jada make 6 cups or blueberry jam and divided the jam equally among 4 containers how much jam is in each container?

The system of linear equations, y = 2x + 4 ;

2y = x + 6 has a unique solution and it is a consistent system of linear equations.

An ordered pair that satisfies all equations of the system is the solution of the system. A system of linear equations can have one solution, no solution, or an infinite number of solutions. The systems of equations can be classified according to the number of solutions. If a system has at least one i.e unique solution, it is called consistent. We have, the system of equations is

y = 2x + 4 => 2x - y + 4 = 0 --(1)

2y = x + 2 => x - 2y + 6 = 0 --(2)

Comparing the equation (1) with a₁x + b₁y + c₁=0

and equation(2) with a₂x + b₂y + c₂=0

We get, a₁ = 2 , a₂= 1 , b₁ = -1 , c₁= 4 , b₂= -2 , c₂ = 2

Now, compute the ratio of coefficients of variables .

a₁/a₂ = 2/1 , b₁/b₂ = -1/-2 = 1/2 , c₁/c₂= 4/6 = 2/3

=> a1/a2 ≠ b1/b2 ,

here, both lines are intersect at a point and a unique solution exist for pair of linear equations. In such a case , the pair of linear equations is said to be consistent. Thus, system is consistent.

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Complete question:

Is the system of equation is consistent and

independent consistent and dependent or inconsistent?

y = 2x + 4 , 2y = x + 6

Answer:

Slope is 5

Step-by-step explanation:

if line is parallel to 5x + 10

then the slope has to be equal

y= mx+ b

m = 5

Answer:

4cm

Step-by-step explanation:

l³= 64cm³

l = ³√64 = 4cm

The conversions are as follows: a) 1101100100012 in hexadecimal is D91., b) 45678 in hexadecimal is B26E.

a) To convert the binary number 1101100100012 to hexadecimal, we can group the binary digits into groups of four from right to left. If there are any remaining digits, we can pad them with leading zeros. Then, we can convert each group of four binary digits to its corresponding hexadecimal digit. The conversion table is as follows:

Binary Hexadecimal

0000 0

0001 1

0010 2

0011 3

0100 4

0101 5

0110 6

0111 7

1000 8

1001 9

1010 A

1011 B

1100 C

1101 D

1110 E

1111 F

Now, let's convert the given binary number to hexadecimal:

1101 1001 0001

Grouping the digits into fours:

1101 1001 0001

Converting each group to hexadecimal:

D 9 1

Putting the hexadecimal digits together, we have:

1101100100012 in hexadecimal is D91.

b) To convert the decimal number 45678 to hexadecimal, we can repeatedly divide the decimal number by 16 and keep track of the remainders. The remainders will represent the hexadecimal digits.

Let's perform the division:

45678 ÷ 16 = 2854 remainder 14 (E in hexadecimal)

2854 ÷ 16 = 178 remainder 6 (6 in hexadecimal)

178 ÷ 16 = 11 remainder 2 (2 in hexadecimal)

11 ÷ 16 = 0 remainder 11 (B in hexadecimal)

Reading the remainders from bottom to top, we have:

45678 in hexadecimal is B26E.

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Usando conjuntos de Venn, se encuentra que 7 estudiantes practican solo atletismo.

Los conjuntos son:

Hay que:

La cantidad que practica ambos es:

\(A \cap B = A + B - A \cup B\)

\(A \cap B = 13 + 10 - 20\)

\(A \cap B = 3\)

Solo atletismo es:

\(B - A \cap B = 10 - 3 = 7\)

7 estudiantes practican solo atletismo.

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This question is incomplete

Complete Question

A baker uses 5.5 Ibs of flour daily

The baker's recipe for a loaf of bread calls for 12 oz of flour. If he uses all of his flour to make loaves of bread, how many loaves can he bake in seven days?

Answer:

51.3 loaves of bread

Step-by-step explanation:

Converting 5.5 Ibs to oz (ounces)

1 Ibs =>12 oz

5.5 Ibs => x

Cross Multiply

12 × 5.5 => 88 oz

1 loaf of bread =>12 oz

Hence, in 1 day

12 oz =>1 loaf of bread

88 oz => x

x =>88 oz/ 12 oz

x => 7.3333333333 loaves of bread

Hence, he can make 7.3333333333 loaves of bread in 1 day

Hence, in 7 days

1 day => 7.3333333333 loaves

7 days => x

x => 7 × 7.3333333333 loaves

x => 51.333333333 loaves of bread

Approximately => 51.3 loaves of bread

Answer:

3 meters per second

Step-by-step explanation:

all you need to do is devise 30 by 10

Answer:

Mixed Number

Step-by-step explanation:

It represents a number greater than or equal to one. Numbers that are not whole numbers, but are greater than one, can be written as improper fractions or mixed numbers. A mixed number has a whole number part and a fraction part.

Answer:

Step-by-step explanation:

so 5 feet as a width and 12 as a height meaning that it would be b 13

The weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, but using mathematical induction, the basis step works, although the inductive step fails.

a) If we try to prove the inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) using mathematical induction, we can see that the basis step works. When n = 1, we have 1/2 < 1/√3, which is true.

Now, let's consider the inductive step. Assuming that the inequality holds for some positive integer k, we need to show that it also holds for k+1, i.e., we assume 1/2 · 3/4 ··· 2k-1/2k < 1/√(3k) and we want to prove 1/2 · 3/4 ··· 2k-1/2k · (2k+1)/(2k+2) < 1/√(3k+3).

If we attempt to manipulate the expression, we can simplify it to (2k+1)/(2k+2) < 1/√(3k+3). However, we cannot proceed further to prove this inequality, as it is not necessarily true. Therefore, the inductive step fails, and we cannot establish the original inequality using mathematical induction.

b) However, mathematical induction can still be used to prove the stronger inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n+1) for all integers greater than 1. We can start by verifying the case where n = 1, which gives us 1/2 < 1/√4, which is true.

Now, assuming the inequality holds for some integer k, we can multiply both sides of the inequality by (2k+3)/(2k+2) to get:

(1/2 · 3/4 ··· 2k-1/2k) · (2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

Simplifying the expression on both sides, we have:

(2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

We can observe that the right side of the inequality is less than 1/√(3k+3) by multiplying the denominator of the right side by (2k+3)/(2k+3). Hence, we obtain:

(2k+3)/(2k+2) < 1/√(3k+3).

This establishes the inequality for k+1, and thus, we have proven the stronger inequality using mathematical induction.

By verifying the case where n = 1 separately, we can conclude that the weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, as it follows from the proven stronger inequality using mathematical induction.

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Congruent Triangles

Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus, two triangles can be superimposed side to side and angle to angle.

The definite integral in this problem has the value given as follows:

B. 42.

The definite integral in the context of this problem is given as follows:

\(\int_0^2 (x^7 + 5) dx\)

Applying the power of x integral rule, the result of the integral is given as follows:

\(\frac{x^8}{8} + 5x\)

At x = 2, the numeric value of the integral is given as follows:

\(\frac{2^8}{8} + 5(2) = 42\)

At x = 0, the numeric value of the integral is given as follows:

0.

(as both terms involve a multiplication by x and x = 0).

Applying the Fundamental Theorem of Calculus, the result of the integral is given as follows:

42 - 0 = 42.

Hence option B is the correct option in the context of this problem.

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Answer: discrete

Step-by-step explanation:

The graph would be discrete, because you can only order a whole number of pizzas. This means you cannot have 0.4 of a pizza or 3/5 of a pizza. Therefore, p can only be whole numbers, so you cannot draw a line through the points, since prices for non-whole pizzas are not possible.  

Answer:

The probability that the individual has the disease is 1/500

Step-by-step explanation:

i found the fraction of 1 in 500 which is 1/500, hope this helps :)

When m = 16, the value of P is 18, given that P is inversely proportional to m and P = 36 when m = 8.

When we say that P is inversely proportional to m, it means that as one variable increases, the other variable decreases, and the product of the two variables remains constant. Mathematically, we can express this relationship using the formula P = k/m, where k is a constant of proportionality.

In the given problem, we are given the initial condition that P = 36 when m = 8. We can use this condition to solve for the constant of proportionality k by substituting the values of P and m into the formula:

36 = k/8

Solving for k, we get:

k = 288

Now that we know the value of k, we can use it to find the value of P when m = 16:

P = k/m

P = 288/16

P = 18

Therefore, when m = 16, P has a value of 18.

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Answer:

256, 64, 16, 4

You are dividing 4 each time for your rule.

64/4 = 16

16/4 = 4

4/4 = 1

1/4 = 0.25

0.25/4 = 0.0625

2 , 6 , 18, 54

You are multiplying 3 each time for your rule.

6 x 3 = 18

18 x 3 = 54

54 x 3 = 162

162 x 3 = 486

486 x 3 = 1458

Answer:

20.4% is the percent discount

Step-by-step explanation:

First, subtract your retail price from the discounted purchase price ($98-$78). You get $20 off.

Then take your $ off and put that over the retail price, then multiply that times 100 (20/98=.20408163 then times it by 100 to get 20.4)

tadaaaa

Answer:

4

Step-by-step explanation:

Answer:

2 and 3

Step-by-step explanation:

consider perfect cubes either side of 23

8 < 23 < 27 , then

\(\sqrt[3]{8}\) < \(\sqrt[3]{23}\) < \(\sqrt[3]{27}\) , that is

2 < \(\sqrt[3]{23}\) < 3

Answer:

It tells you that 1000g are in 1 kg. All you need to do is convert your 15 kg to 15000 g.

Answer:

Step-by-step explanation:

1 kg = 1000 g

15 Kg = 15 *1000 = 15000 g

7.75 g = 1 cm³

1 g = 1 ÷ 7.75 cm³

15000 g = \(\frac{1}{7.75}*15000 = 1935.48\)

              = 1935 cm³

Inner diameter = 6 cm

Inner radius = r = 6/2 = 3 cm

Outer radius = R = inner radius  + thickness

  R = 3 + 2 = 5 cm

Volume of cylindrical pipe = 1935 cm³

\(\pi h*(R +r)(R - r) = 1935\\\\3.14 * h *( 5 + 3)(5 - 3) = 1935 \\\\3.14 * h * 8 *2=1935\\\\h = \frac{1935}{3.14*8*2}\\\\h = 38.52 = 39\)

h = 39 cm

Answer:

The repetition intensifies the speaker's sense of urgency.

Step-by-step explanation:

Answer:

D The repetition intensifies the speaker’s sense of urgency.

Step-by-step explanation:

The repetition intensifies the speaker’s sense of urgency.

The joint probability mass function (PMF) for the random variables x and y can be represented in a table with rows and columns corresponding to the possible values of x and y, respectively.

In this case, x represents the number of heads on the first toss, and y represents the total number of heads over all three tosses. There are two possible outcomes for each coin toss: heads (H) or tails (T). Thus, there are 2^3 = 8 possible outcomes for three coin tosses, which can be listed as follows: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. For the first toss, there are two possible outcomes: H or T. Thus, x can take on the values x = 0 or x = 1, with probabilities P(x = 0) = 1/2 and P(x = 1) = 1/2.

For the total number of heads over all three tosses, there are four possible outcomes: 0, 1, 2, or 3 heads. The joint probabilities can be calculated by considering the possible outcomes for each value of x. For example, if x = 0 (i.e., the first toss is a tail), then y can only be 0 or 1, depending on the outcomes of the second and third tosses. The probabilities of these outcomes are P(x = 0, y = 0) = 1/8 and P(x = 0, y = 1) = 3/8. The joint probability mass function for x and y can be summarized in a table as follows:

y=0 y=1 y=2 y=3

x=0 1/8 3/8 3/8 1/8

x=1 1/8 3/8 3/8 1/8

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Answer: \(\frac{7\sqrt{3}}{2}\)

Step-by-step explanation:

\(\sin 60^{\circ}=\frac{x}{7}\\\\\frac{\sqrt{3}}{2}=\frac{x}{7}\\\\x=\frac{7\sqrt{3}}{2}\)

Answer:

A and C are functions.

The domain is x and the range is y

Step-by-step explanation:

Each x - value can have only one y -value

Function= unique x-values

Y can be the same answer but the X has to be different

Answer:

commutative property

Step-by-step explanation:

because commutative property states that a+b=b+a and a x b=b x a

Answer:

13

Step-by-step explanation:

\(f(x) = 5 \sqrt{x} + 8 \\ f(1) = 5 \sqrt{1} + 8 \\13\)

Hope this helps..

Answer:

The domain is: (-∞,∞)

The range is: (0,∞)

Step-by-step explanation:

Answer:

The domain of y = x2 is

✔ all real numbers

The range of y = x2 is

✔ y >= 0

Step-by-step explanation: Hope this helps!

Answer:

B=12

Step-by-step explanation:

I did the math.

There are 364 different committees of 3 people. There are 436 different committees of 4 people.

There are different scenarios for which we can calculate the number of possible committees. Here are a few examples:

To calculate the number of different committees of 3 people, we can use the combination formula, which is:

\(${n \choose k} = \frac{n!}{k!(n-k)!}$\)

where n is the total number of people and k is the number of people needed for the committee. Using this formula, we get:

\(${14 \choose 3} = \frac{14!}{3!(14-3)!} = \frac{14!}{3!11!} = 364$\)

Therefore, there are 364 different committees of 3 people that can be formed from this group.

To solve this problem, we can use the principle of inclusion-exclusion. First, we calculate the total number of committees of 4 people, which is:

\(${14 \choose 4} = \frac{14!}{4!(14-4)!} = \frac{14!}{4!10!} = 1001$\)

Next, we calculate the number of committees that do not include a freshman, which is:

\(${12 \choose 4} = \frac{12!}{4!(12-4)!} = \frac{12!}{4!8!} = 495$\)

Similarly, we calculate the number of committees that do not include a sophomore, a junior, and a senior, which are:

\(${11 \choose 4} = \frac{11!}{4!(11-4)!} = \frac{11!}{4!7!} = 330$\)

\(${10 \choose 4} = \frac{10!}{4!(10-4)!} = \frac{10!}{4!6!} = 210$\)

\(${9 \choose 4} = \frac{9!}{4!(9-4)!} = \frac{9!}{4!5!} = 126$\)

Now we can apply the principle of inclusion-exclusion, which is:

Total number of committees - (number of committees without a freshman + number of committees without a sophomore + number of committees without a junior + number of committees without a senior) + (number of committees without a freshman and without a sophomore + number of committees without a freshman and without a junior + number of committees without a freshman and without a senior + number of committees without a sophomore and without a junior + number of committees without a sophomore and without a senior + number of committees without a junior and without a senior) - number of committees without any freshmen, sophomores, juniors, or seniors.

Plugging in the values, we get:

$1001 - (495 + 330 + 210 + 126) + (66 + 120 + 165 + 84 + 55 + 35) - 1 = 436$

Therefore, there are 436 different committees of 4 people that can be formed, with at least one person from each grade level.

Note that for the last step, we subtracted 1 because there is only one committee that has no freshmen, sophomores, juniors, or seniors.

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The original cost of the cereal box is $5.00 → this represents a 100% of the price

You saved $2.00 by using a coupon, to determine the % of discount this coupon represents you can use cross multiplication:

If $5 represents 100%

$2 represents x%

Where:

The coupon represented a 40% discount on the cereal box.