Sylvia is going to pick out a souvenir hat while she is on vacation. She knows the price of the hat will increase by 5% when she pays sales tax. She writes the expression h + 0.05h to find the total amount she will pay for the hat if it costs h dollars. Jin correctly writes another expression, 1.05h, that will also find the the total amount Sylvia will pay for the hat if it costs h dollars. Use the drop-down menus to explain what each part of Sylvia's and Jin's expressions mean.

Volume of cube is given by the formula :

[tex] Volume = a * a * a [/tex]

Where a is edge of the cube.

We are given edge of cube as 12 inches.

Plugging the value of edge in given formula:

[tex] Volume = 12 * 12 * 12 [/tex]

Volume = 1728 cubic inches.

Answer : Volume of cube is 1728 cubic inches.

Volume of cube is given by the formula :

[tex] Volume = a * a * a [/tex]

Where a is edge of the cube.

We are given edge of cube as 12 inches.

Plugging the value of edge in given formula:

[tex] Volume = 12 * 12 * 12 [/tex]

Volume = 1728 cubic inches.

Answer : Volume of cube is 1728 cubic inches.

Yes, it is possible to place 158 books on three shelves with the given conditions. The distribution will be 49 books on the first shelf, 57 books on the second, and 52 books on the third shelf.

To solve this problem, let's use algebra. Let x represent the number of books on the second shelf. According to the given conditions, the first shelf would have x - 8 books, and the third shelf would have x - 5. The total number of books on all three shelves is 158, and the equation representing the total number of books is:

x + (x - 8) + (x - 5) = 158

Combining like terms:

3x - 13 = 158

Adding 13 on both sides:

3x = 171

Dividing both sides by 3:

x = 57

Therefore, the second shelf has 57 books, the first shelf has 49 books (57 - 8), and the third shelf has 52 books (57 - 5).

It is possible to place the books on the three shelves as required, and the answer is yes, with the distribution being 49 books on the first shelf, 57 books on the second, and 52 books on the third.

Answer:

Part 1) Option A [tex]x>-4[/tex]

Part 2) Option D [tex]x<3[/tex]

Part 3) [tex]y < 1.1[/tex]  

Part 4) [tex]x<-8/15[/tex]

Part 5) [tex]x>-1[/tex]

Step-by-step explanation:

Part 1) we have

[tex]6x-5>-29[/tex]

[tex]6x>-29+5[/tex]

[tex]x>-24/6[/tex]

[tex]x>-4[/tex]

Part 2) we have

[tex]-4x-8>-20[/tex]

[tex]-4x>-20+8[/tex]

[tex]-4x>-12[/tex] -----> Multiply by [tex]-1[/tex]  both sides

[tex]4x<12[/tex]

[tex]x<12/4[/tex]

[tex]x<3[/tex]

Part 3) we have

[tex]-4.2y+2.1 >-2.52[/tex]

[tex]-4.2y >-2.52-2.1[/tex]

[tex]-4.2y >-4.62[/tex] ----> Multiply by [tex]-1[/tex]  both sides

[tex]4.2y < 4.62[/tex]

[tex]y < 1.1[/tex]

Part 4) we have

[tex]-(1/2)x+(1/3)>3/5[/tex]

[tex]-1/2x>(3/5)-(1/3)[/tex]

[tex]-1/2x>4/15[/tex] ---> Multiply by [tex]-1[/tex]  both sides

[tex]1/2x<-4/15[/tex]

[tex]x<-8/15[/tex]

Part 5) we have

[tex]-2.8x+5.6< 8.4[/tex]

[tex]-2.8x< 8.4-5.6[/tex]

[tex]-2.8x< 2.8[/tex] ---> Multiply by [tex]-1[/tex]  both sides

[tex]2.8x>-2.8[/tex]

[tex]x>-2.8/2.8[/tex]

[tex]x>-1[/tex]

Answer:x= -6 and -8

Step-by-step explanation: I took the test

Answer:

Step-by-step explanation:

Given that the distance light travels in one light second about

[tex]1.86(10^5) miles[/tex]

Distance of Saturn from Sun = Time taken for travel x speed

Here speed = [tex]1.86 x 10^5[/tex]

Time taken = 475 light seconds

Hence distance = [tex]1.86 x 10^5x475\\=883.5x10^5\\=8.835x10^7[/tex] miles

Answer: B) The graph of f(x) is horizontally stretched.

Step-by-step explanation: We are given an absolute function [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex].

The standard equation of an absolute function is [tex]f(x)= a|x-h|+k[/tex].

Where (h,k) is the vertex of the absolute function.

If we compare [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex] and [tex]f(x)= a|x-h|+k[/tex], we can see a=[tex]-\frac{2}{3}[/tex], h= -4 and h= -6.

Therefore, first, third and fourth options are incorrect.

So, the second option would only be applicable.

We can see here that the two consecutive whole numbers that 101 lies between are 100 and 102.

To find two consecutive whole numbers that 101 lies between, we can start by finding the smaller whole number.

Since 101 is greater than 100, the smaller whole number would be 100.

To find the larger whole number, we can add 2 to the smaller whole number:

100 + 2 = 102

Thus, we see here that 100 and 102 are the two consecutive numbers where 101 lies between. As we see above, we see the process of finding the numbers.

Consecutive numbers are numbers that follow each other in order without any gaps and have a difference of 1 between each number. In other words, they are numbers that come one after another in a sequence.

Answer:

24

Step-by-step explanation:

The turtle tank has 24 yellow turtles, computed using the guess and check method.

The guess and check method is the process of guessing a solution to the given conditions that will be satisfying all the conditions.

In the question, we are informed that Bernadette is at the turtle tank, which has 32 green and yellow turtles in the tank. We are also informed that there are 3 times as many yellow turtles as green turtles.

Assuming the number of green turtles to be g, and the number of yellow turtles to be y, we can write the equation g + y = 32, as the total number of turtles is given to be 32.

Now, we are told that the number of yellow turtles is 3 times the number of yellow turtles.

Thus, we can say that y = 3g.

Substituting this in the equation, we get g + 3g = 32, or, 4g = 32.

We are asked to solve this equation by the guess and check method.

If we guess g to be 7, the equation is not satisfied as we get 28 = 32.

If we guess g to be 9, the equation is not satisfied as we get 36 = 32.

If we guess g to be 8, the equation is satisfied as we get 32 = 32.

Thus, the correct value for g is 8.

Thus, y = 3g = 3*8 = 24.

Thus, the turtle tank has 24 yellow turtles, computed using the guess and check method.

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Answer:

Answer is b

Step-by-step explanation:

The next two terms of the given geometric sequence is 810.

The first three terms of a geometric sequence are 10, 30, 90.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The formula to find nth term of the geometric sequence is [tex]a_n = ar^{n - 1[/tex].

Where, a = first term of the sequence, r= common ratio and n = number of terms.

Here, the common ratio is 30/10 = 90/30 = 3

Now, [tex]a_4=10\times 3^{4-1}[/tex]

= 10 × 3³

= 270

[tex]a_5=10\times 3^{5-1}[/tex]

= 810

Therefore, the next two terms of the given geometric sequence is 810.

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Step-by-step explanation:  B

We have ---- >  55, 62, 61, 54, 68, 72, 59 ,61, 70  

In total 9 numbers

step 1

order  the numbers  from smallest to largest

54,55,59,61,61,62,68,70,72

1) What is the minimum of the data set ?

The lowest number is the minimum------------ > 54

2) What is the median of the data set ?

Find the number that is in the middle  

54,55,59,61,61,62,68,70,72

The middle number is 61. That is the median.  

Find the middle of each half. Since these numbers are between 2 numbers, you average the numbers (add then divide by 2).  

55+59=114/2=57 This is the first quartile.  

68+70=138/2=69 This is the third quartile

3) What is the first quartile of the data set ?

the answer is 57

4) What is the third quartile of the data set ?

the answer is 69

5) What is the maximum of the data set ?

The highest is the maximum------------ > 72

Answer:

Minimum = 54

Maximum = 72

Median = 61

First quartile = 57

Third quartile = 69

Step-by-step explanation:

Data : 55 62 61 54 68 72 59 61 70

Arrange the data is ascending order

54 , 55, 59, 61,61 ,62 , 68,70 ,72

So, minimum = 54

Maximum = 72

Median is the mid value .

There are nine observations.

So, 5th observation is the median

So, Median = 61

First quartile = It is the median of data of the left side data of the median .

Left side data : 54 , 55, 59, 61

There are four observations

Median = [tex]\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}[/tex]

Median = [tex]\frac{\frac{4}{2}th+(\frac{4}{2}+1)th}{2}[/tex]

Median = [tex]\frac{2th+3rd}{2}[/tex]

Median = [tex]\frac{55+59}{2}[/tex]

Median = [tex]57[/tex]

First quartile = 57

Third quartile = It is the median of data of the right side data of the median .

Right side data : 62 , 68,70 ,72

There are four observations

Median = [tex]\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}[/tex]

Median = [tex]\frac{\frac{4}{2}th+(\frac{4}{2}+1)th}{2}[/tex]

Median = [tex]\frac{2th+3rd}{2}[/tex]

Median = [tex]\frac{68+70}{2}[/tex]

Median = [tex]69[/tex]

Third quartile = 69

Hence minimum is 54 , maximum is 72 ,median is 61 , first quartile is 57 and third quartile is 69

When you add two rational numbers, each number can be written as a  

✔ fraction .

Step-by-step explanation:

When you add two rational numbers, each number can be written as a fraction.

A Rational number can be defined as any number which can be represented in the form of p/q where q ≠ 0. It can be made by dividing an integer by an integer.

For the given situation,

The sum of two rational numbers is rational.

The closure property of addition of rational number states that if we add two rational number, then the sum of these two rational number will also be a rational number.

Adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication.

Hence we can conclude that when you add two rational numbers, each number can be written as a fraction.

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Answer:

1)  the slant height of the pyramid is 50 meters.

2) there are (approximately) a total of 80 ft of laser beams.

Step-by-step explanation:

1) The height of the pyramid (30 m) and half of the length of its base (40 m) form a rectangular triangle, where the slant height is its hypotenuse (H). From Pythagorean theorem:

H^2 = 30^2 + 40^2

H = √2500

H = 50 m

2) In the figure attached the rectangular prism is shown (point E was added).

The length of the laser beams is the addition of the segments AD to segment CB (which are equal).

We can make a rectangular triangle between points ECD. From Pythagorean theorem:

ED^2 = EC^2 + CD^2

ED = √(12^2 + 35^2)

ED = 37 ft

We can make a rectangular triangle between points AED. From Pythagorean theorem:

AD^2 = EA^2 + ED^2

AD = √(15^2 + 37^2)

AD ≈ 40

Then, there are (approximately) a total of 80 ft of laser beams.