Answers
We will have the following:
First, we calculate AE as follows:
[tex]AE=\sqrt[]{AM^2-EM^2}[/tex]Now, we replace values and solve it:
[tex]AE=\sqrt[]{16^2-11^2}\Rightarrow AE=3\sqrt[]{15}[/tex]From theorem AE = EC therefore EC = esqrt(15); so, the following is true:
[tex]AC=AE+EC\Rightarrow AC=2AE\Rightarrow AC=2(3\sqrt[]{15})\Rightarrow AC=6\sqrt[]{15}[/tex]Knowing this, we then determine FA as follows:
[tex]FA=\sqrt[]{AC^2-CF^2}[/tex]We then determine BE, DM & CM as follows:
Related Questions
i need help with this. for 2nd option, select only one sub-option
Answers
A matrix being in row echelon form means that Gaussian elimination has operated on the rows.
A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions:
- It is in row echelon form.
-The leading entry in each nonzero row is a 1 (called a leading 1).
-Each column containing a leading 1 has zeros in all its other entries.
The matrix presented on the problem satisfies all conditions, therefore, the matrix is indeed in reduced row-echelon form.
Solve the system using algebraic methods.
y = x² + 4x
y = 2x² + 3x - 6
Solution x =
Answers
Two or more expressions with an Equal sign is called as Equation. x is -6 and 7 for equations y = x² + 4x and y = 2x² + 3x - 6
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given two equations are
y = x² + 4x
y = 2x² + 3x - 6
Let us simplify these equations as below.
x² + 4x-y=0..(1)
2x² + 3x -y= 6..(2)
subtract equations (2) from (1)
x² + 4x-y-2x² - 3x+y=-6
-x² +x=-6
x(-x+1)=-6
x=-6
and -x+1=-6
Subtract -1 from both sides
-x=-7
x=7
Hence solution of x is -6 and 7 for equations y = x² + 4x and y = 2x² + 3x - 6
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12 is what percent of 18
Answers
We have that
[tex]12\cdot\text{ }\frac{100}{18}=\text{ }\frac{1200}{18}\text{ = 66.6666}[/tex]So the answer is: 66.6666 .
Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 12 minutes. Consider 49 of the races.
Let
X = the average of the 49 races.
Please see attachment for questions
Answers
Using the normal distribution and the central limit theorem, it is found that:
a) The distribution is approximately N(145, 1.71).
b) P(143 < X < 148) = 0.8389.
c) The 70th percentile of the distribution is of 145.90 minutes.
d) The median is of 145 minutes.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In the context of this problem, the parameters are defined as follows:
[tex]\mu = 145, \sigma = 12, n = 49, s = \frac{12}{\sqrt{49}} = 1.71[/tex]
The distribution of sample means is approximately:
N(145, 1.71) -> Insert the mean and the standard error.
The normal distribution is symmetric, hence the median is equal to the mean, of 145 minutes.
For item b, the probability is the p-value of Z when X = 148 subtracted by the p-value of Z when X = 143, hence:
X = 148:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (148 - 145)/1.71
Z = 1.75
Z = 1.75 has a p-value of 0.9599.
X = 143:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (143 - 145)/1.71
Z = -1.17
Z = -1.17 has a p-value of 0.1210.
Hence the probability is:
0.9599 - 0.1210 = 0.8389.
The 70th percentile is X when Z has a p-value of 0.7, so X when Z = 0.525, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
0.525 = (X - 145)/1.71
X - 145 = 0.525(1.71)
X = 145.90 minutes.
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y = -x +3
x+y = 17
Are these parallel?
Answers
Answer:
Yes
Step-by-step explanation:
The equations need to be in slope intercept form. The first equation is but the second one isn't. Solve the second equation for y to put it in slope intercept form.
x + y = 17
x - x + y = 17 - x
y = -x + 17
To determine if they are parallel the slopes need to be the same.
y = -1x + 3
y = -1x +17
The slope are both -1, so they are parallel
Answer:
Yes
Step-by-step explanation:
For the polynomial below, 1 is a zero.h(x) = x² – 3x? - 2x + 4Express h(x) as a product of linear factors.
Answers
Step 1
Given the zero, 1, we can use synthetic division to acquire the other factors
Using synthetic division we will write out all coefficients of the terms of h(x) and proceed thus
1 | 1 -3 -2 +4
1 -2 -4
-----------------------
1 -2 -4 0
Hence the quadratic equation we will need to split into linear factors is given as
[tex]x^2-2x-4[/tex]Since the remainder is 0
Step 2
Factorize the quadratic equation above completely
[tex]\begin{gathered} x^2-2x-4=0 \\ we\text{ will use} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]Where
a= 1
b= -2
c= -4
[tex]\begin{gathered} x=\frac{-(-2)\pm\sqrt[]{(-2)^2-4\times1\times-4}}{2\times1} \\ x=\frac{2\pm\sqrt[]{4+16}}{2} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{2\pm\sqrt[]{20}}{2} \\ x=\frac{2}{2}+\frac{\sqrt[]{20}}{2}=1+\frac{2\sqrt[]{5}}{2}=1+\sqrt[]{5} \\ Or \\ x=\frac{2}{2}-\frac{\sqrt[]{20}}{2}=1-\frac{2\sqrt[]{5}}{2}=1-\sqrt[]{5} \end{gathered}[/tex]Hence the product of linear factor will be
[tex](x-1)(1+\sqrt[]{5})(1-\sqrt[]{5})[/tex]
if A/B and C/D are rational expressions,then which of the following is true?*PHOTO*
Answers
In general,
[tex]\begin{gathered} \frac{w}{x}*\frac{y}{z}=\frac{w*y}{x*z} \\ x,z\ne0 \end{gathered}[/tex]Therefore, in our case, (Notice that since A/B and C/D are rational expressions, B and D cannot be equal to zero)
[tex]\frac{A}{B}*\frac{C}{D}=\frac{A*C}{B*D}[/tex]Notice that the left side of each option includes the term
[tex]\frac{A}{B}*\frac{D}{C}[/tex]However, we cannot assure that C is different than zero because it is only stated that C/D is rational.
Furthermore,
[tex]\frac{A}{B}*\frac{D}{C}=\frac{A*D}{B*C}[/tex]And (A*D)/(B*C) is not included among the options.
Therefore, the answer has to be option D as it is the only one that correctly expresses the multiplication of two fractions.Remember that there is a mistake in each option, the left side has to be A/B*D/CA museum curator counted the number of paintings in each exhibit at the art museum. Number of paintings Number of exhibits 9 2 21 1 40 1 1 46 3 52 1 67 2 X is the number of paintings that a randomly chosen exhibit has. What is the expected value of x Write your answer as a decimal.
Answers
Answer
Expected number of paintings that a randomly chosen exhibit has = 40.3
Explanation
The expected value of any distribution is calculated as the mean of that distribution.
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Σx = (9 × 2) + (21 × 1) + (40 × 1) + (46 × 3) + (52 × 1) + (67 × 2)
Σx = 18 + 21 + 40 + 138 + 52 + 134
Σx = 403
N = 2 + 1 + 1 + 3 + 1 + 2 = 10
Mean = (Σx)/N
Mean = (403/10) = 40.3
Hope this Helps!!!
Using Calculus with Data in a tablePlease let me know if you have any questions regarding the material, thanks!
Answers
ANSWER
g'(0.1) = 4
EXPLANATION
As stated, g(x) is a composition of two functions: f(x) and 2x. To find its derivative, we have to use the chain rule,
[tex]g^{\prime}(x)=f^{\prime}(x)\cdot(2x)^{\prime}=f^{\prime}(2x)\cdot2[/tex]So, the derivative of g(x) = f(2x) is twice the derivative of f(x) and, therefore,
[tex]g^{\prime}(0.1)=f^{\prime}(2\cdot0.1)\cdot2=f^{\prime}(0.2)\cdot2=2\cdot2=4[/tex]Hence, g'(0.1) = 4.
An asteroid is traveling at 32.0 kilometers per second. At this speed, how much time will it
take the asteroid to travel 1,040 kilometers?
Write your answer to the tenths place.
Answers
Answer:
1040 × 33.0 =
33,280
tenths= 33.3km\s
What is the equation for a line passing through (-2,5) perpendicular to y - 3x = 8
Answers
Consider that the equation of a line with slope 'm' and y-intercept 'c' is given by,
[tex]y=mx+c[/tex]Consider the given equation of line,
[tex]\begin{gathered} y-3x=8 \\ y=3x+8 \end{gathered}[/tex]Comparing the coefficient, it is found that the slope of the given line is 3,
[tex]m=3[/tex]Let 's' be the slope of the line which is perpendicular to this line.
Consider that two lines will be perpendicular if their product of slopes is -1,
[tex]\begin{gathered} m\times s=-1 \\ 3\times s=-1 \\ s=\frac{-1}{3} \end{gathered}[/tex]So the slope of the perpendicular line is given by,
[tex]y=\frac{-1}{3}x+c[/tex]Now, it is given that this line passes through the point (-2,5), so it must satisfy the equation of the line,
[tex]\begin{gathered} 5=\frac{-1}{3}(-2)+c_{} \\ 5=\frac{2}{3}+c \\ c=5-\frac{2}{3} \\ c=\frac{13}{3} \end{gathered}[/tex]Substitute the value of 'c' to get the final equation,
[tex]\begin{gathered} y=\frac{-1}{3}x+\frac{13}{3} \\ 3y=-x+13 \\ x+3y=13 \end{gathered}[/tex]Thus, the required equation of the perpendicular line is x + 3y = 13 .
From least to greatest. -1.4-1.02 -1.20
Answers
We could put these values in the number line:
Therefore, the order of the numbers from least to greatest is:
-1.4 , -1.20 , -1.02
The least number between all the options given is -1.4 because if you see, all numbers are negative, so, when a negative number is greater, as the amount after the negative sign becomes greater, the number is going to be least. That's the reason of the order.
A car used 15 gallons of gasoline when driven 315 miles. Based on this information, which expression should be used to determine the unit rate of miles per gallon of gasoline?
Answers
Given trhat a car used 15 gallons of gasoline to cover 315 miles.
The expression that will be used to determine the unit rate of miles per gallon of gasoline is:
[tex]\frac{315\text{ miles}}{15\text{ gallons}}[/tex]ANSWER:
[tex]\frac{315\text{ miles}}{15\text{ gallons}}[/tex]Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Answers
The binomials x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.
How to derive the equations of the factors of a polynomial
Herein we know the x-values of a polynomial such that the expression is equal to zero. Mathematically speaking, these x-values are known as roots and the mathematical expressions that contain them are known as factors, which are represented by binomials of the form:
a · r - b = 0
Where a, b are real coefficients.
If we know that x₁ = 4, x₂ = - 1, x₃ = 3 / 2, then the factors of the polynomials are listed below:
x₁ = 4:
x - 4 = 0
x₂ = - 1:
x + 1 = 0
x₃ = 3 / 2
2 · x - 3 = 0
x - 4, x + 1 and 2 · x - 3 are factors of the polynomials.
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a turtle swims 15 kilometers in 9 hours how long does it take the turtle to swim 18 kilometers?
Answers
Answer:
10.8 hours or 648 minutes
Step-by-step explanation:
1. Find a factor of 15 and 18 kilometers. A similar factor is 3.
2. Find how long it will take the turtle to swim 3 kilometers.
3. Divide 9 by 5 which is how long it takes to swim three hours. (Keep it in a fraction for now)
4.Multiply 9/5 by 6 to get 18 hours; which is 10.8 hours.
Jordan’s of Boston sold Lee Company of New York computer equipment with a $7,000 list price. Sale terms were 4/10, n/30 FOB Boston. Jordan’s agreed to pay the $400 freight. Lee pays the invoice within the discount period. What does Lee pay Jordan’s?
Answers
If Sale terms were 4/10, n/30 FOB Boston and Jordan’s agreed to prepay the $400 freight. Lee pays the invoice within the discount period. The amount that Lee pay Jordan’ s is $7,120.
What is the amount received?Using this formula
Amount received = [ ( Cost of computer equipment × ( 1 - rate )] + Freight
Let plug in the formula
Amount received = [ $7,000 × ( 1 - 0.04) ] +$400
Amount received = ( $7,000 x .96 ) + $400
Amount received = $6,720 + 400
Amount received = $7,120
Therefore Lee pay Jordan the amount of $7,120.
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in a classroom there are 28 tablets which includes 5 that are defective. if seven tablets are chosen at random to be used by student groups. 12. how many total selections can be made? a. 140 b. 98280 c. 11793600 d. 4037880 e. 1184040 13. how many selections contain 2 defective tablets? a. 10 b. 21 c. 336490 d. 706629 e. 33649
Answers
Using the combination formula, it is found that:
The number of total selections that can be made is: e. 1184040.The number of selections that contain two defective tablets is: c. 336490.Combination formula[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials. It is used when the order in which the elements are chosen does not matter.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In the context of this problem, we have that seven tablets are chosen from a set of 28 tablets, hence the number of selections that can be made is given by:
[tex]C_{28,7} = \frac{28!}{7!21!} = 1,184,040[/tex]
For two defective tablets, the selections are given as follows:
Two defective from a set of five.Five non-defective from a set of 23.Hence the number of selections is calculated as follows:
[tex]C_{23,5}C_{5,2} = \frac{23!}{5!18!} \times \frac{5!}{2!3!} = 336,490[/tex]
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The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d equals 20 times the sine of the quantity pi over 30 times t end quantity plus 10 comma where d represents the distance, in feet, of the person above the ground after t seconds. How long will it take for the Ferris wheel to make one revolution?
Answers
We have the function d, representing the distance from the ground of a person riding on a Ferris wheel:
[tex]d(t)=20\sin (\frac{\pi}{30}t)+10[/tex]If we consider the position of the person at t = 0, which is:
[tex]d(0)=20\sin (\frac{\pi}{30}\cdot0)+10=20\cdot0+10=10[/tex]This position, for t = 0, will be the same position as when the argument of the sine function is equal to 2π, which is equivalent to one cycle of the wheel. Then, we can find the value of t:
[tex]\begin{gathered} \sin (\frac{\pi}{30}t)=\sin (2\pi) \\ \frac{\pi}{30}\cdot t=2\pi \\ t=2\pi\cdot\frac{30}{\pi} \\ t=60 \end{gathered}[/tex]Then, the wheel will repeat its position after t = 60 seconds.
Answer: 60 seconds.
Help me answer these thank u :)
Answers
6. -2
7.-38
8.-15
9.0
10.-13
11.-30
12.38
13.33
14.-23
6. -2
7.-38
8.-15
9. 0
10. -13
11. -30
12. 38
13. 33
14. -23
You have a total of 21 coins, all nickels and dimes. The total value is $1.70. Which of the following is the system of linear equations that represent this scenario? Let n = the number of nickels and let d = the number dimes.
Answers
n = number of nickels
d = number of dimes
1 nickel = 5 cents
1 dime = 10 cents
total number of 21 coins:
n + d = 21
Total value = $1.70
5n + 10 d = 170
Divide by 100
0.05n + 0.10 d = 1.70
Answer:
n + d = 21
0.05n + 0.10 d = 1.70
If z = 12.8, what's is the value of 2(z - 4)?
Answers
The given expression is
[tex]2(z-4)[/tex]Let's replace z = 12.8.
[tex]2(12.8-4)=2(8.8)=17.6[/tex]Therefore, the value is 17.6.Can you please help me out with a question
Answers
Given data:
The given radius is r=16 ft.
The expression for the surface area is,
[tex]\begin{gathered} SA=4\pi(r)^2 \\ =4\pi(16ft)^2 \\ =1024\pi ft^2 \end{gathered}[/tex]The expression for the volume of the sphere is,
[tex]\begin{gathered} V=\frac{4}{3}\pi(r)^3 \\ =\frac{4}{3}\pi(16ft)^3 \\ =\frac{16384\pi}{3}ft^3 \end{gathered}[/tex]Thus, the surface area is 1024π sq-ft, and volume is (16384π)/3 cube-ft.
Find the probability and odds of winning the two-number bet (split) in roulette. Then find expected value of a $1 bet in roulette for the two-number bet.P.S Might not have enough information
Answers
We have to find the probaiblity of winning a split bet in roulette.
Then, we will have 2 numbers that will make us wind the bet out of 37 numbers that make the sample space.
We can then calculate the probability of winning the split bet as the quotient between the number of success outcomes (2) and the number of possible otucomes (37):
[tex]P(w)=\frac{2}{37}\approx0.054[/tex]We can transform this into the odds of winning by taking into account that if 2 are the success outcomes, then 37-2 = 35 are the failure outcomes.
Then, the odds of winning are 2:35.
We now have to calculate the expected value for a $1 bet.
We know the probabilities of winning and losing, but we don't know the value or prize for winning.
The payout for a split bet is 17:1, meaning that winning a split bet of $1 has a prize of $17.
Then, we can use this to calculate the expected value as:
[tex]\begin{gathered} E(x)=P(w)*w+P(l)*l \\ E(x)=\frac{2}{37}*17+\frac{35}{37}*0 \\ E(x)=\frac{34}{37} \\ E(x)\approx0.9189 \end{gathered}[/tex]This means that is expected to win $0.9189 per $1 split bet.
Answer:
Probability of winning: 2/37 ≈ 0.054
Odds of winning: 2:35
Expected value of $1 split bet (17:1 payout): $0.9189
Rectangle CARD has a length of 2x-5 and a width of 6x+10. Triangle BEST has a length of 10x+3 and a width of 4x-7. Find the difference between triangle CARD and triangle BEST. *
Answers
Given:
Rectangle CARD: {length = 2x-5 and width = 6x+10}
Triangle BEST: {length = 10x+3 and width = 4x-7}
To find the differnce, let's first the perimeter of both.
Perimeter of rectangle CARD: 2(length + width)
= 2(2x - 5 + 6x + 10)
= 2(2x + 6x - 5 + 10)
= 2(8x + 5)
= 16x + 10
Perimeter of triangle BEST: 2(length + width)
2(10x + 3 + 4x - 7)
= 2(10x + 4x + 3 - 7)
= 2(14x - 4)
= 28x - 8
Therfore, the difference between both of them is calculated below:
(28x - 8) - (16x + 10)
= 28x - 8 - 16x + 10
= 28x - 16x - 8 10
= 12x - 18
ANSWER:
12x -
Open the most convenient method to graft the following line
Answers
You have the following expression:
3x + 2y = 12
the best method to graph the previous expression is by intercepts.
In this case, you make one of the variables zero and solve for the other one. Next, repeat the procedure wi
Suppose that you follow the same path on the return trip from Dubuque to Council Bluffs. What would be thetotal number of (actual) miles for the round trip?
Answers
We know the trip from Council Bluffs to Dubuque had a total distance of 348 miles; if we take the same route to go back this will mean that we need to travel the same distance, 348 miles. The total distance then we will be 696 miles.
I have already found X . I need help finding m<2
Answers
Given:
[tex]m\angle1=8x-102\text{ and }m\angle4=2x+6[/tex]Required:
[tex]\text{ Find the measure of }\angle2.[/tex]Explanation:
Step 1:
[tex]m\angle1=m\angle4[/tex]Step 2:
[tex]\begin{gathered} 8x-102=2x+6 \\ 6x=108 \\ x=18 \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} m\angle1=8(18)-102 \\ m\angle1=144-102 \\ m\angle1=42 \\ Now, \\ m\angle1+m\angle2=180 \\ 42+m\angle2=180 \\ m\angle2=180-42 \\ m\angle2=138 \end{gathered}[/tex]Answer:
Measure of angle 2 equals 138.
Find two points on the graph of this function other than the origin that fits in the given grid express each coordinate as an integer or simplified fraction or around four decimal places as necessary another coordinates to plot points on
Answers
Substitute arbitrary values of x for which -10 < h(x) < 10.
In this instance, we can use x = 1, and x = -1
[tex]\begin{gathered} h(x)=-\frac{5}{8}x^5 \\ h(1)=-\frac{5}{8}(1)^5 \\ h(1)=-\frac{5}{8} \\ h(1)=-0.625 \\ \\ h(x)=-\frac{5}{8}x^{5} \\ h(-1)=-\frac{5}{8}(-1)^5 \\ h(-1)=\frac{5}{8} \\ h(-1)=0.625 \end{gathered}[/tex]Therefore, the points that fits in the grid in the function h(x) are (1, -0.625) and (-1, 0.625).
Consider the equation. Y=x^2+1The next step in graphing a parabola is to find points that will determine the shape of the curve. Find the point on the graph of this parabola that has the x-coordinated x= -2
Answers
The graph is
[tex]y=x^2+1[/tex]its a upword parabola and vertex of graph is (0,1)
the point on a graph x=-2
[tex]\begin{gathered} y=x^2+1 \\ y=(-2)^2+1 \\ y=4+1 \\ y=5 \end{gathered}[/tex]so graph of function is :
(B)
the coordinate of graph then x=1
[tex]\begin{gathered} y=x^2+1 \\ y=1^2+1 \\ y=2 \end{gathered}[/tex]the value of y is 2 then value of x=1
so I've been using the formula for the volume of a cylinder but I'm still not getting anything even remotely close to my answer choices. the volume is 438.08π mL and the radius is 3.7 cm. I'm solving for the height
Answers
Answer:
H = 32 cm
Explanation:
The area of a cylinder is given by
[tex]V=\pi r^2h[/tex]Now solving for h gives
[tex]h=\frac{V}{\pi r^2}[/tex]Now V = 438.08 π and r = 3.7 cm. Putting these values in the above equations gives
[tex]h=\frac{438.08\pi\operatorname{cm}^3}{\pi(3.7cm)^2}[/tex][tex]\boxed{h=32\operatorname{cm}\text{.}}[/tex]which is our answer!