The princess of the Kingdom of Abundance accidentally drops her magic salamander's feeding bowl into a fire. She orders a new feeding bowl to be made out of Dragon Alloy #18, which is 86% magic steel and the rest titanium. The
dwarfs have a lot of Dragon Alloy #33, which is 28% titanium. How much of
that alloy and how much magic steel should they combine to make 700 grams of Dragon alloy #18?

Answer:

$17.2

Step-by-step explanation:

120 + 16*100 = 120 + 1600 = 1720

The member pays $1720 annually for 100 classes and membership fee combined.

1720/100 = 17.2

The student pays $17.2 per class on average.

1) This is a Two tailed Test.

2) Decision rule is; If the p-value is greater than 4% fail to reject H₀.

3) P-value = 0.00968764 and so we reject H₀

We are given the hypothesis as;

Null Hypothesis; H₀: m₁ = m₂

Alternative Hypothesis; H₁: m₁ ≠ m₂

1) Since the alternative hypothesis has "not equal to sign", then it is a two tailed test.

2) Since we are told to use significance level as 0.04, then we can say that the decision rule is;

If the p-value is greater than 4% fail to reject H₀.

3) Using a 2-Sample Z-Test online TI calculator gives the test statistic as;

z = 2.5868

4) From z-score calculator, p-value equals 0.00968764. This is less than 0.04 and as such the decision regarding H₀ is to reject H₀.

5) P-value = 0.00968764

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Answer:

80

Step-by-step explanation:

1) if the number of hamburgers is 'h', number of cheesburgers is 'c', then

2) the condition 'The number of cheeseburgers sold was three times the number of hamburgers' can be written as c=3h. Also

3) the condition 'combined total of 320' can be written as h+c=320, then

4) it is possible to make up the system of equations:

[tex]\left \{ {{c=3h} \atop {c+h=320}} \right. \ = > \ \left \{ {{c=240} \atop {h=80}} \right.[/tex]

5) finally, number of hamburgers is 80.

Answer: Scott - 18, Kaitlin - 9, Bill - 54

Step-by-step explanation:

Let's view this as units. There are a total of 81 units. If we solve for Scott's orders:

Kaitlin served 9 fewer orders than Scott. We add 9 to 81 --> 9 + 81 = 90.

Now if we view Scott's orders as one unit:

Scott - 1 unit

Kaitlin (after adding 9) - 1 unit

Bill - 3 units (he served 3 times as many orders as Scott)

In total there are 3 + 1 + 1 = 5 units.

90 / 5 = 18.

Therefore, Scott served 18 orders.

18 - 9 = 9.

Kaitlin served 9 orders.

18 x 3 = 54.

Bill served 54 orders.

And to check our answer, 54 + 18 + 9 is 81.

Answer:

0, -3

Step-by-step explanation:

Attachment.

In short, it is way easier to not graph it, however, if you really need to graph it, change it to the correct form, then do some plug and chug if the equation is not so friendly.

Answer:

5.907 km

Step-by-step explanation:

2.783 km + 3.124 km = 5.907 km

Using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df is of Tc = 2.1098.

It is found using a calculator, with two inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df, using the stated two-tailed test, is of Tc = 2.1098.

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Term life insurance has the lower premium because term life insurance pays the face value to your beneficiary if you die within a certain set period of time, whereas whole life insurance covers you your entire life. (Option A)

Insurance is when a third-party (the insurer) promises to indemnify another party (the insured) for losses they might suffer in the future in exchange for agreed upon payments.

Permanent life insurance is a type of insurance that provides a coverage that never expires. The person with a permanent life insurance is covered until he or she passes on. Whole life insurance is a type of permanent life insurance that has a fixed and guaranteed premium and a fixed death benefit.

Term life insurance is a type of insurance that provides coverage to a person only for a scheduled period of time. For example, a person who buys a 10 year term life insurance, the person's insurance only lasts for 10 years. If the person passes on within the 10 years, his beneficiary receives payments. If the person passes on after 10 years, his beneficiary does not receive any payments.

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Answer:

15+15

Step-by-step explanation:

Two 15's added together can equal 30

Answer: The center of the circle will be (1,2) and the radius will be 2.5

Step-by-step explanation: Basically since its (x-1) it would become x=1 so that's ur first value same thign with y but that would be ur second value. And since in your equation it is 6.25 that would be 2.5 because 6.25 is r^2 and you are looking for r.

Using sampling concepts, the population and the sample are given as follows:

d. population: 6,000 batches of 100 cards sample: every 100th batch.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and then:

Hence, in the situation described the population is the 6,000 batches of 100 cards, while the sample is every 100th batch, hence option d is correct.

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The solution of the given expression is 9*[tex]x^{4}[/tex]/100.

GIven an expression equal to 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].

We have to simplify the expression in which variable comes only once.

Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.

The given fraction is 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].

When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.

=27[tex]x^{4}[/tex]/300

Now divide numerator an denominator by 3.

=9[tex]x^{4}[/tex]/300

Hence the expression 27[tex]x^{12} /300x^{8}[/tex] will look like [tex]9x^{4} /100[/tex] after simplifying.

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Answer:

[tex]Simplify:\sqrt\frac{27x^{12} }{300x^{8} }[/tex]

[tex]O \frac{9}{100}x^{4}[/tex]

✔ [tex]\frac{3}{10} x^{2}[/tex]

[tex]O \frac{27}{300} x^{4}[/tex]

[tex]O\frac{9}{10} x^{2}[/tex]

The surface area of the cone is 282.6 square centimeters.

For a cone of radius R and height H, the surface area is given by:

[tex]A = pi*R^2 + pi*R*\sqrt{R^2 + H^2}[/tex]

Where pi = 3.14

In this case, we have:

[tex]A = 3.14*(5cm)^2 + 3.14*5cm*\sqrt{(5cm)^2 + (12cm)^2} = 282.6 cm^2[/tex]

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The common base that can be used to rewrite each side of the equation is 2.

The common base that can be used to rewrite each side of the equation is as follows:

2ˣ⁺³ - 3 = 5

add 3 to both sides

2ˣ⁺³ - 3 + 3 = 5 + 3

2ˣ⁺³ = 8

Hence,

2ˣ⁺³ = 2³

Therefore, the common base that can be used to rewrite each side of the equation is 2.

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The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

To answer the question, we need to know what an equation is

An equation is a mathematical expression that show the relationship between two variables.

Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S

So, L.H.S = 9cos(sin¯¹(x))

= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])

9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]

= √[9² × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - x²}]   (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)

= √(81 – 81x²)

= R.H.S

So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

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The tree diagram representing these reporting relationships is attached.

It should be noted that a tree diagram is a planning tool that is used to show the hierarchy of tasks that are needed to be completed.

In this case, the tree diagram shows the way the employees report to each other.

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The two colors can be chosen in 3 different ways.

If we have a set of N elements, the number of different sets of K elements (such that the order of the K elements does not matter) is:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case, we have 3 colors, so N=3, and we want to choose 2, then K=2.

Replacing that we get:

[tex]C(3, 2) = \frac{3!}{(3- 2)!*2!} = \frac{3*2*1}{1*2*1} = 3[/tex]

The two colors can be chosen in 3 different ways.

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Considering the given regression equation, the number of weeks that will pass before the value of the stock reaches $600 is of:

B. 8.3.

The value of the stock y after x weeks is given as follows:

log(y) = 0.3x + 0.296.

We have to solve for x when y = 600, hence:

log(600) = 0.3x + 0.296

0.3x = 2.7782 - 0.296

x = (2.7782 - 0.296)/0.3

x = 8.3 weeks.

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The percentage of students age 15 and above travel to school by bus is 47%

The table of values is given as:

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15                            18                 165

Age 15 and above    65                                 195

Column totals          152          110        98      360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above  = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15           87              18      60        165

Age 15 and above    65          92        38        195

Column totals          152          110        98      360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

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Answer:

24

Step-by-step explanation:

1) according to the additional (see the attached picture) f(6)= -6 and g(5)= -5. Then

2) the given experssion can be written:

f(6)-6*g(5)=-6-6*(-5)=-6+30=24.

The difference between the functions give:

(f - g)(1) = f(1) - g(1) = -3

For two functions f(x) and g(x), the difference is defined as:

(f - g)(x) = f(x) - g(x).

Then:

(f - g)(1) = f(1) - g(1)

By looking at the given tables, we know that:

f(1) = -2

g(1) = 1

Replacing that we get:

(f - g)(1) = f(1) - g(1) = -2 - 1 = -3

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The two sets of parametric equations for the rectangular equation are;

It follows from the task content that the parametric equations can be determined as follows;

By substituting the x= t+6 into the rectangular equation; we have;

y = (t+6-6)²-7(t+6)

y = t²-7t-42.

By substituting the x= 7t into the rectangular equation; we have;

y = (7t-6)² -7(7t)

y = 49t² - 84t +36 - 49t

y = 49t² - 133t +36.

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Using proportions, it is found that 40 ml of water have to be added to make the ratio of oil to water of 1:3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The jar contains 100 ml of oil and water in the ratio 1:4, hence:

Oil was added to make the ratio 1/2, hence:

[tex]\frac{20 + x}{100 + x} = \frac{1}[3}[/tex]

3(20 + x) = 100 + x

60 + 3x = 100 + x

x = 20.

Then there are 40 ml of oil and 80 ml of water, for a total of 120 ml. Now we want a ratio of 1:3, that is, 3/4 of the mixture being water, hence:

[tex]\frac{80 + x}{120 + x} = \frac{3}{4}[/tex]

4(80 + x) = 3(120 + x)

320 + 4x = 360 + 3x

x = 40

40 ml of water have to be added to make the ratio of oil to water of 1:3.

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The Piecewise -Defined function and how it is graphed is given below..

Given the function in the attached image,

See the attached Graph for better understanding.

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Answer:

Step-by-step explanation:

the legs

Answer:

1050 masks per person.

Step-by-step explanation:

1) Create an equation to find the total number of masks

2) Solve equation and divide total by 2 to get the number of masks that can be given to both Mark and Paula so that they have equal number.

1) Since Paula has 70% of the total masks, it can be represented as 0.7 * t where t is the variable representing the total number of masks. Mark on the other hand has the remaining number of masks out of 100% which is 30%. We can express that as 0.3. We multiply that by t because he has 30% of the masks. The final equation we have is 0.3t + 840 = 0.7t. 840 because Paula has 840 more masks than Mark.

2) Solve by subtracting 0.3t from both sides leaving you with 0.4t = 840. We divide both sides by 0.4 to get 2100. That is the total number of masks. If we divide that number by 2, we get 1050.

Answer:

The ladder is 98 inches tall in inches.

Step-by-step explanation:

⇒ 8 (feet)  × 12 (inches)  = 96 inches

⇒ Add the extra 2 inches

⇒ 98 inches tall.