Which of the graps below best displays this situation?
Which expression can be used to calculate the area of the smaller square?

(a) The number of ways the books can be arranged in any order is 362880,

(b) The number of ways the mathematics books must be together and the novels must be together is 4320.

Part(a) :

The number of mathematics-book is = 3,

The number of novels is = 5,

The number of biology books is = 1,

So, there are total of (5+3+1) = 9 books

These 9 books can be arranged in 9! = 362880 ways.

Part(b) :

If the mathematics book are together we can consider the mathematics books as 1 book and

if the novels are together then these 5 novels can be considered as one.

So, there are total 3 books which can be arranged in 3! Ways.

And these 5 novels can be arranged in themselves in 5! Ways and

these 3 mathematics books can be arranged in themselves in 3! ways.

So, total number of ways = 3!×3!×5! =6×6×120 = 4320 ways.

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The correct statement regarding the solution of the system of equations is given as follows:

A. The solution to the system is viable.

The situation is modeled by a system of equations, for which the variables are given as follows:

From each row of the table, the equations are given as follows:

Subtracting the third equation by the second, the value of x is given as follows:

2x = 178

x = 178/2

x = 89.

From the first equation, the value of y is given as follows:

y = [614 - 4 x 89]/2

y = 129.

From the second equation, the value of z is given as follows:

z = 555 - 3 x 89 - 129

z = 159.

Hence the system has a viable solution.

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Answer:

3x + 12

Step-by-step explanation:

3(x + 4) ​

3x + 12

So, the expand is 3x + 12

Answer:

3x + 12

Step-by-step explanation:

You multiply the outside of the perentheses by everything inside, and 3(x) + 3(4) = 3x + 12

Answer:

I just had to say those numbers because of so I can send it like I'm about

To find the lower bound and upper bound of the difference m-n, we need to first find the possible range of values for m and n.

• For m rounded to 1 decimal place, the actual value could be anywhere between 48.15 and 48.25 (since the digit in the second decimal place could be anything from 0 to 9, and we round to the nearest 0.1).

• For n rounded to 1 decimal place, the actual value could be anywhere between 6.65 and 6.75.

Now, we can calculate the lower bound and upper bound of m-n:

Lower bound of m-n = (48.15 - 6.75) = 41.4

Upper bound of m-n = (48.25 - 6.65) = 41.6

Therefore, the lower and upper bounds of m-n are 41.4 and 41.6, respectively.

5y+15

I think this is correct. Hope this helps:)

Answer: 5y + 15

Step-by-step explanation: 5(y+3)

                                            = 5(y) + 5(3)

                                            = 5y + 15

Answer:

(x-2.5)^2 + 1.75

Step-by-step explanation:

To write that as an equation, we get x^2 - 5x + 8.

now, we need to complete the square:

x^2 - 5x + 6.25 + 1.75 =

(x-2.5)^2 + 1.75.

Answer:

y = - [tex]\frac{1}{2}[/tex] (x + 3)² + 4

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (- 3, 4 ) , then

y = a(x - (- 3) )² + 4 , that is

y = a(x + 3)² + 4

to ind a substitute the point (1, - 4 ) into the equation

- 4 = a(1 + 3)² + 4

- 4 = a(4)² + 4 ( subtract 4 from both sides )

- 8 = 16a ( divide both sides by 16 )

- [tex]\frac{8}{16}[/tex] = a , that is

a = - [tex]\frac{1}{2}[/tex]

y = - [tex]\frac{1}{2}[/tex] (x + 3)² + 4 ← equation of parabola

The probability that each of you orders a different type of sandwich is 72%.

To find the probability that each of you orders a different type of sandwich, we can use the counting principle.
Step 1: Determine the total number of ways you and your friends can order sandwiches.

Since there are 10 types and each of you can choose any type, there are 10 * 10 * 10 = 1000 possible ways to order.
Step 2: Calculate the number of ways you can order different types of sandwiches.

For the first person, there are 10 choices.

For the second person, there are 9 remaining choices (since their sandwich must be different from the first person's). For the third person, there are 8 remaining choices (different from both the first and second person's choices). So there are 10 * 9 * 8 = 720 ways to order different types of sandwiches.
Step 3: Calculate the probability of ordering different types of sandwiches.

Divide the number of ways to order different sandwiches by the total number of ways to order:
Probability = (Number of ways to order different sandwiches) / (Total number of ways to order)
Probability = 720 / 1000 = 0.72 or 72%.

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Answer:

A=1 B=2 C=3   Domain: [2, infinity) Range: (neg. infinity, 3]

Step-by-step explanation:

a is rate B is Horitzontal shift C is vertical shift

Answer:-1.5

Step-by-step explanation:

first distribute 3

to get 6x + 3= 4x

then -6x on right side to get

3= -2x

then divide by -2

3/-2= x

x= -1.5

Hello !

Answer:

[tex]\Large \boxed{\sf x=-\frac{3}{2}}[/tex]

Step-by-step explanation:

We're looking for the value of x that satisfies the following equation :

[tex]\sf 3 (2x+1) = 4x[/tex]

We need to isolate x.

First, let's expand left side :

[tex]\sf 3\times 2x+3\times1=4x\\6x+3=4x[/tex]

Now let's substract 4x from both sides :

[tex]\sf 6x+3-4x=4x-4x\\2x+3=0[/tex]

Substract 3 from both sides :

[tex]\sf 2x+3-3=0-3\\2x=-3[/tex]

Finally, let's divide both sides by 2 :

[tex]\sf \frac{2x}{2} =-\frac{3}{2} \\\boxed{\sf x=-\frac{3}{2}}[/tex]

Have a nice day ;)

Answer:

  64°

Step-by-step explanation:

You want the measure of angle ZOX, the smaller of a linear pair marked (3x -2)° and (5x +6)°.

The angles of a linear pair are supplementary—they total 180°.

  (5x +6) +(3x -2) = 180

  8x +4 = 180 . . . . . simplify

  8x = 176 . . . . . . subtract 4

  x = 22 . . . . . . divide by 8

The measure of angle ZOX is ...

  ∠ZOX = (3x -2)° = (3·22 -2)°

  ∠ZOX = 64°

__

Additional comment

Angle ZOY is ...

  ∠ZOY = (5·22 +6)° = 116°, the supplement of 64°.

If an employee is selected at random, the probability that you will select a person who uses a suv or sedan is 85%.

Given data: Primary vehicles to commute to work :

Percentage of employees who use a boat = 10%

Percentage of employees who use a Sedan = 35%

Percentage of employees who use a SUV = 50%

Percentage of employees who use a Bicycle = 5%

Probability of selecting a person who uses a SUV or Sedan can be calculated as follows:

Probability of selecting a person who uses a SUV or Sedan= Probability of selecting a person who uses a SUV + Probability of selecting a person who uses a Sedan

Probability of selecting a person who uses a SUV or Sedan= 50% + 35%= 85%

Hence, the probability of selecting a person who uses a SUV or Sedan is 85%.

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Answer:

(6,45)

Step-by-step explanation:

To graph each ratio relationship in the coordinate plane, we can plot the ordered pairs (time, distance) for each leg of the trip. For the first leg from Chicago to Los Angeles, the plane travels 15 miles every 2 minutes. So we can plot the following points:

(0, 0) - starting point

(2, 15) - after 2 minutes, the plane has traveled 15 miles

(4, 30) - after 4 minutes, the plane has traveled 30 miles

(6, 45) - after 6 minutes, the plane has traveled 45 miles

(8, 60) - after 8 minutes, the plane has traveled 60 miles

We can plot these points on a coordinate plane, with time on the x-axis and distance on the y-axis. The resulting graph would show a straight line with a slope of 7.5 (rise of 15/2 and run of 1).

For the second leg from Los Angeles to Chicago, the plane travels 25 miles every 3 minutes. So we can plot the following points:

(0, 0) - starting point

(3, 25) - after 3 minutes, the plane has traveled 25 miles

(6, 50) - after 6 minutes, the plane has traveled 50 miles

(9, 75) - after 9 minutes, the plane has traveled 75 miles

(12, 100) - after 12 minutes, the plane has traveled 100 miles

We can plot these points on the same coordinate plane as the first leg. The resulting graph would also show a straight line with a slope of 8.33 (rise of 25/3 and run of 1).

The two graphs would intersect at the point (6, 45), which represents the halfway point of the round trip.

Answer:

(-2/5, 11/5)

Step-by-step explanation:

We can use the formula for finding a point that divides a line segment into a given ratio. Let P be the point on the line segment QR that partitions it in the ratio 2:3. Then we have:

P = ( (3x2 + 2x1)/(3+2), (3y2 + 2y1)/(3+2) )

where (x1, y1) = (-8, -8) is the coordinates of Q and (x2, y2) = (2, 7) is the coordinates of R.

Substituting the values, we get:

P = ( (32 + 2(-8))/(3+2), (37 + 2(-8))/(3+2) )

P = ( (-2/5), (11/5) )

Therefore, the coordinates of the point P on the directed line segment QR that partitions it in the ratio 2:3 are (-2/5, 11/5).

I remember doing this but I don’t seem to remember sorry

Answer:

Step-by-step explanation:

The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2. 3(10 + 2) = ? According to this property, you can add the numbers and then multiply by 3.

Rounding to the nearest whole number, Dr. Powell can expect about 16 micrograms of medication to be remaining in Ruby's body after 4 hours.

In mathematics, an equation is a statement that two expressions are equal. It typically consists of two sides, a left-hand side and a right-hand side, separated by an equal sign (=). Equations are used to represent relationships between variables or to solve for unknown values. They are an important tool in algebra, calculus, and other areas of mathematics and science.

Here,

The exponential equation in the form y = a(b)^x that can model the amount of medication in Ruby's body, y, x hours after it was administered is:

y = 40(0.8)ˣ

where:

a = 40, the initial amount of medication given to Ruby

b = 0.8, the factor by which the medication decreases each hour

To find the amount of medication remaining in Ruby's body after 4 hours, we can substitute x = 4 into the equation and evaluate:

y = 40(0.8)⁴

y = 40(0.4096)

y = 16.384

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The expression that makes the equation true is: (4 x 3) ÷ 2.

option 1 is the correct answer.

In mathematics, an expression is a combination of symbols and/or values that represents a quantity or a relationship between quantities. It can include variables, constants, mathematical operations, and functions.

first, let's simplify the expression within the parentheses:

3 x 5 + 1 = 15 + 1 = 16

Now, we can simplify the entire expression:

1/2 x (3 x 5 + 1) - 2 = 1/2 x 16 - 2 = 8 - 2 = 6

So, we need to select the expression that equals 6:

6 ÷ 3 + 2 = 4

6 + 8 ÷ 4 = 8

(4 x 3) ÷ 2 = 6

Therefore, the expression that makes the equation true is: (4 x 3) ÷ 2.

option 1 is the correct answer.

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Answer:

        .

(4x3)---- 2

         .

B

Step-by-step explanation:

hope this help!

The average speed of NFL players varies by position and other factors, and while the forty-yard dash is a common measure of speed, it's important to consider other factors and potential biases when comparing average times between different years.

The average speed of NFL players can vary depending on their position and other factors such as age, height, and weight. The forty-yard dash is a common measure of speed and agility for NFL players.

Regarding the question about whether NFL players were significantly faster between 2012-2014 compared to previous years, we would need to compare the average forty-yard dash times for running backs and wide receivers from 2012-2014 to the average times from prior years to determine if there was a significant difference.

However, it's worth noting that the average forty-yard dash time can be influenced by a variety of factors, including changes in the testing conditions, differences in the player population being tested, and changes in training and coaching techniques. Therefore, we cannot make any definitive conclusions about changes in player speed based solely on this one measure.

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Answer: To solve this problem, we can start by drawing a diagram of the two triangles and the line connecting their hypotenuses. Let's label the height of the first triangle as h1, the width of the second triangle as w2, and the slope of the line as m.

We know that the hypotenuse of a right triangle is always longer than either of its legs, so we can conclude that h1 < w2. We also know that the height of the second triangle is 12 units, so we can label that as h2 = 12.

Using the Pythagorean theorem, we can express the lengths of the hypotenuses in terms of their legs:

h1^2 + 3^2 = L^2, where L is the length of the first hypotenuse

w2^2 + 12^2 = L^2, where L is the length of the second hypotenuse

Setting these two expressions equal to each other, we can solve for h1 in terms of w2:

h1^2 + 3^2 = w2^2 + 12^2

h1^2 = w2^2 + 12^2 - 3^2

h1^2 = w2^2 + 141

h1 = sqrt(w2^2 + 141)

Now, we can use the fact that the hypotenuses lie on the same line to write an equation for that line:

y = mx + b

where b is the y-intercept of the line. Since the hypotenuses intersect the y-axis at the points (0,h1) and (0,12), we know that b = (h1 + 12)/2. Therefore, our equation becomes:

y = mx + (h1 + 12)/2

To find the slope of the line, we can use the fact that the rise (change in y) over run (change in x) is the same for both triangles. We can express this as:

(h1 - 12) / 3 = 12 / w2

Solving for h1 in terms of w2 and simplifying, we get:

h1 = (36/w2) + 12

Substituting this expression for h1 into our equation for the line, we get:

y = mx + ((36/w2) + 24)/2

y = mx + (18/w2) + 12

Comparing this to the general form of the equation for a line, y = mx + b, we see that the slope is simply:

m = 18/w2

Substituting w2 = 3 (since we were given that the width of the second triangle is 3 units), we get:

m = 18/3 = 6

Therefore, the slope of the line is 6.

Step-by-step explanation:

Answer: 59.02 square inches

Step-by-step explanation:

We can use the formulas for the volume and surface area of a sphere to solve this problem.

The formula for the volume of a sphere is:

V = (4/3)πr^3

Where V is the volume, r is the radius, and π is pi (approximately equal to 3.14159).

We know that the volume of the sphere is 33.51 cubic inches, so we can plug that in and solve for the radius:

33.51 = (4/3)πr^3

r^3 = (3/4) * (33.51/π)

r^3 = 10.56

r ≈ 2.17

Now that we know the radius is approximately 2.17 inches, we can use the formula for the surface area of a sphere to find the surface area:

A = 4πr^2

A = 4π(2.17)^2

A ≈ 59.02 square inches

Therefore, the surface area of the sphere is approximately 59.02 square inches.

Answer:

x=7

Step-by-step explanation:

Check the attachment below:  

Answer:

x² - 9x + 6

Step-by-step explanation:

The polynomial in standard form is:

x² - 9x + 6

This is a quadratic polynomial because it has a degree of 2, and it has three terms.

Real number that is greater than or equal to zero. The only number that is both positive and negative is the number 0.

Answer:

C. 13,200 mm²

Step-by-step explanation:

Overall, we have area of a rectangle which is 12000 and the area of the two triangles are 1200.

We both add them to get the area of the irregular shape.

12000 + 1200 = 13,200 mm²