Based on the provided information, Jerry's Z score will be negative, while Corey's Z score will be positive.
A Z-score refers to a numerical measurement that defines the raw value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it means that the data point's score is identical to the mean score. A negative z-score indicates that the data point is below average or mean and a positive z-score indicates that the data point is above average or mean. Consider the formula for z score which is given by:
z = (x - µ)/σ where x is the given data value, µ is the mean, and σ is the standard deviation.
Hence, if the x < µ, the z score will be negative while if x > µ, the z score will be positive. As Corey scored higher than the mean on his SAT, his z score will be positive, and Jerry scored lower than the mean on his SAT, his z score will be negative.
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What is the probability of getting a ten or a jack from a deck of pocker cards
The probability of getting a 10 or a jack from a deck of poker cards (52 cards) is 15.38%.
What is probability?Probability is concerning about numerical description
Is how likely is an event is occur or how likely it is true.
As per the given sequence -
there are four 10 cards and four jack cards respectively
4+4=8
If you want to get one from the 52 cards, so it's 8 out of 52. 8/52
To calculate the percentage, you must multiply 8 by 100, then divide by 52.
Thus,
8*100/52=15.38
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Help!
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Slope = -8, passing through (-4,-9)
Answer:
-12,-17
Step-by-step explanation:
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
If the diameter of a small red beachball is 8 inches, then the cone with the same radius and a height of a 8 inches would fit into the beachball 1/2 times and the volume of the cone would be about 536 in^3.
What is cone and its formula?They develop as a result of lava pieces being blown into the air by ferocious eruptions, solidifying, and then falling as cinders surrounding the volcanic vent. These cinders, which are typically the size of pebbles, are packed with numerous small bubbles that the lava captured as it solidified. The height of a cinder cone can range from tens to hundreds of metres.A cone has no edges and just one face, which is its round base. A cone only has one vertex or apex point. The cone has a volume of 13 r2h. The cone's total surface area is equal to r(l + r). The cone's slant height is (r2+h2).A cone has a vertex that is not on the base and a single circular base.Explanation :
If the diameter of a small red beachball is 8 inches, then the cone with the same radius and a height of a 8 inches would fit into the beachball 1/2 times, because Centre radius will reduced to point when it reaches its full height.
The volume of the cone would be about 536 in^3.
Volume of a cone = 1/3 π [tex]r^{2}[/tex] *h
= 1/3 x π x [tex]8^{2}[/tex] x 8 = 536
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Answer:
two134Step-by-step explanation:
You want to know how many times the volume of a cone 8 inches in diameter and 8 inches high will fit into the volume of a beachball that is 8 inches in diameter, and you want the approximate volume of the cone.
Sphere volumeThe equation for the volume of a sphere based on its diameter is ...
V = π/6d³
Cone volumeThe equation for the volume of a cone is usually written ...
V = 1/3πr²h
For the cone in this problem, with both diameter and height equal to that of the sphere, we can rewrite the volume equation as ...
V = 1/3π(d/2)²·d = π/12d³ . . . . . . where d=8 inches, the sphere diameter
Volume ratioThen the ratio of the sphere's volume to that of the cone is ...
Vs/Vc = ((π/6)d³)/((π/12)d³) = 12/6 = 2
The volume of the cone will fit into the volume of the sphere two (2) times.
Numerical volume valueThe volume of the cone is ...
V = (π/12)8³ = 128π/3 ≈ 134 . . . . cubic inches
The cone's volume is about 134 in³.
__
Additional comment
Note that we have taken the wording "with the same radius" to mean that the radius of the cone is the same as the radius of the sphere.
Alternatively, it could mean the radius of the cone is the same as the dimension given for the diameter of the sphere. In that case, the volume of the cone is 4 times as great, so its volume of 536 in^3 will fit into the sphere 1/2 times.
57% of all the town's residents own a dog and 61% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible) a. P(Own a Dog)b. P(Own a Cat)- c. P(Own a Cat and a Dog) d. P(Own a Dog GIVEN Own a Cat)
Among dog owners, 40% also keep cats.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured
According to our question-
27% of households only own dogs.
12 percent own a cat but no dog.
18% of people own both dogs and cats.
43% don't own either a dog or a cat.
18/45 dog owners also have cats.
*100% = 40%
Among dog owners, 40% also keep cats.
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a. What is the equation of the line that is perpendicular to the graph and intercepts the y-axis at (0,-6)
b. What is the equation of the line that is perpendicular to the graph and intercepts the y-axis at (2,-2)
a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0,-6) is y = -1/m * x - 6
b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2,-2) is y = -1/m * x - 2
what is intercepts?
The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0, -6) can be written as:
y = mx + b
where m is the slope and b is the y-intercept.
Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-6).
Therefore, the equation of the line is y = -1/m * x - 6
b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2, -2) can be written as:
y = mx + b
where m is the slope and b is the y-intercept.
Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-2).
Therefore, the equation of the line is y = -1/m * x - 2
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Four identical trapeziums are placed on a coordinate grid as shown.
a) Write down algebraic expressions for the coordinates of point L.
b) M has coordinates (9,9).
N has coordinates (15,15).
Work out the value of a and the value of b
a) The algebraic expression for the coordinates of point L is (a-b,b).
b)The value of a is 9, and the value of b is 3
What are coordinate points?
A specific point on a grid referred to as a coordinate plane can be located using coordinates, which are two numbers. In a plane, a point is known to have specific coordinates. The coordinates are the ordered pairs of numbers (x, y) that describe the location of any point on a plane. In our everyday lives, we use coordinates for things like map location, classroom seating, and more.
a) Extending point L towards the y-axis, we see that it corresponds to the given coordinate, i.e., (0,b). Therefore the y coordinate is b.
Next, extending the point L towards the x-axis, we see that the point lands somewhere between the distance 'a' from the origin. As the height is 'b', and as the trapeziums are identical, we can say that the extended point of L lands at a point that is 'b' distance from 'a'. Hence the x coordinate is a-b.
Hence, the coordinates of point L are (a-b,b).
b) Given M(9,9) and N(15,15).
Extending the point M towards the x-axis, we get that it coincides with the point 'a', therefore we get the value of a=9.
Now extending point N towards the x-axis, we get that it lands at a distance of 15 from the origin. We got the value of a=9, so the remaining distance between the point (9,0) and (15,0) is 6 units.
Extending the point (9,0) upwards, we see that it cuts the uppermost trapezium giving us the distance of the trapezium excluding the small triangle formed. Now taking the same information, if we cut the bottom-most trapezium, we see that it cuts at point (6,0).
Now we know the height of the trapezium is 'b'. So, we get b=9-6 (as 9 is the distance of the entire trapezium, and 6 is from the above calculations).
We get b=3.
Hence we got the value of 'a'=9 and 'b'=3.
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A linear function h models a relashinship in which the dependent variable decreases 2 units for every 5 units the independent variable increase. Graph h when h(0)=4
By using slope intercept form of equation of line, the graph of
h(x) = [tex]-\frac{2}{5}x + 4[/tex] has been shown
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Let the independent variable be x and dependent variable be h(x)
The dependent variable decreases 2 units for every 5 units the independent variable increase.
Slope = [tex]-\frac{2}{5}[/tex]
So,
h(x) = [tex]-\frac{2}{5}x + c[/tex]
Now,
h(0) = 4
So, c = 4
h(x) = [tex]-\frac{2}{5}x + 4[/tex]
The graph has been attached here-
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-8x-8 = -49.44
+ 8x+12y=58.20
Step-by-step explanation:
-8x-8 = -49.44+ 8x+12y=58.20
Write this set of rational numbers from lest to greatest -11 3/4, 7, -7, 13, -13
Write this set of rational numbers from least to greatest -11 3/4, 7, -7, 13, -13:
Answer:
-13 , -11 , -7 , 3/4 , 7 , 13
Using the following year-end information for Calvin's Clothing, calculate the current ratio and acid-test ratio for the business:
Cash$52,000
Short-term investments 12,000
Accounts receivable 54,000
Inventory 325,000
Prepaid expenses 17,500
Accounts payable 106,500
Other current payables 25,000
The current ratio and acid-test ratio for the business is 3.50 and 0.90.
What is Working Capital?
Working capital is a gauge of a company's liquidity. This is crucial because it aids the business in making decisions about its current assets and liabilities.
Current ratio = Current Assets / Current Liabilities
Current ratio = 460,500 / 131,500
Current ratio = 3.5 times
Quick ratio
Quick ratio = Quick Assets \ Current Liabilities
Quick ratio = 118,000 / 131,500
Quick ratio = 0.90
Cash 52,000
Short-term investments 12,000
Accounts receivable 54,000
Inventory 325,000
Prepaid expenses 17,500
Total Current Assets 460,500
Total Quick assets 118,000
Accounts payable 106,500
Other current payables 25,000
Total Current Liabilities 131,500
Quick assets include Cash, Short term investments and accounts receivables
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I need help thank you
It follows that someone who watches TV for 11 hours can complete 19 situps.
How to find the calculation?This information was provided to us by the question.
A linear equation in slope-intercept form is one with the formula y = ax + b.
Claim: A line with slope a contains the point (0,b) on the y-axis and the solutions of the equation y = ax + b (where a and b are numbers) form a line with slope a.
a=−1.077
b=30.98
r2=0.744769
r=−0.863
Where
X is the amount of situps.
Y is the quantity of television viewing hours.
X equals 11, so
Including this in the existing formula
Y = (-1.077)(11) + 30.98
Y = −11.847 + 30.98
Y = 19.133
which equals around 19
So, it follows that someone who watches TV for 11 hours can complete 19 situps.
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Find 910−238 . Express your answer as a mixed number in simplest form.
By converting the given improper fraction 910/238 as a mixed number we get the result as 3[tex]\frac{14}{17}[/tex].
What is a mixed number?A mixed number is one that includes both a whole number and a legal fraction. A number with both an integer (whole number) and a correct fraction is referred to as a mixed number or mixed fraction (a fraction whose numerator is less than its denominator).
Pretzels, peanuts, Cheerios, and of course rice and corn Chex make up this mixture, which is dubbed a "mix." Numerals with both an integer and a fraction included are known as mixed numerals. The term "mixed number" refers to the combination of these two types of numbers.
Given,
910/238 is an improper fraction.
Now by dividing both the numerator and denominator by 14, we get
(910/14)/(238/14)
=65/17
Now, 65/17 can be written as a mixed number as 3[tex]\frac{14}{17}[/tex].
Therefore, By converting the given improper fraction 910/238 as a mixed number we get the result as 3[tex]\frac{14}{17}[/tex].
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The complete question is:
"Find 910/238. Express your answer as a mixed number in simplest form."
Explain special rights. Im confused how to find missing sides and angles
Answer:
all triangle sum must be 180 right angles are 90 degree like the top to left in the figuresum what you have and give it ad equals to 180 then solveAnswer to this required:
Please help me <3 What is A, B, C
(If correct i will give you brainlist also u get lots of points)
A= -10140000 B= 3485800 C= 13414200
Step-by-step explanation: hope this helped!!!
a) Work out the minimum number of dogs that could have a mass of more than 24 kg
b) Work out the maximum number of dogs that could have a mass of more than 24 kg}.
Mass(kg) Frequency
0≤x<10 2
10≤x<20 7
20≤x<30 12
30≤x<40 6
a) The minimum number of hikers who could have walker between 6 and 17 miles is of: 9.
b) The maximum number of hikers who could have walker between 6 and 17 miles is of: 19.
What is shown by the frequency table?The frequency table shows the number of times that each range was observed in this problem.
For the minimum number of hikers walking between 6 and 17 miles, we have that:
All the 2 hikers in the interval 5 < x < 10 walked less than 6 miles.All the 8 hikers in the interval 15 < 20 < 20 walked more than 17 miles.Hence the minimum number is of 9, all of which walked between 10 and 15 miles, which is between 6 and 17.
For the maximum number of hikers walking between 6 and 17 miles, we have that:
All the 2 hikers in the interval 5 < x < 10 walked more than 6 miles.All the 8 hikers in the interval 15 < 20 < 20 walked less than 17 miles.Hence the maximum number is of:
2 + 9 + 8 = 19.
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Joe flew his small airplane 1000 km in 4 hours flying with the wind. He flew 700 km against
the wind in 7 hours. Find the rate at which he flew in still air and the rate of the wind.
Answer:
To solve this problem, we can set up the following system of equations:
Let x be the rate at which Joe flew in still air and y be the rate of the wind.
1000 km / 4 hours = x + y
700 km / 7 hours = x - y
Solving this system of equations using the elimination method, we get:
x + y = 250
x - y = 100
Adding these two equations together, we get 2x = 350, so x = 175 km/hour.
Subtracting the second equation from the first equation, we get 2y = 150, so y = 75 km/hour.
Therefore, the rate at which Joe flew in still air is 175 km/hour and the rate of the wind is 75 km/hour.
Step-by-step explanation:
Which answer describes the type of sequence? 1, 6, 7, 13, ...
O arithmetic
O geometric
O neither arithmetic nor geometric
A series that is neither mathematical nor geometric is described by the provided sequence. Which is the proper response would be a choice (B).
What exactly is an algebraic sequence?A grouping of numbers in a specific order is known as an arithmetic sequence.
The following question gives the sequence as follows: 1, 6, 7, 13,...
We must determine the kind of the current sequence.
According to the question, we have 1, 6, 7, 13,...
For verification as an arithmetic series:
The usual deviation between 1 and 6 is given by d = 6 - 1 = 5.
Commonly, 6 and 7 differ by 1 when d = 7 - 6
It is not an arithmetic sequence since the common difference between subsequent terms is not the same.
In order to verify it as a geometric sequence:
r = 6/1 = 6 is a common ratio between 1 and 6.
r = 7/6 is a common ratio between 6 and 7.
It is not a geometric sequence since the common ratio between subsequent terms is not the same.
A series that is neither mathematical nor geometric is described by the provided sequence.
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A solid object is made with the combination of a cylinder and a cone having same radii. The height of the cylinder and the slant height of the cone are 30 cm and 26 cm respectively. If the total cost of painting the total surface of the solid object at the rate of Rs 210 per 100 sq. cm is Rs 6336, find the height of the cone.
The total surface area of the solid object is the sum of the surface area of the cylinder and the surface area of the cone.
The surface area of the cylinder is 2πr(r+h), where r is the radius of the cylinder and h is its height.
The surface area of the cone is πr(l+r), where r is the radius of the cone and l is its slant height.
Since the cylinder and the cone have the same radius, we can call this radius r.
The total surface area of the solid object is therefore 2πr(r+h) + πr(l+r).
We are told that this total surface area is equal to 6336/210 = 30 sq. cm.
Thus, we can set up the equation: 2πr(r+h) + πr(l+r) = 30.
We are trying to find the value of l, which is the slant height of the cone. We are given the value of h, which is the height of the cylinder. We can substitute this value into the equation to get:
2πr(r+30) + πr(l+r) = 30.
This equation can be rearranged and solved for l to find the slant height of the cone.
l = sqrt(900 - 60r).
Since we are given that the slant height of the cone is 26 cm, we can substitute this value into the equation to solve for the radius of the cone:
26 = sqrt(900 - 60r)
Solving for r, we find that the radius of the cone is 15 cm.
Substituting this value back into the equation for the slant height of the cone, we find that the height of the cone is:
l = sqrt(900 - 60(15)) = sqrt(300) = 17.67 cm.
Thus, the height of the cone is approximately 17.67 cm.
14. Find (f +g)(x) if f(x)=4 x²-5x and g(x)=3x²+6x-4.
(f +g)(x)=-x²+11x-4
(f +g)(x)=7x²+x-4
(f +g)(x)=x²-11x+4
(f +g)(x)=-x²-x⁴
Answer:
(f +g)(x)=7x²+x-4
Step by step:
first you have to add both f(x) and g(x) to find (f +g)(x)
If a sample of a certain solution is determined to have a [H3O+] concentration of 8.25×10−3 moles/liter, what is its pH?
where log is the base-10 logarithm and [H+] stands for the hydrogen ion concentration in units of moles per liter solution.
What is this pH?The pH of water determines how acidic or basic it is. The scale runs from 0 to 14, with 7 being neutral. pHs less than 7 indicate acidity, while pHs greater than 7 indicate base. pH is a measure of the relative amount of free hydrogen and hydroxyl ions in water.Hawkes Learning says the answer is 0.0. I tried this problem and got it wrong at first, but they said the correct answer is 0.0.Before attempting to answer this question, it may be useful to review the properties of logarithms and the definition of pH.The pH of a solution is a measure of the concentration of hydrogen ions, as well as its acidity or alkalinity. The pH scale is normally between 0 and 14. Aqueous solutions with a pH less than 7 at 25 ° C are acidic, while basic or alkaline solutions have a pH greater than 7.pH=−log([H3O+])
=−log(8.25×10−3)
=−log(8.25)−log(10−3) loga(xy)=loga(x)+loga(y)
=−log(8.25)+1 log(10x)=x
=0.0 round off to one decimal place
pH is defined as the negative logarithm of hydrogen ion concentration present in a solution.To calculate the pH of the reaction, we use the equation:[tex]pH = -log[H^{+} ][/tex]where,
Putting values in above equation, we get:Hence, the pH of the solution is 1.022To learn more about pH refer to:
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a dining hall had a total of 20 tables— some long rectangular tables and some round ones. Long tables can seat 10 people. Round tables can seat 8 people. on a busy evening, all 182 seats at the tables are occupied. a write a system of equations to represent this scenario
The solution of linear equations in two variables gives the following results.
The number of long tables = 11The number of round tables = 9 What are linear equations in two variables?A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Given:
Total number of tables in dining hall = 20 people
The number of people who can seat at long table = 10 people
The number of people who can seat at the round table = 10 people
According to the question, let’s assume a linear equation in two variables
number of long tables = x
number of round tables = y
⇒ x +y=20 ………… (1)
⇒10 x + 8 y=182 ………...(2)
Multiply equation (1) by 8 and subtract it from equation 2.
⇒ 10x+8y=182 ………… (2)
⇒ 8x+8 y=160 ………....(1)
⇒2x=22
⇒x=11
now put the value of x in equation (1) we get,
⇒11+y=20
⇒y=20-11
⇒y=9
Therefore, the number of long tables = 11
The number of round tables = 9
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2 1/2 divided by 1 3/4
Answer:
10/7 or 1 3/7
Step-by-step explanation:
1. change from mixed fraction to improper fraction, 5/2 and 7/4
2. instead of the dividing the fractions as is, multiply the reciprocal which would be 5/2 multiplied by 4/7. Then you cross multiply. 2 into 2, 1 and 2 into 4, 2. So now you're left with 5 and 2/7 since 5/1 is basically 1.
3. simplify to just 10/7
Answer:
10/7 or 1 3/7
I took a test with that question.
A store owner sells a mix that is 45% cashew nuts. How many pounds of cashews should he add to 36lb of this mix to get a mix that is 60% cashews
SHOW STEPS PLease
To make this mixture 60% cashews, 240 pounds of cashews must be added to 36 pounds of this mixture.
Explain the term proportion?Comparing two integers that each stand for a component of a whole results in a proportion. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.For the stated question-
Let the total amount of mix be 'x'.
45% of the mix is cashew nuts: 0.45x.
Now, 60% cashews is made by making 36 lb; 0.60x.
Then, 0.45x + 36 = 0.6x
x = 36/0.15
x = 240
Thus, 240 pounds of the cashews should be added to 36lb of this mix to get a mix that is 60% cashews.
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sam ran 63756 feet in 70 minutes whats samns rate in mph
Answer:
10.35 miles/hour
Step-by-step explanation:
Hence, Sam ran at the rate of 10.35 miles/hour .
write down in trems of n an expression for the nth term in the following sequences 1 8 15 22 29
The expression which defines the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).
Which expression represents the nth term of the expression in terms of n?It follows from the task content that the expression which represents the nth term of the given sequence be determined.
By observation, the first term, a of the sequence is; 1.
Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.
It follows that the expression is a arithmetic sequence which can be modelled by;
T (n) = a + d (n - 1)
Since the constant common difference of consecutive terms in the sequence is; 7,
The required expression for the nth term of the expression is;
nth = 1 + 7(n -1)
On this note, the nth term is given by the expression; T (n) = 1 + 7 (n -1).
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A box is filled with 5yellow cards, 8blue cards, and 7green cards. A card is chosen at random from the box. What is the probability that the card is not blue?
Probability that a card is chosen is not blue is 3/5
What is Probability?Probability means possibility.
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.topic. One is the probability of every event in a sample space.
According to the probability formula, the likelihood that an event will occur is equal to the proportion of favorable outcomes to all outcomes.
probability that an event will occur P(E) = Number of favorable outcomes/Total Number of outcomes
Total number of cards in the box is 5+8+7=20 cards
Number of cards that are not not blue = 5 + 7 = 12 cards
Probability that a card is chosen is not blue = Number of favorable outcomes/Total Number of outcomes = 12/20 = 3/5
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Probability that a card is chosen is not blue is 3/5
What is Probability?
Probability means possibility. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. topic. One is the probability of every event in a sample space.
According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.
probability that an event will occur P(E) = Number of favorable outcomes/Total Number of outcomes
Total number of cards in the box is 5+8+7=20 cards
Number of cards that are not not blue = 5 + 7 = 12 cards
Probability that a card is chosen is not blue = Number of favorable outcomes/Total Number of outcomes = 12/20 = 3/5
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A polynomial ppp is graphed. What could be the equation of ppp?
Choose 1 answer:
cos^2x+cost^2x cot^2x
Yes, by definition cotx=1tanx, and tanx=sinxcosx, so cotx=1sinx/cosx=cosxsinx.
Step-by-step explanation:Thus, squaring both sides of the equation, we obtain cot2x=cos2xsin2x.The formula of 1 – cos2x is 1 – cos2x = 2sin²x. Through this, you can identify trigonometric identities.They're very different and your example is not correct.2cosx is twice the cosine of angle x.[tex]osx2=cos(x2)=cos(x[/tex]×[tex]x) while cos2(x)=cos(x)[/tex]×[tex]cos(x)=(cos(x))2.[/tex]
[tex]cos^2xcot^2+cos^2x\\= cos^2x(cot^2x+1)\\= cos^2x csc^2x\\= cot^2x < ==Answer[/tex]
[tex]cos2x = 1 - 2 sin 2x.\\cos2x = (1 - tan 2x) / (1 + tan2x)[/tex]
To learn more about trigonometric identities refer to:
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You are given the figure below as well as the following information: m <9 = 110⁰ m<8 = 70° p parallel q. Use the figure and the given information to answer Question
what is m < 15
A. 70
B. 110
C. 80
D. 100
Answer:
B. 110°
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Given:
m∠9 = 110°m∠8 = 70°p || qApply the Vertical Angle Theorem to find the measure of angle 8:
⇒ m∠3 = m∠8 = 70°
As angles 7 and 8 form a linear pair:
⇒ m∠7 + m∠8 = 180°
⇒ m∠7 + 70° = 180°
⇒ m∠7 = 110°
As line p is parallel to line q, apply the Corresponding Angles Postulate to find the measure of angle 15:
⇒ m∠15 = m∠7 = 110°
Therefore, the measure of angle 15 is 110°.