Answer:
Check the answer. 1. ... 5 times a number plus 8 is equal to 3 times the number minus 4. 7 times a ... Twice a number is equal to 5 times the sum of the number and 6. The product ... If the equation is an identity, write the answer as “All real numbers.
Step-by-step explanation:
A line passes through the point (3,-8) and has a slope of 3. Write an equation in point-slope form for this line.
Answer:
y+8 = 3(x-3)
Step-by-step explanation:
The point slope form of the equation for a line is
y-y1 = m(x-x1)
y- -8 = 3(x -3)
y+8 = 3(x-3)
Calculate the derivative indicated.
dy
1
where
y=51
+ 4x2
dx2
x=6
73
Answer:
8 5/648
Step-by-step explanation:
y = 5x ^ -3 + 4x^2
dy /dx = 5 * -3 x^ -4 + 4 * 2x ^ 1
= -15 x ^ -4 + 8x
Now take the second derivative
dy^2/ dx^2 = -15 * -4 x^-5 +8
= 60 x^ -5 +8
= 60 /x^5 +8
Evaluate at x = 6
= 60 / 6^5 +8
60/7776 +8
5/648 + 8
8 5/648
A ball thrown into the air from a roof 15 feet above the ground with an initial vertical velocity of 30 ft/sec can be modeled by the equation: . How long will the ball be in the air? What is it’s maximum height?
Answer:
Total time of flight= 6.3 s
Total Max height= 60.87ft
Step-by-step explanation:
Height above ground = 15ft
Velocity=30ft/sec
Angle = 90°
Max height traveled= U²Sin²tita/2g
Max height traveled= ( 30²*1²)/(2*9.81)
Max height traveled= 900/19.62
Max height traveled= 45.87 ft
Total Max height= 15+45.87= 60.87ft
Time travel to Max height
=( usin90)/g
Time travel to initial position
= (30*sin90)/9.81
= 3.1 s
Time to travel to the ground from Max height
H = 1/2gt²
60.87= 1/2 * 9.81*t²
(60.87*2)/9.81= t²
3.5 = t
Total time of flight = 3.5+3.1
Total time of flight= 6.3 s
Classify the triangle based on its angles and sides
Answer:
Options (c) and (f)
Step-by-step explanation:
In the given triangle,
Measure of one angle is 90°.
Therefore, it's a right angle triangle.
Since two angles of the given triangle are equal, opposite sides of this triangle will be equal.
Therefore, the given right triangle is an isosceles triangle.
Options (c) and (f) will be the answer.
HELP ASAP PLS! A random number generator is used to create a real number between 0 and 1, equally likely to fall anywhere in this interval of values. (For the instance, 0.3794259832... is a possible outcome). a. Sketch a curve of the probability distribution of this random variable, which is the continuous version of the uniform distribution. b. What is the mean of this probability distribution?
Answer:
a. Attached.
b. Mean = 0.5
Step-by-step explanation:
This random number generator con be modeled with an uniform continous random variable X that has values within 0 and 1, each with the same constant probability within this range.
The probability for the values within the interval [a,b] in a continous uniform distribution can be calculated as:
[tex]f(x)=\dfrac{1}{b-a}\;\;\;x\in[0; 1][/tex]
In this case, b=1 and a=0, so f(x)=1.
The sketched curve of the probability distribution of this random variable is attached.
The mean of this distribution can be calculated as the mean for any uniform distribution:
[tex]E(X)=\dfrac{a+b}{2}=\dfrac{0+1}{2}=0.5[/tex]
Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and the length of side S T is 16. The length of side T U is 8 and the length of U V is 6. Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem? StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
Answer:
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
Step-by-step explanation:
The expression below means RS/VU = ST/UT
See the attachment for better explanation.
Answer:
A
Step-by-step explanation:
I took the test
Solve this equation for x: 2x^2 + 12x - 7 = 0
What is the first step to solve this equation?
-combine like terms
-factor the trinomial
-isolate the constant term by adding 7 to both sides
Answer:
x=0.5355 or x=-6.5355
First step is to: Isolate the constant term by adding 7 to both sides
Step-by-step explanation:
We want to solve this equation: [tex]2x^2 + 12x - 7 = 0[/tex]
On observation, the trinomial is not factorizable so we use the Completing the square method.
Step 1: Isolate the constant term by adding 7 to both sides
[tex]2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7[/tex]
Step 2: Divide the equation all through by the coefficient of [tex]x^2[/tex] which is 2.
[tex]x^2 + 6x=\frac{7}{2}[/tex]
Step 3: Divide the coefficient of x by 2, square it and add it to both sides.
Coefficient of x=6
Divided by 2=3
Square of 3=[tex]3^2[/tex]
Therefore, we have:
[tex]x^2 + 6x+3^2=\frac{7}{2}+3^2[/tex]
Step 4: Write the Left Hand side in the form [tex](x+k)^2[/tex]
[tex](x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\[/tex]
Step 5: Take the square root of both sides and solve for x
[tex]x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355[/tex]
Answer:
Step-by-step explanation:
Step 1: Isolate the constant term by adding 7 to both sides of the equation.
Step 2: Factor 2 from the binomial.
Step 3: 9
Step 3 b: 18
Step4: write the trinomial as the square root of a binomial.
Step 5: divide both sides of the equation by 2 Step
6: Apply the square root property of equality Step
7: subtract 3 from both sides of the equation.
The time, T (seconds) it takes for a pot of water to boil is inversely proportional to the cooker setting, H , applied to the pot. When H = 7 , T = 150 . What must the cooker setting be if it takes 7 minutes to boil the water?
Answer:
150
Step-by-step explanation:
Given the following parameters;
Time, T = 150mins
Cooker setting, H = 7
Since the time for a pot of water to boil is inversely proportional to the cooker setting;
[tex]T * 1/H[/tex]
[tex]T = K/H[/tex] ........equation 1
Where, K is the constant of proportionality.
Substituting the parameters into the equation 1, we have;
150 = K/7
K = 150*7
K = 1050
To find the cooker setting at 7mins;
[tex]T = K/H[/tex]
H = K/T
H = 1050 ÷ 7
H = 150.
Hence, the cooker setting must be at 150.
The height of a ball above the ground as a function of time is given by the function h(t)= -32t^2+8t+3 where h is the height of the ball in feet and t is the time in seconds. When is the ball at a maximum height
Answer:
The ball is at a maximum height when t = 0.125s.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, f(x_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]f(x_{v})[/tex]
In this question:
[tex]h(t) = -32t^{2} + 8t + 3[/tex]
So [tex]a = -32, b = 8[/tex]
When is the ball at a maximum height
[tex]t_{v} = -\frac{8}{2*(-32)} = 0.125[/tex]
The ball is at a maximum height when t = 0.125s.
Express as a ratio: the speed of 1 km/min to
the speed of 10 m/s.
Answer:
10 : 6
Step-by-step explanation:
1km / min = 1000m / 60 sec = 100/6 m/s
Ratio :
100/6 : 10
10/6 : 1
10 : 6
From 1985 to 2003, the total attendance A (in thousands) at NCAA women’s basketball games can be modeled by =−1.95^3 +70.1x^2 −188+2150 where x is the number of years since 1985.
a. What is the initial value of this function (the attendance in 1985)?
b. Find the attendance for the year 1998.
Answer:
21507269Step-by-step explanation:
We assume your intended attendance equation is ...
A = -1.95x^3 +70.1x^2 -188x +2150
a. For x=0 (corresponding to 1985), the first three terms are 0, so we have ...
A = 2150 . . . . the initial value of the function
__
b. For x=13 (corresponding to 1985) we have ...
A = ((-1.95(13) +70.1)(13) -188)(13) +2150 = (44.75(13) -188)(13) +2150
= 393.75(13) +2150 = 7268.75
Attendance in the year 1998 is modeled to be about 7269.
Marts is solving the equation S=2nrh+2nr2 for h. Which should be the result?
Step-by-step explanation:
Hope you understand this
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix C. Group of answer choices A. -14 B. 14 C. -22 D. The determinant cannot be found for a matrix with these dimensions.
Answer: d) determinant cannot be found
Step-by-step explanation:
You can only find the determinant of a SQUARE matrix.
In other words, the dimensions must be 2 × 2 or 3 × 3 or ... n × n
The dimensions of the given matrix is 2 x 3, so the determinant cannot be calculated.
I need help not good at graphs
Answer:
a, b
Step-by-step explanation:
a and b cause all the data are not in a form of a line
What’s the correct answer for this?
Answer:
1/2
Step-by-step explanation:
The formula that relates two independent events is provided as below:
P(A) x P(B) = P(A⋂B)
=> P(A) x (1/3) = 1/6
=> P(A) = (1/6) x 3
=> P(A) = 3/6 = 1/2
=> Option D is correct
Hope this helps!
Express the complex number in trigonometric form.
-6 + 6\sqrt(3) i
Answer:
12(cos120°+isin120°)Step-by-step explanation:
The rectangular form of a complex number is expressed as z = x+iy
where the modulus |r| = [tex]\sqrt{x^{2}+y^{2}[/tex] and the argument [tex]\theta = tan^{-1}\frac{y}{x}[/tex]
In polar form, x = [tex]rcos\theta \ and\ y = rsin\theta[/tex]
[tex]z = rcos\theta+i(rsin\theta)\\z = r(cos\theta+isin\theta)[/tex]
Given the complex number, [tex]z = -6+6\sqrt{3} i[/tex]. To express in trigonometric form, we need to get the modulus and argument of the complex number.
[tex]r = \sqrt{(-6)^{2}+(6\sqrt{3} )^{2}}\\r = \sqrt{36+(36*3)} \\r = \sqrt{144}\\ r = 12[/tex]
For the argument;
[tex]\theta = tan^{-1} \frac{6\sqrt{3} }{-6} \\\theta = tan^{-1}-\sqrt{3} \\\theta = -60^{0}[/tex]
Since tan is negative in the 2nd and 4th quadrant, in the 2nd quadrant,
[tex]\theta =180-60\\\theta = 120^{0}[/tex]
z = 12(cos120°+isin120°)
This gives the required expression.
A Lake Tahoe Community College instructor is interested in the average number of days Lake Tahoe Community College math students are absent from class during a quarter that lasts 9 weeks. What is the population she is interested in
Answer:
All Lake Tahoe Community College math students
Step-by-step explanation:
From the question itself it is clear that the instructor is interested in the average number of days Lake Tahoe Community College math students are absent from class during a quarter that lasts 9 weeks, which clearly indicates that the teacher is interested in population of all Lake Tahoe Community College math students.
Are these calculated correctly?
14. Was the perimeter calculated correctly?
Length = 4 yards Breadth = 1 *2/5 yards = 7/5 yardsWe know that,
Perimeter of rectangle = 2 ( l + b )
= 2 ( 4 + 7 / 5 )
= 2 ( 20 + 7 / 5 )
= 2 × 27/5
= 54 / 5
= 1 * 4/5
No ...
7 days 8 hours 20 minutes
- 4 days 10 hours 30 minutes
F 2 days 21 hours
50 minutes
G 3 days 2 hours
10 minutes
H 7 days 8 hours
20 minutes
J 11 days 8 hours
50 minutes
K none of these
These box plots show daily low temperatures for a sample of days in two different towns.
Town A. 10,15,20,30, and 55
Town B. 5,20,30,40, and 55
*The question is incomplete. Attached below is the diagram of the box plots being referred to followed by the complete question and options.
Answer:
D. The median for town A, 20 degrees, is less than the median of town B, 30 degrees
Step-by-step Explanation:
From the given diagram of the box plots showing the daily low temperatures for town A and B, the median of town A and B is shown on the box plots by the line that divides the box. Therefore, the median of town A is where the line that divides the box is. Median for town A is 20⁰. Same applies for town B. Town B median is 30⁰.
Therefore, option D is the most appropriate comparison of the centers. Median of town A is less than median of town B.
What’s the correct answer for this?
Answer:
x = 12
Step-by-step explanation:
Since they are equidistant from the centre, they are equal in length i.e.
JK = LM
4x+37 = 5(x+5)
4x+37 = 5x+25
37-25 = 5x-4x
12 = x
OR
x = 12
Which expression represents the composition [g o f o h](x) for the functions below?
f(x) = 5x – 4
g(x) = 5x3
h(x) = 3x
Answer: 16875x³-13500x²+3600x-320
Step-by-step explanation:
[gοfοh](x) means g(f(h(x))). So you plug in h(x) into f(x) and that into g(x).
f(3x)=5(3x)-4=15x-4
g(f(3x))=5(15x-4)³
g(f(3x))=5(3375x³-2700x²+720x-64)
g(f(3x))=16875x³-13500x²+3600x-320
Answer:
A
Step-by-step explanation:
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
Answer:
a) 0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less
b) 0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours
c) 0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours
d) 86 should have a battery life of at least 9 hours.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
The probability of being higher than x is:
[tex]P(X > x) = \frac{b - x}{b-a}[/tex]
The probability of being between c and d is:
[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]
Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
This means that [tex]a = 8.5, b = 12[/tex]
a. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]P(X \leq 10) = \frac{10 - 8.5}{12 - 8.5} = 0.4286[/tex]
0.4286 = 42.86% probability that the battery life for an iPad Mini will be 10 hours or less.
b. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?
[tex]P(X > x) = \frac{b - x}{b-a}[/tex]
[tex]P(X > 11) = \frac{12 - 11}{12 - 8.5} = 0.2857[/tex]
0.2857 = 28.57% probability that the battery life for an iPad Mini will be at least 11 hours
c. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?
[tex]P(c \leq X \leq d) = \frac{d-c}{b-a}[/tex]
[tex]P(9.5 \leq X \leq 11.5) = \frac{11.5 - 9.5}{12 - 8.5} = 0.5714[/tex]
0.5714 = 57.14% probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours.
d. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?
Proportion of iPad Minis with a battery life of at least 9 hours.
[tex]P(X > 11) = \frac{12 - 9}{12 - 8.5} = 0.8571[/tex]
Out of 100:
0.8571*100 = 85.71
To the nearest whole number
86 should have a battery life of at least 9 hours.
Solve the following quadratic equation using the quadratic formula. Separate multiple answers with a comma if necessary.
[tex]−yx^{2} +4y−6=0[/tex]
Answer:
[tex] y^2 -4y +6=0[/tex]
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where [tex] a = 1, b= -4 ,c =6[/tex]
And replacing we got:
[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]
And solving we got:
[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]
Where [tex] i =\sqrt{-1}[/tex]
And the possible solutions are:
[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]
Step-by-step explanation:
For this case we use the equation given by the image and we have:
[tex] -y^2 +4y -6=0[/tex]
We can rewrite the last expression like this if we multiply both sides of the equation by -1.
[tex] y^2 -4y +6=0[/tex]
Now we can use the quadratic formula given by:
[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
Where [tex] a = 1, b= -4 ,c =6[/tex]
And replacing we got:
[tex] y = \frac{-(-4) \pm \sqrt{4^2 -4(1)(6)}}{2*1}[/tex]
And solving we got:
[tex] y = \frac{4 \pm \sqrt{-8}}{2} =2 \pm 2\sqrt{2} i[/tex]
Where [tex] i =\sqrt{-1}[/tex]
And the possible solutions are:
[tex] y_1=2 + 2\sqrt{2} i , y_2 = 2 - 2\sqrt{2} i [/tex]
Some parts of California are particularly earthquake-prone. Suppose that in one metropolitan area, 33% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random. Let X denote the number among the four who have earthquake insurance. A) Find the probability distribution of X.B) What is the most likely value for X?
C) What is the probability that at least two of the four selected have earthquake insurance?
Answer:
(a) The probability mass function of X is:
[tex]P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...[/tex]
(b) The most likely value for X is 1.32.
(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.
Step-by-step explanation:
The random variable X is defined as the number among the four homeowners who have earthquake insurance.
The probability that a homeowner has earthquake insurance is, p = 0.33.
The random sample of homeowners selected is, n = 4.
The event of a homeowner having an earthquake insurance is independent of the other three homeowners.
(a)
All the statements above clearly indicate that the random variable X follows a Binomial distribution with parameters n = 4 and p = 0.33.
The probability mass function of X is:
[tex]P(X=x)={4\choose x}\ (0.33)^{x}\ (1-0.33)^{4-x};\ x=0,1,2,3...[/tex]
(b)
The most likely value of a random variable is the expected value.
The expected value of a Binomial random variable is:
[tex]E(X)=np[/tex]
Compute the expected value of X as follows:
[tex]E(X)=np[/tex]
[tex]=4\times 0.33\\=1.32[/tex]
Thus, the most likely value for X is 1.32.
(c)
Compute the probability that at least two of the four selected have earthquake insurance as follows:
P (X ≥ 2) = 1 - P (X < 2)
= 1 - P (X = 0) - P (X = 1)
[tex]=1-{4\choose 0}\ (0.33)^{0}\ (1-0.33)^{4-0}-{4\choose 1}\ (0.33)^{1}\ (1-0.33)^{4-1}\\\\=1-0.20151121-0.39700716\\\\=0.40148163\\\\\approx 0.4015[/tex]
Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.
Please someone help me !
Step-by-step explanation:
a. If x is the total numbers of students in school, 35%x = 140.
0.35x = 140
x = 140/0.35 = 400
b. Since there are 400 kids in the school, 15% of them take the bus which is 0.15 * 400 = 60 kids.
What’s the correct answer for this?
Answer:
x = 7
Step-by-step explanation:
<ACF = 90° (since AB is the diameter and it is perpendicular to EF)
But <ACF = 2(7x-4)
So
2(7x-4) = 90
14x-8 = 90
14x = 90+8
14x = 98
Dividing both sides by 14
x = 7
Solve for x: -3x-3=-3(x+1)
Answer:
x= -6 broo
Step-by-step explanation:
The range of which function includes -4?
A y=-x-5
B y=√x+5
C y=√x+5
D y=-{X-5
Range of the given function y=-x-5 includes -4
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
For the given function,
y = -x-5
Wen we put x = -1
we get y = -4
Also,
The range of this function is (-∞, ∞)
Hence,
The function y = -x-5 includes the -4.
To learn more about function visit:
https://brainly.com/question/8892191
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What’s the correct answer for this?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
A tangent meets with the radius to form a right angle
Thus, we can use Pythagoras' theorem
b^2 = c^2 - a^2
Sub the values in:
b^2 = 5^2 - 3^2
b^2 = 16
Square root for the answer:
b = 4
Thus, the answer is option A.
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Answer:
option 1 is the answer
Step-by-step explanation:
IN A CIRCLE , THE TANGENT IS THE PERPENDICULAR TO THE RADIUS DRAWN TO THE POINT OF CONTACT
SO AC ⊥ BC
ie angle ACB= 90 degree
therefore in triangle ABC , ACB = 90 DEGREE
By applying pythagorus theorem ,
AB^2 = AC^2 + BC^2
5^2 = r^2 + 3^2
25 -9 = r^2
16 = r^2
r = square root o f 16
therefore r= 4
please mark me as the brainliest...
