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Answer:

  25.5 years

Step-by-step explanation:

The multiplier for continuous compounding at annual rate r for t years is ...

  e^(rt)

You want the value of t when that is 3 and r=0.043.

  3 = e^(0.043t)

  ln(3) = 0.043t

  t = ln(3)/0.043 ≈ 25.549 . . . . years

Multiply 0.625/1 by 1000/1000 to get 625/1000. Reducing we get 5/8  

Answer:

The inequality is 2 ≤ x < 8.

A closed dot represents ≤, and an open dot represents <. Since x can represent all values between 2 and 8, you will shade in between 2 and 8 on the number line. x is greater than or equal to 2, so there will be a closed dot on 2. x is less than 8, so there will be an open dot on 8.

The answer is 'number line with a closed dot on 2 and an open dot on 8 and shading in between'.

The solution to the inequality c ≤ -2 is closed dot at –2; shade all the points to the left of –2

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

A number line can be used to represent numbers placed on regular intervals. A number line can be used to represent an inequality.

The solution to the inequality c ≤ -2 is closed dot at –2; shade all the points to the left of –2

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Answer:Formular for simple interest is

I = P X R XT

————

100

where P is the amount borrowed or loan , Rate is the percentage of interest in P while T is the Time range for the loan

Now to find the Principal, we now change the original subject of the formula to suit or reflect P.
P = I X 100

———-

R X T

= 11, 178

———

6 X 9

=. 11, 178

——

54

=. $20,700

Step-by-step explanation:

Answer:

$20,700

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

Given:

Substitute the given values into the formula and solve for P:

\(\implies \sf 11178=P(0.06)(9)\)

\(\implies \sf 11178=0.54P\)

\(\implies \sf P=\dfrac{11178}{0.54}\)

\(\implies \sf P=20700\)

Therefore, the principal amount is $20,700.

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Samantha was receiving an interest rate of 12% on her account.

Present value is the present value of future cash flows discounted at a certain rate. Present value is based on the concept of the time value of money, where a dollar today is worth more than a dollar in the future.

PV = FV /(1 + r )ⁿ

Information provided to us ,

time period , n = 6 years

let " $x " be the present value of Samantha's account money.

After 6 years it becomes double that is

future value, F = $2x

let "r" be rate of interest was Samantha receiving on her account.

plugging all known values in above formula,

$x = $2x /(1+r)⁶

=> (1+r)^6 = 2

=> 1 + r = (2)^1/6 = 1.122

=> r = 1.122 - 1 = 0.122

=> r = 12%

So, rate of interest is 12% .

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Answer:

Step-by-step explanation:

Step 1:

Make a proportion:

10/5 = 22/x

Step 2:

Cross multiply:

10x=22*5

10x=110

Step 3:

Divide by 10 to isolate x:

x=11

The vector function u(t) is linearly independent (and not linearly dependent).

To determine if the vector function u(t) = (9cos t, 9sin t, 0) is linearly dependent, we need to check if there exist constants c1 and c2, not both zero, such that:

c1u(t) + c2u(t) = 0

where 0 represents the zero vector of the same dimension as u(t).

So, let's assume that such constants exist, and write:

c1(9cos t, 9sin t, 0) + c2(9cos t, 9sin t, 0) = (0, 0, 0)

Simplifying each component, we get:

(9c1 + 9c2)cos t = 0

(9c1 + 9c2)sin t = 0

0 = 0

From the third equation, we know that 0 = 0, so we don't gain any new information from it. However, the first two equations tell us that either cos t = 0 or sin t = 0, since c1 and c2 cannot both be zero. This implies that t must be a multiple of pi/2 (i.e., t = k(pi/2), where k is an integer).

Substituting t = k(pi/2) into the original vector function, we get:

u(k(pi/2)) = (9cos(k(pi/2)), 9sin(k(pi/2)), 0)

For k = 0, 1, 2, 3, we get the vectors:

u(0) = (9, 0, 0)

u(pi/2) = (0, 9, 0)

u(pi) = (-9, 0, 0)

u(3pi/2) = (0, -9, 0)

Since these four vectors are all distinct, we know that no two of them are scalar multiples of each other.

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The formula for the final velocity,\(v_{f}\) , in terms of initial velocity, vi, acceleration, a, and time, t is given by \(V_{f}=at+V_{i}\)

A =\((V_{f}-V_{i} )/t\)  You can put \(1\) under A and then cross multiply.

\(at =V_{f} -V_{i}\)

Get \(V_{f}\)  by adding  \(V_{i}\) in both sides of the equation.

\(at+V_{i} =V_{f}\)

                                                OR

The final speed \(V_{f}\) in terms of other parameters is given by the relation \(V_{f}\)\(=at+V_{i}\)

How to calculate the acceleration of an object?

Mathematically, acceleration is calculated using this formula:

\(a=(V_{f}-V_{i} )/t\)

Where:

Making \(V_{f}\) the subject of the formula, we have:

\(at =V_{f} -V_{i}\)

\(V_{f} =V_{i} +at\)

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Answer:

15

Step-by-step explanation:

If you do the Pythagorean theorem or use the right triangle triples, you’ll get 15 as your answer, hope this helps :)

To compute C(7,5), or the number of combinations of choosing 5 items from a set of 7, you can use the formula for combinations: C(n, r) = n! / (r!(n - r)!)

Where "n" is the total number of items, "r" is the number of items you want to choose, and "!" denotes the factorial of a number (the product of all positive integers up to that number).
C(7,5) = 7! / (5!(7 - 5)!)

Step-by-step explanation:
1. Calculate the factorial of 7: 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
2. Calculate the factorial of 5: 5! = 5 × 4 × 3 × 2 × 1 = 120
3. Subtract 5 from 7: (7 - 5) = 2
4. Calculate the factorial of 2: 2! = 2 × 1 = 2
5. Multiply the factorial of 5 and the factorial of 2: (5! × 2!) = 120 × 2 = 240
6. Divide the factorial of 7 by the product of the factorials from step 5: (7! / (5! × 2!)) = 5040 / 240
C(7,5) = 21
In conclusion, there are 21 different ways to choose 5 items from a set of 7.

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Hence, 1) 6 cm (smallest value), 2) 6 cm, and 3)15.167 cm are the approximate dimensions which will result in a material with the biggest volume (largest value).

A 3D object's surface area is indeed the entire area that all of its faces cover. For instance, the surface area of a cube has been its surface area if we need to determine how much paint is needed to paint it. It's always calculated in square units.

Let the height be y as well as the side length of a square base be x. The rectangular solid's surface area is then determined by:

When we simplify this equation, we obtain:

The rectangular solid's volume is determined by:

V = x² × y = x² × (433.5 - 4x²) / (2x)

When we simplify this equation, we obtain:

V = 216.75x - 2x³

We must determine the value of x that maximizes V in order to determine the dimensions that lead to a solid with the maximum volume. Using V's derivative with x as the base, we can calculate:

dV/dx = 216.75 - 6x²

By setting this to 0 and figuring out x, we obtain:

216.75 - 6x² = 0

x² = 36.125

x ≈ 6.005

When we rewrite the equation for y using this value of x, we obtain:

y ≈ 15.167

Thus, the following dimensions will produce a solid with the largest volume:

1. 6 cm (smallest value)

2. 6 cm

3.15.167 cm (largest value)

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Answer:

What do you need from this question? Its not asking anything.

Step-by-step explanation:

Answer:

Step-by-step explanation:

They're both right angle triangles and have the same length and size , hence congruency

Answer:

-2 1/4 = 4/5x + (-2)

explanation:

Because read it closely

Answer:

A.)-2 1/4 = 4/5x + (-2)

Step-by-step explanation:

I took the K12 test

Answer:

deductive

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Answer: yes

Step-by-step explanation:

The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.

The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).

The total amount she earns can be represented by

y = 15x + 20

where y is her daily earnings and x is the number of bikes she assembles

If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).

domain : {x| 0 ≤ x ≤ 6}

where x is a whole number

Substituting the minimum and maximum value of x in the function.

y = 15(0) + 20     when x = 0

y = 20

y = 15(6) + 20     when x = 6

y = 110

range : $20 ≤ y ≤ $110

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Answer:

4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The left most line is 2 units above the x axis on the black shape.

The left most line is 8 units above the x axis on the green shape

the dilation factor is

green / black = 8 / 2

green / black = 4

The required probability is 0.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Mean = μ = 34641

Standard deviation = σ = 2480

Sample space = n = 121

s = σ/√n = 2480/√121 = 22.5.45

The probability required is the difference of  p-value of Z when X = 34641 + 344 = 34985 and the p-value of Z when X = 34641 - 344 = 34297.

When X =  34985,

z = (X - μ)/σ

= 34985 - 34641 / 2480

= 344 /2480

= 0.138

p-value of z = 0.138 is 0.8902

When X =  34985,

z = (X - μ)/σ

= 34297 - 34641 / 2480

= -344 /2480

= -0.138

p-value of z = -0.138 is 0.8902

∴ Probability = 0.8902 - 0.8902 = 0

Thus, the required probability is 0.

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The lifting force if the speed is 220 miles per hour is F' = 708.53 N.

The force of light, or simply light, is the sum of all forces on an object that cause the object to move perpendicular to the direction of flow.

The most common type of lift is the wing lift. But there are many other common uses, such as propellers on airplanes and ships, rotors on helicopters, fan blades, sails on sailboats, and wind turbines.

We have,

The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. It, means that,

\(F=kAv^{2}\)

Where

k is constant

If, A = 190 Ft², v = 220 mph, F = 950 pounds

Now, find k first from the above data. So,

    \(k=\frac{F}{Av^{2} }\)

⇒ \(k=\frac{950}{190* (220)^2}\)

⇒ k = 0.0001033

It is required to find the lifting force on the wing if the plane slows down to 190 miles per hour.

Let F' is a new force. So,

    F' = 0.0001033 × 190 × (190)²

⇒ F' = 708.53 pounds.

So, the lifting force is 708.53 pounds if the plane slows down to 190 miles per hour.

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A. If the radius of the sphere is r, what is the height of the cylinder H=4√r

B The volume of the sphere will be V=4πr³

Volume is defined as the space occupied by any object in the three-Dimenions. All three parameters are required for the volume like length, width and height of cube or cuboid.

Here for the part A If the radius of the sphere is r, what is the height of the cylinder the solution will be given as:-

The Volume of sphere = Volume of cylinder

4πr³=(π÷4) r²H

H=16r

H=4√r

Hence the height of the cylinder will be H=4√r

B. The volume of the shapes will be given as:-

(1) Volume of cylinder = (π÷4)r²H

Here r= radius of the cylinder

H = height of the cylinder

(2) The Volume of the Sphere=4πr³

Here r= radius of the cylinder

(3) The Volume of cone=(1÷3)πr³l

Here r = radius of the base

l=slant height of the cone

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Answer:

I believe that it would be 22

The score that is 1 standard deviation below the mean is µ - σ = -5. Hence, the answer is -5.

Given that the scores on a test are normally distributed with a mean of µ and a standard deviation of σ.

The Z-score or Standard score is a dimensionless measure and it describes the number of standard deviations a given value x lies above or below the mean µ.

Mathematically, it can be represented as;

Z = (x - µ)/ σNow, we have to find the score that is standard the mean or the score that is 1 standard deviation below the mean.

Using the formula for the Z-score,

Z = (x - µ)/ σZ = -1

(Since we have to find the score which is 1 standard deviation below the mean)We know that the z-score of -1 corresponds to the 15.87th percentile.

From the standard normal table, the corresponding value of x is;z = -1 corresponds to x = µ - σz = -1 corresponds to x = µ - σ = -5

Therefore, the score that is 1 standard deviation below the mean is µ - σ = -5. Hence, the answer is -5.

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1) The coordinates of the vertex are; (-6, -1)

2) The x-intercepts are; (-5, 0) and (-7, 0)

3) The y-intercept is; (0, 35)

4) There is no vertical stretch

We are given the factored form of the quadratic function as;

y = (x + 5)(x + 7)

1) y = (x + 5)(x + 7)

Expanding gives;

y = x² + 12x + 35

The vertex is at;

x = -b/2a

Thus;

x = -12/(2 * 1)

x = -6

The y-coordinate of the vertex is;

y = (-6)² + 12(-6) + 35

y = 36 - 72 + 35

y = -1

Vertex coordinate = (-6, -1)

2) The x-intercept is the point where y =- 0

Thus;

(x + 5)(x + 7) = 0

x + 5 = 0 or x + 7 = 0

x = -5 or -7

Thus;

x-intercept is (-5, 0) and (-7, 0)

3) y-intercept is the point where x = 0. Thus;

y = (0 + 5)(0 + 7)

y = 35

y-intercept is (0, 35)

4) There is no vertical stretch because there is no number before the brackets.

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Answer: (-1,2)

Step-by-step explanation:

Your solution is the intersecting point.

Answer:

1. 3 = 5x2 – 10x

2. 8 = 5(x2 – 2x + 1)

3. StartFraction 8 Over 5 EndFraction = (x – 1)2

Step-by-step explanation:

3-4x=5x^2-14x

3=5x^2-14x+4x

3=5x^2-10x

5x^2-10x-3=0

1. 3 = 5x2 – 10x

2. 8 = 5(x2 – 2x + 1)

8=5x^2-10x+5

8-5=5x^2-10x

3=5x^2-10x

3. StartFraction 8 Over 5 EndFraction = (x – 1)2

8/5=x^2-2x+1

Cross product

8=5(x^2-2x+1)

8=5x^2-10x+5

8-5=5x^2-10x

3=5x^2-10x

Answer:

3 - 4x = 5x2 - 14x

= 3 - 5x2 = - 14x + 4x

=  3 - 10 = 10x

= 7 = 10x

= x = 7/10

= x = 0.7

Step-by-step explanation:

the standard equation of the circle having the given center and radius is \((x-9)^2+(y-2)^2=\frac{9}{25}\).