Find the surface area of the triangular prism. Be sure to include the correct unit in your answer.

A Cartesian coordinate system is a coordinate system that employs a pair of perpendicular number lines, one horizontal axis and the other vertical axis.

Each point in the plane is defined by an ordered pair of numbers known as its coordinates. plot an athlete running from point A (3,0) to point B (0,5) then to point C (-4,-2) and ending at point D (3, -1) and clear marking of your coordinate system and plotting your athlete’s movement, using vector arrows depicting direction.

Step 1: Determine the maximum and minimum values on the x-axis and y-axis. Choose suitable values for both axes.
Step 2: Draw a horizontal x-axis and a vertical y-axis intersecting at the origin (0, 0). Ensure that the length of the axes is sufficient to accommodate the points.
Step 3: On the x-axis, mark the point A (3,0) which is located 3 units from the origin towards the right. Label the point A.
Step 4: On the y-axis, mark the point B (0,5) which is located 5 units from the origin towards the top. Label the point B.
Step 5: On the x-axis, mark the point C (-4,-2) which is located 4 units from the origin towards the left. Label the point C.
Step 6: On the y-axis, mark the point D (3,-1) which is located 1 unit from the origin towards the bottom. Label the pointD.
Step 7: Join the points A, B, C, and D to form a quadrilateral.
Step 8: Draw vectors (vector arrows) that depict the movement of the athlete in the order from A to B, from B to C, and from C to D. Repeat this for all the movements of the athlete from A to B, from B to C, and from C to D.

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Answer:

65%

Step-by-step explanation:

To find percentage, we take the fraction of the total and multiply it by 100.

\(\frac{325}{500} \times=\frac{325}{5}=65\)

Answer:

\(153.84\%\)

Step-by-step explanation:

\( 1. \: \frac{500}{3.25} \\ 2. \: 153.84\%\)

Answer:

−15, 0, 27, 1102

Step-by-step explanation:

Answer:

1, 2, 3...

Step-by-step explanation:

Integers can be whole numbers, counting numbers, etc. I hope this helps!

Answer:

x = 2  is the correct answer :)

A prime date is a date where both the month and day form a prime number, for example 2/2 or 3/3.

There were 10 prime dates in 2007:

January 2nd (1/2)

February 2nd (2/2)

March 3rd (3/3)

April 5th (4/5)

May 7th (5/7)

June 11th (6/11)

July 13th (7/13)

August 17th (8/17)

September 19th (9/19)

November 23rd (11/23)

December 29th (12/29)

A prime date is a date where both the month and day form a prime number, for example 2/2 or 3/3. To find the number of prime dates in 2007, we must first identify which months and days form prime numbers. January 2nd (1/2), February 2nd (2/2), March 3rd (3/3), April 5th (4/5), May 7th (5/7), June 11th (6/11), July 13th (7/13), August 17th (8/17), September 19th (9/19), November 23rd (11/23), and December 29th (12/29) are all prime dates in 2007. Therefore, there were 10 prime dates in 2007.

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The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

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Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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Answer:

6.3%

Step-by-step explanation:

We're gonna use the simple interest formula: A = P(1 + rt)

A = Final amount (500 + 15.75 = 515.75)

P = Starting amount (500)

r = rate (?)

t = number of years (.5 since it's been half a year)

515.75 = 500(1 + 0.5r)

Disitribute the 500 to the equation inside the parenthesis

515.75 = 500 + 250r

Subtract 500 from both sides

515.75 = 500 + 250r

- 500   - 500

15.75 = 250r

Divide both sides by 250

15.75/250 = 250r/250

r = 0.063

11\44 for the dime, and 12\44 for the penny.

Step-by-step explanation:

11 dimes + 21 nickels + 12 pennies = 44 coins. 12\44 probability of randomly choosing a penny from the jar. And 11\44 probability of randomly choosing a dime AFTER the penny is replaced.

In what form?!?!?!?!?!?!?

Your question has been heard loud and clear.

Answer is option D.

The point (-2,3)  is the solution to the equation of option D.

5(-2)-2(3) = -10+-6 = -16

2(-2)-5(3) = -4+-15 = -19

Here , in the equation , x = -2 and y = 3  ,when we substitute these values in the equation(D) , we get the correct answer.

Answer:

D) y= -1/2x+9

Step-by-step explanation:

if u substitute y with 8 u will get 2

if u substitute y with 5 u will get 8

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}=xy_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 8) and (x₂, y₂ ) = (8, 5)

m = \(\frac{5-8}{8-2}\) = \(\frac{-3}{6}\) = - \(\frac{1}{2}\)

The line crosses the y- axis at (0, 9) ⇒ c = 9

y = - \(\frac{1}{2}\) x + 9 → D

Range is R={n^2: n is natural number} U {n(n+1) : n is natural number}

The expression ⌈y⌉⋅⌊y⌋ represents the product of the ceiling and floor functions of y.

To find the range of all possible values of y, we need to consider the possible values of the ceiling and floor functions individually.

1. Ceiling function (⌈y⌉): This function rounds y up to the nearest integer. Since y is greater than 0, the ceiling of y will always be greater than or equal to y.

2. Floor function (⌊y⌋): This function rounds y down to the nearest integer. Again, since y is greater than 0, the floor of y will always be less than or equal to y.

Now, let's consider the product of the ceiling and floor functions, ⌈y⌉⋅⌊y⌋.

The product ⌈y⌉⋅⌊y⌋ will always be greater than or equal to 0 since y > 0 and this can take only integral values.

Therefore, the range of all possible values of y such that ⌈y⌉⋅⌊y⌋ is the set R={n^2: n is natural number} U {n(n+1): n is natural number}

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Please make sure your question is formatted correctly and ill answer it for you.

Answer:

D) x = -8

Step-by-step explanation:

All the values less than 7 are included in the number line. The graph on number line is shown in figure attached. In the options given, all values in Option A, B and C are greater than 7 so these cannot be included.

Answer:

What is it?

Step-by-step explanation:

Answer:

21.8 degrees

Step-by-step explanation:

edge

As per the formula of surface area of cube, the length of the cube is 5.45 meters.

The general formula to calculate the surface area of the cube is calculated as,

=> SA = 6a²

here a represents the length of cube.

Here we know that  the side of a cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters.

When we apply the value on the formula, then we get the expression like the following,

=> 180 = 6a²

where a refers the length of the cube.

=> a² = 30

=> a = 5.45

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The total amount in the bank after the specific number of years is;

9.  $476. 1

11. $7, 128. 8

The formula for calculating simple interest is expressed as;

I = PRT/100

Where;

From the information given, we have that;

9.Principal amount = $450

Interest rate = 1.45

Time = 5

Substitute the values into the formula

SImple interest = $450 ×1. 45× 5/100

Multiply the values, we get;

Simple interest, I = 2610/100

Divide through

Simple interest = $26. 1

Total amount = $450 + $26.1 = $476. 1

11. Principal amount = $5600

Interest rate = 3.9

Time = 7 years

Substitute the values

Simple interest = $5600× 3. 9 × 7/100

Multiply the values

Simple interest = 152,880/100

Simple interest = $1528. 8

Total amount = $7, 128. 8

Hence, the values are $476. 1 and  $7, 128. 8

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\(\sqrt[3]{27x^6y^4}\implies \sqrt[3]{3^3 (x^2)^3 y^3 y^1}\implies 3x^2 y\sqrt[3]{y}\)

If the limit of f(x) as x approaches 8 is 3, can you conclude anything about f(8)? The answer is No. We cannot. See the explanation below.

Again, 'No,' is the response to this question. The justification for this is that the value of a function does not depend on the function's limit at a given moment.

This is particularly clear when we consider a question with a gap. A rational function with a hole is an excellent example that will help you answer this question.

The limit of a function at a position where there is a hole in the function will exist, but the value of the function will not.

A limit is the result that a function (or sequence) approaches when the input (or index) near some value in mathematics.

Limits are used to set continuity, derivatives, and integrals in calculus and mathematical analysis.

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Answer:

a = 45

b = 45

c = 73

The order doesn't matter as long as we have two copies of 45 and one copy of 73.

============================================================

Explanation:

If a,b,c are all different values, then there's no way to have a mode since the mode is the most frequent item. We need 45 to repeat itself more than once.

This means either a,b,c are the same value (45) or exactly two of those variables are equal (either a = b, b = c or a = c) to 45.

Let's assume that a = b = c = 45. If so, then

{41,46,a,b,c}

would update to

{41,46,45,45,45}

Adding those items up and dividing by 5 gets us

(41+46+45+45+45)/5 = 44.4

We don't get the mean of 50 we want. So all three a,b,c values cannot be 45.

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

Instead, we have the case that exactly two of a,b,c are 45 and the third is something else.

Without loss of generality, let's say a = b = 45 and c is something else.

The set {41,46,a,b,c} updates to {41,46,45,45,c}

Add those values up, divide by 5, and set the result equal to the target goal of 50. The idea is to solve for c.

(41+46+45+45+c)/5 = 50

(177+c)/5 = 50

177+c = 5*50

177+c = 250

c = 250-177

c = 73

As a check,

(41+46+45+45+73)/5 = 50

which works out.

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

So that's how we arrive to a = 45, b = 45, c = 73

The order of the letters doesn't matter. We could easily have a = 45, c = 73 and b = 45; or we could have a = 73, b = 45, c = 45.

All that matters is exactly two of the a,b,c are 45 and the third variable is 73.

Answer:

840 has 6 odd factors

Step-by-step explanation:

Answer:

x = 2 and y = -4

Step-by-step explanation:

To solve using substitution, we define one unknown variable in terms of another and sub this into a second equation with both.

We are told y=2x-8 and -3x+4y=-22, so let's sub '2x-8' in for y in -3x+4y=-22:

-3x+4y=-22

-3x+4(2x-8)=-22

-3x+8x-32=-22

5x=10

x=2

If x=2 and y=2x-8, let's sub 2 in for x to find y:

y=2x-8

y=2(2)-8=4-8=-4

answer: 10

step by step explanation:

this is not a textbook way but

4:5 means 4/5 and we know that the numbers will be equal to this number so we can multiply the number 4/5*2/2 so we will get 8/10

8/10=4/5

and 8*10=80

so 1st no. is 8 and 2nd is 10

10>8

Answer:

greater number is 10

Step-by-step explanation:

the ratio of the 2 numbers = 4 : 5 = 4x : 5x ( x is a multiplier )

their product is 80 , that is

4x × 5x = 80

20x² = 80 ( divide both sides by 20 )

x² = 4 ( take square root of both sides )

x = \(\sqrt{4}\) = 2

then greater number = 5x = 5 × 2 = 10

Sophia did Calculus test better ompared to the rest of her class, as her z-score for Statistics  was lower than her z-score for Calculus

We know that the formula for the z-score is: \(z=\frac{x-\mu}{\sigma}\)

where x is the observed value

μ is the mean of the sample

σ is the standard deviation of the sample

Sophia got a 95% on her statistics. The grades had a mean of 87%, with a standard deviation of 7%

So, her z-score for statistics would be:

\(z_s=\frac{95-87}{7}\\\\z_s=1.14\)

She got a 91% on her calculus mid-term. The grades had a mean of 85%, with a standard deviation of 47%

So, her z-score for statistics would be:

\(z_c=\frac{91-85}{4}\\\\z_c=1.5\)

Since her z-score for Statistics  was lower than her z-score for Calculus,  she did Calculus test better.

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The basis for h is {v2,v3}.

To find a basis for h=span{v1,v2,v3}, we need to determine which of these vectors are linearly independent and which are not.

We know that v1-3v2+5v3=0, which means that v1 can be expressed as a linear combination of v2 and v3.

Therefore, v1 is not linearly independent and we can remove it from our list of vectors.

Now we have v2 and v3 left. To determine if they are linearly independent, we can try to express one of them as a linear combination of the other. Let's try to express v2 as a linear combination of v3:

v2 = a*v3 + b*v1

Since we already know that v1 can be expressed as a linear combination of v2 and v3, we can substitute v1 with that expression:

v2 = a*v3 + b*(v1-3v2+5v3)

Simplifying this expression, we get:

(1+3b)v2 + (-a+5b)v3 = v1

We want the left side to be equal to zero, so we set up a system of equations:

1+3b = 0

-a+5b = 0

Solving this system, we get a=15 and b=-1. This means that v1 can be expressed as:

v1 = 15v3 - v2

Therefore, v2 and v3 are linearly independent and form a basis for h=span{v1,v2,v3}.

So the basis for h is {v2,v3}.

Using the given information, we can find a basis for H = span {v1, v2, v3}.

It is verified that v1 - 3v2 + 5v3 = 0. This implies that v1 is a linear combination of v2 and v3. Therefore, v1 is not linearly independent from v2 and v3.

To find a basis for H, we can consider only the linearly independent vectors. In this case, the basis for H would be {v2, v3}.

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Antinuclear antibodies (ANAs) are most likely to be elevated in this patient. The correct answer is option C.

In this situation, the patient's most likely diagnosis is lupus erythematosus. Lupus erythematosus is a complex autoimmune disorder that affects the body's normal functioning by damaging tissues and organs. ANA testing is used to help identify individuals who have an autoimmune disorder, such as lupus erythematosus or Sjogren's syndrome, which are two common autoimmune disorders.

Antibodies to specific nuclear antigens, such as double-stranded DNA and anti-cyclic citrullinated peptide (anti-CCP) antibodies, are also found in lupus erythematosus and rheumatoid arthritis, respectively. However, these antibodies are less common in other autoimmune disorders, whereas ANAs are found in a greater number of autoimmune disorders, which makes them a valuable initial screening test.

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Answer:

Congrats.

Step-by-step explanation:

Thanks for the free points btw :)

Answer:

cogradulations

Step-by-step explanation:

Answer:

2 face cards

Step-by-step explanation:

By definition, there are 12 face cards (Kings, queens, and jacks) and 36 numbered cards (2's through 10's) in a standard deck of 52 cards.  Aces are not considered face cards (no face on the card).

The ratio of face cards in a full deck is (12/52) or slightly over 23%.

The likelihood of a face card in a hand of 8 cards is:

(8 cards)*(12 face cards/52 cards) = 1.85 cards.  We need to round to the nearest whole card, so the expected number of face cards in a hand of 8 is 2 cards.