The value of B on the table is given as follows:
D. 90.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
From the table, the constant is obtained as follows:
k = 20/14 = 40/28 = 10/7.
Hence the relationship is given as follows:
y = 10x/7.
The value of B is the value of y when x = 63, hence:
y = 10 x 63/7
y = 10 x 9
y = 90.
Meaning that the correct option is given by option D.
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Please help me with the following question.
The probability that an individual with a positive screening test will indeed have the disease is 0.9798.
What is probability?The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
A medical study team wanted to assess a suggested diabetic screening.
When administered to a random sample of 150 diabetic individuals, the test produced 34 positive findings.
While it produced 9830 negative findings when administered to a random sample of 9850 healthy people.
Assume that 30% of the population has diabetes.
The probability that an individual with a positive screening test will indeed have the disease is 0.9798.
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How would you find x?
Step-by-step explanation:
n (TUB)=100-20
=80
from formula,
80 = x (x-5)+x+2x
80= x^2-5x+3x
80=x^2-2x
x^2-2x-80=0
x^2-10x+8x-80=0
x(x-10)+8 (x-10)=0
(x+8)(x-10)=0
either,
x+8=0
×=-8 (neglected)
Or,
x-10=0
×=10
A six-sided die is rolled, and the number N on the uppermost face is recorded. From a jar containing 10 tags numbered 1,2,...,10 we then select N tags at random without replacement. Let X be the smallest number on the drawn tags. Determine Pr{X=2}and E[X].
Please solve it step by step especially the expectation part. appreciate it.
You can draw some intuition graph and picture to help you explain
As per the probability the equation of E[X] = 2 * P(X=2) + 3 * P(X=3) + ... + 10 * P(X=10)
A die is a cube-shaped object with six faces numbered from 1 to 6. Each face has an equal chance of landing face up when the die is rolled. When you roll a die, you are randomly selecting one of the six numbers.
Let's first calculate the probability that X is equal to 2. To do this, we need to consider two cases:
The first case is when N = 2. In this case, there is only one way to select 2 tags, both with the number 2.
The second case is when N is greater than 2. In this case, there are 9 ways to select the first two tags, both with the number 2. The rest of the tags can be selected in any order.
The probability that X is equal to 2 can be calculated as follows:
P(X=2) = (1/45) + (9/45 * (9/44) * (8/43) * ... * ((10-N+1)/(10-N+2)))
Next, we calculate the expected value of X. The expected value of X is calculated as follows:
E[X] = sum of (each value of X multiplied by its probability)
E[X] = 2 * P(X=2) + 3 * P(X=3) + ... + 10 * P(X=10)
The expected value of X gives us an idea of the average value of X over many trials of rolling the die and selecting the tags.
In conclusion, the probability that X is equal to 2 is calculated by considering two cases, and the expected value of X is calculated by summing up each value of X multiplied by its probability.
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16. _______________________ has one outcome or collection of outcomes.
An event has one outcome or collection of outcomes.
How to complete the statementAn event in probability is a set of one or more outcomes from a sample space, which is a set of all possible outcomes of a random experiment.
An event represents a situation or condition of interest in a random experiment.
The event can have one outcome or multiple outcomes, and it can be either simple (consisting of a single outcome) or compound (consisting of multiple outcomes).
For example, the event of rolling a six on a single die is a simple event with one outcome
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Which Number line represents the solution set of the inequality
Answer:
Second option
Step-by-step explanation:
Given inequality
[tex]-8t\:+\:2\:\dfrac{1}{4}\ge 42\dfrac{1}{4}[/tex]
Convert mixed fractions to improper fractions:
[tex]2\dfrac{1}{4}=\dfrac{9}{4}[/tex]
[tex]2\dfrac{1}{4}=\dfrac{169}{4}[/tex]
The inequality becomes
[tex]-8t+\dfrac{9}{4}\ge \dfrac{169}{4}[/tex]
Multiply throughout by 4
[tex]-32t + 9 \ge 169[/tex]
[tex]\rightarrow -32t \ge 169-9\\\\-32t \ge 160\\\\-t \ge \dfrac{160}{32}\\\\-t \ge 5\\\\[/tex]
Multiply throughout by -1 (the inequality is reversed):
[tex]t \le -5[/tex]
The second option correctly represents this inequality
Option #1: Solve the inequality and graph the solution set.
Option #2: Test out the options to see which has solutions.
Let's do Option #2:
The first possible answer shows t < -5, so if we pick t = -10, we'd be in that interval. Let's test if t = -10 is a solution:
[tex]\begin{aligned}-8(-10) + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]80 + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]82\frac{1}{4} &\stackrel{\checkmark}{\geq} 42\frac{1}{4}\end{aligned}[/tex]
That checked!
So this alone tells us that the bottom two answers are not possible answers, since they do not include -10 in their sets.
But now we need to decide between the top answer or the one right below it. The only difference between the two number lines is that the top one does NOT include x = -5, while the second one does. So we need to test out if x = -5 is a solution, just like we did for x = -10.
[tex]\begin{aligned}-8(-5) + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]40 + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]42\frac{1}{4} &\stackrel{\checkmark}{\geq} 42\frac{1}{4}\end{aligned}[/tex]
Because of the "or equal to" in the inequality, this does check.
Our answer is the second number line, with a closed circle at x = -5 and the shading to the left.
If you wanted to do this by solving the inequality, that work would look like this:
[tex]\begin{aligned}-8t + 2\frac{1}{4} &\geq 42\frac{1}{4}\\[0.75em]-8t + 2\frac{1}{4}-2\frac{1}{4} &\geq 42\frac{1}{4}-2\frac{1}{4}\\[0.75em]-8t &\geq 40\\[0.75em]\dfrac{-8t}{-8}~ &{\boldsymbol{\leq}}~ \dfrac{40}{-8}\\[0.75em]t &\leq -5\end{aligned}[/tex]
Note that the inequality flipped because we divided both sides of the inequality by a negative number.
The area of of 20 yards
Correct option is D, using area of playground the length and width of the playground is length = 10 yd, breadth = 2 yd.
What is area in math?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy. A plane figure's area is the space that its perimeter encompasses. The area of a closed figure is the total number of unit squares covering its surface. Area is measured in square units like cm2 and m2.
The area of a shape is the area enclosed by its perimeter or boundary.
A = b × h is the formula for calculating the area, A, of a square or rectangle.
The playground's length is 5 times more than its breadth,
thus l=5w.
However, 10=2 x 5 allows us to write
l=5w, and
area = 20
=l x w
= (5x2) x 2
=20.
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Complete question -
The area of a playground is 20 square yards. The length of the playground is 5 times longer than its width. Find the length and width of the playground.
length = 1 yd, width = 20 yd
length = 2 yd, width = 10 yd
length = 10 yd, width = 2 yd
length = 20 yd, width = 1 y
Original Price %
100%
100%
100%
100%
100%
Markdown Amount Original Sales Price - New Sales
Original Sales Price X Markdown Percentage Markdown/Discount Amount
Original Sales Price minus Markdown/Discount Amount = New Sales Price
Original Sales Price X (100% minus Markdown Percentage) = New Sales Price
Paid Percentage
Discount Percent
10%
20%
33%
Price
50%
75%
The "Markdown%" is defined by RICS and the majority of the retail business as "Markdown dollars divided by Sales."
How do I calculate the quantity and percentage of markdown?Establish the markdown. Subtract the actual selling price from the difference in pricing. After that, multiply this outcome by 100. The outcome is a percentage markdown.
Here,
The "Markdown%" is defined by RICS and the majority of the retail business as "Markdown dollars divided by Sales." The dollar discount is divided by the NET retail sales price to determine the markdown percentage (times 100). As an illustration, a
=> $30 item is reduced to $24 and sold.
=> The markdown percentage is 25% ($6/$24).
=> Original Sales Price X (100% minus Markdown Percentage)
=> New Sales Price Paid Percentage= Discount Percent is 10%
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The bed is a scale drawing with the width, w, of the bed measuring exactly 2 inches. With a scale of 1 in. = 1 1/2 ft, what is the width of the actual bed?
Make a proportion and solve for w.
Answer:
The answer is 24 inches
Step-by-step explanation:
A restaurant plans to use a new food delivery service. The food delivery service charges $4.98 for every 2 meal’s delivered, plus $2.00 service fee. What is the slope of this situation? 2.00 2.49 4.49 4.98
Answer: 2.49
Step-by-step explanation:
$2.00 is an automatic fee, so this is our y-intercept.
$4.98 for every two meals, so if we divide that by two, we get the price for one meal, which is $2.49.
In a typing class, the average number of words per minute N typed after t weeks of lessons was found to be
N =157/1 + 5.4e^-0.12t
Find the time necessary to type (a) 50 words per minute and (b) 75 words per minute
Answer:
i hope this helpes
Step-by-step explanation:
(a) To find the time necessary to type 50 words per minute, we need to solve the equation:
157/1 + 5.4e^-0.12t = 50
Rearranging the equation to isolate e^-0.12t and using the natural logarithm, we can find t:
ln(N - 157) = ln(5.4) - 0.12t
-ln(N - 157) = 0.12t - ln(5.4)
0.12t = ln(5.4) + ln(N - 157)
t = (ln(5.4) + ln(N - 157)) / 0.12
Plugging in N = 50, we get:
t ≈ 11.52 weeks
(b) To find the time necessary to type 75 words per minute, we follow the same steps as above:
157/1 + 5.4e^-0.12t = 75
ln(N - 157) = ln(5.4) - 0.12t
-ln(N - 157) = 0.12t - ln(5.4)
0.12t = ln(5.4) + ln(N - 157)
t = (ln(5.4) + ln(N - 157)) / 0.12
Plugging in N = 75, we get:
t ≈ 9.32 weeks
Answer:
For 50 wpm : 7.7 weeks approximately
For 75 wpm : 13.3 weeks approximately
Step-by-step explanation:
Given the relationship between N, the typing speed and t, the number of weeks of lessons as:
[tex]\mbox{\large N= \dfrac{157}{1+5.4e^{-0.12t}}}[/tex]
To solve for t for a particular N
cross-multiply the left side with the right side denominator to get
[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{N}}[/tex]
For N= 50 this works out to
[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{50}}[/tex]
[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157}{50} - 1}\\[/tex]
[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157-50}{50} } = \dfrac{107}{5} = 2.14[/tex]
Divide by 5.4 both sides:
[tex]\mbox{\large e^{-0.12t } = \dfrac{2.14}{5.4}} = 0.3963\\[/tex]
Take natural logs on both sides
[tex]\mbox{\large \ln(e^{-0.12t}) = \ln(0.3963)\\}[/tex]
[tex]\mbox{\large \ln(e^{-0.12t}) = -0.12 \;\textrm{since $ln(e^x)$ = x}}[/tex] since ln(eˣ) = x
ln(0.3963) = -0.9256
Therefore
[tex]t = \dfrac{-0.9256}{-0.12} = \dfrac{0.9256}{0.12} = {7.7133 \;weeks\approx \mbox{\large \boxed{7.7 \;weeks}}[/tex]
For N = 75, follow the same strategy and you will end up with
[tex]1+5.4e^{-0.12t}=\dfrac{157}{75} \\\\\\1+5.4e^{-0.12t}= 2.0933\\\\5.4e^{-0.12t} = 2.0933 - 1 = 1.0933\\\\e^{-0.12t} = \dfrac{1.0933}{5.4} = 0.2025\\\\[/tex]
Taking logs on both sides
[tex]-0.12t =-1.5971[/tex]
[tex]t = \dfrac{-1.5971}{-0.12} = 13.3097 \;weeks \approx \boxed{\mbox{\large 13.3 \;weeks}}[/tex]
solve each integral using the information from groupwork question 2. (1) (0.25 points)z sin(x) cos3 (x) dx
The solution of the integral ∫sin ( x ) cos³( x )dx is equal to ( cos⁴(x) / 4 ) + c , where 'c' is the constant.
Solution of the integral is solved by substitution method :
∫∫sin ( x ) cos³( x )dx ___( 1 )
Let us consider cos ( x ) = t ____( 2 )
Now differentiate both the side we get,
-sin (x ) dx = dt
⇒ sin (x ) dx = -dt ____( 3 )
Substitute the value of ( 2 ) and ( 3 ) in ( 1 ) we get,
∫ t³ ( -dt )
= - ∫ t³ dt
= - t⁴ / 4 + c
Where 'c' is the integral constant .
Relace t = cos (x)
= - cos⁴ ( x ) / 4 + c
Therefore, the integral of the ∫sin ( x ) cos³( x )dx is equal to
( cos⁴(x) / 4 ) + c .
The above question is incomplete, the complete question is:
solve each integral using the information : ∫sinx cos³x dx
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whatcis 626362737287387287373 times 77474747743874837847348734463763786837
The result of 626362737287387287373 times 77474747743874837847348734463763786837 represented in scientific notation is 4.80498727057566113882339366151788673587 × 10⁹⁵.
The number you provided in your question can be represented in scientific notation. Scientific notation is a way of expressing numbers in a compact form that is especially useful for very large or very small numbers. The number you provided in your question can be represented in scientific notation as:
7.7474747743874837847348734463763786837 × 10⁷⁷
And 626362737287387287373 can be represented as:
6.26362737287387287373 × 10¹⁸
The product of these two numbers can be calculated as follows:
(7.7474747743874837847348734463763786837 × 10⁷⁷) × (6.26362737287387287373 × 10¹⁸) =
= (7.7474747743874837847348734463763786837 × 6.26362737287387287373) × (10⁷⁷ × 10¹⁸) =
= 48.0498727057566113882339366151788673587 x 10⁹⁵
So, the result of 626362737287387287373 times 77474747743874837847348734463763786837 in scientific notation is:
4.80498727057566113882339366151788673587 × 10⁹⁵
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What is the slope of the linear relationship? a graph of a line that passes through the points 0 comma 1 and 4 comma 0 one fourth negative one fourth four over 1 negative one fourth
The slope of the linear qeuation is -1/4 = -0.25
What is the slope of the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if a line passes through (x₁, y₁) and (x₂, y₂) the slope will be:
a = (y₂ - y₁)/(x₂ - x₁)
We can see the points (0, 1) and (4,0). Then the slope is:
a = (0 - 1)/(4 - 0) = -1/4
The slope is -1/4.
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find all rational zeros
The zeros of a polynomial are the values of x for which the polynomial is equal to 0.
What is polynomial?
A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a non-negative integer power. It is an algebraic expression that can involve constants, variables, and exponents.
To find the rational zeros of a polynomial, use the Rational Zero Theorem. This theorem states that if the polynomial is written in standard form, ax^n + bx^n-1 + cx^n-2 + ... + k = 0, then the possible rational zeros are any rational number that can be expressed as p/q, where p is a factor of k (the constant) and q is a factor of a (the leading coefficient).
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Complete question is:
How to Find All Possible Rational Zeros Using the Rational Zeros Theorem With Repeated Possible Zeros?
Jayden is handing out chocolate candies and bubble gum for Halloween. He wants to have a total of 8 pounds of candy, but he doesn't want to spend more than $19.00 total on the candy. If chocolate candies cost $1.50 per pound, and bubble gum cost $2.90 per pound, how many pounds of each type of candy should he buy?
He should buy (blank) pounds of chocolate candies and (blank) pounds of bubble gum.
Answer:
He should buy 4 pounds of chocolate candies and 4 pounds of bubble gum.
Step-by-step explanation:
1.50x4 (4 pounds) equals = $6
2.90x4 (4 pounds) equals = $11.6
$11.6 + $6 = $17.6
Hope this helps! <3 (so sorry if this is wrong :C)
Given the figure, and MN || QR, what can be concluded?
PM
PN
PQ = PR
Q
M
MN = QR
P
N
R
MP=2-QM
PM
NR
=
PN
MQ
As segments MN and QR are parallel, the correct statement regarding the triangles is given as follows:
PM/PQ = PN/PR.
How to obtain the correct statement?The theorem used to solve this problem is given as follows:
A line parallel to one side of a triangle divides the other two proportionately.
The parallel segments are given as follows:
MN and QR.
Hence the segments that have proportional length are given as follows:
PQ and PQ.
As these segments are divided by segment MN, the proportional relationship is given as follows:
PM/PQ = PN/PR.
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The answers please I’ll give you points fast
The length of the hypotenuse for all the right-angled triangles are found using trigonometric functions.
What is the hypotenuse?
The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.
11) when angle = 30°
perpendicular = 3
sin 30 = perpendicular/ hypotenuse
0.5 = 3/hypotenuse
hypotenuse = 6
12) sin 30 =perpendicular/ hypotenuse
0.5 = 8/ hypotenuse
hypotenuse = 16
13) sin 60 = 11√3 / x
Hypotenuse = x = 11√3/ sin 60 = 11√3 / (√3/2) = 22
14) sin 30 = perpendicular/ hypotenuse
0.5 = 9/x
x = 18
15) cos 60 = base/ hypotenuse
0.5 = 1 /x
x = 2
16) sin 60 = 12√3/x
√3/2 = 12√3/x
Hypotenuse = x = 24
Therefore the length of the hypotenuse for all the right-angled triangles are found.
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The expression (3x - 4y²) (3x + 4y²) is equivalent to:
O9x²-16y^4
O9x²-8y^4
O9x² +16y^4
O6x²-16y^4
O6x²-8y^4
Answer:
9x²-16y^4
Step-by-step explanation:
(3x - 4y²) (3x + 4y²)
→ expand the expression
(3x²) - (4y²)
→ simplify the expression
3² × x² - 4² × (y²)²
→ calculate
9x² - 16(y²)²
→ simplify (use (a^m)^n = a^mn
9x² - 16x^4
Answer: 9x² - 16x^4
hope this helps!
What is the answer 1/2 = 5d-1/2
Answer:
d=1/5
Step-by-step explanation:
Answer: d=2/5
Step-by-step explanation:
A basketball team played a total of 28 games. The ratio of the total number of games they won to the number of games they lost is 43. How many games did they win? How many games did they lose?
Answer:
win=16, lose=12
Step-by-step explanation:
total is 28, and win to lose is 4:3
so 4+3=7 , which means we put them into 7 part
and 28/7=4, each part equal to 4
so the win= 4 time 4=16
lose = 3 time 4= 12
Anyone good with geometry please help with as many questions ASAP. I would greatly appreciate it!
Answer: it is Konnachair, dm me there
Step-by-step explanation:
25d^3 +210d^2-640=0
solve for d with steps please
Answer:
Step-by-step explanation:
The equation 25d^3 + 210d^2 - 640 = 0 can be reduced to a quadratic equation by using the factor theorem:
(d - 8)(25d^2 + 182d + 80) = 0
So, one root of the equation is d = 8. To find the other two roots, you can solve the quadratic equation:
25d^2 + 182d + 80 = 0
Using the quadratic formula, the roots can be calculated as:
d = (-b ± √(b^2 - 4ac)) / 2a
Where a = 25, b = 182, and c = 80.
So,
d = (-182 ± √(182^2 - 4 * 25 * 80)) / 2 * 25
d = (-182 ± √(33124 - 8000)) / 50
d = (-182 ± √(25124)) / 50
d = (-182 ± 158) / 50
Therefore, the roots of the equation are:
d = (-340 + 158) / 50 = (-182 + 158) / 50 = (-24) / 50 = -0.48
d = (-340 - 158) / 50 = (-182 - 158) / 50 = -340 / 50 = -6.8
So, the solutions to the equation are d = 8, -0.48, and -6.8.
Alexander is working two summer jobs, making $10 per hour washing cars and $8 per hour landscaping. Last week Alexander worked twice as many hours washing cars as he worked landscaping and earned a total of $84. Write a system of equations that could be used to determine the number of hours Alexander worked washing cars last week and the number of hours he worked landscaping last week. Define the variables that you use to write the system.
x = 2y and x*$10 + y*8 = $84 are the required system of equations and when we solve it, we can observe that he spent 6 hours cleaning vehicles and 3 hours gardening.
What is a system of equations?A group of equations comprising one or more variables is known as a system of equations.
The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
We must first define the variables:
x is the amount of time spent cleaning autos.
x = the number of landscaping hours.
Since we know Alexander spent twice as much time cleaning vehicles as he did landscaping, we can say:
x = 2y
Additionally, we know that he made $84 in total, so:
x*$10 + y*8 = $84
The set of equations is thus:
x = 2y
x*$10 + y*8 = $84
We simply swap the first equation with the second one to answer it:
(2y)*$10 + y*8 = $84
y*$28 = $84
y = $84/$28 = 3
He thus spent three hours landscaping, and:
x = 2*y = 2*3 = 6
6 hours washing cars.
Therefore, x = 2y and x*$10 + y*8 = $84 are the required system of equations and when we solve it, we can observe that he spent 6 hours cleaning vehicles and 3 hours gardening.
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There were 125 females and 100 males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answer:
4:9
Step-by-step explanation:
To find the ratio of males to the total number of people present, we need to divide the number of males by the total number of people.
The total number of people present is the sum of the number of females and the number of males:
Total = 125 females + 100 males = 225 people
So the ratio of males to the total number of people present is:
100 males / 225 people
To simplify this ratio, we can divide both the numerator and denominator by the greatest common factor, which is 25.
So the simplified ratio is:
100/225 = 4/9
So the ratio of males to the total number of people present is 4:9
compare how men and women rate their general state of health using a comparative chart. using your chart, briefly compare and contrast how men and women rate their general state of health.
Men are more likely to have diabetes, heart disease, and stroke, whereas women are more likely to have arthritis and depression, with significant regional variation.
What is the main difference between man and woman?In contrast to a woman, who has a smaller body and bone structure, weaker muscles, and thinner skin and a thinner skull, a man has a larger body, greater bone structure, stronger muscles, and thicker skin and skull. 3. Men and women experienced chronic disease at different rates (2.09 vs 1.90 per 100 person-years, respectively).
The most frequent disease was diabetes (40.9%), which was then followed by COPD (32.8%), stroke (9.6%), CHF (8.2%), MI (5.9%), and lung cancer (2.6%).
Males have one X and one Y chromosome, while females typically have two X chromosomes in their pair. The series of developmental events that give bodies and brains male features are brought on by a gene on the Y chromosome.
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The complete question is"The Most Recent Round Of Data Collection Occurred Over The Course Of September 2013–November, 2013 In HINTS 4 Cycle 3.In This Lab, You Will Be Using A Subset Of The HINTS 4 Cycle 3 Data To Practice Creating Effective And Informative Graphical Representations Of Data, Which May Include Histograms And Circle Graphs. About The Data For This Lab, You Need To
The most recent round of data collection occurred over the course of September 2013–November, 2013 in HINTS 4 Cycle 3.In this lab, you will be using a subset of the HINTS 4 Cycle 3 data to practice creating effective and informative graphical representations of data, which may include histograms and circle graphs. "
A system of linear inequalities is shown.{ >1/2 − 2, <1/2 + 1}
Which graph shows the solution to the system
of inequalities?
Answer:
The graph that shows the solution to the system of linear inequalities is the one that has a line with a slope of -2 and y-intercept of 1/2, and another line with a slope of 1 and y-intercept of 1/2. The region of the plane that lies between the two lines and satisfies both inequalities is the solution set.
UGENT!!!!!!
Dataset 1: [10 8 22 5 6 1 7]
Dataset 2: [122.5 123.8 121.2 125.8 120.2]
Please calculate the range, variance, and standard deviation for Dataset 1 and
Dataset 2. Please show all math involved.
Dataset 1:
Range = 21
Variance: = 150.33
Standard deviation: = 12.37
Dataset 2:
Range: = 5.6
Variance: = 1.44
Standard deviation: = 1.2
How to calculate the valueVariance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed.
Dataset 1:
Range: 22-1 = 21
Variance: (sum of squares of deviations from mean) / (number of items - 1) = (902/6) = 150.33
Standard deviation: square root of variance = sqrt(150.33) = 12.37
Dataset 2:
Range: 125.8-120.2 = 5.6
Variance: (sum of squares of deviations from mean) / (number of items - 1) = (7.2) = 1.44
Standard deviation: square root of variance = sqrt(1.44) = 1.2
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Modeling with Composite Functions
A department store has marked down its merchandise by 25%. It later decreases by $5 the price of items that have not sold.
a. Write a function f(x) to represent the price after the 25% markdown.
b. Write a function g(x) to represent the price after the $5 markdown.
c. Use a composition function to find the price of a $50 item after both price adjustments.
d. Does the order in which the adjustments are applied make a difference? Explain.
a. f(x) = 0.75x.
b. g(x) = x - 5.
c. f(50) = 0.75×50 - 5 ⇒ f(50) = 32.5.
d. Yes, The order in which the adjustments are taken does make a difference.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, A department store has marked down its merchandise by 25%. It later decreases by $5 the price of items that have not sold.
Let, 'x' be the price of the merchandise.
Therefore, After 25% mark down it would be (75/100)×x = 0.75x and a $5 decrease would be (- $5).
a. A function f(x) to represent the price after the 25% markdown is,
f(x) = 0.75x.
b. A function g(x) to represent the price after the $5 markdown is,
f(x) = x - 5.
c. A composition function to find the price of a $50 item after both price adjustments is f(50) = 0.75x - 5.
f(50) = 0.75×50 - 5.
f(50) = 37.5 - 5.
f(50) = 32.5.
d. It would make a difference, Let's assume the price is $100,
Then a 25% markdown would be $75 and with a decrease of $5 the final price would be $70.
Again, Assuming the price to be $100, 5$ decrease is $95 and 75% of $95 is 0.75×95 = $71.25.
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The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Which of the following is the best interpretation of the standard deviation? A. The number of breakdowns on a randomly selected day is expected to be 0.28. B. The number of breakdowns on a randomly selected day will be 0.28 away from the mean. C. The average number of breakdowns per day for a random sample of days is expected to be 0.28 D. On average, the number of breakdowns per day varies from the mean by about 0.28. E. The number of breakdowns per day for a random sample of days is expected to be 0.28 away from the mean.
The correct option is (D). On average, the number of breakdowns per day varies from the mean by about 0.28.
Because standard deviation represents the typical distance between each data point and the mean.
The variability in a dataset is condensed into a single value called the standard deviation (SD). It shows the typical separation between the mean and each data point. Smaller values show that the data points are more evenly distributed around the mean, indicating that the dataset's values are generally stable.The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is.
A discrete random variable's variance and standard deviation can be seen as measurements of the variability of the values the random variable assumes throughout the course of an experiment's multiple trials.So, the correct answer is On average, the number of breakdowns per day varies from the mean by about 0.28.
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You have a special computer that is cooled by a water tank. The water evaporates a little bit
each day but each day the same amount evaporates. At first the level of the water in the
tank is 15 cm. After 2 days have passed it is down to the tank has 14 cm of water. When will
the water run out?
Step-by-step explanation:
We know that the water level in the tank is 15 cm initially, and after 2 days it has dropped to 14 cm. Therefore, the water level is dropping by 1 cm per day. To find out when the water will run out, we need to know how many days it will take for the water level to drop to 0 cm.
To find this out, we can use the following formula:
Days = (Initial water level - Final water level) / Rate of evaporation per day
Plugging in the values, we get:
Days = (15 - 0) / 1 = 15 days
So, the water will run out in 15 days.
