The 100th number of the sequence 1, 4, 7, 10..., is 298.
The given series 1, 4, 7, 10..., is an AP.
Arithmetic Progression (AP) is a sequence of numerals in order, in which the difference between any two consecutive digits is a constant value. A progression is a type of sequence for which it is possible to get a formula for the nth term.
The Arithmetic Progression is the most generally used sequence in maths with easy-to-understand formulas. The nth-term formula of the AP (arithmetic progression) is
aₙ = a₁+ d(n-1)
Where
n = number of terms
a = first term
d = common difference
Here, n = 100, d = 3 and a₁ = 1
[tex]a_{100}[/tex] = 1 + 3(100-1)
[tex]a_{100}[/tex] = 1 + 3(99)
[tex]a_{100}[/tex] = 1 + 297
[tex]a_{100}[/tex] = 298
--The given question is incorrect, the correct question is
''If we count by 3's starting with 1, the following sequence is obtained: 1, 4, 7, 10..., what is the 100th number in this sequence?"--
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what is the probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?
The probability that 3 hearts are chosen if 7 cards are selected from a well-shuffled deck of 52 playing cards is [tex]\\& =0.175823334\end{aligned}[/tex]
A probability simple definition is what?The probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging between 0% to 100% can be used to describe probabilities.
A probability may it be negative?Although a quasiprobability distributed enables a negative probability, called quasiprobability, for some events, the probability of the result of an experiment is never negative. These distributions may be applicable to conditional probability or unobservable occurrences.
The number of choosing cards out of 52 is = ⁵²C₃
Number of ways of choosing 3 cards of heart out of 13 cards and 4 out of remaining 39 cards = ¹³C₅ × ³⁹C₃
Probability of choosing 5 hearts = ¹³C₃ × ³⁹C₄ / ⁵²C₃
[tex]\begin{aligned}\frac{13 \times 2 \times 11 \times 13 \times 19 \times 3 \times 9}{26 \times 17 \times 10 \times 7 \times 2 \times 47 \times 46} & =\frac{23523786}{133784560} \\& =0.175823334\end{aligned}[/tex]
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A circle centered at $A$ with a radius of $1$ and a circle centered at $B$ with a radius of $4$ are externally tangent. A third circle is tangent to the first two and to one of their common external tangents as shown. What is the radius of the third circle
The radius of the third circle is found out to be as , 1cm.
The radius of 1st circle = 1
radius of second circle = 4
Let XYR be external tangent of the circle which is centered at C,.
Then if we will extend the line PQ to R ,
the result will be , XPR being similar to triangle YQR ,
Therefore,
RQ = x
and length of RP = x + 5
Therefore, x / x+ 5 = 1/4
=> 4x = x + 5
=> x = 1
So , the length of QR is found out to be as 1cm.
A tangent to a circle is known as a straight line which touches the circle exactly at one point . A circle can have infinite number of tangents.
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2 7/9 divided by 2. Write in simplest form
Answer:
Step-by-step explanation:
2 7/9 divided by 2
First, convert the mixed number into a improper fraction:
25/9
Then multiply by the reciprocal of 2, by multiplying it by 1/2,
which turns into 25/8
Turn it into a mixed number: 1 7/18 OR 25/8
tyrone went to the pet store to buy 5 goldfish for his fish tank. he spent less than $15 in all to buy the fish. let x represent how much each goldfish cost. which inequality describes the problem?
Each goldfish cost less than $3.
Now, According to the question:
As per the question information:
Tyrone went to the pet store to buy 5 goldfish for his fish tank.
He spent less than $15 in all to buy the fish.
Let x represent how much each goldfish cost.
which inequality describes the problem?
5x < 15 , 5x ≤ 15
To solve the inequality :
Based on the given condition :
Formulate:
x = 15 ÷ 5
Reduce the fraction :
x = 3
Hence, Each goldfish cost less than $3.
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The given question is incomplete, the complete is :
Tyrone went to the pet store to buy $5 goldfish for his fish tank. He spent less than$15 in all to buy the fish. Let x represent how much each goldfish cost. Which inequality describes the problem?
5x < 15 , 5x ≤ 15
Solve the inequality. Then, complete the sentence to describe the solution. Each goldfish cost less than $
Which transformations could be performed to show that △ABC is similar to △A"B"C"?
Answer:
A [tex]180^{\circ}[/tex] rotation about the origin, then a dilation by a scale factor of [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The preimage is larger than the image.
Eliminate options 1 and 3.Also, the orientiation of the triangle didn't change.
Eliminate option 2.Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 21 pipes has a standard deviation of 14.6 inches. Show each step.
The 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)
given that
95% confidence interval for the standard deviation of the lengths of pipes
a sample of 21 pipes
standard deviation of 14.6 inches
chi-squared(1 - a/2) < or = (n-1)s^2/(std. dev.)^2 < or = chi-squared(a/2)
in the above
a is alpha
std is standard deviation
a = (1-95/100) = 1 - 0.95 = 0.05
then, degree of freedom = 21 - 1 = 20
chi-squared(0.975) = 20.5
chi-squared(0.025) = 3.25
chi-squared for 20.5 = (21-1)×[tex](14.6)^{2}[/tex] / 20.5 = 103.98
chi - squared for 3.25 = (21-1)×[tex](14.6)^{2}[/tex] / 3.25 = 655.8
we need to square-root of the above values
chi-squared for 20.5 = [tex]\sqrt{103.98}[/tex] = 10.2
chi - squared for 3.25 = [tex]\sqrt{655.8}[/tex] = 25.6
the 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)
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a toy company packages modeling clay in the shape of a rectangular prism with dimensions 6 inches by 1 inch by 1/2 inch. they want to change the shape to rectangular pyramid that uses the same amount of clay. determine 2 sets of possible dimensions for the pyramid.
Two sets of possible dimensions for the rectangular pyramid that uses the same amount of clay as the rectangular prism are 2 inches base and 1.5 inches height, and 3 inches by a 1-inch base and 1-inch height.
The volume of the rectangular prism is 6 inches * 1 inch * 1/2 inch = 3 cubic inches. To determine the possible dimensions for the pyramid, we need to find the dimensions that will give us the same volume.
One set of possible dimensions for the pyramid would be a base that is 2 inches by 2 inches, and a height of 1.5 inches. This would give a volume of 2 inches * 2 inches * 1.5 inches / 3 = 2 cubic inches, which is the same as the original rectangular prism.
Another set of possible dimensions would be a base that is 3 inches by 1 inch and a height of 1 inch. This would give a volume of 3 inches * 1 inch * 1 inch / 3 = 1 cubic inch, which is the same as the original rectangular prism.
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Could any of you guys help me answer this question pls the homework is due today!
Step-by-step explanation:
y = 37 + x
the 4th angle (bottom right) is
360 - 90 - 90 - 125 = 55°
because the sum of all angles in any quadrilateral is 360°.
now we can assume a right-angled triangle on the right side of the trapezium.
one leg is 15 cm (like the left side), the other leg is x cm. and the right side of the trapezium is the Hypotenuse.
the bottom right angle is 55°.
the upper angle is 125 - 90 = 35°.
we can use the law of sine to get x.
the law of sine is
a/sin(A) = b/(sin(B) = c/sin(C)
with a, b, c being the sides of the triangle opposite of the corresponding angles A, B, C.
so,
15/sin(55) = x/sin(35)
x = 15×sin(35)/sin(55) = 10.50311307... cm
y = 37 + 10.50311307... = 47.50311307... ≈
≈ 47.5 cm
the basketball team won 20 games, which is 80%, of the games they played. how many total games did they play?
The total number of games did they played is 80
The term total in math is also known as sum is defined as the result of arithmetically adding numbers or quantities.
Here we have given that the team wins 20 games.
And the number of games won by the team is 80% of the number of games played.
Then the calculation is done as follows:
Here let us consider that the total number of games played be 100 units.
As we can say that the number of games won by the team will be 80 units.
Then according to the question it can be written as
=> 50 units = 40
Then for 100 units (40 x 100)/80 = 80
Therefore the total number of games played by the team is 80.
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Add the polynomial. 2a+b-c-d and 4a-3b-2c+5d
Answer:
6a-2b-3c+4d
Step-by-step explanation:
2a+4a = 6a
b-3b = -2b
-c-2c = -3c
-d+5d = 4d
Answer:
6a - b - 3c + 4d
Step-by-step explanation:
⭐What is a polynomial?
if "poly" means "many" and "nomial" means "terms", then polynomial means "many terms"Whenever you add polynomials, the only terms you can perform addition or subtraction on are like terms.
⭐What are like terms?
terms with the same variable AND exponentWe are asked to add the two given polynomials. Therefore, we have to add the like terms.
[tex]2a + b - c - d + (4a - 3b - 2c + 5d)[/tex]
a and a, b and b, c and c, and d and d all have the same variable with an exponent of 1.
When adding, make sure to utilize the correct addition rules.
⭐What are the rules for adding real numbers?
NEGATIVE + positive = NEGATIVEnegative + POSITIVE = POSITIVEPOSITIVE + POSITIVE = POSITIVENEGATIVE + NEGATIVE = NEGATIVE2a and 4a are positive. Therefore, 2a + 4a = 6a.
-3b is negative, but b is positive. -3b > b. Therefore, -3b + b = -2b.
-c and -2c are both negative. Therefore, -2c - c = -3c.
-d is negative, but 5d is positive. 5d > -d. Therefore, -d + 5d = 4d.
∴ [tex]2a + b - c - d + (4a - 3b - 2c + 5d) = 6a -b -3c + 4d[/tex]
⭐if this response helped you, please mark it the "brainliest"!⭐
Potatoes cost janice $1. 00 per pound, and she has $6. 00 that she could possibly spend on potatoes or other items. Suppose she feels that the first pound of potatoes is worth $1. 50, the second pound is worth $1. 14, the third pound is worth $1. 05, and all subsequent pounds are worth $0. 30 per pound.
Janice will spend $3.00 on 3 pounds of potatoes. If she only has $3.00, she will spend it all on potatoes and purchase 3 pounds of potatoes.
a) 3 pounds of potatoes
b) 3 pounds of potatoes
What is pounds?A pound is defined as 16 ounces, 7,000 grains (or 0.45359237 kg) of avoirdupois weight and 12 ounces, 5,760 grains (or 0.37324171216 kg) of troy and apothecaries' weight. The initials "lb" come from the Latin word "libra," which was the Roman equivalent of the modern "pound."
Janice can get potatoes once the price is set. As a result, she will buy those potatoes whose value is less than her willingness to pay. Her disposition to pay is what she feels the pound of potatoes is "worth". If the worth of the primary, second, and third pounds exceeds the price of the potato ($1.50, $1.14, $1.05 > $1.00), Janice will not purchase these because the worth is less than the price. (0.30 USD 1.00 USD).
Thus, Janice will spend $3.00 on 3 pounds of potatoes. If she only has $3.00, she will spend it all on potatoes and purchase 3 pounds of potatoes.
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Alexandra is fishing from a small boat. A fish swimming at the same depth as the hook
at the end of her fishing line is 5 meters away from the hook. If Alexandra is 13 meters away
from the fish, how far below Alexandra is the hook?
Answer:
12 m
Step-by-step explanation:
Here's a picture to show the problem.
boat
--------------------------------------------
~~~~~~~~~~~\ /~~~~~~~~~~~~~~~~~~~~~~~~
\-----------Alexandra ---------/ surface of the water
|\
| \
| \
| \
d | \ 13 m
| \
| \
| \
| --- rt < \
hook -----|------------------------------ fish
5 m
There is a right angle at the hook. We have a right triangle with leg d, the distance we need to find, leg 5 m, and hypotenuse 13 m.
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = √144
b = 12
Answer: 12 m
Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation. What is YT? using point T as the center of dilation.3units6units12units15units
The value of TY using point T as the center of dilation = 12.
What is a line segment?A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Here, we have
Given: Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation.
X'Y' and XY are parallels, which means X'Y' = means XY, there is a similarity between the two triangles, we can find YT by using the theorem of Thales,
TY' / TY =TX' / TX =X'Y' /XY,
TY' / TY = TX' / TX = 9/ TY =6/ 2+6=6/8
9/ TY = 6/8
TY= 12
Hence, the value of TY = 12.
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answer follow up questions
reference:
2.3 birthdays
Rule B
John March 23
Kelly June 15
Julia April 8
Rule P
August 10 Josh
October 19 Peter
January 27 Angela
Observational data that contains a numerical value or amount is called: _________
Observational data that contains a numerical value or amount is called Quantitative observation.
What is observational data?
An observational study draws conclusions from a sample to a population in disciplines like epidemiology, social sciences, psychology, and statistics when the independent variable is not under the researcher's control due to ethical considerations or logistical limitations.
Observational data in market research refers to information gathered without the research subject (such as a specific client, patient, employee, etc.) having to be explicitly involved in documenting what they are doing.
An objective collection of data, quantitative observation refers to "associated to, of or depicted in terms of a quantity" and is primarily focused on numbers and values.
Methods of statistical and numerical analysis are used to derive the results of quantitative observation.
Hence, observational data that contains a numerical value or amount is called Quantitative observation.
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Top one
A princess is on the top of a 167 foot tower looking down at a 37° angle of depression at a package attached to a rope on the ground. How long is the rope?
The length of the rope in the question is; 277.5 ft
How to solve Angle of depression problems?The angle of depression is defined as the angle between the horizontal line of sight and the line of sight down to an object. For example, if you were standing on top of a hill or a building, and looking down at an object, you could measure the angle of depression.
The rope length can be calculated using the trigonometric ratio which is;
167/x = sin 37
x = 167/sin 37
x = 167/0.6018
x = 277.5 ft
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If the measure of ∠4 = 55°, then the measure of ∠2
Step-by-step explanation:
∠4=55
or, ∠=55/4 or,∠=13.75
∠2=?
or, ∠2=13.75*2
or,∠2=27.5
2/4 Marks
Frequency density
42/44 Marks
The histogram shows information about how 550 people travel to work.
40
35-
30-
25-
20-
15-
10-
5-
0+
0 5 10 15 20 25 30 35 40 45 50 55 60
Distance (miles)
56%
a) How many people travel more than 30 miles to work?
b) 205 of the 550 people travel further than Sam. Estimate how far Sam travels.
Answer: Based on the histogram, it is not possible to determine the exact number of people who travel more than 30 miles to work. However, we can estimate the number of people by using the histogram.
Step-by-step explanation: The histogram shows the frequency density of people traveling different distances to work.
The Y-axis shows the frequency density, and the X-axis shows the distance in miles.
The histogram is divided into bars, each representing a range of distances.
We can see that the majority of people travel less than 30 miles to work, with the highest frequency density being around 20 miles.
However, the histogram does not provide the exact number of people for each bar. Therefore, we cannot determine the exact number of people who travel more than 30 miles to work.
b) Sam travels around 20 miles to work.
Explanation:
205 people out of 550 people is approximately 37% of the total number of people surveyed.
The closest bar on the histogram to 37% is the one around 20 miles.
Therefore, it can be estimated that the distance that Sam travels is around 20 miles.
Melanie babysits for $14 per hour.
If she earned $91 last week,
how many hours did she work?
Define the variable. Write and
solve the equation.
Answer:
Equation is 14h = 91
It solves to h = 6.5
===========================================
Work Shown:
h = number of hours worked
14h = amount earned at $14 per hour
14h = 91 is the equation
To solve this equation, divide both sides by 14.
14h = 91
14h/14 = 91/14
h = 6.5
She worked 6.5 hours last week.
What are the 8 types of operating system?
The types of operating system are:-
1. Batch Operating System.
2. Real-Time Operating System.
3. Time-Sharing Operating System.
4. Distributed Operating System.
5. Embedded Operating System.
6. Network Operating System.
7. Mobile Operating System.
What is an operating system?
An operating system can be thought of as a hardware and user interface. It is in charge of several different activities, including resource allocation, CPU management, file management, and the execution of all programmes. An operating system's function is to offer a setting in which a user can run programmes conveniently and effectively.
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Given that a is an odd multiple of 1183, find the greatest common divisor of 2a^2+29a+65 and a+13
The solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and k = 1,3,5,7,9...
Let d = [tex](2a^{2} +29a + 65, a+ 13)[/tex]
Now, we can split [tex]2a^{2} + 29a + 65[/tex] in the following way, so that it becomes easier to factorise.
[tex]2a^{2} + 29a + 65 = (2a^{2} + 29a + 39) + 26[/tex]
From this, we can quantify and notice that -13 is one root of this equation, while the other root is -3/2.
Therefore, [tex]2a^{2} + 29a + 39 = (a+13)(2a+3)+26[/tex]
Thus, [tex]d = ((a+13)(2a+3)+26, a+ 13)[/tex]
The greatest common divisor (GCD) of two or more numbers is the greatest common factor number that divides them, exactly. It is also called the highest common factor (HCF).
Now, we can use Euclid's Algorithm.
[tex]= gcd (2a^{2} + 29a + 65, a + 13)\\= gcd (2a^{2} + 29a + 65 - 2a(a+13), a+13)\\= gcd (3a + 65, a + 13)\\= gcd (3a + 65 - 3a(a+13), a+13)\\= gcd (26, a + 13)[/tex]
This is necessarily 1, 2, 13, or 26, which we can see by just looking at the first term. By factoring 1183 and considering that [tex]a[/tex] is an odd multiple, then we should be able to conclude the answer.
Hence, the conclusion is that the solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and k = 1,3,5,7,9...
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Solve for X, Leave in simplest radical form
Answer: X = [tex]\frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation: Because the two angles are equal (You circled them, also 45 degs), and there is a right triangle, which means that the 90-degree angle's adjacent sides are equal, in this case, both sides equal to X.
Using the special triangle ratio ( 1, 1, [tex]\sqrt{2}[/tex]), in this case, the "2" is equal to [tex]\sqrt{2}[/tex] times [tex]\sqrt{2}[/tex], so you have to divide the "1" (X) by [tex]\sqrt{2}[/tex], you simply get [tex]\frac{1}{\sqrt{2} }[/tex].
Sorry for my bad english
Complete. 64 yd = in.
Answer: 2304
Step-by-step explanation: 64 x 36 = 2304
Answer:
2,304 in.
Step-by-step explanation:
I attached a pic of my work.
List five vectors in Span {v1,v2}. Do not make a sketch.v1=6 4 −8v2=−6 2 0
The five vectors in span {v1,v2} are we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together.
1. v3 = (3v1 + 2v2) = (18 8 −16)
2. v4 = (2v1 + 3v2) = (−12 6 0)
3. v5 = (4v1 + v2) = (0 6 −32)
4. v6 = (−2v1 + 5v2) = (36 10 0)
5. v7 = (−v1 + 4v2) = (−36 8 0)
To calculate the vectors, we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together. For example, for v3 we multiplied v1 by 3 and v2 by 2 and then added the components together to get the vector (18 8 −16). We performed similar calculations for the other vectors.
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Jessica is measuring two line segments. The first line segment is 30 cm long while the second line segment is 500 mm long. How long are the two line segments together?A. 80 cmB. 25 cmC. 47 cmD. 49 cm
The length of the two line segments together is 80 cm
Step 1: Convert 500mm into cm.
We know that the value of 1mm is equal to 0.1 cm.
Then, 500mm will be 500mm*0.1 = 50 cm.
Therefore, the second line segment is 50 cm long.
Step 2: Calculate total length.
Let the first line segment be L1= 30 cm long and the second line segment be L2= 50 cm long.
Now, the total length is
L = L1 + L2
Substitute the values L1= 30 cm and L2= 50 cm in L = L1 + L2.
Hence, the length of the two line segments together is 80 cm
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a blackjack dealer lays out five cards, face down, from a single deck of 52 cards. what is the probability that at least one of them is an ace?
0.6928 or 69.28% is the probability of at least one ace among five cards .
in order to get the probability that at least one of the five cards is an ace, then we implement the use of complement rule.
as we know this rule states that the probability of an event happening which is equal to 1 minus the probability of the event which is not happening.
In this order of situation the event is drawing no aces from the five cards. hence the probability of drawing no aces is (48/52)^5, as we are having 48 non-ace cards in the deck and the value of the probability of drawing a non-ace is 48/52.
the calculation to get the probability of drawing at least one ace is:
1 - (48/52)^5 = 1 - (0.9231)^5 = 0.6928
hence the probability value of at least one ace among five cards is 0.6928 or 69.28%.
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Aiden measured a line to be 4.1 inches long. If the actual length of the line is 5.3 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
22.6%.
Step-by-step explanation:
To calculate the percent error of a measurement, you can use the following formula:
Percent Error = (|measured value - actual value| / actual value) x 100%
Plugging in the values from the problem:
Percent Error = (|4.1 inches - 5.3 inches| / 5.3 inches) x 100% = (1.2 inches / 5.3 inches) x 100% = 0.226 x 100% = 22.6%
To the nearest tenth of a percent, the percent error is 22.6%.
A piece of a cow’s leg bone with a volume of 10 cm3 has a mass of 18 g. What is the density of the bone please answer
]Mariam has $560 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $275.67.
She buys 3 bicycle reflectors for $16.32 each and a pair of bike gloves for $24.39.
She plans to spend some or all of the money she has left to buy new biking outfits for $27.40 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Mariam can purchase while staying within her budget.
The number of outfits Mariam can purchase is 7.
The inequality to represent the situation is 560 ≤ 349.02 + 27.40x.
How to represent a situation with an inequality?Mariam has $560 to spend at a bicycle store for some new gear and biking outfits. The price list are as follows:
She buys a new bicycle for $275.67.She buys 3 bicycle reflectors for $16.32 eachA pair of bike gloves for $24.39.She plans to spend some or all of the money she has left to buy new biking outfits for $27.40 each.
The inequality that can be used to determine x, the number of outfits Mariam can purchase within her budget can be calculated as follows:
560 ≤ 275.67 + 3(16.32) + 24.39 + 27.40x
where
x = number of biking outfits
560 ≤ 275.67 + 3(16.32) + 24.39 + 27.40x
560 ≤ 275.67 + 48.96 + 24.39 + 27.40x
560 ≤ 349.02 + 27.40x
560 - 349.02 ≤ 27.40x
divide both sides by 27.40
210.98 ≤ 27.40x
divide both sides by 27.40
210.98 / 27.40 ≤ x
7.7 ≤ x
Therefore, the number of outfit he can purchase is 7.
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If m < 1 equals (6x + 3) and m < 2 equals 117 what is the value of x
The value of x is 19.
What is the slope intercept?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.
We can start by using the information given in the problem to set up an equation. We know that:
m < 1 = 6x + 3
m < 2 = 117
We are also given that m < 1 and m < 2 represent different values.
Now we can substitute the second equation into the first equation:
6x + 3 = 117
To solve for x, we can subtract 3 from both sides:
6x = 114
Finally, we can divide both sides by 6:
x = 19
Hence, the value of x is 19.
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