what is listed below in the picture

The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer:

63.2

Step-by-step explanation:

The triangles are similar so corresponding angles are congruent. Angle K corresponds to angle P so the answer is 63.2 degrees.

Step-by-step explanation:

3. (c) complementary since the sum of the angles is 90°

4. 5x + 95 = 180 ---> 5x = 85 or x = 17 ans (d)

5. 68 + x + 90 = 180

x + 158 = 180

x = 22

ans. (b)

The order of rotational symmetry for a regular polygon with five (5) sides is equal to five (5).

A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:

The order of rotational symmetry of a regular polygon or geometrical shape can be defined as the number of times the polygon can be rotated around a full (complete) circle and still look the same.

As a general rule in geometry, a regular polygon with number of sides (n) has "n" lines of symmetry and its order of rotational symmetry is equal to "n."

Note: The number of sides (n) of a pentagon is 5.

Based on this rule, the order of rotational symmetry for a regular polygon with five (5) sides is equal to five (5).

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Answer:

rectangle that measures 22cm x

25cm

A rectangle that measures 22cm x 25cm is more square.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

To determine which rectangle is more square, we need to compare their aspect ratios, which is the ratio of the length to the width of the rectangle. A rectangle is considered to be more square when its aspect ratio is closer to 1.

In the first rectangle, the aspect ratio is 35cm/39cm = 0.897. In the second rectangle, the aspect ratio is 22cm/25cm = 0.88. Since the aspect ratio of the second rectangle is closer to 1, it is considered to be more square.

It's worth mentioning that a square is a special type of rectangle where all four sides are equal in length. So, if we compare the rectangles with a square, the rectangle that measures 22cm x 25cm is less square than a square with a side length of 22cm or 25cm.

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Answer:

170 students were attending

Step-by-step explanation:

use a system of equations:

\(\left \{ {{x+y=300} \atop {9x+6y=2190}} \right.\)  

let x be the adults and y be the students

\(\left \{ {{-9(x+y=300)} \atop {9x+6y=2190}} \right.\)    multiply the top equation by -9 and add the two systems together to cancel out x. you are then left with:

\(-3y=-510\)

divide both sides by -3 to leave y alone:

\(\frac{-3y}{-3}=\frac{-510}{-3}\)

that would leave you with:

y=170

Answer:

20/7 dollars per hour

Step-by-step explanation:

He pays 10 dollars per 3 1/2 hours. To find the unit rate, we divide the two.

10 / (3 1/2) =

10 / (7/2) =

(10/1) x (2/7) =

20/7

a) Probability that the flight will accommodate all ticketed passengers who show up is 0.16

b) Probability that not all ticketed passengers who show up can be accommodated is 0.67

c) The probability that you will be able to take the flight is 96%

Probability is a powerful tool to understand the likelihood of different outcomes in various situations, including overbooking of flights

In this scenario, the random variable y represents the number of ticketed passengers who actually show up for the flight, out of a total of 55 ticketed passengers for a plane with only 50 seats. The probability mass function of y provides the probabilities for each possible outcome.

(a) The probability that the flight will accommodate all ticketed passengers who show up is the probability of y being equal to 50, which is 0.16.

(b) The probability that not all ticketed passengers who show up can be accommodated is the sum of the probabilities of y being greater than 50, which is

=> 0.05 + 0.10 + 0.13 + 0.14 + 0.25 = 0.67.

(c) If you are the first person on the standby list, the probability of being able to take the flight is the probability of y being less than or equal to 50, which is 0.89. This means that there is an 89% chance that you will get on the plane. If you are the third person on the standby list, the probability is the probability of y being less than or equal to 52 (since two people need to cancel or not show up for you to get on), which is 0.96. This means that there is a 96% chance that you will get on the plane.

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Answer:

1/4 or .25

Step-by-step explanation:

Anser: there would be 5 groups with six penanuts each and a remainder group with only 4 peanuts

Step-by-step explanation:

since 34/5 gives a remainder

calculate 30/5 which gives you 6

then you would be left with 4 since 30 +4 is 34

The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled, obtained from the volume of the wheelbarrow and the volume of the truck is about 41 times.

The volume of a solid is the three dimensional space the solid occupies.

The specified dimensions of the wheelbarrow and truck indicates that the volumes of the wheelbarrow and the truck are;

Volume of the wheelbarrow = 2 ft × 1.5 ft × 3 ft = 9 ft³

Volume of the truck = 11 ft × 8 ft × 6 ft = 528 ft³

70% of the volume of the truck = 70% × 528 ft³ = 369.6 ft³

The number of times Johnny uses the wheelbarrow = 369.6 ft³ ÷ 9 ft³ ≈ 41.0

The number of times Johnny needs to use the wheelbarrow is about 41 times

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Answer:

Step-by-step explanation:

So the two lines before and after the expression means absolute value, or modulus of, knowing this, it means that the answer must always yield positive. So if x-6 is positive, it will stay positive, if x-6 is negative, it will turn positive, therefore it can never yield a negative value.

Now im assuming the second question is meant to be absolute value of x-5 is less than 0, because it makes no sense otherwise.

So now knowing that x-5 is always positive, or 0, but this inequality only wants less than 0, this means there are no solutions for the inequality.

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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Answer:

40

Step-by-step explanation:

Answer:

The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 37 - 1 = 36

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 36 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.0262

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.0262\frac{5}{\sqrt{37}} = 1.67\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 31 - 1.67 = 29.33 minutes

The upper end of the interval is the sample mean added to M. So it is 31 + 1.67 = 32.67 minutes.

The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.

It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

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The value of f(6) is -5.

What are coordinates?

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

The position of a point or a shape in a given space is determined by coordinates, which are numbers (a map or a graph ).

Observe the graph:

Locate +6  on x-axis

From there, move down to touch the curve.

Then, the corresponding y value on y axis is -5

So, f(6) = -5

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The number line that shows the solution to the inequality is given as follows:

First number line.

The inequality in the context of this problem is defined as follows:

-6x + 5 >= 17

-6x >= 12.

Due to the negative sign of the leading coefficient, we should change the sign of all terms, including the sign, as follows:

6x <= -12.

Then the solution is given as follows:

x <= -2.

Which is composed by the numbers to the left of the closed interval at x = -2, hence the first number line gives the solution to the inequality.

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The number line that shows the solution to the inequality is: C. graph C.

In Mathematics and Geometry, an inequality refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

-6x + 5 ≥ 17

By subtracting 5 from both sides of the equation (inequality), we have;

-6x + 5 - 5 ≥ 17 - 5

-6x ≥ 12

x ≤ 12/6

x ≤ 2 (it would be shaded to the left with a closed circle at 2).

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Answer:

Hello! answer: D. 180

Step-by-step explanation:

What you do for these is find the surface area for each face separately then add them up so...

for the sides its 18 for the top and bottom it's 48 for the front and back it's 24 so now we add all 6 up so... 18 + 18 + 48 + 48 + 24 + 24 = 180 Hope that helps!

Answer:

180 in²

Step-by-step explanation:

To wrap the given box, we need to find the total surface area of the figure.

TSA of cuboid = 2 (lb + bh + hl)

= 2 { (6*8) + (8*3) + (3*6) }

= 2 ( 48 + 24 + 18 )

= 2 * 90

= 180 in²

Answer:

a.(2 × 25) + 105

Step-by-step explanation:

Let the number of hours spent repairing the bike = x

Mr. Jones charged Roberta $105 for parts and $25 per hour for labor to repair her bicycle.

Therefore, our algebraic expression

= $25× x + $105

= 25x + 105

We were told in the question that He spent 2 hours repairing her bike.

Hence:

25 × 2 + 105

Therefore, the correct option is option a

a.(2 × 25) + 105

Answer:

x=6,36

Step-by-step explanation:

step 1 : cross multiply

x-3=3.36

x=3.36+3

x=6.36

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\stackrel{vertex}{(\stackrel{h}{2}~~,~~\stackrel{k}{-11})}\qquad y=a(x-2)^2-11\qquad \qquad \textit{we also know that} \begin{cases} x=0\\ y=5 \end{cases} \\\\\\ 5=a(0-2)^2-11\implies 16=4a\implies \cfrac{16}{4}=a\implies 4=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=4(x-2)^2-11~\hfill\)

The equation of the parabola that has the vertex at point (2,-11) and passes through the point (0,5) is y = 4 (x - 2)² - 11.

A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.

The general form of a parabola is,

y = a (x - h)² + k

where (h, k) is the vertex.

Given vertex is (2, -11).

Equation is,

y = a(x - 2)² - 11

Also, given that the parabola passes through the point (0, 5).

Substituting,

5 = a (0 - 2)² - 11

⇒ 5 = 4a - 11

⇒ a = 4

So the required equation is, y = 4 (x - 2)² - 11.

Hence the equation of the given parabola is y = 4 (x - 2)² - 11.

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Answer:

y=1/5x-4

Step-by-step explanation:

So, first we're gonna put this into point slope form, (y-y1)=m(x-x1), then we'll convert it. When you plug the numbers in, you get (y+9)=1/5(x+25)

Then, you simplify!

y= 1/5(x+25)-9

y=1/5x+5-9

y=1/5x-4

Hope this helped!

There are 50 predicted rolls for 5 in 300 times of rolls.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, Janet rolls a 6-sided number cube 300 times,

Probability = (Favourable Outcomes)/(Possible Outcomes)

Favourable Outcomes: 5 (1 total)

Possible Outcomes: 1,2,3,4,5,6 (6 total)

Probability of a 5 in any given roll of a die = 1/6

1/6x300 = 50 = 50 predicted roll with 5.

Hence, There are 50 predicted rolls for 5 in 300 times of rolls.

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The probability that either event will occur is 0.33

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

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

Total = A + B + C

So, we have

Total = 8 + 7 + 30

Evaluate

Total = 45

So, we have

P(A) = 8/45

P(B) = 7/45

For either events, we have

P(A or B) = 8/45 + 7/45

P(A or B) = 15/45

Evaluate

P(A or B) = 0.33

Hence, the probability that either event will occur is 0.33

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The correct formula to find the z-value for a sample mean when applying the central limit theorem is (A) Z = [x-μ]/[σ/√n].

Here, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. The central limit theorem states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the population distribution. The z-value is used to determine the probability of obtaining a sample mean that is a certain number of standard deviations away from the population mean. Formula (A) calculates this z-value by standardizing the sample mean with respect to the population mean and the standard error of the mean.

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Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

The answer will be 11.78

Step-by-step explanation:

The first step to dividing fractions of 412.3 and 35. Next to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed. You will get the answer in no time!