Answer:
[tex]\Huge \boxed{9}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3a}{b} -6= 21[/tex]
Add 6 to both sides.
[tex]\displaystyle \frac{3a}{b} =27[/tex]
Dividing both sides by 3.
[tex]\displaystyle \frac{a}{b} = 9[/tex]
A bag contains 3 red apples and 6 yellow apples. 3 apples are selected at random. Find the probability of selecting 1 red apple and 2 yellow apple.
Step-by-step explanation:
[tex]number \: of \: ways \: to \: select \: 3 \: out \: of \: 9 = {C}^{9}_3 = 84[/tex]
[tex]ways \: to \: select \: 1red \: and \: 2yellow \: apples \: = {C}^{3}_1 \times {C}^{6}_2 = 3 \times 15 = 45[/tex]
Probability of selecting 1 red and 2 yellow apples = 45 / 84 = 0.53
( 4a + 1 )( 7a 2 - 3a - 5 ) simplified
Answer:
28a³ - 5a² - 23a - 5
Step-by-step explanation:
FOIL and Distribute Parenthesis
Step 1: Write out expression
(4a + 1)(7a² - 3a - 5)
Step 2: Distribute 4a
28a³ - 12a² - 20a
Step 3: Distribute 1
7a² - 3a - 5
Step 4: Combine
28a³ - 12a² - 20a + 7a² - 3a - 5
Step 5: Combine like terms
28a³ - 5a² - 23a - 5
The angles in a triangle are such that one angle is 85∘ more than the smallest angle, while the third angle is 3 times as large as the smallest angle. Find the measures of all three angles.
Answer:
Step-by-step explanation:
x + x + 85 + 3x = 180
5x + 85 = 180
5x = 95
x = 19°
3(19)= 57°
x + 85 = 19 + 85 = 104°
The angles in a triangle are such that one angle is 85° more than the smallest angle, while the third angle is 3 times as large as the smallest angle. On solving the linear equation, the measures of all three angles are 17°, 51° and 102°.
Linear equation in one variable is an equation with an equals to sign with expressions on either side of it being equal. There must only be one variable. Also, the degree of each term must be one.
Given in the question:
Let the smallest angle be x°
the second angle = (x+85)°
the third angle = 3x°
Sum of all interior angle of a triangle = 180°
The linear equation becomes:
x + (x+85) + 3x = 180
5x + 85 = 180
5x = 95
x = 17°
x + 85 = 17 + 85 = 102°
3x = 17 * 3 = 51°
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Find the missing length to the nearest tenth.
13.3
9.7
Answer:
≈ 9.1
Step-by-step explanation:
As per Pythagorean theorem, the missing leg has length of:
[tex]\sqrt{13.3^2 - 9.7^2}[/tex] = [tex]\sqrt{82.8}[/tex] ≈ 9.1
Heather wants to purchase a pet from her local pet store. The pet store is offering 50% off rare exotic parrots. The original purchase price of a parrot is $956.50. Heather has a coupon for 10% off her entire purchase. How much will she pay if she also purchases a birdcage for $47.05?
$525.66
$478.25
$472.77
$903.20
C) $472.77
Step-by-step explanation: The parrot is half off so it goes from $956.50 to $478.25. Add the bird cage for $47.05 and she has a total of $523.3 to pay. The 10% off coupon makes her need to pay $472.77.
Answer:
$472.77
Step-by-step explanation:
To to this you would just do 50% of 956.50 so you would multiply 956.50 and 50 so you get 48,725 and divide by 100 so you get 487.25 as the price of the bird. So then you you would add 47.05 to the number so you get 525.30 and you would multiply by 10 then divide by 100 so you get 52.53 and subtract that from 525.30 so you get $472.77
solve for x: 2+3 (x+2x) = -2x(2-4) +1
Answer:
x = -1/5
Step-by-step explanation:
2+3 (x+2x) = -2x(2-4) +1
Combine like terms
2+3(3x) = -2x (-2) +1
Distribute
2+9x = 4x +1
Subtract 4x from each side
2+9x-4x = 4x+1-4x
2+5x = 1
Subtract 2 from each sdie
5x = 1-2
5x = -1
Divide by 5
5x/5 = -1/5
x = -1/5
how many gallons of a 80% antifreeze solution must be mixed with 70 gallons of 30% antifreeze to get a mixture that is 70% antifreeze
On a drawing of a model airplane, the scale used is 1 in.:3 ft. How many feet would 4.5 inches represent?
A.13.5ft
B.6.5ft
C.1.5ft
D.4.5ft
Answer:
A. 13.5ft
Step-by-step explanation:
8(−5d−9)−3(−6d+10) in simplest terms?
Answer:
-22d+42
Step-by-step explanation:
-40d+72+18d-30=-22d+42
What is the y-intercept of the graph
of 3x - 4y = 12
Pls help
Answer:
Hey there!
3x-4y=12
-4y=-3x+12
y=3/4x-3
So the y-intercept is -3.
Let me know if this helps :)
Answer:
The y-intercept is at (0, -3).
Step-by-step explanation:
Where the graph intercepts the y axis x = 0 so we have the equation:
3(0) - 4y = 12
-4y = 12
y = 12/ -4
y = -3.
Find the output, d, when the input, t, is 11. d= -20+11t d= ______
Answer:
d = 101
Step-by-step explanation:
d= -20+11t
Let t=11
= -20 + 11(11)
= -20 + 121
101
Answer:
the output is 101
Step-by-step explanation:
d= -20+11t
in the question it is given that t=11
substituting t=11 in the given equation
d=-20+11(11)d=-20+121d=101so the output is 99
hope it will help ^_^
Find the unknown. Identify the property that completes the number sentence. 24 + ___ = 18 + 24 Need a Hint? 18; Commutative Property of Addition 18; Associative Property of Addition 18; Identity Property of AdditionNEED A ANSWER RIGHT NOW!!!!!!
Answer: 18
Step-by-step explanation:
24+18= 42, and so does 18+24
;)
I need help! Please! Geometry! I don't know what I'm doing!
find the solutions of the quadratic equation 5x^2 +3x+1=0
Answer:
The answer is
[tex]x = - \frac{3}{10} + \frac{ \sqrt{11} }{10} \: i \\ \\ \: OR \\ \\ x = - \frac{ 3}{10} - \frac{ \sqrt{11} }{10} \: i[/tex]Step-by-step explanation:
5x² + 3x + 1 = 0
Using the quadratic formula
[tex]x = \frac{ - b\pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]From the question
a = 5 , b = 3 , c = 1
Substitute the values into the above formula and solve
That's
[tex]x = \frac{ - 3\pm \sqrt{ {3}^{2} - 4(5)(1) } }{2(5)} \\ x = \frac{ - 3\pm \sqrt{9 - 20} }{10} \\ x = \frac{ - 3\pm \sqrt{ - 11} }{10} \\ x = \frac{ - 3\pm \sqrt{11 } \: i}{10} \\ x = \frac{ - 3 + \sqrt{11} \: i}{10} \: \: or \: \: \: x = \frac{ - 3 - \sqrt{11} \: i}{10} [/tex]Separate the real and imaginary parts
We have the final answer as
[tex]x = - \frac{3}{10} + \frac{ \sqrt{11} }{10} \: i \\ \\ x = - \frac{ 3}{10} - \frac{ \sqrt{11} }{10} \: i[/tex]The equation has complex roots
Hope this helps you
the sum of 14 and a number n is equal to 17. what is the number
Answer:
3
Step-by-step explanation:
14 + n = 17
you have to isolate n by subtracting 14
n = 3
Answer:
x=3
Step-by-step explanation:
14+x=17 subtract 14 from both sides and you get x=3
(3 + 2i) + (4 – 5i) solve the equation .
Answer:
7 - 3 i
Step-by-step explanation:
Simplifying
(3 + -2i) + (4 + -5i) = 0
Remove parenthesis around (3 + -2i)
3 + -2i + (4 + -5i) = 0
Remove parenthesis around (4 + -5i)
3 + -2i + 4 + -5i = 0
Reorder the terms:
3 + 4 + -2i + -5i = 0
Combine like terms: 3 + 4 = 7
7 + -2i + -5i = 0
Combine like terms: -2i + -5i = -7i
7 + -7i = 0
Solving
7 + -7i = 0
Solving for variable 'i'.
Move all terms containing i to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -7i = 0 + -7
Combine like terms: 7 + -7 = 0
0 + -7i = 0 + -7
-7i = 0 + -7
Combine like terms: 0 + -7 = -7
-7i = -7
Divide each side by '-7'.
i = 1
Simplifying
i = 1
A bicycle is traveling at 20 miles per hour.
How many feet will it cover in 55 seconds?
Round your answer to the nearest tenth of a foot.
Answer:
1613.3 feetStep-by-step explanation:
Given the conversion 1mile = 5280feet
If a bicycle is traveling at 20 miles per hour, then the bicycke must have been travelling at (20*5280)feet per hour which is equivalent to 105,600 feet per hour.
To know the number of feet that will be covered in 55seconds, we will solve the equality operation;
If 105,600 feet = 1hour (3600secs)
x foot = 55secs
where x is the amount of feet it will cover in 55 seconds?
Cross multiply
3600 * x = 105,600*55
3600x = 5,808,000
divide both sides by 3600
3600x/3600 = 5,808,000/3600
x = 1613.3 feet (to the nearest tenth)
Hence the amount of feet covered in 55seconds to the nearest tenth is 1613.3 feet
5x - 7x + 6 = -2(x - 3)?
Answer: infinite number of answers
Step-by-step explanation:
5x - 7x + 6 = -2(x - 3) Distribute the -2
5x - 7x + 6 = -2x + 6 Combine like terms on the left side
-2x + 6 = -2x + 6 Add 2x to both sides
6 = 6
This means there’s an infinite number of answers. To test this, you could for example plug in 1 and -1. You’d find that they both solve the equation.
The table shows the ratio of nuts to raisins in different snack mixes. Which graph shows these equivalent ratios?
Answer:
figure 3
Step-by-step explanation:
see attached
x coordinates is the nuts
and y coordinates is the raisings
These corresponding ratios are only visible in graph 3.
What is the ratio?The ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
Given, The table shows the ratio of nuts to raisins in different snack mixes.
to compare the graph in Figure 1 with the graph in Figure 2 you would say that as both independent variables increase so do the Raisins.
but the first two graphs are not satisfying the value given in the chart or table.
By comparing Graph 3 and graph 4
SinceNuts should be on the x-axis and raisins on the y-axis
thus only graph 3 is satisfying all the criteria given in the problem.
Therefore, only graph 3 shows these equivalent ratios Also see the attached picture below.
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a. How many ways can the letters of the word ALGORITHM be arranged in a row?
b. How many ways can the letters of the word ALGORITHM be arranged in a row if A and L must remain together (in order) as a unit?
c. How many ways can the letters of the word ALGORITHM be arranged in a row if the letters GOR must remain together (in order) as a unit?
Answer: a) 362880 b) 40320 c)720
Step-by-step explanation:
a) There are 9 letters in the word ALGORITHM. Pls note that all 9 letters are different.
So to find the number of the ways which the letters can be arranged lets imagine , that in 1st place can stay any of 9 letters, in second place any of remaining 8 letters, in 3-rd place - any of 7 letters etc
So total number of the ways is
N= 9*8*7*6*5*4*3*2*1=9!=362880
b) If A and L must remain togetherin order AL ( LA is forbidden !) so we can imagine that AL is 1 special letter.
So total number of the letters is 8. Similarly to a) we can find the number of the ways as:
N=8*7*6*5*4*3*2*1=40320
c) Similarly to b) lets imagine that GOR is 1 special letter. So there are only 7 letters . Similarly to a) the number of the ways is
N=7*6*5*4*3*2=720
Step-by-step explanation:
a.362880 b.40320. c.720
1. The speed at which an automated assembly line produces a product follows a normal distribution with mean production time of 32.20 seconds and standard deviation of 1.05 seconds. A full production run from this line consists of 20 completed products. What is the probability that a full production run will take less than 32 seconds on average to produce?2. Recent homebuyers from a local developer allege that 30% of the houses this developer constructs have some major defect that will require substantial repairs. To test this allegation, we randomly sample 20 homes constructed by the developer and find that two of the homes did indeed have some major defect. If the allegation is correct, what is the probability of observing at most two defective homes out of a random sample of 20?3.It is believed that 15% of people who fly on commercial airliners are "very concerned" about the safety of the carrier they have chosen. If this is accurate, what is the probability that out of 150 randomly selected people who fly on commercial airliners, between 20 and 25 of them are "very concerned" about the safety of the carrier which they have chosen?
Answer: Probability = 0.2
Step-by-step explanation:
Given data:
Mean production time = 32.20 seconds
Standard deviation = 1,05seconds
probability that a full production run will take less than 32 seconds on average to produce
= P(Xbar<32)
= P(Z<-0.8518)
= 0.2
A photocopy of a polygon was reduced to 70% of its original size. Then, the copy was again reduced to 70% of its size.
a.is the second photocopy similar to the original?
b.what is the ratio of the corresponding sides of the second photocopy to the original?
Step-by-step explanation:
Step 1 of 4
a) Yes, since the photo copy, is same which is reduced by 80% it remains similar. Because the angles stay the same and the ratios responding sides are proportional.
The following is the figure:

a). Photocopy of a polygon reduced the size of the original polygon by
70%.
But the shape and angles of the the polygon remains unchanged.
Therefore, all the photocopies will be similar to the original polygon.
b). Let the measure of a side of the original polygon measures 'x' unit.
Size of the original polygon gets reduced by 70% in the photocopy.
Then the measure of the side in the photocopy = x - (70% of x)
= [tex]x-\frac{70x}{100}[/tex]
= [tex]x-0.7x[/tex]
= [tex]0.3x[/tex] units
Size of the second photocopy was reduced again by 70%.
Therefore, measure of the side of the second polygon = [tex]0.3x-(\frac{70}{100}\times 0.3x)[/tex]
= [tex]0.3x-0.21x[/tex]
= [tex]0.09x[/tex] units
Ratio of the corresponding sides of the second photocopy and the
original = [tex]\frac{0.09x}{x}[/tex]
= 0.09 : 1
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For the given function, find the vertical and horizontal asymptote(s) (if there are any). f(x) = the quantity x minus five divided by the quantity x squared minus one
Answer:
Step-by-step explanation:
The function is:
x - 5
f(x) = ---------------
x^2 - 1
Horizontal asymptote: observe that as x grows towards infinity, the function (and graph) approaches y = 0. This is the horizontal asymptote.
Vertical asymptote: These occur whenever the denominator of a rational function becomes zero. Here the vertical asymptotes are x = ± 1.
Please help I’m confused.
Answer:
What is the most common month? That is the answer
Step-by-step explanation:
Answer:
January is the most common month
Step-by-step explanation:
january=7
march=4
august=3
april=5
june=5
july=4
november=1
december=6
may=2
october=1
february=1
At the farmers market 2 pounds of peaches cost $4.20 how much will 4 pounds cost
Answer:
$8.4
Step-by-step explanation:
2 pounds of peaches cost $4.20
1 pound of peaches costs = 4.20 /2
4 pounds of peaches cost =[tex]\frac{4.20 *4}{2} \\8.4[/tex]
4 pounds of peaches cost $8.4
NEED HELP FAST!! A group of students performed an experiment to prove the law of conservation of energy. In the experiment, a flask containing water at room temperature was shaken vigorously for a few minutes. The table shows a partial record of the temperature of the water before and after shaking. Experimental Record Temperature Before Shaking 20 °C After Shaking Unknown What best predicts the unknown temperature? A- Less than 20 °C because the total energy of the system after shaking is lower B- Greater than 20 °C because the total energy of the system after shaking is higher C- Less than 20 °C, because the mechanical energy from shaking transforms to thermal energy D -Greater than 20 °C, because the mechanical energy from shaking transforms to thermal energy
Answer:
I think option D is the answer.
Answer:
D
Step-by-step explanation:
true answer ;)
Consider the ratio of 153 per 108. Write this ratio in different forms below. A ratio written as a reduced fraction: ____ A ration written as a decimal rounded to the hundredths: ___
Answer:
17/12 and 1.42Step-by-step explanation:
Ratios can be used to compare values and also can be written in various forms.
Given the following example
the ratio of 153 per 108.
153:108
A. this ratio can expressed in the reduced fraction as
dividing both the numerator and the denominator by a common factor of 3 will give
=153/108 = 51/36
we can further divide by a common factor of 3 to further reduce the ratio
= 51/36= 17/12
hence the ratio expressed as a reduced fraction is 17/12
B. ration written as a decimal rounded to the hundredths:
A ratio written as a decimal rounded to the hundredths:
to express the ratio as a decimal we have to divide the numerator by the value of the denominator i.e 153/108= 1.4166
to the nearest hundredth we have 1
1.42
Simplify the expression (4x^3y^-5)^4
Answer:
64x^12 / y^20
Step-by-step explanation:
(4x^3y^-5)^4
Distribute the exponential value of 4 to all terms in the parentheses.
4^4 * x^(3*4) * y^(-5*4)
Multiply each exponent.
64x^12 * y^-20
Make the negative exponent positive by making it a fraction.
64x^12 / y^20
June bought three books. For the first book, she paid one half of her allowance plus $1 more. For the second book, she paid one half of her left-over money plus $2 more. For the third book, she paid one half of her left-over money plus $3 more. At this point, she had no money left. How much was her allowance?
Answer:
$34
Step-by-step explanation:
I'd work backwards.
For the third book, she paid all her remaining money. The problem says she paid "1/2 her leftover money + $3". This means that: (let m = money used to buy book 3)
m = 1/2m + 3
1/2m = 3
m = 6
For the second book: (let n = money before book 2)
n - m (money left after book 2) = 1/2n + 2
1/2n +2 is money used up for book, which is the same as n-m.
n = 1/2n + 2 + m
1/2n = 2 + m = 2 + 6
1/2n =8
n = 16
For the first book, she spent 1/2 her money + 1. If o = money before book 1 (or the whole allowance):
o - n = 1/2o + 1
o = 1/2o + n + 1 = 1/2o + 16 + 1
1/2o = 17
o = 34
Check!
Spent 17 (half 34) + 1 on book 1
16 left
Spent 8 (half 16) +2 on book 2
6 left
Spent 3 (half 6) + 3 on book 3
0 left
Please.... I need answers for these fractions.
1 whole, 1 whole, 3/5, 1 whole,6/7, 1 whole,6/9, 8/10, 6/13, and 6/7 i think but im not positive