Final answer:
To find out how much more was cut from the skirt than the pants, convert fractions to have a common denominator and subtract: 3/4 inch minus 1/6 inch equals 7/12 inch.
Explanation:
To determine how much more the tailor cut off the skirt than the pants, we need to subtract the length cut from the pants from the length cut from the skirt. The tailor cut 3/4 of an inch off the skirt and 1/6 of an inch off the pants. To perform the subtraction, we need a common denominator, in this case, 12 is suitable. So we convert 3/4 to 9/12 and 1/6 to 2/12.
Now, we subtract the smaller fraction from the larger one:
9/12 - 2/12 = 7/12 of an inch.
Therefore, the tailor cut 7/12 of an inch more off the skirt than the pants.
what is the sum of the finite arithmetic series? 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)
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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7 of every 20 employees at v&b bank company are between the ages of 20 and 30 if there are 13220 employees at B&B Bank company how many are between the ages of 20 and 30
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.
joey's little sister must take four steps for every three steps joey takes. suppose one step of joey's covers one foot. how many feet would his sister
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.
A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 . What is the volume of the dilated prism? Enter your answer, as a decimal, in the box.
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]
At the beginning of a call to the cable company, a message tells customers, “After you finish talking to our customer service representative, you will be asked to take a five-question survey about the level of service you received. It would be appreciated if you could please stay on the line to answer the survey questions.” What type of sampling is the cable company using? systematic random sampling voluntary sampling cluster sampling convenience sampling
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.
Why do we do 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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A helicopter flies 200 miles against the wind in 2 hours, with the wind, it can fly 300 miles in the same amount of time. Find the speed of the helicopter in still air.
To find a power series for the function, centered at 0. f(x) = 18 (x + 1)3
whats a square root?
Searches related to Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.10, point, 1 meters per second. When it reached the water's surface after 35 seconds, Elon found it was only an old shoe. Graph the shoe's altitude (in meters relative to the water's surface) as a function of time (in seconds).
If the two equal sides of an isosceles triangle are 2 cm long, find the length of the third side thatmaximizes the area of the triangle.
a sperical water tank holds 12,500 ft^3 of water what is the diameter of the tank
if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.
What is Three dimensional shape?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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j is 25 more than 3 help
what score must a student make on an algebra test to have an average score of 90 for the grading period. If his other test scores are 88, 84, and 92?
complete the two column proof
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.
Choose the triangle that seems to be congruent to the given one
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.
Therefore, triangle ADB is congruent to triangle BAC by Side Side Side (SSS) congruence theorem.what is the length of MN?
The lengths of pregnancies are normally distributed 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.
b. if the length of pregnancy is in the lowest 44%, then the baby is premature. find the length that separates premature babies from those who are not premature.
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.
PLEASE HELP!!!!
A. Y=|x+4|+2
B. y=|x-4|+2
C. y=|x+4|-2
D. y=|x-4|-2
A veterinary clinic plans to build four identical dog kennels along the side of its building using 210 feet of fencing. (See the picture.) What should be the dimensions of each kennel to maximize the enclosed area? (Note: No fencing is needed along the side of the building.)
Final answer:
To maximize the enclosed area, each kennel should be in the shape of a square with dimensions of 52.5 feet by 52.5 feet.
Explanation:
To maximize the enclosed area, each kennel should be in the shape of a square. Let's assume that each side of the square kennel has a length of x feet.
Each kennel has four sides, so the total length of fencing required for all four kennels is 4x feet.
Given that there are 210 feet of fencing available, we can set up the equation 4x = 210 and solve for x to find the length of each side of the square kennel.
Dividing both sides of the equation by 4, we get x = 52.5 feet.
Therefore, each kennel should have dimensions of 52.5 feet by 52.5 feet to maximize the enclosed area.
what is the greatest common factor that could be used to reduce 36/90
what can you say about his average speed?
What is 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?
y = x – 8
y = x + 1
y = x + 1
y = x + 10
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]
What is the equation for 5n+7=21
about 45 of every 300 apples are picked at the Newberry apple orchard are rotten if 3560 apples were picked one week about how many apples rotten
What is the common difference between the elements of the arithmetic sequence below? -18, -22.5,-27,-31.5,-36
Answer:
-4.5
Step-by-step explanation:
are the solutions of the quadric x^2 -7x+4
A pond is 50 m long 30 m wide and 2m deep find the capacity of the pond in cubic meters
Today Ian wants to run less than 7/12 mile. Write a fraction with a denominator of 4 to respresent a distance that is less than 7/12.
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
What would be the slope of the line perpendicular to the line 4x + 2y = 12?
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.
Do the table and the equation represent the same function?
y = 115 + 32(x)
0 115
2 179
4 243
6 307
8 371
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.
For x = 0: y = 115 + 32(0) = 115, which matches the table.For x = 2: y = 115 + 32(2) = 115 + 64 = 179, which matches the table.For x = 4: y = 115 + 32(4) = 115 + 128 = 243, which matches the table.For x = 6: y = 115 + 32(6) = 115 + 192 = 307, which matches the table.For x = 8: y = 115 + 32(8) = 115 + 256 = 371, which matches 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.