Answer:
8:07:12 am
Step-by-step explanation:
The lights will change simultaneously after any multiple of the least common multiple of their cycle times.
LCMThe least common multiple of a set of numbers is the product of the highest powers of their prime factors.
48 = 2⁴×3
72 = 2³×3²
108 = 2²×3³
The highest power of the factor 2 is 4. The highest power of the factor 3 is 3, so the LCM of the numbers 48, 72, and 108 is ...
LCM = 2⁴×3³ = 16×27 = 432
The lights will change simultaneously after each period of 7 minutes 12 seconds. They will change simultaneously again at 8:07:12 am.
subtract the squre of m from the ratio of p andq
The expression that represent the given statement is p/q - m²
Writing an expressionFrom the question, we are to write an expression for the word problem
We are to write an expression for the statement
"Subtract the square of m from the ratio of p and q"
Square of m = m²
Ratio of p and q = p/q
Thus,
subtract the square of m from the ratio of p and q, becomes
p/q - m²
Hence, the expression that represent the given statement is p/q - m²
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Write an equation that represents the line.
Use exact numbers.
(-2,-1)
(4,6)
Check the picture below.
to get the equation of any straight line, we simply need two points off of it, so let's use those in the picture
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{6 -1}{4 +2} \implies \cfrac{ 5 }{ 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}{1}=\stackrel{m}{\cfrac{5}{6}}(x-\stackrel{x_1}{(-2)})\implies y-1=\cfrac{5}{6}(x+2) \\\\\\ y-1=\cfrac{5}{6}x+\cfrac{5}{3}\implies y=\cfrac{5}{6}x+\cfrac{5}{3}+1\implies y=\cfrac{5}{6}x+\cfrac{8}{3}[/tex]
Frank went to the playground at 5:20 P.M. He played on the slide for 45 minutes and the swings for 5 minutes, then went home. What time was it when Frank left the playground?
The time it was when Frank left the playground is; 6:10 PM.
How to calculate time difference?We are given;
Time at which Frank went to the playground; 5:20 p.m
Amount of time that frank played on the slide = 45 minutes
Amount of time that frank swings on the play ground = 5 minutes
Now, we are told that after he played on the slide and swung on the playground, that he went home.
Thus, he spent a total time of 45 + 5 = 50 minutes on the playground before going home.
Thus, time he went home = 5:20 p.m + 50 minutes = 6:10 p.m
Thus, we can conclude that the time it was when Frank left the playground is; 6:10 PM.
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Can someone help me find the value of x for the triangle?
Answer:
109°
Step-by-step explanation:
The sum of angles in all triangles is equal to 180. For this given triangle, we can solve for x.
48° + 23° + x° = 180°
180° - 71° = x°
x = 109°
Hey I'm sunny, and i request someone's help (please)
1. Value of b (b - 4.21 = 87.654)
2. Divide: 1.86 and 8.4
3: Compare: 1.92
that's it
Bye! - SunnyBunny <3
The computation shows that the value of b will be 91.864.
How to illustrate the information?From the information given, we are told to find the value of b (b - 4.21 = 87.654). This will be:
b - 4.21 = 87.654
b = 87.654 + 4.21
b = 91.864
Also. dividing 1.86 and 8.4 will be:
= 1.86/8.4
= 0.2213
Therefore, the values are 91.864 and 0.2213.
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The peak current passing through an inductor is 2. 0 aa. part a what is the peak current if the peak emf e0e0 is doubled?
Answer:
22
I remember this question in school
Apply the distributive property to create an equivalent expression. 9(a + 4b + 3c)
[tex] \rm9(a + 4b + 3c) \\ 9(a) + 9(4b) \rm+ 9(3c) \\ \rm 9a + 36b + 27c \\ \therefore \tt9(a + 4b + 3c) = 9a + 36b + 27c[/tex]
Which of these is a simplified form of the equation 7y 8 = 9 3y 2y? 7y = 6 2y = 1 12y = 17 5y = 17
The simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1
How to simplify an equation?The equation can be simplified as follows:
7y + 8 = 9 + 3y + 2y
We have to combine like terms
Hence,
7y + 8 = 9 + 3y + 2y
7y + 8 = 9 + 5y
subtract 5y from both sides
7y - 5y + 8 = 9 + 5y - 5y
2y + 8 = 9
Let's subtract 8 from both sides
2y + 8 - 8 = 9 - 8
2y = 1
Therefore, the simplified equation of 7y + 8 = 9 + 3y + 2y is 2y = 1
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What is the following quotient?6-3(^3√6)/3/9
O 2(3√3)-3√/18
O 2(³√/3)-3(³/2)
O 3(3/3)-3√/18
O 3(³√/3)-3(3√/2)
Applying properties of exponents, the quotient is given as follows:
[tex]2\sqrt[3]{3} - \sqrt[3]{18}[/tex]
What is the quotient?The expression is given by:
[tex]\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}}[/tex]
The 3 can be inserted into the cube root, as follows:
[tex]\frac{6 - 3\sqrt[3]{6}}{\sqrt[3]{9}} = \frac{6 - \sqrt[3]{6 \times 3³}}{\sqrt[3]{9}}[/tex]
Applying the subtraction, we have that the expression is:
[tex]\frac{6}{\sqrt[3]{9}} - \frac{\sqrt[3]{162}}{\sqrt[3]{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{\frac{162}{9}} = \frac{6}{\sqrt[3]{9}} - \sqrt[3]{18}[/tex]
The denominator can be simplified as follows:
[tex]\sqrt[3]{9} = \sqrt[3]{3^2} = 3^{\frac{2}{3}}[/tex]
Then:
[tex]\frac{6}{\sqrt[3]{9}} = \frac{2 \times 3}{3^{\frac{2}{3}}} = 2 \times 3^{1 - \frac{2}{3}} = 2 \times 3^{\frac{1}{3}} = 2\sqrt[3]{3}[/tex]
Hence the quotient is given by:
[tex]2\sqrt[3]{3} - \sqrt[3]{18}[/tex]
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StartFraction 6 Over 7 EndFraction x + one-half = StartFraction 7 Over 8 EndFraction for x?
The value of x in 6/7x + 1/2 = 7/8 is 7/16
How to solve for x?The equation is given as:
6/7x + 1/2 = 7/8
Subtract 1/2 from both sides
6/7x + 1/2 -1/2 = 7/8 -1/2
Evaluate the difference
6/7x = 3/8
Multiply both sides by 7
6x = 21/8
Divides both sides by 6
[tex]x = \frac {7}{16}[/tex]
Hence, the value of x is 7/16
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Geometry: complete this proof of theorem 14, ASAP!
(Theorem 14: if a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel.)
Answer:
1. Transversal y intersects lines m and n; <1 ~= <2 (Given)
2. <1 ~= <3 (Vertical Angles Theorem)
3. <2 ~= <3 (Transitive Property of Congruence)
4. m || n (Converse of Alternate Interior Angles Theorem)
Suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally adjacent seat. How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?
688,747,536 ways in which the people can take the seats.
How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.
When the whistle blows, each person needs to change to an orthogonally adjacent seat.
(This means that the person can go to the seat in front, or the seats in the sides).
This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.
Now, if we take the options that each seat has, and we take the product, we will get:
P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.
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A line passes through the point (7, 3. and has a slope of 2. Write an equation for this line.
Answer:
y = 2x - 11.
Step-by-step explanation:
Use the point-slope form of the straight line.
y - y1 = m(x - x1) where m = slope and (x1, y1) is the given point.
Here m = 2 and (x1, y1) = (7,3) so the equation is:
y - 3 = 2(x - 7)
y - 3 = 2x - 14
y = 2x - 11
6 Find the value of x from the following figures.
1)
please help if u cannot skip
The statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
How to determine which statement is true?To determine which statement is true, we need to know the conditions for continuity and differentiablity of a function.
Conditions for continuity and differentiablity of a function.For a function f(x) to be continuous at a point x = a, then both the left hand limit of f(x) and the right hand limit of f(x) as x → a must be equal. That is [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x)[/tex]. So, [tex]\lim_{x \to a^{} } f(x)[/tex] must exist since [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x) = \lim_{x \to a^{} } f(x)[/tex]Also, for a function to be differentiable at a point x = a, it must also exist at x = a
So, since f(x) = {x² - 1 if -1 ≤ x ≤ 3 and x²/3 if 3 < x ≤ 8}
From the equality on the first condition,we see that f(x) is exists at x = 3 but is not continuous since f(x) changes to another function when x > 3. So,left hand limit of f(x) and the right hand limit of f(x) as x → 3 are not equal.
That is [tex]\lim_{x \to 3^{-} } f(x) \neq \lim_{x \to 3^{+} } f(x)[/tex] . Thus, the function is discontinuous at x = 3.
For differentiability, both conditions must be met. Since only one condition is met, it is non-differentiable.
So, the function is discontinuous and non-differentiable at x = 3.
So, the statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
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The terminal side of an angle
intersects the unit circle at point
Answer:
[tex] - \frac{ \sqrt{2} }{2} [/tex]
Step-by-step explanation:
The sine of an angle is equal to the y coordinate point where the terminal side of the angle intersects the unit circle.
What would be the coefficient of determination r2 if the total sum of squares (sst) is 90 and the sum of squares due to error (sse) is 0 (zero)?
The coefficient of determination is 1.
Given
Total Sum of squares (SST) = 90
Sum of squares due to error (SSE) = 0
We have to find coefficient of determination.
The correlation of determination is the ratio of the explained variation to the total variation.
The coefficient of determination is used to analyze how differences in one variable can be explained by a difference in a second variable.
The coefficient of determination is also called r-squared or r-square.
Its the percentage of variation in the y-variable(response) that can be explained by the least squares regression line of y on x.
Coefficient of determination can be found with the following formula:
Formula of coefficient of determination :
[tex]R^{2} = 1 - \frac{SSE}{SST}[/tex]
= 1 - [tex]\frac{0}{90}[/tex]
= 1 - 0
= 1
[tex]R^{2}[/tex] = 1
Therefore,
The coefficient of determination is 1.
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triangle ABC is reflected across the y-axis and then dilated by a factor of 1/2 centered at the origin. which statement correctly describes the resulting image
Answer:
Step-by-step explanation:
The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths.
What is the circumference of a circle (to the nearest whole number) whose diameter is 12?
Step-by-step explanation:
Circumference = πd
= π × 12
= 37.6991
=38
Answer:38
Step-by-step explanation:
Convert 352 base 6 to base 4.
Answer:
(2030)4
Step-by-step explanation:
Base 6 to decimal calculation:
(352)6 = (3 × 62) + (5 × 61) + (2 × 60) = (140)10
Decimal to base 4 calculation:
Divide by the base to get the digits from the remainders:
= (2030)4
Still have any questions?
Do hit me up or contact me
The answer is 2030.
First, convert from base 6 to base 10.
3 × 6² + 5 × 6¹ + 2 × 6⁰108 + 30 + 2140Now, convert from base 10 to base 4.
140 ÷ 4 = 35 ⇒ R = 035 ÷ 4 = 8 ⇒ R = 38 ÷ 4 = 2 ⇒ R = 02 ÷ 4 = 0 ⇒ R = 2Connecting the digits, the answer is : 2030
A private jet flies the same distance in 10 hours that a commercial jet flies in 7 hours. if the speed of the commercial jet was 144mph less than 2 times the speed of the private jet, find the speed of each jet.
The speed of private jet is = 252 mph
The speed of commercial jet is = 360 mph
What is speed ?
Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement. Put another way, speed is a scalar value, while velocity is a vector.Let the speed of private jet be x mph.
Then the speed of commercial jet will be = 2x - 144
Equation forms:
10x = 7 ( 2x - 144 )
Solving for x
10x = 14x - 1008
⇒ 10x - 14x = - 1008
⇒ - 4x = - 1008
⇒ x = 252
So, x = 252
Hence, the speed of private jet is = 252 mph
The speed of commercial jet is = = 2(252) - 144 = 360 mph
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If the population standard deviation σ=25. What is the required minimum sample size to construct a 95 confidence level for the population mean with an allowable error of ±3?
The required minimum sample size to construct a 95% confidence level for the population mean is 267.
In this question,
In the probability and statistics theory, the confidence interval of the population parameter is the estimated range of values we are sure with a certainty that our parameter will lie within, the range being calculated from the sample obtained. The smaller is the margin of error, the more confidence we have in our results.
The population standard deviation, σ = 25
Confidence level for the population mean = 95%
Margin of error = ±3
Let n be the sample size of the population
The z-score for the confidence level of 95% for the population mean is 1.96.
The formula of margin of error is
[tex]E=\frac{z \sigma}{\sqrt{n} }[/tex]
Now, the sample size of the population can be calculated as
[tex]n=(\frac{z\sigma}{E} )^{2}[/tex]
On substituting the above values,
⇒ [tex]n=(\frac{(1.96)(25)}{3} )^{2}[/tex]
⇒ [tex]n=(\frac{49}{3}) ^{2}[/tex]
⇒ [tex]n=(16.33)^{2}[/tex]
⇒ n = 266.77 ≈ 267
Hence we can conclude that the required minimum sample size to construct a 95% confidence level for the population mean is 267.
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Question 1 of 10
Which expression is the simplest form of - (3x³ + x²) +2 (x³ - 4x²)?
OA.-2³-32²
OB.-2³-92²
O C. 5x³-7x2²
OD. 52³-82²
SUBMIT
Answer:
B. -x³ - 9x².
Step-by-step explanation:
- (3x³ + x²) +2 (x³ - 4x²)
= -3x³ + 2x³ - x² - 8x²
= -x³ - 9x²
Answer: [tex]\Large\boxed{-x^3-9x^2}[/tex]
Hi there! By my calculation, I got the answer above. However, it doesn't fit any one of the answer choices. I am not sure if I am totally correct, but I have been double-checking my answers. Please let me know whether it's the answer choices mistaken or I am wrong so that I could modify my answer if necessary.
Step-by-step explanation:
Given expression
- (3x³ + x²) +2 (x³ - 4x²)
Expand parenthesis by the distributive property
= -3x³ - x² + 2x³ - 8x²
Combine like terms
= -3x³ + 2x³ - x² - 8x²
[tex]\Large\boxed{=-x^3-9x^2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
In an aquarium, the ratio of sharks to dolphins is 3 : 5 and the ratio of
dolphins to starfish is 2 : 7.
There are 6 sharks in the aquarium.
How many starfish are there?
Step-by-step explanation:
step 1: how many dolphins
there are 6 sharks
sharks to dolphins is 3 to 5
3 S to 5 D
we can divide 6 (amount of sharks known) by 3, to get what a ratio of 1 is
6 ÷ 3 = 2
so 2 sharks is = 1 part or ratio
now we can times by 5 to get a ratio of 5
5 × 2 = 10
there are 10 Dolphins
Step 2: How many starfish
repeat the steps above but for the ratio 2: 7 where 2 is the Dolfin ratio and there are 10 dolphins
put in questions answer you got
Answer:
35 starfish
Step-by-step explanation:
shark/dolphin * dolphin /starfish = shark / starfish
Now. put in the numbers given:
3/5 * 2/7 = 6/35 = shark / starfish put in '6' for shark (given)
6/35 = 6/starfish cross multiply
6 * starfish = 35* 6
starfish = 35
Consider the graph of the function f(x)=2^x which statements describe key features of function g if g(x)=3f(x)?
it's multiple choice, select all the correct answers:
y-intercept at (0,1)
y-intercept at (0,3)
horizontal asymptote of y=3
x-intercept at (3,0)
horizontal asymptote of y=0
no x-intercept
Answer:
A, C, D
Step-by-step explanation:
4/7+3/7 1/5.3/2-4/10
Answer:
3/10
Step-by-step explanation:
=4/7 + 9/70 - 4/10
=l.C.M of 7 , 70 and 10 =70
=4/7 .10/10 +9/70 -4/10 .7/7
=40/70 +9/70 -28/70
=40+9-28/70
=49-28/70
=21/70
=3/10
In a game, a player earns 100 points for each question answered correctly and earns -30 points for each question answered incorrectly. A player answered 14 questions correctly and 6 questions incorrectly.
Part A) Write a numeric expression to represent the total number of points the player earned.
Part B) Determine the total number of points.
The general expression is 130 x - 600 and total points scored by the player is 1220
A) Let the number of correctly answered questions be x.
∴ Number of incorrectly answered questions will be 20 - x.
+ 100 points is awarded for each question answered correctly while -30 points is awarded for each question answered incorrectly.
Thus, the general equation becomes
= 100x - (20 - x)(-30)
= 100x +30x - 600
= 130x - 600
Thus the general expression becomes 130 x - 600
B) The player answers 14 questions correctly, thus x = 14
Substituting the value of x =14 in the general equation we get,
= 130(14) - 600
= 1820 - 600
= 1220.
Thus the total points scored by the player will be 1220
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A cupcake store has 5 different kinds of cupcakes: chocolate, vanilla, lemon, strawberry, and coffee. Assuming there are at least 12 of each kind of cupcake, how many ways can you choose 12 cupcakes
Assuming there are at least 12 of each kind of cupcake, number of ways can you choose 12 cupcakes is; 1399358844975 ways
How to solve probability combination?We are given the quantity of each type of cupcake as follows;
Number of types of cupcakes = 5
Number of Chocolate Cupcakes = 12
Number of Vanilla Cupcakes = 12
Number of Lemon cupcakes = 12
Number of Strawberry Cupcakes = 12
Number of coffee cupcakes = 12
Thus, total number of cupcakes will be gotten by adding all the quantities given above of the different types of cupcakes and we will get; Total number of cupcakes = 12 + 12 + 12 + 12 + 12
Total number of cupcakes = 60
Now, since there is no order of selection, then the number of ways that you can choose 12 cupcakes will be gotten by using the combination formula which is; nCr = n!/(n!(n - r)!)
Thus, number of ways that you can choose 12 cupcakes =
60C12 = 60!/(12! * (60 - 12)!) = 1399358844975 ways
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Given a polynomial function f(x)=2x²+ 7x+6 and an exponential function g(x)=2+ 5, what key features do f(x) and g(x) have in common?
Both f(x) and g(x) increase over the interval of [-4,∞)
Both f(x) and g(x) have the same x-intercepts of (-2, 0) and (-1.5, 0).
Both fox) and gox) have the same y-intercept of (0,6)
Both f(x) and g(x) have the same range of (-00.01]
Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:
Both f(x) and g(x) have the same y-intercept of (0,6)What is the polynomial function about?Polynomial functions are known to be a kind of an expressions that is made up of a set of variables of different extent or degrees, non-zero coefficients, positive exponents (of variables), and also it is made up of constants.
Note that the equation of the functions are stated as:
f(x) = 2x² + 7x + 6
g(x) = 2^x + 5
The right and next thing to do is to plot a graph of both functions (see image attached)
From the graph, we have the fact that Both f(x) and g(x) have the same y-intercept of (0,6)
Therefore, Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:
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Question 10 of 28
Which of the following expressions are equivalent to
2. ? Choose all that apply.
ھر - 20
A.
B.
c.
2
(3)2 - (13 )2
1
1
(x3 - 3 ) ( + 13 )
2
1
(3 - 13) (3 - 13)
مردم زمرے
2
1
D. (x3 - 3 ) ( + 13 )
Answer: A, D
Step-by-step explanation:
A) Correct. [tex](x^3)^2=x^{(3)(2)}=x^6[/tex]. Similar logic for y.
B) Incorrect. The numerators are different.
C. Incorrect. The denominators are not the same.
D. Correct. The denominators are the same by difference of squares.