The 99% confidence interval for the mean wage of all judges is given as follows:
($61.5, $68.5).
How to obtain the confidence interval?We have the standard deviation only for the sample, hence the t-distribution is used to obtain the confidence interval.
The equation that defines the bounds of the confidence interval is given as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 25 - 1 = 24 df, is t = 2.797
The remaining parameters are given as follows:
[tex]\overline{x} = 65, s = 6.25, n = 25[/tex]
Hence the lower bound of the interval is calculated as follows:
65 - 2.797 x 6.25/5 = $61.5.
The upper bound of the interval is of:
65 - 2.797 x 6.25/5 = $68.5.
Missing InformationThe problem asks for the 99% confidence interval for the mean wage of all judges.
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1. Find the slope of a line that passes through (3,-5) and (6,-6)
m=____
2. y=7 x+2
m=___
5. Find the slope of a line that passes through ( 4.5, 3.5) and (9.5, 5.5)
m=_____
6. y=-3 x-4
m=_____
The slope the lines in the given functions are -1/3, 7, 0.4 and -3
Slope of a LineThe is the ratio of the rise to run of the graph or the ratio of change in y- coordinate to the change in the x-coordinate.
The formula of slope is given as;
m = y₂ - y₁ / x₂ - x₁
1)
The points are
A = (3, -5)B = (6, -6)Applying the formula of slope of a line
m = -6 - (-5) / 6 - 3)
m = -6 + 5 / 3
m = -1/3
slope is - 1/3
2) The equation 7x + 2 is a linear equation which is modeled as y = mx + c
where m is the slope and c is the y - intercept
The slope of the linear equation y = 7x + 2 is 7
slope is 7
5) Using the formula of slope of a line
m = y₂ - y₁ / x₂ - x₁
m = 5.5 - 3.5 / 9.5 - 4.5
m = 0.4
Slope is 0.4
6) The linear function y = -3x - 4
Comparing the function with y = mx + c
The slope is -3
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Evaluate the expression when y=6 and x=9.
5y-x
Answer:
21
Step-by-step explanation:
y=6 and x=9.
5y – x
= 5(6) – 9
= 30 – 9
= 21
i hope this helped
What is the volume of this figure?
The Volume of the given figure is 264 cubic units
What is Volume?
Volume is a measurement of three-dimensional space that is occupied. It is frequently mathematically quantified using SI-derived units or different imperial or US customary units. The concept of length is linked to the definition of volume.
Solution:
Volume of Cuboid = Length * Breadth * Height
Volume of Cuboid 1 = 8*5*5 = 200 cubic units
Volume of Cuboid 2 = 8*8*1 = 64 cubic units
Total Volume = 200 + 64 = 264 cubic units
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Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an additional
charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $222.00. On her second business trip she drove 200 miles in 3 days, and
paid $139.00 for the rental. Find the daily fee, and find the mileage charge.
Daily fee is $, and the mileage charge is $.
Answer:
Daily fee is $13.75, and the mileage charge is $0.37.
Find the missing fraction
_+ 1/16=3/2
Answer:
23/16?
Step-by-step explanation:
23/16 + 1/16 = 3/2
Select the correct answer. Consider the following equation. − 16 p + 37 = 49 − 21 p Select the equation that has the same solution as the given equation. A. − 55 + 12 p = 5 p + 16 B. − 14 + 6 p = − 9 − 6 p C. 2 + 1.25 p = − 3.75 p + 10 D. 3 2 p − 5 + 9 4 p = 7 − 5 4 p
The equation that has the same solution as − 16 p + 37 = 49 − 21 p is (3/2)p - 5 + (9/4)p = 7 - (5/4)p thus option (C) is correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation.
As per the given equation,
− 16 p + 37 = 49 − 21 p
-16p + 21p = 49 - 37
5p = 12
p = 12/5 = 2.4
In the equation,(3/2)p - 5 + (9/4)p = 7 - (5/4)p
(3/2)p + (9/4)p + (5/4)p = 7 + 5
5p = 12
p = 2.4
Hence "The equation (3/2)p - 5 + (9/4)p = 7 - (5/4)p has the same solution as − 16 p + 37 = 49 − 21 p ".
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6and 3/4 divided by 1 and 1/18
Answer:
Your answer is 6.
Step-by-step explanation:
If this is correct can i get branilest? Hope this helps :)
The population of a certain single-cell organism doubles every hour, starting with 100 cells. Which COULD be an equation to model th
situation, where f(t) is the number of organisms and t is time in hours?
geometric progression with common ratio 2.
so, f(t) = 100 x [tex]2^t[/tex] be an equation to model the situation.
What is geometric progression ?A sort of sequence known as geometric progression (GP) is one in which each following phrase is created by multiplying each preceding term by a fixed number, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers.A geometric progression, also termed a geometric sequence, is a set of integers where each term after the first is obtained by multiplying the one before it by a constant, non-zero quantity known as the common ratio.Given :
starting with 100 cells.
a=100
r = 2
a certain single-cell organism doubles every hour
f(t) is the number of organisms and t is time in hours.
f(t) = 100 x [tex]2^t[/tex]
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Using - your favorite statistics software package, you generate scatter plot which displays a linear form You find regression equation and the standard deviation for both variablesThe standard deviation for X is 1.34, and the standard deviation for y is 3.6. The regression equation is reported 4 1.891 What fraction of the variation in y can be explained by the variation in the values of x? (
The regression line is yˆ = 4 + 1.891x , the coefficient of determination of two variables or the fraction of the variation in y that can be explained by the variation in the values of x is 0.51..
Here the fitted regression equation of y on x is
yˆ = 4 + 1.891x ---(*)
where, x --> Independent variable
yˆ --> predicted value of the dependent variable
Now, b₁ = slope cofficient = 1.891 ~ 1.91
(estimated from least squares method)
We have given that,
Standard deviations for X = 1.34 = sₓ say
Standard deviations for Y = 3.6 = sᵧ say
we know, b₁ = r₀( sₓ/sᵧ ) where ro is corr(X,Y)
=> 1.91 = r₀ (3.6/1.34)
=> 1.91×1.34/ 3.6 = r₀
=> r₀ = 0.71944
Defining, R² = cofficient of determination of two variables = Proportion of variation in Y , explained by the variation in the value of X, through the regression model.
= (r₀)² = (0.71944)² = 0.505442
R² = 0.505442 ~ 0.51 (in two decimals)
Hence, the cofficient of determination is 0.51..
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Complete question:
Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.34 , and the standard deviation for y is 3.6 . The regression equation is reported as y = 4 + 1.891x . What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 1 and 2.)
Rocky spends 1 3/4 hours working out
on Monday, 2½ hours on Wednesday and 5/6 of
an hour on Friday. How much time did he spend
working out this week.
Answer:
5 1/12 hours
Step-by-step explanation:
You need a common denominator and that would be 12
1 [tex]\frac{9}{12}[/tex] ([tex]\frac{3}{4}[/tex] x [tex]\frac{3}{3}[/tex]) another name for [tex]\frac{3}{3}[/tex] is 1. You are making an equivalent fraction
2 [tex]\frac{6}{12}[/tex] ([tex]\frac{1}{2}[/tex] x [tex]\frac{6}{6}[/tex])
[tex]\frac{10}{12}[/tex] ([tex]\frac{5}{6}[/tex] x [tex]\frac{2}{2}[/tex])
1 [tex]\frac{9}{12}[/tex] + 2 [tex]\frac{6}{12}[/tex] + [tex]\frac{10}{12}[/tex] = 3 [tex]\frac{25}{12}[/tex]
I can break [tex]\frac{25}{12}[/tex] into [tex]\frac{12}{12}[/tex] + [tex]\frac{12}{12}[/tex] + [tex]\frac{1}{12}[/tex] Another name for [tex]\frac{12}{12}[/tex] is 1
3 + 1 + 1 + [tex]\frac{1}{12}[/tex]
5 [tex]\frac{1}{12}[/tex]
Solve the following equation:
3x^2= -12
a.
X = 2
b. x=-2
C.
No real solutions
d.
X = ‡2
3x^2= -12
Divide each side by factors that do NOT contain the variable
This means X = +/- 2 (with imaginary number)
Olivia and liam paint their houses. Olivia can paint her house in 9 hours while liam paints his in 7 hours. If olivia and liam painted together, write an equation that would find the time in hours t it. would take them to paint a house.
Answer:
t = 7/9 * 9 + 7/9 * 7 = 14 hours
Step-by-step explanation:
The product of a number and 3 less than the number is 18. Find the number
Answer: n = 6 or n = -3
Step-by-step explanation:
n(n-3)=18
n^2 - 3n = 18
n^2 - 3n - 18 = 0
n = 6 or n = -3
Question 1 of 10
What is the slope formula?
OA. ₂-₁,
Y/₂-1/₁
OB. -
X₂-X₁
O c. 2-₁
X₂-1/₁
D. +₁
Y/₂+1/₁
SUBMIT
Answer:
(y2-y1)/(x2/x1)
Step-by-step explanation:
Well uh I hope you get it
Weston Inc. just agreed to pay £19632 today, £19827 in one year later, £32464 in two years later to a landlord to explore for, but not extract valuable materials. If the landlord invests the money at a rate of 5.81% compounded annually, what is the investment worth two years from today?
Your deposit must be returned by the landlord within 30 days, less any sum subtracted for damages.
What is the most a landlord can raise rent?To maximize their earnings, landlords set the rent on rental properties at market rates. Should they... Your reported income plays a big part in how much rent you will have to pay.
3% of the existing rent or the local Consumer Price Index (CPI), whichever is higher, is the maximum increase in rent that the landlord is permitted to make once every 12 months. The requirements of California Tenant Protection Act (AB1482) are expressly applicable to rent hikes.
A renter may be evicted even without a lease. Considering that there isn't a lease or rental agreement, a landlord or property management is free to evict a renter for any reason. The sole need under law would be that the renter being evicted receive a formal notice before being removed.
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NO LINKS!! Find the sum of the infinite geometric series:
-125/36 + 25/6 - 5 + 6 - . . .
Answer:
[tex]S_{\infty}=-\dfrac{625}{396}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given geometric series:
[tex]-\dfrac{125}{36}+\dfrac{25}{6}-5+6-...[/tex]
To find the common ratio, divide a term by the previous term:
[tex]\implies r=\dfrac{a_4}{a_3}=-\dfrac{6}{5}[/tex]
Substitute the found common ratio and given first term into the sum formula:
[tex]\implies S_{\infty}=\dfrac{-\frac{125}{36}}{1-\left(-\frac{6}{5}\right)}[/tex]
[tex]\implies S_{\infty}=\dfrac{-\frac{125}{36}}{1+\frac{6}{5}}[/tex]
[tex]\implies S_{\infty}=\dfrac{-\frac{125}{36}}{\frac{11}{5}}[/tex]
[tex]\implies S_{\infty}=-\dfrac{125}{36} \times\dfrac{5}{11}[/tex]
[tex]\implies S_{\infty}=-\dfrac{625}{396}[/tex]
Find the multiplicative inverse of −1/2.
Answer:
2
Step-by-step explanation:
To determine the multiplicative inverse of a number, we use the following rule: The multiplicative inverse of a number a/b is b/a.
Are there any circles for which the relationship between the diameter and the circumference cannot be represented by π? explain
Well, the diameter and circumference scale perfectly. Therefore, the ratio will remain the same regardless of how big or tiny the circle is. For all circles, circumference is equal to x diameter. There are no exceptions because this is the definition of.
Give an example of diameter.
If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.
What is a circle's circumference?
A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).
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I'm not sure about this question DO NOT MIND THE TEXT IN THE BOX JUST ANSWER PLEASEEE!!
DONT ASNWER IF YOU DONT KNOW!
Answer:
You had it right, now all you have to do it add 18 and 30 and 4 and 3 and you should get your answer, than you take the answer and write 48r+7w=55rw
Step-by-step explanation:
I added 18, 30, 4, and 3. I got 48 for the 18 and 30 and 7 for the 4 and 3
Question 3 Write a method that solves for x in the quadratic equation. The parameters are a, b, c, and boolean flag that indicates whether it will solve the equation with addition or subtraction in the numerator. 2-4ac ㄨㄧ- 2a Source: Wikipedia The method will return the value of x
On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )
What is quadratic equation?A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.
public static double solve(double a, double b, double c, boolean flag)
{ double d = Math.sqrt(b*b - 4*a*c); if(flag)
{ return (-b + d) / (2*a); }
else { return (-b - d) / (2*a); } }
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the amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.4 years and a standard deviation of 2.1 years. random samples of size 12 are drawn from the population and the mean of each sample is determined.
O 5.4 years, 0.48 years O 5.4 years, 0.10 years O 1.18 years, 2.2 years
O 1.18 years, 0.48 years
Using statistics we know that the mean value is 5.6 years, and the standard error is 0.4478.
What are statistics?The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics.
Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
So, we have:
μ = 5.6
σ = 1.9
n = 18
Figuring out each sample's mean:
Therefore, the population means itself serves as the best estimator of the sample mean.
μₓ = μ = 5.6
The sample mean is 5.6 years as a result.
Estimating the standard deviation:
By using the formula:
Standard error = σ/√n
Given that the samples are of size n = 18 and the standard deviation is = 1.9:
Standard error = 1.9/√18 = 0.4478
Therefore, using statistics we know that the mean value is 5.6 years, and the standard error is 0.4478.
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Complete question:
The amount of time employees of a telecommunications company have worked for the company is normally distributed with a mean of 5.6 years and a standard deviation of 1.9 years. Random samples of size 18 are drawn from the population and the mean of each sample is determined. Find the mean and the standard error.
Find the z-score such that the area under the standard normal curve to its left is 0.2
The z-score such that the area under standard normal curve to its left is 0.2 is found as -0.84.
Explain the term Z-score?A mathematical table known as the Z table, also known as the Z-score table or the standard normal table, is used to determine the likelihood that the z-score number is below, above, or in between the values just on standard normal distribution.
Z-scores are the most used name for standard scores. Its similar concepts, like as z-values, standardized factors, and normal scores, are utilized in this article.A positive Z score score implies that the raw score is higher than the distribution's mean.For instance, a z-score of 2 indicates that the result is two standard deviations above the mean.If the Z score is negative, the distribution's mean is below the raw score value.For the stated question,
You simply need to discover the location of 0.2 on the z-score table and then its z-score. (The area to the left of a z-score is shown in the table)
Our z-score is -(0.8 + 0.04) = - 0.84 as a result.
Thus, the z-score such that the area under the standard normal curve to its left is 0.2 is found as -0.84.
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Choose answers that describe the quadrilateral STUV if ST|| UV,TU||VS
and diagonals are congruent: SU≅TV
Parallelogram
Triangle
Rhombus
Square
Trapezoid
By using properties of quadrilateral, it can be concluded that-
Square describes the quadrilateral STUV
What is a quadrilateral?
Quadrilateral is a two dimensional four sided figure.
Here the properties of quadrilateral STUV is
Pair of opposite sides are parallel
Diagonals are congruent.
In a parallelogram, the pair of opposite sides are parallel but diagonals are not congruent
Triangle is not a quadrilateral
In Rhombus, the pair of opposite sides are parallel but the diagonals are not congruent
In square, the pair of opposite sides are parallel and the diagonals are congruent
In Trapezoid, one pair of opposite sides are parallel and one pair of opposite sides are non parallel.
So Square describes the quadrilateral STUV
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Determine the end behavior of the polynomial function.
f(x)= -2x^3 +3x^2 +2x -1
The correct option is (a)
As x ⇒ ∞, f(x) ⇒ -∞ and As x ⇒ -∞, f(x) ⇒ ∞.
What is Polynomial function ?
The terms poly and nomial combine to form the word polynomial. We can define polynomials as "algebraic expressions with many terms" because "poly" means many and "nomial" denotes the term.
Given : f(x)= -2x^3 +3x^2 +2x -1
In order to determine the end behavior of the polynomial function, we are required to check the highest degree of the polynomial and the coefficient of the term which has highest degree.
Here, The highest degree of the polynomial is 3 and the coefficient of the term which has highest degree is -2.
Since, the coefficient is negative, the graph will move right down which means as x ⇒ ∞, f(x) ⇒ -∞.
Similarly, the degree is odd which states that the sign will be opposite of what the coefficient has. So, As x ⇒ -∞, f(x) ⇒ ∞.
Hence, As x ⇒ ∞, f(x) ⇒ -∞ and As x ⇒ -∞, f(x) ⇒ ∞.
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Write an equation of the line below.
Answer: Recommended to simplify to y=1/4x+3
y=2/8x+3
*Note slope may need to be simplified to (1/4 depends)
Step-by-step explanation: Formula y=mx+b
Slope m=2/8 >>>>simplify to 1/4 up 1 over 4 (the x goes beside this)
Look on y-axis count up to the dot y=3
To compare the means of three samples -- perhaps three experimental treatments -- we should use this test:
A. Pooled variance t-test assuming equal variance.
B. Separate variance t-test assuming unequal variance.
C. Z-test of difference of means.
D. Analysis of variance
The correct answer is D. Analysis of variance (ANOVA). To compare the means of three samples -- perhaps three experimental treatments -- we should use ANOVA Test.
ANOVA is a statistical test that is used to compare the means of two or more samples. It can be used to determine whether there is a significant difference between the means of the samples, and to identify which samples are significantly different from one another.
A pooled variance t-test is a statistical test that is used to compare the means of two samples, assuming that the variances of the two samples are equal. This test is not suitable for comparing the means of three or more samples.
A separate variance t-test is a statistical test that is used to compare the means of two samples, assuming that the variances of the two samples are not equal. This test is also not suitable for comparing the means of three or more samples.
A z-test of difference of means is a statistical test that is used to compare the means of two independent samples. It is not suitable for comparing the means of three or more samples.
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Realiza las siguientes potencias
The powers is 5 - 1/2³.
What is Exponents and Powers?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
The number of times a number has been multiplied by itself is referred to as an exponent.
Given:
(5 - [tex]2^{-3}[/tex])
As, we know that
[tex]a^{-m[/tex] = 1/ [tex]a^m[/tex]
Then, (5 - [tex]2^{-3}[/tex])
= 5 - 1/2³
= 5-1/8
= 40-1/8
= 39/8
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The Translation of attached question is
Make the following powers
The greatest common factor of 250 and 300 is?
Answer:
250 / 50 = 5
300 / 50 = 6
Therefore, the greatest common factor of 250 and 300 is 50.its also known as a number to be divided so you can get the lowest fractionStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-The greatest common factor of 250 and 300 is 50
What is the greatest common factor of two numbers?The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number.
Given here: The numbers as 250 and 350
Steps to find GCF
Find the prime factorization of 250
250 = 2 × 5 × 5 × 5
Find the prime factorization of 300
300 = 2 × 2 × 3 × 5 × 5
To find the GCF, multiply all the prime factors common to both numbers
Hence, GCF = 2 × 5 × 5 GCF = 50
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A rectangle is split into four triangle as shown. What is the area of shade triangle?
Answer:
First of all u need to find the rectangle area then subtract the area of three triangles.
step1 : 3×4=12
step2: 1×4/2 + 2×3/2 + 3×1/2 = 6.5
Answer = 12 - 6.5 = 5.5
Which expression is equal to 7 + 6X5-2?
A) 13X5-2
B) 7+11-2
C) 13 X 3
D) 37-2
Answer:
So, in the expression 7 + 6X5-2, we must first multiply 6 and 5, which gives 30. Then we must add 7 and 30, which gives 37. Finally, we must subtract 2 from 37, which gives a final score of 35.
Therefore, the expression 7 + 6X5-2 is equal to 37-2. The correct answer is D) 37-2.