A recipe for cake for 3/4 cup of sugar and 2 cups of flour. How much sugar would be needed for 1 cup of flour?

Answer:

Step-by-step explanation: I think it's D

Bonnie will have gained a total of £210 in interest from her investments in these two accounts.

Bonnie initially invests £600 in an account with a 4% simple interest per year. After 2 years, the interest earned on this investment would be:

Interest = Principal × Rate × Time

= £600 × 0.04 × 2

= £48

So after 2 years, Bonnie would have a total of £600 + £48 = £648.

Next, Bonnie reinvests half of the amount (£648/2 = £324) in another account with a 5% simple interest per year. She leaves this money in the account for 10 years. The interest earned on this investment would be:

Interest = Principal × Rate × Time

= £324 × 0.05 × 10

= £162

Therefore, the interest Bonnie gains from this second investment after 10 years is £162.

To calculate the total interest gained from both investments, we add the interest from the first investment (£48) to the interest from the second investment (£162):

Total interest = £48 + £162

= £210

Therefore, Bonnie will have gained a total of £210 in interest from her investments in these two accounts.

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Answer:

volume = 174.8 sq. units.

Answer:

61.5752159 units³

Step-by-step explanation:

The height of a cone can be found using the following formula:

\(v=\frac{1}{3} \pi r^2h\)

We know that the height is 14.7 and the radius is 2.

\(h=14.7 \\r=2\)

Substitute the values into the formula.

\(v=\frac{1}{3} \pi (2)^2(14.7)\)

Evaluate the exponent.

⇒ 2²= 2*2 = 4

\(v=\frac{1}{3} \pi (4)(14.7)\)

Multiply 4 and 14.7

\(v=\frac{1}{3} \pi (58.8)\)

Multiply 1/3 and pi.

\(v=1.04719755*58.8\)

Multiply the two numbers together.

\(v=61.5752159\)

Add appropriate units. Volume is cubic units, and we aren't given units. So, we should use cubic units.

\(v=61.5752159 units^3\)

The volume of the cone is 61.5752159 cubic units.

Answer:

NOT a single ordered pair satisfies the equation.

Step-by-step explanation:

Given the equation

\(x^2+y^2=100\)

Let us substitute all the given ordered pairs to find which ordered pair satisfies the equation.

For (0, -100)

\(x^2+y^2=100\)

substitute x=0 and y=-100

\(0^2+\left(-100\right)^2=100\)

\(10000=100\)

FALSE

Thus, the ordered pair (0, -100) does NOT satisfy the equation.

For (10, -10)

\(x^2+y^2=100\)

substitute x=10 and y=-10

\(10^2+\left(-10\right)^2=100\)

\(200=100\)

FALSE

Thus, the ordered pair (10, -10) does NOT satisfy the equation.

For (25, 75)

\(x^2+y^2=100\)

substitute x=25 and y=75

\(25^2+\left(75\right)^2=100\)

\(6250=100\)

FALSE

Thus, the ordered pair (25, 75) does NOT satisfy the equation.

Therefore, NOT a single ordered pair satisfies the equation.

5.30 % rate of return would you expect on a 5-year treasury security, assuming the pure expectations theory is valid.

To reflect the true cost and purchasing power of money that is borrowed or invested, an interest rate is called a real interest rate that has been adjusted for inflation. The nominal interest rate depicts the cost of money and reflects the state of the market. A good's nominal value is its price in terms of money. Its value in relation to another good, service, or collection of goods is what determines its true worth. Given that it is the current interest rate in the economy, it is frequently referred to as the market interest rate (usually charged by banks and other institutions). Depending on the bank or the type of loans or deposits, this nominal interest rate may be 8%, 10%, or 12%.

Nominal interest rate = Real interest rate + Inflation rate

= 2.5% + 2.8%

= 5.30%

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An equation is formed of two equal expressions. The number of cakes that are made by Sam this week is $10.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Sam gets paid $20 a week in addition to $4 for every cake she bakes. Let y be the total amount that is made by Sam this week, while x represents the number of cakes she bakes. Therefore, the equation for the total amount made by sam in a week can be written as,

y = 20 + 4x

Since her total income for this week is $60, therefore, we can write,

60 = 20 + 4x

40 = 4x

x = 10

Hence, the number of cakes that are made by Sam this week is $10.

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the kangaroo real height is 3 feet and shadow height is 5 feet

if the height of the tree is 7 feet so the real height of the tree is 5 feet

Answer: The measure of angle 3 is 50 degrees.

Step-by-step explanation:

We know that angle 2 is 130 degrees.

Angle 1 and angle 2 are verticle angles which means that they are across and equal to each other.

So angle 1 and angle 2 are 130 degrees.

Add up both angle 1 and angle 2, 130 + 130 = 260.

Now, all of these angles add up to be 360 degrees in total as they make a circle and there are 360 degrees in one.

Subtract 260 from 360, 360 - 260 = 100.

Since both angle 3 and angle 4 are also verticle angles we need to split the 100 degrees evenly, 100 ÷ 2 = 50.

So, angle 3 is 50 degrees.

Answer: 12,000n

Step-by-step explanation:

Jane want to save $12,000 every year.

Assuming there are n number of years, she would have saved:

= 12,000 * n

That therefore, is the total amount she would have given a certain number of years.

For instance, in 10 years she would have:

= 12,000 * n

= 12,000 * 10

= $120,000

Answer:

angle Q is 68°

angle R is 112°

Answer:

Terms: 7, 5c, 2k, 15

Variables: C, K

Co efficients: 5, 2

Constants: 7, 15

The average speed for the trip was 90 mph Given that a trip of 900 miles would have taken 1 hour less if the average speed for the trip had been greater by 10 miles per hour. We are supposed to calculate the average speed for the trip.

Let the original speed be 'x' mph. Then, new speed will be (x + 10) mph

Time taken at the original speed to cover 900 miles:900 / x hours

Time taken at the new speed to cover 900 miles:900 / (x + 10) hours

According to the question,1 hour less when the average speed is increased by 10 mph:

900 / x - 900 / (x + 10) = 1

Multiplying by (x)(x+10) on both sides:

900(x+10) - 900x = x(x+10)

Solving for x:

x² + 10x - 9000 = 0x

= (−10 ± √(10² + 4×1×9000)) / 2x

= (−10 ± √(100 + 36000)) / 2x

= (−10 ± √36100) / 2

On ignoring the negative value, we get the value of 'x' to be:

x = (−10 + 190) / 2x

= 180 / 2

= 90 mph

Therefore, the average speed for the trip was 90 mph.

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Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0.

Several real-world scenarios use exponential functions, including population increase, compound interest, radioactive decay, and the spread of diseases. For instance, an exponential function may be used to simulate the expansion of a bacterial population, with the rate of increase being proportional to the population size. Similarly, compound interest, which applies the rate of interest to the principal sum across a number of periods, can be represented by an exponential function.

Positive value of a vertically stretches the graph of f when a > 1 or shrinks the graph of f when a < 1. h translates the graph of f to the left when h < 0 or right when h > 0 and k translates the graph of f up when k > 0 and down when k < 0.

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Root x = 2 is an extraneous solution for radical equation √(4 · x - 7) - √(2 · x) = 1, whose roots are 2 and 8, respectively.

In this problem we find the definition of a radical equation, whose roots must be found by combining algebra properties and power properties. A root is an extraneous solution if the result lead to an absurdity. (i.e. 1 = 0).

First, write the complete expression:

√(4 · x - 7) - √(2 · x) = 1

Second, apply algebraic substitution formula u = 2 · x to simplify the model:

√(2 · u - 7) - √u = 1

Third, use algebra properties to clear square roots:

√(2 · u - 7) = 1 + √u

Fourth, square both sides of the expression:

2 · u - 7 = (1 + √u)²

2 · u - 7 = 1 + 2 · √u + u

u - 7 = 1 + 2 · √u

u - 2 · √u - 8 = 0

Fifth, use algebraic substitution k = √u and solve the quadratic-like equation by factorization:

k² - 2 · k - 8 = 0

(k - 4) · (k + 2) = 0

k₁ = 4 or k₂ = - 2

Sixth, find the values of x by reversing algebraic substitutions:

√u₁ = 4 or √u₂ = - 2

u₁ = 4² or u₂ = (- 2)²

2 · x₁ = 4² or 2 · x₂ = (- 2)²

x₁ = 8 or x₂ = 2

Seventh, look for any extraneous solution:

x₁ = 8

√(4 · 8 - 7) - √(2 · 8) = 1

√25 - √16 = 1

5 - 4 = 1

1 = 1

x₂ = 2

√(4 · 2 - 7) - √(2 · 2) = 1

√1 - √4 = 1

1 - 2 = 1

- 1 = 1 (CRASH!)

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Answer:

4x - 5 ft

Step-by-step explanation:

Perimeter = 4 × side

16x - 20 = 4 × side

(16x - 20)/4 = side

4x - 5 = side

Answer:

\(perimeter = 2(l + b) \\ 16x - 20 = 2(2l)(square \: so \: l = b) \\ 16x - 20 = 4l \\ l =( 16x - 20 )\div 4 = 4x - 5 \\ thank \: you\)

Answer:

they are 2 lines that look ;like this =

Step-by-step explanation: the 2 lines of the equal sign are parallel

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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The area of the triangle PQR that has a side length of p = 14 inches, q = 37 inches, and r = 38 inches is 257.2 inches².

area of triangle = √s(s - a)(s - b)(s - c)

where

Therefore,

s = 14 + 37 + 38  / 2 = 89 / 2 = 44.5

area of triangle = √44.5(44.5 - 14)(44.5 - 37)(44.5 - 38)

area of triangle = √44.5 × 30.5 × 7.5 × 6.5

area of triangle = √66165.9375

area of the triangle = 257.227404255

area of the triangle ≈ 257.2 inches²

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36m, 9 x 4 = 36

.

.

.

.

.

Answer:

im think its B

Step-by-step explanation:

Answer:

7 to the left, and up 2.

Step-by-step explanation:

The length of one side of each triangle is 15 inches.

To find the length of one side of each triangle, we can start by calculating the total length of the sides of the rectangle and square. Then, we can subtract that value from the total length of wire used to find the remaining length for the two triangles. Finally, we can divide the remaining length by the number of sides in the two triangles to find the length of one side of each triangle.

The total length of the sides of the rectangle is:

2(15 inches) + 2(12 inches) = 30 inches + 24 inches = 54 inches

The total length of the sides of the square is:

4(19 inches) = 76 inches

The remaining length for the two triangles is:

220 inches - 54 inches - 76 inches = 90 inches

The length of one side of each triangle is:

90 inches ÷ 6 sides = 15 inches

Therefore, the length of one side of each triangle is 15 inches.

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Answer: 125.00$

Step-by-step explanation:

the answers in the question

Answer: $62.50

Step-by-step explanation:

125/2=62.50

9514 1404 393

Answer:

  B  -11 4/15

Step-by-step explanation:

  -7 3/5 -3 2/3 = -(7 3/5 +3 2/3)

  = -((7 +3) +(3/5 +2/3)) = -(10 +9/15 +10/15)*

  = -(10 +19/15) = -(10 +1 4/15)

  = -11 4/15

___

* you know at this point that the correct answer is B. The integer part cannot be 10, but must be 11.

The distance between two boats travelling in a canal in opposite direction given by the equation 2 ( x -1 ) = 2x + 5, will have no solution.

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.

For example:

1. x + y = 2

2. 5x + y + z = 5

1. Unique Solution

2. Infinite Solution

3. No Solution.

Unique solution: 3x + 5 = -10

here, x will have only one solution i.e. x = -5

Infinite solution: 2x + 3 = x + x + 3

here, x will have infinitely solution

No solution: 3x + 5 = 3x - 5

here, 5 ≠ -5

We have given that:

2(x -1 ) = 2x + 5

2x - 2 = 2x + 5

-2 ≠ 5

here, x will have no solution.

Hence,

The distance between two boats travelling in a canal in opposite direction given by the equation 2 ( x -1 ) = 2x + 5, will have no solution.

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The probability that gas is not used for cooking at a household can be determined by considering the probabilities of shopping at Prime Foods and using gas for cooking.

Let's denote the event of using gas for cooking as G and the event of shopping at Prime Foods as P. We are given that the probability of G is 0.18, and the conditional probabilities are as follows: P(G) = 0.7 and P(~G) = 0.35.

To find the probability of gas not being used for cooking, we need to calculate P(~G|~P), which represents the probability of not using gas for cooking given that a person does not shop at Prime Foods.

Using conditional probability, we have P(~G|~P) = P(~G∩~P) / P(~P). Here, P(~G∩~P) represents the probability of both not using gas for cooking and not shopping at Prime Foods, and P(~P) represents the probability of not shopping at Prime Foods.

Since P(~G∩~P) + P(G∩~P) = P(~P), we can rewrite the equation as P(~G|~P) = [P(~G∩~P) + P(G∩~P)] / P(~P).

We are given P(G∩~P) = P(G) * P(~P|G) = 0.18 * (1 - 0.7) = 0.054.

Therefore, P(~G|~P) = [P(~G∩~P) + P(G∩~P)] / P(~P) = (0.054 + 0) / (1 - 0.35) = 0.054 / 0.65 ≈ 0.083.

So, the probability that gas is not used for cooking at the household, given that a person does not shop at Prime Foods, is approximately 0.083, which is option (a).

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Answer:

7.875

Step-by-step explanation:

AB+BC=AC

(4x-9)+(4x-9)=45

8x-18=45

8x=63

x=7.875

Answer:

1) 1/17

2) 1/111

3) 1/15

They're all fractions

Hope that helped, just divide the result with the number available

Example :

1÷17 =1/17