Numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.
Given a paragraph in which there are blanks:
A _____ is a number whose only factors are 1 and itself. If a number has factors besides 1 and itself, it is called a _____. You can use divisibility rules or _______ to help you determine whether a number is prime or composite.
We are required to fill the blank with appropriate options.
We have to fill "prime numbers" in the first blank.
We have to fill "composite numbers" in the second blank.
We have to fill "the sieve of Eratosthenes" in the third blank.
Hence numbers whose only factors are 1 and itself is known as prime numbers , numbers whose factors besides 1 and itself are composite numbers, we can use the sieve of Eratosthenes to determine whether the number is prime or composite.
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The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a videocassette recorder over the past 12 months are satisfied with their products. If there are 4 different brands of videocassette recorders made by the company, the best sampling strategy would be to use a
The best sampling strategy would be a stratified sample.
How are samples classified?Samples may be classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.For this problem, the 4 different brands of the recorders must be considered, hence the buyers should be divided into groups, and a proportion of each group should be sampled, hence a stratified sample should be used.
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HELP PLS
Name the intersection of plane K and plane L.
Answer:
line MN
Step-by-step explanation:
If two planes intersect, then the intersection is a line.
Answer: line MN
Example
A soccer league has 60 returning players and 36 new players. Each team will have
the same ratio of returning players to new players as the league has. How many
new players will a team with 10 returning players have?
You can use a double number line to find ratios equivalent to 60: 36.
Number pairs that line up vertically represent equivalent ratios.
Returning Players 0
New Players 0
10
++
6
+6
+
-6
60
36
You can divide each quantity in 60: 36 by 6 to find the equivalent ratio 10:6.
A team with 10 returning players will have 6 new players.
1 Sophia says that you can solve the problem in the Example by multiplying both
quantities in the ratio 60:36 by. Is Sophia correct? Explain.
Answer:
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
The net of a pyramid is shown below. 4in 4in 4in 4in 8in. The surface area of the solid is __ square inches.
Answer:
80 in.²
Step-by-step explanation:
The total surface area of the pyramid is the sum of the area of the base and the areas of the 4 triangular sides.
Square: area = s²
Square: side = 4 in.
Triangular side: area = bh/2
Triangular side: base = 4 in.; height = 8 in.
Area of the base: s² = (4 in.)² = 16 in.²
Total area of the 4 triangular sides: 4 × bh/2 = 2bh = 2 × 4 in. × 8 in. = 64 in.²
Surface area = 16 in.² + 64 in.² = 80 in.²
Will give brainliest !!
Type the correct answer in the box.
Which trigonometric expression can be used to find value of x? Replace a and b with the correct values.
(trigonometry)
Answer:
x = 12cos(35)
Step-by-step explanation:
Well you have hyp and adj, meaning cosine. and u have the angle and need the adjacent, so side(cos(theta)).
12cos(35).
I need help… a lot of it im so confused
[tex] \sqrt[3]{b {}^{2} } = b {}^{ \frac{2}{3} } [/tex]
2)[tex]f(4) = 2(3) {}^{4} = 2 \times 81 = 162[/tex]
3)[tex]f( \frac{1}{2} ) = \frac{1}{3} (9) {}^{ \frac{1}{2} } + 5 = \frac{ \sqrt{9} }{ 3} + 5 = 6[/tex]
4)
[tex]f(5) = - 4(2) {}^{ - 5 + 1} = - 4(2) {}^{ -4} = \frac{2 {}^{2} }{2 {}^{4} } = \frac{1}{2 {}^{2} } = \frac{1}{4} [/tex]
5)[tex]f(10) = 2e {}^{0.15 \times 10} = 2e {}^{1.5} = 8.96[/tex]
6)[tex]y = 10(b) {}^{x} \: \: \\ 10 = 10(b) {}^{0} \: duh \\ 2 = 10b {}^{1} \\ b = \frac{2}{10} = \frac{1}{5} [/tex]
7)[tex]y = a(b) {}^{x} \\ 3 = a(b) {}^{0} \\ a = 3 \\ \\75 = 3(b) {}^{2} \\ b {}^{2} = 25 \\ b = + 5 \: \: \: or \: \: \: \: b = - 5[/tex]
8)[tex]s = 1000(1 + \frac{0.045}{4} ) {}^{4 \times 10} = 1564.38[/tex]
9)[tex]s = 2500.e {}^{0.07 \times 20} = 10138[/tex]
what is (4x8) divided by (8+2)
Answer:
3.2
Step-by-step explanation:
4 x 8 / 8 + 2
32/10
=3.2
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What is the behavior of the graph y=−x6−6x5+50x3+45x2−108x−108 at each of its zeros
The behavior of the graph with the equation y=x66x5+50x3+45x2108x108 at each of its zeros will be as follows: two of them will resemble a quadratic function, while one of them will resemble a linear function.
This is further explained below.
What is a graph?Generally, a diagram that illustrates the relationship between variable quantities, usually consisting of two variables, with each variable being measured along one of a pair of axes that are intersected at right angles.
In conclusion, At each of its zeroes, the graph y=x66x5+50x3+45x2108x108 will exhibit one linear behavior and two behaviors that resemble quadratic functions.
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* Let S = Span {(2,-1, 1), (3, 1, 1), (1, 2, 0)}. (i) Calculate the dimension of S.
1
2
3
9
The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.
Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars [tex]c_1,c_2,c_3[/tex] (not all zero) such that
[tex]c_1 (2,-1,1) + c_2 (3,1,1) + c_3 (1,2,0) = (0,0,0)[/tex]
which leads to the system of linear equations,
[tex]\begin{cases} 2c_1 + 3c_2 + c_3 = 0 \\ -c_1 + c_2 + 2c_3 = 0 \\ c_1 + c_2 = 0 \end{cases}[/tex]
From the third equation, we have [tex]c_1=-c_2[/tex], and substituting this into the second equation gives
[tex]-c_1 + c_2 + 2c_3 = 2c_2 + 2c_3 = 0 \implies c_2 + c_3 = 0 \implies c_2 = -c_3[/tex]
and in turn, [tex]c_1=c_3[/tex]. Substituting these into the first equation gives
[tex]2c_1 + 3c_2 + c_3 = 2c_3 - 3c_3 + c_3 = 0 \implies 0=0[/tex]
which tells us that any value of [tex]c_3[/tex] will work. If [tex]c_3 = t[/tex], then [tex]c_1=t[/tex] and [tex]c_2 = -t[/tex]. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.
Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.
Write the ratio 6 sodas out of 16 drinks.
Answer:
3:8 3 sodas for 8 drinks
Step-by-step explanation:
6/16
3/8
Figure ABCD Is a kite. Find x
Answer:
x = 8
Step-by-step explanation:
Diagonals of a kite cross at right angles. That gives us a relation that can be solved for x.
SetupThe measure shown is equal to the angle measure of 90°.
14x -22 = 90
SolutionWe can solve this 2-step linear equation in the usual way.
14x = 112 . . . . . . step 1, add the opposite of the constant to get x alone
x = 112/14 = 8 . . . step 2, divide by the coefficient of x
The value of x is 8.
A block exerts a force of 84 Newtons on a table.
The pressure on the table is 30 N/m².
Work out the area of the box that is in contact with the table.
Total for question 5 is 2 marks)
pressure =
force
area
Answer:
2.8m²
Step-by-step explanation:
p = F / A
A = F / p
A = 84 / 30
A = 2.8m²
H2 Worksheet #8
Complete the table for the following rule
y = 2x + 2.
X
1
3
9
10
y
A1
Answer:
It's easy to solve the problem.
let's start...
given equation:- y = 2x+2
X y
1 (2× 1 )+ 2 = 4 .
3 (3×2)+2 = 8 .
9 (9×2) + 2 = 20 .
10. (10× 2)+2 = 22 .( table completed)
just put the value of X in the expression.
train travelling at a uniform speed covers a distance of 255 km in Find the speed of the train and 3 4/5 1 1/2 the distance covered in hours. hours.
The speed of the train is 150 km/hour.
The distance covered by the train in 3 4/5 hours is 570 km.
The speed of a body is calculated using the formula, speed = distance/time.
The distance covered is calculated using the formula, distance = speed*time.
The time taken by a body is calculated using the formula, time = distance/speed.
In the question, we are asked for the speed of a train, when it covers a distance of 225 km in 1 1/2 hours.
Distance = 225 km.
Time = 1 1/2 hours = 1.5 hours.
Speed = Distance/Time = 225/1.5 km/hour = 150 km/hour.
Now, we are asked to calculate the distance covered by the train in 3 4/5 hours.
Speed = 150 km/hour.
Time = 3 4/5 hours = 3.8 hours.
Distance = Speed*Time = 150*3.8 km = 570 km.
Thus, the speed of the train is 150 km/hour.
The distance covered by the train in 3 4/5 hours is 570 km.
The provided question is incorrect. The correct question is:
"A train at a uniform speed covers a distance of 225 km in 1 1/2 hours. Find the speed of the train and the distance covered in 3 4/5 hours.
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What is the difference? \frac{x+5}{x+2}-\frac{x+1}{x^{2}+2x}
Answer:
Step-by-step explanation:
x² + 2x = x(x + 2)
[tex]\sf \dfrac{x +5}{x + 2}-\dfrac{x+1}{x^2+2x}=\dfrac{x + 5}{x +2}-\dfrac{x+1}{x(x+2)}[/tex]
LCM = x(x+2)
[tex]\sf =\dfrac{(x+5)*x}{(x+2)*x}-\dfrac{x+1}{x(x+2)}\\\\=\dfrac{x*x + 5*x}{x^2+2x}-\dfrac{x+1}{x^2+2x}\\\\=\dfrac{x^2+5x - (x+1)}{x^2+2}\\\\=\dfrac{x^2+5x -x - 1}{x^2+2x)}\\\\=\dfrac{x^2+4x-1}{x^2+2x}[/tex]
The volume of a packing box is 5 - x cubic feet. The width of the box is x feet and the length is x - 2 feet
Answer:
Step-by-step explanation:
Can someone help me with a step by step process of how to solve this? Calculus 2
If you fix a point on the curve in the given interval, and revolve that point about the [tex]x[/tex]-axis, it will trace out a circle with radius given by the function value [tex]y[/tex] for that point [tex]x[/tex]. The perimeter of this circle is then [tex]2\pi(8\sqrt x) = 16\pi \sqrt x[/tex].
The surface in question is essentially what you get by joining infinitely many of these circles at every point in the interval [0, 9].
So, the surface area is given by the definite integral
[tex]\displaystyle \int_0^9 16\pi \sqrt x \, dx = 16\pi\times\frac23 x^{3/2}\bigg|_{x=0}^{x=9} = \frac{32\pi}3 \left(9^{3/2} - 0^{3/2}\right) = \boxed{288\pi}[/tex]
A rhombus is a four-sided figure with all sides the same length. Points F(-2,-2), G(-2, 3), and H(2, 6) are three vertices of rhombus FGHJ. Vertex J is directly below vertex H. What is the perimeter of the rhombus? Show your work.
Answer:
20
Step-by-step explanation:
The sides of the 4-sided figure are the same length, so we can find the perimeter (sum of side lengths) by multiplying one side length by 4.
Side lengthPoints F(-2, -2) and G(-2, 3) lie on the same vertical line: x = -2. The distance between them is the difference of their y-coordinates:
FG = (3 -(-2)) = 5
Each side is 5 units long.
PerimeterThe length of the four sides is ...
P = 4s = 4(5) = 20
The perimeter of the rhombus is 20 units.
Question 3 Now change the central angle, ∠CAB, and see how it affects the inscribed angle, ∠CDB. To do this, move point B around the circle without crossing points D and C, and do the same for point C without crossing points B and D. Record five data sets for m∠BAC and m∠BDC in the table.
ANSWER FAST!
By changing the central angle, ∠CAB, the inscribed angle, ∠CDB has the following data sets:
m∠BAC (β) m∠BDC (α)
42° 84°
40° 80°
45° 90°
35° 70°
52° 104°
What is a circle?A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
In Geometry, a circle is considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.
What is the inscribed angle theorem?The inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle. Thus, this is given by this mathematical expression:
m∠BDC = ½ × m∠BAC.
For this exercise, we would change the central angle, ∠CAB, so that the inscribed angle, ∠CDB can have the following data sets:
m∠BAC (β) m∠BDC (α)
42° 84°
40° 80°
45° 90°
35° 70°
52° 104°
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Answer:
plato
Step-by-step explanation:
m∠BAC m∠BDC
50° 25°
70° 35°
90° 45°
125° 62.5°
150° 75°
urgent help thank you
Answer:
-4
Step-by-step explanation:
7x^3 + 5x^2 - 2
= 7*-1 + 5*1 - 2
= -7 + 5 - 2
= -4
Solve the equation: (1-x)2³ = 8
Answer:
0
Step-by-step explanation:
because 1-0=1*2^3=8
because2^3=8
Consider the following figure:
The value of a is
Answer:
125
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation according to this information and that will help us find the value of x:
65 + 60 = x add like terms
125 = x is the answer we are looking for.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{equation:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\huge\textsf{solving:}[/tex]
[tex]\large\textsf{a = 60 + 65}[/tex]
[tex]\large\textsf{60 + 65 = a}[/tex]
[tex]\huge\textsf{simplify it:}[/tex]
[tex]\large\textsf{a = 125}[/tex]
[tex]\huge\textsf{therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{a =} \frak{125}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which geometric sequence has a common ratio of -9? (only one is correct)
a) {-1, -9, 81, 729, …}
b) {-9; -81; -729; -6,561; …}
c) {1, -9, 81, -729, …}
d) {81; 729; 6,561; 59,049; …}
C
1, -9 , 81 , -729 .....
ratio :-
R1 = -9/1 = -9
R2 = 81/-9 = -9
R3 = -729 / 81 =-9
so ,. R1= R2= R3
1. What is the measure of angle x? O 60° O 90° O 45° O 30°
Answer:
Angle x= 60°
Step-by-step explanation:
For the triangle HIL, you're going to add 30+90=120
Angles in a triangle add up to 180.
So, therefore,
180-120=60 so angle L must equal 60.
HJ is a straight line and angles in a straight line add up to 180.
180-90=90
Angle JIL is equal to 90.
To find y you add 90+45 which equals 135.
Again, angles in a triangle add up to 180.
180-135=45
So,
y = 45
Now we are told that IJK is a right angle and that we are given that IJL is 45. 45 is half of 90 so LJK must be 45.
To find angle JLK we must add angle L and angle y.
60+45=105
Angles in a straight line add up to 180. So,
180-105=75
75 = Angle JLK
75+45=120
Angles in a triangle add up to 180 so,
180-120= 60
Angle x= 60°
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questions c, d, e please!
Answer:
c) 3 units
d) g(x) - f(x) = x² + 2x
e) (-∞, -2] ∪ [0, ∞)
Step-by-step explanation:
Part (c)To calculate the length of FC, first find the coordinates of point C.
The y-value of point C is zero since this is where the function f(x) intercepts the x-axis. Therefore, set f(x) to zero and solve for x:
[tex]\implies 1-x^2=0[/tex]
[tex]\implies x^2=1[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{1}[/tex]
[tex]\implies x= \pm 1[/tex]
As point C has a positive x-value, C = (1, 0).
To find point F, substitute the x-value of point C into g(x):
[tex]\implies g(1)=2(1)+1=3[/tex]
⇒ F = (1, 3).
Length FC is the difference in the y-value of points C and F:
[tex]\begin{aligned} \implies \sf FC& = \sf y_F-y_C\\ & = \sf 3-0\\ & =\sf 3\:units \end{aligned}[/tex]
Part (d)Given functions:
[tex]\begin{cases}f(x)=1-x^2\\ g(x)=2x+1 \end{cases}[/tex]
Therefore:
[tex]\begin{aligned}\implies g(x)-f(x) & = (2x+1) - (1-x^2)\\& = 2x+1-1+x^2\\& = x^2+2x\end{aligned}[/tex]
Part (e)The values of x for which g(x) ≥ f(x) are where the line of g(x) is above the curve of f(x):
point A → ∞point E → -∞Point A is the y-intercept of both functions, therefore the x-value of point A is 0.
To find the x-value of point E, equate the two functions and solve for x:
[tex]\begin{aligned}g(x) & = f(x)\\\implies 2x+1 & = 1-x^2\\x^2+2x & = 0\\x(x+2) & = 0\\\implies x & = 0, -2\end{aligned}[/tex]
As the x-value of point E is negative ⇒ x = -2.
Therefore, the values of x for which g(x) ≥ f(x) are:
Solution: x ≤ -2 or x ≥ 0Interval notation: (-∞, -2] ∪ [0, ∞)Answer:
a)
A = (0, 1)
B = (-1, 0)
C = (1, 0)
D = (-0.5, 0)
b) E = (-2, -3)
c) FC = 3 units
d) x² + 2x
e) x ≤ -2 and x ≥ 0
Explanation:
This question displays one equation of a linear function g(x) = 2x + 1 and a parabolic function f(x) = 1 - x².
a)
A point is where the linear function cuts the y axis.
y = 1 - (0)²
y = 1
A = (0, 1)
B and C point is where the parabolic function cuts the x axis.
1 - x² = 0
-x² = -1
x² = 1
x = ±√1
x = -1, 1
B = (-1, 0), C = (1, 0)
D point is where the linear function cuts x axis.
2x + 1 = 0
2x = -1
x = -1/2 or -0.5
D = (-0.5, 0)
b)
E point is where both equations intersect each other.
y = y
2x + 1 = 1 - x²
x² + 2x = 0
x(x + 2) = 0
x = 0, x = -2
y = 1, y = -3
E = (-2, -3)
c)
C : (1, 0)
To find F point
y = 2(1) + 1
y = 3
F : (1, 3)
[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]\sf d = \sqrt{(1 - 1)^2 + (3 - 0)^2}[/tex]
[tex]\sf d = \sqrt{0 + 3^2}[/tex]
[tex]\sf d = 3[/tex]
FC length = 3 units
d)
g(x) - f(x)
(2x + 1) - (1 - x²)
2x + 1 - 1 + x²
x² + 2x
e)
g(x) ≥ f(x)
2x + 1 ≥ 1 - x²
x² + 2x ≥ 0
x(x + 2) ≥ 0
[tex]\boxed{If \ x \ \geq \ \pm \ a \ then \ -a \ \leq x \ \ and \ x \ \geq \ a }[/tex]
x ≤ -2 and x ≥ 0
Find the length of UX
Answer:
[tex]\dfrac{8}{\sin(6^\circ)} \approx 76.53[/tex]
Step-by-step explanation:
[tex]UX \sin(6^\circ) = 8 \Rightarrow \boxed{UX = \dfrac{8}{\sin(6^\circ)} \approx 76.53}[/tex]
What is The solution to -122 < -3(-2 - 8x) - 8x
A. x<8
B. x<-2
C. x>5
D. x>-8
Answer:
D.
Step-by-step explanation:
We can solve by simply isolating x:
[tex]-122 < -3(-2-8x)-8x\\-122 < 6+24x-8x\\-122 < 6+16x\\-128 < 16x\\-8 < x\\OR\\x > -8[/tex]
You can check by plugging in any value greater than -8
-122<-3(-2-8(-7))-8*-7
-122<-3(-2+56)+56
-122<-3(54)+56
-122<-162+56
-122<-106
Find all the missing values to make the equation true
The missing value in the logarithm are as follows:
log₃ 7 - log₃ 2 = log₃ (7 / 2)log₉ 7 + log₉ 4 = log₉ 28log₆ 1 / 81 = - 4 log₆ 3How to solve logarithm?Using logarithm rule,
logₐ b - logₐ c = logₐ (b / c)
logₐ b + logₐ c = logₐ (b × c)
Therefore,
log₃ 7 - log₃ 2 = log₃ (7 / 2)
log₉ 7 + log₉ 4 = log₉ (7 × 4) = log₉ 28
log₆ 1 / 81 = log₆ 81⁻¹ = log₆ 3⁻⁴ = - 4 log₆ 3
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Time to use my tools
96 100 132
6 ... 4 ....6
5....7......3
21...32...?
1)32
2)20
3)25
4)30
find the missing one
Answer:
the correct answer is 25
please help! will give brainliest to whoever answers
maths functions
Answer:
1. f(x) is reflected across the x-axis
2. f(x) is translated 1 unit up
3. f(x) is vertically scaled by a factor of 2
4. f(x) is reflected across the x-axis AND is vertically scaled by a factor of 2
5. f(x) is vertically scaled by a factor of 3 AND is translated 1 unit down
6. f(x) is vertically scaled by a factor of 1/6 AND is translated 1 unit up
Solving question:
(1) [tex]g(x) = -f(x)[/tex]
This graph has been reflected in the x axis. Equation: [tex]\sf g(x) = -\dfrac{2}{x}[/tex]
(2) [tex]g(x) = f(x) + 1[/tex]
Graph has been translated 1 units up vertically. Equation: [tex]\sf g(x) = \dfrac{2}{x} +1[/tex]
(3) [tex]g(x) = 2f(x)[/tex]
This graph has been stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = \dfrac{4}{x}[/tex]
(4) [tex]g(x) = -2f(x)[/tex]
This graph has been reflected in the x axis and stretched vertically by a factor of 2. Equation: [tex]\sf g(x) = -\dfrac{4}{x}[/tex]
(5) [tex]g(x) = 3f(x) - 1[/tex]
This graph has been stretched vertically by a factor of 3 and translated 1 units down. Equation: [tex]\sf g(x) = \dfrac{6}{x} -1[/tex]
(6) [tex]g(x) = \frac{1}{6} f(x) + 1[/tex]
This graph has been stretched vertically by a factor of 1/6 and translated 1 units up. Equation: [tex]\sf g(x) = \dfrac{1}{3x} +1[/tex]
