We are given a fixed number of samples, n = 100.
We are given two conditions:
x = 45, z = 0.50
x = 52, z = 1.00
The relevant equation we can use here is:
z = (x – m) / s
where m is the mean and s is the std dev
So for the two conditions:
0.50 = (45 – m) / s --> eqtn 1
1.00 = (52 – m) / s --> eqtn 2
Rewriting eqtn 1 in terms of m:
0.5 s = 45 – m
m = 45 – 0.5 s --> eqtn 3
Rewriting eqtn 2 in terms of m:
1.00 s = 52 – m
m = 52 – 1.00 s --> eqtn 4
Equating eqtn 3 and 4:
45 – 0.5 s = 52 – 1.00 s
0.5 s = 7
s = 14
From eqtn 4:
m = 52 - 1.00 * 14
m = 38
Therefore answers are:
m = 38 and s = 14
The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0
The equation of this circle in standard form is
A. (x - 2)^2 + (y + 3)^2 = 5
B. (x - 2)^2 + (y + 3)^2 = 18
C. (x - 4)^2 + (y + 6)^2 = 24
D. (x + 4)^2 + (y - 6)^2 = 24
E. (x + 2)^2 + (y - 3)^2 = 35
The center of the circle is at the point __
A. (-14,21)
B. (-2,3)
C. (2,-3)
D. (-4,6)
E. (4,-6)
And it's radius is ___ units.
A. 5 1/2
B. 3(2 1/2)
C. 2(6 1/2)
D. 35 1/2
Answer:
The standard form equation is B.
The centre of the circle is B
The radius is B.
Step-by-step explanation:
Firstly, the equation can all be divided by 7:
(7x² + 7y²− 28x + 42y − 35) ÷ 7 =
x² + y² - 4x + 6y - 5 = 0
x² - 4x + y² + 6y - 5 = 0
Now add [tex]\frac{1}{2}* b[/tex]
0.5 * 4 = 2, 2² = 4 so 4
0.5 * 6 = 3. 3² = 9 so 9
(x² - 4x + 4) + (y² + 6y + 9) - 4 - 9 - 5 = 0
As the standard form of a circle is (x - a)² + (y - b)²= r² , we need to change this to this. Simply find a number that multiplies to 4 and adds to -4 ( -2 ) and a number that multitplies to 9 and adds to 6 (3):
(x - 2)² + (y + 3)²
Also, we need to subtract the square of the number inside the brackets, as this is completing the square:
-2 * -2 = 4
3 * 3 = 9
So we need to subtract 4 and 9, and 5 as that was in the original:
(x - 2)² + (y + 3)² - 4 - 9 - 5 = 0
To find the radius, we need to move this numbers over to the other side making them positives:
(x - 2)² + (y + 3)² = 4 + 9 + 5
(x - 2)² + (y + 3)² = 18
So the equation is B.The centre of the circle in (x - a)² + (y - b)² is [tex]a[/tex] and [tex]b[/tex]
So in this equation the centre is -2, 3. Which is B.The radius is the square root of whatever (x - a)² + (y - b)² equals, so the square root of 18 is the radius:
√18 = √9√2
= 3√2
= [tex]3 * (2x^{\frac{1}{2} } )[/tex]
So your answer is B.Is there a number that is exactly 3 more than its cube?
For a given number X, its cube is written as X^3.
Here we want to see if we can find a number that is exactly 3 more than its cube, this means that:
[tex]X = X^3 + 3[/tex]
We will see that yes, there exists a number with this property.
Then we can try to solve this to find the number with that given property.
We can rewrite it as:
[tex]-X^3 + X - 3 = 0[/tex]
Now we can solve this for X, as the question asks about existence and not for the exact number, we can graph this the above function:
[tex]f(X) = -X^3 + X - 3[/tex]
And if it crosses the x-axis, then at some point we have:
[tex]f(X) = 0[/tex]
This would imply that there exists a real number that is 3 more than its cube.
The graph can be seen below, and we can see that it intersects the X-axis, then yes, there is a number that is exactly 3 more than its cube.
And by watching the graph, we can see that the number is:
[tex]X = -1.672[/tex]
If you want to learn more, you can read:
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The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?
The measure of base angle is [tex]$$\boxed{{{70}^ \circ }} if the vertex angle is {40^ \circ }$$[/tex] .
Further explanation:
Given:
Vertex angle of the isosceles triangle is [tex]{40^ \circ }[/tex] .
Explanation:
The triangle three sided close Figure.
There are three type of triangles.
1. Equilateral triangle
2. Isosceles triangle
3. Scalene triangle
Equilateral triangle has all sides equal and all the angles are equal.
Isosceles triangle has 2 sides equal to each other and the two base angles are equal to each other.
Scalene triangle has all sides unequal and the angles are also not equal to each other.
The sum of all the angles of the triangle is [tex]{180^ \circ }[/tex].
Consider the base angle as y.
The value of y can be obtained as follows,
[tex]\begin{aligned}y+y+40&=180\\2y+40&=180\\2y&=180-40\\2y&=140\\y&=\frac{{140}}{2}\\y&={70^ \circ }\\\end{aligned}[/tex]
The measure of base angle is [tex]$$\boxed{{{70}^ \circ}} if the vertex angle is {40^ \circ}$$[/tex].
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: vertex angle, isosceles triangle, base angle, perpendicular, altitudes, point, triangle, circumcenter, bisectors, perpendicular bisectors, angles, angle bisectors, median, intersection, incenter, right angle triangle, equilateral triangle, obtuse, acute.
Describe or show two ways to find the following product: 3 x 3/4 .
I need help will give brilenst Write an expression where you multiply 0.035 times a power of ten so that the product is greater than 1, but less than 100.
The required expression is:
0.035 × [tex]10^2[/tex] = 3.5 where the product is 1 < [tex]10^x[/tex] < 100.
To ensure that the product is greater than 1 but less than 100 when multiplying 0.035 by a power of ten, we need to find the appropriate exponent that will give us a result within this range.
Let's express 0.035 as a product of a number between 1 and 10 and a power of ten:
0.035 = 3.5 × [tex]10^{-2}[/tex]
Multiplying by a power of ten increases the value. We want the product to be greater than 1 but less than 100. So, we need to increase the exponent of ten until we reach a value within this range.
0.035 × [tex]10^x[/tex]
To ensure that the product is greater than 1, we need to increase the exponent enough to make the coefficient (3.5) greater than 1:
3.5 × [tex]10^x[/tex] > 1
[tex]10^x[/tex] > [tex]\frac{1}{3.5}[/tex]
[tex]10^x[/tex] > 0.29
To ensure that the product is less than 100, we need to find an exponent that doesn't increase the coefficient (3.5) too much:
3.5 × [tex]10^x[/tex] < 100
[tex]10^x[/tex] < [tex]\frac{100}{3.5}[/tex]
[tex]10^x[/tex] < 28.57
Now, we need to find the appropriate exponent x that satisfies both conditions. This exponent should make the product greater than 1 but less than 100.
To simplify, we can use the fact that [tex]10^1[/tex] = 10 and [tex]10^2[/tex] = 100:
[tex]\[ 10^0[/tex] < [tex]10^x[/tex] < [tex]10^2[/tex]
Now, we can choose any exponent between 0 and 2 that satisfies the inequality. For example, we can choose x = 1:
0.035 × [tex]10^1[/tex] = 0.035 × 10 = 0.35
The product of 0.035 multiplied by [tex]10^1[/tex] is 0.35, which is not greater than 1 but less than 100.
Putting x = 2,
0.035 × [tex]10^2[/tex] = 0.035 × 100 = 3.5
Here, the product is greater than 1 but less than 100.
The question is:
Write an expression to multiply 0.035 times a power of ten so that the product is greater than 1, but less than 100.
calculate the area of the circle , round your answer to the nearest hundredth
how can place value help me multiply a two digit number by a multiple of ten?
the length of a rectangle 15 inch longer than twice it's width. if the perimeter is 78 inches. find the length of the retangle
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP
In the 1939 movie The Wizard of Oz, when the brainless Scarecrow is given the confidence to think by the Wizard(by merely handing him a diploma, by the way), the first words the Scarecrow utters are, “The sum of the square roots of any two side of an isosceles triangle is equal to the square root of the remaining side.” An isosceles right triangle is just a right triangle having both legs the same length. Supposed that an isosceles right triangle has legs each length of 3. What is the length of the hypotenuse? Is the Scarecrow’s assertion valid? This question illustrated the true value of a diploma without studying.
The equation that the scarecrow uttered can be expressed mathematically as:
sqrt (C) = sqrt (A) + sqrt (B)
where A, B, and C are the sides of the triangle
Since the triangle is an isosceles, therefore A = B and
sqrt (C) = 2 sqrt (A)
given that the measure of the leg is 3, A = 3, C is:
sqrt C = 2 sqrt (3)
sqrt C = 3.464
C = 12
In a any triangle, the sum of two sides must be greater than the third side, since in this case C > A + B therefore the Scarecrow is not correct because the correct relationship should be A + B > C.
To find the correct hypotenuse, we start with the Pythagorean equation:
C^2 = A^2 + B^2
So what the scarecrow mistakenly did was to ignore the “+” symbol during the square root. Taking the square root on both sides, the correct equation is:
C = sqrt (A^2 + B^2)
Calculate for C, since A = B = 3:
C = sqrt (3^2 + 3^2)
C = 4.24
So now A + B > C and this is now correct.
Which of the following illustrates the truth value of the given conditional statement? If ice is hot, then rain is wet.
F T → T
T T → T
T F → F
F F → T
Answer: The correct option is (A) F T → T.
Step-by-step explanation: We are given to select the correct illustration of the truth value of the following conditional statement :
"If ice is hot, then rain is wet".
Let p : Ice is hot. This is a false statement.
And
q : rain is wet. This statement is true.
We know that
The statement "if p then q" is written as p ⇒ q.
Since p is false and q is true, so p ⇒ q will be true.
That is,
p q p ⇒ q
F T T
Thus, the correct illustration is F T → T.
Option (A) is CORRECT.
Ava picks a number greater than 3 tens 6 ones. The number is less than 52. It has more than 6 ones. What could the number be?
A body is moving along a straight line with a velocity which varies according to the equation v = 9 t2 + 2t, where v is in feet per second and t is in seconds. Find the expression for the distance as a function of time. A. 3t3 + 2t2 + C B. 3t3 + t2 + C C. 20t + C D. 18t + C
If you need to be at the party in 2.5 hours, how fast would you need to drive to get there?
The answer would be 60 km/h. :D
If $3000 is deposited in an account that pays 5% interest, what is the difference in the amount after 4 years between the amount earned if the principal is compounded annually and the amount earned calculated using simple interest?
$30.72
$41.12
$46.52
$53.76
How many minutes does it take to put 42 gallons of water in the tub at a rate of 5 1/4 gallons per minute?
Assume that 2 cards are drawn in succession and without replacement from an ordinary deck of 52 cards. Find the probability that the following occurs.
1 diamond and 1 jack other than the jack of diamonds (in that order) are drawn
You deposit $18,000 into a savings account at a bank that has a rate of 66% compounded monthly. Find the amount of money in the account after 44 years.
find the x in the parallelogram there’s an x in the left corner and 73 degrees in the right bottom corner
One-fourth equals the quotient of a number and 8. Find the number.
A quotient is a quantity produced by the division of two numbers. Hence, the quotient number is [tex]2[/tex].
What is quotient ?
A quotient is a quantity produced by the division of two numbers.
Let us assume that the quotient is [tex]x[/tex]
So, by using the given information it is of the form
[tex]\frac{1}{4}=\frac{x}{8}\\x=\frac{8}{4}\\x=2[/tex]
Hence, the quotient number is [tex]2[/tex].
To know more about quotient
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Help me please ASAP need to get this done.
Answer:
39 mph
15 mph and 28 mph
Median
Median
It shows the median speed.
Step-by-step explanation:
PLEASE HELP!!!!!!!!
A business reports a net income of −$5,040 over a 9-month period.
What is the average income per month for that period? −$45,360
−$560
$560
$45,360
On the coldest night in Vostok Station, Antarctica, the temperature dropped from 0°C to −24°C in 4 hours.
What is the average temperature change per hour?
HURRY ILL PICK BRAINLIEST!!!!!!!
Melinda and Paul shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paul shoveled for 25 minutes to complete 345 square feet of driveway. 30x + 30y = 450 20x + 25y = 345 How much more can Paul shovel in 1 minute than Melinda? 3 square feet per minute 6 square feet per minute 9 square feet per minute 15 square feet per minute
A certain number is 5 less than another number. If their sum is 11 find the two numbers
6.2 * 10 to the third power equals
What is the common ratio of this geometric sequence? 5, 10, 20, 40, 80.
A. -40
B. 0.5
C. 2
D. 40
Answer:
its -2
please brainleist
What is a rule for the sequence below?
1.8, 2.85, 3.90, 4.95, 6
Find the product of 20×9×5. Tell which property you used.
the cost of an item is 100% of its price. what number goes in place of ? in the addition problem?
The answer is 100 thats all you have to put trust me.
Answer 2 and 4 please