Step-by-step explanation:
easy how thick it is we need a picture
which of the following would be an acceptable first step in simplifying the expression tan^x/1+sec^x
The first step is replacing the given trigonometric functions by simpler ones and then taking the product of the denominators.
Which is the first step to simplifying the given expression?
Here we have the expression:
[tex]\frac{tan(x)}{1 + sec(x)}[/tex]
Remember that:
[tex]tan(x) = \frac{sin(x)}{cos(x)}\\ \\sec(x) = \frac{1}{cos(x)}[/tex]
Replacing that would be the "step zero", we can write:
[tex]\frac{tan(x)}{1 + sec(x)} = tan(x)*\frac{1}{1 + sec(x)} = \frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} }[/tex]
The first step to simplify this, is taking the product between the denominators:
[tex]\frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} } = sin(x)*\frac{1}{cos(x) + \frac{cos(x)} {cos(x)} } = \frac{sin(x)}{cos(x) + 1}[/tex]
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Answer:
tanx(1-secx)/(1+secx)(1-secx)
Step-by-step explanation:
aP E
Please help me find the area of this trapeziod.
Answer:
37.5 m
Step-by-step explanation:
Since the trapezoid area formula is ((base 1+base 2)/2)*height, we can plug in the values.
((8+7)/2)*5
(15/2)*5
7.5*5=37.5
Now we add the unit, "m" to get 37.5 m!
Dakota has four yardsticks and two 12-inch rulers.If she lays all four of the yardsticks and both rulers end-to-end,what is the maximum number of feet she can measure accurately at once? PLEASE EXPLAIN
E.12 ft
F.14ft
G.16 ft
H.!8ft
Answer:
[tex]\huge\boxed{\sf 14\ ft}[/tex]
Step-by-step explanation:
Yard sticks = 4
12-inch rulers = 2
All are placed end to end.
Converting yard and inch to feet:4 yardsticks into feets:We know that,
1 yard = 3 feet
4 yards = 3 × 4 feet
4 yards = 12 feet
2 12-inch ruler into feet:We know that:
1 inch = 0.083 feet
24 inch = 0.083 × 24 feet
24 inch = 2 feet
The maximum number of feet she can measure exactly:= 4 yardsticks + 2 12-inch rules
= 12 ft + 2 ft
= 14 ft
[tex]\rule[225]{225}{2}[/tex]
convert 0.390 as a fraction
Answer:
390/1000
This is the answer and hope it helps
Fill in the blanks find P A And si
The answer will be Rs. 4330.
Step-by-step explanation:
Because if you subtract 340 from 4670, you will get the answer which is 4330.
If 3x − 6 ≤ f(x) ≤ x2 − 3x + 3 for x ≥ 0, find lim x→3 f(x).
Answer:
Step-by-step explanation:
Find the reciprocal of 8 2/5
[tex]\huge\underline\red{Answer -}[/tex]
[tex]\bold{8 \frac{2}{5} }\: \\\\ \implies \: \frac{5 × 8 + 2}{5} \: \\ \\ \implies \: \frac{ 40 + 2}{5} \\\\ \implies \frac{42}{5} \\\\ \rightarrow \:\boxed {reciprocal \: = \frac{5}{42} } \\ \\[/tex]
hope helpful ~
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{8 \dfrac{2}{5}}\\\\\mathsf{= \dfrac{8\times5+2}{5}}\\\\\mathsf{= \dfrac{40 + 2}{5}}\\\\\mathsf{= \dfrac{42}{5}}\\\\\mathsf{=\dfrac{5}{42}}\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{\dfrac{5}{42}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Given statements:
If a shape is a parallelogram, then opposite angles are congruent.
. A rhombus is a parallelogram.
Which is a logical conclusion from the given statements?
O A rhombus has opposite angles that are congruent.
O The opposite sides of a rhombus are congruent.
O The diagonals of a rhombus are congruent.
O A rhombus is a quadrilateral.
The logical conclusion from the statement is that
B. The opposite sides of a rhombus are congruent.
How to deduce the information?From the information given, if shape is a parallelogram, then opposite angles are congruent.
In this case, since the rhombus is a parallelogram, then the opposite sides of a rhombus are congruent.
In conclusion, the correct option is B.
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Given sinθ=1/2 determine the value of sec θ. 0°<θ<90°
Given Choices
2/√3
√3/2
2
1
Answer:
[tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]
Step-by-step explanation:
Given [tex]sin(\theta)=\frac{1}{2}[/tex] , to find [tex]sec(\theta)[/tex], it will be helpful to visualize a right triangle (triangle with a 90 degree angle) associated with that particular θ. There are a few ways to go about this:
A general solution methodAll of the basic trigonometric functions, applied to an angle) are a ratio of two specific sides of any right triangle that holds that angle.
Remember that the Sine of an angle is defined specifically, the ratio of the opposite side (the side across from the angle in the Sine function), and the hypotenuse (the side across from the right angle). You might remember this through SohCahToa
[tex]sin(\theta)=\frac{opp}{hyp}[/tex]
In our case, since [tex]sin(\theta)=\frac{1}{2}[/tex] , so [tex]\frac{opp}{hyp}=\frac{1}{2}[/tex] . While there are an infinite number of triangles that have that ratio of those sides, they are all "similar" triangles (corresponding angles congruent, and corresponding sides are proportional, yielding common ratios of sides), and for ease, we can consider simply the triangle where the value of the numerator is the length of the opposite side, and the value of the denominator is equal to the hypotenuse. So, [tex]opp=1[/tex], and [tex]hyp=2[/tex].
While we haven't actually talked about θ yet, we can still set up the triangle that has these sides so that we can visualize what the triangle looks like. (see image)
This triangle represents the triangle for the unknown θ in the original sine function. We're tasked with finding the secant of that particular unknown θ.
Working toward Secant
Here, it will be helpful to remember either the reciprocal identities for[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex], or the definition of the secant function [tex]sec(\theta)=\frac{hyp}{adj}[/tex].
I find that most people remember the reciprocal identities more easily than keeping track of the definitions, so, since secant is related to cosine, it will be important to remember that [tex]cos(\theta)=\frac{adj}{hyp}[/tex]. From there, take the reciprocal of the cosine-value to get the secant-value (which matches the definition of the secant function).
Either way, it comes down to knowing the lengths of the side adjacent to theta, and the hypotenuse. We already know the length of the hypotenuse, so we just need the length of the adjacent side.
Applying the Pythagorean Theorem
Fortunately, because it is a right triangle, the Pythagorean Theorem applies: [tex]a^{2} +b^{2} =c^{2}[/tex] (where c is the length of the hypotenuse, and a & b are the lengths of the legs)
Substituting the known values for the sides we do know...[tex](adj)^{2} +(1)^{2} =(2)^{2}\\(adj)^{2} +1 =4[/tex]
...isolating "adj" by subtraction...
[tex](adj)^2=4-1\\(adj)^2=3[/tex]
...applying the square root property...
[tex]adj=\sqrt{3}[/tex] or [tex]adj=-\sqrt{3}[/tex]
Identifying which Quadrant the triangle is in
Since we were given that [tex]0^o < \theta < 90^o[/tex], our triangle is an acute triangle (as drawn in the diagram), and is in quadrant I (indicating that both legs will be measured with a positive value.
Thus, we discard the negative solution and conclude that [tex]adj=\sqrt{3}[/tex].
Finding the final solution
From there, [tex]cos(\theta)=\frac{adj}{hyp}[/tex] implies [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex], and through the reciprocal relationship (or simply the definition of secant, whichever is easier for you to remember), [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]
Note: This method did not require knowing what the angle θ was.
Alternative method using the Unit CircleIf you know well the values of special triangles in the unit circle, you may have identified that [tex]sin(\theta)=\frac{1}{2}[/tex] is associated with [tex]\theta=30^o[/tex]. If so, if you also recall that the ordered pair associated with that point on the unit circle is [tex](\frac{\sqrt3}{2} ,\frac{1}{2} )[/tex], and that the [tex]cos(\theta)=x\text{-coordinate on the unit circle}[/tex], then you can quickly identify that [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex].
This method still ends the same: recalling the reciprocal relationship between cosine and secant, giving [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex].
Barbara buys a box of pens for $4. For every additional box she buys, she gets a $1 discount. Which expression represents the total cost of the -
pens, c, as a function of the number of boxes, b?
Answer:
Step-by-step explanation:
I need to use factorial the! When you use the binomial probability formula and I need to show step-by-step for for a through c
Given the number of trials and the probability of success, determine the probability indicated: (Hint use binomial distribution formula use factorials ! in showing your work)
n = 15, p = 0.4, find P(4 successes)
n = 12, p = 0.2, find P(2 success )
n = 20, p = 0.05, find P(at most 3 successes)
(hint for c.
P (at most 3 successes) = P(x ≤3)= P(x= 0) + P(x = 1)+ P(x = 2)+ P(x = 3)
Using the binomial distribution, it is found that the probabilities are:
P(X = 4) = 0.1268.P(X = 2) = 0.2835.[tex]P(X \leq 3) = 0.9841[/tex]What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.Exercise 1:
The parameters are:
n = 15, p = 0.4, x = 4.
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228[/tex]
Exercise 2:
The parameters are:
n = 12, p = 0.2, x = 2.
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835[/tex]
Exercise 3:
The parameters are:
n = 20, p = 0.05.
The probability is:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Using the binomial formula for each value and adding them:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841[/tex]
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24. This week, Cristina eamed P594.65 from selling burgers for 35 days. How much he will earn in 5 days?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter. You got 88.75 for the first quiz, 85.5, 90.5, and 87.25 in the second, third and fourth quizzes, respectively. What is your average in the four quizzes this quarter?
A. 86.5
B. 88
C. 89.5
D. 90 26. Amberich put P580.00 into a savings account for one year. The rate of interest on the account was 6.5%. How much was the interest for one year in pesos and centavos?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
24. This week , Cristina eamed P594.65 from selling burgers for 35 days . How much he will earn in 5 days ?
A. P84.95
B. P94.95
C. P104.95
D. P114.95
25. You have four quizzes in your math subject in a quarter . You got 88.75 for the first quiz , 85.5 , 90.5 , and 87.25 in the second , third and fourth quizzes , respectively . What is your average in the four quizzes this quarter ?
A. 86.5
B. 88
C. 89.5
D. 90
26. Amberich put P580.00 into a savings account for one year . The rate of interest on the account was 6.5 % . How much was the interest for one year in pesos and centavos ?
A. P67.70
B. P37.70
C. P57.70
D. P17.70
Question 24 :
P594.65 : 35 days
P594.65/7 : 35/7 days
P84.95 : 5 days
⇒ A. P84.95
Question 25 :
88.75 + 85.5 + 90.5 + 87.25 / 4
352/4
88
⇒ B. 88
Question 26 :
I = P × r × t
I = 580.00 × 0.065 × 1
I = P37.70
⇒ B. P37.70
How much acetic acid is in a 5 - liter container of acetic acid and water that is marked 80% acetic acid ? How much is water ?
what is the value of the fourth term in a geometric sequence for which a1=10 and r =0.5
Answer: 1.25
Step-by-step explanation:
The explicit formula for the sequence is [tex]a_{n}=10(0.5)^{n-1}[/tex]
Substituting in n=4,
[tex]a_{4}=10(0.5)^{4-1}=\boxed{1.25}[/tex]
A company has 200 machines. Each machine has 129 probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is and the probability that at least one machine would be working is the probability that all would be working is
The probability that 5 would not be working is 0.18665, the probability that at least one machine would be working is 0.00602 and the probability that all would be working is 1.
Given a company has 200 machines. Each machine has a 12% probability of not working.
If we working pick 40 machines randomly then we have to find the probability that 5 would not be working, the probability that at least one machine would be working, and the probability that all would be working.
So
1) probability that 5 would not be working
C(40,5)·0.12⁵·0.88³⁵= 40!/(5!(40-5)!)·0.12⁵·0.88³⁵
≈ 0.18665
2) probability that at least one machine would be working
0.88⁴⁰ ≈ 0.00602
3) probability that all would be working
1 - 0.12⁴⁰ ≈ 1.0000
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2x-3<1 or 3x-1<17
Solve compound inequality
The union consists of all of the elements that are contained in each interval.
Inequality Form:
x<6
Interval Notation:
(−∞,6)
Help me to solve this answer below :((!!!
Answer:
3/2+1/2+17/2=21/2
Answer: 21/2 hours or 10 1/2 hours
Step-by-step explanation:
To find out the total number of hours needed for all activities scheduled for the day, simply add the needed hours for each activity.
You just need to add them because they have the same denominator.
3/2 for homework
1/2 for home chores
17/2 for sleep
[tex]\frac{3}{2} + \frac{1}{2} + \frac{17}{2} = \frac{21}{2}[/tex] hours
A linear function contains the following points: 0,-3 and 6,15.
WHat is the slope and y-intercept
The slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
A linear function contains the following points: (0,-3) and (6,15)
The slope:
[tex]\rm m =\dfrac{15-(-3)}{6-0}[/tex]
m = 18/6
m = 3
The equation of a line:
y = mx + c
Plug x = 0, y = -3
-3 = c
Thus, the slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)
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Explain how to graph a scatterplot and its regression line using a regression calculator
Press the Linear Regression button to generate the regression line.
We have given that, regression line using a regression calculator
We have to determine how to graph a scatterplot and its regression line using a regression calculator.
Before entering data into the regression calculator, it is important to determine which variable should be associated with the x-axis and which with the y-axis.
What is the regression line?
Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.
Enter the data pairs.
Press the Linear Regression button to generate the regression line.
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Determine whether each ordered pair is a solution to the inequality x+5y<2.
Select all that apply:
(−8,−1)
(−1,0)
(4,2)
(9,6)
(0,10)
Two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
Given inequality is:-
x + 5y < 2.We will check all the points for the inequality:-
(−8,−1) → x + 5y < 2. → -8 +(5 x -1) < 2 → -13 < 2 It is inequality
(−1,0) → x + 5y < 2 → -1 < 2 It is inequality
(4,2) → x + 5y < 2 → 14 < 2 wrong
(9,6) → x + 5y < 2 → 39 < 2 wrong
(0,10) → x + 5y < 2 → 50 < 2 wrong
Therefore the two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.
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Over what interval is the function in this graph increasing? A. –5 ≤ x ≤ 5 B. –3 ≤ x ≤ 2 C. –4 ≤ x ≤ –2 D. –2 ≤ x ≤ 3
The function in this graph is increasing in the interval –2 ≤ x ≤ 3 , Option D is the right answer.
What is a function ?A function is a mathematical statement used to relate a dependent and an independent variable.
From the graph it can be seen that the graph is increasing in the interval
–2 ≤ x ≤ 3
The graph is said to be increasing when the value of y is getting more and more positive
As –2 ≤ x ≤ 3 , y varies from -3 to +3
Therefore Option D is the right answer.
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Answer:
–2 ≤ x ≤ 3
Step-by-step explanation:
A carpet installer charges a flat rate of $40 + $1.50 per square foot for labor so the total cost for the labor depends on the amount of carpet installed the relationship between the total cost for labor and the amount of corporate installed is the domain of the relation is the range of the relation is
The domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
A carpet installer charges a flat rate of $40 and $1.50 per square foot for labor.
So the total cost for the labor depends on the amount of carpet installed, the relationship between the total cost for labor and the amount of corporate installed.
Then the domain of the relation is the range of the relation will be
Let y be the total amount and x be the number of square foot.
y = 1.5x + 40
Then the domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).
The graph is given below.
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find the value of x y and z?
Answer:
Step-by-step explanation:
(-7x^2+3)-(-4x-3)
(−7x
2
+3)−(−4x−3)
Answer:
-28x^3-28x^2+16x+15
Step-by-step explanation:-28x^3-28x^2+16x+15
An 8-pack of clay pots costs $15.76. What is the unit price?
If f(x) = 3x + 2 what is f(5)?
Answer:
f(1)= 3×1 + 2 = 5
....
.....
....
f(5)= 3×5 + 2 = 17
Answer:
f(5) = 17
Step-by-step explanation:
Given: f(x) = 3x + 2
We are asked to find the value of the function when the value of x is 5
Substitute 5 as the value of x in the function:
⇒ f(x) = 3x + 2
⇒ f(5) = 3(5) + 2 [multiply]
⇒ f(5) = 15 + 2 [add]
⇒ f(5) = 17
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a telephone company charges $0.98 for the first minute, $0.82 for each additional minute, and a$1.56 service charge if the cost is 11.56 how long did the person talk
Answer:
12 minutes
Step-by-step explanation:
added in the picture
James has available a 10% alcohol solution and a 60% alcohol solution find how many liters of each solution he shouldn’t mix to make 50 L of a 40% alcohol solution
Answer:
20 L
Step-by-step explanation:
I am guessing that you meant should instead of shouldn't.
To solve this we can set the amount of 10% solution needed equal to x. This means that the 60% solution will be the remaining amount needed, so 50 L - x.
We can do 10%*x+60%*(50-x)=50*40%. Solving for x we get:
0.1*x+0.6*50-0.6*x=50*0.4
0.1*x+30-0.6*x=20
-0.5*x=-10
x=20
V
On March 8, 2017, one U.S. dollar was worth 66.79 Indian rupees.
(a) On that date, how many dollars was 110.66 rupees worth?
Round your answer to the nearest hundredth of a dollar.
dollars
(b) On that date, how many rupees was 125.29 dollars worth?
Round your answer to the nearest hundredth of a rupee.
I need help with this problem.
Answer:
a=1.66
b=8368.12
Step-by-step explanation:
hope it helps
Move the slider on the graph on the right to graph each function:
For the function: y = StartRoot x minus 7 EndRoot + 1
The domain is : x ≥
The range is: y ≥
Answer:
domain: x ≥ 7 . . . [7, ∞) in interval notationrange: y ≥ 1 . . . [1, ∞) in interval notationStep-by-step explanation:
You want the domain and range of the function y = √(x -7) +1.
DomainThe domain is the horizontal extent of the graph. The graph of the given function extends to the right from x=7, which is included in the solution set.
The domain is x ≥ 7.
RangeThe range is the vertical extent of the graph. The graph of the given function extends upward from y=1, which is included in the solution set.
The range is y ≥ 1.
Answer: domain: 7
range: 1
Step-by-step explanation:
