The equation of line s is y + 7 = -7/6(x - 7).
What is slope of a line?
A line's steepness and direction are measured by the line's slope. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, Δy, Δx respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx
Given equation of line r is y = 6/7x+1.
The slope of line r is m = 6/7
The slope of the line that is perpendicular to line r is -1/m = - 7/6.
The equation of line that passes through the point (x₁, y₁) with slope m is y - y₁ = m(x - x₁).
Putting m = - 7/6, x₁ = 7 and y₁ = -7 in y - y₁ = m(x - x₁):
y - (-7) = - 7/6(x - 7)
y + 7 = - 7/6(x - 7)
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Solve each system by elimination: 7x+3y=-1 4x+y=3
Using elimination method, the solution to the system of equation is as follows:
x = 2 and y = -5
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's use elimination method to solve the system of equation as follows:
7x + 3y = - 1
4x + y = 3
multiply equation(ii) by 3
Hence,
7x + 3y = - 1
12x + 3y = 9
subtract equation(i) from equation(ii)
5x = 10
x = 10 / 5
x = 2
Let's find y
7x + 3y = - 1
7(2) + 3y = -1
14 + 3y = -1
3y = -15
y = -15 / 3
y = -5
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Write an equation of the line in point plice form, through the point (4,-1) and ha a lope a 6
The equation of the line will be y = 6x - 25
Given, the point is (4, -1)
The slope is m = 6.
We have to write an equation of the line in slope-intercept form.
The standard form of equation of the line in slope-intercept form is given by
y = mx + c
Where, m is the slope.
Now, substituting the values of x, y and m in the equation,
-1 = 6(4) + c
-1 = 24 + c
c = -1 - 24
c = -25
Put the value of c in the standard equation,
y = 6x - 25
Therefore, the equation of the line is y = 6x - 25
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Solve for x . Round to the nearest tenth, if necessary.
Answer: 52.5°
Step-by-step explanation:
sin59 = 45/x
sin59(x) = 45
x = 45/sin59 = 52.5°
A full pond containing 625 gallons of water begins losing its water at a rate of 20% per week. If the pond now contains 320 gallons of water, how many weeks has it been since the pond was at full capacity?
(Use the digits 0 – 9 to enter a number. Use a decimal point only if necessary.)
Using an exponential function to represent the exponential decay, it will take approximately 4 weeks to reach 320 gallons
Exponential EquationAn exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
To solve this problem, we have to write an exponential equation to calculate the exponential decay.
Data;
A = 320P = 625r = 20% = 0.2t = ?A = P(1 + r)⁻ˣ
320 = 625(1 + 0.2)⁻ˣ
x = 3.67
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calculate the p-value associated with the null hypothesis that 50% of the students at eastern work more than 10 hours a week.
The p-value associated with the null hypothesis = 0.05
Fail to reject the null hypothesis. The P-value is greater than the level of significance.
Candice should reject the null hypothesis as the 50% confidence interval does not contain 10 hours
Small p-values offer proof that the null hypothesis is false. The stronger the evidence is against the null hypothesis, the smaller (closer to 0) the p-value. The null hypothesis is rejected if the p-value is less than or equal to the chosen significance level; otherwise, it is not.
You have the Hypothesis that "students study less than 10 hours, on average, per week"
Symbolically:
H₀:μ≥10hours
H₁:μ<10hours
The significant level for this case study is 50% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.
The p-value of 0.05 is one of the most often used numbers. When the calculated p-values are less than 0.05, the faulty hypothesis is considered to be fraudulent or invalid (subsequently the name invalid theory). Additionally, the faulty theory is taken into consideration to be clear if the value is greater than 0.05.
The edge for that likelihood in our model is 0.05, and it represents the probability that our results will be similar to the invalid speculation. Therefore, if the calculated p-value is less than 0.05, it actually means that there is a very little likelihood that we would have the same results as the flawed hypothesis. Additionally, if the p-value is greater than 0.05, there is a very strong probability that the results will be similar to the flawed speculation, leading us to conclude that it is legitimate.
Therefore,
Fail to reject the null hypothesis. The P-value is greater than the level of significance.
The p-value associated with the null hypothesis = 0.05
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please help need an answer ASAP!!!!!!!!!!!!
Answer:
1/9
Step-by-step explanation:
The y intercept of a line is when x = 0
y = 1/9
Answer:
y = 1/9
Step-by-step explanation:
y = -10x + 1/9
Substitute 0 for x
y = -10 x 0 +1/9
-10 x 0 = 0
y = 1/9
Write an equation of the line that passes through $\left(7,10\right)$ and is perpendicular to the line $y=\frac{1}{2}x-9$.
The equation of the line that passes through (7, 10) and its perpendicular to the line y = (1/2)x - 9 is y = -2x + 24
The coordinates of the line passing through the point = (7, 10)
The equation of the perpendicular line
y = (1/2)x - 9
The slope of the line = 1/2
The slope of the original line = - 1 / (1/2)
= -1 × 2
= -2
The slope intercept form is
y = mx + b
Substitute the values in the equation and find the value of b
10 = -2(7) + b
10 = -14 + b
b = 10 + 14
b = 24
Substitute the value of b and m is the equation
y = -2x + 24
Therefore, the slope of the line is y = -2x + 24
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question in the image below!!!!!!
Part a: The significance of the piece-wise function is define.
Part b: r(t) be the total amount of snow in cubic ft. is calulated.
Part c: Total volume of the ice is not removed.
Define the term rate of change of volume?The term "rate of change" (ROC) describes the rate which something transforms over time.The indicator that demonstrates how much a volume tendency is developing either in the up or down direction is the volume rate of change.For the given question, the rate function is given as;
f(t) = { 0, 0 ≤ t < 6 ,
125, 6 ≤ t < 7
108, 7 ≤ 9 }
Part a: The significance of the piece-wise function is-
f(t) = { 0, 0 ≤ t < 6 } define the volume of ice per hour accumulated in between 0 to 6 hours is 0 cubic ft/hr.f(t) = {125, 6 ≤ t < 7 } define the volume of ice per hour accumulated in between 6 to 7 hours is 125 cubic ft/hr.f(t) = { 108, 7 ≤ 9} define the volume of ice accumulated per hour in between 7 to 7 hours is 108 cubic ft/hr.
Part b: r(t) be the total amount of snow in cubic ft.
r(t) = { 0, 0 ≤ r < 6 } define the volume of ice accumulated in between 0 to 6 hours is 0 cubic ft: 0 cubic ft.f(t) = {125, 6 ≤ t < 7 } define the volume of ice accumulated in between 6 to 7 hours is 125 cubic ft. is 62.5 cubic ftf(t) = { 108, 7 ≤ 9} define the volume of ice accumulated in between 7 to 7 hours is 108 cubic ft. is 54 cubic ft.Part c: total ice accumulated is;
62.5 ft + 54 ft. = 116.5 cubic ft.
Total volume of the ice accumulated = 367.5 cubic ft.
Thus, no total volume of the ice is not removed.
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Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula?
Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction
An expression which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula is: expression A. Therefore, the correct answer option is A.
What is a quadratic equation?A quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
Mathematically, the quadratic formula is modeled or represented by this mathematical expression:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
From the information provided, we have the following values;
0 = -3x² - 2x + 6
Where:
a = -3
b = -2
c = 6
Substituting the values into the quadratic formula, we have;
[tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2 - 4(-3)(6)}}{2(-3)}\\\\x = \frac{2\; \pm \;\sqrt{4^2 - 4(-3)(6)}}{2(-3)}[/tex]
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What is the length of segment AB? (4 points) A coordinate plane is shown. Point A is located at 0, 12, and point B is located at 5, 0. The two points are connected by a line segment. 10 12 13 15
The length of segment AB is 13 units.
What is the distance formula?The distance between the two points (a,b) and (c,d) is given by:
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex].
The given coordinates of A and B are A(0,12) and B(5,0).
The length of segment AB is given by:
[tex]AB = \sqrt{(5-0)^2 + (0 - 12)^2}\\\\AB=\sqrt{25 + 144}\\\\AB = \sqrt{169}\\\\AB = 13[/tex]
Hence, the length of segment AB is 13 units.
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Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales. Last week, she sold $843 worth of goods. How much was she paid?
The amount that Josephine will be paid is $644.30.
How much was Josephine paid?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
In this situation, Josephine earns a salary of $560.00 per week, plus a commission of 10% on all sales and she sold $843 worth of goods.
The amount she'll be paid will be:
= $560 + (10% × $843)
= $560 + $84.3
= $644.30
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The results of a series of surveys revealed a population with a mean of 15 and a standard deviation of 1.88. If each survey has a sample size of 70, which value falls within the interval where 95% of the sample means occur?
A) 15.66
B) 15.49
C) 14.96
D) 14.34
If each survey has a sample size of 70, a value which falls within the interval where 95% of the sample means occur is: C) 14.96.
What is a confidence interval?In this scenario, the confidence interval at 95% can be represented by this mathematical expression p - E < p < p + E
Based on the parameters provided, we would determine both the lower limit and upper limit for the interval where 95% of the sample means occur as follows;
Lower limit = 15 - 1.88/√70
Lower limit = 15 - 0.23
Lower limit = 14.77
For the upper limit, we have:
Upper limit = 15 + 1.88/√70
Upper limit = 15 + 0.23
Upper limit = 15.23
For 95% of the sample means to occur, the confidence interval is given by;
Confidence interval = (14.77, 15.23)
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1. (*) Tres amigos, Alex, Beto y Valentín, van al cine y se sientan en una fila de tres asientos contiguos vacíos. Si se sabe que:
• Alex se sienta adyacente a Beto y Valentín.
• Valentín se sienta a la derecha de Beto.
¿Cuál es el orden en que se sientan dichos amigos, empezando de izquierda a derecha?
Beto, Alex, Valentín
O Valentín, Beto, Alex
Valentín, Alex, Beto
O Alex, Valentín, Beto
By using the concept of arrangement, it can be concluded that-
The correct order is Beto, Alex, Valentin
What is arrangement?The act of arranging people and things towards a certain goal is referred to as arrangement. the arrangement or arrangement of details in a written work. Readers to whom a piece of writing is addressed; those who read or hear what you have written.
Why is writing arrangement crucial?Your reader could feel disoriented and lose interest if there is no obvious organizational structure. Your essay's organization will aid readers in making connections between the essay's body and thesis, as well as help you stay on task as you plan and compose the essay.
It is known that:
• Alex sits next to Beto and Valentin.
• Valentin sits to the right of Beto.
So the correct order is Beto, Alex, Valentin
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A shipping container is in the shape of a right rectangular prism with a length of 20 feet, a width of 8.5 feet, and a height of 8 feet. The container is filled with contents that weigh 0.25 pound per cubic foot. What is the weight of the contents in the container?
5440 pounds
1360 pounds
240 pounds
340 pounds
The weight of the contents in the container is 340 pounds
How to calculate the weight of the contents in the container ?The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units. Volume and the definition of length are related.
Given ,
volume of container = 20 x 8.5 x 8= 1360 cubic feet
weight = 0.25 pounds per cubic foot
0.25 x 1360 = 340 pounds
Therefore the weight of the contents in the container is 340 pounds
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For this function, what is the average rate of change over the interval 3.5 ≤ x ≤ 4?
The average rate of change for 3.5 ≤ x ≤ 4 is 2[f(4) - f(3.5)]
What is Average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
given:
Interval: 3.5 ≤ x ≤ 4
Now, For average rate
= [f(4) - f(3.5)]/(4 - 3.5)
= 2[f(4) - f(3.5)]
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Please help me thank you
The slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The parallel lines have same slope
The slope of LM = the slope of NO
The slope of LM = (-1-(-5))/(4-(-2))
The slope of LM = 4/6 = 2/3
Slope of NO = 2/3
If LMNO is rectangle:
The slope of LO = -1/(slope of LM)
The slope of LO = -1(2/3)
The slope of LO = -3/2
Thus, the slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.
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Which expression is equivalent to this polynomial?
15x - 24
A.3(5x-8)
B. 5(3x-8)
C. 3(5x-24)
D.3(5x - 5)
Answer: A 3(5x-8)
Step-by-step explanation: 3 times 5x is 15x and 3 times -8 is -24
Help guysss happy holidays
The Type of taxation system in this table represent is Option C Regressive Tax.
What is Taxation System?Taxation System is an obligatory fee or financial charge is referred to as a tax when it is imposed by a government on a person or an organisation in order to raise money for public projects that fund the greatest services and infrastructure. Various public spending programmes are then funded with the money that was gathered.
Type of Taxation
There are mainly four types of Taxes, these are Regressive, progressive, Indirect, and Proportional. In the given question the Regressive Taxation system is represented.
A Regressive Taxation system is one where Companies which have lower income have higher tax rate in comparison to big companies. In the given question the company which have lowest income is giving 15% of total income, while the largest company is giving 10% of their income.
Therefore, taxation system in this table represent is Option C Regressive Tax.
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Which of these expense types and answers is true?
a. Fixed expenses - change each month
b. Periodic fixed expenses - are monthly expenses like your water bill and electric or gas bill.
c. Flexible expenses - monthly expenses whose cost is the same each month
d. Indebtedness expense - minimum monthly payments you make on your loans and credit cards
The expense type which is true is , indebtedness expense as because they are the minimum monthly payments you make on your loans and credit card.
Being in debt to someone else or owing them money is the state of being indebted. A person who owes money has either borrowed money or obtained goods or services in exchange for a promise to repay the money.
Someone can owe money for both present-day obligations and obligations that they anticipate having in the future. For instance, the term "indebtedness" can relate to a person's mortgage or a car loan.
The majority of people cannot afford to buy a home or a car outright, thus they owe the bank the amount of the loan that was granted to them. When you use a credit card to make purchases like apparel or travel expenses, you become indebted. Being in debt is not the same as not making payments.
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Write the
equation
of the line In
Slope-Intercept
Form.
Type your
answer here.
The equation of line in slope intercept form is y = -1/3 x + 1.
What is equation of a line?
The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. The slope of the line and a point on the line can be used to create the equation of a line.
The points on the line are (3,0) and (0,1).
The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of line is (1 - 0)/(0 - 3) = -1/3.
The line cuts y-axis at (0,1). Thus y-intercept of the line is 1.
The slope-intercept form of the line is
y = -1/3 x + 1
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which is more likely rolling a total of 8 when two dice are rolled or rolling a total of 8 when thre dices are roled
Answer: Two dice
Step-by-step explanation:
For the two dice, there are 5 possible: (6, 2);(5, 3);(4, 4);(3, 5);(2, 6)
So two dice, the probability is 5/36 = 30/216
For three dice, the number of favorable cases is 21
The probability is 21/216
So the two dice are more likely
An airline finds that about 888 percent of the time, a person who makes an advance reservation does not keep the reservation. Therefore, for each of their 105105105-passenger planes, the company schedules 113113113 people with advance reservations. Based on this information, about how many of the scheduled people will not keep their reservation?.
Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.
Given,
In the question:
An airline finds that about 8 percent of the time, a person who makes an advance reservation does not keep the reservation.
Therefore, for each of their 105105105-passenger planes, the company schedules 113113113 people with advance reservations.
Now, According to the question:
Capacity of the airline per trip = 105 only
But company schedules = 113 people with advance reservations
Since 8% do not turn up
Out of 113 passengers who reserved in advance we can say
that 8% of 113 passengers will not keep their reservation
Based on this information, number of the scheduled people will not keep their reservation
= 8% x 113
= 0.08*113
=9.04
Hence, Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.
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chi-square tests are used for testing hypotheses of the association between two categorical values.
true
false
The given statement " chi-square tests are used for testing hypotheses of the association between two categorical values. " is true
The term chi square test defines if there is a significant relationship between two nominal variables.
Here we have given the statement, chi-square tests are used for testing hypotheses of the association between two categorical values.
And we need to find whether the statement is true or not.
As per the definition of chi square test, we know that the frequency of each category for one nominal variable is compared across the categories of the second nominal variable.
Here we also know that the data can be displayed in a contingency table where each row represents a category for one variable and each column represents a category for the other variable.
Therefore, based on these facts the given statement is true.
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What is the value of x?
Answer: 71
Step-by-step explanation:
Calculate c, ∠B, and ∠A based on given b, a, and ∠C.c = √b2 + a2 - 2ba·cos(C) = 13.67386∠B = arccos(c2 + a2 - b22ca)= 1.23918 rad = 71°∠A = arccos(c2 + b2 - a22cb)= 1.23918 rad = 71°
Construct a quadrilateral PQRS with PQ= 5cm, QR = 5.5cm, RS = 5.5cm, SP= 6.5cm & angle PQR = 75°.Also construct a Triangle QRM whose area is equal to quadrilateral PQRS.
The image for quadrilateral PQRS is attached below
The image for Triangle QRM is attached below
What is the construction of a quadrilateral PQRS?Generally, To construct a quadrilateral PQRS with the given dimensions, you can use a straightedge and a compass. Here is a step-by-step guide:
Start by drawing a straight line segment PQ of length 5 cm.Place the compass on point P and draw an arc with a radius of 5.5 cm.Place the compass on point Q and draw an arc with a radius of 5.5 cm. The two arcs should intersect at a point R.Place the compass on point R and draw an arc with a radius of 6.5 cm.Place the compass on point P and draw an arc with a radius of 6.5 cm. The two arcs should intersect at a point S.Connect points S and R to complete the quadrilateral PQRS.To construct a triangle QRM with an area equal to quadrilateral PQRS, you can use the same method as above. Here is a step-by-step guide:
Start by drawing a straight line segment QM of length 5 cm.Place the compass on point Q and draw an arc with a radius of 5.5 cm.Place the compass on point M and draw an arc with a radius of 5.5 cm. The two arcs should intersect at a point R.Connect points Q and R to complete the triangle QRM.To verify that the area of triangle QRM is equal to the area of quadrilateral PQRS, you can use the formula for the area of a triangle:
Area of triangle QRM = (1/2) * QM * QR * sin(angle QRM)
And the formula for the area of a quadrilateral:
Area of quadrilateral PQRS = (PQ * QR * sin(angle PQR))/2
Substituting the given values and solving for sin(angle QRM), we find that:
sin(angle QRM) = (2 * area of quadrilateral PQRS)/(QM * QR)
= (2 * (5 * 5.5 * sin(75)))/(5 * 5.5)
= sin(75)
Thus, the area of triangle QRM is equal to the area of quadrilateral PQRS, as desired.
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∠ABC and ∠KLC form a linear pair with m∠ABC = 74° and m∠KLC = x°.
Answer:
106
Step-by-step explanation:
A linear pair adds to 180
180 - 74 = 106
At the Wheatley School, the probability that a student takes Math 8 and Technology is 0.12. The probability the student takes Math 8 is 0.16. Find the probability that the student takes technology given that he is taking Math 8.
The probability that the student takes technology given that he is taking Math 8 is 0.075.
What is conditional probability?
Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Here, we have
Given:
The probability that a student takes Technology and Math 8 is 0.012.
P(Technology and Math 8) = 0.012
The probability that a student takes Math 8 is 0.16.
P(Math 8) = 0.16
We have to find the probability that a student takes Technology given that the student is taking Math 8
we use conditional probability
P(Technology|Math 8) = P(Technology and Math 8)/P(Math 8)
P = 0.012/0.16
P = 0.075
Hence, the probability that the student takes technology given that he is taking Math 8 is 0.075.
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For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
a. stays the same
b. increases
c. decreases
The minimum sample size needed to guarantee a given margin of error increases , the correct option is (b) .
What is Margin Of Error ?
The term margin of error is defined as an estimate of a small sample that is drawn from a relatively large population data.
the margin of error is usually governed by the parameters such as the standard deviation , sample size and desired confidence level.
to find missing term in the given statement , let us consider the values ,
where σ ⇒ Standard deviation for population
and m as "Margin of error" and Z as "Empirical value of Z-score" at a given confidence level .
So , minimum sample size for given confidence level is given by
⇒ (Z×σ)²/m²
from above formula we can conclude that minimum sample size is directly related to population's standard deviation.
Therefore, the minimum sample size required would "increase" with the increase in population "standard deviation" .
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Simplify the expression:
5t+
–
9+
–
8t+
–
5
The expression 5t + (-9) + (-8t) + (-5) in the simplified form will be negative (3t + 14).
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 5t + (-9) + (-8t) + (-5)
Simplify the expression, then the value of the expression is given as,
⇒ 5t + (-9) + (-8t) + (-5)
⇒ 5t - 9 - 8t - 5
⇒ – 3t – 14
⇒ – (3t + 14)
The expression 5t + (-9) + (-8t) + (-5) in the simplified form will be negative (3t + 14).
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a linear function has slope of -5/3. What does the slope tell us about the graph of the function
Answer:
Step-by-step explanation:
The slope of a linear function is a measure of the rate at which the value of the function changes as the input (x) changes. A slope of -5/3 means that for every 3 units of change in the input, the output (y) changes by -5 units.
In general, a negative slope indicates that the graph of the function is decreasing. As the input increases, the output decreases. A slope of -5/3 is a relatively steep negative slope, which means that the graph of the function will have a steep downward slope.
A slope of -5/3 also tells us that the function is not a horizontal line. A horizontal line has a slope of 0, which means that the output does not change as the input changes. A slope of -5/3 is not equal to 0, which means that the function is not a horizontal line.
Overall, the slope of a linear function tells us about the direction and steepness of the graph of the function. A slope of -5/3 indicates that the graph of the function is decreasing and relatively steep.