45 equals the quotient of a number n and 3

Answer: At the end of May, there will be $372.

Explanation:

Since we have given that

On the first day of May, each one save =$0.25

Number of friends = 3

Total save on the first day of May is given by

[tex]0.25\times 3=\$0.75[/tex]

Similarly,

On the second day of May, each one save =$0.25

Total save on the second day of May is given by

[tex]0.50\times 3=\$1.5[/tex]

Similarly,

On the third day of May, each one save =$0.25

Total save on the third day of May is given by

[tex]0.75\times 3=\$2.25[/tex]

This series becomes arithmetic progression,

[tex]0.75,1.5,2.25......[/tex]

Here, a = 0.75

d=common difference is given by

[tex]d=a_2-a_1=1.5-0.75=0.75\\d=a_3-a_2=2.25-1.5=0.75[/tex]

Since there are 31 days in the month of May,

So, n=31

We need to calculate the sum of 31 terms to get our answer,

[tex]S_n=\frac{n}{2}(2a+(n-1)d)\\\\S_{31}=\frac{31}{2}(2\times 0.75+(31-1)\times 0.75)\\\\=\frac{31}{2}(1.5+30\times 0.75)\\\\=\frac{31}{2}(24)\\\\=31\times 12\\\\=\$372[/tex]

Hence, at the end of May, there will be $372.

The total amount in the fund at the end of May is 239.25.

To find the total amount of money in the fund at the end of May, we need to calculate the sum of the money put into the fund on each day. The students decide to put 0.25 on the first day, 0.50 on the second day, 0.75 on the third day, and so on. This is an arithmetic sequence, where the first term (a) is 0.25 and the common difference (d) is 0.25. The formula to find the sum of an arithmetic sequence is:

S = (n/2)(2a + (n-1)d)

In this case, n = 31 (since there are 31 days in May), a = 0.25, and d = 0.25. Plugging these values into the formula, we get:

S = (31/2)(2 * 0.25 + (31-1) * 0.25) = 239.25

Therefore, at the end of May, there will be 239.25 in their fund.

Answer:

16 years

Step-by-step explanation:

Given,

Number of students in group A = X,

Sum of their ages = 221,

So, the average age of students in group A = [tex]\frac{\text{Sum of ages}}{\text{Total students}}[/tex]

[tex]=\frac{221}{X}[/tex]

According to the question,

[tex]\frac{221}{X}=\text{Integer}[/tex]

∴ X must be a factor of 221,

∵ 221 = 13 × 17,

Now, If X = 13,

Then the number of students in group B = 26 ( NOT POSSIBLE )

If X = 17,

Then the number of students in group B = 34

Which is between 30 and 40,

Now, Let S be the sum of ages of students in group B,

So, the average age in group B = [tex]\frac{S}{34}[/tex]

Again according to the question,

[tex]\frac{S+221}{17+34}=\frac{S}{34}-1[/tex]

[tex]\frac{S+221}{51}=\frac{S-34}{34}[/tex]

[tex]34S+7514 = 51S - 1734[/tex]

[tex]34S - 51S = -1734 - 7514[/tex]

[tex]17S = 9248[/tex]

[tex]\implies S = 544[/tex]

Therefore, the average age of B = [tex]\frac{544}{34}[/tex] = 16 years.

Answer:

x + 3 is a factor of the polynomial.

Step-by-step explanation:

We have been given that p(x) is a polynomial with integer coefficient.

Also p(-3)=0

Since, p(-3) =0, hence, we can say that -3 is a zero of the polynomial.

Now, we apply factor theorem.

Factor Theorem: If 'a' is a zero of a function f(x) then (x-a) must be a factor of the function f(x).

Applying this theorem, we can say that (x+3) must be a factor of the polynomial.

Hence, first statement must be true.

Answer:  The correct option is (A) (x + 3) is a factor of the polynomial.

Step-by-step explanation:  Given that p(x) is a polynomial with integer coefficients and p(-3)=0.

We are to select the true statement from the given options.

Factor Theorem:  If q(x) is a polynomial with integer coefficients and q(a) = 0, then (q - a) will be a factor of q(x).

Here, it is given that

p(x) is a polynomial with integer coefficients and p(-3) = 0.

Therefore, by Factor theorem, we can say that (x-(-3)), ie., (x + 3) is a factor of the polynomial p(x).

Thus, (x + 3) is a factor of the polynomial.

Option (A) is CORRECT.

The average daily balance for the given billing cycle is calculated by summing the product of each daily balance and the length of time it was held, and then dividing by the number of days in the billing cycle. After doing this, the average daily balance comes out to be $755.17.

The subject of this question is finance and it involves calculating the average daily balance for a billing cycle. In this method, the daily outstanding balances are added together and then divided by the total number of days in the billing period.

Here, the billing cycle lasts for 29 days, from 4/17 to 5/17.

Like this, you calculate the balance for each portion of the billing cycle, then multiply each by the number of days that balance was held, add those up, and finally, divide by the number of days in the billing cycle:

((1100*10) + (400*2) + (700*8) + (640*11)) / 29 = $755.17

Therefore, the average daily balance is $755.17.

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Answer:

C

Step-by-step explanation:

Answer:

-3-6i/5 is the answer it was also correct on the test ! :D

Answer:

The System of inequality is ,

1. y > 2 x + p

2. y < 2 x + p

Suppose we assign some values to p and q and draw its graph

And, then the inequality sign on both inequalities is reversed

3. y < 2 x + p

4. y > 2 x + p

And , then draw it's graph

it has been found that, the solution set of both the inequality remains same.That is there is no point or set of points , which satisfy both the system of inequality.

The system has no solution.

Answer:

There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.

Step-by-step explanation:

edge - 2023 :)

In a scatterplot that depicts an exponential model, the data points will form a curve that resembles the shape of an exponential function.

In a scatterplot that depicts an exponential model, the data points will form a curve that resembles the shape of an exponential function. The x-axis represents the independent variable, while the y-axis represents the dependent variable. As the x-values increase, the corresponding y-values will increase at an exponential rate. For example, if we are graphing the growth of a population over time, the scatterplot will show the population size increasing rapidly as time progresses.

On a scatterplot depicting an exponential model, the data points are represented as points on a curvy line. The correct answer is option D) points on a curvy line.

In a scatterplot depicting an exponential model, the data points typically form a curvy line. Exponential relationships show rapid growth or decay, which is reflected in the scatterplot as a smooth, non-linear curve.

As the independent variable increases, the dependent variable changes exponentially, resulting in data points that do not lie along a straight line but instead form a distinctive curve. This curve can either rise sharply or decrease rapidly, depending on whether the exponential function involves growth or decay.

For instance, in exponential growth, the data points start small and then rapidly increase, forming a curve that steepens over time. Conversely, in exponential decay, the data points start large and decrease rapidly, forming a curve that flattens out as it approaches zero.

Therefore, on a scatterplot representing an exponential model, the data points are typically observed to form a curvy line, as seen in option **D)**.

Complete question : How is the data represented on a scatterplot that depicts an exponential model?

A) points on a line

B) random points

C) points on a horizontal line

D) points on a curvy line

The maximum height the football reaches is 147 feet, and it takes 3 seconds for the football to reach that height. To determine when the football is above 122 feet, the equation is set equal to 122 and solved for time t.

To find the maximum height reached by the football, we need to determine the vertex of the parabolic function given by y = -[tex]16t^2[/tex] + 96t + 3. Since the coefficient of [tex]t^2[/tex]is negative, the parabola opens downwards, and the vertex will give us the maximum height.

To find the time at which the maximum height occurs, use the formula t = -b/2a, where a is the coefficient of [tex]t^2[/tex] and b is the coefficient of t.

In this equation, a = -16 and b = 96, so t = -96/(2 x -16) = 3 seconds. Plugging this back into the original equation gives us the maximum height: y = -16[tex](3)^2[/tex] + 96(3) + 3 = 147 feet.

To determine when the football is above 122 feet, we set the equation equal to 122 and solve for t:

122 = -[tex]16t^2[/tex] + 96t + 3. We simplify and solve the quadratic equation, which may yield two possible times, one during the ascent and one during the descent of the football's path.

The equation that represents the profit for the month is: y = 33.09x - (2,137.00 + 15.15x).

The ongoing expenses incurred from the normal day-to-day operations of a business are referred to as operating costs.

The equation that represents the profit for the month is:

y = 33.09x - (2,137.00 + 15.15x)

This equation takes into account the revenue generated by selling x units, which is 33.09x, and subtracts the total cost of producing those x units, which is (2,137.00 + 15.15x). The result is the total profit generated for the month.

We can simplify the equation by combining like terms:

y = 17.94x - 2,137.00

This equation can be used to determine the total profit for any given number of units produced.

The coefficient of x (17.94) represents the profit generated per unit sold, and the constant term (-2,137.00) represents the fixed costs that must be subtracted from the revenue to calculate the profit.

Therefore, the correct equation is y = 33.09x - (2,137.00 + 15.15x), because it takes into account both the revenue and the total costs associated with producing x units.

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Answer:

y = (x + 1)^2

Step-by-step explanation:

I used desmos and put each answer choice into the graphing calculator and answer choice D was the only one that matched with the image in the question.

Random sample - choosing a sample so that every member has an equal chance of being chosen (this is the absolute definition of random sampling)

Sample - a portion of a large group is termed as a sample.

Biased sample -  choosing a sample from people who are under 15 years old (biased sampling states that all the members of a group are not included in survey)  

Estimating from a sample - using the responses of a small group to make conclusions about the large group.(estimation means roughly judging something based on some sample )

If m∠CXP = 106.02°, m∠SYD is 73.98°. Among the given ones the correct option is 1.

In geometry, a transversal is a line that intersects two or more other lines in a plane.

When a transversal intersects two parallel lines, it forms a set of eight angles, including alternate interior angles, alternate exterior angles, corresponding angles, and consecutive interior angles.

If the lines PQ←→ and RS←→ are parallel, then the alternate interior angles formed by transversal CD←→ are congruent. Therefore, we have:

m∠CXP = m∠DYX (alternate interior angles)

m∠CXD + m∠DXP = 180° (linear pair)

We can use these two equations to find m∠SYD. First, we need to find m∠CXD, which is the same as m∠YXC because they are vertical angles. We know that:

m∠CXP = 106.02°

So, we can use the linear pair equation to find m∠DXP:

m∠CXD + m∠DXP = 180°

m∠DXP = 180° - m∠CXD

Substituting m∠CXD = m∠YXC, we get:

m∠DXP = 180° - m∠YXC

Now, using the alternate interior angles equation, we can replace m∠CXP with m∠DYX:

m∠DYX = m∠CXP = 106.02°

Finally, we can use the linear pair equation again to find m∠SYD:

m∠DYX + m∠SYD = 180°

m∠SYD = 180° - m∠DYX

m∠SYD = 180° - 106.02°

m∠SYD = 73.98°

Therefore, m∠SYD is 73.98°, i.e., option 1.

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