Look at this prism and its net. Rectangular prism with length labeled 5 meters, width labeled 7 meters, and height labeled 12 meters. Net of the same rectangular prism with the same dimensionsn labeled. What is the surface area of this rectangular prism? cm²

Final answer:

No, not every even number can be written as a sum of two primes. This is known as the Goldbach Conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers.

Explanation:

No, not every even number can be written as a sum of two primes. This is known as the Goldbach Conjecture, which states that every even number greater than 2 can be expressed as the sum of two prime numbers. So far, this conjecture has been tested for even numbers up to at least 4, and no counterexamples have been found. However, it has not been proven to be true for all even numbers.

For example, the number 4 can be expressed as the sum of two primes (2 + 2), but the number 6 cannot be expressed as the sum of two primes. On the other hand, the number 8 can be expressed as the sum of two primes (3 + 5). This pattern continues, with some even numbers being expressible as the sum of two primes and others not.

The number of stamps each could have purchased is 84

How to determine the number of stamps each purchased

From the question, we have the following parameters that can be used in our computation:

Andy = packs of 4

Erin = packs of 6

Jarred = packs of 7

Expand 4, 6 and 7

So, we have

4 = 2 * 2

6 = 2 * 3

7 = 7

The LCM of 4, 6 and 7 is then calculated as

LCM = 2 * 2 * 3 * 7

Evaluate

LCM = 84

Hence, the number of stamps each could have purchased is 84

Let the number of stickers in each pack be 'x'

Finn bought 2 packs of stickers.

Number of stickers in 2 packs = [tex] 2 \times x [/tex] = 2x

According to the question, a friend gave him 4 more stickers and now he has 24 stickers in all.

Therefore, [tex] 2x+4=24 [/tex]

[tex] 2x=24-4 [/tex]

[tex] 2x=20 [/tex]

x = 10

Therefore, number of stickers in each pack are 10.

Fraction is a way to describe a part of a whole. The fraction is represented by the shaded part of the model is [tex]\dfrac{2}{1}[/tex].

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25

If we look at each of the shapes, we can observe that the whole of the shape is shaded therefore, the shaded part of the shape is equal to the shape which is represented by 1.

Now, in the image, there are two shapes given each of which is completely shaded, and the whole shape is represented by 1. therefore, these two shapes will be represented by 2.

The shaded shape can be written as,

[tex]2 = \dfrac{2}{1}[/tex]

Hence, the fraction is represented by the shaded part of the model is [tex]\dfrac{2}{1}[/tex].

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a) π · (12 · tan 70°)2. To find the area of the ground covered by the conical tent, use the formula for the surface area of a cone, A = πr(r+√(r^2+h^2)).

To find the area of the ground covered by the conical tent, we can use the formula for the surface area of a cone. The formula is A = πr(r+√(r^2+h^2)), where r is the radius and h is the height of the cone.

In this case, the height of the cone is 12 feet and the angle it makes with the ground is 70°. To find the radius, we can use trigonometry. The radius is given by r = h tanθ, where θ is the angle with the ground. Plugging in the values, we get r = 12 tan(70°).

Now, substituting the value of r into the formula for the surface area of the cone, we get A = π(12 tan(70°))(12 tan(70°)+√((12 tan(70°))^2 + 12^2)). This simplifies to option a) π · (12 · tan 70°)2.

A geometric series is the sum of an unlimited number of terms with a fixed ratio between them. The correct option is B.

A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.

The given statement "If all terms of a series are​ positive, then the series sums to a positive number" is true because the series will converge to a positive number because the series contains no negative terms.

Hence, the correct option is B.

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Answer with explanation:

→→Information given about Parabola

Vertex of the Parabola = (0,0)

Focus is located on the positive x- axis.

Definition of Parabola: A parabola is locus of all the points such that distance from a fixed point known as focus to distance from a fixed line called, Directrix  is always constant.

Let focus of the parabola be (k,0), where , k>0.

Distance between vertex (0,0) and focus(k,0) = Distance between vertex (0,0) and point on negative x-axis (-k,0).

Directrix will pass through point (-k,0).

So, equation of Directrix will be, x= -k

Directrix will pass through

Option B: The Negative part of the x -axis.

Answer with Step-by-step explanation:

Let

A:selecting a heart

Total cards=52

number of hearts=13

P(A)=13/52

B:selecting a 8

number of 8=4

P(B)=4/52

A∩B:selecting a heart with 8 on it

number of hearts with 8 on it=1

P(A∩B)=1/52

A∪B:selecting a heart or a 8

We have to find P(A∪B)

P(A∪B)=P(A)+P(B)-P(A∩B)

          = [tex]\dfrac{13}{52}+\dfrac{4}{52}-\dfrac{1}{52}[/tex]

          =[tex]\dfrac{13+4-1}{52}[/tex]

          = 16/52

          = 4/13

Hence, the probability of selecting a heart or a 8 is:

4/13

Answer:

I think its 5

Step-by-step explanation:

I may be wrong

Answer: The answer in order are false, false, true, true, false and (3,1)

Step-by-step explanation:

We know that image of a point (x,y) under the y-axis

is (-x,y) i.e. the sign of x coordinate changes

Similarly in case of x-axis sign of y coordinate changes

i.e (x,y) is reflected to (x,-y)

Also the reflection of (x,y) under the line y=x is (y,x)

and the reflection of (x,y) under the line y=-x is(-y,-x)

So  

a) Given image of (-3,-5) under x-axis is (3,-5).

Hence statement is false

b) Given image of (1,9) under y-axis is (1,-9)

Hence the statement is false

c) Given image of (8,7) under y=-x is (-7,-8)

i.e. the statement is true

d) Given image of (-6,-6) under y=x is (-6,-6)

i.e the statement is true

e) Given image of (2,4) under y axis followed by x-axis is (-2,-2)

Hence the statement is false

f) (3,-1) is reflected in x-axis to (3,1)

Hence the point k is (3,1)

Answer:

a

b

e

g

Step-by-step explanation:

I just did the assignment lol-

Answer: The damaged area is equal to 8831.25ft^2

Step-by-step explanation:

We know that we have a circular area, where half of the grass has died. We know that the circular picnic is "150 feet across" I guess this means that if you walk in a straight line from the edge of the circular area, through the middle, and to the next edge, the distance is 150ft.

This would mean that the diameter is equal to 150ft.

With this we can calculate the total area of the circle; this is:

A = pi*r^2

where r is the radius, that is half the diameter, so we have r = 150ft/2 = 75ft

and pi = 3.14

so we have:

A = 3.14*(75ft^)^2 = 17662.5ft^2

And we know that half of that area has the grass damaged, so the amount of square feet of grass needed is equal to A/2 = (17662.5ft^2)/2 = 8831.25ft^2

To determine the value of ↑ which the equation ax²-3x-5=0 has 1 as a root, we substitute x=1 into the equation and solve for a, yielding the result that a=8.

To find the value of a for which the equation ax² - 3x-5=0 has 1 as one of its roots, we can substitute x=1 into the equation and solve for a. When x=1, the equation simplifies to:

a(1)² - 3(1) - 5 = 0

a - 3 - 5 = 0

a - 8 = 0

Therefore, a = 8.

This means that the value of a is 8 for the equation to have 1 as one of its roots. This is a direct application of the fact that if a polynomial has a certain number as a root, then by substituting that number in place of the variable, the equation should result in zero.