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4 years ago

7

Cory knows that 16 tablespoons are the same as 1 cup he needs to measure 3/4 cup,but all he has is a table spoon how many tables

poons would Cory use

1 answer:

Murljashka [212]4 years ago

8 0

He would need to use 12 tablespoons for 3/4 cups.

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Does consuming beer attract mosquitoes? A study done in Burkino Faso, Africa, about the spread of malaria investigated the conne

Pachacha [2.7K]

Answer:

Take u1 = average number of mosquitoes attracted after drinking beer

u2 = average number of mosquitoes attracted after drinking water

a) The null and alternative hypotheses:

H0 : u1 = u2

H1 : u1 > u2

b) i) The average number of mosquitoes per volunteer before drinking (beer group) :

$x'1 = \frac{x_1}{n} = \frac{434}{25} = 17.36$

Sample mean for mosquitoes attracted before consumption for beer group is 17.36

The average number of mosquitoes per volunteer before drinking (water group) :

$x'2 = \frac{x_2}{n} = \frac{337}{18} = 18.72$

Sample mean for mosquitoes attracted before consumption for water group is 18.72

The two means are different.

The difference in the two means are as a result of random choice.

c) i) The average number of mosquitoes per volunteer after drinking (beer group) :

$x'1 = \frac{x_1}{n} = \frac{590}{25} = 23.60$

Sample mean for mosquitoes attracted after consumption for beer group is 23.60

ii) The average number of mosquitoes per volunteer after drinking (water group) :

$x'2 = \frac{x_2}{n} = \frac{345}{18} = 19.17$

Sample mean for mosquitoes attracted after consumption for water group is 19.17

The two sample means are different.

This difference here is likely not to be as a result of random choice, because the mean difference here is greater than the mean difference before consumption.

d) A statistically significant difference provides evidence that beer consumption increases mosquito attraction, as the average number of mosquitoes attracted when drinking beer is higher than the mean number of mosquitoes attracted when drinking water.

5 0

3 years ago

Tim spent $24 at the grocery store. This was six dollars less than two times what he spent at the game store. How much did he sp

belka [17]

The answer to the question is A

3 0

4 years ago

find the equation of a circle which passes through the point (2,-2) and (3,4) and whose centre lies on the line x+y=2

Nadusha1986 [10]

Answer:

Equation of the circle

(x - 0.7)² + (y - 1.3)² = 12.58

Step-by-step explanation:

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle.

a) We are told in the question that the equation of the circle passes through point(2, -2)

Hence,

Substituting 2 for x and -2 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(2 - a)² +(-2 - b)² = r²

Expanding the bracket

(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²

4 - 2a - 2a +a² +4 +2b +2b +b² = r²

4 - 4a + a² + 4 + 4b + b² = r²

a² + b² -4a + 4b + 4 + 4 = r²

a² + b² -4a + 4b + 8 = r²............Equation 1

We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y

Hence,

Substituting 3 for x and 4 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(3 - a)² +(4 - b)² = r²

Expanding the bracket

(3 - a) (3 - a) + (4 - b)(4- b) = r²

9 - 3a - 3a +a² +16 -4b -4b +b² = r²

9 -6a + a² + 16 -8b + b² = r²

a² + b² -6a -8b + 9 + 16 = r²

a² + b² -6a -8b + 25 = r²..........Equation 2

The next step would be to subtract Equation 1 from Equation 2

a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²

a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²

Collecting like terms

a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0

2a + 12b -17 = 0

2a + 12b = 17...........Equation 3

Step 2

We are going to have to find the values of a and b in other to get our equation of the circle.

Since the center of the circle(a, b) lies on x + y = 2

Therefore, we have

a + b = 2

a = 2 - b

2a + 12b = 17 ..........Equation 3

Substituting 2 - b for a in

2(2 - b) + 12b = 17

4 - 2b + 12b = 17

4 + 10b = 17

10b = 17 - 4

10b = 13

b = 13/10

b = 1.3

Substituting 1.3 for b in

a + b = 2

a + 1.3 = 2

a = 2 - 1.3

a = 0.7

hence, a = 0.7, b = 1.3

Step 3

We have to find the value of r using points (2, -2)

(x - a)² + (y - b)² = r²

Where x = 2 and y = -2

(-2 - 0.7)² + (-2 - 1.3)² = r²

(-2.7)² + (-3.3)² = r²

1.69 + 10.89 = r²

r² = 12.58

r = √12.58 = 3.55

Step 4

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle

a = 0.7

b = 1.3

r² = 12.58

Equation of the circle =

(x - 0.7)² + (y - 1.3)² = 12.58

7 0

4 years ago

The length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensi

artcher [175]

Length of rectangle = 5 less than 2x width
Perimeter = 146 cm

<u>Equations we will use...</u>
w = width
(2w - 5) = length (l)
perimeter (p) = 2(l + w)

<u>Substitute equation for </u><u>length</u><u> into equation for </u><u>perimeter</u>
p = 2(l + w)
146 = 2((2w - 5) + w) [use distributive prop.]
146 = 4w - 10 + 2w [combine like terms]
146 = 6w -10 [solve for w]
156 = 6w
w = 26 cm

<u>Now substitute width back into the </u><u>equation</u><u> for length...</u>
l = 2w - 5
l = 2(26) - 5
l = 47

Double check to make sure values added up to 146 cm
w + w + l + l = 146
26 + 26 + 47 + 47 = 146
146 = 146

Therefore, the width is 26 cm and the length is 47 cm.

8 0

4 years ago

Divide. Simplify your answer as much as possible.

Reil [10]

Step-by-step explanation:

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4 0

3 years ago