Perform the operation and simplify the resulting fraction: 7/3a - 8/5 + 4/15a

Answer:12

Step-by-step explanation:

8 times 3 equals 24.24 subtract36 get 12

By factorizing the polynomials, the HCF of the expressions 3(x-y)^2 and 12x^2(x^2+y^2+2xy) is 3.

HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).

To obtain the HCF of algebraic expression, take the common of all the prime factors of two polynomials.

We first factorize the given algebraic expressions:

3(x - y)^2 = 3 × (x - y) × (x - y)

12x^2(x^2+y^2+2xy) = 12x^2(x + y)^2

12x^2(x + y)^2 = 2 × 2 × 3 × x × x ×  (x + y) × (x + y)

so, the highest common factor between the both expressions is 3.

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The model that would model the ratio is 4 : 1

the penalties made is given as 12

To get the penalty kicks that he made given that he made 9 more penalty kicks than he missed

let the penalty kicks be

= x

if he made more than 9 than missed we would have

x + 9 = 4

x = 1

cross multiply

1 (x + 9) = 4 * X

x + 9 = 4x

9 = 3x

x = 3

since x + 9 penalties made

3 + 9 = 12

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The correct option is C, P - value is 0.0718.

A sample proportion in statistics is a measurement of the proportion or percentage of a sample that demonstrates an important characteristic or quality. It is computed by dividing the sample's overall population by the proportion of participants who exhibit the characteristic.

For instance, if a sample of 100 individuals is chosen to estimate the percentage of people who love chocolate ice cream, and 30 of those individuals state that they do, the sample proportion would be 0.3 or 30%, as 30 out of 100 individuals state that they do.

We must first compute the test statistic in order to determine the P-value for Aurelia's test. The test statistic has a typical normal distribution when the null hypothesis is true.

The sample proportion of heads is:

p' = 43/100 = 0.43

The test statistic is:

[tex]z = \frac{(p' - p)}{ \sqrt{(p(1-p) / n)}}[/tex]

where p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Substituting the given values, we get:

[tex]z = \frac{(0.43 - 0.5)}{/ {sqrt(0.5 \times 0.5 / 100)}} = -1.8[/tex]

Since this is a two-sided test, we need to find the area under the standard normal distribution curve in both tails of the distribution that is more extreme than the observed test statistic.

Using a standard normal distribution table, we find that the area to the left of -1.8 is 0.0359. Therefore, the area in both tails is:

P-value = 2 × 0.0359 = 0.0718

So, the correct answer is:

c) 0.0718

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Answer:C

Step-by-step explanation: Kahn Academy

The mode of the data set given is 63.

Statistics uses the terms mean, median, and mode to describe central tendency. They each provide information about what value in a data set is conventional or representative of the data set in their own unique ways.

The number that appears the most frequently in a piece of data is the mode. Count the occurrences of each number in the data collection. The figure with the largest total is the mode. More than one mode is acceptable. Additionally, there is no mode if all numbers appear exactly once.

Given that:

62,63,67,66,66,63,62,68,69,65,67,63,64,

By rearrangement, we have:

62, 62, 63, 63, 63, 64, 65, 66, 66, 67, 67, 68, 69

Therefore, the highest occurring number(mode) is 63.

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To estimate the probability that a randomly selected person would pass the driving test on the first attempt, we can divide the number of people who passed on the first attempt (6500) by the total number of people who took the test (10,000).

Probability = Number of favorable outcomes / Total number of possible outcomes.In this case, the favorable outcome is passing the test on the first attempt, and the possible outcomes are all the people who took the test.

Probability = 6500 / 10000= 0.65

Therefore, the estimated probability that a randomly selected person would pass the driving test on the first attempt is 0.65 or 65%. This means that there is a 65% chance that a randomly selected person from the group of 10,000 would pass the driving test on their first try.

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The two numbers are 3 and 11 respectively

From the information given, we have that

The first number is x

The second number is y

Also,

2x - y = -5

x + y = 14

Make 'x' the subject from equation 2

x = 14 - y

Make 'x' the subject

2(14-y) - y = -5

28 - 2y - y= -5

collect like terms

-3y = -33

y = 11

Substitute the values

x = 3

Hence, the values are 3 and 11

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The height of the tree to the nearest foot is 27 feet.

The height of the tree can be found as follows:

The height of the tree can be found using trigonometric ratios. Therefore,

let

tan ∅ = opposite / adjacent

Therefore,

opposite side = adjacent tan ∅

Hence,

height of the tree = 20 + x tan 45° = x tan 75°

20 + x tan 45° = x tan 75°

20 tan 45 + x tan 45° = x tan 75°

20 tan 45 =  x tan 75° -  x tan 45°

20 tan 45 =  x(tan 75 - tan 45)

20 tan 45 = x(3.73205080757 - 1)

2.73205x = 20

x = 20 / 2.73

x  = 7.32600732601

x = 7.34

Therefore,

height of the tree = x tan 75°

height of the tree = 7.34 × tan 75°

height of the tree = 27.3186119114

height of the tree = 27 ft

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The function operation (f-g)(x) in the functions f(x) = 2√3x and g(x) = -4√3x is 6√3x and  the value of (f-g)(12) is 36.

A function is simply a relationship that maps one input to one output.

Given that;

First, set up the function;

(f - g)(x) = f(x) - g(x)

Replace the function designators with the actual function.

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 2√3x - (-4√3x)

(f - g)(x) = 2√3x + 4√3x

(f - g)(x) = 6√3x

Now, we evaluate when x = 12.

(f - g)(x) = 6√3x

Replace x with 12

(f - g)( 12 ) = 6√3(12)

(f - g)( 12 ) = 6√36

(f - g)( 12 ) = 6 × 6

(f - g)( 12 ) = 36

Therefore, the function operation (f-g)(x) is 6√3x and (f-g)(12) is 36.

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Given the equation AB = BC, we want to find B, assuming that A, B, and C are square matrices and B is invertible. We can conclude that B is invertible.

To do this, we will use the fact that if A is invertible, then we can multiply both sides of the equation by its inverse to isolate B:

AB = BC

[tex]A^-1 AB = A^-1 BC[/tex]

B = A^-1 BC

Here, A^-1 is the inverse of A, and it satisfies the equation[tex]A A^-1 = A^-1 A[/tex]= I, where I is the identity matrix. By multiplying both sides of the equation [tex]AB = BC by A^-1[/tex], we obtain the expression for B.

Now, let's consider the invertibility of B. If A and B are invertible, then the product AB is also invertible. This is because the product of two invertible matrices is invertible, and its inverse is given by the formula [tex](AB)^-1 = B^-1A^-1[/tex]. In this case, since[tex]B = A^-1 BC,[/tex] we can conclude that B is invertible.

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Answer:

He is correct.

Step-by-step explanation:

Shown in picture.

Hope its clear.

The measure of the length NO after dilation will be 15.

The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.

Given that to make JNO, Megan enlarges JKL by a scale factor of 3/5 around point J.

The measure of side NO will be calculated as:-

NO = 3 / 5  x 25

NO = 3 x 5

NO = 15

Therefore, the length of the side NO is 15.

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The distance of the rope to the base of the flagpole is 27.05 ft.

A rope is tied from the top of a flag pole to the ground. If the rope is 28 ft long and makes a 15 degree angle with the ground, the distance of the rope to the base of the flag pole can be calculated as follows:

The situation forms a right angle triangle.

Hence,

using trigonometric ratios,

cos 15° = adjacent / hypotenuse

cos 15° = x / 28

cross multiply

Therefore,

x = 28 cos 15

x = 28 × 0.96592582628

x =  27.0459231361

x = 27.05 ft

Therefore,

distance of the flagpole to the base of the ground  = 27.05 ft

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706.5 in³

The volume of a shape describes the amount of space a shape takes up.

Volume Formula

For a cylinder, the volume formula is V = πr²h. In this formula, V represents the total volume. Additionally, π represents the constant pi, which is approximately 3.14. The variable r represents the radius. Remember that radius is the distance from the center of the circle to the edge. Finally, h is the height of the cylinder.

Solving for Volume

The diagram shows that the radius is 5in. We know this because the distance from the center to the edge of the circle is 5in. Additionally, the height is 9in. Now, we can plug these values into the formula.

For this calculation, I used 3.14 for π. The unrounded volume in terms of pi is 225π.

The volume of the cylinder is 706.5 in³.

The tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

What is Circle?

A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are a fixed distance away from a given point, called the center of the circle. This distance is known as the radius of the circle.

A circle can also be defined as the locus of a point that moves in a plane in such a way that its distance from a fixed point is constant. The constant distance is the radius of the circle.

The minute hand on a clock makes a full rotation in 60 minutes, which means it travels the circumference of a circle with a radius of 23 cm in 60 minutes. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

Therefore, the circumference of the circle traced by the tip of the minute hand is:

C = 2πr = 2 × 3.14 × 23 cm ≈ 144.44 cm

To find out how far the minute hand travels in 11 minutes, we need to calculate what fraction of the circumference it covers in that time. Since 11 minutes is about 18.3% of an hour (60 minutes), the minute hand travels 18.3% of the circumference of the circle in that time:

Distance traveled = 0.183 × 144.44 cm ≈ 26.4 cm

Therefore, the tip of the minute hand on a clock travels approximately 26.4 cm in 11 minutes if the minute hand is 23 cm long.

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Chandra spends 3 minutes on each math problem if she spends a total of 15 minutes on math problems and spends the same amount of time on each problem

Chandra spends the same amount of time on each math problem. Let's call the amount of time she spends on each problem "t".

We know that Chandra spends a total of 15 minutes on math problems. If she spends the same amount of time on each problem, then the total time spent on all the problems is equal to the number of problems multiplied by the time spent on each problem.

So, we can write the following equation:

total time spent on all problems = number of problems * time spent on each problem

We know that the total time spent on all problems is 15 minutes, so we can substitute this into the equation:

15 = number of problems * t

We don't know the number of problems, but we can solve for t by rearranging the equation:

t = 15 / number of problems

So, the amount of time Chandra spends on each math problem is equal to 15 divided by the number of problems.

For example, if Chandra works on 5 math problems, then the amount of time she spends on each problem is:

t = 15 / 5 = 3

So, Chandra spends 3 minutes on each math problem if she spends a total of 15 minutes on math problems and spends the same amount of time on each problem.

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The area of the trapezoid would be 42.5 m².

What is the area of a trapezoid?

The area of a trapezoid is given by the formula:

Area = (1/2) × (sum of the bases) × height

where the bases are the two parallel sides of the trapezoid and the height is the perpendicular distance between the bases.

The parameters of the trapezoid are;

Short base length = 3 m

Height = 5

Large base length = 4 + 3 + 7 = 14 m

Thus;

Area of a trapezoid = 1/2 * (Short base + Large base) * h

Area = 1/2 * (3 + 14) * 5

= 1/2 * 17 * 5

= 42.5 m²

Hence, the area of the trapezoid would be 42.5 m².

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The reliability of the machine can be estimated to be 0.9833, calculated as (1000 - 1) / 1000 + (600 - 5) / 600.  we can take the average of the two reliability estimates, giving us a reliability of 0.9833.

The reliability of a machine can be estimated by taking the ratio of machines that did not fail to the total number of machines operated in a given period. In this case, the reliability of the machine from Factory A can be estimated to be 0.99 (1000 - 1 / 1000). The reliability of the machine from Factory B can be estimated to be 0.9833 (600 - 5 / 600). To estimate the reliability of the machine based on both factories, we can take the average of the two reliability estimates, giving us a reliability of 0.9833.

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The height of the rectangle must be greater than 4 inches if the perimeter of the rectangle is greater than 30 inches.

In geometry, a rectangle is a quadrilateral with four right angles, and opposite sides are equal in length. The perimeter of a rectangle is the total distance around it.

Let's assume that the height of the rectangle is x inches. According to the problem, the base is 7 more than its height, which means the base is (x + 7) inches.

Now, we can calculate the perimeter of the rectangle using the formula:

Perimeter = 2(length + width)

In a rectangle, the length and width are the same as the base and height, respectively. So, in our case, the perimeter of the rectangle will be:

Perimeter = 2(x + (x + 7)) = 4x + 14

As we are given that the perimeter of the rectangle is greater than 30 inches, we can write the inequality:

4x + 14 > 30

Solving for x, we get:

4x > 16

x > 4

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the angle BAD is 75 degrees and  we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD .

To work out angle BAD, we need to use the properties of angles in a circle and the tangent-secant theorem. Here are the steps to solve the problem:

Identify the relevant angles First, we need to draw a diagram to visualize the problem. We have a circle with center O, points A, B, C, and D on the circumference, and tangent ED. Angle ODB is given as 25 degrees. We need to find angle BAD. We can label the angles in the diagram as follows:

Angle AOB = 2x (angle at the center is twice the angle at the circumference)

Angle BCD = x (angles in the same segment are equal)

Angle OBD = 90 degrees (tangent and radius are perpendicular)

Angle OED = 90 degrees (tangent and radius are perpendicular)

Angle ABD = y (we need to find this angle)

Angle BAD = z (we need to find this angle)

Use the sum of angles in a triangle

We notice that triangle ABD is a right triangle, with right angle at B. Therefore, angles ABD and BAD are complementary. That is, ABD + BAD = 90 degrees. Use the tangent-secant theorem

We can use the tangent-secant theorem to find the value of angle ABD. The tangent-secant theorem states that if a tangent and a secant intersect at a point on a circle, then the angle between the tangent and the secant is equal to the half the difference of the intercepted arcs. In our diagram, ED is a tangent, and BD is a secant. Therefore, angle ODB = 25 degrees is half the difference of the intercepted arcs AD and AB. That is, angle ABD = (2x - x)/2 = x/2.

Solve for x

To find x, we can use the fact that the angles in a triangle add up to 180 degrees. Therefore, x + 2x + 90 = 180 (sum of angles in triangle AOB). Solving for x, we get x = 30 degrees.

Find angle ABD and angle BAD

Using the result from step 3, we get ABD = x/2 = 15 degrees. Using the result from step 2, we get BAD = 90 - ABD = 75 degrees.

Therefore, the angle BAD is 75 degrees. In summary, we used the properties of angles in a circle and the tangent-secant theorem to find angle BAD. We noticed that ABD and BAD are complementary, and we used the tangent-secant theorem to find ABD. Then, we solved for x using the fact that the angles in a triangle add up to 180 degrees. Finally, we used the results from steps 2 and 3 to find BAD.

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The above-shown note is labeled B based on the information provided.

A point is considered to really be equidistant from both of two other points when they are equally distanced from one another. The distance between any two given points may be calculated using the distance formula utilizing the coordinates of the two points.

Example: Given that points A and B have the coordinates (1, -2) and (5, 6), respectively, determine the midpoint of line segment AB. Find the midpoint's distance between points A and B to confirm it. The midpoint is confirmed to be equally far from points A and B because both of those places are from it.

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Using the vertices given, the area of triangle PQR is 18 squared units

The area of triangle PQR can be found using the Shoelace Theorem. This theorem states that the area of a polygon can be calculated by taking the sum of the products of the coordinates of its vertices and subtracting the sum of the products of the coordinates of its vertices in reverse order.

In this case, the vertices of triangle PQR are P(-8, 2), Q(-2, 4), and R(-6, 8), so the area can be calculated as follows:

A = 1/2 * |(-8 * 4) + (-2 * 8) + (-6 * 2) - (2 * -2) - (4 * -6) - (8 * -8)| = 1/2 * |-32 + 16 + -12 - 4 + 24 + 64| = 1/2 * |36| = 18 square units

So the area of triangle PQR is 18 square units.

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The vertical intercept for the table showing the relationship for Jada's grandparents starting a savings account for her is starting savings amount in the account of $ 600.

The vertical intercept in a graph is the point where a line intersects the vertical axis of the coordinate plane. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.

The vertical intercept would therefore be first amount in the savings account by Jada's grandparents which is the $ 600.  This is the amount when x = 0 or rather when x was the starting year of 2006.

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PLEASE GIVE BRAINLIEST!
thank you and have a good day :)

Answer:

5)1/12

6) 25%

Step-by-step explanation:

5)The odds of Mr Douglas eating two slices of cheese pizza can be calculated by doing 3/(5 + 1 +3) = 1/3

the second slice's odds can be calculated by doing 2/(5+1+2) = 1/4

Multiply these to get the odds of two being eaten

1/4 times 1/3 is 1/12.

6) the odds of her selecting a red pen the first time is 50%. to do it again would be another 50% chance. 50% times 50% is 25%.

Let's first assign variables to the numbers given.

We're given:

Plug the second equation into the first one and solve for y:

[tex]x+y=367\\(y+95)+y=367\\2y+95=367\\2y=272\\y=136[/tex]

Therefore, they sold 136 chocolate cones.

They sold 136 chocolate ice cream cones.

In the preceding equation the measure of the smallest angle is 52° in length.

Internal angles 2 and 3 are alternate options. Two angles that share a vertex and a side but no interior points in common. two angles that don't have any shared interior points but do have a common vertex and side.

We know that a triangle has 180 angles altogether.

So, 2x + 3x - 11 + 2x + 9 = 180

7x - 2 = 180

7x = 180 + 2

x = 182 / 7

x = 26

Now, magnitude of angles = 2x = 2(26) = 52  [ Smallest ]

3x - 11 = 3(26) - 11 = 78 - 11 = 67  [ Largest ]

2x +9 = 2(26) + 9 = 52 + 9 = 61

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The numbers on a centimeter ruler represent that There are 10 millimeters unit for each centimeter.

What is a unit?

Units are the instruments used to measure and compare various things. When all measuring units are the same, comparison is simple. Various units can be categorised based on their intended usage. A couple of the units are classed as follows:

The seven SI basic units (The International System of Units (SI), sometimes known as the metric system, is the international measurement standard) are as follows:

Length - meter (m)

Time - second (s)

Amount of substance - mole (mole)

Electric current - ampere (A)

Temperature - kelvin (K)

Luminous intensity - candela (cd)

Mass - kilogram (kg)

Now,

As we have seen in a ruler from any two numbers 1 and 2 or 4 and 5

there are always 10 vertical lines which represents a millimeter

and 10 lines means 10 millimeter.

hence,

          The numbers on a centimeter ruler represent that There are 10 millimeters unit for each centimeter.

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The range of values for the third side must be 5 < C < 13 this means that the third side must be a value greater than 5 and less than 13.

What is triangle?

A triangle is a two-dimensional geometric shape with three sides and three angles. It is a basic polygon and one of the simplest shapes in geometry. Triangles come in different types based on the length of their sides or the measure of their angles, such as equilateral triangles (all sides are equal), isosceles triangles (two sides are equal), scalene triangles (no sides are equal), right triangles (one angle measures 90 degrees), and obtuse triangles (one angle measures greater than 90 degrees).

The third side of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides A, B, and C, we have:

                                    A + B > C

                                    B + C > A

                                    A + C > B

For the given sides of 8 and 5, the range of values for the third side can be found by considering the two inequalities:

                                    5 + C > 8

                                     8 + C > 5

Adding the two inequalities, we get:

                        13 > C

So the range of values for the third side must be:

                         5 < C < 13

This means that the third side must be a value greater than 5 and less than 13.

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The difference in height between Sarah and Tayjen kite is 1060 cm (10.6 m)

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

1 m = 100 cm

Sara's kite flew 48 meters in the air. Hence:

Height of Sarah kite = 48 m = 48 m * 100 cm per m = 4800 cm

Tayjen's kite flew 5,860 centimeters in the air. Therefore:

Difference in height = 5860 - 4800 = 1060 cm = 1060 cm * 1 m per 100 cm = 10.6 m

The difference in height is 1060 cm (10.6 m)

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