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3 years ago

Juanita says that 3.5[4d - (2) (1.5)] and 2[7d - (5)(1.05)] are equivalent. Is Juanita correct? Explain your reasoning.

Mathematics

1 answer:

valkas [14]3 years ago

8 0

Answer:

Yes

Step-by-step explanation:

3.5 [4d - 2*1.5] = 3.5*4d - 3.5*2*1.5

= 14d - 10.5

2*[7d - 5*1.05] = 2*7d - 2*5*1.05

= 14d - 10.5

When we are simplifying both the expression using distributive property, we get the same expression at the end.

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Four expressions are shown:

Oksana_A [137]

The answer is 12x+4 and 2(6x+2)

Hope it helps.

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3 years ago

Read 2 more answers

Duck #1 lays eggs whose weights are normally distributed with a mean of 70gramsand a standard deviation of 6 grams.Duck #2 lays

Genrish500 [490]

Answer:

26.11% probability that Duck #2’s egg weighs more than Duck #1’s egg

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If an egg is randomly chosen from each duck, what is the probability that Duck #2’s egg weighs more than Duck #1’s egg?

Duck #2 egg will weigh more if the subtraction of duck's 2 egg by duck's 1 egg is larger than 0.

When we subtract normal distributions, the mean is the subtraction of the means. So

$\mu = 65 - 70 = -5$

The standard deviation is the square root of the sum of the variances. So

$\sigma = \sqrt{6^2+5^2} = \sqrt{61} = 7.81$

Now, we have to find 1 subtracted by the pvalue of Z when X = 0. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0 - (-5)}{7.81}$

$Z = 0.64$

$Z = 0.64$ has a pvalue of 0.7389

1 - 0.7389 = 0.2611

26.11% probability that Duck #2’s egg weighs more than Duck #1’s egg

4 0

3 years ago

Emma is making a recipe that needs 2 1/2 cups of sugar. Each

IrinaVladis [17]

The given partial fraction divided by the fraction of sugar in a scoop is

equal to multiplying the partial fraction by the reciprocal of the fraction.

The number of scoops of sugar needed is <u>10 scoops</u>.

Reasons:

The amount of sugar the recipe Emma is making needs = 2 1/2 cups

Amount of sugar in each scoop of sugar = 1/4 cups

Required:

The amount of scoops Emma needs to add for the entire recipe

Solution:

The amount of sugar needed = 2 1/2 cups

Amount of sugar per scoop = 1/4 cups/scoop

Therefore;

$\displaystyle Number \ of \ scoops = \mathbf{\frac{Cups \ of \ sugar \ needed}{Cups \ of \ of \ sugar \ per \ scoop}}$

Which gives;

$\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}}$

$\displaystyle 2 \frac{1}{2} = \frac{5}{2}$

$\displaystyle \frac{ \frac{5}{2}}{\frac{1}{4} } = \mathbf{ \frac{5}{2} \times \frac{4}{1} = \frac{20}{2 }} = 10$

Therefore;

$\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}} = 10 \, scoops$

The number of scoops she needs for the entire recipe is <u>10 scoops</u>

Learn more about division by fractions here:

brainly.com/question/20591763

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2 years ago

How is the graph of y = (x + 1)^2- 5 transformed from the graph of y=x^2?

Ainat [17]

$\text{Hi there! :D}$

$\boxed{\text{There is a horizontal shift of 1 unit left and 5 units down.}}$

$\text{Recall that the transformations form of a quadratic function is:}\\\\y = \pm a(b(x-h))+k \text{ where:}\\\\a = \text{ vertical stretch/compression}\\\\b = \text{ horizontal stretch/compression}\\\\h = \text{ shift left/right}\\\\k = \text{ shift up/down}\\\\\text{Therefore, in this instance:}\\\\h = -1\\\\k = -5, \text{ so:}\\\\\text{There is a horizontal shift of 1 unit left and 5 units down.}$

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3 years ago

What is the are and perimeter of these 4 problems

Allisa [31]

Answer:

1.A:32 P:24

2.A:40 P:26

Step-by-step e1.xplanation:

2. its the same as a rectangle if you cut it you can turn it into a rectangle

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3 years ago