Answer:
Proved
Step-by-step explanation:
Given
Integers: a, b, c
Required
Show that c is a multiple of a⁶
First, we need to list out the multiples of a³
[tex]a^3 -> a^3, a^6, a^9, a^{12}...[/tex]
Since b is a multiple of a³, then b can be any of the listed multiples
Next, is to list out the multiples of b²
[tex]b^2 -> b^2,b^4,b^6,b^8,b^{10}....[/tex]
Since c is a multiple of b², then c can be any of the listed multiples
To list out the multiples of a⁶, we have to get the common multiples of a³ and b² in terms of a
Substitute a³ for b in
[tex]b^2 -> b^2,b^4,b^6,b^8,b^{10}....[/tex]
[tex](a^3)^2 -> (a^3)^2,(a^3)^4,(a^3)^6,(a^3)^8,(a^3)^{10}....[/tex]
[tex]a^6 -> a^6,a^{12},a^{18},a^{24},a^{30}....[/tex]
Recall that c is a multiple of b²
From the above listed multiples, we have a⁶ listed as one of the multiple; Hence, c is a multiple of a⁶
Yes C should be multiple of [tex]a^6[/tex]
Calculation of the multiple:Since it is mentioned that b should be the multiple of [tex]a^3[/tex]
So,
[tex]b = a^3R[/tex] here some integer should be R
And, the c should be multiple of [tex]b^2[/tex]
So,
[tex]C = b^2 r[/tex] for some integer r
Now we have to substitute the value of b from the first equation
i.e.
[tex]C = (a^3R)^2r = a^6 (R^2r)[/tex]
Here [tex]R^2r[/tex] is some integer
so,
[tex]C = a^6R'[/tex]
Therefore, we can say that Yes C should be multiple of [tex]a^6[/tex]
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Can you please help me with this I’ll give you a Brainly list please it’s hard
Answer:
Your answer will be 6+6-17 hope this helps :)
Step-by-step explanation:
Jen classifies the number 4.567 as an irrational number because it does not repeat. Is Jen correct? Explain.
Answer: Jen is wrong about her classification.
Step-by-step explanation:
First of all, we know that the definition of an irrational number is that they are numbers that cannot be represented by a simple fraction and that they are never repeating decimals and they never end.
So, considering this, Jen is wrong because, yes it does not repeat but it DOES END unless it is not written in this problem that it continues on irrationally like pi. Hence, this number is not irrational.
The Jen classifies the number 4.567 as an irrational number is false.
It is required to find the number is rational and irrational numbers.
What is real number?Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
Given :
Jen's argument
We have
4.567 as an irrational number
The above claim is false because
4.567 =
4567/1000
When we divide the above number in the form of p/q and q≠0 then then number is rational number.
Therefore, the Jen classifies the number 4.567 as an irrational number is false.
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help I need to determine the slopes
Answer:
y-int: (0, -45)
x-int: (-10, 0)
Step-by-step explanation:
x-intercept is the x-value when y = 0
y-intercept is the y-value when x = 0
x-int:
When y = 0, x = -10, so (-10, 0)
y-in:
when x = 0, y = -45, so (0, -45)
please help me with this
which expression is equivalent to (12^4) 2/9^?
Answer:
(124)(29)
=10616832
Step-by-step explanation:
if you know the ratio of students to teachers is 5 to 1 and you know there are 15 teachers, how many students are there?
Answer:
Ratio = 5:1
= 5 / 1
Number of teachers = 15
Lets take the number of students = x
Therefore,
5:1 = x:15
= 5/1 = x/15
x = 15 × 5
= 75 students
Hope it helps!!
What is 4 4/5+7 3/5-6
Answer:
17.4
Step-by-step explanation:
44/5 = 8.8
73/5 = 14.6
8.8 + 14.6 = 23.4
23.4 - 6 = 17.4
Which of the following statements are always true? Justify your answers. a. If A + B = C, then AD' + BD' = CD' b. If A'B + A'C = A'D, then B + C = D c. If A + B = C, then A + B + D = C + D d. If A + B + C = C + D, then A + B = D
Answer:
a. True
B. False
C. True
D. False
Step-by-step explanation:
a.) A+B = C then AD' + BD' = CD'
AD'+BD' = D'(A+B)
and we already have that A+B = C
such that D'C = C'D
this statement is true
b.) A'B + A'C = A'D then B+C = D
let's have A = 1 and B= 0, C= 0 and D = 1
A'(0) + A'(0) = 1(1)
0+0 = 1
0 = 1
This is false because 0 is not equal to 1
c.) A+ B=C then A+B+D= C+D
If A+B+D= C+D
Then A+B=C
The statement is true
d.) A+B+C=C+D
A+B = D
let's equate A = 0
B= 0
C= 1
D= 1
from a+b = D
We have
0+0 = 1
0 is not equal to 1
The statement is false
Answer:
a. True
B. False
C. True
D. False
Step-by-step explanation:
a.) A+B = C then AD' + BD' = CD'
AD'+BD' = D'(A+B)
and we already have that A+B = C
such that D'C = C'D
this statement is true
b.) A'B + A'C = A'D then B+C = D
let's have A = 1 and B= 0, C= 0 and D = 1
A'(0) + A'(0) = 1(1)
0+0 = 1
0 = 1
This is false because 0 is not equal to 1
c.) A+ B=C then A+B+D= C+D
If A+B+D= C+D
Then A+B=C
The statement is true
d.) A+B+C=C+D
A+B = D
let's equate A = 0
B= 0
C= 1
D= 1
from a+b = D
We have
0+0 = 1
0 is not equal to 1
The statement is false
Step-by-step explanation:
Assume the random variable x is normally distributed with mean and standard deviation . Find the indicated probability.
Complete Question
Assume the random variable x is normally distributed with mean u=87 and standard deviation o=5. Find the indicated probability.
P(x<81)
P(x<81)=__(Round to four decimal places).
Answer:
The value is [tex]P(x < 81) = 0.11507[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 87[/tex]
The standard deviation is [tex]\sigma = 5[/tex]
The probability is mathematically represented as
[tex]P(x < 81) = P (\frac{X - \mu }{\sigma } < \frac{81 - 87 }{5 } )[/tex]
Generally [tex]\frac{X - \mu}{\sigma} = Z (The \ z-score \ of X )[/tex]
[tex]P(x < 81) = P (Z < - 1.2)[/tex]
From the z-table
[tex]P (Z < - 1.2) = 0.11507[/tex]
So [tex]P(x < 81) = 0.11507[/tex]
Tom Thomas took tennis lessons. He traveled 12 miles one way at an average cost of $0.42 per mile. His racket cost $94, balls cost $12.50, shoes cost $44.50, his warm-up was $34, and his shorts were $19.95. He paid 5% sales tax on his equipment, clothes, and warm-up. Tom also paid $20.00 per lesson for 12 lessons. He only had to pay for the warm-up one time. Including the cost of round trip travel, what is the total cost? $
Answer:
One Way Trip There = ($460.22)
There and Back Trip = ($465.26)
Enter the correct answer in the box replacing the values of m and b
Answer: f(x) = -2X + 5
Step-by-step explanation:
Which of the following is most likely the next step in the series?
o
Answer:
C
Step-by-step explanation:
the first shape has 6 edges, the second shape has 5 edges, the third shape has 4 edges, therefore the fourth shape has 3 edges (c)
is 7.69669669 a rational number
Answer:
yes it is
Step-by-step explanation:
hope this helps✨
A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of drawing a strawberry? (Please simplify your answer) 3 3 5 5 1/6 1/6 1/5
Answer:
[tex]Probability = \frac{1}{6}[/tex]
Step-by-step explanation:
Given
Grape = 15
Cherry = 7
Lemon = 3
Strawberry = 5
Total = 30
Required
Determine the probability of picking a strawberry
The probability of drawing a strawberry is calculated by dividing the number of strawberry by the total number of fruits as follows;
[tex]Probability = \frac{Strawberry}{Total}[/tex]
Substitute 5 for Strawberry and 30 for Total
[tex]Probability = \frac{5}{30}[/tex]
Divide the numerator and denominator by 5
[tex]Probability = \frac{1}{6}[/tex]
Hence, the required probability is [tex]\frac{1}{6}[/tex]
Use the ruler to measure the length of this object. (IMAGE BELOW)
Answer: 5 cm
Step-by-step explanation:
To use a ruler, you read it from left to right, where the numbers get larger and larger. The blue end of the ruler starts at 0 cm, where it should start. Going right, we see that it ends at 5 cm. Therefore, our answer is 5 cm.
Help me please! LAST TWO QUESTIONS.
Answer:
1) [tex](4x)(x+2)-x(3x+5)[/tex]
2A) [tex]w^2+3w[/tex]
2B) [tex]28\text{ in}^2[/tex]
Step-by-step explanation:
1)
First, let's write the expressions for the area of the entire shaded region and the white area.
The formula for the area of a rectangle is given by:
[tex]A=lw[/tex]
For the entire shaded rectangle, the length is (4x) and the width is (x+2). So, the area is:
[tex](4x)(x+2)[/tex]
For the white rectangle, the length is (3x+5) and the width is (x). So, the area is:
[tex]x(3x+5)[/tex]
The shaded area is the entire shaded rectangle minus the area of the white rectangle. Therefore, our expression would be:
[tex](4x)(x+2)-x(3x+5)[/tex]
2)
Part A)
So, we are given that the length of the rectangle is 3 inches greater than the width.
The area of a rectangle is given by:
[tex]A=lw[/tex]
So, let w be width and let l be the length.
Since the length is 3 inches greater than the width, this means that the l is (w+3).
Thus, substitute. Our expression will therefore be:
[tex]lw\\w(w+3)[/tex]
Since we want a polynomial, let's expand:
[tex]=w^2+3w[/tex]
Part B)
To find the area when the width is 4, substitute 4 for w:
[tex]w^2+3w\\=(4)^2+3(4)[/tex]
Square and multiply:
[tex]=16+12[/tex]
Add:
[tex]=28\text{ in}^2[/tex]
So the area is 28 square inches.
What is the average of 74 and 57?
Answer:
65.5
Step-by-step explanation:
(74 + 57)divided by 2 = 65.5
Write 3,141,500 in scientific notation.
Answer:
The answer is 3.14 * 10^-6
Answer:
3.1415 * 10^6
Step-by-step explanation:
Scientific notation is of the form a* 10 ^b where a is between 1 and less than 10
3,141,500
Move the decimal 6 places to the left
The exponent is the number of places you move the decimal
Since we move it to the left, it is positive
3.141500 * 10^6
Drop the trailing zeros
3.1415 * 10^6
Which number rounds to 4.3 when rounded to the nearest tenth?
Answer:
it is the same 4.3
Step-by-step explanation:
this numbers didn't add one number when you round(0,1,2.3.4)
this numbers(5,6,7,8,9), you add one number when you add
4.3 (the three is the tenth)and no number after it so its stell the same
The rounding number of 4.3 when rounded to the nearest tenth is 4.3
Here,
The number is 4.3
We have to find the rounding number of 4.3 nearest tenth.
What is Rounding number?
A method of approximating a number to its nearest place value is called Rounding of Numbers.
Now,
The number is 4.3
To round the decimal number to its nearest tenth, look at the hundredth place.
But here is no any number on hundredth number, hence no change occur for rounding 4.3 to the nearest tenth.
So, The rounding number of 4.3 when rounded to the nearest tenth is same as the number 4.3
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38 animals are at the aquarium. 22 animals are manatees and the rest are sea lions.
How many of the animals are sea lions?
22 manatees
? sea lions
38 animals
Answer:
16
Step-by-step explanation:
38-22=16
16 sea lions
Answer:
38-22=16.
16 sea lions.
when graphing the function f(x)=-|x+5|+12 on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function
Answer: is B
Step-by-step explanation:
-20, xmax
The most appropriate viewing window for determining the domain and range of the function is Xmin: –20, Xmax: 20Ymin: –20, Ymax: 20.
The given function is f(x)=-|x+5|+12.
We need to find the most appropriate viewing window for determining the domain and range of the function.
What is the domain and range of the function?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (-∞, ∞), {x|x∈R}
Range: (-∞, 12], {y|y≤12}
So,window=Xmin: –20, Xmax: 20Ymin: –20, Ymax: 20
Therefore, the most appropriate viewing window for determining the domain and range of the function is Xmin: –20, Xmax: 20Ymin: –20, Ymax: 20.
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Help will give brainliest
Answer:
[tex](-1)+(-3)=-4[/tex]
Step-by-step explanation:
We were originally on -1.
But we jumped to -4.
-4 is 3 spaces to the left of -1.
In other words, we subtract 3 into -1.
Another way of saying this is that we added -3 to -1.
Therefore, our equation is:
[tex](-1)+(-3)=-4[/tex]
A visitor guide for a downtown area lists many restaurants. Which of the following is an example of a quantitative variable the guide could report for each restaurant? A. the zip code of the restaurant B. the number of seats in the restaurant C. the type of cuisine the restaurant offers D. a restaurant critic’s letter grade (A–F)
The correct answer is B. The number of seats in the restaurant
Explanation:
The number of seats is a quantitative variable because this is expressed using numbers and can be understood through numbers. For example, the average of seats in the restaurants in the area can be calculated by finding the total of seats and dividing the number into the number of restaurants.
On the other hand, the type of cuisine and the restaurant critic's letter grade do not involve numbers but qualities, which make them qualitative variables. Also, even if zip codes are expressed using numbers these cannot be understood through them, for example, you cannot add two zip codes.
Answer:
B
Step-by-step explanation:
195.21 is 24.10% of what number?
Turn the percentage into a decimal.
24.10 / 100 = 0.241
Divide.
195.21 / 0.241 = 810
Therefore, 195.21 is 24.10% of 810
Best of Luck!
f(x)=-4x+1 Find the average rate of change from 2 to 5.
Answer:
- 4
Step-by-step explanation:
The slope of the line is the average rate of change of f(x)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
f(x) = - 4x + 1 ← is in slope- intercept form
with m = - 4 ← average rate of change
Round 630,379,982 to the nearest hundred thousand
Answer:
630,400,000
Step-by-step explanation:
630,379,982
The 3 above that is bold, between the 0 and the 7, is in the hundred thousands place.
To round to a place, change all digits to the right of that place to zero. If the digit immediately to the right is 0 through 4, you're done. If the digit immediately to the right is from 5 to 9, then you raise the digit you are rounding to by 1.
Step 1. Make all digits to the right of the hundred thousands digit 0.
630,300,000
Step 2. Since the digit immediately to the right of the hundred thousands digit was a 7, which is from 5 to 9, the digit we are rounding to goes up by 1. The 3 becomes 4.
630,400,000
Answer: 630,400,000
Can someone help? This is from Kahn Academy
Answer:
B. [tex] \frac{ {7}^{36} }{ {9}^{24} } [/tex]
Step-by-step explanation:
[tex] \bigg( {9}^{6} . {7}^{ - 9} \bigg ) ^{ - 4} \\ \\ = {9}^{6 \times ( - 4)} \times {7}^{ - 9 \times ( - 4)} \\ \\ = {9}^{ - 24} \times {7}^{36} \\ \\ = \frac{ {7}^{36} }{ {9}^{24} } \\ [/tex]
Which step in the problem-solving process includes the following statement? Identify the information the problem gives you. A. Understand B. Look back C. Solve D. Plan
Answer:plan
Step-by-step explanation:
Example
The size of a playground is 160 feet by 360
feet. A model is created that measures 4
inches by 9 inches.
Unit Rates
Answer:
The playground is 160ft by 360ft.
The model is 4in by 9in
First, 1ft = 12 inches.
Then the measures of the playground, in inches, is:
160*12in = 1920 in
360*12in = 4320in
The playground is 1920in by 4320in.
Then, the ratios between the measures of the playground and the model are:
1920in/4in = 480
4320in/9in = 480
This means that each inch in the model, represents 480 inches in the actual playground.
You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?
Answer:
y = 7.8x + 26
Step-by-step explanation:
Given the following :
Pearson's r = 0.78
Average consumption of ice cream = 5 grams per week (m) with Standard deviation (sd) = 1.5 grams
Average weight = 65 kg with standard deviation of 15kg
Formular for the regression line :
General regression formula :
y = mx + c
y = predicted variable ; m = slope or gradient ; x = predictor variable ; c = intercept
Gradient (m) = change in y / change in x
m = (sd y / sd x) * r
m = (sd weight / sd ice cream) × r
m = (15 / 1.5) × r
m = 10 × 0.78 = 7.8
Intercept:
mean of weight(y) - [Slope×mean of icecream(x)]
65 - [7.8 × 5]
65 - 39 = 26
Hence,
y = 7.8x + 26
PART 5 - Mathematical knowledge
If 4x + 12 = 0, then x=
A -16
B -12
С-3
D
1/3
Click the button or type the letter tot
Answer: C) -3
Step-by-step explanation: 4(-3) + 12 = 0