Given
To find the value of x.
Now,
By the external angle sum property of triangle, we have,
\((4x+2)\degree+(2x-9)\degree=5x+13\degree\)That implies,
\(\begin{gathered} 4x+2+2x-9=5x+13 \\ 6x-7=5x+13 \\ 6x-5x=13+7 \\ x=20\degree \end{gathered}\)Hence, the value of x is 20 degrees.
The measures of the angles of a triangle are shown in the figure below. Solve for x.
34°
46°
x°
The measures of the angle x in the triangle is 100 degrees
How to determine the measures of the angle?From the question, we have the following parameters that can be used in our computation:
Angles = 34, 46 and x
The sum of angles in a triangle add up to 180 degrees
This is represented as
Sum of angles = 180
Substitute the known values in the above equation
So, we have
34 + 46 + x = 180
Evaluate the like terms in the above equation
So, we have
80 + x = 180
Evaluate the like terms in the above equation
So, we have
x = 100
Hence, the value of x is 100
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Find the circumference.
Use 3.14 for it.
r= 4 cm
C = [?] cm
C=d
Answer:
C = 25.12
Step-by-step explanation:
Knowing Pie is 3.14, and r = 4, for radius. We can get the diameter(d) by multiplying the radius by 2. So 3.14 times 8. Equals C, which is 25.12
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Is Canada‘s population is 1/10 of the United States and Canada‘s population is 32 million how many people live in the United States
Answer:
320M
Step-by-step explanation:
It is given that Canada's population is 1/10th of the USA's population, essentially meaning that the US's population is 10x that of Canada's. Therefore, if Canada's population is 32M, multiply 10 to that:
32,000,000 x 10 = 320,000,000
320,000,000 people live in the US.
~
The functions f (x) = 1/2x-3 and g(x) = -2x+ 2 intersect
at x = -2. True or false?
9514 1404 393
Answer:
False
Step-by-step explanation:
f(-2) = (1/2)(-2) -3 = -1 -3 = -4
g(-2) = -2(-2) +2 = 4 +2 = 6
The function values are not the same at x=-2, so the graphs do not intersect there.
__
The graphs intersect at x=2.
the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone
Answer:
Step-by-step explanation:
V = 3.9V
I = 0.12A
Ohm's Law, V = IR
Rearranging Ohm's Law, R = V/I
R = 3.9/0.12 = 32.5Ω
help please help mesda
Answer:
25, 25, 22.5, 22
Step-by-step explanation:
It gives you a hint; K = y/x. They give you what x and y are so use that to solve for the last row.
We are given all of these values:
x -> 2, 3, 4, 5
y -> 50, 75, 90, 110
Use the formula given and solve for K.
50/2 = 25
75/3 = 25
90/4 = 22.5
110/5 = 22
Best of Luck!
2. In a random sample of 87 college students, the average number of GroupMe messages handled in
one day is 49. The 95% confidence interval for the mean number of messages handled by students
daily is given as 47 to 51.
a. What is the population standard deviation of the sample?
b. If the number of samples were doubled, by what factor would the confidence interval change
(keeping the same confidence level?)
We have that the population standard deviation and confidence interval is mathematically given as
SD=1
W = 2.8284
Standard deviation and the new widtha) Generally, normal distribution 95% of the values lies within 2 standard deviations from the mean.
Therefore, we have here:
2*2SD = 51 - 47
2*2SD
SD=1
Hence, the standard deviation is
SD=1
b)
Where,the margin of error is inversely proportional to the square root of sample size.
1 / sqrt{2}
Hence, the new width is
1 / sqrt{2}\(1 \ sqrt{2}\)
W = 2.8284
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can someone help me with this
Answer:
146, 146
Step-by-step explanation:
\(AB^2 = (-4-4)^2 + (11-8)^2 = 73 \\ \\ BC^2 = (4-1)^2+ (8-0)^2 =73 \\ \\ \therefore AB^2 + BC^2 = 146 \\ \\ \\ AC^2 = (-4-1)^2 + (11-0)^2 = 146\)
in the illustration below ,The two lights are designed tc pperate at 6 volts, 5 amps each,
5
f the power source is12 volts, what will be the value of the Resistor?
Round to the tenth position. (0.00)
The value of the resistor needed in this scenario is approximately 1.2 ohms.
To find the value of the resistor in the given scenario, we can apply Ohm's Law, which states that the current (I) flowing through a resistor is directly proportional to the voltage (V) across it, and inversely proportional to the resistance (R) of the resistor.
Using Ohm's Law, we have the formula:
V = I * R
Where:
V is the voltage across the resistor (12 volts in this case),
I is the current flowing through the resistor (5 amps for each light, so a total of 10 amps),
R is the resistance of the resistor (which we need to find).
Rearranging the formula, we have:
R = V / I
Plugging in the values:
R = 12 volts / 10 amps
R = 1.2 ohms
Therefore, the value of the resistor needed in this scenario is approximately 1.2 ohms.
It's worth noting that this calculation assumes the lights are connected in parallel, as the current remains the same for each light. If the lights were connected in series, the total resistance would be the sum of the individual resistances, and the calculation would be different.
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What is the area of a triangle with side lengths 17, 18, and 19? Express your answer in simplest radical form.
The area of a triangle with side lengths 17, 18, and 19 in simplest radical form is 18√7770
How to find the area of the triangleThe area of the triangle is calculated using the formula
Area of triangle = √[s(s – a)(s – b)(s – c)]
s = perimeter o the triangle
a, b and c are the lengths of the triangle
s = a + b + c = 17 + 18 + 19 = 54
Area of triangle = √[54 * (54 – 17)(54 – 18)(54 – 19)]
Area of triangle = √[2517480]
Area of triangle = 18√7770
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A bag of the same size balls contains six blue balls firebrand balls five yellow balls and four green balls what is the probability of selecting a blue or green ball on the first draw
The probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.
What is probability ?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur. If an event has a probability of 0.5, it means that the event is equally likely to occur or not occur. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability is an important concept in mathematics, statistics, and many other fields, as it allows us to make predictions and decisions based on the likelihood of certain outcomes.
According to the question:
The total number of balls in the bag is:
6 blue balls + 5 yellow balls + 4 green balls = 15 balls
The probability of selecting a blue or green ball on the first draw can be found by dividing the number of blue and green balls by the total number of balls:
P(blue or green) = (number of blue balls + number of green balls) / (total number of balls)
P(blue or green) = (6 + 4) / 15
P(blue or green) = 10 / 15
P(blue or green) = 2/3
Therefore, the probability of selecting a blue or green ball on the first draw is 2/3 or approximately 0.67.
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What are the characteristics of the F distribution
What is the rate of change of y with respect to x for this function?
Answer:
-9/2
Step-by-step explanation:
For a standard normal distribution, which of the following variables always equals 1?
Answer:
B.
Step-by-step explanation:
The standard deviation for a standard normal distribution is always equal to 1.
σ = 1
Option B is the correct answer.
What is z-score?A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.
It measures the unusual or extreme a particular data point is compared to the rest of the distribution
We have,
The variable that always equals 1 for a standard normal distribution is the standard deviation, which is denoted by the Greek letter sigma (σ).
The standard normal distribution has a mean of 0 and a standard deviation of 1, so its probability density function is:
f(x) = (1/√(2π)) \(e^{-x^2/2}\)
where e is the mathematical constant approximately equal to 2.71828, π is the mathematical constant approximately equal to 3.14159, and √(2π) is the square root of 2 times π, which is approximately equal to 2.50663.
The probability density function represents the relative likelihood of observing a value x in the standard normal distribution.
Since the standard deviation is always 1, the formula for calculating the probability of observing a value x is:
P(x) = f(x) = (1/√(2π)) \(e^{-x^2/2}\)
Therefore,
The standard deviation for a standard normal distribution is always equal to 1.
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if m angle TOK = 49° what is the measure of the angle supplement of TOK?
Answer:
67
Step-by-step explanation:
The measure of the angle supplement of TOK is 131°.
What is a supplementary angle?Supplementary angles refer to the pair of angles that always sum up to 180°. These two angles are called supplements of each other.
Now the given angle is,
m TOK = 49°
Let the supplement of 49° be x.
Now, 49° + x = 180°
Taking alike terms together we get,
⇒ x = 180° - 49°
Solving we get,
⇒ x = 131°
which is the required supplement of TOK.
Thus, the measure of the angle supplement of TOK is 131°.
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What is the degree of the polynomial, y^2+7x^14-10x^2?
The degree of the polynomial is 14
How to determine the degree of the polynomial?The polynomial is given as:
y^2+7x^14-10x^2
Here, we assume that the variable of the polynomial is x
The highest power of x in the polynomial y^2+7x^14-10x^2 is 14
Hence, the degree of the polynomial is 14
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O
Which of the following could be used to calculate the area of the sector in the circle sho
O
m(Sin)
O
WE OD
m(Sin)2
O n(30in)2
O
r-5 in 30
m(30in)
O
above? (5 points)
The Circle Sector Area correct answer is: O n(30in)2
To calculate the area of the sector in the circle, you would typically use the formula:
Area = (θ/360) * π *\(r^2\)
where θ is the angle of the sector in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
From the options you provided, the correct choice would be:
O n(30in)2
This option represents the square of the radius (30in) squared, which gives you the value of \(r^2.\)
Therefore, the Circle Sector Area correct answer is: O n(30in)2
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Based on the information in the two-way table, what is the probability that a person
selected at random both bikes and runs?
Round your answer to the nearest tenth of a percent.
Answer:
Step-by-step explanation:
What is (I^2)+(I^2)+3x if x=I^2?
Show your work.
Answer:
-5
Step-by-step explanation:
(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5
Question 3 -
of 4 Step 1 of 1
A box contains 17 green marbles and 8 white marbles. If the first marble chosen was a white marble, what is the probability of choosing, without
replacement, a green marble? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
Step-by-step explanation:
17/25
The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?
There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.
First, we can standardize the problem by using the z-score formula:
z = (x - μ) / σ
Where:
x = the weight value we want to find the probability for (345 g in this case)
μ = the mean weight (350 g)
σ = the standard deviation (4 g)
Substituting the values into the formula:
z = (345 - 350) / 4 = -1.25
Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.
The probability of obtaining a z-score less than -1.25 is approximately 0.1056.
However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.
The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.
Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.
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Combine the like terms to create an equivalent expression.
10k+1+8k+2=10k+1+8k+2
Literally I really need this question pls help points and brainlest
Answer:
C
Step-by-step explanation:
Can I get brainliest
C because it is the only option that depicts 2 blue marbles and one red one
Answer:
Step-by-step explanation:
whatever nobody cares and that person gave you the wrong answer
A rectangle has a perimeter of 28 feet. The width of the rectangle is two foot less than the length of the rectangle. What is the width of the rectangle?
Step-by-step explanation:
perimeter of a rectangle = 2×length + 2×width = 28 ft
width = length - 2
length = width + 2
2×(width + 2) + 2×width = 28
2×width + 4 + 2×width = 28
4×width + 4 = 28
4×width = 24
width = 6 ft
and the length is width + 2 = 6+2 = 8 ft.
What is the Probability.
The value of the conditional Probability is P(A|B) is 1/3.
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The main distinction between a probability and a conditional probability is that a probability is the likelihood of an event, such as A, occurring, whereas a conditional probability assumes that another event, such as B, has already happened in order to define the probability of an event, such as in the conditional probability of A given B.
Conditional probability is the likelihood that any event A will occur in the presence of another event B that is related to A. P(A|B) illustrates it.
By, Conditional Probability :
P (A∩B) =P (A∩B') - P(B)= 4/9 - 1/3 = 1/9
P(A|B) = P (A∩B)/ P(B)
= (1/9)/(1/3) = 1/3
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Does anyone know please
Answer:
the answer would be A 16cm
Select the correct answer from the drop-down menu. The graphed linear equation is . (a) 3x-2y=-12 (b)2x-3y=-12(c) 3x+2y=12(d)3x+3y=-12
Answer:
Option (C) will be the answer.
Step-by-step explanation:
Let the equation of the given line is,
y = mx + b
Where 'm' is the slope of the line and 'b' is the y-intercept
Slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is represented by,
Slope of the line (m) = \(\frac{y_2-y_1}{x_2-x_1}\)
For a line passing through (0, 6) and (4, 0)
Slope 'm' = \(\frac{6-0}{0-4}\)
m = \(-\frac{3}{2}\)
y-intercept of the line 'b' = 6
Therefore, equation of the line will be,
y = \(-\frac{3}{2}x+6\)
2y = -3x + 12
3x + 2y = 12
Option (C) will be the answer.
Answer:
c is the answer
Step-by-step explanation:
3x+2y=12
Shireen decided to deposit her graduation gift money in two different savings accounts. Account X has an interest rate of .5% and Account Y has an interest rate of .25%. Altogether, she received $5000 from graduation. If after the first year Her interest earned was $21.25, how much was deposited into each account?a. Define your variables by assigning them to the real-world quantities in the problem.b. Write a system of equations in standard form you can use to solve for those quantities.c. Calculate the x and y intercepts for both equations.d. How much was deposited in each account? Use whatever method you want to solve thesystem of equations.
Let x= be the amount in the account with .5%
Let y be the amount in the account with .25%
We know that interest is
I = PRT
I = 21.25 and time is 1 year so t=1
I = x(.005)(1) + y (.0025)
We also know that the amount invested is 5000
x+y = 5000
The system of equations is
21.25 = .005x + .0025y
x+y = 5000
21.25 = .005x+.0025y
Let x = 0
21.25 = .0025y
21.25/.0025 =y
The y intercept is 8500
Let y =0
21.25 = .005x
21.25/.005 =x
The x intercept is 4250
x+y = 5000
Let x = 0
The y intercept is 5000
Let y =0
The x intercept is 5000
Using substitution
x = 5000-y
21.25 = .005(5000-y) + .0025y
21.25 = 25 - .005y +.0025y
21.25-25 = -.0025y
-3.75 = -.0025y
-3.75/-.0025 = y
1500 = y
Now find x
x+y = 5000
x+1500=5000
x = 5000-1500
x = 3500
Learning Task 3 Answer the questions that follow. Put a check mark (/) on the space provided. Copy and answer in your math notebook. 1. The units for Volume are always ______squared _____cubed 2. Volume is the amount of space an object takes up. ___True ___False Calculate for the volume of solid. 3. Chona is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 4. A 3-tier cake with the same height of 10 in and radius of 12 in, 8 in, 5 in respectively is to be delivered to a birthday party. How much space does this cake take up? Use 3.14 for π. 5. A Styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for π.
3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.
4. The cake takes up approximately 7317 cubic inches of space.
5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.
1. The units for Volume are always cubed.
2. Volume is the amount of space an object takes up. True.
3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:
V = 3.14 * (4.5)^2 * 32
V = 3.14 * 20.25 * 32
V ≈ 2034.72 cubic inches
4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.
Tier 1:
V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches
Tier 2:
V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches
Tier 3:
V3 = 3.14 * (5)^2 * 10 = 785 cubic inches
Total volume:
Total V = V1 + V2 + V3
Total V = 4521.6 + 2010.4 + 785
Total V ≈ 7317 cubic inches
5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:
V = (1/3) * 3.14 * (24)^2 * 12
V = (1/3) * 3.14 * 576 * 12
V ≈ 7234.08 cubic centimeters
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round 1456 to nearest 10
Answer:
1460
Step-by-step explanation:
rounding to the nearest ten, that is nearest to 1456 which would be 1460 (hope this helps! ) ♡
Answer:
1460
Step-by-step explanation:
Original number is 1 4 5 6
To round to the nearest ten, look at the digit in the 10's place and the digit immediately to the right of it
The digit in the tens place is 5
If the digit to the immediate right of this digit is 5 or greater, round the digit in the tens place up by one digit and set the immediate right digit to 0
So 5 rounds up to 6
The 6 to the immediate right(units place becomes 0)
1 4 5 6 rounded to nearest ten==> 1 4 6 0