Final answer:
To calculate the new mean after adding a score of 12 to the original 6 scores with a mean of 5, determine the total sum of the original scores, add 12, and divide by the new number of scores. The new mean for the 7 scores is 6.
Explanation:
To find the new mean when one person with a score of x = 12 is added to a sample of n = 6 scores with a current mean of m = 5, first calculate the total sum of the scores before the new score is added. This can be done by multiplying the mean by the number of scores. Then add the new score to this total and divide by the new number of scores.
Calculate the total sum of the original scores: Total sum = mean × number of scores = 5 × 6 = 30.Add the new score to the total sum: New total sum = 30 + 12 = 42.Calculate the new mean by dividing the new total sum by the new number of scores: New mean = New total sum ÷ new number of scores = 42 ÷ 7 = 6.So, the mean for the new set of scores is 6.
are the graphs of the lines in the pair parallel? Explain. y = 5x + 6 –18x + 3y = –54
A store buys items at a wholesale price of $45 each. If the store marks up the price, and no discounts are given, which could be possible retail prices?
hurry
Answer:49 65
Step-by-step explanation:
Help find the segment indicated please !
Two numbers have a sum of 22 and a difference of 6. find the two numbers.
Joo-Eun wants to draw a triangle with sides measuring 6 mm, 8 mm, and 11 mm. Which is true about Joo-Eun’s plan?
Answer:
The answer is B, he can only draw one unique triangle with these side lengths.
Step-by-step explanation:
I did the quiz
Simplify b ( a + b ) - a ( a - b ).
a^2 + 2 ab + b^2
a^2 - 2 ab + b^2
-a^2 + 2 ab + b^2
-a^2 - 2 ab - b^2
Answer:
-a^2 + 2 ab + b^2
Step-by-step explanation:
To solve this, you need to distribute the letters into the parenthesis.
Then, you sum equal things, and you get the result.
[tex]b(a+b)-a(a-b)=\\ba + b^{2} -a^{2} + ab=\\ b^{2} + 2ab -a^{2}[/tex]
So, the rigth answer is number three: -a^2 + 2 ab + b^2
The graph of a translated exponential function is shown below. Its parent function is y = 4x.
If the graph is asymptotic to y = -3 and contains the points (2, -2) and (3, 1), what is the equation of the function?
The equation of the graph is [tex]y = -3 +4^{x -2[/tex]
How to determine the equation of the function?The parent function is given as:
[tex]y = 4^x[/tex]
From the graph, we can see that the function is translated 3 units down and 2 units right.
This means that the transformation rule
(x, y) -> (x - 2, y - 3)
So, we have:
[tex]y = -3 +4^{x -2[/tex]
Hence, the equation of the graph is [tex]y = -3 +4^{x -2[/tex]
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In a paddock there are emus and wombats. If there are 52 heads and 148 feet, how many emus are in the paddock?
Anybody got some answers????
If 543 planes leave from JFK airport and each plane has 228 passengers, how many people have flown out of JFK? people;
123,804 people have flown out of JF-K airport based on the assumption of full plane occupancy. Real-world variations and logistical complexities may impact the actual number.
To find the total number of people who have flown out of JF-K, you can multiply the number of planes by the number of passengers per plane.
543 planes * 228 passengers/plane = 123,804 people
Therefore, 123,804 people have flown out of JF-K airport.
It's important to note that this calculation assumes each plane is fully occupied and that there are no variations in passenger counts.
In reality, the number of passengers on each plane may vary, and factors such as seat availability, ticket sales, and other considerations can affect the actual number of people who have flown out of JF-K. Additionally, this calculation does not account for return flights, layovers, or other complexities in air travel logistics.
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These data show the ring size for a sample of 8 men 12 10 11.5,11.5, 12, 9, 9 , 11 what is the best approximation of the standard deviation of the ring size data
Answer:
Standard deviation of ring size is 1.253
Step-by-step explanation:
We are given the following data-set:
12, 10, 11.5, 11.5, 12, 9, 9, 11
n = 8
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{86}{8} = 10.75[/tex]
Sum of squares of differences = 1.5625 + 0.5625 + 0.5625 + 0.5625 + 1.5625 + 3.0625 + 3.0625 + 0.0625 = 11
[tex]S.D = \sqrt{\displaystyle\frac{11}{7}} = 1.253[/tex]
A scientist wants to measure out 0.62 liters of a liquid, but she can only find a beaker that measures volume in milliliters. How many milliliters should she measure to equal 0.62 liters?
To convert 0.62 liters to milliliters, you multiply 0.62 by 1,000, which equals 620 milliliters. Therefore, the scientist should measure out 620 milliliters of the liquid.
Explanation:When a scientist wants to measure out 0.62 liters of a liquid, but only has a beaker that measures volume in milliliters, she needs to first understand the conversion between liters and milliliters. 1 liter is equal to 1,000 milliliters. So, she would need to convert 0.62 liters to milliliters. She can do this by multiplying 0.62 liters by 1,000. This gives her 620 milliliters. Therefore, if a scientist wants to measure out 0.62 liters of a liquid, but the beaker only measures volume in milliliters, then she should measure out 620 milliliters.
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1. find the sum of the measures of exterior angles, one at each vertex, of an octagon.
a. 180*
b. 360*
c. 1080*
d. 1440*
2. If the sum of the interior angles of a polygon is 900* ( * = degrees) , then how many sides does the polygon have?
a. 6
b. 7
c. 8
d. 9
10. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.
11. The parallelogram has the angle measures shown. Can you conclude that it is a rhombus, rectangle, or a square? Explain.
Answer: First question: b. 360°
Second question : b. 7
Third question: Yes, it is a parallelogram.
Fourth question: It is a rhombus.
Step-by-step explanation:
1. Since, The sum of exterior angles in a polygon is always equal to 360 degrees.
And, an octagon is also a polygon.
Therefore the sum of the all exterior angle of an octagon = 360°
2. Since, the sum of the interior angles of a polygon of n sides is (n-2)×180°
But here (n-2)×180°=900
⇒ n-2 = 5 ( After dividing both sides by 180° )
⇒ n = 5 + 2 = 7
Thus, If the sum of the interior angles of a polygon is 900° then the polygon has 7 sides.
10. Since, In triangles XNY and WNZ,
XN≅NZ (Given)
NY≅NW ( Given)
∠XNY≅∠WNZ ( vertically opposite angles)
Thus, By SAS postulate of congruence,
ΔXNY≅ΔWNZ,
By CPCTC, XY≅WZ
Similarly, Δ XNW≅ Δ YNZ,
By CPCTC, XW≅YZ
Therefore, In quadrilateral XYZW, Opposite sides are equal.
⇒ XYZW is a parallelogram.
11. Let ABCD is a parallelogram,
In which AC is a diagonal.
Also, AB = CD and AD= BC ( By the property of parallelogram)
And, It is given that ∠DAC=∠DCA = 72°
Therefore ADC is an isosceles triangle ( By the property of isosceles triangle)
Thus, AD=DC
Similarly, ABC is an isosceles triangle.
Thus, AB= BC
Thus, AB=BC=CD=DA.
Also, ∠ADC=∠ABC ( By the property of parallelogram)
Therefore, In ABCD all sides are equal and Opposite angles are equal.
⇒ ABCD is a rhombus. ( The diagram is shown below)
the formula, P=v^2/R, gives the relationship between resistance (R), voltage (V) and power P). solve the formula for resistance.
Answer: [tex]R=\frac{V^2}{P}[/tex]
Step-by-step explanation:
Given formula : [tex]P=\frac{V^2}{R}[/tex], gives the relationship between resistance (R), voltage (V) and power P).
When we multiply R to the both sides of the above equation, we get
[tex]PR=v^2[/tex]
Now, divide P on the sides, we get
[tex]R=\frac{V^2}{P}[/tex]
Hence, the formula for resistance will be
[tex]R=\frac{V^2}{P}[/tex], gives the relationship between resistance (R), voltage (V) and power (P).
Which of the following reasons will complete the proof?
SAS
ASA
SSS
The reason that will complete the proof is SSS (Side-Side-Side) which states that if three corresponding sides of two triangles are congruent, then the triangles are congruent.
Explanation:Out of the given options, the reason that will complete the proof is SSS which stands for Side-Side-Side. SSS is a congruence postulate that states that if three corresponding sides of two triangles are congruent, then the triangles are congruent.
In this case, since both 'o' and 'sx' are given, we can apply the SSS congruence postulate to show that the triangles are congruent. This is because two sides 'o' and 'sx' are congruent, and the third side of each triangle can be determined by adding up the length of the other sides.
The correct reason that completes the proof is "SAS" which stands for Side-Angle-Side.
SAS is a postulate in geometry that states: "If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent."
To prove two triangles congruent using the SAS postulate, you need to show that two sides of one triangle are congruent to two sides of another triangle, and the included angle (the angle formed by the two sides) of one triangle is congruent to the included angle of the other triangle.
For example, let's say we have two triangles, Triangle ABC and Triangle DEF. To prove them congruent using the SAS postulate, we need to show that AB is congruent to DE, BC is congruent to EF, and the angle at B is congruent to the angle at E.
Once we have established these congruencies, we can conclude that Triangle ABC is congruent to Triangle DEF.
Therefore, in the context of the given question, the reason that completes the proof is SAS.
Before a renovation, a movie theater had 134 seats. After the renovation, the theater has 196 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
Answer:46.3%
Step-by-step explanation:
Final answer:
46.3%
Explanation:
To find the approximate percentage increase in the number of seats at the theater, subtract the initial number of seats from the final number, then calculate the percentage increase using this difference.
Percentage Increase:
To calculate the approximate percentage increase in the number of seats at the theater:
Find the difference in the number of seats after and before the renovation: 196 - 134 = 62 seats.Calculate the percentage increase: (62 / 134) * 100% ≈ 46.3%What number does x stand for in this equation?
-7x + 6=27
Based on the given information and the algebraic and geometric properties presented or proven thus far, choose the congruence theorem that could be used to prove the triangles congruent. If it is not possible to prove the triangles are congruent, choose "not possible".
SSS
SAS
SSA
not possible
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: DC║AB, DC=AB.
If a transversal line intersect two parallel lines, then the alternative interior angles are equal.
In triangle ABC and CDA,
[tex]AB=DC[/tex] (Given)
[tex]\angle 2=\angle 3[/tex] (Alternative interior angles)
[tex]CA=CA[/tex] (Common side)
Two corresponding sides and their including angle are equal.
By SAS postulate of congruent triangles,
[tex]\triangle ABC\cong \triangle CDA[/tex]
Since both triangles are congruent by SAS postulate, therefore the correct option is 2.
Please help with this question. 15 points.
Which graph represents the function?
Solve. −4.2y+2.1>−2.52 Drag and drop a number or symbol into each box to show the solution. <>0.11.14.62−4.62 y
According to these three facts, which statements are true?
- Circle D has center (2, 3) and radius 7.
- Circle F is a translation of circle D, 2 units right.
- Circle F is a dilation of circle D with a scale factor of 2.
A) Circle F and circle D are similar.
B) The center of circle F is (0, 3).
C) The radius of circle F is 28.
D) Circle F and circle D are congruent.
(Again, you can choose more than one option.)
Using the stated facts, the statements from the listed options which are true are given by: Option A) Circle F and circle D are similar.
How to find if a pair of figure is not dilated version of each other?Dilation of a figure will leave its size get scaled (multiplied) by same number.
Thus, suppose if a circle is dilated with its center as center of dilation, with some scale factor, that will affect its radius.
So, if the current circle is having the radius 'r' units, and the circle is dilated from its center with scale factor of S, then, we get:
New circle's radius = [tex]S \times r \: \rm units[/tex]
For the given case, the three facts to be considered are:
Circle D has center (2, 3) and radius 7.Circle F is a translation of circle D, 2 units right.Circle F is a dilation of circle D with a scale factor of 2.Since circle F is translation of circle D, 2 units right, so its all points will be shifted 2 units right, which makes coordinate (x,y) - > (x + 2, y) (since height is same, only the x coordinates shifted to right side).
Thus, center of F would be (2 + 2, 3) = (4,3).
Since there is scaling of the circle D scale factor 2, thus, radius of circle F will be twice the radius of the circle D, which will be 2 times 7 = 14 units.
Since dilated figures are similar, thus, Circle F and Circle D are similar.
(similar figures are those who look alike, although may be smaller or larger versions, but congruent figures are exact same dimension holding figures, their all properties match, but positions can be different).
Thus, the correct statement is only option A: Circle F and circle D are similar.
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1/4 of 96= ? without using a fraction
Solve. x² + 20x + 100 = 50
A)x=−10±52√
B)x=50±252√
C) x=10±52√
D)x=50±52√
x = −10 ± 5√2
Solve. x²+ 20x + 100 = 50
Subtracting 50 from both sides
[tex] x^{2} +20x+100-50=50-50 [/tex]
[tex] x^{2} +20x+50=0 [/tex]
To solve the quadratic equation, let us use quadratic formula
For, [tex] ax^{2} +bx+c=0 [/tex] , [tex] x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a} [/tex]
So, a=1, b=20, c=50
So, we get,
x=[tex] \frac{-20+-\sqrt{20^{2}-4*1*50}}{2*1} [/tex]
[tex] x=\frac{-20+-\sqrt{400-200}}{2} [/tex]
[tex] x=\frac{-20+-\sqrt{200}}{2} [/tex]
[tex] x=\frac{-20+-10\sqrt{2}}{2} [/tex]
[tex] x=\frac{-10+-5\sqrt{2}}{1} [/tex]
[tex] x=-10+-5\sqrt{2} [/tex]
Option(a) Answer
So, x=-10+5[tex] \sqrt{2} [/tex]
or, x=-10-5[tex] \sqrt{2} [/tex]
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Given the equation 2x^2 - 5x + 7 = 0.
Find the discriminant.
Describe the roots and explain your reasoning.
It takes mario 5 minutes to type 225 words.how many many minutes does it take him to type 360 words?enter your answer in the box.
Answer:
the answer is 8
Step-by-step explanation:
because if you multiply 8 times 45 it equals 360
There is your answer
Quick help: Explain how to solve the following system of equations. What is the solution to the system?
2x+2y+z=-5
3x+4y+2z=0
x+3y+2z=1
Write a decimal that represents the value of $1 bill and 5 quarters
Why do we need to construct a confidence interval?
Joseph is going on a trip and he needs to rent a car. He looks online and finds two companies that offer different pricing options for car rentals. Company A charges $0.25 per mile plus a $50 rental fee. Company B charges $0.45 per mile plus a $20 rental fee.
Which statement is true about the pricing plans for Company A and Company B?
A) Company A is a better deal if Joseph drives 150 miles.
B) Company B is a better deal if Joseph drives 150 miles.
C) Company B is a better deal if Joseph drives more than 150 miles.
D) Company A is a better deal if Joseph drives less than 150 miles.
E) The price for traveling 150 miles is the same for both compan
Answer:
E.The price for travelling 150 miles is same for both company.
Step-by-step explanation:
We are given that Joseph is going on a trip and he needs to rent a car.
Company A
Charge $0.25 per mile plus $50 rental fee.
Company B charges 40.45 per mile plus $20 rental fee.
A.Total distance=150 miles
Company A
Charges for 150 miles=[tex]150\times 0.25=[/tex]$37.5
Total charges=37.5+50=$87.5
Company B
Charges for 150 miles=[tex]150\times 0.45[/tex]=$67.5
Total charge=20+67.5=$87.5
The price for travelling 150 miles is same for both company.
But if distance greater than 150 miles such 155 miles
Company A
Total charge=[tex]155\times 0.25+50=[/tex]$88.75
Company B
Total charges=[tex]155\times 0.45+20=[/tex]$89.75
Company A is better deal if Joseph more than 150 miles.
If distance 145 miles
Price form company A=[tex]145\times 0.25+50=[/tex]$86.25
Price form company B=[tex]145\times 0.45+20=[/tex]$85.25
Company B is better deal if Joseph travel less than 150 miles.
Hence, option E is true.