Answer:
Length x = 36ft
Breadth y = 15 ft
Therefore, the dimensions of the room x by y is 36ft by 15ft.
Step-by-step explanation:
Let x and y represent the length and breadth of the room
And r represent the diagonal of the room.
Given;
One wall measures 21 ft longer than the adjacent wall
x = y + 21 .......1
The diagonal of a rectangular room is 39 ft long
r = 39ft
Since r is the diagonal, applying Pythagoras theorem;
r = √(x^2 + y^2) = 39
√(x^2 + y^2) = 39
Square both sides and substitute equation 1;
(x^2 + y^2) = 39^2
((y+21)^2 +y^2) = 39^2
(y^2 + 42y + 21^2 + y^2) -39^2 = 0
2y^2 +42y - 1080 = 0
y^2 + 21y - 540 = 0
Solving the quadratic equation, we have;
y = - 39 or y = 15
Since length cannot be negative then;
y = 15 ft
From equation 1;
x = y + 21
x = 15 + 21
x = 36 ft
Length x = 36ft
Breadth y = 15 ft
Therefore, the dimensions of the room x by y is 36ft by 15ft.
Given that (0,0) is on the graph of f(x), find the
corresponding point for the function
f(x) – 5.
Answer:
(0, -5)
Step-by-step explanation:
You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).
That would be ...
(x, f(x) -5) = (0, 0 -5) = (0, -5)
If function g is defined by the equation y − 3x = -14, which equation represents the function in function notation?
Answer:
A
Step-by-step explanation:
First, we can change the equation into y = mx + b form:
y - 3x = -14
y = 3x - 14
Now, we can just replace y with g(x):
g(x) = 3x - 14
the number of locally owned businesses in our town seems to be decreasing at a rate of 35 per year. If there are 860 locally owned businesses today, what number can we expect to have in 5 years?
Answer:
685
Step-by-step explanation:
today: 860
in 1 year: 860 - 35 = 825
in 2 years: 825 - 35 = 790
in 3 years: 790 - 35 = 755
in 4 years: 755 - 35 = 720
in 5 years: 720 - 35 = 685
if there are about 3.346x10^26 molecules of water in a liter of water and the ocean is about 1.26x10^21 liters in volume, how many water molecules are there in the ocean?
Answer: 4.21596 x 10⁴⁷
Step-by-step explanation:
(3.346 x 10²⁶) (1.26 x 10²¹)
= (3.346 x 1.26) x 10²⁶⁺²¹
= 4.21596 x 10⁴⁷
You just purchased two coins at a price of $1,030 each. Because one of the coins is more collectible, you believe that its value will increase at a rate of 7.7 percent per year, while you believe the second coin will only increase at 7.1 percent per year. If you are correct, how much more will the first coin be worth in 20 years
Answer:4541(Rounded) 4541.99779(Unrounded)
Step-by-step explanation:
A= P(1 + r)^T
A= answer
P=principle(amount of money)
r=Rate(percent / 100)
T=Time(Annually)
1030(1 + .077)^20
Brainliest would be appericiated!
No one is helping me :( Can someone please give me a hand? :(
Which statement best describes the graph of x^3 – 3x^2
- X + 3?
A.It starts down on the left and goes up on the right
and intersects the x-axis at x = -1, 2, and 3.
B.It starts down on the left and goes up on the right
and intersects the x-axis at x = -1, 1, and 3.
C.It starts up on the left and goes down on the right
and intersects the x-axis at x = -1, 2, and 3.
D.It starts up on the left and goes down on the right
and intersects the x-axis at x = -1, 1, and 3.
What is this expression in simplified form?
3^3 x 6^6
Answer:
i think its 1259712.
Step-by-step explanation:
when we find3^3 and 6^6 we get, 27×46656
and by multiplying them we get, 1259712...
is answer
Answer:
1,259,712
Step-by-step explanation:
Follow the order of operations, evaluating exponents first:
3^3 × 6^6 = 27 × 46,656 = 1,259,712
_____
When in doubt, the Google calculator can be relied upon to follow the order of operations. (Use an asterisk (*) for multiplication.)
Solve the equation. dx/dt =3/xet +9x An implicit solution in the form F(t.x)C, where C is an arbitrary constant.
Answer:
[tex]\text{The implicit solution:} \frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C[/tex]
Step-by-step explanation:
It is given that there is arbitrary constant C and we have to find the implicit solution. Therefore, first separate the variable that is given in equation and then use integration to find the implicit solution. Here, below is the calculation.
The given equation is:
[tex]\frac{dx}{dt} = \frac{3}{xe^{t-9x}}[/tex]
Now, if we use separation of variable.
[tex]\frac{dx}{dt} = \frac{3}{xe^{t-9x}} \\\frac{dx}{dt} = \frac{3}{xe^{9x}e^{t}} \\xe^{9x}dx = \frac{3}{e^{t}}dt \\[/tex]
Now integrate both side:
[tex]\int xe^{9x} dx = \int \frac{3}{e^{t}} dt \\\frac{e^{9x}}{9}(x) - \int \left [ \frac{e^{9x}}{9} \right]dx = -3e^{-t} + C \\[/tex]
[tex]\frac{xe^{9x}}{9} - \frac{e^{9x}}{81} = -3e^{-t} + C \\\frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C \\[/tex]
Thus, the implicit solution is:
[tex]\frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C[/tex]
You wish to accumulate $14,580 in 6 years. Payments are made at the end of every six-month period into an account earning 7.2% compounded semi-annually. Find the required payment amount to accomplish your goal.
If a sample of size 41 is selected, the value of A for the probability P(-A ≤ t ≤ A) = 0.90 is:
Answer: 1.684
Step-by-step explanation:
since sample size (n) is 41
confidence level = 0.90 = 90%
df = n - 1
df = 41 - 1
df = 40
that is For Degrees of Freedom = 40
significance level α = 1 - (confidence level / 100)
Significance Level α = 1 - (90/100 ) = 0.10
using the z-score
critical values of t = 1.684
A graph has been attached to further assist.
The mean weight of an adult is 6767 kilograms with a variance of 121121. If 164164 adults are randomly selected, what is the probability that the sample mean would be greater than 64.864.8 kilograms
Answer:
99.48% probability that the sample mean would be greater than 64.8 kilograms.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 67, \sigma = \sqrt{121} = 11, n = 164, s = \frac{11}{\sqrt{164}} = 0.86[/tex]
What is the probability that the sample mean would be greater than 64.8 kilograms?
This is 1 subtracted by the pvalue of Z when X = 64.8.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.8 - 67}{0.86}[/tex]
[tex]Z = -2.56[/tex]
[tex]Z = -2.56[/tex] has a pvalue of 0.0052
1 - 0.0052 = 0.9948
99.48% probability that the sample mean would be greater than 64.8 kilograms.
Solve and check: 3 x2 + 5x + 6 + x − 1 x + 2 = 7 x + 3
Answer:
3[tex]x^{2}[/tex] -2x +5=0
Step-by-step explanation:
Combine liked terms:
3[tex]x^{2}[/tex]+5x+x-1x+6+2=7x+3
3[tex]x^{2}[/tex]+6x-1x+8=7x+3
3[tex]x^{2}[/tex]+5x+8=7x+3
Subtract 3: 3[tex]x^{2}[/tex]+5x+8-3=7x+3-3
3[tex]x^{2}[/tex]+5x+5=7x
Now subtract 7x:
3[tex]x^{2}[/tex]+5x+5-7x=7x-7x
If you want combine liked terms:
3[tex]x^{2}[/tex]-7x+5x+5=0
3[tex]x^{2}[/tex]-2x+5=0
Hope this helps!
The width of a rectangle is 6 less than the length. Let L represent the length of the rectangle. Write an expression for the width of the rectangle.
Answer:
W+6 = Y.
Or
Y -6 = W
Step-by-step explanation:
Let's call the length of the rectangle L.
And let W represent the width of the rectangle.
Let's write an expression to determine the width of the rectangle relative to the length of the rectangle.
From the question, the width W is 6 less than the length L of the rectangle.
It means the length is greater than the width with 6 units.
The expression is
W+6 = Y.
Or
Y -6 = W
factor the polynomial -5x^3-10x^2-15x
Answer:
-5x(x^2 + 2x + 3)
Explanation:
-5x is the highest common factor of all terms in the polynomial
-5x^3 - 10x^2 - 15x = -5x(x^2 + 2x + 3)
www.g A bag contains 3 white counters, 10 black counters, and 4 green counters. What is the probability of drawing (a) a white counter or a green counter
Answer:
41.18% probability of drawing a white counter or a green counter
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
There are 3+10+4 = 17 counters.
Of those, 3+4 = 7 are white or green
7/17 = 0.4118
41.18% probability of drawing a white counter or a green counter
Solve for y: |6y - 3| + 8 = 35 Select one: a. y = -5 b. y = 5 or y = -4 c. =5=−203 y = 5 o r y = − 20 3 d. y = 5
Answer:
y=5 or y=-4
Step-by-step explanation:
6y - 3| + 8 = 35
|6y-3|=35-8
|6y-3|=27
either 6y-3=-27 then 6y=27+3
y=30/6=5
or 6y-3=-27
6y=-27+3
y=-24/6
y=-4
Graph the equation y = 1/8x-7
Answer:
[tex]slope:1/8y-intercept:-7\\COORDINATES(x,-7)\\\\(56,0)[/tex]
Step-by-step explanation:
I NEED HELP PLEASE THANKS!
An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S47°E. Find a vector that represents the resultant velocity of the plane relative to the point of takeoff. Let i point east, j point north, and k point up.
(Show work)
Answer:
30.7i + 135.9j + 53.4k
Step-by-step explanation:
The ' horizontal ' may act as the x - axis in this case, the airplane taking off at an angle of 173 cos 18 respective to this x - axis. Respectively it travels restricted to an angle of 173 sin 18 from the y - axis. The following shows this angle at vector( s ) j and k relative to the air -
j - ( 173 cos 18 ),
k - ( 173 sin 18 )
Thus, one can assume such -
[tex]0i + ( 173 cos 18 )j + ( 173 sin 18 )k[/tex]
Knowing that, this second bit here should be similar to the first bit above, given that the wind is now blowing with a velocity of 42 miles per hour at an angle of 47 degrees. Therefore, j = 42 cos 47, i = 42 sin 47 -
[tex]( 42 sin 47 )i + ( 42 cos 47 )j + 0k[/tex]
Adding the two we should get the following -
[tex]30.7i +135.9j + 53.4k[/tex]
Answer:
30.72i+ 135.89j +53.46k
Step-by-step explanation:
If we measure angle φ up from the horizontal and angle θ CCW from east, the direction vector of the airplane at take-off is ...
(ρ, θ, φ) = (173 mph, 90°, 18°)
The rectangular expression of this vector will be ...
(ρ·cos(θ)·cos(φ), ρ·sin(θ)·cos(φ), ρ·sin(φ)) = (0, 164.53, 53.46) . . . mph
__
The wind vector is ...
(ρ, θ, φ) = (42, -43°, 0°) ⇒ (30.72, -28.64, 0) . . . mph
And the rectangular coordinate sum of these vectors is ...
(0, 164.53, 53.46) +(30.72, -28.64, 0) = (30.72, 135.89, 53.46)
The resultant velocity vector of the airplane is ...
30.72i+ 135.89j +53.46k
The correlation matrix obtained for the variables bp (y) (blood pressure), age (x1) (age), smk (x2) (smoke) and WET(X3) (Weight), is given by:
BP AGE SMK WET
BP 1 0.64 0.72 0.48
AGE 1 0.32 0.78
SMK 1 0.40
WET 1
Based on this matrix please calculate the partial correlation.
a. 0.53
b. 0.48
c. 0.62
d. 0.32
Answer:
c) 0.62
Step-by-step explanation:
In this case, we are required to find the partial correlation, [tex] r_Y_X_1_|_X_2[/tex].
To find the partial correlation, use the formula:
[tex] r_Y_X_1_|_X_2 = \frac{r_Y_X_1 - r_Y_X_2 * r_X_1_X_2}{\sqrt{1 - r_X_1_X_2}^2 - \sqrt{1 - r_Y_X_2}^2} [/tex]
[tex] r_Y_X_1_|_X_2 = \frac{0.64 - 0.72 * 0.32}{\sqrt{1 - 0.32}^2 - \sqrt{1 - 0.72}^2} [/tex]
[tex] = \frac{0.410}{0.657}[/tex]
[tex] r_Y_X_1_|_X_2 = 0.62 [/tex]
The partial correlation is 0.62.
Option C
What is 27 rounded to the nearest ten? Use the number line to find the answer.
A number line from 10 to 50. An arrow points to 27.
The number 27 when rounded to the nearest ten using the number line will give the number 30.
On the number line, the numbers are marked from 10 to 50.
So, the tens are 10, 20, 30, 40, and 50.
The number 27 has to be rounded to the nearest ten.
The one position will be 0.
Now, 27 lies in between the tens 20 and 30 on the number line.
Now, it is required to find which number is 27 closer to.
There are 7 units from 20 to 27.
But there are only 3 units far from 27 to 30.
So, 27 can be rounded to 30 to the nearest ten.
Learn more about Rounding Off here :
https://brainly.com/question/24234983
#SPJ6
there are 480 students in a class. the ratio of boys to girls is 1:3 how many students in the class are boys
Answer:
120
Step-by-step explanation:
480/(1+3)
480/4
= 120
1 × 120 : 3 × 120
120 : 360
Boys to girls are in the ratio 120:360.
There are 120 boys.
can someone help me asap pls?
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Trigonometry.
so here, we gonna use the cosine ratios.
so here, we also use the Pythagoras Theorem.
[tex] {h}^{2} + {k}^{2} = {r}^{2} [/tex]
so we here, we get
h= 1 ,
[tex]h = 1 \: r = 2 \: k = \sqrt{3} \: \\ \alpha = 60 \: \beta = 30[/tex]
18. You are standing beside the Colorado River, 400 feet
from the base of Hoover Dam. Using an electronic distance
measuring device, you find the distance to the top of the dam
to be 965 feet. Use the diagram at the right to find the height
of the dam.
965ft
a.
561.6 ft
b. 781.6 ft
c. 566 ft
400 ft
166 ft
=======================================================
Work Shown:
The horizontal portion is 400+166 = 566 feet. Label this as 'a', so a = 566. The vertical side is unknown, so b = x. The hypotenuse is c = 965
Use the pythagorean theorem
a^2+b^2 = c^2
566^2+x^2 = 965^2
x^2 = 965^2 - 566^2
x = sqrt( 965^2 - 566^2 )
x = 781.58108984289 which is approximate
x = 781.6 feet when rounding to one decimal place
Mary Jo spends $2,690 to buy stock in two companies. She pays $24 a share to one of the companies and $25 a share to the other. If she ends up with a total of 110 shares, how many shares did she buy at $24 a share and how many did she buy at $25 a share?
Answer:
60 of 24 dollars each and 50 of 25 dollars
Step-by-step explanation:
x= 24 dollars
110 shares, total x at 24 dollars each
110-x at 25 dollars each
24x+25 (110-x)=2690
24x+ 2750 - 25x= 2690
-1x= -60
x= 60
24 multiplied by 60 =1440
2690-1440 =1250
1250 / 25 = 50
can u vote me as brainliest ?
identify which graphs are functions and which graphs are not.
Answer:
Step-by-step explanation:
We will apply the vertical line test in the given graphs to test them for a function.
Option (1) [First in top row]
If we draw a vertical line from any point, none other point of the graph passes through it.
Therefore, Graph (1) is a function.
Option (2) [2nd in the top row]
When we draw a vertical line through (2, 1), another point (2, -1) will pass through this line.
Therefore, Graph (2) is not a function.
Option (3) [1st in the second row]
In this option when a vertical line is drawn from (2, 1) two more points (2, 2) and (2, 3) pass through this line.
Therefore, graph (4) is not a function.
Option (4). [2nd in the 2nd row]
In this graph only one point lie on the vertical lines drawn.
Therefore, Graph (4) is a function.
Which equation represents a population of 250 animals that decrease at the annual rate of 12%
Answer:
P = 250(1 - 0.12)^t
Step-by-step explanation:
Since it is a decrease in population, we have 1 minus the rate. Since we start out with 250, we have 250 times 1 minus the rate. Since we are dealing with annual loss, we get 250(1 - 0.12)^t.
250 - starting population
1 - rate (0.12) - decreasing rate
t - time elapsed
Answer: p = 250(0.88)^t
Write an expression involving integers for each statement a) moving 4 steps left, then moving 9 steps right b) on 3 separate occasions, Shari lost 2 pencils
Answer:
a) x-4+9
b) x-2
For part b, I am not 100% sure about my answer, but I am sure about part a.
Precalculus Help Needed!
Answer:
It approaches 1
Step-by-step explanation:
f(x)=1
The equinoxGroup of answer choicesis when the subsolar point is at one of the tropics.is the longest day of the year at any given place.has 12 hours of day and 12 hours of night for all locations.occurs four times during the year.
Answer:
c. has 12 hours of day and 12 hours of night for all locations
Step-by-step explanation:
The equinox is the time of the year marked by a nearly equal length of day and night. This word has a Latin root meaning which stands for equality, hence the word 'equinox'. It usually falls on March 21, and September 23 of every year. On these days the sun is above the equator.
The equinox which occurs around September happens in the Northern Hemisphere and is also known as the Fall or Autumnal equinox. Whereas, the equinox which occurs at the Southern Hemisphere is also known as the Spring or Vernal equinox. During an equinox, the tilt of the earth is perpendicular to the sun.
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion
Answer:
A sample of 385 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample:
We need a sample of n.
n is found when M = 0.05.
We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]
[tex]n = 384.16[/tex]
Rounding up
A sample of 385 is needed.