The objective function is . z=6x+4y
A. Find the value of the objective function at each corner of the graphed region.
B. Find the maximum value of the objective function.
C. Find the minimum value of the objective function.

A(2,10)
B(8,5)
C(9,4)
D(1,3)

Step-by-step explanation:

First, let's calculate the amount that Eleanor would need to finance after the down payment:

$1,987.00 - $87.00 = $1,900.00

Option 1: Financing through the dealer

Finance charge:

Total amount paid - amount financed = finance charge

$169.00 x 12 months = $2,028.00

$2,028.00 - $1,900.00 = $128.00

APR:

We need to use the following formula to calculate APR:

APR = ((finance charge / amount financed) x (12 / loan term in months)) x 100

APR = (($128.00 / $1,900.00) x (12 / 12)) x 100

APR = 0.0674 x 100

APR = 6.74%

Total amount paid:

Amount financed + finance charge = total amount paid

$1,900.00 + $128.00 = $2,028.00

Option 2: Credit union loan

Finance charge:

Total amount paid - amount financed = finance charge

$114.19 x 18 months = $2,055.42

$2,055.42 - $1,900.00 = $155.42

APR:

We can use the same formula as before to calculate APR:

APR = ((finance charge / amount financed) x (12 / loan term in months)) x 100

APR = (($155.42 / $1,900.00) x (12 / 18)) x 100

APR = 0.0458 x 100

APR = 4.58%

Total amount paid:

Amount financed + finance charge = total amount paid

$1,900.00 + $155.42 = $2,055.42

The credit union loan is the better deal. Here's why:

The finance charge is lower for the credit union loan ($155.42 vs. $128.00).

The APR is also lower for the credit union loan (4.58% vs. 6.74%).

The total amount paid is higher for the credit union loan, but this is because it has a longer repayment period (18 months vs. 12 months). If we look at the total amount paid per month, the credit union loan is still the better deal ($114.19 vs. $169.00).

Therefore, Eleanor should choose the credit union loan.

B u A = 48

B = 45

The part of set B not included in A is B - A∩B  = 45 - 7 = 38

Since B u A = 48,  A must have 48-38 = 10 elements (3 exclusive of B, 7 shared with B).

------

Alternatively, the inclusion-exclusion principle may be used:   A  +  B  - (A ∩ B) = A u B  

  A + 45 - 7 = 48

  A  = 48 - 45 + 7  

   A = 10

NOTE that I'm using A and B  to indicate the number of elements in each set, respectively.

More formally, one would write |A|  and |B| to indicate the cardinality (number of elements) of the set.

Answer:

Because 6th grade math is the abosulute worst. other than every other math above 6th grade

Step-by-step explanation:

Answer:

one 2

one 3

two 4's

one 5

one 6

Step-by-step explanation:

We can use the combination formula to derive how many sets of two can be obtained from this set of 4 numbers. We are using the combination formula instead of the permutation formula because, in this situation, order doesn't matter; the mean of 1 and 3 is the same as the mean of 3 and 1.

\(_nC_r = \dfrac{n!}{r!(n-r)!}\) where \(n\) is the number of things to choose from and \(r\) is the number of things we are choosing. Hence the equation for this problem is:

\(_4C_2 = \dfrac{4!}{2!(4-2)!}\)

\(_4C_2=\dfrac{24}{2(2)}\)

\(_4C_2 = 6\)

So, there are 6 ways to pick 2 cards from a total of 4. We can lay out these 6 possibilities from the given numbers on each card:

(1, 3)     (3, 5)     (5, 7)

(1, 5)     (3, 7)

(1, 7)

Then, we can calculate the mean, or average, of each.

2           4           6

3           5

4

Finally, we can conclude that the distribution of the means for each possible set of number pairs is:

one 2

one 3

two 4's

one 5

one 6

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

  (a)  5440.42 g

Step-by-step explanation:

The amount remaining (Q) is given in terms of the initial amount (Q₀) by the exponential decay formula ...

  Q = Q₀(1/2)^(t/330) . . . . . where t is in days

__

The amount after 540 days is ...

  1750 g = Q₀(1/2)^(540/330) = 0.321666Q₀

  Q₀ = (1750 g)/(0.321666) ≈ 5440.42 g

The initial quantity was about 5440.42 grams.

To prove that a function is one to one function with an inverse, the graph  of the function should not intersect the horizontal line more than once.

The function is defined as the mathematical statement that shows the relationship between one variable and another variable. If one variable is independent variable other variable will be dependent variables. The function that consist off variables numbers and the mathematical operators

To prove the function is one to one then first draw the graph of the function using the values. If the graph is not intersecting the horizonal line of the graph then its a one to one function

If the function is one to one, then only the function has inverse

Therefore, if the graph is not intersecting horizontal line more than once, then the function is one to one function with an inverse

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Answer:

0

Step-by-step explanation:

\(~~~(-37+37 )\div(-15)\\\\=0\div (-15)\\\\=0\)

Answer:

0

Step-by-step explanation:

Following PEMDAS -37+37 is 0 and 0/-15 is also 0

1/6

The probability of an event is the number of ways the event can happen divided by the number of possible outcomes. In this case, the possible outcomes are the numbers on the die, which are 1, 2, 3, 4, 5, and 6.

The event of rolling a number greater than 5 or less than 3 can happen in two ways: rolling a 6 or rolling a 1 or 2. So the probability of this event is:

P(greater than 5 or less than 3) = (number of ways the event can happen) / (number of possible outcomes) = 2/6 = 1/3

So the answer is option D. 1/6

Answer:

0.00236

Step-by-step explanation:

Move the decimal left 3 times as the exponent is negitiave 3

Answer:

359.13

Step-by-step explanation:

Sales tax rate: 10.5%;

Price without tax: $325 dollars;

Amount of sales tax ≈ $34.13 dollars;

Price with sales tax ≈ $359.13 dollars;

Answer:

6.3 Cubic cm

Step-by-step explanation:

\(V=A*h=(1.8*1.2+.5*1.1*1.8)*2=6.3cm^{3}\)

Answer:

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;

\(\frac{\pi }{2} [e^2 - 1 ]\)  or 10.036

Step-by-step explanation:

Given the data in the question;

y = \(y = e^{(x - 1 )\), y = 0, x = 1, x = 2.

Now, using the integration capabilities of a graphing utility

y = \(y = e_2}^{(x - 1 )_\), y = 0

Volume = \(\pi \int\limits^2_1 ( e^{x-1)^2} - (0)^2 dx\)

Volume = \(\pi \int\limits^2_1 ( e^{x-1)^2 dx\)

Volume = \(\pi \int\limits^2_1 e^{2x-2}dx\)

Volume = \(\frac{\pi }{e^2} \int\limits^2_1 e^{2x}dx\)

Volume = \(\frac{\pi }{e^2} [\frac{e^{2x}}{2}]^2_1\)

Volume = \(\frac{\pi }{2e^2} [e^4 - e^2 ]\)  

Volume = \(\frac{\pi }{2} [e^2 - 1 ]\)  or 10.036

Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;

\(\frac{\pi }{2} [e^2 - 1 ]\)  or 10.036

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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We get sin88° ≈ 0.99. Rounding to the nearest hundredth, sin88° ≈ 0.99.

In trigonometry, the sine function is one of the primary trigonometric functions that relates the ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse. The sine function is defined as:

sine (θ) = opposite / hypotenuse

where θ is the measure of the acute angle in radians or degrees.

The sine function is a periodic function, meaning it repeats itself after every 2π radians or 360 degrees. The graph of the sine function is a wave that oscillates between -1 and 1, with the midline at y = 0. The amplitude of the wave is 1, which represents the maximum height of the wave above and below the midline.

The sine function is used in many real-world applications, such as in engineering, physics, and astronomy to model waves, oscillations, and periodic phenomena. It is also used in geometry to calculate the sides and angles of triangles, as well as in calculus to solve differential equations and to describe the motion and behavior of complex systems.

Using a calculator, we get sin88° ≈ 0.99. Rounding to the nearest hundredth, sin88° ≈ 0.99.

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69200000 in scientific notation is  6.92 × 10⁷.

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

Scientific Notation is a special way of writing numbers:

For example 800 is written as 8 × 10² in Scientific Notation.

Therefore, let's write the scientific notation of the number 69200000.

Hence,

69, 200, 000 = 6.92 × 10⁷

The logic is that we will count backwards until we meet the last number. Since we counted towards the left side, the exponent will be positive.

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The preceding polynomial equation has three solutions: z = 0, z = 3/4, and z = -1/5.

First, we can factor out a common factor of z:

z(20z² - 11z - 3) = 0

Now we need to factor the quadratic expression in the parentheses.

We can use the quadratic formula or factor by grouping to do this. Factoring by grouping yields:

z(20z² - 11z - 3) = 0

z(4z - 3)(5z + 1) = 0

Setting each of the factored terms equal to zero, we have:

z = 0, 3/4, -1/5

Therefore, the solutions to the given polynomial equation are z = 0, z = 3/4, and z = -1/5.

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Answer:

\(6x^2-2x-6\)

Step-by-step explanation:

\(f(x)=6x^2-4 \\\\g(x)=2x+2 \\\\(f-g)(x)= (6x^2-4)-(2x+2)=6x^2-2x-6\)

Hope this helps!

The value of the evaluated function f(x) = -3x² + 2x  at  

(i) f(-2) is -16   ;

(ii) f(a) is -3a² + 2a .

The Function is represented as : f(x) = -3x² + 2x  ;

(i) We have to evaluate the above function at f(-2),

So, we substitute x = -2 into the function:

we get ;

⇒ f(-2) = -3(-2)² + 2(-2)

⇒ f(-2) = -12 - 4 = -16  .

So ,  f(-2) = -16  .

(ii) Next we have to evaluate f(a),

So , we substitute x = a into the function:

⇒ f(a) = -3a² + 2a

So , f(a) = -3a² + 2a   .

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The given question is incomplete , the complete question is

For the following exercises, evaluate the function f(x) = -3x² + 2x ; at the given input: (i) f(-2) (ii) f(a)  .

Answer:

\((x + 3) {}^{2} = x {}^{2} + 9\)

\((x + 3) {}^{2} \\ = {x}^{2} + 2 \times x \times 3 + 3 {}^{2} \\ = x {}^{2} + 6x + 9\)

Note - (a + b)² = a² + 2ab + b²

✐ La expansión de Mary está mal. Correcta expansión ⇻ x² + 6x + 9

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

# ꧁❣ RainbowSalt2²2² ࿐

We know that z varies directly as √√x and inversely as y, which can be written as:

z = k(√√x)/y

where k is the constant of proportionality.

To find the value of k, we can use the values given when x = 25 and y = 7:

179 = k(√√25)/7

179 = k(5/7)

k = (179*7)/5

k = 250.6

Now we can use this value of k to find z when x = 64 and y = 4:

z = 250.6(√√64)/4

z = 250.6(2)/4

z = 125.3

Therefore, z ≈ 125.3 when x = 64 and y = 4.

Answer:

\(\boxed {1)log_{b}(75) = 4.317}\)

\(\boxed {2)ln(20) = 2.9957}\)

Step-by-step explanation:

\(\textsf {Question l :}\)

\(\longrightarrow \mathsf {log_{b}(3) = 1.099}\)

\(\longrightarrow \mathsf {log_{b}(5) = 1.609}\)

\(\textsf {Identities applied :}\)

\(\boxed {log(ab) = loga + logb}\)

\(\boxed {log(a)^{x} = xloga}\)

\(\textsf {We can rewrite the problem as :}\)

\(\longrightarrow \mathsf {log_{b}(75)}\)

\(\longrightarrow \mathsf {log_{b}(25 \times 3)}\)

\(\longrightarrow \mathsf {log_{b}(5^{2} \times 3)}\)

\(\longrightarrow \mathsf {log_{b}(5)^{2} + log_{b}(3)}\)

\(\longrightarrow \mathsf {2log_{b}(5) + log_{b}(3)}\)

\(\textsf {Now, substitute the values :}\)

\(\longrightarrow \mathsf {2(1.609) + (1.099)}\)

\(\longrightarrow \mathsf {3.218 + 1.099}\)

\(\longrightarrow \mathsf {4.317}\)

\(\boxed {log_{b}(75) = 4.317}\)

\(\textsf {Question ll :}\)

\(\longrightarrow \mathsf {ln(4) = 1.3863}\)

\(\longrightarrow \mathsf {ln(5) = 1.6094}\)

\(\textsf {Rewriting the problem :}\)

\(\longrightarrow \mathsf {ln(20)}\)

\(\longrightarrow \mathsf {ln(4 \times 5)}\)

\(\longrightarrow \mathsf {ln(4) + ln(5)}\)

\(\longrightarrow \mathsf {1.3863 + 1.6094}\)

\(\longrightarrow \mathsf {2.9957}\)

\(\boxed {ln(20) = 2.9957}\)

Answer:

\(\sf \log_b(75)=4.317\)

\(\sf \ln (20)=2.9957\)

Step-by-step explanation:

Question 1

Given:

  \(\sf \log_b(3)=1.099\)

  \(\sf \log_b(5)=1.609\)

To evaluate \(\sf \log_b(75)\),  replace 75 with (5 × 5 × 3):

\(\implies \sf \log_b(5 \cdot 5 \cdot 3)\)

\(\textsf{Apply the Product log law}: \quad \log_axy=\log_ax + \log_ay\)

\(\implies \sf \log_b5+\log_b5+\log_b3\)

Substitute the given values to solve:

\(\implies \sf 1.609 + 1.609 + 1.099=4.317\)

Question 2

Given:

  \(\sf \ln(4)=1.3863\)

  \(\sf \ln(5)=1.6094\)

To evaluate ln(20) replace 20 with (4 × 5):

\(\implies \sf \ln (4 \cdot 5)\)

\(\textsf{Apply the Product log law}: \quad \ln xy=\ln x + \ln y\)

\(\implies \sf \ln (4)+\ln (5)\)

Substitute the given values to solve:

\(\implies \sf 1.3863+1.6094=2.9957\)

Answer:

It is counter clockwise

Step-by-step explanation:

The description of the transformation from f(x) = 3x + 7 to g(x) = 8x + 7 will be counterclockwise rotation.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The equations are given below.

f(x) = 3x + 7  and g(x) = 8x + 7

The slope of f(x) is 3 and the slope of g(x) is 8.

It is clear that the slope is increased, then the line rotates counterclockwise about the y-intercept.

Then the correct option is D.

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The set of points related to an exponential function and matched with set of translated points are, respectively:

(x, y) = (- 1, 0.5) → (x', y') = (2, - 1.5)

(x, y) = (0, 1) → (x', y') = (3, - 1)

(x, y) = (2, 4) → (x', y') = (5, 2)

(x, y) = (3, 8) → (x', y') = (6, 6)

(x, y) = (1, 2) → (x', y') = (4, 0)

(x, y) = (- 2, 0.25) → (x', y') = (1, - 1.75)

According to statemente, we find the case of set of points related to an exponential function and a set of translated points, after a quick inspection we derive the transformation rule:

Horizontal translation: 3 units right, vertical translation: 2 units down.

Now we check the statement on each ordered pair:

(x, y) = (- 1, 0.5):

(x', y') = (- 1, 0.5) + (3, - 2) = (2, - 1.5)

(x, y) = (0, 1):

(x', y') = (0, 1) + (3, - 2) = (3, - 1)

(x, y) = (2, 4):

(x', y') = (2, 4) + (3, - 2) = (5, 2)

(x, y) = (3, 8):

(x', y') = (3, 8) + (3, - 2) = (6, 6)

(x, y) = (1, 2):

(x', y') = (1, 2) + (3, - 2) = (4, 0)

(x, y) = (- 2, 0.25):

(x', y') = (- 2, 0.25) + (3, - 2) = (1, - 1.75)

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\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Inequalities.

so we get as,

(w+6)/2 < 5

so we get as,

w+6 < 10

=> w < 10-6

=> w < 4

so the answer is,

w < 4