Hunter has $50 in is savings and deposits $30 each week. Max has $175 in his savings and deposits $5 each week. Find the number of weeks it will take for each person has

The probability that the iPhone will not die before t hours, given an average battery life of 10 hours, can be calculated using the exponential distribution. The reliability of the device is equal to the probability of surviving beyond t hours, which is given by the equation \(\[P(T > t) = e^{-\lambda t}\]\), where \(\(\lambda\)\) is the rate parameter. In this case, since the average battery life is 10 hours, \(\(\lambda = \frac{1}{10}\)\). Therefore, the probability of reliability is \(\[P(T > t) = e^{-\frac{t}{10}}\]\).

To find the probability of reliability, we use the exponential distribution formula. The exponential distribution is commonly used to model the time until an event occurs, such as the battery dying in this case. The rate parameter, \(\(\lambda\)\), is the reciprocal of the average time until the event occurs.

In this scenario, the average battery life is given as 10 hours. Therefore, the rate parameter \(\(\lambda\)\) is \(\(\frac{1}{10}\)\). The probability that the iPhone will not die before t hours is calculated by finding the complement of the probability that it will die before t hours.

The complement of the event "the iPhone will die before t hours" is "the iPhone will survive beyond t hours." This is represented as \(\(P(T > t)\)\), where T is the time until the battery dies.

Substituting the value of \(\(\lambda\)\) into the exponential distribution formula, we get \(\(P(T > t) = e^{-\frac{t}{10}}\)\). This equation gives us the probability that the iPhone will not die before t hours, which is the reliability of the device.

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The conditional probability is 3/8

From the question, we have

total number in bit string =16

let s be the set of all bit strings

number of strings =8

probability of selecting A

P(A)=8/16=1/2

P(A∩B)=3/16

the conditional probability is,

P(A∩B)/P(A)=3/16/1/2

=3/8

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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The statistic is the average diameter of 100 bearings from the lot, which is 2.515 cm. This is outside the specified limits, resulting in the lot being mistakenly rejected.

The statistic in this case is the average diameter of the inspected bearings from the lot. The lot contains a boxcar of ball bearings, and the specified acceptance of the lot is that the average diameter must be 2.503 cm. The inspector happens to inspect 100 bearings from the lot and determines that the average diameter of these bearings is 2.515 cm, which is outside the specified limits. As a result, the lot is mistakenly rejected. The value of the statistic is the average diameter of the inspected bearings from the lot, which is 2.515 cm. This is the value that determined the lot's rejection, as it is outside the specified limits.

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Answer:

x<1/2

Step-by-step explanation:

Hope this helps!

Answer:

5*(2*x+1)-+10)<0

10x-5=5•2x-1

5•(2x-1)<0

divide both sides by 5

divide both sides by 2

x-1/2<0

add 1/2 on both sides x<1/2

so, x<1/2

Step-by-step explanation:

hope it helps

Answer:

cos0 = 1

sin30= 1/2

tan0 = 0

Answer:

\(a) cos0^o = 1\\b) sin30^o = \frac{1}{2} \\c) tan0^o =0\)

The given question is based on differentiation and partial differentiation. In order to solve this problem we will use the chain rule and partial differentiation. The question says to find du/dt for the given function. Given, u=xy+yz+zx;x=t,y=e−t,z=cost.

Now we have to find du/dt.Using chain rule,du/dt=∂u/∂x(dx/dt)+∂u/∂y(dy/dt)+∂u/∂z(dz/dt).

Differentiate u with respect to x, y and z we get,∂u/∂x=y+z (as the derivative of xy with respect to x is y and that of zx with respect to x is z)∂u/∂y=x+z (as the derivative of xy with respect to y is x and that of yz with respect to y is z)

∂u/∂z=x+y (as the derivative of yz with respect to z is y and that of zx with respect to z is x)Differentiating x, y and z with respect to t we get, x=t, y=e^−t, z=cos t. Thus dx/dt=1, dy/dt=−e^−t and dz/dt=−sin t.

Substituting the values we get,du/dt=(y+z) dt/dx +(x+z) dt/dy +(x+y) dt/dz=(e^−t) (1−t−cos t−sin t)−tsin t.

Thus, du/dt=(e^−t) (1−t−cos t−sin t)−tsin t.

The given problem belongs to the chapter of differentiation and partial differentiation. It says to find du/dt for the given function. The question can be solved using the chain rule and partial differentiation.

Firstly, the partial differentiation of u with respect to x, y and z needs to be found. We know that partial derivative of xy with respect to x is y and that of zx with respect to x is z, hence ∂u/∂x=y+z.

In the same way, partial derivative of xy with respect to y is x and that of yz with respect to y is z, thus ∂u/∂y=x+z. Also, partial derivative of yz with respect to z is y and that of zx with respect to z is x, hence ∂u/∂z=x+y. Now, we need to find the values of x, y and z with respect to t. x=t, y=e^−t and z=cos t.

Then, differentiating x, y and z with respect to t, we get dx/dt=1, dy/dt=−e^−t and dz/dt=−sin t. Finally, substituting the above values in the given formula, we get the answer of du/dt which is (e^−t) (1−t−cos t−sin t)−tsin t. Hence, the answer is found to be (e^−t) (1−t−cos t−sin t)−tsin t.

Thus, we can conclude that the given problem was solved using the chain rule and partial differentiation. The answer of du/dt was found to be (e^−t) (1−t−cos t−sin t)−tsin t.

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Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

All apply values to the equation are:

0 ⇒ A

π/3 ⇒ B

5π/3 ⇒ E

What is an equation?

A formula known as an equation shows the equality of two expressions by joining them with the equals sign =.

Main Body:

∵ 0 ≤ x ≤ 2π is the domain for angle x

∴ 0 ≤x/2  ≤ π is the domain of angle

∵ sin(x/2) + cos(x) - 1 = 0

→ To solve the equation we should use the rule of cosine double angle

∵ cos(x) = 1 - 2 sin²(x/2)

→ Substitute it in the equation above

∴ sin(x/2) + (1 - 2 sin²(x/2) = 0

∴ sin(x/2) + 1 - 2 sin²(x/2) = 0

→ Add the like terms

∴ sin(x/2) + (1 - 1) - 2 sin²(x/2) = 0

∴ sin(x/2) - 2 sin²(x/2) = 0

→ Take sin(x/2) as a common factor

∴ sin(x/2) [1 - 2sin(x/2)] = 0

→ Equate each factor by 0

∵ sin(x/2) = 0

→ The value of sine equal zero on the x-axis

∴ x/2 = 0, π, 2π

∵ The domain of x/2  is 0 ≤ (x/2) ≤ π

∴  x/2 = 0 and π ⇒ 2π refused because ∉ the domain

→ Multiply both sides by 2 to find x

∴ x = 0 and 2π

∵ 1 - 2sin(x/2) = 0

→ Subtract 1 from both sides

∴ - 2sin(x/2) = -1

→ Divide both sides by -2

∴ sin(x/2) = 1/2

→ The sine is positive in the 1st and 2nd quadrants

∴ (x/2) lies on the 1st OR 2nd quadrants

∵ (x/2) = sin⁻¹(1/2)

∴ (x/2) =  π/6 =  ⇒ 1st quadrant

→ Multiply both sides by 2

∴ x = π/3

∵ (x/2) = π -π/6  = 5π/6 ⇒ 2nd quadrant

→ Multiply both sides by 2

∴ x = 5π/3

∴ The values of x are 0,π/3 , 5π/3 , 2π

Hence  apply values are:

0 ⇒ A

π/3⇒ B

5π/3⇒ E

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Answer:

its 1.4

Step-by-step explanation:

Answer:

1.4

Step-by-step explanation:

(a) The probability that both Anderson and Box will be selected is 0.1

(b) The probability that at least one of the two members whose name begins with C is selected is 0.7

(c) The probability that the two chosen representatives have a total of at least 17 years teaching experience there is 0.6

(a) You will have to consider the 10 different outcomes. Each combination of "A−B","B−Cox", "B−Cramer",... is equally likely to be drawn.

There are \(\left \{ {{5} \atop {2}} \right. =10\)

10 ways to choose 2 people from a group of 5. Since we are only considering 1 possibility, the answer will be 1/10=0.1

(b), there are a few possibilities where at least 1 "C" member gets selected. Consider

"Cox−A", "Cox−B", "Cox−Cramer", "Cox−F"

and

"Cramer−A", "Cramer−B", "Cramer−Cox", "Cramer−F"

Notice that "Cox−Cramer" appears twice, so one needs to be eliminated. Turns out there are 7 different possibilities out of 10...so we have 0.7

(c), I'd personally recommend taking the "compliment" of events. ie, how many combinations have LESS than 17 years? Turns out there are 4 combinations - (3,6),(3,7),(3,10),(6,7).

You can use the answer from (a) and evaluate this to become

1−4/10=0.6.

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From the graph of a function over the interval [-4,4]. the following are found for each function

The domain of a function refers to the input variables, often times the domain comprises of the x axis. for the given graph the domain is -4 ≤ x ≤ 4.

This would be through the points in the function. We are given  [-4,4]

-4 is the negative side while 4 is the positive. We have to write this out as

-4 ≤ x ≤ 4.

The positive part part of the function is at 4. This is because we can assume a +4 sign.

The negative part is the point -4.

Hence we can say that the domain is -4 ≤ x ≤ 4 with the positive and negative at 4 and -4 respectively

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Answer:

You basically just square then square root it all for distance and whatever; herons formula, magnitude, whatever formulae

You should get:

6.3245 --> 6.33 -> 6.3

Answer:

regular

Step-by-step explanation:

because an irregular polyhedron is formed by polygons of different shapes where all the components are not the same.

Answer:

-174

Math is hard but calculator harder, also english is hard too.

Answer:

-174

Step-by-step explanation:

−2(3+5)2−46

=−2(82)−46

=(−2)(64)−46

=−128−46

=−174

Answer: 16 yards would be your answer

The  scale factor of ABCD to QRST is 1:2

The perimeter of rectangles ABCD and QRST are 56 yards and 112 yards respectively.

Rectangle ABCD has a width of 8 yards and a length of 20 yards.

Rectangle QRST is similar to rectangle ABCD.

Rectangle QRST has a length of 40 yards.

Therefore, the scale factor of ABCD to QRST can be calculated as follows:

let

x = width of rectangle QRST

8 / x = 20 / 40

8 / x = 1 / 2

x = 16

The scale factor of  ABCD to QRST is 1:2

perimeter ABCD = 2(8 + 20) = 56 yards

perimeter QRST = 2(16 + 40) = 112 yards.

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we know that

The probability of losing the national treasure from A to Q is 0.02

so

The probability that not losing the national treasure from A to Q is 1-0.02=0.98

The probability that not losing the national treasure from Q to U is 1-0.04=0.96

The probability that not losing the national treasure from U to W is 1-0.05=0.95

The probability that not losing the national treasure from W to Z is 1-0.03=0.97

therefore

The probability that not losing the national treasure from A to Z is equal to

P=0.98*0.96*0.95*0.97

The limit of the sequence (1) {2}, (2) {(-1)^n}, and (3) {n sin(n)}, converges to DNE (does not exist) or the sequence diverges. The limit of the sequence (4) {sin(nπ)} is undefined, as it oscillates between -1 and 1.

In the case of sequence (1) {2}, the limit is a constant value, and the sequence converges to that value. However, in the case of sequence (2) {(-1)^n}, the sequence oscillates between -1 and 1, and there is no single value that it approaches as n tends to infinity. Therefore, the limit does not exist, and the sequence diverges.

Sequence (3) {n sin(n)} also does not have a limit as n tends to infinity. The term n sin(n) oscillates between positive and negative values without approaching a specific value. Hence, the limit of this sequence is DNE, and it diverges.

In the case of sequence (4) {sin(nπ)}, the term sin(nπ) oscillates between -1 and 1 as n varies. Since there is no convergence to a specific value, the limit of this sequence is undefined.

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Answer:

2nd option: \(3 \frac{65}{72} \) pounds

Step-by-step explanation:

backpack +math book ----- \(18 \frac{7}{9} \) pounds

backpack ----- \(14 \frac{7}{8} \) pounds

Weight of math book

= (weight of backpack +math book) -(weight of math book)

\( = 18 \frac{7}{9} - 14 \frac{7}{8} \\ = 3 \frac{65}{72} \)

Answer:

B. 3 and StartFraction 65 over 72 EndFraction pounds

Step-by-step explanation:

Answer:

\(a=0.8\bar{3}m/s^2\)

Step-by-step explanation:

\(a=\frac{v}{t} \\a=\frac{25m/s}{30s}\\ \\a=0.8\bar{3}m/s^2\)

The two numbers which add to 6 and multiply to 58 are; 3+7i and 3-7i

According to the question;

Hence;

(6-y)y = 58

6y -y² = 58

y² - 6y +58 = 0

By solving quadratically; we have;

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We have two equations :

x=y-9

5x+2y = 11

We just have to plug the value of x in the second equation to find y :

5(y-9) + 2y = 11

5y - 45 + 2y = 11

7y - 45 = 11

7y = 11 + 45

7y = 56

y = 56/7 = 8

Finally, since x = y -9

x = 8-9 = -1

Good Luck

Answer:

X = -1 Y = 8

try downloading mathaway it might help with these problem types

Answer:

Step-by-step explanation:

Divide 5 by 3

5 divided by 3 is 1 (in the set of integers). The remainder is 2.

5/3 is 1.666666666666666666666666666666666666666666666666666666666666667 (in the set of reals).

Solution for 5 divided by 3

✍️See below how to solve this division manually.

5 divided by 3 - Long Division Solution

The solution below uses the "Long Division With Remainders Method". It is one of two existing methods of doing long division.

Start by setting the divisor 3 on the left side and the dividend 5 on the right:

 1 ⇐ Quotient

 ―

3)5 ⇐ Dividend

 3

 -

 2 ⇐ Remainder

The result of the division of 5 divided by 3 is 1.6666666666666667, as a decimal number.

5/3 as a mixed number

5 divided by 3 equals to the mixed number 1 2

3

.

Note that the result of the division 5÷3 is not an exact value and is equivalent to a recurring decimal 1.66... (which has 6 as the period).

Answer:

\(5(4)^x=320\\\frac{5(4)^x}{5}=\frac{320}{5}\\ 4^x=64\\x*(log(4) )=log(64)\\x=\frac{log(64)}{log(4)}\\ x=3\)

Step-by-step explanation:

Answer:

A) 1.25

Step-by-step explanation:

Use L'Hôpital's Rule and differentiate both top and bottom expressions:

\(\lim_{x \to 3} \frac{x^{2}-x-6 }{x^{2}-2x-3}\)

\(\lim_{x \to 3} \frac{2x-1-0 }{2x-2-0}\)

\(\lim_{x \to 3} \frac{2x-1}{2x-2}\)

Substitute x=3 into the expression:

\(\frac{2(3)-1}{2(3)-2}\)

\(\frac{6-1}{6-2}\)

\(\frac{5}{4}\)

Therefore, \(\lim_{x \to 3} \frac{x^{2}-x-6 }{x^{2}-2x-3}=\frac{5}{4}=1.25\), making the correct answer A.

Answer:

0=11

Step-by-step explanation:

Answer:

4)d)9/10

5)a)20

6)b)3/10

7)b)3/7

Step-by-step explanation:

According to the given information the line integral is \(=\frac{8}{15}(1+125.\sqrt{10})\).

Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.

\(\int_C\hairsp xyds,C:x=t^2,y=2t,0\le t\le3\\x^\prime=2t\\y^\prime=2\\ds=\sqrt{\left(x^\prime\right)^2+\left(y^\prime\right)^2}\\\sqrt{{4\left(t\right)}^2+4}\\\int C\ xy\ ds\ =\int_0^3\hairspt^2\cdot2t\cdot2\cdot\sqrt{1+t^2}\mathrm{\ }dt\\t=\ \ tan\ \theta\\dt=(1+{tan}^2\theta)d\theta=({Sec}^2\theta)d\theta\ \\{=\int}_0^3\hairsp4t^3\sqrt{1+t^2}\mathrm{\ }dt\\=\frac{8}{15}(1+125.\sqrt{10})\)

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There were 128 children and 155 adults.

Let us first set up our system by assigning x and y to mean something. Let x = the number of children and y = the number of adults.

First equation: Children cost $1.50 and Adults cost $4.00. In order to find the amount of money a group of children will cost, we multiply the number of children, x, by 1.5.

This is represented by 1.5x. For adults, who cost 4 dollars to enter, we will use 4y. The total amount of money made on the given day was $632. To get this amount, we must add 1.5x and 4y.

1.5x+4y=632 --------(1)

Second equation: Total amount of people on the given day is 238. To get this number, we must add together x and y, or the number of children and adults.

x + y = 238-----(2)

System of equations:

1.5x+4y=632

x+y = 238

Let's use the substitution of the x variable to solve the system.

x+y=238.

y=238-x

Substitute y = 238 - x into the first equation.

1.5x + 4 (238 - x) =632

1.5x + 952 - 4x = 632  

952- 2.5x = 632

-2.5x = -320

x = 128

Substitute x =128 back into y = 238 - x

y = 283-128

y=155

There were 128 children and 155 adults.

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