A garden hose can fill a swimming pool in 4 days and a larger hose can fill the pool in 2 days. How long will it take to fill the pool if both the hoses are used?

Answer:

5

Step-by-step explanation:

Plug in 24 for x in your g(x) equation.

[tex]g(24)=\sqrt{24-8} \\g(24)=\sqrt{16} \\g(24)=4[/tex]

Next, plug in your g(x) value, 4, to your f(x) equation for x.

[tex]f(4)=2(4)-3\\f(4)=8-3\\f(4)=5[/tex]

Answer:

See explanation.

Step-by-step explanation:

Part C)

[tex]5+(-10)[/tex]

When adding a positive to a negative, the result will be the sign of the larger absolute value. In this case, 10 is greater than 5, so the result will be negative.

Adding a negative is also the same thing as subtracting a positive.

[tex]5+(-10)\\5-10\\-5[/tex]

For your second problem, 5 is larger than 3, so the result will be positive.

[tex]5+(-3)\\5-3\\2[/tex]

-----

When adding a positive to another positive, the result will be positive.

[tex]5+3\\8[/tex]

When adding a number to zero, the answer will always be the number.

[tex]5+0\\5[/tex]

Part D)

When multiplying a positive times a negative, the result will always be negative.

[tex]5*(-10)\\-50[/tex]

[tex]5*(-3)\\-15[/tex]

-----

When multiplying a positive times a positive, the result will always be positive.

[tex]5*10\\50[/tex]

When multiplying a positive or a negative times zero, the result will always be zero.

[tex]5*0\\0[/tex]

Answer:

A) Apples: $30x

    Cherry: $40y

B) ($30x)+($40y)=600

The simplified expression for [tex]\((5 \cdot x^3) / (x^2)\) is \(5 \cdot x\).[/tex]

When x = 2, the result is [tex]\(5 \times 2 = 10.[/tex]

The answer is 10.

To evaluate the expression[tex]\((5 \cdot x^3) / (x^2)\) for \(x = 2\),[/tex]  we first need to simplify the given expression.

Given:

[tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]

Simplifying, we divide the powers of x :

[tex]\[ x^3 / x^2 = x^{3-2} = x^1 = x. \][/tex]

So the expression simplifies to:

[tex]\[ 5 \cdot x. \][/tex]

Now substitute x = 2 :

[tex]\[ 5 \cdot 2 = 10[/tex]

Thus, the value of [tex]\((5 \cdot x^3) / (x^2)\) when \(x = 2\)[/tex] is: 10.

Question : Evaluate the expression [tex]\[ \dfrac{5 \cdot x^3}{x^2} \][/tex]for  x = 2.​ start fraction, 5, dot, x, cubed, divided by, x, squared, end fraction for x=2x=2x, equals, 2.

Answer:

Option 2: Yes, the distance from (-2,0) to (1,√7) is 4 units

Step-by-step explanation:

The point is:

(1,√7)

If the point lies on the circle, then the distance of point and the center of circle should be equal to the radius of the circle.

The radius can be viewed from the diagram that it is 4 units.

The center is: (-2,0)

Now, distance:

[tex]d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}}\\ d = \sqrt{(-2-1)^{2}+ (0-\sqrt{7} )^{2}}\\ d = \sqrt{(-3)^{2}+ (-\sqrt{7} )^{2}}\\=\sqrt{9+7}\\ =\sqrt{16}\\ =4[/tex]

Hence, option 2 is correct ..

Answer:

18 stamp increase

15 % increase

Step-by-step explanation:

To find the increase in number , we take the number of stamps in march and subtract the stamps in october

128-120 = 18

To find the percent increase, we take the number of stamps that we gained over the original amount of stamps * 100%

percent increase = 18/120 * 100%

                              .15 * 100%

                              15% increase

Myra's stamp collection increased by 18 stamps from October to the following March. This is calculated by subtracting the number of stamps she had in October (120 stamps) from the number she had in March (138 stamps).

To find out by how much Myra's stamp collection has increased between October and March, you simply need to subtract the number of stamps she had in October from the number she had in March. She had 120 stamps in October, and by March, she had 138 stamps.

To calculate the increase, we'll use the following steps:

Doing the math:

138 stamps (in March) - 120 stamps (in October) = 18 stamps

So, Myra's collection increased by 18 stamps between October and March.

Answer:

  $26.40

Step-by-step explanation:

For a linear function, the mean of the function is the function of the mean:

  20 + 2.00·μX = 20 + 2.00·3.2 = 20 + 6.40 = 26.40 . . . . dollars

The mean total amount collected per car entering the Safari Adventure Theme Park is $26.40.

The mean of the total amount of money collected per car entering the park can be calculated by finding the expected value of the total amount, considering the price per car and per person. In this case, the mean total amount collected per car = price per car + (mean number of people per car) * price per person. Substituting the given values: 20 + 3.2 * 2 = $26.40.

Answer:

Step-by-step explanation:

Because 48 and 89 have the same sign, that is, the negative sign, their sum takes on that sign:

 -48

 -89

---------

 -137

Answer:

C

Step-by-step explanation:

An angle whose vertex lies on a circle and whose sides are 2 chords of the circle is one half the measure of the intercepted arc.

arc CED is the intercepted arc, hence

arc CED = 2 × 99° = 198°

Answer:

C) 198

Step-by-step explanation:I took the test

For this case, we have by definition that:

[tex]C = (F-32) * \frac {5} {9}[/tex]

If they tell us that the base temperature is 50 degrees Fahrenheit, then we substitute:

[tex]C = (50-32) * \frac {5} {9}\\C = 18 * \frac {5} {9}\\C = 2 * 5\\C = 10[/tex]

Finally, the temperature equals 10 degrees Celsius.

Answer:

10 degrees Celsius

The temperature in Celsius when it is 50 degrees Fahrenheit is 10 degrees Celsius, calculated using the conversion formula Celsius = (Fahrenheit - 32) × 5/9.

To convert a temperature from Fahrenheit to Celsius, we use the formula: Celsius = (Fahrenheit - 32) × 5/9. If the temperature is 50 degrees Fahrenheit, we subtract 32 from 50, giving us 18. Then we multiply 18 by 5/9, resulting in 10. Therefore, the temperature in Celsius is 10 degrees Celsius.

Thus, when the temperature is 50°F, it is equivalent to 10°C.

Answer:

y = 500(1.05)^x.

Step-by-step explanation:

551.25 = 500x^2    where x is the multiplier for each year.

x^2 = 551.25/500

x =  1.05

So the value after x years is 500(1.05)^x.

Answer: [tex]y=500(1.05)^x[/tex]

Step-by-step explanation:

The exponential growth equation is given by :-

[tex]y=A(1+r)^x[/tex]              (1)

, where A is the initial value of ,  r is the rate of growth ( in decimal) and t is the time period ( in years).

Given : The value of a collector’s item is expected to increase exponentially each year.

The item is purchased for $500. After 2 years, the item is worth $551.25.

Put A= 500 ;  t= 2 and y= 551.25 in (1), we get

[tex]551.25=500(1+r)^2\\\\\Rightarrow\ (1+r)^2=\dfrac{551.25}{500}\\\\\Rightarrow (1+r)^2=1.1025[/tex]    

Taking square root on both sides , we get

[tex]1+r=\sqrt{1.1025}=1.05\\\\\Rightarrow\ r=1.05-1=0.5[/tex]

Now, put A= 500 and r= 0.5 in (1), we get the equation represents y, the value of the item after x years as :

[tex]y=500(1+0.5)^x\\\\\Rightarrow\ y=500(1.05)^x[/tex]    

Answer:

Step-by-step explanation:

when logs are added, they can be multiplied to produce a simplified log.

log_5(4*7) + log_5(2)

log_5(4*7*2)

log_5(56)

Answer:

1/3 = .33

THE UNIT RATE IS 1 TO 3

Answer:

infinite slope

Step-by-step explanation:

Note that x=3 is simply a vertical straight line that passes through the point (3,y) for all real values of y

Also recall that the slope of a vertical straight line is undefined  (or infinite slope)

hence the slope of x=3 is infinite.

Answer: OPTION D.

Step-by-step explanation:

The vertex form of a quadratic function is:

[tex]y= a(x - h)^2 + k[/tex]

Where (h, k) is the vertex of the parabola and "a" is the coefficient of the squared in the parabola's equation.

We know that the vertex of this parabola is at (5,5) and we also know that when the x-value is 6, the y-value is -1.

Then  we can substitute values into  [tex]f (x) = a(x - h)^2 + k[/tex] and solve for "a". This is:

[tex]-1= a(6- 5)^2 + 5\\\\-1=a+5\\\\-1-5=a\\\\a=-6[/tex]

Answer:

D

Step-by-step explanation:

Answer: Hypothesis testing

Step-by-step explanation:

In statistics , Hypothesis testing is a general procedure to check the results of a experiment or a survey to confirm that they have actual and valid  results.

Given claim : A recent study claimed that half of all college students "drink to get drunk" at least once in a while. By believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk".

Here the College Alcohol Study is just testing the results of the survey .

Hence, this is is s a type of Hypothesis testing.

Answer:

ΔKLJ ~ ΔRPQ by AA~

Step-by-step explanation:

Angle angle similarity needs two corresponding angles in two triangles to be same. The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~

It is a theorem in mathematics that sum of internal angles of a triangle equate to [tex]180^\circ[/tex]

Suppose that two angles are given as   [tex]a^\circ[/tex] and  [tex]b^\circ[/tex] and let there is one angle missing. Let its measure be [tex]x^\circ[/tex]

Then, by the aforesaid theorem, we get:

[tex]a^\circ + b^\circ + x^\circ = 180^\circ\\\\ \text{Subtracting a + b degrees from both sides} \\\\x^\circ = 180^\circ - (a^\circ + b^\circ)[/tex]

Two triangles are similar if two corresponding angles of them are of same measure. It is because when two pairs of angles are similar, then as the third angle is fixed if two angles are fixed, thus, third angle pair also gets proved to be of same measure. This makes all three angles same and thus, those two triangles are scaled copies of each other. Thus, they're called similar.

For given case, we've got

[tex]m\angle K = m\angle R\\m\angle J = m\angle Q\\[/tex]

Thus, for the rest of the angle pair, we have:

[tex]m\angle L = 180 - (m\angle J + m\angle K) = 180 - (m\angle Q + m\angle R) = m\angle P\\\\m\angle L = m\angle P[/tex]

Thus, given two triangles are similar by angle-angle similarity.

Thus,

The two given triangles are similar by: ΔKLJ ~ ΔRPQ by AA~

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Answer:

C.(5 sqrt(2), 5 sqrt(2)

Step-by-step explanation:

The point which lie on the circle is :

          [tex](5\sqrt{2},5\sqrt{2})[/tex]        

It is given that the circle is centered at origin and has a radius of 10 units.

We know that if (h, k) represents the coordinate of the center of circle and r is the radius of the circle then the equation of circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here we have:

[tex]h=0\ ,\ k=0\ and\ r=10[/tex]

Hence, the equation of circle is given by:

[tex](x-0)^2+(y-0)^2=10^2\\\\i.e.\\\\x^2+y^2=100------------(1)[/tex]

If we substitute the given point into the equation of the circle and it makes the equation true then the point lie on the circle and if it doesn't make the equation true then the point do not lie on the circle.

a)

[tex](\sqrt{10},0)[/tex]

i.e.  

[tex]x=\sqrt{10}\ and\ y=0[/tex]

i.e. we put these points in the equation(1)

[tex](\sqrt{10})^2+(0)^2=100\\\\i.e.\\\\10=100[/tex]

which is a false statement .

Hence, this point do not lie on the circle.

b)

[tex](0,2\sqrt{5})[/tex]

i.e.

[tex]x=0\ and\ y=2\sqrt{5}[/tex]

i.e. we put these points in the equation(1)

[tex](0)^2+(2\sqrt{5})^2=100\\\\i.e.\\\\20=100[/tex]

which is a false statement .

Hence, this point do not lie on the circle.

c)

 [tex](5\sqrt{2},5\sqrt{2})[/tex]      

i.e.

[tex]x=5\sqrt{2}\ and\ y=5\sqrt{2}[/tex]

i.e. we put these points in the equation(1)

[tex](5\sqrt{2})^2+(5\sqrt{2})^2=100\\\\i.e.\\\\50

+50=100\\\\i.e.\\\\100=100[/tex]

which is a true statement .

Hence, this point  lie on the circle.

Answer:

  A: factor the equation to (x -3)(x +4) = 0

  B: solutions are x=-4, x=3

Step-by-step explanation:

A: Santos has the equation in standard form. Several options for solution are available: graphing (see attached), completing the square, factoring, using the quadratic formula. I find factoring to get to the solution most directly. The other methods work just as well.

To factor the equation, Santos needs to find two factors of -12 that have a sum of +1. Those would be +4 and -3. Putting these numbers into the binomial factors, Santos would have ...

  (x +4)(x -3) = 0

__

B: The values of x that make the factors zero are ...

  x = -4, x = 3

To solve the equation, Santos should first factor the quadratic equation, then use the Zero Product Property to find the solutions, which are x = 3 and x = -4.

For Part A, Santos should factor the quadratic equation x2 + x - 12 = 0. This can be done by finding two numbers that add to 1 (the coefficient of x) and multiply to -12 (the constant term). These numbers are 4 and -3. So the factored form of the equation is (x - 3)(x + 4) = 0.

For Part B, to find the solutions to the proportion, he should use the Zero Product Property which states that if the product of two factors is zero, then at least one of the factors must equal zero. This gives us the solutions x - 3 = 0 and x + 4 = 0. Solving for x in each case provides the solutions: x = 3 and x = -4.

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Answer:

Step-by-step explanation:

The vertical asymptotes are found where a denominator factor is zero (and there is no corresponding numerator factor to cancel it). Here, that is at x = 7.

There is no horizontal asymptote because the numerator is of higher degree than the denominator.

When you divide the numerator by the denominator, you get ...

  y = (x +9) +60/(x -7)

Then when x gets large, the behavior is governed by the terms not having a denominator: y = x +9. This is the equation of the slant asymptote.

The function y = (x^2 + 2x - 3) / (x - 7) has a vertical asymptote at x = 7 and a slant asymptote at y = x. It does not have a horizontal asymptote.

The function given is y = (x^2 + 2x - 3) / (x - 7). When identifying the asymptotes, we need to consider three types: horizontal, vertical, and slant.

For vertical asymptotes, we look for values of x that make the denominator of the function zero. In this case, x = 7 is a vertical asymptote.

For horizontal or slant asymptotes, we compare the degree of the polynomial in the numerator with the degree of the polynomial in the denominator. Since the degree of the numerator (which is 2) is larger than the degree of the denominator (which is 1), there's no horizontal asymptote. However, we have a slant asymptote which is determined by long division of the polynomials or using synthetic division.  

The slant asymptote is therefore y = x.

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Answer:

58

Step-by-step explanation:

Rule: the exterior angle = the sum of the two angles that do not share a side with the exterior angle. Put in much simpler terms <DAB = <B + <C

Solution

<C + <B = <DAB

<C + 56 = 114                    Subtract 56 from both sides

<C +56-56 = 114-56          Combine

<C = 58

x = 58

Answer:

-27a³b⁶+ 8a⁹b¹²

Step-by-step explanation:

In the expression above -27 is a perfect cube of -3, 8 is a perfect cube of 2.

The exponents of a and b in both terms in the expression are divisible by 3.

The cube root of x, that is ∛xⁿ=x∧(n/3) where n is an integer.

ANSWER

[tex]- 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]

EXPLANATION

When we can write an expression in the form

[tex] {(x)}^{3} + {(y)}^{3} [/tex]

then it is a sum of cubes.

To write a given sum as sum of cubes, then the coefficients of the terms should cube be numbers and the exponents of any power should be a multiple of 3.

This tells us that the first option will be the best choice.

[tex] - 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]

We can rewrite this as:

[tex] { (- 3)}^{3} {a}^{3} {b}^{2 \times 3} + {2}^{3} {a}^{3 \times 3} {b}^{4 \times 3} [/tex]

We apply this property of exponents:

[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]

This gives us

[tex] {( - 3a {b}^{2}) }^{3} + {(2{a}^{3} {b}^{4} })^{3} [/tex]

Therefore the correct option is A

Answer:

  216

Step-by-step explanation:

(g∘f)(x) = g(f(x))

f(2) = 2·2 +2 = 6

g(f(2)) = g(6) = 6³ = 216

Answer:

216

Step-by-step explanation:

Correct Plato

Answer:

A

Step-by-step explanation:

Subtraction means "difference".  The only choice there that has the word "difference" in it is choice A.  

For this case we must find the product of the following expression:

[tex]8y ^ 3 (-3y ^ 2) =[/tex]

We have to by law of signs of multiplication:

[tex]+ * - = -[/tex]

Also, by definition of multiplication of powers of the same base, we put the same base and add the exponents, then the expression is rewritten as:

[tex]-24y ^ {3 + 2} =\\-24y ^ 5[/tex]

Answer:

[tex]-24y ^ 5[/tex]

Answer:

The Answer is -24y^5

Step-by-step explanation:

We know this because multiplying 8 by -3 = -24

Then we have to combine the exponents and we get 5.  

Hope I helped.  I used a website called mathwa3 to help, the 3 stands for a y.

Have a great day!!!

Answer:

[tex](-\frac{3}{4})(\frac{7}{8})[/tex] ↔ [tex]-\frac{21}{32}[/tex]

[tex](\frac{2}{3})(-4)(9)[/tex] ↔ [tex]-24[/tex]

[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})[/tex] ↔ [tex]-2[/tex]

[tex](2\frac{3}{5})(\frac{7}{9})[/tex] ↔ [tex]\frac{91}{45}[/tex]

Step-by-step explanation:

The first expression is

[tex](-\frac{3}{4})(\frac{7}{8})[/tex]

On simplification we get

[tex]-\frac{3\times 7}{4\times 8}[/tex]

[tex]-\frac{21}{32}[/tex]

Therefore the product of [tex](-\frac{3}{4})(\frac{7}{8})[/tex] is [tex]-\frac{21}{32}[/tex].

The second expression is

[tex](\frac{2}{3})(-4)(9)[/tex]

On simplification we get

[tex](\frac{2}{3})(-36)[/tex]

[tex]-\frac{72}{3}[/tex]

[tex]-24[/tex]

Therefore, the product of [tex](\frac{2}{3})(-4)(9)[/tex] is [tex]-24[/tex].

Similarly,

[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})\Rightarrow (\frac{5}{16})(8)(-\frac{4}{5})=(\frac{5}{2})(-\frac{4}{5})=-2[/tex]

[tex](2\frac{3}{5})(\frac{7}{9})=(\frac{13}{5})(\frac{7}{9})=\frac{91}{45}[/tex]

The sets of numbers are:

(-7)(-1.2) <-> 8.4

(-2 1/2)(-2) <-> 5

(2.5)(-2)<->-5              

(7) (-1.2) <-> -8.4  

The given expressions involve multiplication and follow the product rule of signs. According to this rule, the product of two numbers with the same sign is positive, while the product of two numbers with different signs is negative.

(-7)(-1.2) = 8.4: Both numbers have the same sign (negative * negative), so the product is positive. The result is 8.4.

(-2 1/2)(-2) = (-5/2)(-2) = 5: Again, both numbers are negative, so the product is positive. The calculation involves multiplying mixed numbers, where -2 1/2 is equivalent to -5/2. The result is 5.

(2.5)(-2) = -5: The numbers have different signs (positive * negative), so the product is negative. The result is -5.

(7)(-1.2) = -8.4: Once more, the numbers have different signs (positive * negative), leading to a negative product. The result is -8.4.

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Answer: Adjacent Angles

A pair of angles which share a common side and vertex is called adjacent angles.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given:

A pair of angles which share a common side and vertex.

If two angles share a side and a vertex, they are said to be adjacent in geometry.

In other words, adjacent angles do not overlap and are placed precisely next to one another.

Therefore, the right definition is adjacent angles.

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Answer: The total volume of air contained in the bubbles of one sheet of bubble wrap is about 0.5 cubic meters.

Step-by-step explanation:

Volume of sphere :-

[tex]V=\dfrac{4}{3}\pi r^3[/tex], where r is the radius of the sphere.

Given : Diameter of the bubble = 0.01 m

Then Radius of the bubble = [tex]\dfrac{0.01}{2}=0.005\ m[/tex]

Volume of each bubble:-

[tex]V=\dfrac{4}{3}(3.14) (0.005)^3[/tex]

Also, Number of bubbles in each sheet = 1,000,000

Then , the total volume of air contained in the bubbles of one sheet of bubble wrap will be :-

[tex]\dfrac{4}{3}(3.14) (0.005)^3\times1,000,000=0.52333333\approx0.5\ \text{cubic meters} [/tex]

Hence, the total volume of air contained in the bubbles of one sheet of bubble wrap is about 0.5 cubic meters.

Answer:

Step-by-step explanation:

Apply the weights to the scores and add them up:

  5% × midterm + 15% × project + 35% × homework + 45% × final

  = 0.05(75) +0.15(93) +0.35(78) +0.45(70)

  = 76.5

The student has a solid letter grade of C.

The student's overall final score is 76.5  which is between 70 and 79, the students earned a C.

To calculate the student's overall final score, we can use the following formula:

Final grade = (midterm score * midterm weight) + (project score * project weight) + (homework score * homework weight) + (final exam score * final exam weight)

where midterm weight is the percentage of the final grade that the midterm counts for, project weight is the percentage of the final grade that the project counts for, homework weight is the percentage of the final grade that the homework assignments count for, and final exam weight is the percentage of the final grade that the final exam counts for.

In this case, the midterm weight is 5%, the project weight is 15%, the homework weight is 35%, and the final exam weight is 45%. The student's midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70.

Therefore, the student's overall final score is calculated as follows:

Final grade = (75 * 0.05) + (93 * 0.15) + (78 * 0.35) + (70 * 0.45)

Final grade = 3.75 + 13.95 + 27.3 + 31.5

Final grade = 76.5

Therefore, the student's overall final score is 76.5.

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Answer:

The sample size must be greater than or equal to 756

Step-by-step explanation:

The formula to calculate the error of the proportion is the following

[tex]E=z_{\alpha/2}*\sqrt{\frac{p(1-p)}{n}}[/tex]

where p is the proportion, n the sample size, E is the error and z is the z-score for a confidence level of 95%

For a confidence level of 95% [tex]z_{\alpha/2}=1.96[/tex]

We know that for this case [tex]p=0.23[/tex]

We require that the error be 0.03 as maximum

Therefore we solve for the variable n

[tex]z_{\alpha/2}*\sqrt{\frac{p(1-p)}{n}}\leq0.03\\\\1.96*\sqrt{\frac{0.23(1-0.23)}{n}}\leq0.03\\\\\sqrt{\frac{0.23(1-0.23)}{n}}\leq \frac{0.03}{1.96}\\\\(\sqrt{\frac{0.23(1-0.23)}{n}})^2\leq (\frac{0.03}{1.96})^2\\\\\frac{0.23(1-0.23)}{n}\leq (\frac{0.03}{1.96})^2\\\\\frac{0.23(1-0.23)}{(\frac{0.03}{1.96})^2}\leq n\\\\n\geq\frac{0.23(1-0.23)}{(\frac{0.03}{1.96})^2}\\\\n\geq756[/tex]

Answer:

1305

Step-by-step explanation:

Answer:

23 out of 91

around 1/3 of the class

Step-by-step explanation:

the total number of students so around the third part of the class