A banquet hall has just two sizes of tables.
One size seats exactly 5 people, and the other size seats exactly 8 people.
At tonight’s banquet, exactly 79 people will be seated at less than one dozen tables, and there will be no empty places.
How many tables of each size will there be at the banquet?

Binomial probability states that the probability of x successes on n repeated trials in an experiment which has two possible outcomes can be obtained by

(nCx).(p^x)⋅((1−p)^(n−x))

Where success on an individual trial is represented by p.

In the given question, obtaining heads in a trial is the success whose probability is 1/2.

Probability of 6 heads with 6 trials = (6C6).((1/2)^6).((1/2)^(6–6))

= 1/(2^6)

= 1/64

Answer:

We have

tan 12.5  = 60 / adj       rearrange  as

adj = 60 / tan 12.5  = about 270.64 m

Step-by-step explanation:

Mark me brainllest

In the triangle below, ΔABE≅ΔCBD. Reason (AAS)

We should know that the postulates talk about the proofs about the given diagram or flowchart

There is an attached diagram to support our answer

Below gives the correct explanations

S/n         Statement                                     Reason

1               <ABE≅<CDE                             Given in the diagram

2            <AEB≅CED           The theory of vertical angles  are      equal        3             BE≅ED                                 Also given in the diagram

4          ΔABE≅ΔCDE            The rule of Angle, Side Angle proof

In conclusion the triangle below, ΔABE≅ΔCBD. Reason (AAS)

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Complete question:

Given AC 1 BD, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you

Answer:

The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.

Step-by-step explanation:

This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.

Answer:

y=3x

Step-by-step explanation:

-6/-2=3, -3/-1=3, 3/1=3. 6/2=3

Answer:

50

Step-by-step explanation:

i got it correct on the iready quiz

The graph of the line does not change except only in the y - intercept. The slope of the line remains same.

        y = mx + c

        [m] : slope of line.

        [c] : y - intercept

Given is a graph that shows the relationship between time and the distance a train travels.

From the graph, we can write the coordinates as -

(1, 60) and (2, 120)

So, we can write the slope of the line as -

m = (120 - 60)/(2 - 1)

m = 60/1

m = 60

Therefore, the slope of the line given in the graph will be 60 miles/hr.

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Answer:

y = 1/3x

Step-by-step explanation:

The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)

From the question, we have the following parameters that can be used in our computation:

35/100,5/10,65/100

In the above sequence, we can see that 15/100 is added to the previous term to get the new term

This means that

First term, a = 35/100

Common difference, d = 15/100

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 35/100 + 15/100(n - 1)

So, we have

f(n) = 7/20 + 3/20(n - 1)

Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)

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The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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the formula for the area of the circle is

it is given that the area of the circle is 201.1

we know that the diameter of the circle is twice of the radius

so, diameter D = 2r = 2 x 8 = 16

so the answer is approx 16

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

Answer:

-3

Step-by-step explanation:

Negative 3 because Emmet had 14 points, then lost 17 points, landing him with the score of -3

Answer:B

Step-by-step explanation:I’m not completely sure but y is going up twice as much as x.

Answer:

The correct answer: a line

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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Answer:

16 this is the real answer

Step-by-step explanation:

Hope this help

In order to construct a Venn diagram for a survey, first enter the cardinality of the universal set to obtain subsequent cardinalities.

The universal set is the set of all possible outcomes, and the cardinality of a set is the number of elements in the set. Once you have the cardinality of the universal set, you can use it to calculate the cardinality of any other set in the survey.

For example, if the universal set has a cardinality of 100, and the survey asks people whether they like dogs or cats, you can calculate the number of people who like dogs by subtracting the number of people who like cats from the total number of people surveyed.

In order to construct a Venn diagram, you will need to draw two or more circles, each representing a set in the survey. The circles should be overlapping to represent the sets that have members in common.

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In order to construct a Venn diagram for a survey, first enter the cardinality of the to obtain subsequent cardinalities region. Then use

Answer:

The state can issue 456,976,000 license plates.

Step-by-step explanation:

For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.

For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.

For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:

\(\frac{10}\) \(\frac{26}\) \(\frac{26}\) \(\frac{26}\) \(\frac{26}\) \(\frac{10}\) \(\frac{10}\)

= 10*26*26*26*26*10*10

=456,976,000.

Therefore, the state can issue 456,976,000 license plates.

In the given graph, the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

To find the equation of the quadratic function, we start by using the vertex form:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex. Plugging in the given vertex (4,-2), we get:

\(y = a(x - 4)^2 - 2\)

Next, we use the other two points to find two additional equations:

\(6 = a(8 - 4)^2 - 2 (plugging in (8,6))\\0 = a(2 - 4)^2 - 2 (plugging in (2,0))\)

Simplifying these equations, we get:

\(6 = 16a - 2\\8a = 4 -- > a = 1/2 \\0 = 4a - 2 \\4a = 2 -- > a = 1/2 \\\)

So the equation of the quadratic function is:

\(y = (1/2)(x - 4)^2 - 2\)

Now, we can answer the questions:

The y-intercept is the point where the graph intersects the y-axis. To find it, we set x = 0 in the equation:

\(y = (1/2)(0 - 4)^2 - 2 = 6\)

So the y-intercept is (0,6).

To find the x-intercepts, we set y = 0 in the equation:

\(0 = (1/2)(x - 4)^2 - 2\)

Simplifying, we get:

\((x - 4)^2 = 4\\ - 4 = \pm 2 \\= 2, 6\)

So the x-intercepts are (2,0) and (6,0).

The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is at (4,-2), the axis of symmetry is the line x = 4.

The interval on which the graph is increasing is (-∞,4), and the interval on which it is decreasing is (4,∞).

The sign of the leading coefficient is positive, since it is 1/2.

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Step-by-step explanation:

7! = 5040 ways

Answer:

The sample space of rolling two six-sided dice at the same time consists of all possible outcomes of the two dice. Each die can show any number from 1 to 6, so the sample space contains 6 x 6 = 36 possible outcomes.

Each outcome is represented by an ordered pair (a,b) where a and b are integers from 1 to 6 representing the numbers shown on each die, respectively. For example, (1,1), (1,2), (1,3),......., (6,5), (6,6) are all possible outcomes in the sample space.

Answer:

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

There are various combinations of coins.

In total there are:

Answer:

no solution

y=x^3

y= 2-1 x 1

Step-by-step explanation:

Answer:

The next two terms are  92 and 105.

Step-by-step explanation:

79 + 13 = 92

92 + 13 = 105

Answer:

325/3

Step-by-step explanation:

\(48+4^2+\frac{3}{5}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:48=\frac{48\cdot \:5}{5}\\\\=\frac{48\cdot \:5}{5}+\frac{3}{5}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\\\\\:combine\:the\:fractions}:\\\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{48\cdot \:5+3}{5}\\\\48\cdot \:5+3=243\\\\=4^2+\frac{243}{5}\\\\=16+\frac{243}{5}\\\\=\frac{16\cdot \:5}{5}+\frac{243}{5}\\\\=\frac{16\cdot \:5+243}{5}\\\\16\cdot \:5+243=323\\\\=\frac{323}{5}\)

Answer:

180,300= $480

Step-by-step explanation: multiply the % by the total (600) and you will get the answer. then add together

Answer:

1,880

Step-by-step explanation:

add them togther:) hope its right.

Answer:

-1

Step-by-step explanation:

If you multiply x by -1 you will get the y value to be the negative of that number.

Hope this helps!!

Answer:

so first find what y equals then put the negative in front of it lol there is a pattern positive and negative

3,-3

4,-4

5,-5

6,-6

y,-y

Step-by-step explanation:

x = 13 (option A), y = 22 (option D)

In a parallelogram, the opposite angles are equal

∠G = ∠E

∠D = ∠F

Also any two adjacent angles are supplementary:

∠G + ∠F = 180

∠D + ∠E = 180

∠G = 128, ∠F = 52, ∠D = 4x, ∠E = 6y - 4

∠G = ∠E

128 = 6y - 4

solve for y:

128 + 4 = 6y

132 = 6y

divide both sides by 6:

132/6 = 6y/6

y = 22

∠D = ∠F

4x = 52

divide both sides by 4:

x = 52/4

x = 13

x = 13 (option A), y = 22 (option D)

Answer:

\(\displaystyle \frac{cd^6}{a^4b^2}\)

Step-by-step explanation:

\(\displaystyle \frac{a^{-4}b^{-2}cd^6}{e^{-7}}\\\\=a^{-4}b^{-2}cd^6e^7\\\\=\frac{cd^6}{a^4b^2}\)

Notice that the variables with negative exponent that were originally in the denominator went to the numerator (like with \(e^{-7}\)) and became positive, and vice versa with those originally in the numerator went in the denominator (like with \(a^{-4}b^{-2}\)) and also became positive.

Step-by-step explanation:

a‐⁴b‐²cd⁶

_______

e‐⁷

cd⁶e⁷

_____

a⁴b²