Answer:
Common ratio r = [tex]\dfrac{2}{3}[/tex]
Sequence is described by
[tex]a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\[/tex]
Step-by-step explanation:
[tex]S_n = \dfrac{a_1(1-r^n)}{1-r}[/tex]
where
r = common ratio
a₁ = first term
Sum of first two terms
[tex]S_2 = \dfrac{a_1(1-r^2)}{1-r}[/tex]
Sum of first four terms:
[tex]S_4 = \dfrac{a_1(1-r^4)}{1-r}[/tex]
[tex]\dfrac{S_4}{S_2} = a_1 \cdot \dfrac{1-r^4}{1-r} \div a_1 \cdot \dfrac{1-r^2}{1-r}\\[/tex]
To divide, flip the divisor and multiply
[tex]\dfrac{S_4}{S_2} =\dfrac{a_1(1-r^4)}{1-r} \times \dfrac{1-r}{a_1(1-r^2)}[/tex]
The a₁ and (1-r) terms cancel out from numerator and denominator leaving
[tex]\dfrac{S_4}{S_2} =\dfrac{1-r^4}{1-r^2} \cdots [1][/tex]
Using the identity
[tex]a^2 - b^2 = (a- b)(a+b)[/tex]
[tex]1- r^4 = 1^4 - r^4 = (1^2 - r^2)(1^2+r^2) = (1-r^2)(1+r^2)[/tex]
Plugging this into equation 1 we get
[tex]\dfrac{S_4}{S_2} =\dfrac{(1-r^{2})(1+r^{2})}{1-r^{2}}[/tex]
The [tex]1- r^2[/tex] terms cancel out leaving:
[tex]\dfrac{S_4}{S_2} =1 + r^2[/tex]
We are given
[tex]S_4 =\dfrac{65}{18}\\\\S_2 = \dfrac{5}{2}[/tex]
[tex]\dfrac{S_4}{S_2} = \dfrac{65}{18} \div \dfrac{5}{2}[/tex]
To divide, flip the denominator [tex]\dfrac{5}{2}[/tex] and multiply
[tex]\dfrac{S_4}{S_2} = \dfrac{65}{18} \times \dfrac{2}{5}\\\\= \dfrac{13}{9}[/tex]
Therefore
[tex]1 + r^2 = \dfrac{13}{9}\\\\r^2 = \dfrac{13}{9} - 1\\\\= \dfrac{13}{9} - \dfrac{9}{9}\\\\= \dfrac{4}{9}[/tex]
[tex]r = \sqrt{\dfrac{4}{9}}\\\\= \dfrac{\sqrt{4}}{\sqrt{9}}\\\\= \dfrac{2}{3}[/tex]
So the common ratio
[tex]r = \dfrac{2}{3}[/tex]
To find the first term we have sum of first two terms = 5/2
[tex]S_2 = \dfrac{a_1(1-r^2)}{(1-r)} = a_1 (1+ r)[/tex]
Plugging in knowns
[tex]\dfrac{5}{2} = a_1(1+\dfrac{2}{3})\\\\= a_1 \cdot \dfrac{5}{3}[/tex]
Multiply both sides by 3/5 to get
[tex]a_1 = \dfrac{5}{2} \times \dfrac{3}{5}\\\\a_1 = \dfrac{3}{2}[/tex]
The nth term of a GP is
[tex]a_n = a_1 \cdot r^{n-1}\\[/tex]
Plugging in the values obtained
[tex]a_n = \dfrac{3}{2}\cdot \left(\dfrac{2}{3}\right)^{n-1}\\[/tex]
Select the equation that is true. A. 2 2/3 × 4 = 8 2/3 B. 2 2/3 × 5/8 = 1/2 3 C. 2 2/3 × 2/3 = 2 4/9 D. 2 2/3 × 4 3/5 = 8 6/15
Question 1
Find the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made. The interest charge for unpaid balances is 18% per year.
Credit Card Balance = $5000
Credit Limit = $5000
Minimum Payment = $125.00
The credit card's outstanding amount is [tex]4875[/tex], the new interest rate is [tex]75[/tex], as well as the buying power is [tex]50[/tex] after paying the required minimum payment of [tex]125[/tex].
What does the word "interest" mean?The urge to become interested with something, give it your whole attention, and learn more about it My entire life, astronomy has captivated me. He never seems to be concerned about his children.
Why is there an interest?You pay the interest on almost any loans and bank debt of money. The proportion of the loan balance used by lenders to compute interest. Clients who lend money can earn interest
We determine the monthly interest charge,
Interest charge = (1.5% per month) [tex]*[/tex] (5000 unpaid balance)
Interest charge [tex]= 75[/tex]
The new overdue debt is obtained by deducting the minimum monthly payment from the original unpaid balance:
Unpaid balance [tex]= 5000 - 125[/tex]
Unpaid balance [tex]= 4875[/tex]
we add the interest charge to the new unpaid balance to get the new balance:
New balance [tex]= 4875 + 75[/tex]
New balance [tex]= 4950[/tex]
Lastly, we may determine the purchasing power by deducting the new balance from the credit limit:
Purchasing power [tex]= 5000 - 4950[/tex]
Purchasing power [tex]= 50[/tex]
Therefore the unpaid balance on the credit card is [tex]4875[/tex], the new interest charge is [tex]75[/tex], and the purchasing power is [tex]50[/tex].
To know more about interest visit:
https://brainly.com/question/31000593
#SPJ1
Find the value of x. (Pic)
122°
Step-by-step explanation:
the formula is (n-2)180
n = the number of sides of a polygon
in this case (n-2)180;
=(4-2)180
=(2)180
=360 the total interior angle
add everything and minus them with the total interior angle to get your answer
# of rolls per trial 20 50 100
# of times a 3 was rolled 8 18 30
Julia made a die for a game. It had 5 faces, labeled 1-5. Because of the shape of the die, it was biased in favor of rolling a 3. We do not know the amount of bias. She experimented to extimate how likely it was for a 3 to be rolled and her results are in the above table.
In question #1, you found the best estimate of the probability of rolling a 3. Using that estimate, how many times would a 3 be rolled after 200 rolls?
We can conclude after answering the provided question that We can estimate that a 3 would be rolled probability 71 times after 200 rolls if we round off to the nearest integer.
What is probability?Probability is a way of measuring of how likely an event is to occur. It is represented by a number respectively 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Switching a valid coin and coin flips has such a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a branch of mathematics that studies random events instead than their properties. It is applied in many fields, including facts and figures, finance, science, and construction.
Based on the information provided, the estimated probability of rolling a 3 can be calculated as follows:
8/20 = 0.4 for 20 rolls
18/50 = 0.36 for 50 rolls
For 100 rolls: 30/100 = 0.3
We can take the average of these values to get the best estimate:
(0.4 + 0.36+ 0.3) / 3 = 0.3533
As a result, the best estimate of the likelihood of rolling a 3 is 0.3533.
We can estimate the number of times a 3 would be rolled after 200 rolls using this probability as:
The number of times a 3 would be rolled equals the probability of rolling a 3 multiplied by the number of rolls.
= 0.3533 x 200
= 70.66
We can estimate that a 3 would be rolled approximately 71 times after 200 rolls if we round off to the nearest integer.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
What is the domain of the function
Answer: x[tex]\neq[/tex]6
Step-by-step explanation
The inverse function is f^-1(x)=1/x-4+6 and the domain is x[tex]\neq[/tex]6
Express f(x) as y
Swap the positions of x and y
Add 6 to both sides
Multiply both sides by y-4
Divide both sides by x + 6
Add 4 to both sides
Rewrite as: f-1(x)=1/x+6-4
Hence, the inverse function is 4 and the domain is x[tex]\neq[/tex]6
A chef need to 12 pound of sliced carrots. This preparation of carrots has a yield percent of 86. What he peed quantity of carrots does the chef need to pull from the walk-in?
The chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.
What is quantity?Quantity is the amount or magnitude of something. It can be measured in terms of units, such as length, weight, volume, area, speed, temperature and time. Quantity also refers to the size or number of something, such as the number of items in a package or the number of people in a room. In mathematics, quantity is usually represented by a number or symbol.
In order to calculate the quantity of carrots the chef needs to pull from the walk-in, we can use the following formula:
Quantity Needed = 12 lb / 0.86 (yield percent)
Therefore, the chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.
To know more about quantity click-
https://brainly.com/question/30545084
#SPJ1
The chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.
What is quantity?Quantity is the amount or magnitude of something. It can be measured in terms of units, such as length, weight, volume, area, speed, temperature and time. Quantity also refers to the size or number of something, such as the number of items in a package or the number of people in a room. In mathematics, quantity is usually represented by a number or symbol.
In order to calculate the quantity of carrots the chef needs to pull from the walk-in, we can use the following formula:
Quantity Needed = 12 lb / 0.86 (yield percent)
Therefore, the chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.
To know more quantity click-
https://brainly.com/question/28294142
#SPJ1
Select the graph that correctly represents ƒ(x) = 1∕2(x – 3)^2 – 6.
Option (b) correctly represent the graph f(x) = 1/2 (x-3)² -6, we can find by coordinate geometry.
What is Coordinate geometry?
A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one (1) or more numbers, or coordinates.
In coordinate geometry, many geometric figures are described using graphs and coordinates. The coordinate plane must be described in a definition of coordinate geometry. The intersection of 2 number lines, referred to as axes, yields the coordinate plane, also known as the coordinate graph, which is a grid system.
In option (b), if we put x = 7 , we get y = 2.
and , if we put x =4, we get y = -5.5
Hence, the option (b) is correct.
To learn more about space, visit:
https://brainly.com/question/14445084
#SPJ1
I will mark you brainiest!
If the triangle above is translated two units to the right, what is the correct coordinate for A'?
A) A'(5, 5)
B) A'(5, 0)
C) A'(0, 5)
D) A'(0, 0)
If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?
A) A'(0, 5)
B) A'(2, 5)
C) A'(5, 2)
D) A'(-5, -2)
Answer:
Step-by-step explanation:
1. (0,5) or A
2.(2,5) or B
Write a function rule P(m) to represent Evelyn’s profit per mask so that she can always find what her profits will be for any amount of masks (m) she sells.
By answering the presented question, we may conclude that Evelyn will equation need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.
Initially, we must determine the entire cost of producing and transporting one mask:
Total cost per mask = $1.25 plus $2.15 for delivery = $3.40
Profit per mask is selling price minus total cost per mask, which equals $5 - $3.40 = $1.60.
As a result, Evelyn will profit $1.60 for each mask she sells. We may use the following calculation to calculate how many masks she needs to sell to recoup her $450 initial project costs:
Total beginning project expenditures / profit per mask = number of masks to sell
Total number of masks to be sold = $450 / $1.60 per mask = 281 masks
Evelyn will need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Please see the picture. Can anyone help me whats the correct arrangement of cooking? Thank you
According to the information, the correct order of the steps would be: 5, 2, 3, 6, 7, 4, 1.
How to organize the steps properly?To properly organize the steps we must read each one of them and identify the procedure they are describing. In this case, they are describing the procedure for cooking a fried food. According to the above, the steps to follow would be:
5. Wash your hands.
2. Take strips out of the freezer and put a maximum of 15 into a basket. Lower the basket into preheated oil.
3. Start the strip' timer by pressing the button on the front of the fryer.
6. When the timer sounds, shake the basket once during cooking without removing the basket from the oil.
7. When the timer sounds, remove the basket from the fryer and drain well.
4. Hold food in warming drawer or cabinet. Press the strips' hold timer button on the cabinet timer.
1. Use tongs to place strips in the package (3 for a small order, 5 for a large order).
Learn more about cooking in: https://brainly.com/question/5190639
#SPJ1
Solve the indefinite integral (linear):
Answer:
[tex] \rm \: a. \: \displaystyle \int \rm \: (3 {x}^{2} + 4x)dx[/tex]
[tex] = \displaystyle \int \rm 3 {x}^{2} dx + \displaystyle \int \rm4x \: dx[/tex]
[tex] \rm = 3 \displaystyle \int \rm {x}^{2} \: dx + 4\displaystyle \int \rm \: x \: dx[/tex]
[tex] \rm \: = 3 \times \dfrac{ {x}^{3} }{3} + 4 \dfrac{ {x}^{2} }{2} + c[/tex]
[tex] \boxed{\rm = {x}^{3} + 2 {x}^{2} + c}[/tex]
[tex]b. \displaystyle \int \rm \bigg( \dfrac{1}{ {t}^{2} } + \sqrt{t} \bigg)dt[/tex]
[tex] = \displaystyle \int \rm \frac{1}{ {t}^{2} } dt + \displaystyle \int \rm \sqrt{t} \: dt[/tex]
[tex] = \displaystyle \int \rm \: {t}^{ - 2} dt \: +\displaystyle \int \rm {t}^{ \frac{1}{2} } dt[/tex]
[tex] \rm \: = \dfrac{ {t}^{ - 1} }{ - 1} + \frac{ {t}^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ [/tex]
[tex] \rm = - \dfrac{1}{t} + \dfrac{2}{3} {t}^{ \frac{3}{2} } + c \\ [/tex]
[ In Second question I used dt instead of dx ]
Where is there a striking deviation in the dot plot above
The is a striking deviation at the value of 5.5.
This deviation is seen in the form of a cluster of dots that are significantly higher than the rest of the data points. This cluster of dots represents a group of observations that share a similar characteristic or variable that sets them apart from the rest of the data set.
The presence of this deviation at the value of 5.5 indicates that there is a unique factor or characteristic present in this group of observations that is not shared by the rest of the data set. This could be due to a number of factors, such as a different population, different data collection methods, or even measurement error.
It is important to note this deviation when analyzing the data set, as it can have a significant impact on any conclusions drawn from the data.
for such more questions on striking deviation
https://brainly.com/question/20632412
#SPJ11
A passenger train has tickets available for 12 window seats and 8 aisle seats. The next person to buy a ticket will be randomly selected to one of those seats. What is the probability that the next passenger will be assigned to an aisle seat?
The answer is 2/5.
There is an 8/20 chance that the next person will receive a window seat. You simplify that probability to get your answer. 8/20 becomes 2/5. So the answer is 2/5.
Evaluate the following using Cauchy Integral Theorem; The integral of 3z+1/(z(z-2)^2)
Hence, in response to the provided question, we can say that As a result, derivatives the integral has a value of -i/2.
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value changes in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. einsteinerupload of. Derivatives are rate of change metrics that apply to almost any function.
To use the Cauchy Integral Theorem to evaluate the integral (3z+1)/(z(z-2)2), we must first determine whether the function has any singularities in the region we are integrating across.
We can write the function to find the residue at z=0 as:
A/z + B/(z-2) + C/(z-2)2 = (3z+1)/(z(z-2)2)
3z+1 = A(z-2)^2 + Bz(z-2) + Cz
When we set z=0, we get:
1 = 4A
So, A = 1/4.
Set z=2 in the following equation and its derivative to determine B and C:
9 = 4B + 2C
3 = 4A - 2B - C
B = -1/2 and C = 7/4.
So, A=1/4 is the remnant at z=0, while B=-1/2 is the residue at z=2.
Applying the residue theorem, the integral is as follows:
dz = 2i [Res(z=0) + Res(z=2)] = 3z+1/(z(z-2)2
= 2πi [1/4 - 1/2]
= -πi/2.
As a result, the integral has a value of -i/2.
To know more about derivatives visit:
https://brainly.com/question/25324584
#SPJ1
I need all of the angles shown please help
The unknown angles of the kites are as follows:
m∠1 = 90°
m∠2 = 65°
m∠3 = 90
m∠4 = 65°
m∠5 = 25°
How to find the angles of a kite?A kite is a quadrilateral that has 90° angles at the point of intersection of the two diagonals. The sum of angles in a kite is 360 degrees.
Therefore, the diagonal of a kite bisect each other at right angle.
Diagonals also bisect each angles.
Using the diagonal theorem of the kite,
m∠1 = 90 degrees
m∠2 = 180 - 25 - 90 = 65 degrees(sum of angles in a triangle)
m∠3 = 90 degrees
m∠4 = 65 degrees(Base angles of an isosceles triangles are congruent)
m∠5 = 25 degrees
learn more on kite here: https://brainly.com/question/30482906
#SPJ1
Express the perimeter of the following triangle in simplest form: 3a + 8 4a +2b + 7 5a + b
The perimeter of the triangle when expressed in simplest form is 12a + 3b + 15
How to express the perimeter of the triangleThe dimensions of the triangle are given as
3a + 8 4a +2b + 7 5a + b
Perimeter refers to the total length of the boundary or outer edge of a two-dimensional shape.
The perimeter is measured in linear units such as centimeters, meters, feet, or inches.
The formula for finding the perimeter of a shape depends on the type of shape
For the triangle, we have
Perimeter = 3a + 8 + 4a +2b + 7 + 5a + b
Evaluate
Perimeter = 12a + 3b + 15
Hence, teh perimeter is 12a + 3b + 15
Read more about perimeter at
https://brainly.com/question/24571594
#SPJ1
Which triangle has the greater area? What is its area?
Triangle A
Triangle B
4 cm
8 cm
A. Triangle A: A = 16 cm²
B. Triangle B: A = 15 cm²
C. Triangle A: A = 32 cm²
D. Triangle A: A = 30 cm²
5 cm
6 cm
HELP ASAP PLEASE
Answer:
A. Triangle A= 16cm^2
Step-by-step explanation:
triangle A area=8×4=32
32÷2=16cm^2
triangle B area= 5×6=30
30÷2=15cm^2
so triangle A has the greater area of 16 cm^2
Answer:
A. 16cm2 triangle
Explanation in detail: triangle A area=84=32 32÷2=16cm^2 area of triangle B = 56=30
30÷2=15cm^2 As a result, triangle A has a bigger area of 16 cm2.
Step-by-step explanation:
Calculus(Question in picture)
The percentage error in the volume calculation is estimated to be 24%.
What is the percentage error?The formula for the volume of a sphere is V = (4/3)πr³
where;
r is the radius of the sphere.Since the diameter is given as 50 ± 4 cm, the radius can be calculated as:
r = (1/2)d = (1/2)(50 ± 4) cm = 25 ± 2 cm
The percentage error in the radius is:
Δr/r = (2 cm) / (25 cm) = 0.08
This means that the radius measurement has an error of 8%.
Using the formula for the volume of a sphere, we can calculate the volume as:
V = (4/3)π(25 ± 2)³ = (4/3)π(27 ± 18) × 10³ cm³
The percentage error in the volume calculation can be found by:
ΔV/V = (Δr/r) × 3
ΔV/V = 0.08 × 3 = 0.24 = 24%
Learn more about percentage error here: https://brainly.com/question/5493941
#SPJ1
Récrire sous forma an
(5^2)^3×7^2×7^3
Answer:
262609375 is the answer.
n 8.1 Homework
K
Part 1 of 2
Suppose that the local sales tax rate is 3% and you purchase a car for $21,100.
a. How much tax is paid?
b. What is the car's total cost?
This same car's purchase amount, which would include tax, is $21,733.
Which tax is this?A tax is a compulsory fee / financial charge imposed by a government on a person or an entity in order to raise money for public works projects that provide the greatest infrastructure and facilities.
a. To determine the amount of tax paid, multiply the cost of the car even by applicable sales tax rate.
3% times $21,100 is the amount of tax paid.
Taxes paid = 0.03 times $21,100.
Total tax paid: $633
Hence, $633 in taxes were paid on the vehicle.
b. To get the entire cost of the vehicle, we must add the purchase price and any applicable taxes:
Total price equals automobile price plus tax paid.
Cost in total is $21,100 plus $633.
Cost in total is $21,733
To know more about tax visit:
https://brainly.com/question/29115944
#SPJ1
A consulting company has a project to launch, Project MI, and two potential consultants that will take over the project as project leaders, Jim and Joe. The project will succeed with probability 0.8 if Jim is the project leader, and with probability 0.6 if Joe is the project leader. The manager of the company said that Jim or Joe would lead the project with probabilities 0.4 and 0.6, respectively. Two months later, we have been told that the project has succeeded. What is the probability that Jim was the project leader?
Answer:
Jim was the project leader given that the project has succeeded is approximately 0.57.
Investment A: $800 compounded continuously at 3.5%
Investment B: $900 compounded quarterly at 3%
a. Which investment would be worth more after 20 years? (2 points)
b. How long will it take investment A to triple?
Round to the nearest tenth of a year. (2 points)
URGENT ! 100 POINTS !
Mali is preparing for a competition that involves running and biking. This past weekend, they ran and biked for a total of 34 miles in 3.5 hours. Their average speed
for running was 6mph, and for biking it was 12.5mph.
If "x" represents the total hours Mali ran, and "y" represents the total hours Mali biked....
Which equation is a representation of the TOTAL TIME Mali spent training?
A. x+y = 3.5
B. 6x +12.5y = 34(3.5)
C. 6x +12.5y = 3.5
D. x+y=34
E. 12.5x+6y= 3.5
A. x + y = 3.5 equation is a representation of the TOTAL TIME Mali spent training
What is distance?An amοunt οf space between twο things οr peοple
The tοtal distance Mali cοvered can be expressed as the sum οf the distance run and the distance biked, which is equal tο 34 miles:
distance run + distance biked = 34
We can express the distance run and the distance biked in terms οf their speeds and the time spent running and biking, respectively:
distance run = 6x (where x is the time spent running in hοurs)
distance biked = 12.5y (where y is the time spent biking in hοurs)
Using the fοrmula distance = rate × time, we can write twο equatiοns fοr the time Mali spent running and biking:
6x + 12.5y = 34 (tοtal time equatiοn)
x + y = 3.5 (tοtal time equatiοn)
Optiοn A, x + y = 3.5, is a representatiοn οf the tοtal time Mali spent training, but οptiοn B, 6x + 12.5y = 34(3.5), is nοt a representatiοn οf the tοtal time Mali spent training, but rather a representatiοn οf the tοtal distance cοvered by Mali in terms οf their speeds and time spent training. Optiοns C, D, and E are nοt cοrrect representatiοns οf the tοtal time Mali spent training either. Therefοre, the cοrrect answer is:
A. x+y = 3.5
To learn more about Distance, click on the link:
https://brainly.com/question/15461491
#SPJ1
Use set-builder notation to indicate set numbers as described.
Answer
4
The set of all real numbers between 1 and 3, including 1
The set of all real numbers between 1 and 3, including 1 can be represented using set-builder notation as: { x ∈ R | 1 ≤ x ≤ 3 }
set-builder notation:
{ x ∈ R | 1 ≤ x ≤ 3 }
"The set of all x in the set of real numbers such that x is bigger than or equal to 1 and less than or equal to 3" can be understood from this notation. The word "such that" is denoted by the vertical bar "|," and the condition that follows lists the requirements that each element of the set must meet.
When the criteria is "more than or equal to 1" in this instance, the set contains 1. As they also meet the requirement of being "less than or equal to 3," the set also includes all real numbers between 1 and 3. Observe that no numbers outside of the range [1,3] are included in the collection.
In conclusion, the set of all real numbers between 1 and 3, including 1, may be written as x R | 1 x 3 in set-builder notation.
Learn more about set-builder notation here:
https://brainly.com/question/29531272
#SPJ1
pls help! show work!
Answer:
6 cm
Step-by-step explanation:
Volume of the given cylinder is calculated using the formula
V = π r ² l
r = radius of the cylinder = diameter/2
Here r = 4/2 = 2 cm
V = 150 cm³
and we are asked to calculate l
Plugging in known values
150 = π · 2³ · l
switch side:
π · 2³ · l = 150
π · 8 · l = 150
l = 150/8π
= 5.96831 cm
To the nearest centimeter we would round this up to 6 cm (Answer)
Find the value of x. Round to the
nearest tenth.
12
X =
The measure of the angle x is 70.53 degrees
How to determine the value of the angleIt is important to know that trigonometric identities are defined as equalities that relate to different trigonometric functions and also holds true for any value of the variable that is in the domain.
There are different trigonometric identities namely;
tangentcosecantsecantsinecosinecotangentThe ratio for the identity cosine is;
cos θ = adjacent/hypotenuse
substitute the values, we get;
cos x = 4/12
divide the values
cos x = 0. 3333
Take the inverse cosine of the values
x = 70. 53 degrees
Learn about trigonometric identities at: https://brainly.com/question/7331447
#SPJ1
Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs 15. (Take p = 3.14). (show working too) stop copying from others
The required length of lace = 4.17m and the cos for lace of 4.17m is ₹ 70.65.
[tex]\text{Circumference of the circle}=2\pi r[/tex][tex]\text{Radius of circle}=\dfrac{\text{diameter}}{2}[/tex]
Step 1:
Find the radius, r of the circular table.
Given that, Salma wants to put a lace on the edge of a circular table of diameter
Diameter of circle, d=1.5m
Radius of circle, [tex]\text{r}=\dfrac{1.5}{2}\text{m}[/tex]
Step 2:
Find circumference of the circle.
Substitute [tex]\text{r}=\dfrac{1.5}{2}\text{m}[/tex] in formula
[tex]\text{Circumference of the circle}=2\pi r[/tex]
Take [tex]\pi =3.14[/tex]
[tex]=2\times3.14\times\dfrac{1.5}{2}[/tex]
[tex]=3.14\times1.5[/tex]
[tex]=4.71 \ \text{m}[/tex]
[tex]\text{Circumference of circle} = 4.71 \ \text{m}[/tex]
[tex]\text{The length of lace required is 4.71} \ \text{m}[/tex]
Step 3:
Find the cost of rope.
From step 2
[tex]\text{Length of lace required} =\it{4.17} \ \text{m}[/tex]
Given that, of the lace costs ₹ 15
From the above statement, form an equation.
Cost of 1m lace = ₹ 15
Therefore, cost of 4.17m lace
Required length of lace = 4.17m. Cost for lace of 4.17m is₹ 70.65.
Determine which translations would map Figure F onto Figure G.
Press "try" to test a translation or sequence of translations.
Figure G
12 11
Figure F
-12-11-10-9 -8 -7
5 6 7 8 9 10 11 12
-10 11
A translation ___ units and ___ units.
The translations that would map Figure F onto Figure G are given as follows:
A translation right 4 units and up 3 units.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically on the coordinate plane.
The four translation rules for coordinates are defined as follows:
Translation left a units: (x,y) -> (x - a, y).Translation right a units: (x,y) -> (x + a, y).Translation up a units: (x,y) -> (x, y + a).Translation down a units: (x,y) -> (y - a).The rule applied to the coordinates of each point on the figure F to obtain Figure G is given as follows:
(x,y) -> (x + 4, y + 3).
Hence the translation is defined as follows:
4 units right.3 units up.More can be learned about translations at brainly.com/question/28174785
#SPJ1
What is the area of the triangle in the coordinate plane?
(A) 36 units²
(B) 38 units²
(C) 66 units²
(D) 72 units²
_______________________________
(reporting wrong/spam answers)
(giving brainliest to correct answers)
_______________________________
The area of the triangle in this coordinate plane will be 36 square units. Then the correct option is A.
What is the area of the triangle?Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
[tex]\text{A} = (\dfrac{1}{2} ) \times h\times b[/tex]
From the graph, the length of the height of the triangle is 9 units and the length of the base of the triangle is 8 units. Then the area is given as,
[tex]\text{A} = (\dfrac{1}{2} ) \times 9\times 8[/tex]
[tex]\text{A = 36 square units}[/tex]
The area of the triangle in this coordinate plane will be 36 square units. Then the correct option is A.
More about the area of the triangle link is given below.
https://brainly.com/question/19305981
PLEASE HELPP!!!!
Philip and Laura want to build a pool in their backyard. The length and width of the pool can be represented by the equation f(x)=(x-3)(5x+2) feet. What is the area of Philip and Laura’s pool? You must show your work and include your units.
Answer:
5 by 2, 13 by 4, and 6 by 6.
The pool at Philip and Laura's home is therefore 5 x 2 x 13 x 6 square feet in size.
Step-by-step explanation:
We must multiply the pool's length by its breadth to determine its area. The formula f(x) = (x-3)(5x+2) yields the length and width, so:
Size equals (x-3) feet
Size is (5x+2) feet wide.
Length times Width equals (x-3) times (5x+2) square feet.
Increasing the brackets results in:
Area: 5 by 2, 13 by 4, and 6 by 6.
The pool at Philip and Laura's home is therefore 5 x 2 x 13 x 6 square feet in size.