[tex]\cfrac{tan(\theta )+1}{sec(\theta )}~~ = ~~sin(\theta )+cos(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{tan(\theta )+1}{sec(\theta )}\implies \cfrac{~~ \frac{ sin(\theta )}{cos(\theta ) } +1~~}{\frac{1}{cos(\theta )}}\implies \cfrac{~~ \frac{ sin(\theta )+cos(\theta )}{cos(\theta ) } ~~}{\frac{1}{cos(\theta )}}[/tex]
[tex]\cfrac{ sin(\theta )+cos(\theta )}{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ } \cdot \cfrac{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1}\implies sin(\theta )+cos(\theta )[/tex]
You take a new job as a tutor and you get paid $100 whether students come or
not. What type of pay is this?
Salary
Vacation Pay
Piece Rate
Hourly Pay
A survey of 600 students yielded the following information: 129 were seniors, 249 were commuters, and 68 were seniors and commuters. how many students were neither seniors nor commuters?
A survey of 600 students yielded the following information: 129 were seniors, 249 were commuters, and 68 were seniors and commuters.
The answer provided below has been developed in a clear step by step manner.
Step: 1
Total number of students are 600
n(T) = 600
The number of seniors are:
n(S) = 129
The total number of commuters are:
n(C) = 249
The total number of seniors and commuters are:
n(S∩C) = 68
Total number of seniors or commuters is:
n(S∪C) = n(S)+n(C) - n(S∩C)
n(S∪C) = 129+249-68
= 310
Explanation:
The given information has been shown as.
Step: 2
Calculate the total value of n(S∪C):
So the total number of seniors and commuters are 310.
Now we have to calculate the students who are neither seniors nor commuters are:
Total students - n(S∪C)
S∪C = 600 - 310
= 290
Hence the students that are neither senior nor commuters are 290.
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y=2x-1
y = 5-x
What is the solution to this system
of equations?
Answer:
mother....... pure the water by boilingit
What is proof of perpendicular?.
To prove that given is perpendicular we have show that one make right angle, i.e. 90 degree.
What does perpendicular mean?A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with that other line. In other words, two lines become perpendicular to one another if they connect at a right angle.
For proof of perpendicular-
Theorm 1 : If two lines intersect to form a pair of lines with a "congruent angle," then the lines are perpendicular to one another. Angles that are equivalent to one another are known as congruent angles.
Theorm 2 : Four right angles will be formed if two perpendicular lines cross.
Theorm 3 : The "adjacent acute angles" are complimentary if two of their sides are perpendicular. As you presumably remember, acute angles are angles that are fewer than 90 degrees, whereas adjacent angles are angles that are next to one another.
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Write the equation of the line in fully simplified slope-intercept form. PLS HELP ME IM FAILING THIS CLASS
Answer:
The answer is: y = x + 7
Step-by-step explanation:
happy learning
Your uncle Jim lives in England, where the current exchange rate iS 1.64 US dollars for each
British pound. Solve for the amount of your monthly bill,
England.
to the nearest hundredth, if you lived in
Answer:
Since we need your monthly bill we will call it the variable B for now, (Unless you have the bill, if so replace it with the variable)
Multiply 1.64 x B since the exchange rate is different than the US bill,
For example, say your bill is $100 in the U.S.
You do 1.64 x 100 = A monthly bill of $164 if you lived in Britain
Step-by-step explanation:
identify the vertex, axis of symmetry, maximum or minimum, and domain and range of each function. f(x)
The vertex is (7, -27)
The line of symmetry is x = 7.
The minimum is y = -27
The domain is the set of all real numbers.
The range is y ≥ -27.
Given,
The quadratic equation is as follows:
f(x) = (x - 7)^2 - 27
The quadratic equation is in vertex form, hence if the vertex is (h, k), the vertex form will be as follows:
f(x) = (x - h)^2 + k
Then the vertex in this instance is (7, -27).
A line of the form x = h is the line of symmetry, and in this instance the line is x = 7.
The minimum of the quadratic equation is y = -27 since the function has a positive leading coefficient, indicating that the vertex is a minimum.
Finally, the domain is the set of all real numbers, much like the domain of any quadratic equation.
The range includes all real numbers that are greater than or equal to -27.
R = y ≥ -27.
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The given question is incomplete. Completed question is given below;
Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of the function. f(x)=(x-7)^(2)-27
what is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book?
The probability that nadia randomly picks up a reference book and then without replacing it picks up a nonfiction book is 5/136.
Given:
17 total number books out of which 10 are fiction books,2 are reference books , 5 non fiction books.
Number of ways of picking reference book = [tex]2_C_1[/tex]
Probability of picking a reference book = [tex]2_C_1/17_C_1[/tex]
= 2/17
The total number of books left on the shelf is 16.
The number of ways in which a non fiction book can be picked after a reference book is already picked = [tex]5_C_1/16_C_1[/tex]
= 5/16.
Total probability = 2/17*5/17
= 10/272
= 5/136.
Therefore The probability that nadia randomly picks up a reference book and then without replacing it picks up a nonfiction book is 5/136.
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3 * 2x * 4
simplify
in my textbook answer is shown as 24x i need to know it is 24x
* represents multiply symbol
Answer:
yes
Step-by-step explanation:
24 * 2 represents 24 × 2
I am not a fan of the use of the asterix to represent multiplication
Please help will mark brainiest!!!
2.) These students want to make more money at their job which pays hourly. If they want their hourly wages to increase, what is an appropriate transformation to accomplish this task? Why? Use a complete sentence.
The appropriate transformation to increase the hourly wage is a vertical stretch of the function.
What is the definition of the payment function?The payment function, as a function of the number of hours worked, is a linear function with definition given as follows:
P(h) = mh + b.
In which the coefficients of the payment function are listed as follows:
m is the slope of the linear function, which is equivalent to the hourly pay of the students.b is the intercept of the linear function, which is equivalent to the fixed pay of the students.To increase the hourly pay, the slope needed to be increased, meaning that the slope m has to be multiplied by a constant k, and this multiplication is a transformation called a vertical stretch by a factor of k.
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The appropriate transformation to increase the hourly wage is a vertical stretch of the function.
What is the definition of the payment function?
The payment function, as a function of the number of hours worked, is a linear function with definition given as follows:
P(h) = mh + b.
In which the coefficients of the payment function are listed as follows:
m is the slope of the linear function, which is equivalent to the hourly pay of the students.
b is the intercept of the linear function, which is equivalent to the fixed pay of the students.
To increase the hourly pay, the slope needed to be increased, meaning that the slope m has to be multiplied by a constant k, and this multiplication is a transformation called a vertical stretch by a factor of k.
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help asaap
Calculate the area of the pavement surrounding the swimming pool.
Answer:
5x2=10. 7x2=14. 10+14=24.
Step-by-step explanation:
A table is 6 feet long and 3 feet wide. You extend the length of the table by inserting two identical table leaves. The extended table is rectangular with an area of $\left(18+6x\right)$ square feet. Write an expression that represents the length (in feet) of the extended table.
Given that a table is 6 feet long and 3 feet wide. You extend the length of the table by inserting two identical table leaves. The extended table is rectangular with an area of (18+6x) square feet.
The area of a rectangle is the product of the width and the length
The required values are given as;
6 + 2x
Here x represents the width of the leaves
Total length = (6 + 2x) feet
Width = 3 feet
Area, A = (6 + 2x) ft. × 3 ft. = (18 + 6x) ft.²
The expression that represents the length of the table is 6 + 2x
The variable x represents the width of the leaves
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Find the length of the side x.
Give your answer rounded to 1 DP.
14.2cm
9.7cm
3.6cm
The diagram is not drawn accurately.
The value of x using the Pythagoras Theorem is 6.08 cm.
What is Pythagoras' Theorem?
The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares. The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC,is present. The base in this equation is AB, the height is AC, and the hypotenuse is BC.
In the given figure, we have:
A right angles triangle.
So, the Hypotenuse meaure is 14.2 cm;
The measure of the base side is 3.6 + 9.7 cm = 13.3 cm;
So, we can find the perpendicular side length using the Pythagorean Theorem
So, using the Pythagoras theorem,
[tex]c^{2} = x^{2} + y^{2}[/tex]
[tex](14.2)^{2} = (13.3)^{2} + x^{2}[/tex]
201.64 = 176.89 + [tex]x^{2}[/tex]
24.75 = [tex]x^{2}[/tex]
So, x = 4.97
So, The perpendicular side is 4.97 cm;
Now using the Pythagoras theorem again in the smaller triangle, we get:
[tex](3.6)^{2} + (4.9)^{2} = x^{2}[/tex]
12.96 + 24.01 = [tex]x^{2}[/tex]
36.97 = [tex]x^{2}[/tex]
So, The value of x is 6.08 cm;
Hence,
The value of x is 6.08 cm;.
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staceys long jump was 10 feet. that is 5/6 foot longer than rons long jump. did ron jump more or less than 10 feet
Ron jump is less than 10 feet. Ron jump is actually 5.45 feet.
How to find who jump more ?Stacey long jump was 10 feet. That is 5/6 foot longer than Ron's long jump.
Let's find if Ron jump more or less than 10 feet's.
Therefore,
Ron's Jump = x
Hence,
x + 5 / 6 x = 10
6x + 5x / 6 = 10
cross multiply
6x + 5x = 60
11x = 60
x = 60 / 11
x = 5.45
Therefore, Ron jump less than 10 feet.
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What are the domain and range?
Answer:
-2,2
4
Step-by-step explanation:
hospital records show that 16% of all patients are admitted for heart disease, 26% are admitted for cancer (oncology) treatment, and 8% receive both coronary and oncology care. what is the probability that a randomly selected patient is admitted for something other than coronary care? (note that heart disease is a coronary care issue.)
0.86 is the probability that a randomly selected patient is admitted for something other than coronary care.
What is probability ?
The likelihood that something will occur is the foundation of it. The justification for probability serves as the basic foundation for theoretical probability.A coin is tossed, for instance, and the theoretical likelihood of receiving a head is 1 in 2.Let H denotes the patients are admitted for heart disease.
Let C denotes the patients are admitted for cancer treatment.
We are given:
P(H) = 0.16
P(C) = 0.26
P( H ∩ C ) = 0.8
P(Hc ) = 1 - P(H) = 1 - 0.16 = 0.86
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Subtract. Simplify your answer and write it as a mixed number. 12 5/12 - 4 1/6
After the subtraction, the simplified form of the mixed number is 33/4
Mixed numbers
Mixed fraction means a fraction represented with its quotient and remainder.
Given,
Here we have the mixed numbers 12 5/12 - 4 1/6
Now, we have to perform the subtraction in it and then we have to simplifies it.
Firs we have to convert the mixed numbers into normal fraction, for that we have to do the following:
12 5/12 = (12 x 12) + 5/12
=> (144 + 5)/12
=> 149/12
Similarly, when we simplifies the second one, then we get,
=> 4 1/6 = (6 x 4) + 1/6
=> (24 + 1) / 6
=> 25/6
Here the fractions have unlike denominators.
So, first we have to find the Least Common Denominator and rewrite the fractions with the common denominator.
Therefore, the LCD(149/12, 25/6) = 12
Now, we have to multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD.
=> 149/12 - 50/12
The two fractions now have like denominators so you can subtract the numerators.
Then:
=> 99/12
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 99 and 12 using GCF(99,12) = 3
So, the simplified form of the fraction is
=> 33/4
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a path diagram allows you to determine the effect of one variable upon another both directly and indirectly through an intervening variable. true false
The given statement "a path diagram allows you to determine the effect of one variable upon another both directly and indirectly through an intervening variable. " is true.
Given that,
To justify the given statement whether it is true or not.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
According to the question,
Let the two interdependent numbers be x and y,
y ∝ x
y = kx
Or
x = y/k
Thus, a path diagram allows you to determine the effect of one variable upon another both directly and indirectly through an intervening variable.
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X
Estimate the solution to the system of equations graphed on the grid:
-10-9-3-7-5-5--3-
10
8
6
-10
4 5 6 7 8 9 10
A (1.5, 4.2)
B (-4.1,-1.5)
C (-1.6, 1.4)
D (1.4,-2.1)
The solution is
y=x+4
y=-2x-4
Slope of a Line :
The ratio of the change in the y coordinate to the change in the x coordinate is known as a line's slope in mathematics.
Y and X, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate.
As a result, the formula for the change in y-coordinate with respect to the change in x-coordinate is m = change in y/change in x = y/x.
where the slope of a line is denoted by "m".
The graph of the equation y = mx + c has a slope of m, an intercept of m, and a y-intercept of c. In the slope-intercept version of the linear equation, m and c are real integer values.
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h(x)=1-3x, domain= {1, 0, 1, 2}
Write the range of h using set notation. Then graph h.
The domain of the given function h(x) = 1 - 3x is {-2, 1, -2, -5}.
What are the domain and the range of a set of ordered pairs?The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.
The function is given in the question as:
h(x) = 1 - 3x ....(i)
Here domain= {1, 0, 1, 2}
The range includes all possible y values of a set of ordered pairs.
Substitute the values of the domain i.e. x = 1, 0, 1, 2 in the equation (i),
h(x) = 1 - 3(1)
h(x) = 1 - 3
h(x) = -2
h(x) = 1 - 3(0)
h(x) = 1
h(x) = 1 - 3(1)
h(x) = 1 - 3
h(x) = -2
h(x) = 1 - 3(2)
h(x) = 1 - 6
h(x) = -5
Therefore, the domain of the given function is {-2, 1, -2, -5}.
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Makayla paid $3. 36 for 1. 4 pounds of grapes. What is the unit rate per pound of grapes?.
Answer:2.4
Step-by-step explanation:
Based on the information given the unit rate per pound is 2.4.
Using this formula
Unit rate per pound=Costs/Pounds
Where:
Cost=$3.36
Pounds=1.4 pounds of grapes
Let plug in the formula
Unit rate per pound=$3.36/1.4
Unit rate per pound=2.4
the unit rate per pound is 2.4.
Write 35/3 as a mixed number.
Answer:
Step-by-step explanation:
11 2/3
explain why it is reasonable to use a one-sample t confidence interval to estimate the population mean even though the population distribution is not approximately normal. (select all that apply.)
The general form of a Confidence Interval Estimate for a population mean is
Sample mean ± Critical Value × Standard Error of statistics.
Confidence intervals are one type of statistical interference. They allow us to range values where we can be relatively confident the true value will be. In this case, we are constructing a confidence interval for a population mean. For example: - Suppose that our sample has a mean of X bar = 10 and have constructed the 90% confidence interval.
From the above discussion, we get to know that:
It is reasonable to use a one sample t confidence interval to estimate the population mean since all freshman at a mid western university where surveyed.
It is reasonable to use a one sample t confidence interval to estimate the population mean since the sample size is at least 30.
It is reasonable to use a one sample t confidence interval to estimate the population mean since the sample size is the sample is representative of the population.
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If the mean of the data in the column graph is 6, how many people caught a bus?
Thank you for helping.
Answer:
4 people caught the bus
Step-by-step explanation:
Azaan scored 42 points in 3 games. How many points would you expect him to make in an 11 game season?
Answer: 154
Step-by-step explanation:
= [tex]11x\frac{42}{3} \\[/tex]
= 154
1) Use the compound-angle formulae to write the following as surds.
(i) sin 75° = sin(45° +30°)
(ii) cos 135º = cos(90° +45°)
Problem 1:
[tex]sin(75^o)=sin(45^o+30^o)\\sin(A+B)=sinAcosB+cosAsinB\\sin(45^o+30^o)=sin45^ocos30^o+cos45^osin30^o\\\frac{1}{\sqrt{2} } *\frac{\sqrt{3} }{2} +\frac{1}{\sqrt{2} } ]\times\frac{1}{2} \\\frac{\sqrt{3} }{2\sqrt{2} } +\frac{1}{2\sqrt{2} } ---- > \frac{\sqrt{3}+1}{2\sqrt{2} } (ANS)[/tex]
Problem 2:
[tex]cos135^o=-cos45^o=-\frac{1}{\sqrt{2} }[/tex]
Explanation:
Cos 135° is an angle in the second quadrant.
In the second quadrant, cos is negative. [tex]cos\theta=\frac{x}{r}[/tex]
[tex]cos135=cos(180-45)=-cos45^o[/tex]
An angle of 45° is found in a right-angled triangle of sides [tex]1:1:\sqrt{2}[/tex]
[tex]cos45^o=\frac{1}{\sqrt{2} }[/tex]
[tex]cos135^o=-cos45^o=-\frac{1}{\sqrt{2} }[/tex]
Note that [tex]\sqrt{2}[/tex] is an irrational number and cannot be given as an exact decimal.
Little messy math, but thanks for asking the question.
- Eddie
68. if the radius of a circle is an exponential random variable, find the density function of the area.
The density function of area is is ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}}).
A random variable can be defined as a variable whose value is unknown or as a function that assigns numerical values to each of the outcomes of an experiment. It can also be defined as a rule that assigns a numerical value to each outcome in a sample space.
The density function (1.4-5)P(x) = an exp(-ax), if x0,0, if x>0, where an is any positive real number, defines the exponential random variable.
radius R has df f(r) ={\lambdae}^{-\lambdar}
area Y= *r2
r = \pm (Y/(\pi))1/2
hence P(Y<y) =F(Y) =P( *r2<y) =P(r<+/- (Y/( ))1/2 ) = \int_{{-y/\pi}^{1/2}}^{{(y/\pi)}^{1/2}}{\lambdae}^{-\lambdar} dr
= e^{{\lambda(y/\pi)}^{1/2}}- e^{{-\lambda(y/\pi)}^{1/2}}
Therefore P(df of y) = f(y) = d/dyf(y) =(d/dy) (e^{{\lambda(y/\pi)}^{1/2}}- e^{{-\lambda(y/\pi)}^{1/2}})
= ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}})
Therefore the density function of area is ½({(y/\pi)}^{1/2}(e^{{\lambda(y/\pi)}^{1/2}}+ e^{{-\lambda(y/\pi)}^{1/2}})
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14. 2x² - 9x - 5≥0
Solve each of the quadratic inequalities.
Answer: x > _5
Step-by-step explanation:
Help on all problems but mostly #6 & #7 parts a,b, and c
hello here is number 4 & 6
6:
the graph for number 6 is listed below.
table:
(-2,5)
(-1,0)
(0,-3)
(1,-4)
(2,-3)
4:
all of them can be, look at the listed images below.
A basketball player recorded for 11 consecutive games her points 13 20 15 22 24 21 18 20 25 17 27 how many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
She need 6 points to score in her 12th game in order to decrease the interquartile range by 1 point.
What is Interquartile range?
An Interquartile range is one of the measure of variability that measures the spread of middle 50% of the data.
Given that;
A basketball player recorded for 11 consecutive games her points as;
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
Now,
Since, We know that;
The formula for the interquartile range is,
⇒ IQR = Q₃ - Q₁
Where, Q₃ is the third quartile , Q₁ is the first quartile.
Here, We arrange the points in the increasing order as;
⇒ 13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27
The first quartile is calculated as;
Q₁ = (n + 1) / 4 th term
Where, n is number of terms.
Q₁ = (11 + 1) / 4
Q₁ = 3rd term
Q₁ = 17
The third quartile Q₃ is calculated as;
Q₃ = 3(n + 1) / 4
Q₃ = 3 x 3
Q₃ = 9th term
Q₃ = 24
Thus, The interquartile range is,
⇒ IQR = Q₃ - Q₁
⇒ IQR = 24 - 17
⇒ IQR = 7
So, The desired interquartile range is,
⇒ IQR = 7 - 1
⇒ IQR = 6
Therefore, She need 6 points to score in her 12th game in order to decrease the interquartile range by 1 point.
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