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3 years ago

6x squared plus 12x plus 13 equals 2x squared plus 4

1 answer:

6 0

$12x^2+12x+3=2x^2+4\\\\12x^2-2x^2+12x+3-4=0\\\\10x^2+12x-1=0\\\\a=10;\ b=12;\ c=-1\\\\\Delta=12^2-4\cdot10\cdot(-1)=144+40=184\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{184}=\sqrt{4\cdot46}=2\sqrt{46}\\\\x_1=\frac{-12-2\sqrt{46}}{2\cdot10}=\frac{-6-\sqrt{46}}{10};\ x_2=\frac{-12+2\sqrt{46}}{2\cdot10}=\frac{-6+\sqrt{46}}{10}$

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Specify the set of all integers that are congruent to 5 (mod 7) using (a) the roster method and (b) set-builder notation

IrinaVladis [17]

Answer:

(a) A = {... -23, -16, -9, -2, 5, 12, 19, 26, ....}

(b) $A = {x\in Z: x = 5 - 7t,\ t\in Z}$

Solution:

For two integers x and y to be congruent, we know that:

If 't' divides y - x, we say that x is congruent to y modulo t, written x ≡ y mod t.

Now,

In roster form, we include each element in the representation of the set.

In set-builder form, we use mathematical notation and properties of the elements of the set.

Now,

As per the question;

(a) To represent all the integers congruent to 5 (mod 7) by roaster method of a set A (say):

where

$x\in Z$ such that

x ≡ 5 (mod 7)

Then

A = {... -23, -16, -9, -2, 5, 12, 19, 26, ....}

(b) In set builder form,

$A = {x\in Z: x = 5 - 7t,\ t\in Z}$

4 0

3 years ago

the manager at a hotel wants to know how often do his costomers rent boats at the nearby lake.Which sampling method will give va

Korvikt [17]

Answer: ❤️Hello!❤️He asks every tenth customer who checks into the hotel. Hope this helps! ↪️ Autumn ↩️

6 0

3 years ago

Based on the figure, select all true equations

Lady bird [3.3K]

Answer:

a) no

b) true

c) true

d) no

e) true

f) true

3 0

2 years ago

A half-century ago, the mean height of women in a particular country in their 20s was 64.7 inches. Assume that the heights of

Ainat [17]

Answer:

99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.

Step-by-step explanation:

We are given that a half-century ago, the mean height of women in a particular country in their 20's was 64.7 inches. Assume that the heights of today's women in their 20's are approximately normally distributed with a standard deviation of 2.07 inches.

Also, a samples of 21 of today's women in their 20's have been taken.

Let $\bar X$ = sample mean heights

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean height of women = 64.7 inches

$\sigma$ = standard deviation = 2.07 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the sample of 21 of today's women in their 20's have mean heights of at least 65.86 inches is given by = P( $\bar X$ $\geq$ 65.86 inches)

P( $\bar X$ $\geq$ 65.86 inches) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ $\geq$ $\frac{65.86-64.7}{\frac{2.07}{\sqrt{21} } }$ ) = P(Z $\geq$ -2.57) = P(Z $\leq$ 2.57)

= 0.99492 or 99.5%

The above probability is calculated by looking at the value of x = 2.57 in the z table which has an area of 0.99492.

Therefore, 99.5% of all samples of 21 of today's women in their 20's have mean heights of at least 65.86 inches.

3 0

3 years ago

Can I someone help me answer this?

ikadub [295]

The dependent is the childrens hospital

7 0

3 years ago