What is the value of this limit?




Please help, its important!!! No link please. Just the answer!​

Answer:

412.92

Step-by-step explanation:

\(A = P(1+\frac{r}{n} )^{nt}\)

A: Amount, P: Principal, r: interest, n: no.of times compounded yearly and t: time in years

We have P = 300

r = 4% = 0.04

n = 12 (compounded monthly)

t = 8

\(A = 300(1+\frac{0.04}{12} )^{12*8}\\\\300(\frac{12.04}{12} )^{96}\\\\= 412.92\)

Answer:

x = 3.5

Step-by-step explanation:

Since the triangles are similar we can use ratios to solve

4           7

------  = ------

(4+2)    ( 7+x)

Using cross products

4(7+x) = 7*(4+2)

Distribute

28+4x = 42

Subtract 28 from each side

4x = 42-28

4x= 14

Divide by 4

4x/4 = 14/4

x = 7/2

In fraction form, the answer is 1/4, which represents the simplified probability of the given event occurring.

To find the probability of picking a prime number and then picking another prime number, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Given the four numbers: 5, 6, 7, and 8, we can see that there are two prime numbers (5 and 7) and two non-prime numbers (6 and 8).

The total number of possible outcomes is 4 since there are four cards to choose from.

Now, let's consider the favorable outcomes, which are picking a prime number and then picking another prime number.

The probability of picking a prime number on the first draw is 2/4, as there are two prime numbers out of the four total cards.

Since we replace the card before the second draw, the probability of picking a prime number on the second draw is also 2/4.

To find the probability of both events occurring, we multiply the individual probabilities:

(2/4) * (2/4) = 4/16 = 1/4

Therefore, the probability of picking a prime number and then picking another prime number is 1/4.

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Answer:

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

Collinear points are the points on the same line.

There are two lines in the diagram.

The collinear points:

The points that are collinear are  D,G and E  and another set of points which are collinear are L,G and J.

The points which lie on the same straight line are known as collinear points.

Similarly, if three or more number of points are collinear then they form a straight line.

If we observe the figure, the points D,G and E are collinear points as they are on same line.

Similarly the points L, G and H are in the straight line which makes them collinear.

Therefore , the points L,G and J are collinear points.

Hence, the points that are collinear are  D,G and E and another set of points which are collinear are L,G and J

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The inequality expression 2x³ - 3x² - 32x + 48 > 0 has a solution of x >3/2 or x > -4 or x > 4

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

2x³ - 3x² - 32x + 48 > 0

When the above expression is factored, we have

2x³ - 3x² - 32x + 48 = (2x - 3)(x + 4)(x - 4)

So, we have the following

(2x - 3)(x + 4)(x - 4) > 0

Expanding the expression we have

2x - 3 > 0 or x + 4 > 0 or x - 4 > 0

When the values of x is solved, we have

x >3/2 or x > -4 or x > 4

Hence, the inequality expression has a solution of x >3/2 or x > -4 or x > 4

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Answer:

ok

Step-by-step explanation:

Answer:

16n

Step-by-step explanation:

Answer:

11 degrees

Step-by-step explanation:

We can write an equation

x - 13 = -2  Add 13 to both sides

x = 11

Answer:

Step-by-step explanation:

5¾ + (-¼)

Turn the mixed number to an improper fraction.

5¾ + (-¼) = 23/4 - ¼ = (23-1)/4 = 22/4 = 11/2 = 5½

:::::

-⅔ + ⅙

Give the fractions a common denominator. The least common multiple of 3 and 6 is 6.

-⅔ + ⅙ =  -4/6 + 1/6 = -3/6 = - ½

:::::

-8/5 + (-¾)

Give the fractions a common denominator. The least common multiple of 5 and 4 is 20.

-8/5 + (-¾) = -32/20 - ¾ = -32/20 - 15/20 = -47/20

Answer:

UV

Step-by-step explanation:

You just match the line from the 1st figure to the second to get the answer, the shapes have to match.

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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The simplified form of the expression (2 1/6 ) × (1 1/3) is 26/9.

Given the expression in the question;

(2 1/6 ) × (1 1/3)

To simplify, first convert from mixed to improper fraction.

(2 1/6 ) × (1 1/3)

( (2×6 + 1)/6 ) × (1 1/3)

( (12 + 1)/6 ) × (1 1/3)

( 13/6 ) × (1 1/3)

( 13/6 ) × (1×3 + 1/3)

( 13/6 ) × (3 + 1/3)

( 13/6 ) × (4/3)

Now, cancel the common factor 2.

13/6 × 4/3

13/3 × 2/3

( 13 × 2 ) / ( 3 × 3 )

( 26 ) / ( 9 )

26/9

Therefore, the simplified form is 26/9.

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If the pattern (see attachment) below was tripled, the ratio of black squares to gray squares would be equal to 1:2.

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented by the following equation:

y = kx

Where:

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

For this exercise, the ratio of black square to gray squares is given by:

B:G = 1:2

Tripling the pattern, we would multiply by three (3) as follows:

B:G = [1:2] × 3

B:G = 3:6

Dividing all through by 3, we have:

B:G = [3:6]/3

B:G = 3/3 : 6/3

B:G = 1:2.

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The rule that best describes this transformation is  option A) (x, y) (x, y-7)

The term  Coordinate geometry entails is the study of of geometric shapes by plotting them in the coordinate axes.

Note that from the image attached:

Coordinates of A  = (2,6)     Coordinates of A' = (2,-1)

Coordinates of B= (1,2)      Coordinates of B'=(1,-5)

Coordinates of C=(4,2)      Coordinates of C'=(4,-5)

From the above,  the x-coordinate is not altered but there is a difference of 7 units in y-coordinates. Hence, The rule that best describes this transformation is (x, y-7)

Hence, The rule that best describes this transformation is ( (x, y) (x, y-7)

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See full question below

Triangle ABC was transformed to create triangle A’B’C’. Which rule best describes this transformation?

A) (x, y) (x, y-7)

B) (x, y) (x, -y)

C) (x, y) (x-7, y)

D) (x, y) (-x, y)

Answer:

Step-by-step explanation:

Therefore, the set of numbers can be measures of a triangle. ... a triangle with the given measures will be a right triangle. ... The perimeter is the sum of the lengths of the three sides. ... an area of 2 square units, the irrational number √2 is.

Answer:

V≈1150.35cm³

Step-by-step explanation:

Using the formulas

V=4 /3πr3

d=2r

Solving for V

V=1/ 6πd^3=1/ 6·π·13^3≈1150.34651cm³

Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.

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They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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Answer:

\(range=5.1\)

Step-by-step explanation:

The range of a set is found by subtracting the lowest number from the greatest number.

The greatest number is 2.8 , and the lowest is -2.3. Subtract the values:

\(2.8-(-2.3)\)

Two negatives make a positive, so:

\(2.8+2.3=5.1\)

:Done

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The given table does not represent a function. The correct answer is D. No, because one x-value corresponds to two different y-values.

To determine if the table represents a function, we need to check if every x-value corresponds to exactly one y-value. Let's analyze the given table:

x | y

-------

O | 1

X | 4

2 | 3

3 | 2

3 | 5

4 |

5 |

From the table, we can see that the x-values are not unique. Both the values 3 and 4 appear twice in the x-column, but they have different corresponding y-values.

This violates the definition of a function, which states that each input (x-value) should have only one output (y-value).

Therefore, the given table does not represent a function.

The correct answer is D. No, because one x-value corresponds to two different y-values.

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Answer:

y = -7x + 2

Step-by-step explanation:

Use the slope-intercept form y = mx + b.

Substitute -7 for m, 0 for x and 2 for y.  Then

2 = (-7)(0) + b, so b must be 2.

The desired equation is y = -7x + 2.

The value of x will be 18.67 for the given data of the triangle.

We have,

Thale's theorem:

When a line parallel to one side of a triangle intersects the other two sides in distinct points, the other two sides are divided in the same ratio.

Given that the sides of the triangle are divided into two parts,

For the left part the parts will be x and x + 7 for the right side the parts will be 16 and 22.

The ratio will be the same according to Thale's theorem. The value of x will be calculated as:-

x / ( x + 7 ) = 16 / 22

22x = 16x + 112

6x = 112

x = 112 / 6

x = 18.67

Therefore, the value of x will be 18.67.

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complete question;

Find the values of x and y. Find value of x.

The amount of wax needed to make 288 candles is  41472 inches³.

A company makes wax candles in the shape of a rectangular prism. Each candle is 6 inches long, 3 inches wide, and 8 inches tall.

Therefore, the amount of wax to make 288 candles can be calculated as follows:

Hence,

volume of each rectangular prism = 6 × 3 × 8

volume of each rectangular prism = 18 × 8

volume of each rectangular prism = 144 inches cube

Therefore,

1 candle =  144 inches cube

288 candles = ?

cross multiply

volume of wax for 288 candles = 288 × 144

volume of wax for 288 candles = 41472 inches³

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The value of angle x is 133 degree

And the equation of line be of the form,

⇒  y - y₁ = 133(x - x₁)

In the given line,

one angle is of 47 degree

And other is x degree

To find the value of x,

Since we know that,

The angle  of line is 180 degree.

Therefore,

⇒ x + 47 = 180

⇒         x = 133 degree

Therefore slope of this line be 133 degree

Now let this line is  passing through (x₁, y₁)

Hence,

The equation of  line be,

⇒ y - y₁ = (slope)(x - x₁)

⇒  y - y₁ = 133(x - x₁)

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Answer:

0.6

Step-by-step explanation:

probability of choosing a composite number, since all composite numbers from 12 are, 2,4,6,8,10,12 (might have left some out) but those are 6 chances you can pick a composite number :)

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

The domain and the range of the function are [0, 4] and [0, 19.6] respectively

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The function is given as

h(t) = -4.9t² + 19.6t

The domain is the set of valid time the function can take

To do this, we simply plot the graph of h(t) = -4.9t² + 19.6t

On the graph, we can see that:

The t values start from 0 and ends at 4

This means that the domain is [0, 4]

On the graph, we can see that:

The y values start from 0 and ends at 19.6

This means that the range is [0, 19.6]

Hence, the domain and the range of the function are [0, 4] and [0, 19.6] respectively

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