Answer:
The center of the circle represented by given equation is (−1,3) and its radius is 3.
Explanation:
An equation of the form (x−h)2+(y−k)2=r2, is the equation of a circle of radius r, with a center at (h,k).
Hence as the equation
(x+1)2+(y−3)2=9
⇔(x−(−1))2+(y−3)2=9=32
and hence the center of the circle represented by this equation is (−1,3) and radius is 3.
Answer: just took the test, this is wrong
Step-by-step explanation:
Find the difference between points P (4,6) and Q (8,9)
[tex]distance = \sqrt{x2 - x1 + y2 - y1} \\ here \\ \: \: \: \: x1 = 4 \\ \: \: \: \: x2 = 8 \\ \: \: \: \: y1 = 6 \\ \: \: \: \: y2 = 9 \\ now \: we \: have \: to \: substitute \: the \: given \: values \: in \: the \: above \: formula \\ we \: get \\ \: \: \: \: \: \: = \sqrt{8 - 4 + 9 - 6} \\ \: \: \: \: \: \: = \sqrt{4 + 3} \\ \: \: \: \: \: \: = \sqrt{7} \\ \\ hope \: it \: helped[/tex]
13 different cut flowers and I plan on using 7 of them. How many different selections of the 7 flowers are possible?
Answer:
7/13
Step-by-step explanation:
Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent. What additional information is needed to prove that the triangles are congruent using the AAS congruence theorem? LO ≅ LM OA ≅ MA AngleLOA ≅ AngleLMA AngleLAO ≅ AngleLAM
Answer:
Angle LOA = angle LMA
Step-by-step explanation:
I just took the test
From the diagram, the two triangles have an indication of a pair of
congruent angles.
The additional information needed is; ∠LOA ≅ ∠LMAReasons:
The given parameters of ΔLOA and ΔLAM are;
The shared side of the triangles = Side LA
From the attached diagram, we have;
∠ALO = ∠ALM
Required:
The additional information needed to prove that the triangles are congruent using AAS
Solution:
The AAS congruency is an acronym for Angle Angle Side, which states
that, two triangles are similar if two angles and a non included side of one
triangle are equal to two angles and a non included side on another
triangle, then the two triangles are congruent.
The angle on ΔLOA that will make the side LA a non included side is ∠LOA.
Similarly;
The angle on ΔLAM that will make the side LA a non included side is ∠LMA.
Therefore, the additional information needed to prove that the triangle are congruent using the AAS congruency theorem is; ∠LOA ≅ ∠LMA
Learn more about Angle Angle Side, AAS, rule of congruency here:
https://brainly.com/question/17033697
Two lines intersect and two of the vertical angles measure 37°. What is the measure of the other two vertical angles?
Answer:
286 degrees and 143 degrees
Step-by-step explanation:
When line intersect the two vertical angle adds up to 180 degrees
To find the other vertical angle:
180 -37=143 degrees
So for two vertical angles
we take (180*2)-(37*2)=286 degrees
What is the frequency of the function y=2sin(1/2 x)-3 *
Options::
1
1/2
2π
-3
Answer:
-3
Step-by-step explanation:
y = 2sin (1/2 x 0) -3
y = -3
A store that sells skis buys them from a manufacturer at a wholesale price of $87. The store’s markup rate is 50%
Answer: $130.50
Step-by-step explanation: $87 x .50 = $43.50 / $87 + $43.50 = $130.50
G(x) =19.60 + 1.75x what is the value of g (30) ?
Answer:
72.1
Step-by-step explanation:
G(x) =19.60 + 1.75x
Let x = 30
G(30) =19.60 + 1.75*30
=19.60 +52.5
72.1
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8548 g and a standard deviation of 0.0512 g. A sample of these candies came from a package containing 444 candies, and the package label stated that the net weight is 379.3 g. (If every package has 444 candies, the mean weight of the candies must exceed 379.3/444 = 0.8543 g for the net contents to weigh at least 379.3 g.)
(a) If 1 candy is randomly selected, find the probability that it weighs more than 0.8542g. (Round to four decimal places as needed.)
(b) If 447 candies are randomly selected find the probability that their mean weight is at least 0.8542 g. (Round to four decimal places as needed.)
(c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Answer:
a) 0.5047
b) 0.5978
c) Yes
Step-by-step explanation:
Given:
Mean, u = 0.8548
Standard deviation = 0.0512
Sample mean, X' = 0.8542
a) If 1 candy is randomly selected, the probability that it weighs more than 0.8542 would be:
[tex] z = \frac{X' - u}{\sigma} = \frac{0.8542 - 0.8548}{0.0512} = -0.0117 [/tex]
From standard normal table, NORMSTD(-0.0117) = 0.4953
P(z > -0.0117) = 1 - 0.4953 = 0.5047
Probability = 0.5047
b) If 447 candies are randomly selected the probability that their mean weight is at least 0.8542:
Here, we are to find the probability that the men weight is greater or equal to 0.8542
[tex] z = \frac{X' - u}{\sigma / \sqrt{n}} = \frac{0.8542 - 0.8548}{0.0512/ \sqrt{447}} = -0.24776 [/tex]
From standard normal table, NORMSTD(-0.24776) = 0.40216
P(z > -0.0117) = 1 - 0.40216 = 0.5978
Probability = 0.5978
c) Yes, it seems the candy company is providing consumers with the amount claimed on the label, because the probability of getting a sample mean of 0.8542 or greater when 447 candies are selected is not exceptionally small
A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 51 months and a standard deviation of 11 months. Using the Empirical Rule rule, what is the approximate percentage of cars that remain in service between 73 and 84 months
Answer:
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = 0.02145 = 2.1 %
Step-by-step explanation:
Explanation:-
Given mean of the Population 'μ ' = 51 months
Standard deviation of the Population 'σ' = 11 months
Let 'X' be the random variable of Normal distribution
Let 'X' = 73
[tex]Z = \frac{x-mean}{S.D} = \frac{73-51}{11} = 2[/tex]
Let 'X' = 84
[tex]Z = \frac{84-51}{11} = 3[/tex]
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = P( 2 < Z < 3)
= P( Z<3) - P( Z <2)
= 0.5 + A(3) - ( 0.5 + A(2))
= A(3) - A( 2)
= 0.49865 - 0.4772 ( From Normal table)
= 0.02145
P( 73 < x < 84 ) = 0.02145
The approximate percentage of cars that remain in service between 73 and 84 months
P( 73 < x < 84 ) = 0.02145 = 2.1 %
The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the____
of the triangle
A. Median
B. Angles
C. Sides
D. Vertices
Answer: sides
Step-by-step explanation:
The orthocenter of the triangle will be the intersection of the three altitudes of a triangle. The orthocenter has several vital properties with other parts of a triangle, including the area ,incenter circumcenter and more. Typically, the orthocenter is represented by letter H.
The altitude of a triangle is a line that passes through the vertex of a triangle and it is also perpendicular to the opposite side. The orthocenter of a triangle can lie outside the triangle because an altitude may not necessarily intersect the side.
Suppose we want to choose a value of x within 3 units of 11. [This means a value of x that is less than 3 units away from 11.] Think about some values of x that meet this constraint. Write an inequality that represents all values of x that meet this constraint. On the number line below, represent all values of x that meet this constraint.
Answer:
(a) [8, 14]
(b) [tex]8 \leq x \leq 14[/tex]
(c)See attachment
Step-by-step explanation:
We want to choose a value of x within 3 units of 11.
(a)Now, 11-3=8 and 11+3=14
The possible values of x ranges is in the closed interval [8,14]
(b) Since x is within 3 units of 11., we have:
[tex]|11-x|\leq3[/tex]
Solving the absolute inequality
[tex]-3 \leq 11-x \leq 3\\$In $ -3 \leq 11-x\\ x \leq 11+3\\x \leq 14\\\\$In $ 11-x \leq 3\\ 11-3 \leq x\\8 \leq x\\$Therefore,an inequality that represents all values of x that meet this constraint is:$\\8 \leq x \leq 14[/tex]
(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.
The solution of the inequality is [tex]8\leq x\leq14[/tex]
According to the question, we need to choose a value of x within 3 units of 11. This can be represented by the inequality
[tex]|11-x|\leq3[/tex]
The expression in modulus can be negative or positive:
For the positive inequality
[tex]11-x \leq3\\-x \leq3 -11\\x\geq8\\8\leq x[/tex]
For the negative inequality
[tex]-11+x \leq3\\x \leq3 +11\\x\leq14\\[/tex]
Combining the inequalities
[tex]8\leq x\leq14[/tex]
Hence the solution of the inequality is [tex]8\leq x\leq14[/tex]
Learn more here: https://brainly.com/question/15816805
A poster of area 3840 cm? has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the sides. Find the
dimensions that maximize the printed area.
(Use decimal notation. Give your answers as whole or exact numbers.)
width:
cm
height:
cm
Answer:
Dear user,
Answer to your query is provided below
The dimensions to maximise the printed area to 2160 is length = 100cm and width = 60cm
Step-by-step explanation:
Explanation for the answer is attached in the image
Put this equation into slope-
intercept form.
3x – 2y = 4
Answer:
y= 3/2x -2
Step-by-step explanation:
make y be on one side by itself ( -2y = -3x + 4 )
divide by negative 2 in order to get y by itself ( -2y/-2 = -3/-2 + 4/-2 )
two negatives make a positive ( y = 3/2 + -2 )
According to the National Education Association (NEA), teachers generally spend more than hours each week working on instructional duties (NEA website, April 2012). The following data show the number of hours worked per week for a sample of high school Science teachers and a sample of high school English teachers.
High School Science Teachers: 53 56 54 54 55 58 49 61 54 54 52 53 54
High School English Teachers: 52 47 50 46 47 48 49 46 55 44 47
A. What is the median number of hours worked per week for the sample of 13 high school Science teachers?
B. What is the median number of hours worked per week for the sample of 11 high.
C. Which group has the higher median number of hours worked per week? What is the difference between the median number of hours worked per week?
Answer/Step-by-step explanation:
=>Given the no. of hrs a sample of high school Science and English Teachers spend on instructional duties weekly as follows:
Science teachers: 53 56 54 54 55 58 49 61 54 54 52 53 54
English teachers: 52 47 50 46 47 48 49 46 55 44 47
=>Required:
a. Median number of hours worked by Science teachers weekly:
First step to take is to arrange our given data in ascending order as follows =>
49, 52, 53, 53, 54, 54, (54), 54, 54, 55, 56, 58, 61
Next is to find our median which is the the middle value of our data point = 54
b. Median number of hours worked by English teachers weekly:
First, order the data given as follows =>
44, 46, 46, 47, 47, (47), 48, 49, 50, 52, 55
Next is to find the middle data point = 47
C. The group with the highest median number of hours is Science Teachers = 54 hours per week
The difference in the median number of hours worked per week between both groups = 54 - 47 = 7hours
Can someone help me with this?
Answer:
Step-by-step explanation:
These are mostly calculator problems. The only trick is the last one. Your calculator will have either a y^x button or ^ button. They both do the same thing.
So for the last one, you must do it as
64 y/x (1÷6)= and you will get 2. Perhaps all of them should be done that way.
If your calculator uses ^ then you would do it
64^(1÷6)= which is the same thing.
Answers
a 4
b 10
c 5
d 2
The line whose equation is 3x - 5y = 4 is dilated by a scale factor of 3
centered at the origin. Which statement is correct? *
Answer:
Answer 1.
Step-by-step explanation:
The complete question is:
The line whose equation is 3x - 5y = 4 is dilated by a scale factor of 3 centered at the origin. Which statement is correct?
1. The image of the line has the same slope as the pre-image but a different y-intercept.
2. The image of the line has the same y-intercept as the pre-image but a different slope.
3. The image of the line has the same slope and the same y-intercept as the pre-image.
4. The image of the line has a different slope and a different y-intercept from the pre-image.
Recall that a dilation by a scale factor r centered at the origin takes a point (x,y) and maps it to the point (r*x,r*y).
Consider also a line of equation [tex]ax+by=c[/tex]. From this equation, the slope of the line is given by the number [tex]\frac{-a}{b}[/tex] and the y-intercept is given by [tex]\frac{c}{b}[/tex].
Consider the given equation 3x-5y =4. If we replace (x,y) with (3x,3y), we get
[tex]3(3x)-5(3y) = 4 = 3 (3x-5y) = 4 [/tex]
which is equivalent to
[tex] 3x-5y = \frac{4}{3}[/tex]
Note that comparing the equations 3x-5y=4 and [tex]3x-5y=\frac{4}{3}[/tex] the values of a and b are equal but the value of c is different. This means that they have the same slope but a different y-intercept.
12 m 20 m 16 m 6m 10m x find the length represented by x for each pair of similar triangles
Answer:
x = 8mStep-by-step explanation:
Let the two triangles be represented as A and B.
Given two triangles with sides 12m 20m 16m and 6m 10m x.
Lengths of sides of triangle A = 12m, 20m, 16m
Lengths of sides of triangle B = 6m, 10m, x
It can be seen that each length of triangle A are twice that of B i.e triangle B dilated by a factor of 1/2.
A = 2B
Considering the 16m length in triangle A and comparing it with the 'x'm length in triangle B, we can get the unknown length x as shown;
16 = 2x
x = 16/2
x = 8m
How many ways can Carlos choose 2 pizza toppings from a menu of 4 toppings if each topping can only be chosen once?
Answer:
30 different ways
Step-by-step explanation:
Hi
for the first topping she can choose 1 of 6 items
so she has 6 choices
and then the second topping she has 5 choices as each topping can only be chosen once
so it comes 6 * 5 = 30
A country commits to decreasing spending for infrastructure in various ways at a rate of 30% per year. At the time of the announcement, the country is spending $12 billion per year. Which graph models the amount of infrastructure spending for future years?
Answer:
You want the curve to be decreasing from left to right since they are decreasing the amount spent so we can eliminate options 2 and 3. The initial amount (when x = 0) has to be 12 so the answer is the last option.
Who failed to support civil rights for freed slaves? (wrong category by mistake, not mathematics)
Answer:
The Supreme Court.
Step-by-step explanation:
After the end of the Civil War and the enactment of the Thirteenth Amendment in 1865, slavery was officially abolished in the United States. Thus, the millions of African American slaves that inhabited the southern states of the country won their freedom and equality before the law against whites.
Now this situation began to dismember in 1877, when federal troops left the southern states and Reconstruction officially came to an end. From then on, Democratic governors and legislators began to sanction the Black Codes and Jim Crow Laws, aimed at curtailing the civil and political rights of African-Americans.
This situation was tested before the Supreme Court in 1896 in the case Plessy v. Ferguson. But in the ruling of said case, the Supreme Court established that racial segregation was constitutional and therefore neglected African Americans and their rights.
Jack and Rebecca Pearson just had triplets. They want to have enough money for their
children's college fund. So they decide to deposit $100 at the end of each quarter for 20
years into an account paying 4.2% annual interest compounded quarterly.
a) How much is in the account at the end of 20 years?
b) How much did the Pearsons actually contribute to the college fund account?
c) How much interest did the account earn in those 20 years?
Answer:
a) $12,440.43
b) $8,000.00
c) $4,440.43
Step-by-step explanation:
the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.
a) $12,671.05
b) $8,100
c) $4,571.05
a) $12,440.43
b) $8,000.00
c) $4,440.43
Step-by-step explanation:
the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.
a) $12,671.05
b) $8,100
c) $4,571.05
Please answer this correctly
Answer:
1-5: Make it 1 unit tall
6-10: Make it 4 units tall
11-15: Make it 1 unit tall
16-20: Make it 0 units tall (Change nothing)
21-25: Make it 5 units tall
Step-by-step explanation:
1-5: 1 (1 number)
6-10: 7, 9, 9, 10 (4 numbers)
11-15: 13 (1 number)
16-20: (0 numbers)
21-25: 21, 23, 23, 25, 25 (5 numbers)
DAN Summer 2020
English
Determining an unknown Angle measure
m26 is (2x - 5)' and m 28 is (x + 5)
What is m 23?
1 2
3 4
5 6
78
Dona
Answer:
m∠3 = 115°
Step-by-step explanation:
Since measure of angle 6 = (2x - 5)°
And measure of angle 8 = (x + 5)°
Since ∠6 and ∠8 are the supplementary angles,
m∠6 + m∠8 = 180°
(2x - 5)° + (x + 5)° = 180°
3x = 180°
x = 60°
Therefore, m∠6 = (2x - 5) = (120 - 5) = 115°
and m∠8 = (x + 5) = 65°
Since angle 6 and angle 3 are interior alternate angles,
Therefore, m∠6 = m∠3 = 115° will be the answer.
Find the factorization of the polynomial below.
81x2 - 18x + 1
Answer:
(9x - 1)²
Step-by-step explanation:
If you can tell, the square root of 81 is 9. This should be a clue that the polynomial could be one binomial squared. If you tried factoring starting out with 9x in both parenthesis, you could see that you would get (9x - 1)² as your answer.
Answer:
(9x-1)²
Step-by-step explanation:
81x² - 18x + 1= (9x)²- 2*9x+1²= (9x-1)²
A publisher reports that 41% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually less than the reported percentage. A random sample of 320 found that 36% of the readers owned a laptop. Is there sufficient evidence at the 0.05 level to support the executive's claim? Find the value of the test statistic. Round your answer to two decimal places. Specify if the test is one-tailed or two-tailed. Determine the decision rule for rejecting the null hypothesis, H0. Make the decision to reject or fail to reject the null hypothesis. State the conclusion of the hypothesis test.
Step 1 of 6: State the null and alternative hypotheses.
Answer:
Step-by-step explanation:
Hello!
The objective is to test the claim that less than 41% of the publisher's readers own a laptop.
To do so, a sample of 320 readers was taken and the proportion of readers that own a laptop resulted in 36%
Be X: number of readers that own a laptop.
X~Bi(n;p)
n=320
Sample proportion p'= 0.36
The hypotheses are:
H₀: p ≥ 0.41
H₁: p < 0.41
α: 0.05
[tex]Z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)
[tex]Z_{H_0}=\frac{0.36-0.41}{\sqrt{\frac{0.41(1-0.41)}{320} } }= -1.82[/tex]
This test is one-tailed to the left, meaning, that you'll reject the null hypothesis to small values of Z, there is only one critical value that defined the rejection region:
[tex]Z_{\alpha }= Z_{0.05}= -1.645[/tex]
The decision rule is:
If [tex]Z_{H_0}[/tex] ≤ -1.645, reject the null hypothesis.
If [tex]Z_{H_0}[/tex] > -1.645, do not reject the null hypothesis.
The calculated value is less than the critical value, then the decision is to reject the null hypothesis.
So at a 5% significance level, the test is significant. You can conclude that the population proportion of the publisher's readers that own a laptop is less than 41%.
I hope this helps!
What is the value of a3 - b2 for a=3 and b = 1/2
Answer:
Answer = 26.75
Answer = 27
Step-by-step explanation:
[tex]a^{3} -b^{2} \\a =3\\b =\frac{1}{2} \\3^{3} -(\frac{1}{2} )^{2} \\27 -\frac{1}{4} \\\\\\Answer = 26.75\\Answer = 27[/tex]
Answer:
26 3/4 God bless!
Step-by-step explanation:
Help ?!!!!?!?????????????????
a tree needs to be stake with four wires, each wire is attached to the trunk 6 feet above the ground, and then anchored to the ground 8 feet from the base of the tree. How many feet of the wire is needed for 5 trees???
Answer:
89
Step-by-step explanation:
the correct
9. 5(x - 2) = 15
a. 10
b. 5
c. 1
Answer:
the answer is 5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
5x-10=15
5x=25
x=5
SOMEONE PLEASE HELP ME !! ASAP!!
Answer:
A
Step-by-step explanation:
RT=12
TU=5
RU=12+5=17
RS=17+7=24
SU=√(RS²-RU²)=√(24²-17²)=√(24-17)(24+17)=√(7×41)=√287
area=1/2×12×√287=6×√287≈101.6 unit²