Answer:
Your answer is 96.5606 Kilometers.
Step-by-step explanation:
1.609 x 60 = 96.5606
Mark as brainliest if it's correct!
Answer:
96.5606kms
Step-by-step explanation:
A box with a square base and an open top is to be constructed using 7500 sq. in. of cardboard. Find the dimensions of the box that will maximize its volume. What is the maximum volume
Answer:
Step-by-step explanation:
Let the length of one side of the square base be x
Let the height of the box by y
Volume of the box V = x²y
Since the box is opened at the top, the total surface area S = x² + 2xy + 2xy
S = x² + 4xy
Given
S = 7500sq in.
Substitute into the formula for calculating the total surface area
7500 = x² + 4xy
Make y the subject of the formula;
7500 - x² = 4xy
y = (7500-x²)/4x
Since V = x²y
V = x² (7500-x²)/4x
V = x(7500-x²)/4
V = 1/4(7500x-x³)
For us to maximize the volume, then dV/dx = 0
dV/dx = 1/4(7500-3x²)
1/4(7500-3x²) = 0
(7500-3x²) = 0
7500 = 3x²
x² = 7500/3
x² = 2500
x = √2500
x = 50in
Since y = (7500-x²)/4x
y = 7500-2500/4(50)
y = 5000/200
y = 25in
Hence the dimensions of the box that will maximize its volume is 50in by 50in by 25in.
The Volume of the box V = 50²*25
V = 2500*25
V= 62,500in³
Hence the maximum volume is 62,500in³
Two cyclists start from different locations and simultaneously begin heading toward each other. One of the cyclists travels 16 mph, while the other cyclists travels 22 mph. If the two cyclists are 342 miles apart, how many hours will it take for them to meet?
Answer:
The cyclists will meet after 9 hours.
Step-by-step explanation:
Let t be the time the cyclists need to meet.
16t + 22t = 342
38t = 342
t = 9
A music store has 1,440 CDs. Each CD rack holds 90 CDs. How many racks does the store need to use to hold all the CDs?
Answer:
16 cd racks
Step-by-step explanation:
1,440%90
16. If there are 75 calories in 220 grams of an artificial sweetener, how many calories would be
in 484 grams of that same artificial sweetener?
d. 165 calories
a. 150 calories
b. 155 calories
c. 160 calories
Answer:
d. 165 calories
Step-by-step explanation:
First of all, we would find the amount of calories in 1 gram of the artificial sweetener
1 gram = 220/75
1 gram = 2.93 calories
Therefore, 484 grams has;
484 * 2.93 = 165.2
Approximately, this is equal to 165 calories.
Method 2
220 grams of the artificial sweetener has 75 calories.
484 grams of the artificial sweetener has x calories.
Translating the word problem into an algebraic equation, we have;
220 = 75
484 = x
Cross-multiplying, we have;
220x = 75*484
220x = 36300
x = 36300/220
x = 165 calories.
Which expressions is equivalent to 21-(-5)
Answer:
21 + 5
Step-by-step explanation:
A negate minus a negative equals a positive
Answer:
(-5)-21
Step-by-step explanation:
use the cummutitive property to make a new equation out of the original one to get (-5)-21
How do you do these problems?
Answer:
18e⁶
⁵/₁₂₈
Step-by-step explanation:
Rₙ(x) = f⁽ⁿ⁺¹⁾(c) / (n+1)! (x − a)ⁿ⁺¹, and a < c < x.
f(x) = eˣ, a = 0, and n = 1. Thus R₁ is:
R₁(x) = f"(z)/2! x²
R₁(x) = eᶻ/2 x²
|R₁| is a maximum when |f"(z)| is a maximum. On the domain 0 < z < 6, that maximum is e⁶. At x = 6, the upper bound of |R₁| is:
|R₁| = 18e⁶
This time, f(x) = 1 / √(1 + x) = (1 + x)^-½. a = 0, and n = 2.
R₂(x) = f⁽³⁾(z)/3! x³
Find f⁽³⁾(x):
f'(x) = -½ (1 + x)^-³/₂
f"(x) = ¾ (1 + x)^-⁵/₂
f⁽³⁾(x) = -¹⁵/₈ (1 + x)^-⁷/₂
On the domain -½ < z < 0, |f⁽³⁾(z)| is a maximum at z = 0.
|f⁽³⁾(z)| = ¹⁵/₈
Therefore, at x = -½, the upper bound of R₂ is:
|R₂| = (¹⁵/₈)/6 |(-½)³|
|R₂| = ⁵/₁₂₈
The slope is the same as the unit rate and constant of a proportionality in a _______.
A. Prortional relationship
B. Slope
C. Rise
D. x2- x1
E. Run
F.y2 - y1
Answer:
I think the answer is B: Slope
Step-by-step explanation:
On a graph, proportional relationships are straight lines that extend through the origin. The relative steepness of the line is called slope; the slope of a graph is the same as the constant of proportionality of the equation.
Hope this helped, Have a Wonderful Day!!
The slope is the same as the unit rate and constant of proportionality in a slope. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The slope is the same as the unit rate and constant of proportionality in a slope. Then the correct option is B.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ5
105 people must be split into 3 equal groups. How many people in each group?
Answer:
35 people in each
Step-by-step explanation:
105÷3=35
please answer the full question
To demonstrate probabilities, a mathematics teacher had students draw cards from a bag which contained 26 red cards and 26 black cards. During class, the bag was dropped, and 5 red cards and 1 black card were lost.
Tell whether the loss of cards changes the probability of drawing a black card from the bag.
If so, was the probability increased or decreased? Support your answer by calculating the probability for each situation.
Answer:
The probability of drawing increases from drawing a black card from the bag.
Step-by-step explanation:
If 5 were dropped from red it would leave red with 21 cards and if 1 was dropped from black cards it would leave 25 cards in black cards. It does change the probability of drawing a red card it is more likely now to draw a black card than a red card because there are more black cards than red.
Hope this helps <3
What is 4x2 - x + 17 when x = -7?
Answer:
32
Step-by-step explanation:
4 times 2 is 8, - -7 is 15 plus 17 is 32
Given the following system of equations, identify the type of system.
x + y = 6
2x - y = -4
A. Consistent
B. Inconsistent
C. Equivalent
Step-by-step explanation:
I think is b i hope this works
4d + 3 - d + c Simplified Answer-Type Answer Here,
may someone please help me find the increasing and decreasing
Answer:
from [- infinity to (2, 0)] is when it is increasing. (both included).
from [(2, 0) to infinity ] is when it is decreasing. (both included).
By looking at the graph, we can determine this.
The slope of the increasing line is positive, and the slope of the decreasing line is negative.
Tell Me what 37/5 x 19/14 equal
Answer:
10 3/70
Step-by-step explanation:
Answer: 10.06
Step-by-step explanation:
You move down 6 units. You end at (-5, -5). Where did you start?
Answer:
(-5, 1)
Step-by-step explanation:
(x, y)
x moves left/right
y moves up/down
x = -5
y = -5 + 6 = 1
(-5, 1)
A typical tip in a restaurant is 15% of the total bill. If the bill is $90, what would the typical tip be
Answer:$13.50
Step-by-step explanation:
Find the value of x and y.
12
9
y
X=
y =
Answer:
the value of x is 12, and the value of y is 9
Answer:
y=9
x=12
Step-by-step explanation:
this is because the top and bottom of the square are equal as well as from the sides of left to right.
pls answer this asap will give brainliest
Answer:
C: The American antelope
Step-by-step explanation:
Please answer the question in the picture
What is the first step needed to solve 4 over 7 multiplied by x minus 5 equals negative 13 ? (1 point) Subtract 13 from both sides Divide both sides by 7 Add 5 to both sides Multiply both sides by 4\
It is add five two both sides.
For triangle EFG shown below, what is the measure of the exterior angle at vertex G?
E
(1) 27°
(3) 74°
47°
(2) 47°
(4) 94°
27°
106°
G
F
What is an equation of the line that passes through the point (-8,0) and is perpendicular to the line x+2y=14
Step-by-step explanation:
let eqn be y = mx + b.
Since perpendicular, m = - 1/(-0.5) = 2
sub (-8, 0):
0 = 2(8) + b
b = - 16
therefore equation is y = 2x - 16
Topic: coordinate geometry
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
find the slope of the line that passes through the point (-5,3) and (5,-3).
Answer:
-6/10 or -0.6
Step-by-step explanation:
m=y2-y1/x2-x1
-3-3=(-6)
5-(-5)=10
-6/10
hope this helps :3
if it did pls mark brainliest
Write an equivalent addition expression to : -10 – (-4)
Answer:
-6
Step-by-step explanation:
-10-(-4)=-1+4=-6
Hope this helps plz mark brainliest ;D
show that 4/9 - 1/6 = 5/18
Answer:
Step-by-step explanation:
4/9-1/6=5/18
Step-by-step explanation:
[tex] \frac{4}{9} - \frac{1}{6} [/tex]
[tex] (\frac{4}{9} \times \frac{2}{2} ) - ( \frac{1}{6} \times \frac{3}{3} )[/tex]
[tex] \frac{8}{18} - \frac{3}{18} [/tex]
5/18
The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all employees at the company and wants to conduct a systematic sample of size.
Required:
a. What is k?
b. Determine the individuals who will be administered the survey.
Answer:
Explained below.
Step-by-step explanation:
The human resource department at a certain company wants to conduct a survey regarding worker morale. The department has an alphabetical list of all 4,502 employees at the company and wants to conduct a systematic sample of size 50.
Systematic sampling is a kind of probability sampling method in which individuals from a larger population are nominated according to a random initial point and a static, periodic interval.
(a)
A sample of size 50.
Then the value of k will be: [tex]k=\frac{4502}{50}=90.04\approx 50[/tex]
Thus, the value of k is 90.
(b)
Label the employees from 1 to 4502.
And select every 90th employee.
So, the individuals who will be administered the survey are:
90th, 180th, 270th,...
a nursery sells kentucky bluegrass seed for $5.75 per pound and tall fescue seed for $4.50 per pound. the nursery sells a mixture of the two kinds of seed for $5.25 per pound. let k represent the amount of kentucky blue grass seed the nusery uses in in 5 pounds of the mixture
Answer:
[tex]k=3[/tex]
Step-by-step explanation:
Given that:
Per pound cost of kentucky bluegrass seed = $5.75
Per pound cost of tall fescue seed = $4.50
Per pound cost of mixture of seeds = $5.25
[tex]k[/tex] is the amount of kentucky blue grass.
Total amount of the mixture = 5 pounds
Therefore, amount of tall fescue seed = (5 - [tex]k[/tex]) pounds
To find:
The value of [tex]k[/tex].
Cost of [tex]k[/tex] pounds of kentucky bluegrass seed = [tex]\$5.75k[/tex]
Cost of (5 - [tex]k[/tex]) pounds of tall fescue seed = [tex]\$(5-k)4.50[/tex]
As per question statement:
[tex]5.75k+(5-k)4.50=5.25\times 5\\\Rightarrow 575k+5\times 450 -450k=525\times5\\\Rightarrow 125k=75\times5\\\Rightarrow k =3\ pounds[/tex]
Amount of kentucky blue grass seed used = 3 pounds
Amount of tall fescue seed used = 5-3 = 2 pounds
Which algebraic expression is equivalent to the expression below?
(13x - 7) + (12 - 3x)
A.
10x + 5
B.
25x - 10
C.
16x + 19
D.
10x + 19
Answer:
10x + 5
A is the correct answer
Step-by-step explanation:
what is 5+5 and then divided by 8
Two math questions
Among all pairs of numbers whose sum is 14, find a pair whose product is as large as possible. What is the maximum product?
The pair of numbers whose sum is 14 and whose product is as large as possible is nothing.
(Use a comma to separate answers.)
The maximum product is nothing.
and
- refer to picture
