What is the volume of the following rectangular prism?

Answer:

a) The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms, b) The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.

Step-by-step explanation:

a) The total weight of fruits ([tex]m_{T}[/tex]) is calculated by the following formula:

[tex]m_{T} = m_{a} + m_{m}+m_{o}[/tex]

Where:

[tex]m_{a}[/tex] - Total weight of apples, measured in kilograms.

[tex]m_{m}[/tex] - Total weight of mangoes, measured in kilograms.

[tex]m_{o}[/tex] - Total weight of oranges, measured in kilograms.

If [tex]m_{a} = 1\,\frac{1}{2} \,kg[/tex], [tex]m_{m} = 5\,\frac{1}{4}\,kg[/tex] and [tex]m_{o} = 1\,\frac{1}{2}\,kg[/tex], then:

[tex]m_{T} = 1\,\frac{1}{2}\,kg + 5\,\frac{1}{4}\,kg + 1\,\frac{1}{2}\,kg[/tex]

[tex]m_{T} = \frac{6}{4}\,kg + \frac{21}{4}\,kg + \frac{6}{4}\,kg[/tex]

[tex]m_{T} = \frac{33}{4}\,kg[/tex]

[tex]m_{T} = 8\,\frac{1}{4}\,kg[/tex]

The total weight of fruits is [tex]8\,\frac{1}{4}[/tex] kilograms.

b) The weight eaten by her family is determined by the following expression:

[tex]m_{E} = m_{a,e} + m_{m,e} + m_{o,e}[/tex]

Where:

[tex]m_{a,e}[/tex] - Eaten weight of apples, measured in kilograms.

[tex]m_{m,e}[/tex] - Eaten weight of mangoes, measured in kilograms.

[tex]m_{o,e}[/tex] - Eaten weight of oranges, measured in kilograms.

Given that [tex]m_{a,e} = \frac{3}{4}\,kg[/tex], [tex]m_{m,e} = 2\,\frac{1}{2}\,kg[/tex] and [tex]m_{o,e} = \frac{1}{2}\,kg[/tex], the weight eaten by her family is:

[tex]m_{E} = \frac{3}{4}\,kg + 2\,\frac{1}{2}\,kg + \frac{1}{2}\,kg[/tex]

[tex]m_{E} = \frac{3}{4}\,kg + \frac{10}{4}\,kg + \frac{2}{4}\,kg[/tex]

[tex]m_{E} = \frac{15}{4}\,kg[/tex]

[tex]m_{E} = 3\,\frac{3}{4}\,kg[/tex]

The weight of the fruits left is found by subtraction:

[tex]m_{R} = m_{T}-m_{E}[/tex]

[tex]m_{R} = 8\,\frac{1}{4} \,kg -3\,\frac{3}{4}\,kg[/tex]

[tex]m_{R} = \frac{33}{4}\,kg-\frac{15}{4}\,kg[/tex]

[tex]m_{R} = \frac{18}{4}\,kg[/tex]

[tex]m_{R} = 4 \,\frac{1}{2}\,kg[/tex]

The weight of the fruits left is [tex]4\,\frac{1}{2}[/tex] kilograms.

Answer:

y=6x-23

Step-by-step explanation:

-5=6(3)+b

-5=18+b

b=-23

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Answer:

6x-23

Step-by-step explanation:

Step-by-step explanation:

distance around the running track means to find the perimeter of whole solid figure

radius(r) = 30/2 =15m

perimeter = 50+ pi× r + 50+ pi × r

= 100 + 2 × pi ×r

= 100 + 2× 22÷7 × 15

= 1360/ 7 m

= 194.285 m

Answer:

6x^2 + 15

Step-by-step explanation:

We don't know what the square of a number is, so we represent it as x^2

The first part tells us to find the product of 6 and the square of a number, so

6x^2

The second part tells us to add 15 so,

6x^2 + 15

The expression that should be represented is [tex]6x^2 + 15[/tex]

Given that

Based on the above information,

Let us assume the number should be x

So, from the above information, the expression should be [tex]6x^2 + 15[/tex]

Therefore we can conclude that The expression that should be represented is [tex]6x^2 + 15[/tex]

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Answer:

A) The number halfway between -2 and 6 is 2.

B) -10 is halfway between -18 and 8

Answer:

p = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given

p = [tex]\frac{x^2-y^2}{x^2+xy}[/tex] ( factorise numerator and denominator )

x² - y² ← is a difference of squares and factors as (x - y)(x + y)

x² + xy ← factor out x from each term

= x(x + y) , thus

p = [tex]\frac{(x-y)(x+y)}{x(x+y)}[/tex] ← cancel (x + y) on numerator/ denominator

   = [tex]\frac{x-y}{x}[/tex] ← substitute x = - 4, y = - 6

   = [tex]\frac{-4-(-6)}{-4}[/tex]

   = [tex]\frac{-4+6}{-4}[/tex]

    = [tex]\frac{2}{-4}[/tex] = - [tex]\frac{1}{2}[/tex]

Answer:

list in the explanation

Step-by-step explanation:

BOOT x2

SKINNY x2

RELAXED x2

BOOT, SKINNY

BOOT, RELAXED

SKINNY, BOOT

SKINNY, RELAXED

RELAXED, BOOT

RELAXED, SKINNY

The solution set is given by Set A = { BB , SS , RR , BS , BR , SR } , where B , S and R are boot cut (B), skinny (S), and relaxed fit (R) respectively

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set be represented as A

Now , the equation will be

Marcus is shopping for pants and the available pants are boot cut (B), skinny (S), and relaxed fit (R)

He wants to buy 2 pair of pants , and the possible ways of 2 pants are

Set A = { BB , SS , RR , BS , BR , SR }

So , the total number of elements in set A = 6 pairs

Therefore , the value of A is 6 pairs

Hence , the set A is { BB , SS , RR , BS , BR , SR }

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Answer:

98

Step-by-step explanation:

So we have the two functions:

[tex]g(x)=-2x-2\text{ and } r(x)=x^2-2[/tex]

And we want to find the value of r(g(4)).

To do so, first find the value of g(4):

[tex]g(x)=-2x-2\\g(4)=-2(4)-2\\[/tex]

Multiply:

[tex]g(4)=(-8)-2[/tex]

Subtract:

[tex]g(4)=-10[/tex]

Now, substitute this into r(g(4)):

[tex]r(g(4))\\=r(-10)[/tex]

And substitute this value into r(x):

[tex]r(-10)=(-10)^2-2[/tex]

Square:

[tex]r(-10)=100-2[/tex]

Subtract:

[tex]r(-10)=98[/tex]

Therefore:

[tex]r(-10)=r(g(4))=98[/tex]

Answer:

Step-by-step explanation:

Answer:

10:5 OR 2:1

Step-by-step explanation:

Let x be the parts of 25% dextrose and

y be the parts of 10% dextrose are mixed so that

20% dextrose mixture is obtained.

amount of dextrose in the mixture will be 20% of (x+y).

We have to find the value of [tex]\frac{x}y \ OR\ x:y[/tex]

Now, we can apply the concept that sum of amount of dextrose in the two liquids will be equal to the amount of dextrose in the mixture.

[tex]\Rightarrow x \times 25\% + y \times 10\%=(x+y)\times 20\%\\\Rightarrow x \times\dfrac{25}{100} + y \times \dfrac{10}{100}=(x+y)\times \dfrac{20}{100}\\\Rightarrow x \times25 + y \times 10=(x+y)\times 20\\\Rightarrow 25x + 10y=20x+20y\\\Rightarrow 25x -20x =20y-10y\\\Rightarrow 5x=10y\\\Rightarrow \dfrac{x}{y} = \dfrac{10}{5}\\\Rightarrow \bold{x:y=10:5\ OR\ 2:1}[/tex]

So, the answer is 10:5 or 2:1.

Answer:

4.90% is approximately the new Dextrose concentration.

Explanation:

Volume by Volume percent is given by ;

Volume percentage of dextrose solution = 5%

In 100 mL of solution 5 ml of dextrose is present.

Now, volume sterile water added was equal to the 40% of volume of dextrose volume.

So, volume of the sterile water added =  

Total volume of the solution after addition of water = 100 mL + 1 mL = 102 mL

New concentration of dextrose will be;

4.90% is approximately the new Dextrose concentration.

Step-by-step explanation:

Answer:

60 miles per hour

Step-by-step explanation:

Total distance= 180 miles

Total time =3 hours

Average rate of change= ?

Distance= Rate × time

Make Time the subject of the formula

Time= Distance / Rate

Make average rate of change the subject of the formula

Average rate of change = Distance / time

= 180 miles / 3 hours

= 60 miles per hour

Answer:

The correct option is;

2. (750 - w)(13) = d (750 + w)(11) = d - 250

Step-by-step explanation:

The items with information given are;

The cruising speed of the planes = 750 km/h

The first plane flies against a constant headwind = w

The second plane flies against a constant tailwind  in magnitude to the headwind

The time duration of flight of the first plane = 13 hours

The time duration of flight of the second plane = 11 hours

The distance flown by the second plane = The distance flown by the first plane - 250 km

When we take the headwind magnitude as, w and the distance flown by the first plane as d, we have;

Speed of flight of the first plane = 750 - w

Speed of flight of the second plane = 750 + w

Therefore, the distance flown by the first plane in 13 hours is given as follows;

(750 - w) × (13) = d

Then we have;

The distance flown by the second plane in 11 hours is (750 + w) × (11) = d.

The correct option is (750 - w)(13) = d, (750 + w)(11) = d - 250

Answer:

Step-by-step explanation:

Hello, please consider the following.

The "vertex form" is as below.

[tex]y=a(x-h)^2+k\\\\\text{Where (h, k) is the vertex of the parabola.}\\[/tex]

Let's do it!

[tex]f(x)=\dfrac{1}{2}x^2+3x-2\\\\f(x)=\dfrac{1}{2}\left(x^2+3*2*x\right) -2\\\\f(x)=\dfrac{1}{2}\left( (x+3)^2-3^2\right)-2\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9}{2}-\dfrac{4}{2}\\\\f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{9+4}{2}\\\\\large \boxed{\sf \bf \ \ f(x)=\dfrac{1}{2}(x+3)^2-\dfrac{13}{2} \ \ }[/tex]

Thank you.

Answer:

D. All real numbers

Step-by-step explanation:

The domain is the set of values that can be used for x. There is no restriction on x, so the domain is all real numbers.

Answer:

all real numbers

Step-by-step explanation:

The domain is the possible input values

Since x can be any value, the domain is all real numbers

Answer:

The angles are 63 , 97

Step-by-step explanation:

Let one angle be x

As sum of two angles is 160, the other angle = 160 - x

Their difference  = 34

x - [160- x] = 34

Use distributive property to remove the brackets

x - 160 + x = 34

Add like terms

x + x - 160 = 34

2x - 160 = 34

Add 160 to both sides

2x  = 34 + 160

2x = 194

Divide both sides by 2

2x/2 = 194/2

x = 97°

One angle = 97°

Other angle = 160 - 97 = 63°

Answer:

Step-by-step explanation:

Step1: find the interval of roots. Consider -3 and -2

[tex]f(-3) = -7 <0[/tex]

[tex]f(-2) = 18 >0[/tex]

Hence, the root must be on [-3,-2]

Step2:  consider the middle point -2.5

[tex]f(-2.5) = 3.875 >0[/tex]

Then, the root must be on [-3, -2.5]

Step 3: Repeat step 2 by finding the value of f at the middle point -2.75

[tex]f(-2.75) = -1.0468 <0[/tex]

Step 3: Repeat step 2 by finding the value of f at the middle point of the interval [-2.75,-2.5] which is -2.625

[tex]f(-2.625) = 1.537 >0[/tex]

Step4: Repeat step 2 on [-2.75, -2.625]

Repeat step 2 until you got the root which is -2.701

Step-by-step explanation:

[tex]c^{2} = {a}^{2} + { b}^{2} [/tex]

Pythagoras theorem

x²=12² + 5²

x²=144+25

x²=169

[tex]x = \sqrt{169} [/tex]

x=13

Answer:

x = 13

Step-by-step explanation:

Using the Pythagorean Theorem to find the missing hypotenuse side:

[tex]a^2+b^2=c^2[/tex]

12 and 5 are a and b. 'x' would be c.

[tex]12^2+5^2=c^2\\\\12^2=144\\5^2=25\\\\144+25=c^2\\\\169=c^2\\\\\sqrt{169}=\sqrt{c^2}\\\\\boxed{13=c}[/tex]

'x' should be equal to 13.

Answer:

Step-by-step explanation:

You cannot add these because they are not like. IF you have a value for x, then the expression could be evaluated at the x value, but you can't add them.

Answer:

Step-by-step explanation:

a). 'Per ml' cost of the small size = [tex]\frac{\text{Sale price of small cane}}{\text{Amount of liquid}}[/tex]

                                                       = [tex]\frac{4.50}{250}[/tex]

                                                       = $0.018

'Per ml' cost of the medium size = [tex]\frac{\text{Sale price of medium cane}}{\text{Amount of liquid}}[/tex]

                                                        = [tex]\frac{9.95}{500}[/tex]

                                                        = $0.0199

     'Per ml' cost of the large size = [tex]\frac{\text{Sale price of large cane}}{\text{Amount of liquid}}[/tex]

                                                      = [tex]\frac{16.95}{1000}[/tex]

                                                      = $0.01695

Therefore, expression to compare per ml cost of three containers will be,

$0.0199 > $0.018 > $0.01695  

b). Least expensive way to buy the cleaner is to choose the container with least per ml cost.

Cost of 1500 ml cleaner = Cost of 1000 ml cleaner + Cost of 500 ml of cleaner

                                        = Cost of 1000 ml cleaner container + Cost of 'n' containers of 250 ml container

Total cost of 1500 ml = $16.95 + $4.50n

                                    = 16.95 + 2(4.5) [For n = 2]

                                    = $25.95

c). Most expensive way to purchase 1500 ml cleaner is to choose the most expensive cleaners

Cost of 1500 ml cleaner = Cost of 'n' containers of medium size containers

                                        = 9.95(n)

                                        = 9.95(3)

                                        = $29.85

Answer:

Step-by-step explanation:

convert mixed fraction into improper fraction

[tex]5\frac{3}{4}=\frac{23}{4}\\\\\\3\frac{7}{8}=\frac{31}{8}\\\\5\frac{3}{4}-[-3\frac{7}{8}]=\frac{23}{4}+\frac{31}{8}\\\\=\frac{23*2}{4*2}+\frac{31}{8}\\\\=\frac{46}{8}+\frac{31}{8}\\\\=\frac{46+31}{8}\\\\\\=\frac{77}{8}\\\\=9\frac{5}{8}[/tex]

Answer:

9 5/8.

Step-by-step explanation:

5 3/4 - (-3 7/8)

= 5 3/4 + 3 7/8

= 5 + 3 + 3/4 + 7/8

= 8 + 3/4 + 7/8    

The LCD of 4 and 8 is 8 so we get

8 + 6/8 + 7/8

= 8 + 13/8

= 8 + 1 5/8

= 9 5/8.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Answer: Hi!

The solution to positive 6 and -6 is 0. A negative and a positive of the same absolute value cancel out.

Hope this helps!

Answer:

the answer is zero !

Step-by-step explanation:

when a negative and a positive of the same number  go against each other they cancel out

We simplify the expression by subtracting 1 from 8, resulting in 7. We then multiply 7 by -2 to obtain the final answer of -14.

To simplify the given expression, -2(8 - 1), we can start by evaluating the expression inside the parentheses,

8 - 1 = 7

Now, we substitute this value back into the original expression:

-2(7)

Multiplying -2 by 7, we get:

-2 * 7 = -14

Therefore, -2(8 - 1) simplifies to -14.

In this case, we simplified the expression inside the parentheses first and then applied the multiplication operation. It's important to remember that when there is a negative sign in front of parentheses, it distributes to each term inside the parentheses. So, -2 multiplied by 8 gives -16, and -2 multiplied by -1 gives +2. The sum of -16 and +2 is -14.

In summary, when we evaluate the expression -2(8 - 1), the result is -14. This means that if we follow the order of operations (parentheses first, then multiplication), we simplify the expression by subtracting 1 from 8, resulting in 7. We then multiply 7 by -2 to obtain the final answer of -14.

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Answer:

68 square cm

Step-by-step explanation:

Interior square WXYZ is making four right triangles of equal bases (8 cm) and heights (2 cm) inside the square ABCD. Therefore,

Area of shaded Square = Area of square ABCD - 4 times area of one right triangle.

[tex] = {10}^{2} - 4 \times \frac{1}{2} \times 8 \times 2 \\ = 100 - 32 \\ = 68 \: {cm}^{2} [/tex]

Answer:

3.625 gpm

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is not properly written. Find the correct question below.

If x – 5y = -15 . Complete the missing value in the solution to the equation (-5, ____)

Let the coordinate of the variables be (x, y). Comparing the coordinates (x, y) with the given coordinate (-5, __), we will discover that x = -5. To get the y coordinate, we will substitute x = -5 into the given expression as shown;

If x – 5y = -15

-5 - 5y = -15

Adding 5 both sides

-5-5y+5 = -15+5

-5y = -10

Dividing both sides by -5;

-5y/-5 = -10/-5

y = 2

Hence the missing value in the solution of the equation is 2. The coordinate will be (-5, 2)

Answer:

2

Step-by-step explanation:

I did the khan :)

Answer:

The graph f(x) was shifted 3 units to the right and shifted 2 units up to get the graph of g(x).

Step-by-step explanation:

From the original graph to the transformed one, we can see that the transformations (x - 3) and + 2 were added to the equation.

The (x - 3) means that the x-value of the vertex will increase by 3, meaning that the graph will shift 3 units to the right.

The +2 will increase the y-value of the vertex by 2, meaning that the graph will move up 2 units.

So, the graph of g(x) relates to f(x) as it is a transformation 3 units to the right and 2 units upwards.

Answer:Answer:

[tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]

Step-by-step explanation:

Given the sequence -4,-6,-8..., in order to get sigma notation to represent the sum of the first seven terms of the sequence, we need to first calculate the sum of the first seven terms of the sequence as shown;

The sum of an arithmetic series is expressed as [tex]S_n = \frac{n}{2}[2a+(n-1)d][/tex]

n is the number of terms

a is the first term of the sequence

d is the common difference

Given parameters

n = 7, a = -4 and d = -6-(-4) = -8-(-6) = -2

Required

Sum of the first seven terms of the sequence

[tex]S_7 = \frac{7}{2}[2(-4)+(7-1)(-2)]\\\\S_7 = \frac{7}{2}[-8+(6)(-2)]\\\\S_7 = \frac{7}{2}[-8-12]\\\\\\S_7 = \frac{7}{2} * -20\\\\S_7 = -70[/tex]

The sum of the nth term of the sequence will be;

[tex]S_n = \frac{n}{2}[2(-4)+(n-1)(-2)]\\\\S_n = \frac{n}{2}[-8+(-2n+2)]\\\\S_n = \frac{n}{2}[-6-2n]\\\\S_n = \frac{-6n}{2} - \frac{2n^2}{2}\\S_n = -3n-n^2\\\\S_n = -n(3+n)[/tex]

The sigma notation will be expressed as [tex]\sum\left {{7} \atop {1}} \right -n(3+n)[/tex]. The limit ranges from 1 to 7 since we are to  find  the sum of the first seven terms of the series.