Answer:
Step-by-step explanation:
[tex]\frac{1}{cosx} . \frac{1}{sinx} =\frac{2}{sinx}\\ \frac{1}{cosx} . \frac{1}{sinx} - \frac{2}{sinx} = 0\\\frac{1}{sinx}(\frac{1}{cosx} - 2) = 0\\\frac{1}{cosx} = 2\\cosx = \frac{1}{2} \\x = 60[/tex]
A charity run has prizes for the top finisher in each of 10 age categories. The
times of the prize-winners are shown. Which scatterplot accurately reflects these data?
Age 13 17 21 26 34 36 44 51 62 70
Time (minutes) 23 17 17 15 19 20 24 25 29 30
The scatter plot that accurately describes the data is given as follows:
Scatter plot A.
What is the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following input-output format:
(Input, Output).
The input and output variables for this problem are given as follows:
Input variable: age.Output variable: time.Hence the points are given as follows:
(13, 23), (17, 17), (21, 17), ..., (70,30).
And all these points are marked on the scatter plot given by option A.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The period of the trigonometric function in this problem is given as follows:
A) 540º.
How to define a trigonometric function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For the tangent function, we have that it is similar to the sine function, that we use tan() instead of sin().
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The coefficient B for the equation is given as follows:
B = 2/3.
Hence the period of the function is given as follows:
2π/(2/3) = 3π = 540º.
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in a water tank there's a depth of 9cm, imagine the tank is sealed and put onto it's side, whats the depth of the water now (photo included)
The depth of water when the tank is on its side is 4.2 cm.
We are given that;
tank measurement is 13*8*17
Now,
A cube is a three-dimensional representation of a square. it has 6 faces 2 on the bottom and top, 4 on the sides faces.
To find the volume of water in the tank when it is upright. To do this, you multiply the depth of water by the area of the base:
Volume = Depth * Area Volume = 9 cm * (13 cm * 8 cm) Volume = 936 cm^3
This volume does not change when you put the tank on its side. However, the area of the base does change. Depending on which side you put the tank on, the area of the base will be either 13 cm by 17 cm or 8 cm by 17 cm. Let’s assume you put the tank on its longer side, so that the area of the base is 13 cm by 17 cm.
Now, you can find the depth of water by dividing the volume by the area:
Depth = Volume / Area Depth = 936 cm^3 / (13 cm * 17 cm) Depth= 4.2 cm
Therefore, by the cube answer will be 4.2cm.
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Describe the transformations from the parent y=1/x :
y=3/x+5 -3
The transformations to the parent function are given as follows:
Vertical stretch by a factor of 3.Translation left 5 units.Translation down 3 units.How to obtain the transformations?The parent function for this problem is given as follows:
y = 1/x.
The transformed function for this problem is given as follows:
y = 3/(x + 5) - 3.
Hence the transformations to the parent function are given as follows:
Vertical stretch by a factor of 3. -> multiplication by 3 in the numerator.Translation left 5 units, as x -> x + 5.Translation down 3 units, as y -> y - 3.More can be learned about transformations at https://brainly.com/question/28687396
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The graph of f(x) and table for g(x)= f(kx) are given.
A coordinate plane with a quadratic function labeled f of x that passes through the points negative 2 comma 4 and negative 1 comma one and vertex 0 comma 0 and 1 comma 1 and 2 comma 4
x g(x)
−8 4
−4 1
0 0
4 1
8 4
What is the value of k?
k = −4
k is equal to one fourth
k is equal to negative one fourth
k = 4
------------------------------
The quadratic functions f(x) and g(x) are described in the table.
x f(x) g(x)
−6 36 4
−5 25 1
−4 16 0
−3 9 1
−2 4 4
−1 1 9
0 0 16
1 1 25
2 4 36
In which direction and by how many units should f(x) be shifted to match g(x)?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units
------------------
Answer both questions for brainliest! (as long as correct)
For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth.
For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.
Received message. For the first question, we can see that g(x) = f(kx). To find k, we can compare the x values of f(x) and g(x). We can see that when x = -8 for g(x), x = -2 for f(x). This means that k(-8) = -2. Solving for k gives us k = -2/-8 = 1/4. Therefore, k is equal to one fourth. For the second question, we can see that g(x) is f(x) shifted to the right by 4 units. Therefore, f(x) should be shifted to the left by 4 units to match g(x). The answer is left by 4 units.
hopes thats help thank you
Calculator
A computer generates 90 integers from 1 to 8 at random. The results are recorded in this table.
Outcome
Number of times outcome occurred
9%
What is the experimental probability of the computer generating a 3 or a 5?
O 20%
O 18%
1
O 40%
26
2 3
8
10
4
12
ស
5
8
6
6
7
9
8
11
The experimental probability of the computer generating a 3 or a 5 is given as follows:
20%.
How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The total number of outcomes in the table is given as follows:
90.
The desired number of outcomes is given as follows:
10 + 8 = 18.
Hence the experimental probability is given as follows:
p = 18/90 = 0.2 = 20%.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Which of these numbers is between 1/3
and 87/100
on a number line? the options are
11/100
3/5
92/10
3/10
3/5 is the fraction between the numbers 1/3 and 87/100
Measuring fractions using number lineA number line is a graphical representation of numbers that can be used to understand and visualize numerical relationships. It is a straight line that extends infinitely in both directions and is usually drawn horizontally.
Writing the fractions as percentage:
1/3 * 100 = 33.3%
87/100 = 87%
This shows that the required number must be between 33.3% and 87%
From the given options:
3/5 * 100 = 3 * 20
3/5 * 100 = 60%
Hence the value in between the numbers 1/3 and 87/100 is 3/5
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Help Due!!!! HELP ASAP!!!
The interval representing the range of the graphed function in this problem is given as follows:
a) (0, ∞).
How to define the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.From the image of the problem, the output y of the function is composed by the positive values, hence the interval representing the range is given as follows:
(0, ∞).
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I need help, I was trying to solve it but I got lost.
Answer: [tex]x\approx 6.2[/tex]
Step-by-step explanation:
Detailed explanation is attached below.
8cm into kilometres
Answer:
[tex]\huge\boxed{\sf 0.00008\ km}[/tex]
Step-by-step explanation:
Statement:To convert cm to km, we need to divide by 100,000.Solution:= 8 cm
= 8 / 100,000 km
= 0.00008 km[tex]\rule[225]{225}{2}[/tex]
Answer:
0.00008
80 cm is 0.0008 so you know I just assumed
Could someone kindly give me a detailed explanation with step-by-step instructions for the solution? I would greatly appreciate it.
Let f: N → Q be defined by f(x) = x / 1 + x for any x ∈ N. Prove or disprove each of the following:
(a) The function f is injective.
(b) The function f is surjective.
A. The function f is injective.
B. The function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.
How to prove it is injectiveTo prove that the function f is injective, we need to show that if f(x) = f(y), then x = y.
Let f(x) = f(y). Then we have:
x / (1 + x) = y / (1 + y)
Cross-multiplying, we get:
x(1 + y) = y(1 + x)
x + xy = y + xy
Now, subtract xy from both sides:
x = y
Since x = y when f(x) = f(y), we can conclude that the function f is injective.
(b) To prove or disprove that the function f is surjective, we need to determine whether for every y ∈ Q, there exists an x ∈ N such that f(x) = y.
Consider the case where y = 1/2. We need to find x ∈ N such that:
f(x) = x / (1 + x) = 1/2
Cross-multiplying, we get:
2x = 1 + x
Subtract x from both sides:
x = 1
In this case, there exists an x ∈ N (x = 1) such that f(x) = 1/2. However, we need to consider all y ∈ Q. Let's try another case.
Consider the case where y = 1. There is no x ∈ N that satisfies the following equation:
f(x) = x / (1 + x) = 1
Cross-multiplying, we get:
x = 1 + x
Subtract x from both sides:
0 = 1
This is a contradiction, so there is no x ∈ N such that f(x) = 1. Therefore, the function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.
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Makayla leans a 18 foot ladder aginst a wall so that it forms and angle of 64 degrees with the ground. what the horizontal distance between the base of the ladder and the wall
The horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.
To answer the question, we need to use trigonometry. In this case, we can use the sine function, which relates the opposite side of a right triangle to its hypotenuse. In this case, the ladder is the hypotenuse, and the horizontal distance between the base of the ladder and the wall is the opposite side.
The angle formed by the ladder and the ground is the angle of interest.
Let x be the horizontal distance between the base of the ladder and the wall. Then, using the sine function, we have:
sin(64 degrees) = x/18
Multiplying both sides by 18, we get:
x = 18 sin(64 degrees) ≈ 16.2 feet
Therefore, the horizontal distance between the base of the ladder and the wall is approximately 16.2 feet.
It is important to note that when using trigonometry, we need to use the appropriate trigonometric function depending on the sides and angles we are given. In this case, we were given the hypotenuse and the angle opposite the horizontal distance, so we used the sine function.
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Use the 68-95-99.7 rule to find the following quantities. Do not round any answers.
What portion of scores are between 59 and 91?
What portion of exam scores are less than 67?
What portion of exam scores are between 67 and 91?
The portion of scores that are between 59 and 91 is 98%.
The portion of exam scores that are less than 67 is 16%.
The portion of exam scores that are between 67 and 91 is 82%.
What is a normal distribution curve?A normal distribution curve is a type of probability distribution that is commonly used in statistics to represent a large set of data. It is also known as a bell curve. The curve is bell-shaped, symmetrical, and smooth.
Comparing the exam score diagram in the question, to a standard normal distribution curve, we will have the following;
The portion of scores that are between 59 and 91 is;
= 100% - (59 to 43 portion)
= 100% - 2%
= 98%
The portion of exam scores that are less than 67 is;
= (67 to 59) + (59 to 43)
= 14% + 2%
= 16%
The portion of exam scores that are between 67 and 91 is ;
= (67 to 75) + (75 to 83) + (83 to 91)
= 34% + 34% + 14%
= 82%
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Write a polynomial function in factored form that has roots at x=7, x=-10, and x=3. Each root should have a multiplicity of 1.
The polynomial function in factored form with roots x = 7, x = -10, and x = 3, each with a multiplicity of 1, is [tex]f(x) = x^3 - 76x + 210.[/tex]
To write a polynomial function in factored form with the given roots, we can use the factored form equation:
f(x) = (x - r1)(x - r2)(x - r3)...
Where r1, r2, r3 represent the roots of the polynomial.
Given the roots x = 7, x = -10, and x = 3, we can write the factored form equation as:
f(x) = (x - 7)(x + 10)(x - 3)
Expanding this equation will give us the polynomial function in factored form:
[tex]f(x) = (x - 7)(x + 10)(x - 3)[/tex]
[tex]= (x^2 - 7x + 10x - 70)(x - 3)[/tex]
[tex]= (x^2 + 3x - 70)(x - 3)[/tex]
[tex]= x^3 - 3x^2 + 3x^2 - 9x - 70x + 210[/tex]
[tex]= x^3 - 76x + 210[/tex]
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
We can start by finding the value of the expression inside the tangent function: tan(1/2 (0 + π/2)) = tan(π/4) = 1
Now we can substitute this value into the original equation and simplify:
y = -3 + tan(1/2 (0 + π/2))
y = -3 + 1
y = -2
The vertical shift of the graph is the constant term in the equation, which is -2. Since this value is negative, the graph is shifted downwards. Therefore, the correct answer is (A) 3 units down
Teams in the National Football League in America are divided into two conferences: the AFC and the NFC. Some teams have animals as their mascots, and others do not. The following two-way table displays this data.
How many teams are in the NFC?
The total number of teams that are in the NFC from the given two way frequency table is: 16 teams
How to Interpret a two way frequency table?A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data
From the attached two way table, we see that:
Total number of animals = 15
Total number of non-animals = 17
Total Number of NFC = 16
Total number of AFC = 16
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A coffee house blended 16 pounds of espresso flavored
coffee beans with 10 pounds of vanilla flavored coffee
beans. The 26 pound mixture cost $229. A second mixture
included 14 pounds of espresso flavored coffee beans and 11
pounds of vanilla flavored coffee beans. The 25 pound
mixture cost $219.50. Find the cost per pound of the
espresso and vanilla flavored coffee beans.
Answer:
Use systems of equations to solve.
Let x represent the cost per pound of the espresso coffee beans and
y represent the cost per pound of the vanilla coffee beans.
6x + 5y = 77.50
20x + 13y = 234.50, both of these are given.
Rewrite these equations so you can eliminate one of the variables;
60x + 50y = 775, Multiply both sides of the equation by 10
60x + 39y = 703.5, Multiply both sides of the equation by 3
Now Subtract equation 2 from equation 1,
11y = 71.5
y = 6.5
Solve for x,
6x + 5(6.50)= 77.50
x = 7.50
Therefore, the cost per pound of the espresso coffee beans is $7.50, and
the cost per pound of the vanilla coffee beans is $6.50.
Find the volume of the sphere use three
Answer: 2916 cubic feet
Step-by-step explanation:
V=(4/3)*3*(9^3)
V=(4/3)*3*729
V=2916
Recipe for fruit punch orange juice 6 cups pineapple juice 3 cups cranberry juice one cup Felicia has 32 fluid ounces of pineapple juice does she have enough pineapple juice to make one recipe?
PART- A
A-Yes she has just enough pineapple juice.
B-yes she has more than enough pineapple juice.
C- No she needs 8 more fluid ounces of pineapple juice.
D- No she needs 16 more fluid ounces of pineapple juice.
PART B- Jared also wants to make fruit punch. He has 8 pints of each Orange juice, pineapple juice, and cranberry juice. Which of the following are true…
A- he doesn’t have enough of each type of juice to make 1 recipe.
B- He has enough of each type of juice to make 1 recipe.
C- he has enough of each type of juice to make 2 recipes.
D- he has enough of each type of juice to make 3 recipes.
The statement which is true is he has enough of each type of juice to make 1 recipe, the correct option is B.
We are given that;
Orange juice cup= 6
Pineapple juice cup=3
Now,
PART A: To answer this question, we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Felicia has pineapple juice in fluid ounces. We can use the fact that 1 cup = 8 fluid ounces to convert Felicia’s amount of pineapple juice to cups:
32 fluid ounces = 32 / 8 cups = 4 cups
The recipe requires 3 cups of pineapple juice, so Felicia has more than enough pineapple juice. The correct answer is B.
PART B: we need to convert the units of measurement to be consistent. The recipe uses cups as the unit of measurement, while Jared has each type of juice in pints. We can use the fact that 1 pint = 2 cups to convert Jared’s amounts of juice to cups:
8 pints = 8 * 2 cups = 16 cups
Jared has 16 cups of each type of juice. The recipe requires 6 cups of orange juice, 3 cups of pineapple juice, and 1 cup of cranberry juice. This adds up to 10 cups of juice for one recipe. So, Jared has enough of each type of juice to make one recipe and have some left over. However, he does not have enough of each type of juice to make two recipes, since that would require 20 cups of juice in total. T
Therefore, by unitary method the answer will be He has enough of each type of juice to make 1 recipe.
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Find the measure of the red arc or chord in ⊙C.
The calculated measure of the red arc in ⊙C is 11
How to find the measure of the red arc or chord in ⊙C.From the question, we have the following parameters that can be used in our computation:
The congruent circles
From the circles, we have
Centers = C and P
Also, we have
Corresponding segments are equal segments
Using the above as a guide, we have the following:
QR = LM
Where
LM = 11
This gives
QR = 11
Hence, the value of QR is 11
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Robbie grew 6 inches in eight months. What is his average growth rate per month?
Two coins are tossed simultaneously for 360 times.
The number of times '2. Talls' appeared was three times 'No Tall' appeared and number of times '1 tall* appeared is double the number of times 'No Tail' appeared. Find the probabilly of getting Two tails.
The probability of getting Two Tails is 0.1 or 10%.
Let's assume that '2. Tails' appeared x times.
According to the given information, 'No Tail' appeared 3x times, and '1 Tail' appeared 2 × 3x = 6x times.
The total number of tosses is 360. We can express this information in an equation:
x + 3x + 6x = 360
Simplifying the equation:
10x = 360
x = 36
Now we know that '2. Tails' appeared 36 times, 'No Tail' appeared 3x = 3 × 36 = 108 times, and '1 Tail' appeared 6x = 6 × 36 = 216 times.
To find the probability of getting Two Tails, we divide the number of times '2. Tails' appeared by the total number of tosses:
Probability of Two Tails = Number of times '2. Tails' appeared / Total number of tosses
= 36 / 360
= 0.1
Therefore, the probability of getting Two Tails is 0.1 or 10%.
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Rewrite the following equation in exponential form. log2 (16) = 4 /5
Answer: 2^(4/5)=16
Step-by-step explanation:
log a (b)=c
this converts to:
a^c=b
so...
2^(4/5)=16
Find the slope and the y intercept of the line -6x + 3y =-3
The slope and y-intercept include the following:
Slope = 2.
y-intercept = -1.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, we have the linear equation:
-6x + 3y =-3
By making y the subject of formula, we have:
3y = 6x - 3
y = 2x - 1
By comparison, the slope and the y-intercept include the following:
Slope, m = 2.
y-intercept, b = -1.
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What is the mode of the data set below? 0, 4 , 3, 4, 0, 9, 1
The mode of the data is 0
What are the measures of central tendency?Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.
It provides an accurate description of the entire data.
The three major measures of central tendency are given as;
ModeMeanMedianThe mode is defined as the measure of central tendency representing the most occurring number in a given data set
From the information given, we have;
0, 4 , 3, 4, 0, 9, 1
Then, the mode is 0
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Log2x + log4x + log16 = 7
the solution to the equation log2x + log4x + log16 = 7 the logarithms using the properties of Logarithms is x ≈ 53.408.
To solve the equation log2x + log4x + log16 = 7, we can simplify the logarithms using the properties of logarithms.
First, we can use the property loga + logb = log(ab) to combine the logarithms:
log2x + log4x + log16 = log(2x * 4x * 16)
Next, we simplify the expression inside the logarithm:
log(2x * 4x * 16) = log(32x^3)
Now, our equation becomes:
log(32x^3) = 7
To eliminate the logarithm, we can rewrite the equation in exponential form:
32x^3 = 10^7
Simplifying further:
32x^3 = 10,000,000
Now, we can solve for x by dividing both sides of the equation by 32:
x^3 = 10,000,000 / 32
x^3 = 312,500
To find the value of x, we take the cube root of both sides:
x = ∛312,500
x ≈ 53.408
Therefore, the solution to the equation log2x + log4x + log16 = 7 is x ≈ 53.408.
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Teams in the National Football League in America are divided into two conferences: the AFC and the NFC. Some teams have animals as their mascots, and others do not. The following two-way table displays this data.
how many teams are in the NFC
The total number of teams that are in the NFC from the given two way frequency table is: 16 teams
How to Interpret a two way frequency table?A two-way table is one way to display frequencies for two different categories collected from a single group of people. One category is represented by the rows and the other is represented by the columns.
Two-way frequency tables are also referred to as a visual representation of the possible relationships between two sets of categorical data
From the attached two way table, we see that:
Total number of animals = 15
Total number of non-animals = 17
Total Number of NFC = 16
Total number of AFC = 16
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What type of angles are angle 1 and angle 8 ?
Answer:
Angles 1 and 8 are alternate exterior angles.
PLEASE HELPPPP I AM CONFUSED AND NOBODY can help meee
Using substitution method to solve the system of linear equation, the number of calculator is 50 and calender is 30
What is system of linear equations?The collection of two or more linear equations involving the same variables is known as a system of linear equations. In this case, linear equations are first-order equations, where the maximum power of the variable is 1.
To solve this problem, we can set the variables for this;
Let;
calculator = xcalendar = yTo write the system of linear equations;
x + y = 80 ...eq(i)
12x + 10y = 900 ...eq(ii)
Part B;
Using substitution method;
From equ(i)
x + y = 80
x = 80 - y ...equ(iii)
Put equ(iii) into equ(ii)
12(80 - y) + 10y = 900
y = 30
x = 50
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What are the values of the trigonometric ratios for this triangle?
sin θ =
cos θ =
tan θ =
4/3 3/5 4/5 5/3 5/4 3/4
Answer:
Sin θ = 3/5 cos θ = 4/5 tan θ= 3/4