The formula A=15.7e^(0.0433t) models the population of a US state, A, in millions, t years after 2000. When will the population of the state reach 18.7 milion?

The number of cords in 1 m^3 are four.

Here , volume of a cuboid is involved. If l, b, h are respectively the length, breadth and the height of the cuboid , then its volume is given by

V = l x b x h cubic units.

Now, here we know that 1 m =3.28 ft.

So, 1 m^3 = (3.28)^3 cubic feet. = 35.288 cubic feet.

So, we have to find the number of cords in 35.288 cubic feet.

Now, volume of a single cord = l x b x h = 8 x 4 x 4 = 128 cubic feet.

So, no. of cord = 128/35.288 = 3.66.

Since, the number of cords is always a whole number , so 3.66 can treated as 4 by rounding it off to unit's place.

Hence, The number of cords in 1 m^3 are four.

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The number of cords in 1 m^3 is four.

Here, the volume of a cuboid is involved. If l, b, h are respectively the length, breadth and height of the cuboid, then its volume is given by

V = l x b x h cubic units.

Now, here we know that 1 m =3.28 ft.

So, 1 m^3 = (3.28)^3 cubic feet. = 35.288 cubic feet.

So, we have to find the number of cords in 35.288 cubic feet.

Now, the volume of a single cord = l x b x h = 8 x 4 x 4 = 128 cubic feet.

So, no. of cord = 128/35.288 = 3.66.

Since the number of cords is always a whole number, 3.66 can be treated as 4 by rounding it off to the unit's place.

Hence, The number of cords in 1 m^3 is four.

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Answer: (-2,4)

Step-by-step explanation:

A solution is an intersection point between the parabola and the linear function. We can see 2 intersections, one of which is (-2,4)

Therefore, (-2,4) is the solution.

Answer:

y = 6

Step-by-step explanation:

8y+1 + 6y+3 = 90

14y+6=90

14y=84

y = 6

Answer:

Step-by-step explanation:

This is a right scalene triangle as it has 90° angle and all sides have different lengths.

Correct choices are C and D

Answer:

Solution:

the given TRAINGLE is right angled and scale traingle .

The difference between the number of adults cats at the pet centre on Monday and Wednesday is 3.

Ratio, in math, is a term that is used to compare two or more numbers.

The ratio of adult cats to kittens at a pet care centre on Wednesday was 5:3. There were 27 kittens there that day.

Hence, let

total number of cat on Wednesday = x

Hence,

27  = 3 / 8 x

cross multiply

3x = 216

x = 216 / 3

x = 72

Hence,

adult cat on Wednesday = 72 - 27 = 45

The difference between the number of adult cats at the pet centre on Monday and Wednesday can be computed as follows:

difference = 48 - 45 = 3

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The value is 7/4 = 1.75

From the question, we have

\(2\frac{1}{2} -\frac{3}{4} \\=\frac{5}{2} -\frac{3}{4} \\=\frac{10-3}{4}\\=\frac{7}{4}=1.75\)

Subtraction:

The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign. For instance, supposing there are nine oranges stacked together (as indicated in the above image), four oranges are taken out and put in a basket, leaving nine – four oranges, or five oranges, in the stack. Therefore, 9 minus 4 equals 5, or the difference between 9 and 4. Different kinds of numbers can also use subtraction, which is not just applicable to natural numbers. This means that we can use several sets of objects, such as negative numbers, fractions, rational and irrational numbers, decimals, functions, matrices, and vectors, to explain reducing or eliminating physical and abstract values.

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Answer:

- 5√2 / 2   ,   - √2

Step-by-step explanation:

√2 x² + 7x + 5√2 = 0

√2          5

1              √2

(√2 x + 5) (x + √2) = 0

√2 x + 5 =0            x = - 5/√2 = - 5√2 / 2

or x + √2 = 0          x = -√2

Answer:

in five hours you will travel 153.75 miles

Hello!

What does this problem want:

==> how far will the car have traveled in 5 hours

What we must find ==> how many miles does the car travel in an hour

  \(\text{Rate}=\frac{61.5 \text{ miles}}{2 \text{ hours}} =30.75\text{ miles per hour}\)

Therefore: the car will travel in 5 hours

   5 * 30.75 = 153.75 miles

Hope that helps!

Answer: \(-\frac{5}{7}\)

Step-by-step explanation:

To find the slope of the line, you want to use the formula \(m=\frac{y_2-y_1}{x_2-x_1}\).

\(m=\frac{-3-2}{3-(-4)} =\frac{-5}{7}\)

Now we know the slope is \(-\frac{5}{7}\).

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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The cosine of the angle of intersection is approximately 0.965.

The point of intersection between the curves r1(t)=⟨t,3−t,9 t2⟩ and r2(s)=⟨1−s,s 2,s2⟩ can be found by setting their respective components equal to each other and solving for the values of t and s. This gives us the following system of equations:
t = 1 - s
3 - t = s^2
9t^2 = s^2

Solving for t in the first equation and substituting into the second equation gives us:
3 - (1 - s) = s^2
s^2 - s - 2 = 0

Using the quadratic formula, we find that s = 2 or s = -1. Substituting these values back into the first equation gives us t = -1 or t = 2.

The point of intersection is therefore (x,y,z) = (-1,2,9) or (2,1,4).
To find the angle of intersection, we can use the dot product formula:
cos(θ) = (r1(t) · r2(s)) / (|r1(t)| |r2(s)|)

Substituting in the values of t and s from the point of intersection and simplifying gives us:
cos(θ) = (-1)(1-2) + (2)(2) + (9)(4) / (√((-1)^2 + 2^2 + 9^2) √((1-2)^2 + 2^2 + 4^2))
cos(θ) = 41 / (√86 √21)
cos(θ) = 41 / √1806

Therefore, the cosine of the angle of intersection is approximately 0.965.

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Step-by-step explanation:

milli means thousandths.

in 1 gram there are therefore 1000 milligrams.

so, when you have milligrams, you need to divide them by 1000 to get the grams.

so, 1g/1000mg

The answer is 10,077,696,000 different 10-letter words that can be formed using these letters.

To find the number of different 10-letter words that can be formed using the given letters, we can use the formula for permutations with repetition:

where n is the number of distinct objects (letters in this case), and r is the number of positions (10 in this case).

we can calculate the number of different 10-letter words as follows:

The formula states that the number of permutations with repetition of n distinct objects in r positions is equal to n^r. In this case, we have 2 distinct objects for the first set of letters (E and B), 3 for the second set (O, J, and 0), 1 for the third set (P), and 4 for the fourth set (B, V, I, and T).

we have a total of 2 + 3 + 1 + 4 = 10 distinct objects to choose from, and we need to fill 10 positions.

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Answer:

140, 60

Step-by-step explanation:

15x+5 + < CDB =180 line form an 180 angle

180-80-6x-6 = < CDB sum of angles in a triangle is 180

substitute < CDB from second to first

15x+5+180 -80-6x-6 =180

combine like terms

9x -81 =0

x=81/9=9

so angle YDC = 15*9+5 = 140 degrees

and angle DBC = 6*9+6= 60 degrees

Answer:

p ≤ 15

Step-by-step explanation:

8p ≤ 120

/8 on both sides

p ≤ 15

Answer:

100 x 3

Step-by-step explanation:

Well, it's a pretty simple problem.

If she already has 100 ants and it triples every month then, we'd multiply.

Key words like triple, double, twice as much can signal that a problem requires multiplication.

In this case, we'd do 100 x 3

which means that after one month, she'd have 300 ants.

Symbolically, they correspond to the relationships between the coefficients of the equations.

A system of 2 linear equations in 2 variables can have one of the following three possible solutions:

One unique solution: In this case, the two lines intersect at exactly one point, and this point is the solution to the system. Visually, the two lines are not parallel, but they are not the same either. Symbolically, the system is represented as:

a1x + b1y = c1

a2x + b2y = c2

where a1, b1, c1, a2, b2, and c2 are constants, and x and y are variables.

Infinitely many solutions: In this case, the two lines coincide and are on top of each other, meaning they have the same slope and the same y-intercept. Visually, the two lines are identical. Symbolically, the system is represented as:

a1x + b1y = c1

ka1x + kb1y = kc1

where a1, b1, and c1 are constants, x and y are variables, and k is any non-zero constant.

No solution: In this case, the two lines are parallel and never intersect. Visually, the two lines are distinct and never meet. Symbolically, the system is represented as:

a1x + b1y = c1

a2x + b2y = c2

where a1, b1, c1, a2, b2, and c2 are constants, and x and y are variables, and the slope of one line is not equal to the slope of the other.

Geometrically, these cases correspond to the three possible positions of two lines in the coordinate plane. Symbolically, they correspond to the relationships between the coefficients of the equations.

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Answer:

37/100 = 0.37 (the first one)

Step-by-step explanation:

a percentage is out of 100.

If you divide 37 by 100, you get 0.37

Answer:

37%=0.37=37/100

Step-by-step explanation:

Convert the percentage to an equivalent decimal number by placing the percentage sign with x1/100. The decimal equivalent to the percentage by moving the decimal 2 places to the left from the convert postion.

Answer:

Number of bagels = 10

Number of donuts = 25

Step-by-step explanation:

Let Number of bagels = b

Number of donuts = d

As given,

Each donut cost $0.55 and each bagel cost $1.20

⇒ Cost of d donuts = $0.55d

   Cost of b bagels = $1.20b

Also given,

Jamian bought a total of 35 bagels and donuts

⇒ b + d = 35     ........(1)

Also,

He paid a total of  $25.75.

⇒ 1.20b + 0.55d = 25.75          .........(2)

Now,

Multiply equation (1) by 1.20 , we get

1.20( b + d = 35 )

⇒1.20b + 1.20d = 42               ..........(3)

Now,

Subtract equation (2) from equation (3), we get

1.20b + 1.20d  - ( 1.20b + 0.55d ) = 42 - 25.75

⇒1.20b + 1.20d  - 1.20b - 0.55d  = 16.25

⇒0.65d = 16.25

⇒d = \(\frac{16.25}{0.65}\) = 25

⇒d = 25

Put the value of d in equation (1) , we get

b + d = 35

⇒b + 25 = 35

⇒b = 35 - 25 = 10

⇒b = 10

∴ we get

Number of bagels = b = 10

Number of donuts = d = 25

\(\huge{ \mathfrak{  \underline{ Answer} \:  \:  ✓ }}\)

Figure - 1 :

The given triangles are similar, so their corresponding sides will be proportional.

Let the missing side be x

_____________________________

Figure - 2 :

The given figure is a Cylinder :

\( \large \boxed{ \mathrm{volume = \pi {r}^{2}h }}\)

_____________________________

\(\mathrm{☠ \: TeeNForeveR \: ☠}\)

Step-by-step explanation:

7 + x/3 =2x - 5

7 + 5=2x - x/3

12 = 5x/3

cross multiply

36=5x

x=36/5

x=7.2

Answer:

Step-by-step explanation:

I believe the answer is

C) Laura mixed more vinegar per cup of olive oil, because 3:1 is greater than 4:2

Per 1 cup, Laura has 3 tbsp of vinegar, but Juliette only has 2 tbsp per cup.

It wouldn't be D) because 3 tbsps aren't bigger than 2 cups....

Answer:

6

Step-by-step explanation:

Step-by-step explanation:

the correct answer is option a 6a-7

The solution to (11cis61.5 ∘ )(5cis159.5 ∘ ) is approximately 55.6158 + 34.1628i in rectangular form.

Explanation:

To multiply complex numbers in polar form, we multiply their magnitudes and add their angles. In this case, we have (11cis61.5 ∘ )(5cis159.5 ∘ ).

First, we multiply the magnitudes: 11 * 5 = 55.

Then, we add the angles: 61.5 ∘ + 159.5 ∘ = 221 ∘.

Now we have the product in polar form, which is 55cis221 ∘.

To convert it to rectangular form, we use Euler's formula: z = r(cosθ + isinθ).

The rectangular form of 55cis221 ∘ is 55(cos221 ∘ + isin221 ∘).

Using a calculator to evaluate cos221 ∘ and sin221 ∘, we find that cos221 ∘ ≈ 0.616 and sin221 ∘ ≈ -0.787.

Finally, we multiply the magnitude (55) by the real part (cos221 ∘) and the imaginary part (sin221 ∘) to obtain the rectangular form of the product:

55 * 0.616 ≈ 33.880 and 55 * (-0.787) ≈ -34.283.

So, the solution in rectangular form is approximately 33.880 - 34.283i, which can be rounded to 55.6158 + 34.1628i to four decimal places.

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The transfer function allow us to determine the appropriate value of Ki that satisfies the desired overshoot and settling time specifications ≈ 16.67.

To design a compensator that guarantees a steady-state error less than 0.01 and a settling time (Ts) of 5 seconds with 5% maximum overshoot (PO), we can use a proportional-integral (PI) controller.

The transfer function of the compensator can be represented as:

C(s) = Kp + Ki/s

where Kp is the proportional gain and Ki is the integral gain.

To achieve a steady-state error less than 0.01, we need to ensure that the open-loop transfer function with the compensator, G(s)C(s), has a DC gain of at least 100.

To calculate the values of Kp and Ki, we can follow these steps:

Determine the open-loop transfer function without the compensator, G(s):

G(s) = 2(s + 3)(s + 1)

Calculate the DC gain of G(s) by evaluating G(s) at s = 0:

DC_gain = G(0) = 2(0 + 3)(0 + 1) = 6

Determine the required DC gain with the compensator to achieve a steady-state error less than 0.01:

Required_DC_gain = 100

Calculate the proportional gain Kp to achieve the required DC gain:

Kp = Required_DC_gain / DC_gain = 100 / 6 ≈ 16.67

Determine the integral gain Ki to achieve the desired overshoot and settling time.

To achieve a settling time of 5 seconds and a 5% maximum overshoot, we can use standard control design techniques such as root locus or frequency response methods.

Using these methods, you can determine the proper Ki value to meet the required overshoot and settling time specifications.

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Answer:

j + 5 = 80

Step-by-step explanation:

i think thats right