Find the volume of the triangular prism as pictured below with a = 10 cm, b =
cm, and h = 10 cm.

The approximate length of arc CB is given as follows:

14.17 cm.

The circumference of a circle of radius r is given by the multiplication of 2 by the number π = 3.14 and the radius r, as follows, hence the equation is given as follows:

C = 6.28r.

The radius for this problem is given as follows:

r = 7 cm.

The angle relative to arc CB is given as follows:

2 x 58º = 116º.

As an entire circumference has an angle of 360º, the approximate length of arc CB is obtained as follows:

116/360 x 6.28 x 7 = 14.17 cm.

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In the triangle QRS the sum of square of 6 and square root of 85 is equal to 11 and RT is height.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

Given ,

AQRS is an isosceles triangle. Complete the statement that explains whether RT is the height of the triangle.

So, from the given triangle we can say that ,

[tex]6^{2}[/tex] + [tex]\sqrt{85 }^2[/tex] = [tex]11^{2}[/tex]

By the pythagorean theorem , we can say that ,

the sum of squares of base and opposite side is always equals to square of hypothenuse.

so it is equal to square of 11 and RT is height.

Therefore, in the triangle QRS the sum of square of 6 and square root of 85 is equal to 11 and RT is height.

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The solution is Option A.

The conversion factor should have gallons in the denominator and the equation will be 350 gallons = 92.3 L

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the amount of gallons of water be = 350 gallons

And , 1 gallon = 3.79 liters

So , the amount of 350 gallons = ( 350 ) x ( 1/3.79 ) L

Substituting the values in the equation , we get

The amount of 350 gallons = ( 350 / 3.79 ) L

On simplifying the equation , we get

The amount of 350 gallons = 92.3 L

Therefore , while converting the gallons to liters , the factor of gallons should be in the denominator

Hence , the equation is 350 gallons = 92.3 L

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Answer:

3x² + 9x + 1

Step-by-step explanation:

5x - 2 + 3x² + 4x + 3

= 9x - 2 + 3x² + 3

= 9x + 1 + 3x²

= 3x² + 9x + 1

Answer:

x = 4

Step-by-step explanation:

2x - 3 = 5   Add 3 to each side

2x - 3 + 3 = 5 + 3

2x = 8  Divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]

x = 4

Answer: 6 containers

Step-by-step explanation:

Fraction division.

2/3 divided by 1/8.

Keep-change-flip. (or a similar method for dividing fractions)

2/3 times 8/1 is 16/3.

He will fill 5 and 1/3 containers, so 6 containers will have paint in them.

(っ◔◡◔)っ ♥

Hope this helps.

MM4343

The sample taken by Sam is Biased sampling.

A subset of a population is chosen at random in a basic random sampling. Each person in the population has an exact equal probability of getting chosen using this sampling technique.

Given:

Sam asked 15 of his friends what they thought about the pizza they just had.

Sam here chooses his friend that means the people are selective already.

He already chooses the people which were known to him.

So, the selection here is biased sample.

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The steps to set up the study and the limitations that would be faced are explained below .

The Steps to setup the study are  :

(i) Recruit a large and diverse group of participants who are willing to stick to the prescribed diets for the duration of the study.

(ii) Divide the participants randomly into two or more groups. One group would be given a diet high in trans fats, and the other group(s) would be given a diet low in trans fats.

(iii) Monitor the health status of the participants closely throughout the study .

(iv) At the end of the study, compare the health outcomes of the different groups of participants to determine whether there is a significant difference in health outcomes .

The Limitations of this type of study include :

⇒ the difficulty of controlling all aspects of participants' diets, since participants may consume other foods outside of what is provided to them.

⇒ the study may not be long enough to detect long-term effects of trans fats on health.

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The given question is incomplete , the complete question is

One way that researchers study the effects of trans fats on people's health is by setting up controlled experiments. For example, in an experimental feeding trial, participants agree to stick to specific diets that the researchers prescribe. In this case, the researchers might vary the proportions of saturated, unsaturated, and trans fats in the diet of each participant. Throughout the study, the health status of the participants is monitored closely.

Suppose that you are a researcher designing an experimental feeding trial. How would you set up your study and what limitations would you face ?

Answer:

150

Step-by-step explanation:

5/6= ?/180

We can use cross-products to solve.

5 * 180 = 6 * ?

Divide each side by 6.

5 * 180/6 = ?

5 * 30 = ?

150

The missing number is 150.

Answer:

150/180

Step-by-step explanation:

Solution by Cross Multiplication;

The equation:

[tex]\frac{5}{6} = \frac{x}{180}[/tex]

The cross-product is:  

5(180)  =  6(x)

Solving for x:

x = [tex]\frac{5(180)}{6} \\[/tex]

x = 150

Answer: 27

Step-by-step explanation:

8^x+1 = 64

8^x+1 = 8²

x+1 =2

x = 2 - 1

x = 1

To Find :

3^2x +1

Substitute the value of x :

3^2(1)+ 1

3^2+1

3^3

27

Answer:

Step-by-step explanation:

The correct answer is C. Shading will be above the y=-2x+1 line but below the y= 3x-1 line.

The line y=-2x+1 is a line with a slope of -2 and a y-intercept of 1. It represents the solutions that are greater than -2x+1.

The line y=3x-1 is a line with a slope of 3 and a y-intercept of -1. It represents the solutions that are less than 3x-1.

So, when you graph both of these lines on the same coordinate plane, the solutions that satisfy both inequalities will be the region that is above the line y=-2x+1 but below the line y=3x-1, and this is the region that will be shaded.

Answer:

1020 handshakes including the bride and the groom. 980 excluding the groom and the bride.

Step-by-step explanation:

(20*19) twenty people on the brides side shake hands with the other 19 people (19 because you can't really shake your own hand).

+(20*30) twenty people on the brides side shake hand with 30 people on the grooms side.

+(20*2) twenty people on the brides side shake hands with the bride and the groom.

this equalssss......

1020!!!!

Since the grooms family does hugs instead of handshakes, you'd only calculate how many the brides side does.

Answer:

123.88 square units

Step-by-step explanation:

r = radius of circle

  = radius of sector

 = Length of LM

 = Length of MN

 = 13 units

When the angle is measured in degrees:
Area of a sector: [tex]\frac{Angle OfSector}{360^{o}}[/tex]× [tex]\pi r^{2}[/tex]

                = [tex]\frac{84}{360}[/tex]×[tex][\pi (13)^{2}][/tex]

                = 123.883 [tex]units^{2}[/tex]

                = 123.88 square units (Rounded to the nearest hundredth)

Overall, the article has given me a deeper appreciation for the role that statistics plays in the political landscape.

One statistical discussion that stood out to me was the concept of margin of error. This is a measure of the accuracy of a poll and is calculated by taking into account the sample size and the variability in responses. I now have a better understanding of how pollsters use this measure to determine the reliability of their results.

Additionally, the article highlighted the importance of understanding statistical significance, which refers to the likelihood that a particular result occurred by chance. This is an essential concept in statistics that helps to determine whether a particular result is reliable or not.

It has also emphasized the need to interpret polling data with caution and to be mindful of the potential for errors and biases.

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Answer: about 1587 cm^2

Step-by-step explanation: The equation for area of circle is A= πr^2 OR A= (pi/4)d^2

Given the diameter is 46.7, the radius would be half of that which is 23.35.

Simply plug it into the equation

A =  π23.35^2

OR

A= (π/4)46.7^2

Since you are using 3 in place of pie, it would be 3(23.35)^2  OR (3/4)46.7^2

the answer i got was 1,635 cm^2 so your closest choice to that is 4

Using the unitary method, we find that the store created approximately 37 bags with 15 random cards in each bag.

This problem can be solved using the unitary method. It is given that the

number of Anniversary cards is 163,

number of Birthday cards is 258,

number of Get Well cards is 98

and the number of Thank you cards is 47

So, the total number of cards will be equal to the sum of all these cards, that is,

163+258+98+47

= 566 cards

To create bags of 15 random cards, we have to divide the total number of cards by 15  which gives,

566/15 = 37.734

Thereby, we can say that the store created approximately 37 bags with 15 random cards in each bag.

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68.5% of Colton's gross pay is take-home pay. To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and then multiply by 100 to convert the resulting decimal to a percentage.

To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and multiply the resulting decimal by 100 to express it as a percentage. Colton's gross pay is $1421.50 and his net pay is $973.48. Dividing the net pay by the gross pay gives a result of 0.685, or 68.5% when converted to a percentage. This means that 68.5% of Colton's gross pay is take-home pay, or the amount of money that he receives after deductions are made. Therefore, Colton's take-home pay is $973.48, which is 68.5% of his gross pay.

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The speed of both the trains would be 400 mph and 450 mph respectively.

The formula to calculate the distance travelled is -

Distance = Speed x Time

Given is that two cities are 1020 miles apart. Two trains simultaneously left these cities heading toward one another. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours, the trains had not met yet and were 170 miles apart.

Let the speed of one train be {x} mph. Then, the speed of the other train would be {x + 10} mph.

Distance covered by both the trains would be -

train { 1 } = 5x                             ... { 1 }

train { 2 } = 5(x + 10)                          ... { 2 }

Now, we can write -

1020 - {5x + 5(x + 10)} = 170

1020 - 170 = 10x + 50

10x = 800

x = 80

Speed of train { 1 } = 400 mph

Speed of train { 2 } = 450 mph

Therefore, the speed of both the trains would be 400 mph and 450 mph respectively.

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On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

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Step-by-step explanation:

Use PEMDAS (Order of operations).

Simplify exponents

33554432 - 1048576 + 54288

Add and subtract (left to right)

33030144

63 goes into 33030144 524288 times.

Answer:

2^19(63)

Step-by-step explanation:

(2^5)^5-(2^4)^5+2^19

2^25-2^20+2^19

2^19(2^6-2+1)

2^19(64-2+1)

2^19(63)

Answer: -5r+8r+5=3r+5

Step-by-step explanation:

First add like terms, so -5r and 8r. For a second lets pretend the r doesn't exist. So, what is -5 + 8, 3, so 3r. Since 3r and 5 cannot be combined, the equivalent expression is 3r+5.

well, since we know that one root is 5, that is a factor of it is (x-5), so hmmm by the remainder theorem we also know that if we plug "5" as our argument in our f(x), that is, if we do f(5), it must result to 0. so f(5) = 0, if that's so then

[tex]2x^2+bx-10=f(x)\implies 2(5)^2+b(5)-10=f(5) \\\\\\ 2(5)^2+b(5)-10=0\implies 50+5b-10=0\implies 5b=-40 \\\\\\ b=\cfrac{-40}{5}\implies \boxed{b=-8} \\\\[-0.35em] ~\dotfill\\\\ 2x^2-8x-10=0\implies 2(x^2-4x-5)=0\implies 2\stackrel{ {\Large \begin{array}{llll} x=-1 \end{array}} }{(x+1)}(x-5)=0[/tex]

Answer: 5 Months

Step-by-step explanation:

Alright, we know he will make $120 a month (since 50 + 70 = 120)

(Let's have months=m)

So now we need to figure out for how many months (m) will he need to get to $600.

We know 120 a month so we can get the equation: 120m=600

Now all we have to do is solve for m

Divide both sides by two to get m=5

Checking Answers

70(5)=350

50(5)=250

250+350=600

So this solution works.

Answer: 5 months

Step-by-step explanation: so, what you have to do is add up 120 5 times so in total you will have 600 so the answer is 5 months.

Answer: 135

Step-by-step explanation:

Counting by 5 The last point at the end of the box and whisker plot is 135

Answer:

304

Step-by-step explanation

it was on my quiz

Answer:

The number 304 is exactly halfway between 61 and 547.

Step-by-step explanation:

To find the halfway point between two given numbers we can simply add them together then divide them by 2.

Note:

let [tex]N[/tex] be the number that is halfway

[tex]N=\frac{547+61}{2}[/tex]

[tex]N=\frac{608}{2}[/tex]

[tex]N=304[/tex]

Using unit conversions the total height change from the top of mount Everest to the bottom of the Mariana trench is 12.3 miles

We know that 1 km = 0.62136 miles and 1 foot = 0.000189 miles

Depth of Mariana Trench (d) = 11 km = 11 × 0.62136

                                                          = 6.835 miles

Height of Mount Everest (h) = 29000 ft = 29000 × 0.000189

                                                              = 5.492 miles

Therefore the total height difference top of Mount Everest and to bottom of the Mariana Trench is given by

H = Depth of Mariana Trench + Height of Mount Everest

H = d + h

H = 6.835 miles + 5.492 miles

H = 12.327 miles

H = 12.3 miles

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The value of x that makes the shape a parallelogram is 2/3

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are kite, square, rectangle, parallelogram and so on.

A parallelogram is a quadrilateral with two pairs of parallel sides. Each parallel sides are equal. Also, the diagonals of a parallelogram bisect each other.

From the diagram, the diagonals bisect each other in other to be a parallelogram, hence:

6x = 3x + 2

3x = 2

x = 2/3

The value of x is 2/3

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Answer:answer

Step-by-step explanation:because