A water tank is built in the form of a right rectangular prism, with dimensions that measure 13.1 ft by 7.5 ft by 7.2 ft. How many cubic feet of water would it hold when it is full? Round your answer to the nearest tenth if necessary.

Answer:

Sandwich = 2

Cookie = 1

Step-by-step explanation:

Let

This would mean :

3x + 2y = 8  and 7x + 2y = 16

Because we have two similar terms in the equations, (2y) we can subtract the two equations from each other cancelling out the terms resulting in us having one term that we can solve for. This is known as the elimination method

  7x + 2y = 16

-  3x + 2y  = 8

-----------------------

4x   +   0y   = 8

==> 4x = 8

==> x = 2

We can now plug in the value of x into one of the equations and solve for y

==> 7x + 2y = 16

==> 7(2) + 2y = 16

==> 14 + 2y = 16

==> 2y = 2

==> y = 1

We can conclude that the cost of a sandwich is 2 and the cost of a cookie is 1

The value of the angle x in the triangle is; x = 70°

Looking at the given image, it is clear that both triangles are similar triangles. This is because we see that after the duplicate, 2 sides apiece are equal.

Thus, the third angle bordering the center of the triangle with one angle as 15° is;

y = 180 - (15 + 20)

Since sum of angles in a triangle equals 180 degrees.

y = 180 - 35

y = 145°

Similarly,

z = 180 - (20 + 15)

z = 180 - 35

z = 145°

Now, sum of angles at a point is 360 degrees. Thus;

x = 360 - (145 - 145)

x = 70°

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[tex]~~~~~~~~~~~~\stackrel{\textit{\LARGE Sydney}}{\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}}}[/tex]

[tex]A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 100\\ r=rate\to 0.8\%\to \frac{0.8}{100}\dotfill &0.008\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=100\left[ \cfrac{\left( 1+\frac{0.008}{12} \right)^{12 \cdot 10}-1}{\frac{0.008}{12}} \right]\left(1+\frac{0.008}{12}\right) \\\\\\ A=100\left[ \cfrac{\left( \frac{1501}{1500} \right)^{120}-1}{\frac{1}{500}} \right]\left(\frac{1501}{1500}\right) \implies {\Large \begin{array}{llll} A \approx 12497.05 \end{array}}[/tex]

Total number of students is 70.

What do you mean by ratio?

A ratio is a comparison of two quantities. The ratio of a to b can also be expressed as:  a:b

A ratio is the equality of two ratios. Write ratios to help you find equivalent ratios and solve for unknown quantities.

Two common types of relationships are part-to-part and part-to-whole.

In a library, the ratio of students with younger siblings to those without younger siblings was 4:3

There were 42 students without younger siblings.

As the given ratio is 4:3

So, let the number of students with younger siblings  = 4x

let the number of students without younger siblings = 3x

There were 42 students without younger siblings.

3x = 42

x = 42/3

x = 14

Let y be the number of students with younger siblings

y = 4x = 4(14) = 56

Total students = students with younger siblings + students without younger siblings

= 14 + 56

= 70

Therefore, total number of students is 70.

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Answer:

1 hour

Step-by-step explanation:

Answer: 1hour

Step-by-step explanation: lol

Answer: Accounting profit=$90,000 and Economic profit loss= $28,500

Step-by-step explanation:

Accounting profit = Total revenue - Explicit costs Accounting profit = ($65 × 4,000) - ($50,000 + $120,000) Accounting profit = $260,000 - $170,000 Accounting profit = $90,000

Economic profit = Total revenue - (Explicit costs + Implicit costs) Economic profit = ($65 × 4,000) - ($50,000 + $120,000 + Forgone interest on savings + Forgone wages) Economic profit = ($65 × 4,000) - [$50,000 + $120,000 + (0.06 x $25,000) + $60,000] Economic profit (loss) = $28,500

Answer:

Below

Step-by-step explanation:

Any 5 points you want

pick out 5 values of x      say     -4    -1     0      3   7  

  and calculate the value of the corresponding 'y' using the equation....then plot those points

Answer:

Step-by-step explanation:

There a few ways to solve this system. Since each equation is set equal to y on the left side, that means that we can set the right side of each equation to be equal to each other. So,

3x - 4 = -2x + 6

This can now be solved for x:

5x - 4 = 6 (added 2x to each side)

5x = 10 (added 4 to each side)

x = 2 (divided each side by 5)

Now that we know what x must be, we can plug 5 in for x in either of the equations and solve for y:

y = 3(5) - 4

y = 6 -4

y=2

This means y should be 2. To make sure this answer is correct, we can plug our y and x numbers into the OTHER equation to see if it makes sense:

(2) = -2(2) + 6

2 = -4 + 6

2=2

That looks right, so x = 2 and y = 2

The value of p is -5

Simply use cross multiplication :

The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.

Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.

[tex]14p-8=22+20p\\or, 14p-20p=22+8\\or, -6p=30\\or, p=-\frac{30}{6} \\or, p= -5[/tex]

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The value of (1 + i)^5 is -2 * 2^1.5 * (1 + i). De Moivre's describes how the power of a complex number can be calculated using the properties of its modulus and argument.

De Moivre's theorem states that for any complex number z and any integer n, we have (z^n) = (r^n)(cos(nθ) + i * sin(nθ)), where r is the magnitude of z and θ is the angle that z makes with the positive real axis in the complex plane. Using this theorem, we can easily find the fifth power of 1+i as follows:

First, we need to express 1+i in polar form, which is given by z = r * cis(θ), where r is the magnitude of z and cis(θ) is the complex number with magnitude 1 and angle θ in the complex plane. In this case, we have z = 1+i = sqrt(2) * cis(π/4), where sqrt(2) is the magnitude of 1+i and cis(π/4) is the complex number with magnitude 1 and angle π/4 in the complex plane.

Next, we substitute this expression for z into the formula for (z^n) given by De Moivre's theorem, which gives us

(1 + i)^5 = √2^5 * (cos(5 * 45) + i * sin(5 * 45))

        = 2^2.5 * (cos(225) + i * sin(225))

(1 + i)^5 = 2^2.5 * (-cos(45) + i * -sin(45))

        = 2^2.5 * (-1 + i * -1)

        = -2 * 2^1.5 * (1 + i)

Therefore, the value of (1 + i)^5 is -2 * 2^1.5 * (1 + i).

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The measure of the smallest angle in the triangle is 10.8°

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.

The corresponding angles of the two equal lengths in an isosceles triangle are equal. This means that if we represent the two angles by x and the the third angle by y , then 2x+y = 180.

using cosine rule c² = a²+b²+2abcosC

a = 8, b = 8 and c = 3

3² = 8²+8²+2×8×8cos C

9 = 64+64+128cos C

128cosC = 9- 128

cos C = -119/128

cos C = -0.93

C = cos^-1 0.93

C = 158.4°

therefore 158.4 + A+ B = 180

A= B

2A = 180-158.4

2A = 21.6

A = 21.6/2

A = 10.8°

therefore A = B = 10.8°. This means the value of the smallest angle is 10.8°

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The value of x will be;

⇒ x = 4

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

On a Right triangle,

⇒ A = 18x - 2 , B = 20 , C = ?

Now,

Since, On a Right triangle,

One angle is at 90 degree.

Hence, C = 90°

Since,  A = 18x - 2 , B = 20 , C = 90°

Hence, We get;

⇒ 18x - 2 + 20 + 90 = 180

⇒ 18x - 2 + 110 = 180

⇒ 18x + 108 = 180

⇒ 18x = 180 - 108

⇒ 18x = 72

⇒ x = 4

Thus, The value of x will be;

⇒ x = 4

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The missing value after solving is 280 seconds .

Given :

james rode his bike 7 yards in 3 seconds. set up the table with the information you know. yards seconds 7 3 you got it!

Seconds :

The second ( s or sec ) is the International System of Units ( SI ) unit of time measurement.

Table :

yards           seconds

7                     3

120                 x

we need to find x :

1 yard = 7/3 seconds

120 yards = 7 / 3 * 120 seconds

= 7 / 1 * 40 seconds

= 7 * 40 seconds

= 280 seconds.

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Answer:

The property tax that must be paid on the lot is $864.

Step-by-step explanation:

The assessment value of the lot is $36,000, and the tax rate is 2.4 cents per $1, or 0.024. So the total amount of tax due is calculated as follows:

$36,000 * 0.024 = $<<36000*0.024=864>>864

Answer:

3 days.

Step-by-step explanation:

The first sentence states that Michael ate a whole bag in 3 days.  That's how long it will rtake him to eat a bag of candy, assuming it is the same size and tastiness as the first.

The simplified form of the given expression, (2c7)(9c), is 18c⁸

From the question, we are to simplify the given expression
The given expression is

(2c7)(9c)

First, we will write the expression properly

The given expression written properly is

(2c⁷)(9c)

Now, we will simplify the expression

Simplifying the expression

(2c⁷)(9c)

Multiply

2c⁷ × 9c

Collect like terms

2×9 × c⁷ × c

18 × c⁷⁺¹

18 × c⁸

18c⁸

Hence, the expression is 18c⁸

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28° & 62° are the measure of each acute angle.

What is acute angle and example?

Acute angles are defined as those that are less than 90 degrees. Compared to the right angle, this angle is smaller (which is equal to 90 degrees).

            For instance, acute angles include 30°, 45°, 60°, 75°, 33°, 55°, and 85°, among others.

In a right triangle we know that one of the angles is 90°. We also know that the 3 angles must add up to 180°.

Let x = acute angle 1

     y = acute angle 2

We have 2 unknowns, therefore we must have 2 equations to solve this.

Eq. I                                                       Eq. II

90 + x + y = 180                                  

x + y = 180 - 90                                    

x + y = 90

Using the value for x in terms of y from Eq. II in Eq. I we can solve for y:

x = 2y + 6                

x + y = 90                

2y + 6 + y =90        

3y = 90 - 6                

3y = 84                  

y = 84/3                    

y = 28                      

Using this value for y in Eq. II we can solve for x:

x = 2y + 6                

x = 2(28) + 6            

x = 56 + 6              

x = 62                      

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The complete question is -

In a right triangle, the measure of one acute angle is 2 times the sum of the measure of the other acute angle and 3. Find the measure of each acute angle

To find the sum of 52 + 23 is the value is worked to be 75

Combining things and counting them as one big group is done through addition.

In math, addition is the process of adding two or more integers together.

Addends are the numbers that are added, and the outcome of the operation, or the final response, is referred to as the sum.

In this problem the addends include

The applying the addition operation

= 52 + 23

= 45

The sum is solved to be 75

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The plane with an angle of depression of 70° is closer to the airport.

The distance between the plane and the airport is 15957 feet.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Two planes are flying at an altitude of 15,000 feet.

The angle of depression from one plane to the airport is 70°.

This means,

The distance of the plane from the airport.

Sin 70 = 15,000 / Distance

Distance = 15,000/ sin 70 = 15,000 / 0.94 = 15957 feet _____(1)

The angle of depression from one plane to the airport is 60°.

The distance of the plane from the airport.

Sin 60 = 15,000 / Distance

Distance = 15,000/ sin 60 = 15,000 / 0.87 = 17241 feet _____(2)

Thus,

The plane with an angle of depression of 70° is closer to the airport.

The distance between the plane and the airport is 15957 feet.

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Her total salary for the month would be $8300.

We have a women with $3,200 as a base salary each month. She gets 8.5% of everything she sells. If she sold $60,000 worth of items this month.

Assume her total salary to be y = $(3200 + x). Then, we can write -

y = $(3200 + {8.5/100} x 60000}

y = $(3200 + 5100)

y = $8300

Therefore, her total salary for the month would be $8300.

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In linear equation, Joshua should buy is 255 + 6s ≥ 333.

What is linear equation in math?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let the sets of spoons be represented by s

The restaurant needs at least 333 spoons.

Each set on sale contains 8 spoons

There are currently 333 spoons.

At least as an inequality is ≥

Hence:

255 + 6 × s ≥ 333

255 + 6s ≥ 333

Therefore, inequality tha can be used to determine s the minimum number of sets of spoons Joshua should buy is

255 + 6s ≥ 333

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The test is proved that hypothesis that the population mean is atleast 3-miles per gallon.

A hypothesis is the proposed explanation for any kind of  phenomenon.

So here are the values of X  BAR i=2.4. S is 1.8.

Our sample n =100.

The null hypothesis here is that mu is greater than or equal to 3.

Against the alternative hypothesis that  is less than three. Now the calculated value for the test statistic is going to be the  equal to X bar is in (-)  knots. That's 2.4 -3. divided by S over  2^2 of end. So 1.8 divided by the square root of the  100 gives us negative 3.33. So we can refer to that box of the T distribution and we are  get the value. The p value for the test is going to be less than 0.5. Therefore we have the  strong evidence that the not hypothesis is going to be the  read checked it.  So  therefore we can reject to the  null hypothesis and then it can accept the alternative by the  hypothesis that  is less than three. Where it is  here is the mean of the population, the noting the average increase per gallon.

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Answer:

n = -21

Step-by-step explanation:

Five More Than One Third Of A Number Is Negative 2 What Is The Number?

1/3n + 5 = -2

subtract 5 from both sides:

1/3n + 5 - 5 = -2 - 5

1/3n = -7

multiply both sides by 3:

3(1/3n) = 3(-7)

n = -21

ur not the smartest person

65,760,000

Answer:

x = 1 1/2

Step-by-step explanation:

1/3 x + 1/4 = 3/4

Solving for x

Subtract 1/4 from each side

1/3 x + 1/4 -1/4 = 3/4-1/4

1/3 x = 2/4

Simplify

1/3x = 1/2

Multiply each side by 3

1/3 x * 3 = 1/2 * 3

x = 3/2

Changing to a mixed number

x = 1 1/2

Answer:

[tex]\sf \frac{3}{2} = 1 \frac{1}{2} \\ [/tex]

Step-by-step explanation:

[tex] \sf \frac{1x}{3} + \frac{1}{4} = \frac{3}{4} \\ [/tex]

To solve easily, multiply the whole equation by it's LCM ( LCM of 3 & 4 is 12 ).

[tex] \sf12 \times ( \sf \frac{1x}{3} + \frac{1}{4} = \frac{3}{4} ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \\ \\ \sf \frac{1x}{3} \times 12 + \frac{1}{4} \times 12= \frac{3}{4} \times 12\\ \\ \sf \sf \frac{12x}{3} + \frac{12}{4} = \frac{36}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf4x + 3 = 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

And now solve for x.

First, subtract 3 from both sides.

[tex] \sf4x = 9 - 3 \\ \sf4x = 6[/tex]

Divide both sides by 4.

[tex] \sf \: x = \frac{6}{4} \\ [/tex]

To write the fraction in its simplest form, divide both the numerator and denominator by 2.

[tex] \sf \frac{3}{2} = 1 \frac{1}{2} \\ [/tex]

In the figure of triangles given figure C is not similar

Not similar

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

In figure  C no information is given about the angles hence they are not similar.

Figure B is similar by Side - Side - Side (SSS) and shows a proportion of 2

Figure D is similar by Side - Angle - Side (SAS), the include angle here are equal by vertical angle theorem

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The truth value of the ~[P v (Q v R)] >~ (S v P) is true.

Truth-value, in logic, is the degree to which a particular proposition or assertion is true (T or 1) or false (F or 0). Because the truth-value of a compound proposition is a function of, or a quantity depending upon, the truth-values of its component components, logical connectives like disjunction and negation can be conceived of as truth-functions.

Given, ~[P v (Q v R)] >~ (S v P) since P v (Q v R) is true, thus ~ [ P v ( Q v R ) ] is false, therefore the implication is true.

⇒~[T v (F v T)] >~ (F v T)

⇒[F v (F v T)]>(T v T)

⇒[F v (F v T)]>(T v T)

⇒F v T

⇒T

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