A water tank initially contained 65 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 109 seconds? Round answers to the nearest whole liter.

Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.

What is the relation between power and base?

Compare  7² and 2⁷.

7 ≠ 2

So, write the power as repeated multiplication of the given expression:

7²  = 7 * 7

2⁷ = 2*2*2*2*2*2*2

Evaluate:

7² = 49

2⁷ = 128

Compare the values:

128 > 49

2⁷ > 7²

Hence, Write each power as repeated multiplication. Then evaluate and compare their values is the correct option to compare the value of each expression.

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Answer:

Step-by-step explanation:

If a number is squared and then divided by 15, the resulting expression can be written as (x^2)/15, where x is the number. For example, if the number is 5, then the expression can be written as (5^2)/15 = 25/15. In general, the value of the expression (x^2)/15 will be the square of the number x divided by 15.

Answer:

64/100

Step-by-step explanation:

Answer: 16/25or64/100

Step-by-step explanation: 64/100 and divide it by 4 . To change a percent to a fraction, put the percentage over 100 (after removing the % sign) and simplify if necessary

The total cost of installing a fence around all sides of the rectangular yard would be $38250.

What is the area of the rectangle?

For the dimensions of the rectangle of length 'l' and breadth 'b', the area can be computed by using the formula,

           Area = Length ×  Breadth

Given data:

The length of the yard is 90 feet. and the breadth is 50 feet.

Area of the yard = length * breadth

                           = 90 * 50

                           = 4500 square foot

Now per square foot, the cost is $8.50 so the total cost of installing a fence around all sides of the yard would be = 4500 * 8.5

                                                                          = $38250.

Hence, the total cost of installing a fence around all sides of the rectangular yard would be $38250.

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Answer:

1: 50

2: 1

3: 2

4: 36

5: 0

6: -12

7: -2

8: 3

Step-by-step explanation: Use PEMDAS

P: Parentheses

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

Answer:

5, -11. -3, 8. 10, 17. -15, 13.

Step-by-step explanation:

All you have to do is switch x and y

The equivalent expressions are 16a + b, 17b + 11a, and 17b.

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.

In general, if anything is considered equal then the two of them are said to be equivalent. Similarly to this, if any two or more algebraic equations have identical solutions or roots then the equations are Equivalent expressions even they look different.        

Here we have

Expressions

3a +b +13a

20b +11a -3b

20b -5b +2b  

To simplify given expressions add or subtract like terms as given below

3a +b +13a => (3a+13a) +b = 16a + b

Therefore,

The equivalent expression of 3a +b +13a is 16a + b        

20b +11a -3b => (20b-3b) + 11a = 17b + 11a

Therefore

The equivalent expression of 20b +11a -3b is 17b + 11a  

20b-5b+2b => 20b+2b - 5b = 22b -5b = 17b

Therefore,

The equivalent expression of 20b-5b+2b is 17b

Therefore,

The equivalent expressions are 16a + b, 17b + 11a, and 17b.

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The angles of the cyclic quadrilateral and the arc angle is as follows:

A cyclic quadrilateral is a quadrilateral drawn inside a circle. In other words, a cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.

A cyclic Quadrilateral's opposite angles add to 180°.

Therefore,

∠PSR = 180 - 93 = 87 degrees.

An inscribed angle is one-half of the measure of the arc that it intercepts.

Therefore,

87 = 1 / 2 arc PQR

cross multiply

arc PQR = 87 × 2

arc PQR  = 174 degrees

Hence,

arc QR = 174 - 126

arc QR = 48 degrees

arc RS = 360 - 90 - 174

arc RS = 96 degrees.

∠QPS = 1 / 2 (96 + 48)

∠QPS = 1 / 2 (144)

∠QPS = 144 / 2

∠QPS = 72 degrees

∠SRQ = 180 - 72

∠SRQ = 108 degrees

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Answer:    

   48°

   96°

    72°

    87°

   108°

Step-by-step explanation:

   arc QR = 48°

   arc RS = 96°

   ∠QPS = 72°

   ∠PSR = 87°

   ∠SRQ = 108°

Using Pythagorean Theorrem the length of AE = 46 units

What is a Right Angle Triangle?

A right triangle or right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Solution:

In Triangle ABC using Pythagorean Theorem

AC = √(21*21 + 20*20)

AC = √841

AC = 29

In Triangle CDE using Pythagorean Theorem

CE = √(8*8 + 15*15)

CE = √289

CE = 17

From the figure we can say that AE = AC + CE

AE = 29 + 17

AE = 46 units

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The next time they will meet again is 08:44 (next day)

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

EZPlanes Airways depart = every 264 minutes

Bryanair Airlines depart = every 198 minutes

Both airlines depart = at 06:20

Using the above as a guide, we have the following departure times

EZPlanes Airways depart = 264, 528, 792, 1056, 1320, 1584, 1848, 2112, 2376 and 2640 minutes,

Bryanair Airlines depart = 198, 396, 594, 792, 990, 1188, 1386, 1584, 1782 and 1980 minutes

The common departure time in the above is

Time = 1584 minute

So, we have

Common departure time = 06:20 + 1584 minutes

Evaluate the sum

Common departure time = 06:20 + 26 hours + 24 minutes

Evaluate the sum

Common departure time = 08:44 (next day)

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The roots of the quadratic equation 3y² + 3(4y² - 2) is ± √(1/7).

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, 3y² + 3(4y² - 2).

3y² + 12y² - 2.

14y² - 2.

Let 14y² - 2 = 0.

14y² = 2.

y² = (2/14).

y = ± √(2/14) Or ± √(2/2×7) Or ± √(1/7).

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The equation of the line that passes through the point (3,4) and has an undefined slope is y = 3

An undefined slope is an infinite slope. This is the slope of a vertical line. The x values never changes no matter the changes in the y values.

The equation of a line in slope intercept form can be represented as follows:

y = mx + c

where

m = slope

c = y-intercept

Since the slope, m is undefined, the expression that has an undefined slope is a vertical line

Therefore,

y = 3

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Answer:

The possible values of k are -0.56, -3.56, -2 and -1.

Step-by-step explanation:

We have the equation of the parabola, .

Substituting x=0, we get that  i.e. y = -1.5k

So, the y-intercept is (0,-1.5k).

Thus, the height of the triangle becomes |-1.5k| = 1.5k

Again, substituting y=0,  i.e.  i.e. x=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.

We see that 'k' cannot be 0 or -3 as if k=0, then height = 0, which is not possible. If k= -3, then the base = 0, which is also not possible.

As, area of a triangle = .

Substituting the values, we get,

1.5=

i.e.

i.e. k = -0.56 and k = -3.56

or

1.5=

i.e.

i.e. k = -2 and k = -1.

Thus, the possible values of k are -0.56, -3.56, -2 and -1.

Answer:

70

Step-by-step explanation:

Substitute the value -3 into the expression and simplify:

10(4 - -3)

10(4 + 3)

10(7)

70

Answer

hello I have provided a picture of the answer

Step-by-step explanation:

ur welcome and have a nice day

The required solution (1, 4) of a linear system of the equation is determined by the elimination method.

Given the linear system of equations:

8x - 2y = 0 or 4x - y = 0 …(i)

-6x + 14y = 50 or -3x + 7y = 25 …(ii)

Equations (i) and (ii) constitute a system of two first-degree equations in the two variables x and y.

So, we have to find out the value of 'x’ and 'y’.

By multiplying 7 by equation (i) and adding both equations

28x - 7y -3x + 7y = 25

25x = 25

x = 25/25

x = 1

Substitute the value of x = 1 in the equation (i), and solve for y

4(1) - y = 0

y = 4

Hence, the required solutions are x = 1 and y = 4.

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The required distance between the points  (−1,6) and (−1,7). is 1 unit.

Given that,
using the distance formula to evaluate the distance between the points  (−1,6) and (−1,7).

Distance is defined as the object traveling at a particular speed in time from one point to another.

Here,
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
Substitute the values in the above equation,
D = √[[-1 + 1]² + [7 - 6]²]
D = √[0 + 1]
D = 1

Thus, the required distance between the points  (−1,6) and (−1,7). is 1 unit.

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Answer:

1.25 es la respuesta

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

Each picture costs $7.50

One time shipping cost = $3.25

Total cost of the order = $85.75

To FInd:

An equation to determine the number of pictures ordered.

Solution:

Define x:

Let x be the number of pictures bought.

Let y be the total amount of money collected.

Form the equation:

The $3.25 one time shipping cost is a fixed cost.

The $7.50 is a variable cost depending on the number of pictures ordered.

Therefore the equation:

⇒ y = 3.25 + 7.5x

Find the number of pictures bought.

The total cost is $85.75

3.25 + 7.5x = 85.75

7.5x = 82.50

x = 11

Answer: The equation is y = 3.25 + 7.5x and Todd bought 11 pictures.

(a) Minimum payment to be paid is $22

(b) Minimum payment to be paid is $35

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.

The formula for simple interest is:

Simple Interest=P×R×T

where:

P=Principal Amount

R=Daily interest rate

T=Number of days between payments​

(a)The minimum monthly payment is calculated by taking 1.5 percent of the outstanding principle

(0.015) ×$ (677+452+139+141) = $21.135

as there is no additional interest due.

The minimum monthly payment required on December 1 is $22, rounded up to the nearest whole dollar.

(b) The minimum monthly payment will be equal to 1.5 percent of the outstanding principle plus the new interest charges.

We will apply the simple interest formula, S.I = p×r×t, to get his new interest costs.

Because Dec contains 31 days, the

Principle amount, p = (677+452+139+141) - 300 = 1109,

the rate, r = 0.05163% each day

Time, t = 31 days.

S.I =p×r×t=1109×0.0005163×31= $17.75

0.015×1109 = 16.64, which is 1.5 percent of the outstanding amount.

To reach $17.75 + $16.64 = $34.39, we must now add the additional interest to 1.5 percent of the outstanding principal.

The minimum monthly payment required on January 1 is $35, rounded up to the next whole dollar.

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The number of One-person tubes and two-person tubes is 3 and 12 respectively.

It is the basic arithmetic operation, in which you are separating the number into some parts.

Given:

A group spends $277.50 to rent 15 tubes for a float down the Lchetucknee River. One-person tubes cost $12.50 and two-person tubes cost $20.

The equation can be written as,

12.5x + 20y = 277.5

Here, x is the number of One-person tubes and y is two-person tubes.

Also, x + y = 15

Solve the above equation by elimination method,

x = 3 and y = 15 - 3 = 12

Therefore, the number of One-person tubes and two-person tubes is 3 and 12 respectively.

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Evan's error was that he subtracted  -2 1/2 from 4, and thus he got  6 1/2.  On adding he would be getting  1 1/2

A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.

It is given that Evan added -2 1/2 and 4 but got 6 1/2

The mistake that Evan did was instead of adding, he substracted -2 1/2 from 4, and thus he got 6 1/2. This is because

4 -  (-2 1/2)

= 4 + 2 1/2

=  6 1/2

This is wrong as he was asked to add -2 1/2 and 4 not to subtract.

Therefore, on adding -2 1/2 and 4, we get,

= 4 - 2 1/2

= 1 1/2

Evan's error was that he subtracted  -2 1/2 from 4, and thus he got 6 1/2         .  On Evan's error was that he subtracted  from 4, and thus he got          .  On adding he would be getting  1 1/2

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The point at which the given lines intersect is (6,0,2) and an equation of the plane that contains these lines is x+y=6.

(a) In the given question we have to find the point at which the given lines intersect.

r = [3,3,0] + t[3,-3,2]

r = [6,0,2] + s[-3,3,0]

The equations of the lines can be written as :

The points for first line is

L(1)⟹x=3+3t, y=3-3t, z=0+2t and

The points for second line is

L(2)⟹x=6-3s , y=0+3s , z=2+0s .

Set the z coordinates equal from the line one and two, and we get :

2t = 2

Divide by 2 we get

t=1 .

Substitute the value of t into the point of x of first line :

x=3+3(1)

x=3+3

x=6

Equating the value of x equal to the coordinate of x of line two

6=6-3s

Subtract 6 on both side, we get

-3s=0

s=0

Now substitute the value of t into the point of y of first line:

y=3-3(1)

y=3-3

y=0

Equating the value of y equal to the coordinate of y of line two

0=0+3s

s=0

Now substitute the value of t into the point of z of first line:

z=0+2(1)

z=2

Equating the value of z equal to the coordinate of z of line two

2=2+0(s=0)=2 .

We thus have the point of intersection is :

P=(x,y,z)

P=(6,0,2)

Hence, the point at which the given lines intersect is (6,0,2)

(b) The direction vector for the first line is

[tex]\vec{v_{1}}=3\hat{i}-3\hat{j}+2\hat{k}[/tex]

and the direction vector for the second line is

[tex]\vec{v_{2}}=-3\hat{i}+3\hat{j}+0\hat{k}[/tex]

We can find a normal vector to the line as :

[tex]\vec{N_{1}}=\vec{v_{1}}\times\vec{v_{2}}[/tex]

[tex]\vec{N_{1}}=\begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\-3 &3 &-2 \\ -3 &3 & 0 \end{vmatrix}[/tex]

[tex]\vec{N_{1}}=\hat{i}(0-(-6))-\hat{j}(0-6)+\hat{k}(-9-(-9))[/tex]

[tex]\vec{N_{1}}=6\hat{i}+6\hat{j}[/tex]

is a normal vector

But , we can also use

[tex]\vec{N}=\frac{\vec{N_{1}}}{6}[/tex]

[tex]\vec{N}=\hat i+\hat j[/tex]

as the normal vector to the plane .

We can thus use the point P=(6,0,2) and the normal vector [tex]\vec{N}=\hat i+\hat j[/tex] to write the equation of the plane :

1(x-6)+1(y-0)+0(z-2)=0

x-6+y+0=0

x+y=6

Hence, an equation of the plane that contains these lines is x+y=6.

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The right question is

(a) Find the point at which the given lines intersect.

r = [3,3,0] + t[3,-3,2] r = [6,0,2] + s[-3,3,0]

(x,y,z) = ( )

(b) Find an equation of the plane that contains these lines.

By using the concept of algebraic expression, it can be calculated that

The number that makes the expressions equivalent is -0.7

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

The given algebraic expression is

−1.1−1.4m + 0.4

On simplifying −1.1−1.4m + 0.4

−1.1−1.4m + 0.4

-0.7 - 1.4m

So the number that makes the expressions equivalent is -0.7

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In 11.61 years the given principal amount of $ 900 will be double.

Compound interest is interest charged on a loan and is determined by both the principal amount and the rate of interest compounding per year.

The formula for the Amount when compound interest is calculated is given by

P = Principal amount

r = Rate of interest

n = Number of compounds

t = Time period in years

Here from the given data,

Principal amount = $ 900

Rate of interest = 6% = 6/100 = 0.06

Number of compounds = 12    [ ∵ compounded monthly]

Here we need to find the time period

Assume that after 't' years the amount will be doubled

From the given data and formula,

Amount, A = 900(1+0.06/12)^12t        

= 900(1+0.06/12)^12t

= 900(1 + 0.005)^12t

= 900 (1.005)^12t  

As we assumed after 't' years the amount is double

=> 900 (1.005)^12t  = 2 × 900

=> (1.005)^12t  = 2    

Applying log on both sides

=> log (1.005)^12t  = log 2

=> 12t log(1.005) = log 2

=> 12t = log 2/log(1.005)

[ we can use a calculator for log (1.005) and log 2]

=> 12t = 0.30108/ 0.00216  

=> 12t = 139.888

=>  t =  11.61

Therefore,

In 11.61 years the given principal amount of $ 900 will be double.

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The value of (f  o g)(-6) will be;

⇒  (f  o g)(- 6) = - 157

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

⇒ f (x) = - 4x - 1

And,  g (x) = x² + 3

Now,

Since, The values are,

⇒ f (x) = - 4x - 1

And,  g (x) = x² + 3

Hence, The value of function  (f  o g)(x) is,

⇒  (f  o g)(x) = f (g (x) )

                  = f (x² + 3)

                  = - 4 (x² + 3) - 1

                  = - 4x² - 12 - 1

                  = - 4x² - 13

Thus, (f  o g)(- 6) = - 4 (-6)² - 13

                         = - 4 × 36 - 13

                         = - 144 - 13

                         = - 157

So, The value of (f  o g)(-6) will be;

⇒  (f  o g)(- 6) = - 157

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The area under the graph using first two and then four rectangles f(x) = x³ between x = 2 and x = 4 is 0.2421875.

Here a=0, b=1 and n=2( two rectangles), so

Δx = (1 - 0)/2

Δx = 1/2

Δx = 0.5

M2 = (0.5) * ( f((0+0.5)/2)) + f((0.5+1)/2)) )

= (0.5) * ( f(0.25) + f(0.75) )

Using  f(x) = x^3

=(0.5) * ( 0.015625 + 0.421875 )

=0.21875

Here a=0, b=1 and n=4( four rectangles), so

Δx = (1 - 0)/4

Δx = 1/4

Δx = 0.25

M4 = (0.25) * ( f((0+0.25)/2)) + f((0.25+0.5)/2)) + f((0.5+0.75)/2)) + f((0.75+1)/2)) )

=(0.25) * ( f(0.125) + f(0.375) + f(0.625) + f(0.875) )

Using  f(x) = x^3

= (0.25) * ( 0.001953125 + 0.052734375 + 0.244140625 + 0.669921875 )

= 0.2421875

Hence,  the area under the graph using first two and then four rectangles f(x) = x³ between x = 2 and x = 4 is 0.2421875.

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For the given data

(a) sample mean is 17 and sample standard deviation = 8.91 .

(b) the 95% confidence interval is (9.551 , 24.449)  .

(c) the 90% confidence interval is (11.032 , 22.968) .  .

In the question ,

the data is given as 25, 11, 12, 27,26, 22, 8,5.

So , the number of terms (n) = 8

Part(a)

the sample mean(μ)  is = (25+11+12+27+26+22+8+5)/8 = 17

the standard deviation is calculated as :

= √[(25 - 17)² + (11 - 17)² + (12 - 17)² + (27 - 17)² + (26  - 17)² + (22 - 17)² + (8 - 17)² + (5 - 17)²)]/7

Simplifying the above data further ,

we get

= 8.91

Part(b)

we know that at 95% confidence interval , the critical value is t₀.₀₂₅,₇ = 2.3646

So , the 95% confidence interval is :

= μ ± t₀.₀₂₅,₇*s/√n

= 17 ± 2.3646*8.91/√8

= 17 ± 7.449

So , the interval is ⇒ (9.551 , 24.449) .

Part(c)

we know that at 90% confidence interval , the critical value is t₀.₀₅,₇=1.8946

So , the 90% confidence interval is :

= μ ± t₀.₂₅,₇*s/√n

= 17 ± 1.8946*8.91/√8

= 17 ± 5.968

So , the interval is ⇒ (11.032 , 22.968) .

Therefore ,(a)  the sample mean and standard deviation are 17 and 8.91

(b) the 95% interval is (9.551 , 24.449) .

(c) the 90% interval is (11.032 , 22.968) .

The given question is incomplete , the complete question is

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 25, 11, 12, 27,26, 22, 8,5.

(a) Calculate the sample mean and the sample standard deviation.

(b) Construct the 95% confidence interval for the population mean.

(c) Construct the 90% confidence interval for the population mean.

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