Answer: 3
Step-by-step explanation:
Given
The equation of the circle is [tex]x^2+y^2-4x-6y-k=0[/tex]
Using completing the square method
[tex]\Rightarrow x^2+y^2-4x-6y+4-4+9-9-k=0\\\Rightarrow \left( x^2-4x+4\right)+\left( y^2-6y+9\right)-\left( k+4+9\right)=0\\\Rightarrow \left( x-2\right)^2+\left( y-3\right)^2=\left( k+13\right)[/tex]
on comparing with standard form, [tex]r^2=k+13[/tex]
Insert the value of r
[tex]\Rightarrow 4^2=k+13\\\Rightarrow k=16-13\\\Rightarrow k=3[/tex]
question in picture attached
Answer:
True
Step-by-step explanation:
Right angles (shown on the diagram) are perpindicular by definition.
Mrs. Wigen conducted a survey in her math class. She asked each of her students to tell her how many pets they have at home. The dot plot below represents the results of Mrs. Wigen's math class survey. 12-----3 4:25 Number of pets at home Find the Measures of Center for the data: Mean Round to the nearest tenths place Median Mode
Answer:
4 : 25 to round off we have to see that
4 : 25 to round off we have to see that If in ones place it is more than 5 or not
4 : 25 to round off we have to see that If in ones place it is more than 5 or not if yes we will add to 1 no to tenths place
4 : 25 to round off we have to see that If in ones place it is more than 5 or not if yes we will add to 1 no to tenths place Finally 4 : 25 it has 5 in its ones place
So the answer will be 4 : 30g A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam. We are interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%. The test statistic is
Answer:
The test statistic is [tex]z = 1.25[/tex]
Step-by-step explanation:
We are interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%.
At the null hypothesis, we test if the proportion is 80%, that is:
[tex]H_0: p = 0.8[/tex]
At the alternate hypothesis, we test if the proportion is more than 80%, that is:
[tex]H_a: p > 0.8[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
80% is tested at the null hypothesis:
This means that [tex]\mu = 0.8, \sigma = \sqrt{0.2*0.8} = 0.4[/tex]
A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam.
This means that [tex]n = 100, X = \frac{85}{100} = 0.85[/tex]
The test statistic is
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.85 - 0.8}{\frac{0.4}{\sqrt{10}}}[/tex]
[tex]z = 1.25[/tex]
The test statistic is [tex]z = 1.25[/tex]
which one is right please help
Dolve for theta. С 13 4 o o A B Your answer
Answer:
θ ≈ 17.1°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan θ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{4}{13}[/tex] , then
θ = [tex]tan^{-1}[/tex] ([tex]\frac{4}{13}[/tex] ) ≈ 17.1° ( to the nearest tenth )
Solve for x.
-30 = 5(x + 1)
x=
Answer: -7
Step-by-step explanation:
-30 = 5(x + 1)
-30 = 5x + 5. ( After distrbuting the 5)
-5. -5
-30 - 5. = 5x
-35 = 5x
x = -7
The function graphed to the left is function. The curve has and continues infinitely in one direction. Each y-value is each corresponding x-value.
Answer:
1. A square root
2. one distinct endpoint
3. The square root of
on edg
have a nice day! :)
Step-by-step explanation:
1. The function graphed to the left is function. A square root
2. The curve has and continues infinitely in one direction.
one distinct endpoint
3. Each y-value is each corresponding x-value. the square root of
what is square root function?The principal square root function. (usually just referred to as the "square root function") is a function that maps the set of nonnegative real numbers onto itself.
1. A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions.
The graph shown is known as the graph for square root functions.
2. The curve has one distinct end point and continues infinitely in one direction.
3. The square root of each corresponding x-value.
Each value of y is the corresponding square root of x- values.
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Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept.
Answer:
Step-by-step explanation:it’s c
Carson has a package to mail the package is 87 inches Long the shipping company only Mail Packages that are up to seven feet long can Carson mail the package show your work and add complete sentences to your answer. ASAP PLS
Answer:
Carson can't mail the package
The reasoning for why he can't mail it is because in every foot there is 12 inches and if u multiply 12 by 7 you get 84 meaning Carson's package is larger then 7ft
Packaging and Branding; Your Small Business Shipping Strategy; 5 Ways ... Download the complete in-depth, 16 chapter guide. ... USPS offers cubic pricing for Priority Mail shipments
Please mark me as brainlistKyle boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 5 radians per minute and has a radius of 40 feet. The center of the Ferris wheel is 47 feet above the ground. Let t represent the number of minutes since the Ferris wheel started rotating.
Required:
Write an expression (in terms of t) to represent the varying number of radians θ Ryan has swept out since the ride started.
Answer:
a) The expression for the change in angular position is [tex]\theta = 5\cdot t[/tex].
b) The expression for the height of Ryan regarding the center of the Ferris wheel is [tex]H(t) = 40\cdot \sin (5\cdot t)[/tex].
c) The expression for the height of Ryan above the ground is [tex]H(t) = 40\cdot \sin (5\cdot t) + 47[/tex].
Step-by-step explanation:
The statement is incomplete. Complete form is introduced below:
Kyle boards a Ferris wheel at the 3-o'clock position and rides the Ferris wheel for multiple revolutions. The Ferris wheel rotates at a constant angular speed of 5 radians per minute and has a radius of 40 feet. The center of the Ferris wheel is 47 feet above the ground. Let t represent the number of minutes since the Ferris wheel stated rotating.
a) Write an expression (in terms of t) to represent the varying number of radians [tex]\theta[/tex] Ryan has swept out since the ride started.
b) Write an expression (in terms of t) to represent Ryan's height (in feet) above the center of the Ferris wheel.
c) Write an expression (in terms of t) to represent Ryan's height (in feet) above the ground.
a) Let suppose that Ferris wheel rotates counterclockwise. As the Ferris wheel rotates at constant rate, this kinematic expression can be used to determine the change in angular position ([tex]\theta[/tex]), in radians:
[tex]\theta = \omega \cdot t[/tex] (1)
Where:
[tex]\omega[/tex] - Angular velocity, in radians per minute.
[tex]t[/tex] - Time, in second.
If we know that [tex]\omega = 5\,\frac{rad}{min}[/tex], then the expression for the change in angular position is [tex]\theta = 5\cdot t[/tex].
b) Geometrically speaking, Ryan's height with respect to the center of the Ferris wheel is described by the following formula:
[tex]H(t) = r \cdot \sin (\omega\cdot t)[/tex] (2)
Where:
[tex]r[/tex] - Radius of the Ferris wheel, in feet.
[tex]H(t)[/tex] - Height of Ryan with respect to the center of the Ferris wheel, in feet.
If we know that [tex]\omega = 5\,\frac{rad}{min}[/tex] and [tex]r = 40\,ft[/tex], then the expression for the height of Ryan regarding the center of the Ferris wheel is [tex]H(t) = 40\cdot \sin (5\cdot t)[/tex].
c) We use the following geometric expression to model Ryan's height above the ground:
[tex]H(t) = r\cdot \sin (\omega\cdot t) +h_{o}[/tex] (3)
Where [tex]h_{o}[/tex] is the height of the center of the Ferris wheel above the ground, in feet.
If we know that [tex]h_{o} = 47\,ft[/tex], [tex]\omega = 5\,\frac{rad}{min}[/tex] and [tex]r = 40\,ft[/tex], then the expression for the height of Ryan above the ground is [tex]H(t) = 40\cdot \sin (5\cdot t) + 47[/tex].
Help pls
Is either x = 7 or x = 9 a solution to 23 >19?
A. Neither is a solution.
B. They are both solutions.
C. x = 7 is a solution, but x = 9 is not.
D. x = 9 is a solution, but x = 7 is not
Answer:
b they are both solution
(3w-8)(5=w)=0 ,What is w?
Answer:
- 1. 5 as decimal
-3 / 2 as a fraction
Step-by-step explanation:
Can somebody please help in this question?
First find the area of one side.
The area of the side of a cube is s^2 where s is the length if one edge.
The edge length is given as 2/3, so the area of a side is 2/3^2 which is equal to 2/3 x 2/3 = 4/9 square units.
A cube has 6 sides so now to find the surface area of the cube multiply the area of one side by 6 sides:
4/9 square units x 6 = (4 x6)/9 = 24/9 which can be rewritten as 2 2/3 square units
The answer is 2 2/3 units^2
Solve the inequality:
5x - 7 ≥ 3x + 9
Answer:
x≥8
Step-by-step explanation:
Answer:
x ≥ 8
Step-by-step explanation:
Subtract 3x from both sides:
2x - 7 ≥ 9
Then add 7 to both sides:
2x ≥ 16, or
x ≥ 8
an initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. how long will it take to double the investment?
Answer:
20 years
Step-by-step explanation:
9000/ 100= 900 = 10%
900/2= 450
450 x 2= 900
900 x 10= 9000
Now we multiply 10 by 2 because we doubled the value of our 450 into a 900 and now we get 20.
Compound interest is the interest that is made from the principal and the interest as well in consecutive years.
The number of years it will take to double the investment is 15 years.
What is compound interest?Compound interest is the interest that is made from the principal and the interest as well in consecutive years.
We have,
Principal = $9000
Rate = 5%
The formula is given as:
A = p [tex](1 + \frac{R}{100} )^{n}[/tex]
n = number of years
Double the investment:
Amount = 2 x 9000 = 18000
Now,
18000 = 9000 [tex](1 + \frac{R}{100} )^{n}[/tex]
2 = [tex](1 + 0.05)^{n}[/tex]
2 = [tex]1.05^{n}[/tex]
Taking log on both sides.
[ log a² = 2 log a ]
log 2 = n log 1.05
0.30 = n 0.02
n = 0.30 / 0.02
n = 15
Thus,
The number of years it will take to double the investment is 15 years.
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g(r) r²6r 55 1) What are the zeros of the function? Write the smaller r first, and the larger r second. smaller r = larger r = 2) What is the vertex of the parabola?
Answer:
smaller r = -8
larger r = 2
vertex of the parabola
(-8,2)
Step-by-step explanation:
Solve equation by using the quadratic formula.
6x² – 2x=8
Answer:
D
Step-by-step explanation:
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!! ALL LINKS WILL BE REPORTED!!!!!!!!!!!
Answer:
1. Dot Plot
2, The histogram
You are at the top of a lighthouse that is 500 ft tall. You look down towards the ocean and see a boat located 800 ft. from the shore.
a) What is the angle of depression from your position to the boat? Round to the nearest whole number.
b) If the boat travels away from the lighthouse an additional 1000 feet, what is the angle of depression from your position to the boat? Round to the nearest whole number.
C) By how many degrees did your line of sight change.
Answer:
a) 32° (nearest whole number)
b) 16° (nearest whole number)
c) 16.5° (1 d.p.)
Step-by-step explanation:
Please see the attached picture for the full solution.
On Saturday, Emily's mother gave birth to twins and named them Nyra and Ishaan. When they were first born, Nyra weighted
3.96 kilograms , and Ishaan weighed
2.56 kilograms. How much did the babies weigh in total?
part of the object is a rectangle that is twice as tall it is wide one of the rectangles sides is also a side of a pentagon
Answer:
c
Step-by-step explanation:
During one month, there were 2,000 people who used the advertiser links on a website. The percent of people who clicked on each
advertisement link is shown in the circle graph. Calculate the number of people who clicked on the link for each type of advertisement. How
many people used the Music link?
Advertiser Links
Computers
2396
Music
25%
TVS
3%
Movies
1796
Cell phones
32%
340
450
500
540
Answer:
500
Step-by-step explanation:
During one month, there were 2,000 people who used the advertiser links on a website. The percent of people who clicked on each
advertisement link is shown in the circle graph. Calculate the number of people who clicked on the link for each type of advertisement. How
many people used the Music link?
Advertiser Links
Computers
2396
Music
25%
TVS
3%
Movies
1796
Cell phones
32%
340
450
500
540
Then You Turn The Music Percent Into A Decimal Which Is .25% Then Times That By 2000 And You Get .25 X 2000 = 500
Help please!!! Best answer will get brainliest!!!
Can some one help me ASAP
Answer:
To get the Angle
Cos=46/59
tita=
[tex] {cos}^{ - 1} [/tex]
46/59
tita=37.667
tita=38°
Which statement about the angle 0 is true
Answer:
Option C, sin(Ф) = 7/25
Hope this helps!
Suppose that your drawer contains 8 AAA batteries but only 6 of them are good. If you randomly select 4 batteries what is the probability all 4 will work ?
Answer:
Step-by-step explanation:
[tex]P=\frac{6}{8} \times\frac{5}{7} \times\frac{4}{6} \times\frac{3}{5} =\frac{3}{14}[/tex]
Step-by-step explanation:
the probability of the 4 batterys work was %30 because if you take randomly 4 battery you take good and bad batterys and the most probability is the 4 batterys don't work or the 4 batterys work or like 1 or 2 batterys work thats why like %30 the batterys work
Which is the graph of the system of equations?
2x - 3y = 12
4x - y = 8
YA
1
-
6
-21
The solution of the linear system is (1.2, -3.2). Then the correct option is A.
What is linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The system of the equations is given below.
2x - 3y = 12 ..1
4x - y = 8 ..2
By solving the equations 1 and 2. Then we have
x = 1.2 and y = -3.2
Then the correct option is A.
The graph of the system of the equation is given below.
More about the linear system link is given below.
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Calculate sales tax using the following information:
Taxable amount of the sale: $150
Sales tax percentage: 7%
What is the amount of the sales tax?
Round the answer to the nearest cent (hundredths).
A percentage is a way to describe a part of a whole. The amount of the sales tax is $10.5.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given the taxable amount of the sale is $150, while the Sales tax percentage is 7%. Therefore, the amount of sales tax is,
Amount of sales tax = 7% of $150 = 0.07 × 150 = $10.5
Hence, the amount of the sales tax is $10.5.
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What is the slope of the line that passes through the points
(
9
,
4
)
(9,4) and
(
9
,
−
5
)
?
(9,−5)? Write your answer in simplest form.
We are given:
The line passes through the points (9,4) and (9,-5)
We know that:
Slope of a line = (change in y) / (change in x)
Finding the slope:
Change in x = final x - initial x
Change in x = 9 - 9 = 0
Slope of line = (change in y) / 0
because division by 0 is undefined:
Slope of the line is Undefined
We could've solved for the change in y but there's no reason to because no matter what's in the numerator, as long as the denominator is 0, the value is undefined
Find the surface area of rectangular prism.
s=
Answer:
16
Step-by-step explanation:
For rectangular prisms you do L, W, H.
4 = Length
x
2 = Width
x
2 = Height
=
Volume = 2 x 2 x 4 = 16
~ LadyBrain