SOLUTION:
Case: Probability from a normal distribution
Given: Mean = 430, Standard deviation: 34
Required: To find the probability that the score of a randomly selected examinee is between 400 and 480
Method:
Steps
Step 1: Get the z-score with the lesser value:
[tex]undefined[/tex]Final answer:
Find the volume of a road construction marker, a cone with height 2 ft and base radius 1/5 ft. Use 3.14 as an approximation for π.The volume of the cone is __. (ft^2, ft^3, ft)(Simplify your answer. Type an integer or decimal rounded go the nearest hundredth as needed.)
Remember that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]we have
r=1/5 ft
pi=3.14
h=2 ft
substitute given values
[tex]\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot(\frac{1}{5})^2\cdot2 \\ V=0.08\text{ ft3} \end{gathered}[/tex]the answer is 0.08 ft^3is √4 a perfect square root
A perfect square is a value that has a whole number square root. So, if the square root of anumber gives a whole number then the square root is called a perfect square root. The square root of 4, √4 is 2 . 2 is a whole number. So,Its square root is a whole number. Thus, √4 is a perfect square root.
-7(x - 2) = 38 - 3x
We need to solve the following expression:
[tex]-7(x-2)=38-3x[/tex]The first step to solve this problem is to apply the distributive property on the left side of the equation. This is given by the sum of the products. We have:
[tex]\begin{gathered} -7x-2\cdot(-7)=38-3x \\ -7x+14=38-3x \end{gathered}[/tex]We need to change the terms that have "x" from the right to the left. To do that we need to add "3x" on both sides.
[tex]\begin{gathered} -7x+14+3x=38-3x+3x \\ -7x+3x+14=38 \\ -4x+14=38 \end{gathered}[/tex]Then we need to subtract "14" on both sides to isolate the term with x on the left. We have:
[tex]\begin{gathered} -4x+14-14=38-14 \\ -4x=24 \end{gathered}[/tex]Then we need to divide both sides by "-4".
[tex]\begin{gathered} \frac{-4x}{-4}=\frac{24}{-4} \\ x=-6 \end{gathered}[/tex]The value of "x" that solves this equation is -6.
Write an expression to represent the perimeter of the figure below: p=
Answer:
[tex]P=6x-8[/tex]
Step-by-step explanation:
Using the formula for the perimeter of a rectangle,
[tex]P=2(x+4+2x-8) \\ \\ =2(3x-4) \\ \\ =6x-8[/tex]
John has three parts that he mows each Park measures 2 and 1/2 miles by 2 3/4 miles how many square miles does he know in all
We will determine the number of square miles he mows as follows:
[tex]A=(2\frac{1}{2})(2\frac{3}{4})\Rightarrow A=(\frac{4}{2}+\frac{1}{2})(\frac{8}{4}+\frac{3}{4})[/tex][tex]\Rightarrow A=(\frac{5}{2})(\frac{11}{4})\Rightarrow A=\frac{55}{8}\Rightarrow A=6\frac{7}{8}\Rightarrow A=6.875[/tex]So, he mows 55/8 square miles for each park.
Given that sino =V48and cotê is negative, determine 0 and coté. Enter the angle O in degrees from the interval [0°, 360). Write the exact answer. Do not round.
In this problem
we have that
sin(theta) is positive and cos(theta) is negative
That means
the angle theta lies on the II quadrant
Remember that
[tex]\cot (\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]Find out the value of cos(theta)
[tex]\sin ^2(\theta)+\cos ^2(\theta)=1[/tex]substitute the given value
[tex](\frac{\sqrt[]{48}}{8})^2+\cos ^2(\theta)=1[/tex][tex]\cos ^2(\theta)=1-\frac{48}{64}[/tex][tex]\begin{gathered} \cos ^2(\theta)=\frac{16}{64} \\ \cos ^{}(\theta)=-\frac{4}{8} \end{gathered}[/tex]Find out the value of cot(theta)
substitute given values
[tex]\cot (\theta)=-\frac{4}{\sqrt[\square]{48}}[/tex]simplify
[tex]\cot (\theta)=-\frac{4}{\sqrt[\square]{48}}\cdot\frac{\sqrt[]{48}}{\sqrt[]{48}}=-\frac{4\sqrt[]{48}}{48}=-\frac{\sqrt[]{48}}{12}=-\frac{4\sqrt[]{3}}{12}=-\frac{\sqrt[]{3}}{3}[/tex]Find out the angle theta
using a calculator
angle in II quadrant
theta=120 degreesConvert to radians ---->Please provide the slope and the work showing how you got the slope for each equation please!
Slope for (16, -10) and (16, 15) is undefined, slope for (-19, -6) and (15, 16) is 11/17, slope for (19, -2) and (-11, 10) is -2/5, and slope for (12, -18) and (-15, 18) is -4/3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
For (16, -10) and (16, 15)
m=15-(-10)/16-16=15+10/0=25/0=undefined
For (-19, -6) and (15, 16)
m=16-(-6)/15-(-19)
=22/34=11/17
For (19, -2) and (-11, 10)
m=10-(-2)/-11-19
=10+2/-30
=-12/30=-2/5
For (12, -18) and (-15, 18)
m=18-(-18)/-15-12
=36/-27
=-12/9
=-4/3
Hence slope for (16, -10) and (16, 15) is undefined, slope for (-19, -6) and (15, 16) is 11/17, slope for (19, -2) and (-11, 10) is -2/5, and slope for (12, -18) and (-15, 18) is -4/3.
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What is the value of x if the acute angles of a right triangle measure 8xº and12xº? Remember the interior angles of a triangle measures 18. degrees. *4.59.527
We have a right triangle (one of its angle is a 90 degrees angle).
We know that
Sophie is going to drive from her house to City A without stopping. Let D represent Sophie's distance from City A t hours after leaving her house. The table below has select values showing the linear relationship between t and D. Determine the average speed that Sophie travels, in miles per hour.
Answer:
55 miles per hour.
Explanation:
To determine the average speed traveled by Sophie, we find the slope of the function given from the linear table.
[tex]\begin{gathered} \text{Slope}=\frac{82.5-165}{2.5-1} \\ =-\frac{82.5}{1.5} \\ =-55 \end{gathered}[/tex]What this means is that Sophie's distance from City A is reducing at a rate of 55 miles per hour.
Thus, the average speed that Sophie travels, is 55 miles per hour.
If angle A is a complement to angle B and the m
If Angle A is a complement to Angle B, then mIf we know the value of m[tex]\begin{gathered} m\measuredangle a+m\measuredangle b=90 \\ 31+m\measuredangle b=90 \\ m\measuredangle b=90-31 \\ m\measuredangle b=59 \end{gathered}[/tex]The measure of Angle B is 59°,
A circle has a diameter of 12 m. What is its circumference? Use 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer. Explanation Check 12 m 4
To find the circumference of a circle , we use the formula
[tex]C=\pi d[/tex]C = Circumference
d= diameter
[tex]\begin{gathered} C=3.14\times12 \\ C=37.68m^2 \end{gathered}[/tex]Write an equation in slope-intercept form of a line passingthrough the given point and parallel to the given line.3. (-3, -1);2y- 3x= 8
It's required to find the equation of a line that passes through (-3, -1) and is parallel to the line 2y - 3x = 8.
Solving for y:
[tex]y=\frac{3}{2}x+4[/tex]The slope of this line is 3/2 and the required line must have the same slope because they are parallel.
The point-slope form of a line passing through the point (h, k) and slope m is:
y = m(x - h) + k
Substituting:
[tex]\begin{gathered} y=\frac{3}{2}(x+3)-1 \\ Operate. \\ y=\frac{3}{2}x+\frac{9}{2}-1 \end{gathered}[/tex]Simplifying, the required line is:
[tex]y=\frac{3}{2}x+\frac{7}{2}[/tex]Suppose 18 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 85% a month. If the yard can only sustain 100 plants, use a logistic growth model to estimate the number of plants after 3 months.
Answer
The estimated number of plants after 3 months using the logistic model = 70 blackberry plants
Explanation
If a population is growing in a constrained environment with carrying capacity K, and absent constraint would grow exponentially with growth rate r, then the population behavior can be described by the logistic growth model:
[tex]P_n=P_{n-1}+r(1-\frac{P_{n-1}}{K})P_{n-1}[/tex]From the question,
[tex]\begin{gathered} P_0=18,r=85\%=0.85,K=100 \\ \\ So, \\ \\ P_n=P_{n-1}=+0.85(1-\frac{P_{n-1}}{100})P_{n-1} \end{gathered}[/tex]After the first month,
[tex]\begin{gathered} P_{n-1}=P_0=18 \\ \\ \therefore P_1=P_0+0.85(1-\frac{P_0}{100})P_0 \\ \\ P_1=18+0.85(1-\frac{18}{100})18 \\ \\ P_1=18+0.85(1-0.18)18=18+0.85\times0.82\times18 \\ \\ P_1=18+12.546 \\ \\ P_1=30.546\text{ }plants \end{gathered}[/tex]After the second month,
[tex]\begin{gathered} P_1=30.546 \\ \\ \therefore P_2=P_1+0.85(1-\frac{P_1}{100})P_1 \\ \\ P_2=30.546+0.85(1-\frac{30.546}{100})30.546 \\ \\ P_2=30.546+0.85(1-0.30546)30.546=30.546+0.85\times0.69454\times30.546 \\ \\ P_2=30.546+18.033 \\ \\ P_2=48.579\text{ }plants \end{gathered}[/tex]So after 3 months,
[tex]\begin{gathered} P_2=48.579 \\ \\ \therefore P_3=P_2+0.85(1-\frac{P_2}{100})P_2 \\ \\ P_3=48.579+0.85(1-\frac{48.579}{100})48.579 \\ \\ P_3=48.579+0.85(1-0.48579)48.579=48.5796+0.85\times0.5142\times48.579 \\ \\ P_3=48.579+21.232 \\ \\ P_3=69.811\text{ }plants \\ \\ P_3\approx70\text{ }blackberry\text{ }plants \end{gathered}[/tex]The estimated number of plants after 3 months using the logistic model = 70 blackberry plants.
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.Passing through (5,3) with x-intercept 6Write an equation for the line in point-slope form.
In general, the equations of a line in point-slope form and slope-intercept form are:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y=mx+b \end{gathered}[/tex]respectively. Where m is the slope of the line, b is a constant, and (x_1, y_1) is a point on the line.
Thus, the point-slope form of the line described by the problem is:
[tex]y-3=m(x-5)[/tex]We simply need to calculate the slope of the line. For that, we simply require 2 points, we already have (5, 3) and, since the x-intercept is 6, we can deduce that the line goes through (0,6).
Therefore, the slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-3}{0-5}=-\frac{3}{5}[/tex]Then, the solution is:
[tex]y-3=-\frac{3}{5}(x-5)[/tex]-121+17:[(93:3+3):2]x50=? 1) 2) 3) 4) 5) 6)
Write the standard form of the equation of the circle with the given center and radius.Center (−2,−5), r=6
Given, center of the circle (-2,-5)
The radius is r=6
Now the form of the equation of circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Thus,
[tex]\begin{gathered} (x-(-2))^2+(y-(-5))^2=6^2 \\ \Rightarrow(x+2)^2+(y+5)^2=36 \\ \Rightarrow x^2+4+4x+y^2+25+10y=36 \\ \Rightarrow x^2+y^2+4x+10y+29=36 \\ \Rightarrow x^2+y^2+4x+10y-7=0 \end{gathered}[/tex]The answer is
[tex]x^2+y^2+4x+10y-7=0[/tex]2) Write an equation of a line that is parallel to the line whose equation is 3y = x + 6 and that passes through the point (-3,4). Y-Y=m(x-x) y = mx + b ino
SOLUTION:
Step 1:
In this question, we are given the following:
Write an equation of a line that is parallel to the line whose equation is
[tex]\text{3 y = x + 6}[/tex]and that passes through the point (-3,4)
Step 2:
From the question, we can see that the given equation is given as:
[tex]\begin{gathered} 3\text{ y = x + 6} \\ \text{Divide both sides by 3, we have that:} \\ y\text{ = }\frac{1}{3}x\text{ + 2} \end{gathered}[/tex]Comparing this, with the equation of a line, we have that:
[tex]\begin{gathered} y\text{ = mx + c} \\ \text{Then, the gradient of line, m = }\frac{1}{3} \end{gathered}[/tex]Step 3:
Now, using the equation of a line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where (x }_1,y_1)\text{ = ( -3 , 4 )} \\ m\text{ = }\frac{1}{3} \end{gathered}[/tex][tex]\begin{gathered} y\text{ - }4\text{ = }\frac{1}{3}(\text{ x -- 3)} \\ y\text{ - 4 =}\frac{1}{3}(\text{ x+ 3)} \end{gathered}[/tex]Multiply through by 3, we have that:
[tex]\begin{gathered} \text{3 ( y - 4 ) = ( x + 3)} \\ 3y\text{ - 12 = x + 3} \\ \text{Hence, we have that:} \\ 3y\text{ = x + 3 +1 2} \\ 3\text{ y = x + 15} \end{gathered}[/tex]CONCLUSION:
The equation of the line that is parallel to the given line is:
[tex]3y\text{ = x + 15}[/tex]
What is the slope of (17, 11) (5, 0)
Solution
- The formula for the slope is given below:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ (x_1,y_2)\text{ and (}x_2,y_2)\text{ are the coordinates of the points given} \end{gathered}[/tex]- We have been given the points (17, 11) and (5, 0).
- Thus, we can proceed to find the slope as follows:
[tex]\begin{gathered} x_1=17,y_1=11 \\ x_2=5,y_2=0 \\ \\ \therefore m=\frac{0-11}{5-17}=-\frac{11}{-12} \\ \\ \therefore m=\frac{11}{12} \end{gathered}[/tex]Final Answer
The value for the slope is
[tex]\therefore m=\frac{11}{12}[/tex]I need help with this I was absent in school and the teacher won’t help me
Step-by-step explanation:
Given the equation
-45n + 45 = 90
Step 1: Isolate n
We can isolate n by subtracting 45 from both sides
-45n + 45 - 45 = 90 - 45
-45n + 0 = 45
-45n = 45
Divide through by -45
-45n/-45 = 45/-45
n = -1
Hence, the value of n is -1
the line on the coordinate plane makes an angle of depression 32 degrees
From the given figure
The angle is in the third quadrant
This means we must add 180 degrees to the given angle to get the true angle
Since 32 + 180 = 212,
Then look at the third row on the table to find the sine of the angle
sine the true angle is the number in the 3rd-row 1st column is -0.5299
The answer is B
b.
The slope of the line is
[tex]\begin{gathered} m=\tan (212) \\ m=0.6249 \end{gathered}[/tex]The slope of the line is 0.6249
|||RATIOS, PROPORTIONS, AND PERCENTSFinding the original amount given the result of a percentage...Va o- httpemployeesA company has been forced to reduce its number of employees. Today the company has 28% fewer employees than it did a year ago. If there are currently306 employees, how many employees did the company have a year ago?I need help with this math problem
The amount of employees on the previous year represents 100%. If today the company has 28% fewer employees, then the current amount of employees represents:
[tex]100\%-28\%=72\%[/tex]72% of the amount of employees of the previous year. Rewritting this percentage as a decimal, we have:
[tex]72\%=\frac{72}{100}=0.72[/tex]If we divide the current amount of employees by 0.72, we're going to find the original amount.
[tex]\frac{306}{0.72}=425[/tex]The company had 425 employees on the previous year.
Write the equation to solve and then find the measure of each acute angle(3x + 8° (2x + 12)°
We have here a right triangle, and that is why we have two acute angles (that is, the measure of each of them is less than 90 degrees).
We also know that the sum of the inner angles of a triangle is 180 degrees.
Having this information at hand, we can proceed as follows:
[tex](3x+8)+(2x+12)+90=180[/tex]This is the equation. Now, we need to solve this equation to find x, and then we need to use the algebraical equations to find each of the acute angles.
Solving the equation
1. Sum the like terms (like terms have the same variable or they are constants.)
[tex]3x+2x+8+12+90=180[/tex]Then, we have:
[tex]5x+110=180\Rightarrow5x=180-110\Rightarrow5x=70[/tex]2. We need to divide each side of the equation by 5 to isolate x:
[tex]\frac{5x}{5}=\frac{70}{5}\Rightarrow x=14[/tex]Now, we have x = 14. Therefore, the values for each of the acute angles are (we need to substitute the value of x in each equation):
a. 3x + 8 ---> 3 * (14) +8 = 42 + 8 =50. Hence, one acute angle measures 50 degrees.
b. 2x + 12 ---> 2 * (14) + 12 = 28 + 12 = 40 degrees. Therefore, the other acute angle measures 40 degrees.
In summary, the equation to solve is:
[tex](3x+8)+(2x+12)+90=180[/tex]And the values for each of the acute angles are 50 and 40 degrees.
Please help me with a question Rewrite the polar equation r=3sin(0) as a Cartesian equation.
Given,
The expression is,
[tex]r=3sin\theta[/tex]Required
The cartesian form of the given expression.
The cartesian form of the expression is,
Consider the function f(x) = 22 - 102 – 24. Given that one of the solutions of thefunction is r = -2 , what is the other solution of the function?
The initial function is:
[tex]f(x)=x^2-10x-24[/tex]And we know that one solution is r=-2
could someone help me with this math problem? thanks a lot if you do (:
We will have the following:
First, we determine the slope of the linear relationship:
[tex]m=\frac{320-380}{2.75-2.5}\Rightarrow m=-240[/tex]a) Now, using this information and one point (2.50, 380) we will replace in the general equation for a linear function, that is:
[tex]\begin{gathered} N(p)-y_1=m(p-x_1)\Rightarrow N(p)-380=-240(p-2.5) \\ \\ \Rightarrow N(p)-380=-240p+600 \\ \\ \Rightarrow N(p)=-240p+980 \end{gathered}[/tex]So, the equation is:
[tex]N(p)=-240p+980[/tex]b) We determine the revenue function as follows:
[tex]\begin{gathered} R(p)=pN(p)\Rightarrow R(p)=p(-240p+980) \\ \\ \Rightarrow R(p)=-240p^2+980p \end{gathered}[/tex]So, the equation of revenue is:
[tex]R(p)=-240p^2+980p[/tex]c) We determine the critical points of the revenue:
[tex]\begin{gathered} R^{\prime}(p)=-480p+980=0\Rightarrow480p=980 \\ \\ \Rightarrow p=\frac{49}{24}\Rightarrow p\approx2.04 \end{gathered}[/tex]So, the price that maximizes revenue is approximately $2.04.
The maximum revenue will be:
[tex]\begin{gathered} R(2.04)=-240(2.04)^2+980(2.04)\Rightarrow R(2.04)=1000.416... \\ \\ \Rightarrow R(2.04)\approx1000.42 \end{gathered}[/tex]So, the maximum revenue is approximately $1000.42.
Write a rule for the nth term of the geometric sequence given a_7=58, a_11=94
We are told the sequence is arithmetic. This means that the difference between one therm and the next is a constant.
We are also given two terms of the sequence. Let's see what their difference is
[tex]a_{11}-a_7=94-58=36[/tex]This means that, in general
[tex]a_{k+4}-a_k=36[/tex]With this, we can deduce that the difference between any two cnsecutive terms will be 9, for example
[tex]a_7=58,a_6=49,a_5=40,a_4=31,a_3=22[/tex]Indeed,
[tex]a_7-a_3=58-22=36[/tex]Now we should find the first term of the sequence, a₀, in order to find the rule for the nth term.
[tex]a_2=13,a_1=4,a_0=-5[/tex]In general, the rule for the nth term of an arithmetic sequence is given by
[tex]a_n=a_0+d(n)[/tex]where d is the difference between two consecutive term. In this case we have
[tex]a_n=-5+9\cdot n[/tex]with n=0,1,2,....
Which list includes the most important factors to consider when opening a savings account? O The fees, the interest rates, and the minimum deposit to open the account O The fees, the interest rates, and the bank's brand recognition O The fees, which bank your friend uses, and the minimum deposit to open the account O The fees, which bank your friend uses, and the bank's brand recognition
Answer:
The fees, the interest rates, and the minimum deposit to open the account
Answer: Based on the sales made by Micro Sales on bank credit cards, the journal entries would be:
Date Account Title Debit Credit
March 4 Cash $13,095
Card Service expense $ 405
Sales Revenue $13,500
How is the transaction by Micro Sales recorded?
The cash account will be debited with:
= 13,500 x (1 - 3%)
= $13,095
The Card service expense is:
= 13,500 x 3%
= $405
Sales revenue will be credited by the amount of sales which is $13,500.
Step-by-step explanation:
y=2/3x-2y=-x+3solve for x and y
EXPLANATION
Given the system of equations:
(1) y = 2x/3 - 2
(2) y = -x +3
Substitute y= -x+3
-x + 3 = 2x/3 - 2
Isolate x for -x+3 = 2x/3 - 2
Subtract 3 from both sides:
-x + 3 - 3 = 2x/3 -2 - 3
Simplify:
-x = 2x/3 -5
Subtract 2x/3 from both sides:
-x - 2x/3 = 2x/3 - 5 -2x/3
Simplify:
-5x/3 = -5
Multiply both sides by 3:
3(-5x/3) = 3(-5)
Simplify:
-5x = -15
Divide both sides by -5
-5x/-5 = -15/-5
Simplify:
x = 3
Then, for y = -x + 3
Substitute x = 3
y = -3 + 3
Simplify:
y = 0
The solutions to the system of equations are:
y = 0 , x = 3
the Venn diagram below models the possibility of three events a b and c the probabilities for each event or given by the ratio of the area of the event to the total area of 72 for example event C is read-only so for the probability that event C,you haveP(C)=area Red/total area =18/12×6=18/72=1/4=0.25are A&B dependent or independent events use conditional probability to support your conclusion
The events A and B are dependent events. This is because unlike the red area, event A means green given that blue has already occured. Event A includes blue and green and then event B includes green and yellow. Therefore event B cannot take place unless event A (which includes green area) has already taken place. Same goes for event A, it cannot take place unless event B has occured because the green area occurs in event B. Both events are dependent events. The result of one will influence the result of the other on.
**Event C is the only independent event**
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced. Assume that you take out a $3000 loan for 30 months at 9% APR. How much of the first month's payment is interest? (Round your answer to the nearest cent.)
Given parameters:
[tex]\begin{gathered} P=Loan\text{ amount=\$3000} \\ r=rate\text{ intersest per period=9\%=}\frac{9}{100\times12}=\frac{0.09}{12}=0.0075 \\ n=n\nu mber\text{ of payments=30 months} \\ \end{gathered}[/tex]We can now apply the formula below to calculate the payment amount per period
[tex]A=P\frac{r(1+r)^n}{(1+r)^n-1}[/tex][tex]\begin{gathered} A=3000\times\frac{0.0075(1+0.0075)^{30}}{(1+0.0075)^{30}-1} \\ \\ A=3000\times\frac{0.0075(1.25127)}{(1.25127)-1}=\frac{28.1536}{0.25127}=112.05 \end{gathered}[/tex]Thus his monthly payment will be $112.05
But since we have to get the interest on the first month's pay,
The interest is
[tex]r\times P=0.0075\times3000=\text{ \$22.5}[/tex]Thus, $22.50 is the interest on the first month's payment