A construction worker needs to move 120 ft squared (3) of dirt by using a wheelbarrow. One
wheelbarrow load holds 8 ft squared(3) of dirt and each load takes him 10 minutes to complete
. One
correct way to figure out the number of hours he would need to complete this job is

Answer:

c. 0.3974

Step-by-step explanation:

Given;

number of white balls, W = 17

number of red balls, R = 18

Total number of balls, T = 35

The number of ways the event will occur is given by

= P(2 whites) and P(2 reds)

= P(2whites) x P(2 reds)

= 17C2 x 18C2

= 136 x 153

= 20,808

The total number of possible outcome

= 35C4

= 52,360

The probability = 20,808 / 52,360

                          = 0.3974

The correct option is "C"

Probability that the sample contains two white balls and two red ones is equal to 0.3974.

So, option c. is correct.

Probability is a discipline of mathematics concerned with numerical explanations of the likelihood of an event occurring or the truth of a claim.

Number of white balls \(=\boldsymbol{17}\)

Number of red balls \(=\boldsymbol{18}\)

Total number of balls \(=\boldsymbol{35}\)

Probability that the sample contains two white balls and two red ones  

\(=\frac{\binom{17}{2}\binom{18}{2}}{\binom{35}{4}}\)

\(=\frac{\frac{17!}{15!2!}\frac{18!}{16!2!}}{\binom{35!}{31!4!}}\)

\(=\boldsymbol{0.3974}\)

So, option c. is correct.

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a) The distance of the stone above ground level at any time t is given by h(t) = 950 + 4.9t², where h(t) is measured in meters and t is measured in seconds.

b) It takes approximately 13.93 seconds for the stone to reach the ground.

c) The stone strikes the ground with a velocity of approximately 136.04 m/s.

d) It takes approximately 16.75 seconds for the stone thrown downward with a speed of 6 m/s to reach the ground.

When objects are dropped or thrown from a height, their speed and position can be determined using physics equations. In this problem, we will calculate the distance, time, and velocity of a stone dropped from a tower.

First, we need to determine the equation for the height of the stone above the ground at any given time t. We can use the formula:

h(t) = h0 + vt + 0.5at²

where h0 is the initial height, v is the initial velocity (which is zero for a dropped object), a is the acceleration due to gravity (g = 9.8 m/s^2), and t is the time since the stone was dropped.

Using the given values, we can plug in the numbers and simplify:

h(t) = 950 + 0t + 0.5(9.8)t²

h(t) = 950 + 4.9t²

To find the time it takes for the stone to reach the ground, we need to set h(t) = 0 and solve for t:

0 = 950 + 4.9t^2

t^2 = 193.88

t ≈ 13.93 seconds

To find the velocity at which the stone strikes the ground, we can use the formula:

v = v₀ + at

where v₀ is the initial velocity (which is zero for a dropped object) and a is the acceleration due to gravity (g = 9.8 m/s²). We can plug in the values for t and solve for v:

v = 0 + 9.8(13.93)

v ≈ 136.04 m/s

Finally, if the stone is thrown downward with a speed of 6 m/s, we can use the same formula for h(t) as before, but with an initial velocity of -6 m/s. We can then find the time it takes to reach the ground using the same method as before:

h(t) = 950 - 6t + 0.5(9.8)t²

0 = 950 - 6t + 4.9t²

t² - 1.22t - 193.88 = 0

t ≈ 16.75 seconds

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Rectangle volume formula: Volume = length × width × height

V = 2.75 × 1.80 × 1.40 = 6.93 meters³

1m³ = 1000 litres

6.93 × 1000 = 6930 litres

Answer:

6930 litres of water can hold when filled to the brim.

Answer: 6930 liters

2.75 * 1.80 * 1.40

6.93

6.93*1000 is 6930 liters

Brainliest pls if it is correct!

given a parabola in standard form

y

=

a

x

2

+

b

x

+

c

then the x-coordinate of the vertex can be found using

∙

x

x

vertex

=

−

b

2

a

y

=

x

2

−

6

x

+

5

is in standard form

with

a

=

1

,

b

=

−

6

,

c

=

5

⇒

x

vertex

=

−

−

6

2

=

3

substitute this value into equation for y-coordinate

y

vertex

=

3

2

−

6

(

3

)

+

5

=

−

4

⇒

vertex

=

(

3

,

−

4

)

the axis of symmetry is vertical and passes through the

vertex with equation

x

=

3

to find x-intercepts let y = 0

⇒

x

2

−

6

x

+

5

=

0

the factors of + 5 which sum to - 6 are - 1 and - 5

⇒

(

x

−

1

)

(

x

−

5

)

=

0

equate each factor to zero and solve for x

x

−

1

=

0

⇒

x

=

1

x

−

5

=

0

⇒

x

=

5

⇒

x

=

1

and

x

=

5

←

x-intercepts

graph{(y-x^2+6x-5)(y-1000x+3000)=0 [-10, 10, -5, 5]}

Answer:

Step-by-step explanation:

A because the gcf of 20 is 4 and the gcf of 4 is 4

Answer:

b

..,..............................................is my answer

Answer: \(2,412cm^{3}\)

Step-by-step explanation:

trust

The volume of the cylinder is the extension of the base area throughout its length thus the volume of the given cylinder will be 198.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

The volume of the cuboid = length × height × width.

As per the given cylinder,

The radius of the base of the cylinder = 3

Height = 7

Base area = π(radius)²

Base area = π(3)²

Base area = 9π

The volume of the cylinder = Base area × Height

Volume = 9π × 7 = 198.

Hence "The volume of the cylinder is the extension of the base area throughout its length thus the volume of the given cylinder will be 198".

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Answer:

Step-by-step explanation:

equal

Answer:

0.5054

Step-by-step explanation:

This is a question on conditional probability.

We solve using Baye's Theorem of conditional probability

From the question

The probability of having a particular disease = 0.08.

The probability of not having a particular disease = 1 - 0.08 = 0.92

The probability of testing positive for the disease is given that a person has the disease = 0.94

The probability of testing positive given that the person does not have the disease = 0.08

Given that a person tests positive for the disease, the probability that they actually have the disease is

= (0.08 × 0.94)/(0.08 × 0.94) + (0.08 × 0.92)

= 0.0752/0.0752 + 0.0736

=0.0752/ 0.1488

= 0.5053763441

≈ Approximately to 4 decimal places = 0.5054

, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: The fraction 3/9

Now we can simplify the fraction further by dividing both the numerator and denominator by 3

let p=3/9

then p=3/3 / 9/3

       p= 1/3

Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

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Answer:

3/4

Step-by-step explanation:

Convert the fractions into decimals.

5/8 = 0.625

3/4 = 0.75

0.75 is greater than 0.625.

Answer:

I believe the answer is d because it couldn't be any smaller than either box.

Answer:

D)

Step-by-step explanation:

We know, that looking from Solid #1, there is 192 M&M's. Since the width is 4 cm, and the length is 5 cm, and the height is 4 cm, we know that with a square of length and width of 7cm, and a height of 6.5, it would have a larger volume, and would hole more M&M's. Which means...

we could eliminate options A), B), and C),

Which leaves us with D).

Hope this helps...

Answer:

The compound statement is a conjunction (AND) of two expressions, (p^q) and r. The truth value of the conjunction is true only if both expressions are true. In this case, since p is true, q is true, and r is false, the expression (p^q) is true (since both p and q are true), but the conjunction of (p^q) and r is false, because one of the expressions in the conjunction is false. Therefore, the truth value of the compound statement is False.

Answer:

1. D

2. Is A $0.87 for each song

Step-by-step explanation:

12 x $0.87 = $10.44

$10.44 + $5.04 = $15.48

I hope this helped you

Answer: 0.9554

Step-by-step explanation:

Let \(\overline{X}\) be the sample mean.

Given: Mean weight\((\mu)\) of an adult is 65 kilograms with a standard deviation\((\sigma)\) of 13 kilograms.

Sample space = 92

The probability that the sample mean would be greater than 62.7 kilograms:

\(P(\overline{X}>62.7)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{62.7-65}{\dfrac{13}{\sqrt{92}}})\\\\=P(Z>-1.70)\\\\=P(Z<1.70)\ \ \ \[P(Z>-z)=P(Z<z)]\\\\=0.9554\)[ By p-value table]

Hence, the required probability= 0.9554

Answer:

  (f∘g)(1) = 2; (f∘g)'(1) = 2

  (f∘g)(2) = -2; (f∘g)'(2) = -2

Step-by-step explanation:

You want (f∘g)(x) and (f∘g)'(x) for x=1 and x=2 given the function values and derivatives in the table.

This composition means f(g(x)). The value is found by first determining the value of z = g(x), then using that to find the value of f(z).

For x=1, the value of g(1) is seen to be -2.

For x=-2, the value of f(-2) is seen to be 2.

This means f(g(1)) = 2.

For x=2, the value of g(2) is 0.

For x= 0, the value of f(0) is -2.

This means f(g(2)) = -2.

This is a little trickier, as you need to find the derivative of the composition:

  f(g(x))' = f'(g(x))·g'(x)

In the attached table, we have made a column for f'(g(x)) to help find this product.

For x=1, f'(g(1)) = f'(-2) = 1; and g'(1) = 2, so f'(g(1))g'(1) = 1·2 = 2 = (f∘g)'(1)

For x=2, f'(g(2)) = f'(0) = 2; and g'(2) = -1, so f'(g(2))g'(2) = 2(-1) = -2 = (f∘g)'(2)

Answer:

103

Step-by-step explanation:

x = 180 - 77 = 103

Answer:

103

Step-by-step explanation:

X + 77 = 180

Solve for x

x = 180-77

x = 103

A small aircraft takes off from the ground. The height of the aircraft increases by 1,000 feet for every minute that has passed since the aircraft left the ground.

Which function best represents the height of the aircraft in feet, as a function of time in minutes?

___________________________________________

f(x ) = 1000x

y= mx+b

b= 0

The slope m (feet for every minute) (y/x) (variation of y with respect to x)

Answer:

Step-by-step explanation:

As per properties mentioned above we have:

ΔABD is right triangle with ∠B - 30°, ∠A- 90°, ∠D - 60°

Side opposite to 30 is half of the length of the hypotenuse

AD is opposite to ∠B and BD is the hypotenuse, then:

and

Answer:

Step-by-step explanation:

Slope of line passing through (2, 7) and (1, -2) = (-2-7)/(1-2) = 9

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

19.

I hope this answer helped! please mark brainliest and vote 5 stars >:)

Answer:

x=4

Step-by-step explanation:

i used mathaway

3x+2 = 7x-14

The distance between each tick mark on this number line= 1/5 units

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

5 equal spaces between 0 and 1 shows,

5 equal spaces= 1 unit

1 equal space = x units

Do the cross multiplication.

5*x=1*1

5x=1

x=1/5

So, the distance between each tick mark on this number line= 1/5 units

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Answer:

1/5 is the answer