A blue whale is currently diving down beneath the ocean. After 4 minutes, the blue whale is 33.7 meters below sea level, and after 13mins, the blue whale is 99.4 meters below sea level. If the blue whale is diving at a constant rate, how long will it take to reach a depth of 190.65 meters below sea level? To answer this, construct a linear function.

please hurry i dont want to fail

Answer:

Sarah earns R6 100 in total for her work to the value of R12 000.

Step-by-step explanation:

To calculate Sarah's earnings, we need to break down her income into two parts: the commission she earns on income up to R5 000, and the bonus commission she earns on income above R5 000.

Commission on income up to R5 000:

Sarah's basic salary is R3 000 per month, and she earns 20% commission on income up to R5 000. So for the first R5 000 of income, Sarah's commission is:

[tex]\text{Commission on income up to} \ R5, 000 = 20\% \ \text{of} \ R5, 000 = R1 ,000[/tex]

Bonus commission on income above R5 000:

Sarah also receives a 10% bonus on top of the normal commission rate on earning above R5 000. So for the amount earned above R5 000, her commission is:

[tex]\text{Commission on income above} \ R5, 000 = (20\% + 10\%) of (R12, 000 - R5, 000) = 30\% \ \text{of} \ R7, 000 = R2 ,100[/tex]

Total earnings:

Sarah's total earnings are the sum of her basic salary and the commission she earns:

Total earnings = Basic salary + Commission on income up to R5 000 + Commission on income above R5 000

[tex]\text{Total earnings} = R3, 000 + R1 ,000 + R2 ,100[/tex]

[tex]\text{Total earnings} = 6,100[/tex]

Therefore, Sarah earns R6 100 in total for her work to the value of R12 000.

Explanation: The evolution of numbers developed differently with disparate versions, which include the Egyptian, Babylonians, Hindu-Arabic, Mayans, Romans, and the modern American number systems.

Answer:

Step-by-step explanation:

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According to bayes therom the conditional probability thst x is greater than 26 is zero.

Bayes' theorem may be used to compute the conditional probability that x is greater than 26 if x is less than or equal to 12.

P(x > 26 | x 12) = P(x > 26 plus x 12) / P(x > 26 plus x 12) (x 12).

Because x cannot be more than 26 and less than or equal to 12, the numerator of the preceding formula is zero. As a consequence, the conditional probability is equal to zero:

P(x > 26 | x ≤ 12) = 0

This means that knowing x is less than or equal to 12 does not inform us if x is more than or less than 26.

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At equilibrium we expect [Reactants} < [Products)  from the the profile that has been shown.

An energy profile diagram, also known as an energy diagram or reaction coordinate diagram, is a graphical representation of the energy changes that occur during a chemical reaction or a physical process. It shows the energy levels of the reactants, products, and any intermediate species that may form during the reaction.

The horizontal axis of an energy profile diagram represents the reaction coordinate, which is a measure of the progress of the reaction from the reactants to the products. The vertical axis represents the energy of the system.

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To conduct a hypothesis test comparing variances of independent samples from two populations, the test statistic will have an F-distribution.

The F-distribution is a probability distribution that describes the ratio of two independent chi-squared distributions divided by their degrees of freedom. In this case, the numerator and denominator degrees of freedom are based on the sample sizes and variances of the two populations being compared.

The null hypothesis for the F-test is that the variances of the two populations are equal, and the alternative hypothesis is that they are not equal. The F-test allows us to determine if the difference in variances is statistically significant, and if we reject the null hypothesis, we can conclude that the variances are significantly different.

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An equation is a statement that two expressions are equal. The expressions on both sides of the equation can be made up of variables, constants, and mathematical operations.

For example, the equation:

[tex]2x + 5 = 11[/tex]

Has two expressions on either side of the equals sign. The expression on the left side is 2x + 5, which consists of the variable x, the constant 2, and the constant 5, combined using the mathematical operation of addition.

The expression on the right side is 11, which is a constant. The equation states that the two expressions are equal, which means that the value of x can be determined to be 3 by solving the equation.

Part A:

The value for x that is a solution to  [tex]2x - 5 = 3 is x = 4.[/tex]  

The value for x that is a solution to   [tex]2x - 5 > 3[/tex] is   [tex]x > 4[/tex] .

Part B:

The solution to  [tex]-2x - 5 = 3[/tex] is [tex]x = -4[/tex] .

The solution to   [tex]-2x - 5 > 3[/tex] is  [tex]x < -4[/tex]  .

A value for x that is a solution to  [tex]-2x - 5 = 3[/tex] is [tex]x = -4[/tex]  .

A value for x that is a solution to  [tex]-2x - 5 > 3[/tex] is [tex]x = -5[/tex]  .

Therefore, The value for x that is a solution to  [tex]2x - 5 > 3[/tex] is [tex]x > 4[/tex] . and A value for x that is a solution to [tex]-2x - 5 > 3[/tex]   is [tex]x = -5[/tex]  .

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The number of times larger Cell S is compared to Cell W is 4 x 10²,

Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

When the power of the scientific notation is negative, it means that the number is less than 1. 0.01 would be written as 1 x [tex]10^{-2}[/tex]. Cell S is larger than Cell W.

(7.2 x [tex]10^{-5}[/tex]) ÷ (1.8 x [tex]10^{-7}[/tex])

(7.2 / 1.8) x [tex]10^{-5--7}[/tex]

4 x 10²

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Answer:

Step-by-step explanation:

The given sequence is geometric.

To find the common ratio (r) of the sequence, we need to divide any term by its preceding term. Let's divide the second term (8) by the first term (32):

r = 8/32 = 1/4

Now, we can use the formula for a geometric sequence to find any term:

an = a1 * r^(n-1)

where:

an = nth term of the sequence

a1 = first term of the sequence

r = common ratio

n = position of the term we want to find

Let's use this formula to find the third term:

a3 = 32 * (1/4)^(3-1) = 2

So, the common ratio of the sequence is 1/4, and each term is obtained by multiplying the preceding term by 1/4. The sequence is decreasing rapidly because the ratio is less than 1.

Answer:

Step-by-step explanation:

[tex]diameter=\sqrt{(5+2)^2+(5+2)^2} \\=\sqrt{49+49} \\=\sqrt{98} \\=7\sqrt{2} \\radius=\frac{7\sqrt{2} }{2} \\\approx 4.95[/tex]

Three youngsters are interviewed at random. Population variation is around [tex]18.67[/tex].

The standard deviation refers to the square base of variance, which is the average of the squares departures from the mean. Both metrics capture distributional variability, although they use different measurement units: The units used to indicate standard deviation are the same as the values' original ones.

In statistics, population standard deviation is a crucial indicator of dispersion. further reading. Statisticians compute variance to determine how order to overcome the drawbacks in a data gathering interact to one another. By calculating the population variance, one may also compute the dispersion in relation to the population means.

we need to first find the population mean [tex]u[/tex]

[tex]u = (2 + 4 + 12)/3 = 6[/tex]

To calculate the population variance

[tex]= [(-4)^{2} + (-2)^{2} + 6^{2} ]/3[/tex]

[tex]= (16 + 4 + 36)/3[/tex]

[tex]= 56/3[/tex]

[tex]= 18.67[/tex] (rounded to two decimal places)

Therefore, the population variance is approximately [tex]18.67[/tex].

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The value of length of side g using the  similar triangles is found as 20 ft.

In the given figures:

DC || EA

So,

∠D = ∠A

∠C = ∠E

By Angle -Angle similarity both triangles are similar.

Thus,

Taking the ratios of their side, it will be also equal.

EA / DC = EB / BC

5 / 10 = g / 10

g = 10*10 / 5

g = 100 / 5

g = 20

Thus, the value of length of side g using the  similar triangles is found as 20 ft.

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The probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time is 0.000055

The multiplication rule of probability can be used to determine the likelihood of drawing three kings consecutively from a standard deck of cards when the drawn card is not put back into the deck each time.

Since there are four kings in a deck of 52 cards, the likelihood of drawing a king from a standard 52-card deck is 4/52 or 1/13.

There are still 51 cards in the deck after the first king is drawn, and three of them are kings. Therefore, there is a 3/51 chance of drawing another king.

There are 50 cards left in the deck after drawing the second king, and two of them are kings. The likelihood of drawing a third king is therefore 2/50 or 1/25.

Therefore, the probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time is:

(1/13) x (3/51) x (1/25) = 3/54,600 or approximately 0.000055.

Hence, 0.000055 is the probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time.

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Answer:

12/2652

Step-by-step explanation:

First, the probability of drawing a king for the first time is 4/52. The chance of drawing another is 3/51. Multiplying, we get the 3rd answer choice, 12/2652

The bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.

Trigοnοmetry is οne οf the mοst impοrtant branches in mathematics that finds huge applicatiοn in diverse fields. The branch called “Trigοnοmetry” basically deals with the study οf the relatiοnship between the sides and angles οf the right-angle triangle.

Hence, it helps tο find the missing οr unknοwn angles οr sides οf a right triangle using the trigοnοmetric fοrmulas, functiοns οr trigοnοmetric identities. In trigοnοmetry, the angles can be either measured in degrees οr radians. Sοme οf the mοst cοmmοnly used trigοnοmetric angles fοr calculatiοns are 0°, 30°, 45°, 60° and 90°.

We can use trigοnοmetry tο sοlve fοr the hοrizοntal distance. Let x be the hοrizοntal distance frοm the bοat tο the lighthοuse.

Then, tan(5°) = οppοsite/adjacent = 139/x

Sοlving fοr x, we get:

x = 139/tan(5°) ≈ 1592.53 feet

Therefοre, the bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.

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1. The diagonals are equal. Rectangle

2. All sides are equal, and one angle is 60°. Rhombus

3. All sides are equal, and one angle is 90°. Square

4. It has all the properties of parallelogram, rectangle, and rhombus. Square

5. It is an equilateral parallelogram. Rhombus

A rectangle is a four-sided figure with two sets of parallel sides, with each side being a different length. The opposite sides of a rectangle are always equal in length, so the angles of a rectangle are all 90 degrees. A rectangle can also be referred to as a quadrilateral.

A rhombus is a four-sided figure with all sides the same length. The angles of a rhombus are not all 90 degrees, but the opposite sides of a rhombus are equal in length. A rhombus can also be referred to as a diamond.

A square is a four-sided figure with all sides being the same length and all angles being 90 degrees. A square can also be referred to as a regular quadrilateral.

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The complete question is:

Identify whether the following statements describe a rectangle, rhombus or square.

1. The diagonals are equal. ____________

2. All sides are equal, and one angle is 60°. ____________

3. All sides are equal, and one angle is 90°. ____________

4. It has all the properties of parallelogram, rectangle, and rhombus. ____________

5. It is an equilateral parallelogram. ____________

Answer:

The critique of the sample method and survey used by the guild is as follows:

In summary, the survey used by the guild suffers from various types of bias, which may affect the validity and generalizability of the results. To improve the validity and reliability of the survey, the guild should use random sampling and address issues such as non-response and response bias.

[tex]T(11) = -1[/tex] represents the initial negative term inside the series.

A phrase that acknowledges a characteristic or trait in anything is said to be positive. Negative terms are those that downplay some aspect or characteristic of something. The positive or negativizes of a phrase is termed its quality.

Positive simply denotes excellent or the polar opposite of negative. For instance, you're less likely to receive favorable feedback on your scorecard if you've a good mindset toward your assignments. It might be difficult to keep track of all the different definitions of the word positive.

T(n) is negative when [tex]32 - 3n < 0[/tex], which can be rearranged as:

[tex]3n > 32[/tex]

[tex]n > 32/3[/tex]

Since [tex]n[/tex] is an integer, the smallest value of n that satisfies this inequality is [tex]n = 11[/tex].

Therefore, the [tex]11th[/tex] term of the sequence is:

[tex]T(11) = 32 - 3(11) = -1[/tex]

So the first negative term in the sequence is [tex]T(11) = -1.[/tex]

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Step-by-step explanation:

it was not clear if an average change rate would be sufficient, or if you needed an immediate change rate (as I also don't know if you covered derivatives already or not).

so, it would be helpful, if you could put a message to an answer that was not giving you what you need.

so, here now an answer for an immediate change rate (hopefully that is what you need) :

we have a right-angled triangle.

the direct line of sight (the direct distance between police and red car) is the Hypotenuse (the baseline opposite of the 90° angle).

the 50 ft and 180 ft are the legs.

Pythagoras gives us the length of the Hypotenuse :

Hypotenuse² = 50² + 180² = 2500 + 32400 = 34,900

Hypotenuse = sqrt(34900) = 186.8154169... ft

in general terms let's say x is the distance of the cop to the road, y is the distance on the road to the crossing point with the distance cop to road, and z is the line of sight distance between the red car and the cop (the Hypotenuse).

x² + y² = z²

now, the first derivative of distance is the change of distance = speed.

then dy/dt (= y') is how fast the car is traveling down the road. dx/dt (= x') is how fast the cop is traveling toward the road. and dz/dt (= z') is how fast the distance between the cop and the car is changing.

now, we take the derivative of our equation

x² + y² = z² with respect to time, variable by variable :

d(x² + y² = z²)/dt =

dx²/dx × dx/dt + dy²/dy × dy/dt = dz²/dz × dz/dt

that gives us the equation

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

x(dx/dt) + y(dy/dt) = z(dz/dt)

from the problem we know x (50 ft), y (180 ft), dz/dt (85 ft/s). we calculated z (the Hypotenuse = sqrt(34900), and since the cop is not moving, we know dx/dt = 0.

and we get

50ft×0ft/s + 180ft×(y') = sqrt(34900)ft×(85)ft/s

we solve for y' (the speed of the car on the road)

y' = sqrt(34900)×85/180 = 88.21839132... ft/s

≈ 88.22 ft/s

and now here the difference for an average change rate over the unrevealed of 1 second :

the radar measured the change of the distance (Hypotenuse) from 1 second ago to now.

so, 1 second ago, the distance was

186.8154169... + 85 = 271.8154169... ft

the 50 ft leg stays the same, but the 180 ft leg was (again via Pythagoras)

271.8154169...² = 50² + leg²

leg² = 271.8154169...² - 50² = 71,383.62088...

leg = 267.1771339... ft

so, the red car traveled

267.1771339... - 180 = 87.1771339... ft/s

as you can see, it is close, but there has to be a difference, as the average change rate is only an approximation to the immediate change rate.

Step-by-step explanation:

Area of parallelogram = base × height or say b×h

Given: h=8 inches

Area=120 sq.inches

⇒120=8×b

⇒120/8=b

⇒120/8=b = 15

Answer = 15 inches b

Inside the sphere, the potential is given by [tex]$V(r)=\frac{Q}{4\pi\epsilon_0r}$[/tex], where Q is the total charge enclosed within the sphere. Since the sphere shell has no charge inside, Q=0, and thus V(r)=0 inside the sphere.

Outside the sphere, the potential is given by

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{Q'}{4\pi\epsilon_0r'}$[/tex]

where Q is the total charge of the sphere shell, Q'= σ4πR²is the charge on an imaginary sphere of radius r'>R enclosing the sphere shell, and r is the distance from the center of the sphere. Using the result from Ex. 3.9, the potential outside the sphere becomes

[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{\sigma_0 R^2}{2\epsilon_0 r}$[/tex]

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The correct answer is C. This is not a probability model because the sum of the probabilities is not 1.Therefore, the sum of the probabilities must be equal to 1 for a set of probabilities to be considered a probability model.

Probability is a measure of the probability of an event, expressed as a number between 0 and 1.

For example, the probability of rolling a 6 on a fair six-sided die is 1/6 or approximately 0.17.

In order for a set of probabilities to represent a probability model, the sum of all the probabilities must be equal to 1. This ensures that there is a 100% chance that one of the possible outcomes will occur.

If the sum of the probabilities is less than 1, then there is a possibility that none of the outcomes will occur.

If the sum of the probabilities is greater than 1, then there is a possibility that more than one outcome will occur, which is not possible in a probability model.

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the largest integer [tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]

To find the largest integer[tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$[/tex], we need to count how many factors of 3 are in the product of the odd integers from 1 to 99.

One way to do this is to factor each odd integer into its prime factors and count how many factors of 3 are present. However, this would be quite tedious and time-consuming.

A quicker approach is to use the fact that every third odd integer is a multiple of 3. Thus, we can count how many multiples of 3 are present in the product of the odd integers from 1 to 99.

Let [tex]$m$[/tex] be the number of multiples of 3 in the range from 1 to 99. Then we have:

[tex]m = \left\lfloor \frac{99}{3} \right\rfloor = 33[/tex]

This is because there are 33 multiples of 3 in the range from 1 to 99 (namely, 3, 6, 9, ..., 96, 99).

Each multiple of 3 contributes at least one factor of 3 to the product of the odd integers. However, some multiples of 3 contribute two or more factors of 3, depending on how many factors of 3 they contain.

To count how many multiples of 3 contribute two or more factors of 3, we need to count how many multiples of 9, 27, and 81 are present in the range from 1 to 99.

There are [tex]$\left\lfloor \frac{99}{9} \right\rfloor = 11$[/tex]multiples of 9, namely 9, 18, 27, ..., 81, 90, 99. Each multiple of 9 contributes at least two factors of 3 to the product of the odd integers.

There are [tex]$\left\lfloor \frac{99}{27} \right\rfloor = 3$[/tex] multiples of 27, namely 27, 54, 81. Each multiple of 27 contributes at least three factors of 3 to the product of the odd integers.

There is only one multiple of 81 in the range from 1 to 99, namely 81, which contributes at least four factors of 3 to the product of the odd integers.

Thus, the total number of factors of 3 in the product of the odd integers from 1 to 99 is:

[tex]n = m + 2\times\text{number of multiples of 9} + 3\times\text{number of multiples of 27} + 4\times\text{number of multiples of 81}[/tex]

[tex]n = 33 + 2\times 11 + 3\times 3 + 4\times 1 = 62[/tex]

Therefore, [tex]the $ largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]

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Step-by-step explanation:

The formula for calculating the balance on a CD (Certificate of Deposit) after a certain amount of time is:

A = P(1 + r/n)^(nt)

Where: A = the ending balance P = the principal (initial investment) r = the annual interest rate (as a decimal) n = the number of times interest is compounded per year t = the time in years

In this case, the initial investment is $1,800.00, the annual interest rate is 2.3% (or 0.023 as a decimal), and the investment period is 2 years. Assuming that the interest is compounded annually, we can substitute these values into the formula:

A = 1800(1 + 0.023/1)^(1*2) A = 1800(1.046729) A = 1883.12

Rounding to the nearest cent, the ending balance after 2 years on the CD is $1,883.75 (option B). Therefore, option B is the correct answer.

Option C) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.

Relative frequency is a measure of the proportion or percentage of times an event occurs in a given sample. It is calculated by dividing the frequency of an event by the total number of events in the sample. The formula for relative frequency is given as follows:

Relative frequency = Frequency of an event / Total number of events in the sample

For the joint relative frequency of 10th grade students in geometry, the parameters are given as follows:

Hence the joint relative frequency is obtained as follows:

20.7/100 x 100%= 20.7%.

Hence option C is correct.

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The amount that LeeCo pays Macy for the office equipment at the $6,300 list price, sales terms of 3/10, n/30 FOB with payment made within the discount window, is $6,111.

A cash discount refers to a reduction in the price of an item due to payment within the discount period.

A cash discount incentivizes the customer to make prompt payments.

The list price of the equipment = $6,300

Sales terms: 3/10, n/30 FOB

Prepaid freight = $40

Cash discount = $189 ($6,300 x 3%)

Payment after the discount = $6,111 ($6,300 - $189)

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The conditions in which is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal : (C) A random sample of 10 taken from a population distribution that is skewed to the right.

In statistics, the normal or Gaussian distribution is a continuous probability distribution for real-valued random variables.

The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distribution is unknown. Their importance is partly due to the central limit theorem. It states that in some cases the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable - whose distribution converges to a normal distribution as the size of the l sample increases.

Now,

If we look at the options given below, we see that the random samples in options A and B are normally distributed, so their sample means will be approximately normally distributed.

Similarly, option E indicates that the population is uniform, so the sample mean will also be approximately normal.

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