Ost< and cost is given. Use the Pythagorean identity sin2 t + cos2 t = 1 to find sin t.18) cos i =316I need help with #18
Answers
sin^2t + cos^2t = 1
sint = 1/4
(1/4)^2 + cos^2 t = 1
1/16 + cos^2 t = 1
cos^2 t = 1 - 1/16
cos^2 t = (16 - 1)/16
cos^2 t = 15/16
take root both side,
[tex]\begin{gathered} cost=\sqrt[]{\frac{15}{16}} \\ \cos t=\frac{\sqrt[]{15}}{4} \end{gathered}[/tex]so the answer is option D
Related Questions
Sophie put $3330 in a savings account at a simple interest rate of 7.4% per year.
Adam put $2795 in a savings account at a simple interest rate of 8.1% per year.
Who will have earned more interest after 5 years? How much more?
Answers
Sophie earned more simple interest of $100.
Simple interest is a short and easy technique for calculating the interest price on a mortgage. simple interest is decided with the aid of multiplying each day's interest charge via the most important by the variety of days that elapse among bills.
To calculate Simple interest, multiply the main quantity by using the interest charge and the time. The method written out is Simple interest = principle x interest price x Time." This equation is the most effective way of calculating interest.
Calculation:-
For Sophie
SI = PRT/100
= ($3330 × 7.4 × 5 ) /100
= $1232
For Adam
SI = PRT/100
= ($2795 × 8.1 × 5 ) /100
= $1132
Therefore, Sophie earned more interest of $1232 - $1132 = $100
simple interest is based on the most important amount of a loan or the primary deposit in a financial savings account. simple interest doesn't compound, and because of this a creditor will most effectively pay interest on the foremost amount, and a borrower might in no way have to pay extra interest at the previously amassed interest.
Learn more about simple interests here:-https://brainly.com/question/25793394
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Help Dalton explain his work. Complete the paragraph.One way to show that FGHI is a rectangle is to show that all 4 of its angles are rightangles. So, I found the slope of each side. The slope of FG and IH wasTheslope of FI and GH wasThen I knew that ZF, LG, ZH, and ZI were all rightangles becauselines have
Answers
ANSWERS
...The slope of FG and IH was 4/5. The slope of FI and GH was -5/4. Then I knew that ∠F, ∠G, ∠H, and ∠I were all right angles because perpendicular lines have opposite reciprocal slopes.
EXPLANATION
The slope of a line is given by,
[tex]m=\frac{\Delta y}{\Delta x}[/tex]For lines FG and IH, the slope is,
[tex]m_{FG}=m_{IH}=\frac{8}{10}=\frac{4}{5}[/tex]Similarly, the slope of lines FI and GH is,
[tex]m_{FI}=m_{GH}=\frac{5}{-4}=-\frac{5}{4}[/tex]Note that the slopes are opposite reciprocals, which makes each pair of lines perpendicular lines.
Find the value of x and the value of y.A. x = 15, y = 10sqrt3B. r = 20, y = 10sqrt3C. r = 20sqrt3, y = 5sqrt3D. x=15, y = 5sqrt3
Answers
To find the values of x and y it is necessary to use trigonometric ratios.
To find x it is necessary to use sine. Sine is the ratio between the opposite side to a given angle and the hypotenuse. In this case, the given angle is 60°, the opposite side is x and the hypotenuse is 10 sqrt 3. Use this information to find x:
[tex]\begin{gathered} \sin 60=\frac{x}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\sin 60=x \\ x=15 \end{gathered}[/tex]To find y it is necessary to use cosine. It is the ratio between the adjacent side to a given angle and the hypotenuse. The given angle is 60°, the adjacent side is y and the hypotenuse is 10 sqrt 3. Follow the same procedure as with sine:
[tex]\begin{gathered} \cos 60=\frac{y}{10\sqrt[]{3}} \\ 10\sqrt[]{3}\cdot\cos 60=y \\ y=5\sqrt[]{3} \end{gathered}[/tex]The correct answer is D. x=15, y=5sqrt3.
what's false 16 / 10 equal 25 / 40
Answers
10/16 = 25/40
Divide each
0.625 = 0.625
Second option:
15/60= 35/140
0.25 = 0.25
Third option
24/36=50/75
0.6666= 0.6666
Fourth option
14/35=35/70
0.4=0.5
FALSE
Please help me on my hw I need help on #2
Answers
Given:
The number is,
[tex]5.232323\ldots\text{.}[/tex]To express the given number into fraction . it means in the form,
[tex]\frac{a}{b}[/tex]We can express the given number into geometric series as,
[tex]\begin{gathered} 5.232323\ldots=5+\frac{23}{100}+\frac{23}{10000}+\frac{23}{100000}+\text{.}\ldots\ldots \\ =5+\frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots\ldots\text{.}\mathrm{}(1) \\ \frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots=-23+\sum ^{\infty}_{n\mathop=1}23(\frac{1}{100})^{n-1} \\ =-23+\frac{23}{1-\frac{1}{100}} \\ =-23+\frac{23(100)}{99} \\ =-23+\frac{2300}{99} \\ =\frac{-2277+2300}{99} \\ =\frac{23}{99} \end{gathered}[/tex]Now, equation (1) becomes,
[tex]5+\frac{23}{99}=\frac{518}{99}[/tex]Answer:
[tex]\frac{518}{99}[/tex]if f(x) = 13 when f(x)=5x -√8, find x.
Answers
Given that we have the function f(x) = 5x-√8, it is equal to 13 at some value of x. This relation can be written in equation as
[tex]5x-\sqrt[]{8}=13[/tex]Move √8 to the other side of the equation so that only the term with x will be left on the left-hand side. We have
[tex]5x=13+\sqrt[]{8}[/tex]Divide both sides by 5, we get
[tex]\begin{gathered} \frac{5x}{5}=\frac{13+\sqrt[]{8}}{5} \\ x=\frac{13+\sqrt[]{8}}{5} \end{gathered}[/tex]The square root of 8 can be further simplified as
[tex]\sqrt[]{8}=\sqrt[]{4\cdot2}=2\sqrt[]{2}[/tex]Hence, the value of x can also be rewritten as
[tex]x=\frac{13+2\sqrt[]{2}}{5}[/tex]Thus, the value of x to satisfy f(x) = 13 when f(x)=5x -√8 is
[tex]x=\frac{13+\sqrt[]{8}}{5}=\frac{13+2\sqrt[]{2}}{5}=\frac{13}{5}+\frac{2\sqrt[]{2}}{5}[/tex]Probability of dependent events2/5EspanolA department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 5 live in the town of Gaston,2 live in Pike, and 2 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Gaston? Write your answer as afraction in simplest form.0DOХ5?
Answers
Given there are 9 customers who have entered the drawing, 5 live in the town of Gaston, 2 live in Pike, and 2 live in wells. Two winners will be selected at random.
We have to find the probability that both winners live in Gaston.
The probability that the first winner selected is from Gaston is:
[tex]P(A)=\frac{5}{9}[/tex]The probability that the second winner selected is from Gaston is:
[tex]P(B|A)=\frac{4}{8}=\frac{1}{2}[/tex]The probability that both winners live in Gaston is:
[tex]\begin{gathered} P(A\cap B)=P(A)\cdot P(B|A) \\ =\frac{5}{9}\cdot\frac{1}{2} \\ =\frac{5}{18} \end{gathered}[/tex]Thus, the answer is 5/18.
What is the volume of a sphere with a diameter of 7.5 cm, rounded to the nearesttenth of a cubic centimeter?
Answers
The number of protozoa in a biology laboratory experiment is given by the polynomial functionp(t) = 0.02t^4 + 0.3t^3 + 7t^2, where p is the number of protozoa after t hours.Step 2 of 2: How many protozoa are present after 2 days? Round your answer to the nearest wholenumber.
Answers
In order to calculate the number of protozoa after 2 days (that is, 48 hours), let's use t = 48 in the function p(t) and calculate its value:
[tex]\begin{gathered} p(t)+0.02t^4+0.3t^3+7t^2 \\ p(48)=0.02\cdot48^4+0.3\cdot48^3+7\cdot48^2 \\ p(48)=0.02\cdot5308416+0.3\cdot110592+7\cdot2304 \\ p(48)=106168.32+33177.6+16128 \\ p(48)=155473.92 \end{gathered}[/tex]Rounding to the nearest whole number, the number of protozoa is 155474.
A city is built on the banks of a river and some islands in the river. The map below shows the bridges connecting the various land masses. Draw a graph that models the connecting relationships in the map below. The vertices represent the land masses and the edges represent bridges connecting them. Is it possible to find a circuit through the city that uses each bridge once? If so, enter the sequence of land masses(vertices) visited, for example ABDEA. If it is not possible, enter DNE. Use Fleury's algorithm and show all work and the graph as demonstrated in class.
Answers
We can graph the model as:
The Fleury's algorithm start with any vertex, and then select an edge that start from this vertex and go to another vertex. Then we pick another edge that starts from the last vertex, and so on. The condition is that all the vertices in the graph are always connected to each other: that is, there is always a path to conect any two vertices.
We start with A.
We can go to C, then B, then D, then E, then A.
After this part, we are left with these edges:
As the last vertex was A, we start from there.
We go to D, then to B, then to C, then to A again and we end in E.
We are never able to go back to the vertex we start (A), so there is no possible sequence.
Answer: DNE
How many radians are in a full rotation around a circle, or 360°?
Answers
Given:-
A full rotation.
To find the correct radians.
So as we know full rotation means 360 degree.
Also we know,
[tex]\pi=180[/tex]So for getting 360 degree. we get,
[tex]2\times180=360[/tex]So the required solution is,
[tex]2\pi[/tex]In the figure below, AB is an angle bisector. What is the value of x? Show and explain work
Answers
Since AB is the angle bisector:
[tex]\begin{gathered} m\angle CAB=m\angle DAB \\ so\colon \\ 33=4x+1 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 4x=33-1 \\ 4x=32 \\ x=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Answer:
x = 8
Find the lowest multiple of each group.show the factors you used.1. 5,20,28
Answers
Given the following question:
1, 5, 20, 28
1 = 1
5 = 5
20 = 2 × 2 × 5
28 = 2 × 2 × 7
2 × 2 × 5 × 7
2 × 2 = 4
4 × 5 = 20
20 × 7 = 140
LmM = 140
Disprove each statement , and then find all values of a and b for which the statement happens to be true . Explain your results If f(x) = x ^ (1/3) does f(a + b) = f(a) + f(b) ?
Answers
We are given the following function:
[tex]f(x)=x^{\frac{1}{3}}[/tex]To determine the value of f(a) we will replace the value of "x" for "a" in the function:
[tex]f(a)=a^{\frac{1}{3}}[/tex]Using the same procedure we determine the value of f(b):
[tex]f(b)=b^{\frac{1}{3}}[/tex]Now we determine the value of f(a+b):
[tex]f(a+b)=(a+b)^{\frac{1}{3}}[/tex]We are asked about the equatity:
[tex]f\mleft(a+b\mright)=f\mleft(a\mright)+f\mleft(b\mright)[/tex]replacing the values we get:
[tex](a+b)^{\frac{1}{3}}=a^{\frac{1}{3}}+b^{\frac{1}{3}}[/tex]We get an equality that is not true for any value of "a" and "b" since the left expression can't be converted into the right expression for any "a" or "b". The statement is false.
The statement could be right if "a" or "b" equal zero, for example, let's take a = 0, we get:
[tex](0+b)^{\frac{1}{3}}=(0)^{\frac{1}{3}}+b^{\frac{1}{3}}[/tex]Simplifying:
[tex]b^{\frac{1}{3}}=b^{\frac{1}{3}}[/tex]Which is a true statement. .
Which of the following is an arithmetic sequence? A. 1, 0, 1, 0, 1, 0, ...B. 800, 200, 50, ...C. 10, 7, 4, 1, -2, ...D. 1, 3, 9, 27,...
Answers
Given:
The sequences in options.
Required:
Which of the sequence is an arithmetic sequence.
Explanation:
The arithmetic sequence has a common ration, that is equal for every pair of number
[tex]d=a_2-a_1,d=a_3-a_2[/tex]Now, in option c
[tex]\begin{gathered} d=7-10=-3 \\ d=4-7=-3 \\ d=1-4=-3 \end{gathered}[/tex]So, common ratio is -3 and hence sequence is arithmetic sequence.
Answer:
So, option c is correct.
Hello, I need help on how to read attached graph based on the questions.Thank you
Answers
As can be seen in the above graph:
(a) g(x) > 0 in the interval: (-4, -2) U (0, 2)
(b) g(x) < 0 in the interval: (-2, 0)
(c) g(x) = 0 at the next x-values: -4, -2, 0, 2
Graphically, the derivative of a function evaluated at a point is seen as the slope of the tangent line that passes through that point of the function.
Then, if the slope is positive, the derivative is positive, if the slope is zero (a horizontal line), the derivative is zero, and if the slope is negative, the derivative is negative.
In the next graph, we can see some of these slopes:
Therefore, the intervals where g'(x) is positive, negative or zero are:
(d) g'(x) > 0 in the interval: (-4, -3) U (-1, 1)
(e) g'(x) < 0 in the interval: (-3, -1) U (1, 2)
(f) g'(x) = 0 at the next x-values: -3, -1, 1
The Young family has collected movies. They have 18 action movies. 16 comedies. 8 mysteries, and 12 dramas. How many movies do they have in total?
Answers
The family has 54 movies in total
Explanation:The movies the family have in total is the addition of the number of movies in each category:
18 + 16 + 8 + 12
= 54
A triangle has side lengths of 6, 8, and 10Is it a right triangle?
Answers
To be a right triangle it must comply with the following:
[tex]a^2+b^2=c^2[/tex]Where:
a = 6
b = 8
c = 10
So:
[tex]\begin{gathered} 6^2+8^2=10^2 \\ 36+64=100 \\ 100=100 \end{gathered}[/tex]This means that it is a right triangle.
Answer: Yes, It is a right triangle
Perform the indicated operation 4.8L +12.6L
Answers
To perform a operation with the same variable (L), add or subtract the coefficients before the variable and keep the variable.
4.8 L + 12.6 L
(4.8 + 12.6) L
17.4L
Answer: 17.4 L.
> Next question Get a similar question You can retry this a 8.1 ft 9.7 10.6 Name the Shape: • triangle trapezoid kite parallelogram
Answers
The given figure is has three sides and three vertices : Triangle
In the given triangle, height = 9.7 ft, base = 8.1 ft,
Area of triangle = 1/2 x Base x Height
Area of traingle = 1/2 x 8.1 x 9.7
Area of traingle = 39.28 ft²
Area of the given figure = 39.28 ft²
three points a b and c exist in space such that b is between a and C it is known that AB = 7 , BC= 4 and AC = 9 . Ar epoints a b and c Collinear? give a written explanation supported by mathematical evidence for your answer.
Answers
Points are collinear if they are in the same line.
So:
AB+BC = AC
Replacing with the values given:
7+4 = 9
11 =9 False
A,b, and c aren't collinear.
Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. What is the probability distribution forthe 30 pieces of fruit, in the order listed?FruitNumber ofpiecesProbabiltyApples Bananas62
Answers
Answer:
D.
Explanation:
We were given that:
A company provides fruit for its employees
The employees can pick among five kinds of fruit
The fruits obtained this week is:
Apples = 6 pieces
Bananas =2 pieces
Lemons = 10 pieces
Oranges = 8 pieces
Pears = 4 pieces
Total = 30 pieces
The probability distribution for this is given by:
[tex]\begin{gathered} P(apples)=\frac{Number\text{ of apples}}{Total}=\frac{6}{30}=\frac{1}{5} \\ P(apples)=\frac{1}{5} \\ \\ P(bananas)=\frac{Number\text{ of bananas}}{Total}=\frac{2}{30}=\frac{1}{15} \\ P(bananas)=\frac{1}{15} \\ \\ P(lemons)=\frac{Number\text{ of lemons}}{Total}=\frac{10}{30}=\frac{1}{3} \\ P(lemons)=\frac{1}{3} \\ \\ P(oranges)=\frac{Number\text{ of oranges}}{Total}=\frac{8}{30}=\frac{4}{15} \\ \\ P(pears)=\frac{Number\text{ of pears}}{Total}=\frac{4}{30}=\frac{2}{15} \\ P(pears)=\frac{2}{15} \\ \\ \therefore P=\frac{1}{5},\frac{1}{15},\frac{1}{3},\frac{4}{15},\frac{2}{15} \end{gathered}[/tex]Therefore, the answer is D
Find the measure of chord EF. Enter your numerical answer.
Answers
Notice that each chord (CD and EF) defines a segment in the circle whose arc length has the same value. Thus, the length of both chords has to be the same; then,
[tex]\begin{gathered} CD=EF \\ \Rightarrow9x-1=41-5x \\ \Rightarrow14x=42 \\ \Rightarrow x=3 \end{gathered}[/tex]Finding the length of EF,
[tex]\begin{gathered} x=3 \\ \Rightarrow EF=41-5*3=26 \end{gathered}[/tex]Therefore, the answer is 26
A straw is placed in a rectangular box that is 6 inches by 4 inches by 8 inches, as shown. If the straw fits exactly in the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
Answers
Explanation
you can solve this by using the distance between 2 points formula
[tex]D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}[/tex]then
Step 1
Let
P1(0,0,0)
P2(6,4,8)
now , replace
[tex]\begin{gathered} D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2} \\ D_{ab}=\sqrt[]{(6-0)^2+(4-0)^2+(8-0)^2} \\ D_{ab}=\sqrt[]{(6)^2+(4)^2+(8)^2} \\ D_{ab}=\sqrt[]{36^{}+16+64} \\ D_{ab}=\sqrt[]{116} \\ D_{ab}=\sqrt[]{4\cdot29} \\ D_{ab}=2\sqrt[]{29} \end{gathered}[/tex]I hope this helps you
A. 12in ^2B. 30 in ^2C. 24 in ^2 D. 27 in 2pls help with guided practice
Answers
The given figure is a parallelogram. The formula for determining the area of a parallelogram is expressed as
Area = base * height
From the diagram,
base = 9 inches
height = 3 inches
Area = 9 * 3 = 27 in^2
The correct option is D
Solve x2-12x + 11 = 0 by completing the square.
Answers
Given: A quadratic equation-
[tex]x^2-12x+11=0[/tex]Required: To solve the equation by completing the square method.
Explanation: The general form of a quadratic equation is-
[tex]ax^2+bx+c=0[/tex]The given equation can be solved by the method of completing the square by adding and subtracting the term-
[tex](\frac{b}{2})^2[/tex]Hence, the given equation can be written as-
[tex]x^2-12x+36-36+11=0[/tex]Now solving further as-
[tex]\begin{gathered} x^2-2\times6\times x+6^2-25=0 \\ (x-6)^2=25 \\ (x-6)=\sqrt{25} \\ (x-6)=\pm5 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} x-6=5\text{ or } \\ x-6=-5 \end{gathered}[/tex]This gives-
[tex]\begin{gathered} x=11\text{ or} \\ x=1 \end{gathered}[/tex]Final Answer: The solution to the equation is x=11 or x=1.
13. If a trapezoid has base lengths of 18and 40, what is the length of themedian?I●
Answers
The median of a trapezoid is a straight line that goes from the midpoint of one of the sides to the midpoint of the opposite side and is parallel to both bases.
Its length is the average of the lengths of both bases:
[tex]median=\frac{(upper.base+lower.base)}{2}[/tex]One of the bases of the trapezoid has a length of 18 units and the other base has a length of 40 units. Average both bases to determine the length of the median:
[tex]\begin{gathered} median=\frac{18+40}{2} \\ median=\frac{58}{2} \\ median=29 \end{gathered}[/tex]The length of the median is 29 units.
graph the equation shown below by transforming the given graph of the parent function. y = 2x²
Answers
We have that the parent function is multiplied by 2, therefore, the graph for y = 2x^2 will compress in comparison with the graph of y=x^2
Both graphs would looke like this:
where the black graph represents the functon y = 2x^2 and the red graph represents the function y = x^2
percentage of the people surveyed said Lombardi?
The grade a student makes on a test varies directly with the amount of time the student spends studying. Suppose a student spends 5 hours studying and makes a grade of 89 on the test. What is an equation that relates the grade earned on a test, g, with the amount of time spent studying, t. in hours?
Answers
It is given that,
A student spends 5 hours studying and makes a grade of 89 on the test.
To write an equation that relates the grade earned on a test in t hours.
Let us take,
For 5 hours, the grade is 89
For 1 hour, the grade will be,
[tex]\frac{89}{5}=17.8[/tex]Then for t hours, the general equation will be,
[tex]g=17.8t[/tex]Hence, the answer is g=17.8t.
2. The line plot shows the results of a survey about kitchen sinks. Kitchen Sink Survey + 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Capacity (gallons) Write a paragraph summarizing the data set. In your summary include the following A description of the data, including the unit of measure The number of data values The shape of the distribution The value of an appropriate measure of center The value of an appropriate measure of spread
Answers
Given: The information and line plot showing
..
From the plot we can write a table of values for the data
From the table we can get the mean
[tex]\begin{gathered} M_{\text{ean}}=\frac{\Sigma fx}{\Sigma f} \\ M_{\text{ean}}=\frac{(12\times0+13\times1+\ldots+24\times1+25\times0)}{1+2+4+5+...+1+0} \\ M_{\text{ean}}=\frac{354}{21} \\ M_{\text{ean}}=16.86 \\ M_{\text{ean}}\approx17 \end{gathered}[/tex]The standard deviation
[tex]\begin{gathered} S_{\text{tandard deviation}}=\sqrt[]{\frac{\Sigma f(x-\mu)^2}{\Sigma f}} \\ S_{\text{tandard deviation}}=\sqrt[]{\frac{0(12-17)^2+1(13-17)^2+\cdots+1(24-17)^2}{21}} \\ S_{\text{tandard deviation}}=\sqrt[]{\frac{150.571}{21}} \\ S_{\text{tandard deviation}}=2.68 \end{gathered}[/tex]ANSWER SUMMARY
It can be observed that the capacity of the kitchen sink ranges from 12 gallons to 25 gallons. There are 21 kitchen sink with different capacity in gallons. The shape of the distribution is skewed right with an appropriate measure of centre (that is the mean) as 17 gallons. The measure of spread including the range (between 13 gallons to 24 gallons) is 11 gallons, the median is 16 gallons sink and the standard deviation is 2.68 gallons
Answer:
poopsicle
Step-by-step explanation: