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3 years ago

The square root of 5 less than twice a number is 7. Find the number.

Mathematics

1 answer:

densk [106]3 years ago

3 0

Answer:

4.618

Step-by-step explanation:

Let's use x to represent the number so we can write an equation to solve it.

'twice the number' is represented by 2x so we have our equation:

2x-5^0.5=7

(5^0.5 is just square root 5 because I can't do a square root symbol.)

Now we need to isolate the x term so:

2x-5^0.5+5^0.5=7+5^0.5

2x=7+5^0.5

Square root 5 = 2.236 (3dp)

2x=7+2.236

2x=9.236

2x/2=9.236/2

x=4.618

Hope this helped!

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Two times a number is equal to six less than three times the number

Mekhanik [1.2K]

2 times a number, x, is equal to 6 less than 3 times the number, x.

2x = 3x - 6
-1x = -6
x = 6

The number is 6.

8 0

3 years ago

(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the prop

zalisa [80]

Answer:

(a) The sample sizes are 6787.

(b) The sample sizes are 6666.

Step-by-step explanation:

(a)

The information provided is:

Confidence level = 98%

MOE = 0.02

n₁ = n₂ = n

$\hat p_{1} = \hat p_{2} = \hat p = 0.50\ (\text{Assume})$

Compute the sample sizes as follows:

$MOE=z_{\alpha/2}\times\sqrt{\frac{2\times\hat p(1-\hat p)}{n}$

$n=\frac{2\times\hat p(1-\hat p)\times (z_{\alpha/2})^{2}}{MOE^{2}}$

$=\frac{2\times0.50(1-0.50)\times (2.33)^{2}}{0.02^{2}}\\\\=6786.125\\\\\approx 6787$

Thus, the sample sizes are 6787.

(b)

Now it is provided that:

$\hat p_{1}=0.45\\\hat p_{2}=0.58$

Compute the sample size as follows:

$MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}$

$n=\frac{(z_{\alpha/2})^{2}\times [\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})]}{MOE^{2}}$

$=\frac{2.33^{2}\times [0.45(1-0.45)+0.58(1-0.58)]}{0.02^{2}}\\\\=6665.331975\\\\\approx 6666$

Thus, the sample sizes are 6666.

7 0

2 years ago

A distance travaled by train in three hours with a constant speed of r miles per hour

True [87]

The distance travelled by the train with constant speed of r miles will be 3r.

<h3><u>What is Speed?</u></h3>

The most crucial scientific notion is measurement. Base or physical fundamental units are used to quantify a wide range of quantifiable quantities.
One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance. Let's explore speed in-depth in this session.
The pace at which an object's location changes in any direction. When an object travels the same distance in the same amount of time, it is said to be moving at a uniform speed.
When an object travels a different distance at regular intervals, it is said to have variable speed.

We know the formula of distance linking the speed and the time.

Distance = speed × time

Substituting the given values to get:

Distance = r × 3

Distance = 3r

Know more about Speed with the help of the given link:

brainly.com/question/6280317

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2 years ago

What is the lowest term of 110/33

andrew11 [14]