The height of the giraffe whose shadow is 5 feet 9 inches at the same time will be 10 feet and 6.5 inches.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
The next stop on the road trip is the zoo.
Jacob goes to find his favorite animal, the giraffe.
Jacob wonders how tall the tallest giraffe at the zoo is.
If Jacob is 5 feet 6 inches and his shadow at the time is 3 feet long.
Then the height of the giraffe whose shadow is 5 feet 9 inches at the same time will be
Let x be the hieght of the giraffe. Then we have
The ratio will remain constant.
x / 5.75 = 5.5 / 3
x = 10.54
x = 10 feet 6.5 inches
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Uppose a jar contains 12 red marbles and 18 blue marbles. if you reach in the jar and pull out 2 marbles at random without replacement, (a) find the probability of getting two red marbles:
[tex] \displaystyle
|\Omega|=\binom{30}{2}=\dfrac{30!}{2!28!}=\dfrac{29\cdot30}{2}=435\\
|A|=\binom{12}{2}=\dfrac{12!}{2!10!}=\dfrac{11\cdot12}{2}=66\\\\
P(A)=\dfrac{66}{435}=\dfrac{22}{145}\approx15\% [/tex]
The period T in seconds of a simple pendulum of length L in feet is given by T=2π√L/32. Determine the length in feet of a simple pendulum whose period is 8.72 seconds. Round your answer to the nearest foot.
1972 feet.
387 feet.
62 feet.
256 feet.
if f(x) and it’s inverse function, f-1(x) are both plotted on the same coordinate plane, what is their point of intersection?
By using basic property of inverse function we got that if f(x) and it’s inverse function are both plotted on the same coordinate plane, then their point of intersection is (3,3)
What is function ?Function is relation between a set to another set with a property that every element of first set has a unique image in second set.
Here graph of f(x) is given and we have to find the point of intersection of function and it's inverse function
We know that a function and it's inverse function are mirror image of each other with respect to line y=x hence they intersect only at y=x line
By drawing y=x line with the given graph we got that f(x) intersect y=x line at (3,3) hence inverse function will intersect at (3,3)
By using basic property of inverse function we got that if f(x) and it’s inverse function are both plotted on the same coordinate plane, then their point of intersection is (3,3)
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When the graph of a function and its inverse function are plotted on the same coordinate plane, the point of intersection is the point where the two graphs intersect. Therefore, the point of intersection is (x, y).
Explanation:When the graph of a function and its inverse function are plotted on the same coordinate plane, the point of intersection is the point where the two graphs intersect.
Let's say the point of intersection is (x, y).
This means that both f(x) and f-1(x) have the same x-coordinate, which is x, and the same y-coordinate, which is y.
Therefore, the point of intersection is (x, y).
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what is 17.5 of 50???
On n − {1}, the relation r given by a r b iff the prime factorizations of a and b have the same number of 2's. for example, 48 r 80 because 48 = 24 · 3 and 80 = 24 · 5. name three elements in each of these classes: 7, 10, 72.
i need help with number 2 please p
Find the slope of the line that passes through the pair of points. (4, 8), (8, 11)
How do find the measure of side a?
The measure of side a is 14.
We have,
We use the trigonometric identites:
Sin function
Now,
Sin A = Perpendicular / Hypotenuse
Sin 34 = a / 25
0.56 = a / 25
a = 0.56 x 25
a = 14
Thus,
The measure of side a is 14.
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For a function p(x)= x^2-9, what is the inverse function for the domain [0, infinity\
Please help me on this ?!?!?!
You want to draft a four player tennis team. There are eight players to choose from. How many different teams can you form?
We want to make a 4 players team, and there are total 8 players. As we know the order of selection does not matter in a team of players, only the combination of players matters.
So we would use concept of Combinations and It will be choose 4 out of 8 players.
The formula for Combination is given as follows :-
[tex]nCr = \frac{n!}{r!*(n-r)!} \\\\ Choose \;4 \;out \;of \;8 \;players \\\\ 8C4 = \frac{8!}{4!*(8-4)!} = \frac{8!}{4!*4!} \\\\ 8C4 = \frac{8*7*6*5*4*3*2*1}{(4*3*2*1)*(4*3*2*1)} = \frac{8*7*6*5}{4*3*2*1} =\frac{1,680}{24} = 70 \;combinations[/tex]
Hence, Total number of different teams = 70 combinations.
TIMED, anyone know the answer?
A culture started with 3,000 bacteria. After 7 hours, it grew to 3,300 bacteria. Predict how many bacteria will be present after 17 hours. Round your answer to the nearest whole number. P=Ae^kt
Answer:3,780
What is the area of a circle with a radius is of 6 inches?
determine the amount of an investment if $400 is invested at an annual interest rate of 7.25% for 7 years. round to the nearest penny.
A class of 24 students was asked to identify a team spot in which they have participated. Their responses are shown in the line plot.
a. How many total responses are recorded in the line plot for the five sports?
b. What is the total number of students polled?
c. Give a possible explanation as to why the answers of part (a) and (b) are different.
Enter your answer in the box.
If 25 people play the game how many people do you expect to hit HHH?
Answer:
Almost 3 persons are expected to hit HHH.Step-by-step explanation:
To find the answer we must use the diagram, we see that among 8 possible results, there's one possible outcome to hit HHH.
So, to find the amount of people that are expected to hit HHH, we just have to multiply each percentage assigned to the HHH outcome:
[tex](0.7)(0.5)(0.3)=0.105[/tex]
Now, we see that a 10.5% of the people will be expected to hit HHH.
The approximate number of people would be:
[tex]25(0.105) \approx 3[/tex]
Therefore, almost 3 persons are expected to hit HHH.
What is the value, after 7 years, of a 2014 mustang that was originally 25,000.00, if it depreciates at a rate of 8% per year??
The estimated answer would be =14000
Paul took out a 2-year loan for $1450 at a computer retailer to be paid back with monthly payments at an 18% APR, compounded monthly. If the loan offers no payments for the first 4 months, about how much in total will Paul pay in interest for the loan?
To solve this system of equations by elimination, what operation could be used to eliminate the y-variable and find the value of x? 2x − 4y = 6 −3x + 3y = 12 A) add 3 times the second equation to 4 times the first equation B) add 4 times the second equation to 3 times the first equation C) subtract 3 times the second equation from 4 times the first equation D) subtract 4 times the second equation from 3 times the first equation
Answer:
Option B is correct.
add 4 times the second equation to 3 times the first equation
Step-by-step explanation:
Given the system of equation:
[tex]2x - 4y = 6[/tex] ......[1]
[tex]-3x + 3y =12[/tex] .....[2]
Multiply equation [1] by 3 we get;
[tex]3(2x-4y) = 3 \cdot 6[/tex]
Using distributive property; [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
6x - 12y = 18 .......[3]
Multiply equation [2] by 4 we get;
[tex]4(-3x+3y) = 4 \cdot 12[/tex]
Using distributive property we get;
-12x + 12y = 48 ......[4]
Add equation [3] and [4] to eliminate y and solve for x;
(6x -12y) + ( -12x +12y ) = 18 + 48
6x - 12y -12x + 12y = 66
Combine like terms;
6x - 12x = 66
or
-6x = 66
Simplify:
x = -11
Therefore, the operation which could be used to eliminate the y-variable and find the value of x is;
add 4 times the second equation to 3 times the first equation.
Answer:
Option B
Step-by-step explanation:
Given is a system of two equations as
[tex]2x − 4y = 6 \\−3x + 3y = 12[/tex]
To solve them using elimination:
Elimination method is the method of making coefficients of one variable numerically equal
IN the given system we have -4 as coefficient for y in I equation and 3 for y in II equation.
To make them numerically equal with opposite signs we can multiply I equation by 3 and II by 4
WE get
[tex]6x-12y =18\\-12x+12y=48[/tex]
Now if we add these two we are able to eliminate y from the system
Adding gives
[tex]-6x=66\\x=-11[/tex]
So option B is right
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Sathish is going on a 200020002000-kilometer road trip with two friends. The car consumes 666 liters of gas for every 100100100 kilometers, and gas costs \$1.20$1.20dollar sign, 1, point, 20 per liter.If Sathish and his two friends want to split the cost evenly, how much should they each pay?\$
The scale factor of a figure and its enlargement is 6. What is the new length of the enlarged figure if the original length is 3 cm?
3 cm
6 cm
18 cm
36 cm
Answer:
The new length of the enlarged figure will 18 cm.
Step-by-step explanation:
A scale factor is a number which scales, or multiplies the original figure by some quantity.
In the equation [tex]y = Cx[/tex], C is a scale factor for x. It is called the constant of proportionality or scale factor of y to x.
As the given length is 3 cm, so with a scale factor of 6, the length of the enlarged figure will be [tex]3\times 6=18[/tex] cm
Therefore, the new length of the enlarged figure will 18 cm.
One angle of a triangle is three times as large as another. the measure of the third angle is 65 degrees more than that of the smallest angle. find the measure of each angle.
A group of people are going on a 5 mil hike. They walked 2 1/10 miles in the morning and 1 1/4 mils during the first hr of the afternoon. How many miles do they have to walk?
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Use a calculator to find the mean and standard deviation of the data. Round to the nearest tenth.
946, 726, 956, 519, 104, 415, 428, 457, 614, 201, 772, 801
A. mean = 566.5; standard deviation = 261.9
B. mean = 578.3; standard deviation = 261.9
C. mean = 578.3; standard deviation = 68572.4
D. mean = 566.5; standard deviation = 68572.4
Answer:
mean is 578.3 deviation 261.9
Step-by-step explanation:
Find the height of the cylinder.
options;
4.8 in.
2.4 in.
14.4
7.2 in.
The height of cylinder is,
⇒ h = 2.4 inches
We have to given that,
In a cylinder,
Volume = 271.4 inches³
And, Radius = 6 inch
Since, We know that,
Volume of cylinder is,
⇒ V = πr²h
Where, V is volume , r is radius and h is height.
Substitute all the values, we get;
⇒ 271.4 = 3.14 × 6² × h
⇒ 271.4 = 3.14 × 36 × h
⇒ 271.4 = 113.04 × h
⇒ h = 2.4 inches
Thus, The height of cylinder is,
⇒ h = 2.4 inches
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Write an equation for a line
g(x)
perpendicular to
f(x) = 5x − 8
and passing through the point
(5, 10)
Which linear expression is a factor of the polynomial function f(x) = x3 + 2x2 − x − 2? x − 2 x + 2 x + 3 x − 3