Answer:
5 out of 9
Step-by-step explanation:
You have 5 blue marbles and for red marbles which makes a total of 9 marbles in a bag. If you take one marble out and put it back in another marble out and put it back at random the probability of getting a blue marble is 5 out of 9.
The probability of getting exactly 1 blue marble from a bag which is filled with 5 blue and 4 red marbles is 40/81.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
There is a bag filled with 5 blue and 4 red marbles. Thus, the total number of marble in the bag are,
[tex]5+4=9[/tex]
One marble is taken at random from the bag, the color is noted and then it is replaced. The probability of getting blue marble is,
[tex]P(B)=\dfrac{5}{9}[/tex]
The probability of getting red marble is,
[tex]P(R)=\dfrac{4}{9}[/tex]
The Probability of getting red marble in first pick and probability of getting blue marble in second pick is,
[tex]P_1=\dfrac{4}{9}\times\dfrac{5}{9}=\dfrac{20}{81}[/tex]
The Probability of getting blue marble in first pick and probability of getting red marble in second pick is,
[tex]P_2=\dfrac{5}{9}\times\dfrac{4}{9}=\dfrac{20}{81}[/tex]
The exactly 1 blue is taken out, when first marble is red and second is blue or the first one is blue and second one is red. Thus, the probability of getting exactly 1 blue is,
[tex]P=P_1+P_2\\P=\dfrac{20}{81}+\dfrac{20}{81}\\P=\dfrac{40}{81}[/tex]
Thus, the probability of getting exactly 1 blue marble from a bag which is filled with 5 blue and 4 red marbles is 40/81.
Learn more about the probability here;
https://brainly.com/question/24756209
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help me please, guys
Answer:
7.7
Step-by-step explanation:
The area of the wall is 4 * 2 = 8.
The radius of each clock is 0.3 / 2 = 0.15.
The area of all 4 circles is 4 * (πr²) = 4 * 3.14 * 0.15² = 0.3.
8 - 0.3 = 7.7
Answer:
6.9
Step-by-step explanation:
Total area of the wall is 4 x 2 = 8
Area for a circle is π x radius^2
Therefore total area of 4 clocks = 4 (π x 0.3^2)
Which is: 1.13...
Now we take away this answer from the area of the wall:
8 - 1.13... = 6.9 (1 d.p)
Let Aequals [Start 2 By 2 Matrix 1st Row 1st Column 3 2nd Column 2 2nd Row 1st Column negative 1 2nd Column 2 EndMatrix ]and Bequals [Start 2 By 2 Matrix 1st Row 1st Column 2 2nd Column 6 2nd Row 1st Column negative 3 2nd Column k EndMatrix ]. What value(s) of k, if any, will make ABequals BA?
Answer:
No value of k will make AB=BA
Step-by-step explanation:
[tex]A=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right), $ $B=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right) \\\\\\AB=\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)=\left(\begin{array}{ccc}3*2+2*-3&3*6+2*k\\-1*2+2*-3&-1*6+2k\end{array}\right)=\left(\begin{array}{ccc}0&18+2k\\-8&-6+2k\end{array}\right)[/tex]
[tex]BA=\left(\begin{array}{ccc}2&6\\-3&k\end{array}\right)\left(\begin{array}{ccc}3&2\\-1&2\end{array}\right)=\left(\begin{array}{ccc}0&16\\-6&-6+2k\end{array}\right)[/tex]
We can see that [tex]AB \neq BA[/tex]. Therefore, there is no value of k that will make it equal. In general, matrix multiplication is not commutative.
The height of Maury’s room is 8.4 feet from the floor to the ceiling. Maury wants to install a ceiling fan that hangs 1.875 feet below the ceiling. If Maury is 6.6 feet tall, which explains whether Maury’s head will hit the fan? Maury’s head will hit the fan because there are 6.525 feet between the floor and the fan, and 6.525 is less than 6.6. Maury’s head will not hit the fan because there are 6.525 feet between the floor and the fan, and 6.525 is less than 6.6. Maury’s head will hit the fan because there are 6.675 feet between the floor and the fan, and 6.675 is less than 6.6. Maury’s head will not hit the fan because there are 6.675 feet between the floor and the fan, and 6.675 is less than 6.6.
Subtract the ceiling fan from the height of the room:
8.4 - 1.875 = 6.525 feet
The answer is:
Maury’s head will hit the fan because there are 6.525 feet between the floor and the fan, and 6.525 is less than 6.6.
Answer:
it is A
Step-by-step explanation:
solve for x
2x/3 + 2 = 16
Answer:
2x/3 + 2= 16
=21
Step-by-step explanation:
Standard form:
2
3
x − 14 = 0
Factorization:
2
3 (x − 21) = 0
Solutions:
x = 42
2
= 21
The probability that a house in an urban area will be burglarized is 6%. If 10 houses are randomly selected, what is the probability that none of the houses will be burglarized?
Answer:
[tex](\dfrac{94}{100})^{10} \ or\ \approx 0.54[/tex]
Step-by-step explanation:
Given :
Probability that a house in an urban area will be burglarized,
[tex]p =6\%=\dfrac{6}{100}[/tex]
To find:
Probability that none of the houses randomly selected from 10 houses will be burglarized = ?
[tex]P(r=0) =?[/tex]
Solution:
This question is related to binomial distribution where:
[tex]p =\dfrac{6}{100}[/tex]
[tex]\Rightarrow[/tex] Probability that a house in an urban area will not be burglarized,
[tex]q =1-6\%=94\%=\dfrac{94}{100}[/tex]
Formula is:
[tex]P(r=x)=_nC_xp^xq^{n-x}[/tex]
Where n is the total number of elements in sample space and
x is the number selected from the sample space.
Here, x = 10 and
x = 0
[tex]\therefore P(r=0)=_nC_0p^0q^{10-0}\\\Rightarrow 1 \times (\dfrac{6}{100})^0\times (\dfrac{94}{100})^{10}\\\Rightarrow 1\times (\dfrac{94}{100})^{10}\\\Rightarrow (\dfrac{94}{100})^{10}\\\\\Rightarrow (0.94)^{10}\\\Rightarrow \approx 0.54[/tex]
A human resource manager for a large company takes a random sample of 60 employees from the company database. Based on the sample she calculates a 95% confidence interval for the mean time of employment for all employees to be 8.7 to 15.2 years. Which of the following will provide a more informative (i.e., narrower) confidence interval than the 95% confidence interval?
A. Using a 90% confidence level (instead of 95%)
B. Using a 99% confidence level (instead of 95%)
C. Using a sample size of 40 employees (instead of 60)
D. Using a sample size of 90 employees (instead of 60)
Answer:
A. Using a 90% confidence level (instead of 95%)
D. Using a sample size of 90 employees (instead of 60)
Step-by-step explanation:
The margin of error of a confidence interval is given by:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The higher the margin of error, the less precise the confidence interval is.
We have:
A 95% confidence interval, with a sample of 60.
We want to make it more precise:
Two options, decrease z(decrease the confidence level), or increase n(increase the sample size).
So the correct options are:
A. Using a 90% confidence level (instead of 95%)
D. Using a sample size of 90 employees (instead of 60)
Keith Rollag (2007) noticed that coworkers evaluate and treat "new" employees differently from other staff members. He was interested in how long a new employee is considered "new" in an organization. He surveyed four organizations ranging in size from 34 to 89 employees. He found that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
A) In this study, what was the real range of employees hired by each organization surveyed?
B) What was the cumulative percent of "new" employees with the lowest tenure?
Answer:
a) Real range of employees hired by each organization surveyed = 56
b) The cumulative percent of "new" employees with the lowest tenure = 30%
Step-by-step explanation:
a) Note: To get the real range of employees hired by each organization, you would do a head count from 34 to 89 employees. This means that this can be done mathematically by finding the difference between 34 and 89 and add the 1 to ensure that "34" is included.
Real range of employees hired by each organization surveyed = (89 - 34) + 1
Real range of employees hired by each organization surveyed = 56
b) It is clearly stated in the question that the "new" employee status was mostly reserved for the 30% of employees in the organization with the lowest tenure.
Therefore, the cumulative percent of "new" employees with the lowest tenure = 30%
Allie Maxudywishes to retire 25 years. She has decided that she should be able to invest $5000 per year in her retirement fund. If she makes the payments in quarterly installments at the beginning of the each year, and earn an annual percentage rate of 8% on her money how much she will have at the time of her retirement?
Answer:
$394,772.11
Step-by-step explanation:
This requires using compound interest as follows:
Principal = $5,000
Time = 25 years
Interest rate per annum = 8%
1st year: principal = 5000
Interest capitalized (5000*0.08) = 400
Amount (5000 + 400) = $5400
2nd year: principal = 5400 + 5000 = 10,400
Interest capitalized (10,400*0.08) = 832
Amount (10,400 + 832) = $11,232
3rd year: principal = 11,232+5000 = $16,232
Interest capitalized (16,232*0.08) = 1,298.56
Amount (16,232+1,298.56) = $17,530.56
4th year: principal = 17,530.56+5000 = $22,530.56
Interest capitalized (22,530.56*0.08) = 1,802.45
Amount (22,530.56+1,802.45) = $24,333.01
5th year: principal = 24,333.01+5000 = $29,333.01
Interest capitalized (29,333.01 * 0.08) = 2,346.64
Amount (29,333.01 + 2,346.64) = $31,679.65
6th year: principal = 31,679.65 + 5000 = $36,679.65
Interest capitalized (36,679.65 * 0.08) = 2,934.37
Amount (36,679.65 + 2,934.37) = $39,614.02
7th year: principal = 39,614.02 + 5000 = $44,614.02
Interest capitalized (44,614.02 * 0.08) = 3,569.12
Amount (44,614.02 + 3,569.12) = $48,183.14
8th year: principal = 48,183.14 + 5000 = $53,183.14
Interest capitalized (53,183.14 * 0.08) = 4,254.65
Amount (53,183.14 + 4,254.65) = $57,437.79
9th year: principal = 57,437.79 + 5000 = $62,437.79
Interest capitalized (62,437.79 * 0.08) = 4,995.02
Amount (62,437.79 + 4,995.02) = $67,432.81
10th year: principal = 67,432.81 + 5000 = $72,432.81
Interest capitalized (72,432.81 * 0.08) = 5,794.63
Amount (72,432.81 + 5,794.63) = $78,227.44
11th year: principal = 78,227.44 + 5000 = $83,227.44
Interest capitalized (83,227.44 * 0.08) = 6,658.20
Amount (83,227.44 + 6,658.20) = $89,885.64
12th year: principal = 89,885.64 + 5000 = $94,885.64
Interest capitalized (94,885.64 * 0.08) = 7,590.85
Amount (94,885.64 + 7,590.85) = $102,476.49
13th year: principal = 102,476.49 + 5000 = $107,476.49
Interest capitalized (107,476.49 * 0.08) = 8,598.12
Amount (107,476.49 + 8,598.12) = $116,074.61
14th year: principal = 116,074.61 + 5000 = $121,074.61
Interest capitalized (121,074.61 * 0.08) = 9,685.97
Amount (121,074.61 + 9,685.97) = $130,760.58
15th year: principal = 130,760.58 + 5000 = $135,760.58
Interest capitalized (135,760.58 * 0.08) = 10,860.85
Amount (135,760.58 + 10,860.85) = $146,621.43
16th year: principal = 146,621.43 + 5000 = $151,621.43
Interest capitalized (151,621.43 * 0.08) = 12,129.71
Amount (151,621.43 + 12,129.71) = $163,751.14
17th year: principal = 163,751.14 + 5000 = $168,751.14
Interest capitalized (168,751.14 * 0.08) = 13,500.09
Amount (168,751.14 + 13,500.09) = $182,251.23
18th year: principal = 182,251.23 + 5000 = $187,251.23
Interest capitalized (187,251.23 * 0.08) = 14,980.10
Amount (187,251.23 + 14,980.10) = $202,231.33
19th year: principal = 202,231.33 + 5000 = $207,231.33
Interest capitalized (207,231.33 * 0.08) = 16,578.51
Amount (207,231.33 + 16,578.51) = $223,809.84
20th year: principal = 223,809.84 + 5000 = $228,809.84
Interest capitalized (228,809.84 * 0.08) = 18,304.79
Amount (228,809.84 + 18,304.79) = $247,114.63
21st year: principal = 247,114.63 + 5000 = $252,114.63
Interest capitalized (252,114.63 * 0.08) = 20,169.17
Amount (252,114.63 + 20,169.17) = $272,283.8
22nd year: principal = 272,283.8 + 5000 = $277,283.8
Interest capitalized (277,283.8 * 0.08) = 22,182.70
Amount (277,283.8 + 22,182.70) = $299,466.5
23rd year: principal = 299,466.5 + 5000 = $304,466.5
Interest capitalized (304,466.5 * 0.08) = 24,357.32
Amount (304,466.5 + 24,357.32) = $328,823.82
24th year: principal = 328,823.82 + 5000 = $333,823.82
Interest capitalized (333,823.82 * 0.08) = 26,705.91
Amount (333,823.82 + 26,705.91) = $360,529.73
25th year: principal = 360,529.73 + 5000 = $365,529.73
Interest capitalized (365,529.73 * 0.08) = 29,242.38
Amount (365,529.73 + 29,242.38) = $394,772.11
what is 7/9 x 5 2/5 please!
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
=>[tex]\frac{7}{9} * 5 \frac{2}{5}[/tex]
=> [tex]\frac{7}{9} * \frac{27}{5}[/tex]
=> [tex]\frac{7*3}{5}[/tex]
=> [tex]\frac{21}{5}[/tex]
=> [tex]4\frac{1}{5}[/tex]
Answer:
[tex]4\frac{1}{5}[/tex]
Step-by-step explanation:
[tex]\frac{7}{9} \times 5 \frac{2}{5}[/tex]
[tex]\frac{7}{9} \times \frac{27}{5}[/tex]
[tex]\frac{7 \times 27}{9 \times 5 }[/tex]
[tex]\frac{189}{45}[/tex]
[tex]\frac{21}{5}[/tex]
[tex]=4\frac{1}{5}[/tex]
In triangle ABC, the measure of angle A is half the measure of angle B, and the measure of angle C is 50° less than the measure of angle B. Find the measure of the smallest angle. (Recall that the sum of the measures of the angles in a triangle is 180°.)
Answer:
42º
Step-by-step explanation:
You can start by setting up the equations that are given in the stem of the problem: a=.5b, c=b-50, a+b+c=180. Then plug in the values of b in relation to the other values into the equation a+b+c=180. This will give you (.5b)+b+(b-50)=180. By expanding this and combining like terms, we will get 2.5b=230. By dividing each side by 2.5, we get b=92. Then, referencing the first equations, a=.5(92)=46, and c=92-50=42. The smallest of all of these is c, 42.
Janice really likes potatoes. Potatoes cost $1.00 per pound, and she has $6.00 that she could possibly spend on potatoes or other items. Suppose she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30. how many pounds of potatoes will she purchase?
Answer:
6 pounds
Step-by-step explanation:
HELP ME Answer it from the forst one to the last one with the rght answer please.This is Urgent so do it Faster if u now the answers
Step-by-step explanation:
2) 63
3) 7000
4) 10
These are some answers
Write an expression without exponent that is equivalent to 2 to 3rd power nd 4 to the 3rd power
Answer:
2 to the 3rd power,
2*2*2
4 to the 3rd power,
4*4*4
Step-by-step explanation:
The "3rd power" means how many times the number given to it would be multiplied. Aka, 2 to the 4th power would mean 2 times 2 times 2 times 2, (2 four times).
Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?
Answer:
d on edge
Step-by-step explanation:
-3(x+4)(x-2)/x^2-1`
The equation of the rational function is: [tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
The x-intercepts of the rational function are given as: -4 and 2.
This means that, the zeroes of the function are (x + 4) and (x -2)
Multiply the zeroes of the function
[tex]f(x) = (x + 4)(x -2)[/tex]
The vertical asymptotes of the rational function are given as: 1 and -1.
This means that, the denominator is the product of (x + 1) and (x -1)
So, we have:
[tex]f(x) = \frac{(x + 4)(x -2)}{(x + 1)(x-1)}[/tex]
Express the denominator as the difference of two squares
[tex]f(x) = \frac{(x + 4)(x -2)}{x^2-1}[/tex]
Lastly, the horizontal asymptote is given as y = -3.
So, the actual function is:
[tex]f(x) = y \times \frac{(x + 4)(x -2)}{x^2-1}[/tex]
Substitute -3 for x
[tex]f(x) = -3 \times \frac{(x + 4)(x -2)}{x^2-1}[/tex]
This gives
[tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
Hence, the equation of the rational function is: [tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
Read more about rational functions at:
https://brainly.com/question/1851758
Please answer this correctly
Answer:
101-120=4
Step-by-step explanation:
All that you need to do is count how many data points fall into this category. In this case, there are four data points that fall into the category of 101-120 pushups
111111105113Therefore, the answer to the blank is 4. If possible, please mark brainliest.
Answer:
There are 4 numbers between 101 and 120.
Step-by-step explanation:
101-120: 105, 111, 111, 113 (4 numbers)
11. cos theta = 3/4, in quadrant 1
Answer:
Step-by-step explanation:sin
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f(x) = 2x – 1 g(x) = 7x – 12 What is h(x) = f(x) + g(x)?
Answer:
h(x)=9x-13Solution,
[tex]h(x) = f(x) + g(x) \\ \: \: \: \: \: \: \: = 2x - 1 + 7x - 12 \\ \: \: \: \: \: \: = 2x + 7x - 1 - 12 \\ \: \: \: \: \: \: = 9x - 13[/tex]
hope this helps...
Good luck on your assignment..
Answer:
h(x)=9x-13
Step-by-step explanation:
We want to find out what h(x) is. We know what h(x) is equal to, which is
h(x)= f(x)+g(x)
We know that f(x)=2x-1 and g(x)=7x-12. Substitute the expressions in.
h(x)= (2x-1)+(7x-12)
Simplify by combining like terms. Add all the terms with a variable (x), then all the terms without a variable, or constants.
h(x)=(2x+7x)+(-1+-12)
Add 2x and 7x.
h(x)=(2+7)(x)+(-1+-12)
h(x)= 9x+(-1+-12)
Add -1 and -12.
h(x)= 9x+(-13)
h(x)=9x-13
Hee lllp!!! Now 70 points
Answer:
[tex]\huge\boxed{Option \ 1}[/tex]
Step-by-step explanation:
Since, AE = CE and BE = DE , then E is the midpoint of AC and BD. Causius can use that to show that AC and BD bisect each other which means that they both are the diagonals of a parallelogram bisecting each other. Hence, It will be proved that ABCD is a || gm.
Hope this helped!
~AnonymousHelper1807SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
plane
Step-by-step explanation:
Answer:
D. Plane
Step-by-step explanation:
A plane extends in two dimensions. This figure is a plane. It is not a point, a segment or a ray.
Suppose the solutions of a homogeneous system of four linear equations in five unknowns are all multiples of one nonzero solution. Will the system necessarily have have a solution for every possible choice of constants on the right sides of the equations? Explain.
Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.
Yes, it's miles true.
Consider the machine as Ax = 0. in which A is 4x5 matrix.
From given dim Nul A=1. Since, the rank theorem states that
The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation
rank A+ dim NulA = n
dim NulA =n- rank A
Rank A = 5 - dim Nul A
Rank A = 4
Thus, the measurement of dim Col A = rank A = five
And since Col A is a subspace of R^4, Col A = R^4.
So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.
Express the following ratio in it’s simplest form
5:20
Answer:
1:4
Step-by-step explanation:
Answer:
1 : 4
Step-by-step explanation:
5:20
Divide each side by 5
5/5 : 20/5
1 : 4
Find the perimeter ? Plsss
Hey there!
Answer:
25.1 units.
Step-by-step explanation:
Calculate the lengths of sides AB, BC and AC. Use the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Solving for AB:
[tex]d = \sqrt{(4 -(-4))^2 + (5-(-1))^2}[/tex]
[tex]d = \sqrt{8^2 + 6^2}[/tex]
[tex]d = \sqrt{100}[/tex]
[tex]AB = 10[/tex]
Solving for BC:
This side is a vertical line, meaning simply find the difference of y values between each endpoint.
[tex]5-(-2) = 7[/tex]
[tex]BC = 7[/tex]
Solving for AC:
[tex]d = \sqrt{(4-(-4))^2 + (-2-(-1))^2}[/tex]
[tex]d = \sqrt{(8)^2 + (-1)^2}[/tex]
[tex]d = \sqrt{65}[/tex]
d≈ 8.06 units
Add up all of the side lengths:
10 + 7 + 8.06 = 25.06 ≈ 25.1 units.
Diego planted a 8 inch tall magical beanstalk. The height of the beanstalk increases by 16% each day.Write a function ff that determines the height of the beanstalk in inches in terms of the number of days tt since Diego planted the beanstalk f(t)=f(1)/f(0)=f(2)/f(1)=f(5.28)/f(4.28)=For any value of x, what is the value of f(x+1)/f(x)?
Answer:
The expression for the height of the plant is: f(x) = 8*(1.16)^x;
The value of f(x+1)/f(x) is 1.16.
Step-by-step explanation:
Since Diego's beanstalk grows at an exponential rate of 16% per day, then the expression that represents the height of the plant, "f", in function of days, "x", can be found as shown below:
Initially the height of the plant was:
[tex]f(0) = 8[/tex]
After the first day however it was:
f(1) = 8*(1 + \frac{16}{100}) = 8*(1.16)
While after the second day:
f(2) = f(1)*(1.16) = 8*(1.16)*(1.16) = 8*(1.16)²
And so on, therefore the expression is:
f(x) = 8*(1.16)^x
The value of f(x + 1)/f(x) is:
[8*(1.16)^(x + 1)]/[8*(1.16)^x]
[8*(1.16)*(1.16)^(x)]/[8*(1.16)^x] = 1.16
x + 7 = 6x - 3
answer plssss
Answer:
x=2
Step-by-step explanation:
x + 7 = 6x - 3
Subtract x from each side
x+7-x = 6x-x
7 = 5x-3
Add 3 to each side
7+3 = 5x-3+3
10 =5x
divide by 5
10/5 = 5x/5
2 =x
Answer:
x= 2
hope it helps!
Step-by-step explanation:
x + 7 = 6x - 3
Bring all the variables to one side
So get 6x to the other side
x+7-6x = -3
-5x +7 = -3
Take 7 to the other side
-5x= -3 -7
-5x = -3 + -7
-5x = -10
x = -10/-5
minus n minus becomes plus
x= 10/5
= 2
❗️❗️❗️Find the length of side x in simplest radical form with a rational denominator.❗️❗️❗️
Plzzz helppp meeee
Answer:
[tex]x=\frac{\sqrt{14} }{2}[/tex]
Step-by-step explanation:
Notice that you are given an isosceles right-angle triangle to solve, since each of its two acute angles measures [tex]45^o[/tex]. Then such means that the sides opposite to these acute angles (the so called "legs" of this right angle triangle) must also be of the same length (x).
We can then use the Pythagorean theorem that relates the square of the hypotenuse to the addition of the squares of the triangles legs:
[tex](\sqrt{7})^2=x^2+x^2\\7=2\,x^2\\x^2=\frac{7}{2} \\x=+/-\sqrt{\frac{7}{2}} \\x=+/-\frac{\sqrt{14} }{2}[/tex]
We use just the positive root, since we are looking for an actual length. then, the requested side is:
[tex]x=\frac{\sqrt{14} }{2}[/tex]
Find the area of a circle with radius, r = 59cm.
Give your answer rounded to 3 SF.
Answer:
3481π or 10935.884
Step-by-step explanation:
Area = πr^2
Area = 3481π or 10935.884
find the x value to make L||M
Answer:
X=7[tex]solution \\ 2x - 3 = x + 4(being \: alternate \: exterior \: angles) \\ or \: 2x - x = 4 + 3 \\ x = 7 \\ hope \: it \: helps[/tex]
John took all his money from his savings account. He spent $48 on a radio and 3/8 of what was left on presents for his friends. Of the money remaining, John put 2/3 into a checking account and the last remaining $100 was left to charity. How much money did John orginally have in his savings account?
Answer:
Step-by-step explanation:
Let a = original amt in the savings account
"He spent $48 on a radio and 3/8 of what was left on presents for his friends."
Therefore he kept 5/8 of what was left
5/8(a - 48)
5/8(a - 30) left
:
John then put 2/3 of his remaining money into a checking account and donated the $100 that was left to charity.
a = 2/3(5/8a - 30) + 100
a = 5/12a - 20 + 100
a = 5/12a + 80
a - 5/12a = 80
7/12a = 80
a = $137.17 originally in his saving acct
PLEASE HELP ME WITH THIS, HELP NEEDED ASAP
Answer:
x = 16.5
Step-by-step-explanation:
The height of the larger triangle is 11, and the height of smaller triangle is 2. Which means that the larger triangle height is 5.5 times greater than the smaller triangle's height.
If the base of the smaller triangle is 3, that means that base of the whole/larger triangle is 16.5 because 3 * 5.5 = 16.5
Given that 9 x − 4 y = 20 Find y when x = − 2 Give your answer as an improper fraction in its simplest form.
Answer:
y = [tex]-9 \frac{1}{2}[/tex]
Step-by-step explanation:
9x-4y = 20
Given that x = -2
Putting in the above equation
9(-2) -4y = 20
-18 - 4y = 20
-4y = 20+18
-4y = 38
Dividing both sides by -4
y = [tex]-\frac{38}{4}[/tex]
y = [tex]-\frac{19}{2}[/tex]
y = [tex]-9 \frac{1}{2}[/tex]
Answer:
19/-2
Step-by-step explanation:
the answer is referred in the picture with the working out. hope it was helpful