It took 5.5 hours to drive 154 miles. What was the average rate of speed?
Answers
Answer:
The average speed would be about 28 miles per hour.
Step-by-step explanation:
154 divided by 5.5 is 28.
Related Questions
2. In 2008, the maximum taxable income for Social Security was
$ 102,000 and the tax rate was 6.2%.
paid in the year 2008?
What is the maximum Social Security tax anyone could have
b. Randy had two jobs in 2008. One employer paid him $67,010
and the other paid him $51,200. Each employer took out 6.2%
for Social Security taxes. How much did Randy overpay for Social
rity taxes in 2008?
Answers
Answer: A: $6324
B: by $1005.04 more
Step-by-step explanation:
A: 6.2% of 102,000 is 6324
B: find the tax rate of each job by finding 6.2% of what was paid, add them together, then subtract the maximum tax rate from that to see how he over paid
A boat is heading towards a lighthouse, whose beacon-light is 104 feet above the
water. From point A, the boat's crew measures the angle of elevation to the beacon,
, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 22°. Find the distance from point A to point
Round your answer to the nearest foot if necessary.
Answers
The distance between points A and B is 482.86 feet.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Fro, The given information,
tan8° = 104/x.
x = 742.86 feet.
Again,
tan22° = 104/y.
y = 260 feet.
Therefore, The distance between points A and B is,
x - y = 742.86 - 260 feet.
= 482.86 feet.
Q. A boat is heading towards a lighthouse, whose beacon light is 104 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon is 8° before they draw closer.
They measure the angle of elevation a second time from point B to be 22°. Find the distance from point A to point B, Round your answer to the nearest foot if necessary.
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Find the slope and reduce.
P=(-3, 3) Q=(1, 3)
Slope =
Answers
Answer:
Slope is 0.
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in frame of reference s, an electron moving along the x-axis has energy 4mc^2 what is the momentum magnitude observed in frame s'
Answers
The momentum magnitude observed in frame s' is √(15m^2c^4).
In special relativity, the relationship between energy (E) and momentum (p) is given by the equation:
E^2 = (pc)^2 + (mc^2)^2
where m is the rest mass of the particle, c is the speed of light, and p is the momentum of the particle.
In frame of reference s, the energy of the electron is given as 4mc^2. Plugging this into the equation, we have:
(4mc^2)^2 = (pc)^2 + (mc^2)^2
Simplifying this equation, we get:
16m^2c^4 = p^2c^2 + m^2c^4
Canceling out the common terms, we have:
15m^2c^4 = p^2c^2
Taking the square root of both sides, we get:
pc = √(15m^2c^4)
The momentum magnitude observed in frame s', denoted as p', is related to the momentum in frame s (p) by the relativistic velocity addition formula:
p' = γ(p - βE/c)
where γ is the Lorentz factor and β is the velocity of frame s' relative to frame s. Since the electron is moving along the x-axis, the velocity β is zero, and the Lorentz factor γ is equal to 1.
Therefore, the momentum magnitude observed in frame s' is the same as the momentum magnitude in frame s:
p' = p
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The mccarthy family is installing a rectangular patio in their backyard that will be 18 3 4 feet by 12 feet. what will be the area of the patio in square fe
Answers
The area of a rectangular patio with the dimensions of 18-3/4 feet and 12 feet will be determined by using the formula for the area of rectangle.
Area of rectangle is calculated by multiplying the length of the rectangle to the width of the rectangle. i.e.,
Area of rectangle= Length*Width
In the given situation,
Length= 18-3/4feet
Width=12 feet.
1. Convert the value of length to improper fraction:
18-3/4=75/4
2. Multiply the length and width to find the area:
Area=(75/4)x12
Solving the expression:
3. Area=75x3=225 sq. feet
The area of a 18-3/4 feet and 12 feet rectangular patio is 225 sq. feet.
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pls help there are 3 pics with multiple questions inside of them pls thank you
Answers
Answer:
Step-by-step explanation:
17. Rotation
18. Always
19. 4
20.
21. Acute triangle/ Isosceles triangle. All angels are acute and there are none of the sides are equal.
22. The transformation was a reflection. I know this because all the colors flipped, but everything else is the same.
Answer:
17. rotation
18. never
19. 4
20. The third one
21. It is an acute ASA triangle because all of the angles are less then 90 degree and since you are given the sides as well, it is ASA.
22. A rotation was used, because the colors are rotated 90 degrees, even though the shape itself stays the same.
Step-by-step explanation:
AD and EC are diameters of 0. OB is a radius. Classify each statement as true or false. AOE = 50
Answers
Applying the definition of a diameter, we can conclude that m<AOE = 80 degrees. Therefore, m<AOE = 50 is FALSE.
What is a Diameter and a Radius?The diameter is the longest chord passing through the center of a circle, while the radius is the distance from the center to any point on the circumference. The diameter forms two semicircles or divides the circle into two halves.
We are given that AD and EC are diameters of the circle O. This means that EOC is a straight angle or semicircle, which is equal to 180 degrees. Therefore:
m<EOC - m<AOB - m<BOC = m<AOE
Substitute:
180 - 50 - 50 = m<AOE
80 = m<AOE
m<AOE = 80°
Therefore, the statement, m<AOE = 50 is FALSE.
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Give an example from the image of each kind of segment.
1. a diameter
2. a chord that is not a diameter
3. a radius
Answers
Answer:
Diameter: Line segment BC
Chord: line segment DE
Radius: line segment GA
Step-by-step explanation:
Diameter: all the way across circle, going through center
Radius: half of diameter
Chord: connects two points of circle, not through center (since then it would be diameter)
Suppose (x1,...,xn) is a sample from a Bernoulli(0) with 0 € [0, 1] unknown. (a) Show that X"=(xi – 7)2 = nx (1 – X). (Hint: x} = xi.) (b) If X ~ Bernoulli(o), then o2 = Var(x) = 0(1 – 6). Record the relationship between the plug-in estimate of o2 and that given by s2 in (5.5.5). (c) Since s2 is an unbiased estimator of o2 (see Problem 6.3.23), use the results in part (b) to determine the bias in the plug-in estimate. What happens to this bias as n → 00?
Answers
(a) Showing that X"=(xi – 7)2 = nx (1 – X) which is a sample from a Bernoulli(0).
We have that X~Bernoulli(0), so E(X) = 0 and Var(X) = 0(1-0) = 0. Let's define Y = (X - 7)^2. Then, we have:
Y = (X - 7)^2
= X^2 - 14X + 49
= X(X-1) - 14X + 49
= X - X^2 -14X + 49
= -X^2 -13X + 49
Taking the expected value of Y, we get:
E(Y) = E(-X^2 -13X + 49)
= -E(X^2) -13E(X) + 49
= -Var(X) + 49
= -0 + 49
= 49
Now, let's calculate the expected value of nx(1-X):
E(nx(1-X)) = nE(X) - nE(X^2)
Since X~Bernoulli(0), we have E(X) = 0 and E(X^2) = Var(X) + E(X)^2 = 0. Therefore, E(nx(1-X)) = 0.
So, we have shown that E(Y) = E(nx(1-X)), which implies that they are equal with probability one. Therefore, we have:
(nx(1-X)) = (X-7)^2
(b) The relationship between the plug-in estimate of o^2 = p(1-p) = X(1-X)
and s^2 = nx(1-X)/(n-1).
We know that Var(X) = o^2 = p(1-p), where p is the unknown parameter of the Bernoulli distribution. The plug-in estimate of o^2 is given by:
s^2 = sum((Xi - Xbar)^2)/(n-1)
where Xbar is the sample mean and Xi are the sample values. Using the fact that Xi ~ Bernoulli(p), we have:
E(Xi) = p and Var(Xi) = p(1-p)
Therefore, the sample mean Xbar is an unbiased estimator of p, and the sample variance s^2 is an unbiased estimator of o^2. We can write:
s^2 = sum((Xi - Xbar)^2)/(n-1)
= sum(Xi^2 - 2XiXbar + Xbar^2)/(n-1)
= (sum(Xi^2) - 2nXbar^2 + nXbar^2)/(n-1)
= (sum(Xi^2) - nXbar^2)/(n-1)
sum(Xi^2) = nx(1-X) + nXbar
s^2 = [nx(1-X) + nXbar - nXbar^2]/(n-1)
= nx(1-X)/(n-1)
Therefore, the plug-in estimate of o^2 is given by:
o^2 = p(1-p) = X(1-X)
s^2 = nx(1-X)/(n-1)
(c) The bias in the plug-in estimate is Bias = Xbar^2 - nx(1-X)/(n-1).
We can calculate the bias of the plug-in estimate as follows:
Bias = E(o^2) - o_hat^2
= E(X(1-X)) - nx(1-X)/(n-1)
= E(X) - E(X^2) - nx(1-X)/(n-1)
= p - (p(1-p)) - nx(1-X)/(n-1)
= p^2 - nx(1-X)/(n-1)
p = Xbar
Bias = Xbar^2 - nx(1-X)/(n-1)
As n approaches infinity, the bias approaches zero. This is because as n gets larger, the sample estimate of o^2 becomes more accurate, and the plug-in estimate becomes closer to the true value of o^2. Therefore, the bias in the plug-in estimate decreases as n increases.
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If a block is drawn from the box as shown above 150 times with replacement, predict the number of times the block drawn will have the vowel U.
A.
The letter U would be drawn roughly 30 times, but probably not exactly 30 times.
B.
The letter U would be drawn roughly 12 times, but probably not exactly 12 times.
C.
The letter U would be drawn roughly 15 times.
D.
The letter U would be drawn exactly 30 times.
Answers
The letter U would be drawn roughly 30 times, but probably not exactly 30 times.
How to determine the number of times the outcome is UThe box is given as
Box = Vowels
The letters of a vowel are A E I O U
This means that
The probability of drawing a U on any single draw is 1/5
When the trials is repeated 150 times, the expected value can be calculated using the formula:
E(X) = np
where X is the random variable representing the number of times a U is drawn.
Plugging in n=150 and p=1/5, we get:
E(X) = 150 x 1/5 = 30
So, we can predict that the block will be drawn with the vowel U approximately 30 times out of the 150 draws
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Determine two posotive decimals a and b that make the following statement true if a< 1 and b <1, then a÷b< 1
Answers
Answer:
many
a = 0.2
b = 0.7
Step-by-step explanation:
if a÷b is less than 1, then a must be smaller than b, so you can use any two decimals as long as a is the smaller of the two.
Tom drives 200 miles in 4 hours.
He drives the first 32 miles at an average speed of 64 mph
Work out his average speed for the rest of the journey, in mph.
Please help??
Answers
His average speed for the rest of the journey was of 48mph.
Find the y-intercept of an equation whose slope is 2 and has the point (1, 5)
Answers
Answer:
The y-intercept is 3.
Step-by-step explanation:
I had to use a graph but if you mark the point on the graph. The slope is 2 so you would go up 2 right 1. But you can also do it the opposite way, go down 2 left 1. I hope this helps!
Determine whether the sequence converges or diverges. If it converges, find the limit. an = 3 + 5n^2 / 1+n
Answers
After considering the given data and given set of options we conclude that sequence projects a divergence therefore the correct option is diverges.
To estimate and find whether the sequence \(an = 3 + 5n^2 / 1+n\) converges or diverges, we can apply the following steps:
We can apply divison of both the numerator and denominator of the sequence by \(n^2\) to get an equivalent expression: \(an = (5/n) + 3n / (1/n + 1).\)
As n comes towards infinity, the term 5/n approaches zero and the term 3n approaches infinity.
Hence, the sequence diverges to infinity.
Finally, the sequence \(an = 3 + 5n^2 / 1+n\)diverges.
Then after carefully evaluating we can projects that,l the sequence diverges which can be seen in the given figure.
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Multiply using the distributive property (X+4)(X^2+6x-3)
Answers
Answer:
x^3 + 10x^2 + 21x - 12
Step-by-step explanation:
(x + 4)(x^2 + 6x - 3)
you can separate to make it easier for u
x(x^2 + 6x - 3) + 4(x^2 + 6x - 3), this is optional u don't have to do this part
x^3 + 6x^2 - 3x + 4x^2 + 24x - 12
add like terms together
x^3 + 10x^2 + 21x - 12
What is the length of the missing side?
Answers
Answer:
4 Feet
Step-by-step explanation: Cut the rectangle in half and you get squares and half of eight is and they'd all have equal sides of 4
Calculate the pay for the following day of a
weekly time card given a wage of $13/hr.
Name
Week of:
Morning
In Out
Monday 08:00 12:00
Afternoon
In Out
12:45
17.30
pay = $[?]
Round your answer to the nearest hundredth.
Please help if you can.
Answers
Answer:
$113.62
Step-by-step explanation:
so for the first day it's pretty simple, they go to work for 4 hours so 4•13=52
for the second day they go to work for 4 hours and 45 minutes. now 45 minutes is 75% of an hour so you do 13•.75 to get the amount of money they'd receive for 45 minutes. then 52+52+9.62= 113.62
A retailer is offering 5% off your total order, if you sign up for their email list. If your total is $254.20, how much will you save by signing up?
Answers
Answer:
$254.20 - 5%= 241.49 US$
so you will save up to 14
Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 2.5%/year compounded monthly. If the future value of the annuity after 10 years is $60,000, what was the size of each payment? (Round your answer to the nearest cent.) $
Answers
Answer:
Monthly payment= $440.71
Step-by-step explanation:
Giving the following information:
Mothly interest rate (i)= 0.025/12= 0.00208
Number of periods (n)= 12*10= 120 months
Future Value (FV)= $60,000
To calculate the monthly payment, we need to use the following formula:
Monthly payment= (FV*i) / [(1+i)^(n) - 1]
Monthly payment= (60,000*0.00208) / [(1.00208^120) - 1]
Monthly payment= $440.71
Question 14 (5 points)
Which of the following is equivalent to cos (23º)?
cos (90°)
sin (67°)
sin (23°)
cos (67°)
Answers
Answer:
Sin (67°)
Step-by-step explanation:
Cos (23°) = sin(90-23) = sin (67°)
Answered by GAUTHMATH
Which expression is equivalent to 15x + 3.
I need help ASAP !
Answers
Answer:
Because if you think about it , 5×3 is 15 so you divide 15 by 3 which gives you 5 then you replace 3 with a 1
Step-by-step explanation:
3 (5x +1 )
Answer is :
(15x)+3
Reasoning: In PEMDAS, multiplication/ division (left to right) comes before add/ subtract (left and right) , meaning it will only matter IF we put x+3 in parenthesis.
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Algebra 2 Trig Unk 1 Test 2020 / 2 of 10
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The park in Springtown has a 2.13 km hiking trail. How many miles long is the hiking trail? (1 km =
0.6214 miles)
Answers
Answer:
1.32
Step-by-step explanation:
we have the known,
2.13 km * 0.6214 miles = 1.323521 or 1.32 miles
1 km
Smith City received 2. 45 inche of rain on Monday and 1. 72 inche of rain on Tueday. Write an equation howing a way to etimate to the nearet inch the total rainfall for the two day
Answers
an equation showing a way to estimate to the neasrt inch the total rainfall for the two day 2.45 + 1.72 ≈ 4.2 inches
1. Add the two amounts of rainfall together: 2.45 + 1.72
2. Round the answer to the nearest inch: 4.2 inches
3. The equation to estimate the total rainfall for the two days is 2.45 + 1.72 ≈ 4.2 inches.
This equation provides a simple way to estimate the total rainfall for two days. By adding the two amounts of rainfall, we can then round the answer to the nearest inch to obtain the estimated total rainfall. This equation can be used to quickly and accurately estimate rainfall totals for any two-day period.
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define a function named (prod-inv-indirect? a1 b1 c1 d1 a2 b2 c2 d2)whichdetermines iftheproduct of two matrices is invertible by this method.
Answers
The product of two matrices is invertible by this method, then the determinant of a product of two matrices is equal to the product of their determinants. Thus, we have proved that the statement in the proposition is true also in the case when the two matrices are non-singular.
We say that a square matrix is invertible if and only if the determinant is not equal to zero. In other words, a 2 x 2 matrix is only invertible if the determinant of the matrix is not 0. If the determinant is 0, then the matrix is not invertible and has no inverse.
If A and B are each invertible and are both n x n matrices, then the product AB is invertible.
The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one). The determinant of a matrix A is denoted \(det(A)\), \(det A\), or \(|A|\).
Therefore,
The product of two matrices is invertible by this method, then the determinant of a product of two matrices is equal to the product of their determinants. Thus, we have proved that the statement in the proposition is true also in the case when the two matrices are non-singular.
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Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $210. Now the cost is $320. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answers
The percent increase is 56%
The percent increase if the airline charges an additional $50 baggage fee with the new ticket price is 76%
How to determine the percent increaseThe formula for determining percent increase is expressed as;
Percent increase = x₂ - x₁/x₁ × 100/ 1
Where;
x₁ is the initial valuex₂ is the final valueNow, substitute the values, we have;
Percent increase = $320 - $210/$210 × 100/ 1
Find the difference
Percent increase = $110/$210 × 100/ 1
Percent increase = 0. 52 × 100/ 1
Multiply through
Percent increase = 52%
If there is an increase of $50
Percent increase = $370-210/210 × 100/ 1
= 160/210 × 100/ 1
= 76%
Hence, the values are 52% and 76% respectively,
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Quadrilateral A’B’C’D is the image of quadrilateral ABCD under a translation.
Answers
Answer:
The translation is (-1, -3)
Step-by-step explanation:
Arjun begins the calendar year with $4000 in his bank account. he earns 9% simple interest annually. after how many years will the valance of the account be $6500?
Answers
The number of years that it will take for the Valence of the account to be $6500 = 6.9 years
What is annual simple interest?Annual simple interest is defined as the amount of money that is being paid to an individual who invested a specific amount of money for a period of time.
The principal amount = $4000
The rate for earnings= 9%
The simple interest= $6500 - 4000 = 2500
Time = X
Using the formula:
Simple interest = P ×T×R/100
Make T the subject of formula;
T = Simple interest × 100/ P × R
T = 2500 × 100/ 4000× 9
T = 250000/36000
T = 6.9 years
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A candy manufacturer is marketing a gift box containing four cream-filled nuggets and five pieces of fudge. The manufacturing process for each candyis designed so that the mean weight of a cream-filled nugget is 3 ounces with a standard deviation of 0.2 ounces and the mean weight of a piece of fudge is 4 ounces with a standard deviation of 0.3 ounces. The boxes have a mean weight of 3 ounces with a standard deviation of 0.1 ounces. If three gift boxes are selected at random, what is the probability that at least one box will weigh less than 34 ounces?
Answers
The probability that at least one box in a selection of three candy gift boxes will weigh less than 34 ounces needs to be found.
To calculate the probability, the weight of a box can be considered as the sum of the weights of the individual candies in the box. The weights of the individual candies are normally distributed with known means and standard deviations.
Using the properties of normal distributions, the weights of the boxes can be modeled as normally distributed with a mean of 27 ounces (9 candies x 3 ounces per candy) and a standard deviation of 0.374 ounces (sqrt(4*(0.2^2)+5*(0.3^2)+0.1^2)). Then, the probability of at least one box weighing less than 34 ounces can be calculated using the normal distribution function.
The calculated probability is 0.0569, or approximately 5.69%. Thus, there is a 5.69% chance that at least one of the three selected candy gift boxes will weigh less than 34 ounces.
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The probability that at least one box will weigh less than 34 ounces is approximately 0.117.
To solve this problem, we can use the Central Limit Theorem to approximate the distribution of the total weight of three gift boxes. The mean weight of one gift box is 3*(4)+5*(3) = 27 ounces, and the standard deviation is sqrt((4*(0.2)^2 + 5*(0.3)^2)) = 0.69 ounces.
The probability that one gift box weighs less than 34 ounces is given by the standard normal distribution, which we can find using a z-score of (34-27)/0.69 = 10.14.
The probability that all three boxes weigh at least 34 ounces is (1-0.117)^3 = 0.770, so the probability that at least one box weighs less than 34 ounces is approximately 1 - 0.770 = 0.117.
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What is an expression for the radius of the circle? What is the least possible integer value of x for the circle to exist? Explain
Answers
The area of a circle is given by the next formula:
\(A=\pi *r^2\)___________
For the given expression of area:
\(\pi *r^2=4\pi x^2+12\pi x+9\pi\)Use the equation above to solve r (radius):
1. Divide both sides of the equation into π
\(\begin{gathered} \frac{\pi *r^2}{\pi}=\frac{4\pi x^2+12\pi x+9\pi}{\pi} \\ \\ r^2=4x^2+12x+9 \end{gathered}\)2. Factor the expression on the right using the notable product perfect square binomial:
\(\begin{gathered} (a+b)\placeholder{⬚}^2=a^2+2ab+b^2 \\ \\ 4x^2+12x+9=(2x)\placeholder{⬚}^2+2(2x)(3)+3^2 \\ 4x^2+12x+9=(2x+3)\placeholder{⬚}^2 \\ \\ \\ r^2=(2x+3)\placeholder{⬚}^2 \end{gathered}\)3. Find square root of both sides of the equation:
\(\begin{gathered} \sqrt{r^2}=\sqrt{(2x+3)\placeholder{⬚}^2} \\ \\ r=2x+3 \end{gathered}\)Then, the radius is given by the expression 2x+3.______________________________
To find the least possible integer value of x: As r is the radius of a circle, it cannot be a negative amount or 0, then r needs to be greather than 0:
\(\begin{gathered} 2x+3>0 \\ \end{gathered}\)Solve the ineqaulity above:
\(\begin{gathered} 2x+3-3>0-3 \\ 2x>-3 \\ \\ \frac{2x}{2}>-\frac{3}{2} \\ \\ x>-\frac{3}{2} \end{gathered}\)x needs to be greater than -3/2 (-1.5).
Then, the least possible integer value of x is -1Answer:
450
Step-by-step explanation:
calculate it by solving the radius as you get the radius you will be able to do th question
Consider the following function f(x)=x4+3, x>=0.Find an explicit formula for f^-1
Answers
The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.
To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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