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IRISSAK [1]
3 years ago
6

Simplify sqrt 3× sqrt 27

Mathematics
2 answers:
lidiya [134]3 years ago
7 0
[√3] * [√27] = √3 * √[9*3] = √3 *3√3 = 3 * 3 = 9,
or [√3] * [√27] = √[3*27] = √[81] = 9.
sleet_krkn [62]3 years ago
4 0
√3√27

=√(3*27)

=√81

=9

As 9*9=81.

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

RULES:

√a√b=√ab

As (√a√b)²=((√a)²(√b)²)=√a√a√b√b=ab

When:

(√a√b)²=ab

√a√b=√ab
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5. The superintendent of the local school district claims that the children in her district are brighter, on average, than the g
anygoal [31]

Answer:

We conclude that children in district are brighter, on average, than the general population.

Step-by-step explanation:

We are given the following data set:

105, 109, 115, 112, 124, 115, 103, 110, 125, 99

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{1117}{10} = 111.7

Sum of squares of differences = 642.1

S.D = \sqrt{\frac{642.1}{49}} = 8.44

We are given the following in the question:  

Population mean, μ = 106

Sample mean, \bar{x} = 111.7

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 8.44

First, we design the null and the alternate hypothesis

H_{0}: \mu = 106\\H_A: \mu > 106

We use one-tailed(right) t test to perform this hypothesis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{111.7 - 106}{\frac{8.44}{\sqrt{10}} } = 2.135

Now,

t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = 1.833

Since,                  

t_{stat} > t_{critical}

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

We conclude that children in district are brighter, on average, than the general population.

4 0
3 years ago
A contractor bought 6.4 ft2 of sheet metal. He has used 2.1 ft2 so far and has $77.40 worth of
son4ous [18]

Answer:

$18

Step-by-step explanation:

Given:

6.4x - 2.1x = 77.4

Where,

x = cost of sheet metal per square foot

How much does sheet metal cost per square foot?

6.4x - 2.1x = 77.4

4.3x = 77.4

Divide both sides by 4.3

x = 77.4 / 4.3

= 18

x = $18

Sheet metal per square foot cost $18

8 0
3 years ago
Which unit is used to measure film size? pixels in cm mm
tatuchka [14]
Mm is the unit used to measure film size. It stands for millimeter.

The standard film size is 35 mm. The standard frame size of a still camera film was 24 x 36 mm.

mm is the smallest unit to measure length of an object. It is followed by cm then in and so on.

1 cm = 10 mm
1 in = 2.54 cm
1 in = 25.4 mm
3 0
3 years ago
F(x)=3x-4 and g(x) = x2 find the value of f(3)-g(2) <br><br> show all work
zheka24 [161]

Answer: 1

f(x) = 3x - 4 => f(3) = 3.3 - 4 = 9 - 4 = 5

g(x) = x² => g(2) = 2² = 4

=> f(3) - g(2) = 5 - 4 = 1

Step-by-step explanation:

3 0
3 years ago
Complete the proof given below.
allochka39001 [22]

Given that the opposite sides of a parallelogram are congruent, a diagonal

of the parallelogram forms two congruent triangles.

The correct options to complete the proof are;

  • <u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram
  • <u>Reflexive property of congruency</u>
  • <u>SSS</u>

Reasons:

The completed two column proof is presented as follows;

Statement  {}                                  Reason

1. ABCD is a parallelogram  {}       1. Given

2. \overline{AB} ≅ \overline{DC} and \overline{BC} ≅ \overline{DA}  {}      2. <u>Opposite sides of a parallelogram</u>

3. \overline{AC} ≅ \overline{CA}    {}                             3. <u>Reflexive property of congruency</u>

4. ΔABC ≅ ΔCDA     {}                   4. <u>SSS</u>

The correct options are therefore;

<u>Opposite sides of a parallelogram;</u> ABCD is a parallelogram

Reflexive property of congruency

SSS;

Reason 2. Opposite sides of a parallelogram, which is based on the

properties of a parallelogram and that ABCD is a parallelogram.

Reason 3. The reflexive property of congruency, states that a side is

congruent to itself.

Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency

postulate that states that if the three sides of one triangle are equal to the

three sides of another triangle, then the two triangles are congruent.

Learn more about parallelograms here:

brainly.com/question/4218263

brainly.com/question/21390857

8 0
2 years ago
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