Larry's Lemons is a street vendor business that sells lemonade and lemon bars. A cup of lemonade sells for $2 and a lemon bar sells for $1.50. When all related business expenses are included, a cup of lemonade costs $0.25 to prepare and a lemon bar costs $0.20 to prepare.
Last Monday, one of the vendors selling Larry's Lemons sold at least $500 worth of lemonade and lemon bars and its expenses were no more than $100. At least 150 cups of lemonade were sold.
Let x be the number of cups of lemonade sold last Monday and y be the number of lemon bars sold last Monday.
Which ordered pairs representing a combination of cups of lemonade and lemon bars could have been sold last Monday and make sense in the context of the situation?
Select each correct answer.
(160,110)(160,110)
(232.5,200)(232.5,200)
(155,305.5)(155,305.5)
(150,200)(150,200)
(180,100)
Answers
We can let x and y represent cups of lemonade and numbers of lemon bars, respectively. Then the constraints are ...
x ≥ 150y ≥ 02x +1.5y ≥ 5000.25x +0.20y ≤ 100A graph is shown in the attachment, with the ordered pairs plotted. It is not feasible to sell half cups of lemonade or half lemon bars, so the second and third choices must be excluded. The point (160, 110) falls outside the feasible region, so is not a correct choice.
The correct choices are ...
(150, 200)(180, 100)
Final answer:
The only ordered pairs that meet the constraints of Larry's Lemons business situation are (150,200) and (180,100), as these combinations satisfy the conditions for revenue, expenses, and minimum amount of lemonade sold.
Explanation:
To find which ordered pairs (x, y) make sense in the context of Larry's Lemons' business situation, we need to consider the given conditions and set up inequalities to express the sales and expense constraints.
The conditions are:
A cup of lemonade sells for $2 and a lemon bar for $1.50.The cost to prepare a cup of lemonade is $0.25, and a lemon bar is $0.20.The vendor sold at least $500 worth of products.The vendor's expenses were no more than $100.At least 150 cups of lemonade were sold.Revenue Constraint:
For the revenue, we need to ensure that the seller made at least $500.
2x + 1.5y ≥ 500
Expense Constraint:
For the expenses, they should not exceed $100.
0.25x + 0.20y ≤ 100
Lemonade Sold Constraint:
Since at least 150 cups of lemonade were sold:
x ≥ 150
Now we check the given ordered pairs against these constraints:
(160,110): Given the constraints, this pair is feasible because the revenue is $2(160) + $1.50(110) = $470, which does not meet the revenue condition. Therefore, it is not a correct answer.(232.5,200): This pair does not represent whole units of lemonade and lemon bars, which doesn't make sense in this context as you can't sell half a cup of lemonade or half a lemon bar.(155,305.5): Similar to the above, this also includes half units and is thus not feasible.(150,200): Meets the revenue constraint, $2(150) + $1.50(200) = $500 in sales, and the expense constraint, $0.25(150) + $0.20(200) = $92.5 in expenses. It is a correct answer.(180,100): Also meets the constraints with revenue $2(180) + $1.50(100) = $510 and expenses $0.25(180) + $0.20(100) = $85. It is a correct answer.Only the ordered pairs (150,200) and (180,100) satisfy all the conditions of the problem.
Related Questions
there is a photo attached
drop down 1:
161/289 -- incorrect
-161/289 -- CORRECT
64/289
-64/289
drop down 2:
-30/217 -- incorrect
-30/161 -- INCORRECT
-240/217 -- incorrect
-240/161
Answers
Your question answers itself.
You have shown the correct answer for the first drop-down: -161/289
You have shown the 3 incorrect answers out of the 4 choices for the second drop-down. The correct choice is the remaining one: -240/161.
_____
Even if all you know is that tan = sin/cos, you would suspect that answer choice based on the numerator of the cosine: 161. That value is likely the one in the denominator of the tangent value.
_____
cos(2θ) = 2cos(θ)² . . . . trig identity
... = 2(-8/17)² -1 = 128/289 -1 = -161/289
sin(2θ) = √(1-cos(2θ)²) . . . . trig identity
... = √(289² -161²)/289 = √57600/289 = 240/289
tan(2θ) = sin(2θ)/cos(2θ) . . . . trig identity
... = (240/289)/(-161/289) = -240/161
Q # 8 please I need your help
Answers
A. -2/3 because you would go down two and then to the right three. I hope that helps.
Solution :
Given ,line that passes through the pair of points (1,7) and (10,1)
The slope of the line passing through the points [tex](x_{1},y_{1} ) \:and \:(x_{2},y_{2})[/tex] is given by,
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here, [tex](x_{1},y_{1} ) =(1,7)\:and \:(x_{2},y_{2})=(10,1).[/tex]
[tex]\Rightarrow m=\frac{1-7}{10-1} \\\Rightarrow m=\frac{-6}{9}=\frac{-2}{3}[/tex]
Hence , slope of the line passing through the pir of points (1,7) and (10,1) is [tex] \frac{-2}{3}[/tex] ( first option)
Which of the graphs below would result if you made the leading term of the following function negative?
Answers
We are given function F(x) = x^3 +3x^2.
Leading term is the term that has highest power of a variable.
For the given function we have highest power 3 of x.
Therefore, leading term is x^3. We don't have any sign in front of x^3. Therefore, it's a positive leading term.
And degree of the is highest power, that is 3.
Therefore, degree is an odd number.
According to problem, we need to make the leading term as a negative number.
So, we need to find a rule for end behaviour of the graph with:
Leading coefficent = Negative.
Degree : Odd.
Please note the rule, when leading coefficent a negative number and degree is odd.
x--> + ∞ f(x) ---> - ∞
x--> - ∞ f(x) ---> + ∞
We can see option D has f(x) ---> - ∞ for x--> + ∞ and f(x) ---> + ∞ for x--> - ∞.
Therefore, correct option is D.Answer: graph D
Step-by-step explanation: just took the test
13. Model the function rule y = -2x - 3 with a table of values. Show your work.
Answers
y = -2x - 3
To make a table, we assume any number for x and find out y
Lets assume x= -1
y = -2x - 3 = -2(-1) -3 = 2-3 = -1
Lets assume x= 0
y = -2x - 3 = -2(0) -3 = 0-3 = -3
Lets assume x= 1
y = -2x - 3 = -2(1) -3 = -2-3 = -5
Lets assume x= 2
y = -2x - 3 = -2(2) -3 = -4-3 = -7
Table is
x y = -2x-3
-1 -1
0 -3
1 -5
2 -7
what is the equation of the line
y = 1/2x - 4
y = 2x - 4
y = 2x + 2
y = 1/2x + 2
Answers
y = [tex]\frac{1}{2}[/tex] x + 2
the equation of a line in slope-intercept form is
y = mx + c (m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 4, 0 ) ← points from graph
m = [tex]\frac{0-2}{-4-0}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]
from the graph the y-intercept = (0, 2 ) → c = 2
y = [tex]\frac{1}{2}[/tex] x + 2 ← is the equation
The equation of the line is [tex]y = \frac{1}{2}x + 2[/tex]
The calculation is as follows:The equation of a line in slope-intercept form is
y = mx + c
Here m is the slope and c is the y-intercept
Now
[tex]m = ( y_2 - y_1 ) \div (x_2 - x_1 )[/tex]
Here
[tex](x_1, y_1 )[/tex]= (0, 2 ) and [tex](x_2, y_2 )[/tex] = (- 4, 0 )
Now
[tex]m = (0-2) \div (-4-0)\\\\= -2\div -4\\\\= \frac{1}{2}[/tex]
From the graph the y-intercept = (0, 2 ) i.e. c = 2
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The princess traces one plant’s roots to discover that it has exactly 5 roots. One of the roots she can trace to 2−3√5. At least two of the roots are the same and labeled −4.
What conclusions can the princess draw about the other two roots?
There may be more than one correct answer. Select all correct answers.
-One of the other roots is 2+ 3√5
-One of the other roots could be another −4.
-One of the other roots could be another 2− 3√5
-One of the other roots is 3+ 2√5
-One of the other roots is 3− 2√5
Answers
complex roots occur in conjugate pairs
given 2 - 3√5 is a root then 2 + 3√5 is also a root
one of the other roots is 2 + 3√5
there are 2 roots of - 4
one of the other roots could be another - 4
Final answer:
The princess can conclude that one of the other roots is 2+ 3√5, one of the other roots could be another −4, and one of the other roots could be another 2− 3√5.
Explanation:
The princess can draw the following conclusions about the other two roots:
One of the other roots is 2+ 3√5.One of the other roots could be another −4.One of the other roots could be another 2− 3√5.These conclusions are based on the fact that the princess has already traced one root to be 2−3√5 and at least two roots are labeled −4.
Help me please very confused
Answers
Read the problem and answer choices. You want to get from ABCD to EFGH, so you need to figure out how to do that with reflection, translation, and dilation—in that order.
The reflection part is fairly easy. ABC is a bottom-to-top order, and EFG is a top-to-bottom order, so the reflection is one that changes top to bottom. It must be reflection across a horizontal line. The only horizontal line offered in the answer choices is the x-axis. Selection B is indicated right away.
The dimensions of EFGH are 3 times those of ABCD, so the dilation scale factor is 3. This means that prior to dilation, the point H (for example), now at (-12, -3) would have been at (-4, -1), a factor of 3 closer to the origin. H corresponds to D in the original figure, which would be located at (0, -2) after reflection across the x-axis.
So, the translation from (0, -2) to (-4, -1) is 4 units left (0 to -4) and 1 unit up (-2 to -1).
The appropriate choice and fill-in would be ...
... B. Reflection across the x-axis, translation 4 units left and 1 unit up, dilation with center (0, 0) and scale factor 3.
_____
You can check to see that these transformations also map the other points appropriately. They do.
Tom is putting cartons of ice-cream in one of the freezers. There are 13 boxes and each box contains 24 cartons. How many cartons of ice-cream are there in total?
Answers
24x13=312
There are a total of 312 total ice cream cartons.
There are a total of 312 cartons or ice cream in total.
Jon Ericson bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan.
At the end of 2 years he owes the bank $50,000. Now that interest rates have gone up to 13%, the bank will renew the mortgage at this rate or Jon can pay $50,000.
Jon decides to renew and will now pay $11.72 monthly per thousand on his loan. You can ignore the small amount of principal that has been paid.
What is the amount of the old monthly payment? $ ____
What is the amount of the new monthly payment? $ ____
What is the percent of increase in his new monthly payment? ____ %
Answers
You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.
a) The old monthly payment was $10.67×50 = $533.50
b) The new monthly payment is $11.72×50 = $586.00
c) The increase in monthly payment is figured in the usual way:
... (new/old -1)×100% = (1.0984-1)×100% = 9.84%
_____
In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.
Remark
The first fact you need to know is that the bank has taken money from you and nothing has been reduced from the principle. Crafty people those bankers; you are going to pay off the interest before touching the principle. They're like you to refinance for the rest of your life at the rates you currently have.
Point. You started out with a 50k debt. You still have that same debt.
Solution
Givens
number of thousands (n) = 50000/1000 = 50
Amount paid per thousand (A) = 10.67
Total monthly payments (T) = ?
Part A
T = n * A
T = 50 * 10.67
T = 533.50 is the old monthly payment
Part B
T = n * A
T = 50 * 11.72
T = 586.00 new monthly payment.
Part C
This is a notes question. What have you been told in your notes on this question. You can find the raw amount just by subtracting 586 - 533.50 = 52.50
But how do you find the % increase. Which one of the payments do you use as your base?
In point of fact, you should be using the first number 533.5
What % will you get when you multiply that by 533.5 and get 52.50?
You are not trying to find 586. You are trying to find the number that you add to 533.5 to get to 586
The answer is (52.50 / 533.5)*100% = 9.84% is the % increase.
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4. Work out the value of k.
Answers
The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.
Gradient is the slope
So the slope of the line joining the points A(3,-5) and B(6,k) is 4
Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
A(3,-5) and B(6,k) are (x1,y1) and (x2,y2)
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]
We know slope =4
[tex]\frac{k+5)}{3}=4[/tex]
Cross multiply and solve for k
k + 5 = 12
k = 7
The value of k = 7
Explain how (13 + 10) + 5 is solved differently from 13 + (10 + 5). A) For (13 + 10) + 5, you add 13 + 5 first, then add 10. For 13 + (10 + 5), you add the 10 + 13 first, then add 5. Eliminate B) For (13 + 10) + 5, you add 13 + 10 first, then add 5. For 13 + (10 + 5), you add the 10 + 5 first, then add 13. C) For (13 + 10) + 5, you add 13 - 10 first, then add 5. For 13 + (10 + 5), you add the 10 - 5 first, then add 13. D) For (13 + 10) + 5, you add 13 + 10 first, then subtract 5. For 13 + (10 + 5), you add the 10 + 5 first, then subtract 13.
Answers
Answer:
The answer is B
Step-by-step explanation:
Simple use P.E.M.D.A.S
Parentheses are always first, you add 13+10 then evaluate everything else.
Have a great day.
3 and 5 form what type of angle pair? A. corresponding angles B. alternate interior angles C. consecutive interior angles D. alternate exterior angles
Answers
Answer:
C. consecutive interior angles
Step-by-step explanation:
The subject angles are between lines a and b, so are interior (not exterior). They are on different corners of the intersection, so are not corresponding. They are on the same side of line c, so are not alternate. The share a side, but not a vertex, so they are consecutive. The appropriate choice is ...
... C. consecutive interior angles
Answer: C. consecutive interior angles
solve the system by graphing or using a table.
2x+4y=12
x+y=2
Answers
Answer: x = -2 and y = 4
Step-by-step explanation:
We have given a system of equations
2x + 4y =12 ...........(1)
and
x + y = 2 .............(2)
Now to plot them in graph we need to find the points of the above linear equations .
From equation 1 ,we get
[tex]4y=12-2x\\\Rightarrow\ y=\frac{12-2x}{4}\\ \Rightarrow\ y=3-\frac{x}{2}\\\text{Put x=0, then} \\y=3-\frac{0}{2}=3\\\Rightarrow\ \text{Put x=6}\\y=3-\frac{6}{2} =3-3=0[/tex]
So get the points (0,3) and (6,0).
From equation 2 ,we get
[tex]y=2-x\\\text{Put x=0}\\y=2-0=2\\\text{Put x=2}\\y=2-2=0[/tex]
So we get the points (0,2) and (2,0).
So after plotting these points we get two lines intersecting at (-2,4).
Therefore our solution is x=-2 and y= 4.
Answer:
(-2, 4)
Step-by-step explanation:
how many times larger is 9 X 10 to the 6 exponent than 3 x 10 to the 4th exponent
Answers
300
divide 9 × [tex]10^{6}[/tex] by 3 × [tex]10^{4}[/tex]
= [tex]\frac{9}{3}[/tex] × [tex]10^{6}[/tex] / [tex]10^{4}[/tex]
= 3 × [tex]10^{6-4}[/tex] = 3 × [tex]10^{2}[/tex] = 300
97 POINTS WILL MARK BRAINLESS
I need help with these i'm so confused could you show me on how you got the answers Thank you so much
Answers
Answer:
2.
x = 15∠1 = 45°1.
x = 5∠A = 85°Step-by-step explanation:
2.Angles 135° and (2x+15)° together make up a line (the transversal crossing m and n). Such angles are called a "linear pair" and their sum is always 180°. That means we can write the equation ...
... 135° + (2x+15)° = 180°
... 150 +2x = 180 . . . . . . . remove the degree symbol, combine terms
... 2x = 30 . . . . . . . . . . . . subtract 150
... x = 15 . . . . . . . . . . . . . . divide by 2
Angle 1 and angle (2x+15)° are on opposite sides of the transversal line, and are both between the parallel lines m and n. This makes them alternate interior angles. Such angles are congruent—they have the same measure. We know the measure of angle (2x+15)° is (2·15+15)° = 45°, so we know the measure of ∠1 is also 45°.
1.a) The sum of angles in a triangle is always 180°. This means ...
... (15x +10)° + (15x -10)° + (3x +15)° = 180°
... 33x +15 = 180 . . . . . . . drop the ° symbol, combine terms
... 33x = 165 . . . . . . . . . . subtract 15
... x = 5 . . . . . . . . . . . . . . . divide by 33
b) ∠A = (15x+10)° = (15·5 +10)°
... ∠A = 85°
(1)
(a)
the sum of the angles in a triangle = 180°, hence
3x + 15 + 15x - 10 + 15x + 10 = 180
33x + 15 = 180 ( subtract 15 from both sides )
33x = 165 ( divide both sides by 33 )
x = 5
(b) ∠A = 15x + 10 = (15 × 5 ) + 10 = 75 + 10 = 85°
(2)
2x + 15 + 135 = 180 ( straight angle )
2x + 150 = 180 ( subtract 150 from both sides )
2x = 30 ( divide both sides by 2 )
x = 15 ⇒ 2x + 15 = 45
∠1 = 45° ( alternate angles are congruent )
what is 352 divided by 53 please reply to this within a hour im timed....
Answers
352 divided by 53 is 6.64150943
Hi TaeArmy23,
352 / 53
= 6.6415
= 6.6
Hope This Helps!
If (c) were f(k) = -3/k+2, what value of k would be excluded from the domain?
Answers
k = - 2 is excluded from the domain
the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that k cannot be
solve k + 2 = 0 ⇒ k = - 2 ← excluded value
HURRYYY!!! 20 POINTS AND BRAINLIEST IF CORRECT.
Which represents where f(x) = g(x)?
f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answers
Its A i did the test
please help!!!
The value of " X " is...
2x + y − z = 3
−x + y + 2z = 0
3x + 2y + z = 9
12
2
3
-4
Answers
x = 3
2x + y - z = 3 → (1)
- x + y + 2z = 0 → (2)
3x + 2y + z = 9 → (3)
we require to eliminate the y and z terms from the equations
(1) + (3) : 5x + 3y = 12 → (4)
multiply (1) by 2
4x +2y - 2z = 6 → (5)
(2) + (5) : 3x + 3y = 6 → (6)
(4) - (6) : 2x = 6 ⇒ x = 3
Consider the following investment. (Round your answers to the nearest cent.)
$3,000 at 6% compounded annually for 15 years
(a) FIND the future value of the given amount.
(b) INTERPRET the future value of the given amount.
After 15 years, the investment is worth $?
Answers
(a) 6% of the value of the investment is added each year. This means the value of the investment is multiplied by 1.06 each year. After 15 multiplications, the value is ...
... $3000×1.06¹⁵ ≈ $7189.67
(b) The interpretation of this result is ...
... After 15 years, the investment is worth $7189.67.
The future value of a $3000 investment at an annual interest rate of 6%, compounded annually for 15 years, is approximately $8093.97. This means that the original sum will grow to this amount after the set period.
Explanation:To find the future value of an investment, we use the formula for compound interest which is A = P(1 + r/n)^(nt). Where:
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount you borrowed or deposited). r is the annual interest rate (in decimal form). n is the number of times that interest is compounded per unit t. t is the time the money is invested for in years.Given are P = $3000, r = 6%/100 = 0.06 (annually), n = 1 (since it's compounded annually), and t = 15 years. Plugging these into the formula, we get A = $3000(1 + 0.06/1)^(1*15) = $3000(1.06)^15 = $8093.97.
Interpreting this, it means that investing $3000 at 6% compounded annually would grow to approximately $8093.97 after 15 years.
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what is the answer for 300/2 by changing the number from mixed to improper and simplify at the end if needed
Answers
Simplify. Divide the number
300/2 = 150
150 is your answer (it is a whole number, no need to change to improper, unless you want 150/1)
hope this helps
A pair of sneakers on sale for $51. This is 75% off the original price. How much less than the original price is the sales price?
Answers
75% of X = $51, thus x or the original price is $68 . Thus the sales price is $17 less.
__________ are pairs of angles formed when a third line (transversal) intersects two other lines. These angles are on the opposite sides of the transversal and are between the other two lines.
Answers
"Opposite sides of the transversal..." Alternate
"Between the other two lines." Interior
Alternate Interior angles.
If they were outside the two lines they would be alternate exterior angles and if they were on the same side of the transversal then they would be corresponding angles.
A polynomial function has a root of –6 with multiplicity 1, a root of –2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?
Answers
because the leading coefficient is positive and the highest degree is odd (9) the function is negative for (-inf, -6). Then it crosses the -6 root to become positive until it crosses again the root -2. (it crosses because both roots have an odd multiplicity). then it touches on root 0 (does not cross due to an even multiplicity there), so function remains negative from -2 till root 4 where it crosses into the positive.
Given the above, only the first choice is a correct statement.
The true statement about the graph is: (a) the graph of the function is positive on [tex]\mathbf{(-6,-2)}[/tex]
The given parameters are:
[tex]\mathbf{Root = -6, Multiplicity = 1}[/tex]
[tex]\mathbf{Root = -2, Multiplicity = 3}[/tex]
[tex]\mathbf{Root = 0, Multiplicity = 2}[/tex]
[tex]\mathbf{Root = 4, Multiplicity = 3}[/tex]
Add up the multiplicities, to calculate the degree of the polynomial function
[tex]\mathbf{Degree = 1 + 3 + 2 + 3}[/tex]
[tex]\mathbf{Degree = 9}[/tex] --- odd number
The interval of the first root is:
[tex]\mathbf{Interval = (-\infty,-6)}[/tex]
The interval of the second root is:
[tex]\mathbf{Interval = (-6,-2)}[/tex]
A polynomial function with an odd degree, and a positive leading coefficient will start with negative values, until it reaches the smallest root, before it switched to positive values.
This means that, the function increases at: [tex]\mathbf{Interval = (-6,-2)}[/tex]
Hence, option (a) is correct.
Read more about polynomial functions at:
https://brainly.com/question/9338204
The price of a round trip ticket to San Francisco increases from $525.00 to $650.00. To the nearest whole percent, what is the percent of increase?
A) 18%
B) 24%
C) 28%
D) 30%
E) 34%
Answers
B
to calculate percent increase use
[tex]\frac{increase}{original}[/tex] × 100%
increase = $650 - $525 = $125
percent increase = [tex]\frac{125}{525}[/tex] × 100% = 24% → B
Answer:
The answer is B) 24%
Step-by-step explanation:
The formula for percentage increase is given as:-
Percentage Increase = ( New Price - Old Price ) /old price * 100
old price = $525
New Price = $650
Percentage Increase = 24%
Hence the price increases by 24%
given the function f(x)=3^x, find the value of f^-1(27)
Answers
This is asking you to solve the equation ...
... 27 = 3^x
You can use logarithms to find
... log(27) = x·log(3)
... log(27)/log(3) = x = 1.43136376.../0.47712125...
... x = 3
Or, you can use your knowledge of small cubes and match exponents.
... 3^3 = 3^x
... 3 = x
Solve the inequality |x| < 5. {x|-5 < x < 5} {x|x < -5 ∪ x > 5} {x|x -5 ∪ x < 5}
Answers
ANSWER
The correct answer is A
{[tex]x|-5<\:x<\:5[/tex]}
EXPLANATION
[tex]|x|<5[/tex]
This implies that
[tex]x<5\:or\:-x<5[/tex]
We solve the compound inequality to obtain,
[tex]x<5\:or\:x>-5[/tex]
Remember that, dividing through by negative 1 reverses the inequality sign
The solution set is
{[tex]x|-5<\:x<\:5[/tex]}
How does sin 30degrees compare to sin -30degrees?
Answers
The sine function is an odd function, so the sine of -30° is the opposite of the sine of 30°.
sin(30°) = 1/2
sin(-30°) = -1/2
The sine of 30° is greater than the sine of -30°.
Jo flips a coin {H, T}; then rolls a 6-sided die {1, 2, 3, 4, 5, 6}.
How many possible outcomes are in the sample space of this experiment?
A. 4
B. 8
C. 12
D. 36
Answers
Answer:
Option C
Step-by-step explanation:
A coin has two outcomes Head (H) and tail (T).
So, the number of outcomes when a coin is tossed = 2
A coin has six outcomes [tex]\left \{ 1,2,3,4,5,6 \right \}[/tex]
So, the number of outcomes when a coin is tossed = 6
Therefore, possible outcomes when Jo flips a coin and then rolls a 6-sided die are [tex]\left \{ H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6 \right \}[/tex]
So, the number of possible outcomes = 12
Option C. is correct.
Using the concept of sample space, it is found that the number of possible outcomes in the experiment is given by:
C. 12
The sample space of an experiment is the set that contains all possible outcomes.
In this problem:
For the coin, there are 2 outcomes.For the dice, there are 6 outcomes.The coin and the dice are independent, thus, there are 2 x 6 = 12 possible outcomes, which means that the correct option is:
C. 12
A similar problem is given at https://brainly.com/question/15006554
What is the Equivalent ratio of 6:_= 9:12
Answers
[tex]\frac{6}{8}[/tex]
let x be the unknown value in the ratio, hence
[tex]\frac{6}{x}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )
9x = 72 ( divide both sides by 9 )
x = 8
thus [tex]\frac{6}{8}[/tex] = [tex]\frac{9}{12}[/tex]