is -3.5 greater than 17/5

Consider the following problem.

A student library has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student academic meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.

The conditions of this problem give rise to the following system of equations

Multiplying the second equation by 1/2 and the third equation by 12, we get:

Now, multiply the first equation by -2 and add it to the second equation. In this way we obtain:

Multiply the first equation by -6 and add it to the last equation. In this way we obtain:

Finally, the process is completed by adding the second multiplied by 3 to the third equation.

then, if we perform back substitution we get the desired solutions:

and

We can conclude that the correct answer is:

Problem:

A student cafeteria has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.

System of equations:

Solution for this system of equations:

x=27

I think it's because if 3 is to 2 then 18+9=27. which means 27 is to 18.

The probability that the selected three digit number is an exact match with the winning three digit number = 1/1000

The 10 digits are 0, 1, 2, 3, 4, 5, 6,7, 8, 9. From these 10 digits 3 digits are selected.

Total number of ways of selecting a three-digit number = Number of ways of selecting a digit from 10 digits for each place(one's, ten's and hundred's place)

Thus a three-digit number can be selected in 10 x 10 x 10 = 1000 ways.

So there are 1000 possibilities for a three digit number.

From this only one choice matches exactly with the winning number.

So the number of favorable outcome = 1

Hence, The probability that the selected three digit number is an exact match with the winning three digit number = 1/1000

Learn more about probability at https://brainly.com/question/24756209

#SPJ4

The equation of u when it is the subject is u = 9/t - 12at

From the question, the original equation is given as

9 = 12at2 + ut

Next, we rewrite the equation to show the exponents

This is represented as

9 = 12at² + ut

To solve further, we simply isolate the variable term ut

This is done by subtracting 12at²  from both sides of the equation

So, we have the following equation

9 - 12at² = 12at² - 12at² ut

Evaluate the like terms in the equation

So, we have

9 - 12at² = ut

Lastly, divide both sides of the equation by t

So, we have

(9 - 12at²)/t = ut/t

Evaluate the quotients

9/t - 12at = u

Make us the subject

u = 9/t - 12at

Hence, the solution for the equation for u is u = 9/t - 12at

Read more about subject of formula t

https://brainly.com/question/10643782

#SPJ1

Answer: [tex]x=90[/tex]

Step-by-step explanation:

Using the alternate exterior angles theorem,

[tex]180-x=x\\\\180=2x\\\\x=90[/tex]

To get the inverse of this function you need two steps. First, we leave the variable [tex]x[/tex] alone in the function. Finally, write [tex]f^{-1}(x)[/tex] where you see the letter [tex]x[/tex] and [tex]x[/tex] where you see the letter [tex]y[/tex].

Leave the variable [tex]x[/tex] alone.

Make lettering according to the rule above.

Answer:

3=6 5=10 7=14

Step-by-step explanation:

here's how to do it u wwould have to sum (+) up all the ratios then it would give u 15 after then u divide the sum by 15 hen u multiply by ratios .

Answer:

where's the rest of the question⁉️

To construct the graph of the hyperbola, the procedure is as follows:

The equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:

(y - y*)²/a² - (x - x*)²/b² = 1.

A vertical hyperbola opens up and down.

In this problem, the equation is:

(y + 2)²/36 - (x + 5)²/64 = 1.

Hence the center is:

(-5, 2).

The value of coefficient a is:

a² = 36 -> a = 6.

Then the vertices of the hyperbola are:

The slopes of the asymptotes of the parabola are given as follows:

±a/b.

Hence:

Since the asymptotes pass through the center, the equation is:

y - 2 = ± 3/4(x + 5).

More can be learned about the graph of a hyperbola at https://brainly.com/question/12050850

#SPJ1

The increase in the selling price is 1.818.

Test statistic:

A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.

The given values are:

a = 0.1

x = 94

μ = 90

The formula for test statistic will be:

t = ((x- μ) / ([tex]\frac{s}{vn}[/tex])

Now put the values in the given equation we have:

t = (94-90) / ([tex]\frac{22}{10}[/tex])

 = 4/2.2

  = 1.818

Therefore the increase in the selling price is 1.818.

To know more about the selling price refer to the link given below:

https://brainly.com/question/1153322

#SPJ4

Answer:

Bottom right

Step-by-step explanation

Answer:

first answer is correct

ANSWER:

Therefore there are about 234 grams

STEP-BY-STEP EXPLANATION:

We have that the density is given by this formula

We have the value of the density and the volume, therefore we can calculate the number of grams as follows:

It is to be noted that the absolute expression that shows how far the student's score is from the average is given as: "| x - 74| (Option C)

The student obtained a score of x% based on the question. As a result, x% might be larger or lower than the average score of 74%.

To establish how distant the student's score is from the average, we must subtract the student's score from the average score; i.e. (x - 74)

This difference, however, might be negative: as a result, the absolute value of (x - 78) must be calculated, yielding |x - 74|.

As a result, the phrase that may be used to assess how distant the student's score is from the average is as follows: |x - 74| which is the same as option c - An Absolute expression.

Absolute expressions are or modulus of a real number x, abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.

Learn more about absolute expressions:
https://brainly.com/question/28433835
#SPJ1

By solving  ( 3 / x - 4) = (x - 5) / x equation we get ,

x = 10 and x = 2 .

Given ( 3 / x - 4) = (x - 5) / x,

3x = (x - 5) (x - 4)

By solving this equation,

3x = x( x - 5 ) - 4( x- 5)

3x = x² - 5x - 4( x - 5)

3x = x² - 5x  - 4x + 20

3x = x² - 9x + 20 = 0

3x - x² + 9x -20 = 0

12x - x² - 20 = 0

-x² + 12x -20 = 0

-1(x(x - 2 ) - 10( x - 2 )) = 0

-1( x - 10) ( x - 2) = 0

x - 10 = 0

x - 2 = 0

∴  x = 10

    x = 2

To learn more about factorization refer to :

https://brainly.com/question/25829061

#SPJ13

2.6

Given the expression;

Simplify the expression in the bracket to have:

Simplify the result to have;

Hence the result of the given function on simplification is 2.6

SOLUTION

The question is

Now let's solve. This becomes

This becomes

So we have our x as

The kite's height above the earth is 287 feet.

A right-angled triangle is formed by the length of the string, the height of the kite (h) above ground, and the perpendicular distance from the end of the kite string to the man.

The link between the lengths and angles of a right-angled triangle is demonstrated through trigonometry.

Using trigonometric ratios,

the height of the kite above the ground is

sin(55) = h ÷ 350

h = 287 ft

As a result, the kite's height above ground is 287 feet.

A trigonometric function is a real function in mathematics that relates the angle of a right triangle to the ratio of the lengths of the sides. They are frequently used in earth sciences such as navigation, structural mechanics, astrophysics, geography, and many other fields.

Learn more about trigonometry at

https://brainly.com/question/19509227?referrer=searchResults

#SPJ4

Alana's conclusion from the study is not appropriate.

Why is Alana's conclusion from the study is not appropriate?

What is an appropriate study?

To learn more about appropriate studies, refer:

https://brainly.com/question/25257437

#SPJ4

The value of k - 0.3753, used  to predict the population in 2017,  the population in 2017 is 508861.

population of given by P = 289.81e^Kt

in 2000 population P(0)=289.81 thousand

in 2006 population P(6) = 363000

363000 = 289810[tex]e^{k6}[/tex]

k = 1/6 ln | 363000 /289810 |

k = 0.3753

Population in 2017  --> t =17

P(15) = 289810[tex]e^{k6}[/tex]

P(15) = 508861.32

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from which a statistical sample is taken in statistics. It could be a collection of people, things, occasions, organizations, etc. To make inferences, use populations. A population can be all the students at a particular school. It would contain all the students who study in that school at the time of data collection

To learn more about population, visit;

https://brainly.com/question/27779235

#SPJ4

The Conditional Probability that the coin is weighted towards heads is 0.25/0.75 . Conditional probability is the result of Bayes’ Theorem .

A coin is tossed twice . So, total outcomes are { HH , TH , HT, TT} that is 4 .

Probability= favourable outcomes / total outcomes

Probability of getting two heads = ¼ = 0.25

Favourable outcomes are { HH , HT, TH}

Probability of getting at least one head = ¾ = 0.75

Conditional probability is measure of the probability of an event occurring, given that another event has already occurred.

Formula , P(A|B) = P(A and B)/ P(B)

Here, p(A|B) is conditional probability of A given B

P(B) is probability of event B occur

P(A and B) is probability of both events A and B occur

We have to find conditional probability that coin is weighted towards heads and it is = Probability of getting both heads / probability of getting at least one head

= ¼ / ¾ = 0.25 / 0.75

Which is required result .

To learn more about Conditional Probability, refer :

https://brainly.com/question/11899923

#SPJ4

Step 1

Plot a graph with the given table.

Step 2

Calculate r, the correlation coefficient between the two variables.

Step 3

Interprete the value of r

Step 3

Compute the regression line for predicting price from mileage

Step 4

Predict the price of a car with 30,000 miles

Step 5

Answer:

Step-by-step explanation:

Let the green graph be G and the blue graph, be B:

1) Be cognate of the fact that the function in blue is completely negative, while the upper green graph is positive

Note: First, we should note that the blue function must therefore be a transformation of the Green function.

This means B takes the form:

y = (s)*a*|X+b|

We are required to find a, b, and s, where s is the sign.

2) From (1), we can deduce that, if graph G was transformed into B, then the first transformation begins by reflecting G along the X-axis (multiplying by -1).

Therefore, s = -1

3) From (2), it follows that the first transformation produces the following effect:

y = |X| transformed to y = -|X|

and B now takes the form y = -a*|X+b|

4) We notice again that the apexes of both functions do not touch. This means G was not only reflected along the X-axis but was also shifted or translated along the X-axis.

5) Building from (4), we notice that the Blue function takes a value of 0 when x is 1. If we put this in the general equation for B;

y = -a*|X+b| implies;

0= -a*|1+b|      

|1+b| = 0/-a

|1+b| = 0

1+b = 0

and y becomes:

Notice also that when the x is 5, the Blue function now takes a value of -1. If we put this in a general equation for B;

y = -a*|X-1|

-1 = -a*|5-1|

-1 = -a*|4|

-4a = -1

Blaise M.

SOLUTION:

Step 1:

In this question, we are given the following:

The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury​ (mm Hg), find the volume when the pressure is 200 mm Hg.

Step 2:

This is an application of Boyle's law which states that:

Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.

Next:

CONCLUSION:

The volume when the pressure is 200 mm Hg is:

The answer of the linear equation for Y=2x+5 is x = (y-5)/2.

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0.  Now in this equation, x is a variable, A is a coefficient, and B is constant.

The given linear equation is,

Y=2x+5

Now, solve this linear equation for x

Take 5 to LHS it will change sign to -ve

y-5 = 2x

Next, take coefficient of x below to LHS

(y-5)/2 = x

Now, swap the sides

x = (y-5)/2

To read more about the Linear equation.

https://brainly.com/question/25870256

#SPJ13

Coterminal Angles are angles that share the same initial side and terminal sides.

Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

QUESTION A

The angle is given as 600°.

To find the coterminal angle between 0° and 360°, we subtract 360° from the angle.

Therefore,

The coterminal angle is 240°.

QUESTION B

The angle is given as

To get an angle between 0 and 2π, we will add 2π to it.

Hence, we have

The coterminal angle is π/2.

We are given that Jane used 200 minutes and the cost was $75, and also she used 680 minutes and the cost was $195. To determine a function of the cost "C" as a function of the minutes "x" we will assume that the behavior of this function is that of a line. Therefore, the function must have the following form:

Where "m" is the slope and "b" the y-intercept. We will determine the slope using the following formula:

Where:

Are points in the line. The given points are:

Substituting in the formula for the slope we get:

Solving the operations we get:

Now we substitute in the formula for the line:

Now we determine the value if "b" by substituting the first point. This means that when C = 200, x = 75.

Solving the product:

Now we subtract 18.75 from both sides:

Therefore, the formula of the cost is:

Part B. We are asked to determine the cost is there is a consumption of 323 minutes. To do that we will substitute in the formula for "C" the value of x = 323.

Solving the operations we get:

Therefore, the cost is $262.

Answer:

Step-by-step explanation:

We will make use of algebra here.

First of all, we know that the monthly fee will be the same throughout all the months.
So, let's consider that cost to be the yet-to-find constant: [tex]a[/tex].

A charge is accumulated for every minute on the call, so let's consider that minutely charge to be the constant: [tex]b[/tex].

[tex]x[/tex] is the number of minutes spent on the call.
So, the total charge after talking for [tex]x[/tex] minutes would be:

[tex]b \times x\\=bx[/tex]

The monthly cost is the sum of the monthly fee and the total charge.

So, if this is represented mathematically, we get:

[tex]C(x)= a+bx[/tex]

A piece of information that we have is that, after calling for 200 minutes (which means [tex]x=200[/tex]), the monthly cost ( [tex]C(x)[/tex] ) would be $75.

Upon substituting these values in the equation we found above, we get:

[tex]C(x)=a+bx\\\\75=a+200b[/tex]

Similarly, we have another piece of information, which states that calling for 680 minutes ([tex]x=680[/tex]) produced a monthly cost of $195.

Upon substituting these values in the equation we found above, we get:

[tex]C(x)=a+bx\\\\195=a+680b[/tex]

And, thus we have found a system of equations:

 [tex]a+200b=75\\a+680b=195[/tex]

For the first equation, let's make [tex]a[/tex] the subject:

[tex]a+200b=75\\\\a+200b-200b=75-200b\\\\a=75-200b[/tex]

Substitute this expression for [tex]a[/tex] into the second equation:

[tex]a+680b=195\\\\75-200b+680b=195\\\\75+480b=195[/tex]

Find the value of [tex]b[/tex] using this equation:

[tex]75+480b=195\\\\75+480b-75=195-75\\\\480b=120\\\\\frac{480b}{480}=\frac{120}{480}\\\\b=\frac{1}{4}[/tex]

Insert the value for [tex]b[/tex] into the expression for [tex]a[/tex]:

[tex]a=75-200b\\\\a=75-200(\frac{1}{4})\\\\a=75-50\\\\a=25[/tex]

Since we have the values for the constants [tex]a[/tex] and [tex]b[/tex], we can complete the function/equation  [tex]C(x)[/tex]:

[tex]C(x)=a+bx\\\\C(x)=25+\frac{1}{4}x[/tex]

So, the answer for (A) is:

[tex]C(x)=25+\frac{1}{4}x[/tex]

For (B), we have to find the monthly bill/cost ( [tex]C(x)[/tex] ) when 323 minutes have been spent on calling.

So, we just have to substitute [tex]x[/tex] for 323, since [tex]x[/tex] represents the number of minutes spent on calling:

[tex]C(x)=25+\frac{1}{4}x\\\\C(x)=25+\frac{1}{4}(323)\\\\C(x)=25+80.75\\\\C(x)=100.75[/tex]

The answer for (B) is [tex]\$100.75[/tex]

Answer: m = 24

Step-by-step explanation:

The right side of the table is the x value, and the left side is the y value.

Pick two points, I will pick (1,35) and (3,83).

Once you pick the points, input them in the rise over run formula:

y2-y1/x2-x1

83-35/3-1 = 48/2 = 24

7069 are the minimum number of balls that must be drawn without replacement to complete the requirement that all balls of a single color be drawn.

First of all, we’ll look at the worst possible scenario and determine the minimum number of balls needed. We know that the color we are looking for is not blue, nor white, nor black (as there are less than 1515 of the same color when talking about those). In our worst possible scenario, we’ll first pull out all the blue, white, and black balls. Add them up. That means that we’ll definitely pull out 2523 balls( 1111 white + 1313 blue + 99 black). We are not done yet. From all the given balls, we are left with red, green, and yellow colored balls. In our worst scenario, we’ll pull out 1514 balls of every single color, and then we’ll finish it with one color (it doesn’t matter which). Since, we have 3 different colors left, that’s 3*1515+1 = 4545+1 = 4546 that is 4546 more balls.

To finish, we simply add the first 2523 balls with 4546, yielding 2523+4546 = 7069 balls.

To learn more about withdraw arrangement ways , refer :

https://brainly.com/question/13654367

#SPJ4