Answer:
[tex]\boxed{a_5 = 40.5}[/tex]
Step-by-step explanation:
Common ratio r of a geometric sequence is the ratio of each term to the previous term and is a constant
Thus if you have a sequence a₁, a₂, a₃, a,...
[tex]r = \dfrac{a_2}{a_1} = \dfrac{a_3}{a_2} = \dfrac{a_4}{a_3} \cdots[/tex]
For a geometric sequence with common ratio [tex]r[/tex] and a starting value of [tex]a_1[/tex]the nth term is given by the formula:
[tex]a_n = a_1r^{n-1}[/tex]
Here [tex]a_1 = 8, r = 1.5[/tex]
and we are asked to find the 5th term
[tex]a_5 = 8 \times 1.5^{(5-1)}\\\\= 8 \times 1.5^4\\\\=40.5\\\\[/tex]ANSWER
The terms of the sequence are
8, 12, 18, 27, 40.5 with 8 being the first term and 40.5 the 5th term
Whether the function is even or odd
The given graph is not symmetric with respect to the y-axis. Hence, this is not even function.
What is Function?
A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
An example of a rule is a function, which produces one output for a single input.
If the graph of a function is symmetric with respect to the y-axis, then it is said to be an even function. Otherwise, it is odd function.
The given graph is not symmetric with respect to the y-axis. Hence, this is not even function.
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sat math scores are approximately normally distributed, with a mean of 508 and a standard deviation of 120. skye decides to take the sat exam, and scores 920. what is the probability someone scored less than her on the sat math test?
On solving the provided question, we can say that standard deviation and mean, The equivalent ACT score is using 1.545 as the z score [tex]= > X = 1.545 * 3.9 + 19.2 = 25.5[/tex]
What is standard deviation?Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.
[tex]X = 0.675 * 198 + 1101 = 1235[/tex]
standard deviation and mean
[tex]X = 0.675 * 3.9 + 19.2 = 21.8[/tex]
scores 1407 standardized score z for 1407
[tex]z = (X-μ)/σ = (1407-1101)/198 = 1.545[/tex]
The equivalent ACT score is using 1.545 as the z score
[tex]= > X = 1.545 * 3.9 + 19.2 = 25.5[/tex]
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Write all names that apply to each number
5.45
the altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 9.5 centimeters and the area is 100 square centimeters?
So, the base of the triangle is decreasing at the rate of 1.6 cm/min.
Given that:
The altitude of is increasing at a rate of 1 centimeters/minute, which means;
dh/dt = 1 cm/min
The area of the triangle is increasing at a rate of 4 square centimeters/minute;
dA/dt = 4 cm2/min
When A = 100 cm2, h = 10 cm
We know that, area of a triangle is given by:
A = 1/2 × b × h
b = 20 cm
Let us differentiate both sides with respect to time:
dA/dt = 1/2 [b dh/dt + h db/dt]
Substituting the values
2 = 1/2 [20 × 1 + 10 × db/dt]
By further simplification, we get
4 = 20 + 10 db/dt
db/dt = -1.6 cm/min
Therefore, the base of the triangle is decreasing at the rate of 1.6 cm/min.
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2.6 an srs? the leader of a student organization wishes to form a committee that will consist of 5 of the 50 members. he decides to take an srs of size five from the members and those selected will comprise the committee. he chooses an srs of size five and all are men. he would like to have some women on the task force, so he decides to take another srs. this time there are three women and two men in the sample, so he decides these five will form the committee. we can conclude the sample obtained is an srs because the final sample was obtained by simple random sampling. an srs because all members had the same chance of being in the final sample. not an srs because a sample consisting entirely of men is not allowed. not an srs because the first sample was not balanced between men and women.
We can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling. not an SRS because the first sample was not balanced between men and women
an SRS?
the leader of a student organization wishes to form a committee that will consist of 5 of the 50 members.
he decides to take an SRS of size five from the members and those selected will comprise the committee.
he chooses an SRS of size five and all are men.
he would like to have some women on the task force, so he decides to take another SRS.
this time there are three women and two men in the sample, so he decides these five will form the committee.
we can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling.
an SRS because all members had the same chance of being in the final sample.
not an SRS because a sample consisting entirely of men is not allowed.
not an SRS because the first sample was not balanced between men and women.
we can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling. not an SRS because the first sample was not balanced between men and women.
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Solve for the missing side y
12
8
y
The missing side is 6√13 in the given right-angled triangle.
What is right-angled triangle?If one of a triangle's angles is a right angle (90 degrees), the triangle is known as a right-angled triangle or just a right triangle, according to the definition of a right triangle. Triangle ABC is a right triangle that contains the base, altitude, and hypotenuse in the example image.
Base AB, altitude AC, and hypotenuse BC are shown in this equation. The largest side and the side that faces away from the right angle in a right triangle is the hypotenuse, and it is this side that is significant.
Given that A right angle triangle has sides 12cm and 18 cm
y = [tex]\sqrt{12^2 + 18^2}[/tex]
y = 6√13
Thus, the missing side y is 6√13.
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a ship leaves port at noon and has a bearing of the ship sails at 20 knots. how many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 p.m.?
On solving the provided question we can say that the equation gives us 101.77 mi S; 63.59 mi W and S 39.4° W; 131.7 nautical miles
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.
The ship will have traveled 120 nautical miles in the six hours between noon and six o'clock using the formula distance = speed time distance (20 nm/h) (6 h).
The location of the ship will be in (S, W) coordinates.
[tex]120(cos(32), sin(32)) ≈ 120(0.848048, 0.529919) ≈ (101.77, 63.59)[/tex]
The ship will have traveled 101.77 miles south and 63.59 miles west.
83.59). The distance from port will be ...
[tex]d = √(101.77^2 +83.59^2) = 131.7\\ arctan(83.59/101.77) ≈ 39.4[/tex]
The bearing and distance are ...
S 39.4° W
131.7 nautical miles
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*Round to the nearest TENTH!!*
Perimeter =
Therefore , the solution of the given problem of the perimeter of given figure is 18 + √34 cm or 18 + 5.83 = 23.83 cm
What is a perimeter?In geometry, a shape's perimeter is referred as the entire length of its boundary. The perimeter of a form is created by adding the dimensions of all of its edges and the edges that surround it. Utilizing linear distance measures like centimeters, meters, inches, or feet, it is calculated.
Given:
5 + 8 + 5 + x = 18 +x
=> To find the value of x ,
We use pythagoras theorem :
thus,
=> 5² + 3² = x²
=> x² = 34
=> x = √34
The perimeter of given figure is 18 + √34 cm or 18 + 5.83 = 23.83 cm
Therefore , the solution of the given problem of the perimeter of given figure is 18 + √34 cm or 18 + 5.83 = 23.83 cm
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will, tim and harry are going to have dinner together. will pays for 2 pizza costing 3.75 each. tim pays for 3 desserts costing 1.09 each. tim says I´ve paid my fair share of the total cost. Find out if Tim is correct. You must justify your answer.
Answer:
To determine if Tim is correct in stating that he has paid his fair share of the total cost, we need to calculate the total cost of the dinner and compare it to the cost of the desserts Tim paid for.
Will paid for 2 pizzas at a cost of $3.75 each, for a total of 2 * $3.75 = $7.50
Tim paid for 3 desserts at a cost of $1.09 each, for a total of 3 * $1.09 = $3.27
The total cost of the dinner is $7.50 + $3.27 = $10.77
To check if Tim has paid his fair share, we need to compare the cost of the desserts he paid for ($3.27) to the total cost of the dinner ($10.77)
$3.27 is 30.3% of $10.77, meaning Tim paid for around 30% of the dinner.
In this case, it's not fair to say that Tim has paid his fair share of the total cost, since he paid for only around 30% of the dinner, and as such, this cost should be split among the three of them.
It would be more accurate to say that Tim has paid a portion of the dinner, but not his fair share.
The cost of a council tax bill increased by 5%.
The council tax bill increased by £62.
Work out the cost of the council tax bill before the increase
Answer:
To work out the cost of the council tax bill before the increase, we can use the formula:
Original cost = New cost / (1 + increase percentage)
We know that the council tax bill increased by 5% and the increase is £62. So the new cost of the council tax bill is £62 more than the original cost.
We can use the formula above to find the original cost:
Original cost = £62 / (1 + 0.05)
Original cost = £62 / 1.05
Original cost = £59.04
So the cost of the council tax bill before the increase was £59.04.
Factorise fully x²+X
Answer:
x(x+1)
Step-by-step explanation:
x^2+x=x(x+1)
Answer: x (x + 1)
Step-by-step explanation: Factor out the X
Alonso brings $21 to the market to buy eggs and avocados. he gets eggs that cost $2.50. then, he notices that
the store only sells avocados in bags of 3 for $5. he wants to buy as many avocados as he can with his
remaining money.
let b represent the number of bags of avocados that alonso buys.
1) which inequality describes this scenario?
choose 1 answer:
2.50 + 5b < 21
b
2.50 +5b > 21
2.50 + 3b < 21
2.50 + 3b > 21
j
Answer:
£2.50+5b>21
Step-by-step explanation:
this is because a bag is b and they cost £5 so therefore it's 5b then they have to be under 21 pounds so you use the less than symbol.
At a research facility that designs rocket engines, researchers know that some engines fail to ignite as a result of fuel system error. From a random sample of 40 engines of one design, 14 failed to ignite as a result of fuel system error. From a random sample of 30 engines of a second design, 9 failed to ignite as a result of fuel system error. The researchers want to estimate the difference in the proportion of engine failures for the two designs. Which of the following is the most appropriate method to create the estimate
It is solved using the concept of z-table. Correct option is: (E)
What is z-table?The difference from the mean is expressed as a z-score in standard deviation units. It is not clear either one agree or disagree with the null hypothesis. The likelihood that a point as severe as their statistic would be seen that under null hypothesis is known as the p-value.
A z-table, sometimes referred to as the standard normal table, gives the area beneath the curve to the left of a z-score. This region indicates the likelihood that z-values will fall inside a particular area of the standard normal distribution.
Here, we have to calculate the confidence interval for determine the population interval.
Now, P₁ - P₂, this is the difference between the two population proportion.
thus, option (E) is the correct answer.
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The complete question is as follows:
16. if you change your lights to high beam when the driver of an approaching vehicle fails to dim his lights, the probability of an accident increases because:
If blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle which is denoted as option C.
What is a Vehicle?This refers to something which is used to transport people and goods from one place to another and examples include car, lorry etc. The lights are used at night for proper vision of the road so as to reduce the risk of accidents on the road.
here,
In a situation whereby an individual is blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle so as to prevent temporary vision impairment.
This helps to prevent accidents on the road and for the safety of the driver thereby making it the correct choice.
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Select the simplified polynomial, in standard form (7w^2 - 12w + 8) - (w^2+6w-2)
The simplified polynomial is 6w^2 - 18w + 10.
What is polynomial?A polynomial is an expression consisting of variables and coefficients and are used to model real-world situations. It is an equation of degree greater than one, where the exponents of the variables can be any non-negative integer. For example, the polynomial equation x2 + 3x + 2 represents a parabola when graphed. Polynomials are used in a variety of fields, such as mathematics and physics.
It is in standard form because it is written as ax^2 + bx + c, where a, b, and c are the coefficients of the terms and x is the variable. The coefficients are in decreasing order of powers of the variable, and there are no fractions or radicals in the equation.
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There is a 25% chance that you will have to work tonight and cannot study for the big
math test. if you study, then you have an 80% chance of earning a good grade. if
do not study, you only have a 30% chance of earning a good grade.
you
Therefore ,as a result, the answer to the probability problem is 67.5% chance that you get good scores.
What exactly does the probability process entail?Probability theory is a branch of mathematics that focuses on calculating the likelihood that a statement is true or that an event will occur. Any number in 0 and 1, with 1 signifying certainty and 0 generally reflecting the likelihood of occurrence, can be used to represent a chance. Probability is a diagrammatic model of range the chance or likelihood that an event will occur.
Here,
Given : There is a 0.25 percent probability that we work tonight without studying,
a 0.80 percent chance that you study and get high grades, and
a 0.30 percent chance that you don't study and get a good grade.
To calculate the likelihood that we will receive high marks,
multiply by: 0.25 * 0.30 + 0.75 * 0.8
=> 0.075 + 0.60 => 0.675
You have a 67.5% chance of getting good grades.
As a result, the answer to the probability problem is 67.5% chance that you get good scores.
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what kind of triangle is this?
The kind of triangle in the image above is a scalene triangle.
What is a Scalene Triangle?A scalene triangle is a type of triangle that has three sides with different lengths. It is one of the three main types of triangles, the other two being isosceles and equilateral triangles. They also have three different angles.
Scalene triangles do not have any congruent sides or angles, making them the most diverse and versatile type of triangle. They can be used to construct many different shapes and figures, and have many unique properties and characteristics that make them useful in a variety of fields, including mathematics, physics, and engineering.
In the image given, the three sides of the triangle appears to be of different sizes.
Therefore, we can conclude that the triangle is a scalene triangle.
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a right triangle has sides that measure 24 and 32, but the length of the hypotenuse is unknown. what is the perimeter measurement of this triangle? round your answer to the nearest hundredth
The perimeter of the triangle is 96, rounded to the nearest hundredth.
To calculate the perimeter of the triangle, we need to first calculate the length of the hypotenuse.
The hypotenuse of a right triangle is calculated using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two sides.
Therefore, for this triangle, we have:
(Hypotenuse)² = (24)² + (32)²
Therefore, the Hypotenuse = √(24² + 32²)
Hypotenuse = √(576 + 1024)
Hypotenuse = √1600
Hypotenuse = 40
To calculate the perimeter, we need to add up all three sides of the triangle.
the perimeter = 24 + 32 + 40
the perimeter = 96
Therefore, the perimeter of the triangle is 96, rounded to the nearest hundredth.
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The expression 62.4d-21062.4d−21062, point, 4, d, minus, 210 gives the number of Indian rupees you receive when you exchange \$d$ddollar sign, d at the local currency exchange.
How many Indian rupees do you receive when you exchange \$13$13dollar sign, 13?
The amount of Indian rupees that I would be able to receive when $13 is exchanged would be = 601.2
Indian rupees.
What is local currency exchange?Local currency exchange is defined as the exchange of a money currency from its local form to another form which depends of its current exchange rate.
From the expression given;
= 62.4d -210
Where d = $13, substitute into the given equation.
= (62.4 ×13) - 210
= 811.2 -210
= 601.2
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What is the name of the fee charged by a financial institution for withdrawing money from an account before the maturity date?
O A. Surrender charge
O B. Liquidity fee
O C. Early redemption fee
Surrender charges safeguard against such losses. Surrender costs on some annuities and insurance products can apply for as short as 30 days or as long as 15 years. If you cash in your investment in year one, the surrender cost for annuities and life insurance is typically 10%.
The surrender period is the amount of time that an investor must wait before withdrawing cash from an annuity without penalty. Surrender periods can last many years, and withdrawing funds before the conclusion of the surrender term may result in a surrender charge, which is basically a delayed sales cost.
The longer the surrender time, in general, but not always, the better the annuity's other terms.
The surrender period is the period during which an investor may withdraw funds from an annuity without incurring a surrender charge.
The surrender term can last many years, and annuitants may face large fines if they remove their invested assets before the time has finished.
Other financial instruments include a surrender period as well B-share mutual funds and entire life insurance plans are two examples.
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HELLP! EASY POINTS!
Explain how to use a graph to determine a point on the coordinate plane that you could use to form a right triangle with the ordered pairs shown.
Answer:
In this problem, we need to add a point to this graph which creates a right triangle with the given points.
The easiest way to do this is to find a point that is perpendicular to both of the points; more simply put, it has to have the x-coordinate of one of the given points and the y-coordinate of the other given point.
For example, adding the point (50, -14) to the graph satisfies this criteria, using the x-coordinate of (50, 25) and the y-coordinate of (130, -14). However, you could also use the y-coord of the first point and the x-coord of the second to add the point (130, 25). Both points in bold satisfy the criteria.
See the attached image for a graph of these points and the right triangles they create.
(2a−13)÷b15 when a=−35 and b=−6.75
Please and Thank You! :)
Answer:
-.56296296296...
Step-by-step explanation:
[tex]\frac{(2)(-35)-13}{(-6.75)(15)}[/tex]
[tex]\frac{70-13}{-101.25}[/tex]
[tex]\frac{57}{-101.25}[/tex]
-.56296296296... The 296 is repeating
What is the base if the portion is $4,570 and the rate is 55%?
Answer:
8309.09
Step-by-step explanation:
Base = Total
So we know that 4570 is 55% of the total
55% = 55/100 = 0.55
It is the same as:
4570 = 0.55 * total
Total = 4570/0.55 = about 8309.09
Hope this helps :)
Let me know if this is correct or not
Have a great day!
The measure of angle FGH is 60°.
The measure of angle
JGH is 35%.
FGJ is x°.
The measure of angle
Find the value of x.
x = 0
X
S
G
F
to
35°
60°
H
x = 60° - 35°
x = 25°
The measure of angle FGJ is 25°
Question 1
Divide £1530 in the ratio 5 : 12
fill in the blank: if the factor (x-a)^n shows up in the complete factorization of a polynomial, then the multiplicity of a is____.
a. n
b. a
c. a-n
d. x-a
If the factor (x - a)^n shows up in the complete factorization of a polynomial, then the multiplicity of a is: A. n.
What is a polynomial function?In Mathematics, a polynomial function can be defined as a type of mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.
This ultimately implies that, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
In this context, we can logically deduce that the graph of a polynomial function would touch the x-axis (x-coordinate) and turns around at r when the value of r is a zero of even multiplicity.
In conclusion, the multiplicity of a must be n since the factored form in the complete factorization of this polynomial function is (x - a)^n.
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Imagine you have a classmate who has never had an introduction to statistics in a math course. Explain to that person how the probability of selecting a red tile is determined. Use complete sentences.
The probability of selecting a red tile is determined by the formula number of red tiles/total number of tiles.
Probability is used to determine the chances of events.
To calculate the probability of selecting a red tile, we start by:
Get the number of red tiles
The total number of tiles
Then we need to divide the number of red tiles by the total number of tiles.
According to the question, there are 15 red tiles in a total of 60 tiles, then the probability of selecting a red tile is:
P(red) = 15/60
Divide 15 by 60
P(red) = 0.25
Thus, the probability of selecting a red tile for the given values is 0.25.
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Given the data set 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, which of the mean, median or mode would you use to describe the typical or central value in this date set? Why? O None of these as this data set is qualitative.O The mode as this data set is dominated by a single value. O The median as there are outliers at the high end of the data set causing the mean to be skewed high. O The mean as this data set has no outliers causing the mean to be skewed.
The mean as this data set has no outliers causing the mean to be skewed. option ( D )
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle value when a data set is ordered from least to greatest.
The mode is the number that occurs most often in a data set.
Mean - Add all numbers and divide by the total number of numbers
-> 5.5
Median - When all the numbers are put in order least to greatest, the middle value (if there are two numbers, find the average of the two numbers)
-> 5.5
Mode - Number that shows up most often
-> None
I would use the mean or median to describe the typical central value because they are the same value.
Therefore, The mean as this data set has no outliers causing the mean to be skewed. option ( D )
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a gazebo in the shape of a regular octagon has equal sides of 9 feet and an apothem of 10.9 feet. a. if one side of a gazebo is open, and the other sides have a railing, find the cost of the railing if it sells for $7.90 per foot. b. find the area of the gazebo. (express your answer in square feet) c. find the cost of the gazebo's flooring if it costs $3 per square foot. round to the nearest hundred dollars
The maximum number of pens he can buy now is 71.
We are given that;
A regular octagon has equal sides = 9 feet and an apothem of 10.9 feet
The cost of the railing if it sells = $7.90 per foot
Now,
Let’s assume that the person has bought x pens.
The total cost of the pens would be 9x dollars.
The shopkeeper has given a discount of 70 dollars. So the total cost of the pens after discount would be 9x - 70 dollars.
We need to find the maximum number of pens he can buy now.
we need to find the maximum value of x such that 9x - 70 ≤ 0.
Solving this inequality gives us x ≤ 70/9 ≈ 7.78.
Therefore, by algebra the answer will be 71.
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An ant walk along a tick. The tick i 1 1/2 ft long. The ant travel 3/10 ft every econd. How long doe it take the ant to walk the whole length of the tick?
The required time taken by the ant to complete whole length of the brick is 5 seconds.
What is speed?Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
According to question:Length of brick = 1(1/2) = 3/2
Speed of ant = 0.3 ft/sec
Then,
Speed = distance/time
Time = distance/speed
Time = 1.5/0.3 = 5 seconds
Thus, time taken by ant to cover whole length is 5 seconds
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