The driver that is predict to win the next drag race will be A. Driver A had a mean race time of 3.81 seconds and a standard deviation of 0.21 seconds.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation implies that the values are dispersed over a wider range, a low standard deviation shows that the values tend to be close to the mean of the collection.
Given that we are aware that standard deviations indicate variability in a data collection, the variability is greater the higher the standard deviations.
In this case, A has the higher standard deviation. Therefore, the driver that is predict to win the next drag race will be Driver A had a mean race time of 3.81 seconds and a standard deviation of 0.21 seconds.
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[tex] \rm If \: \beta = \lim_{x \to0} \frac{ {e}^{ {x}^{3} } - (1 - {x}^{3} {)}^{ \frac{1}3 } + ((1 - {x}^{2} {)}^{ \frac{1}{2} } - 1) \sin x}{x \sin^{2} x} ,\\ [/tex]
then the value of [tex]6 \beta [/tex] is
Expand the limand as
[tex]\dfrac{e^{x^3} - (1 - x^3)^{1/3} + \left((1-x^2)^{1/2} - 1\right) \sin(x)}{x \sin^2(x)} \\\\ ~~~~~~~~ = \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} \cdot \dfrac{x^2}{\sin^2(x)} + \dfrac{(1-x^2)^{1/2} - 1}{x^2} \cdot \dfrac{x}{\sin(x)}[/tex]
Recall that for [tex]a\neq0[/tex],
[tex]\displaystyle \lim_{x\to0} \frac{\sin(ax)}{ax} = 1[/tex]
Then
[tex]\displaystyle \beta = \lim_{x\to0} \left( \dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} + \dfrac{(1-x^2)^{1/2} - 1}{x^2}\right)[/tex]
Rationalize the numerators.
[tex]\dfrac{e^{x^3} - (1-x^3)^{1/3}}{x^3} = \dfrac{e^{3x^3} - (1 - x^3)}{x^3 \left(e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}\right)} \\\\ ~~~~~~~~~~~ = \left(\dfrac{e^{3x^3} - 1}{x^3} + 1\right) \cdot\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}}[/tex]
and observe that
[tex]\dfrac1{e^{2x^3} + e^{x^3} (1-x^3)^{1/3} + (1-x^3)^{2/3}} \to \dfrac13[/tex]
[tex]\dfrac{(1-x^2)^{1/2}-1}{x^2} = \dfrac{(1-x^2) - 1}{x^2 \left((1-x^2)^{1/2} + 1\right)} \\\\ ~~~~~~~~ = -\dfrac1{(1-x^2)^{1/2} + 1} \to -\dfrac12[/tex]
This leaves us with
[tex]\displaystyle \beta = \lim_{x\to0} \frac{e^{3x^3} - 1}{3x^3} - \frac16[/tex]
The remaining limit is the derivative of [tex]e^{3x^3}[/tex] at [tex]x=0[/tex], so its value is 1, and we find
[tex]\beta = 1 - \dfrac16 = \dfrac56 \implies 6\beta = \boxed{5}[/tex]
the area A of a rectectangle is represented by the formula A=Lw where I is the length and W is the width. write an equation that would make it easy to find the length of the rectangle
Answer: L=A/W
Step-by-step explanation: If you do this then you will find the length because L x W = A. So if the area is determined by l and w then you could divide A by the width to find the length because you multiply length and width to find the area
Look for acute, obtuse, and right angles in your environment or find one of each online. Post an image of each. Can you find all three in one spot?
Identify the acute, obtuse, and right angles in your image or images.
Answer: Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees.
Step-by-step explanation:
help me do this plroblem
Answer: $640
Step-by-step explanation:
Answer:
640
Step-by-step explanation:
A copy machine makes 91 copies in 3 minutes and 15 seconds. How many copies does it make per minute?
copies per minute
X
5
Find the area of the semicircle. (Take pi=22/7) Diameter=14
Area of semicircle is 77.
What is semicircle?
A semicircle is defined as half circle formed by cutting the circle into two halves.
Given that;
Diameter of semicircle = 14
Radius of semicircle = 14/2 = 7
Now, Area of semicircle = 1/2 (πr²)
Substitute π = 22/7 and r = 7, we get;
Area of semicircle = 1/2 (πr²)
= 1/2 × (22/7) × 7 × 7
= 77
So, Area of semicircle is 77.
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I need help to find the degree
Answer:
Step-by-step explanation:
Find the degree, leading term, and leading coefficient.
Polynomial Degree:
2
Leading Term:
5x²
Leading Coefficient:
5
An angle measures 124° less than the measure of its supplementary angle. What is the
measure of each angle?
Answer:
56°
Step-by-step explanation:
Supplementary angles are = to 180° so you have to subtract 124 from 180 which gives you 56°
A square window has an area of 9 square feet. What is the perimeter of the window?
Answer:
12
Step-by-step explanation:
For Exercises 1 and 2, use the table. It shows the types of
and prices of Jolly Juice Orange Juice.
Bottles of Jolly Juice Orange Juic
Containers
Price
8 oz
$0.96
16 oz
$1.60
32 oz
$2.56
64 oz
$3.84
1. Find the unit rate for an 8-ounce
container of Jolly Juice. Explain your
answer.
2. Find the unit rate for each size. Then order the sizes from least to greatest unit rate
Answer:
I have 5 apples and give u 2 how much I have
the graph shows two points from the table representing a proportional relationship. Which point corresponds to the last entry in the table?
Answer:
Step-by-step explanation: second point correspond to the last entry in the table
16. Vocabulary A number written in
expanded form is written as the sum
of each …..
.Write 39,005
in expanded form...
If m∠3 = 4x + 10 and m∠4 = 5x, find x.
The value of x is 10.
Given m∠3 = 4x+10 and m∠4 = 5x
Now, we need to determine what value of x it is.
We know that in quadrilateral four angles are there in that two angles are equal it is said to be as Rhombus.
Two angles are given in this question. We assume those are equal angles.
∴ m∠3 = m∠4
By substituting the values of two angles, we get
4x+10 = 5x
By deducting '4x' on both sides, we get
4x+10-4x = 5x - 4x
10 = x
∴ x = 10
The final value for x is 10.
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[ne
How many solutions for x does the following equation have?
(6x + 6) = 4x + 4
O A. 0
OB. 1
O C. infinite
OD. 4
HELP PLEASE? THE PICTURE IS ATTACHED FOR ANYONE THAT WANTS TO HELP, I’D APPRECIATE IF SOMEONE HELP ME ANSWER THIS
Answer:
$32.00
Step-by-step explanation:
The easiest way of calculating discount is, in this case, to multiply the normal price $80 by 40 then divide it by one hundred. So, the discount is equal to $32. To calculate the sales price, simply deduct the discount of $32 from the original price $80 then get $48 as the sales price.
HELP PLEASE? THE PICTURE IS ATTACHED FOR ANYONE THAT WANTS TO HELP, I’D APPRECIATE IF SOMEONE HELP ME ANSWER THIS
Answer:
40% Of 80 is 32
Solve for x.
6/9=x/12
Simplify as much as possible
- - - - - - - - - - - - - - - - - - - - - - - -
Find common denominators :)
6/9
Divide by 4 (the common factor of 9 and 12)
2/3
Multiply by 4
8/12
8/12 = 8/12
Now, simplify.
2/3
- - - - - - - - - - - - - - - - - - - - - - - -
Have a great day/night! :)
(Please consider leaving a Brainliest!)
~pinetreee
The leg of a right triangle is 8 ft in length while
the hypotenuse is 15 ft in length. Find the missing
side of the triangle. Write the answer in simplified
radical form
Answer:
[tex]\sqrt{161}[/tex] ft
Step-by-step explanation:
According to the pythagorean theorem, in a right-angle triangle, the sum of of the squared legs is equal to the hypotenuse squared.
In simpler words, if we have legs [tex]a[/tex] and [tex]b[/tex], as well as hypotenuse [tex]c[/tex], then [tex]a^2 + b^2 = c^2[/tex].
In our case, we know that [tex]a = 8[/tex] and [tex]c = 15[/tex], therefore, we should try and find b.
[tex]8^2 + b^2 = 15^2\\\to 64 + b^2 = 225 \text{ // Subtract by 64}\\\to b^2 = 161 \text{ // Take the square root of both sides}\\\to b = \sqrt{161}[/tex]
:52:26 ATI
f(x) =
wer.
-(x+8)² + 4 for
for
Find f(-5)
x < -5
x ≥ 3
The value of f(-5) when we solve the function f(x) is -5.
What does the mathematical function mean?A function is a statement, tenet, or rule that creates a correlation between two variables. In mathematics, functions are used often and are required to build complicated connections.
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The function can be solved as:
[tex]f(x) = -(x+8)^{2} +4[/tex]
[tex]=-(-5+8)^{2}+4[/tex]
[tex]=-(3)^{2}+4[/tex]
[tex]=-9+4[/tex]
[tex]=-5[/tex]
Hence, f(-5) = -5
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Which translation(s) will take Triangle T to Triangle U? Explain your answer
For Triangle T to translate Triangle U
1. Translate (-3, 0) to (1, 2).
2. Translate (-2, -1) to (2, 1) .
3. Translate (-4, -3) to (0, -1).
Options A and C
This is further explained below.
What is translation?Generally, A translation is a kind of geometric transformation that is used in Euclidean geometry. This type of transformation involves moving each point of a figure, shape, or space by the same distance in a certain direction.
In conclusion, for Triangle T to translate Triangle U
1. Translate (-3, 0) to (1, 2).
2. Translate (-2, -1) to (2, 1) .
3. Translate (-4, -3) to (0, -1).
Therefore, Options A and C are valid
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There is a pair of parallel sides in the following shape.
What is the area of the shape?
If there is a pair of parallel sides in the following shape. the area of the shape is: 21 unit².
Area of the shapeUsing this formula to determine or find the area of the shape
Area = (1/2)× (Area+ breadth )height
Where:
Area= 9
Breadth= 5
Height = 3
Now Let plug in the formula so as to find the area
Area of the shape = (1/2)× (9 + 5) ×3
Area of the shape = (1/2)× (14)×3
Area of the shape = (1/2)× 42
Area of the shape= 21 unit²
Therefore If there is a pair of parallel sides in the following shape. the area of the shape is: 21 unit².
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A turtle was swimming 2 feet below the surface of a pond. While looking for food, he went down 7 more feet
-6(w +5 ) +9<-51
Solve the inequality
Answer:
w>5
Step-by-step explanation:
Go onto symbolab it's a website good for solving math problems like this
the lengths of the four sides as a quadrilateral (in feet) are consecutive integers if the perimeter is 86 ft find the value of the longest of the four side lengths
Let x be the shortest side
Let x+1 be the second side
Let x+2 be the third side
Let x+3 be the fourth and longest side
[tex]perimeter = s_{1} + s_{2} + s_{3} + s_{4} \\ 86 = x + (x + 1) + (x + 2) + (x + 3) \\ 86 = x + x + 1 + x + 2 + x + 3 \\ 86 = 4x + 6 \\ 4x = 80 \\ x = 20[/tex]
Shortest side is 20 cm
Longest side is x+3 so 20+3=23
Answer: 23Find the value of X then find the measure of each labeled angle.
The value of the angle x is 108 degree.
According to the statement
We have to find that the value of the x in the adjacent angle.
So, For this purpose, we know that the
The adjacent angles is the two angles are said to be adjacent angles when they share the common vertex and side.
From the given information:
When we extend line AB to E
Then ∠EBC is created
Since BC is parallel to AD
So, ∠EBC =∠BAD = x° (corresponding angles are equal )
Linear pair : Two angles are said to be linear if they're adjacent angles formed by two intersecting lines. The measure of a angular unit is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Now With the linear pair property
x+(x-36) = 180
2x - 36 = 180
2x = 180+36
2x = 216
x = 216/2
x = 108.
Then one angle is of 108 degree and second angle is 72 degree.
So, The value of the angle x is 108 degree.
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investment will pay $332,640 at the end of next year for an investment of $220,000 at the start of the year. If the market interest rate is 8% over the same period, should this investment be made?
A.
Yes, because the investment will yield $85,536 more than putting the money in a bank.
B.
Yes, because the investment will yield $76,032 more than putting the money in a bank.
C.
Yes, because the investment will yield $95,040 more than putting the money in a bank.
D.
No, because the investment will yield $95,040 less than putting the money in a bank.
Based on the amount the investment would pay at the end of next year, and the market interest rate, C. Yes, because the investment will yield $95,040 more than putting the money in a bank.
How to know if the investment should be made?The investment of $220,000 at the market rate of 8% would earned:
= 220,000 x 8%
= $17,600
The amount that the investment would make instead is:
= 332,640 - 220,000
= $112,640
The difference is:
= 112,640 - 17,600
= $95,040
In conclusion, the investment should be made.
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h(x) = 3x - 5, find h(-2).
Answer:
h= 3x/x −5
Step-by-step explanation:
hx=3x−5
Step 1: Divide both sides by x.
hx/x = 3x/x −5
h= 3x/x −5
x
Answer:
h= 3x/x −5
I need help with 4 and 5
4. The two triangles are similar by virtue of the AAA triangle congruence theorem as a result of the corresponding angles which have equal measures.
5. The length of segment CE to the nearest tenth is; 46.7 in.
What is the length of segment CE as required in the task content?4. The ∆CBD and ∆CAE are similar (congruent) following the fact that angle C is common to both triangles and the angles A and E have equal measures as E and D respectively by virtue of corresponding angles theorem. Ultimately, the two triangles; ∆CBD and ∆CAE are congruent since all three angle measures are the same in the triangles.
The corresponding angles in discuss is due to the fact that the lines ED and AE are parallel lines.
5. Also, upon establishing the congruence of the two triangles, it follows that the ratio of their corresponding sides is same for all three sides.
Therefore, we can establish that;
BD/AE = CD/CE
6/14 = 20/CE
CE = (14 × 20)/6
CE = 140/3
CE = 46.667 in.
Ultimately, the length of segment CE to the nearest tenth is; 46.7 in.
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solve 6/58 x -1 2/5 -371/40 -6 1/4 1 1/2 371/40
The simpliified value of the expression 6 5/8 x -1 2/5 is - 371/40
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
6 5/8 x -1 2/5
Convert the mixed fractions to improper fractions
So, we have
6 5/8 x -1 2/5 = 53/8 x - 7/5
Evaluate the product of the numerators in the above expression
So, we have
6 5/8 x -1 2/5 = 53/8 x - 7/5
Evaluate the product of the numerators in the above expression
So, we have
6 5/8 x -1 2/5 = - 371/8 x 1/5
Evaluate the product of the denominators in the above expression
So, we have
6 5/8 x -1 2/5 = - 371/40
Hence, the simpliified value of the expression 6 5/8 x -1 2/5 is - 371/40
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6. BUILDING A horse farm is developing a new indoor arena in a rectangular building. They want the width of the building to be 2y feet and the length to be 4y – 9 feet. Write an expression in simplest form to represent the area A of the building in terms of y.
The area of the rectangular arena can be represented as A = (8y2 - 18y) square feet.
Here, we are given the dimensions of a rectangular arena, which are as follows-
Length = 4y - 9 feet
width = 2y feet
The area of a rectangle is given by the formula-
Area of a rectangle = length x breadth
Thus, in this case, area (A) can be calculated as follows
A = (4y - 9) * 2y
Now, we simplify the equation-
A = (4y)(2y) - 9(2y)
A = 8 - 18y
Thus, the area of the rectangular arena can be represented by the following equation- A = (8 - 18y) square feet.
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PLEASE HELP! DUE IN LESS THAN 2 HOURS! IM STUCK! PLEASE HELP ME! YOU WILL GET 100 POINTS! THANKS QUESTION DOWN BELOW!!! PLEASE SHOW THE WORK!
Answer:
Do you want the equation?
y = [tex]x^{2}[/tex]
Step-by-step explanation:
Answer:
1. One square
2. Four squares
3. Nine squares
4. Sixteen squares
5. Twenty-five squares
6. Thirty six squares
7. 49 squares
8. 64 squares
9. 81 squares
10. 100 squares
Step-by-step explanation:
The pattern is add six squares to the image before the one you’re working.