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3 years ago

Which expression is equivalent to 6(3+0.05)?

Mathematics

2 answers:

Gnesinka [82]3 years ago

6 0

$\huge{\boxed{6(3)+6(0.05)}}$

The distributive property shows that you need to multiply the $6$ separately by each term in the parentheses. This means you multiply $6*3$ and $6*0.05$ , then add them together to get $6*3+6*0.05$ , or in the terms of your answer choices, $\boxed{6(3)+6(0.05)}$ .

Elan Coil [88]3 years ago

5 0

D. The answer is d because it correctly resembles the distributive property

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During a thunderstorm yesterday, 600 millimeters of rain fell in 30 minutes. What is the unit rate for millimeters per minute?

eimsori [14]

Answer:

.33

Step-by-step explanation:

7 0

2 years ago

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What is the surface area of this solid?

Anna007 [38]

Answer:

SA. = 62.8 +87.92= 150.72

Step-by-step explanation:

surface area of cone without base = pi*r*s = 3.14 * 2* 10 = 62.8

Surface area of cylinder without base = 2*pi*r*h + pi*r*r

= 2* 3.14 * 2 * 6 + 3.14*2*2

= 75.36 + 12.56 = 87.92

SA. = 62.8 +87.92= 150.72

6 0

3 years ago

Teacher raises A school system employs teachers at

Cerrena [4.2K]

By adding a constant value to every salary amount, the measures of

central tendency are increased by the amount, while the measures of

dispersion, remains the same

The correct responses are;

(a) The shape of the data remains the same

(b) The mean and median are increased by $1,000

Reasons:

The given parameters are;

Present teachers salary = Between $38,000 and $70,000

Amount of raise given to every teacher = $1,000

Required:

Effect of the raise on the following characteristics of the data

(a) Effect on the shape of distribution

The outline shape of the distribution will the same but higher by $1,000

(b) The mean of the data is given as follows;

$\overline x = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i}$

Therefore, following an increase of $1,000, we have;

$\overline x_{New} = \dfrac{\sum (f_i \cdot (x_i + 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i + f_i \cdot 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i}$

$\overline x_{New} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + 1000 = \overline x + 1000$

Therefore, the new mean, is equal to the initial mean increased by 1,000

Median;

Given that all salaries, $x_i$ , are increased by $1,000, the median salary, $x_{med}$ , is also increased by $1,000

Therefore;

The correct response is that the median is increased by $1,000

Where;

n = The number of teaches;

Given that, we have both a salary, $x_i$ , and the mean, $\overline x$ , increased by $1,000, we can write;

$\sigma_{new} =\sqrt{\dfrac{\sum \left ((x_i + 1000) -(\overline x + 1000)\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x - 1000\right )^{2} }{n}}$

$\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x - 1000\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}}$

$\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}} =\sqrt{\dfrac{\sum \left (x_i-\overline x \right )^{2} }{n}} = \sigma$

Therefore;

$\sigma_{new} = \sigma$ ; The standard deviation stays the same

Interquartile range;

The interquartile range, IQR = Q₃ - Q₁

New interquartile range, IQR $_{new}$ = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR

Therefore;

The interquartile range stays the same

Learn more here:

brainly.com/question/9995782

6 0

2 years ago

The number of measles cases increased 13.6 % to 57 cases this year, what was the number of cases prior to the increase? (Express

ELEN [110]

Answer:

The number of cases prior to the increase is 50.

Step-by-step explanation:

It is given that the number of measles cases increased by 13.6% and the number of cases after increase is 57.

We need to find the number of cases prior to the increase.

Let x be the number of cases prior to the increase.

x + 13.6% of x = 57

$x+x\times \frac{13.6}{100}=57$

$x+0.136x=57$

$1.136x=57$

Divide both the sides by 1.136.

$\frac{1.136x}{1.136}=\frac{57}{1.136}$

$x=50.176$

$x\approx 50$

Therefore the number of cases prior to the increase is 50.

7 0

3 years ago

Which is greater: 25% of 15 or 15% of 25? Explain your reasoning using algerbreaic representations or visual models

Bingel [31]

25% of 15 is the same as 15% of 25
25%=25/100
25% of 15=(25/100)15=(25*15)/100

15%=15/100
15% of 25=(15/100)25=(25*15)/100

Therefore:
25% of 15=15% of 25
because:
(25/100)15=(15/100)25
(25*15)/100=(25*15)/100
3.75=3.75

5 0

3 years ago