The probability that John selected a red marble on the first draw and then selected red again on the second draw is 1/9.
To calculate the probability of John selecting a red marble and then selecting red again, we need to determine the probability of each event separately and then multiply them together.
The probability of selecting a red marble on the first draw is the number of red marbles divided by the total number of marbles:
P(Red on first draw) = 4 / (8 + 4) = 4 / 12 = 1/3
Since John replaced the marble back into the bag before the second draw, the probability of selecting a red marble on the second draw is also 1/3.
To find the probability of both events happening together (independent events), we multiply the probabilities:
P(Red on first draw and Red on second draw) = P(Red on first draw) × P(Red on second draw)
= (1/3) × (1/3)
= 1/9
Therefore, the probability that John selected a red marble on the first draw and then selected red again on the second draw is 1/9.
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1. Find the pattern in this sequence. Then write
the next three terms in the sequence.
5,2,1,...
Answer:
-1,-3,-4 it is just subtracting the same amount.
Step-by-step explanation:
16. c= vλ. If c = 2.998 x 10^8 m/s, v= 4.41 x 10¹4 s-¹; find a value for λ.
Answer:
6.80 x 10⁻⁷ m
Step-by-step explanation:
You can find the value of λ by inserting the given values into the equation and simplifying.
c = vλ <----- Given equation
2.998 x 10⁸ m/s = (4.41 x 10¹⁴ s⁻¹)λ <----- Insert values
6.80 x 10⁻⁷ m = λ <----- Divide both sides by 4.41 x 10¹⁴
A bag contains lettered tiles. the theoretical probability of choosing a vowel is 40%. the bag contains 78 consonants. how many tiles are in the bag?
The total number of ties present in the bag are 130.
What is probability?Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."
Formula for probability is -
Probability(Event) = Favourable Outcomes/Total Outcomes
It P(E) is the probability for occurring any event.
'x' be the favourable outcome.
'n' be the total outcome.
Then,
P(E) = x/n.
Calculation for the total tiles present the bag.
The probability of choosing a vowel is 40% = 0.4.
Then, the probability of choosing a consonants will be 1 - 0.4 = 0.6 or 60%.
Let P(E) be the probability of the occurrence of the consonants.
Then,
P(E) = total number of consonants/total tiles in the bag.
Let 'T' be the total tiles in the bag.
0.6 = 78/T
T = 78/0.6
T = 130
Therefore, the total tiles present in the bag are 130.
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3\sqrt(6)*6\sqrt(6)
Please quick reply!
Answer: 3
Step-by-step explanation:
Multiply the numerator to get 3 x 6 is 18
Multiply the denominator to get √6 x √6 = 6
Divide 18 by 6 to get the answer is 3
the diagonal of the rectangle is 15 cm and one of its sides is 9 cm. find the area of the rectangle.
The area of the rectangle is 108 square centimeters.
Given Information
The following information has been given in the question,
Length of the diagonal of the rectangle, l = 15 cm
Length of one of the sides of the rectangle, a = 9 cm
Let the other side of the rectangle be b.
Finding the Other Side of the Rectangle
According to Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Applying this theorem in the right-angle triangle formed by the diagonal and 9cm side of the rectangle, we get,
l² = a² + b² [∵ The diagonal makes the hypotenuse]
(15)² = (9)² + b²
b² = (15)² - (9)²
b² = 225 - 81
b² = 144
b = √144
b = 12 cm
Calculating the Area of the Rectangle
Area of the rectangle, A = a × b
A = 9 × 12
A = 108 cm²
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Question 12
From the given graph, use two points to write an equation in point-
slope form and then change to slope-intercept form.
Step 1: Use the two points to find the slope.
Step 2: Use the slope and one point to complete point-slope form.
y-y₁ = m(x-x₁)
Step 3: Change point-slope form into slope intercept form by solving
for y. Show your work!
y=mx+b
A square pool is surrounded by a paved area that is 2 metres wide. If the area of the paving is 72m2, what is the length of the pool?
The length of the square pool is 8. 49cm
How to determine the areaNote that the formula for finding the area of a square is given as;
Area = length^2
We have
Area = 72 m²
Substitute into the formula
I^2 = 72
Find the square root of both sides
I= √72
I = 8. 49cm
The length of the square pool given as I is 8. 49cm
Thus, the length of the square pool is 8. 49cm
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Find the area of the figure.
Answer:
60 ft^2
Step-by-step explanation:
Solve:
2a + 6 = 12
a =
Answer:
8
Step-by-step explanation:
because hhhhhh
gghhhh
jkkkkk
lllll
vvvvv
dddfff
oooooo
eeeerer
kkkkkk
lllll.ssss
(Refer to the attached image)
Answer:
D. 10
Step-by-step explanation:
To find the distance between two points, use the distance formula:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Define the two points:
[tex]\textsf{Let }(x_1,y_1)=(4,-3)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(-4,3)[/tex]
Substitute the two defined points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(-4-4)^2+(3-(-3))^2}[/tex]
[tex]\implies d=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\implies d=\sqrt{(-8)^2+6^2}[/tex]
[tex]\implies d=\sqrt{64+36}[/tex]
[tex]\implies d=\sqrt{100}[/tex]
[tex]\implies d=\sqrt{10^2}[/tex]
[tex]\implies d=10[/tex]
Therefore, the distance between the two given points is 10 units.
Formula given by
[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{8^2+6^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{10^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=10units[/tex]
Option D
Given the right triangle, use the pythagorean theorem to find "a" (one of the legs) when c=85 and b= 53. (round answer to nearest tenth).
Answer:
a= 100.2
Step-by-step explanation:
You solve it like you ate looking for the hypotenuse
check out the pic first
Answer: (0, 16)
Step-by-step explanation:
y = mx + c
c is the y intercept
from the equation, c = 16
(it's not exactly mx but you don't need to solve for x)
At 3:20, what is the measure in degrees of the lesser angle formed by the hour hand and the minute hand
Answer: 30 degrees
Step-by-step explanation:
A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°
The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, angle of depression from the helicopter can be found as follows:
tan x = opposite / adjacent
where
x = angle of depression
Hence,
tan x = 660 / 280
tan x = 2.35714285714
x = tan⁻¹ 2.35714285714
x = 67.1231281953
x = 67°
Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
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Answer:
D = 67
Step-by-step explanation:
solve for x -
[tex] x^{2} + 5x + 6 = 0 \\ \\ [/tex]
ty! :)
Hello,
x² + 5x + 6 = 0
a = 1 ; b = 5 ; c = 6
∆ = b² - 4ac = 5² - 4 × 1 × 6 = 25 - 24 = 1 > 0
2 solutions :
[tex] x_{1} = \frac{ - b - \sqrt{\Delta} }{2a} = \frac{ - 5 - 1}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]
[tex]x_{2} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - 5 + 1}{2 \times 1} = \frac{ - 4}{2} = - 2[/tex]
S = { -3 ; -2}
What addition/subtraction equation should I put?
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
When solving an equation, Anne's first step is shown below. Which property justifies
Anne's first step?
The justification used is multiplicative property of equality because both sides are multiplied by the same value
Solving linear equationsGiven the expression below
-1/3(4x^2 - 3) - 3 = 5x^2 - 2
We are to determine the justification by Anne to get the step 2 as shown
(4x^2 - 3) - 3 = -3(5x^2 - 2)
Expand
(4x^2 - 3) - 3 = -15x^2 + 6
Hence the justification used is multiplicative property of equality because both sides are multiplied by the same value
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On purchasing a cell phone, Tia got an offer and got the cell phone for $35\%$ less than the tag price. If she saved $\$140$ on that cell phone. Then price on the tag must be $\$$
On purchasing a cell phone, Tia got an offer and got the cell phone for 35% less than the tag price. If she saved 140 on that cell phone. Then price on the tag is 400.
Since, the cell pone is sold with 35% discount on it.
Tia got that phone at selling price with 35% discount on tag price. Also, she saved around 140 on buying the cell phone.
Therefore, the discount on the cell phone on the tag price is her saving on buying the cell phone.
Hence,
35% discount on tag price=Saved amount
(35/100)×T=140
where T is the tag price.
T=(140×100)35
T=14000/34
T=400
Therefore, on buying the cell phone with 35% discount on tag price costs around 140. Then the tag price is 400.
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mel cuts a slice of cake if her slice is 4/15 of the cake, what is the central angle of her slice, please give answer in degrees
Answer:
Below in bold.
Step-by-step explanation:
That would be 4/15 * 360 as there are 360 degrees in a circle
= 96 degrees.
A plane can cover 9904 km in 8 hours how mucb distance will it cover in 1 hour?
In one hour the plane will cover a distance of 1238 km.
What is a linear equation?
A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y is x is given.
calculation:-
today distance = 9904 km.
total time is taken = 8 hours.
∴total distance covered in one hour = 9904/8
= 1238 km.
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Convenience sampling Multiple Choice is the same as simple random sampling. ensures that samples are representative of the population. is an unbiased sampling method. collects sample information from groups that are easy to obtain.
Option (d) is correct. Convenience sampling collects sample information from easy-to-collect groups.
Given convenient sampling.
Convenience sampling is defined as a method adopted by researchers in which they collect market research data from a pre-existing group of respondents. This is the most commonly used sampling technique because it is extremely fast, simple and economical. In many cases, members are easily accessible to be part of the template. It is non-probability sampling and therefore different from random sampling. Since the samples are taken for convenience, the samples are not always representative of the population and therefore have bias. In this case, people were sampled simply because they were convenient.
Thus, convenience sampling collects sample information from easy-to-collect groups.
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A movie ends at 7:45 P.M. The next movie begins 50 minutes later. What time does the next movie begin?
Answer:
8:35 PM
Step-by-step explanation:
First, subtract 15 from 50.
50-15=35
Add that 15 taken from 50 to 7:45.
7:45 + 0:15 = 8:00
Add 35 to 8:00
8:00 + 0:35 = 8:35
The next movie will start at 8:35 PM.
Hope this helps!
10 points please help me!!!
Step-by-step explanation:
16-19 -> 3 (16, 17, 19)20-23 -> 1 (21)24-27 -> 3 (24, 26, 26)28-31 -> 4 (28, 29, 30, 31)32-35 -> 5 (32, 33, 34, 34, 35)find the value of x from the figure
Answer:
x = 30
Step-by-step explanation:
110 and 3x - 20 are supplementary angles, sum to 180° , then
110 + 3x - 20 = 180
90 + 3x = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Answer:
x = 30
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
For this question, you must be clear of the angle properties.
z + 110 = 180 (Sum of Angles on a straight line)
z = 180 - 110 = 70
z = 3x - 20 (Corresponding Angles)
3x - 20 = z
3x - 20 = 70
3x = 70 + 20
3x = 90
x = 90 / 3 = 30
Select the equivalent expression. 2^-4 = ?
Answer:
1/16
Step-by-step explanation:
This means 1/2x2x2x2 = 1/16
How would you describe the graph for the equation |x| <4?
a.) An open circle on 4 with a solid line drawn to an open circle on -4.
b.) A closed circle on 4 with a solid line drawn to a closed circle on -4.
c.) A closed circle on 4 with a solid line drawn to an open circle on -4.
d.) An open circle on 4 with a solid line drawn to a closed circle on -4.
Answer:
a.) An open circle on 4 with a solid line drawn to an open circle on -4.
Explanation:
Open circles are used for signs: < and >
Closed circles are used for signs: ≤ and ≥
Here in the given expression: |x| < 4
[<] sign is used so open circle is used
If |y| < a then -a < y < a
so here, -4 < x < 4
Both circles should be opened, drawn with a solid line from -4 to 4.
Nina thought of a number. she added 24 , tripled the result, subtracted 18 , multiplied the result by 2 and got 120 . what was nina's number?
Answer:
Step-by-step explanation:
If we subtract 3 from the unknown number, we get just as much as if we subtracted 7 from the unknown number and we multiplied the result by 2
The weights of certain machine components are normally distributed with a mean of 7.75 ounces and a standard deviation of 0.07 ounces. Find the two weights that separate the top 4% and the bottom 4%. These weights could serve as limits used to identify which components should be rejected. Round your answer to the nearest hundredth, if necessary.
The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .
The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).
What is normal distribution?The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.
The probability for values that are farther from of the mean tapered down equally both in directions.
Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.
The values of z = +1.75 and z = -1.75
Let the weight of the machines be 'x'.
Use the formula for z- value
z = (x - μ)/ σ
Where,
σ is standard deviation = 0.07 ounces.
μ is mean = 7.75 ounces.
Substitute all the values and calculate the weight.
case 1: when z = +1.75
1.75 = (x - 7.75)/0.07
x = (1.75×0.07) + 7.75
x = 7.872
x = 7.87 (round nearest hundredth)
case 2: when z = -1.75
-1.75 = (x - 7.75)/0.07
x = (-1.75×0.07) + 7.75
x = 7.6275
x = 7.63 (round nearest hundredth)
Therefore,
x = 7.87 (round nearest hundredth) is weight which separates top 4%.
x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.
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Read the following description of a relationship:
Ron is making a banner by stringing letters on a cord. The cord weighs 8
ounces, and each letter weighs 10 ounces.
Let n represent the number of letters and w represent the weight of the banner.
This relationship can also be shown in a table. Complete the equation that represents the
relationship between n and w
The equation that represents the relationship between n and w is w = 10n + 8.
How to illustrate the expression?From the information, Ron is making a banner by stringing letters on a cord and the cord weighs 8
ounces and each letter weighs 10 ounces.
Let represent the number of letters
Let w represent the weight of the banner.
In this case, when n = 6, w = 68 and when n = 7, w = 78.
Therefore, the relationship will be:
w = 10n + 8
To confirm let's use n = 6
10n + 8
10(6) + 8
= 68
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Answer:
Step-by-step explanation:
w=10n+8
The probability is .80 that a standard normal random variable is between -z and +z. The value of z is approximately:________
The z value for the probability in the standard normal table is 1.29.
In this question,
Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.
The value of probability is 0.80
A standard normal random variable is between -z and +z, So
P(-z < 0 < z) = 0.80
⇒ 2P(0 < z) = 0.80
⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]
⇒ P(0 < z) = 0.40
From the standard normal table, z value for the probability 0.40 is
⇒ z = 1.29
Thus P(0 < 1.29) = 0.40
Hence we can conclude that the z value for the probability in the standard normal table is 1.29.
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