A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere with a radius of 0.5 cm, are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots dropped in the vessel. Use n =3.14

Answer: It should be 33.5%

The amount in the account is decreasing and at the decreasing percentage is 10%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

r (number of years)      g(r) (amount in dollars)

1                                      8,972

2                                     8,074.80

3                                     7,267.32

4                                     6,540.59

The amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 9,628(0.92)x

To know amount increasing or decreasing,

we can subtract amounts in the account in two consecutive years,

⇒ 8074.80 - 89 72

⇒  -897.2

It is negative so it can be say that amount is decreasing.

Percentage = (89 72 - 8074.80)/8972 x 100

                    = 10

Hence, the percentage is 10%

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Principal is $6000.

Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows $5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years. 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.

Given Data

Using simple interest formula,

| = $14,400

R = 8%

T = 30 years

I = \(\frac{PRT}{100}\)

14400 = \(\frac{P(8)(30)}{100}\)

\(\frac{14400(100)}{8(30)}\) = P

P = 6000

Principal is $6000.

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The trigonometric function on the graph is:

f(x)= -cos(x)

So the correct option is B.

Here we can see the graph of a trigonometric function. We can see that the x-intercept is -1.

Notice that:

sin(0)= 0

cos(0) = 1

So the function can be an inversion over the x-axis of the cosine function, we coulod write this as:

f(x) = -cos(x)

That is the graphed function.

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The relation that can not be supported by the evidence in the image is option B

Corresponding angles are those that are located on the same side of the transversal and in identical relative positions to the parallel lines. Angles that correspond to one another have the same measure.

Alternate interior angles are those that are located on the transverse and within the area between the parallel lines, respectively. Congruent alternate interior angles exist.

Alternate external angles are those that are outside of the space between the parallel lines and on the opposing sides of the transversal. Congruent external angles exist between the two.

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The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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Answer:

D. y = x - 4

Step-by-step explanation:

Given the following data;

Points (x, y) = (3, -1)

To find the equation of line;

First of all, we would determine the slope of the graph.

Mathematically, slope is given by the formula;

\( Slope = \frac{Change \; in \; y \; axis}{Change \; in \; x \; axis} \)

\( Slope, m = \frac {y_{2} - y_{1}}{x_{2} - x_{1}} \)

Substituting into the equation, we have;

\( Slope, m = \frac {5 - 5}{5 - 5} \)

Slope, m = 1

Generally, the equation of straight line is y = mx + c

Where;

m is the slope.

x and y are the points

c is the intercept.

Substituting the values in order to find the intercept, we have;

Using points (x, y) = (3, -1)

-1 = 1*3 + c

-1 = 3 + c

c = -1 - 3

Intercept, c = -4

Therefore, the equation of line becomes;

y = x - 4.

Answer:

18 cm

Step-by-step:

The formula for the volume of a triangular prism is given by:

V_triangular_prism = (1/2) * base * height * length

where the base is the area of the base triangle, height is the perpendicular distance between the two parallel base planes, and length is the distance between the two triangular faces.

We are given that the base area of the triangular prism is 36 cm² and the volume is 432 cm³. Using these values, we can solve for the height:

432 = (1/2) * 36 * height * length

height * length = 24

Since we want to find the base side length of a rectangular prism that has the same volume, we can use the formula for the volume of a rectangular prism:

V_rectangular_prism = length * width * height

We know that the volume of the rectangular prism is also 432 cm³, so we can substitute this value and the value we found for the height * length product:

432 = length * width * height

432 = length * width * (24/length)

432 = 24 * width

width = 18

Therefore, the base side length of the rectangular prism needs to be 18 cm.

Hope this helps!

Answer:

so no answer

Step-by-step explanation:

no answer

An equation 6(2x+4)²=(2x+4)+2 has degree 2, so it is quadratic equation. Therefore, option D is the correct answer.

The standard form of a quadratic equation is given as:

ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.

Quadratics are the polynomial equation which has highest degree of 2.

A) x⁴-6x²-27=0

Here, the highest degree is 4 so, it is biquadratic equation.

B) 3x⁴=2x

3x³=2

Here, the highest degree is 3 so, it is cubic equation.

C) 2(x + 5)⁴+2x²+5=0

Here, the highest degree is 4 so, it is biquadratic equation.

D) 6(2x+4)²=(2x+4)+2

6(4x²+16x+16)=(2x+4)+2

24x²+96x+96=2x+4+2

24x²+94x+90=0

Here, the highest degree is 2 so, it is quadratic equation.

E) 6x⁴= -x²+5

6x⁴+x²+5=0

Here, the highest degree is 4 so, it is biquadratic equation.

F) 8x⁴+2x²-4x=0

Here, the highest degree is 4 so, it is biquadratic equation.

Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Select all of the following equation(s) that are quadratic in form.

a) x⁴-6x²-27=0

b) 3x⁴=2x

c) 2(x + 5)⁴+2x²+5=0

d) 6(2x+4)²=(2x+4)+2

e) 6x⁴= -x²+5

f) 8x⁴+2x²-4x=0

Answer:

The answer is 8x - 6

Step-by-step explanation:

2(4x - 3)

2 × 4x - 2 × 3

8x - 6

Thus, The answer is 8x - 6

-TheUnknownScientist 72

Answer:

-8x+6

Step-by-step explanation:

For this problem, we can use distributive property.

-2(4x-3) = (-2*4x) - (-2*3)

-8x - (-6)

When we have two negatives signs, it turns into a positive sign

-8x+6

Hope this helps :)

6f+21=-15

6f+21-21=-15-21

6f=-36

6f/6=-36/6

f=-6

Answer: f=-6

Step-by-step explanation:

Earnings per hour: $13.75

Tuesday = 8 am to 2 pm = 6 hours

Thursday= 8 am to 1 pm = 5 hours

Friday = 10:00 am to 12:15 pm = 2.15 hours

Add all the hours:

6+5+2.15 = 13.15 hours

Multiply by the amount she earns per hour:

hours x earnings per hour = 13.15 x 13.75= $180.81

Gross pay $180.81

Answer:

(7x + 6) tickets

Step-by-step explanation:

Tickets Ross has : 8x - 5

Tickets Ross needs : 15x + 1

To find out the remaining amount, subtract the tickets Ross has from the number of tickets he needs.

Must ticket win

Answer:

3a^2

Step-by-step explanation:

one way of answering this question is by finding the area of the whole shape, including the non-shaded shape, then taking away the area of the non-shaded shape from the whole thing, leaving you the area of the shaded shape

Step-by-step

find the area of the whole shape

2a x 2a

= 4a^2 (or 4a to the power of 2)

Now that we have the area of the whole shape, we must find the area of the non-shaded shape and take it away from 4a^2, we do this by

a x a

= a^2 (or a to the power of 2)

now we minus the non-shaded shape away from the total area

4a^2 - a^2

= 3a^2 (or 3a to the power of 2)

Answer:

the zeros of the function are those that result, when plugged into the equation, in zero; the zeros are -3, 1, and 1/2

Step-by-step explanation:

all possible factors:

±3/2,  ±1/2,  ±3,  ±1

2x³ + 3x² - 8x + 3

let '2' = p and let '3' = q

factors of 'p' are 1 and 2

let '3' = q

factors of 'q' are 1 and 3

possible factors are q/p

in essence it boils down to, when investing, you take risks all the time, the money is going to be invested on some expenditure that may work or not work, if it doesn't work, your money is Kaput, and if it works, how much are you getting back?  2%, 17%? or whatever.

If a company would like you to invest and provides you with 2% return, is kinda low but the issue is that whatever they're going to use it for and the health of their finances is such that you'll get 2%, or the probability of you getting that much is pretty good.

Now, if the same company instead offers 35% return on investment, hell that's high, the hell is going on?  Why are they so generous?

Well, they're not really being generous, the issue is the probability that you'll get that much is not really that good, there's a good chance your money will go Kaput, so the risk is really much higher, before you invest you're told of those chances, hmmmm should you do it knowing there's a good chance of being left just holding an empty bag?  So you'd hesitate and possibly say forget it, unless  the returns make it tilt that balance.  So the investors get attracted by the higher percent of return, but is always counter-balanced with the risk associated with it.

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Domain :

\(x \leqslant - 1\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Range :

\(y \geqslant 0\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Thus the correct answer is (( B )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

YES

Step-by-step explanation:

4(Z-3)=16

4Z-12=16

  +12 +12

4Z=28

Z=7

Answer:7

Step-by-step explanation:

4(z-3)=16

4z-12=16

4z=28

4z/4=28/4

z =7

Answer:

Step-by-step explanation:

Steps to solve:

-4z + 4 + 12z = 3z + 4 + 5z

~Combine like terms

8z + 4 = 8z + 4

~Subtract 4 to both sides

8z = 8z

~Divide 8 to both sides

0 = 0

All real numbers are solutions.

Set builder notation: {x | R}

This is an identity since every value can be a solution to the equation.

Best of Luck!

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer:

Step-by-step explanation:

x=24/5

Answer:

Answer: n is 110

Step-by-step explanation:

Formular:

\(mean = \frac{ \sum(n_{1}, \: n _{2}, \: ...n_{n} ) }{n} \\ \)

therefore:

\(140 = \frac{(120 + 145 + 130 + 80 + 95 + 100 + 340 + n)}{8} \\ \\ (8 \times 140) = 1010 + n \\ 1010 + n = 1120 \\ n = 1120 - 1010 \\ n = 110\)

Answer:

for 6, you drag 36. for 7, you drag 42.

Step-by-step explanation:

It is using time tables by x6

The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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Distance traveled after toll payment is 1.2 miles on highway 40.

The distance may be calculated using a curved route. Displacement measurements can only be made along straight lines. Distance is path-dependent, meaning it varies depending on the direction followed. Displacement simply depends on the body's beginning and ending positions; it is independent of the route.

Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.

The size or extent of the displacement between two points is referred to as distance. Keep in mind that the distance between two points and the distance traveled between them are not the same. The entire length of the journey taken between two points is known as the distance traveled. Travel distance is not a vector.

Distance traveled before toll payment =3/5 miles on highway 40

Distance traveled after toll payment =2*3/5  = 6/5 =

1.2 miles on highway 40.

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The answer choice which is a function among the given answer choices is; Choice B as they are all correct.

From conventional mathematics, a function from a set x to a set y assigns to each element of X exactly one element of Y.

The set of values x is called the domain of the function and the set of values y is called the codomain/range of the function.

Functions basically represents the idealization of how a varying quantity depends on another quantity.

It therefore follows from the paragraph above that all of the answer choices are functions.

Therefore, the answer choice which is a function among the given answer choices is; Choice B as they are all correct.

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