The conditional probability that an adult who lifts weights regularly, also runs regularly is 0.219 or 21.9% if the 18% lift weights regularly, 32% run regularly, and 7% lift weights and run regularly.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
Let's suppose P(A) is the probability of adults who lift weights regularly.
P(A) = 18% = 0.18
Similarly,
P(B) = 32% = 0.32
P(A∩B) = 0.07
We know:
[tex]\rm P(A|B) = \dfrac{P(A\cap B)}{P(B)}[/tex]
[tex]\rm P(A|B) = \dfrac{0.07}{0.32}[/tex]
P(A|B) = 0.219 or
P(A|B) = 21.9%
Thus, the conditional probability that an adult who lifts weights regularly, also runs regularly is 0.219 or 21.9% if the 18% lift weights regularly, 32% run regularly, and 7% lift weights and run regularly.
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Find the surface area of the prism. Enter your answer in the box.
Answer:
Area of the prism = 2(lw + lh + wh)
l = length = 6 m
w = width = 3 m
h = height = 12 m
—
Area of the prism = 2(6*3 + 6*12 + 3*12) = 2(18 + 72 + 36) = 2(126) = 252 m²
—
Have a nice day!!
Write the equality in the given diagram below
Answer:
The inequality for this diagram is x≥-1
Please the explanation... it always helpsssss....
Step-by-step explanation:
The first step is to look at the circle... is it filled in or not... in this case it is...
meaning the symbol is greater than or equal to OR less than or equal to
next the arrow is pointing to the right meaning the symbol must be greater than or equal to
then look at the value at the filled in circle (which in this case is -1)
meaning the inequality must be x≥-1
i really hope this helps!!!!
Please help me I don’t how to do this
Answer:
C. 5f +25
Step-by-step explanation:
When Tariq goes bowling, his scores are normally distributed with a mean of 110 and a standard deviation of 10. Using the empirical rule, what percentage of the games that Tariq bowls does he score between 80 and 140
Using the Empirical Rule, it is found that Tariq scores between 80 and 140 in 99.7% of the games that he bowls.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, considering the mean of 110 and the standard deviation of 10, scores between 80 and 140 are within 3 standard deviations of the mean, hence Tariq scores between 80 and 140 in 99.7% of the games that he bowls.
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Question 1 (1 point)
Consider this right triangle. Determine whether each equation is correct. Select Yes or No fo
each equation
А
5
3
4
4
С
00
B
COS(A)
5
3
O Yes
ONO
Next Page
Yes
Step-by-step explanation:
[tex] \cos( \alpha ) = \frac{base}{hypoteneuse} [/tex]
Its just correct..
A box of chocolates contains 10 milk chocolates, 8 dark chocolates and 6 white chocolates. Sung randomly chooses a chocolate, eats it, then randomly chooses another. What is the probability Sung chose a milk chololate then a white chocolate
Using it's concept, it is found that there is a 0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
Initially, there are 10 + 8 + 6 = 24 chocolates, out of which 10 are milk, hence the probability of eating a milk chocolate first is given by: [tex]\frac{10}{24} = \frac{5}{12}[/tex].Then, there will be 23 chocolates, out of which 6 will be white, hence the probability of eating a white chocolate first is given by: [tex]\frac{6}{23}[/tex].Thus, the probability of milk then white is given by:
[tex]p = \frac{5}{12} \times \frac{6}{23} = \frac{30}{12 \times 23} = 0.1087[/tex]
0.1087 = 10.87% probability Sung chose a milk chocolate then a white chocolate.
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part of a line having two end points
Answer:
a line segment
Step-by-step explanation:
Answer:
A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.
Step-by-step explanation:
hope this helps
Is this true or false?
Answer:
true
Step-by-step explanation:
Use the table below to answer this question:
x y
−1
7
3
3
5
1
Find the average rate of change for the given function from x = −1 to x = 5. (5 points)
−6
−1
1
6
Using it's concept, it is found that the average rate of change of the function from x = -1 to x = 5 is of -1.
What is the average rate of change of a function?It is given by the change in the output divided by the change in the input.
In this problem, the output changes by -6(from 7 to 1) when the input changes by 6(from -1 to 5), hence the average rate is given by:
r = -6/6 = -1.
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20 cm
10 cm
Find the area of this figure.
[?] square centimeters
6 cm
Answer:
260 cm^2
Step-by-step explanation:
Area of rectangle = 20 x 10 = 200 cm^2
Area of triangle = 6 x 20 /2 = 60 cm ^2
Area of figure = 200 + 60 = 260 cm^2
3. The FFA had a fundraiser by selling hot dogs for $1.50 and drinks for $2.00. Their total sales were $400.
a) Write an equation to calculate the total of $400 based on the hot dog and drink sales.
b) Graph the relationship between hot dog sales.
The equation that represents the total of $400 based on the hot dog and drink sales is $400= $1.50H + $2.00D
Using equation for expressionsThe amount sold for each hot dog = $1.50
The total number of hot dogs sold = H × $1.50
The amount sold for each drink = $2.00
The total number of drinks sold = D× $2.00
The total sales made was = $400
Therefore the equation that represents the total of $400 based on the hot dog and drink sales is;
$400= $1.50H + $2.00D
The relationship that exists between the hot dog sales is that the cost is the drinks is higher than the cost of the hot dog.
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please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answer:
6.1 km
Step-by-step explanation:
The Pythagorean theorem tells you the relationship between the lengths of the sides of a right triangle.
c² = a² +b² . . . . a, b are the short sides; c is the hypotenuse
__
The geometry of this problem can be modeled by a right triangle with legs 3.7 km and 4.9 km. The distance of interest is the hypotenuse of the triangle.
c² = 3.7² +4.9² = 13.69 +24.01 = 37.70
c = √37.70 ≈ 6.1
The straight-line distance is about 6.1 km.
Given that ‘z’ is in set of complex number and ‘a’ is any real numbers. Solve the trigonometric equation sin(z) = a for all general solutions.
Recall that for all [tex]z\in\Bbb C[/tex],
[tex]\sin(z) = \dfrac{e^{iz} - e^{-iz}}{2i}[/tex]
so that
[tex]\sin(z) = a \iff e^{iz} - e^{-iz} = 2ia[/tex]
Multiply both sides by [tex]e^{iz}[/tex] to get a quadratic equation,
[tex]e^{2iz} - 2iae^{iz} - 1 = 0[/tex]
Solve for [tex]e^{iz}[/tex]. By completing the square,
[tex]e^{2iz} - 2ia e^{iz} + i^2a^2 = 1 + i^2a^2[/tex]
[tex]\left(e^{iz} - ia\right)^2 = 1 - a^2[/tex]
[tex]e^{iz} - ia = \pm \sqrt{1-a^2}[/tex]
[tex]e^{iz} = ia \pm \sqrt{1-a^2}[/tex]
[tex]iz = \log\left(ia \pm \sqrt{1-a^2}\right)[/tex]
[tex]iz = \ln\left|ia \pm \sqrt{1-a^2}\right| + i \left(\arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n\right)[/tex]
[tex]\boxed{z = -i \ln\left|ia \pm \sqrt{1-a^2}\right| + \arg\left(ia \pm \sqrt{1-a^2}\right) + 2\pi n}[/tex]
where n is any integer.
We are given with:
[tex]{\quad \qquad \longrightarrow \sin (z)={\sf a}\:,\:z\in \mathbb{C}}[/tex]
Recall the identity what we have for the sine function of complex numbers
[tex]{\boxed{\bf{\sin (z)=\dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}}}}[/tex]Put the values to thus obtain:
[tex]{:\implies \quad \sf \dfrac{e^{\iota z}-e^{-\iota z}}{2\iota}=a}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}-e^{-\iota z}=2a\iota}[/tex]
Multiply both sides by [tex]{\sf e^{\iota z}}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}\cdot e^{\iota z}-e^{-\iota z}\cdot e^{\iota z}=2a\iota e^{\iota z}}[/tex]
[tex]{:\implies \quad \sf (e^{\iota z})^{2}-2a\iota e^{\iota z}-1=0}[/tex]
Put x = [tex]{\sf e^{\iota z}}[/tex]:
[tex]{:\implies \quad \sf x^{2}-2a\iota x-1=0}[/tex]
Find the discriminant, here D will be, D = (-2ai)² - 4 × 1 × (-1) = 4 - 4a² = 4(1-a²)
Now, By quadratic formula:
[tex]{:\implies \quad \sf x=\dfrac{-(-2a\iota)\pm \sqrt{4(1-a^{2})}}{2}}[/tex]
[tex]{:\implies \quad \sf x=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]
[tex]{:\implies \quad \sf e^{\iota z}=\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}}[/tex]
[tex]{:\implies \quad \sf \iota z=log\bigg(\dfrac{a\iota \pm \sqrt{1-a^{2}}}{2}\bigg)}[/tex]
Using the formula for logarithms, we have:
[tex]{:\implies \quad \sf \iota z=log(a\iota \pm \sqrt{1-a^{2}})-log(2)}[/tex]
[tex]{:\implies \quad \sf z=\dfrac{1}{\iota}log(a\iota \pm \sqrt{1-a^{2}})-\dfrac{1}{\iota}log(2)}[/tex]
The sine function is periodic on 2πn and zero on (π/2), and the logarithmic expression becomes undefined for all ia±√(1-a²) < 0, so we will take modulus of it
[tex]{:\implies \quad \boxed{\bf{z=\dfrac{1}{\iota}log\bigg|a\iota \pm \sqrt{1-a^{2}}\bigg|-\dfrac{1}{\iota}log(2)+\dfrac{\pi}{2}+2\pi n\:\:\forall \:n\in \mathbb{Z}}}}[/tex]
PLSSS HELP ME WITH MATH
Step-by-step explanation:
always remember, equations and inequalities are like a scale with 2 pans (left and right).
a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.
for an equation the scale has to stay balanced all the time.
and in an inequality one side is heavier that the other (it normally does not matter how much heavier) with "<" or ">" signs, or the scale can be also balanced with "<=" or ">=" signs. just the other side must never be heavier.
A
so, in our case here
2x - 5 = 3
yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.
2x - 5 >= 3
well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.
but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?
2×5 - 5 >= 3
10 - 5 >= 3
5 >= 3
true, great ! so, e.g. x = 5 is also a valid solution.
what else ?
let's simplify the inequality
2x - 5 >= 3
2x >= 8
x >= 4
so, really every value of x that is greater or equal to 4 is a valid solution for the inequality.
B
-2x - 5 = 3
yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.
-2x - 5 >= 3
well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.
but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?
-2×-5 - 5 >= 3
remember, -×- = +
10 - 5 >= 3
5 >= 3
true, great ! so, e.g. x = -5 is also a valid solution.
what else ?
let's simplify the inequality
-2x - 5 >= 3
-2x >= 8
x <= -4
a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.
so, really every value of x that is less or equal to -4 is a valid solution for the inequality.
a boat is traveling east across a river that is 112 meters wide at 8 meters per second. if the river has a northwest current of 5 meters per second, what is the resultant speed of the motorboat rounded to the nearest 10?
boat speed= 8 m/s
river current= 5 m/s
to find:the resultant speed of the motorboat rounded to the nearest 10.
solution:use pythagorean theorem.
let the unknown be "x".
[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]
[tex] {c}^{2} = \sqrt{ {a}^{2} + {b}^{2} } [/tex]
[tex]x = \sqrt{ {8}^{2} + {5}^{2} } [/tex]
[tex]x = \sqrt{64 + 25} [/tex]
[tex]x = 9.4 \: m |s[/tex]
hence, the resultant speed of the motorboat is 9.4 m/s
Use the distributive property to write an equivalent expression.
10(y-7z+1)
Answer:
10y - 70z + 10.
Step-by-step explanation:
10(y-7z+1) Multiply each term in the brackets by 10:
= 10y - 70z + 10
If anyone can help me with this, please feel free to answer
Pam has 15 candies in a jar, her sister threw in some more ( the ones she doesn’t like) and now Pam has 27. Write an equation to determine how many candies ( x) her sister put in the jar. Solve using both inverse operations and balance scale.
Answer:
Step-by-step explanation:
Number of candies that her sister gave = x
Total candies that Pam has now = 27
x + 15 = 27
Inverse operation:
x + 15 = 27
x + 15 - 15 = 27 - 15
x = 12
Answer:
Equations :
27 - 15 = x
15 + x = 27
Step-by-step explanation:
So, we know that 1. Pam starts with 15 candies. and 2. Pam ends up having 27 candies. This means, that she gained candy.
To figure out how many candies her sister gave, her, we have to find the difference between 27 and 15 becuase she goes from having 15 to having 27 after her sister had given some.
x will represent how many cadies Pams' sister had given her :
27 - 15 = x
12 = x
This means Pams' sister gave 12 candies to Pam. To make sure we are correct, we can simply start with how many candies Pam started with (15). And add how many we think her sister added (12)
15 + 12
15 + 12 = 27
Therefore proving, and meaning, that Pams' sister gave her 12 candies.
Possible Equations :
27 - 15 = x
End total (27) minus starting total (15).
15 + x = 27
Starting total (15) plus how many she gained (x) equal to end total (27).
5 cm
3 cm
5 cm
8 cm
2 cm
7 cm
what is the volume of the prism? show your thinking. organize it so it can be followed by others.
8400
Step-by-step explanation:
use multiplication
I cant reveal any more things that I know
A company that makes boxes finds that 7 out of 25 boxes are damaged. What percent of the boxes are damaged
Answer:
15%
Step-by-step explanation:
see the picture for explanation
Answer:
28%.
Step-by-step explanation:
That would be 100 * 7/25
= (100/25) * 7
= 4*7
= 28.
I know the answer but I would like to know how to solve it
Step-by-step explanation:
We can use long division to solve this
First place a 5 in the tens place, this means we are multiplying 5 by 50. This will subtract 250 from 280, leaving us with 30.
Next place a 6 in the ones place, this means we are multiplying 5 by 6. This will subtract 30 from 30, leaving us with 0.
This means we have found our answer of 56.
Answer:
See explanation
Step-by-step explanation:
Basically, division is just saying "how many numbers would go into this number this many times?" We can break this problem down into 200/5 and 80/5. 200/5 is 40, and 80/5 is 16. 40+16 is 56, so the answer is 56.
(I can elaborate further if needed)
Hope this helps!
the area is 72 square meters. the lenght is 9 meters. what is the width
Answer: 8 meters
Step-by-step explanation: 72/9 = 8
Answer:
8 meters
Step-by-step explanation:
Since there is so little information given, I'm assuming this is just the area of a rectangle. The formula you used to find the area of a rectangle is "area = length * width" or "A = l*w".
We are given the area and the length, so we can fill in those spaces in the formula-
72 = 9 * w
Now, in order to find the width. we have to undo in reverse order. We have to divide 72 by 9.
72 (/ 9) = 9 * w (/ 9)
8 = w
Therefore, the width is 8 meters. I hope this helps! Have a lovely day!! :)
exponential function question
Answer: [tex]y = 850(0.943)^t[/tex]
Reason:
The exponential of the form [tex]y = a*b^x[/tex] has 'a' as the initial term and b as the growth or decay factor.
a = 850 is the starting amount
b = 1 + r = 1 + (-0.057) = 0.943 is the decay factor
If the sample loses 5.7% of its mass each year, then it keeps the remaining 94.3% of it.
What is the range of the function represented by this graph?
Answer:
The range of the function given in the graph is the values of all y for any input x.
Therefore, as shown in the graph the value of y for any input of x is below y = 1. Therefore, the range is y <= 1
Which functions have a y-intercept that is greater than the y-intercept of the function g(x) = |x 3| 4? check three options. f(x) = –2 (x – 8)2 h(x) = –5 |x| 10 j(x) = –4(x 2)2 8
Using it's concept, it is found that the functions that have a greater y-intercept than g(x) = |x + 3| + 4 are given as follows:
h(x) = -5|x| + 10.k(x) = 0.25(x - 4)² + 4.m(x) = 0.25|x - 8| + 6.What is the y-intercept of a function?It is the value of the function when the input is of zero, that is, f(0).
For g(x) = |x + 3| + 4, we have that g(0) = 7. As for the other functions, we have that:
f(x) = -2(x - 8)² -> f(0) = -128.h(x) = -5|x| + 10 -> f(0) = 10 -> Greater than g(x).j(x) = -4(x + 2)² + 8 = f(0) = -8.k(x) = 0.25(x - 4)² + 4 -> f(0) = 8 -> Greater than g(x).m(x) = 0.25|x - 8| + 6 -> f(0) = 8 -> Greater than g(x).More can be learned about the y-intercept of a function at https://brainly.com/question/24737967
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!!!40 POINTS AND BRAINLIEST!!! PLEASE SHOW WORK!!!
How much ribbon would be needed to go around a package that had a length [tex]2x^2+3x-5/x^2+x-3[/tex] centimeters and width [tex]x^2-x-5/x^2+x-3[/tex] centimeters?
(SHOW YOUR WORK IF YOU CAN)
Answer:
(6x² +4x -20)/(x² +x -3) cm
Step-by-step explanation:
The perimeter of a rectangle is twice the sum of its length and width. Here, length and width are rational functions. The same relation to perimeter applies.
__
[tex]P = 2(L+W)\\\\P=2\left(\dfrac{2x^2 +3x-5}{x^2+x-3}+\dfrac{x^2-x-5}{x^2+x-3}\right)\qquad\text{use given values for $L$ and $W$}\\\\P=2\left(\dfrac{2x^2+3x-5+x^2-x-5}{x^2+x-3}\right)=\dfrac{2(3x^2 +2x-10)}{x^2+x-3}\\\\P=\dfrac{6x^2+4x-20}{x^2+x-3}\\\\\underline{\ \qquad}\\\\\textsf{It would take $\dfrac{6x^2+4x-20}{x^2+x-3}$ cm of ribbon to go around the package.}[/tex]
Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or
nelther (If the set is not a relation).
A={(1, 2) (2, 2) (3, 2) (4, 2)
A. Function
B. Relation
C. Neither
Answer:
C neither
the coordinates shows that only the x intercepts are moving not y the line of the graph will be horizontal and straight . it is not a function
9. Draw a right triangle that has the 90° angle
between 6 cm and 8 cm sides. What is the
length of the third side? How do you know
without measuring?
What is the area of a square with sides that each have a length of 1 meter?
Answer:
1 m^2
Step-by-step explanation:
A = W * L
1 * 1 = 1
Charlie raked 23 piles of leaves. jessie raked 14 piles of leaves.
how many more piles of leaves did charlie rake than jessie?
2. The annual cost of science club membership is $ 95. The cost
increases by $20 every year. How much will it cost in 9 years?
Answer:
275
Step-by-step explanation:
20 x 9 = 180
180 + 95 = 275
