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The surface area of the rectangular prism is 172cm^2

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross sections. The faces of the prism are parallelograms or rectangles.

The surface area of prism is 2A+ pH

where A is the base area

P is the perimeter of the base

and h is the height

for a rectangular prism, the base area is 2×8=16cm^2

perimeter of a rectangle= 2(l+b)

= 2(8+2)

= 20cm

surface area =( 2× 16) + 20× 7

= 32+ 140

= 172cm^2

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Answer:

Step-by-step explanation:

The distance between the two points (5,6) and (10,12) is [tex]\sqrt{61}[/tex]

What is the distance between two points formula?

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a standard formula to calculate the distance between two points. This equation can calculate the separation between any two locations on an x-y plane.

Solution explained:

First, Write the distance formula:

[tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]

Now,

Substitute (5,6) and (10,12) into [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex] :

[tex]\sqrt{(10 - 5)^{2} + (12 - 6)^{2}}[/tex]      Calculate

[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex]                      Calculate

[tex]\sqrt{25 + 36}[/tex]                            Calculate

Hence. the distance between points (5,6) and (10,12) is [tex]\sqrt{61}[/tex].

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The cost of feed for a cow in a month is $15.08

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

Similarly the ratio of the cost of cow's food to pig is 2:1

represent the cost of feed of a cow by x and the cost of feed for a pig to be y

therefore x= 2y

there are 46 cows, therefore the cost of feed for 46 cows is 46x

there are 22 pigs, therefore the cost of pig is 22y

46x+22y= 860

representing 2y for x

46(2y)+22y= 860

114y= 860

y= 860/114

y=$ 7.54

recall x=2y

x= 7.54×2= $15.08

therefore $15.08 is spent on a cow in a month

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The triangle does not exist, as the property, the sum of two sides of a triangle is greater than the third side length of the triangle does not hold true.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric forms is represented by the symbol △ and consists of three connected vertices. Triangles may be categorized into a number of different varieties according to their sides and angles.

It is a triangle's property that the sum of any two sides of a triangle is greater than the third side.

Here sides given are 3 m, 5 m, 9 m.

Let us add the sides length 3 m and 5 m

3 m + 5 m = 8 m

Compare this with the third-side length of the triangle

8 m < 9 m

So, the property does not hold true.

So, the triangle does not exist.

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The expression that shows the distance you would drive from the gym to the office along this road is b.|-6|+|4|

Distance is a numerical or qualitative measurement of the distance between two objects or points. Distance is defined as an object's total movement without regard for direction. The distance can be defined as how much ground an object has covered regardless of its starting or ending point.

To find the distance between two points in a number line we do the absolute value of the points subtracted. That is if we need to find the distance between point a and point b in a number line we do |a-b|.

Now, the Gym is at point -6 in the number line and the office is at point 4 in the number line, then the distance from -6 to 4 is |-6-4| = |-10| = 10.

Now, option a is |-6+4| ≠ |-6-4|.

The option b is |-6|+|4| = 6+4 = 10 =|-6-4|. Then, option b is correct.

Option c is -6+4 ≠ |-6-4|.

The option d is -|6|+|4| = -6+4 ≠ |-6-4|.

Then, the correct answer is b.

The complete question is given below.

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Complete question

Which expression shows the distance you would drive from the gym to the office along this road?

a.|-6 + 4|

b.|-6|+|4|

c.-6+4

d.-|6|+|4|

The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].

Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "."

The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].

Expressions using linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values might be either numerical, algebraic, or both.

The number of apps Kumiko buy is a and the number of games she can buy is g.

The gift card has 50$.

Total amount of apps = 1.25a

Total amount of games = 2.5g

So, the linear equality will be [tex]1.25a+2.5g\leq50[/tex].

She can can only games and apps for amount less than and equal to $50.

Therefore, The linear inequality representing the number of apps and games that Kumiko can buy is [tex]1.25a+2.5g\leq50[/tex].

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The given question is Incomplete. Here is the complete question:

Kumiko has a $50 gift card for a Web site that sells apps and games. Games cost $2.50 each, and apps cost $1.25 each. Write an inequality that represents the number of apps a and the number of games g that Kumiko can buy and describe any constraints.

The answer is 6 groups of 0.7 tenths is 4.2. in the decimal form.

What is Decimals?

Decimals are a form of a number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

6 groups of ____ tenths is 4.2

4.2 ÷ 6 = 0.7

Hence,  6 groups of 0.7 tenths is 4.2

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The time taken by the rocket to reach its maximum height is 1.25 seconds  and the maximum height is 32 feet.

Given equation:

h(t) = -16t^2+40t+7 and initial velocity is 40 feet per second and launching pad is 7 feet tall.

a = 1

t = -b/2a

= -40/2*-16

= -40/-32

= 40/32

= 1.25 seconds

h(2.5) = -16(1.25)^2+40*1.25+7

= -1.5625*16+50+7

= -25+57

= 32 feet.

Therefore The time taken by the rocket to reach its maximum height is 1.25 seconds  and the maximum height is 32 feet.

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The system of inequalities that best matches the graph is Option C

Step-by-step explanation:

To find the system of inequalities, we simply need to find the equation of each line.

Thus, let's find the inequality that is represented by each line.

Red Line:

First, let’s determine the slope. To do so, we can use the slope formula:

m = (y₂-y₁) / (x₂-x₁)

We can use any two points that's on the Red Line. Using (3, -2) and (6, -4) and substituting them into the slope formula yields:

m = (-4+2) / (6-3)    = -2/3

Therefore, the slope of the red line is 2.

To write the equation of the red line, we can use the slope-intercept form:

y = mx + c

Notice that our y-intercept of our red line is (0, 3). Therefore, b = 3 and we already determined that m = -2/3:

y = ((-2/3)x) + (-3)

y   = (-2/3)x -3

Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.

And since our line is shaded, our sign will be less than or equal to. Therefore:

y ≤ (-2/3)x - 3

Blue line:

Again, let’s first find the slope. We can use the two points (3,0) and (0, -3). Hence:

m = (-3-0) / (3-0)  = -3/3  = -1

So, the slope is -1.

We can now use the slope-intercept form. Notice that our y-intercept is (0, 0). Thus, we will substitute -1 for m and 0 for b. This yields:

y = -1x + 0

y = -x

Finally, we will determine our sign. Since the shaded region is above the blue line, our y is lesser than our equation. Therefore, our equation is:

y < -x

Thus, all together, our inequalities are:

y ≤ (-2/3)x - 3

y < -x

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The expression that is equivalent is y(x + 2) and xy + 2y and x(x + y + 2) and  x² + xy + 2x

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

y(x + 2) and xy + 2y

xy + 2y and xy + 2y

Therefore, the expressions are equivalent.

x(x + y + 2) and  x² + xy + 2x

x² + xy + 2x and x² + xy + 2x

They are equivalent expression.

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Answer:

[tex] - 8(9 - ( - 33 - 15) \div 12[/tex]

[tex] - 8(9 - ( - 48) \div 12[/tex]

[tex] - 8(9 + 4)[/tex]

[tex] - 8(13)[/tex]

[tex] - 104[/tex]

Answer:

-104

Step-by-step explanation:

Divide 108 by 12

Calculate -3 × 11 - 15 which is 48

Remove the parentheses

Divide 48 by 12 which is 4

9 + 4 is 13

-8 × 13 = -104

Answer:

[tex]-9 (9x -6) = 3 (4x+6) \\ - 9 \times 9x + 9 \times 6 = 3 \times 4x + 3 \times 6 \\ - 81x + 54 = 12x + 18 \\ -81x - 12x = - 54 + 18 \\ - 93x = - 36 \\ x = \frac{36}{93} \\ x = \frac{18}{46.5} \\ x = 0.3870967742[/tex]

Answer: C. (2, 1)

Step-by-step explanation:

The numbers labeled are

(-5, -8)

(-2, 1)

(4, 0)

(2, 9)

Find coordinates by looking at each line. (x, y)

The x-axis is the horizontal line in the middle.

The y-axis is the vertical line going across.

The x-axis always goes first when plotting down coordinates, and y goes second.

So, the one NOT labeled is C (2, 1)

Answer: $9.76

Step-by-step explanation: If you multiply f, the order of fries (5) by the cost of it ($1.08) you would get $5.40 & if you multiply d, the order of drinks (4) by the cost of it ($1.09) you would get $4.36. If you add up both the total numbers, you would get a final answer of $9.76.

Answer:

$9.76

Step-by-step explanation:

1.08f + 1.09d= Total

1.08(5)+1.09(4)= Total

5.40+4.36= Total

The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.

What is least common denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Given fractions are

2/3 and 8/11

L.C.M of 3 and 11 is 33.

We get,

2/3 ×11/11 = 22/33

and

8/11×3/3 = 24/33

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A 12-ounce can of beer contains the same amount of alcohol as a five-ounce glass of wine.

In a five-ounce glass of wine, the percentage of alcohol is 12%, which is the same in the 12-ounce can or bottle of beer, and 1.5 ounces of 86-proof liquor. Although a person under the influence of alcohol will have impaired judgment and therefore must avoid driving, doesn't matter what kind of alcoholic beverage they drink. Digestion of alcohol doesn't take place as soon as you drink it, it is absorbed in your bloodstream which reaches the brain and thus creates impaired judgment.

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The solution of the given equation [tex]y=6x+20[/tex] is [tex]x = \frac{y + 20}{6}[/tex]

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

We have,

                        [tex]y = 6x + 20[/tex]

Arrange the equation both sides so that all variable terms are on the left hand side.

                        [tex]6x - 20 = y[/tex]

Add 20 to both sides of the equation.

                   [tex](6x - 20) + 20 = y + 20[/tex]

                        [tex]6x = y + 20[/tex]

Divide both sides by 6 we get,

                          [tex]\frac{6x}{6} = \frac{y + 20}{6}[/tex]

                      ∴   [tex]x = \frac{y + 20}{6}[/tex]

Hence, final solution is [tex]x = \frac{y + 20}{6}[/tex] .

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The expected value of the sum of these events will be 2 / 3.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that the expected value for getting heads, on 30 coin tosses, is 15. The expected value for rolling a 1, after 30 die rolls is 5.

The probability of the sum will be calculated as,

P = ( 15 / 30 ) + ( 5 / 30 )

P =  ( 20 / 30 )

P = 2 / 3

Therefore, the expected value of the sum of these events will be 2 / 3.

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The circumference of the circle to the nearest hundredth is 21.98 inches.

The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.

The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.

The circumference of the circle can be found as follows:

circumference of a circle = 2πr

where

Therefore,

diameter of the circle = 7 inches

radius of the circle = 7 / 2 = 3.5 inches

Hence,

circumference of a circle = 2 × 3.14 × 3.5

circumference of a circle = 21.98 inches

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Salinity and density decrease as temperature rises. Salinity and density, therefore, have a negative relationship with temperature. The density rises as salinity rises. As the temperature drops, ocean water becomes denser. Therefore, water becomes denser as it becomes colder. The density of seawater also rises as salinity does.

Water that is less dense floats above water that is denser. The warmer water will float on top of the colder water if there are two layers of water with the same salinity. However, there is a catch! Salinity has less of an impact on water density than temperature does. Therefore, if the layer with higher salinity is considerably warmer than the layer with lower salinity, the layer with higher salinity can actually float on top of the layer with lower salinity.

As you descend to the ocean's bottom, the temperature of the water continues to drop. So, as you descend to the ocean's bottom, the density of the water keeps rising. The deep ocean is divided into layers, with the lightest water at the top and the densest water at the bottom. The ocean's depths have horizontal circulation. In other words, water flows in strata of equal density.

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8.08 percent of babies are born prematurely .

We have following information,

lengths of pregnancy of humans are Normally distributed.

mean of distribution ( μ ) = 268 days

standard deviations of distribution = 15 days

We shall find out the pecent of babies are born. prematurely.

Using the Normal distribution formula ,

Z = ( X - μ ) /σ

where X---> sample mean

μ --> poplution mean

putting the possble values of variables we get,

if a baby born three weaks early then he is considered as premature.

X = 21 , μ = 268 , r =

Z = ( 21-268)/ 15 = - 247/15 = - 16.4

Now, p-value corresponding to Z-value= -16.4 is

8.08..

thus for z= -16.4 , p-value will be 8.08 .. So, 8.08 percent of babies are born prematurely.

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Answer:717 calories

Step-by-step explanation:

first you need to find what one ounce would be:

430/12=35.83...

then you multiply the answer by 20

35.83*20=716.6...=717

Answer:

c = 11.46 yd

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ c² = (8.1)² + (8.1)²

→ c² = 65.61 + 65.61

→ c² = 131.22

→ c = √131.22

→ [ c = 11.46 yd ]

Hence, value of c is 11.46 yd.

The equation of the line is y = -3/4x + 10, the graph of the equation has been plotted

The slope of the line = -3/4

The slope of the line the change in y coordinate with respect to the change in x coordinate of the function

The line is passing through the point (0,10)

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

y-10 = -3/4(x-0)

y - 10 = -3/4x

y = -3/4x + 10

The equation of the line in slope intercept form is

y = -3/4x + 10

Plot the graph using the slope intercept form

Hence, the equation of the line is y = -3/4x + 10, the graph of the equation has been plotted

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The probability that Sara will pick a blue marker is 3/20.

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math's to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given,

the box contains red markers = 5

blue marker = 3

purple marker = 9

pink markers = 3

Total number of markers = 20

The probability that she picks blue marker = 3/20

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