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The table below shows a relationship between hours and miles traveled:

After reading the table, a student writes this equation to show the proportional relationship between hours and miles traveled. The constant of proportionality is 30.

m = 30h

Based on the table and the equation, how many miles would they travel after 12 hours?

A: 360 miles

B: 600 miles

C: 240 miles

D: 42 miles

Answer:

Below

Step-by-step explanation:

EVERY triangle's angles add up to 180 degrees

  a RIGHT triangle has a 90 degree angle

       this right triangle also has a 45 degree angle

              let x° = third angle

                     90°  + 45°  + x° = 180°

                                 x = 180 - 90 - 45 = 45 degrees

The equation for the number of cells after t-15 minute periods is C = 157 x [tex]2^{t/15}[/tex].

The number of cells after 2 hours is  40,192.

The equation for the number of cells after t-15 minute periods is an exponential equation.

The form of the equation will be:

Future population = present population x [tex]2^{number of minutes / 15}[/tex]

C = 157 x x [tex]2^{t/15}[/tex].

Number of cells after 2 hours :

First convert 2 hours to minutes = 2 x 60 = 120 minutes

C =  157 x [tex]2^{120/15}[/tex]

157 x [tex]2^{8}[/tex]

C = 40,192

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Answer: 14.5 and 5.5

Step-by-step explanation:

The issue is using whole numbers. 14+6=20, but 14-6=8.   15+5=20, but 15-5=10. If we use decimals, we can get in between the numbers a little to get 9. 14.5+5.5=20, but unlike 14+6, 14.5 gives 5 a tiny boost to push it to 14.5-5.5=9. Hope that helps!

Answer:

14.5

5.5

Step-by-step explanation:

14.5+5.5=20

14.5-5.5=9

We can state this by responding to the provided question December 31: equation Interest Paid 184 Interest Expensed 184 (To charge interest for one month on the Paola Bank note)

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The journal entries for the mentioned transactions are as follows:

Jan. 2: 40,000 in product inventory and 40,000 in accounts payable (To record the purchase of merchandise on account)

April 1: Cash 40,600 Accounts Payable 40,000 Interest Payable 600 (To record the payment of the Nunez note and interest)

Oct. 1: Cash 70,110 Notes Payable 68,400 Interest Payable 1,710 (To record the payment of the Marson note and interest)

Cash 27,600 Notes Payable 27,600 as of December 1

(In order to document the note's issuance to Paola Bank)

December 31: Interest Paid 184 Interest Expensed 184

(To charge interest for one month on the Paola Bank note)

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The type of triangle AABC is an equilateral triangle, as it is formed by the midsegments of the equilateral triangle ADEF.

Since the midsegments of a triangle are parallel to its opposite sides and half the length of the opposite sides, the midsegments of an equilateral triangle are congruent to each other, and their length is half the length of the sides of the equilateral triangle.

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2} and y = \dfrac{q+n}{2}[/tex]

We are given that;

An equilateral triangle DEF

AAB is formed by the midsegments of triangle ADEF, which means that AAB is also an equilateral triangle. To see why this is true, we can use the following argument:

The midsegment of DE is parallel to AB and has half the length of AB.

The midsegment of EF is parallel to AA' and has half the length of AA'.

The midsegment of FD is parallel to BB' and has half the length of BB'.

Therefore, AB = AA' = BB', and the angles at A and B are both 60 degrees (since DEF is equilateral).

Thus, AAB is an equilateral triangle, because all its sides are equal in length and all its angles are equal to 60 degrees.

Therefore, by midpoint the answer will be equilateral triangle.

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Answer:

201.5km

Step-by-step explanation:

50000cm = 500m

1000m + 500m = 1500m

1km = 1000m

So 1.5km = 1500m then..

200km + 1.5km = 201.5km

Answer: $4.35

Step-by-step explanation:

320.38 rupees / 73.6500 rupees = $4.35

The value of angle mXUV is 76⁰.

The value of angle mXUV is  109⁰.

The measure of angle mWXU is calculated by applying the following circle theorem.

mWXU  = ¹/₂ ( 152⁰ ) (angle at tangent is half the angle subtended by an arc )

mWXU  =  76⁰

The value of angle mXUV is calculated as follows;

mXUV + mXWV = 180 (opposite angles of a cyclic quadrilateral)

mXWV + 71 = 180

mXWV = 180 - 71

mXWV = 109⁰

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Answer x is 7

Step-by-step explanation:

The three angles are 104degrees, (9x-25) and unknown

The pictures shows that the two sides are equal therefore the two opposite angles are equal

104 + (9x-25) +(9x-25) =180

RE write

104 +2(9x-25) =180

Subract 104 from both sides

2(9x-25) = 180-104

2(9x-25) = 76

Divide both sides by 2

9x - 25 = 38

Add 25 to both sides

9x = 63

Divide both sides by 9

X =7

The angle is 9x-25 = 38

Answer:

The polynomials are:

-7x²+ 5/3x

6x² + 5x

-x^2+5x

The expression x^2+ 5x1/5 is not a polynomial because it contains a fraction with x in the denominator.

Answer:

Step-by-step explanation:

10 + 10 = 20

☁️Answer☁️ I think D.

️Step-by-step explanation️ hope this helps

The scale factor for the given transformation is -

{k} = 2/3.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Given is a figure {Q} that is a transformation of figure {P}.

The base length of the figure {P} is 15 cm. The base length for figure {Q} is 10 cm. So, we can write the scale factor as -

{K} = 10/15

{K} = 2/3

Therefore, the scale factor for the given transformation is -

{k} = 2/3.

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The best estimate of the time it will take Andrea and her friend to paint the fence together is 2.4 hours.

What is work and time in mathematics?

In mathematics, work refers to the amount of effort or energy needed to complete a task or achieve a goal. Work is often measured in units such as joules or calories.

Time refers to the duration or amount of time it takes to complete a task or achieve a goal. Time is often measured in units such as seconds, minutes, hours, or days.

To estimate the time it will take Andrea and her friend to paint the fence together, we can use the formula:

Total Time = (Time for Person 1 x Time for Person 2) / (Time for Person 1 + Time for Person 2)

Using this formula, we can estimate the time it will take Andrea and her friend to paint the fence together as:

Total Time = (6 hours x 4 hours) / (6 hours + 4 hours) = 24/10 = 2.4 hours

Therefore, the best estimate of the time it will take Andrea and her friend to paint the fence together is 2.4 hours.

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a. The mean of the sampling distribution is 0.2 and the standard deviation is 0.027. b. The probability that Cindy will get at least 48 orange Stattle is approximately 0.0901.

A method for estimating the probability of a binomial distribution using a normal distribution is known as the normal approximation to the binomial distribution. When the sample size is sizable and the success probability is not too close to 0 or 1, it can be employed. To utilise this approximation, we must first get the binomial distribution's mean and standard deviation, then normalise the distribution using the z-score calculation.

As 20% of the candies are orange, the mean of the sampling distribution of p is equal to the population percentage, which is 0.2.

The standard deviation of the sampling distribution of p can be found using the formula:

σp = sqrt((p * (1 - p)) / n)

Substituting the values:

σp = sqrt((0.2 * 0.8) / 220) = 0.027

So the mean of the sampling distribution is 0.2 and the standard deviation is 0.027.

b. Let X be the number of orange Stattles in the bag.

The z-score is given as:

z = (X - μ) / σ

z = (48 - 44) / 2.974 = 1.34

So the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag is approximately 0.0901.

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Therefore , the solution of the given problem of linear equation comes out to be y= (3/2)x + 5 .

The equation y=mx+b is the basis of a linear regression model. B is the slope, and m is the y-intercept. The aforementioned sentence is repeatedly alluded to as a "math problem with two variables," despite the fact that y and y are distinct parts. In bivariate linear equations, there are only two variables. The application regions for linear equations have no definitive solutions.

Here,

We must first determine the slope of the line before using the point-slope form of the equation of a line to determine the equation of the line that goes through two points.

The angle of the line that connects the coordinates (2, 8) and (8, 7) is:

=> slope = (−7 − 8) / (−8 − 2)

=> slope = −15 / −10

=> slope = 3/2

When we express the equation of a line in the point-slope format, where (x1, y1) is one of the line's points and m is its slope, we get the following result:

=> y − y1 = m(x − x1)

By selecting the line's origin (2, 8) and substituting the slope m = 3/2, we obtain:

=> y − 8 = (3/2)(x − 2)

The equation y = mx + b is transformed into the slope-intercept form by condensing and reordering the variables.

=> y = (3/2)x + 5

Consequently, y = (3/2)x + 5 represents the equation of the line going through the points (2, 8) and (8, 7) respectively.

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In response to the aforementioned query, we may say that Point M's slope coordinates are therefore (39/25, 69/25).

A line's slope determines how steep it is. The gradient is mathematically expressed as gradient overflow. By dividing the vertical change (run) between two spots by the height change (rise) between the same two locations, the slope is determined. The equation for a straight line, y = mx + b, is written as a curve form of an expression. When the slope is m, b is b, and the line's y-intercept is located (0, b). For instance, the y-intercept and slope of the equation y = 3x - 7 (0, 7). The location of the y-intercept is where the slope of the path is m, b is b, and (0, b).

A and B's respective y-coordinates are at the midpoint of the triangle AB.

[tex]((x A + x B)/2, (y A + y B)/2)[/tex]is the midpoint.

[tex]((-4 + 2)/2, (2 + 10)/2)[/tex] is the midpoint.

Midway = [tex]( -1, 6 )\\[/tex]

Slope of AB: The slope of AB is equal to the product of the y-value and the x-value, or:

slope is equal to [tex](y B-y A) / (x B-x A).\\[/tex]

slope = [tex](10 - 2) / (2 - (-4))\\[/tex]

slope = 8/6 = 4/3

[tex]y - y 1 = m * (x - x 1)\\y - 6 = (-3/4) * (x + 1)\\y - 6 = (-3/4)\\x - (3/4)\sy = (-3/4)x + (21/4)[/tex]

Point M's coordinates are:

[tex]y = (-3/4)x + (21/4)\\4x/3 + 2 = (-3/4)x + (21/4)\\16x + 24 = -9x + 63\s25x = 39\ = 39/25\\y = (-3/4)(39/25) + (21/4) = 69/25\\[/tex]

Point M's coordinates are therefore (39/25, 69/25).

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Answer:

ambiguous question dear!!

Step-by-step explanation:

π - This is an irrational number. 22/7 - The number is rational but not an integer. 3.3 - The number is an integer but not a whole number.

The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it may be expressed as p/q.

Irrational numbers are those that are not logical in nature. Let's explain; irrational numbers may be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.

π - This is an irrational number.

22/7 - The number is rational but not an integer.

3.3 - The number is an integer but not a whole number.

The number is a whole number but not a natural number.

9 -This number can be written as a natural number.

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Answer:

22² · π

Step-by-step explanation:

The formula to find the area of the circle is

A = π · r²

r = 22

Looking at the options, the answer is 22² · π

An equivalent expression of (5.1u + 8) + 6 is 5.1u + (8 + 6)

From the question, we have the following parameters that can be used in our computation:

(5.1u + 8) + 6

The associative property states that

(a + b) + c = a + (b + c)

Using the above as a guide, we have the following equation

(5.1u + 8) + 6 = 5.1u + (8 + 6)

Hence, the expression is 5.1u + (8 + 6)

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A triangular pyramid is a solid figure made of only triangular faces.

A triangular pyramid is a type of pyramid that has a triangular base and three triangular faces that meet at a common point or apex. The triangular base is usually referred to as the base face of the pyramid, while the remaining three triangular faces are called lateral faces.

The properties of a triangular pyramid include:

It has one base face and three lateral faces.

All four faces are triangles.

It has four vertices or points.

It has six edges or line segments.

To find the volume of a triangular pyramid, the area of the base face and the height of the pyramid must be known.

Triangular pyramids can be found in many real-world applications, such as in the design of buildings and structures, in geometry and mathematics, and in the study of crystals and minerals. They are also used in computer graphics to create 3D models of objects and environments.

A triangular pyramid is a solid figure made of only triangular faces.

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With a scaling ratio of 5:2, the larger cylinder's volume is (C) 70m³.

A scale factor is used when a shape is enlarged and each side is multiplied by the same quantity.

This number represents the scaling factor. Map scale factors are used to show distances between locations accurately.

The new shape created by scaling the original shape is twice as big when the scale factor is 2.

Thus, calculate the larger cylinder's volume as follows:

x/5 = 28/2

2x = 28*5

2x = 140

x = 70m³

Therefore, with a scaling ratio of 5:2, the larger cylinder's volume is (C) 70m³.

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Complete question:

The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?

Question 8 options:

A. 700 m3

B. 350 m3

C. 70 m3

D, 437.5 m3

E. 175 m3

Answer: 70m^3

Step-by-step explanation:

I took the test

Answer:

less than

Step-by-step explanation:

just multiply top and bottom untill the denominator is the same

The ratio of the diameter of the nucleus to the diameter of the atom is   [tex]2 \times 10^{-5}[/tex] .

A ratio is a mathematical relationship between two or more numbers that shows how much one number is in relation to the other.

As per the given data:

Diameter of an atom = [tex]4 \times 10^{-8}[/tex] cm

Diameter of the nucleus = [tex]8 \times 10^{-13}[/tex] cm

To find the ratio of the diameter of the nucleus to the diameter of the atom:

Ratio = (diameter of the nucleus) / (diameter of the atom)

Ratio = [tex]\frac{8 \times 10^{-13}}{4 \times 10^{-8}}[/tex]

[tex]= 2 \times 10^{-13 + 8}\\ = 2 \times 10^{-5}\\[/tex]

Hence, the ratio of the diameter of the nucleus to the diameter of the atom is  [tex]2 \times 10^{-5}[/tex] .

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The probability that a random sample of 50 seniors has a mean score of at most 415 is given as follows:

0.1894 = 18.94%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters are given as follows:

[tex]\mu = 425, \sigma = 80, n = 50, s = \frac{80}{\sqrt{50}} = 11.31[/tex]

The probability that they scored at most 415 is the p-value of Z when X = 415, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (415 - 425)/11.31

Z = -0.88

Z = -0.88 has a p-value of 0.1894.

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If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:

Total number of hours of work / Number of hours of work done by 4 men in a day

= 224 / (4 x 8)

= 7

So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.

II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:

Total number of men x Total number of days x Number of hours worked by each man per day

= 4 x 7 x 8

= 224 hours

Therefore, the total cost of employing all 4 men is:

Total number of hours x Rate per hour

= 224 x $57.50

= $12,880

III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:

Total number of hours of work / Total number of days to complete the project

= 224 / 4

= 56 hours

Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:

Number of hours of work per day - Number of hours worked by each man per day

= 56 - 8

= 48 hours

Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.

IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:

l x $57.50

= $57.50l

Let the overtime rate of payment be $r per hour. Then:

r = $57.50l

The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:

Number of regular hours x Regular hourly rate

= 4 x 8 x 7 x $57.50

= $16,240

The cost of overtime hours is:

Number of overtime hours x Overtime hourly rate

= 4 x 6 x 7 x $57.50l

= $12,180l

So, the total cost of the project is:

Total cost = Cost of regular hours + Cost of overtime hours

= $16,240 + $12,180l

Answer:

Step-by-step explanation:

(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:

Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days

So it will take 4 men, each working 8 hours per day, 7 days to complete the project.

(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:

Total cost = 4 men x $57.50/hour x 56 hours = $12,320

(iii) If the project is to be completed in 4 days, each man will need to work for a total of:

224 total hours / (4 men x 4 days) = 14 hours per day

Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.

(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:

Overtime rate = $57.50 x 1.5 = $86.25/hour

To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:

Regular hours cost = 224 regular hours x $57.50/hour = $12,880

The cost of the overtime hours is:

Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour

= 96 x $86.25

Therefore, the total cost of the project is:

Total cost = Regular hours cost + Overtime cost

= $12,880 + $8,280

= $21,160

where the overtime rate is 1.5 times the regular hourly rate.

Answer:

We can simplify the expression as follows:

First, we need to evaluate the exponent in parentheses:

2-3 = -1

Next, we need to square -1:

(-1)^2 = 1

Now, we can substitute 1 back into the expression:

+(-4)(1)

Finally, we can simplify:

+(-4) = -4

Therefore,

+(-4)(2-3)^2 = -4.

Step-by-step explanation:

The scale factor of the dilation is 1/2.

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Here given that blue figure is the dilated image of the black figure.

Dilation is the reduction.

The bottom left point is (2, 2) and top let point is (2, 4) of blue figure.

Length of the left segment of blue figure = [tex]\sqrt{(2-2)^2+(4-2)^2}[/tex]

                                                                    = 2

The bottom left point is (4, 4) and top let point is (4, 8) of black figure.

Length of the left segment of black figure = [tex]\sqrt{(4-4)^2+(8-4)^2}[/tex]

                                                                      = 4

Scale factor = Ratio of corresponding sides

                    = 2/4

                    = 1/2

This will be the same if we take another corresponding sides.

Hence the scale factor is 1/2.

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Answer:

Where's the question...