ANSWER
The light intensity is 7.0
STEP-BY-STEP EXPLANATION:
What to find? The value of the proportionality constant.
Given parameters
• Light intensity = 569 lumens
,• Distance = 9
According to the question, Light intensity (I) is proportional to the inverse square of the distance.
This can be expressed mathematically as
Let the intensity of light be represented as I
Let the distance be represented as d
[tex]I\text{ }\propto\text{ }\frac{1}{d^2}[/tex]The next thing is to introduce a constant k
[tex]\begin{gathered} I\text{ = }\frac{K\cdot\text{ 1}}{d^2} \\ I\text{ = }\frac{K}{d^2} \end{gathered}[/tex]Recall that,
I = 569 lumens
d = 9
The next thing is to substitute the parameters into the above formula
[tex]\begin{gathered} \frac{Lumens\text{ at current distance}}{\text{Lumens at origin or source}}\text{ = }\frac{1}{d^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{(9)^2} \\ \frac{\text{Lumens at current distance}}{\text{5}69}\text{ = }\frac{1}{81} \\ \text{Cross multiply} \\ 569\cdot\text{ }1\text{ = Lumens at current distance }\cdot\text{ 81} \\ \text{Divide both sides by 81} \\ \frac{569}{81}\text{ = }\frac{Lumens\text{ at current distance }\cdot\text{ 81}}{81} \\ \text{Lumens at current distance = 7.0} \end{gathered}[/tex]What is the cube root of 3 and 512
Answer:
1.4422
Step-by-step explanation:
Depends what they are asking for in some cases they will want you to simplify it to 1.4 or
[tex]\sqrt[n]{x}[/tex] It might also look like this with a 3 on top and bottom
sry if this is confusing
If you have any questions just ask : )
Select the correct answer.
Consider the graph of function g.
A parabola labeled lowercase g declines through the points (negative 4, 4), (negative 3, 2 point 2), (negative 2, 1), (0, 0), (2, 1) and (3 point 5, 3) on the x y coordinate plane.
If f(x) = x2, which equation represents function g?
A. g(x) = f(2x)
B. g(x) = f(4x)
C. g(x) = 2 f(x)
D. g(x) = f(1/2x)
The correct option is B that is g(x)=f(4x) as the condition says, "A parabola labeled lowercase g declines through the points (negative 4, 4), (negative 3, 2 point 2), (negative 2, 1), (0, 0), (2, 1) and (3 point 5, 3) on the x y coordinate plane".
What is parabola?A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side intersect. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one. A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
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help please! will give brainliest
Answer:
I believe the top is 50 because 50 is the b value while the bottom would be 25 because that is the ac value of the expression
Step-by-step explanation:
above
When spinning a wheel with 1 red, 2 blue, and 3 green spaces, what
is the probability that you will not spin a red?
Step-by-step explanation:
so, we have 1 + 2 + 3 = 6 total spaces.
a probability is always the ratio
desired cases / totally possible cases
the probability to spin red is therefore
1 desired case
6 total possible cases
1/6 = 0.166666666...
a probability of 1 means a sure result = anyone of the totally possible cases.
so, 6/6 = 1 in our case.
if the desired cases are everything but red, we need to eliminate the possible red results (1) from the amount of our desired cases : 6 - 1 = 5
so the probability of not spinning a red is
5/6 = 0.833333333...
formally we can also say this is the sure thing minus the opposite of what we want to have. the opposite of not spinning a red is spinning a red (1/6) :
1 - 1/6 = 5/6 = 0.833333333...
what is y+2=-6(x-3) in standard form?
Answer: 6x + y = 16
Step-by-step explanation:
Petrol has a density of: 740 kg/m³ A container holds 12 litres of petrol. One litre is equal to 0.001 m³. What is the mass of the petrol?
The mass of the petrol is 8.88 kg.
Given, Petrol has a density of 740 kg/m³.
A container holds 12 litres of petrol.
One litre is equal to 0.001 m³.
As, Density = Mass/Volume
1 litre = 0.001 m³
12 litres = 0.012 m³
Now, using the formula, we get
740 = mass/0.012
mass = 740×0.012
mass = 8.88 kg
Hence, the mass of the petrol is 8.88 kg.
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How many ways can the letters in the word PARALLEL be arranged?
Answer:
3,360 ways.
Explanation:
In the word PARALLEL
• Number of letters = 8
,• Number of Ls = 3
,• Number of As = 2
Since no other restriction is given, the number of ways in which the letters can be arranged is:
[tex]\frac{8!}{3!\times2!}[/tex]We solve to obtain our result.
[tex]\begin{gathered} \frac{8!}{3!\times2!}=\frac{8\times7\times6\times5\times4\times3!}{3!\times2!} \\ =\frac{8\times7\times6\times5\times4}{2!} \\ =8\times7\times6\times5\times2 \\ =3360\text{ ways} \end{gathered}[/tex]The word can be arranged in 3,360 ways.
Based on the diagram below, we can say that the two triangles ___.
Solution
Step1
The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.
Step2
Two pairs angles are equal, hence they are similar
Answer
Are similar by AA
please help with circles
Answer:
≈ 466 cm
Step-by-step explanation:
the total length of wire required is
outside sides of square + 4 straight pieces + circumference of circle
= (4 × 70) + (4 × 15) + (π d ← d is the diameter )
= 280 + 60 + 40π
= 340 + 125.66
= 465.66
≈ 466 cm ( to the nearest cm )
We need to find out the total length of wire needed to make this design. We can do this by finding out the perimeter of square and Circle and finally adding the lengths of the four 15cm wire used .
Given data:-
length of side of square= 70cmdiameter of Circle= 40cm , r = 20cm 15cm four wiresPerimeter of the square:-
[tex]\longrightarrow p_s = 4(side) \\ [/tex]
[tex]\longrightarrow p_s = 4(70cm) \\ [/tex]
[tex]\longrightarrow p_s = 280cm \\ [/tex]
Perimeter/circumference of the circle:-
[tex]\longrightarrow p_c = 2\pi r \\ [/tex]
[tex]\longrightarrow p_c = 2(3.14)(20cm) \\ [/tex]
[tex]\longrightarrow p_c = 125.71 cm \\ [/tex]
Additionally length of four wires would be 15cm*4 = 60cm .
So , total length of the wire required,
[tex]\longrightarrow l =( 125.71 + 280+60)cm \approx \boxed{466\ cm}\\ [/tex]
and we are done!
Multiply: -3/10 • -5/12
Answer:
15/120 simplified is 1/8
For t(x) = 3x - 5, find the value of x
for which /(x) = 4.
Answer:7
Step-by-step explanation:
3x-5
replace x for 4
3(4)-5
=12-5
=7
Selena and Luis are building a model bridge out of balsa wood. To make a strong bridge, they create each post by laying out two long wooden poles horizontally, as shown in the diagram, and connecting them with smaller strips of balsa wood laid diagonally in a triangle pattern. The triangle pattern is continued down the entire length of the wooden poles.
The poles are 12 centimeters apart, and each small strip of balsa wood is 13 centimeters long.
If the two poles are each 100 centimeters long, how many small strips of balsa wood will they need to connect them?
Pythagoras theorem is used to find the length of sides in geometry. The number of strips of Balsa wood having length of 13cm is 8 approximately.
What is Pythagoras theorem?Pythagoras theorem states that the square of the hypotenuse in a right angled triangle is equal to the sum of the squares of the remaining two sides.
Given that,
The length of each pole = 100cm.
The distance between the pole = 12cm.
The length of each strip of Balsa wood = 13cm.
The diagram for the given question is as follows,
Apply Pythagoras theorem, h² = p² + b² in the given triangle to find the hypotenuse as,
h² = 100² + 12²
=> h² = 10144
=> h = 100.71
Now, the number of strips of balsa wood is equal to hypotenuse divided by 13 which is given as,
100.71 ÷ 13 = 7.74.
Hence, the number of small strips of Balsa wood is 8 approximately.
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50 points to the first person to answer this for me. Solve.
−2 1/3x=−1 3/4
What is the solution to the equation?
Enter your answer as a simplified fraction in the box.
Answer: [tex]x= \frac{3}{4}[/tex]
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Divide each amount in the ratio given. $84in the ratio 2:1
The ratio shows how many times one value is contained in another value.
1 part = $28
2 parts = $56
3 parts = $84
The amount 84 in the ratio 2:1 is 56:28.
What is a ratio?
The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Amount = $84.
We will divide the amount into 2:1
This means,
There are 3 parts.
2 + 1 = 3
The amount for each part.
= 84/3
= 28
Now,
1 parts = $28
2 parts = 2 x $28
2 parts = $56
The ratio 2:1 of 84 is 56:28
Thus,
The amount 84 in the ratio 2:1 is 56:28.
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each day for three weeks, keisha recods the number of eggs her chickens lay. The frequency table shows her data. which statement describes the data distribution
The greatest number of eggs laid by the chicken any day is 7
What is frequency table?A frequency table is a table that lists items and shows the number of times the items occur.Frequency refers to the number of times an event or a value occurs.
A frequency table lists a set of values and how often each one appears.
The frequency table above shows the number of eggs laid for 3weeks.
From the table, the least number of egg laid in anyday is 3 and the greatest number of egg laid in a day is 7.
Therefore the greatest number of egg that can be laid by the chickens in anyday is 7
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Answer:
The distribution is spread from 3 eggs to 7 eggs.
A knitter is planning to knit a blanket and refers to a chart showing the size of blanket that can be knited based on the amount of yarn available.Which statement is true?A.The dependent variable is the amount of yarn because that is the input and the independent variable is the size of the blanket because that is the output B. The dependent variable is the size of the blanket because that is the input and the independent variable is the amount of yarn became that's is the output C. The Independent variable is the amount of yarn because that is the input, and the dependent variable is the size of the blanket became is the output D.The independent variable is the size of the blanket because that is the input, and the dependent variable is the amount of yarn became that is the output for
Since the amount of yarn available is what defines the size of the blanket, the amount of yarn is the independent variable, and it is the input for the table or equation.
The size of the blanket depends on the amount of yarn, so the size of the blanket is the dependent variable, and it is the output of the table or equation.
Therefore the option that shows the true statement is C.
2x-5x-9 = -3x+2-9
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. X=
O B. The solution is all real numbers.
O C. There is no solution.
By simplifiying the linear equation we will see that it is false, then the correct option is C, there are no solutions.
How to solve the linear equation?Here we have the following linear equation:
2x - 5x - 9 = -3x + 2 - 9
We want to solve this linear equation for the variable x, to do so, we need to isolate the variable x in one of the sides of the equation, so let's do that.
First we move all te terms with x to the left side and the terms without x to the right side, so we get:
2x - 5x + 3x = 2 - 9 + 9
(2 - 5 + 3)*x = 2
0*x = 2
0 = 2
So we have a false equation, this means that there is no value of x such that the equation is true, then the equation has no solutions, and the correct option is C.
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Literal equation
6 = 2(m-b)/m+b
for b.
Answer:
b= −1/2m
Step-by-step explanation:
Step 1: Multiply both sides by b+m.
6b+6m=−2b+2m
Step 2: Add 2b to both sides.
6b+6m+2b=−2b+2m+2b
8b+6m=2m
Step 3: Add -6m to both sides.
8b+6m+−6m=2m+−6m
8b=−4m
Step 4: Divide both sides by 8.
The population of a small town is said to be decreasing exponentially at a rate of 2% every year. In the year 2020 the population is 24,597.If this rate continues what is the expected population in the year 2025? Round your answer to the nearest whole number
Using exponential function to calculate the exponential decrease, the population in 2025 is 22278
Exponential FunctionAn exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on. Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
We can write the function as
A = N(1 + r)⁻ˣ
x = timer = rateN = initial valueLet's plug in our values and solve
A = 24597(1 + 0.02)⁻⁵
A = 22,278
The population in 2025 is 22278
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Sarah is going to invest $79,000 and leave it in an account for 7 years. Assuming the
interest is compounded quarterly, what interest rate, to the nearest tenth of a
percent, would be required in order for Sarah to end up with $121,000?
The interest rate that would be required in order for Sarah to end up with $121,000 is R=6.1%
What is meant by compound interest?Compound interest, often known as interest on principal and interest, is the adding of interest to the loan or deposit principal. It occurs when interest is reinvested, added to the lent capital instead of being paid out, or the borrower is required to pay it, resulting in the next period's interest being generated on the principal amount plus any accumulated interest. Finance and economics both use compound interest frequently.
compound interest allows for the accumulation of interest from prior periods.
Given that Sarah is going to invest $79,000 and leave it in an account for 7 years.
We have to assume that the interest is compounded quarterly then,
A=P[tex](1+(R/400))^{4n}[/tex]
121000=79000[tex](1+(R/400))^{28}[/tex]
(121000/79000)=[tex](1+(R/400))^{28}[/tex]
[tex](1.53)^{1/28}[/tex]= [tex](1+(R/400))[/tex]
1.0153=[tex](1+(R/400))[/tex]
0.0153=R/400
R=6.1372
R=6.1%
Therefore, the interest rate is R=6.1%
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Solve the following inequality and select all possible solutions.
You drove 18 miles in 20 minutes at a constant speed and did NOT exceed the speed limit, given in miles per hour. Among the following, which is the lowest that the speed limit could have been?
Answer:
54 mph
Step-by-step explanation:
18 miles / 20 minutes = 18 miles / 1/3 hour
18 ÷ 1/3 = 18 × 3 = 54 mph
The constant speed with given distance and time is 54 miles per hour.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, you drove 18 miles in 20 minutes at a constant speed.
Here, 20 minutes =20/60 =1/3 hours
Now, Speed = Distance÷Time
Speed= 18÷1/3
Speed=54 miles per hour
Therefore, the constant speed is 54 miles per hour.
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The triangle has the sides AB = 4cm BC = 6cm AC = 8cmCalculate the triangles highest corner
Given: A triangle ABC with sides, AB= 4cm
BC=6cm and
AC=8cm
Required: To find out the triangle's highest corner.
Explanation: Let us first draw a triangle with given sides,
Which function is best represented by this graph?
Responses
A
y = - 2 x + 2
5y = - 2 x + 2 5
B
y = - 5 x + 5
2y = - 5 x + 5 2
C
y = - 5 x + 2
2y = - 5 x + 2 2
D
y = 2 x + 2
5
The function best represented by the graph is y = - 5 x + 5 2y = - 5 x + 5². Option B.
Use the vertical line test to determine if a graph represents a function. A graph is a function if a vertical line moves across it and touches it only at one point at a time. If a vertical line touches a graph at multiple points, the graph is not a function.
Calculation:-
X intercept = 2
y intercept = 5
slopt = y/x
= 5/2
= 2.5
For the line to be perpendicular to each other angle must be 90⁰.
Hence option B.
B.y = - 5 x + 5
2y = - 5 x + 5 2
slope m = 5/2
2.5.
A function is defined as a relation between a set of inputs each with an output. Simply put, a function is a relationship between inputs, each associated with exactly one output. Each function has a domain and a codomain or scope. The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of the parabola is the vertex.
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4 Friends shot free throws for a charity event. Adam scored 8 more points than cheryl. Laura scored twice as many points as Adam. Tom scored 10 points less than Laura. Together the four friends scored a total of 66 points.Cheryl's Expression = Adam's Expression = Laura's Expression = Tom's Expression =State each person's points :Cheryl's points = Adam's points = Laura's points = Tom's points =
Let cheryl score "c", Adam score "a", Laura score "l" and Tom score "t", points.
Now, let's write equations for statements given.
Adam scores 8 more than Cheryl, so:
a = c + 8
or
c = a - 8
Laura scored twice as Adam, so:
l = 2a
Tom scores 10 less than Laura:
t = l - 10
or
t = 2a - 10
Altogether, they scored 66, so:
c + a + l + t = 66
Putting the 3 bold equations in the last one, we can solve for "a" first. Shown below:
[tex]\begin{gathered} c+a+l+t=66 \\ a-8+a+2a+2a-10=66 \\ 6a-18=66 \\ 6a=66+18 \\ 6a=84 \\ a=\frac{84}{6} \\ a=14 \end{gathered}[/tex]So,
c = a - 8
c = 14 - 8
c = 6
l = 2a
l = 2(14)
l = 28
t = 2a - 10
t = 2(14) - 10
t = 28 - 10
t = 18
So,
Adam = 14 points
Cheryl = 6 points
Laura = 28 points
Tom = 18 points
find the y-intercept of the graph of the linear equation 2y=x-4
The y intercept of the graph of the linear equation 2y = x - 4 is -2 obtained through the following graph.
Linear equation:
Linear equation means an equation in which the highest power of the variable is always 1 also known as a one-degree equation.
The standard form of a linear equation is ax + b = c
Given,
Here we have the linear equation 2y = x - 4.
Now, we have to find the y - intercept from this equation's graph.
In order to plot the graph for this equation we have to rewrite the given equation then we get,
=> 2y = x - 4
=> y = (x-4)/2
Now we have to take sample value for x, in order to get the table for the equation.
For that we have to take the sample value of x as -2, -1, 0, 1, and 2, then we get the table like the following.
By using the table we have to plot the graph, then the resulting graph is attached below.
Through the graph we have identified that the y - intercept is -2.
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4x - 3y = –6 solve it
Answer:
3ggjurfyeyryeyryryryr
Answer:
see the answer
Step-by-step explanation:
4x-3y=1xy
Two integers, c and d, have a product of -6. What is the greatest possible sum of cand d?
The greatest possible sum of c and d? is 5.
How to calculate the value?From the information, the product is -6. The numbers that can given this value include:
(-1) × (6) = -6
(-2) × (3) = -6
(-6) × 1 = -6
(-3) × (2) = -6
Therefore from the information, the number that will give the greatest sum will be:
-1 + 6
= 5
Therefore, the greatest sum is 5.
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I need help to solve part B and give my reasoning in two collum proof.
SOLUTION
3(a)
The diagram below would be helpful
From the diagram above, a segment has been made from C to O indicating the radius of the circle, so CO is a radius.
Also any line drawn from the center of a circle to touch the circumference is a radius, So, OB is a radius too.
Since CO and OB are radii of the circle, then their sides are equal,
Hence triangle COB is an isosceles triangle.
Also the line OA represents the radius of the circle just like CO. Since OA and CO are radii,
Hence triangle COA is an isosceles triangle.
(b) Statement: AOB is a straight line and at the center of a circle
Reason: Given
Statement: AOB is also an angle, which is 180 degrees
Reason: Angle on a straight line is 180 degrees
Statement: Angle AOB is an angle at the center of the circle, and angle C is at the circumference
Reason: same arc AB
Statement: Angle AOB = 2C
Reason: Angle at the center of a circle is twice angle at the circumference.
Hence
[tex]\begin{gathered} \angle AOB=2\angle C \\ 180\degree=2C \\ C=\frac{180}{90} \\ C=90\degree \end{gathered}[/tex]Therefore C is a right-angle (90 degrees)
17. Is the following statement true or false? A triangle can have two angles that measure 100°.Explain.
the interior angles of the triangle must sum 180°
if we have two angles that measure 100° the sum of interior angles of a triangle will be more than 180°, and that can't be true.
so the answer is FALSE