to train for a race nathon bikes every 2 days and swims every 5 days he biked on October 2 and he swam on October 5

the first day nathan's will bike and swim is October?

4

8

10

12

15

20​

7x + 5y = 43 --------(i)

5x + 5y = 5 --------(ii)

for solving, eqn (i) - eqn (ii)

7x + 5y = 43

5x + 5y = 5

- - -

__________

2x = 38

=> x = 19

putting x = 19 in eqn (ii)

we get, y = -18

(x,y) = (19,-18)

The length of the rectangular painting is equal to 76 cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The area of a rectangular painting is 4636 cm². The width of the painting is equal to 61 cm.

The length of the painting is calculated as,

Area of rectangle = Length x Width

4636 = Length x 61

Length = 4636 / 61

Length = 76 cm

The length is 76 cm for the rectangle.

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Answer:

piece c

Step-by-step explanation:

Answer:

The answer is 12

Step-by-step explanation:

let Linda's present age = x

Linda =x

(4x+6)=3(x+3)

4x+6= 3x+18

x=12

Answer:

v1 positive v2 negative

Step-by-step explanation:

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Using the trigonometric symmetries we can rewrite  the expression in terms of sin(z) as:  

\(\[\frac{1}{{\sqrt{{1 - \sin^2(z)}}}} + \frac{1}{{\sin(z)}}\]\)

Let's complete the identities using the trigonometric symmetries from the table:

a. sin(-a) = -sin(a) (Using the symmetry: sin(-a) = -sin(a))

b. cos(-x) = cos(x) (Using the symmetry: cos(-x) = cos(x))

c. tan(-2) = -tan(2) (Using the symmetry: tan(-x) = -tan(x))

Now, let's rewrite the expression in terms of sin(z):

\(\sec(z) + \csc(z) = \frac{1}{\cos(z)} + \frac{1}{\sin(z)}\)

To rewrite this expression in terms of sin(z), we can use the identity:

\(\[\sec(z) = \frac{1}{\cos(z)} = \frac{1}{\sqrt{1 - \sin^2(z)}}\]\csc(z) = \frac{1}{\sin(z)}\]\)

So, the expression becomes:

\(\[\frac{1}{{\sqrt{{1 - \sin^2(z)}}}} + \frac{1}{{\sin(z)}}\]\)

This is the rewritten expression in terms of sin(z).

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Answer:

n<5

Step-by-step explanation:

6(3+n)<48

Step 1: Simplify both sides of the inequality.

6n+18<48

Step 2: Subtract 18 from both sides.

6n+18−18<48−18

6n<30

Step 3: Divide both sides by 6.

6n /6 < 30 /6

n<5

Answer:

The answer is 3

Step-by-step explanation:

x×108=y

x×2²×3³=y

3×108=324

The 90% confidence interval for the number of chocolate chips per cookie in Big Chip cookies, based on a sample of 52 cookies with a mean of 18.5 and a standard deviation of 3.8, can be calculated.

To calculate the 90% confidence interval, we can use the formula:

Confidence interval = sample mean ± (critical value × standard error)

First, we need to calculate the standard error, which represents the variability of the sample mean. The standard error is calculated by dividing the sample standard deviation by the square root of the sample size:

Standard error = sample standard deviation / √(sample size)

In this case, the sample mean is 18.5, the sample standard deviation is 3.8, and the sample size is 52. Therefore, the standard error is 3.8 / √52 ≈ 0.528.

Next, we need to determine the critical value corresponding to a 90% confidence level. The critical value depends on the desired confidence level and the sample size. Since the sample size is 52 and the confidence level is 90%, we can use a t-distribution and look up the critical value from the t-table or use statistical software. Let's assume the critical value is 1.67 for this calculation.

Plugging the values into the confidence interval formula:

Confidence interval = 18.5 ± (1.67 × 0.528) = 18.5 ± 0.882

Therefore, the 90% confidence interval for the number of chocolate chips per cookie in Big Chip cookies is approximately (17.618, 19.382). This means we are 90% confident that the true mean number of chocolate chips per cookie falls within this interval based on the given sample.

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To find the maximum or minimum value of the function f(x, y, z) = x^2y^2z^2 subject to the given constraint, we need to apply the method of Lagrange multipliers.

To find the maximum or minimum value of f(x, y, z) = x^2y^2z^2 subject to a constraint, we introduce a Lagrange multiplier λ and form the Lagrangian function L(x, y, z, λ) = f(x, y, z) - λg(x, y, z), where g(x, y, z) is the constraint equation.

In this case, there is no specific constraint equation given, so we assume that the function is subject to some constraint. Let's denote the constraint equation as h(x, y, z) = 0.

To find the maximum or minimum value, we solve the following system of equations:

∇L = λ∇h,

h(x, y, z) = 0.

Taking the partial derivatives of L with respect to x, y, z, and λ, we obtain:

2xy^2z^2 = λhₓ,

2x^2yz^2 = λhᵧ,

2x^2y^2z = λh_z,

h(x, y, z) = 0.

Solving this system of equations will yield the critical points where the maximum or minimum of f(x, y, z) occurs subject to the given constraint.

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Answer:

$65

Step-by-step explanation:

169 ÷ 13 = 13

13 × 5 = 65

The first derivative of the given vector function r(t) = \(e^{t^{{7} }}\))i - j ln(13t) k is equal to r'(t) = 7t⁶×  \(e^{t^{{7} }}\)i - j/t k.

To find the derivative of the vector function,

Simply take the derivative of each component of the vector separately.

Let's calculate the derivatives of each component,

Vector function is,

r(t) = \(e^{t^{{7} }}\)i -jln(13t)k

Taking the derivative of the first component with respect to t,

r₁(t) =  \(e^{t^{{7} }}\)

r₁'(t) = (d/dt)  \(e^{t^{{7} }}\)

r₁'(t) = 7t⁶×  \(e^{t^{{7} }}\)

Taking the derivative of the second component with respect to t,

r₂(t) = -j ln(13t)

r₂'(t) = (d/dt) (-j ln(13t))

r₂'(t) = -j × (1/(13t)) × 13

r₂'(t) = -j/t

Taking the derivative of the third component with respect to t,

r₃(t) = k

r₃'(t) = 0

Therefore, the derivative of the vector function r(t) is r'(t) = 7t⁶×  \(e^{t^{{7} }}\)i - j/t k.

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The above question is incomplete , the complete question is:

Find the derivative, r'(t), of the vector function.

\(\[\mathbf{r}(t) = e^{t^{{7} }} \mathbf{i} - \mathbf{j} \ln(13} t)\mathbf{k}\]\)

Data:

• Monthly budget: $15

• Price of a package of ramen: $1.48

• Price of a music download: $1.15

Procedure:

Answer: 10.1

Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:

So the matching pairs are:

The line integral of (x⁸y + sin(x)) dy along the arc of the parabola y = x² is equal to 1/9.

To evaluate this line integral, we need to parameterize the curve C, which is the arc of the parabola y = x². Let's choose the parameterization x = t and y = t², where t ranges from 0 to 1.

Now we can express dy in terms of dt: dy = (dy/dt) dt = (2t) dt.

Substituting this into the integrand, we have (x⁸y + sin(x)) dy = (t⁸(t²) + sin(t)) (2t) dt = 2t¹⁰ + 2tsin(t) dt.

The integral of 2t¹⁰ with respect to t is (2/11)t¹¹. The integral of 2tsin(t) with respect to t is -2tcos(t) - 2sin(t).

Evaluating these integrals from t = 0 to t = 1, we have

\(\[\left(\frac{2}{11}(1^{11}) - 2(1)\cos(1) - 2\sin(1)\right) - \left(\frac{2}{11}(0^{11}) - 2(0)\cos(0) - 2\sin(0)\right)\]\).

Simplifying further, we get  \(\(\frac{2}{11} - 2\cos(1) - 2\sin(1)\)\).

This is approximately equal to 0.0893.

Hence, the line integral is approximately 0.0893, or equivalently, 1/9.

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To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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Answer:

(x+3)²=25

Explanation:

(in progress)

Answer:

(x+3)² = 25

Step-by-step explanation:

We are given the following equation:
2x² + 12x = 32

We want to find what the equation of this will be when we complete the square.

To start, we can divide both sides by 2. The resulting equation will be:

x² + 6x = 16

When completing the square, we add a third number to both sides. This is because we will factor the left side into the form (a+b)².

Recall that (a+b)² = a² + 2ab + b². The 6x is the 2ab in this sense, but because the value of a would be x (a² is x²), 6 = 2b.

If we solve 6 = 2b, then b = 3.

Now, square it to get the third number in the equation. 3² = 9.

We now add 9 to both sides of the equation. We do this in order to balance the equation, because if we add 9 to only one side, the equation will become unbalanced.

x² + 6x + 9 = 16 + 9

x² + 6x + 9 = 25

We can factor the left side to get:

(x+3)² = 25

Answer:

Y = 6

X = 10

Step-by-step explanation:

Answer:

the answer is 8 very easy and very simple have a great

day ☺️

Answer:

no solutions

Step-by-step explanation:

6n - 6n - 12 = 14 - 2 = 12 ( add 12 to both sides )

0 = 24 ← not possible

this indicates the equation has no solution

There are 64 teams in the sample space. There are 16 teams in the event W. p(W) = 0.25, is the probability that a randomly chosen team is in event W.

Since the teams are divided equally into four regions, there are 16 teams in the event W (assigned to the West region). The probability that a randomly chosen team is in event W, p(W), is the number of teams in event W divided by the total number of teams in the sample space. So, p(W) = 16/64 = 1/4 or 0.25. There are 64 teams in the sample space. There are 16 teams in the event W (since each region has 16 teams). P(W) = 16/64 = 0.25, which is the probability that a randomly chosen team is assigned to the West region.

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Seating arrangement would best suit a family restaurant is c) a space with all booths.

This restaurant with a comfortable atmosphere usually serves food in large quantities by placing it in the middle of the table.

So, each family member can take food from the middle and enjoy it on their respective plates. This concept is exactly the same as how to eat at home with the family.

Apart from that, the characteristics of this restaurant are almost the same as a casual dining restaurant, the difference is the absence of alcoholic beverages in family restaurants.

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Answer:

222,547.5 cm^3.

Step-by-step explanation:

The formula for the volume of a cylinder is pi * r^2 * h.

In this case, h = 315.

r = 30 / 2 = 15.

pi * (15)^2 * 315

= pi * 225 * 315

= pi * 70,875

= 3.14 * 70,875

= 222,547.5 cm^3.

Hope this helps!

The inequality which allow able for width x is 0 ≤ x ≤ 10.

According to the given question.

The sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches.

Width

Let the length, and height of the box be l, and h respectively.

Therefore,

The perimeter of the base of box = 2(width + l) = 2(x + l)

Also, it is given that

l = 2.5x

So,

perimeter of the base = 2(x + 2.5x) = 2(3.5x)

Now, according to the given condition.

The sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches.So, the inequlaity which represent this scenario is

2(3.5x) + 60 ≤ 130

⇒ 7x ≤ 130-60

⇒ 7x ≤ 70

⇒ x ≤ 10  

Also, x is the width of the box, so it must have some measure and cant be negative therefore

0 ≤ x ≤ 10.

Hence, the inequality which allow able for width x is 0 ≤ x ≤ 10.

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The correct answer is option 1: 8.46 g and 8.80 g. The given information is: The weights of certain machine components are normally distributed with a mean of 8.61 g and a standard deviation of 0.07 g. We need to find the two weights that separate the top 3% and the bottom 3%.Solution:The given distribution is a normal distribution, which is continuous and symmetric about its mean µ= 8.61 g. The standard deviation is given as σ= 0.07 g. Here, it is required to calculate the two weights that separate the top 3% and the bottom 3%.

Here, we can use the Z-score formula which is given by: Z = (X - µ)/σWhere, Z is the standardized score; X is the raw score or variable, µ is the mean of the population, and σ is the standard deviation of the population.Using the Z-score formula, we can find the Z-scores for the given data as follows: For top 3%, the Z-score is Z₃ = 1.88 (approx.)For bottom 3%, the Z-score is Z₁ = -1.88 (approx.)

The value of Z is calculated using the Z-table, which gives the area to the left of the Z-score. Since the area required is in the tails of the distribution, we can calculate it using the following relation:area in the tail = (100% - desired area)/2area in the tail = (100% - 3%)/2 = 48.5%Using the Z-score formula, we can find the two weights that separate the top 3% and the bottom 3% as follows:X = Zσ + µFor top 3%: X₃ = Z₃σ + µ = 1.88(0.07) + 8.61= 8.80 g (approx.)X₁ = Z₁σ + µ = -1.88(0.07) + 8.61= 8.46 g (approx.)Therefore, the two weights that separate the top 3% and the bottom 3% are 8.46 g and 8.80 g.

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Answer:

$ 17 off

Step-by-step explanation:

20% is one fifth of the price

So divide 85 by 5  you get 17

Since you only get one 1/5 of the price off you save $17

Just to check and make sure you can do 17 * 5 = 85

Answer:

69.3548%

Step-by-step explanation:

43 divided by 62 is 69.3548

Answer:

your mom

Step-by-step explanation: