The probability of having exactly 10 successes in 32 independent trials, with a success probability of 0.34, is approximately 0.0122 (rounded to four decimal places).
To compute the probability of having exactly x successes in a binomial experiment, we can use the binomial probability formula:
[tex]P(x) = C(n, x) \times p^x \times (1 - p)^{(n - x)[/tex]
where:
P(x) is the likelihood that x successes will occur.
n is the total number of trials
P is the likelihood that a trial will be successful.
C(n, x) is the binomial coefficient, which represents the number of ways to choose x successes out of n trials.
In this case, n = 32, p = 0.34, and x = 10. Let's calculate the probability:
P(10) = C(32, 10) * (0.34)^10 * (1 - 0.34)^(32 - 10)
The binomial coefficient C(32, 10) can be calculated as:
C(32, 10) = 32! / (10! * (32 - 10)!)
Now, let's compute the value:
C(32, 10) = 32! / (10! * 22!)
= (32 * 31 * 30 * 29 * 28 * 27 * 26 * 25 * 24 * 23) / (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= 57,032,707,456 / 3,628,800
= 15,504
Now, substitute the values back into the binomial probability formula:
P(10) = 15,504 * (0.34)^10 * (1 - 0.34)^(32 - 10)
P(10) ≈ 0.0122
Therefore, the probability of having exactly 10 successes in 32 independent trials, with a success probability of 0.34, is approximately 0.0122 (rounded to four decimal places).
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What is (m+2z)^2+12tz
The expression [tex](m+2z)^2+12tz[/tex] simplifies to [tex]m^2 + 4mz + 4z^2 + 12tz[/tex]
The expression [tex](m+2z)^2+12tz[/tex] represents a mathematical equation involving variables m and z, as well as the constant t.
To simplify the expression, we can expand the square and then combine like terms.
Expanding the square, we have:
[tex](m+2z)^2 = (m+2z)(m+2z) = m^2 + 4mz + 4z^2[/tex]
Substituting this result back into the original expression, we have:
[tex](m+2z)^2 + 12tz = m^2 + 4mz + 4z^2 + 12tz[/tex]
At this point, we have combined all the terms in the expression, and there are no more like terms to be simplified.
Therefore, the final simplified form of the expression [tex](m+2z)^2+12tz is m^2 + 4mz + 4z^2 + 12tz.[/tex]
It is important to note that this simplified expression is still in terms of the original variables m, z, and t, and no further simplification can be done unless specific values are assigned to these variables.
This equation can be further manipulated or solved depending on the context or purpose it serves within a mathematical problem or equation system.
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4. At the time of retirement, a couple has $200,000 in an account that pays 8.4 % compounded monthly. If
they decide to withdraw equal monthly payments for 10 years, at the end of which time the account will have
zero balance, how much should they withdraw each month?
The couple should withdraw approximately $1,120.28 each month for a period of 10 years in order to deplete the account balance to zero by the end of the term.
To calculate the monthly withdrawal amount for the couple, we can use the concept of an annuity.
Principal amount (P) = $200,000
Interest rate (r) = 8.4% per year = 8.4/100 = 0.084
Number of compounding periods per year (n) = 12 (monthly compounding)
Number of years (t) = 10
The formula for calculating the monthly withdrawal amount from an annuity is:
Withdrawal Amount [tex]= P \times (r/n) / (1 - (1 + r/n)^{(-n\times t)})[/tex]
Plugging in the given values, we get:
Withdrawal Amount [tex]= $200,000 \times (0.084/12) / (1 - (1 + 0.084/12)^{(-12\times 10)})[/tex]
Now, let's calculate it step by step:
Calculate the value inside the parentheses:[tex](1 + 0.084/12)^{(-1210)}[/tex]
(1 + 0.084/12) = 1.007
(-1210) = -120
[tex](1.007)^{(-120)[/tex] ≈ 0.433
Substitute the value into the formula:
Withdrawal Amount [tex]= $200,000 \times (0.084/12) / (1 - 0.433)[/tex]
Simplify the denominator:
Withdrawal Amount [tex]= $200,000 \times (0.084/12) / 0.567[/tex]
Perform the division:
Withdrawal Amount ≈ $1,120.28
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A formula for speed is given. distance speed= ______________ Time Which units are possible for the formula?
The speed=distance ÷ Time , the units that are possible for the formula is m/s and km/h.
What is speed?Speed is what it means. the speed at which an object's location changes in any direction. The distance traveled divided by the time it took to travel that distance is how fast something is moving.
The units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s).
The formula speed = distance divided by time, which can be expressed as;
[tex]speed = \frac{distance}{ time}[/tex]
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Mercury, if ingested can cause severe health problems. The amount of mercury in Tuna’s body tissue is much higher than other fish.
It is known that the amount of mercury in Albacore tuna is normally distributed with mean 10.13 micrograms and standard deviation of 2.03 micrograms per ounce.
A food company has a production line for canned albacore tuna. They regularly take random samples of 10 cans of tuna and test the amount of mercury. If the sample mean amount of mercury in tuna exceeds 12 micrograms per ounce, the production line will be stopped to find the source of contamination.
Let μ denote the actual population mean amount of mercury in tuna per ounce. The hypotheses for this testing situation are:
H
0
:
μ
=
10.13 vs
H
A
:
μ
>
10.13.
To calculate the chance of making a Type I error using the decision rule above, what would you use as the mean for the normal distribution in your graphing calculator?
The probability of making a Type I error using the decision rule above is 0.00045 or 0.045%.
The hypothesis for this testing situation are given below:H0: μ = 10.13HA: μ > 10.13μ denotes the actual population mean amount of mercury in tuna per ounce.
Therefore, the company has set a limit of 12 micrograms of mercury per ounce of albacore tuna. If the sample mean amount of mercury in tuna exceeds this amount, the production line will be stopped to find the source of contamination.
To calculate the chance of making a Type I error using the decision rule above, we will use the mean for the normal distribution in the graphing calculator, which is 10.13. The standard deviation is 2.03 and the sample size is 10 cans of tuna. We need to find the z-value that corresponds to a sample mean of 12 or greater.
The formula for calculating the z-value is shown below z = (x - μ) / (σ / sqrt(n))where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Using the given information, we can calculate the z-value as follows:z = (12 - 10.13) / (2.03 / sqrt(10))z = 3.32Therefore, the probability of making a Type I error using the decision rule above is the area to the right of the z-value of 3.32. To calculate this probability, we can use a standard normal distribution table or a graphing calculator.
Using a graphing calculator, we can find the probability by graphing a standard normal distribution with a mean of 0 and a standard deviation of 1 and shading the area to the right of the z-value of 3.32.
The graphing calculator gives the probability of 0.00045.
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The length of a triangle's base is 5x'y' cm and its height is 4xy? cm.
* Determine a simplified expression for the area of the triangle.
* If the triangle is the base of a prism with a length of & cm, find a simplified expression for the volume of the prism.
* If x= 4cm and y =3 cm, determine the area of the triangle and the volume of the triangular prism
1. The simplified expression for the area of the triangle is 10x²y²
2. The expression for the volume of the prism is 80x²y²
3. The area of the triangle 1440 cm² and the volume of the prism is 11520cm³
What is area of triangle?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
The area of a triangle is expressed as
A = 1/2bh
where b is the base and h is the height.
base = 5x'y'
height = 4xy
A = 1/2 × 5xy × 4xy
A = 10x²y²
The volume of a prism is expressed as;
V = base area × height
height = 8cm
The expression for the volume = 10x²y² × 8
= 80x²y²
When x = 4 and y = 3
A = 10x²y² = 10 × 16 × 9
= 1440 cm²
Volume of the prism = 1440 × 8
= 11520 cm³
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Suppose Boris places $9500 in an account that pays 12% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
At the end of 1 year, the amount in the account is $10,640, and at the end of 2 years, the amount is $11,910.40.
To calculate the amount in the account at the end of each year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, Boris placed $9500 in an account that pays 12% interest compounded annually.
(a) To find the amount in the account at the end of 1 year, we have:
P = $9500
r = 12% = 0.12
n = 1 (compounded annually)
t = 1 year
Using the formula, we have:
A = 9500(1 + 0.12/1)^(1*1)
A = 9500(1 + 0.12)^1
A = 9500(1.12)
A = $10640
Therefore, the amount in the account at the end of 1 year is $10,640.
(b) To find the amount in the account at the end of 2 years, we have:
P = $9500
r = 12% = 0.12
n = 1 (compounded annually)
t = 2 years
Using the formula, we have:
A = 9500(1 + 0.12/1)^(1*2)
A = 9500(1 + 0.12)^2
A = 9500(1.12)^2
A = $11910.40
Therefore, the amount in the account at the end of 2 years is $11,910.40.
In summary, at the end of 1 year, the amount in the account is $10,640, and at the end of 2 years, the amount is $11,910.40.
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CO
2
3 4
The graph of the function f(x) = -(x+3)(x-1) is
shown below.
-6 -4 2
Mark this and return
6
←
-2-
-6
2
4
6
X
Which statement about the function is true?
O The function is positive for all real values of .x
where
x < -1.
TIME REMAINING
54:49
O The function is negative for all real values of x
where
x<-3 and where x> 1.
O The function is positive for all real values of x
where
x>0.
O The function is negative for all real values of x
where
x<-3 or x>-1.
Save and Exit
Next
Submit
The true statement about this function is that: the function is negative for all real values of x, where x < -3 and where x > 1.
What is a function?A function is a mathematical expression which can be used to define and indicate the relationship existing between two or more variables in a data set.
By critically observing the graph which models the given function (see attachment), we can logically deduce that the true statement about this function is that it's negative for all real values of x, where x is less than -3 and where x is greater than 1.
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Solve by using whole number
Step-by-step explanation:
8 x x 2 first x can be 0 - 9 <==== 10 choices
second x can also be 0 -9 <====10 choices for each of the FIRST 10 choices
10 x 10 = 100 possible plates.
8 00 2
8012
8022
.
.
.
8 99 2
Answer:
a) see below
b) 100
Step-by-step explanation:
a)
8 _ _ 2
8002
8012
8022
8032
8042
8052
8062
8072
8082
8092
8002
8112
8122
8132
8142
8152
8162
8172
8182
8192
8202
8212
8222
8232
8242
8252
8262
8272
8282
8292
8302
8312
8322
8332
8342
8352
8362
8372
8382
8392
8402
8412
8422
8432
8442
8452
8462
8472
8482
8492
8502
8512
8522
8532
8542
8552
8562
8572
8582
8592
8602
8612
8622
8632
8642
8652
8662
8672
8682
8692
8702
8712
8722
8732
8742
8752
8762
8772
8782
8792
8802
8812
8822
8832
8842
8852
8862
8872
8882
8892
8902
8912
8922
8932
8942
8952
8962
8972
8982
8992
b) There are 100 different license plates.
Range,median,mean,mode for 79,83,94,86,90,84,86
The range is 5. The mean is 86. The mode is 86. The median is 86.
What is the range, median, mean and mode?The numbers arranged in ascending order is 79, 83, 84, 86, 86, 90, 94
Range is the difference between the highest and lowest values of a set of observations
Range = highest value - lowest value
94 - 79 = 5
Mean is the average of a set of numbers.
Mean = sum of numbers / total number in the dataset
(79 + 83 + 84 + 86 + 86 + 90 + 94) / 7 = 602 / 7 = 86
Mode is the number that appears with the most frequency in the dataset. 86 appears twice in the dataset.
Median is the number at the center of the dataset.
Median = (n + 1) / 2
Where n is the numbers in the observation
(7 + 1) / 2 = 4th number = 86
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I spent half of my savings on cloths and half of what was left on shoes. if I had#100.00 balance, what had I at first?
Answer:
Step-by-step explanation:
50$
Let R be the region bounded by the following curves. Use the method of your choice to find the volume of the solid generated when R is revolved around the x-axis.
y=[tex]\sqrt{ln(x^2/64)[/tex]
y = [tex]\sqrt{ln(x/8)[/tex]
y = 1
about the x-axis
The volume of the solid generated when R is revolved around the x-axis is 20π/3 cubic units.
To find the volume of the solid generated when the region R is revolved around the x-axis, we can use the method of disks or washers.
First, let's find the points of intersection of the curves.
Setting the first two equations equal to each other, we have:
√(x^2/64) = √(x/8)
Squaring both sides, we get:
x^2/64 = x/8
Multiplying both sides by 64, we have:
x^2 = 8x
Rearranging, we get:
x^2 - 8x = 0
Factoring out x, we have:
x(x - 8) = 0
So, x = 0 and x = 8 are the points of intersection.
Now, let's integrate to find the volume of the solid.
We can split the region R into two parts: the part below y = 1 and the part between the curves y = √(x^2/64) and y = √(x/8).
For the part below y = 1, the radius of each disk is given by the corresponding x-value, and the height is 1. So the volume of this part is given by:
V1 = π * ∫[0,8] (1)^2 dx
Simplifying, we get:
V1 = π * ∫[0,8] dx
Integrating from 0 to 8, we have:
V1 = π * [x] evaluated from 0 to 8
V1 = π * (8 - 0)
V1 = 8π
For the part between the curves, the radius of each washer is given by the corresponding x-value, and the height is the difference between the curves: √(x^2/64) - √(x/8). So the volume of this part is given by:
V2 = π * ∫[0,8] [(√(x^2/64))^2 - (√(x/8))^2] dx
Simplifying, we get:
V2 = π * ∫[0,8] [(x^2/64) - (x/8)] dx
Integrating from 0 to 8, we have:
V2 = π * [(x^3/192) - (x^2/16)] evaluated from 0 to 8
V2 = π * [(8^3/192) - (8^2/16) - (0^3/192) + (0^2/16)]
V2 = π * [256/192 - 64/16]
V2 = π * [4/3 - 4]
V2 = -4π/3
The total volume of the solid is the sum of V1 and V2:
V = V1 + V2
V = 8π - 4π/3
V = (24 - 4)π/3
V = 20π/3
As a result, the solid created when R is rotated about the x-axis has a volume of 20/3 cubic units.
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The bike you have saved for is discounted 25%. You have $600 saved to purchase it. The original non-discounted price of the bike is $625. There is 5.53% sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax how much money will you have left over?
After purchasing the bike with the discount and sales tax, you will have approximately $105.331 left over.
How much money will you have left?In order to determine how much will be left, we can do this;
1. The discounted price of the bike is;
Discounted price = Original price - (Discount percentage * Original price)
Discounted price = $625 - (0.25 * $625)
Discounted price = $625 - $156.25
Discounted price = $468.75
2. Calculate the sales tax:
Sales tax is added to the price of the bike, so we need to calculate 5.53% of the discounted price.
Sales tax = Sales tax percentage * Discounted price
Sales tax = 0.0553 * $468.75
Sales tax = $25.912
3. Calculate the total amount to be paid:
Total amount to be paid = Discounted price + Sales tax
Total amount to be paid = $468.75 + $25.919
Total amount to be paid ≈ $494.669 (rounded to three decimal places)
4. Calculate the money left over:
Money left over = Total amount saved - Total amount to be paid
Money left over = $600 - $494.669
Money left over = $105.331
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The function g(x) is graphed.
3-
2
4-
-5-4-3-2-1₁
-2
3
++
2
3 4 5 X
Which statements about the function are true? Choose
three options.
g(1) = -1
Og(0) = 0
g(4) = -2
g(1) = 1
Og(-1) = 1
The three true statements of the function g(x) = x² are
g(0) = 0, g(-1) = 1, and g(-1) = 1.
Options B, D, and E are the correct answer.
We have,
Function:
g(x) = x²
Substitute x = 0, 1, -1, 4 in the function.
So,
g(0) = x² = 0² = 0
This is true.
g(1) = x²= 1² = 1
This is true.
g(-1) = x² = (-1)² = 1
This is true.
g(4) = x² = 4² = 16
This s not true.
Thus,
The three true statements of the function g(x) = x² are
B. g(0) = 0
D. g(-01) = 1
E. g(-1) = 1
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The complete question:
The function g(x) = x² is graphed. Which statements about the function are true?
g(1) = -1
g(0) = 0
g(4) = -2
g(1) = 1
g(-1) = 1
A small tree that is 5 feet tall casts a 3-foot shadow, while a building that is 45 feet tall casts a shadow in the same direction. Determine the length of the building's shadow.
9 feet
10 feet
15 feet
27 feet
a circular wheel of a diameter 35 cm makes 100 revolutions in 1 min. Calculate the distance covered by the wheel in half an hour.express answer in km. take pie 22/7
Answer ASAP
Answer:
Circumference = Diameter × π
Circumference = 35 cm × 3.14
Circumference = 109.9 cm
The number of revolutions in 1 minute is given as 100, so the distance covered in 1 minute can be calculated as:
Distance in 1 minute = Circumference × Revolutions
Distance in 1 minute = 109.9 cm × 100
Distance in 1 minute = 10990 cm
To find the distance covered in half an hour, we need to multiply the distance in 1 minute by 30, since there are 30 minutes in half an hour:
Distance in half an hour = Distance in 1 minute × 30
Distance in half an hour = 10990 cm × 30
Distance in half an hour = 329700 cm
To express the answer in km, we need to divide the distance in cm by 100000, since there are 100000 cm in a km:
Distance in km = Distance in cm / 100000
Distance in km = 329700 cm / 100000
Distance in km = 3.297 km
Therefore the distance covered by the wheel in half an hour is 3.297 km.
See the attached math problem, please help!
The equations of the rows are
x + 3y - z = 44x - 2y + 7 = 20-3x + y + 5 = 8How to determine the equations of the rowsFrom the question, we have the following parameters that can be used in our computation:
The augmented matrix given as
[tex]\left[\begin{array}{ccc|c}1&3&-1&4\\4&-2&7&20\\-3&1&5&8\end{array}\right][/tex]
From the above, we set the columns as follows:
x = first row
y = second row
z = third row
constant = fourth row
Using the above as a guide, we have the following:
x + 3y - z = 4
4x - 2y + 7 = 20
-3x + y + 5 = 8
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. In a test (+5) marks are given for every correct answer and (-2) marks are
given for every incorrect answer and 0 for answer not attempted. Ram gets 3
correct and 4 incorrect out of 7 questions he attempted. What is his score
If Ram gets 3 correct and 4 incorrect out of 7 questions he attempted then Ram's score in the test is 7.
To find Ram's score, we will use the given formula:S = 5c - 2w
where S is the score, c is the number of correct answers and w is the number of wrong answers.
Ram attempted 7 questions and answered 3 of them correctly and 4 of them incorrectly.
So:
c = 3 (number of correct answers)w = 4 (number of wrong answers)
We can now substitute these values in the formula to get Ram's score:
S = 5c - 2w
S = (5 x 3) - (2 x 4)
S = 15 - 8
S = 7
Therefore, Ram's score is 7.
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The question is provided in the picture below! Thank you!
The surface area written as a function of time is expressed as:
S(t) = ⁹/₄πt⁴
How to change the subject of the formula?The subject of a formula is defined as the variable that is being worked out. It can be recognized as the letter on its own on one side of the equals sign.
We are told that the formula for the surface area of the hot air balloon is given as: S(r) = 4πr²
Now, the radius with respect to time is given by the formula:
r(t) = ³/₄t²
where t is time.
Thus, Putting ³/₄t² for r in the surface area formula gives us:
S(t) = 4π(³/₄t²)²
S(t) = 4π(⁹/₁₆t⁴)
S(t) = ⁹/₄πt⁴
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Segments AC and BD are diameters of Circle E. If, arc ACD = 326 degrees then what does BCA equal?
Answer:
Since arc ACD is 326 degrees and arc AD is a semicircle (180 degrees), then arc ACB is:
arc ACB = arc ACD - arc AD
arc ACB = 326 - 180
arc ACB = 146 degrees
Since arc ACB is a central angle, it is equal to twice the inscribed angle BCA:
2 * BCA = arc ACB
BCA = arc ACB / 2
BCA = 146 / 2
BCA = 73 degrees
Therefore, BCA is 73 degrees.
What is the measure of ZMOP, given that figure MNOP is a rectangle?
OA. 35°
OB. 45°
OC. 90°
D. 55°
N
M
55%
O
P
"What is the measure of ZMOP, given that figure MNOP is a rectangle" is D. 55°.
In a rectangle, all interior angles are 90°.
Therefore, NM is perpendicular to OP.Since NM = 55% of OP, we can construct a right triangle where ON is the hypotenuse and NM is one leg.
Since this is a 45°-45°-90° triangle, the measure of angle ZMO is 45°.
Thus, the measure of angle ZMOP can be found by subtracting 90° (the measure of angle NMO) from 45°.
This gives us 55° as the measure of angle ZMOP.Therefore, the answer is D. 55°.
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The following table shows the number of fire hydrants in each neighborhood overseen by Fire District
9
99.
Neighborhood Number of fire hydrants
Clearwater Estates
17
1717
Babbling Brooke
8
88
Hidden Village
21
2121
Shamrock Oak
15
1515
Tower Terrace
12
1212
Find the median number of fire hydrants.
Without considering any external factors or influences, the median number of fire hydrants in the neighborhoods overseen by Fire District 9 is 15, as determined by the given data.
To find the median number of fire hydrants in the neighborhoods overseen by Fire District 9, we need to arrange the given numbers in ascending order and determine the middle value.
Here are the numbers sorted in ascending order:
8, 12, 15, 17, 21
Since we have an odd number of values, the median will be the middle number, which in this case is 15.
Therefore, the median number of fire hydrants in the neighborhoods overseen by Fire District 9 is 15.
To explain this concept further, the median is a measure of central tendency that represents the middle value in a set of numbers.
It is calculated by arranging the numbers in ascending or descending order and selecting the middle value.
In cases where there is an even number of values, the median is the average of the two middle numbers.
In this scenario, we have five numbers representing the number of fire hydrants in each neighborhood.
By sorting them in ascending order, we can easily identify the middle value as 15, which serves as the median.
This indicates that half of the neighborhoods have fewer than 15 fire hydrants, while the other half have more than 15 fire hydrants.
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Can you guys pls answer this question
Examining the figure, quadrilateral PQUV is a parallelogram
What is a parallelogram?
A parallelogram is a quadrilateral, which is a polygon with four sides. It is a special type of quadrilateral characterized by several distinct properties.
In this case, we assumed that
UV = PQUP = VQIn addition, the sides as mentioned are parallel to each other
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raj bought 300 mangoes at per 10 mangoes for RS 100 and sold them at a profit of 25% At what rate did he sell per 15 mangoes
Raj sold the mangoes at a rate of Rs. 12.50 per 15 mangoes.
Raj purchased 300 mangoes at a cost of Rs. 100 per 10 mangoes. Later, he sold all the mangoes at a profit of 25%. Now we need to determine the rate at which he sold 15 mangoes.
To find the selling rate per 15 mangoes, we first calculate the selling price of the entire batch of 300 mangoes.
Raj initially bought 10 mangoes for Rs. 100. Therefore, the cost of one mango is Rs. 100/10 = Rs. 10.
Since Raj sold the mangoes at a profit of 25%, the selling price per mango can be calculated as the cost price plus 25% of the cost price. Thus, the selling price per mango is Rs. 10 + (25/100)*Rs. 10 = Rs. 12.50.
To find the selling price of the entire batch of 300 mangoes, we multiply the selling price per mango by the total number of mangoes: Rs. 12.50 * 300 = Rs. 3750.
Finally, to determine the selling rate per 15 mangoes, we divide the total selling price by the number of mangoes: Rs. 3750 / 300 = Rs. 12.50.
Therefore, Raj sold the mangoes at a rate of Rs. 12.50 per 15 mangoes.
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NO LINKS!!! URGENT HELP PLEASE!!
In a right triangle ABC, C being the right angle, the cosine of angle B is equal to option A: cos(90° - B).
How to Find the Cosine of an Angle in a Right Triangle?Using the definition of cosine, we can express the cosine of angle B in the right triangle as cos(B) = adjacent side / hypotenuse, which is A / C.
To find an alternative expression for cos(B), we can use the fact that the sum of the angles in a triangle is 180°.
In a right triangle, angle A + angle B + angle C = 180°.
Since angle C is 90°, we have angle A + angle B + 90° = 180°, which simplifies to angle A + angle B = 90°.
By rearranging the equation, we get angle A = 90° - angle B.
Now, we can substitute angle A in the cosine expression: cos(B) = adjacent side / hypotenuse = A / C = (90° - B) / C.
Therefore, cos(B) is equal to cos(90° - B), corresponding to option A.
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Answer:
B) sin(90° - B)
Step-by-step explanation:
The interior angles of a triangle sum to 180°.
As angle C is the right angle in right triangle ABC, the other two angles, A and B, must be complementary angles (sum to 90°). Therefore, we can say:
A = 90° - BB = 90° - AFor two complementary angles, the cosine of one equals the sine of the other. Therefore, in our right triangle ABC, the cosine of A equals the sine of B, and the cosine of B equals the sine of A:
cos A = sin Bcos B = sin AIf we substitute A = 90° - B into the first equation, we can say that:
[tex]\large\boxed{\cos B = \sin (90^{\circ} - B)}[/tex]
At the beginning of an experiment, a scientist has 296 grams of radioactive goo. After 135 minutes, her sample has decayed to 9.25 grams.
What is the half-life of the goo in minutes? (Round to one decimal place)
The half-life of the goo is
Find a formula for
G
(
t
)
, the amount of goo remaining at time
t
.
G
(
t
)
=
How many grams of goo will remain after 38 minutes? (Round to one decimal place)
There will be
grams of goo after 38 minutes.
The half-life of the radioactive goo is approximately 41.82 minutes. The formula for the amount of goo remaining at time t is G(t) = 296 * (1/2)^(t/41.82). After 38 minutes, there will be approximately 66.5 grams of goo remaining.
To find the half-life of the radioactive goo, we can use the formula for exponential decay:
N(t) = N₀ * (1/2)^(t/h)
where N(t) is the amount of goo remaining at time t, N₀ is the initial amount of goo, t is the time elapsed, and h is the half-life of the goo.
In this case, N₀ = 296 grams, N(t) = 9.25 grams, and t = 135 minutes. We can plug these values into the formula and solve for h:
9.25 = 296 * (1/2)^(135/h)
To solve for h, we can take the logarithm of both sides:
log(9.25) = log(296) + (135/h) * log(1/2)
Simplifying further:
(135/h) = (log(9.25) - log(296)) / log(1/2)
(135/h) ≈ -3.2279
h ≈ 135 / (-3.2279)
h ≈ -41.82
Since the half-life cannot be negative, we take the absolute value:
half-life ≈ 41.82 minutes (rounded to one decimal place)
The formula for the amount of goo remaining at time t (in minutes) can be written as:
G(t) = 296 * (1/2)^(t/41.82)
To find the amount of goo remaining after 38 minutes, we can substitute t = 38 into the formula:
G(38) = 296 * (1/2)^(38/41.82)
G(38) ≈ 66.5 grams (rounded to one decimal place)
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Pls help with my homework
The volume of the larger boat is 3840 cm³.
How to find the volume of similar solid?If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.
Therefore, let's find the volume of the larger boat as follows:
Hence,
(5 / 20)³ = 60 / v
5³ / 20³ = 60 / v
125 / 8000 = 60 / v
cross multiply
125v = 480000
divide both sides by 125
v = 480000 / 125
v = 3840
Therefore,
volume of the larger boat = 3840 cm³
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pay terest as shown below. Michelle wants to invest £2900 in one of these accounts for 19 years. a) Which account will pay Michelle more interest after 19 years? b) How much more interest will that account pay? Give your answer in pounds (£) to the nearest 1p. Account 1 Simple interest at a rate of 8% per year Account 2 Compound interest at a rate of 5% per year
a) Michelle wants to invest £2900 in one of these accounts for 19 years. Compound interest at a rate of 5% per year in Account 2 will pay Michelle more interest after 19 years.
b) The interest paid by Account 2 is £2202.55 which is £331.87 more than the interest paid by Account 1.
Account 2 will pay Michelle £331.87 more interest than Account 1 after 19 years.
Account 1 pays simple interest at a rate of 8% per year. The formula for simple interest is given as follows:
I = P * r * t
Where, I = Interest earned
P = Principal (initial amount invested)
r = Rate of interest per year (in decimals
)t = Time period for which money is invested A
ccount 2 pays compound interest at a rate of 5% per year.
The formula for compound interest is given as follows:
A = P * (1 + r/n)^(n*t)
Where, A = Amount earned
P = Principal (initial amount invested)
r = Rate of interest per year (in decimals)
n = Number of times interest is compounded per year (in this case, n = 1 as interest is compounded annually)
t = Time period for which money is investedIn this case, Michelle invests £2900 in both accounts for 19 years.
Account 1: I = P * r * tI = 2900 * 0.08 * 19I = £4396.00
Account 2: A = P * (1 + r/n)^(n*t)A = 2900 * (1 + 0.05/1)^(1*19)A = £5102.55
The interest earned in Account 2 is A - P = £5102.55 - £2900 = £2202.55.
The difference in interest earned between Account 2 and Account 1 is £2202.55 - £4396.00 = £-2193.45.
Therefore, Account 2 pays Michelle £2193.45 more interest than Account 1.
However, the question asks for the amount in pounds to the nearest 1p.
Rounding off the values of interest earned to 2 decimal places gives the interest earned by Account 1 as £4396.00 and the interest earned by Account 2 as £2202.55.
The difference in interest earned is £2202.55 - £4396.00 = £-2193.45 ≈ £-2193.44.
Rounding this value to the nearest 1p gives the difference in interest earned as £-2193.44 ≈ £-2193.44 ≈ -£2193.44.
The value is negative because Account 2 pays Michelle less interest than Account 1.
Therefore, Account 1 pays £2193.44 more interest than Account 2.
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What is the order of the rotational symmetry for the figure?
The order of the rotational symmetry of the figure is
C. 1What is rotational symmetry?Rotational symmetry refers to the property of an object or shape that remains unchanged or appears the same after a rotation of a certain angle around a fixed point called the center of rotation.
The degree or order of rotational symmetry of an object is determined by the number of distinct positions in which it looks the same during a full rotation of 360 degrees (or 2π radians).
In this case the figure will have only one rotational symmetry
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Firestation B is 15 miles due east from Firestation A. firefighters at station a spot a fire at N 60° E or 30° . firefighters at station B spot the same fire at N 40° W or 320° 
The approximate distance between station B and Fire is 29.5 miles.
The missing angle in the triangle :
180 - (30 + 50) = 100°
Let distance between fire and station B = b
Using the sine rule :
a/sinA = b/sinB = c/sinCb/sin(30) = 15/sin(15)
b = (15 * sin(30)) / sin(15)
b = 7.5/sin(15)
b = 28.97
Hence, the approximate distance is 29.5 miles.
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Which of the following is NOT a rational expression? (Answers in image below.)
The expression that is NOT a rational expression is 2x/1.
What is a rational expression?A rational expression is a ratio of two polynomials. Note that a polynomial has a coefficient a power and a variable. In all of the expressions provided, there are polynomials that contain a coefficient like 2, a variable x, and a power that is either 1, 2, 3, or any other number.
The only exception to this is option 3 which has no polynomial as a denominator.
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