Note that;
secθ = 1/cosθ cotθ= cosθ/sinθ
substitute into into the expression
[tex]\sec \theta.\cot \theta.\sin \theta=\frac{1}{\cos\theta}.\frac{\cos \theta}{\sin \theta}\text{. sin}\theta[/tex]cosθ at the numerator will cancel out the cosθ at the denominator, also sinθ at the numerator will cancel out the sinθ at the denominator
[tex]=1[/tex]Question 811pA ship is travelling due north with a speed of 12 km hr-1 relative to the water.The current in the water is flowing at 1.1 km hr-1 to the east. Determine themagnitude of the velocity of the ship.
We have the following excerpt for the analysis:
" A ship is travelling due north with a speed of 12 km/hr relative to the water. The current in the water is flowing at 1.1 km/hr to the east. Determine the magnitude and the velocity of the ship "
We will investigate the application for the concept of relative velocity. The following variables can be extracted from the given excerpt:
[tex]\begin{gathered} V_{sw}\text{ = 12 }\frac{\operatorname{km}}{hr}\ldots\text{ due north} \\ \\ V_w\text{ = }1.1\text{ }\frac{\operatorname{km}}{hr}\ldots\text{ due east} \end{gathered}[/tex]In such cases of application we seek help by formulating a velocity triangle. We need to determine the direction and magnitude of ship's velocity that it must traverse in and by the effect of current due east the ship starts to move north.
We can go ahead and express the above information graphically in form a velocity triangle as follows:
Think of the above velocity triangle as such:
" The ship initital moves with a velocity ( Vs ) which is unknown at a certain angle. During the course the current of the water ( Vw ) pushes the ship nose from east side towards north. With the effect of the current the ship "seems" to be moving due north ( Vsw ) "
The above triangle is represented as a right angled triangle. We will recall the properties and the application of pythagoream theorem that only applies to right angle triangle as follows:
[tex]H^2=P^2+B^2[/tex]Where,
[tex]H=V_s,P=V_w,B=V_{sw}[/tex]We will plug in the respective quantities in the pythagorean theorem relation expressed above:
[tex]\begin{gathered} (V_s)\text{ = }\sqrt[]{(V_w)^2+(V_{sw})^2} \\ \\ (V_s)\text{ = }\sqrt[]{(1.1)^2+(12_{})^2} \\ \\ (V_s)\text{ = }\sqrt[]{(145.21)} \\ \\ (V_s)\text{ = 12.05 }\frac{\operatorname{km}}{hr}\ldots Answer \end{gathered}[/tex]
Angles A and B are complementary. If the measure of ∠A is 20°, what is the measure of ∠B?
Answer
Option A is correct.
Angle B = 70°
Explanation
Complementary angles sum up to give 90°
If A and B are complementary angles, then,
A + B = 90°
20° + B = 90°
B = 90° - 20°
B = 70°
Hope this Helps!!!
The laminated block consists of a layer of wood between two layers of plastic. If each plastic layer is one-third as thick as the wooden layer, and the thickness of each layer is an integer, what is one possible height of a stack of such blocks? A. 18 B. 33 C. 42 D. 45
The possible height of a stack of such laminated blocks is 45
How to determine the possible height of the laminated blockinformation given in the question
each plastic layer is one-third as thick as the wooden layer
the thickness of each layer is an integer
The laminated block has three layers
2 plastic layers and one wooden layer
let the thickness of the plastic layer be x
such that the thickness of the wooden layer = 3x
the total thickness
= x + x + 3x
= 5x
for x to be an integer it is a multiple of 5. the only multiple of five in the options is D hence the answer
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This is a math problem that involves finding the height of a stack of laminated blocks. Let’s try to solve it together.
First, we need to find the thickness of each layer in a single block. Let x be the thickness of the wooden layer in centimeters. Then, each plastic layer is one-third as thick as the wooden layer, so it has a thickness of 3x centimeters. The total thickness of one block is the sum of the thicknesses of all three layers, which is x+3x+3x=35x centimeters.
Next, we need to find the number of blocks in a stack. Since the thickness of each layer is an integer, we can assume that the thickness of one block is also an integer. Therefore, we can divide the height of the stack by the thickness of one block to get the number of blocks. Let h be the height of the stack in centimeters, and n be the number of blocks. Then, we have n=35xh=5x3h.
Finally, we need to check which of the given options for h satisfies the condition that n is also an integer. We can do this by plugging in each value of h and simplifying the fraction 5x3h. If the fraction has no remainder, then n is an integer.
Option A: h=18. Then, 5x3h=5x3(18)=5x54. This fraction has a remainder of 4 when divided by 5, so n is not an integer.
Option B: h=33. Then, 5x3h=5x3(33)=5x99. This fraction has a remainder of 4 when divided by 5, so n is not an integer.
Option C: h=42. Then, 5x3h=5x3(42)=5x126. This fraction has no remainder when divided by 5, so n is an integer. For example, if x = 3, then n = 5(3)126=15126=8.4.
Option D: h=45. Then, 5x3h=5x3(45)=5x135. This fraction has no remainder when divided by 5, so n is an integer. For example, if x = 6, then n = 5(6)135=30135=4.5.
Therefore, one possible height of a stack of such blocks is 42 centimeters or 45 centimeters. Option C and option D are both correct answers.
Slove equation with variables on both sides4 - m = -1 + 4m
Which sum or difference is modeled by the algebra tiles?
The most appropriate choice of Quadratic equation will be given by
Second option is correct
What is quadratic equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A two degree equation is known as quadratic equation.
Here,
In the upper row, there are one tile of [tex]-x^2[/tex], two tiles of [tex]-x[/tex] and four tiles of 1
Required equation = [tex]-x^2[/tex][tex]-2x[/tex] + 4
In the lower row, there are one tile of [tex]-x^2[/tex], two tiles of [tex]-x[/tex] and 1 tiles of -1
Required equation = [tex]-x^2[/tex][tex]-2x[/tex] -1
( [tex]-x^2[/tex][tex]-2x[/tex] + 4) + ( [tex]-x^2[/tex][tex]-2x[/tex] -1) = [tex]-2x^2 -4x + 3[/tex]
Second option is correct
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee please
Answer:
Equation of the vertical asymptote is x = 0
Graph B is the correct graph
Step-by-step explanation:
The easiest way to answer this question would be to graph the function instead of attempting to solve for it algebraically which can also be done
The attached graph shows the function g(x) = -9/x
What is an asymptote?
In simple terms, an asymptote is a line that a curve approaches, as it heads towards infinity:
From the figure it is seen that the vertical asymptote occurs at x = 0 and the horizontal asymptote at y = 0
That's because at x = 0, the line almost touches but not quite the y-axis and is in a vertical direction both up and down
Help please my last tutor got it wrong thank you
In order to solve this, the first thing we have to do is to determine the value of g(-2), this is possible by evaluating -2 for x in g(x), like this:
g(-2) = 3(-2)²= 3×4 = 12
Now that we know the value of g(-2), we can determine the value of f(g(-2)) by evaluating g(-2) = 12 in f(x), like this:
f(g(-2)) = f(12) = 5(g(-2)) + 3 = 5(12) + 3 = 60 + 3 = 63
Then, f(g(-2)) = 63
In ADEF, the measure of ZF=90°, FE = 84, ED = 85, and DF = 13. What ratiorepresents the sine of ZE?
ANSWER:
[tex]\frac{13}{85}[/tex]STEP-BY-STEP EXPLANATION:
The first thing is to draw the triangle DEF
The sine of an angle is given as follows:
[tex]\begin{gathered} \sin \theta=\frac{\text{ opposite}}{\text{ hypotenuse}} \\ \text{ForA smaller number and a larger number add up to 8 and have a difference of 6. (Let X be the larger number and Y be the smaller number) A. 2x=8 x-y=6 B. 2x+2y=8 x-y=6 C. x+y=8 x-y=6D. x+y+8=0 x-y+6=0Which one is it A, B, C or D
Answer
Option C is correct.
x + y = 8
x - y = 6
Explanation
The larger number is x
The smaller number is y
The two numbers sum up to give 8
x + y = 8
The two numbers have a difference of 6
x - y = 6
Hope this Helps!!!
From the image sent, we can tell that the total ounces of solution is 28 ounces.
x + y = 28
Then, the second equation will be formed using the pure acid content
0.07x + 0.14y = 0.12 (28) = 3.36
So, the two equations are
x + y = 28
0.07x + 0.14y = 3.36
We can then solve this simultaneous equation and obtain that
x = 8 ounces, y = 20 ounces
Hope this Helps!!!
Dwayne stated that the slope of the line perpendicular to y = -2x is 2. Describe Dwayne's error.
The product of slople of two lines wchich are perpendicular to each other is negetive one.
The given expression of the line is,
[tex]y=-2x[/tex]The general expression for a stright line with slope 'm' is,
[tex]y=mx+c[/tex]Here, 'm' is the slope and 'c' is a constant.
Conparing the given equation of line with the general expression of a stright line,
[tex]m=-2[/tex]Thus, the slope of the given line is -2.
Let the slope of the perpendicular line to the given line be 'k'. Since the product of slope of perpendicular line is -1.
[tex]\begin{gathered} m\times k=-1 \\ k=\frac{-1}{k} \end{gathered}[/tex]Substitute value of m=-2 in the above expression.
[tex]\begin{gathered} k=\frac{-1}{-2} \\ k=\frac{1}{2} \end{gathered}[/tex]Thus, the slope of the perpendicular line is -1/2, and thus Dyne's statement is wrong.
The slope of the perpendicular line is -1/2, and the Dyne's statement is wrong.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
The given expression of the line; y = -2x
The general expression for a straight line with slope 'm' is;
y = mx + c
where 'm' is the slope and 'c' is a constant.
Therefore, the slope of the given line is; -2.
Assume the slope of the perpendicular line to the given line be 'k'. Since the product of slope of perpendicular line is -1.
m x k = -1
m = -1/k
Substitute value of m=-2 in the given expression.
k = 1/2
Hence, the slope of the perpendicular line is -1/2, and the Dyne's statement is wrong.
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. In a recent year, the U.S. Postal Service handled approximately 0.459 of the world's card and letter mail volume. Write this decimal as a percent.
The percentage of of the given decimal value is 45.9%
Decimal to PercentageTo solve this problem, we have to express the decimal value into a percentage and this can be done by simply multiplying the ratio of world's card to letter mail volume by 100.
To change a fraction to a percentage, you can divide the numerator by the denominator which will give us a decimal number then multiply the result by 100. Alternatively, you can multiply the numerator by 100 first then divide the result by the denominator of the fraction.
Mathematically, this can be achieved by
[tex]0.459 * 100[/tex]
Solving this, we would have
[tex]0.459 * 100 = 45.9\%[/tex]
The percentage of world's card to letter mail volume is 45.9%
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$55,000 at 16% compounded annually for 2 years.
Explanation:
The question wants us to find the amount that will be obtained when $55,000 at 16% is compounded annually for 2 years
To do so, we will use the formula below
[tex]\begin{gathered} A=P(1+\frac{r}{100})^t \\ \text{where} \\ r=16\text{ \%=0.16} \\ t=2 \\ P=55,000 \end{gathered}[/tex]Thus, we will have
[tex]\begin{gathered} A=55000(1+0.16)^2 \\ A=55000(1.16)^2 \\ A=55000\times1.3456 \\ A=74008 \end{gathered}[/tex]Thus, the amount will be $74,008
Remember, the equation to be solved is5x + 8 = 43. When the first step of subtractingeight is completed, what is the new equation thatresults?
Explanation
We are given the equation
[tex]5x+8=43[/tex]We are also asked to find the next step to be followed when the first step of subtracting eight is completed
To do so, the steps will be
Step 1: Subtract 8 from both sides
[tex]\begin{gathered} 5x+8-8=43-8 \\ 5x=35 \end{gathered}[/tex]The new equation will be
[tex]5x=35[/tex]Step 2: Divide both sides by the coefficient of x (5)
We will divide both sides by 5
[tex]\begin{gathered} \frac{5x}{5}=\frac{35}{5} \\ \\ x=7 \end{gathered}[/tex]Thus, the answer is 7.
QuestionThe graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation.Three normal distribution curves.A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is evenly spread out, curve Upper B is tall and the least spread out, and curve Upper C is short and more evenly spread out from the center.Select the correct answer below:ABC
Curve B normal distribution has the smallest standard deviation.
What is Normal Distribution?The normal distribution describes a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation
Given,
Three normal distribution curves.
A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C.
Curve Upper A is evenly spread out,
curve Upper B is tall and the least spread out,
and curve Upper C is short and more evenly spread out from the center.
We need to find which curve shows low standard deviation.
Among the three curves, curve B has less width. Hence standard deviation will be small for curve B.
Hence curve B normal distribution has the smallest standard deviation.
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help me please
thank you
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
What is science?
Tel in ditels
Answer:
Science is the systematic study of the structure and behavior of the physical and natural world through observation, experimentation,and the testing of theories against the evidence obtained
Which fraction that is not equivalent to the other fractions.
Simplify each fraction as follows:
[tex]\begin{gathered} \frac{4}{12}=\frac{4\times1}{4\times3}=\frac{1}{3} \\ \frac{2}{5}=\frac{2}{5} \\ \frac{3}{9}=\frac{3\times1}{3\times3}=\frac{1}{3} \\ \frac{1}{3}=\frac{1}{3} \end{gathered}[/tex]As seen above, the three fractions 4/12,3/9 and 1/3 are equivalent.
The fraction 2/5 is not equivalent to the other three.
Hence 2/5 does not belong and is not equivalent to the other three given fractions.
The population (in millions) of a certain country can be approximated by the function: P(x)=50*1.02^x where x is the number of years after 2000. Which of the following calculations will tell in what year the population can be expected to reach 100 million? a. ln(2/1.02)+2000 b. ln(2)/ln(1.02)+2000 c. ln(2/1.02) d. ln(2)/ln(1.02)
The calculation that tells us the year the population can be expected to reach 100 million is log 2/log 1.02 + 2000.
i.e
x = log 2/log 1.02 + 2000
Option B is the correct answer.
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
P(x) = 50 x [tex]1.02^x[/tex]
P(x) = Number of population in millions after x years
For 100 million populations we have,
100 = 50 x [tex]1.02^x[/tex]
Divide both sides by 50.
100/50 = [tex]1.02^x[/tex]
2 = [tex]1.02^x[/tex]
Putting log on both sides.
log 2 = x log 1.02
x = log 2 / log 1.02
Since x is the number of years after 2000 we have,
x = log 2/log 1.02 + 2000
Thus,
The calculation that tells us the year the population can be expected to reach 100 million is log 2/log 1.02 + 2000.
i.e
x = log 2/log 1.02 + 2000
Option B is the correct answer.
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Help needed! please help math
PLEASEEE!!!
t = 4.738 * 10³ would take the rocket to travel the speed.
What is speed, for instance?
Speed is a way to gauge how rapidly something is happening, moving, or moving swiftly. The speed of a car being driven at 45 mph serves as an illustration. A person cleaning a room in 10 minutes is an illustration of speed.Speed indicates how quickly something or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time.d = 1.701 * 10⁸
s= 3.59 * 10⁴
s = d/t
t = d/s
t = 1.701 * 10⁸/3.59 * 10⁴
t = 0.4738 * 10⁸⁻⁴
t = 0.4738 * 10⁴
t = 4.738 * 10³
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i need help i also put a screenshot
Answer:
6.2
Step-by-step explanation:
every minute 6.2 gallons fill into the pool.
Factor the polynomial if possible. If the expression cannot be factored enter
x^2 -19x + 88
Replace -19x by -8x -11x
x^2 -8x - 11x + 88
Common factor of both pairs:
x (x-8) - 11(x-8)
Write in factor form
(x-11) (x-8)
"The surface area of a sphere is 205 in^2. If its radius is tripled, what will be the new surface area of the sphere? " If you could help explain how to solve this that would be great! Thank you!
Question:
The surface area of a sphere is 205 in^2. If its radius is tripled, what will be the new surface area of the sphere?
Solution:
The surface area of a sphere is given by the following formula:
[tex]SA=4\pi r^2[/tex]where r is the radius of the sphere. Now, if the surface area of the sphere is 205 in^2, by the above equation we have that:
[tex]205=4\pi r^2[/tex]solving for r^2, we get:
[tex]r^2\text{ = }\frac{205}{4\pi}[/tex]and solving for r, we get:
[tex]r\text{ = }\sqrt[]{\frac{205}{4\pi}}\text{ = 4.03}[/tex]this means that the radius of the sphere with a surface area of 205 in^2 is 4.03. Then, if this radius is tripled, we get a new radius of
r = 3 x 4.03 = 12.09
then, replacing this new value in the first equation (surface area), we get:
[tex]SA=4\pi(12.09)^2\text{ = 1836.80}[/tex]Then, we can conclude that the correct answer is:
[tex]SA=\text{ 1836.80}[/tex]I need to solve for each part the part above the red line and the part under the red line please help QUICK
So upper most rectangle area is given as,
[tex]\begin{gathered} \text{A}_1=\text{ length}\times breadth\text{ } \\ \text{A}_1=\text{ 8}\times2 \\ \text{A}_1=16\text{ sq.ft.} \\ A_2=\text{ (8-3)}\times6 \\ \text{A}_2=5\times6 \\ \text{A}_2=30\text{ sq.ft.} \end{gathered}[/tex]Makhail currently has a balance of $5,400 in his bank account. this is 60% of the balance he had when he opened the account. How much money will be in his account when the balance is down to 35% of the balance he had when he opened the account?
Mikhail will have $2940 in his bank account when he has 35% balance left.
The difference between the amount of debit entries and the total of credit entries made into an account during a specific financial period is referred to as the "balance" in bookkeeping.
When total debits spent exceed total credits, the account displays a debit balance. When total credits surpass total debits, the account balance is displayed as a credit. If the debit and credit totals are equal, the balances are regarded as being eliminated. The term "balance" in an accounting period should represent the net worth of assets and liabilities so that the accounting equation's concept of equilibrium may be better understood.Let Mikhail has $x in his account.
Now 60% of x = 5400
or, 0.6x = 5040
or, x = $8400
When he has 35% he will have = 35% of 8400 = $2940
Hence he will have $2940 in his account.
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the question is in the pic! Also, you have to give the answer in simplified, decimalized, and percentaged form!!
The total number of pieces in the domino is 28.
a)
The number of pieces that have an odd number of dots is 12, so the probability of choosing a piece with an odd number of dots is:
[tex]P=\frac{12}{28}=\frac{3}{7}=\text{0}.4286=42.86\text{\%}[/tex]b)
The number of pieces that have 2 dots is 2, so:
[tex]P=\frac{2}{28}=\frac{1}{14}=0.0714=7.14\text{\%}[/tex]c)
The number of pieces that don't have 7 dots is 25, so:
[tex]P=\frac{25}{28}=0.8929=89.29\text{\%}[/tex]d)
The number of pieces that have at most 8 dots is 22, so:
[tex]P=\frac{22}{28}=\frac{11}{14}=0.7857=78.57\text{\%}[/tex]e)
The number of pieces that have more than 10 dots is 2, so:
[tex]P=\frac{2}{28}=\frac{1}{14}=0.0714=7.14\text{\%}[/tex]f)
The number of pieces that have a number of dots multiple of 4 is 7, so:
[tex]P=\frac{7}{28}=\frac{1}{4}=0.25=25\text{\%}[/tex]According to data released in 2016, 69% of students in the United States enroll in college directly after high school graduation. Suppose a sample of 178 recent high school graduates israndomly selected. After ventying the conditons for the Central Limit Theorem are met. find the probability that at most 67 % enrolled in college directiy after high school graduaton
Given
students enroll = 69%
n = 178
Find
probability that at most 67 % enrolled in college directiy after high school graduation
Explanation
Let p be the proportion of students in the united states enroll directly after high school graduation.
p = 69% = 0.69
q = 1 - p = 1 - 0.69 = 0.31
n = 178
we have to find
[tex]\begin{gathered} P(p\leq0.67)=P(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\leq\frac{0.67-0.69}{\sqrt{\frac{0.69\times0.31}{178}}}) \\ \\ P(p\leq0.67)=P(Z\leq-0.58) \\ P(p\leq0.67)=0.280 \end{gathered}[/tex]Final Answer
probability that at most 67 % enrolled in college directiy after high school graduation = 0.280
polynomials - mixed practicesimplify the polynomials write your answer in standard form please make the minimum of step thank you!
The given expression is
[tex](4x+1)(x+8)[/tex]We have to use the distributive property
[tex](4x+1)(x+8)=4x\cdot x+4x\cdot8+1\cdot x+1\cdot8=4x^2+32x+x+8[/tex]Then, we reduce like terms.
[tex]4x^2+33x+8[/tex]Hence, the final expression is[tex]4x^2+33x+8[/tex]Mr. Jones has a box of t-shirts to distribute to his students for Field Day. There are 30 red and 60 blue t- shirts in the box. If the first student chooses a t-shirt without looking , what is the probability that she will choose a blue t- shirt?
Given:
Number of blue t-shirst, B=60.
Number of red t-shirs, R=30.
The number of total t-shirts is,
[tex]\begin{gathered} T=B+R \\ T=60+30 \\ T=90 \end{gathered}[/tex]The probabilty of choosing a blue t-shirt is,
[tex]\begin{gathered} P(B)=\frac{B}{T} \\ =\frac{60}{90} \\ =\frac{2}{3} \end{gathered}[/tex]Therefore, the probabilty of choosing a blue t-shirt is 2/3.
2a² + b²-8a²
+ x²y - 3x + 9xy²
Answer:
mi madre va a entender eso
Decide whether there is enough information to prove that mln. If so, state the theroem you would use.#O No, there is not enough information.O Yes. Alternate Interior Angles ConverseO Yes. Alternate Exterior Angles ConverseOYes. Consecutive Interior Angles ConverseO Yes. Corresponding Angles Converse
Explanation
The converse of alternate interior angles theorem states that if two lines are intersected by a transversal forming congruent alternate interior angles, then the lines are parallel.
For the given question, we can then conclude that
Line m and n are parallel because of the Alternate Interior Angles Converse
Therefore, the answer is
