The value of x is 7/2
How to solve for x?The equation is given as:
x/3 - 3/4 = 5/12
Multiply through by 12
4x - 9 = 5
Add 9 to both sides
4x = 14
Divide by 4
x = 7/2
Hence, the value of x is 7/2
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Find the midpoint of a and b when a has coordinates (2,3) and b has coordinates (8,9)
The midpoint of co-ordinate is (5, 6)
Add both "x" coordinates, and divide by 2.
Add both "y" coordinates, and divide by 2.
Given that;
Coordinates of A = (2,3)
Coordinates of B = (8,9)
Find:
Midpoint of co-ordinate
Computation:
Midpoint of co-ordinate = [(x1 + x2) / 2], [(y1 + y2) / 2]
Midpoint of co-ordinate = [(2 + 8) / 2], [(3 + 9) / 2]
Midpoint of co-ordinate = [10 / 2], [12 / 2]
Midpoint of co-ordinate = (5, 6)
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Suppose you are an engineer trying to recreate an experiment involving a weight on the end of a spring. This simulation will give you an idea of what the experiment will look like. For more information, you can visit this simple harmonic motion website. You are given the equation y(t)=2 sin 4 pi t + 5 cos 4pi t, which models the position of the weight, with respect to time. You need to find the amplitude of the oscillation, the angular frequency, and the initial conditions of the motion. You will also be required to find the time(s) at which the weight is at a particular position. To find this information, you need to convert the equation to the first form, y(t) = A sin (wt+0).
The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .
How to find the canonical form of the equation for simple harmonic motion
Herein we have a simple harmonic motion model represented by a sinusoidal expression of the form y(t) = A · sin (C · t) + B · cos (C · t), which must be transformed into its canonical form, that is, y(t) = A' · sin (C · t + D). We proceed to perform the procedure by algebraic and trigonometric handling.
The amplitude of the canonical function is determined by the Pythagorean theorem:
A' = √(2² + 5²)
A' = √ 29
The angular frequency C is the constant within the trigonometric functions from the non-canonical formula:
C = 4π
Then, we find the initial position of the weight in time: (t = 0)
y(0) = 2 · sin (4π · 0) + 5 · cos (4π · 0)
y(0) = 5
And now we calculate the angular phase below: (A' = √ 29, C = 4π, y = 5)
5 = √ 29 · sin (4π · 0 + D)
5 / √ 29 = sin D
D ≈ 0.379π rad
The canonical expression equivalent to sinusoidal model y(t) = 2 · sin (4π · t) + 5 · cos (4π · t) is y(t) = (√ 29) · sin (4π · t + 0.379π) .
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A probability that it will rain on a given day during the rainy season in Miami is 70%. If there are 140 days in the rainy season. On how many days should you except it to rain?
Answer:
98 days
Step-by-step explanation:
140*70%=140*(7/10)=14*7=98
One student can paint a wall in 12 minutes. Another student can paint the same wall in 24minutes. Working together, how long will it take for them to paint the wall?
Answer:
8 minutes.
Step-by-step explanation:
We work in fractions of the wall they can paint in 1 minute, so
1/12 + 1/24 = 1/x where x is the time it takes when working together.
Multiplying through by 24x:
2x + 1x = 24
3x = 24
x = 8 minutes.
Which two ratios form a proportion? a) 4 20 and 1 5 b) 4 20 and 2 5 c) 20 4 and 1 5 d) 20 4 and 2 5
A is proportional.
Lets simplify the problem,
← divide numerator/ denominator by 4
= 4/20= 1/5
Thus A form a proportion
≠ 1/5
Thus B is not a proportion
← divide numerator/ denominator by 4
= 2/5 ≠ 1/5
Thus C is not a proportion
5/1 ≠ 1/5
Thus D is not a proportion
A is proportional.
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Flies Mosquitoes The table shows the number of flies and the number of mosquitoes that the frog eats for two lunches. Based on the ratio,
complete the missing values in the table.
On Monday: 35 mosquitos.
On Tuesday: 6 flies.
How to estimate the missing values of the table?As you can notice in the diagram, the frog eats 3 flies for every 7 mosquitoes (for lunch). Then you can define this ratio as pursues:
3: 7 or 3/7.
Based on the table below:
If the frog swallows 15 flies on Monday, then the number of mosquitos that it eats can be estimated as pursues:
3/7 = 15/mosquitoes
mosquitoes [tex]$= \frac{15*7}{3}[/tex]
mosquitoes = 35
If the frog eats 14 mosquitoes on Tuesday, then the number of flies that it eats can be estimated as pursues:
3/7 = flies/14
flies [tex]$= \frac{14*3}{7}[/tex]
flies = 6
The complete question is:
A frog catches insects for his lunch. The frog likes to eat flies and mosquitoes in a certain ratio, which is shown in the diagram. The table shows the number of flies and the number of mosquitoes that the frog eats for two lunches.
Based on the ratio, complete the missing values in the table.
Day Flies Mosquitoes
Monday 151515
Tuesday
141414
Disregard Above
Use Picture
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1. Find the length of each side of the triangle if its perimeter is 86cm the sides are. 3a-2, 5a+3, 6a+1
Hello,
3a - 2 + 5a + 3 + 6a + 1 = 86
14a + 2 = 86
14a = 86 - 2
14a = 84
a = 84/14
a = 6
lengths :
3a - 2 = 3 × 6 - 2 = 18 - 2 = 16 cm
5a + 3 = 5 × 6 + 3 = 30 + 3 = 33 cm
6a + 1 = 6 × 6 + 1 = 36 + 1 = 37 cm
Which are the solutions of x² = 19x + 12
Answer:
[tex]\{x=\frac{19-\sqrt{409} }{2}\ , \ x=\frac{19+\sqrt{409} }{2}\}[/tex]
Step-by-step explanation:
x² = 19x + 12
⇔ x² - 19x - 12 = 0
Calculating the discriminant :
b² - 4ac = (-19)² - 4×1×(-12) = 409
The discriminant is positive ,then the equation has two solutions.
[tex]x=\frac{19-\sqrt{409} }{2} \ \ or\ \ x=\frac{19+\sqrt{409} }{2}[/tex]
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
Answer:
b
Step-by-step explanation:
b shows direct variation because we can clearly tell that the slope of the graph is 1/2. The graph is also linear, and it crosses the origin (0,0).
a: This graph can be represented as y=2, and that is not a direct variation.
b: Above explanation. This graph is a direct variation.
c: This graph can be represented as x=-8, and that is not a direct variation.
d: This graph has the slope, but it does not cross the origin, so it is not a direct variation.
Answer:
Graph b
Step-by-step explanation:
Direct variation means "y varies directly as x”:
Direct variation equation:
[tex]y=kx[/tex]
where k is the (non-zero) constant of variation.
Note, therefore, that a direct variation equation passes through the origin, as when x = 0:
[tex]\implies y=k(0) \implies y=0[/tex]
Graph a
y does not change as x varies.
Therefore this graph does not model a direct variation.
Graph b
As x gets bigger, so does y. As x gets smaller, so does y.
The line passes through the origin (0, 0).
Therefore this graph models a direct variation.
Graph c
x does not change as y varies.
Therefore this graph does not model a direct variation.
Graph d
As x gets bigger, so does y. As x gets smaller, so does y.
However, the line does not pass through the origin (0, 0).
Therefore this graph does not model a direct variation.
Alice and Bob each arrive at a party at a random time between $1:00$ and $2:00$. If Alice arrives after Bob, what is the probability that Bob arrived before $1:30$
The probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.
According to the question,
Alice and Bob each arrive at a party at a random time between 1.00 P.M and 2.00 P.M.
In probability theory, the sample space(s) of a random trial is the set all possible results of that trial.
Let 'x' be the arrival time of Alice and 'y' be the arrival time of Bob.
s = {(x, y) /1≤x≤2 and 1≤y≤2}
In order to find the probability of the Bob arrived before 1.30 P.M, if the Alice arrives after Bob.
Formula for Probability = [tex]\frac{Number of favorable events}{Total number of events}[/tex]
= 1/2
Hence, the probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.
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Which type of graph would you want to use to show the frequency of an interval?
line graph
histogram
box-and-whisker plot
stem-and-leaf plot
The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(0) = g(0) and f(2) = g(2)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answer:
first option
Step-by-step explanation:
Always remember to graph a diagram :)
Given the series below, find S29.
{13+4+(−5)+(−14)+(−23)+...}
Select one:
a. -2,480
b. -2,752
c. -3,016
d. -3,277
Answer:
d
Step-by-step explanation:
there is a common difference between consecutive terms in the series, that is
4 - 13 = - 5 - 4 = - 14 - (- 5) = - 23 - (- 14) = - 9
this indicates the series is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = 13 and d = - 9 , then
S₂₉ = [tex]\frac{29}{2}[/tex] [ (2 × 13) + (28 × - 9) ]
= 14.4(26 + (- 252))
= 14.5(26 - 252)
= 14.5 × - 226
= - 3,277
A jar is filled with 50 different colored marbles, 8 of which are red, 20 of which are blue, and 22 of which are green. a player is asked to draw a single marble from the jar and if they draw a red marble they will win $20, if they draw a blue marble they will lose $10, and if they draw a green marble they will lose $5. round your answer to the nearest cent.
The expected value of drawing a marble from the jar is -$0.8.
Given that jar is filled with 50 coloured marbles out of which 8 are red , 20 are blue and 22 are green and we have to find the expected value that a player will get by drawing one marble from the jar if the prize of drawing red marble is $20 and loss of $10 if blue marble is drawn.
Probability that a red marble is drawn from jar=8/50
Probability that a blue marble is drawn from jar=20/50
Probability that a green marble is drawn from jar=22/50
Value that player can expect by drawing a red marble from jar=
=P(X=red)*20-P(X=blue)*10+P(X=green)*0
=8/50*20-20/50*10+0
=16/5-20/5
=-4/5
=-0.8
It is negative ,means that player will not get any money. In fact player will lose $0.8.
Hence the expected value that player can expect is -$0.8.
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Question is incomplete as it should include that calculate the expected value of drawing a marble.
c) tan²0 - cot²0 = sec²0 (1- cot²0)
Prove that LHS = RHS So that LHS will be the sec²0 (1- cot²0)
Answer:
Maybe this could help?
You have 7 balls that are each a different color of the rainbow. in how many distinct ways can these balls be ordered? a. 1 b. 7 c. 49 d. 343 e. 5,040
Answer:
5040 ways
Step-by-step explanation:
here we need to find the number of permutations of the 7 balls :
= 7!
= 7×6×5×4×3×2×1
= 5 040
what operation is evaluated first in the expression 4 + 9 2 /3 x 2 - 2 =
Answer:
You add the numerator
multiply the denominator and substract
then you can divide the expression.
Step-by-step explanation:
According to BODMAS
division comes before multiplication, addition and subtraction.
but in some cases like this, it's difficult to follow that procedure
WILL GIVE BRAINLIEST FOR CORRECT ANSWER AND EXPLANATION Belinda is buying fencing for her vegetable garden to keep her dogs out. The length of her garden is 15.6 feet, and the width is 10.8 feet. How much fencing material should she purchase to build the fence around the garden?
A. 168.48 ft
B. 54 ft
C. 52.8 ft
D. 26.4 ft
Answer:
C. 52.8 ft.
Step-by-step explanation:
Calculate the perimeter of the garden
[tex]P=2l+2w=2(15.6)+2(10.8)=31.2+21.6=52.8[/tex]
The perimeter represents the length of the fencing material she needs
Hope this helps
Answer:
52.8 if u give me brainliest tht will be so help full:)
Step-by-step explanation:
The data below show the hourly wages earned by six employees. The second column shows the number of years of work experience for each employee. The third column is a binary variable indicating whether or not the employee has completed a training program. For the following questions, you may check your work using a calculator but must show how you set up the expression you are using (i.e. show your work).
wage experience training
8 1 0
20 10 0
10 2 0
12 4 0
16 4 1
14 6 1
a) What are the mean, variance, and standard deviation of wages?
b) What is the mean, variance, and standard deviation of experience?
c) Draw a scatter plot with experience on the horizontal axis and wages on the vertical axis. Draw a straight line that best fits the data points. Based on this line, what is the approximate wage of someone with 0 years of experience?
d) What is the covariance of wages and experience? Is this consistent with the line you drew in part c)? Explain.
e) What is the correlation of wages and experience?
The approximate wage of someone with 0 years of experience is -4.64
a) What are the mean, variance, and standard deviation of wages?The dataset of wages is
Wages = 8, 20, 10, 12, 16, 14
The mean is calculated as:
Mean = Sum/Count
This gives
Mean = (8+ 20+ 10+ 12+ 16+ 14)/6
Mean = 13.33
The variance is
Variance = ∑(x- mean)²/n-1
This gives
Variance = [(8 - 13.33)^2 + (20 - 13.33)^2 + (10 - 13.33)^2 + (12 - 13.33)^2 + (16 - 13.33)^2 + (14 - 13.33)^2]/5
Evaluate
Variance = 18.67
The standard deviation is
Standard deviation = √Variance
This gives
Standard deviation = √18.67
Evaluate
Standard deviation = 4.32
b) What is the mean, variance, and standard deviation of experience?The dataset of experience is
Wages = 1, 10, 2, 4, 4, 6
The mean is calculated as:
Mean = Sum/Count
This gives
Mean = (1+ 10+ 2+ 4+ 4+ 6)/6
Mean = 4.5
The variance is
Variance = ∑(x- mean)²/n-1
This gives
Variance = [(1 - 4.5)^2 + (10 - 4.5)^2 + (2 - 4.5)^2 + (4 - 4.5)^2 + (4 - 4.5)^2 + (6 - 4.5)^2]/5
Evaluate
Variance = 10.3
The standard deviation is
Standard deviation = √Variance
This gives
Standard deviation = √10.3
Evaluate
Standard deviation = 3.21
c) Draw a scatter plot with experience on the horizontal axis and wages on the vertical axis.See attachment for the scatter plot and the straight line that best fits the data points.
The equation of the straight line is
y = 0.69x - 4.64
The approximate wage of someone with 0 years of experience is
y = 0.69 * 0 - 4.64
Evaluate
y = -4.64
Hence, the approximate wage of someone with 0 years of experience is -4.64
d) What is the covariance of wages and experience?This is calculated as:
Cov(x,y) = ∑(x - x mean)(y - y mean)/N - 1
So, we have:
Cov(x,y) = [(8 - 13.33) * (1 - 4.5) + (20 - 13.33)*(10 - 4.5) + (10 - 13.33)*(2 - 4.5) + (12 - 13.33)*(4 - 4.5) + (16 - 13.33)*(4 - 4.5) + (14 - 13.33)*(6 - 4.5)]/5
Evaluate
Cov(x,y) = 12.80
Hence, the covariance of wages and experience is 12.80
Is this consistent with the line you drew in part c?
Yes it is
e) What is the correlation of wages and experience?Here, we use a graphing calculator.
From the graphing calculator, we have:
r = 0.9231
Hence, the correlation of wages and experience is 0.9231
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Translate to algebra numbers, the difference of a number times 3 and 6 equals 9.
Answer:
The equation is ×=-3
Step-by-step explanation:
Let x be the number
Difference between a number tines 3 and 6 is 9
3x-6x=9
-3x=9
x=-3
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If you could help me on 1 and 2 that would be great!!!
The conversion of the vectors into coordinate notation rule are as follows;
(-3, 1) ==> (x-3, y+1)(4, -7) ==> (x+4, y-7)What are the coordinate notation form of the given vectors?It follows from the task content that the vectors given in the task content can be converted to coordinate notation form by mapping x and y to their respective transformation units. It therefore follows that the coordinate notation form of the vectors are;
(-3, 1) ==> (x-3, y+1)(4, -7) ==> (x+4, y-7)Read more on coordinate notation;
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PLEASE HELPPPPPPPPPPPPPPPPPPPPPPP
Answer:
x intercepts: (1,0), (-3,0)
the roots are 1 and -3
Step-by-step explanation:
Using the Quadratic Formula:
x=−b±sqrt(b2−4ac)/2a
Substitute:
x= -8±sqrt(8^2-4(4)(-12))/2(4)
x=-8±sqrt((64- -192))/8
x=-8±sqrt(256)/8
Solve two equations (±)
x=-8±16/8
x=8/8 and x=-24/8
x=1 and x=-3
Answer:
x = -3
x = 1
Step-by-step explanation:
Hello!
We can solve the quadratic by Factoring the Equation and using the Zero Product Property.
Factor[tex]y = 4x^2 + 8x - 12[/tex][tex]y = 4(x^2 + 2x - 3)[/tex]
We want to find two numbers that multiply out to -3, but add up to 2. The numbers that work are -1 and 3. We can expand 2x to -x and 3x and factor by grouping.
[tex]y = 4(x^2 -x + 3x - 3)[/tex][tex]y = 4(x(x - 1) + 3(x - 1))[/tex][tex]y = 4(x + 3)(x - 1)[/tex]Solve for x
Set each factor to 0 and solve for x in both.
[tex]0 = 4(x + 3)(x - 1)[/tex][tex]0 = (x + 3), x = -3[/tex][tex]0 = (x - 1), x = 1[/tex]Therefore, the x-interecpts are -3 and 1.
Find the measure of angle C.
D
118°
C
The measurement of angle C in the given figure is 118°.
Given that are two lines intersecting at a point making 4 angles, 118°, C, D and B.
B and D are opposite to each other and C and 118° are opposite to each other.
We need to find the measurement of angle C.
To find the measurement of angle C, we can use the concept of vertical angles.
Vertical angles are a pair of non-adjacent angles formed when two lines intersect.
They are always congruent, meaning they have the same measure.
In this case, angle 118° and angle C are vertical angles. So, their measures are equal:
Angle C = 118°
Therefore, the measurement of angle C is 118°.
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The slope of the line is -2 use the coordinates (4,-6) to find the point-slope equation of the line
Answer: [tex]y+6=-2(x-4)[/tex]
Step-by-step explanation:
See attached image.
Can someone help? ASAP
[tex]\tan 45^{\circ}=\frac{x}{2\sqrt{10}}\\\\1=\frac{x}{2\sqrt{10}}\\\\\boxed{x=2\sqrt{10}}\\\\\\\\\sin 45^{\circ}=\frac{2\sqrt{10}}{y}\\\\\frac{1}{\sqrt{2}}=\frac{2\sqrt{10}}{y}\\\\y=2\sqrt[20}\\\\\boxed{y=4\sqrt{5}}[/tex]
Can someone help me please
Answer:
[tex]y=7x[/tex]
I hope this helps and that you can give a brainliest!
Step-by-step explanation:
If x and y vary directly, that means that y is directly proportional to x. So, the parent function is y = kx.
So, by plugging in the given y=42 when x=6 into this parent function, we get:
42=6k
If we solve for k, we end up with 7.
Now if we plug in the value of k back into the parent function of this scenario, we get:
[tex]y=7x[/tex]
ALL U NEED TO TO IS IDENTIFY THE PROPERTYS OF EACH PROBLEM. PLS
Experiments done without replacement will result in:
When sampling is finished without replacement, each member of a population could also be chosen just once. during this case, the chances for the second pick are full of the results of the primary pick. The events are considered to be dependent or not independent.
lets understand with the help of an Example
You have a good, well-shuffled deck of 52 cards. It consists of 4 suits. The suits are clubs, diamonds, hearts and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king) of that suit.
Sampling without replacement:
Suppose you decide three cards without replacement. the primary card you choose out of the 52 cards is that the K of hearts. you place this card aside and pick the second card from the 51 cards remaining within the deck. it's the three of diamonds. you place this card aside and pick the third card from the remaining 50 cards within the deck. The third card is that the J of spades. Your picks are . Because you have got picked the cards without replacement, you can not pick the identical card twice.
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Which of the following aquatic organisms is classified as a fish?
whale
jellyfish
octopus
shark
I think the octopus is right but i am not sure !
Answer:
Shark
Step-by-step explanation:
They have gills,scales,swim bladders to float,most produce eggs and also in ectothermic.
======================================================
Further explanation:
Whales are not fish. This is a common misconception many people have (the same goes for dolphins as well). Whales are mammals that don't have gills, which is why they occasionally come to the surface for oxygen. Despite "fish" being literally right in their name, jellyfish aren't fish. It's confusing I know. Jellyfish belong to the phylum Cnidaria, while fish belong to the phylum Chordata. Octopus aren't fish either. They are molluscs and are related to animals like snails, squid, and slugs.Sharks are fish. They have gills and fins like any other fish does.A study analyzed the average yearly salt intake in the united states from 2012 thru 2017. the data is summarized in the table: the study found that the data after the year 2012 can be modeled by the function f(x) = 52.3x + 3,548, where x is the the number of years since 2012 and f(x) is the total amount of salt ingested in grams. describe the significance of 3,548.
The significance of 3,548 estimates the average grams of salt used in 2012.
A connection between independent variables and the dependent variable.is defined by the function.
Functions help to represent graphs and equations. A function is represented by two variables, one is dependent, and another one is an independent function.
The study discovered that the function can represent the data after the year 2012 as,
f(x) = 52.3x + 3,548
Where x is the number of years since 2012.
Hence, The significance of 3,548 estimates the average grams of salt used in 2012.
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