The interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.
What is empirical rule?According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
Here we had where mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex].
When Ryan runs the 400 meter dash, his finishing times are normally distributed with a mean of 75 seconds and a standard deviation of 0.5 seconds.
The interval of times that represents the middle 68% of his finishing times in the 400 meter race is,
[tex]P(75 - 0.5 < X < 75 + 0.5) = 68\%\\P(74.5 < X < 75.5) = 68\%[/tex]
Thus. the interval of times which represents the middle 68% of Ryan's finishing times in the 400 meter race, using the empirical rule, is 74.5 seconds to 75.5 seconds.
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The sales of new products over time are found to follow a quadratic model before dropping off to zero at the end of the product’s lifetime. A new product is released with sales modeled by the equation
S
=
−
(
t
−
3
)
2
+
81
, where S represents the sales in millions of dollars and t represents the number of years the product will be sold. According to the equation, what will be the lifetime of this product?
The sales equation of the product is an illustration of a quadratic function, and the lifeline of the product is 12 years
How to determine the lifeline of the product?The sales equation is given as:
S(t) = -(t - 3)² + 81
The lifeline of the product is when the sales hits 0.
This means that S(t) = 0
So, we have:
-(t - 3)² + 81 = 0
Subtract 81 from both sides
-(t - 3)² = -81
Divide both sides by -1
(t - 3)² = 81
Take the square root of both sides
t - 3 = 9
Add 3 to both sides
t = 12
Hence, the lifeline of the product is 12 years
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Find the measures of x and y.
2.
145°
55°
Answer:
x = 35° , y = 90°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
145° is an exterior angle of the triangle , then
y + 55° = 145° ( subtract 55° from both sides )
y = 90°
the sum of the 3 angles in a triangle = 180° , then
x + y + 55° = 180°
x + 90° + 55° = 180°
x + 145° = 180° ( subtract 145° from both sides )
x = 35°
Describe the transformation that maps the pre-image (ΔA) to the image (ΔA').
Step-by-step explanation:
90 degrees rotation, clockwise
Need help plezzzzzzzzzzzzzzzz
Answer:
The answer is B. 60°
Step-by-step explanation:
The Unit Circle.
A = sin^-1 ( [tex]\frac{\sqrt{3} }{2}[/tex]) = 60°
If tan 8
3
what does sin 8 = ?
4
Answer:
The answer is option B
3/5
what is the greatest ten you can multiply by 2 to get close to but not over 58?
Answer:
20
Step-by-step explanation:
20 x 2 =40
40 is under 58 and the closest to 58
the next 10 is 30 and 30 x 30 is over 58 with 60
Your cousin's age is the cube of your little sister's age. If your
cousin is 8 years old, how old is your little cousin?
Answer:
2
Step-by-step explanation:
2 times 2 times 2 equals 8
Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
Answer:
27<AB<81
Step-by-step explanation:
The sum of two sides of a triangle have to be than the length of the third side. 27+54 is 81, so the AB has to be less than 81. Now, to find the minimum, I can say 27+x has to be greater than 54, so x has to be greater than 27. Therefore, the answer has to be between 27 and 81, so the 2nd one is correct.
Answer:
B. 27 < AB < 81
Step-by-step explanation:
Nice
Apply the 45°-45°-90° Triangle Theorem to find the length of a leg of a right triangle if the length of the hypotenuse is 8/2
inches.
Answer:
d
Step-by-step explanation:
d
What is the largest circle contained in a triangle where the center of the circle is the incenter of the triangle?
Answer:
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter.
Helppppppp
Miguel thinks that his data do not support the article's claim because 63.5%
of the students who made the honor roll at his school do not exercise.
Using data from the table, explain what is wrong with Miguel's reasoning.
The 63.5% of the students who do not exercise is the wrong percentage because 70% of the students do not exercise.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Miguel thinks that his data do not support the article's claim because 63.5% of the students who made the honor roll at his school do not exercise.
The percentage of the students who do not exercise will be
[tex]\rm P = \dfrac{112}{160} \times 100\\\\P = 70\%[/tex]
The 63.5% of the students who do not exercise is the wrong percentage because 70% of the students do not exercise.
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Andy is building a model train. A train in real life has a wheel diameter of 33 inches, a length of 20 feet, a width of 10 feet, and a height of 12 feet. If his model has a width of 8 inches, what does the height need to be?
By finding and using the scale factor for the model, we conclude that the height of the model is 9.6 inches.
How to apply a scale factor?The ratio between the model's width and the real width is the scale factor, and all the dimensions change following that scale factor.
We have:
8 in = 10ft
1 ft = (8/10) in
This means that each feet in the real life, will be represented with (8/10) inches in the model.
Now we know that the real height is 12ft, then the model's height will be:
12* (8/10) in = 9.6 in
So the correct option is B.
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Answer:
9.6
Step-by-step explanation:
took usatest prep got a 100%
11 divided by 15?
Help me
Answer:
0.733 repeating
Step-by-step explanation:
use your calculator
what is the equation that represents the sentence, twenty four is the sum of a number and six use x for the variable
Answer:
24 = x + 6
Step-by-step explanation:
24 = x + 6
which number has the least value? (a) 5.61 (b) 16.5 (c) 56.1 (d) 51.6
Answer:
(a) 5.61
Step-by-step explanation:
Rearrange from smallest to largest:
☟︎︎︎
5.61 < 16.5 < 51.6 <56.1
Find the value of x
Please answer ASAP!!!!!
Answer:
x = 8
Step-by-step explanation:
24x = 6 x 32
24x = 192
x = 192/24
x = 8
Someone pls help me I don't know what to do
Answer:
14 in
Step-by-step explanation:
area cylinder= area of base × height of cylinder
area of cylinder = (pi × radius²) × H
(sub in values )
196×pi = (pi x r²) × 1
(196×pi)/1 = pi × r²
(196×pi)/pi = r²
(pics cancel each other )
then, square root 196= r
14 in = radius
Help me with this im confused
Answer:
y=6x
Step-by-step explanation:
1. find the slope m. Pick two points on the line, such as (0,0) and (1,6). Plug those points into the slope formula.
m=change in y/change in x
m=6-0/1-0 Plug in (0,0)(1,6)
m=6/1 simplify
m=6
The slope is 6
2. Find the y-intercept. Since the line crosses the y-axis at 0, the y-intercept is 0.
3. Use the slope m=6 and the y-intercept b=0 to write the equation in slope-intercept form.
y=mx+b
y=6x+0 Plug in m=6 and b=0
y=6x
If 12(x -7) = -11 then x =?
Answer:
x = 73/12
Step-by-step explanation:
Given:
[tex]\displaystyle \large{12(x-7)=-11}[/tex]
Distribute 12 in x-7:
[tex]\displaystyle \large{12x-84=-11}[/tex]
Add both sides by 84:
[tex]\displaystyle \large{12x-84+84=-11+84}\\\displaystyle \large{12x=73}[/tex]
Divide both sides by 12:
[tex]\displaystyle \large{\dfrac{12x}{12}=\dfrac{73}{12}}\\\displaystyle \large{x=\dfrac{73}{12}}[/tex]
Therefore, the solution is x = 73/12
Answer:
[tex]\large\boxed{\bf\:x = \frac{73}{12} = 6\frac{1}{12} \approx 6.083}[/tex]
Step-by-step explanation:
[tex]12(x - 7) = -11[/tex]
Multiply 12 by x & 7 (distributive property) in the left hand side of the equation .
[tex]12(x-7)=-11\\(12*x)-(12*7)=-11\\12x - 84 =-11[/tex]
Bring -84 to the right hand side of the equation. Then,
[tex]12x = -11 + 84\\12x = 73\\x=\frac{73}{12} \\\\\boxed{\bf\:x = \frac{73}{12} = 6\frac{1}{12} \approx 6.083}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
On our vacation we traveled 416 miles using 16 gallons of gas how many miles were we able to go on 1 gallon of gas?
Answer:
26 miles per gallon
Step-by-step explanation:
Divide 416 by 16 to find miles per gallon :)
Point A is located at (-6, 5). After it is transformed, point A' is located at (6, 5). What could the transformation be?
A reflection in the x-axis
A reflection in the y-axis
A transiation 12 units Up
A translation 12 to the right
Answer:
A reflection on the y axis, and 12 units to the right
Step-by-step explanation:
This is true because if you translate something from one variable, you are going over the second variable.
Please HELP Me with this problem!
Answer:
B
Step-by-step explanation:
because 30÷3=10
Answer:
Your answer is B
Step-by-step explanation:
Solve for x. Your answer must be simplified
x/7 ≥ -6??
Find the volume of this triangular prism.
6 cm
7 cm
10 cm
Answer:
L×W×B
10×7×6
=420cm of triangular prism
please help me outt on this round to nearest tenth
A cheetah can run for a short time at 3 m/s (70 mph). How far can it travel in 19 s?
distance =
Answer: 57m
Step-by-step explanation: Speed is 3m/s
Time is 19seconds
distance =speed × time
Distance = 19 × 3
Answer:
57 m.
Step-by-step explanation:
In 1 second it can run 3 m
So in 19 s it can run 3*19
= 57 m.
What fraction of 720 is 80
Answer:
9/36.Step-by-step explanation:
Fraction:
80/720Simplify:
80/720= 9/36Answer would be 9/36.
write 4200 as a power whose base is e
Answer:
Step-by-step explanation:
First find the natural log of 4200: It is 8.343.
Then 4200 = e^8.343
HELP will give brainliest
complete the worksheet 2-18
Answer: 1/10, 1/7, 2/9, 2/5, 7/11, 1/4, 1/10, 1/7, 1/9, 1/2 , 1/8, 1/12, 0/1, 0/0
1/13, 1/3, 1/4
Step-by-step explanation: i think i know all the answers
Flying against the wind, an airplane travels 2610 kilometers in 3 hours. Flying with the wind, the same plane travels 8750 kilometers in 7 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answer:
200 km/hr
Step-by-step explanation:
Let Va = the velocity of the airplane
Let Vw = the velocity of the wind
When flying with the wind:
(Va+Vw)*(4 hours) = 4000
4Va + 4Vw = 4000
4Vw = 4000 - 4Va
Vw = 1000 - Va
When flying against the wind:
(Va-Vw)*(7 hours) = 4200 km
7Va - 7Vw = 4200
Substitute 1000-Va for Vw and solve for Va:
7Va - 7(1000-Va) = 4200
7Va -7000 + 7Va = 4200
14Va = 11200
Va = 800 km/hr
Rate of wind:
Vw = 1000 - Va = 1000 - 800 = 200 km/hour