Answer:
2 hours
Step-by-step explanation:
Mike has a six hour head start so he is 6 x 2 = 12 miles ahead
their 'closing speed' is 8-2 = 6 m/hr
it will take Kim 12 / 6 = two hours to catch Mike
A solid sphere is cut into 12 equal wedges. The volume of each wedge is
V=³. Solve the formula for r.
The complete question is
"A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. Solve the formula for r."
A solid sphere is cut into 12 equal wedges. The volume of each wedge is V= 4/3πr³. The value of r is (9V/π)^1/3.
What is the volume of the sphere?It is given that;
The Volume of a sphere = V = 4/3πr³
Dividing into 12
4/3 x 1/12 πr³ = 1/9πr³
V = 1/9πr³
Cross multiply
9V = πr³
Divide both sides by π
9V/ π = πr³/ π
9V/ π = r³
Take the cube root of both sides
r = (9V/π)^1/3
Thus, The value of r is (9V/π)^1/3.
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A cylindrical cup with a base diameter of 4 inches and a height of 12 inches is filled with orange juice that occupies 67% of the cup. What is the volume of the orange juice in the cup?
Volume
πr²hπ(2)²(12)48π150.7in³Volume of orange juice
67% of 150.70.67(150.7)100.969in³Answer:
101.0 in³ = 1.656 liters
Step-by-step explanation:
Formulas
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
[tex]\textsf{Diameter of a circle}=2r \quad\textsf{(where r is the radius)}[/tex]
Given dimensions of cylinder:
diameter = 4 inheight = 12 inFirst, calculate the radius by halving the diameter:
[tex]\implies \textsf{Radius }(r)=4 \div 2=2\: \sf inches[/tex]
Substitute the given values into the formula to find the volume of the cup:
[tex]\begin{aligned}\textsf{Volume of a cylinder} & = \pi r^2h\\ \implies \textsf{Volume of the cup} & = \pi \cdot (2)^2 \cdot 12\\& = \pi \cdot 4 \cdot 12\\& = 48\pi \sf \:\:in^3 \end{aligned}[/tex]
The cup is filled with orange juice that occupies 67% of the cup. To find the volume of orange juice in the cup, multiply the found volume of the cup by 67%:
[tex]\begin{aligned}\implies\textsf{Volume of orange juice} & = 67\% \textsf{ of }48 \pi \\\\& = \dfrac{67}{100} \cdot 48 \pi \\\\& = \dfrac{3216}{100} \pi \\\\& = 101.0336197...\\\\& = 101.0\:\: \sf in^3\:(nearest\:tenth) \end{aligned}[/tex]
Liquid is usually measured in liters.
To convert cubic inches to liters, multiply by 0.016387064:
[tex]\implies \sf 101.0336197...in^3 \times 0.016387064 = 1.656 \: liters\:(3\:dp)[/tex]
Solving Linear Equations: Variable on One Side
ssignment Active
Determining the Input Value That Produces the Same Output
Value for Two Functions
If f(x) = -3x + 4 and g(x) = 2, solve for the value of x
for which f(x) = g(x) is true.
ty
X =
y = f(x)
y = g(x)
x
2 3
Done
-2
Intro
-1
4
3
2
1
1
answer 2/3
check the attachments for more info
hope it helps :)
The functions f(x) and g(x) are equal for the x = 2/3
What is a function?A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given that, are two functions, f(x) = -3x + 4 and g(x) = 2, we need to find the value of x for which both are equal,
So,
For f(x) = g(x) we should equate the two functions to get the value of x.
f(x) = g(x)
-3x + 4 = 2
-3x + 4 - 4 = 2 - 4
-3x = -2
Dividing by -3 on both sides;
(-3x)/-3 = (-2)/-3
x = 2/3
Hence, the functions f(x) and g(x) are equal for the x = 2/3
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What is the volume of the cylinder below?
-----
-
2112
O O
A. 408 units3 B. 2448 units3
O
C. 204772 units 3
O
D. 20471 units
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
We need to find volume of the given Cylinder, with information :
radius (r) = 12 units height (h) = 17 units[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi r²h[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot(12) {}^{2} \sdot17[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = \pi \sdot144{}^{} \sdot17[/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(Cylinder)} = 2448 \pi \: \: unit {}^{3} [/tex]
So, correct choice is B
The volume of the given cylinder is 2448π cubic units
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the volume of the given cylinder
Radius is 12 units
Height is 17 units
Volume of cylinder= πr²h
Plug in the values of radius and height
Volume = π×12²×17
=π×144×17
=2448π cubic units
Hence, the volume of the given cylinder is 2448π cubic units
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What is the solurion to h/-24 < 18
Let's solve
h/-24<18Multiply- on both sides
h/24>-18Multiply 24 on boths sides
h>-18(24)h>-432Solution set
(-432,oo)Answer:
Step-by-step explanation:
Given inequality:
[tex]\sf \dfrac{h}{-24} < 18[/tex]
Eliminate the denominator of the fraction by multiplying both sides by -24, remembering to flip the relation (inequality symbol) as the factor is negative.
[tex]\implies \sf \dfrac{h}{-24} \cdot -24 > 18 \cdot -24[/tex]
[tex]\implies \sf h > -432[/tex]
Therefore, the solution is [tex]\sf h > -432[/tex]
Howard and Jane are surveying their neighbors about the community garden. Their questions, written on the survey, are below: Howard: Did you visit the garden this month? Jane: How many times do you visit the garden in a month? Who wrote a statistical question and why?
Answer:
Step-by-step explanation:
Note
Answer: Jane's question
Howard merely asked if a visit had taken place. There isn't a number anywhere or one that can be implied.
Jane asked for a number. It requires that the responder gives a number with no embellishment. The question asks for the number of times something has occurred and there is a time frame for the answer. That usually is the characteristic of a statistical survey.
Which shows one way to determine the factors of Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? by grouping?
The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
How to determine the factors?The expression is given as:
x^3 + 4x^2 +5x + 20
Group the expression into two
(x^3 + 4x^2) + (5x + 20)
Factorize each group
x^2(x + 4) + 5(x + 4)
Factor out x + 4
(x^2 + 5)(x + 4)
Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
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The table shows the number of cups of water required when cooking different amount of rice
Which statements apply to the ratio of rice and water? Choose two options.
A) The amount of rice is the dependent value.
B) the amount of the water is the dependent value.
C) the amount of rice is the independent value
D) the amount of water is the independent value.
E) the values cannot be labeled as dependent or independent without a given equation.
Forming quadratic expression.Two consecutive odd numbers are such that their product is 35.find the numbers
Answer:
Numbers are 5 , 7
Step-by-step explanation:
Forming quadratic equation and solving:Let the two consecutive odd numbers be (2x + 1) and (2x + 3)
Their product = 35
(2x + 1)(2x + 3) = 35
Use FOIL method.
2x*2x + 2x*3 + 1*2x + 1*3 = 35
4x² + 6x + 2x + 3 = 35
Combine like terms
4x² + 8x + 3 = 35
4x² + 8x + 3 - 35 = 0
4x² + 8x - 32 = 0
Quadratic equation: 4x² + 8x - 32 = 0Solving:
4x² + 8x - 32 = 0
Divide the entire equation by 2
[tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]
2x² + 4x - 16 = 0
Sum = 4
Product = -32
Factors = 8 , (-4)
When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.
Rewrite the middle term
2x² + 8x - 4x - 16 = 0
2x(x + 4) - 4(x + 4) = 0
(x + 4) (2x - 4) = 0
2x - 4 = 0 {Ignore x +4 = 0 as it gives negative number}
2x = 4
x = 4/2
x= 2
2x + 1 = 2*2 + 1 = 5
2x + 3 = 2*2 +3 = 7
The numbers are 5 , 7
5 ⟌94.3
108.86
18.86
188.6
18.68
Answer:
18.86
Step-by-step explanation:
5 ⟌94.3
90 ÷ 5 = 18
18
5 ⟌94.3
-90
-----------------
4.3
cant divide by 4 so add a decimal
5 × 0.8 = 4
18.8
5 ⟌4.3
- 4.0
---------------
0.3
5 × 0.06 = 0.3
18.86
5 ⟌0.3
- 0.3
--------------
0
I hope this helps!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the graph of the function .
Match each transformation of function f with a feature of the transformed function.
vertical asymptote of
function decreases as x increases
y-intercept at
x-intercept at
arrowRight
arrowRight
arrowRight
g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)
h(x) = f(x - ¹/₂) -------> x-intercept at (1.5, 0)
j(x) = f(x) - ¹/₂ -------> vertical asymptote at x = 0
m(x) = function decreases as x increases
How to Interpret Graphs?We are given the function;
f(x) = In (x)
Now, from the given tiles and when we punch the respective values for the given functions, we can say that;
g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)
h(x) = f(x - ¹/₂) -------> x-intercept at (1.5, 0)
j(x) = f(x) - ¹/₂ -------> vertical asymptote at x = 0
m(x) = function decreases as x increases
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Khloe goes to a store an buys an item that costs xx dollars. She has a coupon for 15% off, and then a 8% tax is added to the discounted price. Write an expression in terms of xx that represents the total amount that Khloe paid at the register.
Answer:
0.93x
Step-by-step explanation:
the total amount is:
x(1-15%+8%)=0.93x
so the answer is 0.93x
this venn diagram shows sports played by 10 students what is p
P(A | B) is 2/10 = 0.2.
What is P(A | B) ?P(A | B) means the probability that a students pays both basketball and football. It is the intersection of both circles on the venn diagram.
P(A | B) = number of students that play both games / total number of students
2/10 = 0.2
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Find all solutions.
x +4x=0
Answer: x = 0
Step-by-step explanation:
Given:
x + 4x = 0
Combine like terms:
5x = 0
Divide both sides of the equation by 5:
x = 0
We can also check our work by graphing. See attached, intercepts of the x-axis are solutions.
9, 16, 23, ...
Find the 46th term.
Answer:
324
Step-by-step explanation:
Formula: [tex]a_{n} =a_{1} +(n-1)d[/tex]
=> [tex]a_{46} =9_{1} +(n-1)7\\[/tex]
= [tex]9_{1} +(46-1)7\\[/tex]
= [tex]9+(45)7\\[/tex]
= [tex]9+315[/tex]
= [tex]324[/tex]
:D
identify the matrix transformation of angle TUV, which has coordinates T(0,1), U(1,2), and V(2,0) for 90 degree rotation clockwise. Then identify the correct vertices of the image
Cost of Bikes ($) at Bike Shop
312, 352, 480, 392, 368, 352, 416, 640
Ic. mode
The mode is.
Answer:
352
Step-by-step explanation:
it repeated more than once
ASAP HELP NOWWWWW
What are the solutions for the following system of equations? –3x2 + 4y = 21 4x2 + y = 10 (1, 6) and (0, 10) (–1, 6) and (1, 6) (1, 6) and (3, 12) (–1, 6) and (3, 12)
The solutions for the following system of equations will be (–1, 6) and (1, 6). Then the correct option is B.
What is the solution of the equations?The equations are given below.
–3x² + 4y = 21 ...1
4x² + y = 10 ...2
Multiply equation 1 by 4 and equation 2 by 3, then we have
–12x² + 16y = 84
12x² + 3y = 30
Add both equations, then we have
19y = 114
y = 6
From equation 2, we have
4x² + 6 = 10
4x² = 4
x² = 1
x = ±1
x = 1, –1
Then the correct option is B.
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The mean price of a textbook is $82, and the range of prices are $16. What are the possible prices for the textbook?
$82, $82, $82, $82, $98
$90, $90, $74, $74, $74
$82, $82, $88, $76, $82
$82, $84, $90, $80, $74
Answer: D (82, 84, 90, 80, 74)
Finding Range:
To find range, you must subtract the smallest number to the highest number in that number pattern.
For example, the highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).
Range is basically the most easiest to find out of median, mean, and mode. You just have to find the greatest-smallest = range.
Finding Mean:
To find mean, you must add all the numbers up then divide the sum by the QUANTITIY of all the numbers.
For example, if we add 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).
Mean is basically easy to find as you just add all the numbers and divide it by how much numbers make that sum.
Conclusion:
In conclusion, the mean and range all match a possible price of the textbook, having a range of $16 and a mean of $82. Thus, D is the right answer.
The correct option is D (82, 84, 90, 74)
What is range?Range is subtract the smallest number to the highest number in that number pattern.
What is mean?Mean is addition of all the numbers up then divide the sum by the quantities of all the numbers.
The highest in D is 90, and the smallest is 74. 90-74 is 16, which matches the range for a possible price (16 = 16).
Addition of 82, 84, 90, 80, and 74, we would get 410. Since there are 5 numbers that make up 410, we divide 410 by 5, and therefore getting 82. This matches the mean of the price of a textbook (82 = 82).
Therefore, the possible prices for the textbook is the possible prices for the textbook is (82, 84, 90, 74).
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If Bank A charges a monthly service
fee of $2.50 and a per-check fee of
$0.15, while Bank B charges a
monthly service fee of $4 and a per-
check fee of $0.05, which bank will
charge a customer more in fees if
she writes 18 checks per month, and
by how much?
The bank which will charge a customer more in fees if she writes 18 checks per month, and by how much is Bank A by $0.30
How to write and solve equation?let
x = number of checksBank A = 2.50 + 0.15x
= 2.50 + 0.15(18)
= 2.50 + 2.7
= $5.20
Bank B = 4 + 0.05x
= 4 + 0.05(18)
= 4 + 0.9
= $4.9
Difference in charges = $5.20 - $4.90
= $0.30
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Find the volume of the figure. Use 3.14 for .
5 m
12 m
Answer:
1203.6 ---- the six is recurring ( .666666...)
Step-by-step explanation:
volume of hemisphere= [tex]\frac{2}{3}[/tex] x 3.14 x r^3
volume of cylinder= 3.14 x r^3 x h
1. Volume of hemisphere= 2/3 x 3.14 x 5^3 = 261.6 recurring
2. volume of cylinder = 3.14 x 5^2 x12 = 942
3. add the two together -----------> 1203.6
x y
-1 -10
3 14
Complete the slope-intercept form of the linear equation that represents the relationship in the table.
to get the equation of any straight line, we simply need two points off of it, let's use the ones in the table.
[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -1&-10\\ 3&14\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{(-10)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{14 +10}{3 +1}\implies \cfrac{24}{4}\implies 6[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-10)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-1)}) \\\\\\ y+10=6(x+1)\implies y+10=6x+6\implies y=6x-4[/tex]
6. A department store uses a
market research survey to
determine the types of products
various consumer groups are
buying.
Choose all that apply.
The characteristics that best
describe surveys are:
Answer choices:
Work with a wide variety of
formats
Involve studying subjects in their
environment, which is not
controlled in any way
May collect either facts or
opinions
Find the product 3 radical -3 and 3 radical -5
[tex]\left(\sqrt[3]{-3} \right) \left(\sqrt[3]{-5}\right)\\\\=\left( \sqrt[3]{-1}\right \sqrt[3]{3}) \left(\sqrt[3]{-1} \sqrt[3]{5} \right)\\\\=\sqrt[3]{(-1)(-1)} \cdot \sqrt[3]{(3)(5)}\\\\=\sqrt[3]{1} \cdot \sqrt[3]{15}\\\\=1\cdot \sqrt[3]{15}\\\\=\sqrt[3]{15}[/tex]
Community Gardens
In 1977, in New York City, people noticed something surprising. It was there in a vacant lot. It wasn’t the heaps of garbage. It was the tomato plants that were growing wild. “If vegetable plants can grow there,” some of the people thought, “why can’t we plant vegetables ourselves?” So the people cleared away the garbage. They began growing vegetables, fruits, herbs, and even flowers. The Clinton Community Garden was started.
Community gardens are found in cities all around the country. People start community gardens in vacant lots and on apartment balconies. As unbelievable as it sounds, they even tend gardens on rooftops.
What exactly is a community garden? It’s a garden that different people in a neighborhood plant and tend. It does not belong to any one person. Community gardeners eat and sometimes share the food they grow. Some community gardeners donate their food to local food banks. They give it to people who cannot afford to buy food.
Some community gardens are one large plot of land. Everyone shares in the work. They all plant seeds, weed, water, and share in the rewards. In other community gardens, the larger piece of land is divided up. People tend to their plots.
Community gardens offer many benefits. For one thing, they bring people together. Community gardeners get to know each other. Older people work alongside kids. Another benefit is the low-cost food, of course. The vegetables and fruits are also fresher and more healthful. And people tending a garden are getting fresh air and exercise.
A community garden benefits the whole community. It makes the neighborhood more beautiful. There can be no disagreement about that. A community garden creates a green space among concrete streets and sidewalks. This helps reduce heat in the summer. The plants soak up sunlight. Concrete reflects the sun’s heat into the air. Community gardens indirectly help save fuel resources, too. Trucks don’t have to deliver as much food from long distances to grocery stores. People don’t have to drive as much to grocery stores, so less gas is used.
More community gardens should be started. With all the benefits they bring us, who could argue with that?
A family of three works in a community garden in the middle of a city with tall buildings.
Reread the sentence from the article.
There can be no disagreement about that.
What does the word disagreement most likely suggest?
A.
taking action
B.
getting along
C.
not taking action
D.
not getting along
Answer:
not taking action
Step-by-step explanation:
because it is talking about how beautiful the gardens are and it could be said like this, "It makes the neighborhood more beautiful. There can be not taking action about that."
Which point lies on the line described by the equation below? y+ 4 = 4(x-3) O A. (3,-4) O B. (2,9) O C. (0,0) O D. (1,-11) E. (1,11) OF. (-2, 3) PREVIOUS SUBMIT 22949
The point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have an equation of a line:
y + 4 = 4(x - 3)
A (3,-4)
Plug the above points in the equation of the line.
-4 + 4 = 4(3 -3)
0 = 0 (true)
The point lies on the line
Similarly checking for others points we will find that points (2,9), (0,0) , (1,-11), (1,11), and (-2, 3) does not lie on the line y + 4 = 4(x - 3)
Thus, the point (3, -4) lie on the line y + 4 = 4(x - 3) because the point (3,-4) satisfy the line option (A) is correct.
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Solve the system of equations.
y=x²-5
y 2x+3
Answer:
[tex]x=4,\:x=-2[/tex]
Step-by-step explanation:
Both equations are equal to y, so we can simply set them equal to each other and solve for x:
[tex]x^2-5=2x+3\\\\x^2-8=2x\\\\x^2-2x-8=0\\\\(x-4)(x+2)=0\\\\x=4,\:x=-2[/tex]
What is the solution to the equation |x − 4| = 17?
[tex]~~~~~~|x-4| = 17\\\\\implies x -4 = 17~~~~ \text{or}~~~~~ x -4 = -17\\\\\implies x = 17+4~~~~\text{or}~~~~~ x = -17+4\\\\\implies x = 21~~~~~~~~~\text{or}~~~~~x = -13[/tex]
Work out (5*10^3)*(9*10^7).
Give your answer in standard form.
Work out (7*10^5) / (2*10^2).
Give your answer in standard form.
Answer:
(5*10^3)*(9*10^7) = 4.5*10^11
(7*10^5) / (2*10^2) = 3.5*10^3
Step-by-step explanation:
calculate 5 multiply by 9
5*9=45
the multiple of the power in the same base of number is calculated by using addition(+)
(10^3)*(10^7) = 10^(3+7)
= 10^10
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
45*(10^10)
= (4.5*10^1) * (10^10)
= 4.5*10^(1+10)
= 4.5*10^11
calculate 7 divide by 2
7/2=3.5
the dividing of the power in the same base of number is calculated by using subtraction(-)
(10^5)/(10^2)
= 10^(5-2)
= 10^3
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
3.5*10^3
Answer:
→ (5×10³)×(9×10⁷) = 4.5 × 10¹¹→ (7×10⁵) / (2×10²) = 3.5 × 10³Step-by-step explanation:
(5×10³)×(9×10⁷)
= 5×10³×9×10⁷
= 5×9×10³×10⁷ (commutative property)
= (5×9)×(10³×10⁷) (associative property)
= 45 × 10³⁺⁷
= 45 × 10¹⁰. (Exponent property)
= 4.5 × 10¹¹
…………………………………………
(7×10⁵) / (2×10²)
= (7/2) × (10⁵/10²)
= 3.5 × 10⁵⁻²
= 3.5 × 10³
A line, y mx + b, passes through the point (2, 3) and is parallel to y 2x + 5. What is the value of b?
Answer:
Step-by-step explanation:
If a line is parallel to another it must have the same slope
The slope/intercept form of a line is y = mx + b where m is the slope and b the y intercept
The line y = 2x + 5 has slope 2
So the slope of the line that passes through (2,3) must also have the slope 2
We have
y = 2x + b; Substituting x =2, y =3 in this equation gives us
3 = 2 (2) + b or b = -1
Hence the equation of the line is
y = 2x -1
Cross-check
Substitute for x = 2 ==> y = 2(2) - 1 = 3 which is consistent