The line equation that passing through point (6,-1) and perpendicular to y = -2x + 8 is
From the case we know that:
Point = (6, -1)
Line 1: y = -2x + 8
Line 2?
If line 1 and line 2 is perpendicular, hence the slope of both lines should fulfill this rule:
m1 x m2 = -1
(-2) x m2 = -1
m2 = 1/2
Next, we will try to find the line equation using the passed through point:
y - y1 = m (x - x1)
y - (-1) = 1/2 (x - 6)
y + 1 = 1/2 (x - 6)
y + 1 = 1/2 x - 3
y = 1/2 x - 4
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T/F two lines either intersect or are parallel.
The given statement is True.
What are parallel lines?
Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
True. Two lines either intersect or are parallel.
This means that there are only two possibilities for the relationship between two lines: they either meet at a single point, in which case they are said to intersect, or they never meet, in which case they are said to be parallel.
If two lines are intersecting, then they are not parallel, and if two lines are parallel, then they do not intersect.
Hence, The given statement is True.
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PLEASE HELP! What is another way to write the expression x(14 + 19) + 30
Answer:
33x+30
Step-by-step explanation:
If you distribute the x to 14 and 19, you will end up with:
14x+19x+30
Then, if you add the two x values together, you'll end up with:
33x+30
Another way you can do it is adding the numbers in the parentheses first:
x(33)+30
Then distribute the x:
33x+30
Find the range for the measure of the third side of a triangle when the measures of the other two sides are 22 in. and 17 in.
Answer:
The range for the third side is 11 in. to 40 in.
Step-by-step explanation:
The third side of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the two sides have lengths of 22 in. and 17 in., so the third side must have a length between 11 in. (the smaller of the two given lengths) and 40 in. (the sum of the two given lengths).
problem 5. signal transformations given the signal x[n] shown below, sketch and carefully label each of the following signals: a) x[2(n 1)] b) x[n-1]u[-1-n]
a) x[2(n-1)] is a signal that has been shifted to the right by 1 sample and then scaled by a factor of 2. , b) x[n-1]u[-1-n] is a signal that has been shifted to the left by 1 sample and then multiplied by a unit step function.
a) x[2(n-1)] is a signal that has been shifted to the right by 1 sample and then scaled by a factor of 2. This can be shown graphically by shifting the signal to the right by 1 sample and then halving the width of each sample.
b) x[n-1]u[-1-n] is a signal that has been shifted to the left by 1 sample and then multiplied by a unit step function which is used to clip off all values of the signal before -1. This can be shown graphically by shifting the signal to the left by 1 sample and then removing all values before the -1 sample.
a) x[2(n-1)] is a signal that has been shifted to the right by 1 sample and then scaled by a factor of 2.
b) x[n-1]u[-1-n] is a signal that has been shifted to the left by 1 sample and then multiplied by a unit step function.
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The diameter of a cone's circular base measures 10 inches, and the slant height of the cone is 8 inches.
What is the approximate surface area of the cone?
Responses
146.3 in²
146.3 in²
204.1 in²
204.1 in²
314.2 in²
314.2 in²
565.2 in²
The surface area of the cone with a slant height of 8in and diameter of 10in is 204.1 in².
What is the surface area of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The surface area of a cone is expressed as;
A = πrl + πr²
Given that;
Diameter d = 10inRadius = diameter/2 = 10/2 = 5inSlant height h = 8inSurface area A = ?Plug the given values into the above formula and simplify
A = πrl + πr²
A = ( 3.14 × 5 × 8 ) + ( 3.14 × 5² )
A = 125.6 + 78.5
A = 204.1 in²
Therefore, the surface area is 204.1 in²
Option B) 204.1 in² is the correct answer.
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93 x 10 with the power of 3
Answer:93000
—————————————-
The first, second and fourth terms of a proportion are 16, 24 and 54 respectively. Find the third
term.
(a) 8
(b) 36
(c) 24
(d) 7.1
Answer:
Third term is 36
Step-by-step explanation:
According to the definition of proportion, if two sets of given numbers are in the same ratio, then the ratios are said to be directly proportional to each other
We use the symbol :: to denote proportion
So if
a:b :: c:d
Then a/b = c/d
We are given that first number = 16, second is 24 and the last is 54
Let the third number be x
We have that
16:24 :: x : 54
In other words
16/24 = x/ 54
Simplifying left side
2/3 = x/54
x = 2/3 x 54 = 36
What is the slope - intercept form (y=mx+b) of the equation of each line?
Answer:
7. y = -8/3x+4
8. y = -2/1 + 1
Step-by-step explanation:
Here we can use either rise over run or the slope formula(y2-y1/x2-x1) in order to find the slope. Then looking at the y-axis we can find the y intercept. In the image follow the steps using rise over run.
-Hope this helped
Someone please help me on thisss
The upcoming championship high school football game is a big deal in your little town. The problem is, it is being played in the next biggest town, which is two hours away! To get as many people as you can to attend the game, you decide to come up with a ride-sharing app, but you want to be sure it will be used before you put all the time in to creating it. You determine that if more than three students share a ride, on average, you will create the app. You conduct simple random sampling of 20 students in a school with a population of 300 students to determine how many students are in each ride-share (carpool) on the way to school every day to get a good idea of who would use the app. The following data are collected:
6 5 5 5 3 2 3 6 2 2
5 4 3 3 4 2 5 3 4 5
The parameter used in the probability is the average number of students represented by u.
How to calculate the probability?The confidence interval based on the information will be:
= 3.85 - 2.09(1.348 / ✓20)
= 3.22
Also, 3.85 + 2.09(1.348 / ✓20) = 4.48
The confidence interval simply means that one is 95% confident that the true mean is between 3.22 and 4.48.
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Need answers before Friday
The discounted prices are given below.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
a)
Price = $1.20
Off = 25% = 1/4
Discounted amount = 1/4 x 1.20 = $0.3
Discounted price = 1.20 - 0.3 = $0.9
b)
Price = $18
Off = 25% = 1/4
Discounted amount = 1/4 x 18 = $4.5
Discounted price = 18 - 4.5 = $13.5
c)
Price = $150
Off = 30% = 0.3
Discounted amount = 0.3 x 150 = $45
Discounted price = 150 - 45 = $105
d)
Price = $20
Off = 40% = 0.4
Discounted amount = 0.4 x 20 = $8
Discounted price = 20 - 8 = $12
e)
Price = $2.20
Off = 10% = 1/10
Discounted amount = 1/10 x 2.20 = $0.22
Discounted price = 2.20 - 0.22 = $1.98
f)
Price = $1.30
Off = 50% = 1/2
Discounted amount = 1/2 x 1.30 = $0.65
Discounted price = 1.30 - 0.65 = $0.65
Thus,
The discounted prices are given above.
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Your school is selling tickets for the band concert. On the first day of ticket sales the school sold five adult tickets and three student tickets for a total of $18. The school took in $22 on the second day by selling seven adult tickets and one student ticket.
What is the price of a student ticket?
Adult ticket costs $3 and the student $1.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
1) Gathering the data
1st day
5a +3s =18
2nd day:
7a +1s= 22
2) Let's set a system of Linear equations, given those two equations:
solving we get,
a=3
s=1
3) Hence, the adult ticket costs $ 3 and the student $1.
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. Generally, which one of the following is the least appropriate measure of central tendency for a data set that contains outliers? a.mean b.median c.2ndquartile d.50thpercentile
The following is the least appropriate measure of central tendency for a data set that contains outliers is 2ndquartile.
A single number that seeks to characterise a set of data by pinpointing the centre position within that set of data is referred to as a measure of central tendency. As a result, measures of central location are occasionally used to refer to measures of central tendency. They also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.
The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, some indicators are more useful than others.
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a. Find the ratio of the number of nonfiction book to the number of fiction books give your answer in fraction form. Give your answer in fraction form
b. How many times the number of nonfiction books is the number of fiction books? Give your answer in fraction form.
c. Suppose the number fiction books is 2/7 times the number of nonfiction books what would be the ratio of the number of nonfiction books to the number of TOTAL number of books give your answer in fraction form.
The ratio of nonfiction to fiction books is 49 : 2.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, The number of fiction books is 2/7 times the number of nonfiction books.
So, If we have 7 nonfiction books then we have 2/7 fiction books.
Therefore, The ratio Nonfiction : Fiction = 7 : 2/7.
Nonfiction : Fiction = 49 : 2.
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Classify the following triangle. Check all that apply. Angle 120
In the given triangle the length of the two sides of the triangle is equal hence the triangle is an isosceles triangle, and the angle is 120 degree hence the triangle is obtuse triangle.
What is an isosceles triangle?An isosceles triangle is one with two equally sized sides. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.
In the given triangle the length of the two sides of the triangle is equal hence the triangle is an isosceles triangle, and the angle is 120 degree hence the triangle is obtuse triangle.
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A company has two large computers. The slower computer can send all the company's emails in 30 minutes. The faster computer can complete the same job in 15 minutes. If both computers are working together, how long will it take them to do the job?
The two computers simultaneously can send the email in 10 minutes.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the company has two large computers. The slower computer can send all the company's emails in 30 minutes. The faster computer can complete the same job in 15 minutes.
The time taken by both the computers together will be:-
1 / t = 1 / 30 + 1 / 15
1 / t = ( 1 + 2) / 30
1 / t = 3 / 30
1 / t = 1 / 10
t = 10 minutes
Hence, the time taken by both computers will be 10 minutes.
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in assessing the validity of a test, you randomly assign 100 individuals to two groups: one group assesses intelligence through a newly developed test, and a second group assesses intelligence through a traditional intelligence test that has been shown to be valid. you then conduct a statistical analysis to see if there are significant differences between the groups. your hypothesis states that there will be no significant differences. this type of validity is called:
This type of validity is called concurrent validity.
Concurrent validity refers to the extent to which a new test measures the same construct as an established, well-validated test. In this scenario, the newly developed test is being compared to a traditional intelligence test that has already been shown to be valid, and the hypothesis is that there will be no significant differences between the results obtained from the two tests. By comparing the scores of the two groups, the researchers are attempting to determine whether the new test is measuring the same construct (intelligence) as the established test.
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evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 41 x3 − 27 dx
The integral of 41x^3 - 27 dx is 41/4 x^4 - 27x + c.
Calculating an integral is called integration. To determine the functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.
The concept of limit is employed broadly in calculus whenever algebra and geometry are applied. Limits assist us in analyzing how points on a graph behave, such as how they approach one another until their distance approaches zero.
The indefinite integral of 41x^3 - 27 dx is given by:
∫(41x^3 - 27)dx = 41/4 x^4 - 27x + c
where c is the constant of integration.
Correct Question :
evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 41x^3 - 27 dx
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La expresión algebraica de la relación sigue siendo y = 10x, donde x es la cantidad
de entregas a domicilio que realizan, mientras y es el ingreso en soles que
obtienen por ellas.
Representa, mediante un gráfico de valores, la relación entre la cantidad de
envíos a domicilio y el ingreso (S/).
¿Consideras que, para representar la función mediante un gráfico, primero e
fundamental dibujar el plano cartesiano? Justifica tu respuesta.
Algunos estudiantes dibujan la siguiente gráfica, asignan valores al eje de la
abscisas de uno en uno y al eje de las ordenadas de 10 en 10.
Sí, considero que para representar la función mediante un gráfico, es necesario primero dibujar el plano cartesiano. Esto es porque el plano cartesiano permite representar gráficamente una relación entre dos variables.
Esto también le permite al usuario visualizar los valores que están relacionados y ver cómo se comportan las variables en relación con el otro. El plano cartesiano también le permite al usuario ver los valores que se encuentran fuera del rango de los datos y ayuda a entender mejor la relación entre los datos.
El hecho de asignar valores al eje de la abscisas de uno en uno y al eje de las ordenadas de 10 en 10 no es necesario para representar la función mediante un gráfico, ya que esto depende de las escalas que se elijan para los ejes. Por ejemplo, si la cantidad de envíos a domicilio es el eje x y el ingreso es el eje y, el usuario puede elegir diferentes escalas para los ejes para representar la relación. Por ejemplo, el usuario puede elegir una escala de 1 en 1 para el eje x y una escala de 10 en 10 para el eje y, o una escala de 2 en 2 para el eje x y una escala de 5 en 5 para el eje y.
English version:Yes, I believe that in order to represent the function using a graph, it is essential to first draw the Cartesian plane. This is because the Cartesian plane allows for graphically representing a relationship between two variables. This also allows the user to visualize the values that are related and see how the variables behave in relation to one another. The Cartesian plane also allows the user to see the values that are outside of the range of the data and helps to better understand the relationship between the data.
Assigning values to the x-axis one by one and to the y-axis 10 by 10 is not necessary to represent the function using a graph, as this depends on the scales chosen for the axes. For example, if the number of deliveries is the x-axis and the income is the y-axis, the user can choose different scales for the axes to represent the relationship. For example, the user can choose a scale of 1 to 1 for the x-axis and a scale of 10 to 10 for the y-axis, or a scale of 2 to 2 for the x-axis and a scale of 5 to 5 for the y-axis.
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which of the following are good principles for building an interface? select all that apply. a. giving the user control. b. using touchscreens. c. requiring multiple instances of identity verification. d. being consistent (in terminology, layout, and so on)
The good principles for building an interface are:
(a) Giving the user control
(b) Being consistent (in terminology, layout, and so on).
The User Interface is the full form of the term UI.
It is based on the principle of the way that the user takes control of the devices or computer.
The users mark a website or app by the performance of it as a whole, which is not only the functions of that particular website or app but also the design.
There are many good principles for an interface to be great.
It is important for the interface to be in control for the user. Then, only the user will interact with it more.
Using touchscreens is not that important, since buttons can also be used.
If there came multiple instances to verify the identity, the users will be more prone to get fed up. So, it is not good.
Consistency is very important in interface design. This means that the users should feel easy to go through the interface.
Hence, the good principles are giving the user control and consistency.
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The value of the digit 2 in the number 25.381 is 10 times greater then the value of the digit 2 in which of the following numbers
The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in 52.
The correct option is A.
What is a place value?Place value, which is related to a digit's location in a number, is the amount that each digit is worth.
Given:
We have a decimal number 25.381.
From the given choices;
We have number 52.
In the number 52:
The place value of 2 is 2.
The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in 52.
Therefore, the number is 52.
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The complete question:
The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in which of the following numbers:
A) 52.
B) 25534.675
FILL THE BLANK. the term statistics refers to a set of mathematical procedures for ______, _______, and ________ information
Statistics is a set of mathematical procedures used to collect, analyze, and interpret data.
Generally, it involves collecting data from a sample population, organizing the data into a meaningful manner, and then applying statistical methods to draw conclusions from the data. Statistical methods include descriptive statistics, which summarize the data, and inferential statistics, which use the data to make predictions about a larger population.
Descriptive statistics uses various measures to summarize a population, such as the mean, median, and mode. The mean is the average of all the values in a population and is calculated by adding up all the values and dividing by the number of values. The median is the middle value when all the values in a population are arranged from smallest to largest. The mode is the most frequently occurring value in a population.
Inferential statistics uses the data from a sample population to make predictions about a larger population. For example, a researcher might use a statistical test to determine if a certain treatment is effective. The researcher would collect data from a sample of the population, then use a statistical test to determine if the treatment had an effect on the sample population. If the test is statistically significant, then the researcher can conclude that the treatment is likely to have an effect on the larger population.
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82.1% of cincinnati households have a computer. if 111,804 households in cincinnati have a computer, how many households are there altogether in cincinnati? show your work. round to the nearest whole number.
82.1% of cincinnati household have a computer . If 111,804 households in cincinnati have a computer then 136 households are there altogether in cincinnati.
Given that, 82.1% of Cincinnati households have a computer.
111,804 households in Cincinnati have a computer.
Ratios: It is the realtion between two numbers which shows how much bigger on quantity is than another.
Proportion: It is the an equality of two ratios.
Let total number of houses be x;
According to ratio and proportions we have,
(111,804/x)*100=percentage of Cincinnati households having a computer.
then (111,804/x)*100=82.1
cross multiplying we have
x=(111,804*100)/82.1
x=136 households (Round to the nearest whole number.)
so total households present are 136
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82.1% of Cincinnati households have a computer. If 111,804 households in Cincinnati have a computer then 136 households are there altogether in Cincinnati.
Given that, 82.1% of Cincinnati households have a computer.
111,804 households in Cincinnati have a computer.
Ratios: It is the relation between two numbers that shows how much bigger one quantity is than another.
Proportion: It is the equality of two ratios.
Let the total number of houses be x;
According to the ratio and proportions we have,
(111,804/x)*100=percentage of Cincinnati households having a computer.
then (111,804/x)*100=82.1
cross multiplying we have
x=(111,804*100)/82.1
x=136 households (Round to the nearest whole number.)
so total number of households present are 136
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9) Refer to the table which summarizes the results of testing for a certain disease.
Positive Test Negative Test
Result Result
Subject has the disease
Subject does not have the disease
111
11
4
172
one of the results is randomly selected, what is the probability that it is a false negative (test
indicates the person does not have the disease when in fact they do)? What does this probability
suggest about the accuracy of the test?
A) 0. 591, The probability of this error is high so the test is not very accurate.
B) 0. 0348, The probability of this error is low so the test is fairly accurate.
C) 0. 0134; The probability of this error is low so the test is fairly accurate.
D) 0. 0369; The probability of this error is low so the test is fairly accurate.
The probability that it is a false negative (test indicates the person does not have the disease when in fact they do) is 0.0348.
This probability indicates that the test's accuracy is 0. 0348; as the likelihood of this inaccuracy is minimal, the test is quite accurate.
The likelihood that a randomly chosen result will be a false negative, meaning that the test will show that the person does not have the condition while in fact they do:
[tex]P(NP|D) = \frac{4}{115} \\\\P(NP|D) = 0.0348[/tex]
We may infer that the occurrence is unlikely to occur and that the test is reasonably accurate because the probability is less than 0.0500.
Probability is simply the possibility that something will happen. When we don't know how something will turn out, we might talk about the possibility of one result or the likelihood of several. The study of occurrences that fit into a probability distribution is known as statistics.
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What is a 5 number summary with an example?
The five-number summary would therefore be 0, 0.5, 7.5, 44, and 63.
What is a 5 number summary with an example?The first group's median, which is equal to (0 + 1)/2 = 0.5, is in the first quartile's bottom half.The median of the second group is (27 + 61)/2 = 44, which corresponds to the upper or third quartile.The two observations that are the smallest and largest are 0 and 63.The five-number summary would therefore be 0, 0.5, 7.5, 44, and 63.Summary in Five Numbers: ProcedureStarting with the smallest number, arrange your numbers in ascending order.Locate your data set's minimum and maximum in step two.Discover the median in step three.The numbers above and below the median are enclosed in parentheses in step four.Identify Q1 and Q3 in step 5.To learn more about five-number summary refer
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If the highest exponent of a polynomial function is ___, then the range of the function is always all real numbers.
The highest exponent of a polynomial function is 0 or positive, then the range of the function is always all real numbers.
When only addition, subtraction, multiplication, and non-negative integer exponentiation of variables are used in an expression, it is referred to as a polynomial. It is made up of variables and coefficients.In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
The degree of a polynomial is the highest power of x in its expression. Constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively, are polynomials of degree 0, 1, 2, 3, and 4.The highest exponent of a polynomial's variable is known as the polynomial's degree.Hence, the highest exponent of a polynomial function is 0 or positive, then the range of the function is always all real numbers.
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The value of a certain car after t years is modeled by the expresslon 15,000(0. 7)^ What are the initial cost, and the rate of depreciation of this car?
The initial cost of the car was $15,000 and the rate of depreciation is 30%.
The equation [tex]15,000(0.7)^t[/tex] models the value of a car after t years. The value of the car after 0 years, or its initial cost, is [tex]15,000(0.7)^0[/tex] = 15,000. The rate of depreciation can be calculated as 1 - 0.7, which equals 0.3 or 30%. This means that each year, the value of the car decreases by 30% of its previous value. This model assumes a constant rate of depreciation, which may not always reflect real-world situations. However, it provides a simple estimate of the decline in value over time for this car.
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Describe all solution of Ax = b, where A = [2 -5 3 -2 6 -5 -4 7 0] and b = [-3 4 3] Describe the general solution in parametric vector form.
The system has no solution, there is no particular solution x₀, and the general solution does not exist in this case.
The equation Ax = b, where A is a 3x3 matrix and b is a 3x1 column vector, represents a system of linear equations. To find all solutions of this system, we can either use Gaussian elimination or Cramer's rule.
In this case, A = [[2, -5, 3], [-2, 6, -5], [-4, 7, 0]] and b = [[-3], [4], [3]].
Using Gaussian elimination, we can transform the matrix A into its reduced row echelon form and then use back substitution to solve for the variables. The reduced row echelon form of A is:
[[1, 0, 1/2], [0, 1, -5/2], [0, 0, 0]]
Since the last row is all zeros except for the last entry, the system is inconsistent and has no solution.
Alternatively, we can use Cramer's rule to find the solution. The formula for Cramer's rule is:
x_i = det(A_i) / det(A), where A_i is the matrix A with the i th column replaced by the vector b.
In this case, det(A) = 0, so the system has no solution.
The general solution of this system of linear equations is the set of all linear combinations of the columns of A. If the system has a solution, the general solution can be expressed in the parametric vector form as:
x = x₀ + t₁ * v₁ + t₂ * v₂, where x₀ is a particular solution, v₁ and v₂ are the non-trivial solutions, and t₁ and t₂ are scalar parameters.
Since the system has no solution, there is no particular solution x_0, and the general solution does not exist in this case.
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In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Harold has scored 83, 84, and 77 on the first three. What range of scores on the fourth test will give Harold a B for the semester (an average between 80 and 89, inclusive)? Assume that all test scores have a non-negative value. Express your answer in interval notation.
76≤x≤100 is the range of scores on the fourth test will give Harold a B for the semester.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests
Harold has scored 83, 84, and 77 on the first three
We have to find the range of scores on the fourth test will give Harold a B for the semester
The sum of the first three is 244
For 4 the sum must be between 320 and 356, for 320/4 is 80 and 356/4 is 89
Therefore 320-244≤ average ≤ 356-244
76≤x≤112
If the score can't be >100, then 100 is the upper limit. From the wording of the question, I would say 76≤x≤100
Hence, 76≤x≤100 is the range of scores on the fourth test will give Harold a B for the semester.
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from the top of a 250-ft lighthouse, the angle of depression to a ship in the ocean is 21°. how far is the ship from the base of the lighthouse? (round your answer to the nearest foot.)
The ship is at a distance of 651 feet away from the lighthouse.
Therefore the answer is 651.
Let's call the distance from the base of the lighthouse to the ship "d". Then, using basic trigonometry:
tan∅ = opposite side/ adjacent side
So here opposite side is the height of the lighthouse and adjacent side is the distance from the base of the lighthouse.
tan(21°) = height of lighthouse/ d
d = height of lighthouse/ tan(21°)
d = 250 / tan(21°)
d = 250 / 0.384 = 651.3 ft
Rounding to the nearest foot, the ship is 651 ft away from the base of the lighthouse.
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