Answers
a)
[tex]\dfrac{42}{65}\cdot\dfrac{25}{36}\cdot\dfrac{26}{49}=\dfrac{2\cdot3\cdot7}{5\cdot13}\cdot\dfrac{5\cdot5}{2\cdot2\cdot3\cdot3}\cdot\dfrac{2\cdot13}{7\cdot7}=\dfrac{7}{13}\cdot\dfrac{5}{2\cdot3}\cdot\dfrac{2\cdot13}{7\cdot7}=\\\\\\=\dfrac{1}{1}\cdot\dfrac{5}{2\cdot3}\cdot\dfrac{2}{7}=\dfrac{5}{3}\cdot\dfrac{1}{7}=\dfrac{5}{21}[/tex]
b)
[tex]\dfrac{21}{32}\cdot\dfrac{39}{120}\cdot\dfrac{40}{65}=\dfrac{21}{32}\cdot\dfrac{3\cdot13}{2\cdot2\cdot2\cdot3\cdot5}\cdot\dfrac{2\cdot2\cdot2\cdot5}{5\cdot13}=\\\\\\=\dfrac{3\cdot7}{32}\cdot\dfrac{13}{2\cdot2\cdot2\cdot5}\cdot\dfrac{2\cdot2\cdot2}{13}=\dfrac{21}{32}\cdot\dfrac{1}{5}\cdot\dfrac{1}{1}=\dfrac{21}{160}[/tex]
c)
[tex]\dfrac{15}{90}\cdot\dfrac{36}{75}\cdot\dfrac{27}{42}=\dfrac{3\cdot5}{2\cdot3\cdot3\cdot5}\cdot\dfrac{2\cdot2\cdot3\cdot3}{3\cdot5\cdot5}\cdot\dfrac{3\cdot3\cdot3}{2\cdot3\cdot7}=\\\\\\=\dfrac{1}{2\cdot3}\cdot\dfrac{2\cdot2\cdot3}{5\cdot5}\cdot\dfrac{3\cdot3}{2\cdot7}=\dfrac{1}{1}\cdot\dfrac{2}{5\cdot5}\cdot\dfrac{3\cdot3}{2\cdot7}=\dfrac{1}{25}\cdot\dfrac{9}{7}=\dfrac{9}{175}[/tex]
Related Questions
I need help knowing which graphs represent that y is a function of x
Answers
Answer:
B, C, F
Step-by-step explanation:
The choices B, C, and F are right because if you do the Vertical line test, the vertical line only intersects one point in the graph. The function only has one output value for each input value.
what's the distance between (-14,-18) and (-25,-23)
Answers
Answer:
the answer is 12.08
Step-by-step explanation:
Use the distance between point formula
[tex](8 + 4 + 3) + (6 + 5 + 11) = [/tex]
Answers
Answer:
= 37
Step-by-step explanation:
(8+4+3) + (6+5+11)
= 15 + 22
= 37
Round the following whole number to the nearest thousand.
9474
Answers
Answer:
9,000
Step-by-step explanation:
9474
Locate the thousands place:
9474
Check the number to the right:
9474
If the number is greater than or equal to 5, we round up. If the number is less than or equal to 4, we round down.
Since there is a '4', we round down.
9474 ≈ 9000
Hope this helps.
You deposit $6000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years?
Answers
Answer:
13,200
Step-by-step explanation:
6000/100=60
60x8=480
480x15=7,200
6,000+7,200=13,200
If the initial amount is $6000 , rate of interest 8% then after 15 years the amount willbe $19957.218.
What is compound interest?Compound interest is the interest calculated on the principal and the aggregate interest. It may be copounded annually,semi annually, monthly, bimonthly,etc.
How to calculate interest?We have been given that the deposit is $6000,rate is 8% which is compounded monthly.
So effective rate of interest will be 8/1200=0.0067.
n will be 15*12=180
The sum after 15 years=6000[tex](1+0.0067)^{180}[/tex]
S=6000[tex](1+0.0067)^{180}[/tex]
Take log both sides.
log S=log 6000[tex](1+0.0067)^{180}[/tex]
log S=log 6000+log [tex](1+0.0067)^{180}[/tex]
log S=log 6000+180 log (1.0067)
log S=3.7781+180*0.0029
log S=3.7781+0.522
log S=4.3001
S=AL (4.3001)
S=19957.218
Hence if the initial amount is $6000 , rate of interest 8% then after 15 years the amount willbe $19957.218.
Learn more about compound interest at https://brainly.com/question/24924853
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Construct a square whose area is
36 cm²
Answers
Squares have equal sides and 6^2 = 36
Sparkle Cleaners uses 2 3 of a jug of window cleaner in 3 weeks. How much window cleaner do they use in 1 week? Simplify your answer and write it as a proper fraction, mixed number, or whole number.
Answers
Answer:
7⅔ window cleaner
Step-by-step explanation:
23 =3w
x= 1w
3x =23
x= 7⅔ window cleaner
Gina has 2/3 pounds of apples. Jane has 3/5 pound of apples. Gina and Jane want to combine their apples to make an apple pie. The recipe calls for 1 1/2 pounds of apples. How many pounds of apples do they need for their pie? Show all work.
Answers
Answer:
Step-by-step explanation:
1. 3x5=15
2. 2x5=10 and 3x3=9
3 10/15 + 9/15= 19/15 or 1 and .3 so they need approx .2 more pounds
slope 5/6, passes through (12,4)
Answers
Answer:
y= 5/6x -6
Step-by-step explanation:
[tex]m =\frac{5}{6} \\(12,4)=(x_1,y_1)\\\\[/tex]
Substitute values into point slope form
[tex]y-y_1 =m(x-x_1)\\\\y - 4 = \frac{5}{6} (x-12)\\\\y-4 = \frac{5}{6} x -10\\\\y=\frac{5}{6} x -10+4\\\\y = \frac{5}{6} x -6[/tex]
The equation of the line that has a slope of 5/6 and passes through (12, 4) will be y = 5/6) x - 6.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 5/6. Then the equation of the line will be
y = (5/6)x + c
The equation of the line is passing through (12, 4), then the value of c will be
4 = (5/6) 12 + c
4 = 10 + c
c = -6
Then the equation of the line will be y = (5/6)x - 6.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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g(x)= 2x-4
f(x)= -3x-4
Find (g • f)(x)
Answers
Answer:
Step-by-step explanation:
(2x - 4)(-3x -4)
-6x^2 - 8x + 12x + 16
-6x^2 + 4x + 16
in grouped data each of the group is called?
Answers
Answer:
The class interval.
Other than replacing the equal sign with some sort of inequality sign, what is the one big difference we need to keep in mind when solving a linear inequality?
Answers
Step-by-step explanation:
In response to this question,
When solving a linear equality, one difference that we must keep in mind other than replacement of = sign with some equality sign is that when we do multiplication or division with a negative number, we are then required as a must to change the direction of the inequality sign.
Jessica makes overtime pay when she works more than 40 hours in a week. So far this week she has worked 29 hours. She will continue to work h hours this week. Write, solve, and graph an inequality to show the values of h that will allow Jessica to earn overtime pay.
Answers
Answer:11 more hours
Step-by-step explanation:
Factor out gcf
16x5 – 12x3
Answers
Answer:
(16 and 5 = gcf of 1) 12 and 3 = gcf of 3
Step-by-step explanation:
divid both to find the answer
-5x + 3 = 8x + 9 – 3
Answers
[tex]\text {Hi There! The answer to your problem is}[/tex]
[tex]\fbox {x=-3/13}[/tex]
[tex]\text {Your 1st Step will be to Simplify the Equation}[/tex]
[tex]\text {-5x+3=8x+9+-3}[/tex]
[tex]\text {-5x+3=(8x)+(9+-3) (Combine Like Terms)}[/tex]
[tex]\text {-5x+3=8x+6}[/tex]
[tex]\text {The Next Step is to Subtract 8x}[/tex]
[tex]\text {-13x+3-3=6-3}[/tex]
[tex]\text {-13x=3}[/tex]
[tex]\text {The Final Step is to Divide by -13}[/tex]
[tex]\text {-13x/13=3/-13}[/tex]
[tex]\text {x=-3/13}[/tex]
[tex]\text {Best of Luck!}[/tex]
[tex]\text {-LimitedX}[/tex]
which of these comparisons is correct?
A. -2 < -5
B. 0 > 2
C. 4 > -4
D. -6 < -5
Answers
please help ill mark branilest
Answers
I think it's the third choice :)) the one you currently have
What angle is exactly 90 degrees?
7
Answers
Answer:
a Right angle is an angle of exactly 90 degrees
Answer:
A right angle is exactly 90 degrees
Step-by-step explanation:
A right angel is like an L pretty much
plz mark brainest, trying to get to next rank and only need two more.
The human resource department at a certain company wants to conduct a survey regarding worker benefits. The department has an alphabetical list of all 7148 employees at the company and wants to conduct a systematic sample of size 70.
Answers
Answer:
The answer is "K= 102"
Step-by-step explanation:
Given:
Number of employees = 7128
sample size =70
k=?
Formula:
[tex]\to K= \frac{\text{Number of employees}}{\text{sample size}} \\\\[/tex]
[tex]= \frac{7148}{70} \\\\= 102.11\ \ \ \ or \ \ \ 102[/tex]
Find the perimeter of the figure below, in feet.
5.1 ft
14.8 ft
14.8 ft
14.8 ft
19.9 ft
10 ft
34.7 ft
24.8 ft
14.8 ft
5.1 ft
(Note: diagram is NOT to scale)
Answers
Answer:
158.8ft
Step-by-step explanation:
Please help me I am confused- qwq
Answers
$162.50 because if you add the percentages together, you get 35%
If you subtract 35% off of 250, you get 162.50
If x2 + 3x + 7 is divided by x + 2, then what is the remainder?
Answers
Answer:
ok but thx for the points
Step-by-step explanation:
The remainder when the polynomial x² + 3x + 7 is divided by x + 2 is 5.
A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables.
The remainder theorem states that for a polynomial, f(x) divided by a linear polynomial , x - a, the remainder is equal to f(a).
Given the polynomial; f(x) = x² + 3x + 7, since it is divided by x + 2, hence:
x + 2 = 0
x = -2
f(-2) = (-2)² + 3(-2) + 7 = 5
Hence the remainder when the polynomial x² + 3x + 7 is divided by x + 2 is 5.
Find out more at: https://brainly.com/question/19030073
What is £36 in the ratio 2:1:1
Answers
Answer:
$18, $9, $9
Step-by-step explanation:
First get the sum of all the ratios 2+1+1 =4
Divide $36 by the sum of the ratios $36/4 =$9
Multiply each ratio by $9 to get each of the amount.
I. 2x$9= $18
ii. 1x$9= $9
Iii. 1x $9 = $9
In the given figure, PQ=PR and QS is the bisector of angle PQR. If angle PQS=30°, find angle PSQ.
Answers
Answer:
90°
Step-by-step explanation:
PQ=PR ⇒
∠PQR = ∠PRQQS is the bisector of angle PQR ⇒
∠PQS= ∠RQSIf angle PQS=30°, find angle PSQ
∠PQS=30° ⇒
∠PQR = 2*∠PQS = 2*30° = 60°As ∠PQR = 60°,
∠PRQ = 60° and ∠QPR = 60° as remaining angleSo,
∠PSQ = 180° - (∠QPR + ∠PQS) = 180° - 90° = 90°Approximately 2,094,800 people took a
vacation to a state park this year. 25
years ago 158,975 people vacationed to
state parks. Approximately how many
more people visited the park than 25
years ago?
Answers
Answer: 1935825
Step-by-step explanation:
y=2x+3 help please ...
Answers
Answer:
x=-3/2
y=3
Step-by-step explanation:
i hope this helps
Answer:
x=2x+3 Improper question not enough details The only answer can be found right now is 3x+3
Step-by-step explanation:
Combine like terms and give me brainliest please
if de = 6x , EF =4x, and df =10 what is DE
Answers
Answer: 6
Step-by-step explanation:
Given DE, EF and DF, we know that DE and EF make up DF. We add DE and EF and set it equal to DF.
6x+4x=10 [add]
10x=10 [divide both sides by 10]
x=1
Now that we know x=1, we can plug that into DE.
6(1)=6
Now, we know that DE is 6.
I not sure how to find the value of the letters
Answers
Answer:
a = 31°
b = 66°
Step-by-step explanation:
Reason for the answer to a:
It is an alternate angle. So, a = 31°.
Reason for the answer to b:
It is also an alternate angle. So, b = 35° + 31° = 66°.
x-6y<-12 in slope intercept form
Answers
X-6y<-12 in slope intercept form is y > 1/6X + 2
7(1 - 2n) < 33 - n
solve the inequality
show work
Answers
Answer:
n > -2
Step-by-step explanation:
7(1 - 2n) < 33 - n
7 - 14n < 33 - n
Subtract 7
-14n < 26 - n
Add n
-13n < 26
Divide by -13
n > -2
Answer:
n > -2
Step-by-step explanation:
Distribution property:
7 - 14n < 33 - n
Bring n over:
7 - 13n < 33
Bring 7 over:
-13n < 26
n > -2