Find the solution set for the following system graphically:
2\3x+4 = y and y < 4x

If the money box has 600 coins that consist of 20 cents and 50 cents, the total amount of cents in the money box is 24,000 cents.

To determine the total amount of cents in Thabang's money box, we need to know how many of the 600 coins are 20 cents and how many are 50 cents. Let's use variables to represent these quantities.

Let x be the number of 20 cent coins, and y be the number of 50 cent coins. We know that the total number of coins is 600, so we have:

x + y = 600

We also know that the value of each 20 cent coin is 20 cents, and the value of each 50 cent coin is 50 cents. So the total value of the coins in the money box is:

20x + 50y

To find the total amount of cents in the money box, we need to simplify and solve for the value of the expression above. We can do this by using the equation we have for x and y and substituting y = 600 - x:

20x + 50(600 - x) = 20x + 30000 - 50x = -30x + 30000

So the total value of the coins in the money box is -30x + 30000 cents. We don't know the value of x yet, but we know that x and y must be non-negative integers and x + y = 600.

We can solve for x by trying different values of x until we find one that satisfies these conditions. For example, if we set x = 200, then y = 400 and the conditions are satisfied. Therefore, the total amount of cents in the money box is:

-30x + 30000 = -30(200) + 30000 = 24000

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The probability that Ben will make three out of his next five free throws is approximately 0.3456

Assuming that each free throw attempt is independent of the others, we can use the binomial distribution to calculate the probability of Ben making three out of his next five free throws.

The probability of making a free throw is 0.6, so the probability of missing a free throw is 0.4. Let X be the number of successful free throws out of 5 attempts. Then X follows a binomial distribution with n = 5 and p = 0.6.

The probability of making three out of five free throws can be calculated as follows

P(X = 3) = (5 choose 3) × (0.6)^3 × (0.4)^2

where (5 choose 3) = 10 is the number of ways to choose 3 successful free throws out of 5 attempts.

Using a calculator, we get

P(X = 3) = 0.3456

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The value for theta is 16.7 degrees and that of alpha is 73.3 degrees.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions

The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio.

To find alpha, we can take the inverse tangent of both sides of the equation:

tan α = 10/3

tan⁻¹(tan α) = tan⁻¹(10/3)

α = tan⁻¹(10/3)

Using a calculator, we get:

α ≈ 73.3 degrees (rounded to one decimal place)

Therefore, the value of alpha is approximately 73.3 degrees.

To find theta, we can take the inverse tangent of both sides of the equation:

tan θ = 3/10

tan⁻¹(tan θ) = tan⁻¹(3/10)

θ = tan⁻¹(3/10)

Using a calculator, we get:

θ ≈ 16.7 degrees (rounded to one decimal place)

Therefore, the value of theta is approximately 16.7 degrees.\

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The area of the blue paper obtained by subtracting the 6 circle areas from the rectangle is 20.64 sq. cm.

A circle is made up of all points in a single plane that are equidistant from one another. Only the bordering points make up the circle. The radius is the distance from the centre to the outside of the circle.

The diameter is the length of a line that connects the circle's ends to its middle point. The radius is half as large as the diameter.

Given data:

length l = 12 cm

width w = 8 cm

radius r = 4/2 = 2 cm.

Area of blue page = Total area of rectangle - 6*area of circle

Area of blue page = length * width - 6*π*r²

Area of blue page = 12*8 - 6*3.14*2²

Area of blue page = 20.64 sq. cm.

Thus, the area of the blue paper obtained by subtracting the 6 circle areas from the rectangle is 20.64 sq. cm.

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Answer:

sin(theta) = -3/5.

Step-by-step explanation:

We know that tan(theta) = 3/4, which means that the ratio of the opposite side to the adjacent side of a right triangle with angle theta is 3/4. We can use the Pythagorean theorem to find the hypotenuse of the triangle:

hypotenuse^2 = opposite^2 + adjacent^2

hypotenuse^2 = (3^2) + (4^2)

hypotenuse^2 = 9 + 16

hypotenuse^2 = 25

hypotenuse = 5

Since 180 degrees < theta < 270 degrees, we know that theta is in the third quadrant, where the sine function is negative. Therefore, sin(theta) = -opposite/hypotenuse = -3/5.

So, sin(theta) = -3/5.

Answer:

1/4

Step-by-step explanation:

As given the figure, 3 out of 4 rectangles are shaded,

So,

4/4-3/4=1/4

Answer:

Common difference = 2

Step-by-step explanation:

We can find the common difference by subtracting any two consecutive terms with the smaller number being subtracted from the larger:

Thus, to find the common difference, d, we can subtract -13 from -15:

d = -15 - (-13) = -15 + 13 = 2

The total space that the cargo will take up is 7 x 10⁷ cubic feet.

In geometry, a prism is a three-dimensional solid shape that consists of two congruent bases (which can be any polygon) and a set of parallel line segments that connect the corresponding vertices of the two bases. The bases are usually parallel and of the same shape and size, and the line segments connecting the vertices are known as the lateral faces of the prism.

Prisms are commonly found in architecture and engineering, where they are used to create structures such as buildings, bridges, and towers. They are also used in optics, where they are used to refract and reflect light, and in mathematics, where they are used to study geometric properties and relationships.

To find the total space that the energy prisms will take up, we need to multiply the number of prisms by the amount of space each prism takes up. We can use scientific notation to simplify the calculation:

3.5 x 10⁵ energy prisms * 2 x 10² cubic feet per prism

= (3.5 * 2) x 10⁵⁺² cubic feet

= 7 x 10⁷ cubic feet

Therefore, the total space that the cargo will take up is 7 x 10⁷ cubic feet.

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Answer:

501.5

Step-by-step explanation:

Hope this helps!

Answer:

501.50

Step-by-step explanation:

Let 425 = 100%

(because 425 is the original quantity)

=>18% more than 425 = 100% + 18% = 118%

(because 425 = 100%)

If 100% = 425

118% = ?

=118 ÷ 100 × 425

= 501.50

Therefore the number which is 18% more then 425 is 501.50.

Answer:

Let the length of the rectangle be x and the width of the rectangle be y.

Then, we can use the Pythagorean Theorem to find the value of x and y:

x2 + y2 = 62

x2 + y2 = 36

We can use trigonometry to find the value of x and y:

x = 6 sin 30°

y = 6 cos 30°

Therefore, the length of the rectangle is 6 sin 30° cm and the width of the rectangle is 6 cos 30° cm.

Answer:

30.5 or 61/2 cm²

Step-by-step explanation:

So the area of the figure is shown by this equation.

Area = Area of triangle - Area of rectangle cut out

        = (0.5)(9)(9) - (2)(5)

        = 40.5 - 10

        = 30.5 or 61/2 cm²

The measure of angle ABD is 30 (optionD)

Angle addition postulate states that: The sum of the measure of two adjacent angles is equal to the measure of the angle formed by the non-common sides of the two adjacent angles.

angle ADB and DBC are adjascent angles. And the sum of the two adjascent angles is angle ABC

Therefore using angle addition postulate;

Angle ABC = < ABD + < DBC

70 = < ABD + 40

< ABD= 70 - 40

< ABD = 30°

therefore the measure of angle ABD = 30°

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The measure of angle subtended by the arc CEB is 210⁰.

The value of m∠CDB is 30⁰.

The measure of angle subtended by the arc CEB is calculated by applying the following formula.

The sum of angles in a circle = 360⁰, so the value of arc CEB is calculated as;

arc CEB = 360 - 150⁰

arc CEB = 210⁰

Based on the angle of intersecting chord theorem, we will have the following equation to determine the value of m∠CDB.

m∠CDB = ¹/₂ (210 - 150)

m∠CDB = 30⁰

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A 95% confidence interval for the average is 3898.

In statistics, the confidence interval formula is used to express the degree of uncertainty surrounding a sample estimate of a population parameter.

Formula of confidence interval:

If n ≥ 30,

Confidence Interval = m ± z(SD/√n)

where,

n = Number of terms

m = Sample average

SD = Standard Deviation

Value for the confidence interval in the z table is z.

Table of Confidence interval  and Z

CI      z

0.70 1.04

0.75 1.15

0.80 1.28

0.85 1.44

0.90  1.645

0.92 1.75

0.95 1.96

0.96 2.05

0.98 2.33

0.99 2.58

According to the question

random sample of student (n) =  99

average savings = 3800 dollars

Standard deviation =  500 dollars

95% confidence interval for the average needed

i.e , z = 1.96

Now, By using Formula of confidence interval:

Confidence Interval = m ±  z(SD/√n)

substituting the values

Confidence Interval = 3800 ± 1.96(500/√99)

                                 = 3800 ± 98.49

                                 = 3898.49

values to the nearest whole number

Confidence Interval = 3898

Hence,  A 95% confidence interval for the average is 3898 .

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Answer:

The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides. The sum of exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.

Step-by-step explanation:

Answer:

2. Where is the point of discontinuity of y =

=

O x = 5

O x = 49

O x=-10

O x = -5

-10x+49

x-5

?

Answer:

A

Step-by-step explanation:

Answer:

To multiply 9200 and 2.3 x 10^3 in scientific notation, we need to multiply their coefficients and add their exponents.

9200 x 2.3 x 10^3 = 21,160,000

Since the product is greater than 10, we need to adjust the coefficient and the exponent to express the number in scientific notation. We can move the decimal point to the left until there is only one digit to the left of the decimal point, and count how many places we moved the decimal point. In this case, we need to move the decimal point 7 places to the left:

2.116 x 10^7

Therefore, the product of 9200 and 2.3 x 10^3 expressed in scientific notation is 2.116 x 10^7.

Answer:

4

Step-by-step explanation:

Have a good day :-)

The principal from difference between Simple interest and Compound interest of a certain sum of money is 50.4 at 6% p.a. for 2 years is $14,000.

Let the principal be P.

Simple interest = P x 0.06 x 2 = 0.12P

Compound interest = P(1 + 0.06)^2 - P = 1.1236P - P = 0.1236P

Given: Compound interest - Simple interest = 50.4

0.1236P - 0.12P = 50.4

0.0036P = 50.4

P = 50.4 / 0.0036

P = 14000

Therefore, the principal is $14,000.

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Answer:

Step-by-step explanation:

The circumference is the perimeter of a circle, which is equal to 131.88ft.

Circumference = [tex]2\pi r^{2}[/tex]

[tex]131.88=2\pi r^{2} \\r^{2} =\frac{131.88}{2\pi } \\r=\sqrt{20.989} \\r=4.581[/tex]

This means that the diameter is:

[tex]d=2r\\d=9.163[/tex]

So our area is:

[tex]A=\pi r^{2} \\A=\pi (4.581)^{2} \\A=65.940[/tex]

Hope this helped!

A sphere's volume may be calculated using the formula [tex]137.25[/tex] cm cube.

V = 4/3 r3, where V is the volume and r is the radius, is the formula for a sphere's volume. 1/2 of a sphere's radius makes up its radius. Therefore, you may determine the radius first, followed by the volume, to get the surface of a circle given its diameter.

The radius of a sphere is the distance between its center and its outside surface. The amount of space a satellite's surface covers is known as its surface area, and it is equal to 4r2.

The diameter of the sphere, [tex]d = 6.4[/tex] cm

Radius,[tex]r = 3.2[/tex] cm

We need to find the volume of the sphere. The formula for the volume of a sphere is given by :

[tex]V=4/3pir^{3}[/tex]

[tex]4/3pi*(3.2)^{3}[/tex]

[tex]=137.25 cm^{3}[/tex]

The radius of the bowling ball is [tex]6.4 cm/2 = 3.2 cm[/tex], and its volume is [tex]V[/tex] bowling [tex]= 4/3 pi(3.2)^{3} * 8 = 1,100.8[/tex] cubic cm.

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Answer:

[tex] \frac{y - y1}{m} = x - x1 \\ x1 = x - \frac{y - y1}{m} [/tex]

so,A is the correct answer...

The area of the triangle with vertices (-1, 1), (-1, 5), and (4, 1) is 10 square units.

The area of a triangle is a measure of the amount of space inside the triangle. It is defined as half the product of the base of the triangle and its corresponding height.

If a triangle has base length b and corresponding height h, then its area A is given by the formula:

A = (1/2) × b ×h.

In the given question,

To find the area of the triangle with vertices (-1, 1), (-1, 5), and (4, 1), we can use the formula: A = (1/2) × b ×h.

where the base is the distance between two vertices of the triangle and the height is the perpendicular distance from the third vertex to the base.

We can choose any two points as the endpoints of the base, but it may be easiest to use the points (-1, 1) and (4, 1), since the height will be the vertical distance from the third vertex (which is ( -1, 5)) to the base.

The distance between (-1, 1) and (4, 1) is: base = 4 - (-1) = 5

To find the height, we need to determine the perpendicular distance from the point (-1, 5) to the line containing the base. This can be done by finding the equation of the line containing the base and then finding the distance from the point (-1, 5) to that line.

The equation of the line containing the base is: y = 1

since the line is horizontal and passes through the point (4, 1) and (-1, 1).

The distance from the point (-1, 5) to the line y = 1 is:

height = |5 - 1| = 4

where the absolute value is taken to ensure that the height is positive.

Now, we can substitute the values of the base and height into the formula for the area:

Area = (1/2) × base × height

= (1/2) * 5 * 4

= 10

Therefore, the area of the triangle with vertices (-1, 1), (-1, 5), and (4, 1) is 10 square units.

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Therefore, the probability of Mrs. Vo winning is 1 - 91/300 - 8/21 = 11/30.

Probability refers to the likelihood or chance that a particular event or outcome will occur. It is a mathematical concept that quantifies the degree of uncertainty associated with an event or situation. Probability is typically expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that it is certain to occur.

by the question.

let's consider the first case: Mrs. Vo spins a number greater than 65 on her first spin. There are a total of 8 numbers greater than 65 on the wheel: 70, 75, 80, 85, 90, 95, 100. Since there are 21 sections on the wheel, the probability of spinning a number greater than 65 on the first spin is 8/21.

The number of possible outcomes for Mrs. Vo's spin is 21, since there are 21 equal portions on the wheel. However, we need to exclude the outcomes that would cause Mrs. Vo's sum to exceed 100, since that would result in an automatic loss. The largest possible outcome on the wheel is 100, so Mrs. Vo cannot spin a number greater than or equal to 35 on her first spin.

The number of outcomes that would give Mrs. Vo a winning sum of at least 66 is the number of outcomes greater than 65, which are 70, 75, 80, 85, 90, 95, and 100. There are 7 such outcomes.

If Mrs. Vo spins a number less than or equal to 65 on her first spin, the probability of this happening is 13/21. The probability of her second spin being between 1 and 35 is 35/100 (since there are 35 numbers between 1 and 35 on the wheel). So, the probability of her total sum being less than or equal to 65 is (13/21) * (35/100) = 91/300.

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Answer:

a=3 d=6 n=45

A45= 3+44×6=267

Step-by-step explanation:

i hope you find it helpful

Given the first three terms of the sequence to be

[tex]3,9,15,...[/tex]

It is observed that each successive term of the sequence is obtained by the addition of 6 to the preceding term.

Thus, the sequence is an arithmetic sequence.

The nth term of an arithmetic sequence is given as

[tex]a_n=ar^{r-1}[/tex]

Thus, from the given sequence,

               [tex]a=3[/tex]

[tex]d=9-3=6 \ \text{OR} \ 15-9=6[/tex]

              [tex]n=45[/tex]

[tex]T_{45} \ \text{is thus evaluated as}[/tex]

     [tex]T_{45}=3+(45-1)6[/tex]

    [tex]T_{45}=3+(44\times6)[/tex]

        [tex]T_{45}=3+264[/tex]

             [tex]T_{45}=267[/tex]

The 45th term of the sequence is thus 267

The evaluation of expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) and simplification to get the final result of 2√5 - 2√6 + 6.

To evaluate the expression is

7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2)

we need to rationalize the denominators of each fraction. To do this, we can multiply both the numerator and denominator of each fraction by the conjugate of the denominator.

For the first fraction, we can multiply the numerator and denominator by (√10 - √3):

7√3(√10 - √3) / [(√10 + √3)(√10 - √3)]

Simplifying the denominator gives:

7√3(√10 - √3) / 10 - 3

For the second fraction, we can multiply the numerator and denominator by (√6 - √5):

-2√5(√6 - √5) / [(√6 + √5)(√6 - √5)]

Simplifying the denominator gives:

-2√5(√6 - √5) / 6 - 5

For the third fraction, we can multiply the numerator and denominator by (√15 - 3√2):

-3√2(√15 - 3√2) / [(√15 + 3√2)(√15 - 3√2)]

Simplifying the denominator gives:

-3√2(√15 - 3√2) / 15 - 9

Now, we can simplify each expression separately and then combine them:

7√3(√10 - √3) / 7 = √30 - 3

-2√5(√6 - √5) / 1 = -2√6 + 2√5

-3√2(√15 - 3√2) / 6 = -√30 + 9

Combining the expressions gives:

√30 - 3 - 2√6 + 2√5 - √30 + 9

Simplifying further gives:

2√5 - 2√6 + 6

Therefore, the value of the expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) is 2√5 - 2√6 + 6.

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