The solution is, : d) 255 ≤ f(x) ≤ 340.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
The function
f(x)= 8.5x
represents the amount of money that Steve earns given the number of hours, x, he works.
The dependent variable is the total amount that he earns, f(x) while the independent variable is the number if hours, x that he works. The range is the possible values of the dependent variable that satisfies the equation.
Steve works between 30 and 40 hours per week.
This means that the lowest amount that he earns is 8.5×30 = $255
The highest amount that he earns is 8.5× 40 = 340.
Therefore, the range is
255 ≤ f(x) ≤ 340
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Use the circle graph shown below to answer the question.
If 30 sixth graders own birds, how many sixth graders were surveyed?
The total number of sixth graders surveyed is 600 sixth graders
Solving statistics problem using pie chartsThe given diagram is a pie chart with different percent of pet owned by sixth graders.
We need to determine the number of sixth grader surveyed if 30 sixth graders own birds.
Number of birds = 5% of the total sixth graders
Substitute the given parameters
30 = 0.05 * T
T = 30/0.05
T = 600
Hence is 30 sixth graders own birds, then 600 sixth graders were surveyed.
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What is the linear equation represented by the graph?
The linear equation represented by the graph is y = 8x.
Describe Linear equation?A linear equation is a mathematical equation that describes a straight line in a two-dimensional space. It can be written in the form of:
y = mx + b
where y and x are variables, m is the slope of the line, and b is the y-intercept of the line (the point where the line crosses the y-axis).
The slope, represented by "m", describes the steepness of the line, while the y-intercept, represented by "b", is the point where the line intersects with the y-axis.
Linear equations can also be written in other forms, such as the standard form:
Ax + By = C
where A, B, and C are constants, and x and y are variables. In this form, the equation describes a line in terms of its x and y intercepts.
Linear equations are used in a variety of fields, including mathematics, physics, engineering, economics, and more. They are useful for describing and predicting relationships between variables that exhibit a linear pattern.
The equation represented by the graph is a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1)/(x2 - x1)
Let's choose the first two points (0.5, 4) and (1, 8):
m = (8 - 4)/(1 - 0.5) = 8
So, the slope is 8.
To find the y-intercept, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Let's choose the point (0.5, 4) and the slope we just found:
y - 4 = 8(x - 0.5)
y - 4 = 8x - 4
y = 8x
So, the linear equation represented by the graph is y = 8x.
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The cost of putting on a play is $500 for the theater rental, $500 for the actors, and $750 for set decorations and costumes. If tickets are sold for $25 each, how many tickets need to be sold to reach the break-even point?
Answer:
The total cost of putting on the play is $500 for theater rental + $500 for actors + $750 for set decorations and costumes = $1750.
To reach the break-even point, the revenue from ticket sales needs to equal the total cost, so $1750 = $25 x (number of tickets sold).
Solving for the number of tickets sold, we can divide both sides by $25: $1750 / $25 = (number of tickets sold).
This gives us: 70 = number of tickets sold.
Therefore, Mr. Curry needs to sell 70 tickets to reach the break-even point.
Step-by-step explanation:
in the xy-plane, the lines y=3x-5 and y=-2x+10 intersect at a point (h,k). what is the value of k?
Answer:
(3,4)
k is 4
Step-by-step explanation:
See attached graph.
Help! I need to solve this! Show work please
A x=3 hope it helps-parker have a nice day
f(x) = − ³/2 x and g(x) = (½)² – 1
-
Graph the functions on the same coordinate plane.
Let
What are the solutions to the equation
?
f(x) = g(x) ₂
The solution to the equations have the coordinates of (-6.61, 9.91) and (0.61, -0.91)
How to determine the solution to the system of equationFrom the question, we have the following parameters that can be used in our computation:
f(x) = − ³/2 x and g(x) = (½)² – 1
Express the equation properly
So, we have
f(x) = -3/2x
g(x) = (1/2x)^2 - 1
Next, we make a plot of the system to determine the solution
The point of intersection in the plot represent the solution to the equations
In this case, the point of intersection has a coordinate of (-6.61, 9.91) and (0.61, -0.91)
Hence, the solution is (-6.61, 9.91) and (0.61, -0.91)
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What is 10 percent of 20000?
To find 10 percent of 20000, you can multiply 20000 by 0.1, which gives you the answer of 2000.
0.1 × 20000 = 2000.
Here's the explanation of the calculation: When we want to find a certain percentage of a number, we can convert the percentage into a decimal by dividing it by 100. In this case, 10% is equivalent to 10/100, which simplifies to 0.1. Then, we can multiply 20000 by 0.1 to find the answer, which is 2000. In summary, to find 10% of a number, we can convert the percentage into a decimal by dividing it by 100, and then multiply the decimal by the original number.
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Pls help 23736 x 2858=?
Answer:
23736 x 2858
= 67837488
Step-by-step explanation:
You're welcome.
Answer:
67837488
Step-by-step explanation:
24 X 3 X 23 X 43 X 1429
PLEASE HELPPP
WILL GIVE BRAINLIEST!!!!!!
Julie is correct. If n=0 then you would get the fraction [tex]\frac{0}{0}[/tex] which is indeterminant (or undefined) since a zero is present in the denominator.
arge telescopes often have small fields of view. For example, the Hubble Space Telescope’s (HST’s) advanced camera has a field of view that is roughly square and about 0.06 degree on a side.
Calculate the angular area of the HST’s field of view in square degrees.
A. 0.006 Square degrees
B. 0.36 Square degrees
C. 0.0036 Square degrees
D. 0.06 Square degrees
The correct response is C. 0.0036 Square degrees The field of vision of the Hubble Space Telescope is only 0.006 degrees, which is around 100 times less than that of the Micro Observatory telescopes. But it has a 100 times better angular resolution!
Skywatchers can readily view planets with just a modest or medium-sized telescope. How much of our solar system is visible will wow you! Additionally, you don't need a completely dark sky to see all of the planets in our solar system; a telescope can still make Venus, Mars, Jupiter, and Saturn easily visible even when viewed in a city. From $100 to well over $10,000, a telescope can be purchased. In 2022, you can anticipate that a good telescope for visual observing will start around $300 and a telescope capable of deep-sky astrophotography would start around $800. With a 25x telescope, even the tiniest telescope should be able to see Saturn's rings.
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Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST's) advanced camera has a field of view that is roughly square and about 0.06 degree on a side. Calculate the angular area of the HST's field of view in square degrees.
A. 0.006 Square degrees
B. 0.36 Square degrees
C. 0.0036 Square degrees
D. 0.06 Square degrees
The list below shows prices of several houses on Hill Street. 45,000, 50,000, 60,000, 60,000. 65,000, and 1,820,000. Which of the following statements is true regarding this data? Select three that apply.
One possible true statement regarding the data is that there is a significant outlier in the dataset, which is the value of 1,820,000.
What is an Outlier?An outlier is an observation that is significantly different from other observations in the dataset, and it can have a big impact on the results of statistical analyses, such as the mean or the median.
In this case, the outlier value of 1,820,000 is much larger than the other values, which range from 45,000 to 65,000.
It is possible that this value represents a different type of house, or that it has some unique characteristics that make it much more expensive than the other houses on Hill Street.
Therefore, if we are interested in analyzing the prices of houses on Hill Street, it may be important to remove the outlier value before conducting any statistical analysis.
P.S: Your question is incomplete, so I gave you a general overview on how to interpret data.
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The sum of deviations of the individual observations from their sample mean isO sometimes greater than and sometimes less than zero, depending on the observations O always less than zero O always greater than zero O We do not have enough info to answer this questionO always equal to zero
The sum of deviations of the individual observations from their sample mean is always equal to zero.
The sum of deviations of the individual observations from their sample mean is always equal to zero. This is because the sum of all the deviations is the sum of a positive and a negative value. When we add the negative value to the positive value, the net result is always zero.To illustrate this, let's take an example. Suppose we have a sample of 5 observations: 2, 4, 6, 8, 10. The mean of the sample is 6. The deviations of the individual observations from the sample mean can be calculated as follows:
2-6=-4
4-6=-2
6-6= 0
8-6= 2
10-6=4
When we add the deviations, we get: -4+(-2)+0+2+4=0. The sum of all the deviations is always equal to zero.
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whats is 5.2r-2.4=8.7
The value of r is 2.134
in the equation, we would first
add 2.4
to both sides:
5.2r - 2.4 + 2.4 = 8.7+ 2.4
5.2r = 11.1
now we will
divide both sides by 5.2
to isolate the variable "r"
[tex]\frac{5.2r}{5.2} = \frac{11.1}{5.2}[/tex]
1r = 2.13461538
thus, the value of r = 2.134 approximately
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What is the definition of covariance
Answer:
indicates the relationship of two variables whenever one variable changes.
Step-by-step explanation:
2, 10, 50, 250, 1250
Write the explicit form of the sequence above.
The explicit function of the sequence is a(n) = 2(5)^n-1
How to determine the explicit function of the sequenceThe definition of the function is given as
2, 10, 50, 250, 1250
The above definitions imply that we simply multiply 5 to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a(1) = 2
Common ratio, r = 5
So, we have
a(n) = a * r^n-1
This givs
a(n) = 2(5)^n-1
Hence, the sequence is a(n) = 2(5)^n-1
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H
116
What does it mean when a two-way table shows an association between
two data sets?
The solution is given below.
What is a two-way table?A table in which the rows represent the categories for one category variable, the columns represent the categories of a second category variable and each cell displays the frequency (or proportion) resulting for that row and column combination for the two variables.
here, we have,
1. Positive association - direct relationship: increase = increase and vice versa
2. Scatterplot - scattered data
3. Bivariate data - two variables
4. Two-way table - displays two variables into rows and columns
5. Two-way relative frequency table - shows the relative frequencies in the table
6. Association - how sets of data are related
7. Negative association - reverse relationship: increase = decrease and vice versa
8. Relative frequency - frequency of a specific data value divided by the total number of data values
9. No association - no relationship
10. Strength of association
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How do I solve this?
The given triangles are similar by SSS theorem
Similarity property of a triangleThe given figures are similar triangles with 3 sides and angles. There are several ways triangles can be proved to be similar such as the AAS, SSS, SAS etc theorems.
For the given triangles, if the ratio of their similar sides is equivalent to the same constant, then the triangles are similar.
AC/HF = AB/HG = CB/GF = k
84/14 = 72/12 = 48/8
84/14 = 6
72/12 = 6
48/8 = 6
Since the ratios are all equal, hence the triangles are similar
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An air navigation system spots two planes converging to a point at right angles and at colliding speeds. The planes are flying at 560 mph and 900 mph and are at 280 miles and 450 miles from the point, respectively. At what rate, in mph, is the distance between the planes decreasing?
The distance is decreasing at a rate of 1028.30 miles/hour.
What is Rate of Change?An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.
Plane X: The first plane is due west of you, or at x = -280
traveling towards you at 560 mph
Plane Y: The second plane is due south of you, or at y = -450
traveling towards you at 900 mph.
D = Distance between the two planes.
D = √( x² + y² )
d/dt [ D ] = d/dt [ √( x² + y² ) ]
dD/dt = 1 / 2√( x² + y² ) (2XX' + 2YY')
dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900)
dD/ dt = 1/2 √(-280)² + (-450)² (2 (-280)(560) + 2(-450)(900))
dD/ dt = 1/ 530 (-140,000 - 405, 000)
dD/ dt = -1028.30
Thus, The distance is decreasing at a rate of 500 miles/hour
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Suppose the cumulative distribution function of the random variable X is F(x) = 0 when x<-2 , F(x) = .25x + .5 when -2 <= x < 2 and F(x) = 1 when 2<=x (<= means greater than or equal). Determine the following a. P(X<1.8) b. P(X>-1.5) c. P(X<-2) d. P(-1
the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0.
a. P(X<1.8) = .25(1.8) + .5 = .95
b. P(X>-1.5) = .25(-1.5) + .5 = .375
c. P(X<-2) = 0
d. P(-1.5<X<2) = .25(2) + .5 - (.25(-1.5) + .5) = .875
a. For the probability P(X<1.8), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in 1.8 for x in the function to get F(1.8) = 0.25(1.8) + 0.5 = 0.95. Therefore, P(X<1.8) = 0.95.
b. For the probability P(X>-1.5), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375. Therefore, P(X>-1.5) = 0.375.
c. For the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0. Therefore, P(X<-2) = 0.
d. For the probability P(-1.5<X<2), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 and 2 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375 and F(2) = 0.25(2) + 0.5 = 0.95. Therefore, P(-1.5<X<2) = 0.95 - 0.375 = 0.875.
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Emily parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded annually. What will be the total balance after 2 years?
Responses
$3,273.50
$3,273.50
$1,757.71
$1,757.71
$2,385.72
$2,385.72
$1,314.08
Answer:
B
Step-by-step explanation:
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal (starting amount)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = time (in years)
We can plug in the given values:
P = $1,500
r = 0.0825 (8.25% expressed as a decimal)
n = 1 (compounded annually)
t = 2
A = $1,500(1 + 0.0825/1)^(1*2)
A = $1,500(1.0825)^2
A = $1,757.71
Therefore, the total balance after 2 years will be $1,757.71. Answer choice B is correct.
3.In an online quiz, positive points are awarded for a correct answer, and negative
points are awarded for an incorrect answer. Elena answers 10 questions correctly and
4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.
a. Write a system of equations that describes Elena's and Kiran's scores. Usex to
represent the number of points for a correct answer and y to represent the
number of points for an incorrect answer.
that
X represents number of points and y represents incorrect answer
The system of equations can be written as:-
10x + 4y = 42
6x + 8y = 14
What is a system of equations?A system of equations, also known as a set of simultaneous equations or an equation system, is a finite set of equations for which we sought common solutions in mathematics. A system of equations can be classified in the same way that a single equation can.
Given that in an online quiz, positive points are awarded for a correct answer, and negative points are awarded for an incorrect answer. Elena answers 10 questions correctly and 4 incorrectly and scores 42 points. Kiran answers 6 questions correctly and 8 incorrectly and scores 14 points.
The system of equations can be written as:-
10x + 4y = 42
6x + 8y = 14
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Solve for x and y
5x + y = 9
10x -7y = -18
Answer:
x=1; y=4
Step-by-step explanation:
for this system, you could use either substitution or elimination
i'll solve it both ways
SUBSTITUTION:
5x+y=9 becomes y=-5x+9
10x-7y=-18; substitue y from y=-5x+9
10x-7(-5x+9)=-18
10x+35x-63=-18
45x=45
x=1
substitue x into y=-5x+9
y=-5(1)+9
y=4
ELIMINATION
5x+y=9
10x-7y=-18
multiple the top equation by 7 to get 35x+7y=63
now, 7y and -7y cancel out
add the two equations to get 45x=45
x=1
substitute into 5x+y=9
5(1)+y=9
y=4
Urgent! Can you help me solve these 3 numbers with detailed steps please!
d) whenther there the limit is going to infinity like that
take the large term on the top and the largest one on the bottom
so;
4x^5/12x^2 =
basically if you continued to plug it in it would give you
4x^5/12x^2
eventually 12x^2 would = 24 because you would get 12x^2 to 24x^1, take the dervative = 24
for the top it would go from 4x^5; 20x^4; 80x^3
then you would have 80x^3/24
plug in infinity for x
infinity/24
the longer diagonal of a field in the shape of a quadrilateral is 120 m and the length of the perpendiculars from the opposite vertex upon a longer diagonal is 20 m and 30 m find the area of the field Step by Step Explaination class 8 lesson no 11 mensuration
The area of the field is 900√10 m².
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Quadrilateral ABCD.
The longer diagonal connects vertices A and C, and let E and F be the feet of the perpendiculars from vertices B and D to the longer diagonal AC.
From the figure,
BE = 20 m
DF = 30 m
AE = EC = 120/2 = 60 m
Now,
The area of the quadrilateral.
The area of a trapezoid.
= (sum of parallel sides) x (height) / 2
Using the Pythagorean theorem,
AB² = AE² + BE²
60² + 20² = 4000
AB = √(4000)
AB = 20 √10
And,
CD² = CE² + DF²
CD² = 60² + 30²
CD² = 4500
CD = √(4500)
CD = 15 √20
Now,
Area = AB + CD x 1/2 x AC
= 20√10 + 15√20 x 1/2 x 120
= 900√10
Therefore,
The area of the field is 900√10 m².
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A company is designing a new cylindrical package. The volume of the package is 87.92 in.3. The radius is 2 inches. Use the formula V = Bh and 3.14 to approximate π
to answer the questions.
Part A
To the nearest inch, how many inches is the height of the cylindrical package?
Part B
The company decides to keep the radius the same and double the height. Rounded to the nearest hundredth, how many cubic inches is the new volume of the package?
The height of the cylindrical package is 6 inches.
The new volume of the package is 88.26 cubic inches.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
Part A:
The formula for the volume of a cylinder is V = Bh, where B is the area of the base of the cylinder and h is its height.
For a cylinder with radius r and height h, the base area B is given by
B = πr².
Substituting the given values, we have:
V = Bh
87.92 = π(2²)h
h = 87.92 / (4π)
h ≈ 5.57
Rounding to the nearest inch, the height of the cylindrical package is 6 inches.
Part B:
If the company doubles the height of the cylinder while keeping the radius the same, the new height will be 2h = 2(5.57) = 11.14 inches.
The new volume can be calculated using the same formula:
V = Bh
V = π(2²)(11.14)
V ≈ 88.26 cubic inches
Rounding to the nearest hundredth, the new volume of the package is 88.26 cubic inches.
Thus,
The height of the cylindrical package is 6 inches.
The new volume of the package is 88.26 cubic inches.
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Helppp
A circle has an arc whose measure is 80 degrees and whose length is 88pi. What is the diameter of the circle?
The diameter of the circle is 396 units
What is a diameter?The diameter is the length of the line through the center that touches two points on the edge of the circle.
A diameter is twice the radius of a circle.All diameters are segment but not all segments are diameter.
length of an arc = tetha/360 × πd
l = 80/360 × π d
88π = 80/360 × π d
80d = 88× 360
80d = 31680
divide both sides by 80
d = 31680/ 80
d = 396 units
therefore the diameter of the circle is 396 units
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Help!!! I need help I don't know how to do it
Ted jogged a total of 11.2 miles in 4 days. He jogged the same distance each day.
Part A
How far did he jog each day? Enter your answer in the box.
2.8
miles
Part B
How many total miles would Ted jog if he continued to jog the same number of miles each day for 6 days? Enter your answer in the box.
miles? put answer bellow for part b
Answer: 16.8 miles
Step-by-step explanation:
Multiply 2.8 miles by 6 to find the number of miles jogged after 6 days.
Answer:
16.8 miles!
Step-by-step explanation:
What does alpha 0.05 mean in stats?
An alpha value of 0.05 means that there is a 5% chance of incorrectly rejecting the null hypothesis.
In statistics, "alpha" is used to represent the significance level in a hypothesis test. The significance level, denoted by α, is the probability of rejecting the null hypothesis when it is actually true.
In other words, if the p-value in a hypothesis test is less than or equal to 0.05, we can reject the null hypothesis and conclude that there is a statistically significant difference between the groups or variables being tested.
An alpha value of 0.05 is commonly used in research studies, but other values such as 0.01 or 0.10 may also be used depending on the desired level of significance.
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How do you calculate the arc length of a circle?
To calculate the arc length of a circle, you need to use the formula: arc length = (central angle in radians) x (radius)
where the central angle is measured in radians and the radius is the distance from the center of the circle to the edge. To use this formula, first convert the central angle from degrees to radians by multiplying it by π/180. Then, multiply the result by the radius to find the arc length. For example, if you have a circle with a radius of 5 units and a central angle of 45 degrees, you can calculate the arc length as follows: Convert the central angle to radians: 45 x π/180 = 0.7854 radians. Multiply the central angle in radians by the radius: 0.7854 x 5 = 3.927 unit. Therefore, the arc length of a circle with a radius of 5 units and a central angle of 45 degrees is 3.927 units.
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