To find the missing leg, we use Pythagorean's Theorem
\(c^2=a^2+b^2\)Where c = 6 and a = 3. Let's use these values to find b-
\(\begin{gathered} 6^2=3^2+b^2 \\ b^2=36-9 \\ b=\sqrt[]{27} \\ b=\sqrt[]{9\cdot3} \\ b=3\sqrt[]{3} \end{gathered}\)Hence, the length of the third side is\(b=3\sqrt[]{3}\)What is the equation of the line in slope-intercept form 
Answer:
y=3/5x+3
3 is where the line goes through the y-axis
3/5 is the slope (rise/run)
Step-by-step explanation:
choose the points that lies in the line and do the above process.
Ciara throws four fair six-sided dice. The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6 Work out the probability that at least one of the dice lands on an even number.
The likelihood that one or more of the dice will land on an even number is 1296.
How does probability work?The likelihood of an event is quantified by its probability, which is a number. It is stated as a number between 0 and 1, or in percentage form, as a range between 0% and 100%. The likelihood of an event increasing with probability of occurrence.
According to the given information:Four 6-sided dice are rolled what is the probability that at least two dice show least 2 die the same.
For 2 of the same: 5×5×642) =900
For 3 of the same: 5×643) =120
For 4 of the same: 644) =6
Combined: 900+120+6=1026
Total possibilities: 64=1296
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The probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
We can solve this problem by finding the probability that all four dice land on odd numbers and then subtracting this probability from 1 to get the probability that at least one of the dice lands on an even number.
The probability that one dice lands on an odd number is 3/6 = 1/2, and the probability that all four dice land on odd numbers is:
(1/2) × (1/2) × (1/2) × (1/2) = 1/16
Therefore, the probability that at least one of the dice lands on an even number is:
1 - 1/16 = 15/16
So the probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
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Jamaal is mixing blue and yellow paint to make green. He adds 2 parts blue paint to 2 parts yellow paint.
For every 1 part blue paint, there
yellow paint.
Jamaal is not happy with thecolor and adds 1 more part of blue paint. This will make the green paint more
For every 1 part blue paint, there
✔ is 1 part
yellow paint.
Jamaal is not happy with the color and adds 1 more part of blue paint. This will make the green paint more
✔ blue
.
Write an expression for the height, h, of a cylinder with a volume of 547 cubic inches
in terms of its radius, r.
The expression for the height (h) in terms of radius r is h = 547/(∏r²).
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
Given that the volume of the cylinder is 547 cubic inches.
The volume of a cylinder is V = ∏r²h
Where r is the radius of the cylinder.
h is the height of the cylinder.
Putting V = 547, r = r and h = h in V = ∏r²h
547 = ∏r²h
∏r²h = 547
Divide both sides by ∏r²:
h = 547/∏r².
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A quality control inspector has drawn a sample of 20 light bulbs from a recent production lot. Suppose 20% of the bulbs in the lot are defective. What is the probability that less than 8 but more than 4 bulbs from the sample are defective? Round your answer to four decimal places.
Explanation
We are given a sample 20 bulbs
the percentage of defective = 20% =0.2
So we are told to find the probability that less than 8 but more than 4 bulbs from the sample are defective
\(P(4So we will have\(P(5)+P(6)+P(7)\)We will use the binomial probability formula
\(\)Which equation can be used to find the area of the blue triangle?
A) A=2(7)(12)
B) A= 1/2 (7)(12)
C)A=2(7²)(12²)
D)A= 1/2(7²)(12²)
Answer:
The answer is D. A=1/2(7 to the power of 2) 12 to the power of 2)
Step-by-step explanation:
Sorry I keep asking questions I'm just need to finish this assignment HELP ASAP
Answer:
2,100x3/7 = 2,100x3/7=6,300/7= 900
Step-by-step explanation:
multiply 2,100 x 3 = 6,300 divide by 7 = 900
Answer:
1st box=2100
2nd box=6300
3rd box=900
Step-by-step explanation:
Ryan and Carlos decided to sell their cups of hot chocolate for $2.75. They sold 12 cups. They spent $9.45 on supplies that they will need to pay back to the bank.
How much profit did Ryan and Carlos make?
Answer:
$23.55
Step-by-step explanation:
First we will need to determine the total amount of sales Ryan and Carlos made. To do that we will multiply the amount of products sold by the product cost.
$2.75 x 12 = $33
Now we need to deduct the cost of supplies they need to pay back from their profits.
$33- $9.45= $23.55
Now we are left with Ryan and Carlos' total profit, which is $23.55
Kai, a seventh grader, wants to determine the average number of times the families in his neighborhood visit the pool during the summer. He samples the families of four of his classmates. Which improvements could Kai make to his sample to increase the validity of the results? Check all that apply. Sample more families/ sample families that have children who are not in seventh grade/ sample families that do not have children /sample families whose answer to the survey question is predetermined/ sample families living in every third house in the neighborhood
The correct options are sample more families, sample families having children who are not in seventh grade.
Sample families that do not have children. Sample families living in every third house in neighborhood.
To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:
Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.
Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.
Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.
Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of
sampling bias.
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what is the measure of
Help i need asaaaaaap °∠°
Answer:
Cube 1 = 30 cubic
Cube 2 = 48 cubic
Cube 3 = 72 cubic
Step-by-step explanation:
Cube 1 = 5x2x3
Cube 2 = 6x2x4
Cube 3 = 8x3x3
Find the angle on the unit circle
The angle on the unit circle is solved to be
56.01 degrees (to the nearest tenth)
How to find the angleTo find the angle of the terminal side through the given point on the unit circle, we can use the inverse trigonometric functions.
given that P = ((√5)/4, (√11)/4)
θ = arctan ((√11)/4 / (√5)/4)
θ = arctan((√11)/(√5))
θ ≈ 56.01 degrees
hence to the nearest tenth of a degree, the angle of the terminal side through the point P = ((√5)/4, (√11)/4) on the unit circle is approximately 56.01 degrees.
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An office building worth $1 million when completed in 2010 is being depreciated linearly over 50 years. What was the book value of the building in 2014? What will it be in 2022? (Assume the scrap value is $0.)
Answer:
To calculate the book value of the building, we need to calculate the annual depreciation amount and multiply it by the number of years elapsed since the building was completed.
The annual depreciation amount is calculated as: $1 million / 50 years = $20,000
In 2014, the book value of the building was: $1 million - ($20,000 * (2014 - 2010)) = $1 million - ($20,000 * 4) = $960,000
In 2022, the book value of the building will be: $1 million - ($20,000 * (2022 - 2010)) = $1 million - ($20,000 * 12) = $680,000
based on the graph how many tiles are im figure 0
For figure {0}, the number of tiles will be equal to 2.
What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a graph as shown in the image.
The line passes through point -
(3, 8) and (4, 10)
So, the slope of the line will be -
m = (10 - 8)/(4 - 3)
m = 2
y = 2x + c
For the point (3, 8), we can write -
8 = 6 + c
c = 2
For figure {0}, the number of tiles will be equal to 2.
Therefore, for figure {0}, the number of tiles will be equal to 2.
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Evaluate
∫
π
−
π
cos
2
(
5
x
)
d
x
.
Answer:
\( _{ - \pi} \int ^{\pi} \cos(2(5x) dx = _{ - \pi} \int ^{\pi} \cos(10x) dx \\ let \: 10x \: be \: u \\ \frac{d(10x)}{dx} = du \\ dx = \frac{du}{10} \\ignore \: limits \\ _{ - \pi} \int ^{\pi} \cos(2(5x) dx = \int \cos(u) \frac{du}{10} \\ = \frac{1}{10} \sin(u) + c \\ substitute \: for \: u \\ = \frac{1}{10} \sin(10x) |^{\pi} _{ - \pi} \\ = \frac{1}{10} (( \sin(10\pi) - ( \sin( -10 \pi) ) \\ \)
10x10-5(300x2)/5 Ian theb jkkkkj
Answer:
=10x¹⁰−300x²
Step-by-step explanation:
Refer to the Attachment for steps.
Answer:
dffd
Step-by-step explanation:
Which of the following expression is equivalent to 8x^2~5x+3x(4-2x)?
Answer:
2x^2 + 7x.
Step-by-step explanation:
8x^2 - 5x + 3x(4 - 2x)
= 8x^2 - 5x + 12x - 6x^2
= 2x^2 + 7x.
Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4
simplify (-4/5)^9/(-4/5)^10
Answer:
- 5/4
Step-by-step explanation:
exact form:-5/4
decimal form:-1.25
mixed number form: -1 1/4
The Fairview Chamber of Commerce researched the number of employees working at local companies. Number of employees Number of companies 273 1 350 4 357 1 873 4 X is the number of employees that a randomly chosen company has. What is the expected value of X? Write your answer as a decimal.
In order to find the expected value of x, we just need to divide the total number of employees by the total number of companies:
\(\begin{gathered} E(x)=\frac{273\cdot1+350\cdot4+357\cdot1+873\cdot4}{10} \\ E(x)=\frac{5522}{10} \\ E(x)=552.2 \end{gathered}\)So the expected value of x is 552.2.
Un hombre posee 50 acciones con un valor de 30 cada una , la corporación declaró un dividendo del 6% pagadero en acciones ¿cuantas acciones poseía entonces?
el hombre tenía 50 acciones.
La pregunta es, ¿cuántas acciones poseía el hombre si declararon un dividendo del 6% pagadero en acciones y tenía 50 acciones con un valor de $30 cada una?Para calcular cuántas acciones tenía el hombre,
se puede utilizar la siguiente fórmula:Dividendos = Número de acciones * Precio por acción * Tasa de dividendosDe esta fórmula,
podemos despejar el número de acciones. Así, tenemos:Número de acciones = Dividendos / (Precio por acción * Tasa de dividendos)De los datos del problema, se sabe que el hombre tenía 50 acciones con un valor de $30 cada una.
Además, la corporación declaró un dividendo del 6% pagadero en acciones. Por lo tanto, la tasa de dividendos es del 6%.Para resolver el problema, primero debemos calcular el valor del dividendo que se pagará en acciones.
Para ello, se debe multiplicar el valor de las acciones del hombre por la tasa de dividendos.
Así, tenemos:Valor del dividendo = 50 acciones * $30 * 0.06 = $90El valor del dividendo es de $90. Ahora, podemos sustituir este valor en la fórmula para calcular el número de acciones que tenía el hombre.
Así, tenemos:Número de acciones = $90 / ($30 * 0.06) = 50 accionesPor lo tanto,
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Given that a = 24 cm and b = 7 cm, work out x
Simplify the fraction
18
60
as much as possible.
3
10
18
60
12
54
Answer:
3/10
Hope this helps!
Have a good day :)
Is the sum of 3.04 and √20 rational or irrational? Explain.
Answer:
Irrational
Step-by-step explanation:
A rational number can be expressed as p/q where p and q are integers
3.04 is rational since it can be expressed as 304/100
√20 is not rational. √20 = √(4·5) = √4·√5 = 2√5
While 2 is a rational number, √5 is irrational since 5 is a prime number and square roots of primes are not rational
An irrational number multiplied by a rational number is irrational so √20 is irrational
An irrational number added to a rational number results in an irrational number.
So 3.04 + √20 is irrational
Solve X- (-2) = 21 please help me
Answer:
x=19
Step-by-step explanation:
I hope this helps you out and if your feeling generous plz mark brainliest it helps me a lot thank you:)
if a triangle has one side with a length of 20 meters and a second side with a length of 18 meters
Answer:
see attached
Step-by-step explanation:
You want the possible lengths of the third side of a triangle with side lengths 20 m and 18 m.
Triangle inequalityIf the third side is length c, the triangle inequality requires ...
18 +c > 20 ⇒ c > 2
20 +c > 18 ⇒ c > -2
18 +20 > c ⇒ c < 38
The possible lengths for the third side (c) are ...
2 < c < 38
That is, the third side must lie between the difference and the sum of the given sides.
The attachment shows the values on the list that are in this range.
Suppose y varies directly with x. When x is 5, y is 15. What is y when x is 12?
Answer:
y = 36
Step-by-step explanation:
given y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition when x = 5 , y = 15
15 = 5k ( divide both sides by 5 )
3 = k
y = 3x ← equation of variation
when x = 12 , then
y = 3 × 12 = 36
What do you need to make on your final exam to make an 80 for this class S1.
If your T1 = 73, T2 = 90, grades count as 3/7 each and the final is 1/7?
The score that you need to make in your final exam to ensure you make at least an 80 for the class is; 71
How to calculate the grade point average?
To calculate the Grade point Average, the unit value for each course that a student receives one of the utilized grades is multiplied by the number of grade points that are assigned for that grade. Then, the sum of these products is then divided by the sum of the units. Thereafter, the cumulative GPA is the sum of the grade points divided by the sum of the units.
We are told that;
You need to make on your final exam to make an 80 for this class S1.
T1 = 73, T2 = 90, grades count as 3/7 each.
The final is 1/7.
Thus, we can develop the equation with x as the required final score as;
(219/7) + (270/7) + (x/7) = 80
Multiply through by 7 to get;
219 + 270 + x = 80
489 + x = 560
x = 560 - 489
x = 71
Thus, that is the required score.
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Line ac and df are parallel they are cut by transversal Hj with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E
The measure of the unknown angles in the parallel lines AC and DF with transversal HJ are as follow,
m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.
Two lines AC and DF are parallel to each other in the attached figure
Transversal HJ cut lines AC and DF at point B and E respectively.
Measure of ∠ABE = 63°.
Using the result based on corresponding angles, alternate interior angles , and vertically opposite angles of a parallel lines we get,
Measure of ∠ABE ≅ Measure of ∠DEH ( corresponding angles)
⇒Measure of ∠DEH = 63°
Measure of ∠ABE ≅ Measure of ∠BEF ( alternate interior angles)
⇒Measure of ∠BEF = 63°
Measure of ∠ABE ≅ Measure of ∠CBJ ( vertically opposite angles)
⇒Measure of ∠CBJ = 63°
Using the result of linear pair angles,
Measure of ∠ABE + Measure of ∠CBE = 180°
⇒ Measure of ∠CBE = 180° -63°
⇒ Measure of ∠CBE = 117°
Measure of ∠CBE ≅ Measure of ∠FEH ( corresponding angles)
⇒Measure of ∠FEH = 117°
Measure of ∠CBE ≅ Measure of ∠BED ( alternate interior angles)
⇒Measure of ∠BED = 117°
Measure of ∠CBE ≅ Measure of ∠ABJ ( vertically opposite angles)
⇒Measure of ∠ABJ = 117°
Therefore, the measure of the seven unknown angles formed in the parallel line are given by m ∠DEH = 63° , m ∠BEF = 63° ,m ∠CBJ = 63°, m ∠CBE = 117° , m ∠FEH = 117° , m ∠BED = 117° , and m ∠ABJ = 117°.
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The above question is incomplete, the complete question is:
Lines AC and DF are parallel. They are cut by transversal HJ with your partner find the seven unknown angle measures in the diagram explain your reasoning. What do you notice about the angles with vertex B and the angles with vertex E.
In the attached figure.
what is the slope of a line that is parallel to the line connecting point O (-5,1) and point P (2,3)?
Answer:
2/7
Step-by-step explanation:
2 parallel lines have the same slope
we just need to find the slope of the line with the point’s connecting O and P
We use y2-y1/x2-x1 to find slope
3-1/2-(-5)
2/7
2/7 is the slope
Hopes this helps please mark brainliest