Answer:
option D is correct.
Step-by-step explanation:
We need to find the value of
[tex]\sum_{n=1}^{6} 4(3)^{n-1}[/tex]
Here value of n starts from 1 and goes on till 6
And we need to add the values of all the terms by putting value of n from 1 to 6
This can be written as:
[tex]=4(3)^{1-1}+4(3)^{2-1}+4(3)^{3-1}+4(3)^{4-1}+4(3)^{5-1}+4(3)^{6-1} \\ Solving\\=4(3)^0+4(3)^1+4(3)^2+4(3)^3+4(3)^4+4(3)^5\\=4(1)+4(3)+4(9)+4(27)+4(81)+4(243)\\=4+12+36+108+324+972\\=1456[/tex]
So, option D is correct.
Answer:
1456
Step-by-step explanation:
This is the sum of a geometric sequence
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
4[tex](3)^{n-1}[/tex] ← is in this form
with a = 4 and r = 3
The sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex], hence
[tex]S_{6}[/tex] = [tex]\frac{4(3^6-1)}{3-1}[/tex] = [tex]\frac{4(729-1)}{2}[/tex] = 2 × 728 = 1456
PLEASE HELP PLEASE PLEASE
44% of a number is 88. What is 1% of the number?
A) 2
B) 200
C) 38.72
D) 132
Answer: The answer to your question is 200
Step-by-step explanation: because when you are multiply a percentage by a whole number, you are trying to find what percentage of the whole number makes the problem true. In your case, the problem would be set up like this:
44% of what number is 88
0.44 of x is 88
So, now that you have the problem set up, the final answer would be 200 after you have gone through each answer and substituted each value to come up with a true statement
help asap, please!!!!!!!!
1/6p + (-4/5) is the equivalent expression. You have to add like terms, meaning constants are added to constants, variables are added to variables, etc. the result you get from adding like variables leaves you with 1/6p + (-4/5) or 1/6p - 4/5
1.) are positive fractions irrational numbers?
2.) are negative fractions irrational number?
thanks !
Answer:
1)no
2)no
Fractions are rational numbers
Step-by-step explanation:
irrational numbers are numbers which can't be written as ratios, fractions, or rational decimals
hope this helps!
For the inverse variation equation xy=k, what is the constant of variation, k, when x=-2 and y=5?
-10
-2/5
5/2
10
Answer:
-10
Step-by-step explanation:
xy = k
(-2)(5) = k
-10 = k
Answer: -10
Step-by-step explanation:
Given: The inverse variation equation is given by :-
[tex]xy=k[/tex]
To find : The constant of variation, k, when x=-2 and y=5
Substitute the given values of x and y in the given inverse equation , we get
[tex]-2\times 5=k\\\\\Rightarrow\ k=-10[/tex]
Hence, the value of constant of variation = -10
Which linear inequality is represented by the graph
For this case we have that the boundary line of inequality is dotted, therefore equality is not included.
We find the slope of the line, substituting two points that pass through it:
[tex](0,3)\\(3,5)\\m = \frac {5-3} {3-0} = \frac {2} {3}[/tex]
We evaluate a point within the region and see which case is met:
[tex](x, y) :( 0.6)[/tex]
We replace:
[tex]A) y <\frac {2} {3} x + 3\\6 <0 + 3\\6 <3[/tex]
It is not fulfilled, we discard the first option.
[tex]C) y> \frac {2} {3} x + 3\\6> 0 + 3\\6> 3[/tex]
Is fulfilled!
Answer:
Option C
find the given angle to the nearest degree.
Answer:
[tex]\alpha=44\°[/tex]
Step-by-step explanation:
By definition, the tangent of an angle is the quotient between the side opposite the angle and the side adjacent to the angle
In other words:
[tex]tan(\alpha) = \frac{opposite}{adjacent}[/tex]
In this triangle, the length of the side adjacent to the desired angle is 50, and the length of the opposite side is 48
So:
[tex]tan(\alpha) = \frac{48}{50}\\\\tan(\alpha)= 0.96[/tex]
Finally
[tex]\alpha =arctan(0.96)\\\\\alpha=44\°[/tex]
Answer:
Final answer is [tex]?=44[/tex] degree.
Step-by-step explanation:
Using given information in the picture, we need to find the missing value of angle "?"
Apply formula of tangent function which is :
[tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]
[tex]\tan\left(?^o\right)=\frac{48}{50}[/tex]
[tex]\tan\left(?^o\right)=0.96[/tex]
[tex]?=\tan^{-1}\left(0.96\right)[/tex] degree
[tex]?=43.830860672092581097187030418859[/tex] degree
Hence final answer is [tex]?=44[/tex] degree.
does this have a. Proportional relationship
No, to be proportional, there would be a consistent pattern between x and y. For example 2 times 2.5 is 5. And 3 times 2 is 6. The ratio is not the same.
how do i divide fractions ΓΓΓ
Dividing fractions is basically the same thing as multiplying but by the reciprocal. I will give an example.
1/2 divided by 1/3
To solve this you do 1/2 multiplied by 3/1 so you switch the numerator and denominator.
M is directly proportional to r cubed when r = 4, m = 160. Find the value of r when m = 540
Answer:
r = 6
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportionality
To find k use the condition r = 4 when M = 160
k = [tex]\frac{M}{r^3}[/tex] = [tex]\frac{160}{64}[/tex] = 2.5, so
M = 2.5r³ ← equation of proportionality
When M = 540, then
540 = 2.5 r³ ( divide both sides by 2.5 )
216 = r³ ( take the cube root of both sides )
r = [tex]\sqrt[3]{216}[/tex] = 6
Which expression is equivalent to −1/12x−1/3 ?
1/12(−x+4)
1/12(−x−1/4)
1/12(−x−1/3)
1/12(−x−4)
The answer is the last one, 1/12(-x-4).
Explanation:
Find the domain and range !!! 10 points math 3
Answer:
The domain = (-∞ , -1/4) ∪ (-1/4 , ∞)
The range = (-∞ , 21/4)∪(21/4 , ∞)
The answer is not in the choices
Step-by-step explanation:
* Lets revise how to find the inverse function
- At first write the function as y = f(x)
- Then switch x and y
- Then solve for y
- The domain of f(x) will be the range of f^-1(x)
- The range of f(x) will be the domain of f^-1(x)
* Now lets solve the problem
- At first find the domain and the range of f(x)
∵ f(x) = (x - 9)/(21 - 4x)
- The domain is all real numbers except the value which
makes the denominator = 0
- To find this value put the denominator = 0
∴ 21 - 4x = 0 ⇒ subtract 21 from both sides
∴ -4x = -21 ⇒ ÷ -4 both sides
∴ x = 21/4
∴ The domain = R - {21/4} OR the domain = (-∞ , 21/4)∪(21/4 , ∞)
* Now lets find the range
- The range will be all the values of real numbers except -1/4
because the horizontal asymptote equation is y = -1/4
- To find the horizontal asymptote we find the equation y = a/b
where a is the coefficient of x up and b is the coefficient of x down
∵ The coefficient of x up is 1 and down is -4
∴ The equation y = 1/-4
∴ The value of y = -1/4 does not exist
∴ The range = R - {-1/4} OR the range = (-∞ , -1/4) ∪ (-1/4 , ∞)
* Switch the domain and the range for the f^-1(x)
∴ The domain = (-∞ , -1/4) ∪ (-1/4 , ∞)
∴ The range = (-∞ , 21/4)∪(21/4 , ∞)
The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 7.4% per hour. How many hours does it take for the size of the sample to double
Answer:18.12
Step-by-step explanation:
which value makes this equation true -4x = 20
Answer:
x= -5 makes the given equation -4x = 20 true
Step-by-step explanation:
We have been given the equation;
-4x = 20
we are to determine the value of x that will make the equation true. We simply make x the subject of the formula;
divide both sides of the equation by -4;
(-4x)/(-4) = 20/(-4)
x = -5
Therefore, x= -5 makes the given equation -4x = 20 true
Answer:
[tex]x=-5[/tex]
Step-by-step explanation:
The given linear equation is:
-4x = 20
To find the value of x that makes the equation true, we need to solve for x.
We divide both sides by -4 to obtain:
[tex]\frac{-4x}{-4}=\frac{20}{-4}[/tex]
This is the sane as:
[tex]\frac{-4x}{-4}=\frac{-5\times-4}{-4}[/tex]
We cancel out the common factors to get:
[tex]x=-5[/tex]
a rectangular prism with dimensions 3 by 4 by 8 has the same volume as a different rectangular prism with dimensions 4 by 4 by what?
let's recall that the volume of a rectangular prism is simply the product of its 3 dimensions.
so the volume for the first one is simply 3*4*8 = 96.
now, let's do some quick prime factoring of that 96
96 = 2*2*2*2*2*3
since we know the factors of 96, and we can rearrange them in any way we wish and will always have a product of 96, well, le'ts do some rearranging for the second prism.
the second prism has 4 and 4, namely 2*2 and 2*2, what's leftover? 2*3.
so the second prism must be (2*2) * (2*2) * (2*3), namely a 4x4x6.
Help please and explanation please
For this case we must add the given series. We expanded the series for each of the values of i, that is, from 1 to 5:[tex]3 (1) +3 (2) +3 (3) +3 (4) +3 (5) =\\3 + 6 + 9 + 12 + 15 =[/tex]
We add the terms:
[tex]9 + 9 + 12 + 15 =\\18 + 12 + 15 =\\30 + 15 =\\45[/tex]
Finally, the value of the given series is 45.
Answer:
45
Write an equation for the sentence "The product of a number n and 7.7 equals 112.42." Solve for the variable.
Answer:
[tex]7.7n=112.42[/tex]
[tex]n=14.6[/tex]
Step-by-step explanation:
The product is the result obtained by multiplying two factors. Then, the sentence ""The product of a number n and 7.7 equals 112.42" can be expressed with the following equation:
[tex]7.7n=112.42[/tex]
To solve for the variable "n", you has two apply the Division property of equality and divide both sides of the equation by 7.7
Therefore, the value of "n" is:
[tex]\frac{7.7n}{7.7}=\frac{112.42}{7.7}\\\\n=14.6[/tex]
Scientists discovered a large star 250,000 light-years from Earth. A light-year
is about 5,880,000,000,000 miles. What is the distance of the large star from
Earth in scientific notation?
Answer:
B. 1.47*10^18
Step-by-step explanation:
Given
Distance of largest start from earth in light years = 250000
1 light year = 5880000000000 miles
So,
Distance of largest star from earth in miles = 250000 * 5880000000000
= 1470000000000000000 miles
In order to convert in scientific notation, point will be moved 18 places to the left, so the number will become:
1.47* 10^18 miles
So option B is correct..
Answer: OPTION B
Step-by-step explanation:
Scientific notation has the form:
[tex]a10^n[/tex]
Where "a" is a number between 1 and 10 but is not less than 10 and "n" is an integer.
If a light-year is about 5,880,000,000,000 miles and the large star is 250,000 light-years from Earth, then this distance in miles is:
[tex]d=(250,000)(5,880,000,000,000)\\d=1,470,000,000,000,000,000.0\ mi[/tex]
To express this distance in scientific notation, the decimal point must be after the first digit. You can observe that the decimal point must be moved 18 places, then:
[tex]a=1.47[/tex] and [tex]n=18[/tex]
Therefore, you get that the distance of the large star from Earth in scientific notation is:
[tex]d=1.47*10^{18}\ mi[/tex]
18 more than a number is 29
This is the answer (I believe): 18 + x = 29
Answer:
11
Step-by-step explanation:
29-18 is 11
I need the answer for this problem please
Answer:
B
Step-by-step explanation:
Find all probabilities:
A. False
[tex]Pr(\text{red shirt}|\text{large shirt})=\dfrac{\text{number red large shirts}}{\text{number large shirts}}=\dfrac{42}{77}=\dfrac{6}{11}\\ \\Pr(\text{large shirt})=\dfrac{\text{number large shirts}}{\text{number shirts}}=\dfrac{77}{165}=\dfrac{7}{15}[/tex]
B. True
[tex]Pr(\text{blue shirt}|\text{large shirt})=\dfrac{\text{number blue large shirts}}{\text{number large shirts}}=\dfrac{35}{77}=\dfrac{5}{11}\\ \\Pr(\text{blue shirt})=\dfrac{\text{number blue shirts}}{\text{number shirts}}=\dfrac{75}{165}=\dfrac{5}{11}[/tex]
C. False
[tex]Pr(\text{shirt is medium and blue})=\dfrac{\text{number medium and blue shirts}}{\text{number shirts}}=\dfrac{48}{165}=\dfrac{16}{55}\\ \\Pr(\text{medium shirt})=\dfrac{\text{number medium shirts}}{\text{number shirts}}=\dfrac{88}{165}=\dfrac{8}{15}[/tex]
D. False
[tex]Pr(\text{large shirt}|\text{red shirt})=\dfrac{\text{number red large shirts}}{\text{number red shirts}}=\dfrac{42}{90}=\dfrac{7}{15}\\ \\Pr(\text{red shirt})=\dfrac{\text{number red shirts}}{\text{number shirts}}=\dfrac{90}{165}=\dfrac{6}{11}[/tex]
Point S is _____.
1.inside the circle
2.on the circle
3.collinear with the diameter AC.
4.outside the circle
Answer:
point s is inside the circle.
Point s is inside the circle
Plz help god blees if you do it all i will give u BRAINLIEST
IF YOU DO ONE THAT WILL NOT BE HELPING AND I WILL REPORT YOU!!!!!!!!!!
Answer:
the first one is 23
the second one is 70-79
the third one is 11
Step-by-step explanation:
this is because frequency refers to the amount of people who got the scores on the x-axis.
so for the first one you would count up how many people participated i.e. 2+9+7+5 = 23
the second one is asking for the mode test score and mode refers to the most common, so the most common test score is the 70-79 bar
the third one is asking for how many people scored below 80, which is 11 as 2 people scored 60-69 and 9 scored 70-79 on the test (2+9=11)
Hope this helps :)
the answer is 23
hope this helps
5x=3x+14
Solve for x and name the steps taken.
Answer:
Simplifying
5x = 3x + 14
Reorder the terms:
5x = 14 + 3x
Solving
5x = 14 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
5x + -3x = 14 + 3x + -3x
Combine like terms: 5x + -3x = 2x
2x = 14 + 3x + -3x
Combine like terms: 3x + -3x = 0
2x = 14 + 0
2x = 14
Divide each side by '2'.
x = 7
Simplifying
x = 7
Step-by-step explanation:
What is the inverse equation of the function, y=5x-4
Answer:
y^-1 = (x + 4)/5
Step-by-step explanation:
To find the inverse equation of the function y=5x - 4, first we need to switch the x and y:
→ y = 5x - 4
→ x = 5y - 4
Now, solving for 'y':
→ x = 5y - 4
→ x + 4 = 5y
→ y = (x + 4)/5
therefore, the inverse equation is: y^-1 = (x + 4)/5
What is the complete factorization of the polynomial below x^3+x^2+9x+9
The complete factorization of the polynomial [tex]x^3 + x^2 + 9x + 9[/tex] is [tex]x + 1)(x^2 + 9)[/tex] using real coefficients, and [tex](x + 1)(x + 3i)(x - 3i)[/tex] using complex coefficients.
The complete factorization of the polynomial [tex]x^3 + x^2 + 9x + 9[/tex] can be found by grouping and factoring terms with common factors.
To proceed, let's group the terms as follows: [tex](x^3 + x^2) + (9x + 9).[/tex]
Factoring out the common factors in each group gives us [tex]x^2(x + 1) + 9(x + 1).[/tex]
Now, we notice that (x + 1) is a common factor in both terms, so we can factor it out to get our complete factorization: [tex](x + 1)(x^2 + 9).[/tex]
As [tex]x^2 + 9[/tex] can't be factored further using real coefficients, this is the fullest factorization in the realm of real numbers.
However, if complex numbers are considered, [tex]x^2 + 9[/tex] can be expressed as [tex](x + 3i)(x - 3i)[/tex], where i is the imaginary unit.
So, the complete factorization using complex coefficients is [tex](x + 3i)(x - 3i)[/tex]
What is the point slope form of a line with slope -5 that contains the point (2,-1)?
A.y+1=-5(x-2)
B.y-1=5(x+2)
C.y-1=-5(x-2)
D.y+1=5(x+2)
Answer:
a
Step-by-step explanation:
What is the measure of ced?
Answer:
212°
Step-by-step explanation:
We have the measure of CE and the measure of ED, so all we have to do is combine those two to get the measure of CED.
The arc CE measures 52 degrees.
The arc ED measures 160 degrees
The arc CED is the sum of arc CE and ED, so:
CED = 52° + 160° = 212°
We don't have any length measurement inside that circle to calculate the length of the arc CED in inches, centimeters or otherwise... so we can only measure it degrees.
6. When making adjusting entries, which account is never affected?
A. Capital
B. Withdrawal
C. Fees Expense
D. Cash
It never affects D. Cash
Answer:
Cash is never affected.
Step-by-step explanation:
When making adjusting entries, cash is never impacted.
Adjusting entries means to make the account up to date at the end of the accounting period.
All adjusting entries affect a minimum of one income statement account and one balance sheet account, but this never affects cash.
Which linear function represents the line given by the point-slope equation y – 2 = 4(x – 3)?
y = 4x - 10. The linear functions y = 4x - 10 represent the line given by the point-slope equation y - 2 = 4(x - 3).
In order to solve this problem, we have to take the point-slope equation y - 2 = 4(x - 3) and convert it to the linear function form y = mx + b as follow:
y - 2 = 4(x - 3)
y - 2 = 4(x) - (4)(3)
y - 2 = 4x - 12
y - 2 + 2 = 4x -12 +2
y = 4x - 10 (Linear function)
Which graph represent the equation y=-2
Answer:
The top left graph.
Step-by-step explanation:
That is because it goes through y=-2
Final answer:
To find the total cost per mile to rent the car, add the rental cost for 5 days to the gasoline cost, then divide by the miles driven. Ruth Barr's total cost per mile was approximately $0.3785.
Explanation:
To calculate the total cost per mile to rent the car, we need to add the cost of renting the car for 5 days to the cost of gasoline and then divide the sum by the number of miles driven.
Calculate the rental cost for 5 days: 5 days × $59.95/day = $299.75.
Add the cost for gasoline: $299.75 (rental cost) + $137.76 (gasoline) = $437.51.
Divide the total cost by the number of miles driven: $437.51 ÷ 1156 miles = approximately $0.3785 per mile.
The total cost per mile Ruth Barr spent to rent the car was approximately $0.3785.
What is the sokution of -(x)=-8
Answer:
x = 8
Step-by-step explanation:
Given
- x = - 8 ( multiply both sides by - 1
- x × - 1 = - 8 × - 1, that is
x = 8
Answer:
x = 8
Step-by-step explanation:
Given
- x = - 8 ( multiply both sides by - 1
- x × - 1 = - 8 × - 1, that is
x = 8