can someone please explain how they got this final answer.
how did they get the 3? and why is the 18 gone! :( i am so confused
The rationalization of the given surd gives the answer as √2/3
What is rationalization?Rationalization is a process that finds application in elementary algebra, where it is used to eliminate the irrational number in the denominator.
Given here: The surd 2/√18
Thus rationalizing we get as follows:
2/√18
=2×√18/√18×√18 ( multiplying both numerator and denominator by √18)
=2√18/√18² ( since 18²ˣ¹/₂=18)
=2√18/18
=2√3²×2 / 18 ( ∵ 18=3²×2)
=2×3×√2/18
=(6/18) × √2
=(1/3)×√2
=√2/3
Hence, The rationalization of the given surd gives the answer as √2/3
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asap Last week, Toby bought 11 books and 8 movies for a total of $207.
Today, Toby bought 16 books and 9 movies for a total of $280.
Assuming neither item has changed in price, what is the cost of a book in dollars?
Assuming neither item has changed in price, the cost of a book is $13.
System of EquationsA system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
Firstly, you should convert the text of the problem into equations, thus you can write:
11b+8m=207 (1)
16b+9m=280 (2)
where: b=book and m= movie
From the substitution method, you can solve this question following the steps below:
The equation 1, you can re-write as: b=(207-8m)/11. This relation, you can apply in equation2. See below.
16b+9m=280
[tex]{16*\frac{(207-8m)}{11} }+ 9m=280 \\ \\ \frac{3312-128m}{11} + \frac{99m}{11} =\frac{3080}{11} \\ \\ 3312-128m+99m=3080\\ \\ -29m= -232\\ \\ m=8[/tex]
If m=8, you can find the value of the cost of a book from the relation (207-8m)/11. Then,
[tex]b=\frac{(207-8m)}{11}=\frac{207-8*8}{11} =\frac{207-64}{11} \\ \\b=\frac{143}{11} =13[/tex]
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what is the smallest number of cars that can tailgate in a straight line at a football game so that one car is in front of four cars, one car is behind four cars, and three cars are between two cars?
The smallest number of cars that can tailgate in a straight line at a football game is 12.
Smallest Tailgate Cars NumberThis can be determined by using a logic puzzle approach. If one car is in front of four cars, that's 5 cars in total. If one car is behind four cars, that's also 5 cars. And if three cars are between two cars, that's 5 sets of two cars, or 10 cars. The total number of cars is 5 + 5 + 10 = 20.
This logic puzzle approach is not applicable for all problems. It depends on the specific problem and the information provided. For certain types of problems, a different approach or method may be more appropriate. The key is to understand the problem, determine the necessary information, and select the best approach to solve it.
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If marc r v = marc v u , what is marc v u ?a. 47° b. 52° c. 64° d. 87°
If marc r v = marc v u , the value of marc v u is given as 64°.
mArc R V = mArc V U, Angle S O R = 13 x degrees and angle T O U = 15 x - 8 degrees
∠SOR = ∠TOU (Vertically opposite angles are equal). Therefore:
13 x = 15x - 8
solving by calculating the value of x to satisfy the equation: Subtracting 13x from both sides
13x - 13x = 15x - 8 - 13x
0 = 15x - 13x - 8
2x - 8 = 0
Adding 8 to both sides:
2x - 8 + 8 = 0 + 8
2x = 8
2x/2 = 8/2
x = 4
∠SOR = 13x = 13(4) = 52°
∠TOU = 15x - 8 = 15(4) - 8 = 60 - 8 = 52°
Let a = mArc R V = mArc V U
Therefore:
mArc R V + mArc V U + ∠TOU = 180 (sum of angles on a straight line)
Substituting:
a + a + 52 = 180
2a = 180-52
2a = 128
a = 128/2
a= 64°
mArc R V = mArc V U = 64°
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Hannah's monthly bank statement showed the following deposits and withdrawals:
-−$99.01, $1.20, -−$35.92, -−$68.67, $52.41
If Hannah's balance in the account was $66.11 at the beginning of the month, what was the account balance at the end of the month?
Answer: - $83.88
Step-by-step explanation:
$66.11 - $99.01 + $1.20 - $35.92 - $68.67+ $52.41 = $83.88
PQ = 9x - 31 and QR = 43; Find x.
Answer:
We can't solve this problem if there is no context given. Since nothing is mentioned, it is safe to assume that PR and QR are line segments. Based on the nomenclature, it may be a collinear system of 3 points: P, Q and R. The equation should be:
PR = PQ + QR
Assume x is referred to line PQ
(9x - 31) = x + 43
9x - x = 43 + 31 = 74
8x = 74
x = 9.25
Which of the following is equal to the number sentence listed below?
(21 × 25) + (21 × 12)
21 + 25 = 46
21 + 12 = 33
46 + 33 = 79
therefore the answer is 79
Step-by-step explanation: thank you for listening
The 4th term of a geometric sequence is -25 and the 9th term is 25/32. Find the 15th term
The 15th element of the geometric sequence generated by exponential function y = 200 · (- 1 / 2)ⁿ⁻¹ is 25 / 2048.
How to determine the value from a geometric sequence
In this question we find the case of geometric sequence, that is, a set of values generated by a exponential function, whose definition is shown below:
y = a · rⁿ⁻¹, n ≥ 1
Where:
a - Value of the first element of the series.r - Common raten - Index of the n-th element of the series.If we know that y₄ = - 25 and y₉ = 25 / 32, then the expression that generates the geometric sequence is:
- 25 = a · r³
25 / 32 = a · r⁸
- 1 / 32 = r⁵
r = - 1 / 2
a = - 25 / r³
a = - 25 / (- 1 / 2)³
a = - 25 / (- 1 / 8)
a = 200
y = 200 · (- 1 / 2)ⁿ⁻¹
And the 15-th term of the geometric series is:
y = 200 · (- 1 / 2)¹⁴
y = 25 / 2048
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AB and CD are parallel lines and EH is a transversal.
What is the size of angle AFG?
The value of the consecutive interior angles formed by the parallel lines is : ∠CGF = 61°
Define the term co-interior angles?The two angles which it are on the same side of both the transversal are known as co-interior angles as well as consecutive interior angles. The inside angles total 180 degrees and are known as co-interior angles. It indicates that two internal angles that reside on the same sides of the transversal have a sum that is additional.For the stated question:
∠HGD = ∠CGF = 119° (vertically opposite angles)
And,
∠AFG + ∠CGF = 180° (consecutive interior angles)
∠CGF = 180° - 119°
∠CGF = 61°
Thus, the value of the consecutive interior angles formed by the parallel lines is : ∠CGF = 61°
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Which number does point A represent?
In the diagram below, ST is parallel to PQ. If SR = 2.4, PQ = 1.8, RQ = 3,
and ST = 1.2, find the length of PR. Figures are not necessarily drawn to scale.
P
R
T
The length of PR from triangle PQR is 3.6
Since we know that ST is parallel to PQ, we can conclude that the triangle RST is somehow similar to triangle PQR. We can try to find each side pairs that share equals angles. Those side pairs are:
ST and PQ
RS and RP
TR and QR
From the question, we know that:
SR =2.4
PQ = 1.8
RQ = 3
ST = 1.2
We can find the lenght of PR by finding the ratio between the two triangles:
PQ = PR
ST SR
1.8 = PR
1.2 2.4
6 = PR
4 2.4
PR = 3.6
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If the side ratio is 9:16, the perimeter ratio is
Answer:
the answer to this question is 2.25
what is the maximum length of instruction for 8086 based-ibm pc?
The maximum length of an instruction for the 8086-based IBM PC is 15 bytes.
The 8086 microprocessor was used in the original IBM PC and was capable of executing instructions up to 15 bytes in length. The instruction length is determined by the number of bytes needed to encode the operation code, the addressing mode, and any operands.
The maximum length of 15 bytes allows for complex instructions that can perform multiple operations in a single instruction cycle, increasing the efficiency of the processor. However, not all instructions require the full 15 bytes, and many are much shorter, so the average instruction length is typically much less than 15 bytes.
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an engineer designs an improved light bulb. the previous design had an average lifetime of 1200 hours. the new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs. although the difference is quite small, the effect was statistically significant. the explanation is that
The difference is quite small, the effect was statistically significant. the explanation is that the sample size is very large.
As per the given data:
An engineer designs an improved light bulb.
The previous design had an average lifetime of 1200 hours.
The new bulb had a lifetime of 1201 hours, using a sample of 2000 bulbs.
Let us assume the null and alternative hypothesis
Null: The average lifespan of old and new designs is the same.
Alternative: The lifespans of new and ancient designs differ.
Because of the huge sample size, the p-value is lower. Reject the null hypothesis as a result, and the effect is now considered statistically significant.
Although the difference between 1200 hours and 1201 hours is quite tiny, the effect was statistically significant because of the high sample size.
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An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The new bulb has a lifetime of 1201 hours, using a sample of 2000 bulbs. Although the difference is quite small, the effect is statistically significant. The explanation is:
(a) that new designs typically have more variability than standard designs.
(b) that the sample size is very large.
(c) that the mean of 1200 is large.
(d) all of the above.
the simple interest on $600 for t years at 5 per cent annum is $120. the vale of t is
Answer:
t = 4 years
Step-by-step explanation:
Simple Interest = Prt where r = rate in decimal, t = time in years, P = principal
r = 5/100 = 0.05
Plugging in knowns
120 = 600 x 0.05 x t
120 = 30t
30t = 120
t = 120/30
t= 4 years
define a parallel or meridian in a geographic coordinate system. describe where the zero lines occur.
The Parallel , Meridian in the geographical coordinate system is defined below and zero Line is where prime meridian is at 0° longitude .
In a Geographic Coordinate system, a Meridian is a line of longitude that runs from the North Pole to the South Pole and is used to indicate the east-west position of a location on the Earth's surface.
A Parallel is a line of latitude that circles the Earth parallel to the equator and is used to indicate the north-south position of a location on the Earth's surface.
The Zero Line is the line of longitude that is defined as 0° and runs from the North Pole to the South Pole, passing through Greenwich, England. The equator is the line of latitude that is defined as 0° and circles the Earth at an equal distance from the North and South Poles.
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Looking at the incomes in the piecewise function before Example 2 that are over $74,900 but not over $151,200, the equation is y = 10,312.50 + 0.25(x - 74,900). (a) What does the $10,312 mean? (b) What does the 0.25(x - 74,900) mean? c) Simplify the equation. show work
The simplified equation is y = 10,312.50 + 0.25x - 18,672.50
What is the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
(a) The $10,312.50 represents the fixed amount of income tax owed for the range of incomes between $74,900 and $151,200.
(b) The 0.25(x - 74,900) represents the additional amount of income tax owed based on a tax rate of 0.25 (25%) of the income above $74,900. The x-74,900 term represents the amount of income that is above $74,900, and multiplying by 0.25 calculates the additional tax owed for this portion of the income.
(c) To simplify the equation:
y = 10,312.50 + 0.25(x - 74,900)
y = 10,312.50 + 0.25x - 74,900 * 0.25
y = 10,312.50 + 0.25x - 18,672.50
Hence, the simplified equation is y = 10,312.50 + 0.25x - 18,672.50
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supose you have the equattion x=12. use the addition property of equality to write 3 equations that have the same soulition
Based on the addition property of equality, from the equation x=12, we can generate the following equations and solutions:
x+3 = 15x+7 = 19x+20 = 32.What is the addition property of equality?The addition property of equality states that you can add the same value to both sides of an equation and still maintain an equivalent equation.
It states that if two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.
If x = 12, using the addition property of equality, the following equations can be generated.
x+3 = 15 (12+3)
x+7 = 19 (12+7)
x+3 = 32 (12+20)
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When evaluating a histogram it is desirable for which of the following to be true?Histograms are a waste of time and provide no meaningful information about process variation.As wide as possible as long as it is between the spec limits.Skewed is better than symmetricalAs narrow as possible as long as it is between the spec limits.
Histograms are a waste of time and provide no meaningful information about process variation are true statement
A machine should be calibrated closer to the lower spec limit than the upper spec limit if the cost of fixing output that is too high is greater than the cost of fixing output that is too low.
If the cost of fixing output that is too high is greater than the cost of fixing output that is too low then it make sense to calibrate the machine closer to the lower spec limit.
This way if the machine produces less output than is required, it can be fixed at a lower cost than if the machine had been set to the upper spec and produces output that is too high.
Histograms are a waste of time and provide no meaningful information about process variation
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Xavier needs to print some color copies for a presentation, and he has a coupon. His cost y in dollars to print x copies is y = 0.08x – 2.50.
2.50 is the coupon amount and 0.08 is the cost for one copy from the equation y = 0.08x - 2.50.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
y = 0.08x - 2.50
Where x is the number of copies and y is the cost of printing x copies.
Now,
From the equation,
y = 0.08x - 2.50
2.50 is the coupon amount.
0.08 is the cost for one copy.
Thus,
2.50 is the coupon amount.
0.08 is the cost for one copy.
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two hundred fifty people were surveyed to determine their favorite mode of transportation. what number of people chose walking?
If two hundred fifty people were surveyed to determine their favorite mode of transportation. The number of people that chose walking is 35?
What is the survey about?A survey is a research method used to collect information from a sample of individuals about their opinions, beliefs, behaviors, or other characteristics.
The purpose of a survey is to gather data to help understand a specific population or topic, and the results of a survey can be used to make decisions, inform policy, or guide further research.
From the question (image attached)
14 people - Walking
Total surveyed =250
Therefore: 14/100 * 250
= 35
Hence 35 people were walking.
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PLEASEEE HELPP MEE
What the answer to number 3 the question the circled in red
Answer:
Step-by-step explanation:
it will ride at 45 miles because if you know every 2 hours she rides 18 miles and your trying to see how many in 5 hours you just do 18 + 18 +9 because half of 18 is 9 and you get 45.
Together, two wildlife refuge tour guides each lead ten 45-minute tours each day. The wildlife refuge needs to calculate the person-hours for the tours to allocate enough money in their budget to pay the tour guides. What is the number of person-hours per day for the tours?
A.
600
B.
300
C.
15
D.
30
Answer:
Step-by-step explanation:
The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to____(mm)^2
Answer:
150.72
Step-by-step explanation:
area of a cylinder = top circle + bottom circle + lateral
lateral = perimeter of the circle * height = 2π*2 * 10 =40π
area of a circle = πr² = 4π
top & bottom =8π
total = 40π+8π =48π = 150.72
The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is [tex]$$150.8 \mathrm{~cm}^2$$[/tex].
What is the surface area of a solid cylinder?The sum of the areas of all the faces or surfaces that surround a solid results in its total surface area. The tops and bottoms (bases) as well as the remaining surfaces make up the faces. The surface area of a solid without its bases is known as its lateral surface area.
The area of the cylinder is determined by adding the areas of the curving surface and its two circular bases.
A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².
Total surface area [tex]$S=2 \pi r h+2 \pi r^2$[/tex]
Substitute the values in the above equation, we get
[tex]$$\Rightarrow \mathrm{S}=2 \pi \mathrm{r}(\mathrm{r}+\mathrm{h})=2 \times 3.1416 \times 2 \times 12$$[/tex]
simplifying the equation, we get
[tex]$$\Rightarrow \mathrm{S}=150.8 \mathrm{~cm}^2$$[/tex]
[tex]$\Rightarrow \mathrm{S} \approx 1.51 \times 10^4 \mathrm{~mm}^2$$[/tex]
Therefore, the surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is [tex]$$\mathrm{S}=150.8 \mathrm{~cm}^2$$[/tex].
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Se tiene una balanza de 2 platillos y tres pesas de 1 kg, 3 Kg y 9 Kg ¿Cuantos objetos de diferente peso se podran pesar?m
Con la balanza de 2 platillos y las 3 pesas de 1 Kg, 3 Kg y 9 Kg se pueden pesar 7 objetos de diferente peso.
Esto se puede calcular usando la fórmula de combinaciones: nCr, donde n es el número total de elementos y r es el número de elementos a seleccionar. En este caso, n es igual a 5 (2 platillos y 3 pesas) y r es igual a 2 (porque se están seleccionando 2 elementos). Por lo tanto, la fórmula se convierte en 5C2, lo que equivale a 10. Sin embargo, se descartan 3 combinaciones en las que se utilizan dos pesas iguales, lo que reduce el resultado a 7. Por lo tanto, con la balanza de dos platillos y las 3 pesas de 1 Kg, 3 Kg y 9 Kg se pueden pesar 7 objetos de diferente peso.
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Bethan and Siobhan are cousins.
They both live in the same city but do not attend the same school.
The graph represents each of their journeys to school and back.
Distance from
home (km)
2
08:00
Key:
10:00
Bethan's journey
Siobhan's journey
12:00
14:00
a) At what time does Bethan arrive
home from school?
14:45 15:15 15:30 16:00
A
D
B
B
16:00 4 km
Time
A
C
C
b) What distance does Siobhan
travel each day when going to
school and back?
5 km
B
8 km
C
16 km
D
Answer:
A) 15:30
B) 8 km
Step-by-step explanation:
a) At 15:30, Bethan's journey line intersects the y-axis, indicating her arrival at home from school.
b) Siobhan's journey line starts and ends at 2 km on the x-axis, which represents the distance from her home. Therefore, Siobhan travels a total of 4 km to school and 4 km back, so she travels a total distance of 8 km each day.
The cot of pen and three ruler i le29 while two ruler and ix pen cot le48. Find the cot of eight ruler and three pen
The cost of eight ruler and three pens is le79.125.
Let's call the cost of a pen x and the cost of a ruler y. From the first statement, we can create the equation:
x + 3y = 29
And from the second statement:
6x + 2y = 48
That is dividing by 2, 3x + y = 24
Now we have two equations with two variables and can use substitution or elimination method to find the values of x and y.
Let's use substitution:
x = 29 - 3y
Substituting this into the second equation:
3(29 - 3y) + y = 24
87 - 9y + y = 24
8y = 63
y = 63/ 8
y = 7.875
Now that we have the value of y, we can use the first equation to find the value of x:
x = 29 - 3y = 29 - 3 * 63/8
= 5.375
So, a pen costs le5.375 and a ruler costs le7.875. To find the cost of 8 rulers and 3 pens, we multiply:
8 * 7.875 + 3 * 5.375 = le79.125
The cost of 8 rulers and 3 pens is le79.125.
--The question is incomplete, the complete question is as follows--
"The cost of a pen and three ruler is le29 while two ruler and six pen cost le48. Find the cost of eight ruler and three pen."
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you and your roomate are hosting a party, you invited 20 other pair of roommate, during the party you pull everyone at the party excluding yourself and ask everyone how mnya hnads each person shook, 2 condition each person did not shake his roomates hands each person shook a different number of hands how many hands did my roommate shake?
Your roommate shook 10 hands at the party you and your roommate hosted.
If each person at the party shakes hands with a different number of people, and each person did not shake hands with their own roommate, then the number of hands each person shakes will form a set of integers from 0 to 19, with no duplicates. Since there are 20 people at the party, the sum of the numbers from 0 to 19 is 20 * 19 / 2 = 190.
If we subtract the number of hands that each person shakes from this sum, we find that the number of hands that my roommate shook is equal to 190 - (0 + 1 + 2 + ... + 19) = 190 - (0 + 19) * 20 / 2 = 190 - 20 * (19 / 2) = 190 - 20 * 9.5 = 190 - 190 = 0. This is not possible, since each person must shake at least one hand. The only possible answer is 10, which satisfies the conditions.
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Assume you are solving a linear system. In the process of solving it, you get a final statement of 5 = 0. Which of the following statements is true?
dont guess
The true statement about the solution to the system is (e) none of the above
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
Solving a linear system
You get a final statement of 5 = 0
This equation is false
This is so because 0 and 5 do not have the same value
This statement creates a contradiction, which means that there is no solution to the linear system.
This means that the sytsem of equation has no solution and the solution to the system does not exist
Hence, the system has no solution
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describe the state plane coordinate system. what type of projections are used in a state plane coordinate system?
Answer:
Step-by-step explanation: north-south and east-west lines are perpendicular
