Answer:
Option C) is correct
Step-by-step explanation:
Given: Endpoints of the diameter of the circle are A(-1, -2) and B(3,10)
To find: slope of the tangent drawn to the circle at point B
Solution:
Let [tex](x_1,y_1)=(-1,-2)\,,\,(x_2,y_2)=(3,10)[/tex]
Centre of the circle = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{-1+3}{2},\frac{-2+10}{2})=(1,4)[/tex]
Let [tex](h,k)=(1,4)[/tex]
Distance formula states that distance between points (a,b) and (c,d) is given by [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex]
Radius of the circle = Distance between points [tex](-1,-2)[/tex] and [tex](1,4)[/tex] = [tex]\sqrt{(1+1)^2+(4+2)^2}=\sqrt{4+36}=\sqrt{40}[/tex] units
Let r = [tex]\sqrt{40}[/tex] units
Equation of a circle is given by [tex](x-h)^2+(y-k)^2=r^2[/tex]
[tex](x-1)^2+(y-4)^2=\left ( \sqrt{40} \right )^2\\(x-1)^2+(y-4)^2=40[/tex]
Differentiate with respect to x
[tex]2(x-1)+2(y-4)\frac{\mathrm{d} y}{\mathrm{d} x}=0\\\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{1-x}{y-4}[/tex]
Put [tex](x,y)=(3,10)[/tex]
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{1-3}{10-4}=\frac{-2}{6}=\frac{-1}{3}[/tex]
So,
slope of the tangent drawn to this circle at point B = [tex]\frac{-1}{3}[/tex]
How many solutions does the equation –2(3x – 1) = –6x – 1 have?
What about 2(3x – 1) = 6x – 2?
What about 2(3x – 1) = –6x – 2?
Answer: See below
Step-by-step explanation:
–2(3x – 1) = –6x – 1
-6x + 2 = -6x - 1 (IMPOSSIBLE, ZERO)
2(3x – 1) = 6x – 2
6x - 2 = 6x - 2 (INFINITE)
2(3x – 1) = –6x – 2
6x - 2 = -6x - 2 (ONE, x can be the number 0)
Apple would like to estimate the web browsing battery life of the iPad. The following data represents the battery life, in hours, experienced by six users.
10 14 14 16 13 8
Using this sample, the point estimate for the web browsing battery life of the iPad is:________
Answer:
12.5 hours
Step-by-step explanation:
The data which represents the battery life, in hours, experienced by six users is given below:
10 14 14 16 13 8
To determine the point estimate for the web browsing battery life of the iPad, we find the mean number of hours.
[tex]Mean=\dfrac{10+14+14+16+13+8}{6} \\\\=\dfrac{75}{6} \\\\=12.5[/tex]
The point estimate for the web browsing battery life of the iPad is: 12.5 hours
Watch help video
Find the distance between the two points rounding to the nearest tenth (if necessary).
(4,4) and (-2,-4)
Answer:
1
Submit Answer
attempt 1 out of 2
Answer:
10
Step-by-step explanation:
Using the distance formula, the distance is ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = √((-2-4)^2 +(-4-4)^2) = √((-6)^2 +(-8)^2) = √(36 +64)
d = √100 = 10
The distance between the two points is 10 units.
Help ill give you brainliest and points !!!!!
Answer:
1.12
2.85
3.60
Step-by-step explanation:
1.
if m = 12 you solve by dividing 144/12
144/12 = 12
2.
when m = 11 you solve by computing 7(11) + 8
7(11) = 77 so you solve from there 77 + 8 which equals 85
3.
When g = 4 you solve my multiplying 15(4)
15(4) = 60
Answer:
first question: 12
second question: 85
third question: 60
Step-by-step explanation:
first question: plug in 12 for m and you would get 144/12 which equals 12.
Second question: plug in 11 for m and you have 7(11) + 8.
77+8 = 85
third question: plug in 4 for g and you have 15(4)
15 x 4 = 60.
*parentheses mean multiplication when next to a number
ex: 7(11)
not ex: 3 + (2/3) since it isn't directly next to the first number, instead its adding
What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?
3
4
Ο Ο Ο Ο
5
9
Answer:
The answer is 4
Step-by-step explanation:
1.5(4+4)-3= 9
4.5(4-2)=9
9=9
Answer:
[tex]x=4[/tex]
Explanation:
[tex]1.5x+6+-3=4.5x+-9\\1.5x+3=4.5x-9\\-3x+3=-9\\-3x=-12\\x=4[/tex]
Line segment Q R , Line segment R S are Line segment S Q midsegments of ΔWXY. Triangle R Q S is inside triangle X Y W. Point R is the midpoint of side X Y, point S is the midpoint of side Y W, and point Q is the midpoint of side X W. The length of Q R is 2.93 centimeters, the length of R S is 2.04 centimeters, and the length of Q S is 2.28 centimeters. What is the perimeter of ΔWXY? 11.57 cm 12.22 cm 12.46 cm 14.50 cm
Answer:
14.50 cm
Step-by-step explanation:
The Midsegment Theorem states that the midsegment connecting the two sides of a triangle is parallel to the third side, and its length is half that of the third side.
Thus, ∆XYZ is similar to ∆QRS with a scale factor of 2.
Also, the perimeter of ∆XYZ is twice that of ∆QRS.
For ∆QRS, P = 2.93 cm + 2.04 cm + 2.28 cm = 7.25 cm
∴ The perimeter of ∆XYZ = 2 × 7.25 cm =14.50 cm
The Perimeter of triangle WXY is 14.5cm
The formula for calculating the perimeter of the triangle WXY is given as:
Perimeter of triangle WXY = XY + YZ + XY
From the given triangle;
QR = 2.93cmQS = 2.28cmRS = 2.04cmAlso,
XR = RY = QR = 2.93cmZS = SY = QS = 2.28cmZQ = QX = RS = 2.04cmPerimeter of triangle WXY = 2QR + 2QS + 2RS
Perimeter of triangle WXY = 2(2.93) + 2(2.28) + 2(2.04)
Perimeter of triangle WXY = 5.86 + 4.56 + 4.08
Perimeter of triangle WXY = 14.5cm
Hence the Perimeter of triangle WXY is 14.5cm
Learn more on perimeter of triangles here: https://brainly.com/question/24382052
What is the y value?
Answer:
y =34
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
63+ 2y+ y+15 = 180
Combine like terms
78+ 3y = 180
Subtract 78 from each side
78+3y-78 = 180-78
3y = 102
Divide each side by 3
3y/3 = 102/3
y =34
Answer:
[tex]y = 34[/tex]
Step-by-step explanation:
Sum of the angles in a triangle is 180 degrees
[tex]2y + 63 + y + 15 = 180 \\ 3y + 63 + 15= 180 \\ 3y +7 8 = 180 \\ 3y = 180 - 78 \\ 3y =10 2 \\ \frac{3y}{3} = \frac{102}{3} \\ y = 34 [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The tree diagram represents an
experiment consisting of two trials.
.4
.5
.6
D
.3
С
.5
.7
D
Þ(B and D) = [?]
ter
Answer:
0.35
Step-by-step explanation:
.5x.7
(3xy)*x*у
х
Зуз
Зхуз
9xуз
9x5уз
Answer:
3 x^2 y^2
Step-by-step explanation:
Simplify the following:
3 x y x y
3 x y x y = 3 x^2 y^2:
Answer: 3 x^2 y^2
Which inequality represents the sentence below? Four and nine tenths less than the product of a number and six is no more than eighteen and one-eighth. 4 and StartFraction 9 over 10 EndFraction minus 6 x less-than-or-equal-to 18 and StartFraction 1 over 8 EndFraction 6 x minus 4 and StartFraction 9 over 10 EndFraction less-than-or-equal-to 18 and StartFraction 1 over 8 EndFraction 4 and StartFraction 9 over 10 EndFraction less-than 6 x + 18 and StartFraction 1 over 8 EndFraction 6 x minus 4 and StartFraction 9 over 10 EndFraction less-than 18 and StartFraction 1 over 8 EndFraction
Answer:
D. 6x-4 9/10<= 18 1/8
Step-by-step explanation:
Sorry I'm a little late :(
Please answer this correctly
72+72+36= 144+36= 180
Answer:
Area of the figure = 176 m²
Step-by-step explanation:
Area of Rectangle = Length × Width
Dividing the whole figure
Rectangle 1:
6 × 18 = 108 m²
Rectangle 2 :
10 × 6 = 60 m²
Rectangle 3:
2 × 4 = 8 m²
Adding All
Area of the figure = 108 + 60 + 8
Area of the figure = 176 m²
Solve the following equation using the quadratic formula: 3(x+4)2 - 81 = 0
Answer:
[tex]-4\pm 3\sqrt{3}[/tex]
Step-by-step explanation:
[tex]3(x+4)^2-81=0 \\\\3(x^2+8x+16)-81=0 \\\\3x^2+24x+48-81=0 \\\\3x^2+24x-33=0 \\\\x=\dfrac{-24\pm\sqrt{24^2+4(3)(33)}}{2(3)}= \\\\\dfrac{-24\pm\sqrt{972}}{6}= \\\\\dfrac{-24\pm 18\sqrt{3}}{6}= \\\\-4\pm 3\sqrt{3}[/tex]
Hope this helps!
Twenty students from Sherman High School were accepted at Wallaby University. Of those students, eight were offered military scholarships and 12 were not. Mr. Dory believes Wallaby University may be accepting students with lower SAT scores if they have a military scholarship. The newly accepted student SAT scores are shown here.
Military scholarship: 850, 925, 980, 1080, 1200, 1220, 1240, 1300
No military scholarship: 820, 850, 980, 1010, 1020, 1080, 1100, 1120, 1120, 1200, 1220, 1330
Part A: Do these data provide convincing evidence of a difference in SAT scores between students with and without a military scholarship? Carry out an appropriate test at the α = 0.05 significance level.
Part B: Create and interpret a 95% confidence interval for the difference in SAT scores between students with and without a military scholarship.
Answer:
Step-by-step explanation:
For military scholarship,
Mean, x1 = (850 + 925 + 980 + 1080 + 1200 + 1220 + 1240 + 1300)/8
x1 = 1099.375
Standard deviation = √(summation(x - mean)²/n
n1 = 8
Summation(x - mean)² = (850 - 1099.375)^2 + (925 - 1099.375)^2 + (980 - 1099.375)^2 + (1080 - 1099.375)^2 + (1200 - 1099.375)^2 + (1220 - 1099.375)^2 + (1240 - 1099.375)^2 + (1300 - 1099.375)^2 = 191921.875
Standard deviation, s1 = √(191921.875/8
s1 = 154.89
For no military scholarship,
Mean, x2 = (820 + 850 + 980 + 1010 + 1020 + 1080 + 1100 + 1120 + 1120 + 1200 + 1220 + 1330)/12
x2 = 1070.83
Standard deviation = √(summation(x - mean)²/n
n2 = 12
Summation(x - mean)² = (820 - 1070.83)^2 + (850 - 1070.83)^2 + (980 - 1070.83)^2 + (1010 - 1070.83)^2 + (1020 - 1070.83)^2 + (1080 - 1070.83)^2 + (1100 - 1070.83)^2 + (1120 - 1070.83)^2 + (1120 - 1070.83)^2 + (1200 - 1070.83)^2 + (1220 - 1070.83)^2 + (1330 - 1070.83)^2 = 238091.6668
Standard deviation, s2 = =√(238091.6668/12
s2 = 140.86
Part A)
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean score of students with military scholarship and μ2 be the mean score of students without military scholarship.
The random variable is μ1 - μ2 = difference in the mean score between students with military scholarship and without military scholarship
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (1099.375 - 1070.83)/√(154.89²/8 + 140.86²/12)
t = 0.42
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [154.89²/8 + 140.86²/12]²/[(1/8 - 1)(154.89²/8)² + (1/12 - 1)(140.86²/12)²] = 21644133.914878543/1533280.3458504018
df = 14
We would determine the probability value from the t test calculator. It becomes
p value = 0.68
Since alpha, 0.05 < than the p value, 0.68, then we would fail to reject the null hypothesis. Therefore, at a significance level of 5%, these data do not provide convincing evidence of a difference in SAT scores between students with and without a military scholarship
Part B)
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 95% confidence interval, we would determine the z score from the t distribution table because the number of samples are small
Degree of freedom =
(n1 - 1) + (n2 - 1) = (8 - 1) + (12 - 1) = 18
z = 2.101
x1 - x2 = 1099.375 - 1070.83 = 28.545
Margin of error = 2.101√(154.89²/8 + 140.86²/12) = 143.3
The 95% confidence interval is 28.545 ± 143.3
Need help ASAP thank you!!!
Answer:
= 180 yd^3
Step-by-step explanation:
The volume of a triangle prism is
V= Bh where B is the area of the base
B = area of the triangle
= 1/2 *8* 5
= 20 yd^2
V = 20 yd^2 * 9 yd
= 180 yd^3
What’s the correct answer for this?
Answer:
B
Step-by-step explanation:
OP = OQ
Answer:
B
Step-by-step explanation:
Look at the shape closely observe the following the imaginary lines;
OC = OA , OB = OD {these is the raduis of the circle;
note also line CQ = CD { the perpendicular line bisects line CD in two equal halves;
Similarly ;
note also line AP= PB { the perpendicular line bisects line OP in two equal halves}
Hence;
OP is congruent to the OQ
In maths we say something is congruent when they are the same shape and have same angles but we are allowed to flip it's side.
George is curious. He has been told that the average body temperature of humans is 98.6 degrees Fahrenheit. However, he believes it is much lower than that. He randomly selects 60 people from those passing by him on a street and takes their temperature. The average temperature of these 60 people is 98.2 degrees Fahrenheit. The standard deviation, sigma Subscript x,is known to be 0.62 degrees Fahrenheit. The p-value is less than 0.0001. What is the correct conclusion?
Answer:
[tex]p_v =P(t_{(59)}>t_{calc})<0.0001[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.
Step-by-step explanation:
Information given
[tex]\bar X=98.2[/tex] represent the sample mean
[tex]\sigma=0.62[/tex] represent the population standard deviation
[tex]n=60[/tex] sample size
[tex]\mu_o =98.6[/tex] represent the value that we want to test
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the true mean is equal to 98.6 F, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 98.6[/tex]
Alternative hypothesis:[tex]\mu \neq 98.6[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
The degrees of freedom, on this case:
[tex]df=n-1=60-1=59[/tex]
The p value would be given by:
[tex]p_v =P(t_{(59)}>t_{calc})<0.0001[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis and we can conclude that the true mean for this case is significantly different from 98.6 F at any usual significance level used.
A community center sells a total of 305 tickets for a basketball game. An adult ticket costs $5. A student ticket costs $1. The sponsors collect $693 in ticket sales. Find the number of each type of ticket sold.
Answer: student tickets = 208
Adult tickets = 97
Step-by-step explanation:
x + y = 305
x = 305 - y
5x + y = 693
Substituting
5 (305 - y) + y = 693
1525 - 5y + y = 693
-4y = -832
y = 832 / 4 = 208
The sum of two numbers is 41. One number is 1 less than the other.
Answer:
s must be 21 and r is 20
Step-by-step explanation:
Represent the two numbers using variables r and s.
Then r + s = 41, and r = s - 1
Substituting the 2nd equation for r into the first equation, we get:
s - 1 + s = 41, or 2s = 42. Then s must be 21 and r is 20.
Find the area of the trapezoid with the numbers 4, 3, 3 ,1
Answer:
The answer depends on the shape of the trapezoid...
Step-by-step explanation:
A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. (trapezium)
Area = (a+b/2) * h
IF the sides are a = 3 ,b = 3 and height = 4
THEREFORE:
(3+3/2) * 4
6/2 * 4
3 * 4
12
Hope it helped.... Please mark as brainliest..thanks!!!
A researcher was interested about the weekly average usage of a local park in San Antonia, Texas. A study was designed to study the relationship between age and number of times residents visited the park each week. They were interested to see if age tends to impact the number of times residents visit the park. The surveyor collected responses information about age and the number of visits per week from 118 residents of San Antonia, Texas. They provided them with an anonymous paper survey to fill out.
Required:
a. What are the observational units in this study?
b. Is number of visits per week the explanatory or response variable?
c. Is age the explanatory or response variable?
d. Is this an observational study or a randomized experiment?
e. What is the most concerning type of bias in this study? Why?
f. What is the appropriate scope of inference in this study
Answer:
a) Residents of San Antonia, Texas
b) Response variable
c) Explanatory variable
d) Observational study
e) Response bias
f) The appropriate scope of interest is the " relationship between age and the weekly average usage of local parks in San Antonia"
Step-by-step explanation:
a) In this study, the objects or entities on which observation is done are the residents of San Antonia, hence they are the observational units.
b) In this observation, the number of visits per week is the response variable because it is the outcome of the observation. It is a dependent variable that varies due to variation in the ages.
c) Age is the variable that helps to predict the average number of visits to the park, it can then be called the predictor variable. It is independent of any external variable.
d) This is an observational study because it is meant to observe the relationship between the ages and the average number of visits to the park per week. The variables are not randomly assigned.
e ) The type of bias that is most concerning in this study is response bias. This is because it is a paper survey and their can be invalid responses either due to unfaithfulness or ignorance of the respondents.
f) The appropriate scope of the inference in this study is the relationship between the ages and the weekly average usage of local parks in San Antonia.
2.1.40: The police records of a city contain the following statistics on offenses for the month of May: 430 assaults, 146 robberies, and 131 drug sales. The records also show that 26 people were involved in both assault and robbery and that 33 people were involved in both assault and drug sales. What is the greatest possible number of offenders for May who satisfy these statistics
Answer:
648
Step-by-step explanation:
Number of Assaults, n(A)=430
Number of Robberies, n(R)=146
Number of Drug Sales Offenses, n(D)=131
Number involved in both assault and robbery= [tex]n(A\cap R)=26[/tex]
Number involved in both assault and drug sales= [tex]n(A\cap D)=33[/tex]
Therefore, to find the greatest possible number of offenders for May who satisfy these statistics, we remove the number of those who were involved in more than one crime.
This gives us:
[tex]=n(A)+n(R)+n(D)-n(A\cap R)-n(A\cap D)\\=430+146+131-26-33\\=648[/tex]
The greatest possible numbers of offenders in May is 648.
What is the square root of -1
Answer:
i
Step-by-step explanation:
It's imaginary, or it can also be referred to as i.
You are shopping online for a new TV. The one you want costs $2,500. You live in New York where the state sales tax rate is 8.49%. Your sister lives a short distance over the border in CT where the state sales tax rate is 6.35%. If you have the TV shipped to her and you pick it up. How much will you save?
Answer:
$5350
Step-by-step explanation:
see attachment
Answer:
Its 53.50
Step-by-step explanation:
What is the range of a function?
Answer:
The set of all output values of a function. Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then the range is {1,4,9,...}
Solve (x + 1)2 - 4(x + 1) + 2 = 0 using substitution.
U=
х
4(x +1)
O x +1
(x + 1)2
Answer:
Step-by-step explanation:
We are given the equation [tex](x+1)^2-4(x+1)+2=0[/tex]. Consider the substitution u = (x+1). Then the equation turns out to be [tex]u^2-4u+2=0[/tex]
Recall that given a second degree polynomial of the form [tex]ax^2+bx+c =0[/tex] then its solutions are given by the expression
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In our case, a = 1, b = -4 and c =2. Then the solutions are
[tex]u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}[/tex]
[tex]u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}[/tex]
We have that x = u-1. So the original solutions are
[tex]x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}[/tex]
[tex]x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}[/tex]
Answer: x+4
Step-by-step explanation: part one- x+4
Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4
Please answer this correctly
Answer:
x = 6
Step-by-step explanation:
Assuming these rectangles are similar, you can set up a proportion like this:
[tex]\frac{15}{10} =\frac{x}{4}[/tex]
→Cross multiply:
[tex]\frac{60}{10x}[/tex]
→Divide 60 by 10:
x = 6
If s(x) = 2 – x2 and t(x) = 3x, which value is equivalent to (s circle t) (negative 7)?
Answer:
153
Step-by-step explanation:
What can you conclude about the hypotenuse of the two triangles?
Answer: C
Step-by-step explanation:
Since the sides are marked with the little lines, you know they are congruent with each other. Since the sides are congruent, you know the hypotenuse will be congruent.
You can argue that these triangles are similar, but the difference is that similar triangles are the same shape, but not the same size. These triangles are congruent because they are the same size and shape. Therefore, the hypotenuse is congruent.
To the nearest degree, what is the measure of the central angle for faucets?
Answer:
43°
Step-by-step explanation:
Solve the system using substitution.
5x+ 4y = 10
4x - y = 8
Answer:
Step-by-step explanation:
hello
from 4x-y=8 we can say that y = 4x-8
we substitute in the first equation to get
5x + 4 (4x-8) = 10
then
5x + 16 x -32 = 10
<=> 21x = 32+10=42
<=> x = 42/21 = 2
and then y = 8-8=0
don t hesitate if you need any further explanation
thanks
Answer: x = 2, y = 0 or (2 , 0)
Step-by-step explanation:
Solving using substitution is where you solve for a variable in one of the two equations in the system then plug it into the other.
For an easier plug in we can take the second equation. 4x-y = 8.
From here we need to isolate the y variable which is easier to isolate than x, in my opinion.
Subtract the 4x over.
-y = 8-4x
Now divide by a -1 so y is positive.
y= -8 + 4x
Now plug this in for y in the other equation.
5x + 4(-8 + 4x) = 10
Distribute the 4.
5x - 32 + 16x = 10
Combine like terms
21x - 32 = 10
Add the 32.
21x = 42
Divide by 21.
x = 2
Now that we have solved for one variable we can plug this into either equation and solve for the other.
I will plug it into the second equation.
4(2) - y = 8
Simplify.
8 - y = 8
Subtract 8.
-y = 0
Divide by -1.
y = 0
So the x and y values are.
x = 2
y = 0
