Answer:
To find the directional derivative in the direction of the vector (1,2), we need to find a unit vector in the direction of the vector (1,2). We simply divide by the magnitude of (1,2). u=(1,2)∥(1,2)∥=(1,2)√12+22=(1,2)√5=(1/√5,2/√5).
Answer:To find the directional derivative in the direction of the vector (1,2), we need to find a unit vector in the direction of the vector (1,2). We simply divide by the magnitude of (1,2). u=(1,2)∥(1,2)∥=(1,2)√12+22=(1,2)√5=(1/√5,2/√5).
Step-by-step explanation:
There are 750 toothpicks in a regular-size box. A jumbo-size box is made by doubling the length, width, and height of the regular box. How many toothpicks will the jumbo box hold?
2250 toothpicks
1500 toothpicks
3000 toothpicks
6000 toothpicks
Answer:
The last option: 6,000 toothpicks.
Step-by-step explanation:
The formula I used: (2L) (2W) (2H)
If a jumbo sized box is made by doubling the length, width, and height then each measurment will be doubled so length x2, width x2, height x2 so therefore those added up would be 8. Then just do 8 times the volume. 8 x 750 = 6,000.
The best basketball player on a college team kept track of the number of baskets she made in her last eight games.
11 15 19 12 11 16 11 17
Calculate the mean, median, range, and midrange of the number of baskets she made in her last eight games.
The set is 11, 15, 19, 12, 11, 16, 11, 17
Mean = 14
Median = 13.5
Range = 8
Midrange = 15
What is a mean?
It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
The set:
11 15 19 12 11 16 11 17
The sum of the set:
= 11 + 15 + 19 + 12 +11 +16 + 11 + 17
= 112
Mean:
= 112 / 8
= 14
Median:
Arrange the set in ascending order.
11, 11, 11, 12, 15, 16, 17, 19
The Median is the mid-value of the set.
Median = (12 + 15) / 2 = 27/2 = 13.5
Range:
Highest value in the set = 19
Lowest value in the set = 11
Range = Highest value - Lowest value
= 19 - 11
= 8
Midrange:
= (Highest value + Lowest value) / 2
= (19 + 11) / 2
= 30/2
= 15
Thus,
If the set is 1, 15, 19, 12, 11, 16, 11, 17.
Mean = 14
Median = 13.5
Range = 8
Midrange = 15
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Michael stacks 14 identical disks to form a cylinder. Each disk is 1/4 inch thick. The diameter of each disk is 3 inches. Which measurement is closest to the volume, in cubic inches of the stack of disks? 7 99 396 25
adult tickets to the game are sold for $7 and student tickets are sold for $5. what combination of tickets must be sold to have total sales of at least $5000?
The combination of tickets that must be sold to have total sales of at least $5000 is 7x + 5y ≥ 5000
How to construct inequality?
The situation forms an inequality. Inequality expression has <, >, ≤ or ≥. Therefore,
let
x = number of adult ticket sold
y = number of students ticket sold
Therefore, the combination of tickets must be sold to have total sales of at least $5000 is as follows:
7x + 5y ≥ 5000
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6
Select the correct answer.
Which of the following is a non-real complex number?
OA. 9-
А.
-
5 — 2√7
4
ОВ.
O C.
-8√ - 3/12
OD.
3√² + √
Answer:
D
Step-by-step explanation:
In order to find a non-real number we look for a part of the expression that cannot exist.
Answer choice D stands out as you cannot take a square root of a negative number.
That's our answer!
Option D is correct, the given number 3√(7/5) + √-(9/5) is a non real complex number.
What are Complex Numbers?The complex number is basically the combination of a real number and an imaginary number.
3√(7/5) +√(-9/5) is a non real complex number
We know that a+ib is a complex number where a is real number and b represents the imaginary number
3√(7/5) +√i²(9/5)
3√(7/5) + i√9/5 it is in the form of a+ib.
where a is 3√(7/5) and b is √9/5
3√(7/5) + √-(9/5) is non real complex number
Hence, among the given numbers 3√(7/5) + √-(9/5) is a non real complex number.
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Please answer the first question
Answer:
12 inStep-by-step explanation:
The volume fomula of cylinder
V = πr²hGiven
d = 9 in, V = 763 inSubstitute the values into formula, considering d = 2r, solve for h
763 = 3.14(9/2)²h763 = 63.585hh = 763/63.585h = 11.999 ≈ 12The height is approximately 12 inches
Answer:
12 inches
Step-by-step explanation:
The vase can be modeled as a cylinder.
Volume of cylinder
[tex]\sf V= \pi r^2 h[/tex]
where:
r is the radiush is the heightGiven:
V = 763 in³Diameter = 9 inSubstitute the given values into the formula and solve for h:
[tex]\begin{aligned}\sf V & = \sf \pi r^2 h\\\\\implies \sf 763 & = \sf \pi (4.5)^2 h\\\\\sf h & = \sf \dfrac{763}{\pi (4.5)^2}\\\\\sf h & = \sf 11.99360213...\end{aligned}[/tex]
Therefore, the height of the vase is 12 inches (to the nearest inch).
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May is designing a triangular pyramid made of all glass to go on top of a building. All of the faces of the pyramid have a height of 17 feet and a base of 20 feet. How much glass is needed? A. 680 sq ft B. 340 sq ft C. 2,040 sq ft D. 1,360 sq ft.
Area of a triangle is 1/2 x base x height.
area of triangle = 1/2 x 20 x 17 = 170 square feet.
the image shows 4 triangles, total area = 170 x 4 = 680 square feet.
the answer is A. 680 sq. ft.
Answer:
Area of a triangle is 1/2 x base x height.
area of triangle = 1/2 x 20 x 17 = 170 square feet.
the image shows 4 triangles, total area = 170 x 4 = 680 square feet.
the answer is A. 680 sq. ft.
Hope this helps you!!
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A rental car company charges $31.91 per day to rent a car and $0.07 for every mile
driven. Hudson wants to rent a car, knowing that:
• He plans to drive 100 miles.
• He has at most $70 to spend.
Answer:
1.97 day; 1 day.
Step-by-step explanation:
0.07*100 = 7
31.91x - 7 = 70
70 - 7 = 63
31.91x = 63
63 / 31.91 = 1.97
Hudson can afford to drive the car for 2 days and stay under his budget.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We know that it costs $0.07 for every mile driven and we plan to drive 100 miles, that means we can set the inequality as:
31.91x + 0.07(100) ≤ 70
31.91x + 7 ≤ 70
Rearranging the inequality so we have the variable isolated on one side, we get:
31.91x ≤ 63
Divide both sides by 31.91 to get x alone.
x ≤ 1.97430
x ≤ 2
From obtaining the solution, Hudson can afford to drive the car for 2 days and stay under his budget.
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The question seems incomplete, the complete question would be as:
A rental car company charges $31.91 per day to rent a car and $0.07 for every mile driven. Hudson wants to rent a car, knowing that:
• He plans to drive 100 miles.
• He has at most $70 to spend.
Which inequality can be used to determine, the maximum number of days Hudson can afford to rent for while staying within his budget?
Find the total surface area
Answer:
585
Step-by-step explanation:
Explanation in picture below.
Can someone pls help
Answer:
12cm
Step-by-step explanation:
Answer:
Step-by-step explanation:
x/18 = 4/6
6x = 72
x = 12 cm
What type of number is √25? Whole number , integer , rational or irrational . SELECT ALL THAT APPLY
Answer:
A, B, and C.
Step-by-step explanation:
The square root of 25 is 5. 5 is rational, a whole number, and an integer.
PLEASE HELP ASAP, WILL GIVE BRAINLIEST IF CORRECT
Which line best represents the line of best fit for this scatter plot? Graph shows numbers from 0 to 10 at increments of 1 on the x axis and numbers from 0 to 18 at increments of 2. Scatter plot shows ordered pairs 1, 2 and 2, 6 and 3, 4 and 4, 10 and 5, 8 and 6, 8 and 7, 12 and 8, 10 and 9, 12 and 10, 14. A line labeled P joins ordered pair 0, 2.4 and 9, 18. A line labeled Q joins ordered pairs 0, 2.4 and 10, 18. A line labeled R joins ordered pairs 0, 2.4 and 10, 13.6. A line labeled S joins ordered pairs 0, 2.4 and 10, 10.
Line P
Line Q
Line R
Line S
Answer:
Line R
Step-by-step explanation:
Find the total surface area
Find the value of each determinant:
Help!
Answer:
Matrix 1: -4269
Matrix 2: 1768
Matrix 3: 647.3561
Step-by-step explanation:
Matrix 1: [tex](7*19)-(31*142)=-4269[/tex]
Matrix 2: 1768
[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]
Determinant = [tex]a(ei-fh)-b(di-fg)+c(dh-eg)[/tex]
Matrix 3: 647.3561
[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]
Determinant = [tex]a(ei-fh)-b(di-fg)+c(dh-eg)[/tex]
A bus company is replacing all the old seats in its buses with new ones. The company owns 15 buses and each bus has 22 seats. It costs $91.20 to purchase each new seat, as well as an additional $26.50 to install each new seat. What is the total cost the company will pay?
Answer:
30112.50. 15x22x91.20+26.50
Katy has a choice. She can buy a book of 6 round trip bus tickets from
Houston to Austin for a total of $522 or she can buy a book of 9 round trip
bus tickets from Houston to Austin for a total of $702. Which is the better
deal? Why?
Answer:
buying a book of 9 round trip bus tickets from Houston to Austin for a total of $702 is a better deal because 702/9 = 78 which is less than 522/6 = 87
Step-by-step explanation:
You deposit $25,000 into a bank that pays % 4 annual interest compounded monthly.
a) What is the account balance after 3 years?
b) When will the balance reach $40,000 ?
Answer
A: $28,000
B: 15 years
Step-by-step explanation:
A: Since $25,000 is deposited in the bank and you earn 4% interest annually over 3 years you would earn 12% interest. 12% of 25,000 is 3,000. The sum of 25,000 and 3,000 is 28,000 having you earn $28,000 over 3 years.
B: Since every year you earn 4% annual interest and you have $25,000 deposited in the bank you have to find what percentage of 25,000 equals 15,000. Since 25,000 isn't exactly easy to find multiply it by 4. That leaves you with 100,000 which we know you don't have in the bank but it will make it easier to find the percentage. You will also have to multiply 15,000 by 4 giving you 60,000. Now divide the 60,000 by 1,000 which equals 60. What's the point of the number 60? Well, that's the percentage it takes. Now divide 60 by the annual interest which is 4 and that gives you 15. 15 is the number of years it will take for the balance to reach $40,000.
Hope this helps!
(2 times the square root of 5 plus 3 times the square root of 7) squared
Answer:
10.19
Step-by-step explanation:
The graph shown compares the number of pages of the same book read by Emily and Serena over time.
How many minutes after Serena started reading would the number of pages read by them be equal?
Using linear equations, the number of minutes that both would read for them to read equal number of pages is: 30 minutes.
What is the Equation of a Linear Graph?Equation of a linear graph is given as, y = mx + b, where m and b are the slope and y-intercept of the graph respectively.
Equation for Emily's graph:
Slope (m) = rise/run = 1/3
y-intercept (b) = 2
Substitute m = 1/3 and b = 2 into y = mx + b
y = 1/3x + 2
Equation for Serena's graph:
Slope (m) = rise/run = 2/5
y-intercept (b) = 0
Substitute m = 2/5 and b = 0 into y = mx + b
y = 2/5x + 0
y = 2/5x
To find how many minutes for both of them to read the same number of pages, make both equations equal to each other.
2/5x = 1/3x + 2
2/5x - 1/3x = 2
1/15x = 2
Multiply both sides by 15
x = (2)(15)
x = 30
The answer is 30 minutes for both to read the same number of pages.
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what is the mean for 1500 338 588 850
Answer:
819
Step-by-step explanation:
The mean is the average. Add up all the values and then divide that by the total amount of values. 1500+338+588+850=3276. 3276/4=819.
2. Given: A drug for the relief of asthma can be purchased
from 5 different Manufactures in liquid, tablet, or capsule
form, all of which come in regular or extra strength.
Required: In how many ways can a nurse administer the
drug for a patient suffering for asthma?
Answer:
5*3*2=30ways
Step-by-step explanation:
Since we have 5 different manufacturers who manufactures the drug in 3 different forms and 2 type of strengths, then;
Number of ways in which a nurse can administer the drug for a patient
are; Ways=5*3*2=30ways
It takes Hugh 27 minutes to make of a basket. Enter the time, in hours, it would take Hugh to make 12 baskets.
Two adjacent angles form a straight angle. Which term best describes these two angles?
1. Supplementary angles.
2. Vertical angles.
3. Corresponding angles.
4. Complementary angles.
the answer would be supplementary angle, as an angle is supplementary when the measurements add up to 180 degrees
i need help this exact minute
no fake answers, seriously no.
Answer:
h is the horizontal translation
k is the vertical translation
a is the stretch parallel to the y-axis
Step-by-step explanation:
Parent equation: [tex]y=x^2[/tex]
Translate [tex]h[/tex] units right: [tex]y=(x-h)^2[/tex]
(if [tex]h < 0[/tex], then the translation is [tex]h[/tex] units left)
Stretched parallel to the y-axis by a factor of [tex]a[/tex]: [tex]y=a(x-h)^2[/tex]
(if [tex]a < 0[/tex], the graph is also reflected in the x-axis)
Translated k units up: [tex]y=a(x-h)^2+k[/tex]
(if [tex]k < 0[/tex] then the translation is k units down)
Example attached for [tex]y=2(x-3)^2+4[/tex]
How many outcomes are possible?
2 quarters, 4 dimes, and 1 nickel are tossed
Answer:
70
Step-by-step explanation:
2 quarters are 50¢
4 dimes are 40¢
1 nickel is 5¢
if you add it all together you will get 70¢
What is the surface area of the cylinder with height 4 km and radius 5 km?
y = kx
If y = 54 when x = 60, what is the value of k?
Give any decimal answers to 1 d.p.
Rubin has 6 rolls of pennies containing 50 coins each, 5 rolls of nickels
containing 40 coins each, 4 rolls of dimes containing 50 coins each, and 3
rolls of quarters containing 40 coins each. How much money does he have?
A. $68.40
B. $63.00
C. $8.20
D. $17.50
Answer:
300 cents in pennies
1000 cents in nickles
2000 cents in dimes
3000 cents in quarters
the answer would be B. 63.00
can someone help me with this problem please and give examples im clueless on this one
Ready Mathematics
Unit 6 Unit Assessment
Solve the problems.
1 Look at the triangles.
3 cm
3 cm
3 cm
3 cm
4 cm
7 cm
4 cm
3 cm
Date
3 cm
Answer:
Talking Ben Thinks It 7 cm
Step-by-step explanation:
7m Cause Ben Told me