From a Word Problem
Jack has $10 in his lunch account. He plans to
spend $2 a week on snacks. How long until
Jack's lunch account reaches zero?

\(10x\)

Solution:

If \(f(x) = 3x +3\) and \(g(x) = -3 +2x\), then \(2g(x) +2f(x)\) is:

\(2(-3 +2x) +2(3x +3) \\ -6 +4x +6x +6 \\ (-6 +6) +(4 +6)x \\ 0 +10x \\ 10x\)

The cost of '10' hotdogs and '8' hotdog buns is given by '10x + 8y.'

it is their job to plan and cost a media schedule for the campaign

an amount that has to be paid or spent to buy or obtain something:

"we are able to cover the cost of the event"

The system of equations that represents the total amount of money you spent on hotdogs and hotdog buns at each store is given by:

a) 10x + 8y

The above equation represents the cost of hotdogs and hotdog buns purchased at a store.

The cost of a hotdog is represented by 'x', and the cost of a hotdog bun is represented by 'y.'

Thus, the cost of '10' hotdogs and '8' hotdog buns is given by '10x + 8y.'

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Answer:

A. Makes the most sense. If you are using multiplication you'd get 18 1/16

Step-by-step explanation:

The critical point q = 1 is a relative minimum for the function \(p(q) = q^2 - 2q - 9\).

To find the critical points of the function \(p(q) = q^2 - 2q - 9\), we need to determine the values of q where the derivative of p(q) is equal to zero or undefined.

First, let's find the derivative of p(q):

p'(q) = 2q - 2

Next, we set p'(q) equal to zero and solve for q:

2q - 2 = 0

2q = 2

q = 1

So, q = 1 is a critical point.

To determine the nature of this critical point, we can examine the second derivative of p(q):

p''(q) = 2

The second derivative is a constant, which means it doesn't change with q. Since p''(q) is positive (2 > 0) for all q, this indicates that the critical point q = 1 is a relative minimum.

Therefore, the critical point q = 1 is a relative minimum for the function \(p(q) = q^2 - 2q - 9\).

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Answer:   1/4 chance

Step-by-step explan1ation:

5+3=8

8 / 2 = 1/4

To estimate the sum, we need to round the decimals as:

186,231 ≈ 186

88,941 ≈ 89

So, we sum 186 and 89 as:

186 + 89 = 275

Therefore, the estimated sum of 186,231 + 88,941​ is 275

Answer: 275

The point estimate of the population proportion defective will be 0.0945

The formula for calculating the point estimate is expressed as;

p = x/n,

where p is the proportion of successes in the sample

n is the total sample

Given the following

n = 550 items

x = 52

Substitute

p = 52/550

p = 0.0945

Hence the point estimate of the population proportion defective will be 0.0945

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Answer: 5, 10, 15, 20, 25

Step-by-step explanation:

a(1)=1

a(2)=5(2-1)

a(2)=5

a(3)=5(3-1)

a(3)=10

a(4)=5(4-1)

a(4)=15

5, 10, 15, 20, 25

The volume of a prism is V = Bh = πr2h, therefore the volume of a cylinder is also V = Bh = πr2h. Where, B is the area of ​​the base, h is the height, and r is the radius of the base.

A prism is a polyhedron all of whose faces are flat and whose bases are parallel to each other. It is a solid object with flat surfaces, identical ends, identical diameter and length. The volume of a prism is defined as the total space occupied by a three-dimensional object. Mathematically, it is defined as the product of the area of ​​the base and the length.

Therefore, the volume of the prism = base area × length

Volume of Cylinder:

The volume of a cylinder is the number of unit cubes (cubes per unit length) that can fit in it. It is the space occupied by the cylinder, because the volume of any three-dimensional shape is the space it occupies. The volume of a cylinder is measured in cubic units, such as cm³, m³, in³, etc.

The volume of cylinder is :

V = πr2h

where

'r' is the radius of the cylinder

'h' is the height of the cylinder

And, π is a constant whose value

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To meet the given requirements, the account would need to have around $4,378 at time t=3/5.

To solve this problem, let's break it down into different parts and calculate the required amount in the account at time t=3/5.

1. Calculate the dollar-weighted rate of return:

The dollar-weighted rate of return can be calculated by dividing the total gain or loss by the total investment.

Total Gain/Loss = Account Value at t=1 - Total Investment

             = $3,300 - ($2,000 + $1,000)

             = $3,300 - $3,000

             = $300

Dollar-weighted Rate of Return = Total Gain/Loss / Total Investment

                             = $300 / $3,000

                             = 0.10 or 10% (in decimal form)

2. Calculate the time-weighted rate of return:

The time-weighted rate of return is given as 0.0175 higher than the dollar-weighted rate of return.

Time-weighted Rate of Return = Dollar-weighted Rate of Return + 0.0175

                           = 0.10 + 0.0175

                           = 0.1175 or 11.75% (in decimal form)

3. Calculate the additional investment at time t=3/5:

Let's assume the required amount to be in the account at time t=3/5 is X.

To calculate the additional investment needed at t=3/5, we need to consider the dollar-weighted rate of return and the time period between t=1 and t=3/5.

Account Value at t=1 = Total Investment + Gain/Loss

$3,300 = ($2,000 + $1,000) + ($2,000 + $1,000) × Dollar-weighted Rate of Return

Simplifying the equation:

$3,300 = $3,000 + $3,000 × 0.10

$3,300 = $3,000 + $300

At t=3/5, the additional investment would be:

X = $3,000 × (1 + 0.10) + $1,000 × (1 + 0.10)^(3/5)

Calculating the expression:

X = $3,000 × 1.10 + $1,000 × 1.10^(3/5)

X ≈ $3,300 + $1,000 × 1.078

X ≈ $3,300 + $1,078

X ≈ $4,378

Therefore, the amount that would have to be in your account at time t=3/5 is approximately $4,378.

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Answer:

We have sin² x + cos² x =1 for all real x.

Therefore, sin² x = 1 – cos² x = 1 – (8/17)² = 1 – 64/289 = 225/289 = (15/17)².

However, remember that if x² = a², then x can be +a or –a.

Therefore, sin x can be either –15/17 or +15/17.

Everyone but Anirban so far has forgotten the negative solution.

Step-by-step explanation:

Given that sinθ=817 and cosθ<0 , we have: cosθ=−√1−sin2θ. cosθ=−√1−(817)2. cosθ=−√1−64289.

Answer:

255

Step-by-step explanation:

12x^(2) + 39x + 30

x = 3

Substitute in"3" for "x" and solve;

12(3)^(2) + 39(3) + 30

= 12 * 9 + 117 + 30

= 108 + 117 + 30

= 255

Answer:

255

Step-by-step explanation:

f(x) = \(12x^{2}\\\) + 39x + 30

f(3) = 12(3)\(^{2}\) + 39(3) + 30

= 108 + 117 + 30

= 255

Answer:

w(t-4)=t^2-9t+20

Step-by-step explanation:

w(t)=t^2-t

w(t-4)=(t-4)^2-(t-4)

w(t-4)= t^2-8t+16-t+4

w(t-4)=t^2-9t+20

Answer:

My answer is

7+9-18-19+18= -3.

Answer:

3.75

Explanation:

Given the equation 4x+4y = 15, we are to find the x coordinate of equation

To do this we will find the x intercept of the equation.

when y = 0

4x+4y = 15

4x + 4(0) = 15

4x = 15

x = 15/4

x = 3.75

Hence the x coordinate of the equation is 3.75

Answer:

Step-by-step explanation:

i need points goodluck tho

Answer:

im pretty sure its 43.5

Step-by-step explanation:

Answer:

About 5 hours

Step-by-step explanation:

Hope it helps

Answer:

Step-by-step explanation:

The answers are:

A)  {[(-15+5)×2+8]-32÷8}-(-7)

Calculate within parentheses: -16 - (-7)

Add and subtract (left to right): -16 - (-7) = -9

B) (5-2)³×2+[-4+(-7)]÷(-2+4)²

To solve this problem, you need to follow the steps of order of operations.

Calculate within parentheses: \(3^{3}\) * 2 + [-4 + (-7)] ÷ (-2+4)²

Calculate within parentheses: \(3^{3}\) *2 -11 ÷ (-2+4)²

Calculate within parentheses: 27 × 2 - 11 ÷ (-2+4)²

Calculate exponents: 27 × 2 -11 ÷ 4

Multiply and divide: 54 - 11 ÷ 4

Multiply and divide: 54 - \(\frac{11}{4}\)

Add and Subtract:  \(\frac{205}{4}\)

Convert improper fractions to mixed numbers: \(\frac{205}{4}\) = \(51\frac{1}{4}\)

C) {-10-[12+(-3)²] + 3³}+3³}÷(-3)

Calculate within parentheses: -4 ÷ (-3)

Multiply and divide:  \(\frac{-4}{(-3)}\)

Simplify and convert improper fraction to a mixed number:

\(\frac{-4}{(-3)}\) = \(\frac{4}{3}\) = \(1\frac{1}{3}\)

Hope this helped! If so, please mark brainliest.

Answer:

x = 5    y = -13

Step-by-step explanation:

5(5) - 3 = 22 and 5 - (-13) = 18

The value of x and y is △ABC ≅ △DEF are 5 and -13 respectively

Since △ABC is congruent to △DEF. hence all the sides of △ABC will be equal to △DEF.

Given the sides of △ABC to be 18, 25, and 5x − 3.

Sides of △DEF to be 25, 22, and 5 − y

This shows that the third side of triangle △ABC is 22, hence

5x - 3 = 22

5x = 22 + 3

5x = 25

x = 5

Similarly, the thirs side of △DEF will be 18, hence;

5 - y = 18

y = 5 - 18

y = -13

Hence the value of x and y is △ABC ≅ △DEF are 5 and -13 respectively

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Answer:

2/3

Step-by-step explanation:

Have a good day :)

Answer:

$93.75

Step-by-step explanation:

First step, we need to find 25% of 125, we can do this by multiplying .25 by 125. This leaves us with $31.25. Now, we subtract 31.25 from 125, this leaves us with $93.75. There is your answer. Another way to do this is to find 75% of 125 because 25+75 equals 100.

The number of bows Lulu can make  from the remaining ribbon is 13 bows.

To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.

10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.

She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:

(26/3) * 12 = 104 inches of ribbon remaining.

Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:

104 / 8 = 13 bows.

Lulu can make 13 bows with the remaining ribbon.

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Answer:  the awnser is 43

Step-by-step explanation:

The slope of the tangent line to the witch of Agnesi graph at the point (2, 1) can be found by taking the derivative of the equation and evaluating it at the given point. The slope is 1/2 .

The equation of the witch of Agnesi curve is given by (x^2 + 4)y = 8. To find the slope of the tangent line at a specific point on the curve, we need to take the derivative of the equation with respect to x.
Differentiating the equation implicitly, we get:
2xy + (x^2 + 4)dy/dx = 0.
To find the slope of the tangent line at a particular point, we substitute the x and y coordinates of that point into the derivative expression. In this case, we substitute x = 2 and y = 1:
2(2)(1) + (2^2 + 4)dy/dx = 0.
Simplifying the equation, we have:
4 + (4 + 4)dy/dx = 0,
8dy/dx = -4,
dy/dx = -4/8,
dy/dx = -1/2.
Therefore, the slope of the tangent line to the witch of Agnesi graph at the point (2, 1) is -1/2, or equivalently, -0.5.

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Answer:

C

Step-by-step explanation:

The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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The vector-valued function at each given value of t  is :

a) i

b)  1/√2i+9/√2j

c)−cos(θ)i+9sin(θ)j

d)  −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

The given problem is related to trigonometric Ratios of Angle, where there are six trigonometric ratios sine, cosine, tangent, cotangent, cosecant, and secant. Since it is given that a  vector valued function:

r(t)= cos(t)i + 9 sin(t)j

r(t)=cos(t)i+9sin(t)j

so ,  r(0)=  cos(0)i+9sin(0)j = i ( sine cos0 =1 and sin0 =0)

r(π/4) =  cos(0)i+4sin(0)j = cos(π/4)i+9sin(π/4)j

           = 1/√2i+9/√2j

r(θ−π)= cos(θ−π)i+9sin(θ−π)j= −cos(θ)i+9sin(θ)j

(π/6+△t)−r(π/6)= cos(π/6+△t)i+9sin(π/6+△t)j−cos(π/6)i−9sin(π/6)j

=  cos(π/6+△t)i−cos(π/6)i+9sin(π/6+△t)j−9sin(π/6)j

= −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

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Evaluate (If possible) the vector-valued function at each given value of t. (If an answer does not exist, enter DNE.)

r(t)=cos(t)i+9sin(t)jr(t)

a)r(0)=?

b)r(π/4)=?

c)r(θ−π)=?

d)r(π/6+△t)−r(π/6)=?