4 miles east and 4 miles north of the City Center. The park is 2 miles west and 4 miles south of the Center. How far is it from the mall to the park to the nearest tenth of a mile?
11.1 miles
5.7 miles
10.0 miles
4.5 miles
Answers
Answer:
10.0 is the correct answer
Step-by-step explanation:
Fred has a savings account balance of $1728.57. The interest-rate on the account is 3.4% compounded daily. If he opened the account nine years ago, what was the value of his initial deposit?
Answers
A=p (1+r/k)^kt
A current balance 1728.57
P initial deposit ?
R interest rate 0.034
K compounded daily 365
T time 9 years
Solve the formula for p
P=A÷(1+r/k)^kt
P=1,728.57÷(1+0.034÷365)^(365×9)
p=1,272.91
Hope it helps!
Fred's initial deposit, considering a 3.4% interest rate compounded daily over nine years, was approximately $1258.16.
To find Fred's initial deposit, we need to use the formula for compound interest:
A = P(1 + r/n)ⁿᵗ, where:
Here, we know:
A = $1728.57r = 0.034 (3.4% interest rate)n = 365 (compounded daily)t = 9 yearsWe need to find P. Rearrange the formula to solve for P:
P = A / (1 + r/n)ⁿᵗ
Substitute the known values:
P = 1728.57 / (1 + 0.034/365)³⁶⁵×⁹
First, calculate the daily interest rate
0.034 / 365 = 0.00009315
Next, calculate the exponent:
(365 × 9) = 3285
Now, compute (1 + daily interest rate) raised to the power of 3285:
(1 + 0.00009315)³²⁸⁵ = 1.37423
Finally, divide the final amount by this value:
P = 1728.57 / 1.37423 = 1258.16.
find cos B.
a. cosB= 41/40
b. cosB=9/41
c. cosB=40/41
d. cosB=9/40
Answers
The graph shows the number of each kind of book in Hero's personal library. A book is chosen randomly. What is the probability that the book chosen is a biography?
A)2/15
B)4/15
C)1/30
D)1/4
Answers
Answer: A is the right answer .Probability of the book chosen is a biography is [tex]\frac{2}{15}[/tex].
Step-by-step explanation:
According to the given graph or pie chart
The number of biography books=4
Total books= Romance books+ Science fiction books+ Biography books+Adventure books =2+14+4+10=30
Let B be the event of choosing a biography book then
Probability of the book chosen is a biography P(B)=[tex]=\frac{biography\ books}{total\ books}=\frac{4}{30}=\frac{2}{15}[/tex]
Therefore, Probability of the book chosen is a biography is [tex]\frac{2}{15}[/tex].
From the graph, it is found that there is a [tex]\mathbf{\frac{2}{15}}[/tex] probability that the book chosen is a biography, and the correct option is given by option A.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
There are 4 + 2 + 10 + 14 = 30 books in the hero's library.Of those, 4 are biographies.[tex]p = \frac{4}{30} = \frac{2}{15}[/tex]
Thus:
[tex]\mathbf{\frac{2}{15}}[/tex] probability that the book chosen is a biography, and the correct option is given by option A.
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sin x°= 4/15 round to nearest tenth find x
Answers
Let x = the angle you need to find.
arcsin(sin x) = arcsin(4/15)
x = arcsin(4/15)
x = 15.4660099534
x = 15.47°
Done!
An astronaut who weighed 150 pounds on Earth found that his weight on Jupiter was 400 pounds. He captured an alien that weighed 120 pounds on Jupiter. What is the alien's weight on Earth?
Answers
Answer:
45 pounds
Step-by-step explanation:
20 POINTS if you answer!!!!
Clarence sells yearly subscriptions to a particular magazine. He sells at least 10 and no more than 25 subscriptions each week. The function f(t)=48tf(t)=48t represents the amount of money earned for selling t subscriptions each week. What is the practical range of the function?
Answers
Answer:
All multiples of 48 between 480 and 1200, inclusive
Step-by-step explanation:
I took the test;)
The practical range of the function is [480, 1200].
Explanation:The function f(t)=48t represents the amount of money earned by Clarence for selling t subscriptions each week. To find the practical range of the function, we need to determine the minimum and maximum value of t that satisfy the given conditions. Since Clarence sells at least 10 and no more than 25 subscriptions each week, the practical range of the function is [480, 1200]. This means that the amount of money earned by Clarence each week can range from $480 to $1200.
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The 55 bridesmaids want to make 325 favors for a wedding. Each favor takes about 2 1/2 minutes to make.
About how long will each bridesmaid have to spend making favors?
A.First pic
B.2nd
C.3rd pic
Answers
This means that each bridesmaid will be making on the average [tex]\frac{325}{55}=5\frac{10}{11}[/tex] favors.
Given that aach favor takes about [tex]2 \frac{1}{2}[/tex] minutes to make.
Thus, each bridesmaid will be spending about
[tex]5\frac{10}{11}\times2 \frac{1}{2}= \frac{65}{11} \times \frac{5}{2} \\ \\ = \frac{35}{22} =14.77\approx15 \ minutes[/tex]
Bernard solved the equation 5x+(-4)=6x+4 using algebra tiles. Which explains why Bernard added 5 negative x-tiles to both sides in the first step of the solution?
A) He wanted to create zero pairs on the left side of the equation to get a positive coefficient of x on the right side.
B) He wanted to combine more negative tiles with the 4 negative tiles on the left side of the equation.
C) He wanted to remove the larger coefficient on the left side of the equation.
D) He wanted to have 10 x-tiles on the left side of the equation.
Answers
You could add 4 to both sides.
You could subtract 4 from both sides.
You could subtract 5x from both sides.
You could subtract 6x from both sides.
Any of these work. In Bernard's case, he added 5 negative x tiles, meaning he subtracted. C and D already make no sense, but allow me to further explain. By him subtracting 5x from both sides, the equation turns into:
-4 = x + 4
By this point, he can just subtract 4 from both sides to find the value of x. But the question asks for why he did the first step. Therefore, it would be A.
Answer:
a
Step-by-step explanation:
if dont want to read
A market sells a six-pound bag of potatoes for $6.27 and a 7.5-pound bag of potatoes for $7.65. Which bag of potatoes is a better buy??
Answers
Which principle helps us to determine the total number of outcomes in a sample space?
Answers
The Fundamental Counting Principle: If there are “a” ways for one event to happen, and “b” ways for a second event to happen, then there are “a * b” ways for both events to happen.