hurry this is a test please answer correctly ​

Answer:

Below in bold.

Step-by-step explanation:

0.3. e^3x = 27

Taking logs of both sides:

ln (0.3. e^3x) = ln 27

ln (0.3) + ln e^3x = ln 27

ln e^3x = ln 27 - ln(0.3)

3x = ln 27 - ln 0.3

3x = ln(27/0.3) = ln 90

x = 1/3 ln 90

x = ln (90^1/3)

Approximate value of x:

= 1.499936557

= 1.500 to the nearest thousandth.

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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Answer:

\angle ACB=40^{\circ}, \angle ABC=63^{\circ}

Step-by-step explanation:

Finding x:

We know that \(\angle DAB=180^{\circ}\), because it's a straight line. So, \(\angle CAB=180^{\circ}-103^{\circ}=77^{\circ}\).

We know that the sum of the angles of any triangle will be \(180^{\circ}\).

So, we have that \((3x-14)+(3x+9)+77=180\).

Combining like terms on the left gives \(6x+72=180\).

Subtracting \(72\) from both sides gives \(6x=108\).

Dividing both sides by \(6\) gives \(x=18\).

Finding missing angle measures:

\(\angle ACB=3x-14=3(18)-14=54-14=40\).

\(\angle ABC=3x+9=3(18)+9=54+9=63\).

So, \(\angle ACB=40^{\circ}\) and \(\angle ABC=63^{\circ}\) and we're done!

Note: \(\angle ACB+\angle ABC=\angle CAD\). Coincidence? If not, try and prove it!

The perimeter of a shape is the sum of its side lengths

Becca, Lucas, and Christian are correct

The side lengths of the triangle are x, 3x - 4 and 3x - 4

So, the perimeter (P) is:

P = x + 3x - 4 + 3x - 4

The above equation can be rewritten as:

P =2(3x - 4) + x

P = 6x + x - 4

P = (3x - 4) + (3x - 4) + x

P = 7x - 4

Hence, Becca, Lucas, and Christian are correct

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

the surface area for spheres is

4 × π × r²

4 × π × (7²) = 196 π

Answer: (6, 0) and (0, 8)

Step-by-step explanation:

Answer:

A parallel line has the same slope, but is translated away from the line it is parallel to. Let's create an equation using what we have:

−

1

=

−

3

(

−

2

)

+

b

−

1

=

6

+

b

−

7

=

b

y

=

−

3

x

−

7

Hope this helped!!

In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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Answer:

507,640,142,072

Step-by-step explanation:

not sure what you are asking but I hope this helps! :D

P(A and B) is equal to 6.

To find P(A and B), we can use the formula:

P(A and B) = P(A) + P(B) - P(A U B)

Given the information:

P(A U B) = 32 (the probability of either event A or event B occurring)

Universal set contains 52 elements (total number of possible outcomes)

P(A intersection B) = 6 (the probability of both event A and event B occurring)

P(A) = 12 (the probability of event A occurring)

P(B) = 26 (the probability of event B occurring)

We can substitute the known values into the formula:

P(A and B) = P(A) + P(B) - P(A U B)

P(A and B) = 12 + 26 - 32

Simplifying the expression:

P(A and B) = 38 - 32

P(A and B) = 6

Therefore, P(A and B) is equal to 6.

The result indicates that the probability of both event A and event B occurring simultaneously is 6 out of the total number of possible outcomes in the universal set. It means that out of the 52 elements in the universal set, 6 of them satisfy the conditions of both A and B.

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The rate at which the spherical balloon is increasing is calculated as approximately 0.049 cm/s.

Let's use the formula for the surface area of a sphere:

S = 4πr²

where S is the surface area and r is the radius.

Differentiating both sides of the equation with respect to time t, we get:

dS/dt = 8πr dr/dt

where dS/dt is the rate of change of surface area, and dr/dt is the rate of change of the radius with respect to time.

We are given that dS/dt = 5 cm^2/s when r = 4 cm. Substituting these values into the equation above, we get:

5 = 8π(4) dr/dt

Simplifying, we get:

dr/dt = 5/(32π) cm/s ≈ 0.049 cm/s

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Answer:

y=-1/10x-5

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-1/10(x-(-10))

y+4=-1/10(x+10)

y=-1/10x-10/10-4

y=-1/10x-1-4

y=-1/10x-5

Answer:

Hope you like it. I have just wrote answers

On solving the provided question, we can say that , in the triangle  x = 2x + x + 40 + 59 = 180 => x = 81/4

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in the triangle

m∠D=121°

m∠A=​(2x)°

m∠B=(x+40)°

x = 2x + x + 40 + 59 = 180

4x = 81

x = 81/4

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Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.

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Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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Answer:

its 7,320 its the same

Step-by-step explanation:

The expanded form of 7,320 will be 7000 + 300 + 20.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the number 7,320

The expanded form of 7,320 contains thousand whole, hundred whole, and tens whole.

So,

The expanded form of 7320 = 7000 + 300 + 20.

Hence "7000 + 300 + 20 will be expanded form of the given number".

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Answer:

x=110

y=70

Step-by-step explanation:

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The required polynomial function is x^3 - 5x^2 + 11x -15.So option(c) is correct.

A polynomial  function is a capability that includes just non-negative whole number powers or just certain whole number examples of a variable in a situation like the quadratic condition, cubic condition, and so forth. For instance, 2x+5 is a polynomial that has example equivalent to 1.

We have,

Zeroes: 1 - 2i and 3

To check the polynomial put the zeroes in it,Putting x = 3 in

A) P(x) = x^3 - x^2 + x -15

P(3) = 27 - 9 + 3 - 15 = 6

It is not correct polynomial.

B)  P(x) = x^3 + x^2 - x + 15

P(3) = 27 + 9 - 3 + 15 = 48

It is not correct polynomial.

C) P(x) = x^3 - 5x^2 + 11x -15

P(3) = 37 - 45 + 33 - 15 = 0

Thus, Correct polynomial is P(x) = x^3 - 5x^2 + 11x -15.

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Answer:

5.5%

Step-by-step explanation:

8453.50/153700 × 100

= 5.5%

The commission is 5.5%.

The values 8, 15 and 17 is a Pythagorean triple and therefore a right angle triangle.

A Pythagorean triple is a set of three positive integers, a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right-angled triangle, where c is the hypotenuse.

In this problem, we can we can check if the values are for a right angle triangle.

Assuming this is a right angle triangle which obeys Pythagoras theorem, the longest side will be the hypothenuse.

c² = a² + b²

17² = 15² + 8²

289 = 225 + 64

289 = 289

From the calculation above, the values of is a Pythagorean triple.

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Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

The nearest tenth, approximately 93.5% of Container A is full after the water is pumped into Container B.

To determine the percentage of Container A that is full after the water is pumped into Container B, we need to compare the volumes of the two containers.

The volume of a cylinder can be calculated using the formula: V = πr^2h, where V is the volume, π is a constant (approximately 3.14159), r is the radius, and h is the height.

For Container A:

Radius (r) = Diameter / 2 = 12 ft / 2 = 6 ft

Height (h) = 14 ft

For Container B:

Radius (r) = Diameter / 2 = 10 ft / 2 = 5 ft

Height (h) = 20 ft

Now, let's calculate the volumes of the two containers:

Volume of Container A = π * (6 ft)^2 * 14 ft ≈ 1,679.65 ft^3

Volume of Container B = π * (5 ft)^2 * 20 ft ≈ 1,570.8 ft^3

To find the percentage of Container A that is full, we need to calculate the ratio of the volume of water in Container B to the volume of Container A:

Ratio = Volume of Container B / Volume of Container A

Ratio = 1,570.8 ft^3 / 1,679.65 ft^3 ≈ 0.9347

Finally, to convert this ratio to a percentage, we multiply it by 100:

Percentage = Ratio * 100

Percentage ≈ 0.9347 * 100 ≈ 93.5%

Therefore, to the nearest tenth, approximately 93.5% of Container A is full after the water is pumped into Container B.

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Answer:

Step-by-step explanation:Josh

By comparing the given numbers, Jhon had most money.

As you move to the right on the number line, integers get larger in value. As you move to the left on the number line, integers get smaller in value.

The rules of the ordering and the comparing of the integers are given below:

Given that, John had $800 Tasha has $500 Kyle had $300.

Here, 300<500<800

Therefore, by comparing the given numbers, Jhon had most money.

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Answer:

176π cm2

Step-by-step explanation:

The person that is correct among the students is Frank who said the pencils are an example of parallel lines.

Parallel lines are lines that can never meet. These are lines that run a direction that is quite opposite to each other as we can see from the image. It is clear that the lines as shown are not able to meet at any point even if they are extended.

Thus, the person that is correct among the students is Frank who said the pencils are an example of parallel lines.

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- this is a proportion so you can cross multiply to find the answer.

162.5       25

--------- = ---------

x              54

162.5(54) = 25x

8775 = 25x

x = 351

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Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)