Evaluate the expression when b = 7 and x = -2.
-b+7x
4
X
$

Answer:

The time value, at the end of the fifth year, of a 5-year annuity that pays $200 every month, starting from the beginning of the second month, when the continuously compounded interest rate is 9.959%, is $11,828. To calculate this, we can use the formula A = PMT x [((1 + r)n - 1) / r], where PMT is the payment amount, r is the continuously compounded interest rate, and n is the number of payments. In this case, PMT = $200, r = 0.09959, and n = 60. Plugging these values into the formula, we get A = $200 x [((1 + 0.09959)60 - 1) / 0.09959] = $11,828.

Step-by-step explanation:

I assume we're naming the graph

Seeing the situation:

We have $4 for bonus bucks

We have $50 for amount spent

On the bottom we have the 50, so we can put "Amount spent" in that box

On the left, we have 4, so we can put "Bonus bucks" in that box

At the top, the name is your choice, but we can combine the names in a way... "Bonus Bucks per amount spent"... I guess that works

Looking at the graph, it's correct, but it's in reverse. you want your first dot where the 50 and 4 intersect, then you go diagonally upwards

The explicit formula for aₙ is a formula for the nth term of this sequence aₙ = 8n + 17.

What is the explicit formula?

The explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by Riemann for the Riemann zeta function.

The formula for the nth term of this sequence is a_n = 8n + 17.

This means that each term in the sequence is equal to 8 multiplied by the position of the term (n) plus 17.

For example, the first term (n = 1) is 25, which can be calculated as 8 * 1 + 17 = 25.

The second term (n = 2) is 33, which can be calculated as 8 * 2 + 17 = 33, and so on.

hence, the explicit formula for aₙ is a formula for the nth term of this sequence is aₙ = 8n + 17.

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Answer: 16 grasses, 41 weeds, and 51 trees

Step-by-step explanation:

You can use a variable for the different pollen sources. Use g for grass, w for weeds, and t for trees. w=3g-7.  t=3g+3.  g+w+t=108. In that last equation, you can substitute other values for w and t. g+(3g-7)+(3g+3)=108. combine like terms to get, 7g-4=108. This equation simplifies to g=16. Substitute 16 for g in the first 2 equations, and find that w=41, and t=51.

(Sorry if my explanation didn't make sense)

Answer:

s - 37 = 73

Step-by-step explanation:

We already have the end result which is 73.

We also know that the sale on Sunday is $37 less than Saturday's sales. This means we'll need to take away the 37 from s (Saturday).

Contrapositive represents the implication of conditional statement to the logical statement if p then q to be false where as contradiction we prove that our supposition is false that implies the given condition is true.

Comparison in the proof of contrapositive and contradiction:

Contrapositive represents the hypothesis is true that implies conclusion is also true or the conclusion is false that implies hypothesis is also false.

Example of contrapositive: For any integer a , b a + b ≥ 17 , a≥9 , b≥ 9.

Using contrapositive :

If a < 9 , b < 9 then a + b < 17

a < 9, b < 9 consider a ≤8 , b≤8

a + b = 8 + 8

        = 16

        < 17

It proves a < 9 , b < 9 then a + b < 17 implies ,when  a≥9 , b≥ 9 then

a + b ≥ 17 .

Contradiction : Here we suppose the statement which is against the required statement and prove it wrong which implies our given statement is true.

Example: For any integer a, a²  is even then a is even .

Here we assume a is an odd integer then prove it wrong.

Therefore, comparing contrapositive and contradiction provides contrapositive is conditional to logical and contradiction required to our supposition is wrong.

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Answer:

i don't know

Step-by-step explanation:

The equations that have the same solution are:

2.3p – 10.1 = 6.49p – 4

230p – 1010 = 650p – 400 – p

23p – 101 = 65p – 40 – p

Options B, C, and D are the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We have,

2.3p - 10.1 = 6.5p - 4 - 0.01p

2.3p - 6.5p + 0.01p = 10.1 - 4

2.31p - 6.5p = 6.1

-4.19p = 6.1

p = -6.1/4.19

p = -1.5

Now,

Solve for p.

2.3p – 10.1 = 6.4p – 4

2.3p - 6.4p = 10.1 - 4

-4.1p - 6.4

p = -6.4/4.1

p = -1.6

2.3p – 10.1 = 6.49p – 4

2.3p - 6.49p = 10.1 - 4

-4.19p = 6.1

p = -1.5

230p – 1010 = 650p – 400 – p

230p - 649p = 1010 - 400

-419p = 610

p = -1.5

23p – 101 = 65p – 40 – p

23p - 64p = 101 - 40

-41p = 61

p = -1.5

2.3p – 14.1 = 6.4p – 4

2.3p - 6.4p = 14.1 - 4

-4.1p = 10.1

p = 2.5

Thus,

Equations that have the same solution

2.3p – 10.1 = 6.49p – 4

230p – 1010 = 650p – 400 – p

23p – 101 = 65p – 40 – p

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Based on the information, it can be inferred that the correct answer is option A. Qualitative-ordinal since this variable would yield categories with an order.

An ordinal qualitative variable is a term that refers to a type of variable that is characterized by representing non-numerical modalities, in which there is an order.

According to the above, the level of allergens (low, medium, high) is a non-numeric variable that has an order because each one represents a specific value that is organized in a certain order.

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Answer:

it's already rounded to the nearest hundredth

Step-by-step explanation:

because there is no numbers after the hundredth.

Answer:

  (a) 5.78%

  (b) $10,594.63

  (c) 5.95%

Step-by-step explanation:

You want the annual rate, the 1-year balance, and the effective yield on an account in which $10,000 is deposited, and the value doubles in 12 years.

The compound interest formula is ...

  A = Pe^(rt)

where P is the amount invested at annual rate r for t years, and A is the account balance.

Solving for r, we have ...

  ln(A/P)/t = r

The account value will have doubled when A/P = 2, so the rate is ...

  r = ln(2)/12 ≈ 0.057762 ≈ 5.78%

The annual rate is about 5.78%.

The balance after 1 year is ...

  A = 10000·e^(ln(2)/12·1) = 10000·2^(1/12) = 10594.63

The balance after 1 year will be $10,594.63.

The APR (r) will be ...

  A = P(1 +r)^t

  10594.63 = 10000(1 +r)¹

  r = 10594.63/10000 -1 = 0.059463 ≈ 5.95%

The effective yield is about 5.95%.

The three methods are used to select a sample from a larger population in order to make inferences about the population as a whole.

Probability-proportional-to-size sampling is a method where the probability of an item being selected is proportional to its size. In this case, the size is represented by the dollar amount of the sale.

Systematic selection involves selecting items at regular intervals. In this case, the starting point is 13 and the interval is 30. Every 30th item is selected, starting from the 13th item.

The starting dollar is $17,240 and the interval is $220,000. Every item with a sales amount that falls within the interval is selected with a probability proportional to its size.

The random-number table selection technique involves using a random number table to select items. The last four digits of the invoice number are used to determine which item is selected.

The selection process starts at row (0004) and column (01) and continues across the row and then down to the next row.

The probability of an item being selected in each method differs and is important in ensuring a representative sample is obtained.

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a. Linearly dependent. Notice that u = 3w, so w can be written as a scalar multiple of u, meaning the set is linearly dependent.

b. Linearly independent. The vectors are not scalar multiples of each other, meaning they are linearly independent.

c. Linearly dependent. Notice that v = -2u, so v can be written as a scalar multiple of u, meaning the set is linearly dependent.

d. Linearly independent. The vectors are not scalar multiples of each other, meaning they are linearly independent.

e. Linearly dependent. If (ui, u2, ..., um) is a set of vectors in R" and n < m, then the set is linearly dependent. This means that the set of vectors {u, v, w} is linearly dependent as n = 2 and m = 3.

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The value of function f' (x)=28 and G' (x)=63

    x           f(x)       g(x)      f' (x)       g' (x)
      1            3           2          4            6

      2            1           3          5             7
      3             2          1          7             9        


                                       
F(X)=f(f(x))

F' (X)=(F' (f(x)) x F' (x)⇒ (chain rule)

F' (1)=F' (F(1)x f' (1))

=f' (3) x f' (1)   (( ∵  f(1)=3))

=7 x 4        (∵f' (3)=7, f' (1)=4))

=28

G(x)=g(g(x))

G' (x)=g' (g(x) X  g' (x) ⇒   (chain rule)

G' (2)=g' (g(2) x g' (2)

=g' (3) x g' (2)     (∵g(2)=3))

=9x7        ((∵g' (3)=9, g' (2)=7))

=63


The chain rule is a formula in calculus that expresses the derivative of the composition of two differentiable functions f and g in terms of f and g's derivatives.
d/dx(f(g(x)=f'(g(x)g'(x).


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Answer:

B, D, and F

Step-by-step explanation:

The inequality is x< -3, which pretty much says, on the (x,y) function, any x that is less than -3 is valid.

B, D, F are correct because the x value is less than negative 3

C, and G are incorrect because the value of x is greater than negative 3

A, and E are incorrect because the value of x is the same as 3

The dimensions of the square is [tex]\frac{30}{9+4 \sqrt{3}}[/tex] and equilateral triangle is [tex]& \frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex] that produce a minimum total area.

The sum of the perimeter of an equilateral triangle and a square is 10

Differentiation is a derivative of the value of an independent variable that can be used to measure features of an independent variable per unit change.

The objective is to find the dimensions of the equilateral triangle and square that produce a minimum total area.

Consider,

⇒4a+3b=10

⇒4a=10-3b

⇒a=[tex]\frac{10-3b}{4}[/tex]

The total area of the circle and square is,

[tex]A=a^2+\frac{\sqrt{3}}{4} b^2[/tex]

Substitute the value of a in the formula,

[tex]$$\begin{aligned}A & =\left(\frac{10-3 b}{4}\right)^2+\frac{\sqrt{3}}{4} b^2 \\& =\frac{100-60 b+9 b^2}{16}+\frac{\sqrt{3}}{4} b^2 \\& =\frac{100-60 b+9 b^2+4 \sqrt{3} b^2}{16} \\& =\frac{100-60 b+(9+4 \sqrt{3}) b^2}{16}\end{aligned}$$[/tex]

Differentiate the total area and equate with 0 ,

[tex]$$\begin{aligned}\frac{d A}{d r} & =\frac{0-60+2(9+4 \sqrt{3}) b}{16} \\0 & =\frac{0-60+2(9+4 \sqrt{3}) b}{16} \\\end{aligned}$$[/tex]

[tex]0-60+2(9+4 \sqrt{3}) b & =0 \\2(9+4 \sqrt{3}) b & =60[/tex]

And,

b[tex]=\frac{30}{9+4 \sqrt{3}}[/tex]

Substitute the value of b in the value of a,

[tex]$$\begin{aligned}a & =\frac{10-3\left(\frac{30}{9+4 \sqrt{3}}\right)}{4} \\& =\frac{90+40 \sqrt{3}-90}{4(9+4 \sqrt{3})} \\& =\frac{40 \sqrt{3}}{4(9+4 \sqrt{3})} \\& =\frac{10 \sqrt{3}}{9+4 \sqrt{3}}\end{aligned}$$[/tex]

a[tex]& =\frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex]

Therefore, the dimensions of the square is [tex]\frac{30}{9+4 \sqrt{3}}[/tex] and equilateral triangle is [tex]& \frac{10 \sqrt{3}}{9+4 \sqrt{3}}[/tex] that produce a minimum total area.

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The zeros of the function f(x) = x^4 - x² - 2 are given as follows:

+/-squareroot of 2, +/- i

The function for this problem is defined as follows:

f(x) = x^4 - x² - 2

The zeros are the values of x for which:

f(x) = 0.

Applying the transformation y = x², the function can be reduced to a quadratic function as follows:

y² - y - 2 = 0.

Hence:

(y - 2)(y + 1) = 0.

Meaning that the solutions for y are given as follows:

Then the solutions for x are given as follows:

Meaning that the third option is correct.

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Answer:

-18

Step-by-step explanation:

missing 1 question means losing 3 points so if we mutliply the amout of questions he missed, 6, times the points yoy lose per question,3, we get 18.

Your daughter is 7 years old.

Let "x" be your age.

According to the statement, your age is 34. Thus, x= 34.

Let "y" be the age of your daughter.

According to the statement, your daughter's age is given by the following equation:

[tex]2y+20=x\\ \\2y+20=34[/tex]

[tex]2y+20-20=34-20\\ \\2y=14[/tex]

[tex]\frac{2y}{2} =\frac{14}{2} \\ \\y=7[/tex]

Let's see if number 7 makes the original condition be true.

So, you are 20 years older than twice your daughter's age. Let's multiply your daughter○s age by 2 and add 20, it should return your age (34).

[tex]2(7)+20=\\ \\14+20=\\ \\34[/tex]

That's correct, it means that 7 is the correct answer.

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Two angles are considered to be supplementary angles if their sum of measurements is 180 degrees and the required angle B in the given situation is 142°.

When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Subtract the specified angle from 180 degrees to determine the angle that is supplementary to another angle.

If one angle is 60 degrees, for instance, the next angle will be 180 - 60 = 120 degrees.

The pair of angles known as supplementary angles always add up to 180 degrees.

These two perspectives are known as each other's supplements.

So, we have angle A which is 38°.

Now, calculate angle B as follows:

A + B = 180

38 + B = 180

B = 180 - 38

B = 142°

Therefore, two angles are considered to be supplementary angles if their sum of measurements is 180 degrees and the required angle B in the given situation is 142°.

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348 are the total number of customers visited the theatre.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that at a cinema, films are shown on screen 1 and screen 2

screen 2 customers pay full price or child price

There are three times as many customers in screen 1.

68 customers paid child price in screen 1

In screen 1 the number of customers are 87

In screen 2 the number of customers are three times the screen 1.

87×3=261 in screen 2.

72 are full in screen 1.

53 are in child of screen 2

208 in screen 2 full screen

261+87=348

Hence, 348 are the total number of customers visited the theatre.

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Mosaic Tile Company produces two kinds of tiles, that:

We will solve this problem using the linear programming concept.

From the given case, we know that:

x --> larger tiles

y --> smaller tiles

molding: 0.45x + 0.30y ≤ 75

baking: 0.40x +0.60y ≤ 105

glazing: 0.15x + 0.25y ≤ 60

materials: 30x + 20y ≤ 6,000

Profit: 190x + 240y

We need to find each functions respective constraints and construct a graph containing all of these function constraints.

0.45x + 0.30y = 75

(x = 0)

0.45(0) + 0.30y = 75

y = 250

(y = 0)

0.45x + 0.30(0) = 75

x = 166

0.4x + 0.6y = 105

(x = 0)

0.4(0) + 0.6y = 105

y = 175

(y = 0)

0.4x + 0.6(0) = 105

x = 262

0.15x + 0.25y = 60

(x = 0)

0.15(0) + 0.25y = 60

y = 240

(y = 0)

0.15x + 0.25(0) = 60

x = 400

30x + 20y = 6000

(x = 0)

30(0) + 20y = 6000

y = 300

(y = 0)

30x + 20(0) = 6000

x = 200

We can construct the graph of these constraints such as the attached graph below. From the graph we know that the contraints of molding and baking are intersecting with each other under all of the given constraints. We need to find the intersection point:

0.4x + 0.6y = 105 | x 1| 0.4x + 0.6y = 105

0.45x + 0.3y = 75 | x 2| 0.9x + 0.6y = 150

                                       -0.5x          = -45

                                              x   = 90

0.45(90) + 0.3y = 75

40.5 + 0.3y = 75

0.3y = 34.5

y = 115

The intersection point is (90,115)

We have 3 possible scenario points, their position and each possible profit are:

(0, 175) --> P = 190(0) +240(175) = $42,000

(90, 115) --> P = 190(90) + 240(115) = $44,700

(166,0) --> P = 190(166) + 240(0) = $31,540

The optimum scenario is producing 90 larger tiles and 115 smaller tiles.

By producing the optimum scenario tiles, the baking resources will have:

Baking: 0.40x + 0.6y ... 105

              0.40(90) + 0.6(115) = 105 --> no left over resources

If Mosaic add another hour for Molding, there will be some additional profit, which is can be calculated by trying to create a new equation:

0.45x + 0.30y =< 75+1

0.45x + 0.30y =< 76

0.45x + 0.30y = 76

(y = 0)

0.45x + 0.30(0) = 76

x = 168

We can compare with the initial condition of available molding resources of 75 by producing 166 larger tiles:

Additional profit = (168 x 190) - (166 x 190)

Additional profit = $31,920 - $31,540

Additional profit = $380

Mosaic Tile should not accept the supplier offer because the most critical bottleneck at the time is the molding and baking capacities. Both lines are below the other resources lines and acting as the direct constraint on deciding the optimum possible output. If Mosaic wants to increase its profit, it should look for a solution to increase either or both molding and baking capacities.

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The fruit salad recipe requires 1/3 cup of strawberries and the smoothie recipe requires 3/4 cup of strawberries. So in total, 1/3 + 3/4 = 5/12 cup of strawberries are required for both recipes.

Now we know that Cindy and Borling are both making the recipes. So we need to multiply the 5/12 cup of strawberries by 2 to find out how many cups of strawberries are needed for both of them.

5/12 cup * 2 = 10/12 cup or 5/6 cup of strawberries.

Now if two more friends are joining them, we need to multiply the 5/6 cup of strawberries by 4 to find the total number of cups of strawberries required for all 4 of them.

5/6 cup * 4 = 2 and 1/6 cups.

So in total, 2 and 1/6 cups of strawberries would be required for both girls and two of their friends.

Answer:

Find x.

1/3+3/4=x

4/12+9/12=x

13/12=x

1 1/12 cups of strawberries for one person.

3*1 1/12=3 1/4

Step-by-step explanation:

The equation of the set of algebra tiles is x + 8 = 12.

Algebra tiles are mathematical manipulatives that help students comprehend the principles of algebra and strategies to think algebraically. For introductory algebra pupils at the level of elementary school, middle school, high school, and college, these tiles have been demonstrated to offer solid examples.

Given set,

x 1 1 1 1 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1

the set has one positive x and eight positive units,

the equation is x + 8.

and on the right side of the equation, there are 12 positive units,

equation is x + 8 = 12

Hence the equation s x + 8 = 12.

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Answer:

x + 8 = 12.

Step-by-step explanation:

in case you need it (x=4)

The value of f(g(3)) is   19

f(x)=2x-5

g(x)=4x,

f(g(3))= ?

Solution:

g(3) = 4*3 = 12

f(g(3)) = f(12) = 2*12 - 5 = 24 - 5= 19

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The value of f(g(3)) is 29.

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Answer:

[tex]n \leqslant 312[/tex]

Step-by-step explanation:

[tex]45 + 7 \geqslant \frac{1}{6}n - 7 + 7 [/tex]

[tex]52 \times 6\geqslant \frac{1}{6} n \times 6[/tex]

[tex]312 \geqslant n[/tex]

You can multiply by 6 without changing the sign as 6 > 0