Given a coordinate plane
For each point, we will make a rotation about the origin
A: ( 9, 3) Clockwise by 90
The rule of rotation will be:
[tex](x,y)\rightarrow(y,-x)[/tex]So, the image of A will be A' = ( 3, -9)
B: ( -4, 7 ) counterclockwise 90
the rule of rotation will be:
[tex](x,y)\rightarrow(-y,x)[/tex]So, the image of B will be B' = ( -7, -4)
C: ( 6, -5) by 180
The rule of rotation will be:
[tex](x,y)\rightarrow(-x,-y)[/tex]so, the image of C will be C' = (-6, 5)
D: ( -8, -2) clockwise by 90
So, the image of D will be D' = ( -2, 8)
A committee of six people is chosen from five senators and eleven representatives. How many committees are possiblethere are to be three senators and three representatives on the Committee
SOLUTION
This means we are to select 3 persons from 5 senators and 3 persons from 11 representatives. This can be done by
[tex]^5C_3\times^{11}C_3\text{ ways }[/tex]So we have
[tex]\begin{gathered} ^5C_3\times^{11}C_3\text{ ways } \\ 10\times165 \\ =1650\text{ ways } \end{gathered}[/tex]Hence the answer is 1650 ways
am I correct? Somone please help
Answer:
≠Step-by-step explanation:
7/5 = 1.4
15/10 = 1.5
so 7/5 is not equal to 15/10
the good answer is ≠Find the midpoint for the line segment whose endpoints are (-10,11) and (-1,-15).
Answer:
( -11/2, -2)
Step-by-step explanation:
Finding the midpoint
To find the x coordinate of the midpoint, add the x coordinates of the endpoints and then divide by 2
(-10+-1)/2 = -11/2
To find the y coordinate of the midpoint, add the y coordinates of the endpoints and then divide by 2
(11+-15)/2 = -4/2 = -2
The mid point is ( -11/2, -2)
What is the area of this rectangle?
3
7b ft
7
3
b+21 ft
Step-by-step explanation:
the area of a rectangle is
length × width.
in our case that is
(7/3 × b + 21) × (3/7 × b) =
= 7/3 × 3/7 × b × b + 21 × 3/7 × b =
= 1 × b² + 3×3 × b = b² + 9b = b(b + 9) ft²
so, the area is
b² + 9b = b(b + 9) ft²
remember, an area is always a square "something".
a volume a cubic "something".
so, when the lengths are given in feet, the areas are square feet or ft².
Hi, I always have a hard time with these, the whole question is in the picture.
we have that
x1 ----> number of cars with a 7,000 gal capacity
x2 ---> number of cats with a 14,000 gal capacity
x3 ---> number of cars with a 28,000 gal capacity
so
7000x1+14000x2+28000x3=462000
using a 3x3 system of equations solver
the solution is
x1=-2s-4t+66
x2=s
x3=t
The answer is option B
name the sets of numbers to which the number 62 belongs
62
real numbers (not imaginary or infinity)
rational numbers
Integers ( no fraction, included negative numbers)
Whole numbers (no fraction)
Natural numbers (counting and whole numbers)
(h) through (5,0), y-intercepto 0
We first need to calculate the slope of the line.
m=(0-0)/(5-0)=0 since the slope is equal to zero we have that the line is horizontal.Then the equation is
[tex](y-0)=0(x-0)\Rightarrow y=0[/tex]the equation is y=0
Please answer part a and b questions are in the picture
Part A
we have that
A(4) ----> looking at the graph
A(4) means----> population in the year 1994
so
A(4)----> less than 2 million
and
B(4) -----> greater than 2 million
therefore
the answer Part a is option B
Part B
there is only one value of t where A(t)=B(t)
the value of t is 6 (the year 1996)
Convert degrees to radians:288° = __ πEnter your answer to the tenths place
Given:
[tex]288^{\circ}[/tex]To convert degrees into radians:
We know that,
[tex]\text{Radian}=\theta\times\frac{\pi}{180}[/tex]So, we get
[tex]\begin{gathered} \text{Radian}=288\times\frac{\pi}{180} \\ =\frac{144\pi}{90} \\ =\frac{16\pi}{10} \\ =\frac{8\pi}{5} \end{gathered}[/tex]Thus, the answer is,
[tex]\frac{8\pi}{5}[/tex]Find the percent change to the nearest percent for the function following
f(x) = 3(1 -.2)^-x
The percentage change of the function given in the task content as required is; 20%.
Percent change in exponential functions.It follows from the task content that the percentage change of the function is to be determined.
The percentage change in exponential functions is represented by the change factor, an expression on which the exponent is applied.
On this note, since the function given is an exponential function in which case, the change factor is; (1 - .2).
It consequently follows that the change implies a 20% decrease. This follows from the fact that 20% is equivalent to; 0.2.
Ultimately, the percentage change of the function is; 20%.
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Using the origin as the center of dilation and a scale factor of k=1/2 find the coordinates of the vertices of the image of the polygon below
Given
Using the scale of 1/2
This means we divide each coordinate by 2
[tex]\begin{gathered} (0,3)=(0,1.5) \\ (-4,0)=(-2,0) \\ (2,0)=(1,0) \\ (0,-3)=(0,-1.5)_{} \end{gathered}[/tex]es26. Name the relationship between the anglesand solve for x.12x + 417x + 2
From the given figure, we can see that the angle (12x+4) and the angle (17x+2) lie on the same straight line.
Theerfore, they are supplimentary to each other.
Write the following phrase as a variable expression. Use x to represent “a number” The sum of a number and fourteen
we can write "the sum of a number and fourteen", given that x represents any number, like this:
[tex]x+14[/tex]From the diagram below, if side AB is 36 cm., side DE would be ______.
Given
AB = 36 cm
Find
Side DE
Explanation
here we use mid segment theorem ,
this theorem states that the mid segment connecting the mid points of two sides of a triangle is parallel to the third side of the triangle and the length of the midsegment is half the length of the third side.
so , DE = 1/2 AC
DE = 36/2 = 18 cm
final Answer
therefore , the correct option is c
Write a word problem to fit the following rates: 72 tokens/12 games, ◾️ tokens/10 games
We have to write a word problem using,
• 72 tokens/12 games
,• tokens/10 games
We can first give an information related to 72 tokens PER 12 games.
Then we can ask "how many tokens" per 10 games.
Let us devise a word problem.
The local game center sells tokens to play online games. Jeremy used 72 token to play 12 online games. At this rate, how many token would Jeremy use to play 10 online games?
The above problem uses both the information provided.
find the point that is symmetric to the point (-7,6) with respect to the x axis, y axis and origin
Answer:
[tex]\begin{gathered} a)(-7,-6)\text{ } \\ b)\text{ (7,6)} \\ c)\text{ (7,-6)} \end{gathered}[/tex]Explanation:
a) We want to get the point symmetric to the given point with respect to the x-axis
To get this, we have to multiply the y-value by -1
Mathematically, we have the symmetric point as (-7,-6)
b) To get the point that is symmetric to the given point with respect to the y-axis, we have to multiply the x-value by -1
Mathematically, we have that as (7,6)
c) To get the point symmetric with respect to the origin, we multiply both of the coordinate values by -1
Mathematically, we have that as:
(7,-6)
In July, Lee Realty sold 10 homes at the following prices: $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000. Calculate the mean and median.
The mean is 143000 and Median is 141000 for data $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000.
What is Statistics?A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data
The mean is give by sum of n numbers to the total number of observations
Mean=Sum of observations/ Number of observations
Given,
10 homes at the following prices: $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000.
Sum of observations=$140,000+$166,000+$80,000+$98,000+ $185,000+$150,000+ $108,000+$114,000+$142,000+ $250,000=1433000
n=10
Mean=1433000/10=143000
So mean is 143000
Now let us find the median, Median is the middle most number.
First we have to arrange the observation in ascending order.
$80,000, $98,000, $108,000, $114,000, $140,000, $142,000, $150,000, $166,000, $185,000, $250,000
Now Median= ($140,000+$142,000)/2
=282000/2=141000
Hence Mean is 143000 and Median is 141000.
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which description compass the domains of function a and function be correctly rest of the information in the picture below please answer with the answer choices
Given:
Function A: f(x) = -3x + 2
And the graph of the function B
We will compare the domains of the functions
Function A is a linear function, the domain of the linear function is all real numbers
Function B: as shown in the figure the graph starts at x = 0 and the function is graphed for all positive real numbers So, Domain is x ≥ 0
So, the answer will be the last option
The domain of function A is the set of real numbers
The domain of function B: x ≥ 0
you decide to work part time at a local supermarket. The job pays $14.50 per hour and you work 24 hours per week. Your employer withhold 10% of your gross pay for federal taxes, 7.65% for FICA taxes and 3% for state taxes. Complete parts a through F
The gross pay that the employee will get is $276.14.
How to calculate the amount?The job regarding the question pays $14.50 and the person works 24 hours per week. The weekly pay will be:
= 24 × $14.50
= $348
Also, the employer withhold 10% of your gross pay for federal taxes, 7.65% for FICA taxes and 3% for state taxes. Therefore, the gross pay will be:
= Weekly pay - Federal tax - Fica tax - state tax
= $348 - (10% × $348) - (7.65% × $348) - (3% × $348)
= $348 - $34.80 - $26.62 - $10.44
= $276.14
The pay is $276.14.
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Which expression is equivalent to cot2B(1 – cos-B) for all values of ß for which cot2B(1 - cos2B) is defined?
From the Pythagorean identity,
[tex]\sin ^2\beta+\cos ^2\beta=1[/tex]we have
[tex]\sin ^2\beta=1-\cos ^2\beta[/tex]Then, the given expression can be rewritten as
[tex]\cot ^2\beta\sin ^2\beta\ldots(a)[/tex]On the other hand, we know that
[tex]\begin{gathered} \cot \beta=\frac{\cos\beta}{\sin\beta} \\ \text{then} \\ \cot ^2\beta=\frac{\cos^2\beta}{\sin^2\beta} \end{gathered}[/tex]Then, by substituting this result into equation (a), we get
[tex]\begin{gathered} \frac{\cos^2\beta}{\sin^2\beta}\sin ^2\beta \\ \frac{\cos ^2\beta\times\sin ^2\beta}{\sin ^2\beta} \end{gathered}[/tex]so by canceling out the squared sine, we get
[tex]\cos ^2\beta[/tex]Therefore, the answer is the last option
The lengths of adult males' hands are normally distributed with mean 189 mm and standard deviation is 7.4 mm. Suppose that 15 individuals are randomly chosen. Round all answers to 4 where possible.
a. What is the distribution of ¯x? x¯ ~ N( , )
b. For the group of 15, find the probability that the average hand length is less than 191.
c. Find the first quartile for the average adult male hand length for this sample size.
d. For part b), is the assumption that the distribution is normal necessary? No Yes
Considering the normal distribution and the central limit theorem, it is found that:
a) The distribution is: x¯ ~ N(189, 1.91).
b) The probability that the average hand length is less than 191 is of 0.8531 = 85.31%.
c) The first quartile is of 187.7 mm.
d) The assumption is necessary, as the sample size is less than 30.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]. The mean is the same as the population mean.For sample size less than 30, such as in this problem, the assumption of normality is needed to apply the Central Limit Theorem.The parameters in this problem are given as follows:
[tex]\mu = 189, \sigma = 7.4, n = 15, s = \frac{7.4}{\sqrt{15}} = 1.91[/tex]
Hence the sampling distribution of sample means is classified as follows:
x¯ ~ N(189, 1.91).
The probability that the average hand length is less than 191 is the p-value of Z when X = 191, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (191 - 189)/1.91
Z = 1.05
Z = 1.05 has a p-value of 0.8531, which is the probability.
The first quartile of the distribution is X when Z has a p-value of 0.25, so X when Z = -0.675, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.675 = (X - 189)/1.91
X - 189 = -0.675 x 1.91
X = 187.7 mm.
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during happy hour appetizers are at 30% off how much would each appetize your cost show the original price your math and discounted price
EXPLANATION
Let's see the facts:
Appetizers = 30%
The discount price is given by the following equation:
Discount percentage=
Could you send me a screenshot of the question for better understanding, please?
Fill in each blanks so that the resulting statement is true
The next step is to subtract -21x from 9x, which obtains 30x.
Then bring down -2 and form the new dividend 30x - 2
Explanation:Given:
[tex]\frac{9x^2+9x\text{ - 2}}{3x\text{ - 7}}[/tex]To determine the next step in the division, we need to solve the long division:
From our calculation, we subtract -21x from +9x and this gives 30x. We bring down -2 to combine with 30x. The result is 30x - 2
The next step is to subtract -21x from 9x, which obtains 30x.
Then bring down -2 and form the new dividend 30x - 2
you are running a fuel economy study. one of the cars you find where blue
Answer:
Explanation:
For Blue Car:
Distance = 33 & 1/2 miles
Gasoline = 1 & 1/4 gallons
For Red Car:
Distance = 22 & 2/5 miles
Gasoline = 4/5 gallon
To determine the rate unit rate for miles per gallon for each car, we use the following formula:
[tex]Unit\text{ Rate = }\frac{\text{Distance}}{\text{Gasoline consumption}}[/tex]First, we find the unit rate for blue car:
[tex]\begin{gathered} \text{Unit Rate=}\frac{33\text{ }\frac{1}{2}\text{ miles}}{1\text{ }\frac{1}{4}\text{ gallons}} \\ \end{gathered}[/tex]Convert mixed numbers to improper fractions: 33 & 1/2 = 67/2 and 1 & 1/4 = 5/4
[tex]\begin{gathered} \text{Unit Rate = }\frac{\frac{67}{2}}{\frac{5}{4}} \\ \text{Simplify and rearrange:} \\ =\frac{67(4)}{2(5)} \\ \text{Calculate} \\ =\frac{134\text{ miles}}{5\text{ gallon}}\text{ } \\ or\text{ }26.8\text{ miles/gallon} \end{gathered}[/tex]Next, we find the unit rate for red car:
[tex]\begin{gathered} \text{Unit Rate = }\frac{22\frac{2}{5}}{\frac{4}{5}} \\ \text{Simplify and rearrange} \\ =\frac{\frac{112}{5}}{\frac{4}{5}} \\ =\frac{112(5)}{5(4)} \\ \text{Calculate} \\ =28\text{ miles/gallon} \end{gathered}[/tex]Therefore, the car that could travel the greater distance on 1 gallon of gasoline is the red car.
The price of Stock A at 9 A.M. was $15.21. Since then, the price has been increasing at the rate of $0.07 each hour. At noon the price of Stock B was $15.96. It begins to decrease at the rate of $0.15 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the same?
The price of the two stocks will be same in 1 hours .
in the question ,
it is given that
the price of the stock A at 9 A.M is $15.21
price increases at the rate of 0.07 each hour .
so the price of the stock A at 12 P.M. is 15.21 + 0.21 = $15.42
and the price of the stock A after x hours from 12 P.M. is given by the equation
stock A = 15.42 + 0.07(x)
the price of stock B at 12 P.M. is $15.96
price decreases at the rate of 0.15 each hour .
the price of the stock B after x hours from 12 P.M. is given by the equation
stock B = 15.96 - 0.15(x)
since the price of the two stocks is same , we equate both the equations .
15.42 + 0.07(x) = 15.96 - 0.15(x)
15.42 + 0.07x = 15.96 - 0.15x
0.15x + 0.07x = 15.42 - 15.21
0.22x = 0.21
x = 0.9545
x ≈ 1
Therefore , The price of the two stocks will be same in 1 hours .
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Here is a list of questions about the students and teachers at a school. Select the questions that are statistical questions.
As observed, all the questions in the list can be answered on the basis of some data collection and analysis.
So they all can be considered as statistical questions.
Thus, all the questions in the given list are statistical questions.
1.
If you have to answer the question for most popular lunch choice, you have to collect data of the lunch choices by a large portion of the called population. Then the lunch choice corresponding to highest frequency will be considered as the most popular lunch choice. Since the conclusion is data driven, this is a statistical question.
2.
In order to answer the question, you need to collect the information about the name of school each of the called population is admitted to. If all the students are found to be admitted to the same school, then the name of that school would be the answer.
Here also, the conclusion is data driven, so this is also a statistical question.
3.
To answer this question, you have to gather all the teaching staff of the school, and take individual answers to which subject they teach. The number of teachers who answered math will be the answer for this question.
Here also, the conclusion is data driven, so this is also a statistical question.
4.
To answer this question, you have to gather the individual age of each teacher in the school. The age corresponding to the maximum frequency would be the answer to this question.
Here also, the conclusion is data driven, so this is also a statistical question.
5.
To answer this question, you have to collect data about how much sleep each student gets in the school. Then only you can answer this question.
Since the conclusion is data driven, this is a statistical question.
6.
To answer this question, you have to collect data that how many students travel by which mode of transport to travel from home to school. The mode corresponding to highest frequency is the answer to this question.
Here also, the conclusion is data driven, so this is also a statistical question.
Thus, it is seen that all the six questions are statistical questions.
How do you solve letter b using a subtraction equation with one variable that has a solution of 2/3. A step by step guide would be helpful.
Let's set x as the variable that has a solution of 2/3.
A possible equation is:
[tex]1-x=y[/tex]Now, in order to know the y-value, replace the x-value=2/3 and solve for y:
[tex]\begin{gathered} 1-\frac{2}{3}=y \\ we\text{ can replace 1 by 1/1} \\ \frac{1}{1}-\frac{2}{3}=y \\ \text{The subtraction of fractions can be solved as} \\ \frac{1\times3-1\times2}{1\times3}=y \\ \frac{3-2}{3}=y \\ \frac{1}{3}=y \end{gathered}[/tex]Now, replace the y-value in the initial equation, and we obtain:
[tex]1-x=\frac{1}{3}[/tex]If you solve this equation, you will get x=2/3.
Triangle FGH is similar to triangle IJK. Find the measure of side JK. Round youranswer to the nearest tenth if necessary.
Let x be the measure of JK so we get that
[tex]\frac{23}{5}=\frac{x}{3.5}\rightarrow x=3.5\cdot\frac{23}{5}=16.1[/tex]What is the intermediate step in the form (x+a)^2=b(x+a)
2
=b as a result of completing the square for the following equation?
x^2+6x+19=4x
The intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method is (x + (√3 - 2)/2)² = 77/4.
The standard form of a quadratic equation.In Mathematics, the standard form of a quadratic equation is given by:
ax² + bx + c = 0.
In this exercise, you're required to determine the intermediate step in the form (x + a)² = b when you solve the given quadratic equation by using completing the square method. Therefore, we would re-write the quadratic equation by subtracting 19 from both sides as follows:
x² + 6x + 19 = 4x
x² + 6x + 19 - 19 = 4x - 19
x² + 6x = 4x - 19
x² + 6x - 4x = 19
x² + 2x = 19
In order to complete the square, we would have to add (half the coefficient of the x- term)² to both sides of the quadratic equation as follows:
x² + 2x + (1/2)² = 19 + (1/2)²
x² + 2x + 1/4 = 19 + 1/4
(x + (√3 - 2)/2)² = 77/4
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Complete Question:
What is the intermediate step in the form (x + a)² = b as a result of completing the square for the following equation?
x² + 6x + 19 = 4x
Growing up, Mrs. Reeder's favorite book was THE ADVENTURES of TOM SAWYER.Now that she is a teacher, she buys 25 copies to read with her class. If each book coast $7.19, how much does Mrs. Reeder spend?
According to the given data we have the following:
Total copies she buys= 25 copies
book cost=$7.19
Therefore, in order to calculate the amount of money that Mrs. Reeder spend we would have to make the following calculation:
Amount of money that Mrs. Reeder spend= quantity of copies * book cost
Amount of money that Mrs. Reeder spend=25 copies*$7.19
Amount of money that Mrs. Reeder spend=$180
The amount of money that Mrs. Reeder spend was $180