A recipe calls for 4 2/3 cups of stock. If 4 1/2 times the recipe needs to be made, how much stock will be needed?

Answer:

The length of each side of the original square was [tex]15[/tex] inches

Step-by-step explanation:

Let

x------> the length side of the original square

we know that

The perimeter of a square is equal to

[tex]P=4b[/tex]

where

b is the length side of the square

In this problem

[tex]b=(x+2.5)\ in[/tex]

[tex]P=70\ in[/tex]

substitute

[tex]70=4(x+2.5)[/tex]

solve for x

[tex]70=4x+10[/tex]

[tex]4x=70-10[/tex]

[tex]x=60/4=15\ in[/tex]

f(x) = 4x − 12

f−1(x) =1/4 x + 3

The inverse of the function f(x) = 4x - 12 is f^-1(x) = (x + 12)/4.

To find the inverse of the function f(x) = 4x - 12, we need to switch the roles of x and y and solve for y.  

Step 1: Replace f(x) with y: y = 4x - 12.

Step 2: Swap x and y: x = 4y - 12.

Step 3: Solve for y: x + 12 = 4y.  

Step 4: Divide both sides by 4: (x + 12)/4 = y.

Therefore, the inverse function is f-1(x) = (x + 12)/4.

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Answer:

Step-by-step explanation:

[tex]\text{The formula of a distance between two points on a number line:}\\\\d=|a-b|\\\\\text{for}\ a\geq b:\ d=a-b\\=========================\\\\\text{We have}\ 4.7\ \text{and}\ -11.2.\ \text{Substitute:}\\\\d=4.7-(-11.2)=4.7+11.2=15.9[/tex]

The distance between 4.7 and -11.2 on the number line is 15.9.

The distance between two points on a number line can be found by taking the positive difference between their coordinates. In this case, the distance between 4.7 and -11.2 is found by subtracting the smaller number from the larger number and taking the absolute value.

Distance = |-11.2 - 4.7| = |-15.9| = 15.9

Therefore, the correct expression is Distance = 15.9.

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Answer:

m = (12 - 7) / (-39 - 26) = 5/(-65) = -1/13

Final answer:

The 8 in the number 8.4 has a value that is 100 times greater than the 8 in the number 0.084. The first 8 represents 8 ones, while the second represents 8 hundredths.

Explanation:

The value of the 8 in 8.4 is 100 times greater than the 8 in 0.084. To understand why, let's remember that each position in a decimal number has a place value that is 10 times less than the place value to its left. For instance, in the number 8.4, the 8 is in the ones place, meaning its value is 8 ones or '8'. However, in the number 0.084, the 8 is in the hundredths place, so its value is 8 hundredths or '0.08'.

Therefore, when comparing the two eights, we see that:

The 8 in 8.4 equals 8 ones (8 × 1 = 8).

The 8 in 0.084 equals 8 hundredths (8 × 0.01 = 0.08).

To find a number whose 8 is worth 100 times less than the 8 in 8.4, we need the 8 to be two places to the right of the decimal point, which is the hundredths place. The number 0.084 satisfies this because 8 ones (the value of the 8 in 8.4) are 100 times greater than 8 hundredths (the value of the 8 in 0.084).

Answer:

A

Step-by-step explanation:

a. The 50 independent network servers would be needed if each has 98% reliability.

b. Approximately 9 independent network servers would be needed if each has 89% reliability.

To calculate the number of independent network servers needed for a given level of reliability, we can use the following formula:

[tex][ \text{Number of servers} = \frac{1}{1 - \text{Reliability}} ][/tex]

a) For servers with 98% reliability:

[tex][ \text{Number of servers} = \frac{1}{1 - 0.98} = \frac{1}{0.02} = 50 ][/tex]

Therefore, 50 independent network servers would be needed if each has 98% reliability.

b) For servers with 89% reliability:

[tex][ \text{Number of servers} = \frac{1}{1 - 0.89} = \frac{1}{0.11} \approx 9 ][/tex]

Therefore, approximately 9 independent network servers would be needed if each has 89% reliability.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='. The solution of the given equation,−2 − (+7) is −9.

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

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Given an equation, −2 − (+7) which is needed to be solved. Therefore, The given equation can be solved as shown below.

−2 − (+7)

Open the brackets,

= −2 − 7

Add the two terms,

= −9

Hence, the solution of the given equation,−2 − (+7) is −9.

Learn more about Equation:

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Marta's wire is 19.2 cm longer than Tia's wire.

Given:

Tia 's wire is 4m 8 cm ⇒ cut into 10 equal pieces

Marta's wire 540 cm ⇒ cut into 9 equal pieces

Question:

How much longer is one of Marta's wires then one of Tia's?

1. Tia's wire is in m and cm unit, so we can not divide it straightly into its equal pieces. First step, we are going to convert meter (m) to millimeter (mm):

Tia's wire = 4 m 8 cm

[tex]\boxed {1 m = 100 cm }[/tex]

[tex]\boxed {= (4 m \times \frac{100 cm}{ 1 m}) + 8 cm ) } \\\boxed {= 400 cm + 8 cm }\\\boxed {= 408 }[/tex]

2. Second step, calculate each pieces Tia's wire:

She cut this wire into 10 equal pieces:

[tex]\boxed {= \frac{408}{10} } \\\boxed {= 40.8 cm }[/tex]

Each piece of Tia's s ribbon is is 40.8 cm long

3. Third step, we are going to calculate Marta's wire:

She has 540 cm and cut it into 9 equal pieces

[tex]\boxed {= \frac{540 cm}{9} }[/tex]

[tex]\boxed {=60 cm }[/tex]

Each pieces Marta's wire is 60 cm long

4. Last step, find the difference between Tia's wire and Marta's:

[tex]\boxed {=60 cm -40.8 cm }\\\boxed {=19.2 cm }[/tex]

So, Marta's wire is 19.2 cm longer than Tia's wire

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Keywords: converting, conversion, dividing, subtraction, find the difference, converting meter to centimeter, converting unit of length

Final answer:

To find the critical value for α = 0.025 in a one-tailed test, we look at the standard normal distribution tables; the critical value is approximately -1.96.

Explanation:

The question pertains to hypothesis testing in the context of proportion analysis. To determine the critical value for a significance level α = 0.025 in a one-tailed test about a proportion, we use the standard normal distribution (Z-distribution). Given that the sample size is large (n=400), it is appropriate to use a Z-test for this calculation. The critical value corresponds to the Z-score that has 0.025 of the distribution's area to its right (since we are checking for 'less than 10% defective').

Referring to standard normal (Z) distribution tables or using statistical software, we can find that the critical value for α = 0.025 for a one-tailed test is approximately -1.96. This is the Z-score such that the area under the normal curve to the right of this value is 0.025. If the calculated Z-score obtained from the sample proportion is less than -1.96, we would reject the null hypothesis that the proportion of defective peaches is less than 10%.

To find the value of x in a system of equations, you can use the substitution or elimination method. In this case, x = 2 is the solution.

To find the value of x in the system of equations x − 2y = 2 and 3x + y = 6, we can use the method of substitution or elimination.

Substitution method:

Therefore, the value of x in the solution to the system of equations is x = 2.

Answer:

1/3

Step-by-step explanation:

The distance between the ships is changing at a rate of 39 km/hr at 4:00 PM. This is calculated using differentiation of the Pythagorean theorem relating distances between the ships.

This is a typical

related rates problem

in calculus. Before we start, let's mark the distance between ship A and ship B as C, the distance that A traveled as X (X=35 km/hr*4 hr = 140 km), and the distance B traveled as Y (Y=20 km/hr*4 hr = 80 km). Note that X, Y, and C form a right triangle. By using the Pythagorean theorem, we get C²=X²+Y², which we can differentiate with respect to time (t) to obtain, 2C * dC/dt = 2X * dX/dt + 2Y * dY/dt. As we're solving for dC/dt (rate of change of the distance between the two ships), we get dC/dt = (X * dX/dt + Y * dY/dt) / C. Plugging in the known values (X=140 km, Y=80 km, dX/dt=35 km/hr, dY/dt=20 km/hr, and C=170 km, as it hasn't changed since they started), we get dC/dt = (140*35 + 80*20) / 170 = 39 km/hr. So, the distance between the ships is changing at a rate of 39 km/hr at 4:00 PM.

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Answer:

The required equation of line is y=-6x-57.

Step-by-step explanation:

The point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

Where m is slope of the line.

It is given that a line that passes through (–9, –3) and has a slope of –6.

Substitute m=-6, x₁=-9 and y₁=-3 in the above equation.

[tex]y-(-3)=-6(x-(-9))[/tex]

[tex]y+3=-6x-54[/tex]

Subtract 3 from both the sides.

[tex]y=-6x-54-3[/tex]

[tex]y=-6x-57[/tex]

Therefore the required equation of line is y=-6x-57.

Answer:

D).y+3=-6(x+9)

Step-by-step explanation:

took it on edge

To solve this problem, all we have to do is to use a conversion factor to convert millisecond into seconds. We know that there are 1000 milliseconds in a second, therefore:

pitcher’s arm rotation = 7 degrees / millisecond * (1000 milliseconds / second)

pitcher’s arm rotation = 7,000 degrees / second

Answer:

7000 Hope this helps and if it does remember to give me a like , please and thank you!