P(z < -2.08) = 0.018763
Explanations:From the standard normal distribution table, we can check the probability given any z-score
Therefore, checking P(z < -2.08) from the standard normal distribution:
P(z < -2.08) = 0.018763
Let x equals negative 16 times pi over 3 periodPart A: Determine the reference angle of x. (4 points)Part B: Find the exact values of sin x, tan x, and sec x in simplest form. (6 points)
The reference angle of x is -60 degree. The exact values of sin x, tan x, and sec x is [tex]$\sin \left(-60^{\circ}\right)=-\frac{\sqrt{3}}{2}$[/tex], [tex]$\tan \left(-60^{\circ}\right)=-\sqrt{3}$[/tex], [tex]$\sec \left(-60^{\circ}\right)=2$[/tex]
[tex]x=-\frac{16 \times 180}{3}$$[/tex]
Multiply the numbers: [tex]$16 \times 180=2880$[/tex]
[tex]$x=-\frac{2880}{3}$[/tex]
Divide the numbers: [tex]$\frac{2880}{3}=960$[/tex]
x=-960
Or, x = 2 [tex]\times[/tex] 360 - 960
Follow the PEMDAS order of operations
Multiply and divide (left to right) 2 [tex]\times[/tex]360 : 720 =720-960
Add and subtract (left to right) 720-960: -240
x= -240
Reference angle =180-240
Reference angle= -60
Sin (-60 degree)= [tex]$\sin \left(-60^{\circ}\right)=-\frac{\sqrt{3}}{2}$[/tex]
[tex]$\tan \left(-60^{\circ}\right)=-\sqrt{3}$[/tex]
[tex]$\sec \left(-60^{\circ}\right)=2$[/tex]
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find slope -1,4 3,15
Answer:11/4
Step-by-step explanation: First you put the points in m=x1-x2/y1-y2
m=15-4/3+1=15
Round to the nearest tenths 62.32
Answer:62.3
Step-by-step explanation:
What is the first point you would graph the function 3x+1/2y=2
First, let's clear y to get the slope-intercept form:
[tex]\begin{gathered} 3x+\frac{1}{2}y=2 \\ \\ \rightarrow6x+y=4 \\ \Rightarrow y=-6x+4 \end{gathered}[/tex]This way, we can conclude that the y-intercept is 4. This is the first point we have to graph:
[tex](0,4)[/tex]solve P=2M+2M for G
G=?
G=P-2M/2
Step-by-step explanation:
P=2G+2M
p - 2M = 2G
G=P - 2M/2
Alpha Industries is considering a project with an initial cost of $7.9 million. The project will produce cash inflows of $1.63 million per year for 7 years. The project has the same risk as the firm. The firm has a pretax cost of debt of 5.58 percent and a cost of equity of 11.25 percent. The debt-equity ratio is .59 and the tax rate is 21 percent. What is the net present value of the project?
The net present value of the project of the company Alpha Industries is $494,918.
Given,
The initial cost of the project = $7.9 million
Cost of debt = 5.58 percent
Cost of equity = 11.25 percent
The debt-equity ratio= .59
Tax rate = 40 percent.
Let us assume
Equity be $x, then
Total = $1.59x
Respective weights = Pretax cost of debt × (1 - tax rate)
=5.58% × (1 - 0.4)
Respective weights = 3.348%
WACC = Respective costs × Respective weights
WACC = (x ÷ 1.59x × 11.25%) + (0.59x ÷ 1.59x × 3.348)
WACC = 8.318%
The present value of annuity = Annuity × (1 - (1 + interest rate)^ - time period] ÷ Rate
=1.63 × [1 - (1.08317811321)^-7]÷ 0.08317811321
= $1.63 × 5.150256501
The present value of annuity = $8,394,918.10
The net present value = The present value of cash inflows - The present value of cash outflows
= $8,394,918.10 - $7,900,000
The net present value of the the project = $494,918
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Simplify 2f+ 6f help me pls
Answer:
[tex]{ \tt{ = 2f + 6f}}[/tex]
- Factorise out f as the common factor;
[tex]{ \tt{ = f(2 + 6)}} \\ = 8f[/tex]
whats an inequality to compare the numbers
11 and -9
The inequality comparison
What is Inequality?
Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.
Given, numbers are
11 and -9
an inequality to show all numbers: from (11) to (–9) inclusive
-9 ≤ x ≤ 11
Hence, inequality to compare the numbers
11 and -9 is -9 ≤ x ≤ 11
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find the surface area of the triangular prism 7 6 7 9
The surface area of the triangular prism will be 217.95 cm²
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
It is given that,
Base side, a = 7 sm
Base side, b = 6 cm
Base side, c = 7 cm
Height, h = 9 cm
The surface area of a triangle prism: The formula for a triangular prism's surface area is,
A=bh+(b₁+b₂+b₃) units²
where b is the base of a triangular face, h is the height of a triangular face, b₁ is the side of the triangular base, b₂ is the side of the triangular base, and l is the prism's length.
The surface area of the triangular prism will be,
[tex]\rm A = ah + bh + ch + \dfrca{1}{2} \sqrt{-a^4 +2(ab)^2 +2(ac)^2 -b^4+2(bc)^2 -c^4}[/tex]
Substitute the given values,
[tex]\rm A = 7 \times 9 + 6 \times 9 + 7 \times 9 + \dfrac{1}{2} \times \sqrt{-7^4 + 2(7 \times 6)^2 +2 (7\times 7)^2 -6^4 + 2(6 \times 7)^2 - 7^4} \\\\ A = 217.94 \ cm^2[/tex]
Thus, the surface area of the triangular prism will be 217.95 cm².
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can you check to see if my work is correct?
The Solution.
[tex]P=-\frac{1}{250}T^2+2.8T-394[/tex]To obtain the maximum value of T, we differentiate with respect to x and equate to zero.
[tex]\begin{gathered} \frac{dP}{dT}=2(-\frac{1}{250}T)+2.8\text{ =0} \\ \\ -\frac{1}{125}T+2.8=0 \\ \\ -\frac{T}{125}=-2.8 \\ \text{Cross multiplying, we get} \\ T=125\times2.8=350^oF \end{gathered}[/tex]To get the maximum value of P, we shall substitute 350 for T in the given function.
[tex]\begin{gathered} P=-\frac{1}{250}(350^2)+2.8(350)-394 \\ \\ P=-490+980-394 \\ P=96\text{ percent} \end{gathered}[/tex]The correct answer is T = 350 degrees Fahrenheit , and P = 96 percent.
Work out the following sums and write the answers correctly.
a) £1.76 + £2.04
b) £5.62 + £2.38
Answer of a is €3.8
Answer of b is €8
Solution :
To get the answer add two decimal number
ie. the sum of first question is €1.76 + €2.04 = €3.8
the sum of second question is €5.62 + €2.38 = €8
Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined.Addends are the numbers added, and the result or the final answer we get after the process is called the sum.To learn more about Addition refer :
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The sum of a number and 4 times it’s reciprocal is 13/3. Find the number(s).
Let the unknown number be "x"
We will write an algebraic equation from the word problem given. Then we will solve for "x".
Given,
Sum of number (x) and 4 times the reciprocal is 13/3
We can convert it into an algebraic equation:
[tex]x+(4\times\frac{1}{x})=\frac{13}{3}[/tex]Now, let's solve for the unknow, x,
[tex]\begin{gathered} x+(4\times\frac{1}{x})=\frac{13}{3} \\ x+\frac{4}{x}=\frac{13}{3} \\ \frac{x^2+4}{x}=\frac{13}{3} \\ 3(x^2+4)=13\times x \\ 3x^2+12=13x \\ 3x^2-13x+12=0 \\ (x-3)(x-\frac{4}{3})=0 \\ x=3 \\ x=\frac{4}{3} \end{gathered}[/tex]The numbers are
[tex]\begin{gathered} 3 \\ \text{and} \\ \frac{4}{3} \end{gathered}[/tex]Please helpp..Use the simple interest formula to determine the missing value.
p=$951.63, r= 6.5%, t= ?, i = $123.71
t=years
Using the simple interest formula, the value of time (t) is 103 years.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest. Ordinary simple interest and exact simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest. The simple interest calculation formula is the same for both approaches.So, the simple interest rate formula:
A = P (1 + rt)We need to find the value of time (t), then the formula will become:
t = (1/r)(A/P - 1)Insert the values as follows:
t = (1/6.5)(951.63/123.71) - 1)t = 102.96Rounding off: t = 103 years
Therefore, using the simple interest formula, the value of time (t) is 103 years.
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6. Takao scores a 90, an 84, and an 89 on three out of four math tests. Whatmust Takao score on the fourth test to have an 87 average (mean)?a. 87b. 88c. 85d. 84e. 86
Consider x as Takao's fourth score.
Then, to achieve an 87 average, we have:
[tex]\begin{gathered} 87=\frac{90+84+89+x}{4} \\ x+263=4\cdot87 \\ x=348-263 \\ x=85 \end{gathered}[/tex]Answer:
c. 85
Circle O shown below has an are of length 47 inches subtended by an angle of 102°.Find the length of the radius, x, to the nearest tenth of an inch.
We will have the following:
[tex]\begin{gathered} 47=\frac{102}{360}\ast2\pi(x)\Rightarrow\pi(x)=\frac{1410}{17} \\ \\ \Rightarrow x=\frac{1410}{17\pi}\Rightarrow x\approx26.4 \end{gathered}[/tex]So, the radius is approximately 26.4 inches.
-5 ( -10-2(-3)) to the 2nd power . numerical exponents
The value of -5 ( -10-2(-3)) to the 2nd power is -6480.
What is an exponent?It should be noted that an exponent simply means the number through which another number can be multiplied by itself.
Based on the information given, it should be noted that PEDMAS will be used. This implies:
P = parentheses
E = Exponents
D = division
M = multiplication
A = addition
S = subtraction
-5 ( -10-2(-3)² will be illustrated thus:
It's important to calculate the value in the parentheses first according to PEDMAS.
= -5 [(-12(-3)]²
= -5 (36)²
= -5 × 1296
= -6480
The value is -6480.
In this case, the concept of PEDMAS is used to get the value.
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find the volume of a conebase diameter of 10 ydheight 6 ydsuse the value 3.14 for pie
Given
The formula
[tex]\begin{gathered} \text{The volume of a cone =}\frac{1}{3}\pi r^2h \\ \\ \pi=3.14 \\ r=5 \\ h=6 \end{gathered}[/tex][tex]\begin{gathered} \text{The volume of a cone =}\frac{1}{3}\pi r^2h \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times5^2\times6 \\ \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times25^{}\times6 \\ \\ \text{The volume of a cone =}\frac{1}{3}\times3.14\times150 \\ \\ \text{The volume of a cone =}3.14\times50 \\ \\ \text{The volume of a cone =}157yd^3 \end{gathered}[/tex]The final answer
[tex]\text{The volume of a cone =}157yd^3[/tex]Two people start walking at the same time in the same direction. One person walks at 2 mph and the other person walks at 6 mph. In how many hours will they be 2 mile(s) apart?
Let's define the following variable:
t = number of hours for them to be 2 miles apart
Distance covered by Person A after "t"hours would be 2t or 2 miles times "t" hours.
Distance covered by Person B after "t" hours would be 6t or 6 miles times "t" hours.
If the distance of Person A and B is 2 miles apart after "t" hours, we can say that:
[tex]\begin{gathered} \text{Person B}-PersonA=2miles \\ 6t-2t=2miles\text{ } \end{gathered}[/tex]From that equation, we can solve for t.
[tex]\begin{gathered} 6t-2t=2miles\text{ } \\ 4t=2miles\text{ } \\ \text{Divide both sides by 4.} \\ t=0.5hrs \end{gathered}[/tex]Therefore, at t = 0.5 hours or 30 minutes, the two persons 2 miles apart.
At 0.5 hours, Person A will
Translate PreImage coordinates left 9 units and down 1 unit.
Given
A(11,9)
B(11,3)
C(5,3)
D(5,9)
In the coordinate system (x,y), x determines the horizontal position, and y determines the vertical position. Having a translation of 9 units left, and 1 unit down, means that each coordinate system will be translated as (x-9 , y-1).
[tex]\begin{gathered} (x,y)\Longrightarrow(x-9,y-1) \\ \\ A(11,9)\Longrightarrow A^{\prime}(11-9,9-1)\Rightarrow A^{\prime}(2,8) \\ B(11,3)\operatorname{\Longrightarrow}B^{\prime}(11-9,3-1)\operatorname{\Rightarrow}B^{\prime}(2,2) \\ C(5,3)\operatorname{\Longrightarrow}C^{\prime}(5-9,3-1)\operatorname{\Rightarrow}C^{\prime}(-4,2) \\ D(5,9)\operatorname{\Longrightarrow}D^{\prime}(5-9,9-1)\operatorname{\Rightarrow}D^{\prime}(-4,8) \end{gathered}[/tex]Therefore, the coordinates of the post image are A'(2,8), B'(2,2), C'(-4,2), D'(-4,8).
The probability that an individual is left-handed is 12%, In a randomly selected class of 30students, what is the probability of finding exactly 4 left-handed students?
Given that:
- The probability that an individual is left-handed is 12%.
- There are 30 students in the class.
You need to use this Binomial Distribution Formula, in order to find the probability of finding exactly 4 left-handed students :
[tex]P(x)=\frac{n!}{(n-x)!x!}p^x(1-p)^{n-x}[/tex]Where "n" is the number being sampled, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.
In this case:
[tex]\begin{gathered} n=30 \\ x=4 \\ p=\frac{12}{100}=0.12 \end{gathered}[/tex]Therefore, by substituting values into the formula and evaluating, you get:
[tex]P(x=4)=\frac{30!}{(30-4)!4!}(0.12)^4(1-0.12)^{30-4}[/tex][tex]P(x=4)\approx0.2047[/tex]Hence, the answer is:
[tex]P(x=4)\approx0.2047[/tex]How many solutions does the system have? 2x + 3y = -6 3a - 4y = -12 no solutions O exactly one solution O infinitely many solutions
Therefore, it has exactly one solution.
Finding the vertex focus directrix and axis of symmetry of a parabola
Equation:
[tex](y+1)^2=6(x-5)[/tex]The vertex is given by the following formula:
[tex](y-k)^2=4p(x-h)[/tex]where the vertex is (h, k). Thus, in our equation k = -1 and h = 5, and the vertex
is (5, -1).
Additionally, the focus is given by (h+p, k). In our case:
[tex]p=\frac{6}{4}=\frac{3}{2}[/tex]Then, the focus is:
[tex](5+\frac{3}{2},-1)[/tex]Simplifying:
[tex](\frac{13}{2},-1)[/tex]The directrix is x = h - p:
[tex]x=5-\frac{3}{2}=\frac{7}{2}[/tex]Finally, the axis of symmetry is y = -1.
ahmed want to make a triangle, he has rods that measure 9 inch and 15 inches. the rods cannot be cut. which is the length of a rod he could use to complete the triangle?
The length of the rod that he could use to complete the triangle is 12 inches. This is solved based on the principle of Pythagorean Triples.
What are the Principles of Pythagorean Triples?Pythagorean triples are a collection of three positive numbers that fit into the Pythagorean theorem formula, which is written as a² + b² = c², where a, b, and c are positive integers. In this case, 'c' is the 'hypotenuse,' or the triangle's longest side, while 'a' and 'b' are the other two legs of the right-angled triangle.
Pythagorean triples are denoted as (a,b, c). The most well-known Pythagorean triple example is (3, 4, 5). We can see that the numbers 3, 4, and 5 meet the equation a² + b² = c².
To prove that the length of the rod that should be used to complete the triangle is 12. Let's subject the values to the Principles of Pythagorean Triples.
Given:
9,
let's assume that 15 is the longest side.
Thus,
If we are correct,
9² + 12² should equal 15²
9² = 81
12² = 144
15² = 225
81 + 144 =225
Hence the length of the rod that must be used to complete the triangle is 12 inches.
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A money market account offers 1.25% interest compounded monthly. If you want to save $500 in two years, how much money would you need to save per month?
If you want to save $500 in two years, you need to save $20.58 per month with a 1.25% interest compounded monthly.
How is the periodic saving determined?The monthly savings can be determined using an online finance calculator as follows:
N (# of periods) = 24 months (2 x 12)
I/Y (Interest per year) = 1.25%
PV (Present Value) = $0
FV (Future Value) = $500
Results:
Monthly Savings = $20.58
Sum of all periodic savings = $494.04
Total Interest = $5.96
Thus, the investor needs to save $500 in two years to save $20.58 monthly.
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Murray has tossed a coin 120 times. The coin landed on heads 54 times. What is the experimental probability that the coin will land on heads on the next toss?
Answer:
Explanation:
Experimental probability = number of favorable outcomes/number of total outcomes
From the information given,
number of favorable outcomes = 54
number of total outcomes = 120
The experimental probability that the coin will land on heads on the next toss = 54/120
Dividing the numerator and denominator by 6,
The experimental probability that the coin will land on heads on the next toss = 9/20
The length of a rectangle is 5yd less than twice the width, and the area of the rectangle is 33yd^. Find the dimensions of the rectangle.
Let l be the length of the rectangle and w its width.
From this, we have:
I) w - l = 5
II) l*w = 33
From I, we have w = 5 + l
Applying this to equation II, we have: l(5+l) = 33
l^2 + 5l - 33 = 0
The positive root of this equation is l = [sqrt(157) - 5]/2 = 3.8 yd (rounded to the nearest tenth)
Applying this to equation I, we have: w - 3.8 = 5, which implies w = 5 + 3.8 = 8.8 yd
which integer could represent the fact that the water level of a pool decreases by 4 feet
-4
1) In this question, there's not much information so let's think of a rule
2) We can sketch this out:
We could even write a function that describes this, which "W" stands for Water Level and "t":
3) So if the level of water is decreasing by 4 feet each and every water level from now on is negative.
How can I solve this equation if x = -2 and y = -3? 3y (x + x² - y) I've also included a picture of the equation.
In order to calculate the value of the equation, let's first use the values of x = -2 and y = -3 in the equation and then calculate every operation:
[tex]\begin{gathered} 3y(x+x^2-y) \\ =3\cdot(-3)\cdot(-2+(-2)^2-(-3)) \\ =-9(-2+4+3) \\ =-9\cdot5 \\ =-45 \end{gathered}[/tex]Therefore the final result is -45.
What is the product in simplest form? State any restrictions on the variable9X^2+9X+18)/(X+2) TIMES (x^2-3x-10)/(x^2+2x-24)
So, here we have the following expression:
[tex]\frac{9x^2+9x+18}{x+2}\cdot\frac{x^2-3x-10}{x^2+2x-24}[/tex]The first thing we need to notice before simplifying, is that the denominator can't be zero.
As you can see,
[tex]\begin{gathered} x+2\ne0\to x\ne-2 \\ x^2+2x-24\ne0\to(x+6)(x-4)\ne0\to\begin{cases}x\ne-6 \\ x\ne4\end{cases} \end{gathered}[/tex]These are the restrictions on the given variable.
Now, we could start simplyfing factoring each term:
[tex]\begin{gathered} \frac{9x^2+9x+18}{x+2}\cdot\frac{x^2-3x-10}{x^2+2x-24},x\ne\mleft\lbrace2,4,-6\mright\rbrace \\ \\ \frac{9(x^2+x+2)}{x+2}\cdot\frac{(x-5)(x+2)}{(x+6)(x-4)},x\ne\lbrace2,4,-6\rbrace \end{gathered}[/tex]This is,
[tex]9(x^2+x+2)\cdot\frac{(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]So, the answer is:
[tex]\frac{9(x^2+x+2)(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]It could be also written as:
[tex]\frac{(9x^2+9x+18)(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]Round the decimal number to the nearest thousandth.
11.59978
Answer:
Step-by-step explanation:
