bob, mary, and jen go to dinner. each orders a different meal. the waiter forgets who ordered which meal, so he randomly places the meals before the three diners. let c be the event that a diner gets the correct meal and let n be the event that a diner gets an incorrect meal. enumerate the sample space and then find the probability that:

Step-by-step explanation:

Since it's a right triangle, you can use Pythagoras

a^2 + b^2 = c^2

We have b and c, we just need a, so let's plug it in

\( {x}^{2} + {24}^{2} = {25}^{2} \)

\( {x}^{2} + 576 = 625\)

\( {x}^{2} = 49\)

\(x = 7\)

Answer: 7ft

Step-by-step explanation:

hypotenuse (h) = 25

perpendicular (p) = 24

base (b) = ?

We know by using Pythagoras theorem

b = √h² - p²

= √ 25² - 24²

= √ 49

= 7 ft

Answer: y - 6 = -(1/2)(x+1)

Step-by-step explanation:

1. First step is to remember point slope form (a common way of expressing the equation for a line).

y - y1 = m(x - x1)

2. Next fill in the data we are given.

y - 6 = m(x -(-1)) ----> y - 6 = m(x + 1)

3. Next step is to find the value of the slope (m) using slope formula.

m = (y2 - y1) / (x2 - x1)

4. Fill in the data

m = (5 - 6) / (1 +1) = - 1 /2

5. Add the calculated slope to the point slope form.

y - 6 = -(1/2)(x+1)

Answer:

Step-by-step explanation:

\(tan^2 \theta+1=-2 \tan \theta \\tan^2 \theta +2 tan \theta +1=0\\(tan \theta+1)^2=0\\tan \theta=-1=-tan 45=tan (360-45)=tan 315\\\theta =315 ^\circ\)

Answer:

0.02

infinete 0.0222222222

Step-by-step explanation:

or 45

The  rate of change of Wayne's hours of sleep with respect to each day is  5  hours per day.

The rate of change of Wayne's hours of sleep with respect to each day is calculated as follows;

Mathematically, the formula is given as;

rate of change of sleep = change in sleep / change in time of sleep

The change in the sleep pattern = 30 - 15 = 15 hours

The change in the time of sleep = 6 - 3 = 3 days

The  rate of change of Wayne's hours of sleep with respect to each day is calculated as

rate of change of sleep = ( 15 hours ) / ( 3 days )

rate of change of sleep = 5  hours per day

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Answer: 38

Step-by-step explanation:

Subtract 1/8 from 1/2

12 - 18 is 38.

Steps for subtracting fractions

Find the least common denominator or LCM of the two denominators:

LCM of 2 and 8 is 8

Next, find the equivalent fraction of both fractional numbers with denominator 8

For the 1st fraction, since 2 × 4 = 8,

12 = 1 × 42 × 4 = 48

Likewise, for the 2nd fraction, since 8 × 1 = 8,

18 = 1 × 18 × 1 = 18

Subtract the two like fractions:

48 - 18 = 4 - 18 = 38

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

3,8,11

Step-by-step explanation:

if line d was parallel there might be more but it is not so the only ones that are congruent are 3,8 and 11

Answer:

69.8°

Step-by-step explanation:

Since cosФ = -0.3456

Ф = cos⁻¹(-0.3456)

Ф = 110.2°

Since the angles are supplementary, let the acute angle be x

So, x + 110.2° = 180°

x = 180° - 110.2°

x = 69.8°

The game was originally priced at £48, but after a \(\frac{1}{3}\) decrease in price, it was reduced to £32.

To solve this problem, we need to work backwards from the reduced price of £32 to determine the original price of the game before the decrease.
If the game was reduced in price by \(\frac{1}{3}\), then this means that the new price is \(\frac{2}{3}\) of the original price.
We can set up an equation to represent this relationship:
\(\frac{2}{3} x = 32\)
To solve for \(x\) (the original price), we can multiply both sides of the equation by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\):
\(\frac{3}{2}\) × \(\frac{2}{3} x\) = \(\frac{3}{2}\) × \(32\)
\(x = 48\)
Therefore, the original price of the game was £48.

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Answer:

p = -7/4 or -1 3/4

Step-by-step explanation:

-1 23/40 = 9/10p

-1 23/40 = -63/40

So, our equation is

-63/40 = 9/10p

Divided both sides by 9/10

p = -7/4

So, the answer is

p = -7/4

or

-1 3/4

The percentage of all patients who took the test had a true negative result is given as follows:

18%.

Two parameters are used to calculate a percentage, as follows:

The proportion is given by the number of desired outcomes divided by the number of total outcomes, while the percentage is the proportion multiplied by 100%.

For the true negative tests, we have those are the people that tested negative and did not have the disease, hence the percentage is given as follows:

18%.

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Answer:

-2+i

Step-by-step explanation:

-7+4i represents (-7,4) and 3-2i represents (3,-2).

So, the midpoint is (-2,1), which represents -2+i.

Answer: its a little blurry not to be rood :c

Step-by-step explanation:

There are 5354 people were in the arena.

Percentage:

The term percentage is referred as a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

The formula for calculating the percentage is,

Percentage = (Actual value/Total value) x 100

Given,

Here we have that, 4550 men in the arena comprised 85% of the people in the arena.

Now we need to find how many people were in the arena.

Let p be the number of people in Arena.

So, based on the percentage formula,

It can be written as,

=> 85% = (4550 / p) x 100

=> 85/100 = 4550 /p

=> 0.85 = 4550/p

=> 4550/0.85 = p

=> p = 5354

Therefore, there are 5354 people were in the arena.

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The test statistic is approximately -2.03.

To calculate the test statistic, we can use the one-sample t-test formula:

t = (x - μ) / (s / √n)

Where:

x is the sample mean,

μ is the hypothesized population mean,

s is the sample standard deviation,

n is the sample size.

In this case, we have:

x = 44.3 (sample mean)

μ = 44.6 (hypothesized population mean)

s = 1.01 (sample standard deviation)

n = 46 (sample size)

Plugging in the values, we can calculate the test statistic:

t = (44.3 - 44.6) / (1.01 / √46)

= -0.3 / (1.01 / √46)

= -0.3 / (1.01 / 6.782)

≈ -0.3 / 0.148

Rounding to 2 decimal places, the test statistic is approximately -2.03.

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Complete question =

Testing:

H0:μ=44.6

H1:μ<44.6

Your sample consists of 46 subjects, with a mean of 44.3 and standard deviation of 1.01.

Calculate the test statistic, rounded to 2 decimal places.

Answer:

11.03

Step-by-step explanation:

To find this answer, you would need to find how many miles 1 gallon of gas will take them. To find this, you would do 290÷8=36.25. So with this information, you will be able to find out how much gas it would take to travel 400 miles. You would do 400÷36.25=11.03. 11.03 would be how many gallons of gas is used to travel 400 miles.

The centre line of a control chart is calculated by computing the average (mean) of the data for every period.

In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.

The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.

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Answer:

i think its -10

Step-by-step explanation:

hope im not wrong

The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.

This is referred to as a quadrilateral which has four right angles and the area is calculated by multiplying the length with the breadth.

In as situation where the algebra tile rectangles is used , it is best to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 8cm and the breadth is 5cm then the area will be  8cm × 5cm = 40cm²

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We are 92% confident that the true population proportion of Americans who support legalizing marijuana is between 0.61 and 0.65. Therefore, option B. is correct.

To construct a 92% confidence interval for the true population proportion of Americans who support legalizing marijuana, we need to follow these steps:

1. Calculate the sample proportion (p):
p = (number of people in favor) / (total number surveyed)

= 1147 / 1821 ≈ 0.6298

2. Determine the critical value (z*) for a 92% confidence interval using a standard normal (z) table or calculator. In this case, z* ≈ 1.75.

3. Calculate the margin of error (ME):
ME \(=z^{*} \times \sqrt{\frac{p \times(1-p)}{n}}\)

≈ \(1.75 \times \sqrt{[(0.6298 \times (1 - 0.6298)) / 1821]}\) ≈ 0.0198

4. Construct the confidence interval:
Lower bound = p - ME ≈ 0.6298 - 0.0198 ≈ 0.61
Upper bound = p + ME ≈ 0.6298 + 0.0198 ≈ 0.65

So, the 92% confidence interval for the true population proportion of Americans who support legalizing marijuana is between 0.61 and 0.65 (rounded to 2 decimal places).

Answer: B. We are 92% confident that the true population proportion of Americans who support legalizing marijuana is between .61 and .65.

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Answer:

C(x) = 25 + 2x

Step-by-step explanation:

He already has 25 cards.

He is collecting 2 cards per month. In x months, he will have collected:

2 * x = 2x cards

That means that the number of cards he will have after x months will be the sum of the cards he already has and the cards he collects per month:

C(x) = 25 + 2x

The percentage of ball that hit into the outfield would be represented by the equation = 15/8 = X/100. That is A.

The total number of balls that that where present at the battling practice by Alexis = 15.

The number of balls that hit into the outfield = 8

The number of balls that hit outside the outfield = 15-8= 7

The percentage (x) of the balls that are outside the outfield;

X = 8/15 × 100/1

x ×15 = 8 × 100

15/8 = X/100.

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Amy's grade in a sociology course is to be determined by averaging her four test grades. Amy scored 86, 88, and 90 on the first three tests, respectively.

The sum of the first three scores Amy obtained in her tests is 86 + 88 + 90 = 264.

To figure out what grade she requires to receive on the fourth test to maintain an average grade of B or higher,

we must first identify what a B is. To get a B, Amy needs to have a total grade point average (GPA) of 3.0 or greater.
To maintain a GPA of 3.0 or greater, Amy's total GPA is found by adding up the scores of her four tests and then dividing by 4. So, her total score must be equal to or greater than 4 x 3.0 = 12.0.
The score that Amy requires on the fourth test to maintain an average GPA of B or higher is calculated as follows:
x + 264 = 4 × 3.0
where x is the score on the fourth test.
x = (4 x 3.0) - 264
x = 12 - 264
x = -252
As a result, Amy needs a score of 252 or greater on the fourth test to maintain a B grade point average in the sociology course.

Amy needs to achieve a score of 252 or higher on the fourth test to maintain a B grade point average in the sociology course. The GPA of 3.0 or higher is required to maintain a B grade point average, and to do this, her overall score must be 4 x 3.0 = 12.0 or higher.

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Answer:

In mathematics, a variable is a symbol which functions as a placeholder for varying expression or quantities, and is often used to represent an arbitrary element of a set. In addition to numbers, variables are commonly used to represent vectors, matrices and functions. In science, there is a independent and dependent variable.

Step-by-step explanation:

Answer:

VARIABLE MEANING: A variable is a letter used to describe an unknown number. A quantity that can change or vary, taking on different values. A letter or symbol representing a varying quantity.

CO EFFICIENT MEANING: A number next a variable behind the letter examples: 4m -3x 6y 5w

EXPRESSION MEANING: An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division.

TERM MEANING: It's either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs, or sometimes by divide.