2/3(4a-15)-1/9(6a-2)

we can shown that the areas of △PMS and △SOR are equal, and the areas of △MQT and △NRT are equal,

we can then conclude that △PMS+△MQT = △SOR + △NRT.

We will label the points in the figure as follows:

PQ = RS (given that PQRS is a parallelogram)

MN = OS (given that MNOS is a parallelogram)

T is the point of intersection of MQ and PR

R is the point of intersection of PS and NT

considering  △PMS and △SOR. We can see that they share a base, PS, and that the heights of both triangles are equal, since PS is parallel to MN and therefore the distance between PS and MN is the same at both ends. Therefore, the areas of these two triangles are equal.

Also  considering  △MQT and △NRT.

It is obvious that they share a base, QT, and that the heights of both triangles are equal, since QT is parallel to RS and therefore the distance between QT and RS is the same at both ends.

Therefore, the areas of these two triangles are also equal.

Since we have shown that the areas of △PMS and △SOR are equal, and the areas of △MQT and △NRT are equal, we can conclude that △PMS+△MQT = △SOR + △NRT.

This was  using the properties of parallelograms and the fact that the triangles share a common base with equal heights.

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Hello and regards 24kendalllove.

The given function is y = x^2 - 2x - 1.

The domain of a quadratic function, like this one, is the set of all values of x for which the function is defined. Since a quadratic function is defined for all real values of x, the domain of this function is all real numbers.

To find the range of the quadratic function, we must first identify whether the parabola opens up or down. In this case, the coefficient of the x^2 term is positive (1), which means that the parabola opens up.

Since the parabola opens up, the vertex of the parabola will be the lowest point on the graph. To find the vertex, we use the formula x = -b / 2a, where a and b are the coefficients of the terms x^2 and x, respectively. In this case, a = 1 and b = -2, so x = -(-2) / (2 * 1) = 1. We then plug this value of x into the function to find the corresponding y value: y = (1)^2 - 2(1) - 1 = -2.

So, the vertex of the parabola is (1, -2). Since the parabola opens up, the range of the function will be all y-values greater than or equal to the y-value of the vertex. Therefore, the range of the function is y ≥ -2.

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After converting 5²/53³  in simplest form we get 25/148,877 as the correct answer.

To simplify the expression 5²/53³, we first evaluate the exponents of 5 and 53.

5² means 5 multiplied by itself, or 5 × 5, which equals 25.

53³ means 53 multiplied by itself three times, or 53 × 53 × 53. This can be calculated using a calculator or by multiplying the numbers out by hand. The result is 148,877.

So, we can rewrite the expression 5²/53³ as: 25/148,877

This expression cannot be simplified any further because 25 and 148,877 have no common factors other than 1.

Therefore, the expression in its simplest form is 25/148,877.

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The value of k for the  logarithmic function f(x)=log0.5 x+k is k = log2 (1/2x).

Here we need to understand that the logarithmic function f(x)=log0.5 x+k can be written in the form f(x)=log0.5 x + log0.5 b.

The given logarithmic function is of the form f(x) = log0.5 x + k.

We want to express this function in terms of a logarithm with base 0.5 and a constant b.

Using the property of logarithms that states that the logarithm of a product is the sum of the logarithms of the factors, we can write:

f(x) = log0.5 x + log0.5 b

where b is a constant that we need to determine.

We want to find a value of b such that the expression above is equivalent to the original function f(x) = log0.5 x + k. We can do this by setting the two expressions equal to each other:

log0.5 x + log0.5 b = log0.5 x + k

b = [tex]0.5^k[/tex]

Substituting this value of b into the expression we obtained earlier gives:

f(x) = log0.5 x + log0.5 (0.5^k)

f(x) = log0.5 (x([tex]0.5^k[/tex]))

Using the property of logarithms that states that the logarithm of a power is the product of the exponent and the logarithm of the base, we can simplify this expression:

f(x) = log2 x - k

We are now given that the function f(x) T z the x-axis, which means that f(x) = 0.

Setting this equal to the expression we obtained above, we get:

log2 x - k = 0

log2 x = k

Solving for k gives:

k = log2 x

Substituting this expression for k back into the original function f(x) = log0.5 x + k, we get:

f(x) = log0.5 x + log0.5 ([tex]0.5^{(log2 x)[/tex])

f(x) = log0.5 (x ( [tex]0.5^{(log2 x)[/tex]))

f(x) = log0.5 (x ( [tex](1/2)^{log2[/tex]))

f(x) = log0.5 (x ( (1/2)))

f(x) = log0.5 (x/2)

Therefore, the value of k for the function f(x) = log0.5 x + k is k = log2 x, and the equivalent expression for the function is f(x) = log0.5 (x/2).

The value of k for the function f(x) = log0.5 x + k is k = log2 (1/2x).

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The absolute value equation is |x - 11| = 6.

Givent he values 5 and 17 on the numberr line, we want to write an absolute value equation in the form |x - c| = d.

Now, given two numbers a and b, we have that

So, given that

we have that

c = (a + b)/2

= (5 + 17)/2

= 22/2

= 11

Also, given that

we have that

d = (b - a)/2

= (17 - 5)/2

= 12/2

= 6

So, to write the absoiute value equation, we substitute the values of the variables into the equation

|x - c| = d.

So, substituting the values of the variables into the equation, we have that

|x - c| = d.

|x - 11| = 6.

So, the absolute value equation is |x - 11| = 6.

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For the given Cuboid, the width will be equal to 4.5 cm.

What exactly is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where opposite faces are equal in size and shape. A cuboid is also known as a rectangular parallelepiped or rectangular prism.

In a cuboid, the three pairs of opposite faces are parallel to each other and perpendicular to the other pair of faces. The cuboid has eight vertices or corners, twelve edges, and six rectangular faces.

Now,

We can use the formula for the volume of a cuboid to find the missing dimension:

Volume = Length x Width x Height

In this case, we are given the length and height of the cuboid, but we do not know its width. Let's assume that the width of the cuboid is "w". Then, we can write the equation:

220.5 = 7 x w x 7

Simplifying this equation, we get:

220.5 = 49w

Dividing both sides by 49, we get:

w = 4.5

Therefore, the third dimension of the cuboid is:

Width = 4.5 cm

So, the cuboid has three dimensions of 7 x 4.5 x 7 cm.

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Rosa bought 8 cans of juice for herself and her friends.

To calculate how many cans of juice Rosa bought, we first need to calculate the total amount of money she gave the cashier:

2/3 of 15 quarters = (2/3) x 15 = 10 quarters (since each quarter is worth 25 cents,

10 quarters are worth 10 x 25 = 250 cents)

3/5 of 10 nickels = (3/5) x 10 = 6 nickels (since each nickel is worth 5 cents, 6 nickels are worth 6 x 5 = 30 cents)

Therefore, Rosa gave the cashier 250 + 30 = 280 cents.

Now, we need to find out how many cans of juice Rosa can buy with 280 cents:

1 can of juice costs 35 cents, so 280 cents can buy 280/35 = 8 cans of juice.

Therefore, Rosa bought 8 cans of juice for herself and her friends.

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Answer:

4.75 kg

Step-by-step explanation:

Bottles of jam given by Sakshi to her friends =7

Bottles of jam prepare by sakshi for herself =12

Total bottles of jam made =7+12=19

Weight of jam in 1 bottles =250 gm

Total weight of jam made by sakshi

=250×19

=4,750 gm

Total weight of jam =4.75 kg.

To check whether the point (2, √5) lies on the circle centered at the origin with radius 3, we can use the distance formula for a point (x, y) on the circle:

d = √((x - 0)^2 + (y - 0)^2)

Since the center of the circle is at the origin, the x-coordinate is 0 and the y-coordinate is 0. The radius is given as 3. So, substituting these values in the above formula, we get:

3 = √((2 - 0)^2 + (√5 - 0)^2)

Simplifying the right side of the equation:

3 = √(4 + 5)

3 = √9

3 = 3

Since both sides of the equation are equal, the point (2, √5) lies on the circle centered at the origin with radius 3.

A population standard deviation of 8.5 minutes. Then, the p-value is 0.0436.

We know the length of the show based on the assumption that shoppers spend an average of 8 minutes in line at the store checkout.

A sample of 100 buyers reported an average sample wait time of 8.5 minutes. For example, the population standard deviation is 3.2 minutes.

Null Hypothesis, H₀: μ =8 minutes    {means that the actual mean waiting time does not differs from the standard}

Alternate Hypothesis, Hₐ: μ ≠ 8 minutes    {means that the actual mean waiting time differs from the standard}

The test statistics that would be used here are One-sample z-test statistics as we know about the population standard deviation;

                      T.S. = x-μ/σ/√n   ~ N(0,1)

where, X = sample mean waiting time = 8.5 minutes

            σ  = population standard deviation = 3.2 minutes

             n = sample of shoppers = 100

So, test statistics  =  8.5 -8/3.2/√100

                             =  1.75

The value of t-test statistics is 1.75.

Now, the P-value of the test statistics is given by;

   P-value = P(Z > 1.71) = 1 - P(Z ≤ 1.75)

                 = 1 - 0.9568 = 0.0438

Complete Question:

A sample of 100 shoppers showed a sample mean waiting time of 8.5 minutes. Assume a population standard deviation of 3.2 minutes. What is the p-value?

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Answer: 3300

Explanation: V=lwh/3=22x30x15/3=3300

At the Digital animation studio, character designers outnumber interns by 320.

Let's break down the information given in the circle graph and find out how many more character designers there are than interns.

1. Determine the number of employees for each job type by multiplying the percentage by the total number of employees (1600):
- Interns: 5% * 1600 = 80 employees
- Set Shading: 10% * 1600 = 160 employees
- Character Shading: 10% * 1600 = 160 employees
- Story Artist: 20% * 1600 = 320 employees
- Character Design: 25% * 1600 = 400 employees
- Animator: 30% * 1600 = 480 employees

2. To find how many more character designers there are than interns, subtract the number of interns from the number of character designers:
- Character Design - Interns = 400 - 80 = 320 employees

In conclusion, there are 320 more character designers than interns at the digital animation company.

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The mean travel time for the 7 students is approximately 8.6 minutes, and the median travel time is 8.5 minutes.

To find the mean travel time, we need to add up all the travel times and divide by the total number of students:

Mean = (8 + 14 + 12 + 9 + 7 + 5 + 5) / 7

Mean = 60 / 7

Mean ≈ 8.6 (rounded to one decimal place)

So, the mean travel time for the 7 students is approximately 8.6 minutes.

To find the median travel time, we need to arrange the travel times in order from smallest to largest:

5, 5, 7, 8, 9, 12, 14

There are 7 students, so the median is the middle value. In this case, the middle value is the average of the 4th and 5th numbers:

Median = (8 + 9) / 2

Median = 8.5

So, the median travel time for the 7 students is 8.5 minutes.

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Answer:

  C.  25

Step-by-step explanation:

You want to know the first quartile as shown in the given box plot.

A box plot has vertical lines at (left to right) ...

The left end of the "box" is the first quartile.

The first quartile of the dataset represented by this box plot is 25.

Answer:

Step-by-step explanation:

The given surface is the pyramid and the area of the pyramid is [tex]301.98978[/tex].

The formula to calculate the total surface area of a triangular pyramid is[tex]\frac{1}{2} (a*b)+\frac{3}{2}(b*s)[/tex]

Calculate the area of each triangular face. This can be done using the formula for the area of a triangle: [tex]\frac{1}{2} bh[/tex], where b is the base of the triangle and h is the height of the triangle.

In this case, the base is one of the sides of the base triangle, and the height is the slant height of the pyramid.

Add up the areas of all the triangular faces and the area of the base to get the total surface area of the pyramid.

Add the area of the square.

Therefore the  given surface is the pyramid and the area of the pyramid is [tex]301.98978[/tex].

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In this case, the IQR should be used because the data in both Sunny Town and Desert Landing is not normally distributed and has different shapes.

What is outliers ?

Outliers are pieces of information that dramatically deviate from the rest of the information in a dataset. These could be values that are atypically high or low or values which vary significantly from the data's central trend. Outliers can appear for a number of causes, including measurement or record errors, inherent data variability, or unusual events. It is frequently required to recognize and effectively handle outliers because of their potential to significantly affect statistical analyses.

given,

IQR, as it can provide a better measurement of the variability of the middle 50% of the data and is less impacted by outliers.

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The linear scale factor of the enlargement is 6.7 (580 cm³/87 cm³). To the nearest hundredth, the linear scale factor of the enlargement is 6.70.
The surface area scale factor of the enlargement is 33.2 (290 cm³/8.7 cm³). To the nearest hundredth, the surface area scale factor of the enlargement is 33.17.

Surface area is the combined area of all the faces of a three-dimensional object. It is the area that is visible when looking at the outside of the object. It is often used to calculate the amount of material needed for a certain project or product. It is also used to calculate the cost and energy required to heat or cool a certain space. Surface area can be calculated using geometry and calculus, or it can be measured directly.

1. Linear scale factor: The linear scale factor of the enlargement is the ratio of the volume of the larger jar to the volume of the smaller jar. The volume of the larger jar is 0.58 L which is equivalent to 580 cm³. The volume of the smaller jar is 87 cm³. Therefore, the linear scale factor of the enlargement is 6.7 (580 cm³/87 cm³). To the nearest hundredth, the linear scale factor of the enlargement is 6.70.

2. Surface area scale factor: The surface area scale factor of the enlargement is the ratio of the surface area of the larger jar to the surface area of the smaller jar. The surface area of a jar depends on its radius. Since the radius of the larger jar is larger than the radius of the smaller jar, the surface area of the larger jar is larger than the surface area of the smaller jar.

Therefore, the surface area scale factor of the enlargement is greater than 1. To calculate this factor, we can use the formula for the surface area of a cylinder: A = 2πrh, where r is the radius and h is the height. The height of both jars is the same, so we can calculate the surface area scale factor by dividing the radius of the larger jar by the radius of the smaller jar. The radius of the larger jar is 0.29 L, which is equivalent to 290 cm³. The radius of the smaller jar is 8.7 cm³.

Therefore, the surface area scale factor of the enlargement is 33.2 (290 cm³/8.7 cm³). To the nearest hundredth, the surface area scale factor of the enlargement is 33.17.
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Complete questions as follows-
Use the following information to answer the next two questions Raj Jars Ltd. Sells different types of similar jars. One of their jars has a volume of 87 cm³ and another has a volume of 0.58 L. 1. What is the linear scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³ 2. What is the surface area scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³

Answer:

9(2x + 1) < 9x - 18

9(2x + 1) < 9(x - 2)

2x + 1 < x - 2

x < -3

So -4 is in the solution set.

Answer: y = (3/2)x - 7

Step-by-step explanation:To find the equation of a line perpendicular to another line, we need to know that the slopes of two perpendicular lines are negative reciprocals of each other. Therefore, the slope of the line we're looking for will be the negative reciprocal of -2/3, which is 3/2.

Now we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

We know that the line we're looking for goes through the point (6,2), so x1 = 6 and y1 = 2. We also know that the slope is 3/2. Substituting these values into the point-slope form, we get:

y - 2 = (3/2)(x - 6)

Simplifying and putting the equation into slope-intercept form, we get:

y = (3/2)x - 7

So the equation of the line perpendicular to y = -2/3x -1 that goes through the point (6,2) is y = (3/2)x - 7.

Answer:

f(x) =x^2 - 3x^2 - 6x + 8.

Step-by-step explanation:

If 40% of adults questioned reported that their health was excellent, then the probability that when 13 adults are randomly selected, 3 or fewer are in excellent-health is (b) 0.169.

The number of adults randomly selected is = 13 adults,

We need to find probability of getting 3 or fewer people reporting excellent health which is considered as success , in 13 trials

The probability of success = 0.4     ...because proportion of adults reporting excellent health in general population.

We use "binomial-probability" formula to calculate probability:

⇒ P(X ≤ 3) = ΣP(X = k), for k = 0, 1, 2, 3

where X = number of successes = people reporting excellent health and P(X = k) = probability of getting exactly k successes;

⇒ P(X = k) = C(n,k) × p^k × (1-p)^(n-k),

where n = number of trials, p = probability of success, and

substituting values,

We get,

⇒ P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3),

⇒ C(13,0) × (0.4)⁰ × (0.6)¹³ + C(13,1) × (0.4)¹ × (0.6)¹² + C(13,2) × (0.4)² × (0.6)¹¹ + C(13,3) × (0.4)³ × (0.6)¹⁰,

≈ 0.1686 ≈ 0.169.

Therefore, the required probability is approximately 0.169, the correct option is (b).

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F(x) is a degree 6 polynomial having roots at x = 0, I -5, and 3.

As F(x) contains six elements in the form of (x-a), where an is a root, the degree of F(x) is 6. We discover that the roots are x=0, I -5, and 3 when we set each component to zero. By resolving each issue independently, their roots can be discovered. For instance, x=0, I is obtained from x(x2+1)=0. We obtain x=-5 from (x+5)=0. We get x=3 from (x2-3)=0. The roots of F(x) are significant because they reveal where the function crosses the x-axis and where its extrema are.

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f(x) = 7 is the output for only one input value, which is x = 3, because this is the only value that results in the maximum value of the function.

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

The function f(x) = −(x−3)²+7 is a quadratic function in vertex form. The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

In this case, the vertex is (3, 7), which means that the parabola opens downwards and has a maximum value of 7. This also means that any value of f(x) less than 7 can be obtained from two different values of x, since the parabola is symmetric around its vertex.

However, f(x) = 7 is the maximum value of the function and can only be obtained for a single value of x, which is the x-coordinate of the vertex, namely x = 3. This is because the vertex is the highest point on the parabola, and any other value of x will result in a lower value of f(x).

Therefore, f(x) = 7 is the output for only one input value, which is x = 3, because this is the only value that results in the maximum value of the function.

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The error in the calculation above is that the order of operations was not followed correctly. Multiplication should be performed before division. the correct answer is [tex]4[/tex]  , not  [tex]1/9[/tex] .

The error in the calculation above is in the first step. When performing multiplication and division in the same step, you should always perform the multiplication before the division. This is known as the order of operations.

The correct calculation would be:

[tex]8/12 \times6 = (8/12) \times 6[/tex]   (perform the multiplication first)

[tex]= (2/3) \times 6[/tex] (simplify the fraction)

[tex]= 12/3[/tex]

[tex]= 4[/tex]

The error in the calculation above is that the order of operations was not followed correctly. Multiplication should be performed before division.

The correct calculation is as follows:

[tex]8/12 \times 6 = (8/12) x\times6[/tex] // Multiplication first

[tex]= (2/3) \times 6 /[/tex]  / Simplify 8/12 to 2/3

= [tex]12/3[/tex] // Multiply 2/3 by 6

=  [tex]4[/tex] // Simplify 12/3 to 4

Therefore, the correct answer is [tex]4[/tex] , not [tex]1/9[/tex]  .

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To find the length of side BC, we'll use right-triangle trigonometry as follows:

The value of the tangent function for the measure of angle A = (the length of the side opposite angle A)/(the length of the side adjacent to angle A)

tan 40° = BC/AC

tan 40° = BC/15 cm

Now, multiply both sides by 15 cm:

(tan 40°)(15 cm) = (BC/15 cm)(15 cm)

(tan 40°)(15 cm) = (BC)(15 cm/15 cm)

(tan 40°)(15 cm) = (BC)(1)

BC = (tan 40°)(15 cm)

Now, using a table of values for the trigonometric functions for angles from 0° to 90° or using a scientific calculator, we find that tan 40° = .8391 (to 4 decimal places). Now, substituting on the right side we get:

BC = (.8391)(15 cm)

BC = 12.6 cm to the nearest tenth of a centimeter.

Answer:

[tex]≈7.07 \: {ft}^{2} [/tex]

Step-by-step explanation:

Given:

d = 3 ft

Find: A (area) - ?

First, we can find the length of the radius, since we know the diameter:

r = 0,5× d

r = 0,5 × 3 = 1,5 ft

[tex]a = \pi {r}^{2} = \pi \times( {1.5})^{2} = 2.25\pi ≈7.07 \: {ft}^{2} [/tex]

The area of the circular tablecloth is approximately 7 square feet.

To find the area of a circle, you use the formula A = πr^2, where A is the area and r is the radius of the circle. The diameter of the tablecloth is 3 feet, so the radius is 1.5 feet. Plugging this into the formula, we get A = π(1.5)^2 ≈ 7.07 square feet. However, the question asks for the measurement closest to the area of the tablecloth in feet, so we can round the answer to 7 square feet.

Therefore, the area of the tablecloth is approximately 7 square feet.

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Answer:

B

Step-by-step explanation:

you would fill in x for 0 and 3 times 0 is 0

then it would be zero plus 1 which would be !

Answer:

B. 1

Explanation:
3(0)+1

0+1=1

Answer:

  I = 12my -p

Step-by-step explanation:

You want to express the interest I on a mortgage of principal p that has a monthly payment of m for y years.

The number of monthly payments in y years is 12y.

The value of those monthly payments is (12y)(m).

The interest paid is the difference between the value of payments and the principal amount of the loan:

  I = 12my -p