Answer:
a) Let’s assume that the moose population, p, changes linearly with time t (in years since 1991). We can use the given data to find the slope of the line that represents the population change. The slope is (5850-4330)/(1999-1991) = 190 moose/year. The equation of the line is p = 190(t) + 4330.
b) According to this model, the moose population in 2002 would be p = 190(2002-1991) + 4330 = 6490 moose.
Step-by-step explanation:
You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
With given compound interest, it will take approximately 31 years and 5 months to pay off the loan.
What is Compound interest?
Compound interest is computed on both the starting principal and the accrued interest from prior periods. In other words, it is the interest gained not just on the principle amount but also on any past interest earned.
Now,
Using the given formula:
N = (-log(1 - i * A / P)) / (log(1 + i))
where i = 0.0025 (0.25% monthly interest rate), A = $70,000, and P = $250
N = (-log(1 - 0.0025 * 70000 / 250)) / (log(1 + 0.0025))
N = (-log(1 - 175)) / (log(1.0025))
N = (-log(0.9883)) / (0.0025)
N = 376.48
Rounding up to the nearest whole number, it will take 377 months to pay off the loan.
Therefore, it will take approximately 31 years and 5 months to pay off the loan.
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A Bakery sold 382 cakes in one week. this was twice as the day so the previous week. write an equation that can be used to find the number of cakes and that were sold the previous week 
Answer:
164 Cakes
Step-by-step explanation:
382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.
Melissa collected the data in the table.
When x = 4, what is the residual?
–3
–1
1
3
From the data in the table, we can conclude that when x = 4, then the residual will equal -1.
How to determine the residualTo determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.
So, Residual = Gven value - Predicted value.
When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.
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Answer:
The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.
Step-by-step explanation:
In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.
If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.
What does a residual value of –0.8 mean in reference to the line of best fit?
The given point is 0.8 units above the line of best fit.
The given point is 0.8 units below the line of best fit.
The line of best fit is not appropriate to the data.
The line of best fit has a slope of 0.8.
Which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?
y = –55x + 407
y = –41x + 814
y = –38x + 922
y = –26x + 723
Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.
The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:
y = –38x + 922.
Therefore, the answer is y = –38x + 922.
Step-by-step explanation:
Consider a triangle ABC.
.............................
Mr. Wang and Mrs. Wang have 3 sons. Every son has 1 wife, 1 son, 1 sister. How many people in this family?
If Mr. Wang and Mrs. Wang have 3 sons and every son has 1 wife, 1 son, and 1 sister, the total number of people in the family, based on mathematical operations, is 14.
How is the total number determined?The total number of people in the family can be determined using the mathematical operations of multiplication and addition.
Multiplication and addition are two of the four basic mathematical operations.
Multiplication involves the multiplicand, the multiplier, and the product, while addition involves two or more addends added to get the sum.
The number of parents = 2
The number of sons = 3
The number of additional family members for each son = 3
The total number of additional family members = 9 (3 x 3)
The total number of persons in the family = 14 (9 + 3 + 2)
Thus, there are 14 people in the family of Mr. Wang and Mrs. Wang.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Therefore , the solution of the given problem of angles comes out to be the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6.
An angle's meaning is what?The point of intersection of the paths joining a skew ends yields the skew's greatest and smallest walls. A crossroads may be where two paths converge. Angle is another outcome of two things interacting. They approach dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various configurations between their endpoints.
Here,
Regarding the illustrated diagram, the appropriate statements are:
=> m∠3 + m∠4 + m∠5 = 180°
This is accurate since every triangle's internal angles add up to 180°.
=> m∠5 + m∠6 = 180°
This is true because a triangle's internal angle and outside angle are always equal to 180 degrees.
=> m∠2 + m∠3 = m∠6
This is accurate because, based on the information provided,
the exterior angle at angle 2 (m2) of the triangle is equal to the corresponding interior angle at angle 6 (m6) of the triangle.
Therefore, the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. are always true in relation to the given figure.
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15 POINTS
please help
#2
AA Similarity Theorem is required to prove that both triangles are similar
What is AA Similarity Theorem
AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In other words, if two angles of one triangle are equal to two angles of another triangle, then the third angles must also be equal, and the two triangles are said to be similar.
One of the equal angle is marked while the other is equal using the concept of vertical angle theorem. Angles formed where the line intersect are the ones equal by vertical angle theorem
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Which equation best represents the relationship between X and Y in the graph?
A- y = 3x + 3
B- y = 3x - 1
C- y = 1/3x + 3
D- y = 1/3x - 1
Nora bought 100 shares of a technology stock and 200 shares of a mutual fund for $3600. Her sister, Erin, bought 300 shares of
the technology stock and 50 shares of the same mutual fund for $5300. Find the cost per share of the technology stock, and the
cost per share of the mutual fund.
The cost per share of the technology stock is $14.
What is a variable?
In mathematics, a variable is a symbol or letter that represents a value or a quantity that can change or vary in a given context or problem. Variables are used to express mathematical relationships and to formulate equations and functions.
Let's use variables to represent the cost per share of the technology stock and the mutual fund. We can call the cost per share of the technology stock "T" and the cost per share of the mutual fund "M".
From the problem, we know:
Nora bought 100 shares of the technology stock and 200 shares of the mutual fund for a total of $3600:
100T + 200M = 3600
Erin bought 300 shares of the technology stock and 50 shares of the mutual fund for a total of $5300:
300T + 50M = 5300
We now have a system of two equations with two variables. We can solve for T and M by using elimination or substitution. Here, we will use the substitution method:
From the first equation, we can isolate T by subtracting 200M from both sides:
100T = 3600 - 200M
Divide both sides by 100 to get:
T = 36 - 2M
Now substitute this expression for T into the second equation:
300(36 - 2M) + 50M = 5300
Expand and simplify:
10M = 1100
Divide both sides by 10 to get:
M = 110
So the cost per share of the mutual fund is $110.
To find the cost per share of the technology stock, we can substitute M = 110 into either of the original equations. Let's use the first equation:
100T + 200(110) = 3600
Simplify:
100T = 1400
Divide both sides by 100 to get:
T = 14
So the cost per share of the technology stock is $14.
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Oriana's Pizza Kitchen has an oven that is shaped like a
rectangular prism. Inside, the oven is 5 feet wide and 4
feet deep so it can bake
their super large pizzas. It is also 3 feet high. What is
the oven's volume?
12 ft³
15 ft3
60 ft³
20 ft³
Answer:
Step-by-step explanation:
For questions 16, write the negation of each conditional statement.
16. If you don’t look both ways before crossing the street, then you will get hit by a car.
Answer:
The symbols used to represent the negation of a statement are “~” or “¬”. For example, the given sentence is “If you don’t look both ways before crossing the street, then you will get hit by a car." Then, the negation of the given statement is “that u won't get hit”. Thus, if the given statement is true, then the negation of the given statement is false.
4. Greta's neighborhood is having a picnic to celebrate the end of the school year. She has been
asked to prepare potato salad. Greta actually has to work at 2pm when the picnic is scheduled, so
she asks Lynn, the neighbor coordinating food, if she can drop off the potato salad at the park
when she goes into work at 10am. Lynn is not sure this will work. Describe why Lynn is hesitant
and what might happen if Greta's potato salad sits out in the sun until the picnic begins at 2pm.
Then offer at least one suggestion to solve Greta and Lynn's problem.
Lynn is hesitant to allow Greta to drop off the potato salad at 10am .
How to solve Greta and Lynn's problem?Greta could make the potato salad the night before and keep it in the refrigerator to solve the problem she and Lynn were having. She could then transport the potato salad at a safe temperature in a cooler filled with ice packs on the day of the picnic.
She could ask Lynn to store the potato salad in a cooler or refrigerator until the picnic starts when she gets to the park. Along these lines, the potato salad will be protected to eat and won't represent a gamble of food contamination.
The mayonnaise in Greta's potato salad will spoil, leading to the growth of bacteria that could result in foodborne illness, if it is left outside in the sun until the picnic begins at 2 p.m. The potato salad may cause nausea, vomiting, diarrhea, and stomach cramps in those who consume it.
Because food safety guidelines state that perishable foods, like potato salad, should not be kept at room temperature for more than two hours, Lynn is hesitant to let Greta drop off the potato salad at 10 a.m.
If the potato salad is left out in the sun from 10 a.m. to 2 p.m., bacteria can grow on it, and eating it could make you sick.
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Use L’hospital if it applies
Lim x—> infinity
(lnx)^3/x^2
The calculated value of the limit of (ln x)^3 / x^2 as x approaches infinity is 0.
Calculating the limits of the derivativesTo apply L'Hopital's rule, we need to take the derivative of the numerator and denominator separately with respect to x.
We can apply this rule repeatedly until we get a determinate form.
lim x → ∞ [(ln x)^3 / x^2]
Taking the derivative of the numerator:
= 3(ln x)^2 (1/x)
Taking the derivative of the denominator:
= 2x
Applying L'Hopital's rule again by taking the derivative of the numerator and denominator:
= lim x → ∞ [6(ln x) / x]
Taking the derivative of the numerator:
= 6/x
Taking the derivative of the denominator:
= 1
Applying L'Hopital's rule one last time:
= lim x → ∞ 6 / x^2
= 0
Therefore, the limit of (ln x)^3 / x^2 as x approaches infinity is 0.
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One hundred adults were asked to name
their favorite sport, and the results are
shown in the circle graph. What percent of
adults preferred soccer or baseball?
Volleyball, 3
Other. 4
Golf, 7
Soccer, 11.
Baseball, 14
Football,39
Basketball, 22
The percentage of adults who preferred soccer or basketball is 25%.
What is circle graph?The size of each slice in a circle graph, also called a pie chart, indicates the proportion or percentage of each category, and the information is displayed as a circle divided into sections or slices. Circle graphs are frequently used to compare various categories in a dataset or to illustrate how various components contribute to the overall. They are particularly helpful when working with data that can be broken down into distinct categories, such survey results or demographic data.
From the circle graph we see that, percentage of adults who preferred soccer is 11%, and the percentage who preferred baseball is 14%.
Thus,
11% + 14% = 25%
Hence, the percentage of adults who preferred soccer or basketball is 25%.
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if a square has length of its side is 8cm then find length of its diagonal
Answer:
8√2 cm
Step-by-step explanation:
Which is more, 19 ounces or 1 pound?
Consequently, 1 pound weighs more than 19 ounces.
What additional weight units are there?
The weight can also be expressed in terms of grams, kilograms, pounds, and tons.
What is a pound?Pound has two different definitions. When used as a noun, it refers to a 16 oz. weight unit. Or it can be used as a verb to strike or hit hard and frequently.
What does ounce mean?The weight unit known as an ounce is 1/16th of a pound.
What fraction of a ton is one pound?A ton weighs 2000 pounds.
16 ounces make up one pound. Consequently, 1 pound weighs more than 19 ounces.
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A fair coin is tossed three times in succession. The set of equally likely outcomes is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Find the probability of getting exactly one tail.
The probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
What is probability?Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
In the given question,
There are 8 possible outcomes, and we want to find the probability of getting exactly one tail. We can list the outcomes with exactly one tail as HHT, HTH, and THH.
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH)
We know that each individual toss of a fair coin has a probability of 1/2 of resulting in either heads or tails. Using the multiplication rule of probability, we can find the probabilities of each of these outcomes:
P(HHT) = (1/2) * (1/2) * (1/2) = 1/8
P(HTH) = (1/2) * (1/2) * (1/2) = 1/8
P(THH) = (1/2) * (1/2) * (1/2) = 1/8
So, the probability of getting exactly one tail is:
P(exactly one tail) = P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 = 3/8
Therefore, the probability of getting exactly one tail when a fair coin is tossed three times is 3/8.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the system of equations algebraically. Show all of your steps.
y=x2+2x
y=3x+20
There are two solutions for given system of equations: (5, 35) and (-4, 8).
What does "system of equations" and its solution means ?A system of equations is a grouping of two or more equations with numerous variables that are treated as a whole. The solution to a system of equations is the set of variable values that satisfies all of the equations in the system at the same time.
Typical approaches for resolving equation systems include:
Substitution MethodElimination MethodMatrix MethodGraphical MethodGiven system of equations is,
[tex]y=x^2+2x[/tex]..................(1)
[tex]y=3x+20[/tex]..................(2)
Solving equations algebraically,
Equating the formulas for 'y' in both equations:
[tex]x^2 + 2x = 3x + 20[/tex]
Rearranging the equation :
[tex]x^2 - x - 20 = 0[/tex]
Here, we got a quadratic equation,Solving for values of x,
[tex](x - 5)(x + 4) = 0[/tex]
[tex]x - 5 = 0 \\x=5\\or\\x + 4 = 0\\x=(-4)[/tex]
For values of 'y', putting values of x in equation (1),
for x = 5,
[tex]y = 5^2 + 2(5)=25 + 10 = 35[/tex]
Thus, (5, 35) is one of the solution.
for x= -4,
[tex]y = (-4)^2 + 2(-4)=16 - 8 = 8[/tex]
Thus, (-4, 8) is other solution.
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Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Identify the interquartile range from the box and whisker plot above
Answer:
interquartile range = 6
Step-by-step explanation:
the interquartile range is the difference between the upper quartile Q₃ and the lower quartile Q₁
Q₃ is the value at the right side of the box, that is 86
Q₁ is the value at the left side of the box, that is 80
interquartile range = Q₃ - Q₁ = 86 - 80 = 6
Expand the expressions and simplify 5(x + 4) + 3(x + 2) =
8x + 4
6x + 18
8x+ 26
7x - 18
Answer:
8x+26
Step-by-step explanation:
distribute the 5 into the numbers in the parentheses. you get (5x+20) then do the same with 3(x+2) which wll be (3x+6) now add like terms, which are 5x+3x=8x and 20+6=26. boom 8x+26.
8x + 26
multiply the outside number by the inside numbers and add them. remember, if the variable is singular example x, then it equals 1 :) I hope this helps you understand, I'm currently doing algebraic expressions.
What is the the slope-intercept form of (-5,-2)
Answer:
Step-by-step explanation:
we can't say because we don't have a couple of coordinates
I believe I missed the lesson on how to solve for x and y from this photo. Any help would be appreciated!
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
Explain about the Pythagorean theorem:The Pythagorean Theorem, a well-known geometric principle that states that the square just on hypotenuse (the side across from the right angle) of a right triangle equals the sum of the squares on its legs, is also known as the
a² + b² = c².
For the larger triangle, applying Pythagorean theorem:
4² + (4√3)² = x²
x² = 16 + 16*3
x² = 16 + 48
x² = 64
x = 8
Then, x - 6 = 8 - 6 = 2
Now applying Pythagorean theorem for smaller triangle:
y² + (x - 6)² = 4²
y² = 4² - 2²
y² = 16 - 4
y² = 12
y² = √12
y = 2√3
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
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5. Jay cuts identical squares from the corners of a
rectangular sheet of paper as shown in the adjoining
figure. Find the area of remaining portion.
The area of the remaining portion of the sheet is -4x² + 12x + 6.
How to find the area of a figure?Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.
Therefore, the area of the remaining portion can be found as follows:
area of the rectangle = 3(4x + 2)
area of the rectangle = 12x + 6
Therefore,
area of each square cut out = x²
area of the 4 square cut out = 4x²
Therefore,
area of the remaining portion = 12x + 6 - 4x²
area of the remaining portion = -4x² + 12x + 6
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Shandra is giving a snack bag to each of her
4 friends. She puts 4 pear slices in each bag.
How many pear slices are there in all?
In a case whereby Shandra is giving a snack bag to each of her 4 friends. She puts 4 pear slices in each bag the number of pear slices that are there in all is 16 pear slices.
How can the slice be calculated?The calculation can be done in a simple way, If Shandra puts 4 pear slices in each of the 4 snack bags, then the total number of pear slices will be:
4 friends x 4 pear slices per bag = 16 pear slices
Therefore, there are 16 pear slices in all.
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Can you please help me with this.
The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.
The total number of ways to develop the complex would be 665, 280 ways.
How to find the probability ?To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.
Using combinations, we have:
Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)
Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)
Now, we find the probability:
Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members
Probability = (C(28, 6) x C(12, 4)) / C(40, 10)
Probability = 0.3633
How to find the number of ways ?To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:
The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:
P(11, 5) = 11! / (11 - 5)!
Total ways to develop the complex = 12 x P(11, 5)
= 12 x 55440 = 665,280 ways
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someone help me plss
The fraction of the panel, that is left after cutting out the hole is [tex]\frac{11}{12}[/tex]
What are the areas of some common plane figuresThe area of a rectangle equals the product of its 2 sides. The area of a triangle is equal to half of the product of the base and height.. If we choose one of the sides as the base, then for area calculation, for height we have to use the height of the opposite vertex from this base. To find it, we have to drop a perpendicular from the opposite vertex onto the base. The area of a parallelogram is the product of the length of the base and the perpendicular distance between the two parallel sides of the parallelogram. Area of a trapezium = half of the product of the distance between the parallel sides and the sum of the length of the parallel sides. Area of a circle is [tex]\pi r^2[/tex], in which r is the radius of the given circle. Sometimes the plane figure maynot be a standard shape. In that case we have to divide the figure into suitably many parts such that, each part is a standard figure whose area we can calculate. Also sometimes we can represent an area as the difference of the area of two standard figures. In that case to find the area we have to take the difference of the areas of the two standard figures.
In our question. Initial area of the panel is (3)(2) = 6 square ft.
Area of the cutout = (1)([tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{2}[/tex] square ft.
Using the formula, fraction left = [tex]\frac{6 - \frac{1}{2}}{6} = 1 - \frac{1}{12} = \frac{11}{12}[/tex]
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Required fraction left is 11/12 square feet.
What is area of rectangle?
A rectangle is a geometric shape that has four sides and four right angles. It is a type of quadrilateral and is characterized by its two pairs of parallel sides. The opposite sides of a rectangle are congruent, which means they have the same length, and the adjacent sides are perpendicular to each other.
The area of a rectangle is the total amount of space inside the rectangle and is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is Area = length x width
For example, if a rectangle has a length of 6 units and a width of 4 units, the area can be calculated as:
Area = 6 units x 4 units = 24 square units
The area of the panel is 3 feet x 2 feet = 6 square feet
The area of the hole is 1 foot x 1/2 foot = 1/2 square feet
Therefore, the area left is 6 square feet - 1/2 square feet = 11/2 square feet
The fraction left is (11/2 square feet) / (6 square feet) = 11/12
Therefore, the required correct option is C.
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Which measurement is equivalent to 47 mL?
47 mL is equivalent to 0.047 L (liters).
What is measurement refers to?Measurement refers to the process of quantifying or determining the amount, size, or degree of something using a standard unit of measurement. It is a way of expressing the quantity or magnitude of a physical property, such as length, mass, volume, time, temperature, etc.
Define the term equivalent?Equivalent means having the same value, function, or meaning as something else. In mathematics, two values are said to be equivalent if they have the same numerical value or satisfy the same equation or inequality. In chemistry, equivalent refers to the amount of a substance that can react with or replace a given amount of another substance in a chemical reaction. In general, equivalent is used to indicate that two things are equal in some way or have the same effect or significance.
1L =1000mL
1mL=1/1000L
Therefore 47 mL=.047 L
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a red car travels 20km in one hour .
a blue car travels 130km in the sAME TIME
which car thas greater average speed???
Answer:
The answer is the Blue car
Step-by-step explanation:
let Red car be x
let blue car be y
x=120km---->1hr
y=130km----->1hr
Average speed =distance(km)/time(hr)=km/hr
let A be average speed
A(x)=120/1=120km/hr
A(y)=130/1=130km/hr
therefore,
the blue car has the greatest average speed