Suppose that you are organizing your texts for the semester at your desk consist-ing of 3 Computer Science, 2 Mathematics, and 2 Sociology textbooks. Assume alltextbooks are distinct. In how many ways can this be done ifa) the books can be arranged in any order?b) the Computer Science books must be together, but all other books can bearranged in any order?c) the Mathematics books and the Computer Science books must be together?

Answer:

If it is a simple average, the average is 2.8 points.

If it is a weigthed-by-credits average, the average is 2.86 points.

Step-by-step explanation:

To calculate the simple average of this 5 grades, we sum all the points and divide it by 5:

In Algebra: A = 4 points

In History: B = 3 points

In Sociology: A = 4 points

In English: D = 1 point

In Seminar: C = 2 points

Average = (4+3+4+1+2)/5 = 2.8 points

If the average is weighted by the credits, we must add each score multiplied by the credits and, in total, divide it by the total amount of credits.

[tex]weighted-average = \sum(points_i*credits_i)/\sum(credits_i)\\\\weighted-average = (4*3+3*3+4*3+1*3+2*2)/(3+3+3+3+2)\\weighted-average = 40 / 14 = 2.86[/tex]

Final answer:

To find the student's semester GPA, assign points to each grade based on the grading scale, multiply by the credits for each course, sum these totals, and divide by total credit hours. The student's GPA is approximately 2.86.

Explanation:

To calculate the student's semester grade point average (GPA), we first multiply each grade by its respective credit hours, then sum these numbers, and finally divide by the total number of credit hours. Here is the breakdown:

Algebra: A (4 points) × 3 credits = 12

History: B (3 points) × 3 credits = 9

Sociology: A (4 points) × 3 credits = 12

English: D (1 point) × 3 credits = 3

Seminar: C (2 points) × 2 credits = 4

Next, we add these totals: 12 + 9 + 12 + 3 + 4 = 40. The sum of the credit hours is 3 + 3 + 3 + 3 + 2 = 14. The GPA is calculated as the total points divided by the total credit hours, which is:

GPA = Total Points / Total Credit Hours = 40 / 14 ≈ 2.86

Therefore, the student's semester GPA is approximately 2.86.

Answer:

[tex]0.950796[/tex]

Step-by-step explanation:

Given that a shuttle launch depends on three key devices that may fail independently of each other with probabilities 0.01, 0.02, and 0.02, respectively.

Required probability =  the probability for the shuttle to be launched on time

= Probability that all three do not fail

Since each key device is independent of the other

we have

prob that all three do not fail = [tex](1-0.01)(1-0.02)(1-0.02)\\=0.99*0.98*0.98\\=0.950796[/tex]

Answer:

You can complete your schedule in 13 different ways.

Step-by-step explanation:

You initially have two general options:

1) You  can take Calculus at 9.30 and Physics at 11.30 OR

2) You can take Physics at 9.30 and Calculus at 11.30.

Let's examine each option:

1) If you take Calculus at 9.30 you'd have 3 options (since there are 3 Calculus sections), and then you'd have 3 options at 11.30 to take Physics. This makes 3 x 3 = 9 options.

2) If you choose to take Physics at 9.30, you'd have 2 options and then you'd have 2 Calculus options at 11.30. This makes 2x2 = 4 options.

Since you can take either option one OR two, we will sum up both results, and therefore you have 9 +4 = 13 different ways to complete your schedule.

Answer: 376.98192 mL

Step-by-step explanation:

We are going to use this equation.

V  = π  *  r²  * h

according to the question we have the value for r and h, if you replace the values into the equation we will get  following product:

note: also keep in mind that value of π is 3.141516

V  = π  *  r²  * h

V  = π  *  (4in)²  * (10in)

V = 502.64256 in³

after we can divide this value in 4 equals parts

then  we get the following equation:

502.64256 in³ / 4 = 125.66064 in³

after that that you can multiply this value by 3 to get the 3 parts of the cylinder vase for example:

125.66064 in³ * 3 = 376.98192 in³

and this result is the volume of water that we have to pour into the vase

Answer:

a) yes

b) no

Step-by-step explanation:

[tex](\mathbb{Z}, *)[/tex] is a gruop if satisfies the following conditions:

1. If a and b are two elements in [tex]\mathbb{Z}[/tex], then the product a*b is also in [tex]\mathbb{Z}[/tex].

2. The defined multiplication is associative, i.e., for all a,b,c in [tex]\mathbb{Z}[/tex], (a*b)*c=a*(b*c).

3. There is an identity element e such that e*a=a*e=a for every element a in [tex]\mathbb{Z}[/tex].

4. There must be an inverse of each element. Therefore, for each element a of [tex]\mathbb{Z}[/tex], the set contains an element b=a^(-1) such that a*a^(-1)=a^(-1)*a=e.

Let's see if the conditions are satisfied:

a)

1. if x and y are integers then x+y-1=a*y is an integer

2. If x,y and z are integers then

   (x*y)*z= (x+y-1)*z= (x+y-1) + z - 1= x +y+z-2,

   x*(y*z)= x*(y+z-1)= x + (y+z-1) -1 = x+ y + z -2

  Then (x*y)*z=x*(y*z), i.e, * is associative.

3. Let e=1 and b an integer. Observe that

    1*b=1+b-1=b and b*1= b + 1 -1= b.

  Then e is an identity element.

4. a and integer and b= 2- a. Observe that

    b*a= 2-a+a-1= 1 and a*b= a+2-a-1=1,

the b= a^(-1) is the inverse of a.

We conclude that [tex](\mathbb{Z}, *)[/tex] is a group.

b)

1. If x,y and z are integers then

   (x*y)*z= (x-y+xy)*z= (x-y+xy) - z + (x-y+xy)z= x -y-z+xy+xz-yz+xyz

   x*(y*z)= x*(y-z+yz)= x - (y-z+yz) +x(y-z+yz) = x-y +z + xy -xz -yz+xyz

  Then (x*y)*z≠x*(y*z), i.e, * isn't associative.

We conclude that [tex](\mathbb{Z}, *)[/tex] isn't a group.

Answer:

Hence the current weighted average of student = 87.60

Step-by-step explanation:

Grades obtained by student are

Q1= 100

Q2= 93

IW1= 82

IW2= 83

H1= 80

the weighted average = sum of all the grades/ number of subjects

[tex]= \frac{100+93+82+83+80}{5}[/tex]= 87.60

Hence the current weighted average of student = 87.60

Answer:

1) 15

2) 4.5

Step-by-step explanation:

1 ) 10, 12, 16, 17,20

Average = [tex]\frac{\text{Sum of all observations}}{\text{Total no. of observations}}[/tex]

Average = [tex]\frac{10+12+16+17+20}{5}[/tex]

Average = [tex]15[/tex]

2) 0, 3,6,9

Average = [tex]\frac{\text{Sum of all observations}}{\text{Total no. of observations}}[/tex]

Average = [tex]\frac{0+3+6+9}{4}[/tex]

Average = [tex]4.5[/tex]

Answer:

178 meters in 2 seconds = 890 meters in 10 seconds.

Step-by-step explanation:

Given : 178 meters in 2 seconds.

To find : How many meters in 10 seconds ?

Solution :

Applying unitary method,

In 2 seconds there is 178 meter.

In 1 second there is [tex]\frac{178}{2}[/tex] meter.

In 1 second there is 89 meter.

In 10 seconds there is [tex]10\times 89[/tex] meter.

In 10 seconds there is 890 meter.

Therefore, 178 meters in 2 seconds = 890 meters in 10 seconds.

Answer:

Using the rule of 72, the doubling time is 9.35 years.

The exact answer is that the doubling time is 8.89 years.

Step-by-step explanation:

By the rule of 72, we have that the doubling time D is given by:

[tex]D = \frac{72}{Interest Rate}[/tex]

The interest rate is in %.

In our exercise, the interest rate is 7.7%. So, by the rule of 72:

[tex]D = \frac{72}{7.7} = 9.35[/tex].

Exact answer:

The exact answer is going to be found using the compound interest formula(since the rule of 72 is a simplification of this formula).

The compound interest formula is given by:

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

[tex]A = 2P[/tex]

[tex]r = 0.077[/tex]

There are 52 weeks in a year, so [tex]n = 52[/tex]

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]2P = P(1 + \frac{0.077}{52})^{52t}[/tex]

[tex]2 = (1.0015)^{52t}[/tex]

Now, we apply the following log propriety:

[tex]\log_{a} a^{n} = n[/tex]

So:

[tex]\log_{1.0015}(1.0015)^{52t} = \log_{1.0015} 2[/tex]

[tex]52t = 462.44[/tex]

[tex]t = \frac{462.44}{52}[/tex]

[tex]t = 8.89[/tex]

The exact answer is that the doubling time is 8.89 years.

Answer:

a) $765.13 b) $277,601.23

Step-by-step explanation:

a) The problem is an example of an ordinary annuity (deposits at the end of the period).

The future value of this type of annuity is:

[tex]FV=A*\frac{(1+i)^{n} -1}{i}[/tex]

Clearing the annual deposit A

[tex]A=FV*\frac{i}{(1+i)^{n} -1}[/tex]

[tex]A=360,000*\frac{0.11}{(1.11)^{38}-1 } =360,000*0,002125351=765.13[/tex]

The deposit needed to have $360,000 in 38 years is $765.13

b) We can use the same formula to compute the FV of a known deposit:

[tex]FV=A*\frac{(1+i)^{n} -1}{i}[/tex]

[tex]FV=590*\frac{(1.11)^{38} -1}{0.11}=590*470,5105644=277,601.23[/tex]

With annual deposits of $590 you will have at 38 years an ammount of $277,601.23

Answer:

B.) 100 in2

Explanation:

20 x 10 = 200

200 ÷ 2 = 100

B.) 100 in2

Answer: It's b

Step-by-step explanation:

Answer:

1.5 ml

Step-by-step explanation:

We have been given that the concentration on hand is 10 mg per ml.

We know that gr stands for grains.

We know that 1 gr equals 60 mg.

First of all, we will convert 1/4 gr to mg as:

[tex]\frac{1}{4}\text{ gr}\times \frac{60\text{ mg}}{\text{ gr}}[/tex]

[tex]\frac{1}{4}\times 60\text{ mg}[/tex]

[tex]15\text{ mg}[/tex]

1 ml equals 10 mg. We can set an a proportion as:

[tex]\frac{x}{15\text{ mg}}=\frac{\text{1 ml}}{10\text{ mg}}[/tex]

[tex]\frac{x}{15\text{ mg}}*15\text{ mg}=\frac{\text{1 ml}}{10\text{ mg}}*15\text{ mg}[/tex]

[tex]x=\text{1 ml}*1.5[/tex]

[tex]x=\text{1.5 ml}[/tex]

Therefore, 1.5 ml is needed for the dose.

Answer:

120 MW/hour

Step-by-step explanation:

The formula of the average rate of change between two points in a function is:

Average rate of change (ARC) = f(x2) -f(x1)/(x2-x1)

Let's think  the power demad as a function d(x) depending of the hour of the day, so the variable x= hour of the day.

Now we have:

d(5)= 1600

d(8)= 1960

If we apply the mentioned ARC formula = [d(8)-d(5)] MW/(8-5)hour= (1960-1600)MW/3hour= 360/3=120 MW/Hour

Answer:

[tex]r=5.23\%[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=1\ years\\ P=\$27,580\\I=\$1,442.43\\r=?[/tex]

substitute in the formula above

[tex]1,442.43=27,580(r*1)[/tex]

Solve for r

[tex]r=1,442.43/27,580[/tex]

[tex]r=0.0523[/tex]

convert to percent

[tex]r=0.0523*100=5.23\%[/tex]

This is the set of all integers greater than -2, excluded. So, the elements of the set are

[tex]\{-1,0,1,2,3,4,5,\ldots\}[/tex]

Given:

Set defining the rule → {y | y is an integer and y > -2}

To find:

The set following the given property

Solution:

Set defined by {y | y is an integer and y > -2} where y is the set of integers greater than -2.

Option (1)

{3,4,5,6........}

All the integers are greater than -2, therefore, this set will the answer.

Option (2)

{2, 3, 4, 5, 6.....}

All integers are greater than -2, therefore, this set will be the answer.

Option (3)

{-2, -1, 0, 1, 2, 3....}

There is an element which is equal to -2.

Therefore, given set will not be the answer.

Option (4)

{0, 1, 2, 3.....}

All elements are greater than -2.

Therefore, given set will be the answer.

Options (1), (2), (4) will be the answer.

Learn more about the integers,

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Answer:

No, irrational numbers are not closed under multiplication.

Step-by-step explanation:

Irrational numbers are the numbers that cannot be demonstrated in the form of a fraction [tex]\frac{x}{y}[/tex]. We can define rational numbers in other ways as well. Irrational numbers are the numbers which when written in decimal form, the decimal expansion does not end. For example √2, √3, etc.

The closed property of multiplication of irrational numbers state that if two irrational numbers are multiplied, then their product is also an irrational number.

Let a and b be two irrational numbers, then a×b = c(c is product of a and b), c should also be an irrational number.

Irrational numbers are not closed under multiplication and this can be illustrated with the help of an example:

√2 × √2 = 2

It is clear that 2 is not an irrational number.

Hence, irrational numbers are not closed under multiplication.

Answer:

Step-by-step explanation:

1. Number of boys in the group = 25

Number of girls in the group = 18

Total children = 25 + 18 = 43

Number of ways to arrange the children in a way = 43!

2. If we consider all the boys as an individual then number of ways children can be arranged = 19!

Number of ways boys can sit next to each other = 25!

So the number of ways can be arranged = 19!×25!

3. Number of ways boys can sit next to each other = 25!

Number of ways girls can sit next to each other = 19!

Then number of ways to arrange the children in a row with all boys next to each other and all the girls next to each other will be = 2 × 18! × 25!

4. 1. To choose a chess team if anyone can be chosen

= [tex]^{43}C_{6}[/tex]

= 6096454

4. 2. Exactly 2 girls must be chosen then number of ways

= [tex]^{18}C_{2}\times ^{25}C_{4}=1935450[/tex]

4. 3. At least two boys must be chosen

= [tex]^{25}C_{2}\times ^{18}C_{4}+^{25}C_{3}\times ^{18}C_{3}+^{25}C_{4}\times ^{18}C_{2}+^{25}C_{5}\times ^{18}C_{1}+^{25}C_{6}[/tex]

= 5863690

Answer:

500 cubic feet equals 14158.4 liters or 3740.25 gallons.

Step-by-step explanation:

We are asked to convert 500 cubic feet to liters then to gallons.

We know that one cubic feet equals 28.3168 liters.

[tex]\text{500 cubic feet to liters}=\text{500 cubic feet}\times \frac{\text{28.3168 liters}}{\text{cubic feet}}[/tex]

[tex]\text{500 cubic feet to liters}=500\times \text{28.3168 liters}[/tex]

[tex]\text{500 cubic feet to liters}=\text{14158.4 liters}[/tex]

We know one liter equals 0.264172 gallons.

[tex]\text{14158.4 liters to gallons}=\text{14158.4 liters}\times\frac{0.264172\text{ gallons}}{\text{liter}}[/tex]

[tex]\text{14158.4 liters to gallons}=14158.4 \times 0.264172\text{ gallons}[/tex]

[tex]\text{14158.4 liters to gallons}=3740.2528448\text{ gallons}[/tex]

[tex]\text{14158.4 liters to gallons}\approx 3740.25\text{ gallons}[/tex]

Therefore, 500 cubic feet equals 14158.4 liters or 3740.25 gallons.

Answer:  0.8531

Step-by-step explanation:

Let x be the random variable that represents the readings on scientific thermometers .

Given : The readings on scientific thermometers are normally distributed,

Population mean : [tex]\mu=0^{\circ}\ C[/tex]

Standard deviation : [tex]\sigma=1^{\circ}\ C[/tex]

Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

Now, the z-value corresponding to -1.05 :  [tex]z=\dfrac{-1.05.-0}{1}=-1.05[/tex]

P-value = [tex]P(x>-1.05)=P(z>-1.05)=1-P(z\leq-1.05)[/tex]

[tex]=1-0.1468591=0.8531409\approx0.8531\text{ (Rounded to four decimal places)}[/tex]

Hence, the probability of the reading greater than -1.05 in degrees Celsius.= 0.8531

Answer:

Open system

Step-by-step explanation:

We are putting can of soft drink in the refrigerator so that it will cool down. As we can see the can of soft drink cool down when it releases its heat to the refrigerator. As it can exchange its temperature with it's surrounding so it will be an open system. If it would be a closed system then it won't be able to release its heat to the surrounding so it won't be able to cool down.

Answer:

The sum of two rational numbers is always a rational number.

Step-by-step explanation:

Rational Number is the number of the form [tex]\frac{p}{q}[/tex], q≠0 and p and q are integers.

Further, when we add or subtract two rational number it is always a rational number. Example:

[tex]\dfrac{4}{64} +\dfrac{25}{4} = \dfrac{4+25\times 16}{64} \\= \dfrac{4+400}{64} = \dfrac{404}{64} =\dfrac{101}{16}[/tex]

which is also a rational number.

Thus, the sum of two rational numbers is always a rational number.

Answer:

D. 65.7-65.6

(the exact difference is 10.1, which is "about" 10)

The difference that is about 10 is 70.9-58.7. The correct option is B. 70.9-58.7

To determine the difference that is about 10, we will evaluate the given expressions one after the other.

The result that is closest to 10 gives the difference that is about 10

Evaluating this, we get

33.2-28.4 = 4.8

Evaluating this, we get

70.9-58.7 = 12.2

Evaluating this, we get

42.5-16.8 = 25.7

Evaluating this, we get

65.7-65.6 = 0.1

From above, we can observe that from A to D, the answer that is closest to 10 is 12.2

Hence, the difference that is about 10 is 70.9-58.7. The correct option is B. 70.9-58.7

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Answer: 8 inches

Step-by-step explanation:

We know that the area of a rectangle is given by :-

[tex]A=l\times w[/tex], where l is length and w is width of the rectangle.

Given : The width of rectangle : w=4 inches

The area of rectangle : A =32 inches.

Then substitute these values in the above formula, we have

[tex]32=l\times4\\\\\Rightarrow\ l=\dfrac{32}{4}=8[/tex]

hence, the length of rectangle = 8 inches.

To determine the maximum length of the shipping carton given a maximum combined length and girth of 108 inches, we calculate the girth as 52 inches using the provided width and height. Subtracting this from 108 inches gives us a maximum allowable length of 56 inches.

The problem is a geometry optimization problem where we need to maximize the length of a shipping carton given a constraint on its combined length and girth. Girth is the perimeter around the width and height sides of the package. According to the U.S. postal regulations, the maximum combined length and girth is 108 inches.

First, let's calculate the girth using the given dimensions of the carton. The width is 14 inches and the height is 12 inches. The girth is twice the width plus twice the height (since girth is the perimeter of the cross-section):

girth = 2  × width + 2 × height

girth = 2  × 14in + 2 × 12in

girth = 28in + 24in

girth = 52in

Now, to find the maximum length, we can subtract the girth from the maximum allowed combined length and girth:

max length = max combined length and girth - girth

max length = 108in - 52in

max length = 56in

Therefore, the maximum length that the carton can be is 56 inches.

Answer:

[tex]0\le P\le 1[/tex]

Step-by-step explanation:

The probability of an event is a number describing the chance that the event will happen.

Definition: The probability of an evant is

[tex]P=\dfrac{\text{Number of favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]

1. An event that is certain to happen (Number of favorable outcomes = Number of all possible outcomes) has a probability of 1.

2. An event that cannot possibly happen (Number of favorable outcomes = 0) has a probability of 0.

3. If there is a chance that an event will happen, then its probability is between 0 and 1.

Thus,

[tex]0\le P\le 1[/tex]

The probability of an event occurring is always between 0 and 1, inclusive. Therefore, the correct inequality is 0≤P≤1.

The probability of an event (P) in a standard probability model is always defined between 0 and 1. Here, 0 represents the impossibility of the event, whereas 1 represents the certainty of the event. Therefore, the inequality that best describes the probability P is 0≤P≤1. Any other range for probability does not fit into the standard probability model used in mathematics.

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Answer:

So, the times the ball will be 48 feet above the ground are t = 0 and t = 2.

Step-by-step explanation:

The height h of the ball is modeled by the following equation

[tex]h(t)=-16t^2+32t+48[/tex]

The problem want you to find the times the ball will be 48 feet above the ground.

It is going to be when:

[tex]h(t) = 48[/tex]

[tex]h(t)=-16t^{2}+32t+48[/tex]

[tex]48=-16t^{2}+32t+48[/tex]

[tex]0=-16t^{2}+32t+48 - 48[/tex]

[tex]16t^{2} - 32t = 0[/tex]

We can simplify by 16t. So

[tex]16t(t-2)= 0[/tex]

It means that

16t = 0

t = 0

or

t - 2 = 0

t = 2

So, the times the ball will be 48 feet above the ground are t = 0 and t = 2.

Answer:

The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.

There is a 61.92% probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

Step-by-step explanation:

This can be solved by the the z-score formula:

On a normaly distributed set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a value X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Each z-score value has an equivalent p-value, that represents the percentile that the value X is:

The problem states that:

Mean = 35, so [tex]\mu = 35[/tex]

Variance = 81. The standard deviation is the square root of the variance, so [tex]\sigma = \sqrt{81} = 9[/tex].

Find the 33rd percentile of the time it takes Finn to get to work on any given day. Do not include any units in your answer.

Looking at the z-score table, [tex]z = -0.44[/tex] has a pvalue of 0.333. So what is the value of X when [tex]z = -0.44[/tex].

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.44 = \frac{X - 35}{9}[/tex]

[tex]X - 35 = -3.96[/tex]

[tex]X = 31.04[/tex]

The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.

Over the next 2 days, find the probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

[tex]P = P_{1} + P_{2}[/tex]

[tex]P_{1}[/tex] is the probability that Finn took more than 40.5 minutes to get to work on the first day. The first step to solve this problem is finding the z-value of [tex]X = 40.5[/tex].

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{40.5 - 35}{9}[/tex]

[tex]Z = 0.61[/tex]

[tex]Z = 0.61[/tex] has a pvalue of 0.7291. This means that the probability that it took LESS than 40.5 minutes for Finn to get to work is 72.91%. The probability that it took more than 40.5 minutes if [tex]P_{1} = 100% - 72.91% = 27.09% = 0.2709[/tex]

[tex]P_{2}[/tex] is the probability that Finn took more than 38.5 minutes to get to work on the second day. Sine the probabilities are independent, we can solve it the same way we did for the first day, we find the z-score of

[tex]X = 38.5[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{38.5 - 35}{9}[/tex]

[tex]Z = 0.39[/tex]

[tex]Z = 0.39[/tex] has a pvalue of 0.6517. This means that the probability that it took LESS than 38.5 minutes for Finn to get to work is 65.17%. The probability that it took more than 38 minutes if [tex]P_{1} = 100% - 65.17% = 34.83% = 0.3483[/tex]

So:

[tex]P = P_{1} + P_{2} = 0.2709 + 0.3483 = 0.6192[/tex]

There is a 61.92% probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

Answer:

The interior angles for this triangle are 80º, 30º and 70º.

Step-by-step explanation:

The sum of a interior angle with it's respective exterior angle is also always 180º.

So, for the exterior angle that is 100º, we can find the first interior angle of the triangle

100º + A1 = 180º

A1 = 180º - 100º

A1 = 80º

The first interior angle of this triangle is A1 = 80º;

For the exterior angle that is 150º, we can find the second interior angle of the triangle.

150º + A2 = 180º

A2 = 180º - 150º

A2 = 30º

The second interior angle of this triangle is A2 = 30º.

From here, to find the third interior angle, we apply the following definition

The sum of the three interior angles of a triangle is always 180º.

So:

A1 + A2 + A3 = 180º

80º + 30º + A3 = 180º

110º + A3 = 180º

A3 = 180º - 110º

A3 = 70º

The third interior angle of this triangle is A3 = 70º.

The interior angles for this triangle are 80º, 30º and 70º.

Answer:

when graphing f(x) between x=-3 & x=3, the result is a function that comes from x=-infinite and positive y, crosses the x-axis at (-2.646,0), continues to decrease until (-1.871,-12.25) and then increases until (0,0).

This function is symetrical by the y axis, therefore, after reaching (0,0), f(x) decreases until (1.871,-12.25), starts to increase until it crosses the x axis at (2-646,0) and continues to increase until x=+infinite

Step-by-step explanation:

This funcion appears as a large W, with it's points on (-1.871,-12.25) , (0,0) & (1.871,-12.25)

Answer:

amount of pepper required= 7.5 tsp

amount of garlic powder required = 30 tsp

Step-by-step explanation:

Given,

amount of salt used for small batch of the recipe = 2 tsp

amount of pepper used for small batch of the recipe = 1 tsp

amount of garlic powder used for small batch of the recipe = 4 tsp

amount of salt used for the larger batch = 15 tsp

                                                             = 2 x 7.5 tsp

                                                             = amount of salt used for small batch the recipe x 7.5

So,

the amount of pepper needed for the larger batch= 7.5 x amount of pepper used for the small batch of recipe

                                                                      = 7.5 x 1 tsp

                                                                       = 7.5 tsp

the amount of garlic powder needed for the larger batch= 7.5 x amount of garlic powder used for the small batch of recipe

                                                                                          = 7.5 x 4 tsp

                                                                                          = 30 tsp

Final answer:

To adjust the recipe for 15 tsp of salt, you will need 7.5 tsp of pepper and 30 tsp of garlic powder, by applying a scaling factor based on the original recipe proportions.

Explanation:

The question asks how much pepper and garlic powder are needed if a recipe is scaled up to use 15 tsp of salt, from an original recipe that calls for 2 tsp of salt, 1 tsp of pepper, and 4 tsp of garlic powder. To solve this, we first determine the scaling factor for the recipe by dividing the new quantity of salt by the original quantity of salt, which is 15 tsp ÷ 2 tsp = 7.5. Next, we apply this scaling factor to the measurements for pepper and garlic powder.

Pepper needed = 1 tsp (original amount) x 7.5 (scaling factor) = 7.5 tsp of pepper.

Garlic Powder needed = 4 tsp (original amount) x 7.5 (scaling factor) = 30 tsp of garlic powder.