The first skater has a 40 meter d and is traveling at a rate of 12 meters second, second skater is traveling rate of 14 meters per second. it will take 20 seconds for second skater to pass the first skater.
What is the definition of time?Time is continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in conscious experience. Time is often referred to as fourth dimension, along with three spatial dimensions.
Time has long been an important subject of study in religion, philosophy, and science, but defining it in manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and performing arts all incorporate some notion of time into their respective measuring systems.
12x+40=14x
40=2x
x=20
it will take 20 seconds for second skater to pass the first skater.
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Consider the equation shown.
24
2"
What is the value of n?
Applying the rules of exponents, the value of n in the equation given is calculated as: n = 8.
How to Apply the Rules of Exponents?The product rule of exponents says that when the base are the same, add their exponents together.
For example, m × m² = m^(1 + 2) = m³.
The exponents are 1 and 2. The expression has similar base of m. Therefore, to multiply m and m² together, we would simply add their exponents together while the final result will be the same base.
Also, the negative rule of exponents states that we subtract their exponents if they have he same base.
For example:
m³/m² = m³ ÷ m² = m^(3 - 2) = m.
Given the equation:
[tex]\frac{4^3 \times 8^2}{2^n} = 2^4[/tex]
Simplify the bases to make all equal
= [tex]\frac{2^{(2)(3)} \times 2^{(3)(2)}}{2^n} = 2^4[/tex]
= [tex]\frac{2^{6} \times 2^{6}}{2^n} = 2^4[/tex]
Apply the product rule and the negative rule of exponents to find the value of n in tye equation:
[tex]2^{(6 + 6 - n)} = 2^4\\\\2^{(12 - n)} = 2^4\\\\[/tex]
The bases will cancel each other:
12 - n = 4
Subtract 12 from both sides
12 - n - 12 = 4 - 12
-n = -8
Divide both sides by -1
n = 8
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What is the solution to the given equation 2(y-5)=14
Answer: y=12
Step-by-step explanation:
Distribute
Add 10 to both sides
Simplify.
Answer: y = 12
Step-by-step explanation:
2 ( [tex]y\\[/tex] - 5 ) = 14
2[tex]y\\[/tex] - 2 · 5 = 14
2[tex]y\\[/tex] - 10 = 14
(2[tex]y\\[/tex] - 10) + 10 = 14 + 10
2[tex]y\\[/tex] = 24
[tex]\frac{2y}{2} = \frac{24}{2}[/tex]
What is the surface area of a cylinder that has a radius of 5 m and a height of 13 m?
Surface area of a cylinder= 2πr(h+r)
=2×22/7×5×(13+5)
=31.43×(18)
=565.74meter squared
What are the perimeters of this
perimeter of triangle is = 3 + 5 + 4 = 12 cm
perimeter of rectangle is = 2( 3 + 6 ) = 18 cm
perimeter of parallelogram is = 2 (5+7) = 24 cm
What is perimeter ?A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape. The circumference of a circle or an ellipse is referred to as its perimeter. Perimeter calculations have many practical applications.
Calculationperimeter of triangle is = 3 + 5 + 4 = 12 cm
perimeter of rectangle is = 2( 3 + 6 ) = 18 cm
perimeter of parallelogram is = 2 (5+7) = 24 cm
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The diameter of
one species of bacteria is shown. Bonnie
approximates this measure as 3 × 10-11 meter.
Is she correct? Explain.
No, i don't think she is correct as she didn't rounded-off correctly while measuring the diameter of bacteria.
What is rounding- off?Rounding off is a type of estimation. Estimation is used in everyday life and also in subjects like Mathematics and Physics. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number.
According to the picture it shows the diameter of the bacteria is 0.00000025691m
So , [tex]2.5691 * 10^-^7m[/tex] is rounded off and will be equal to [tex]3*10^-^7m\\[/tex]
As, The digit right to 2 is 5 and which already passed halfway up
So, the number 2 will be rounded off to 3 as it being the nearest digit.
Therefore, Bonnie is wrong as she did mistake while rounding - off measurments.
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question is in the photo
The values for the parabola are found as-
Focus, a = 4x axis vertex; h = 5y-axis vertex; k = 8What is meant by the parabola?A parabola is a curve equation in which a point on a curve is equidistant out of a fixed point and a fixed line. The fixed point is known as the parabola's focus, and also the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie just on fixed line.The focus of the parabola is the point (a, 0).The parabola's directrix is the line sketched parallel to a y-axis and passing through point (-a, 0). The directrix is perpendicular to a parabola's axis.For the given question.
The total horizontal distance covered by water is 10 feet.
The maximum height attained by nozzle of water is 8 feet.
Thus, the vertex of parabola (h, k) = (5, 8)
The nozzle was 4 foot above the ground, a = 4.
The equation of parabola becomes;
y = a(x - h)² + k
y = 4(x - 5)² + 8
Thus, the equation of parabola becomes; y = 4(x - 5)² + 8.
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use the range rule of thumb to find the minimum usual value μ–2σ and the maximum usual value μ 2σ. enter answer as an interval using square-brackets only with whole numbers.
The range thumb rule The minimum and maximum values for the usual value, which is two, are 812.14 and 885.85, respectively.
Range thumb rule: what is it?An efficient way to calculate the range from the standard deviation is to use the range rule of thumb. The range is normally around four times the standard deviation, according to this information. Inferring that your range is around eight if your standard deviation is 2, for example.
As an illustration of a binomial distribution, we'll utilize seeds.
According to given data;
Let "X" represent the number of tomato seeds that actually germinate based on the data provided.
With the knowledge provided above, we can now determine the:
The median number of seeds that we may anticipate to germinate
standard deviation (σ): sqrt of n*p*(1-p)
Once you calculate the mean and standard deviation, you can calculate the minimum usual value and the max usual value.
Now, in your problem:
n = 1415
p = 3/5
so,
the mean would be: (1415)(3/5) = 849
the standard deviation would be: sqrt (mean)(1-3/5) = 18.4282
Next, we find the minimum and maximum usual values according to the equations you gave:
minimum: mean - 2(standard deviation)
= 849 - 2(18.4282)
= 812.1436
maximum: mean + 2(standard deviation)
= 849 + 2(18.4282)
= 885.8564
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Choose the multiplication problem that matches this model: I Dan studied for of an hour for 4 days in a row. How many hours did he study? Dan studied for 2 hours for 4 days in a row. How many hours did he study? O Dan studied for of an hour for 4 days in a row. How many hours did he study? O Dan studied for of an hour for 4 days in a row. How many hours did he study?
The number of bars of the same color could be used to show the number of hours that Dan studies hence he studied for 2/3 hours in four days.
What is multiplication?The term multiplication refers to the number of times that a number is added to itself. For instance, if I add four three times, I could shorten the expression as four multiplied by three.
If we look at the diagram, we can see that in each tile, there are always two bars of the same color out the whole three bars. The bars that are of the same color shows the number of hours that Dan studied.
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Name the property shown and explain
in a complete sentence supporting
your answer choice.
a (b + c) = ab+ac
Need help with this question!!!!
Using the exterior angle of a polygon theorem, the value of the missing angle is 58°
Calculating the value of a missing angleFrom the question, we are to calculate the value of the missing angle.
From the given information, the missing angle is (3x -2)°.
To calculate the value of the missing angle,
First, we will determine the value of x
From the Exterior angle of a polygon theorem, we can write that
90° + (3x + 12)° + (4x - 10)° + (3x - 2)° + 70° = 360°
(3x + 12)° + (4x - 10)° + (3x - 2)° = 360° - 70° - 90°
3x° + 12° + 4x° - 10° + 3x° - 2° = 200°
10x° = 200° + 2° + 10° - 12°
10x° = 200°
x = 200/10
x = 20
The missing angle is (3x -2)°
Substitute the value of x
(3(20) -2)°
= (60 -2)°
= 58°
Thus,
The missing angle measure is 58°
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804
X 79
Explain step by step
The correct answer to task 804 × 79 is 63,516.
Understanding the multiplication of numbersWhen we multiply a number and another together, or a number and a variable, or even a variable with another variable, we mean the product of the two factors. The multiplication sign is " × " .
The step by step explanation of the task above is given below:
804 × 79 = 63,516.
Another example of Multiplication is
40 × 2 = 80.
The product of a and b also means Multiplication.
a and b means a × b = ab.
The product or the multiplication of g and 5 means g × 5 = 5g.
In conclusion, from the detailed information and explanation given above, the product of 804 × 79 is 63,516.
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The range of a set of numbers is 19.
The minimum value is 9.
What is the maximum value?
If the range of the data set is 19. Then the maximum value of the set will be 28.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.
The range of the data is the difference between the maximum number to the minimum number. Then the formula is written as,
Range = Maximum value - Minimum value
The range of a set of numbers is 19. And the minimum value is 9.
Then the maximum value of the set is calculated as,
Range = Maximum value - Minimum value
19 = Maximum value - 9
Maximum value = 19 + 9
Maximum value 28
If the range of the data set is 19. Then the maximum value of the set will be 28.
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If you double a number and then add 28 , you get
{4}{9} of the original number. what is the original number?
In this mathematical expression, the original number is 4.
How is the original number determined?We can use a mathematical equation to work out the original number.
A mathematical equation uses variables, numbers, and constants to show that two values are equal.
Mathematical equations connect two mathematical expressions using the equal sign (=).
Let the original number = x
According to the statement:
2x + 28 = {4}{9}
This implies that:
2x + 28 = 36
Subtracting 28 from both sides gives:
2x = 8
x = 4
Thus, the original number is 4.
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marlena surveyed classmates and found that the ratio of the numbers of text messages sent by girls varies directly with the number of texts sent to boys. The girls sent 27 texts for 9 texts sent by the boys.How Many texts did the girls send if the boys sent 7 texts
Find the range of the following
function given that
ƒ(x) = x² − 1
Domain: -2
Answer:
Hope the picture will help you
Choose a rational number expressed as an infinite periodic decimal greater than 0.6(3) and less than 0.64.
Answer:
0.635
Step-by-step explanation:
This is half way between 0.63 and 0.64.
Hope this helps!
PLEASE HELP ASAP!!!!!
The definition for the function is y = {-2x +1 x < 1 ; -x + 2 x ≥ 1. The correct option is b.
Equation of a functionFrom the question, we are to determine the equation for the function
First, we will determine the equation for when x < 1
Picking the points (-1, 3) and (0, 1)
Using the formula,
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
(y - 3) / (x - -1) = (1 - 3) / (0 - -1)
(y - 3) / (x + 1) = -2 / (0 + 1)
(y - 3) / (x + 1) = -2 / 1
(y - 3) / (x + 1) = -2
y - 3 = -2(x + 1)
y - 3 = -2x - 2
y = -2x - 2 + 3
y = -2x + 1
Thus,
When x < 1, the function is y = -2x + 1
Now, determine the equation for when x ≥ 1
Picking the points (1, 1) and (2, 0)
(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)
(y - 1) / (x - 1) = (0 - 1) / (2 - 1)
(y - 1) / (x - 1) = -1 / 1
(y - 1) / (x - 1) = -1
y - 1 = -1(x - 1)
y - 1 = -x + 1
y = -x + 1 + 1
y = -x + 2
Thus,
When x ≥ 1, the function is y = -x + 2
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in a survey of u.s. cities it is discovered there is a positive correlation between the number of paved streets in the city and the number of registered cars.does this mean that paving more streets will result in the increase of registered cars?
Yes if there is a positive correlation existing between the paving of streets and the number of registered cars then paving more streets would result in the increase in the registered cars.
What does a positive correlation mean?This is the term that is used to tell us that there is the presence of a correlation that would make the two variables that we are talking about to move in the same direction. That is when one increases, the other would have to increase as well.
Such that we would have the increase in the number of paved street to cause an increase in the number of registered cars in the place.
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If an experiment with a random outcome is repeated a large number of times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called what?.
Answer: The correct answer is the Law of Large Numbers
Step-by-step explanation:
Imagine flipping a coin. There is a 50% likelihood that you would get tails. However, it doesn't happen all the time. If you flipped it just a few times, you could get all tails and have 100% tails.
However, if you experimented a lot of times (a large number), you almost certainly wouldn't get all tails. You would get close to 50%. That is the main point of the law.
The more trials you do, the more likely you will get close to the theoretical value.
3 of your 5 teachers are females what percent of your teachers are females
Answer: 60% of your teachers are female
Step-by-step explanation: 3 out of 5 is 60%
Whats the answer for the math problem
Answer:
the answer is -60........
Answer:
-60! 1560 divided by 26 is 60, but any negative divided by a positive is a negative, so the product will be negative as well.
Step-by-step explanation:
Hope it helps! =D
How many 135-inch-thick books can fit on a 1412-inch-long bookshelf?
You can fit ? books on the bookshelf.
Fully simplify 5√/20 - 4√5
[tex]5\sqrt{20} = 5\sqrt{4.5} = 5.2\sqrt{5} = 10\sqrt{5}[/tex]
[tex]10\sqrt{5} - 4\sqrt{5} = 6\sqrt{5}[/tex]
katrina can arrange the chairs in the classroom in 5 minutes. one day peter helped her and took both of them 2 minutes to arrange the chairs. how long will it take peter to arrange the chairs all by himself?
The time taken by Peter to arrange the chairs all by himself is 10/3 minutes.
Given that :-
Katrina can arrange the chairs in the classroom in 5 minutes.
One day peter helped her and took both of them 2 minutes to arrange the chairs.
We have to find the time taken by Peter to arrange the chairs all by himself.
LCM (5,2) = 10
Let the total work of arranging the chairs is of 10 units.
We know that,
Efficiency of a person = Total Work/Time taken by person
Hence,
Efficiency of Katrina = 10/5 = 2 units
Efficiency of Katrina + Efficiency of Peter = 10/2 = 5 units
Hence,
Efficiency of Peter = 5 - 2 = 3 units
Hence, time taken by Peter to arrange the chairs all by himself = 10/3 minutes.
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what is x and what is the am of the segment
Answer:
-0.5 or -1/2
Step-by-step explanation:
(5x) + (3x+4) = 8x+4
8x+4 = 0
8x = -4
x = -0.5
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Which of the following statements best describes the value of the expression 2x – 7, when x = 5?
A. The result is not a whole number.
B. The result is a prime number.
C. The result is a composite number.
D. The result is a whole number that is neither prime nor composite.
7TH grade math
The best description of the value of the expression 2x - 7, when x = 5 is B. The result is a prime number.
What is a prime number?A prime number cannot be divided by another number except by itself or 1.
Common prime numbers include 2, 3, 5, 7, 11, 13, 17, and 19.
The value of 2x – 7, when x = 5 is 3.
3 is a prime number as well as a whole number, but it is not a composite number.
Thus, we can conclude that the result of solving the expression is the prime number 3.
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QR = 5x - 15, and QS = 100
The value of x if R is the midpoint of QS is 31 units.
How to find value of x using midpoint?The midpoint is the middle point of a line segment.
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
The midpoint is halfway between the two end points.
Therefore, R is the midpoint of QS
Hence,
QS = QR + RS
QR = 5x - 15
QS = 100
Therefore, QR and RS are congruent because R is the midpoint of QS
QR = RS
Hence,
100 = 5x - 15 + 5x - 15
100 = 10x - 30
100 + 30 = 10x
130 = 10x
divide both sides by 10
x = 130 / 10
x = 13
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consider a spinner that, after a spin, will point to a number between 0 and 1 with uniform probability. 1. what is the probability that the spinner will land on something less than 0.75? 2. determine p(1/5
Hence the probability that the spinner will land on something less than 0.75 is 37/50
As we know in between 0 and 1 the decimal numbers are ( 0.1, 0.2, 0.3, 0.4 _ _ _ _ _ 0.95, 0.96, 0.97, 0.98, 0.99, 1.00)
So,
To find the probability = favorable outcomes/ total numbers of outcomes
Favorable outcomes = 0.74 / 1.00
solve the decimal numbers in the simplified form
The probability that the spinner will land on something less than the decimal number 0.75 is 37/50.
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jaylin has a wooden cube which is painted blue on the outside. she cuts the cube into $1000$ identical cubes, some of which have some sides painted blue, then rolls the resulting cubes like dice. the probability that no blue faces land up after jaylin rolls the $1000$ cubes can be expressed as $2^a \times 3^b \times 5^c$ where $a$, $b$ and $c$ are integers. what is the value of $a b c$?
The probability is a + b + c = -382
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Every cube's side is [tex]\sqrt[3]{1000}[/tex] = 10
Since there are 512 unpainted cubes within, the likelihood is 1⁵¹² = 1
There are 8 corners, and each one has a chance of 3 / 6 = 1 / 2 = 2⁻¹ so the probability is 1⁸ / 2 = 1 / 2⁸
There are 8 * 12 = 96 edge pieces (12 edges total, with 8 on each edge; each cube has a probability of 4 / 6 = 2 / 3, so the probability is 2⁹⁶ / 3 = 2⁹⁶ / 3⁹⁶
There are 8 * 8 * 6 = 384 center cubes, each having a chance of 5 / 6, so the probability is 5³⁸⁴ / 6 = 5³⁸⁴ / 6³⁸⁴ = 5³⁸⁴ / (2³⁸⁴ * 3³⁸⁴)
So, the probability is:
(1 / 2⁸) * (2⁹⁶ / 3⁹⁶) * [5³⁸⁴ / (2³⁸⁴ * 3³⁸⁴)]
= (5³⁸⁴ * 2⁹⁶) / (2³⁹² * 3⁴⁷⁰)
= 5³⁹⁴ * 2⁹⁶ * 2⁻³⁹² * 3⁻⁴⁷⁰
= 5³⁸⁴ * 2⁻²⁹⁶ * 3⁻⁴⁷⁰
Thus, a + b + c = -382
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a scale drawing of a rectangular building is 4 inches wide and 5 inches long. the actual building is 240 yards wide. what is the area of the actual building in yards
Answer:
72,000 yards
Step-by-step explanation:
The scale factor can be found by doing:
[tex]240 \div 4 = 60[/tex]
This means that 60 is the scale factor. You can apply the scale factor to the length of the rectangular building, meaning that the length of the actual building is:
[tex]5 \cdot 60 = 300[/tex] yards
So, if the building is 240 yards wide, and 300 yards long. You can find the area of the actual building just like any other rectangle using:
[tex]A = l \cdot w[/tex]
(Area = length * width)
So, the final answer is:
[tex]A = 300 \cdot 240\\ A= 72,000[/tex]
This means that the area of the actual building is 72,000 yards.