Answer:
[tex]\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }[/tex]
Step-by-step explanation:
Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;
let;
[tex]y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\[/tex]
[tex]\frac{dy}{dx} = \frac{-1}{sin y} \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}[/tex]
Therefore;
[tex]\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }[/tex]
Since x = cos y from the above substitute;
[tex]\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }[/tex]
Hence, [tex]\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }[/tex] gives the required proof
Researchers wanted to know whether it is better to give the diphtheria, tetanus and pertussis (DTaP) vaccine in the thigh or the arm. They collect data on severe reactions to this vaccine in children aged 3 to 6 years old. What would be the best statistical test for them to utilize?
A. One-sample chi-square
B. Linear regression
C. T-test
D. Two-sample chi-square
Answer:
D. Two-sample chi-square
Step-by-step explanation:
A chi-square test is a test used to compare the data that is observed, from the data that is expected.
In a two-sample chi-square test the observed data should be similar to the expected data if the two data samples are from the same distribution.
The hypotheses of the two-sample chi-square test is given as:
H0: The two samples come from a common distribution.
Ha: The two samples do not come from a common distribution
Therefore, in this case, the best statistical test to utilize is the two-sample chi-square test.
A pet store has 10 puppies, including 2 poodles, 3 terriers, and 5 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement find the probability that both select a poodle.
The probability is
Answer:
2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.
Step-by-step explanation:
do some math
Translate into an algebraic expression and simplify if possible. I have a total of 10 gigabytes of data on my computer, x gigabytes are movies and the rest is music. How many gigabytes of music is stored on my computer?
Answer:
simple really
Step-by-step explanation:
10 gigabytes of data on my computer, x gigabytes are movies and the rest is music.
so it will have to be 10-X= remaining gigabites of music
Answer:
Movies: x gig
pictures: x/2 gig
music: 10 - x - x/2 = 10 - (3/2)x
excel A car insurance company has determined that 8% of all drivers were involved in a car accident last year. If 15 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year
Answer:
[tex] P(X \geq 3)= 1- P(X<3)= 1-P(X \leq 2)= 1- [P(X=0) +P(X=1) +P(X=2)][/tex]
And we can find the individual probabilites using the probability mass function and we got:
[tex] P(X=0) = (15C0) (0.08)^{0} (1-0.08)^{15-0}=0.286 [/tex]
[tex] P(X=1) = (15C1) (0.08)^{1} (1-0.08)^{15-1}=0.373 [/tex]
[tex] P(X=2) = (15C2) (0.08)^{2} (1-0.08)^{15-2}=0.227 [/tex]
And replacing we got:
[tex] P(X\geq 3) = 1-[0.286+0.373+0.227 ]= 0.114[/tex]
Step-by-step explanation:
For this case we can assume that the variable of interest is "drivers were involved in a car accident last year" and for this case we can model this variable with this distribution:
[tex] X \sim Bin (n =15, p =0.08)[/tex]
And for this case we want to find this probability;
[tex] P(X \geq 3)[/tex]
and we can use the complement rule and we got:
[tex] P(X \geq 3)= 1- P(X<3)= 1-P(X \leq 2)= 1- [P(X=0) +P(X=1) +P(X=2)][/tex]
And we can find the individual probabilites using the probability mass function and we got:
[tex] P(X=0) = (15C0) (0.08)^{0} (1-0.08)^{15-0}=0.286 [/tex]
[tex] P(X=1) = (15C1) (0.08)^{1} (1-0.08)^{15-1}=0.373 [/tex]
[tex] P(X=2) = (15C2) (0.08)^{2} (1-0.08)^{15-2}=0.227 [/tex]
And replacing we got:
[tex] P(X\geq 3) = 1-[0.286+0.373+0.227 ]= 0.114[/tex]
a geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .
Answer: [tex]\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}[/tex]
Step-by-step explanation:
a₁, 375, a₃, a₄, 81
First, let's find the ratio (r). There are three multiple from 375 to 81.
[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]
Next, let's find a₁
[tex]a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625[/tex]
Lastly, Use the Infinite Geometric Sum Formula to find the sum:
[tex]S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}[/tex]
Which steps would be used to solve the equation? Check all that apply. 2 and two-thirds + r = 8 Subtract 2 and two-thirds from both sides of the equation. Add 2 and two-thirds to both sides of the equation. 8 minus 2 and two-thirds = 5 and one-third 8 + 2 and two-thirds = 10 and two-thirds Substitute the value for r to check the solution.
Answer:
Subtract 2 and two-thirds from both sides of the equation
8 minus 2 and two-thirds = 5 and one-third
Substitute the value for r to check the solution.
Step-by-step explanation:
2 2/3 + r = 8
Subtract 2 2/3 from each side
2 2/3 + r - 2 2/3 = 8 - 2 2/3
r = 5 1/3
Check the solution
2 2/3 +5 1/3 =8
8 =8
Answer:
1, 3, 5
Step-by-step explanation:
edge
Find the surface area of this composite solid. I Need answer ASAP Will give brainliest
Answer:
B. 120 m²
Step-by-step explanation:
To find the surface area of the composite solid, we would need to calculate the area of each solid (square pyramid and square prism), then subtract the areas of the sides that are not included as surface area. The sides not included as surface area is the side the pyramid and the prism is joint together.
Step 1: find the surface area of the pyramid:
Surface area of pyramid with equal base sides = Base Area (B) + ½ × Perimeter (P) × Slant height (l)
Base area = 4² = 16 m
Perimeter = 4(4) = 16 m
Slant height = 3 m
Total surface area of pyramid = 16 + ½ × 16 × 3
= 16 + 8 × 3 = 16 + 24
= 40 m²
Step 2: find the area of the prism
Area = 2(wl + hl + hw)
Area = 2[(4*4) + (5*4) + (5*4)]
Area = 2[16 + 20 + 20]
Area of prism = 2[56] = 112 m²
Step 3: Find the area of the sides not included
Area of the sides not included = 2 × area of the square base where both solids are joint
Area = 2 × (4²)
Area excluded = 2(16) = 32 m²
Step 4: find the surface area of the composite shape
Surface area of the composite shape = (area of pyramid + area of prism) - excluded areas
= (40m²+112m²) - 32m²
= 152 - 32
Surface area of composite solid = 120 m²
Give examples of three sets A,B,C for which A-(B-C)=(A-B)-C.
How do you determine whether the sign of a trigonometric function (sine, cosine, tangent) is positive or negative when dealing with half angles? Explain your reasoning and cite examples. Why do you think the half-angle identities include positive and negative options but the other identities don't seem to have this option built in?
Answer:
This question is about:
sin(A/2) and cos(A/2)
First, how we know when we need to use the positive or negative signs?
Ok, this part is kinda intuitive:
First, you need to know the negative/positve regions for the sine and cosine function.
Cos(x) is positive between 270 and 90, and negative between 90 and 270.
sin(x) is positive between 0 and 180, and negative between 180 and 360.
Then we need to see at the half-angle and see in which region it lies.
If the half-angle is larger than 360°, then you subtract 360° enough times such that the angle lies in the range between (0° and 360°)
and: Tan(A/2) = Sin(A/2)/Cos(A/2)
So using that you can infer the sign of the Tan(A/2)
Now, why these relationships use the two signs?
Well... this is because of the square root in the construction of the relationships.
This happens because:
(-√x)*(-√x) = (-1)*(-1)*(√x*√x) = (√x*√x)
For any value of x.
so both -√x and √x are possible solutions of these type of equations, but for the periodic nature of the sine and cosine functions, we can only select one of them.
So we should include the two possible signs, and we select the correct one based on the reasoning above.
a silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by
Question:
A silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by
s(t) = -16t² + v₀t + s₀
Determine the position and velocity functions for the coin.
Answer:
position function: s(t) = (-16t² + 64) ft
velocity function: v(t) = (-32t) ft/s
Step-by-step explanation:
Given position equation;
s(t) = -16t² + v₀t + s₀ ---------(i)
v₀ and s₀ are the initial values of the velocity and position of the coin respectively.
(a) Since the coin is dropped, the initial velocity, v₀, of the coin is 0 at t = 0. i.e
v₀ = 0.
Also since the drop is from the top of a building that is 64 feet tall, this implies that the initial position, s₀, of the coin is 64 ft at t=0. i.e
s₀ = 64ft
Substitute the values of v₀ = 0 and s₀ = 64 into equation (i) as follows;
s(t) = -16t² + (0)t + 64
s(t) = -16t² + 64
Therefore, the position function of the coin is;
s(t) = (-16t² + 64) ft
(b) To get the velocity function, v(t), the position function, s(t), calculated above is differentiated with respect to t as follows;
v(t) = [tex]\frac{ds(t)}{dt}[/tex]
v(t) = [tex]\frac{d(-16t^2 + 64)}{dt}[/tex]
v(t) = -32t + 0
v(t) = -32t
Therefore, the velocity function of the coin is;
v(t) = (-32t) ft/s
Please help me this
And show your working out
Thanks I will appreciate it
Answer:
3x / 2 + 9 = 5
3x / 2 = -4
3x = -8
x = -8/3
(2 + v) / 3 = 9
2 + v = 27
v = 25
32 / (d - 2) = 10
32 = 10 * (d - 2)
3.2 = d - 2
d = 5.2
2p - 4 = 3p / 2
2 * (2p - 4) = 3p
4p - 8 = 3p
p - 8 = 0
p = 8
3b / 2 = 12
3b = 24
b = 8
PLEASEEE HELP ME ITS DUE ASAP PLS
Answer:
V ≈ 1436.03 cm³
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}[/tex]πr³. r represents the radius, which is 7 cm since the diameter is 14 cm, so plug 7 into the equation as r. Also remember that the question states to use 3.14 for pi/π.
V = [tex]\frac{4}{3}[/tex] (3.14)(7)³
V ≈ 1436.03 cm³
What is m<3 ? M<6 is and m<8 is (x+5
Answer:
m∠3 = 115 degrees
Step-by-step explanation:
angle 6 and angle 8 are on a straight line
we know that sum of angles on straight line is 180
therefore
m∠8 = x+5
m∠6 + m∠8 = 180
2x - 5 + x+5 = 180
=> 3x = 180
=> x = 180/3 = 60
Thus,
m∠6 = 2x-5 = 2*60 - 5 = 115
we know that for two parallel lines cut by a transversal
alternate opposite angles are equal
m∠6 and m∠3 are alternate opposite angles
thus
m∠6 = m∠3 = 115 (answer)
Evaluate. Write your answer as a fraction or whole number without exponents. 1/10^-3 =
Answer:
1000
Step-by-step explanation:
=> [tex]\frac{1}{10^{-3}}[/tex]
According to the law of exponents, [tex]\frac{1}{a^{-m}} = a^{m}[/tex]
So, it becomes
=> [tex]10^{3}[/tex]
=> 1000
Find the distance of the line segment joining the two points:
segment joining the two points: (√ 2,0) and(0, - √ 2)
Answer:
2
Step-by-step explanation:
[tex]\sqrt{((\sqrt{2} - 0)^2 + (0 - (-\sqrt{2}))^2)[/tex]
what is the simplest form of this expression 2(w-1) +(-2)(2w+1)
Answer:
-2w - 4
Step-by-step explanation:
What is the simplest form of this expression
2(w - 1) + (-2)(2w + 1) =
= 2w - 2 - 4w - 2
= -2w - 4
Answer: -2w-4
Step-by-step explanation:
subtract 4w of 2w
2w-2-4w-2
subtract 2 of -2
-2w-2-2
final answer
-2w-4
Suppose that you have 9 cards. 5 are green and 4 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 4 yellow cards are numbered 1, 2, 3, and 4. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, and without replacement. • G1 = first card is green • G2 = second card is green a) Draw a tree diagram of the situation. (Enter your answers as fractions.) b) Enter the probability as a fraction. P(G1 AND G2) = c)Enter the probability as a fraction. P(at least one green) = d)Enter the probability as a fraction. P(G2 | G1) = _______.
The probability of picking greens on both occasions will be 5/18.
How to explain the probability?The probability of picking greens cards will be:
= 5/9 × 4/8
= 5/18
The probability of picking at least one green will be:
= 1 - P(both aren't green)
= 1 - (4/9 × 3/8)
= 1 - 1/6.
= 5/6
From the tree diagram, the probability as a fraction of P(G2 | G1) will be:
= 4/8 = 1/2
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
The mean student loan debt for college graduates in Illinois is $30000 with a standard deviation of $9000. Suppose a random sample of 100 college grads in Illinois is collected. What is the probability that the mean student loan debt for these people is between $31000 and $33000?
Answer:
the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331
Step-by-step explanation:
Given that:
Mean = 30000
Standard deviation = 9000
sample size = 100
The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:
[tex]P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)[/tex]
[tex]P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})[/tex]
From Z tables:
[tex]P(31000 < X <33000) = 0.9996 -0.8665[/tex]
[tex]P(31000 < X <33000) = 0.1331[/tex]
Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331
If 3/4 and 12/x are equivalent what is the value of x
Answer:
x = 16
Step-by-step explanation:
Simply set them equal to each other and solve:
3/4 = 12/x
3x = 48
x = 16
Answer:
16
Step-by-step explanation:
3/4 = 12/x
Cross multiply.
3 × x = 12 × 4
3x = 48
Divide both sides by 3.
3/3x = 48/3
x = 16
the diagram shows a circle drawn inside a square the circle touches the edges of the square
Answer:
69.5309950592 cm²
Step-by-step explanation:
Area of Square:
Area = [tex]Length * Length[/tex]
Area = 18*18
Area = 324 square cm
Area of circle:
Diameter = 18 cm
Radius = 9 cm
Area = [tex]\pi r^2[/tex]
Area = (3.14)(9)²
Area = (3.14)(81)
Area = 254.469004941 square cm
Area of Shaded area:
=> Area of square - Area of circle
=> 324 - 254.469004941
=> 69.5309950592 cm²
Brainliest for correct awnser! Hannah thinks of a number. She multiplies the number by 2, adds 4, and then divides the result by 3. The number she ends up with is 6. What number did Anna start with? If you work backward to solve this problem, what do you do first?A.Multiply 6 by 2B.Multiply 6 by 3C.Divide 6 by 2D.Subtract 4 from 6
Answer:
B. Multiply 6 by 3
Step-by-step explanation:
Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:
B. Multiply 6 by 3
Your step by step for getting the number Hannah started with:
First, multiply 6 with 3:
6 x 3 = 18
Next, subtract 4:
18 - 4 = 14
Next, divide by 2:
14/2 = 7
Hannah started with the number 7.
~
Answer: Hannah started with 7.
B. Multiply 6 by 3
Explanation:
Let the number be y
2 × y = 2y
(2y + 4)/3 = 6
2y + 4 = 6×3 = 18
2y + 4 = 18
2y = 18 - 4 = 14
y = 14/2 = 7
To solve the problem backward, the first step is to multiply 6 by 3.
Applying the Segment Addition Postulate
Point D is on segment BC. Segment BC measures 8x
units in length.
С
D
B
What is the length of segment BC?
units
3x + 8
4x + 10
Answer:
144
Step-by-step explanation:
Find: Length of segment BC
CD+DB=BC
3x+8+4x+10=BC
7x+18=BC
BC also equals 8x (given on the screen shot)
7x+18= 8x
x=18
18 times 8 = 144
Check:
3( 18) + 8 + 4(18) + 10
54+8 + 72+10
64+ 80= 144 TRUE
The graph shows a gasoline tank being filled at a rate of 2,500 gallons of gas per
hour. How will the graph change if the rate slows?
The correct answer is The line will be less steep because the rate will be slower
Explanation:
The rate of the graph is defined by the number of gallons filled vs the time; this relation is shown through the horizontal axis (time) and the vertical axis (gallons). Additionally, there is a constant rate because each hour 2,500 gallons are filled, which creates a steep constant line.
However, if the rate decreases, fewer gallons would be filled every hour, and the line will be less steep, this is because the number of gallons will not increase as fast as with the original rate. For example, if the rate is 1,250 gallons per hour (half the original rate), after 8 hours the total of gallons would be 1000 gallons (half the amount of gallons); and this would make the line to be less steep or more horizontal.
the number 117 is divisible by nine and only if the sum of the digits in 117 are evenly divisible by 9, truth or false
Answer:
true
Step-by-step explanation:
The test for divisibility by 9 is to add all the digits of the number. If that sum is divisible by 9, then the number is divisible by 9.
The total area under the standard normal curve to the left of zequalsnegative 1 or to the right of zequals1 is
Answer:
0.3174
Step-by-step explanation:
Z-score:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the area under the normal curve to the left of Z. Subtracting 1 by the pvalue, we find the area under the normal curve to the right of Z.
Left of z = -1
z = -1 has a pvalue of 0.1587
So the area under the standard normal curve to the left of z = -1 is 0.1587
Right of z = 1
z = 1 has a pvalue of 0.8413
1 - 0.8413 = 0.1587
So the area under the standard normal curve to the right of z = 1 is 0.1587
Left of z = -1 or right of z = 1
0.1587 + 0.1587 = 0.3174
The area is 0.3174
Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 86 and 125 miles in a day. Round your answer to four decimal places.
Answer:
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles
Step-by-step explanation:
Step(i):-
Given mean of the Population = 100 miles per day
Given standard deviation of the Population = 23 miles per day
Let 'X' be the normal distribution
Let x₁ = 86
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61[/tex]
Let x₂= 86
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086[/tex]
Step(ii):-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)
= P(Z≤ 1.08) - P(Z≤ -0.61)
= 0.5 +A(1.08) - ( 0.5 - A(-0.61))
= A(1.08) + A(0.61) ( A(-Z)= A(Z)
= 0.3599 + 0.2291
= 0.5890
Conclusion:-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles per day
A lady buys bananas at 3 Rs 5 and sells them at 2 Rs for Rs 5; find her gain percent.
Answer:
50%
Step-by-step explanation:
Cost of 3 bananas= Rs. 5 ⇒ cost of 1 banana= Rs. 5/3
Selling price of 2 bananas= Rs. 5 ⇒ selling price of 1 banana= Rs. 5/2
Gain= Rs. (5/2- 5/3)= Rs. (15/6- 10/6)= Rs. 5/6
Gain %= 5/6÷5/3 × 100%= 50%
Adelphi Company purchased a machine on January 1, 2017, for $60,000. The machine was estimated to have a service life of ten years with an estimated residual value of $5,000. Adelphi sold the machine on January 1, 2021 for $21,000. Adelphi uses the double declining method for depreciation. Using this information, how much is the gain or (loss) for the equipment sale entry made on January 1, 2021. Enter a loss as a negative number.
Answer:
-$3576
Step-by-step explanation:
Depreciation using double declining method=100%/useful life*2
Depreciation using double declining method=100%/10*2=20%
2017 depreciation=$60,000*20%=$12000
2018 depreciation=($60,000-$12000)*20%=$9600
2019 depreciation=($60,000-$12000-$9600 )*20%=$7680
2020 depreciation=($60,000-$12000-$9600-$7680 )*20%=$6144
carrying value in 2021=$60000-$12000-$9600 -$7680-$6144 =$24576
Loss on disposal of machine=$21,000-$24576 =-$3576
if my medical expenses are $40,000 per year for 35 years with an increase of 6% a year what is the total amount?
Answer:
$4,457,391.19
Step-by-step explanation:
The sum of n terms of a geometric sequence with common ratio r and initial value "a" is ...
S = a(r^n -1)/(r -1)
Here, your growth factor is r = 1 +6% = 1.06. So, the sum of expenses over 35 years will be ...
S = $40,000(1.06^35 -1)/(1.06 -1) = $4,457,391.19
Need help with number 20
Answer:
A
Step-by-step explanation:
Since we are given BC is congruent to DC and angle b and d are 90. We can prove that <C is congruent to itself by reflexive property of congruence. We can also you use linear pair theorem to prove <CDA is congruent to <CBE. Since they are right angles, we can prove that they are congruent by rt <s thm. Thus, we cna prove they are congruent by ASA. Hope it helps