If a pizza is cut into 8 pieces and 3 children each eat one piece, what fraction of the pizza is gone

The distance that John walk more than Don is 356.60 ft.

A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.

Given that John is walking home with his younger brother and their home is on opposite corner of a rectangle lot with dimensions of 500 feet by 800 feet.

Since John is walking on the sides, the lenght covered by John will be the sum of the sides.

Sum of the sides of the rectangle = 500 ft + 800 ft

Sum of the sides of the rectangle = 1300 ft

Further, Don is walkin on the diagonal, the lenght covered by Don will be the diagonal of the rectangle.

(Diagonal)² = (500 ft)² + (800 ft)²

(Diagonal)² = 250000 ft² + 640000 ft²

Diagonal²  = 890000 ft²

Diagonal  = 943.39811 ft

The distance that John walk more than Don is:

Distance = 1300 ft - 943.39811 ft = 356.60 ft

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[tex]\\ \text{Given that the base salary of Vanessa is }\$400.00 \text{ every week}\\ \\ \text{And she gets an additional }5\% \text{ commission on everything she sells}.\\ \\ \text{Given that last week Vanessa sold }\$1650.00 \text{ worth of items,}\\ \text{so her commission last week was}\\ \\ =5\% \text{ of 1650}\\ \\ =0.05\times 1650\\ \\ =\$ 82.5\\ \\ \text{hence the total salary of Vanessa for last week}=400+82.5=\$482.5[/tex]

Hence the total salary of Vanessa last week was $482.5

Jack  saving 2.25 $ each month

We have given that monthly allowance of jack is 15$

He decides to save 15% of his monthly allowances

We have to calculate the saving of each moth.

Therefore,

we have to find the 15% in decimal form,

What is the formula for finding the percentage in decimal form:

[tex]decimal form =\frac{x}{100}[/tex]

Where x is in %

Therefore,

15%=15/100=0.15

Jack want to save 0.15 from his monthly allowance of 15$

Therefore,

15(0.15)=2.25

Therefore,

Jack  saving 2.25 $ each month.

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Final answer:

To determine the decimal value of a signed binary number in sign-magnitude form, consider the sign and magnitude separately. (a) -102 (b) +116 (c) -64.

Explanation:

To determine the decimal value of a signed binary number in sign-magnitude form, you need to consider the sign and the magnitude separately.

(a) 10011001:

This number is negative in sign-magnitude form because the leftmost bit is 1. To find its magnitude, you invert the remaining bits (01100110) and convert it to decimal (102).

The final decimal value is -102.

(b) 01110100:

This number is positive in sign-magnitude form because the leftmost bit is 0. The magnitude is obtained by converting the bits (01110100) to decimal (116).

The final decimal value is +116.

(c) 10111111:

This number is negative in sign-magnitude form because the leftmost bit is 1. The magnitude is obtained by inverting the remaining bits (01000000) and converting it to decimal (64).

The final decimal value is -64.

(a) -25, (b) 116, (c) -63; sign bit denotes sign, remaining bits represent magnitude converted to decimal.

Let's go through each signed binary number in sign-magnitude form:

(a) 10011001:

Step 1: Determine the sign bit:

The leftmost bit, or the most significant bit (MSB), is the sign bit. In sign-magnitude representation, 1 denotes a negative number and 0 denotes a positive number. So, the sign bit here is 1, indicating a negative number.

Step 2: Convert the magnitude:

To find the magnitude, we ignore the sign bit and treat the remaining bits as a magnitude in binary form. So, the magnitude here is 0011001.

Step 3: Convert the magnitude to decimal:

The magnitude 0011001 in binary is equivalent to:

(1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0) = 16 + 8 + 1 = 25

Step 4: Apply the sign:

Since the sign bit is 1, indicating a negative number, we negate the magnitude we found in step 3. Therefore, the decimal value of 10011001 in sign-magnitude form is -25.

(b) 01110100:

Step 1: Determine the sign bit:

The leftmost bit is 0, indicating a positive number.

Step 2: Convert the magnitude:

The magnitude here is 1110100.

Step 3: Convert the magnitude to decimal:

The magnitude 1110100 in binary is equivalent to:

(1 * 2^6) + (1 * 2^5) + (1 * 2^4) + (0 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0) = 64 + 32 + 16 + 4 = 116

Step 4: Apply the sign:

Since the sign bit is 0, indicating a positive number, the decimal value remains positive. Therefore, the decimal value of 01110100 in sign-magnitude form is 116.

(c) 10111111:

Step 1: Determine the sign bit:

The leftmost bit is 1, indicating a negative number.

Step 2: Convert the magnitude:

The magnitude here is 0111111.

Step 3: Convert the magnitude to decimal:

The magnitude 0111111 in binary is equivalent to:

(0 * 2^6) + (1 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (1 * 2^1) + (1 * 2^0) = 32 + 16 + 8 + 4 + 2 + 1 = 63

Step 4: Apply the sign:

Since the sign bit is 1, indicating a negative number, we negate the magnitude we found in step 3. Therefore, the decimal value of 10111111 in sign-magnitude form is -63.

So, the decimal values for each signed binary number in sign-magnitude form are:

(a) -25

(b) 116

(c) -63

Answer with Step-by-step explanation:

The volume of cylinder is given by

V=πr²h

Where r is the radius and h is the height

The volume of a cylinder is 50.265 cubic inches when the radius is 2 inches and the height is 4 inches.

50.265=π×2²×4

⇒ π=50.265/16

Now when r=3 inches and h=7 inches

V=π×3²×7

[tex]V=\dfrac{50.265}{16}\times 9\times 7\\ \\V=199.336[/tex]

Hence, volume of the cylinder when the radius is 3 inches and the height is 7 inches is:

199.336 cubic inches

The sum of the interior angle measures of an 18-gon is calculated using the formula (n-2)  imes 180 degrees, which equals 2880 degrees.

The sum of the interior angles of an n-gon (a polygon with n sides) can be found using the formula (n-2)  imes 180 degrees. For an 18-gon, we can substitute 18 for n in the formula to calculate the sum of interior angles.

Sum of interior angles = (18-2)  imes 180
Sum of interior angles = 16  imes 180
Sum of interior angles = 2880 degrees

Therefore, the sum of the interior angle measures of an 18-gon is 2880 degrees.

Answer:

1/8

4

Step-by-step explanation:

She got an A on 5/8 of all tests.

She got a perfect score on 1/5 of the 5/8.

1/5 * 5/8 = 5/40 = 1/8

She took a total of 32 tests.

1/8 * 32 = 4

Answer:

1/8

4

Explanation of why 1/12+1/12+1/12 equals 1/4 through adding fractions with common denominators.

Adding fractions:

Convert all fractions to have a common denominator.

Add the numerators together.

Keep the denominator the same.

Therefore, 1/12 + 1/12 + 1/12 = 3/12 = 1/4.

Answer:  The correct option is (C) 3 cm, 4 cm, 5 cm.

Step-by-step explanation:  We are given to select the correct side lengths that could form a triangle.

We know that

the sum of the lengths of any two sides of a triangle is always greater than the third side.

That is, if a, b and c represents the lengths of three sides of a triangle, then we must have

[tex]a+b>c,~~b+c>a,~~c+a>b.[/tex]

Option (A) is

a = 2 cm, b = 2 cm, c = 4 cm.

We have

[tex]a+b=2+2=4=c~~~\Rightarrow a+b=c.[/tex]

Hence, this option is NOT correct.

Option (B) is

a = 3 cm, b = 5 cm, c = 10 cm.

We have

[tex]a+b=3+5=8<10=c~~~\Rightarrow a+b<c.[/tex]

So, this option is NOT correct.

Option (C) is

a = 3 cm, b = 4 cm, c = 5 cm.

We have

[tex]a+b=3+4=7>5=c~~~\Rightarrow a+b>c,\\\\b+c=4+5=9>3=a~~~\Rightarrow b+c>a,\\\\c+a=5+3=8>4=b~~~\Rightarrow c+a>b.[/tex]

So, this option is CORRECT.

Option (D) is

a = 4 cm, b = 8 cm, c = 15 cm.

We have

[tex]a+b=4+8=12<15=c~~~\Rightarrow a+b<c.[/tex]

So, this option is NOT correct.

Thus, (C) is the correct option.

Answer:

Option C.

Step-by-step explanation:

To form a triangle we should always remember that a triangle is possible when sum of two smaller sides of the triangle is greater than the largest side.

If smaller sides are a, b and largest side is c

Then a + b > c

Now we take each option given

Option A) 2 cm, 2 cm, 4 cm

2 + 2 = 4 which equal to the largest side so to form a triangle is not possible.

Option B) 3 cm, 5 cm, 10 cm

3 + 5 = 8 < 10 cm

Here sum of smaller sides is less than to the largest side so triangle will not be formed.

Option C. 3 cm, 4 cm, 5 cm

3 + 4 = 7 > 5 cm

Therefore triangle can be formed.

Option D) 4 cm, 8 cm, 15 cm

4 + 8 = 12 < 15 cm

so triangle can not be formed.

Option C is the correct option.

Sasha drank a total of 51⁄2 cups of water by converting the pints to cups and then adding the half cup she drank on the way home.

To calculate the total amount of water Sasha drank, we need to add the volume of water she drank during practice and the volume she drank on the way home. However, we first need to convert the measurements so that they are in the same unit.

There are 2 cups in a pint, so 21⁄2 pints of water is equivalent to 5 cups of water (since 2 pints = 4 cups and 1/2 pint = 1 cup). Adding the additional 1/2 cup she drank on the way home gives us:

5 cups (from 21⁄2 pints)+ 1/2 cup (drank on the way home)

5 + 1/2 = 51⁄2 cups in total

Therefore, Sasha drank a total of 51⁄2 cups of water.

The estimated stopping distance when the car is traveling at [tex]71\ miles\ per\ hour[/tex] is approximately [tex]{91.84}\ feet[/tex].

To find the mathematical model that relates the stopping distance [tex]\( d \)[/tex] to the speed [tex]\( v \)[/tex], given that stopping distance is directly proportional to the square of the speed, we can write:

[tex]\[ d = k v^2 \][/tex]

where [tex]\( k \)[/tex] is the proportionality constant.

Given that the car required [tex]90\ feet[/tex] to stop when its speed was[tex]70\ miles \ per\ hour[/tex], we can use this information to find [tex]\( k \)[/tex]

Convert the speed from miles per hour to feet per second (since [tex]1 \ mile = 5280 \ feet\ and\ 1\ hour = 3600 \ seconds[/tex]):

[tex]\[ 70 \text{ mph} = 70 \times \frac{5280}{3600} \text{ fps} = 102.67 \text{ fps} \][/tex]

Now, substitute [tex]\( v = 102.67 \) fps[/tex] and [tex]\( d = 90 \) feet[/tex] into the equation:

[tex]\[ 90 = k \times (102.67)^2 \][/tex]

Calculate [tex]\( (102.67)^2 \)[/tex]

[tex]\[ (102.67)^2 = 10545.84 \][/tex]

[tex]\[ 90 = k \times 10545.84 \][/tex]

Solve for [tex]\( k \)[/tex]

[tex]\[ k = \frac{90}{10545.84} = 0.00853 \][/tex]

Now, substitute [tex]\( k \)[/tex] back into the model:

[tex]\[ d = 0.00853 v^2 \][/tex]

Estimate the Stopping Distance at [tex]71 \ miles\ per\ hour[/tex]

Convert [tex]71 \ miles\ per\ hour[/tex] to feet per second:

[tex]\[ 71 \text{ mph} = 71 \times \frac{5280}{3600} \text{ fps} = 103.87 \text{ fps} \][/tex]

Now, calculate the stopping distance [tex]\( d \)[/tex] at this speed:

[tex]\[ d = 0.00853 \times (103.87)^2 \][/tex]

[tex]\[ d = 0.00853 \times 10781.14 \][/tex]

[tex]\[ d = 91.84 \][/tex]

Its all five of them

number of successful trials/ total number of trials

Step-by-step explanation:

A catering company’s recipe for salad uses a ratio of 2 cups of dressing to 12 cups of vegetables. (a) Mrs. Roberts simplified this ratio to 2:6. Explain/show how you know she is incorrect. Can you tell where she might have made a mistake while simplifying?

Solution:

So, A catering company’s recipe for salad uses a ratio of 2 cups of dressing to 12 cups of vegetables.

Ratio of dressing:vegetables=2:12.

Let us divide 2 and 12 by 2

Ratio of dressing: vegetables= [tex] \frac{2}{2} [/tex] : [tex] \frac{12}{2} [/tex]

So, finally we get ratio=1:6 and not 2:6. The mistake is in this step while simplifying.

So, Simplified Ratio of dressing:vegetables=1:6.

Answer:B

Step-by-step explanation:

Given:Ranger Station to Nature Center = 90°Nature Center to petting zoo = 40°Petting Zoo to Tennis Court = 120°Tennis Court to Pool = 65°Pool to Ranger Station = 45°radius = 1 milearc length = 2πr angle/360°Ranger station to nature center.arc length = 2 * 3.14 * 1 mile * 90°/360°arc length = 2 * 3.14 * 1 mile * 0.25arc length = 1.57 milesNature center to Petting Zooarc length = 2 * 3.14 * 1 mile * 40°/360°arc length = 2 * 3.14 * 1 mile * 0.11arc length = 0.70 miles1.57 miles + 0.70 miles = 2.27 miles or 2.3 miles CHOICE B