a triangle with three acute angles and no congruent sides

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:

Step-by-step explanation:

The place value of the '3' in 27.4359 is in the tenths place, and therefore its value is 0.3. The position of the '3' relative to the decimal point determines its place value.

The place value of the '3' in 27.4359 is determined by its position relative to the decimal point. In this example, the '3' is located in the first space to the right of the decimal point, which represents the tenths place.

So, the value of the '3' in this decimal is three-tenths, or 0.3. Looking at other numbers for comparison, consider 0.00347. Here, the '3' is three places to the right of the decimal, but the place value would be significantly lower, as it is in the thousandths place.

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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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Final answer:

To find the length and width of the rectangle with an area of 156 square inches and a perimeter of 50 inches, we can set up and solve a system of equations based on the area and perimeter formulas. After solving, we determine that the length is 13 inches and the width is 12 inches.

Explanation:

The student has asked to find the length and width of a rectangle given that it has an area of 156 square inches and a perimeter of 50 inches. To solve this problem, we need to use the formulas for the area and perimeter of a rectangle.

Area and Perimeter Formulas

Area formula: A = length × width

Perimeter formula: P = 2(length + width)

Let's denote the length as 'l' and the width as 'w'. The area of the rectangle is 156, so we can write:

l × w = 156

The perimeter of the rectangle is 50, so we can write the perimeter formula as:

2(l + w) = 50

This simplifies to:

l + w = 25

Now, we have two equations:

l × w = 156

l + w = 25

We can solve this system of equations by expressing one variable in terms of another. Let's express 'w' in terms of 'l' from the second equation:

w = 25 - l

Now, substitute 'w' in the area equation:

l × (25 - l) = 156

This is a quadratic equation that can be solved to find the values of 'l'. Once we have 'l', we can find 'w' using the second equation.

After solving, we find that the length is 13 inches and the width is 12 inches. Therefore, the rectangle's dimensions are 13 inches by 12 inches.

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.

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.

Final answer:

The letter 'z' in mathematics can refer to various concepts including complex numbers with arguments measured in degrees, z-scores in statistics indicating deviation from the mean, and as a variable within equations and inequalities.

Explanation:

The concept of 'z' seems to refer to multiple mathematical contexts, including complex numbers, z-scores in statistics, and equations involving z. Specific examples from the information provided include:

Complex numbers where z's argument could be positive or negative, and use of degrees in the context of a circle's 360 degrees showing that -30 and 330 degrees represent the same angle.

The z-score, which measures how many standard deviations a data point is from the mean in statistics, such as z = -4 indicating a data point four standard deviations to the left of the mean.

Equations where z is a variable representing a number, which could be within a certain range or satisfying a given condition.

Understanding these uses of z in the mathematical context allows for precise interpretation of equations, probabilities, and analyses of data sets.

The inequality that represents the statement "A number z is fewer than 34." is: z < 3/4.

How to express the inequality?

The inequality that represents the word sentence "A number z is fewer than 3/4" is z < 3/4.

To explain this, we can compare z to 3/4. If z is smaller than 3/4, we can use the less than symbol (<) to represent this relationship.

So, the inequality is z < 3/4.

For example, if z is 1/2, which is smaller than 3/4, the inequality holds true: 1/2 < 3/4.

Complete question is:

Write the word sentences as an inequality.

A number z is fewer than 3/4.

An inequality that represent this word sentences is?

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.

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]

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.

The length of line segment WU is 4 cm.

Hence, 4 cm is correct.

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Now, As given that, RSTU is an parallelogram.

RT and SU are its two diagonals.

They intersect each other at point W.

Properties of parallelogram is that they bisect each other.

i.e SW = WU and RW = WT

As given that, SW = 4 cm.

So, WU = SW = 4 cm

Therefore, the length of line segment WU is 4 cm.

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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 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.

The answer is (B) Their measures should add up to be 100°.

We know that the sum of all angles of a triangle is equal to 180 degrees. Stefan has calculated the first angle and it came out to be 80 degrees. So the other two angles must be equal to 100 in order to complete the total measurement of triangle angles which is 180.