The solutions are:
(a) Standard error is 957.04. (b) The probability is 50%. (c)The probability is 0.8491. (d) The probability is 0.8617.
To calculate the values, use the standard error formula for the sample mean:
(a)
The standard error is given by:
[tex]Standard\ error =\dfrac{ Population \ standard \ deviation}{\sqrt{sample\ size}}\\Standard\ error=\dfrac {\$ 7,400 }{ \sqrt60}\\Standard\ error =\ $957.04[/tex]
(b)
To find the probability that the sample mean will be more than $27,175, convert it into a z-score and then find the area under the normal distribution curve:
z = (sample mean - population mean) / standard error
z = ($27,175 - $27,175) / $957.04
z = 0
Since the z-score is 0, the area under the curve to the right of this point is 0.5 or 50%.
c. To find the probability that the sample mean will be within $1,000 of the population mean, we need to find the area between the range of $(27,175 - $1,000) and $(27,175 + $1,000).
Lower limit: $27,175 - $1,000 = $26,175
Upper limit: $27,175 + $1,000 = $28,175
Now, we calculate the z-scores for both limits:
lower = ($26,175 - $27,175) / $957.04 ≈ -1.045
upper = ($28,175 - $27,175) / $957.04 ≈ 1.045
Using a standard normal distribution table or calculator, the probability of a z-score being between -1.045 and 1.045 is approximately 0.8491.
(d)
If the sample size were increased to 100.
[tex]Standard error = \dfrac{ \$7,400}{ \sqrt{100}} \\Standard error = \$740[/tex]
Find the probability that the sample mean will be within $1,000 of the population mean, did in part c:
Lower limit: $27,175 - $1,000 = $26,175
Upper limit: $27,175 + $1,000 = $28,175
lower = ($26,175 - $27,175) / $740
lower ≈ -1.351
upper = ($28,175 - $27,175) / $740
upper ≈ 1.351
Using a standard normal distribution table or calculator, the probability of a z-score being between -1.351 and 1.351 is approximately 0.8617.
Hence,
Standard error is 957.04.The probability is 50%.The probability is 0.8491.The probability is 0.8617.Learn more about Probability here:
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I want a way to solve such a problem
Answer: please calculate the answer.
Step-by-step explanation:\\ Bro use this formula (sum of all numbers of the question) \ no. of seen numbers.
Arithmetic mean = ( 24+124+243+...) \ 12
need help solving this
Answer:
x = (√21)/2
Step-by-step explanation:
The sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. That means the middle-length side is (√3)/2 times the length of the longest side.
x = (√3)/2·√7
[tex]\boxed{x=\dfrac{\sqrt{21}}{2}}[/tex]
Help help math math good luck
Use rigid motions to explain whether the triangles in the figure are congruent. Be sure to describe specific rigid motions in your explanation . ( Will Mark Brainliest if answered correctly).
Step-by-step explanation:
I don't really know what demonstrating with rigid motion means, never heard that before. But a method for demonstrating it could be drawing circumferences of radius:
1) R1 = d(O,S)
2) R2 = d(O,J)
3) R3 = d(O,M)
With O being the origin of the reference system.
*Note: d(A,B) means distance between point A and point B
After you've done that you can show that the points S and P are on the same circumference, J and W are on the same circumference (different from the one of S and P), M and D are on the same circumference.
After you've done that you calculate the angle between the points on the same circumference and demonstrating that they are all the same.
Answer:
Step-by-step explanation:
Congruent
Shift right 1 unit and up 5 units
Rotate 90 degrees clockwise about (-1, 2)
Or
just rotate 90 degrees clockwise about (1, -1)
given parallelogram EFGH, where EF = 5x + 18, HE = 3x + 4 and the perimeter is 60, which value of GH
Given the perimeter of the parallelogram in the image below is 60, the value of GH will be: 23.
Recall:
Perimeter of a parallelogram = 2(a + b), where a is the side length and b is the base length.Opposite sides of a parallelogram are equal.Given the parallelogram as shown in the diagram below, where:
base (b) = EF = 5x + 18
side (a) = HE = 3x + 4
Perimeter = 60
Plug in the values into the formula:
60 = 2[(3x + 4) + (5x + 18)]
60 = 2[3x + 4 + 5x + 18]
60 = 2[8x + 22]
60 = 16x + 44
60 - 44 = 16x
16 = 16x
1 = x
x = 1
GH = EF = 5x + 18 (equal opposite sides of parallelogram)
GH = 5x + 18
Plug in the value of xGH = 5(1) + 18
GH = 23
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Triangle DNO has vertices at D(5, 8), N(– 3, 10), and O(– 3, 6). If vertex D is translated 4 units to the right, the best name for Triangle DNO is:
Answer Choices:
a. Scalene
b. Isosceles
c. Equilateral
d. Right
e. none of these
Using distance between two points to find the lengths of the edges of the triangle, the correct option is:
b. Isosceles
The distance between two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Vertex D is translated 4 units to the right is (9,8).
The lengths of the edges are:
[tex]DN = \sqrt{(9 - (-3))^2 + (8 - 10)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}[/tex]
[tex]DO = \sqrt{(9 - (-3))^2 + (8 - 6)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}[/tex]
[tex]NO = \sqrt{(-3 - (-3))^2 + (10 - 6)^2} = \sqrt{0^2 + 4^2} = 4[/tex]
Two edges of the same length, hence, it is an isosceles triangle, given by option b.
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At Cheesecake Factory, the cost of your meal before the tip is $77.23. You leave a 15% tip. How much
money did you leave for tip? What is the total cost of your meal?
Answer:
$88.81
Step-by-step explanation:
to find tip, multiply 77.23 and .15 to get $11.58
total cost = meal + tip
total cost = 77.23 + 11.58 which equals $88.81
Simplify 1.25 (-x -4)
Answer:
-1.25x-5
Step-by-step explanation:
Multiply using Distribution:
1.25(-x-4)
-1.25x-5
My answer can't be simplified anymore, since there isn't any like terms.
MAX POINTS!!!! Please help me solve the problem in the picture and tell me what I’m doing also explain each step.
I know myself that the answer is 0.4
34/23 as a decimal rounded to the nearest tenth
Answer:
1.5
Step-by-step explanation:
1.47826086
rounded to the nearest tenth is 1.5
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )
Answer:
x=7.85
Step-by-step explanation:
Give the triangles we know that:
[tex] \frac{cd}{fh} = \frac{de}{hg} = \frac{ce}{gf} [/tex]
Now we can substitute like usual
[tex] \frac{78}{fh} = \frac{117}{54} = \frac{ce}{5x + 1} [/tex]
Now we simplify the fraction in the middle
the middles fraction will =13/6
Therefore:
[tex] \frac{78}{fh} = \frac{13}{6} [/tex]
so 13fh=468
Therefore: fh=36
Now we can use the Pythagorean theorem
so
[tex]gf = \sqrt{ {54}^{2} - {36}^{2} } [/tex]
so gf=18√5
so 5x+1=18√5
so 5x=-1+18√5
so x=7.85
(I'm not too sure about this one tho)
What are the center and radius of the circle?
Answer:
R = 4
Step-by-step explanation:
Beause when we say (-1,4)
It say the center of it
Help!!! I will reward lots of points! QUESTION: At Walmart, 6 apples and 5 oranges cost $11. At Publix, 2 apples and 3 oranges cost $7. Set up a system of two equations which you will solve to find the cost of one apple and one orange. Also step by step
Answer: I do not think this problem is solvable; the cost of apples and oranges at the stores are different
-5x + 7y = -3
-3x - y = 19
Answer:
x=-5, y=-4
Step-by-step explanation:
to solve this system of equations, first multiply the second equation by 7 to get -21x-7y=133. this allows for the y terms in both equations to cancel once you add the two equations together.
adding these together, the y term cancels and you are left with -26x=130. so dividing both sides by -26 will get x=-5. then plug this x value back into either original equation (i chose -3x-y=19) so solve for y.
-3(-5)-y=19 so -y=4 so y=4
so the answer to the system of equations is x=-5 and y=-4
Hello please help straight up answer I’ll give points thanks I’m just trying to pass
Answer:
I think it's 34°.
Step-by-step explanation:
The angle to the right of 3x+7 is the alternate interior angle to 2x+3, meaning that they are the same.
Now, that angle, 2x+3, and 3x+7, are on a line, which I'm assuming is a straight line with an angle of 180°. If it is, then (2x+3)+(3x+7)=180
Now you can solve for x.
2x+3+3x+7=180
5x+10=180
5x=170
x=34
Therefore, x=34°
Hope I helped!
Find all real values of $x$ such that $x^2-5x + 4=0$.
Answer:
x=4 && x=1
Step-by-step explanation:
x^2 - x - 4x + 4=0
x(x-1) - 4(x - 1)=0
(x-4)(x-1)=0
X=4 and x=1
All real values of $x$ such that $x²-5x + 4=0$ will be x=4 and x=1.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the quadratic equation is, x²-5x+4=0
Any equation of form ax²+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
We have to find the value of x as,
x²-5x + 4=0
x² - x - 4x + 4=0
x(x-1) - 4(x - 1)=0
(x-4)(x-1)=0
X=4 and x=1
Thus, all real values of $x$ such that $x²-5x + 4=0$ will be x=4 and x=1.
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Four tour buses depart the terminal on the same day. The itinerary of the first bus takes 6 days, for the second bus it takes 8 days, for the third bus it takes 10 days, and the fourth bus takes 15 days. Assuming that another tour begins the same day that the bus returns to the terminal, how many days will it take until all four buses return to the terminal on the same day?
Using the least common factor, it is found that it will take 120 days until all four buses return to the terminal on the same day.
Considering their itineraries, the number of days it will take until all four buses return to the terminal on the same day is the lcm of 6, 8, 10 and 15.To find their least common factor, we factor each number by prime numbers, hence:
6 - 8 - 10 - 15|2
3 - 4 - 5 - 15|2
3 - 2 - 5 - 15|2
3 - 1 - 5 - 15|3
1 - 1 - 5 - 5|5
1 - 1 - 1 - 1
Hence, lcm(6, 8, 10, 15) = 2³ x 3 x 5 = 8 x 15 = 120.
It will take 120 days until all four buses return to the terminal on the same day.
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help me plssssssssssssssssssssss
Answer:
p < 319
Step-by-step explanation:
Image attached giving 25 points please help
There are 30 cats and 50 dogs at the local animal shelter. Of these animals, 15% were adopted last week. How many animals were adopted?
Solve each system using substitution or additions
(elimination).
-x+2y=-1
5x-10y=6
Answer:
Step-by-step explanation:
L1 -x + 2y = -1
L2 5x - 10y = 6
-x + 2y = - 1 multiply by -1
x - 2y = 1 multiply by 5
5x - 10y = 5 is similar that 5x - 10y = 6
The system has no solution
The simplified equation after clearing the decimals is
-12.2 + 2.8w - 8.8 = 1.05w
Answer:
-21=-4w
w=5.25
but you don’t want decimals
so- you round down
w=5
Step-by-step explanation:
You combine like terms, and then make sure your variable is alone, the only way to get it alone from a ”mixed number” is to divide
you do the same thing to both sides
so divde each side by -4
-21/-4 = 5.25
or with it rounded down since it’s under a five
It’s 5 with the decimals removed
i hope this helps
A regular 10-sided polygon has a perimeter of 540 feet. What is
the length of one side?
A.540 feet
B.360 feet
C.270 feet
D.54 feet
Answer:
D. 54 feet
Step-by-step explanation:
One side will be 1/10 of the total length of all 10 sides.
(1/10)(540 ft) = 54 feet . . . length of one side
What is 10 1/2 divided by 2 1/4
Answer:
4.666666667 or 4.6_ (repeating decimal)
Help help help math math math
Answer:
1/4
Step-by-step explanation:
the x decreases by 1 the y decreases by 4
Answer:
-4
Step-by-step explanation:
A box contains four bags of sugar. The total mass of all four bags is 6 kg. What is the mass of each bag in grams?
help me plssssssssssssss
Answer:
C .......
Step-by-step explanation:
A Math book is 6. 15 centimeters. How thick will 21 Math books on a shelf be? A. 130.15 cm B. 129.16 cm. C. 129. 15 cm. D. 128. 16 cm
Multiply:
6.15 x 21 = 129.15
Answer: C. 129.15 cm.
Solve for x: x /6−y/3= 1
SHOW WORK
[tex]\dfrac x6 - \dfrac y3 =1\\\\\\\implies \dfrac x6 - \dfrac{2y}6 = 1\\\\\\\implies \dfrac{x-2y}6 =1\\\\\\\implies x -2y =6\\\\\\\implies x =6+2y\\\\\\\implies x = 2(3 +y)[/tex]
HELLO?? WHY ISNT ANYONE HELPING ME!!?!?!? HELP ME