Suppose y = 2x + 1 , where x and y are functions of t. (a) if dx/dt = 3, find dy/dt when x = 4. dy dt = (b) if dy/dt = 2, find dx/dt when x = 40. dx dt =

Answer:

The height of the building is approximately [tex]34\ ft[/tex]

Step-by-step explanation:

Let

h------> height of the building from the student's eye level

H----> height of the building from the ground (H=h+5 ft)

we know that

[tex]tan(30\°)=\frac{h}{50}[/tex]

[tex]h=tan(30\°)(50)=28.87\ ft[/tex]

Find the height of the building H

[tex]H=h+5=28.87+5=33.87\ ft[/tex]

The height of the building is approximately [tex]34\ ft[/tex]

The statistical technique applicable here is simple random sampling and binomial distribution. The formula for a binomial distribution is used to estimate the probabilities of a specific number of satisfactions among the randomly selected 15 adults. The average number and variability can also be calculated for this binomial distribution.

This question is about statistics, particularly a technique called simple random sampling. In the given scenario, it's reported that 66% of adults are satisfied with the major airlines' job. We're asked to conjecture about a scenario where 15 adults are chosen at random and the number who are satisfied is observed.

First, this scenario is modeled with a binomial distribution. A binomial distribution is appropriate here because you're considering a certain number of 'trials' (15 adults), and for each trial, there are two possible outcomes - the adult is either satisfied or not satisfied with the airlines. The 'success' probability (satisfaction) remains constant (66%).

A. If we want to know the probability of exactly x adults satisfied, the formula for a binomial distribution is used: P(X = k) = C(n, k) * (p^k) * ((1 - p)^(n - k)), where C(n, k) is combinations of n things taken k at a time, n is number of trials (15), p is the probability of success (66% or 0.66), and k is the number of successes we want exact probability for.

B. If we want to know the expected value or the average number of adults satisfied, it's simply n*p, in this case 15*0.66 = 9.9, meaning, on average, about 10 adults out of 15 should be satisfied according to the poll report.

C. If we want to compute the variability, we can calculate the standard deviation. For a binomial distribution, the standard deviation, sigma, is square root of [ n*p*q ], where q = 1-p is the probability of 'failure', or an adult not satisfied.

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Answer:

The times were Lily 9.5 hours and Andrea 6.5 hours.

Equation "D" is correct using those numbers.

Step-by-step explanation:

Divide the area into 6 portions and find the sum of each one to find the value of the final integral:

f(x)dx = 2(8+4)/2 + 1 (8+6)/2 + 2 (6+10)/2 + 1(10+10)/2 + 2 (10+12)/2 + 1 (12+16)/2

= 12 + 7 + 16 + 10 + 22 + 14 = 81 sq units

Answer:

Step-by-step explanation:

Given is a table of x, f(x) as below

x             1   3   4   6   7  9  10

f(x)         4   8  6  10  10  12  16

Mid pt      6   7   8  10   11  14

width of

interval    2   1     2   1    2    1

dA1         12   7   16  10  22  14

area = area of all rectangles= 81 sq units.

Answer:

  3.9

Step-by-step explanation:

A calculator is useful for this.

Answer:

7.75 F

Step-by-step explanation:

you will do 7/2 *

convert 2.25 to imporper fraction

multiply the denomintor

Answer:

7.75

Step-by-step explanation:

Answer:

18.15

Step-by-step explanation:

Percent means per hundred, so we can convert 4.6% and 3.65% to equivalent decimals.

4.6%= 4.6 divided by 100 = 0.046

3.65%= 3.65 divided by 100 = 0.0365

Since both sales tax rates apply to $220, we can add the two rates.

0.046 + 0.0365= 0.0825

0.0825 x 220 = 18.15

And so, Yuki pays$18.15 in sales tax for her handbag purchase.

Answer:

A=158

Step-by-step explanation: SA = 2 × l × w  +  2 × l × h  +  2 × w × h

Answer: Option D

(D) 158 square feet

Step-by-step explanation:

A=2(wl+hl+hw)=2·(3·8+5·8+5·3)=158ft²

Answer:

  [tex]r=\dfrac{I}{Pt}[/tex]

Step-by-step explanation:

Solve this the way you do any "solve for" problem. Locate the variable of interest and identify what has been done to it. Undo that.

Here, the variable of interest is "r". It has been multiplied by Pt. We undo that multiplication by dividing by that product:

  [tex]I=Prt\\\\\dfrac{I}{Pt}=\dfrac{Prt}{Pt}\\\\\dfrac{I}{Pt}=r \quad\text{simplify}[/tex]

Answer:

  yes, and no

Step-by-step explanation:

There are a few trig functions that are "simple" and can be memorized. Usually, these are the ones for angles of 0°, 30°, 45°, 60°, 90°. See below for a table.

To solve an equation like this for DE, you multiply both sides of the equation by 4 (cancelling the denominator).

  4·tan(90°) = DE

The tangent of 90° is "infinity." So, the length of DE will be infinite for an angle of 90°.

_____

Trig functions of multiple angles and half angles can be derived from those in the table using the appropriate formulas. The math can get messy fast.

Of course, SOH CAH TOA reminds you of the relationships between trig function values and right triangle side measures. You may not know the angle measure (and it may be irrelevant), but you can find the trig function value.

Answer:

See below.

Step-by-step explanation:

You can find them by constructing a right angled triangle with the given angle and measuring the sides  giving sin = opposite / hypotenuse , cos = adjacent / hypotenuse and tan = opposite / adjacent ( SOH-CAH-TOA).

For  tan 90 degrees you think of an 'imaginary' triangle where opposite side = hypotenuse and the adjacent side = 0 ( in fact a vertical line!) .Now tan  x = opposite / adjacent  =  opposite / 0 which is indeterminate. There is no value for the tan of 90 degrees and so there is no solution to your problem.

Answer:

c. [tex]\frac{5}{33}[/tex]

Step-by-step explanation:

The given decimal is  [tex]0.\bar {15}[/tex]

Let  [tex]y=0.\bar {15}...(1)[/tex]

Multiply equation (1) by 100.

[tex]100y=15.\bar {15}...(2)[/tex]

Subtract equation (1) from equation (2)

[tex]\Rightarrow 100y-y=15.\bar {15}-0.\bar {15}[/tex]

[tex]\Rightarrow 99y=15[/tex]

Divide both sides by 99.

[tex]\Rightarrow y=\frac{15}{99}[/tex]

Simplify;

[tex]\Rightarrow y=\frac{5}{33}[/tex]

The recurring decimal 0.15 can be converted to the fraction 5/33.

To convert the repeating decimal 0.15 to a fraction, follow these steps:

Let x be the repeating decimal: x = 0.151515...

Express this equation by multiplying both sides by 100 to shift the decimal point two places: 100x = 15.151515...

Next, subtract the original equation from this new equation: 100x - x = 15.151515... - 0.151515...

This simplifies to: 99x = 15

Solve for x by dividing both sides by 99: x = 15/99

Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 3: x = 5/33

Therefore, the repeating decimal 0.15 can be expressed as the fraction 5/33.

Answer:

72 members

Step-by-step explanation:

Total surveyed members = 40

members voting yes = 12

probability of the members voting yes = 12/40 = 3/10

It is observed that, out of every 'n' members, n*(3/10) members are expected to vote yes:

Therefore,

number of members expecting to voye yes out of 240 are = 240 * 3/10

=> 24 * 3 = 72 members

Answer:

a) 20.16; b) 20.49 and 21.51

Step-by-step explanation:

We use z scores for each of these.  The formula for a z score is

[tex]z=\frac{X-\mu}{\sigma}[/tex].

For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.

Using this, 21 as the mean and 1 as the standard deviation,

-0.84 = (X-21)/1

-0.84 = X-21

Add 21 to each side:

-0.84+21 = X-21+21

20.16 = X

For part b, we want the middle 39%.  This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want

50-19.5 = 30.5% = 0.305 and

50+19.5 = 69.5% = 0.695.

Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:

-0.51 = (X-21)/1

-0.51 = X-21

Add 21 to each side:

-0.51+21 = X-21+21

20.49 = X

0.51 = (X-21)/1

0.51 = X-21

Add 21 to each side:

0.51+21 = X-21+21

21.51 = X

The 20th percentile for incubation times is approximately 20.16 days. The incubation times that make up the middle 39% of fertilized eggs fall between roughly 20.5 days and 21.5 days.

This question focuses on statistics and their application in a biological context, specifically about the incubation time of fertilized eggs. In statistics, the normal distribution is a common continuous probability distribution that is symmetric about the mean.

(a) The 20th percentile of the normal distribution can be found using the z-table or a calculator that has the capability. Using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value in the data set, μ is the mean, and σ is the standard deviation, a Z-score associated with the 20th percentile is approximately -0.84. So the incubation time in days for the 20th percentile is (0.84 * 1) + 21 = 20.16 days.

(b) Similarly, to find the incubation times that make up the middle 39% of the fertilized eggs, note that since this is symmetric, this implies the incubation times falls between the 30.5 percentile and the 69.5 percentile. Using the formula Z = (X - μ) / σ and the Z-table, the Z-scores associated with these percentiles are approximately -0.5 and 0.5 respectively. Hence the incubation time falls between (0.5 * 1) + 21 = 20.5 days and (0.5 * 1) + 21 = 21.5 days

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Answer:

a) 0.789, this is the complement of the probability of no repeat offenders; b) 0.411; c) 0.033; d) μ = 1.429; e) σ = 9.58

Step-by-step explanation:

For part a,

The probability that no parolees are repeat offenders is 0.211.  This means the probability of at least one is a repeat offender is the complement of this event.  To find this probability, subtract from 1:

1-0.211 = 0.789.

For part b,

To find the probability that 2 or more are repeat offenders, add together the probability that 2, 3, 4 or 5 parolees are repeat offenders:

0.216+0.162+0.032+0.001 = 0.411.

For part c,

To find the probability that 4 or more are repeat offenders, add together the probabilities that 4 or 5 parolees are repeat offenders:

0.032+0.001 = 0.033.

For part d,

To find the mean, we multiply each number of parolees by their probability and add them together:

0(0.211)+1(0.378)+2(0.216)+3(0.162)+4(0.032)+5(0.001)

= 0 + 0.378 + 0.432 + 0.486 + 0.128 + 0.005 = 1.429

For part e,

To find the mean, we first subtract each number of parolees and the mean to find the amount of deviation.  We then square it and multiply it by its probability.  Then we add these values together and find the square root.

First the differences between each value and the mean:

0-1.429 = -1.429;

1-1.429 = -0.429;

2-1.429 = 0.571;

3-1.429 = 1.571;

4-1.429 = 2.571;

5-1.429 = 3.571

Next the differences squared:

(-1.429)^2 = 2.0420

(-0.429)^2 = 0.1840

(0.571)^2 = 0.3260

(1.571)^2 = 2.4680

(2.571)^2 = 6.6100

(3.571)^2 = 12.7520

Next the squares multiplied by the probabilities:

0(2.0420) = 0

1(0.1840) = 0.1840

2(0.3260) = 0.652

3(2.4680) = 7.404

4(6.6100) = 26.44

5(12.7520) = 63.76

Next the sum of these products:

0+0.1840+0.652+0.7404+26.44+63.76 = 91.7764

Lastly the square root:

√(91.7764) = 9.58

Probabilities are used to determine the outcomes of events.

The table is given as:

[tex]\left[\begin{array}{ccccccc}x &0 &1 &2 &3 &4 &5 &P(x) &0.211 &0.378 &0.216& 0.162 &0.032 &0.001\end{array}\right][/tex]

(a) Probability that one or more are repeat offenders

This is represented as: [tex]P(x \ge 1)[/tex]

Using the complement rule, we have:

[tex]P(x \ge 1) = 1 - P(x = 0)[/tex]

So, we have:

[tex]P(x \ge 1) = 1 - 0.211[/tex]

[tex]P(x \ge 1) = 0.789[/tex]

The probability that one or more are repeat offenders is 0.789

(b) Probability that two or more are repeat offenders

This is represented as: [tex]P(x \ge 2)[/tex]

Using the complement rule, we have:

[tex]P(x \ge 2) = 1 - P(x = 0) - P(x = 1)[/tex]

So, we have:

[tex]P(x \ge 2) = 1 - 0.211 - 0.378[/tex]

[tex]P(x \ge 2) = 0.411[/tex]

The probability that two or more are repeat offenders is 0.411

(c) Probability that four or more are repeat offenders

This is represented as: [tex]P(x \ge 4)[/tex]

So, we have:

[tex]P(x \ge 4) = P(x = 4) + P(x = 5)[/tex]

[tex]P(x \ge 4) = 0.032 + 0.001[/tex]

[tex]P(x \ge 4) = 0.033[/tex]

The probability that four or more are repeat offenders is 0.033

(d) The expected number of repeat offenders

This is calculated as:

[tex]\mu = \sum x \times P(x)[/tex]

So, we have:

[tex]\mu = 0 \times 0.211+ 1\times 0.378 + 2 \times 0.216 + 3 \times 0.162 + 4 \times 0.032 + 5 \times 0.001[/tex]

[tex]\mu = 1.429[/tex]

The expected number of repeat offenders is 1.429

(e) The standard deviation

This is calculated as:

[tex]\sigma= \sqrt{\sum (x^2 \times P(x)) - \mu^2}[/tex]

[tex]\sum (x^2 \times P(x))[/tex] is calculated as:

[tex]\sum (x^2 \times P(x)) = 0^2 \times 0.211+ 1^2 \times 0.378 + 2^2 \times 0.216 + 3^2 \times 0.162 + 4^2 \times 0.032 + 5^2 \times 0.001[/tex]

[tex]\sum (x^2 \times P(x)) = 3.237[/tex]

So, we have:

[tex]\sigma= \sqrt{\sum (x^2 \times P(x)) - \mu^2}[/tex]

[tex]\sigma = \sqrt{3.237 - 1.429^2}[/tex]

[tex]\sigma = \sqrt{1.194959}[/tex]

[tex]\sigma = 1.093[/tex]

The standard deviation of repeat offenders is 1.093

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To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic. For each congruence, we substitute the given values of a and b and simplify the congruences to solve for c. The possible values of c are then determined using the Chinese Remainder Theorem when appropriate.

To find the integer c that satisfies the given congruences, we can use the properties of modular arithmetic:

a) To find c such that a.c ≡ 13a (mod 19), we divide both sides of the congruence by a. This gives us c ≡ 13 (mod 19).

b) To find c such that b.c ≡ 8b (mod 19), we divide both sides of the congruence by b. This gives us c ≡ 8 (mod 19).

c) To find c such that c.c ≡ a - b (mod 19), we square both sides of the congruence. This gives us c^2 ≡ (a - b)^2 (mod 19). Since we know a ≡ 11 (mod 19) and b ≡ 3 (mod 19), we substitute these values and simplify the congruence to c^2 ≡ 8 (mod 19). To solve this quadratic congruence, we can use the Chinese Remainder Theorem to find the two square roots of 8 modulo 19, which are 7 and 12. Therefore, c ≡ 7 (mod 19) or c ≡ 12 (mod 19).

d) To find c such that c.c ≡ 7a + 3b (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 7(11) + 3(3) ≡ 4 (mod 19). Similar to part (c), we use the Chinese Remainder Theorem to find the square roots of 4 modulo 19, which are 2 and 17. Therefore, c ≡ 2 (mod 19) or c ≡ 17 (mod 19).

e) To find c such that c.c ≡ 2a^2 + 3b^2 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c^2 ≡ 2(11^2) + 3(3^2) ≡ 2(121) + 3(9) ≡ 149 ≡ 2 (mod 19). Therefore, c ≡ ±4 (mod 19).

f) To find c such that c ≡ a^3 + 4b^3 (mod 19), we substitute the given congruences for a and b into the congruence and simplify to obtain c ≡ 11^3 + 4(3^3) ≡ 11^3 + 4(27) ≡ 11^3 + 4(8) ≡ 11 + 32 ≡ 17 (mod 19). Therefore, c ≡ 17 (mod 19).

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ANSWER

[tex] P(G)= \frac{1}{3}[/tex]

EXPLANATION

The number of green marbles in the bag is

[tex]n(G) = 2[/tex]

The total number of marbles in the bag is

[tex]n(S)=1+2+3 = 6[/tex]

The probability of selecting a green marble from the bag without looking is

[tex]P(G)= \frac{n(G)}{n(S)} [/tex]

Substitute the values to get,

[tex]P(G)= \frac{2}{6} [/tex]

[tex]P(G)= \frac{1}{3} [/tex]

Answer:

The probability of drawing a green marble out of the bag without looking = 1/3

Step-by-step explanation:

It is given that, a bag contains 1 blue, 2 green, and 3 red marbles

Therefore total number of marble in the  bag = 1 + 2 + 3 = 6

To find the probability

Total number of marble = 6

Number of green marble  = 2

The probability of drawing a green marble = 2/6 = 1/3

Answer:

C) 120 degrees

Step-by-step explanation:

m<A + m<B + m<C = 180

45 + m<B + 15 = 180

m<B + 60 = 180

m<B = 120

The answer is C) 120

Answer: The temperature would be -2 degrees at midnight.

Step-by-step explanation:

If you take 8 and minus 10 then you get -2!

Answer:

-2

Step-by-step explanation:

hope it will help youu!!!

Answer:

Option C. [tex]65[/tex]

Step-by-step explanation:

we know that

The discriminant of a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]D=b^{2}-4ac[/tex]

in this problem we have

[tex]2x^{2} +3x-7[/tex]  

so

[tex]a=2\\b=3\\c=-7[/tex]

substitute

[tex]D=3^{2}-4(2)*(-7)[/tex]

[tex]D=9+56[/tex]

[tex]D=65[/tex]

The discriminant of the giving polynomial is 65. The correct option is C. 65

From the question, we are to determine the discriminant of the given polynomial

The given polynomial is

2x²+3x-7

This is a quadratic function

The discriminant of a quadratic function is simply the value in the square root of the quadratic formula

That is,

Discriminant, D = b² - 4ac

In the given quadratic function, 2x²+3x-7

a = 2, b = 3 and c = -7

∴ D = 3² -4(2)(-7)

D = 9 +56

D = 65

Hence, the discriminant of the giving polynomial is 65. The correct option is C. 65

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Answer: First option and last option.

Step-by-step explanation:

By definition, an equation of direct proportion has the following form:

[tex]y=kx[/tex]

Where k is the constant of proportionality.

The equation of the line [tex]y=mx+b[/tex], where m is the slope and b the y-intercept.

When b=0, means that the line passes through the origin. Therefore, it would be:

[tex]y=mx[/tex]

(which is similar to  [tex]y=kx[/tex])

Then, the slope of the line would be the constant of proportionality.

By definition, the slope can be positive or negative.

Keeping on mind the information above, you can see that the equation that have that form are:

[tex]y=-2x\\\\y=4x[/tex]

Answer:

y=−2x

Step-by-step explanation:

I got it right on Imagine math.

Answer:

It would be $13.05

Step-by-step explanation:

Since you're dividing negative $65.25 with a negative number of 5 stores. The five stores are negative because he bought from those stores. So, when dividing the 2 negatives you get a positive $13.05.

If Tom has bought only one t-shirt  the change to Tom's account balance

would have been - $13.05.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Tom bought 5 t-shirts from a store.

After he bought the t-shirts, his account balance showed a change of

- $65.25.

Assuming all 5 t-shirts cost the same so the cost of 1 t-shirt would be

= - (65.25/5).

= - 13.05 dollars.

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Answer:

$42

Step-by-step explanation:

Divide $18 by 3 to get a unit rate of $6 per hour. Then, multiply by 7 hours to get $42.

All you need to do is divide 1470 by 35, which is 42.

Is there answer choices?

Answer:

C

Step-by-step explanation:

If the parent function is function [tex]y=f(x)[/tex] and [tex]a>0,[/tex] then

In your case, the grapgh of the function [tex]y=2^x+2[/tex] is translated 2 units up the graph of the function [tex]y=2^x.[/tex]

Answer:

[tex]f(x)=2^{x} +2[/tex] relative to [tex]f(x)=2^{x}[/tex]

This is called translation of functions, and it refers to the movement of a specific function, either upwards, downwards, leftwards or rightwards. To be able to translate a function, we have to use the next rules.

In this case, the problem is saying that we have to move the function upwards by two units, because [tex]f(x)=2^{x} +2[/tex] is the same function as    [tex]f(x)=2^{x}[/tex], but moved 2 units upwards.

In addition, the graph is attached, there you can see the difference between those two functions, you will se that they are the same, but one is moved two units upwards.

The coefficient of q in the sum of the two expressions is 17/24.

We have,

The given expression is:

(2/3q - 3/4(-1/6q - r))

Let's simplify this expression step by step:

Step 1: Distribute -3/4 to (-1/6q - r):

(2/3q - 3/4 * -1/6q + 3/4 * r)

Step 2: Simplify the multiplication of fractions:

(2/3q + 1/8q + 3/4 * r)

Step 3: Combine like terms:

(17/24q + 3/4 * r)

Thus,

The coefficient of q in the sum of the two expressions is 17/24.

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The coefficient of q in the sum of the expressions is found by simplifying the terms individually and then combining them. After finding a common denominator and adding the terms, the coefficient of q is 19/24.

To find the coefficient of q in the sum of the given expressions (2/3q - 3/4*(-1/6q - r)), we first need to simplify the expression step by step. Starting with the second term, we distribute the -3/4 across the parentheses:

Now adding this to the first term:

To add the q terms, they need to have a common denominator. The common denominator for 3 and 8 is 24. We convert both fractions:

Now we can add them:

The coefficient of q in the sum of the given expressions is 19/24.

Answer:

300°

Step-by-step explanation:

This may seem really strange and counterintuitive to you, but when you turn 1° 300 times, you have turned 300°.

_____

If you don't want to add it up ...

1° + 1° + 1° ... + 1° . . . . . 300 times

you can use multiplication. It was invented as a shortcut to repeated addition:

1° × 300 = 300°

The gear has turned a total of 300 degrees.

To solve this problem, we need to consider the information given and apply basic multiplication. The gear turns in 1° sections, and it does so a total of 300 times. Since each section is 1°, we can simply multiply the number of sections by the size of each section to find the total degrees turned.

So, the calculation is as follows:

Number of sections = 300

Size of each section = 1°

Total degrees turned = Number of sections × Size of each section

Total degrees turned = 300 × 1°

Total degrees turned = 300°

Therefore, the gear has turned 300 degrees in total.

Rolling a 5 in 300 rolls: Probability of 1/6 [tex]*[/tex] 300 ≈ 50 times.

Sure, let's break it down step by step:

1. Understand Experimental Probability : Experimental probability is based on actual outcomes from an experiment or trial. It's calculated by dividing the number of favorable outcomes by the total number of outcomes.

2. Identify the Probability of Rolling a 5 : Since a standard number cube has 6 faces numbered 1 through 6, each face has an equal probability of 1/6 of showing up in a single roll.

3. Calculate the Probability of Rolling a 5 : The probability of rolling a 5 is 1/6, since there's one favorable outcome (rolling a 5) out of the total 6 possible outcomes.

4. Use Probability to Predict Outcomes : To predict how many times you'll roll a 5 in 300 rolls, multiply the probability of rolling a 5 by the total number of rolls.

Let's calculate:

Probability of rolling a 5 = 1/6

Total number of rolls = 300

Number of times you'll roll a 5 = (Probability of rolling a 5) * (Total number of rolls)

= (1/6) [tex]*[/tex] 300

≈ 50

So, based on experimental probability, you can predict that you will roll a 5 approximately 50 times if you roll the number cube 300 times.