Answers
The two numbers have 1 as a common factor and nothing else. Hence 1 is the HCF. This proves that the HCF of any two consecutive numbers is always a one.
Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.
Related Questions
2(x+1)=3x+5. solve for x
Answers
Answer:
x = -3
Step-by-step explanation:
1. Which are true of x = log10 31,500? Select all that apply.
a. x < 4
b. x = 4
C. X > 4
d. x < 5
e. X = 5
f.x > 5
I don’t get this
Answers
Given:
[tex]x=\log_{10}31,500[/tex]
To find:
Select the true statements from the given options about the given value.
Solution:
We have,
[tex]x=\log_{10}31,500[/tex]
It can be written as
[tex]x=\log_{10}(2^23^25^37)[/tex]
[tex]x=\log_{10}(2^2)+\log_{10}(3^2)+\log_{10}(5^3)+\log_{10}(7)[/tex] [tex][\because \log(ab)=\log a+\log b][/tex]
[tex]x=2\log_{10}2+2\log_{10}3+3\log_{10}5+\log_{10}(7)[/tex]
[tex]x=2\left(0.30105\right)+2\left(0.47712\right)+3\left(0.69897\right)+0.8451[/tex]
[tex]x=4.49835[/tex]
Clearly, the value of x lies between 4 and 5. So, [tex]x>4[/tex] and [tex]x<5[/tex].
Therefore, the correct options are C and D.
The true statements are: (c) x > 4 and (d). x < 5
The logarithmic expression is given as:
[tex]x = \log_{10}(31500)[/tex]
Express 31500 as a product of 100
[tex]x = \log_{10}(315 * 100)[/tex]
Apply the law of logarithm
[tex]x = \log_{10}(315) + \log_{10}(100)[/tex]
Evaluate log 100 base 10
[tex]x = \log_{10}(315) + 2[/tex]
Evaluate log 315 base 10
[tex]x = 2.50 + 2[/tex]
Add the expressions
[tex]x \approx 4.50[/tex]
4.5 is greater than 4 and less than 5
Hence, the true statements are: (c) x > 4 and (d). x < 5
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Kristen owns a bakery and is making a cake for a wedding. The dimensions of the cake are shown below. Answer each of the questions below.
What is the frosted area of the top cake? (Round to the nearest tenth)
What is the frosted area of the bottom cake? (Round to the nearest tenth)
What is the total surface area of cake that will be frosted?
Answers
Answer:
$22.5.
Step-by-step explanation:
The total revenue that is gained from the sales of the cakes is determined by multiplying the number of cakes by the price. If we let x be the number of $1 that should be deducted from the price and y be the total revenue,
y = (25 - x)(100 + 5x)
Simplifying,
y = 2500 + 25x - 5x²
We get the value of x that will give us the maximum revenue by differentiating the equation and equating the differential to zero.
dy/dx = 0 = 25 - 10x
From a random sample of 16 people in a jail, the number of days remaining in each their sentences was noted. The 16 people have a mean remaining sentence of 645 days with a standard deviation of 31 days. Assume the population of remaining sentences is normally distributed. Construct a 95% confidence interval for the mean remaining sentence of all people in the jail. Round final answer to one decimal place.
Answers
Answer:
The 95% confidence interval for the mean remaining sentence of all people in the jail is between 628.5 days and 661.5 days.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 16 - 1 = 15
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1315
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.1315\frac{31}{\sqrt{16}} = 16.5[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 645 - 16.5 = 628.5 days
The upper end of the interval is the sample mean added to M. So it is 645 + 16.5 = 661.5 days
The 95% confidence interval for the mean remaining sentence of all people in the jail is between 628.5 days and 661.5 days.
.......,,,,,,;,,.,.........
Answers
Answer:
lol dababy ur my idol
Step-by-step explanation:
84b /32b
3b
Answer:
3b^2
Step-by-step explanation:
12b^7 / 4b^5
=12b^7/ 4b^5
=12b^2/4
=3b^2
The Holbrooks ordered 25 gallons of orange juice and 16 pints of cranberry juice for their resturant. How much juice do they have in all?
Answers = a- 57 gallons b- 29 gallons
c- 216 gallons d- 164 gallons
Answers
Answer:
27gallons
Step-by-step explanation:
First we need to convert 16pints to gallons
Since;
1 pint = 0.125gallons
16 pints = x
Cross multiply
1 * x = 16 * 0.125
x = 2gallons
Since Holbrooks ordered 25 gallons of orange juice and 16 pints of cranberry juice for their resturant, the total juice he has is 25gallons + 2 gallons = 27gallons
PLS HELP!
2x + 4 > 8
Answers
2x 4 =- 8
2 x + 4 = 8 2x+4=8 2x+4=8. Subtract 4 from both sides. Simplify 8 − 4 8-4 8−4 to 4. Divide both sides by 2.
Can someone please help I really need the answer I give anyone a brainliest
Quadratic vs Exponential Functions
X
- 1000000x y-2
0
1
0
1
1000000
2
2
4000000
4
3
9000000
8
4
16
5
32
16000000
25000000
36000000
49000000
6
64
7
128
Question:
The table shows the behavior of a quadratic and an exponential function near the origin
A. Which function is growing more rapidly?
B. Between which X-values does the table indicate that the functions graphs have crossed?
C. Will the functions graphs ever intersect again? Can you prove this?
1)
Answers
Answer:
A) The first function (the quadratic one) is growing more rapidly.
B) Between x=0 and x=1.
C) We can assume that they don't intersect again.
Step-by-step explanation:
A)
The first function (the quadratic one) is growing more rapidly. We can see this because the difference between its y values is so much greater than the difference between the y values for the exponential function.
B)
Between x=0 and x=1. When functions intersect, their y and x values are equal. The y-values are equal at some point over x=0 and x=1 because they both cross over the same range (y=1 and y=2)
C)
We can assume that they don't intersect again because the y-values for the exponential equation will never reach the corresponding values for the quadratic equation; it simply isn't growing rapidly enough.
Factor this polynomial completely x2-8x+16
Answers
Answer:
X^2-8x+16
X^2-4x-4x+16
Factorise by gouping terms
X(x-4)-4(x-4)
=(x-4)(x-4)
There are a couple of formulas that we should know about quadratic functions, and this one utilizes this one:
(x - a)^2 = x^2 -2ax + a^2
Notice how x^2 - 8x + 16 fits into the formula:
x^2 - 8x + 16
x^2 - 2*x*4 + 4^2
(x - 4)^2
(x - 4)(x - 4)
Of course, not all expanded quadratic expressions fit into that formula, so there is a universal method to factor quadratic expressions:
x^2 + x(a + b) + ab —> (x + a)(x + b)
Basically, the middle term is the sum of an and b times x, and the last term is the product of an and b. So, if we are using the expression given in the problem, notice how -4 * -4 is 16, and the sum of -4 and -4 is -8. Thus, a and b are both -4 and the factored form is (x - 4)(x - 4)
Sammy finds satellite images of a school and a museum. They put the images on a coordinate grid (shown
below).
School
Coordinate values are in meters.
Compare the area of the school and the museum.
Answers
Answer:
c
Step-by-step explanation:
ka
The area of the school is about 827 m² less than the area of the museum.
What is area?Area is the amount of area occupied by an object's flat (2-D) surface or shape.
Given:
Sammy finds satellite images of a school and a museum. They put the images on a coordinate grid (shown below).
School coordinate values are in meters.
To find the area of the school:
The school is rectangular.
Area of the rectangle = length x width
To find the length,
use distance formula.
We interpreted coordinates,
Fort length (-20, 20) and (-40, 80)
For width (-50, 10) and (80, -20)
Distance of length = √(60)²+(-20)² = 20√10
Distance of width = √(30)²+(10)² = 10√10
Area of the rectangle = length x width
Area of the rectangle = 20√10 x 10√10 = 2000 m²
The area of the museum is πr².
And r = 30
The area of the museum = π(30)². ≈ 2827 m².
Subtracting the area's = 827 m².
Therefore, the area of the school is about 827 m² less than the area of the museum.
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What are equivalent expressions for
3 (y + 1) + 4 + 3y
Answers
Answer:2yu
Step-by-step explanation:if you see this hi
please help !! A store sells packs of 3 mini-pizzas for $5. Complete the ratio table to show the price for up to 15 mini-pizzas. Mini-Pizzas 6 12 15 Price ($) 5 15 PART B A store sells packs of 3 mini-pizzas for $5. How much would 24 mini-pizzas cost?
Answers
Answer:
Step-by-step explanation:
6-$10 12-$20 15-$25
part 2 $40
Determine the value of w and x in circle M below.
H
w
106
A
Y
M
W=
Answers
Answer:
x= 32
w=74
Step-by-step explanation:
my explanation is in the picture
The value of w and x in circle M below mathematically given as
w = 74 , x = 32
What is the value of w and x in circle M below?
Generally, the equation for the sum of angle of a triangle is mathematically given as
w+x+c = 180
w+a = 106
w+x = 106
therefore,
106 +c = 180
c = 180-106
c = 74
w = 74
thus,
w+x+c = 180
74 + x + 74 = 180
x = 180 -148
x = 32
In conclusion, the value of w and x in circle M below is
w = 74 , x = 32
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You and a friend want to know how much rope you need to climb a large rock. Your friend is 5.5 feet tall and casts a shadow that is 18 feet long. If the rock casts a shadow that is 209.5 feet long, calculate the height of the rock from the ground. Round your answer to the nearest foot. (Hint: make a drawing) a. 64 ft b. 18 ft c. 210 ft d. 219 ft
Answers
Answer: The value of x from the equation is 64 ft. Thus, they will be needing approximately 64 ft of rope.
Step-by-step explanation: The concept that is useful in order to answer this item is the concept of ratio and proportion. Let x be the height of the rock from the ground. We use the equation below to answer.
5.5 ft / 18 ft = x ft / 209.5 ft
I will mark you brainlist!
How many triangles and rectangles/squares do you need to solve for?
Answers
Answer:
8 triangles
Step-by-step explanation:
1 Triangle = 2 needed to be solve. 4 triangle × 2 =8.
HELP!!! “Fill in the boxes with the values that make the statement true.”
Answers
Answer:
[tex]\sqrt{21m^{17} } = 3m \sqrt[17]{7m}[/tex]
(look attachment)
A quality control inspector has drawn a sample of 11 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that less than 7, but more than 4 bulbs from the sample are defective
Answers
Answer:
0.04845
Step-by-step explanation:
Probability that less than 7 but more than 4 bulbs from the sample are defective :
P(4 < X < 7) = P(x = 5) + P(x = 6)
Using the binomial probability formula :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
From the question :
p = 0.2 ; 1 - p = 0.8 ; n = 11
P(x =5) = 11C5 * 0.2^5 * 0.8^6 = 0.03876
P(x = 6) = 11C6 * 0.2^6 * 0.8^5 = 0.00969
P(4 < X < 7) = P(x = 5) + P(x = 6)
P(4 < X < 7) = 0.03876 + 0.00969
P(4 < X < 7) = 0.04845
427 × 1,000 jnjnnjnjnnjjjjjjjjjjjjjjjjjj
Answers
Answer:
427,000...
Step-by-step explanation:
just search it up. Anywayyysss cute copy and paste☏ ♡ ☆⋆◦★◦⋆°*•°
. * . . ° . ● ° .
¸ . ★ ° :. . • ° . * :. ☆
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★ ★°★ . * . °☆ . ● . ★ ° . • ○ ● . ☆ ★ ° ☆ ¸. ¸ ★ . • ° . *
¸ . ★ ° :. :. . ¸ . ● ¸ ° ¸. * ● ¸ °☆
☆ °☆ . * ● ¸ . ★¸ .
. * . . ° . ● ° .
° :. ° . ☆ . . • . ● .° °★ Not sure how to copy and paste? Just right click your mouse and choose copy in options, to release repeat the process and just paste it. No mouse? Select the text with your computer pad and use ctrl c to release, ctrl v. On mobile? Press on your screen and select the text, use the option copy and paste wherever you would like!
I need help please.
Answers
Answer:
i think the anwser is 2
Step-by-step explanation:
Answer: 24 cubes
Step-by-step explanation:
Give the equation of the circle centered at the origin and passing through the point -7 0
Answers
Answer: 7.0 because you add 10 to - 3 it makes7.0
Step-by-step explanation:
Each base in this right prism-like figure is a quarter of a circle with a radius of 2 m.
10 m
2 m
2 m
What is the volume of the figure?
Give an exact answer in terms of pi.
Answers
Answer:
Volume of the figure = 10π cubic meters
Step-by-step explanation:
Volume of the right prism like figure = Area of the base × Height
Area of the base of the prism = [tex]\frac{1}{4}(\pi r^{2})[/tex]
= [tex]\frac{1}{4}(\pi)(2)^2[/tex]
= π m²
Height of the prism = 10 m
Volume of the prism given in picture = π × 10
= 10π cubic meters
Answer: 10π
Step-by-step explanation:
Helpppppppppppppy pls
Answers
Answer:
Step-by-step explanation:
Touch screen maze portfolio if you need more info please comment on the question not answer it all troll answers will be removed
Answers
A maze game can be constructed successfully by abiding by the specified guidelines in a systematic manner. Here is a comprehensive guide consisting of multiple steps to create it:
What are the steps?1. Initially, plot the initiation point and conclusion point across different quadrants.
2. Commence the game: Participants must start from the starting point and locate the ending spot through the shortest possible route.
3. Illustrate two sample games through drawing colored paths utilizing pencils or markers which should then be described using coordinates for each route.
4. Compute the overall distance travelled by extracting geographical details available from the used path's coordinates via the distance formula.
5. Finally, determine the most concise path course among all other alternatives.
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Tara has two bags of marbles. Bag 1 contains 6 red marbles, 5 blue marbles, and 4 green marbles. Bag 2 contains 3 red marbles, 2 blue marbles, and 4 green marbles. Tara will randomly select 1 marble from each bag. What is the probability that Tara will select a red marble from each bag?
Answers
Answer: 26 - 6
Step-by-step explanation: i think sorry if rong
Review the graph of complex number z. What is the conjugate of z?
7 – 6i
6 – 7i
–7 + 6i
–6 + 7i
Answers
Answer: B. 6 - 7i
Step-by-step explanation:
The complex conjugate of the given graph of the complex number is 6-7i.
We have given that,
7 – 6i
6 – 7i
–7 + 6i
–6 + 7i
We have to determine the conjugate of z.
What is the conjugate of complex numbers?
changing the sign of the imaginary part of the complex number. To find the complex conjugate of 4+7i we change the sign of the imaginary part. Thus the complex conjugate of 4+7i is 4 - 7i.
Therefore the complex conjugate of the given graph of the complex number is 6-7i.
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A banner measures 5.4 feet long. How long does the banner measure in inches and yards?
Answers
Answer:
64.8 and 1.8
Step-by-step explanation:
The banner measure inches in yards are 64.8 and 1.8.
We have given that,
We have to determine the length does the banner measure in inches and yards.
What is the meaning of inches and yards?
An inch is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to 136 yard or 112 of a foot.
Therefore we get the banner measure inches in yards are 64.8 and 1.8.
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17.
Which pair of numbers is relatively prime? *
7 & 21
4 & 15
ОООО
6 & 9
9 & 27
Answers
Answer:
9 & 27
Step-by-step explanation:
since all prime numbers above 5 end in 1,3,7 and 9then to find a prime number between say 70 and 80 the only possibilities are 71,73,77,79
Answer:
9 & 27
Step-by-step explanation:
Plz mark as Brainliest...
What is the fraction ⁸⁄₂₀ in its simplest form?
Answers
Answer:
2/5
Step-by-step explanation:
dsadsadasddsadsadasddsadsadasddsadsadasddsadsadasd
Step-by-step explanation:
8/20=4/10=2/5
done by cancelling
hope it helps
If a triangle has a perimeter of 36 inches, which of the following would be the perimeter of the triangle
formed by connecting its midpoints?
(1) 18 inches
(3) 24 inches
(2) 20 inches
(4) 72 inches
Answers
Answer:
1) 18 inches
Step-by-step explanation:
By the Midsegment Theorem: A midsegment connecting two sides of a triangle is parallel to the third side and is half as long the third side.
ans: 36/2 = 18
Harry manages a sales force which sells several products in different sales territories. A random sample of 25 territories were selected and the data is provided in an Excel worksheet labelled Harrys. The variables include total sales credited to the sales representative (Sales), the length of time employed in months (time), the market potential (Poten), the advertising expense for the territory (AdvExp), the market share (Share), the change in market share over the previous three years (Change), the number accounts assigned to the sales representative (accounts), an index representing the workload (work), the rating on the last performance review (rating) and whether it is a star territory (star territories have performed well in the past).
Using the methods discussed in this class, determine the “best” regression model to predict Sales. Write a brief report (less than two pages) summarizing your analysis, including key statistical results, conclusions, and recommendations. Include any appropriate technical material in an appendix.
Answers
Answer:
13,000 i think
Step-by-step explanation: