Identify all the real roots of 4x^4+31x^3-4x^2-89x+22=0

Lan wants to run less than 7/12 miles. It says to find out a fraction with a denominator of 4 and which is less than 7/12.

Let's assume the required fraction to be x/4 such that x/4 is less than 7/12.

[tex] \frac{x}{4} < \frac{7}{12} \\\\
3*\frac{x}{4} < \frac{7}{12}*3 \\\\
\frac{3x}{4} < \frac{21}{12} \\\\
\frac{3x}{4} < \frac{7}{4} \\\\
3x < 7 [/tex]

So we must have multiples of 3's that should be less than 7, we have only two choices 3 < 7 or 6 < 7.

It means x = 1 or x = 2, and the required fraction would be 1/4 or 2/4.

2/4 is simplified to 1/2 and the question says to have denominator 4.

Hence, final answer is 1/4

Answer:

[tex]y=\frac{3}{2}x+10[/tex]

Step-by-step explanation:

Given equation of line : [tex]2x + 3y = -5[/tex]

Standard form of equation of line = [tex]y=mx+c[/tex]  ---A

Where m is the slope

Convert the given equation in standard form

[tex]2x + 3y = -5[/tex]

[tex] 3y = -5-2x[/tex]

[tex] y =\frac{-5}{3}-\frac{2}{3}x[/tex]

So, slope =[tex]m = -\frac{2}{3}[/tex]

If the two lines are perpendicular then the product of their slopes is -1

Let n be the slope of required equation of line

So, [tex]m \times n = -1[/tex]

[tex]-\frac{2}{3}\times n = -1[/tex]

[tex]n=\frac{3}{2}[/tex]

Substitute this value in A

[tex]y=\frac{3}{2}x+c[/tex]  --B

Now we are given that the required perpendicular line passes through the point (–6, 1)

So, substitute  (–6, 1)  in B

[tex]1=\frac{3}{2}(-6)+c[/tex]  

[tex]1-(\frac{3}{2}(-6))=c[/tex]  

[tex]10=c[/tex]  

Substitute the value of c in B

[tex]y=\frac{3}{2}x+10[/tex]

Hence the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5? is  [tex]y=\frac{3}{2}x+10[/tex]

Final answer:

The probability of a pregnancy lasting 309 days or longer is approximately 0.32%. Pregnancies shorter than 266 days are considered premature, which is determined based on the lowest 44% criterion.

Explanation:

The questions deal with calculating probabilities and determining specific values based on a normal distribution of pregnancy lengths, with a mean of 268 days and a standard deviation of 15 days.

a. Find the probability of a pregnancy lasting 309 days or longer.

To find this probability, we first calculate the z-score for 309 days:
Z = (X - μ) / σ = (309 - 268) / 15 ≈ 2.73.

Looking up the z-score of 2.73 in a standard normal distribution table or using a calculator with normal distribution functions, we find the area to the right is approximately 0.0032. This represents the probability of a pregnancy lasting 309 days or longer, which is 0.32%.

b. Find the length that separates premature babies from those who are not premature.

To determine the length of pregnancy that separates the lowest 44% (premature babies), we look for the z-score corresponding to the 44th percentile in a standard normal distribution table, which is approximately -0.15.

Then, we use the formula to find the specific value: X = μ + Zσ = 268 + (-0.15)(15) ≈ 266 days. Therefore, pregnancies shorter than 266 days are considered premature in this context.

Final answer:

To calculate the number of employees at V&B Bank Company between the ages of 20 and 30 out of the total 13,220 employees, we multiply 13,220 by the ratio of 7/20, yielding 4,627 employees in that age range.

Explanation:

The question asks how many employees at V&B Bank Company are between the ages of 20 and 30, given that 7 out of every 20 employees are in that age bracket and that the total number of employees is 13,220.

First, find the fraction of employees that are between the ages of 20 and 30 by dividing 7 by 20.

Fraction of employees aged 20-30 = 7 / 20

Next, calculate the number of employees in that age bracket by multiplying the total number of employees (13,220) by the fraction calculated above.

Number of employees aged 20-30 = 13,220 * (7 / 20)

By performing that multiplication:

Number of employees aged 20-30 = 13,220 * 0.35

Number of employees aged 20-30 = 4,627

Therefore, there are 4,627 employees at V&B Bank Company who are between the ages of 20 and 30.

WEBCASTING

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if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that the spherical water tank holds 12,500 ft³of water

We need to find the volume of the spherical water tank.

We know that volume of sphere=4/3πr³

Volume of sphere is 12,500  ft³

12500=4/3×3.14r³

12500=4.186r³

Divide both sides by 4.186

12500/4.186=r³

2986.144=r³

Take cube root on both sides

∛2986.144=r

14.40=r

We know diameter=2r

Diameter=2×14.4

=28.8=29

Hence, if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.

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Answer with Step-by-step explanation:

We are given that

Angle 2 and angle 5 are supplementary.

We have to prove that l is parallel to m.

Step 1:[tex]\angle 2+\angle 5=180^{\circ}[/tex]

Reason:By definition of supplementary angles.]

Step 2:[tex]\angle 2\cong \angle 3[/tex]

Reason:Vertical angle theorem.

Step 3:[tex]\angle 3+\angl 5=180^{\circ}[/tex]

Reason : substitute property

Step 4:angle 3 and angle 5 are  supplementary.

Reason: By definition of supplementary angles.

Step 5: [tex]l\parallel m[/tex]

Reason:Converse of same side  interior angles theorem.

We are given a figure with composite triangles.

We need to find a congruent triangle to triangle ADB.

Two figures are congruent if their corresponding sides and angles are congruent.

We can see

AB congruent to AB

AD congruent to BC and

AC congruent to BD.

Here are the calculations to find the percentages:

1. [tex]15\text{m}$ is what percent of $60\text{m}?[/tex]

[tex]\frac{15\text{m}}{60\text{m}} \times 100\% = \frac{1}{4} \times 100\% = 25\%[/tex]

2. [tex]15\text{m}$ is what percent of $3\text{m}?[/tex]

[tex]\frac{15\text{m}}{3\text{m}} \times 100\% = 5 \times 100\% = 500\%[/tex]

3. [tex]15\text{m}$ is what percent of $30\text{m}?[/tex]

[tex]\frac{15\text{m}}{30\text{m}} \times 100\% = \frac{1}{2} \times 100\% = 50\%[/tex]

4. [tex]15\text{m}$ is what percent of $1.5\text{km}?[/tex]

[tex]1.5\text{km} = 1500\text{m}[/tex]

[tex]\frac{15\text{m}}{1500\text{m}} \times 100\% = \frac{1}{100} \times 100\% = 1\%[/tex]

Therefore, the percentages are:

1. [tex]15\text{m}$ is $25\%$ of $60\text{m}[/tex]

2.[tex]15\text{m}$ is $500\%$ of $3\text{m}[/tex]

3. [tex]15\text{m}$ is $50\%$ of $30\text{m}[/tex]

4. [tex]15\text{m}$ is $1\%$ of $1.5\text{km}[/tex]

Answer:

Third option 30° 28' 10"

Brainlist?

Step-by-step explanation:

m∠ROT, formed by adjacent angles m∠ROS (20° 15' 40") and m∠SOT (10° 12' 30"), measures 30° 28' 10" according to the Angle Addition Postulate.

Attached diagram.

To find the measure of angle ROT (m∠ROT), you can use the Angle Addition Postulate.

The Angle Addition Postulate states that the measure of an angle formed by two adjacent angles is equal to the sum of the measures of those two angles.

Here m∠ROS and m∠SOT as adjacent angles forming m∠ROT.

m∠ROS = 20 degrees 15 minutes 40 seconds

m∠SOT = 10 degrees 12 minutes 30 seconds

To find m∠ROT, add the measures of m∠ROS and m∠SOT:

m∠ROT = m∠ROS + m∠SOT

First, add the degrees, then the minutes, and finally the seconds separately:

Degrees: 20 degrees + 10 degrees = 30 degrees

Minutes: 15 minutes + 12 minutes = 27 minutes

Seconds: 40 seconds + 30 seconds = 70 seconds

Now, simplify the seconds by converting any excess seconds into minutes:

70 seconds = 1 minute and 10 seconds

Now, add the minutes to the total:

27 minutes + 1 minute = 28 minutes

So, m∠ROT is:

30 degrees 28 minutes 10 seconds

Therefore, the measure of the angle m∠ROT = 30 degrees 28 minutes 10 seconds.

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The above question is incomplete, the complete question is:

Use the following diagram to complete the required information. m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30"

m∠ROT =

30 ° 27' 10"

31 ° 28' 10"

30 ° 28' 10"

Attached diagram.

Answer:

-4.5

Step-by-step explanation:

Solution:

We have been asked to find the sum of the given geometric series.

The given Arithmetic series is

[tex] 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5) [/tex]

As we know the sum of the Arithmetic series is given by

[tex] S_n=\frac{n}{2}[2a+(n-1)d] \\
\\
\text{where a= first term, n=Total number of terms , d=Common diffrence}\\
\\
\text{Here we have}\\
\\
a=7.6, d=-1.3, n=8\\
\\
\text{Substitute the values in the above formula we get}\\
\\
S_8=\frac{8}{2}[2*7.6+(8-1)(-1.3)] \\
\\
S_8=4[15.2-9.1]\\
[/tex]

[tex] \\
S_8=4*6.1=24.4\\ [/tex]

Hence Required Sum=24.4

The sum of the finite arithmetic series

7.6 + 6.3 + 5 + 3.7 + 2.4 + 1.1 + (-0.2) + (-1.5) is 24.4.

We have,

To find the sum of a finite arithmetic series, you can use the formula:

Sum = (n/2) * (first term + last term)

In this case,

The first term is 7.6 and the last term is -1.5.

The common difference between terms is -1.3.

Sum = (8/2) * (7.6 + (-1.5))

= 4 * 6.1

= 24.4

Therefore,

The sum of the finite arithmetic series

7.6 + 6.3 + 5 + 3.7 + 2.4 + 1.1 + (-0.2) + (-1.5) is 24.4.

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Answer: Option B

x = 10

Step-by-step explanation:

just did it on edge