Melissa and Joey enjoyed dinner at a restaurant. They paid the waiter $100.50 plus a 20% tip. How much did each person pay if they split the total bill in half?

Here, we know that 1 pint = 2 cups

Thus, 1 cup = [tex] \frac{1 pints}{2} [/tex]

3 ponds apples are needed for 4 cups i.e. 3 ponds of apples = 4 cups of applesauce

1 cup of applesauce = [tex] \frac{3 ponds}{4} [/tex]

Now, 6 pints will have 12 cups of applesauce

Multiplying this equation by 12 ⇒ 1 cup of applesauce = [tex] \frac{3 ponds}{4} [/tex]

12 ×1 cup of applesauce = 12 × [tex] \frac{3 ponds}{4} [/tex]

So, 12 cups of applesauce = 9 ponds of apple.

Thus, 9 ponds of apple will be needed to make 6 pints of applesauce.

Following are the calculation to the given equation:

Given:

[tex]\to \frac{1}{4}(8x+56)=20[/tex]

To find:

x=?

Solution:

[tex]\to \frac{1}{4}(8x+56)=20\\\\\to \frac{8x}{4} + \frac{56}{4}=20\\\\\to 2x + 14=20\\\\\to 2x = 20-14\\\\\to 2x= 6\\\\\to x=\frac{6}{2}\\\\\to x= 3[/tex]

Therefore, the final answer is "3".

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Answer:[tex]8x^{8}[/tex]

Step-by-step explanation:

When multiplying two numbers with exponents you adding the exponents

[tex](x^{m} )(x^{n} )=x^{m+n}[/tex]

[tex]\sqrt{64x^{16} }[/tex] = [tex]\sqrt{64x^{8+8} }[/tex] = [tex]\sqrt{8(8)(x^{8}) (x^{8} )}[/tex] =8[tex]x^{8}[/tex]

Answer: In an observational study, researchers do not control treatment, and in an experiment they do .

Step-by-step explanation:

Observational study is the study where the researcher observes the subjects and measures variables, but does not influence the population where as in an experiment the experimenter has control on the independent variable to see the effect on the dependent variable.

So the correct difference between an observational study and an experiment is that "in an observational study, researchers do not control treatment, and in an experiment they do."

Answer:

B on EDG

Step-by-step explanation:

Final answer:

Avenue A is perpendicular to North Street, and it would also be perpendicular to South Street since they run parallel. The concept of vector components Ax and Ay, being perpendicular and analogous to these streets, helps illustrate the perpendicular relationship between Avenue A and South Street.

Explanation:

Given that Avenue A is perpendicular to North Street, we can infer that Avenue A is also perpendicular to South Street because in a typical city grid, north and south streets run parallel to each other. When two lines are perpendicular to a third line, they are parallel to each other and form a 90° angle with the perpendicular line.

The relationships among vectors can help further illustrate this idea. If we look at the components of a vector, Ax and Ay, where Ax is the movement in the east-west direction (like Avenue A) and Ay is the movement in the north-south direction (like North Street), they form a right angle with each other. If you walk along Avenue A (the Ax component), then along North Street (the Ay component), you construct a path that is the resultant vector A with its own magnitude and direction.

The sum of these vectors is represented as Ax + Ay = A. This combination holds only for vector quantities, which include both magnitude and direction. This principle does not apply when we're summing up the magnitudes alone, as in the example where if Ax is 3 m east and Ay is 4 m north, the direct path A would not simply be their sum in magnitudes but would instead be a diagonal 5 m northeast according to the Pythagorean theorem.

Answer:

a, the first graph

Step-by-step explanation:

The probability distribution represents the likelihood of each possible value of a random variable. In this case, the random variable X represents the number of times red is spun. The graph that represents this probability distribution would have the values 0, 9/33, and 24/33 plotted for X=0, X=1, and X=2.

The probability distribution represents the likelihood of each possible value of a random variable. In this case, the random variable X represents the number of times red is spun. The sample space S consists of nine outcomes with one red spin and twenty-four outcomes with two red spins.

To find the probability distribution, we calculate the probability of each possible value of X. The probability of X=0 (no red spins) is 0, the probability of X=1 (one red spin) is 9/33, and the probability of X=2 (two red spins) is 24/33.

The graph that represents this probability distribution would have the values 0, 9/33, and 24/33 plotted on the y-axis for the corresponding values of X=0, X=1, and X=2 on the x-axis.

Answer:

B) 68

Step-by-step explanation:

56*2=112

180-112=68.

Answer:

Use a double-sided coin and assign heads as females and tails as males.

Step-by-step explanation:

I did the I-Ready lesson.

When dealing with null coefficient terms in mathematics or chemistry, they can be a tool to simplify calculations. Replacing zero coefficients with a positive approximation or selecting rows with zeroes in matrices can ease the process. Always verify solutions by substituting them back into the original equations to ensure correctness.

When you encounter situations where there are no matching coefficients in your algebraic equations, it is important to look for null coefficient terms. Such terms can help simplify the computations. For instance, if you are working on balancing chemical equations or solving systems of equations, and one of the coefficients is zero, this can be advantageous because multiplying by zero is a straight-forward operation.

If a coefficient equals zero, like one in a characteristic equation, replace it with a positive quantity approaching zero from the right-hand side. Continue with the analysis after this adjustment. Additionally, when working with matrices, selecting a row with zeros as the coefficient row can simplify the process of expansion by minors since some minors will not need to be computed and can just be multiplied by the zero coefficient.

In the case of balancing equations in chemistry or optimizing coefficients in a mathematical model, practice and a methodical approach are necessary. Make sure to double-check your computations and if you are unsure about the correctness of your solution, substitute it back into the original equation.

The required √5 on the number line is shown in the image attached.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here

To locate √5 on a number line, we can begin by locating the integers that √5 lies between. We know that 2² = 4 and 3² = 9, so √5 must be between 2 and 3.

To get a more accurate estimate, we can divide the distance between 2 and 3 into 10 equal parts (tenths). Each tenth represents 0.1 units on the number line. We know that 0.5 is halfway between 0 and 1, so √5 must be a little more than halfway between 2 and 3.

By estimating the position of √5 on the number line, we can approximate it as being around 2.2 to 2.3.

Thus, the required √5 is shown in the image attached.

Learn more about number line here:

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Final answer:

The probability that no girls and 3 boys will be chosen is 1/55 or approximately 1.82%.

Explanation:

To find the probability that no girls and 3 boys will be chosen, we need to determine the total number of possible outcomes and the number of favorable outcomes.

There are a total of 12 children (8 girls + 4 boys) in the family. Since 3 children are being chosen, the total number of possible outcomes is the combination of 12 children taken 3 at a time, which is denoted as C(12, 3) = 220.

The number of favorable outcomes is choosing 3 boys from the 4 available boys, which is denoted as C(4, 3) = 4.

Therefore, the probability of choosing no girls and 3 boys is 4/220 = 1/55, which can be reduced to approximately 0.0182 or 1.82%.

The probability stated as P(blue) = 1/4 illustrates theoretical probability, which is determined by the number of favorable outcomes divided by the total number of outcomes without the need for any experiment or past data.

The type of probability illustrated by the statement "A jar contains blue, red, yellow, and green marbles with P(blue) = 1/4" is theoretical probability. This is because the probability value is based on the known possible outcomes and the assumption that each outcome has an equal chance of occurring. For example, if a bag contains four green marbles, three red marbles, and two yellow marbles, the theoretical probability of drawing a yellow marble followed by a green marble without replacement would be calculated using the number of ways these events can happen divided by the total number of outcomes.

Theoretical probability does not require experimental results or past data and is often used in problems involving equally likely events, such as drawing marbles from a jar or flipping a fair coin. In contrast, experimental probability is based on the frequency of an event happening from trials or experiments. In the given example with the jar of marbles, we assume that each marble color is equally likely to be drawn.

To know if 2 triangles are similar, we would need at least 2 angles, why?

Since a triangle has 3 angles, and those angles add up to 180°, we can easily determine the third angle.

Example: If 2 angles of a triangle were 13 and 97, we would know that 13 + 97 = 110, then 180° - 110° = 70°, so the missing angle is worth 70°.

Hope this helped! c:

Answer:

B. Kendra should have divided by 2 instead of multiplying by 2 in the denominator.

Step-by-step explanation:

In Kendra’s class, 40 percent of the students earned an A on the math test.

Let the total students in the class be = x

So, as per the situation given, we can say that

[tex]0.40\times x=20[/tex]

x = 50

Hence, there are 50 students in the class.

We can cross check this as:

[tex]0.4\times50=20[/tex]

So, Kendra surely did a mistake.

Kendra should have divided 100 by 2. But she multiplied by 2.