Answer: f(3) = 0.84375
Step-by-step explanation:
f(3) is asking for the value of the function when x = 3, not multiplying f by 3. (f(x) is basically the output, y)
So we just plug in 3 for x and simplify (use PEMDAS)
f(3) = 2(0.75)^3
f(3) = 2(0.421875)
f(3) = 0.84375
Answer:
[tex]\frac{27}{32}[/tex]
Step-by-step explanation:
It may be a bit easier to represent 0.75 as a fraction, since we can use the following property of exponents: [tex](\frac{a}{b})^x = \frac{a^x}{b^x}[/tex]
We can represent 0.75 as: [tex]\frac{3}{4}[/tex]
And substituting this into the function we get: [tex]f(x)=2(\frac{3}{4})^x[/tex]
calculating the value when x=3, we get: [tex]f(3)=2(\frac{3}{4})^3[/tex]
using the property previously stated we get: [tex]f(3)=2(\frac{3^3}{4^3})[/tex]
Raising each value to the exponent we get: [tex]f(3)=2(\frac{27}{64})[/tex]
When we multiply by two, we can simplify by splitting up 64, into two factors: 2 and 32, to get: [tex]\frac{2*27}{32*2}[/tex]
From here it's easy to see that we can cancel out the values 2, to get: [tex]\frac{27}{32}[/tex]
Which is our answer!
Sketch a right triangle corresponding to the trigonometric function of the acute angle 8. Then find the exact values of the other five trigonometric functions of
Solution:
Given:
[tex]cot(\theta)=2[/tex]Using the trig ratio of cot;
[tex]\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ tan\theta=\frac{opposite}{adjacent} \\ Hence, \\ cot\theta=\frac{adjacent}{opposite} \\ cot\theta=\frac{2}{1} \\ adjacent=2 \\ opposite=1 \end{gathered}[/tex]The hypotenuse is gotten using the Pythagoras theorem;
[tex]\begin{gathered} h^2=2^2+1^2 \\ h^2=4+1 \\ h^2=5 \\ h=\sqrt{5} \end{gathered}[/tex]Thus, the sketch of the right triangle is;
[tex]\begin{gathered} Thus, \\ opposite=1 \\ adjacent=2 \\ hypotenuse=\sqrt{5} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} sin\theta=\frac{opposite}{hypotenuse} \\ sin\theta=\frac{1}{\sqrt{5}} \\ sin\theta=\frac{1}{\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}}{5} \\ sin\theta=\frac{\sqrt{5}}{5} \end{gathered}[/tex][tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ cos\theta=\frac{2}{\sqrt{5}} \\ cos\theta=\frac{2\sqrt{5}}{5} \end{gathered}[/tex][tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ tan\theta=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} csc\theta=\frac{1}{sin\theta} \\ csc\theta=\frac{1}{\frac{\sqrt{5}}{5}} \\ csc\theta=\sqrt{5} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta} \\ sec\theta=\frac{1}{\frac{2\sqrt{5}}{5}} \\ sec\theta=\frac{\sqrt{5}}{2} \end{gathered}[/tex]which candy is better to buy $4.12 for 4 bars of 7.14 for 7 bars?
Its better to buy second set of candy. That is, candy which is $7.14 for 7 bars.
Given,
The cost for first candy = $4.12 for 4 bars.
The cost for second candy = $7.14 for 7 bars.
We have to determine which candy is better to buy.
For that we have to find the cost of one candy.
That is,
The cost for one candy in first candy set = 4.12/4 = 1.03
The cost for one candy in second candy set = 7.14/7 = 1.02
Here,
1.02 is less than 1.03.
That is, second set of candy has lesser cost than first set.
So, its better to buy second set of candy. That is, candy which is $7.14 for 7 bars.
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what is the value of x in the equation negative x equals 2 - 3x + 6
Given the equation
-x = 2 -3x + 6
To solve this:
Step 1: collect like terms
-x + 3x = 2 + 6
2x = 8
Step 2: Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}\text{ =}\frac{8}{2} \\ \\ x=\text{ 4} \end{gathered}[/tex]The value of x = 4
The volume of a spherical balloon with radius 2.6 cm is about 74 cm3. Estimate the volume of a similar balloon with radius 10,4 cm,
To find the volume of a similar ballon with radius 10.4 cm, we will simply take the proportion
Let v be the volume of the similar ballon;
[tex]\frac{74}{v}=\frac{2.6}{10.4}[/tex]Cross -multiply
[tex]2.6v\text{ = 769.6}[/tex]Divide both-side by 2.6
[tex]v=296\operatorname{cm}^3[/tex]a certain linear function can be described by the equation below
We are given the information that the equation of the line is of the form:
y = a x + b
where a is a negative number and b is a positive number.
And we are asked to select among a number of options that represent the situation.
SInce b is a positive number (being "b" what is understood as the y-intercept) the line DOESN'T pass through the origing of coordinates. So the first option is discarded.
SInce "a"is a negative number (this is the so called "slope' of the line) the line must be slanted, and dropping from left to right Therefore option b is also discarded because that represents a line going up from left to right.
Option c is also discarded, because a is a negative number (not a zero) and lines parallel to the x axis have slope zero.
The last option is the correct one, since the intercept oo the y-axis is at a positive value for y, the line must be going down due to the negative slope, and therefore going across the II, I and IV quadrant as shown below: (give me a few minutes to draw a line with this characteristics)
Then, please mark the last option (d) as the correct answer.
List the improper fractions in order from greatest to least:9/7, 7/6, 17/14, 26/21
Answer:
[tex]\frac{9}{7},\frac{26}{21},\frac{17}{14},\frac{7}{6}[/tex]Explanation:
Given the improper fractions:
[tex]\frac{9}{7},\frac{7}{6},\frac{17}{14},\frac{26}{21}[/tex]In order to arrange the fractions, first, find the lowest common multiple of the denominators.
• LCM of 7, 6, 14, and 21 = 42
Next, rewrite each fraction as an equivalent fraction using the LCM as the new denominator.
[tex]\begin{gathered} \frac{9}{7}=\frac{9\times6}{7\times6}=\frac{54}{42} \\ \frac{7}{6}=\frac{7\times7}{6\times7}=\frac{49}{42} \\ \frac{17}{14}=\frac{17\times3}{14\times3}=\frac{51}{42} \\ \frac{26}{21}=\frac{26\times2}{21\times2}=\frac{52}{42} \end{gathered}[/tex]Since all the denominators are the same, order the numerators from the greatest to the least:
[tex]\begin{gathered} \frac{9}{7}=\frac{9\times6}{7\times6}=\frac{54}{42} \\ \frac{26}{21}=\frac{26\times2}{21\times2}=\frac{52}{42} \\ \frac{17}{14}=\frac{17\times3}{14\times3}=\frac{51}{42} \\ \frac{7}{6}=\frac{7\times7}{6\times7}=\frac{49}{42} \end{gathered}[/tex]Thus, the fractions ordered from greatest to least is:
[tex]\frac{9}{7},\frac{26}{21},\frac{17}{14},\frac{7}{6}[/tex]
Given m∥n, find the value of x
Answer:
x=55
Step-by-step explanation:
2x+6+x+9=180
3x=165
x=55
:]
Answer: x=55
Step-by-step explanation:
Since the lines are parallel, the two angles on the line are supplementary angles.
It means they would add to 180.
1) Set up the equation
(2x+6)+(x+9)=180
2) Combine like terms
3x+15 = 180
3) Move the 15 to the other side to leave x
3x = 180 - 15
3x = 165
4) Set x by itself
x = 165/3
x=55
"What happens if the slope is equal to zero? Provide an example of two points that would be on a line with a zero slope."
The line which is parallel to X-axis or which is drawn horizontally in the cartesian plane has its slope equal to zero.
As per the question statement, we are supposed to tell the significance of a zero sloped line. Before solving it, we need to know the formula for calculating the slope i.e., m = tanθ, where θ is the inclination angle of the line wrt X-axis.
Slope zero means m = 0 i.e., tanθ = 0 i.e., θ = 0 degrees
Hence a line having NO inclination or in simple words, is parallel to X-axis is known as a zero sloped line.
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The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.Is f one-to-one?
A function is called being one-to-one if, for every value of x, there is only one value of y and vice-versa.
If the graph of the function is given, a practical rule to determine if the function is one-to-one is to use the horizontal-line test.
This test is as follows: Imagine you have a horizontal line (maybe a ruler) and you can move it up and down the grid.
If your line touches the graph only once at every vertical position, then your function is one-to-one.
Now if we test our function drawn in blue, we can touch it only once as we move our line up and down, thus:
Is f one-to-one?
Yes
The table represents a quadratic function. Write an equation of the function in standard form.
x -3 -1 1 3
y 0 -12 -16 -12
y =
The standard form of the quadratic equation is given as follows:
y = x² - 2x - 15.
What is a quadratic equation?A quadratic equation is modeled according to the following rule:
y = ax² + bx + c.
From the given table, when x = -3, y = 0, hence the first equation is given by:
(-3)²a + (-3)b + c = 0
9a - 3b + c = 0.
When x = -1, y = -12, hence the second equation is given by:
-12 = a(-1)² + b(-1) + c
a - b + c = -12.
When x = 1, y = -16, hence the third equation is given by:
-16 = a(1)² + b(1) + c
a + b + c = -16.
Then the system of equations to find the coefficients is given as follows:
9a - 3b + c = 0.a - b + c = -12.a + b + c = -16.Using a calculator, the solution to the system is:
a = 1, b = -2, c = -15.
Hence the equation is given by:
y = x² - 2x - 15.
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I'll give you brainliest if it's right =D
Which equation shows a proportional relationship between x and y?
A) y = 12x + 1
B) y = 3.5x
C) y = 2
D) y=−4x−6
Answer:
C.
Step-by-step explanation:
The relationship is proportion if y/x is constant.
So it is C because 12/4 = 15/5 = 18/6 = 3.
The figure below is a parallelogram. Find RQ.-1+4xPeO 15O 1004O 123x+3SR
We have a parallelogram and we have to find the length of side RQ.
Opposite sides of a parallelogram besides being parallel, they also have the same length.
Then, we can write:
[tex]PS=QR[/tex]We can use that to find the value of x as:
[tex]\begin{gathered} PS=QR \\ -1+4x=3x+3 \\ 4x-3x=3+1 \\ x=4 \end{gathered}[/tex]Knowing x = 4, we can find RQ as:
[tex]QR=3x+3=3(4)+3=12+3=15[/tex]Answer: QR = 15
In ΔJKL, \overline{JL} JL is extended through point L to point M, \text{m}\angle KLM =(7x+3)^{\circ}m∠KLM(7x+3) ∘,\text{m}\angle LJK = (2x+12)^{\circ}m∠LJK=(2x+12)∘,and \text{m}\angle JKL = (3x+7)^{\circ}m∠JKL=(3x+7) ∘.Find \text{m}\angle LJK.m∠LJK.
Applying the exterior angle theorem, the measure of angle LJK is: 28°.
What is the Exterior Angle Theorem?Where an external angle is formed by an extended side of a triangle, its measure is equal to the two remote angles of the triangle, according to the exterior angle theorem.
Given the following:
m∠KLM = (7x + 3)°m∠LJK = (2x + 12)°m∠JKL = (3x + 7)°Angles LJK and JKL are remote angles of the triangle which are opposite the exterior angle KLM.
Therefore:
m∠LJK + m∠JKL = m∠KLM
Substitute
2x + 12 + 3x + 7 = 7x + 3
Combine like terms and find the value of x:
5x + 19 = 7x + 3
5x - 7x = -19 + 3
-2x = -16
-2x/-2 = -16/-2
x = 8
Find
m∠LJK = 2x + 12
Plug in the value of x:
m∠LJK = 2(8) + 12
m∠LJK = 28°
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What is the sign of -2 to the power of 49
Answer:
negative
Step-by-step explanation:
-2 to the power of odd numbers is negative
to the power of even numbers is positive
Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer.
1. Angle j and k
j || k is a result of the Converse of Corresponding Angles Postulate.
2. The alternating inner angles of the lines j and k are angles 2 and 5. If angle 2 = angle 5, then
Alternate Interior Angles in Reverse According to the theorem, j || k.
Alternate interior angles are conversed by J and K.
How do parallel angles work?
3. Similarly Angle 3 equals Angle 10.
Angle 3 and Angle 10 are the exterior angles of the lines l and m, respectively. Angle 3 equals angle 10 according to the Converse of Alternate Exterior Angles Theorem, therefore l || m.
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Line j has an equation of y=–
9
7
x+
10
7
. Line k is parallel to line j and passes through (–
4,4). What is the equation of line k?
The equation of the line k parallel to line j and passes through (-4, 4) is
y = - 9 / 7 x - 8 / 7
How to find equation of a line?Equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line k is parallel to the line j, y = - 9 / 7 x + 10 / 7 and passes through (-4, 4),
Parallel lines have the same slope.
Hence, let's find the y-intercept of the equation k using (-4, 4)
4 = - 9 / 7 (-4) + b
4 - 36 / 7 = b
b = - 8 / 7
Therefore,
the equation is y = - 9 / 7 x - 8 / 7
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Fill in the blank so that the resulting statement is true.To divide x³+4x²-3x+6 by x-2 using synthetic division, the first step is to write
Answer:
Explanation:
Given the polynomial:
[tex]x^3+4x^2-3x+6[/tex]To divide the polynomial by the linear function x-2 using synthetic division, first, set the linear function equal to 0 and solve for x:
[tex]x-2=0\implies x=2[/tex]The result is written outside the line as shown below:
Next, write the coefficients of the polynomial inside as shown above:
Question 10(Multiple Choice Worth 1 points)
(08.01 LC)
Susan wants to conduct a survey to find how much time the students of her school spent eating in a local cafeteria. Which of the following is an appropriate statistical question for this survey?
Who eats at the cafeteria on weekends?
How many students eat in the cafeteria on Mondays?
How many students eat in the cafeteria once a week?
How many hours during the week do you eat in the cafeteria?
Answer:
How many hours during the week do you eat in the cafeteria?
Step-by-step explanation:
since susan wants to find out how much time they are spending, the appropriate question would be the one asking about how many hours (time) they spend in the cafeteria
A nurse is given instructions to give a nitroglycerin drip at 10 mcg/minute. The nitroglycerin is mixed at 50 mg per 500 mL. The flow rate needs to be in mL/hr. Complete parts a through c.
a) What is the dosage in milligrams per minute (mg/min)?
b) What is the dosage in milligrams per hour, mg/hr?
c) How many milliliters per hour, ml/hr, should be administered?
The Dosage in milligrams per min, mg/min : 0.01mg / min
The Dosage in milligrams per hour, mg/hr : 0.6mg/hr
The dosage available in milliliters per hour, ml/hr: 6ml/hr
What is Dosage ?
A dosage is a predetermined amount of a drug, food, or pathogen that is administered as a single unit. The dose increases with the amount administered. In medicine, doses are most frequently calculated for substances.
Given,
Dose(mcg) = 10mcg/min
Dose available = 50mg
Volume of dose available = 500ml
a) The dosage in milligram per minute will be:
= 10mcg / 1000mcg
= 0.01mg / min
b) The dosage in milligrams per hour, mg/hr :
= 10mcg x 60min / 1000mcg
= 0.6mg/hr
c) By dosage formula we can write:
= OxV / A
Where,
O = Dose ordered
V = Volume of dose available
A = Dose available
So that we know,
Dose ordered (mg) = 0.6 mg
Volume of dose available (mL) = 500 mL
Dose available (mg) = 50 mg
= 0.6 x 500 / 50
= 6ml/hr
Hence,
The Dosage in milligrams per min, mg/min : 0.01mg / min
The dosage in milligrams per hour, mg/hr : 0.6mg/hr
The dosage available in milliliters per hour, ml/hr: 6ml/hr
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What is the slope of a line perpendicular to the
line whose equation is 6x - 9y = 216. Fully
simplify your answer.
Answer:
Slope is 2/3
Step-by-step explanation:
Ghost, Inc., has no debt outstanding and a total market value of $395,600. Earnings before interest and taxes, EBIT, are projected to be $53,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 13 percent higher. If there is a recession, then EBIT will be 22 percent lower. The company is considering a $195,000 debt issue with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 8,600 shares outstanding. The company has a tax rate of 21 percent, a market-to-book ratio of 1.0, and the stock price remains constant. Calculate earnings per share (EPS) under each of the three economic scenarios before any debt is issued.
a-1.
Calculate earnings per share (EPS) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
a-2. Calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1. Calculate earnings per share (EPS) under each of the three economic scenarios assuming the company goes through with recapitalization. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
b-2. Given the recapitalization, calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
EPS for recession is $3.7975, EPS for normal is $4.8686, EPS for expansion is $5.5015, and Percentage change in EPS for expansion is 13% and for recession is -22%, EPS under each of the three scenarios after recapitalization is 4360 and percentage change in EPS after the recapitalization is -31.17% and 18.42% for recession and expansion respectively.
A-1) Calculation of EPS under each scenario:
EBIT for expansion condition,
= EBIT × 113%
= $53,000 × 113%
= $59,890
EBIT for recession conditions,
= EBIT × 78%
= $53,000 × 78%
= $41,340
Tax = EBT × 21%
Net income = EBT - Taxes
EPS = Net income ÷ No. of shares
EPS for recession = $3.7975
EPS for normal = $4.8686
EPS for expansion = $5.5015
A-2) Calculation of Percentage change in EPS,
For Expansion = (Expansion EPS - Normal EPS) ÷ Normal EPS
= (5.05 - 4.86) ÷ 4.86
= 13%
For Recession = (Recession EPS - Recession EPS) ÷ Recession EPS
= (4.86 - 3.79) ÷ 4.86
= -22%
B-1) Calculation of EPS under each of the three scenarios after recapitalization,
Market to Book ratio (l) = Market value ÷ Book value
l = $395,600 ÷ Book Value
Book Value = $395,600
Stock Price = Book Value ÷ No. of outstanding shares
= $395600 ÷ 8,600
= 46
No. of shares repurchased = Debt ÷ Stock Price
= $195,000 ÷ 46
= 4240
No. of shares after repurchasing = No. of outstanding shares - No. of shares repurchased
= 8,600 - 4240
= 4360
B-2) Calculating percentage change in EPS after recapitalization,
For Recession = (Recession EPS - Recession EPS) ÷ Recession EPS
= (4.66 - 6.77) ÷ 6.77
= -31.17%
For Expansion = (Expansion EPS - Normal EPS) ÷ Normal EPS
= (8.02 - 6.77) ÷ 6.77
= 18.42%
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In the diagram below, assume that all points are given in polar coordinates. Determine the rectangular coordinates for each point. Visually check your answers to ensure they make sense.(r,θ)=(6.9,0.7) corresponds to (x,y)=(r,θ)=(7.2,1.5) corresponds to (x,y)=(r,θ)=(8,3.4) corresponds to (x,y)= (r,θ)=(4.7,3π/2) corresponds to (x,y)=
use the equation 1/4+s=18/20 pls help
The value of (s) that satisfy the given equation → 1/4+s=18/20 is 0.65.
What is equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. There are different types of equation such as - Linear Equations, Radical Equations, Exponential Equations, Rational Equations etc.
Given is the following equation written in variable (s)
1/4 + s = 18/20
We have -
1/4 + s = 18/20
We will solve the given expression using the transpose method -
1/4 + s = 18/20
Shifting (s) to the left hand side and constant numbers to right hand side, and then solving for (s), we get -
s = 18/20 - 1/4
s = 9/10 - 1/4
s = 0.9 - 0.25
s = 0.65
The value of s will be 0.65
Therefore, the value of (s) that satisfy the given equation → 1/4+s=18/20 is 0.65.
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Rewrite the expression as an equivalent exponential expression with a positive exponent.
you can do this I know you can !!!!!
5.8. The lifetime in hours of an electronic tube is a random variable having a probability density function given by
f(x)= xe^-x. x>-0
The lifetime in hours of an electronic tube will be of 2 hours.
A probability density function, also known as the density of a continuous random variable, is a function used in probability theory whose value at any given sample (or point) in the sample space can be interpreted as giving a relative likelihood that the random variable's value would be close to that sample. While the absolute likelihood of a continuous random variable taking on any given value is 0, probability density (PDF) at two different samples can be used to infer, in any given draw of the random variable, how much more likely it would be that the random variable would be close to one sample compared to the other sample.
We have,
f(x) = xe^(-x) x>0
= 0 o.w.
Consider,
[tex]E(X) = \int\limits^a_0 {xf} (x)\, dx \\\\E(X) = \int\limits^a_0 {xxe}^{-x} \, dx \\\\E(X) = \int\limits^a_0 {x}^{2}e^{-x} \, dx \\\\E(X) = \int\limits^a_0 {x}^{b-1}e^{-mx} \, dx = \frac{n}{m^{n} } \\\\= 2! = 2[/tex]
Therefore, a tube of this type should last for 2 hours.
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Batman’s age is 12 less than triple Robin’s age. When you add Batman’s age to Robin’s age, you get 68. How old is Batman and how old is Robin? Show work. Handwritten. Complete Sentence.
Answer: Mr. Bond is gonna be mad at youuuuuuuuuuu.
Step-by-step explanation: But I think Batman is like 40 and robin's like 18. I had problems with this too and I can't rlly give u proof rn. Good luck with the unit testtt.
Name the number of degrees in the monomial.8abcd
Given: 8abcd
The number of degrees is the sum of the exponent of each variable in the monomial
The answer is 4
Which of the following is a solution of the inequality h + 9 < 20?
Answer:
h < 11
Step-by-step explanation:
Thats what i get when i work it out lol
can you show me step by step on how to answer this problem 11/5 + 23/10 = ?
Answer: 45/10
Explanation:
We want to add
11/5 + 23/10
The first step is to find the lowest common multiple, LCM of the denominators. The LCM of 5 and 10 is 10. We would divide the LCM by each denominator and multiply each numerator by the results. The common denominator of the final fraction would be the LCM. We have
For the first fraction,
10/5 = 2
2 x 11 = 22
For the second fraction,
10/10 = 1
1 x 23 = 23
Thus, the final fraction would be
(22 + 23)/10
= 45/10
Given the sequence -7, -3, 1, 5,What is the explicit formula to represent this sequence?A. a^n= 4n-7B. a^n= -7n+4C. a^n= 5-7nD. a^n= 4n-11
The given sequence is
[tex]-7,-3,1,5[/tex]To find the explicit formula, first, we have to find the difference by subtracting two consecutive terms.
[tex]-3-(-7)=-3+7=4[/tex]As you can observe, the difference is 4.
[tex]d=4[/tex]From the sequence, we observe that the first term is -7.
[tex]a_1=-7[/tex]The formula for arithmetic sequences is
[tex]a_n=a_1+(n-1)d[/tex]Now, let's replace the values we've got.
[tex]a_n=-7+(n-1)\cdot4[/tex]Then, we simplify.
[tex]\begin{gathered} a_n=-7+4n-4 \\ a_n=4n-11 \end{gathered}[/tex]Therefore, the right answer is D.