It takes 14 hours for a tap with a flow of 18 litres per minute to fill a reservoir with water. How long will it take if the flow is reduced to 7 litres per minute? I need formulas

Answer:20%

Step-by-step explanation:

The distance that the end of the pendulum travels when it swings is given by the relation D = 27.3 cm

Given data ,

A pendulum of length 18 cm is swinging from a fixed point

Now ,  it swings through an angle of 87°

So , Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

Now , D = ( θ/360 ) x 2πr

On simplifying , we get

D = ( 87 / 360 ) x 2 ( 3.14 ) ( 18 )

D = ( 0.241667 ) ( 113.04 )

D = 27.3 cm

Hence , the pendulum travels a distance of 27.3 cm

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The length of BC is determined as  6√31  by applying trigonometry ratio.

The length of BC is calculated by applying the following formulas for trig ratios.

The trig ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The hypothenuse side of the right triangle is given as 12√31 and the opposite side is length BC.

The length of BC is calculated as follows;

sin 30 = BC / 12√31

BC = 12√31 x sin (30)

BC = 12√31 x ¹/₂

BC = 6√31

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Answer:

  $15,200

Step-by-step explanation:

You want to know the amount deposited at 1.5% that will earn the same simple interest in a year as $12,000 deposited at 1.9%.

The interest amount is given by the formula ...

  I = Prt

For the two accounts, the interest and the time are the same, so we have ...

  P1·r1 = P2·r2

  12000·1.9% = P2·1.5% . . . . . . . . . . . equate interest amounts for t=1

  P2 = 1.9/1.5·12000 = 15200 . . . . . . divide by 1.5%

Ruth deposited $15,200.

<95141404393>

The scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex] where 10 raised to an exponent (-2).

In scientific notation, a number is expressed as the product of a coefficient and a power of 10.

To write the number 0.08 in scientific notation, it as a decimal number multiplied by a power of 10.

So, 0.08 can be written in scientific notation as 8 x [tex]10^{(-2)[/tex].

In scientific notation, the number is written as the product of a coefficient (8) and a power of 10 raised to an exponent (-2), indicating the decimal's position relative to the coefficient.

Therefore, the scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex].

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Answer:

The volume of the cylinder is 500 π cubic kilometers.

Step-by-step explanation:

Formula: V = πr²h

r = d/2

r = 20km/2

r = 10 km

h = 5km

Solve for the volume using the formula.

Substitute the given

V = π(10km)²(5km)

V = 500π km³

I hope this helps you

Answer:

Step-by-step explanation:

Let’s define the number of rides that Zeek can ride as “r”.

To determine how many rides Zeek can ride, we need to first subtract the cost of admission from his total budget:

$30 - $13 = $17

This means that Zeek has $17 left to spend on rides. Since each ride costs $2, we can set up the following equation:

$2r = $17

To solve for “r”, we divide both sides of the equation by $2:

r = $8.50

So Zeek can ride a maximum of 8 rides with the $17 he has left after paying for admission. However, since he cannot ride a fraction of a ride, he may be limited to only 8 rides or fewer.

The relation is a function because (d) Yes because for each output there is exactly one input.

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

The graph

The graph can be represented as

x  g(x)

-5  1

-2  0

-1   -1

0  2

1  3

5   1

The above table of values is a function

This is so because each output values have different input values.

i.e. it would pass the vertical line test when represented on a graph

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Answer:

98 is a whole number

Step-by-step explanation:

0.86 is a decimal

2/5 is a fraction

35% is a percentage

Answer:

31 years

Step-by-step explanation:

A = P(interest rate)^number of years (n)

if the money is to quadruple, A = 4 X 22,000 = 88,000.

P = investment amount = 22,000.

interest rate is 4.5%. so we have the whole (100%) + 4.5% = 1.045%.

n is number of years.

22,000 (1.045)^n = 88, 000

divide both sides by 22, 000:

(1.045)^n = 4

take logs for both sides:

log (1.045)^n = log 4

simplify using log laws (by bringing down the n):

n log (1.045) = log 4

divide both sides by log (1.045):

n = (log 4) / log (1.045)

= 31.49 (31 years to nearest year)

After considering all the given data we conclude that the the probability of rolling a number less than 7 is 1/2, under the condition that the set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12).

The evaluated probability of rolling a number less than 7 on a 12-sided die is the number of outcomes that are less than 7 divided by the total number of possible outcomes.

The set of equally likely outcomes is (1,2,3,4,5,6,7,8,9,10,11,12). There are 6 numbers less than 7 in this set (1,2,3,4,5,6) and 12 possible outcomes.

Hence , the probability of rolling a number less than 7 is:

6/12 = 1/2

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Answer: there is one solution

Step-by-step explanation:

12x − 13y = 5

x = 23y + 10

lets substitute x into the first equation.

12(23y + 10) - 13y = 5

276y + 120 - 13y = 5

263y = -115

y = -115/263

substituting for x:

x = 23(-115/263) + 10

x = -2645/263 + 10

x = -15/263

As we can see, we get one value of x;

this means there is one solution

Given WX is tangent to OS at point V, the statements that must be true include:

A. m∠TVX =m∠TVX

C. m∠TVW = m∠TSV

D. m∠TUV =m∠TVW

In mathematics, a tangent is a line that touches a curve at exactly one point, without intersecting it at that point. The tangent line at a point on a curve represents the slope of the curve at that point. The concept of tangent is important in calculus, where it is used to calculate derivatives of functions.

TUV = 1/2MTU = TVW

TUV = TVW

Also, MTV = TSV = 2TVW

TVW = TSV

The correct options are A, C and D.

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(a) The result of row 1 and row 2 interchange is [3     -2    3]

                                                                                 [2     3     1]

(b) The result of multiplying and adding the matrix is [-1       5     -2]

                                                                                         [3      -2      3]

The row operation of the matrix is calculated as follows;

The given matrix;

[2     3     1]

[3     -2    3]

To interchange row 1 and row 2, we determine it as follows;

R₁ ↔ R₂   = [3     -2    3]

                  [2     3     1]

The product of row 2 and -1 is calculated as;

-1 (R₂) = [-3      2     -3]

The addition of -1(R₂) + R₁ is calculated as;

-1(R₂) + R₁ = [-3      2     -3] + [2     3     1]

-1(R₂) + R₁ = [-1       5     -2]

new matrix =  [-1       5     -2]

                       [3      -2      3]

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The probability that a randomly selected point within the square falls in the red-shaded square is 0.11

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

The areas of the above shapes are

Red square = 1² = 1

White square = 3² = 9

The probability is then calculated as

P = Red square/White square

So, we have

P = 1/9

Evaluate

P = 0.11

Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.11

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The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8

The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point

The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;

f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8

The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8

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If the volume is 133 1/3 in³, the value of x is equal to 5 inches.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

133 1/3 = 10 × x ×  2 2/3

400/3 = 10 × x × 8/3

400/3 = 80x/3

80x = 400

x = 400/80

x = 5 inches.

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After considering all the given options we come to the conclusion that the inequality that represents the  values of x for the give triangle ABC is 15/11 < x < 17/5, which is Option A.

Here, the sides of a triangle should gradually satisfy the triangle  inequality theorem which projects that the summation of the lengths considering any two sides of a triangle should be bigger than or equivalent towards the length of the third side.
Then, for the given sides of triangle ABC,
3x+1 + 16 > 8x

Applying this inequality,
x > 15/11
So,
16 + 8x > 3x+1
Applying simplification
x < 17/5
Hence , the inequality that represents the values of x for which triangle ABC exists is 15/11 < x < 17/5.
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The surface area of the given cylinder is approximately 1758.4 square yards.

To find the surface area of a cylinder, we need to calculate the sum of the areas of its curved surface (lateral surface area) and its two circular bases.

Given:

Height (h) = 18 yards

Radius (r) = 10 yards

π (pi) ≈ 3.14

Lateral Surface Area:

The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius and h is the height.

Lateral Surface Area = 2πrh

Substituting the given values, we have:

Lateral Surface Area = 2 × 3.14 × 10 × 18

Lateral Surface Area = 1130.4 square yards (rounded to the nearest hundredth)

Circular Bases:

The area of a circle can be calculated using the formula πr^2, where r is the radius.

Area of a Circular Base = π[tex]r^2[/tex]

Substituting the given radius, we have:

Area of a Circular Base = 3.14 × [tex]10^2[/tex]

Area of a Circular Base = 314 square yards

To find the total surface area, we need to add the lateral surface area and the areas of the two circular bases.

Total Surface Area = Lateral Surface Area + 2 × Area of a Circular Base

Substituting the values, we get:

Total Surface Area = 1130.4 + 2 × 314

Total Surface Area = 1758.4 square yards (rounded to the nearest hundredth)

Therefore, the surface area of the given cylinder is approximately 1758.4 square yards.

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Question

'What is the surface area of this cylinder? What is the surface area of this cylinder? Use I ~ 3.14 and round your answer to the nearest hundredth_ 18 yd 10 yd square yards'

The assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.

To estimate the number of fossils after 10 years, we need to solve the given equation. However, since the equation is not provided, we'll assume a simple exponential decay model for the population of fossils.

Let's assume the equation for the population of fossils is:

N(t) = N0 * e^(-kt)

where:

N(t) is the number of fossils after t years,

N0 is the initial number of fossils,

k is a decay constant, and

e is the base of the natural logarithm (approximately 2.71828).

Since the initial number of fossils is given as 100, we have N0 = 100. Now, we need to find the value of the decay constant (k) to estimate the number of fossils after 10 years.

Without further information, it's challenging to determine the exact decay constant. However, let's assume a hypothetical value of k = 0.1 for this example.

Plugging the values into the equation, we get:

N(10) = 100 * e^(-0.1 * 10)

= 100 * e^(-1)

≈ 100 * 0.36788

≈ 36.788

So, with the assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.

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Answer:

B. 2333.59

Step-by-step explanation:

We have been given the following differential equation:

[tex]\dfrac{dN}{dt}=\dfrac{5000}{6+5t}[/tex]

To find the number of fossils N(t) after t = 10 years, we first need to solve the differential equation using integration and the given parameters to create an equation for N(t) in terms of t.

Solving a differential equation means using it to find an equation in terms of the two variables, without a derivative term.

Rearrange the equation so that all the terms containing N are on the left-hand side, and all the terms containing t are on the right-hand side:

[tex]1\;dN=\dfrac{5000}{6+5t}\; dt[/tex]

Integrate both sides:

[tex]\displaystyle \int 1 \;dN=\int \dfrac{5000}{6+5t}\; dt[/tex]

Use the following integration rules:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Integration rulest}\\\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\;\;(where $n$ is any constant value)\\\\\\$\displaystyle \int \dfrac{n}{a+bx}\:\text{d}x=\dfrac{n}{b}\ln |a+bx|+\text{C}$\\\\ \end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int 1\;dN&=\int \dfrac{5000}{6+5t}\; dt\\\\\implies N&=\frac{5000}{5}\ln \left|6+5t\right|+C\\\\N&=1000\ln \left|6+5t\right|+C\end{aligned}[/tex]

As the initial number of fossils is 100, then N = 100 when t = 0.

Substitute these values into the equation and solve for C:

[tex]100=1000\ln \left|6+5(0)\right|+C[/tex]

[tex]C=100-1000\ln (6)[/tex]

Therefore, the equation for N in terms of t is:

[tex]N=1000\ln \left|6+5t\right|+100-1000\ln(6)[/tex]

Use the quotient log rule to simplify:

[tex]N=1000\ln \left|6+5t\right|-1000\ln(6)+100[/tex]

[tex]N=1000\ln \left(\dfrac{\left|6+5t\right|}{6}\right)+100[/tex]

To estimate the number of fossils after 10 years, substitute t = 10 into the equation:

[tex]N=1000\ln \left(\dfrac{\left|6+5(10)\right|}{6}\right)+100[/tex]

[tex]N=1000\ln \left(\dfrac{56}{6}\right)+100[/tex]

[tex]N=2333.59\; \sf (2\;d.p.)[/tex]

Therefore, the number of fossils after 10 years is 2333.59.

Answer:

Step-by-step explanation:

Amount in 4.6% acct= 15000*(1/3)= 5000

Amount in bonds = 1/4*15000= 3750

Amount in stock= 15000-(5000+3750)= 6250

Amount in each account at the end of three years

5000*(1.046)^3= 5722.22668

3750*(1.052)^3=4365.94728

6250*1.03*(1-.08)*1.06= 6277.85

total: 5722.22668+4365.94728+6277.85=16366.02396

gain= 16366.02396-15000=1366.02396

or (16366.02396/15000)-1= 9.1068264%

The statements that will be true about parallelogram ABCD are: A, B, D, and E.

Properties of a Parallelogram -

Diagonals of a parallelogram bisect each other into congruent segments.

Opposite angles and sides of a parallelogram are always congruent.

Alternate interior angles are always congruent in measure.

Thus, the following would be true of parallelogram ABCD:

AP ≅ CP (congruent segment's of a bisected diagonal)

BC ≅ AD (congruent opposite sides)

∠CAD ≅ ∠ACB (congruent angles)

∠BPC ≅ ∠APD (congruent angles)

Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.

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After applying factorization of the given functions the evaluated expression comes out to be (2x + 1)(x² - x - 4.8), under the condition the given function is P(x)=2x × 3- 5.6x +1

In order to factorize the given polynomial P(x) = 2x³ - 5.6x + 1, we can apply the Rational Root Theorem. The theorem projects that in an incident when a  polynomial has integer coefficients, then any rational roots must have a numerator that divides the constant term and a denominator that divides the leading coefficient.
For the given case, the leading coefficient is 2 and the constant term is 1.
Hence, any rational roots must be of the form p/q where p divides 1 and q divides 2. This elaborates that the possible rational roots are ±1/2 and ±1.
We can observe these roots applying synthetic division. Using synthetic division with root -1/2 gives us:
-1/2 | 2   0   -5.6   1
    |    -1    0.8  -0.5
    -------------------
          2   -1   -4.8  0.5
This means that P(x) can be factored as:
P(x) = (2x + 1)(x² - x - 4.8)
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A set of two or more equations with the same variables.

A system of linear equations with EXACTLY ONE solution.

A system of linear equations with INFINITELY MANY solutions.

A system of equations with NO solution.

A number representing how many times the Base number should be multiplied by itself.

A chart of the different values for an equation or graph.

Systems of Equations:

A set of two or more equations with the same variables.

These equations are solved simultaneously to find the values of the variables.
Consistent Independent:

A system of linear equations with EXACTLY ONE solution.

This means that the lines represented by the equations intersect at a single point.
Consistent Dependent (Coincident):

A system of linear equations with INFINITELY MANY solutions.

In this case, the equations represent the same line or overlapping lines, and every point on the line is a solution.
Inconsistent:

A system of equations with NO solution.

This occurs when the lines represented by the equations are parallel and never intersect.
Exponent:

A number representing how many times the base number should be multiplied by itself.

For example, in the expression[tex]2^3,[/tex] the exponent is 3, which means 2 should be multiplied by itself 3 times [tex](2 \times  2 \times  2 = 8).[/tex]
T-Table:

A chart of the different values for an equation or graph.

It typically includes two columns: one for the input values (usually x) and one for the corresponding output values (usually y).

T-tables are helpful for understanding the relationship between the variables in an equation and for plotting points on a graph.

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Answer:

B and D

Step-by-step explanation:

4²= 16

it's a perfect square

2³= 8

it's a perfect cube

This given function does not have an end behavior since it is not a polynomial.

The end behavior of a function describes the behavior or trend of the function as the input values (x) approach positive or negative infinity. It helps us understand what happens to the function's values as x becomes very large or very small.

We have three possible cases of end behavior of a function which are;

The end behavior of a function is often determined by using the leading term of the function, which is the term with the highest power of x.

In the given problem;

[tex]f(x) = \frac{8x^6 - 16x^3 + 8}{4x^2 - 4x - 24}[/tex]

The end behavior of this function does not exist because this function is not a polynomial

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The perimeter of the given triangle is: 19.2 units

The formula for the distance between two coordinates is:

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus: (0, 3)(4, -2)

Slant distance on left side of triangle = √[(-2 - 3)² + (-3 - 0)²] = 5.8 units

Slant distance on right side of triangle = √[(-2 - 3)² + (4 - 0)²] = 6.40 units

Length of horizontal part of triangle = 7 units

Thus:

Perimeter of triangle = 5.83 + 6.40 + 7 = 19.2 units

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