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astra-53 [7]
2 years ago
5

6. What is the minimum vertical distance between the parabolas

t%20%7B%20and%20%7D%20y%3Dx-x%5E%7B2%7D%20%3F%20" id="TexFormula1" title=" y=x^{2}+1 \text { and } y=x-x^{2} ? " alt=" y=x^{2}+1 \text { and } y=x-x^{2} ? " align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Arada [10]2 years ago
5 0

Answer:

0.75.

Step-by-step explanation:

1) the required vertical distance is the distance between two vertexes.

2) according to the item 1, the coordinates of the vertexes are:

(y=x²+1): x₀=0; y₀=1;

(y=x-x²): x₀=0.5; y₀=0.25;

3) according to the item 2, the distance between 1 and 0.25 is 0.75.

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A biologist is studying the composition of birds on a lake and counts 61 ducks, 17 geese, 11 cranes, 15 swans, and 6 herons. Fro
Klio2033 [76]

Answer:

Expected counts: 55 ducks, 25 geese, 13 cranes, 11 swans, 6 heron

Observed counts:

61 ducks, 17 geese, 11 cranes, 15 swans, and 6 herons.

Step-by-step explanation:

There are 61+17+11+15+6 = 110 birds on the lake.

The expected counts are:

0.50*110 = 55 ducks

0.23*110 = 25 geese

0.12*110 = 13 cranes

0.10*110 = 11 swans

0.05*110 = 6 herons

What the biologist counted were the observed counts.

7 0
3 years ago
Miss Connor asks her class to guess her mystery number she tells him this number has two digits is a prime less than 20 and a fa
babymother [125]
You are to follow the clues. Since is is 2 digits and is prime, go through the prime numbers between 10 and 20. They are 11, 13, 17, and 19. Then you find the factors of 34 which are 1×34 2x17. That leaves only 1 possible answer: 17
7 0
4 years ago
The cone pictured has a surface area of ______ square centimeters. (Use 3.14 for π.)
Marina86 [1]
Assuming that the units are in cm
Given,

Diameter of the cone = 12 cm


Using the above, the radius of the cone can be determined, which is half the diameter of the cone

∴ Radius of the cone (r) = 12/2 = 6 cm
Height of the cone (h) = 7 cm

Using the above, slant height (s) = √(r² + h²) = √(6² + 7²) = √36 + 49 = √85 = 9.22 cm

π = 3.14

Now using the above values, we can calculate the total surface area of the cone.
Total surface area of the cone (A) = Lateral surface area of the cone (L) + Base surface area of the cone (B)

Lateral surface area of the cone (L) = π r s = 3.14 x 6 x 9.22 = 173.70 cm²
Base surface area of the cone (B) = π r² = 3.14 x 6² = 113.04 cm²

Total surface area of the cone = L + B = 173.70 + 113.04 = 286.74 cm²


6 0
3 years ago
A 600-ft tall building is represented by a 30-in. tall model.
alexdok [17]

\huge\boxed{19\ \text{inches}}

First, find the scale factor by dividing the first building's real-life height by its model height.

\frac{600}{30}=\frac{60}{3}=20

Now, we'll write an equation to find the model height of the second building.

r=20m

Here is an equation where r represents the real-life height of a building, 20 represents the scale factor, and m represents the model height of the same building.

Fill in the information we already know.

380=20m

Divide both sides by 20.

\frac{380}{20} = \frac{20m}{20}

\large{\boxed{19}}=m

So, the model height of the second building is 19 inches.

5 0
3 years ago
Ms. johnson owns a spice shop. she combines 5 pounds of dried rose hips and 1 pound of five-spice powder to make a new seasoning
Burka [1]

Given the 6 pound weight of the new seasoning having ingredients that cost $8, and $11, the amount she should charge for 1 ounce is $0.53125

<h3>Which method can be used to calculate the price of the new seasoning?</h3>

The ingredients in the new seasoning are;

5 pounds of dried rose hips + 1 pounds of five-spice powder

Cost of the ingredients are;

1 pound of dried rose hips = $8

1 pound of five-spice powder = $11

The cost of combined spice, <em>C</em>, is therefore;

C = $8 × 5 + $11 × 1 = $51

The weight of the new combined seasoning = (5 + 1) pounds = 6 pounds

Cost of 1 pound of the new seasoning is therefore;

1 \: lb =  \frac{51}{6}  = 8.5

  • 1 lb of the new seasoning = $8.5

  • 1 lb = 16 ounces

Therefore;

1 \: ounce =  \frac{8.5}{16}  = \mathbf{0.53125}

  • The amount she should charge for 1 ounce is $0.53125

Learn more about unit conversion calculation here:

brainly.com/question/4845674

#SPJ1

7 0
2 years ago
Read 2 more answers
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