Rick received better results for his Maths test than for his English test. If the sum of his two marks is 163 and the difference is 31, find the mark for each subject.

The volume of the region in first octant is 9.

Given that the region in the first octant bounded by the cylinder r=3 and the plane z=y.

The graph is shown below.

we are given that first octant is bound by r=3  and z=y

We will use the conversion formula, i.e.

x²+y²=r² where x=rcos∅ and y=rsin∅

Firstly, we will find bound octant

0≤∅≤π/2

0≤r≤3

0≤z≤r sin∅

Now, we can set up integral

[tex]V=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}\int_{0}^{rsin(\theta)}rdzdrd\theta[/tex]

Further, we can solve it.

Firstly, we solve integral for z then we solve for r and after that we will solve for ∅, we get

[tex]\begin{aligned}V&=\int_{0}^{\frac{\pi}{2}}\int_{0}^{3}r^2 \sin (\theta)dr d\theta\\&=\int_{0}^{\frac{\pi}{2}}\frac{1}{3}r^3\sin \theta d\theta\left|_{0}^{3}\\ &=\int_{0}^{\frac{\pi}{2}}\left(\frac{1}{3}\sin\theta d\theta(27-0)\right)\\ &=\int_{0}^{\frac{\pi}{2}}9\sin \theta d\theta\\ &=0-(-9)\\ &=9\end[/tex]

Hence, the volume of the region in the first octant is bounded by the cylinder r=3 and the plane z=y is 9.

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Answer:

The total surface area of the the cylinder is 640.56cm², surface are is always give in cm² not in cm³ b/c cm³ indicates the volume of the cylinder not the surface area.

Step-by-step explanation:

Hello!

. SA=2πr(r+h) ,or 2πr²+h(2πr)

Answer:

204π cm^2

which is 640.88 cm^2 to the nearest hundredth.

Step-by-step explanation:

Surface area = 2 * area of the base + area of the curved side.

= 2*π *r^2  + 2*π*r*h

= 2π(6)^2 + 2π(6)(11)

= 72π + 132π

= 204π cm^2.

The scale factor that can be applied to Cone 1 to make Cone 2 is 0.8

This are constants that is used to enlarge of diminish a given figure of sides of a figure

We can determine the scale factor by finding the ratio of the similar sides of two figures, From the given cones, the ratio of their radius can determine the scale factor that is applied to Cone 1 to make Cone 2

From the given figure;

scale factor = radius of cone 2/radius of cone 1

Given the following parameters

radius of cone 2 = 2 ft

radius of cone 1 = 2.5ft

Substitute

scale factor =  2/2.5

scale factor = 0.8

Hence the scale factor that can be applied to Cone 1 to make Cone 2 is 0.8

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Based on the Venn diagram, the number of employers who ask employees to be skilled in both communication (C) and handling money (M) is equal to 47 employers.

A Venn diagram is a circular graphical tool that is used to graphically show, logically compare and contrast two (2) or more finite data set or samples in a given population.

From the Venn diagram, we can deduce that the number of employers who ask employees to be skilled in both communication (C) and handling money (M) is given by:

C∩M = 22 + 25

C∩M = 47 employers.

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Answer:

21655

Step-by-step explanation:

minus the values

The linear inequality of the graph is: -x + 2y + 1 > 0

First, we calculate the slope of the dashed line using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Two points on the graph are:

(1, 0) and (3, 1)

The slope (m) is:

[tex]m = \frac{1 - 0}{3 - 1}[/tex]

This gives

m = 0.5

The equation of the line is calculated as:

[tex]y = m(x -x_1) + y_1[/tex]

So, we have;

[tex]y = 0.5(x -1) + 0[/tex]

This gives

[tex]y = 0.5x -0.5[/tex]

Multiply through by 2

[tex]2y = x - 1[/tex]

Now, we convert the equation to an inequality.

The line on the graph is a dashed line. This means that the inequality is either > or <.

Also, the upper region of the graph that is shaded means that the inequality  is >.

So, the equation becomes

2y > x - 1

Rewrite as:

-x + 2y + 1 > 0

So, the linear inequality is: -x + 2y + 1 > 0

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Complete question

Find a linear inequality with the following solution set. Each grid line represents one unit. (Give your answer in the form ax+by+c>0 or ax+by+c [tex]\geq[/tex] 0 where a, b, and c are integers with no common factor greater than 1.)

Answer:

[tex]\huge\boxed{\sf Option \ B}[/tex]

Step-by-step explanation:

[tex]\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}[/tex] --------------------(1)

Take the expression

[tex]\displaystyle x^2 + \frac{bx}{a}[/tex]

We can also write it as:

[tex]\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )[/tex]

According to the formula [tex]a^2+2ab+b^2[/tex], the b of this expression is [tex]\displaystyle \frac{b}{2a}[/tex]. So,

b² will be:

[tex]\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}[/tex]

So, we will add [tex]\displaystyle \frac{b^2}{4a^2}[/tex] to both sides in Eq. (1)

For STEP 4, the equation will become:

[tex]\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The next step is to divide b/a by 2 then square it and add to both sides.

This creates a perfect square quadratic on left side.

So the answer is :

x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared

The y-intercept of the linear function is y = 0.

A linear function is modeled by:

y = mx + b

In which:

The y-intercept is given by (0,a) = (0,-a). From this, we have that for it to be a function, a = -a, and the only value that respects this condition is a = 0, hence the y-intercept of the linear function is y = 0.

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If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒  x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

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The measure of the ∠1 is 35 degrees.

it is important to know that the measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.

Also, the angle subtended by the arc at the center of the circle is the angle of the arc

From the diagram, we have

m ∠ of external angle = half of the difference of arc angles

The arc angles are

m ∠ of external angle = ∠ 1

Let's substitute the angles

∠1 = [tex]\frac{106 - 36}{2}[/tex]

∠ 1 = [tex]\frac{70}{2}[/tex]

∠ 1 = 35°

We can see that the external angle 1 measures 35 degrees.

Note that the complete image is added.

Thus, the measure of the ∠1 is 35 degrees.

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Answer:

12.2 cm

Step-by-step explanation:

we are going to use the formula (below).

Our a and b are going to be our two legs: 10cm and 7cm

[tex]C^{2} =10^{2} +7^{2} \\C^{2}=100+49\\C^{2}=149\\C=\sqrt{149} \\C=12.2cm[/tex]

Answer:

[tex]\huge\boxed{\sf y = 1/3}[/tex]

Step-by-step explanation:

-4 + 3y = -3

Add 4 to both sides

3y = -3 + 4

3y = 1

Divide 3 to both sides

[tex]\rule[225]{225}{2}[/tex]

Answer:

13

Step-by-step explanation:

Given x = 2, y = 3 and z = 4. We'll evaluate the value of x² + y² with given condition.

First, remind that we are only given the expression of x-term and y-term only and therefore, z-term is not included - it's not to be considered.

Substitute x = 2 and y = 3 in the expression:

[tex]\displaystyle{2^2+3^2 = 4+9}\\\\\displaystyle{4+9 = 13}[/tex]

Hence, the value of x² + y² when x = 2 and y = 3 is 13.

Please let me know if you have any questions!

#1

#b

#c

#f

#i

Answer:

a) 3₁₀

b) 6₁₀

c) 7₁₀

f) 19₁₀

i) 181₁₀

Step-by-step explanation:

Binary to Decimal Conversion (Positional Notation Method)

For a binary number with 'n' digits:

For example, to convert the binary number 111001₂ into a decimal:

[tex]\begin{array}{ c c c c c c}1 & 1 & 1 & 0 & 0 & 1\\\downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0\\\end{array}[/tex]

Multiply each digit by the base (2) raised to the power as indicated above and sum them:

[tex]=(1 \times 2^5)+(1 \times 2^4)+(1 \times 2^3)+(0 \times 2^2)+(0 \times 2^1)+(1 \times 2^0)[/tex]

[tex]= 32+16+8+0+0+1[/tex]

[tex]= 57[/tex]

Finally, express as a decimal number ⇒ 111001₂ = 57₁₀

Question (a)

[tex]\begin{aligned}\implies 11_2 & = (1 \times 2^1)+(1 \times 2^0)\\& = 2+1\\& = 3\end{aligned}[/tex]

Therefore, 11₂ = 3₁₀

Question (b)

[tex]\begin{aligned}\implies 110_2 & = (1 \times 2^2)+(1 \times 2^1)+(0 \times 2^0)\\& = 4+2+0\\& = 6\end{aligned}[/tex]

Therefore, 110₂ = 6₁₀

Question (c)

[tex]\begin{aligned}\implies 111_2 & = (1 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =4+2+1\\& = 7\end{aligned}[/tex]

Therefore, 111₂ = 7₁₀

Question (f)

[tex]\begin{aligned}\implies 10011_2 & =(1 \times 2^4)+(0 \times 2^3)+ (0 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =16+0+0+2+1\\& = 19\end{aligned}[/tex]

Therefore, 10011₂ = 19₁₀

Question (i)

[tex]\phantom{)))}10110101_2 \\\\=(1 \times 2^7)+(0 \times 2^6)+(1 \times 2^5)+(1 \times 2^4)+(0 \times 2^3)+ (1 \times 2^2) +(0 \times 2^1)+(1 \times 2^0)\\\\=128+0+32+16+0+4+0+1\\\\= 181[/tex]

Therefore, 10110101₂ = 181₁₀

Answer:

A, B, F

- The radius of the circle is 3 units

- The center of the circle lies on the x-axis

- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

Step-by-step explanation:

The first option is correct because the standard equation of the circle is:

[tex](x - 1)^{2} + {y}^{2} = 9[/tex]

making the radius equal to 3.

The center is at (-1,0), therefore it lies on the x-axis.

And lastly, the last option is correct because both options have the radius of 3.

The missing side of a right triangle x is 24 units.

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

The side x can be found using similar triangle ratios,

Hence,

x / 400 = 144 / x

cross multiply

x × x = 400 × 144

x² = 57600

square root both sides

√x² = √57600

x = 240

Therefore, the value of x in the right triangle is 240 units.

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As x increases, y value decreases.

The rate of change for y as a function of x is decreasing, therefore the function is a decreasing function.

For all values of x, the function value y, decreases to 0.

The y intercept of the graph is the function value y=8

When x=1, the function value y=5.

From the given graph, it is clear that the curve is decreasing for all values of x. Hence, the rate of change of the give curve is decreasing.

Therefore, the giving function is called as decreasing function.

Since, the function is decreasing for all values of x, the value of y decreases to 0.

Form the graph, it is clear that the y-intercepts is at y=8.

Also, the value of y at x=1 is 5 from the graph.

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Answer:

The answer is 75 and here's why.

Let's figure out the amount of remaining votes to prove this.

250 total votes   -    150 votes for candidate a = 100 votes.

               minus ↑ sign

Candidate B received 25% of the votes, so let's find 25% of 100

100 * 0.25 = 25 votes

Candidate B only got 25 votes (that's kinda sad, poor guy)

100 - 25 votes = the # of votes candidate C got

Candidate C got 75 votes!

The order of the numbers which satisfies commutative property exists 1/7 + (-1)+ 2/7.

The commutative property exists a math rule that states that the order in which we multiply numbers does not change the product. The commutative property uses for addition and multiplication. The property states that phrases can “commute,” or transfer locations, and the outcome will not be affected. This exists described as a + b = b + a for addition, and a × b = b × a for multiplication.

Arranging the order of the numbers the fractions

[tex]$& \frac{1}{7}+(-1)+\frac{2}{7} \\[/tex]

[tex]$=& \frac{1}{7}+\frac{2}{7}+(-1) \\[/tex]

Simplifying the equation, we get

[tex]$= \frac{1}{7}+(-1) \\[/tex]

[tex]$&=\frac{4}{7}[/tex]

Therefore, the correct answer is option A. 1/7 + (-1)+ 2/7

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Answer: 22.5

Step-by-step explanation:

[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]

The equation which has the values as given in the task content is; y= x² -3x -5.

By convention, the general form representation of a quadratic equations is;

y = ax² + bx +c.

Hence, it follows that when the equation has an a-value of 1 a b-value of -3 and a c-value of -5, the equation is; y= x² -3x -5.

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Answer:

a) 25830

b)9975

Step-by-step explanation:

a) 287

x 90

25830

b) 105

x 95

9975

Use the given function to find the [tex]y[/tex]-coordinate of [tex]A[/tex].

[tex]x=2 \implies y = 10+8\cdot2+2^2-2^3 = 22[/tex]

Find the equation of the line through the origin and [tex]A[/tex]. This line has slope

[tex]\mathrm{slope} = \dfrac{22-0}{2-0} = 11[/tex]

and passes through (0, 0), so its equation is

[tex]y - 0 = 11 (x-0) \implies y = 11x[/tex]

Then the area of the shaded region is given by the definite integral

[tex]\displaystyle \int_0^2 (y - 11x) \, dx = \int_0^2 (10 + 7x + x^2 - x^3) \, dx \\\\ ~~~~~~~~ = \left(10x + \frac72 x^2 + \frac13 x^3 - \frac14 x^4\right)\bigg|_0^2 \\\\ ~~~~~~~~ = 10\cdot2+\frac72\cdot2^2+\frac13\cdot2^3-\frac14\cdot2^4 = \boxed{\frac{98}3}[/tex]

"The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location."

Polynomial functions are equations such as quadratic and cubic equations that take only the non-negative integer power of a variable or a positive integer exponent. For example, 2x + 5 is a polynomial with an exponent equal to 1.

A polynomial function is an expression that is a combination of variables of different degrees, non-zero coefficients, positive exponents (of variables), and constants. For example, f (b) = 4b2 – 6 is a polynomial of'b'and has a degree of 2.

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Check each number's prime factorization, then add any factors necessary to make each one a cube.

(a) 3

[tex]3087 = 3^2 \times 7^3 \implies \boxed{3}\times3087 = (3\times7)^3 \implies 9261=21^3[/tex]

(b) 25

[tex]2560 = 2^9\times5^1 \implies \boxed{5^2}\times2560 = \left(2^3\times5\right)^3 \implies 64000 = 40^3[/tex]

The largest possible area of one of the circles would be 314. 2 cm²

It is important to note that the formula for finding the area of a circle is given as;

Area = [tex]\pi r^2[/tex]

From the information given, we have the sides of the square to have a value of 20cm

Also note that the measure of the sides of the square is the size of the diameter of the circle

But we need to find the radius

radius = diameter/2

radius = 20/ 2 = 10cm

Substitute value of radius into the formula for area

Area = 3. 142 × 10^2

Area = 3. 142 × 10 × 10

Area = 314. 2 cm²

The area of the circle is 314. 2cm^2

Thus, the largest possible area of one of the circles would be 314. 2 cm²

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Answer:

[tex]\displaystyle \\\sum_{k=0}^4 45-2.5k=200[/tex]

Step-by-step explanation:

We start off with the term 45 and decrease by 2.5 each term, ending with four 2.5's subtracted from 45.

Therefore, our index starts at k=0 and ends at 4. The general term can be defined then as [tex]\displaystyle \\\sum_{k=0}^4 45-2.5k[/tex] and evaluating yields 200.

There is a 9/25 chance that two numbers will be added together such that their total exceeds their product.

The set of positive numbers are:

{1,2,3,4,5}

We have to independently select two numbers from these sets.

We are trying to determine the likelihood that the sum is larger than the product of the integers.

When one of the chosen numbers is 1, the total will always be greater than the product because:

1*1=1 & 1+1=2

1*2=2 & 1+2=3

1*3=3 & 1+3=4

1*4=4 & 1+4=5

1*5=5 & 1+5=6

and so on.

If we select 2 as both numbers then,

2*2=4 & 2+2=4

Here sum and the product are equal.

If not, the product will be bigger than the sum.

Now, the first stage is to evaluate the total number of two combinations that are feasible:

We have 5 alternatives for the first number and 5 alternatives for the second number.

The product of the number of possibilities in each scenario yields the total number of combinations:

C= 5*5=25

The following combinations have a sum that is greater than the product :

1 and 1

1 and 2

1 and 3

1 and 4

1 and 5

2 and 1

3 and 1

4 and 1

5 and 1

So, we get 9 combinations.

So, Probability,p=9/25

Therefore it is concluded that the probability is 9/25.

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