The average score in an examination taken by 52 students of a class is 85. If the scores of the best 5 performers are not considered, the average score of the remaining students falls by 2. If, none of the first five highest scorers is not below 80 and if each of the 5 top scorers had distinct integral scores, find the maximum possible score of the topper.​

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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Answer:

Step-by-step explanation:

b varies inversely as h, the equation is:

b = 8 when h = 5, find the value of k:

The equation is now:

Find b when h = 4:

As

\(\\ \sf\longmapsto b\propto \dfrac{1}{h}\)

\(\\ \sf\longmapsto b1h1=b2h2\)

\(\\ \sf\longmapsto 8(5)=4b_2\)

\(\\ \sf\longmapsto 4b_2=40\)

\(\\ \sf\longmapsto b_2=10\)

Since one angle measures 18°, and the other angle measures (8x − 28)°, the value of x is equal to 12.5.

In Mathematics, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).

Mathematically, a complementary angle can be calculated by using this mathematical expression:

Q + R = 90°

Where:

Q and R are measure of the angles subtended.

Substituting the given parameters into the complementary angle formula, the sum of the angles is given by;

(8x - 28)° + 18° = 90°

8x - 10 = 90

8x = 90 + 10

8x = 100

x = 100/8

x = 12.5

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Answer: 24 km/hour

Step-by-step explanation: 120/5= 24

Answer:

27

Step-by-step explanation:

15+7=22+7=22

Answer: 27

Step-by-step explanation:

15+7=22

22+5=27

I hope this helped!!

The linear regression equation that best fits the data is y = 3.04x + 5.8.

Using a graphing calculator, we can plot the data points and find the linear regression model that best fits the data.

The linear regression equation that best fits the data is

y = 3.04x + 5.8.

Therefore, the answer is: y=3.04x+5.8.

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Answer: 16.75

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Add all of the number and divide by the amount of numbers there is

Answer:

4600 tenths as a Fraction

Since 4600 tenths is 4600 over ten, 4600 tenths as a Fraction is 4600/10.

4600 tenths as a Decimal

If you divide 4600 by ten you get 4600 tenths as a decimal which is 460.00.

4600 tenths as a Percent

To get 4600 tenths as a Percent, you multiply the decimal with 100 to get the answer of 46000 percent.

4600 tenths of a dollar

First we divide a dollar into ten parts where each part is 10 cents. Then we multiply 10 cents with 4600 and get 46000 cents or 460 dollars and 0 cents.

Step-by-step explanation:

Hope this helped!

Stay safe!!!

Answer:

Step-by-step explanation:

To answer this, multiply 4600 by 10:  46000.  There are 46000 tenths in 4600.

The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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Answer:

y = 50x +30

Step-by-step explanation:

Answer:

y = 50x + 30

Step-by-step explanation:

When it says "per" it means you have to multiply x by that number (mx), when it says plus or something that doesn't include the word "per" it means that you just add it with the mx... or in other words, the addition part is (b).

The vertex of the graphed function f(x) = [x - 4] + 3 is (4, 3).

The function f(x) = [x - 4] + 3 is in the form of an absolute value function, where the expression inside the absolute value brackets represents the input value shifted horizontally by 4 units to the right.

The constant term of 3 represents a vertical shift upwards by 3 units.

To find the vertex of this function, we need to determine the x-coordinate that corresponds to the minimum value of the absolute value function.

In this case, since the absolute value function is within brackets and not being multiplied or divided by a coefficient, the minimum value occurs at the point where the expression inside the brackets equals zero.

Therefore, setting x - 4 = 0, we find x = 4.

Substituting this x-value into the function, we find f(4) = [4 - 4] + 3 = 3. So the vertex of the graphed function is located at the point (4, 3), where x = 4 and y = 3. This means that the graph is shifted 4 units to the right and 3 units upward from the origin.

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The solution of the expression, \(x^{\frac{9}{7} }\) is \(\sqrt[7]{x^{9} }\).

An expression is a combination of numbers, variables, functions such as addition, subtraction, multiplication or division etc.

Therefore, let's rewrite the expression to it's equivalent expression.

An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same.

Therefore, using indices rule

\(x^{\frac{9}{7} }\) = \(\sqrt[7]{x^{9} }\)

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Answer:

I'm not going to answer this, but this should just think about the 29 students and put each outcome to the test.

Step-by-step explanation:

Answer:

0.0579

Step-by-step explanation:

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³

P(X≤2) = 0.00032 + 0.0064 + 0.0512

P(X≤2) = 0.0579

Probability of obtaining a success is 0.0579 .

Here,

Binomial distribution formula:

P(x:n,p) = nCx px (1-p)n-x Or P(x:n,p) = nCx px (q)n-x

Substituting the values of n and p

n = 5

p = 0.8

So,

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³

P(X≤2) = 0.00032 + 0.0064 + 0.0512

P(X≤2) = 0.0579

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After transformation, the point (-1,2) in the image would be (-1,-2)

Each transformation applied to the prior image is combined into a composition of transformations. The result of a translation is identical to a composition of reflections across parallel lines (twice the distance between the parallel lines). The composite transformation is carried out by multiplying the matrix in order from the right to the left side if it is represented as a column. The output from the preceding matrix is multiplied by the new matrix that will follow.

First, we must mirror the point (-1, 2) around the line y=-x.

(X, Y) is the rule (-y,-x)

you obtain (-1,2)—>(-2,1) (-2,1)

At this point, you must rotate (-2,1) by 90 degrees.

(X, Y) is the rule ( -y,x)

so (-2,1)—> (-1,-2) (-1,-2)

After transformation, the point (-1,2) in the image would be (-1,-2)

The complete question is,

What is the image point of (-1,2) after the transformation R 90° ry=-x

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The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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Answer:

48

Step-by-step explanation:

12 x 4 = ?

Can I get a crown?

Answer:

Step-by-step explanation:

Protein ,fat and, calories. I think that’s it

1. Simplifying the exponent (a⁵a⁹)⁻⁵/a⁻¹⁵ = a⁻⁵⁵

2. Simplifying the exponent  [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = m⁻¹⁰

Exponents are powers to which a number is raised.

1. Given the exponential expression, (a⁵a⁹)⁻⁵/a⁻¹⁵, we desire to simplify the expression. We proceed as follows

Since we have  (a⁵a⁹)⁻⁵/a⁻¹⁵

Using the multiplication law of exponents which is xᵃ x xᵇ = xᵃ⁺ᵇ, the numerator becomes

(a⁵a⁹)⁻⁵/a⁻¹⁵ =  (a⁵⁺⁹)⁻⁵/a⁻¹⁵

=  (a¹⁴)⁻⁵/a⁻¹⁵

Also, using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

 (a¹⁴)⁻⁵/a⁻¹⁵ = (a¹⁴×⁻⁵)/a⁻¹⁵

=  (a⁻⁷⁰)/a⁻¹⁵

Now using the division law of exponents, we have xᵃ/xᵇ = xᵃ⁻ᵇ

So,   (a⁻⁷⁰)/a⁻¹⁵ = a⁻⁷⁰ ⁻⁽⁻¹⁵⁾

= a⁻⁷⁰⁺¹⁵

= a⁻⁵⁵

So, (a⁵a⁹)⁻⁵/a⁻¹⁵ = a⁻⁵⁵

2. Given the exponential expression, [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵, we desire to simplify the expression. We proceed as follows

Since we have [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵

Using the multiplication law of exponents which is xᵃ x xᵇ = xᵃ⁺ᵇ, the numerator becomes

[(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = [(m⁻³⁺⁽⁻⁷⁾)/(m⁻⁴)⁻³]⁵

= [(m⁻³⁻⁷)/(m⁻⁴)⁻³]⁵

= [(m⁻¹⁰)/(m⁻⁴)⁻³]⁵

Also, using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

= [m⁻¹⁰/(m⁻⁴)⁻³]⁵ = [(m⁻¹⁰)/(m⁻⁴×⁽⁻³⁾)]⁵

= [(m⁻¹⁰)/m⁻¹²]⁵

Now using the division law of exponents, we have xᵃ/xᵇ = xᵃ⁻ᵇ

So, [(m⁻¹⁰)/m⁻¹²]⁵ = [m⁻¹⁰ ⁻⁽⁻¹²⁾]⁵

= [m⁻¹⁰⁺¹²]⁵

= [m⁻²]⁵

Using the factor law (xᵃ)ᵇ = xᵃᵇ, we have that

[m⁻²]⁵ = m⁻²ˣ⁵

= m⁻¹⁰

So, [(m⁻³m⁻⁷)/(m⁻⁴)⁻³]⁵ = m⁻¹⁰

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Answer:

0.25

Step-by-step explanation:

Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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x=3.5 and y=2.5

First, combine the equations in such a way that you can eliminate a variable. Then solve for the variable. Insert this value into one of the original equations and solve for the unknown variable.

See details:

Answer:

Step-by-step explanation:

Quadratic means squared equation so

the first one is your answer.

y= 4x²

Answer:

D)  

Step-by-step explanation:

y = 12x.

A) x=8, so that y = 12(8) = 96.  It's on the line

B) x = 10, so that y = 12(10) = 120.  It's on the line

C) x = 15, so that y = 15(12) = 180.  It's on the line

D) x = 18, so that y = 18(12) = 216, not equal to 206.  So, the point is not on the line.

The work required to pump the water out of the spout is approximately 64,307,077 ft-lb

To find the work required to pump the water out of the spout, we need to calculate the weight of the water in the tank and then convert it to work using the formula: work = force × distance.

First, let's calculate the volume of water in the tank. The frustum of a cone can be represented by the formula: V = (1/3)πh(r1² + r2² + r1r2), where r1 and r2 are the radii of the two bases and h is the height.

Given r1 = 3 ft, r2 = 6 ft, and h = 12 ft, we can calculate the volume:

V = (1/3)π(12)(9 + 36 + 18) = 270π ft³

Now, we can calculate the weight of the water using the density of water:

Weight = density × volume = 62.5 lb/ft³ × 270π ft³ ≈ 53125π lb

Next, we convert the weight to force by multiplying it by the acceleration due to gravity (32.2 ft/s²):

Force = Weight × acceleration due to gravity = 53125π lb × 32.2 ft/s² ≈ 1709125π lb·ft/s²

Finally, we can calculate the work by multiplying the force by the distance. Since the water is being pumped out of the spout, the distance is equal to the height of the frustum, which is 12 ft:

Work = Force × distance = 1709125π lb·ft/s² × 12 ft ≈ 20509500π lb·ft ≈ 64307077 lb·ft

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Answer:

Step-by-step explanation:

Given is the quadratic equation

It has the maximum height at its vertex, x-coordinate of which is calculated by the formula:

Calculating the highest point:

The number of days that this solution will probably last would be = 8 days.

To calculate the number of days the solution will last the following is taken into consideration.

The parameters given which are not in ml should be converted to ml as follows;

2 Oz of Lidocaine to ml = 2×29.6=59.2ml

½tsp of banana flavouring;

= 1/2×4.92

= 2.5ml

Therefore the total volume of the solution = 100+59.2+2.5 = 161.7ml

But 2×10 = 1 day

20ml = 1 day

161.7ml = X

Make X the subject of formula;

X = 161.7/20

= 8.1

= 8 days.

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Answer:

A ≈ 117.3 cm²

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

Area of a Triangle: A = 1/2bh

If Triangle A ≅ Triangle B, then the bottom side length of A would be 11 cm and the hypotenuse will stay 24 cm.

Step 1: Find the vertical leg of A

11² + b² = 24²

121 + b² = 576

b² = 455

b = 21.3307 cm

Step 2: Find area of A

A = 1/2(11)(21.3307)

A = 1/2(234.638)

A = 117.319

A ≈ 117.3 cm²

The equation -6 = 0 is not true, which means that there is no solution to the equation 9t+6 in standard form. This is because we cannot write the equation in the form \(ax + by = c\)  , since there is no value of c that would satisfy the equation.

To write 9t+6 in standard form, we need to rearrange the expression to have the variables first, followed by the constant term. The standard form of a linear equation is:

\(ax + by = c\)

where a, b, and c are constants, and x and y are variables.

To rearrange 9t+6, we first need to group the t term and the constant term together. We can do this by adding 0t to the expression:

\(9t + 0t + 6\)

Now, we can rearrange the terms so that the variable term comes first:

\(9t + 0t = 9t\)

Finally, we can write the expression in the standard form:

\(9t + 0t = 9t + 6\)

This can be simplified further by removing the 0t term:

\(9t = 9t + 6\)

We can now move the constant term to the other side of the equation by subtracting 6 from both sides:

\(9t - 6 = 9t + 6 - 6\)

\(9t - 6 = 9t\)

\(-6 = 0\)

Therefore, The equation  \(-6 = 0\) is not true, which means that there is no solution to the equation   \(9t+6\) in standard form. This is because we cannot write the equation in the form  \(ax + by = c\)  , since there is no value of c that would satisfy the equation.

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