Answer:
Volume = 2,143.57 mm³
Step-by-step explanation:
Given:
radius (r) = 8 mm
π = 3.14
Required:
Volume of the sphere
Solution:
Volume of the sphere = ⁴/3πr³
Plug in the values
Volume = ⁴/3 × 3.14 × 8³
= ⁴/3 × 3.14 × 512
= 6,430.72/3
Volume = 2,143.57333
Volume = 2,143.57 mm³ (nearest hundredth)
Consider a triangle ABC like the one below. Suppose that a = 47, b = 59, and A = 37" (The figure is not drawn to scale.) Solve the triangle,
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or",
Answer:
B = 49.1°
C = 93.9°
c = 77.9
Step-by-step explanation:
Given:
a = 47, b = 59, and A = 37°
Required:
B, C, and c
Solution:
✔️To find B, apply the law of sines:
[tex] \frac{sin(A)}{a} = \frac{sin(B)}{b} [/tex]
Plug in the values
[tex] \frac{sin(37)}{47} = \frac{sin(B)}{59} [/tex]
Cross multiply
[tex] 47*sin(B) = sin(37)*59 [/tex]
Divide both sides by 47
[tex] \frac{47*sin(B)}{47} = \frac{sin(37)*59}{47} [/tex]
[tex] sin(B) = 0.7555 [/tex]
[tex] B = sin^{-1}(0.7555) [/tex]
[tex] B = sin^{-1}(0.7555) [/tex]
B = 49.0690779° ≈ 49.1° (nearest tenth)
✔️C = 180° - (A + B) (sum of triangle)
C = 180° - (37° + 49.1°)
C = 93.9°
✔️To find c, apply the law of sines:
[tex] \frac{sin(B)}{b} = \frac{sin(C)}{c} [/tex]
Plug in the values
[tex] \frac{sin(49.1)}{59} = \frac{sin(93.9)}{c} [/tex]
Cross multiply
[tex] c*sin(49.1) = sin(93.9)*59 [/tex]
Divide both sides by sin(49.1)
[tex] c = \frac{sin(93.9)*59}{sin(49.1)} [/tex]
c = 77.8766982
c ≈ 77.9 (nearest tenth)
What is the approximate volume of a cone with a height of 12 inches and a diameter of 10 inches?
Use 3.14 for 7 and round the answer to the nearest whole number.
Answer:
314
Step-by-step explanation:
V=πr^2(h/3)
diameter is 10 so /2 and you get radius
plug values in and solve for x
Answer:
314
yea im sure thats the answear
If the gradient of the tangent to
[tex]y = \sqrt{x} [/tex]
is
[tex] \frac{1}{6} [/tex]
at point A, find the coordinates of A.
Answer:
Point A(9, 3)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y) Functions Function Notation Terms/Coefficients Anything to the 0th power is 1Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{x}[/tex]
[tex]\displaystyle y' = \frac{1}{6}[/tex]
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y = x^{\frac{1}{2}}[/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}x^{\frac{1}{2} - 1}[/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}x^{-\frac{1}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2x^{\frac{1}{2}}}[/tex][Derivative] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}[/tex]Step 3: Solve
Find coordinates of A.
x-coordinate
Substitute in y' [Derivative]: [tex]\displaystyle \frac{1}{6} = \frac{1}{2\sqrt{x}}[/tex][Multiplication Property of Equality] Multiply 2 on both sides: [tex]\displaystyle \frac{1}{3} = \frac{1}{\sqrt{x}}[/tex][Multiplication Property of Equality] Cross-multiply: [tex]\displaystyle \sqrt{x} = 3[/tex][Equality Property] Square both sides: [tex]\displaystyle x = 9[/tex]y-coordinate
Substitute in x [Function]: [tex]\displaystyle y = \sqrt{9}[/tex][√Radical] Evaluate: [tex]\displaystyle y = 3[/tex]∴ Coordinates of A is (9, 3).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
The ratio of two sums of money is 5:7 if the smaller amount is $250, what is the largest amount?
Answer:
$350
Step-by-step explanation:
[tex]\frac{250}{y} :\frac{5}{7}[/tex]
y · 5 = 250 · 7
5y = 1750
5y ÷ 5 = 1750 ÷ 5
y = 350
Answer:
$350
Step-by-step explanation:
5 is to 250 as 7 is to 'x'
5/250 = 7/x
cross-multiply:
5x = 1750
x = 350
Evaluate Vb2 - 4ac when a = -2, b = 8 and c = 1/2 Write your answer in simplest form and in decimal form rounded to the
nearest hundredth
Simplest form:
Decimal form:
plz plz answer this 10pts
Answer:
PART A
$4.25×2.9$12.325PART B
cost of milk chocolate=$5.15×1.6$8.24total cost =12.325+8.24
$20.565hope it helps
stay safe healthy and happy.Answer:
Part A: $12.325
Part B: $20.565
Step-by-step explanation:
PART A:
To find the answer, we multiply 2.9 and 4.25 together: 2.9 * 4.25 = 12.325
The cost of 2.9 pounds of dark chocolate is $12.325
PART B:
To find the answer, we multiply 1.6 and 5.15 together: 1.6 * 5.15 = 8.24
After that, to find the cost of the dark and milk chocolate together, we add up the two answers: 12.325 + 8.24 = 20.565
The total cost of the milk and dark chocolate is $20.565
Note: You might need to round it up. In this case, Part A is $12.33 and Part B is $20.57
David wanted to go on an amusement park ride. A sign posted at the entrance read “You must be greater than 42 inches tall and no more than 57 inches tall for this ride.” Which inequality would model the height, x, required for this amusement park ride?
Answer:
42 < x less than or equal to 57
Step-by-step explanation:
The inequality that would model the height, x, required for this amusement park ride is 57 > h > 42.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations
Now it is given that,
Lower limit of height must be greater than 42 inches
Upper limit of height must be less than 57 inches
If h is the height used for model.
Thus, h < 57 inches
and, h > 42 inches
Therefore the inequality model will be,
57 > h > 42
Thus, the inequality that would model the height, x, required for this amusement park ride is 57 > h > 42.
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WILL MARK BRAINLIEST!!! Plz help me with my math!
y varies directly with x. If y = -4 when x = 2, find y when x = -6.
Answer:
y = 12
Step-by-step explanation:
y = kx
-4 = k * 2
k = -4/2 = -2
y = -2x
y = -2 * (-6)
y = 12
Fahad is 140 cm tall. Fareed is 1090 mm tall.
Who is taller? How much taller?
Answer:
Fahad is taller with 31 centimeters
Step-by-step explanation:
1090mm=109cm
Fahad is taller than Fareed by 31 centimeters.
1090 mm = 109 cm
140 cm - 109 cm = 31 cm
Hope this helps; please mark brainliest!
Have an amazing day!
Gabe purchased a razor for $9.99, a refill pack of razor blades forthe
regular price of $12.99, shaving cream for $2.99, and lotion for$5.55. He
had a $4.00 coupon for the razor, a $0.75 coupon for the shaving cream,
and a $2.00 manufacturer's rebate form for the refill. Determine the final
price.
A. $ 27.47
B. $ 27.44
C. $ 24,47
D. $ 24.77
Answer:
24.77
Step-by-step explanation:
The final without coupons is 31.52, but because you use 4.75 in coupons and 2.00 in manufacturer's rebate, it drops down to 24.77.
Hope this helps!
Above are two different models of the same rectangle. If the length of the model on the top is 6 cm, what is the length of the model on
the bottom?
A. 15 cm
В. 12cm
C. 21cm
D.36cm
Answer:
D.36cm
Step-by-step explanation:
If the top rectangle have 6 cm, it means 6×16=108 ft
If the two rectangles are the same, it means that the bottom rectangle have also 108 ft, so:
108÷3= 36 cm
Find the selling price
Cost of the computer; $1,850.00
Markup: 75%
Answer:
2466.67
Step-by-step explanation:
1850/.75=2466.67
The cost of selling price of the computer is, $3,237.5
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Cost of the computer = $1,850.00
Markup = 75%
Now,
The cost of selling price of the computer is,
⇒ $1,850 + 75% of $1,850
⇒ $1850 + 75 /100 × $1850
⇒ $1850 + $1387.5
⇒ $3,237.5
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Bill had 5 tests over the marking period. He knows he is receiving a 85 on his report card. He was looking back at his test and only has four grades: 80, 90, 100, 85. What was the score of the missing test? Please no silly answers or links ill report you.
Answer:
70
Step-by-step explanation:
(Not the most streamlined way but.)
Knowing that if he had 5 tests, and a mark of 85, we can determine the total average grade Bill received. 85*5=425
Then subtract the known grades
425-(90+85+100+80)=x
425-(355)=x
70=x
Bill would have scored 70 on that 5th test
1.) Determine the type of solutions for the function (Picture 1)
2.) Determine the type of solutions for the function (Picture 2)
3.) Use the formula b2−4ac to determine the value of the discriminant of the function f(x)=2x2+8x+6
Use Desmos Scientific (Picture 3)
4.) Describe the transformations of the function
g(x)=−25(x−4)2+6 from the transformation of the parent function
Use phrases such as: the graph is reflected or not reflected/ the graph gets wider or narrower/ the graph slides left or right _________ units and slides up or down _________ (Picture 4)
Answer:
1) 2 nonreal complex roots
2) 1 Real Solution
3) 16
4) Reflected, narrower by a factor of 2/5, slides right 4 units and slides up 6 (units)
Step-by-step explanation:
1) The graph does not intercept the x-axis, therefore, there are no real solutions at the point y = 0
We get;
y = a·x² + b·x + c
At y = 6, x = -2
Therefore;
6 = a·(-2)² - 2·b + c = 4·a - 2·b + c
6 = 4·a - 2·b + c...(1)
At y = 8, x = 0
8 = a·(0)² + b·0 + c
∴ c = 8...(2)
Similarly, we have;
At y = 8, x = -4
8 = a·(-4)² - 4·b + c = 16·a - 4·b + 8
16·a - 4·b = 0
∴ b = 16·a/4 = 4·a
b = 4·a...(3)
From equation (1), (2) and (3), we have;
6 = 4·a - 2·b + c
∴ 6 = b - 2·b + 8 = -b + 8
6 - 8 = -b
∴ -b = -2
b = 2
b = 4·a
∴ a = b/4 = 2/4 = 1/2
The equation is therefor;
y = (1/2)·x² + 2·x + 8
Solving we get;
x = (-2 ± √(2² - 4 × (1/2) × 8))/(2 × (1/2))
x =( -2 ± √(-12))/1 = -2 ± √(-12)
Therefore, we have;
2 nonreal complex roots
2) Give that the graph of the function touches the x-axis once, we have;
1 Real Solution
3) The given function is f(x) = 2·x² + 8·x + 6
The general form of the quadratic function is f(x) = a·x² + b·x + c
Comparing, we have;
a = 2, b = 8, c = 6
The discriminant of the function, D = b² - 4·a·c, therefore, for the function, we have;
D = 8² - 4 × 2 × 6 = 16
The discriminant of the function, D = 16
4.) The given function is g(x) = (-2/5)·(x - 4)² + 6
The parent function of a quadratic equation is y = x²
A vertical translation is given by the following equation;
y = f(x) + b
A horizontal to the right by 'a' translation is given by an equation of the form; y = f(x - a)
A vertical reflection is given by an equation of the form; y = -f(x) = -x²
A narrowing is given by an equation of the form; y = b·f(x), where b < 1
Therefore, the transformations of g(x) from the parent function are;
g(x) is a reflection of the parent function, with the graph of g(x) being narrower by 2/5 than the graph of the parent function. The graph of g(x) is shifted right by 4 units and is then slides up by 6 units.
How do you find the unknown length for a special right angel
Answer: Pythagorean theroem
Step-by-step explanation:
The easiest method to use in terms of a missing side as long as you know at least two other variables whether its another side or angle
BRAINLY PEOPLE HELP!!!
Answer:
A)
Step-by-step explanation:
Hope I helped! Ask me anything if you have questions! Brainiest plz. Hope You make a 100%! Have a nice day! -Amelia♥
Which is greater 6 cups or 4 quarts
Answer:
not sure but 4 quarts i think
Answer:
4 quarts is greater because it is equal to 16 cups
3/4 x 2/5 x 4/3 please helpppppppppppppppppppp
Answer:
24/60 or 0.4
Step-by-step explanation:
3/4×2/5=6/20
4/3×6/20=24/60
24/60
ILL GIVE YOU BRAINLIEST!! 33 POINTS!!!
(ONLY IF YOU GET IT CORRECT)
Answer:
80 ft
Step-by-step explanation:
the length of an arc is equal to the degree the arc makes
Answer:
A. 28π/9 ftStep-by-step explanation:
Arc length is:
2πr*80°/360° ft = 4π*7/9 ft =28π/9 ftCorrect choice is A
There is a hole that is 6ft deep and has a diameter of 5t how much dirt is in the hole?
Lily is 90 cm tall. If Anika is 3/5 of the height of Lily, and Sadaf is 4/3 of the height of Anika, how tall is Sadaf?
Based upon risk, which of the following answers ranks from high to low?
Collectables
Bonds
Stocks
Mutual Funds
Answer:
stocks, bonds, mutual funds, and collectables
Step-by-step explanation:
Find the length of the following sides:
DF
AB
EF
Answer:
DF) = 10
AB) = 5
EF) = 12.5
Step-by-step explanation:
For length AB
[tex]3^{2} +4^{2} = AB^{2}[/tex] -> 9+16=[tex]\sqrt{25}[/tex] -> 5
For length DF
We know that AD is 2.5 times smaller than DE (7.5 / 3)
Now we can use that to determine length DF
BD = 4, DF = 4*2.5 = 10
using the Pythagorean theorem, you can find EF:
[tex]DE^{2} +DF^{2} =EF^{2}[/tex]
[tex]7.5^{2}+ 10^{2} =12.5[/tex]
Josh orders 12 soccer jerseys for his team, including his coach. He pays a total
of R594,60 for the jerseys. What did each jersey cost?
Answer:
4955
Step-by-step explanation:
soccer jerseys--> 12
total--> R 59460
= 59460 divided by 12
= 4955
Ans: Each jersey costs R 4955.
thenks and mark me brainliestt pls :))
We had a surprise party for Grandmama she was very surprised. Find the error in the sentence
Answer:
There needs to be a (.) or an (;)
Step-by-step explanation:
Drag a company name into each box to show the total cost from least to greatest.
Answer:
Company A:
$3 each6% for shipping150*3*1.06 = $477 total costCompany B:
$3.10 each4% for shipping150*3.1*1.04 = $483.60 total costCompany C:
$3.20 eachNo shipping charge150*3.2 = $480 total costLeast cost | Medium cost | Greatest cost
Company A | Company C | Company B
Who could help me please and thank you
Only answer if you know how to do the equation
Let's find the slope of the line passing through it :
[tex] \boxed{ slope = \frac{y_2-y_1}{ x_2- x_1} }[/tex]
[tex] \dfrac{ -5 - ( - 6)}{0 - ( - 5)} [/tex][tex] \dfrac{1}{5} [/tex]Now, we know, equation of a line is :
[tex]\longrightarrow y = mx + b[/tex]
where,
m represents the slopeTherefore,
[tex]\longrightarrow \: y = \dfrac{1}{5} x + b[/tex]
let's put the value of x and y from the first coordinates .
[tex]y = \dfrac{x}{5} + b[/tex][tex] - 5 = \dfrac{0}{5} + b[/tex][tex]b = - 5[/tex]Hence, we got the equation of line as :
[tex]y = \dfrac{x}{5} - 5[/tex]or
[tex]5y = x - 25[/tex]_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
6 + y= -8 ????????????????
Answer:
y = -14
Step-by-step explanation:
6 + y = -8
Subtract 6 from both sides to get y by itself.
y = -14.
Proof:
6 + y = -8
Substitute the variable.
6 + (-14) = -8
Add the negative/Subtract.
-8 = -8.
Answer:
y=−14
Step-by-step explanation:
Let's solve your equation step-by-step.
6+y=−8
Step 1: Simplify both sides of the equation.
y+6=−8
Step 2: Subtract 6 from both sides.
y+6−6=−8−6
y=−14
brainliest please?If we remove all of the jacks, queens and kings from a 52-card deck, how many unique three card hand combinations can we create?
59,280
44,200
132,600
19,760
The no. of unique card combinations we can create is 59280
What is permutation and combination?
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented.
There are 52 cards in a deck in which, there are 12 face cards and 40 numbered cards.
So, by using fundamental principle of counting=40x39x38 =59280
Therefore, the no. of unique card combinations we can create is 59280
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The Kitchen committee purchased 76 boxes of cookies for Vacation Bible School,
Monday, 14 2/3 boxes were used; Tuesday 15 boxes; and Wednesday 13 3/4 boxes.
How many boxes were used during the three days?
(Write the operation and the answer)