3x² = 20 - 7х ?????????????????

Answer: 6

Step-by-step explanation:

Given: Gomez has 30 cans of regular soda and 18 cans of diet soda.

He wants to create some identical refreshment tables that will operate during the football game and doesn't want any sodas left over.

Then, the greatest number of refreshment tables that Gomez can stock = GCD (30,18).

Since, 30=  2 x 5 x x 3

18= 2 x 3 x 3

GCD (30,18) = 2 x 3 = 6

Hence, the greatest number of refreshment tables that Gomez can stock is 6.

The expected winning and the value of that prize, which gives an expected winning is c. $3.13 per ticket.

The expected winnings per ticket in the raffle can be calculated by adding the products of the probability of the expected value of winning each prize. The predicted wins per ticket may be computed as the total of each prize's value multiplied by its probability of winning, i.e.

Expected winnings per ticket

= (1/800) × $400 + (4/800) × $200 + (12/800) × $125 + (30/800) × $60 + (753/800) × $0

If we condense the equation, we obtain:

Calculating the total wins anticipated per ticket

= $0.50 + $1.00 + $1.88 + $0.75 + $0

Expected winnings per ticket = $3.13

Therefore, if you buy a ticket, the expected winnings per ticket are $3.13.

Read more about equation on:

https://brainly.com/question/25976025

#SPJ4

Complete question:

For a fundraiser, there is a raffle with 800 tickets, each costing $15. 1 ticket will win a $400 prize, 4 tickets will win a $200 prize, 12 tickets will win a $125 prize, 30 tickets will win a $60 prize, and the remaining tickets will win nothing. if you buy a ticket, what are the expected winnings per ticket? question options:

a) $5.36

b) $5.63

c) $5.33

d) $5.66

Answer:

Around 25

Step-by-step explanation:

452 candies/18 children

= 25.11111111

Meaning there are around 25 left

Answer:

452 divided by 18 equals

25 with a remainder of 2

Step-by-step explanation:

The x-coordinate of the solution for the system of equations is -455.

To find the x-coordinate of the solution for the system of equations, we can substitute the value of y from the first equation into the second equation and solve for x.

Given equations:

y - x = 910

2x = -2y

From the first equation, we can rearrange it to solve for y:

y = x + 910

Now we substitute this value of y into the second equation:

2x = -2(x + 910)

Let's simplify the equation:

2x = -2x - 1820

Adding 2x to both sides:

4x = -1820

Dividing both sides by 4:

x = -455

Therefore, the x-coordinate of the solution for the system of equations is -455.

Learn more about coordinate system here:

https://brainly.com/question/28913580

#SPJ11

The dimensions of the rectangular pen that maximize the area are 75ft x 75ft.

The rectangular pen that maximizes the area with 300ft of fencing is the one with dimensions 75ft x 75ft.

Let the length of the rectangular pen be xft and the width be yft.

Then the perimeter of the rectangular pen will be given as:

P = 2x + y

= 300ft

On one side of the property, there is a river, so we do not need fencing for that side;

hence we can consider the area of the rectangular pen without one side (the side facing the river).

The area of the rectangular pen without one side is given as:

A = xy

We have an expression for y in terms of x and P, which is:

P = 2x + y

⇒ y = P − 2x

Substituting for y in the expression for the area, we get:

A = xy

= x(P − 2x)

= Px − 2x²

Differentiating A with respect to x and equating to zero, we get:

dA/dx

= P − 4x = 0

⇒ x = P/4

= 75ft

So the length of the rectangular pen will be

2x = 2(75ft)

= 150ft

and the width will be y = P − 2x

= 300ft − 150ft

= 150ft

The dimensions of the rectangular pen that maximize the area are 75ft x 75ft.

to know more about dimensions visit:

https://brainly.com/question/31106945

#SPJ11

The probability that the date sara chose is a prime number is 0.2.

Given that, sara chose a date from the calendar.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Here, total number of outcomes = 30

Number of favourable outcomes = 6

Now, probability = 6/30

= 1/5

= 0.2

Therefore, the probability that the date sara chose is a prime number is 0.2.

To learn more about the probability visit:

https://brainly.com/question/11234923.

#SPJ1

Answer:

8+2g

Step-by-step explanation:

Answer:

1.  Y = -1/4x + 1

3. Y = 2/5x + 1

5. Y = 4/5x + 5

7. Y = -x + 5

9. Y = -5/2x - 16

Step-by-step explanation:

Find the slope using the formula

Use the slope and one of the points to find the y-intercept

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

Answer:

b = \(\frac{ac-2c}{2a}\)

Step-by-step explanation:

Given

\(\frac{1}{2}\) = \(\frac{1}{a}\) + \(\frac{b}{c}\)

Multiply through by 2ac to clear the fractions

ac = 2c + 2ab ( subtract 2c from both sides )

ac- 2c = 2ab ( divide both sides by 2a )

\(\frac{ac-2c}{2a}\) = b

The angle of elevation of the sun will be 65.56 degrees.

Given that:

Height, h = 297 feet

Shadow, x = 135 feet

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The angle of elevation of the sun will be given as,

tan θ = 297 / 135

tan θ = 2.2

θ = 65.56°

The angle of elevation of the sun will be 65.56 degrees.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

#SPJ1

There are four levels of measurement: nominal, ordinal, interval, and ratio.

The level of measurement of a variable refers to the type or scale of measurement used to quantify or categorize the data. There are four levels of measurement: nominal, ordinal, interval, and ratio.

1. Nominal level: This level of measurement involves categorical data that cannot be ranked or ordered. Examples include gender, eye color, or types of cars. The data can only be classified into different categories or groups.

2. Ordinal level: This level of measurement involves data that can be ranked or ordered, but the differences between the categories are not equal or measurable. Examples include rankings in a race (1st, 2nd, 3rd) or satisfaction levels (very satisfied, satisfied, dissatisfied).

3. Interval level: This level of measurement involves data that can be ranked and the differences between the categories are equal or measurable. However, there is no meaningful zero point. Examples include temperature measured in degrees Celsius or Fahrenheit.

4. Ratio level: This level of measurement involves data that can be ranked, the differences between the categories are equal, and there is a meaningful zero point. Examples include height, weight, or age.

It's important to note that the level of measurement affects the type of statistical analysis that can be performed on the data.

Know more about measurement here,

https://brainly.com/question/2107310

#SPJ11

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

Learn more about area here

https://brainly.com/question/25292087

#SPJ11

Answer:

86 cm^2.

Step-by-step explanation:

We can split this into 2 small trapezia at the top, a rectangle in the centre and one triangle at the bottom.

Area of one small trapezium =  1/2 * 2 * (2 + 6) = 8 unt^2

Area of two of these = 16 unit^2.

Area of rectangle = 3*12 = 36 units^2.

Area of the triangle =  1/2 * 6 * 12 = 36 unit^2.

Total area = 16 +36 + 36

=  86 cm^2.

The circumference of the circle is approximately 31.42 cm and the area of the circle is approximately 157.08 cm².

A circle circumscribed about a square with sides of 10cm has a circumference of approximately 31.42 cm and an area of approximately 157.08 cm².

If a circle is circumscribed about a square, the diameter of the circle is equal to the diagonal of the square. In this case, the diagonal of the square is:

d = √(10² + 10²) = √(200) = 10√(2) cm

The radius of the circle is half the diameter, so:

r = 5√(2) cm

The circumference of the circle is:

C = 2πr = 10π√(2) cm

The area of the circle is:

A = πr² = 50π cm²

Learn more about circumference at

https://brainly.com/question/28757341

#SPJ4

The equation would be (qn + 1 = rqn + c)

A statement that defines the equality of two mathematical expressions is called an equation. The goal is frequently to ascertain the values of the variables that make the equation true, and it may have one or more variables.

An equation that expresses qn+1, the quantity of the antibiotic just after taking the (n+1)th tablet, in terms of qn, the quantity just after taking the nth tablet, is given by:

qn+1 = rqn, assuming the quantity of the antibiotic in the body decreases over time.

Alternatively, if the quantity of the antibiotic in the body increases over time, the equation would be: qn+1 = rqn + c, where c is a constant representing the additional amount of the antibiotic added by taking the (n+1)th tablet.

To know more about equation, visit:

https://brainly.com/question/2228446

#SPJ1

We need to find the angle (rounded to the nearest whole degree) of a circle that would represent the percent of students taking mathematics.

Since a complete turn around the circle has 360º, we have the following proportion:

Number of students Angle

734 360º

442 x

Then, cross multiplying the above values, we obtain:

Answer: 217º

Answer:

217°

Step-by-step explanation:

The fraction of students taking math is   442/734

 we need this same fraction of the 360 degrees in a circle

442/734 * 360 = 217°

i) As the quotient between consecutive terms is the same, the data is a geometric sequence.

ii) The recursive formula is: f(x) = f(x-1)\(2^{x-1\) and f(1)= 2.

iii) She will need a time of 1024 units to complete the 10th station.

Any term of a series can be defined by its preceding term in a recursive formula (s).

A recursive function is one that generates a series of phrases by repeating or using its own prior term as input.

i). As the quotient between consecutive terms is the same, the data is a geometric sequence.

ii) The data is a geometric series because when x increases by 1, y increases by 2, and thus the quotient between consecutive terms is the same.

The recursive formula for a geometric sequence is

f(x) = f(x-1)\(q^{x-1\) and f(1)= \(a_1\)

As, \(a_1\) = 2, q=1

f(x) = f(x-1)\(2^{x-1\) and f(1)= 2

iii) The explicit formula for a geometric sequence

\(a_n=a_1 q^{n-1\)

\(a_n=2 (2^{n-1})\)

\(a_n=2^n\)

and, for n=10

\(a_{10\) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

     = 1024.

Learn more about recursive formula here:

https://brainly.com/question/8972906

#SPJ1

Answer:

I suppose the equation would be something like b = 6x, where x is equal to the amount of chocolate chips and b equals to amount of butter.

The dimensions of the rectangle are width = 6 cm and length = 18 cm.

Let's begin by putting variables on the rectangle's measurements.

Let's call the width "w" and the length "l".

From the problem statement, we know that:

l = 4w - 6 (since the length is 6 centimeters less than 4 times the width)

We also understand that the following formula determines a rectangle's perimeter:

perimeter = 2(length + width)

So, for this rectangle, we have:

perimeter = 2(l + w)

perimeter = 2((4w - 6) + w)

perimeter = 2(5w - 6)

perimeter = 10w - 12

We are given that the perimeter is 48 centimeters, so we can set up an equation and solve for "w":

10w - 12 = 48

10w = 60

w = 6

Now that we know the width is 6 centimeters, we can use the equation we derived earlier to find the length:

l = 4w - 6

l = 4(6) - 6

l = 18

for such more question on dimensions

https://brainly.com/question/13847072

#SPJ11

We successfully proved the given identity cot(A) = sin(2A) / (1 - cos(2A)).

To prove the identity cot(A) = sin(2A) / (1 - cos(2A)), we'll start with the left-hand side (LHS) and simplify it to match the right-hand side (RHS).

LHS: cot(A)

Using the reciprocal identity, cot(A) = 1 / tan(A), we can rewrite it as:

LHS: 1 / tan(A)

Now let's simplify the right-hand side (RHS):

RHS: sin(2A) / (1 - cos(2A))

Using the double-angle identity for sine, sin(2A) = 2sin(A)cos(A), we can substitute it into the RHS:

RHS: (2sin(A)cos(A)) / (1 - cos(2A))

Now, let's manipulate the RHS to match the LHS:

RHS: (2sin(A)cos(A)) / (1 - cos(2A))

To simplify further, we'll use the double-angle identity for cosine, cos(2A) = cos²(A) - sin²(A):

RHS: (2sin(A)cos(A)) / (1 - (cos²(A) - sin²(A)))

Simplifying the denominator:

RHS: (2sin(A)cos(A)) / (1 - cos²(A) + sin²(A))

Since cos²(A) + sin²(A) = 1 (from the Pythagorean identity), we can replace it:

RHS: (2sin(A)cos(A)) / (2 - cos²(A))

Canceling out the common factor of 2:

RHS: sin(A)cos(A) / (1 - cos²(A))

Using the identity sin²(A) = 1 - cos²(A), we can rewrite it:

RHS: sin(A)cos(A) / sin²(A)

Now, let's simplify the right-hand side further:

RHS: sin(A)cos(A) / sin²(A)

Using the identity sin(A) / sin²(A) = 1 / sin(A), we can rewrite it:

RHS: cos(A) / sin(A)

Since cot(A) = 1 / tan(A) = cos(A) / sin(A), we have:

LHS: cot(A) = RHS: cos(A) / sin(A)

Therefore, we have successfully proved the given identity cot(A) = sin(2A) / (1 - cos(2A)).

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ4

Prove the following identity cotA=sin2A/(1-cos2A)

Probability -  The 25th percentile of the sample mean is 1829

What is probability?

A probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

What is mean?

The sum of a set of numbers divided by the number of numbers in the set is known as the arithmetic mean or arithmetic average in mathematics and statistics.

µ or mu = 1.3

sigma=0.13

n = 200

a) P(X'<x)=0.25

or,

P[(X'-mu)/sigma-√n < (x-mu)/sigma/√n]=0.25

or,

P(Z<(x-1.3)/0.13/√200)=0.25

or,

(x-1.3)/(0.13/√200)=-0.6745

or, x = 1.2938

P(X'>1.305)=0.05

or,

P[(Z>X'-mu)/sigma/√n]=0.05

or,P[(Z>1.305-mu)/sigma/√n]=0.05

or,

(1.305-1.3)/(0.13/√n)=1.645

or, n = 1829.27

or, n = 1829

to learn more about mean visit:

https://brainly.com/question/1136789

#SPJ4

Answer:

See below

Step-by-step explanation:

(2m+1)(2n+1)

=4mn+2m+2n+1

=2(2mn+m+n)+1

=odd

An odd time and an odd equals an odd has been proved below.

An odd number is a number if we divide by 2, leave a remainder as 1.

⇒The sum of two odd numbers is always even(which can be divided by 2 ).

⇒The product of two or more odd numbers is always odd.

The sum of the even number and odd numbers is always an odd number, while the sum of an odd number of odd numbers is always even. For example, the sum of the given odd numbers 7, 3, 1, and 5 is 16, while the sum of given odd numbers 7, 1, 9, and 13 is 30.

Given that the expression

⇒ (2m + 1)(2n + 1)

⇒ 4mn+2m+2n+1

⇒ 2(2mn+m+n)+1

hence, it comes out of 2 ×something which will always even +1 which gives an odd number.

For more information about odd number

https://brainly.com/question/240064

#SPJ2

Answer:

YZ ≅ AB

Step-by-step explanation:

A translation is a correspondence between two mathematical figures, for instance, the coordinates of each point in a straight line of one figure that is added to the coordinates of the corresponding point on the other figure.

But here, we are given a Δ XYZ which is translated to ΔCAB. This tells us more about how the corresponding points preserve their congruence nature.

i.e.

X corresponds to C

Y  corresponds to A

Z  corresponds to B

Similarly;

XY  corresponds to CA

YZ  corresponds to AB

XZ  corresponds to CB

Since both triangles preserve their congruence nature, then all corresponding points are congruent as well.

Therefore, from the choice of options given, only YZ  corresponds to AB is the right answer.

i.e.

YZ ≅ AB

Answer:

C

Step-by-step explanation:

The statement that best describes the Central Limit Theorem is (a) The distribution of means of random samples pulled from a population will be normally distributed if the sample size is large enough.

The Central Limit Theorem (CLT) states that if repeated random samples is taken from a population with a finite mean and standard deviation, then the distribution of the sample means will approach a normal distribution, even if the original population is not normally distributed.

The larger the sample size, the more closely the sample means will approximate a normal distribution.

which means that, for example, if we take multiple samples of size 100 from a population and calculate the average of each sample, the distribution of those sample means will be approximately normally distributed, regardless of the original shape of the population.

The given question is incomplete , the complete question is

Which best describes what the Central Limit Theorem states ?

(a) The distribution of means of random samples pulled from a population will be normally distributed if the sample size is large enough.

(b) All distributions have the same mean.

(c) The distribution of standard deviations of random samples pulled from a population will be normally distributed if the sample size is large enough.

(d) All distributions are close enough to normally distributed to use the normal distribution as a approximation.

Learn more about Central Limit Theorem here

https://brainly.com/question/18403552

#SPJ4

Answer:

one-solution

Step-by-step explanation:

(x + 2y = 6)2

2x - 3y = 26

2x + 4y = 12

2x - 3y = 26

7y = -14

y = -2

x + 2(-2) = 6

x + -4 = 6

x = 10

Answer:

Step-by-step explanation:

It is two lines, if they intersect there is one solution, if parallel- no solution, if  same lines- infinitely many solutions

Lets put them in slope-intercept form and compare:

As we see the lines have different slopes, so they intersect which means one solution only.

Answer:

-4<-1 and -1<4

Step-by-step explanation:

Step-by-step explanation:

\(2x + y = 5 \\ - x + y = 2\)

\(y = 2 + x\)

\(2x + x + 2 = 5 \\ 3x + 2 = 5 \\ 3x = 3 \\ x = 1 \\ y = 2 + x \\ y = 3\)

The answer is four cubed

Answer: 4 squared

Step-by-step explanation: