The number of ways of selecting 3 items from a total of 7 items, where order does not matter is (a) 35 ways.
The number of ways to choose three items from a group of seven, where order does not matter, is given by the combination formula:
⇒ C(n,r) = n!/(r! × (n-r)!),
where n is = total number of items, and r is = number of items to be chosen,
We have, total items (n) = 7 and items to be selected (r) = 3.
Substituting the values,
We get;
⇒ C(7,3) = 7!/(3! × (7-3)!),
⇒ 7!/(3! × 4!),
⇒ (7 × 6 × 5)/(3 × 2 × 1),
⇒ 35 ways.
Therefore, the correct option is (a).
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The number 0 is a solution to which of the following inequalities? Select all that apply. x – 5 ≤ -3 x/-2 ≥ 0 x + 11 > 12 4x < 0
Answer: the inequalities for which 0 is a solution are x - 5 ≤ -3 and x/-2 ≥ 0.
Step-by-step explanation: x - 5 ≤ -3 (0 is less than or equal to 2)
x/-2 ≥ 0 (0 is greater than or equal to 0)
In mathematical form, this can be written as:
0 ≤ x - 5 ≤ -3 or x - 5 ≤ 0 and x ≤ -3
Consider a figure in a coordinate plane. For each of the transformations below, first transform the figure as stated. Then reverse the order of the sentences and transform the original figure a second time. Did the sequences result in the same image or a different image? Drag and drop each transformation in the cell with the appropriate heading.
Transformation is a function that takes points on the plane and maps them to other points on the plane.
Transformations can be applied one after the other in a sequence where you use the image of the first transformation as the pre image for the next transformation.
Find the image for each sequence of transformations.
Using geometry software, draw a triangle and label the
vertices A, B, and C. Then draw a point outside the
triangle and label it P.
Rotate △ABC 30° around point P and label the image as
△A′B′C ′. Then rotate △A′B′C ′ 45° around point P and
label the image as △A″B″C ″. Sketch your result.
Make a conjecture regarding a single rotation that will map △ABC to △A″B″C″.
Check your conjecture, and describe what you did.
Using geometry software, draw a triangle and label the
vertices D, E, and F.
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Help please (time limit)
Answer:
It is a function
Step-by-step explanation:
It's a function because it does not over lapp
Select the correct answer.
What is the simplest form of this expression?
(2x-3)(3x²+2x-1)
O A 6x³-5x²²-8x+3
OB. 6x³-5x² - 6x + 2
OC. 6x³-9x² - 4x +3
OD. 6x³-2²-8x+3
The simplest form of the expression (2x-3)(3x²+2x-1) is 6x³ - 5x² - 8x + 3.
What is the simplest form of this expression?Given the expression in the question:
( 2x - 3 )( 3x² + 2x - 1 )
To simplify the expression (2x-3)(3x²+2x-1), we need to use the distributive property of multiplication,
which states that: a(b+c) = ab + ac
Using this property, we can expand the expression as follows:
(2x-3)(3x²+2x-1)
2x(3x²+2x-1) - 3(3x²+2x-1)
6x³ + 4x² - 2x - 9x² - 6x + 3
Add like terms
= 6x³ - 5x² - 8x + 3
Therefore, the simplest form is 6x³ - 5x² - 8x + 3.
Option A) 6x³ - 5x² - 8x + 3 is the correct answer.
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Use the equation to answer ALL of the questions below.
f(x) = 2x² + 8x - 4
What is the axis of symmetry? You can use the equation
What is the vertex of the parabola (x, y)?
What is the y-intercept of the parabola?
Answer:
see explanation
Step-by-step explanation:
given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
then the equation of the axis of symmetry is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = 2x² + 8x - 4 ← is in standard form
with a = 2, b = 8 , then equation of axis of symmetry is
x = - [tex]\frac{8}{2(2)}[/tex] = - [tex]\frac{8}{4}[/tex] = - 2
that is equation of axis of symmetry is x = - 2
the axis of symmetry passes through the vertex of the parabola
substitute x = - 2 into f(x) for corresponding y- coordinate
f(- 2) = 2(- 2)² + 8(- 2) - 4 = 2(4) - 16 - 4 = 8 - 20 = - 12
vertex = (- 2, - 12 )
the y- intercept is on the y- axis, where the x- coordinate is zero
substitute x = 0 into f(x)
f(0) = 2(0)² + 8(0) - 4 = 0 + 0 - 4 = - 4
y- intercept = - 4
Find the volume of the following Cylinders Diameter 150mm, height 100m
Answer:
I am not sure if you wanted the answer in mm or m. I gave the answer is m
v = 0.58875[tex]m^{3}[/tex]
Step-by-step explanation:
v = 1/3[tex]\pi r^{2} h[/tex]
v = 1/3 (3.14)([tex].075^{2}[/tex])(100) The diameter 150mm is .0150m Take have of that to find the radius
v = 0.58875[tex]m^{3}[/tex]
with each heartbeat, blood pressure increases as the heart contracts, then decreases as the heart rests between beats. The maximum blood pressure is called
the systolic pressure and the minimum blood pressure is called diastolic pressure. When a doctor records an individual's blood pressure such as "120 over 80" it
is understood as "systolic over diastolic". Suppose that the blood pressure for a certain individual is approximated by p (t)-80+30 sin (120xt) where p is the
blood pressure in mmHg (millimeters of mercury) and is the time in minutes after recording begins.
(a) Find the period of the function and interpret the results.
(b) Find the maximum and minimum values and interpret this as a blood pressure reading.
(c) Find the times at which the blood pressure is at its maximum.
Part: 0/3
Part 1 of 3
(a) Find the period of the function and interpret the results.
The period is minutes and represents the time for one complete heartbeat.
This implies that the heart rate is beats per minute. (Write your answers as simplified fractions, if necessary.)
The period of the function is 1/60 minutes
As a result, blood pressure changes between each heartbeat as a consequence of these oscilllations happening every second.
Max value = 110 mmHg
the minimum = 50 mmHg.
This suggests that systolic pressure remains at 110 mmHg and diastolic pressure is still maintained at 50 mmHg.
blood pressure peaks occur at times t = (1/2 + 2 * k) / 120 seconds.
How to find the period(a) The given function is:
p(t) = 80 + 30 * sin(120 * pi * t)
This is equivalent to sinusoidal function in the form of:
p(t) = A + B * sin(C * t)
Where:
A is the baseline value,
B is the amplitude, and
C determines the frequency of the function.
Information given in the problem
A = 80, B = 30, and C = 120 * pi.
The period of a sinusoidal function is given by:
Period = 2 * pi / C
Period = 2 * pi / (120 * pi) = 1/60 minutes
The period of the function is 1/60 minutes, which means that the blood pressure oscillates every 1/60 minutes or 1 second. As a result, blood pressure changes between each heartbeat as a consequence of these oscilllations happening every second.
(b) maximum and minimum values of a sinusoidal function
Max value = A + B
Min value = A - B
Substituting the values of A and B:
Max value = 80 + 30 = 110 mmHg
Min value = 80 - 30 = 50 mmHg
Max value = A + B giving values of 110 mmHg
the minimum is A - B delivering 50 mmHg.
This suggests that systolic pressure remains at 110 mmHg and diastolic pressure is still maintained at 50 mmHg.
(c) the time at which the blood pressure is at its maximum, we solve for t when the sinusoidal function is at its peak.
sin(120 * pi * t) = 1
Taking the inverse sine of both sides:
120 * pi * t = pi/2 + 2 * pi * k (where k is an integer)
Solving for t:
t = (1/2 + 2 x k)/120 (for k = 0, 1, 2, ......)
implying that blood pressure peaks occur at times t = (1/2 + 2 * k) / 120 seconds.
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Find the remainder when f(x) is divided by x-k, ( SYNTHETIC DIVISION)
[tex]f(x)=2x^3 +5x^2 -12x ; k=-1[/tex]
Explain well, please.
Answer:
15
Step-by-step explanation:
You want the remainder from division of f(x) = 2x³ +5x² -12x by x -(-1).
Synthetic divisionThe table used for synthetic division is built by listing the zero of the divisor at upper left, and the coefficients of the polynomial across the top to the right of that. They are listed in order of decreasing degree, with any necessary zero coefficients put in the appropriate place(s).
The attachment shows the table and the instructions for filling it out. The value at the bottom in the rightmost column is the remainder from the division.
The remainder theorem tells you that is also the value of the function for x = k.
The remainder from f(x) ÷ (x +1) is 15.
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Which of the following is equal to 6,000 mL can someone also like give me like a step to step explanation for i can write it down
6,000 mL is equal to 6 litres
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
We know that 6,000 mL is equal to 6L
One litre is equal to 1000 ml
1 l = 1000 ml
6 l=6000 ml
Hence, 6,000 mL is equal to 6 litres
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Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is
inconsistent.
2x-4y= -4
3x+3y= 2
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
OA. The solution is.
(Simplify your answers.)
OB. There are infinitely many solutions. The solution can be written as {(x,y) |x=y is any real number).
(Simplify your answer. Type an expression using y as the variable.)
OC. The system is inconsistent.
Inc
The line 3x+5y = 10 is dilated by a scale factor of 3. What is the equation of the dialted line
The equation of the dilated line is 9x + 15y = 10.
What is scale factor?In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects, which can be used to either vertically or horizontally enlarge (increase) or reduce (compress) a function representing their size.
Generally speaking, the transformation rule for the dilation of a geometric object or equation based on a specific scale factor of 3 is given by this mathematical expression:
(x, y) → (SFx, SFy)
Where:
x and y represents the data points.SF represents the scale factor.Therefore, the transformation rule for this dilation is given by;
(x, y) → (3x, 3y)
3(3x + 5y) = 10
9x + 15y = 10.
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find the volume of the image below.
The volume of the image is given as follows:
10626 ft³.
How to calculate the volume of a prism?The volume of a prism is calculated as the multiplication of the base area of the prism by the height of the prism.
The bottom of the prism in this problem square base of side length 23 ft, along with height of 18 ft, hence:
Bottom volume = 18 x 18 x 23
Bottom volume = 7452 ft³.
The top of the prism also has square base of side length 23 ft, along with triangular height of 12 ft, hence:
Top volume = 0.5 x 12 x 23 x 23 (multiplies by 0.5 as the top is a triangle).
Top volume = 3174 ft³.
Hence the total volume of the prism is given as follows:
7452 + 3174 = 10626 ft³.
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the function f(x) = x^2-1 and g(x) = -x^2+4 are shown on the graph
Answer: Given the following equations, determine the x value(s) that result in an equal output for both functions. f(x) = 3* g(x)=4x+1. C0 and 2.
Step-by-step explanation:
Given the following equations, determine the x value(s) that result in an equal output for both functions. f(x) = 3* g(x)=4x+1. C0 and 2.
f(x)=5x+4, g(x)= x+7 find f(g(3))
Answer: 54
Step-by-step explanation:
Start from the middle of the equation and work your way out.
First find g(3) :
g(3) = 3+7 = 10
Then plug g(3) into the f equation:
f(g(3)) = 5(10) + 4 = 54
A triangle with an area of 0.45m squared and a perimeter of about 325cm?
pls help meee
Answer:To solve this problem, we need to use the formulas for the area and perimeter of a triangle.
Let's start by using the formula for the area of a triangle:
Area = (base x height) / 2
where base and height are the length and height of the triangle's base, respectively.
Let's assume that the base of the triangle is x meters, and the height is y meters. Then we have:
Area = (x*y)/2 = 0.45 m²
Solving for y, we get:
y = (2*0.45)/x
y = 0.9/x
Now, let's use the formula for the perimeter of a triangle:
Perimeter = a + b + c
where a, b, and c are the lengths of the three sides of the triangle.
Since we know that the perimeter is about 325 cm, we can assume that the three sides are close to each other in length. Let's assume that each side has a length of 325/3 = 108.33 cm.
Converting to meters, we get:
a = b = c = 108.33/100 = 1.0833 m
Now, we can use the formula for the area of a triangle again to solve for x:
Area = (base x height) / 2
0.45 = (x * 0.9/x) / 2
0.9 = x²
x = √0.9 = 0.9487 m
Therefore, the base of the triangle is approximately 0.9487 meters, and the height is approximately 0.9/0.9487 = 0.9487 meters.
So the triangle has sides of length 1.0833 meters and a base of length 0.9487 meters, which gives us a perimeter of approximately 3.215 meters (rounded to three decimal places).
Step-by-step explanation:
Answer both please
Find the domain of the function. (Enter your answer using interval notation.)
f(x) =
4x³-3
x² + 4x - 5
7. [-/3 Points]
f(-8)
=
Evaluate f(-8), f(0), and f(4) for the piecewise defined function.
f(x) =
x+4 if x < 0
2-x if x 20
f(0) =
f(4) =
The solution is, the domain is: x ∈ (-∞, ∞).
Here, we have,
When we have two functions, f(x) and g(x), the composite function:
(f°g)(x)
is just the first function evaluated in the second one, or:
f( g(x))
And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:
f(x) = 1/(x + 1)
where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.
Now, we have:
f(x) = x^2
g(x) = x + 9
then:
(f ∘ g)(x) = (x + 9)^2
And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:
x ∈ (-∞, ∞)
(g ∘ f)(x)
this is g(f(x)) = (x^2) + 9 = x^2 + 9
And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:
x ∈ (-∞, ∞)
(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4
And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:
x ∈ (-∞, ∞)
(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18
And again, there are no values of x that cause a problem here,
so the domain is:
x ∈ (-∞, ∞)
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complete question:
Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat
2. The postmaster of a small western town receives a certain number of complaints each
day about mall delivery.
DAY 1 2 3 4 5 6 7
Number of Complaints 4 12 15 8 9 6 5
a. Determine two-sigma control limits using the above data.
b. Is the process in control?
To calculate the three-sigma control limits, we first need to find the mean and standard deviation of the sample.
Here, we have,
The mean is:
μ = (4 + 12 + 16 + 8 + 9 + 6 + 5 + 12 + 15 + 7 + 6 + 4 + 2 + 11) / 14 = 8.071
The standard deviation is calculated using the standard deviation formula and is arrived at:
σ = 4.319
The three-sigma control limits are:
Upper control limit = μ + 3σ = 8.071 + (3 × 4.319) = 20.027
Lower control limit = μ - 3σ = 8.071 - (3 × 4.319) = -3.886
b. We can check if the process is in control by looking at whether any of the data points fall outside of the control limits.
From the given data, we can see that the maximum number of complaints is 16, which is well within the upper control limit of 20.027. The minimum number of complaints is 2, which is also well within the lower control limit of -3.886.
Therefore, based on the given data, we can conclude that the process is in control.
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solve each rational equation. list excluded values
x+4/x+5=6/x^2+10+25
Write the equation for the following sequences in standard form.
30, 150, 750, 3750, ...
PLEASE HELP ASAP
worth 10 points
Answer:
The common ratio is 5.
30 ÷ 5 = 6.
Let n = 1 be the first term of this sequence.
[tex]a(n) = 6( {5}^{n} )[/tex]
Find the perimeter of the
similar figure.
24cm
Perimeter = 72cm
32cm
Perimeter = [?]cm
The value of the unknown perimeter is derived to be 96 cm using the ratio of the known side of the similar figures.
What is ratioA ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. It can be used to express one quantity as a fraction of the other ones.
By comparison using the variable x to represent the unknown perimeter, and the ratio of the known side lengths;
24/32 = 72cm/x
x = (32 × 72cm)/24 {cross multiplication}
x = 2304cm/24
x = 96 cm
Therefore, the value of the unknown perimeter is derived to be 96 cm using the ratio of the known side of the similar figures.
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If 2:3 is expressed in the form x: 12, what is the value of x?
Answer:
If 2:3 = x:12, then:
2/3 = x/12
Multiplying both sides by 12, we get:
x = 2/3 x 12 = 8
Therefore, the value of x is 8.
How many roots, real or complex, does the polynomial 7 + 5x* - 3z? have in all?
Answer:
One.
Step-by-step explanation:
This polynomial has only one variable, which is x*. We can treat z and 7 as constants. Therefore, the polynomial is linear and can be written as:
5x* + c
where c = 7 - 3z.
A linear polynomial has either one root (when the coefficient is non-zero) or zero roots (when the coefficient is zero). Therefore, the given polynomial has exactly one root, which is:
x* = -c/5 = -(7 - 3z)/5 = (3z - 7)/5
Two cars left Sunnyside City at the same time and traveled for 5 hours. The average speed of the faster car was 10 kilometers per hour greater than the average speed of the slower car. In the 5 hours, the two cars traveled a total of 550 kilometers
The velocity of the two cars are 50km/hr and 60km/h
What is velocity?Velocity is the rate of change of distance with time. it is measured in meter per second and it is a vector quantity.
let the faster car be A and slower car be B
V(A) = V(B) +10
S( A) = v × t
S(B) = v(b) × t
S( A) = 5( v(b) +10)
S(A) +S(B) = 550
5v(b) +50+5vb = 550
10v(b) = 550-50
v(b) = 500/10
v(b) = 50km/h
v(a) = 50 +10
v(a) = 60km/h
Therefore the velocity of the two cars are 50km/h and 60 km/h
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Solve the following equation exactly on the interval [0,2π).
3cos2θ−2cosθ−2=0
Select all correct answers, assuming they are rounded to two decimal places.
Select all that apply:
θ≈1.24
θ≈2.15
θ≈2.41
θ≈3.55
θ≈4.13
θ≈5.36
Answer:θ≈2.15
θ≈4.13 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
3u^2 - 2u - 2 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3, b = -2, and c = -2. Substituting these values, we get:
u = (2 ± sqrt(4 + 24)) / 6
u = (2 ± 2sqrt(7)) / 6
Simplifying this expression, we get:
u = (1 ± sqrt(7)) / 3
Therefore, either:
Ok this isnt hard but i need help
Answer:
C is correct because parallel lines cut by a transversal form congruent alternate interior angles.
The essay, "I, Pencil," illustrates that production of an ordinary wood pencil used for writing
a. is so complex that only a few manufacturers know how to produce it.
b. is simple enough that it can be produced by millions of people.
c. looks simple, but for many years only government officials in centrally planned economies were able to figure out how to produce it.
d. involves the cooperative efforts of millions of people, whose actions are directed through markets.
The essay, "I, Pencil," illustrates that production of an ordinary wood pencil used for writing d. involves the cooperative efforts of millions of people, whose actions are directed through markets.
What is shown in " I, Pencil"?I, Pencil, an essay by Leonard Read portrays that the manufacture of a common wood pencil utilized for writing necessitates the collective efforts of millions of human beings whose activities are strictly regulated through markets.
The paper conveys that though an ordinary pencil looks like such a straightforward item, it is actually created from a complex system of people, procedures, and materials from far and wide. From timber harvesters who procure the wood, to the miners who take graphite out from the ground, to the employees in manufacturing plants who produce the finished article, the lead holder necessitates the orderly collaboration of multiple individuals and enterprises.
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Which function is a translation one unit right of the function f(x) = log x?
Answer:
Step-by-step explanation:The function y=log(x) is translated 1 unit right and 2 units down.
Nine to the second power +4 to the second power
Answer:
Step-by-step explanation:
9 * 9 = 81
4 * 4 = 16
81 + 16 = 97
Apply the k-means algorithm on the following dataset (x,y):(-1,-0.75),(-1,-1),(-0.75,- 1.0), (- 0.25, - 0.25), (0.25, 0.25), (0.75, 1.0), (1.0, 1.0), (1.0, 0.75) and create two clusters. Let the initial cluster prototypes be located at (0.0, 0.0) and (0.75, 0.75) respectively.
Find area of polygon where n=14 and radius= 1
Answer:16.484
Step-by-step explanation:
find the area of a regular polygon with n sides and radius r, we can use the formula:
Area = (n * r^2 * sin(2*pi/n)) / 2
where pi is the mathematical constant pi (approximately equal to 3.14159).
Plugging in n = 14 and r = 1, we get:
Area = (14 * 1^2 * sin(2*pi/14)) / 2
= (14 * sin(pi/7)) / 2
≈ 16.484
Therefore, the area of the polygon with 14 sides and a radius of 1 unit is approximately 16.484 square units.