Therefore (t) can be written as **(2 - 3Q) / (Q + 4)**.
Define Q?Within the given equation, Q is a variable. It stands for an unknowable amount or value that can be ascertained by equation-solving.
What exactly is variable?A quantity that can take on any one of a number of values is referred to as a variable. A variable in mathematics is a symbol or letter that denotes an unknowable amount or value. The variable Q in the given equation stands for an unknowable quantity or value that can be ascertained by resolving the equation.
The equation is as follows:
Q = (2 - 4t) / (t + 3)
When we divide both sides by (t + 3), we obtain:
Q(t + 3) = 2 - 4t
When we increase the left side of the equation, we obtain:
Qt + 3Q = 2 - 4t
The result of adding 4t to both sides of the equation is:
Qt + 3Q + 4t = 2
Combining related concepts gives us:
t(Q + 4) = 2 - 3Q
The result of dividing both sides by (Q + 4) is:
t = (2 - 3Q) / (Q + 4)
t can therefore be written as **(2 - 3Q) / (Q + 4)**.
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three bolts and three nuts are in a box. two parts are chosen at random. find the probability that one is a bolt and one is a nut.
The probability of picking one bolt and one nut is 1/2 or 50%.
To find the probability that one is a bolt and one is a nut, we need to use the formula for calculating the probability of two independent events happening together: P(A and B) = P(A) × P(B)
Let's first calculate the probability of picking a bolt from the box:
P(bolt) = number of bolts / total number of parts = 3/6 = 1/2
Now, let's calculate the probability of picking a nut from the box:
P(nut) = number of nuts / total number of parts = 3/6 = 1/2
Since the events are independent, the probability of picking a bolt and a nut in any order is:
P(bolt and nut) = P(bolt) × P(nut) + P(nut) × P(bolt)
P(bolt and nut) = (1/2) × (1/2) + (1/2) × (1/2)
P(bolt and nut) = 1/2
Therefore, the probability of picking one bolt and one nut is 1/2 or 50%.
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the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
To find the probability that one chosen part is a bolt and the other chosen part is a nut, we need to use the formula for probability:
Probability = (number of desired outcomes) / (total number of outcomes)
There are two ways we could choose one bolt and one nut: we could choose a bolt first and a nut second, or we could choose a nut first and a bolt second. Each of these choices corresponds to one desired outcome.
To find the number of ways to choose a bolt first and a nut second, we multiply the number of bolts (3) by the number of nuts (3), since there are 3 possible bolts and 3 possible nuts to choose from. This gives us 3 x 3 = 9 total outcomes.
Similarly, there are 3 x 3 = 9 total outcomes if we choose a nut first and a bolt second.
Therefore, the total number of desired outcomes is 9 + 9 = 18.
The total number of possible outcomes is the number of ways we could choose two parts from the box, which is the number of ways to choose 2 items from a set of 6 items. This is given by the formula:
Total outcomes = (6 choose 2) = (6! / (2! * 4!)) = 15
Putting it all together, we have:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 18 / 15
Probability = 1.2
However, this answer doesn't make sense because probabilities should always be between 0 and 1. So we made a mistake somewhere. The mistake is that we double-counted some outcomes. For example, if we choose a bolt first and a nut second, this is the same as choosing a nut first and a bolt second, so we shouldn't count it twice.
To correct for this, we need to subtract the number of outcomes we double-counted. There are 3 outcomes that we double-counted: choosing two bolts, choosing two nuts, and choosing the same part twice (e.g. choosing the same bolt twice). So we need to subtract 3 from the total number of desired outcomes:
Number of desired outcomes = 18 - 3 = 15
Now we can calculate the correct probability:
Probability = (number of desired outcomes) / (total number of outcomes)
Probability = 15 / 15
Probability = 1
So the probability that one chosen part is a bolt and the other chosen part is a nut is 1, or 100%. This makes sense because if we choose two parts at random, we must get one bolt and one nut since there are three of each in the box.
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Find the measure of the line segment indicated, assume that lines which appear tangent, are tangent.
Find FS
Possible answers —>
A. 17
B. 21
C. None of the other answers are correct
D. 18
E. 45
The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18
What is the properties of intersecting chordsThe property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
UF × FS = VF × FT
8(10x - 1) = 9 × 16
80x - 8 = 144
80x = 144 + 8 {collect like terms}
80x = 152
x = 152/80 {divide through by 80}
x = 1.9
FS = 10(1.9) - 1 = 18
Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18
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The radius of a circle is 10 cm. Find its area in terms of π.
The area of a circle is given by the formula:
A = πr^2
where r is the radius of the circle.
Substituting the value of the radius as r = 10 cm, we get:
A = π(10)^2
A = 100π
Therefore, the area of the circle with radius 10 cm is 100π square centimeters.
~~~Harsha~~~
Question 9(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 10(Multiple Choice Worth 2 points)
(Circle Graphs MC)
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 11(Multiple Choice Worth 2 points)
(Circle Graphs LC)
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 54°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
Question 12(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Question 13(Multiple Choice Worth 2 points)
(Making Predictions MC)
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students. 2) The correct circle graph is option 2. 3) Option 4: Paddleboarding.
What is a histogram?The frequency or relative frequency of the data points falling within each interval is depicted by the height of the bars in a histogram, which is a graphical representation of the distribution of continuous data. Histograms are frequently used in data analysis to show how a single variable is distributed and to spot any patterns or trends. Additionally, they can be used to compare the distributions of two or more variables or to spot anomalies or outliers in the data.
1) A histogram would be the best graphical representation for the teacher's data on the subject preferences of students.
2) Given the type of transportation we have he total number of visitors as:
(120+24+45+30+81=300)
Now, for walk we have:
120/300 = 40/100 = 40%
For Bicycle we have:
24/300 = 8%
Thus, the correct circle graph is option 2: circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
3) For the central angle to be 54 the number of campers needs to correspond to this number. The activity that corresponds to 54 degrees is Paddleboarding.
4) For the number of principals in conference we set up a proportionality with total people as follows:
We know that, 52 principals out of 70 people thus:
52/70 = x/750
Now,
x = (52/70) * 750
x = 557.14
Hence, we can predict that there were about 557 principals in attendance at the conference.
5) Given that, out of 225 students 27 prefer cookies thus,
27/225 = 0.12
That is 12% students like cookies.
Now, for the total number of students we have:
0.12 * 4000 = 480
Thus, option A: The college will have about 480 students who prefer cookies.
6) For the given description of the line plot the median is:
For Bus 47 = 16
For Bus 18 = 13
The faster bus is Bus 47, with a median of 16.
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a culture contains 10,000 bacteria initially. after an hour the bacteria count is 25,000. (a) find the doubling period. (b) find the number of bacteria after 3 hours.
we call a number a mountain number if its middle digit is larger than any other digit. for example, 284 is a mountain number. how many 3-digit mountain numbers are there?
If we consider a mountain number with its middle digit is larger than any other digit, then there are possible three-digit mountain numbers are equals the 240.
A number is called a 'mountain' if its decimal digits insitiate with 1, i.e. 'base camp', increase continuously to one largest digit, then decrease continuously back to one i.e. back to base camp. We have a number is called a mountain number. Now, there are 100 to 999 total 3-digit numbers. Now, with 2 in the middle, we have = 2 numbers[1 x 2] - 120 = 121
With 3 in the we have = 6 numbers[2 x 3] - 130, 131, 132, 230, 231, 232.......and so on.With 4 in the middle,we have = 12 numbers[3 x4]With 5 in the middle, we have = 20 numbers[4 x 5]With 6 in the middle, we have = 30 numbers[5 x 6]With 7 in the middle, we have = 42 numbers[6 x 7]With 8 in the middle, we have = 56 numbers[7 x 8]With 9 in the middle, we have = 72 numbers[8 x 9]So, we have a total of Total Number = 2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 = 240 "mountain numbers". Hence, the required number , value is 240.
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Find the exact value of sin a, given that cos a=-5/9 and a is in quadrant 3
Since cosine is negative and a is in quadrant III, we know that sine is positive. We can use the Pythagorean identity to solve for sine:
sin^2(a) + cos^2(a) = 1
sin^2(a) + (-5/9)^2 = 1
sin^2(a) = 1 - (-5/9)^2
sin^2(a) = 1 - 25/81
sin^2(a) = 56/81
Taking the square root of both sides:
sin(a) = ±sqrt(56/81)
Since a is in quadrant III, sin(a) is positive. Therefore:
sin(a) = sqrt(56/81) = (2/3)sqrt(14)
Becca is construction triangle d e f using the following angles 50°, 65°, 65°,
what mistake did she make?
Becca made a mistake while constructing triangle DEF by using the angles 50°, 65°, and 65°. The mistake she made was violating the triangle inequality theorem.
According to the theorem, the sum of any two sides of a triangle must be greater than the third side. In other words, if we add the lengths of two sides of a triangle, it must be greater than the length of the third side.
Since Becca only used angles to construct the triangle, she did not consider the side lengths of the triangle. Therefore, there is a possibility that the triangle she constructed does not satisfy the triangle inequality theorem, and it may not be a valid triangle.
In order to ensure the triangle is valid, Becca needs to consider the side lengths while constructing the triangle. She could use trigonometric ratios or a ruler and protractor to measure the side lengths and angles accurately.
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The cost of 1 cup of tea and 6 cakes is £13. The cost of 1 cup of tea and 4 cakes is £9 a) How much do 2 cakes cost? b) How much does 1 cake cost?
The answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
To find the cost of 1 cupcake, we need to subtract the cost of the tea from the total cost of 3 cupcakes:
3 cupcakes + 1 tea = £9
3 cupcakes = £9 - 1 tea = £9 - £1.5 (assuming the cost of 1 tea is the same in both cases) = £7.5
1 cupcake = £7.5 ÷ 3 = £2.5
So 2 cupcakes would cost:
2 cupcakes = 2 × £2.5 = £5
Therefore, the answers are:
a) 2 cakes cost £5
b) 1 cake costs £2.5.
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What is the answer to this problem?
The area of the shaded area is 3.27 ft²
How to the area of the shaded area?We can find the area of the shaded area by subtracting the area of the triangle from the area of the sector. That is;
Area of shaded area = Area of sector - area of triangle
Area of shaded area = (60/360 * π * 6²) - (1/2 * 6 * 6 * sin 60)
Area of shaded area = (60/360 * 22/7 * 36) - (1/2 * 36 * 0.866)
Area of shaded area = 3.27 ft²
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Which comparison is not correct?
A. 1 > -9
B. 3 < 6
C. -8 > -6
D. -3 < 4
Answer:
The comparison that is not correct is:
C. -8 > -6
This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.
The other comparisons are correct:
A. 1 > -9 (true, because 1 is greater than -9)
B. 3 < 6 (true, because 3 is less than 6)
D. -3 < 4 (true, because -3 is less than 4)
3 out of 7 questions. PLEASE help me.
Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar
Transforming the circles(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:
Translate the solid circle 2 units to the left and 2 units down.Dilate the solid circle by a scale factor of 2.Therefore, the blank spaces should be filled as follows:
Translate the solid circle 2 units to the left and 2 units down.
Dilate the solid circle by a scale factor of 2.
(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.
This is because all circles are similar
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Find the avatar rate of change f(x)=3√x-1 +2; 9 ≤ x ≤ 65
Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.
Plugging in these values, we get:
average rate of change = (f(65) - f(9)) / (65 - 9)
average rate of change = (3√64 + 2 - 3√8 - 2) / 56
average rate of change = (3(4) + 2 - 3(2) - 2) / 56
average rate of change = (12 - 4) / 56
average rate of change = 8 / 56
average rate of change = 1 / 7
Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer: To find the average rate of change of the function f(x) over the interval [9, 65], we can use the formula:
average rate of change = (f(b) - f(a)) / (b - a)
where a = 9, b = 65, f(a) = f(9) = 3√8 + 2, and f(b) = f(65) = 3√64 + 2.
Plugging in these values, we get:
average rate of change = (f(65) - f(9)) / (65 - 9)
average rate of change = (3√64 + 2 - 3√8 - 2) / 56
average rate of change = (3(4) + 2 - 3(2) - 2) / 56
average rate of change = (12 - 4) / 56
average rate of change = 8 / 56
average rate of change = 1 / 7
Therefore, the average rate of change of the function f(x) over the interval [9, 65] is 1/7.
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
The construction and the resulting triangles are interesting because they allow us to explore the properties of perpendicular lines and the angles they form.
Now, let's look at the two triangles that are formed as a result of this construction - ΔABD and ΔBCD. Since line BD is perpendicular to line AC, we know that angle ABD and angle CBD are both right angles. This is because any line that is perpendicular to another line forms a right angle with that line.
Now, let's look at the other sides of the triangles. In ΔABD, we have side AB, which is different from side BC in ΔBCD. Similarly, in ΔBCD, we have side CD, which is different from side AD in ΔABD.
So, although the two triangles share a common side (BD), they have different lengths for their other sides. This means that the two triangles are not congruent, since congruent triangles must have the same length for all their sides.
However, we can still find some similarities between the two triangles. For example, since angle ABD and angle CBD are both right angles, we know that they are congruent. Additionally, we can use the fact that angle ADB is congruent to angle CDB, since they are alternate interior angles formed by a transversal (line BD) intersecting two parallel lines (line AC and the line perpendicular to it passing through point B).
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Complete Question:
Draw a line through point B that is perpendicular to line AC Label the intersection of the line and line AC as point D. Take a screenshot of your work, save it, and insert the image in the space below.
Part B
Based on your construction, what do you know about ΔABD and ΔBCD?
A rectangular garden has a walkway around it. The area of the garden is 4(4.5x+3.5). The combined area of the garden and the walkway is 5.5(6x+5). Find the area of the walkway around the garden as the sum of two terms.
The product of two terms gives the walkway's area around the garden: 15x+13.5.
Define rectangleA rectangle is a four-sided polygon with two pairs of parallel and congruent sides, and four right angles. The opposite sides of a rectangle are equal in length and parallel to each other, while the adjacent sides are perpendicular to each other.
Area of garden = 4(4.5x + 3.5) = 18x+14
The combined area of the garden and the walkway = 5.5(6x+5) =33x+27.5
The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:
Aw=combined area -Area of garden
=33x+27.5-18x-14
=15x+13.5
Thus, we can say that the area of the walkway around the garden is the sum of two terms: 15x+13.5.
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Using the graph, determine the coordinates of the y-intercept of the parabola.
Answer:
The y-intercept is at (0, 8).
Answer: (0,8)
Step-by-step explanation: The line only touches the Y-axis Once and its on 8
Select the GCF of these numbers. 48 and 60 22 ·3 2· 112 32 23 · 5 13· 193 ·232
The GCF of 48 and 60 is 12
To find the greatest common factor (GCF) of 48 and 60, we can start by finding the prime factorization of each number
48 = 2^4 × 3
60 = 2^2 × 3 × 5
Next, we can identify the common factors of both numbers by looking at their prime factorization
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors of 48 and 60 are: 1, 2, 3, 4, 6, and 12.
The greatest common factor is the largest number that both 48 and 60 can be divided evenly by. In this case, that number is 12. Therefore, the GCF is 12.
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The given question is incomplete, the complete question is:
Find the GCF of 48 and 60.
There is 6/8 of a cake
leftover after a birthday
party. How many 1/4
pieces can be made from
the leftover cake?
Answer: 3 pieces
Step-by-step explanation:First, 6/8 can be converted into fourths by dividing the numerator and the denominator by 2 and we get 3/4. if we want 1/4 slices we divide 3/4 by 1/4 and get 3.
Grupo textil M & M destaca que los ingresos de este año vienen dados por la funcion f(x) = (x+2)(-x+9-3) donde "x" es el precio de cada unidad y f(x) es la ganancia expresada en dolares
Para entender mejor esta función, podemos expandirla y simplificarla:
f(x) = (x+2)(-x+6)
f(x) = [tex]-x^2 + 4x + 12[/tex]
Esta es una función cuadrática, lo que significa que tiene la forma de una parábola. El término cuadrático ([tex]-x^2[/tex]) hace que la parábola tenga una concavidad hacia abajo, lo que significa que el valor máximo de la función se encuentra en el vértice de la parábola.
Podemos encontrar el valor del precio de venta que maximiza la ganancia utilizando la fórmula x = -b/(2a), donde "a" es el coeficiente del término cuadrático y "b" es el coeficiente del término lineal.
En este caso, a = -1 y b = 4, por lo que:
x = -4/(2-1)
x = -4/-2
x = 2
Por lo tanto, el precio de venta que maximiza la ganancia es de 2 por unidad. Si se venden las unidades a este precio, la ganancia total sería de:
f(2) = [tex]-2^2 + 4(2) + 12[/tex]
f(2) = -4 + 8 + 12
f(2) = 16 dólares
Es importante tener en cuenta que la función f(x) también puede ser utilizada para calcular la ganancia total para cualquier precio de venta "x". Por ejemplo, si se venden las unidades a 3 por unidad, la ganancia sería:
f(3) = [tex]-3^2 + 4(3) + 12[/tex]
f(3) = -9 + 12 + 12
f(3) = 15 dólares
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I need help answering this question and understanding it
The amount of money less per hour which Melanie earn than Olivia is equal to $268.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about Melanie's earnings, we have the following:
y = 22.2x
When x = 40 hours, the y-value is given by;
y = 22.2(40)
y = $888.
Difference in earnings can be calculated as follows;
Difference = $1156 - $888
Difference = $268.
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the mean iq of the population of osu students is 100. a random sample of 5 students will be taken from the population, but the first student scored 150. what do expect the average to be for the 5 students?
Even though the first student scored 150, the expected average IQ score for the remaining four students is still 100.
Explain average
The average is a statistical measure that represents the central tendency of a set of values. It is calculated by adding up all the values and dividing them by the total number of values. The average provides a single value that represents the typical value in the set and is often used to compare different sets of data or to summarize large amounts of data.
According to the given information
Let X be the random variable representing the IQ score of an individual student. Then, the sample mean of the five students, denoted by Y, can be expressed as:
Y = (X1 + X2 + X3 + X4 + X5) / 5
Given that the first student scored 150, the expected value of the sample mean of the remaining four students, denoted by E(Y|X1=150), can be calculated as follows:
E(Y|X1=150) = E((X2 + X3 + X4 + X5) / 4 | X1 = 150)
Since X1 = 150 is an observed value, we can treat it as a constant and apply the linearity of expectation:
E((X2 + X3 + X4 + X5) / 4 | X1 = 150) = (E(X2 | X1 = 150) + E(X3 | X1 = 150) + E(X4 | X1 = 150) + E(X5 | X1 = 150)) / 4
Now, since the sample is random, the remaining four IQ scores are also independent and identically distributed as X, with the same mean of 100. Therefore, we have:
E(X2 | X1 = 150) = E(X3 | X1 = 150) = E(X4 | X1 = 150) = E(X5 | X1 = 150) = E(X)
Thus, we can simplify the expression as:
E(Y|X1=150) = (4E(X) / 4) = E(X) = 100
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state the nameof this quadrilateral...70 points
Answer:
Step-by-step explanation:
its a rectanlge
Find the measure of the missing side.
1. 8.2
2. 9.9
3. 7.4
4. 10.9
Answer:
1
Step-by-step explanation:
First of all we use the "law of sines"
to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x
and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°
180°=70°+51°+ x
x = 180°-121°
=59°
Using law of sines:
(sides are represented by small letters/capital letters are the angles)
a/sinA= b/sinB= c/sinC
We have one given side which is "9"
so,
9/sin70= x/sin59
doing the criss-cross method,
9×sin59=sin70×x
9×sin59/sin70=x
x=8.2 (answer 1)
I hope this was helpful <3
Sam makes tote bags for a school fundraiser. The fixed costs for making the bags is $30. The cost of the materials for each bag is $8.50. Sam can spend less than a total of $200 on the tote bags. Write an inequality that can be used to determine b , the number of tote bags that can be made.
Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
why would you use a trigonometric function to set-up an application problem instead of a non-trigonometric function
Trigonometric functions are used to model relationships between angles and sides of a right triangle. They are particularly useful in solving problems that involve angles, distances, heights, and lengths that are difficult to measure directly.
For example, consider a problem that involves finding the height of a building. By measuring the length of the shadow cast by the building at a particular time of day, the angle of the sun's rays can be calculated using trigonometry. Once the angle is known, the height of the building can be determined using the tangent function.
In contrast, a non-trigonometric function may not be able to model the relationship between the given quantities in such problems, and may not provide an accurate solution. Therefore, when a problem involves angles or distances that are not directly measurable, trigonometric functions are typically the best tool for setting up and solving the problem.
To know more about trigonometric functions
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when a researcher uses the pearson product moment correlation, two highly correlated variables will appear on a scatter diagram as what?
When a researcher uses the Pearson product-moment correlation, two highly correlated variables will appear on a scatter diagram as a tightly clustered group of points that form a linear pattern.
The scatter diagram is a visual representation of the correlation between two variables, where one variable is plotted on the x-axis, and the other variable is plotted on the y-axis. If the two variables have a high positive correlation, then the points on the scatter diagram will form a cluster that slopes upwards to the right.
On the other hand, if the two variables have a high negative correlation, then the points will form a cluster that slopes downwards to the right. The tighter the cluster of points, the higher the correlation between the variables.
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Given the quadratic equation x^(2)+4x+c=0, what must the value of c be in order for the equation to have solutions at x=-3 and x=-1 ?
Answer:
Step-by-step explanation:
If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,
(x - 3) (x - 1)
x^2 - x - 3x + 3
x^3 - 4x + 3 = 0
Your answer is 3
ASAP I really need help doing a two column proof for this please.
The two column proof is written as follows
Statement Reason
MA = XR given (opposite sides of rectangle)
MK = AR given (opposite sides of rectangle)
arc MA = arc RK Equal chords have equal arcs
arc MK = arc AK Equal chords have equal arcs
Equal chords have equal arcsAn arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.
If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.
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in a role playing game two special dice are rolled. one die has 4 faces numbered 1 through 4 and the other has 6 faces numbered 1 thorugh 6. what is the probabilty that the total shown on the two dice after they are rolled is greater than or equal to 8?
The probability that the total shown on the two dice after they are rolled is greater than or equal to 8 is 1/9.