A group of 7 friends is planning a hike. Each friend will need of a gallon of water to drink during the hike. How many gallons of water will the group need for the hike? ​

Given, that the volume of the cube is 3375 cubic inches.

The formula of the volume of the cube is,

Replacing the given volume into the above formula we get,

Hence, the correct option is option B.

Answer:

A decimal that never ends is called A repeating decimal or recurring decimal

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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The simplified version of the expression would be 31-w

The numerical part of the expression given is :

Simplifying using Subtraction operation:

Adding the alphabetical part :

Therefore, the simplified form of the expression is 31-w.

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When Kayla was instructed to rewrite the polynomial expression x2 + 6x + 9, she wrote \(x^2+2 x-3+3^2=(x+3)^2\).

Factor \($ x^2+6 x+9: \quad(x+3)^2$\)

\($$x^2+6 x+9$$\)

Rephrase in the manner of \($a^2+2 a b+b^2$\) :

\($9=3^2$\)

\($6 x=2 x \cdot 3$\\$=x^2+2 x \cdot 3+3^2$\)

Using the Perfect Square Formula : \($\quad a^2+2 a b+b^2=(a+b)^2$\)

\($$\begin{aligned}& x^2+2 x-3+3^2=(x+3)^2 \\& =(x+3)^2\end{aligned}$$\)

An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial. x2 4x + 7 is an illustration of a polynomial of one uncertain x.

An expression with a single or a number of terms is referred to as a polynomial. The words "polynomial" and "nomial," which are two distinct phrases, are the origins of the term. Nominal is another word for many, while poly is another word for many. An algebraic expression with two or more algebraic terms is referred to as a polynomial.

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Answer:

-11-(-5)= -6

25-(-3)= 28

-7-(-2)= -5

4-15= -11

6-(-9)= 15

Answer:

3) 3 3/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.

For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.

Point of view:

Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!

:)

To produce 60 liters of a 55% acid solution, we need 18 liters of a 50% acid solution and 42 liters of a 60% acid solution.

Let x be the number of liters of the 50% acid solution needed, and y be the number of liters of the 60% acid solution needed.

We can set up two equations based on the amount of acid and the total volume:

0.50x + 0.60y = 0.55(60)

x + y = 60

Simplifying the first equation:

0.50x + 0.60y = 33

5x + 6y = 330 (multiplying both sides by 10)

We can solve for one variable in terms of the other in the second equation, and substitute into the first equation:

y = 60 - x

5x + 6(60 - x) = 330

Simplifying:

x = 18

So we need 18 liters of the 50% acid solution, and:

y = 60 - x = 42

So we need 42 liters of the 60% acid solution.

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Answer:

Step-by-step explanation:

seventy-thousand I believe.

Answer:

Step-by-step explanation:

From the given information:

The number of children that were randomly allocated to each vaccination group; n₁ = 200,000

No of polio cases X₁ = 57

Now, in the vaccine group:

the proportion of polio cases is:

\(\hat p_1 = \dfrac{57}{200000}\)

=  0.000285

The number of children that were randomly allocated to the placebo group, n₂ = 200,000

No of polio cases X₂ = 142

In the placebo group

the proportion of polio cases is:

\(\hat p_2 = \dfrac{142}{200000}\)

Null and alternative hypothesis is computed as follows:

H₀: There is no difference in the proportions of polio cases between both groups.  

H₁: There is a difference in the proportions of polio cases between both groups.

Let assume that the level of significance ∝ = 0.05

The test statistic  can be computed as:

\(Z = \dfrac{\hat p_1-\hat p_2}{\sqrt{\dfrac{\hat p_1 \hat q_1}{n_1}+ \dfrac{\hat p_2 \hat q_2}{n_2}}}\)

\(Z = \dfrac{0.000285-0.000710}{\sqrt{\dfrac{0.000285(1-0.000285)}{200000}+ \dfrac{0.000710(1-0.000710)}{200000}}}\)

\(Z = \dfrac{-4.25\times 10^{-4}}{\sqrt{\dfrac{0.000285(0.999715)}{200000}+ \dfrac{0.000710(0.99929)}{200000}}}\)

Z = - 6.03

P-value =  2P(Z < -6.03)

From the Z - tables

P-value =  2 × 0.0000

= 0.000

We reject the H₀ provided that P-value is very less.

Therefore, we may conclude that there is a difference in the proportions of polio cases between the vaccine group and placebo group not due to chance.

The number of customers that got a cofee is 50.

We know that the cafe had 125 customers, of these 125 customers 40% got a cofee.

Then we need to find the 40% of 125, to get that we need to take the product between 40% (in decimal form, this is 40%/100% = 0.4) and the number of customers, which is 125.

Then the number of customers that got a coffee is:

N = 0.4*125 = 50

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Answer: 80:120

Step-by-step explanation:

hi <3

2 + 3 = 5

200/5 = 40

2 x 40 = 80

3 x 40 = 120

sita gets 80 and geeta gets 120

hope this helps :)

Answer:

4th option

Step-by-step explanation:

The points R', S', T', U' are obtained by a reflection in the line y = - 3

This is a horizontal line passing through all points with a y- coordinate of - 3

RSTU and R'S'T'U' are equidistant from this line

Answer:

41.93 degrees

Step-by-step explanation:

Answer:

23816

Step-by-step explanation:

Hope this helps you

The differential equation representing the model of the number of words memorized by the students is equal to option C. dL/dt = k(100 - L).

Let us consider function 'L' represents the number of words memorized at time 't'

Total number of words students asked to memorized = 100 words

Rate of change of number of words with time 't' is equal to ( dL/dt )

Number of words left to memorized by the students = 100 - L

Differential equation representing the situation is

= Rate of change of number of words memorized ∝ number of words left to memorized

= dL/dt ∝ ( 100 - L )

⇒ dL/dt = k( 100 - L )

Where 'k' is the constant of proportionality .

k is a positive number.

Therefore, the differential equation representing the situation of memorizing word is given by option c. dL/dt = k( 100 - L ).

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The above question is incomplete, the complete question is:

Students are asked to memorize a list of 100 words. The students are given periodic quizzes to see how many words they have memorized. The function L gives the number of words memorized at time t. The rate of change of the number of words memorized is proportional to the number of words left to be memorized.

1. Which of the following differential equations could be used to model this situation, where k is a positive constant?

A. dL/dt = kL

B. dL/dt = 100 - kL

C. dL/dt = k(100 - L)

D. dL/dt = kL - 100

Answer: -1

Step-by-step explanation:

Evaluate 4x if x = -1/4

4(-1/4) = -1

Answer: -1

Step-by-step explanation:

4x and x = -1/4

plug x into the expression

\(4(-\frac{1}{4} )\)

simplifies to:

\(-\frac{4}{4}\)

4 divided by 4 is just 1, but it is negative so your final answer is

-1

The input (x) that satisfies the condition of being multiplied by 6 and then Subtracted by 80 to give the same value as the output is 16.

The input as "x." According to the given information, the input (x) is multiplied by 6 and then subtracted by 80, resulting in the output. In mathematical terms, this can be expressed as:

Output = (6 * x) - 80

The problem states that the input and output are the same. Therefore, we can set up the equation:

x = (6 * x) - 80

To solve for x, we'll rearrange the equation and isolate the variable:

x - 6 * x = -80

Combine like terms:

-5 * x = -80

Divide both sides by -5:

x = (-80) / (-5)

Simplifying the division:

x = 16

Hence, the input (x) that satisfies the condition of being multiplied by 6 and then subtracted by 80 to give the same value as the output is 16.

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Step-by-step explanation:

1. 27

2. 15

3. 22

Answer:

v = 13.5m/sec

Step-by-step explanation:

v = u + at

u = 3m/s

a = 1.5m/s^2

t = 7 sec

v = 3 + 1.5×7

v = 3 + 10.5

v = 13.5m/s

Answer:

\(12\pi\)

Step-by-step explanation:

\(L=\frac{\pi (120)(18)}{180} =\frac{2160\pi }{180}= 12\pi\)

Hope this helps

1.6 ounces of tin does the bar contain.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Bronze is an alloy of tin and copper combined at a ratio of 8:2.

i.e., Ratio = tin : Copper= 8:2

let the common ratio be x.

So, tin = 8x and Copper= 2x

We have Bronze = 2 ounces then the amount tin the bar contain

= 8/10 x 2

= 0.8 x 2

= 1.6 ounce

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Let's denote the quantities of each type of cookie sold by:

• A = # of chocolate chip cookies,

• B = # of sugar cookies,

• C = # of peanut butter cookies.

From the statement, we know that:

• Bod sold five times as many chocolate chips as peanut butter: A = 5C,

• Bod sold seven fewer sugar than chocolate chip: B = A - 7,

• Bod sold 9 peanut butter cookies: C = 9,

Replacing the value C = 9 in the equation of A we find that: A = 5 * 9 = 45.

Replacing the value A = 45 in the equation of B we find that: B = 45 - 7 = 38.

Answer

• Bod sold A = 45 butter cookies,

• Bod sold B = 38 sugar cookies,

• Bod sold C = 9 peanut butter cookies.

Answer:

Eduardo will get $4.03

Step-by-step explanation:

To solve this problem, first add 4.99 and 0.98 together, remember to line up the decimals

4.99

+ 0.98

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

5.97

Now take 5.97 from 10.00

first you can't take 7 from 0 so you take 1 from the tens place making 10.00 into 9.9 10, now you can take 7 from 10 which equals 3. Into the tenths place you can take 9 from 9 which is a 0. Lastly 9 - 5 is 4, adding the decimal back you get

10.00

- 05.97

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

$ 4.03

The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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The set of side measurement could be used to form a triangle is option(4) 7, 12 and 18

If the sides of the triangles are a, b and c. There will be three condition

a + b > c

b + c > a

c + a > b

We have to check these condition

Part 1

The sides are 3, 5 and 7

3 + 5 > 11

8 < 11

It does not form a triangle

Part 2

The sides are 4, 18 and 23

4+18 >23

22 < 23

It does not form a triangle

Part 3

The sides are 5, 9 and 14

5+9 > 14

14 = 14

It does not form a triangle

Part 4

The sides are 7, 12 and 18

7+12 > 18

19 > 18

12 + 18 > 7

30 > 7

7+18 > 12

25 > 12

It forms a triangle

Hence, the set of side measurement could be used to form a triangle is option(4) 7, 12 and 18

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