Homework 4: Trigonometry:Finding Sides and Angle** This is a 2-page document! **x=7.3Directions: Solve for x. Round to the nearest tenth.
Using trigonometric ratio. SOHCAHTOA
[tex]\begin{gathered} \cos 63^{\circ}=\frac{adjacent}{\text{hypotenus}} \\ \cos 63^{\circ}=\frac{x}{16} \\ x=16\cos 63^{\circ} \\ x=16\times0.45399049974 \\ x=7.26384799583 \\ x\approx7.3 \end{gathered}[/tex]2(q + 4) = 10
Solve for q
Answer:
q=1
Step-by-step explanation:
2(q+4)=10
q+4=5
q=1
:]
Answer:
3
Step-by-step explanation:
2 x 3 6 4 10
Let f(x) = 9x - 8. Find (f o f)(1).
Let f(x) = 9x - 8. Find (f o f)(1).
we know that
(f o f)(1).=f(f(1))
step 1
find f(1)
f(1)=9(1)-8
f(1)=1
substitute
f(f(1))=f(1)=1
therefore
the answer is 1
Find the distance between the points P (3, 5) and Q (8,7).
Answer:
The distance between two points (x₁,y₁) and (x₂,y₂) on the coordinate plane is d=√((x₂-x₁)²+(y₂-y₁)²)
√(8 - 3)² + (7 - 5)² = √29 ≈ 5.3851648071345
The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars)
t
years after 1995.
420
t
+
5750
Use this expression to predict what the total average credit card debt was or will be in the year 2006.
Answer: In the year 2006, the total average credit card debt for a U.S. household will be (or was)
dollars.
In the year 2006, the total average credit card debt for a U.S. household was 10370 dollars.
How to solve Exponential functions?
We are given the expression that gives an approximate value of the total average credit card debt in a U.S. household (in dollars), t years after 1995 as;
420t + 5750
where t represents number of years after the year 1995. Thus, for the year 2006, the value of t is;
t = 2006 - 1995
t = 11 years
Thus;
f(11) = 420(11) + 5750
f(11) = 10370 dollars
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Tobin's friend Rose claims that she can read minds. To test
Rose's abilities, Tobin draws 3 cards without replacement
from a standard deck of 52 playing cards. Tobin asks Rose
to identify each of the 3 cards she drew in order.
Assume that Rose has no special abilities and is randomly
guessing the cards.
What is the probability that Rose identifies all 3 cards in
the correct order?
The probability that rose identifies all 3 cards in the correct order is 1/132,600 by the concept of permutation.
What is permutation?It is the separate arrangements of a given number of associates taken all at once, or some of them, or just a few of them. There are two possible meanings, AB and BA, for instance, if we have the two elements A and B.
Following the arrangement of 'r' items from a total of 'n' elements, the number of permutations is,
nPr = n! / (n – r)!
Here to obtain the probability in correct order use permutation formula
Recall that, Probability is calculated as favorable outcomes divided by all possible outcomes.
Favorable number of outcomes = 1 (as only one order is correct)
Total outcomes = 52p3 (since 3 cards to be arranged from pack of 52)
So, the probability of rose identifies all 3 cards in correct order =1/52p3
Probability = [tex]\frac{1}{52!/(52-3)!}[/tex]
Probability = 49! /52!
Probability = 49! /52*51*50*49!
Probability = 1/52*51*50
Probability = 1/132,600
Therefore, the probability that rose identifies all 3 cards in the correct order is 1/132,600.
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Define a variable, write an inequality, and solve: A number decreased by 7 is at least 15
Inequality: [tex]x-7\ge 15[/tex]
Solution: [tex]x\ge 22[/tex]
Inequality is a mathematical statement which depicts the relation between two or more mathematical variable or quantities which involves in relation which is not equal or inequal.
Given the statement is "A number decreased by 7 is at least 15"
Let the number be the variable x.
Now decreased by 7 = x-7
Suitable inequality sign for at least statement is [tex]\ge[/tex]
So the required inequality is given by,
[tex]x-7\ge15[/tex]
Solving the same we get,
[tex]x-7+7\ge 15+7[/tex]
[tex]x\ge 22[/tex]
Thus the number is [tex]x\ge 22[/tex]
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Use the function below to find f(-2).
f(x) = 3x
A. -6
B. -9
O C.
O D.
996
610
9
Answer:
option d is the correct answer
The graph below shows the number of bushels of soybeans a farmer harvested from his field.NUMBER OF ACRES HARVESTEDwhich set of ordered pairs could have been used to make the graph?A. (3, 125), (4, 200), (5, 225)B. (50, 1), (200, 4), (300, 6)C. (100, 2), (250, 5), (350, 7)D. (2, 100), (3, 150), (5, 250)And don't worry this is just a practice :)
From the graph, we can see that the set of ordered pairs which belongs to the line are
D). (2, 100), (3, 150), (5, 250)
Because x-axis is the first coordinate and y-axis is the second coordinate. In options B and C, they are
arranged in the wrong place. In option A, point (3,125) doesn´t belong to the line.
he table shows the gallons of water in a pool over time. A two column table with six rows. The first column, Time in minutes, has the entries, 0, 1, 2, 3, 4, 5. The second column, Water in Pool in gallons, has the entries, 50, 44, 38, 32, 26, 20. Choose the term that describes the slope of the line of a graph representing the data in the table. The slope of a line graphed to represent the volume of water in a pool over time would be described as .
The slope of the line to represent the volume of water in a pool over time would described as -10
From the given table we have to choose points to find the slope of the line
The domain is defined as the set of possible inputs of the function.
The range is defined as the set of all possible outputs of the function.
The slope of the line is the change in y coordinate with respect to the change in y coordinates
Slope of the line m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Where m is the slope of the line
[tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] are the coordinates of the two points
We have to choose two points
The two points (2,44) and (4,26)
m = [tex]\frac{26-46}{4-2}[/tex]
m = -20/2
m = -10
Hence, the slope of the line to represent the volume of water in a pool over time would described as -10
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Barnaby decided to count the number of ducks and geese flying south for the winter. Thefirst day he counted 175 ducks and 63 geese. What is the ratio of ducks to the total num-ber of birds flying overhead in simplest terms?
So, here we have that there are 175+63 = 238 birds in total.
We want to know the ratio of ducks to the total number of birds flying overhead. There are 175 ducks for a total of 238, so the ratio is:
175:238
A map of a park has no scale. The distance between the campground and the entrance station on the map is 2 inches. The actual distance between them is 8 miles. On the map, the distance between the campground and the lake is 12 inch.
What is the actual distance in miles between the campground and the lake?
The distance between the lake and campground is 48 miles.
Given
The distance between the campground and the entrance is 2
The actual distance between them is 8 miles
Hence the scale is 2 for 8 miles
Also, Distance on the map between campground and lake is 12 inch.
Let us say actual distance is x
There fore we can form equation as
2x = 12x18
2x = 216
x=48
Hence the actual distance between campground and lake is 48 miles.
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Use the rule for the order of operations to simplify: 8+6(6-2(5-4))
Given the expression below
[tex]8+6(6-2(5-4))[/tex]Step 1: Using PEMDAS rule
P=> Parenthesis
E=>Exponent
M=>Multiplication
D=>Division
A=>Addition
S=> Subtraction
From the rule above, we will start our simplification with the parenthesis
Step 1: simplify (5-4)
[tex]\begin{gathered} 8+6(6-2(5-4) \\ 8+6(6-2(1)) \end{gathered}[/tex]Step 2: Expand 2(1)=> 2x1, then simplify (6-2(1))
[tex]8+6(6-2(1))\Rightarrow8+6(6-2)\Rightarrow\cdot=8+6(4)[/tex]Step 3: Expand 6(4)=>6 x 4
[tex]8+6(4)\Rightarrow8+6\times4\Rightarrow8+24[/tex]Step 4: Add 8 and 24
[tex]8+24=32[/tex]Hence, the final answer is 32
Answer: your answer would be 32
Step-by-step explanation:
using PEMDAS we would first go by parentheses and use the order by each step.
can someone help me please ?
The most appropriate choice for HCF of two numbers will be given by -
Maximum number of performers in each row so that all the rows are equal in length = 8
What is HCF?
HCF means Highest Common Factor. HCF of two numbers a and b is the largest number that is divides both a and b.
Number of instruments = 24
Number of flag bearers = 16
Maximum number of performers in each row so that all the rows are equal in length = HCF of 24 , 16
[tex]24 = 2^3 \times 3\\16 = 2^4[/tex]
HCF = [tex]2^3[/tex] = 8
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3. Using the diagram below, answer the following questions. Remember, you must
show your work for credit.
LA = 6y+42
ZC
ZD
A. Solve for y. (2 points)
ZA=
y=
I
B. Find the measure of angles A, C and D showing all work. (2 points)
ZC=
LB = 66
ZD =
Using vertical angles, it is found that:
A. The solution for y is of y = 4.
B. The angle measures are given as follows:
<A = 66º.<C = 114º.<D = 114º.Vertical AnglesIf two angles are opposite by the same vertex in crossing segments, these angles are called vertical angles, and they are congruent, that is, they have the same measure.
In the context of this problem, the angles of 6y + 42 and of 66 are vertical, hence the value of y is calculated as follows:
6y + 42 = 66
6y = 24
y = 24/6
y = 4.
Angles A and C are supplementary, meaning that the sum of their measures is of 180º, hence:
<C + 66º = 180º
<C = 180º - 66º
<C = 114º.
Angles C and D are vertical, hence the measure of angle D is calculated as follows:
<D = 114º.
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Classify the triangle with the following angle measure: 20^, 50^, 110^
An acute triangle is a triangle with three acute angles, whereas an obtuse triangle is a triangle with one obtuse angle and two acute angles.
An obtuse angle is a angle which is more than 90°.
In our problem, the triangle has a 110° angle, and 110°>90°; therefore, the answer is obtuse triangle
Please help I was sick today and I don’t understand
Answer:
This is a 30 60 90 triangle. They are saying the hypotenuse is 3x + 6 and the shortest side is 8x - 4. In a 30 60 90 triangle, the hypotenuse is 2 times the short side meaning that/
3x + 6 = 16x - 4
Now we can solve...
10 = 13x
x= [tex]\frac{10}{13}[/tex]
The amount of water a bag of salt can treat is known in cubic feet.
Given:
There is a rectangular prism shape water tank given with 23yd 15yd anf 4yd measurements
Required:
A) We need to find the volume of tank in cubic ft
B) 18.8 cubic ft need 1 salt bag then we need to find to total needed salt bag
C) $4.65 per bag then find total cost
Explanation:
first pf all we need to convert given measures in feet from yd
[tex]\begin{gathered} 1yd=3ft \\ 23yd=69ft \\ 15yd=45ft \\ 4yd=12ft \end{gathered}[/tex]A)
Volume
[tex]V=lwh=69*45*15=37260ft^3[/tex]B)
18.8 cubic ft need 1 bag
then
37260 cubic ft need x
[tex]x=\frac{37260}{18.8}=1981.9\approx1982\text{ bags}[/tex]C)
Cost for 1 bag is $4.65
then
cost for 1982 bags is y
[tex]y=1982*4.65=9216.3[/tex]Final answer:
A) volume of tank in cubic ft is 37260
B) 18.8 cubic ft need 1 salt bag then we need total 1982 needed salt bags
C) $4.65 per bag then total cost is $9216.3
Michael has a twelve gallon gas tank. When he filled
his tank up, he pumped nine gallons of gas. What
fraction of his tank had been empty?
Answer:
3/4
Step-by-step explanation:
9/12 Divide the top and bottom by 3
3/4
Classify the four angles of the quadrilateral. С 750 B 1050 90° 90-
Anlges A and D are right angles becuase they measure 90
Angle C is Acute because it is smaller than 90
Angle B is Obtuse because it is grather than 90
The graph depicts the growth in costs using a line segment. Use the midpoint formula to approximate the cost during the year 1987.The approximate cost during the year 1987 was $ ____.
Answer:
The approximate cost during the years 1987 was $7527
Explanation:
The midpoint formula is:
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]For two given points.
In this case, we can see in the graph the points (1983, 5021) and (1991, 10033)
Then, using the midpoint formula:
[tex]M(\frac{1983+1991}{2},\frac{5021+10033}{2})=M(1987,7527)[/tex]Thus, the approximation for the year 1987 is $7527
Find the slope of the line passing through the pair of points or state that the slope is
undefined. Then indicate whether the line through the points rises, falls, is horizontal, or
is vertical.
(3,-5) and (-7,-5)
...
Select the correct choice below and, if necessary, fill in the answer box within your
choice.
Answer:
The slope is o. The line will be vertical and the equation of the line is y = -5
Step-by-step explanation:
help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeee
Step-by-step explanation:
I just answered this. how often did you post this basic question ?
Please help if you can!!!
!!PLEASE HELP!!
Stefan is baking taquitos for a school fundraiser. The recipe calls for 2 1/2 cups of beans and 3 1/4 cups of rice. What is the ratio between cups of beans and cups of rice?
The ratio between cups of beans and cups of rice is 10/13 . Option C
What is ratio?
A ratio can described as an ordered pair of numbers, like y and z, that is written mathematically in the form y / z where the denominator of the fraction is not equal to zero.
It is known to describe the number of times an element or number contains another number proportionally.
It is also seen as the comparison of two quantities, elements or numbers that has the same units and likewise, explains how much one of the elements or quantity is found in the another one.
This is done based on their sizes or magnitudes.
A proportion is a mathematical equation with two ratios set equivalent or equal to each other.
Given that;
Beans = 2 1/ 2 cups
Rice = 3 1/4 cups
Convert to mixed fractions;
Beans = 5/2
Rice = 13/4
Now, divide the cups of beans by that of rice;
= 5/ 2 ÷ 13/4
= 5/2 × 4/13
= 10/13
Hence, the ratio is 10/13
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At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph?
A) approximately 16%
B) at most 34%
C) at most 2.5%
D) at most 13.5%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
Given :
The statistician reported that the mean serve speed was 100 miles per hour
the standard deviation of the serve speeds was 15 mph
Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric
To find :
What percentage of the player's serves were between 115 mph and 145 mph?
Solution :
μ =100
σ = 15
P ( 115 < x <145)
= P ( [tex]\frac{115-100}{15}[/tex] < x-μ /6 <[tex]\frac{145-100}{15}[/tex] )
= P ( [tex]\frac{15}{15}[/tex] < z < [tex]\frac{15}{15}[/tex] )
= p ( 1<z<3)
= p( z<3)-p(z-1)
=0.9987-0.8413
=0.1574
p ( 115<xx<145)= 15.74 %
p( 115<x<145)= approximately 16%
The percentage of players serves were between 115 mph and 145 mph is approximately 16%.
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Complete sheet given
Answer:
good jb
Step-by-step explanation:
Integers greater than -6 and less than 2
IN OTHER WORDS WE ARE LOOKING FOR WHOLE NUMBERS BETWEEN -6 AND 2
[tex] - 5 \\ - 4 \\ - 3 \\ - 2 \\ - 1 \\ 0 \\ 1[/tex]
ATTACHED IS THE SOLUTION
Answer:
1,0,-1,-2,-3,-4,-5
Step-by-step explanation:
Write an equation. Let X represent the number described in the exercise. Then solve the equation & find the number. Four subtracted from the product of 5 and a number is 51.Write an equation.
We have to write an equation from the word problem,
Four subtracted from the product of 5 and a number is 51
Let's break it down:
--- product of 5 and a number can be written as,
[tex]\begin{gathered} 5\times x \\ =5x \end{gathered}[/tex]--- four subtracted from "product of 5 and a number" can be written as,
[tex]5x-4[/tex]^^ All this is equal to 51, so we can write,
[tex]5x-4=51[/tex]To find the unknown number, we solve the above equation. The steps are shown below:
[tex]undefined[/tex].5t + .1 < 10t + .05
Answer: t> -4/95
Step-by-step explanation: times both sides by 10(just make the calculation easier, no need to do that)
5t+1<100t+5
-95t<4
t > -4/95