What function is inverse of the exponential function y=(1. 5)^x

Answer: 729

Step-by-step explanation:

3^2 is the same has 3 to the power of 2

9^2 is the same as 9 to the power of 2

When you see an expression like 3^2 x 9^2, it means you must raise 3 and 9 to the power of 2, multiply those numbers, and then do it again.

3 raised to the power of 2, often known as 3 times itself or 3 x 3, equals 9.

9 raised to the power of 2, often known as 9 times itself (9 x 9), equals 81.

As a result, when we change these values in the original expression, we obtain:

3^2 x 9^2 = 9 x 81

Now that we have these two integers, we can easily multiply them to obtain the result:

9 x 81 = 729

Therefore, 729 is the answer to the equation 3^2 x 9^2.

The value of one square in each sample is:

(a) 2

(b) 6

(c) 3

(d) 5

Let x represent the value one square. Thus, the value of one square in each sample can be determined as follow.

(a) 2x + 1 = 5        (Left side is equal to right side)

2x = 5 - 1

2x = 4

x = 4/2

x = 2

(b) 10 = x + 2 + 2

10 = x + 4

x = 10 - 4

x = 6

(c) 5 + 1 + x = 9

6 + x = 9

x = 9 - 6

x = 3

(d) 25 = 5x

x = 25/5

x = 5

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As a result, for the two schools, the measures of variability are:

Mountain View School:

Range = 4, Variance = 9.1733, Standard deviation = 3.029

Bay Side School:

Range = 10, Variance = 7.84, Standard deviation = 2.8.

The degree of variance or dispersion in a set of data values is measured by standard deviation. The degree to which the data values deviate or vary from the mean or average value of the data set is indicated by this statistical indicator.

We must ascertain the range, variance, and standard deviation for each dataset in order to determine the measures of variability for the two schools.

Mountain View School:

Range: The smallest class size is 5 and the largest is 9, so the range is 9-5 = 4.

Variance: To calculate the variance, we need to find the mean first.

Mean = (5+6+8+9+8+2+0+10+2+4+5+6+8)/15

= 5.6

Then, we can find the variance using the formula:

Variance = Σ(xi - μ)²/n

= [(5-5.6)² + (6-5.6)² + (8-5.6)² + (9-5.6)² + (8-5.6)² + (2-5.6)² + (0-5.6)² + (10-5.6)² + (2-5.6)² + (4-5.6)² + (5-5.6)² + (6-5.6)² + (8-5.6)²]/15

= 9.1733

Standard deviation = √(9.1733) = 3.029

Bay Side School:

Range: The smallest class size is 0 and the largest is 10, so the range is 10-0 = 10.

Variance: To calculate the variance, we need to find the mean first.

So,

Mean will be = (8+7+6+5+5+4+4+3+1+0+2+0+0+2+3+5)/15

= 3.6

Then, we can find the variance using the following formula:

Variance = Σ(xi - μ)²/n

= [(8-3.6)² + (7-3.6)² + (6-3.6)² + (5-3.6)² + (5-3.6)² + (4-3.6)² + (4-3.6)² + (3-3.6)² + (1-3.6)² + (0-3.6)² + (2-3.6)² + (0-3.6)² + (0-3.6)² + (2-3.6)² + (3-3.6)² + (5-3.6)²]/15

= 7.84

Standard deviation will be = √(7.84)

= 2.8

As a result, for the two schools, the measures of variability are:

Mountain View School:

Range = 4, Variance = 9.1733, Standard deviation = 3.029

Bay Side School:

Range = 10, Variance = 7.84, Standard deviation = 2.8

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The area of the composite shape are

1. Orange

2. Light blue

3. Purple

4. Green

5. Red

6. Yellow

7. Light green

8. Yellow

9. Dark blue

10. Pink

The area of the composite shapes are solved as follows

1. rectangles

= 7 * 3 + (15 - 7) * 1.5

= 21 + 12

= 33 square cm

2.

= 39 x 4 + 0.5(39 + 26) x (18 - 4)

= 156 + 455

= 611 square m

3.

= 12 * 15 + 0.5 x 15 x 10

= 180 + 75

= 255 square ft

4.

= 15 x 7 + 0.5 x π x 3.5 x 3.5

= 105 + 19.24

= 124.2 square cm

5.

= 0.5 x 10 x 22 - 0.5 x 6 x 12

= 110 - 36

= 74 square yd

6.

= 0.5 x π x 3 x 3 + 0.5 x 6 x 11

= 14.14 + 33

= 47.1 square m

7.

= 18 x 6 - 2 x π x 2 x 2

= 108 - 25.13

= 82.8 square m

8.

= 4 x 16 + 0.5 (16 + 10) x (8 - 4)

= 64 + 52

= 116 square cm

9.

= 18 x 8 - 4 * 0.5 x 4 x 4

= 144 - 32

= 112 square cm

10.

= [0.5 (7 + (9 + 3)) x (15 + 6 - 17)] + [(17 - 6) x (9 + 3)] + [6 x 9]

= 38 + 132 + 54

= 224 square cm

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Answer:

Step-by-step explanation:

18 pizzas were eaten at the party in total.

The term "total number" refers to the complete count or sum of a set of numbers or objects. It is the result of adding up all the individual numbers or objects in a set to get a final value that represents the entire set.

If each pizza was cut into 8 slices, then 2 and 1/2 pizzas is equivalent to 20 slices of pizza because:

2\frac{1}{2} \times 8 = 20

Since there were 7 groups of children, the total number of slices of pizza eaten at the party is:

20 slices/pizza x 7 groups = 140 slices

To convert this to the number of pizzas eaten, we divide the total number of slices by the number of slices per pizza:

140 slices ÷ 8 slices/pizza = 17.5 pizzas

Therefore, 17.5 pizzas were eaten at the party in total. However, since a pizza cannot be divided into fractions, we should round up to the nearest whole number, giving us a final answer of 18 pizzas.

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For a loan of $24,000 at 6% interest over 60 months, the monthly payment is $466.47.

A monthly payment is the sum of money that is made towards a debt or loan on a regular basis; it normally consists of both the main and interest. It is a set sum that the borrower must consistently pay until the debt is repaid in full. Mortgages, auto loans, student loans, and personal loans all frequently include monthly installments. The loan amount, the interest rate, and the term of the loan all affect how much will be paid each month.

We can use the following calculation to determine a loan's monthly payment:

M = P * (r * (1 + r)ⁿ) / ((1 + r)ⁿ⁻¹)

where:

M = payment each month

P = Principal (the loaned amount)

r = (Divide the annual interest rate by 12 to get the monthly interest rate)

n = total payments (12 divided by the number of years)

By entering the specified values, we obtain:

P = 24000

r = 6% / 12 = 0.005

n = 60

M = 24000 * (0.005 * (1 + 0.005)⁶⁰) / ((1 + 0.005)^60 - 1)

M = $466.47 (rounded to the nearest cent)

So, $466.47 is the monthly payment for a $24,000 loan with a 6% interest rate over 60 months.

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The supplementary angle means the sum of angles will be 180°. Hence the supplementary angle (or supplement) to a 55º angle is 125°.

When adding two or more angles, the result is 180°, and such pairs of angles are called linear pairs. The word 'linear' means 'straight', and 180° is also referred to as a straight angle. That is why a linear pair is always 180°.

Given angle is 55°.

To find the supplementary angle or supplement of 55º we must subtract 55º from 180°.

That is Supplement = 180 - 55 = 125°.

This is because supplementary angle means sum of two angles results in 180°.

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there were 28,800 handshakes that occurred at the meeting.

How to solve the question?

In order to calculate the number of handshakes that occurred, we can use the formula for the sum of the first n-1 positive integers. The reason we use n-1 is because each person shakes hands with n-1 other people (themselves excluded).

The formula is:

(n-1) + (n-2) + (n-3) + ... + 1

where n is the number of people in the group.

In this case, n = 240, so we plug in:

(240-1) + (240-2) + (240-3) + ... + 1

Simplifying:

239 + 238 + 237 + ... + 1

We can see that this is an arithmetic series with a common difference of -1 and a first term of 239. Using the formula for the sum of an arithmetic series, we get:

S = n/2 * (first term + last term)

S = 240/2 * (239 + 1)

S = 240/2 * 240

S = 28,800

Therefore, there were 28,800 handshakes that occurred at the meeting.

It's worth noting that this calculation assumes that each handshake is counted twice (once for each person involved). If we only counted each handshake once, then we would need to divide our final answer by 2, giving us 14,400 handshakes.

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Based on the information, we can infer that the most accurate method would be method 3 because it randomly selects the participants without any preference.

The most appropriate method for this survey would be method three (option D) because it will have a group of people who were chosen randomly. This means that people can have different ranges of age, gender, preferences, among others.

This is important because they will represent all the diversity of characteristics of the public, which will allow a study in this population to be more accurate.

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The area of the irregular polygon is equal to 30.5 square units.

In this problem we find the representation of an irregular pentagon, that is, a polygon of five sides of different length. Whose area can be found by adding the areas of rectangles and triangles:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

Now we proceed to determine the area of the irregular polygon:

A = 0.5 · 1 · 4 + 0.5 · 3 · 2 + 2 · 4 + 0.5 · 3 · 2 + 3 · 4 + 0.5 · 5 · 1

A = 2 + 3 + 8 + 3 + 12 + 2.5

A = 30.5

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The function f has only one critical value on the open interval (0,10), and the answer is (a) one.

To find the critical values of the function f(x) on the open interval (0,10), we need to find the values of x where f'(x) is equal to zero or undefined.

First, we need to find the values of x where f'(x) is undefined. Since f'(x) contains a term of x in the denominator, it will be undefined at x = 0. However, since the interval we are interested in is (0,10), we can exclude this value.

Next, we need to find the values of x where f'(x) is equal to zero. We can set the numerator of f'(x) equal to zero and solve for x

cos(x²) = 1/5

Taking the inverse cosine of both sides, we get

x² = arccos(1/5)

x = ±√(arccos(1/5))

However, since we are only interested in the interval (0,10), we can discard the negative root. Using a calculator, we can find that

√(arccos(1/5)) ≈ 2.6779

Therefore, the correct option is (a) one

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Answer:

(x+2)^2+(y-5)^2=81

Step-by-step explanation:

standard form equation is (x-h)^2+(y-k)^2=r^2

so, input the values:

(x+2)^2+(y-5)^2=9^2

simplify:

(x+2)^2+(y-5)^2=81

Katie's claim can be represented by the equation: a² ¢= 4(1/2ab) + b²

Katie's claim can be represented by the equation:

Outer square area = Sum of areas of four triangles + Inner square area or mathematically, a² = 4(1/2ab) + b²

where "a" and "b" are the lengths of the legs of the right triangle and "a²" represents the area of the outer square, while "b²" represents the area of the inner square.

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C) 36 yards   18*6=108

108ft to yards is 36

Answer:C

Step-by-step explanation:

Each jump rope is 6 feet long, so 18 jump ropes would require a total of:

18 x 6 = 108 feet of rope

Since there are 3 feet in a yard, we can convert 108 feet to yards by dividing by 3:

108 ÷ 3 = 36 yards

Therefore, the football coach should buy 36 yards of rope. The answer is (C).

Andrew has $28, and Matthew has 5 times that amount, or $140.

The term "amount" typically refers to a quantity or sum of something. It can refer to a physical quantity of something, such as the amount of water in a glass, or an abstract quantity, such as the amount of time it takes to complete a task.

Let x be the amount of money that Andrew has.

Then, the amount of money that Matthew has is 5 times x, which is 5x.

Together, they have a total of $168, so we can write an equation:

x + 5x = 168

Simplifying, we get:

6x = 168

Dividing both sides by 6, we get:

x = 28

Therefore, Andrew has $28, and Matthew has 5 times that amount, or $140.

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Answer:

1 crown and 1 coin

Step-by-step explanation:

1 crown =10 cents

1 coin = 25 cents

10 +25 = 35

Ms. Roberts will pay $9.375 for the grapes.

We have,

To calculate the cost of the grapes, you can multiply the weight of the grapes by their price per pound.

Weight of grapes = 4 3/4 pounds

Price per pound = $2.50

Total cost of grapes = (4 3/4 pounds) x ($2.50/pound)

First, we need to convert the mixed number 4 3/4 to an improper fraction:

= 4(3/4)

= (4 x 4 + 3)/4

= 19/4

Now, we can multiply:

Total cost of grapes = (19/4) x ($2.50/pound)

Simplifying the fractions:

Total cost of grapes = $9.375

Therefore,

Ms. Roberts will pay $9.375 for the grapes.

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Answer:

40 beads

Step-by-step explanation:

First, let's find the length of string that the beads will be on.

The string is originally 20 cm, but 2 cm is taken off each side.

So, the string that the beads will be on is only 16 cm now.

Each bead is 4 mm wide, so we have to convert the bead width to centimeters.

4/10=0.4

So each bead is 0.4 cm.

Now to find how many beads will fit, we have to divide the length by the width of the bead.

16/0.4=40

So, Mona will need 40 beads.  Hope this helps ;)

The expression (x^2 -3x+7) cannot be simplified further because there are no like terms to combine or any other operations to perform. It is already in its simplest form.

The expression (x^2 -3x+7) is a quadratic expression, meaning it has a degree of 2. It cannot be simplified further because there are no like terms to combine, which is the only operation that can be performed to simplify polynomials.

To understand this, let's look at the individual terms of the expression. The term x^2 is the highest degree term, which means it has the greatest power of x.

The term -3x is the linear term, which means it has a degree of 1. And the constant term is 7, which means it has a degree of 0.

Since the terms have different degrees and there are no like terms, there is no way to simplify the expression any further.

Therefore, (x^2 -3x+7) is already in its simplest form.

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The digit 5 in 89.059 is greater than the digit 5 in 78.365.

To compare the digit 5 in the numbers 89.059 and 78.365, we need to look at the place value of the digit 5 in both numbers. In 89.059, the digit 5 is in the thousandth place, while in 78.365, the digit 5 is in the hundredth place.

Since the digit 5 in the thousandth place has a greater place value than the digit 5 in the hundredth place, it means that the digit 5 in 89.059 is greater than the digit 5 in 78.365.

To understand this concept better, consider the place value system of decimal numbers, where each digit represents a specific place value. The rightmost digit represents the units, the next digit to the left represents the tens, and so on.

Moving leftwards, each digit's place value increases by a factor of 10. Thus, the digit 5 in the thousandth place has a place value of 0.001, which is greater than the place value of the digit 5 in the hundredth place, which is 0.01. Therefore, the digit 5 in 89.059 is greater than the digit 5 in 78.365.

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The length or value of d is 3m

What is meant by length?

Length is a measurement of how long something is, typically referring to the longest dimension of an object or space. It is a fundamental physical quantity and can be measured in various units, such as meters, feet, or inches. Length is important in many fields, including mathematics, science, and engineering.

According to the given information

In a right-angled triangle, the side opposite to the 90-degree angle is called the hypotenuse. The side opposite to the 60-degree angle is equal to the hypotenuse multiplied by the square root of 3 divided by 2. Since AC is the hypotenuse and its length is given as 2*(√(3))m, we can find the length of BC (d) as follows:

d = (AC * √(3)) / 2 d = (2 * √(3) * √(3)) / 2

d = 3m

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However, 2/7 is not equivalent to any fraction with denominator 6. Therefore, Maria's claim is incorrect.

A fraction is a way of representing a part of a whole or a ratio between two quantities. It consists of two numbers, the numerator (located above the fraction line) and the denominator (located below the fraction line), separated by a horizontal fraction bar. The numerator represents the number of parts of the whole or the ratio, while the denominator represents the total number of equal parts or the denominator of the ratio.

For example, the fraction 3/4 represents three out of four equal parts or three parts out of a total of four parts. It can also be interpreted as a ratio of three to four. Fractions can be simplified by dividing both the numerator and denominator by their greatest common factor. For instance, the fraction 6/8 can be simplified to 3/4 by dividing both the numerator and denominator by 2.

A counterexample to Maria's claim is the fraction 2/7.

To see this, note that 1/5 is equivalent to 14/70 and 1/7 is equivalent to 10/70. Therefore, any fraction between 1/5 and 1/7 can be expressed in the form n/70, where 10 < n < 14.

However, 2/7 is not equivalent to any fraction with denominator 6. Therefore, Maria's claim is incorrect.

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Opposite rays can be defined as a figure formed by two collinear rays with a common endpoint, since the two rays lie on the same line.

The value of x is given as follows:

x = 12.25

Similar triangles are triangles that share these two features listed as follows:

The proportional relationship for the side lengths in this problem is given as follows:

x/7 = 3.5/2

Applying cross multiplication, the value of x is obtained as follows:

2x = 7 x 3.5

x = 7 x 3.5/2

x = 12.25.

The triangle is given by the image presented at the end of the answer.

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Six semicircles lie in the interior of a regular hexagon with a side length of 2 so that the diameters of the semicircles coincide with the sides of the hexagon. The zone of the shaded locale is around 10.3923 square units.

 We will approach this problem by first finding the region of the hexagon and after that subtracting the zones of the six semicircles from it. The zone of a customary hexagon with side length 2 can be found utilizing the equation:

Region of hexagon = (3√3/2) x side[tex]^{2}[/tex]

Substituting the given esteem of side length, we get:

Area of hexagon = (3√3/2) x 2[tex]^{2}[/tex] = 6√3

The range of a crescent is half the region of the comparing circle. So, the zone of each crescent is:

Range of semicircle = 1/2 x π x radius[tex]^{2}[/tex] = 1/2 x π x 1^[tex]^{2}[/tex]= π/2

There are six semicircles, so the whole range of the semicircles is:

Add up to the zone of semicircles = 6 x π/2 = 3π At long last, able to find the zone of the shaded locale by subtracting the region of the semicircles from the range of the hexagon:

Zone of shaded locale = Range of hexagon - Add up to a range of semicircles

= 6√3 - 3π

≈ 10.3923 thus, the zone of the shaded locale is around 10.3923 square units. 

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