Using trigonometric identities, it is found that the exact value of the secant of the angle is given by:
c. [tex]\sec{\theta} = - \sqrt{5}[/tex]
How is the tangent related to the secant?According to the following identity:
[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]
The tangent is the inverse of the cotangent, hence in this problem, we have that:
[tex]\tan{\theta} = -2[/tex]
Then, the secant is given as follows:
[tex]\sec^2{\theta} = 1 + (-2)^2[/tex]
[tex]\sec^2{\theta} = 5[/tex]
[tex]\sec{\theta} = \pm \sqrt{5}[/tex]
The angle is in the second quadrant, where the cosine is negative, hence the secant also is and option c is correct, that is:
c. [tex]\sec{\theta} = - \sqrt{5}[/tex]
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What is the value of 6 in 640.31?
Answer:
hundred
Step-by-step explanation:
Answer:
600
Step-by-step explanation:
You have been given data about gas prices in 15 states. Comparing the two data sets below, what does the larger mean and median say about gas prices in 2022 compared to gas prices in 2018?
Gas Prices in 2018 Gas Prices in 2022
Max: $2.42
Min: $2.03
Mean: $2.098
Median: $2.06
Mode: $2.04
Variance: 0.0121
Standard Deviation: $0.11
Max: $5.87
Min: $4.48
Mean: $4.83
Median: $4.72
Mode: $4.72
Variance: 0.0142
Standard Deviation: $0.38
Comparing the two data sets shown below
What is standard deviation and variance?Variance is the average squared deviations from the mean, while standard deviation is the square root of this number.
Both the mean and the median can be used to describe where the “center” of a dataset is located.
So, the mean of data in 2022 is more than mean of data in 2018.
It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers.
As the variance of 2022 more than in variance in 2018.
A high variance indicates that the data points are very spread out from the mean, and from one another.
As the standard deviation of 2022 more than in standard deviation in 2018.
The high standard deviation indicates data are more spread out.
The bigger the range, the more spread out the data.
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The hour and minute hand of a clock form an angle that constantly changes. During each hour of the day,the clock hands will form right, acute and obtuse angles. Assume the hour hand points directly at the hour.Write a time of day when the two clock hands form each tyep of angle
The each type of angle are discussed below
What is angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
If the hours hand point to the hour 1 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 2 and minute hand at 12 then
angle will be acute.
If the hours hand point to the hour 3 and minute hand at 12 then
angle will be right angle .
If the hours hand point to the hour 4 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 5 and minute hand at 12 then
angle will be obtuse.
If the hours hand point to the hour 6 and minute hand at 12 then
angle will be straight angle .
If the hours hand point to the hour 7 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 8 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 9 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 10 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 11 and minute hand at 12 then
angle will be reflex.
If the hours hand point to the hour 12 and minute hand at 12 then
angle will be Complete angle.
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A stainless steel patio heater is a square pyramid. The length of one side of the base is 23.4 in. The
slant height of the pyramid is 93.2 in. What is the height of the pyramid?
The height of the pyramid is aboutin.
(Round to one decimal place as needed.)
The height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.
What is a square pyramid?In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.
We have a square pyramid.
Length of the pyramid = 23.4 in
The slant height of the pyramid = 93.2 in
From the figure:
Base length CB = DC = 23.4 in
In a right-angled triangle, BCD
Applying Pythagoras theorem:
DC² + CB² = DB²
23.4² + 23.4² = DB²
DB = 33.092 in
OB = (1/2)DB
OB = (1/2)33.092 = 16.546 in
In the right-angle triangle AOB, again applying Pythagoras theorem:
AO² + OB² = AB²
h² + 16.546² = 93.2²
AO = h (height of the square pyramid)
AB = slant height = 93.2 in
After calculating, we get:
h = 91.719 ≈ 91.72 in
Thus, the height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.
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The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis.
Which of the following is the best interpretation of the standard deviation of the residuals?
The typical arm span is 161 centimeters.
The typical foot length is 16.1 centimeters.
The typical distance between the observed and predicted arm spans is 1.61 centimeters.
The typical distance between the observed and predicted foot lengths is 1.61 centimeters.
Answer:
D
Step-by-step explanation:
The correct answer should have a 63%.
It's probably D. The terminology is a little confusing.
The equation of the output looks like:
-7.611 + .186(x) = y
x --> Arm span
y --> Foot span
The linear relationship is formed with the armspan.
True or False
1. The data given in interval is a grouped data.
2. The specific point where the upper and lower limit meets is the data value.
3. The gap between each data value is called interval.
4. The number of times an observation occurs or appears in a data set is called frequency distribution table.
5. The lowest number in the class interval is the upper limit.
Answer:
true
false
true
false
true
The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled 12 vans and 11 buses with 576 students. High School B rented and filled 4 vans and 9 buses with 384 students. Each van and each bus carried the same number of students. How many students rode in each van?
Answer:
15 students
Step-by-step explanation:
To solve this question, we can set up a system of equations.
Let's start by naming our variables.
We can call the number of students that rode in a van "x".
Then, let's name the number of students that rode a bus "y".
Knowing this, we can create two equations and then solve.
For High School A, the equation would be as follows:
12x+11y=576
For High School B, it would be:
4x+9y=384
What you have to do now, is to eliminate one of the variables.
I'm going to choose to do it with elimination, but substitution also works.
I'm going to multiply the second equation by 3, so that we can subtract the equations to eliminate the x variable.
3(4x+9y=384)
Since we're multiplying 3 to both sides, the equation will remain true.
12x+27y=1152
Now, let's subtract the other equation from this one:
12x+27y=1152
- 12x+11y=576
_____________
0x+16y=576
Our new equation is:
16y=576
Divide both sides by 16 to isolate y
y=36
This means that 36 students rode in each bus.
Let's now use this info to solve for x.
We can do this by plugging in 36 for y.
4x+9y=384
4x+9(36)=384
Simplify
4x+324=384
Subtract 324 from both sides
4x=60
Divide both sides by 4
x=15
This means that 15 students rode in each van.
As I mentioned earlier, this could have also been solved by substitution.
You would have had to isolate one variable so that one of the equations read x= something or y= something
After that, you plug that in to the other equation so you're left with only one variable.
You then simplify, and plug the value back in for the other variable.
Given the nature of this question, that would have involved working with decimals, so I chose elimination instead.
Please let me know if you have any questions!
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Here, we have given that,
The senior classes at High school A and High school B planned separated trips. The number of bus and vans rented by high school class A are 12 vans and 11 buses. The number of bus and vans rented by high school class B are 4 vans and 9 buses. The total number of students in class A are 576 students. The total number of students in class B are 384 students .Let the number of students in van be 'x' and number of students in bus be 'y' .
According to the question,
Linear equation for class A
[tex]\sf{ 12x + 11y = 576 ...eq(1)}[/tex]
Linear equation for class B
[tex]\sf{ 4x + 9y = 384 ...eq(2) }[/tex]
Subtract eq(2) from eq(1) :-
[tex]\sf{ 12x + 11y -( 4x + 9y) = 576 - 384 }[/tex]
[tex]\sf{ 12x + 11y - 4x - 9y = 192 }[/tex]
[tex]\sf{ 8x + 2y = 192 }[/tex]
[tex]\sf{ 2(4x + y) = 192 }[/tex]
[tex]\sf{ 4x + y = {\dfrac{192}{2}}}[/tex]
[tex]\sf{ 4x + y = 96}[/tex]
[tex]\bold{ y = 96 - 4x ...eq(3) }[/tex]
Subsitute eq (3) in eq(1) :-
[tex]\sf{ 12x + 11( 96 - 4x) = 576 }[/tex]
[tex]\sf{ 12x + 1056 - 44x = 576 }[/tex]
[tex]\sf{ 12x - 44x = 576 - 1056}[/tex]
[tex]\sf{ -32x = - 480 }[/tex]
[tex]\sf{ x = {\dfrac{-480}{-32}}}[/tex]
[tex]\bold{ x = 15 }[/tex]
Thus, The value of x is 15 .
Now, subsitute the value of x in eq(2) :-
[tex]\sf{ 4(15) + 9y = 384 }[/tex]
[tex]\sf{ 60 + 9y = 384 }[/tex]
[tex]\sf{ 9y = 384 - 60 }[/tex]
[tex]\sf{ 9y = 324 }[/tex]
[tex]\sf{ y = {\dfrac{324}{9}}}[/tex]
[tex]\bold{ y = 36 }[/tex]
Thus, The value of y is 36
In this question, we have taken x and y are the number of students in each van and a bus.Therefore,
The number of students in each van = 15
The number of students in each bus = 36
Hence, The number of students rode in each van are 15 .
Please answer asap!!!!!! I Inserted photo. Thankssss
Answer:
2nd option
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
given
6xy³z × 3x²yx²
= 6 × 3 × x × x² × x² × y³ × y × z
= 18 × [tex]x^{(1+2+2)}[/tex] × [tex]y^{(3+1)}[/tex] × z
= 18[tex]x^{5}[/tex][tex]y^{4}[/tex]z
HURRY!!!!
If p -> q is true and q is true, then p is ____ true.
-always
-sometimes
-never
If p is true and q is true, then ~ p -> ~ q is ____ true.
-always
-sometimes
-never
Sometimes. p ⇒ q is true if both p and q are true, or whenever p is false.
Always. ¬ p ⇒ ¬q is true if ¬p and ¬q are both true (which means p and q are both false), or whenever ¬p is false (p is true).
For the function f(x) = 3x + 7, find the following:
a) f(2)=
c) f(x) = 8
b) f(-3) =
d) f(x) = 10
Answer:
a) 13
b) 1/3
c) -2
d) 1
Step-by-step explanation:
This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:
For example:
f(x) = 3x + 7
f(2) = 3(2) + 7
f(2) = 6 + 7
f(2) = 13
________
f(-3) = 3x + 7
f(-3) = 3(-3) + 7
f(-3) = -9 + 7
f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.
f(-3) = -2
The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:
For example:
f(x) = 8
f(x) = 3x + 7
8 = 3x + 7
8 - 7 = 3x
1 = 3x
x = 1/3
f(x)= 10
f(x) = 3x + 7
10 = 3x + 7
10 - 7 = 3x
3 = 3x
3/3 = x
1 = x
I hope this helps!
There is £80 in a pot which is shared out amongst 3 people. Anne gets £20 Mark gets £35 and Ben gets £25. What ratio of the money do all of the people get?
i need this done in 20 min please help asap
Answer:
the second one
Step-by-step explanation:
just looking at the y values you get
-24y + 32y so that will give u +8y , there is only one answer with that
50 PTS PLS HELP I'M BEING TIMED!!!!!!!! MY TEACHER IS CRAZY NO SCAMS
Determine the cost of 2 years at a community college or 4 years at a state college (in your home state or out of state). Explain the cost of your chosen college in 4-6 sentences. Remember, the cost of college includes: Tuition Room and board Books/supplies Gas Spending money
In Colorado, the estimated total in-state college tuition cost for two years is $83,832. It is to be noted that this is inclusive of other factors as shown in the computation below.
What is the calculation for the above figure?
Given the following:
Base Tuition (Note that this increases by 20% every year) = $12, 650
Off campus Room and Board - $11, 440
Housing - $5,976
Meals - $ 6, 450
Living Expenses - 1,670
Books and Supplies - $1200
The summary thus is equal to
Base Tuition = $12, 650 * 2 * 1.2
Off campus Room and Board - $11, 440 * 2
Housing - $5,976 * 2
Meals - $ 6, 450 * 2
Living Expenses - 1,670 *2
Books and Supplies - $1200 *2
This results in:
Base Tuition = $30,360
Off campus Room and Board = $22,880
Housing = $11, 952
Meals = $ 12900
Living Expenses = $ 3,340
Books and Supplies = $2,400
Grand Total = $ 83,832.
Note that the base tuition was estimated to increase at the rate of 20% every year.
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on a piece of paper, graph y=3/4x-3 use the graph to find the x-intercept of the line
The x-intercept of the line is (4, 0)
How to find the x-intercept of a lineThe x-intercept of a line is the point where the line crosses the x-axis. Given the equation below:
y=3/4x-3
The x-intercept occurs at the point where y = 0. Substitute:
0 = 3/4x - 3
3/4x = 3
3x = 12
x = 4
Hence the x-intercept of the line is (4, 0)
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The ratio of the number of squares to the number of triangles in simplest form is
added to make the ratlo of the number of squares to the number of triangles 1: 1 Is
The ratio of the number of squares to the number of triangles is 5 : 2
The number of triangles that should be added to make the ratio is 6
What are the ratios?
Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained in another number.
Ratio of the number of squares to the number of triangles = number of squares : number of triangles
10 : 4
5 : 2
The number of triangles that should be added to make the ratio 1 : 1 - 10 - 4 = 6
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Solve the following quadratic by
completing the square.
y = x² + 4x - 2
X
x = [?] ± √ [ ]
Please help me
Answer:
x = -2+- sqrt(6)
Step-by-step explanation:
Using completing the square, let x^2+4x-2 = 0 and solve the steps to get the answerx^2 + 4x - 2 =0
add 2 to both sides to get x^2 + 4x = 2
then add 4 to both sides to get x^2 + 4x + 4 = 6
Get the left hand side to the square formate: (x+2)^2 = 6
then simplify x+2 = sqrt(6) or x+2 = -sqrt(6)
so x = sqrt(6) - 2 or x = -sqrt(6) -2
The construction crew for a new house will dig a hole in the shape of a rectangular prism for the house's foundation. the hole will be 48ft long, 39ft wide, and 9ft deep. to haul away all of the dirt from the hole, a dump truck will take trips to a nearby landfill. the crew knows the amount of dirt the truck can hold each trip in cubic yards.
(a) find the volume of dirt that will be hauled away in cubic yards. use the table of conversion facts, as needed.
____yd3???
(b) each trip, the truck can haul away 11yd3 of dirt. to save gas, the crew wants to take as few trips as necessary to haul all of the dirt away. since all of the dirt needs to be hauled away, the crew might have to take a partial load for one trip. how many trips are needed to haul away all of the dirt? count each trip it makes the same, even if the truck isn't full.
_______trips???
c) if it costs $1175 for each trip that the truck makes, how much will it cost to haul away all the dirt?
$____ ???
The first step is to convert feet to yards.
1 feet = 1/3 yards
48 / 3 = 16 yards 39 / 3 = 13 yards 9/3 = 3 yardsVolume of the dirt hauled away = 16 x 13 x 3 = 624 yards³
Number of trips needed to haul away the dirt = 624 / 11 = 56. 7 = 57 trips
Total cost = 57 x 1175 = $66,975
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1. What is the area of the polygon? Show your work.
There are 760 calculators,6 were defective what is the probability that a calculator chosen at random will be defective
Answer:
Unlikely
Step-by-step explanation:
well if you want the chance it’s unlikely. This is because you only have 6 defective calculators and the rest or majority are not defective.
Find the value of x.
Answer:
Step-by-step explanation:
Remark
What you don't know and what makes the problem confusing, is that where to the given arcs start and end. So I am going to say that both arcs start from E and 119 ends at D, and 174 ends at F which means that the arc FD is not known, but it is not hard to find.
The total number of degrees from beginning to end is 360 degrees. The formula for finding FD is
Formula
FD = 360 - (174 - 119)
The formula for x is (ED - FD)/2
Solution
Arc FD = 360 - (174 - 119)
Arc FD = 67
So x = (119 - 67) / 2
x = 52 /2
x = 26
which of the following demonstrates how the 20 is calculated using the combination pattern
The combination expression that demonstrates how the 20 is calculated using the combination pattern is 6C3
Permutation and CombinationWhile combination has to do with selection, permutation has to do with arrangement.
According to the combination rule
nCr = n!/(n-r)!r!
The expression that gives the result of 20 is expressed below;
6C3 = 6!/(6-3)!3!
6C3 = 6!/3!3!
6C3 = 6!/6*6
6C3 = 720/36
6C3 =20
Hence the combination expression that demonstrates how the 20 is calculated using the combination pattern is 6C3
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Part D
What is the difference of the earnings of movies C and D for that week?
The difference of the earnings of movies C and D for that week is $10,652,270.46 .
What is the difference in earnings?Subtraction is used to determine the difference between two or more numbers.
The difference = earnings of movie D - earnings of movie C
$34.311,887.98 - 23,659,617.52 = $10,652,270.46
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35. the set, s consists of 900,000,000 whole numbers, each being the same number of digits long. howmany digits long is a number from s? (hint: use the fact that a whole number cannot start with the digit 0.)
Answer:
9 digit longLet the number of digits be n and the number of elements in set be s.
When n = 1The set contains 1-digit numbers, 1 through 9,The set consists of 10 - 1 = 9 numbers.When n = 2The set contains 2-digit numbers, 10 through 99,The set contains 100 - 10 = 90 numbers.When n = 3The set contains 3-digit numbers, 100 through 999,The set contains 1000 - 100 = 900 numbers.The pattern we see helps us determine the relationship between s and n as follows.
When set contains n-digit numbers, the set contains:
s = 10ⁿ - 10ⁿ⁻¹ = 10ⁿ⁻¹(10 - 1) = 9*10ⁿ⁻¹ elementsWe have s known, substitute it into equation above and solve for n:
900000000 = 9*10ⁿ¹100000000 = 10ⁿ⁻¹10⁸ = 10ⁿ⁻¹n - 1 = 8n = 9The numbers in the set s are 9-digit long.
If f(x) = x³ +7x²-x and g(x)=x²-3, What is the degree of g(f(x))?
a)2
b)3
c)6
d)8
Answer:
c) 6
Step-by-step explanation:
Given :
⇒ f(x) = x³ + 7x² - x
⇒ g(x) = x² - 3
===============================================================
Finding the degree of g(f(x)) :
⇒ Degree of f(x) = 3
⇒ Degree of g(x) = 2
⇒ Therefore, degree of g(f(x)) = degree of f(x) × degree of g(x)
⇒ Degree of g(f(x)) = 3 × 2
⇒ Degree of g(f(x)) = 6
Degree of g(f(x))
Use Pascal's law
3×26Option C
HELPP PLEASE ASAP Use the Pythagorean theorem to find the missing length in the right triangle
Answer:
c = 10
Step-by-step explanation:
The pythagoras theorem :
a² + b² = c²
a = 6 and b = 8
6² + 8² = c²
36+64 = c²
100 = c²
c = √100
c= 10
Hope this helped and brainliest please
I need help what's the answer
Answer:
[tex]y = 2x - 5[/tex]
Step-by-step explanation:
slope-intercept form is [tex]y = mx + b[/tex] with [tex]m[/tex] being the slope of the line and [tex]b[/tex] being the y-intercept (where the line touches the y-axis)
First we can find [tex]m[/tex] using the formula for slope, [tex]\frac{rise}{run}[/tex] (or [tex]\frac{y_1 - y_2}{x_1 - x_2}[/tex]), which is the change in y over the change in x.
We can use any points on the line, but I am going to use [tex](4, 3)[/tex] and [tex](3, 1)[/tex] for this example. We can now find the slope.
[tex]\frac{3-1}{4-3} = \frac{2}{1}[/tex]
This means your slope is 2, which means [tex]m[/tex] is 2.
Finding the y-intercept is easy. This line crosses the y-axis at -5, and so [tex]b[/tex] is -5.
Now we can plug in the values into our original equation to get the equation of the line.
[tex]y = 2x - 5[/tex]
That is the answer
- Kan Academy Advance
How can I solve this math problem.
Answer:4.6
Step-by-step explanation:
Use the pythagorean theorem, then find the square root using your calculator.
HELP FOR BRAINLIEST & 100
please
Answer:
Hi,
Step-by-step explanation:
1) PC=PD since PC*PA=PD*PB
2)25 since PO²=PA²+r² PO=14.5, PB=14.5+10.5=25
3)
6²=3*x==> x=12
If f(x) = 2x2 + 3 and g(x)=x2-7, find (f- g)(x).
The difference of the given functions is x^2 + 10
Difference of functionsGiven the following functions
f(x) = 2x^2 + 3 and
g(x)=x^2-7
Take the difference
(f-g)(x) = 2x^2 + 3 - (x^2 - 7)
(f-g)(x) = 2x^2 - x^2 +3 + 7
(f-g)(x) = x^2 + 10
Hence the difference of the given functions is x^2 + 10
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find the angle of this sector.
on the image
Answer:
[tex]\alpha =107.4^{o}[/tex]
Step-by-step explanation:
[tex]15=\frac{\pi (8)\alpha }{180}[/tex]
[tex]\alpha =\frac{(15)(180)}{8\pi } =\frac{2700}{25.13}=107.4[/tex]
Hope this helps
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=15\\ r=8 \end{cases}\implies 15=\cfrac{\theta \pi (8)}{180}\implies 15=\cfrac{2\pi \theta }{45} \\\\\\ 675=2\pi \theta \implies \cfrac{657}{2\pi }=\theta \implies 104.56^o\approx \theta =a[/tex]