Find the center and radius of the circle with the equation: (x-0^2 + (y+1)^2 = 4
a.
center: (-5, 1)
radius: 4
c.
center: (-5, 1)
radius: 2
b.
center: (5, -1)
radius: 4
d.
center: (5, -1)
radius: 2
The center and radius of the circle is (b) center: (-5, 1) radius: 2
How to determine the center and the radius?The circle equation is given as:
(x-5)^2 + (y+1)^2 = 4
The circle equation is represented as:
(x-a)^2 + (y-b)^2 = r^2
Where:
Center = (a,b)
Radius = 4
By comparison, we have:
(a, b) = (-5, 1)
r^2 = 4
This gives
(a, b) = (-5, 1)
r = 2
Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2
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how many 3cm cubes can be put in a box 3cm long 6cm wide 12cm high?
Answer:
8
Step-by-step explanation:
A cube is equal on all sides. Therefore the cubes must be 3cm x 3cm x 3cm. Therefore, each cube has an area of 27cm^3. The box that the cube has an area in is 3cm x 6cm x 12 cm which = 216cm^3. If you do [tex]216cm^3/27cm^3 = 8 cubes[/tex]
Determine the unknown length or angle measurement. Round each answer to the nearest whole number.
The unknown sides and angles of the triangle are 18 cm and 39 degrees respectively.
How to find the side and angle of a triangle?The side and angle of a triangle can be found as follows:
using sine law,
Angle A = 180 - 68 - 59 = 53 degrees
19.5 / sin 59 = a / sin 53
19.5 sin 53 = a sin 59
a = 19.5 sin 53 / sin 59
a = 15.5733924459 / 0.8571673007
a = 18.1680280047
a = 18 cm
15 / sin ∅ = 20 / sin 57
15 sin 57 = 20 sin ∅
sin ∅ = 12.5800585192 / 20
sin ∅= 0.62900292595
∅ = sin ⁻¹ 0.62900292595
∅ = 38.9763828249
∅ = 39 degrees.
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Which statement below correctly depicts the expected value of a fair game?
E(X) = 0
E(X) = 1
E(X) > 0
E(X) >1
Answer:
e(x)=0 will be your answer
Step-by-step explanation:
First of all it is important to know about the fair game. A game is said to be fair if it has equal chances of winning for both the parties.
In Statistical terms, this can be said as expected value =0
If E(X) = 1 where X is from the player, then organizer of the game would have more chances of losing.
Similarly if E(X)>0where X is from the player, then organizer of the game would have more chances of losing.
Also if E(X)>1, where X is from the player, then organizer of the game would have more chances of losing.
Hence a fair game is one where
Answer: A. E(X) = 0
Step-by-step explanation:
=
Triangle R S T is shown. Angle T R S is a right angle. The length of R T is 5, the length of R S is 12, and the length of hypotenuse S T is 13.
Given right triangle RST, what is the value of sin(S)?
Five-thirteenths
Five-twelfths
Twelve-thirteenths
Thirteen-twelfths
Answer:
Step-by-step explanation:
I would use the law of sins.
13/sin90 = 5/sin s
sin s = (5 sin 90)/13
sin s = .3846.
Now put in your calculator sin-1 .3846 and you will get the angle of 22.6 degrees rounded to the tenths place.
Answer:
22.6 = 113/5
Step-by-step explanation:
The range, a measure of variability, Group of answer choices is the difference between the largest (L) and smallest (S) value in a list of scores is the most informative when used to describe data sets without outliers includes only two values in its computation, regardless of the number of scores in a distribution all of the above
The correct answer is all of the above.
Why is the range the most convenient measure of variability?
Your data's spread from the lowest to the greatest value in the distribution is indicated by the range. The calculation of this variability index is the simplest. Simply subtract the lowest value from the highest value in the data set to determine the range.How do you find the range?
The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response.Learn more about range
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This figure represents a design found in a glass panel. ABCD is a rectangle with
midpoints X, Y, Z, and W. Emily states that the quadrilateral formed by the segments
that join the midpoints of the sides is a rhombus. Do you agree with her? Explain why
or why not.
Answer: Yes
Step-by-step explanation:
Since ABCD is a rectangle, [tex]\angle AXY[/tex], [tex]\angle YBZ[/tex], [tex]\angle WCZ[/tex], and [tex]\angle WDX[/tex] are all right angles, and are thus all congruent because all right angles are congruent. Furthermore, because ABCD is a rectangle, we know that [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\overline{AD} \cong \overline{BC}[/tex]. Because we are given that X, Y, Z, and W are midpoints, using the fact that halves of congruent segments are congruent, we can conclude that [tex]\overline{AY} \cong \overline{YB} \cong \overline{CW} \cong \overline{WD}[/tex] and that [tex]\overline{AX} \cong \overline{XD} \cong \overline{BZ} \cong \overline{ZC}[/tex]. As a result, we can conclude that [tex]\triangle AYX \cong \triangle DXW \cong \triangle CWZ \cong \triangle BYZ[/tex] by SAS, and thus by CPCTC, [tex]\overline{AY} \cong \overline{XW} \cong \overline{ZW} \cong \overline{YZ}[/tex]. Therefore, since the quadrilateral formed by the midpoints has four congruent sides, it must be a rhombus.
if you buy a computer game for $54, you have a $5 mail-in rebate, and you pay 8% sales tax, how much does your game cost?
Answer:53.32
Step-by-step explanation:
$54 retail price
sales tax 8%
$54x8%= 4.32
sales tax is $4.32
$54+$4.32= $58.32
total with tax is $58.32
$58.32-$5= 53.32
There are 5 different families of triplets at a triplets convention. Each triplet shook hands with all the other triplets, except his or her siblings. How many handshakes took place?
There is a total of 90 handshakes.
How many handshakes took place?
There are 5 sets of triplets.
If we select one of the sets, each of the triplets will have one handshake with the other 12 people. So we have 36 handshakes at this point.
Now we only care for the other 4 sets.
We select one set again, each triple on that set will have one handshake with the other 9 people, so for the 3 triplets, we have a total of 27 new handshakes.
For the remaining 3 sets we do the same, this time we add 18 handshakes.
Finally, there are 2 sets of triplets, this time we add 9 new handshakes.
To get the total number of handshakes we need to add them all:
36 + 27 + 18 + 9 = 90
There is a total of 90 handshakes.
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PLEASE HELP!!!!
Question 8(Multiple Choice Worth 5 points)
(05.02 MC)
Based on the figure below, what is the value of x?
A right angle is shown divided in two parts. The measure of the angle of one part is 20 degrees and the measure of the other part is 5x plus 15 degrees.
A) 1
B) 9
C) 11
D) 15
The value of x from the given figure is 11
Complementary anglesThe sum of two complementary angles is 90 degrees.
The angles shown in the diagram are complementary such that;
20 + 5x + 15 = 90
5x + 35 = 90
5x = 90- 35
5x = 55
x = 55/5
x = 11
Hence the value of x from the given figure is 11
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The Random Variable is normally distributed with mean = 98 and standard deviation =
20.41.
On the sampling distribution with n = 81, for what value of the sample mean (X) would have
10% of the possible sample means less than it? Round your answer to 2 decimal places.
If mean is 98, standard deviation is 20.41, n=81 then sample mean will be 131.57445 which would have 10% of the possible mean less than it.
Given that mean is 98,standard deviation is 20.41,n=81 and significance level be 10%.
We are required to find the value of sample mean.
Because the value of n is greater than 30 so we will use z statistics in the problem.
We know that,
Z=(X-μ)/σ in which μ is population mean, σ is standard deviation.
Confidence level=1-0.01=0.09 means 90%.
Z value for 90% confidence level be 1.645.
we have to put the value of Z=1.645 , μ=98,σ=20.41 to get the value of X.
1.645=(X-98)/20.41
1.645*20.41=X-98
33.57445=X-98
X=98+33.57445
X=131.57445
Hence if mean is 98, standard deviation is 20.41, n=81 then sample mean will be 131.57445 which would have 10% of the possible mean less than it.
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Solve for x: 12x^2 – 6 (a^2 + b^2)x + 3a^2b^2 = 0
Step-by-step explanation:
[tex]12 {x}^{2} - 6( {a}^{2} + {b}^{2} )x + 3 {a}^{2} {b}^{2} = 0[/tex]
Using quadratic formula, we get
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( - 6) {}^{2}( {a}^{2} + {b}^{2}) {}^{2} - 4(12)(3 {a}^{2} {b}^{2} )} }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( {a}^{2} + {b}^{2} ) {}^{2} - 144 {a}^{2} {b}^{2} } }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{36( ({a}^{2} + {b}^{2}) {}^{2} - 4 {a}^{2} {b}^{2} }) }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{6 \sqrt{ ({a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{24} [/tex]
[tex]x = 6( {a}^{2} + {b}^{2} )± \frac{ \sqrt{( {a}^{2} + {b}^{2} ) {}^{2} - 4 {a}^{2} {b}^{2} } }{4} [/tex]
Answer: x₁=6b², x₂=6a².
Step-by-step explanation:
[tex]12x^2-6*(a^2+b^2)+3a^2b^2=0\\D=(6*(a^2+b^2))^2-4*12*3a^2b^2\\D=6^2*(a^2+b^2)^2-144a^2b^2\\D=36*(a^4+2a^2b^2+b^4)-144a^2b^2\\D=36a^4+72a^2b^2+b^4-144a^2b^2\\D=36a^4-72a^2b^2+36b^4\\D=(6a^2)^2-2*6a^2*6b^2+(6b^2)^2\\D=(6a^2-6b^2)^2\\\sqrt{D}=\sqrt{(6a^2-6b^2)^2}=|6a^2-6b^2|=б(6a^2-6b^2).\\\displaystyle x_{1,2}=\frac{-(-6*(a^2+b^2))б(6a^2-6b^2)}{2} .\\x_1=\frac{6a^2+6b^2-6a^2+6b^2}{2} \\x_1=\frac{12b^2}{2} \\x_1=6b^2.\\x_2=\frac{6a^2+6b^2+6a^2-6b^2}{2} \\x_2=\frac{12a^2}{2} \\x_2=6a^2.[/tex]
60÷8 explained well and not in a decimal form
Answer: 15/2
Step-by-step explanation: if you fraction it, it'll be 60/8 so you can simplify it by 4. So 60÷4/8÷4 will be 15/2. So the answer is 15/2
Answer:
15/2 or 7 1/2.
Step-by-step explanation:
60 / 8 divide top and bottom by 4:-
= (60/4) / (8/4)
= 15/2.
Select the correct answer from each drop-down menu.
Given: line AB ||line DC and DF_~BF
Prove: DFC _~BFA
Angles are formed when two or more lines intersect. Angles are majorly measured in degrees.
The required proof is as shown below:
Whenever a transversal passes through two parallel lines, angles are formed which have some similar properties.
STATEMENTS REASONS
1. AB ║DC Given.
2. < FDC ≅ < FBA Alternate angle theorem.
3. <AFB ≅ < DFC Vertical opposite angle rule.
4. DF ≅ BF Given
5. ΔDFC ≅ Δ BFA Angle-Angle-Side property
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What elements does a strong body paragraph in a literary analysis always contain? Select three options.
The elements which must be contain in a body paragraph of a literary analysis are;
An introduction to a text.Reasons that support a viewpoint.Supporting evidence and commentary.What elements does a strong body paragraph in a literary analysis always contain?A strong body paragraph basically is characterized as a medium of stating facts regarding a viewpoint and these statements must be accompanied by supporting evidence and commentary.
On this note, the three elements which should be contained in a strong body paragraph are;
An introduction to a text.Reasons that support a viewpoint.Supporting evidence and commentary.Remarks:
an introduction to a text
reasons that support a viewpoint
O a thesis statement
supporting evidence and commentary
Da summary of the main points
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Ummm can y’all solve these problems I’ll give extra points for this
Pls solve step by step and label which is which
Which best describes how to Sovle the equation below?
26x = 74
A. Multiply both sides by 74.
B. Multiply both sides by 26.
C. Divide both sides by 26.
D. Divide both sides by 74.
You are flying a kite in a competition and the length of the string is 725 feet and the angle at which the kite is flying mesures 35” with the ground. How high is your kite flying?
The kite is flying 415.84 feet from the ground
How to determine the height?The given parameters are:
Length of the string, L = 725 feetAngle, x = 35 degreesLet the height be h.
So, we have the following sine function
sin(x) = h/L
Make h the subject
h = L * sin(x)
This gives
h = 725 * sin(35)
Evaluate
h = 415.84
Hence, the kite is flying 415.84 feet from the ground
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A comet is estimated to be about 960,000,000 km from Earth. Write this distance in scientific notation. [?] × 10 km Enter 13
Answer:
[tex](9*10^{9})( 6*10^{8})[/tex] or 9.6×10^8
Step-by-step explanation:
The answer is written above.
Hope this helps!
Answer:
9.6 * 10^8 km.
Step-by-step explanation:
960,000,000
= 9.6 * 10^8 km.
The value of the exponent = number of digits after the 9, which = 8.
PLSS HELP ASAP
A bag of marbles contains 7 red, 8 orange, 9 purple, 7 white, and 5 yellow. Mark reaches into the bag and randomly picks out 3 marbles all at once.
How many different 3-marble groups are possible?
What is the probability that he will select 2 red and 1 yellow marbles?
based on the number of marbles in the bag, the number of marble groups possible is 7,140 groups.
the probability of selecting 2 red and 1 yellow is 1/68.
what number of 3-marble groups can be made?first, find the number of marbles:
= 7 + 8 + 9 + 7 + 5
= 36
the number of marble groups are:
= 36 ! / (3 ! x 33 !)
= 7,140 groups
the probability of picking 2 red and 1 yellow is:
= (( (7! / (2! x 5!)) x ( ( 5! / (1! x 4!))) / 7,140
= 1 / 68
= 1.47%
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A random sample of n = 16 scores is obtained from a normal population with m = 40 and s = 8. what is the probability that the sample mean will be within 2 points of the population mean?
Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, the parameters are given as follows:
[tex]\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]
The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:
X = 42:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (42 - 40)/2
Z = 1
Z = 1 has a p-value of 0.8413.
X = 38:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (38 - 40)/2
Z = -1
Z = -1 has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.
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A model pirate ship uses the scale
5 inch: 20 meters. If the model is
50 inches long, how long is the
pirate ship?
Answer:
200 meters
Step-by-step explanation:
If the ratio is 5 inches to 20 meters that means for every 5 inches in the model there will be 20 meters on the real ship.
If the model is 50 inches long that means that there are 10 5 inch segments, multiply this 10 by the 20 meters in the ratio and you will get 200 meters as the final length for the ship.
what is 12(w-3) if w= 10
Hey there!
12(w - 3)
= 12(10 - 3)
= 12(10) + 12(-3)
= 120 - 36
= 84
OR
12(w - 3)
= 12(10 - 3)
= 12(7)
= 84
Therefore, your answer should be:
84
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
HELP, WILL GIVE BRAINLEST..
Factor the GCF: -6x³y + 9x²y2 - 12xy³ (5 points)
O 3xy(-2x² + 3xy - 4y²)
O-3xy(2x² + 3xy - 4y²)
O-3xy(2x2-3xy + 4y²)
O-3(2x³y - 3x²y² + 4xy³)
Answer:
[tex]\sf -3xy\left(2x^2-3xy+4y^2\right)[/tex]
Step-by-step explanation:
[tex]\sf -6x^3y+9x^2y^2-12xy^3[/tex]
To factor the GCF of 6x³y + 9x²y2 - 12xy³ let's apply the exponent rule:-
[tex]\boxed{\sf a^{b+c}=a^ba^c}[/tex]
[tex]\boxed{\sf x^3y=xx^2y,\:x^2y^2=xxyy,\:xy^3=xyy^2}[/tex]
[tex]\sf -6xx^2y+9xxyy-12xyy^2[/tex]
Rewrite,
-6 as 2 * 39 as 3 * 3-12 as 4 * 3[tex]\sf 2\cdot \:3xx^2y+3\cdot \:3xxyy+4\cdot \:3xyy^2[/tex]
Now, factor out the common term [tex]\sf -3xy[/tex]:-
[tex]\sf -3xy\left(2x^2-3xy+4y^2\right)[/tex]__________________________
The gross domestic product of the United States in 2020 was $20,940,000,000. What is the gross domestic product of the United States in 2020 expressed in scientific notion?
Answer:
2.094 x 10¹⁰ I have to add more words soo
PLEASE I NEED HELP ON THIS QUESTION
Answer:
Option c is the correct answer
Step-by-step explanation:
distance of satrun - distance of jupiter
To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that
Answer:
2 sides and angle between them are congruent to the same 2 sides and angle on the other triangle
Step-by-step explanation:
A kite is made up of two isosceles triangles, KIT and KET, with the lengths shown. The top triangle of the kite, ΔKIT, is made from approximately 17 square inches of material.
Isosceles triangles K I T and K E T are connected at side K T. The length of K T is 10 inches. The length of sides K E and E T are 8 inches. The lengths of sides K I and I T are 6 inches.
Heron’s formula: Area = StartRoot s (s minus a) (s minus b) (s minus c) EndRoot
How much material is used for the entire kite, quadrilateral KITE? Round to the nearest square inch.
31 square inches
34 square inches
48 square inches
62 square inches
The amount of material needed for the entire kite is 48 square inches
How to determine the amount of material?The given parameters:
KI =6 inches
ET = 8 inches
KT=10 inches
Area of ΔKIT = 17 square inches
Start by calculating the area of the bottom triangle using:
A = 0.5 * Base * Height
This gives
A = 0.5 * 10 * 6
Evaluate
A = 30
The amount of material is
A = 30 + 17
A = 47
Hence, 48 square inches of material is used for the entire kite, quadrilateral KITE
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A rectangular gate measures 1.2 m by 2.3 m with a 2.4 m diagonal. Is the gate
square? If not, should the diagonal be longer or shorter?
You buy 4 health bars and 3 health drinks for $10. your friend buys 6 health bars and 2 health drinks for $10.
Answer:
The bars cost 1 each and the drinks cost 2 each.
Step-by-step explanation:
Let b = bars and d = drinks
4b + 3d = 10 6b + 2d = 10
There are a few ways to solve this. If I want to eliminate the b's from both equations. I would multiple the first equation all the way through by -6 and the second equation all the way through by 4.
4b+ 3d = 10
-6(4b + 3d) =(10)-6 Multiple all the way through by -6
-24b -18d = -60 A positive multiplies by a negative is a negative
6b + 2d = 10
4(6b + 2d) = (10)4 Multiple all the way through by 4
24b + 8d = 40
Take the two bold equations from above and add them together
-24b - 18d = -60
24 b + 8d = 40
-10d = -20 Divide both sides by -10
d = 20 A negative divided by a positive is a negative.
Plug in 2o for d in either of the top two equations and get b = 1.