Is 17,077 a prime number? Think step by step and then answer Yes or No
To determine if 17,077 is a prime number, we need to check if it is divisible by any number other than 1 and itself.
First, let's check if it is divisible by 2. Since 17,077 is an odd number (not divisible by 2), we move on to check further.
Next, we check if it is divisible by 3. To do this, we add up the individual digits in 17,077: 1 + 7 + 0 + 7 + 7 = 22. Since 22 is not divisible by 3, 17,077 is also not divisible by 3.
We can continue this process to check if it is divisible by 5, 7, 11, and so on. However, a shortcut can be taken by checking divisibility up to the square root of 17,077.
The square root of 17,077 is approximately 130.558. We can check if 17,077 is divisible by any number up to 130. Since it is not divisible by 2, 3, 5, 7, 11, or any other smaller prime numbers, we can conclude that 17,077 is a prime number.
Therefore, the answer is: Yes, 17,077 is a prime number.
Cara and Beejal make a poster for school. The poster is in the shape of a rectangle. The left side of the poster measures 7 units; the top side of the poster measures 6 units. What is the area in square units of the completed poster? (1 point)
26 square units
42 square units
48 square units
13 square units
To find the area of a rectangle, we need to multiply the length by the width.
In this case, the left side measures 7 units and the top side measures 6 units.
Therefore, the area of the poster is 7 units * 6 units = 42 square units.
So the correct answer is: 42 square units.
Ja'Miles designs a sign for a store in the shape of a triangle. His design is 7.5 square feet in area, and the triangle has a height of 2.5 feet. What is the length of the base of his sign? (1 point)
10 feet
0.6 feet
3 feet
6 feet
To find the length of the base of the triangle, we can use the formula for the area of a triangle:
Area = (base * height) / 2
Given that the area is 7.5 square feet and the height is 2.5 feet, we can rearrange the formula to solve for the base:
base = (2 * Area) / height
Substituting the values, we have:
base = (2 * 7.5) / 2.5
base = 15 / 2.5
base = 6
So, the length of the base of Ja'Miles' sign is 6 feet.
The correct answer is: 6 feet.
Ethan writes the ratio x/8 = y/16 to help him reduce the size of a two-dimensional shape 16
If the new value of y is 3 units, what will be the value of x? (1 point)
1.5 units
6 units
3/16 units
0.5 units
To solve for the value of x, we can use the given ratio x/8 = y/16.
Given that the new value of y is 3 units, we can substitute y with 3 in the equation:
x/8 = 3/16
To isolate x, we can cross-multiply:
16x = 8 * 3
16x = 24
Finally, divide both sides by 16 to solve for x:
x = 24/16
x = 1.5 units
So, the value of x is 1.5 units.
The correct answer is: 1.5 units.
Li is a professional nature photographer. She takes a photograph of a spider web and prints a copy. The original dimensions of her copy are 6 inches by 4 inches. Li decides to advertise her business by printing smaller copies of the spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of the original printed photograph? (1 point)
1 inch by 0.5 inches
1.5 inches by 1 inch
2 inches by 1 inch
12 inches by 8 inches
To find a smaller scale drawing of the original printed photograph, we need to decrease the dimensions proportionally.
The original dimensions of the photograph are 6 inches by 4 inches. To find a smaller scale, we can divide both dimensions by the same factor.
Let's try each option:
1 inch by 0.5 inches:
Dividing the original dimensions by 6, we get 1 inch by 0.67 inches.
1.5 inches by 1 inch:
Dividing the original dimensions by 4, we get 1.5 inches by 1 inch.
2 inches by 1 inch:
Dividing the original dimensions by 3, we get 2 inches by 1.33 inches.
12 inches by 8 inches:
Dividing the original dimensions by 0.5, we get 12 inches by 8 inches, which is larger than the original.
Based on these calculations, the option that represents a smaller scale drawing of the original printed photograph is:
1.5 inches by 1 inch.
So the correct answer is: 1.5 inches by 1 inch.
what is the approximate circumference of a circle with the radius of 90
To find the approximate circumference of a circle, we can use the formula:
Circumference = 2 * π * radius
Given that the radius is 90, we can substitute it into the formula:
Circumference = 2 * π * 90
Approximating π to 3.14, we have:
Circumference ≈ 2 * 3.14 * 90
Circumference ≈ 564.6
Therefore, the approximate circumference of a circle with a radius of 90 is 564.6 units.
The approximate circumference of a circle is 7,459 miles. What is the diameter rounded to the nearest hundredths place? Use 3.14 for π. (1 point)
To find the diameter of a circle, we can use the formula:
Diameter = Circumference / π
Given that the approximate circumference is 7,459 miles and using the value of π as 3.14, we can substitute these values into the formula:
Diameter = 7459 / 3.14 ≈ 2373.89
Rounded to the nearest hundredths place, the diameter is approximately 2373.89.
So the answer is: 2373.89
The radius of a circle is 98 mm. What is the area of the circle? Write your answer
hundredths place. Use 3.14 for π. (1 point)
To find the area of a circle, we can use the formula:
Area = π * (radius)^2
Given that the radius is 98 mm and using the value of π as 3.14, we can substitute these values into the formula:
Area = 3.14 * (98)^2 ≈ 30171.52
Rounded to the nearest hundredths place, the area of the circle is approximately 30171.52 square mm.
So the answer is: 30171.52 square mm.
If the area of a circle is 28.26 cm², what is the radius of the circle? (1 point)
To find the radius of a circle when its area is given, we can use the formula:
Area = π * (radius)^2
Given that the area is 28.26 cm², we can rearrange the formula to solve for the radius:
(radius)^2 = Area / π
radius = √(Area / π)
Substituting the values, we have:
radius = √(28.26 / 3.14) ≈ √9 ≈ 3
So, the radius of the circle is approximately 3 cm.
The correct answer is: 3 cm.
Complete the table by finding the circumference and area of a circle with a radius of 279 inches. Substitute 3.14 for pi. Express your answers to the hundredths place.
To find the circumference and area of a circle with a radius of 279 inches, we can use the formulas:
Circumference = 2 * π * radius
Area = π * (radius)^2
Given that the radius is 279 inches and using the value of π as 3.14, we can substitute these values into the formulas:
Circumference = 2 * 3.14 * 279 ≈ 1750.92 inches
Area = 3.14 * (279)^2 ≈ 244029.66 square inches
Rounded to the hundredths place, the circumference is approximately 1750.92 inches and the area is approximately 244029.66 square inches.
A triangular flag has a height of 15 inches and a base length of 25 inches. Magnolia makes a scale drawing of the flag in which the base length is 10 inches. What is the area of Magnolia's scale drawing? Solve the problem by computing the actual area from the scale drawing. Show your work. (4 points)
To find the area of Magnolia's scale drawing, we can use the concept of similarity. The ratio of corresponding sides in similar figures is the same.
In this case, the ratio of corresponding sides is 10 inches for the base length of the scale drawing versus 25 inches for the actual flag. This means that every dimension in the scale drawing is 10/25, or 2/5, of the actual flag's dimension.
The height of the actual flag is 15 inches. Thus, the height of the scale drawing would be (2/5) * 15 = 6 inches.
Now, we can find the area of the scale drawing using the formula for the area of a triangle:
Area = (base * height) / 2
For the scale drawing, the base length is 10 inches and the height is 6 inches. Plugging these values into the formula, we get:
Area of the scale drawing = (10 * 6) / 2 = 30 square inches
Therefore, the area of Magnolia's scale drawing is 30 square inches.
What is a two-dimensional representation of a three-dimensional figure? (1 point)
a net
a rectangle
a triangular prism
a triangle
A two-dimensional representation of a three-dimensional figure is called a net.
So, the correct answer is: a net.
Which of the following describes a valid method for calculating the surface area of a triangular prism? (1 point)
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.
The correct method for calculating the surface area of a triangular prism is:
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Find the surface area of a cube with sides measuring 11 meters. (1 point)
66 m²
132 m²
726 m²
121 m²
To find the surface area of a cube, we can use the formula:
Surface Area = 6 * (side length)^2
Given that the side length of the cube is 11 meters, we can substitute this value into the formula:
Surface Area = 6 * (11)^2
Surface Area = 6 * 121
Surface Area = 726 square meters
Therefore, the surface area of a cube with sides measuring 11 meters is 726 m².
The correct answer is: 726 m².
Cherese needs to buy some cardboard to build a box 10 inches long, 9 inches wide, and 7 inches high. If she purchases 500 square inches of cardboard, how much will b left over? (1 point)
406 in.2
54 in.2
426 in.2
446 in.2
To calculate the total surface area of the box, we need to find the area of each face and sum them up. Since a box has six faces, the formula to find the surface area is:
Surface Area = 2 * (length * width + length * height + width * height)
Given that the dimensions are 10 inches long, 9 inches wide, and 7 inches high, we can substitute these values into the formula:
Surface Area = 2 * (10 * 9 + 10 * 7 + 9 * 7)
Surface Area = 2 * (90 + 70 + 63)
Surface Area = 2 * 223
Surface Area = 446 square inches
If Cherese purchases 500 square inches of cardboard, then the amount left over would be:
Leftover = Purchased - Surface Area
Leftover = 500 - 446
Leftover = 54 square inches
Therefore, Cherese will have 54 square inches of cardboard left over.
The correct answer is: 54 in.².
A slice is made parallel to the base of a right rectangular pyramid that has four equal edges. Which shape does the cross section make? (1 point)
hexagon
triangle
square
trapezoid
When a slice is made parallel to the base of a right rectangular pyramid with four equal edges, the shape of the cross-section made will be a square.
So, the correct answer is: square.
After you break apart a rectangular pyramid, what two-dimensional shapes appear in
the net? (1 point)
square and triangle
rectangles
triangles
rectangle and triangles
After breaking apart a rectangular pyramid, the two-dimensional shapes that appear in the net will be rectangles and triangles.
So, the correct answer is: rectangle and triangles.
What is the formula to solve for the slant height of the side triangles in the rectangular pyramid?
(1 point)
O = h
= l times w
= √(l/2)² + h²
= √(w/1)² + h²