=======================================================
Explanation:
Draw a circle and split it into 4 equal pieces.
We'll split the 160 students into four equal groups
160/4 = 40
Write the number 40 in each slice. Shade 3 of those slices to represent 3*40 = 120 students went to the pep rally (the remaining 40 did not go).
Answer:
120
Step-by-step explanation:
Take the 160 divide by ¾ to get 120.. These are the number of students who went
George found that he blinked 85 times in 15 minutes. At this rate, how many seconds passed during the 51 blinks?
alpha writes the infinite arithmetic sequence \[10, 8, 6, 4, 2, 0 ,\ldots.\]beta writes the infinite geometric sequence \[9, 6, 4, \frac{8}{3}, \frac{16}{9}, \ldots.\]gamma makes a sequence whose $n^{\text{th}}$ term is the product of the $n^{\text{th}}$ term of alpha's sequence and the $n^{\text{th}}$ term of beta's sequence: \[10\cdot 9 \quad,\quad 8\cdot 6\quad ,\quad 6\cdot 4\quad,\quad 4\cdot \frac83\quad,\quad 2\cdot \frac{16}{9}\quad,\quad \ldots.\]what is the sum of gamma's entire sequence?
Consecutive terms in the α sequence have a common difference of
8 - 10 = 6 - 8 = 4 - 6 = … = -2
so they are given recursively by
[tex]\begin{cases} \alpha_1 = 10 \\ \alpha_n = \alpha_{n-1} - 2 & \text{for } n\ge2 \end{cases}[/tex]
By substitution, we have
[tex]\alpha_n = \alpha_{n-1} - 2 \\\\ \alpha_n = \alpha_{n-2} - 2\cdot2 \\\\ \alpha_n = \alpha_{n-3} - 3\cdot2 \\\\ \vdots \\\\ \alpha_n = \alpha_{n-(n-1)} - (n-1)\cdot 2 = \alpha_1 - 2(n-1) = 12-2n[/tex]
Consecutive terms in the β sequence have a common ratio of
6/9 = 4/6 = (8/3)/4 = … = 2/3
so the recurrence for these terms is
[tex]\begin{cases} \beta_1 = 9 \\\\ \beta_n = \frac23 \beta_{n-1} & \text{for } n\ge2 \end{cases}[/tex]
We can solve for [tex]\beta_n[/tex] similarly:
[tex]\beta_n = \dfrac23 \beta_{n-1} \\\\ \beta_n = \left(\dfrac23\right)^2 \beta_{n-2} \\\\ \beta_n = \left(\dfrac23\right)^3 \beta_{n-3} \\\\ \vdots \\\\ \beta_n = \left(\dfrac23\right)^{n-1} \beta_{n-(n-1)} = \left(\dfrac23\right)^{n-1} \beta_1 = \dfrac{2^{n-1}}{3^{n-1}} \cdot 3^2 = \dfrac{2^{n-1}}{3^{n-3}}[/tex]
The γ sequence has [tex]n[/tex]-th term
[tex]\gamma_n = \alpha_n \beta_n = (12-2n) \dfrac{2^{n-1}}{3^{n-3}} = (108-18n) \left(\dfrac23\right)^{n-1}[/tex]
and we want to compute
[tex]\displaystyle \sum_{n=1}^\infty \gamma_n = 108 \sum_{n=1}^\infty \left(\frac23\right)^{n-1} - 18 \sum_{n=1}^\infty n \left(\frac23\right)^{n-1}[/tex]
Recall the sum of an infinite geometric series with common ratio [tex]|r|<1[/tex] converges to
[tex]\displaystyle \sum_{n=1}^\infty r^{n-1} = \frac1{1-r}[/tex]
so that
[tex]\displaystyle \sum_{n=1}^\infty \left(\frac23\right)^{n-1} = \frac1{1-\frac23} = 3[/tex]
For the remaining sum, we can use the method shown in question [24494877] to compute
[tex]\displaystyle \sum_{n=1}^\infty nr^{n-1} = \frac1{(1-r)^2}[/tex]
which gives
[tex]\displaystyle \sum_{n=1}^\infty n \left(\frac23\right)^{n-1} = \frac1{\left(1-\frac23\right)^2} = 9[/tex]
Then the infinite sum of the terms of γ converges to
[tex]\displaystyle \sum_{n=1}^\infty \gamma_n = 108 \cdot 3 - 18 \cdot 9 = \boxed{162}[/tex]
rewrite cos^4 2x in terms of the first power of cosine.
cos2x = (1+cos(2x))/2
What is meant by first power of cosine?The cosine power is odd (n odd): u = sin x and du = cos x dx should be used. d u = cos To create an even number of cosine powers, replace dx with (a), canceling one power of cos x by substituting du. The Power Factor is the sine of the angle formed by Current and Voltage.
P = VI Cosθ OR.Cosθ = P ÷ V I OR.Cosθ = kW ÷ kVA OR.Cosθ = True Power ÷ Apparent Power.The ratio of the length of the side next to the angle to the length of the hypotenuse is known as the cosine, sometimes abbreviated as "cos." The ratio of the length of the side across from the angle to the length of the side next to it is called the tangent, which is frequently abbreviated as "tan."
cos2(2x) = (1+cos(4x))/2
cos4(2x)= [(1+cos(4x))/2]²
[tex]cos^{4}[/tex](2x) = [(1+cos(4x))/2]²
[tex]cos^{4}[/tex] (2x) = (1/4) × [1 + cos(4x)]²
[tex]cos^{4}[/tex](2x) = (1/4) × (1 + 2cos(4x) + cos²(4x))
[tex]cos^{4}[/tex](2x) = (1/4)*[1 + 2cos(4x) + (1 + cos(2x))/2]
[tex]cos^{4}[/tex](2x) = (1/4)*[1 + 2cos(4x) + (1/2)*(1 + cos(2x))]
[tex]cos^{4}[/tex](2x) = (1/8)*[2 + 4cos(4x) + 1 + cos(2x)]
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X-3 is a factor of x³+ax²–2x+3
Answer:X-3 is a factor of x³+ax²–2x+3
Step-by-step explanation:X-3 is a factor of x³+ax²–2x+3
p(x)=x
3
−ax
2
+2x+a−1
⇒ p(a)=(a)
3
−a(a)
2
+2(a)+a−1
⇒ 0=a
+2a+a−1=0
⇒ 3a−1=0
⇒ 3a=1 a=
3
1
Ms. Juhal was making t-shirts. One of the designs had the instructions to make points at the following locations and then draw lines to connect the points in order: A (-5,5) ; B (-5,3) ; C (-5,1) ; and D (2,1) . ⦁ Use graph paper to plot the points. ⦁ Connect them in order: A to B, B to C, C to D, and then D back to A. What shape is created?
HELP PLS
Identify that the shape created is a Triangle.
For this exercise it is important to remember that, given a point P (x , y), "x" is the the x-coordinate of the point and "y" is the y-coordinate of the point.
In this case, Ms. Juhal has the following points:
1) Point A (-5 , 5)
x = -5 and y = 5
2) Point B (-5 , 3)
Where:
x = -5 band y = 3
3) Point C (-5 , 1)
x = -5 and y = 1
4) Point D (2,1)
Where:
x = 2 and y = 1
Therefore, knowing the coordinates of each point, you can plot them and connect them in order (Observe the picture attached).
Finally, you can identify that the shape created is a Triangle.
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Micah is planning a road trip. He estimates that he will drive a total of of 7 hours. He wants to stop for gas after ⅓ of the total time has passed. How long will he drive before he stops for gas? Express your answer as a mixed number.
Answer:
After 2 1/3 hours.
Step-by-step explanation:
For this you have to calculate how much hours is 1/3 of 7 hours. The word 'of' implies a multiplication function.
1/3 * 7 = 7/3 = 2 1/3
Do number 12 and 13 please thank you!!
12. The statement ' x+3 = 9' is true sometimes.
How is this explained?
Let x= 6,
6 + 3 = 9 (true)
Let x= 5 ,
5 + 3 = 8 (not true)
13. Option c. The statement 'multiplicative inverse of a number is less than the original number' is true for all numbers greater than 1.
How is this explained?
Let us consider some numbers,
a) 1
The multiplicative inverse of 1 = 1
Thus, multiplicative inverse of this number is not less than the original number.
b) 2 (greater than 1)
The multiplicative inverse of 2 = 1/2
multiplicative inverse of this number is less than the original number.
c) 8/7 (greater than 1)
The multiplicative inverse of 8/7 = 7/8
Here, multiplicative inverse of this number is less than the original number.
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-Determine the equation of the line that passes through the point (9, -42)and is parallel to the line y = -5x + 1.Enter your answer in slope-intercept form.Pls see picture
Two parallel lines have the same slope. Given the equation of one of the lines, you can determine the slope of the other line:
[tex]y=-5x+1[/tex]The slope of the line is the coefficient of the x-term, in this case, that coefficient is -5. Then the slope of both parallel lines is m= -5.
The line you have to find must cross through the point (9,-42). Using the point-slope form you can determine the equation of the parallel line:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line:
[tex]\begin{gathered} y-(-42)=-5(x-9) \\ y+42=-5(x-9) \end{gathered}[/tex]To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+42=(-5)\cdot x+(-5)\cdot(-9) \\ y+42=-5x+45 \end{gathered}[/tex]Subtract 42 to both sides of the expression to pass the term to the right side of the equal sign:
[tex]\begin{gathered} y+42-42=-5x+45-42 \\ y=-5x+3 \end{gathered}[/tex]The equation of the line is y= -5x + 3
Help please
I don’t understand
1) Let the value of yellow circles = x
Let the value of green butterflies = y
Consider the left string,
3x + y = 15 ----(1)
Consider the right string,
x + 2y = 15 ----(2)
Let us solve the linear equations
(1) *2 => 6x+ 2y = 30 ---(3)
(3) - (2) => 6x+ 2y = 30 - ( x + 2y = 15)
=> 5x = 15
=> x = 3
Substituting x in (1)
3(3) + y = 15
y = 15- 9
y = 6
The value of yellow circles = 3
The value of green butterflies = 6
2) Let the yellow circles = c
Let the green butterflies = b
The linear equations that could be formed are:
a) Left string equation:
3c+b = 15
b) Right string equation:
2b +c = 15
c) Equation of both strings:
4c +3b = 30
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Which could be the first step in solving the equation represented by the model below? XX X X Add 4 negative unit tiles to both sides. Add 4 negative unit tiles to the left side, and add 6 negative unit tiles to the right side. Add 4 positive unit tiles to both sides. Add 6 negative unit tiles to the left side, and add 4 negative unit tiles to the right side.
The most appropriate choice for linear equation will be given by -
First option is the correct option
Adding 4 units negative tiles to both sides.
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expression by an equal to sign.
A one degree equation is called linear equation.
Here,
The equation is 3x + 4 = 2x + 6
For the second option,
If we have to add 4 units negative tiles to left side, we will also have to add 4 units negative tiles to right side.
Second option is wrong
For the third option
We have to add four units negative tiles to both sides, not 4 units positive tiles.
For the fourth option
Adding 6 units negative tiles to left side and 4 units negative tiles to right side will not eliminate any of 6 or 4.
So the first option is correct.
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Complete Question
The diagram has been attached below
WILL GIVE BRAINLY IF WRITE PLS HEP ASAP
Pls help!
if you have to work it out pls work it out my teacher will be mad if no work!
Answer:
1st one: 50%, 0.5, 1/2
2nd one: 25%, 0.25, 1/4
3rd one: 18%, 0.18, 9/50
4th one: 10%, 0.1, 1/10
5th one: 20%, 0.2, 1/5
Step-by-step explanation:
Hope this helps!
I need help with this question
The proportional relationship modeled by Table A is graphed on the image given at the end of the answer.
Direct proportional relationshipA direct proportional relationship is defined when the output variable y is calculated with the multiplication of the input variable x and the constant of proportionality r as follows:
y = rx.
The meaning of this is that a proportional relationship is only represented when the division of y by x for all pairs of points (x,y) are the same.
Hence, the proportional relationship in this problem is represented by table A, as:
r = 10/5 = 8/4 = 6/3 = 2/1.
Hence the equation is:
y = 2x.
For table B, a proportional relationship is not shown, as:
3/1 is different of 4/2.
The graph containing the points listed on table A are given at the end of the answer.
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For a certain airline, flight attendants need to be between 63 and 73 inches tall. Which of the following absolute value equations can be used to represent these minimum and maximum heights
Flight attendants for one carrier must be between 63 and 73 inches tall. The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.
Given that,
Flight attendants for one carrier must be between 63 and 73 inches tall.
We have to find what absolute value equations from the list below can be used to express these minimum and maximum heights.
In algebra, an absolute value function is a function where the variable is inside the bars denoting absolute values. The absolute value function is also known as the modulus function, and its most popular representation is function of x = |x|, where x is a real number. The absolute value function is typically written as function of x = a |x - h| + k, where a denotes the vertical stretch of the graph, h denotes the horizontal shift, and k denotes the vertical shift from the graph of function of x = |x|.
Therefore, The absolute value equations from the list below can be used to express these minimum and maximum heights is |x+68|<5.
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Differentiate the function, f(x) = ln (2x + 4) with respect to x?
Answer:
f'(x) = [tex]\frac{1}{x+2}[/tex]
Step-by-step explanation:
using the chain rule to differentiate
f(x) = g(h(x)) , then
f'(x) = g'(x) × h'(x)
f(x) = ln(2x + 4) , then
f'(x) = [tex]\frac{1}{2x+4}[/tex] × [tex]\frac{d}{dx}[/tex] (2x + 4)
= [tex]\frac{1}{2x+4}[/tex] × 2
= [tex]\frac{2}{2x+4}[/tex]
= [tex]\frac{1}{x+2}[/tex]
Three students are participating in a walkathon. The data for each student is shown. Student A: the equation y = 14x represents the amount of money raised (y) for walking (x) miles
Student B:$42 is raised after walking 3 miles.
Student C: miles walked 6 and 9 money raised $72 and $108
Answer choses
Student A
Student B
Student C
All three students raised the same amount of money after walking 8 miles.
The student that raised the least amount based on the information is student C.
How to illustrate the information?For student A, the equation illustrated is y = 14x and this represents the amount of money raised (y) for walking (x) miles.
For student B, $42 is raised after walking 3 miles. The amount raised per mile will be:
= $42 / 3
= $14 per mile
For C, The miles walked 6 and 9 and the money raised $72 and $108. This shows that the amount is:
= $72 / 6
= $12 per mile.
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Three students are participating in a walkathon. The data for each student is shown. Student A: the equation y = 14x represents the amount of money raised (y) for walking (x) miles
Student B:$42 is raised after walking 3 miles.
Student C: miles walked 6 and 9 money raised $72 and $108
Who raised the least amount
Answer:
The student that raised the least amount based on the information is student C.
Step-by-step explanation:
Eugene is deciding between two payment plans when purchasing a new car. If Eugene chooses payment plan A, he will pay $429.47 a month for 36 months for the car. If Eugene chooses payment plan B, he will pay $340.89 a month for 48 months for the car. How much money will Eugene save on the car overall if he chooses payment plan A?
Eugene will save $901.8 on the car overall if he chooses payment plan A.
Eugene has to buy a new car, and there are two payment plans from which he has to decide which to opt for.The two plans are, namely, plan A and plan B.In plan A, he has to pay an amount of $429.47 a month for 36 months for the car.In plan B, he has to pay an amount of $340.89 a month for 48 months for the car.The total amount to be paid if he chooses plan A is 36*429.47 = $15,460.92.The total amount to be paid if he chooses plan B is 48*340.89 = $16,362.72.We can see that plan A is better than plan B.The amount saved by Eugene by selecting plan A is represented in the equation below:$16,362.72 - $15,460.92 = $901.8To learn more about equations, visit :
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a one way train ticket in the city costs $1.95. A monthly pass costs $50. For what numbers of rides should you buy the monthly pass?
For 26 rides in a month, a monthly pass should be made, while for rides less than 26 using a one-way ticket will be a cost-effective method
Cost of one way train ticket = $.195
Cost of monthly pass = $50
Monthly pass: It is a prepaid fare card good for one month of limitless travel. This saves cost and time in terms of commuting costs and time of getting the tickets issues
Let x represent the number of rides one takes
Formulating the equation we get:
Cost of one-way ticket*Number of rides = Cost of a monthly pass
= 1.95*x = 50
x = 25.64 or 26 rides
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Point Q has coordinates (5,6). If you rotate Q 90° about the origin, (0,0), what are the coordinates of Q′
The coordinates of the image after 90° about the origin is (6, -5)
What is a 90 degrees rotation?A 90 degrees rotation denoted by R(90, 0) is a rotation that has the same effect as the 270 degrees counterclockwise of a figure.
How to determine the image of the rotation?The coordinate of the point is given as
(5, 6)
The rotation is given as 90° about the origin
So, we have
(x, y) => (y, -x)
Substitute (5, 6) in (x, y) => (y, -x)
So, we have
(5, 6) => (6, -5)
Hence, the coordinates of the image is (6, -5)
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A pile of sand has a weight of 65 kg.
Some of the sand is put into a small sack.
The rest of the sand is put into a large sack.
The sand in the large sack weighs 15 kg more than the sand in the small sack.
What is the weight of the sand in the small sack?
Answer:
25 kg
Step-by-step explanation:
The sum of the weights of the small and large sacks is 65 kg. The larger sack weighs 15 kg more. You want the weight of the smaller sack.
SetupLet w represent the weight of the sand in the small sack. Then (w+15) is the weight of the sand in the larger sack. The total weight is 65 kg, so we have ...
w +(w+15) = 65
SolutionSubtracting 15 from both sides gives ...
2w = 50
w = 25
The weight of the sand in the small sack is 25 kg.
Yvonne is training for the marathon. She calculates to see whether she can cover 9 miles in 10 minutes. But she completes the distance in 8 minutes. What is the percent error in Yvonne's calculation?
The relative error exists multiplied by 100 to estimate the percent error. The percent error in Yvonne's calculation exists 11% error.
What is meant by percent error?The difference between the estimated value and the actual value in relation to the actual value is known as the percent error. To calculate the percent error, the relative error is multiplied by 100.
Percent error calculates the difference between an estimate and a correct value and expresses it as a percentage. Analysts can use this statistic to determine how big the error is in relation to the actual value. It is also referred to as % error and percentage error.
%error = (calculated value - experimental value) / calculated × 100%
%error = (10 - 9)/9 × 100%
= 1/9 × 100%
= 11.11111 ≈ 11% error
Therefore, the percent error in Yvonne's calculation exists 11% error.
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can someone help me with this
Answer: Slope intercept from is y= 4/13x-5/13
Step-by-step explanation:
Cody biked a total of 22 kilometers
by making 11 trips to work. How
many trips will Cody have to make to
bike a total of 30 kilometers?
Answer: 15
Step-by-step explanation:
This is the answer because 22 divided by 11 equals 2 kilometer each trip to work so 30 kilometer divided by 2 is 15.
Ian is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $1.25 per mile driven. How much would a taxi ride cost if Ian is riding for 2 miles? How much would a taxi ride cost that is mm miles long?
It would cost him $ 5 to cover a distance of 2 miles.
Amount charged by the taxi driver which is mandatory to be paid is $ 2.50
Additional amount charged by the driver is $1.25
Since Ian is driving 2 miles thus we can write it as follows :
2.50 + (1.25 × 2) = 2.50 + 2.5
= $5
The additional charges are basically the amount which is charged by the driver to cover a particular distance and thus this distance changes as the distance changes.
However the mandatory fees is constant and it never changes.
It would cost him $ 5 to cover a distance of 2 miles.
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A ticket to see your favorite baseball team costs 37.26$. That price decreases by 0.28$ for every game lost during the regular season. What equation could you use to find the cost C of a ticket after L losses? Represent the total change in the cost of a ticket after the team loses 37 games. What is the price of a ticket after the team loses 37 games?
Equation: (C Stands for Cost and L stands for losses)
37.26 C-0.28 L
The total change in the cost of a ticket is dollars.
The equation that represents the given situation is required.The cost of the ticket after L losses is a. Initial cost of the ticket = $49.64Price decrease per game lost = $0.41Number of games lost = LMoney lost after L losses is So, the cost of the ticket after L losses would be the initial cost of the ticket minus the money lost after L losses.The cost of the ticket after L losses is a.
Pls help me how did I get the question wrong
Answer:
see explanation
Step-by-step explanation:
the equation of a line (linear equation) has slope- intercept form
y = mx + c ( m is the slope (gradient)) and c the y- intercept )
y = 12 + 2x or y = 2x + 12 ← is in slope- intercept form
with gradient m = 2
--------------------------------------------------------
the only graphs in linear form are
y = [tex]\frac{1}{2}[/tex] x and y = 12 - x
the other 2 have an x² term which indicates they are quadratic
10y-2y + 30 = 8y - 15 + 5
Answer:
No Solution
Step-by-step explanation:
Question 5 (1 point)
(03.06 MC)
Use function notation to write a recursive formula to represent the sequence: 3, 6, 12, ...
The recursive formula is f(n - 1) . 3
The correct option is (c)
What are Recursive Formula ?
A recursive formula refers to a formula that defines each term of a sequence using the preceding term(s). The recursive formulas define the following parameters:
The first term of the sequenceThe pattern rule to get any term from its previous termGiven,
The sequence is:
3, 6 , 12 ....
To find the recursive formula of above sequence :
Now, The first term is 3.
Recursive formula is :
f(n - 1) . 3
Hence, The recursive formula is f(n - 1) . 3
The correct option is (c)
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Find the circumference and area of the figure if each unit on the graph measures 1 centimeter Round answers to the nearest tenth, if necessary
A(2,3)
B(4,1)
Circumference of the circle = 17.8 units
Area of the circle = 25.1 square unit
What is circumference of circle ?An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle."
Formula to get the circumference of a circle = 2πr
Where r = radius of the circle
Radius of the given circle = Distance between the points A(2, 3) and B(4, 1)
r = [tex]\sqrt{(2-4)^{2} +(3-1)^{2} }[/tex]
r = 2√2units
Therefore, circumference = 2π(2√2)
= 17.77
≈ 17.8 units
Area of the circle = πr²
= π(2√2)²
= 8π
= 25.13
≈ 25.1 square unit
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Determine the unknown angle in the triangle pictured below: