The net of a pyramid is shown below. The net of a square based pyramid, with base edges labeled 4 inches and the height of the triangle labeled 8 inches. The surface area of the solid is ____ square inches.

Answers

Answer 1

The answer is 80 square inches. The bottom part is a square. You need to do length times width which is 4 times 4 (the base edges) and it is 16. The formula of area for a triangle is half times length times width. This is 4 times 8 which is 32 and times half or divide by 2 and you get 16 square feet for each triangle face. Multiply 16 by 4 for all triangular faces and you get 64 and add the square surface area (16 squ.feet) and the total surface area is 80.

Related Questions

Pamela is 13 years older than Jiri. The sum of their ages is 53 what is Jiri's age?

Answers

You are first told that Pamela is 13 years older than Jiri so:

p=j+13

Then you are told that the sum of their ages is 53 so:

p+j=53

We already know from the first statement that p=j+13, this makes p+j=53 become:

(j+13)+j=53 so we combine the two j's on the left side

2j+13=53 subtract 13 from both sides

2j=40 divide both sides by 2

j=20

So Jiri is 20 years old.

The solution is: Jiri is 20 years old.

What is addition?

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Pamela is 13 years older than Jiri so:

p=j+13

Then you are told that the sum of their ages is 53 so:

p+j=53

We already know from the first statement that p=j+13, this makes p+j=53 become:

(j+13)+j=53 so we combine the two j's on the left side

2j+13=53 subtract 13 from both sides

2j=40 divide both sides by 2

j=20

So Jiri is 20 years old.

Hence, The solution is: Jiri is 20 years old.

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Rewrite the equation in standard form and identify a, b, and c. 2x^2 + 6x - 9 = 3x^2 - 11x - 7

Answers

[tex]2x^2 + 6x - 9 = 3x^2 - 11x - 7\\ x^2-17x+2=0\\ a=1\\ b=-17\\ c=2[/tex]

2x^2 + 6x - 9 = 3x^2 - 11x - 7

Subtract 2x^2 from both sides
6x - 9 = x^2 - 11x - 7

Substract 6x from both sides
-9 = x^2 - 17x - 7

Add 9 to both sides
0 = x^2 - 17x + 2

a = 1
b = -17
c = 2

y=-x y=2x+3 graph the equation to solve the system

Answers

If Y=-x y=2x+3 was graphed it would be (-1,1)

Well to solve by graphing, you would graph both equations and then see where the two lines intersect. This graphical intersection is the point where both equations are equal to each other.

To solve using math :P

If a solution exists, (x,y)=(x,y) so we can say y=y and then we can say:

2x+3=-x add x to both sides

3x+3=0

3(x+1)=0

So x=-1, and since y=-x

y=1

So the solution to the system of equations, and the graphical intersection, is the point (-1, 1)

Find the surface area of a regular pentagonal prism with side length 8, altitude 20, and apothem approximately 5.5

Answers

Final answer:

The surface area of a regular pentagonal prism can be found by calculating the area of the pentagonal bases and the area of the rectangular sides and then summing those areas together.

Explanation:

Calculating the Surface Area of a Regular Pentagonal Prism

To find the surface area of a regular pentagonal prism with given dimensions, we need to calculate the area of two components: the area of the pentagonal bases and the area of the rectangular sides (also called the lateral faces). We are given that the side length (s) of the pentagon is 8 units, the prism's altitude (h), or height, is 20 units, and the apothem (a) is approximately 5.5 units.

Firstly, the area of a pentagon (Apentagon) is calculated using the formula Apentagon = ½ * perimeter * apothem, where the perimeter (P) of a regular pentagon is the side length multiplied by 5. Thus, the area of one pentagonal base is ½ * 5 * 8 * 5.5. Next, to find the entire area of the two pentagonal bases, we multiply this result by 2.

The area of each of the rectangular sides can be found by multiplying the side length by the prism's altitude. Since there are 5 identical rectangular sides in a regular pentagonal prism, their total area is 5 * 8 * 20.

Adding these two results together gives us the total surface area of the prism. So, the formula for the surface area is Total Surface Area = (2 * ½ * 5 * 8 * 5.5) + (5 * 8 * 20).

What is the next number of 2 7 8 3 12 9

Answers

6 would be the next number in pattern

Answer with Step-by-step explanation:

We are given a pattern

2 7 8 3 12 9

and we are asked to find the next term of this pattern

2+1=3

7+5=12

and 8+1=9

We can view this pattern in the set of three numbers and then, the next three are formed by adding one, five & one, respectively.

See these COLUMNS of groups of three:

2 3 4

7 12 17

8 9 10

Hence, next number in the pattern is:

Translate to an algebraic expression. 5 INCREASED BY y

Answers

easy............5 + y

Write 337,060 in expanded form using exponents

Answers

3x10^5 \\ +3x10^4 \\ +7x10^3 \\ + 0x10^2 \\ +6x10^1 \\ +0x10^0

The length of the hypotenuse is:
0.
1.
2.
4.

Answers

divide the base by the sin of the opposite angle

base = 2

opposite angle = 30 degrees

2/sin(30) = 4

x = 4

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

Answers

Final answer:

The probability is approximately 0.267.

Explanation:

To find the approximate probability that the mean salary of the 100 players exceeded $4.0 million, we can use the Central Limit Theorem and the Z-score formula. The Z-score formula is:

Z = (x - μ) / (σ / sqrt(n))

where x is the value we want to find the probability for (in this case $4.0 million), μ is the mean of the population ($3.26 million), σ is the standard deviation of the population ($1.2 million), and n is the sample size (100).

We calculate the Z-score as follows:

Z = (4.0 - 3.26) / (1.2 / sqrt(100)) = 0.617

We then use a Z-table or a calculator to find the probability corresponding to a Z-score of 0.617. The probability is approximately 0.267.

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=52t-16t^2 . What is the maximum height that the ball will reach? Do not round your answer.
Height: ________Feet

Answers

A quick way to do this problem is to use the vertex formula as if you were trying to graph the parabolic function.
We know that in this case the vertex is at a maximum height because the leading coefficient is negative. If it were positive, then the vertex would be at the lowest point, in other words, they would ask you to solve for the lowest point. In this case we are solving for the highest point.
Primarily, we can use the axis of symmetry formula to solve for the x-coordinate of the vertex which demonstrates the time the object takes to reach its apex. Once we find the t or the x-coordinate, we can plug it back into the equation to solve for the h or height.
Axis of symmetry formula: -b/ 2a

(b) is 52 in this case. (a) is -16 in this case. Just plug the numbers in but be mindful of the signs included in the formula.
-(52)/ 2(-16) = -52/-32
The quotient would be a terminating decimal: 1.625

Therefore, the time it takes for the ball to reach its highest point would be 1.625 seconds. Now you can plug this number back in as a substitution for the variable t and you can solve for h.

h = -16(1.625)^2 + 52(1.625)
h = -16(2.640625) + 84.5
h= -42.25 + 84.5
h = 42.25
Therefore, the maximum height that the ball will reach in 1.625 seconds is 42.25 feet.

The maximum height would be 42.25 feet that the ball will reach.

What is the velocity?

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

A vertical upward throwing of a ball Its height h after t seconds (in feet) is given by the function h(t) = 52t - 16t²

Here h(t) = 52t - 16t²

Differentiate with respect to t to get maximum height

h'(t) = 52 - 2 × 16t

h'(t) = 52 - 32t

In this position, the acceleration would be zero,

So 0 = 52 - 32t

32t = 52

t = 52/ 32

t = 1.625

Substitute the value of t = 1.625 in the given function,

⇒ h = 52(1.625) - 16(1.625)²

⇒ h = 84.5 - 42.25

⇒ h = 42.25

Therefore, the maximum height would be 42.25 feet that the ball will reach.

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this box can be packed with 48 unit cubes the edge length each unit cube is 1 meter what is the voume of the box

Answers

Since each cube has a volume of 1 cubic meter and the box and fit 48 unit cubes the volume of the box is 48 cubic meters.

Answer:

48 cubic meters.

Step-by-step explanation:

48x1

unit meter is cubic meters

Differentiate
1/√x^2-1

Answers

the function is [tex]f(x)= \frac{1}{ \sqrt{ x^{2} -1}} [/tex]

write f again as [tex]f(x)= (x^{2} -1)^{- \frac{1}{2} } [/tex]

(the power -1 takes the expression to the denominator, and the power 1/2 is square root)

writing rational expressions as power expressions, generally makes differentiation more practical.

In [tex]f(x)= (x^{2} -1)^{- \frac{1}{2} } [/tex] we notice 2 functions:

the outer function [tex]u^{ -\frac{1}{2} } [/tex], where [tex]u=x^{2} -1[/tex], and the inner, u itself , which is a function of x.

So we differentiate by using the chain rule:

[tex]f'(x)= -\frac{1}{2}u^{- \frac{1}{2}-1 }*u'= -\frac{1}{2}u^{- \frac{3}{2} }*(2x)=- \frac{x}{ \sqrt{ u^{3} } } =- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }[/tex]

Answer: [tex]- \frac{x}{ \sqrt{ (x^{2} -1)^{3} } }[/tex]

A student was asked to use the formula for the perimeter of a rectangle, P = 2l + 2w, to solve for l. The student came up with an answer, P -2w=2l. What error did The student make? Explain. Then solve for l

Answers

The student solved for 2l, not l. Dividing P -2w=2l by 2, we get l=P/2-w

A fish is 5 feet below the surface of a lake. If its position can be recorded as −5 feet, what would the position of 0 represent?

Answers

Hey!

According to your question, we can see that if we got a negative number, that would represent that we are below sea level, that may mean being underwater. If we got a positive number, then that means we are above the sea level. The position of 0 would represent sea level.

Thanks
-TetraFish

What is a ratio equivalent to 8/10 with lower terms

Answers

You divide both the top and bottom by the GCF (Greatest common factor)

In this case the gcf is 2 so you divide both 8 and 10 by 2, and you get 4/5.

A line passes through the point (6−6) and has a slope of 3/2 . Write an equation in point-slope form for this line.

Answers

y= (3/2)x-15 is the equation

Write 935.97 in expanded form

Answers

935.97 = 900 + 30 + 5 + 0.9 + 0.07

hope it helps

there were 137 tickets purchased for a major league baseball game the lower box tickets cost $12.50 and the upper box tickets cost $10 the total amount of money spent was $1,502.50 how much of each kind of ticket

Answers

lower box = x

upper box = y

x+y=137

x=137-y

12.50x + 10y=1502.50

12.50(137-y) + 10y=1502.50

1712.5-12.50y+10y=1502.50

1712.5-2.50y=1502.50

-2.5y=-210

y=-210/-2.50 = 84

y = 84

x=137-84=53

53 lower box tickets

84 upper box tickets

Perform the indicated operation. (5 - 2i 2) 2

Answers

[tex]\bf (5-2i^2)^2\qquad \textit{now recall }i^2=\sqrt{-1}\cdot \sqrt{-1}=\sqrt{(-1)^2}=-1 \\\\\\ (5-2(-1))^2\implies (5+2)^2\implies 7^2\implies 49[/tex]

ANSWER

[tex](5 - 2 {i}^{2} ) ^{2} = 49[/tex]

EXPLANATION

The given expression is

[tex](5 - 2 {i}^{2} ) ^{2} [/tex]

This is an expression containing a complex number.

Recall that in complex numbers,

[tex] {i}^{2} = - 1[/tex]

The expression now becomes,

[tex](5 - 2 {i}^{2} ) ^{2} = (5 - 2 ( - 1) ) ^{2} [/tex]

This implies that,

[tex](5 - 2 {i}^{2} ) ^{2} = (5 + 2 ) ^{2} [/tex]

This will simplify to,

[tex](5 - 2 {i}^{2} ) ^{2} = {7}^{2} [/tex]

This eventually gives us,

[tex](5 - 2 {i}^{2} ) ^{2} = 49[/tex]

The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 25 feet. Round your answer to the nearest tenth.

Answers

I assume you are looking for the formula, and the velocity.

The formula:
v1^2-v0^2=2aS

where
v0=initial velocity (0 if object falls from rest), ft/s
v1=velocity reached after falling a distance S, ft/s
S=distance from initial position, positive downwards (for falling objects), ft
a=acceleration due to gravity, 32.2 ft/s^2 in imperial units

So substituting numbers, assuming initial velocity is zero (from rest), then
S=25 ft
v1^2-0^2=2*32.2*25
v1^2=1610
v1=sqrt(1610)
=40.1 ft/s

if f(x) = 3x - 2 then f (8) - f(-5)=

Answers

f(8) = 3(8) - 2 = 22
f(-5) = 3(-5) - 2 = -17
so....
f(8) - f(-5) = 22 - -17 = 39

A triangle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?

Answers

you must first subrtact 4 -6 to get 42 then add 99

Ricky is filling an 8 inch by 4 inch by 4 1/2 inch rectangular box with packing peanuts. The peanuts are cubes that come in two different sizes ,1 cubic inch and 1/8 inch .How many peanuts of each size are needed to fill the box?

Answers

First find the volume of the box: 8•4•4.5=144 cubic inches.
8 of the 1/8 inch=1 of the 1 cubic inch
He could do 144 and 0
143 and 8
142 or 16
Or just keep following the pattern... Hope that helped

A collection of quarters and nickels is worth $3.75. There are 27 coins in all. Find how many of each there are.

Answers

Q +N =27

Q=27-N

0.25Q + 0.05N =3.75

0.25(27-N) + 0.05 =3.75

6.75-0.25N+0.05N=3.75

6.75-0.2N=3.75

-0.2N=-3

N=-3/-0.2 = 15

15 nickels

27-15 = 12

12 quarters

15x0.05 = 0.75

12 x 0.25 = 3.00

3.00 + 0.75 = 3.75

12 quarters & 15 nickels

Find the value of x, rounded to the nearest tenth. Please help me!!

Answers

When two secant lines intersect each other outside a circle, the products of their segments are equal.

5(x+5) = 7(15+7)
5x + 25 = 7 * 22
5x + 25 = 154
5x = 154 - 25
5x = 129
x = 129/5
x = 25.8

The value of x for the circle is 25.8. The correct option from the following is (D).

Simple closed shapes include circles. It is the collection of all points in a plane that are a certain distance from the center. A segment is a section of a straight line that has every point on the line that lies in its middle and is enclosed by two clearly defined endpoints.

The products of two secant lines that cross one another outside of a circle are equal.

The value of x is:

5(x+5) = 7(15+7)

5x + 25 = 7 × 22

5x + 25 = 154

5x = 154 - 25

5x = 129

x = 129/5

x = 25.8

Hence, the value of x is 25.8.

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Assume the Poisson distribution applies. Use the given mean to find the indicated probability.

Find P(4) when μ = 8.

Answers

For given Poisson distribution, μ=8.

P(k)=μ^k*e^(-μ)/k!
so
P(4)=8^4*e^(-8)/4!=0.05725 approx.

Final answer:

Using the Poisson distribution formula, substitute the given mean and the number of occurrences into the formula to find the probability. Hence P(4; 8)= e^-8 * 8^4 / 4!. The answer will be in decimal form, signifying the probability.

Explanation:

The probability in a Poisson distribution that an event happens exactly k times when the mean occurrence rate (μ or Lambda) is given is determined using the following formula:

P(k; μ) = (e^-μ * μ^k) / k!

Where e is Euler's number (approximately equal to 2.71828), k is the number of occurrences (in this case, it is 4) and μ is the mean number of occurrences (in this case, it is 8).

Applying the values into the formula, we have:

P(4;8) = (e^-8 * 8^4) / 4!

You can calculate the above expression using a calculator to find the probability. Remember, the answer will be in decimal form, representing the probability of the event occurring 4 times when the average rate of occurrence is 8.

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A cylinder has a base area of 169π cm2 . Its height is 4 cm more than the radius. Identify the volume of the cylinder. Round to the nearest tenth, if necessary.

Answers

check the picture below.

Answer:

V = 9025.8 cm3

Step-by-step explanation:

what is the product x 2-16/2 x+8 . x3-2x2+x/x2+3x-4

Answers

x^2 - 16 x^3 - 2x^2+x
------------- * ---------------------
2x+8 x^2 + 3x -4

(x+4)(x-4) x (x - 1)(x - 1)
= ----------------- * ----------------------
2(x+4) (x + 4)(x - 1)

x(x- 4) (x - 1)
= -----------------
2 (x + 4)

Answer:

A on Edge 2021

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

Preston goes on a camel safari in Africa. They travel 5 km north, then 3km east and then 1 km north again. What distance did he cover? What was his displacement?

Answers

what distance did he cover? well, he went 5km first, then 3km, then 1km, 5 + 3 + 1, is how much he covered.

what was his displacement? well, he has a north displacement of 6, 5 + 1, and a horizontal displacement of 3, check picture below.

so, his total displacement is "c" northeast.

The total distance Preston covered on his camel safari is 9 km, and his displacement is 6.71 km toward the northeast.

Determining Distance and Displacement

To answer the student's question about Preston's journey during his camel safari, we need to consider the definitions of distance and displacement.

Distance is the total length of the path traveled regardless of direction. In Preston's case, he traveled 5 km north, then 3 km east, and then 1 km north again. Therefore, the total distance covered is the sum of these individual distances

Displacement, on the other hand, measures the change in position from the starting point to the final point and is direction-dependent. It is a vector quantity with both magnitude and direction. To find the displacement, we can represent Preston's movement on a coordinate system with north being the positive y-direction and east being the positive x-direction.

From the starting point, moving 5 km north and then 1 km north results in a total of 6 km in the positive y-direction.

The magnitude of the displacement can be calculated using the Pythagorean theorem:

√((6 km)² + (3 km)²) = √(36 km² + 9 km²) = √(45 km²) = 6.71 km (rounded to two decimal places)The direction of the displacement would be to the northeast. Therefore, Preston's displacement is 6.71 km toward the northeast.

Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?

Answers

inequation 1:

[tex] \frac{2}{3}x-3 \geq y[/tex]

to plot the pairs (x, y) for which the inequation holds, draw the line [tex]y=\frac{2}{3}x-3[/tex]

then pick a point in either side of the line. If that point is a solution of the inequation, than color that region of the line, if that point is not a solution, then color the other part of the line.

we do the same for the second inequation. Then the solution, is the region of the x-y axes colored in both cases.

inequation 2:

[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]

[tex]y\ \textless \ - \frac{2}{3} x+ 4 [/tex]

draw the lines

i) [tex]y=\frac{2}{3}x-3[/tex] use points (0, -3), (3, -1)

ii)[tex]y=- \frac{2}{3} x+ 4 [/tex] use points ( 0, 4), (3, 2)

let's use the point P(3, 3) to see what region of the lines need to be coloured:

[tex]\frac{2}{3}x-3 \geq y[/tex] ;
[tex]\frac{2}{3}(3)-3 \geq 3[/tex]
[tex]2-3 \geq 3[/tex], not true so we color the region not containing this point

[tex]y+ \frac{2}{3}x\ \textless \ 4 [/tex]
[tex](3)+ \frac{2}{3}(3)\ \textless \ 4 [/tex]
[tex]3+ 5\ \textless \ 4 [/tex] not true, so we color the region not containing the point (3, 3)

The graph representing the system of inequalities is the region colored both red and blue, with the blue line not dashed, and the red line dashed.

Answer:

in other words b

Step-by-step explanation:

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