Answer:
2/3
Step-by-step explanation:
3(y - 1) = 2x + 2
3y - 3 = 2x + 2
3y = 2x + 5
3y/3 = 2x/3 + 5/3
y = 2/3x + 5/3
Does that help?
An animal shelter spends $2.00 per day to care for each bird and $5.00 per day to care for each cat. Gabriel noticed that the shelter spent $44.00 caring for birds and cats on Friday. Gabriel found a record showing that there were a total of 13 birds and cats on Friday. How many birds were at the shelter on Friday?
Answer:
7 birds
Step-by-step explanation:
Let b = number of birds
c = number of cats
We know there were 13 birds and cats
b+c =13
It is $2 per bird and $5 per cat for a total of $44
2b+5c =44
Solve b+c =13 for c by subtracting b from each side
c = 13-b
Now we can substitute this into the second equation
2b+5c =44
2b + 5(13-b) =44
Now distribute
2b+65 -5b = 44
Combine like terms
-3b +65 =44
Subtract 65 from each side
-3b +65-65 =44-65
-3b = -21
Divide each side by -3
-3b/-3 = -21/-3
b=7
There were 7 birds
We could also find the number of cats
c =13-7
c =6
Answer:
7 birds
Step-by-step explanation:
No. of birds: x
No. of cats: y
2x + 5y = 44
x + y = 13
x = 13 - y
2(13 - y) + 5y = 44
26 - 2y + 5y = 44
3y = 18
y = 6
x = 13 - 6
x = 7
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?
A) 0.1
B) 1/2
C) 1
D) 10
What is the ratio for the surface areas of the cones shown below, given that
they are similar and that the ratio of their radii and altitudes is 4:3?
---
--
A. 16:9
B. 9:16
C. 64:27
D. 27:64
The ratio of the surface areas of the cone shown is 16 : 9.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Given are two cones.
Also given that,
Ratio of the radii of the cones = 4 : 3
It is given that both cones are similar figures.
So scale factor = 4/3
Surface area of a cone = πr² + πr√h²+r²
Now the surface area is proportional to the square of the radii of the cone.
So ratio of surface area = 4² / 3² = 16 / 9
Hence ratio of the surface area of the cones is 16 : 9.
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PLEASE I NEED HELP WITH THIS!!!!
Answer:
oh yeah thats the 3rd one
Step-by-step explanation:
What is the slope of the line 6x+10y=8 ?
Answer:
-3/5
Step-by-step explanation:
6x + 10y = 8
10y = -6x + 8
10y/10 = -6x/10 + 8/10
y = -3/5x + 4/5
Does that help?
The top two nets represent the triangular prisms that are attached to the bases of a rectangular prism. The composite figure is composed of all three prisms. The shaded areas are faces that are shared between the prisms. What is the total surface area of the composite figure?
78 square units
144 square units
282 square units
342 square units
Answer:
282 square units
Step-by-step explanation:
I just answered this question
The total surface area of the composite figure is 282 square units. Thus, the correct option is C.
What is the area?The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.
The top two nets are triangular prisms connected to the bases of a rectangular prism. The composite image is made up of all three prisms. The dark sections represent faces shared by the prisms.
The total surface area of the composite figure is calculated as,
A = 4(1/2 x 3 x 4) + 2(5 x 10) + 2(4 x 10) + 2(3 x 3) + 2(3 x 10)
A = 24 + 100 + 80 + 18 + 60
A = 282 square units
Thus, the correct option is C.
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1 point
The area of an airplane's wings is related to the airplane's lifting force,
which holds the airplane in the air. The table below lists several wing areas
and the corresponding lifting forces. The ratio of lifting force to area is
equivalent for all pairs in the table. What are the values of x and y?*
AIRPLANE LIFTING FORCE
Area of Wings Lifting Force
(square feet) (pounds)
125
1,875
150
175
2,625
250
3,750
x
5,625
420
2,250
O
x = 375 square feet and y = 7,500 pounds
O
x= 335 square feet and y = 6,300 pounds
O
x= 335 square feet and y = 7,500 pounds
O
x = 375 square feet and y = 6,300 pounds
Answer:
x = 375 square feet and y = 6,300 pounds.
Explanation:
The table is:
AIRPLANE LIFTING FORCE
Area of Wings Lifting Force
(square feet) (pounds)
125 1,875
150 2,250
175 2,625
250 3,750
x 5,625
420 y
The ratio of lifting force to the area is equivalent for all pairs in the table. What are the values of x and y?
1. Calculate x:
Ratio of lifting force to the area for the first pair (row):
125/1,875Ratio of lifting force to area for the pair with x:
x/5,625Set the proportion:
Equal the two ratios
x/5,625 = 125/1,875Multiply both sides by 5,625 (multiplication property of equalities):
x = 5,625 × 125/1,875x = 375 ← answer2. Calculate y:
You can use the same know ratio for the first pair: 125/1,875
And set the corresponding proportion, with y:
420/y = 125/1,875Invert both sides:
y/420 = 1,875/125Multiply both sides by 420
y = 420 × 1,875/125 y = 6,300 ← answerThe answer is x = 375 square feet and y = 6,300 pounds.
Suppose there is a simple index of three stocks, stock ABC, stock XYZ, and
stock QRS. Stock ABC opens on day 1 with 4000 shares at $3.15 per share.
Stock XYZ opens on day 1 with 5000 shares at $4.30 per share. Stock QRS
opens on day 1 with 6000 shares at $4.60 per share. The price of stock ABC
on day 8 begins at $3.50. The price of stock XYZ on day 8 begins at $3.90.
Stock QRS opens on day 8 with a price of $4.50 per share. Assume that each
stock has the same number of shares that it opened with on day 1. What is
the rate of change of this simple index over 1 week?
O A. 1.9%
O B. 2.0%
O C. -1.9%
O D. -2.0%
Answer: C -1.9
Step-by-step explanation:
The rate of change of this simple index over 1 week given the change in the stock prices is -1.9%.
What is the rate of change?
The rate of change is the difference in the total value of the simple index.
Total value of the simple index at day 1 = (4000 x $3.15) + (5000 x $4.30) + (6000 x $4.60) = $61,700
Total value of the simple index at day 8 = (4000 x $3.50) + (5000 x $3.90) + (6000 x $4.50) = $60,500
Rate of change = (60,500 / 61700) - 1 = -1.9%
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what is 14991.1 rounded to the nearest hundredth
Answer:
15000.0
Step-by-step explanation:
Answer:
Step 1: Round to the nearest hundredth
It is already rounded to the tenth so rounded to the hundredth would just add a 0.
14991.10
Answer: 14991.10
If you meant hundreds:
14991.10
Since the tens place is greater or equal to 5, you round up the hundreds place. This will make the thousands place go up by one.
14991.10
15000
sorry if it’s hard to see . can anybody help me with this ?
Answer:
5
Step-by-step explanation:
4/4 crosses out and 20/4=5 so x=5
Answer:
x = 5
Step-by-step explanation:
since the work is already done for you, all you have to do is divide 20 by 4, which gives you 5.
you can also check this answer by multiplying 4 by 5, which would give you 20, further proving the answer.
The Smiths spend 8% of their budget on entertainment. Their total budget this year is $3,000 more than last year, and this year they plan to spend $3,600 on entertainment. What was their total budget last year?
Answer:
$6600
Step-by-step explanation:
3000+3600=6600
Answer:
Their total budget was $42000 last year.
Step-by-step explanation:
8% = 0.08
1.) 0.08( x + 3000 ) = 3600
2.) Distribute:
0.08x + 240 = 3600
3.) Use inverse operation to solve. Subtract 240 from each side:
0.08x + 240 = 3600
- 240 = - 240
0.08x = 3360
3.) divide 0.08 from each side:
0.08x = 3360
x = 42000
Theo's Survey Results
Eye Color
Brown Blue
Boy
25
25
Gender
Girl
25
25
Theo recorded the gender and eye color of students walking in the hallway at his middle school. What is the
experimental probability in simplest form that the next student he sees will be a boy with brown eyes?
Answer:
25% or 1/4
Step-by-step explanation:
There altogether 100 boys and girls together and the probability of one color would be 25. Therefore 25/100 would your fraction but it has to be simplified so then the answer would be 1/4
Find the inverse of function f.
f(x) = 1/3 - 1/21x
Answer:f⁻ (x) = 7 - 21 x.
We can also write it as:
y = 1/3 - 1/21 x
1 / 21 x = 1 / 3 - y
x = 7 - 21
To find the inverse of the function f(x) = 1/3 - 1/21x, interchange x and y in the equation, solve for y, and denote it as the inverse function, resulting in [tex]f^-1(x) = 7 - 21x[/tex].
The student is asking to find the inverse of the function f(x) = 1/3 - 1/21x. To find the inverse function, we need to first rewrite the function in the form y = 1/3 - 1/21x. Next, we switch x and y to get x = 1/3 - 1/21y. Then, solve for y, giving us the inverse. The steps are:
Replace f(x) with y: y = 1/3 - 1/21xInterchange x and y: x = 1/3 - 1/21yMultiply both sides by 21 to clear the fraction: 21x = 7 - yAdd y to both sides and subtract 7 from both sides: y + 21x = 7Isolate y: y = 7 - 21xFinally, replace y with f-1(x) to denote the inverse function:f-1(x) = 7 - 21x
An athlete can run 9 kilometers in 1 hour. If the athlete runs at that same average speed for 30 minutes, how far will the athlete travel? *
1 point
A 18 kilometers
B 9 kilometers
C 4.5 kilometers
D It travels right at an increasing speed.
The athlete can cover 4.5 km in 30 minutes. Hence, option C is correct.
Important information:
An athlete can run 9 kilometers in 1 hour.We need to find the distance covered by the athlete in 30 minutes.
Average speed:We know that 1 hour = 60 minutes. So,
The distance covered in 60 minutes is 9 km.
The distance covered in 1 minute is [tex]\dfrac{9}{60}[/tex] km.
The distance covered in 30 minutes is [tex]\dfrac{9}{60}\times 30=4.5[/tex] km.
Therefore, the athlete can cover 4.5 km in 30 minutes. Hence, option C is correct.
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Lynn put 3 7/8 gallons of gas in her gas tank. if there are now 18 1/6 gallons in the tank, how many gallons did she start with?? Please I need an answer ASAP worth 25 points!!!!
Lynn starts with 14.3 gallons in her gas tank.
What is the Subtraction operation?Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
She put 3 7/8 gallons of gas in her gas tank. if there are now 18 1/6 gallons in the tank.
We have to determine the number of gallons did she start with
As per the given question, the required evaluation would be as:
Initial gallons = current gallons - put gallons
Initial gallons = 18 1/6 - 3 7/8
Convert the improper fractions into decimals,
Initial gallons = 18.167 - 3.875
Apply the subtraction operation, and we get
Initial gallons = 14.292 ≈ 14.3
Therefore, she starts with 14.3 gallons in her gas tank.
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A penny is tossed and a number cube is rolled. Find probability P(tails and 3). Please select one answer.
1/12
1/2
1/6
Answer:
the probability is 1/12
Step-by-step explanation:
The probability, P(Tails) to get tails is equal to:
[tex]P(Tails)=\frac{1}{2}[/tex]
Because a penny have two possible options heads or tails and tails is one option.
Additionally, the probability P(3) that the number cube get a 3 is equal to:
[tex]P(3)=\frac{1}{6}[/tex]
Because the cube have 6 possible options and 3 is one option.
Now, the probability P(tails and 3) is calculated as a multiplication of P(tails) and P(3). then, P(tails and 3) is equal to:
P(tails and 3) [tex]=\frac{1}{2}*\frac{1}{6}=\frac{1}{12}[/tex]
Answer:
1/12
Step-by-step explanation:
First we calculate the probability of the coin tossed being a tails.
The coin has two sides (heads and tails), so the probability of each case is 1/2, so the probabilty of having a tails is 1/2
For the number cube, we have six possibilities, so the probability of having a number 3 is 1/6
Now, to find the final probability P(tails and 3) we just need to multiply both probabilities:
P(tails and 3) = P(tails) * P(3) = (1/2) * (1/6) = 1/12
What is the answer for 10 and 11 step by step. Please
Answer:
sOoRrY bUt i cAnT rEaD
4(x-2)=3(x-3) what is the answer
The answer is -1
Step-by-step explanation:
A room has a rectangular floor that is 15 feet by 21 feet. What is the area of the floor in square yards?
A. 24
B. 35
C. 36
D. 105
E. 144
Answer:
B. 35
Step-by-step explanation:
1. Multiply 15 by 21 to get 315 ft.
2. Convert square feet to square yards to get 35
3. There are 3 feet in ONE yard. The question asks you to convert the area from SQUARE feet to SQUARE yards. Squared means two. Three feet (or one yard) doubled is 9, so divide 315ft by 9.
4. 315 divided by 9 gives you 35
(This answer is correct according to the Official 2020-2021 ACT Practice Test answer sheet)
The area of the floor in square yards will be 315 square feet's.
What is the area of square and a rectangle?
The area of the square and rectangle is -
Square = [x]² {x is the side of a square]
Rectangle = L x B {L is the length and B is breadth}
Given is a room has a rectangular floor that is 15 feet by 21 feet.
We have room that has a rectangular floor that is 15 feet by 21 feet.
The area of the rectangle will be -
A = 15 x 21
A = 315 square feet's.
Therefore, the area of the floor in square yards will be 315 square feet's.
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What is the domain of F(x) = In(x)?
A. all real numbers except 0
B. all real numbers greater than 0
C. all real numbers
D. all real numbers less than
Answer: all real numbers expect ZERO
Step-by-step explanation:
find the area of that shape please and show work
Given:
AB = 9 in, BC = 2 in
DE = 3 in, EF = 3 in
To find:
The area of the shape
Solution:
ABCH is a rectangle.
Area of rectangle = length × width
= AB × BC
= 9 × 2
Area of ABCH = 18 in²
GDEF is a square.
Area of square = side × side
= DE × EF
= 3 × 3
Area of GDEF = 9 in²
Area of the shape = Area of ABCH + Area of GDEF
= 18 in² + 9 in²
= 27 in²
The area of the shape is 27 in².
2. Evaluate 5xy
if x = 2 and y = 6.
Answer:
[tex]5(2)(6) = 60[/tex]
Kishuana rode her bike for 35 minutes each on Monday, Wednesday, and Saturday and 55 minutes each on Tuesday and Thursday. Write an expression that shows the total amount of time she spent riding her bike. Then evaluate the expression.
order of operations
Answer:
35a+55b=c
35x3=105
55x2=110
105+110=215
c=215
she rode her bike for 215 mins= 3 hours and 58 mins
Step-by-step explanation:
What is the area of the circle whose diameter is 16 ft?
201.1 sq ft
802.2 sq ft
50.3 sq ft
Answer:
Step-by-step explanation:
The area of a circle is
[tex]A=\pi r^2[/tex]
We are given the diameter, but need the radius. The radius is half the diameter, so the radius is 8 feet. Plugging into the formula and using 3.14 for π:
A = (3.14)(64) so
A = 200.96 sq feet which rounds to 201. I guess that's the first choice there, but not quite exact...
Final answer:
The area of the circle with a diameter of 16 ft is (Option A) 201.1 sq ft.
Explanation:
The area of a circle can be found using the formula A = πr², where A is the area and r is the radius. However, in this case, we are given the diameter instead of the radius. The diameter is twice the length of the radius, so we can calculate the radius by dividing the diameter by 2. Given that the diameter of the circle is 16 ft, the radius would be 16/2 = 8 ft.
Now, we can use the formula A = πr² to find the area. Plugging in the radius value, we get A = π(8 ft)² = π(64 ft²) ≈ 201.1 sq ft.
if tan 0= -3/8 which expression is equivalent to cot0?
Answer:
-8/3
Step-by-step explanation:
should be -8/3
cotangent is the reciprocal of tangent
tan 0 = -3/8
cot 0 = 1/tan 0 = 1 / (-3/8) = 8/-3 = -8/3
Answer: 1/-3/8
Step-by-step explanation:
Circumference and Area of a circle
#5 please
Answer: the circumference is 25.13 and the area is 50.26 if rounding up then 50.27
Step-by-step explanation: to find circumference it is 2piR and to find the area it is piR^2
f(1)=−3
f(n)=2⋅f(n−1)+1
f(2)=
Answer:
-5
Step-by-step explanation:
f(2) = 2 * f(2-1) + 1
f(2) = 2 * f(1) + 1
f(2) = 2(-3) + 1
f(2) = (-6) + 1
f(2) = -5
anyone know how to do this?
The dot plot below shows the number of books 26 students read in a month:
Dot plot labeled Number of Books Read shows 10 dots over 0, 7 dots over 1, 3 dots over 2, 2 dots over 3, 1 dot over 4, and 3 dots over 10.
Is the median or the mean a better center for this data, and why?
Mean; because the data is skewed and there are outliers
Mean; because the data is symmetric and there are outliers
Median; because the data is skewed and there are outliers
Median; because the data is symmetric and there are outliers
Francine is selling ice cream from her shack on the ocean. She opens the shack
with 500 servings of ice cream. During the day she sells enough ice cream to
decrease her total ice cream by 65%. How many servings of ice cream does
Francine have left? *
Answer:
325 servings
Step-by-step explanation: