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AfilCa [17]
3 years ago
11

Roberta wants to create 17 ounces of new hand lotion, with a minimum 15% concentration of beeswax, from a mixture of two lotions

. One lotion has a 21% concentration of beeswax, and the second lotion has a concentration of 5% beeswax. Based on the inequality below, how much of the 21% lotion, x, will she need? 0.21x + 0.05(17 - x) > 2.55
Mathematics
1 answer:
Zarrin [17]3 years ago
6 0

Answer:

Step-by-step explanation:

Given the inequality

0.21x + 0.05(17 - x) > 2.55 where x is the amount of 21% lotion needed

Given

0.21x + 0.05(17 - x) > 2.55

Open the parenthesis

0.21x + 0.85-0.05x > 2.55

Collect like terms

0.21x-0.05x+0.85>2.55

0.16x+0.85>2.55

0.16x>2.55-0.85

0.16x > 1.7

x > 1.7/0.16

x > 10.625

Hence she will need 21% lotion approximately greater than 10 ounces

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Graph and label the image of the figure below after a dilation by a factor of 1/2.
neonofarm [45]
Answer:

M' (1.5, -1), F' (2, -1), L' (0.5 -2.5), W' (2.5, -2.5)

see graph below

Explanation:

Given:

The image of a quadrilateral on a coordinate plane

To find:

The coordinates of the new image after dilation of 1/2 have been applied to the original image.

Then graph the coordinates

First, we need to state the coordinates of the original image:

M = (3, -2)

F = (4, -2)

L = (1, -5)

W = (5, -5)

Next, we will apply a scale factor of 1/2:

\begin{gathered} Dilation\text{ rule:} \\ (x,\text{ y\rparen}\rightarrow(kx,\text{ ky\rparen} \\ where\text{ k = scale factor} \\  \\ scale\text{ factor = 1/2} \\ M^{\prime}\text{ = \lparen}\frac{1}{2}(3),\text{ }\frac{1}{2}(-2)) \\ M^{\prime}\text{ = \lparen}\frac{3}{2},\text{ -1\rparen} \\  \\ F\text{ = \lparen}\frac{1}{2}(4),\text{ }\frac{1}{2}(-2)) \\ F^{\prime}\text{ = \lparen2, -1\rparen} \end{gathered}\begin{gathered} L\text{ = \lparen}\frac{1}{2}(1),\text{ }\frac{1}{2}(-5)) \\ L^{\prime}\text{ = \lparen}\frac{1}{2},\text{ }\frac{-5}{2}) \\  \\ W\text{ = \lparen}\frac{1}{2}(5),\text{ }\frac{1}{2}(-5)) \\ W^{\prime}\text{ = \lparen}\frac{5}{2},\text{ }\frac{-5}{2}) \end{gathered}

The new coordinates:

M' (3/2, -1), F' (2, -1), L' (1/2, -5/2), W' (5/2, -5/2)

M' (1.5, -1), F' (2, -1), L' (0.5 -2.5), W' (2.5, -2.5)

Plotting the coordinates:

3 0
10 months ago
I need help with the incorrect ones please
Morgarella [4.7K]

Answer:

73.6

61.824

.2776

2.3

1.342

.4129

*note* I had trouble reading the standard deviation of the second part, so if it's not 3 then leave a comment and i will fix it*

Step-by-step explanation:

1.)

the mean would be something like 460*.16= 73.6

The variance should be 460*.16(1-.16)= 61.824 which means the standard deviation is √61.824= 7.863

for p to be less than .15 it would have to be less than .15*460= 69

(69-73.6)/7.863= -.59 which has a probability of .2776

2.)

the mean is 2.3

I am not sure if the standard deviation is 3 or .3 (picture is kind of blurry)

I am thinking that it's three which would mean that the standard deviation would be √(3²*(1/5))= 1.342

(2-2.3)/1.342= -.22 = .4129

5 0
2 years ago
Find the value of each variables in the parallelogram
Ksju [112]

Answer:

C = 6

D = 10

Step-by-step explanation:

C + 5 = 11

C + 5 -5 = 11 -5

C = 6

D + 4 = 14

D + 4 -4 = 14 -4

D = 10

4 0
3 years ago
In a cross between two individuals who are heterozygous for two traits determined by dominant and recessive alleles (Aa Bb), wha
cricket20 [7]

Answer: A

Step-by-step explanation:

4 0
3 years ago
What is the perimeter of a rectangle with a length of 13 feet and a width of 9 feet
koban [17]
Length (l) = 13 feet
Width (b) = 9 feet

Perimeter = 2(l + b)

= 2(13 + 9)

= 2×21

= 42 feet
6 0
2 years ago
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