What is 3x = 99 - 35x + 12

If average of 3 quantities is 15 , sum of quantities is....?

Verizon [17]

Answer:

45

Step-by-step explanation:

Let the three quantities be x, y and z.

$\because \: average = \frac{sum \: of \: quantities}{no \: of \: quantities} \\ \\ \therefore \: 15 = \frac{x + y + z}{3} \\ \\ 15 \times 3 = x + y + z \\ \\ \huge \purple{ 45 = x + y + z}$

8 0

2 years ago

570 mL = ? oz,show work

Natali5045456 [20]

Conversion from milliliters to ounces can be done using the following relation: 1 mL = 0.033814 ounce.

Given 570mL, we multiply it to the amount of ounces as shown in the relation. This is done below:

570 mL * (0.033814 oz / 1 mL) = 19.274 oz

8 0

2 years ago

If a =7 inches and c = 14 inches in a right angle, then what is the measure of angle a

strojnjashka [21]

Answer:

Its 63.435

Step-by-step explanation:

https://www.calculator.net/triangle-calculator.html?vc=&vx=7&vy=&va=90&vz=14&vb=&angleunits=d&x=104&y=23

I always used this when it came to triangles

7 0

2 years ago

a media statistics agency reports that the mean number of televisions in a household in a particular country is 2.24. assume tha

KatRina [158]

The probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household is 0.48173.

Given: Mean(μ) = 2.24, Standard deviation(σ) = 1.38, Sample size(n) = 1.28 and a random variable for X = 2.55

What is a probability distribution?

A probability distribution is a kind of function for a discrete variable X, whose distribution over a certain interval is discrete or it shows the density of a random variable X that occurs over a given interval in the given distribution.

What is the z-score?

The z-score or the z-value shows the number of standard deviations unit away lies the given random variable from the mean.

Or it shows how dense is the value for a random variable near or away from the mean.

The formula to calculate the z-score from the mean. The standard deviation is:

z = (X - μ) / ( σ / √(n)) where,

z = z-score,

X = random variable,

μ = mean,

σ = standard deviation, and

n = sample size

Let's solve the given question:

We have,

Mean(μ) = 2.24,

Standard deviation(σ) = 1.38,

Sample size(n) = 1.28, and

a random variable for X = 2.55

As it is given sample means at least 2.55 so we have to find the Z(x ≥ 2.55).

Therefore, Z(x ≥ 2.55) = (2.55 - μ) / ( σ / √(n))

Substituting all values we get:

Z(x ≥ 2.55) = (2.55 - 2.24) / ( 1.38 / √(40))

Z(x ≥ 2.55) = 0.01 / 0.21819

Z(x ≥ 2.55) = 0.48173

Hence the probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household is 0.48173.

Know more about “probability distribution” here: brainly.com/question/11234923

#SPJ4

Disclaimer: The given question is incomplete. The complete question is mentioned below:

a media statistics agency reports that the mean number of televisions in a household in a particular country is 2.24 with a standard deviation of 1.38 what is the probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household?

7 0

1 year ago

The figure below shows two triangles EFG and KLM.

grandymaker [24]

A right triangle is a triangle that has a right angle of 90 degrees. In this exercise, we have two of this type of triangles. To solve this problem, we will apply some properties of triangles, so:

1. Which step can be used to prove that triangle EFG is also a right triangle?

To prove this, we need to use Pythagorean Theorem. So, for triangle EGF, if the formula:

$c^{2}=a^{2}+b^{2}$

is true, then EFG is also a right triangle. The steps are:

Square a

Square b

Square c

If the sum of the square of a and the sum of the square of b equals the square of c, then this is a right triangle.

2. Prove that the sum of a and c is greater than b.

We need to prove that:

$a+c>b$

From trigonometry, we know that:

$a=c \times sin(\theta) \\ \\ b=c \times cos(\theta) \\ \\ where \ \theta=\angle EFG \\ \\$

By substituting these values in the previous inequality:

$c \times sin(\theta)+c>c \times cos(\theta) \\ \\ Since \ c>0 \\ \\ sin(\theta)+1>cos(\theta) \\ \\ 1>cos(\theta)-sin(\theta)$

Since $\theta$ is an angle greater than 0 and less than 90 degrees, $cos(\theta) \ and \ sin(\theta)$ are numbers between 0 (greater than) and 1. Therefore, this inequality is always true. So, the statement has been proved.

3. Prove that the sum of a and b is greater than c.

We need to prove that:

$a+b>c$

Applying the same reasoning as in 2:

$c \times sin(\theta)+c \times cos(\theta)>c \\ \\ Since \ c>0 \\ \\ sin(\theta)+cos(\theta)>1$

This inequality is always true. So, the statement has been proved.

4. Prove that triangles are congruent by SSS property and hence angle EGF is equal to angle KML.

SSS means that we know the three sides of the triangle and want to find the missing angles. For ΔEGF, we know the three sides, and for KML, since this is a right triangle KL = c, therefore the corresponding sides of these two triangles are equal. Accordingly, these two triangles are congruent by SSS and angle EGF is equal to angle KML.

5. Prove that the ratio of EF and KL is greater than 1 and hence the triangles are similar by AA postulate.

The ratio of EF and KL is:

$\frac{EF}{KL}$

The statement is true if and only if EF > KL. Then, according to AA postulate, two triangles are similar if they have two corresponding angles congruent. So:

EGF is congruent to KML and equals 90 degrees
GEF is congruent to MKL
EFG is conguent to KLM

Accordingly, the triangles are similar.

3 0

2 years ago

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