Answer:
Step-by-step explanation:
The third term of the geometric progression will be 1 / 27 with common ratio 2 / 3.
We are given that:
2nd term of geometric progression = 1 / 18
5th term = 4 / 243
Now, we can also write it as:
2nd term = a r ( where r is the common ratio and a is the initial term.)
a r = 1 / 18
5th term = a r⁴
a r⁴ = 4 / 243
Now divide 5th term by 2nd term, we get that:
a r⁴ / a r = ( 4 / 243 ) / ( 1 / 18 )
r³ = 72 / 243
r³ = 8 / 27
r = ∛ (8 / 27)
r = 2 / 3
3rd term = a r²
a r² = a r × r
= 1 / 18 × 2 / 3
3rd term = 1 / 27
Therefore, the third term of the geometric progression will be 1 / 27 with common ratio 2 / 3.
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Your question was incomplete. Please refer the content below:
The 2nd and 5th term of a GP are 1/18 and 4/243 respectively find the 3rd term
What is the answer to (-3.4)(5)
Answer:
-17
here is what yourrrr looking for
Answer:
-17
Step-by-step explanation:
Straight multiplication of a negative times a positive
A graphic designer enlarges a 12 inch long picture to a 2 1/2 foot long banner. At this setting if the picture is 16 inches wide how wide is the banner
Based on the enlargement the graphic designer applied to the length of the picture, the banner is as wide as 3 ⁸/₁₂ foot long
What is the width of the banner?The fact that 12 inch was enlarged to 2.5 foot means that every inch is:
= 2.5 / 12
= 2.5/12 foot
This means that if the picture was 16 inches wide, the enlarged size of the banner would be:
= 16 x 2.5/12
= 40 / 12
= 3.33
= 3 ⁸/₁₂ foot long
In conclusion, the width of the banner is 3 ⁸/₁₂ foot long
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1. m/A
= 62°
Complement
Supplement
For the given value of angle;
∠A = 62°
The complement of ∠A is; 90 - ∠A
complement = 90 - 62
complement = 28°
Now, for supplementary angle:
If the sum of the two angles equals 180°, the angles are supplementary. Each angle is referred to as a supplement from another angle.For the given: ∠A = 62°
supplementary = 180 - 62
supplementary = 118°
Thus, the complement and supplement are obtained as 28° and 118°.
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Can you guys help me solve this ?
Answer:
48,485
Step-by-step explanation:
I don't know if that would fit in the box but it wants a rounded form of the answer in a whole number. It was actually 48484.84 and so on, but since we want it in a whole number, I decided to round the .8 since it is above 5 which would round up the answer to 48485. the 4 after the .8 can't do anything besides round down since it isn't higher than 5.
3(−5.8 + w) = 22.62 what dose the W =
w = −1.3
w = 1.3
w = 5.6
w = 13.34
Answer:
d. w=13.34
Step-by-step explanation:
The value of w is 13.34 for the given equation. The correct answer is option D.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
The equation is given as follows:
3(−5.8 + w) = 22.62
First, we distribute the 3 on the left side of the equation:
-17.4 + 3w = 22.62
Next, we isolate the variable by adding 17.4 to both sides of the equation:
-17.4 + 3w + 17.4 = 22.62 + 17.4
3w = 40.02
Finally, we solve for w by dividing both sides of the equation by 3:
w = 13.34
Therefore, the value of w is 13.34, so the answer is option D.
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Use the table to write an expression that shows how many total baskets the Cavaliers made during the season. Simplify the expression.
The expression that shows how many total basket the Cavaliers made during the season is 1978+f
The total number of free throws = 1484
The number of two point field goals = f
The number of 3 point field goals = 494
Total number of basket Cavaliers made during the season = Number of free throws + Number of two point goals + Number of three point field goals
Substitute the values in the equation
Total number of basket Cavaliers made during the season= 1484 + f +494
Add them together
1484+ f +494= 1978+f
Hence, the expression that shows how many total basket the Cavaliers made during the season is 1978+f
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Express the solution graphically 2/3(x-9)>-8
The solution of the inequality given as 2/3(x - 9) > 8 is x > 21
How to express the solution graphically?The inequality is given as
2/3(x - 9) > 8
Multiply both sides by 3/2
So, we have
x - 9 > 12
Add 9 to both sides of the inequality
So, we have
x > 21
Hence, the solution of the inequality given as 2/3(x - 9) > 8 is x > 21
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Can anybody help me with this
Answer:
C. triangle 1 and triangle 2
Step-by-step explanation:
Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Write an equation of a parabola in vertex form. Vertex (0,-3) and passes through (-8,5)
The equation of the parabola that has vertex (0, -3) and also passes through the point (-8,5) is y = -1(x - 0)² - 3.
The vertex form of the equation of a parabola is:
y = a(x-h)² + k
where the vertex = (h, k)
The given vertex, (h, k) = (0, -3)
The line passes through the (-8, 5)
x = -8, y = 5
Substitute x = -8, y = 5, h = 0, y = -3 into the equation to solve for a
y = a(x - h)² + k
5 = a(-8-0)² + (-3)
5 = a(-8)² - 3
-8a = 5+3
-8a = 8
a = 8/-8
a = -1
Substitute a = -1, h = 0, k = -3 into y = a(x - h)² + k
y = -1(x - 0)² - 3
The equation of the parabola that has vertex (0, -3) and also passes through the point (-8,5) is y = -1(x - 0)² - 3
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If the length of a rectangle is L and the width is w, write an algebraic expression for the perimeter of the rectangle.
Tysm in advance!
Answer: P=2L+2w
Step-by-step explanation:
P=perimeter.
P=2L+2w ==> there are two lengths and two widths in a rectangle. That totals to 4 sides in a rectangle.
Write the equation of a line that is parallel y = 4x - 7 and goes through the point (4,1).
The equation of a line that is parallel to y = 4x - 7 and goes through the point (4,1) is y = 4x - 15.
How do we find the equation of a line when two lines are parallel?We can infer that the two lines are parallel because they are distinct and share the same slopes. We can determine whether any two lines are parallel using this characteristic.Then we determine the equation of the line by point-slope form.A point on the line and the slope of the line are required in the point-slope version of the equation of a line. The line's slope is m, and the referred point on the line is (x₁,y₁).Given line: y = 4x - 7
Slope of line m₁ = 4
Two lines are parallel lines when the slopes of the lines are the same.
so, m₁ = m₂
m₂ = 4
Now, the equation of a line with slope 4 and passing through the point (4,1) is:
⇒ y - y₁ = m (x - x₁)
⇒ y - 1 = 4(x - 4)
⇒ y - 1 = 4x -16
⇒ y = 4x - 15
Hence the equation of a line that is parallel to y = 4x - 7 and goes through the point (4,1) is y = 4x - 15.
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W to the power of 3 = 125 when W =
Answer:
W to the power of 3 =125
And 125 is same as 5 power power 3.
Therefore W = 5.
Use the value of the ratio to fill in the following two multiplicative comparison statements. a. The number of pancakes made is ________ times the amount of cups of flour needed. b. The amount of cups of flour needed is ________ of the number of pancakes made
The value of the ratio to fill in the following two multiplicative comparison statements are:
(A) The number of pancakes made is 5 times the amount of flour required. (B) The amount of flour required is 1/5 of the number of pancakes made.What do we mean by ratio?A ratio in mathematics indicates how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio of 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), and the proportion of oranges to total fruit is 8:14. (or 4:7).The number of pancakes made is five times the amount of flour required. The amount of flour required is one-fifth of the number of pancakes made.Therefore, the value of the ratio to fill in the following two multiplicative comparison statements are:
(A) The number of pancakes made is 5 times the amount of flour required. (B) The amount of flour required is 1/5 of the number of pancakes made.Know more about ratios here:
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36- x=3 help me xdddddddd
The linear equation is
x=33
A linear equation in one variable is defined as an equation with only one variable. The standard form of linear equation in one variable is stated as Ax + B = 0, where A and B can be any two numbers, and x has just one possible value.
36- x=3
x=33
The coefficients can be considered as parameters of the equation, and may be arbitrary expressions, supplied they do no longer incorporate any of the variables. To yield a significant equation, the coefficients required to now not all be 0.
alternatively, a linear equation can be obtained by using equating to zero a linear polynomial over a few area, from which the coefficients are taken.
The answers of such an equation are the values that, whilst substituted for the unknowns, make the equality true.
within the case of just one variable, there may be precisely one solution
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If the measure of angle is 3pi/4 , which statements are true?
If the measure about an angle is 3pi/4, the sentences are:
sinθ = sin135 = √2/2cosθ = cos135 = √2/2The correct option are A , D.
What is a trigonometric function?a function of an arc or angle represented most simply in terms of the ratios of pairs of sides of a right-angled triangle (such as the sine, cosine, tangent, cotangent, secant, or cosecant). also known as a circular function.
Why do we utilize trigonometric functions?Trigonometry is used to set directions such as north, south, east, and west; it tells you which direction to go using the compass to get on a straight path. It is used in trace to locate a location. It is also used to determine the distance between the shore and a point in the water.
According to the given data:Investigation trigonometric function:
θ = 3π/4
= 3/4 * 180
= 135
tanθ = sin135/cos135
= -1
sinθ = sin135 = √2/2
cosθ = cos135 = √2/2
The reference angle for stuff in Q2 is 180 - theta = 180 - 135 = 45 degrees.
If the measure about an angle is 3pi/4, the sentences are:
sinθ = sin135 = √2/2
cosθ = cos135 = √2/2
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I understand that the question you are looking for is:
If the measure of angle 0 is 3pi/4 which statements are true (multiple choice)
A. sin(0)=sqrt2/2
B. The measure of the reference angle is 45
C. The measure of the reference angle is 30
D. The measure of the reference angle is 60
E. cos(0)=sqrt2/2
F. tan(0)=1
A man has 19 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 355
cents, how many dimes and how many quarters does he have?
Let a be the number of dimes and y be the number of quarters.
Write an equation that expresses the information in the sentence "A man has 19 coins."
Write an equation that expresses the information in the sentence "The total value of change is 355 cents."
Solve the system you have written above.
The number of dimes, a is
The number of quarters, y is
Answer:
8 dimes11 quartersStep-by-step explanation:
You want to find the number of dimes (x) and the number of quarters (y) in 19 coins that have a total value of $3.55.
SetupUsing the given variables, we can write two equations. One is for the number of coins; the other is for their value.
x + y = 19 . . . . . . . . . . . number of coins
10x +25y = 355 . . . . . value in cents
SolutionIt usually works well to solve an equation involving the highest-value coin. That means we want to eliminate the x-variable. Using the first equation, we can write ...
x = 19 -y
Substituting into the second equation, we get ...
10(19 -y) +25y = 355
190 +15y = 355 . . . simplify
15y = 165 . . . . . . . subtract 190
y = 11 . . . . . . . . . . divide by 15
x = 19 -11 = 8
The number of dimes is 8.
The number of quarters is 11.
__
Alternate solution
The average coin value is 355/19 = 18 13/19 cents. The proportion of the highest-value coins is the ratio of the difference between this value and the lowest value, divided by the difference in values.
proportion of quarters = (18 13/19 -10)/(25 -10) = (8 13/19)/15 = (165/19)/15
proportion of quarters = 11/19
Multiplying this by the number of coins (19) gives the number of quarters:
(11/19)×19 = 11 . . . . quarters
You may recognize some similarities to the above solution.
__
Additional comment
Once you understand this generic solution to a mixture problem, you can use it to write down the answer without bothering with variables and equations.
Why doesn’t 4.5x100=4.500 make sense?
Answer:
it doesnt make sense because when u add 0's you move the decimal for every 0 added so it would be 450
Step-by-step explanation:
Consider the composite function g(f(x)) = x√6.
If f(x) = 3x², what is g(x)?
O g(x)=√2x
O g(x)=√x+3
O g(x)=√6x
O g(x)=√9-x
100 points hellpppp look at the image below
The values of JL, EF and KM are -19units, 29 units and 22 units respectively.
How to determine the values13. From the diagram shown, we have;
JL = JK + KL
where;
JK = x + 2
KL = 4x - 16
JL = 6x - 13
Substitute the expressions
6x - 13 = x + 2 + 4x - 16
collect like terms
x = -1
JL = 6x - 13 = 6(-1) - 13 = -6 -13 = -19 units
14. EG = 2x + 13
EF = x + 14
FG = 14
2x + 13 = x + 14 + 14
collect like terms
x = 15
EF = 15 + 14 = 29 units
15. KL = 6
LM = 2x
KM = 3x - 2
3x - 2 = 6 + 2x
collect like terms
x = 8
KM = 3x - 2 = 22 units
Thus, the values of JL, EF and KM are -19units, 29 units and 22 units respectively.
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a safety inspector found flaws in 3 out of 540 lamps built in a factory what is the probability that the next lamp she expects is flawed.
The probability that the next lamp safety inspector expects will be defective is 1/180.
What is probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.Formula: P = favourable events/Total events
Put the values in the formula and solve as follows:
P = favourable events/Total eventsP = 3/540P = 1/180Therefore, the probability that the next lamp safety inspector expects will be defective is 1/180.
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7x-2y-10x+5+8y simplified please show steps
Answer:-3x-10y+5
Step-by-step explanation:
7x-2y-10x+5+8y
-3x-2y+5-8y
-3x-10y+5
Ava has a part-time job at a store. She earns a weekly salary. She also
earns a $0.60 bonus for each gift card she sells. The expression
65 +0.60g shows Ava's total weekly earnings. Identify any variables,
Defficients, and terms in the expression. Tell what each represents.
Based on the given expression, the parameters are:
The variable = gThe coefficient = 0.60The constant = 65AlgebraThis is a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols, that is substituting one thing for another.
Given expression: 65 + 0.60g
Bonus for each gift card = $0.60Weekly salary = $65Number of gift cards sold = gFrom the expression:
The variable = gThe coefficient = 0.60The constant = 65Learn more about algebra:
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16. A collection of dimes and nickels is worth $3.10. If there are 45 coins in all, how many of each kind of coin are there?
Answer:
28 nickels and 17 dimes
Step-by-step explanation:
A nickel is worth 5 cents and a dime is worth 10 cents
If there are X nickels and Y dimes
Total value = 5X + 10Y cents
$3.10 == 3.10 x 100 = 310 cents
So 5X + 10 Y = 310
Divide both sides by 5 to get
5X/5 + 10Y/5 = 310/5
X + 2Y = 62 (1)
The total number of coins is X + Y and is given to be 45
X + Y = 45 (2)
Subtract Eq(2) from Eq(1) to get
X + 2Y - (X + Y) = 62-45 = 17
X + 2Y - X - Y = 17
Collecting like terms
(X - X) + (2Y - Y) = 17
Y = 17
So number of dimes = 17
To find X, the number of nickels use equation (2)
X + 17 = 45
Subtract 17 from both sides
X + 17 - 17 = 45 - 17
X = 28
So number of nickels = 28
in the diagram, CD || EF, G, -70° and HI - HG. Calculate the values of x, y and z
The measures of the angles are x = 40, x = 110 and y = 70
What are angles?Angles are formed when two or more lines intersect
How to calculate the values of x, y and z?The figure represents the given parameters
On the figure, we have the following highlights
Angle 3 and angle y are corresponding angles.
Corresponding angles are congruent
So, we have
y = Angle 3
From the figure
Angle 3 = 70
So, we have
y = 70
The angle on a straight line is 180 degrees
So, we have
x + y = 180
This gives
x + 70 = 180
Evaluate the like terms
x = 110
The triangle is an isosceles triangle.
So, we have
y = Angle 2
This means that
Angle 2 = 70
The sum of angles in a triangle is 180
So, we have
z + y + Angle 2 = 180
This gives
z + 70 + 70 = 180
Evaluate
z = 40
Hence, the measures of the angles are x = 40, x = 110 and y = 70
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Which number sentence is true?
PLEASE HELPP
twenty professiional athlets were asked what age did you graduate from college the responses are displayed in the histogram below
According to the given graph:
Age at graduation (in years) between 45 to 50 years.Age at graduation (in years) between 20 to 25 years.What is histogram?A histogram is a data representation that looks like a bar graph that bins a variety of classifications into columns and along the horizontal x-axis. The number count or percentage of occurrences inside this data for each column is represented by the vertical y-axis. Columns can be utilized to display data distribution patterns.
When should a histogram be used?When you're taking continuous measurements and you want to understand the distribution of results and look for outliers, use histograms. These graphs divide your continuous measurements into value ranges known as bins.
According to the given data:Based on these data, the numbers below appear to represent the smallest.:
= Age at graduation (in years) between 45 to 50 years.
Based on these data, the numbers below appear to represent the largest.
= Age at graduation (in years) between 20 to 25 years.
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I understand that the question you are looking for is:
Twenty professional athletes were asked, “What age did you graduate from college?” The responses are displayed in the histogram below.
Frequency 20 30 Age at graduation (in years) 40 50
(a) Which of the statistics below appear to be the smallest based on these data?
(b) Which of the statistics below appear to be the largest based on these data?
Jamie paid the rent well past the due date for the months of April, May and June,
As a result, he had been charged a total of $75 as late fee. How much did he pay as
late fee per month?
According to the arrangement, he must pay a late fee of $25 each month.
Describe division:The inverse of multiplication is division. If three groups of four add up to twelve, twelve divided into three equal groups adds up to four in each group. The basic purpose of splitting is to determine how many equal groups have been formed or how many people are in each group when equitably sharing.
What exactly is a division formula?To divide two numbers, use the formula Dividend Divisor = Quotient + Remainder. The dividend seems to be the number being divided in this case. The number that divides the number (dividend) into equally equal parts is known as the divisor.:
According to the given data:Total late fee = $75.
Rent late for 3 months.
Late fee per month= total late fee/ months
= 75/3
= 25.
Late fee per month= $25.
According to the arrangement, he must pay a late fee of $25 each month.
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Suppose that you purchase a machine for $800 at the beginning of the year and that the value of the machine on the retail market drops by $16 per month. Write a linear model for the current value P of the machine on the retail market (in dollars) at year
t (with t=0 being the year that the machine was purchased).
Note: the '' P(t)= '' is already provided and pay attention to units.
Hi
T (0) = 800
T(n+1) = T (n) - 16
General formula is : T(n) = 800- 16*n
with "n" the year you are.
exemple : if you search value of machine at year 3, it's value is :
t(3) =800 -16*3
t(3)= 800 -48
t(3) = 752
London answered 51 questions correctly on her multiple choice science final and earned a grade of 85%. How many total questions were on the final exam?
Quadrilateral ABCD is a rectangle. Find the coordinates for Point B.
Answer:
(8,25)
Step-by-step explanation: