A baker uses 2 lbs of butter to make 7


dozen cookies. How many pounds of


butter would be used to make 132


cookies?

To double the initial deposit of $500 at an annual interest rate of 10% compounded annually, it will take approximately 7 years.

To determine the time it takes for the money to double, we need to consider the concept of compound interest. In this case, the interest is compounded annually at a rate of 10%.

When money is compounded annually, the formula to calculate the future value (FV) is given by the formula: FV = PV(1 + r)^n, where PV is the initial deposit, r is the interest rate, and n is the number of years.

We want to find the value of n when the future value (FV) is equal to double the initial deposit (2 * $500 = $1000). Therefore, the equation becomes: $1000 = $500(1 + 0.10)^n.

To solve for n, we can take the natural logarithm of both sides of the equation: ln($1000/$500) = ln(1.10)^n. Simplifying, we get: ln(2) = n * ln(1.10).

Using the logarithmic properties, we can isolate n: n = ln(2) / ln(1.10). Evaluating this expression, we find that n is approximately 7 years.

Hence, it will take approximately 7 years for the initial deposit of $500 to double at a 10% interest rate compounded annually.

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Answer:

Step-by-step explanation:

y = a(x-h)^2+k   ← vertex form of parabola equation with vertex (h, k)

So:

y = a(x-5)^2 + (-2)    ←  vertex form of our parabola equation

Parabola goes through (8, 25) so if x=8 then y=25

25 = a(8-5)^2 - 2

25 +2  = a(3)^2 - 2 +2

27 = 9a

a = 3

That means, the equation of a parabola in vertex form that passes through (8,  25) and has vertex (5, -2):

                                             y = 3(x - 5)^2 - 2

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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Using the range concept, it is found that the range of \(y = \csc^{-1}(x)\) is [-1,1].

The range of a function is the set that contains all possible output values.

Co-secant is 1 divided by sine, hence:

\(\csc{x} = \frac{1}{\sin{x}}\)

Then:

\(\csc^{-1}{x} = \frac{1}{\csc{x}} = \frac{1}{\frac{1}{\sin{x}}} = \sin{x}\)

The sine function assumes values between -1 and 1, inclusive, hence the range of \(y = \csc^{-1}(x)\) is [-1,1].

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Answer:

-pi/2,0 & 0,pi2

Step-by-step explanation:

i got you if nobody else do gang

Answer:

B

Step-by-step explanation:

The function is increasing anywhere the slope is positive.  This corresponds to the intervals -4<x<-2 and 0<x<2.  So, answer B is correct.

If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.

To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.

To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).

Plugging in the values, we have:

FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06

≈ $12,350

Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.

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The value of n corresponding to AIG = 11.6 and i = 7%, compounded annually, using the given known points (n, A/G) (all at i = 7%) is 41 years.

Given Points are as follows:(35, 10.6687), (40, 11.4234), (45,12.0360)Here, we have to find the value of "n" such that A/G = 11.6A/G is given by the following formula:A/G = (1 - (1+i)^-n)/i * (F/A, i, n)

By substituting the values of the above given points in the formula, we get:(35, 10.6687)  => A/G = 10.6687 = (1 - (1+0.07)^-35)/0.07 * (F/A, 0.07, 35) (1)(40, 11.4234) => A/G = 11.4234 = (1 - (1+0.07)^-40)/0.07 * (F/A, 0.07, 40) (2)(45, 12.0360) => A/G = 12.0360 = (1 - (1+0.07)^-45)/0.07 * (F/A, 0.07, 45) (3)Now, we will use the value of equation (2) and (3) to get the value of "n".

Equation (2) => 11.4234 = (1 - (1+0.07)^-40)/0.07 * (F/A, 0.07, 40) => (F/A, 0.07, 40) = 11.4234 * 0.07 / (1 - (1+0.07)^-40)Equation (3) => 12.0360 = (1 - (1+0.07)^-45)/0.07 * (F/A, 0.07, 45) => (F/A, 0.07, 45) = 12.0360 * 0.07 / (1 - (1+0.07)^-45)

Now, using the above value of (F/A, 0.07, 40) and (F/A, 0.07, 45) in equation (1)10.6687 = (1 - (1+0.07)^-35)/0.07 * (11.4234 * 0.07 / (1 - (1+0.07)^-40)) => n = 40 years11.4234 = (1 - (1+0.07)^-40)/0.07 * (12.0360 * 0.07 / (1 - (1+0.07)^-45)) => n = 41 years12.0360 = (1 - (1+0.07)^-45)/0.07 * (11.4234 * 0.07 / (1 - (1+0.07)^-40)) => n = 43 years

Therefore, the value of n corresponding to AIG = 11.6 and i = 7%, compounded annually, using the given known points (n, A/G) (all at i = 7%) is 41 years.

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The percentage of the data set within the range of 10 to 22 is 68.26%.

To find the percentage of the data set for a normally distributed variable with a mean of 16 and a standard deviation of 6, we can use the concept of z-scores and the standard normal distribution.

First, we need to convert the values to z-scores, which measure the number of standard deviations a particular value is from the mean. The formula for calculating the z-score is:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

In this case, we want to find the percentage of the data set within a certain range. Let's say we want to find the percentage of the data set between 10 and 22. We can calculate the z-scores for these values:

\(z1 = (10 - 16) / 6 = -1.0\)

\(z2 = (22 - 16) / 6 = 1.0\)

Next, we can use a standard normal distribution table or a calculator to find the area under the curve between these z-scores. The area between -1.0 and 1.0 represents the percentage of the data set within the range of 10 to 22.

Looking up the z-scores in the standard normal distribution table, we find that the area between -1.0 and 1.0 is approximately 0.6826. This means that approximately 68.26% of the data set falls within the range of 10 to 22.

Therefore, the percentage of the data set within the range of 10 to 22 is 68.26%.

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At the 5% level of significance, the data suggests that the average zinc concentration in the bottom of the water column exceeds that in surface water.

To determine if the average zinc concentration in the bottom of the water column exceeds that in surface water, you can perform a paired t-test. The null hypothesis (H0) would be that the average zinc concentration in the bottom of the water column is equal to or less than that in surface water.

To perform the test, you would calculate the difference between each paired measurement (bottom - surface) and then calculate the mean and standard deviation of these differences. Using these values, you can calculate the t-statistic and compare it to the critical value from the t-distribution table at the 5% level of significance.

If the calculated t-statistic is greater than the critical value, you would reject the null hypothesis and conclude that the average zinc concentration in the bottom of the water column exceeds that in surface water at the 5% level of significance.

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Answer:

\( h \le 30 \)

Step-by-step explanation:

Let h = number of hours of work.

At most 30 hours means 30 hours or less.

\( h \le 30 \)

Answer:

12.5 inches

Step-by-step explanation:

Given the equation for the cross section of a parabolic satellite TV dish:

y=1/50x^2

Equation of a parabola :

(y - k) = 1/4p * (x - h)^2

Distance of the focus from the Vertex = p

Comparing both equations :

1/4p * (x - h)^2 = 1/50 * x^2

4p = 50

Divide both sides by 4

4p/4 = 50/4

p = 12.5 inches

This is Right answer....

I hope you understand....

give me Brainliest.....

Thanks....

Answer: $1,312.5 difference

Step-by-step explanation:

1050 x 1.5 = 1575

1575 x 1.5 = 2,362.5

2,362.5 - 1050 = 1,312.5

Answer:

see explanation

Step-by-step explanation:

y(x + 1) = 51 ← substitute y = 3 into the equation

3(x + 1) = 51 ( divide both sides by 3 )

x + 1 = 17 ( subtract 1 from both sides )

x = 16

Given:

What to prove: x = 16

We have now proved that x = 16.

Hoped this helped.

\(BrainiacUSer1357\)

Answer:

y = − 2 /3 x − 7

Step-by-step explanation:

Use the slope formula and slope-intercept form  y = m x + b  to find the equation.

❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

Hey buddy ....

I really appreciate God to give me this chance to help u.

Let's see what to do...

-----------------------------------------------------------

First we need to find the slope of the line using this equation :

Suppose a = ( - 6 , - 3 ) , b = ( - 3 , - 5 )

\(slope = m = \frac{y(b) - y(a)}{x(b) - x(a)} \\ \)

Just need to put the coordinates in the equation:

\(slope = \frac{ - 5 - ( - 3)}{ - 3 - ( - 6)} \\ \)

\(slope = \frac{ - 5 + 3}{ - 3 + 6} \\ \)

\(slope = \frac{ - 2}{ - 3} \\ \)

\(slope = \frac{3}{2} \\ \)

====================================

We have this equation as the point-slope form of the linear functions :

\(y - y(one \: \: of \: \: the \: \: given \: \: points) = (slope) \times ( \: x - x(o \: o \: f \: t \: g \: p) \: ) \\ \)

Now just need to put the slope and one the given points ( a or b ) in the above equation:

I like to use a ( you can use b bro )

\(y - ( - 3) = \frac{3}{2} \times (x - ( - 6) \: ) \\ \)

\(y + 3 = \frac{3}{2} \times (x + 6) \\ \)

\(y + 3 = \frac{3}{2} x + 9 \\ \)

Subtract sides 3

\(y + 3 - 3 = \frac{3}{2} x + 9 - 3 \\ \)

\(y = \frac{3}{2} x + 6 \\ \)

And this is the equation of the line.

So we're done.....

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Take care dude ❤❤❤❤❤

❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

Answer:

Madeline picks 6 pieces of fruit per hour

Step-by-step explanation:

divide total amount of fruit she picked on that day by the amount of hours she spent picking

12/2 = 6

42/7 = 6

Answer:

579.67 yards

Step-by-step explanation:

Answer:

≈579.67 yards

Step-by-step explanation:

1. convert feet into yards

1 foot = 1/3 yards

2. use dimensional analysis

\(\frac{1739feet}{1}\) * \(\frac{1/3 yards}{1 foot}\)

3. multiple straight across

1739 feet * 1/3 yards

answer: ≈579.67 yards

Answer:

Mr Batista should bring more 82 cups.

Step-by-step explanation:

solve:

→ 514 - 36(12)

→ 514 - 432

→ 82

He needs more 82 cups and did not bring enough.

Answer:

(-2, 8)

Step-by-step explanation:

When rotating an image 90 degrees, x and y switch places and te new x coordinate becomes the opposite sign.

(x,y) -> (-y, x)

so

(8,2) -> (-2,8)

Answer:

is you are not adding in the 24 then 40 if you are adding in the 24 then 64

Step-by-step explanation:

The probability of having 3 earthquakes in the same year that all measure 6.0 or more is approximately 0.1106 or 11.06%.

What is probability?

Probability is a measure of the likelihood or chance that an event will occur. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

Assuming that the number of earthquakes measuring 6.0 or more on the Richter scale in a year follows a Poisson distribution with a mean of 0.93 (i.e., an average of 0.93 such earthquakes per year over the past 100 years), we can use the Poisson probability formula to find the probability of having exactly 3 such earthquakes in a year:

\(P(X = 3) = (e^{(-0.93)} * 0.93^3) / 3!\)

where X is the number of earthquakes measuring 6.0 or more on the Richter scale in a year.

Plugging in the values, we get:

\(P(X = 3) = (e^{(-0.93)} * 0.93^3) / 3! = 0.1106\)

Therefore, the probability of having 3 earthquakes in the same year that all measure 6.0 or more on the Richter scale, given that there have been 93 such earthquakes in the past 100 years, is approximately 0.1106 or 11.06%.

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Sorry, I could only solve #12.

Answer:

Step-by-step explanation:

To put the equations 5x - 9 = y and 2x = 7y in matrix form, we can write them as a system of equations by rearranging the terms. The matrix form can be represented as:

| 5  -1 |   | x |   | -9 |

| 2   -7 | * | y | = |  0 |

In matrix form, a system of linear equations can be represented as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

For the equation 5x - 9 = y, we can rearrange it as 5x - y = 9. This equation corresponds to the row [5 -1]X = [-9] in the matrix form.

For the equation 2x = 7y, we can rearrange it as 2x - 7y = 0. This equation corresponds to the row [2 -7]X = [0] in the matrix form.

Combining these two equations, we can write the system of equations in matrix form as:

| 5  -1 |   | x |   | -9 |

| 2   -7 | * | y | = |  0 |

This matrix form allows us to solve the system of equations using various methods, such as Gaussian elimination or matrix inversion.

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Answer: the three given points are the vertices of a triangle. solve the triangle, rounding lengths tot he nearest tenth and angle measures to the nearest degree A(0,0) B(-3,5) C(3,-2)

***

Plot given points to form a triangle with angle A at (0,0), B at (-3,5) and C at (3,-2).

Using distance formula:

AB=√(0+3)^2+(0-5)^2)=√(9+25)=√34

AC=√(0-3)^2+(0+2)^2)=√(9+4)=√13

BC=√(-3-3)^2+(5+2)^2)=√(36+49)=√85

..

Law of cosine: c^2=a^2+b^2-2abcosA

(BC)^2=(AB)^2+(AC)^2-2*AB*ACcosA

√85^2=34+13-2*√34*√13cosA

85=47-2√442cosA

38=-42cosA

cosx=-38/42

A=154.8˚

..

using law of sin:

BC/sin(154.8˚)=AC/sinB

sinB=AC*sin(154.8˚)/BC=0.1665

B=9.6˚

..

BC/sin(154.8˚)=AB/sinC

sinC=AB*sin(154.8˚)/BC=0.2693

C=15.6˚

Step-by-step explanation:

Answer:

Step-by-step explanation:

500+70=570

500+50=550

550+50+50+50+50+50+50=850

570+70+70+70+70=850

6 months

Answer:

x=-5, y=-2

Step-by-step explanation:

3x+2y= -19  

-3x-5y= 25

Add the two equations together

3x+2y= -19  

-3x-5y= 25

------------------

0x -3y = 6

Divide each side by -3

-3y/-3 = 6/-3

y = -2

Now find x

3x+2y = -19

3x +2(-2) =-19

3x-4 = -19

Add 4 to each side

3x -4+4 = -19+4

3x= -15

divide by 3

3x/3 = -15/3

x = -5

Answer:

x = -5, y = -2

Step-by-step explanation:

3x + 2y = -19

-3x - 5y = 25

Add both equation together.

Divide each side by -3.

Now, find x.

Substitute the value of y into the equation 3x + 2y = -19

Move the constant to the right hand side and change their sign.

Divide both side by 3.

Therefore, x = -5 and y = -2

The value of P(1.41 < Z < 2.85)  is 0.0771.

Hence, the correct answer is d.

A normally distributed random variable with mean μ= 0 and standard deviation σ= 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Because the Standard Normal Distribution is a probability distribution, the area under the curve between two points indicates the likelihood that variables will take on a range of values.

The whole area under the curve is one, or one hundred percent.

The mean and variance of a normal distribution are governed by two factors.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

The probability that a standard normal random variable Z is between 1.41 and 2.85 can be found using a standard normal table with a standard normal cumulative distribution function.

The answer is approximate:

P(1.41 < Z < 2.85)

= P(Z < 2.85) - P(Z < 1.41)

= 0.9927 - 0.9185

= 0.0742

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