Answer:
A 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].
Step-by-step explanation:
We are given below the ages (in years) of randomly selected race car drivers;
Ages: 32, 40, 27, 36, 29, 28.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean age = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{32+40+27+36+29+28}{6}[/tex] = 32 years
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 5.1 years
n = sample of car drivers = 6
[tex]\mu[/tex] = population mean age of all race car drivers
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.571 < [tex]t_5[/tex] < 2.571) = 0.95 {As the critical value of t at 5 degrees of
freedom are -2.571 & 2.571 with P = 2.5%}
P(-2.571 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.571) = 0.95
P( [tex]-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.571 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.571 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]32-2.571 \times {\frac{5.1}{\sqrt{6} } }[/tex] , [tex]32+2.571 \times {\frac{5.1}{\sqrt{6} } }[/tex] ]
= [26.65, 37.35]
Therefore, a 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].
Will give you brainiest
Answer:
[tex]\boxed{<a = 62 degrees}[/tex]
[tex]\boxed{<b = 118 degrees}[/tex]
Step-by-step explanation:
A) If AB is a diameter, Then ACB is a 90 degrees angle because In a semi-circle (AB is a diameter which divides the circle into 2 equal parts), the angle opposite to the diameter is of 90 degrees.
So, <ACB = 90 degrees
Then <a = 180-90-28
=> <a = 62 degrees
B) The opposite interior angles of a quadrilateral inscribed in a circle add up to 180 degrees.
So,
=> <a + <b = 180
=> <b = 180-62
=> <b = 118 degrees
Which function has the same graph as x+y= 11?
A. Ax) = -y + 11
B.
Rx) = -x + 11
C.
A x) = x-11
D.
*x) = y- 11
Answer:
the answer is b= -x+11
Answer:b
Step-by-step explanation:
Please help me find the surface area please?????
Answer: 4032 squared feet
Step-by-step explanation:
1. Identify the figure. Rectangular Pyramid
2. Find the area of the four triangle faces. 1/2*47*32 = 752. Then, 752*4 = 3008.
3. Find the area of the rectangular base. 32*32 = 1024
4. Add the areas together, 3008+1024 = 4032
Image attached: Triangle measurement Theorem
Answer:
17
Step-by-step explanation:
Using Triangle Midsegment theorem, it states that if :
Q is the midpoint of MN and R is the midpoint of NP
Then, QR is parallel to MP and QR = 1/2 of MP
Mathematically
QR = 1/2MP
From the above question, we are given the following values:
QR = 3x - 4
MP = 55 - 3x
Since
QR = 1/2MP
3x - 4 = 1/2(55 - 3x)
3x - 4 = 55/2 - 3x/2
Collect like terms
3x + 3x/ 2 = 55/2 + 4
9x/ 2 = 31.5
Cross Multiply
9x = 31.5 × 2
9x = 63
x = 63/9
x = 7
Since QR = 3x - 4
x = 7
QR = 3×7 - 4
= 21 - 4
= 17
Hence, QR = 17
. The perimeter of a rectangle is 38 inches. If the length is 3 inches more than the width, find the width.
Answer:
w = 8 inchesStep-by-step explanation:
P = 2w + 2l
l = 3 + w
38 = 2w + 2(3 + w)
38 = 2w + 6 + 2w
38 - 6 = 4w
32 = 4w
w = 32 : 4
w = 8 inches
l = 3 + w
l = 3inches + 8inches
l = 11 inches
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HELP FAST
Figure ABCD is a parallelogram.
What is the value of x?
A
B
6
7
5x + 3
8
38
9
D
с
Answer:
hope it helps uh.......
CORRECT ANSWER GETS BRAINLIEST!! PLSS HELP!!!
Answer:
Method: Roll, pick, and replace a marble 70 times. Count the number of times you... Roll greater than 2 and pick a yellow marble.
Step-by-step explanation:
Please help me for precalculus ):
Answer:
The correct answer would be D.
Step-by-step explanation:
Find the missing length indicated.
Answer:
x=60
Step-by-step explanation:
in similar triangles ratio of sides is equal.
[tex]\frac{100}{x} =\frac{x}{36}\\x^{2} =100 \times 36\\x=10 \times 6=60[/tex]
The ratio of the corresponding sides of the triangle is constant. Then the missing length x is 60 units.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
If the two triangles are similar, the ratio of the corresponding sides will be constant.
The ratio of the corresponding sides of the triangle is constant.
100 / x = x / 36
x² = 100 x 36
x² = 3600
x = 60
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approximately 13% of the USA population is left handed. Hiw many lefties would expect in a school of 420 students
Answer:
Approximately 55 students
Step-by-step explanation:
13% of 420 is 54.6 which you can then round up to 55
Hope this helped!
Answer:
55 students
Step-by-step explanation:
Take the percent and multiply by the number of students
13% * 420
.13 * 420
54.6
Rounding up
55 students
Find the missing segment in the attached image
Answer:
The length of the missing segment is 24
Step-by-step explanation:
Given
The figure above
Required
Determine the missing segment
Let the missing segment be represented with x
Given that, there exist parallel lines between the two triangles;
The relationship between the sides of the triangles is as follows;
[tex]\frac{15}{x} = \frac{15+5}{8+x}[/tex]
[tex]\frac{15}{x} = \frac{20}{8+x}[/tex]
Cross Multiply
[tex]15 * (8 + x) = 20 * x[/tex]
Open bracket
[tex]15*8 + 15 * x = 20 * x[/tex]
[tex]120 + 15x = 20x[/tex]
Subtract 15x from both sides
[tex]120 + 15x -15x= 20x-15x[/tex]
[tex]120 = 20x-15x[/tex]
[tex]120 = 5x[/tex]
Divide both sides by 5
[tex]\frac{120}{5} = \frac{5x}{5}[/tex]
[tex]\frac{120}{5} = x[/tex]
[tex]24 = x[/tex]
[tex]x = 24[/tex]
Hence, the length of the missing segment is 24
310
Which law would you use to simplify the expression
quotient of powers
power of a quotient
product of powers
power of a product
power of a quotient
edge 2021
The law used to simplify the expression is quotient of powers.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,
3¹⁰ / 3⁴
For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.
By the definition we have the property of the power quotient of the same base set:
xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾
So, using the same,
3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶
Thus, to simplify the expression we must use the property of the power quotient of the same base.
Hence, the law used to simplify the expression is quotient of powers.
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A grid map marks the plot of Harold’s garden in meters. The coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5). He wants to build a short fence around the garden. The perimeter of his garden is meters.
Answer: 46
Step-by-step explanation:
Given that the coordinates of the quadrilateral-shaped property are G(–8, 3), A(4, 8), R(10, 0), and D(–2, –5).
You need to find length GA, GD, RA and RD by using the formula
L = sqrt[ ( X2 - X1)^2 + ( Y2 -Y1 )^2 ]
Length GA will be
L = sqrt [ ( 8-3 )^2 + ( 4+8 )^2 ]
L = sqrt ( 5^2 + 12^2 )
L = sqrt(25 + 144)
L = sqrt (169)
L = 13.
Length GD will be
L = sqrt [ ( -5-3 )^2 + ( -2+8 )^2 ]
L = sqrt ( -8^2 + 6^2 )
L = sqrt(64 + 36)
L = sqrt (100)
L = 10.
Length RA will be
L = sqrt [ ( 10-4 )^2 + ( 0-8 )^2 ]
L = sqrt ( 6^2 + 8^2 )
L = sqrt(36 + 64)
L = sqrt (100)
L = 10.
Length RD will be
L = sqrt [ ( 10+2 )^2 + ( 0+5 )^2 ]
L = sqrt ( 12^2 + 5^2 )
L = sqrt(144 + 25)
L = sqrt (169)
L = 13.
The perimeter P will be
Substitute all the parameters into the formula below
P = GA + GD + RA + RD
P = 13 + 10 + 10 + 13
P = 46
Angelo cuts a piece of wood for a project. The first cut is shown and can be represented by the equation y - 5x-1. The second cut needs to be parallel to the first. It will pass through the point (0,6). Identify the equation that
represents Angelo's second cut.
PLEASE HELP!
Answer:
y=5x+6
Step-by-step explanation:
Please see attached
5.
Solve the inequality.
9 +6 > 5
9 > 11
g > 1
g> -1
Answer: g> -1
Step-by-step explanation:
The given inequality is [tex]g+6>5\ .[/tex]
To solve the above inequality for g, we just need to remove 6 from the left side by subtracting it, for that we have to subtract 6 from both the sides, we get
[tex]g+6-6>5-6\\\\\Rightarrow\ g>-1[/tex]
i.e. The value of g is strictly greater than -1.
Hence, the correct answer is g> -1.
Subtraction Property of Inequality says that if the same number is subtracted from both sides on the inequality then the sense (equality symbol) of the inequality remains unchanged.
What exactly is a 'Factorial'? Give Brainlist to the finest answer
hi
It's a kind of multiplication where you do a serie of multiplication starting from your number until one. It written with a "!" after the number.
ex : 3! = 3*2*1 = 6
10! = 10*9*8*7**6*5*4*3*2*1 = 2628800
Answer:
answer is below
Explanation:
A factorial multiplies a number by the numbers below it. A factorial also acts as a function.
An example of a factorial can be:
[tex]5!=5 \times 4 \times 3 \times 2 \times 1[/tex]
[tex]5!=120[/tex]
Factorial of zero is defined as 1.
After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola. The equation for this parabola is y = -x2 + 36. Graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. Analyze the two functions. Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents. Is the linear function you created with your table positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent. Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).
Answer:
what is this
Step-by-step explanation:
oof
On a coordinate plane, a curved line with minimum values of (negative 1.5, negative 2) and (1.5, 2), and a maximum value of (0, 4), crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 4). Which is an x-intercept of the graphed function?
Answer:
(-2, 0), (-1, 0), (1, 0), (2, 0)
Step-by-step explanation:
The x-intercept of function can be defined as the values of x at which the graph of the function intercepts the x-axis, or where the values of the function, y, is equals to zero.
As it is already given that the graph crosses x-axis at points (-2, 0), (-1, 0), (1, 0), and (2, 0), and as we know that the point where the graph crosses x-axis has the value of the function equal to zero, so the x-intercepts of the given function are (-2, 0), (-1, 0), (1, 0), and (2, 0)
Answer:
(–3, 0) and (1,0)
Step-by-step explanation:
on edge
Choose the word that has the same connotation as the word fouled
Answer:
contaminated
Step-by-step explanation:
The word fouled is used in the "The grapes of wrath"
where in writer says that "the water fouled the ignition wire and water fouled the carburetors".
In this context fouled means that some impurity is being added to the carburetor and wire frames.
Hence the best suitable word from the option will be "contaminated".
Contamination means " the act of making anything impure "
Oliwia made a scaled copy of the following triangle. She used a scale factor greater than 111. What could be the height of the scaled copy of the triangle? Choose 3 answers: (A) 3 1/3 units (B) 10.5 units (C) 11.1 units (D) 18 units (E) 35 1/2 units
Answer:
C & D & E
Step-by-step explanation:
The correct options are C, D, and E.
Scaled copyA scaled copy is an enlarged image of the previously given figure.
Scale factorA scale factor is a factor by which the image is been enlarged. for example, the scale factor of 10 means each side will be multiplied by 10, resulting in a figure that is 10 times the real figure.
As given in the problem the scale factor is anything greater than 1.
We know that when we multiply 11 by 1 or a number greater than 1 the value will be the same or changed.
Therefore, the height of the scaled copy of the triangle will be anything equal to 11 or greater than 11.
Looking at the options available,
(A) 3 1/3 units
It is less than 11, therefore, not the right option.
(B) 10.5 units
It is less than 11, therefore, not the right option.
(C) 11.1 units
It is greater than 11, therefore, can be the possible option.
(D) 18 units
It is greater than 11, therefore, can be the possible option.
(E) 35 1/2 units
It is greater than 11, therefore, can be the possible option.
Thus, the correct options are C, D, and E.
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The graph below shows the price of different numbers of mats at a store: A graph is shown. The values on the x axis are 0, 2, 4, 6, 8, 10. The values on the y axis are 0, 21, 42, 63, 84, and 105. Points are shown on ordered pairs 0, 0 and 2, 21 and 4, 42 and 6, 63 and 8, 84. These points are connected by a line. The label on the x axis is Number of Mats. The title on the y axis is Price in dollars. Which equation can be used to determine p, the cost of b mats? p = 10.50 + b b = 10.50 + p b = 10.50p p = 10.50b
Answer:
p = 10.5b
Step-by-step explanation:
The equation has this form:
y = ax+c
a = [tex]\frac{21-0}{2-0}[/tex] a = 21/2 a= 10.5so the slope is 10.5
c is the y-intercept wich is given by the output of 0
here it's 0
0⇒0so the equation is y = 10.5x ⇒ p=10.5b
Answer:
P=10.5b
Step-by-step explanation:
What is the hypotenuse of a right triangle ABC with sides a=12 and b=5?
A)169
B)13
C)17
D)7
Answer:
B: 13
Step-by-step explanation:
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem if you know the length of the other two sides. Basically, you square the length of the 2 sides, a and b, and then add them together. Take the square root of the result to get the hypotenuse.
1. Square the length of a and b.
12 * 12 = 144
5 * 5 = 25
2. Add them together.
144 + 25 = 169
3. Take the square root.
The square root of 169 is 13.
In other words, the hypotenuse of this triangle is equal to √a^2 + b^2 = √12^2 + 5^2 = 13
Answer:
13
Step-by-step explanation:
12 x 12 =144
5 x5=25
Blah blah blah
Answer 13
Find the y-intercept and x-intercept of the line.
-x+4y = 8
Answer:
x-intercept(s): ( − 8 , 0 )
y-intercept(s): ( 0 , 2 )
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y-intercept, substitute in 0 for x and solve for y.
What is the inverse of the function f(x)= 1/4x-12
Answer:
The inverse is 4x+48
Step-by-step explanation:
y = 1/4x - 12
Exchange x and y
Solve for y
x = 1/4y -12
Add 12 to each side
x+12 = 1/4 y -12+12
x+12 = 1/4y
Multiply each side by 4
4(x+12) = 4*1/4y
4x+48 = y
The inverse is 4x+48
Answer:
4x + 48
Step-by-step explanation:
f(x) = 1/4x-12
y = 1/4x - 12
Switch variables.
x = 1/4y - 12
Solve for y.
x = 1/4y - 12
Add 12 on both sides.
x + 12 = 1/4y - 12 + 12
x + 12 = 1/4y
Multiply both sides by 4/1.
4/1(x + 12) = 1/4y × 4/1
4x + 48 = y
Find the solution(s) to 22 +57-3 = 0. Check all that apply.
DAX=3
O B x=-3
O x=2
Ex=-
SU
Answer:
x = -3 and x = 1/2
Step-by-step explanation:
To find the solutions to
2x² + 5x - 3 = 0
we can use the quadratic formula, as follows:
[tex] x = \frac{-b \pm \sqrt{b^2- 4(a)(c)}}{2(a)} [/tex]
[tex] x = \frac{-5 \pm \sqrt{5^2- 4(2)(-3)}}{2(2)} [/tex]
[tex] x = \frac{-5 \pm 7}{4} [/tex]
[tex] x_1 = \frac{-5 + 7}{4} [/tex]
[tex] x_1 = 0.5 [/tex]
[tex] x_2 = \frac{-5 - 7}{4} [/tex]
[tex] x_2 = -3 [/tex]
1) Explain the Distributive Property in your own words.
2) Give an example that shows how to use the Distributive Property to rewrite a one-variable expression.
Answer:
The Distributive Property states that when a number in parentheses is next to a number, you distribute the number outside of the parentheses and multiply by each of the numbers in parentheses.
5(10+x)=5(10)+5(x)=50+5x
:)
Which statement about the function is true?
The graph of the function f(x) = (x - 4)(x + 1) is shown
below.
The function is increasing for all real values of x
where
x<0.
O The function is increasing for all real values of x
where
x < -1 and where x>4
6
4-
2
O The function is decreasing for all real values of x
where
-1<x<4.
The function is decreasing for all real values of x
where
x < 1.5.
2
4
6
-6-4-2
-2
X
27
4
6
Answer:
The correct option is:
The function is decreasing for all real values of x where x < 1.5.
Step-by-step explanation:
We are given a function f(x) which is a product of two linear polynomial as:
Now, we know that on multiplying the two linear polynomial we will obtain a quadratic polynomial.
So, the function f(x) will be represented as:
So, we will plot the graph of the function and check which statements about the function hold true.
1)
The function is increasing for all real values of x where x < 0.
This statement is false.
Since we get from the graph that function f(x) is decreasing for x<0.
2)
The function is increasing for all real values of x where x < –1 and where x > 4.
This option is incorrect as the function is decreasing for x<-1
whereas it is increasing for x>4.
3)
The function is decreasing for all real values of x where –1 < x < 4.
This option is incorrect.
Since, the function is both decreasing as well as increasing in the interval (-1,4).
4)
The function is decreasing for all real values of x where x < 1.5.
This option is correct.
Since it could be observed from the graph that the function is decreasing for x<1.5.
given that (-3 3) is on the graph of f(x) find the corresponding point for the function f(x+1)
Answer:
(-3, 4).
Step-by-step explanation:
When f(x) becomes f(x + 1), all that is happening is that the y-value increases by 1.
So, (-3, 3) becomes (-3, 3 + 1). That is (-3, 4).
Hope this helps!
Answer:
(-2, 3)
Step-by-step explanation:
Find f(x + 1) by adding 1 to the x-coordinate -3 of (-3, 3): (-2, 3)
What is the surface area of a cylinder
396 pi ft^2
180 pi ft^2
192 pi ft^2
252 pi ft^2
Answer:
252pi ft^2
Step-by-step explanation:
The surface area of a cylinder is given by
SA = 2 pi r^2 + 2pi rh
The diameter is 12 so the radius is 12/2 = 6
= 2 pi (6)^2 +2 pi *6*15
= 72 pi + 180pi
= 252pi ft^2
Solve equation by using the quadratic formula.
15x2 + 13x = 0
13
x = -—,0
15
a.
C.
13
x= —.0
15
b. x=0
d.
13
x=+—
15
Answer:
Step-by-step explanation:
Here the coefficients of the x terms in this quadratic are a = 15, b = 13 and c = 0. The discriminant is b^2 - 4ac, or 13^2 - 4(15)(0) = 169 - 60, or 109.
The solutions are:
-13 ± √109
x = -----------------
30
Hence, the roots of the quadratic equation is
[tex]x=0,x=-\frac{13}{15}[/tex]
What is the quadratic equation?
A quadratic equation is any equation that can be rearranged in standard form as + or offer insight into other areas of mathematics.
Here given equation is [tex]15x^2+13x=0[/tex].
As the general formula is
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}\\\\[/tex]
Here, [tex]a=15,b=13[/tex]
Substituting these values in general formula
[tex]x=\frac{-13+-\sqrt{(13)^2-4(15)(0)}}{2(15)}\\\\x=\frac{-13+-\sqrt{169-0}}{30}\\\\x=\frac{-13+-\sqrt{169}}{30}\\\\x=\frac{-13+-13}{30}\\\\\\x=\frac{-13-13}{30},x=\frac{-13+13}{30}\\\\x=\frac{-26}{30},x=0\\\\x=\frac{-13}{15},x=0[/tex]
Hence, the roots of the quadratic equation is
[tex]x=0,x=-\frac{13}{15}[/tex]
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