If I drove at the speed of a light year it would take me 1.152×10⁻⁴ seconds.
What is scientific notation?In scientific notations numbers are written in the form of a base that is
0 ≤ b < 10 and multiplied by 10ⁿ where n represents integers.
We write large standard numbers in the scientific form in a compact manner.
We know 1 meter is 0.000621371 miles.
∴ 34700 meters is (34700× 0.000621371) = 21.56 = 2.156×10¹ miles.
Given, A light year is equivalent to 6.7x10^8 miles/hour.
∴ It would take (2.156×10¹/6.7x10^8) = 0.32×10⁻⁷ miles per hour.
Or (0.32×10⁻⁷×3600) = 1.152×10⁻⁴ seconds.
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Which of the following is a diagonal matrix?
O
2
0
0 -42
0
0
1
6
0
0
16 -7.5
0
0
3.5 -18
0 9
-4
0
0
0
-22 0
0 7.5
0
0 7.5
0-22 0
Mark this and return
Save and Exit
4
Answer: the second one
Step-by-step explanation: trust me bro
The graph shows the relationship between the amount of peaches in pounds, x, and the amount of peaches in dollars, y. What is the slope of the line?
Answer: 5/2 or 2.5
Step-by-step explanation: Rise/Run = 5/2
find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = sin(x), a = ????
The taylor series of sin x at x= π is ∑( for n=0,∞) [tex]\frac{-1^{n+1}(x-\pi )^{2n+1} }{(2n+1)! }[/tex]
the Taylor series n of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.
since the function we are given is :
sin(x), since we need to find the Taylor series of sin(x) at x=π, which can also be written as : sin(x+π)
we can find find the Taylor series of sin(x+π) at x=0
sin(x+π)=−sin(x)
= ∑( for n=0,∞) [tex]\frac{(-1)^{n}x^(2n+1) }{(2n+1)!}[/tex]
= ∑( for n=0,∞) [tex]\frac{-1^{n+1}x^{2n+1} }{(2n+1)!}[/tex]
so sin (x)= ∑( for n=0,∞) [tex]\frac{-1^{n+1}(x-\pi )^{2n+1} }{(2n+1)! }[/tex]
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find the Taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = sin(x), a = π????
a dental student is conducting a study on the number of people who visit their dentist regularly. of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
For samples of size n = 60, the mean of the sampling distribution is 0.6
and the standard deviation of the sampling distribution is 0.0632
Here, N = 520 and X = 312
So, the population proportion is calculated as;
p = X / N
p = 312/520
p ≈ 0.600
So, the mean of the sampling distribution would be,
μ = 0.600
And for samples of size n = 60, the standard deviation of the sampling distribution would be,
σ = √[p(1 - p)] / n
σ = √[0.6(1 - 0.4)] / 60
σ = √[(0.6 * 0.4) / 60]
σ = √(0.004)
σ = 0.0632
Therefore, the mean of the sampling distribution = 0.6
and the standard deviation of the sampling distribution = 0.0632
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Given question is incomplete.
A complete question is:
a dental student is conducting a study on the number of people who visit their dentist regularly. of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n = 60
stocks a and b each have an expected return of 12%, a beta of 1.2, and a standard deviation of 25%. the returns on the two stocks have a correlation of 0.6. portfolio p has 50% in stock a and 50% in stock b. which of the following statements is correct?
d. Portfolio P has a standard deviation that is less than 25%
This response is accurate because a portfolio made up of two stocks with a correlation of less than one will always have a standard deviation that is lower than the standard deviation of the stocks added in accordance with their weight in the portfolio. For example, in this scenario, both stocks have a weight of 50% and a standard deviation of 25%, so their sum will be.
The portfolio standard deviation will be smaller than 25% since (0.5*25%) + (0.5*25%) = 25%.
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Use the number line to represent the solution to 5x > 15
Select a ray. Move the point on the ray to the correct place on the number line.
The solution to the inequality expression is x > 3 and the number line is attached
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
5x > 15
To start with, we divide both sides of the inequality expression by 5
So, we have the following representation
5x/5 > 15/5
Evaluate the quotient
So, we have the following representation
5x/5 > 3
Evaluate the quotient
So, we have the following representation
x > 3
So, the solution is x > 3
See attachment for the inequality graph
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The triangles below are congruent and their corresponding parts are marked.
B
(a) LA = 40
LB = 40
LC = 40
(c) AACB A
X
Z
Name all the corresponding congruent angles and sides.
Then, complete the triangle congruence statement.
(b) AB
AC
BC
X
Ś
Answer:
AB = YZ
AC = XY
BC =XZ
Statement : The given two triangles are congurent by all axiom.
4. Assume a manufacturer makes an item that costs $2.50 to produce. The
markup when sold to the distributor is 35 percent. What is the cost to the
distributor? When the distributor sells the item to the retailer, the markup is 40
percent. How much will the retailer pay for the item?
Answer: Cost to distributer $3.38
Cost to retailer $4.73
Step-by-step explanation: First find 35 percent of $2.50
2.50 x 0.35 = 0.875 this is 35% of 2.50
Then add this amount to 2.50
2.50 + 0.875 = 3.375 or $3.38
Then to find the cost to the retailer repeat this process with 40%
3.38 x 0.40 = 1.352
1.352 + 3.38. = 4.732 or $4.73
In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)°, what is the value of x?
O 51
0 29
026
O 25
The value of x, if In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)° is 25, so correct option is D.
What is triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.
Given:
In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)°
Calculate the value of x as shown below,
The sum of triangles will be equal to 180°,
mZD + mZE + mZF = 180
4x + 2x - 3 + x + 8 = 180
7x = 180 - 5
x = 175 / 7
x = 25
Therefore, the value of x, if In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)° is 25.
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Jade pent 1/2 of an hour playing on her phone. That ued up 1/9 of her batter. How long would he have to play on her phone to ue her entire battery
She has to play 4.5 hours to discharge the whole phone.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Jade spent 1/2 of an hour playing on her phone which uses 1/9th of her battery.
For 1/9th battery, it took 1/2 hour.
So for the whole charge to discharge it will take, (1/2)/ (1/9) = 9/2 =4.5.
Hence, She has to play 4.5 hours to discharge the whole phone.
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Your team has contracted to design and build a 500 ft, square-based, open-top, rectangular steal holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible.
The first step is to calculate the approximate weight of the tank. This can be done by calculating the weight of the stainless steel plates and multiplying it by the surface area of the tank.
The surface area can be calculated by multiplying the length of the sides by the height. The weight of the stainless steel plates can be found online or by consulting a materials engineer.Once the approximate weight of the tank has been calculated, the base and height dimensions can be determined by trial and error. Start with a base length and a height and calculate the approximate weight of the tank. Then, adjust the base length and/or height and recalculate the weight. Continue this process until the lightest weight is achieved.It is important to consider the structural integrity of the tank when selecting the dimensions. A tank with too little height or too wide a base may not be able to withstand the pressure of the contents within. Consulting a structural engineer may be necessary to ensure that the tank is strong enough to withstand the pressure of the contents.
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Line v is perpendicular to the graph of y= 2x - 11. Line w is parallel to line v and passes through point (-6,10)What is the equation in slope-intercept form of line w?
Answer:
y=26x-+8
Step-by-step explanation:
When the height of the cylinder increased from 100 m to 1000 m, what happened to the amount of heat generated in the system? it decreased by a factor of 10. it decreased by a factor of 5. it increased by a factor of 5. it increased by a factor of 10.
When the height of the cylinder increased from 100 m to 1000 m, what happened to the amount of heat generated in the system is decreased by a factor of 10.
Define the term potential energy?Potential energy is the energy that a body possesses as a result of its position. Heat is produced when this energy is transformed.The potential energy formula is provided by
P.E. = m g h
In which m is the body's mass, h its height, and g its gravitational acceleration.When a body is at a height of 100 m, its potential energy is
P = mgx100x100=100mg
When a body is at a height of 1000 m, its potential energy is
P' = mxgx1000x1000
P' = 1000 mg
P' to P have a 10:1 ratio.
Thus, ten times as much heat is produced in the cylinder.
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The answer is D: It increased by a factor of 10.
Graph negative 3.5 and negative 1.5 on the number line
The required graph has been attached which represents negative 3.5 and negative 1.5 on the number line.
What is Number Line?To indicate their position, all rational numbers can be plotted on a number line. Every point on the number line indicates how many units a number is away from zero and in which direction.
As per the question, the negative 3.5 placed on the number line is 3.5 units to the left of zero, and the negative 1.5 placed on the number line is 1.5 units to the left of zero. The number zero is the most essential position on the number line. All of the other locations on the number line are predicated on zero.
Thus, the required graph has been attached which represents negative 3.5 and negative 1.5 on the number line.
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let x denote the number of canon slr cameras sold during a particular week by a certain store. the pmf of x is x 0 1 2 3 4 px(x) 0.1 0.2 0.3 0.25 0.15
the value of P(X=4,Y=2) is 0.0518.
Given that, X denote the number of Canon SLR cameras sold during a particular week by a certain store.
The probability mass function (pmf) of X is,
X 0 1 2 3 4
PX(x) 0.1 0.2 0.3 0.25 0.15
Let Y denote the number of purchasers during this week who buy an extended warranty.
The value of P(X=4,Y=2) is the probability that 4 cameras are sold and 2 extended warranties are sold in a week.
P(X=4,Y=2)=p(4,2)=P(Y=2|X=4)×P(X=4)
The number of purchasers purchasing the extended warranty can be 0, 1, ……, x.
Here x is cameras are sold.
Assuming that each customer buys at most 1 camera.
Considering that the event “a purchaser buys extended warranty” as “success” and the event “a purchaser does not buy extended warranty” as “failure”.
In that case, all the customers purchasing cameras buy extended is 60%.
The probability of failure is 0.4.
This follows the binomial distribution, where total number of trials is the number of purchasers of camera and x is the probability of success is 0.6.
The probability that 2 out of 4 cameras purchasers buys extended warranty with probability of success 0.6 is,
P(Y=2|X=4)=4C2(0.6)2(0.4)4−2=6×0.36×0.16=0.3456
Given that,
P(X=4)=0.15
Therefore,
P(X=4,Y=2)=P(Y=2|X=4)×P(X=4)=0.3456×0.15=0.0518
Therefore, the value of
P(X=4,Y=2) is 0.0518.
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I really need someone to help me understand this problem
The linear function in slope intercept form is y = -2x - 5.
How to represent linear function in slope intercept form?Linear function can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope in the linear function.
Using (-1, -3) and (3, - 11)
m = -11 + 3 / 3 + 1
m = -8 / 4
m = -2
Therefore, let's find the y-intercept as follows:
using (-1, -3)
y = -2x + b
-3 = -2(-1) + b
-3 = 2 + b
b = -3 - 2
b = -5
Therefore, the equation in slope intercept form is y = -2x - 5
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How to solve 3(1+p)=-5(p+1)
The value of P in the equation is -1
Answer:
p=-1
Step-by-step explanation:
3(1+p)=-5(p+1)
Remove the parenthesis:
3+3p=-5p-5
Subtract 3 from both sides.
3p=-5p-5-3
Simplify:
3p=-5p-8
Rearrange:
3p=-8-5p
Add 5p to both sides:
8p=-8
Divide both sides by 8:
p=-1
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solve the inequality
15t>180
Answer: t=12
Step-by-step explanation:
To isolate the t, divide both sides by 15. The 15 on the left cancels out, and 180 divided by 15 is 12.
Find the perimeter and area of triangle RST if each unit on the graph measures 1 centimeter. Round your answer to the nearest centimeter, if necessary.
y
8
S-4,5)-6
Q-6,1)
-876
R(-8,-3)
Perimeter
Area
4
-6
81
468x
7(6,-5)
cm²
jcm
The perimeter and the area of the triangle are given as follows:
Perimeter: 21 cm.Area: 16 cm².How to obtain the perimeter of the triangle?The perimeter of the triangle is given by the sum of the lengths of the outer edges of the triangle.
From the image given at the end of the answer, these lengths are of:
AB = 4.AC = 8.BC = 8.83 -> Pythagorean Theorem -> hypotenuse of a right triangle of sides 4 and 8.Hence the perimeter of the triangle is of:
P = 4 + 8 + 8.83 = 21 cm.
(rounded to the nearest cm, as each unit represents 1 cm).
How to obtain the area of the triangle?The triangle in this problem is a right triangle, hence the area is obtained by half the multiplication of the sides, as follows:
A = 0.5 x 4 x 8 = 16 cm².
Missing InformationThe problem is incomplete, hence a similar problem was given and solved, by the triangle in the image at the end of the answer.
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what is surface area of the cuboid 4cm.5cm.9cm.
Answer:202 surface area
Step-by-step explanation:
16. Find the direction of the force
F=(-√12 i-2j) N.
Answer:
240° ( Quadrant III)
Step-by-step explanation:
Arctan ( -sqrt(12) /-2) = 240 degrees
Suppose are running a study/poll about the probability of catching the flu this year. You randomly sample 142 people and find that 69 of them match the condition you are testing. Suppose you have the following null and alternative hypotheses for a test you are running: H 0 : p = 0.54 H a : p < 0.54 Calculate the test statistic, rounded to 3 decimal places
The test statistic of null and alternative hypotheses for a test is 0.811.
69 of the 142 persons that were randomly chosen from a sample are found to meet the condition we are testing.
The sample proportion phat = 69 ÷ 142 = 0.489
n = 69
p = 0.54
the following are your test's null and alternate hypotheses:
[tex]H_0[/tex] : p = 0.54
[tex]H_a[/tex] : p < 0.54,
test statistic,
z = (phat - p) ÷ √(p × (1 - p) ÷ n)
z = (0.489 - 0.54) ÷ √((0.79 × 0.21) ÷ 42) = 0.811
A test statistic is a figure obtained from a statistical analysis. It explains how distant the observational values seem to be from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.
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Consider the division of 4h2 + 2h + 6 by 2h. What are the values of a and b? a = 2 and b = 1 a = 2h and b = 1 a = and b = a = and b =.
When the dividend is 4h²+2h+6 and the divisor is 2h, the value of a is 2h and the value of b is 1.
What is polynomial?A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The terms degree, standard form, monomial, binomial, and trinomial are all covered in this video.
Here,
Dividend=4h²+2h+6
Divisor=2h
The value of a and b,
=(4h²+2h+6)/2h
=4h²/2h+2h/2h+6/2h
=2h+1+3/h
a=2h
b=1
The value of a is 2h and b is 1 where the dividend is 4h²+2h+6 and divisor is 2h.
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Answer:What are the values of A and B?
A = 2 and B = 1
A = 2h and B = 1
A = and B =
A = and B =
Step-by-step explanation:
The number of bagels sold daily for two bakeries is shown in the table:
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median?
A. Mean for both bakeries because the data is symmetric
B. Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric
C. Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric
D. Median for both bakeries because the data is not symmetric
It is better to describe the centers of distribution in terms of the
D. Median for both bakeries because the data is not symmetric.
What are mean, median, and mode?The three main methods for identifying the average value of a set of integers are mean, median, and mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.
The middle value in a list that is arranged from smallest to greatest is called the median.
The value that appears the most frequently on the list is the mode.
We know symmetric data sets have a graph that is bell-shaped.
Here the data for both bakeries are not symmetric we can conclude that from the given table itself so it is better to describe the centers of distribution in terms of the median for both bakeries because the data is not symmetric.
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a coin is weighted so that the probability of obtaining a head in a single toss is 0.25. if the coin is tossed 45 times, what is the probability of obtaining between 9 and 14 heads, exclusive. a. 0.0537 b. 0.5051 c. 0.7201 d. 0.6975 e. 0.4836
The probability of obtaining between 9 and 14 heads is .0.0408
Probability:
in statistics, probability refers the possibility of the outcome of any random event.
Given,
A coin is weighted so that the probability of obtaining a head in a single toss is 0.25.
Here we need to find the probability of obtaining between 9 and 14 heads if the coin is tossed 45 times.
While we looking into the given question,
Probability of obtaining a head in a single toss = 0.25
Number of toss = 45
Here we need to find the probability of getting head between 9 and 14, is calculated as,
=> mean = 45 x 0.25 = 11.25
=> standard deviation = √11.25 x(1 - 0.25) = 2.9
Here the probability is written as,
=> P(9 < x < 14) = P(8.5 < x < 14.5)
Then the z score, is
=> z = (8.5 - 11.25)/2.9 = -0.9483
=> z = (14.5 - 11.25)/2.9 = 1.1207
So, the given probability is rewritten as,
=> P(9 < x < 14) = P(z < 1.1207) - P(z < 0.9483)
When we apply the value of z score on it then we get,
= > P(z < -0.9483) = 0.17149
=> P(z > 1.1207) = 0.13121
=> P(9 < x < 14) = 0.13121 - 0.17149
=> 0.0403
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Find x in the right triangle. 324−−−√324
B 147−−−√147
C 63−−√63
D 175−−−√175
E 21−−√21
Answer:
I believe it is 3rd one but not 100% sure
Step-by-step explanation:
hope this helps
Find the perimeter of a rectangle in simplest expression form that has an area of 6x2 +17x + 12 square feet. Please make sure you show all your work for full credit. (10 points)
Answer: P=14x-8
Step-by-step explanation:
I will solve this by factoring the numbers
(3x+1)(4x-5)=0
so L and w would be 3x+1,4x-5 order does not matter
Plug in to the perimeter formula and solve
P = 2(L+W)
P = 2(4x-5+3x+1)
P = 2(7x-4)
P = 14x - 8
given a fair 6-sided die if you roll it 5 times and add up the results, what is the probability that the sum is divisible by 6
1/6 is the Dice roll probability that the sum is divisible by 6
What is Dice roll Probability ?
An event is a specific subset of the sample space in probability. The sample space, for instance, is equal to all of the values on the die, or the set, when just one die is rolled, as in the example above (1, 2, 3, 4, 5, 6). Each number in the set only appears once since the die is impartial. The frequency of each number is thus 1. We divide the event frequency (1) by the size of the sample space (6) to get the chance of rolling any one of the die's numbers, which comes out to 1/6.
The difficulty of computing probability more than doubles when two fair dice are rolled. This is so that rolling one die does not affect rolling another. A roll does not affect another roll. We apply the multiplication rule when dealing with independent occurrences. A tree diagram is used to show that there are 6 × 6 = 36 possibilities that can result from rolling two dice.
We know that whatever be the first four numbers , the fifth number will decide whether the sum is divisible by 6 or not
That is let , S= N+N5
Before adding N5 , we cannot say whether S is divisible by 6
N5 is chosen from 6 equally likely numbers ,1,2,3,4,5,6
P(N5) =1/6
Therefore Dice roll probability that sum is divisible by 6 is 1/6
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the lengths, in inches, of adult corn snakes are normally distributed with a population standard deviation of 8 inches and an unknown population mean. a random sample of 25 snakes is taken and results in a sample mean of 58 inches. identify the parameters needed to calculate a confidence interval at the 99% confidence level. then find the confidence interval. z0.10z0.10 z0.05z0.05 z0.025z0.025 z0.01z0.01 z0.005z0.005 1.282 1.645 1.960 2.326 2.576
We can estimate with standard deviation of 8 that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
x = 58
σ = 8
n = 25
z α/2 = 2.576
(53.88, 62.12)
the given values σ=8, n=25, and z α/2=2.576 for a confidence level of 99%, we have
margin of error=(2.576)(8/√25)
≈ (2.576)(1.6)
≈4.12
With x¯=58 and a margin of error of 4.12, the confidence interval is
(58−4.12,58+4.12)
= (53.88 , 62.12).
therefore we can estimate with 99% confidence that the true population mean length of adult corn snakes is between 53.88 and 62.12 inches.
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(0.5- 0.3) power of 2?
Solving the Question
[tex](0.5- 0.3)^2[/tex]
⇒ Subtract inside the parentheses:
[tex]= (0.2)^2[/tex]
⇒ Evaluate the exponent by multiplying 0.2 by 0.2:
[tex]= 0.04[/tex]
Answer0.04
Answer:
0.04
Step-by-step explanation: