A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid.

A solid right pyramid has a square base. The base edge length is 2 centimeters longer than the height of the pyramid. The height of the pyramid is 6 centimeters.

If the height is 6 cm, what is the volume of the pyramid?
24 cm3
48 cm3
128 cm3
144 cm3

Answer:

See below

Step-by-step explanation:

x = largest

x-1   previous

x -2  smallest

sum =   x   +    x-1      +   x-2

sum = 3x -3    

The perimeter of the triangle can be express as follows:

12b + 11d + 2c

The perimeter of a figure is the sum of the whole sides of the figure.

A triangle has three sides. Therefore, the perimeter of a triangle is the sum of the three sides.

Therefore, the sides of the triangle are of lengths (2b + 5c) centimetres, (10b + 7d) centimetres, and (4d-3c) centimetres.

Hence, the perimeter of the triangle can be represented as follows:

Perimeter of the triangle = 2b + 5c + 10b + 7d + 4d - 3c

Perimeter of the triangle = 2b + 10b + 7d + 4d + 5c - 3c

Perimeter of the triangle = 12b + 11d + 2c

Therefore, the perimeter of the triangle can be express as follows:

12b + 11d + 2c

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Answer:r=14°

Step-by-step explanation:

(5r-5)°+ (8r+3)°=180

(Sum of angles on a straight line =180°)

Collect like terms

5r+8r-5+3=180

13r-2=180

13r=180+2

13r=182

r=182/13

r=14°

Answer:

(a) k = 4
(b) y = - 2x + 9

Step-by-step explanation:

x2-x1, y2-y1  
= 3-2, 3-5

= 1,-2
3,3 + 1,-2 = (4,1)

x=4

The volume of the cone is  84.9 km³

Volume of a cone = 1 / 3 πr²h

where

Therefore,

radius = 3 km

height = √9.5² - 3²

height = √81.25

height = 9.01387818866

height = 9.014 km

Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014

volume of the cone = 254.732197612 / 3

volume of the cone = 84.9107325372

volume of the cone = 84.9 km³

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Answer:

Step-by-step explanation:

12

480 Ways can the letters be arranged.

What is the meaning of probability ?

First letter can't be n or l

=   4! × [tex]5P_{3}[/tex]

=    24 × 5! /3!

=     24 × 5 × 4

=         480

Therefore, 480 ways can the letters be arranged.

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Answer: 480 ways

Step-by-step explanation:

Your net worth change by zero dollars.

Net worth is the difference between asset and liability.  

In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.

Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.

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Step-by-step explanation:

g(f(a))=4(a²+2a) + 5

= 4a²+8a+5

Answer:

The answer is B, 2.78 hours

Step-by-step explanation:

Answer:

  6 hours 15 minutes, or 6.25 hours

Step-by-step explanation:

We assume Hank reads at a constant rate. His reading time will be proportional to the number of pages.

We know that 15 minutes is 1/4 hour, so the proportion can be written ...

  hours/pages = (book hours)/(250 pages) = (1/4 hour)/(10 pages)

Multiplying by 250 pages gives ...

  book hours = 250(1/4 hour)/10 = 25/4 hour = 6 1/4 hour

It will take Hank 6 1/4 hours to read the book.

Answer:

J

Step-by-step explanation:

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

Equivalent functions are different functions that have equal values when evaluated and compared

The function is given as:

f(x) = 36x^2 - 1

Express 1 as 1^2

f(x) = 36x^2 - 1^2

Express 36x^2 as (6x)^2

f(x) = (6x)^2 - 1^2

Apply the difference of two squares.

This is represented as:

(a + b)(a - b) = a^2 - b^2

So, we have the following equation

f(x) = (6x - 1)(6x + 1)

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

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The solution to the following mathematical problems are;

Solve using

BODMAS

5² -3⁴ / (2³-5)(6² ÷ 9)

= 25-81 / (8-5)(36÷9)

= -56 / (3)(4)

= -56/12

= - 14/3

20² ÷ {3(5-9)² + 2}

= 400 ÷ {3(-4)² + 2}

= 400 ÷ {3(16) + 2}

= 400 ÷ (48+3)

= 400 ÷ 50

= 8

84/12 + (5-7)² -72 ÷ 6×2

= 7 + (-2)² - 12 × 2

= 7 + (4) - 24

= 11 - 24

= -13

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Answer:Maria

Step-by-step explanation: Maria uses a cup per 2 gallons while Franco uses a cup for 5 gallons. Maria has a 1:16 ratio while Franco has a ratio of 1: 80 because a gallon is 16 cups. It is clear now that Franco has a smaller ratio so, Maria's sports drink is stronger.

Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:

The value of h is the same for all the shape so assume the value of h is 2 units.

The volume of a cylinder is:

= πr²h

First cylinder area:

= 22/7 x 3 x 2

= 56.54867 units

The second cylinder area:

= 22/7 x 6 x 2

= 226.19467 units

The volume of a cone is:

= πr²h/3

First cone volume:

= 22/7 x 3 x 2/3

= 18.84956 units

Second cone volume:

= 22/7 x 6 x 2/3

= 75.39822 units

The order is therefore:

Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units

In conclusion, the shapes with the larger radius of 6 units will have more volume.

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If they work together, they need 15/8 hours to assemble one shelving unit.

What does work mean in math?

According to tittle, we know worker A can  assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.

If A & B work together , they will spend the same time t to assemble only one shelving .

That means,                  1/5t + 1/3 t = 1                         (equation)

1/5 t is worker A's workload during time t , 1/3 t is worker B workload.

So,   1/5 t + 1/3t = 1  is the answer

     ⇒ 5t + 3t = 15

     ⇒ t = 15/8 hours

If they work together, they need 15/8 hours to assemble one shelving unit.

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Answer:

Letter C is the correct answer or  1/5 t + 1/3t = 1

Answer:

the triangle is a right angle triangle. I can't see the correct explanation here so I will explain

Step-by-step explanation:

to work out whether triangles are right angle you do :

square root of (5² + 12²) so it would be 25 + 144 =169 and the square root of 169 is 13 . we do this because the square root of both of the side lengths squares should make ths longer side in this case it makes 13 so it is a right angled triangled

i hope this helps . if you need any more help pls ask :)

Using the arrangements formula, it is found that:

a) There are 1365 possible outcomes that contain exactly four tails.

b) There are 1,307,674,399,889 possible outcomes that contain at least three heads.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repetitions, the number of ways is given as follows:

[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

In which [tex]n_1, n_2, \cdots, n_n[/tex] are the numbers of repetitions.

Item a:

11 heads and 4 tails, hence:

[tex]A_{15}^{11,4} = \frac{15!}{11!4!} = 1365[/tex]

There are 1365 possible outcomes that contain exactly four tails.

Item b:

The total number is:

[tex]A_{15} = 15! = 1,307,674,400,000[/tex]

With no heads:

[tex]A_{15}^{15,0} = \frac{15!}{15!0!} = 1[/tex]

With one head:

[tex]A_{15}^{14,1} = \frac{15!}{14!1!} = 15[/tex]

With two heads:

[tex]A_{15}^{13,2} = \frac{15!}{13!2!} = 95[/tex]

Hence the number of outcomes with less than three heads is:

1 + 15 + 95 = 111

With at least three heads, the number of outcomes is:

[tex]1,307,674,400,000 - 111 = 1,307,674,399,889[/tex]

There are 1,307,674,399,889 possible outcomes that contain at least three heads.

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The expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The local gym is offering this new promotion:

An enrollment fee of $40 and a monthly fee of $30.

Let m be the total number of months

Total monthly fee = 30m

Total cost(including the enrollment fee of $40) = 40 + 30m

Let the total cost is c:

c = 40 + 30m

If in the linear expression, one variable is present, then the bis known as the linear expression in one variable.

Thus, the expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.

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For Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14.

To calculate the sum of money they must deposit, use the compound interest formula.

From the compound interest formula;

P = A / ( 1 + r/n )^(nt)

Given that;

P = A / ( 1 + r/n )^(nt)

P = 20,000 / ( 1 + 0.12/4 )^(4×10)

P = 20,000 / ( 1.03)^40

P = 20,000 / 3.26203779

P = $6,131.14

Therefore, for Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14.

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Using the normal distribution, we have that the desired information is given as follows:

a) X ~ N(3,1.8).

b) 3 days.

c) Z = 0.5556.

d) 0.33 = 33%.

e) 0.2048 = 20.48%.

f) 5.3 days.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 3, \sigma = 1.8[/tex]

Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.

The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:

Z = (4 - 3)/1.8 = 0.5556.

The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:

Z = (3.8 - 3)/1.8 = 0.44.

Z = 0.44 has a p-value of 0.67.

1 - 0.67 = 0.33.

The probability is of 0.33 = 33%.

The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:

X = 4.2:

Z = (4.2 - 3)/1.8

Z = 0.67.

Z = 0.67 has a p-value of 0.7486.

X = 3.2:

Z = (3.2 - 3)/1.8

Z = 0.11.

Z = 0.11 has a p-value of 0.5438.

0.7486 - 0.5438 = 0.2048 = 20.48%.

The 90th percentile is X when Z = 1.28, hence:

1.28 = (X - 3)/1.8

X - 3 = 1.8 x 1.28

X = 5.3 days.

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Answer:

You did not list any choices but if you simplify that the answer is 6√2x-3√2

Step-by-step explanation:

If they want you to factor it instead of simplifying the answer is 3√2(2x-1)

Answer:

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

Step-by-step explanation:

So you haven't provided any options, but I'm assuming they want it in most simplified form.

To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.

So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y

[tex]5xy-3y+xy[/tex]

So in here, think of y as the variable and the 5x, -3, and x as the coefficients.

In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))

[tex](5x-3+x)y[/tex]

Simplify this expression to get

[tex](6x-3)y[/tex]

Now just plug the sqrt(2) back in as y and you get the expression

[tex](6x-3)\sqrt{2}[/tex]

Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

Answer: 26.39

Step-by-step explanation:

2xπxr

The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a linear equation is given as:

y = mx + b

Where m is the rate of change and b is the y intercept (initial value of y)

Let y represent the amount of water Jaquan uses to wash x cars, Using the point (2, 24) and (5, 60):

y - 24 = [(60 - 24)/(5- 2)](x - 2)

y = 12x

For 6 cars:

y = 12(6) = 72

The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.

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Answer: Jaquan uses 72 L to wash 6 cars

Step-by-step explanation:

The amount in the ira's account s = $187,159.62.

How do you interest rate?

Future Value of an Ordinary Annuity

[tex]s = R(( 1 + i)^{n} - 1 ) / i[/tex]

where

S = the future value;

R = the periodic payment;

i = the interest rate per period;

n = the number of periods.

[tex]s = 5000 ( 1 + 0.032)^{25} - 1)/ 0.032[/tex]

[tex]s = 5000((1.032)^{25} - 1 )/0.032[/tex]

[tex]s = 5000( 2.19782157471 - 1)/0.032[/tex]

[tex]s = 5000(1.19782157471)/0.032[/tex]

[tex]s = 5000 * 37.4319242096[/tex]

s = $187,159.62

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The option A is correct. A circle is the shape of the cross section taken parallel to the base of a cylinder.

According to the statement

We have given that the cylinder and we have to tell that the which shape required for the cross section taken parallel to the base of a cylinder.

So, For this purpose,

We know that the

A cylinder is a three-dimensional solid, one of the most basic geometric shapes.

In this shape the surface formed by the points at a fixed distance from a  line segment, which is  known as the axis of the cylinder.

As the bases of cylinder are two identical circles which are parallel to the curved surface.

The curved surface when we open will be circle rather than the circle.

So, Due to this reason the answer is a circle.

Therefore, a circle is the shape of the cross section taken parallel to the base of a cylinder.

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Answer:296 m

I’m assuming “breadth” is width and garderean is just the park.

(25+25+12+12) times 4.

A is never defined

Answer: 10

Step-by-step explanation: 5 less than 15 is 10 because 15 - 5 is 10. If it was 15 less from 5, only then it would be -10.

Answer:

5 less than 15 is Option D, 10. This is because using mathematical symbols, it says 15-5 which equals to 10.