In June, the Zavala family's NIPSCO bill was $150. In July their NIPSCO bill was $180. Mrs. Zavala said that the bill increased by 30%. Mr. Zavala said it increased by 20%. Who is correct?

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

Not a question, and also incorrect (sorry)

Step-by-step explanation:

The rate of change for a vertical line is undefined.

The rate of change for a HORIZONTAL line is 0

Theoretically, the rate of change for a vertical line is not zero it is undefined.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Zero rates of change refer to a quantity that does not fluctuate over time.

But bear in mind these two separate circumstances: Horizontal lines have a slope of 0 since the vertical change is 0.

As 0 cannot be split into any integer, there is no slope for vertical lines since there is no horizontal change.

Because of this, the rate of change for a vertical line is not zero but rather is unknown.

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The Perimeter of the polygon = 22.43 units.

Given the vertices of the polygon as:

The perimeter of the polygon is the sum of all its sides, UV + VW + UW.

Apply the distance formula, d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) to find the length of each of the three sides of the polygon as shown below:

UV = √[(3−(−2))² + (4−4)²]

UV = √[(5)² + (0)²]

UV = √25

UV = 5 units

VW = √[(3−3)² + (4−(−4))²]

VW = √64 = 8 units

UW = √[(−2−3)² + (4−(−4))²]

UW = √89 = 9.43 units

Perimeter of the polygon = 5 + 8 + 9.43

Perimeter of the polygon = 22.43 units

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Simplify the left side of the equation.

Simplify the right side of equation.

Both side of equation give same results so Hugo is correct.

Muscular strength can be measured based on the amount of weight lifted.

Muscular strength can be measured based on the amount of weight lifted. The upper-body and lower-body strength are measured separately. Muscular strength is typically measured which is known as a One Rep Max (1RM).

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Answer:

The one with arrows are the answers

->Line segment E B  is bisected by Line segment D F .

->A is the midpoint of Line segment F C .

Line segment F C  bisects Line segment D B.

->Line segment E B  is a segment bisector.

->FA = One-halfFC.

Line segment D A is congruent to Line segment A B .

Step-by-step explanation:

I did it on edge and got it right

Answer:

1. Line segment E B  is bisected by Line segment D F .

2. A is the midpoint of Line segment F C .

4.Line segment E B  is a segment bisector.

5. FA = One-halfFC.

The linear equation that compares the population y of spoonerville as it relates to the number of years since 2000 be,

y - 150x

Given, In the year 2000, the state of Florida named an existing town after their great and brightest resident.

The town of Spoonerville was founded in 2000 but unfortunately the population decreased by 150 people per year. In 2007 the population was 75,450 people.

Let the population of Spoonerville be y,

and the number of years since 2000 be x

So, the equation be

Population = y - 150x

Hence, the linear equation that compares the population y of spoonerville as it relates to the number of years since 2000 be,

y - 150x

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Answer:

First you need to know how many feet are in a mile (5280 ft) and so you would multiply this by 3 and to show your work because teachers need that now sadly you do this

\(3x5280=\)

15820

:)

The value of the expression , where , , and are real numbers with and , we can rationalize the denominator and simplify the expression. The value of is .

Given the expression , we need to simplify it by rationalizing the denominator. We start by multiplying the numerator and denominator by the conjugate of the denominator, which is . This results in the expression . By using the difference of squares identity, we simplify the denominator to . Next, we can cancel out the common factors of 2 in both the numerator and denominator, which gives us . Simplifying further, we have . To find the value of , we need to determine the values of , , and . Since and , we substitute these values into the expression, which yields . Therefore, the value of is .

In summary, by rationalizing the denominator and simplifying the expression , we find that the value of is .

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Answer:

$59.33

Step-by-step explanation:

To begin, let's start with what we know

Item = 69.80

Discount = 15% or 0.15

So, let's put it into this formula

New Price = Item ( 1 - Discount)              Note: P is the final price

                 = 69.80 ( 1 - 0.15)

                 = 69.80 ( 0.85 )

                 = 59.33

The new price is $59.33.

If you have any questions, please let me know in the comments. If you could mark this answer as the brainliest, I would greatly appreciate it!

Answer:

$59.33

Step-by-step explanation:

To find the new price, we need to know what is 15% of 69.80, and then subtract the result from 69.80. To find the percent, we multiply the number by the percent using decimals for the percent. 15% is 0.15, so we multiply 69.80 * 0.15 = 10.47

Next, subtract 10.47 from 69.80.

69.80 - 10.47 = 59.33

The new price is 59.33.

Another method is that since 69.80 is 100 percent, then the new price will be 100% - 15% = 85%. Multiply the 85 percent by 69.80, and find your answer.

0.85 * 69.80 = 59.33

Hope this helps.

4(3)(2)/2 + 2² = 12 + 4 = 16

The distance from -4 to 1 is 5 units.

The correct number line and expression to find the distance from -4 to 1 are:

Number line: -4 -3 -2 -1 0 1

Expression: |-4 - 1|

To find the distance, we subtract the smaller number (-4) from the larger number (1) and take the absolute value:

|-4 - 1| = |-5| = 5

Therefore, the distance from -4 to 1 is 5 units.

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Answer:

A

Step-by-step explanation:

translating the decimal -0.625 to fraction form, you get -5/8, which is equal to B. C is greater, being closer to 0 than -0.625, so that leaves you with A, which is -1.6, and less than -0.625.

Approximately 64 students in the accounting class scored less than 65 or more than 75.

To solve this, we'll use the Empirical Rule, which states that for a normal distribution:

1. Approximately 68% of the data falls within one standard deviation of the mean.
2. Approximately 95% of the data falls within two standard deviations of the mean.
3. Approximately 99.7% of the data falls within three standard deviations of the mean.

In your accounting class, the mean score is 70, and the standard deviation is 5. We want to find the number of students who scored less than 65 (one standard deviation below the mean) or more than 75 (one standard deviation above the mean).

Using the Empirical Rule, we know that about 68% of students scored between 65 and 75 (within one standard deviation of the mean). Therefore, the remaining 32% of students scored either less than 65 or more than 75.

Since there are 200 students in the class, we can calculate the number of students who scored less than 65 or more than 75:

0.32 * 200 = 64 students

So, approximately 64 students in the accounting class scored less than 65 or more than 75.

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Given:

The figure of two semicircles with diameters 6 cm and 5 cm.

To find:

The area of the combined figure.

Solution:

It is given that the diameters of the semicircles are 6 cm and 5 cm so their radii are 3 cm and 2.5 cm respectively.

Area of a semicircle is:

\(A=\dfrac{1}{2}\pi r^2\)

So, the combined area of two semicircles with radii 3 cm and 2.5 cm is:

\(Area=\dfrac{1}{2}\pi (3)^2+\dfrac{1}{2}\pi (2.5)^2\)

\(Area=\dfrac{1}{2}\pi (9)+\dfrac{1}{2}\pi (6.25)\)

\(Area=14.137167+9.817477\)

\(Area=23.954644\)

Round the value to the nearest tenth (one decimal place.

\(Area\approx 24.0\)

Therefore, the area of given figure is 24.0 sq. cm.

Answer:

i think c

Step-by-step explanation:

Answer: I think it's P.E.M.D.A.S

Step-by-step explanation:

Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;

60° + 70° + y = 180°

130° + y = 180°

y = 180° - 130°

y = 50°

Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.

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Answer:

3 feet

Step-by-step explanation:

From the option available the measurement 1 meter is equal to 100 centimeters.

The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

given the measurement is 1 meter

1 meter is equal to 100 centimeters

From unit conversion:

1 meter is also equal to 3.2808 feet

1 meter is also equal to 39.3701 inch

1 meter is also equal to 1000 millimeters

1 meter is also equal to 1.093 yards.

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Complete question:

Answer:

Step-by-step explanation:

"Quadrilateral ABCD is a square. Explanation: Quadrilateral ABCD has four ninety-degree angles, meaning it has four right angles because every right angle measures ninety degrees. A quadrilateral with four right angles must be a rectangle by the definition of a rectangle."

The true statement about hypothesis testing is that option "c. If the test statistic is more extreme than the p-value, then we reject the null hypothesis."

In hypothesis testing, we evaluate whether there is enough evidence to support rejecting the null hypothesis in favor of the alternative hypothesis. The test statistic measures the strength of the evidence against the null hypothesis. The p-value, on the other hand, represents the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

If the test statistic is more extreme than the p-value, it means that the evidence against the null hypothesis is strong. In such cases, we reject the null hypothesis because the observed data is unlikely to occur under the assumption that the null hypothesis is true. This leads us to accept the alternative hypothesis instead.

It is important to note that hypothesis testing does not prove or disprove the truth of the null hypothesis or alternative hypothesis definitively. Instead, it provides statistical evidence to support one hypothesis over the other based on the observed data and the chosen significance level (alpha). The significance level (alpha) determines the threshold at which we consider the evidence strong enough to reject the null hypothesis.

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the area of the regular heptagon is approximately 865.125 cm² when X = 9 cm and a = 11 cm.To find the area of the regular heptagon, we can use the formula:

Area = (perimeter x apothem) / 2

The perimeter of a regular heptagon is given by:

Perimeter = 7 x side length

Since all sides of a regular heptagon are equal, we can find the length of one side by using the apothem:

Side length = 2a x tan(π/7)

Substituting the given values, we get:

Side length = 2 x 11 cm x tan(π/7) ≈ 22.5 cm

Now, we can find the perimeter:

Perimeter = 7 x 22.5 cm = 157.5 cm

Finally, substituting the values of the apothem and perimeter in the formula for area, we get:

Area = (157.5 cm x 11 cm) / 2 ≈ 865.125 cm²

Therefore, the area of the regular heptagon is approximately 865.125 cm² when X = 9 cm and a = 11 cm.

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Answer:

A= 10B/3 +4

Step-by-step explanation:

If Argyle says that she has collected data that only tell her whether the cases are the same or different, one can accurately say that she has collected data on the nominal level.

The nominal level of measurement is the least strict type of data measurement in which the measurements or observations are grouped into distinct categories without a specific order or value structure. At this stage of measurement, variables are defined as categorical because the groups and categories can only be counted, which is usually done using frequencies and proportions.

The nominal level of measurement can take the form of either binary or multichotomous. Binary variables have only two groups, while multichotomous variables have more than two groups. Variables that are frequently used in this level of measurement include gender, race, or political affiliations.

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99% Confidence Interval for the Population Percentage of Defective Disks = (0.1004, 0.1196).

Rules for Decimals. Align up the decimal points. To ensure that every one of the values have the same number of places following the decimal, add 0s. Add the same way you would with complete numbers.

Step 1:

Sample Size: n=7002

Number of non-defective disks =6232

Number of defective disks: x = 7002-6232=770

Sample proportion \(\widehat{p}\) = x/n = 770/ 7002 = 0.110

Estimated proportion of disks which are defective: Sample proportion: \(\widehat{p}\) = 0.110

Step 2:

Range of confidence for the population proportion:

\(=\widehat{p}\pm z_{\alpha /2}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

\(\alpha = (100-99)/100 = 0.01; \alpha/2 = 0.005\)

99% Confidence interval =

\(=\widehat{p}\pm z_{0.005}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

from standard normal tables z0.005 = 2.58

99% Confidence Level for the Population Percentage of Defective Disks =

\(=\widehat{p}\pm z_{0.005}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

\(=0.11\pm 2.58\sqrt{(0.11(1-0.11))/7002}\)

\(=0.11\pm 2.58\sqrt{(0.110\times 0.89)/7002}=0.11\pm 2.58\sqrt{\frac{0.0979}{7002}}\)

\(=0.11\pm 2.58\times 0.0037 = 0.11\pm 0.0096 =(0.1004, 0.1196)\)

99% Confidence interval for population proportion of disks which are defective= (0.1004, 0.1196).

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Answer:

the decimal is 0.375

And the percentage of it would be 37.5(just adding that because why not)