Find the total surface area of the pyramid.

Answer:

The scientific  notation is \(1.7\times 10^{10}\).

Step-by-step explanation:

Consider the provided information.

We need to express 17 billion in scientific notation.

17 billion is: 17,000,000,000

We split the given number into a coefficient and a power of 10.

Move the decimal point of the given number till the coefficient of the given number is greater than 1 and less than 10 and write the power of 10 equal to the number of steps the decimal point was moved.

17 billion in scientific notation = \(1.7\times 10^{10}\).

Hence, the required answer is \(1.7\times 10^{10}\).

Answer:

Marcie has used a total of 170 feet of tape (two 85-foot lengths) from the 50-foot roll, which means that there is 50 - 170 = -120 feet of tape left on the roll, indicating that the roll is empty and there is no tape left.

Answer: 80% or 4/5

Step-by-step explanation:

so I don’t know how many numbers there are on this cube (a standard number cube has #1-6) but I’m going to go with 10 numbers (don’t know how this is possible but anyway-). I’ll edit my answer if needed.

10 numbers

10 (numbers) - 2 (#8 and #10) = 8 (possible numbers)

so 8/10 or 80%

reduced fraction: 4/5

percentage: 80%

fraction: 8/10

*will edit if needed

The shortest total length of fence needed to divide a rectangular field with a total area of into three equal areas is X units.

To divide the rectangular field into three equal areas, the most efficient way is to create two parallel fences that divide the field into three equal strips. The length of these two fences will be equal to the width of the field. Another fence is then required to divide one of the strips into two equal areas. This third fence will have a length equal to the length of the field. Therefore, the total length of fence needed is the sum of the width and length of the field.

Learn more about rectangular field here

https://brainly.com/question/30430121

#SPJ11

Answer:

$750

Step-by-step explanation:

2500 divided by 100 = 25 and 25 x 30 = 750

Sorry if im wrong

The price for 2500 pencils is $750.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have,

A box of 100 personalized pencils costs $30.

So, cost of 1 pencil = $30 / 100 = 3/10

Now, the price to buy the 2500 pencils

= 2500 x 3/10

= 250 x 3

= $750

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ2

Answer:

2 cm per hour

Step-by-step explanation:

1 hour lines up with 2cm

2 hours line up with 4cm

3 hours line up with 6cm

Answer:

2=(3,-2)

3=(-4.75,-6.25)

4=(5/2,3/2)

5=87.8(simplified)

The equation of the plane through the line of intersection of the planes and and perpendicular to the plane is x - 2y + 15z - 51 = 0.

The line of intersection of the planes and can be found by setting the two equations equal to each other and solving for x, y, and z. Doing so gives:

3x - y + 2z = 1

2x + y - 3z = -4

Adding the two equations yields:

5x - z = -3

Solving for z, we get:

z = 5x + 3

Now we need to find a normal vector to the plane . The coefficients of x, y, and z in the equation of the plane give us the normal vector:

n = <1, 2, -3>

The dot product of the normal vector n and the vector parallel to the line of intersection gives us the direction of the plane we are looking for:

n . <5, 0, 1> = 1(5) + 2(0) + (-3)(1) = 2

Thus, the equation of the plane we are looking for is:

1(x - x0) + 2(y - y0) - 3(z - z0) = 0

where (x0, y0, z0) is a point on the line of intersection of the planes and . We can use the solution we found earlier to obtain:

z = 5x + 3

Substituting this into the equation of the plane gives:

x - 2y + 15z - 51 = 0

Thus, the equation of the plane through the line of intersection of the planes and and perpendicular to the plane is:

x - 2y + 15z - 51 = 0.

Learn more about line of intersection here

https://brainly.com/question/30655803

#SPJ11

The measure of angle R, found through the angle sum property of a triangle and corresponding angles in ΔKIX and ΔREM is m∠R = 61°

Corresponding angles are angles in two congruent or similar triangles, located between a pair of segments in one triangle that are congruent to a pair of segment in the other triangle

The details of the question are;

The transformation that maps triangle ΔKIX unto triangle ΔREM is a rotation.

Please see attached the example drawing of ΔKIX and ΔREM created with MS Excel.

A rotation transformation is a rigid transformation, therefore, the side lengths and shape of triangle ΔKIX is preserved in the image of the triangle, ΔREM

The measure of angle ∠X in triangle ΔKIX is ∠X = 117°

The measure of angle ∠I in ΔKIX is ∠I = 2°

∠K + ∠I + ∠X = 180° (angle sum property  of a triangle)

The measure of angle ∠K = 180° - (∠X + ∠I)

Therefore;

m∠K = 180° - (117° + 2°) = 61°

m∠K = 61°

Based on the naming of the triangles ΔKIX and ΔREM, we have;

∠K corresponds to ∠R, ∠I corresponds to ∠E, and ∠X corresponds to angle ∠R, therefore;

∠K ≅ ∠R, ∠I ≅ ∠E, ∠X ≅ ∠R, which by the definition of congruency indicates;

∠K = ∠R, ∠I = ∠E, ∠X = ∠R

m∠R = m∠K = 61°

m∠R = 61°

Learn more about the angle sum property of a triangle here:

https://brainly.com/question/27437134

#SPJ1

A certain discrete mathematics class consists of 26 26 students. of these, 15 15 plan to major in mathematics and 15 15 plan to major in computer science. five students are not planning to major in either subject. 5 students are planning to major in both subjects.

Let M be the set of students planning to major in mathematics.

C be the set of students planning to major in computer science.

N be the set of students who are not planning to major in either subject.

From the question statement,

Total number of students in the class = 26

The number of students planning to major in mathematics = 15

The number of students planning to major in computer science = 15

The number of students who are not planning to major in either subject = 5

Here we have to find the,

Number of students planning to major in both subjects.

Total number of students in the class = Number of students in the set M + Number of students in the set C + Number of students in the set N

The total area enclosed by the circles represents the total population being considered.

The area enclosed by each circle represents the number of people who belong to that set only. The area enclosed by the intersection of the circles represents the number of people who belong to both sets.

Number of students in M only = 10

Number of students in C only = 10

Number of students in N only = 5

Total number of students in the class = 26.

We can summarize our findings in a table as shown below:
Set Notation Number of students M 15 C 15 N 5 M ∩ C x M' ∩ C' ∩ N 0 Total 26
The total number of students in the class = 26

Therefore, the number of students in M ∩ C is 5.

For similar question on Venn Diagram

https://brainly.com/question/28060706

#SPJ11

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

To know more about marginal utility related question visit:

https://brainly.com/question/30841513

#SPJ11

Answer:

48

Step-by-step explanation:

P would equal 30 but you would have to multiply it by 5/8 so you would get 48.

Answer:

This should help

Step-by-step explanation:

1.05, 1.09 and 1.1 are close to each other so I marked where each one should go

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

according to clue no. 1 the number is 760 > x > 740. so, it could be any number between 740 - 760.

according to the 2 & 3 clue we can conclude that thousandths and ones digit are even and thousandth digit is twice the ones digit.

so the ones digit could be, 2 & 4 and the thousandth digit could be 4 & 8.

according to the 4th clue we can say that the tenths digit is 1 and thousandths digit is 4 as, thousandth digit is the 2nd even number after ones digit and also, sum of tenths and thousandth digit is 5 so, 1 + 4 = 5.

so, through this we can conclude that,

• ones digit = 2 as ( thousandth is twice the ones = 2 × 2 = 4 )

• tenths digit = 1 ( as 1 + 4 = 5 )

• thousandths digit = 4 ( as 4 + 1 = 5 )

according to clue no. 5 product of hundredths and hundreds is 7 so, 7 × 1 = 7.

so, according to this we can conclude that hundreds digit is 7 because in the required number the hundreds digit is itself 7

• hundreds digit = 7

&

• hundredths digit is = 1

and also, tens digit is 5 because only ones and thousandths digit are even.

so, the required number is, 752.114

hope this answer helps you dear & may u have a great day ahead!... take care!

Answer:

x ≥ -1 ≤ 4

Step-by-step explanation:

This would be your inequality.

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

Learn more about Scheduling here:

brainly.com/question/30012511

#SPJ4

ANSWER 35

Step-by-step explanation:

7 and 5 - 35

Now just simplify the 3 and 4 :)

The union of two events A ∪ B, represents the event that occurs if either A or B (or both) occurs in a single performance of the experiment. It consists of all the sample points that belong to A or B or both.

In probability theory, events are subsets of the sample space, which is the set of all possible outcomes of an experiment. The union of two events A and B is a new event that combines the outcomes from both A and B. It represents the occurrence of either A or B or both.

Mathematically, the union of A and B is written as A ∪ B. It consists of all the sample points that are in A, in B, or in both A and B. If an outcome belongs to A ∪ B, it means that it satisfies at least one of the conditions: it belongs to A, it belongs to B, or it belongs to both A and B.

The concept of the union of events is essential in probability calculations, such as finding the probability of at least one of two events occurring. By taking the union of events, we can combine their probabilities to analyze the likelihood of specific outcomes in the experiment.

Learn more about union here:

brainly.com/question/29189297

#SPJ11

Therefore, the volume of the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is 96 cubic units.

To find the volume of the solid bounded by the coordinate planes (xy-plane, xz-plane, and yz-plane) and the plane 6x + 4y + z = 24, we need to determine the region in space enclosed by these boundaries.

First, let's consider the plane equation 6x + 4y + z = 24. To find the x-intercept, we set y = 0 and z = 0:

6x + 4(0) + 0 = 24

6x = 24

x = 4

So, the plane intersects the x-axis at (4, 0, 0).

Similarly, to find the y-intercept, we set x = 0 and z = 0:

6(0) + 4y + 0 = 24

4y = 24

y = 6

So, the plane intersects the y-axis at (0, 6, 0).

To find the z-intercept, we set x = 0 and y = 0:

6(0) + 4(0) + z = 24

z = 24

So, the plane intersects the z-axis at (0, 0, 24).

We can visualize that the solid bounded by the coordinate planes and the plane 6x + 4y + z = 24 is a tetrahedron with vertices at (4, 0, 0), (0, 6, 0), (0, 0, 24), and the origin (0, 0, 0).

To find the volume of this tetrahedron, we can use the formula:

Volume = (1/3) * base area * height

The base of the tetrahedron is a right triangle with sides of length 4 and 6. The area of this triangle is (1/2) * base * height = (1/2) * 4 * 6 = 12.

The height of the tetrahedron is the z-coordinate of the vertex (0, 0, 24), which is 24.

Plugging these values into the volume formula:

Volume = (1/3) * 12 * 24

= 96 cubic units

To know more about volume of the solid,

https://brainly.com/question/30079268

#SPJ11

The triple integral of the function ∫∫∫E x²+y²+z²  dV evaluated by using  spherical coordinates is equal to 97.2π.

Triple integral ∫∫∫E x²+y²+z² dV in spherical coordinates,

Express the integrand and the volume element dV in terms of the spherical coordinates ρ, θ, and φ.

In spherical coordinates, the volume element is ,

dV = ρ² sin φ dρ dθ dφ

Since the ball E is defined by x²+y²+z² ≤9,

which is equivalent to ρ≤3, with following limits of integration.

0 ≤ ρ ≤ 3

0 ≤ θ ≤ 2π

0 ≤ φ ≤ π

Therefore, the triple integral can be written as,

∫∫∫E x²+y²+z²  dV

= \(\int_{0}^{2\pi }\int_{0}^{3}\int_{0}^{\pi }\)  ρ² ρ² sin φ dφ dθ dρ

Evaluating the innermost integral first, we get,

\(\int_{0}^{\pi }\)ρ² sin φ dφ

= -ρ² cos φ \(|_{0}^{\pi }\)

= ρ²

Substituting this into the triple integral, we get,

∫∫∫Ex²+y²+z²  dV = \(\int_{0}^{3}\int_{0}^{2\pi }\) ρ⁴ sin φ dθ dρ

Evaluating the θ integral, we get,

\(\int_{0}^{2\pi }\)π ρ⁴ sin φ dθ = 2π ρ⁴ sin φ

Substituting this into the triple integral, we get,

∫∫∫E x²+y²+z²  dV = \(\int_{0}^{3}\)2π ρ⁴ sin φ dρ

Evaluating the ρ integral, we get,

\(\int_{0}^{3}\)2π ρ⁴ sin φ dρ

= (2π/5) [ρ⁵]\(|_{0}^{3}\)

= (2π/5) (3⁵)

= 97.2π

Therefore, the triple integral ∫∫∫E x²+y²+z²  dV evaluated in spherical coordinates is 97.2π.

learn more about triple integral here

brainly.com/question/31482362

#SPJ4

To approximate the area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method, we can use the following formula:

Approximate Area = Δx * [f(x1) + f(x2) + f(x3) + f(x4)]

where Δx is the width of each subinterval and xi represents the right endpoint of each subinterval.

In this case, the interval [2, 4] is divided into four equal subintervals, so Δx = (4 - 2) / 4 = 0.5.

Now, let's evaluate the function at the right endpoints of the subintervals:

f(2.5) = 1/(2.5)^2 = 0.16

f(3) = 1/(3)^2 = 0.1111

f(3.5) = 1/(3.5)^2 = 0.0816

f(4) = 1/(4)^2 = 0.0625

Substituting these values into the formula:

Approximate Area = 0.5 * [0.16 + 0.1111 + 0.0816 + 0.0625]

Approximate Area = 0.5 * 0.4152

Approximate Area = 0.2076

Therefore, the approximate area under the graph of f(x) = 1/x^2 over the interval [2, 4] using four equal subintervals and the right endpoint method is approximately 0.2076.

learn more about graph here

https://brainly.com/question/10712002

#SPJ11

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Answer:

X=0

Step-by-step explanation:

36-3(2-4x0)

33(-2x0)

33(0)

=0

Answer:

b c and f edit: also A

Step-by-step explanation:

just gotta find what is reflexive