what is the volume of the rectangular prism?

The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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ANSWER:

C. linear growth; because the rate of growth is constant

STEP-BY-STEP EXPLANATION:

With the data supplied by the statement we can establish the following function:

We can see that it is a linear function that is increasing, since rate of growth is constant and positive

Answer: she putz 9 in the last shelter

Step-by-step explanation:

Answer:

In explanation

Step-by-step explanation:

x= -1

3(-1)^2+7=0

= 10

x= 0

3(0)^2+7

y=7

x=1

3(1)^2+7

y=10

x=2

3(2)^2+7

=3(4)+7

=12+7

y=19

Step-by-step explanation:

x^2+5x+7x+35=0

x*x+5x+7x+5*7=0

x(x+5)+7(x+5)=0

(x+7)*(x+5)=0

x=-7 or x=-5

So the function is positive (>0) when

x<-7 and when x>-5

Answer: 252 ft²

Step-by-step explanation:

    Based on the picture, the scale drawing of the kitchen is 1.75 in by 2.25 in.

    We will convert these measurements using the scale, \(\frac{1}{4}\) in = 2 ft. We will use dimensional analysis.

1.75 in ➜ \((1.75\;in)(\frac{2\;ft}{0.25\;in})=14\;ft\)

2.25 in ➜ \((2.25\;in)(\frac{2\;ft}{0.25\;in})=18\;ft\)

    Lastly, we will solve for the area using the formula below.

A = LW

A = (14 ft)(18 ft)

A = 252 ft²

\(A=252(ft^{2} ).\)

As you can see on the image, the kitchen forms the shape of a rectangle, therefore, to find the area of its area is:

\(A=WL\); where "W" is the width if the rectangle and "L" is the length.

Check the attached image.

W= \(1 \frac{3}{4}(in)\)

L= \(2\frac{1}{4}(in)\)

For W:

\(1 \frac{3}{4}(in)*\frac{2(ft)}{\frac{1}{4} (in)} =\\ \\1 +\frac{3}{4}(in)*\frac{2(ft)}{\frac{1}{4} (in)}=\\ \\1+0.75(in)*\frac{2(ft)}{0.25(in)} =\\ \\1.75(in)*\frac{2(ft)}{0.25(in)} =\\ \\14ft\)

------------------------------------------------------------------------------------------------------------

For L:

\(2\frac{1}{4}(in)*\frac{2(ft)}{\frac{1}{4} (in)} =\\ \\2+0.25(in)*\frac{2(ft)}{0.25(in)} =\\ \\2.25(in)*\frac{2(ft)}{0.25(in)} \\ \\18ft\)

\(A=14(ft)*18(ft)=252(ft^{2} )\)

Answer:

right square pyramid A≈742.98

Step-by-step explanation:

Height ; 40

base area ; 70

Answer:

False. The center of a semisimple Lie algebra is usually not trivial.

Step-by-step explanation:

The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.

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Answer:

(-1,4)

Step-by-step explanation:

to find out we just fill in the values to see if it’s true

(x,f(x))

4=-1^2+3

4=1+3

4=4

True

-4=-1^2+3

-4=1+3

-4=4

Not true

-4=1^2+3

-4=1+3

-4=4

Not true

-1=-4^2+3

-1=16+3

-1=19

Not true

Hopes this helps please mark brainliest

The margin of error is defined as follows:

M = 1.9z/sqrt(n).

In which:

The bounds of the confidence interval are given as follows:

\(\overline{x} \pm z\frac{\sigma}{\sqrt{n}}\)

In which:

The margin of error is then given as follows:

\(M = z\frac{\sigma}{\sqrt{n}}\)

The problem is incomplete, hence the general procedure to obtain the sample size was presented.

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The equation does not have a unique solution for x. It is true for any value of x.

The given equation is:

(5/7)(x + 2) - (3/7)x = (2/7)(x + 5)

To solve for x, we'll first simplify both sides of the equation using the distributive property and combining like terms:

[(5/7)x + (5/7)(2)] - (3/7)x = [(2/7)x + (2/7)(5)]

Simplifying further:

(5/7)x + 10/7 - (3/7)x = (2/7)x + 10/7

Next, we'll collect the x terms on one side and the constant terms on the other side of the equation:

(5/7)x - (3/7)x - (2/7)x = 10/7 - 10/7

Combining like terms:

[(5/7) - (3/7) - (2/7)]x = 0

Simplifying further:

(0/7)x = 0

Any value of x will satisfy this equation since (0/7)x will always be zero.

Therefore, the equation does not have a unique solution for x. It is true for any value of x.

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Subtracting the old surface area from the new surface area will reveal the surface area growth. the increase in surface area is  \(0.9l + 0.9w + 54\) square cm.

First way to solve the problem:

Let's assume the original dimensions of the rectangular prism are length = L, width = W, and height = 30 cm. Then, the surface area of the box can be calculated as:

Surface area \(= 2(LW + LH + WH)\)

After increasing the height by 0.9 cm, the new height becomes 30.9 cm. So, the new surface area can be calculated as:

New surface area \(= 2(LW + L(30.9) + W(30.9) + WH)\)

The increase in surface area can be found by subtracting the original surface area from the new surface area:

Increase in surface area = New surface area - Surface area

\(= 2(LW + L(30.9) + W(30.9) + WH) - 2(LW + LH + WH)\)

\(= 2(30.9L + 30.9W + 30H + 0.9L + 0.9W) - 2(30L + 30W + 30H)\)

\(= 1.8L + 1.8W + 54\)

Therefore, the increase in surface area is \(1.8L + 1.8W + 54\) square cm.

Second way to solve the problem:

We can also use the formula for the surface area of a rectangular prism, which is:

Surface area \(= 2lw + 2lh + 2wh\)

If the height is increased by 0.9 cm, then the new surface area can be calculated as:

New surface area  \(= 2lw + 2l(30.9) + 2w(30.9)\)

\(= 2lw + 60.9l + 60.9w\)

The increase in surface area can be found by subtracting the original surface area from the new surface area:

Increase in surface area = New surface area - Surface area

\(= (2lw + 60.9l + 60.9w) - (2lw + 60l + 60w)\)

\(= 0.9l + 0.9w + 54\)

Therefore, the increase in surface area is  \(0.9l + 0.9w + 54\) square cm.

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The given question is incomplete. The complete question is given below:

A box has the shape of a rectangular prism with height 30 cm. If the height is increased by 0.9 ​cm, by how much does the surface area of the box​ increase?

Use pencil and paper. Show your work. Then show a second way to solve the problem. Explain which way you like better and why.

The number in an expanded form is 700,000 + 182 + 0.009

The number is given as:

seven hundred thousand one hundred eighty-two and nine thousandths

Next, we split the numbers:

seven hundred thousand = 700,000

one hundred eighty-two = 182

and nine thousandths = 0.009

Next, we add the numbers

700,000 + 182 + 0.009

Hence, the number in an expanded form is 700,000 + 182 + 0.009

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Answer:

Step-by-step explanation:

g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)}

The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.

In Mathematics, the average of these quiz scores can be calculated by using the following formula:

Average = Sum of quiz score/Number of quiz scores

Note: Let the variable q represent the student's score on the third (3rd) quiz.

Substituting the given parameters into the formula, we have the following;

Average = (75 + 83 + q)/3

Average = (158 + q)/3

This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:

85 ≤ (158 + q)/3 ≤ 90

Multiplying all through by 3, we have the following:

255 ≤ (158 + q) ≤ 270

Subtracting 158 from both sides of the inequality, we have the following:

97 ≤ x ≤ 112

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Answer:

see explanation

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle then the median is the average of the values either side of the middle.

Given

3   8   14   19   22   29   33   37   43   49

                            ↑ middle is between 22 and 29

median = \(\frac{22+29}{2}\) = \(\frac{51}{2}\) = 25.5

The upper quartile \(Q_{3}\) is the middle value of the data to the right of the median.

29   33   37   43   49

               ↑

\(Q_{3}\) = 37

The lower quartile \(Q_{1}\) is the middle value of the data to the left of the median.

3   8   14   19   22

           ↑

\(Q_{1}\) = 14

The min is the smallest value in the data set, that is 3

The max is the largest value in the data set, that is 49

The 5 number summary is

3,  14,  25.5,  37,  49

To configure the emergency trauma center within the given 1,500 square feet, consider the dimensions of equipment items such as patient beds, medical carts, examination tables, imaging equipment, surgical equipment, workstations, and storage areas.

To configure the emergency trauma center within the given 1,500 square feet, we need to consider the dimensions of the equipment items and plan an efficient layout. Here is a list of equipment items and their dimensions:

Patient beds: These typically have dimensions of around 3 feet by 6 feet. Depending on the number of beds required, we can allocate sufficient space for them, keeping in mind the need for walkways around each bed.

Medical carts: These can vary in size, but a common dimension is around 2 feet by 3 feet. Allocate a designated area or storage space for the medical carts, ensuring easy access and mobility.

Examination tables: These usually have dimensions of approximately 2.5 feet by 5 feet. Plan a separate area for examination rooms where the tables can be placed along with other necessary equipment.

Imaging equipment: Such as X-ray machines or CT scanners, which may require a designated room or area with specific shielding and safety considerations. Ensure enough space for patient accessibility and the equipment's operation.

Surgical equipment: Depending on the specific surgical procedures performed, allocate adequate space for surgical tables, anesthesia carts, surgical instruments, and any required sterilization equipment.

Workstations: Create workstations for medical staff, including computers, desks, and storage areas for paperwork and supplies. Consider the need for privacy and comfortable working conditions.

Storage areas: Allocate space for storing medical supplies, medications, and other equipment that may not be immediately needed but should be easily accessible.

When planning the layout, consider factors such as patient flow, accessibility, and safety regulations. It's essential to create a functional and efficient floor plan that allows for smooth operations and optimal patient care within the given square footage.

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Answer:

terminating decimals

Step-by-step explanation:

they don't seem to repeat numbers

Answer:

repeating

Step-by-step explanation:

6÷7= 1.111111111111

Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

Algebraic expression is a expression that contains variables,constants with algebraic operations (addition , subtraction , etc)

Answer:

3(2x+2) = 6x + 6

Step-by-step explanation:

Those are algebra tiles, so it is saying (if you read across the top) 2x +2 then if you read down you have 3 units, so the dot means 2x + 2 multiplied by 3

If you write it in algebraic terms it is 3(2x+2) so the answer when you distribute is 3 (2x) + 3(2) so 6x + 6, and if you count the number of red rectangles you have 6 of them, hence the 6x, and if you cound the units in gray you have 6 of them, hence the 6.

Algebra tiles are used to demonstrate algebra concepts

Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

Answer:

m = 25 + 6n

Step-by-step explanation:

To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.

Answer:

  (c)  0

Step-by-step explanation:

Each of the terms in the expression represents a different transformation of a different trig function. Expressing those as the same trig function can make it easier to find the sum.

__

We can start with the identity ...

  cos(x) = sin(x +π/2)

Substituting the argument of the cosine function in the given expression, we have ...

  cos(π/2 -θ) = sin((π/2 -θ) +π/2) = sin(π -θ) = -sin(θ -π)

__

The first term, sin(π +θ), is a left-shift of the sine function by 1/2 cycle, so can be written ...

  sin(π +θ) = -sin(θ)

The second term is the opposite of a right-shift of the sine function by 1/2 cycle, so can be written ...

  cos(π/2 -θ) = -sin(θ -π) = sin(θ)

Then the sum of terms is ...

  sin(π +θ) +cos(π/2 -θ) = -sin(θ) +sin(θ) = 0

The sum of the two terms is identically zero.

The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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Answer:

Step-by-step explanation:

You worked 4 weeks.

You were paid 200 dollars

200  divided by 4 = weekly wage

200 / 4 = 50

She was paid 50 dollars per week.

{(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

When one magnitude depends on another, the relationship between them is known as a mathematical function. So long as they are uniquely and solely connected.

Every mathematical function is the relationship between an element of group A and an element of group B. Consequently, the following algebraic expression can be used to represent this function:

Therefore, the {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The complete question is given below,

Which relation describes a function? What makes it a function?

A) {(-2,3),(-2,5),(-6,7)} Each member of the range is unique.

B) {(2,3),(3,3),(3,4)} Each member of the domain and range is positive.

C) {(2,3),(3,3),(3,4)} Each member of the domain and range is a real number.

D) {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range.

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Answer:

2.2

Step-by-step explanation:

The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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