Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance, adding 5 yards a day for 21 days which explicit formula models this situation

Answer:

The hose is ~70.71 ft long.

Step-by-step explanation:

We need to use Pythagorean theorem to figure this out. ( A^2 + B^2 = C^2)

So we first need to square 50 two times, since that's the length and height of the garden. This equals 5000.

Then we just need to find the root of 5000! This rounds out to about 70.71 ft.

Hope I could help! :)

The length of the hose which is ​stretched from one corner of the garden to another corner across the diagonal of it is 70.72 ft

The diagonal of the square is the distance from opposite vertices of it. There are two diagonals in a square which are equal in measure.

To find the diagonal of the square, the following formula is used.

d=a√2

Here, (a) is the length of the side of the square.

The side of a square garden is 50 ft long. One hose is stretch from one corner of the garden to another corner across the diagonal of it. Thus, the length of the diagonal is,

d=a√2

d=(50)√2

d=70.72 ft

Thus, the length of the hose which is ​stretched from one corner of the garden to another corner across the diagonal of it is 70.72 ft

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Answer:

C

Step-by-step explanation:

Answer:1.) 6/52

Step-by-step explanation:

The answer provides step-by-step solutions to a set of 10 different probability questions based on a standard deck of 52 playing cards. Each solution follows the same basic principle of dividing the number of ways the desired outcome can occur by the number of total possible outcomes.

The probability calculations, based on a 52-card deck, are as follows:

Remember that probabilities are calculated as the desired outcome divided by the total possible outcomes.

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Answer:

x= 8/3 and x= -8/3

Step-by-step explanation:

Remember the difference of two squares method

a²- b²= (a+b) (a-b)

Given;

9x²-64=0

We notice 9 and 64 are in square form thus can be written as

(3x-8) (3x+8)....................................applying the difference in squares method to simplify

Solving for x

(3x-8) (3x+8) =0

3x-8=0

3x=8

x= 8/3

or

3x+8=0

x= -8/3

Answer:

8/3 and -8/3

Step-by-step explanation:

I believe the Surface Area is 37 inches^2 and the Volume is 15 inches^2

The volume of the cylindrical aquarium to the nearest whole number is [tex]\(\boxed{26694}\)[/tex] cubic feet.

The volume [tex]V[/tex] of a cylinder can be calculated using the formula:

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

 where [tex]r[/tex] is the radius of the cylinder's base and [tex]h[/tex] is the height of the cylinder.

 Given:

- Radius [tex]\( r = 18.8 \)[/tex] feet

- Height [tex]\( h = 24 \)[/tex] feet

- [tex]\( \pi \approx 3.14[/tex]

Now, let's calculate the volume:

[tex]\[ V = 3.14 \times (18.8 \text{ feet})^2 \times 24 \text{ feet} \][/tex]

[tex]\[ V = 3.14 \times 18.8^2 \times 24 \][/tex]

[tex]\[ V = 3.14 \times 353.44 \times 24 \][/tex]

[tex]\[ V = 3.14 \times 8482.56 \][/tex]

[tex]\[ V \approx 26694.1216[/tex]

To the nearest whole number, the volume of the aquarium is approximately:

[tex]\[ V \approx 26694 \] cubic feet.[/tex]

Therefore, the volume of the cylindrical aquarium to the nearest whole number is [tex]\(\boxed{26694}\)[/tex] cubic feet.

Angles:

A=76 degrees

C=90 degrees

B=180-(90+76)=180-166

=14 degrees

Answer:

It’s c (B=14,b=3.2,c=13.4)

Step-by-step explanation:

edge

Answer:

She'll need 8143 cubic inches of foam and 1,809.6  square inches of fabric.

Step-by-step explanation:

Assuming you want to know how much foam and fabric she will need...

First the foam... so we need to determine the volume of that footstool.  The Volume of a cylinder is given by:

V = π * r² * h

So, we plug in the numbers:

V = π * 12² * 18 = π * 144 * 18

V = 2,592 π  = 8143 cubic inches.

Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.

The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool.  The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.

So the lateral surface of the cylinder is:

LS = 18 * 75.14 = 1,357.2 sq inches.

Then we need to calculate the area of the top... which is easy:

A = π * r²  = π * 12²  = 144 π = 452.4 sq inches

So, to cover the lateral side of the footstool and its top, she needs to use:

TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.

Answer:

The fabric needed = 2260.8 square inches

Step-by-step explanation:

Points to remember

Surface area of cylinder = 2πr(r + h)

It is given that,

Maria want to make a footstool in the shape of a cylinder.

radius of cylinder = 12 in and height = 18 in

To find the surface area

Here r = 12 in and h = 18 in

Surface area = 2πr( r + h)

 = 2 * 3.14 * 12 (12 + 18)

 = 2260.8 square inches

Answer:b

Step-by-step explanation:

You're answer is b. All you have to do is a measurement

Answer:

B) 1/2 (154° - 46°)

Step-by-step explanation:

Here ∠XYZ is an angle subtended by two chords from a point outside of the circle.

It is a one of the circle.

If the angle subtended by two chords from the outside point of the circle, the measure of the angle is 1/2 times difference of the major arc and minor arc.

Here Major arc = 154° and minor arc = 46°

Applying the rule, we get

m∠XYZ = [tex]\frac{1}{2} (Major arc - Minor arc)[/tex]

m∠XYZ = 1/2 (154° - 46°)

ANSWER

1 bell shape

2 to find probability when sampling

EXPLANATION

1 In a normal distribution, the mode,mean and median are equal.

As a result, the distribution is neither skewed to the right or left.

The shape of the normal distribution looks like a bell.

That is why it is also called the bell curve.

2. The area under the normal curve is 1.

The line of symmetry of the bell shaped distribution divides it into two halves with area 0.5 each.

The normal curve is therefore used to find the probabilities of a sample distributions.

Answer:

200.96 ft²

Step-by-step explanation:

The question is on surface area of a closed cylinder

Formulae= SA=2 ×pi× r² + 2×pi×r×h

Where pi=3.14

SA= 2×3.14×2² + 2×3.14×2×14

SA=25.12+175.84

SA=200.96 ft²

ANSWER

7.8cm

EXPLANATION

Given an acute angle of the right triangle to be 40°, the two sides of the triangles involve are the opposite side and the hypotenuse.

The trigonometric ratio that, involves opposite side and the hypotenuse is the sine ratio.

[tex] \sin(40 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex] \sin(40 \degree) = \frac{5}{hypotenuse} [/tex]

hypotenuse =5÷sin(40°)

hypotenuse=7.77cm

P means permutation, so using the permutation formula:

8P4 = 8! / (8-4)!

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1)

= 8 x 7 x 6 x 5

= 1680

The answer is C.

Answer:

C

Step-by-step explanation:

Its C

18/25= 21/x

18x=525

525/18 = 29.16

29.4

Answer:

92

Step-by-step explanation:

You need to divide the total number of souvenir paperweights divded by how much the box holds.

You will get 91.923 however you cant have only part of a box so you have to round up to 92.

Answer:

123

Step-by-step explanation:

In a parallelogram, both pairs of opposite angles are congruent. Also, both pairs of opposite sides are parallel, meaning there are consecutive interior angles. Consecutive interior angles equal 180, so simply subtract 57 from 180 to find your missing angles.

Find the area of the shaded figure.

40192 mm²

the area of the circle inside

= phi × r × r

= 3,14 × 40 mm × 40 mm

= 314/100 × 40 mm × 40 mm

= 5024 mm²

large circle area

= phi × r × r

= 3,14 × 120 mm × 120 mm

= 314/100 × 120 mm × 120 mm

= 45216 mm²

broad shaded

= 45216 mm² - 5024 mm²

= 40192 mm²

The area of the shaded figure is 10053.08 [tex]mm^2[/tex].

To find the area of the shaded region, we can use the following steps:

Calculate the area of the larger circle.

Calculate the area of the smaller circle.

Subtract the area of the smaller circle from the area of the larger circle.

The area of a circle is calculated by multiplying the radius squared by pi. The radius of the larger circle is 60 mm, so the area of the larger circle is:

[tex]A_l[/tex] = [tex]\pi[/tex] * [tex](60 mm)^2[/tex]

= 11309.72 [tex]mm^2[/tex]

The radius of the smaller circle is 20 mm, so the area of the smaller circle is:

[tex]A_s[/tex] = [tex]\pi[/tex] * [tex](20 mm)^2[/tex]

= 1256.64 [tex]mm^2[/tex]

The area of the shaded figure is calculated by subtracting the area of the smaller circle from the area of the larger circle:

A = [tex]A_l[/tex] - [tex]A_s[/tex]

= 11309.72 [tex]mm^2[/tex] - 1256.64 [tex]mm^2[/tex]

= 10053.08 [tex]mm^2[/tex]

Therefore, the area of the shaded figure is 10053.08 [tex]mm^2[/tex].

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Answer:

x+1, y-9

Step-by-step explanation:

Answer:

(x, y) ----> (x +1, y - 9)

Step-by-step explanation:

A square on a coordinate plane is translated 9 units down and 1 unit to the right.

Let's (x, y) is coordinate plane.

Here x represents the horizontal move and y represents the vertical move.

It is translated 9 units down and 1 unit right.

(x, y) ----> (x +1, y - 9)

Translation (x, y )---> (x+1, y-9)

Answer:

the answer would be y=2x+4

Step-by-step explanation:

The side lengths 10.5 cm, 20.8 cm, and 23.3 cm create a right scalene triangle.

Answer:

The perimeter of the equilateral triangle, P = 24 units

Step-by-step explanation:

All sides of an equilateral triangle are equal. The height of the equilateral triangle is given by :

[tex]h=\dfrac{\sqrt{3} }{2}\times a[/tex]

a is the side of triangle

If the height of an equilateral triangle is, [tex]h=4\sqrt{3}[/tex]

Equation (1) becomes,

[tex]a=\dfrac{2h}{\sqrt{3} }[/tex]

Put h in above formula. So,

[tex]a=\dfrac{2\times 4\sqrt{3}}{\sqrt{3} }[/tex]

a = 8

So, the side of triangle is 8. The sum of all sides is called perimeter of any figure. So,

[tex]P=8\times 3[/tex]

P = 24 units

So, the perimeter of the equilateral triangle is 24 units. Hence, this is the required solution.

Final answer:

To find the perimeter of the equilateral triangle with a height of 4√3, we determine the side length using the relationship between the height and side length of the triangle, and then multiply by three to get a perimeter of 24 units.

Explanation:

The height of an equilateral triangle is given as 4√3. To find the perimeter, we need to determine the length of a side of the triangle. In an equilateral triangle, the height (h) creates a right-angled triangle where the height is opposite to a 60° angle, and the half of a side of the triangle (half-base) is adjacent to it. The relationship is given by the equation h = (a√3)/2, where a is the side length of the equilateral triangle. By substituting the height with 4√3, we get:

4√3 = (a√3)/2 → a = 8

Since all sides of an equilateral triangle are equal, the perimeter is three times the side length, which means the perimeter P = 3 × 8 = 24 units.

Answer:

V=94.5 cm^3

Explanation:

Volume of a Prism: (B)H

B=Base Formula

H=Height of Prism

H=12

Triangle Base Formula: 1/2bh

b=3.5

h=4.5

Substitute Variables in formula:

V=[1/2(3.5)(4.5)](12)

Solve:

V=(7.875)(12)

V=94.5 cm^3

Answer:

Pretty sure it's 140.87 cm

Step-by-step explanation:

Multiply 3 1/2 by 4 1/4

Divide by two which is 7.43

Multiply 3 1/2 by 12

Now add 42+42+42+7.43+7.43

OR

126+14.87  

There is no solution to Kamal's equation because -24 ≠ 7

How to solve the problem

The equations are given as

i. 3(x-8)=x+2x+7

ii. 3x-24=3x+7

iii. -24=7

We have to expand the first equation

3(x-8)=x+2x+7

this would produce the second equation

3 * x - 3 * 8 = 3x + 7

we have

ii. 3x-24=3x+7

from here we have to take like terms on put them on same side

3x - 3x = 7 + 24

0 = 31

or from 3x-24=3x+7

the 3x is eliminated

-24 = 7

But we know that -24 ≠ 7. Hence no solution.

Answer:

The answer is D, 30.4

Step-by-step explanation:

Because the two parallelograms are similar, the relationship between the sides of them are directly proportional.

So:

[tex]\frac{9}{8} =\frac{x}{27}[/tex]

Cross multiply

8x = 243

÷8 both sides

x = 30.375 ≈ 30.4

The answer is D, 30.4

ANSWER

D. 30.4

EXPLANATION

The two parallelograms are similar, therefore the corresponding sides must be in the same proportion:

[tex] \frac{x}{9} = \frac{27}{8} [/tex]

Multiply both sides of the equation by 8. This implies that,

[tex]x = \frac{27}{8} \times 9[/tex]

[tex]x = 30.375[/tex]

Rounding to the nearest tenth gives us:

[tex]x = 30.4 \: units[/tex]

Answer:

1) 46.6

Step-by-step explanation:

Given Data:

s1 of Triangle ABC= 4cm

s2 of Triangle ABC=6cm

s3 of Triangle ABC=8cm

As per the side-side-side SSS of a given triangle

the corresponding angles are found by the following law of cosine formula

cos A = (b2 + c2 − a2) / 2bc

Putting the values we get

cos A= (4^2+8^2-6^2)/2(4)(8)

cos A= (16+64-36)/64

A=cos^-0.6875

A=46.57!

Answer:

84.78

Step-by-step explanation:

Final answer:

To determine the cost of silver needed for a solid sphere with a radius of 1.5 cm, the volume is calculated first, and then multiplied by the cost per cubic centimeter of silver, resulting in a total cost of $84.78.

Explanation:

The problem requires calculating the cost of the silver needed to manufacture a solid sphere. To find the cost, we first need to calculate the volume of the sphere using the formula V = (4/3)πr³, where V is the volume and r is the radius. Then, we multiply the volume by the cost per cubic centimeter of silver to get the total cost.

Given the radius r = 1.5 cm and the cost of silver = $6.00/cm³, we can plug these values into the formula:

Therefore, the silver required to make one solid sphere would cost $84.78.

Answer: the answer is 18

Step-by-step explanation:

[tex]\bf 12+9\times \cfrac{4}{2}\div (2+1)\implies \stackrel{\mathbb{P~E~M~D~A~S}}{12+9\times \cfrac{4}{2}\div (\stackrel{\downarrow }{3})}\implies 12+9\times \stackrel{\downarrow }{2}\div(3) \\\\\\ 12+\stackrel{\downarrow }{18}\div (3)\implies 12+\stackrel{\downarrow }{6}\implies 18[/tex]

Answer:

<CDH = 110°

Step-by-step explanation:

Given <1 = 70°

Because BF ║ CD so <1 = <3 = 70° (corresponding angles are equal)

<CDH = 180° - <3

<CDH = 180° - 70°

<CDH = 110°

Answer:

125

Step-by-step explanation:

We are given that <1=70. Using that, we know that <5 also equals 70 because of the definition of vertical angles, we then can find <2 also by subtracting 70 from 180 and dividing it by 2 to get 55. <4=<2 and <6=<5, so using substitution we can get m<CDH=125

Answer:

White: 2/5

Dark: 3/5

Step-by-step explanation:

There are 5 sections and there are 2 white spots and 3 dark spots.

So, 2 out of the 5 sections are white which is 2/5 and 3 out of the 5 sections is dark which is 3/5.

Answer:

Step-by-step explanation:

Given : The total number of sections = 5

The number of white sections = 2

The number of dark sections =3

Now, the probability that the spinner lands on a white section is given by :-

[tex]\text{P(white)}=\dfrac{\text{Number of white sections}}{\text{total sections}}\\\\=\dfrac{2}{5}[/tex]

Now, the probability that the spinner lands on a dark section is given by :-

[tex]\text{P(dark)}=\dfrac{\text{Number of dark sections}}{\text{total sections}}\\\\=\dfrac{3}{5}[/tex]

Answer:

System #2:

3x - y = 4---->6x - 2y = 8