After considering all the given data we conclude that the the probability of rolling a number less than 7 is 1/2, under the condition that the set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12).
The evaluated probability of rolling a number less than 7 on a 12-sided die is the number of outcomes that are less than 7 divided by the total number of possible outcomes.
The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). There are 6 numbers less than 7 in this set (1,2,3,4,5,6) and 12 possible outcomes.
Hence , the probability of rolling a number less than 7 is:
6/12 = 1/2
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A. Determine if (x+2) is a factor of f(x) =x^3-3x^2-7x+6. Explain your reasoning.
Yes (x+2) is a factor of the function, because the remainder is zero.
No (x+2) is NOT a factor of the function, because the remainder is NOT zero.
B. Use division (long or synthetic) and/or factoring to write f(x) =x^3-3x^2-7x+6 in completely factored form, given that (x+2) is a factor of f(x).
select an answer
f(x)=
DNE
X=
Y=
C. Find all the zeros F(X)= x^3-3x^2-7x+6 . NO DECIMALS!
select an answer
y=
x=
DNE
F(X)=
A. Since the remainder is zero, (x+2) is indeed a factor of f(x).
B. So, f(x) is completely factored as (x+2)(x-1)(x-3).
C. The zeros of F(x) are: -2, 1, and 3.
To determine if (x+2) is a factor of f(x) = x³-3x²-7x+6 can use synthetic division or long division.
Using synthetic division:
-2 | 1 -3 -7 6
-2 10 -6
1 -5 3 0
Using the result from part A we can write:
f(x) = (x+2)(x²-5x+3)
The quadratic factor can be factored further using the quadratic formula or factoring by grouping:
f(x) = (x+2)(x-1)(x-3)
So, f(x) is completely factored as (x+2)(x-1)(x-3).
The zeros of f(x) are the values of x that make f(x) equal to zero.
From the factored form of f(x) we can see that the zeros are -2, 1 and 3. So:
The zeros of F(x) are: -2, 1, and 3.
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Please help me with this 12-14
The arc lengths and the angle measures are arc length = 0.67 meters, AC = 45 degrees and TV = 23 degrees
Calculating the arc lengths and the anglesArc length
Given that
Central angle = 6 degrees
Circumference = 40 meters
The arc length is calculated as
arc length = Central angle/360 * Circumference
So, we have
arc length = 6/360 * 40
Evaluate
arc length = 0.67 meters
The measurement of AC
Here, the arc AC subtends the angle 45 degrees at the center of the circle
This means that
AC = 45 degrees
The measurement of TV
Here, the arc TV subtends the angle 23 degrees at the center of the circle
This means that
TV = 23 degrees
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What time is shown on the clock?
Answer:
3:55
Step-by-step explanation:
3:55
Will Give Brainliest Please Help!
What is one value of x that could replace the missing value in the table
The value of x which could replace the missing value in the table so that y is not a function of x is; 7.
What is the missing value of x that could make y not a function?It follows from the task content that the value of x which could make y not a function of is required to be determined.
Recall that a function is a special kind of relation in which case each value of x is assigned one value of y.
On this note, if we assign 7 as the missing value of x, then y is not a function of x as u has now been assigned more than 1 output, y values.
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what is the difference between a linear functuon and nonlinear function
Answer:
In mathematics, a function is a rule that assigns one unique output value for each input value. A linear function is a function that has a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will form a straight line.
For example, the function f(x) = 2x + 1 is a linear function because its graph is a straight line. As x increases by 1, the output of the function increases by 2.
On the other hand, a nonlinear function is a function that does not have a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will not form a straight line.
For example, the function f(x) = x^2 is a nonlinear function because its graph is a curve. As x increases, the output of the function increases at an increasing rate.
In general, nonlinear functions can take many different forms and can have complex behaviors, whereas linear functions have a simple, predictable behavior.
which equation is NOT true?
A -4+(-3) =-7
B -8(2) = -16
C 3-(-2)=5
D -12 ÷ (-3) = -4
the equation T^2=A^3 shows the relationship between a planets orbital period
The orbital increased by factor [tex]2^3^/^2[/tex] .Hence, correctander is option D by equation T²=A³
The relationship between a planet’s orbital period(T) and the planet’s mean distance from the sun(A) is given by equation T²=A³
Given equation is T²=A³
The distance between the planet X and sun is represented by d
Time-period of the planet X:
T²=d³
Distance between planet Y and the sun is represented by d'
d'= 2d
T'²=d'² = (2d)³ = 8d³
On dividing (1)and (2).
T'/T = 8d³/d³
=8
=2√2
=[tex]2^3^/^2[/tex]
Hence, the orbital increased by factor [tex]2^3^/^2[/tex] .
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The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased? A. 2^1/3. B. 2^1/2. C. 2^2/3. D. 2^3/2
A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
Approximately 95% of the trees in the orchard contain between 375 and 520 suitable apples.
There is a 95% probability that the true mean number of apples per tree is between 375 and 520.
If many random samples of size 40 are selected from the population of all trees in this large orchard, approximately 95% of the sample means will be between 375 and 520 apples.
If many random samples of size 40 are selected from the population of all trees in this large orchard, about 95% of the intervals would capture the true mean number of suitable apples produced per tree.
Answer:
The option that the margin of error accounts for in the given interval is sampling variation.
Step-by-step explanation:
A pentagonal pyramid.
There are
faces on the solid.
There are
edges on the solid.
There are
vertices on the solid.
Answer:
A pentagonal pyramid. There are 6 faces on the solid. There are 10 edges and there are 6 vertices on the solid.
What is a pentagonal pyramid?A pentagonal pyramid is defined as a type of pyramid that has a base with the shape of a regular polygon.
The properties of a pentagonal pyramid include the following:
It has 6 faces. It has 5 triangles as lateral sides. It also has a pentagon at the base. It has 6 vertices.It also has 10 edges.Learn more about polygon here:
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answer it for brainlest and whatever just i need help quikely
Answer:
so do i get brainiliest???
Step-by-step explanation:
Graph the line with equation y=-x-2
The line with the equation y = -x - 2 will pass through the points (0, -2) and (2, -4) and continue infinitely in both directions.
We have,
To graph the line with the equation y = -x - 2, we can follow these steps:
- Step 1:
Plot two points on the graph.
Select any x-value and substitute it into the equation to find the corresponding y-value.
Repeat this process for a different x-value to find another y-value.
Let's choose x = 0:
y = -(0) - 2
y = -2
So we have the point (0, -2).
Let's choose x = 2:
y = -(2) - 2
y = -4
So we have the point (2, -4).
- Step 2:
Plot the points on a coordinate plane.
Plot the points (0, -2) and (2, -4) on a graph.
Step 3: Draw a line passing through the two plotted points.
Using a straightedge or by hand, draw a line that connects the two points.
Thus,
The line with the equation y = -x - 2 will pass through the points (0, -2) and (2, -4) and continue infinitely in both directions.
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Which expression will complete the proof?
O cos(k0-0) + i sin(k0 - 0)
O cos(k0 - 0) + / sin(k0 + 0)
O cos(k0 + 0) + i sin(k0 – 0)
O cos(k0 + 0) + i sin(k0 + 0)
The expression O cos(k0 + 0) + i sin(k0 + 0) is commonly used in proofs involving complex numbers and trigonometric functions, representing the complex exponential function [tex]e^(ik0)[/tex].
The expression that will complete the proof depends on the given context and what exactly needs to be proved. However, in general, the expression O cos(k0 + 0) + i sin(k0 + 0) is often used in proofs involving complex numbers and trigonometric functions.
This expression represents the complex exponential function [tex]e^(ik0)[/tex], where k0 is a constant. The cosine term represents the real part of the complex number, while the sine term represents the imaginary part.
The addition of 0 in the arguments of both cosine and sine indicates that the complex number is in polar form, with a magnitude of 1 ([tex]since cos^2 +[/tex] [tex]sin^2 = 1[/tex] for all angles).
Using this expression, we can perform various operations and manipulations to prove different results, such as De Moivre's theorem or Euler's formula.
Ultimately, the choice of expression will depend on the specific problem and what needs to be proved.
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The volume of a gas was measured as the temperature was increased from 173 K to
423 K in 50 K intervals. The gas volumes recorded, starting at 173 K, were 16, 21, 26, 30, 36, and 40 cm . Determine whether the data is best described by an increasing or decreasing function, and whether it is linear or exponential. Find a regression equation.
The data is best described by an increasing function. The regression equation is y =0.0965x - 0.61.
Here is a table of the data:
Temperature (K) Gas Volume (cm³)
173 16
223 21
273 26
323 30
373 36
423 40
The data is best described by an increasing function, and it is likely to be linear since the volume of the gas increases uniformly with the temperature.
Let x be the temperature and y be the volume of the gas.
The slope is given by (nΣxy - ΣxΣy) / (nΣx² - (Σx)²),
where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x, Σy is the sum of y, and Σx² is the sum of the squares of x.
The y-intercept is given by (Σy - bΣx) / n, where b is the slope.
Using the data, we have n = 6, Σx = 17788, Σy = 169, Σxy = 4225, and Σx² = 43750.
Substituting these values into the formulas gives the slope b = 0.09657 and the y-intercept a = -0.61.
Therefore, the regression equation is y =0.0965x - 0.61.
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A rectangle measures 2 3/4 inches by 2 3/4 inches. What is its area?
The area of the given rectangle is 121/16 square inches.
As know that the area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
To find the area of the rectangle, we need to multiply the length by the width. We have:
Length = 2 3/4 inches = 11/4 inches
Width = 2 3/4 inches = 11/4 inches
Area = Length x Width
Area = (11/4) inches x (11/4) inches
Area = 121/16 square inches
Therefore, the area of the rectangle is 121/16 square inches.
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Please help I am struggling a lot thank you so much have a great day
Answer:
Step-by-step explanation:
To calculate the values of the given function, substitute the given values of x into the function f(x) = 7x^2 - 8x + 8:
f(-2) = 7(-2)^2 - 8(-2) + 8
= 7(4) + 16 + 8
= 28 + 16 + 8
= 52
f(-1) = 7(-1)^2 - 8(-1) + 8
= 7(1) + 8 + 8
= 7 + 8 + 8
= 23
f(0) = 7(0)^2 - 8(0) + 8
= 0 - 0 + 8
= 8
f(1) = 7(1)^2 - 8(1) + 8
= 7(1) - 8 + 8
= 7 - 8 + 8
= 7
f(2) = 7(2)^2 - 8(2) + 8
= 7(4) - 16 + 8
= 28 - 16 + 8
= 20
Therefore, the values of the function for the given inputs are:
f(-2) = 52
f(-1) = 23
f(0) = 8
f(1) = 7
f(2) = 20
While digging in his garden. Tyri pushes a shovel into the ground with a force of 630 newtons at an angle of 70° with the ground. Which diagram shows the resolution of the force Tyri exerts into its rectangular components?
The resolution of the given force applied to the shovel is: A vertical force of 592 NA horizontal force of 215.47 N
How to find the components of the force?The components of a force represent the combined vertical and horizontal forces that combine to make the resultant force. Components are two vectors that add up to the given vector which are perpendicular to each other.
Now, when we apply a force F to an object at an angle θ, it can be said that the resolution of the forces is:
In the horizontal direction: F_x = F * cos θIn the vertical direction: F_y = F * sin θTyri pushes a shovel into the ground with a force of 630 newtons at an angle of 70° with the ground.
Thus, the diagram that shows the resolution of the forces is:
A vertical line showing a force of 630 * sin 70 = 592 N
A horizontal line showing a force of 630 * cos 70 = 215.47 N
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The linear function passes through the point (-1,4) and has a slope of 4. What is the zero of f? Hint: point slope formula.
A: -3
B: 5
C: -2
D: 8
The zero of f is x = -2. C.
The equation of the linear function can be found using the point-slope formula:
y - y1 = m(x - x1)
m is the slope and (x1, y1) is a point on the line.
Plugging in the given values, we get:
y - 4 = 4(x + 1)
Expanding and simplifying, we get:
y = 4x + 8
The zero of f (where f(x) = y) set y = 0 and solve for x:
0 = 4x + 8
4x = -8
x = -2
The point-slope formula may be used to determine the equation of the linear function:
y - y1 = m(x - x1)
(X1, Y1) is a point on the line, and m is the slope.
With the above variables obtain:
y - 4 = 4(x + 1)
By enlarging and condensing, we obtain:
y = 4x + 8
y = 0, you may solve for x using the zero of f (where f(x) = y):
0 = 4x + 8 4x
= -8 x
= -2
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dentify the radius and the center of a circle whose equation is (x – 5)² + y² = 81.
The radius of the circle is units.
The center of the circle is at (, ).
Answer:
Step-by-step explanation:
General formula
(x-h)^2 + (y-k)^2 = r^2
where (h,k) center of circle whose radius r
applying the formula to our Q
(x – 5)² + y² = 81
(x – 5)² + (y-0)² = 9^2
---> center of circle (5,0)
---> radius is 9
The bar graph above shows the number of T-shirts of different colors sold by a store one week. The following
week, the store had a sale, and sales of each color T-shirt sold increased by about 50 percent from the
previous week. Of the following, which is closest to the number of green T-shirts sold the week of the sale?
0 15
0 20
045
0 60
The number of green t-shirts sold are 45.
Given that a bar graph showing the sell of t-shirts of 4 different colour,
It is saying that the sell has increased by 50% next week, we need to find the number of green t-shirts to be sold in next week,
So, the number of green t-shirts sold in previous week = 30
So this week the sell should have been increased by 50%
Therefore, the number of green t-shirts sold this week = 150/100 × 30
= 1.5 × 30 = 45
Hence the number of green t-shirts sold are 45.
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If sinx= 5/13 and x is in quadrant 1, then Tanx/2=
OA. -5
O B. - 1/5
OC. 5
O D. 1/5
Answer: D: 1/5
Step-by-step explanation:
sinx = 5/13
this ratio is special; it is a 5-12-13 right triangle, (pythagorean triple).
there is also a formula to find tan(x/2); It is tan(x/2) = ±[tex]\sqrt{\frac{1-cosx}{1+cosx} }[/tex]
the + or - sign is decided by the quadrant the half angle is in;
since x is in quad one, it is somewhere between 0 and pi/2. To find the half angles position, simply divide it; x/2 is somewhere between 0/2 and pi/4.
so its also in the first quadrant. Since tangent is positive in the first quadrant, we will take the positive answer:
One more thing. we need the cosx in our formula. cosx will be 12/13, since this is a special right triangle as we said before.
tan(x/2) = [tex]\sqrt{\frac{1-12/13}{1+12/13} }[/tex]
tan(x/2) = [tex]\sqrt{\frac{1/13}{25/13} }[/tex]
tan(x/2)= [tex]\sqrt{1/25}[/tex]
tan(x/2) = 1/5
Option D is the answer :)
.
What is the x-coordinate of the solution to the following system of equations?
2x + y = -4
5x + 3y = -6
Ox=-6¹
Ox=6
Ox = -8
Ox=8.
Answer:
Option : A
Step-by-step explanation:
To find the x-coordinate of the solution to the system of equations, we need to solve the system by eliminating either x or y. Let's eliminate y by multiplying the first equation by 3 and the second equation by 1:
Equation 1: 2x + y = -4 (multiply by 3)
Equation 2: 5x + 3y = -6 (multiply by 1)
Multiplying equation 1 by 3 gives us:
6x + 3y = -12
Multiplying equation 2 by 1 gives us:
5x + 3y = -6
Now we can subtract equation 2 from equation 1 to eliminate y:
(6x + 3y) - (5x + 3y) = -12 - (-6)
6x + 3y - 5x - 3y = -12 + 6
x = -6
Therefore, the x-coordinate of the solution to the system of equations is x = -6.
The correct option is: Ox=-6.[tex][/tex]
103. In a sample of 50 cars at a local dealership,
there are 12 red cars and 10 cars with backup
cameras. Of the 12 red cars, 4 have backup
cameras. If a car is selected at random from
the given sample, what is the probability
that both of the following are true: the car is
not red and does not have a backup camera?
A. 3/5
B. 16/25
C. 19/25
D. 4/5
Answer:
The correct answer is (D) 4/5.
Step-by-step explanation:
First, we need to find the number of cars that are neither red nor have a backup camera.
Number of cars that are not red = 50 - 12 = 38
Number of cars that do not have a backup camera = 50 - 10 = 40
Number of cars that are neither red nor have a backup camera = 38 + 10 - 50 = 8
Therefore, the probability of selecting a car that is not red and does not have a backup camera is:
P(not red and no backup camera) = 8/50
Simplifying:
P(not red and no backup camera) = 4/25
So the correct answer is (D) 4/5.
Kendall kept track of the number of hours that she spent in
pep band each week for several weeks. She spent 2, 4, 4, 5,
and 5 hours.
What is the mean number of hours that Kendall spent in pep band each
week?
OA. 5 hours
OB. 4 hours
OC. 20 hours
OD. 3 hours
Suppose you want to purchase a $ 165000 house. If you put 20% down and finance the rest in a 20 year mortgage at an interest rate of 7.5%, what will your monthly payments be?
Monthly payment =
The monthly payments on the 20 yrs mortgage would be $946.69.
According to the question, the down payment on the house is 20% of $165000, which is:
0.2 * $165,000 = $33,000
The amount that is needed to be financed is:
$165,000 - $33,000 = $132,000
This rate of interest on the payment is 7.5% per year, which is equal to 0.075 as a decimal. We know that the mortgage is for 20 yrs or 240 months:
To calculate the monthly payment, we can use the formula:
monthly payment = [tex][P * r * (1 + r)^n] / [(1 + r)^n - 1][/tex]
where P is the principal amount i.e. the amount being borrowed, r is the monthly interest rate, whereas n is the number of payments.
we need to find the monthly interest rate, for which we can use divide the yearly interest by the number of months in a year, we get:
r = 0.075 / 12 = 0.00625
Now substituting the values into the formula above we get:
monthly payment = [tex][$132,000 * 0.00625 * (1 + 0.00625)^240] / [(1 + 0.00625)^240 - 1][/tex]
monthly payment = $946.69 which is rounded to the nearest cent.
Therefore, the monthly payments on the 20 yrs mortgage would be $946.69.
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Betty has a checking account and a non-interest-bearing savings account. Function C represents her checking account balance, where x is the number of months. Function S represents her saving account balance which function represents Betty's total account balance,
Answer: t(x) or total amount
Step-by-step explanation:
Answer:
Step-by-step explanation:
d
A dairy farm has a real estate tax rate of $57.26 per thousand dollars of assessed
value. If the farm is assessed at $665,500.00 what is the real estate tax?
Benjamin is planning what to wear tomorrow evening.
• He has 3 shirts to choose from: red, white, and green.
• He has 2 pairs of pants to choose from: blue jeans and khaki pants.
• He has 3 pairs of shoes to choose from: sneakers, flip flops, and boots.
Benjamin randomly chooses one item from each group. What is the probability that he chooses
sneakers and the green shirt? Type in simplest form!!! Anything else will be considered correct, no exceptions
Answer:
1/9
Step-by-step explanation:
P =
[tex](no \: of \: favorable \: outcomes) \div (total \: numeber \: of \: outcomes \: )[/tex]
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Peace
1. Allison is buying a home. It cost her $230,000. She has to put a down payment of 10% of the purchase price. How much is her down
payment?
$13,000
$23,000
$30,000
$2,000
Determine the equation of the circle with center
(
0
,
9
)
(0,9) containing the point
(
65
,
12
)
(
65
,12).
A circle with Centre [tex](a,b)[/tex] has the general equation:
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
where [tex]r[/tex] is the radius and [tex](a,b)[/tex] is the Centre.
Given that the Centre is at [tex](0,9)[/tex], the equation is as follows:
[tex](x-0)^2 + (y-9)^2 = r^2[/tex]
If we simplify, we get:
[tex]x^2 + (y-9)^2 = r^2[/tex]
The fact that the circle comprises the coordinates [tex](65,12)[/tex] is also provided. Therefore, we may change these values into the equation and find [tex]r[/tex]:
[tex]65^2 + (12-9)^2 = r^2[/tex]
[tex]4225 + 9 = r^2[/tex]
[tex]r^2 = 4234[/tex]
When we square the two sides, we obtain:
[tex]r = \sqrt{4234}[/tex]
The circle's equation is as follows:
[tex]x^2 + (y-9)^2 = 4234[/tex]
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