Answer:
the integer is 5
Step-by-step explanation:
x^2+3(x+1)=43
x^2+3x+3=43
x^2+3x+(9/4)=43-3+(9/4)
(x+(3/2))^2=42 1/4
x+(3/2)=sqrt(42 1/4)
x+(3/2)=6 1/2
x=(6 1/2)-(3/2)
x=5
check:
5^2+3(6)=43
25+18=43
43=43
Answer:
5
Step-by-step explanation:
let positive integer be x
x² + 3(x+1)=43
x²+3x+3-43=0
x² + 3x - 40 = 0
x² + 8x - 5x - 40 = 0
x(x+8) - 5(x+8)=0
(x-5)(x+8)=0
x-5=0 or x+8=0
x=5. or x=-8
but the question says positive integer,
therefore, x=5
Thank you for all the help guys
Answer:
a is the right answer thanksFind the missing side. Round your answer to the nearest tenth
Answer:
14.7
Step-by-step explanation:
tan(73)=48/x
or, x=48/tan(73)
or, x=14.7 (rounded to the nearest tenth)
Answered by GAUTHMATH
How many sides does a regular polygon have if each interior angle measures 178°?
The number of sides of a regular polygon with an interior angle [tex]\[{178^ \circ }\][/tex] is 180.
What is the regular polygon?
A polygon is regular when all angles are equal and all sides are equal.
A regular polygon has if each interior angle.
Interior angle of given polygon =178
An exterior angle of polygon =180 −178 =2
The sum of exterior angles of any polygon is 360
Number of sides of a regular polygon
[tex]=\frac{360}{2}[/tex]
[tex]=180[/tex]
Therefore, The number of sides of a regular polygon is 180.
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A population proportion is 0.57. Suppose a random sample of 657 items is sampled randomly from this population.
a. What is the probability that the sample proportion is greater than 0.58?
b. What is the probability that the sample proportion is between 0.54 and 0.60?
c. What is the probability that the sample proportion is greater than 0.56?
d. What is the probability that the sample proportion is between 0.53 and 0.55?
e. What is the probability that the sample proportion is less than 0.48?
A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area
Answer:
11 meters
Step-by-step explanation:
First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).
The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is
(√3/4)((11-4x)/3)²
= (√3/4)(11/3 - 4x/3)²
= (√3/4)(121/9 - 88x/9 + 16x²/9)
= (16√3/36)x² - (88√3/36)x + (121√3/36)
The total area is then
(16√3/36)x² - (88√3/36)x + (121√3/36) + x²
= (16√3/36 + 1)x² - (88√3/36)x + (121√3/36)
Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)
When x=0, each side of the triangle is 11/3 meters long and its area is
(√3/4)a² ≈ 5.82
When x=2.75, each side of the square is 2.75 meters long and its area is
2.75² = 7.5625
Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters
The length of the square must be 4 m in order to maximize the total area.
What are the maxima and minima of a function?When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.
We have,
Length of the wire = 11 m
Let the length of the wire bent into a square = x.
The length of the wire bent into an equilateral triangle = (11 - x)
Now,
The perimeter of a square = 4 side
4 side = x
side = x/4
The perimeter of an equilateral triangle = 3 side
11 - x = 3 side
side = (11 - x)/3
Area of square = side²
Area of equilateral triangle = (√3/4) side²
Total area:
T = (x/4)² + √3/4 {(11 -x)/3}² _____(1)
Now,
To find the maximum we will differentiate (1)
dT/dx = 0
2x/4 + (√3/4) x 2(11 - x)/3 x -1 = 0
2x / 4 - (√3/4) x 2(11 - x)/3 = 0
2x/4 - (√3/6)(11 - x) = 0
2x / 4 = (√3/6)(11 - x)
√3x = 11 - x
√3x + x = 11
x (√3 + 1) = 11
x = 11 / (1.732 + 1)
x = 11/2.732
x = 4
Thus,
The length of the square must be 4 m in order to maximize the total area.
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3. You buy butter for $3 a pound. One portion of onion compote requires 2 oz of butter. How much does the butter for one portion cost?
Answer:
The butter for one portion cost $ 0.375.
Step-by-step explanation:
Given that you buy butter for $ 3 a pound, and one portion of onion compote requires 2 oz of butter, to determine how much does the butter for one portion cost, the following calculation must be performed:
2 oz = 0.125 lb
1 = 3
0.125 = X
3 x 0.125 = X
0.375 = X
Therefore, the butter for one portion cost $ 0.375.
The SAT and ACT college entrance exams are taken by thousands of students each year. The scores on the exam for any one year produce a histogram that looks very much like a normal curve. Thus, we can say that the scores are approximately normally distributed. In recent years, the SAT mathematics scores have averaged around 480 with standard deviation of 100. The ACT mathematics scores have averaged around 18 with a standard deviation of 6.
a. An engineering school sets 550 as the minimum SAT math score for new students. What percent of students would score less than 550 in a typical year?
b. What would the engineering school set as comparable standard on the ACT math test?
c. What is the probability that a randomly selected student will score over 700 on the SAT math test?
Answer:
a) 75.8% of students would score less than 550 in a typical year.
b) The comparable standard would be a minimum ACT score of 22.2.
c) 0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Question a:
SAT, so mean of 480 and standard deviation of 100, that is, [tex]\mu = 480, \sigma = 100[/tex]
The proportion is the p-value of Z when X = 550. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{550 - 480}{100}[/tex]
[tex]Z = 0.7[/tex]
[tex]Z = 0.7[/tex] has a p-value of 0.758.
0.758*100% = 75.8%
75.8% of students would score less than 550 in a typical year.
b. What would the engineering school set as comparable standard on the ACT math test?
ACT, with a mean of 18 and a standard deviation of 6, so [tex]\mu = 18, \sigma = 6[/tex]
The comparable score is X when Z = 0.7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.7 = \frac{X - 18}{6}[/tex]
[tex]X - 18 = 0.7*6[/tex]
[tex]X = 22.2[/tex]
The comparable standard would be a minimum ACT score of 22.2.
c. What is the probability that a randomly selected student will score over 700 on the SAT math test?
This is 1 subtracted by the p-value of Z when X = 700, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 480}{100}[/tex]
[tex]Z = 2.2[/tex]
[tex]Z = 2.2[/tex] has a p-value of 0.9861.
1 - 0.9861 = 0.0139
0.0139 = 1.39% probability that a randomly selected student will score over 700 on the SAT math test.
To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used
Answer:
Cluster Sampling
Step-by-step explanation:
Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.
The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. Which of the following correctly labels the population?
1–1020
01–1020
001–1020
0001–1020
I think its (B), 01-1020.
Answer:
Should be (B)
01-1020
ED2021
The correct label for the population is 1 - 1020,
Option A is the correct answer.
What is random sampling?It is the way of choosing a number of required items from a number of population given.
Each items has an equal probability of being chosen.
We have,
The population in this case refers to the entire group of interest, which is the entire student body of the school.
The total number of students is 1,020.
The population is usually labeled with a range or interval that includes all the possible values of the variable of interest.
In this case, the variable of interest is whether or not a student has an opinion on parking.
The correct label for the population is 1-1020, as this range includes all possible student identification numbers at the school.
The other options (01-1020, 001-1020, and 0001-1020) are not correct because they suggest that there are leading zeros in the student identification numbers, which is not usually the case.
Thus,
The correct label for the population is 1-1020,
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write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
FH ≈ 6.0
Step-by-step explanation:
Using the sine ratio in the right triangle
sin49° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FH}{FG}[/tex] = [tex]\frac{FH}{8}[/tex] ( multiply both sides by 8 )
8 × sin49° = FH , then
FH ≈ 6.0 ( to the nearest tenth )
Answer:
6
Step-by-step explanation:
sin = opposite/hypotenuse
opposite = sin * hypotenuse
sin (49) = 0,75471
opposite = 0,75471 * 8 = 6,037677 = 6
please can anyone help me with this question what is the probability of the spinner landing on an even number.
2. How many solutions does this system of equations have? *
y = 5x – 2
y = 5x + 7
Answer:
No solution.
Step-by-step explanation:
[tex]{ \sf{y = ±∞ \: \: and \: \: x = ±∞}}[/tex]
You randomly select one card from a 52-card deck. Find the probability of selecting the 9 of spades or the 3 of clubs.
The probabilitiy is ___.
(Type an integer or a fraction. Simplify your answer.)
Answer:
2/52=1/26
Step-by-step explanation:
Exercise 6.2
1.
a.
The total cost function is given by C = 100 - 5x + 7x2, find
the average cost and marginal cost.
9514 1404 393
Answer:
average cost = 7x -5 +100/xmarginal cost = 14x -5Step-by-step explanation:
The average cost is the total cost divided by the number of units produced:
average cost = C/x = 100/x -5 +7x
__
The marginal cost is the derivative of the total cost function.
marginal cost = -5 +14x
If a system including the quadratic equation representing the parabola and a linear equation has no solution, which linear equation could be the second equation in the system? A. 1/2x=y+4 B. 2x-y=0 C.y=6 D.y=2x+6
9514 1404 393
Answer:
D. y=2x+6
Step-by-step explanation:
The line cannot intersect the parabola if it has a y-intercept greater than 5 and a suitable slope. The only sensible answer choice is ...
y = 2x +6
Answer:
D. y = 2x + 6.
Step-by-step explanation:
The required equation would not intersect the parabola at any point.
The only one to fit that is D.
What is the value of the x variable in the solution to the following system of equations? (5 points) 2x − 3y = 3 5x − 4y = 4 Select one: a. −1 b. 0 c. x can be any number as there are infinitely many solutions to this system d. There is no x value as there is no solution to this system
Answer:
D. There is no x value as there is no solution to this system
Step-by-step explanation:
2x − 3y = 3 5x − 4y = 4
5x - 4y = 4 -4y = -5x + 4 y = 5/4x - 1
2x - 3(5/4x - 1) = 3
2x - 15/4x + 3 = 3
-7/4x = 0
x = 0
the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)
9514 1404 393
Answer:
all real numbers
Step-by-step explanation:
The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.
The domain of g(x) = f(-x) is all real numbers.
5/10+4/16 in simplest form
Use the substitution method to solve this system.
y = 2x+4
3x+y = 9
Answer:
x = 1; y=6
Step-by-step explanation:
y = 2x +4
3x + y = 9
Substitute 2x+4 for y in 3x+y = 9
3x + y = 9
3x + 2x+4 = 9
5x + 4 = 9
5x = 9-4
5x = 5
5x/5 = 5/5
x = 1
Substitute 1 for x in y = 2x +4
2(1) + 4
2 + 4
= 6
Answered by Gauthmath
Which of the following points would fall on the line produced by the point-slope form equation y - 10 = 3(x - 11) when graphed?
Answer:
(-5,-37)
(-4,-34)
(-3,-31)
(-2,-28)
(-1,-25)
(0,-22)
(1,-19)
(2,-16)
(3,-13)
(4,-10)
(5,-7)
(6,-4)
Step-by-step explanation:
y - 10 = 3(x - 11)
y - 10 = 3x - 33
y = 3x -22
Find the arc length of the 3/4 of a circle with a radius of 5
Answer:
7.5 pi
Step-by-step explanation:
The formula for arc length of a sector is denoted as
[tex]\frac{x}{360}2\pi r[/tex], where x is the central angle of the sector.
Since the sector is 3/4 of a circle, the central angle will be 3/4 of 360 degrees.
3/4 of 360 is 270, so we have our central angle. We also have our radius which we can plug into the formula.
[tex]\frac{270}{360}2(5)\pi[/tex]
2 times 5 is equal to 10, and 270/360 simplifies to 3/4. 3/4 times 10 is equal to 7.5, so the answer is 7.5 pi
Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected and the diameter is measured. The resulting data (in millimeters) are as follows: No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24 Use the data above to calculate a 95% two-sided confidence interval on the mean rod diameter. Assume the data are normally distributed. (a) Calculate the sample mean and standard deviation. Round the sample mean and the sample standard deviation to 2 and 3 decimal places respectively (e.g. 98.76 and 98.765). (b) Calculate the 95% two-sided confidence interval on the true mean rod diameter. Round your answers to 3 decimal places (e.g. 98.765).
Answer:
(8.213 ; 8.247)
Step-by-step explanation:
Given the data :
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Dia. 8.23 8.16 8.23 8.25 8.26 8.23 8.20 8.26 8.19 8.23 8.20 8.28 8.24 8.25 8.24
Sanple size, n = 15
Sample mean, xbar = Σx / n = 123.45 / 15 = 8.23
The sample standard deviation, s = √(x -xbar)²/n-1
Using calculator :
Sample standard deviation, s = 0.03116
s = 0.031 (3 decimal places)
The 95% confidence interval :
C.I = xbar ± (Tcritical * s/√n)
Tcritical at 95%, df = 15 - 1 = 14
Tcritical = 2.145
C.I = 8.23 ± (2.145 * 0.031/√15)
C.I = 8.23 ± 0.0171689
C.I = (8.213 ; 8.247)
ive gotten it wrong like 4 times n i cannot figure it out pls help
Answer:
x = 74.74 m
Step-by-step explanation:
you need simple trigonometry to solve it
cosine of an angle is the ratio of the adjacent side to the hypotenuse
cos(42.2) is about 0.74
so X / Hypotenuse = 0.74
we know hypotenuse is 101 m
X / 101 = 0.74
x = 74.74 m
hope this helped!
A bank wishes to estimate the mean balances owed by customers holding Mastercard. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?
A. 76
B. 85
C. 86
D. 77
Answer:
D. 77
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population standard deviation is estimated to be $300
This means that [tex]\sigma = 300[/tex]
If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?
This is n for which M = 80. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]80 = 2.327\frac{300}{\sqrt{n}}[/tex]
[tex]80\sqrt{n} = 2.327*300[/tex]
[tex]\sqrt{n} = \frac{2.327*300}{80}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*300}{80})^2[/tex]
[tex]n = 76.15[/tex]
Rounding up:
77 cardholders should be sampled, and the correct answer is given by option d.
plzzzzz helllllllppppppp worth 25 points
Answer:
Step-by-step explanation:
Let's fill that in with what the variables are "worth":
(3)(-3)+2(-2) and simplify to
-9 + (-4) which, when you add those 2 negatives, gives you
-13, choice B.
Answer:
[tex]x = 3 \\ y = - 3 \\ z = - 2 \\ xy + 2z = 3 \times - 3 + 2 \times - 2 \\ = - 9 - 4 \\ = - 13 \\ thank \: you[/tex]
Which of the following behaviors would best describe someone who is listening and paying attention? a) Leaning toward the speaker O b) Interrupting the speaker to share their opinion c) Avoiding eye contact d) Asking questions to make sure they understand what's being said
Answer:
d) Asking questions to make sure they understand what's being said
Step-by-step explanation:
Asking questions is important for learning and clears up any confusion.
need help with math plz thanks
Answer:
0
Step-by-step explanation:
[tex]f(x)=2x-4\\f(2)=2(2)-4\\f(2)=4-4\\f(2)=0[/tex]
Answer:
0
Step-by-step explanation:
If f(x) = 2x - 4
Then f(2) = 2(2) -4
f(2) = 4 - 4
= 0
A survey asked 25 students about their favorite sport. A frequency table of their responses is below.
Basketball, 4; football, 7; lacrosse, 3; soccer, 8; volleyball, 3.
Which of the following is the correct relative frequency table for the students’ favorite sport?
Answer: The second one
Step-by-step explanation:
response/25=x/100 and then you solve for x
A percentage is a way to describe a part of a whole. The correct table is B.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given the number of students who play different sports as,
Basketball = 4
Football = 7
Lacrosse = 3
Soccer = 8
Volleyball = 3
Now, the percentage of students for each sport can be written as,
Basketball = 4/25 = 0.16
Football = 7/25 = 0.28
Lacrosse = 3/25 = 0.12
Soccer = 8/25 = 0.32
Volleyball = 3/25 = 0.12
Hence, the correct table is B.
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If f(x)=-4x-5 and g(x)=3-x whats is g(-4)+f(1)
Answer: -2
Step-by-step explanation:
g(-4) = 3 - (-4) = 3 + 4 = 7f(1) = -4(1) - 5 = -4 - 5 = -9g(-4) + f(1) = 7 + (-9) = 7 - 9 = -2
Use the confidence level and sample data to find a confidence interval for estimating the population μ. Round your answer to the same number of decimal places as the sample mean.
Test scores: n = 92, = 90.6, σ = 8.9; 99% confidence
Options:
A.) 88.2 < μ < 93.0
B.) 88.4 < μ < 92.8
C.) 89.1 < μ < 92.1
D.) 88.8 < μ < 92.4
Answer: Choice A.) 88.2 < μ < 93.0
=============================================================
Explanation:
We have this given info:
n = 92 = sample sizexbar = 90.6 = sample meansigma = 8.9 = population standard deviationC = 99% = confidence levelBecause n > 30 and because we know sigma, this allows us to use the Z distribution (aka standard normal distribution).
At 99% confidence, the z critical value is roughly z = 2.576; use a reference sheet, table, or calculator to determine this.
The lower bound of the confidence interval (L) is roughly
L = xbar - z*sigma/sqrt(n)
L = 90.6 - 2.576*8.9/sqrt(92)
L = 88.209757568781
L = 88.2
The upper bound (U) of this confidence interval is roughly
U = xbar + z*sigma/sqrt(n)
U = 90.6 + 2.576*8.9/sqrt(92)
U = 92.990242431219
U = 93.0
Therefore, the confidence interval in the format (L, U) is approximately (88.2, 93.0)
When converted to L < μ < U format, then we get approximately 88.2 < μ < 93.0 which shows that the final answer is choice A.
We're 99% confident that the population mean mu is somewhere between 88.2 and 93.0
