Answer:
12, 20, 5, 30, 10, 14, 10, 20, 10, 16
Step-by-step explanation:
1.) 21-9=12
2.)35-15=20
3.) 30-25=5
4.) 40-10=30
5.) 30-20=10
11.) 34-20=14
12.) 22-12=10
13.) 30-10=20
14.) 19-9=10
15.) 28-12=16
express 2^6 × 2^2 in the form 8^p
The value of the expression 2^6 × 2^2 is 8^2 * 4
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the value of the expression?The expression is given as
2^6 × 2^2
Apply the product law of indices to the above expression
So, we have
2^6 × 2^2 = 2^(6 + 2)
Evaluate the sum in the above expression
So, we have
2^6 × 2^2 = 2^8
Expand the expression
So, we have
2^6 × 2^2 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
This gives
2^6 × 2^2 = 8 * 8 * 4
So, we have
2^6 × 2^2 = 8^2 * 4
Hence, the value of the expression 2^6 × 2^2 is 8^2 * 4
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A population has a mean = 79 and a standard deviation = 18. Find the mean and standard deviation of a sampling distribution of sampling means with sample size = 36.
The sampling distribution of sample means is a mean of 79 and a standard deviation of 3.
What is the standard deviation?The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.
Given that,
Population mean, [tex]\bar{x}[/tex] = 79
Population standard deviation, σ = 18
Sample size, n = 36
We have to determine the mean and standard deviation of a sampling distribution of sample means.
Let X denotes a random variable distributed with a mean and standard deviation of 85 and 28 respectively.
Also, if a random sample of size n is drawn from the population, then the sample mean is denoted by [tex]\bar{x}[/tex].
The sampling distribution of sample means [tex]\bar{x}[/tex] is given by:
ц [tex]\bar{x}[/tex] = ц
σ [tex]\bar{x}[/tex] = σ/√n
Therefore, for the sample size n = 36, the sampling distribution of sample means [tex]\bar{x}[/tex] is obtained as:
ц [tex]\bar{x}[/tex] = 79
σ [tex]\bar{x}[/tex] = 18/√36 = 3
Hence, the required sampling distribution of sample means is mean of 79 and a standard deviation of 3.
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Find the volume of the solid generated by revolving the region r bounded by y=e^-2x, y=0, x=0, x=ln9
The volume of the solid generated by revolving the region R bounded by
y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9 around x-axis = 0.25 cubic units
Given the region R bounded by y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9.
We will find the volume of the solid obtained by revolving this region around the x-axis through disc integration method.
The disc integration method is used to find the volume of a solid obtained by revolving a region around an axis parallel to x-axis.
Then, volume, V = [tex]\int\limits^0_{ln9} {y^2} \, dx[/tex]
= [tex]\int\limits^0_{ln9} {(e^{-2x})^2} \, dx[/tex]
= [tex]\int\limits^0_{ln9} {e^{-4x}} \, dx[/tex]
= [tex]\frac{e^{-4x}}{-4} |_{x=0\ to \ x=ln9}[/tex]
= [tex]\frac{e^{-4 ln9}}{-4} +\frac{1}{4}[/tex]
= [tex]\frac{9^{-4}+1}{4}[/tex] ≈ 0.25 cubic units
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5 - 4k = -7
please help
Answer:
k = 1.75
Step-by-step explanation:
5 - 4k = -7
k = 1.75, because if you subtract 4 from both sides, you are left with 1.75 = -7.
Answer:
k = 3
Step-by-step explanation:
5 - 4k = - 7 ( subtract 5 from both sides )
- 4k = - 12 ( divide both sides by - 4 )
k = 3
(2a^-5)(-5a^9)
simplify the expression. show your work and justify each step.
Step-by-step explanation:
[tex] = (2 {a}^{ - 5} ) \times ( - 5 {a}^{9} )[/tex]
[tex] = (2 \times ( - 5)) {a}^{ - 5 + 9} [/tex]
[tex] = - 10 {a}^{4} [/tex]
4) Sara took a ferry to a nearby island that lasted for 5 days. Although she forgot to check the date when she departed, during the trip she heard someone say the date was August 14". When she arrived on the island, a native told Sara it was August 16th. What date did Sara start her trip?
A random sample of 100 diabetics undergoes genotyping and it was found that 23 of them have the gene. compute the z test statistic needed for this hypothesis test.
The z test statistic needed for this hypothesis test is 0.75 .
Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.
NOW,
sample proportion = p = x / n = 0.23
Test statistics
z = ( p - p0 ) / [tex]\sqrt{ p0*(1-p0)}[/tex] / n
= ( 0.23 - 0.20) / [tex]\sqrt{ (0.20*0.80) / 100}[/tex]
= 0.75
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An 8ft length of 4 inch wide crown molding costs $14. how much will it cost to buy 40ft of crown molding?
It would cost $70 to buy 40 ft of crown molding.
What is cost explain?
Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.8 ft length costs $14
To find the cost of 1 ft length,
Divide through by 8
8ft/8 length costs $14/8
1ft costs $1.75
Now, to find the cost of 40 ft length
1ft costs $1.75
1 ft x 40 would cost $1.75
40 ft would cost $70
Therefore, it would cost $70 to buy 40 ft of crown molding.
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is the point with coordintaes (-2,-9) on the line whose equation is y=4x - 1?
Answer:
Yes
Step-by-step explanation:
If you have a graphing calculator or something similar, that could really help because all you would have to do is plug in the equation and look up the table and it would show that coordinate in there.
A. Independent Activity 1 Identify whether the following equations are quadratic equations or not? m( 2m + 3) =0 11t2 (t - 4 ) = 0 5h + h2 = - 7 4b (b - 2 ) = - 8 y2 + 7y - 6 = 0 please answer
1, 3, 4,5
The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfill the equation (α, β).
It is a given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.
1)m( 2m + 3) =0
2m²+3m=0
Yes it is a quadratic equation.
2) 11t² (t - 4 ) = 0
11t³-44t²=0
NO
3) 5h + h² = - 7
Yes it is a quadratic equation.
4)4b (b - 2 ) = - 8
4b²-8b +8 =0
Yes, it is a quadratic equation.
5) y² + 7y - 6 = 0
Yes it is a quadratic equation.
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Three consecutive even integers such that the sum of the smallest integer and twice the middle integer is 20 more than the largest integer. What is the largest integer?
14 is the largest integer.
Let x, x+2 & x+4 be the 3 integers.
x + 2 (x+2)= (x+4)+20
x + 2x + 4 = x + 4 + 20
3x + 4 = x + 24
3x - x = 24 - 4
2x = 20
x = 20/2
x=10 for the smallest integer.
10 + 2 = 12 for the middle integer.
10 + 4 = 14 for the largest integer.
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The distance between A(-2,4) and B (1,0) is?
A. 2.24
B. 5
C. 25
D. 4
E. -5
=========================================================
Work Shown:
[tex]A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (1,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-1)^2 + (4-0)^2}\\\\d = \sqrt{(-3)^2 + (4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
I used the distance formula.
A slight alternative is to plot the points to form a right triangle. The hypotenuse is the segment from A to B. Then use the pythagorean theorem to find the hypotenuse. Take note how a 3-4-5 right triangle forms.
Mr. Morris borrowed $25,000 from the bank. The time of the loan was 4 years. How much will he pay if the interest rate is 5.25%? (Use simple interest.)
X-6
=
Solve:
4(x-8) = 28
Answer: 34
Step-by-step explanation:
equation for y.
1. 2x + y = -9
2x+y=-9
If you want to solve for y, then you would get y = -2x-9
This is the result after subtracting 2x from both sides. This is so we can undo the +2x that happens to the y variable.
Answer:
Infinitely many solutions (If its solved by systems of equations)
y = -2x - 9 (if you ONLY want to solve for y)
Step-by-step explanation:
Well you can solve this is 2 ways. Substitution and Elimination
SUBSTITUTION
2x + y = -9
2x+y=-9
Step 1: Solve 2x+y =−9 for y:
2x+y=−9
2x+y+−2x=−9+−2x(Add -2x to both sides)
y=−2x−9
Step: Substitute −2x−9 for y in 2x+y=−9:
2x+y=−9
2x+−2x−9=−9
−9=−9(Simplify both sides of the equation)
−9+9=−9+9(Add 9 to both sides)
Final answer -----> 0=0
ELIMINATION
2x + y = -9
2x+y=-9
Step 1: Multiply the second equation by -1, then add the equations together.
(2x + y = -9)
-1(2x+y=-9)
Which then becomes:
2x + y = -9
-2x - y = 9
Step 2: Add these equations to eliminate x:
Final answer -----> 0 = 0
Calculate the 95onfidence interval for the true population mean based on a sample with =225, =8.5, and =45. function
The true population mean is (222.52, 227.48) with a 95% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true population mean is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95
⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95
⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95
95% confidence interval for
⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))
Here, x = 225, s = 8.5, and n = 45
⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))
⇒ μ = (222.52, 227.48)
Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.
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The question seems to be incomplete the correct question would be
Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.
Dan and David are marking exam papers. Each set takes Dan 35 minutes and David 1 hour. Express the times Dan and David take as a ratio.
Give your answer in its simplest form
Answer:
35:1
Step-by-step explanation:
Answer:
7 : 12
Step-by-step explanation:
the times must be of the same measure.
1 hour = 60 minutes , then
Dan : David = 35 : 60 = 7 : 12 ← in simplest form
(3x5x7) (1/3 + 1/5 -1/7)
Answer:
41
Step-by-step explanation:
(3*5*7)((1)/(3) +( 1)/(5) -(1)/(7))
When you simplify this, the answer is 41.
Answer: 41
Step-by-step explanation:
Can someone solve it please?
What is the polynomial regression?
In order to transform linear regression into polynomial regression, certain polynomial terms are added to it due to the non-linear relationship between the dependent and independent variables.
Let's say we have independent data X and dependent data Y. In the preprocessing stage, we turn the input variables into polynomial terms to some extent before feeding the data to a mode.
As a specific example of multiple linear regression, polynomial regression is a type of linear regression that estimates the connection as an nth degree polynomial. The performance can also be negatively impacted by the existence of one or two outliers since Polynomial Regression is sensitive to outliers.
The connection between the dependent and independent variables is best approximated by polynomial. It may be used for a wide range of functions. In general, polynomial suits a large range of curvature.
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Please help me with the photo below thanks
Answer:
A) -12-4-5
B) X^2-X
Step-by-step explanation:
..
..
Is the function [tex]f(x)=\sqrt{x}[/tex] differentiable at x=0 and continuous over R?
Answer: No
Explanation:
Apply the derivative
[tex]f(x) = \sqrt{x}\\\\f(x) = x^{1/2}\\\\f'(x) = (1/2)x^{-1/2}\\\\f'(x) = \frac{1}{2x^{1/2}}\\\\f'(x) = \frac{1}{2\sqrt{x}}\\\\[/tex]
Though we run into a problem since f ' (0) is undefined, due to the zero in the denominator.
Therefore, f(x) is not differentiable at x = 0.
The function is continuous, but only on the interval [tex]x \ge 0[/tex] and not over the entire set of real numbers R.
this is so in the morning & i need these answers!! :\
Find two consecutive whole numbers that √130 lies between.
b. calculate the probability that 30% or more of the sample will be living in poverty. assume the sample is collected in such a way that the conditions for using the clt are met.
0.0 65 is the probability that 30% or more of the sample will be living in poverty.
What is an probability in statistics?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.P(P ≥ 0.34 ) = P ( [tex]\frac{p' - p}{\sqrt{p( 1- p )/n} }[/tex] ≥ [tex]{\frac{0.34 - 0.30}{\sqrt{\frac{0.30 ( 1- 0.30)}{300} } } }[/tex]
= P ( 2 ≥ 1.5119)
= 0.0653
= 0.0 65
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The puppy shelter where Clara works is moving to a new building. The rooms in the new building are built to hold 6 puppies each. Clara needs to figure out how many rooms she'll need to house a total of 78 puppies.
Use an equation to find the number of rooms Clara needs.
Answer:
Equation: 6x = 78Rooms: 13Step-by-step explanation:
Let the number of rooms is x.
Each room is built to hold 6 puppies, so x rooms hold 6x puppies.
The equation for this is:
6x = 78x = 78/6x = 13And the solution is 13 rooms.
Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6. How many books did she buy?
Solve the recurrence relation: t(n) = 3t(n-1) 1, with initial condition of t(0) = 1
A linear recurrence relation is a function or sequence in which each term is a linear combination of the terms that came before it.
The recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].
What is meant by "recurrence relation"?Recurrence relations are used to simplify complex problems by reducing them to an iterative process based on simpler versions of the problem.
Using the substitution method, we find out that
[tex]T(n) &=n+3 T(n-1) \\[/tex]
[tex]&=n+3(n-1)+3^2 T(n-2) \\[/tex]
[tex]&=n+3(n-1)+3^2(n-2)+3^3 T(n-3) \\[/tex]
[tex]&=\cdots \\[/tex]
[tex]&=n+3(n-1)+3^2(n-2)+\cdots+3^{n-1}(n-(n-1))+3^n T(0) \\[/tex]
simplifying the above equation, we get
[tex]$&=\frac{3^{n+1}-2 n-3}{4}+3^n T(0) \\[/tex]
[tex]&=\Theta\left(3^n\right)[/tex]
Even without doing the full calculation it is not hard to check that [tex]$T(n) \geq 3^{n-1}+3^n T(0)$[/tex], and so [tex]$T(n)=\Omega\left(3^n\right)$[/tex].
A cheap way to obtain the corresponding upper bound is by considering
[tex]$S(n)=T(n) / 3^n$[/tex], which satisfies the recurrence relation
[tex]$S(n)=S(n-1)+n / 3^n$[/tex].
Repeated substitution then gives
[tex]$\frac{T(n)}{3^n}=\sum_{m=1}^n \frac{m}{3^m}+T(0)[/tex]
Since the infinite series [tex]$\sum_{m=1}^{\infty} \frac{m}{3^m}$[/tex] converges, this implies that [tex]$\frac{T(n)}{3^n}=\Theta(1)$[/tex] and so [tex]$T(n)=\Theta\left(3^n\right)$[/tex]
Therefore, the recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].
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The following is a list of P/E ratios (current stock price divided by company's earnings per share) for 17 companies. 57, 53, 50, 46, 42, 35, 31, 56, 52, 34, 34, 34, 30, 30, 55, 55, 51. Draw the histogram for these data using an initial class boundary of 29.5, an ending class boundary of 59.5, and 5 classes of equal width. Note that you can add or remove classes. Label each class with its endpoints.
The histogram for these data is given at the end of the answer.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
For this problem, there are 5 classes with a range of 30, as 59.5 - 29.5 = 30, hence the class width is of:
30/5 = 6.
From the data-set, we have that:
There are 7 values between 29.5 and 35.5.There are 0 values between 35.5 and 41.5.There are 2 values between 41.5 and 47.5.There are 4 values between 47.5 and 53.5.There are 4 values between 53.5 and 59.5.Considering this, the histogram is given at the end of the answer.
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The area A of a rectangle with dimensions 4x and 5 is described with the inequality 100 ≤ A ≤ 1,000.
Select the compound inequality for the area written in terms of x.
OA. 100 ≤ 10+ 8x ≤ 1,000
OB. 100 ≤ 18x ≤ 1,000
O C. 100 ≤ 9x ≤ 1,000
OD 100 ≤ 20x ≤ 1,000
The compound inequality for the area written in terms of x is 100 ≤ 20x ≤ 1,000.
We know that, the area of rectangle is given by:
Area = Length × Breadth
Now, we will substitute the values of length as 4x and breadth as 5 in the formula:
= 4x × 5
= 20x
Now. we will substitute this value in the inequality 100 ≤ A ≤ 1,000 to get the compound inequality:
100 ≤ 20 x ≤ 1,000.
Therefore, the compound inequality for the area written in terms of x is 100 ≤ 20x ≤ 1,000.
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