We can find a and b using inverse trig functions,
[tex]
\cos(a)=\frac{4}{5}\implies a=\arccos\Big(\frac{4}{5}\Big)\approx36.87 \\
\sin(b)=-\frac{5}{13}\implies b=\arcsin\Big(-\frac{5}{13}\Big)\approx-22.62
[/tex]
[tex]\tan(36.87-(-22.62))\approx1.7[/tex]
Hope this helps.
A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi. Find the probability that the sample mean comprehensive strength exceeds 4985 psi.
Answer:
Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.
Step-by-step explanation:
We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.
Let [tex]\bar X[/tex] = sample mean comprehensive strength
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean comprehensive strength = 5500 psi
[tex]\sigma[/tex] = standard deviation = 100 psi
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P([tex]\bar X[/tex] > 4985 psi)
P([tex]\bar X[/tex] > 4985 psi) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{4985-5500}{\frac{100}{\sqrt{9} } }[/tex] ) = P(Z > -15.45) = P(Z < 15.45)
= 0.99999
Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.
Which is 23,578,000 written in scientific
notation?
Answer:
[tex]23,578,000 = 2.3578 \times {10}^{7} \\ [/tex]
Is 3 5/2 an acceptable answer?
Please explain your answer.
thx
yes, if the question is asking for a mixed number.
Answer:
5 1/2 would be a better answer or 5.5 in decimal form
hope this helps :)
Roy wants to buy a new wireless phone for $200. Two stores offer different payment options. Which plan has a greater initial value? Which phone will be paid for at a faster rate
Answer:
store A
Step-by-step explanation:
Seutas tali yang panjangnya 121 meter dipotong menjadi beberapa bagian sehingga dibuat deret geometri. Jika jumlah potongan terpendek 4 meter dan jumlah potongan terpanjang 108 meter, maka jumlah potongan tali yang terbentuk adalah …… .. 14
Answer:
orehwfociuxsh8tq23rjwfhdfyvbndm
Step-by-step explanation:
Valentina va de compras al mall con $50.000. Gasta 3/5 de esa cantidad en un buzo y la mitad del resto en una falda.¿cuanto dinero le queda a valentina?
Answer:
The amount left with Valentina is $10,000.
Step-by-step explanation:
The question is:
Valentina goes shopping at the mall with $50,000. She spends 3/5 of that amount on a diver and half the rest on a skirt. How much money does Valentina have left?
The original amount Valentina had was, P = $50,000.
Compute the amount spent on a diver as follows:
D = [tex]\frac{3}{5}th[/tex] of $50,000
[tex]=\frac{3}{5}\times 50000\\=30000[/tex]
The amount spent on a diver was, D = $30,000.
Amount left:
A = P - D
= 50000 - 30000
= 20000
Compute the amount spent on a skirt as follows:
S = [tex]\frac{1}{2}[/tex] of $20,000
[tex]=\frac{1}{2}\times 20000\\=10000[/tex]
Amount left:
A₁ = A - S
= 20000 - 10000
= 10000
Thus, the amount left with Valentina is $10,000.
Sarah bought 3 1/2 pints of blueberries to make jelly. She ate 3/4 of a pint of berries on her way home. How many pints of berries does she have left to make jelly?
Answer:
11/4 or 2.75 pints
Step-by-step explanation:
We want to find the difference between the original amount of blueberries and the amount she ate
original amount-amount ate
3 1/2 -3/4
To subtract, we need common denominators
The common denominator of 2 and 4 is 4
3 1/2=7/2
Multiply by 2/2 to get a common denominator of 4
7/2*2/2=14/4
Now, we have common denominators and can subtract
14/4-3/4
Subtract the numerators, and leave the denominators as 4
11/4 =2.75
She has 11/4 or 2.75 pints left
In the city of Manhattan, it takes about 13 Starbucks to serve every 100,000 people. As of 2019, Manhattan has
approximately 1,629,000 people. If Manhattan is approximately 23 square miles, what is the density of Starbucks per
square mile in the city?
___Starbucks per square mile
Answer:
9.207
Step-by-step explanation:
To get the amount of starbucks for the population we can do
[tex]\frac{13 * 1629000}{100000}[/tex]
which gives us 211.77 total Starbucks in 23 miles.
To get starbucks per mile, we divide this number by 23.
This gives us 9.207
if angle y measures 33 degrees what does angle x measure?
Answer:
<x = 147
Step-by-step explanation:
Supplementary angles is when the sum of the two angles are equal to 180
So the sum of angle x and angle y is equal to 180
y = 33
x + y = 180
x + 33 = 180
x = 180 - 33
x = 147
Answer:
x = 147°
Step-by-step explanation:
x ; y = suplementary =>
x + y = 180° } => x = 180° - 33° = 147°
y = 33°
8 yd
6 yd
Surface Area?
The surface area of a rectangle can be calculated by multiplying its length by its width. Since the given dimensions are 8yd and 6yd, the surface area, or more accurately the area, would be 48yd2.
The answer is 48yd2.
Surface area in mathematics refers to the total measure of the exposed outer surfaces of a three-dimensional object, like a cube, sphere, or cylinder. It is calculated by finding the sum of the areas of all the individual surfaces. For example, in a cube, you would add the areas of all six square faces. Surface area plays a crucial role in geometry and real-life applications like packaging design and construction. It helps quantify the amount of material needed and aids in solving problems related to shapes and volumes.
The surface area of a rectangular prism (which includes a box or cuboid shape) is found using the formula: 2lw + 2lh + 2wh, where l equals length, w equals width (or breadth), and h equals height. However, if we are dealing with a rectangle, since it's a two-dimensional figure, the surface area would be its area, which can be found with the formula length x width.
In your case, you only provided the length and width so I would assume that we are dealing with a rectangle. Therefore, to find the area, you just need to multiply the length by the width: 8yd x 6yd = 48yd2.
The answer is 48yd2.
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A bowl contains 4 tangerines and 5 clementines. John randomly selects one piece of fruit, and then Pam randomly selects one of the remaining pieces of fruit. What is the probability that John selects a tangerine and Pam selects a clementine?
Answer:
5/18
Step-by-step explanation:
There are 9 pieces of fruit in the bowl, tangerines and 5 clementines.
Assuming that they do not put the fruit back
P (tangerine) = number of tangerines/ total = 4/9
Then John keeps his and there are 8 pieces of fruit in the bowl,
3 tangerines and 5 clementines.
P (Clementine) = number of clementines/ total = 5/8
P (tangerine, no replacement, Clementine) = P (tangerine) * P (Clementine)
= 4/9 * 5/8 =5/18
Answer:
5/18
Step-by-step explanation:
1. Find each of their probabilities separately
2. John= # of tangerines/ total # of fruit
3. John = 4/9
4. Pam = # of clementines/ total # of fruit left
5. Pam= 5/8
6. Multiply the two together to get the probability that both pick the fruit they want
7. 4/9 times 5/8
8. 5/18
20 points if you help me on this proublem
Answer:
1) f(x) = x/8 - 7
2) f(x) = 1 - x/3
3) f(x) = 20 - 0.25x
4) f(x) = x + 7
Step-by-step explanation:
f^-1 = 8(x + 7)
x + 7 = y/8
x = y/8 - 7
f(x) = x/8 - 7
f^-1 = -3(x - 1)
y/-3 = x - 1
x = 1 - y/3
f(x) = 1 - x/3
f^-1 = 4(20 - x)
y/4 = 20 - x
x = 20 - y/4
f(x) = 20 - x/4
f(x) = 20 - 0.25x
f^-1 = x - 7
y = x - 7
x = y + 7
f(x) = x + 7
Penny makes deposits into two separate accounts for 5 years: option A: $800; 6% annual simple interest option B: $800; 6% annual compound interest. A. What is the interest earned on option A? B. What is the total value of option A? C. What is the interest earned on option B? D. What is the total value on option B? E. Which is the better option?
Answer:
A) P = 240
B) P + Po = 1040
C) P = 270.58
D) P+Po = 1070.58
E) Option B (compound interest) is better, as it generates more interest for the same inicial value, rate of interest and time
Step-by-step explanation:
The formula for simple interest is:
P = Po*r*t
Where P is the interest earned, Po is the inicial value, r is the rate of interest and t is the time.
The formula for compound interest is:
P+Po = Po*(1+r)^t
So we have that:
A) P = 800*0.06*5 = 240
B) P + Po = 800 + 240 = 1040
C) P+Po = 800*(1+0.06)^5 = 1070.58 -> P = 1070.58 - 800 = 270.58
D) P+Po = 1070.58
E) Option B (compound interest) is better, as it generates more interest for the same inicial value, rate of interest and time
Find the solutions. Show steps please!
Answer:
x = 0, π/4, π, 7π/4
Step-by-step explanation:
sin(2x) = √2 sin x
Use double angle formula.
2 sin x cos x = √2 sin x
Move everything to one side.
2 sin x cos x − √2 sin x = 0
Factor.
sin x (2 cos x − √2) = 0
Solve.
sin x = 0, cos x = ½√2
x = 0, π/4, π, 7π/4
Using this tree diagram, compute the probability of system failure. Follow each branch to find all possible favorable outcomes for success, and then use that value to find the probability of system failure.
Answer: The system will succeed when the first alarm rings or when the first one fails, but the second one rings. The probability of this is 0.98
The probability of system failure is 1-(probability of success)= 1-0.98= 0.02
Step-by-step explanation:
Answer:
The system will succeed when the first alarm rings or when the first one fails, but the second one rings. The probability of this is 0.98
The probability of system failure is 1-(probability of success)= 1-0.98= 0.02
Step-by-step explanation:
Plato
A bag contains 50 pieces of gum flavored cherry, grape, and watermelon.
· William will randomly pick a piece of gum.
· The probability of picking cherry is 1/5 .
· The probability of picking watermelon is 3/10 .
What is the probability William will pick a piece of grape gum?
Answer:
1/10
Step-by-step explanation:
The probability William will pick a piece of grape gum is 1/5.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
Total gums= 50
The probability of picking cherry is 1/5.
and, probability of picking watermelon is 3/10.
As, we know the probability of all vents sum upto 1.
So, P(picking a grape gum)
= 1- 1/5 - 3/10
= 10-2-3/ 10
=5/10
=0.5
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second. y=-16x^2+128x+136
Answer: The rocket will reach its max after 4 seconds
Step-by-step explanation:
Hi, to find the maximum height, we have to set the first derivative of the equation equal to zero.
y=-16x^2+128x+136
0 = (2)-16x +128
0= -32x+128
Solving for x:
32x = 128
x = 128/32
x = 4 seconds
The rocket will reach its max after 4 seconds
Feel free to ask for more if needed or if you did not understand something.
If two equations in a linear system have the same slope and the same -intercepts, the system will have:'
a ; infinite solutions
b ; no solution
c ; one solution
d ; two solutions
Answer:
The answer to your question is a. Infinite solution
Step-by-step explanation:
When two lines have the same slope and the same intercepts, this means that these lines are the same so they system of equations will have infinite solutions.
If the lines do not cross, there will be no solution.
If the lines cross in one point there will be one solution
If there are a quadratic and a linear function they will cross in two points.
Math math math math mathematics maths
Answer:
Answer is 3
Step-by-step explanation:
Claudio bought tickets to a music festival that 225,000 people were expected to attend.what is the scientific notation?
Answer:
The number of people that attended in scientific notation is 2.25 x 10^5.
Step-by-step explanation:
Triangle ABC goes through a series of three transformations, resulting in triangle A^ prime B^ prime C^ prime . The three transformations are listed below. Rotation 180clockwise about the origin • a reflection over the x-axis • reflection over the y- axis Triangle ABC has vertex A located at (2, - 3) . Using the coordinates of this point, explain how the three transformations map vertex A onto vertex A^ prime .
Answer:
After the first rotation
A^ prime = (- 2, 3)
After the next two transformations, A^ = A = (2. -3)
Step-by-step explanation:
Here we have that
Rotation of 180 °clockwise about the origin will result in the inversion of the vertex point A such that the coordinates will be (- 2, 3)
Reflection over the x axis and a reflection over the y axis combined will revert the triangle back to its initial position
Therefore after the first rotation
A^ prime = (- 2, 3)
After the next two transformations, A^ = A = (2. -3).
As a brickmason's apprentice, you need to move the correct number bricks. The mason needs enough bricks to lay the next 4 rows. Each course is 24 bricks long. How many bricks do you need to move to complete the four rows?
Answer:
96 bricks
Step-by-step explanation:
In this question, we are asked to calculate the number of bricks which are needed by a mason given the number of bricks needed to complete each of the course.
From the question, we can identify that we have 4 rows to be filled with each of the rows being 24 bricks long.
now , to calculate the number of bricks needed to be moved by the mason, our work is pretty straightforward. what we simply need to do is to multiply the number of rows by the number of bricks per course.
According to this question specifically, this is equal to a value of 4 * 24 = 96 bricks
plz help ive been stuck on this question for so long
Multiply each exponent inside the parentheses by the exponent on the outside:
8^(-5 x -4) / 2^(-2 x -4)
8^20 / 2^8
The answer is C
A lighthouse is set 10 meters back from the edge of the shoreline, and it's beacon is 52 meters above sea level. Lucy can see the beacon from her ship, and the of elevation is 18 degrees. Her eyes are 12 meters above sea level. How far is the ship from the shoreline to the nearest meter?
Answer:
The distance of the ship from the shoreline is 113 metres.
Step-by-step explanation:
Please kindly check the attached files for explanation
Answer:
The distance of the ship to the shoreline is 113 meters
Step-by-step explanation:
Here we have the following information
Location of lighthouse = 10 m back from the edge of the shoreline
Height of beacon above sea level = 52 m
Level of the eyes of Lucy above sea level = 12 m
Angle of elevation of the beacon from Lucy = 18°
Therefore, the beacon, the elevation of the eyes of Lucy and the base of the lighthouse at the same elevation with Lucy form a right triangle with opposite side to angle = 52 m and angle = 18 °
Therefore, from
[tex]Tan\theta =\frac{sin\theta }{cos\theta } = \frac{Opposite \, side \, to\, angle}{Adjacent\, side \, to\, angle}[/tex]
We have
[tex]Tan18 =\frac{52-12}{Adjacent } = \frac{40}{Adjacent}[/tex]
0.325 = [tex]\frac{40}{Adjacent}[/tex]
Where the adjacent side is the distance of the ship from the lighthouse
Adjacent side = 40/0.325 = 123.107 meters
We recall that the lighthouse is 10 m back from the edge of the shoreline, therefore the ship is 123.107 - 10 or 113.107 meters from the shore line which is 113 meters to the nearest meter.
What is the y-intercept of y=3x-2
Answer:
This formula is in slope-intercept form. 3 is the slope (positive slope) and -2 is the y-intercept.
Hi there!
Your answer is:
The slope is 3 and the y-intercept is 2 or (0, 2).
Have a good day
~ Mqddie
What the answer to this plz need help ASAP
Answer:
A) 9841
Step-by-step explanation:
Formula of geometric sequence:
[tex]S_n=\frac{a_1*(r^n-1)}{r-1} \\[/tex]
First, calculate the common ratio (r) of the sequence.
It can be calculated by dividing any term of the geometric sequence by the term preceding it.
[tex]r = \frac{27}{9}\\ \\r=3[/tex]
Then
[tex]Sum = \frac{1(3^9-1)}{3-1} \\\\Sum = \frac{3^9-1}{2}\\ \\Sum=\frac{19683-1}{2} \\\\Sum = \frac{19682}{2} \\\\Sum=9841[/tex]
David has two cylinder shaped bottles of punch, each with a height of 12 inches and a radius of 2 inches. He wants to fill a half-sphere punch bowl to the brim with the punch. What should the radius of the punch bowl be to the nearest tenth of an inch to fill it entirely with the two bottles of punch?
Answer: 5.2 inches
Step-by-step explanation:
Hi, first we have to find the volume of the cylinder shaped bottles:
V = π r^2 h
where:
V =volume
r= radius
h= height
Replacing with the values given:
V = π 2^2 (12)= 150.80 cubic inches
Since there are 2 bottles
Total punch: 2V = 301.59 cubic inches
The formula for the volume of a half-sphere is
V = (2 / 3) π r3.
Since the half-sphere is filled with the two bottles of punch (301.59 cubic inches)
301.59 =(2 / 3) π r3.
301.59/ (2/3) π =r3
144 =r3
∛144 =r
5.2 inches =r
A paining measures 2.4 feet from the left to right it's hung on the center of the rectangle or wall measuring to 20 feet from left to right what is the distance between the right edge in the painting of the page of the wall reason that the paining does not tilt
Answer:
the distance between the right edge of the painting and right edge of the wall = 8.8 ft
Step-by-step explanation:
From the question, the painting is hung in center of a rectangular wall and so the distance between them on either side will be the same.
Thus, we will divide the length of the painting and wall by 2 to get 2.4/2 = 1.2 ft and 20/2 = 10 ft .
So, the distance between the right edge of the painting and right edge of the wall will be;
D = 10 - 1.2 = 8.8 ft
Michelle walks at a speed of 320 feet per minute her friend Diana Liz 400 yards from the shelves house approximately how many minutes will Michelle need to walk from her house to Diana's house and back
Answer:
3 mins 45 seconds
Step-by-step explanation:
According to the question, Michelle walks at a speed of 320 feet per minute her friend Diana Liz 400 yards from the shelves house approximately how many minutes will Michelle need to walk from her house to Diana's house and back
----First of all we have to work out in only a unit(since there are 2 units involved;feet and yards)
So,let's change the feet to yards
1 foot = 3 yards
X = 400 yards
X = 400 × 3
X = 1200 feet
Speed = distance/time
320 = 1200/x
X = 1200/320
X = 3.75 mins or 3 mins 45 secs
Without solving them, say whether these equations have a positive solution, a negative solution,
a zero solution, or no solution.
Positive solution= the answer is a positive number.
Negative solution= the answer is a negative number.
Zero solution= the answer is zero.
Negative solution= the variable goes away, so you can't solve it.
a. 3x=5
b. 5z+7=3
c. 7-5w=3
d. 4a=9
e. y=y+1
Answer:
a. 3x=5 Positive Solution
Reasoning: You're working with only positives
b. 5z+7=3 Negative Solution
Reasoning: If you carry the 7 over the non-coefficient numbers will be negative thus making your answer negative
c. 7-5w=3 Positive Solution
Reasoning: both the coefficients and the non coefficients will be negative if solved and thus will result in the negatives becoming positive when dividing the 5w
d. 4a=9 Positive
Reasoning: The first step would be to divide the 9 by 4 and the resulting number would be positive
e. y=y+1 Negative Solution (No solution)
Reasoning: y can never equal itself with changing. Thats like saying 0 is 1. This has no solution but based on the rules this is negative solution
The solutions to the equations are: a. Positive solution, b. Negative solution, c. Negative solution, d. Positive solution, and e. No solution.
Explanation:Let us analyze these equations one by one:
a. 3x=5: This equation involves multiplying a number by 3 to get 5. The solution here would be a positive number because 5/3 is positive.b. 5z+7=3: To find the value of 'z', we'd subtract 7 from both sides and then divide by 5. Considering that 3-7 is negative, and dividing a negative number by a positive number results in a negative answer, the solution of this equation will be negative.c. 7-5w=3: In this equation, subtracting 7 from 3 gives a negative number. Therefore, 'w' would be negative as dividing a negative number with a negative number results in a positive solution, which we can't have. Therefore, the solution of this equation will be negative.d. 4a=9: This equation involves dividing 9 by 4. The solution would be a positive number because 9/4 is positive.e. y=y+1: In this equation, when we attempt to isolate 'y', we're left with 0=1, which is not possible. Therefore, this equation has no solution.Learn more about Finding Solutions to Equations here:https://brainly.com/question/35067340
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