Therefore, the solutions of the equation in the interval [0, 2) are: x = π/6, -π/6 (in radians) or x = 30°, -30° (in degrees). Note that the solutions are listed in ascending order.
How to Solve the Equation?The equation is:
sec(x) = 2√3/3
First, we can find the values of x for which sec(x) = 2√3/3. Recall that sec(x) = 1/cos(x), so we have:
1/cos(x) = 2√3/3
Multiplying both sides by cos(x), we get:
1 = 2√3/3 cos(x)
cos(x) = 3/(2√3) = √3/2
Now, we can use the unit circle to find the solutions of the equation in the interval [0, 2).
cos(x) = √3/2 when x is π/6 or 11π/6 (in radians), or 30° or 330° (in degrees), since these are the angles in the unit circle where the x-coordinate is √3/2.
However, we need to make sure that these solutions are in the interval [0, 2). Since the period of sec(x) is 2π, we can add or subtract 2π to any solution to get another solution. Therefore, we need to find the solutions in the interval [0, 2π) that correspond to the solutions we found above.
π/6 is already in the interval [0, 2π), so it is a solution in the interval [0, 2). To find the other solution in the interval [0, 2), we can add 2π to 11π/6:
11π/6 + 2π = 23π/6
23π/6 is not in the interval [0, 2), so we need to subtract 2π instead:
11π/6 - 2π = -π/6
-π/6 is in the interval [0, 2), so it is also a solution in the interval [0, 2).
Therefore, the solutions of the equation in the interval [0, 2) are:
x = π/6, -π/6 (in radians) or x = 30°, -30° (in degrees)
Note that the solutions are listed in ascending order.
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a research methods professor creates a computer tutor to help students understand confounding and obscuring variables. before the second exam in the class, volunteers are randomly assigned to either interact with the computer tutor on the materials or to play angry birds on the computer for an equivalent time (30 minutes). although the students in the tutor group do significantly better on the exam the following day, many of the practice questions from the tutor are exactly the same as those on the exam. what is the main threat to concluding that the tutor was effective?
The main threat to concluding that the tutor was effective in helping students understand confounding and obscuring variables is the issue of 'practice effects'.
Practice effects occur when exposure to specific materials or questions during a study can artificially inflate performance on subsequent measures, such as an exam.
In this case, if the practice questions from the tutor were exactly the same as those on the exam.
Then the students who interacted with the tutor may have had an advantage on the exam .
Due to familiarity with the questions rather than a true understanding of the material.
The use of the same practice questions in the tutor and on the exam .
It represents a potential confounding variable that could affect the interpretation of the results.
It is possible that the tutor may have been effective.
But it is also possible that the practice effect of the repeated questions contributed to the observed improvement in performance.
Future research could use different practice questions in the tutor and on the exam.
Use a different exam altogether to assess performance.
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Write a function to model the volume of a rectangular prism if the length is 26cm and the sum of the width and height is 32cm. what is the maximum possible volume of the prism?
To model the volume of a rectangular prism with length 26cm and width w and height h such that the sum of the width and height is 32cm, we can use the following function:
V(w, h) = 26wh
subject to the constraint:
w + h = 32
We can solve for one of the variables in the constraint equation and substitute it into the volume equation, giving us:
w + h = 32 => h = 32 - w
V(w) = 26w(32 - w) = 832w - 26w^2
To find the maximum possible volume, we can take the derivative of this function with respect to w and set it equal to zero
dv/dw= 832 - 52w = 0
Solving for w, we get:
w = 16
Substituting this value back into the constraint equation, we get:
h = 32 - w = 16
Therefore, the maximum possible volume of the prism is:
V(16, 16) = 26(16)(16) = 6656 cubic cm
So the function to model the volume of the rectangular prism is V(w) = 832w - 26w^2, and the maximum possible volume is 6656 cubic cm when the width and height are both 16cm.
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Question 1 2 pts A researcher is interested in determining whether sugar consumption increases memory. She recruits 100 participants and randomly assigns them to one of two groups, sugar vs. No sugar. She then measures their word recall: Sugar group: M = 4. 5, SD = 1. 8, n = 55 • No sugar group: M = 2. 6, SD =. 68, n = 45 1. Is this an example of a quasi-experimental design? (yes or no) 2. What is the dependent variable? 3. What is the independent variable?
1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.
2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.
3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.
The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.
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Can someone please help me ASAP? It’s due tomorrow
Answer:
0.30.400.1Step-by-step explanation:
tried my best as the first two got me stuck
wouldn't recommend trying my answer and Id wait for another answer
What is the missing value of G if G is two and one-half times smaller than 19. 02 cm? A. 7. 608 cm B. 7. 808 cm C. 8. 608 cm D. 9. 51 cm
Therefore, the missing value of G is 7.608 cm, which is option A.
What is the missing value of G?If G is two and one-half times smaller than 19.02 cm, we can find the value of G by multiplying 19.02 cm by 2/5, since two and one-half is equal to five halves, or 2/5 when expressed as a fraction.
G = (2/5) x 19.02 cm
Simplifying this expression:
G = 7.608 cm
Therefore, the missing value of G is 7.608 cm, which is option A.
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A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 19. 1 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 18. 1, 21. 1, 22. 1, 23. 1, 21. 1, 27. 1, and 27. 1 pounds. If α = 0. 200, what is the critical value? The population standard deviation is unknown
Since the population standard deviation is unknown, we use a t-distribution to find the critical value. The degrees of freedom for the t-distribution is n-1, where n is the sample size. In this case, n = 7, so the degrees of freedom is 7-1 = 6. The critical value for a t-distribution with 6 degrees of freedom and a significance level of α = 0.200 (two-tailed) can be found using a t-table or calculator. The critical value is approximately ±1.94.
A cake is in the shape of a rectangular prism. It has a length of 13 inches, a width of 8 inches, and a height
of 5 inches. A baker will put frosting on all sides of the cake except for the bottom. What is the total surface area
of the cake that will be covered in frosting?
Show Your Work
O 114 in.
0 334 in.
O 449 in?
O 573 in?
If the cake is in the shape of a rectangular prism, the total surface area of the cake that will be covered in frosting is 314 sq. inches.
To find the total surface area of the cake that will be covered in frosting, we need to calculate the area of all sides except the bottom. A rectangular prism has 6 sides, and we will be considering 5 of them.
Surface area of top: length × width = 13 × 8 = 104 sq. inches
Surface area of front: length × height = 13 × 5 = 65 sq. inches
Surface area of back: length × height = 13 × 5 = 65 sq. inches
Surface area of left side: width × height = 8 × 5 = 40 sq. inches
Surface area of right side: width × height = 8 × 5 = 40 sq. inches
Now, we will sum the areas of all these sides:
104 + 65 + 65 + 40 + 40 = 314 sq. inches
So, the total surface area of the cake that will be covered in frosting is 314 sq. inches. None of the provided options match this answer, so it is important to double-check the question for any discrepancies.
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Will give brainliest!
given that the slope of the consecutive sides is -2/3 and 3/2
can you prove that it is a parallelogram or a rectangle.
explain your answer.
A figure with slope of consecutive sides -2/3 and 3/2 is a rectangle and it is not a parallelogram.
To prove that it is a parallelogram or a rectangle, we need to show that the opposite sides are parallel and the adjacent sides are perpendicular.
Let's first check if the opposite sides are parallel. The slope of one side is -2/3, and the slope of the adjacent side is 3/2. For opposite sides to be parallel, the slopes must be equal. However, -2/3 and 3/2 are not equal, so we can conclude that the given figure is not a parallelogram.
Now, let's check if the adjacent sides are perpendicular. The product of the slopes of the adjacent sides is
(-2/3) x (3/2) = -1, which is the slope of a line perpendicular to both sides. Since the product of the slopes is -1, we can conclude that the adjacent sides are perpendicular.
Therefore, figure is not a parallelogram, but it is a rectangle.
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Malachi ask students in his class, “ how long does it take you to get to school?“ The histogram shows the data
Answer: C Distribution is symmetric
Step-by-step explanation:
The charge for a mission to the zoo is $3.25 for each adult and $1.50 for each student. on a day when 400 people paid to visit the zoo, the receipts totaled 1,237. find the number of adult tickets purchased that day
The number of adult tickets purchased that day was 36 if the charge is $3.25 for each adult and $1.50 for each student and 400 people paid $1237
Let the number of adults be x
the number of students be y
Total people = 400
x + y = 400
Total receipts = $1,237
Cost of an adult ticket = $3.25
Cost of a student ticket = $1.50
Cost of x adults tickets = 3.25x
Cost of y student tickets = 1.50y
3.25x + 1.50y = 1237
Multiply the first equation by 1.50
1.50x + 1.50y = 600
Subtract the second and above equation
1.75x = 637
x = 364
364 + y = 400
y = 36
Thus, the number of adult tickets purchased is 36.
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(4,7);y=3x+6
Write an equation passing through the point and parallel to the given line.
The Equation of the line which is parallel to the line "y = 3x + 6", and also passes through (4,7) is "y = 3x - 5".
In order to find an equation of a line which passes through point (4,7) and is parallel to line "y = 3x + 6", we use the fact that parallel lines have the same slope.
The given line ""y = 3x + 6" has a slope of 3,
So, the "parallel-line" we want to find must also have a slope of 3.
Now, by using the "point-slope" form of the equation of a line, which is : y - y₁ = m(x - x₁),
where m is slope and (x₁, y₁) is a point on the line,
So, we substitute "m = 3" and (x₁, y₁) = (4,7) to get:
⇒ y - 7 = 3(x - 4),
⇒ y - 7 = 3x - 12,
⇒ y = 3x - 5
Therefore, the equation of the required line is y = 3x - 5.
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An office manager orders one calculator or one calendar for each of the office's 80 employees. Each calculator costs $12, and each calendar costs $10. The entire order totaled $900.
Part A: Write the system of equations that models this scenario.
Part B: Use substitution method or elimination method to determine the number of calculators and calendars ordered. Show all necessary steps.
The system of equations is.
x + y = 80
12x + 10y = 900
And the solutions are y = 30 and x = 50
How to write and solve the system of equations?Let's define the two variables:
x = number of calculators.
y = number of calendars.
With the given information we can write two equations, then the system will be:
x + y = 80
12x + 10y = 900
Now let's solve it.
We can isolate x on the first equation to get:
x = 80 - y
Replace that in the other equation to get:
12*(80 - y) + 10y = 900
-2y = 900 - 960
-2y = -60
y = -60/-2 = 30
Then x = 50
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What is the mean of the data set fifth grade jump distance
The mean of the fifth-grade jump distance data set.
How to calculate the mean of fifth-grade jump distances?To determine the mean of the data set for fifth-grade jump distances, we need the actual data values. Without the specific data set, it is not possible to calculate the mean.
The mean is the sum of all the values in a data set divided by the number of values. Therefore, we would need the individual jump distances for each fifth-grade student to calculate the mean accurately.
Once we have the complete data set, we can add up all the distances and divide by the total number of students to find the mean. Without the specific data, we cannot provide a numerical answer for the mean of the fifth-grade jump distance.
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Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 22 ties, 13 of which he feels go well with the sportscoat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sportscoat.
The probability the tie goes well with the jacket is?
The probability the tie will not go well with the jacket is?
The odds against the tie going well with the jacket is?
(Simplify your answer. Type an integer or a fraction.)
The odds in favor of the tie going well with the jacket is?
(Simplify your answer. Type a ratio using a colon.)
The sum of the roots of a quadratic is 1 and the product of the roots is -35/4.
a. find the quadratic.
b. find the roots
If the sum of the roots of a quadratic equation is 1 and the product of the roots is -35/4 and the equation is [tex]4x^2-4x-35=0[/tex] and the roots are 3.5 and -2.5
If the quadratic equation is [tex]ax^2+bx+c=0[/tex]
The sum of the roots = [tex]-\frac{b}{a}[/tex]
The product of the roots = [tex]\frac{c}{a}[/tex]
Sum of the roots = 1 = [tex]-\frac{b}{a}[/tex]
Product of the roots = [tex]-\frac{35}{4}[/tex] = [tex]\frac{c}{a}[/tex]
If we assume a as 1, then the equation comes out to be:
[tex]x^2-x-\frac{35}{4} =0[/tex]
Multiply the equation by 4 to get a simplified equation:
[tex]4x^2-4x-35=0[/tex]
[tex]4x^2[/tex] - 14x + 10x - 35 = 0
2x (2x - 7) + 5 (2x - 7) = 0
(2x - 7)(2x + 5) = 0
x = 3.5 and -2.5
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Given that in an arithmetic series a8 = 1 and a30=-43, find the sum of terms 8 to 30.
The sum of terms 8 to 30 in the arithmetic series is -826.
In an arithmetic series, the nth term is given by the formula an = a1 + (n-1)d, where a1 is the first term and d is the common difference between terms.
We are given that a8 = 1 and a30 = -43. Using the formula above, we can write:
a8 = a1 + 7d = 1 (1)
a30 = a1 + 29d = -43 (2)
Subtracting equation (1) from equation (2), we get:
22d = -44
d = -2
Substituting d = -2 into equation (1) and solving for a1, we get:
a1 = 15
Now we can use the formula for the sum of an arithmetic series to find the sum of terms 8 to 30:
S = (n/2)(a1 + an)
S = (23/2)(15 + (-43))
S = -826
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Ivan created a scale drawing of the Grand Canyon using a scale of 1 inch for every 25
miles. His drawing is 11 inches long. What is the actual length of the canyon?
Answer:
275 miles
Step-by-step explanation:
Graph the equation shown below by transforming the given graph of the parent function. 2^3x
The graph of the exponential function [tex]y = 2^{3x}[/tex] is given as follows:
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function in this problem is given as follows:
[tex]y = 2^{3x}[/tex]
Hence the parameter values are:
a = 1, hence when x = 0, y = 1.b = 2, hence when x increases by 1/3, y is multiplied by 2 -> increases by 1/3 due to the horizontal compression with the multiplication by 3 in the domain.More can be learned about exponential functions at brainly.com/question/2456547
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What is the length of the segment indicated by the question mark
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4[/tex]
Write an expression for the sequence of operations described below.
Subtract three from the product of seven and eight
Type x if you want to use a multiplication sign. Type / if you want to use a division sign. Do not simplify any part of the expression.
An expression for the sequence of operations described "Subtract three from the product of seven and eight." is (7 × 8) - 3.
How to evaluate and solve the given expression?In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.
Based on the information provided, we have the following mathematical expression:
Expression: (7 × 8) - 3
56 - 3
53
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Consider the concentration, C, (in mg/liter) of a drug in the blood as a function of the amount of drug given, x, and the time since injection, t For 0 <= x <= 5 and t >= 0 hours, we have C = f(x,t) = 26te^-(5-x) f (3,5) = _____
Using the given function, we can plug in x=3 and t=5 to find the concentration of the drug in the blood:
C = f(x,t) = 26te^-(5-x)
C = f(3,5) = 26(5)e^-(5-3)
C = f(3,5) = 130e^-2
Using a calculator, we can simplify this to:
C = f(3,5) ≈ 32.22 mg/liter
Therefore, the concentration of the drug in the blood 3 hours after injection with a dosage of 5 mg is approximately 32.22 mg/liter.
Hi! To find the concentration C at f(3,5), you'll need to plug in the values for x and t into the given function f(x,t) = 26te^-(5-x).
So, f(3,5) = 26(5)e^-(5-3) = 130e^(-2).
Now, calculate the exponential value: e^(-2) ≈ 0.1353.
Finally, multiply this value by 130: 130 * 0.1353 ≈ 17.589.
Thus, f(3,5) = 17.589 mg/liter (rounded to 3 decimal places).
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Mohal is a waiter at a restaurant. Each day he works, Mohal will make a guaranteed wage of $25, however the additional amount that Mohal earns from tips depends on the number of tables he waits on that day. From past experience, Mohal noticed that he will get about $15 in tips for each table he waits on. How much would Mohal expect to earn in a day on which he waits on 16 tables? How much would Mohal expect to make in a day when waiting on
�
t tables?
Answer:
If Mohal waits on 16 tables, he can expect to earn $25 wages + ($15 tips x 16 tables) = $265 in a day.
If Mohal waits on 1 table, he can expect to earn $25 wages + ($15 tips x 1 table) = $40 in a day.
A cuboid is placed on top of a cube, as shown in the diagram, to form a solid.
2 cm
3 cm
The cube has edges of length 7 cm.
The cuboid has dimensions 2 cm by 3 cm by 5 cm.
Work out the total surface area of the solid.
Optional working
Ansv
cm²
+
5 cm
7 cm
Answer: 344cm²
Step-by-step explanation:
7x7=49
49x5=245
3x2=6
49-6=43
245+43=288
5x2=10 10x2=20
5x3=15 15x2=30
288+30+20+6=344
John owns 10 shirts and needs to select 5 to wear to school next week. How many ways can he choose the shirts? (hint: combinations)
50 ways
B 252 ways
500 ways
D 792 ways
There are 252 different combinations of shirts, the correct option is B.
In how many ways he can choose the shirts?Remember that if you have N elements, and you want to select K of these, the number of combinations is given by:
[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]
Here we have 10 shirts and we want to select 5 of these, so the number of combinations is given by:
[tex]C(10, 5) = \frac{10!}{(10 - 5)!*5!} \\\\C(10, 5) = \frac{10*9*8*7*6}{5*4*3*2} = 252[/tex]
There are 252 different combinations, so the correct option is B.
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Determine the location and value of the absolute extreme values off on the given interval, if they exist 8x? f(x) - +22x2 - 24x on (-7,11 G What in are the absolute maximum maxime off on the given interval? Select the correct choice below and, if necessary, to in the answer bowen to completo your choice A. Tho absolute maximum/maxima isarea- (Use a comma to separato answers as needed. Type exact answers, using radicals as rended) B. There is no absolute maximum off on the given interval What are the absolute minimum/minima off on the given interval? Select the correct choice below and. If necessary, in the wwer boxes to complete your in O A The absolute minimum/minima is/are at (Use a comma to separate answers as needed. Type exact answers, using radical as needed) B. There is no absolute minimum off on the given interval
The absolute maximum will be at (11, 10373).
The absolute minimum is at (-1.963, -25.294).
What in are the absolute maximum maxime off on the given interval?
To determine the location and value of the absolute extreme values of the function f(x) = 8x³+ 22x² - 24x on the interval (-7, 11), follow these steps:
Find the critical points by taking the derivative of the function and setting it equal to zero:
f'(x) = 24x² + 44x - 24
Solve for x:
Factor the equation: 4(6x² + 11x - 6) = 0
Using the quadratic formula, x = (-11 ± √(121 + 144))/12
x ≈ -1.963, 0.630
Check the endpoints and the critical points to find the absolute maximum and minimum:
f(-7) ≈ 461
f(-1.963) ≈ -25.294
f(0.630) ≈ -16.102
f(11) ≈ 10373
Compare the values:
The absolute maximum is at x = 11, with a value of 10373.
The absolute minimum is at x ≈ -1.963, with a value of ≈ -25.294.
Answer:
The absolute maximum is at (11, 10373).
The absolute minimum is at (-1.963, -25.294).
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The number of revolutions
made by a tire traveling over a fixed distance
varies inversely with the radius of the tire. a
12-inch radius tire makes 100 revolutions to
travel a certain distance. how many
revolutions would a 16-inch radius tire require
a
to travel the same distance?
define variables
identify constant of variation
write an equation and show work (please can someone help with this stuff, my deadline is in 4 days)
A 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.
Let's start by defining some variables. Let "r" represent the radius of the tire and "n" represent the number of revolutions it makes over a fixed distance. We are given that the number of revolutions is inversely proportional to the radius of the tire. This means that as the radius increases, the number of revolutions decreases, and vice versa. We can express this relationship mathematically as follows:
n = k/r
Here, "k" is the constant of variation, which remains the same for any given tire traveling over the same distance. To solve the problem, we need to find the value of "k" first. We know that a 12-inch radius tire makes 100 revolutions to travel a certain distance. Substituting these values into the equation, we get:
100 = k/12
Solving for "k," we get k = 1200. Now we can use this value to find the number of revolutions required by a 16-inch radius tire to travel the same distance:
n = 1200/16 = 75
Therefore, a 16-inch radius tire would require 75 revolutions to travel the same distance as a 12-inch radius tire that made 100 revolutions.
In summary, we defined the variables, identified the constant of variation, wrote the equation (n=k/r), found the value of the constant by using the given information, and used it to solve the problem by finding the number of revolutions required by a tire with a different radius.
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Josie had 12 beads on her necklace. Then she added b more beads. Write an expression that shows how many beads are on the necklace in all. please write a expression like b-12 or b+?
The expression that shows how many beads are on the necklace in all is:
b + 12.
What is expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:
Start with the initial number of beads on the necklace, which is 12.
To this, add the number of beads Josie added, which is b.
Combine the two terms to form the final expression: 12 + b.
Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.
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Edro, Lena, Harriet, and Yermin each plot a point to approximate StartRoot 0. 50 EndRoot.
Pedro A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 2 and 0. 3.
Lena A number line going from 0 to 0. 9 in increments of 0. 1. A point is between 0. 4 and 0. 5.
Harriet A number line going from 0 to 0. 9 in increments of 0. 1. A point is at 0. 5.
Yermin A number line going from 0 to 0. 9 in increments of 0. 1. A point is just to the right of 0. 7.
Whose point is the best approximation of StartRoot 0. 50 EndRoot?
Pedro
Lena
Harriet
Yermin
Yermin's point is the best approximation of the square root of 0.50.
To know whose point is the best approximation of the square root of 0.50 on a number line. We have the points plotted by Pedro, Lena, Harriet, and Yermin.
Step 1: Calculate the square root of 0.50.
[tex]\sqrt{0.50} = 0.707[/tex]
Step 2: Compare the plotted points to the calculated square root value.
Pedro: Between 0.2 and 0.3
Lena: Between 0.4 and 0.5
Harriet: At 0.5
Yermin: Just to the right of 0.7
Step 3: Determine the closest approximation.
Yermin's point (just to the right of 0.7) is the closest to the calculated value of 0.707.
Your answer: Yermin's point is the best approximation of the square root of 0.50.
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What is the explicit equation for the nth term of the arithmetic sequence 6.3, 3.6, 0.9, –1.8, –4.5, …? an = 6.3 – 2.7n an = 6.3 – 2.7(n – 1) an = 6.3 + 2.7n an = 6.3 + 2.7(n + 1)
The explicit equation for the nth term of the arithmetic sequence is an = 9 - 2.7n.
What is the implicit equation?
An implicit equation is an equation in which the variables are not explicitly expressed in terms of each other. In other words, the equation does not give a direct formula for one of the variables in terms of the other(s), but rather relates the variables through some function or equation.
What is the explicit equation?
An explicit equation is an equation in which one variable is expressed directly in terms of the other(s). In other words, the equation gives a formula for one of the variables in terms of the other(s).
According to the given information:
the first term of the sequence is a1 = 6.3, and the common difference between consecutive terms is d = -2.7 (since we subtract 2.7 from each term to get to the next term). Therefore, the explicit equation for the nth term of the sequence is:
an = 6.3 + (n - 1)(-2.7)
Simplifying this expression, we get:
an = 6.3 - 2.7n + 2.7
an = 9 - 2.7n
So the correct equation for the nth term of the arithmetic sequence 6.3, 3.6, 0.9, -1.8, -4.5, ... is:
an = 9 - 2.7n
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The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?
O Use the distance formula to find the length of each side, and then add the lengths.
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
O Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicul
O Use the distance formula to find the length of the sides, and then multiply two of the side lengths.
Answer:..
Step-by-step explanation:Use the distance formula to find the length of each side and then add the lengths.
Use the slope formula to find the slope of each of side, and then determine if the opposite sides are parallel.
Use the slope formula to find the slope of each of side, and then determine if the consecutive sides are perpendicular.
Use the distance formula to find the length of the sides, and then multiply two of the side lengths.