7. PART A:
Martin has 1/4 of a bag of chocolate chip cookies. The bag weighs 4 pounds. How
many pounds of cookies does he have?

Answer:

Step-by-step explanation:

To avoid dividing by zero, denominator cannot equal 0:

                   [tex]x^2-9\neq 0[/tex]

       [tex](x+3)(x-3)\neq0[/tex]

        [tex]x\neq-3 \text{ and }x\neq3[/tex]

Solution: We cannot use [tex]x=-3 \text{ and }x=3[/tex].

Answer:

46√3

Sorry, it's a lot of steps to elaborate on.

Natalie owes $18 at the end of every two weeks.

To find the weekly payment amount, we can use the given data to write a system of equations. Let's assume that Natalie borrowed x amount from her parents.

From the given table, we can write the following equations:

At the end of 2 weeks, Natalie still owes:

x - 2d = 180 ...(1)

At the end of 4 weeks, Natalie still owes:

x - 4d = 144 ...(2)

Solving equations (1) and (2), we get:

2d = 36

d = 18

Therefore, Natalie owes $18 at the end of every two weeks.

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The jug used by older adults has a volume of 300 ml. To convert 3 liters to milliliters.

We multiply three by 1000, giving us 3000 ml. The ratio of the jug to the kettle can be simplified to 1:10.

To convert 360°F to °C, we use the formula (360-32) ÷ 1.8, which gives us 182°C rounded off to the nearest 10°C.

Answer:

  (x, y, z) = (-1, -1, 0)

Step-by-step explanation:

You want the solution to the system of equations ...

The calculator solution is shown in the attachment.

  (x, y, z) = (-1, -1, 0)

The coefficient of the y-variable is 2 or -2, which means we can eliminate y terms by adding pairs of equations. Adding the first equation to each of the other two reduces the system to ...

Adding these two equations together gives ...

  -14z = 0   ⇒   z = 0

Substituting this into the second of the reduced equations gives ...

  9x = -9   ⇒   x = -1

And substituting for x and z in the first of the original equations gives ...

  -3(-1) +2y = 1

  2y = -2 . . . . . . . . subtract 3

  y = -1

The solution is (x, y, z) = (-1, -1, 0).

#95141404393

Answer:

4√10

Step-by-step explanation:

distance = √((16-4)²+ (12-8)²)

= √(144 + 16)

=√160

=√(4X4X10)

=√4 X √4 X √10

= 2 X 2 X √10

= 4√10

Answer:

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

The general equation for conditional probability is:

Using this equation and the given values, we can calculate P(A | B) as follows:

Therefore, P(A | B) = 2/3.

Step-by-step explanation:

To compute the monthly sales forecast using a 4-month moving average with the given weights, we can follow these steps:

1. Determine the weights for each of the four months. Based on the provided weights (25%, 20%, 15%, 12%), we can assign the following weights to the respective months in reverse order:

Month 1: 12%

Month 2: 15%

Month 3: 20%

Month 4: 25%

2. Calculate the forecast for each month by multiplying the demand for the corresponding month by the assigned weight and summing them up.

For Month 5:

Forecast = (Demand for Month 5 * Weight for Month 1) + (Demand for Month 4 * Weight for Month 2) + (Demand for Month 3 * Weight for Month 3) + (Demand for Month 2 * Weight for Month 4)

Forecast = (41 * 0.12) + (40 * 0.15) + (33 * 0.20) + (29 * 0.25)

Forecast = 4.92 + 6 + 6.6 + 7.25

Forecast ≈ 24.77

Similarly, you can calculate the forecasts for the remaining months using the same approach.

Month 6:

Forecast = (43 * 0.12) + (41 * 0.15) + (40 * 0.20) + (33 * 0.25)

Month 7:

Forecast = (49 * 0.12) + (43 * 0.15) + (41 * 0.20) + (40 * 0.25)

Month 8:

Forecast = (52 * 0.12) + (49 * 0.15) + (43 * 0.20) + (41 * 0.25)

By performing these calculations, you can determine the monthly sales forecasts for each of the remaining months based on the given demand and weights.

Answer:

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

Given sequence:

This is a AP since the difference is common:

The previous term is going to be 7 less than the subsequent term:

Applying the Triangle Midsegment Theorem, the length of CD in the triangle is: 44 cm.

Based on the Triangle Midsegment Theorem, the line segment that joins the midpoints of two sides of a triangle is parallel to the third side of the triangle and is also half of the length of the third side.

Thus, BE is the midsegment of the triangle with length of 22 cm. Since CD is the third side of the triangle, therefore we have:

Length of BE = 1/2(length of CD)

Plug in the values:

22 = 1/2(CD)

2 * 22 = CD

44 = CD

Length of CD = 44 cm.

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Peter invested $138 in the 12% account and $288 in the 13% account.

Let x be the amount invested in the 12% account and y be the amount invested in the 13% account.

We know that the total amount invested is the sum of the two accounts, so: x + y = total amount invested

We also know that Peter has $150 more in the 13% account, so:

y = x + 150

The total interest earned is $54, which can be expressed as:

0.12x + 0.13y = 54

Substituting y with x + 150, we get:

0.12x + 0.13(x + 150) = 54

Simplifying and solving for x, we get:

0.12x + 0.13x + 19.5 = 54

0.25x = 34.5

x = 138

Therefore, Peter invested $138 in the 12% account and $288 in the 13% account.

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The equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28.

To determine the equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28, we need to use the standard form of the equation of a parabola:
(x - h)^2 = -4p(y - k)
where (h,k) is the vertex and p is the distance from the vertex to the focus (which is half the focal diameter in this case).
Using the given information, we can plug in the values for h, k, and p:
(h,k) = (-8,5)
p = 28/2 = 14
(x + 8)^2 = -4(14)(y - 5)
Simplifying this equation, we get:
(x + 8)^2 = -56(y - 5)
And that is the equation of the parabola that opens down, has vertex (-8,5) and a focal diameter of 28.

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Looking at these angles, we can see that they are alternate interior angles. Alternate interior angles are congruent. This means that to solve we will simply need to set the given expressions equal to each other and solve for x.

4x - 23 = 3x + 18

x - 23 = 18

x = 41

Answer: x = 41

Hope this helps!

Answer:

V = 25 cm³

Step-by-step explanation:

the volume (V) of a rectangular prism is calculated as

V = Ah ( A is the area of the base and h the height )

V = 15 × 5 = 75 cm³

the volume of the pyramid is one third the volume of the prism , then

V = 75 × [tex]\frac{1}{3}[/tex] = 25 cm³

The sequence -19, -11, -3, 5,... is arithmetic with a common difference of 8.

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant value, called the common difference (d), to the preceding term. To determine if the given sequence is arithmetic, we can find the differences between consecutive terms.

The difference between the second and first terms is 11 - (-19) = 30, and the difference between the third and second terms is -3 - (-11) = 8. The difference between the fourth and third terms is 5 - (-3) = 8. Since the differences between consecutive terms are the same, the sequence is arithmetic.

The common difference can be found by subtracting any term from the term that follows it. For example, the common difference can be obtained by subtracting the second term (-11) from the third term (-3), or by subtracting the third term (-3) from the fourth term (5).

In both cases, we get a common difference of 8. Therefore, the common difference of the given sequence is 8.

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She will need to use 4 bottles of plant food in 12 weeks.

To feed one plant, Juba mixes 15ml of plant food with 1 liter of water. She will therefore require the following to feed nine plants in the greenhouse once a week:

9 plants × 15 ml plant food every week = 135 ml plant food.

To feed 11 plants in the vegetable plot twice a week, she will need:

11 plants x 15 ml plant food x 2 times = 330 ml plant food per week

Juba will therefore require a total of 135 ml + 330 ml = 465 ml of plant food per week.

She will require: 465 ml  x 12 weeks = 5580 ml.

Plant food comes in bottles of 1500 ml each. Juba will therefore require:5580 ml ÷ 1500 ml/bottle = 3.72

Therefore, She will need to use 4 bottles of plant food in 12 weeks.

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The acceleration for each section is shown below.

We know the formula

Acceleration = change in haste/ time taken

1. For a

= (12-0)/4

= 12/4

= 3

For b:

= (12-12)/ 5

=0

For c:

= (6-12)/ (2)

= -3

For d:

= (10-6) / 4

= 4/4

= 1

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To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

The equation help us to get the response to the statements as follows

1. False

2. False

3. True

4. False

The statement is true when the solution of the equation is true with the statement

The given equation is

f(x) = 32 / ( 1 + e⁰°⁵ˣ)

first statement

For x = 3, f(3) = 5.84

For x = 6, f(6) = 1.52

5.82 - 1.52 ≠ 9 ft

False

second statement

For x = 0, f(0) = 16

False

third statement

For x = 1, f(1) = 12.08

this shows a decline hence this is True

fourth statement

The trees maximum height, captured should be 16 ft as it started declining

False

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hmm well, let's firstly convert all the mixed fractions to improper fractions, then we'll get the dot product.

[tex]\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > \hspace{5em}\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{4\frac{2}{3}} \implies \cfrac{4\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{14}{3}} \\\\\\ \stackrel{mixed}{7\frac{1}{4}}\implies \cfrac{7\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{29}{4}}~\hfill \stackrel{mixed}{8\frac{1}{2}} \implies \cfrac{8\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > ~~\cdot~~\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{29}{4} \right)\left( \cfrac{7}{2} \right)~~ + ~~\left( -\cfrac{17}{2} \right)\left( \cfrac{14}{3} \right)\implies \cfrac{203}{8}-\cfrac{119}{3}\implies \cfrac{-343}{24} ~~ \approx ~~ \stackrel{ \textit{dot product} }{-14.29}[/tex]

Answer:

14.0

Step-by-step explanation:

Using sine rule

sin A/a = sin B/b

sin 70/15 = sin 61/b

b sin 70 = 15 sin 61

b = (15 sin 61) / sin 70

b = 13.96126278

b = 14.0

Nam needs to pay VND 63,000 for the two toys after receiving the 10% discount.

Nam asked his mother for permission to buy toys as a gift for Tuan's friend on his birthday.

He chose two toys with list prices of VND 45,000 and VND 25,000, respectively.

However, the good news is that he was able to receive a 10% discount on the total cost of both toys.
To calculate the amount that Nam has to pay for both toys, we first need to calculate the total cost of the two toys.

The cost of the first toy is VND 45,000 and the cost of the second toy is VND 25,000, so the total cost of both toys is:
Total cost = VND 45,000 + VND 25,000 = VND 70,000
Now that we have calculated the total cost of both toys, we can calculate the amount of discount that Nam will receive. The discount is equal to 10% of the total cost, which is:
Discount = 10% x VND 70,000 = VND 7,000
Therefore, the amount that Nam has to pay for both toys after the discount is:
Amount to pay = Total cost - Discount

= VND 70,000 - VND 7,000

= VND 63,000
In conclusion, Nam has to pay VND 63,000 to buy both toys after receiving a 10% discount.

It's a great deal, and Tuan's friend will surely love the toys as his birthday gift.

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1) The mean of the number of children is ≈ 1.5

2) the median is 1

3) the 5 number summary is

4) See the box plot attached.

A) Mean = sum of all the children reported by the adults/ number of adults

(0 × 5) + (1 × 3) + (2 × 4) + (3 × 2) + (4 × 0) + (5 × 1) = 22

number of adults
5 + 3 + 4 + 2 + 0 + 1 = 15

Mean = 22/15 ≈ 1.5

B)  to find the median we must arrange all the number in ascending order

0, 0, 0, 0, 0, 1, 1, 1, 2,  2, 2, 2, 3,  3, 5

Thus, 1 is the median when we select the number in the middle.

C) the 5 number summary is

D) See the box plot attached.

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Every adult's meal costs $26, and every child's meal costs $17.

Let

cost of adults = x

Cost of child = y

78x + 78y = $3,354

58x + 76y = $2,800

From (1)

Divide through by 78

x + y = 43

x = 43 - y

Substitute into (2)

58x + 76y = $2,800

58(43 - y) + 76y = 2800

2494 - 58y + 76y = 2800

- 58y + 76y = 2800 - 2494

18y = 306

y = 306/18

y = 17

Substitute the value of y into

x = 43 - y

x = 43 - 17

x = 26

Therefore, the cost of adults meal is $26 and child's meal is $17

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The scale factor here is 2.1.

To calculate the scale factor, you need two corresponding measurements from two similar objects or figures. The scale factor is the ratio of the corresponding lengths or dimensions between the two objects.

Now, the scale factor is

= 12.5 / 5

= 125/50

= 21/10

= 2.1 : 1

Thus, the scale factor here is 2.1.

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Answer: Length 105 Width 105

There are other possible answers

Step-by-step explanation:

Perimeter of the field is = (2)*(125) + (2)*(85) = 420

Area of the field is = (85)*(125) = 10,625

You need to find two other numbers that when doubled add up to 420, and when multiplied together are greater than 10,625. Guess and check can work, however making a square will yield the highest results, you can find the dimensions of said square by dividing 420 by 4 to get 105.

(2)*(105) + (2)*(105) = 420

(105)(105) = 11,025

420 = 420

11,025 > 10,625

The mean score to the nearest whole number is equal to 5.0

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of data based on the frequency, we have;

Total score, F(x) = 1(3) + 2(1) + 3(4) + 4(10) + 5(15) + 6(9) + 7(3) + 8(5)

Total score, F(x) = 3 + 2 + 12 + 40 + 75 + 54 + 21 + 40

Total score, F(x) = 247

Now, we can calculate the mean score as follows;

Mean = 247/50

Mean = 4.94 ≈ 5.0.

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The matrix after the operation is:

[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]

We have,

Matrix

[tex]\left[\begin{array}{ccc}3&8&67\\-5&-13&-109\end{array}\right][/tex]

To get a 1 in row 1.

We apply the operation:

Row 1 ÷ 3

So,

[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]

Thus,

The matrix after the operation is:

[tex]\left[\begin{array}{ccc}1&8/3&67/3\\-5&-13&-109\end{array}\right][/tex]

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