The value of source of illumination (I) is 32 luxes when the distance d = 4 m.
The brightness of illumination that is denoted by I of ab object varies inversely as the square of of its distance which is denoted by variable 'd'.
So, I ∝ 1/d²
Therefore, I = k/d².......... (i), where k is a non zero proportionality constant.
It is given that if the source of illumination I = 18 luxes when d = 4 m.
Substituting I = 18 and d = 4 in the equation (i) we get,
18 = k/4²
k/16 = 18
k = 18*16 = 288
Now we have to find the value of I when d = 3m.
Now the relation becomes. I = 288/d²
Substituting the value d = 3 in equation (ii) we get,
I = 288/3² = 288/9 = 32 Iuxes.
Hence the source of illumination now is 32 Iuxes.
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Answer this based on the question. Thank you.
The interval of systolic blood pressure that represents the middle 95% of males is [94, 126].
What is the mean and standard deviation?The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
According to the given information:According to the empirical rule (also known as the 68-95-99.7 rule), for a normal distribution, approximately 68% of the observations fall within one standard deviation of the mean, approximately 95% of the observations fall within two standard deviations of the mean, and approximately 99.7% of the observations fall within three standard deviations of the mean.
In this case, we want to find the interval that contains the middle 95% of observations. Since the distribution is normal, we know that approximately 95% of the observations will be within two standard deviations of the mean. Therefore, we need to find the values that are two standard deviations away from the mean in both directions.
Using the formula for z-scores, we can find the z-score corresponding to the upper and lower endpoints of this interval:
z_lower = (x_lower - mu) / sigma = (x_lower - 110) / 8 = -2
z_upper = (x_upper - mu) / sigma = (x_upper - 110) / 8 = 2
Solving for x_lower and x_upper, we get:
x_lower = mu + z_lower * sigma = 110 + (-2) * 8 = 94
x_upper = mu + z_upper * sigma = 110 + 2 * 8 = 126
Therefore, the interval of systolic blood pressure that represents the middle 95% of males is [94, 126].
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The graph shows g(x), which is a translation of f(x)=x2. Write the function rule for g(x)
Answer:
g(x) = x^2 -3
Step-by-step explanation:
First of all we see that the graph is shifted downward (f(0)=0^2=0)
let g(x) = f(x) + c = x^2 + c
where c is a constant
from the graph we know that:
g(0) = -3
0^2 + c = -3
c = -3
so g(x) = x^2 -3
then plug in some points to see if its true:
g(2) = 2^2 - 3 = 1 ### correct
g(3) = 3^2 - 3 = 6 ### correct
Find the measure of the indicated angle to the nearest degree
Answer:
D
Step-by-step explanation:
using the cosine ratio in the right triangle
cos ? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{27}{40}[/tex] , then
? = [tex]cos^{-1}[/tex] ( [tex]\frac{27}{40}[/tex] ) ≈ 48° ( to the nearest degree )
proportional? x −4 −2 0 y 0 2 4 x 3 1 −1 y −2 0 2 x 0 1 2 y −1 0 1 x 6 3 0 y −2 −1 0
Answer:
The first set of data is not proportional because the ratio between the input and output values is not constant. For example, when x decreases from -4 to -2, y increases by 2 (from 0 to 2), which is a ratio of 1:1. When x decreases from -2 to 0, y increases by 2 (from 2 to 4), which is a ratio of 1:2.
The second set of data is proportional because the ratio between the input and output values is constant. For example, when x decreases from 3 to 1, y increases by 2 (from -2 to 0), which is a ratio of 1:1. When x decreases from 1 to -1, y increases by 2 (from 0 to 2), which is also a ratio of 1:1.
The third set of data is proportional because the ratio between the input and output values is constant. For example, when x increases from 0 to 1, y increases by 1 (from -1 to 0), which is a ratio of 1:1. When x increases from 1 to 2, y increases by 1 (from 0 to 1), which is also a ratio of 1:1.
The fourth set of data is not proportional because the ratio between the input and output values is not constant. For example, when x decreases from 6 to 3, y decreases by 1 (from -2 to -1), which is a ratio of 1:3. When x decreases from 3 to 0, y decreases by 1 (from -1 to 0), which is a ratio of 1:3, but from x=0 to x=-3, y does not decrease by 1, meaning that the ratio among changes varies.
Mateo is thinking of a whole number .If he multiplies his number by 3, the answer is less than 30 .If he multiplies his number by 6, the answer is more that 40.There is more than one number that Mateo could be thinking off.
What is the sum of all of the numbers Mateo could be thinking of?
In art class students are mixing blue and red paint to make purple paint. Justin mixes 7 cups of blue paint and 6 cups of red paint. Latanya mixes 4 cups of blue paint and 3 cups of red paint. Whose purple paint will be bluer?
Answer:
mark me brilliant
Step-by-step explanation:
To determine whose purple paint will be bluer, we need to compare the ratios of blue to red in their mixes.
Justin's ratio of blue to red is 7:6 or 7/6.
Latanya's ratio of blue to red is 4:3 or 4/3.
To compare which ratio has more blue, we can simplify each ratio so that they have the same denominator:
- Justin's ratio: 7/6
- Latanya's ratio: 4/3 = 8/6
Now we can see that Justin's mix has a slightly higher ratio of blue to red than Latanya's mix. Therefore, Justin's purple paint will be bluer.
Answer:
Step-by-step explanation:
For Justin, the ratio is 7 cups of blue paint to 6 cups of red paint. For Latanya, the ratio is 4 cups of blue paint to 3 cups of red paint.
To compare the blueness of their purple paint, we must simplify these ratios. Justin's ratio simplifies to 7/6, while Latanya's ratio simplifies to 4/3. Now, let's convert these fractions to decimals for easier comparison:
Justin: 7 ÷ 6 ≈ 1.167
Latanya: 4 ÷ 3 ≈ 1.333
As you can see, Latanya's ratio (1.333) is greater than Justin's (1.167), which means her purple paint will be bluer.
if sin(theta) = -2/5, and theta is in quadrant 111, then find
In the quadrant III, all except tangent and cotangent have negative values.
Given,
sinθ = -3/5
sinθ = opposite/hypotenuse
So, adjacent = √5² - 3²
Adjacent = 4
So, cosθ = -4/5
tanθ = sinθ/cosθ
tanθ = 3/4
cosecθ = 1/sinθ = -5/3
secθ = 1/cosθ = -4/5
cotθ = 1/tanθ = 4/3
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Your question was incomplete, but most probably your question will be:
If sin(theta) = -3/5, and theta is in quadrant 111, then find cosθ, tanθ, cosecθ, secθ and cotθ.
8.88=4.44(x+7) answer pls I need it asap!!!
To solve for x in the equation 8.88 = 4.44(x+7), we need to isolate x on one side of the equation. Here are the steps:
Distribute the 4.44 on the right side of the equation:
8.88 = 4.44x + 31.08
Subtract 31.08 from both sides of the equation:
-22.2 = 4.44x
Divide both sides by 4.44:
x = -5
Therefore, the solution for x in the equation 8.88 = 4.44(x+7) is x = -5.
One way to determine if a square root is rational or irrational is
to_
-Determine if it is the square root of any rational number
-Find out if it is the square root of a perfect square
-Rewrite the square root as a rational exponent
19) Grace competes on her school's archery team. On average she hits a bullseye 2 out of every 3
arrows. She shoots 5 arrows during each round of competition. Describe a simulation that you
could run to estimate the number of bullseyes Grace will hit during her next round. Explain
In order to simulate the amount of bullseyes that Grace will strike during her upcoming turn, we can carry out the following steps:
Within each loop cycle, generate 5 random integers between 0 and 1 to represent the likelihood of hitting a bullseye with each missile.
Accumulate the total number of bullseyes achieved for each round by adding the number of times the generated figure is less than or equal to 2/3.
After successfully running the simulation through 10,000 rounds, divide the total number of bullseyes hit by 10,000 to get the average number of bullseyes struck every round.
Finally, state the expected number of bullseyes that Grace will hit on her next turn by saying the average from step 4.
As a result, by prudently repeating numerous rounds, our algorithm can factor in the differential element instinctive throughout this process and eventually obtain a more precise tally of the predicted number of bullseyes Grace may potentially hit during her upcoming turn.
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Sami’s puppy went form weighting 21 pounds to 37 pounds. What is the percent increase in weight?
Answer:
76% increase (approximately)
Step-by-step explanation:
21 lbs ➜ 37 lbs.
To calculate percentage increase, you must first find the difference of the final value and the starting value.
[tex]37-21=16[/tex]
Second, take the difference and divide it from the starting value.
[tex]16/21\\=0.76[/tex] (approximately)
Lastly, take the quotient and multiply it by 100.
[tex]0.76 *100\\=76[/tex]
Therefore, there was a 76% increase in weight.
Can some figure out the answer here?
Answer:
Step-by-step explanation:
d=71 vertical angles-angles across 2 intersecting are =
e=180-71=109 supplementary angles are =180
g=19
boxes 3,4, 5, 6, 8 are true
The equation for line f can be written as y=
9
5
x–2. Perpendicular to line f is line g, which passes through the point (5,–
3). What is the equation of line g?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
y = -5x/9 - 2/9
Step-by-step explanation:
if two lines are perpendicular to each other,
the product of their slopes are -1
(slope of f)(slope of g) = -1
(9/5)(slope of g) = -1
(slope of g) = -5/9
equation of g:
(y - (-3))/(x - 5) = -5/9
(y+3) = -5/9 * (x-5)
y = -5x/9 + 25/9 - 3
y = -5x/9 - 2/9
NO LINKS!!! URGENT HELP PLEASE!!!
Show that the triangle with vertices A, B, and C is a right triangle.
Answer:
[tex]\left[d(A,C)\right]^2=\boxed{178}[/tex]
[tex]\left[d(A,B)\right]^2+\left[d(B,C)\right]^2=\boxed{128+50=178}[/tex]
[tex]\text{Area of the triangle}=\boxed{40}\; \text{units}^2[/tex]
Step-by-step explanation:
From inspection of the given triangle, the coordinates of vertices A, B and C are:
A = (9, 4)B = (1, -4)C = (-4, 1)We can use the distance formula to find the lengths of the sides of triangle ABC.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}d(A, C) & =\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\& =\sqrt{(-4-9)^2+(1-4)^2}\\& =\sqrt{(-13)^2+(-3)^2}\\& =\sqrt{169+9}\\& =\sqrt{178}\end{aligned}[/tex]
[tex]\begin{aligned}d(A, B) & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(1-9)^2+(-4-4)^2}\\& =\sqrt{(-8)^2+(-8)^2}\\& =\sqrt{64+64}\\& =\sqrt{128}\end{aligned}[/tex]
[tex]\begin{aligned}d(B, C) & =\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\& =\sqrt{(-4-1)^2+(1-(-4))^2}\\& =\sqrt{(-5)^2+(5)^2}\\& =\sqrt{25+25}\\& =\sqrt{50}\end{aligned}[/tex]
Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Therefore, to determine if triangle ABC is a right triangle, substitute the found side lengths into the Pythagoras Theorem:
[tex]\begin{aligned}\implies \left[d(A, B)\right]^2 + \left[d(B, C)\right]^2 &= \left[d(A, C)\right]^2\\\left[\sqrt{128}\right]^2+\left[\sqrt{50}\right]^2&=\left[\sqrt{178}\right]^2\\128+50&=178\\178&=178\end{aligned}[/tex]
As the equation is true, this proves that triangle ABC is a right triangle.
The area of a right triangle is half the product of the lengths of its legs.
The legs of triangle ABC are AB and BC.
Therefore, the area of triangle ABC is:
[tex]\begin{aligned}\text{Area\;of\;triangle\;$ABC$}&=\dfrac{1}{2} \cdot d(A,B) \cdot d(B,C)\\\\&=\dfrac{1}{2} \cdot \sqrt{128} \cdot \sqrt{50}\\\\&=\dfrac{1}{2} \cdot \sqrt{128 \cdot 50}\\\\&=\dfrac{1}{2} \cdot \sqrt{6400}\\\\&=\dfrac{1}{2} \cdot \sqrt{80^2}\\\\&=\dfrac{1}{2} \cdot 80\\\\&=40\; \text{square\;units}\end{aligned}[/tex]
Therefore, the area of the triangle is 40 square units.
1)
B 80°
A X+40°
E 125
C x+50
D x+5
Sum of the interior angles=
x=
Sum of the interior angles is 540°.
The value of x is 81.67°, and angle A, C, D are 121.67°, 131.67°, 86.67° respectively.
What is the sum of interior angles of a pentagon?
Sum of interior angles of pentagon = (n-2) ×180° = (5 - 2) × 180° = 540°
Where n is number of side of the polygon.
Here given that values of angle A, B, C, D, E are (x + 40°), 80°, (x + 50°), (x + 5°), 125° respectively.
So,
angle A + angle B + angle C + angle D + angle E = 540°
We are Substituting the given values and get,
(x + 40) + 80 + (x + 50) + (x + 5) + 125 = 540
Or, 3x + 295° = 540°
Or,3x = 245°
Or, x = 81.67°
Now,
angle A = x + 40° = 81.67° + 40° = 121.67°
angle C = x + 50° = 81.67° + 50° = 131.67°
angle D = x + 5° = 81.67° + 5° = 86.67°
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Please help me I need this
The equations that can be used to find the length of the base are a and d
The formula for the volume of a rectangular prism is V = lwh
V = volume, l = length
w = width
h = height
In this problem, the volume of the rectangular prism is given as 1,392 cubic centimeters, the height is given as 12 centimeters, and the width is given as 8 centimeters. We can use the formula to find the length of the base as:
l = V / wh
Substituting the given values, we get:
l = 1,392 / (8 x 12)
Simplifying, we get:
l = 14.5
Therefore, the length of the base of the rectangular prism is 14.5 centimeters.
The two equations that can be used to find the length of the base are:
a. 1392 = 96l (multiplying both sides of the equation by 8 x 12)
d. 12 x 8 x l = 1392 (rearranging the formula V = lwh to solve for l)
Therefore, the equations that can be used to find the length of the base are a and d
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A wooden cube has lengths 8cm. It has a mass of 307.2g. Find the density of the cube.
The density of the wooden cube is 0.6 g/cm³ when length is 8cm and has a mass of 307.2g.
To find the density of the wooden cube, we use the formula:
Density = Mass / Volume
Given that the length of the cube is 8 cm, all sides are equal in length.
The volume of a cube is given by the formula:
Volume = side length³
Substituting the given values:
Volume = 8 cm × 8 cm × 8 cm = 512 cm³
Now we can calculate the density:
Density = Mass / Volume = 307.2 g / 512 cm³
Simplifying:
Density = 0.6 g/cm³
Therefore, the density of the wooden cube is 0.6 g/cm³
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condense 51loga-27logb+25logc
The condensed form of the expression is log [(a⁵¹× c²⁵) / b²⁷
We can use the logarithmic identities:
log aˣ = x log a
to simplify the expression:
51 log a - 27 log b + 25 log c
= log a⁵¹- log b²⁷ + log c²⁵
using the identity log (a/b) = log a - log b
= log [(a⁵¹× c²⁵) / b²⁷
Therefore, the condensed form of the expression is log [(a⁵¹× c²⁵) / b²⁷
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For each z-score below, find the percentile (percent of individuals scoring at or below):
a) z = -0.47
b) z = 2.24
The percentile for each z-score is solved
a) z = -0.47 , P₁ = 32.84%
b) z = 2.24 , P₂ = 98.89%
Given data ,
To find the percentile corresponding to a given z-score, we can use a standard normal distribution table or a calculator that can compute the cumulative distribution function (CDF) of the standard normal distribution.
The CDF gives the probability that a value from a standard normal distribution is less than or equal to a given z-score.
a) For z = -0.47, we can use a standard normal distribution table or a calculator to find the percentile. Let's assume that the percentile corresponding to z = -0.47 is P₁
P₁ = Percentile for z = -0.47
Using a standard normal distribution table or a calculator, we find that P₁ is approximately 32.84%. This means that about 32.84% of individuals scored at or below a z-score of -0.47.
b) For z = 2.24, we can use a standard normal distribution table or a calculator to find the percentile. Let's assume that the percentile corresponding to z = 2.24 is P₂
P₂ = Percentile for z = 2.24
Using a standard normal distribution table or a calculator, we find that P₂ is approximately 98.89%. This means that about 98.89% of individuals scored at or below a z-score of 2.24.
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expand and simplify (x+5)(x-1)
The expanded and simplified form of the expression (x + 5)(x - 1) is x² - x + 5x - 5.
What is the expanded form of the expression?Given the expression in the question;
(x + 5)(x - 1)
To expand and simplify the expression (x+5)(x-1),
we use the distributive property:
(x + 5)(x - 1)
x(x - 1) + 5(x - 1)
Now we can simplify each term by using the distributive property again:
x(x - 1) = x² - x
5(x - 1) = 5x - 5
Putting these terms back together, we have:
(x+5)(x-1) = x² - x + 5x - 5
Combining like terms, we get:
(x+5)(x-1) = x² + 4x - 5
Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.
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Need help will give brainliest and 5 stars for quick answers! I have 20 minutes to do this!
Answer:
Step-by-step explanation:
[tex]\frac{4(x+9)(x-4)^{2}(x+2) }{(x-3)(x+5)^{2} (x+2)}[/tex]
The only think i'm unsure of is the square on bottom. I know the exponents need to add up because there is a horizontal asymptote vs. slant. Everything else is right
4 on top is for the HA
x+9 is for going through x
x-4 touches
x+2 on top and bottom is hole
x-3 and x+5 is VA
A scientist wants to find the radius, in meters, of this hemispherical dome. She finds that the surface area of the entire sphere containing the dome is 520 square meters. Which equation could she use to find the dome's radius?
I NEED HELP PLEASE! WILL MARK BRAINLIEST IF CORRECT !
Answer: 71.57
Step-by-step explanation:
You are going to use SOH CAH TOA to find the angle
because the opposite and adjacent are the sides from the reference angle use TOA (tanΘ=opp/adj)
TanΘ=[tex]\frac{9}{3}[/tex]
now use that tan^-1 (9/3) on your calculator (make sure your calc is in degree mode)
71.57
Can somone help with this
If the cylindrical-barrel's volume is 785.4 ft³, then the radius of barrel is approximately 5 ft, so option(c) is correct.
We know that cylindrical barrel's volume is given by formula : V = πr²h
where V represents volume, r represents radius, and h represents height of the cylinder.
In this case, we know that the volume of barrel is 785.4 ft³ and the height is 10 ft.
Substituting these values and π ≈ 3.14, into the Volume-formula,
We get,
785.4 = 3.14 × r² × (10);
785.4/31.4 = r²,
r = √(785.4/31.4),
r ≈ 5 ft
Therefore, the radius of the barrel is (c) 5 feet.
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what is the slope of y=3/4x?
Answer: [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
In a slope-intercept equation written in the form as y = mx + b, the slope is equal to m
y = 3/4x
The slope is [tex]\frac{3}{4}[/tex]
4. Samantha received $59 for her birthday. She spent $25 on a
charm bracelet. Her brother now has twice as much money as
Samantha. How much money does Samantha's brother have?
The answer will be $68 and Here's Why:
Samantha received $59 for her birthday. That will be the base of the equation. She spent $25 on a charm bracelet so that will be the number being subtracted.
$59 - $25 = $34
We also know that he brother has twice as much money as she does. So that means he has 2x more money than her.
So: $34 x 2 = $68.
So here brother has $68 more than her.
Solve the following system of equations:
x+y=−4
y=x2−6x
Answer:
We can start by substituting y from the first equation into the second equation:
y = x^2 - 6x
x + y = -4
x + (x^2 - 6x) = -4
x^2 - 5x - 4 = 0
We can solve for x by factoring:
(x - 4)(x + 1) = 0
So x = 4 or x = -1.
If x = 4, then y = -8 from the first equation, and y = 4^2 - 6(4) = -8 from the second equation, so (x,y) = (4,-8) is a solution.
If x = -1, then y = 3 from the first equation, and y = (-1)^2 - 6(-1) = 7 from the second equation, so (x,y) = (-1,3) is another solution.
Therefore, the system of equations has two solutions: (4,-8) and (-1,3).
If f(x) = 3x − 4, which of these is the inverse of f(x)?
-
O A. f¹(x) = 24
O B. f¹(x) = + 4
O C. ¹(x)=-4
○) D. ƒ¨¯¹(x) = 2-3 4
The inverse of the function f(x) = 3x - 4 is f⁻¹(x) = x/3 + 4/3.
What is the inverse of the given function?The inverse of a function is simply a new function that "reverses" the action of the original function.
Given the function in the question:
f(x) = 3x - 4
To find the inverse of f(x) = 3x - 4, we simply need to solve for x in terms of y.
f(x) = 3x - 4
y = 3x - 4
Interchange the variables
x = 3y - 4
Solve for y
Adding 4 to both sides:
x + 4 = 3y - 4 + 4
x + 4 = 3y
3y = x + 4
Dividing both sides by 3:
3y/3 = x/3 + 4/3
y = x/3 + 4/3
Replace y with f⁻¹(x)
f⁻¹(x) = x/3 + 4/3
Therefore, the inverse is f⁻¹(x) = x/3 + 4/3
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Solve the proportion.
3x/9=7/4
Answer:
exact form: x=21/4
decimal form: 5.25.
mixed number form: x=5 1/4
Step-by-step explanation:
have a good day :)
Answer:
x = 5.25 or 21/4 or 5 1/4
Step-by-step explanation:
3x : 9 = 7 : 4
3x = 9 x 7 : 4
3x = 63 : 4
3x = 15.75
x = 15.75 : 3
x = 5.25 or 21/4 or 5 1/4
-----------------
check
(3 × 5.25) : 9 = 7 : 4
15.75 : 9 = 7 : 4
1.75 = 1.75
same value, the answer is good
Please help! will mark brainliest!
Answer:
6 teaspoons!
Step-by-step explanation:
if he is doubling the recipe (4 divided by 2 = 2) then 3 * 2 would give you 6!
