Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $12.50 per hour at her job, and Jack is paid $10 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $750 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?
Answers
The inequality representing their combined pay would be
[tex]12.50x+10.00y \geq 750[/tex]. This is because Jane makes 12.50/hr, Jack makes 10.00/hr, and they want to make at least, so greater than or equal to, $750 combined.
The inequality representing their combined hours working would be
[tex]x+y \leq 65[/tex], since they do not want their combined hours to be over 65. In both of these inequalities, x represents the number of hours Jane works and y represent the number of hours Jack works.
To graph these, we solve both of them for y:
[tex]x+y \leq 65 \\ x+y-x \leq 65-x \\ y \leq 65-x[/tex]
[tex]12.50x+10.00y \geq750 \\12.50x+10.00y-12.50x \geq 750-12.50x \\10.00y \geq 750-12.50x \\ \frac{10.00y}{10.00} \geq \frac{750}{10.00} - \frac{12.50x}{10.00} \\y \geq 75-1.25x[/tex]
The attached screenshot shows what the graph looks like. Going to the point where they intersect, we see that the shaded region that satisfies both inequalities begins when Jane works 40 hours and Jack works 25.
Answer:
20
Step-by-step explanation:
just did it on study island
Related Questions
Help me I don’t get this!!!
Answers
One owl has a wingspan of 1⁄2 foot. A second owl's wingspan is 3⁄4 foot. How much longer is the wingspan of the second owl?
Answers
First, we'll need to find the common denominator:
1/2 = 2/4
Then, we can subtract.
3/4 - 2/4 = 1/4
With this, we now know that 1/4 is the answer.
The wingspan of the second owl is 3 inches longer than that of the first owl.
The question asks to find out how much longer the wingspan of the second owl is compared to the first owl. The first owl has a wingspan of 1/2 foot, while the second owl has a wingspan of 3/4 foot. To find the difference in wingspan, we subtract the first owl's wingspan from the second owl's wingspan:
3/4 foot - 1/2 foot = 2/4 foot - 1/2 foot = 2/4 foot - 2/4 foot = 1/4 foot.
Since there are 12 inches in a foot, we can convert this difference to inches:
1/4 foot times 12 inches/foot = 3 inches.
Hi guys can you help me factor these two equations?
5x^2-13x-6
4x^4 – 28x^3 + 48x^2
please show your work on both of them, and thank you so much!
Answers
1. First, you must find the roots of the quadratic equation, by applying the quadratic formula, which is:
x=-b√(b²-4ac)/2a
2. The roots are:
x1=3
x2=-2/5
3. Then, you have:
5(x-3)(x+2/5)
4. When you simplify, you obtain:
(x-3)(5x+2)
B) 4x^4-28x^3+48x^2
1. First, you must factor the common term, which is 4x^2. Then:
4x^2(x^2-7x+12)
2. Now, you must apply the quadratic formula to obtain the roots of the quadratic equation: x^2-7x+12. Then, you have:
x1=4
x2=3
3. Finally, you obtain:
4x^2(x-4)(x-3)
what is the answer to g(r)=−5r+13
Answers
The function g(r) is a linear equation with a slope of -5 and a y-intercept of 13. You can find the value of g(r) by plugging in different values for r.
Explanation:The student's question is regarding the function g(r)=−5r+13. However, the rest of the information provided appears to be disjointed and not directly related to the function in question.
To answer their question, g(r)=−5r+13 is a linear function where -5 is the slope and 13 is the y-intercept. In this equation, r is the independent variable, and g(r) is the dependent variable. You would insert a value for r to find the corresponding output of g(r). For example, if r = 2, then g(2) = -5(2) + 13 = -10 + 13 = 3.
Which of the following values could represent the probabilities of complementary events and 28% and 82% and 10% and 80%
1/7and2/7
2/5and3/5
Answers
Answer:
2/5 and 3/5
Step-by-step explanation:
Complementary events have probabilities that sum to 100%, or 1.
28+82 = 110; this is not 100.
10+80 = 90; this is not 100.
1/7+2/7 = 3/7; this is not 1.
2/5+3/5 = 1; this is correct.
factor the following polynomial completely 30y^6+25y^5-10y^4
Answers
a. In order for ΔABC to be similar to ΔDEF, what must be true about the angles? Be specific. b. If you know that ΔABC is similar to ΔDEF, and you know that m∠A = 52° and m∠E = 65°, what is m∠C? Explain how you arrived at your answer. c. What is the difference between two figures being similar and two figures being congruent?
Answers
ii) If ΔABC is similar to ΔDEF, therefore; m∠A = m∠D, m∠B=m∠E, and m∠C=m∠F,
thus, if m∠A= 52, m∠D=52, and if m∠E=65, then m∠B=65, thus to get m∠C;
180- (52+65)
= 63 , therefore; m∠C= 63
iii) if two figures are similar they have the same shape and not necessarily the same size while if two figures are congruent then they have the same shape and size
Answer:
If ΔABC is similar to ΔDEF, therefore; m∠A = m∠D, m∠B=m∠E, and m∠C=m∠F,
though, if m∠A= 52, m∠D=52, and if m∠E=65, then m∠B=65, though to get m∠C;
180- (52+65)
= 63 , so then, m∠C= 63
Step-by-step explanation:
What values of c and d make the equation true? mc011-1.jpg c = 2, d = 2 c = 2, d = 4 c = 6, d = 2 c = 6, d = 4
Answers
We can simplify the equation by first cubing both sides
= 162x^cy^5 = (27x^6y^3)6y^d
= 162x^cy^5 = 162 x^6y^3y^d
dividing both sides by 162
= x^cy^5 =x^6y^3y^d
equating the values with similar bases
x^c = x^6, therefore c=6
and y^5=y^3y^d
y ^5 = y^(3+d)
hence, 5 = 3+d
thus, d= 2
Therefore, the values of d and c that will satisfy the equation are, c =6 and d=2
The answer is C.
c=6 d=2
PLZ HELP!!!!!!! Can a kite be formed by drawing a triangle and then reflecting one or more times? Explain.
Select one:
a. Yes. Draw any triangle ABC. Reflect this triangle across the perpendicular bisector of line AB, creating triangle A'B'C' for which A'=B and B'=A. By the definition of a reflection, sides A'C and B'C' are congruent. In addition, sides B'C and A'C' are congruent. The quadrilateral CC'B'A' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
b. Yes. Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
c. No. Since the reflection of a triangle is always another triangle, there is no way to create a quadrilateral using a triangle or its reflection.
d. No. It is not possible to reflect a triangle in such a way that the result is quadrilateral with any consecutive sides that are congruent.
Answers
The answer is (B).
Draw any triangle ABC. Reflect this triangle across the line AB, creating triangle A'B'C' for which A'=A and B'=B. By definition of a reflection, sides B'C and B'C' are congruent. In addition, sides A'C and A'C' are congruent. The quadrilateral CA'C'B' has two pairs of consecutive sides that are congruent and no congruent opposite sides. By definition, this is a kite.
What is the probability of drawing a heart from a standard deck of cards on a second draw, given that a heart was drawn on the first draw and not replaced?
A) one over fifty one
B) one over fifty two
C) twelve over fifty one
D) thirteen over fifty two
Answers
Answer: C) twelve over fifty one
Step-by-step explanation:
Formula for probability =[tex]\dfrac{\text{Favorable outcomes}}{\text{Total ouctomes}}[/tex]
We know that , a standard deck has 52 cards.
Number of hearts = 13
If a heart was drawn on the first draw and not replaced, then the number of hearts left = 13-1=12 (favorable outcomes)
The total number of cards left = 52-1=51 (total outcomes)
Therefore, the probability of drawing a heart from a standard deck of cards on a second draw, given that a heart was drawn on the first draw and not replaced would be :-
[tex]\dfrac{\text{Number of hearts left}}{\text{Total cards left}}\\\\=\dfrac{12}{51}[/tex]
Hence, the correct answer is option C) twelve over fifty one
Rectangle FGHJ is transformed according to the rule T(–3, –2)ry = x. What is the y-coordinate of J”?
Answers
the point J (10,-6)
the rule is-----------(x,y)-------------------> (x-3, y-2)
therefore
J (10,-6)----------------- > (10-3,-6-2)--------> (7,-8)
the answer is
the y-coordinate of J” is -8
Answer:
The y-coordinate of J'' is 8.
Step-by-step explanation:
The given rule of transformation is
[tex]T(-3,-2)r_{y=x}[/tex]
It means, first the figure is reflected across the line y=x and then translated by the rule T(-3,-2).
From the given figure it is clear that the coordinates of point J are (10,-6).
If a figure is reflected across the line y=x, then
[tex](x,y)\rightarrow (y,x)[/tex]
The coordinate of point J'.
[tex]J(10,-6)\rightarrow J'(-6,10)[/tex]
If a figure is translate by the rule T(-3,-2), then
[tex](x,y)\rightarrow (x-3,x-2)[/tex]
The coordinate of point J''.
[tex]J'(-6,10)\rightarrow J''(-6-3,10-2)=J''(-9,8)[/tex]
Therefore the y-coordinate of J'' is 8.
Charlotte bought packs of hot dogs for $4 each. Eack pack has 8 hot dogs. If she spent $16 how many hot dogs did she get
Answers
16/4=4
8*4=32
ms.black paid $32 intrest at the rate of 8% on a loan of $200. For how long was the loan?
Answers
What is the answer I need help now!!!!
Answers
The probability of heads is 0.50, or 50%.
I hope this helps!
PLEASE HELP!!!!!
TIME SENSITIVE! Will mark brainliest!
Part 1.] Match the following items.
1. 2, 4, 8, 16, . . ., 64
2. 3, 6, 9, 12, . . .
3. 3 + 9 + 27 + 81 + . . .
4. 3 + 5 + 7 + 9 + . . .
5. 3, -3, 3, -3, 3,-3, . . .
A. arithmetic series
B. finite sequence
C. infinite sequence
D. geometric series
E. alternating sequence
Part 2.]-3, 6, -9, 12, -15, . . .
Which of the following represents the general term for the sequence given?
A. [tex] (-1)^{n} 3^{n} [/tex]
B. [tex] (-1)^{n} 3n[/tex]
C. [tex] (-1)^{n+1}3[/tex]
Part 3.] The first attached picture
A. 35
B. 14
C. 11
Part 4.] The second attached picture
A. 6
B. 9
C. 18
Part 5.] The third attached picture
A. 10
B. 14
C. 28
Part 6.] Which of the following best describes the following set of numbers?
6+8+10+12+...+(4+2n)+...
A. Arithmetic Sequence
B. Geometric Series
C. Geometric Sequence
D. Arithmetic Series
Answers
Part 1.] Match the following items.
1. 2, 4, 8, 16, . . ., 64---------- > B. finite sequence
2. 3, 6, 9, 12, . . . ------------- > C. infinite sequence
3. 3 + 9 + 27 + 81 + . . .------> D. geometric series
4. 3 + 5 + 7 + 9 + . . .----------> A. arithmetic series
5. 3, -3, 3, -3, 3,-3, . . .-------- >E. alternating sequence
Part 2.]-3, 6, -9, 12, -15, . . .
Which of the following represents the general term for the sequence given?
A. (-1^n)*(3^n)
for n=1-----------> (-1^1)*(3^1)=-3
for n=2-----------> (-1^2)*(3^2)=9 -------------- a2=6 no represents
B. (-1^n)*(3n)
for n=1-----------> (-1^1)*(3*1)=-3
for n=2-----------> (-1^2)*(3*2)=6
for n=3-----------> (-1^3)*(3*3)=-9
for n=4-----------> (-1^4)*(3*4)=12
for n=5-----------> (-1^5)*(3*5)=-15
C. (-1^(n+1))*(3)
for n=1-----------> (-1^(1+1))*(3)=3---------- > a1=-3 no represents
the answer part B is option B. (-1^n)*(3n)
Part 3.] The first attached picture
Σ (2n+1) for n=1 to 5
n1---------> (2*1+1)=3
n2---------> (2*2+1)=5
n3---------> (2*3+1)=7
n4---------> (2*4+1)=9
n5---------> (2*5+1)=11
Σ (2n+1) for n=1 to 5=[3+5+7+9+11]=35
the answer part C is 35
Part 4.] The second attached picture
Σ (3n) for n=1 to 3
n1---------> (3*1)=3
n2---------> (3*2)=6
n3---------> (3*3)=9
Σ (3n) for n=1 to 3=[3+6+9]=18
the answer part 4 is 18
Part 5.] The third attached picture
Σ (2n+2) for n=1 to 4
n1---------> (2*1+2)=4
n2---------> (2*2+2)=6
n3---------> (2*3+2)=8
n4---------> (2*4+2)=10
Σ (2n+2) for n=1 to 4=[4+6+8+10]=28
the answer part 5 is 28
Part 6.] Which of the following best describes the following set of numbers?
6+8+10+12+...+(4+2n)+...
8-6=2
10-8=2
12-10=2
the next number is obtained by adding 2 to the previous number
this is an Arithmetic Series
the answer is the option D. Arithmetic Series
The area of a rectangle is 77ft^2 , and the length of the rectangle is 3ft more than twice the width. What are the dimensions of the rectangle ?
Answers
W = W
L = 2W + 3
Area = L * W
Area = (2W + 3)*W
Area = 2W^2 + 3W
The area is also 77
So
Area = 2w^2 + 3W = 77
Area = 2w^2 + 3W - 77 = 0
Now factor the question
77 can only factor into 1,77 which is highly unlikely and 7 and 11
As a guess I'm going to try 7. It that's true, we get
(x + 7)(2x - 11) = 0 This might work.
x^2 + 14x - 11x - 77 = 0
x^2 + 3x - 77 = 0 So the factoring is correct.
x + 7 = 0
x = - 7
2x - 11 = 0
2x = 11
x = 11/2
x = 5.5
W = 5.5 <<<< Answer
The minus seven is meaningless.
Width = 5.5
Length = 2*5.5 + 3
Length = 11 + 3
Length = 14 <<<< answer
Now we have to check the area.
Area = L * W
Area = 14 * 5.5
Area = 77. You have a complete answer.
What is log5(4*7)+log5^2 as a single log?
Answers
It would be better if you sent a photo task
I'm not sure what I understood correctly
Answer with explanation:
The four options are
(A) log5 21 (B) log5 26 (C) log5 30 (D) log5 56
[tex]\rightarrow\log_{5}(4\times 7) +\log_{5}(2)\\\\ \rightarrow \log_{5}28+\log_{5}2\\\\\rightarrow \log_{5}(28 \times 2)\\\\=\log_{5}(56)\\\\ \text{Used this property of log}\\\\ \log_{m} a+\log_{m} b=\log_{m} ab[/tex]
Option D
What do you say when you meet a two headed dragon
Answers
In literature, when a character meets a two-headed dragon, their response may vary based on the story's context. Dragons often symbolize challenges; thus, a character may respond with caution and respect. This concept, however, is symbolic and represents various elements in different literatures.
Explanation:In literature, the response to meeting a two-headed dragon can vary greatly depending on the context of the story and the characteristics assigned to the creature. Dragons, particularly two-headed ones, often symbolize challenges or adversities. So, one way to respond practically when you meet a two-headed dragon would be with caution and respect.
For example, in fantasy literature, a protagonist might say 'Well met, noble dragon. What do you require of me?' This politeness and respect can often turn a potentially dangerous encounter into an opportunity for dialogue. Remember, in literature, fantastic creatures like headed dragons are often symbolic, representing something else entirely in the context of the story.
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Which conversion requires multiplication?
A. Deciliter to liter
B. Liter to kiloliter
C. Kiloliter to liter
D. Milliliter to centiliter
Answers
milli-, centi-, deci-, unit, deca-, hecto-, kilo-.
Converting from the left to right (from smallest to largest) means you divide to get your answer.
Converting from the right to the left (from largest to smallest) means you multiply to get your answer. Deciliter to liter goes from left to right, so that would be division. Liter to kiloliter goes from left to right, so it is division. Kiloliter to liter goes from right to left, so it is multiplication. Milliliter to centiliter goes from left to right, so it is division.
Answer:
I believe it is B
Step-by-step explanation:
Given the functions f(x)= [tex] \frac{1}{x-2} + 1 [/tex] and g(x) = [tex] \frac{1}{x+5} + 9[/tex]
Which statement describes the transformation of the graph of function f onto the graph of function g?
The graph shifts 8 units right and 7 units down.
The graph shifts 8 units left and 7 units up.
The graph shifts 7 units right and 8 units down.
The graph shifts 7 units left and 8 units up.
Answers
Transformation of functions:
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
To graph y = f (x) -k, move the graph of k units down.
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right.
To graph y = f (x + h), move the graph of h units to the left.
f (x) = (1 / (x-2)) + 1
To graph y = f (x) + k, move the graph of k units up.
h (x) = (1 / (x-2)) + 1 + 8
To graph y = f (x + h), move the graph of h units to the left.
g (x) = (1 / (x-2 + 7)) + 1 + 8
g (x) = (1 / (x + 5)) + 9
Answer:
The graph shifts 7 units left and 8 units up.
Find the sum of the first thirty consecutive whole numbers.
Answers
The sum of the first thirty consecutive whole numbers can be represented by the following series
[tex] 0+1+2+3+4+....+29\\ \\Sum \; of\; first \; 30\; whole \; numbers\; =\; Sum\; of\; first \; 29\; Natural\; Numbers\\ \\1+2+3+4+...+29 \\ \\ Formula\\ 1+2+3+....+n=\frac{n(n+1)}{2} \\ \\ Substituting\; 29\; for\; n,\; we\; get...\\ \\ 1+2+3+4+...+29=\frac{29(30)}{2}=29 \times 15=435 [/tex]
Conclusion:
The sum of the first thirty consecutive whole numbers is 435.
Answer:
435
Step-by-step explanation:
The gouse method or something.
(29*30)/2=435
what is the solution to the proportion? 3y-8/12 = y/5
Answers
Justification:
A proportion is the equality of two ratios.
Your equality is:
3y - 8 y
--------- = ---
12 5
That equality is an equation. Now you must solve for y.
These are the steps:
1) Multilpy both sides by 12 * 5
=> 5 (3y - 8) = 12y
2) Expand the parentesis (distributive property)
15y - 40 = 12y
3) Transpose 12 and - 40
15y - 12y = 40
4) Combine the like terms
3y = 40
5) Divide both sides by 3
y = 40 / 3
Answer: y = 40 / 3
Classify the model as exponential growth or exponential decay. Identify the growth or decay factor AND the percent of increase or decrease per time period.
y=100(1.05)^t
Plz help!
Answers
The growth factor is 1.05.
The increase is (1.05 -1)*100% = 5% per period.
Which algebraic expression is equivalent to the expression below? (3x + 12) + 8x
A.
(3x + 8x) + 12
B.
(3x - 8x) + 12
C.
23x
D.
(3x + 12x) + 8
Answers
A rental company charges $75 a day and 20 cents a mile for renting a truck. michael rents a truck for 2 days, and his bill came to $238. how many miles did he drive?
Answers
You then solve for x by multiplying 75 by 2 to get 150. Then subtract 150 from both sides of the equation, so this is what you get .20x=88. Finally divide by .20 on both sides to get x= 440
Answer:
440 miles.
Step-by-step explanation:
A rental company charges for rent a truck = $75 per day
and the charges per mile = 20 cents
100 cents = 1 dollar
20 cents = [tex]\frac{20}{100}[/tex]
= $0.20
Michael rents a truck for 2 days.
Let Michael drove the truck in 2 days = x miles
and his bill came to $238.
the equation will be : (75 × 2) + 0.20x = 238
150 + 0.20x = 238
0.20x = 238 - 150
0.20x = 88
x = [tex]\frac{88}{0.20}[/tex]
x = 440
Michael drove the truck 440 miles in 2 days.
Keith had 1 1/2 cups of flour.he used 5 2/3 cups to make bread.How many cups of flour does Keith have left
Answers
What is the slope of a line parallel to line B?
-1/3
2/5
5/2
5/3
Answers
what is the answer im so confused
Answers
Answer:
Step-by-step explanation:
their income for the month of may is $3500
2% of this income was spent on movies
2% of $3500 = 2/100 × 3500
=0.02 ×3500
= $70
What makes a parallelogram, a square, a rhombus, a rectangle, a kite and a trapezoid unique?
Answers
Square: All sides are congruent.
Rhombus: Is a four-sided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal.
Rectangle: It is a quadrilateral which has two pairs of parallel and equal sides. It is also a parallelogram with its all four internal angles equal to right angles.
Kite: Is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
Trapezoid: Has a pair of parallel sides. is an Isosceles trapezoid when both angles coming from a parallel side are equal, and the sides that aren't parallel are equal in length
30 POINTS!!!!! WILL MARK BRAINLIEST!
Karel and her family have just moved into a new neighborhood. Karel wants to earn money by baby-sitting for families with young children. She asked other students her age how much they charged for babysitting. The results are listed in the chart below.
LOOK AT CHART!
1. Suppose Karel wants to be the least expensive babysitter in the neighborhood. How much should she charge? This response will be graded for the correct numerical information.
2. Suppose Karel wants to charge the same hourly rate as most of the other baby-sitters. How much should she charge? This response will be graded for the correct numerical information.
3. Suppose Karel wants her hourly rate to be higher than the rate of half of other baby-sitters, but lower than the hourly rate of the rest of the babysitters. How much should she charge? This response will be graded for the correct numerical information.
4. In addition to the babysitting rates charged by others, what might Karel consider when she sets her rates? Respond in complete sentences, not only with calculations. Write as if you are verbally explaining what you are thinking.
Answers
Since the cheapest babysitter charges $2.00, Karel should charge less to be cheapest.
2. $3.25
Most of the other babysitters charge $3.25.
3. $2.50
The median of this set is $2.50, so she should be at the median of $2.50 for this question.
4. Karel should also consider the range of the hourly costs of the babysitters. For this, she would charge $1.00.
Karel should charge $7 per hour to be the least expensive babysitter, $10 per hour to charge the same rate as most other babysitters, and $12 per hour to have a higher rate than half of the other babysitters.
Explanation:1. To be the least expensive babysitter, Karel should charge $7 per hour as it is the minimum rate.
2. To charge the same hourly rate as most other babysitters, Karel should charge $10 per hour as it is the mode or the most frequently occurring rate.
3. To have a higher rate than half of the other babysitters but lower than the rest, Karel should charge $12 per hour as it lies in the middle of the range from $7 to $15.
4. When setting her rates, Karel should consider factors like her experience, qualifications, the number of children she can handle, the neighborhood's average income, and any additional tasks she may be asked to perform.
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