The length of the boston marathon is 138,435 ft. each stride, or step, by a particular runner is 3ft. long. does the number of strides the runner takes fit evenly into the length of the race? explain.
Yes 138,435 can be divided by 3 it equals to 46,145
If k= am + 3mx, Express the value of m in terms of a, k and x?
(a + b)2 = 1a^2 + 2ab + 1b^2
(a + b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3
How are binomial expansions related to Pascal’s triangle?
Answer:
The coefficients of the terms come from rows of the triangle.
If the exponent is n, look at the entries in row n.
Study the Proof: Give the reasons for the missing reason. List the number and then state the reason
What is the domain of the function on the graph
Answer:
The correct option is all real numbers greater than or equal to -3.
Step-by-step explanation:
The concept of domain of a function refers to all the points in the x axis for which the function is defined. In the graph as you can see the function starts in x = -3 (includes that point) and growths towards positive values of x, to +∞. So its domain is [-3, ∞) or {R, x≥ -3} in other words "all real numbers greater than or equal to -3."
The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) using a point and the slope. Which point did Harold use?
Answer: equation of a linear function in point-slope form
Step-by-step explanation:
Given : The equation of a linear function in point-slope form passing through point [tex](x_1,y_1)[/tex] is
[tex]y -y_1 = m(x -x_1)[/tex]
The equation written by Harold correctly
[tex]y = 3(x - 7)[/tex]
It can be written as:[tex]y-0 = 3(x - 7)[/tex]
When we compare to the equation of a linear function in point-slope form, we get [tex]y_1=0,\ x_1=7[/tex]
Hence, the point used by Harold = [tex](x_1,y_1)=(7,0)[/tex]
What are the domain and range of the function
Answer:
The domain is the all possible value of x which give the real value of y whereas Range is the all possible value of y after putting the values of x.
For example: We have function: f(x) = x²
Here Domain = All Real Numbers = (-∞, ∞) {∵ For every value of x f(x) give real value)
and, Range = All positive real number = (0, ∞) {∵ f(x) is giving only positive value no matter what the value of x is}
Determine the total number of roots of each polynomial function
g(x) = 5x - 12x2 + 3
Answer:- The total number of roots in the given polynomial function is 2.
Explanation:-
We know that corollary of Fundamental Theorem of Algebra tells that polynomial will have exactly as many roots(m) as its degree(m>0).
The given polynomial function [tex]g(x)=5x-12x^2+3[/tex] is a quadratic polynomial with degree 2.
Thus by corollary of Fundamental theorem of algebra
The total number of roots in the given polynomial function must be 2.
Lesson 1: identify pairs of lines and angles draw two lines intersected by a transversal. label corresponding angles ∠1 and ∠2. label alternate interior angles ∠3 and ∠4. label alternate exterior angles ∠5 and ∠6. label consecutive interior angles ∠7 and ∠8. label vertical angles ∠9 and ∠10. answers
What is the probability that a point chosen at random on the grid will lie in the unshaded region?
a. 5/8
b. 2/5
c. 3/8
d. 3/5?
Name three decimals between 0.55 and 0.56
The required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.
We have to determine the three decimals between 0.55 and 0.56
As per the attached number line,
Three decimals between 0.55 and 0.56 are :
⇒ 0.552, 0.553, and 0.554
Hence, the required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.
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Which lines or segments are parallel? Justify your answer.
What are the new coordinates of the point (-3, 7) after it has been rotated 90° counterclockwise about the origin?
20 points!!!! What number needs to be added to both sides of the equation in order to complete the square?
x²+16x=18
( x² + 16 +_____= 18+______
(x^2 + 16 + 8^2 = 18 + 8^2
Two cars leave the origin; one goes north at 45 mph and the other goes south at 30 mph. after how many hours will they be 400 miles apart?
you learn from your science teacher that the water expands when you freeze it. the next time you freeze your water bottle,you will leave room for the water to expand so that the bottle dose not crack.
what kinda reasoning did you use
One inlet pipe can fill an empty pool in 12 hours, and a drain can empty the pool in 20 hours. How long will it take the pipe to fill the pool if the drain is left open?
If one inlet pipe can fill the pool in 12 hours and the drain can empty it in 20 hours, the combined rate of the two is 1/30 pools per hour. Therefore, it will take 30 hours to fill the pool with the drain open.
Explanation:The question addresses a common concept in mathematics, which is rates and work problems. To determine the time it takes for the inlet pipe to fill the pool with the drain open, we first have to figure out the rates at which the pipe fills and the drain empties the pool.
If an inlet pipe can fill the pool in 12 hours, its rate of work is 1/12 pool per hour. Similarly, if the drain can empty the pool in 20 hours, then its rate is 1/20 pool per hour.
When both the inlet and drain are open, their combined rate will be the fill rate minus the drain rate, which is (1/12) - (1/20) = 1/30 pool per hour.
Therefore, at the combined rate, it will take 1 divided by 1/30 = 30 hours to fill the pool with the drain open.
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When both the inlet pipe and drain are open, it will take 30 hours to fill the pool, computed by dividing the total work done (1 pool) by the net rate (1/30 pool/hour).
Explanation:In mathematics, problems such as these are usually solved by working with the concept of rates. In this scenario, we have two rates: the inlet pipe, and the drain. The rate of the inlet pipe is 1 pool per 12 hours, or 1/12 pool/hour. The rate of the drain is 1 pool per 20 hours, or 1/20 pool/hour. The net rate when both are open is thus (1/12 - 1/20) pool/hour, which simplifies to 1/30 pool/hour. To find out how long (t) it will take to fill the pool with both the inlet and drain open, we would use the fact that Rate x Time = Work Done. The Work Done in this case is 1 (equivalent to one pool), and the rate we’ve calculated as 1/30 pool/hour.
So, solving for time, we get:
t = Work Done / Rate = 1 pool / (1/30 pool/hour) = 30 hours.
So, it would take 30 hours to fill the pool with the inlet pipe and the drain open.
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After selling a dozen copies of the daily newspaper a newsstand had fewer than 75 copies left how many copies did the newsstand have at the beginning of the day
How do you find what a variable means?
f f(x) = x2 – 25 and g(x) = x – 5, what is the domain of (F/g)(x)
Mille pays 4 percent state income tax on his earnings if he earns 1867 how much income tax can he expect to pay?
Is 267 the largest number in the sum of 3 integers evaluated from 269?
Determine the dimensions of the rectangle that requires a minimum amount of fence.
[tex] \sqrt{ \frac{3}{16} } [/tex]
Rational or irrational?
The triangles are similar
What is the value of x?
Enter your answer in the box.
x=
The triangles are similar
What is the value of x?
Enter your answer in the box.
x=
What is AE ?
Enter your answer in the box.
Hunter designs two flags for his adventure club.
What is the length of the base, x, of the larger flag?
Enter your answer, as a decimal, in the box.
A man throws a basketball from 30 in. above the ground. The basketball bounces off the floor and a boy catches it. The distance the ball traveled from the man to the floor is 45 in., and the distance the ball traveled from the floor to the boy is 40 in. The angles formed from by the basketball's path are congruent.
What is the distance, x, from the floor that the boy caught the ball?
Enter your answer, as a decimal, in the box. Round your answer to the nearest hundredth.
The value of x is AB/3, which is equal to KD/3.
Explanation:In the given scenario, we have two similar triangles, HKD and KFD. Since they are similar, their corresponding sides are proportional. In triangle HKD, the width KD is equal to x, and in triangle KFD, the base KF is equal to 3x (proportional to AB). Therefore, the value of x is AB/3, which is equal to KD/3.
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Answer: x=16
Step-by-step explanation:
In the processes of the dilation each number displayed in the first triangle is multiplied by four in order for the second figure to be created. Therefore you would also multiple 4 x 4 in order to get 16.
Write the identity of the missing nucleus for the following nuclear decay reaction: 232 90Th→228 88Ra+?
The missing nucleus in the nuclear decay reaction of Thorium-232 into Radium-228 is an alpha particle, or Helium-4.
Explanation:The question pertains to a nuclear decay reaction where Thorium-232 decays into Radium-228 and a missing nucleus. The missing nucleus can be determined by subtracting the atomic mass and atomic number of the daughter nucleus (Radium-228 with atomic number 88) from the parent nucleus (Thorium-232 with atomic number 90). This yields an alpha particle (He), which has an atomic mass of 4 and atomic number of 2. Here's how it works:
232 90Th (parent nucleus) → 228 88Ra (daughter nucleus) + 4 2He (missing nucleus).
Thus, the missing nucleus is an alpha particle (Helium-4).
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One mile is 5280 feet. there are 3600 seconds in one hour. how many feet per second, rounded to the nearest hundredth, does a car travel when it is traveling at 60 miles per hours
What is the simplified form of the left side of the following equation?
2x-4+5x=8
Select the correct answer below.
A.2x+1
B.3x-4
C.5x-2
D.7x-4
Answer:
D. 7x -4
Step-by-step explanation:
You want the simplified form of the expression 2x-4+5x.
Like termsAn expression is simplified by eliminating parentheses and combining like terms. Here, there are no parentheses, but there are like terms: 2x and 5x. Combining them gives ...
2x -4 +5x
= (2 +5)x -4
= 7x -4 . . . . . . . . . matches choice D
A particular investment account offers an interest rate of 8% each year. An investor puts $3,500 into the account. For tax purposes, he wants to determine the number of years, t, for which the account will have less than $6,000. Write an inequality to represent this situation, and use it to determine the number of years for which the account will have less than $6,000.
Final answer:
The compound interest inequality for the investment account is 3500(1 + 0.08)^t < 6000. Solving this, we find that the account will have less than $6,000 for approximately 6 years.
Explanation:
To solve this problem, we will use the formula for compound interest which is [tex]A = P(1 + r)^t,[/tex] where:
A is the future value of the investment/loan, including interestP is the principal investment amount ($3,500 in this case)r is the annual interest rate (decimal)t is the number of years the money is invested or borrowed forWe are trying to find the number of years, t, when the account will have less than $6,000, at an annual interest rate of 8%, i.e., r = 0.08.
The inequality will be:
[tex]3500(1 + 0.08)^t < 6000[/tex]
To solve for t, we first divide both sides by 3,500:
[tex](1 + 0.08)^t[/tex]< ≈ 1.7143
Now, take the natural logarithm of both sides:
[tex]ln((1 + 0.08)^t) < ln( 1.7143)[/tex]
t · ln(1.08) < ln(≈ 1.7143)
Divide both sides by ln(1.08) to isolate t and calculate:
t < ≈ ln(≈ 1.7143) / ln(1.08) < ≈ 6.6
Therefore, the investment account will have less than $6,000 for approximately 6 years.
On average, a shooter can hit his target one time in four. if he fires 4 shots in a row, what is the probability that he will hit his target?