Answer:
The value of x is [tex]\frac{7}{4}[/tex].
Step-by-step explanation:
It is given that the inverse variation equation is
[tex]xy=k[/tex] ..... (1)
The value of y is 4 and the value of k is 7.
Substitute y=4 and k=7 in equation (1).
[tex]x\times 4=7[/tex]
Divide both sides by 4.
[tex]\frac{x\times 4}{4}=\frac{7}{4}[/tex]
[tex]x=\frac{7}{4}[/tex]
Therefore the value of x is [tex]\frac{7}{4}[/tex].
For women at hartford college, times to run 400 meters are normally distributed with a mean of 84 seconds and a standard deviation of 7 seconds. what percentage of the times are more than 91 seconds? more than 63 seconds?
Approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.
To find the percentage of times that are more than 91 seconds and more than 63 seconds, we can use the properties of a normal distribution and the standard normal distribution table (also known as the z-table).
Given:
Mean (μ) = 84 seconds
Standard deviation (σ) = 7 seconds
1. Probability of times more than 91 seconds:
First, we need to find the z-score for the value 91 seconds:
[tex]\(z = \frac{X - \mu}{\sigma} = \frac{91 - 84}{7} = \frac{7}{7} = 1\)[/tex]
Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = 1\)[/tex]. The z-table provides the percentage of values below a given z-score, so we need to find the complement (1 - percentage) to get the percentage of values above [tex]\(z = 1\).[/tex]
From the z-table, the area to the right of [tex]\(z = 1\)[/tex] is approximately 0.1587.
So, the percentage of times more than 91 seconds is [tex]\(1 - 0.1587 = 0.8413\)[/tex] or 84.13%.
2. Probability of times more than 63 seconds:
Similarly, we need to find the z-score for the value 63 seconds:
[tex]\(z = \frac{X - \mu}{\sigma} = \frac{63 - 84}{7} = \frac{-21}{7} = -3\)[/tex]
Now, using the z-table, find the area under the standard normal curve to the right of [tex]\(z = -3\)[/tex]. Again, we need to find the complement to get the percentage of values above [tex]\(z = -3\).[/tex]
From the z-table, the area to the right of [tex]\(z = -3\)[/tex] is approximately 0.9987.
So, the percentage of times more than 63 seconds is [tex]\(1 - 0.9987 = 0.0013\)[/tex] or 0.13%.
Therefore, approximately 84.13% of times are more than 91 seconds, and approximately 0.13% of times are more than 63 seconds.
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What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
13.4 units
17.9 units
26.8 units
40.0 units
see the attached figure to better understand the problem
Let
x------> the length side of a rectangle
y-------> the width side of a rectangle
we know that
the perimeter of a rectangle is equal to the formula
[tex]P=2x+2y[/tex]
in this problem
[tex]AB=DC=x[/tex]
[tex]AD=BC=y[/tex]
Step 1
Find the distance AB
[tex]A(-6,4)\\B(2,8)[/tex]
we know that
the distance's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(8-4)^{2} +(2+6)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2} +(8)^{2}}[/tex]
[tex]dAB=\sqrt{80}\ units[/tex]
Step 2
Find the distance BC
tex]B(2,8)\\C(4,4)[/tex]
we know that
the distance's formula between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2} +(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(4-8)^{2} +(4-2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2} +(2)^{2}}[/tex]
[tex]dBC=\sqrt{20}\ units[/tex]
Step 3
Find the perimeter
we know that
the perimeter of a rectangle is equal to the formula
[tex]P=2x+2y[/tex]
[tex]P=2AB+2BC[/tex]
we have
[tex]dAB=\sqrt{80}\ units=8.9\ units[/tex]
[tex]dBC=\sqrt{20}\ units=4.5\ units[/tex]
substitute the values of the distance in the formula
[tex]P=2*8.9+2*4.5=26.8\ units[/tex]
therefore
the answer is
The perimeter of the rectangle is equal to [tex]26.8\ units[/tex]
How many possible outcomes exist when four fair coins are flipped
Answer: 16
Step-by-step explanation:
The number of outcomes exist , when a coin is flipped (tails , head) = 2
The number of possible outcomes , when 'n' number of coins are flipped :_
[tex]2^n[/tex]
For n= 4, the number of possible outcomes , when four coins are flipped :_
[tex]2^4=2\times2\times2\times2=16[/tex]
Hence, the possible outcomes exist when four fair coins are flipped = 16
Please Help!!!
In isosceles triangle ∆ABC with base
BC
draw the median
AM
. Find AM, if the perimeter of ∆ABC is 32 cm and perimeter of ∆ABM is 24 cm.
A cashier always starts the day with $60 in pennies, nickels, dimes, and quarters. She begins with five times as many pennies as quarters, and the number of nickels and dimes are both twice the number of quarters. How many pennies does she start with?
6 pennies
26 pennies
100 pennies
500 pennies
Which of the following is the solution set of the given equation?
14 + 8m = 14 - 3m - 5m
A.) Ø
B.) {0}
C.) {all reals}
EXPERTS ONLY!! Ill mark as brainlist!
What is the intersection of planes ADE and BEA?
a.) Plane BED
b.) Plane ABC
c.) Line BD
d.) Line AE
Answer:
d.) Line AE
Step-by-step explanation:
We have been given a diagram. We are asked to find the intersection of planes ADE and BEA.
Upon looking at our given diagram, we can see that both planes intersect only at two points that are point A and E respectively.
We can also see that the line AE is a common side of both planes, therefore, line AE is the intersection of planes ADE and BEA.
How do you simplify 2√5+3√5-√5
The functions f(x) and g(x) are described below: f(x) = 7x + 9 g(x) = 7x − 4 The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units.
PLEASE HELP
Write the linear inequality shown in the graph. The gray area represents the shaded region.
y ≤ –3x + 5
y ≥ –3x + 5
y ≥ –3x – 5
y ≤ –3x – 5
Answer:
[tex]y\leq-3x+5[/tex]
Step-by-step explanation:
we know that
The solution of the inequality is the shaded area below the solid line (the gray area)
The slope of the solid line is negative
The y-intercept of the solid line is positive
The equation of the solid line is equal to [tex]y=-3x+5[/tex]
therefore
the equation of the inequality is equal to
[tex]y\leq-3x+5[/tex]
Darryl has $5 left in his pocket. He spent $16 on a book, $20 on a compact disc, and $2 on a magazine. How much money did he have at the beginning of the day?
Answer:
He had a total of $43 at the beginning of the day
Step-by-step explanation:
Step 1
Express the amount of money Darryl had in the beginning as follows;
A=E+R
where;
A=initial amount he had at the beginning
E=total expenditure
R=total remainder after spending
In our case;
A=unknown
E=Amount spent on book+amount spent on compact disc+amount spent on magazine
E=(16+20+2)=$38
R=$5
Step 2
Substitute the values in the expression and solve for A;
A=(38+5)=43
He had a total of $43 at the beginning of the day
Only four countries have not officially adopted the metric system
True or false?
Answer:
true
Step-by-step explanation:
The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 =1/2 (x – 1). What is the slope-intercept form of the equation for this line?
y = 1/2x + 2
y = 1/2x – 4
y = 1/2x + 5/2
y =1/2x – 7/2
Imran and Aubrey were asked to find an explicit formula for the sequence 14,5,-4,-13...
Imran said the formula is g(n)=14-9(n-1)
Aubrey said the formula is g(n)=14-9n
Which one of them is right?
Just Irman
Just Aubrey
Both
Neither
PLEASE HELP ASAP!!!
Answer with Step-by-step explanation:
An explicit formula for the sequence
14,5,-4,-13...
given by Imran is g(n)=14-9(n-1)
and by Aubrey is g(n)=14-9n
We have to determine who is right
g(n)= 14-9n
g(1)=14-9
= 5
Hence, formula given by Aubrey is wrong
g(n)=14-9(n-1)
g(1)=14-9(0)=14
g(2)=14-9(1)=5
g(3)=14-9(2)= -4
g(4)=14-9(3)= -13
Hence, formula given by Imran is correct
Hence, correct option is:
Just Imran
Answer:
Only Imran
Step-by-step explanation:
Which of the following is important in a two-column proof?
A.) a list of all theorems
B.) staircase Logic
C.) order
D.) detailed explanations for each step
You are enclosing a rectangular garden with 60 feet of ornamental fencing. the area of the garden is 200 square feet. what are the dimensions of the garden?
The perimeter is equal to 60 feet and has the formula:
Perimeter = 2 l + 2 w
60 = 2 l + 2 w
The area is equal to 200 square feet and has the formula:
Area = l w
200 = l w
Rewriting area in terms of l:
l = 200 / w
Combining this with the perimeter formula:
60 = 2 (200 / w) + 2 w
60 = 400 / w + 2 w
Multiplying all by w:
60 w = 400 + 2 w^2
Dividing by 2 and rearranging:
w^2 – 30 w = - 200
Completing the square:
(w – 15)^2 = - 200 + (-15)^2
(w – 15)^2 = 25
w – 15 = ±5
w = 10, 20
Hence the dimensions of the garden is 10 feet by 20 feet
The width and length of the rectangular garden, given an area of 200 square feet and a total available perimeter of 60 feet, are 10 feet and 20 feet respectively.
Explanation:To solve this problem, we can use the formula for the area of a rectangle, which is length × width = area, and the perimeter of a rectangle, which is 2(length + width) = perimeter. We know the total perimeter available (which is the ornamental fencing) is 60 feet and the area is 200 square feet.
Let's denote the length of the rectangle as L and the width as W. We can then set up these two equations:
2L + 2W = 60L × W = 200We can simplify the first equation to get L + W = 30 and then isolate either L or W to substitute into the area equation. Let's isolate L to get L = 30 - W.
We then substitute this into the area equation to get: (30 - W)W = 200. Solving this quadratic equation, the possible solutions are W=10 and W=20. However, if W=20, that would leave 0 feet for the length, which is not possible. Therefore, we have W=10 and L=20.
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A theater has 500 seats. Three-fourths of the seats are filled. How many seats are filled?
Express the area a of an equilateral triangle as a function of the length of its side s
A cyclist rides her bike at a rate of 10 meters per second. What is this rate in kilometers per hour? How many kilometers will the cyclist travel in 3 hours? Do not round your answers.
Which linear inequality is represented by the graph?
A) y > 2/3x - 2
B) y < 2/3x + 2
C) y > 2/3x + 1
D) y < 2/3x - 1
I NEED THE ANSWER ASAP ‼️
Find the difference.
(8 - 6i) ( -1 -3i )
a) 7 - 9i
b) 9 - 9i
c) 7 - 3i
d) 9 - 3i
Thank you!
The width of the rectangle shown below is 8 inches (in.). The length is 3 feet (ft.). What is the area of the rectangle in square inches?
Answer:
3 feet = 36 inches...
THEN
8 x 36 = 288 inches squared!
Step-by-step explanation:
hope this helped
Some of the steps in the derivation of the quadratic formula are shown. Step 4: Step 5: Step 6: Step 7: Which best explains why the expression cannot be rewritten as during the next step? Negative values, like −4ac, do not have a square root. The ± symbol prevents the square root from being evaluated. The square root of terms separated by addition and subtraction cannot be calculated individually. The entire term b2 − 4ac must be divided by 2a before its square root can be determined.
Answer:c
Step-by-step explanation:
The answer is the square root of terms separated by addition and subtraction cannot be calculated individually.
To find expression cannot be rewritten as during the next step and explain.
What is expression?Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.
The statement that best explains why the expression cannot be rewritten as during the next step is that the square root of terms separated by addition and subtraction cannot be calculated individually.
So, the square root of terms separated by addition and subtraction cannot be calculated individually.
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Which point on the graph represents the y-intercept?
V
W
Y
Z
Find (x - 6)2
a. x2 + 12x + 36
b. x2 - 12x + 36
c. x2 + 6x + 36
s. x2 - 6x + 36
This graph shows the costs of purchasing two types of laundry detergent.
Which statement is true?
a.) Detergent A is less expensive than Detergent B.
b.) Detergent B is less expensive than Detergent A.
c.) Detergent A and Detergent B cost about the same.
Answer:
the other person is correct
Step-by-step explanation:
What is the solution to 2x^2+x+2=0 ??
Answer:
[tex]x=\frac{-1+-i\sqrt{15}}{4}[/tex]
Step-by-step explanation:
[tex]2x^2+x+2=0[/tex]
Apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=2, b= 1, c=2
Plug in the value in the quadratic formula
[tex]x=\frac{-1+-\sqrt{1^2-4(2)(2)}}{2(2)}[/tex]
[tex]x=\frac{-1+-\sqrt{-15}}{4}[/tex]
Square root of -1 is 'i'
[tex]x=\frac{-1+-i\sqrt{15}}{4}[/tex]
The solution of the given quadratic equation is,
x = [-1±i√15]/4
Hence option 3rd is correct.
The given quadratic equation is,
2x²+x+2=0
Here we can see that it is of the form of ax² + bx + c = 0.
Since we know that
The quadrature formula for ax² + bx + c = 0 is
⇒ x = [-b±√(b²- 4ac)]/2a
Here we have,
a = 2
b = 1
c = 2
Put these value in quadrature formula we get,
⇒ x = [-1±√(1²- 4x2x1)]/2x2
= [-1±√(1- 16)]/4
= [-1±√(-15)]/4
Since we know that, i = √-1
Therefore,
⇒ x = [-1±i√15]/4
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Help finding angles 4, 3 ,2 ,5... Picture attached this time
He ratio of black socks to white socks in the sock drawer is 1:4. there are 8 black socks. how many white socks are there? white socks
Final answer:
Based on the ratio of 1:4 for black socks to white socks, and knowing there are 8 black socks, we calculate the number of white socks to be 32.
Explanation:
The question asks us to find the number of white socks when given the ratio of black socks to white socks in a drawer and the number of black socks. The ratio is 1:4, which implies for every black sock, there are 4 white socks. Since there are 8 black socks, to find the number of white socks, we multiply the number of black socks by the ratio of white socks to black socks, which would be 8 * 4 = 32. Therefore, there are 32 white socks in the drawer.