If the mean of 6 numbers increased by 3, by how much would the sum of
the 6 numbers have to increase? *
O 18
O 21
O 12
O 3
O 6

System of Equations

Let:

x = cost of each notebook.

y = cost of each thumb drive.

Three notebooks and 2 thumb drives cost $43, thus:

3x + 2y = 43

Three notebooks and three thumb drives cost $57, thus:

3x + 3y = 57

Subtracting both equations:

3x - 3x + 3y - 2y = 57 - 43

Simplifying:

y = 14

Substituting into the first equation:

3x + 28 = 43

Subtracting 28:

3x = 15

Dividing by 3:

x = 5

Each notebook cost $5 and each thumb drive cost $14

Answer:

4a plus or minus 1b

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 44\ units}\)

Step-by-step explanation:

Solution:

So,

= 3 + 8 + 3 + 6 + 5 + 6 (again) + 4 + 5 + 4

\(\rule[225]{225}{2}\)

Answer:

8-4=4

therefore 6+4=10

then perimeter =2(5)+10+6+2(3)+8+4=44units

Answer: 5.25 square inches

Step-by-step explanation:

A=(1/2)bh=(1/2)(3.5)(3)=5.25

The surface area generated by revolving the curve about the x-axis is 18π square units. and the surface area generated by revolving the curve about the y-axis is 81π square units.

To find the area of the surface generated by revolving the curve x = 9t, y = 2t, 0 ≤ t ≤ 3, we can use the formula for the surface area of a solid of revolution.

(a) Revolving the curve about the x-axis:

In this case, the curve forms a straight line parallel to the x-axis. To find the surface area, we integrate the circumference of each small circle along the length of the curve.

The circumference of a circle is given by C = 2πr, where r is the distance between the curve and the axis of revolution (in this case, the x-axis). Since y = 2t is the distance between the curve and the x-axis, we have r = 2t.

To find the surface area, we integrate the circumference along the curve:

Surface area = ∫[0, 3] 2π(2t) dt

= 4π ∫[0, 3] t dt

= 4π [t^2/2] [0, 3]

= 4π (9/2)

= 18π

So, the surface area generated by revolving the curve about the x-axis is 18π square units.

(b) Revolving the curve about the y-axis:

In this case, the curve forms a straight line parallel to the y-axis. The approach is similar to part (a), but now the distance between the curve and the axis of revolution is given by x = 9t.

Using the same process as before, we find:

Surface area = ∫[0, 3] 2π(9t) dt

= 18π ∫[0, 3] t dt

= 18π [t^2/2] [0, 3]

= 18π (9/2)

= 81π

Therefore, the surface area generated by revolving the curve about the y-axis is 81π square units.

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The value of cos (x + pi) is -✓3/2, based on the stated information and known trigonometric values.

As per the known fact, the value of x wil be 30° as it is the specific value whose cosine or cos is ✓3/2. Now, we also know that π represents 180°. Also, the formula for cos (a + b) is cos A cos B - sin A sin B.

So, cos (x + pi) will be -

cos x cos pi - sin x sin pi

Keeping the values and solving -

cos (x + pi) = cos 30 cos 180 - sin 30 sin 180

cos (x + pi) = (✓3/2 × -1) - (1/2 × 0)

cos (x + pi) = -✓3/2

Hence, the value of cos (x + pi) is -✓3/2.

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The claim that less than 50% of people following a particular diet will experience increased energy is not supported by the sample data.

Hypotheses:H0: p = 0.50 (Null hypothesis)p < 0.50 (Alternative hypothesis)Conditions:Sample size n = 100 is greater than 30 and less than 10% of the population.

Individuals are randomly selected and have to follow the diet. Multiple trials can be considered as binomial distribution trials. Based on this, we can conclude that it is possible to test the claim that less than 50% of people following a particular diet will experience increased energy.Level of Significance:α = 0.05 (Given)Test statistic:We use the standard normal distribution to calculate the test statistic.

Z = (p - p0) / [p0(1 - p0) / n]P-value:Using the p-value approach, we can reject the null hypothesis if the p-value is less than or equal to the level of significance (α).

The p-value is the probability of obtaining the observed sample proportion of successes or more extreme values, given that the null hypothesis is true. Conclusion: Since the calculated test statistic value (-0.70) is less than the critical value of -1.645 (from standard normal distribution table for 0.05 level of significance), we fail to reject the null hypothesis (H0) and conclude that there is not sufficient evidence to claim that less than 50% of people following a particular diet will experience increased energy.

Therefore, the claim that less than 50% of people following a particular diet will experience increased energy is not supported by the sample data.

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The shadow of the 24-foot tree will be 9.6 feet.

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

Given that:-

If a 40-foot tree casts a 16-foot shadow, find the length of the shadow cast by a 24-foot tree.

Now, The shadow of the 24-foot tree will be calculated as follows:-

40/16 = 24/x

x = 24 x 16 / 40

x = 9.6

Therefore, the shadow of the 24-foot tree will be 9.6 feet.

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Answer:

x=15 y=12 z=2

Step-by-step explanation:

4x=60 x=15

5y=60 y=12

2z=4 z=2

Answer:

x+y=85 and x-y=20

x=85-y x=20+y

85-y=20+y

85-20-y-y=0

65-2y

-2y=65

y=-65/-2

y=32.5

finding x by substituting y=32.5

x+y=85

x+32.5=85

x=85-32.5

x=52.5

.

To serve 24 people with turkey, carter need to spend around 18 pounds for it  when he needs to pay three quarter for each.

Carter need to serve turkey for a total of 24 members. He wants to provide three quarter of a pound of turkey for each person.

Now, we need to calculate for total members attending the event.

Calculation for total amount of turkey = Total members * Amount for each person the to be  needed

Total amount of turkey = Members x Amount per person

Total amount of turkey = 24*(3/4)

Total amount of turkey= 6*3

Total amount of turkey=18

Therefore, 18 pounds of Total amount of turkey is needed to serve the total number of 24 people. In that way carter can have enough turkey to feed every one in the group who are attending the event.

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Answer:

4.69 in

Step-by-step explanation:

By sine rule:

\( \frac{ \sin \: 23 \degree}{a} = \frac{ \sin \: 90 \degree}{12} \\ \\ \frac{ \sin \: 23 \degree}{a} = \frac{1}{12} \\ \\ a = 12 \: \sin 23 \degree \\ \\ a = 12 \times 0.3907311285 \\ \\ a = 4.68877354 \\ \\ a \approx 4.69\: in\)

Using probability concepts, it is found that:

1. P(B|A) = 0.4.

2. \(P(A \cap B) = 0.1575\)

3. B. A is true given that B is true

4. Since \(P(A \cap B) = P(A)P(B)\), they are dependent.

5. Since \(P(A \cap B) \neq P(A)P(B)\), they are independent.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

Item 1:

Applying conditional probability:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.14}{0.35} = 0.4\)

Hence, P(B|A) = 0.4.

Item 2:

\(P(A|B) = \frac{P(A \cap B)}{P(B)}\)

\(0.35 = \frac{P(A \cap B)}{0.45}\)

\(P(A \cap B) = 0.35(0.45)\)

\(P(A \cap B) = 0.1575\)

Item 3:

A is true given that B is true, hence, option B.

Item 4:

Two events, A and B, are dependent if:

\(P(A \cap B) = P(A)P(B)\)

In this problem:

\(P(A \cap B) = \frac{3}{25}\)

\(P(A)P(B) = \frac{3}{10} \times \frac{2}{5} = \frac{6}{50} = \frac{3}{25}\)

Since \(P(A \cap B) = P(A)P(B)\), they are dependent.

Item 5:

\(P(A|B) = \frac{P(A \cap B)}{P(B)}\)

\(P(A \cap B) = P(B)P(A|B)\)

\(P(A \cap B) = \frac{1}{4} \times \frac{21}{100}\)

\(P(A \cap B) = \frac{21}{400}\)

\(P(A)P(B) = \frac{7}{20} \times \frac{1}{4} = \frac{7}{80}\)

Since \(P(A \cap B) \neq P(A)P(B)\), they are independent.

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Answer:

Biotic factors of a marine ecosystem typically include algae, plankton, bacteria, seaweed, corals, fish, sharks, seals, whales, penguins and jellyfish.

Step-by-step explanation:

i hope this answer helped

Thanks for choosing brainly

Answer:

b

Step-by-step explanation:

The length of side x in simplest radical form is √3 units.

In Mathematics, Pythagorean's theorem is modeled or represented by the following mathematical equation:

c² = a² + b²

Where:

a, b, and c are the side lengths of a right-angled triangle.

By critically observing the image of the right-angled triangle, we can logically deduce that the opposite side is equal to the adjacent side (corresponding sides).

In order to determine the length of side x, we would have to apply Pythagorean's theorem.

c² = a² + b²

(√6)² = x² + x²

6 = 2x²

x² = 6/2

x² = 3

x = √3 units.

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Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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Answer:

X = 2 x − 10

 y = − 2 /x 3 − 7 /3

Step-by-step explanation:

To get this you must solve y first. There are no variables to x so find y and put it into the equation. Substitute it and find X

Answer:

x = 10, y = - 9

Step-by-step explanation:

Given the 2 equations

x = - 3y - 17 → (1)

2x + 3y = - 7 → (2)

Substitute x = - 3y - 17 into (2)

2(- 3y - 17) + 3y = - 7 ← distribute and simplify left side

- 6y - 34 + 3y = - 7

- 3y - 34 = - 7 ( add 34 to both sides )

- 3y = 27 ( divide both sides by - 3 )

y = - 9

Substitute y = - 9 into (1) for corresponding value of x

x = - 3(- 9) - 17 = 27 - 17 = 10

James has $37.67 now after all his expenses

James had $x, his brother had $y, and his sister had $z when the morning began.

By using algebra,

James's sibling had twice as much money as James.

Now, x =y/2..... (i)

James had $27 fewer dollars than his sister did.

So, x = z - 27 ........ (ii)

⇒  {From equation (1)}

⇒ y/2 = z -27

⇒ y = 2z - 54

⇒ 2z - y =54 ..........(3)

Now, James and his sister each received $12 from his brother.

James now has $(x + 12), his brother now has $(y -24), and his sister now has $(z + 12).

Given that James' sister has twice as much money as James' brother after payoff,

So, z+12/2 = y-24

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

The result of resolving equations (3) and (4) is

3y = 54 + 100 = 154

⇒ y =  51.33.

The result of equation (3) is now z = 52.67.

And from equation (1), x = 51.3/2= 25.67

So, now, James has (25.67 + 12) = $37.67

Hence, James has $37.67 now after all his expenses

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Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

Answer:

70/5 = 14 which then means it 14/1

Answer:

2

Step-by-step explanation:

.

On solving the fractional equations, the values are -

9. w = 3 2/30

10. a = 16/21

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The first fractional equation is -

5 9/10 = w + 2 5/6

Convert the mixed fractions to normal fractions -

59/10 = w + 17/6

Collect the like terms -

w = 59/10 - 17/6

w = (177 - 85) / 30

Use the arithmetic operation of subtraction and division -

w = 92/30

w = 3 2/30

The second fractional equation is -

1 1/3 = a / 1 3/4

Convert the mixed fractions to normal fractions -

4/3 = a / 7/4

Collect the like terms -

a = 4/3 × 4/7

Use the arithmetic operation of multiplication and division -

a = 16/21

Therefore, the value for w is 3 2/30 and for a is 16/21.

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The number of years that the deposit was held for is 3 years.

From the information, Mr. Johnson deposited $2000 in an account that earns simple interest at an annual interest rate of 6%. and he received $360 as interest at the end of the tenure.

It should be noted that simple interest is Illustrated as:

I = PRT

Therefore, T = Interest / Principal × Rate

Time = 360 / (2000 × 6%)

Time = 360 / 120

Time = 3 years

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Answer:

A. 2x2+8x+6

Step-by-step explanation:

two x squared plus 8x plus 6.

Answer:(5x+8)/[(x+4)(x-1)(x+3)]

Step-by-step explanation:

1. First factorize the quad expressions in the denomeneter of both fractions.

2. Then choose you arithmetic common denomeneter .

3. And the rest is child's play.

Answer:

\(f=\frac{3+4d}{3+d}\)

Step-by-step explanation:

\(d= \frac{3(1-f)}{(f-4)} \\(f-4)d=3-3f\\f-4=\frac{3-3f}{d} \\f=\frac{3-3f+4d}{d} \\f+\frac{3f}{d} =\frac{3+4d}{d} \\fd+3f=3+4d\\f(d+3)=3+4d\\f=\frac{3+4d}{3+d}\)

Based on the given information, the product should be distributed from {S}1 to the retailers located at R1, R2, R3, and R4.

To determine the most efficient distribution route, several factors need to be considered. These factors include the distance between the origin point {S}1 and each retailer, transportation costs, logistical infrastructure, and delivery timeframes. By evaluating these factors, a decision can be made regarding the optimal distribution route.

One approach could be to assess the geographical proximity of {S}1 to each retailer. If {S}1 is closest to R1 compared to the other retailers, it would make logistical sense to prioritize R1 for distribution. However, other factors such as transportation costs and delivery timeframes must also be considered. If the transportation costs are significantly higher or the delivery timeframes are longer for R1 compared to the other retailers, it might be more efficient to distribute the product to a different retailer.

Moreover, the logistical infrastructure and transportation networks available between {S}1 and the retailers should be evaluated. If there are direct and efficient transportation routes between {S}1 and one or more retailers, it would make sense to utilize those routes for distribution. This consideration would help minimize transportation costs and delivery times.

Ultimately, the decision on the optimal distribution route depends on a comprehensive analysis of various factors such as geographical proximity, transportation costs, logistical infrastructure, and delivery timeframes. By carefully evaluating these factors, a well-informed decision can be made regarding the distribution of the product from {S}1 to retailers R1, R2, R3, and R4.

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Answer:

x = 1/48

Step-by-step explanation:

3x + 2x + 1/6 - 1/4 = x

5x + 1/6 - 1/4 = x

5x + 2/12 - 3/12 = x (find a multiple by a common denominator)

5x - 1/12 = x

5x - x - 1/12 = 0

4x - 1/12 = 0

x = 1/12 / 4

x = 1 / 12×4

x = 1/48