The proof of trigonometric identity (sin(x) + tan(x))/sin(x) = 1 +secx is given below.
The given trigonometric identity is,
(sin(x) + tan(x))/sin(x).
We know that tan(x) = sin(x)/cos(x), so we can substitute that in:
sin(x)/ sin(x) + sin(x)/cos(x) / sin(x)
We can simplify the fraction in the numerator:
sin(x)/ sin(x) + sin(x)/sin(x)cos(x)
We know that sin(x)/sin(x) = 1, so we can simplify further:
1+ 1/cos(x)
We know that 1/cos(x) = sec(x), so we can substitute that in:
1 + sec(x).
Now we have the same expression as the right-hand side of the identity, so we have proven that:
sin(x) + tan(x)/sin(x) = 1 + sec(x)
Therefore, (sin(x) + tan(x))/sin(x) = 1 +secx.
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which function is NOT increasing for all values of x
Answer: The function that is NOT increasing for all values of x is A. f(x) = x^2
Rita is a software saleswoman. Her base salary is $1800, and she makes an additional $60 for every copy of Math is Fun she sells.
Let P represent her total pay (in dollars), and let N represent the number of copies of Math is Fun she sells. Write an equation
relating P to N. Then use this equation to find her total pay if she sells 24 copies of Math is Fun.
Answer: P = 1800 + 60n
$3240
Step-by-step explanation:
her pay (P) would start at 1800, and she would gain 60 dollars for every copy (N) she sells.
Paul earns
every
days. At that rate, how much will Paul earn after
days?
Paul will earn $1,500 after 30 days of work.
How much will Paul earn after 30 days?A work wages means the fixed regular payment earned for work or services which is typically paid on a daily or weekly basis.
To find out how much Paul will earn after 30 days, we wlll multiply his daily earnings by the number of days he works which gives us:
= $50/day x 30 days
= $1500.
Full question "Let assume Paul earns $50 every days. At that rate, how much will Paul earn after 30 days?".
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Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AABCE AUVW?
Check all that apply.
The congruency theorem that would match the triangles shown is AAS. Option B
What is AAS?The Angle-Angle-Side (AAS) congruence theorem states that two angles and one side of one triangle must match two angles and one side of another triangle in order for two triangles to be considered congruent.
To put it another way, two triangles are said to be congruent if their included sides (the sides between the two angles) and their two neighboring angles are both identical.
Thus looking at the triangles we can see that two angles and one side are the same for the both triangles.
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Im not sure what the solution is-
Answer: it’s -0,6 which is C
Step-by-step explanation:
Please solve this. I’m so bad at this type of math
Answer:
See explanation
Step-by-step explanation:
Combine terms into a single fraction
-1/2 (-3x/2 + 6x + 1) - 3x
Find common denominator
-1/2 (-3x/2 + 2⋅6x / 2 + 2/2) - 3x
Multiply the numbers
-1/2 (-3x/2 + 12x / 2 + 2/2) - 3x
Combine like terms
-1/2 (9x + 2/2) - 3x
Distribute
-9x-2 / 2 ⋅ 2 - 3x
Multiply
-9x-2 / 4 - 3x
Solution
-21x-2 / 4
x = y -16
solve for y
Answer:
x+16=y
Step-by-step explanation:
[tex]x=y-16\\x+16=y[/tex]
help me with my online homework question about midsegments
The length of the midsegment x is given as follows:
x = 9.
How to obtain the value of x?The value of x for this problem are obtained considering the triangle midsegment theorem, which states that the midsegment of the triangle has a length that is equals to half the length of the base of the triangle.
The length of the base of the triangle in this problem is given as follows:
18 units.
Hence the length of the midsegment x is given as follows:
x = 0.5 x 18.
x = 9 units.
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9
How are Francisco’s feelings about Earth different from his parents’ feelings about Earth?
Answer
Si ya tienen 2/3 y 13/7, cuanto falta para completar 4 enteros?
To complete 4 whole numbers using the fractions 2/3 and 13/7, a total of 31/21 is needed.
To determine how much is needed to complete 4 whole numbers using the fractions 2/3 and 13/7, we need to find the sum of these fractions and subtract it from 4.
First, we need to find a common denominator for the fractions. In this case, the least common multiple (LCM) of 3 and 7 is 21.
We convert the fractions to have the same denominator:
(2/3) x (7/7) = 14/21
(13/7) x (3/3) = 39/21
Now we add the fractions:
14/21 + 39/21 = 53/21
We subtract this sum from 4 whole numbers:
4 - 53/21
To perform this subtraction, we need to have the same denominator:
4 = (4/1) x (21/21) = 84/21
We subtract the fractions:
84/21 - 53/21 = 31/21
Therefore, to complete 4 whole numbers using the fractions 2/3 and 13/7, a total of 31/21 is needed.
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Which of the following statements is true?
a. sin 18° cos 72°
b.
sin 55° = cos 55°
c. sin 72°= cos 18°
d. Both a and c.
Please select the best answer from the choices provided
OA
OO
ABCD
OD
(b) and (c) are correct
value of sin 55 = cos 55
sin 72 = cos 18
The blue object (D) has been roadster 180 degrees clockwise about the point (1,2). Which is the correct image
• Brown: image C
•Purple: image B
•None of the images
•Green: image A
Answer:
(D). Therefore, the correct answer is
Step-by-step explanation:
the other images. A rotation of 180 degrees clockwise about the point (1,2) means that every point on the blue object (D) will move to a new position that is 180 degrees away from the point (1,2) on a circle. The distance from the point (1,2) to the new position will be the same as the distance from the point (1,2) to the original position.
One way to find the new position is to use the formula:
(x′,y′)=(2x−x0,2y−y0)
where (x′,y′) is the new position, (x,y) is the original position, and (x0,y0) is the center of rotation. In this case, (x0,y0)=(1,2).
For example, let’s take the point (3, 4) on the blue object (D). Applying the formula, we get:
(x′,y′)=(2×3−1,2×4−2)
(x′,y′)=(5,6)
This means that the point (3, 4) on the blue object (D) will move to the point (5, 6) after the rotation.
We can repeat this process for all the points on the blue object (D) and see which image matches the new positions. Alternatively, we can use a visual method by drawing a line from each point on the blue object (D) to the point (1,2) and extending it until it reaches another point on the same circle. That point will be the new position after the rotation.
Using either method, we can see that none of the images match the rotation of the blue object (D). Therefore, the correct answer is:
A pail of water was 1 /4 full. Kassia added some water until the pail was 2/ 3 full. How much water did she add?
Answer: 5/12
Step-by-step explanation:
2/3 - 1/4
Find equivalent fractions that have the same denominator.
2/3 is the same as 8/12
1/4 is the same as 3/12
8/12 - 3/12 = 5/12
5/12
Ross family buys a washer and dryer set for $1135 and agrees to make 9 payments of $132. 51 each. Find the annual percentage rate of the loan
The annual percentage rate (APR) of the loan is 2.7%.
To find the annual percentage rate (APR) of the loan, we need to use the formula
APR = (2 × P × R / N) × 100
where P is the principal amount (in this case, $1135), R is the interest rate (in decimal form), and N is the total number of payments (in this case, 9).
We can solve for R by first finding the total amount paid over the course of the loan, which is
Total amount paid = 9 × $132.51 = $1192.59
The amount of interest paid on the loan is therefore
Interest paid = $1192.59 - $1135 = $57.59
Now we can use the formula to solve for R
R = (Interest paid × N) / (2 × P × N)
R = ($57.59 × 9) / (2 × $1135 × 9)
R = 0.027 or 2.7%
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Solve for x.
12
x+5
X =
15
Answer:
Step-by-step explanation:
4.2
12/(x+5) = 15
We can start by cross-multiplying:
12 = 15(x+5)
Then, we can distribute the 15:
12 = 15x + 75
Next, we can subtract 75 from both sides:
-63 = 15x
Finally, we can divide both sides by 15:
x = -63/15
Therefore, x = -4.2.
If the figure is a regular polygon find the value of x
The value of the x in the given octagon is 26.
Given is regular polygon with 8 sides, we need to find the measure of the x,
Since, the polygon is 8-sided therefore, it is an octagon,
The sum of the interior angles of a polygon =
= (number of sides - 2) × 180°
= (8-2) × 180°
= 6 × 180°
= 1080°
Therefore, one angle = 1080° / 8 = 135°
Therefore,
135° = 6x-21
135°+21 = 6x
6x = 156
x = 26
Hence, the value of the x in the given octagon is 26.
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Solve for missing sides:
b
60°
a
5√3
Answer:
b = 5, a = 10.
Step-by-step explanation:
sin 60 = 5√3 / a
√3/2 = 5√3 / a
a = 5√3 / √3/2
= 5√3 * 2/ √3
= 10
By pythagoras:
10^2 = (5√3)^ 2 + b^2
100 = 75 + b^2
b^2 = 25
b = 5
What is the measure of minor arc JP
Answer:130
Step-by-step explanation:
2 x 115 to find measure of major arc. Then 360 - 230 = 130
The area of a circle is 36ft what is the circumference
Step-by-step explanation:
area = pi * radius ^2
36 ft^2 = pi * radius^2
radius = 3.39 feet diameter = 2 x radius = 6.77 ft
Circumference = pi * diameter = 21.27 ft
A study was done about people that watch the Superbowl and World Series.
Did not watch the World Series Did watch the World series Totals
Male 57 64 121
Female 43 36 79
Totals 100 100 200
Are gender and watching the World Series Independent?
Draw the conclusion that there is insufficient evidence to support a relationship between gender and World Series viewing based on the findings of the chi-square test.
Use a chi-square test of independence to evaluate whether gender and World Series viewership are independent variables.
Let's begin by calculating the predicted frequencies for each cell based on the supposition that gender and World Series viewing are unrelated. The formula is as follows:
Expected frequency = (row total x column total) / grand total
Expected frequencies table:
Male | 60.5 60.5 121
Female | 39.5 39.5 79
Total | 100 100 200
Next, we can calculate the chi-square test statistic using the formula:
χ² = Σ (observed frequency - expected frequency)2 / expected frequency
where the sum is taken over all cells in the table.
Calculating the chi-square test statistic:
χ² = ((57 - 60.5)2 / 60.5) + ((64 - 60.5)2 / 60.5) + ((43 - 39.5)2 / 39.5) + ((36 - 39.5)2 / 39.5)
= 0.36 + 0.36 + 0.36 + 0.36
= 1.44
Finally, we need to compare the calculated chi-square value with the critical value from the chi-square distribution with (rows - 1) x (columns -
1) degrees of freedom at a chosen level of significance. For a 2x2 contingency table, the degrees of freedom are (2-1) x (2-1) = 1.
The critical value is 3.84 at a 5% level of significance and one degree of freedom. We fail to reject the null hypothesis that gender and viewing the World Series are independent since our calculated chi-square value of 1.44 is lower than the crucial value of 3.84.
Therefore, We can draw the conclusion that there is insufficient evidence to support a relationship between gender and World Series viewing based on the findings of the chi-square test.
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A city has a population of 230,000 people. Suppose that each year the population grows by 5%. What will the population be after 5 years?
There will be about 288,207.08 people living in the city in five years.
The population of a city with a 230,000-person population that increases by 5% year can be determined using the compound interest formula. Compound interest is calculated as follows: A = P(1 + r/n)nt
Where n is the number for times it is added up per year, r is the yearly interest rate, A is the potential value, P is the current value, and t is the length of the period in years. In this instance, the present value was 230,000, the yearly interest rate was 5%, the duration of the period is 5, and the interest compounded once a year. When these values are added for the formula, we obtain:
[tex]A = 230000(1 + 0.05/1)^(1 \times 5)[/tex]
[tex]A = 230000(1.05)^5[/tex]
A = 288,207.08
The growth rate is assumed to stay constant throughout at all times period, which could sometimes not be the case. When predicting population increase, it is also important to take into account additional variables like migration, birth rate, as well as mortality rate.
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which is true for a binomial distribution?multiple choicethe probability of success remains the same from trial to trial.
b) 'The probability of success remains the same from trial to trial' is true for a binomial distribution.
A binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where the probability of success remains constant from trial to trial.
The Poisson distribution, on the other hand, is a discrete probability distribution that describes the number of events occurring in a fixed interval of time or space, where the events are rare and random, and the mean number of events per interval is constant.
The number of possible outcomes in a binomial distribution depends on the number of trials and the number of possible outcomes in each trial, and there is no specific requirement for a minimum number of outcomes.
The value of T is not relevant or defined in the context of a binomial distribution.
Correct Question :
Which is true for a binomial distribution?
a) It approximates the Poisson distribution
b) The probability of success remains the same from trial to trial
c) There are ten or more possible outcomes
d) The value of T Is equal to 1.50,
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Which expanded form of 12x^2-8x-15 could be used to factor the expression by grouping?
Answer:
To factor the expression 12x^2 - 8x - 15 by grouping, we need to rewrite it as a sum of two terms, each of which has a common factor. One possible way to do this is:
12x^2 - 8x - 15 = (4x - 5)(3x + 3)
To check if this is correct, we can use the distributive property to expand the product (4x - 5)(3x + 3), which gives:
(4x - 5)(3x + 3) = 12x^2 + 2x - 15
We can see that this is equivalent to the original expression 12x^2 - 8x - 15, so the factoring is correct.
To obtain this factored form by grouping, we can group the first two terms and the last two terms of the expression:
12x^2 - 8x - 15 = (12x^2 - 18x) + (10x - 15)
We can then factor out the GCF from each group:
12x^2 - 8x - 15 = 6x(2x - 3) + 5(2x - 3)
Notice that the terms 6x and 5 have a common factor of (2x - 3). Factoring out this common factor, we get:
12x^2 - 8x - 15 = (2x - 3)(6x + 5)
Therefore, the expanded form of 12x^2 - 8x - 15 that can be used to factor the expression by grouping is:
(2x - 3)(6x + 5)
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Question is below :)
The x-intercept is 5.5 and the y-intercept is -7.5 for the given line.
The point on a graph where a line or curve meets the y-axis or x-axis is referred to as an intercept in mathematics and statistics. It also goes by the names y-intercept and x-intercept.
The intercept is the value of y when x is 0 in a linear equation of the form y = mx + b. When the independent variable (x) is zero, the value of y is represented by the intercept term (b). Similarly, the x-intercept indicates the value of x when y is zero, and the constant term (a) reflects the value of x when the dependent variable (y) is zero in an equation of type x = a + by.
The x-axis is cut at point 5.5 by the straight line and the y-axis is cut by the line at -7.5.
Therefore, the x-intercept is 5.5 and the y-intercept is -7.5.
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A, B, C, or D? Im a little confused.
Answer:
D
Step-by-step explanation:
The answer is D
To find this answer you find the need to find the equation of the lines. The equation of the first line is [tex]-\frac{5}{2} + 40[/tex] . I found this because I looked at the rise/run or how much the graph is moving up or down. In this graph, it is moving down by 1. But the graph is incremented by 5 so the rise is 5. Next, the graph is moving left by 2 so the slope is -5/2. The y-intercept is 40 because it is the place where the line hits the y-axis.
The next equation for the line is repeating the same steps and you get [tex]-\frac{5}{3}+15[/tex].
The next part would be the solution of the lines. The solution is where the two lines intersect. The lines intersect at (6, 25). Only answer D has all these parts correct.
onsider rolling two number cubes, each of which has its faces numbered from 1 to 6. the cubes will be rolled and the sum of the numbers landing face up will be recorded. let the event e represent the event of rolling a sum of 5. how many outcomes are in the collection for event e ?
The collection of outcomes for the event e of rolling a sum of 5 contains 4 possible outcomes: {1, 4}, {2, 3}, {3, 2}, {4, 1}.
To find the number of outcomes in the event of rolling a sum of 5, we need to determine all the possible ways to get a sum of 5 when rolling two number cubes.
There are several ways to get a sum of 5
The first cube lands on 1 and the second cube lands on 4.
The first cube lands on 2 and the second cube lands on 3.
The first cube lands on 3 and the second cube lands on 2.
The first cube lands on 4 and the second cube lands on 1.
Therefore, the collection of outcomes for the event e of rolling a sum of 5 contains 4 possible outcomes
{1, 4}, {2, 3}, {3, 2}, {4, 1}
So, there are 4 outcomes in the collection for event e.
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How many distinct rays are there given n collinear points?
Answer:
(n * (n - 1)) / 2
Step-by-step explanation:
If we have n collinear points, then we can draw n - 1 non-overlapping rays starting from any point on the line. This is because if we choose any two points on the line, then we can draw a unique ray passing through them, and since there are n choose 2 pairs of points on the line, we can draw n choose 2 = (n * (n - 1)) / 2 rays passing through them. However, each of these rays is counted twice (once for each of its endpoints), so we divide by 2 to get the final answer.
Therefore, the number of distinct rays that can be drawn from n collinear points is:
(n * (n - 1)) / 2
Note that this formula assumes that no three points are collinear, as otherwise, the number of rays would be infinite.
In parallelogram PSQSR, what is Pq
Answer:
In parallelogram PSQSR, Pq represents the length of the side PQ.
Since PSQR is a parallelogram, opposite sides are equal in length. Therefore, Pq is equal in length to the side SR, which is opposite to Pq in the parallelogram.
So, if the length of SR is given, then Pq is also equal to that length. If the length of SR is not given, then Pq cannot be determined.
Step-by-step explanation:
What is the intercepted arc for angle G ?
Look at what angle G is looking at what arc
As you can kinda tell it is arc CDF
And also here an image for the intercepted arc rule and how it works
you have 100 balls (50 black balls and 50 white balls) and 2 buckets. how do you divide the balls into the two buckets so as to maximize the probability of selecting a black ball if 1 ball is chosen from 1 of the buckets at random?
To maximize the probability of selecting a black ball if one ball is chosen at random from one of two buckets containing 50 black and 50 white balls, all 50 black balls should be put in one bucket and the other bucket should contain 49 white balls and 1 black ball.
To maximize the probability of selecting a black ball, you need to ensure that there are more black balls in one of the buckets than in the other.
Here's one possible way to divide the balls
Put all 50 black balls in one bucket (Bucket A).
Put 49 white balls and 1 black ball in the other bucket (Bucket B).
With this arrangement, Bucket A has a 100% chance of yielding a black ball if a ball is chosen at random, and Bucket B has a slightly less than 50% chance of yielding a black ball (specifically, a 1/50 chance, since there is only 1 black ball among the 50 balls in that bucket).
Therefore, the overall probability of selecting a black ball from one of the two buckets is maximized using this arrangement.
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