Caleb is making lemonade and cookies for the school bake sale. He has 10 cups of
sugar. He needs two cups of sugar for lemonade. Each batch of cookies uses 11/2 cups
of sugar. What is the maximum number of cookie batches he can make?

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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Answer:

The number of hours Jackie worked  = 80hours

Step-by-step explanation:

Last summer:

Jackie made $960

Rachel made $960

let number of hours Jackie worked = x

Rachel worked 16 hours more than Jackie:

Number of hours Rachel worked = x + 16

if Jackie earned $y  per hour

Rachel earned $2 less per hour = y-2

Jackie: 960 = x × y = xy

Rachel: 960 = (x+16)(y-2)

960 = xy -2x +16y -32

recall xy = 960, insert the value for xy

960 = 960 - 2x +16y -32

- 2x +16y -32 = 0

2x -16y = -32

x-8y = -16

x = 8y-16

recall xy = 960, insert the expression for x

(8y-16)y = 960

8y² -16y = 960

y² -2y - 120 = 0

y²+10y-12y -120 = 0

y(y+10) -12(y+10) = 0

(y-12) = 0 or (y+10) = 0

y = 12 or -10

since y can't be negative, y = 12

x = 8y-16

x = 8(12) -16 = 80

The number of hours Jackie worked = x = 80 hours

Answer:

Therefore, the Panthers had a better overall record for the season, with a total of 212 points earned compared to the Cowboys' total of 173 points.

Step-by-step explanation:

To compare the measures of center, we can calculate the mean and median points earned by each team:

Panthers: Mean = 212/15 = 14.13 points, Median = 14 points

Cowboys: Mean = 173/15 = 11.53 points, Median = 10 points

Based on these calculations, we can see that the Panthers have a larger mean value of about 14.13 points compared to the Cowboys' mean value of about 11.53 points. However, the median value for both teams is less useful for comparison since they are only one point apart. Therefore, we can conclude that the Panthers had the better overall record for the season based on both the total points earned and their larger mean value.

So, the answer is Panthers; they have a larger mean value of about 14.8 points (Option C is incorrect as the mean value of Panthers is approximately 14.13 and not 14.8).

Answer:

thye answer is -5f

Step-by-step explanation

Answer:

answer is <-8/5

and x <-22/12

Answer:

300x4 =1200

20x4 = 80

1x4 =8

1288

Step-by-step explanation:

Break apart 321 = 300+20+ 1

This is the hundreds, tens, and ones

Then multiply each by 4

Add all together to get answer

Answer:

n = - 7

Step-by-step explanation:

\(0.0000003 = 3 \times {10}^{ - 7} \\ \implies \: n \: = - 7\)

Answer:

\(209.43 \: \: {units}^{3} \)

Step-by-step explanation:

\(v = \pi {r}^{2} \frac{h}{3} \\ = \pi \times {5}^{2} \times \frac{8}{3} \\ = 209.439\)

Answer:

28800

Step-by-step explanation:

first find Gerard's salary and then divide it by 1.25

Answer:

28800

Step-by-step explanation:

Let M be Martin and G be Gerard

Let 12:7 be 12x:7x

21000 = 7x

x = 3000

12x = 3000*12 = G after pay rise

12x = 36000 = G after pay rise

36000 = 125% G before pay rise

1.25G = 36000

G = 28800

Hope this helps ;)

9514 1404 393

Answer:

Step-by-step explanation:

The function will be linear if the differences in y-values are proportional to the differences in x-values. The constant of that proportionality is the slope of the line. A linear equation can be written using the point-slope form:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

__

Table 1

x-differences: 2-0 = 2, 4-2 = 2, 6-4 = 2

y-differences: -19-6 = -25, -44-(-19) = -25, -69-(-44) = -25

m = -25/2; (h, k) = (0, 6)

  linear relation: y -6 = (-25/2)x

__

Table 2

x-differences: 2, 4, 2

y-differences: 10, 20, 10

m = 10/2 = 20/4 = 10/2 = 5; (h, k) = (2, 13)

  linear relation: y -13 = 5(x -2)

__

Table 3

x-differences: 2, 2, 2

y-differences: 20, 20, 20

m = 20/2 = 10; (h, k) = (2, -4)

  linear relation: y +4 = 10(x -2)

__

Table 4

x-differences: 2, 4, 2

y-differences: 25, 75, 125

  not a linear relation

Answer:

Step-by-step explanation:

(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2

Answer: y21600x281=1 y 2 1600 - x 2

Step-by-step explanation: for sure chfjjgffjfj ;)

Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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Answer:

81x^8

Step-by-step explanation:

i hope this helps :)

Answer:

5/2

Step-by-step explanation:

5 divided by 2 is 2.5 and then 2.5 as a fraction is 5/2

Answer:

0.4 or 2/5

Step-by-step explanation:

I divided 2 by 5 because 2 bags were being split by 5 friends and got 2/5 which is also 0.4.

(hope this helps :P)

The ratio shows how many times one value is contained in another value.

The number of top dogs is 192.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of top dogs to fat cats was 24 to 19.

if they were 152 fat cats.

This means,

Number of top dogs = 24x

Number of fat cats = 19x

Now,

Number of fat cats = 152

This means,

152 = 19x

x = 8

Now,

Number of top dogs = 24x

= 24x

= 24 x 8

= 192

Thus,

The number of top dogs is 192.

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The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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Answer:

\(\huge\boxed{\boxed{49}}\)

Step-by-step explanation:

Hello.

In order to simplify this expression, we need to add

2+5, which is equal to 7

Multiply that times 7:

49

And we're done!

I hope it helps & have an outstanding day!

~ST2710 :)

Answer:

48 ≥ 4x + 2y

44 ≥ 2x + 2y

    First, we will look at assembling hours.

"The standard model requires 4 hours to assemble [and] the artisan model requires 2 hours to assemble"

    We also know they have 48 hours per day for assembly, x is standard model and y is artisan model.

48 = 4x + 2y

    Lastly, they do not need to make that many, but they can so we will use greater than or equal to.

48 ≥ 4x + 2y

    Now let us look at finishing hours.

"The standard model requires ... 2 hours for finishing touches. The artisan model requires ... 2 hours for finishing touches."

    We also know they have 44 hours per day for assembly, x is standard model and y is artisan model.

44 = 2x + 2y

    Again, they do not need to make that many, but they can so we will use greater than or equal to.

44 ≥ 2x + 2y

Step-by-step explanation:

math is all about repetition. the more you do it and use it, the easier it gets. but burning yourself out by putting in to much time is no good either.

there is not a one sized fits all answer, do what's best for you.

Answer:

I'd say 20 minutes to 4 hours, but it really depends on what you're learning. For example, if you're having trouble with a math subject, you may want to divide it in half and practice a little each day.

Step-by-step explanation:

Answer:

maybe : 1,2,5,6,9,10,13,14,17,

Step-by-step explanation:

I think it's in odd/even number pattern but it'll always skip a number???

or it's just in +1 then +3 pattern

The next terms of the pattern 1,2,5,6,9 are 10, 13,14,17,18,21.

Sequence is a collection of terms which are related in some way which is common to all the terms or some of the terms.

The pattern is given as 1,2,5,6,9 and we have to find the next terms of the pattern.

The First term is 1, the second term is 2. The difference between them is 1.

Second term is 2 and the third term is 5. The difference between them is 3.

Third term is 5 and the fourth term is 6. The difference between them is 1.

Fourth term is 6 and fifth term is 9. The difference between them is 3.

If we observe pattern in them them we can find that in first term they have added 1 , in second term 3 , in third term 1, in fourth term 3. It means first add 1 and then 3.

The next terms will be :

9+1=10

10+3=13

13+1=14

14+3=17

17+1=18

18+3=21.

Hence the next terms of the pattern 1,2,5,6,9 are 10,13,14,17,18,21.

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Answer:

The maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Step-by-step explanation:

We are given that weight P is inversely proportional to the distance D between the supports of the beam, and for this certain type of wooden beam, we have:

P = 7200/D

To find the distance between supports needed to carry 1600 lb, we can substitute P = 1600 in the above equation and solve for D:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

So the distance between supports needed to carry 1600 lb is 4.5 feet.

To find the maximum distance between supports for the beam to support a weight of 1600 lb, we can use the same equation and solve for P = 1600:

1600 = 7200/D

D = 7200/1600

D = 4.5 feet

Therefore, the maximum distance between supports for the beam to support a weight of 1600 lb is also 4.5 feet.

Answer:

On a number line, −2 is located to the right of −3

Explanation:

It's better constructing a graph

In any case:

A.) On a number line, −2 is located to the left of −3.

-This is wrong. -2 is closer to the zero on the right thus, -3 is on the left of -2 and -2 is on the right of -3

B.) On a number line, −2 is located to the right of −3.

-This is correct

3.) On a number line, −2 is located to the left of 0 and −3 is located to the right of 0.

-This is wrong. Since both -2 and -3 are negative integers, both must be in the left of 0

4.) On a number line, −2 is located to the right of 0 and −3 is located to the left of 0.

-This is wrong. Since both -2 and -3 are negative integers, both must be in the left of 0

please please please please please please

Answer:

  2.  Tenths place

Step-by-step explanation:

When you're concerned with the precision of a sum, the final value must be rounded to the precision of the least-precise contributor.

The numbers contributing to this sum are ...

  7.273, with least significant digit in the thousandth's place.

  -12.4, with least significant digit in the tenths place.

The smaller the place value of the least significant digit of a number, the greater the precision it has. The least-precise number will have the largest place value of its least-significant digit.

  tenths > thousandths, so -12.4 has less precision

First of all, we compute the sum as though every contributor were exact. This is especially important when there are more than two contributors. With only two contributors, you get the same result if you round the more precise number first.

  7.273 -12.4 = -5.127 . . . . . preferred method of finding the sum

  7.3 -12.4 = -5.1 . . . . . . . . . . alternate approach for 2 contributors

Finally, we round that sum to the nearest tenth, reflecting the precision of -12.4:

  sum = -5.1

__

Additional comment

As a general rule, this fixation on precision applies to quantities that are measured, estimated, or rounded.

For example, it doesn't make much sense to report a financial value to the penny if one of the contributors has already been rounded to the nearest hundred-thousand dollars. The amount could already be in error by up to $50,000, so precision to the penny is meaningless.

When working many kinds of problems, it can be useful to report answers to the same precision used for the problem values. In some cases, you are told exactly what precision to use for an answer (nearest integer, tenth, or hundredth). Where you are not told, it usually doesn't make much sense to use 6 significant digits for an answer to a problem with values given as one significant digit. However, it can be sensible to report the answer to 2 or 3 significant digits.

__

Here (in this problem), we're concerned with a sum. When you are computing a product or ratio, the rules are different. In those cases, the (least) number of significant digits in the contributors will determine the number of significant digits in the answer. Where mixed arithmetic (products and sums) is involved, the rounding of the final answer will depend on the final operation:

  a(b+c) . . . the final operation is multiplication

  ab +ac . . . the final operation is addition

As with all computation, the intermediate results should be carried to full calculator precision (unless directed otherwise). Only the final answer should be rounded to the necessary precision.

Answer:

Step-by-step explanation:

Therefore, the values of

a

1

and r are 2 and -1, respectively.

The values of a₁ and r of the geometric series are 2 and -1 respectively.

Any term divided by the preceding term is a constant in a geometric series. The common ratio of the sequence is the name given to this constant. Any term in the sequence can be divided by the prior term to determine the common ratio.

We have the series 2, -2, 2, -2, ......

Here, The first term is 2.

and, the Common Ratio = -2 / 2

                                        = 2/(-2)

                                         = -1

So, the first term is 2 and r is -1.

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Answer:

Step-by-step explanation:

58 ft (1/10 inch/ft) = 5.8 inch

A and B is not, because if you were to make the A bigger it'll be the same as B, so I think is C

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

To determine which set of side measurements could form a triangle, we need to check if the sum of the lengths of the two shorter sides is greater than the length of the longest side. This is known as the Triangle Inequality Theorem.

Let's check each set of side measurements:

13, 19, 7:

The sum of the two shorter sides is 7 + 13 = 20, which is greater than the longest side (19). Therefore, this set of side measurements could form a triangle.

25, 12, 13:

The sum of the two shorter sides is 12 + 13 = 25, which is equal to the longest side (25). Therefore, this set of side measurements could form a triangle.

18, 2, 24:

The sum of the two shorter sides is 2 + 18 = 20, which is greater than the longest side (24). Therefore, this set of side measurements could form a triangle.

3, 1, 5:

The sum of the two shorter sides is 1 + 3 = 4, which is less than the longest side (5). Therefore, this set of side measurements could not form a triangle.

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

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Many companies are moving online or are entirely online already. This includes credit card companies. Also, these same companies may send a bill in the mail as well, but it depends on the company. It effectively depends on if you select the "paperless billing" option or not.