Answer:
Width = 2
Length = 5
Step-by-step explanation:
let A be the area of the rectangle
L be the length of the rectangle
w be the width of the rectangle
Formula: ‘area of a rectangle’
A = L × w
…………………………………………………
A = L × w
⇔ 10 = (w + 3) × w
⇔ 10 = w² + 3w
⇔ w² + 3w - 10 = 0
Solving the quadratic equation w² + 3w - 10 = 0 :
Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49
then √Δ = 7
[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]
[tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]
-5 is not valid ,because w represents the width
which must be a positive number
Then w = 2
Conclusion:
Width = 2
Length = 2 + 3 = 5
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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I need this answer as soon as possible! 50 points!
[tex]20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5[/tex]
Answer:
[tex]800\sqrt{5}[/tex]
Step-by-step explanation:
Given: [tex]\large (20)^\text{$ \dfrac{5}{2} $}[/tex]
Properties of Exponents:
Rational Exponent Property: [tex]\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}[/tex]
a number raised to a fraction, can be converted to a radical. the numerator becomes the exponent, and the denominator becomes the index of the radical.Product of Powers Property:
when multiplying powers with the same base, add the exponents.1. Convert into a radical:
[tex]\sqrt[2]{20^5} \implies \sqrt{20^5}[/tex]
2. Simplify the expression:
[tex]\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}[/tex]
3. Evaluate the power:
[tex]20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}[/tex]
4. Multiply:
[tex](400\times2)\sqrt{5}\\\\\implies800\sqrt{5}[/tex]
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 :)
help and thank youu~
Answer:
Perimeter=150cm
Step-by-step explanation:
25cm×6=150cm
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
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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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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A patient has been prescribed 1 gram (g) of Drug A. The stock dose is available in 250 milligram (mg) tablets. How many tablets would you administer per dose?
The patient would be administered 4 tablets per dose.
How do we use word problems to solve real-life problems?In mathematics, solving word problems involves a careful understanding of the content of the problem. This will enable the use of appropriate variables and data representation.
From the given information:
A patient has been prescribed = 1 gram of Drug A.A stock dose is available in = 250 mgFrom the standard conversion rate, we know that:
1 g = 1000 mgHere, to determine the number of dose to be administered, we have:
(x) /dose = 1000 mg/250 mg
x = 4 dose.
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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.
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
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.
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~Just a smiley person helping fellow students :)
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
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.
Select the correct
What is the solution to this system of equations?
3x + y = 17
x + 2y = 49
O A.It has no solution.
OB. It has infinite solutions.
O C. It has a single solution: x = 15, y = 17.
OD. It has a single solution: x = -3, y = 26.
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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Worth 40 points! Select the correct answer.
What is the value of x in the triangle? (file of the picture is attached below)
Answer:
Its A
Step-by-step explanation:
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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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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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:
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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12 to 30 Express as a fraction in the lowest terms?
Answer:
2/5
Step-by-step explanation:
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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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:
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)
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
Factor the polynomial using the greatest common factor.
x^2+3x
x²+3x
= x×x+3×x
= x(x+3)
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)
Solve 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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This data set represents the widths in yards of pieces of fabric used by a sewing group. What is the mean of this data set? {113, 14, 23, 12, 114}
Answer:
55.2 is the mean
Explanation:
Given data set: {113, 14, 23, 12, 114}
Mean = sum of the terms/number of terms
Mean = (113 + 14 + 23 + 12 + 114)/5
= (276)/5
= 55.2
Answer:
Mean = 55.2
Step-by-step explanation:
Given data set: 113, 14, 23, 12, 114
To find the mean of a data set, divide the sum of all data values by the total number of data values:
[tex]\large \begin{aligned}\sf Mean & = \sf\dfrac{sum\:of\:all\:data\:values}{total\:number\:of\:data\:values} \\\\\implies \sf Mean & = \sf \dfrac{113 + 14 + 23 + 12 + 114}{5}\\\\& = \sf \dfrac{276}{5}\\\\& = \sf 55.2\end{aligned}[/tex]
convert the following equation into standard form y=-5x/8 + 3