the correlation coefficient of X and Y is Cov ( X, Y ) = 1/2
X = Number of heads in the first 20 flips
Y = Number of heads in the last 20 flips
Given that X and Y are binomial variables hence
P( probability ) = 1/2
Find Cov( X; Y )
xi = result of the ith flip ∴ X = x1 + x2 + x3 + x4+....x20
yj = result of the jth flip ∴ Y = y3 + y4 + y5 + y6+ ....x20
covariance of xi and yi = 1/2 * 1/2 = 1/4 when i = j and it is = 0 when i ≠ j
hence Cov( X; Y ) can be expressed as
Cov( X; Y ) = ∑^4 ∑^6 ∴ Cov( Xi , Yj ) = 2/4 = 1/2 ( given that i = j )
Hence he correlation coefficient of X and Y is Cov ( X, Y ) = 1/2
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Ms. Morales bought the kiddie pool shown below for her children. pleas help thank you
A diagram of a kiddie pool is shown. The height of the pool is labeled twelve inches. A line drawn under the pool from one side of the pool to the other is labeled fifty-four inches.
If she filled the pool 3/4 of the way with water, how much water did Ms. Morales put in the pool in terms of π?
Responses
A)5,832π in.3
B) 6,561π in.3
C) 7,776π in.3
D) 8,748π in.3
The water Ms. Morales put in the pool in terms of π is [tex]\pi[/tex]6561inch^3
What is the volume of a right circular cylinder?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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harold tosses a nickel four times. then find the probability that he gets at least as many heads as tails.
As a result, there is an 11/16 chance that there will be at least as many heads as tails.
What is probability?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:
In a certain school district, it was observed that 33% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 130 out of 345 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.05α=0.05 level of significance. What is the hypothesized population proportion for this test?
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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Find the limit of the function as x approaches 1 by inspecting the graph.
O 2 O oo O -1 O 5 O 0
The limit of the function is 2 as x approaches 1.
What is limit of a function?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]
the sum of two numbers is 22, and their difference is 12. set up two equations to solve using elimination to help you find the numbers. enter the lesser of the two numbers here:
When the sum of two numbers is 22, and their difference is 12, the lesser of the two numbers is 5.
What is equation?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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A kite has angle measures of 7x°, 65°, 85°, and 105°. Find the value of x.
Which of the angles are opposite angles? Explain your reasoning.
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.
A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100(extremely good quality). The stem-and-leaf display of the data is shown to the right. What percentage of the respondents rated overall television quality with a rating of 50 or below? show answer please A. 56 B. 44 C. 11 D. 40
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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Toby and his little sister are saving up money to buy a joint birthday present for their mother. Toby already has $26 saved and plans to save $14 per week from his allowance. His sister has $28 saved so far and will save $12 per week from hers. The two siblings will soon have saved the same amount towards their mother's gift. How long will that take? How much will each one have saved?
In ------- weeks, Toby and his sister will each have saved $---------
In 1 week, Toby and his sister will each have saved $40.
In how many weeks would the siblings have saved the same amount?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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An individual was making blankets for a few friends. The individual used 6.25 feet of fabric for one blanket. If the individual makes 7 blankets, how many feet of fabric will the individual have used to make 7 blankets (round to the nearest whole number)?
Landon had one string that was 10 meters long. He used 6.275 meters of this string for a project.
What was the length of string in meters that Landon had left?
16.275 m
4.275 m
3.725 m
6.265 m
Answer:
3.725
Step-by-step explanation:
10-6.275
4-0.275
3.725
Use the figure showing two parallel lines cut by a transversal. Find the measure of angle 2 if the measure of angleUse the figure showing two parallel lines cut by a transversal. Find the measure of angle 2 if the measure of angle 1 is 65 degrees.
1 is 65 degrees.
The measure of angle 2 is given as follows:
115º.
What are linear pairs?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.
Missing InformationThe figure giving context to the problem, without scaling, is given at the end of the answer.
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What is the end behavior of the graph?
The end behaviour of the graph shows that the range of the graph ranges from 0 to ∞.
What are domain and range?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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Which of these strategies would eliminate a variable in the system of equations?
{
6
�
+
5
�
=
1
6
�
−
5
�
=
7
⎩
⎪
⎪
⎨
⎪
⎪
⎧
6x+5y=1
6x−5y=7
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
Subtract the bottom equation from the top equation.
(Choice B)
B
Add the equations.
(Choice C)
C
Multiply the top equation by
7
77, then subtract the bottom equation from the top equation.
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 x and y -intercepts of a line are -5/3 and 3/5 respectively. What is its equation?
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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Vlad spent 20 minutes on his history homework and then completely solve X math problems that took two minutes to complete what is the equation that could be used to find the value of why the total time that Vlad spent on his homework and what are the constraints on the values of X and y
The total time of homework is represented by T = 2x + 20.
What is an expression?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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For the reaction A + B -> C, explain at least two ways in which the rate law could be zero order in chemical A.
Chemical A's rate law may be zero order and is unaffected by the ratio of reactant to product concentrations.
What is meant by ratio?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls). This suggests that there are more individuals who disapprove of your opinion than who approve of it.The mathematical formula for the ratio is commenting/(reposts + likes), where the ratio is the number of comments a post receives in comparison to likes and reposts.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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Find the constant rate of change
Age Height
9 54
10 56
11 58
12 60
The constant change rate will be straight according to the solution.
What does "constant rate of change" mean?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 rate of change is it always the same?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.
According to the given data: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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1850-120w=b (the answer of part A)
How would you interpret the statement that b(14)=170?
The statement b(14) = 170 is interpreted using the function 1850 - 120w = b to be:
When w is 14 b is equal to 170
How to interpret a functionThe 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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Lines L and M are perpendicular to each other. Line L has an undefined slope. Find the possible equation of line M.
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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Which expression shows the first step in evaluating
2+7.12-3²?
6
A 2+84-3²
6
B 9.12-3²
C 2+7.122
1.12-9
6
D 2+7.2-3²
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.
What is evaluating?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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S is the sum of 12, 8, 6, 4 and x. What is the value of x if x = 2/5S?
(Linear equations)
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
Calcular el valor numerico de la funcion polinomica.
Gracias al que respondio :)
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
¿Como resolver las expresiones?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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The impedance Z, in ohms, of a circuit element is defined as the ratio of the phasor voltage V, in volts, across the element to the phasor current I, in amperes, through the elements. That is, z= v/i. If the voltage across a circuit element is 12+5i volts and the current through the element is 3-2i amperes, determine the impedance.
The impedance of the circuit in this problem is given as follows:
Z = (26 + 39i)/11.
How to obtain the impedance of a circuit?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:
V = 12 + 5i.I = 3 - 2i.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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There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)
The probability that the next piece of fruit out of the bag will be an apple is ²/₃.
What is the probability?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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(a) If you invest Po dollars at 7% annual interest and the future value is computed by continuous com- pounding, how long will it take for your money to double?
(b) Suppose you invest Po dollars at r% annual interest and the future value is computed by continuous compounding. If you want the value of the account to double in 2 years, what is the required interest rate?
(c)A rule of thumb used by many people to determine the length of time to double an investment is the rule of 70. The rule says it takes about t = 70/r years to double the investment. Graphically compare this rule to the one isolated in part b. of this problem.
(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 three interior angles of a triangle measure x°, (x+5)°, and (x+25)°, which is the measure of the three angles
* 45°
* 65°
* 70°
* 50°
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.
1
Which of the following lists the terms in
x^2-7x + 11?
A. x, 7, 11
B. x², -7x, 11
C. x, -7x, 7, 11
D. x, x², 7, -7x, 11
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.
How do quadratic equations work?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.
Evaluating :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
Why do we use quadratic equations?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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Write in point slope form and slope intercept form.
When given the point-slope form of a line, we first must identify the point and the slope in order to create a graph of the line.
How do you write point-slope form with a point slope?The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept). In order to emphasise the slope and y-intercept of the same line, we can rewrite an equation in point-slope form to be in slope-intercept form, y=mx+b.
Plug the slope and the (x, y) point values into y = mx + b, then solve for b using the substitution method.Point-slope form is represented as y y 1 = m (x x 1), where (x 1, y 1) is the supplied point and m is the given slope.
Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). A graph is usually simple to make.
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The given points can be written in point-slope form as y - 6 = -6(x - 4) and slope intercept form as y = -6x + 30.
How do you write point-slope form with a point slope?The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept). In order to emphasise the slope and y-intercept of the same line, we can rewrite an equation in point-slope form to be in slope-intercept form, y=mx+b.
Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). A graph is usually simple to make.
Given, x intercept = 5
which means when y = 0, x = 5 i.e. (5, 0)
And given a point (4, 6)
using the two points in slope formula
[tex]$\mathrm{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
[tex]$\mathrm{m = \frac{6- 0}{4 - 5}}[/tex]
m = 6/-1
m = -6
Now, as we have slope, put the data in point-slope form
y-y₁ = m(x -x₁)
y - 6 = -6(x - 4) ⇒ point-slope form
y - 6 = -6x + 24
y = -6x + 24 + 6
y = -6x + 30 ⇒ slope intercept form
Thus, the given points can be written in point-slope form as y - 6 = -6(x - 4) and slope intercept form as y = -6x + 30.
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A town has a population of 78,000 and shrinks at a rate of 3% every year. Which equation represents the town’s population after 5 years?
The equation that represents the town's population is p = 78,000 x 0.97^5.
What is the equation?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:
x = the variable e = constantThe 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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A person cycles from their home to a library which is 8 kilometers away. It takes them 20 minutes to reach the library. They stay there for 30 minutes to read, and then walk to their friend's home which is 4 kilometers from the library and reach there in 20 minutes. Which graph best represents this situation?
It’s cAnswer:
Step-by-step explanation:
it’s right
The graph that represents the situation is added as an attachment
How to determine the graph of the situationFrom the question, we have the following parameters that can be used in our computation:
Library = 8 kilometers for 20 minutesTime at rest = 30 minutesFriend = 4 kilometers for 20 minutesThis 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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