Let's begin by identifying key information given to us in the graph:
The reciprocal parent function is given as 1/f(x). This is better written as shown below
[tex]\begin{gathered} f(x)=\frac{a}{(x-h)}+k \\ when\colon h=0,k=0,a=1 \\ f(x)=\frac{1}{x-0}+0 \\ f(x)=\frac{1}{x} \\ f(x)=y \\ \Rightarrow y=\frac{1}{x} \end{gathered}[/tex]When the value for x is greater than zero, the function is positive as shown below:
[tex]\begin{gathered} x=2 \\ y=\frac{1}{2}=\frac{1}{2} \\ y=\frac{1}{2} \end{gathered}[/tex]When the value of x is lesser than zero, the function is negative as shown below:
[tex]\begin{gathered} x=-1 \\ y=\frac{1}{-1}=-1 \\ y=-1 \end{gathered}[/tex]Therefore, the correct answer is option A (The function is negative when x < 0)
The number of students in the tutoring center was recorded for 27 randomly selected times. The data is summarized in the frequency table below. What is the class width for this frequency distribution table
The class width for this frequency table is 5.
What is class width?The class width is described as the distance between the lower class of two consecutive classes.
How to calculate class width?One can calculate class width by finding the difference between the two consecutive lower classes.
In the figure above, the first two classes are described as
0-4
5-9
So, the lower classes of these intervals are 0,5
Thus the difference between them is 5
Therefore, the class width for this frequency distribution table is 5.
To know more about class width, visit:
https://brainly.com/question/28359316
#SPJ13
Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 neighborhood residents are displayed in the histogram below. A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8. Which interval shows the greatest change in water bills? $150–$175 $175–$200 $200–$225 $225–$250
$200-$225 interval shows the greatest change in water bills
What is Histogram?A diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
The interval which contains the median water bill is $200 - $225
The tabulated data is given in the attachment.
The median class = Cummulative frequency / 2
The median class = 40 / 2
The class interval which contains the 20th frequency.
This is the 200 - 225 class
The interval which contains the median water bill is $200 - $225
Hence $200-$225 interval shows the greatest change in water bills
To Learn more on Histogram click:
brainly.com/question/300591
#SPJ1
Answer:
C)$200–$225
Step-by-step explanation:
edge 2023
Determine the open intervals on which the function is increasing, decreasing, or constant.(Enter your answers using interval notation. If an answer does not exist, enter DNE.)
Given:
[tex]f(x)=\sqrt{x^2-4}[/tex]To find:
The interval at which the function is increasing, decreasing and constant.
Explanation:
We know that,
For a function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function.
For a function, y = F(x), if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.
According to the graph,
The function is increasing in the interval,
[tex][2,\infty)[/tex]Because, if x increases from 2, the value of y increases.
The function is decreasing in the interval,
[tex](-\infty,-2][/tex]Because, if x increases from negative infinity, the value of y decreases.
As we know, a constant function is a function whose output value is the same for every input value.
Here, the function is not constant at any of the intervals.
Final answer:
Increasing:
[tex][2,\infty)[/tex]Decreasing:
[tex](-\infty,-2][/tex]Constant: DNE.
M=W(1+rt) (solve the following formula for "t"
Given the following formula given in the exercise:
[tex]M=W\mleft(1+rt\mright)[/tex]You can solve for the variable "t" by following the steps shown below:
1. You must apply the Disrtributive proprerty on the right side of the equation:
[tex]\begin{gathered} M=(W)\mleft(1)+(W)(rt\mright) \\ M=W+Wrt \end{gathered}[/tex]2. Now you need to apply the Subtraction property of equality by subtracting "W" from both sides of the equation:
[tex]\begin{gathered} M-(W)=W+rtW-(W) \\ M-W=Wrt \end{gathered}[/tex]3. Finally, you can apply the Division property of equality by dividing both sides of the equation by "Wr":
[tex]\begin{gathered} \frac{M-W}{Wr}=\frac{Wrt}{Wr} \\ \\ t=\frac{M-W}{Wr} \end{gathered}[/tex]The answer is:
[tex]t=\frac{M-W}{Wr}[/tex]What is 372.7332 rounded to the nearest thousandth?
Please help rn I have until 3pm
Can you help me answer part A and part B?
Now, Now,We are given the following vectors:
[tex]P\left(5,4\right),Q\left(7,3\right),R\left(8,6\right),S\left(4,1\right)[/tex]We are asked to determine the following vector:
[tex]PQ+3RS[/tex]First, we will determine the vector PQ and RS. To determine PQ we use the following:
[tex]PQ=Q-P[/tex]This means we need to subtract "P" from "Q". We do that by subtracting each component of the points, like this:
[tex]PQ=\left(7,3\right)-\lparen5,4)=\left(7-5,3-4\right)[/tex]Solving the operations:
[tex]PQ=\left(2,-1\right)[/tex]Now, we use a similar procedure to determine RS:
[tex]RS=S-R[/tex]Substituting we get:
[tex]RS=\left(4,1\right)-\left(8,6\right)=\left(4-8,1-6\right)[/tex]Solving the operations:
[tex]RS=\left(-4,-5\right)[/tex]Now, we substitute the values in the vector we are looking for:
[tex]PQ+3RS=\left(2,-1\right)+3\left(-4,-5\right)[/tex]Now, we solve the product by multiplying both components of RS:
[tex]PQ+3RS=(2,-1)+(-12,-15)[/tex]Now, we solve the addition by adding each corresponding component:
[tex]PQ+3RS=(2-12,-1-15)[/tex]Solving the operations:
[tex]PQ+3RS=(-10,-16)[/tex]And thus we have determined the components.
Part B. We area asked to determine the magnitude of the vector. To do that we will use the following:
Given a vector of the form:
[tex]X=\left(x,y\right)[/tex]Its magnitude is:
[tex]\lvert X\rvert=\sqrt{x^2+y^2}[/tex]This means that the magnitude is the square root of the sum of the square of the components. Applying the formula we get:
[tex]\lvert\begin{equation*}PQ+3RS\end{equation*}\rvert=\sqrt{\left(-10\right)^2+\left(-16\right)^2}[/tex]Now, we solve the squares:
[tex]\lvert\begin{equation*}PQ+3RS\end{equation*}\rvert=\sqrt{100+256}[/tex]Solving the addition:
[tex]\lvert\begin{equation*}PQ+3RS\end{equation*}\rvert=\sqrt{356}[/tex]Now, we factor the term inside the radical as follows:
[tex]\lvert PQ+3RS\rvert=\sqrt{4\left(89\right)}[/tex]Now, we distribute the radical:
[tex]\lvert PQ+3RS\rvert=\sqrt{4}\sqrt{89}[/tex]Taking the left square root:
[tex]\lvert PQ+3RS\rvert=2\sqrt{89}[/tex]And thus we have determined the magnitude.
What are the dimensions of the rectangle with Maximum area?
Let x be the length of the rectangle and y be the width of the rectangle, then we can set the following equations:
[tex]\begin{gathered} 2x+2y=40, \\ A=x\cdot y\text{.} \end{gathered}[/tex]Solving the first equation for x we get:
[tex]\begin{gathered} 2x=40-2y, \\ x=\frac{40}{2}-\frac{2y}{2}, \\ x=20-y\text{.} \end{gathered}[/tex]Substituting x=20-y in the second equation we get:
[tex]\begin{gathered} A=(20-y)\times y, \\ A=20y-y^2. \end{gathered}[/tex]Now, we will use the first and second derivative criteria to find the maximum.
The first and second derivatives are:
[tex]\begin{gathered} A^{\prime}(y)=20-2y. \\ A^{\prime\prime}(y)=-2. \end{gathered}[/tex]Since the second derivative is a negative number that means that A(y) reaches a maximum when A´(y)=0.
Solving A´(y)=0 for y we get:
[tex]\begin{gathered} 20-2y=0, \\ 20=2y, \\ 10=y\text{.} \end{gathered}[/tex]Now, substituting y=10 in x=20-y, we get:
[tex]x=20-10=10.[/tex]Answer:
Length 10 yards.
Width 10 yards.
three fourths of w + 5 is one half of w increased by 9
let's put the information given in a mathematical equation:
[tex]\frac{3}{4}w+5=\frac{1}{2}w+9[/tex]we pass all the terms thas has w in them to the left side and left the other terms in the right side:
[tex]undefined[/tex]Rotate this hexagon 180º.
(0, -8)
(3, -8)
(6,-5)
(6, 1)
(3, 2)
(0, 2)
After rotation the coordinates of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)
Upon rotation of this hexagon by 180
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
After rotation, the co- ordinates change from
(0, -8) → (0, 8)
(3, -8) → (-3, 8)
(6,-5) → (-6, 5)
(6, 1) → (-6, -1)
(3, 2) → (-3, -2)
(0, 2) → (0, -2)
Therefore, after rotation the coordinates of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)
To learn more about rotation about origin refer here
https://brainly.com/question/11053791
#SPJ1
Write an inequality that represents the graph below
An inequality that represents the given graph is; 2 < x < ∞.
What is referred as the term inequality?In mathematics, an inequality is a link between two expressions as well as values that aren't equal to each other.Inequality results from a lack of balance. For instance, suppose you would like to buy a new vehicle that costs $250 but only have 225. It is also a inequality because you are comparing these two non-equal numbers.For the given question.
The inequality is given by the values of the number line.
The value is starting from 2 and goes up to infinity.
But, It is a hollow dot at 2 means 2 is with open interval, as 2 will not be taken for the value of x.
The values lies between, (2, ∞)
Thus, the inequality that represents the given graph is; 2 < x < ∞.
To know more about the inequality, here
https://brainly.com/question/25799000
#SPJ13
Put 3/4, -1/2, -1/4 in order from least to greatest.
Answer:
-1/2, -1/4, 3/4.
Explanation:
If we draw the number in a number line, we get:
So, if we order them from least to greatest, we get:
-1/2, -1/4, 3/4.
Answer:
-1/2, -1/4, 3/4
Step-by-step explanation:
The hypotenuse of right triangle XYZ is 28 and m
Solution
For this case we can do the following:
m < X = 60
One angle in a right triangle needs to be 90º
So then we can find the measure of the other angle like this.
180 -90-60 = 30º
We can find the following identity:
[tex]\sin 60=\frac{y}{28}[/tex]And solving for thw leg opposite we got:
[tex]y=28\cdot\sin 60=24.25[/tex]
Sun lei bought a computer for $1800. The total cost, including tax, came to $1890. What is the tax rate?
Given:
Cost of computer without tax $1800.
Total cost including tax is $1890
[tex]\text{Tax amount =1890-1800}[/tex][tex]\text{Tax amount = \$90}[/tex]Let the tax rate be x
[tex]90=1800\times\frac{x}{100}[/tex][tex]\frac{90}{18}=x[/tex][tex]x=5[/tex]Tax rate is 5%
2) Convert this fraction into a mixed number in lowest terms 60/25
Please I need step by step explanation.
The given fraction 60/25 into a mixed number would be 2 2/5 in the lowest terms.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
First, we have to find the whole number,
Determine how many times the denominator enters the numerator. Divide 60 by 25 and preserve just the numbers to the left of the decimal point:
⇒ 60 / 25 = 2.4000 = 2
Then, find a new numerator :
Multiply the result by the denominator and subtract it from the original numerator.
⇒ 60 - (25 x 2) = 10
Now, put together
To obtain this, keep the original denominator and use the solutions from Steps 1 and 2:
⇒ 2 10/25 ⇒ 2 2/5
Thus, the given fraction 60/25 into a mixed number would be 2 2/5 in the lowest terms.
Learn more about the fraction here:
brainly.com/question/10354322
#SPJ1
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8543 g and a standard deviation of 0.0519 g. A sample of these candies came from a package containing 469 candies, and the package label stated that the net weight is 400.3 g. (If every package has 469 candies, the mean weight of the candies must exceed
400.3
469=0.8536 g for the net contents to weigh at least 400.3 g.)
Given,
The weight of candies normally distributed ;
Mean weight of candies = 0.8543 g
Standard deviation, σ = 0.0519 g
Sample of candy came from a packet of 469 candies
Net weight of the packet = 400.3 g
Average weight of the candies in the packet;
[tex]x_{avg} =[/tex] ∑xi/n = 400.3/469 = 0.8535
The population standard deviation (sigma=0.0519 g) is the standard deviation for a confectionery that was chosen at random (sample size n=1).
The z-score can be used to determine the likelihood that an element has a weight greater than 0.8536z = (X - μ) / (σ/√n) = (0.8536 - 0.8535) / (0.0519/√1) = 0.0001/0.0519 = 0.002
P(X > 0.8536) = P(z > 0.002) = 0.4992
A randomly chosen candy has a probability P=0.4992 of weighing at least 0.8536 g.
The z-score needs to be computed if the sample now has n=441 candies and we want to know the likelihood that the mean weight is at least 0.8543 g:z = (X - μ) / (σ/√n) = (0.8543 - 0.8535) / (0.0519/√441) = 0.0008/0.0024 = 0.3288
P(X > 0.8543) = P(z > 0.3288) = 0.37115
A sample of 441 candies chosen at random has a probability P=0.3712 of having an average weight of at least 0.8543 g.
We may determine the likelihood that, for a package of 469 candies and using the mean of 0.8535 g that we previously determined, the average weight is at least 0.8556 g in order to be more certain of the claim that the mean weight is 0.8556 g.z = (X - μ) / (σ/√n) = (0.8556 - 0.8535) / (0.0519/√469) = 0.0021/0.0024 = 0.89
P(X > 0.8556) = P(z > 0.89) = 0.18673
Given that the likelihood is P=0.187, the brand's claim that it delivers the amount promised to customers on the label needs to be reevaluated.
Learn more about probability here;
https://brainly.com/question/16012391
#SPJ1
Find the critical value (tα/2) for a 99% confidence interval if the sample size is 15. Round your answer to three decimal places.
tα/2 =
The critical value (tα/2) for a 99% confidence interval for the sample size 15 is 2.977 .
We have to find the critical value tα/2 for 99% confidence interval, we are given the sample size.
First we will find the alpha value to get the critical value.
=100%-99%
=1-0.99
=0.01
α=0.01
α/2=0.01/2
α/2=0.005
degrees of freedom(df)= n-1=15-1=14
We will use degrees of freedom and α/2 values to find the critical value that is tα/2.
By using the t table we get the critical value of tα/2=2.977.
Therefore, the critical value for 99% confidence interval with sample size 15 is 2.977.
To know more about critical value here
https://brainly.com/question/14100623#
#SPJ1
A car travels 238 miles in 4 hours and 15 minutes. How many miles does it travel per
hour?
We can conclude that the distance traveled in 1 hour is 57 miles after doing some mathematical operations.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So, the distance traveled in 1 hour:
Distance traveled in 4 hours and 15 minutes = 238 milesThen divide 238 by 4.15 as follows:
238 ÷ 4.1557.34Rounding off: 57 miles
Therefore, we can conclude that the distance traveled in 1 hour is 57 miles after doing some mathematical operations.
Know more about mathematical operations here:
https://brainly.com/question/20628271
#SPJ13
Here is an ordered set of sample data.87 109 156 166 204210 279 416 500 534592 609 655 677 777837 873 998Identify the 5 number summary: (min, Q1, median, Q3, max).
Solution:
A boxplot is a standardized way of displaying the dataset based on a five-number summary: the minimum, the maximum, the median, the first quartile, and the third quartile.
The general representation for a box plot is given below;
Comparing this to the box plot given in the question, the following can be deduced;
[tex]\begin{gathered} \text{minimum, }\min =11 \\ lowerquartileQ_1=12 \\ \text{Median}=15 \\ \text{upper quartile, Q}_3=17 \\ \max imum,\text{ max=20} \end{gathered}[/tex]Therefore, the answer as arranged is;
[tex](11,12,15,17,20)[/tex]The interquartile range, IQR is given by;
[tex]\begin{gathered} Q_3-Q_1 \\ \text{where;} \\ Q_3=17 \\ Q_1=12 \\ \\ \text{IQR}=17-12 \\ \text{IQR}=5 \end{gathered}[/tex]Therefore, the interquartile range is 5.
Sam bought 9 tickets all in the same row to a KC Royals game for himself and his
friends next week. His friends are Eric, Sarah, Renee, David, Julie, Derek, Kelsey and
Kyle.
(a) How many different ways can the friends be seated in the row?
(b) Sam has a crush on Sarah, so he wants to make sure his seat is next to hers. How
many ways are there to assign the seats now?
(c) How many ways are there to assign the seats if Sam wants to ensure that they
are all seated boy-girl-boy-girl?
Using the arrangements formula, the number of ways that they can be seated for each case is given as follows:
a) No restrictions: 362,880.
b) Sam next to Sarah: 80,640.
c) Boy-girl-boy-girl: 2,880.
What is the arrangements formula?The number of possible arrangements of a set containing n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
For item a, we consider that 9 people will be seated with no restrictions, hence the number of ways is given as follows:
9! = 362,880
For item b, there is the restriction that Sam has to be seated next to Sarah, hence:
There are 8 pairs of seats in which they can be seat, each in 2 ways(Sam-Sarah or Sarah-Sam).The other 7 people can be seated in 7! ways, as there are no restrictions for them.Hence the number of ways is:
2 x 8 x 7! = 80,640.
For item c, we can treat the boys and the girls places as independent, hence:
There are 5! ways for the boys to sit, as there are five boys in the group.There are 4! ways for the girls to sit, as there are four girls in the group.Hence the number of ways is:
5! x 4! = 2,880.
More can be learned about the arrangements formula at https://brainly.com/question/20255195
#SPJ1
Which equation represents a horizontal line that passes through the point (2, 7)? А x=2 В y = 2 C X= 7 D y=7
It is important to know that horizontal lines are represented by the equation y = k, where k is a real numbers.
In this case, if the equation passes thorugh (2,7), then the equation would be y = 7.
Hence, the answer is D.CD is the mid segment of trapezoid WXYZ.-What is the value of X?-What is XY?-What is WZ?
The midsegment theorem states that the length of the midsegment is equal to half the length of the base. From the information given,
midsegment = CD = 22
base = XY = 4x + 1
By applying the midsegment theorem, we have
CD = 1/2XY
22 = 1/2(4x + 1)
By crossmultiplying, we have
22 * 2 = 4x + 1
44 = 4x + 1
4x = 44 - 1
4x = 43
x = 43/4
x = 10.75
Thus,
Substituting x = 10.75 into XY = 4x + 1, it becomes
XY = 4(10.75) + 1
XY = 43 + 1
XY = 44
Substituting x = 10.75 into WZ = x + 3, it becomes
WZ = 10.75 + 3
WZ = 13.75
Nandita earned 224 dollars last month. she earned 28 dollars by selling cards at a craft fair and the rest of the money by babysitting. Complete an equation that models the situation and can be used to determine x, the number of dollars Nandita earned last month by babysitting.
the selling price of each card is = 28 $
let she sold x number of cards,
so, the equation is,
28x = 224
x = 224/28
x = 8
thus, the answer is number of cards sold by nandita is 8
so, the equation is
28x = 224
A train travels 150 km in 2 hours and 30 minutes. What is its average speed?
Answer:
It's average speed is 48 km per hour
Step-by-step explanation:
Answer:
60 km/hr
Step-by-step explanation:
150 km / 2.5 hr = 60 km/hr
I can’t figure this out I need help. I’ve been stuck on it for about an hour and a half.
SOLUTION
From the question, we are told to distribute the multiplication across in
[tex](4v^4-6z^5).4z^4[/tex]This means we should expand.
This becomes
in thr figure,, PQ =PR, and PS & ST are medians. What QT and QR
QR = QS + SR
QS = y+1/2
QS= SR
SR= y+1/2
QR= y+1/2 +y+ 1/2 = 2y + 1
QT = TP
RP = 2 TP
RP = 10
10 = 2 TP
10/2= TP
5 = TP
TP= QT
QT= 5
Since y= 5
QR = 2y + 1 = 2 (5) + 1 = 10 + 1 = 11
Answers:
QT= 5
QR= 11
In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between chirps and outdoor temperature is , where c is the number of chirps per minute and f is the temperature in degrees Fahrenheit.
Suppose 110 chirps are heard in a minute. If it is 75°F outside, about how many chirps can we expect to hear in one minute? Do not include units (chirps) in your answer. Round your answer to the nearest whole number.
Answer:
The crickets do not chirp at all below 40 degrees and at 75 degrees they chirp about 161 times per minute.
17. The rent for a store is GH¢420.00 a year.
What is the rent for the store in six
months?
Answer:
GH¢210Step-by-step explanation:
The rent is 420 a year.
6 months is half a year.
The rent for 6 months is half the rent for a year:
420/2 = 210In isosceles △ABC where AC≅BC, altitiude CD is drawn. If AC= 17 and AB= 30. Determine the altitiude of the triangle.
By definition, an Isosceles triangle is a triangle that have two congruent sides, and the altitude divides the triangle into two equal Right triangles.
Remember that a Right triangle is a triangle that has an angle whose measure is 90 degrees.
Based on this, you know that:
[tex]\begin{gathered} AD=BD=\frac{AB}{2} \\ \\ AC=BC \end{gathered}[/tex]Knowing that:
[tex]\begin{gathered} AB=30 \\ AC=17 \end{gathered}[/tex]You get that:
[tex]\begin{gathered} AD=BD=\frac{30}{2}=15 \\ \\ AC=BC=17 \end{gathered}[/tex]The Pythagorean Theorem states that:
[tex]a^2=b^2+c^2[/tex]Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.
So you can identify that, for this case:
[tex]\begin{gathered} a=17 \\ b=15 \\ c=CD \end{gathered}[/tex]Where "CD" is the altitude of the triangle.
Therefore, substituting values and solving for "CD", you get this result:
[tex]\begin{gathered} 17^2=15^2+CD^2 \\ \sqrt[]{17^2-15^2}=CD \\ CD=8 \end{gathered}[/tex]The answer is: Option (1)
Find the number, if 0.7 of it is 42.
The number whose 0.7 is 42 is 5.715.
What do you mean by number?
In mathematics, a number serves as both a unit of measurement and a label. The first examples are the natural numbers 1, 2, 3, 4, and so forth. Language can express numbers by the use of number terms. Numerals are symbols that are used to symbolize specific numbers; for example, the number "5" can be symbolize as number five.
Let the required number be X
As given in the question 0.7 of X is 42,
We can write it as:
(0.7)X = 42
If a number make to change its side around the equal sign then if it is in divide on one side so it will become in multiplication on the other side.
So,
X = 4/0.7
X = 5.715 (approximately)
Therefore, The number whose 0.7 is 42 is 5.715
To know more about numbers, go to link
https://brainly.com/question/25734188
#SPJ9
Use the equation below and the indicated value to find an ordered pair that is a solution.
y=2x-1 Let x = 4.
The ordered pair is 4.
The ordered pair is 4 is 7.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Given that,
The equation is
y = 2x-1
Substitute the value of x =4
y = 2x-1
y = 2×4-1
y = 7
The value of y at x = 4 is 7.
Hence, the ordered pair of 4 is 7.
To learn more about the equation from the given link:
https://brainly.com/question/22688504
#SPJ10