Answer.
a. Population is the total number of voters in the constituency, that is 10000
b. the parameter is the unknown character of the population, that is 35% of 10000= 3,500
c. Statistics of interest is know character from the sample, that is 40% of 200= 80
d. The two answers are not surprisingly, because the sample is a portion of the population and we expect it to be smaller that the population. Thus, parameter must be bigger than statistics of interest.
d) ii. If another 200 sample was to be taken, we expect to see an increase in a statistics of interest.
Thus my answer, please help by your approval as fast as you can
Which of the following is a geometric sequence?
A. 5, 12, 17, 29, 46
B. 3, 7, 11, 15, 19
C. 4, 6, 10, 16, 26
D. 4, 16, 64, 256
The given geometric sequence is 4, 16, 64, 256.
What is Geometric Sequence?It is defined as the sequence where the ratio between the adjacent numbers is constant.It is represented as: G = arⁿ (a = first term; r = common ratio; n = nth term).Given: Geometric Sequences
Among the given sequences, geometric sequence will be identified if the ration between two adjacent numbers is constant for the given sequence.
Option (A): 5, 12, 17, 29, 46
Common ratio (r) is:
r = 12/5 = 2.4
r = 17/12 = 1.4
r = 29/17 = 1.7
r = 46/29 = 1.6
Here, common ratio is not constant.
Hence, option (A) is incorrect.
Option (B): 3, 7, 11, 15, 19
Common ratio (r) is:
r = 7/3 = 2.3
r = 11/7 = 1.5
r = 15/11 = 1.3
r = 19/15 = 1.3
Here, common ratio is not constant.
Hence, option (B) is incorrect.
Option (C): 4, 6, 10, 16, 26
Common ratio (r) is:
r = 6/4 = 1.5
r = 10/6 = 1.66
r = 16/10 = 1.6
r = 26/16 = 1.62
Here, common ratio is not constant.
Hence, option (C) is incorrect.
Option (D): 4, 16, 64, 256
Common ratio (r) is:
r = 16/4 = 4
r = 64/16 = 4
r = 256/64 = 4
Here, common ratio is constant.
Hence, option (D) is correct.
Therefore, the geometric sequence is 4, 16, 64, 256.
Correct option is (D).
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Given circle P, find mDBC
Answer:
240 i think
Step-by-step explanation:
Answer:
[tex]m\widehat {DBC}=240^{\circ}[/tex]
Step-by-step explanation:
We have been given image of a circle. We are asked to find measure of arc DBC.
[tex]m\widehat {DBC}=\widehat {DB}+\widehat {BA}+\widehat {AC}[/tex]
We know that central angle is equal to measure of corresponding arc, so measure of arc DB will be equal to measure of angle DPB.
Since angle APC and angle DPB are vertical angles, so measure of angle DPB will be equal to measure of angle APC that is 60 degrees.
[tex]m\widehat {DBC}=60^{\circ}+120^{\circ}+60^{\circ}[/tex]
[tex]m\widehat {DBC}=120^{\circ}+120^{\circ}[/tex]
[tex]m\widehat {DBC}=240^{\circ}[/tex]
Therefore, the measure of arc DBC is 240 degrees.
The length of a rectangle is 5 more than 3 times its width. The perimeter of the rectangle is 58 in. What is the length of the rectangle?
A. 23 in.
B. 29 in.
C. 32 in.
D. 35 in.
Answer:
The correct answer is option A. 23 in
Step-by-step explanation:
It us given that, the length of a rectangle is 5 more than 3 times its width. The perimeter of the rectangle is 58 in.
To find the length of rectangle
Let 'x' be the width of rectangle.
Length = 3x + 5
Perimeter of rectangle = 2(length + width)
58 = 2(3x + 5 + x)
58 = 2(4x + 5)
29 = 4x + 5
4x = 29 - 5
4x = 24
x = 24/4 = 6
Therefore length of rectangle = 3x + 5
= 3*6 + 5 = 23 in
The correct answer is option A. 23 in
Using the following Venn Diagram what is the probability of selecting a letter that is neither blue nor red?
Every letter is either red or blue. So the probability is 0.
[tex]|\Omega|=7\\|A|=0\\\\P(A)=\dfrac{0}{7}=0[/tex]
Rachel read 30 minutes for every 10 minutes that she spent watching television. Nicolas read 45 minutes for every 15 minutes that he watched television. The ratio of time that Rachel and Nicolas spent reading to the time they spent watching television is
Answer:
Both 3:1
Step-by-step explanation:
30:10 Divide by 10
3:1
45:15 Divided by 15
3 : 1
Answer:
the same
Step-by-step explanation:
I really need help with this problem
Answer:
(g◦f)(-6) = -9
Step-by-step explanation:
(g◦f)(-6) means g(f(-6))
Put the number where the variable is and evaluate.
f(-6) = 3/2(-6) +5 = -9 +5 = -4
g(f(-6)) = g(-4) = 7 -(-4)² = 7 -16 = -9
Then ...
(g◦f)(-6) = -9
What are the zeros of the following quadratic equation: y = 6x^2 - 17x - 3 Step by Step
Answer:
x = 3, x = -1/6 are the zeros
Step-by-step explanation:
I find graphing the equation using a graphing calculator to be about the fastest way to find the zeros.
__
For this equation, you can look for factors of 6·(-3) = -18 that have a sum of -17. Those are -18 and +1, so the factorization of the equation is ...
y = (1/6)(6x -18)(6x +1) = (x -3)(6x +1)
The roots are the values of x that make the factors be zero, so x=3 and x=-1/6.
__
You can also use the quadratic formula to find the zeros. That tells you the solution to ...
ax² +bx +c = 0
is
x = (-b ±√(b²-4ac))/(2a)
Comparing your equation to the standard form, you can identify the coefficients as ...
a = 6, b = -17, c = -3
so the zeros are ...
x = (-(-17) ±√((-17)² -4(6)(-3)))/(2(6))
x = (17 ±√369)/12 = (17 ±19)/12 = {-2, 36}/12 = {-1/6, 3}
The zeros are x = -1/6 and x = 3.
To find zeros of a quadratic equation, you use the quadratic formula. Applying this formula to the equation y = 6x^2 - 17x - 3 yields two solutions, representing the two points where the function intersects the x-axis.
Explanation:The subject of this question concerns finding the zeros of a given quadratic equation, y = 6x^2 - 17x - 3. Zeros are the x-values that make the equation equal to zero or to point where the function intersects the x-axis.
To find the zeros, we'll use the quadratic formula, which is derived from an equation of the form ax² + bx + c = 0: x = [ -b ± sqrt(b^2 - 4ac) ] / (2a).
Applying the quadratic formula to your equation, with a = 6, b = -17, and c = -3, we get the two solutions, which are the zeros of the equation: x = [ 17 ± sqrt((-17)^2 - 4*6*-3) ] / (2*6). Computing this, we get two solutions, or two zeros, which are the points where your function y = 6x^2 - 17x -3 crosses the x-axis.
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On the morning of June 4, the stock of Nagasaki Corporation opened at a price of $331⁄8 per share. At the end of the day, the price had risen $41⁄4 per share. What was the price at the end of the day?
Answer:
$37 3/8
Step-by-step explanation:
Add the rise to the opening price to find the closing price.
33 1/8 + 4 1/4 = (33 +4) + (1/8 +2/8) = 37 3/8 . . . . . . dollars per share
Final answer:
The closing price of Nagasaki Corporation's stock, after adding the increase of [tex]\$4 \frac{1}{4}[/tex]to the opening price of [tex]\$33\frac{1}{8}[/tex], was [tex]\$37\frac{3}{8}[/tex] per share.
Explanation:
The student asked: On the morning of June 4, the stock of Nagasaki Corporation opened at a price of [tex]$33\frac{1}{8}[/tex]per share. At the end of the day, the price had risen [tex]$4 \frac{1}{4}[/tex] per share. What was the price at the end of the day?
To find the closing price of the stock, we need to add the increase to the opening price:
Convert the mixed numbers to improper fractions: [tex]\$33\frac{1}{8} = \frac{265}{8} \ and\ \$4\frac{1}{4} = \frac{17}{4}[/tex]
Find a common denominator to add the fractions: Since 8 and 4 are both multiples of 4, we will convert [tex]\frac{17}{4} to \frac{34}{8}.[/tex]
Add the fractions [tex]: \frac{265}{8} + \frac{34}{8} = \frac{299}{8}[/tex]
Convert the improper fraction back to a mixed number: [tex]\frac{299}{8} = $37\frac{3}{8}[/tex]
Therefore, the closing price of the stock was [tex]$37\frac{3}{8}[/tex]per share.
Look at the figure:
An image of a right triangle is shown with an angle labeled x.
If tan x° = 11 divided by r and cos x° = r divided by s, what is the value of sin x°?
sin x° = s divided by 11
sin x° = 11 divided by s
sin x° = 11r
sin x° = 11s
Answer:
sin(x°) = 11/s
Step-by-step explanation:
The tangent is the ratio of sine to cosine, so ...
tan(x°) = sin(x°)/cos(x°)
Multiplying by cos(x°) gives ...
sin(x°) = cos(x°)·tan(x°) = (r/s)·(11/r)
sin(x°) = 11/s
Answer:
sin x° = 11 divided by s
Step-by-step explanation:
Given,
tan x° = 11 divided by r
[tex]\implies tan x^{\circ}=\frac{11}{r}[/tex]
Also, cos x° = r divided by s
[tex]\implies cos x^{\circ}=\frac{r}{s}[/tex]
We know that,
[tex]\frac{sinx^{\circ}}{cos x^{\circ}}=tan x^{\circ}[/tex]
[tex]\implies sinx^{\circ}= tan x^{\circ}\times cos x^{\circ}[/tex] ( by cross multiplication )
By substituting the values,
[tex]sin x^{\circ}=\frac{11}{r}\times \frac{r}{s}=\frac{11r}{rs}=\frac{11}{s}[/tex]
⇒ sin x° = 11 divided by s
20 points if you help
(08.02 MC)
A pair of equations is shown below:
y = 6x − 4
y = 5x − 3
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
A
The first equation has slope 6 and y intercept -4. I'd plot y intercept (0,-4) and (1,2), and connect the dots and extend for the first line.
The second equation has slope 5 and y intercept -3. I'd plot y intercept (0,-3) and (1,2), and connect the dots and extend for the second line.
We stumbled on the solution, both lines contain (1,2)
B
I don't like the graphing. This is algebra, not connect the dots.
We have two equations for y, we equate them to find the x where they meet.
6x - 4 = 5x - 3
6x - 5x = -3 + 4
x = 1
y = 6(1) - 4 = 2
Check: y = 5(1) - 3 = 2, good
Answer: (1, 2)
Find the area of the trapezoid
Answer:
C. [tex]52\sqrt{3}\ ft^2[/tex]
Step-by-step explanation:
Use formula for the area of trapezoid
[tex]A=\dfrac{a+b}{2}\cdot h,[/tex]
where a is the smaller base, b is the larger base and h is the height.
From the diagram,
[tex]a=11\ ft\\ \\b=15\ ft\\ \\h=4\sqrt{3}\ ft[/tex]
So, the area of trapezoid is
[tex]A=\dfrac{11+15}{2}\cdot 4\sqrt{3}=13\cdot 4\sqrt{3}=52\sqrt{3}\ ft^2[/tex]
Which formula can be used to sum the first n terms of a geometric sequence?
Answer:
The correct answer option is B. [tex] S _ n = a _ 1 [ \frac { 1 - r ^ n } { 1 - r } ] [/tex].
Step-by-step explanation:
The following is the formula that is used to find the sum of a geometric progession:
[tex] S _ n = a _ 1 [ \frac { 1 - r ^ n } { 1 - r } ] [/tex]
where [tex]S_n[/tex] is the sum, [tex]a_1[/tex] is the first term, [tex]r[/tex] is the common ratio while [tex]n[/tex] is the number of terms.
The formula which can be used to find the sum of the first n terms of a geometric sequence is:
[tex]S_n=a_1(\dfrac{1-r^n}{1-r})[/tex]
Step-by-step explanation:Geometric sequence--
A sequence is said to be a geometric sequence if each of the term of a sequence is a constant multiple of the preceding term of the sequence.
This constant multiple is known as a common ratio and is denoted by r.
Also, if the first term of the sequence is: [tex]a_1[/tex]
Then the sequence is given by:
[tex]a_1,\ a_2=a_1r,\ a_3=a_1r^2,\ a_4=a_1r^3,\ .............a_n=a_1r^{n-1},\ .....[/tex]
The sum of the first n terms of the sequence is given by:
[tex]S_n=a_1(\dfrac{1-r^n}{1-r})[/tex]
A box has a length of 4 feet, a width of 2 1/2 feet, and a height of 1 3/4 feet. What is the volume of the box? A. 17 1/2 B. 8 3/8 C. 8 3/4 D.35 cubic inches
Answer:
A. 17 1/2 . . . cubic feet
Step-by-step explanation:
The volume is the product of the length, width, and height. If your calculator doesn't deal with mixed numbers, it can be convenient to use one that does.
(4 ft)(2 1/2 ft)(1 3/4 ft) = 17 1/2 ft³
The volume of the box is 17 1/2 cubic feet.
____
You can also convert the numbers to decimal to use on your calculator:
4 × 2.5 × 1.75 = 17.500
Or convert them to improper fractions:
4 × 5/2 × 7/4 = 35/2 = 17 1/2
Final answer:
The volume of the box is 17 1/2 cubic feet, making the correct answer A. 17 1/2.
Explanation:
To find the volume of the box, we need to multiply its length, width, and height together.
The formula for volume is Volume = length × width × height.
Given that the box has a length of 4 feet, a width of 2 1/2 feet, and a height of 1 3/4 feet, we first need to convert these measurements into improper fractions or decimals to make the multiplication easier.
Width: 2 1/2 feet = 5/2 feet
Height: 1 3/4 feet = 7/4 feet
Volume = 4 feet × (5/2 feet) × (7/4 feet) = 20/2 × 7/4 = 10 × 7/4 = 70/4 = 17 1/2 cubic feet.
Therefore, the correct answer is A. 17 1/2 cubic feet.
How would you describe the difference between the graphs of f(x)=x^2 + 4 and g(y)=y^2+4?
On a hike, 5 children equally shared a box of granola bars. There were g granola bars in the box. Which equation shows the number of granola bars, n, each child received?
Answer: n = g/5
Step-by-step explanation:
Divide 1/3 yd by 9/13 ? please show work
Answer:
13/27
Step-by-step explanation:
1/3 ÷ 9/13
Copy dot flip
1/3 * 13/9
13/27
One number is two more than four times another. If their sum is decreased by two, the result is twenty-five. Find the
numbers
Step-by-step explanation & answer:
Let
x = "one number", then
4x+2 = "the other number"
If the sum is decreased by two, that gives
sum decreased by two = (x+4x+2) - 2 = 5x
The sum decreased by two = 25 (given)
therefore
5x = 25
x = 5
So
"one number" = 5
"another number" = 4x+2 = 4*5+2 = 22
What is the sum of the geometric sequence 3,12,48... if there are 8 terms?
A) 21,845
B)43,690
C)65,535
D)87,380
Answer:
C) 65,535
Step-by-step explanation:
You can add up the 8 terms ...
3, 12, 48, 192, 768, 3072, 12288, 49152
to find their sum is 65535.
_____
Estimating
Knowing the last term (49152) allows you to make the correct choice, since the sum will be more than that and less than double that.
_____
Using the formula
You know the formula for the sum of a geometric sequence is ...
S = a1(r^n -1)/(r -1)
where a1 is the first term (3), r is the common ratio (4), and n is the number of terms (8).
Filling in the values, you find the sum is ...
S = 3(4^8 -1)/(4-1) = 4^8 -1 = 65535
The sum of the geometric sequence 3, 12, 48, ... with 8 terms is 65,535. We use the geometric sum formula and identify a common ratio of 4 to compute the answer, which is option C.
Explanation:To find the sum of a geometric sequence, we use the formula S = a * (1 - r^n) / (1 - r), where S is the sum of the sequence, a is the first term, r is the common ratio, and n is the number of terms. In this sequence, the first term a is 3, and we can find the common ratio r by dividing the second term by the first term: r = 12 / 3 = 4. With 8 terms in the sequence, we can calculate the sum.
S = 3 * (1 - 4^8) / (1 - 4) = 3 * (1 - 65536) / (1 - 4) = 3 * (-65535) / (-3) = 65535.
Therefore, the sum of the sequence is 65,535, which corresponds to option C.
CHOOSE 1 ANSWER:
A
B
C
D
The equation used to solve for x in the given diagram is 7x + 11x = 90, representing the total sum as 90 degrees.
In the diagram, you have an angle formed by two given lines. To find the value of x, you can use the fact that the total sum is 90 degrees.
1. The first angle of the diagram is labeled as 7x.
2. The second angle of the diagram is labeled as 11x.
So, the equation for the sum of these angles should equal 90 degrees:
7x + 11x = 90
Now, you can simplify the equation:
18x = 90
To isolate x, divide both sides by 18:
18x / 18 = 90/ 18
x = 5
So, the equation used to solve for x is indeed 7x + 11x = 90, which simplifies to 18x = 90 when considering the angles around the point.
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The given question pertains to different aspects of probability in Mathematics, such as combinations, proportions and matched pairs. Each concept is used to determine the likelihood of an event occurring and they all play integral roles in statistical analysis.
Explanation:The details indicate that this question pertains to probability in Mathematics especially applied to situations like combinatorics, proportions and matched pairs. So let's explore each of those concepts with the details given:
Combinations and Probability
In probability, the concept of combinations is important because it helps to determine the likelihood of a particular event occurring. For instance, P(choosing all five numbers correctly) relates to the probability of choosing numbers correctly in a given set. It's determined by P(choosing 1st number correctly) * P(choosing 2nd number correctly) * P(choosing 5th number correctly).
Proportions
The term 'two proportions' perhaps refers to odds ratio or probability comparison between two events.
Matched pairs, dependent groups
This is a statistical technique often used in studies where each individual or item has a unique match - for example, a study comparing the math scores of twins. Here, it seems like an insight into statistical analysis where outcomes are compared within matched pairs. Therefore, these different concepts are all part of probability and statistics.
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The volume of a cube with side length x inches is x^3 cubic inches. If a cube has volume 1000 cubic inches, what is its side length (in inches)?
Answer:
10"
Step-by-step explanation:
The volume for a cube is V = l × w × h
But since this is a cube, all the sides aree the same length, so we could rewrite this in terms of x as:
V = [tex]x^3[/tex]
If we know the volume to be 1000, we sub it in for V:
[tex]1000=x^3[/tex]
We "undo" a cube by taking the cubed root of both sides. The cubd root of x cubed is just x, and the cubed root of 1000 is 10. Therefore, x = 10
How to subtract a negative number from a positive number
Answer:
googles explanation is below
Step-by-step explanation:
Rule 3: Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. Basically, - (-4) becomes +4, and then you add the numbers. For example, say we have the problem -2 - –4.
What is the answer
Square EFGH stretches vertically by a factor of 2.5 to create rectangle E′F′G′H′. The square stretches with respect to the x-axis. If point H is located at (-2, 0), what are the coordinates of H′ ?
Answer:
The coordinates of H′ are (-2,0).
Step-by-step explanation:
It is given that square EFGH stretches vertically by a factor of 2.5 with respect to the x-axis to create rectangle E′F′G′H′.
If a figure stretches vertically by a factor of 2.5 with respect to the x-axis, then the x-coordinates remains same and the points which lie on the axis are also remains the same after stretch.
It is given that the coordinates of H are (-2,0). This point lie on the x-axis, therefore it will remains the same after stretch.
Therefore the coordinates of H′ are (-2,0).
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Check the picture below.
make sure your calculator is in Degree mode.
Answer:
x=56.7
Step-by-step explanation:
From the given triangle, the opposite side of angle x is 66 mm
79 mm is opposite to the right angle, so hypotenuse = 79 mm
we know the opposite side and the hypotenuse
To find the angle we use sin
[tex]sin(x)= \frac{opposite side}{hypotenuse}[/tex]
opposite side = 66
hypotenuse = 79
[tex]sin(x)= \frac{66}{79}[/tex]
[tex]x=sin^{-1}(\frac{66}{79})[/tex]
x=56.66199855
Round the answer to nearest tenth
x=56.7
Simplify the fraction (4t^2-16/8) / (t-2/6)
Answer:
A. 3(t+2)
Step-by-step explanation:
We can easily solve your question by using any computational tool or calculator
Please see attached images for a full analysis of your problem
The result is
A. 3(t+2)
[tex]\bf \cfrac{~~\frac{4t^2-16}{8}~~}{\frac{t-2}{6}}\implies \cfrac{4(t^2-4)}{8}\cdot\cfrac{6}{t-2}\implies \cfrac{4\stackrel{\stackrel{difference}{of~squares}}{(t^2-2^2)}}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot\cfrac{\stackrel{3}{\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}~~}{t-2}[/tex]
[tex]\bf \cfrac{\begin{matrix} 4 (t-2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(t+2)}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{3}{~~\begin{matrix} t-2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 3(t+2)[/tex]
The pH scale measures how acidic or basic a substance is. Lemon juice is said to have a pH of less than 4 and greater than 1.5. Model the normal range of pH values of lemon juice, using a compound inequality.
1.5 > x > 4
1.5 < x < 4
1.5 ≤ x ≤ 4
1.5 ≥ x ≥ 4
Let's say x is J because it's Lemon Juice.
It's said that the pH of J is less than 4 so: pH(J) < 4 and pH(J) is greater than 1.5 so: pH(J) > 1.5
Now we can construct:
[tex]1.5 < pH(J) \wedge pH(J) < 4[/tex]
Or simply:
[tex]1.5 < pH(J) < 4[/tex]
We can also write this with an interval:
[tex]pH(J)\in(1.5, 4)[/tex]
Hope this helps.
r3t40
Inequalities are used to relate unequal expressions.
The compound inequality that represents the normal range of pH values of lemon juice: (b) 1.5 < x < 4
Let the pH of lemon juice be represented with x.
x less than 4 means: x < 4
x greater than 1.5 means x > 1.5
So, we have:
x < 4 and x > 1.5
Rewrite as:
x > 1.5 and x < 4
Express x > 1.5 as 1.5 < x
1.5 < x and x < 4
Combine the inequalities
1.5 < x < 4
Hence, the required compound inequality is: (b) 1.5 < x < 4
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Which of the following is a geometric sequence with a common ratio of 2?
A. 14, 16, 18, 20, ...
B. 64, 32, 16, 8, ...
C. 14, 28, 56, 112, ...
D. 87, 85, 83, 81, ...
The geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...
What is a geometric sequence?There are three parameters which differentiate between which geometric sequence we're talking about.
The first parameter is the initial value of the sequence.
The second parameter is the quantity by which we multiply previous term to get the next term.
The third parameter is the length of the sequence. It can be finite or infinite.
Suppose the initial term of a geometric sequence is 'a'
and the term by which we multiply the previous term to get the next term is 'r' (also called the common ratio)
Then the sequence would look like
[tex]a, \: ar, \: ar^2, \: ar^3, \: \cdots[/tex]
(till the terms to which it is defined)
If the initial term is 'a', then the geometric sequence with common ratio = 2 would look like:
[tex]a, \: a(2), \: a(2)^2, \: a(2)^3, \: \cdots\\\\a, \: a(2), \: a(4), \: a(8), \: \cdots[/tex]
Checking all the options to see which one has got common ratio 2:
A. 14, 16, 18, 20, ...Initial term a = 14,
The geometric sequence with a = 14, and r = 2 would be:
[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]
The sequence 14, 16, 18, 20, ... doesn't match with it, so its not correct option.
B. 64, 32, 16, 8, ...Initial term a = 64,
The geometric sequence with a = 14, and r = 2 would be:
[tex]64, 64(2), 64(4), 64(8), \cdots\\\\64, 128, 256, 512, \cdots\\[/tex]
The sequence 64, 32, 16, 8, ... doesn't match with it, so its not correct option.
C. 14, 28, 56, 112, ...Initial term a = 64,
The geometric sequence with a = 14, and r = 2 would be:
[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]
The sequence 14, 28, 56, 112, ... matches with it, so its correct option.
D. 87, 85, 83, 81, ...Initial term a = 87,
The geometric sequence with a = 87, and r = 2 would be:
[tex]87, 87(2), 87(4), 87(8), \cdots\\\\87, 174, 348, 696, \cdots\\[/tex]
The sequence 87, 85, 83, 81, ... doesn't match with it, so its not correct option.
Thus, the geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...
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X + 35/17 = 4 The answer is 33/17 but I got it wrong because I multiplied 4 by 17. Why do I minus 35/17 from 4 instead of multiplying 17 to four? Do I always minus a positive fraction instead of multiplying the denominator when solving linear equations?
X=33/17
Here is how it works
By the way what you are working with is called improper factions, which is when the big number is placed over the smaller number.
Now 33/17 is also 1 16/17
35/17 is also 2 1/17
Now we can the proper fractions which are 1 16/17 and 2 1/17
1+2=3 and 16/17 + 1/17 equals 1
3+1=4
I enjoyed solving your problem. please vote my answer brainliest..thanks
Find the missing factor. Write your answer in exponential form.
8^-1 = _ • 8^-2
Answer:
The answer is 8, so 8^1
Step-by-step explanation:
You add and subtract exponents when multiplying and dividing.
PLS HELP SHOW ALL YOUR WORKING OUT :D
[tex]AB=\sqrt{(10-1)^2+(3-7)^2}=\sqrt{81+16}=\sqrt{97}\approx9.85[/tex]
A high school guidance counselor wants to find the probability that students who study geometry as freshmen will go on to study calculus before graduating. To do this, he has constructed a table, shown below, which shows the number of students who study geometry as freshmen in a given year, and the number of those students who study calculus before graduating.
Year
2000
2001
2002
2003
2004
2005
Geometry Students
680
577
822
743
859
804
Calculus Students
391
336
512
374
465
361
Which year had the highest experimental probability that a freshman studying geometry would take a calculus class before graduation?
a.
2001
b.
2002
c.
2003
d.
2004
Answer:
b. 2002
Step-by-step explanation:
divide the geometry kids by total kids to take calculus.
The experimental probability of a freshman studying geometry taking a calculus class before graduation was greatest in 2002.Option B is correct.
What is the probability?
The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts.
The The experimental probability of a freshman studying geometry taking a calculus class before graduation is obtained by dividing the number of students taking calculus to the number of students of student taking statics.
Referred to the excel table in the attachment for the probability.
The experimental probability of a freshman studying geometry taking a calculus class before graduation in 2002 is found at;
[tex]\rm P_{2002}(\%) = \frac{512}{822} \times 100 \\\\ P_{2002}(\%) =62.29[/tex]
The experimental probability of a freshman studying geometry taking a calculus class before graduation was greatest in 2002.Option B is correct.
Hence,Option B is correct.
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