The probability of drawing a white marble on the first draw and another white marble on the second draw is 1/3.
What is probability?Probability theory is an area of mathematics that examines random events. A random event's outcome cannot be predicted before it happens, although it could take any of several different forms. The final result is thought to have been determined by chance.
In everyday speech, the word "probability" has numerous meanings. For the growth and applicability of the mathematical theory of probability, two of these are particularly crucial. One is the representation of probabilities as relative frequencies, which is illustrated by examples from basic teams playing coins, cards, dice, and roulette wheels.
Given that, a bag contains 6 white marbles and 4 black marbles. a marble is drawn from the bag and then a second marble is drawn without replacing the first one.
The total number of balls = 10 marbles.
The probability of drawing a white marble on first draw = 6/10.
The probability of drawing a white marble on the second draw = 5/9.
The probability of drawing a white marble on the first draw and another white marble on the second draw is:
6/10 × 5/9 = 30/90 = 1/3
Hence, the probability of drawing a white marble on the first draw and another white marble on the second draw is 1/3.
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Suav deposits $450 every quarter into an account earning a quarterly interest rate of 2.225%. How much would he have in the account after 10 years, to the nearest dollar?
The amount in the account after 10 years is $4,978.365.
What is Interest?Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principle refers to the borrowed or lent funds. The Amount is the total of the principal plus interest. The term "rate of interest" refers to the rate at which interest is applied to the principal.
Given:
P= $450
R= 2.225%
n= 10
So, Amount = d [[tex](1+i)^n[/tex] - 1 ] / i
A = 450 x [[tex](1+0.02225)^{10[/tex] - 1 ] / 0.02225
A = 450 x (1.24615249763-1) / 0.02225
A = 450 x 0.24615249763/ 0.02225
A = 4,978.365
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The temperature in Austria one morning was -5 degrees celcius at eight o clock and increased by 2 degrees celcius every hour until twelve o clock . What will be the temperature be at half past eleven
The temperature at half past eleven would be 2 °C.
What is algebraic expression?In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.
Given is that the temperature in Austria one morning was -5 degrees Celsius at eight o clock and increased by 2 degrees Celsius every hour until twelve o clock.
We can write the temperature variation as a function of hour {x} as -
T{x} = (- 5 + 2{x})°C
For half past eleven, we will have -
{x} = 3.5
So, we can write -
T{x} = (- 5 + 2 x 3.5)°C
T{x} = 2 °C
Therefore, the temperature at half past eleven would be 2 °C.
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Suppose you started at the point (7, 2). From there, you moved up 5 units,
and right 3. At what coordinate would you be?
Answer:(10,7)
Step-by-step explanation:
Answer:
(10 , 7)
Step-by-step explanation:
You start at the point (7 , 2)
Moving up 5 units is going up on the y axis, therefore add 5 to 2.
(7 , 7)
Moving to the right 3 times is going to the right on the x-axis, and since moving to the right is positive, add 3 to 7.
[(10 , 7)]
Find the length of side in simplest radical form with a rational denominator.
Answer:
x=2sqrt2
Step-by-step explanation:
The legs are equal, thus the sides are x, x, and hypotenuse is 4. This means that x^2+x^2=4^2. Thus, 2x^2=16 => x^2=8 => x= sqrt8 => x=2sqrt2
The width of the rectangle is the length minus 5 units. The area of the rectangle is 6 square units. What is the width, in units, if the rectangle?
Answer:The width of the rectangle is 1 unit
Step-by-step explanation:Let the length of the rectangle be x
let the breadth be x-5
Since ,area of rectangle=length*breadth
area = x*(x-5)
6=x^2-5x
x^2-5x-6=0
solving the above equation,
x^2-(6x-x)-6=0
x^2-6x+x-6=0
x(x-6)+1(x-6)=0
(x-6)(x+1)=0
x=6 and x=-1
since the breadth cannot have negative value
Hence ,the breadth of rectangle is 1 unit
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What is the volume area of a cylinder with base radius 2 and height 6?
Answer:
75.4
Step-by-step explanation:
Volume of cylinder=πr2h
=π·22·6≈75.39822
Which of the following shows the simplified form of sine of x over the quantity 1 plus cosine of x (end quantity)?
A. sin x − tan x
B. sin x − cot x
C. csc x − cot x
D. 1
The simplified form of sine of x over the quantity 1 plus cosine of x (end quantity) is 1. Option D
How to find the simplified form of the expressionThe question can be interpreted as sin(x) / (1 + cos(x))
sin(x) / (1 + cos(x)) = (sin(x) / cos(x)) / (1/cos(x) + cos(x)/cos(x))
= tan(x) / (1 + sec(x))
= (sin(x)/cos(x)) / (cos(x)/(cos(x)+1))
= (sin(x)/cos(x)) / ((cos(x)+1)/cos(x))
= sin(x) / (cos(x) + 1)
Therefore, the simplified form of sin(x) / (1 + cos(x)) is:
sin(x) / (1 + cos(x)) = sin(x) / (cos(x) + 1) = 1
Hence, The simplified form of sine of x over the quantity 1 plus cosine of x (end quantity) is 1
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Use <,>, or =
1.9 ? 1.90
0.05 ? 0.2
3.88 ? 6.38
The comparision between decimal number are 1.9 = 1.90, 0.05 < 0.2, 3.88 < 6.38
How can we express numbers belonging to decimal numeral system?Suppose that the number is abcd.efg and belongs to the decimal numerical system.
Therefore, one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.
Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.
Here we can see that
1.9 = 1.90
0.05 < 0.2
3.88 < 6.38
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Express 4 + ln 2 - ln 4 as a single natural logarithm. a. ln 2 b. ln 4 c. ln 64
The single natural logarithm expression is ln(2). Therefore, correct answer is (a)
Logarithmic Equations:The expression in the form [tex]e^a=b[/tex] can also be written as In b = a which is called as logarithmic expression.
Properties of Logarithms:
1. In (mn) = In m + In n
2. In [tex]a^m =[/tex] m In a
3. In [tex]e^a[/tex] = a.
How to express as a single natural logarithm?The natural logarithm expression is:
4 + ln 2 - ln 4
Apply the product and quotient rule of natural logarithm:
4 + ln 2 - ln 4 = In (4 × 2/4)
Evaluate the quotient:
4 + ln 2 - ln 4 = In (2)
Hence, the single natural logarithm expression is ln(2).
The correct option is (a)
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Answer:
B: ln 4.
Step-by-step explanation:
Mrs. Mack is looking at the blueprints for a new factory. On the blueprint, the factory floor is a rectangle with a length of 0.3 meter and a width of
0.25 meter. The factory will be built by using a scale factor of 140.
Mrs. Mack wants to know the area of the factory floor. She decides to do this by first determining the dimensions of the factory floor.
What will be the length of the factory floor?
Enter your answer in the box
Answer:
42 meters
Step-by-step explanation:
The length of the factory floor will be 42 meters. This is found by multiplying the length of 0.3 meters by the scale factor of 140, which yields 42 meters.
Answer:
42 meters
Step-by-step explanation:
its correct :)
Turn the (a) Are they taking the test? (b) Write a letter. a lette (c) Don't make a noise. (d) Please bring some noodles. (e) Let him complete his work. (f) Does she compose poems? (g) Has she composed a song? (h) Did he To following sentences into passive voice. Opleted Linder
The diameter of a cylindrical water tank is 13 ft, and its height is 17 ft. What is the volume of the tank?
Use the value 3.14 for I, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
13 ft
17 ft
ft ft²
X
Hello Everyone, please help me with this blanks
Note that the prompt is geared at testing the ability of the to understand certain vocabulary terms. The terms are given as follows:
aggrandizebombastdeignelicitendemicflauntmendaciousobviateorthographypaleontologypanacheparoxysmrecoilsaturnineshibbolethThe completed paragraphs are given below.
The first paragraph is completed as follows:
When Dr. Carter is not fulfilling his duties as the professor of paleontology at Ganton College, he is in the jungles of South America supervising excavations of ancient creatures. During the last dig, Dr. Carter recoiled when a poisonous snake tried to bite him. Now he wears tall boots and gloves to obviate the risk of dangerous animals endemic to the region.
He will definitely elicit the need for such safety measures. Some of the incoming scientists will accuse him of self-aggrandizement despite the fact that the sociable doctor always avoids using too much panache when speaking about safety; he'll flaunt his amazing findings when he returns to the campus at the end of the summer. He can put his bombast to better use in the classroom.
The second paragraph is completed as follows:
Baker deigned to give a semi-friendly nod to his Nazi captors, and he immediately suffered the consequences. Baker then endured the loud paroxysm of his cellmates: "What was that? What, are you working for them, too?"
He understood their paranoia. Just weeks before, a(n) mendacious rebel captive had revealed the escape plan to the guard. The prisoners, including Baker, had to abandon months of secrecy and labor that went into the construction of the tunnel. They had not yet regrouped; most of the saturnine prisoners simply lay in their cells, defeated.
Baker sat against the wall and thought about his capture. He had misused the shibboleth that the Nazis used to identify foreign spies. and the lack of orthography on his forged travel documents instantly signaled that he was not the German officer he claimed to have been. They must need information, he reasoned, or they would have executed him by now.
The definition of terms are given as follows:
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-0.75, -3, -12, -48... Find the 9th term
Answer:
-49,152
Step-by-step explanation:
if you multiply -0.75, times 4 it equals -3 so do that until you get the ninth term. (Multiply each term by 4).
**NEED HELP. OFFERING25 POINTS!!!**
Graph and analyze the function f(x)=2〖(x-1)〗^2.
A.) Use the graph provided below to graph f(x). Include at least 5 points and the vertex.
B.) Describe the transformation from the parent function y=x^2 to the function f(x).
C.) State the domain and range of f(x). Use either set notation or interval notation.
D.) State axis of symmetry. Write as an equation of a line.
Providing a graph to use!! TY!
The points and the vertex are (1, 0), (2, 2), (0, 2), (-1, 8) and (-2, 18)
The points and the vertexFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2(x - 1)²
See attachment for the graph
From the attached, the points are (1, 0), (2, 2), (0, 2), (-1, 8) and (-2, 18)
Where the vertex is (1, 0)
Describe the transformationWe have
y = x^2
f(x) = 2(x - 1)²
The transformation is described as follows:
A vertical stretch by a factor of 2A shift to the right by 1 unitsThe domain and rangeThe input has no restriction
So, we have
Domain: (-∝, ∝)
The output starts or ends at the vertex
So, we have
Range: [0, ∝)
The axis of symmetryIn (a), we have
vertex is (1, 0)
So, we have
(x, y) = (1, 0)
Remove the y coordinate
x = 1
Hence, the axis of symmetry is x = 1
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Hugh poured 100 kilograms of water into 10 kg of salt.He made ...... kilograms of ......% salt solution.
NEED HELP ASAP!!!!! PLEASEEE!
Hugh made 110 kilograms of 9.1% salt solution.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Hugh poured 100 kilograms of water into 10 kg of salt.
So, the total mass is the sum of the mass of water and the mass of salt.
Thus, 100+10=110 kg.
The ratio between the mass of the salt (10 kg) and the combined mass of the mixture is the concentration.
Now, C=10/110 ×100
= 100/11
= 9.1%
Therefore, Hugh made 110 kilograms of 9.1% salt solution.
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Sections taken through the narrow width of an entire building are known as ______________________________ sections.
Sections taken through the narrow width of an entire building are known as transverse sections.
What is building?A building is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory.
Given is a structural analysis blank statement as -
"Sections taken through the narrow width of an entire building are known as __________ sections.
Sections taken through the narrow width of an entire building are known as transverse sections. Those through the long dimension are known as longitudinal sections.
Therefore, Sections taken through the narrow width of an entire building are known as transverse sections.
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you can compare two marginal distributions to see if the corresponding two variables are related. true/false
Yes, you can compare two marginal distributions to see if the corresponding two variables are related. This is done by plotting the two distributions and visually inspecting them for evidence of a relationship. Additionally, you can use statistical tests to measure the strength of the relationship between the two variables.
Comparing two marginal distributions can help you identify if there is a relationship between two variables. You can plot the distributions and look for evidence of a relationship such as a linear trend or a pattern of higher or lower values compared to one another. Additionally, you can use statistical tests such as the Pearson correlation coefficient or Spearman's rank correlation coefficient to measure the strength of the relationship between the two variables.
Yes, you can compare two marginal distributions to see if the corresponding two variables are related. This is done by plotting the two distributions and visually inspecting them for evidence of a relationship. Additionally, you can use statistical tests to measure the strength of the relationship between the two .
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Find the measure of the largest exterior angle
Answer:
sum of all side of Pentagon= 540
10x+6x+4x+3x+x=540
24x. =540x. =540/24x. = 22.5According to question
10x = 10×22.5=225how to calculate inverse sin?
The inverse of the sine can be calculated by using the formula sin^-1(x) = arcsin(x)
To calculate the inverse sine (sin^-1) of a value, you can use a scientific calculator or look up the value in a trigonometric table. However, if you want to understand how to do it manually, follow these steps:
Make sure the value you are calculating the inverse sine of is between -1 and 1, inclusive. If it is not, the inverse sine is undefined.
Write down the value you want to find the inverse sine of.
Use the formula: sin^-1(x) = arcsin(x), where x is the value you wrote down.
Substitute the value of x into the formula and calculate the inverse sine using a calculator or by using a series expansion or Taylor series approximation.
The inverse sine function returns a value in radians, so you may need to convert it to degrees if that's the unit you're working with.
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I ride four times faster than I jog. If a trip took me 45 minutes and I spent 15 of these minutes jogging 3km, how far did I ride ?
Answer:
24km
Step-by-step explanation:
15 min (jogging)
30 min (cycling)
3km/15 min (jogging)
1km/5min (jogging)
4km/5min (cycling)
30÷5= 6
4×6= 24km
Distance covered during riding is 24 km.
What is meant by speed ?Speed of an object is defined as the rate of change of the distance travelled.
Here,
Speed is the distance travelled in a given time.
Total time given, t = 45 minutes
Time taken for jogging, t₁ = 15 minutes
So, time taken for riding, t₂ = t - t₁
t₂ = 45 - 15
t₂ = 30 minutes
Distance covered during jogging, d₁ = 3 km
Therefore speed of jogging, v₁ = d₁/t₁ = 3/15
v₁ = 0.2 km/min
So, speed of riding, v₂ = 4v₁ = 4 x 0.2
v₂ = 0.8 km/min
Therefore distance covered during riding, d₂ = v₂ x t₂
d₂ = 0.8 x 30
d₂ = 24 km
Hence,
Distance covered during riding is 24 km.
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a rectangular room is 3 meters longer than it is wide, and its perimeter is 30 meters. find the dimension of the room.
how to convert 250 ml to l?
250 milliliters is equal to 0.25 liter
The conversion factor to convert milliliter to liters is 0.001
Therefore, the equation will be,
1 ml = 0.001 liter
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The volume in liters = The volume in ml × conversion factor
Substitute the values in the equation
1 ml = 0.001 liters
250 ml = 0.001 × 250
Multiply the numbers
= 0.25 liters
Therefore, 250 ml is 0.25 liters
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Find an equation of the plane that contains the curve with the given vector equation. r(t) = (t, t3, t)
The equation of the plane can be expressed as 3t2x - y - 3t2z = d, where d is a constant.
What is equation?Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.
The equation of the plane that contains the curve with the vector equation r(t) = (t, t3, t) can be found by taking the cross product of two vectors that are on the plane. Let the two vectors be v1 = (1, 0, 1) and v2 = (1, 3t2, 1). Taking the cross product of these two vectors yields v1 x v2 = (3t2, -1, -3t2). This vector is perpendicular to the plane. Therefore, the equation of the plane can be expressed as 3t2x - y - 3t2z = d, where d is a constant.
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mike wrote 4 checks for $30 each, withdrew another $40 and deposited $80. What was the overall change in the amount of money he had?
((30$ x4)+40$)-80$=80$
solving systems of equations by substitution examples 3x + y = 13. 5x -2y = 7.
Answer:
x = 3, y = 4
Step-by-step explanation:
3x + y = 13
5x - 2y = 7
To solve by substitution, you solve one of the equations for a variable, and then plug it into the other equation.
I'm going to choose to solve the first equation for y, as that will be the easiest.
y = -3x + 13 (subtract 3x from both sides)
Now we plug this equation into the y in the second equation and solve for x.
5x - 2(-3x + 13) = 7 (distribute)
5x + 6x - 26 = 7 (combine like terms)
11x - 26 = 7 (add 26 to both sides)
11x = 33
x = 3
Now that we know x is 3, we can plug it in a solve either equation for y.
y = -3(3) + 13
y = -9 + 13
y = 4
Solve for x; Then find the length of PM AND OM
Answer:
[tex]x=12[/tex], PM = 27, OM = 54
Step-by-step explanation:
To find x, we can notice that MP is similar to OP. Therefore, we can create an equation:
[tex]2x+3=4x-21[/tex]
[tex]2x-4x=-21-3[/tex]
[tex]-2x=-24[/tex]
[tex]x=12[/tex]
To solve for PM, we can plug in x from [tex]2x+3[/tex]:
[tex]2(12)+3[/tex]
= 27
To solve for OM, we will need to add OP and PM values and plug in x:
[tex]4x-21+2x+3[/tex]
Plug in x:
[tex]4(12)-21+2(12)+3[/tex]
= 54
Determine the unknown angle measures of △DEF. Round to the nearest degree.
m∠D =
°
m∠F =
°
m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.
What is angle?Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.
To determine the unknown angle measures of △DEF, we can use the fact that the sum of the angles of a triangle is 180°. Thus, if we know two angle measures in the triangle, we can use them to calculate the third.
Let's denote the two known angle measures as m∠D and m∠F. We can use the following equation to solve for the unknown angle measure:
m∠D + m∠F + m∠E = 180°
We can rearrange the equation to solve for m∠E:
m∠E = 180° - m∠D - m∠F
Therefore, once we know the measures of m∠D and m∠F, we can calculate the measure of m∠E.
For example, if m∠D = 40° and m∠F = 65°, then the measure of m∠E would be:
m∠E = 180° - 40° - 65° = 75°
Therefore, m∠D = 40°, m∠F = 65°, and m∠E = 75°. Round to the nearest degree.
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Answer: the answer is
m∠D = ✔ 46°
m∠F = ✔ 44°
Step-by-step explanation: I got it correct. it will be show below.
50% of the machines at Bud's Suds are washing machines. If there are 10 washing machines, how many machines are at Bud's Suds in all?
Answer:
20
Step-by-step explanation:
If 50% of machines are washing machines and there are 10, then add 10 again to get 100% of the total machines
What is the measure of arc e b c? 40° 90° 140° 220°
The measure of the arc is option (c) 140°
In geometry, an arc is a curved line that is a part of a circle's circumference. The measure of an arc can be calculated using the angle of the arc, which is measured in degrees.
In the case of EBC, the measure of the arc is 140°. This is because we can use the Angle-Side-Angle (ASA) congruence theorem, which states that two triangles are congruent if and only if two angles and the included side are equal.
In the case of EBC, we know that angle A equals 40° and angle C equals 90° so the only variable left is the measure of the arc, which is equal to 140°.
Therefore, the measure of EBC is 140°. This can be verified by drawing the triangle and measuring the arc with a protractor.
Therefore, option (c) is the right one.
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Complete Question:
What is the measure of arc EBC when the values of Angle a nd c are 90 and 40 degree respectively.
a) 40°
b) 90°
c) 140°
d) 220°
