0.78 can be written as the fraction 71/90 after simplifying by dividing both the numerator and denominator by the greatest common divisor, which is 0.1.
To rewrite the repeating decimal 0.78 as a simplified fraction, we can use the concept of geometric series.
Let x = 0.78
Multiply both sides by 10 to shift the decimal point:
10x = 7.88
Subtract the original equation from the multiplied equation to eliminate the repeating part:
10x - x = 7.88 - 0.78
This simplifies to:
9x = 7.1
Now, divide both sides of the equation by 9 to isolate x:
x = 7.1/9
To express the fraction in simplest form, we can find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD:
GCD(7.1, 9) = 0.1
Dividing both the numerator and denominator by 0.1 yields:
7.1/9 ÷ 0.1/0.1 = 71/90
Therefore, the repeating decimal 0.78 is equivalent to the simplified fraction 71/90.
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The function 1=21.55 cos m-7 +43.75models the average high temperature in degrees Fahrenheit each month b throughout the year in Anchorage, Alaska, where m 1 for January and m 12 for December. Approximate y how many nmonths is the average high temperature above freezing (32 F)?
Answer:
8
Step-by-step explanation:
The number of months that having average high temperature above freezing (32 F) is approximately for 3 months.
What is a function?A function is defined as a relation between a set of inputs having one output each. It is a set of permissible outputs with the property that each input is related to exactly one output.
For the given situation,
The function is [tex]t=21.55 cos(\frac{\pi }{6}(m-7) )+43.75[/tex]
The temperature for months are calculated using the function t.
Here m = 1 refers January,
m = 2 refers February and so on.
Now substitute m = 1 for January,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(1-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-6) )+43.75[/tex]
⇒ [tex]t=22.2[/tex]
For February m = 2,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(2-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-5) )+43.75[/tex]
⇒ [tex]t=25.08[/tex]
For march m = 3,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(3-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-4) )+43.75[/tex]
⇒ [tex]t=32.9[/tex]
For April m = 4,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(4-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-3) )+43.75[/tex]
⇒ [tex]t=43.75[/tex]
For May m = 5,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(5-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-2) )+43.75[/tex]
⇒ [tex]t=54.525[/tex]
For June m = 6,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(6-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(-1) )+43.75[/tex]
⇒ [tex]t=62.41[/tex]
For July m = 7,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(7-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(0) )+43.75[/tex]
⇒ [tex]t=65.3[/tex]
For August m = 8,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(8-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(1) )+43.75[/tex]
⇒ [tex]t=62.41[/tex]
For September m = 9,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(9-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(2) )+43.75[/tex]
⇒ [tex]t=54.525[/tex]
For October m = 10,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(10-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(3) )+43.75[/tex]
⇒ [tex]t=43.75[/tex]
For November m = 11,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(11-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(4) )+43.75[/tex]
⇒ [tex]t=32.975[/tex]
For December m = 12,
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(12-7) )+43.75[/tex]
⇒ [tex]t=21.55 cos(\frac{\pi }{6}(5) )+43.75[/tex]
⇒ [tex]t=25.087[/tex]
Thus from the above temperatures of each month, the temperature for three months are less than 32°F.
Hence we can conclude that the number of months that having average high temperature above freezing (32 F) is approximately for 3 months.
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A sweater that originally cost $40 is on sale for 10 percent off. What is the amount of the discount?
Answer:
$36
Step-by-step explanation:
orig price = $40
discount=10%
40*10/100= 400/100 = 4
$40-4= $36
Answer:
$4
Step-by-step explanation:
x percent = x/100
10 percent = 10/100 = 0.10
10% of $40 = 0.10*40 = 4
You save $4
The old price is $40 and changes to $36 after the discount is applied. This is ignoring any taxes or other surcharges
Anyways I'm going a bit off tangent. The final answer is choice B) $4
Question 5
Given the sequence, 35, 32, 29, 26, 23, ...
Find the following:
a1 =
Answer:
a1 = 2
Step-by-step explanation:
what does a1 mean?
35, 32 29, 26, 23, 20 , 17, 14, 11, 8, 5, (2)
Divide.
8.64÷(−0.27)
Enter your answer in the box.
The answer is -2.3328
A mall is designing an outdoor space. The available space is 127 feet by 46 feet. The
plan is for a grassy section with a width of 40 feet. Next to the grass will be a cement
sidewalk with a width of 6 feet. What is the area of the available space in square feet?
Answer:
5882
Step-by-step explanation:
Answer:
5842
Step-by-step explanation:
The grass and sidewalk is extraneous information (not needed) since it only asks for the available space total. so 127 x 46
whats 8/10 = ?/20
I REALLYYYYYYYYYY NEED HELP WITH THIS!!!!!!!!!!!!!!!!!!
Answer:
16
Step-by-step explanation:
Answer:
16/20
Step-by-step explanation:
8x2=16 and the remainder is 20 so that makes 16/20
Find the missing measure x° 65°
Given the following expression. 2 1/4 - (-3 2/5) A. Rewrite the expression using addition. B. Evaluate the expression.
Answer:
[tex]2\frac{1}{4} + 3 \frac{2}{5}[/tex]
Step-by-step explanation:
[tex]2\frac{1}{4} - (-3 \frac{2}{5}[/tex][tex])[/tex]
However, - × - equals +
[tex]2\frac{1}{4} + 3 \frac{2}{5}[/tex]
What is the value of n in the equation in = 9?
n =
Answer:
n=0
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
PLEASE HELP Identify and solve the inequality that
represents how many $20 bills, n , you can withdraw from the account without
going below the minimum balance. Current amount $320.00 minimum $100.00
you can withdraw 11 times before it reaches the minimum of $100
42 is 84% of what number
Answer:
50
Step-by-step explanation:
Because 84% out of 50 is 42
y = 15 when x = 60, find y when x = 45
Answer:
y=0
Step-by-step explanation:
Answer: y = 30
hope it helps!
Find the factored form of the expression. Check your answer.
5x2 +5
5x² +5= 1 (Type an exact answer, using radicals and i as needed.)
Answer:
5² × 5
5²: 10
karena ada pangkat 2
jadi kita kalikan dengan jumlah yang
dihitung yang sesuai dengan pangkat nya
Contoh:
5×10+5 =
55
Step-by-step explanation:
( Type an exact answer,using radicals and i as
needed) .
HELP!!! ITS DUE TODAY
Answer:
Well one thing that created a demand was the fact that more and more people were getting farms and also slaves were dying. It was mainly the colonization of the new world
Step-by-step explanation:
The history is the Portugese came to africa and started kidnapping them and taking them to portugal. they were looked at as a novelty so more and more people started to get them and also bring them to america with them
When negative five is subtracted from a number the result is 10. Find the number.
15
5
-5
-15
A hot air balloon is released at ground level, and it rises into the air at a constant rate. After 5 seconds the height of the balloon is 20 feet. The balloon continues to rise at the same rate.
Which table shows the relationship between the time in seconds, x , and the height of the balloon in feet, y?
Answer: D
Step-by-step explanation:
If after 5 seconds the height was 20 feet then in 10 seconds it will be 40 feet and in 20 seconds it will be 80 seconds.
To get from 5 to 10 you multiply by 2
To get from 20 to 40 you multiply by 2.
Since you have a constant change then it works for D only.
The linear equation that represents the height of the balloon at a time will be y = 4x. Then the correct option is D.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
A hot air balloon is launched from the ground and climbs into the air at a consistent velocity. The balloon's elevation is 20 feet after 5 seconds. The balloon keeps rising at the same rate.
The height per second is given as,
m = 20 / 5
m = 4 ft/sec
Then the equation is given as,
y = 4x
At x = 10 sec, then the value of y will be
y = 4 (10)
y = 40 ft
At x = 20 sec, then the value of y will be
y = 4 (20)
y = 80ft
The linear equation that represents the height of the balloon at a time will be y = 4x. Then the correct option is D.
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Retha is building a rock display for her science project. She put 72 rocks in the first row, 63 rocks in the second row, and 54 rocks in the third
row.
If the pattern continues, how many rocks will she use in the sixth row?
OA. 54
OB. 45
O c. 36
O D. 27
O E. 18
Answer:
b
Step-by-step explanation:
What is this expression in simplified form?
3V3 • 6V6
Answer:
18V^9
Step-by-step explanation:
Answer:
54
Step-by-step explanation:
1 When the product of 4 and a number x is added to 12, the result is 16. What is the difference between x and 8?
Answer:
x = 1
Step-by-step explanation:
12 + 4 x = 16
Subtract 12 from both sides.
4x = 4
Divide 4 on both sides.
x = 1
Find the real-number root -81
solve for y
7x-5y=17
Answer: 7*x-5*y-(17)=0
Step-by-step explanation:
f(x)= -x + 6x² - 10x +4
Iliana’s math grade increased from 65 to 86. Fiona’s math grade increased from 70 to 80. What is the difference, rounded to the nearest whole number, between the approximate percent increases?
10 percent
15 percent
18 percent
21 percent
Answer:
C
Step-by-step explanation:
Answer:
it is C
Step-by-step explanation:
i did the test
a basketball weights approximately 1.35kg what is this mass in grams
Answer:
1350
Step-by-step explanation:
Answer:
1,350 grams is the answer.
Pleaseeeee helppppppp
Answer:
1.) y=3x
2.) y= -2/3 x + 1
3.)y = -2/3 x - 4
4.) y = 4
5.) y = x + 5
6.) y = 2x
What are the values of x, y and z in the diagram below? x 107° N z w
Answer:
73,107,73
Step-by-step explanation:
x=73 ,y=107 ,z=73
Drag each tile to the correct location on the table. Each tile can be used more than once, but not all tiles will be used.
Choose the justification for each step in the solution to the given equation.
multiplication property of equality
subtraction property of equality
division property of equality
addition property of equality
simplification
Multiple tiles can be used.
From up to down in justification :
1) Subtraction property of equality
2) Simplification
3) Subtraction property of equality
4) Simplification
5) Division property of equality (( I'm not sure))
6) Simplification
Answer:
Subtract
simp
subtract
simp
multiply
simp
Step-by-step explanation:
-f(a) Think of this as “the opposite of f(a).”
-f(a)=
F) does f(3)=f(-3)? (Yes or No)
D) does f(a) = f(-a)? ( Yes or No)
Answer:
F) yes
D)no
no
bfhdfthjfyktyrztjkgtwfhdhdgdrdrdth
Help please!! Due today I'll give brainliest and a 5 star rating to everyone ILL DO ANYTHING JUST HELPADWIEFHRJ
Answer:
i think the answer would be B i think if its wrong i am sorry
Step-by-step explanation:
Write the exponent for the expression.
3x3
Answer:
First, rewrite the expression as:
3
x
3
×
1
8
Next, use this rule of exponents to rewrite the expression again as:
x
a
×
b
=
(
x
a
)
b
3
x
3
×
1
8
⇒
3
(
x
3
)
1
8
Now, use this rule of exponents to write the expression as a radical:
x
1
n
=
n
√
x
3
(
x
3
)
1
8
=
3
8
√
x
3
Step-by-step explanation:
Step-by-step explanation:
it is 3 to the power of 3 or 3 with a tiny three next to it. The answer to 3 to the power of three is 27. 3x3=9 9x3=27