Answer:
width = 10 m
length = 16 m
Step-by-step explanation:
Formula
[tex]\textsf{Area of a rectangle} = wl[/tex]
[tex]\textsf{Perimeter of a rectangle}=2(w+l)[/tex]
(where [tex]w[/tex] is width and [tex]l[/tex] is length)
Given:
Area = 160 m²Perimeter = 52 mSubstituting the given values into the formulae to create two equations:
[tex]\textsf{Equation 1}: \quad wl=160[/tex]
[tex]\textsf{Equation 2}: \quad 2(w+l)=52[/tex]
Rearranging Equation 1 to make w the subject:
[tex]\implies w=\dfrac{160}{l}[/tex]
Substituting expression for w into Equation 2 and solving for [tex]l[/tex]:
[tex]\implies 2\left(\dfrac{160}{l}+l\right)=52[/tex]
[tex]\implies \dfrac{160}{l}+l=26[/tex]
[tex]\implies 160+l^2=26l[/tex]
[tex]\implies l^2-26l+160=0[/tex]
[tex]\implies l^2-10l-16l+160=0[/tex]
[tex]\implies l(l-10)-16(l-10)=0[/tex]
[tex]\implies (l-10)(l-16)=0[/tex]
[tex]\implies l=10, 16[/tex]
According to Equation 1:
If length = 10 m ⇒ width = 16 mIf length = 16 m ⇒ width = 10 mAs width < length, the dimensions of the shop are:
width = 10 mlength = 16 mSolve the triangle: α = 40°, β = 35°, and a = 10.
b = 8.9, γ = 105°, c = 6.7
b = 11.2, γ = 105°, c = 6.7
b = 11.2, γ = 105°, c = 15.0
b = 8.9, γ = 105°, c = 15.0
The triangle: α = 40°, β = 35°, and a = 10. is b = 8.9, γ = 105°, c = 15.0
What is Sine Law?If A, B, and C are the measurements of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite of the corresponding angles, then the ratios of the a side’s length to the sine of the angle opposite the side must all be the same.
a/ sin A = b/ sin B = c/ sin C
Using Angle sum property in a triangle we have,
α+β+ γ = 180
40+35+ γ=180
γ= 180-75
γ= 105°
Now,
c/ sin γ= a/ sin α
c/ sin 105= 10/ sin 40
c/ 0.96592 = 10 /0.6427
c = 15
again,
b/ sin β= a/ sin α
b/ sin 35= 10/ sin 40
b/0.5737= 15.559
b= 8.92
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Write these ratios in their simplest form. You must show all your workings:
a. 2 litres:600ml
b.8h:1day
c.3km:250m
The simplest form of the given ratios are : 10:3 , 1:3 , and 12:1
What is Ratio?A ratio indicates how many times one number contains another.
Here, for given ratio
2 litres : 600 ml = 2000 ml : 600 ml
= 20 : 6
= 10 : 3
8 h : 1 day = 8 hrs : 24 hrs
= 8:24
= 1 : 3
3 km : 250 m = 3000 m : 250 m
= 3000 : 250
= 300 : 25
= 12 : 1
Thus, the simplest form of the given ratios are : 10:3 , 1:3 , and 12:1.
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9. A computer chip manufacturer knows that 72% of the chips produced are defective.
Suppose 3000 chips are produced every hour, what is the probability that exactly 800
chips are acceptable? Compare the results of using the binomial distributions with
those found using the normal approximation.
The probability that exactly 800 chips are acceptable is less than 0.000001
How to determine the probability?The given parameters are:
Sample, n = 3000Percentage acceptable, p = 72%Acceptable chips, x = 800The binomial probability is represented as:
[tex]P(x) = ^nC_x * p^x * (1- p)^{n - x}[/tex]
So, we have:
[tex]P(300) = ^{3000}C_{800} * (72\%)^{800} * (1- 72\%)^{3000 - 800}[/tex]
The data values are large.
So, we use a statistical calculator to evaluate the expression
Using the calculator, we have:
P(300) < 0.000001
Hence, the probability that exactly 800 chips are acceptable is very small i.e. less than 0.000001
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A train leaves Thorn Junction at 1:25 P.M. and arrives in Niles at 3:05 P.M. The train makes two stops along the route for a total of 15 minutes.
A second train leaves Thorn Junction at 4:30 P.M. and heads to Niles. This train does not make any stops.
What time will the second train arrive in Niles? Enter your answer in the boxes.
:
P.M.
Answer: It will arrive at 5:55 P.M
Step-by-step explanation:
Someone, please help!! if u actually know how to do it
Answer:
[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]
distance = 16.2788
Step-by-step explanation:
This question is asking you to correctly apply the distance formula. This formula determines the straight line distance between two points by applying Pythagorean's Theorem ([tex]h = \sqrt{x^{2}+y^{2} }[/tex]). The distance formula can be thought of as [tex]distance=\sqrt{(x_{1}-x_{2})^{2} +(y_{1}-y_{2})^{2}}[/tex]. It doesn't matter which order you put your coordinates into the equation as long as it's the square root of the change in x-coordinates squared + change in y-coordinates squared.
Step 1: change in x-coordinates
x1 = -2
x2 = -5
x1 - x2 = -2 - (-5) = 3
Step 2: change in y-coordinates
y1 = 6
y2 = -10
y1 - y2 = 6 - (-10) = 16
Step 3: plug into distance formula
[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]
[tex]distance=\sqrt{(3)^{2} +(16)^{2}}[/tex]
[tex]distance=\sqrt{9 +256}[/tex]
[tex]distance=\sqrt{265}[/tex]
distance = 16.2788
convert the following equation into standard form y=-5x/8 + 3
EASY POINTS Find the domain of the graphed function.
Using it's concept, it is found that the domain of the graphed function is given as follows:
D. [tex]-4 \leq x \leq 2[/tex]
What is the domain of a function?It is the set that contains all possible input values for the function. In a graph, it is given by the values of x.
In this graph, x assumes values between -4 and 2, inclusive due to the closed circle, hence the domain is given by:
D. [tex]-4 \leq x \leq 2[/tex]
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12 to 30 Express as a fraction in the lowest terms?
Answer:
2/5
Step-by-step explanation:
Find the quotient and remainder using long division.
x + x - 13
x - 2
The quotient is
The remainder is
Answer:
[tex]\text{The quotient is}~ x^2 +2x +5 \\\\\text{The remainder is}~ -3[/tex]
Step-by-step explanation:
what's the answer to this
Answer:
AC ≈ 17.3 , BC ≈ 5.3
Step-by-step explanation:
using the tangent ratio in right triangle ACD
tan51° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AD}[/tex] = [tex]\frac{AC}{14}[/tex] ( multiply both sides by 14 )
14 × tan51° = AC , then
AC ≈ 17.3 ( to the nearest tenth )
using the cosine ratio in right triangle ABC
cos72° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{17.3}[/tex] ( multiply both sides by 17.3 )
17.3 × cos72° = BC , then
BC ≈ 5.3 ( to the nearest tenth )
Which algebraic expression is equivalent to the expression below?
3(5x + 7)-6(4- 2x)
3(5x+7)-6(4-2x) - given
15x+21-24+12x - distributive property
27x-3 - combine like terms
write 25.59 in scientific notation
Answer:
2.559 × 10 to the 1st power
Step-by-step explanation:
using a SNC
Answer:
2.559 * 10^1
Step-by-step explanation:
Rules of scientific notation (that I always remember)
- the number must be between 1 and 9
- if number gets smaller, exponent gets bigger; if number gets bigger, exponents gets smaller
25.59 is bigger than 9 so we move the decimal one place value to the left
and the number gets smaller meaning the exponent increases
help please? 50 points if correct
Answer:
15400 in² :)))!
Step-by-step explanation:
Input Data:
Radius = 70 in
Objective:
Find the area of the circle.
Solution:
Area = πr2
= 3.14 x (70) ^2
= 3.14 x (4900)
Area = 15400 in²
Solve for x.
x³ = 216
Enter your answer in the box.
x =
[tex]x^3=216\\x=\sqrt[3]{216}=6[/tex]
This is a simple example. You (should) know that [tex]6^3=216[/tex].
But you can solve it like this:
[tex]\begin{array}{r|l}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}[/tex]
Therefore
[tex]\sqrt[3]{216}=\sqrt[3]{2^3\cdot3^3}=\sqrt[3]{2^3}\cdot\sqrt[3]{3^3}=2\cdot3=6[/tex]
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the value of x in the equation [tex]\pmb{x^3=216}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
The goal is to get x all by itself on one side of the equal sign.Is x by itself? No, it's cubed, or multiplied times itself three times.
So we need to use the opposite operation.
The opposite of cubing is taking the cube root, so we take the cube root of both sides:
[tex]\star~\large\pmb{\sqrt[3]{x^3}=\sqrt[3]{216}}[/tex]
On the left, the cube root sign and the cube cancel, because they're opposite, and we're left with x.
On the right, we take the cube root of 216, which gives us:
[tex]\star~\large\pmb{x=6}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
El parámetro a de una distribución exponencial cumple que
Pregunta 7 opciones:
a = 0
a < 0
a ≥ 0
a > 0
The parameters of an Exponential Distribution is D. a > 0
What is an Exponential Distribution?This refers to the distribution of probability with respects to time taken in a Poisson point process.
Hence, we can see that from the previous knowledge of exponential distributions, it is stated that λ > 0 is the parameter of the distribution, and is supported on the interval [0, ∞).
Therefore, option D is correct.
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6. Dana measured the height of her
bedroom wall to be 3 yards tall. Which of
these is closest to the equivalent
measurement?
Answer:
9 feet, 108 inches, 274.32 cm, 2.7432 meters
Step-by-step explanation:
Not enough information is given to answer.
You didn't provide the list of "these" to choose from, but I can just list some potential answers I could see being an option.
3 yards = 9 feet [1 yard = 3 feet. 3 yards = 9 feet]
9 feet is also 108 inches [1 foot = 12 inches. 9 feet = 108 inches]
3 yards = 108 inches
{There are 91.44 cm in a yard} (1 yard = 91.44 cm. 3 yards = 274.32 cm),
3 yards = 274.32 cm
3 yards = 2.7432 meters (1 yard = 0.9144 meters; 3 yards = 2.7432 meters)
The next model of a sports car will cost 11.8% more than the current model The current model costs 37,000.How much will the price increase in dollars?What will be the price of the next model
$0
$0
?
Answer:
436.6
Step-by-step explanation:
3700×0.118=436.6
A gardener has 75 clients, 45% of whom are businesses. Find the number of business clients.
Answer:
33,75 clients(huh?)
Step-by-step explanation:
75 / 100 = 0,75(1% of all clients)
0,75 * 45 = 33,75(number of business clients)
Factor the polynomial using the greatest common factor.
x^2+3x
x²+3x
= x×x+3×x
= x(x+3)
Suppose the scores of seven members of a women’s golf team are 68, 62, 60, 64, 70, 66, and 72. Find the mean, median, and midrange.
a.
Mean = 64, median = 64, midrange = 64
b.
Mean = 65, median = 64, midrange = 66
c.
Mean = 66, median = 77, midrange = 65
d.
Mean = 66, median = 66, midrange = 66
Please select the best answer from the choices provided
A
B
C
D
The mean, median, and midrange of the given that are 66, 66 and 66 respectively.
Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.
What is the mean, median, and midrange?Mean is the sum total of the number divided by number of terms
Median is the middle number when arranged in ascending or descending order.
Midrange is the average of the sum of the maximum number and the minimum number.
Given that;
Data set: 68, 62, 60, 64, 70, 66, and 72n = 7First, we arrange in ascending order.
60, 62. 64, 66, 68, 70, 72
Mean = ( 60 + 62 + 64 + 66 + 68 + 70 + 72 ) / 7
Mean = 462 / 7
Mean = 66
Median = 66
66 is the middle number.
Range = ( Max + Min ) / 2
Range = ( 72 + 60 ) / 2
Range = 132 / 2
Range = 66
Therefore, the mean, median, and midrange of the given that are 66, 66 and 66 respectively.
Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.
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please please help me I'll give whaever
answer:
1769.344983 or 1769.34 (depends on what you’re rounding to)
explanation:
- the equation for a cylinder‘s surface area is: (2 π r h)+(2 π r^2)
so 2 just means x2
π is just pi
r is your radius and for this equation your radius is 8 cm
and h is your height so for this equation your height is 27.2 cm
- so the equation filled in is:
(2 x π x 8 x 27.2) + (2 x π8^2) = 1769.344983 or 1769.34
(2 x π x 8 x 27.2) = 1367.221123
(2 x π8^2) = 402.1238597
1367.221123 + 402.1238597 = 1769.344983
hope this helps :)
Rani uses a container that can hold 2 liters of water to fill a
fish tank. The fish tank can hold 8 liters of water. How many
times must she fill the smaller container to fill the fish tank?
Answer:
4 times
Step-by-step explanation:
If the smaller container only holds 2 liters, you would have to divide 8 by 2 which is 4.
Answer:
4 times
Step-by-step explanation:
Its 4 times cause 8/2=4
Explain why the "+ C" is not needed in the antiderivative when evaluating a definite integral.
The reason the "+ C" is not needed in the antiderivative when evaluating a definite integral is; The C's cancel each other out as desired.
How to represent Integrals?
Let us say we want to estimate the definite integral;
I = [tex]\int\limits^a_b {f'(x)} \, dx[/tex]
Now, for any C, f(x) + C is an antiderivative of f′(x).
From fundamental theorem of Calculus, we can say that;
[tex]I = \int\limits^a_b {f'(x)} \, dx = \phi(a) - \phi(b)[/tex]
where Ф(x) is any antiderivative of f'(x). Thus, Ф(x) = f(x) + C would not work because the C's will cancel each other.
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The final exam scores in a statistics class were normally distributed with a mean of
70 and a standard deviation of five. What is the probability that a student scored
more than 65% and less than 75% on the exam?
Answer:
68.27%
Step-by-step explanation:
By the Empirical Rule, as 65% and 75% are both one standard deviation apart from the mean of 70%, then this represents 68.27% of the data.
Suppose that 950 couples each have a baby find the mean and standard deviation for the number of boys in the 950 babies
The mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively
How to determine the mean and the standard deviation?From the complete question, we have:
P(boy)= 0.5
Sample size = 950
The mean is then calculated as:
[tex]\bar x = np[/tex]
This gives
[tex]\bar x = 950 * 0.5[/tex]
Evaluate
[tex]\bar x = 475[/tex]
The standard deviation is calculated as:
[tex]\sigma = \sqrt{np(1 - p)[/tex]
This gives
[tex]\sigma = \sqrt{950 * 0.5(1 - 0.5)[/tex]
Evaluate
[tex]\sigma = 15.41[/tex]
Hence, the mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively
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The cost of printing books C varies partly as the amount A charged by the printer
and partly varies inversely as the number n of books printed. When 1000 books
were printed, the amount charged was GHC5000 and the cost of printing was
GHC75010 and when 2500 books were printed, the amount charged was
GHC10000 and the cost of printing was GHC50,004.
Find an equation connecting C,A and n
The equation connecting C,A and n is C = 25A - [tex]\frac{49990000}{n}[/tex]
What is variation?Variation is a mathematical term used to show how a quantity behaves when one quantity increases or decreases.
Analysis:
C = AK + M/n
where K and M are constants
when n = 1000, A = 5000, C = 75010
75010 = 5000K + M/1000-----------1
50004 = 10000k + M/200-------------2
solving simultaneously, K = 25, M = -49990000
C = 25A - 49990000/n
In conclusion, the equation connecting C,A and n is C = 25A - 49990000/n
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Which graph shows the axis of symmetry for the function f(x) = (x - 2)2 + 1?
Answer:
x=2
Step-by-step explanation:
axis of symmetry is
x-2=0
or
x=2
Answer:
Graph B. On a coordinate plane, a vertical dashed line at (2, 0) is parallel to the y-axis.
Find x to the equation
Triangles 3 and 4 are identical. They are joined in the poster to form a square. Construct a math argument to show why triangles 3 and 4 are isosceles right angles.
Triangles 3 and 4 are isosceles right angles because they have same length.
How to explain the triangle?It should be noted be noted that the square has all right angles equal. The largest angle of the triangle is the right angle m.
Here, the triangles are isosceles right angles as both the legs and the acute angles are congruent.
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What is the greatest common factor of 4xy2 and 20x2y4?
4xy
4
Answer:
4 x y ^2
Step-by-step explanation:
4 x y^2 would be the GFC