Given sin(-t) = 2/3, find csc (t).

For a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. It is intended for the quick growth to be a "exponential increase".

The species of bacteria follow an exponential growth pattern.

The exponential growth is given as:

[tex]A(t) = A_0e^{kt}[/tex]

Where, A₀ is the initial population = 4000

k = constant

t = time = 30 minutes = 1/2 hour.

The bacteria doubles in 30 minutes, thus A(t) = 2(4000) = 8000.

Substituting the values in the equation:

[tex]8000 = 4000e^{k(\frac{1}{2} )}\\\\2 = e^{k(\frac{1}{2} )}[/tex]

Takin ln on both sides of the equation:

ln(2) = 1/2 k

2(ln(2)) = k

k = 1.38

The number of bacteria present after 3 hours:

[tex]A(t) = 4000e^{(1.38)(3)}\\\\[/tex]

A(t) = 256000

Hence, for a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.

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A triangular fence having dimensions 2x + 3, y − 6, and 4x − 3, has a perimeter of Option D: 6x + y - 6 feet.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

A triangular fence has measurements -

a = (2x + 3) feet

b = (y - 6) feet

c = (4x - 3) feet

The formula for perimeter of a triangle is -

Perimeter = sum of all three sides

So the equation will be -

Perimeter = a + b + c

Substitute the values in the equation -

Perimeter = (2x + 3) + (y - 6) + (4x - 3)

Perimeter = 2x + 3 + y - 6 + 4x - 3

Perimeter = 6x + y - 6

Therefore, the value for perimeter is 6x + y - 6 feet.

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In third-angle projection, the view of a component is drawn next to where the view was taken. In first-angle projection, the view is drawn on the other end of the component, at the opposite end from where the view was taken.

First angle Protuberance is a system of creating a 2D delineation of a 3D object. It's substantially used in Europe and Asia and has not been officially used in Australia for numerous times. In Australia, third angle protuberance is the favored system of orthographic protuberance. Note the symbol for first angle orthographic protuberance

Third Angle Projection the Object is placed in the Third Quadrant. This means that the Vertical Aeroplane is in front of the object and the Vertical Aeroplane is above the object. These changes in the position of the views are the only difference between protuberance styles.

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The value of P(-3) is -12, Quotient is (-2x² + x - 3) and Remainder is 6.

Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that a polynomial P(x) divided by a factor (x - a) is not really an element of the polynomial.

Given:

P(x) = -2x³-5x²-3.

Using the remainder theorem, the value of P(3) is given by:

P(-3)=  -2x³-5x²-3.

P(-3) =  -2(-3)³-5(-3)²-3

P(-3) = -2(-27) -5(-9) -3

P(-3) = -54 + 45 - 3

P(-3) = -12

As, the divisor of P(x) is (x+3).

so, the division is

                                  (x+3) | -2x³-5x²-3 | -2x² + x - 3

                                             -2x³-6x²

                                          __________

                                                        x² - 3

                                                        x² + 3x

                                                     ________

                                                               -3x - 3

                                                               -3x - 9

                                                              _______

                                                                      6

So, the Quotient is (-2x² + x - 3) and Remainder is 6.

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Answer:

9°

Step-by-step explanation:

x + 4x + 5x + 6x + 7x + 8x + 9x = 360

40x = 360

x = 9

The smallest angle measures x, and x = 9, so its measure is 9°.

Answer: 9°

Based on the information in the graph, it can be inferred that Josephine must have painted 1/4 of the painting.

To find the amount (fraction) of the paint, Josephine should have painted the section marked on the image. To know how much that section is equivalent to, we must take as a reference that the entire painting would be 1.

So, if we divide the painting in half, it would be 1/2, that is, we paint 1 of 2 possible parts. However, in the case of Josephine there are 4 possible parts and she only painted one. From the above, what she should have painted was 1/4.

Note: This question is incomplete. Here is the complete information:

question:

Approximately what portion of the painting was Josephine supposed to paint?

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Answer:

x=12

Step-by-step explanation:

Since b would equal E

We can make an equation.

x^2 -5x = 84

So that can be solved down to

x^2 -5x -84= 0

(x-12)(x+7)=0

x=12

x=-7

Now we see which one equals 84.

(12)^2 -5(12)=84

-7^2-5(-7)=14

therefore 12 is the correct answer and -7 does not work.

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, we can be multiply two polynomials step by step.

Distribute each term of the first polynomial to every term of the second polynomial.

Combine like terms by adding the coefficients of the terms that have the same variables raised to the same powers.

Simplify the result by arranging the terms in descending order of the exponent of the variable.

For example, let's say you want to multiply (2x + 3) and (x - 4):

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

Simplify the terms: 2x^2 - 8x + 3x - 12

Combine like terms: 2x^2 - 5x - 12

Therefore, the product of (2x + 3) and (x - 4) is 2x^2 - 5x - 12.

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The correct expression for 7c-3+2c=15 is c = -1

An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division. The structure of an expression is: Expression = (Number, Math Operator, Number) For example, = 7 + 9 = 23 × 4 = 37 – 6 = 25 + 9 – 4 ÷ 2

Move all terms containing c to the left side of the equation.

Subtract 3c from both sides of the equation:

[tex]= > 7c+6-3c=2[/tex]

Subtract 3c from 7c:

[tex]= > 4c+6=2[/tex]

Move all terms not containing c to the right side of the equation.

Subtract 6 from both sides of the equation:

[tex]= > 4c=2-6[/tex]

Subtract 6 from 2:

[tex]4c=-4[/tex]

Divide each term in [tex]4c=-4[/tex] by [tex]4[/tex] and simplify.

Divide each term in [tex]4c=-4[/tex] by [tex]4[/tex]:

[tex]\frac{4c}{4} =\frac{-4}{4}[/tex]

Simplify the left side:

Cancel the common factor of [tex]4[/tex]:

[tex]c=\frac{-4}{4}[/tex]

Simplify the right side.

Divide [tex]-4[/tex] by [tex]4[/tex]:

[tex]c=-1[/tex]

Therefore, the correct expression for 7c-3+2c=15 is c = -1

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The question is:

How to solve this 7c-3+2c=15

The t-test yields the probability (p value) that the null hypothesis is option (B) incorrect

The p-value in a t-test represents the probability of obtaining the observed test statistic (or one more extreme) assuming that the null hypothesis is true. The null hypothesis is typically a statement of "no effect" or "no difference" between two groups being compared in the test.

Therefore, a low p-value (generally less than 0.05) indicates that the observed data is unlikely to have occurred by chance under the null hypothesis and suggests that the null hypothesis is likely to be false.

In other words, a low p-value provides evidence against the null hypothesis and in favor of the alternative hypothesis (which typically represents the hypothesis that the researchers are interested in testing).

Thus, the p-value does not directly tell us whether the null hypothesis is correct or incorrect, but rather whether the evidence supports rejecting it or not.

Therefore, the correct option is (B) incorrect

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Answer:

36°

--------------------

Incenter is the intersection of angle bisectors.

It means ST is angle bisector of ∠VSW, therefore:

The sector area of the sector defined by the minor arc CB is given as follows:

7.5 cm².

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

A = πr².

We have that the radius is half the diameter, hence it's measure is given as follows:

r = 3 cm.

The angle measure of arc CB is given as follows, considering that BD is half the circle = 180º.

CB + 84º = 180º.

CB = 96º.

An entire circle has an angle of 360º, hence the area of the sector is given as follows:

A = 96/360 x π x 3²

A = 7.5 cm².

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Step-by-step explanation:

the first equation is already (without any transformation) expressing y in terms of x.

we can use that identity in the second equation :

-2x - 4(5x + 3) = 10

-2x - 20x - 12 = 10

-22x = 22

x = -22/22 = -1

and then we use the first equation to solve for y :

y = 5×-1 + 3 = -5 + 3 = -2

so,

x = -1

y = -2

The equivalent expression is -0.45t - 0. 05. Option D

Equivalent expressions are those expressions having the same solution.

From the information given, we have the expression as;

(0.35t -0.4) - (0.8t - 0.35)

Now, to simply the expression, take the steps;

expand the bracket;

0.35t - 0.4 - 0.8t+ 0.35

Now, collect the like terms

0.35t  - 0.8t - 0.4 + 0.35

Add or subtract the like terms

-0.45t - 0. 05

Hence, the expression is -0.45t - 0. 05

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The length and width of a rectangle is Positively correlated variables and the base and height of a triangle is negativley correlated variables.

In mathematics, there are many examples of variables that can be positively or negatively correlated. Here are two examples:

a. Positively correlated variables: The length and width of a rectangle. If you increase the length of a rectangle, the width tends to increase as well. So, there is a positive correlation between the length and width of a rectangle.

b. Negatively correlated variables: The base and height of a triangle. If you increase the base of a triangle, you can keep the area the same by decreasing the height, and vice versa. So, there is a negative correlation between the base and height of a triangle.

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The weight of Franklin’s mountain bike in kilograms which  weighs 17,000 grams is equal to option A. 17 kilograms.

Weight of Franklin’s mountain bike  in grams is equal to 17,000 grams

Convert the grams into kilograms.

One kilograms is equal to one thousand grams

1 kilograms = 1000 grams

⇒ 1 grams = ( 1 / 1000 ) kilograms

⇒ 17,000 grams = ( 17,000 / 1000 ) kilograms

⇒ 17,000 grams = 17 kilograms

Therefore, after converting grams into kilograms the weight of Franklin’s mountain bike whose weight in grams is 17,000 grams  is equal to option A. 17 kilograms.

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Answer: The tip is $14.00

Step-by-step explanation: 20% of 70 is 14.

Answer:

10 packages

Step-by-step explanation:

When Mr. Rankin opens the box and looks straight down on it, he could see two packages. The 12x9 paper package can fit two, side by side in the 18X12 box.

Then there also can fit a stack 5 packages tall. Each bundle is 2 inches tall and the box is 10 inches tall.

Two stacks, 5 deep is 10 packages. see image.

There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

The area of the trapezoid is approximately 42.5 square meters. So, the answer closest to this value is 38 m^2.

What is trapezoid ?

A trapezoid is a quadrilateral with at least one pair of parallel sides. In a trapezoid, the parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. The height of a trapezoid is the perpendicular distance between the bases.

There are several types of trapezoids, including isosceles trapezoids, where the legs are of equal length, and right trapezoids, where one leg is perpendicular to both bases. Trapezoids are commonly used in geometry and can be used to find the area of various shapes, such as triangles and rectangles.

To find the area of the trapezoid, we can use the formula:

Area = (1/2) x (sum of bases) x height

Since the trapezoid is isosceles, the length of the two parallel sides are the same. Let's call that length "x". We can use this information to set up an equation:

3 + 4 + 7 + x = 2x

Simplifying, we get:

14 + x = 2x

x = 14

So the length of both parallel sides is 14 meters.

Now we can plug in the values into the area formula:

Area = (1/2) x (3 + 14) x 5

Area = 8.5 x 5

Area = 42.5

Therefore, the area of the trapezoid is approximately 42.5 square meters. So, the answer closest to this value is 38 m^2.

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Answer: B 38m squared.

Step-by-step explanation:

I took the test and got this question correct.

Answer:

(-x+2)(2x+1) — first option

Step-by-step explanation:

The rectangles represent an x, red means negative and yellow is positive.

The squares represent a unit (the number 1).

The diagram attached below demonstrates how this works.

Basically the top row of this tile equation is (-x + 2)

And the column is (2x+1).

Expanding this makes -2x²+3x+2

The area of the shaded region is 12.5 square inches.

First we can subtract the area of the smaller triangle from the area of the larger triangle.

The larger triangle has a base of 8 inches and a height of 5 inches, so its area is:

(1/2) * base * height = (1/2) * 8 in. * 5 in. = 20 in²

The smaller triangle has a base of 3 inches and a height of 5 inches, so its area is:

(1/2) * base * height = (1/2) * 3 in. * 5 in. = 7.5 in²

Subtracting the area of the smaller triangle from the area of the larger triangle, we get:

20 in² - 7.5 in² = 12.5 in²

Therefore, the area of the shaded region is 12.5 square inches.

Therefore the option is F. 15 in² (none of the given answer choices match the calculated area of 12.5 in²)

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The required interior angle of 20-gon measures 162 degrees.

The interior angle measure for the n-sided polygon is given by
Interior angle measure = (n-2) x 180° / n, where n is the number of sides (or vertices) of the polygon.

Here,

To find the measure of each interior angle of a 20-gon (icosagon), we can use the formula:

For a 20-gon, n = 20. Substituting this into the formula, we get:

Interior angle measure = (20-2) x 180° / 20

= 18 x 180° / 20

= 162°

Therefore, each interior angle of 20-gon measures 162 degrees.

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Answer:

1.666... or 1 2/3

Step-by-step explanation:

The table needs to change number of Bags to Clementines.

And we know that they are only sold in pairs of 3 so we divide 5 by 3 to find the unit price

Answer:

the length of the edge of the cube is 5 meters

Step-by-step explanation:

The surface area of a cube can be found using the formula:

Surface Area = 6 x (side length)^2.

Since the surface area of this cube is 150 square meters, we can set up an equation to solve for the side length:

150 = 6 x (side length)^2

Dividing both sides by 6, we get:

25 = (side length)^2

Taking the square root of both sides, we find the side length:

side length = sqrt(25) = 5 meters.

So the length of the edge of the cube is 5 meters.

Answer:

Step-by-step explanation:

60(12*5) as a square has 4 on the top same for the bottom and has 4 vertices. I hope this helps

Answer:

1. x = 0.75

2. p = 4

3. L = 11

4. t = 42

Step-by-step explanation:

1. The price of pen is x, then

=> 6x + 24 = 28.5

=> 6x = 4.5

x = 4.5/6 = 0.75

2. p is the number of lbs

=> 2p + 50 = 58

2p = 8

p = 4

3. Perimeter = 2(L + W)

2(L + 4) = 30

=> 2L + 8 = 30

2L = 22

L = 11

4. t is the number of tickets

3t + 24 = 150

3t = 126

t = 126/3 = 42

The greatest common factor ( GCF ) of 21 , 14 and 7 is given by A = 7

The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF

Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers

Product of HCF x LCM = product of two numbers

Given data ,

Let the GCF of the numbers be represented as A

Now , the equation will be

Let the first number be p = 21

Let the second number be q = 14

Let the third number be r = 7

Now , the factors of 21 = 1 , 2 , 3 , 7 and 21

The factors of 14 = 1 , 2 , 7 and 14

The factors of 7 = 1 and 7

So , the greatest common factors of 21 , 14 and 7 is 7

Hence , the GCF is 7

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Answer:

Step-by-step explanation:

The formula to calculate the future value of an investment with compounded interest is:

Future value = Principal * (1 + rate/compoundings per year)^(number of years * compoundings per year)

In this case, the principal is $10,000, the interest rate is 2.5%, compounded annually, and the number of years is 20. So, the future value can be calculated as follows:

Future value = $10,000 * (1 + 2.5%/1)^(20 * 1)

Future value = $10,000 * (1.025)^20

Future value = $10,000 * 1.62897526

Future value = $16,289.75

Therefore, $10,000 deposited in an account earning 2.5% interest compounded annually would be worth $16,289.75 in 20 years.

The number of chips sold is 10

The number of candy bars sold is 23

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

The price of each candy bar = $1.50.

The price of each bag of chips = $1.25.

Number of chips = x

Number of candy bar = x + 13

Yesterday Melanie made $33.25.

So,

x + x + 13 = 33.25

Solve for x.

x + x + 13 = 33.25

2x + 13 = 33.25

2x = 33.25 - 13

2x = 20.25

x = 10.125

x = 10

Now,

Number of chips = 10

Number of candy bar = 10 + 13 = 23

Thus,

Number of chips sold = 10

Number of candy bar sold = 23

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