Mathematics College

calculate the distance nathan rides his bike if he rides 9/12 mile each day for 3 days

Answers

Answer 1
[tex]\bf 3\cdot \cfrac{9}{12}\implies 3\cdot \cfrac{\underline{3}\cdot 3}{\underline{3}\cdot 4}\implies 3\cdot \cfrac{3}{4}\implies \cfrac{3\cdot 3}{4}\implies \cfrac{9}{4}\implies 2\frac{1}{4}[/tex]
Answer 2

Final answer:

Nathan rides a total distance of 2 1/4 miles when he rides 9/12 of a mile each day for 3 days. To calculate this, multiply the daily distance by the number of days and simplify the result.

Explanation:

To calculate the distance Nathan rides his bike if he rides 9/12 of a mile each day for 3 days, you need to multiply the distance he rides in a day by the number of days he rides.

Distance per day: 9/12 mileNumber of days: 3 days

So, the total distance Nathan rides is:

9/12 mile/day × 3 days = 27/12 miles

To simplify the fraction:

Divide the numerator (27) and the denominator (12) by their greatest common divisor, which is 3.This gives us 9/4 miles.Convert 9/4 to a mixed number: 9 ÷ 4 = 2 with a remainder of 1, so it's 2 1/4 miles.

Therefore, Nathan rides a total distance of 2 1/4 miles over the three days.

Related Questions

×
[tex] \frac{x}{4} = \frac{6}{12} [/tex] solve the proportions

Answers

To solve a problem like this, you can use a method called cross-multiplying. This is when you multiply the denominator of the first fraction by the numerator of the other and then multiply the two remaining numbers.

[tex] \frac{x}{4} = \frac{6}{12} [/tex]  To make this easier on yourself, simplify first!
[tex] \frac{x}{4} = \frac{1}{2} [/tex]   Multiply x by 2 and multiply 4 by 1.
2x = 4   Divide both sides by 2.
x = 2

You can check this by comparing the fractions with 2 in the place of x.

[tex] \frac{2}{4} = \frac{6}{12} [/tex]   Simplify!
[tex] \frac{1}{2} = \frac{1}{2} [/tex]

The fractions are equal, so x = 2 .

In a local survey, 100 citizens indicated their opinions on a revision to a local land use plan. of the 62 favorable responses, there were 40 males. of the 38 unfavorable responses, there were 15 males. if one citizen is randomly selected find the probability a male and has a favorable opinion

Answers

This is a conditional probability. 
Denote the events like this:
F: Getting a favorable response .
First compute the number of participants: 62+38= 100.
The number of Male with favorable opinion: 40. 
We deduce the probability:
[tex]P(F\vert M)=\dfrac{40}{100}=\dfrac{2}{5}[/tex]

The probability that a male and has a favorable opinion is selected is 2/5

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]

Combination ( Selection )

Combination is the number of ways to select objects.

[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]

Let us tackle the problem.

This problem is about Probability.

Given:

Of the 62 favorable responses, there were 40 males and 22 females.

Of the 38 unfavorable responses, there were 15 males and 23 females.

There were total (40+15) males = 55 males

Let P(M) = probability a male is selected

[tex]P(M) = \frac{\texttt{Number of Male Citizens}}{\texttt{Total Number of Citizens}}[/tex]

[tex]P(M) = \boxed{\frac{55}{100}}[/tex]

There were 62 favorable responses

Let P(F) = probability citizens has a favorable opinion is selected

[tex]P(F) = \frac{\texttt{Number of Favorable Opinion Citizens}}{\texttt{Total Number of Citizens}}[/tex]

[tex]P(F) = \boxed{\frac{62}{100}}[/tex]

Let P(M ∪ F) = probability a male or citizens has a favorable opinion is selected

[tex]P(M \cup F) = \frac{\texttt{Number of Favorable Opinion Citizens or Male Citizens}}{\texttt{Total Number of Citizens}}[/tex]

[tex]P(M \cup F) = \frac{40 + 15 + 22}{100}[/tex]

[tex]P(M \cup F) = \boxed{\frac{77}{100}}[/tex]

At last , the probability a male and has a favorable opinion could be calculated as follows:

[tex]P(M \cap F) = P(M) + P(F) - P(M \cup F)[/tex]

[tex]P(M \cap F) = \frac{55}{100} + \frac{62}{100} - \frac{77}{100}[/tex]

[tex]P(M \cap F) = \frac{40}{100}[/tex]

[tex]P(M \cap F) = \large{\boxed {\frac{2}{5}} }[/tex]

Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation

What is the beat estimate for the quotient? 591.3 device by 29

Answers

Hi there!

To estimate, we can round:

591.3 is approximately 600
29 is approximately 30

Now, we divide:

600 / 30 = 20

Hope this helps!

Can someone explain? Please help! 15 pts!!!!

Answers

Let 
x--------------> the third stone measure

we know that
the recommended height for the bench is ------> 20 in
20=[4 3/8]+[4 1/2]+[5 1/4]+[x]
4 3/8---------> (4*8+3)/8=35/8
4 1/2---------> (4*2+1)/2=9/2
5 1/4---------> (5*4+1)/4=21/4

20=[35/8]+[9/2]+[21/4]+[x]

x=20-(35/8)-(9/2)-(21/4)

x=20-(35+4*9+2*21)/8-----> 20-113/8------- > (8*20-113)/8

x=47/8---------- > 5.875=5 7/8


the answer is 5 7/8 in



jack has 3 quarters, 2 dimes, and one penny. how much money does jack have in all? show your work.

Answers

75+20+1=96 cents


your welcome

a motorboat travels 432 kilometers on 6 hours going upstream and 384 km in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current.
please help slove and steps

Answers

Going upstream: 432 km / 6 hours = 72 km/h
Going downstream: 384 km / 4 hours = 96 km/h
Going upstream against the current means that the effective speed is:
r_boat - r_current = 72
Meanwhile, going downstream with the current means;
r_boat + r_current = 96
Adding both equations (to cancel out r_current) gives:
2r_boat = 72 + 96
r_boat = 84 km/h
Substituting back into one of the original equations: r_current = 12 km/h.

Chris has $100 in his savings account and he adds $20 a month to the account. The total amount can be represented by the linear function T = 20x + 100. His goal is to have a total of $300 in four more months. What should he change in the function to reach this goal? A) Change the amount he adds each month to $50. B) Change the amount he adds each month to $40. C) Change the y-intercept of the linear function to $20. D) Change the y-intercept of the linear function to $50.

Answers

he will need 200 more in 4 months
200/4 = 50
 so A) Change the amount he adds each month to $50.

Answer:

Its A i did USAtestprep

Step-by-step explanation:

A

If an object is projected upward with an initial velocity of 125 125 ft per​ sec, its height h after t seconds is h equals negative 16 t squared plus 125 t h=−16t2+125t. Find the height of the object after 5 5 seconds.

Answers

for this problem all we need to do is ignore everything except the equation and the input (5.5)

so the steps for this problem are below
we need to plug in 5.5 into our equation as it's our input of time to get our output of height
[tex]t(5.5) = - 16(5.5) {}^{2} + 125(5.5)[/tex]
after simplifying you get

remember to square the 5.5 first (order of operations)

[tex]t(5.5) = - 16(30.25) + 687.5[/tex]

simplify just a tad more and we get this as the final answer
[tex]t(5.5) = - 484 + 687.5 = 203.5[/tex]
[tex]203.5 \: ft[/tex]

244 ft I’m pretty sure

Which of the following is equivalent to the expression below?

(8x + 10) + (13 - 8x)

A.
3
B.
8x + 23
C.
16x + 23
D.
23

Answers

= x(8 -8) +(10 +13)
= 0 +23
= 23

Selection D is appropriate.

What is the value of h?

Answers

The value of x can be found by adding the two angles and setting them equal to 180 because they are on a straight line.

3h + 18 + 15h = 180
18h + 18 = 180
18h = 162
h = 9

So the value of h is 9

Answer:

Step-by-step explanation:

H=9 is the answer

round 543,873 to nearest ten thousand

Answers

For this case we have the following number.
 543,873

 1) Remember that when rounding the number to the nearest tousand, the number must have the first three digits (from right to left) equal to zero.

 2) The fourth digit of the number (from right to left) must be rounded to the next number only if the third digit (from right to left) is greater than or equal to 5.

 3) Following steps 1) and 2) we have the number rounded to the nearest tousand is:544,000

 Answer:
 Round to the nearest tousand:
 544,000

Final answer:

To round 543,873 to the nearest ten thousand, we assess the digit in the ten thousand's place (4) and the digit to its right (3). Since the latter is less than 5, we round down, resulting in 540,000.

Explanation:

The question asks to round the number 543,873 to the nearest ten thousand. To do this, we look at the digit in the ten thousand's place, which is 4, and then look at the digit to its right, which is 3. If the digit to the right is 5 or above, we would round up. However, since it's less than 5, we round down. Therefore, 543,873 rounded to the nearest ten thousand is 540,000.

Which term is the perfect square of 3x4 ?

Answers

A perfect square is the product when a number is multiplied to itself. Hence,the square of (3x4) is (3 x 4 x 3 x 4). We can rearrange this and have (3 x 3) x (4 x 4) which gives you 9 x 16. We now have the perfect square of (3x4) re-written as (9 x 16). Thus, the answer is: 9 x 16.

Hope it helps m8!

Answer:

just took the test answer is D

Step-by-step explanation:

There are 1,505 fruits for sale at at farmer’s market. 39% of them are apples, 28% are oranges, 13% are honeydrew melons, and the rest are watermelons. How many watermelons are there ?

Answers

100% - (39% + 28% + 13%) = 100% - 80% = 20%
so 20% are watermelons.

20% of 1505...
0.20(1505) = 301

so 301 are watermelons

Answer:

13

Step-by-step explanation:

What is the equation for the vertical asymptote of f(x)= (x+2)/(4x+4)

Answers

Try this option:
if   [tex]f(x)= \frac{x+2}{4x+4} [/tex]
then according to 
[tex] \lim_{x \to (-1-0)} ( \frac{x+2}{4x+4})=+ \infty[/tex]
and [tex]\lim_{x \to (-1+0)} ( \frac{x+2}{4x+4})=- \infty[/tex]
an equation for vertical asymptote is x=-1.
The graph of this function is in the attached picture.

For which set of lines is it reasonable to state that The two lines are ALMOST perpendicular to each other? A) y = 2.1x + 3, y = 2.1x + 5 B) y = 0.9x + 5, y = -1.26x + 8 C) y = 5x + 1.25, y = -5x + 1.25 D) y = 3 4 x + 0.28, y = 4 3 x + 0.29

Answers

Selection B is the best.

The product of the slopes of the lines is closest to -1 for that pair of lines.

What value is equivalent to ∣ −14 ∣?

Answers

It is positive 14
The absolute value of any negative number becomes positive.
Your answer is 14

The two lines on each sides mean the number is an absolute value. The absolute value of a number is always positive, even if the number is positive itself!

Hope this helps!

Koji is installing a rectangular window in an office building. The window is 8/23 feet wide and 5/34 feet high. The formula for the area of a rectangle is A=bh. What is the area of the window? Enter your answer as a mixed number in simplest form in the box. $$ ft2

Answers

Here, We know, Area = Base * Height
We have: b = 823 Ft
h = 534 Ft

Substitute their values, 
A = 823 * 534
A = 439482 Ft²

In short, Your Answer would be: 439482 Ft²

I really hope this helps!

How do you solve 7.2>0.9(n+8.6)

Answers

7.2>0.9(n+8.6)
multiply 0.9 by all in parentheses

7.2> (0.9*n) + (0.9*8.6)
7.2> 0.9n + 7.74

subtract 7.74 from both sides
-0.54> 0.9n

divide both sides by 0.9
-0.6> n

ANSWER: -0.6> n

Hope this helps! :)

After solving the given equation, the value obtained for n will be equal to n < -0.6.

What is an equation?

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the equation given in the question,

7.2 > 0.9(n + 8.6)

Solve the equation for n,

7.2 > 0.9n + 7.74

7.2 - 7.74 > 0.9n

-0.54/0.9 > n

-0.6 > n or,

n < -0.6

To know more about equation:

https://brainly.com/question/29657983

#SPJ2

The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers. Find the two integers.

Answers

Assume the first even integer is x.
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.

The reciprocals of these two even integers can be written as [tex] \frac{1}{x} [/tex] and [tex] \frac{1}{x+2} [/tex] respectively.

The sum of their reciprocals is 7/24. So we can set up the equation as:

[tex] \frac{1}{x}+ \frac{1}{x+2}= \frac{7}{24} [/tex]

Taking LCM on left hand side:

[tex] \frac{x+2+x}{x(x+2)}= \frac{7}{24} \\ \\ \frac{2x+2}{ x^{2} +2x}= \frac{7}{24} [/tex]

Cross Multiplying the denominators:

[tex]24(2x+2)=7({ x^{2} +2x}) \\ \\ 48x+48=7 x^{2} +14x \\ \\ 7 x^{2} +14x-48x-48=0 \\ \\ 7 x^{2} -34x-48=0 \\ \\ [/tex]

Using the quadratic formula to solve the above equation:
[tex]7 x^{2} -34x-48=0 \\ \\ x= \frac{34+- \sqrt{1156+1344} }{14} \\ \\ x= \frac{34+- \sqrt{2500} }{14} \\ \\ x=\frac{34+-50 }{14} \\ \\ x=6 \\ x=- \frac{8}{7} [/tex]

Since, the value of x can only be an integer, we discard the fractional value and keep x=6

So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24

Algebra Functions and Data Analysis

Answers

Hello there!


The correct answer is option C (-∞,10)

Best of luck with your study!

Help with this math question please

Answers

Re-arranging the inequality to find the test points:

[tex]x- \frac{70}{x}\ \textless \ -3 \\ \\ x- \frac{70}{x}+3\ \textless \ 0 \\ \\ \frac{ x^{2} -70+3x}{x}\ \textless \ 0 \\ \\ \frac{(x-7)(x+10)}{x}\ \textless \ 0 [/tex]

This means, we need to test the inequality for x = -10, x = 0 and x = 7

Since question assumes that x > 0, so we ignore the values less than 0.
So the test points are x = 0 and x = 7

At x = 0 the expression is undefined.
Between x = 0 and x = 7 the value of expression [tex] \frac{(x-7)(x+10)}{x}[/tex] is negative. At x = 7 the value of expression is 0. Above x = 7 the value of expression is positive. 

So, the solution to the given inequality will be 0 < x < 7.
In Interval notation, the solution can be written as (0,7)

Two mechanics can assemble 10 bicycles in 8 hours. How many bicycles could one mechanic assemble in 8 hours?

Answers

Answer:

5 bicycles

Step-by-step explanation:

In the same time period (8 hours), half as many mechanics can assemble half as many bicyles: 10/2 = 5.

Two ships leave the same port in different directions, forming a 120° angle between them. One ship travels 70 mi. and the other 52 mi. before they each drop their anchors. What is the distance between the ships to the nearest mile?

Answers

Answer : Distance between the ships to the nearest miles = 106.03 ≈ 106 mi.

Explanation :

Since we have shown in the figure below :

a=70 mi.

b=52 mi.

c=x mi.

[tex]\text{Since two ships leaves the same port in different directions forming a }120\textdegree\text{angle between them.}[/tex]

So, we use the cosine rule , which states that

 [tex]c^2=a^2+b^2-2ab.cosC\\\\x^2=70^2+52^2-2\times 70\times 52\times cos(120\textdegree)\\\\x^2=4900+2704-7280\times (-0.5)\\\\x^2=7604+3640\\\\x^2=11244\\\\x=\sqrt{11244}\\\\x=106.03[/tex]

So, c = x= 106.03 mi.

Hence, distance between the ships to the nearest miles = 106.03 ≈ 106 mi.


what is the product of (2p+7)(3p^2+4p-3)

Answers

we know that
(2p+7)(3p²+4p-3)=2p*[3p²+4p-3]+7*[3p²+4p-3]
resolving by parts

part 1
2p*[3p²+4p-3]=6p³+8p²-6p

and 
part2
7*[3p²+4p-3]=21p²+28p-21

adding part 1 and part 2
[6p³+8p²-6p]+[21p²+28p-21]=6p³+29p²+22p-21

the answer is (6p³+29p²+22p-21)

A prism is comply filled with 3996 cubes that have edge lengths of 1/3 inches. What is the volume of the prism

Answers

The volume of a cube by definition is:
 V = L ^ 3
 Where:
 L: side.
 We have then that the volume of a cube is:
 V = (1/3) ^ 3
 V = 1/27
 Then, the prism volume is:
 Vtotal = 3996 * V
 Vtotal = 3996 * (1/27)
 Vtotal 148 inches ^ 3
 Answer:
 the volume of the prism is:
 Vtotal 148 inches ^ 3

10 Points Here come get them

Answers

The answer is option D. (15°)

Two angles are said to be supplementary when both angles together make a straight line. Since the measure of a straight line is 180°, it then follows that the sum of two supplementary angle is 180°

Let the unknown angle = x
x is supplementary to 165°
⇒ x + 165° = 180°
x = 180° - 165°
x = 15°
The answer to this is d. 15. 

Supplementary angles are two angles that equal to 180. So you take the known angle (165) and subtract it from 180 to find the other angle measure.

180-165=15

15 is your answer. 

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. what is the expected value of m, the mean of the distribution of sample means?​

Answers

Answer: 
80

Explanation:
The mean of the distribution of sample means always target the population mean. What this line tells is that whatever the population mean will be, the mean of the distribution of sample means will be same. Since the population mean is 80, the mean of distribution of sample means will also be 80.

However, the standard deviation of the sample distributions is different and is equal to the population standard deviation divided by square root of sample size. So in this case the standard deviation of distribution of sample means will be 6 .

Can someone help please? solve by system on inequalities solve each system by graphing

Answers

If you're going to solve by graphing, a graphing calculator is helpful.

The doubly-shaded area to the right of both lines is the solution space. The line at the upper boundary of that space is also part of the solution. The line at the lower boundary is not. The marked point where the lines intersect is not part of the solution space.

152.5225 to two decimal places

Answers

152.52 is your Answer
If you want 152.5225 2 decimal places to the left:
1.525225
If you want 152.5225 2 decimal places to the right:
15252.25

Hope this helps..... ;)

Mario buys 2 pounds of hamburger and 1 pound of sausage. Sausage costs 10 cents more per pound than hamburger. If the total cost of the meat is $5.50, what is the cost of the hamburger per pound?

Answers

Hamburger 1.80lbs sausage is 1.90lbs
1.80+ 1.80+ 1.90=$5.50
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