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2 years ago

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Calculate 12 x 15 by changing the numbers into friendlier numbers as we saw in the videos. Show how you work it out – write out

your methods using the number keys on your computer here: Please write your response.

1 answer:

kondor19780726 [428]2 years ago

7 0

Answer:

The product 12 × 15 in friendlier numbers is (10 + 2) × (10 + 5) = 180

Step-by-step explanation:

The parameter given are;

To 12 × 15 by changing the numbers into friendlier numbers

The product in 12 × 15 written with friendlier numbers (or in a simplified format can be given as follows;

12 × 15 = (10 + 2) × (10 + 5)

Which gives;

(10 + 2) × (10 + 5) = 10² + 10 × 5 + 2 × 10 + 2 × 5

From which we have;

10² + 10 × 5 + 2 × 10 + 2 × 5 = 100 + 50 + 20 + 10 = 180

Therefore;

12 × 15 = 180.

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A team of dermatological researchers were studying skin cancer among 60-70 year old American men. Suppose you were a part of the

Lostsunrise [7]

Answer:

The correct answer is Option A.) The standard deviation of the distribution of sample means is less than the population standard deviation of the number of cancer spots.

Step-by-step explanation:

The standard deviation of the distribution of sample means is less than the population standard deviation of the number of cancer spots.

3 0

1 year ago

If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

kiruha [24]

Answer:

$[1,\infty)$

Step-by-step explanation:

$b(x)=\sqrt{x-4}$

$a(x)=3x+1$

Since we want to know the domain of $(b \circ a)(x)$ , let's first consider the domain of the inside function, that is, that of $a(x)=3x+1$ . Every polynomial function has domain all real numbers.

So we can plug anything for function $a$ and get a number back.

Now the other function is going to be worrisome because it has a square root. You cannot take square root of negative numbers if you are only considering real numbers which that is the case with most texts.

Let's find $(b \circ a)(x)$ and simplify now.

$(b \circ a)(x)$

$b(a(x))$

$b(3x+1)$

$\sqrt{(3x+1)-4}$

$\sqrt{3x+1-4}$

$\sqrt{3x-3}$

Now again we can only square root positive or zero numbers so we want $3x-3 \ge 0$ .

Let's solve this to find the domain of $(b \circ a)(x)$ .

$3x-3 \ge 0$

Add 3 on both sides:

$3x \ge 3$

Divide both sides by 3:

$x \ge 1$

So we want $x$ to be a number greater than or equal to 1.

The option that says this is $[1,\infty)$

-------------------------------

Give an example why option A fails:

A number in the given set is -2.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(-2)=3(-2)+1=-6+1=-5$ and $b(-5)=\sqrt{-5-4}=\sqrt{-9} \text{ which is not real}$ .

Give an example why option B fails:

A number in the given set is 0.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(0)=3(0)+1=0+1=1$ and $b(1)=\sqrt{1-4}=\sqrt{-3} \text{ which is not real}$ .

Give an example why option D fails:

While all the numbers in set D work, there are more numbers outside that range of numbers that also work.

A number not in the given set that works is 3.

$a(x)=3x+1$

$b(x)=\sqrt{x-4}$

So $a(3)=3(3)+1=9+1=10$ and $b(1)=\sqrt{10-4}=\sqrt{6} \text{ which is real}$ .

4 0

2 years ago

Read 2 more answers

Each vertical cross-section of the triangular prism shown below is an isosceles triangle.

vova2212 [387]

Answer:

Height is 3

Step-by-step explanation:

4.24 x 4.24 x 6

Right triangle base = a + b + c

a^2 + 3^2 = 4.24^2

= a^2 + 9 = 17.98

We cross out b to subtract.

a^2 = 17.98 - 9

a^2 = 8.98

We then square √a^2 = √8.98

a = 2.996

We round up a = 3

We have found the height is 3

5 0

2 years ago

QUESTION THREE (30 MARKS) 3.1 The mass of a standard loaf of white bread is, by law meant to be 700g with a population standard

kiruha [24]

Using the normal distribution and the central limit theorem, it is found that there is a 0.0284 = 2.84% probability of finding a sample mean mass of 695g or below.

----------------------------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

----------------------------------

Mean of 700g means that $\mu = 700$
Standard deviation of 21g means that $\sigma = 21$
Sample of 64, thus $n = 64$
<u>For the sampling distribution of the sample mean</u>, the standard deviation is of $s = \frac{21}{\sqrt{64}} = \frac{21}{8} = 2.625$

The probability of finding a sample mean mass of 695g or below is the p-value of Z when X = 695, thus:

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

By the Central Limit Theorem

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

$Z = \frac{695 - 700}{2.625}$

$Z = -1.905$

$Z = -1.905$ has a p-value of 0.0284.

0.0284 = 2.84% probability of finding a sample mean mass of 695g or below.

A similar problem is given at brainly.com/question/22934264

7 0

2 years ago

A multiple must be greater than or equal to the largest starting number. True or False

podryga [215]

I'll use multiples of 2 and 4 as an example:

Multiples of 2: 2, 4, 6, 8...

Multiples of 4: 4, 8, 12, 16...

The least common multiple in this case is 4. The LCM is always ≥ the largest starting number, which is 4 for this example. Therefore, the statement is true.

<em>Hope this helps! :)</em>

8 0

2 years ago