The table shows the number of ounces of butter
Marti used in different recipes. She has 6 ounces of
butter left. How many ounces of butter did she have
at the beginning? Is your answer reasonable? Explain.

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

For more questions on share

https://brainly.com/question/30319374

#SPJ8

Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

More can be learned about transformations at https://brainly.com/question/28687396

#SPJ1

The original amount of the sale is $165

The given parameters are:

Bill after discount = $140

Discount = 15%

The original amount of the sale is calculated as:

Bill after discount = original amount * (1 - Discount)

So, we have:

140 = original amount * (1 - 15%)

This gives:

140 = original amount * 0.85

Divide by 0.85

Original amount = 165

Hence, the original amount of the sale is $165

Read more about discounts at:

https://brainly.com/question/7459025

#SPJ1

For the function and given domain, the range is  {-9,-1,5,7}.

A linear function can be represented by a line. The standard form for this equation is: \(y=ax+b\), for example, y=2x+7.

The domain of a function is the set of input values for which the function is real and defined. On the other words, when you define the domain, you are indicating for which values x the function is real and defined.

While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

The equation of this exercise, 2x+1,  is a linear equation because it presents the form: ax+b. Thus, you already know that your graph will be a line.

For this, you should replace -5,-1, 2,3 for x in the equation 2x+1.

For x=-5,  \(y=2*(-5)+1=-10+1=-9\)

For x=-1, \(y=2*(-1)+1=-2+1=-1\)

For x=2, \(y=2*(2)+1=4+1=5\)

For x=3, \(y=2*(3)+1=6+1=7\)

Therefore, the range is {-9,-1,5,7}

From the  values x of domain and the values of  y calculated previously, plot the points and draw the line. See the image attached.

Learn more about the range and the domain here:

brainly.com/question/10197594  

Answer:

Multiply and simplify as always

Step-by-step explanation:

8/9 x 3/4 = 24/36

simplify 24/36 into 2/3

Answer:  \(\frac{24}{36}\)

8×3=24

9×4=36

I hope this is good enough:

Answer:

1st question, see attachment (-32 is answer). 2nd question, answer is (x+3).

Step-by-step explanation:

please see attachment for 1st question.

2nd question:

-3 means x + 3

for any number A

(-A) is x + A

(A) is x - A

f(0) just means put 0 wherever x is in equation

Answer:

Mean - 5

Standard Deviation - 4.5

Step-by-step explanation:

Just got it correct on Khan Academy :)

80% is her free throw shooting percentage.

A fraction represents a part of a whole.

We can construct a fraction in which the numerator is how many shots she makes, and the denominator is how many shots she took overall.

We now have the following fraction:4/5

To convert this to a percentage, we want the denominator to be 20/20

4/5×20/20

80/100

0.8

Now multiply 0.8 with 100

0.8×100=80

Hence, 80% is her free throw shooting percentage.

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ2

Answer:

6x2-10x-4

Step-by-step explanation:

hx=(2x-4)(3x+1)

hx=2x(3x+1)-4(3x+1)

hx=6x2+2x-12x-4

hx=6x2-10x-4

We can estimate that the percent change in the number of club members from last year to this year is approximately 94.1%. This represents an almost doubling of the club membership.

What is the percent change?

Percentage change is a way to describe the difference between an old value and a new value, expressed as a ratio and then multiplied by 100.

To estimate the percent change in the number of club members, we can use the percent change formula:

percent change = (new value - old value) / old value x 100%

where the "old value" is the number of club members last year and the "new value" is the number of club members this year.

Plugging in the numbers we have:

percent change = (33 - 17) / 17 x 100%

percent change = 16 / 17 x 100%

percent change ≈ 94.1%

Therefore, we can estimate that the percent change in the number of club members from last year to this year is approximately 94.1%. This represents an almost doubling of the club membership.

To learn more about the percent change visit:

https://brainly.com/question/809966

#SPJ1

Answer:

y = 7

Step-by-step explanation:

y = 3(2-1) 2 + 1

y = 3(1)(2) + 1

y = 6 + 1

y = 7

Answer:

Contributions to a 401(k) are pre-tax, meaning they are deposited before your income taxes are deducted from your paycheck. However, when in retirement, withdrawals are taxed at your then-current income tax rate. Conversely, there is no tax savings or deduction for contributions to a Roth IRA

Answer:

20%

Step-by-step explanation:

Answer:

The hourly cost is 17 dollars.

Step-by-step explanation:

1. Subtract the damage deposit from the total cost to get 68.

2. Divide 4 from 68 to get 17. Which is the hourly cost.

Answer:

the answer is going to be b because u going to say In8=×

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

Read more about  Laws of Exponents at: https://brainly.com/question/11761858

#SPJ1

The definite integral for this problem has the result given as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}\)

The definite integral for this problem is defined as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx\)

We have an integral of the sum, hence we can integrate each term, and then add them.

For the first two terms, applying the power rule, the integrals are given as follows:

The integral of the tangent is given as follows:

ln|sec(x)|

Then the integral is given as follows:

I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.

Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:

I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)

I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 212 - ln|sec(5)| + ln|sec(1)|.

More can be learned about definite integrals at https://brainly.com/question/22008756

#SPJ1

The coordinates of B are (-7,-2).

What do you mean by x and y coordinates?

The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.

According to the given data in the question,

if M is the location where line segment AB meets its midpoint.

Then, we will using the midpoint formula,

\((-5,2)=(\frac{-3+x}{2},\frac{6+y}{2})..............(1)\)

Putting the x-coordinates in (1),

\(-5=\frac{-3+x}{2}\\ -10=-3+x\\-10+3=x\\x=-7\)

Similarly, putting the y-coordinates in (1),

\(2=\frac{6+y}{2} \\4=6+y\\4-6=y\\y=-2\)

Hence, the coordinates of B are (-7,-2).

To learn more about x and y coordinates visit to the  given link:

https://brainly.com/question/27749090?referrer=searchResults

#SPJ13

The central angles for the categories with the numbers 40, 100, 50, and 50 are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

To calculate the central angles for each category based on the given numbers 40, 100, 50, and 50, we need to find the proportion of each value to the total sum of all the values. Let's proceed with the following steps:

Step 1: Calculate the total sum of the given numbers: 40 + 100 + 50 + 50 = 240.

Step 2: Find the proportion of each value by dividing it by the total sum and multiplying it by 360 (since a full circle has 360 degrees).

Central angle for the first category: (40/240) * 360 = 60 degrees.

Central angle for the second category: (100/240) * 360 = 150 degrees.

Central angle for the third category: (50/240) * 360 = 75 degrees.

Central angle for the fourth category: (50/240) * 360 = 75 degrees.

The central angles for each category based on the given numbers are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

These central angles represent the relative proportions of each category's spending in relation to the total spending. They can be used to create a pie chart or visualize the distribution of expenses in a circular graph.

For more question on angles visit:

https://brainly.com/question/31615777

#SPJ8

Note the search engine cannot find the complete question

Answer:

36.5 degrees

Step-by-step explanation:

draw a line from B to H then you'll notice that  all the angles on the base are right angles as its a rectangle;e so when you connect BH and AH it makes a right triangle whose base can be found by using 23^2+21^2=c^2

and c=31.1cm so now you have a right triangle with two sides BA=23cm and AH=31.1cm so do tan^-1(23cm/31.1cm) which is equal to 36.5 degrees( correct to 1 d.p.)

Answer:

Step-by-step explanation:

To find the angle between the line BH and plane AEHD, we first need to identify these two elements in the given cube.

From the description of the cube, we can see that the line BH lies on the front plane of the cube, which is formed by the lines AB, BC, CD, and AD.

Also, the plane AEHD is the base plane of the cube, which is formed by the lines AE, EH, HD, and AD.

Therefore, to find the angle between line BH and plane AEHD, we need to determine the direction vectors of both BH and the plane AEHD.

Let's start with BH:

The line BH passes through points B and H. To find the direction vector of BH, we can subtract the position vectors of B and H:

BH = vector(H) - vector(B)

To do this, we need to find the position vectors of B and H with respect to some chosen origin. We can use the vector AD as one of the basis vectors for our coordinate system, and choose A as the origin.

The position vector of B is:

vector(B) = vector(A) + vector(AB)

= (0, 0, 0) + (7, 0, 0)

= (7, 0, 0)

The position vector of H is:

vector(H) = vector(A) + vector(AD) + vector(AE) + vector(AH)

= (0, 0, 0) + (0, 0, 21) + (7, 0, 0) + (0, 23, 0)

= (7, 23, 21)

Therefore, the direction vector of BH is:

BH = vector(H) - vector(B)

= (7, 23, 21) - (7, 0, 0)

= (0, 23, 21)

Next, let's find the normal vector of the plane AEHD:

The plane AEHD is the base plane of the cube, which means it is parallel to the X-Y plane. Therefore, its normal vector is in the Z direction.

To find the normal vector of the plane AEHD, we can take the cross product of two vectors lying in the plane, such as AE and AD:

normal vector = AE x AD

= (7, -23, 0) x (0, 0, 21)

= (-483, -147, 0)

(Note: We could also take the cross product of other pairs of vectors lying in the plane, such as EH and HD, to get the same normal vector.)

Now that we have the direction vector of BH and the normal vector of the plane AEHD, we can find the angle between them using the dot product:

cos(angle) = (BH . normal vector) / (|BH| |normal vector|)

where BH . normal vector is the dot product of BH and the normal vector, and |BH| and |normal vector| are the magnitudes of BH and the normal vector, respectively.

BH . normal vector = (0, 23, 21) . (-483, -147, 0)

= 0 - 3393 + 0

= -3393

|BH| = sqrt(0^2 + 23^2 + 21^2) = sqrt(1102)

|normal vector| = sqrt((-483)^2 + (-147)^2 + 0^2) = sqrt(234018)

Therefore,

cos(angle) = -3393 / (sqrt(1102) * sqrt(234018))

= -0.0662

Finally, we can find the angle between BH and the plane AEHD by taking the inverse cosine. cos(angle) = -0.0662

To find the angle, we take the inverse cosine of both sides:

angle = arccos(-0.0662)

Using a calculator, we get:

angle ≈ 1.649 radians ≈ 94.53 degrees

Therefore, the angle between the line BH and plane AEHD is approximately 94.53 degrees.

The expression that represents the product of t and 9 is 9t

The product of t and 9 can be represented by the following expressions:

All three of these expressions represent the same thing: the result of multiplying t and 9 together.

The expression "t * 9" uses the multiplication operator (*) to indicate that t and 9 are being multiplied.

The expression "9 * t" is equivalent, as multiplication is commutative and the order of the factors doesn't affect the result.

The expression "9t" is a shorthand way of writing the product, using the distributive property of multiplication.

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

https://brainly.com/question/30144287

#SPJ1

Answer:

Answer is A) HL

Step-by-step explanation:

The equation f(x)=x² + 2x is a quadratic equation, and it passes through the points (0,0) and (1,3)

The equation is given as:

f(x)=x² + 2x

Set x = 0

f(0)= 0² + 2(0) = 0

Set x = 1

f(1)= 1² + 2(1) = 3

The above means that the equation f(x)=x² + 2x passes through the points (0,0) and (1,3)

See attachment for the graph of f(x)=x² + 2x

Read more about quadratic graphs at:

https://brainly.com/question/18797214

#SPJ1

Answer: 2

Step-by-step explanation:

We can simplify the given logarithmic expression using the logarithmic property that states:

log a base b - log c base b = log (a/c) base b

Using this property, we can rewrite the expression as follows:

log 16 base 2 - log 4 base 2 = log (16/4) base 2

Simplifying the numerator of the logarithm, we get:

log (16/4) base 2 = log 4 base 2

Now, we can evaluate the logarithm using the definition of logarithm, which states that:

log b base a = x if and only if a = b^x

In this case, we have:

log 4 base 2 = x if and only if 2^x = 4

We know that 2 raised to what power gives 4? It is 2, because 2^2 = 4.

Therefore, we have:

log 4 base 2 = 2

Hence, the value of the given logarithmic expression is 2.

The answer of the given question based on the cost of mailing is , the cost of mailing a 2.5-ounce letter to Vienna, Austria would be $6.63 (rounded to the nearest cent).

An equation is  mathematical statement that shows  two expressions are equal. It contains variables, constants, and mathematical operations like  addition, subtraction, multiplication, and division.

For example, a simple equation could be:

2x + 3 = 9

The equation y = 0.25x + 6.00 represents the cost y of mailing a letter to Vienna, Austria based on the weight x of the letter in ounces. The flat rate of $6.00 is represented by the constant term 6.00 in the equation, and the additional charge of $0.25 per ounce is represented by the coefficient of x, which is 0.25.

To use this equation to determine the cost of mailing a specific letter, you would need to know the weight of the letter in ounces. You could then substitute this value for x in the equation and solve for y, which would give you the cost of postage in dollars.

For example, if a letter weighs 2.5 ounces, you could plug in x = 2.5 into the equation:

y = 0.25(2.5) + 6.00

y = 0.625 + 6.00

y = 6.625

So the cost of mailing a 2.5-ounce letter to Vienna, Austria would be $6.63 (rounded to the nearest cent).

To know more about Weight visit:

https://brainly.com/question/14767944

#SPJ1

In the given information, we know the previous step is:

And the next step is:

As we can observe, between the previous and the next step, the square root has disappeared.

Then, to eliminate a square root we need to square both sides