What is the answer to this math problem? -0.4w=4.2

The first tank hold 1088 - 5t gallons of water after t weeks, while the seocnd tank holds 1360 - 9t gallons after t weeks.

Both tanks hold the same amount of water when

1088 - 5t = 1360 - 9t

Solve for t :

4t = 272

t = 68

So the tanks will hold the same amount of water after 68 weeks.

Jane can select 80 different types of dinner consisting of 3 different items from 5 different vegetarian items and 4 different meat items available.

For finding the various combination of dinners available which has atleast one vegetarian item we will apply combination formula with the given data i.e., \(^{n} C_{r} = \frac{n!}{(n-r)!.r!}\)

A combination is a way of selecting items from a collection where the order of selection does not matter.

We will have to apply the formula separately for vegetarian and meat items.

Combinations available

A. 1 vegetarian item and 2 meat items              

    \(^{5} C_{1} and ^{4} C_{2}\)                                 (In combination "and" means to multiply)                                                                                        

   = \(\frac{5!}{(5-1)!.1!} . \frac{4!}{(4-2)!.2!}\)

   = \(\frac{5!}{(4)!.1!} . \frac{4!}{(2)!.2!}\)

   = \(\frac{5.4.3.2.1}{(4.3.2.1).(1)}. \frac{4.3.2.1}{(2.1).(2.1)}\)

   = 5.3.2

   = 5.6

   = 30

B. 2 vegetarian items and 1 meat item

    \(^{5} C_{2} and ^{4} C_{1}\)

   = \(\frac{5!}{(5-2)!.2!} . \frac{4!}{(4-1)!.1!}\)

   = \(\frac{5!}{(3)!.2!} . \frac{4!}{(3)!.1!}\)

   = \(\frac{5.4.3.2.1}{(3.2.1).(2.1)}. \frac{4.3.2.1}{(3.2.1).(1)}\)

   = 5.2.4

   = 10.4

   = 40

C. 3 vegetarian items and no meat item

   = \(^{5} C_{3} and ^{4} C_{0}\)

   = \(\frac{5!}{(5-3)!.3!} . \frac{4!}{(4-0)!.0!}\)

   = \(\frac{5.4.3.2.1}{(2.1).(3.2.1)}. 1\)

   = 5.2

   = 10

Now, we will add all the different combination

Total combinations = 30+40+10

                                = 80 different type of dinners

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Given,

A jet travels 6320 miles in 8 hours.

Flying with the wind, the same jet travels 5950 miles in 5 hours.

To find: The rate of the jet in still air, and the rate of the wind.

Solution:

The jet's velocity against the wind is

The jet's velocity with wind is

Let the velocity of the jet in still air be x miles per hour and velocity of wind be y miles per hour.

As such its velocity against wind is x-y and with wind is x+y and therefore

Solve both equations (1) and (2)

And

Hence, the velocity of the jet in still air is 990 miles per hour and the velocity of wind is 200 miles per hour.

The equation x² y² = 4 corresponds to a hyperbola when only considering x and y as variables. When considering x, y, and z as variables, the equation corresponds to a two-sheeted hyperboloid.

a) When only x and y are the variables being considered, the equation x² y² = 4 corresponds to a circle in the xy-plane. The circle has a center at the origin (0,0) and a radius of 2.

b) If x, y, and z are the only variables being considered, the equation x² y² = 4 still represents a circle in the xy-plane, but it becomes a cylinder along the z-axis. This cylinder has a center on the z-axis and a radius of 2, extending infinitely along the z-axis.

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Answer:

1

Step-by-step explanation:

1

The equation is y = 726020.4 × (0.9800)ˣ is and the population is declining, the value of y will decrease as x increases.

Two or more expressions with an Equal sign is called as Equation.

The rate of population decline per year, r.

We can calculate this by taking the difference between the initial population and the current population and dividing initial population.

r = (711500 - 697270) / 711500 / 1

= 0.01997

So the population is declining at a rate of  1.997% per year.

Since the population is declining, we know that b must be less than 1. We can find b using the formula:

b = 1 - r

b = 1 - 0.01997 = 0.9800...

So the factor by which the population of Lime County declines each year is  0.9800.

Now let us find the value of a.

We know that the initial population was 711,500 when Leslie first moved to the county, so we can use this value and the value of b to find a using the formula:

a = y / bˣ

a = 711500 / 0.9800¹

= 726020.4

So the exponential equation that models the population of Lime County, y, x years after Leslie moved there is:

y = 726020.4 × (0.9800)ˣ

Hence, y = 726020.4 × (0.9800)ˣ is the equation and the population is declining, the value of y will decrease as x increases.

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Answer:

4x - 9

Step-by-step explanation:

4x - 9

The appropriate distribution to use in this case is the discrete probability distribution since the number of missed days of employees at the shoe store is limited to specific values with associated probabilities.

In a discrete probability distribution, the random variable can only take on specific, separate values with associated probabilities. In this scenario, the number of missed days of employees at the shoe store can only take values from 0 to 10, which are distinct and separate values.

To construct the discrete probability distribution, we need to know the probabilities associated with each possible number of missed days. These probabilities will determine the likelihood of each outcome occurring. The sum of all probabilities should be equal to 1, as it represents the total probability of all possible outcomes.

Once we have the probabilities for each possible number of missed days, we can plot the distribution and analyze the likelihood of different outcomes. The distribution will provide insights into the frequency and probability of various levels of employee absenteeism at the shoe store.

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Answer:

3 x 5 is the gcf of 45 and 75. gcf(45,75) = 15.

Step-by-step explanation:

hope this helped! yw :}

The probability of passing the true/false test of 60 questions if the minimum passing grade is 60% and all responses are random guesses is approximately 0.9802 or 98.02%.

Assuming that all responses are random guesses, we may describe this issue using a binomial distribution, where the number of right responses follows a binomial distribution with \(n = 60\) and \(p = 0.5.\)

If X represents the total number of accurate responses, it will follow a binomial distribution with\(n = 60\) and \(p = 0.5\) as its parameters.

If the passing grade is \(60%\), then there must be a minimum of \(36\)accurate responses \((0.6 * 60 = 36).\)

The normal-approximation can be used to calculate the likelihood of receiving at least \(36\) correct responses. We must determine the mean and variance of the binomial distribution in order to utilise the normal approximation.

The variance of a binomial distribution is

\(2 = np(1-p)\)

\(= 60 * 0.5 * 0.5\)

\(= 15\)

and the mean is

\(= np\)

\(= 60 * 0.5\)

\(= 30.\)

To calculate the probability of passing, we can use the normal distribution with mean 30 and variance 15 to approximate the binomial distribution with continuity correction.

\(P(X \geq 36) = P(Z \geq (36 + 0.5 - 30) / \sqrt{15})\)

where Z is a standard normal random variable.

\(P(Z \geq 2.08) = 1 - P(Z \leq 2.08)\)

\(= 1 - 0.0198\)

\(= 0.9802\)

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Temperature of refrigerators - Cannot determine. Horsepower of race car engines - Ratio. Marital status of school board members - Nominal. Ratings of television programs - Ordinal. Ages of children enrolled in a daycare - Interval

The level of measurement for the temperature of refrigerators cannot be determined based on the given information. The temperature could potentially be measured on a nominal scale if the refrigerators were categorized into different temperature ranges. However, without further context, it is not possible to determine the specific level of measurement.

The horsepower of race car engines can be measured on a ratio scale. Ratio scales have a meaningful zero point and allow for meaningful comparisons of values, such as determining that one engine has twice the horsepower of another.

The marital status of school board members can be measured on a nominal scale. Nominal scales are used for categorical data without any inherent order or ranking. Marital status categories, such as "married," "single," "divorced," etc., can be assigned to school board members.

The ratings of television programs, such as "poor," "fair," "good," and "excellent," can be measured on an ordinal scale. Ordinal scales represent data with ordered categories or ranks, but the differences between categories may not be equal or measurable.

The ages of children enrolled in a daycare can be measured on an interval scale. Interval scales have equal intervals between values, allowing for meaningful differences and comparisons. Age, measured in years or months, can be represented on an interval scale.

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The collection of the ages of the 500 women when they first married is a Sample.

The collection of the ages of the 500 women when they first married is a Sample.

What is a Sample?

A sample is a subset of the population. The sample is chosen to represent the entire population. The purpose of using the sample is to draw a conclusion about the population.

The sample is used to represent the population that is being studied. The collection of the ages of the 500 women when they first married is a sample since it is a subset of the entire population of women.

Researchers use a sample to learn more about the population. It's essential to choose the sample carefully so that it accurately represents the population.

The other options include:

A population is the entire group that you want to draw conclusions about.

A statistic is a numerical value calculated from a sample of data.

Parameter is a numerical value calculated from an entire population of data.

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Answer:

14.9

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

Answer:

A-11

Step-by-step explanation:

Correct on EDGE

The value of the function k(h(10)) will be 11. The correct option is A.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

Given h(t) = t²+t+ 12 and k(t) = √t-1, we are to find k(k.h)(10)

k{h(t)} = k{ t²+t+ 12}

Since k(t)= √t-1, we will replace the variable t in the function with t²+t+ 12

k(h(t)) = √{(t²+t+ 12)-1}

k(h(t)) = √t²+t+12-1

k(h(t)) = √t²+t+11

Substituting t = 10 into the resulting function;

k(h(10)) =  √(10)²+(10)+11

k(h(10)) = √100+10+11

k(h(10)) = √121

k(h(10))= 11

Therefore, the value of the function k(h(10)) will be 11. The correct option is A.

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Answer:

21.875

$8.75/2.5

$8.75× 2.5= 21.875

2.5×2.5=1

Answer:

He rented 82 games

Step-by-step explanation:

296=3x+50

246=3x

x=82

Answer:

spent on game rented

= $296 - $50

= $246

games rented

= $246 ÷ $3

= 82

The given box has the shape of a cuboid, since its height is greater than its width. Thus, the maximum volume for such box is 11200 \(in^{3}\).

The volume of an object is a measure of it containing capacity. Since the given box has a taller height than its width, then it has the shape of a cuboid. The volume of a cuboid is given as:

volume = length x width x height

            = area x height

Given that the sum of the perimeter of its base and its height is not more than 108 inches, we can say; let the sides of the square base be represented by l and its height by h.

Then;

4l + h = 108

Therefore, maximum volume for the box can be attained when l = 20 inches and h = 28 inches.

So that;

4(20) + 28 = 80 + 28

                 = 108 inches

Thus;

maximum volume = area of the square base x height

                        = 400 x 28

maximum volume = 11200 \(in^{3}\)

The maximum volume for such a box would be 11200 \(in^{3}\).

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The particular solution to the given differential equation is: y = x^2 - (2^x)(ln2)/ln2 - 1.

The differential equation is dy/dx = 2x - (2^x)(ln2). To find the particular solution, we need to integrate both sides of the equation with respect to x.

∫dy = ∫(2x - (2^x)(ln2))dx

y = x^2 - (2^x)(ln2)/ln2 + C

To find the value of C, we can use the initial condition that y = -2 when x = 0.

-2 = 0^2 - (2^0)(ln2)/ln2 + C

-2 = -1 + C

C = -1

Therefore, the particular solution to the given differential equation is:

y = x^2 - (2^x)(ln2)/ln2 - 1

In summary, the particular solution to the given differential equation is y = x^2 - (2^x)(ln2)/ln2 - 1, obtained by integrating and using the given initial condition.

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Answer:

V =134.4 ft^3

Step-by-step explanation:

Volume is

V = l*w*h

V = 7*4*4.8

V =134.4 ft^3

The probability that a given student is called upon j times during the term

b(32,j,1/80) = (32/j)∗(1/80)j∗(79/80)(32−j)

Probability:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).

given that

In a class of 80 students, the professor calls on 1 at random for a recitation in each class period

there are 32 class periods in a term

the probability that a given student is called upon j times during the term

b(32,j,1/80) = (32/j)∗(1/80)j∗(79/80)(32−j)

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To calculate the annualized rate of return, we can use the formula for compound interest. The correct answer is 11.66%.

The formula for compound interest is given by: A = P(1 + r)^t, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

In this case, the initial investment (P) is BD 14,000, the final amount (A) is BD 52,600, and the time (t) is 12 years. We need to solve for the annual interest rate (r).

\(BD 52,600 = BD 14,000(1 + r)^{12}\)

By rearranging the equation and solving for r, we find:

\((1 + r)^{12} = 52,600/14,000\)

Taking the twelfth root of both sides:

\(1 + r = (52,600/14,000)^{(1/12)}\\r = 0.1166 / 11.66 \%\)

Therefore, Areej has earned an annualized rate of approximately 11.66% on this investment.

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Answer:

28) 42

29) 7

Step-by-step explanation:

check solution above for step-by-step explanation

Rounding to four decimal places, we get the probability that the weight will be less than 4664 grams as 0.9991.

Let X be the weight of a newborn baby boy born at the local hospital. We know that X follows a normal distribution with mean μ = 3996 grams and variance σ² = 111,556 grams².

We want to find the probability that the weight will be less than 4664 grams. That is, we need to find P(X < 4664).

To standardize X, we can use the z-score formula:

z = (X - μ) / σ

Substituting the given values, we get:

z = (4664 - 3996) / √111556

z = 3.1217

Using a standard normal table or calculator, we can find that the probability of a standard normal random variable being less than 3.1217 is approximately 0.9991.

Therefore, P(X < 4664) = P(Z < 3.1217) ≈ 0.9991.

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Answer:

8.433 to the power of 4

Step-by-step explanation:

The reason is because the nukber written in scientific notation always has to be between 1-10. It can't be 84.33 or 843.3. The number has to be between 1 and 10.

The to your question is that we can use the normal distribution to estimate the probability that the product will last between 16.536 and 8.054 years.


In this case, we want to calculate the probability for x = 16.536 and x = 8.054. The mean (μ) is 14.242 years, and the standard deviation (σ) is 3.978 years.

Using the formula, we can calculate the z-scores for both values:
For x = 16.536: z = (16.536 - 14.242) / 3.978
For x = 8.054: z = (8.054 - 14.242) / 3.978

Once we have the z-scores, we can look up the corresponding probabilities in the standard normal distribution table or use a calculator. Subtracting the probability for the lower z-score from the probability for the higher z-score will give us the probability that the product will last between 16.536 and 8.054 years.

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Answer:

75%

Step-by-step explanation:

Step-by-step explanation:

quarter = 25¢

dime = 10¢

nickel = 5¢

1 quarter (25¢) + 3 dimes (3 x 10¢, which is 30¢) + 4 nickels (4 x 5¢, which is 20¢)

25 + 30 + 20

25 + 50

75¢

1 dollar is 100¢

75/100 = 75%

Answer:

20

Step-by-step explanation:

Let Kayla's age be k.

Let Isaac's age be a.

Kayla is 6 years older than Raoul. This means that:

k = y + 6

lsaac is 4 years younger than Raoul. This means that:

a = y - 4

y = 12

=> k = 12 + 6 = 18

and

a = 12 - 4 = 8

The sun of Raoul's age and Isaac's age is:

12 + 8 = 20

Answer:

When a point gets reflected across the x-axis, the sign of its y-coordinate changes so the coordinates of Q' are (3, 4).

3 and -4

Step-by-step explanation:

hope this helps!