30/7 times t plus 9/14 if t equals 13/2

The principal that would need to be invested to have an accrued amount of 1 million dollars after 30 years is $90,717.95.

The formula compound interest where interest is compounded continuously is expressed as;

A = P × e^(rt)

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for P.

A = P × e^(rt)

P = A / e^(rt)

P = $1,000,000 / e^( 0.08 × 30 )

P = $1,000,000 / e^( 2.4 )

P = $90,717.95

Therefore, the amount of principal is $90,717.95.

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The difference in area is of about 1445.1 square miles.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The radius is the distance of the center of the circle to any point on the circumference of the circle.

For the circle with a radius of 18 miles, the area is given as follows:

A = π x 18² = 1017.9 square miles.

For the circle with a radius of 28 miles, the area is given as follows:

A = π x 28² = 2463 square miles.

Hence the difference is of:

2463 - 1017.9 = 1445.1 square miles.

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The volume of the sawdust pile is 3754.667 cubic feet

A cone is a three-dimensional shape that has a circular base with tapers from the flat base into the vertex.

The formula for searching the volume of the cone can be described below :

V = [tex]\frac{1}{3}[/tex] π [tex]r^{2}[/tex] h

which

V = volume of the cone

r = radius of cone circular base

h = height of cone ( tall of the cone )

From the question, we have following information :\

1. Base diameter = 32 feet

  Base radius = Base diameter / 2 = 32 feet / 2 = 16 feet

2. Tall / Height of the cone = 14 feet

Since the known parameter is enough to be put into the formula, we can simply subtitute the formula with known parameter

V = [tex]\frac{1}{3}[/tex] π [tex]r^{2}[/tex] h

  = [tex]\frac{1}{3}[/tex] x π x [tex]16^{2}[/tex] x 14

  = 3754.667 cubic feet

Hence the volume of the cone is 3754.667 cubic feet

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Answer:

24x+96

Step-by-step explanation:

so we could use Distributive property

which means -12time -2x+-12times-8

                                   =24x+96

i hope is helpful

If [tex]\overline{x}$[/tex] represents the mean of n observations x₁, x₂, ……xₙ, then the value of [tex]$\sum_{i=0}^{n} (x_{i} - \overline{x})$[/tex] is 0.

Mean is the average value of the group of values. It shows the equal distribution of values for a given data set.

To calculate the arithmetic mean of a group of data, first, add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed, we obtain the following formula for the mean ([tex]\overline{x}[/tex]):

[tex]\overline{x}= $\sum {\frac{x}{n} $[/tex]

The formula of the mean ([tex]\overline{x}$[/tex]) is:

[tex]\overline{x} = $\sum_{i=0}^{n} {x_{i}$/n[/tex]

[tex]$\sum_{i=0}^{n} {x_{i} = \overline{x}n[/tex]           Eqn(1)

Here, n is total number of observations.

The value of [tex]$\sum_{i=0}^{n} (x_{i} - \overline{x})$[/tex] is calculated as follows:

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = \sum_{i=0}^{n} x_{i} - \sum_{i=0}^{n}\overline{x}[/tex]

Now, from equation (1), we get

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \sum_{i=0}^{n}\overline{x}[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \overline{x}\sum_{i=0}^{n}1[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \overline{x}n[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = 0[/tex]

Hence, the correct answer is B.

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The equation is in slope-intercept form is y = 240t + 0

The equation of a line in slope-intercept form is given by:

y = mx + b

where m is the slope and b is y-intercept

Let's say the number of times the insect beats its wing in t seconds is represented by y. Then the relationship can be expressed as:

y = 240t

The slope (240) shows that for every 1 second increase in time, the number of wing beats increases by 240. The y-intercept (0) indicates that when t = 0, y=0, i.e. when the insect has not started flying, it has not beaten its wing yet.

Therefore, the equation is in slope-intercept form: y = 240t + 0

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The expression that represents the area of the playground is 45x² - 13x - 2 square feet.

The area of a rectangle is found by multiplying its length by its width. Here the length is given as 5x - 2 feet and width is given as 9x + 1 feet. So, the expression that represents the area of the playground is:

Area = Length * Width

= (5x - 2) * (9x + 1)

= 5x × 9x + 5x -2 × 9x - 2

= 45x² + 5x - 18x - 2

= 45x² - 13x - 2

Therefore, the expression that represents the area of the playground is 45x² - 13x - 2 square feet.

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Answer:

In the given triangle △ABC, AB is equal to 4 and m∠F is equal to 30°. In the triangle △DEF, AB is equal to 6 and m∠F is equal to 50°.

The mean of the sample size of 25 would fall between 68 and 72 68% of the time.

Using the 68-95-99.7 rule, if a variable is normally distributed with mean μ and standard deviation σ, then:

Since the interval we are interested in (68 to 72) falls within the 68% of the data that falls within 1 standard deviation of the mean, it means that 100% - 32% = 68% of the data falls within this interval.

Thus, the mean of this sample size of 25 would fall between 68 and 72 68% of the time.

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Sample 3's mercaptoethanol and urea mixture breaks sulphide bonds, resulting in the loss of tertiary structure and activity, whereas in sample 2, urea is introduced. This chemical denaturing agent aims to break up peptide connections, which would then affect the structure and function of the protein.

An experiment data is given below:

This experiment describes how protein denaturing chemicals affect a protein's ability to function.

Sample 1 preserves protein structure and function because it just contains buffer and no denaturing agent.

Enzymatic activity then results in high fluorescence as a result of this.

In sample 2, urea is added, a chemical denaturing agent that seeks to dismantle peptide bonds, disrupting protein structure and activity.

As a result, there are now less fluorescence products and less active enzyme products overall.

In sample 3, when mercaptoethanol and urea are mixed, sulphide bonds are broken and tertiary structure and activity are lost.

After dialysis, sample 4 had both urea and mercaptoethanol eliminated from it.

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Answer:

see explanation

Step-by-step explanation:

for the given angles to form a triangle they must sum to 180°

given

31 [tex]\frac{3}{4}[/tex]°  , 53 [tex]\frac{1}{2}[/tex]° , 94 [tex]\frac{3}{4}[/tex] ° ( changing to decimal form and adding )

= 31.75° + 53.5° + 94.75°

= 180°

Thus the 3 given angle measures can form a triangle.

Answer: the answer is A), normal is 28 + 4fee, but if she buys LOTS its 22 +8

contact me through discord Acathia#0103, its easier to help, I can help with multiple questions aswell

Step-by-step explanation:

Three edges and three vertices make up the three-sided polygon known as a triangle. The fact that a triangle's internal angles can be added up to equal 180 degrees is its most significant characteristic.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Each side is different, and each angle is less than 90 degrees. Obtuse isosceles: two identical sides and identical angles, with one angle more than 90 degrees.

Shapes with three sides are called triangles. The various triangle varieties go under various names. The dimensions of a triangle's sides and angles determine its type (corners).

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Answer:

The properties of multiplication are distributive, commutative, associative, removing a common factor and the neutral element.

Step-by-step explanation:

The distributive, commutative, associative, removes a common factor, and neutral element characteristics of multiplication.

According to the associative property, grouping symbols can be altered during addition or multiplication without affecting the outcome.

A + (b + c) = A + (b + c) is how this is expressed. In order to multiply a number by all of the distinct addends of another number, one must use the distributive property of multiplication.

A mathematical principle known as the associative property states that the product of a multiplication problem is unaffected by the way the factors are organized.

You can arrange the addends in multiple ways without changing the result, according to the associative property of addition. You can reorder the addends and the result won't change, according to the commutative property of addition.

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The system of equation has no solution

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

2y = 6

y = -15

Since these are two different equations with the same variable, y, we can use substitution to find a solution.

Starting with the second equation, y = -15, we can substitute this value into the first equation:

2y = 6

2(-15) = 6

-30 = 6

This equation is false, meaning there is no solution for y that satisfies both equations.

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Answer:

below

Step-by-step explanation:

Use right triangle Pythagorean theorem

L^2 = 8^2 + 4^2

L^2 = 80

L = sqrt (80)   units      <====exact

             approx is sqrt(80) =~8.94 units

The midpoints of the segment is (4, -3.5).

The coordinates of the point A(x, y) which divides the line segment joining the points P(a , b) and Q(c , d) internally in the ratio m : n are given by the formula: P ( x , y ) = ( a x n + c x m / (m+n)  , bn + dn / (m+n))

Given:

Points (-4, -7) and (12, -6).

So, the ratio is line is m:n = 1:1

let (x, y) be the midpoint.

Now, using section formula

x = (-4 x 1 + 12 x 1)/ (1+1)

x= (-4 +12) /2

x= 8/2

x= 4

and, y = (-7 x 1 -6 x 1)/ 2

y = -7-6/2

y = -13/2

y = -3.5

Hence, the midpoints are (4, -3.5).

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The solution to the differential equation y'' + 4y' + 2y = 4 with zero initial conditions is y(t) = 2e^-2t.

CORRECTION: Given the differential equation: y'' + 4y' + 2y = 4

To solve this differential equation using Laplace transforms, we first need to take the Laplace transform of both sides. The Laplace transform of the derivative of y is given by:

L{y'} = sY(s) - y(0) = sY(s) (assuming zero initial conditions)

L{y''} = s^2Y(s) - sy(0) - y'(0) = s^2Y(s) (assuming zero initial conditions)

Now, substituting these Laplace transforms in the given differential equation, we have:

s^2Y(s) + 4sY(s) + 2Y(s) = 4/s

Solving for Y(s), we get:

Y(s) = (4/s) / (s^2 + 4s + 2) = 2 / (s + 2)^2

Finally, taking the inverse Laplace transform of Y(s), we get:

y(t) = L^-1{Y(s)} = 2e^-2t

Therefore, the solution to the differential equation y'' + 4y' + 2y = 4 with zero initial conditions is y(t) = 2e^-2t.

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Answer: D) 15.7

Step-by-step explanation:

Start with the formula C=2 πr

Then solve for r r=C2π = 98.62·π = 15.69(7)204

The radius of the circle is 15.7 mm.

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

We have,

The circumference of Circle = 2πr

Also, The circumference of a circle is 98.596 millimeters.

So, circumference of Circle = 2πr

98.596 = 2πr

98.596 = 6.28r

r= 98. 596 / 6.28

r = 15.7 mm

Thus, the radius is 15.7 mm.

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Answer:

142

Step-by-step explanation:

6 day av 144 / day so total =144*6

first 3 day av 132 so total =132*3

next 2 days av 163 so total =163*2

144*6= 132*3+163*2+final day

so final day = 142

The process of converting a decimal number to its base 7 equivalent is explained below.

The radix point is the point that separates the whole number part of a number from its fractional part in a numerical system.

The process of converting a decimal number to its base 7 equivalent starts by dividing the decimal number by 7. The remainder from this division will be the first digit after the radix point in the base 7 equivalent.

We continue this process by dividing the quotient obtained in the previous step by 7 until we get a quotient of 0. The remainders obtained from each division will be the digits after the radix point in the base 7 equivalent, in the reverse order.

To get the integer part, we keep dividing the decimal number by 7 until we get a quotient of 0. The remainders obtained from each division will be the digits in the integer part of the base 7 equivalent, in the reverse order.

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The number of students actually enrolled is 6000.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a large university accepts 50​% of the students who apply. Of the students the university​ accepts, 40​% actually enroll. If 30,000.

The number of students will be calculated as:-

Number = ( 30000 x 0.5 x 0. 4 )

Number = 6000

Therefore, the number of students will be 6000.

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Three fifth of the vegetable in Alia garden are tomatoes so number of tomatoes are 3/5x in Alias garden.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

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(a) the root of the equation is =4.4.(b) x=31pi for x=100 approx.

the root of an equation is said to be that value where the equation gets zero. And the intersection point of two equations is the same value of equations.

The roots of x =tan(x), graph y = x and y = tan(x), and look at the intersection points of the two curves.

a) Find the smallest nonzero positive root of x = tan(x),

after seeing the graph the root of the equation is =4.4.

(The desired root is greater than pi/2).

b) Solve x =tan(x) for the root that is closest to x = 100.

after examining the graph of the function we can see that 31pi for x=100 approximately.

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Answer:

see explanation

Step-by-step explanation:

solving the inequality

n + 6 < 13 ( subtract 6 from both sides )

n < 7

this means that any value less than, but not including, 7 is a solution

listing the values that are a solution from - 10 through to 10 , then list of solutions is

- 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Cylinder volume: Considering that;

14 feet is the cylindrical tank's diameter.

The cylindrical tank is 40 feet long.

Find:

how much gas is in the tank.

Computation:

14 feet is the cylindrical tank's diameter.

Tank's cylinder's radius is 14/2, or 7 feet.

Volume of the tank: x amount of gas inside it

Volume of gas in the tank equals πr²h.

Portion of gas in the tank = (3.14)(7)²(40)

Fuel level in tank equals (3.14)(49) (40)

6154.4 feet³ of gas have been filled into the tank.

(Hope this helped!)

The probability that X is between 0.5 and 1 is (C) 19/24.

The probability that X is between 0.5 and 1 can be found by calculating the definite integral of the PDF f(x) over the interval [0.5, 1]:

P(0.5 <= X <= 1) = ∫f(x)dx from 0.5 to 1

Given the PDF f(x) = ax + X^2 for 0<=x<=1, we can evaluate this definite integral as:

P(0.5 <= X <= 1) = ∫(ax + X^2)dx from 0.5 to 1

= [ax^2/2 + x^3/3] from 0.5 to 1

= (1.5a + 1/3) - (0.5a + 0.125)

= (1 + 1/6) - (0.5 + 1/8)

= (2/3 - 3/8)

= 5/24

Since 5/24 is equal to 0.2083, the closest answer choice to this value is 19/24.

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The coordinate of the point P that lies on the line segment AB will be (6.6, 3.8).

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

AP to PB is in the ratio of 4 to 1. Then the coordinate of the point P is given as,

x = (4 × 8 + 1 × 1) / (4 + 1)

x = (32 + 1) / 5

x = 33 / 5

x = 6.6

y = (4 × 4 + 1 × 3) / (4 + 1)

y = (16 + 3) / 5

y = 19 / 5

y = 3.8

The coordinate of the point P that lies on the line segment AB will be (6.6, 3.8).

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Answer:

It's already in order

[tex]\frac{3}{4}[/tex] × [tex]\frac{4}{9}[/tex], [tex]\frac{7}{7}[/tex] × [tex]\frac{4}{9}[/tex]  , [tex]1\frac{2}{3}[/tex] × [tex]\frac{4}{9}[/tex], [tex]2[/tex] × [tex]\frac{4}{9}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] × [tex]\frac{4}{9}[/tex]

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

[tex]\frac{7}{7}[/tex] × [tex]\frac{4}{9}[/tex]

[tex]=\frac{4}{9}[/tex]

[tex]1\frac{2}{3}[/tex] × [tex]\frac{4}{9}[/tex]

[tex]=\frac{20}{27}[/tex]

[tex]2[/tex] × [tex]\frac{4}{9}[/tex]

[tex]=\frac{8}{9}[/tex]

Change them all to the same common denominator of 27

[tex]\frac{9}{27}, \frac{12}{27}, \frac{20}{27}, \frac{24}{27}[/tex]

There about 24 hockey tickets were bought by Bryant. Out of which 14 tickets were child tickets.

A mathematical claim containing two equal algebraic expressions is known as an algebraic equation.

Given that the cost of an adult ticket is $5.50, and a child ticket is $2.00. The total spent is $83, and the total number of tickets bought is 24.

Let us consider the number of adult tickets bought is x and the number of children tickets bought is y.

Then x+y=24. From this, x=24-y.

Also, the given situation is written in an expression as,

[tex]\begin{aligned}5.50x+2.00y&=83\\5.50(24-y)+2.00y&=83\\132-5.50y+2.00y&=83\\-3.5y&=-49\\y&=14\end{aligned}[/tex]

The required answer is 14.

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