Given:
The equation is:
[tex]\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}[/tex]
To find:
The value of a.
Solution:
We have,
[tex]\left(3+4\sqrt{3}\right)\left(2-a\sqrt{3}\right)=-18+2\sqrt{3}[/tex]
On simplification, we get
[tex](3)(2)+(4\sqrt{3})(2)+(3)(-a\sqrt{3})+(4\sqrt{3})(-a\sqrt{3})=-18+2\sqrt{3}[/tex]
[tex]6+8\sqrt{3}-3a\sqrt{3}-4a(3)=-18+2\sqrt{3}[/tex]
[tex]6+8\sqrt{3}-3a\sqrt{3}-12a=-18+2\sqrt{3}[/tex]
[tex](6-12a)+(8-3a)\sqrt{3}=-18+2\sqrt{3}[/tex]
On comparing both sides, we get
[tex]6-12a=-18[/tex]
[tex]-12a=-18-6[/tex]
[tex]a=\dfrac{-24}{-12}[/tex]
[tex]a=2[/tex]
And,
[tex]8-3a=2[/tex]
[tex]-3a=2-8[/tex]
[tex]a=\dfrac{-6}{-3}[/tex]
[tex]a=2[/tex]
Therefore, the value of a is 2.
Rosa had 592 stickers. She gave 212 stickers to Meg.
Which is the best estimate for the number of stickers Rosa has left?
A 200
B. 300
C. 400
D.700
E. 800
Answer: I need help with this as fast as someone can. PLS let me know who to do it
Step-by-step explanation:
A llne passes through the two glven points. Is it vertical, horizontal, or neither?
(1, 0), (0, 0)
O Vertical
Horizontal
Neither
Answer:
Horizontal: if y is equal to 0, then there is no vertical movement
Help I’m stuck on this
Answer:
49 is the answer.
Step-by-step explanation:
[tex] - 11 \frac{2}{3} \times - 4 \frac{1}{5} [/tex]
[tex] - \frac{35}{3} \times - \frac{21}{5} [/tex]
[tex] - 7 \times - 7 = 49[/tex]
What is the scale factor of this dilation?
9514 1404 393
Answer:
3/5
Step-by-step explanation:
The scale factor is the ratio ...
(image measure)/(original measure)
The diagram shows that the original measure of 5 becomes a measure of 3 on the image. The scale factor is 3/5.
(no links please and than you! :))
Answer:
Line D represents a proportional relationship.
Step-by-step explanation:
In an easy way to explain what a proportional relationship is, it is basically a line graph that passes through the origin point. When a line graph passes through the origin point (0,0), it is proportional.
Other graphs do not intersect the origin points so they are not proportional.
Answer:
Line D represents a proportional relationship.
Step-by-step explanation:
In an easy way to explain what a proportional relationship is, it is basically a line graph that passes through the origin point. When a line graph passes through the origin point (0,0), it is proportional.
Other graphs do not intersect the origin points so they are not proportional.
What is the quotient if
1/3 of 10 is divided by 1/7 of 8/12? Reduce if possible.
Answer:
2.75
Step-by-step explanation:
Anthony surveys a group of students at his school about whether they play a
sport. This table shows the results broken down by gender.
Play a sport
Total
Do not play a
sport
105
70
175
Boys
Girls
75
50
125
Total
180
120
300
Are being a girl and playing a sport Independent events? Why or why not?
O A. Yes, they are independent, because P(girl) = 0.58 and Pgirl plays
a sport) = 0.6.
O B. Yes, they are independent, because (girl) = 0.42 and girl plays
a sport) - 0.42
O c. No, they are not independent, because P(girl) = 0.42 and
P(girl plays a sport) = 0.42.
D. Yes, they are independent, because (girl) = 0.58 and P(girl plays
a sport) = 0.58
Answer:
A is the answer it sounds more likely
For given data, being a girl and playing a sport are independent events as P(girl) = P(girl plays a sport) = 0.4.
What are independent events?"These are the events whose occurrence is not dependent on any other event.""When the probability of occurrence of an event A is not affected by the occurrence of another event B, then event A and event B are independent events."Formula for probability of independent events:"If A and B are independent events then, P(A∩B) = P(A).P(B)"
What is probability?"It is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
For given question,
We have been given a table that shows the results broken down by gender.
Play sports Do not play sports Total
Boy 105 75 180
Girl 70 50 120
Total 175 125 300
Using the definition of probability:
⇒ P(girl) = Number of girls/ Number of students
⇒ P(girl) = 120/300
⇒ P(girl) = 0.4 ....................(1)
Now we find the probability of girls that play a sport.
Using the definition of probability:
P(girl plays a sport)
= Number of girls who plays a sport/ number of students who plays a sport
= 70/ 175
= 0.4 ......................(2)
From (1) and (2),
P(girl) = P(girl plays a sport)
Thus, being a girl and playing a sport are Independent events.
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Please Round 1.54 thank you
Answer:
okay so it would be 2 or 1.5 i dont know if you want it whole number but i will explain
if the number is 5 or more like 5.1 or even 5 you round up
if the number is under 5 like 4,3,2,1 your round down
Step-by-step explanation:
Answer:
To The Nearest Tenth : 1.5
To The Nearest Whole Number : 2
Tip:
If the number is 4 or below like 1.42 it would be rounded to 1.4
If the number if 5 or above like 2.58 it would be rounded to 2.6 or 3
I didnt know which one you wanted so I put both
which area 100 km or 60km
Answer:
100km
Step-by-step explanation:
Answer:
100
Step-by-step explanation:
Mario made this model to find the 3 digit number and a 1 digit number what multiplication sentence represents marios model
Answer:
Step-by-step explanation:
Ewww
Help! PLEASEEE! THANK YOU FOR HELPING BTW!
Answer:
Use the slope formula and slope-intercept form y = mx + b to find the equation you get:
y = 8x
If thats not what your looking for then for every 1 (x) you get 8 (y)
Step-by-step explanation:
It was estimated that 650 people would attend bowling night, but 676 people actually attended.
What is the percent error, to the nearest percent of the estimate? Enter the answer in the box.
The estimate's percent error is 4%, to the closest percentage.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Find the difference between the estimate and the actual value:
Actual value - Estimated value = 676 - 650 = 26
The absolute value of the difference is 26, indicating that the actual value exceeded the estimated value.
Next, we need to find the relative error, which is the difference divided by the estimated value:
Relative error = Difference / Estimated value = 26 / 650
Finally, we can convert the relative error to a percentage by multiplying it by 100:
Percent error = Relative error x 100 = 26 / 650 x 100 ≈ 4
Therefore, the percent error, to the nearest percent, of the estimate is 4%.
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the diameter of a sphere is 42 centimeters. find the surface area to the nearest tenth
A population of 1,500 insects grows exponentially by a factor of 3 every week. Select all equations that represent or approximate the population, p. as a function of time in days.t, since the population was 1,500.
The required equation that represent or approximate the population is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
To represent the population, P, as a function of time in days, t, we need to find an exponential growth equation.
Since the population grows exponentially by a factor of 3 every week, we need to convert the weekly growth to daily growth.
Let's break down the problem step by step:
The population grows by a factor of 3 every week.There are 7 days in a week, so the daily growth factor can be calculated by taking the 7th root of 3. (Growth factor per day = [tex]3^{(1/7)[/tex])The initial population is 1,500.Now, we can represent the population, P, as a function of time, t, using the exponential growth equation:
[tex]\mathrm P(t) = \mathrm{Initial \ Population} \times \mathrm {Growth \ Factor}^t[/tex]
where:
Initial Population (Po) = 1,500 (given)
Growth Factor per day = [tex]3^{(1/7)[/tex]
So, the equation representing the population as a function of time in days is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
Hence the required equation that represent or approximate the population is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
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Which expression represent the total cost for Ari to rent a bike for b hours and Meg to rent a scooter for s hours?
A,B,C,D
The expression the represent the total cost for Ari to rent a bike for b hours and Meg to rent a scooter for s hours is total cost = 9b + 10s
How to find the expression for total cost?The cost of rent for bike and scooters are different.
cost for bike = $9 per hour
cost for scooter = $10 per hour
Therefore, he expression the represent the total cost for Ari to rent a bike for b hours and Meg to rent a scooter for s hours is as follows:
total cost = 9b + 10s
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Answer: 9b + 10s
Step-by-step explanation:
I - Ready Sucks :)
what is 30x + 40 factored
Answer:
1 0 ( 3 + 4 )
Step-by-step explanation:
What is the value of y?
please hellpp!!!
Answer:
C=54°
Step-by-step explanation:
If u add each angle of a triangle should ways add up to 180°
Find the area of the parallaogram to the nearest tenth
Answer:
sorry I think yr question is incomplete.
u forget to add picture.
stay safe healthy and happy.Solve for x.
x + 14
5x - 74
x = [?]
Answer:
[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]
x + 14 = 5x - 74 (corresponding angles are equal to each other)
[tex]x + 14 = 5x - 74 \\ 14 + 74 = 5x - x \\ 88 = 4x \\ \frac{88}{4} = x \\ 22 = x[/tex]
Answer:
22
Step-by-step explanation:
Angles x + 14 and 5x - 74 are adjacent angles.
Adjacent angles are equal.
5x - 74 = x + 14
5x - x = 14 + 74
4x = 88
x = 88 / 4
x = 22
Ronnie's Rentals
charges $25 plus $15 per hour to rent a
chain saw. David rented a chain saw for
5 hours. Write an expression to show how
you could calculate the total amount
David paid.
191
Answer:
P = 25 + (15)n
Total amount paid by David = $100
Step-by-step explanation:
Given:
Fixed cost of renting chain saw = $25
Variable cost of renting chain saw = $15 per hour
Time taken = 5 hour
Find;
Total amount paid by David
Computation:
Assume;
Total amount paid by David = P
Time taken = n
So,
P = 25 + (15)n
P = 25 + (15)(5)
P = 25 + 75
P = 100
Total amount paid by David = $100
What is the graph of the solution for y+10>12?
Answer:
Your answer is B.
Step-by-step explanation:
simplify x2 + 12x + 35/3x + 15
which set of side lengths can form a triangle?
А: 2 cm, 2cm. 6 cm
B:3 cm 6 cm, 9 cm
C:4 cm, 8 cm, 5 cm
D:8 cm, 3 cm, 4 cm
Answer:
C:4 cm, 8 cm, 5 cm
Step-by-step explanation:
sum of length of any two sides of a triangle will be larger than the third side.
The speed you are going determines the distance you travel before coming to a complete stop after pressing the brake.
Use the computer outputs, scatterplots, and residual plots to determine which statements are true. Check all that apply.
The linear model is most appropriate.
The power model is most appropriate.
Models are always improved by transformations.
The r2 on the linear model is stronger.
The residual plot is more patterned on the linear model.
Answer:
the linear model is most appropriate, the r2 on the linear model is stronger
Step-by-step explanation:
did it on edge
Answer:
The linear model is most appropriate; The r^2 on the linear model is stronger.
Step-by-step explanation:
When compared side bu side you can see the differences.
h(-3), h(5), h(2), h(0)
h(x) = {x+1, x<2
{2x-1, x>2
Solve these:
h(-3) =
h(5) =
h(2) =
h(0) =
Answer:
h(-3) = -3h
h(5) = 5h
h(2) = 2h
h(0) = 0
A bag contains 4 yellow balls, 5 red balls, and 6 blue balls.
Part A: What is the probability of picking a yellow ball from the bag?
Part B: what is the probability of picking a blue ball from the bag?
Part C What is the probability of picking a yellow ball and then a blue ball after
replacement? Determine if the two events are independent events.
Answer:
A) The probability of picking a yellow ball from the bag is 26.66%.
B) The probability of picking a blue ball from the bag is 40%.
C) The probability of picking a yellow ball and then a blue ball is 11.42%.
Step-by-step explanation:
Since a bag contains 4 yellow balls, 5 red balls, and 6 blue balls, to determine what is the probability of picking a yellow ball from the bag, what is the probability of picking a blue ball from the bag and what is the probability of picking a yellow ball and then a blue ball after replacement, the following calculations must be performed:
A)
4 + 5 + 6 = 100
4 = X
15 = 100
4 = X
4 x 100/15 = X
400/15 = X
26.66 = X
Therefore, the probability of picking a yellow ball from the bag is 26.66%.
B)
15 = 100
6 = X
6 x 100/15 = X
600/15 = X
40 = X
Therefore, the probability of picking a blue ball from the bag is 40%.
C)
14 = 100
6 = X
6 x 100/14 = X
600/14 = X
42.85 = X
0.2666 x 0.4285 = X
0.1142 = X
Therefore, the probability of picking a yellow ball and then a blue ball is 11.42%.
What is the slope of the following table?
Answer:
slope: 5/2
Step-by-step explanation:
Convert 15L 25ml into litres
Answer:
15.025 L
Step-by-step explanation:
25 mL = 25 ml * 1 L/1000 mL = 0.025 L
15 L + 0.025 L = 15.025 L
HELP ME PLEASEEEEEEEEEEEE
Answer:
c
Step-by-step explanation:
6x9=54
54/2= 27
Answer:
27 square units
Step-by-step explanation:
Area of a triangle = (1/2)(base)(height)
A = 1/2(6)(9)
A = 1/2(54)
A = 27
Plzzzz Find the value of x
Answer:
the answer is 55
Step-by-step explanation:
x + x + 90 = 180
2x + 90 = 180
2x = 180- 90 = 110
x = 110 ÷ 2 = 55