A right rectangular prism and its net are shown below.

x=15.4 units

First, some definitions before working the problem:

The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.

The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.

Working the problem

For the given triangle, the right angle is at the bottom, so the side on top is the hypotenuse.  We know the angle in the upper right corner, so the side across from it with length 4.5, is the opposite side.

For this triangle, the "opposite" leg is known.  Additionally, the "hypotenuse" is unknown and is our "goal to find" side.

Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".

Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh".  So, the desired function to use for this triangle is the Sine function.

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]sin(17^o)=\dfrac{4.5}{x}[/tex]

Multiply both sides by x, and divide both sides by sin(17°)...

[tex]x=\dfrac{4.5}{sin(17^o)}[/tex]

Make sure your calculator is set to degree mode, and calculate:

[tex]x=\dfrac{4.5}{0.2923717047227...}[/tex]

[tex]x=15.391366289249...[/tex] units

Rounded to the nearest tenth...

[tex]x=15.4[/tex] units

Answer: 44%, 26%, less likely

Step-by-step explanation:

just do the math!!

The "Expression" which is considered equivalent to this expression "(3x-1)-2(x+2)' is (c) x-5.

In mathematics, an algebraic expression is a combination of numbers, variables, which are joined by arithmetic operations (such as addition, subtraction, multiplication, and division).

We have to find the equivalent-expression for (3x-1)-2(x+2);

⇒ (3x-1)-2(x+2),

⇒ (3x - 1) - 2x - 4,

Combing the like-terms together in the above expression,

We get,

⇒ 3x - 2x -1 - 4,

⇒ x - 5,

Therefore, the correct equivalent expression is Option (c).

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The given question is incomplete, the complete question is

Which of the following expression is equivalent to (3x-1)-2(x+2)?

(a) x+3

(b) x+1

(c) x-5

(d) x-3

Answer:

- 9/16

Step-by-step explanation:

When multiplying fractions, you can multiply them straight across.

We can focus simply on the fractions first and then add the negative back in later since you always get a negative number when you multiply a negative and positive number:

- (3 /4) * (3 / 4)

- (3 * 3) / (4 * 4)

- (9/16)

-9/16

The simplified expression of given term  is: -4 + 2 + -2 + -3x = -4 - 3x

Simplification refers to the process of reducing an expression to its simplest form by combining like terms, removing parentheses, and performing any necessary operations such as addition, subtraction, multiplication, and division. The goal of simplification is to make an expression easier to read and work with, and to reveal any patterns or relationships that may not have been obvious in the original expression. Simplification is an important part of solving equations, evaluating expressions, and performing mathematical operations in general.

We can simplify the expression by combining like terms.

Starting with -4, we add 2 to get:

-4 + 2 = -2

Next, we subtract 2 from -2:

-2 - 2 = -4

Finally, we subtract 3x from -4:

-4 - 3x

So the simplified expression is:

-4 + 2 + -2 + -3x = -4 - 3x

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Answer:

1 inch = 0.6 miles

= 9 inches = 0.6 miles*9

= 9 inches = 5.4 miles

Hence, the answer is 5.4 miles.

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The savings amount balance in the account is $ 467.39

Given data ,

You just opened a savings account and deposited $300 at 3% that you plan on withdrawing in 15 years.

Using the formula FV = PV * (1 + i)^n, where FV is the future value, PV is the present value, i is the interest rate, and n is the number of periods, we can calculate the future value of the savings account after 15 years.

PV = $300 (the initial deposit)

i = 0.03 (the interest rate per period)

n = 15 years (the number of periods)

FV = $300 (1 + 0.03)^15

FV = $300 ( 1.5579 )

FV = $467.39

Hence , after 15 years, the savings account will have a balance of $ 467.39

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Answer:

A square's length & width are equal

Step-by-step explanation:

Kamal's shape is not a square, because a square is equilateral (equal length in all sides), but his square is 2:1,

Answer:

Assuming you meant to write "x^2 - 4x - 12", there are a few equivalent forms that you could use to represent this expression. One common form is:

(x - 6)(x + 2)

Step-by-step explanation:

This is the factored form of the expression, which shows that it can be written as a product of two linear factors. To see why this is true, you can use the distributive property to expand the product:

(x - 6)(x + 2) = x(x + 2) - 6(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12

Answer:

Step-by-step explanation:

This is a word problem involving percentages. To solve it, we need to follow these steps:

Identify the given information and the unknown quantity. In this problem, we are given that Natalie has $330 to spend at the amusement park, 5% is spent on games, 5/11 is for food and drinks, and she spends $13 on parking. The unknown quantity is the price of one ticket.

Write an equation that relates the given information and the unknown quantity. We can use the fact that the sum of all parts of the whole is 100%1. Let x be the price of one ticket. Then we have:

games+food and drinks+parking+tickets0.05×330+115​×330+13+2x​=total amount=330​

Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:

16.5+150+13+2x2x2xxx​=330=330−16.5−150−13=150.5=2150.5​=75.25​

Therefore, the price of one ticket is $75.25.

Answer: y = 3/5x - 2/5

Step-by-step explanation: The slope-intercept form is y = mx+b. Hence, solve for y. 3x - 5y = 2.

Move 5y to the right side and move 2 to the left. 3x - 2 = 5y. Divided 5 for all sides: 3/5x - 2/5 = y. Hence, writing in slope-intercept form is y= mx + b, y = 3/5x - 2/5.

A function whose graph is the graph of y = √x, but is shifted to the left 9 units is [tex]y=\sqrt{x+9}[/tex].

In Mathematics and Geometry, the translation of a geometric figure or graph to the left means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

Conversely, the translation a geometric figure upward means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, the transformed function should be written as follows:

y = √x

g(x) = (√x + 9)

[tex]y=\sqrt{x+9}[/tex]

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A: The data provides convincing evidence, at α=0.02 level, that the glucose drug is effective in reducing mean glucose level.

B: The 98% confidence interval for the difference in mean reduction of glucose level between placebo and drug groups is 3.5 to 13.7 mg/dL, supporting the effectiveness of the glucose drug

A: To test whether the glucose drug is effective in producing a reduction in mean glucose level, we will use a two-sample t-test with equal variances assuming normality of the differences.

Let μA be the true mean reduction in glucose level for the placebo group and μB be the true mean reduction in glucose level for the glucose drug group. The null hypothesis is H0: μA - μB = 0, and the alternative hypothesis is Ha: μA - μB < 0

Using the given data, the sample mean reduction for the placebo group is 9.7 mg/dL and for the glucose drug group is 18.3 mg/dL. The pooled sample standard deviation is 8.064 mg/dL, and the t-statistic is calculated to be:

t = (xB - xA) / (sP × √(1/nA + 1/nB))

= (18.3 - 9.7) / (8.064 × √(1/10 + 1/10))

= 2.551

where xA and xB are the sample means, sP is the pooled sample standard deviation, and nA and nB are the sample sizes.

B: To create a 98% confidence interval for the difference in the placebo and the new drug, we will use the formula:

CI = (xB - xA) ± tα/2,sP × √(1/nA + 1/nB)

where xA and xB are the sample means, sP is the pooled sample standard deviation, nA and nB are the sample sizes, and tα/2,sP is the t-value corresponding to a 98% confidence level with 18 degrees of freedom.

Using the values from Part A, we have:

CI = (18.3 - 9.7) ± 2.101 × 8.064 × √(1/10 + 1/10)

= 8.6 ± 5.103

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The correct question is:

Twenty middle-aged men with glucose readings between 90 milligrams per deciliter and 120 milligrams per deciliter of blood were selected randomly from the population of similar male patients at a large local hospital. Ten of the 20 men were assigned randomly to group A and received a placebo. The other 10 men were assigned to group B and received a new glucose drug. After two months, posttreatment glucose readings were taken for all 20 men and were compared with pretreatment readings. The reduction in glucose level (Pretreatment reading − Posttreatment reading) for each man in the study is shown here.

Group A (placebo) reduction (in milligrams per deciliter): 12, 8, 17, 7, 20, 2, 5, 9, 12, 6

Group B (glucose drug) reduction (in milligrams per deciliter): 29, 31, 13, 19, 21, 5, 24, 12, 8, 21

Part A: Do the data provide convincing evidence, at the α = 0.02 level, that the glucose drug is effective in producing a reduction in mean glucose level?

Part B: Create and interpret a 98% confidence interval for the difference in the placebo and the new drug.

Answer:

The y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Step-by-step explanation:

To solve this question, we need to plug in x = 0 into the given equation and simplify. We get:

y = 6(0 - 1/2)(0 + 3) y = 6(-1/2)(3) y = -9

Therefore, the y-intercept of the graph of the equation is -9. This means that the graph crosses the y-axis at the point (0, -9).

Stan used 19/40 of a gallon of gasoline.

Given that;

At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank.

Hence, It means that the number of gallons of gasoline that he has already put in the tank is

1/8 + 6/10 = 29/40 of a gallon.

Now, After he mowed, 1/4 of a gallon was left in the tank.

Therefore, the total amount of gasoline Stan used is

29/40 - 1/4 = 19/40 of a gallon

Thus, the total amount of gasoline Stan used is, 19/40 of a gallon

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The calculated value of the median of the A-list 7 members at the gym is 54

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

10, 64, 52, 46,54,67,54.

When the numbers are sorted in ascending order, we have

Sorted list = 10, 46, 52, 54, 54, 64, 67

The median is the middle number of the sorted list

So, we have

Middle number = 54

Thsis means that

Memdian = 54

Hence. the median of the A-list 7 members at the gym is 54

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The ramp has a volume capacity of around 37.5 cubic feet.

Calculating the volume of a triangular prism shaped ramp follows a specific formula. First, identify the shape and refer to the equation:

Volume = (1/2) * Base Area * Height

To begin, the base is always in a right-angled triangle form, where its area depends on its width denoted as W, and height noted specifically as H.

Based on these computations, knowing that its triangular base measures 5 feet at its length while taking its height equates 3 feet therefore assessing how much it covers can be found using:

Triangle Area = (1/2) * Base * Height

Substituting values into solving areas leads us to have an answer of over 7 square feet.

Next is computing the volume of the said triangular prism. Placing all given data results in the same formula:

Volume = (1/2) * Base Area * Height

With one-half of the product of both areas which resulted in 7.5 square feet and then multiplying the figure by 10 ft, this yields us an approximate volume of 37.5 cubic feet.

In conclusion, we have determined that the ramp has a volume capacity of around 37.5 cubic feet.

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Length (L) = 10 feet

Width (W) = 5 feet

Height (H) = 3 feet

Mr. González designed a ramp for his car with a length of 10 feet, a width of 5 feet, and a height of 3 feet. What is the volume of the ramp in cubic feet?

Answer:

it's an easy one

Step-by-step explanation:

1. combine those -->4v+4=16

2. subtract the like terms--> 4v=16-4--> 4v=12

3. divide--> v=12/4-->3

4. Answer--> v=3

The team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

We can derive an inequality from the problem statement which is:

8X + 12Y >= 1000

This inequality represents the amount of money the basketball team needs to raise by selling donuts.

X is the number of half dozen boxes sold

Y is the number of full dozen boxes sold.

To find a solution in terms of the given context, we can plug in different values for X and Y that satisfy the inequality. For example:

If the team sells 50 half dozen boxes and 50 full dozen boxes, they will make:

8(50) + 12(50) = $400 + $600 = $1000

So this is a valid solution that meets the fundraising goal.

If the team sells 100 half dozen boxes and 0 full dozen boxes, they will make:

8(100) + 12(0) = $800

This is not enough to meet the fundraising goal, so it is not a valid solution.

If the team sells 0 half dozen boxes and 100 full dozen boxes, they will make:

8(0) + 12(100) = $1200

This is more than the fundraising goal, so it is a valid solution, but the team may not want to sell so many full dozen boxes.

Therefore, one solution in terms of the given context is that the team can sell 50 half dozen boxes and 50 full dozen boxes to raise at least $1000.

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Answer:

x^1/4 + 8x^1/4 + 12

Step-by-step explanation:

Using the FOIL method, we get x^1/4 + 8x^1/4 + 12

Therefore, the correct answer is option C that is LM is reflected over the y-axis to L'M.

In mathematics, a transformation refers to a change in the position, shape, or size of a geometric figure. Transformations can be classified into four types: translation, rotation, reflection, and dilation.

Here,

The transformation of LM to L'M' involves both translation and reflection. To see the translation, we can compare the x- and y-coordinates of L and L', as well as M and M':

The x-coordinate of L' is 5 units more than the x-coordinate of L: -2 = -7 + 5.

The y-coordinate of L' is 2 units less than the y-coordinate of L: -4 = -2 - 2.

The x-coordinate of M' is 5 units more than the x-coordinate of M: 5 = 0 + 5.

The y-coordinate of M' is 2 units less than the y-coordinate of M: 3 = 5 - 2.

Therefore, we can conclude that LM is translated 5 units right and 2 units down to L'M'. This eliminates options OB and OD. To see the reflection, we can compare the x-coordinates of L and M, and their respective x-coordinates in L' and M':

The x-coordinate of L is negative and the x-coordinate of M is positive.

The x-coordinate of L' is negative and the x-coordinate of M' is positive.

Therefore, we can conclude that LM is reflected over the y-axis to L'M'. This eliminates option OA. Therefore, the correct answer is option OC.

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The value of expression 14a +7+ 5b+ 2a + 10b will be 16a + 15b + 7

Since Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given the expression as;

14a +7+ 5b+ 2a + 10b

Combine like terms;

14a + 2a + 10b +7+ 5b

16a + 15b + 7

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Answer:

[tex]c. 1/5[/tex]

Step-by-step explanation:

You have the points (-5, 0) and (0, 1).

To find the slope, b, of the original line, you can use the formula [tex](y_{1}-y_2) /(x_1-x_2)[/tex].

[tex]b = (0-1)/(-5-0) = -1/-5 = 1/5.[/tex]

The slope of a line parallel to the original line would have the same slope as the original line, therefore [tex]1/5.[/tex]

Therefore, there are 3,628,800 different routes possible for the delivery truck to visit all 10 locations only once.

Factorial notation is a mathematical notation used to represent the product of all positive integers up to a given number. It is denoted by an exclamation mark (!) placed after the number. Factorial notation is often used in combinatorics to calculate the number of possible permutations and combinations of a set of objects.

Here,

The number of different routes possible for the delivery truck can be calculated using factorial notation.

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

This simplifies to:

10! = 3,628,800

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To represent z+9=14, we can start by subtracting 9 from both sides of the equation:

z + 9 - 9 = 14 - 9

Simplifying the left side of the equation gives:

z = 5

Therefore, the solution to the equation z+9=14 is z=5.

1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions. 2. If the expression is set equal to 10x + 7, there would be no solution. 3. One solution.

In algebra, like terms are those in which the same variables are raised to the same powers. For instance, the fact that the variable x has been raised to the first power makes the expressions 3x, 2x, and -5x similar. Related expressions include 4y², -y², and 7y², all of which have the variable y increased to the second power. By maintaining the variable and its exponent the same, like terms can be joined by adding or removing the coefficients (the numbers placed in front of the variables).

The given expression is given as 12x - 6x + 4x + 5 = 10x + 5.

Simplifying the expression we het 10 x + 5.

1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions as it will always be true.

2. If the expression is set equal to 10x + 7, there would be no solution, as the variable is eliminated.

3. If the expression is set equal to -10x + 5, there would be only one solution.

10x + 5 = -10x + 5

20x = 0

x = 0

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Answer:

Step-by-step explanation:To find the limit of p(x) as x approaches -3, we can first simplify the expression by factoring the numerator:

p(x) = (x^4 - x^3 - 1) / x^2(x + 1)

= [(x - 1)(x^3 + x^2 - x - 1)] / [x^2(x + 1)]

Now, when x approaches -3, the denominator of the fraction becomes zero, which means we have an indeterminate form of the type 0/0. To evaluate the limit, we can use L'Hopital's rule, which states that if we have an indeterminate form of the type 0/0 or infinity/infinity, we can take the derivative of the numerator and denominator separately and then evaluate the limit again.

Taking the derivative of the numerator and denominator, we get:

p'(x) = [(3x^2 - 2x - 1)(x^2 + 2x) - 2(x - 1)(2x + 1)] / [x^3(x + 1)^2]

Now, plugging in x = -3 into the derivative, we get:

p'(-3) = [(3(-3)^2 - 2(-3) - 1)((-3)^2 + 2(-3)) - 2((-3) - 1)(2(-3) + 1)] / [(-3)^3((-3) + 1)^2]

= [28 - 44] / [(-3)^3(-2)^2]

= -16 / 108

= -4 / 27

Since the derivative is defined and nonzero at x = -3, we can conclude that the original limit exists and is equal to the limit of the derivative, which is:

lim x->-3 p(x) = lim x->-3 [(x - 1)(x^3 + x^2 - x - 1)] / [x^2(x + 1)]

= p'(-3)

= -4 / 27

Therefore, the limit of p(x) as x approaches -3 is equal to -4/27.

Answer:

[tex]\lim_{x \to -3}p(x) =-\dfrac{107}{18}[/tex]

Step-by-step explanation:

Given the function [tex]p(x)=\dfrac{x^4-x^3-1}{x^2(x+1)}[/tex]

Let's give the expressions in the numerator and denominator their own function names so they are easy to refer to:

n, for numerator: [tex]n(x)=x^4-x^3-1[/tex]

d, for denominator:  [tex]d(x)=x^2(x+1)[/tex]

So [tex]p(x)=\dfrac{n(x)}{d(x)}[/tex]

Now, we want the limit of p(x) as x goes to -3.

[tex]\lim_{x \to -3}p(x) =\lim_{x \to -3}\dfrac{n(x)}{d(x)}[/tex]

For limits of quotients, it is important to analyze the numerator and the denominator.

Take a moment to observe that inputting -3 into the denominator is defined and does not equal zero:  [tex]d(-3)=(-3)^2((-3)+1)=-18\ne0[/tex]

Also, observe that inputting -3 into the numerator is defined:  [tex]n(-3)=(-3)^4-(-3)^3-1=81+27-1=107[/tex]

Importantly, both functions n & d are polynomials, which are functions that are continuous over [tex]\mathbb{R}[/tex].

Since both functions n & d are continuous, both n & d are defined at [tex]x=-3[/tex], and [tex]d(-3)\ne0[/tex], then the limit of the quotient is the quotient of the limits:

[tex]\lim_{x \to -3}\dfrac{n(x)}{d(x)}=\dfrac{ \lim_{x \to -3}n(x)}{ \lim_{x \to -3}d(x)}[/tex]

From here, again, since n & d are continuous over [tex]\mathbb{R}[/tex] and defined at the limit, [tex]\lim_{x \to -3}n(x)}=n(-3)[/tex] and [tex]\lim_{x \to -3}d(x)}=d(-3)[/tex].

Therefore,

[tex]\lim_{x \to -3}p(x) =\lim_{x \to -3}\dfrac{n(x)}{d(x)}=\dfrac{ \lim_{x \to -3}n(x)}{ \lim_{x \to -3}d(x)}=\dfrac{n(-3)}{d(-3)}=\dfrac{107}{-18}=-\dfrac{107}{18}[/tex]