Identify the pattern in the list of numbers. Then use this pattern to find the next number. 5,7,12,19,31,50

The equation of the line whose x and y -intercepts are -5/3 and 3/5 respectively is  [tex]9x - 25y + 15 = 0\\[/tex] .

Given,

           The x-intercept of a line = -5/3

            The y-intercept of a line = 3/5

   by substituting values in the intercept form of a line:

                         [tex]-\frac{3x}{5} + \frac{5y}{3} = 1\\[/tex]

     On multiplying the equation by 15 both L.H.S. & R.H.S.

                          [tex]-9x + 25y = 15[/tex]

                      ⇒ [tex]9x - 25y + 15 = 0\\[/tex]

Therefore, the Equation of line is   [tex]9x - 25y + 15 = 0\\[/tex] .

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The end behaviour of the graph shows that the range of the graph ranges from 0 to ∞.

The domain of a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the set of values that the function returns after we enter an x value.

In the given image the graph is showing a parabola symmetric about the y-axis. The range of the graph is varying from 0 to ∞. The graph's end behaviour indicates that the graph's range is from 0 to.

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(a) It will take approx 10.2 years to double your principal at 7% interest.

(b) The required rate of interest to double our income in 2 years is approx 44%

(a)    Given,

                  Annual rate of interest = 7%

                    Let the principal be [tex]x[/tex].

         Formulae for compound interest :

                    [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

Substituting the value of   [tex]P , r , n[/tex] in above formulae.

                  [tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{0.07}{1})^{1t}\\\\2 = 1.07^{t} \\\\t=\frac{ln(2)}{ln(1.07)\\}\\\\t = 10.244768[/tex]

Therefore, it took approx. 10.2 years to double your principal at 7% interest.

(b) Given,

                  The annual rate of interest = [tex]r[/tex]%

                    Let the principal be [tex]x[/tex].

         Formulae for compound interest :

                         [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

we want our money to double in 2 years

                         [tex]2P = P(1 + \frac{r}{n})^{nt}\\\\2x = x(1 + \frac{r}{1})^{2}\\\\2 = (1+r)^{2} \\\\\sqrt{2} = 1 + r\\\\r=0.44[/tex]

Therefore, the required Rate of interest is approx 44%.

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The impedance of the circuit in this problem is given as follows:

Z = (26 + 39i)/11.

The impedance of a circuit of Voltage V and Current I is given by the equation presented as follows:

Z = V/I.

The parameters for this problem are given as follows:

Hence the impedance is given as follows:

Z = (12 + 5i)/(3 - 2i).

Removing the complex number from the denominator, we have that:

Z = (12 + 5i)/(3 - 2i) x (3 + 2i)/(3 + 2i)

Z = [(12 + 5i)(3 + 2i)]/11

11 because (3 - 2i)(3 + 2i) = 9 - 2i² = 9 + 2 = 11, as i² = -1.

Hence:

Z = (36 + 39i - 10)/11

Z = (26 + 39i)/11.

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As a result, there is an 11/16 chance that there will be at least as many heads as tails.

The branch of mathematics concerned with probability is known as probability theory. Although there are several different interpretations of probability, probability theory treats the concept rigorously mathematically by expressing it through a set of axioms. The probability is a measure of the likelihood that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the likelihood or chance that a specific event will occur. Probabilities can be expressed as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The likelihood that there will be more tails, more heads, or equal numbers of each is 5/16, 5/16, and 6/16, respectively. Therefore, the probability that there will be at least as many heads as tails is 11/16.

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Complete Question:

Harold tosses a nickel four times. The probability that he gets at least as many heads as tails is:

The limit of the function is 2 as x approaches 1.

in mathematics, the limit of a function is the value that the function approaches as the input (or independent variable) gets closer to a certain value. The limit of a function is a fundamental concept in calculus, and is used to study the behavior of a function as the input gets arbitrarily close to a certain value, but not necessarily equal to it. The limit is usually denoted by the symbol "lim" and it is read as "the limit of f(x) as x approaches a is L" where f(x) is the function, a is the value that x approaches and L is the limit.

so we need to find

[tex]\lim_{x \to \ 1}\frac{x^2-1}{x-1}[/tex]  ---(i)

we will observer that the function reduces to [tex]\frac{0}{0}[/tex] form at x=1

factorisation of x² -1 = (x+1)*(x-1)

substituting the value of x² -1 in equation (i) we get

[tex]\lim_{x \to \ 1} x+1[/tex]

=> 2

so the value of [tex]\lim_{x \to \ 1}\frac{x^2-1}{x-1}[/tex] =2

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Complete question:

Find the limit of the function as x approaches 1 .

f(x) = [tex]\frac{x^2-1}{x-1}[/tex]

Part 1

Angles of a quadrilateral add to 360 degrees.

[tex]7x+65+85+105=360\\\\7x+255=360\\\\7x=105\\\\x=15[/tex]

Part 2

If [tex]x=15[/tex], then [tex]7x=105^{\circ}[/tex]. Thus, the angles measuring [tex]7x[/tex] and [tex]105^{\circ}[/tex] are opposite angles since opposite angles of a kite are congruent.

This means the remaining angles, which are the angles measuring [tex]65^{\circ}[/tex] and [tex]85^{\circ}[/tex], are also opposite using the process of elimination.

Answer:

x = 20

Step-by-step explanation:

Sum of 12, 8, 6, 4 and x is:

S = 12 + 8 + 6 + 4 + x = 30 + x

[tex]\dfrac{2}{5}S = \dfrac{2}{5}\cdot 30 + \dfrac{2}{5}x\\\\=12 + \dfrac{2}{5}x\\\\\\\textrm{But left side is nothing but x}\\\\\textrm{So we get }x = 12 + \dfrac{2}{5}x\\\\\rm{Subtract $\dfrac{2}{5}x$ from both sides}\\\\x - \dfrac{2}{5}x = 12\\\\\dfrac{3}{5}x = 12\\\\x = \dfrac{12 \cdot 5}{3} \\\\x = 20\\\\[/tex]

Verify

12 + 8 + 6 + 4 + 20 = 50

(2/5) x 50 = 20

It’s cAnswer:

Step-by-step explanation:

it’s right

The graph that represents the situation is added as an attachment

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

This means that the graph would be represented using a distance/time graph

Such that the distance would be on the y-axis and the time would be on the x-axis

See attachment for the graph

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Approximately 43.3% of the respondents rated overall television quality with a rating of 50 or below. The closest answer choice is D. 40

What is the range of the data?

The range is the spread of your data from the lowest to the highest value in the distribution. It is a commonly used measure of variability. Along with measures of central tendency, measures of variability give you descriptive statistics for summarizing your data set

The stem-and-leaf display shows that the data ranges from 0 to 100.

The leaves on the stem for the number "5" are 0, 0, 1, 2, 4, 4, 5, 5, 5, 6, 6, 7, 8, 9.

This means that 13 of the respondents rated overall television quality with a rating of 50 or below.

To find the percentage of respondents who rated television quality 50 or below, we need to divide the number of respondents who rated television quality 50 or below (13) by the total number of respondents and multiply by 100.

13/30 * 100 = 43.333...

Hence, approximately 43.3% of the respondents rated overall television quality with a rating of 50 or below. The closest answer choice is D. 40%.

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Answer:

*50

Step-by-step explanation:

Sum of the interior angle

(n - 2) 180

From the question n is 3.

=(3 - 2) 180

=(1) 180

=180

The value of x

x + (x + 5) + (x + 25) 180

=x + x + x + 5 + 25 = 180

=3x + 30 = 180

=3x = 180 - 30

=3x = 150

=3x/3 = 150/3

x = 50

Therefore the value of x is 50.

Chemical A's rate law may be zero order and is unaffected by the ratio of reactant to product concentrations.

For the zero order reaction, [tex]$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$[/tex]

Rate equation is : Rate [tex]$=\mathrm{k}[\mathrm{A}]^0[\mathrm{~B}]^0$[/tex]

As a result, the pace of the reaction is unaffected by the amounts of reactant and product present.

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The equation is x² - 7x+11 is in form of quadratic equation ax²+bx+c where a = x² , b = -7 and c = 11 .

Option B is correct.

Quadratic equations are second-degree algebraic expressions with the form ax² + bx + c = 0. The word "quadratic" comes from the word "quad," which means square. To put it another way, an "equation of degree 2" is a quadratic equation. Numerous situations call for the use of a quadratic equation.

Factoring  x²-7x+11

The first term is,  x²  its coefficient is  1 .

The middle term is,  -7x  its coefficient is  -7 .

The last term, "the constant", is  11

                                                    x² - 7x  + 11  = 0

When two things are multiplied together and both depend on the same variable, quadratic equations are frequently used. A quadratic equation is used, for instance, when working with area when both dimensions are written in terms of the same variable.

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The equation that represents the town's population is p = 78,000 x 0.97^5.

The equation that represents the town's population is an exponential equation. The general form of exponential equation is f(x) = [tex]e^{x}[/tex]

Where:

The form o f the equation is:

Future population = present population x (1 - rate of decline/100)^number of years

p = 78,000 x (1 - 3/100)^5

p = 78,000x (1 - 0.03)^5

p = 78,000 x (0.97^5)

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Los valores de las expresiones polinomicas son:

10*(1/2)^2 - 4*(1/2) = 1/2

(2/3)*(-3/4) - (1/2)*(-3/4)^2 = -25/32

En este problema queremos encontrar los valores de dos expresiones polinomicas.

La primera es:

10*(1/2)^2 - 4*(1/2)

Primero resolvemos el cuadrado del primer termino, esto da:

10*(1/4) - 4*1/2

10/4 - 4/2

Ahora queremos tener el mismo denominador en ambas fracciones, asi reescribimos la primear como:

5/2 - 4/2

1/2

Ese es el valor numerico.

La segunda expression es:

(2/3)*(-3/4) - (1/2)*(-3/4)^2

Primero resolvemos el cuadrado, recordar que esto cancela el signo negativo:

(2/3)*(-3/4) - (1/2)*(9/16)

Ahora tomamos los productos entre fracciones:

(2/3)*(-3/4) - (1/2)*(9/16)

-6/12 - 9/32

Simplificamos ambas fracciones:

-1/2 - 9/32

Escribimos ambas fracciones con el mismo denominador:

-16/32 - 9/32 = -25/32

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In 1 week, Toby and his sister will each have saved $40.

The first step is to form a linear equation that represents the equation in the question. A linear equation is an equation that has a single variable that is raised to the power of one.

The form of a linear equation that represents the amount saved by the siblings is:

Total amount saved = amount they have already saved + (number of weeks x amount saved per week)

Amount saved by Toby = $26 + ($14 x w)

$26 + $14w

Amount saved by his sister = $28 + ($12 x w)

$28 + $12w

When the siblings have saved the same amount of money, the two above linear functions would be equal:

$26 + 14w = $28 + $12w

In order to determine the value of w, take the following steps:

Combine and add similar terms:

$14w - $12w = $28 - $26

2w = 2

Divide both sides of the equation by 2

w = 2 / 2

w = 1 week

Total amount that would have been saved = $28 + $12(1)

$28 + 12 = $40.

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The measure of angle 2 is given as follows:

115º.

When two parallel lines are cut by a transversal, the consecutive angles relative to the same vertex are linear pairs, which are supplementary angles.

When two angles are supplementary, the sum of their measures is of 180º, meaning that the equation for this problem is given as follows:

m < 1 + m < 2 = 180º.

Since m < 1 = 65º, the measure of angle 2 is obtained as follows:

m < 2 = 180 - 65

m < 2 = 115º.

The figure giving context to the problem, without scaling, is given at the end of the answer.

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The probability that the next piece of fruit out of the bag will be an apple is ²/₃.

The probability is the chance that an expected outcome occurs out of many possible outcomes.

Probability is a fractional value that is obtained as the quotient of the expected outcome over the total events.

The number of apples = 4

The number of peaches = 3

The number of plums = 2

Total number = 9

The number of fruits taken out = 3 (2 plumbs and 1 peach)

The remaining fruits in the grocery bag:

The number of apples = 4

The number of peaches = 2 (3 - 1)

The number of plums = 0 (2 - 2)

Total number = 6

The probability of picking an apple out of the remaining fruits = 4/6 = 2/3

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Answer:

3.725

Step-by-step explanation:

10-6.275

4-0.275

3.725

The null hypothesis population proportion for this test is 33%. The test is used to determine if the proportion of only children in the special program is significantly different from the proportion for the school district, at an alpha level of 0.05.

Step 1: Define the parameters:

Population proportion (p): 33%

Significance level (α): 0.05

Step 2: Calculate the test statistic:

Sample proportion (p-hat): 130/345 = 0.37

Step 3: Calculate the critical value:

Critical value (α): 0.05

Step 4: Compare the test statistic to the critical value:

Test statistic (p-hat) > Critical value (α): 0.37 > 0.05

The test statistic is greater than the critical value, so the null hypothesis is rejected. Therefore, the proportion of only children in the special program is significantly different from the proportion for the school district.

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Answer:

B

Step-by-step explanation:

If both signs are the same (++,--), then you subtract.

If the two signs are different(+-,-+), then you add.

The first step in evaluating 2+7. 12/6-3² is to substitute the values for the numbers and calculate the sum of 2+7, which is 9.

Evaluating is the process of making judgments about something based on a set of criteria. It involves analyzing and assessing a subject and making a determination of its value or worth. This can be done for a variety of things, such as an essay, a project, an individual or group, or a product. Evaluation is a crucial part of the decision-making process and involves a careful consideration of all relevant information and factors. It helps to identify strengths and weaknesses, and determine the effectiveness of something. Evaluating is also used to measure performance, identify areas for improvement, and make comparisons.

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The statement b(14) = 170 is interpreted using the function 1850 - 120w = b to be:

When w is 14 b is equal to 170

The function 1850 - 120w = b  as in the problem is a linear function.

A linear function is one which all the parameters has exponents of one. In the linear function parameters are defined below

b = the output value

w = the input value

120 = slope

1850 = the y intercept

The statement b(14) = 170 means that at input of 14 the out put is 170. this is shown mathematically

1850 - 120w = b

1850 - 120 * 14 = b

1850 - 120w = 170 = b

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The categories include,

8th grade: left-skewed unimodal

Unimodal and symmetric birth weight

Computer count is unimodal and skewed to the right.

Bimodal adult weight distribution

A graph called a histogram shows the frequency distribution of a few data points for a single variable. Data is frequently divided into a number of "bins" or "range groups" by histograms, which count the number of data points in each bin.

While bar charts show categorical factors, histograms display numerical or quantitative data. In most situations, a histogram's numerical data will be continuous (having infinite values). To attempt to plot a continuous variable's possible values on an axis would be absurd.

Based on the frequency distribution, there are four different types of histograms.

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The complete question is: Classify each histogram using the appropriate descriptions. Identify all of the descriptions that apply for each histogram.

The water Ms. Morales put in the pool in terms of π is  [tex]\pi[/tex]6561inch^3

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Given;

Diameter= 54 in.

Height of pool= 12ft

Now,

3/4 th height of pool;

3/4 x 12= 9inch

Volume= [tex]\pi r^{2}h[/tex]

=[tex]\pi[/tex]27x27x9

=[tex]\pi[/tex]6561inch^3

Therefore, the volume of pool will be [tex]\pi[/tex]6561inch^3

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y=7 is One of line M's potential equations.

Let L and M be two lines that are perpendicular to each other. Slope of line is given by m=x 2 −x 1/ y 2​ −y 1

If the denominator is zero, or if the value of the x-coordinate is the same at all points, the value of m is undefined. Every point lying on L has the same value of the x-coordinate because L has an undefined slope.

L is a vertical line because it is parallel to the Y-axis.

Lines that are vertical and horizontal are perpendicular to one another.

∴ Line M will be parallel to the X-axis since it is perpendicular to line L.

Every point located on M will have a constant y-coordinate.

∴ m=0 for M.

Thus, y=7 is one of line M's potential equations.

​

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​

The total time of homework is represented by T = 2x + 20.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Vlad spent 20 minutes on his history homework and then completely solved X math problems that took two minutes to complete.

The expression can be written as:-

T = 2x + 20 minutes

Here, T is the total time, and x is the number of math problems.

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The constant change rate will be straight according to the solution.

When the ratio of something like the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope is another name for the constant change rate. For linear functions, the rate of change will be constant.

The change rate (slope) is constant for straight lines (always the same). The rate of change for such lines is constant. With the aid of the resources on this page, you may learn how to calculate slope and change rate as well as the rate of change formula.

Age                        Height

9                                  54

10                                 56

11                                  58

12                                 60

The constant rate of change will be straight. because the given data will form a straight line on the graph.  the rate of change (slope) is constant (always the same). For such lines, the rate of change is constant.

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When the sum of two numbers is 22, and their difference is 12, the lesser of the two numbers is 5.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

Let numbers be a and b.

a+b=22

a=22-b

b-a=12

b-(22-b)=12

2b-22=12

2b=34

b=17

a=5

The lesser of the two numbers is 5 when the sum of two numbers is 22, and their difference is 12.

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