Answer:
1/9
Step-by-step explanation:
Separate the fraction (1/9) from the variable x:
y = (1/9)x.
1/9 is the constant of proportionality.
Someone help me please
Factor by grouping 5x^3+6x^2+25x+30
Answer:
(5x + 6) (x² + 5)
Step-by-step explanation:
5x³ + 6x² + 25x + 30
= x² (5x + 6) + 25x + 30 -- Group 5x³ and 6x²
= x² (5x + 6) + 5 (5x + 6) -- Group 25x and 30
= (5x + 6) (x² + 5) -- Both terms have a common factor of 5x + 6
At a high school, 9th and 10th graders were asked whether they would prefer
robotics or art as an elective. The results are shown in the relative frequency
table.
To the nearest percent, what percentage of 10th graders surveyed preferred robotics?
Using the percentage concept, it is found that 51% of 10th graders surveyed preferred robotics, hence option B is correct.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, we have that 33% out of 65% of the students are 7th graders who preferred robotics, hence the percentage is given by:
[tex]P = \frac{33}{65} \times 100\% = 51%[/tex]
Which means that option B is correct.
More can be learned about percentages at https://brainly.com/question/14398287
#SPJ1
Answer:
It's A. 61% The dude above me is wrong.
Step-by-step explanation:
I just took the test
Make a matrix A whose action is described as follows: The hit by A rotates everything Pi/4 counterclockwise radians, then stretches by a factor of 1.8 along the x-axis and a factor of 0.7 along the y-axis and then rotates the result by Pi/3 clockwise radians.
Answer:
The required matrix is[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]
Step-by-step explanation:
Matrix of rotation:
[tex]P = \left[\begin{array}{ccc}cos\pi/4&-sin\pi/4\\sin\pi/4&cos\pi/4\end{array}\right][/tex]
[tex]P = \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]
x' + iy' = (x + iy)(cosθ + isinθ)
x' = x cosθ - ysinθ
y' = x sinθ + ycosθ
In matrix form:
[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos\theta&-sin\theta\\sin \theta&cos\theta\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]
The matrix stretches by 1.8 on the x axis and 0.7 on the y axis
i.e. x' = 1.8x
y' = 0.7y
[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]
[tex]Q = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right][/tex]
According to the question, the result is rotated by pi/3 clockwise radians
[tex]R = \left[\begin{array}{ccc}cos(-\pi/3)& -sin(-\pi/3)\\-sin(\pi/3)&cos(\pi/3)\end{array}\right][/tex]
[tex]R = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right][/tex]
To get the matrix A, we would multiply matrices R, Q and P together.
[tex]A = RQP = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right] \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]
[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]
If TU = 6 units, what must be true? SU + UT = RT RT + TU = RS RS + SU = RU TU + US = RS
Answer:
Since RT = 12, TU = 6 and RS = 24, T and U are the midpoints of RS and TS respectively. This means that SU + UT = RT.
Answer:
su+ut=rt
Step-by-step explanation:
5x is equal to 8X raise to power - 1/3
Answer:
No solutions.
Step-by-step explanation:
5x = 8x^-1/3
Divide 8 into both sides.
5/8x = x^-1/3
Divide both sides by x.
5/8 = x^-4/3
Multiply both sides by the exponent -3/4.
5/8^-3/4 = x
1.422624 = x
Plug in 1.422624 for x to check.
It does not work. There are no real solutions.
Couple more! Running out of time lol!
Answer:
A translation; (x,y) --> (x-4,y-5)
Step-by-step explanation:
This is because the figures are congruent and in the same orientation but just in different locations on the coordinate plane.
A(0,3) --> A'(-4,-2)
So, the rule is (x,y) --> (x-4,y-5)
Which of the following represents the set of possible rational roots for the
polynomial shown below?
2^2+ 5^2 – 8x– 10 = 0
For the data set represented by this box plot, what is the value of the maximum? maximum:
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
6.1.3
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
Answer:
μ = 0σ = 1Step-by-step explanation:
A standard normal probability distribution is a normal distribution that has a mean of zero and a standard deviation of 1.
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answer:
Answer is Y
Step-by-step explanation:
Find the equation for the parabola that has its vertex at the origin and has directrix at x=1/48
Answer:
The equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].
Step-by-step explanation:
As directrix is a vertical line, the parabola must "horizontal" and increasing in the -x direction. Then, the standard equation for such geometric construction centered at (h, k) is:
[tex]x - h = 4\cdot p \cdot (y-k)^{2}[/tex]
Where:
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the location of vertex with respect to origin, dimensionless.
[tex]p[/tex] - Least distance of directrix with respect to vertex, dimensionless.
Since vertex is located at the origin and horizontal coordinate of the directrix, least distance of directrix is positive. That is:
[tex]p = x_{D} - x_{V}[/tex]
[tex]p = \frac{1}{48}-0[/tex]
[tex]p = \frac{1}{48}[/tex]
Now, the equation for a parabola with vertex at the origin and a directrix at x = 1/48 is [tex]x= \frac{1}{12}\cdot y^{2}[/tex].
The polynomial-7.5x^2 + 103 + 2142 models the yearly number of visitors (in thousands) x years after 2007 to a park. Use this polynomial to estimate the number of visitors to the park in 2021.
Answer:
In that year approximately 2114 thousand people visited the park.
Step-by-step explanation:
Since the expression [tex]y(x) = -7.5*x^2 + 103*x + 2142[/tex] models the number of visitors in the park, where x represents the number of years after 2007 and 2021 is 14 years after that, then we need to find "y" for that as shown below.
[tex]y(14) = -7.5*(14)^2 + 103*14 + 2142\\y(14) = -7.5*196 + 1442 + 2142\\y(14) = -1470 + 3584\\y(14) = 2114[/tex]
In that year approximately 2114 thousand people visited the park.
"a. How many study subjects were cases? b. How many study subjects were controls? c. What was the ratio of controls to cases?"
Answer:
The description is provided following.
Step-by-step explanation:
The given question is incomplete. The complete question will be:
Brain tumors No Brain tumors
Cell Phones 63 185
No Cell Phones 96 292
The further explanation is given below.
a...
Subjects with these symptoms/diseases are recognized as "cases." Consequently, the majority of the instances would be as follows:
⇒ [tex]63+96[/tex]
⇒ [tex]159[/tex]
b...
Subjects who might not have the disorder or infection are classified as "controls." Therefore, the amount of controls is as follows:
⇒ [tex]185+292[/tex]
⇒ [tex]477[/tex]
c...
The proportion of control and monitoring of instances:
⇒ [tex]\frac{478}{159}[/tex]
⇒ [tex]3.006[/tex]
Jennifer has carpet in her square bedroom. She decides to also purchase carpet for her living room which is rectangular in shape and 9 feet longer than her bedroom.
The area of the carpet required in the living room is given by the quadratic expression below, where x represents the side length, in feet, of the carpet in the bedroom.
X^2 + 9X
Match each part of the expression with what is represents.
Answer/Step-by-step explanation:
Let's highlight the dimensions of the bedroom and living room using the information given in the question:
==>Squared Bedroom dimensions:
Side length = w = x ft
Area = x*x = x²
==>Rectangular living room dimensions:
width = side length of the squared bedroom = x
length = (x + 9) ft
Area = L*W = x*(x+9) = x² + 9x
Now let's match each given expression with what they represent:
==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"
As we have shown in the dimensions of the squared bedroom above.
==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room
==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"
i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.
==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".
i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x
Simplify e^ln4
A. 1/4
B. 4
C. 1n4
D. E^4
Answer:
The answer is option B.
4Step-by-step explanation:
Using the expression
[tex] {e}^{ ln(x) } = x[/tex]
[tex] {e}^{ ln(4) } = 4[/tex]
Hope this helps you
Marking Brainliest! 3(x-100)=?
Answer:
3x - 300
Step-by-step explanation:
Expand the brackets or use distribute law.
Answer:
[tex]3x - 300[/tex]solution,
[tex]3(x - 100) \\ = 3 \times x - 3 \times 100 \\ = 3x - 300[/tex]
hope this helps..
An equilateral triangular plate with sides 6 m is submerged vertically in water so that the base is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.) rhog^3(3)^1/2 _______ dx = _______ N
Answer:
26,400 N
Step-by-step explanation:
PLEASE CHECK ATTACHMENT FOR COMPLETE SOLUTION
Pls help me find the volume of this solid
Answer:
240cm³
Step-by-step explanation:
First, let's assume the entire shape is full rectangular prism without that has the middle being cut out.
What this means is that, to get the volume of the solid made out of clay, we would calculate the solid as a full rectangular prism, then find the volume of the assumed middle cut-out portion. Then find the difference between both.
Let's solve:
Find the volume of the rectangular prism assuming the solid is full:
Volume of prism = width (w) × height (h) × length (l)
w = 4cm
h = 7cm
l = 3+6+3 = 12cm
Volume of full solid = 4*7*12 = 336cm³
Next, find the volume of the assumed cut-out portion using same formula for volume of rectangular prism:
w = 4cm
h = 7-3 = 4cm
l = 6cm
Volume of assumed cut-out portion = 4*4*6 = 96cm³
Volume of solid made from clay = 336cm³ - 96cm³ = 240cm³
In a random sample 765 adults in the United States, 322 say they could not cover a $400 unexpected expense without borrowing money or going into debt. (a) What population is under consideration in the data set
Answer:
The population under consideration in the data set are all the adults in the United States.
Step-by-step explanation:
Sampling
This is a common statistics practice, when we want to study something from a population, we find a sample of this population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
The population of interest are all the residents of New York State.
In this question:
Sample of 765 adults in the United states.
So the population under consideration in the data set are all the adults in the United States.
Each of 100 students in the Allen School can only take 1 CSE class each, between the four classes CSE 311, CSE 312, CSE 331, and CSE 332. Each student (independently of others) takes CSE 311 with probability 0.3, CSE 312 with probability 0.4, CSE 331 with probability 0.1, and CSE 332 with probability 0.2. What is the probability that exactly 31 sign up for CSE 311, 39 sign up for CSE 312, 7 sign up for CSE 331, and 23 sign up for CSE 332
Answer:
[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Step-by-step explanation:
Sample space, n = 100
Let the number of students signed up for CSE 311 = a
Let the number of students signed up for CSE 312 = b
Let the number of students signed up for CSE 331 = c
Let the number of students signed up for CSE 332 = d
Probability of taking CSE 311, [tex]P_a[/tex] = 0.3
Probability of taking CSE 312, [tex]P_b[/tex] = 0.4
Probability of taking CSE 331, [tex]P_c[/tex] = 0.1
Probability of taking CSE 332, [tex]P_d[/tex] = 0.2
[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Progress
Question ID: 470099
One student can paint a wall in 12 minutes. Another student can paint the same wall in 24 minutes. Working together, how long will it
take for them to paint the wall?
Answer:
8 minStep-by-step explanation:
Try this:
1 wall 1 288
------------------------ = --------------- = --------------- min = 8 min
1 wall 1 wall 24 + 12 36
(---------) + (---------) ------------
12 min 24 min 288
Simplify -4 • -4 • -4
Answer: -64
Step-by-step explanation: Since we know that -4 x -4 is a positive, it equals 16, then a positive plus a negative equals a negative, so 16 x -4 equals -64
Answer:
-64
Step-by-step explanation:
-4 • -4 • -4
-4*-4 = 16
16*-4
-64
The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. What is the probability that washing dishes tonight will take me between 12 and 14 minutes
Answer:
The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.
Step-by-step explanation:
Let the random variable X represent the time it takes to wash the dishes.
The random variable X is uniformly distributed with parameters a = 10 minutes and b = 15 minutes.
The probability density function of X is as follows:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]
Compute the probability that washing dishes will take between 12 and 14 minutes as follows:
[tex]P(12\leq X\leq 14)=\int\limits^{12}_{14} {\frac{1}{15-10} \, dx[/tex]
[tex]=\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333[/tex]
Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.
When Vlad moved to his new home a few years ago, there was a young oak tree in his backyard. He measured it once a year and found that it grew by 26 centimeters each year. 4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house? centimeters How many years passed from the time Vlad moved in until the tree was 357 centimeters tall? years
Answer:
The tree was 175 centimeters tall when Vlad moved into the house.
7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.
Step-by-step explanation:
The height of the tree, in centimeters, in t years after Vlad moved into the house is given by an equation in the following format:
[tex]H(t) = H(0) + at[/tex]
In which H(0) is the height of the tree when Vlad moved into the house and a is the yearly increase.
He measured it once a year and found that it grew by 26 centimeters each year.
This means that [tex]a = 26[/tex]
So
[tex]H(t) = H(0) + 26t[/tex]
4.5 years after he moved into the house, the tree was 292 centimeters tall. How tall was the tree when Vlad moved into the house?
This means that when t = 4.5, H(t) = 292. We use this to find H(0).
[tex]H(t) = H(0) + 26t[/tex]
[tex]292 = H(0) + 26*4.5[/tex]
[tex]H(0) = 292 - 26*4.5[/tex]
[tex]H(0) = 175[/tex]
The tree was 175 centimeters tall when Vlad moved into the house.
How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?
This is t for which H(t) = 357. So
[tex]H(t) = H(0) + 26t[/tex]
[tex]H(t) = 175 + 26t[/tex]
[tex]357 = 175 + 26t[/tex]
[tex]26t = 182[/tex]
[tex]t = \frac{182}{26}[/tex]
[tex]t = 7[/tex]
7 years passed from the time Vlad moved in until the tree was 357 centimeters tall.
circumference of 6cm ? help plz <3 heyyy b a e (bet you won't reply :)
Answer:
If r = 6 cm, the the circumference is c = 2π(6) = 12π cm
HOPE THIS HELPS AND PLS MARK AS BRAINLIEST
THNXX :)
BIG Corporation advertises that its light bulbs have a mean lifetime, μ, of 2800 hours. Suppose that we have reason to doubt this claim and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 2620 hours and that the sample standard deviation of the lifetimes is 650 hours.
In the context of this test, what is a Type II error?
A type II error is (rejecting/failing to reject) the hypothesis that μ is (less than/less than or equal to/greater than/greater than or equal to/not equal to/equal to) ____ when in fact, μ is (less than/less than or equal to/greater than/greater than or equal to/not equal to/equal to) ______.
Answer:
A type II error is failing to reject the hypothesis that μ is equal to 2800 when in fact, μ is less than 2800.
Step-by-step explanation:
A Type II error happens when a false null hypothesis is failed to be rejected.
The outcome (the sample) probability is still above the level of significance, so it is consider that the result can be due to chance (given that the null hypothesis is true) and there is no enough evidence to claim that the null hypothesis is false.
In this contest, a Type II error would be not rejecting the hypothesis that the mean lifetime of the light bulbs is 2800 hours, when in fact this is false: the mean lifetime is significantly lower than 2800 hours.
which of the following descriptions represent the transformation shown in the image? Part 3c
Answer: c) rotation of 180° & shift right 1 unit and down 2 units
Step-by-step explanation:
Rotation of 180° changes the signs of x and y
(x, y) → (-x, -y)
Shift right one unit adds 1 to x, Shift two down subtracts 2 from y
(-x, -y) → (-x + 1, -y - 2)
(x, y) (-x + 1, -y - 2)
(-1, -2) → (2, 0)
(-4, -1) → (5, -1)
(-4, -3) → (5, 1)
Simplify The square root of 5 (6-4 the square root of 3)
Answer:
7.75
Step-by-step explanation:
6-4=2
2 times the square root of 3=3.46410161514
square root of 5 times 3.46410161514=7.74596669242
to 2dp=7.75
An experiment consists of dealing 7 cards from a standard deck of 52 playing cards. What is the probability of being dealt exactly 4 clubs and 3 spades?
Answer: 0.00153
Step-by-step explanation:
Given: An experiment consists of dealing 7 cards from a standard deck of 52 playing cards.
Number of ways of dealing 7 cards from 52 cards = [tex]^{52}C_7[/tex]
Since there are 13 clubs and 13 spades.
Number of ways of getting exactly 4 clubs and 3 spades=[tex]^{13}C_4\times\ ^{13}C_3[/tex]
Now, the probability of being dealt exactly 4 clubs and 3 spades
[tex]=\dfrac{^{13}C_4\times\ ^{13}C_3}{^{52}C_7}\\\\\\=\dfrac{{\dfrac{13!}{4!(9!)}\times\dfrac{13!}{3!10!}}}{\dfrac{52!}{7!45!}}\\\\=\dfrac{715\times286}{133784560}\\\\=0.00152850224271\approx0.00153[/tex]
Hence, the probability of being dealt exactly 4 clubs and 3 spades = 0.00153