The median, Q₁, Q₃, lower fence and upper fence of the given data set are 82, 75, 83, 63 and 95.
What is Inter quartile range?
In a range of values, from lowest to highest, the IQR denotes the median 50% of values. Find the median (middle value) of the lower and higher half of the data first, then use that number to calculate the interquartile range (IQR). The first quartile (Q1) and third quartile (Q3) of these values (Q3). What separates Q3 from Q1 is known as the IQR.
Given data set : 72, 81, 82, 83, 83, 85, 100, 54, 75, 81, 83
Firstly, we will arrange the data into ascending order.
we get, 54, 72, 75, 81, 81, 82, 83, 83, 83, 85, 100.
Here, no. of terms is 11
So, Median = (n+1)/2 th = (11+1)/2 = 6th term
So, Median = 82.
Q₁ = (n+1)/4 th term = (11+1)4 th = 3rd term
= 75
Q₃ = 3(n+1)/4 th term = 9th term = 83
Inter-quartile range = Q₃ - Q₁
= 83 - 75 = 8.
Now, Lower fence = Q₁ - 1.5*IQR
= 75 - 1.5× 8
= 75 - 12 = 63
Upper fence = Q₃ + 1.5*IQR
= 83 + 1.5×8
= 83 + 12
= 95.
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Find the other endpoint: if Q is the midpoint of segment PR, find the coordinates of R if point P is (11,-2) and point Q is (-2,3)
The coordinates of R are (-15, 8). The solution has been obtained by using Mid point formula.
What is Mid point formula?
The centre point of a straight line can be located using the midpoint formula. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.
We are given that Q is the midpoint of segment PR and point P is (11,-2) and point Q is (-2,3).
Let the coordinates of R be (x₂, y₂)
Using Mid point formula, we get
⇒Point Q = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
⇒(-2,3) = ((11 + x₂) / 2, (-2 + y₂) / 2)
So,
⇒-2 = (11 + x₂) / 2
⇒-4 = 11 + x₂
⇒x₂ = -15
Similarly,
⇒3 = (-2 + y₂) / 2
⇒6 = -2 + y₂
⇒y₂ = 8
Hence, the coordinates of R are (-15, 8).
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Let \( f(x)=6 x-5 \) and \( g(x)=x^{2}-6 x+3 \). \[ \begin{array}{l} (f \circ g)(x)= \\ (g \circ f)(x)= \end{array} \] Question Help: \( \square \) Message instructor
et \( f(x)=\frac{1}{x-5} \) and
The composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).
Given functions are \( f(x)=6x−5 \) and \( g(x)=x^2−6x+3 \). Let's find the composition of functions below:\((f\circ g)(x)\)First, we need to substitute \( g(x) \) in place of \( x \) in \( f(x) \). Hence,\( (f\circ g)(x) = f(g(x)) \)\( f(g(x)) = 6g(x) - 5 \)Substitute \( g(x) \) in the above equation,\( (f\circ g)(x) = 6(x^2-6x+3) - 5 \)\( (f\circ g)(x) = 6x^2 - 36x + 13 \)\((g\circ f)(x)\)First, we need to substitute \( f(x) \) in place of \( x \) in \( g(x) \). Hence,\( (g\circ f)(x) = g(f(x)) \)We are given that \( f(x)=6x−5 \) , substitute this in the above equation,\( (g\circ f)(x) = g(6x-5) \)Substitute this in the function \( g(x) \),\( (g\circ f)(x) = (6x-5)^2 - 6(6x-5) + 3 \)\( (g\circ f)(x) = 36x^2 - 72x + 29 \)Hence, the composition of the given functions are:\( (f\circ g)(x) = 6x^2 - 36x + 13 \) and \( (g\circ f)(x) = 36x^2 - 72x + 29 \).
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Please help me! I’ve been sick and out of school so I don’t understand.. thanks! :)
Answer:
Step-by-step explanation: So first, you're gonna distribute the 4/5 to the b and the -5, by doing that u will get 3.2=4/5b - 4. Then you're gonna cancel out the -4 by adding it on both sides - 3.2+4=4/5b, you get 7.2=4/5b. Multiply by the reciprocal of 4/5 which is 5/4 on both sides. 7.2 x 5/4 = b. you get 9 = b
Compute the x and y coordinates for points on sine and cosine curves. Set up a subplot grid that has height 2 and width 1 and set the first such subplot as active. Plot the sine and cosine graphs. Hint: Use the plt.subplot() function
plt.plot(x, y_sine)
plt.plot(x, y_cosine)
To compute the x and y coordinates for points on sine and cosine curves, you need to use the trigonometric functions sine and cosine. To plot the sine and cosine graphs in the same figure, you need to create a subplot grid using the plt.subplot() function. This function takes in the number of rows, columns and the active plot you want to plot the graphs in.
To create a subplot grid that has height 2 and width 1 and set the first subplot as active, the code will look like this:
plt.subplot(2, 1, 1)
You can then plot the sine and cosine graphs by using the x and y coordinates calculated from the sine and cosine functions. The code for plotting the graphs will look like this:
plt.plot(x, y_sine)
plt.plot(x, y_cosine)
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The circumference of the bike tire above is 82.268 inches.
What is the radius of the bike tire? (Use 3.14 for .)
A.
26.2 in
B.
13.1 in
C.
41.13 in
D.
258.32 in
Step-by-step explanation:
The circumference of the bike tire above is 82.268 inches.
What is the radius of the bike tire? (Use 3.14 for .)
A.
26.2 in
B.
13.1 in
C.
41.13 in
D.
258.32 in
Ps=the answer is B
ASAP A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 7, 1 comma 9, 2 comma 5, 3 comma 6, 3 comma 7, 5 comma 7, 6 comma 5, 7 comma 3, 9 comma 1, and 10 comma 1
Which two points would a line of fit go through to best fit the data?
(3, 6) and (7, 3)
(3, 7) and (9, 1)
(1, 9) and (10, 1)
(1, 7) and (2, 5)
(1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.
What is Scatter Plot ?
A scatter plot is a graph that shows the relationship between two sets of data. Each dot on the plot represents a single data point, and the position of the dot corresponds to the values of the two variables being plotted.
In this specific scatter plot, we have 10 data points represented by dots. To find the two points that a line of best fit would go through, we want to look for a pattern or trend in the data. Ideally, the line of best fit should pass as close as possible to all of the data points, but this is not always possible.
One common method for finding the line of best fit is to choose two points that seem to be close to the middle of the data and that the line passes through. This is because we want the line to be a good representation of the overall trend in the data.
Looking at the scatter plot provided, we can see that there is a general trend of the data points sloping downward from left to right. If we draw a line that passes through the points (3, 7) and (9, 1), we can see that it closely follows the trend of the data points. Therefore, these are the two points that a line of best fit would go through to best fit the data.
Therefore, (1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.
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Angle Q measures 30 degrees. If angle Q is rotated 45 degrees, what is the measure of angle Q'?
Substituting Q = 30 degrees, we get:
Q' = 30 degrees + 45 degrees
Q' = 75 degrees
Therefore, the measure of angle Q' is 75 degrees.
What exactly does a degree angle mean?Acute angles are those that range in degree from 0 to 90. Obtuse angles (90°–180°) are those that fall within this range. • A right angle is one with an angle of 90 degrees (= 90°).
If angle Q measures 30 degrees and is rotated 45 degrees, we can find the measure of the new angle Q' as follows:
Q' = Q + 45 degrees
Substituting Q = 30 degrees, we get:
Q' = 30 degrees + 45 degrees
Simplifying, we get:
Q' = 75 degrees
Therefore, the measure of angle Q' is 75 degrees.
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The motion of a pendulum swinging in the direction of motion of a car moving at a low, constant speed, can be modeled by \[ s=s(t)=0.04 \sin (2 t)+3 t \quad 0 \leq t \leq \pi \] where \( s \) is the d distance in meters and
t
is the time in seconds. Find the velocity
v
and acceleration
a
of the pendulum at time
t
. (Express numbers in exact form. Use symbolic notation and fractions where needed.)
v(t)=
a(t)=
Find the velocity
v
at
t= 8
π
,t= 4
π
, and
t= 2
π
. (Use decimal notation. Give your answers to two decimal places, if needed.)
v( 8
π
)=
m/s
v( 4
π
)=
m/s
v( 2
π
)=
Find the acceleration
a
at
t= 8
π
,t= 4
π
, and
t= 2
π
. (Use decimal notation. Give your answers to two decimal places, if needed.) Find the acceleration
a
at
t= 8
π
,t= 4
π
, and
t= 2
π
. (Use decimal notation. Give your answers to two decimal places, if needed.)
a( 8
π
)=
a( 4
π
)=
a( 2
π
)=
m/s 2
Graph
s=s(t),v=v(t)
, and
a=a(t)
we can graph s=s(t),v=v(t), and a=a(t) by plotting the equations for s, v, and a as functions of t. The graph of s=s(t) is a sinusoidal curve with a linear trend. The graph of v=v(t) is a sinusoidal curve with a constant value. The graph of a=a(t) is a sinusoidal curve with a zero value.
The velocity v of the pendulum is the first derivative of the distance s with respect to time t. That is, \[ v=v(t)=\frac{ds}{dt} \] Similarly, the acceleration a of the pendulum is the first derivative of the velocity v with respect to time t. That is, \[ a=a(t)=\frac{dv}{dt} \] We can find the velocity v and acceleration a by taking the derivatives of the given equation for the distance s. \[ s=s(t)=0.04 \sin (2 t)+3 t \] The first derivative of s with respect to t is \[ v=v(t)=\frac{ds}{dt}=0.08 \cos (2 t)+3 \] The second derivative of s with respect to t is \[ a=a(t)=\frac{dv}{dt}=-0.16 \sin (2 t) \] Now, we can find the velocity v and acceleration a at the given times t= 8π ,t= 4π , and t= 2π by plugging in the values of t into the equations for v and a. \[ v( 8π )=0.08 \cos (2( 8π ))+3=3 \quad \text{m/s} \] \[ v( 4π )=0.08 \cos (2( 4π ))+3=3 \quad \text{m/s} \] \[ v( 2π )=0.08 \cos (2( 2π ))+3=3 \quad \text{m/s} \] \[ a( 8π )=-0.16 \sin (2( 8π ))=0 \quad \text{m/s}^2 \] \[ a( 4π )=-0.16 \sin (2( 4π ))=0 \quad \text{m/s}^2 \] \[ a( 2π )=-0.16 \sin (2( 2π ))=0 \quad \text{m/s}^2 \] Finally, we can graph s=s(t),v=v(t), and a=a(t) by plotting the equations for s, v, and a as functions of t. The graph of s=s(t) is a sinusoidal curve with a linear trend. The graph of v=v(t) is a sinusoidal curve with a constant value. The graph of a=a(t) is a sinusoidal curve with a zero value.
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(1 point) The radius of the circle with a central angle of 6 radians that intercepts an arc with length 88 cm is _____ cm. The radius of the circle with a central angle of 120° that intercepts an arc with length 17 miles is_____ miles.
The radius of the first circle is 14.67 cm and the radius of the second circle is 8.11 miles.
The radius of a circle can be found by using the formula s = rθ, where s is the length of the arc, r is the radius, and θ is the central angle in radians. Rearranging the formula, we can find the radius by dividing the length of the arc by the central angle: r = s/θ.
For the first part of the question, we are given an arc length of 88 cm and a central angle of 6 radians. Plugging these values into the formula, we can find the radius:
r = 88 cm / 6 radians = 14.67 cm
For the second part of the question, we are given an arc length of 17 miles and a central angle of 120°. However, we need to convert the central angle from degrees to radians before plugging it into the formula. We can do this by multiplying the angle in degrees by π/180:
120° × π/180 = 2π/3 radians
Now we can plug the values into the formula to find the radius:
r = 17 miles / (2π/3) radians = 8.11 miles
So the radius of the first circle is 14.67 cm and the radius of the second circle is 8.11 miles.
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hey you can you stop and help me look at the picture pls and thx then can you answer pls
The line which is not transversal to LR would be Line TK.
How are parallel straight lines related?Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.
Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.
Properties of Parallel Lines Cut by a Transversal
The corresponding angles are equal and the vertically opposite angles are equal.
The alternate interior angles are equal and the alternate exterior angles are equal.
Also, pair of interior angles on the same side of the transversal is supplementary.
Since we know that transversal is a line that intersects two or more other lines at different points.
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Line TK is not transversal to line LR.
What are parallel lines?Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines. We can also say Parallel lines meet at infinity.
Given,
Line PR and KT are parallel
By the figure,
PR = LR
and KT = TK
PR || KT
∴ LR || TK
Hence, TK is the line, that is not the transversal line to LR.
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help me out someone i give brainliest to you!!!!!!!!!!!!!!!!!!!!!!
okay i will answer it for you yes
I suck at math, so someone who is good at it please help me.
Alternate interior angles = ∠7 and ∠9.
Corresponding angles = ∠1 and ∠7
Vertical angles = ∠4 and ∠11
∠7 = 60°
∠8 = 120°
∠9 = 60°
How do angles work?When two lines meet, they intersect at an angle. By using the symbol, we may symbolise an angle.
Two lines meet at the common vertex of an angle, which has one common leg. A straight line's one side always has a total angle of 180 degrees. On the other hand, a point's surrounding angles are always added up to 360 degrees.
Here,
We can see that the Alternate interior angles = ∠7 and ∠9.
Corresponding angles = ∠1 and ∠7
Vertical angles = ∠4 and ∠11
Given, ∠1 = 60°
Now similarly, using the angles properties we can ind the rest of the angles.
∠7 = 60°
∠8 = 120°
∠9 = 60°
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Suppose you're deciding where to order a Hawaiian pizza, and waiting time is a concern of yours. You're considering Krazy Karl's Pizza where the average waiting time is 64 minutes, with a standard deviation of 4. 5 minutes. Or, you might call Domino's Pizza where the average waiting time is 54. 6 minutes, with a standard deviation of 8. 1 minutes.
Z-score for a waiting time of
65 minutes at Krazy Karl's: 0. 222
61. 1 minutes at Domino's: 0. 802
1. How many standard deviations away from the average is a wait time of 71. 8 minutes from Krazy Karl's?
2. About 50% of wait times from Krazy Karl's are smaller than ___ minutes
3. About 95% of wait times for Krazy Karl's are approximately between __ minutes and __ minutes.
4. About 99. 7% of wait times for Domino's are approximately between___ minutes and ___ minutes.
5. How long would you have to wait for a Domino's pizza to be in the same percentile as a wait time of 74 minutes from Krazy Karl's? In other words, what wait time for Domino's is "equivalent" to a wait time of 74 minutes from Krazy Karl's?
6. How long would you have to wait for a Krazy Karl's pizza to be in the same percentile as a wait time of 54 minutes from Domino's? In other words, what wait time for Krazy Karl's is "equivalent" to a wait time of 54 minutes from Domino's?
Answer:
vydbskehhwbe
Step-by-step explanation:
bshhdvjebheunsns
3.04 Unit 3 Test
Question 1: Identify the zeros in the given graph.
(the one where its curved pointing downwards)
Question 1: Options:
{-3,-1,1}
{-3,-1,4,1}
{-3,1}
{-3,-4,1}
Question 2: Identify the roots in the given graph.
(the one where its curved pointing upwards)
Question 2: Options:
{-2, -8,4}
{0,-8}
{-8}
{-2, 4}
Question 3: what are the solutions to x^2 + 10x = 24
Question 3: Options:
{0,-12,2}
{-12,2}
{2}
{-12}
Question 4: identify all solutions to x^2 + 18x = 4x - 49
Question 4: Options:
{-7,0,-7}
{-7}
{-7,7}
{-10,7}
Question 5: Identify the zeros of x^2 - 9x = 0
Question 5: Options:
{9}
{-9}
{-9,9}
{0,9}
Question 6: identify the roots of 4x^2 - 24 = 20x
Question 6: Options:
{-1,6}
{-1}
{6}
{-1,0.6}
Question 7: Which equations have solutions of -2 and 3?
Question 7: Options:
y = x^2 + x - 6
y = x^2 - x - 6
y = x^2 + 5x + 6
y = x^2 - 5x + 6
The zeros in the given graph. (the one where its curved pointing downwards) is {-3,1}.
What are zeroes of graph?The solutions to the equation p(x) = 0, where p(x) stands for the polynomial, are the zeros of a polynomial. If we plot this polynomial as y = p, we can see that these are the values of x where y = 0. (x). In other words, these are the x-intercepts of the graph.
The polynomial's zeros can be found by locating the locations where its graph contacts or crosses the x-axis.
When f(x) = 0, or when the graph's y-coordinate is equal to 0, the zeroes of the graph are determined.
From the graph we see that, at y = 0 we have the values of x as:
1. x = -3 and x = 1
Hence, the zeros in the given graph. (the one where its curved pointing downwards) is {-3,1}.
2. Roots of the graph are - x = - 2 and x = 4, {-2, 4}
3. solutions to x² + 10x = 24,
x² + 10x - 24 = 0
x² + 12x - 2x - 24
x(x + 12) -2 (x + 12)
(x - 2) (x + 12)
x = 2 or x = -12
{-12,2}
4. solutions to x² + 18x = 4x - 49
x² + 14x + 49
x² + 7x + 7x + 49
x(x + 7) + 7 (x + 7)
(x + 7)(x + 7)
x = -7
{-7}
5. zeros of x² - 9x = 0
x(x - 9) = 0
Either x = 0 or x = 9,
{0,9}
6. roots of 4x² - 24 = 20x
4x² - 20x - 24 = 0
x² - 5x - 6 = 0
x² -6x + x - 6 = 0
x(x - 6) + 1(x - 6) = 0
(x + 1) (x - 6)
x = -1 and x = 6
{-1,6}
7. correct option is y = x² - x - 6
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Help as much anything is appreciated!
Due to length restrictions, we kindly invite to read the explanation to see the lenghts of each 30-60-90 right triangles.
How to resolve a 30-60-90 right triangle
In this problem we find six cases of 30-60-90 right triangles, that is, right triangles whose inner angles have the following measures: 30°, 60°, 90°. The length of sides can be found by the following relationships:
The leg adjacent to 60° is 1 / 2 times the hypotenuse.The leg adjacent to 30° is √3 / 2 times the hypotenuse.The leg adjacent 30° is √3 times the leg adjacent to 60°.Now we proceed to determine the missing length:
Case 1:
PV = 4 / (1 / 2)
PV = 8
VT = √3 · 4
VT = 4√3
Case 2:
PT = 2 / √3
PT = 2√3 / 3
PV = 2 / (√3 / 2)
PV = 4√3 / 3
Case 3:
PT = (1 / 2) · 3
PT = 3 / 2
VT = 3√3 / 2
Case 4:
PT = 7 / √3
PT = 7√3 / 3
PV = 7 / (√3 / 2)
PV = 14√3 / 3
Case 5:
VT = √3 · (1 / 2)
VT = √3 / 2
PV = (1 / 2) / (1 / 2)
PV = 1
Case 6:
PV = 100
PT = 50
VT = 50√3
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A car drives at a speed of 90km/h for 2 hours and 20 minutes. How far does the car drive
Answer: 210 ( it hope this is a best answer)
Step-by-step explanation:
2 hours and 20 minutes is 2 and a third hours. Multiply 90 by 2 and a third.
90 × 2.333
209.999
If you round to the nearest kilometer, the answer is 210 km
How many real solutions are there to the equation 2(x-1)^(2)(2x+3)(x+5)^(3)=.001?
There are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]
To find the real solutions, we can use the zero product property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. In this case, we can set each of the factors equal to zero and solve for x:
[tex]2(x-1)^(2)=02x+3=0(x+5)^(3)=0[/tex]
Solving each of these equations gives us the following solutions:
[tex]x=1x=-3/2x=-5[/tex]
However, we need to check each of these solutions to see if they satisfy the original equation. Plugging each solution back into the equation gives us:
[tex]2(1-1)^(2)(2(1)+3)(1+5)^(3)=.0012(-3/2-1)^(2)(2(-3/2)+3)(-3/2+5)^(3)=.0012(-5-1)^(2)(2(-5)+3)(-5+5)^(3)=.001[/tex]
The first and third solutions do not satisfy the equation, but the second solution does. Therefore, there are 2 real solutions to the equation [tex]2(x-1)^(2)(2x+3)(x+5)^(3)=.001.[/tex]
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HELP PLS DUE IN FIVE MINS I NEED HELP STRESSING TIMES
The length of the diagonal is between 3 and 4; it is closer to 3.
What is a diagonal?In Mathematics, the diagonal of a rectangle can be defined as a line segment that connects any two (2) of its non-adjacent vertices together while dividing the rectangle into two (2) equal parts.
In any rectangle, each of the two (2) opposite sides are equal and parallel and the two (2) diagonals are equal.
Based on the information provided about the diagonal, we have:
Diagonal = √18
Diagonal = √9 × √2
Diagonal = 3√2 units.
In conclusion, we can logically deduce that the diagonal is closer to 3 units.
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In this picture, the white ball _____________ its momentum to the red ball. fill in the blank.
The white ball is transferring its momentum to the red ball.
The missing blank is "transferring".
The statement "the white ball is transferring its momentum to the red ball" is based on the law of conservation of momentum.
According to this law, the total momentum of a closed system (in which no external forces act on the system) is conserved. This means that the momentum lost by one object in the system must be gained by another object in the system.
So we can conclude that, in the picture, the white ball and the red ball together form a closed system, and the collision between them causes the white ball to transfer some of its momentum to the red ball, in accordance with the law of conservation of momentum.
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Peter mows 7 lawns in 11 hours. If he continues at the same rate, how many lawns will Peter mow in 55 hours?
If Peter mows 7 lawns in 11 hours, then the number of lawns Peter can mow in 55 hours is 35.
How many lawns can he mow?The first step is to determine how many lawns Peter can mow in 1 hour. To do this, divide 7 by 11.
Division is the process of determining the quotient of two or more numbers. It entails putting a number into equal groups using another number.
Number of lawns that Peter can mow in 1 hour = 7 / 11To determine the number of lawns that can be mowed in 55 hours, multiply the fraction derived in the previous step by 55.
Multiplication is the process of determining the product of two or more numbers.
Number of lawns that Peter can mow in 55 hours = 7/11 x 55 = 35 lawns.To learn more about multiplication, please check: https://brainly.com/question/13814687
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Write the solution set in interval notion for 9t+27 <4t-18. Solve the inequality
The solution set of inequality " for 9t+27 <4t-18" in interval notation is (-∞, -9).
To solve the inequality 9t + 27 < 4t - 18, we need to isolate the variable t on one side of the inequality. Here are the steps:
1. Subtract 4t from both sides: 9t - 4t + 27 < -18
2. Simplify: 5t + 27 < -18
3. Subtract 27 from both sides: 5t < -45
4. Divide both sides by 5: t < -9
Now we can write the solution set in interval notation: (-∞, -9)
So the solution set is all values of t that are less than -9.
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simplify the radical expression below 2/9.
The simplification of the radical expression √9. is 3.
What is radical expression?Radical expressions are simplified by taking them down to their most basic form and, if feasible, altogether deleting the radical. When a radical expression appears in the denominator of an algebraic expression, the radical expression is simplified by multiplying the numerator and denominator by the appropriate radical expression (for example, conjugate in the case of a binomial and the same radical in the case of a monomial).
The given expression is √9.
The given expression can be written as:
√(3)(3) = 3
Hence, the simplification of the radical expression √9. is 3.
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Aplumber is fixing a pipe with a an interior diameter of 0.63 inches. He buys a replacement piece that must fit inside the old pipe. He uses plumbing tape that will fill 0.15 inches of the space between the two pieces of pipe. The new pipe much be 0.1 inches smaller than the old pipe and tape, so that it can fit inside.
What is the largest interior diameter pipe he can buy that will still fit inside the old pipe?
Answer____inch
Explain how you found your answer.
Answer:
0.68 inches
Step-by-step explanation:
The interior diameter of the old pipe is 0.63 inches, and the plumbing tape will fill 0.15 inches of the space between the old pipe and the new pipe. Therefore, the total diameter that the new pipe must fit inside is:
0.63 inches + 0.15 inches = 0.78 inches
The new pipe must be 0.1 inches smaller than this diameter to ensure a proper fit. Therefore, the diameter of the new pipe should be:
0.78 inches - 0.1 inches = 0.68 inches
So, the new pipe must have an interior diameter of 0.68 inches to fit correctly inside the old pipe with the plumbing tape.
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Answer:
A= 9/20 B= 45% C=0.45 d= 4.5% E= 3/8 F= 0.375 G= 37.5% H= 15.5% I = 0.8 j=80%
Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3) and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)." What is the scale factor of the dilation that maps Triangle ABC onto triangle XYZ. ((PLS HELP ITS DUE TOMORROW))
The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.
What is scale factor?A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.
here, we have,
given that,
Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3)
and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)."
now, we now that,
distance formula:
d=√(x2−x1)^2+(y2−y1)^2
so, we get,
length of AB = 3√2
and, length of XY = 3
so, scale factor = AB/XY
=3√2/3
=√2
Hence, The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.
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Quadratic worded question
The owner of a fish shop bought x kilograms of salmon for $400 from the wholesale market. At the end of the day, all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. From the sale of the fish, a total of $540 was made. Calculate how many kilograms of salmon the fish-shop owner bought at the market.
Answer: 23 kg
Step-by-step explanation:
Let's begin by using algebra to solve the problem.
Let x be the number of kilograms of salmon the fish-shop owner bought at the market.
We know that the total cost of the salmon was $400, so we can write:
400 = x * c
where c is the cost per kilogram of salmon.
We also know that all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. So the price per kilogram of salmon at the fish shop was c + 10.
The total revenue from the sale of the fish was $540, so we can write:
540 = (x - 2) * (c + 10)
Now we can use these two equations to solve for x.
First, we can use the first equation to solve for c:
c = 400 / x
Then we can substitute this expression for c into the second equation:
540 = (x - 2) * (400/x + 10)
Simplifying this equation:
540 = 4000/x + 10x - 20 - 80/x
Multiplying both sides by x:
540x = 4000 + 10x^2 - 20x - 80
10x^2 - 20x - 4600 = 0
Dividing both sides by 10:
x^2 - 2x - 460 = 0
We can solve for x using the quadratic formula:
x = [2 ± sqrt(4 + 4*460)] / 2
x = [2 ± 44] / 2
Discarding the negative solution, we get:
x = (2 + 44) / 2
x = 23
Therefore, the fish-shop owner bought 23 kilograms of salmon at the market.
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The value of the fractions will be:
a. 1/3 + 1/4 = 7/12
b. 1/3 + 2/7 = 13/21
c. 1/2 + 2/9 = 13/18
d. 3/4 + 1/5 = 19/20
e. 1/3 + 4/9 = 7/9
f. 1/6 + 3/4 = 11/12
How to calculate the value of the fractionA fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
The value of the fractions will be:
a. 1/3 + 1/4
= 4/12 + 3/12
= 7/12
b. 1/3 + 2/7
= 7/21 + 6/21
= 13/21
c. 1/2 + 2/9
= 9/18 + 4/18
= 13/18
d. 3/4 + 1/5
= 15/20 + 4/20
= 19/20
e. 1/3 + 4/9 = 7/9
f. 1/6 + 3/4 = 11/12
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Reference Library. 40. In a standard deck of 52 cards, what is the probability of drawing a King (4 cards ), a Queen ( 4 cards ), or a Jack ( 4 cards )?
The probability of drawing a King, Queen, or Jack from a standard deck of 52 cards is 3/13.
The probability of drawing a King, Queen, or Jack in a standard deck of 52 cards can be calculated by using the formula for the probability of an event happening: P(E) = number of favorable outcomes / total number of possible outcomes.
In this case, the number of favorable outcomes is the total number of Kings, Queens, and Jacks in the deck, which is 4 + 4 + 4 = 12. The total number of possible outcomes is the total number of cards in the deck, which is 52.
So, the probability of drawing a King, Queen, or Jack is:
P(E) = 12 / 52
Simplifying this fraction gives us:
P(E) = 3 / 13
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Write an equation for the graph that passes through (1,7) and (3,3).
We can use the two-point form to find the equation of the line passing through the two given points:
y - y1 = ((y2 - y1)/(x2 - x1))(x - x1)
where (x1, y1) = (1, 7) and (x2, y2) = (3, 3).
Substituting the values, we get:
y - 7 = ((3 - 7)/(3 - 1))(x - 1)
Simplifying the equation, we get:
y - 7 = (-2/2)(x - 1)
y - 7 = -x + 1
Adding 7 to both sides, we get:
y = -x + 8
Therefore, the equation of the line passing through the points (1, 7) and (3, 3) is y = -x + 8.
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2.9. A computer program has produced the following out- put for a hypothesis-testing problem:
Difference in sample means: 2.35
Degrees of freedom: 18
Standard error of the difference in sample means: ?
Test statistic: to = 2.01
P-value: 0.0298
(a) What is the missing value for the standard error?
(b) Is this a two-sided or a one-sided test?
(c) If a = 0.05, what are your conclusions?
(d) Find a 90% two-sided CI on the difference in means.
(a) The standard error is 1.17. (b) IT is a two-sided test. (c) If a = 0.05, it can be concluded that we can reject the null hypothesis and accept the alternative hypothesis. (d) A 90% two-sided CI on the difference in means is (0.33, 4.37).
(a) The missing value for the standard error of the difference in sample means can be calculated using the formula:
Standard error = (Difference in sample means) / (Test statistic) = 2.35 / 2.01 = 1.17
(b) This is a two-sided test because the P-value is given for a two-sided test. If it were a one-sided test, the P-value would be half of the given value, or 0.0149.
(c) If a = 0.05, we can conclude that the difference in sample means is statistically significant because the P-value (0.0298) is less than a (0.05). This means that we can reject the null hypothesis and accept the alternative hypothesis that there is a difference in the means.
(d) A 90% two-sided CI on the difference in means can be calculated using the formula:
CI = (Difference in sample means) ± (t-value) × (Standard error)
The t-value for a 90% two-sided CI with 18 degrees of freedom is 1.734. So the CI is:
CI = 2.35 ± 1.734 × 1.17 = (0.33, 4.37)
Therefore, the 90% two-sided CI on the difference in means is (0.33, 4.37).
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