Mateo wants to make a toy sailboat. He has two pieces of wood to choose from.
His first piece of wood is a block that measures 18'' x 10" x 8". It weighs 46.65 lbs.
His second piece of wood is a log of wood measuring 21" long, with an average circumference of 25.12". It weights 39.25 lbs.
The sailboat needs to float, but both blocks of wood are denser than wood usually is, and he's not sure either piece of wood will float. He doesn't want to get the water wet before he's applied a sealant, so he isn't willing to just drop them in the water to find out.
2a. Which common solid can he use to represent the block? Which common solid can he use to represent the log? (2 points)
2b. What is the density of the block in pounds per cubic inch? Give the formula for density and show your work. (3 points)
2c. What is the density of the log in pounds per cubic inch? Give the formula for density and show your work. Use 3.14 for π. (Hint: you can determine the radius from the circumference.) (3 points)
2d. Water has a density of about 0.0361 pounds/cubic inch. Anything rarer will float, and anything denser will sink. Which of the pieces of wood are suitable for making a toy boat that will float? (2 points)

Answer: Choice B

Step-by-step explanation: The correct answer is 10, because 10 is the largest number that can you can divide both of these numbers by evenly.

Answer:

The length of c = 18.7 units ⇒ answer (d)

Step-by-step explanation:

In triangle ABC:

∵ measure of angle B = 17° 55'

∵ measure of angle C = 98° 15'

∵ The sum of measures of the interior angles of a triangle is 180°

∴ The measure of angle A = 180 - (17° 55' + 98° 15') = 63° 50'

∵ The length of a = 17 units

* To find the length of c use the sin Rule

- a/sin(A) = b/sin(B) = c/sin(C)

- a is the side opposite to angle A, b is the side opposite

  to angle B and c is the side opposite to angle C

∴ 17/sin(63° 50') = c/sin(98° 15')

* By using cross-multiplication

∴ c = (17 × sin(98° 15')) ÷ sin(63° 50')

∴ c = 18.7 units

∴ The length of c = 18.7 units ⇒ answer (d)

Answer:

D) 1

Step-by-step explanation:

Every whole number (including the ones on a die) are either even or odd, nothing else. So it is guaranteed for the number to be even or odd.

Answer:

t < -2.101, and t > 2.101

Step-by-step explanation:

We are running a hypothesis for the difference of 2 sample means, assuming normality, and assuming that population variances are equal.  This determines which test we run.  

We have:

Sample 1: (women)

n = 10

x = 83

s = 7

Sample 2: (men)

n = 10

x = 77

s = 6.4

The hypothesis for the test are:

H0:  µ1 - µ2 = 0

Ha:  µ1 - µ2 ≠ 0

The significance level is 5%.  The degrees of freedom is 2 less than the sum of the sample size, in this case, 18.  Our t-value is:  2.101

Our critical values for the test statistic are:  t < -2.101, and t > 2.101

The critical value(s) for the hypothesis test if A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years is t < -2.101, and t > 2.101.

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

In Sample 1: (women)

n = 10

x = 83

s = 7

In Sample 2: (men)

n = 10

x = 77

s = 6.4

The hypothesis for the test are:

H₀:  µ1 - µ2 = 0

Hₐ:  µ1 - µ2 ≠ 0

The significance level is 5%.  The degrees of freedom is 2 less than the sum of the sample size, in this case, 18.  Our t-value is:  2.101

Our critical values for the test statistic are:  t < -2.101, and t > 2.101

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C.) 3y=15 is not an inequality.

An inequality compares the magnitude of two numbers (greater than, less than, etc.).  Choice C uses an equals sign.

Hope this helps!!

Final answer:

To simplify the expression, factorize the numerator and then cancel out any common terms with the denominator, resulting in the expression 1 / 3 + 2 / (3x).

Explanation:

To simplify the given expression 2x2 - 10x - 28 over 6x × (6x - 7), we need to factorize the numerator and see if any terms cancel out with the denominator. The factored form of the numerator is (2x + 4)(x - 7). The denominator can be written as 6x(6x - 7).

When we place the numerator over the denominator, we see that (x - 7) cancels out, simplifying our expression to (2x + 4) / 6x. This can further be simplified to 1 / 3 + 2 / (3x) by dividing both terms in the numerator by 6x

Answer:

C.

Step-by-step explanation:

Answer:

The correct option is 3.

Step-by-step explanation:

The parent function is

[tex]f(x)=|x|[/tex]

The horizontal stretch and compression is defined as

[tex]g(x)=|bx|[/tex]

If 0<b<1, then it is horizontal stretch and if b>1, then it is horizontal compression.

Graph 1 passing thought the point (1,-1).

[tex]-1=|b(1)|[/tex]

This statement is false for any value of b, because the value of modulus can not be negative.

Graph 2 passing thought the point (1,2).

[tex]2=|b(1)|[/tex]

[tex]2=b[/tex]

Since b>1, therefore this graph represent the horizontal compression.

Graph 3 passing thought the point (2,1).

[tex]1=|b(2)|[/tex]

[tex]\frac{1}{2}=b[/tex]

Since 0<b<1, therefore this graph represent the horizontal stretch.

Thus, the correct option is 3.

Answer:

C

Step-by-step explanation:

An inverse variation is where the product of inputs and outputs is constant. This means x*y is always the same number.

A is not a solution since it has 3*-4 = -12 and -2*4 = -8. It's not the same.

B is not a solution since it has 2*8 = 16 and 3*12 = 36. It's not the same.

C is a solution since 12*4 = 48 and 8*6 = 48 and 4*12 = 48 and 3*16 = 48. It's the same.

D is not a solution since it has 1*6 = 6 and 2*4 = 8. It's not the same.

The solutions to the given problems involve setting up and solving proportions, as well as understanding and applying ratios.

1. To solve for the variable n in the proportion n : 1/2 as 6 : 1, we set up the equation n/0.5 = 6/1.

By cross-multiplying, we get n = 3.

2. To find the variable b in the proportion 1/4 is to 1 1/4 as 2 is to b, we write it as 1/4 : 5/4 = 2/b.

Cross-multiplying gives us b = 10.

3. To find out how many total students are there given the ratio of girls to boys is 3 to 2 and there are 15 girls, we use the ratio to find the number of boys 15 girls * (2 boys/3 girls) = 10 boys.

Adding the number of girls to the number of boys (15 + 10) gives us a total of 25 students, which is option (C).

4. For the field trip with 12 adults and 14 students, the ratio of the number of adults to the total number of people is 12/(12+14) = 12/26, which simplifies to 6/13, giving us option (A).

5. If 2d = 5c, the statement that is not true is D) 2/d = c/5, because when dividing both sides by the respective variables, it should be d/2 = c/5.

Final answer:

1. n = 3

2. b = 10

3. Option C: 25

4. Option A: 6 to 13

5. Option D: 2/d = c/5.

Explanation:

To solve for the variable n in the proportion n : 1/2 = 6 : 1,

you cross-multiply to get n * 1 = 6 * (1/2), which simplifies to n = 3.

Therefore, n=3.

To find the value of b in the proportion 1/4 : 1 1/4 = 2 : b,

we cross-multiply again, which gives us (1/4) * b = 2 * (5/4), after simplifying this, we get b = 10/1.

Therefore, b=10.

For the ratio of girls to boys, which is 3 to 2, if there are 15 girls, then for every 3 girls, there are 2 boys.

So, 15 girls represent 5 groups of 3 (because 15/3=5).

If there are 5 groups, then there must be 5 * 2 = 10 boys.

Therefore, adding the girls and boys gives us 15 + 10 = 25 total students, selecting Answer C) 25.

To determine the ratio of the number of adults to the total number of people on the field trip, we have 12 adults and 14 students, therefore the total number of people is 12 + 14 = 26.

The ratio of adults to the total number of people is 12:26, which simplifies to 6:13 after dividing both numbers by 2.

So, Answer A) 6 to 13 is correct.

If 2d = 5c, then dividing both sides by 2c gives us d/c = 5/2 or 2.5.

We can also divide by 2d to get c/d = 2/5.

The incorrect statement would be D) 2/d = c/5, as this doesn't match the original equation when cross-multiplied.

Answer:

5 sheets.

Step-by-step explanation:

There are 28 / 4 = 7 students in one group.

Each group was given 35 sheets of paper so each student got 35/7

= 5 sheets.

Each student will get 5 sheets of paper. This is found by dividing the total number of sheets per group (35) by the number of students in each group (7).

To solve the problem, we first need to understand that Mr. Lubec's 28 students are divided into four equal groups. We divide 28 by 4 to determine how many students are in each group, which is 7 students. Mr. Lubec gave each group 35 sheets of paper. To find out how many sheets of paper each student receives, we divide the total number of sheets per group by the number of students in each group.

So, we calculate 35 sheets ÷ 7 students, which equals 5 sheets of paper per student. Therefore, each student will get 5 sheets of paper.

1) regular cost for one person is: 32 ×1 = $32

for X people it would be 32X as you should times by the number of people.

= 32x

2)1 person is (20×1) + 84

20 + 84 = $104

for X people it would be 20x + 84

= 20x + 84

Answer:

92m²

Step-by-step explanation:

The height of the triangle is the height of the square plus the height above the square, or 4+8=12 m.

The length of the hypotenuse is 15 m. The length of the known leg is 12 m.

Substitute 12 for b, 15 for c, and solve for a.

a=√15²-12²= √225−144 = √81 = 9

The bottom leg of the right triangle is 9 m.

To find the length of the base of the large triangle multiply the length of the bottom leg of the right triangle by 2.

The length of the base of the large triangle is (9)(2)=18 m.

Use a formula for the area of a triangle, A=12bh, to find the area of the triangle.

18 is base and 12 is height

A=(1/2)(18)(12)= 108

to find the area of the square:

A= 4²=16

A=108-16= 92m²

The general solution of the differential equation [tex]\frac{dy}{dx} = \frac{8x}{y}[/tex] using variable separable method is [tex]y^{2}= 8 x^{2} +C[/tex].

If it is possible to write a differential equation by the transportation of terms, in the form f(x) dx = g(y) dy where f(x) is the function of x and g(y) is the function of y, then we say that variables are separable.

The solution is given by:

[tex]\int\ {f(x)} \, dx = \int\ {g(y)} \, dy + c[/tex]

where c is the arbitrary constant.

[tex]\frac{dy}{dx} = \frac{8x}{y} \\\\y\, dy = 8x \,dx\\\\\int\ {y} \, dy = \int\ {8x} \, dx\\\\\frac{y^{2} }{2} = \frac{8x^{2} }{2} + C \\\\y^{2}= 8 x^{2} +C[/tex]

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Answer:

A) 100%; B) 0.517; C) 0.858

Step-by-step explanation:

For part A,

We find the sum of the probabilities:

45.2+16.4+6.5+6.3+4.2+3.7+2.1+15.6 = 100

Since they sum to 100%, this is a probability distribution.

For part B,

We add together the probabilities for the US and Canada:  

45.2+6.5 = 51.7% = 51.7/100 = 0.517

For part C,

We first add together the probabilities for Italy, the UK and France:

6.3+4.2+3.7 = 14.2%

Next we subtract this from 100%:

100-14.2 = 85.8% = 85.8/100 = 0.858

Final answer:

The table gives a probability distribution. The probability that a U.S. user obtained music from the United States or Canada is 51.7%. The probability that a U.S. user does not obtain music from Italy, the U.K., or France is 85.8%.

Explanation:

To verify that the table gives a probability distribution, we need to show that the sum of the percentages is equal to 100%. Summing the percentages from the table, we get:

45.2 + 16.4 + 6.5 + 6.3 + 4.2 + 3.7 + 2.1 + 15.6 = 100%

This confirms that the table does give a probability distribution for the experiment.

To find the probability that a U.S. user obtained music from either the United States or Canada, we add the percentages for these two countries:

45.2 + 6.5 = 51.7%

Therefore, the probability is 0.517 or 51.7%.

To find the probability that a U.S. user does not obtain music from Italy, the United Kingdom (U.K.), or France, we subtract the percentages for these three countries from 100%:

100% - (6.3 + 4.2 + 3.7) = 100% - 14.2% = 85.8%

Therefore, the probability is 0.858 or 85.8%.

Answer:

  D)  19.5

Step-by-step explanation:

The law of cosines gives you the relation ...

  a² = b² + c² - 2bc·cos(A)

Substituting the given values, you have ...

  a² = 13² + 11² - 2·13·11·cos(108°) ≈ 378.379

  a ≈ √378.379 ≈ 19.452 . . . . take the square root

  a ≈ 19.5

Answer:

1). infer 2). fired 3). filed 4). filer 5). elfin 6). nerdy 7). felid 8). finer 9). liner 10). lined 11). fiery 12). fiend 13). ferly 14). ferny 15). lindy 16). fined 17). lifer 18). field 19). redly 20). riley 21). riled 22). liney 23). rifle 24). drily 25). fried 26). diner 27). flier 28). flied 29). idler 30). deify 31). reify 32). yield 33). refly 34). dynel 35). edify 36). flyer

hope this helps :)

Answer:

(4, 2.4)

Step-by-step explanation:

(2x+5y=20)3

-

6x-5y=12

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

then....

6x+15y=60

-

6x-5y=12

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

0 + 20y = 48

y=2.4

plug in 2.4 into one of the equations and you get that x= 4

Answer:

option D

2x − 7(−3x − 17) = 4

Step-by-step explanation:

Given in the question two equations

2x - 7y = 4

3x + y = -17

Rearranging equation 2 in terms of y

3x + y = -17

y = -17 - 3x

Put this value of y in Equation 1

2x - 7y = 4

2x - 7(-17 - 3x) = 4

So,

If you use the substitution method to solve the following system, new equation will be

Answer:

The correct answer is D.

Step-by-step explanation:

I got it correct on the test. I hope this helps!

1/2 n - 5 or (n/2) - 5

The correct expression which describes joe's age is,

⇒ 1/2n - 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Joes, who is the youngest member of the wrestling team at Northwood High school, is 5 years less than one-half the age of the coach.

Now, Let the coach is n years old.

Hence, We can formulate;

The correct expression which describes joe's age is,

⇒ 1/2n - 5

Thus, the expression which describes joe's age is,

⇒ 1/2n - 5

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Answer:

H0:  µ = 85.1

Ha:  µ ≠ 85.1

Step-by-step explanation:

She wants to see if the number of days is different.  It could be higher or lower, so the alternate hypothesis uses the "not equal to" sign. If she wanted to see if it rained more on the farm, her alternate hypothesis would be

Ha:  µ > 85.1

If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1  

The solution for the null hypothesis is given below,

H0:  µ = 85.1

Ha:  µ ≠ 85.1

When there are two possibilities then we calculate the null hypothesis if the hypothesis is true hypothesis is accepted if it is To conduct a hypothesis test for the above situation. We define the null hypothesis and the alternative hypothesis.

She is checking to see if the number of days has changed. The alternative hypothesis utilizes the "not equal to" marker since it might be either higher or lower. Her alternate hypothesis, if she wanted to determine whether it rained more frequently on the farm, is

Ha:  µ > 85.1

If she wanted to see if it rained less, then she would use the alternate hypothesis of Ha: µ < 85.1.

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Answer:

Option D.75°

Step-by-step explanation:

we know that

The sum of the interior angles of a regular dodecagon is equal to

[tex]S=(n-2)*180[/tex]

where

n is the number of sides

In this problem

n=12 sides

substitute

[tex]S=(12-2)*180[/tex]

[tex]S=1,800\°[/tex]

Find the measure of each interior angle

Divide the sum of the interior angles by the number of sides

[tex]1,800\°/12=150\°[/tex]

The measure of the angle formed by the radius and the side of a regular dodecagon is half the measure of the interior angle

therefore

[tex]150\°/2=75\°[/tex]

Answer:

a. 21 327 hot dogs/run

b. 70 runs/yr

c. 4 da/run

Step-by-step explanation:

Data:

Production rate (p)           = 5000/da

Usage rate (u)                  =    260/da

Setup cost (S)                   = $66

Annual carrying cost (H) = $0.45/hot dog

Production days (d)         = 294 da

Calculations:

a. Optimal run size

(i) Annual demand (D) = pd = (5000 hot dogs/1 day) × (294 days/1 yr)

= 1 470 000 hot dogs/yr

(ii) Economic run size

[tex]Q_{0}= \sqrt{\frac{2DS }{ h}\times\frac{ p}{p-u }}[/tex]

[tex]= \sqrt{\frac{2\times1470000\times66 }{ 0.45}\times\frac{ 5000}{5000-260 }}[/tex]

[tex]= \sqrt{431200000\times\frac{ 5000}{4740 }}[/tex]

[tex]= \sqrt{454852321}[/tex]

= 21 327 hot dogs/run

b. Number of runs per year

Runs = D/Q₀ = (1 470 000 hot dogs/1yr) × (1 run/21 327 hotdogs)

= 70 runs/yr

c. Length of a run

Length = Q₀/p = (21 327 hot dogs/1 run) × (1 da/5000 hot dogs)

= 4 da/run

To find the optimal run size, use the EOQ formula and calculate the square root. Divide the annual demand by the optimal run size to find the number of runs per year. Finally, calculate the length of a run by dividing the days in a year by the number of runs per year.

The optimal run size can be found using the Economic Order Quantity (EOQ) formula. EOQ = sqrt((2DS)/(H)) where D is the annual demand, S is the setup cost per order, and H is the holding cost per unit per year.

Using the given values:

D = 260 per day * 294 days = 76,440

S = $66

H = $0.45

EOQ = sqrt((2 * 76,440 * 66) / (0.45)) ≈ 6868

The optimal run size is approximately 6868 hot dogs.

The number of runs per year can be calculated by dividing the annual demand by the optimal run size:

Number of runs = 76,440 / 6868 ≈ 11.15

Since the factory operates 294 days a year, the number of runs per year is approximately 11.

The length of a run can be calculated by dividing the days in a year by the number of runs per year:

Length of a run = 294 / 11 ≈ 26.73

The length of a run is approximately 27 days.

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Answer:

A. 1 12

Step-by-step explanation:

Answer:

The answer is the first answer

P = 8 + 4√13 cm

A = 36 cm²

Step-by-step explanation:

* Lets study the figure

- Its a kite with two diagonals

- The shortest one is 12 cm

- The longest one is 26 ⇒ axis of symmetry of the kite

- the shortest diagonal divides the longest into two parts

- The smallest part is 8 cm and the largest one is 18 cm

* To find the area reserved for the logo divide

 the hexagonal piece into two congruent trapezium

- The length of the two parallel bases are 4 cm and 8 cm and

  its height is 3 cm

- The length of non-parallel bases can calculated by Pythagoras rule

∵ The lengths of the two perpendicular sides are 2 cm and 3 cm

- 3 cm is the height of the trapezium

- 2 cm its the difference between the 2 parallel bases ÷ 2

  (8 - 4)/2 = 4/2 = 2 cm

∴ The length of the non-parallel base = √(2² + 3²) = √13

* Now we can find the area of the space reserved for the logo

- The area of the trapezium = (1/2)(b1 + b2) × h

∴ The area = (1/2)(4 + 8) × 3 = (1/2)(12)(3) = 18 cm²

∵ The space reserved for the logo are 2 trapezium

∴ The area reserved for the logo = 2 × 18 = 36 cm²

* The area of the reserved space for the logo = 36 cm²

* The perimeter of the reserved space for the logo is the

  perimeter of the hexagon

∵ The lengths of the sides of the hexagon are:

   4 cm , 4 cm , √13 cm , √13 cm , √13 cm , √13 cm

∴ The perimeter = 2(4) + 4(√13) = 8 + 4√13 cm

* The perimeter of the reserved space for the logo = 8 + 4√13 cm

Answer:

Total earnings at the end of 5 years

= $87071.293

Step-by-step explanation:

First year

$64,000

Second year

$64,000 + 8% of previous year

= $64,000 + 0.08*$64,000

= $69120

Third year

$69120 + 8% of previous year

= $69120 + 0.08*$69120

= $74649.6

Fourth year

$74649.6 + 8% of previous year

= $74649.6 + 0.08*$74649.6

= $80621.568

Fifth year

$80621.568 + 8% of previous year

= $80621.568 + 0.08*$80621.568

= $87071.293

Answer:

375.462.46

Step-by-step explanation:

Took the test and the other answer 87071.29 was wrong

Answer:

  see the attachment

Step-by-step explanation:

There are 16 ounces in 1 pound, so 96 ounces is 6 pounds. You solve this problem by making up the difference between the given amount and 6 pounds—basically, you subtract it from 6.

  6 - 3 1/2 = 2 1/2 . . . . for example

The left sum would be f0+f1+f2+f3

The right sum would be f1+f2+f3+f4

The trapezoidal rule value is:

(f0+f1)/2 + (f1+f2)/2+(f2+f3)/2 +(f3+f4)/2

This would put the trapezoidal rule in the middle , which makes the answer:

Lower sum < Trapezoidal rule Value < Upper sum

Answer:

Step-by-step explanation:

Given function f(x) is positive, increasing and concave up on the closed interval [a, b],

it means f(x1) < f(x2) if x1 < x2

So Lower sum < Upper sum

As Trapezoidal is average of f(x1) and f(x2) = [f(x1) + f(x2)] / 2

it is average of the Lower and Upper sum.

The answer is Lower sum < Trapezoidal rule Value < Upper sum

Answer:

Option B. [tex]5.5[/tex]

Step-by-step explanation:

we know that

Applying the law of cosines

Let

c------> the missing side length

[tex]c^{2}=9^{2}+6^{2} -2(9)(6)cos(37)[/tex]

[tex]c^{2}=30.747[/tex]

[tex]c=5.5[/tex]