Step-by-step explanation:
1.
[tex] \tan \beta = \frac{1}{ \cot \beta } = - \frac{3}{2 \sqrt{10} } = - \frac{3 \sqrt{10} }{20} [/tex]
[tex] \csc \beta \tan \beta = \frac{1}{ \cos \beta } = \sec \beta [/tex]
Therefore,
[tex] \sec \beta = ( \frac{7}{3} )( - \frac{3 \sqrt{10} }{20} ) = - \frac{7 \sqrt{10} }{20} [/tex]
2.
[tex] \csc y = \frac{1}{ \sin y} = - \frac{ \sqrt{6} }{2} [/tex]
[tex] = > \sin y = - \frac{ \sqrt{6} }{3} [/tex]
Use the identity
[tex] \cos y = \sqrt{1 - \sin ^{2} y} \: \: \: \: \: \: \: \: \: \: \: \\ = \sqrt{1 - {( - \frac{ \sqrt{6} }{3}) }^{2} } = - \frac{ \sqrt{3} }{3} [/tex]
We chose the negative value of the cosine because of the condition where cot y > 0. Otherwise, choosing the positive root will yield a negative cotangent value. Now that we know the sine and cosine of y, we can now solve for the tangent:
[tex]\tan \beta = \frac{ \sin y}{ \cos y} =( - \frac{ \sqrt{6} }{3} )( - \frac{3}{ \sqrt{3} } ) = \sqrt{2} [/tex]
3. Recall that sec x = 1/cos x, therefore cos x = 5/6. Solving for sin x,
[tex] \sin x = \sqrt{1 - \cos ^{2} x} = \sqrt{ \frac{11}{6} } [/tex]
Solving for tan x:
[tex] \tan x = \frac{ \sin x}{ \cos x} = (\frac{ \sqrt{11} }{ \sqrt{6} } )( \frac{6}{5} ) = \frac{ \sqrt{66} }{5} [/tex]
The linear function graphed below represents Brenda’s monthly cell phone bill based on the number of hours she uses. What is her hourly rate?
Answer:
You didn't attach an image, can't exactly help. sorry!
A bowl has the shape of a hemisphere whose diameter is 14 centimeters. If this bowl is filled with water, how many cubic centimeters will it take to fill the bowl
Answer:
The cubic centimeters of water it will take to fill the bowl is 718.67 cm³
Step-by-step explanation:
Given;
diameter of the hemisphere, d = 14 cm
radius of the hemisphere, r = d/2 = 14/2 = 7 cm
The volume of the hemisphere is calculated as;
[tex]V = \frac{2}{3} \pi r^3\\\\V = \frac{2}{3} \times \frac{22}{7} \times (7 \ cm)^3\\\\V = 718.67 \ cm^3[/tex]
The cubic centimeters of water it will take to fill the bowl is 718.67 cm³
What is the value of log27 165
The solution of the logarithmic function log₂₇165 found using logarithmic properties is :
(1 + log ₃55)/3.
What is a logarithmic function?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. The usage of logarithmic functions makes it simple to determine some of the non-integral exponent values. The common logarithmic function, which has a base of 10, is identified by the symbols log₁₀ or log.
We are asked to solve the following logarithmic function.
log₂₇165
Here the base of the log is 27.
According to logarithmic properties, we can write the above functions as:
log₂₇165 = log 165 / log 27
If we are dividing the numerator and denominator by log 3, then the new base will become 3.
(log 165 / log 3) / (log 27/log3) = log ₃165 / log₃ 27
Now we can solve as follows,
log ₃165 / log₃ 27 = log ₃(3*55) / log₃ (3³) = [log ₃(3)+log ₃(55)] / 3log₃3
= (1 + log ₃55)/3
Therefore the solution of the logarithmic function log₂₇165 is
(1 + log ₃55)/3.
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Find the Value of x from the angles
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]
The value of [tex]x°[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION :}}}[/tex]
[tex]\longrightarrow{\blue{ x°\:=\:35° }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ [tex]x°[/tex] + 125° + 20° = 180°
➪ [tex]x°[/tex] + 145° = 180°
➪ [tex]x°[/tex] = 180° - 145°
➪ [tex]x°[/tex] = 35°
Therefore, the value of [tex]x°[/tex] is 35°.
Now, the three angles of the triangle are 35°, 125° and 20°.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY:}}}[/tex]
✒ 35° + 125° + 20° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
Hence verified.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
show how to solve 1/4 (4 + x) = 4/3
pls solve for 2 brainliest
In a political science class, the teacher gives a midterm exam and a final. The association between midterm and final scores is linear. The summary statistics are shown below. Midterm Mean=75, Midterm Standard Deviation=10 Final Mean=75, Final Standard Deviation=10 r=0.8 According to the regression equation, for a student who gets 85 on the midterm (one standard deviation above average) what is the predicted final exam grade?
Answer:
The predicted final exam grade is 83
Step-by-step explanation:
Given
[tex]\bar x = 75[/tex] -- midterm mean
[tex]\sigma_x = 10[/tex] --- midterm standard deviation
[tex]\mu =75[/tex] --- final mean
[tex]\sigma = 10[/tex] --- final standard deviation
[tex]r = 0.8[/tex]
Required
The predicted final grade of student who score 85 in midterm
The prediction is represented as:
[tex]y = \alpha + \beta x[/tex]
Where:
[tex]\beta = r * \frac{\sigma}{\sigma_x}[/tex]
[tex]\beta = 0.8 * \frac{10}{10}[/tex]
[tex]\beta = 0.8 * 1[/tex]
[tex]\beta = 0.8[/tex]
and
[tex]\alpha = \mu - r * \bar x[/tex]
[tex]\alpha = 75- 0.8 * 75[/tex]
[tex]\alpha = 75- 60[/tex]
[tex]\alpha = 15[/tex]
So:
[tex]y = \alpha + \beta x[/tex]
[tex]y = 15 + 0.8x[/tex]
For a student who gets 85, the prediction is:
[tex]y = 15 + 0.8*85[/tex]
[tex]y = 15 + 68[/tex]
[tex]y = 83[/tex]
Really struggling and stressing out. Anyone mind helping?
Answer:
it should be 314.16, so I would choose 314
4x-2 3x+14 how do I find x?
Answer:
x = 16
Step-by-step explanation:
4x - 2 = 3x + 14
4x - 2 + 2 = 3x + 14 + 2
4x = 3x + 16
4x - 3x = 3x - 3x + 16
x = 16
Please can someone answer quickly
Which graph matches the equation y+3=2(x+3)?
A (0,3) (-3,-3)
B (0,6) (-3,0)
C (0,-3) (-3,-9)
D (3,3) (0,-3)
Answer:
A (0,3) (-3,-3)
Step-by-step explanation:
A graph will match the equation if both the coordinates points replaced in the equation generate a identity.
When x = -3
[tex]y + 3 = 2(x + 3)[/tex]
[tex]y + 3 = 2(-3 + 3)[/tex]
[tex]y + 3 = 0[/tex]
[tex]y = -3[/tex]
So (-3,-3) is part of the graph.
When x = 0
[tex]y + 3 = 2(x + 3)[/tex]
[tex]y + 3 = 2(0 + 3)[/tex]
[tex]y + 3 = 6[/tex]
[tex]y = 3[/tex]
So (0,3) is part of the solution.
(-3,-3) and (0,3), so option A.
Find the future value for a $100,000 investment for 12 years at a compounded continuously at 2.1%?
Answer:
128659.6037
Step-by-step explanation:
contiously compounding interest formula:
PV(e^(i*t))
100000e^(.021*12)=128659.6037
Can anyone help me solve this
[tex]\longrightarrow{\green{ D. \:3 {a}^{4} \sqrt{2a} }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \sqrt{18 {a}^{9} } \\ \\ ➝ \: \sqrt{2 \times 3 \times 3 \times {a}^{9} } \\ \\ ➝ \: \sqrt{2 \times ({3})^{2} \times {( {a}^{4}) }^{2} a } \\ \\ [∵( { {a}^{4} )}^{2} a = {a}^{4 \times 2 + 1} = {a}^{9}] \\ \\ ➝ \: 3 \times {a}^{4} \sqrt{2a} \\ \\ ➝ \: 3 {a}^{4} \sqrt{2a} [/tex]
[tex]\pink{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
Answer:
The answer is [tex]3a^{4}\sqrt{2a}[/tex]
Step-by-step explanation:
To simplify the radical, start by factoring 9 out of 18 for step 1. Next, for step 2, rewrite 9 as [tex]3^{2}[/tex]. Then, factor out [tex]a^{8}[/tex] for step 3. For step 4, rewrite [tex]a^{8}[/tex] as [tex](a^{4})^{2}[/tex]. Then, for step 5, move the 2 in the radical. Rewrite [tex]3^{2}(a^{4})^{2}[/tex]as [tex](3a^{4})^{2}[/tex] for step 6. Then, add parentheses to the radical for step 7. Finally, for step 8 pull the terms out from under the radical, and the answer is [tex]3a^{4}\sqrt{2a}[/tex].
Step 1: [tex]\sqrt{9(2)a^{9} }[/tex]
Step 2: [tex]\sqrt{3^{2}*2a^{9}[/tex]
Step 3: [tex]\sqrt{3^{2}*2(a^{8}a) }[/tex]
Step 4: [tex]\sqrt{3^{2}*2((a^{4})^{2}) }[/tex]
Step 5: [tex]\sqrt{3^{2}(a^{4})^{2}*2a }[/tex]
Step 6: [tex]\sqrt{(3a^{4} )^{2}*2a }[/tex]
Step 7: [tex]\sqrt{(3a^{4})^{2}*(2a) }[/tex]
Step 8: [tex]3a^{4}\sqrt{2a}[/tex]
Find the radius of the circle whose equation is (x - 2)2 + (y - 4)2 = 9.
Hope this help!!!
Have a great day!!!
A laptop company claims up to 8.1 hours of wireless web usage for its newest laptop battery life. However, reviews on this laptop shows many complaints about low battery life. A survey on battery life reported by customers shows that it follows a normal distribution with mean 7.5 hours and standard deviation 27 minutes. (a) What is the probability that the battery life is at least 8.1 hours
Answer:
0.0918 = 9.18% probability that the battery life is at least 8.1 hours.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 7.5 hours
This means that [tex]\mu = 7.5[/tex]
Standard deviation 27 minutes.
An hour has 60 minutes, which means that [tex]\sigma = \frac{27}{60} = 0.45[/tex]
What is the probability that the battery life is at least 8.1 hours?
This is 1 subtracted by the p-value of Z when X = 8.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8.1 - 7.5}{0.45}[/tex]
[tex]Z = 1.33[/tex]
[tex]Z = 1.33[/tex] has a p-value of 0.9082.
1 - 0.9082 = 0.0918
0.0918 = 9.18% probability that the battery life is at least 8.1 hours.
A rectangular piece of plywood 7.00 ft by 10.00 ft is cut from one comer to an opposite comer. What are the angles between the edges of the resulting pieces? Include
all resulting angles
The angle(s) is/are degrees
(Round to the nearest tenth as needed. Use a comma to separate answers as needed. Do not include the degree symbol in your answer. Type each answer only
once.)
Answer:
Step-by-step explanation:
let one angle=a°
second angle=(90-a)°
tan a=7/10=0.7
a=tan^{-1}(0.7)≈35.0°
other angle=90-35=55.0°
Find the inner product for (4,8) (6,-3) and state whether the vectors are perpendicular.
Answer:
[tex] = \binom{4}{8} . \binom{6}{ - 3} \\ = (4 \times 6) + (8 \times - 3) \\ 24 + ( - 24) \\ = 0 \\ since \: inner \: product \: is \: zero : \\ the \: vectors \: are \: perpendicular[/tex]
Answer:
0
The vectors are perpendicular
Step-by-step explanation:
(4,8) (6,-3)
The inner product is also known as the dot product
4*6 + 8*-3 = 24-24 = 0
The vectors are perpendicular since the dot product is zero
Suppose that for a certain company C(x)=35x+300,000 represents the total cost function, and R(x)=75x represents the total revenue function. Find the total-profit function and break-even point.
Which of the following functions represents the total-profit function?
A) 40x-300,000
B) 40x+300,000
C) 110x+300,000
Answer:
40x - 300,000
7,500
Step-by-step explanation:
profit = revenue - cost
p(x) = 75x - (35x + 300,000)
p(x) = 40x - 300,000
Break even is when profit is zero
40x - 300,000 = 0
40x = 300,000
x = 7,500
The functions that represents the total-profit function would be p(x) = 40x - 300,000. so the correct option is A.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Given that for a certain company C(x) =35x+300,000 represents; the total cost function, and R(x)=75x represents the total revenue function.
WE can calculate the profit by the following formula;
Profit = revenue - cost
p(x) = 75x - (35x + 300,000)
p(x) = 40x - 300,000
Now Break even is when profit is zero,
40x - 300,000 = 0
40x = 300,000
x = 7,500
Hence, the break-even point is 7500.
Therefore, the functions that represents the total-profit function would be p(x) = 40x - 300,000. so the correct option is A.
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the place value of 4 in 56437 is:
Answer:
thousands
Step-by-step explanation:
56437
tents hundreds thousands
what is the domain of the function in this table?
Answer:
there is no table appearing so unfortunately no one can answer this for you. sorry!!
There are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 28 seats on the 2nd row, 31 seats on the third row, and so on. How many seats are in the last row?
Answer:
It is a sequence topic.
The general term of the sequence is 25+3(n-1) where n is the number of the term (here it is the row no.)
So the 20th term is the term with n=20. Substitute n=20 into the above general term, we will get 25+3(20-1) .
Please go on by yourself to work out the answer.
D(p) is the price, in dollars per unit, that consumers are willing to pay for p units of an item, and S(p) is the price, in dollars per unit, that producers are willing to accept for p units. Find the equilibrium point. D(p)=3500−20p, S(p)=2500+5p
What are the coordinates of the equilibrium point?
Answer:
(40,2700)
Step-by-step explanation:
Given
[tex]D(p)=3500-20p[/tex]
[tex]S(p)=2500+5p[/tex]
Required
The equilibrium point
To do this, we have:
[tex]D(p) = S(p)[/tex]
So, we have:
[tex]2500+5p = 3500-20p[/tex]
Collect like terms
[tex]20p+5p = 3500-2500[/tex]
[tex]25p = 1000[/tex]
Divide both sides by 25
[tex]p = 40[/tex]
Substitute [tex]p = 40[/tex] in [tex]D(p)=3500-20p[/tex]
[tex]D(40) = 3500 - 20 * 40[/tex]
[tex]D(40) = 2700[/tex]
Hence, the coordinates of the equilibrium is: (40,2700)
Find the exact value of the following.
Find -xy, for x = -75.9 and y = 2.6.
-xy =
Answer:
197.34
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
x = -75.9
y = 2.6
-xy
Step 2: Evaluate
Substitute in variables: -(-75.9)(2.6)Multiply: (75.9)(2.6)Multiply: 197.34Fill in the blank with the correct fraction. Make sure to express your answer in its simplest, most reduced form.
Answer:
3/4
Step-by-step explanation:
as 1 hour is 60 minutes, to express in fraction form, we have to divide.
so
45/60 can be simplified to 3/ 4 when 15 is taken out as common of both. so the answer is 3/4
Answer:
3/4
Step-by-step explanation:
1 hour= 60 minutes
45/60
simplify the fraction by dividing the numerator and denominator by 5
45÷5=9 and 60÷5=12
new fraction =9/12
simplify 9/12 by dividing the numerator and denominator by 3
9÷3=3 and 12÷3=4
Ans.=3/4
45 minutes is 3/4 of an hour
5. In the figure Find X (In the picture) (giving points to best answer/brainlest)
Answer:
x = 93
Step-by-step explanation:
*for angle labels, see picture below
Using angle addition postulate, we can say that angle EAC is the sum of angle CAB and angle BAE:
m<EAC = m<CAB + m<BAE
m<EAC = x + 39
Since line l and m are parallel, you can say that angle ACD is an alternate interior angle to angle EAC. This means they are equal.
Now, we can write an equation to solve for x:
m<EAC = m<ACD
x + 39 = 132
x = 93
Answer:
x=93°
Step-by-step explanation:
If l ıı m
l=180° ; 132°+?(y) =180° (Co-interior angle)
Find the value of y
132°+y=180°(Transpose)
y=180°-132°
y=48°
...
Find x
39°+x+48°=180°(Transpose)
x=180°-48°-39°
x=93°
If the price of ice cream changes by 30 percent and the quantity demanded changes by 75 percent, what is the absolute value of demand elasticity?
which fraction does not belong? 2\3. 6\9. 4\6 6\8
Answer:
6/8
hope this helps
have a good day :)
Step-by-step explanation:
What steps do i have to take to get the proven
Answer:
I can't really see I wish I can help
The symbols for elements with accepted names Group of answer choices consist of a single capital letter consist of a capital letter and a small letter consist of either a single capital letter or a capital letter and a small letter no answer is correct
Answer:
consist of either a single capital letter or a capital letter and a small letter.
Step-by-step explanation:
A chemical reaction can be defined as a reaction in which two or more atoms of a chemical element react to form a chemical compound.
In Chemistry, a chemical element can be defined as any pure substance that is typically made up of only atoms and cannot be broken down into simpler substances through chemical processes. Thus, the atomic number (the number of protons in the nuclei of an atom) of a particular chemical element distinguishes from other chemical elements.
Generally, all chemical elements are denoted or represented by a symbol, which may either be single capital letter or a capital letter and a small letter.
This ultimately implies that, the symbols for elements with accepted names consist of either a single capital letter or a capital letter and a small letter. For example, the symbol for sodium is Na, copper is Cu, carbon is C, oxygen is O, iron is Fe, nitrogen is N, magnesium is Mg, potassium is K, argon is Ag, hydrogen is H, helium is He, phosphorus is P, etc.
how to find the area of a circle with the diameter 21
Answer:
A ≈ 346.36
Step-by-step explanation:
To find the answer, you must use the formula, A=πr²
Since only the diameter was provided, you need to divide it by 2 to find the radius. 21 divided by 2 equals 10.5, so that will be your radius.
Another formula that can be used while using only the diameter would be A= 1/4 π d²
ow many three-letter "words" can be made from 8 letters "FGHIJKLM" if repetition of letters
Answer:
336
Step-by-step explanation:
A total of 512 possible words can be made.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a 8 letters word "FGHIJKLM"
Assume that there are [y] possible combinations. Then, the total number of [x] digit words that can be made are -
y = 8ˣ
y = 8ˣ
y = 8 x 8 x 8
y = 512
Therefore, a total of 512 possible words can be made.
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