Which of the following represents an exponential function? Select one: a. growth of bacteria in a petridish b. The amount billed to a girl who bought a pair of jeans c. The conversion of kelvin to celsiusd. The number of students enrolled in a class

Answer:

y = -3/4x + 6

Step-by-step explanation:

In order to write an equation of the line in slope-intercept form, we first have to look at the equation:

y = mx + b

We have m, the slope, which is -3/4, and we have our y and x values, so in order to find b, we need to plug the other values in and solve for b

(-4,3)

y = 3

x = -4

m = -3/4

y = mx + b

(3) = [tex](\frac{-3}{4} )[/tex](-4) + b

3 = -3 + b

6 = b

So, equation of the line in slope-intercept form that passes through point (-4,3) and has a slope of -3/4, is y = -3/4x + 6

I hope this helps! :)

There is no solution that satisfy the equation (1,1,1) x u = (7, -4, -3).

The term "vector" in mathematics and physics is used informally to refer to some values that cannot be stated by a single integer (a scalar) or to certain members of vector spaces. Though the components of an algebra are frequently not referred to as vectors, any algebra over a field is a vector space. They are sometimes referred to as vectors, mostly for historical reasons.

A real number is a number that can be used to represent a continuous one-dimensional quantity in mathematics, such as a temperature, duration, or distance. Continuous in this context suggests that values may vary by arbitrary little amounts. An infinite decimal expansion can nearly always represent any real number.

There is no value, not even 0, that would satisfy the equation, which is referred to as "no solution."

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The volume of the given solid is 464 cubic inches.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

From the given figure,

We know that, the volume of a cuboid is Length×Width×Height

Volume of two identical cuboid is

2(8×3×7)

= 336 cubic inches

Volume of small cuboid is

8×4×4

= 128 cubic inches

The volume of the solid =336+128

= 464 cubic inches

Therefore, the volume of the given solid is 464 cubic inches.

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K5 is a non-plannar graph with a minimum number of edges on 5 vertices and K3,3 is a non-plannar graph with a minimum number of edges on 6 vertices.

What is the K3-3 graph or K5?

K5 is a five-vertex graph with one edge between each pair of vertices. One edge connects each pair of vertices from opposing sets in graph K3,3 which has six vertices in two sets of three.

Both K5 and K3,3 are non-planar graphs having a minimal number of edges on their respective sets of 5 and 6 vertices, respectively.

Every appropriate sub-graph of a minimum non-planar graph G is a planar non-planar graph. 4.

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Answer:

1÷(5/2×(2×(8-2/5)-1))

1÷(5/2×(2×(6/5)-1))

1÷(5/2×(12/5-1))

1÷(5/2×7/5)

1÷(35/10)

1÷35/10

1×10/35

10/35

2/7

This is the answer hope you understand it

We have to pay $129,216.31; $64,800.

Option (c) is correct.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is the interest on interest, and it is the mechanism that causes an investment to grow at an exponential rate.

To calculate the amount of money you will have in the investment plan after 18 years, we can use the formula for compound interest:

A = P(1 + r)^n

Where:

A is the final amount (the future value)

P is the principal, or the initial deposit, in this case $300

r is the annual interest rate, in this case 7% (expressed as 0.07)

n is the number of years, in this case 18

m is the number of times the interest is compounded per year. in this case 12 (monthly)

By using this formula, the final amount will be:

A = 300(1 + 0.07/12)^(12*18)

A = $129,218.51

To compare this amount to the total deposits made over the time period, we can calculate the total amount of money deposited by multiplying the deposit amount ($300) by the number of deposits made per month (12) by the number of years (18).

Total deposit = 3001218 = $64,800

Hence, we have to pay $129,216.31; $64,800.

Option (c) is correct.

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Since X, Y, and Z are independent random variables, the probability of one event occurring has no bearing on the likelihood of the other events. In this instance, the probabilities of X, Y, and Z are 30%, 40%, and 20%, respectively.

We must take into account the possibility that both events could occur simultaneously when determining the likelihood that either X or Y will occur. The occurrences where both X and Y occur would be doubly counted if we just added the probabilities of X and Y. To circumvent this, we employ the following formula for the chance of two events occurring together:

P(X or Y) = P(X) + P(Y) - P (X and Y)

This formula takes into account the fact that we must deduct the probability of X and Y's intersection (i.e., the likelihood that they both occur) from the total of each variable's individual probabilities.

Given that X and Y are independent events, P(X and Y) = P(X) * P(Y) = 0.3 * 0.4 = 0.12 is known.

P(X or Y) is therefore equal to P(X) + P(Y) - P(X and Y) = 0.3 + 0.4 - 0.12 = 0.68 = 68% 

 So, according to option most approximately option is A.

Therefore, 70% would be the most accurate response.

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The fourth co-ordinate of the rectangle is D (-2, -1). The equation of the line that passes through the points B and D is 3y = 2x + 3.

The given points are:

A(−2,3), B(4,3), C(4,−1)

When we plot these points on the graph we can easily estimate the fourth point which will be equidistant from A as the point C is from B and from the point C as the point A is from B.

Therefore, the diagonal points are B(4, 3) and D(-2, -1).

The equation of the line between these two points is:

(y - y1) = ((y2 - y1)/(x2 - x1)) (x - x1)

(y - 3) = ((-1 -3)/(-2 - 4)) ( x - 4)

y - 3 = (2/3) (x - 4)

3y - 9 = 2x - 8

3y = 2x + 1

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Answer:

A = -5

B = -2

C = 3

The total milliliters of punch is 2x + y.

To find the total amount of milliliters of punch, we need to add together the amount of water, apple juice, and grape juice used to make it. Since the punch is made up of "water by volume" and "the rest is grape juice," we know that the ratio of water to grape juice is 1 : 1. If we know the amount of grape juice used in milliliters, we can use that to find the amount of water and apple juice used, and then add all three amounts together to find the total amount of milliliters of punch.

Let's say that "x" milliliters of grape juice were used to make the punch. Since the ratio of water to grape juice is 1 : 1, we know that the same amount of water, "x" milliliters, were used. To find the total amount of milliliters of water and grape juice, we add x + x = 2x milliliters.

However, the prompt also mention "apple juice" is also included in the punch, so we need to add the amount of apple juice used in the punch to find the total milliliters of punch. If the amount of apple juice used is "y" milliliters, then the total milliliters of punch is 2x + y.

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Answer:

Step-by-step explanation:

80

Answer:

80

Step-by-step explanation:

To find 125% of 64, you can multiply 64 by 1.25.

125% of 64 = 64 x 1.25 = 80

So, 125% of 64 is 80.

Answer:

57 degrees

Step-by-step explanation:

vertical angles are equal. thus, 3x+9 = 4x-7

subtract 3x from both sides to put all x values and their coefficients on one side

9 = x-7

add 7 to both sides to isolate x

x = 16

B = 4x-7 = 4 * 16 - 7 = 57

Answer:

w

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

[tex] \cos(60) = \frac{x}{12} \\ x = 12 \cos(60) = 6[/tex]

Using the Fundamental Counting Theorem, it is found that 6 different possible outcomes are there.

What is the fundamental principle of counting?

The total number of times an event can occur is m n if there are m possible ways for one event to happen and n various ways for another. A rule used to determine the total number of potential outcomes in a circumstance is known as the fundamental counting principle.

                        It states that there are n m times m n times m methods to do both of these activities if there are n ways to perform one action and m ways to perform another action after that.

For the coin, there are two outcomes, hence . n₁ = 2

For the spinner, there are three outcomes, hence n₂ = 3

Then, the number of outcomes is given by:

N = 2 x 3 = 6.

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Answer:

40m + 40

Step-by-step explanation:

8(5m+5)

40m + 40

Answer: because the mean is 48

Step-by-step explanation:

the average (mean) is 48 so therefore its reasonable that half scored under half scored higher

(i) 2.5 cm, 6.5 cm, 6 cm and (iii) 1.5 cm, 2cm, 2.5 cm can be the sides of a right triangle.

To check if the given measurements are possible sides of a right triangle, it must follow the Pythagorean theorem, where the square of the hypotenuse is equal to the sum of the squares of the legs.

c² = a² + b²

where c is the hypotenuse(longest side)

and a and b are the two other sides

(i) 2.5 cm, 6.5 cm, 6 cm

6.5² = 2.5² + 6²

42.25 = 6.25 + 36

42.25 = 42.25

(ii) 2 cm, 2 cm, 5 cm

5² = 2² + 2²

25 = 4 + 4

25 ≠ 8

(iii) 1.5 cm, 2cm, 2.5 cm

2.5² = 1.5² + 2²

6.25 = 2.25 + 4

6.25 = 6.25

Hence, (i) 2.5 cm, 6.5 cm, 6 cm and (iii) 1.5 cm, 2cm, 2.5 cm can be the sides of a right triangle.

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The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.

The formula to generate random numbers between 01 and 99 is (number*99/max_number)+1.

For the first number in the row, 78038, the calculation would be (78038*99/78038)+1 = 99.

For the second number in the row, 18022, the calculation would be (18022*99/78038)+1 = 25.

For the third number in the row, 84755, the calculation would be (84755*99/78038)+1 = 68.

For the fourth number in the row, 23146, the calculation would be (23146*99/78038)+1 = 17.

For the fifth number in the row, 12720, the calculation would be (12720*99/78038)+1 = 9.

For the sixth number in the row, 70910, the calculation would be (70910*99/78038)+1 = 89.

For the seventh number in the row, 49732, the calculation would be (49732*99/78038)+1 = 56.

For the eighth number in the row, 79606, the calculation would be (79606*99/78038)+1 = 97.

The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.

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The supplied statement states that the iterated integral after being converted to interpolation is 32/3.

In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or just a new function, the reverse of which contains the original mechanism (indefinite integral). To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context. Trigonometric functions of functional and equations are a concept in mathematics. Integral is a derivative of Middle English, Latin integer, and Medieval Latin integralis, each of which mean "making up a whole."

Therefore, the area is,

[tex]R=\left\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{2 x-x^2}\right\}[/tex]

So,

[tex]y=\sqrt{2 x-x^2}[/tex]

y² = 2x - x²

x² - 2x + y² = 0

x² - 2x + 1 + y² = 1

(x-1)² + y² = 1

In other words, the area is the middle section of the disk with a radius of 1 and a center at (0,1).

Region R's polar coordinates are

x = r cos∅, y = r sin∅

So,

[tex]y=\sqrt{2 x-x^2}[/tex]

y² = 2x - x²

x² + y² = 2x

r² = 2r cos∅

r = 2 cos∅

The polar coordinates of the sphere of integration as,

[tex]R=\left\{(r, \theta) \mid 0 \leq \theta \leq \frac{\pi}{2}, 0 \leq r \leq 2 \cos \theta\right\}[/tex]

The provided integral then becomes,

[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r \cdot r d r d \theta \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r^2 d r d \theta \\= & \int_0^{\frac{\pi}{2}} 6\left(\frac{r^3}{3}\right)_0^{2 \cos \theta} d \theta\end{aligned}[/tex]

[tex]\begin{aligned}& =\int_0^{\frac{\pi}{2}} 2\left(8 \cos ^3 \theta-0\right) d \theta \\& =16 \int_0^{\frac{\pi}{2}} \cos ^2 \theta \cdot \cos \theta d \theta \\& =16 \int_0^{\frac{\pi}{2}}\left(1-\sin ^2 \theta\right) \cdot \cos \theta d \theta\end{aligned}[/tex]

Let u = sin∅ then du = cos ∅ d∅

If ∅ = 0 then u = 0 and if ∅ = π/2 then u = 1.

The above integral thus becomes,

[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & 16 \int_0^1\left(1-u^2\right) d u \\= & 16\left(u-\frac{u^3}{3}\right)_0^1 \\= & 16\left(1-\frac{1}{3}\right)\end{aligned}[/tex]

= 32/3

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Therefore , the solution of the given problem of fraction comes out to be Stella makes 6 bows.

The definition of a fraction is a portion of a whole. A single object or a collection of objects might be the entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterwards presented in numerical form.

Here,

Given :

Take the amount of ribbon and divide by the amount needed per bow

5 1/3÷ 1/3

Change the mixed number to an improper fraction

(5*1 +1)/3 ÷1/3

6/3 ÷1/3

Copy dot flip

6/3 * 3/1

6

Stella makes 6 bows.

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Answer:

13.75 m.

Step-by-step explanation:

We can start by calculating the total area of the walls of the room by subtracting the area of the door and window from the total area of the room.

The total area of the room is 20m * 14m = 280 m^2

The area of the door is 1m * 1.7m = 1.7 m^2

The area of the window is 1.8m * 1.8m = 3.24 m^2

The total area of the walls is 280m^2 - 1.7m^2 - 3.24m^2 = 275.06 m^2

Now that we have the total area of the walls, we can divide it by the cost of painting per m^2 to find the height of the room.

The cost of painting per m^2 is $12165.9 / 275.06 m^2 = $44.32/m^2

So we can find the height of the room by dividing the cost by the rate of painting, $12165.9 / $44.32/m^2 = 275.06 m^2 / (20m * h) = 275.06 / 20 = 13.75m

Therefore, the height of the room is approximately 13.75 m.

Answer:

No.

Step-by-step explanation:

Using the Pythagorean Theorem, a^2 + b^2 = c^2, this would not be possible, because 4 + 9 does not equal 16.

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16

Answer:

No.

Step-by-step explanation:

the Pythagorean Theorem states that a²+b²=c²

where a and b are the legs and c is the hypotenuse of a right triangle

in this case we need to know if 2²+3²=4²

2²=4

3²=9

4²=16

4+9=13

13≠16

so no, the hypotenuse cannot be 4 inches long.

Answer:no

Step-by-step explanation:

The solution will remain the system since the same two inequalities still make up the system.

The degree of the measure of the exterior angle is 141 3/7°.

the term exterior angle in triangle is defined as angles that are parallel to the inner angles of a polygon but lie on the outside of it

Here we know that A square and a regular heptagon are coplanar and share a common side AD.

And then here we need to find each of the interior angle of the regular heptagon.

As we all know that here we have to use the formula that gives the interior angle measure for a regular polygon with any number of sides is 180(n-2)/n where n is the number of sides.

According to the given formula here we have a regular heptagon's interior angle measures is calculated as

=> 180(7-2)/7 = 128 4/7.

Here we also know that the angle A and D would be 128 4/7 degrees.

Here the next step is to Find angle BAC.

For that here we have to know that a square's interior angle is 90 degrees and a heptagon's is 128 4/7 degrees.

Now we have to subtract those from 360 degrees to find angle BAC then we get the expression like the following,

=> Angle BAC = 360 - (angle A + 90)

=> 360 - (128 4/7 + 90)

When we simplify this one then we get the resulting value as,

=> 360 - 218 4/7 = 141 3/7 degree

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Yes, it is possible to draw a right angled triangle with sides 1.5cm , 2cm , and 2.5cm.

As given in the question,

In the given triangle,

Measure of the side length of the given triangle are :

1.5cm , 2cm , and 2.5cm

In this triangle longest side is equal to 2.5cm.

Given triangle is right angled triangle check whether Pythagoras theorem satisfied the measure of the sides of the triangle.

Hypotenuse represents the longest side.

( Hypotenuse)² = ( Side 1 )² + ( Side 2)²

Right hand side

= ( 1.5 )² + ( 2 )²

= 2.25 + 4

= 6.25

= ( 2.5 )²

= Hypotenuse²

It satisfied the Pythagoras theorem.

Therefore, the given sides of the triangle represents it is a right angled triangle.

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Since 3 doughnuts is more expensive than and closer to pricing at 2, Sally can only eat 2 doughnuts.

In economics, marginal utility refers to the addition of pleasure or benefit utility a buyer gets by purchasing an extra unit of a good or service. When marginal utility is greater than or equal to price, total utility is maximized. Minimum Utility MU It speaks about increased utility as a result of consuming an extra unit of a commodity.

The change in overall utility is known as marginal utility.

When she accepts two donuts, her marginal utility is three (8–5=3).

Her marginal utility for eating three donuts is 1 (9 – 8).

Since 3 is more expensive than and closer to price at 2, she should only eat 2 doughnuts.

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