The prime factorization of 18 is 2 x 3 x 3.
What is the prime factorization?A prime number is a number that is only divisible by 1 and itself. An example is 11. The factors of a number are numbers that divide another number without leaving any remainder. For example, a factor of 10 is 2. The prime factor of a number is the factors of a number that are prime numbers.
The factors of 18 = 1, 2, 3, 6, 9, 18
Prime factors = 1, 2, 3
Prime factorisation = 2 x 2 x 3
Here is the complete question:
The factor tree below provides the factors of 18. A factor tree of 18. 18 branches to 2 and 9. 9 branches to 3 and 3. What is the prime factorization of 18? 2 times 3 2 times 9 2 times 3 times 3 2 times 3 times 9
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pls help quickly pls
Step-by-step explanation:
if I understand your comment correctly, then you need the mean value of the lifetime of these light bulbs.
1. get the midpoint of each interval.
2. multiply each frequency with its midpoint.
3. sum all frequencies.
4. sum all multiplication results if 2. (of frequencies and midpoints).
5. divide 4. by 3.
lifetime midpoints :
(25 + 50)/2 = 75/2 = 37.5
(50 + 100)/2 = 150/2 = 75
(100 + 150)/2 = 250/2 = 125
(150 + 200)/2 = 350/2 = 175
(200 + 250)/2 = 450/2 = 225
(250 + 300)/2 = 550/2 = 275
(300 + 350)/2 = 650/2 = 325
multiply frequencies with their midpoints :
37.5 × 47 = 1762.5
75 × 86 = 6450
125 × 45 = 5625
175 × 36 = 6300
225 × 0 = 0
275 × 37 = 10175
325 × 50 = 16250
sum all frequencies
47+86+45+36+0+37+50 = 301
sum all multiplication results of 2.
1762.5+6450+5625+6300+0+10175+16250 = 46,562.5
divide 4. by 3.
the mean value is
46,562.5 / 301 = 154.692691... hours ≈
≈ 154.69 hours
Determine the amount of interest the principal in each account had earned. (From Example 2)
3. On March 3, Raul Avila deposited $10,000 in a savings account that pays 5.5% interest compounded daily until June 21.
4. On March 26, Samuel Griffin deposited $20,000 in a savings account that pays 5.5% interest compounded daily until July 24.
The amount of interest that the principal in each account had earned is as follows:
Raul Avila = $167.12
Samuel Griffin = $364.91
How is compound interest computed?The compound interest can be calculated using the compound interest formula:
A = P(1 + \frac{r}{n})^{nt}
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
It can also be computed using an online finance calculator as follows:
Data and Calculations:Raul Avila:N (# of periods) = 110 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
FV = $10,167.12
Total Interest = $167.12
Samuel Griffin:N (# of periods) = 120 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $20,000
PMT (Periodic Payment) = $0
Results:
FV = $20,364.91
Total Interest = $364.91
Thus, using the online finance calculator, the compound interests for each principal have been computed as $167.12 and $364.91, respectively.
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The store has p packages of batteries. Each package contains 12 batteries. Write an expression that shows the number of batteries.
The value of the equation is A = 12p , where p is the number of packages of batteries
What is an Equation?Equations are mathematical statements with two algebraic expressions on either side of the equals (=) sign.
It depicts how the expressions on the left and right sides are linked together.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are all parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of packages be represented as p
Let the number of batteries in one package = 12 batteries
So , the total number of batteries in p packages A = number of packages x number of batteries in one package
The total number of batteries in p packages A = 12p
Hence , the equation is A = 12p
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I need help with this please!!!
Answer: 3/11
The question is just asking you to select three people out of the group of eleven. And because we don't know there ages, the probability they are the oldest three in the group would be 3/11 or 3 out of 11.
equation
3/8 + 5/12 =
Answer:
19/24
Step-by-step explanation:
3/8=36/96
5/12=40/96
36/96+40/96=76/96
76/96=19/24
using ruler and set square draw AB 8cm long. construct line PQ parallel to line AB such that distance apart is 2.5cm
Step-by-step explanation:
omg you are looking like
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[tex]\boxed{\red{ \sf \:Correct\ Answer}}[/tex]
[tex]\red{ \rule{500pt}{900000pt}}[/tex]
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#carryonlearning[tex]\boxed{\red{ \sf \:Correct\ Answer}}[/tex]
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In the notation “t(x)=…,” what does “t(x)” represents
The notation "t(x)" represents the statement t is a function of x
How to interpret the notation?The notation is given as:
t(x) = ....
The above notation is a function notation, and it used to relate one element to another
For instance:
f(x) means f is a function of x
Similarly, "t(x)" represents the statement t is a function of x
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A rectangular plot of land is to be fenced in using two types of fencing. Two opposite sides will use heavy-duty fencing selling for $4.50 a foot. The two remaining sides will use standard fencing selling for $3 a foot. How much of the heavy-duty and standard fencing should be used so that the greatest area can be fenced in at a cost of $18,000?
The amount of heavy-duty fencing to be used is 2000 ft for $9000 and the amount of standard fencing to be used is 3000 ft for $9000 in order to make a total cost of $18000.
How do we determine the area of a rectangular plot?The area of the rectangular plot is denoted by the length multiplied by the width.
Let us assume that the length = x and the width = y.
Area = xyThen, for two opposite with heavy fencing for $4.50 a foot and the standard fencing for $3 a foot, we have:
2x (4.50) + 2y(3) = 18000 ---- (1)
⇒ 9x + 6y = 18000
Make (y) the subject, we have:
[tex]\mathbf{y = \dfrac{18000-9x}{6}}[/tex]
Replace the value of y with the area of the rectangle, and we get:
[tex]\mathbf{Area =x(\dfrac{18000 - 9x}{6})}[/tex]
Area = x(3000 - 1.5x)
Area = 3000x - 1.5x²
For the area to be maximum, we take the differentiation of the Area:
dA/dx = 0
dA/dx = 3000 - 3x
x = 3000/3
x = 1000 ft
From equation (1)
2x (4.50) + 2y(3) = 18000
x (4.50) + y(3) = 9000
1000(4.50) + 3y = 9000
3y = 9000 -4500
y = 4500/3
y = 1500 ft
So, there are (1000× 2)ft = 2000ft heavy duty fencing for $9000, and (1500 ×2)ft = 3000ft standard fencing for $9000 to make a cost of $18000.
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The "int()" operator in your calculator is the "greatest integer function." It returns the greatest integer less than or equal to the operand and is written using square brackets: [x] or [[x]]. For example, it would give back 82 for [[82.976]]. In Smalltown, AZ the students receive grade points as follows: 4.0 for any grade 90% or higher. [90,100) 3.0 for any grade 80% or higher. [80,90) 2.0 for any grade 70% or higher. [70,80) 1.0 for any grade 60% or higher. [60,70) (Notice: students NEVER fail! And students never get 100%!)
The function that correctly returns grades from 60 percent to a 100 percent is f(x) = [[(x - 50)/10]]
How to determine this functionThe question tells us that the students do not fail and they do not get a 100 percent score either.
Hence there is no need for worry if the grade is at 5.0 or less than 1.
For example we have
x = 82.976
f(82.976) =[[(82.976-50)/10]
This would then be 3.29
This is then = 3.0
This function is not an odd function and it is not an even function. This is because the domain does not have negative values.
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Use Interval notation to indicate all real numbers between and including -3,8
The interval notation for all real numbers between -3 and 8 is:
[-3, 8].
How to list all real numbers between a and b?There are an infinite number of real numbers between a and b, hence we list all them in interval notation, as follows:
[a,b]: including a and b.(a,b): excluding a and b.In this problem, we include -3 and 8, hence the notation is:
[-3, 8].
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The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object to the center of the Earth. If an astronaut weighs 196 pounds on the surface of the Earth, what will this astronaut weigh 300 miles above the Earth? Assume that the radius of the Earth is 4000 miles. (Round off your answer to the nearest pound.)
the astronaut would weigh 1 pound above the Earth.
How to calculate the weightGiven that;
Gravitational force = Gm/r^2
M1 = 196 pounds
M2 = unknown
R1 = 4000 miles
R2 = 300 miles
We can deduce that;
[tex]\frac{m1}{r^21} = \frac{m2}{r^22}[/tex]
Let's substitute the values
[tex]\frac{196}{4000^2} = \frac{x}{300^2}[/tex]
[tex]\frac{196}{1.6 *10^7} = \frac{x}{9 *10^4}[/tex]
Cross multiply
196 × 9 ×10^4 = x × 1.6 ×10^7
1.76 × 10^7 = x × 1.6 ×10^7
Make 'x' the subject of formula
x = [tex]\frac{1.76* 10^7}{1.6*10^7}[/tex]
x = 1.1
x = 1 pound
Thus, the astronaut would weigh 1 pound above the Earth.
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Solve for x in the triangle. Round your answer to the nearest tenth.
[tex]x = 12.9[/tex]
Step-by-step explanation:Note:
The following is sin formula:
[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]
1) Using the sin formula
[tex]sin(59) = \frac{x}{15} [/tex]
2) Multiply both sides by 15
[tex]15 \sin(59) = \frac{x}{15} \times 15[/tex]
3) Divide both sides by sin(59)
[tex] \frac{15 \sin(59) }{ \sin(59) } = \frac{x}{ \sin(59) } [/tex]
4) Find the value of x
[tex]x = 15 \sin(59) [/tex]
[tex]x = 12.9[/tex]
In the following figure AEDC is a square, BA= BC and AE = AC. The area of AEDC is 25 cm² and angle B=90°, Calculate the length of AB.
A triangular prism is a prism which has both of its base sides as a rectangle. The length of side AB is 5/(√2) cm.
What is a triangular prism?Suppose you've got a triangle. Now, stretch it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, when we talk about a triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
The area of AEDC is 25 cm². Therefore,
AEDC = AC²
25 cm² = AC²
AC = 5 cm
In ΔABC,
AB² + BC² = AC²
Since AB=BC,
2(AB²) = AC²
AB² = 25/2
AB = 5/√2 cm
Hence, the length of side AB is 5/(√2) cm.
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an airplane flies 3300 miles with the wind in 3 hours 18 minutes. it takes 4 hours and 24 mins to make the return flight against the same wind. find the speed of the airplane and the speed of the wind.
Answer:
The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
Step-by-step explanation:
Let’s assume the speed of the plane =x miles/hr
And let the speed of wind =y miles/hr
So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr
Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr
We know that, distance=speed×time
Then according to the given conditions, we have
3300=(x+y)×(3+(18/60))
here convert 18mins to hour by dividing by 60 and add to 3hrs.
⇒x+y= 3300/3.3
⇒x+y=1000 … (i)
And,
3300=(x-y)×(4+(24/60))
here convert 24mins to hour by dividing by 60 and add to 4hrs.
⇒x-y= 3300/4.4
⇒x-y=750 … (ii)
Adding equation (i) and (ii), we get
2x=1750
⇒x= 1750/2
=875
Substituting the value of x in equation (ii), we get
875−y=750
⇒y=875-750
⇒y=125
Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
a = 2√3 ft.;c = 4 ft.
A = 8√3 sq. ft.
True
False
False . The equation a= 2√3 ft.;c = 4 ft is: A= 2√3 ft².
Area of the triangleGiven:
a = 2√3 ft,
c = 4 ft,
Lengths of the sides of a right triangle = a and b
Hypotenuse= c
Hence:
Using Pythagorean theoremc²=a²+b²
4²=(2√3)²+b²
16=12+b²
4=b²
b=2
Area of triangle
A=1/2×a×b
A=1/2×2√3×2
A=4√3÷2
A=2√3 sq.ft
The Area of the triangle is 2√3 ft².
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Graph f(x) = 3/4x - 2
The equation of the function is the graph of line.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The function is given below.
f(x) = (3/4)x – 2
The function is an equation of line.
The graph of the function is given below.
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Given the data set in the image, which of the following equations best represents a line of best fit?
Answer:
C.
Step-by-step explanation:
The following formula gives the total surface area S of a cylinder with radius r and height h.
S=2πr(r+h)
Find the total surface area of a cylinder with radius 4 and height 8. Enter an exact answer in terms of π. Do not include S= in your answer.
The total surface area of a cylinder with radius 4 and height 8 is 96π.
Surface area of a cylinderIt follows from the task content that the total surface area of the cylinder is to be determined. The total surface area of the cylinder is given by the formular;
S=2πr(r+h)
where,S = surface arear = radius = 4h = height = 8S=2πr(r+h)
= 2 × π × 4(4 + 8)
= 2 × π × 4(12)
= 2π × 48
= 96π
Hence, the total surface area of the cylinder in terms of π is; 96π.
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The following data set is given: 122, 130, 145, 154, 165, 178
Adding which number to the set will increase its mean?
140
A)
B)
C)
D)
148
149
150
Answer:
150
Step-by-step explanation:
Mean is average, so adding any number above the original mean would increase the mean.
Oh no! The principal can't unlock her phone, because she can't remember how to solve the puzzle for her password.
At least two numbers that do NOT work, with an explanation of why they don't work.
Your best guess for a number that does work (or almost works).
A reminder of the puzzle:
The number is between 8,500 and 8,800.
When multiplied by 8, the result is a whole number.
The digit in the hundreds place is ¾ the digit in the thousands place.
The sum of all digits in the number is 26.
The digit in the hundredths place is 200% of the digit in the tenths place.
There are no zeros in the decimal places.
The numbers are:
8,640.1258,604.1258,622.1258,613.1258,631.125What is number system?
A number system is defined as a system of writing to express numbers.
First, the number between 8,500 and 8,800.
So, the thousands place digit is 8.
Second, When multiplied by 8, the result is a whole number.
So, multiplying by 8, the decimal has to end in 5.
Because there is no zeroes in the decimal place..
options are:
8 times 0.5
8 times 0.25
8 times 0.125
Now, The digit in the hundredths place is 200% of the digit in the tenths place
considering digit in the hundreds place is ¾ the digit in the thousands place.
So, choose 0.125.
Now, The digit in the hundreds place is 3/4 the digit in the thousandths place.
Digit in Thousandth Place = 5
Digit in Hundreds place=3/4*2=6
Our number now is:86_ _.125
As, The sum of all the numbers is 26
8+6+1+2+5=22
26-22=4
The possible numbers are:
8,640.125
8,604.125
8,622.125
8,613.12
8,631.125
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NO LINKS!! Find an nth-degree polynomial function with real coefficient satisfying the given conditions.
n= 4
-1, 3, and 2+ 4i are zeros;
f(1)= -136
n=3; We need a third degree polynomials with the following given zero's: 2 and 5i are zeros; f(-1)=156.
Since these are solutions
x = 2 ; x = 5i. Since imaginaries travel in pairs, the other answer is x= -5i.
We have (x-2)(x-5i)(x+5i) = 0
Now,
f(-1) = (-1-2)(-1-5i)(-1+5i) = 156.
f(-1) = (-3)(26) = -78.
But -78 x -2 = 156, so our polynomial becomes
Y= -2x (x - 2 ) x (x to the power of 2 + 25) = 0
Answer:
[tex]f(x)=2x^4-12x^3+50x^2-56x-120[/tex]
Step-by-step explanation:
Complex Conjugate Theorem
For a polynomial p(x) with real coefficients, the complex zeros occur in conjugate pairs. So if (a + bi) is a zero, then its conjugate (a - bi) is also a zero.
Given zeros:
-1, 3, and (2 + 4i)
As one of the given zeros is a complex number, (2 - 4i) is also a zero.
Write each zero as part of a factor and multiply them together, adding a leading coefficient [tex]a[/tex]:
[tex]\begin{aligned}f(x) & =a(x+1)(x-3)(x-(2+4i))(x-(2-4i))\\& = a(x+1)(x-3)(x-2-4i)(x-2+4i)\\& = a(x+1)(x-3)(x^2-2x+4ix-2x+4-8i-4ix+8i-16i^2)\\& = a(x+1)(x-3)(x^2-4x+4-16i^2)\end{aligned}[/tex]
Remember that [tex]i^2=-1[/tex], therefore:
[tex]\begin{aligned}f(x)&=a(x+1)(x-3)(x^2-4x+4-16(-1))\\&=a(x+1)(x-3)(x^2-4x+4+16)\\&=a(x+1)(x-3)(x^2-4x+20)\end{aligned}[/tex]
To find the value of the leading coefficient (a), use the given [tex]f(1)=-136[/tex] :
[tex]\begin{aligned}f(1) & = -136\\\implies a(1+1)(1-3)(1^2-4(1)+20) & = -136\\a(2)(-2)(17) & = -136\\-68a & = -136\\\implies a & = 2\end{aligned}[/tex]
Therefore, the polynomial in factored form is:
[tex]f(x)=2(x+1)(x-3)(x^2-4x+20)[/tex]
Finally, expand the brackets:
[tex]\begin{aligned}f(x) & =2(x+1)(x-3)(x^2-4x+20)\\& =2(x^2-2x-3)(x^2-4x+20)\\& =2(x^4-4x^3+20x^2-2x^3+8x^2-40x-3x^2+12x-60)\\& =2(x^4-4x^3-2x^3+20x^2+8x^2-3x^2-40x+12x-60)\\& =2(x^4-6x^3+25x^2-28x-60)\\& =2x^4-12x^3+50x^2-56x-120\end{aligned}[/tex]
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trigonometry question
worth 100 points!
desperately need help
Answer:
Height is 40√2 m or 56.57 m
Explanation:
Use Pythagoras theorem: a² + b² = c²
where 'a' and 'b' are the legs and 'c' is the hypotenuse
Here given:
a = 20 meterb = heightc = 60 meterSubstitute values:
(20)² + (h)² = 60²
400 + h² = 3600
h² = 3600 - 400
h² = 3200
h = √3200
h = 40√2
h = 56.6 meter
-6-5
A. 2
C. 3
3
2
A
1
4-3-2-10
-1
-21B
-3
C
E
D
F
1 2 3
In the similarity
transformation of AABC
to ADFE, AABC was dilated by
a scale factor of [? ], reflected
across the [ ], and moved
through the translaton [ ].
B. 1/2
D. 1/3
Answer: A
Step-by-step explanation:
Following the first two steps of the sequence of transformations,
[tex]A(-4,-2) \longrightarrow (-2,-1) \longrightarrow (-2,1)[/tex]
We need to map this onto D(1,1), which involves a translation 3 units right.
In the similarity transformation of ΔABC to ΔDFE, ΔABC was dilated by a scale factor of [1/2 ], reflected across the [x-axis ], and moved through the translation [(X+3, Y+0)].
So, correct option is: A.
Here, we have,
from the given fugre we get,
A =( -4, -2)
Following the first two steps of the sequence of transformations,
Dilated by a factor of 1/2 => A' = ( -2, -1)
reflected across the X-axis => A''=( -2, 1)
and moved through the translation becomes D = ( 1,1)
We need to map this onto D(1,1), which involves a translation 3 units right.
so, translation=> ( -2 + 3, 1+0) => (X+3, Y+0)
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Consider the quadratic function y equals 4 x squared minus 4 x minus 1.
What is the graph of this function?
First accurate answer gets brainliest
Answer:
Graph D (look in the attached picture)
The way you do this is use the quadratic formula to solve for the x intercepts which are [tex](\frac{1+\sqrt{2} }{2} )[/tex] and [tex](\frac{1-\sqrt{2} }{2})[/tex]
84. A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent’s survey, would you agree with the Newsweek poll? In complete sentences, also give three reasons why the two polls might give different results.
Critical value z_{0.05}=-1.645
Decision Rule, Reject H if z< -1.645
We do not reject the null hypothesis.
What is the Decision?Generally, the equation for the hypothesis is mathematically given as
H P=0.3
H2:P<0.13
Therefore
[tex]z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\z=\frac{0.11-0.13 }{\sqrt{\frac{0.13(1-0.13)}{76}}}[/tex]
z=-0.52
In conclusion, from the table
Critical value z_{0.05}=-1.645
Decision Rule, Reject H if z< -1.645
In conclusion, we do not reject the null hypothesis.
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If one number is three less than five times m, what is the number?
Answer:
Step-by-step explanation:
n = the number
n = 5m - 3
Hayley and Tyler are on the cross-country team. Tyler can run 1 mile (at a
constant speed) in 8 minutes and 20 seconds. Hayley's distances and times
a training run are given by the equation y = 8x, where x represents distance
miles and y represents time in minutes. Who ran farther in 10 minutes? How
much farther?
The person who ran farther is Hayley.
Who ran farther?
Average speed is the total distance travelled per time.
Average speed = total distance / total time
Tyler's average speed = 1 / 8.30 seconds = 0.12 miles per minute
The distance covered by Tyler in 10 minutes = 0.12 x 10 = 1.2 miles
Distance covered by Hayley in 10 minutes : 10 = 8x
x = 10 / 8 = 1.25 miles
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2. David determines that 3 sqrt 2 cis(7pi/4) = -3+3i. When he considers the graphical representation of these numbers, he knows he made an error. Clearly explain in complete sentences what David observed, and where David made his mistake. State the correct rectangular equivalence of 3 sqrt 2 cis(7pi/4).
The correct rectangular equivalence of 3sqrt(2)·cis(7pi/4 ) is:
3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 ) = 3 - 3i.
Where did David go wrong?David mistakenly interchanged the Sin function and the Cos function when he was calculating the problem.
Hence the correct rectangular equivalence is:
3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 ) = 3 - 3i.
What is rectangular equivalence?An equation is rectangular in form when it is comprised of Variables like X and Y and can be represented on a Cartesian Plane.
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SEVEN TIMES THE SUM OF THREE CONSECUTIVE EVEN INTEGERS IS 140 MORE THAN ELEVEN TIMES THE
MIDDLE INTEGER. FIND THE INTEGERS
The integers are 12,14 and 16
How to determine the integers?Consecutive even integers are represented as:
x, x + 2 and x + 4
So, the statement is represented as:
7 * (x + x + 2 + x +4) = 140 + 11 * (x + 2)
Evaluate the like terms
7 * (3x + 6) = 140 + 11 * (x + 2)
Open the brackets
21x + 42 = 140 + 11x + 22
Collect the like terms
21x -11x =
Evaluate
10x = 120
Divide by 10
x = 12
So, we have
x + 2 = 14
x + 4 = 16
Hence, the integers are 12,14 and 16
Read more about consecutive numbers at:
https://brainly.com/question/10853762
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When half of 3,926 is added to a quarter of 1,924
Answer:
Again, this would be 2444.
Step-by-step explanation:
Because of the previous answers 1963 and 481, we can add them together to make 2444.