The combined work rate can be found by using the equation for combined rate.
The correct responses;The time it will take them working together is; [tex]\displaystyle \underline{\frac{1}{t_b} = \frac{1}{t_1} + \frac{1}{t_2} }[/tex]The number of hours it will take them working together to paint the room is approximately 4.24 hours. The method by which the above responses are obtained:The time it takes Irina to paint the room alone, t₁ = 9 hours
Time it takes Paulo to paint the room, t₂ = 8 hours
Required:
To write the equation for the combined rate of Irina and Paulo
Solution:The equation that gives the time, [tex]\mathbf{t_b}[/tex], it will take both Irina and Paulo to paint the room together is given by the combined rate formula, as follows;
[tex]\displaystyle \underline{ \frac{1}{t_b} = \frac{1}{t_1} + \frac{1}{t_2}}[/tex]Required:The duration it will take them to paint the room when working together.
Solution:The time it will take them to paint the room together is found as follows;
[tex]\displaystyle \frac{1}{t_b} = \mathbf{\frac{1}{9} + \frac{1}{8}}[/tex]
Which gives;
[tex]\displaystyle \frac{1}{t_b} = \frac{8 + 9}{9 \times 8} = \mathbf{\frac{17}{72}}[/tex]
Therefore;
[tex]\displaystyle t_b = \frac{72}{17} \approx \mathbf{4.24}[/tex]
The time it takes Irina and Paulo to paint together, [tex]t_b[/tex] ≈ 4.24 hrs.Learn more about combined rate of work here:
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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
Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF.
△ABC: AB = 10, BC = 16, CA = 20
△DEF: DE = 25, EF = 40, FD = 50
I really need someone to explain to me how to do this because i am so confused my teacher didn't give us notes and didn't explain this very well.
Answer:
2/3 i got it right
Step-by-step explanation:
Final answer:
To find the scale factor between △ABC and △DEF, compare their corresponding side lengths and calculate the scale factor as 2.5 or 5/2.
Explanation:
To verify that two triangles △ABC and △DEF are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.
Calculate the scale factor using the corresponding sides of the triangles: AB/DE = BC/EF = CA/FD.
Substitute the values: 10/25 = 16/40 = 20/50. Simplify to find the scale factor.
Therefore, the scale factor of △ABC to △DEF is 2.5 or 5/2.
What is log5(4*7)+log5^2 as a single log?
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
helppppppppppppppppppppppppppppppppp
what is the answer im so confused
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
help me plsss i really need did that but still dont get it
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
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.
A clock is constructed using a regular polygon with 60 sides. The polygon rotates everybody minute. How much has the polygon rotated after 7 minutes
•14 degrees
•21 degrees
•35 degrees
•42 degrees
Write an equation for the translation of y = 4 x that has the given asymptotes. 15. x = 0, y = 3
How many sets of 7 questions can be chosen from a file of 25 questions?
What do you say when you meet a two headed dragon
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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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!
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
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
what is the answer to g(r)=−5r+13
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.
A rhombus exists. This rhombus has 2 diagonals. The diagonals touch the side forming angles. These angles are in the ratio 4:5. Solve for all the angles in this rhombus based on the theorems for rhombuses and parallelograms.
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?
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.
maxine hosted a dinner party at her favorite restaurant. she had to pay $12 per guest. the restaurant took $72 off the bill due to a mistake in the order. if the finale bill is $300, which equation will help the restaurant determine the number of guests at the dinner party
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.
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.
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.
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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ms.black paid $32 intrest at the rate of 8% on a loan of $200. For how long was the loan?
What makes a parallelogram, a square, a rhombus, a rectangle, a kite and a trapezoid unique?
HELP QUICK PLEASE!!!!!
A proof for the Corresponding Angles Theorem is shown below. Next to each reason, choose the statement to which it applies.
Write an expression to show the sum of fourteen and triple eight.
factor the following polynomial completely 30y^6+25y^5-10y^4
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
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
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?
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:
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 ?
What is the slope of a line parallel to line B?
-1/3
2/5
5/2
5/3
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?
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.