The width of a rectangle is 7 inches. Its length is 10 inches. What is the ratio of its width to its length?\

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

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.

Final answer:

The slope of the line perpendicular to the line 4x + 2y = 12 is the negative reciprocal of the original line's slope, which in this case is 0.5 or 1/2.

Explanation:

The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. To find the slope of the line perpendicular to the line 4x + 2y = 12, we first need to rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.

First, we solve for y:

4x + 2y = 12

2y = -4x + 12

y = -2x + 6

From the equation y = -2x + 6, we can see that the slope (m) is -2. The slope of the perpendicular line will be the negative reciprocal of -2, which is ½ or 0.5. Therefore, the slope of the line perpendicular to the line 4x + 2y = 12 is ½.

Answer:

-4.5

Step-by-step explanation:

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.

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.

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]

Step [tex]1[/tex]

Find the volume of the original prism

we know that

the volume of the prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of the prism

h is the height of the prism

in this problem we have

[tex]B=5\ ft^{2}\\h=10\ ft[/tex]

substitute in the formula of volume

[tex]V=5*10=50\ ft^{3}[/tex]

Step [tex]2[/tex]

Find the volume of the dilated prism

we know that

[tex]volume\ of\ the\ dilated\ prism=[scale\ factor^{3}]*volume\ of\ the\ original\ prism[/tex]

we have

[tex]scale\ factor=\frac{6}{5}[/tex]

[tex]volume\ of\ the\ original\ prism=50\ ft^{3}[/tex]

substitute the values

[tex]volume\ of\ the\ dilated\ prism=(\frac{6}{5})^{3}*50[/tex]

[tex]volume\ of\ the\ dilated\ prism=1.728*50\\ \\volume\ of\ the\ dilated\ prism=86.4\ ft^{3}[/tex]

therefore

the answer is

the volume of the dilated prism is [tex]86.4\ ft^{3}[/tex]

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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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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After plugging the x-values from the table into the equation y = 115 + 32(x) and finding matching results with the y-values in the table, it is clear that the table and equation represent the same function.

To determine if the table and the equation y = 115 + 32(x) represent the same function, we can plug the x-values from the table into the equation and see if the resulting y-values match those provided in the table.

Since the y-values for all listed x-values in the table correspond exactly to those calculated using the equation, it is evident that the table and the equation do indeed represent the same function.

Answer:

voluntary sampling

Step-by-step explanation:

Voluntary sampling involves someone opting to be a part of the sample.  In this situation, customers are given the option to stay on the line to answer a survey; this means it is on a voluntary basis.  Thus it is a voluntary sample.

The type of sampling is the cable company using is convenience sampling.

We do sampling so that we don't have to work on entire population of items but only on that sample in a way that we can predict information about population.

Most of the times, it isn't possible in real world to work on entire populations. Samples come out for rescue by assumptions that they will have some properties of the population pertained in them.

Thus, the sample should be taken out such that it includes data of the population as much  as it can in unbiased way so as to imitate population.

We are given that;

The cable company is using convenience sampling.

Convenience sampling involves selecting individuals who are convenient or readily available to participate in the study. In this case, the cable company is selecting individuals who call their customer service and happen to complete their call with a customer service representative. The individuals are not selected based on any specific criteria or randomly selected, but rather because they happen to call the cable company and complete a customer service call.

As the message specifically invites customers to stay on the line to answer the survey questions, it can also be considered a form of voluntary sampling, where individuals are invited to participate in a study and can choose whether or not to participate.

Therefore, by sampling the answer will be convenience sampling.

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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.

Joey's sister takes 0.75 foot for each step she takes since she takes four steps for every three of Joey's, and Joey's step is 1 foot.

The question revolves around a ratio of steps taken by Joey and his sister. Since Joey's one step covers one foot and his sister takes four steps for his three, we need to determine how many feet his sister covers for each of Joey's steps. Let's use a ratio to figure this out.

First, we establish the ratio of steps: for every 3 steps Joey takes, his sister takes 4. If Joey's 3 steps equal 3 feet (because 1 step = 1 foot), we then find the length of his sister's step compared to his. We divide the 3 feet by Joey's 3 steps to find that each step Joey takes is 1 foot long. Then, we calculate his sister's step length in feet by dividing the 3 feet by 4 (since she takes 4 steps to his 3), which equals 0.75 foot per step for his sister.

So, for each of Joey's steps being 1 foot, his sister's step would be 0.75 foot. Therefore, Joey's sister covers 0.75 foot for each step she takes.