QUADRATIC FORMULA
11. The current World Record for the Track event Shot Put is 23.37 meters - meaning the Shot landed
23.37 meters from where it was launched (DO NOT USE THIS VALUE FOR THE EQUATION).
The path of the Shot thrown by an athlete during a track meet can be modeled by the Quadratic Equation
h(t) = -0.09c2 + 2t + 1.67 where he represents its height in meters and m represents the horizontal
distance in meters. How far did the Shot land from where it was thrown? Substitute 0 for h in your Equation
in order to find the horizontal distance from where this Shot was lauchedlaunched.

Answer:

expected loss of 4/30 ≈ 0.13 dollars

Step-by-step explanation:

profit  = revenue - expenses

expected profit= expected revenue - expected expenses

how i solve this is by multiplying each revenue and expense by its probability and solving from there

revenue of gold = 5

revenue of silver = 2

revenue of black = 0

this exhausts all of our revenue options

total marbles = 2+8+20 = 30

# of gold marbles = 2

probability of gold = 2/30

# of silver marbles = 8

probability of silver = 8/30

# of black marbles = 20

probability of black = 20/30

expected revenue = sum of possible revenues multiplied by their probability

= 5 * 2/30 + 2 * 8/30 + 0 * 20/30 = 10/30 + 16/30 = 26/30

cost = 1 no matter what

expected profit = expected revenue - expected expenses

= 26/30 - 1

= -4/30

= an expected loss of 4/30

4/30 ≈ 0.13

3 number of cups will be needed to marinade 4 pounds of chicken for grill.

Ounce is the small unit of weight which is generally equal to the one by 16th of the pounds.

Here we have the data from the question:-

Marcy will use 6 fluid ounces of lemon-garlic marinade for every pound of chicken.

Marcy plans to grill 4 pounds of chicken.

So total marination required will be:-

Total marination =6x4=24 ounces

Now we know that the conversion:-

1 fluid Ounce = 0.125 Cup

24 fluid ounce =0.125 Cup

Hence 3 number of cups will be needed to marinade 4 pounds of chicken for grill.

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Answer: Each person gets £978

Step-by-step explanation: £6846 divided by 7 is £978

Answer:

23.80$

Step-by-step explanation:

[tex]\frac{20}{x} =\frac{100percent}{19percent}[/tex]

X = (20 × 19) ÷ 100

X =380 ÷ 100

X = 3.8$

20.00+ 3.8=

23.80

Answer:

5 lbs cereal squares.

25 Ibs nuts.

Step-by-step explanation:

Let x be the weight of nuts in pounds and y be the weight of cereal squares in pounds.

Total weight of the party mix is 30 pounds.

[tex]x+y=30[/tex]              ..... (1)

It is given that,

Cost of nuts = $7 per pound

Cost of cereal = $4 per pound

The cost of mix = $6.50 per pound.

[tex]7x+4y=6.50*30[/tex]    

[tex]7x+4y=195[/tex]           ..... (2)

Substitute the value of x in equation (2) from equation (1).

[tex]7(30-y)+4y=195[/tex]

[tex]210-7y+4y=195[/tex]

[tex]-3y=195-210[/tex]

[tex]-3y=-15[/tex]

Divide both sides by -3.

[tex]y=5[/tex]

Substitute y=5 in equation (1).

[tex]x+5=30[/tex]

Subtract both sides by 5.

[tex]x=30-5[/tex]

[tex]x=25[/tex]

Therefore, he use 25 lbs of nuts and 5 lbs cereal squares for party mix.

The volume of a standard NBA basketball is 7,329 cm³.

The volume of a sphere is given by the formula,

V = 4/3×π×r³

Given the diameter of the ball is 24.1 cm, therefore, the radius of the ball will be 12.05cm (half the diameter of the ball). Thus, the volume of the NBA basketball will be,

V = 4/3 × π × (12.05)³

V = 7,329.084 cm³ ≈ 7,329 cm³

Hence, the volume of a standard NBA basketball is 7,329 cm³.

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Answer:

A =24.7° ; B = 40.6° ; C =114.7°

Step-by-step explanation:

Answer:

234

Step-by-step explanation:

Answer:

45 units^2

Step-by-step explanation:

W x H = area

9  x  5 = 45 units^2

Answer:

28 units

Step-by-step explanation:

Length (l) = 9 units

Breadth (b) = 5 units

Perimeter of the rectangle will be,

→ 2(l + b)

→ 2(9 + 5)

→ 2 × 14

→ 28 units

Hence, the perimeter is 28 units.

Answer:

169/8

Step-by-step explanation:

9 7/8 = 79 / 8

11 2/8 = 90 / 8

90/8 + 79/8

The denominator (8) stays the same

90+79 = 169

169/8 or 21 1/8

Answer:

1

Step-by-step explanation:

The 2 equations have different slopes, so they have 1 solution.

Answer:

y= -x-5

Step-by-step explanation:

m=1-(-5)/-4-2

m=-1

-1= -x

y=-x-5

If point B (3, -1) has been translated from A by the Vector (4, 3). Then the coordinates of A will be (12, -3)

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Point B (3, -1) has been translated from A by the Vector (4, 3).

Then the coordinates of A will be

Point B (3, -1) x  (4, 3)

Point B (3 x 4, -1 x 3)

Point B (12, -3)

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Answer:

If the number on the other side of the inequality sign is negative

Step-by-step explanation:

I just know okay

Answer:

2/3

Explanation:

total people: 4 + 2 = 6 people

carpenters: 4 carpenters

probability = 4/6 ≈ 2/3

Answer:

P (carpenter) = 2/3 or 0.67

Step-by-step explanation:

Probabilty of seeing a Carpenter first

⇒ P (carpenter) = 4/6

⇒ P (carpenter) = 2/3 = 0.67

Answer:

Step-by-Step explanation:

Given:

Volume of Rectangular Prism is 15,000cm³.

We know that,

★ Volume of Rectangular Prism = whl ★

Let "h" be the height.

➛ 25 × h × 20 = 15,000

➛ h × 20 × 25 = 15,000

➛ h × 500 = 15,000

➛ h = 15,000 ÷ 500

➛ h = 30

Thus, height of the box is 30 cm.

Answer:

A≈113.1km²

Step-by-step explanation:

Answer:432 whats the other option 4300

Step-by-step explanation:

Answer:

x=2.4

Step-by-step explanation:

3x +4/5=8​

3x = 8 -4/5

3x =7.2

x = 7.2/3

x=2.4

Step-by-step explanation:

You can just divide 10 by 2/5 and you get 25 or try this

Set up proportions and cross multiply 2/5 / 1  =  10/x which you can read as : if 2/5 can be done in 1 hour then 10 tons can be done in x hours cross multiplying, you get 2x/5 = 10  and x = 25

The first term is 3 and the common difference is negative 3. Then the sum of the first 20 terms will be negative 510.

A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.

The first term (a₁) = 3 and the common difference (d) = -3. Then the sum of the first 20 terms will be

Sₓ = (x/2) [2a₁ + (x - 1)d]

Then we have

S₂₀ = (20/2) [2 × 3 + (20 - 1)-3]

S₂₀ = 10 [6 + (19)(-3)]

S₂₀ = 10 [6 - 57]

S₂₀ = 10 [51]

S₂₀ = -510

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Answer:

12 students

Step-by-step explanation:

Because the total is 4 sticks, and each student needs 1/3 of a stick, we would have to see how many 1/3 sticks fit into 4 sticks. Because 3 of the 1/3 sticks fit into 1 stick, then 4 sticks would be 4*3=12 of the 1/3 sticks, which means 12 students can do it.

We could also just do: 4/(1/3)= 4*(3/1)=12

This is fractional division. The second value of the division process, we switch the numerator and denominator's, and the expression turns to a multiplication expression, where we can just multiply.

Answer:

slope= x2- x1/y2 -y1

= 5-(-3)/6-4

8/2= 4

[tex]1 \: 3 \: 3 \: 6 \: 6 \: 5 \: 4 \: 3 \: 1 \: 1 \: 2[/tex]

the mode and median of the given numbers set.

the most frequently occurred number.

[tex]mode = 1 \: and \: 3[/tex]

first arrange all the numbers in either decending or ascending order, then find the number in the middle.

[tex]1 \: 1 \: 1 \: 2 \: 3 \: 3 \: 3 \: 4 \: 5 \: 6 \: 6[/tex]

[tex]median = 3[/tex]

hence, the median of the following data set is 3 and the mode is 1 and 3

Answer:

37.7 ft

Step-by-step explanation:

This is Pythagorean Theorem aka A^2+B^2=C^2

20^2+32^2=C^2

400+1024=C^2

1424=C^2 (now square root both sides)

37.7359…

Closest answer is 37.7 ft

Answer: [tex]37.7ft[/tex]

Step-by-step explanation:

[tex]a=32, b=20[/tex]

[tex]look[/tex] [tex]for~ the ~hypotenuse~ c[/tex]

[tex]a^2+b^2=c^2[/tex]

[tex]\sqrt{32^2+20^2} =37.7ft[/tex]

Answer:

14.4

Step-by-step explanation:

6^2+12^2=x^2

64+144+x^2

208=x^2

square root of 208= 14.4

x=14.4

[tex]y = ab^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=14 \end{cases}\implies 14~~ = ~~ab^0\implies 14=a(1)\implies 14=a~\hfill \underline{y=14b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=4802 \end{cases}\implies 4802~~ = ~~14b^3\implies \cfrac{4802}{14}=b^3 \\\\\\ 343=b^3\implies \sqrt[3]{343}=b\implies 7=b~\hfill \underline{y=14(7)^x}[/tex]

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{4\sqrt{2}}\\ a=\stackrel{adjacent}{s}\\ b=\stackrel{opposite}{s}\\ \end{cases}\implies (4\sqrt{2})^2~~ = ~~s^2~~ + ~~s^2 \\\\\\ 4^2\sqrt{2^2}~~ = ~~2s^2\implies 16(2)=2s^2\implies 32=2s^2\implies \cfrac{32}{2}=s^2 \\\\\\ 16=s^2\implies \sqrt{16}=s\implies \boxed{4=s}[/tex]