Answer:
The Bison is faster by 10 miles per hour.
Step-by-step explanation:
The Bison runs at 3520 ft / min
= 3520/ 5280 miles / minute
= (3520/ 5280) * 60 miles per hour
= 40 miles per hour
The ordered pairs for two points are listed in the table. What is the equation, in slope-intercept form, of the line that contains these points?
x l y
-1 l 3
1 l -7
A. y = -5x + 2
B. y = -5x - 2
C. y = 2x + 5
D. y = 2x - 5
Answer:
y = 5x - 2
Step-by-step explanation:
(-1,3) (1,-7)
Slope (m) = (-7-3)/(1+1) = -10/2 = -5
(-1,3)
y-y = m(x-x) = y-3 = -5(x - -1) = y-3= -5(x+1) =
y-3 = 5x-5
y = 5x - 5 + 3
y = 5x - 2
8. Subtract the polynomials: (3x2 + 5x – 8) – (2x2 - 4x + 3)
please give steps!!
[tex]\\ \sf\longmapsto 3x^2+5x-8-(2x^2-4x+3)[/tex]
[tex]\\ \sf\longmapsto 3x^2+5x-8-2x^2+4x-3[/tex]
[tex]\\ \sf\longmapsto 3x^2-2x^2+5x+4x-8-3[/tex]
[tex]\\ \sf\longmapsto x^2+9x-11[/tex]
Answer:
(3×2+5x-8)-(2×2-4x-3) = (6+5x-8)-(4-4x-3)
= 6+5x-8-4+4x+3
= -3+9x
A cylinder shaped can needs to be constructed to hold 550 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.07 cents per square centimeter. Find the dimensions for the can that will minimize production cost.
9514 1404 393
Answer:
radius: 3.685 cmheight: 12.896 cmStep-by-step explanation:
The cost of the ends of the can will be ...
c1 = 0.07(2πr²)
The cost of the side of the can will be ...
c2 = 0.04(2πrh)
The volume of the can will be ...
v = πr²h
We want the derivative of the total cost to be zero, and we want the volume to be 550 cm³. We can take the derivatives of both equations to find a relation between r and h.
d(c1 +c2) = 0.28πr·dr +0.08π(h·dr +r·dh) = 0
d(v) = 2πrh·dr +πr²·dh = 0
Solving the first equation for dh/dr gives ...
dh/dr = -π(0.28r +0.08h)/(π(0.08r)) = -(7r+2h)/(2r)
Solving the second equation for dh/dr gives ...
dh/dr = -2πrh/(πr²) = -2h/r
Equating these expressions, we get ...
-(7r +2h)/(2r) = -2h/r
7r +2h = 4h . . . . . . . multiply by -2r
h = 7/2r . . . . . . . . . . subtract 2h, divide by 2
__
Now, we can find the can dimensions from the volume equation.
550 = πr²(7/2r)
r³ = 1100/(7π)
r ≈ ∛50.02 ≈ 3.685 . . . . . cm
h = 7/2(3.685 cm) = 12.896 cm
The can cost will be a minimum when the radius is 3.685 cm and the height is 12.896 cm.
_____
Additional comment
You may notice that the ratio of height to diameter is the same as the ratio of end cost to side cost: 7/4. This is the generic solution to this sort of problem.
Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answer:
.87
Step-by-step explanation:
She gets 13 off so 100-13 =87
She will pay 87%
Multiply by .87
Kylie must multiply the price by 0.87 to get the discounted price.
Given that,
Kylie has a loyalty card good for a 13% discount at her local hardware store. What number should she multiply the prices on the tags by to find the price she would have to pay, is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
let the price be x,
Now,
According to the question,
discounted price = x - 13% of x
Discounted price = x - 0.13x
Discounted price = 0.87 x
The coefficient of the x represents the multiplication factor for Kylie.
Thus, Kylie must multiply the price by 0.87 to get the discounted price.
Learn more about percentages here:
brainly.com/question/13450942
#SPJ2
Please help me solve it .
9514 1404 393
Answer:
ii)
36 -16 = 206 -5 = 130 -11 = 19iii)
15 -6 = 95 +2 = 720 -4 = 16Step-by-step explanation:
Straightforward addition and subtraction. You could do this in 2nd grade. Work from lower right to upper left.
ii) 30 -11 = 19; 6 -5 = 1 . . . . bottom two rows
20 -1 = 19; 16 -5 = 11 . . . . right two columns
36 -16 = 20 . . . . top row
Check
36 -6 = 30 . . . . left column
Then the solution by row is ...
36 -16 = 206 -5 = 130 -11 = 19__
iii) Same deal, working from lower right.
20 -4 = 16 . . . . bottom row
9 +7 = 16 . . . . right column
6 -2 = 4 . . . . middle column
5 +2 = 7 . . . . middle row
15 -6 = 9 . . . . top row
15 +5 = 20 . . . . left column
The solution by row is ...
15 -6 = 95 +2 = 720 -4 = 162. A dolphin leaps 5 feet in the air at the same time an orca whale dives 12 feet below the water. How far apart are the whale and the dolphin?
A bookstore sells books at a profit of at least 15% of the final selling price. The store buys a certain book at a cost of £17. If the store gives students a 20% discount, what should the selling price of the book before the discount be?
The Selling Price of The Book before discount will be 20
Let f(x)=x^3-6x+3 i. find the domain of the function and f’(x) in the domain.
Domain of a any cubic function [tex]f(x)=ax^3+bx^2+cx+d[/tex] is defined to be always [tex]\mathbb{R}[/tex].
The derivative with respect to x of your cubic function is,
[tex]\dfrac{d}{dx}f(x)=f'(x)[/tex]
to find the derivative of a polynomial function, simply take a derivative of each factor and sum them up,
[tex]\dfrac{d}{dx}x^3=3x^2[/tex] by the rule [tex]\dfrac{d}{dx}x^m=mx^{m-1}[/tex] where [tex]m\in\mathbb{R}[/tex]
[tex]\dfrac{d}{dx}-6x=-6[/tex]
[tex]\dfrac{d}{dx}3=0[/tex]
So the derivative is,
[tex]f'(x)=3x^2-6[/tex]
both derivative and the original function have equal domain.
Hope this helps :)
Step-by-step explanation:
[tex]thank \: you[/tex]
please help me with this
Evaluate -8 × |2|.
Answer:
-16
Step-by-step explanation:
The absolute value of 2 is 2 so -8*2=-16
find the sum of all multiples of 9 between 0 and 200
Answer:
I thick the answer is 2277
The sample survey showed that 72% of Internet users said the Internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends.
Answer:
The 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:
[tex]0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]
In which n is the sample size of the survey.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The sample survey showed that 72% of Internet users said the Internet has generally strengthened their relationship with family and friends.
This means that [tex]\pi = 0.72[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Confidence interval:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]
The 95% confidence interval for the proportion of respondents who say the Internet has strengthened their relationship with family and friends is:
[tex]0.72 \pm 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]
In which n is the sample size of the survey.
in figure , EF=1 and FC=2 What is the length of AC?
Step-by-step explanation:
ae=ec
ec=1+2=3
then ae=3
Answer:
6-most likely (AC=6)
Step-by-step explanation:
Because the 2 sides, AE and EC *look the same. Also you can look at the opposite sides.
*This is what I think
Please answer this question
Which numbers are 9 units from −5 on this number line?
Drag and drop all of the numbers that are 9 units from −5 to their correct position on the number line.
-14,-5 -4 4 5 9
Answer:
-14 and 4
Step-by-step explanation:
To find the values subtract 9 from -5, as well as add 9 to -5
-5-9= -14
-5+9= 4
If 6 pounds of fruit is 96 cents how much is one pound
Answer:
16 cents per pound
Step-by-step explanation:
Take the cost and divide by the number of pounds
96 cents / 6 lbs
16 cents per pound
Amanda has 1 3/4yds of red ribbon and 7/8yds of green
ribbon. What is the total amount of ribbon that
Amanda has? (write answer as a fraction)
Answer:
21/8 yds or 2 5/8 yds
Step-by-step explanation:
First turn 1 3/4 yards into an improper fraction so you can add it to 7/8 yards.
1 3/4 as an improper fraction is 7/4 yds
7/4 yds = 14/8 yds
14/8 yds + 7/8 yds = 21/8 yds
So the total amount of ribbon Amanda has is 21/8 yds or 2 5/8 yds
what is the importance of mathematics?
(100 points) Select the correct answer.
Danny's 7 friends contributed an equal amount of money to buy him a birthday present. The present cost $84. How much money did each friend contribute?
A. 12
B. 36
C. 48
D. 84
Contribution per head
84/712Option A
Determine if f(x, y) = 10 − x^2 − y^2
is increasing or decreasing at (7, −3) if we
take y to be constant and let x vary. Also determine if f(x, y) is increasing at
(7, −3) if we take x to be constant and let y vary.
Answer:
Step-by-step explanation:
f(x,y)=10-x^2-y^2
To find derivative of z w.r.t. x is treat any other variable as a constant.
dz/dx=0-2x-0
dz/dx=-2x
Evaluating this at (7,-3) gives us dz/dx=-2(7)=-14.
Since this result is negative, it mrans as x increases z decreases.
f(x,y)=10-x^2-y^2
To find derivative of z w.r.t. y is treat any other variable as a constant.
dz/dx=0-0-2y
dz/dx=-2y
Evaluating this at (7,-3) gives us dz/dy=-2(-3)=6.
Since this result is positive it mrans as y increases z decreases.
determine the slope and the y intercept of the line 63=-9y
Answer:
-7
Step-by-step explanation:
63 divided by -9 = y
63 divided by -9 = -7
Check answers :
-9 x -7 = a
a= 63
A log of wood weighs 120kg. After drying, it now weighs 80kg. Find the moisture content of the wood in percentage.
Answer: 33% is moisture content
Step-by-step explanation:
120kg - 80kg = 40kg
40 of 120 is %
Work:
40/120 = 0.33
0.33x100
= 33%
what is the smallest number to be subtracted from 9610,so that the remainder will be a perfect square
Answer:
Hello,
Answer 6
Step-by-step explanation:
[tex]\sqrt{9610} =98,03060...\\\\ENT(\sqrt{9610})=98\\\\9610-98^2=9610-9604=6\\\\[/tex]
The smallest number to be susbtracted is 6
Question
Five people, each working 8 hours a day, can assemble 400 toys in a 5-day work week. What is the average
number of toys assembled per hour, per person?
11) Five must be the solution to 2x + 3 = 13 because 2(5) + 3 = 13.
Answer:
Yes, your right!
look at the image to see
Answer:
surface area = perimeter of base x slant height all of it divided by 2 and then add area of base
pb = 4(6)=24 x 9.5 = 228 /2 = 114 + 36 = 150
hope that answers your question :)
1. Write a survey question for which you would expect to collect numerical
data.
2. Write a survey question for which you would expect to collect categorical
data.
Answer:
How many siblings do you have?
I hope this helps you out :)
use the spinner to find the probability
Answer:
P(multiple of 5) = 0.1667
Step-by-step explanation:
The multiples of 5 on the spinner are 5 and 10. This means out of 12 numbers, only 2 multiples of 5. Therefore, there is a 2/12 chance to get a multiple of 5.
[tex]\frac{2}{12}=\frac{1}{6}=0.1667[/tex]
Therefore, P(multiple of 5) = 0.1667.
Solve the system by substitution.
Answer:
1st, keep value of x in 1st equation
Step-by-step explanation:
-6(-2y-1)+2y=48
12y+6+2y=48
14y=48-6
y=42/14
y=3
Now putting value of y in equation ii)
x= - 2y-1
x= - 2×3-1
x= - 6-1
x= - 7
Therefore, x= - 7
y=3
Find the slope m and y-intercept of the equation:
y = (-1/5)x + 7
a babay weighs 8 & 1/4 pounds at birth two weeks later she weighs 8 & 7/8 how much weight did the baby gain
Answer:
⅝ pounds
Step-by-step explanation:
Weight at birth = 8¼ pounds
Weight after two weeks = 8⅞ pounds
[tex]Weight \: gain \\ = Weight \: after \: two \: weeks - Weight \: at \: birth \\ = 8 \frac{7}{8} \: pounds - 8 \frac{1}{4} \: pounds \\ = (8 \frac{7}{8} \: - 8 \frac{1}{4}) \: pounds \\ = (8 \frac{7}{8} \: - 8 \frac{2}{8}) \: pounds \\ = ( \frac{7}{8} \: - \frac{2}{8}) \: pounds \\ = \frac{5}{8} \: pounds[/tex]
