9514 1404 393
Answer:
64 degrees
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relations between triangle sides and trig functions. Here, the marked sides are opposite and adjacent to the marked angle, so the relevant relation is ...
Tan = Opposite/Adjacent
tan(θ) = 29/14
To find the angle measure, we use the inverse function. It may be called tan⁻¹ on your calculator. It also goes by the name "arctangent." The term "arctan" can be thought of, or even pronounced as, "the angle whose tangent is ...".
θ = arctan(29/14) = 64.23°
The measure of angle θ is about 64°.
_____
Additional comment
The default units for angle measure are radians in most spreadsheets and on-line calculators. You need to make sure your hand-held calculator mode is set to give angles in the units you want. Here, we've given the angle in degrees, which is usually what is expected in problems like this.
{ (-2, 4), (0, 2), (-1, 3), (4, -2)}
The set of ordered pairs above:
DONE
Domain
-3
4
-1
5
Range
3
7
-2
The mapping diagram above:
DONE
y=x²
DONE
x
-3
-1
y
5
2
-1
The table above:
DONE ✔
The set of ordered pairs above: is a function.
The mapping diagram above: is a function.
y = x²: is a function.
The table above: is not a function.
What is a function?In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
Based on the set of ordered pairs, mapping diagram, and the equation above, we can reasonably infer and logically deduce that it represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).
In this context, we can reasonably infer and logically deduce that the table does not represent a function because the input value (-1) has more than output values (2 and 4 respectively).
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The two-way frequency table shows the number of social media contacts for 7th- and 8th-graders.
Complete the column two-way relative frequency table.
What is the value of a?
*
Captionless Image
28
29
38
39
49
100
Below is an illustration of the two-way frequency table showing the number of social media contacts for 7th and 8th students.
What is a two-way frequency table method?The definition of a two-way frequency table is a method of organizing data that makes it simple to see how frequently each category occurs.
The two-way frequency table presented here indicates the quantity of social media contacts made by 7th- and 8th-graders.
The proportion is then determined as follows:
Hence, we have written,
=> for 8th = 55/145 = 38%
=> for 7th = 61/155 = 39%
Here, we just add the cells above them in order to determine the total cells.
Equals> 61% + 39% = 100% for the seventh total.
Equals> 38% + 62% = 100% for the eighth total.
As a result, the column two-way relative frequency table is totally finished as follows:
7th 8th Total
0 - 300 61% 38% 50%
300+ 39% 62% 50%
Total 100% 100% 100%
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CAN SOMEONE PLEASE HELP ME WITH MY MATH !!!
Answer:
3√10
Step-by-step explanation:
From the Euclidean theorem x^2 (height) is equal to 9 × 10
x^2 = 90
x = 3√10
How Do I pass my class correctly and the best way possible
Some of the best ways to pass your class include:
Encourage or motivate yourself.Listen and participate in class.Take notes during class and make sure to go through them carefully.Do not hesitate to ask for helpStay focused during your homeworkConsider studying together with your fellow studentsWhat are the steps to pass your class?Motivate yourself: You have to believe and encourage yourself that you can do it. Note down some goals and use them to motivate yourself.Try to listen and participate in class: Participating in class will help your teacher to know you are interested in the subject. You can write down the questions you would like to ask before the class. Take notes during class and make sure to go through them carefully on your own.Do not hesitate to ask for help: You can ask your classmates or teacher for help, and where possible your parents. Stay focused during your homework: You do not need your phone to distract you when doing your homework. A quiet environment that will guarantee you focus helps a lot.Try studying with your fellow students, discussing topics that you are finding hard to understand would be of great help to you.I believe you can do it. Don't be afraid. Try your best and you will be successful. Hope this will be of help to you.
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Find the area of the figure pictured below.
15 yd
10 yd
17 yd
5 yd
A
First find the area of the square, then the triangle.
15 times 17 = 255 sq. yd
Triangle:
(5 times 5)/2 = 12.5 sq. yd
Your answer is 267.5 sq. yd
Hope this helps.
Simplify the expression using
order of operations
12 (10-5) - 40 + (4+1)
ans is 25
Step-by-step explanation:
12(10-5)-40+(4+1)
=12 of 5 - 40 + 5
= 60 - 40 +5
=60 +5 - 40
=65-40
=25
Answer:
-25
Step-by-step explanation:
We start off by using PEMDAS. 10-5 then 4+1.
12(5)-40+5
we multiply, then add and subtract giving us -25
What expression is equivalent to 5(1/3x+7)-3(1/2x-4)
Step-by-step explanation:
5/3x +35-3/2x+12=0
5/3x -3/2x+35+12=0
1/6x+47=0
1/6x=-47
divide through by 6x
×=1/282
- 1/2 (-5/6 + 1/3) simplified
Tania and Miguel are both blog writers. The table listed below shows the number of new followers each of them gained in each of the last 10 days.A.What is the mean absolute deviation of Tanias dataB. What is the mean absolute deviation of Miguels dataC. Whose data is more valid?
ialidMean Absolute Deviation of Tanias Data
55,65,66,73,77,82,88,91,101,113
The formula for calculating the mean absolute deviation is given by:
\(Mean\text{ Absolute Deviation = }\frac{1}{n}\sum_{i\mathop{=}1}^n\lvert{x_{i-}}\bar{x}\rvert\)
where n is the number of observed values, x-bar is the mean of the observed values and xi are the individual values.
Mean Absolute Deviation of Tanias is given below;
\(MeanAbsoluteDeviationMAD:13.9\)Next is Mean Absolute Deviation of Miguel;
Using the formula already stated;
\(MeanAbsoluteDeviation\text{ }MAD:12.3\)To determine whose data is more valid;
Miquel's data is more valid because it has a smaller mean absolute deviation.
Samira wants to carpet her bedroom. She wants
to know the amount of carpeting in square
meters needed to cover the empty space in the
room. The dimensions of the bed and closet are
given in the table.
Samira will need 14.1 square meters of carpeting to cover the empty space in her bedroom.
Samira wants to carpet her bedroom, and she wants to know the amount of carpeting in square meters needed to cover the empty space in the room. The dimensions of the bed and closet are given in the table.
To determine the amount of carpet needed to cover the empty space in the bedroom, we must first calculate the area of the room. To do this, we will multiply the length and width of the room, excluding the bed and closet.
The width of the room is 3.6 m and the length is 5.2 m. The area of the room is therefore: Area of room = length × widthArea of room = 5.2 m × 3.6 mArea of room = 18.72 m²To determine the amount of carpet needed to cover the empty space in the bedroom, we must subtract the area of the bed and closet from the area of the room.
Area of bed = length × width Area of bed = 2 m × 1.5 mArea of bed = 3 m²Area of closet = length × width Area of closet = 1.8 m × 0.9 mArea of closet = 1.62 m²Total area of bed and closet = 3 m² + 1.62 m²Total area of bed and closet = 4.62 m²Area of empty space = area of room - total area of bed and closet Area of empty space = 18.72 m² - 4.62 m²Area of empty space = 14.1 m²
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My last session disconnected.Find rational zeros and other zeros. Solve f(x)=0. Then factor into linear factors: f(x)= x^3+3x^2-2x-6
Given the following function:
\(f\mleft(x\mright)=x^3+3x^2-2x-6\)You can use the Rational Root Theorem to find the Rational zeros of the function. According to this theorem, if a polynomial has Rational zeros, eachey must have this form:
\(\frac{p}{q}\)Where "p" represents all the factors of the Constant term and "q" represents the factors of the Leading Coefficient.
Then, in this case, you can identify that the Constant term is:
\(a_0=-6\)And the Leading coefficient is:
\(a_n=1\)Then, you can set up that:
\(\frac{p}{q}=\frac{\pm1,2,3,6}{\pm1}\)So the possible zeros are:
\(=\pm1,\pm2,\pm3,\pm6\)Now you must evaluate each case by substituting each value into the function, in order to find the actual Rational zeros:
For:
\(\begin{gathered} x=1 \\ x=-1 \\ x=2 \\ x=-2_{} \\ x=3 \\ x=-3 \\ x=6 \\ x=-6 \end{gathered}\)You get:
\(\begin{gathered} f(1)=(1)^3+3(1)^2-2(1)-6=-4 \\ \\ f(-1)=(-1)^3+3(-1)^2-2(-1)-6=-2 \\ \\ f(2)=(2)^3+3(2)^2-2(2)-6=10 \\ \\ f(-2)=(-2)^3+3(-2)^2-2(-2)-6=2 \\ \\ f(3)=(3)^3+3(3)^2-2(3)-6=42 \\ \\ f(-3)=(-3)^3+3(-3)^2-2(-3)-6=0\text{ (It is a Rational root)} \\ \\ f(6)=(6)^3+3(6)^2-2(6)-6=306\text{ } \\ \\ f(-6)=(-6)^3+3(-6)^2-2(-6)-6=-102 \end{gathered}\)Then, you know that this is a Rational zero of the function:
\(x=-3\)To find the other zeros, you can follow these steps:
1. Divide the polynomial:
\(x^3+3x^2-2x-6\)By this polynomial:
\(x+3\)You can do it using Long Division:
Then, you can set up that:
The steps to solve it are shown below:
- Divide the first term of the Dividend by the first term of the Divisor.
- Place the result on the top.
- Multiply the result by the Divisor.
- Place the product below the Dividend.
- Subtract them in order to create a new polynomial.
- Bring down the next term and apply the same procedure.
Then, you get:
2. Therefore, you can rewrite the function as follows:
\(f\mleft(x\mright)=(x+3)(x^2-2)\)2.Make:
\(f(x)=0\)3. And Set up this equation and solve for "x" in order to find the other roots:
\(\begin{gathered} 0=x^2-2 \\ 2=x^2 \\ \\ x=\pm\sqrt[]{2} \\ \\ x_1=\sqrt[]{2} \\ x_2=-\sqrt[]{2} \end{gathered}\)Knowing those roots, you can factor the function into linear factors:
\(f\mleft(x\mright)=(x+3)(x+\sqrt[]{2})(x-\sqrt[]{2})\)Therefore, the answers are:
- Rational zeros:
\(x=-3\)- Other zeros:
\(\begin{gathered} x_1=\sqrt[]{2} \\ x_2=-\sqrt[]{2} \end{gathered}\)- Factored into linear factors:
\(f\mleft(x\mright)=(x+3)(x+\sqrt[]{2})(x-\sqrt[]{2})\)Oki and Stephen are making bags of trail mix to sell. Oki’s trail-mix recipe requires 3 cups of nuts and 3 cups of dried fruit per bag. Stephen’s trail-mix recipe requires 4 cup of nuts and 2 cups of dried fruit per bag. Together, they want to make as many bags of trail mix as possible. They have exactly 120 cups of nuts and 90 cups of dried fruit. Find the maximum number of bags of trail mix Oki and Stephen can make together.
A. write a system of inequalities
B. Graph and find coordinates of the vertices of the feasible region.
C. Find the maximum number of bags of trail mix oki and stehpen can make. How many of each type of recipe should they make to maximize the total number of bags
Answer: Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.
For vertex (15,15):
3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15
3x + 2y = 90 --> 3(15) + 2y = 90 -->
Step-by-step explanation: A. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we can use a system of inequalities to represent the constraints:
Let "x" be the number of bags of trail mix that Oki makes and "y" be the number of bags that Stephen makes. Then we have:
3x + 4y ≤ 120 (constraint on the number of cups of nuts)
3x + 2y ≤ 90 (constraint on the number of cups of dried fruit)
x ≥ 0 (non-negative constraint for Oki's bags)
y ≥ 0 (non-negative constraint for Stephen's bags)
B. To graph the feasible region, we can start by graphing the two constraint equations as lines:
3x + 4y = 120 (line A)
3x + 2y = 90 (line B)
We can find the x and y intercepts for each line:
For line A:
When x = 0, 4y = 120, y = 30 (y-intercept)
When y = 0, 3x = 120, x = 40 (x-intercept)
For line B:
When x = 0, 2y = 90, y = 45 (y-intercept)
When y = 0, 3x = 90, x = 30 (x-intercept)
Next, we can shade the region that satisfies all of the constraints. This region is below line A and to the left of line B, and is bounded by the x and y axes.
We can find the vertices of the feasible region by finding the intersection points of the two lines and the axes. These vertices are (0,0), (0,30), (15,15), and (30,0).
C. To find the maximum number of bags of trail mix that Oki and Stephen can make together, we need to evaluate the objective function at each vertex of the feasible region, and choose the vertex that maximizes the objective function.
The objective function is the total number of bags of trail mix:
z = x + y
Evaluating at the vertices:
Vertex (0,0): z = 0 + 0 = 0
Vertex (0,30): z = 0 + 30 = 30
Vertex (15,15): z = 15 + 15 = 30
Vertex (30,0): z = 30 + 0 = 30
The maximum value of the objective function occurs at vertices (0,30) and (15,15), where z = 30 bags of trail mix.
To determine how many of each type of recipe to make, we can substitute each vertex into the two constraint equations to find the corresponding values of x and y.
For vertex (0,30):
3x + 4y = 120 --> 3x + 4(30) = 120 --> 3x = -90 --> x = -30
3x + 2y = 90 --> 3(-30) + 2(30) = 90 --> y = 15
Therefore, Oki should make 0 bags of her recipe, and Stephen should make 30 bags of his recipe.
For vertex (15,15):
3x + 4y = 120 --> 3(15) + 4(15) = 120 --> x = 15
3x + 2y = 90 --> 3(15) + 2y = 90 -->
Select all of the trips that would take 2 hours.
1.Drive 60 miles per hour between Buffalo and Seneca Falls, which are 120 miles apart.
2.Walk 3 miles per hour to school, which is 1.5 miles away.
3.Take a train going 80 miles per hour from Albany to New York City
Answer:
#1 and #3
Step-by-step explanation:
if you divide the total distance between them you will get 60 for #1 and 80 for #3 if you multiply them both by 2 you get the total amount of miles for 2 hours
Answer:
1 and 3
Step-by-step explanation:
120 divided by 60=2
160 divided by 8=2
hopes this helps!! have a nice day!!
Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
The cost of staying in a hotel is given by the formula C=50d+20, where C is the cost in £ and d is the number of days a person stays. Find the cost of staying for:
a) 6 days
b) 2 weeks
c) If the cost is 120 then how many days the person can stay
Answer:
a) £320
b) £720
c) 2 days
Step-by-step explanation:
The question is all about inputting values and finding a result or rearranging and finding a result.
a) d = 6. C = 50(6)+20 = 320
b) d = 2x7 (7 days a week) C = 50(2x7) + 20 = 720
c) C = 120 ... 120 = 50d+20
100 =50d d = 100/50 = 2
A survey asked people how many siblings they have, and the results were recorded in this line plot.
How many people surveyed have 4 or more siblings?
dot plot
Answer:
we need a pic of the graph to be able. to work this out.
THANK YOU
Answer:
It's 5.
Step-by-step explanation:
8-3= 5
I need help pls how do u do this step by step? ):
Determine the measure of the third angle in a triangle when the other two angles total 165 degrees.
Answer:
15
Step-by-step explanation:
180-15
Hello!
the sum of the angles in the triangle = 180°
so the 3rd angle = 180° - 165° = 15°
The answer is 15°Solve x2 – 8x + 15 < 0.
Select the critical points for the inequality shown.
Answer:
x=3,5
Explanation:
x2−8x+15=0
Try to express the terms of the equation in square form.
Adding 16 both sides of the equation,
(x2−2⋅x⋅4+42)+15=16
or,(x−4)2+15−16=0
or,(x−4)2−1=0
or,(x−4)2−12=0
This is the a2−b2=(a+b)(a−b)form.
(x−4+1)(x−4−1)=0
or,(x−3)(x−5)=0
Now, equate both the terms to zero since both of them when multiplied, give zero.
Either,
x−3=0
∴x=3
Or,
x−5=0
∴x=5
Ans:x=3,5 Hope this helpsXD...!!
Answer:
3<x<5
Step-by-step explanation:
an Univariate quadratic polynomial can be divided into the product of two first order equations
In this example, x2 - 8x + 15 = (x-3) * (x-5) <0
as a result. the answer is 3< x <5
How much money you have to deposit in an acconut today at 3% simple interest rate if you are to receive Br.5,000 as amount in 10 years?
Answer:
invalid question because there is no way multiplying 3 with a number will result to 0
A study was conducted showing the relationship between the average maintenance cost and the age of a car in years.
Number of observations: 13
Least Squares | Standard | T
Parameter | Estimate | Error | Statistic| P-Value
Intercept | 54.7757 | 54.87 | 0.998282 | 0.3396
Slope | 120.689 | 11.8442 | 10.1898 | 0.0000
a) What is the formula for the regression function based on the output above (Write your equation in the context of question)?
b) Interpret the slope of the regression equation (In the context of question)?
c) Construct an 95% interval to predict the maintenance cost for a car that is 7 years old?
d) Based on this analysis, can we conclude that a relationship exists between the maintenance cost and the age of the car in years? What is the null and alternative hypothesis? Justify your answer using three steps process.
Answer:
Step-by-step explanation:
a) The formula for the regression function is:
Maintenance Cost = 54.7757 + 120.689 x Age of Car
b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.
c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:
Y = a + bX ± tα/2 * SE
where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.
Plugging in the values, we get:
Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442
Y = 923.167 ± 26.010
Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.
d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.
To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.
Two identical gardens are to be weeded, each by a two-person team. Team A includes one gardener who could weed the garden in 2 h and another who could weed the garden in 4 h. Team B includes two gardeners, either of whom could weed the garden in 3 h. Which team will finish first? Explain.
Step-by-step explanation:
Team A time is 1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr
Team B = 1 / ( 1/3 + 1/3) = 1 1/2 hr
Team A wins !
Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm
long. How many centimeters long was the actual tank?
cm
Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.
To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.
Let's denote the length of the actual tank as "x".
According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.
So, we can set up the following proportion:
1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)
Cross-multiplying and solving for x, we get:
x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm
The actual tank is 1620 cm long.
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HELP ME raaaaaaaa NOWWWWWWWWWW
Answer:
C: EAF Is the correct answer
the Cowboys have a record of 16 wins to 4 losses. The
Texans have a record of 18 wins to 3 losses. Which team
has a better record
Helpppp THIS IS TIMED NO LINKS OR I WILL Report YOU I will mark brainliest
Answer:
416
Step-by-step explanation:
Answer: 416 cm^2
Step-by-step explanation:
38+14/2 (16)
Ella earned $59.70 selling handmade bracelets at the craft fair. She sold a total of 6 bracelets. If all the bracelets were priced the same, how much did she charge for each bracelet?
Which of the following is the inverse of y=6*?
O y = logo
y = log,6
O y = logix
Y=log, 6x
Answer:
oy=logo 6
Step-by-step explanation:
The inverse of the function y = 6ˣ is y = log₆ x.
What is Inverse Function?Inverse functions are functions which can be reversed in to another function.
Then the function is said to be the inverse of the second function.
The given function is,
y = 6ˣ
A logarithm is simply the opposite function of the exponentiation.
That is, if c = aˣ, then we can write it as x =logₐ c.
We have,
y = 6ˣ
Now swap the variables.
x = \(6^y\)
Using the definition,
y = log₆ x
Hence the correct option is A.
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Several batches of stew were made yesterday. Each batch required 1 and two-thirds pounds of meat. All together, 10 and StartFraction 5 over 6 EndFraction pounds of meat was used. Janice tried to find the number of batches of stew made. Her work is shown below.
10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds = StartFraction 65 over 6 EndFraction divided by five halves = StartFraction 65 over 6 EndFraction times StartFraction 2 over 5 EndFraction = StartFraction 130 over 30 EndFraction = 4 and one-third
When she checked the answer by estimating, it did not make sense. What error did Janice make?
Janice converted a mixed number to the wrong improper fraction.
Janice added the numerators and denominators instead of multiplying.
Janice did not change the division problem to multiplication.
Janice did not convert the improper fraction to a mixed number correctly in the answer.
Mark this and return
The error that Janice made is that she did not convert the improper fraction StartFraction 130 over 30 EndFraction to a mixed number correctly in her final answer.
The error that Janice made can be identified by analyzing her calculations. Let's examine each step she took:
Step 1: 10 and StartFraction 5 over 6 EndFraction divided by 1 and two-thirds
In this step, Janice correctly converted the mixed number to an improper fraction, which becomes 10 and StartFraction 5 over 6 EndFraction = StartFraction 65 over 6 EndFraction.
Step 2: StartFraction 65 over 6 EndFraction divided by five halves
In this step, Janice attempted to divide the fractions. However, she made an error by adding the numerators and denominators instead of multiplying. This is incorrect. The correct operation for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of five halves is two fifths.
Step 3: StartFraction 65 over 6 EndFraction times StartFraction 2 over 5 EndFraction
Here, Janice multiplied the fractions correctly. The product of these fractions is StartFraction 130 over 30 EndFraction.
Step 4: StartFraction 130 over 30 EndFraction = 4 and one-third
In this step, Janice attempted to convert the improper fraction to a mixed number. However, she made another error in her calculation. The fraction StartFraction 130 over 30 EndFraction is not equal to 4 and one-third. The correct conversion would yield 4 and two-sixths or 4 and one-third.
Therefore, the error that Janice made is that she did not convert the improper fraction StartFraction 130 over 30 EndFraction to a mixed number correctly in her final answer.
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Wheels on some in-line skates can be removed using a 5/32 in. Allen wrench. What is 5/32
written as a decimal?
Answer:
0.15625
Step-by-step explanation:
No specific method, but only using calculator
5÷32
=0.15625