Answer:
1. Shorter Side: 4
2. Longer Side: 7
3. Hypotenuse: [tex]\sqrt{65}[/tex]
Step-by-step explanation:
[tex]4^{2} +7^{2} =65[/tex]
D. 17 °F 2. Franky earns $(100+ x) daily for five days, $(175 + 2x) for two days, and $(75 + 2x) for three days. If the average amount she earns is $80 per day, what is the median amount she earned?
The median total of amount Franky earned is A = $81.67 per day.
Given data ,
For the first five days: $(100 + x) per day
For the next two days: $(175 + 2x) per day
For the final three days: $(75 + 2x) per day
Now , the average amount she earns is $80 per day
So , Average earnings = Total earnings / Total number of days
Average earnings = [(100 + x) * 5 + (175 + 2x) * 2 + (75 + 2x) * 3] / 10
Simplifying the equation:
80 = [500 + 5x + 350 + 4x + 225 + 6x] / 10
Multiplying both sides by 10:
800 = 1075 + 15x
Subtracting 1075 from both sides:
15x = -275
Dividing both sides by 15:
x = -18.33
For the first five days: $(100 - 18.33) = $81.67 per day
For the next two days: $(175 + 2*(-18.33)) = $138.34 per day
For the final three days: $(75 + 2*(-18.33)) = $38.34 per day
Arranging the earnings in ascending order: $38.34, $38.34, $38.34, $81.67, $81.67, $81.67, $81.67, $138.34, $138.34
The median is the middle value when the earnings are arranged in ascending order. In this case, the middle value is $81.67
Hence , the median is $81.67
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Since my uncles farmyeard apperas to be overrun with gos and chickens i asked him hom many of each did he have he responded that his dog and chicked had a total of 148 legs and 60 heads. hime mmay of each does he have
There are 14 dogs and 46 chickens in the farmyard.
The supposition that there are d dogs and c chickens.
Each chicken has two legs, but each dog has four.
Consequently, the total number of legs may be written as follows:
4d + 2c
Since we are aware that there are 148 legs in total, we can construct the following equation:
4d + 2c = 148
We may create another equation since we know that there are a total of 60 heads (dogs and chickens):
d + c = 60
Now that we have two equations with two variables, we may answer them both at the same time.
2d + 2c = 120 is the result of multiplying the second equation by two.
When we deduct this from the first equation, we obtain 2d = 28.
So, d = 14.
Reintroducing this into the second equation, we get:
14 + c = 60
So, c = 46.
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Solution for
Y= x+3
Y= 3x+1
Starting with the two equations:
Y = x + 3 (1)
Y = 3x + 1 (2)
We can solve for x and y by equating equation (1) and (2) and solving for x.
x + 3 = 3x + 1
2x = 2
x = 1
Now we can substitute x = 1 into either equation (1) or (2) to solve for y.
Using equation (1):
Y = x + 3
Y = 1 + 3
Y = 4
Therefore, the solution for the system of equations is:
x = 1, y = 4
radius of 18 feet and a central angle of 52° is shown below. Which of the following is the closest to the length of the arc from point C to point D?
The closest length to the arc from point C to point D is 16.34 ft (option c).
To find the length of the arc from point C to point D, we need to calculate the circumference of the circle and then find the fraction of the circumference represented by the central angle.
The circumference of a circle can be calculated using the formula:
Circumference = 2 × π × radius
Given the radius of 18 feet, the circumference is:
Circumference = 2 × π × 18 = 36π feet
To find the length of the arc, we need to find the fraction of the circumference represented by the central angle of 52°. The fraction is calculated by dividing the central angle by 360° and then multiplying it by the circumference.
Length of the arc = (Central angle / 360°) * Circumference
Length of the arc = (52° / 360°) × 36π
Length of the arc = (13/90) × 36π
Length of the arc = 468π / 90
Length of the arc ≈ 16.41 ft
Among the given options, the closest length to the arc from point C to point D is 16.34 ft (option c).
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6 sin θ=5 to the nearest 0.1°
The value of the equation 6 sinθ=5 for θ is 56.4 degrees
How to evaluate the equationFrom the question, we have the following parameters that can be used in our computation:
6 sinθ=5
Express the equation properly
So, we have the following representation
6 sin(θ) = 5
Divide both sides of the equation by 6
This gives
sin(θ) = 5/6
Evaluate the quotient
sin(θ) = 0.833
Take the arc sin of both sides
θ = sin⁻¹(0.833)
Evaluate
θ = 56.4
Hence, the value of the equation for θ is 56.4 degrees
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Complete question
Approximate θ in the equation, to the nearest 0.1 degrees
6 sin(θ) = 5
From a point X, the bearing of a flag pole is 280⁰, from another point Y due south of X the bearing of the flag pole is 330⁰ . if the angle of elevation of the top of the flag pole from Y is 60⁰ and the distance (X,Y) is 92km . Calculate how far Y is from the flag pole
Answer: 37km
Step-by-step explanation:
The carrying capacity of a drain pipe is directly proportional to the area of its cross section.If cylindrical pipe drain can carry 36L/sec,determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second .
Step-by-step explanation:
x and y are directly proportional means that
y = kx
y grows with the same factor k applied to x.
the area of a circle (the cross section of a cylindrical pipe) is
pi × r²
r being the radius (which is half of the diameter).
so, the area in terms of the diameter is
pi × (d/2)² = pi × d²/4
so, we know
36 correlates to pi × (d small)²/4
60 correlates to pi × (d large)²/4
therefore (directly proportional),
d small² = 36×4/pi
d small = 12/sqrt(pi)
d large² = 60×4/pi
d large = sqrt(4×15×4/pi) = 4×sqrt(15/pi)
the difference between large and small diameter (increase from small to large) is then
4×sqrt(15/pi) - 12/sqrt(pi)
d small = 100%
1% = 100%/100 = 12/sqrt(pi) / 100 = 12/(100sqrt(pi))
the % of the diameter increase is then
increase/1% =
(4×sqrt(15/pi) - 12/sqrt(pi)) / 12/(100sqrt(pi)) =
= (400sqrt(pi)×sqrt(15/pi) - 1200sqrt(pi)/sqrt(pi)) / 12 =
= (400×sqrt(15) - 1200) / 12 = 100×sqrt(15)/3 - 100 =
= 100×(sqrt(15)/3 - 1) = 29.09944487...% ≈ 29.1%
the diameter has to increase by about 29.1%, so that the pipe can carry 60 liters per second.
please consider : only the area of the cross section and the carrying capacity are directly proportional.
the diameter of the cross section and the area of the cross section are NOT directly proportional.
they have the pi×(d/2)² relationship.
and so, while the capacity and the cycle area both increase by the same factor, the impact on the diameter (or radius) is different.
so, for capacity and area we have
60 = k×36
k = 60/36 = 5/3 = 1.66666666...
and therefore both increase by 66.66666...%.
but because of the square relation between diameter and cross section area, the diameter only increases by 29.1%.
Britney is a volunteer at the Westside Library. She collects the books that come down the
chute from the outside drop-off and puts them on the library shelves. Of the books that have
come down the chute so far today, 41 have been fiction and 23 have been nonfiction.
Based on the data, estimate how many of the next 100 books that come down the chute will
be nonfiction.
Based on the given data, we can estimate that approximately 36 out of the next 100 books that come down the chute will be nonfiction.
To estimate the number of nonfiction books out of the next 100, we can use the ratio of nonfiction to the total number of books that came down the chute so far today.
The total number of books that came down the chute so far is:
41 (fiction) + 23 (nonfiction) = 64
The ratio of nonfiction books to the total number of books in library is:
[tex]23/64[/tex]
To estimate the number of nonfiction books out of the next 100, we can multiply the ratio by 100:
[tex](23/64)*100=35.9375[/tex]
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The perimeter of a right triangle is equal to 4x + 3. If two sides of the triangle measure: x + 7 and x – 7, what is the measurement of the hypotenuse?
If two sides of the triangle measure: x + 7 and x – 7, the measurement of the hypotenuse is 2x + 3.
In a right triangle, the hypotenuse is the side opposite the right angle and it is the longest side. We can use the Pythagorean theorem to relate the sides of the right triangle:
a² + b² = c²
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.
We are given that the perimeter of the triangle is 4x + 3. The perimeter of a triangle is the sum of the lengths of its sides, so we can write:
a + b + c = 4x + 3
Substituting the given side lengths, we get:
(x + 7) + (x - 7) + c = 4x + 3
Simplifying, we get:
2x + c = 4x + 3 - 7 + 7
2x + c = 4x + 3
Solving for c, we get:
c = 2x + 3
We did not need to use the Pythagorean theorem in this problem, as we were only asked for the measurement of the hypotenuse in terms of x.
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Graph by completing the square x2-2x+y2+6y-6=0
The equation in the standard form of a circle and find the centre and radius:
(x - 1)²/31 + (y + 3)²/31/3 = 1
To graph by completing the square, we need to rearrange the equation so that it has the form:
(x - h)² + (y - k)² = r²
Starting with x² - 2x + y² + 6y - 6 = 0:
First, we can factor out a 2 from the x terms and a 6 from the y terms:
2(x² - 2x) + 6(y² + 6y) - 6 = 0
Next, we need to complete the square for the x and y terms:
2(x² - 2x + 1) + 6(y² + 6y + 9) - 6 = 2(1) + 6(9)
Simplifying, we get:
2(x - 1)² + 6(y + 3)² = 62
Now we can rewrite the equation in the standard form of a circle and find the centre and radius:
(x - 1)²/31 + (y + 3)²/31/3 = 1
The centre of the circle is (1, -3), and the radius is √(31/3).
The graph is attached with the answer below.
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10. Kipp constructed a pentagonal pyramid for his social studies report. The base had an area of 12 cm². It took 48 cubic centimeters of clay to make his model. Find the height of the pyramid.
We can use the formula for the volume of a pentagonal pyramid to solve this problem:
Volume = (1/3) × Base Area × Height
We know that the base area is 12 cm² and the volume is 48 cubic centimeters. We can substitute these values into the formula and solve for the height:
48 = (1/3) × 12 × Height
Multiplying both sides by 3 gives:
144 = 12 × Height
Dividing both sides by 12 gives:
Height = 12
Therefore, the height of the pentagonal pyramid is 12 centimeters.
A shirt manufacturer pays a worker $0.47 for each acceptable shirt inspected under the prescribed job description. If the worker had the following work record, find the gross earnings for the week: Monday, 250 shirts; Tuesday, 300 shirts; Wednesday, 178 shirts; Thursday, 326 shirts; Friday, 296 shirts
Can someone answer this question
The options 2nd and 3rd are the monomials with degree 2.
Given are the expressions we need to find the monomials with degree 2.
So,
The general form of a monomial with degree 2 is:
ax²
The highest exponent of a polynomial's variable(s) in any of its terms is referred to as the polynomial's degree in mathematics.
It controls the polynomial's behavior and complexity.
A non-negative integer is used to represent the degree.
And,
A monomial is a mathematical expression consisting of a single term. It is composed of a coefficient multiplied by one or more variables raised to non-negative integer exponents.
Here, the monomials can be 2x² and x²
Hence the options 2nd and 3rd are the monomials with degree 2.
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How many turning points are in the graph of the polynomial function?
4 turning points
5 turning points
6 turning points
7 turning points
Given f(x) = x³ - 6x + k, and the remainder when f(x) is divided by x - 1 is 14, then what is the value of k?
Answer: 19
Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).
Hope this helps!
A and B are two cylinders that are mathematically similar.
The area of the cross-section
of cylinder A is 18 cm².
Work out the volume of cylinder B.
Optional working
+
18 cm²
A
Answ cm³
5 cm
B
10 cm
The volume of cylinder B can be calculated using the concept of similarity between the cylinders and the relationship between their areas and volumes. Therefore, the volume of cylinder B is approximately 135.346 cm³.
Given that cylinders A and B are mathematically similar, we can establish a ratio between their corresponding measurements. In this case, we are given the area of the cross-section of cylinder A, which is 18 cm², and the dimensions of cylinder B, which has a height of 10 cm and an unknown radius.
To find the volume of cylinder B, we need to determine the corresponding measurements of its cross-section. Since the cylinders are similar, the ratio of their areas is equal to the square of the ratio of their corresponding linear measurements.
Let's assume that the radius of cylinder B is 'r'. Since the height of cylinder B is given as 10 cm, we can calculate the area of its cross-section using the formula for the area of a circle: A = πr².
The ratio of the areas of the cross-sections of cylinders A and B can be expressed as (Area of A) / (Area of B) = 18 / (πr²).
Since the height of cylinder B is twice that of cylinder A (10 cm compared to 5 cm), the ratio of their corresponding linear measurements is 2:1.
Therefore, the ratio of the areas is (2:1)² = 4:1.
Setting up the equation, we have 18 / (πr²) = 4/1.
By rearranging the equation, we can solve for the radius 'r' of cylinder B:
18 = (4/1) * (πr²)
18 = 4πr²
r² = 18 / (4π)
r² = 4.545
r ≈ 2.132 cm
Now that we have the radius of cylinder B, we can calculate its volume using the formula for the volume of a cylinder: V = πr²h.
V = π * (2.132)² * 10
V ≈ 135.346 cm³
Therefore, the volume of cylinder B is approximately 135.346 cm³.
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Question 2 (Multiple Choice Worth 1 points)
(06.02 MC)
Simplify (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab).
O-a³b-8ab2 + 10ab
O-a³b-8ab²
07a³b-8ab² + 10ab
The simplified expression of (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) is (b) -a³b - 8ab²
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab)
Open the bracket
So, we have
(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = 3a³b - 4ab² + 5ab -4a³b - 4ab² - 5ab
Evaluate the like terms
So, we have
(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = -a³b - 8ab²
Hence, the simplified expression is (b) -a³b - 8ab²
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Please help me with this statistics question. Photo attached
a) The data in the above table about the statistics class asked the city where they live are b) Quantitative and Discrete.
b) The completion of the frequency distribution for the data is as follows:
Class Frequency
Fort Pierce 7
Port St. Lucie 6
Vero Beach 7
Sebastian 4
Okeechobee 6
Total 30
c) The completion of relative frequency and percentage distribution for the data is as follows:
Class Frequency Relative Frequency Percentage
Fort Pierce 7 0.233 23.3%
Port St. Lucie 6 0.200 20.0%
Vero Beach 7 0.233 23.3%
Sebastian 4 0.133 13.3%
Okeechobee 6 0.200 20.0%
Total 30
How the relative frequencies and percentages are computed:Class Frequency Relative Frequency Percentage
Fort Pierce 7 0.233 (7/30) 23.33% (7/30 x100)
Port St. Lucie 6 0.200 (6/30) 20.00% (6/30 x100)
Vero Beach 7 0.233 (7/30) 23.33% (7/30 x100)
Sebastian 4 0.133 (4/30) 13.33% (4/30 x100)
Okeechobee 6 0.200 (6/30) 20.00% (6/30 x100)
Total 30
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Answer Options for a):a) Time-Series
b) Quantitative and Discrete
c) Cross-Sectional Qualitative
d) Quantitative and Continuous
Part A: Jan INCORRECTLY
finds the surface area of the
cone using the following
work. Explain Jan's error
and find the
correct volume AND
surface area of the cone.
The volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.
Given the height (h) of a cone as 22 m and the diameter (d) of its circular base as 22 m, we can find the radius (r) of the circular base using the formula:
r = d/2 = 22/2 = 11 m
Here, Jan made a mistake in the work of the surface area of the cone because she used the wrong value of slant height (l=22) in the calculation.
The volume (V) of a cone is given by the formula:
V = (1/3)πr²h
Substituting the values of r and h, we get:
V = (1/3)π(11)²(22)
V = 2786.2 cubic meters
The surface area (A) of a cone is given by the formula:
A = πr(r + l)
here l is the slant height of the cone, which can be found using the Pythagorean theorem:
l = √(r² + h²)
l = √(11² + 22²)
l = √(605)
l = 24.6
Substituting the values of r and l, we get:
A = π(11)(11 + 24.6)
A ≈ 1229.51 square meters
Therefore, the volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.
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Identify the unit rate in each graph. Then, order the graphs by unit rate, from least to greatest.
The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K
How did we determine their unit rates?Step 1: As we know that Unit Rate
Step 2: Notice that the in graph K line passes through the point (1,3)
Step 3: (1,3)
It means the value of function is 3 when x= 1
Step 4: So the unit rate of graph K is, 3/1
Step 5: Simplify the expression.
3/1 = 3
Step 6: Similarly we can see that the graph P have the point (2, 1)
Step 7: So the unit rate of graph P will be 1/2
Step 8: Simplify the expression.
1/2 = 0.5
Step 9: The graph F have point (1, 1) so it have unit rate of 1/1
Step 10: Simplify the expression.
1/1 = 1
Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5
Step 12: Putting them in least to greater order as,
0.5, 1, 3
It follows that;
graph P, graph F, graph K
Therefore, the required answer is,
Unit rate of graph K = 3
Unit rate of graph P = 0.5
Unit rate of graph F = 1
And the order from lower to greater is, Graph P, graph F, graph K
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Geometry problem (possible drop down answers are ellipse rectangle and circle) please help! Will give crown to first to give correct answer.
Answer:
ellipses
a pair of parallel straight
Step-by-step explanation:
you
cou
Recommendations
Florida's B.E.S.T. Standards: Grade 8 > GG.5 Make predictions 38C
thro
Skill plans
pieces of vanilla cake
You have prizes to reveall Go to
Passersby have taken 4 pieces of vanilla cake and 6 pieces of coconut cake from a
sample tray. Based on past data, of the next 30 samples taken, how many should you expect
to be pieces of vanilla cake?
Vid
Out of the following 30 samples, you may expect that about 12 will be portions of vanilla cake.
How to determine probability?To solve this problem, use the concept of probability and make a prediction based on the past data.
In this case, out of the 10 pieces of cake that have been taken, 4 are vanilla and 6 are coconut.
Therefore, the probability of selecting a piece of vanilla cake from the tray is 4/10, or 2/5.
To predict how many of the next 30 samples will be pieces of vanilla cake, multiply the probability of selecting a vanilla cake by the total number of samples:
(2/5) x 30 = 12
So expect that out of the next 30 samples taken, approximately 12 of them will be pieces of vanilla cake.
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Brenda types 15 words per minute. How long will it take her to type 750 words?
It will take Brenda 50 minutes to type 750 words at a rate of 15 words per minute.
To solve this problem, we can use the formula:
time = amount of work / rate
In this case, the amount of work is typing 750 words, and the rate is 15 words per minute. Substituting these values into the formula, we get:
time = 750 / 15 = 50 minutes
This calculation assumes that Brenda types at a constant rate of 15 words per minute. If her typing speed varies, the time it takes her to type 750 words may be different.
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Find the volume of a rectangular prism with a length of 12 inches a width of 4.5 inches and a height of 3.6 inches
Answer:
194.4
Step-by-step explanation:
V=l*w*h
V=12*4.5*3.6
V=194.4
Your math teacher owns 3 pairs of pants and 3 pairs of shoes. He owns a pair of gray pants, green pants, and blue pants. He owns black shoes, brown shoes, and tan shoes. If he randomly chooses one pair of pants and one pair of shoes, what is the sample space of possible combinations of pants and shoes that he could wear on a typical school day?
Answer:
The sample space of possible combinations of pants and shoes for the math teacher is 9. These combinations include gray pants with black, brown, or tan shoes, green pants with black, brown, or tan shoes, and blue pants with black, brown, or tan shoes.
Hope its helpful
you will get 10 points for each question and help
The probability is very high and the event is very likely to occur.
option B.
What is the explanation for the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
If the probability of a rolling a number greater than 1 on a six sided cube die is 5/6, it implies that the chances of obtaining a number greater than 1 is very high.
We will convert 5/6 to percentage to see the actual value of 5/6.
5/6 x 100%
= 83.33 %
So the value of this probability is very high and the event is very likely to occur.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
Simplify (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy).
O4xy³ - x²y - 3xy
O4xy³ - x²y + 3xy
O 10xy³ + x²y - 3xy
O 10xy³x²y + 3xy
Answer: 10xy³ - x²y + 3xy
Step-by-step explanation:
To simplify the expression (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy), we can combine like terms.
Adding the corresponding terms together, we have:
3xy³ + 7xy³ = 10xy³
8x²y - 9x²y = -x²y
-3xy + 6xy = 3xy
Combining these terms, the simplified expression becomes:
10xy³ - x²y + 3xy
Therefore, the correct option is:
O 10xy³ - x²y + 3xy
Which animal swims at a top speed of about 0.33 mile per minute? Explain how you found your answer
The animal that swims at a top speed of 0. 33 miles per minute would be the Dolphin .
How to find the animal ?To find the animal that swims at a top speed of 0. 33 miles per minute, you need to convert their top speeds in miles per hour to miles per minute.
For every 1 mile per hour, the equivalent in minutes is 0.0166667 miles per minute.
Speed of Swordfish is:
= 60 mph x 0.0166667
= 1 mile per minute
Speed of Tuna :
= 45 mph x 0.0166667
= 0. 75 miles per minute
Dolphin :
= 20 mph x 0.0166667
= 0. 33 miles a minute
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Please help me answer this question ASAP!! It’s due tomorrow! Will mark as brainliest if explained very simply and correct.
Answer:
The answer is B:14
Step-by-step explanation:
When you simply multiply 5% by 14, you get 0.7. So you know that 5% of 14 is 7.