Divide total distance of the race by the length each runner runs:
8 miles / 4/5
When dividing by a fraction flip the fraction over and multiply:
8 miles x 5/4 = (8x5)/4 = 40/4 = 10
There are 10 runners
Answer:
10 runners
Step-by-step explanation:
Is 8 Miles which equals to 40/5 miles. 40/5 miles divided by 4/5 = 10 so 10 runners.
Prove that if a and b are positive integers,then there exists a unique integers q and r such that a=bq+r where 0≤r<b
Step-by-step explanation:
Correct option is
C
0≤r<b
If r must satisfy0≤r<b
Proof,
..,a−3b,a−2b,a−b,a,a+b,a+2b,a+3b,..
clearly it is an arithmetic progression with common difference b and it extends infinitely in both directions.
Let r be the smallest non-negative term of this arithmetic progression.Then,there exists a non-negative integer q such that,
a−bq=r
=>a=bq+r
As,r is the smallest non-negative integer satisfying the result.Therefore, 0≤r≤b
Thus, we have
a=bq1+r1, 0≤r1≤b
5
21. The average of 5 consecutive integers starting with m
as the first integer is n. What is the average of 9
consecutive integers that start with m+2?
A) m + 4
B) n + 6
C) n+ 4
D) m + 5
Answer:
n + 4
Step-by-step explanation:
Given
⅕(m + m + 1 + m + 2 + m + 3 + m + 4) = n
Required
⅑(m + 2 + m + 3 +.......+ m + 10)
We have:
⅕(m + m + 1 + m + 2 + m + 3 + m + 4) = n
Multiply both sides by 5
m + m + 1 + m + 2 + m + 3 + m + 4 = 5n
Collect like terms
m + m + m + m + m = 5n - 1 - 2 - 3 - 4
5m = 5n - 10
Divide both sides by 5
m = n - 2
So, we have:
⅑(m + 2 + m + 3 + m + 4 + m + 5 + m + 6 + m + 7 + m + 8 + m + 9 + m + 10)
Collect like terms
= ⅑(m+m+m+m+m+m+m+m+m+2+3+4+5+6+7+8+9+10)
= ⅑(9m + 54)
= m + 6
Substitute n - 2 for m
= n - 2 + 6
= n + 4
What is the value of x?
O x = 32
O x = 36
O x = 37
O x = 40
Answer:
x=40
Step-by-step explanation:
I went through each answer one by one and the only one that satisfies the question is 40.
The line equals 180°, so x + (4x-20) must equal 180.
x+(4x-20)
40+(4(40)-20)
40+(160-20)
40+140=180
x=40
Answer:
x= 40
Step-by-step explanation:
sum of angle on a straight line= 180;
To find X,
sum of angles = 180
x+(4x-20)= 180
: x= 180- [x+(4x-20)]
opening the brackets,
= 180-x-4x+20= 0
taking like terms:
= -x-4x+180+20= 0
= -5x+200=0
= -5x= -200
= x= 200/5
x= 40°
A species of animal is discovered on an island. Suppose that the population size of the species can be modeled by the following function, where time t is measured in years. P(t) = 520/1 + 8e-0.3t Find the initial population size of the species and the population size after years.
Answer:
The initial population size is of 58.
The population size of the specie after t years is given by:
[tex]P(t) = \frac{520}{1 + 8e^{-0.3t}[/tex]
Step-by-step explanation:
Population size of the specie:
The population size of the specie after t years is given by:
[tex]P(t) = \frac{520}{1 + 8e^{-0.3t}[/tex]
Initial population size
This is P when [tex]t = 0[/tex], that is, [tex]P(0)[/tex]. So
[tex]P(0) = \frac{520}{1 + 8e^{-0.3*0} = \frac{520}{1+8} = \frac{520}{9} = 57.7[/tex]
Rounding to the nearest number, 58
The initial population size is of 58.
Jennifer’s pie shop recorded how many pies it recently sold in each flavor. Lemon meringue pies 2 apple pies 3 peach pies 2 blueberry pies 4 coconut cream pies 1 considering this data, how many of the next 15 pies sold should you expect to be blueberry pies?
Answer:
correct me if im wrong but im assuming four just cause if you count what you have all ready not couting the 15 pies. You have at leat 12 and not couting the lemon pies. And from there you basically have to just thing and do the math and I got at least 3 to 5 pies that should be blueberry. srry for my spekling it ducks
We can expect that out of the next 15 pies sold, approximately 5 of them will be blueberry pies.
What is a relative frequency?Relative frequency is a statistical measure that expresses the proportion or percentage of times an event occurs in relation to the total number of events.
We have,
To estimate how many of the next 15 pies sold should be blueberry pies, we can use the relative frequency of blueberry pies in the given data.
The relative frequency of a pie flavor is the ratio of the number of pies of that flavor to the total number of pies.
The total number of pies sold in this data is:
= 2 + 3 + 2 + 4 + 1
= 12
The number of blueberry pies sold is 4.
The relative frequency of blueberry pies.
= 4/12
= 1/3
This means that 1/3 of the pies sold were blueberry pies.
To estimate the number of blueberry pies out of the next 15 pies sold, we can multiply 15 by the relative frequency of blueberry pies.
= 15 x (1/3)
= 5
Therefore,
We can expect that out of the next 15 pies sold, approximately 5 of them will be blueberry pies.
Learn more about relative frequency here:
https://brainly.com/question/29739263
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Tiffany is borrowing 1,200 from her parents to buy a new laptop computer. She plans to pay them back at the rate of $70 a month. Rosie is borrowing $900 from her parents to buy a violin. She plans to pay her parents back at the rate of $40 per month
This isn't really a question so I'll just go through all of it.
1200 dollars will take about 17 months to pay off with installments of 70 dollars.
900 dollars will take 22.5 months to pay off with 40 dollar installments.
Tiffany will pay off her debt first.
The Coffee Counter charges $8.00 per pound for Kenyan French Roast coffee and $10.00 per pound for Sumatran coffee. How much of each type should be used to make an 18 pound blend that sells for $9.00 per pound?
The Coffee Counter should mix ___ pounds of Kenyan Roast coffee and ___ pounds of Sumatran coffee to make 18 pounds of a blend that sells for $9.00 per pound.
Answer:
x = 9
y = 9
Step-by-step explanation:
Given :
Let :
Kenyan French roast coffee = x
Cost per x = $8
Sumatran Coffee = y
Cost per y = $10
x + y = 18 - - - - (1)
8x + 10y = 9 * 18 ;
8x + 10y = 162 - - - - (2)
From (1):
x = 18 - y
Put x = 18 - y in (2)
8(18 - y) + 10y = 162
144 - 8y + 10y = 162
2y = 162 - 144
2y = 18
y = 9
x = 18 - y
x = 18 - 9
x = 9
You deposit $10,000 in an account that pays 4.5% interest compounded quarterly. Using the future value $10,457.65, what is the interest rate if simple interest was used? (I am struggling with formulas)
9514 1404 393
Answer:
4.5765%
Step-by-step explanation:
Apparently, you have to figure out how long it would take to accumulate a balance of $10,457.65 with interest compounded, then use that time period to compute the equivalent simple interest rate. The relevant formulas are ...
A = P(1 +r/n)^(nt) . . . . amount of P at rate r compounded n times per year for t years
A = P(1 +rt) . . . . amount of P at rate r simple interest for t years
We need to use the first formula to find t, then use the second formula to find r. In both cases A=10457.65 and P=10000. Quarterly compounding means n=4. The interest rate is r=0.045 for the first formula.
Looking for t:
A/P = (1 +r/n)^(nt) . . . . . . . . . . divide by P
log(A/P) = nt·log(1 +r/n) . . . . . take logs
t = log(A/P)/(n·log(1 +r/n)) . . . divide by the coefficient of t
Filling in the given values, we find t to be ...
t = log(10457.65/10000)/(4·log(1 +0.045/4)) = 0.999998 ≈ 1.0
The compound interest is applied for 1 year (t=1), so now we can find r using the second formula.
A = P(1 +rt)
A/P -1 = rt
Filling in the known values, we have ...
1.045765 -1 = r = 0.045765 = 4.5765%
The equivalent simple interest rate on the deposit is 4.5765%.
What side is the shortest in the picture?
A. GF
B. DG
C. EF
D. GE
F. DE
Answer:
A. GF
Step-by-step explanation:
The shortest side in a triangle is opposite the smallest angle
<d = 180 -52 -61 =67
The smallest angle is 52 so the smallest side is DG
<f = 180 - 48-85 =50
The smallest angle is 48 so the smallest side is FG
The smallest angle is 48 so the smallest side overall is FG (GF)
Consider the given functions. Select the expression that will produce h(x). A. f(x) + f(x) B. f(x) − g(x) C. f(x) + g(x) D. g(x) − f(x)
Answer:
here is your answer
Step-by-step explanation:
here is your answer
In the expression 5x6 + 3xy − 7yz2 + , which of the following choices is the exponent in the term 5x6?
Answer:
The exponent is 6.
Basically, the term 5x^6 is asking you to raise 'x' to the 6th power (the exponent) and then multiply it by 5.
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
The diameter of a £1 coin is 22.5 mm. Work out its circumference to the nearest centimetre.Required to answer. Single choice.
(2 Points)
68
70
7
11
Answer:
7
Step-by-step explanation:
Circunference:
The circunference of a circle with diameter d is given by:
[tex]C = d\pi[/tex]
The diameter of a £1 coin is 22.5 mm.
Each mm has 0.1 cm, so the diameter, in cm, is of d = 2.25. Then
[tex]C = 2.25\pi = 7[/tex]
The circunference is of 7 centimeters.
Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black, or green. Half of the numbers 1 - 36 are colored red and half are black and the numbers 0 and 00 are green. Each number occurs only once on the wheel. What is the probability of landing on a red space?
Answer:
18/38 or 9/19
Step-by-step explanation:
18 squares are red
18 squares are black
2 squares have 0 or 00
if the bookstore pays $60 to the publisher what will be the selling price?
Answer:
This means that, when the price of a book from a publisher is $60, the bookstore will sell it for $88 to the students.
What is the y-intercept of a line that has a slope of 3 and passes through point (–1, –7)?
Answer:
the y intercept is -4 (as a point it is (0,-4))
Step-by-step explanation:
Hi there!
We are given a slope (m) of 3 and the point (-1,-7).
We need to find the y intercept of the line that has the slope of 3 and passes through (-1,-7)
One way to find the y intercept is to write the equation of the line in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept).
Since we are given the slope, we can immediately substitute it into the equation
Here it is so far:
y=3x+b
now we need to find b (the y intercept)
since the line passes through the point (-1,-7), we can use it to solve for b
substitute -1 as x and -7 as y into the equation
-7=3(-1)+b
multiply
-7=-3+b
add 3 to both sides
-4=b
so the y intercept is -4 . If you need it as a point, its (0,-4) as the y intercept is the point where the equation passes through the y axis, so the value of x is 0.
Hope this helps! :)
*PLEASE HELP ASAP I WILL MARK BRAINLIST*
(Questions and Answers pictured)
Answer:
The first equation, sorry can’t explain.
Answer:
g(x)=3f(2x)
I think
I need help help help
Answer:
use app Gauthmath its will give you the answer
Find the range of the function represented by the list of ordered pairs below.
{(5,-8),(-1, -9),(0, -11), (9,1)}
The ratio of girls to boys in a particular classroom is 8: 7. How many boys are in the class if there are 45 students?
Answer:
8+6=14
So , we can multiply 14 to 45 =630 in ratio 6:30
With the growth of internet service providers, a researcher decides to examine whether there is a correlation between cost of internet service per month and degree of customer satisfaction (higher scores mean high satisfaction). The researcher only includes programs with comparable types of services. Calculate the Pearson's correlation coefficient for the dataset below and interpret what that means.
Answer:
The correlation is 0.373 . There is a moderate positive linear association between Dollars and Satisfaction.
Step-by-step explanation:
Given the data:
Dollars Satisfaction
70.99 32
76.01 34
67.24 27
69.33 17
67.59 23
74.06 29
76.04 25
72.63 31
68.01 26
67.98 31
Using technology, the Pearson correlation Coefficient calculator ; we can obtain the Pearson correlation Coefficient is 0.3729
Interpretating this value, a correlation Coefficient value of 0.3729 is positive, this means a positive linear relationship exists between the values. Also 0.3729 is closer to 0 than 1 ; this mean that the strength of their relationship is moderate to weak .
Hence, a correlation Coefficient value of 0.3729 means that a weak positive relationship exists between dollar and satisfaction
If the first and last terms of a trinomial are perfect squares, the trinomial is a perfect square
trinomial.
True
O False
Answer:
A trinomial is a perfect trinomial if the first and last terms are positive, perfect squares and the middle term is twice the product of their square roots.
Therefore, if you mean perfect as in positive, the answer is True.
What are the zeros of the quadratic function f(x)
128² - 10x - 3?
Answer:
When 2x^2 - 10x - 3 is plugged into the quadratic equation, the resulting zeroes are x = (5 + sqrt(31))/2 and (5 - sqrt(31))/2. Hope this helps!
Step-by-step explanation:
If my answer is incorrect, please correct me! If you like my answer and explanation, mark me as brainliest!
An electrician needs 4 7/10 rolls of electrical wire to wire each room in a house. How many rooms can he wire with 9 2/5 rolls of wire?
Answer:
2 rooms
Step-by-step explanation:
Let; 4 7/10 = 47/10
9 2/5=47/5
So; if each room(1) = 47/10
47/5 should be x rooms
Equation form47/10 = 1
47/5 = x
cross multiplying
47/10x = 47/5
L.C.M = 10
10×47/10x = 10× 47/5
47x = 47 × 2
x = 47 × 2/47
x = 2
Therefore x being 9 2/5 rolls of wire will wire 2 rooms
Plsss help pls...........
Answer: Prime numbers are divisible by themselves ONLY. 11 is a prime number but 8 isn't because it can be divided by both 2 and 4.
Step-by-step explanation:
11 + 2 + 4 + 6 = 23
23 is prime number every time...
I hope you understand...
Pineapples are sold at 'd' cents per pound. The total weight of 3 pineapples
is 5 pounds. What is the average cost of 1 pineapple?
Answer:
(5/3)d cents exact
1.67d cents decimal approximation
Step-by-step explanation:
Average weight
5pounds/3pineapples = (5/3) pounds/pineapple
Cost of 1 pineapple
(5/3) pounds * dcents/pound
(5/3)d cents exact
1.67d cents decimal approximation
What is the length of the hypotenuse of the triangle?
Answer:
[tex]\sqrt{58}[/tex]
Step-by-step explanation:
To find the hypotenuse, we need to use the pythagorean theorem which is [tex]a^2+b^2=c^2[/tex]
[tex]3^2+7^2=c^2[/tex]
[tex]9+49=c^2[/tex]
[tex]58=c^2[/tex]
[tex]\sqrt{58} =c^2[/tex]
Hope this helps
Answer:
Step-by-step explanation:
√58
Solve this math problem 20 points
Answer:
46
Step-by-step explanation:
Diagonals of square are equal, Therefore,
KM=161
JL=4x-23
4x-23=161
4x=161+23
4x=184
x=184/4
x=46
One bag of marbles contains 2 black , 3 red , and 5 white marbles . A second bag contains 3 white and 2 black marbles . What is the probability of selecting one marble from each bag and that they are not both black.
Please help!!
Answer:
NOT BOTH BLACK = 1-2/25 = 23/25
Step-by-step explanation:
Bag 1 : 8 non-black out of 10
P(1) = 8/10
Bag 2: 3 non-black out of 10
P(2)=3/5
Probability of both independent events happening can be calculated using the multiplication rule
P(1) and P(2) = P(1)*P(2) = 8/10 * 3/5 = 24/50 = 12/25 (both are not black, or none is black)
Interpretating not both black meaning at most one black, then
we calculate the probability of both are black,
P(1) = 2/10
P(2) = 2/5
Probability that both balls are black can be calculated using the multiplication rule
P(1) and P(2) = 2/10 * 2/5 = 2/25
Probability that NOT BOTH BLACK = 1-2/25 = 23/25, i.e. at most one black
Are these events independent or dependent?
A) Take a marble out of a bag and putting it back in the bag then take another marble out of the bag.
B) draw a card from a deck of cards and setting it aside. Draw a card again from the same deck.
URGENT PLEASE HELP!!!
Answer:
a) Independent
b) Dependent
Step-by-step explanation:
a) is independent as the first marble does not affect the chance of getting the second marble as you are putting the marble you picked out back in the bag.
b) is dependent as it affects the chance of picking out other cards as you have removed one card from the list of possibilities.
Step-by-step explanation:
the shehejjene
brbnrb grutbdbd
There are four points on a line: A, B, C and D, so that AB=1,BC=2,CD=4. Find the length of segment AD. Consider all possibilities and draw a picture for each one of them.
All possible answers for the length of AD are, _, _, _, _, _.
Answer:
7
Step-by-step explanation:
Since it's on a line, we add up all of the numbers. So 1 + 2 + 4 = 7.
Answer:
7, 1, 5, and 3
Step-by-step explanation:
Because you have to consider all possibilities, you will have multiple different-looking number lines. Using the ratios given in the problem, just by playing around with the letters' placements on the number line you can easily find the length of AD.