Answer:
a1 = 1875
Step-by-step explanation:
You want a1 for the geometric series that has r = 2/5, an = 120, and Sn = 3045.
Series relationsThe n-th term of the geometric series with first term a1 and common ratio r is ...
an = a1·r^(n-1)
The sum of the first n terms of the geometric series is ...
Sn = a1·(r^n -1)/(r -1)
ApplicationWe can use the expression for an to substitute for r^n in the sum equation:
[tex]a_n=a_1(r^n)(r^{-1})\\\\r^n=\dfrac{a_n}{a_1r^{-1}}=\dfrac{a_nr}{a_1}\\\\S_n=a_1\dfrac{r_n-1}{r-1}=a1\dfrac{\dfrac{a_nr}{a_1}-1}{r-1}\\\\S_n=\dfrac{a_nr-a_1}{r-1}\\\\a_1=a_nr-S_n(r-1)=a_nr+(1-r)S_n\\\\a_1=(120)\dfrac{2}{5}+(1-\dfrac{2}{5})(3045)=\dfrac{2\cdot120+3\cdot3045}{5}\\\\\boxed{a_1=1875}[/tex]
__
Additional comment
The sum is of the first four terms:
1875 +750 +300 +120 = 3045
We can also find this by working backward. The previous term is 5/2 times the current term. We need to find the terms that have a sum of 3045.
120 +300 +750 +1875 +4687.5 +...
Clearly, 5 terms is too many. The sum of the first 4 terms of the backward series is 3045, so we know n=4 and the first term is 1875—the last term of our 4-term backward series.
13) Two supplementary angles
are represented by 3y +10 and 2y+30 What are the measures of each angle?
Up to 180 degrees
Your Welcome
If you place a 26-foot ladder against the top of a building and the bottom of the ladder is 20 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot. help please now.
Answer: The building is approximately 16.6 feet tall.
Step-by-step explanation:
Use Pythagorean theorem (a²+b²=c²) to solve this.
We know that the ladder is 26 feet long so that would be our hypotenuse (c²). and the distance between the ladder and the building is 20 feet. So, this is the base. The remaining side is x.
Your equation would be: 20²+x²=26²
subtract 20² from 26² --> 276=x²
then take the square root --> 16.6=x
What is the measure of ∠b (messed up last)
Answer:
b=30
Step-by-step explanation:
The sum of the three angles of a triangle add to 180.
75+75+b = 180
150+b=180
Subtract 150 from each side.
b = 180-150
b=30
Answer:
b=30
Step-by-step explanation:
The sum of all the angles of a triangle add up to 180°
∠b = 75° + 75° = 150°
Now, we need to subtract 150° from 180° to see how much does angle b measure.
∠b = 150° - 180° = 30°
30° = ∠b
The angles of the triangle would be:
75°, 75°, and 30°
To prove this, we will sum all the angles again:
75° + 75° + 30° = 180°
75° + 75° = 150°
150° + 30° = 180°
Hence, the answer is ∠b = 30°
Angles M, N, and P are supplementary.
What is the measure of angle P?
60°
34°
45°
36°
Step-by-step explanation:
The measure of angle p is 60°
video
Let the region R be the area enclosed by the function f(x) = ln (x) + 1 and
g(x)=x-1. If the region R is the base of a solid such that each cross section
perpendicular to the a-axis is a semi-circle with diameters extending through the
region R, find the volume of the solid. You may use a calculator and round to the
nearest thousandth.
The volume of the solid is approximately 0.558 cubic units.
To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.
We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:
d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2
The radius of each semi-circle is half of the diameter, which is:
r(a) = (ln(a) - a + 2) / 2
The area of each semi-circle is π times the square of its radius, which is:
[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]
To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:
V = ∫[e,2] A(a) da
V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]
V ≈ 0.558 (rounded to the nearest thousandth)
Therefore, the volume of the solid is approximately 0.558 cubic units.
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An isosceles triangle whose sides are 5cm, 5cm and 6cm is inscribed in a circle. Find the radius of the circle.
Answer:
To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:
r = (a/2) * cot(π/n)
where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.
In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:
6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)
36 = 50 - 50cos(x)
cos(x) = (50 - 36)/50
cos(x) = 0.28
x = cos^-1(0.28) ≈ 73.7°
Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:
(5/2)^2 + h^2 = 5^2
25/4 + h^2 = 25
h^2 = 75/4
h = sqrt(75)/2 = (5/2)sqrt(3)
Now we can find the radius of the inscribed circle using the formula:
r = (a/2) * cot(π/n)
where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:
r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm
Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.
What is the likelihood
that all 21 students in a class share the same birthday? Explain.
Quick please!
Answer:
it is not likey bc inless the class have over 2 mil ppl in it itis doouptfull
Step-by-step explanation:
ALGEBRA HW!! I WILL GIVE BRAINLYEST
please answer both questions parts.
The table of original value and rounded values are
x y
0.2 0
0.5 1
0.9 1
1.08 1
1.49 1
1.72 2
2.3 2
2.94 3
The graph is attached
How to make the graphThe graph is made in a cartesian coordinate by tracing the point of intersection of the two points
The table is represented as ordered pair as (original value, rounded value) for the given x and y values:
(0.2, 0), (0.5, 1), (0.9, 1), (1.08, 1), (1.49, 1), (1.72, 2), (2.3, 2), (2.94, 3)
The graph is a scattered plot and its attached
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The radius of a circle is 14 centimeters. What is the circle's circumference?
Use 3.14 for л.
The circumference of the circle who radius is 14 centimeters is approximately 87.92 centimeters.
What is circumference?
Circumference is distance around the edge of a circle. It can be thought as the perimeter of the circle. It is a measure of the total length of the circle, and is determined by the size of the circle's radius or diameter. The formula of circumference of circle is C = 2πr
What is radius ?
Radius is a term used in geometry to refer to the distance between the center of a circle or sphere and any point on its circumference or surface, respectively. It is typically denoted by the letter "r"
In the given question,
The circumference of circle is given by the formula:
C = 2πr
where r is the radius of circle and π (pi) is mathematical constant which is approximately equal to 3.14.
Substituting the given value of radius, we get:
C = 2 x 3.14 x 14
= 87.92 centimeters (rounded to two decimal places)
Therefore, the circumference of the circle is 87.92 centimeters.
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i need help on part d.
Answer:
d. 6 seconds
e. 12 seconds
Step-by-step explanation:
Given that a projectile has an altitude of 320 feet at 2 seconds and 10 seconds after launch, you want to know the time to maximum height and the time the projectile lands on the ground.
d. SymmetryThe parabolic path is symmetrical about the vertical line through its vertex. So, the time at maximum height is the average of the two times at which the height is 320 ft:
(2 s + 10 s)/2 = (12/2) s = 6 s
The projectile is at maximum height 6 seconds after launch.
e. LandingThe projectile is launched from ground level at t=0, so will reach ground level again an equal time after reaching maximum height.
2 × (6 s) = 12 s
The projectile will land after 12 seconds.
solve using the standard algorithm. check your quotient and remainder and by using multiplication and addition 93÷7
In the standard algorithm
Reminder = 2
quotient = 13
What does quotient in mathematics mean?
The number being divided is known as the dividend, in this case, 15. The number being divided is known as the divisor (in this case, 3). The remainder following division is the quotient.
When we divide two integers, the result is a quantity known as the quotient. As an example, since the division resulted in the number 2, the quotient in the equation 8 4 = 2 is 2.
= 93÷7
Reminder = 2
quotient = 13
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers
T.A. =
To clear all your answers and start over, click the trashcan icon. Remember to always be accurate, professional, and friendly in your responses.
To answer a student question on Brainly, first, carefully read the question and understand what is being asked. Then, click on an item from the list or group of pictures provided at the bottom of the problem. Hold down the mouse button and drag the item into the correct position in the answer box.
Release the mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Simply click the garbage button to start anew after clearing all your answers. Always be sure to respond with accuracy, professionalism, and friendliness.
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11. At astronomy school, 30% of the students studying stars, 40% are studying black holes, 10% are studying planets, and 20% are studying comets. Use the random-number table to find the experimental probability that in a group of 4 students, at least 2 will be studying stars. Assign values from the table for each field of study: 11. A. Assign values for the number of stars. M. B. Assan values for the number of black holes. chshe 11. C Assign values for the number of planets. 11. D. Assign values for the number of comets. Use the table to simulate the probability that at least 2 will study stars. 3516 D 1388 5476 2802 11 E What is the simulated probability that at least 2 will be studying stars? 6035 5147 1264
Graph the function blue, green,red.
The graph of the functions are given as attached.
How do graphs help us to understand functions?Graphs are visual representations of functions that provide valuable insights into their behavior. They allow us to see the relationship between the input and output of a function, and how it changes over time or across different values.
The relationship between the two functions is that they are reciprocals of each other. Specifically, f(x) = 2sin(2x) + 1 is the reciprocal of f(x) = 2csc(2x) + 1, since csc(2x) is the reciprocal of sin(2x). Therefore, they have the same shape, but their values are inverted. See the attached graph.
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work out the product of 1 and 3/3 and 1 and 2/6 give your answer in its simplest form
Answer:
To multiply 1 3/3 by 1 2/6, we can first convert these mixed numbers to improper fractions, then multiply them together, and finally simplify the result to its simplest form.
1 3/3 can be written as 4/3 (since 1 whole and 3/3 is equivalent to 4/3)
1 2/6 can be written as 8/6 (since 1 whole and 2/6 is equivalent to 8/6)
Now, we can multiply these two fractions together:
4/3 x 8/6 = (4 x 8) / (3 x 6) = 32/18
To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2:
32/18 = (2 x 16) / (2 x 9) = 16/9
Therefore, the product of 1 3/3 and 1 2/6 is 16/9, or 1 and 7/9 in mixed number form, in its simplest form.
What’s the answer to this problem for factoring basic trinomials?
40-22 x +x²
(x-2)(x-20) is the factored form of the trinomial equation
Factoring trinomialsGiven the quadratic equation below
x² - 22x + 40
To factorise this expression, we need to find two factors of 40 that add up to -22.
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.
To get a sum of -22, we can choose the factors -2 and -20.
Therefore, we can write:
x² - 22x + 40 = (x - 2)(x - 20)
Thus, the factored form of the expression 40-22x+x² is (x-2)(x-20).
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Consider the table shown at left . What is the value of g( f ( -1) )
Answer:
4
Step-by-step explanation:
f(-1) = 2
g(2)= 4
A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,120 ft Determine the flag's width and length if the length is 400 ft greater than the width.
The flag's width is and the length is what?
PLEASE HURRY
Answer:
Step-by-step explanation:
Let's assume that the width of the flag is "w" ft.
According to the problem, the length of the flag is 400 ft greater than the width, which means it can be expressed as:
length = w + 400
Now, we know that the perimeter of the flag is 2,120ft. The perimeter of a rectangle is given by:
perimeter = 2(length + width)
Substituting the values, we get:
2120 = 2[(w+400) + w]
2120 = 2[2w + 400]
2120 = 4w + 800
4w = 1320
w = 330
Hence, the width of the flag is 330ft.
From our equation for the length, we have:
length = w + 400
length = 330 + 400
length = 730
Therefore, the length of the flag is 730ft.
abet level 4 Life orientation 2023 final
A company estimates that 2% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $450.
If they want to offer a 2 year extended warranty, what price should they charge so that they'll break even (in other words, so the expected value will be 0)
$
To break even, the company should charge a price that covers their expected loss. Therefore, the price that they should charge for the 2 year extended warranty is $9
What is expected value?
Expected value is a concept in probability theory that represents the average value of a random variable over a large number of trials. It is calculated by multiplying each possible outcome by its probability and adding up the products
Let x be the price that the company charges for the extended warranty. Then, the expected value of the extended warranty is:
E(x) = 0.98(0) + 0.02(-450) = -9
The negative expected value means that the company is expected to lose money on the extended warranty.
To break even, the company should charge a price that covers their expected loss. Therefore, the price that they should charge for the 2 year extended warranty is:
x = -$(-9) = $9
Therefore, the company should charge $9 for the 2 year extended warranty so that they break even.
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please helppppp i’ll give brainlist
For problems 6 and 7 set up a proportion and solve.
6. The ratio of the birth weight to the adult weight of a male black bear is 3:1000.
7. The measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.
What is an angle?An angle is an abstract concept in geometry which is formed by two lines or rays that meet at a common point. An angle is measured in degrees and can be classified by its size as acute, right, obtuse, or reflex. An angle can also be formed by three points or two intersecting planes.
6. The average birth weight is 12 ounces. The average adult weight is 12 x 1000 = 12000 ounces. Since there are 16 ounces in 1 pound, the average adult weight of the male black bear is 12000/16 = 750 pounds.
7. The measures of the angles in a triangle are in the extended ratio 2:15:19.To find the measure of each angle, we can set up an equation using the extended ratio. Let x be the measure of the first angle, then 15x and 19x will be the measures of the other two angles. This can be written as: 2x + 15x + 19x = 360°. Solving this equation, we get x = 36°. Therefore, the measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.
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Suppose for a community the number of rows in gardens is normally distributed with a mean of 7 rows and standard deviation of 2 rows. Find the probability that a given garden has between 1 and 11 rows. Hint: use the 68 - 95 - 99.7 rule.
The given distribution is normal with mean μ = 7 and standard deviation σ = 2. So,The probability that a given garden has between 1 and 11 rows is approximately 0.9772 or 97.72%.
What is probability?Probability is a mathematical concept that is used to measure the likelihood of a particular event occurring. It is a way to quantify uncertainty, and it is expressed as a number between 0 and 1.
We need to find the probability that a given garden has between 1 and 11 rows.
First, we standardize the values using the formula z = (x - μ) / σ, where x is the number of rows.
For x = 1, z = (1 - 7) / 2 = -3. For x = 11, z = (11 - 7) / 2 = 2.
Using the 68 - 95 - 99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Thus, the probability of a garden having between 1 and 11 rows can be calculated as:
P(1 ≤ x ≤ 11) = P(-3 ≤ z ≤ 2)
From the z-table, we can find that the probability of a standard normal distribution having a z-score between -3 and 2 is approximately 0.9772.
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I need help on this
Answer:
first name is pentagon
second is decagon
third is heptagon
Step-by-step explanation:
first is irregular
second is regular
third is irregular
Suppose P(E)=0.43. Find P (Ec)
The probability of the complementary event of E occurring is 0.57.
What is probability?
Probability is a branch of mathematics that deals with the study of random events or phenomena. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to happen.
In probability theory, P(E) represents the probability of an event E occurring, while P(Ec) represents the probability of the complementary event of E occurring. The complementary event of E is the event that E does not occur. In other words, it consists of all outcomes that are not in E.
To find P(Ec), we can use the formula:
P(Ec) = 1 - P(E)
where 1 represents the total probability of all possible outcomes.
In this case, we are given that P(E) = 0.43. Substituting this value into the formula, we get:
P(Ec) = 1 - P(E)
P(Ec) = 1 - 0.43
P(Ec) = 0.57
Therefore, the probability of the complementary event of E occurring is 0.57.
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4. The fence around a circular pool is 75 ft long.
Diameter:0ft
Radius:0ft
Is it radius diameter or circumference
The resultant values are as follows:
Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft
What is the circumference?The circumference of a circle or ellipse in geometry is its perimeter.
That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.
The curve length around any closed figure is more often referred to as the perimeter.
The length of a circle's outline is referred to as its circumference, and the length of a form with straight sides is referred to as its perimeter.
So, since the fence around the circular pool is given, then it will also be the value of the circumference of the pool.
Circumference = 75 ft
Radius:
2πr = 75
r = 75/2π = 75/(2×3.14) ≈ 11.937
radius = 11.94 ft
Diameter:
2r = 2×11 ≈ 23.87 ft
Therefore, the resultant values are as follows:
Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft
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Complete question:
The fence around a circular pool is 75 ft long. Find: Radius, Diameter, and Circumference.
Just curious to know
Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.
what is percentage ?Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.
given
If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.
You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:
1000 x 67% = 670
Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.
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The complete question is :-
Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?
Possible Answers:
3,700
57,000
67
None of the given answers
670
Based on historical data, an insurance company estimates that a particular customer has a 3.3% likelihood of having an accident in the next year, with the average insurance payout being $1500.
If the company charges this customer an annual premium of $120, what is the company's expected value of this insurance policy?
$
Based on this estimate, the insurance company's projected value of this probability insurance policy is negative, implying that the insurance company will lose money on this policy.
What is probability?Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.
The total of the potential payouts multiplied by the odds of each payout occurring equals the anticipated value of the insurance policy. In this scenario, the possible compensation is the $1500 insurance payout, and the likelihood of the client being involved in an accident is 3.3%, or 0.033.
Expected value = (Payout if event happens) x (Probability of event happening) - (Annual premium)
($1500) x (0.033) - ($120) = expected value
Value expected = $49.50 - $120
-$70.50 is the expected value.
Based on this estimate, the insurance company's projected value of this insurance policy is negative, implying that the insurance company will lose money on this policy.
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If you were to travel 6 miles, and catch a train and traveled 8 miles, how many miles have you traveled?
Answer:
The answer would be 14 miles!
Multiply. (4x-3) (2x − 6)
8
8x²-30x+18
6x² +18x - 9
6x²-30x + 18
08x²-18x + 18
Answer:
8x²-30x+18
Step-by-step explanation:
8x²-24x-6x+18
8x²-30x+18
Answer:
[tex]8x^{2} -30x+18[/tex]
Step-by-step explanation:
[tex]8x^{2} -24x-6x+18[/tex]
[tex]8x^{2} -30x+18[/tex]
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No