Of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit to climb the mountain. What is the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?
The probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is 47.2%.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Take 12 of 200 to determine the number of fit men,
Fit men = 12% × 200
Fit men = 0.12 × 200
Fit men = 24
Since they are asking males and the number of people fits enough, you must subtract the fit men from the fit people so you are not doubling the men
60 - 24 = 36
Add the fit people to the male group,
36+200 = 236
The probability will be calculated as,
P = 236/500
P = 118/250
P = 59/125
P = 47.2%
The probability is 47.5%.
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what is the coefficient in the algebraic expression 7XY squared ?
.help me please thank you
the first one because all the other ones are wrong
Find an equation of the tangent line to the function y = 4x4 at the point p(1, 4).
The equation of the tangent line to the function y = 4x⁴ at (1, 4) will be y = 16x - 12.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
The function is given as,
y = 4x⁴
The slope of the line is given as,
m = y'
m = 16x³
m = 16 (1)³
m = 16
Then the equation of the tangent line is given as,
y = 16x + c
The equation is passing through (1, 4). Then we have
4 = 16 (1) + c
4 = 16 + c
c = - 12
The equation of the tangent line to the function y = 4x⁴ at (1, 4) will be y = 16x - 12.
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Please help with #10 and #11
Suppose △ABC≅△EFG. Which congruency statement is true? AB¯¯¯¯¯≅FG¯¯¯¯¯ BC¯¯¯¯¯≅FG¯¯¯¯¯ AC¯¯¯¯¯≅EF¯¯¯¯¯ AB¯¯¯¯¯≅EG¯¯¯¯¯
A = E
B = F
C = G
Look for the equation which has the same placement. Your answer should be B) BC=FG
Answer: Second option [tex]BC\cong FG[/tex] is the correct option.
Explanation:
If two triangles are congruent then their corresponding sides are congruent.
In [tex]\triangle ABC[/tex] and [tex]\triangle EFG[/tex], AB, BC, and CA are corresponding to EF, FG and GE respectively.
Therefore, if [tex]\triangle ABC\cong \triangle EFG[/tex] then,
[tex]AB\cong EF[/tex],
[tex]BC\cong FG[/tex],
And, [tex]CA\cong GE[/tex]
Therefore, only second option is correct.
The point (4,-3) lies on the circle centre (-2,5). Find the radius of the circle
The radius of the circle with the given coordinates is 6.32 units.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Given that, the point (4,-3) lies on the circle center (-2,5).
Using distance formula we can find the radius of a circle
We know that, Distance =√[(x2-x1)²+(y2-y1)²]
Now, radius =√[(-2-4)²+(5-(-3))²]
=√[(-6)²+(2)²]
= √36+4
= √40
= 6.32 units
Therefore, the radius of the circle is 6.32 units.
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Solve for x.
2/5≤x−4
if r is five less than three times L, then r=
Answer: r=L-3
Step-by-step explanation:
type the slope intercept equation of the line that passes through the point (1,1)&(7,4) enter fraction in simplest form
What is the average of all integers from 11 to 35
Molly jogged at a rate of 6 miles per hour. what is her rate in feet per second?
Answer: the correct answer would be 8.8 ft/s
What is the common number between 1, and 100?
Use your calculator to find an interval of length 0.01 that contains a root. (enter your answer using interval notation.)
How can I combine like terms ?
Step-by-step explanation: To understand how to combine like terms, let's look at an example.
9c + 2c
The two parts of this expression, +9c and +2c, are called terms. The numbers in front of the variables, +9 and +2, are called coefficients.
Since the variables, c and c, are identical, the two terms in this problem are called like terms.
Like terms can be added together by simply adding their coefficients.
So in this problem, since 9 + 2 = 11, 9c + 2c is simply 11c.
the vertices of a parallelogram are j (-5,0) K(1,4), L(3,1) and M(-3,-3). How can you use slope to determine whether the parallelogram is a rectangle? is it a rectangle? Justify your answer.
To determine if the parallelogram is a rectangle, we can use the slopes of its sides. Given the coordinates of the vertices, we can calculate the slopes and compare them. If the opposite sides have equal slopes, then the parallelogram is a rectangle.
Explanation:To determine if the parallelogram is a rectangle, we can use the slopes of its sides. A rectangle has opposite sides that are parallel and equal in length, so the opposite sides of a rectangle will have equal slopes.
Using the given vertices, we can find the slopes for the sides:
Slope of JK = (4 - 0) / (1 - (-5)) = 4/6 = 2/3
Slope of KL = (1 - 4) / (3 - 1) = -3/2
Slope of LM = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3
Slope of MJ = (0 - (-3)) / (-5 - (-3)) = 3/(-2) = -3/2
Since the opposite sides JK and LM have equal slopes of 2/3 and the opposite sides KL and MJ have equal slopes of -3/2, we can conclude that the parallelogram is a rectangle.
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A right triangle has a hypotenuse of 50 feet and a leg of 14 feet. Which is the length of the other leg? 24 feet 30 feet 42 feet 48 feet
Answer:
The length of the other leg is 48 feet
Step-by-step explanation:
To find the length of the other leg, we will simply follow the steps below;
We will use the Pythagoras theorem formula to solve;
Write down the Pythagoras theorem formula
opposite² + adjacent² = hypotenuse²
Let the value of the other leg be x
From the question given;
hypotenuse = 50, a leg, say the opposite = 14
Lets substitute into our formula;
opposite² + adjacent² = hypotenuse²
14² + x² = 50²
196 + x² = 2500
subtract 196 from both-side of the equation
196 - 196 + x² = 2500 - 196
x² = 2304
Take the square root of both-side of the equation
√x² = √2304
x = 48 feet
The length of the other leg is 48 feet
In the figure, angle D measures 31° and angle A measures 27°.
The measurement of angle B is °.
The measurement of angle F is °.
Answer:
63 and 59 are correct
Step-by-step explanation:
Which function below is the inverse of f(x)=x^2-25
f(x) = x^2-25
inverse:
y = x^2-25
x = y^2-25
y = sqrt(5 +25)
Answer is B
Please help!
Which of the following functions has the greatest y-intercept?
f(x)
x y
(−3, 9)
( −2, 4)
(−1, 1)
(0,0)
( 1, 1)
(2 ,4)
g(x) = 5 cos(3x) − 5
The answer is both. Desmos graphing calculator is a great tool if you don't have a calculator on you. Hope this helps!
6x equals 7-4y solve for y
The given values of x, the corresponding values of y are:
1. When x = -2, [tex]\(y = \frac{19}{4}\)[/tex]
2. When x = -1, [tex]\(y = \frac{13}{4}\)[/tex]
3. When x = 0, [tex]\(y = \frac{7}{4}\)[/tex]
Let's solve the equation [tex]\(6x = 7 - 4y\)[/tex] for y:
[tex]\[6x = 7 - 4y\][/tex]
First, isolate the term with y:
[tex]\[4y = 7 - 6x\][/tex]
Next, divide both sides by 4 to solve for y:
[tex]\[y = \frac{7 - 6x}{4}\][/tex]
Now, we can find the values of y for each given value of x:
1. For x = -2:
[tex]\[y = \frac{7 - 6(-2)}{4} = \frac{7 + 12}{4} = \frac{19}{4}\][/tex]
2. For x = -1:
[tex]\[y = \frac{7 - 6(-1)}{4} = \frac{7 + 6}{4} = \frac{13}{4}\][/tex]
3. For x = 0:
[tex]\[y = \frac{7 - 6(0)}{4} = \frac{7}{4}\][/tex]
Therefore, for the given values of x, the corresponding values of y are:
1. When x = -2, [tex]\(y = \frac{19}{4}\)[/tex]
2. When x = -1, [tex]\(y = \frac{13}{4}\)[/tex]
3. When x = 0, [tex]\(y = \frac{7}{4}\)[/tex]
Complete question:
Solve equation for y. Then find the value of y for each value of x.
6x = 7 - 4y; x = -2, -1, 0
Final answer:
To solve the equation 6x = 7 - 4y for y, subtract 7 from both sides and divide by -4 to isolate y.
Explanation:
To solve the equation 6x = 7 - 4y for y, we need to isolate y on one side of the equation. First, we can move the 7 to the other side by subtracting it from both sides:
6x - 7 = -4y
Next, we can divide both sides by -4 to solve for y:
y = (6x - 7) / -4
The bases on a baseball diamond are 90 feet apart. how far is it from home plate to second base?
Which mixed number is greater than 6.78?
A.6 2/7
B. 6 3/4
C. 6 7/9
D.6 4/5
Susan's penny bank is 1/4 full. After she adds 360 pennies, it is 5/8 full. How many pennies can Susan's bank hold?
Find f(-5) if f(x) = |x + 1|.
A.4
B.5
C.6
.....Simplify (8^4)^–16.
Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?
S1 = speed of boat 1
t1 = time to do 1400 meters (boat 1)
S1*t1 = 1400
S2 = speed of boat 2
1400 + S2*t1 = X
t2 = time to do X + 600 (boat 2)
S1*t2 = X + 600
S2*t2 = 2X - 600
S1 = 1400/t1
S2 = (X-1400)/t1
T = t2/t1
1400*T = X + 600
X*T - 1400*T = 2X - 600
X = 3600 meters
River is 3600 meters wide
Which set is an example of like fractions?
If the measures of two complimentary angles are 7x and 11x , then find x
X=5
X=10
X=22.5
X=12
Answer:
x = 5
Step-by-step explanation:
Complementary angles are two angles whose sum is 90º
So, if we have two complementary angles 7x and 11x we know that their sum is 90
We are going to write the equation and solve for x:
[tex]7x+11x=90\\18x=90\\x=90/18\\x= 5[/tex]
Therefore, x would be 5. And the angles would be 7(5) = 35º and 11(5) = 55º
How do i solve the square root of 54x^9y^6?