Answer:x=-5.22311 and x=1.72311
Step-by-step explanation:
2x^2-3x+10x-15=3
Then put into quadratic formula and use calculator
If the 4th and 7th terms of a geometric sequence are 1/16 and
1/128, then the sum of the first 7 terms of this sequence is equal
to
Therefore, the sum of the first 7 terms of the given geometric sequence is 127/128.
To find the sum of the first 7 terms of a geometric sequence, we need to determine the common ratio and the first term of the sequence.
Let's denote the first term of the sequence as 'a' and the common ratio as 'r'.
Given that the 4th term is 1/16 and the 7th term is 1/128, we can write the following equations:
a * r^3 = 1/16 (equation 1)
a * r^6 = 1/128 (equation 2)
Dividing equation 2 by equation 1, we get:
(r^6)/(r^3) = (1/128)/(1/16)
r^3 = 1/8
Taking the cube root of both sides, we find:
r = 1/2
Substituting the value of r back into equation 1, we can solve for 'a':
a * (1/2)^3 = 1/16
a * 1/8 = 1/16
a = 1/2
Now we have the first term 'a' as 1/2 and the common ratio 'r' as 1/2.
The sum of the first 7 terms of the geometric sequence can be calculated using the formula:
Sum = a * (1 - r^n) / (1 - r)
Substituting the values into the formula, we have:
Sum = (1/2) * (1 - (1/2)^7) / (1 - 1/2)
Simplifying the expression
Sum = (1/2) * (1 - 1/128) / (1/2)
Sum = (1/2) * (127/128) / (1/2)
Sum = (127/128)
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A point is plotted on the number line at 2 2/5 . A second point is plotted at −4 3/4 .
What is the length of a line segment joining these points?
What is the answer as a simplified mixed number?
Here, we are required to determine the length of a line segment joining the two points.
The length of the line segment is; 143/20The answer as a simplified modes number is; 7 3/4The first point is plotted on the point, 2 2/5.
i.e on point 12/5.
The second point is at -4 3/4.
i.e on point (-19/4).
The length of a line segment joining these points is given by;
12/5 - (-19/4) which yields;
(48+95)/20 = 143/20
Ultimately, the length of the line segment is;
143/20
To express the answer as a simplified modes number is; 7 3/4.
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Write 28/25 as a percentage
To write 28/25 as a percentage we need to multiply the fraction by 100 as follows:
\(\frac{28}{25}=\frac{28}{25}\cdot100=112\text{ \%}\)Which inequalities would have an open circle when graphed? Check all that apply. T Less-than-or-equal-to 25 -2. 5 Less-than-or-equal-to m x > 5. 4 One-half less-than x x > 0.
The inequalities would have an open circle when graphed are as follows;
The inequality shows that it does not contain boundary point 5.
\(\rm x>5.4\)
The inequality shows that it does not contain the boundary point 1/2.
\(\rm \dfrac{1}{2}>x\)
The inequality shows that it does not contain the boundary point 0.
\(\rm x>0\)
What is a circle?A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center):
The graph will have an open circle only if it has the symbol < or > because it indicates that the boundary is not included.
The inequality shows that it does not contain boundary point 5.\(\rm x>5.4\)
The inequality shows that it does not contain the boundary point 1/2.\(\rm \dfrac{1}{2}>x\)
The inequality shows that it does not contain the boundary point 0.\(\rm x>0\)
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what are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section?
The mean (μ) of a hypergeometric distribution is given by: 8.181
The standard deviation (σ) of a hypergeometric distribution is given by:
1.644
Here, we have,
To find the mean value and standard deviation of the number of projects not among the first 15 that are from the second section, we need to calculate the probabilities for different numbers of projects from the second section.
Let's denote:
N1: Number of students in the first section (25)
N2: Number of students in the second section (30)
N: Total number of projects graded (15)
To calculate the probability of exactly 10 projects being from the second section, we can use the hypergeometric distribution.
The formula for the hypergeometric distribution is:
P(X = k) = (C(N2, k) * C(N1, N - k)) / C(N1 + N2, N)
Where:
X is the random variable representing the number of projects from the second section among the first 15 graded projects.
C(a, b) is the binomial coefficient, also known as "a choose b."
Using this formula, we can calculate the probability for X = 10:
P(X = 10) = (C(30, 10) * C(25, 15 - 10)) / C(55, 15)
Next, we can calculate the mean and standard deviation.
The mean (μ) of a hypergeometric distribution is given by:
μ = N * (N2 / (N1 + N2))
= 15 * (30 / (25 + 30) )
= 8.181
The standard deviation (σ) of a hypergeometric distribution is given by:
σ = √(N * (N1 / (N1 + N2)) * (N2 / (N1 + N2)) * ((N1 + N2 - N) / (N1 + N2)) )
= √(15 * (25 / (25 + 30)) * (30 / (25 + 30)) * (25+30 - 15 )/(25+30)) )
= 1.644
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complete question:
An Instructor Who Taught Two Sections Of Engineering Statistics Last Term, The First With 25 Students And The Second With 30, Decided To Assign A Term Project. After All Projects Had Been Turned In, The Instructor Randomly Ordered Them Before Grading. Consider The First 15 Graded Projects. (A) What Is The Probability That Exactly 10 Of These Are From The
An instructor who taught two sections of engineering statistics last term, the first with 25 students and the second with 30, decided to assign a term project. After all projects had been turned in, the instructor randomly ordered them before grading. Consider the first 15 graded projects.
what are the mean value and standard deviation of the number of projects not among these first 15 that are from the second section?
An airline wants to survey customers about their overall satisfaction. They take a random sample of 1{,}0001,0001, comma, 000 customers who have flown in the past month and email them a survey. The email also offers those who complete the survey a \$25$25dollar sign, 25 gift card that can be used almost anywhere.
Which of these is the best example of nonresponse bias?
The correct option is option A.
Satisfied customers might be less likely to complete the survey than dissatisfied customers.
This would be nonresponse, which is when people of interest can't be reached or refuse to participate. If satisfied customers opt out, then the survey results might suggest that customers are less satisfied overall than they really are.
Nonresponse bias refers to a situation that arises where people are less inclined to provide feedback because their experience was different from those who did.
Satisfied customers would be less inclined to talk about their overall satisfaction than unsatisfied customers as the latter would use the opportunity to make their dissatisfaction known.
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any actives ???can y’all please help me
Answer:
B: $2.50
Step-by-step explanation:
Step 1: form an equation
126 = 12(8 + x)
Step 2: isolate the x
126/12 = 8 + x
126/12 - 8 = x
Step 3: solve
10.5 - 8 = x
2.5 = x = raise per hour
how do i use the substitution method for these equations
y=3x+4
y=5x+12
Answer:
hello there mate
Step-by-step explanation:
the measure of ∠abc in the figure is x°. which of the following is an expression for β° ?
An expression for the measure β° is 180 - x
The correct answer is an option (d)
We know that the sum of four angles of the quadrilateral is always 360°
In the attached quadrilateral angle A and angle D measures 90 degrees respectively.
The measure of ∠ABC in the figure is x° and the measure of ∠BCD is β°
From above statement for quadrilateral ABCD we have,
⇒ ∠A + ∠B + ∠C + ∠D = 360°
⇒ 90° + x°+ β° + 90° = 360°
⇒ x° + β° = 360° - 180°
⇒ x° + β° = 180°
⇒ β = 180 - x
Therefore, the required expression is β = 180 - x
The correct answer is an option (d)
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Find the complete question below.
How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?
a. g(x) is shifted 8 units to the left and 3 units up.
b. g(x) is shifted 3 units to the right and 8 units down.
c. g(x) is shifted 8 units to the right and 3 units up.
d. g(x) is shifted 3 units to the right and 8 units up.
Answer:
The right answer is C.
Step-by-step explanation:
The parent function is:
\(f(x)=x^3\)
If something is subtracted from variable \(x\) it means the graph shifted toward right and something is added to \(y\) value then the graph is shifted up.
\(f(x)=(x-8)^3\)
graph shifted toward right by \(8\) units right
\(f(x)=(x-8)^3+3\)
graph shifted toward right by \(3\) units up
Thus the new function is:
\(g(x)=(x-8)^3+3\)
BRUH THIS DUE SOONER THAN I THOUGHT!!!HELP!!!!!
Use the information to answer the following question.
A car travels at a rate of 45 miles per hour for 5 hours. Let y be the distance, in miles, the car travels for a given amount of time, x, in hours. This situation can be modeled by a function.
What is the domain of the function?
A.0 ≤ x ≤ 5
B.0 ≤ y ≤ 5
C.0 ≤ x ≤ 45
D. 0 ≤ y ≤ 45
1) A Freedom 35 financial planner claims you will need
$1,175,000 to retire in 15 years time. How much should you invest
today at 9% simple interest to reach your retirement goal?
2) How long will it
you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.
To determine how much you should invest today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years, we can use the formula for simple interest:
A = P(1 + rt)
Where A is the future value, P is the principal (the amount you should invest today), r is the interest rate, and t is the time in years.
We can rearrange the formula to solve for P:
P = A / (1 + rt)
Plugging in the values, we have:
P = 1,175,000 / (1 + 0.09 * 15)
P = 1,175,000 / (1 + 1.35)
P = 1,175,000 / 2.35
P ≈ $500,000
Therefore, you should invest approximately $500,000 today at 9% simple interest to reach your retirement goal of $1,175,000 in 15 years.
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42
You are going to make a picture frame that is going to be º 2 inches
long and
8 inches wide. You will measure the diagonal distance to
determine if you are making square corners. What would the mea-
surement of the diagonal need to be to ensure that the corners are
square?
in
The measurement of the diagonal for the picture frame would need to be 8.246 inches to ensure that the corners are square.
This can be calculated using the Pythagorean theorem, where a² + b² = c² and a and b represent the length and width of the frame. So, 2² + 8² = c², which simplifies to 4 + 64 = c², and then 68 = c². Taking the square root of both sides gives us c = 8.246 inches.
To ensure that the corners of your picture frame are square, you can use the Pythagorean theorem. The theorem states that for a right-angled triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (length and width). In this case, the length is 2 inches and the width is 8 inches.
Applying the theorem: Diagonal² = Length² + Width²
Diagonal² = 2² + 8²
Diagonal² = 4 + 64
Diagonal² = 68
Diagonal = √68 ≈ 8.25 inches
So, the measurement of the diagonal should be approximately 8.25 inches to ensure that the corners are square.
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let there be a reflection across the line and let there be a transaction along the Victor a b as shown if the S donate a black figure compared the translated figure as followed by the reflected image of the figure s with a reflected figure s followed by the translated image of figure S.
The green lines would be the reflected and translated figure
Point P represents which point of concurrency?
Answer:
Perpendicular Bisector These are the perpendicular lines drawn to the sides of the triangle.
Step-by-step explanation:
Janet bought g number of packs of gum. Each pack of
gum costs $0.79. Write an expression that shows how
much change she will get back from paying with a $20
bill.
USE g FOR THE VARIABLE
Answer:
f(g)=20-0.79*(g)
Step-by-step explanation:
The change will receive depends on the money given subtract to the variable multiply by the price per gum package.
When the coordinates 1 1 7 3 8 0 and 2 − 2 are joined which shape is formed 5 points group of answer choices trapezoid rectangle rhombus square?
the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined which shape is formed as Square
When the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined, a square is formed. The sides are equal length and the angles are all 90 degrees.The coordinates (1,1), (7,3), (8,0) and (2,-2) are points on a two-dimensional plane. When the points are connected, a square is formed. A square is a four sided shape with four 90 degree angles and four equal length sides. The length of each side can be calculated by finding the distance between the two points. For example, the distance between (1,1) and (7,3) is 6 units. Therefore, the length of each side of the square is 6 units.
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solve the inequality below. use the drop down menus to describe the solution and its graph -7x+13 ≥41
Answer:
x ≥-4
Step-by-step explanation:
-7x+13 ≥41
-7x ≥28 (subtraction property of equality on both sides-subtract 13)
x ≥-4 (division property of equality on both sides-divide by -7)
Claim: Fewer than 93% of adults have a cell phone. In a reputable poll of 1232 adults, 87% said that they have a cell phone. Find the value of the test statistic. Question content area bottom
The value of the test statistic is -8.2542.
We have,
p'= 0.87, p= 0.93 and n= 1232
We know, the equation for the Test statistic for a population proportion is mathematically given as
z = (p' - p)/ √p(1-p)/ n
So, z= (0.87 - 0.93)/ √0.93(1-0.93)/ 1232
z = (-0.06) / 0.007269
z = -8.2542
So, the value of the test statistic is -8.2542.
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Which of the following does not describe the graph below?A. The y-intercept is (0, -3).B. The x-intercept is (6, 0).C. The slope is 1/2.D. The change in the y-values is 6, & the change in the x-values is 3.
D.
1) Looking attentively at the graph
The following option does not describe
Let's check the slope
The option that does not describe is
D.
Because the
A, B and C are true.
And the change in the y values is -3, and the change in x- value is 6.
RESOLVER LA INECUACION x ≥ 6
a group of researchers is conducting a study to determine the average time to fix a rivet at a particular location on an assembly line. at a 95% confidence level, they do not want the average time of their sample to be off by more than 3.5 seconds (could also be stated as: the width of the total deviation from the mean time to be at most 7 seconds). from previous studies, the variance is known to be 55 seconds2. what sample size should be used in this study?
The sample size that should be used in this study is approximately 93.
To determine the sample size for the study, we can use the formula:
n = (Z * σ / E)^2,
where n is the sample size, Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the maximum allowable error or margin of error.
In this case, the researchers want the average time to fix a rivet to be off by at most 3.5 seconds, which can be considered as the margin of error (E).
Given that the confidence level is 95%, the corresponding z-score (Z) is 1.96. The population variance (σ^2) is known to be 55 seconds^2.
Plugging these values into the formula, we can calculate the sample size:
n = (1.96 * sqrt(55) / 3.5)^2,
where sqrt denotes the square root.
Evaluating the expression:
n ≈ 92.607.
Sine the sample size should be a whole number, we can round up the value to obtain the final sample size.
Therefore, the recommended sample size for the study is approximately 93.
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Does anyone know how to solve this?
Answer:
2 3/9 + 3 8/9 = 6 2/9
1. The fare of 12 kg of luggage for a distance of 36km is 24 rupees
How much fare will be charged for a luggage of 18kg for a distance
of 12km?
Answer:
16 rs maybe not sure sry if wrong
does anyone know this answer? timed test
Also called regrouping this is when adding numbers results in more than two digits and one digit is placed in the colum to the left
Answer:
Carrying forward.
Step-by-step explanation:
When regrouping is done to add the numbers where results in a more than 2 digit and one digit is placed to left Colum is called as carrying forward. As regrouping refers to carrying the place values in order to perform operations like addition or subtraction.Assume S is a recursively defined set, defined by the following properties: 1∈ S n ∈ S → 2n ∈ S n ∈ S → 3n ∈ S Use structural induction to prove that all members of S are numbers of the form 2ᵃ3ᵇ, with a and b being non-negative integers. Your proof must be concise.
All members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.
We will prove by structural induction that all members of set S can be expressed as numbers of the form 2ᵃ3ᵇ, where a and b are non-negative integers.
Base Case:
We start with the base case, where n = 1. In this case, 1∈ S, and we can see that 1 can be expressed as 2⁰3⁰, which is of the desired form.
Inductive Step:
Now, assume that for some positive integer k, if n = k, then k∈ S can be expressed as 2ᵃ3ᵇ for non-negative integers a and b.
We will show that if n = k + 1, then k + 1 can also be expressed as 2ᵃ3ᵇ for non-negative integers a and b.
Case 1: If n = 2k, then we know that 2k∈ S. By the induction hypothesis, we can express 2k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 2k+1 = 2(2k) = 2ᵃ₊₁3ᵇ, which is still of the desired form.
Case 2: If n = 3k, then we know that 3k∈ S. By the induction hypothesis, we can express 3k as 2ᵃ3ᵇ for some non-negative integers a and b. Now, we can observe that 3k+1 = 3(3k) = 2ᵃ3ᵇ₊₁, which is still of the desired form.
Since we have shown that if n = k + 1, then k + 1 can be expressed as 2ᵃ3ᵇ, the proof by structural induction is complete.
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Calculate the double integral. ∬R5xsin(x+y) dA, R=(0, π6)×(0, π3)
We need to evaluate the double integral:
∬R 5x sin(x+y) dA, R=(0, π/6)×(0, π/3)
Using iterated integrals, we have:
∬R 5x sin(x+y) dA = ∫[0, π/6] ∫[0, π/3] 5x sin(x+y) dy dx
= ∫[0, π/6] [(-5/2)x cos(x+y)]|[0,π/3] dx
= ∫[0, π/6] [(-5/2)x cos(x+π/3) + (5/2)x cos(x)] dx
= (-5/2) ∫[0, π/6] x cos(x+π/3) dx + (5/2) ∫[0, π/6] x cos(x) dx
Let's evaluate each integral separately:
∫[0, π/6] x cos(x+π/3) dx
= ∫[π/3, 2π/3] (u-π/3) cos(u) du (where u = x+π/3)
= ∫[π/3, 2π/3] u cos(u) du - (π/3) ∫[π/3, 2π/3] cos(u) du
= sin(2π/3) - sin(π/3) - (π/3)(sin(2π/3) - sin(π/3))
= -π/3√3
Similarly,
∫[0, π/6] x cos(x) dx = sin(π/6)/2 = 1/4
Therefore,
∬R 5x sin(x+y) dA = (-5/2) (-π/3√3) + (5/2)(1/4) = (5π)/(6√3)
Hence, the value of the double integral is (5π)/(6√3).
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Calculate the slope of the line that contains:
(4, 5) and (-4, 3)
Directions: Select all correct answers.
Select all situation representing independent events.
Question 7 options:
Spinning spinner two times.
Rolling a die and then flipping a coin.
Taking one candy out of a bag of candies, eating it, and then taking another candy.
Taking a card from a set of ten cards, replacing it, and then, taking another card.
Taking a sock from a drawer, placing it on your foot, and then picking another sock from the drawer.
Taking a card from a set of ten card, not replacing it, and then taking another card.
Answer:
Step-by-step explanation: