A camera has a listed price of $665.98 before tax. If the sales tax rate is 9.5%, find the total cost of the camera with sales tax Included. Round your answer to the nearest cent, as necessary.
we know that
100%+9.5%=109.5%=109.5/100=1.095
so
Multiply the listed price of $665.98 by 1.095
$665.98*1.095=$729.25
therefore
the answer is $729.256. The rectangles length can be represented by 3n2 + 2n -1 and its width can be represented by n2 + 3. What is the perimeter of the rectangle?show your work plsbest answer=brainiest
The perimeter P of a retangle is given as
P = 2(L + B) where
L is the length and B is the width
Hence the perimeter of the given rectangle
= 2(3n2 + 2n -1 + n2 + 3)
= 2(3n2 + n2 + 2n -1 + 3)
= 2(4n2 + 2n -2)
= 8n2 + 4n - 4
[tex]8n^{2} +4n+4[/tex] is the perimeter of the rectangle.
Length of the rectangle =[tex]3n^{2} +2n-1[/tex]
Width or Breath of the rectangle = [tex]n^{2} +3[/tex]
Perimeter of rectangle = 2 ( length + width)
= [tex]2( 3n^{2} +2n-1 +n^{2} +3 )[/tex]
= [tex]2(4n^{2}+2n+2)[/tex]
= [tex]8n^{2} +4n+4[/tex]
Perimeter is the boundary line of a closed geometrical figure. It is always measured for a flat figure ie only 2D figures for example circles, squares, rectangles, or triangles.
The perimeter of the triangle = sum of all sides
The perimeter of the square = 4a, where a is the side of the square
The rectangle is a four-dimensional closed figure.
Properties of rectangle:
4 sides4 verticesOpposite sides are equal as well as parallel2 faces the lines form 90 degree angleFor more questions about perimeter of rectangle visit the link: https://brainly.com/question/26584519
Problem 3. Two professors teach the same course and their students have the same mean score (85) and same median score (85). Grades for each professor are listed below. Professor X: 91, 91, 82, 80, 77, 80, 93, 92, 87, 76, 86, 80, 80, 95, 85 Professor Y: 99, 83, 68, 96, 93, 75, 78, 65, 85, 96, 99, 69, 96, 98, 100, 69, 81, 99, 66 a) B. Calculate, by hand or with a software, the Mean Absolute Deviation (MAD) of each grade distribution and use this information to determine which professor’s grades have a larger variability. C. Discuss whose course would you rather be in and why.
ANSWER
MAD for Professor X = 5.33
MAD for Professor Y = 11.68
Hence, Professor Y's grades have a larger variability.
STEP-BY-STEP EXPLANATION
Step 1: Data, Mean and the Absolute values for Professor X using Microsoft Excel software.
Step 2: Mean Absolute Deviation (MAD) for Professor X using Microsoft Excel software.
Step 3: Data, Mean and the Absolute values for Professor Y using Microsoft Excel software.
Step 4: Mean Absolute Deviation (MAD) for Professor Y using Microsoft Excel software.
Step 5: Variability
The higher the Mean Absolute Deviation (MAD), the greater the variability in the data; that is the data far more spread out. Hence, Professor Y's grades have a larger variability.
Step 6: Whose course would you rather be in and why?
From the results above, it is clear that Professor Y's grades are more spread out from the mean. This shows that the grades are more variable and there is quite less consistency in the grades.
However, the results show that Professor X's grades are less spread out from the mean, less variable and far more consistent.
Hence, you should rather be in Professor X's course because of the above facts.
Set up an equation to solve the given word problem
Let a and b be two numbers. The first equation described in the sentence is
[tex]a=22+b[/tex]And the second equation is
[tex]ab=-121[/tex]Notice that the first equation implies that b>a, so we can rename b as x, obtaining the next two equations
[tex]\begin{gathered} a=22+x \\ ax=-121 \end{gathered}[/tex]Then,
[tex]\begin{gathered} \Rightarrow ax=(22+x)x \\ \Rightarrow x(22+x)=-121 \\ \Rightarrow x(x+22)=-121 \end{gathered}[/tex]The answer is option c.
Finally, solve the equation above for x, as shown below
[tex]\begin{gathered} x(x+22)=x^2+22x \\ \Rightarrow x^2+22x=-121 \\ \Rightarrow x^2+22x+121=0 \\ \Rightarrow(x+11)^2=0 \\ \Rightarrow x+11=0 \\ \Rightarrow x=-11 \end{gathered}[/tex]The answer is x= -11
And number a is x+22=-11+22, a=11
Write a formula for the nTh term of the sequence:1,4,7,10,13
Answer:
[tex]a_n=3n-2[/tex]Explanation:
The formula for the nth term of an arithmetic sequence is
[tex]a_n=a_1+d(n-1)[/tex]Where:
a_n is the term we want to find
a_1 is the first term of the sequence
d is the common distance between the terms.
In this sequence, we can see that d = 3. Because any term minus the previous is 3:
[tex]\begin{gathered} 4-1=3 \\ 7-4=3 \\ 10-7=3 \\ 13-10=3 \end{gathered}[/tex]The first term is 1. Then:
[tex]a_n=1+3(n-1)[/tex]Now, we can apply distributive property:
[tex]a_n=1+3n-3=3n-2[/tex]And we get the final expression for the arithmetic sequence formula for the nth term:
[tex]a_=3n-2[/tex]The directions are with the pic below. I have to send a 2nd pic. Couldn’t fit everything on the page
If the pentagon is rotated 360° about the origin, that means the new figure will be exactly in the same position as the original image, because a rotation of 360° about the origin doesn't change the figure position or orientation.
So, if the vertex was located at (10, -8), the new figure will also have a vertex located at (10, -8).
Therefore the correct option is the fourth one.
Of 20 test scores, three are less than or equal to 87. What is the percentile rank ofa test score of 87?
We know that in a data set of 20 test scores, we have 3 that are less than or equal to 87.
A percentile rank describes the percentage of people in the comparison group who scored below a particular score.
In this case, a percentile rank of 87 correspond to:
[tex]PR_{87}=\frac{20-3}{20}=\frac{17}{20}=0.85=85\%[/tex]This means that the students that score 87 or more performed better than 85% of the other students as there are 17 out of 20 test scores that are under 87.
Answer: the percentile rank of a test score of 87 is 85%.
factorise the following
a) x^2- 12x + 32
b) x^2- 14x + 48
c) x^2 - 3x + 2
The factors of x^2 - 12x + 32 is (x-4)(x-8), factors of x^2-14x+48 is (x-6)(x-8), and factors of x^2-3x+2 is (x-1)(x-2)
a) x^2 - 12x + 32
= x^2 - 8x - 4x + 32
= x(x - 8) - 4(x-8)
= (x-4)(x-8)
b) x^2 - 14x + 48
= x^2 - 8x - 6x + 48
= x(x-8) -6(x-8)
= (x-6)(x-8)
c) x^2 - 3x + 2
= x^2 - x - 2x + 2
= x(x-1)- 2(x-1)
= (x-1)(x-2)
Hence, the factors of a) is (x-4)(x-8), factors of b) is (x-6)(x-8), and factors of c) is (x-1)(x-2)
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Solve the volume of the following solid show complete work
Answer:
[tex]V=48cm^3[/tex]Step-by-step explanation:
The volume of a prism is represented by the area of the base multiplied by the height, therefore the equation is given as:
[tex]\begin{gathered} V=(\frac{1}{2}\cdot b\cdot h)\cdot\text{ length} \\ \text{where,} \\ b=3 \\ h=4 \\ l=8 \end{gathered}[/tex]Therefore, the volume of the given triangular prism:
[tex]\begin{gathered} V=(\frac{1}{2}\cdot3\cdot4)\cdot8 \\ V=6\cdot8 \\ V=48cm^3 \end{gathered}[/tex]what equation describe amonth pf money for taco truck 2, where A is the amonth of money and T is the number of tacos sold.?
Okay, here we have this:
Considering that Truck 2 started $2 and sold 2 the tacos for $1. This mean that each taco cost $0.5, so we obtain the following:
Total amounth of money (A)=Initial Money+$0.5*Number of tacos sold (T)
Finally we obtain the following equation A=$2+$0.5(T)
David has a pocket full of change. His change contains 4 pennies, 2 nickels, and 3 dimes. Find the probability if be randomly chooses 2 coins they are both dimes. Dependent or Independent
Given:
A pocket full of change
The change contains 4 pennies, 2 nickels, and 3 dimes.
so, the number of coins = 4 + 2 + 3 = 9
The probability of choosing the first dime = 3/9
so, the number of coins will be = 9 - 1 = 8
The probability of choosing the second dime = 3/8
So, the probability if be randomly choosing 2 coins they are both dimes =
[tex]\frac{3}{9}\cdot\frac{3}{8}=\frac{1}{8}[/tex]Dependent
What is the probability that out of 175 chicks hatched on Peeper Farm, at least 80 will be female? Assume that males and females are equally probable, and round your answer to the nearest tenth of a percent.
Since we have two possible outcomes for each hatch and they are independent of each other this can be seen as a binomial experiment.
We know that the binomial distribution is given by:
[tex]P(X=k)=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}[/tex]where n is the number of trials, k is the number of succeses we want and p is the probability of success.
In this case we have 175 chicks hatched, then the number of trials is n=175; the probability of success is 0.5 (since the probability of having males or females is equal) and we want that the number of succeses to be at least 80, then we are looking for the probability:
[tex]P(X\ge80)[/tex]but using the properties of the distribution this is the same as:
[tex]P(X\ge80)=P(X=80)+P(X=81)+P(X=82)+\cdot\cdot\cdot+P(X=175)[/tex]where each probability is calculated with the values given above.
In this case we would have to calculate 95 probabilities, as an example we would calculate the first one:
[tex]P(X=80)=\frac{175!}{80!(175-80)!}(0.5)^{80}(1-0.5)^{175-80}=0.03175876249[/tex]By doing all the probabilities and adding them we have that the probability is 0.887 that's the same as 88.7%, therefore the answer is b.
1. If E is the midpoint of AB, F is the midpoint of BC, and G is the midpoint of AC , Name each: a. The centroid of AABC OG G 7 b. The orthocenter of AABC B D 2 Inderline the correct mord
a. The centroid of ΔABC is
b. The orthocenter of ΔABC is CD.
What is the centroid of the triangle?
The center of the object is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.
What is the orthocenter of the triangle?
The intersection of altitudes drawn perpendicularly from the vertex to the opposing sides of a triangle is known as the orthocenter of a triangle.
Here,
a. The centroid of ΔABC is
E is the midpoint and joining vertex C
G is the midpoint of AC and joining a vertex B
F is the midpoint of BC and joining vertex A
b. The orthocenter of ΔABC is CD.
Hence,
a. The centroid of ΔABC is
b. The orthocenter of ΔABC is CD.
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Do you think a rotated image would ever coincide with the original figure
Answer:
Yes, the rotated image coincide with the original figure when the angle of translation is 360 degrees or a multiple of 360 degrees because 360 degrees is the measure of a complete rotation.
Find the surface area and volume of the figure below. Round to the hundredths (2decimal places) if necessary.Use it instead of 3.14 for calculations.
Find the surface area of the sphere
A = 4 * pi * r^2
pi = 3.14
circumference = 34
34 = 2 * 3.14 * r
17 = 3.14 * r
r = 5.41
A = 4 * 3.14 * 5.41
A = 67.95 m^2
Volume is found with
v = 4/3 * 3.14 * r^3
v = 4/3 * 3.14 * 5.41^3
v = 4/3 * 3.14 * 158.34
v = 662.92 m^3
which situation could be described as the product of 3 and -4
Option C
because the temperature decreased in 4 units each hour during 3 hours
identify the zeros of the function f(x)=x²-9
The zeros of the function are -3 or 3
Here, we want to find the zero of the function
To find this, we will have to equate the function to zero
Thus, we have it that;
[tex]\begin{gathered} x^2-9\text{ = 0} \\ x^2\text{ = 9} \\ x\text{ = }\sqrt[]{9} \\ x\text{ = }\pm3 \end{gathered}[/tex]That's your Danny had $20,000 to invest. He invest some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $1580 in interest.how much did he invest in each account.first account $second account $
Let the principal of the investment be represnted below
[tex]p_1=20000-p_2[/tex]Therefore,
[tex]\begin{gathered} I=\frac{prt}{100} \\ for\text{ the first one } \\ I=\frac{(20000-p_2)\times7\times1}{100}=\frac{140000-7p_2}{100} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{For the second one} \\ I=\frac{p_2\times10\times1}{100}=\frac{10p_2}{100}=\frac{p_2}{10} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{140000-7p_2}{100}+\frac{p_2}{10}=1580 \\ \frac{140000-7p_2+10p_2}{100}=1580 \\ 140000-7p_2+10p_2=158000 \\ 3p_2=158000-140000 \\ p_2=\frac{18000}{3} \\ p_2=6000 \end{gathered}[/tex][tex]\begin{gathered} P_1=20000-6000 \\ p_1=14000 \end{gathered}[/tex]He invested $14000 in the first account and $6000 in the second account.
Which equation describes the line with slope 5 that contains the point (-1,4)?O A. y+ 4 = 5(x+1)B. y - 4 = 5(x - 1)O c. y+ 4 = 5(x - 1)O D. y - 4 = 5(x+1)P
Answer
D
[tex]y-4=5(x+1)[/tex]Step-by-step explanation
The equation of a line in point slope form is
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x₁, y₁) is a known point.
Substituting m = 5 and the point (-1, 4), we get:
[tex]\begin{gathered} y-4=5(x-(-1)) \\ y-4=5(x+1) \end{gathered}[/tex]
Begin by graphing the standard quadratic function f(x)=x^2. Then use transformations of this graph to graph the given function
EXPLANATION:
1.We must first locate the intersection points for the graph
[tex]\begin{gathered} h(X)=(\frac{1}{2}x-2)^2 \\ (\frac{x}{2}-2)^2 \\ inter\sec t\text{ in x : }(4,0)\text{ } \\ \text{ intersect in y: }(0,4) \end{gathered}[/tex]By giving points to the equation we can have the graph of an upward curve.
The graph is the following:
Translate Each Equation:Twice A Number Divided By 6 Is 42,Two Times The Sum Of A Number And 5 Is 20Four Times The Difference Of A Number And 7 Is 32
this is a word problem
is means = or equal to
let the number be A
twice the number of A means 2 x A
= 2A
twice the the number of A is divided by 6
this means that 2A / 6 = 42
for the first question the answer is 2A / 6 = 42
Second question
sum means +
we have two numbers which are A and 5
their sum = A + 5
two times the sum of A and 5 can be written as
= 2(A + 5)
Recall, that is represent =
therefore, 2(A+5) = 20
The answer for the second question is 2(A+5) = 20
Third question
Difference means minus
We have two numbers which are A and 7
difference of the A and 7 can be written as A - 7
four time the difference can be written as
4(A-7)
4(A-7) = 32
The answer is 4(A-7) = 32
How I Did (Circle one)Learning Goal from Lesson 12.2I can describe and interpret the solutions to a system of linearinequalities graphically.I got it!I'm still learning it.(Lesson 12.2) Graph the system of linear inequalities. Give two ordered pairs that are solutions andtwo that are not solutions. (2 points)9.Sy 3x + 3by <-28 66I42
To answer this question we will graph the solution set of each inequality and then find the intersection of the solution sets.
1)
[tex]y\ge3x+3.[/tex]Since the inequality is not strict, then the border of the solution set is a solid line.
Notice that the solution set of the first inequality consists of all the points on the graph and above the graph of the line:
[tex]y=3x+3.[/tex]Therefore the solution set to the first inequality is:
2)
[tex]y<2.[/tex]The solution set of the above inequality consists of all the points such that its y-coordinate is less than 2, then its graph is:
Therefore the solution set to the given system of inequalities is:
Answer:
Two points on the solution set are (-2,-3) and (-1,0) and two points that are not on the solution set are (-2,2) and (-4,2).
Calculate the mean medium interquartile range IQ art and standard deviation for each data set ( I need help with 9 and 10)
Company A
we have the data set
23,29,35,46,51,50,42,37,30
Part 1
Find out the mean
mean=(23+29+35+46+51+50+42+37+30)/9
mean=343/9
mean=38.11
Part 2
Find out the median
Rewrite the data set, from less to greater
23,29,30,35,37,42,46,50,51
the median is the center
so
23,29,30,35,37,42,46,50,51
median=37
Q1=(29+30)/2=29.5
Q3=(46+50)/2=48
IQR=Q3-Q1=48-29.5=18.5
Part 3
Find out the standard deviation
For each data point, find the square of its distance to the mean
(23-38.11)^2=228.3121
(29-38.11)^2=82.9921
(35-38.11)^2=9.6721
(46-38.11)^2=62.2521
(51-38.11)^2=166.1521
(50-38.11)^2=141.3721
(42-38.11)^2=15.1321
(37-38.11)^2=1.2321
(30-38.11)^2=65.7721
Sum the values
Sum=772.8879
Divide by the number of data points
772.8879/9=85.8764
Take the square root
the result is 9.27
so
the standard deviation is 9.27
A basketball has a diameter of 8 inches. What is the distance around it?
Assuming that the distance arund it refers to the circumference of a circle with the same radius, then, remember that the circumference of a circle is equal to π times its diameter:
[tex]C=\pi D[/tex]Since the diameter is 8 inches, then:
[tex]\begin{gathered} C=\pi\times8\text{in} \\ =25.13274123\ldots\text{in} \\ \Rightarrow C\approx25.1in \end{gathered}[/tex]Therefore, the distance around it is approximately 25 inches.
Find the average rate of change of f(x) = 2x ^ 2 - 9x from x = 2 to x = 5 . Simplify your answer as much as possible.
5
Explanation:
The average rate of change formula:
[tex]\begin{gathered} \frac{\Delta y}{\Delta x}\text{ = }\frac{y2-y1}{x2-x1}\text{ = }\frac{f(b)\text{ -}f(a)}{b-a}\text{ } \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{f(b)\text{f}(a)}{b-a}\text{ = }\frac{f(5)\text{ -f\lparen2\rparen}}{5-2} \\ \end{gathered}[/tex][tex]\begin{gathered} f(5)\text{ = 2*5}^2-9*5\text{ = 5} \\ f(2)\text{ = 2*2}^2-9*2\text{ = -10} \end{gathered}[/tex][tex]\frac{f(b)\text{f}(a)}{b-a}\text{ = }\frac{5-(-10)}{5-2}\text{ = }\frac{15}{3}\text{ = 5}[/tex]john had 84 apples his friend sam took away 22 of them how many apples does john have left. and what percentage did Sam take away.
We have the following:
The apples that John has left would be the difference between the ones he initially had minus the ones that Sam took
[tex]84-22=62[/tex]To calculate the percentage that Sam took, we must divide the amount that Sam took and the total amount, that is, those that John had initially, then multiply by 100 so that it is a percentage.
[tex]\frac{22}{84}\cdot100=26.19[/tex]Therefore, the percentage is 26.19%
John has left with 62 apples.
Sam takes away 26.19% of the total apples.
Given in the question,
John had 84 apples.
Sam took away 22 apples.
So, to find the number of apples left,
we have to subtract the total number of apples from the number of apples taken by sam,
Remaining apple = 84 - 22
= 62.
Therefore, the number of remaining apples is 62.
Now, we will find the Percentage Of apples taken by Sam,
= [tex]\frac{22}{84}[/tex] × 100
= 26.19%
Therefore, the percentage taken away is 26.19%
what value of z makes the equation 2z-9=7 true
We are given the equation
2z - 9 = 7
Firstly, collect the like terms
2z = 7 + 9
2z = 16
Divide both sides by 2
2z/2 = 16/2
z = 8
Substitute z = 8 back to the previous equation
We have
2(8) - 9 = 7
16 - 9 = 7
7 = 7
Therefore, the value of z that makes the equation 2z - 9 = 7 true is 8
The answer is 8
the standard slope for a drainage pope carrying water is 1/4 inch of vertical drop per foot of horizontal distance. How many inches of vertical drop would an 18-ft drainage pipe require?
Given:
The length of the drainage pipe, l=18 ft.
The slope of the drainage pope is 1/4 inch of vertical drop per foot of horizontal distance.
Hence, the slope is m=1/4 in/ft.
Now, the vertical drop can be calculated by multipying the slope 1/4 in/ft by the length of pipe.
Thus, the vertical drop needed for a 18 ft pipe is,
[tex]\begin{gathered} x=m\times l \\ =\frac{1}{4}\frac{in}{ft}\times18\text{ ft} \\ =4.5\text{ in} \end{gathered}[/tex]Therefore, the vertical drop needed for a 18 ft pipe is 4.5 in.
hi I cricled the correct answer but I just need to solve how to get it.
In order to solve this problem we are gonna use a trick that consist in expressing 64 and 16 as powers of 2.
We can write 64 and 16 in the following way:
[tex]\begin{gathered} 64=2^6 \\ 16=2^4 \end{gathered}[/tex]Now, we replace the equations of above in the equation of the statement:
[tex]\begin{gathered} (2^6)^{2x}=2^4 \\ 2^{6\cdot2x}=2^4 \\ 2^{12x}=2^4 \end{gathered}[/tex]In the intermediate steps we have aplied the rule that the powers multiply.
Now, in the last equation, the exponents must be equal if want to have both sides of the equation equal. So:
[tex]\begin{gathered} 12x=4 \\ x=\frac{4}{12}=\frac{1}{3} \end{gathered}[/tex]The correct answer is B
The following sample was obtained from a populationwith unknown parameters. Scores: 13, 7, 6, 12, 0, 4a. Compute the sample mean and standard deviation.(Note that these are descriptive values that sum-marize the sample data.)b. Compute the estimated standard error for M. (Notethat this is an inferential value that describes howaccurately the sample mean represents the un-known population mean.)
a.
The mean of a sample is given by:
[tex]\bar{x}=\frac{\sum_{i=1}^nx_i}{n}[/tex]In this case we have:
[tex]\begin{gathered} \bar{x}=\frac{13+7+6+12+0+4}{6} \\ \bar{x}=\frac{42}{6} \\ \bar{x}=7 \end{gathered}[/tex]Therefore, the mean of the sample is 7
The standard deviation is:
[tex]s=\sqrt{\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2}{n-1}}[/tex]Then we have:
[tex]\begin{gathered} s=\sqrt{\frac{(13-7)^2+(7-7)^2+(6-7)^2+(12-7)^2+(0-7)^2+(4-7)^2}{6-1}} \\ =\sqrt{\frac{36+0+1+25+49+9}{5}} \\ =\sqrt{\frac{120}{5}} \\ =\sqrt{24} \end{gathered}[/tex]Therefore, the standard deviation is √24
b.
The standard error is defined as:
[tex]SE=\frac{s}{\sqrt{n}}[/tex]Then we have:
[tex]SE=\frac{\sqrt{24}}{\sqrt{6}}=\sqrt{\frac{24}{6}}=\sqrt{4}=2[/tex]Therefore, the estimated standard error is 2
What is 4/5 x 5/6 then simplified?
ANSWER
2/3
EXPLANATION
When we have a multiplication of fractions such as this,
[tex]\frac{4}{5}\times\frac{5}{6}[/tex]We can simplify the numerators and denominators before solving the product. In this case, since 5 is in the denominator of the first fraction and also in the numerator of the second fraction, it cancels out,
[tex]\frac{4}{5}\times\frac{5}{6}=\frac{4}{6}[/tex]But note that 4 and 6 are both even numbers - i.e. they are divisible by 2, so by dividing both the numerator and the denominator by 2, we will get the simplified answer,
[tex]\frac{\frac{4}{2}}{\frac{6}{2}}=\frac{2}{3}[/tex]Hence, the product is 2/3.