Pairs of markings a set distance apart are made on highways so that police can detect drivers exceeding the speed limit. Over a fixed distance, the speed R varies inversely with the time T. In one
particular pair of markings, R is 41 mph when Tis 8 seconds. Find the speed of a car that travels the given distance in 5 seconds.
R= ? mph (Round to the nearest whole number.)

Answer:

256[tex]\pi[/tex]

Step-by-step explanation:

The Area of a circle --> A =[tex]\pi*r^{2}[/tex]

Radius = 16 ft,

[tex]16^{2} = 256[/tex], so instead of then multiplying this number by [tex]\pi[/tex], Just leave it as,

256[tex]\pi[/tex]

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:

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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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:

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.

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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Answer:

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

so,A is the correct answer...

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

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:

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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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

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:

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!

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 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:

4

Step-by-step explanation:

Have a good day :-)

The models that represent a probability of 1/4 of pulling a red marble are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

After completing 12 trials, she pulled a red marble 3 times, hence the probability of pulling a red marble is given as follows:

3/12 = 1/4.

The other models with a probability of 1/4 are given as follows:

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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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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 additional variable used to determine the values of the original variables in the ordered pair of a system of equations whose solution is an infinite number of solution is called a parameter.

A parameter is an unknown variable that is not included in the original equations of a system of equations.

In algebra, a system of equations is a collection of two or more equations involving the same set of variables. The solution to a system of equations is the point or points at which the equations are true. A system of equations can have a unique solution, no solution, or an infinite number of solutions.

When a system of equations has an infinite number of solutions, it means that the equations are dependent on each other. This means that one of the equations can be expressed in terms of the other equation. The solution to the system of equations is then written in terms of the parameter, which is the variable that is not included in the original equations.

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Answer:

each term is half the previous one. 1.6 *.5^(n-1). is a geometric sequence.

This is a geometric sequence with a common ratio of 1/2. Therefore, option B is correct.

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed constant called the common ratio (r).

In other words, if the first term of the sequence is "a", then the nth term of the sequence is given by:

an = a * r^(n-1)

where "n" is the position of the term in the sequence.

In this question:

To see why, notice that each term is half of the previous term:

0.8 is half of 1.6

0.4 is half of 0.8

0.2 is half of 0.4

In a geometric sequence, each term is obtained by multiplying the previous term by a fixed constant, which is called the common ratio. In this case, the common ratio is 1/2, because each term is half of the previous term.

So the sequence can be written as:

1.6, 0.8, 0.4, 0.2, …

or

a₁, a₁/2, a₁/4, a₁/8, …

where a₁ is the first term, which is 1.6 in this case.

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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.

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 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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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