aubree and her children went into a movie theatre and she bought $32 worth of bags of popcorn and pretzel. each bag of popcorn costs $8 and each pretzel costs $4. she bought a total of 6 bags of popcorn and pretzels altogether. Graphically solve a system of equations in order to determine the number of bags of popcorn, x, and the number of pretzels,y, that aubree bought.

Time is represented by the variable. Since a person's speed, which can take on nearly any value, determines how long it takes them to complete a mile, this variable is continuous.

If a quantitative variable is often obtained through measuring or counting, it can either be continuous or discrete. If a variable can take on any two particular real values and all other real values in between, it is said to be continuous over a range of real values.

First, when is a variable continuous and when is it discrete?

A variable is continuous if it can take any value (or at least a dense set of values) inside a certain interval as opposed to discrete if it can only take a few specific values on that interval.

For instance, the only possible values for the numbers one can roll on a dice are 1, 2, 3, 4, 5, and 6, to provide one example.

The variable in this instance now stands for time. Time is nearly always a continuous variable; in this instance, the time refers to the duration of a mile run. Therefore, that variable is capable of practically any value (depends on the speed of the person).

Therefore,

Time is represented by the variable. Since a person's speed, which can take on nearly any value, determines how long it takes them to complete a mile, this variable is continuous.

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The value of BC = 25 using properties of triangle.

What are properties of triangle ?

Let us discuss here some of the properties of triangles.

1. A triangle has three sides and three angles.

2. The sum of the angles of a triangle is always 180 degrees.

3. The exterior angles of a triangle always add up to 360 degrees.

4. The sum of consecutive interior and exterior angle is supplementary.

Properties for isosceles:

Isosceles triangles are those triangles that have at least two sides of equal measure.

1. Two equal sides and two equal angles.

2. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.

3. The side opposite the vertex angle is called the base and base angles are equal.

Using 1st property,

in given triangle two angles are equal then opposite side will also be equal.

So, AB = AC

i.e. 4x+4 = 6x-14

4+14 = 6x-4x

18 = 2x

x = 9

Putting value of x in BC

BC = 2*9 +7

     = 18+7

     = 25.

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The rate of change of the line that contains the two points (-1, -4) and (5, 4) is 4/3.

The rate of change for a line is the slope, the rise over run, or the change in over the change in.

The slope of line can be calculated using the formula, slope =(y2-y1)/(x2-x1).

The given coordinate points are (-1, -4) and (5, 4).

Now, slope = (4-(-4))/(5-(-1))

= (4+4)/(5+1)

= 8/6

= 4/3

Therefore, the slope of a line is 4/3.

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The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4

To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.

This value of z is known as the 43rd percentile of the standard normal curve.

We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.

According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4

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Answer:

Step-by-step explanation:

When graphed they intersect at (2, 5)

a pair of congruent angles are:

3x+4 = (3×12) +4 = 40°

5x - 20 = (5×12) -20 = 40°

The sizes of congruent angles are same. Simply by looking at the specified angles' measurements, congruent angles may be discovered. However, it is not necessary for the terminals used to create these angles to be the same length and direction.

We have been given a different description for each angle.

Let, the number referred to be x

four more than three times a number: 3x + 4

twenty less than five times the number: 5x - 20

So, 5x - 20 =  3x + 4

or, 2x = 24

or, x = 12

The angles are:

3x+4 = (3×12) +4 = 40°

5x - 20 = (5×12) -20 = 40°

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Answer: 13

Step-by-step explanation: To find f(2), you can put 2 into all of the x spots, thus making the equation 4(2)+5. From there you can do PEMDAS and multiply 4 and 2 to get 8, and then add 5 to get 13.

A 80% confidence interval for the slope of the population regression line is answers precise to at least two decimal places is Lower limit : 16.4083 and Upper limit : 49.9587 .

Given :

A least-squares regression on the data he collected produces the equation

y =37.67 + 33.18x

where x is metatarsal - to - femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94.

The sample number is 49 species (here we assume that all the individuals of a the same species are summarised with a central tendency measure.

33.18 - 2.1123 ( 7.94 ) ≤ β ≤ 33.18 + 2.1123 ( 7.94 )

16.4083 ≤ β ≤  49.9587 .

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The greatest common divisor is 12. The linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.

The extended Euclidean algorithm is an algorithm to compute integers x and y such that: ax+by=gcd(a,b)The extended Euclidean algorithm can be viewed as the reciprocal of modular exponentiation.

By reversing the steps in the Euclidean algorithm, it is possible to find these integers x and y. The whole idea is to start with the GCD and recursively work our way backwards. This can be done by treating the numbers as variables until we end up with an expression that is a linear combination of our initial numbers.

First use Euclid's algorithm to find the GCD:

3984 = 588 ×6 + 456

588 = 456×1 +132

456= 132 ×3 + 60

132 =  60×2 +12

60 = 12×5+0

The last non-zero remainder is 12.

Thus, the greatest common divisor is 12.

Now we use the extended algorithm:

12 = 132 +(-2)×60

    = 132 + (-2)×(456 + (-3)×132))

    = (-2)×456 + 7×132

    = (-2)×456 + 7×(588 +(-1)×456))

   = 7×588 + (-9)×(3984 +(-6)×588))

   = 61×588 + (-9)×3984

Thus, a = -9 and b = 61.

Thus, the linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.

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The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Now, According to the question:

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Let's know:

What is Confidence Interval?

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.

The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.

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Answer:

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.

For the given diagram 1. d) all of them are correct, 2. d)none of them are correct and Total Revenue is 3. b. $90,125

1.

Marginal Revenue is

the change in Total Revenue/Change in units of output produced

In the given question the price of the output is fixed at $125.

Hence no matter what the quantity of output sold, every additional output produced will generate an additional revenue of $125.

hence option d) all of them are correct has to be chosen.

2.

Now we already know that if the price has been fixed at $125, the marginal revenue generated cannot be anything but $125.

Hence, option d) None of them are correct.

3.

Total Revenue = Price X Quantity

Here it is given that the Price is $175

Output is 515 units

Hence, the Total Revenue will be $(175  X  515)

= $90125

Hence, option b. $90125 is correct.

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The probability that 2 or fewer in the sample will favor the project is  4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%

According to the question,

It is given that according to the student's government

The probability that number of students in favor of increment in fees : p = 0.70

The probability that number of students against the increment : q = 0.30

Sample Size : n = 12

Number of students follows Binomial distribution

(a) We have to find the probability that 2 or fewer in the sample will favor the project

P( x ≤ 2) = P(0) + P(1) + P(2)

As we know ,

P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾

=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰

=>  P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹  + 12×11/2 × (0.70)²(0.30)¹⁰

=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]

=>  P( x ≤ 2) = 5.9×10⁻⁶[0.78]

=>  P( x ≤ 2) = 4.368 × 10⁻⁶

Which is very close to zero

(b) The data doesn't support the student government claim.

The data seem to indicate that the percent favoring the increase in fees is less than 70%.

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Answer:

  y = 2x³-6x²-2x +6

Step-by-step explanation:

You want the equation of a graph with two turning points, and x-intercepts at -1, +1, and +3. The y-intercept is 6.

Each x-intercept of x=p means the equation has a factor of (x -p). This means the factored equation will be ...

  y = a(x +1)(x -1)(x -3) = a(x² -1)(x -3) = a(x³ -3x² -x +3)

The y-intercept is 3a = 6, so a = 2 and the function is ...

  y = 2x³ -6x² -2x +6

The value of the fraction, negative 5 and 1 over 7 ÷ negative 7 and 3 over 4 is 144/217

A fraction can be described as the part of a whole element or value.

The different types of fractions are;

Examples of proper fractions; 2/4, 5/6, 7/9

Examples of improper fractions; 4/2, 3/2, 6/5

Examples of mixed fractions; 2 1/4, 4 6/7, 8 1/2

Examples of simple fractions; 1/ 3, 3/4, 1/2

Now, from the information given, we have;

Convert into improper fractions

-36/7 ÷ -31/4

take inverse of the divisor and multiply

-36/ 7 × 4/-31

-144/-217

144/217

Hence, the value is 144/217

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To solve this system of differential equations using the series method, we can assume that the solution can be expressed as a power series in both x and y:

[tex]u(x,y) = a0 + a1x + a2y + a3xy + a4x^2 + a5y^2 + ...[/tex]

Substituting this expression into each of the differential equations and collecting the coefficients of each term gives us the following system of equations:

a0 + 5a0 = 0

a1 + 5a2 = 0

a2 + 5a1 = 0

a4 + 5a4 = 0

a5 + 5*a5 = 0

Solving this system of equations gives us the following values for the coefficients:

a0 = 0

a1 = 0

a2 = 0

a3 = 0

a4 = 0

a5 = 0

Therefore, the power series expansion of the solution is:

u(x,y) = 0

This means that the only solution to the differential equations is the trivial solution u(x,y) = 0.

Note that this method of solving differential equations using power series is only applicable if the differential equations are linear and homogeneous, which means that the coefficients of the terms in the differential equations do not depend on x and y, and the right-hand sides of the equations are all equal to 0. If the differential equations are nonlinear or inhomogeneous, other methods may be required to find their solutions.

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Answer:

The answer is 28d + 36.

The time management skill and amount of work done is an example of positive correlation.

Correlation or dependency pertains to any statistical link involving two random variables or bivariate data, whether causal or not. Although the term "correlation" can refer to any form of link, in statistics it is most usually used to refer to the degree to which two variables are statistically linearly associated.

The link between the heights of parents and their children, as seen in the enough that demand curve, and the correlation between the price of an item and the quantity of items that buyers are willing to acquire are examples of dependent phenomena.

The Pearson product-moment correlation coefficient (PPMCC), sometimes known as "Pearson's correlation coefficient," is the most commonly used measure of two-value dependency.

It is computed by dividing the covariance ratio of the two variables in our numerical dataset by the square root of their variances. The covariance of the two variables is simply divided by the product of their standard deviations in mathematics. The coefficient was calculated by Karl Pearson from Francis Galton's similar but slightly different idea.

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Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.

It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.

Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.

Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."

∀xA⇒A(x↔a}

for every formula A and every term a, where A(x↔a}  is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of

∀xA.

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The measure of the central angle in degrees subtended by an arc of length 5 meter is 71.61 degrees

The radius of the circle = 4 meters

The circumference of the circle = 2πr

Where r is the radius of the circle

The value of π = 3.14

The circumference of the circle = 2π × 4

= 8π

The arc length = 5 meters

Consider the x as the central angle

The proportion of central angle and circumference will be

5/8π = x radiance / 2π

Cross multiply the terms

x × 8π = 5 × 2π

x = 10π / 8π

x = 5/4 radiance

Convert radiance to degrees

We know

1 radiance = 180/π degrees

5/4 radiance = 5/4 × 180/π degrees

= 71.61 degrees

Therefore, the central angle is 71.61 degrees

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Answer:

12.2 years

Step-by-step explanation:

To solve, use the exponential growth formula:

[tex]A_t=A_0(1+r)^x[/tex]

where

[tex]A_t[/tex] = Amount as a function of time ($15500)

[tex]A_0[/tex] = Original amount ($5400)

[tex]r[/tex] = rate (.09)

[tex]x[/tex] = time in years

So,

[tex]15500=5400(1+.09)^x\\15500(\frac{1}{5400})=5400(1.09)^x(\frac{1}{5400})\\2.87=1.09^x\\\log_{1.09}2.87=\log_{1.09}1.09^x[/tex]

Use the logarithmic rules that state [tex]\log_{a}a=1[/tex] and [tex]\log_{a}a^b=b\log_{a}a[/tex]:

So,

[tex]\log_{1.09}2.87=x\\12.24\ years=x[/tex]

Answer: I believe its:  An equation that can be used to find x is 4x+30.25=52.25, and each game ticket costs $5.50.

Step-by-step explanation:

well, 52.25 - 30.25 is 22$

22 divided by 4 is 5.50

4 times x plus 30.25 is 52.25

so 4x+30.25= 52.25

Answer: -2 1/8

Step-by-step explanation:

3 1/2 = 3 4/8

5 5/8 - 3 4/8 = 2 1/8

Add the negative sign back to get -2 1/8

Answer:

Billy has 295, maria has 360 we can do this by doing 20 x 14 then add 15 = 295 then for maria 25 x 14 then add 10. Maria made more. Billy will have less

OR

less

billy = 15, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20 = 295

maria = 10, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25 = 360

 maria earned more than billy

Answer:

Step-by-step explanation:

The given statement ,the analysis of total variability into between-treatments and within-treatments variability is the same for a repeated-measures ANOVA and an independent-measure ANOVA is true.

The first stage of the repeated-measures ANOVA is identical to the independent-measures analysis and splits the overall variability into two components: between-treatments and within-treatments

Measurements that are repeated ANOVA is the extension of the dependent t-test and is the equivalent of one-way ANOVA for related, rather than independent, groups.

A repeated measures ANOVA is often referred to as a within-subjects ANOVA or ANOVA for correlated samples. The term "responsibility" refers to the act of determining whether or not a person is responsible for his or her own actions.

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Using the completing square method, the value of (C) x = ±√5 - 2.

A quadratic polynomial of the form ax2+bx+c can be transformed to the form in elementary algebra by using the "completing the square" method for certain values of h and k.

In other words, the quadratic expression is completed by inserting a perfect square trinomial.

So, we have:

x² + 4x = 1

The x-coefficient terms must be divided by two:

4/2 = 2

Square:
2² = 4

Add 4 on both sides as follows:

x² + 4x + 4 = 1 + 4

x² + 4x + 4 = 5

Transform into perfect squares:

(x + 2)² = 5

Both sides of the square root:

x + 2 = ±√5

x = ±√5 - 2

Therefore, using the completing the square method, the value of (C) x=±√5-2.

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Complete question:
Solve x2 + 4x = 1 for x by completing the square.

a. x = −3

b. x = −1

c. x equals plus or minus the square root of 5 minus 2

d. x equals plus or minus square root of 5 plus 2

Answer:

is c correct?

Step-by-step explanation:

Answer:

y = - 0.4x -6

Step-by-step explanation:

The slope-intercept form of a line equation is

y = mx + b

where m is the slope and b the y-intercept where the line crosses the y axis.

From the figure it is clear that the line passes through (0, -6) and therefore the y-intercept is -6

To compute the slope, find another  convenient point on the line. Compute the ratio of change in y values(called rise) to the change in x values(called run). This will be the slope

We see that point (10, -10) has been identified on the graph.(Any of the 4 identified points will do, I just chose this)

So two points to consider are (0, -6) and (10, -10)

Change in y values = rise = -10 - (-6) = 1- + 6 = -4

Change in x values = run = 10 - 0 = 10

So slope m = -4/10 = -0.4

Equation of line is y = -0.4x -6

Answer: 15 - h - 3

Step-by-step explanation: