What is the amount of money in an account at the end of 5 years if the
initial deposit is $10,000 and the interest is compounded continuously
at a rate of 6.75% per year?

Answer: yes

Step-by-step explanation:

There are three students in Mrs. Johansen's class who like sightseeing. We cannot estimate the total number of students in the class based solely on this information.

It is not possible to accurately predict the total number of students in Mrs. Johansen's class based on the information provided. However, we can make an estimate based on the assumption that the three students who responded to the survey are representative of the entire class.

It is impossible to create an accurate projection of the total number of pupils in Mrs. Johansen's class without knowing more about the survey or the class.

However, assuming that the survey was distributed to all students in the class, we may create an approximation based on the proportion of students who stated that their favourite holiday was sightseeing. For example, if we believe that the three students who stated that their favourite holiday was touring reflect 25% of the whole class (i.e., one-fourth of the class), we may estimate that the class has about 12 students.

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The given question is incomplete. the complete question is given below:

If three students in Mrs. Johansen's class said their favourite vacation was sightseeing, what is a reasonable estimate for the total number of students in her class based on this survey?

The type of data collected is Quantitative Data.

Quantitative data is a type of numerical data that is collected through methods such as measurements, surveys, or experiments. It involves numerical values that can be measured and analyzed using statistical techniques. This data can be further classified as discrete or continuous.

Discrete quantitative data consists of countable values that can be expressed in whole numbers, such as the number of people in a room, the number of cars in a parking lot, or the number of books in a library.

Continuous quantitative data consists of measurements that can take on any value within a range, such as weight, height, temperature, or time. Continuous data can be further divided into interval and ratio data, depending on the level of measurement and the presence or absence of a true zero point.

The data collected by the usher, which is the number of unoccupied seats in the movie theater, is a type of quantitative data. It involves numerical values that can be measured and analyzed mathematically.

#Complete Question - an usher records the number of occupied seats in a movie theater during each viewing of a film. identify the type of data collected.

(a) Quantitative data

(b) Qualitative data

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Answer:

51

Step-by-step explanation:

Because 5.1 times ten equals 51 because if you times ten by 5 u get 50 and then do .1 times ten you get 1

Answer:

"sixty-three hundredths of a Kilometer"

Step-by-step explanation:

Decimal measurements are read based on the place of their digits. In this case, Ajay would read this measurement as "sixty-three hundredths of a Kilometer". This is because the final digit of the decimal form measurement is in the "hundredths" position. One more to the right and it would be in the "thousandths" while one more to the left would be the "tenths"

Answer: 3750

Step-by-step explanation:

Answer: When viewed from the side, the spire forms an isosceles triangle m, the area of the isosceles triangle is equal to  1/4b√4a²-b².

Step-by-step explanation:

What is isosceles triangle?

A triangle with two equal-length sides is said to be isosceles. The triangle's third side is referred to as the base, while the triangle's two equal sides are known as the legs. The triangle's legs are usually shorter than the base, which is usually the triangle's longest side.

To determine if the spire on top of a building forms an isosceles triangle when viewed from the side, we first need to define the three sides of the triangle. Let's call the two sides that are equal in length "s" and the third side "l".

Next, we need to determine if the triangle satisfies the definition of an isosceles triangle. The two sides "s" of the spire must therefore be of equal length for the spire to create an isosceles triangle.

To confirm this, we can measure the length of the sides "s" and compare them to each other. If they are equal in length, then the spire forms an isosceles triangle. If they are not equal in length, then the spire does not form an isosceles triangle.

For example, if the base of the triangle is 10 feet and the length of the two equal sides is 10 feet, then the triangle is isosceles. Therefore, the spire on the top of the building forms an isosceles triangle when viewed from the side.

Therefore, if the two sides "s" of the spire are equal in length, then the spire forms an isosceles triangle when viewed from the side.

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An isosceles triangle is a triangle with two sides of equal length and two equal angles.

What is isosceles triangle?

An isosceles triangle is a type of triangle that has two sides of equal length and two angles of equal measure. The two sides of equal length are the two legs of the triangle, while the third side is called the base. The angles opposite the two equal sides are equal in measure, while the angle opposite the base is the third angle. Isosceles triangles are classified according to the measure of their angles. An equilateral triangle is an isosceles triangle with all angles equal to 60°. An isosceles triangle with two angles equal to 45° is called an isosceles right triangle. An isosceles triangle with two angles equal to less than 45° is referred to as an acute isosceles triangle, while an isosceles triangle with two angles equal to more than 45° is referred to as an obtuse isosceles triangle. Isosceles triangles have many practical uses in engineering and architecture. For example, buildings and bridges often feature isosceles triangles in their roofs and arches in order to provide strength and stability.

When viewed from the side, the spire on the top of a building forms an isosceles triangle because it has two equal sides (the sides running up the spire) and two equal angles (the angles at the base of the spire).

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When 5.50 g of NO reacts, we can expect to produce approximately 8.42 grams of NO₂ according to the balanced equation 2NO + O₂ → 2NO₂.

To determine the grams of NO₂ produced when 5.50 g of NO reacts completely, we need to use stoichiometry and the molar ratios from the balanced equation.

From the balanced equation: 2NO + O₂ → 2NO₂, we can see that the stoichiometric ratio between NO and NO₂ is 2:2, meaning that for every 2 moles of NO, 2 moles of NO₂ are produced.

To begin, we need to convert the given mass of NO (5.50 g) to moles. The molar mass of NO is 30.01 g/mol (14.01 g/mol for nitrogen + 16.00 g/mol for oxygen).

Number of moles of NO = mass of NO / molar mass of NO = 5.50 g / 30.01 g/mol ≈ 0.183 mol.

Since the stoichiometric ratio is 2:2, we know that 2 moles of NO produce 2 moles of NO₂. Therefore, 0.183 mol of NO will produce 0.183 mol of NO₂.

Next, we convert the moles of NO₂ to grams. The molar mass of NO₂ is 46.01 g/mol (14.01 g/mol for nitrogen + 2 * 16.00 g/mol for oxygen).

Mass of NO₂ = moles of NO₂ * molar mass of NO₂ = 0.183 mol * 46.01 g/mol ≈ 8.42 g.

Therefore, when 5.50 g of NO reacts completely, we can expect to produce approximately 8.42 grams of NO₂.

The correct answer is: b. 8.43 grams.

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Therefore, the correct inequality to find the domain is simply x - 3 < 0, which simplifies to x < 3.

To find the domain of a function, we need to determine all the values of the independent variable (usually represented by x) that the function is defined for. In this case, the function is defined as f(x) = x - 3, which means we can plug in any value of x into the expression x - 3 to get a corresponding value of f(x).

However, there are some values of x that would cause the expression x - 3 to be undefined. For example, if we were trying to find f(x) when x = 2, we would get f(2) = 2 - 3 = -1, which is a valid output. But if we were trying to find f(x) when x = 3, we would get f(3) = 3 - 3 = 0/0, which is undefined.

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Answer:

First do \(\frac{12-6}{4-2}\), then simplify it into \(\frac{6}{2}\), then, divide 6 by 2 to get 3. 3 is your rate of change.

Formula for slope/rate of change: \(\frac{y2-y1}{x2-x1}\)

Hope this helped!

Answer:

9.5

Step-by-step explanation:

Answer: I don't know the triangle if there n picture

Step-by-step explanation:

The maximum height is 20 yards and the total horizontal distance is 36 yards, which is the distance between the point (2, 0) and (38, 0).

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have:

The blackbird starts his flight path from (2, 0). His flight path reaches a maximum height of 20 yards and lands at point (38, 0).

Here the bird path will be a parabola with a maximum height of 20 yards.

The total horizontal distance traveled by the bird = The distance between the points (2, 0) and (38, 0)

= √(38-2)²

= 36 yards

Thus, the maximum height is 20 yards and the total horizontal distance is 36 yards, which is the distance between the point (2, 0) and (38, 0).

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Answer:

\( P(t_{16}>2.583)\)

And for this case we can use the complement rule and we got:

\(P(t_{16}>2.583)= 1- P(t_{16} <2.583)\)

And if we use the t- table with df =16, we got:

\(P(t_{16}>2.583)= 1-0.990= 0.01\)

Step-by-step explanation:

For this case we know that the degrees of freedom are given:

\( df = n-1= 16\)

And we want to find the following probability:

\( P(t_{16}>2.583)\)

And for this case we can use the complement rule and we got:

\(P(t_{16}>2.583)= 1-P(t_{16} <2.583)\)

And if we use the t-table with df =16, we got:

\(P(t_{16}>2.583)= 1-0.990= 0.01\)

A scatter plot in Excel is the type of chart that can plot a point at its Cartesian coordinates using an x-coordinate and a y-coordinate.

The type of chart in Excel that plots a point at its Cartesian coordinates using an x-coordinate and a y-coordinate is a Scatter Plot. A scatter plot is a type of graph in which individual data points are represented by dots on a graph. Each data point has two coordinates: the x-coordinate and the y-coordinate, which are used to plot the point on the graph.

In Excel, to create a scatter plot, you need to first select your data, then go to the Insert tab and click on the Scatter chart button. You can then choose the type of scatter plot you want to create. Once the chart is created, you can add data labels to show the x-coordinate and y-coordinate of each data point.

In summary, a scatter plot in Excel is the type of chart that can plot a point at its Cartesian coordinates using an x-coordinate and a y-coordinate.

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Answer:

y=2x+6

y=2x+6

Explanation:

Given the equation:

The equation written as a system of equations is:

Opening the bracket in the first equation gives:

The equation rewritten as a Bernoulli equation is y = 1/∛(-2t - (1/3)t^3 + C), where C is the constant of integration.

1.1) To solve the given first-order differential equation using the substitution y = vt:

Substituting y = vt into the equation dy/dt = 2y^2 + t^2:

dv/dt * t = 2(vt)^2 + t^2.

Expanding the equation:

t * dv/dt = 2v^2t^2 + t^2.

Dividing both sides by t:

dv/dt = 2v^2t + t.

Now, we have a separable differential equation. We can rewrite it as:

dv/v^2 = 2t dt.

Integrating both sides:

∫(dv/v^2) = 2∫t dt.

This simplifies to:

-1/v = t^2 + C,

where C is the constant of integration.

Solving for v:

v = -1/(t^2 + C).

Substituting y = vt:

y = -t/(t^2 + C).

Therefore, the general solution for y using the substitution y = vt is y = -t/(t^2 + C), where C is an arbitrary constant.

1.2) To rewrite the equation as a Bernoulli equation:

The given differential equation is:

dy/dt = 2y^2 + t^2.

We can rewrite it in the form of a Bernoulli equation by dividing both sides by y^2:

dy/y^2 = 2 + t^2/y^2.

Now, we introduce a substitution u = 1/y:

du = -dy/y^2.

Substituting this into the equation:

-du = 2 + t^2(u^2).

Rearranging the equation:

du/u^2 = -(2 + t^2) dt.

This is now a Bernoulli equation, where n = -2.

To solve the Bernoulli equation, we can introduce a substitution v = u^(1-n) = u^3:

dv = (1-n)u^(n-1) du.

Substituting this into the equation:

dv = 3u^2 du.

Our equation now becomes:

3u^2 dv = -(2 + t^2) dt.

Integrating both sides:

∫3u^2 dv = -∫(2 + t^2) dt.

This simplifies to:

u^3 = -2t - (1/3)t^3 + C,

where C is the constant of integration.

Substituting back u = 1/y:

(1/y)^3 = -2t - (1/3)t^3 + C.

Taking the reciprocal of both sides:

y = 1/∛(-2t - (1/3)t^3 + C).

Therefore, the equation rewritten as a Bernoulli equation is y = 1/∛(-2t - (1/3)t^3 + C), where C is the constant of integration.

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Answer: C. 15x25=375 meters^2

Step-by-step explanation: multiply the two numbered sides.

Answer:

121°

Step-by-step explanation:

These are supplemental angles.  a straight angle is 180 degrees.

180 - 59 = 121

Answer: m2=121 degrees

Step-by-step explanation:

m1+m2=180 ==> m1 and m2 are on a straight line. Straight lines measure 180 degrees and are called straight angles. m1 and m2 are supplementary angles, so they add up to 180 degrees.

59+m2=180

59-59+m2=180-59

m2=180-59

m2=121 degrees

Answer:

80 hope this helps!

Step-by-step explanation:

Answer:

k < -1 or k > 11

Step-by-step explanation:

Given quadratic equation:

\(3x^2-x+ k = kx-1\)

First, rearrange the given quadratic equation in standard form ax² + bx + c = 0:

\(\begin{aligned}3x^2-x+ k &= kx-1\\3x^2-x+ k-kx+1&=0-kx+1\\3x^2-x-kx+ k+1&=0\\3x^2-(1+k)x+ (k+1)&=0\end{aligned}\)

\(3x^2-(1+k)x+ (k+1)=0\)

Comparing this with the standard form, the coefficients a, b and c are:

\(\boxed{\begin{minipage}{7 cm}\underline{Discriminant}\\\\$\boxed{b^2-4ac}$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}\)

If the quadratic equation has two distinct roots, its discriminant is positive.

\(b^2-4ac > 0\)

Substitute the values of a, b and c into the discriminant:

\((-1 - k)^2-4(3)(k+1) > 0\)

Simplify:

\((-1 - k)(-1-k)-12(k+1) > 0\)

\(1+2k+k^2-12k-12 > 0\)

\(k^2+2k-12k+1-12 > 0\)

\(k^2-10k-11 > 0\)

Factor the left side of the inequality:

\(k^2+k-11k-11 > 0\)

\(k(k+1)-11(k+1) > 0\)

\((k-11)(k-1) > 0\)

If we graph the quadratic k² - 10k - 11, it is a parabola that opens upwards (since its leading coefficient is positive), and crosses the x-axis at k = -1 and k = 11. Therefore, the curve will be positive (above the x-axis) either side of the x-intercepts, so when k < -1 or k > 11.

Therefore, the range of values of k for which the given quadratic equation has two distinct roots is:

\(\boxed{k < -1 \; \textsf{or} \;k > 11}\)

Answer:

22%.

Step-by-step explanation:

7/25 = 28%

0.09 = 9%

2/5 = 40%

29% + 9% + 40% = 78%

100% - 78% = 22%

And you have your answer. Hope this helped.

The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)

From the question, we have the following expression that can be used in our computation:

–3(2x – 5) < 5(2 – x)

Divide bot sides of the inequality by -1

So, we have the following representation

3(2x – 5) > -5(2 – x)

Next, we open the brackets

This gives

6x – 15 > -10 + 5x

Hence, the representation is 6x – 15 > -10 + 5x

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Complete question

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

(a) 6x – 15 > -10 + 5x

(b) 6x – 15 < -10 + 5x

(c) 3(2x – 5) > -5(2 – x)

(d) 3(2x – 5) < -5(2 – x)

Answer: 1/7

Step-by-step explanation:

You can add 4+5+3+2 to get 14, and 2/14 can be simplified to 1/7

Answer:

Option B

Step-by-step explanation:

After each round of the tournament one-fourth players are eliminated.

That means the process of elimination will represent the exponential decay.

Equation of exponential decay is given by the expression,

\(y=a(1-r)^n\)

Here, a = Initial number of players

r = Fraction of reduction in the number of players

y = Final number of players

n = Number of rounds

In the given question,

Initial number of the players (a) = 64

Fraction of reduction in the number of players (r) = \(\frac{1}{4}\)

                                                                             = 0.25

Number of rounds (n) = 6

By substituting these values in the expression,

\(y=64(1-0.25)^6\)

Therefore, Option B is the answer.

The given equation "x=y√−1" seems to be incomplete or contains a typographical error.

To calculate the area bounded above by the curve x=y√−1 and x=−59y^7 and below by the x-axis, we need to find the limits of integration and set up the definite integral.

First, we need to find the intersection points of the two curves. Equating y√−1 and −59y^7, we can solve for y to find the y-values at the intersection points. Then we can set up the integral as the definite integral from the lower limit to the upper limit of the curve y√−1. The limits of integration will be the y-values of the intersection points.

Once we have set up the integral, we can integrate the function y√−1 with respect to y and evaluate the result. This will give us the area bounded above by the curve x=y√−1 and x=−59y^7 and below by the x-axis.

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