There are 6 terms in the sequence greater than 1.
What is a geometric series ?A geometric series is sum of infinite numbers which has a common ratio between its successive terms.
The missing common ratio value is -1/2
It is given in the question that
the number of terms in the sequence = 300
Sum = a₁ (1-rⁿ)/(1-r)
nth term is given by
aₙ = a₁r⁽ⁿ⁻ ¹⁾
1337(1/2)^(n - 1) = 1
(1/2)^(n - 1) = 1/1337
Applying log on both sides
log (1/2)^(n - 1) = log (1/1337)
(n - 1) log(1/2) = log(1/1337)
n = log (1/1337)/ log (1/2) + 1 ≈ 11.384
the 11th term is 1337(-1/2)^(10) ≈ 1.305
and
And the 12th term is 1337(-1/2)^11 = -.653
As the even terms are negative , they are less than 1 and , therefore the odd terms from 1 - 11 term will be positive and greater than 1.
Therefore there are 6 terms in the sequence greater than 1.
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Solve for x:
2x² - 2x+5=0
By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
How to solve a quadratic function by the quadratic formula
Let be a quadratic function of the form a · x² + b · x + c = 0, whose roots can be found by means of the following formula:
[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] (1)
Where a, b, c are the coefficients of the quadratic function.
In we know that 2 · x² - 2 · x + 5 = 0, then the roots of the polynomial are, respectively:
[tex]x_{1} = \frac{2 + \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{1} = \frac{2 + \sqrt{4-40}}{4}[/tex]
x₁ = 0.5 + i 1.5
[tex]x_{2} = \frac{2 - \sqrt{(-2)^{2}-4\cdot (2)\cdot (5)}}{2\cdot (2)}[/tex]
[tex]x_{2} = \frac{2 - \sqrt{4-40}}{4}[/tex]
x₂ = 0.5 - i 1.5
By quadratic formula, the roots of the quadratic function 2 · x² - 2 · x + 5 = 0 are two conjugated complex numbers: x₁ = 0.5 + i 1.5 and x₂ = 0.5 - i 1.5, respectively.
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Simplify the following expressions
2x-2y+5z-2x-y+3z
Answer:
-3y+8z
Step-by-step explanation:
2x-2y+5z-2x-y+3z
you don't need to change their signs just place them accordingly
2x-2x-2y-y+5z+3z
-3y+8z
A rocket is launched from a height of 3m with an initial velocity of 15 m/s at what time will the rocket be 13m from the ground? first person to answer gets brainliest
Interest earned or paid on the principal is ___ interest
Answer:
simple interest
Step-by-step explanation:
SI = principal x rate x time
What is the probability that the top-three finishers in the contest will all be seniors?
Type in the correct answer in each box. Use numerals instead of words. If necessary, round your answers to the nearest tenth.
There are __ different orders of top-three finishers that include all seniors.
The probability that the top-three finishers will all be seniors is __%.
CONTEXT: Coach Bennet’s high school basketball team has 14 players, consisting of six juniors and eight seniors. Coach Bennet must select three players from the team to participate in a summer basketball clinic.
Using the combination formula, it is found that:
There are 364 different orders of top-three finishers that include all seniors.
The probability that the top-three finishers will all be seniors is 15.38%.
The order in which the players are taken is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In total, three students are taken from a set of 14, hence:
[tex]C_{14,3} = \frac{14!}{3!11!} = 364[/tex]
Including only seniors, it would be three students from a set of 8, hence:
[tex]C_{8,3} = \frac{8!}{3!5!} = 56[/tex]
Hence the probability is given by:
p = 56/364 = 0.1538 = 15.38%.
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Is the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
The distribution of the values obtained from a simple random sample of size n from the same population is incorrect.
What is sampling distribution?The sampling distribution of a statistic of size n is the distribution of the values obtained from a simple random sample of size n from the same population.
The sampling distribution is the process of getting a sample through simple random techniques from the sample population.
So, it is incorrect that the distribution of all values of the statistic when all possible samples of the same size n are taken from the same population.
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In the triangle below, which of the following best describes AD?
B
D
O A. Median
OB. Altitude
OC. Perpendicular bisector
A
38
38
Answer:
A. median
explain i just aced the test rn
Answer:
Angle bisector
Step-by-step explanation:
The line AD bisects both sides of the triangle. Both angles are congruent to each other since both sides are congruent to each other.
According to the Centers for Disease Control and Prevention (CDC) , 47% of adults in the United States have hypertension. In a random sample of 500 U.S adults, find the probability that sample the proportion of adults with hypertension is greater than 0.5.
The probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090
How to determine the probability?The given parameters are:
p = 47%
Sample size, n =500
The standard deviation is calculated as:
[tex]\sigma = \sqrt{np(1 - p)[/tex]
So, we have:
[tex]\sigma = \sqrt{500 * 47\%(1 - 47\%)[/tex]
Evaluate
σ = 11.16
The number of adults with hypertension is calculated as:
x = 500 * 0.5 = 250
And the mean is:
μ = 500 * 0.47 = 235
Start by calculating the z-score
[tex]z = \frac{x - \mu}{\sigma}[/tex]
This gives
[tex]z = \frac{250 - 235}{11.16}[/tex]
Evaluate
z = 1.34
The probability is then calculated as:
P(z >1.34) = ??
From z table of probabilities, we have:
P(z >1.34) = 0.090
Hence, the probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090
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In a group there are 3 boys and 4 girls. A child is selected from the group at random. Find the probability that the selected child is a boy.
Answer:
3/7
Step-by-step explanation:
Probability=Number of possible items÷Number of total items.
We will make the possible item 3 because we are looking for the probability whether a boy will be picked.
The number of total items will therefore be: the number of boys + the number of girls; that will be 3+4 =7.
So the probability of picking a boy will be 3/7
THANK YOU.
-2h - 8 = 4h - 3(2h + 12)
Need Help with this..
Answer:
119 4/7
Step-by-step explanation:
Add up all the sides
Hi Student!
Looking at the picture that was provided, we see that the problem statement is asking for us to determine the perimeter of the shape is. Perimeter is the outer layer of the shape which would include the lengths of all the sides that are exposed to the outside.
In this case, we are given 7 different values which represent each of the different sides of the shape which we need to add together to get the perimeter.
Create an expression
[tex]\textsf{Perimeter = side_{1}}[/tex][tex]\textsf{Perimeter = side1 + side2 + side3 + side4 + side5 + side6 + side7}[/tex]Using the expression above, all we need to do is combine all of the values which will give us the outline on our shape. However, since some of the values have different denominators, we will first need to combine the whole numbers and then combine those with a common denominator and finally apply a common denominator to be able to add the rest.
Combine the whole numbers
[tex]\textsf{Perimeter = }35\frac{3}{7} + 10\frac{1}{7} + 10\frac{1}{7} + 12\frac{2}{7} + 12\frac{2}{7} + 15\frac{3}{14} + 24\frac{1}{14}[/tex][tex]\textsf{Perimeter = }(35 + 10 + 10+12+12+15+24)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7} + \frac{3}{14} + \frac{1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7} + \frac{3}{14} + \frac{1}{14})[/tex]Combine those with a common denominator
[tex]\textsf{Perimeter = }(118)+(\frac{3}{7} + \frac{1}{7} + \frac{1}{7} + \frac{2}{7} + \frac{2}{7}) + (\frac{3}{14} + \frac{1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{3+1+1+2+2}{7}) + (\frac{3+1}{14})[/tex][tex]\textsf{Perimeter = }(118)+(\frac{9}{7}) + (\frac{4}{14})[/tex]Covert to mixed fraction and simplify
[tex]\textsf{Perimeter = }(118)+(1\frac{2}{7}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{2}{7}) + (\frac{4}{14})[/tex]Find common denominator and combine
[tex]\textsf{Perimeter = }(119)+(\frac{2*2}{7*2}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{14}) + (\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{14}+\frac{4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4+4}{14})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{8}{14})[/tex]Simplify the expression
[tex]\textsf{Perimeter = }(119)+(\frac{8/2}{14/2})[/tex][tex]\textsf{Perimeter = }(119)+(\frac{4}{7})[/tex][tex]\textsf{Perimeter = }119\frac{4}{7}[/tex]Therefore, the final answer for the perimeter of the figure that was provided would be [tex]119\frac{4}{7}[/tex] units.
How many modes does the following data set have?
2, 2, 3, 3, 3, 4, 4, 4, 4, 11, 11, 11, 25, 25, 25, 25, 26, 26, 26
A. 2
B. 6
C. 4
D. 1
SUBT
please someone help me
Answer:
uh I'm not so sure but
Step-by-step explanation:
it might be 1664
What is the Domain and Range of the function f(x)[tex]\sqrt{x-7} +9[/tex]?
For the given function, the domain is D : { x ≥ 7} and the range is R: { y ≥ 9}
How to get the domain and range?
Here we have a square root, remember that the argument of the square root must be equal or larger than zero, so the domain is such that:
x - 7 ≥ 0.
Solving for x we get:
x ≥ 0 + 7
Then the domain is:
x ≥ 7
To get the range, we evaluate in the minimum of the domain:
f(7) = √(7 - 7) + 9 = 9
Then the range is the set of all values larger than 9, because the function is increasing.
So the range is R: y ≥ 9.
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Kapil's robot starts 70cm from its charging base. It faces the base, then turns 60 degrees clockwise, as shown. Finally, the robot moves 50cm. After moving, how far is the robot from the charging base? Do not round during your calculations. Round your final answer to the nearest centimeter.
The distance of the robot from the charging base is gotten as; 62 cm
How to use Cosine Rule?
From the image attached showing the movement of Kapil's robot, we can use cosine rule to find the value of h which is the distance of the robot from the charging base.
The distance of the robot from the charging base is gotten by;
h = x² + b² - 2xb cos 60
h = 50² + 70² - 2*50*70 * 0.5
h = 62 cm
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2x+2y
3x+3y
=5
=7
How many solutions does the system of equations above have?
The system of equations have one solution
How to determine the number of solutions?The equations are given as:
2x + 2y = 5
3x + 3y = 7
The above equations are distinct linear equations.
This means that they would have one point of intersection, if plotted on a graph
Hence, the system of equations have one solution
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This table shows some values of an exponential function.
What is the function?
The exponential function of the table is y = 0.75(2)^x
How to determine the exponential function?From the table, we have the following points
(x,y) = (0,0.75) and (1,1.5)
An exponential function is represented as:
y = ab^x
At (0,0.75), we have:
0.75 = ab^0
a = 0.75
Substitute a = 0.75 in y = ab^x
y = 0.75b^x
At (1,1.5), we have:
1.5 = 0.75b^1
Evaluate
1.5 = 0.75b
Divide both sides by 0.75
b =2
Substitute b =2 in y = 0.75b^x
y = 0.75(2)^x
Hence, the exponential function is y = 0.75(2)^x
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The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.
Step 1: –c = ax2 + bx
Answer:
The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.
[tex] \: first the formula of quadratic equation \: = - b ≠ \: \sqrt{ \frac{ \: {b }^{2} - 4ac}{ \: 2a} } [/tex]
let's begin to solve this equation,,,
[tex]ax² + bx + c = 0 \\
ax² + bx + c =0 \\ {x}^{2} + \frac{b}{a} \: + \frac{ {b}^{2} }{2a} = \frac{b2}{a} - \frac{c}{a}
\\ x + \frac{ {b}^{2} }{2a} = - \frac{ {b}^{2} }{2a} - \frac{c}{a} [/tex]
MORE BASIC INFORMATIONan equation having the maximum power of the variable equal to is called the quadratic equation the general form of quadratic equation is ax² + bx +c =0 where a,b,c are real numbers a ≠0 x is variable •
a quadratic equation can be solved by two method by factorization and by formula
by factorization a quadratic equation can be solved by factorization only when the product AC can be divided into two such part that it had the sum of the difference of the two part is equal to b
[tex]by the formula of quadratic equation can be solved by \ - } [/tex]
[tex]x = \frac{ - b \sqrt{ {b}^{2} - 4ac } }{2a } \\ root \: of \: equation \: {ax}^{2} + bx + c = 0 \\ - b - \sqrt{ \frac{ {b}^{2} - 4ac}{2a} } [/tex]
Write the slope-intercept form of the equation of the line through the given points.
through: (0, 2) and (-1,-5)
Answer:
y = 7x +2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 1, - 5 )
m = [tex]\frac{-5-2}{-1-0}[/tex] = [tex]\frac{-7}{-1}[/tex] = 7
the line crosses the y- axis at (0, 2 ) ⇒ c = 2
y = 7x + 2 ← equation of line
Find the first 3 iterates of the function f(x) = 0.80x when x^0= 150
Based on the calculations, the first three (3) iterations of the given function are 120, 96 and 76.8.
How to find the first three iterations?In this exercise, you're required to find the first three (3) iterations of the given function. Thus, we would substitute the value of x₀ into the function and then evaluate as follows:
First iteration:
f(x) = 0.80x
f(x₀) = 0.80x₀
f(150) = 0.80 × 150
f(150) = 120.
Second iteration:
f(x) = 0.80x
f(x₁) = 0.80x₁
f(120) = 0.80 × 120
f(120) = 96.
Third iteration:
f(x) = 0.80x
f(x₂) = 0.80x₂
f(96) = 0.80 × 96
f(120) = 76.8.
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If a male student is selected at random, what is the probability the student is a freshman?
The probability that the student selected at random is a freshman is; 29%
How to find the Probability?
From the given table;
Total number of male students = 4 + 6 + 2 + 2 = 14
Number of freshmen students = 4 students
Thus;
Probability that the student selected at random is a freshman is;
P(Freshman | Male) = 4/14 * 100% = 28.57% ≈ 29%
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help heelp help help help
[100 POINTS] What is the measure of the arc from A to B that does not pass through C?
(Fill in the blanks)
Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.
What is the Inscribed Angle Theorem?Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).
m∠BAC = 40 degrees.
Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]
Corresponding arc BC = 80 degrees.
Arc AC through point B = 180 degrees [half circle]
Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.
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R FIVE Given that k = 3n+2/n+1 write 'n' in terms of 'k'
[tex]~~~~~~k = \dfrac{3n+2}{n+1}\\\\\implies k(n+1) = 3n+2\\\\\implies kn+k=3n+2\\\\\implies kn -3n= 2-k\\\\\implies n(k-3) = 2-k\\\\\implies n = \dfrac{2-k}{k-3}\\\\\implies n = -\dfrac{k-2}{k-3}~~~~~~~~;[k\neq 3][/tex]
Find the ratio of the perimeter for the pair of similar two regular pentagons with areas 144 in² and 36 in²
The ratio between the perimeter of the largest and smallest pentagon is 2.
How to find the ratio between the perimeters?We know that the pentagons are similar, meaning that the dimensions of one of the pentagons is k times the dimensions of the other.
Because of this, the ratio between the areas is k squared. And because the perimeter depends linearly on the dimensions, the ratio between the perimeters will be equal to k.
So we need to find k, we will have:
[tex]\frac{144 in^2}{36 in^2} = k^2 = 4\\\\k = \sqrt{4} = 2[/tex]
Then we conclude that the ratio between the perimeters is k =2.
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What similarity statement can you write relating the three triangles in the diagram?
Answer:
They are both right-angled triangles.
Step-by-step explanation:
Use Cramer’s rule to solve for x: x + 4y − z = −14 5x + 6y + 3z = 4 −2x + 7y + 2z = −17
Looks like the system is
x + 4y - z = -14
5x + 6y + 3z = 4
-2x + 7y + 2z = -17
or in matrix form,
[tex]\mathbf{Ax} = \mathbf b \iff \begin{bmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -14 \\ 4 \\ -17 \end{bmatrix}[/tex]
Cramer's rule says that
[tex]x_i = \dfrac{\det \mathbf A_i}{\det \mathbf A}[/tex]
where [tex]x_i[/tex] is the solution for i-th variable, and [tex]\mathbf A_i[/tex] is a modified version of [tex]\mathbf A[/tex] with its i-th column replaced by [tex]\mathbf b[/tex].
We have 4 determinants to compute. I'll show the work for det(A) using a cofactor expansion along the first row.
[tex]\det \mathbf A = \begin{vmatrix} 1 & 4 & -1 \\ 5 & 6 & 3 \\ -2 & 7 & 2 \end{vmatrix}[/tex]
[tex]\det \mathbf A = \begin{vmatrix} 6 & 3 \\ 7 & 2 \end{vmatrix} - 4 \begin{vmatrix} 5 & 3 \\ -2 & 2 \end{vmatrix} - \begin{vmatrix} 5 & 6 \\ -2 & 7 \end{vmatrix}[/tex]
[tex]\det \mathbf A = ((6\times2)-(3\times7)) - 4((5\times2)-(3\times(-2)) - ((5\times7)-(6\times(-2)))[/tex]
[tex]\det\mathbf A = 12 - 21 - 40 - 24 - 35 - 12 = -120[/tex]
The modified matrices and their determinants are
[tex]\mathbf A_1 = \begin{bmatrix} -14 & 4 & -1 \\ 4 & 6 & 3 \\ -17 & 7 & 2\end{bmatrix} \implies \det\mathbf A_1 = -240[/tex]
[tex]\mathbf A_2 = \begin{bmatrix} 1 & -14 & -1 \\ 5 & 4 & 3 \\ -2 & -17 & 2 \end{bmatrix} \implies \det\mathbf A_2 = 360[/tex]
[tex]\mathbf A_3 = \begin{bmatrix} 1 & 4 & -14 \\ 5 & 6 & 4 \\ -2 & 7 & -17 \end{bmatrix} \implies \det\mathbf A_3 = -480[/tex]
Then by Cramer's rule, the solution to the system is
[tex]x = \dfrac{-240}{-120} \implies \boxed{x = 2}[/tex]
[tex]y = \dfrac{360}{-120} \implies \boxed{y = -3}[/tex]
[tex]z = \dfrac{-480}{-120} \implies \boxed{z = 4}[/tex]
Answer:
in photo attached.
Step-by-step explanation:
Which of the following expressions are equivalent to
4-3
?
4-8
U
ful foo
45
DONE
Answer: The correct answers are the first and the fourth one.
Step-by-step explanation:
if you help me I will make you branliest
This exercise is about creating two-dimensional shapes. The resulting shape is a quadrilateral - Square. See the attached for the lines drawn.
What was noticed about the two lines drawn?
The two lines are drawn each had parallel pairs; andThey were perpendicular to one another.What is the meaning of perpendicularity?
When two lines intersect with one another such that they create a right angle, perpendicularity has occurred and both lines are said to be perpendicular to one another.
Hence:
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Molly's jump rope is 6 1/3 feet long. Gail's jump rope is 4 2/3 feet long. How much longer is Molly's jump rope? NOT MUTLIPLE CHOICE IM SO SORRY PLS FORGIVE ME
Answer:
Molly's jump rope is 1 2/3 feet longer than Gail's jump rope.
Step-by-step explanation:
To get this answer, you would have to subtract 6 1/3 - 4 2/3 to find the difference between the two lengths.
To solve this subtraction problem: Start by doing 6 - 4 to get 2, because when the fraction parts are like that, start with whole numbers. Then, solve the fraction parts. 1/3 - 2/3 is -1/3 (you can go to negatives)! Lastly, combine the whole number and fraction parts. 2 - 1/3, because the negative symbol changes to a minus symbol, which will get you 1 2/3.
Hope this helped!