The function for the given situation is f=60h+75.
Given that, a plumber's fees f are $75 for house calls and $60 per hour h for each hour worked.
We need to model a function for the given situation.
What is a function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.
According to the question, we can model function as follows:
f=60h+75
Therefore, the function for the given situation is f=60h+75.
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Which points are collinear with points A and B ?
The collinear points with A and B are:
- A, B, R
- B, D, T
- C, D, U
- B, S, G (where G is the centroid of AEDC).
In the given pyramid BAEDC, the collinear points with points A and B are determined by the midpoints and the line coming from B.
1. Midpoint of BA is R:
- Points A, B, and R are collinear.
2. Midpoint of BD is T:
- Points B, D, and T are collinear.
3. Midpoint of CD is U:
- Points C, D, and U are collinear.
4. Line coming from B meets at S, the midpoint of AEDC:
- Points A, E, D, C, and B are vertices of the pyramid, and S is the midpoint of the line segment connecting B to the centroid of the base AEDC.
- Therefore, points B, S, and the centroid (G) of AEDC are collinear.
In summary, the collinear points with A and B are:
- A, B, R
- B, D, T
- C, D, U
- B, S, G (where G is the centroid of AEDC).
Linda spent 3/4 of her saving on furniture and the rest on a tv.If the tv cost her $200,what were her original savings .
Let x represent the amount of savings
[tex]\frac{3}{4}[/tex] of savings minus tv equals zero
[tex]\frac{3}{4}x[/tex] - 200 = 0
[tex]\frac{3}{4}x[/tex] = 200
3x = 4(200)
[tex]x = \frac{4(200)}{3}[/tex]
x = 266.67
Answer: $266.67
Luna into a rifle for a new pair of running shoes. She purchased 20 tickets and she told that she had 20% chance of winning. How many tickets were sold?
Answer:
4 tickets were sold
Step-by-step explanation:if you have 100 of anything. 5 sets of 20=100
Answer:
Answer: x = 100
Step-by-step explanation:
(20)(x) = (5)(x) = 20/5 = 5x/5 = 100
I just answered and got it correct.
Yolanda says 105 is the same as 50 because 10x5 equals 50. What was yolanda's mistake
Answer: Yolanda's mistake is that she is assuming 105 is same as 10 x 5 .
Explanation:Here 105 represents a three digit number where 1 is at hundreds place,0 is at tens place and 5 is at once place and it can be written as the product of its factors 5 and 21 i.e 105=5×21 =21+21+21+21+21+21=105(by adding once place and tens place), where as 10×5 represents 5 times number 10 i.e.10+10+10+10+10=50(by adding once place and tens place)
So ,assuming 105 is same as 10 x 5 is her mistake.
Mr and mrs Wilson hosted their daughters wedding they paid 575
Alejandro needs to buy bird seed from the local pet store for his parrots. A
10
lb. bag of bird seed costs
$12.55.
The pet store also sells loose bird seed for
$1.49
per pound. The sales tax is already included in these prices. Alejandro wants to buy a
10
lb. bag of bird seed and some loose bird seed. If he has
$20,
how many pounds of loose bird seed can he buy after purchasing the
10
lb. bag?
First take note he only has $20 and the bag he must buy is $12.55. Also the loose seeds are $1.49 per pound.
To solve subtract 12.55 from 20
20-12.55=7.45
So after buying the 10 lb bag he has $7.45 left now divide that by 1.49
7.45/1.49=5
So after buying the 10 lb bag he can also buy 5 lb of the loose seeds!
An up-and-coming band has seen a 50% monthly increase in the the number of audience members at their concerts. At the band's first concert, there were 40 people in the audience. If this trend continues, which of the following graphs represents the number of audience members, y, after x months?
We are given that initially there were 40 people in the audience.
And an up-and-coming band has seen a 50% monthly increase in the the number of audience members at their concerts.
The number of audience members is represented by y variable and
Number of months is represented by x variable.
So, the exponential function would be
y= a(b)^x
Where a is the initial value, b is the growth factors.
a= 40 and b= 1+ 0.50 = 1.50.
Therefore,
y= 40(1.50)^x is the exponential function situation.
Let us check some point on the graph.
If we plug x=0, we get initial value 40.
If we pug x=2, we get
y=40(1.50)^2 = 40(2.25) = 90.
Graph C represents y=40 at x=0 and y=90 at x=2.
Therefore, correct option is C option.If you're on Plato the answer would be C
Help plz I WILL MARK BRAINLYST
The median is 6. I hope this helps you out.
The Answer would be 5.5 because it splits between 6 and 5 and the median would be 5.5.
in a certain chemical, the ratio of zinc to copper is 3 to 13. a jar of the chemical contains 403 grams of copper. how many grams of zinc does it contain?
HELP MEHH PLZZZ!!!!!!!!!!!!!
Answer: 93 grams Zinc
Step-by-step explanation:
3 Zinc : 13 Copper
x 31 x 31
93 Zinc, 403 Copper
or
set up a proportion, cross multiply, and solve for the variable:
[tex]\frac{Zinc}{Copper}: \frac{3}{13} = \frac{x}{403}[/tex]
3(403) = 13(x)
[tex]\frac{3(403)}{13} = x[/tex]
3(31) = x
93 = x
The amount of zinc in the chemical is determined by using the given ratio of zinc to copper and applying it to the given amount of copper. Step-by-step calculations reveal the quantity of zinc to be 93 grams.
Explanation:The question is asking for the amount of zinc in a chemical where the ratio of zinc to copper is 3:13. To find out this, we need to solve for zinc in terms of the given amount of copper.
First, understand that the ratio means for every 3 grams of zinc, there are 13 grams of copper. Now, simply set up a proportion where 3/13 = x/403. Here x is the amount of zinc in grams we are trying to find. 3/13 is the zinc to copper ratio and 403 is the known amount of copper in grams.
When you cross multiply and solve for x, you'll find that x = 3 * 403 / 13 = 93 grams. This means, if there are 403 grams of copper, then there must be "93 grams of zinc".
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Mr ramos thumb measures 4 cm.. Express the length in meters
Jessica has 1368 baseball cards Thomas has has 1633 who has more baseball cards
Total number of baseball cards Jessica has = 1368 cards.
Total number of baseball cards Thomas has = 1633 cards.
We need to find who has more baseball cards.
We can see 1633 is greater than 1368, because we have hundreds digit in 1633 is 6 and hundreds digit in 1368 is 3.
6 is greater than 3. Therefore 1633 is greater than 1368.
And finally we could say Thomas has more baseball cards than Jessica has.Answer:Thomas
Step-by-step explanation:
1633 > 1368
Suppose the population of a certain city is 5891 thousand. It is expected to decrease to 5178 thousand in 50 years. Find the percent decrease. The percent decrease is approximately
We are given
initial population is 5891
so, [tex]P_i=5891[/tex]
Population after 50 years is 5178
so, [tex]P_f=5178[/tex]
now, we can find percent error
so, we can use formula
[tex]error=\frac{P_i-P_f}{P_i}\times 100[/tex]
now, we can plug values
[tex]error=\frac{5891-5178}{5891}\times 100[/tex]
now, we can simplify it
so, we get
The percent decrease is 12.1032%.........Answer
First: work out the difference (decrease) between the two numbers you are comparing by the formula
Decrease = Original Number - New Number
In your case,
[tex]\text{Decrease}=5891-5178=713.[/tex]
Second: divide the decrease by the original number and multiply the answer by 100.
% Decrease = Decrease ÷ Original Number × 100
In your case,
[tex]\%\text{Decrease}=\dfrac{713}{5891}\cdot 100\%=12.1\%.[/tex]
Answer: The percent decrease is approximately 12.1%.
Please help asap 30 pts
629g < box + cereal < 633g
629g - 5g = 624g
633g - 5g = 628g
Answer: a. 624 < x < 628
Solve. T + 23 > 1 t > 24 t > –22 t < 24 t < –22
t + 23 > 1 subtract 23 from both sides
t + 23 - 23 > 1 - 23
t > -22
How many square units are in an office that is 18 units by 8 units?
18x8 is 144
The answer is 144 units^Squared
2/3 = 26.
Show work please. I alr know the answer but my teacher want work showed
[tex]\dfrac{2}{3}x=26\\\\x=26\div \dfrac{2}{3}=26\cdot\dfrac{3}{2}=39[/tex]
The temperature decreased overnight by 15.2°C to a temperature of –12.8°C. Suppose t represents the temperature before it decreased.
Which equation can be used to represent this situation?
A.
t – 15.2 = –12.8
B.
t + 12.8 = –15.2
C.
t – 12.8 = 15.2
D.
t – (–15.2) = –12.8
Answer:
Option a
Step-by-step explanation:
Given that temperature originally was t.
It was decreasing continuously overnight.
finally the temperature reading was -12.8 degree C
Given that it decreased by 15.2 degree C
This means original temperature -15.2 = new temperature -12.8
i.e. t-15.2 = -12.8 is the correct equation.
Option a is right.
Verify:
Solve to get t = 15.2-12.8 = 2.4
Hence when 2.4 decreases by 15.2 we get new temperature
= 2.4-15.2 = -12.8
Find a common solution for the system of equations given below:
-1/4x+y=-2
-x+4y=-8
[tex]\left\{\begin{array}{ccc}-\dfrac{1}{4}x+y=-2&|\cdot4\\-x+4y=-8\end{array}\right\\\\\left\{\begin{array}{ccc}-x+4y=-8\\-x+4y=-8\end{array}\right\\\\-x+4y=-8\ \ \ \ |+x\\4y=x-8\ \ \ \ |:4\\y=\dfrac{1}{4}x+2\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\\\y=\dfrac{1}{4}x+2\end{array}\right[/tex]
mary pitches a ball. the initial height is 4 ft and velocity 55 ft per second. when will the ball hit the ground?
Answer:
t = 3.5 sec
Step-by-step explanation:
The equation that represents the position of the ball as a function of time is the following:
[tex]h(t) =P_{o} + V_{o}t+\frac{1}{2}2at^2[/tex]
Where:
[tex]P_{o}[/tex] = Initial position of the ball (4 feet tall)
[tex]V_{0}[/tex] = Initial speed of the ball (55feet / s)
a = acceleration (9.8 [tex]\frac{m}{s^2}[/tex], or in this case 32.16[tex]\frac{ft}{s^2}[/tex])
t = time in seconds
Then we want to know how long it takes to get to the ground, for this we equal h (t) = 0 and clear t.
So:
[tex]0 = 4 + 55t -16.08t ^ 2[/tex]
Solving the second degree equation we have:
[tex]\frac{-b+\sqrt{b ^ 2-4ac}}{2a} \\ \frac{-b-\sqrt{b ^ 2-4ac}}{2a}[/tex]
[tex]\frac{-55+\sqrt{55^2-4 (-16.08) 4}}{2 (-16.08)}= -0.0712\\\frac{-55-\sqrt{55^2-4 (-16.08) 4}}{2 (-16.08)} = 3.492[/tex]
t = -0.071 sec
t = 3.5 sec
We must take the positive solution.
So:
t = 3.5 sec
Here is an addition sentence.
7 + 4 = 11
Choose the related addition sentence that shows the commutative property of addition..
A.
4 + 7 = 11
B.
11 – 4 = 7
C.
11 = 7 + 4
D.
8 + 3 = 11
For this case, we have the expression given by:
[tex]a + b = c\\[/tex]
This expression turns out to be generic.
The commutative property of the addition states that the order of the addends does not alter the sum. Thus it is concluded that the previous expression above can be written as:
[tex]b + a = c\\[/tex]
In this way [tex]7 + 4 = 11[/tex], applying the commutative property of the addition, it can be written as:
[tex]4 + 7 = 11\\[/tex]
Answer:
Option A
How Do you round 4,398,202 to nearest 100
Answer: 4,398,200
Step-by-step explanation:
4, 398, 202
the underlined 2 is in the 100's place. look at the number to the right of it. If that number is greater than or equal to 5, then the 2 is rounded up. Otherwise, the 2 remains the same.
The number to the right of the underlined 2 is 0, so the 2 remains the same. All digits to the right will become 0s.
Of the 36 students in the environmental club, 15 or boys and 21 are girls. The president of the club wants to add more boys so that the boys represent 50% of the students in the club.
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1) Given
2) m∠1 + m∠2 = 90°
3) BD bisects ∠ADC
4) definition of angle bisector
5) definition of congruency
6) m∠1 + m∠3 = 90°
7) ∠1 is complementary to ∠3 (7) definition of complementary
If there is a drop down box, and my answer is not an option, type in the options in the comment box and I will let you know which theorems (or definitions) are the same as my answer.
how did you gett such a hard question (yes im asking in an awnser box)
The volume of the cube below is 1/8cm^2 . What is the value of x?
We are given
edge of cube =x
we know that formula for volume of cube
[tex]V=x^3[/tex]
we are given
[tex]V=\frac{1}{8} cm^3[/tex]
we can plug value
[tex]x^3=\frac{1}{8} cm^3[/tex]
now, we can solve for x
[tex]\sqrt[3]{x^3} =\sqrt[3]{\frac{1}{8} cm^3 }[/tex]
[tex]x=\frac{1}{2} cm[/tex]............Answer
Answer:
1/2 cm
Step-by-step explanation:
In the great flood of 1993, the Mississippi River was so high that it caused the Illinois River to flow backward. If the Illinois River flowed at the rate of -1500 feet per hour, how far would the water travel in 48 hours?
Mary has a planting pot with a circumference of 92 cm. If a plants' directions state that it must be planted directly in the middle of the pot, what would be the exact measurement? Hint: Find the radius.
24.64 cm
14.64 cm
19.64 cm
22.64 cm
Answer:
14.64 cm
Step-by-step explanation:
this problem is finding radius of a circle from the circumference given.
Circumference of a circle = 2(3.14) r
Using the above we can find one if we know the other. In our case we know circumference and calculate radius.
Circumference = 2(3.14)r= 92 cm
Hence r = 92/2(3.14) = 14.6497cm
apprxoximately 14.64 cm is close to the answer
Hence answer is 14.64 cm.
Answer:
14.64 cm
Step-by-step explanation:
The circumference of a planting pot = 92 cm
To find the measurement of the plant which is planted directly planted in the middle of the pot, we need to find the radius of the planting pot.
We know that the formula of the circumference of a circle is:
Circumference = [tex]2\pi r[/tex]
Therefore, putting the value of the circumference in the formula to get:
92 = 2 x 3.14 x r
r = 92 / (3.12 x 2) = 14.64 cm
Therefore the plant is 14.64 cm long.
A standard brick is 3.625 inches wide, 2.25 inches high, and 7.625 inches long. How many bricks could be in a pallet of bricks that measures 4 feet on all sides? (One cubic foot is 12×12×12 cubic inches.)
A. 1,757
B. 1,974
C. 1,709
D. 1,778
Answer: Option D. 1,778
Solution:
Standard brick:
Width: w=3.625 in
Height: h=2.25 in
Length: l=7.625 in
Volumen of one standard brick: v
v=w*h*l
v=(3.625 in)*(2.25 in)*(7.625 in)
v=62.19140625 in^3
Pallet of bricks:
Side: s=4 feet
s=(4 feet)*(12 in / 1 feet)→s=48 in
Volume of a pallet of bricks: V=s^3
V=(48 in)^3
V=110,592 in^3
Number of bricks could be in a pallet: n
n=V/v
n=(110,592 in^3) / (62.19140625 in^3)
n=1,778.252119
n=1,778
Can someone confirm if this is the answer or not?
30 POINTS FOR WHO EVER GIVE ME THE RIGHT ANSWER
Answer:
False.
Step-by-step explanation:
[tex] \dfrac{1}{x^{-3}} = x^3 [/tex]
[tex] x^3 [/tex] is a simplified expression. The given expression is not simplified.
A ferry traveled \dfrac16 6 1 start fraction, 1, divided by, 6, end fraction of the distance between two ports in \dfrac37 7 3 start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
Answer:
The ferry can travel [tex]\frac{7}{18}[/tex] of the distance between the two ports in one hour.
Step-by-step explanation:
A ferry traveled [tex]\frac{1}{6}[/tex] of the distance between two ports in [tex]\frac{3}{7}[/tex] hour.
Suppose, the ferry traveled [tex]x[/tex] of the distance between the two ports in one hour.
So, the equation according to the ratio of "distance" to "time" will be.......
[tex]\frac{\frac{1}{6}}{\frac{3}{7}} =\frac{x}{1} \\ \\ x=\frac{1}{6}\times \frac{7}{3}= \frac{7}{18}[/tex]
Thus, the ferry can travel [tex]\frac{7}{18}[/tex] of the distance between the two ports in one hour.
Sara spent twice as much at the department store if Sara spent 88 how much did Jenni spend
Answer:
Jenni spent 44
Step-by-step explanation:
Let the amount spent by Jenni be x
Let the amount spent by Sara be 2x which also equals 88
2x = 88
x = ?
Cross multiplying gives:
x/2x × 88 = 44
Jenni therefore spent 44