Evaluate:

6!
A.
60
B.
120
C.
360
D.
720

first part: 5% of $94 is 0.05*94=$4.70

second part: 80% of 45 questions is .8*45 = 36

 4 ÷ [tex]\frac{1}{6}[/tex]

= 4 * [tex]\frac{6}{1}[/tex]

= 24

Answer: 24 slices

Craig practiced 15 hours

Nicki practiced his drums for 11 hours, and considering Craig practiced 4 hours more than Nicki, Craig practiced his drums for 15 hours.

Let's start by figuring out how many hours Nicki practiced his drums. We know that Nicki practiced his drums 5 hours less than Marshal, and Marshal practiced his drums 16 hours. This means that Nicki practiced his drums for 16-5= 11 hours.

Next, we move on to figuring out how many hours Craig practiced his drums. The question tells us that Craig practiced his drums 4 hours more than Nicki. Since we now know that Nicki practiced his drums for 11 hours, this means that Craig practiced his drums for 11+4= 15 hours.

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Answers

1.  1,364

2. x⁴ + 2x - 6

3.  x⁵ - 5x⁴ + 4x³ - x² + 5x - 4

4.  x⁴ - 7x³  - 21x² + 63x -108

5.  a(n-1) + 1.4

6. 3/(2× 2ⁿ⁻¹)

Explanation

Q1

Σ4ⁿ = 4¹ + 4² + 4³ + 4⁴ + 4⁵

      = 4 + 16 + 64 + 256 + 1024

       = 1,364

Q2. What is (f−g)(x)?

f(x)=x4−3x2+5x−7

g(x)=x3−3x2+3x−1

(f−g)(x) = (x⁴−3x²+5x−7

) - (x³−3x²+3x−1)

             =x⁴ + 2x - 6

3. What is (f⋅g)(x)?

f(x)=x2−5x+4

g(x)=x3−1

(f⋅g)(x) = (x³−1)(x²−5x+4

)

           = x⁵ - 5x⁴ + 4x³ - x² + 5x - 4

4. Let f(x)=x2−9 ​ and g(x)=x2−7x+12 .

What is (fg)(x)?

(fg)(x) = (x²−9)(x²−7x+12)

           = x⁴ - 7x³  - 12x² - 9x² + 63x -108

            =  x⁴ - 7x³  - 21x² + 63x -108

5. What is the recursive rule for the sequence?

4.4, 5.8, 7.2, 8.6, 10, …

5.8 = 4.4 = 1.4,     10 - 8.6 = 1.4  The sequence is an AP where the common difference is 1.4 and the first term a is 4.4.

We and 1.4 to the previous term in order to get the next term.

an = a(n-1) + d

     = a(n-1) + 1.4

6. Enter the explicit rule for the geometric sequence.

3/2, 3/4, 3/8, 3/16, 3/32, …

common ratio r, = 4/3 ÷3/2 = 1/2

First term a, = 3/2

an =  arⁿ⁻¹

     = (3/2)(1/2)ⁿ⁻¹

      = 3/(2× 2ⁿ⁻¹)

Answer:

The correct answer is C. $5.07

Step-by-step explanation:

Answer:

5.07

Step-by-step explanation:

For the shown graph, we need to find the value of h(2).

h(2) represents the value of h function for x=2.

We need to check the value of function on the graph where h is 2.

From the graph, we can see for x=2, we have a solid dot for y coordinate at 0 and a hollow dot at y coordinate at 3.

Because hollow dot represents excluded value.

Therefore, we would take y coordinate of solid dot of the graph at x=2.

Therefore, f(2) = 0.

Answer:

The cost of 10 cm and 70 cm are  £0.55 and £3.85 respectively.

Step-by-step explanation:

Material for a dress costs £5.50 per meter.

We know that,  1 meter = 100 cm.

Suppose, the cost of 10 cm material is [tex]x[/tex] and the cost of 70 cm material is [tex]y[/tex]

Now, according to the ratio of "cost" to the "length of material" , we will get.......

[tex]\frac{x}{10} =\frac{5.50}{100}\\ \\ 100x=10*5.50=55\\ \\ x=\frac{55}{100}=0.55[/tex]

and

[tex]\frac{y}{70} =\frac{5.50}{100}\\ \\ 100y=70*5.50=385\\ \\ x=\frac{385}{100}=3.85[/tex]

So, the cost of 10 cm material is £0.55 and the cost of 70 cm material is £3.85

The point-slope form of a line:

[tex]y-y_0=m(x-x_0)[/tex]

We have:

[tex]m=\dfrac{2}{5}\\\\(-4,\ -7)\to x_0=-4,\ y_0=-7[/tex]

Substitute:

[tex]y-(-7)=\dfrac{2}{5}(x-(-4))\\\\y+7=\dfrac{2}{5}(x+4)[/tex]

3. AB = CE

4. CE = AC

5. Transitive property of congruence

6. Definition of isosceles triangle

Triangle ABC Is an isosceles triangle because line AB is equal to line AC .

An isosceles triangle is a triangle with two equal sides and two equal angles. The third side and angle may differ in length and measure.

The symmetry in side lengths and angles gives it distinct geometric properties.

Since line BD is equal to line CE and line CE is equal to line AC, this means that line BC is a bisector of line AD and AE,

Therefore we can say triangle ABC is an isosceles triangle because AB = AC.

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Answer:

The bee traveled 11.7 meters.

Step-by-step explanation:

A bee flew 840 cm first to land on a flower to collect some pollen and then flew another 330 cm to get back to her hive.

For finding the total distance traveled, we need to just add 840 cm and 330 cm.

So, [tex](840+330) cm = 1170 cm[/tex]

We know that,  1 meter = 100 cm. That means, for converting 'cm' into 'meter' , we need to divide by 100.

Thus,  [tex]1170 cm= \frac{1170}{100} meter = 11.7 meter[/tex]

So, the bee traveled 11.7 meters.

Answer:

11.7

Step-by-step explanation:

khan academy

Answer:

180%

Step-by-step explanation:

Answer:

160piein^3

Step-by-step explanation:

Answer: C

Step-by-step explanation:

 f(x) =   2x + 1  ⇒       2x + 1

- g(x) = -(x² - 7) ⇒  -x²     + 7

              (f-g)(x) = -x² + 2x + 8

The area of a circle with a radius of 7.5 cm is 176.81 cm² to two decimal places, and the area of a semicircle with a radius of 8.2 cm is 104.8 cm² to one decimal place.

To work out the area of a circle with a radius of 7.5 cm using π (pi) as 3.142, we use the formula A = πr².

First, square the radius: 7.5 cm × 7.5 cm = 56.25 cm².
Then multiply by π: 56.25 cm² × 3.142 = 176.8125 cm².
The area to 2 decimal places is 176.81 cm².

For the area of a semicircle with radius 8.2 cm, we first calculate the area of a full circle and then divide by 2.
Full circle area: 8.2 cm × 8.2 cm × 3.142 = 209.5852 cm².
Area of the semicircle: 209.5852 cm² ÷ 2 = 104.7926 cm², which rounds to 104.8 cm² to 1 decimal place.

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The area of the circle is [tex]177.16[/tex] [tex]cm^2[/tex] and the area of semicircle is [tex]105.0[/tex] [tex]cm^2[/tex].

The area of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.

1. For the first question, the radius [tex]\( r \)[/tex] is given as 7.5 cm. Using the formula for the area of a circle:

[tex]\[ A = \pi r^2 \][/tex]

[tex]\[ A = 3.142 \times (7.5 \text{ cm})^2 \][/tex]

[tex]\[ A = 3.142 \times 56.25 \text{ cm}^2 \][/tex]

[tex]\[ A = 177.1625 \text{ cm}^2 \][/tex]

Rounded to two decimal places, the area of the circle is [tex]\( A = 177.16 \text{ cm}^2 \)[/tex].

2. For the second question, the figure is a semicircle with a radius of 8.2 cm. The area of a semicircle is half the area of a full circle.

Therefore, using the formula for the area of a circle and then dividing by 2:

[tex]\[ A_{\text{semi}} = \frac{1}{2} \pi r^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 3.142 \times (8.2 \text{ cm})^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 3.142 \times 67.24 \text{ cm}^2 \][/tex]

[tex]\[ A_{\text{semi}} = \frac{1}{2} \times 210.0944 \text{ cm}^2 \][/tex]

[tex]\[ A_{\text{semi}} = 105.0472 \text{ cm}^2 \][/tex]

Rounded to one decimal place, the area of the semicircle [tex]\( A_{\text{semi}} = 105.0 \text{ cm}^2 \)[/tex].

Answer:

2539.63

Step-by-step explanation:

A = 1400(1 + 0.06/4)^(4*10)

 =  2539.63

Since, area of square patch of fabric = 2.25 square inches

Area of square of side 's' = [tex]s^2[/tex]

Since, area of square patch of fabric = 2.25 square inches

[tex]2.25 = s^2[/tex]

[tex]s = \sqrt{2.25}[/tex]

s = 1.5 inches

Therefore, the side length of the patch is 1.5 inches.

Final answer:

To determine the side length of a square with an area of 2.25 square inches, take the square root of the area, which is 1.5 inches.

Explanation:

To find the side length of a square patch of fabric that is 2.25 square inches, we need to understand that the area of a square is given by the formula Area = side × side (or side2). Given that the area is 2.25 square inches, we set up the equation side2 = 2.25.

Now, to find the side, we take the square root of both sides of the equation:

Therefore, the side length of the square patch is 1.5 inches.

The values are always interpreted as (x1, y1) and (x2, y2) in order from left to right, so in this case, (7,2) are (x1, y1) and (15, 8) are (x2, y2)

X1 = 7

Y1 = 2

X2 = 15

Y2 = 8

You need to send 360 texts to earn 1800 points and get the prize.

To figure out how many texts you need to send to obtain the prize from your cell phone company's reward club, you'll want to set up a proportion because you earn a set number of points for every several texts sent. In this case, you get 15 points for every three texts.

Let's use the variable T to denote the total number of texts needed to be sent. We know that:

3 texts = 15 points

T texts = 1800 points

To find T, we can set up a ratio and solve for the variable:

[tex]\(\frac{3 texts}{15 points} = \frac{T texts}{1800 points}\)[/tex]

Cross multiply to solve for T:

3 texts * 1800 points = 15 points * T texts

T = [tex]\(\frac{3 * 1800}{15}\)[/tex]

T = 360 texts

Therefore, you need to send 360 texts to earn 1800 points and get the prize.

Answer: The difference is,

[tex]m^2n^2-mn-11[/tex]

Step-by-step explanation:

Given expression is,

[tex](m^2n^2-7)-(mn+4)[/tex]

By distributive property,

[tex]m^2n^2-7-mn-4[/tex]

Combine like terms( that have the same variables and powers ),

[tex]m^2n^2-mn-11[/tex]

Which is the required result.

Hence, option third is correct.

C

G= - 4t + 100 ( add 4t to both sides )

G + 4t = 100 ( subtract G from both sides )

4t = 100 - G ( divide both sides by 4 )

t = [tex]\frac{100-G}{4}[/tex]

t=(G-100)/4 is the equation that correctly solves the given equation for t. So, option C is the correct answer.

Given that, the number of gallons of water in the pool changes with time t according to the equation.

The given equation is G = -4t + 100.

We need to solve the given equation for t.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Now, G = -4t + 100

⇒4t=G-100

⇒t=(G-100)/4

Therefore, t=(G-100)/4 is the equation that correctly solves the given equation for t. So, option C is the correct answer.

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To work this out we have to do 16.9  hours - 13.2 hours = 3.7 hours so there is a 13.7hour difference and to show it as an addition equation you do 13.2 hours + 3.7hours = 16.9 hours

The difference in time spent online by teens in Brooklyn, NY and Charlotte, NC is 16.9 hours.

To find the difference in time spent online by teens in Brooklyn, NY and Charlotte, NC, we can write and solve an addition equation.

Let's define:

The equation is: x + y = difference in time spent online

Given that teens in Brooklyn, NY spend 16.9 hours per week online and teens in Charlotte, NC spend 13.2 hours per week online, we can substitute these values into the equation:

16.9 + 13.2 = difference in time spent online

Simplifying the equation, we get:

difference in time spent online = 30.1 - 13.2

Therefore, the difference in time spent online by teens in Brooklyn, NY and Charlotte, NC is 16.9 hours.

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20 - 6 + 4k = 2 - 2k

    14   + 4k = 2 - 2k    added like terms (20 and -6)

           +2k        +2k

     14 + 6k  =  2

    -14           -14

             6k = -12

             [tex]\frac{6k}{6} = \frac{-12}{6}[/tex]

               k = -2

Answer: k = -2

The solution to the equation is k = -2.

To solve for k in the equation 20 - 6 + 4k = 2 - 2k, we can start by simplifying both sides of the equation.

Combining like terms on each side:

14 + 4k = 2 - 2k

Next, we can isolate the variable k by moving all terms containing k to one side of the equation.

Adding 2k to both sides:

14 + 4k + 2k = 2 - 2k + 2k

14 + 6k = 2

Now, we'll isolate the variable k by subtracting 14 from both sides:

14 + 6k - 14 = 2 - 14

6k = -12

To solve for k, we'll divide both sides by 6:

(6k)/6 = (-12)/6

k = -2

Therefore, the solution to the equation is k = -2.

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Answer:

Each dog will receive [tex]\frac{1}{2}[/tex] pounds of dog food.

Step-by-step explanation:

This is a very straightforward question.

To find the amount each dog gets we have to divide the total number of dog food to 7 equal portions.

Amount of dog food each dog will receive= Total number of dog food / number of dogs

=[tex]\frac{3\frac{1}{2} }{7}[/tex]

=[tex]\frac{\frac{7}{2} }{7}[/tex]

=[tex]\frac{7}{7*2}[/tex]

=[tex]\frac{1}{2}[/tex] pounds

Therefore, each dog will receive [tex]\frac{1}{2}[/tex] pounds of dog food.

The answer to your question  is B.

Ok so here it is:

-67 ≥ 5 + 3n -21

-67+ 21 ≥ 5 + 3n -21 + 21

the 21 cancel each other out

now add -67 and 21

-46 ≥ 5 + 3n

-46 -5 ≥ 5 -5 +3n

the 5 cancel each other out

now subtract -5 from -46

-51 ≥ 3n

-51 / 3 ≥ 3n / 3

3 cancel each other out

now divide -51 and 3

n ≤ -17

B