the spaceship travels around the sun at a speed of 12.6 miles per second. How far will it travel in 45 seconds?

It is found that Yasmine can create 9 cards.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that Yasmine needs to create invitations for the party. She has ¾ of an hour to make the invitations. It will takes her 1/12 of an hour to make each card.

Since Yasmine takes 1/12 hour create number of cards = 1

Yasmine takes 1 hour to create number of cards = 1 x 12/1 = 12

Yasmine takes 3/4 hour to create number of cards = 12 x 3/4 = 9

Therefore, It is found that Yasmine can create 9 cards.

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ2

We know that the volume,V of a cylinder is given by:

[tex] V=\pi r^2h [/tex]

where r is the radius, h is the height of the cylinder.

Now, it has been given to us that the diameter of the cylinder is 8.5 in. Therefore, the radius of the cylinder will be half it's diameter and will be, [tex] r=\frac{1}{2}\times 8.5=4.25 [/tex] in.

The height, h=11.5 inches

Therefore, applying the formula we will get:

Volume, V=[tex] \pi (4.25)^2(11.5)\approx652.57 in^3 [/tex]

Thus, out of the given options, Option A is the correct option.

Prime numbers are those numbers that have only 1 and the number itself as factors.

If a and b are prime numbers.

The greatest common divisor of a and b is 1.

The lowest common multiple of a and b is ab.

Prime numbers are those numbers that have only 1 and the number itself as factors.

2 is the only even prime number.

Examples:

2, 3, 5, 7, 11 are all prime numbers

We have,

Two natural numbers a and b.

a and b are prime numbers.

The greatest common divisor of a and b:

The prime numbers have 1 and the number itself as its factors.

So,
a x 1 = a

b x 1 = b

1 is the GCD of a and b.

The lowest common multiple of a and b:

a x b = ab

ab is the lowest common multiple of a and b.

Thus,

The greatest common divisor of a and b is 1.

The lowest common multiple of a and b is ab.

Learn more about prime numbers here:

https://brainly.com/question/13665423

#SPJ2

The GCD of two different prime numbers is 1, and the LCM is the product of the two primes.

GCD(a,b) is the Greatest Common Divisor, which is the largest positive integer that divides both numbers without a remainder. For two different prime numbers a and b, their GCD will be 1 because there are no common factors other than 1. LCM(a,b) is the Least Common Multiple, which is the smallest multiple that is divisible by both numbers. For prime numbers a and b, their LCM will be the product of the two primes.

The two division equations for 15 times 2/5 = 6 are 15÷(5/2) = 6 and

15 = (5/2)(6) + 0.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

We know, N = DQ + R.

First type,

15×(2/5) = 6.

15÷(5/2) = 6.

Second type,

N = DQ + R.

15÷(5/2) = 6.

15 = (5/2)(6) + 0.

learn more about fractions here :

https://brainly.com/question/10354322

#SPJ2

Natalia's problem involves creating a system of inequalities with limitations on width and perimeter. Possible rectangle dimensions follow this system, such as a width of 10 inches and a length of 26 inches. Dimensions that don't comply, like a width of 9 inches or a width of 10 inches with a length of 27 inches, are not feasible.

To address Natalia's rectangle problem, we need to create a system of inequalities based on her requirements for width and perimeter. Let's denote the width as w and the length as l. The inequalities should look like this:

Possible dimensions for Natalia's rectangle that satisfy these inequalities could be a width of 10 inches and a length of 26 inches. In this case, the perimeter would be 2(10) + 2(26) = 72 inches, which is the maximum allowed.

Impossible dimensions would include a width of 9 inches, as this is less than the minimum required width, or a width of 10 inches with a length of 27 inches, which would make the perimeter 2(10) + 2(27) = 74 inches, exceeding the maximum permitted perimeter.

The volume of a rectangular prism with a base area of 32 cm and a height 6 cm is  192cm³

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases.

We need to find the volume of a rectangular prism with a base area of 32 cm and a height 6 cm

Volume of rectangular prism is base area times of height

Base area = Thirty two =32 cm²

Height=6 cm

Volume of rectangular prism=32×6

=192cm³

Volume of a rectangular prism with a base area of 32 cm and a height 6 cm is 192cm³

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ2

The volume of the rectangular prism with a base area of 18 cm2 and height of 9 1/2 cm is calculated to be 171 cm3, using the formula Volume = area of base x height.

The volume of a rectangular prism is calculated by multiplying the area of the base by the height of the prism. In this case, the area of the base is given as 18 cm2, and the height is 9 1/2 cm, which can also be written as 9.5 cm for easier multiplication.

To find the volume, we use the formula: Volume = area of base * height. Substituting the known values, we get:

Volume = 18 cm2 * 9.5 cm

Volume = 171 cm3

Therefore, the volume of the rectangular prism is 171 cm3.

Given is a mixed number i.e. [tex] 7\frac{95}{125} [/tex].

We can solve it as given below :-

[tex] 7\frac{95}{125} \\\\
=\frac{(125*7)+95}{125} \\\\
=\frac{875+95}{125} \\\\
=\frac{970}{125} \\\\
=\frac{194}{25} \\\\
=7\frac{19}{25} \;\;or\;\; 7.76 [/tex]

Hence, [tex] \frac{194}{25} \;or\; 7\frac{19}{25} \;or\; 7.76 [/tex] would be better representation of given mixed number i.e. [tex] 7\frac{95}{125} [/tex].

Hope, this helps! :)

Final answer:

To find out how many weeks a 3 lb bag of cat food will last for a cat that eats 3/4 lb per week, divide the total weight of the bag by the weekly consumption. One 3 lb bag lasts for 4 weeks.

Explanation:

The question asks how many weeks a bag of cat food will last if the cat eats 3/4 lb each week and the bag is 3 lbs. To find the answer, we need to divide the total weight of the bag by the amount eaten each week.

Here's the step-by-step calculation:

Therefore, one bag of cat food will last for 4 weeks.

To expand (4−7y)(7+4y), apply the FOIL method to get the expanded form: 28 + 16y - 49y - 28y². Combine like terms to get the standard form: -28y² - 33y + 28.

To expand the given expression (4−7y)(7+4y), we need to apply the distributive property (also known as the FOIL method in this case, which stands for First, Outer, Inner, Last):

Combine the middle terms (16y and -49y) and arrange the polynomial in standard form, which is ordering terms from highest to lowest degree:

Expanded form: 28 + 16y - 49y - 28y²

Combine like terms: 28 - 33y - 28y²

Standard form: -28y² - 33y + 28