if a pupil has a score of 60% how many marks out of 150 did he obtain

The volume of a cone will be 209.41 yard³.

What is volume of cone?

The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.

So the

V = (1/3)πr²h.

Given, data r = 5yards

h = 8 yards

Volume = 1/3 * π * r ²* h

= 1/3 * 3.141*25*8

=209.41 yard³

Hence, the volume of a cone will be 209.41 yard³.

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Answer:

2

Step-by-step explanation:

used tiger-algebra.com

The equation that represents circles that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y-3)² = 36

We know that, the standard form of equation of a circle is expressed as:

(x-a)^2 + (y-b)^2 = b=r^2

where;

(a, b) is the center of the circle

r is the radius of the circle

From given information,

diameter = 12 units

radius = 12/2

           = 6 units

It is given that, the center lies on the y-axis, the center will be at (0, 3)

Substituting above values in the formula,

(x-0)^2 + (y-3)^2 = 6^2

x²+ (y-3)² = 36

Therefore, an equation that represent circle that have a diameter of 12 units and a center that lies on the y-axis is x²+ (y - 3)² = 36

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the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.

A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.

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Answer:

\( \huge{ \boxed{y = 4x + 10}}\)

Step-by-step explanation:

The equation of a line in slope-intercept form is given by

\( \bold{y = mx + c}\)

where

m is the slope

c is the y intercept

From the question

m = 4

In order to find c we substitute the point (−3,−2) into the equation y = mx + c

We have

\( - 2 = 4( - 3) + c \\ - 2 = - 12 + c \\ c = - 2 + 12 \\ c = 10\)

We now substitute m and c into the equation

We have the final answer as

\( \bold{y = 4x + 10}\)

Hope this helps you

The answer to this question is after solving definite integration 0,1,-4,-10

What is Definite integration?

It is just basically Simple Integration with limits. In other words it is completely same as area under curve

Solution:

We will proceed by finding area under curve

Here we have to consider the area above x axis as positive and area under x axis as negative area

In First part +ve area and -ve area cancels each other hence answer is 0

In second part after cancellation only 1 square block above x axis remains whose area is 1  hence answer is 1

remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative

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Explanation:

The vertices of the given triangle are the points:

(2, -1), (4, -5), and (5, -3).

To rotate the figure 90 degrees clockwise, we will use the following rule

(x, y) -----> (y, -x)

So, each vertex becomes

(2, -1) ----> (-1, -2)

(4, -5) ---> (-5, -4)

(5, -3) ---> (-3, -5)

Therefore, using the points (-1, -2), (-5, -4), and (-3, -5) we get that the triangle after the clockwise rotation is:

The coordinates of the shadow cast on the xy-plane by the small object placed at (10, 7, 20), assuming the sun's rays are parallel to the vector [5, 3, -2], can be found by projecting the object's position onto the xy-plane. The shadow will have the same x and y coordinates as the object, but the z-coordinate will be zero since the shadow lies on the xy-plane. Therefore, the coordinates of the shadow will be (10, 7, 0).

To find the shadow's coordinates, we need to project the object's position onto the xy-plane.

The projection can be obtained by subtracting the component of the object's position vector in the direction of the sun's rays. In this case, the direction vector of the sun's rays is [5, 3, -2]. We can find the component of the object's position vector in this direction using the dot product.

The dot product of the object's position vector [10, 7, 20] and the sun's rays direction vector [5, 3, -2] is given by: 10*5 + 7*3 + 20*(-2) = 50 + 21 - 40 = 31.

To obtain the projected position, we subtract the component of the object's position vector in the direction of the sun's rays: [10, 7, 20] - 31 * [5, 3, -2] = [10, 7, 20] - [155, 93, -62] = [-145, -86, 82].

Since the shadow lies on the xy-plane, the z-coordinate of the projected position will be zero. Therefore, the coordinates of the shadow are (10, 7, 0).

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The trigonometric ratios for this problem are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the triangle, we have that:

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The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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The function is:

To find the range in the domain 3 < x 8 we can replace the values of the extrems to sind it so:

for x = 3

for x= 8

So the only range between this numbers is:

The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.

Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.

For example, let's say one missing value is x = 3. We can substitute this into the equation:

y = 2(3) + 4

y = 6 + 4

y = 10

So, the missing ordered pair is (3, 10).

Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:

8 = 2x + 4

4 = 2x

x = 2

So, the missing ordered pair is (2, 8).

In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

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The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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The sorter's error is 91 seconds. This means that the sorter miscalculated the time it would take for the water bottle to travel the length of the belt by 91 seconds.

When anything is referred to as being "long," it refers to its overall length. In other words, it is the larger of the third or upper two dimensions of a geometric object. An example of a shape with two dimensions is a rectangle.

To find out how many seconds it takes for the water bottle to travel the length of the belt, we can use the equation:

distance = rate x time

We know the distance (294 feet) and the rate (7 feet per 6 seconds). Let's solve for time:

294 feet = (7 feet/6 seconds) x time

294 feet x 6 seconds = 7 feet x time

1764 seconds = 7 feet x time

time = 1764 seconds / 7 feet

time = 252 seconds

So it takes 252 seconds for the water bottle to travel the length of the belt.

Now let's calculate the sorter's error:

343 seconds - 252 seconds = 91 seconds

The sorter's error is 91 seconds. This means that the sorter miscalculated the time it would take for the water bottle to travel the length of the belt by 91 seconds.

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Answer:

x=3

Step-by-step explanation:

\(-15x+32=13\\-15x=13-32\\-15x=-45\\x=-45/-15\\x=3\)

Step-by-step explanation:

To Solve This Equation You will need to

Original Equation;

-15x+32=-13

•(Firstly you will Group Like Terms)

-15x=-13-32

•(After Grouping you will go ahead and simplify)

-15x=-13-32

(You will have to add the two negative numbers and note that negative plus negative is still negative even though there is no addition sign there but you'll add them because when there is two negatives without a multiplication or division or any other sign you have to add)

-15x=-13-32

-15x=-45

(Then you proceed to divide both sides by -15)

x=3

This is because -45 divided by -15 is positive 3

Positive 3 because the negative signs cancel each other out.

Answer:

x = 4, -2

Step-by-step explanation:

x^2-2x=8

Move the constant term to the right side of the equation.

x^2 - 2x = 8

Take half of the coefficient of x and square it.

(-2/2)^2 = 1

Add the square to both sides of the equation.

x^2 - 2x + 1 = 8 + 1

Factor the perfect square trinomial.

(x - 1)^2 = 9

Take the square root of both sides of the equation.

x-1=\(\sqrt{9}\)
x-1=±3

Isolate x to find the solutions.

Taking positive

x=3+1=4

x=4

Taking negative

x=-3+1

x=-2

The solutions are:

x = 4, -2

Answer:

\(x = -2,\;\;x=4\)

Step-by-step explanation:

To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:

\(x^2-2x-8=8-8\)

\(x^2-2x-8=0\)

Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.

The two numbers whose product is -8 and sum is -2 are -4 and 2.

Rewrite the coefficient of the middle term as the sum of these two numbers:

\(x^2-4x+2x-8=0\)

Factor the first two terms and the last two terms separately:

\(x(x-4)+2(x-4)=0\)

Factor out the common term (x - 4):

\((x+2)(x-4)=0\)

Apply the zero-product property:

\(x+2=0 \implies x=-2\)

\(x-4=0 \implies x=4\)

Therefore, the solutions to the given quadratic equation are:

\(\boxed{x = -2,\;\;x=4}\)

I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

Hence , the instantaneous rate of change of f(x) = e^(2x)e^(7x) at x = -1 will be 9e⁻⁹ .

We have given a function f(x) = e²ˣ e⁷ˣ.

You can realize the fast rate of modification of a perform at a degree by finding the by-product of that perform and plugging within the x-value of the purpose.

On simplifying , we can write f(x) as e⁹ˣ

Differentiating f(x) with respect to x , we get

     f'(x) =  d/dx (e⁹ˣ)

     f'(x) = e⁹ˣ × 9

Putting x = - 1 in f'(x) , we get

     f'(-1) = 9e⁹⁽⁻¹⁾

            = 9e⁻⁹

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Answer:

Try using the Symbolab calculator.

Step-by-step explanation:

Thats what I usually use and it works

Answer:

hello your question is incomplete attached below is the complete question

answer : It would be narrower  ( C )

Step-by-step explanation:

When The 90% confidence interval is compared to the one constructed ( i.e. one with a more conservative value for degrees of freedom ) it would be narrower and this is simply because the conservative df does not put into consideration the fractional part .

The length of the side x of the given right triangle is approximately equal to 12 units when rounded to four decimal places.

This is a right triangle, so we can use the Pythagorean theorem to solve for x.

According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse (the longest side). Therefore, we have:

\(x^2 + 9^2 = 15^2\)

Simplifying and solving for x, we get:

\(x^2 + 81 = 225\)

\(x^2 = 144\)

x = ±12

Since x represents the length of a side of the triangle, it must be positive. Therefore, we take the positive root and get:

x = 12

Rounding to four decimal places, we have:

x ≈ 12.0000

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Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).

To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.

With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.

Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.

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Answer:

opposite side are congruenyt

Step-by-step explanation:

it always has four congruent angles

ut is also a rectangle

the sum of its angles measures is 360°

Answer:

I would say it’s either A or B but go with what you think is best :)

Step-by-step explanation:

Now,

( 4x + 20 )° = ( 5x - 10 )° ( Alternative angle )

20° + 10° = 5x - 4x

30° = x

◆ x = 30°

I hope it's help you...

Mark me as brainliest...

For given functions, The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

What is the definition of a function?

A function is a mathematical rule that gives each input value a distinct output value. A function is officially defined as a collection of ordered pairs (x, y) in which each input value x is coupled with exactly one output value y. The domain of the function refers to the input values, while the range refers to the output values. A graph, table, equation, or verbal explanation can all be used to depict a function. When the input value is x, the notation f(x) is commonly used to express the output value of a function f.

Now,

From given function f(x) and g(x)

For f(x) when x=0 then y=1 or y-intercept=1

for g(x), the y-intercept is 1 from equation y=4x+1

and slope of g(x)=4

and slope of f(x)=(11-1)/(2-0)

=10/5

=2

Hence,

           The y-intercept of f(x) is equal to the y-intercept of g(x). The slope of f(x) is greater than the slope of g(x).

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Answer:

6

Step-by-step explanation:

the numerator of the fraction is

6(t+h) +1 -(6t +1) = 6h

so the fraction is 6h/h =6

Answer:

Yes, Billy will have enough money to buy two denim shirts.

Step-by-step explanation:

£9.60 × (1/3)

= £3.20

On the special offer day, a denim shirt will cost £3.20.

£3.20×2 = £6.40

Two shirts will cost £6.40

Billy has £13, which will be enough for him to buy two shirts and will have a remaining balance of £6.60