Answer:
see explanation
Step-by-step explanation:
calculate the slope m using the slope formula and equate to the given slope
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
(a)
(x₁, y₁ ) = (- 3, - 4 ) and (x₂, y₂ ) = (0, y )
\(\frac{y-(-4)}{0-(-3)}\) = \(\frac{y+4}{0+3}\) = \(\frac{y+4}{3}\) , then
\(\frac{y+4}{3}\) = 2 ( multiply both sides by 3 )
y + 4 = 6 ( subtract 4 from both sides )
y = 2
ordered pair is (0, 2 )
(b)
(x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (x, 5 )
\(\frac{5-2}{x-(-2)}\) = \(\frac{3}{x+2}\) , then
\(\frac{3}{x+2}\) = \(\frac{3}{7}\) ( cross- multiply )
3(x + 2) = 21 ( divide both sides by 3 )
x + 2 = 7 ( subtract 2 from both sides )
x = 5
ordered pair is (5, 5 )
(c)
(x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (1, - 5 )
\(\frac{-5-5}{1-x}\) = \(\frac{-10}{1-x}\) , then
\(\frac{-10}{1-x}\) = \(\frac{-5}{2}\) ( cross- multiply )
- 5(1 - x) = - 20 ( divide both sides by - 5 )
1 - x = 4 ( subtract 1 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
ordered pair is (- 3, 5 )
(e)
(x₁, y₁ ) = (- 6, y ) and (x₂, y₂ ) = (8, 2 )
\(\frac{2-y}{8-(-6)}\) = \(\frac{2-y}{8+6}\) = \(\frac{2-y}{14}\) , then
\(\frac{2-y}{14}\) = - \(\frac{1}{7}\) ( cross- multiply )
- 7(2 - y) = 14 ( divide both sides by - 7 )
2 - y = - 2 ( subtract 2 from both sides )
- y = - 4 ( multiply both sides by - 1 )
y = 4
ordered pair is (- 6, 4 )
I need helpp! Somebody please help me ! Work is hard
1. 9.48
2. 11.1
3. 5.65
4. 26.45 or 26.4
x to the power of 3 plus x to the power of 2 plus x
Answer:
x(x²+x+1)
Step-by-step explanation:
im not surewhat answer u want but take note this is FACTORIZATION
If f(x) =(2,9%), what is f(3)?
A. 1/729
B. 729
C. 1/81
D. 81
Answer:
CCC
Step-by-step explanation:
Answer:
81
Step-by-step explanation:
a p e x (just took the quiz)
in triangle ABC below the measure of angle a is 20 degrees in the measure of angle B is three times larger than a measure of angle C what is the measure of angle B?
Answer:
In triangle ABC,
What are the angles?
the angles are A, B and C
What is the sum of all three angles in a triangle?
A + B + C = 180°
the measure of angle B is three times that of angle A.
What is angle B equal to, mathematically?
B is equal to 3A
the angles are now A, 3A and C
The measure of angle C is 20 degrees more than that of angle A.
What is angle C equal to, algebraically?
C is equal to A+20
the angles are now A, 3A, and A+20
How do you find the angle measures?
What is the sum of all angles in a triangle?
A + B + C = 180°
Write it again, this time with B = 3A, and C = A+20
A + (3A) + (A+20) = 180°
Simplify:
A + 3A + A + 20 = 180°
5A + 20 = 180°
Solve for A and you have angle A, then reread the above to get B and C.
I’m going to let you finish it from here.
What did you get?
Be sure you double check your answer.
Do your three angles add up to 180?
Is B triple the value of A?
Is C 20 more than A?
Step-by-step explanation:
hopefully this helps
Gavin deposited $200 into his savings account that is compounded semi-annually at an interest rate of 9%. Gavin hoped he would have enough money in 8 years to buy a $400 gaming console for college. Is Gavin correct? Write and solve an equation, showing your work to justify your answer
Answer:
His answer was correct:
(200*0.09)=18
18*16=288
200+288=488
You received a 85, 88, and a 94 on your last three math exams. What grade would you need on your next exam to have an average of 90? (Show all work on your scratch paper and make sure you set up an equation)
You would need to get a ??????
to have an average of 90%.
Answer: 93
suppose: the grade we need on the next exam is x (x > 0)
to have an average of 90, we have the equation:
\(\frac{85+88+94+x}{4}=90\\\\<=>267+x=360\\\\<=>x=360-267\\\\<=>x=93\)
so the grade we need on the next exam is 93
Step-by-step explanation:
\(suppose: the grade we need on the next exam is x (x > 0)
to have an average of 90, we have the equation:
\begin{gathered}\frac{85+88+94+x}{4}=90\\\\ < = > 267+x=360\\\\ < = > x=360-267\\\\ < = > x=93\end{gathered}485+88+94+x=90<=>267+x=360<=>x=360−267<=>x=93
so the grade we need on the next exam
\)
can someone please help me with this
Answer:
ABC = 113°
Step-by-step explanation:
If ABD is 70° and DBC is 43°
ABC is 70°+43° = 113°
Need ASAP! Choose the numbers that are irrational. 1. 0. 87 repeating 2. 3.624 3. √2 4. 0. 6 repeating 5. -5 6. 1 over 3 7. Pi. I couldn't use the symbol
Answer:
1, 3, 7
Step-by-step explanation:
A rational number can be written as a ratio or fraction.
1) I wasn't able to determine a fraction for what I'm assuming you meant by 0.878787878787 going on and on so it must be irrational
2) 3.624 can be written as 3 78/125
3) The square root of two is irrational
4) 0.6666666 going on and on can be written as 1/3
5) -5.6 can be written as a fraction too
6) 1/3 is already a fraction
7) Pi is irrational
Hope that helps!
3. Consider the following system: →0.85→0.85→ Determine the probability that the system will operate under each of these conditions: a. The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) b. Each system component has a backup with a probability of .85 and a switch that is 100 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places. c. Each system component has a backup with a probability of .85 and a switch that is 90 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
a. The probability that the system will operate as shown is approximately 0.6141.
b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.
c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.
a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:
Probability = 0.85 × 0.85 × 0.85
Probability ≈ 0.6141
The probability that the system will operate as shown is approximately 0.6141.
b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:
Probability = 0.85 × 0.85 × 0.85
Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.
c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:
Probability = 0.85 × 0.90 × 0.85
Probability ≈ 0.6485
The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.
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What would be the solution for z?
Answer:
\(z = w - 3x + 2y\)
Step-by-step explanation:
\(3x - 2y + z = w\)
\(3x - 2y + z - 3x + 2y = w - 3x + 2y\)
\( - 2y + z + 2y = w - 3x + 2y\)
\(z = w - 3x + 2y\)
\(\boxed{\green{z = w - 3x + 2y}}\)
х - = 5x – 3y = 2 3. Consider the system of equations: kx + 9y = 1 For which values of k does the system above have a unique solution? (A) All k #0 (B) All k #3 (C) All k + -3 (D) All k +1 (E) All
The system of equations given, kx + 9y = 1 and 5x - 3y = 2, will have a unique solution for all values of k except k = -3.
To determine the values of k for which the system has a unique solution, we need to consider the coefficients of x and y in the equations. The system will have a unique solution if and only if the two lines represented by the equations intersect at a single point. This occurs when the slopes of the lines are not equal.
In the given system, the coefficient of x in the first equation is k, and the coefficient of x in the second equation is 5. These coefficients are equal when k = 5. Therefore, for all values of k except k = -3, the system will have a unique solution. Thus, the correct answer is option (C): All k ≠ -3.
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Complete question: Consider the system of equations: kx + 9y = 1 and 5x-3y=2. For which values of k does the system above have a unique solution? (A) All k #0 (B) All k #3 (C) All k + -3 (D) All k +1 (E) All
Please can u help me
Answer: p=8
Step-by-step explanation:
FH ≅ FJ --> diagonals bisect in parallelograms--> rectangle is a form of a parallelogram 4p-22 = p+2 --> Transitivity p = 8 --> Algebrawhile shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent
while shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent
Let
x ------> amount that Curtis spent
we have that
10=2x-26 ------> equation that represent this situation
solve for x
2x=10+26
2x=36
x=$18
therefore
Curtis spent $18find the sum
(2x+6)+(4x-12)
HELp
Answer:
6x-6
Step-by-step explanation:
(2x+6)+(4x-12)=2x+6+4x-12
=6x-6
Consider the following competing hypotheses: (You may find it useful to reference the appropriate table: z table or t table)
Hypotheses: H0: μD ≤ 2; HA: μD > 2
Sample results: d−d− = 6,9, sD = 7.8, n = 10
The following results are obtained using matched samples from two normally distributed populations:
a. Calculate the value of the test statistic, assuming that the sample difference is normally distributed. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
To calculate the value of the test statistic, we need to use the sample results provided: d-bar = 6.9, sD = 7.8, and n = 10. The value of the test statistic is approximately 1.983.
Given:
Sample mean difference (d-bar) = 6.9
Sample standard deviation of the differences (sD) = 7.8
Sample size (n) = 10
To calculate the test statistic, we can use the formula for the t-statistic:
t = (d-bar - μD) / (sD / sqrt(n))
where d-bar is the sample mean difference, μD is the hypothesized mean difference under the null hypothesis, sD is the sample standard deviation of the differences, and n is the sample size.
In this case, the null hypothesis (H0) states that μD is less than or equal to 2. Since the alternative hypothesis (HA) is μD > 2, this is a one-tailed test.
Plugging in the values into the formula:
t = (6.9 - 2) / (7.8 / sqrt(10))
t = 4.9 / (7.8 / 3.162)
t = 4.9 / 2.471
t ≈ 1.983
Therefore, the value of the test statistic is approximately 1.983.
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If 2 of the 1000 test subjects are randomly selected find the probability that they both had false positive results. Is it unlikely to randomly select 2 subjects and get 2 results that are both false positive results
Using the concept of conditional probability and the conditions provided, The answer is \(\frac {p^2}{2pq}\) .
What do you mean by probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities can be calculated using the ratio of the number of favorable outcomes to the total number of possible outcomes. It helps us to understand the uncertainty of events.
What do you mean by false positive results?A false positive result is when a test indicates that a particular condition or attribute is present, when in reality it is not. For example, in medical testing, a false positive result would occur when a test for a disease returns a positive result but the person being tested does not actually have the disease. False positives can have serious consequences, as they can lead to unnecessary treatments, further testing, and anxiety for the person being tested.
p=probability of occurrence
q=1-p
P(false positive for both subjects | false positive for one subject) = P(false positive for both subjects and false positive for one subject) / P(false positive for one subject)
P(false positive for both subjects | false positive for one subject) = p^2 / (2pq)
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Express 121.746 correct to one decimal
Answer:
121.7
Step-by-step explanation:
Use the .746 to round to the nearest decimal place.
To do this you look to the value of the number next to the .7
If it is 5 or higher you round upwards
If it is 4 or lower you round downwards or leave as is.
Therefore .746 rounds to .7
Your answer is 121.7
or
What is the volume of this cone?
Use ≈ 3.14 and round your answer to the nearest hundredth.
6 cm
10 cm
The calculated volume of the cone is 94.29 cubic cm
How to determine the volume of the coneFrom the question, we have the following parameters that can be used in our computation:
Base diameter = 6 cm
Height = 10 cm
Using the above as a guide, we have the following:
r = 6/2 = 3
h = 10
So, we have
V = 1/3πr²h
Substitute the known values in the above equation, so, we have the following representation
V = 1/3 * 22/7 * 3² * 10
Evaluate
V = 94.29
Hence, the volume is 94.29 cubic cm
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a number is multiplied to itself the product is 49/9 find the number
Answer:
the number is 20
Step-by-step explanation:
let 'n' represent the number
2n + 9 = 49
2n = 40
n = 40/2 = 20
a university requires its biology majors to take a course called bioresearch. the prerequisite for this course is that students must have taken either a statistics course or a computer course. by the time they are juniors, 52% of the biology majors have taken statistics, 23% have had a computer course, and 7% have done both. what is the probability that a randomly selected junior biology major has taken either statistics or a computer course (or both)? please enter your answer as a decimal, rounded to two places after the decimal point.
The probability that a randomly selected junior biology major has taken either a statistics or a computer course is 0.68
To find the probability that a randomly selected junior biology major has taken either a statistics or a computer course (or both), we'll use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Where:
- P(A) is the probability of having taken a statistics course (52% or 0.52)
- P(B) is the probability of having taken a computer course (23% or 0.23)
- P(A and B) is the probability of having taken both courses (7% or 0.07)
Now, plug in the values:
P(A or B) = 0.52 + 0.23 - 0.07
P(A or B) = 0.68
So, the probability that a randomly selected junior biology major has taken either a statistics or a computer course (or both) is 0.68, or 68%.
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Estimate ΔyΔy using differentials.
y=cos(5x),=/30,x=0.055
(Give your answer to three decimal places.)
The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin(5x)dx. We are given that y=cos(5x)=π/30y=cos(5x)=π/30 and x=0.055x=0.055.
We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:
Δy≈dy≈dy=-5sin(5x)dx
Plugging in the values of y, x, and dxdx, we get:
Δy≈-5sin(5(0.055))(0.005)≈-0.00679
Therefore, the estimated change in yy using differentials is -0.00679.
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question the random variable x is exponentially distributed, where x represents the time it takes for a whale watcher to spot a whale. if x has an average value of 45 minutes, what is the probability that x is less than 45 minutes? round the final answer to three decimal places.
0.368 .
The probability that a random variable x is exponentially distributed and less than 45 minutes,
given that the average value is 45 minutes, is 0.368.
This can be calculated by taking the negative of the natural logarithm of 1/2 (i.e. -ln(0.5)) and dividing it by the average value of 45 minutes.
The result, -ln(0.5)/45, equals 0.368, rounded to three decimal places.
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BRIDGE Arturo is designing a bridge for science class using parallel supports for the top and bottom beam. Find m angle2 if m angle1=60^
Answer:
Believe it or not, it would be 60 degrees.
Step-by-step explanation:
Here, we are working with ALTERNATE INTERIOR ANGLES. Since we know the beam supports for the top and bottom are parallel, 1&2 will be the same angle measurement.
Here is a diagram of an example of alternate interior angles, where m1=m2.
Answer:
Step-by-step explanation:
A plane crosses the Atlantic Ocean (3000 miles) with an airspeed of 500 miles per hour. The cost C (in dollars) per passenger is given by X 38,000 C(x) = 200 + + 10 X where x is the ground speed (airspeed + wind). (a) What is the cost when the ground speed is 360 miles per hour; 480 miles per hour? (b) Find the domain of C. (c) Use a graphing calculator to graph the function C=C(x). (d) Create a TABLE with TblStart=0 and ATbl = 50. (e) To the nearest 50 miles per hour, what ground speed minimizes the cost per passenger?
The cost C per passenger is given by the equation C(x) = 200 + 10x, where x is the ground speed. To find the cost, we substitute values into the equation.
(a) When the ground speed is 360 miles per hour, we have C(360) = 200 + 10(360) = 200 + 3600 = 3800 dollars per passenger.
When the ground speed is 480 miles per hour, we have C(480) = 200 + 10(480) = 200 + 4800 = 5000 dollars per passenger.
(b) The domain of C represents the valid input values for x, which in this case is the ground speed. Since the airspeed is given as 500 miles per hour, the ground speed must be greater than or equal to 0. Therefore, the domain of C is x ≥ 0.
(c) The graph of the function C(x) = 200 + 10x can be plotted on a graphing calculator to visualize the relationship between ground speed and cost per passenger.
(d) Creating a table with TblStart = 0 and ΔTbl = 50 allows us to generate a set of values for the ground speed (x) and the corresponding cost (C). The table can be used to observe the cost per passenger at different ground speeds.
(e) To determine the ground speed that minimizes the cost per passenger, we can examine the table or graph and identify the value of x where the cost C(x) is the lowest. By looking for the minimum value of C in the table or finding the lowest point on the graph, we can determine the nearest 50 miles per hour that correspond to the ground speed minimizing the cost per passenger.
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19. The present age of brother and sister are in the ration 4:5 Before three years the ration of their age was 3:4. find their present age-
Answer:
Sister = 15 years old
Brother = 12 years old
Step-by-step explanation:
Right now, if the brother is B years old and the sister is S years old, B = (4/5)S because the ratio from brother to sister is 4:5, so if one unit is X, B = 4X and S = 5X
Three years ago, the brother was B-3 years old and the sister was S-3 years old. Keeping one unit as X, we have
B = 3X
S = 4X
B-3 = (3/4)(S-3)
Therefore, we have a system of equations
B = (4/5)S
B-3 = (3/4)(S-3)
Substitute (4/5)S for B into the second equation to only have one variable
(4/5)S - 3 = (3/4)(S-3)
(4/5)S - 3 = (3/4)S - 9/4
add 3 to both sides and subtract (3/4)S from both sides to isolate the variable and its coefficient
(1/20)S = 3/4
multiply both sides by 20 to isolate the S
S = 15
B = (4/5)S = 12
What is 2,520 divide 36
Find m∠IUV if m∠TUI = 65° and m∠TUV = 147°
The measure of the m∠IUV using the addition postulate is equivalent to 82 degrees
Lines and anglesA line is defined as the shortest distance between two points while an angle is the point where two lines meet.
Given the following measure of angles
m∠TUI = 65° and
m∠TUV = 147°
Required angle
m∠IUV
Using the addition postulate below
m∠TUV = m∠TUI + m∠IUV
Substitute the given parameters
147 = 65 + m∠IUV
m∠IUV = 147 - 65
m∠IUV = 82 degrees
Hence the measure of the m∠IUV using the addition postulate is equivalent to 82 degrees
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Please help explanation if possible
Answer:
y = 3x+6
Step-by-step explanation:
refer to the picture
Answer:
y = 3x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 ← is in slope- intercept form
with slope m = 3
Parallel lines have equal slopes, so slope of parallel line is 3
Expressing the equation in point- slope form with m = 3 , (x₁, y₁ ) = (1, 9)
y - 9 = 3(x - 1)
y - 9 = 3x - 3 ( add 9 to both sides )
y = 3x + 6 ← in slope- intercept form
Help me solve this problem please
How do you write – 6 5/9 as a decimal?
Answer: 6.56
Step-by-step explanation:
Here are the detailed math steps we use to convert 6 5/9 mixed number to decimal form:
Step 1: Multiply the whole number by the denominator:6 × 9 = 54
Step 2: Add the product you got in Step 1 to the numerator:54 + 5 = 59
Step 3: Divide the sum from Step 2 by the denominator:59 ÷ 9 = 6.555556
That's it folks! The answer to 6 5/9 in decimal form is displayed below:
6 5/9 ≈ 6.56