The net of a square pyramid is shown below. What is the surface area of the pyramid?

Ok, so

The point slope form of the line is given by the following formula:

Where

Is a point of the line, and m is the slope.

If we replace our values:

Slope = 7

Point = (-6, 1)

We obtain that the equation is:

To find the slope intercept form of the equation, we distribute in the brackets:

And the equation of our line in the slope intercept form will be:

y=7x+43

To solve the following calculation

You have to keep in mind the order of operations. Which states that multiplications and divisions are to be solved before additions or subtractions.

So the first step is to solve the multiplication "4*2" and the division "10÷2"

Now all that is left is to add the numbers when you have to perform the same operation several times, you have to solve them from lef

SOLUTION; Concept

Step1: Identify the giving information in the question

BOX A contains

BOX B contains

Step2: Find the probability of each event

Event 1: Choosing a green pen from the Box B

Event 2: Choosing a black pen from the Box B

Event 3: Choosing a yellow or black pen from the Box A

Since Box A contains only a yellow or black pen then the probability is

Event 4: Choosing a yellow pen from box A

Since there are 9 yellow pens in box A, the probability of choosing the yellow pen is

Probability describes the likelihood of the event.

Hence From least likely to most likely the occurrence of the event is arranged as follows according to the probability of each event

Using the vector form of velocity, it is possible to calculate the airspeed and bearing, which are 165.33 mph and 0.7 degrees respectively.

Given:

A plane may go 360 miles straight north in 2.0 hours if the wind is blowing at 15 mph and 331 degrees from the north.

You can use the following formula to calculate airspeed.

[tex]V^{2} =V_{x} ^{2} + V_{y} ^{2}- 2v_{x} v_{y}cos\beta \\[/tex] ...........equation (1)

[tex]v_{x}[/tex] is the velocity of the wind and [tex]v_{y}[/tex] is the velocity of the plane.

[tex]\beta = 331-180 = 151 degree[/tex]

Putting [tex]v_{x}, v_{y} , \beta[/tex] in equation (1)

[tex]V^{2}= 15^{2} +180^{2} -2*15*180*cos151\\ V^{2} = 225 + 32400 - 5400*cos151\\V^{2} = 27336.49\\V = 165.33[/tex]

Hence, The airspeed of the plane is 165.33 mph

Now,

[tex]\frac{sin\alpha }{v_{x} } =\frac{sin\beta }{V} \\\frac{sin\alpha }{15 } =\frac{sin151 }{165.33} \\\\sin\alpha = 10*0.00122\\\alpha = 0.7[/tex]

Hence bearing required is 0.7 degrees.

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Since the total interest he paid on the loan was $336. Then, The annual interest rate of Juan's loan if there are 365 days in a year  will be as at 8.4%.

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.

The formula of simple interest is given as:

S.I = PRT

Where:

Substituting the values and solving for the rate on the loan

r = {A} {PT}\r

= {5336} {5000*292}

r = 8.4 %

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The numeric value for the given expression is as follows:

[tex]\frac{j(x + h) - j(x)}{h} = \frac{4^{x - 2}(4^h - 1)}{h}[/tex]

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.

In the context of this problem, the function j(x) is given as follows:

[tex]j(x) = 4^{x - 2}[/tex]

At x = x + h, the numeric value of the function is found replacing the lone instance of x by x + h as follows:

[tex]j(x + h) = 4^{x + h - 2}[/tex]

For the fraction, the subtraction at the numerator is given as follows, applying properties of exponents:

[tex]j(x + h) - j(x) = 4^{x + h - 2} - 4^{x - 2} = 4^{x - 2}(4^h - 1)[/tex]

As the x - 2 term is common to both exponents.

Just dividing by h, the numeric value of the entire expression is given as follows:

[tex]\frac{j(x + h) - j(x)}{h} = \frac{4^{x - 2}(4^h - 1)}{h}[/tex]

Which means that the third option is correct.

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168 students are enrolled in both classes.

This is a problem from set theory. We can solve this problem by following a few steps easily.

First of all, we have to calculate the students present in both classes.

Student present in both classes = the total student - the student not enrolled in both classes.

So the percentage of the students enrolled in both classes or any of one class is ( 100% - 42% ) = 58%.

Now, the students only enrolled in chorus class is ( 58% - 34%) = 24%

So, the students who joined both classes is ( 28%- 24%)= 4%

The total student is 1200, then 4% of the total student is

( 1200 × 14 )/100 = 168 students.

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Given:

A table represents a survey to know if residents would like a dog.

a) What is an appropriate first step in finding the experimental probability that a household has 2 or more dogs?

The first step is to find the total households

So, the answer will be option C

Find the sum of the number of households for each category.

b) What is the experimental probability that a household has 2 or more dogs?

First, the total number of households = 513 + 218 + 129 = 860

And the number of households has 2 or more dogs = 129

So, the probability = 129/860 = 0.15 = 15%

So, the answer will be 15%

-3(x+1)<15 ​

Divide both-side of the inequality by -3

(x + 1) > -5

subtract 1 from both-side of the inequality

x > -5 - 1

x > -6

Answer:

Step-by-step explanation:

-3(x+1)<15

Divide the inequality by -3, so we need to change the sides of the less than into greater than

x+1 > -5

x > -5 - 1

x > -6

The vehicle speed is 53 units if s = 24d and d = 245ft

Given the formula for speed is  =  √24 d

s denotes the vehicle's speed.

d = the length of the skid marks

We need to find the speed of the vehicle.

We know that the displacement d is 117 ft

d = 117 ft

And also it is mentioned in the question to use the below-given formula.

s = √24d

Now substituting the value of displacement in the formula we get

=> s = √24 x 117

=> s = √2808

=> s = 52.99

Now approximating to the nearest value of the decimal, we get.

=> s = 53

Therefore the speed of the vehicle is 53 units.

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Given:

Required:

To find the solution of the given equation.

Explanation:

From the given equation,

Now

Therefore,

Final Answer:

The solutions are

Answer:

1280 ft²

Step-by-step explanation:

Perimeter is the addition of all sides of the shape added together. Therefore, if the backyard is the rectangular shape you know that two of the sides are 40 feet wide. By adding both sides you get a total of 80 feet. Subtract the total from the perimeter in order to get the total of the unknown sides. 144 minus 80 is equivalent to 64. Now that you have the total of the unknown sides, divide by two in order to get the single unknown length. So, 64 divided by 2 is equal to 32. The area is the multiplication of two sides with quadrilaterals. Therefore, 40 times 32 equals an area of 1280 feet squared.

Using the sine formula;

sin 60 / x = sin 90 / 16

cross-multiply

x sin 90 = 16 sin 60

Divide both-side of the equation by sin 90

x = 16 sin 60 /sin 90

x= 13.86

To find y, we can simply use the Pythagoras theorem

opp² + adj² = hyp²

13.86² + y² = 16²

192.0996 + y² =256

subtract 192.0996 from both-side of the equation

y² = 256 - 192.0996

y² = 63.9004

Take the square root of both-side

y = 7.99

Answer:

25 more cups

Step-by-step explanation:

1. You need more than $636.00, but you already have $492.00. To find the needed amount of cups needed to sell, you need to find the difference of the two prices first. In other words, you need to subtract the total needed by the amount already raised.

2. You can get the equation, 636 - 492 = 144

3. Now that you have the amount needed, you can divide the number that you got (144) by 6. You divide it by 6 because that is the amount each cup costs.

4. After dividing 144 by 6, you should get 24. This gives your answer for getting EXACTLY 636. However, in this case, you need more to reach your goal. Since you cannot sell fractions of a cup, just raising it by one can reach your goal. We can add one to 24, making it 25.

In conclusion, you need to sell 25 more cups to reach your goal.

Given the following equation:

You need to solve for "x" in order to find its value and solve the equation. To do this, you can follow the steps shown below:

1. You need to apply the Subtraction property of equality by subtracting 2 from both sides of the equation:

2. Now you can apply the Additio property of equality by adding "4x" to both sides of the equation:

Therefore, you get that the solution is:

Step-by-step explanation:

you do know what a percent is ?

1% is the 1/100 part of a whole.

when we have

100,000,000 (one hundred million),

how many 1/100 parts of that are

45,000,000 (45 million)?

well, 45.

45,000,000 is 45/100 of 100,000,000

in other words 45%.

Answer:21

Step-by-step explanation:

Answer:

12-3x=14

Step-by-step explanation:

The average rate of change of a function in the interval [a,b] is given by:

In this case we have that a=1 and b=6; plugging these values in the formula above we have:

Therefore, the average rate of change in the interval is -15

The number when increased by twenty is at least 85, the possible values  of the numbers for this are: 35, 33, 40 and 34.

Given, according to the statement in the question, frame the equation:

2x+20 ≥ 85

⇒ 2x + 20 ≥ 85

⇒ 2x ≥ 85 - 20

⇒ 2x ≥ 65

⇒ x ≥ 65/2

⇒ x ≥ 32.5

hence the numbers greater than or equal to 32.5 are 35, 33, 40 and 34.

Hence the possible values of the number are 35, 33, 40 and 34.

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As we can se from the graph, the maximum value of the function is almost 15 meters, it is reached between t=1s and t=2s, and the height is 0 again when the time is approximately 3 seconds.

We can find the exact values by using the equation.

First, find the zeroes of the function by setting h(t)=0 and solving the quadratic equation for t:

Then, the projectile hits the ground at t=3s.

To find the time at which the projectile reaches its maximum height, find the average between both zeroes:

To find the maximum height, evaluate h at t=1.3s:

Therefore, to the nearest tenth, the projectile reached a maximum height of 14.5 meters in 1.3 seconds and it took 3.0 seconds for it to hit the ground.

The correct option is the second one.

The given function is:

f(x) = 1.5x + 7

Then, since x represents the age of the baby, in months, in order to find its weight with 5 months, that is, f(5), we need to replace x by 5 in the above equation:

f(5) = 1.5 * 5 + 7 = 7.5 + 7 = 14.5

Therefore, the last option is correct.

Given:

The slopr of line is m = -7.

The line passes through point (-6,8).

Explanation:

The equation of line in slope-intercept form is,

Substitute the valus in the equation to determine the value of c.

So equation of line is y = -7x - 34.

By solving a proportional relation, we conclude that he needs 81 hooks to catch 189 fish.

We assume there is a proportional relationship of the form:

F = k*H

where:

We know that with 3 hooks he catches 7 fish, then we can replace that:

7= k*3

7/3 = k

So the proportional relation is:

y = (7/3)*x

Then if he wants to get 189 fish we can write:

189 = (7/3)*x

And solve this for x:

189*(3/7) = x =81

He will need 81 hooks.

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Answer:

The axis of symmetry is -4 because the axis of symmetry is equal to h, in the vertex form!

Budget: $40

Fruit: $4/pound

Granola bars: $1 each

At least 20 granolas

Let's call

f: number of pounds of fruit

g: number of granola bars

Therefore

The total cost of fruit is given by: $4 · f

The total cost of granola is given by: $1 · g

The total cost of everything is given by: $4 · f + $1 · g

Since budget: $40 then

$4 · f + $1 · g = $40

4f + g = 40

g > 20 means we have at least 20 granolas

4f + g > 20 means that we have at least 20 granolas, that cost $20, since 4f + g = 40 and 40 > 20

Answer:

  9

Step-by-step explanation:

You want the minimum value of objective function C=6x+3y, given the constraints x>1, y≥1, 4x+2y<32, and 2x+8y<56.

The objective function has positive coefficients for both x and y, so it will be minimized when x and y are at their minimum values. The constraints tell you these minimum values are x=1 and y=1, so the minimum value of C is ...

  C = 6(1) +3(1) = 9

The minimum value of C is 9.

__

Additional comment

The value of x cannot actually be 1, so the value of C cannot actually be 9. However x may be arbitrarily close to 1, so C may be arbitrarily close to 9.

  C = 6x +3y   ⇒   x = (C -3y)/6

The x-constraint requires ...

  x > 1

  (C -3y)/6 > 1

  C -3y > 6 . . . . . . multiply by 6

  C > 6 +3y . . . . . . add 3y

The minimum value of y is exactly 1, so we have ...

  C > 6 +3(1)

  C > 9

EXPLANATION:

To calculate the number of independent events that occur, the product of the probabilities of the individual events occurring must be calculated.

Therefore if A and B are independent events then:

P (A and B) = P (A) • P (B)

The exercise is as follows:

NOTE:

To obtain the product of two fractions, the numerators must be multiplied with each other and the denominators must also be multiplied with each other.

The decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25

The given mixed fraction = [tex]14\frac{25}{100}[/tex]

The mixed fraction is the fraction that consist of one whole number and the simple fraction.

The simple fraction is the fraction that consist of numerator and denominator as whole number. The top term of the simple fraction is called numerator and bottom term is called denominator

The decimal number is a number that consist of one whole number and the fractional part. The fractional parts are separated by a decimal point.

The number is [tex]14\frac{25}{100}[/tex]

Convert the mixed fraction to simple fraction

[tex]14\frac{25}{100}[/tex] = (100×14+25)/100

= 57/4

Convert the simple fraction to decimal number

57/4 = 14.25

Hence, the decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25

The complete question is:

Rewrite the decimal fraction as a decimal number.

[tex]14\frac{25}{100}[/tex]

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Given:

To Determine: The square root of the given number

Solution

Step 1: Express 225 as the product pf its prime factors of 225

Step 2: Separate the factors into their own square root

Step 3: Solve the individual's squares

Hence, the square root of 225 is 15