The equation can be y = 3x + 7, evaluating it in x = 16 we will get:
y = 55
How to write and evaluate an equation?We can write a linear equation, which is the simplest type of equations.
For example, let's define:
y = 3x + 7
Now the evaluation.
We want to find the value of y when x = 16. To do so, we need to evaluate the equation in x = 16, that means replacing the variable x by the number, then we will get.
y = 3*16 + 7
y = 55
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Find the 8th term of the geometric sequence 10, 50, 250,...
The 8th term of the sequence is 781, 250.
We have geometric sequence 10, 50, 250,...
First term= 10
Common ratio = 50/10 = 5
So, the 8th term of sequence is
= 10 x [tex]r^{8-1[/tex]
= 10 x [tex]r^7[/tex]
= 10 x [tex](5)^7[/tex]
= 10 x 5 x 5 x 5 x 5 x5 x 5 x 5
= 10 x 78125
= 781, 250
Thus, the 8th term of the sequence is 781, 250.
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Nicole made 10 dozen cupcakes. She made 20% with chocolate icing, 30% with vanilla icing, and 50% with powdered sugar. How many of each kind of cupcake did she make?
Answer:
2 Dozen Chocolate, 3 Dozen Vanilla, 5 Dozen Sugar.
Explanation:
0.5 x 10 = 5.
0.3 x 10 = 3.
0.2 x 10 = 2.
can someone please help me what is 11 1/8 + 2 3/4??? please
Answer: 13 7/8
Step-by-step explanation:
11 + 1/8 + 3/4 + 2 = 13 7/8
Select all numbers that are irrational.
Answer:
The irrational numbers are:
368.5468432...
14.19274128...
√.156
The directional derivative of f= x^2 y z^3 along x = e^-t , y = 1 + 2 sint , z = t -cost at t =0
The directional derivative of f = x²yz³ along vector i + 2j + 2k at x = [tex]e^{-t}[/tex] , y = 1 + 2 sin t , z = t -cost at t =0 is 2/3.
Given that the functions are,
x = [tex]e^{-t}[/tex]
y = 1 + 2 sin t
z = t - cos t
At t = 0 the point will be,
x = e⁰ = 1
y = 1 + 2 sin 0 = 1
z = 0 - cos 0 = -1
So the point is (1, 1, -1).
The vector is,
a = i + 2j + 2k
unit vector of a = (i + 2j + 2k)/√(1² + 2² + 2²) = (i + 2j + 2k)/3
Given the function is, f = x²yz³
Grad. f = 2xyz³.i + x²z³.j + 3x²yz².k
directional derivative is given by
= (Grad. f)*(unit vector of a) at (1, 1, -1)
= (2xyz³.i + x²z³.j + 3x²yz².k)*(i + 2j + 2k)/3 at (1, 1, -1)
= (2xyz³ + 2x²z³ + 6x²yz²)/3 at (1, 1, -1)
= (-2 - 2 +6)/3
= 2/3
Hence required directional derivative is 2/3.
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The question is incomplete. The complete question will be -
"The directional derivative of f= x^2 y z^3 along vector i + 2j + 2k at x = e^-t , y = 1 + 2 sin t , z = t -cost at t =0"
Area/ Perimeter question. Any help? i have an assignment to complete.
Answer:
13 + 8 + 13 + (1/2)(8π) = 34 + 4π feet
= 46.57 feet
tia's favorite stargergy for multiplying polynomials is to make a box that fits the two factors
Using Tia's box method, the multiplication of the polynomials (x + 2)(x² -3x + 5) in the standard form is x³ - x² - x + 10
Here, we need to multiply the polynomials (x + 2)(x² -3x + 5)
Tia's stargergy for multiplying polynomials is to make a box that fits the two factors.
Using Tia's box method,
x² -3x +5
x x³ -3x² +5x
+2 +2x² -6x +10
Consider (x + 2)(x² -3x + 5)
= (x . x²) - (x . 3x) + (x . 5) + (2x²) -(2 × 3x) + (2 × 5)
= x³ - 3x² + 5x + 2x² - 6x + 10
= x³ - 3x² + 2x² + 5x - 6x + 10
= x³ - x² - x + 10
This is the required polynomial.
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Find the complete question below.
what is the solution to the equation 0.5x - 1.25 = 3.5?
Answer:
Step-by-step explanation:
Add '-1.25' to each side of the equation.
1.25 + -1.25 + -0.5x = 0.75 + -1.25 + 3.5n
Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -0.5x = 0.75 + -1.25 + 3.5n
-0.5x = 0.75 + -1.25 + 3.5n
Combine like terms: 0.75 + -1.25 = -0.5
-0.5x = -0.5 + 3.5n
Divide each side by '-0.5'.
x = 1 + -7n
Simplifying
x = 1 + -7n
The sun of the 2 digits of a certain number is 5. If 9 is added to the original number, the new number will have the original digits reversed. Find the number
Answer:
23
Step-by-step explanation:
Assume the digits are
1, 4 or 2,3
The number can be 14, 41, 23, 32
Test each one:
14 + 9 = 23 does not work
41 + 9 = 50 does not work
23 + 9 = 32 works
32 + 9 = 41 does not work
According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:
Month
Average Maximum Monthly Temperature
Jan
48.1
Feb
50.9
Mar
62.4
Apr
67.0
May
76.5
Jun
83.9
Jul
86.8
Aug
88.1
Sep
79.2
Oct
69.9
Nov
59.5
Dec
49.6
Let x represent the months and y represent the average maximum monthly temperature.
Plot the data on a scatterplot. Choose the plot that best represents the data.
a.
On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6).
b.
On a coordinate plane, points are around (5, 85), (6, 90), (7, 80), (8, 70), (9, 60), (10, 50), (48, 1), (50, 3), (62, 4), (66, 4), (76, 5), (82, 8).
c.
On a coordinate plane, points are around (0, 49), (1, 52), (2, 62), (3, 68), (4, 78), (5, 85), (50, 12), (60, 10), (70, 10), (80, 9), (88, 8), (87, 9), (89, 9).
d.
On a coordinate plane, points are around (0, 48), (2, 52), (13, 50).
Please select the best answer from the choices provided
a) On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6) best represents the data.
This is because the data represents a set of paired values, with the months as the independent variable (x) and the average maximum monthly temperature as the dependent variable (y). A scatter plot is the appropriate graph for displaying this type of data.
Option a shows the correct placement of the data points on a scatter plot, with the x-axis representing the months and the y-axis representing the average maximum monthly temperature. The points are clearly organized in a sequence from January to December, with an upward trend in temperature from the winter months to the summer months, followed by a gradual decrease in temperature in the fall and winter months.
Option b has the correct range of temperatures, but the points are not arranged in a logical sequence and are scattered randomly across the graph. Option c also has a similar issue with random placement of points and does not reflect the actual values in the data set. Option d only has three points and does not represent the complete data set.
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complete the table AB=1?, BC=3?
Answer:
angle B = 60 degree
AB = 2 cm
BC = 2 cm
Step-by-step explanation:
an equilateral triangle is a triangle with the following properties:
1. all sides equal
2. all angels equal to 60 degree
As a result:
angle B = 60 degree
AB = 2 cm
BC = 2 cm
Suppose you invest $5,000 in an account earning 4.71% APR compounded
monthly. How much money will be in the account after 15 years?
$9,664.47
After 15 years the account will have $9,664.47
2. An equation for a line is = 6/5 . What will the new equation of this line be after it is rotated 90° counterclockwise around the origin
If new equation of this line be after it is rotated 90° counterclockwise around the origin, the equation of the new line after rotation is y = (-5/6)x
To find the new equation of a line after it is rotated 90° counterclockwise around the origin, we need to use the following formula:
(x', y') = (-y, x)
where (x, y) are the coordinates of a point on the original line, and (x', y') are the coordinates of the corresponding point on the new line after rotation.
We can start by finding the slope of the original line, which is given by:
y = (6x/5)
Rearranging this equation, we get:
x = (5/6)y
This tells us that the slope of the original line is 5/6.
To find the equation of the new line after rotation, we need to apply the formula above to two points on the original line. Let's choose two easy points to work with, such as (0,0) and (5,6).
Using the formula, we can find the new coordinates of these points after rotation:
(0', 0') = (-0, 0) = (0,0)
(5', 6') = (-6, 5)
Now we can find the slope of the new line using these two points:
slope = (6' - 0') / (5' - 0') = 5/-6 = -5/6
In summary, to find the new equation of a line after rotating 90° counterclockwise around the origin, we can use the formula (x', y') = (-y, x) to find the new coordinates of two points on the original line, and then use these points to find the slope of the new line. In this case, the new equation of the line is y = (-5/6)x.
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The students at Kayla's school are forming teams of three students for a quiz bowl competition. Kayla is assuming that each member of a team is equally likely to be male or female. She uses a coin toss (heads = female, tails = male) to simulate this probability. Here is Kayla's data from 50 trials of 3 coin tosses:
thh tth tth tht thh htt hth hht hth tth tth hht hth tht tht tth tth thh thh htt tht thh tth hht hth thh tht tth hht thh hhh tth tth hth htt tht thh hhh htt thh htt ttt tht ttt thh hht hth htt hht hth
According to this data, what is the experimental probability that a team will consist of two girls and a boy?
0.33
0.375
0.23
0.46
The required, experimental probability that a team will consist of two girls and a boy is 0.33. Option A is correct.
To find the experimental probability that a team will consist of two girls and a boy, we need to count the number of times that Kayla got a team with two girls and one boy and divide that by the total number of trials.
So, out of 50 trials, there were 17 trials where the team had two girls and one boy. Therefore, the experimental probability is:
17/50 = 0.34
Therefore, it is 0.34, which is closest to option (A) 0.33.
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Write an equation then find the value of y when x =16. Show all work.
Answer:
Answer is A
Step-by-step explanation:
A) y = -1/2x represents a proportional relationship because the equation can be written in the form y = kx, where k is a constant. In this case, k = -1/2, which means that y is proportional to x with a constant of proportionality of -1/2.
B) y = 2x - 4 does not represent a proportional relationship because the equation cannot be written in the form y = kx. If we try to write it in this form, we get y/x = 2 - 4/x, which means that y/x is not constant. Therefore, y is not proportional to x with a constant of proportionality.
Which diagram depicts as a positive angle in standard position?
Answer:
A.
Step-by-step explanation:
A positive angle has the initial side at the positive x-axis and the terminal side rotated counterclockwise from it.
That is shown in diagram A.
can someone help me with this
The sine equation for the object's height is given as follows:
d = -5sin(0.24t).
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(Bx) + C.
The parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The amplitude for this problem is of 5 inches, hence:
A = 5.
The period is of 1.5 seconds, hence the coefficient B is given as follows:
2π/B = 1.5
B = 1.5/2π
B = 0.24.
The function starts moving down, hence it is negative, so:
d = -5sin(0.24t).
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The sales data for July and August of a frozen yogurt shop are approximately normal.
The mean daily sales for July was $270 with a standard deviation of $30. On the 15th of July, the shop sold $315 of yogurt.
The mean daily sales for August was $250 with a standard deviation of $25. On the 15th of August, the shop sold $300 of yogurt.
Which month had a higher z-score for sales on the 15th, and what is the value of that z-score?
a.)
August, with a z-score of 1.67.
b.)
July, with a z-score of 1.5.
c.)
July, with a z-score of 1.8.
d.)
August, with a z-score of 2.
Answer: D
Step-by-step explanation:
To determine which month had a higher z-score for sales on the 15th, we need to calculate the z-scores for each month's sales.
For July:
z-score = (x - μ) / σ
where x is the sales on the 15th, μ is the mean daily sales for July, and σ is the standard deviation of daily sales for July.
Plugging in the values, we get:
z-score for July = (315 - 270) / 30 = 1.5
For August:
z-score = (x - μ) / σ
where x is the sales on the 15th, μ is the mean daily sales for August, and σ is the standard deviation of daily sales for August.
Plugging in the values, we get:
z-score for August = (300 - 250) / 25 = 2
Since the z-score for August is higher than the z-score for July, August had a higher z-score for sales on the 15th.
The value of the z-score for August's sales on the 15th was 2.
7
Select the correct answer from the drop-down menu.
Which term best fits the sentence?
After you make a decision, the next step in the decision-making process is to
whether you made the right choice.
Reset
Next
This step will help you det
Answer:
Step-by-step explanation: bot
-12 divided by 3 5/9
your answer is 3.375
The curve above is the graph of a sinusoidal function. It goes through the points
and
. Find a sinusoidal function that matches the given graph. If needed, you can enter
=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.
The sinusoidal function that matches the specified graph, expressed using π ≈ 3.1416 is; y ≈ 4·sin(0.628·(x + 3))
What is a sinusoidal function?A sinusoidal function is a periodic function that is based on either the sine or the cosine function.
The general form of a sinusoidal function is; y = A·cos(B·(x - C)) + D
The peak and the trough of the graph of the function indicates that the amplitude, A = (4 - (-4))/2 = 4
The vertical shift, D = (4 + (-4))/2 = 0
The period, P = 2·π/B
A cycle is completed in -0.5 - (-10.5) = 10 units of the x-value interval
P = 10 = 2·π/B
Therefore; B = π/5
When x = -8, y = 0, therefore;
0 = 4·sin((π/5)·((-8) - C)) + 0
4·sin((π/5)·((-8) - C)) = 0
sin((π/5)·((-8) - C)) = 0
(π/5)·((-8) - C) = 0
((-8) - C) = 0
C = -8
When x = 2, y = 0, therefore;
0 = 4·sin((π/5)·(2 - C)) + 0
4·sin((π/5)·(2 - C)) = 0
sin((π/5)·(2 - C)) = 0
(π/5)·(2 - C) = 0
(2 - C) = 0
C = 2
Similarly; When x = -3, y = 0, therefore; C = -3
y = 4·sin((π/5)·(x + 3))
The value C = -3, corresponds to the horizontal shift of the graph of the sine function, which is shifted 3 units to the left
The sinusoidal function, where π ≈ 3.1416 is therefore;
y ≈ 4·sin((0.628)·(x + 3))
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what is the area of the square if it’s 15 by 15
Answer:
225 is the answer
15 times 15
Step-by-step explanation:
Find a quadratic equation which has solutions x=7 and x=-9. Write the quadratic form in the simplest standard form x^2+bx+c=0
Answer: x^2+2x-63
Step-by-step explanation:
Quadratic Equation = x^2-(Sum of Solution)x+(Product of Solution)
=x^2-(7-9)+(7*(-9))
=x^2+2x-63
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Find the value of x in the figure below 53° ,24° and x°
Answer:46
Step-by-step explanation:
traingle ABD = 53 + 24 + 47 + x = 180
134+x=180
x=180-134
x=46
Pls help and show how you got the answer :) I really appreciate it
In 2006, the population will reach 109 million.
The correct answer is an option (d)
Here function [tex]f(x)=100(1.0153)^x[/tex] represents the population (in millions) x years after 2000
We need to find the year x when the population will reach 109 million.
i.e., for f(x) = 109, we need to find the value of x.
Consider function f(x),
[tex]f(x)=100(1.0153)^x[/tex]
Substitute f(x) = 109
⇒ [tex]109=100(1.0153)^x[/tex]
⇒ [tex](1.0153)^x=1.09[/tex]
Taking logarithm on both the sides.
⇒ x ln(1.0153) = ln(1.09)
⇒ x = ln(1.09) / ln(1.0153)
⇒ x = 5.675
⇒ x ≈ 6
So, the required year would be,
2000 + 6 = 2006
Therefore, the correct answer is an option (d)
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Homework help?!?!?!
Answer:
1. The slope of the line is 3. The line goes up 3, over 1, and since slope is rise/run, the slope is 3.
2. The slope of the line is 4. The line goes up 4, over 1, and since slope is rise/run, the slope is 4.
3. The slope of the line is 2. The line goes up 2, over 1, and since slope is rise/run, the slope is 2.
4. The slope of the line is -4. The line goes down 4, over 1, and since slope is rise/run, the slope is -4.
The gradients of line equations are listed below:
m = 3m = 4m = 2m = - 3How to determine the gradient of a line
In this question we have four cases of line equations shown on Cartesian plane, whose gradients must be found. The gradient of each line can be computed by means of secant line formula and two points:
m = Δy / Δx
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.Case 1: (x₁, y₁) = (- 1, - 4), (x₂, y₂) = (1, 2)
m = [2 - (- 4)] / [1 - (- 1)]
m = 3
Case 2: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (0, 3)
m = [3 - (- 1)] / [0 - (- 1)]
m = 4
Case 3: (x₁, y₁) = (- 1, - 1), (x₂, y₂) = (1, 3)
m = [3 - (- 1)] / [1 - (- 1)]
m = 2
Case 4: (x₁, y₁) = (0, 4), (x₂, y₂) = (2, - 2)
m = (- 2 - 4) / (2 - 0)
m = - 3
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Laura is 3 ft tall how tall is Laura in inches
A restaurant hired 18 servers for one banquet. They pay a full time server $21.00 per hour and a part time server $15.50 per hour. If the labor cost of the restaurant was $312.00 per hour, how many full time and part time servers were there for the banquet?
Let's assume that x servers were full-time and y servers were part-time. Then we can write two equations based on the given information:
x + y = 18 (since there were 18 servers in total)
21x + 15.5y = 312 (since the labor cost was $312 per hour)
To solve for x and y, we can use elimination or substitution. Here's one way to use elimination:
Multiply the first equation by 15.5 to get 15.5x + 15.5y = 279.
Subtract the first equation from the second equation to get 5.5x = 33.
Divide both sides by 5.5 to get x = 6.
Now we know that there were 6 full-time servers. We can substitute this value into either of the two equations to solve for y:
6 + y = 18
y = 12
Therefore, there were 6 full-time servers and 12 part-time servers at the banquet.
A total of $8000 is invested: part at 6% and the remainder at 10%
. How much is invested at each rate if the annual interest is $760
The requried, $1000 is invested at 6%, and $7000 is invested at 10%
Let x be the amount invested at 6%, and y be the amount invested at 10%. We know that x + y = $8000 since the total amount invested is $8000.
We also know that the annual interest earned on the 6% investment is 0.06x, and the annual interest earned on the 10% investment is 0.1y. The total annual interest earned is given as $760.
So we have the system of equations:
x + y = 8000 (1)
0.06x + 0.1y = 760 (2)
We can use either substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.06, we get:
0.06x + 0.06y = 480 (3)
0.1y - 0.06y = 0.04y = 280
y = $7000.
Substituting y = $7000 into equation 1, we get:
x + $7000 = $8000
So x = $1000.
Therefore, $1000 is invested at 6%, and $7000 is invested at 10%.
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write a quadratic function that passes through points (5,0) (9,0) (7,-20)
The quadratic function that passes through points is P(x) = 5(x - 5)(x - 9)
Writing the quadratic function that passes through pointsFrom the question, we have the following requirements that can be used in our computation:
Zeros at (5,0) (9,0) Point (7,-20)The quadratic function, P(x), in factored form is represented as
P(x) = a * product of (x - zeros)
So, we have
P(x) = a(x - 5)(x - 9)
Using the point (7, -20), we have
a(7 - 5)(7 - 9) = -20
So, we have
a = 5
Recall that
P(x) = a(x - 5)(x - 9)
So, we have
P(x) = 5(x - 5)(x - 9)
Hence, the function is P(x) = 5(x - 5)(x - 9)
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