Answer:
A) Sample bias
Step-by-step explanation:
If a sample of 100 participants includes 20 men and 80 women, then the sample is biased. Women account for;
(80/100)*100 = 80% of the total participants while men only for 20%.
The sample does not represent the entire population in fair proportions hence the sample is biased
Find an equation for the nth term of the sequence.
-1, -4, -16, -64
a. an = -1 • 4^n - 1
b. an = -1 • 4^n
c. an = 4 • -1^n
d. an = 4 • -1^n + 1
Answer:
a. an = -1 • 4^(n - 1)
Step-by-step explanation:
It's easy see that each term is multiplied by 4 to get the next term, so the common ratio will be 4, that reduces the choices to answers A and B (since C and D use -1 as common ratio). Also, normally a geometric progression uses "n-1", so we'll first try with A to see if it works.
a1 = (-1) * 4^0 = -1 * 1 = -1
a2 = (-1) * 4^1 = -1 * 4 = -4
a3 = (-1) * 4^2 = -1 * 16 = -16
Yes, it works... so the answer is an = -1 • 4^(n - 1)
Three people play a game on each spinner in the previos problem.
* Player 1 scores a point if the pointer lands on 1.
* Player 2 scores a point if the pointer lands on 2.
* Player 3 scores a point if the pointer lands on 3.
a. On which spinner(s) is the game a fair game? Explain.
b. Choose a spinner that you think doesn't make a fair game. Then, change the scoring rules to make the fair by assigning different points for landing on different numbers. Explain why your point system works.
Answer:
Step-by-step explanation:
All other things being equal, spinner A is fine. It is a fair spinner.
Spinner B is not fair. Players 1 and 3 have only 1 number each. Player 2 on the other hand, has 2 numbers that work for him. If player 2 puts in two dollars and players 1 and 3 one dollar each, that should even up the odds. Now you want it just to be fair. So I think player 2 has to put up 2 dollars and players 1 and 3 each put up one. The pot is 4 dollars each time it is played.
Spinner 3 is not fair either. Player one has 2 chances. Player 2 has 3 chances and player 3 has but one chance. There are 6 chances in all. Player 1 should put up 2 dollars to play player 1 should put up 3 dollars and player 1 should put up 1 dollar.
What is the area of the triangle
ANSWER
B. 24 sq. units.
EXPLANATION
The area of a triangle is calculated using the formula:
[tex]Area = \frac{1}{2} \times AB \times BC[/tex]
From the graph ,
AB=3--3=6 units.
BC=3--5=8 units
We substitute the values into the formula to get,
[tex]Area = \frac{1}{2} \times 6 \times 8 = 24sq. \: units[/tex]
The correct answer is B
Please help me!
1. Joshua has a ladder that is 17ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5ftabove the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height? Show your work.
make sure you show your work.
Answer:
not safe
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between an angle and the ratio of side opposite to hypotenuse:
Sin = Opposite/Hypotenuse
You have the ratio of lengths and you want to find the angle. You use the inverse sine function (arcsin, or sin⁻¹) for this purpose.
sin(angle with ground) = (16.5 ft)/(17 ft) = 33/34
angle with ground = arcsin(33/34) ≈ 76.1°
This angle is greater than the angle of 70° recommended as a maximum. The ladder will not be safe at this height.
_____
A calculator does all the work. You just need to make sure it is in degrees mode.
The parent function f(x) = x2 is translated such that the function g(x) = –x2 + 6x – 5 represents the new function.
What is true about the transformation that was performed? Check all that apply.
g(x) has an axis of symmetry at x = 3.
g(x) is shifted down 5 units from the graph of f(x).
g(x) is shifted right 3 units from the graph of f(x).
g(x) is shifted up 4 units from the graph of f(x).
g(x) is narrower than f(x).
Answer:
g(x) has an axis of symmetry at x = 3.
g(x) is shifted right 3 units from the graph of f(x)
g(x) is shifted up 4 units from the graph of f(x).
Step-by-step explanation:
The parent function is:
[tex]f(x)=x^2[/tex]
The transformed function is [tex]g(x)=-x^2+6x-5[/tex].
This new function can be rewritten in the vertex form as:
[tex]g(x)=-(x-3)^2+4[/tex]
This function is obtained by shifting the parent function 3 units right and 4 units up.
The axis of symmetry is x=3;(x=h) and h=3.
There is no horizontal stretch or compression.
The new function is however reflected in the x-axis
Step-by-step explanation:
on edge its A,C,D :)
What is the solution for the equation 2x - 3 = - 8
2x - 3 = -8
+3 + 3
2x = -5
/2 /2
x = -2.5 (Answer)
Prove.
2(-2.5) - 3 = -8
-5 - 3 = -8
-8 = -8
True.
Answer:
Answer -2.5
Step-by-step explanation:
Simple:
2x-3=-8
+3 +3, Add 3 on both sides of the equal sign.
2x = -5, Bring the 2x down and add the -8 + 3
2 2, Divide by 2
x= -2.5
Hope my answer has helped you!
What are the relative minimum and relative maximum values over the interval [−4, 4] for the function shown in the graph?
A. relative minimum = −36 , relative maximum = 64
B. relative minimum = 0, relative maximum = 64
C. relative minimum = −3 , relative maximum = 64
D. relative minimum = −3 , relative maximum = −36
A relative minimum = −36 , relative maximum = 64
Answer:
A
Step-by-step explanation:
The relative minimum is where the curve changes directions from down to up. The relative maximum is where the curve changes direction from up to down.
In the interval [-4, 4], there are two relative minimums: y=-36. And there is one relative maximum: y=64.
Answer A.
Valerie took out a loan to pay off some bills. She borrowed $1,200 at an annual interest rate of 9%. How much interest did she pay on the loan the first year?
Answer:
$108
Step-by-step explanation:
Step 1: Find the interest. You do this by multiplying the amount borrowed by the interest rate. In this case, you multiply 1,200 by 9% (0.09). 1,200 * 0.09 is $108. That's the amount she paid on the loan in her first year.
St. Louis, Missouri and Washington, D.C. Have very similar latitudes. (Latitude measures how far north or south a place is, which in turn affects the temperature.) The box plots below show the daily high temperatures (in degrees Celsius) that were recorded during July 201320132013 in each city. Which pieces of information can be gathered from these box plots?
Answer:
The Answer is multiple choice and the answer is B. Only B.
Step-by-step explanation:
The Answer is multiple choice and the answer is B.
We have given that,
St. Louis, Missouri, and Washington, D.C.
Have very similar latitudes. (Latitude measures how far north or south a place is, which in turn affects the temperature.)
What is the latitudes?The latitude is specified by degrees, starting from 0° and ending up with 90° to both sides of the equator, making latitudes Northern and Southern.
The box plots below show the daily high temperatures (in degrees Celsius) that were recorded during July 201320132013 in each city.
The pieces of the information that can be gathered from these box plots are option is B.
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You have a large tree in your front yard. At noon the tree casts a circular shadow with a radius of 9 m. You are now planting a tree in your back yard. At noon it's shadow will have a radius of 4 m. How much of your yard is shaded by the two trees at noon?
Answer:
97π m² ≈ 304.7 m²
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr²
The sum of the areas of the two circles is ...
A = π(9 m)² + π(4 m)² = π(81 +16) m²
= 97π m² ≈ 304.7 m²
Find the value of the indicated angles. HELP PLEASE!!
Answer:
52
Step-by-step explanation:
add add add add add add adddaddd addda
The inscribed angle is half that of the arc it comprises. The measure of both the angle is 52°.
How do we relate the inscribed angle and the arc?we know that the inscribed angle is half that of the arc it comprises.
Here, the arc that the inscribed angles comprise is the same.
2(3m+2)° = (4m+20)°
Solve for m
6m + 4 = 4m + 20
6m - 4m = 20 - 4
2m = 16
m = 8
To find the measure of the angle
(4m+20)°= 4(8) + 20 = 52°
2(3m+2)° = 2(26) = 52
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The play cost $2,600.00 to produce, and they intend to sell tickets for $10 each. After the play, Betsy will take the ticket proceeds and deposit them with the bank. If 741 people attend the play's opening night, what will the balance of the bank account be? A. $7,410 B. $10,010 C. - $2,526 D. $4,810
Answer:
4,810
Step-by-step explanation:
$10 per ticket times 741 people (10 * 741) is 7,410, then subtract the cost to produce the play, 7,410 - 2600 = 4,810.
NEED ANSWER ASAP!
Which of the following represents the graph of f(x) = 2x + 3? (6 points)
The graph of f(x) = [tex]2^{x+3}[/tex] is option "B" .
What is exponential function?An exponential function is a mathematical function of the following form:
f ( x ) = [tex]a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
According to the question
Represents the graph of f(x) = [tex]2^{x+3}[/tex]
f(x) = [tex]2^{x+3}[/tex] is a exponential function
To draw the graph of f(x) = [tex]2^{x+3}[/tex]
The values will be
x f(x)
0 8
1 16
-1 4
-2 2
-3 0
Hence, the graph of f(x) = [tex]2^{x+3}[/tex] is option "B" .
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The graph of the function represented by the equation f(x) = 2ˣ + 3 is (c)
How to determine the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
The function
Where, we have
f(x) = 2ˣ + 3
The above function is an exponential function that has been transformed as follows
Asymptote at y = 3Function increases as x increasesUsing the above as a guide, we have the following:
The graph of the function is (c)
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An object is launched into the air. The projectile motion of the object can be modeled using the function h(t) = –16t2 + 72t + 5, where t is the time in seconds since the launch and h(t) represents the height in feet of the object after t seconds. What is true about the projectile motion of this object? Check all that apply. The initial height is 5 feet. The initial velocity of the object is –72 feet/second. The object will hit the ground after approximately 4.57 seconds. After 3 seconds, the object is 173 feet high. At t = 0, h(t) = 0.
Answer:
Step-by-step explanation:
In the equation, 72t represents the initial upwards velocity and 5 represents the initial launching height. The leading term represents the pull of gravity on the object in the English system of measurement.
So the first question says the initial height is 5 feet. TRUE
The second question says the initial vertical velocity is -72. FALSE (it's positive 72 ft/sec)
The third question says that the object will hit the ground after approximately 4.57 seconds. TRUE. Find this by setting the h(t) on the left equal to 0, since this is the height at any time during the flight. When h(t) = 0, that means that there is NO height, which means the object is on the ground. Set the equation equal to 0 and factor to find t. Putting that into the quadratic formula gives you t values of -.068 and 4.57. Since the 2 things in math that will NEVER EVER be negative are distances and time, we can safely disregard the negative t value and go with t = 4.57.
The fourth question says that after t = 3 seconds, the object is 173 feet high. FALSE. Find this by subbing in a 3 for every t in the equation.
[tex]h(3)=-16(3)^2+72(3)+5[/tex]
This gives you that h(3) = 77 feet
The last question says that at t = 0, h(t) = 0. FALSE again. Sub in a 0 for every t in the equation, and you get h(0) = 5, which is the initial launching height.
Answer:
The initial height is 5 feet.
The object will hit the ground after approximately 4.57 seconds.
A & C
Step-by-step explanation
An object is launched into the air. The projectile motion of the object can be modeled using the function h(t) = -16t^2 + 72t + 5, where t is the time in seconds since the launch and h(t) represents the height in feet of the object after t seconds
General equation is
V_0 is the initial velocity
h_0 is the initial height
From the given equation , the initial height is 5 feet
Initial velocity is +72 feet / sec
When the onbject hits the ground, the height becomes 0
So we plug in 0 for h(t) and solve for t
USe quadratic formula to solve for t
a=-16, b= 72, c= 5
t= -0.06 and t= 4.568
The object will hit the ground after approximately 4.57 seconds.
To find out the height after 3 seconds, plug in 3 for t
At t=0 , h(0) = 5
Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the questions below. Show all your work for full credit. Use the correct units with your answers
This is a problem of projectile motion. A projectile is an object you throw with an initial velocity and whose trajectory is determined by the effect of gravitational acceleration. The general equation in this case is described as:
[tex]h(t)=-\frac{1}{2}gt^2+v_{0}t+h_{0}[/tex]
Where:
[tex]h(t): \ height \ at \ any \ time \\ \\ g: \ acceleration \ due \ to \ gravity \ 9.8m/s^2 \ or \ 32.16ft/s^2 \\ \\ v_{0}= \ Initial \ velocity[/tex]
So:
[tex]v_{0}=64ft/s \\ \\ h_{0}=3ft[/tex]
Finally, the equation is:
[tex]h(t)=-\frac{1}{2}(32.16)t^2+(64)t+3 \\ \\ \boxed{h(t)=-16.08t^2+64t+3}[/tex]
b. How long will it take the rocket to reach its maximum height?The rocket will reach the maximum height at the vertex of the parabola described by the equation [tex]h(t)=-16.08t^2+64t+3[/tex]. Therefore, our goal is to find [tex]t[/tex] at this point. In math, a parabola is described by the quadratic function:
[tex]f(x)=ax^2+bx+c[/tex]
So the x-coordinate of the vertex can be calculated as:
[tex]x=-\frac{b}{2a}[/tex]
From our equation:
[tex]a=-16.08 \\ \\ b=64 \\ \\ c=3[/tex]
So:
[tex]t=-\frac{64}{2(-16.08)} \\ \\ \boxed{t=1.99s}[/tex]
So the rocket will take its maximum value after 1.99 seconds.
c. What is the maximum height the rocket will reach?
From the previous solution, we know that after 1.99 seconds, the rocket will reach its maximum, so it is obvious that the maximum height is given by [tex]h(1.99)[/tex]. Thus, we can find this as follows:
[tex]H_{max}=h(1.99)=-16.08(1.99)^2+64(1.99)+3 \\ \\ \boxed{H_{max}=66.68ft}[/tex]
So the maximum height the rocket will reach is 66.68ft
d. How long is the rocket in the air?
The rocket is in the air until it hits the ground. This can be found setting [tex]h(t)=0[/tex], so:
[tex]0=-16.08t^2+64t+3 \\ \\ Applying \ quadratic \ formula: \\ \\ t_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=-16.08 \\ \\ b=64 \\ \\ c=3 \\ \\ t_{12}=\frac{-64 \pm \sqrt{64^2-4(-16.08)(3)}}{2(-16.08)} \\ \\ t_{1}=4.0264 \\ \\ t_{2}=-0.046[/tex]
We can't have negative value of time, so the only correct option is [tex]t_{1}=4.0264[/tex] and rounding to the nearest hundredth we have definitively:
[tex]\boxed{t=4.03s}[/tex]
If the ratio between the radii of the two sphere is 3:5, what is the ratio of their volumes?
A. 3:25
B. 6:25
C. 9:25
D. 27:125
Answer: Option D
Step-by-step explanation:
You know that the ratio between the radii of the two sphere is 3:5. Knowing this fact, you can calculate the ratio of their volume with this procedure:
[tex]ratio\ volume=\frac{3^3}{5^3}[/tex]
You need to remember that:
[tex]a^3=a*a*a[/tex]
Then, you can rewrite it as:
[tex]ratio\ volume=\frac{3*3*3}{5*5*5}[/tex]
Finally, you get the the ratio of the volumes of the spheres is:
[tex]ratio\ volume=\frac{27}{125}[/tex] or 27:125
This matches with the option D.
Answer:
The ratio of their volumes is 27 : 125
Step-by-step explanation:
Points to remember
Volume of sphere V = 4/3(πr³)
Where r is the radius of sphere
To find the ratio of volume of spheres
It is given that, the ratio between the radii of the two sphere is 3:5
V₁ = 4/3(πr₁³) = 4/3(π3³) and
V₂ = 4/3(πr₂³) = 4/3(π5³)
V₁/V₂ = 4/3(π3³)/4/3(π5³)
= 3³/5³ = 27/125
Therefore the ratio of their volumes = 27 : 125
Solve the following systems of equations:
4x+5y=-4
4x+3y=12
X=?
Y=?
For this case we have the following system of equations:
[tex]4x + 5y = -4\\4x + 3y = 12[/tex]
We multiply the second equation by -1:
[tex]-4x-3y = -12[/tex]
We add the equations:
[tex]4x-4x + 5y-3y = -4-12\\5y-3y = -4-12\\2y = -16\\y = \frac {-16} {2}\\y = -8[/tex]
We find the value of "x":
[tex]4x = 12-3y\\x = \frac {12-3y} {4}\\x = \frac {12-3 (-8)} {4}\\x = \frac {12 + 24} {4}\\x = \frac {36} {4}\\x = 9[/tex]
Thus, the solution of the system is given by:
[tex](x, y) :( 9, -8)[/tex]
ANswer:
(9, -8)
Answer:
x = 9 and y = -8
Step-by-step explanation:
It is given that,
4x + 5y = -4 ----(1)
4x + 3y = 12 -----(2)
To find the value of x and y
eq (1) - eq (2) ⇒
4x + 5y = -4 ----(1)
4x + 3y = 12 -----(2)
0 + 2y = -16
y = -16/2 = -8
Substitute the value of y in eq (1)
4x + 5y = -4 ----(1)
4x + 5*-8 = -4
4x - 40 = -4
4x = -4 + 40 = 36
x = 36/4 = 9
x = 9 and y = -8
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Answer:
okay
Step-by-step explanation:
Which equation most closely represents the line of best fit for the scatter plot below?
I think that the first choice is the correct one
what is the completley factored form of f(x)=x^3-2x^2-5x+6
Answer:
f(x) = (x - 1)(x + 2)(x - 3)
Step-by-step explanation:
We are given the following function and we are to factorize it completely:
[tex] f ( x ) = x ^ 3 - 2 x ^ 2 - 5 x + 6 [/tex]
To factorize this completely, we will use the rational roots theorem.
[tex] x ^ 3 - 2 x ^ 2 - 5 x + 6 [/tex]
P = ± multiples of constant term [tex]6 = \pm1, \pm2, \pm3, \pm6[/tex]
Q = ± multiples of the coefficient of highest degree term [tex] = \pm1[/tex]
So the factors will be [tex]\frac{P}{Q}[/tex].
The possible rational roots are [tex] 1, \pm2, \pm3, \pm6[/tex].
1 is a confirmed root and now we will use synthetic division to find the other rational roots:
1 | 1 -2 -5 6
1 -1 -6
___________
1 -1 -6 0
So the polynomial will be [tex](x^2 - x - 6)[/tex] which can we factorize now.
[tex]x^2 - x - 6 = x^2 - 3x + 2x - 6[/tex]
[tex]x(x - 3) + 2(x - 3) = (x+2)(x-3)[/tex]
Therefore, the completely factorized form of the given function is f(x) = (x - 1)(x + 2)(x - 3).
*20 POINTS PLEASE HELP ME!!!!!!!!*
Answer:
helloooooooooooooooooooo
solve by substitution:
-5x + y = -2
-3x + 6y = -12
please explain
First we pick the equation. Let's say we pick first one. From it we express y.
[tex]-5x+y=-2\Longrightarrow y=-2+5x[/tex]
Then we use this y and plug it in instead of y in the second equation.
[tex]-3x+6(-2+5x)=-12[/tex]
Now just solve for x.
[tex]
-3x-12+30x=-12 \\
-3x=-30x \\
\underline{x=10}
[/tex]
We plug this x in the first equation.
[tex]-5\cdot10+y=-2[/tex]
And solve for y.
[tex]
-50+y=-2 \\
\underline{y=48}
[/tex]
So the solution to the equation is geometrically a point P which lies on the intersection of the two lines.
[tex]\boxed{P(10,48)}[/tex]
Hope this helps.
r3t40
graph the line.
y - 2 = -3(x + 3)
Answer:
see below
Step-by-step explanation:
The equation is in point-slope form, so you know the line goes through the point (x, y) = (-3, 2) and it has a slope of -3. The slope tells you the line goes down 3 units for each 2 units to the right.
Page 2
7. Donald has 6 unit cubes. How many
different rectangular prisms can he
make using all 6 unit cubes?
Answer:
Step-by-step explanation:
2
With 6 unit cubes, it is possible to form 4 distinct rectangular prisms: 1x1x6, 1x2x3, 1x3x2, and 2x3x1.
Explanation:The subject here is combinatorial mathematics focusing specifically on the construction of geometric shapes with a limited number of unit cubes. With 6 unit cubes, Donald can make 4 different rectangular prisms:1x1x6, 1x2x3, 1x3x2, and 2x3x1, each dimension representing length, width, and height in units. Here, the number of ways to arrange the cubes depends on unique combination of dimensions that respect the given total volume (i.e., number of unit cubes), which is 6 in this case.
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Is this shaded below or above the line?
Answer:
below the line
Step-by-step explanation:
The "shading" is the blue/purple color. The graph is shaded below the line y=-2x+6, as it should be when y is less than or equal to -2x + 6.
(Values of y get smaller in the downward direction, to for any given value, ones that are less than that will be below it.)
Which criteria for triangle congruence can be used to prove the pair of triangles below are congruent?
A. SAS
B. ASA
C. AAS
D. none
Answer:
A)SAS
Step-by-step explanation:
The tick marks represent which sides of the triangles are congruent, while the arc represents which angles are congruent.
Since the arc is in between the sides that are congruent therefore the postulate is Side Angle Side
Without visual or informational context, the congruence criteria between the pairs of triangles cannot be determined. It's essential to know specific details about the triangles to apply congruence criteria like Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS). However, with no further details, the answer is 'D. None'.
Explanation:To determine which criterion for triangle congruence can be used to prove that the pair of triangles are equal, we first need to examine the triangles. SAS refers to Side-Angle-Side, which is when two sides and the included angle of one triangle is congruent to two sides and the included angle of another triangle. ASA refers to Angle-Side-Angle, which is when two angles and the included side of one triangle is congruent to two angles and the included side of another triangle. AAS refers to Angle-Angle-Side, which is when two angles and a non-included side of one triangle is congruent to two angles and a non-included side of another triangle. So, without a visual or further information about the triangles, we cannot directly apply any particular congruence criteria and the answer would be 'D. none'. However, with more information, the pair of triangles can possibly be proven congruent using either SAS, ASA, or AAS methods.
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The radius of a sphere is 3 inches. Which represents the volume of the sphere? O 12TT cubic inches O 36TT cubic inches O 64Tt cubic inches O 81Tt cubic inches
Answer:
36π cubic inches
Step-by-step explanation:
The formula for the volume of a sphere is ...
V = (4/3)πr^3
Fill in the given value and simplify:
V = (4/3)π(3 in)^3 = 36π in^3
In the standard (x, y) coordinate plane, if the x-coordinate of each point is 2 times the y-coordinate, what is the slope of the line?
Answer:
the slope is 1/2
Work:
if the x-coordinate is two times the y-coordinate, that means you are going up one over two each time
slope= y2-y1/x2-x1
so you can pick two points, like (2, 1) and (4,2) and use the formula
slope= 2-1/4-2= 1/2
Hiroshi picked 25 apples and gave away 17. Hiroshi divided the rest equally among 2 friends. How many did each friend have?
25-17=8
8÷2=4
4 apples per friend.
Please help me out with this
Answer:
(7, - 4) and r = 7
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 7)² + (y + 4)² = 49 ← is in standard form
with (h, k) = (7, - 4 ) and r = [tex]\sqrt{49}[/tex] = 7