write an explicit formula for an the nth term of the sequence 40, 33, 26

The equation of the line passing through the points (0, 7) and (2, -5) is y = -6x + 7

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The standard form of a linear equation is:

y = mx + b

where m is the slope(rate of change) and b is the y intercept

As shown in the graph, the line passes through the points (0, 7) and (2, -5). Hence:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-7=\frac{-5-7}{2-0} (x-0)\\\\y=-6x+7\)

The equation of the line is y = -6x + 7

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Answer: Logarithmic

Explanation:

This curve is a reflection of the exponential curve over the line y = x, to show that it is the inverse of exponentials. We use logs to help isolate the exponent among other useful properties.

Answer:

A. Nerve cells

Step-by-step explanation:

Answer:

nerve cells

Step-by-step explanation:

Answer:

70 cm³

Step-by-step explanation:

let the total volume be x

copper : zinc = 3:2

copper ==>

3/5 *x = 42

make x the subject if formula

x = 42*5/3

:. x = 70 cm³✅✅

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the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

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Answer:

Dependent

Step-by-step explanation:

He cant choose a pencil that she already gave him.

Answer:

6

Step-by-step explanation:

Answer:

3 cans cost 2

1 can cost 2/3                    

 I wrote 2/3 to make it easier so you don't have to write in cents

2/3 can be spend to buy 1 can

12 can be spend to buy (2/3)(12) can

(2/3)(12)=8 cans

So the answer is 8 cans

You can buy 8 cans of tuna with 12 dollars

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.

To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.

Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.

The total weight equation is given by:

x + y = 1900

The protein content equation is given by:

(0.70x + 0.20y) / 1900 = 0.55

Simplifying the second equation, we get:

0.70x + 0.20y = 0.55 × 1900

0.70x + 0.20y = 1045

Now, we can solve this system of equations to find the values of x and y.

Rearrange the first equation to solve for x:

x = 1900 - y

Substitute this expression for x in the second equation:

0.70(1900 - y) + 0.20y = 1045

1330 - 0.70y + 0.20y = 1045

1330 - 0.50y = 1045

-0.50y = 1045 - 1330

-0.50y = -285

y = -285 / -0.50

y = 570

Now substitute this value of y back into the first equation to find x:

x + 570 = 1900

x = 1900 - 570

x = 1330

Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.

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Answer:

Area of annulus is 40.85cm² to 2d.p

Step-by-step explanation:

Area of shaded part=Area of bigger circle -Area of smaler circle

Area of annulus= πR²- πr²= π(R²-r²)

A=3.142(7²-6²)

A=3.142(49-36)

A=3.142×13

A=40.846cm²

A=40.85cm² to 2d.p

Answer:

0.15

Step-by-step explanation:

Fp: frequency that the pitcher will throw exactly 4 pitches to a batter=15

Fa: frequency that the pitcher will throw any pitches to a batter=15+20+40+15+10=100

P=Fp/Fa=15/100=0.15

The probability that the pitcher will throw fewer than 3 pitches to a batter is 0.35

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

This probability distribution is shown below:

Pitch                   1            2        3          4         5

Frequency         15         20      40        15        10

Probability         0.15     0.2      0.4      0.15      0.1

Thus the probability that the pitcher will throw fewer than 3 pitches to a batter = P(X < 3)

X  is the number of pitches thrown.

Therefore:

P(X < 3) = P(X = 1) or P(X = 2)

The additive rule of the probability states that if two events X and Y are dependent events, the probability of X or Y occurring is the sum of their individual probability.

P(X < 3) = P(X = 1) or

P(X = 2) = P(X = 1) + P(X = 2)

= 0.15 + 0.2

= 0.35

Hence, The probability that the pitcher will throw fewer than 3 pitches to a batter is 0.35

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the student's mistake is that the did not change the sign from negative to positive. When you have -(-x) negative multiplied by a negative, the negative changes to a positive, so instead of subtracting the 2 the student have to add it

4 -(-2)

4+2

=6

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

The radius of the cylinder is 2.25 feet.

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.

400 = 3.14 r² x 25

Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:

r² = 400 / (3.14 x 25)

r² ≈ 5.08

Taking the square root of both sides to solve for r, we get:

r ≈ √5.08

r ≈ 2.25

Therefore, the radius of the cylinder is 2.25 feet.

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Answer:

\(\sqrt{97} \\ \sqrt{9^{2}+4^{2} }\)

Step-by-step explanation:

Answer:

Its gotta be C

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x-2)(x-2)(x-4)

Answer: 24

Step-by-step explanation:

Subtract them. Then, 23.54 would be closest to 24.

Answer:

21.51.....approximately 22

Option (a) is the correct answer. When two figures are similar, it means they have the same shape but different sizes.

How to solve the question?

In other words, their corresponding angles are congruent, and their corresponding side lengths are proportional.

Option (b) and (d) suggest that the corresponding side lengths of A and B are related by a constant factor (either 2 or 1/2). However, this is not necessarily true for all similar figures. The constant of proportionality can be any positive real number.

Option (c) suggests that the corresponding side lengths of A and B are equal, which means that A and B are not just similar but congruent. This is not necessarily true for all similar figures, as similar figures can differ in size.

Therefore, option (a) is the only answer that must always be true for similar figures. The corresponding side lengths of similar figures are proportional, which means that if one side of figure A is twice as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 2:1. Similarly, if one side of figure A is three times as long as a corresponding side of figure B, then all other corresponding sides will also be in the same ratio of 3:1. This proportional relationship holds true for all pairs of corresponding sides in similar figures

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Option (a) is the correct answer.  The corresponding side lengths of A and B are proportional, must always be true if Figure A is similar to Figure B.

When two figures are similar, their corresponding angles are congruent, and their corresponding side lengths are proportional. This means that if we take any two corresponding sides of the figures, the ratio of their lengths will be the same for all pairs of corresponding sides.

Option b and d cannot be true, as they both suggest a specific ratio of corresponding side lengths, which is not necessarily true for all similar figures.

Option c is not necessarily true, as two similar figures can have corresponding side lengths that are not equal but still have the same ratio.

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Answer:

the answer is 105

Step-by-step explanation:

because 5×3=15 so 15×7 =105

The rate of change is 10. This means every 1 ticket sold produces a net profit of $10.00 (option B)

To get the rate of change, we will find the slope using any two points on the table

Slope formula is given as:

using points (tickets sold, net profit): (200, 0) and (225, 250)

Hence, the rate is 10.

Since we are dividing the net profit by tickets sold, 10 represents the change in net profit per number of tickets sold

As a result, every 1 ticket will produce a net profit of $10

The rate of change is 10. This means every 1 ticket sold produces a net profit of $10.00 (option B)

Answer:

-1/4(2x + 5)

Step-by-step explanation:

1/4 out of 1/2 leaves 2 believe it or not.

1/4 out of 5/4 leaves 5 believe it or not

-1/4(2x + 5)

Proof

-1/4 * 2 = - 1/2

-1/4 * 5 = - 5/4

Answer:

\(x∈( - ∞;8]\)

Step-by-step explanation:

\(x + 9 - 3 \leqslant 14\)

Collect like-terms:

\(x \leqslant 14 - 9 + 3\)

\(x \leqslant 8\)

\(x∈( - ∞;8]\)

The equivalent formula that does not involve integrals is A(x) = 2x - 2x^2 + 4x - 4.

The First Fundamental Theorem of Calculus states that if f(x) is a continuous function on the interval [a, b], then the function F(x) = integral^x_a f(t) dt is an antiderivative of f(x), meaning that its derivative is equal to f(x). Therefore, if we have the antiderivative of a function, we can use the derivative to find an equivalent formula without an integral.

In this case, the derivative of the antiderivative of f(t) = 4 - 2t is f(t) = 4 - 2t, which is the original function. So, the equivalent formula for A(x) is A(x) = 2x - 2x^2 + 4x - 4, which does not involve integrals.

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Answer:

\( \sf \: 4 \frac{4}{8} \)

Step-by-step explanation:

Given problem,

\( \sf \rightarrow \: 2 \frac{3}{8} + 2 \frac{1}{8} \)

Let's solve the problem,

\( \sf \rightarrow \: 2 \frac{3}{8} + 2\frac{1}{8} \)

\( \sf \rightarrow \: \frac{19}{8} + \frac{17}{8} \)

\( \sf \rightarrow \: \frac{(19 + 17)}{8} \)

\( \sf \rightarrow \: \frac{36}{8} \)

\( \sf \rightarrow \: 4 \frac{4}{8} \)

Hence, the answer is 4 4/8.

Answer:

slope intercept form: y= -6x+3

point slope form: y-0= -6(x -1/2)

Step-by-step explanation:

point slope form: y - y1 = m(x - x1)

substitute the values  y-0=-6(x-1/2)

slope intercept form:

find the slope using two given points

m = (y2 - y1) / (x2 - x1)

= (3 - 0) / (0 - 1/2)

= 3 / (-1/2)

= -6

substitute into equation

y= -6x+3

Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)