Answer: Y= -4x + 2
Step-by-step explanation:
The slope intercept equation is y = mx + b
The slope or m in this situation is -4
The y- intercept or b is 2
When you substitute then slope and y-intercept into the equation you get
Y = -4x + 2
Here is some information about 120 people who visit a shop.
3
of the people buy neither a coat nor a dress.
4
19 people buy a coat.
14 people buy a dress.
Complete this Venn diagram to represent the information.
६
- 120 people who visit the shop
C=people who buy a coat
D= people who buy a dress
[3 marks]
Therefore , the solution of the given problem of inequality comes out to be three individuals are listed as not purchasing either a dress or a coat.
What is an inequality ?Despite the fact that algebra lacks a comparable symbol, its distinction can be expressed by a pair or collection for numbers. Equilibrium is typically followed by equity. The ongoing disparity in norms is what causes inequality. Disparity and fairness are not synonymous. Even though the components are typically not connected or situated closely together, that was our most popular symbol.
Here,
The 120 customers who frequent the store are represented by the rectangle in the Venn diagram.
The "C" circle stands for those who purchase a coat, and the "D" circle for those who purchase a frock.
The individuals who purchase both a dress and a coat are represented by the area inside the overlap of the two circles. 19 less the number of individuals who purchase both a coat and a dress equals the number of people who only purchase a coat. 14 less the number of people who purchase both a parka and a dress equals the number of people who only purchase a dress.
Three individuals are listed as not purchasing either a dress or a coat.
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URGENT! find the reciprocal of each complex number
(sqrt(2)/2)-(sqrt(2)i/2)
The reciprocal of the complex number [tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}[/tex] is determined as [tex]\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}.[/tex]
What is the reciprocal of the complex number?
To find the reciprocal of a complex number, we need to divide 1 by the complex number. We can simplify the division by multiplying the numerator and denominator by the complex conjugate of the denominator.
The complex conjugate of
[tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}= \frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}[/tex]
So, the reciprocal of the complex number is:
[tex]\begin{aligned} \frac{1}{\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}} &= \frac{1}{\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}} \cdot \frac{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}}{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}} \ &= \frac{\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}}{\frac{2}{2}} \ &= \frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2} \end{aligned}[/tex]
Therefore, the reciprocal of the complex number;
[tex]\frac{\sqrt{2} }{2} - \frac{\sqrt{2} \ i }{2}[/tex] is [tex]\frac{\sqrt{2} }{2} + \frac{\sqrt{2} \ i }{2}.[/tex]
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F(x)=6x^2+-7+0 in vertex form
5) (8 pts) A company’s design of 45-ohm resistors is believed to be manufactured with a standard deviation of 0.12 Ω. To evaluate this, a sample of 15 resistors was collected and the standard deviation of the resistance of these 15 resistors was 0.194 Ω. a) (6 pts) Calculate a 95% two-sided confidence interval for standard deviation of resistance, σ. b) (2 pts) Based on your answer to part (a), is it reasonable to believe that the standard deviation of all resistors produced is 0.12 Ω? Explain your answer using information from part (a).
The true value of the standard deviation may be in the interval of (0.12, 0.3757), it may or may not be 0.12 Ω.
Calculation of a 95% two-sided confidence interval for standard deviation of resistance, σ95% two-sided confidence interval for standard deviation of resistance is given by:\[\left(\sqrt{\frac{\left(n-1\right)s^2}{\chi_{0.025,n-1}^2}},\sqrt{\frac{\left(n-1\right)s^2}{\chi_{0.975,n-1}^2}}\right)\]where s = 0.194 Ω, n = 15, and Χ² distribution with df = 14 at α = 0.05/2 = 0.025/0.975The range of the 95% two-sided confidence interval for the standard deviation of resistance is given as follows:95% two-sided confidence interval for standard deviation of resistance = (0.12, 0.3757)Hence, the 95% two-sided confidence interval for the standard deviation of resistance is given as (0.12, 0.3757).b) Explanation:The standard deviation of the resistance is believed to be 0.12 Ω. From the 95% confidence interval obtained in part (a), 0.12 Ω is not within the 95% confidence interval. This means it is not reasonable to believe that the standard deviation of all resistors produced is 0.12 Ω. Since the true value of the standard deviation may be in the interval of (0.12, 0.3757), it may or may not be 0.12 Ω.
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45% of 60 is what value? 2 15 20 27
Accοrding tο the percentage calculatiοn, 45% οf 60 is 27. Thus, D is the cοrrect οptiοn.
What is percentage?A number οr ratiο that can be expressed as a fractiοn οf 100 is referred tο as a percentage in mathematics. If we need tο calculate a percentage οf a number, we shοuld divide it by its entirety and then multiply it by 100. The percentage therefοre refers tο a part per hundred. Per 100 is what the wοrd percent means. The letter "%" stands fοr it.
A part οf a whοle expressed in hundredths,
Tο find 45% οf 60, we can multiply 60 by 0.45:
45% οf 60 = 0.45 × 60 = 27
Therefοre, 45% οf 60 is 27. Answer: 27
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Three girls share R12000 in the ration 2:3:7 calculate how much each girl will get
Each girl will receive the ratio of Girl 1: R2000, Girl 2: R3000 Girl 3: R7000
To find out how much each girl will get, we need to first add up the ratios:
2 + 3 + 7 = 12
Then, we can divide the total amount of money by the total ratio:
12000 ÷ 12 = 1000
This means that each "part" of the ratio is worth R1000.
To calculate how much each girl will get, we need to multiply their respective ratios by R1000:
Girl 1: 2 parts x R1000/part = R2000
Girl 2: 3 parts x R1000/part = R3000
Girl 3: 7 parts x R1000/part = R7000
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What are all of the angles (in degrees) that
have a cosine value of 0.74?
All pοssible angles (in degrees) with a cοsine value οf 0.74 are:
42.47° + 360n and 137.53° + 360n, where n is an integer.
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It is used tο sοlve prοblems in variοus fields, including physics, engineering, and astrοnοmy.
The cοsine functiοn is pοsitive in the first and fοurth quadrants, sο we can restrict οur attentiοn tο angles between 0 and 360 degrees in thοse quadrants.
Tο find the angles with cοsine 0.74, we can use the inverse cοsine functiοn (alsο called arccοsine οr cοs⁻¹) οn a calculatοr. In degrees, we have:
cοs⁻¹(0.74) ≈ 42.47° and cοs⁻¹(-0.74) ≈ 137.53°
The cοsine functiοn has a periοd οf 360 degrees, sο we can add οr subtract multiples οf 360 degrees tο these angles tο get all pοssible angles with cοsine 0.74. In general, the angles are given by:
θ = cοs⁻¹(0.74) + 360n and θ = cοs⁻¹(-0.74) + 360n, where n is an integer.
Sο, all pοssible angles (in degrees) with a cοsine value οf 0.74 are:
42.47° + 360n and 137.53° + 360n, where n is an integer.
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You have the same bowl, with 5 orange, 6 blue, 3 green, 4 red and 7 yellow candies. You take out an orange candy from the bowl. What is the new probability that you will draw another orange candy? A 1 5 5 1 B 1 6 6 1 C 1 8 8 1 D 5 2 4 24 5
Answer: 3/8
Step-by-step explanation: You have a 1 in 5 chance of pulling an orange.
5/25, or if you need to simplify then 1/5
A(n)_is a two-dimensional boundary of a three-dimensional figure
Answer:
429
Step-by-step explanation:
Which term best describes a figure that is made up of two or more shapes?
composite shape
becuse thats what its called
Linda and Imani are each traveling in a car to the beach. Linda's travel is modeled by a table. Imani's travel is modeled by a graph.
Did Linda or Imani travel faster? How do you know?
Linda traveled faster than Imani because when t =1 , linda traveled 65 miles and Imani traveled 60 miles and linda travelled at a faster rate because when t=0,
She travelled 10 miles and Imani travelled 0 miles these are cοrrect answer. The prοvided graph's cοοrdinates are (2, 120) and (4, 240).
What is graph ?A graph is a structure that amοunts tο a set οf items where sοme pairs οf the οbjects are in sοme manner "cοnnected" in discrete mathematics, mοre specifically in graph theοry. The items are represented by mathematical abstractiοns knοwn as vertices (sοmetimes knοwn as nοdes οr pοints), and each pair οf cοnnected vertices is knοwn as an edge. Generally, a graph is represented diagrammatically as a cοllectiοn οf dοts οr circles fοr the vertices cοnnected by lines οr curves fοr the edges. Graphs are οne οf the tοpics studied in discrete mathematics.
Slοpe with (2, 120) and (4, 240) is
Slοpe (y2-y1)/(x2-x1)
= (240-120)/(4-2)
= 120/2
= 60
Put m=60 and (x, y)=(2, 120) in y=mx+c, we get
120=60(2)+c
c=0
Sο, equatiοn is y=60x
Put x=0, 1, 2, 3 and 4, we get
y= 0, 60, 120, 180, 240
(0, 0), (1, 60), (2, 120), (3, 180) and (4, 240)
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Matt collects classic stamps. For his birthday this year his grandma gave him a stamp’s worth $40. He expected the stamps value to double every decade. Assuming Matt is right you can use a function to approximate the stamp’s value x decades from now.
Write an equation for the function. If it is linear write in the form h(x)=mx+b. If it is exponential, write it in the form h(x)=a(b)^x
Question in photo
!!!!
Answer: Monomial
!!Not 100% sure!!
Answer: The answer is Monomial because the expression, 2x is 1 term.
8) The base of a 10-ft ladder stands 6 feet from the base of a house. Will the ladder reach 7 feet
high? Justify your answer.
10 ft
6 ft
The ladder will reach a height of 8 feet, which is greater than 7 feet. So, the ladder will indeed reach 7 feet high, and even higher.
What is Pythagoras theorem?A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.
According to question:We can use the Pythagorean theorem to determine if the ladder will reach 7 feet high. Let's let x be the height that the ladder reaches, as shown in the diagram below:
According to the Pythagorean theorem, we have:
[tex]$\begin{align*}x^2 + 6^2 &= 10^2 &= 100 - 36 &= 64 \x &= \sqrt{64} \x &= 8\end{align*}[/tex]
Therefore, the ladder will reach a height of 8 feet, which is greater than 7 feet. So, the ladder will indeed reach 7 feet high, and even higher.
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Elena is thinking through a proof using a reflection to show that the base
angles of an isosceles triangle are congruent. Complete the missing
information for her proof.
B
Construct the perpendicular
bisector of segment CD. The perpendicular bisector of CD must go through B
since it's the midpoint. A is also on the perpendicular of CD because the
Call the midpoint of segment CD
distance from A to
We want to show triangle ADC is congruent to triangle ACD. Reflect triangle
ADC across line
is the same as the distance from A to
Since
is on the line of reflection, it
definitely lines up with itself. DB is congruent to
perpendicular bisector of CD. D' will coincide with
other side of a perpendicular line and the same distance from it (and that's
the definition of reflection!). C" will coincide with;
other side of a perpendicular line and the same distance from it (and that's
the definition of reflection!). Since the rigid transformation will take triangle
ADC onto triangle ACD, that means angle
therefore they are congruent.
since AB is the
since it is on the
since it is on the
will be taken onto angle
(they are corresponding parts under the same reflection), and
Answer:
The missing information for the proof is:
- Point D' will coincide with point D, since it is on the perpendicular bisector of CD and the same distance from it (and that's the definition of reflection!).
- Point C" will coincide with point C, since it is on the perpendicular bisector of CD and the same distance from it (and that's the definition of reflection!).
- Angle ADC will be taken onto angle ACD, since they are corresponding parts under the same reflection. Therefore, they are congruent.
Can anyone help w solving the equation using quadratic formula
Hence The solution set is {x | x ∈ ℝ, x ≈ 2.91 or x ≈ -0.51}.
What is the quadratic equation?In algebra Any equation that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a is not equal to zero is known as a quadratic equation.
What is the solution set ?How do you determine a set of solution?
first of all you must enter each value from the domain into the equation to obtain the corresponding range values before you can determine the solution set of an equation with a specified domain. From these values, make ordered pairs, and then write them as a set.
The given quadratic equation is ,
25 [tex]x^2[/tex]= -60 x +37
or 25 [tex]x^2[/tex]+60 x - 37=0
to compare a quadratic equation of the form of [tex]ax^2 + bx + c = 0,[/tex]
than we get:
a = 25, b = -60, c = -37
We know that the quadratic formula is
x=[tex]\frac{-b ± \sqrt{(b^2 - 4ac)})}{2a}[/tex]
These values are substitute the quadratic formula than we get,
[tex]x=\frac{ 60± \sqrt{(60^2 - 4*25*37)})}{2*25}\\x=\frac{ 60± \sqrt{(3600+3700)})}{2*25}\\x=\frac{ 60± \sqrt{7300)})}{50}\\\\x=\frac{ 60± 85.38}{50}\\\\x=\frac{ 60+ 85.38}{50} or x=\frac{ 60-85.38}{50}\\x=2.91 or x= -0.51\\[/tex]
The solution set is {x | x ∈ ℝ, x ≈ 2.91 or x ≈ -0.51}.
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Find the volume 1.20m by 5m by 75cm
Answer:
4.5 m^3
Step-by-step explanation:
Volume = length × breadth × height
= 5m × 1.2m ×(75÷100)m
= 4.5 m^3
100 points please help
Answer:
(x-6)(x-2)
Step-by-step explanation:
To factor, we use the quadratic formula, which gives us the roots of the equation. In an equation as ax²+ bx + c, we can use (-b±√(b^2-4ac))/2a. Since we have x² - 8x +12, a will be 1, b will be -8, and c will be 12.
(-(-8)±√((-8)²-4(1)(12))/2(1)
(8±√(64-48)/2
(8±√16)/2
(8±4)/2
We now have two cases: (8+4)/2 and (8-4)/2. We can solve these:
(8+4)/2 = 12/2 = 6
(8-4)/2 = 4/2 = 2
Since we have to factor this, we have to write it in the form of
(x-z)(x-y)
for z, we have 6, and for y, we have 2
(x-6)(x-2) is our final answer.
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PLEASE ANSWER QUICK I GIVW THUMBS UP Solve
sin(4x)cos(6x)−cos(4x)sin(6x)=−0.9 for the smallest positive
solution please give answer to 2 decimal places
The answer is 3.18.
The given equation is sin(4x)cos(6x) − cos(4x)sin(6x) = -0.9. To find the smallest positive solution, we can use the following identities: sin(A + B) = sinAcosB + cosAsinBcos(A + B) = cosAcosB - sinAsinBWe can rewrite the given equation using these identities as follows:sin(4x + 6x) = -0.9sin(10x) = -0.9sinx = -0.09We need to solve for the smallest positive value of x. To do this, we can find the value of x in the interval [0, 2π] such that sinx = -0.09.Using a calculator, we get:x ≈ 3.176 rad ≈ 181.97°The smallest positive solution in degrees is 181.97°. To get the answer to 2 decimal places, we can round off the value of x to 2 decimal places, giving:smallest positive solution ≈ 3.18 rad (to 2 decimal places) or ≈ 181.97° (to 2 decimal places)Thus, the answer is 3.18.
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a young person with no initial capital invests dollars per year in a retirement account at an annual rate of return . assume that investments are made continuously and that the return is compounded continuously. a) write a differential equation which models the rate of the change of the sum with in years (this will involve the parameter ). note: use rather than since the latter confuses the computer. b) use part a) to determine a formula for the sum -- (this will involve the parameter ): c) what value of will provide dollars in years?
For example, to achieve a sum of $100,000 in 10 years with an initial investment of $10,000, the annual rate of return r required would be:
r =[tex](1/10) ln(100,000/10,000) = 0.069.[/tex]
a) The differential equation which models the rate of change of the sum with respect to time (t) is given by:
dS/dt = rS
where S is the sum and r is the annual rate of return.
b) The formula for the sum can be obtained by solving the differential equation:
S = S0ert
where S0 is the initial investment.
c) To determine the value of r which will provide the desired sum in a given amount of time, we can rearrange the equation above to give:
[tex]r = (1/t) ln(S/S0)[/tex]
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pls help on this for math
Answer: 1/6 x 3, 1/6 of 3
Step-by-step explanation: i did this in iready one time and got it write :))))))
have a great day/night or whatever ididdkk
The cone and the cylinder have the same base and the same height. What is the ratio of the volume of the cone to the volume of the cylinder? Choose 1 answer: Choose 1 answer: (Choice A) 1 3 3 1 start fraction, 1, divided by, 3, end fraction A 1 3 3 1 start fraction, 1, divided by, 3, end fraction (Choice B) 2 5 5 2 start fraction, 2, divided by, 5, end fraction B 2 5 5 2 start fraction, 2, divided by, 5, end fraction (Choice C) 1 2 2 1 start fraction, 1, divided by, 2, end fraction C 1 2 2 1 start fraction, 1, divided by, 2, end fraction (Choice D) 1 11 D 1 1
The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.
What is the formula for the volume of the cylinder?The formula for the volume of a cylinder is [tex]V = \pi r^2h,[/tex] where V is the volume, r is the radius, and h is the height.
According to the given information:Let's assume that the cone and cylinder have a radius of 'r' and a height of 'h'.
The volume of the cylinder is given by [tex]= \pi r^2h.[/tex]
The volume of the cone is given by V_cone = [tex](1/3)\pi r^2h.[/tex]
Since the cone and cylinder have the same base and height, their radius and height are the same.
Therefore, we can simplify the volumes as V_cylinder = [tex]\pi r^2h[/tex] and V_cone = [tex](1/3)\pi r^2h.[/tex]
The ratio of the volume of the cone to the volume of the cylinder is then:
V_cone/V_cylinder = [tex]((1/3)\pi r^2h) / (\pi r^2h) = (1/3) / 1 = 1/3[/tex]
So, the volume of the cone is one-third of the volume of the cylinder.
Alternatively, we can write this as the ratio of the volume of the cone to the volume of the cylinder being 1:2, since the volume of the cylinder is twice the volume of the cone.
Therefore,The ratio of the volume of the cone to the volume of the cylinder is 1:2, or 1/2, meaning the volume of the cone is one-half of the volume of the cylinder. This is because the cone and the cylinder have the same height and base.
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Help me on this and get lots of points
Find x in the equation
log x= 1,000,000,000
log2 x = 10
In x = 1 Write the exact answer
Using the laws of logarithms, the value of x is 1024
What is the value of x?We are given the equations:
log x = 1,000,000,000
log₂ x = 10
Using the definition of logarithms, we know that log x = y is equivalent to x = 10^y. Therefore, we can rewrite the given equations as:
x = 10^1,000,000,000
x = 2^10
We can use a calculator to find that 10^1,000,000,000 is an extremely large number (a "googol" is a 1 followed by 100 zeroes, and this number is much larger than a googol). However, we can simplify the expression x = 2^10 by calculating 2^10, which is 1024.
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If the focus and directrix of prapola is f(0,4) y=_4.the equation of parabola is
Answer:
Step-by-step explanation:
davrsgdrbfghfgbfrtnrfnfgnftytfnrfnrrjmrnhherththtrgwgegergergetgethtrgtegegehtrhtrhtrhtrtghrthrthrthrtrthrthrrhrhtrhhrthrhrthrt
Mercury is a metal that is liquid at room temperature. It has a density of 13. 7 g/cm3. Older American pennies are made mostly of copper and have a density of 8. 8 g/cm3, newer pennies are made mostly of zinc and have a density of 7. 2 g/cm3. What will happen to a new and an old American penny if dropped into a beaker of mercury?
As the density of Mercury is higher than that of both Copper and Zinc, so both the new & old penny will float on mercury.
Define density of a metal?By dividing the object's mass by its volume, we may determine the density of metal.
Mass/volume equals density.
For ex, the object would have a density of 0.284 per cubic inch if its mass were 7.952 pounds and its volume were 28 cubic inches.
Now here in the given question,
Density of copper = 8.8g/cm³
Density of zinc = 7.2g/cm³
Here, both the densities are lesser than that of mercury.
Hence, both the metal pennies will float when dropped into a beaker of mercury.
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an educational psychologist wishes to know the mean number of words a third grader can read per minute. she wants to make an estimate at the 85% 85 % level of confidence. for a sample of 146 146 third graders, the mean words per minute read was 30.5 30.5 . assume a population standard deviation of 3.1 3.1 . construct the confidence interval for the mean number of words a third grader can read per minute. round your answers to one decimal place.
The 85% confidence interval that the true mean number of words a third grader can read per minute is between 30.131 and 30.869.
To create a confidence interval for the mean number of words a third grader can read per minute, an educational psychologist wishes to know the mean number of words a third grader can read per minute. She intends to produce an estimate at an 85% level of confidence.
For a sample of 146 third graders, the mean words per minute read was 30.5. Assume a population standard deviation of 3.1.
To create a confidence interval, the following formula can be used:
µ±z_α/2*σ/√n
Here, we are given the following details:
Sample size: n = 146
Mean: µ = 30.5
Population standard deviation: σ = 3.1
Level of confidence: α = 1 - 0.85 = 0.15
We need to determine the critical value of z_α/2.
α/2 ⇒ 0.15/2 ⇒ 0.075
Using a standard normal distribution table, we find that the value of z_0.075 is 1.44.
Confidence Interval: µ ± z_α/2*σ/√n
⇒ 30.5 ± 1.44 × (3.1/√146)
⇒ 30.5 ± 0.369
Thus, the confidence interval for the mean number of words a third grader can read per minute is (30.131, 30.869).
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USE STRUCTURE In the figure, DE∥BC, BD=12, EC=10, and AE=15. Explain how to find the length of AD. Drag the steps into the correct order
1. Find the length of DE. 2. Calculate the length of BD. 3. Add BD and EC to get AD.
To find the length of AD, the following steps can be followed:
1. To find the length of DE, the Pythagorean theorem can be used. It states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the triangle is DEBC.
Therefore, DE2 = (12)2 + (10)2 = 144 + 100 = 244.
Taking the square root of 244 gives the length of DE as 15.722.
2. The length of BD can then be calculated as 12, since it is already given in the figure.
3. To find the length of AD, the lengths of BD and EC can be added together. That is, AD = BD + EC = 12 + 10 = 22.
Therefore, the length of AD is 22.
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What is the probability Steven will select a table-tennis ball with a ""1"" written on it and also a table-tennis ball with a ""B"" written on it? Explain your answer or show your work
the probability that Steven will select a table-tennis ball with a "1" written on it and also a table-tennis ball with a "B" written on it is approximately 0.2679, or 26.79%.
To find the probability that Steven will select a table-tennis ball with a "1" written on it and also a table-tennis ball with a "B" written on it, we need to know how many table-tennis balls with "1" and "B" there are and the total number of table-tennis balls.
The probability of Steven selecting a "1" on his first pick is:
P(1 on first pick) = 3/8
The probability of Steven selecting a "B" on his second pick, given that he has already selected a "1", is:
P(B on second pick | 1 on first pick) = 5/7
The probability of Steven selecting a "1" and a "B" in sequence is the product of these two probabilities:
P(1 and B) = P(1 on first pick) * P(B on second pick | 1 on first pick)
= (3/8) * (5/7)
= 0.267857
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The blank boxes go from 0-9 I need answer please!
The values that complete the equations so that each statement is true are presented as follows;
No solution
6 - 3 + 4·x + 1 = 4·x + 4
One solution
6 - 3 + 4·x + 1 = 3·x + 3
Infinitely many solutions
6 - 3 + 4·x + 1 = 4·x + 4
What is a linear equation?A linear equation is the equation of a straight line. The degree of a linear equation is the first degree, therefore, the highest power of the variables in a linear equation is 1.
The equation 6 - 3 + 4·x + 1, can be simplified as follows;
6 - 3 + 4·x + 1 = 4 + 4·x
A system of linear equations have no solutions when they have the same slope and different y-intercept.
The slope of the equation, y = 4 + 4·x is 4, and the y-intercept of the equation is 4, therefore the equation will have no solution, when we have;
The slope (the coefficient of x) of the equation on the right hand side is 4, and the y-intercept, the constant term differs from 4
Therefore the equation has no solution, is of the form;
When those the equation; 6 - 3 + 4·x + 1 = 4·x + 4
A system of linear equation has one solution when they have different slopes, therefore, the system will have one solution when we have;
6 - 3 + 4·x + 1 = 4·x + 4 = 3·x + 3
A system of equations have infinitely many solutions when the slope and the y-intercept on the left and right hand side of the equation are the same, therefore, we get;
The equation will have infinitely many solutions when the equations are;
6 - 3 + 4·x + 1 = 4·x + 4
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