There are 109 terms in given series.
Here, we have,
According to the statement
we have given that the sum of series is AP series and
This is 19 20.5 22 23.5 ... 181
And the sum of series is 10,900
Now, we have to find the number of terms in the series.
Then we use the summation formula which is
S = n/2 (a + L)
Substitute the all given values in it like
L = 181
A = 19 and S= 10,900
then
10,900= n/2(19+181)
10,900= n/2(200)
After solve the equation for n
10,900= 100n
n = 10,900 / 100
n = 109
There are 109 terms in given series.
So, There are 109 terms in given series.
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What is the percent of change in 6 yards to 36 yards - - - 7th-grade math show the work
Answer:
Step-by-step explanation:
Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.
I think sorry if I’m wrong
Find the area of the shaded region. Provide an answer accurate to the
nearest tenth.
18 ft
10 ft
Thus, the area of the shaded part is found to be 50 sq. ft.
Define about area of the shaded region:The shaded region's area is most frequently found in common geometry problems. Such problems always have a minimum of two forms, and you must determine the area for each shape as well as the darkened zone by deducting the smaller shape's area from the larger.
Rectangle's area :
Area has two dimensions: length and width. Square units like square inches, square feet, or square metres are used to measure area.
Multiply its length by the width to determine the area of a rectangle. A is equal to L * W, where * denotes multiplication, L is the length, W is the breadth, and A is the area.Length of shaded part = 5 ft
width of shaded part = 10 ft
Area = 5*10
Area = 50 sq. ft
Thus, the area of the shaded part is found to be 50 sq. ft.
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Correct question:
For the given figure find the area of the shaded region.
Length BC = 18 ft
Length CD = 10 ft
What is the area of the trapezoid?
Answer:
33
Step-by-step explanation:
Pythagorean theorem:
6,5^ - 2.5^2= 36
✓36=6 second leg
3×6=18 square area
0,5×6×2,5=7,5 area of a triangle
2×7,5 + 18= 33
Dos personas reciben a los carros que entran a un estacionamiento. La primera persona entrega un boleto verde cada dos carros que entran. La segunda persona entrega un boleto azul cada tres carros que entran. ¿Qué número ocupará en la fila el tercer carro que recibirá boletos de ambos colores?
Por lo tanto, el tercer carro que recibirá boletos de ambos colores ocupará la posición número 18 en la fila.
Hola, entiendo que quieres saber en qué posición de la fila se encontrará el tercer carro que recibirá boletos de ambos colores (verde y azul). Para esto, vamos a analizar la situación:
- La primera persona entrega un boleto verde cada 2 carros.
- La segunda persona entrega un boleto azul cada 3 carros.
Un carro que recibe boletos de ambos colores será aquel que ocupa una posición que es múltiplo común de 2 y 3. El mínimo común múltiplo (MCM) de 2 y 3 es 6. Por lo tanto, cada 6 carros, habrá uno que reciba boletos de ambos colores.
Para encontrar el tercer carro que recibirá boletos de ambos colores, simplemente multiplicamos el MCM (6) por la cantidad de carros que buscamos (3):
6 × 3 = 18
Por lo tanto, el tercer carro que recibirá boletos ición número 18 en la fila.
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Assume that demand equation is given by q=6000-100p. Find the marginal revenue for the given production levels (values of q). (Hint: Solve the demand equation for p and use R(q)=qp)
a). 1000 units
The marginal revenue at 1000 units is ____. (simplify your answer)
b). 3000 units
The marginal revenue at 3000 units is ____. (simplify your answer)
c). 6000 units
The marginal revenue at 6000 units is ____. (simplify your answer)
The marginal revenue at 1000 units is 40, at 3000 units is 0, and at 6000 units is -60.
Find the marginal revenue?
To find the marginal revenue for the given production levels, we first need to solve the demand equation for p and then derive the revenue function R(q).
Solve the demand equation for p.
q = 6000 - 100p
100p = 6000 - q
p = (6000 - q) / 100
Find the revenue function R(q) using R(q) = qp.
R(q) = q * ((6000 - q) / 100)
Derive the marginal revenue function MR(q) by taking the derivative of R(q) with respect to q.
MR(q) = dR(q)/dq = d(q * (6000 - q) / 100)/dq
Using the product rule:
MR(q) = (1 * (6000 - q) - q * 1) / 100
MR(q) = (6000 - 2q) / 100
Now, we can plug in the given production levels to find the marginal revenue at each level.
The marginal revenue at 1000 units is:
MR(1000) = (6000 - 2 * 1000) / 100 = (6000 - 2000) / 100 = 4000 / 100 = 40.
The marginal revenue at 3000 units is:
MR(3000) = (6000 - 2 * 3000) / 100 = (6000 - 6000) / 100 = 0 / 100 = 0.
The marginal revenue at 6000 units is:
MR(6000) = (6000 - 2 * 6000) / 100 = (6000 - 12000) / 100 = -6000 / 100 = -60.
So, the marginal revenue at 1000 units is 40, at 3000 units is 0, and at 6000 units is -60.
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Question 10 9 pts 1 De Let f(x) = 2.3 + 6x? - 150 +3. (a) Compute the first derivative of f'(x) = (c) on what interval is f increasing? interval of increasing = (d) On what interval is f decreasing? interval of decreasing = **Show work, in detail, on the scrap paper to receive full credit.
The First derivative: f'(x) = 12x - 15 and the Interval of increasing: (5/4, ∞) and the Interval of decreasing: (-∞, 5/4)
Hi! I'd be happy to help you with your question. Let's compute the first derivative, and then determine the intervals of increasing and decreasing:
Given function: f(x) = 2.3 + 6x^2 - 15x + 3
(a) Compute the first derivative, f'(x):
f'(x) = d(2.3)/dx + d(6x^2)/dx - d(15x)/dx + d(3)/dx
f'(x) = 0 + 12x - 15 + 0
f'(x) = 12x - 15
(c) To find the interval where f is increasing, we need to find where f'(x) > 0:
12x - 15 > 0
12x > 15
x > 15/12
x > 5/4
So, the interval of increasing is (5/4, ∞).
(d) To find the interval where f is decreasing, we need to find where f'(x) < 0:
12x - 15 < 0
12x < 15
x < 15/12
x < 5/4
So, the interval of decreasing is (-∞, 5/4).
Your answer:
- First derivative: f'(x) = 12x - 15
- Interval of increasing: (5/4, ∞)
- Interval of decreasing: (-∞, 5/4)
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A school wants to rent out a laser tag arena the table shows the cost of renting the arena for different numbers of hours suppose the arena charges a constant hourly rate fill in the missing value in the table
hours _______ 5 9 -___________
cost (in dollars ) 500 1,250 __________ 3,500
The constant hourly rate using the given data points is $100 per hour.
To calculate the constant hourly rate, we can use the given data points. For example, let's use the 5-hour rental for $500:
Hourly rate = Total cost / Number of hours
Hourly rate = $500 / 5 hours
Hourly rate = $100 per hour
Now, we can use this hourly rate to find the cost for the missing hour value in the table:
Cost = Hourly rate × Number of hours
Cost = $100 per hour × 9 hours
Cost = $900
So, the table will look like this:
Hours: _______ 5 | 9 | _______
Cost (in dollars): 500 | 1,250 | 3,500
Now we can calculate the missing hours for the $3,500 cost:
Number of hours = Total cost / Hourly rate
Number of hours = $3,500 / $100 per hour
Number of hours = 35 hours
Now, the completed table is:
Hours: _______ 5 | 9 | 35
Cost (in dollars): 500 | 1,250 | 3,500
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A student at a local high school claimed that three-
quarters of 17-year-old students in her high school had
their driver's licenses. To test this claim, a friend of hers
sent an email survey to 45 of the 17-year-olds in her
school, and 34 of those students had their driver's
license. The computer output shows the significance test
and a 95% confidence interval based on the survey data.
Test and Cl for One Proportion
Test of p = 0. 75 vs p +0. 75
Sample X N Sample p 95% CI Z-Value P-Value
1
34 45 0. 755556 (0. 6300, 0. 086 0. 9315
0. 8811)
Based on the computer output, is there convincing
evidence that p, the true proportion of 17-year olds at this
high school with driver's licenses, is not 0. 75?
O No, the P-value of 0. 9315 is very large.
Yes, the P-value of 0. 9315 is very large.
O Yes, the 95% confidence interval contains 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p > 0. 75.
No, the incorrect significance test was performed.
The alternative hypothesis should be p<0. 75.
No, there is not convincing evidence that p, the true proportion of 17-year-olds at this high school with driver's licenses, is not 0.75.
This is because the P-value of 0.9315 is very large, and the 95% confidence interval contains 0.75 (0.6300, 0.8811). This means that there is not enough evidence to reject the null hypothesis that the true proportion of 17-year olds with driver's licenses is 0.75. The 95% confidence interval also supports this, as it includes 0.75. Therefore, there is no convincing evidence to suggest that the student's claim is incorrect.
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A number 5 times as big as M
Answer:
Step-by-step explanation:
If we let M be a number, then 5 times as big as M would be 5M. Not that hard :/
Liang wants to form a chess club. His principal says that he can do that if Liang can find six players, including himself. How would you conduct a simulated model that estimates the probability that Liang will find at least five other players to join the club if he asks eight players who have a 70% chance of agreeing to join the club? Suggest a simulation model for Liang by describing how you would do the following parts
To conduct a simulated model that estimates the probability that Liang will find at least five other players to join the chess club if he asks eight players who have a 70% chance of agreeing to join.
We can use the following steps:
1. Define the variables:
- n: the number of trials (i.e., the number of times Liang asks eight players to join)
- p: the probability of success (i.e., the probability that a player agrees to join the club, which is 0.7)
- k: the number of successes needed (i.e., the number of players, excluding Liang, that he needs to find to form the club, which is 5)
- success: a counter to keep track of the number of successful trials (i.e., the number of times Liang finds at least five players to join)
2. Set the initial value of the success counter to 0.
3. Start a loop that runs n times. In each iteration of the loop:
- Generate a random number between 0 and 1 using a random number generator.
- If the random number is less than or equal to p, increment a "success count" variable.
- If the success count variable reaches k, break out of the loop.
4. After the loop finishes, divide the success count variable by n to get the simulated probability that Liang will find at least five players to join the chess club.
5. Repeat the simulation multiple times (e.g., 1000 times) to obtain a distribution of simulated probabilities.
6. Calculate the mean and standard deviation of the simulated probabilities to estimate the most likely probability that Liang will find at least five players to join the chess club, and the range of probabilities that he is likely to obtain.
Note: This simulation model assumes that each player's decision to join the club is independent of the other players' decisions and that the probability of success (i.e., agreeing to join) is the same for each player. These assumptions may not always be accurate in practice.
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Let a,b,c and d be distinct real numbers. Show that the equation (x-b)(x-c) (x-d) + (x-a)(x-c)(x - d) + (x-a) (x-b)(x-d) + (x - a)(x-b)(x-c) has exactly 3 distinct roul solutions (Hint: Let p(x)= (x-a)(x-b)(x-c)(x-d). Then p(x) = 0 has how many distinct real solutions? Then use logarithmic differentiation to show that p'(x) is given by the expression on the left hand side of (1). Now, apply Rolle's theorem. )
There exists at least one c in the open interval (a, b) such that f'(c) = 0.
There are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.
To prove that the given equation has exactly 3 distinct real solutions, let's follow the steps mentioned in the question.
First, consider the polynomial p(x) = (x-a)(x-b)(x-c)(x-d). Since a, b, c, and d are distinct real numbers, p(x) has 4 distinct real roots, namely a, b, c, and d.
Now, let's find the derivative p'(x) using logarithmic differentiation. Taking the natural logarithm of both sides, we have:
[tex]ln(p(x)) = ln((x-a)(x-b)(x-c)(x-d))[/tex]
Differentiating both sides with respect to x, we get:
[tex]p'(x)/p(x) = 1/(x-a) + 1/(x-b) + 1/(x-c) + 1/(x-d)[/tex]
Multiplying both sides by p(x) and simplifying, we have:
[tex]p'(x) = (x-b)(x-c)(x-d) + (x-a)(x-c)(x-d) + (x-a)(x-b)(x-d) + (x-a)(x-b)(x-c)[/tex]
Now, we apply Rolle's Theorem, which states that if a function is continuous on the closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in the open interval (a, b) such that f'(c) = 0.
Since p(x) has 4 distinct real roots, there must be 3 intervals between these roots where the function p(x) satisfies the conditions of Rolle's Theorem. Therefore, there are 3 distinct points where p'(x) = 0, which corresponds to the 3 distinct real solutions of the given equation.
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the battery life of the iphone has an approximately normal distribution with a mean of 10 hours and a standard deviation of 2 hours. if you randomly select an iphone, what is the probability that the battery will last more than 10 hours?
If you randomly select an iphone, The probability that the battery will last more than 10 hours is 0.5000.
Population mean, µ = 10
Population standard deviation, σ = 2
The likelihood that the battery will survive more than 10 hours is equal to
[tex]= P( X > 10)\\= P( (X-\mu)/\sigma > (10 - 10)/2)\\= P( z > 0)\\= 1- P( z < 0)\\[/tex]
Using excel function:
= 1- NORM.S.DIST(0, TRUE)
= 0.5000
The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that describes a large class of phenomena observed in nature, social sciences, and engineering. It is often called the bell curve because of its characteristic shape, which is symmetric and bell-shaped.
The mean and the standard deviation are the two factors that define the normal distribution. The mean is the center of the distribution, and the standard deviation measures how much the data varies from the mean. The normal distribution has several important properties, including that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
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The drawing shows a bridge design. the measurement of angle 1 is 125°. the measurement of angle 1 and angle 2 equal 180°. classify the relationship between angle 1 and 2, then find the measurement of angle 2.
The measurement of angle 2 is 55°, if the measurement of angle 1 and angle 2 equal 180° and measurement of angle 1 is 125° in the drawing of the bridge design.
The measurement of angle 1 is 125°, and the sum of angle 1 and angle 2 is 180°. The relationship between angle 1 and angle 2 is supplementary since their sum is equal to 180°. To find the measurement of angle 2,
Recall the given information: angle 1 = 125°, and angle 1 + angle 2 = 180°.Set up an equation using the supplementary relationship: 125° + angle 2 = 180°.Subtract 125° from both sides of the equation: angle 2 = 180° - 125°.Calculate the result: angle 2 = 55°.Therefore, angle 2 has a measurement of 55°.
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An experiment was conducted to test the effect of a new dietary supplement for weight loss. Ten men and ten women were given the supplement daily for a month; then the amount of weight each person lost was determined. A significance test was conducted at the α = 0. 05 level for the mean difference in the number of pounds lost between men and women. The test resulted in t = 2. 178 and p = 0. 3. If the alternative hypothesis in question was Ha: μm − μw ≠ 0, where μm equals the mean number of pounds lost by men and μw equals the mean number of pounds lost by women, what conclusion can be drawn? (2 points)
options:
There is not a significant difference in mean weight loss between men and women.
There is sufficient evidence that there is a difference in mean weight loss between men and women.
There is sufficient evidence that, on average, men lose more weight than women.
The proportion of men who lost weight is greater than the proportion of women.
There is insufficient evidence that the proportion of men and women who lost weight is different
The null hypothesis (H0) is that there is no significant difference in mean weight loss between men and women, or μm - μw = 0. The alternative hypothesis (Ha) is that there is a significant difference in mean weight loss between men and women, or μm - μw ≠ 0.
Is there sufficient evidence to support the claim that there is a difference in mean weight loss between men and women in the dietary supplement experiment?The p-value of 0.3 indicates that there is no significant difference in mean weight loss between men and women. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we can conclude that there is not a significant difference in mean weight loss between men and women.The t-value of 2.178 indicates that there is some difference in the mean weight loss between men and women, but the p-value of 0.3 indicates that this difference is not statistically significant. In other words, the observed difference in mean weight loss could have occurred by chance, and we cannot reject the null hypothesis that there is no difference in mean weight loss between men and women. Therefore, we conclude that there is not a significant difference in mean weight loss between men and women.Learn more about experiment,
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Find the probability that a randomly selected within the square falls in the red shaded area
Therefore, the probability that a randomly selected point within the square falls in the red-shaded area is 68%.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event A is denoted as P(A). To calculate the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes.
Here,
The area of the red-shaded region is the area of the square minus the area of the white right-angled triangle. The area of the square is the length of one side squared, which is:
Area of square = 5 cm × 5 cm
= 25 cm²
The area of the right-angled triangle is one-half the base times the perpendicular height, which is:
Area of triangle = (1/2) × base × height
= (1/2) × 4 cm × 4 cm
= 8 cm²
Therefore, the area of the red-shaded region is:
Area of red-shaded region = Area of square - Area of triangle
= 25 cm² - 8 cm²
= 17 cm²
To find the probability that a randomly selected point within the square falls in the red-shaded area, we need to divide the area of the red-shaded region by the total area of the square, which is:
Probability = Area of red-shaded region / Area of square
Probability = 17 cm² / 25 cm²
= 0.68 or 68%
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Simplify (4x − 6) + (5x + 1). Group of answer choices 9x + 5 9x − 5 x − 5 −x − 5
Answer:
Combining like terms,
(4x - 6) + (5x + 1) = 9x - 5
On a coordinate plane, 2 triangles are shown. Triangle D E F has points (6, 4), (5, 8) and (1, 2). Triangle R S U has points (negative 2, 4), (negative 3, 0), and (2, negative 2).
Triangle DEF is reflected over the y-axis, and then translated down 4 units and right 3 units. Which congruency statement describes the figures?
ΔDEF ≅ ΔSUR
ΔDEF ≅ ΔSRU
ΔDEF ≅ ΔRSU
ΔDEF ≅ ΔRUS
The congruency statement that describes the figures is:
ΔDEF ≅ ΔRSU
To answer your question, let's first find the image of triangle DEF after reflecting over the y-axis and then translating down 4 units and right 3 units.
1. Reflect ΔDEF over the y-axis:
D'(−6, 4), E'(−5, 8), F'(−1, 2)
2. Translate ΔD'E'F' down 4 units and right 3 units:
D''(−3, 0), E''(−2, 4), F''(2, −2)
Now, we have ΔD''E''F'' with points (−3, 0), (−2, 4), and (2, −2). Comparing this to ΔRSU with points (−2, 4), (−3, 0), and (2, −2), we can see that:
ΔD''E''F'' ≅ ΔRSU
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Answer:
ΔDEF ≅ ΔRSU
Step-by-step explanation:
Find the length of the radius r
Step-by-step explanation:
Use Pythagorean theorem for right triangles
c^2 = a^2 + b^2 where c = hypotenuse and a and b are the legs
8.6^2 = 5^2 + r^2
8.6^2 - 5^2 = r^2
r = ~ 7 units
Solve for x.
Round to the nearest tenth.
The measure of the angle x in the circle is 65 degrees
Solving for x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
On the circle, we have the angle at the vertex of the triangle to be
Angle = 100/2
Angle = 50
The sum of angles in a triangle is 180
So, we have
x + x + 50 = 180
Evaluate the like terms,
2x = 130
So, we have
x = 65
Hence, the angle is 65 degrees
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Can someone please help me ASAP? It’s due tomorrow. Show work please
The number of possible outcomes of the compound event of selecting a card, spinning the spinner, and tossing a coin is B. 72 outcomes.
How to find the number of possible outcomes ?To determine the number of possible outcomes for the compound event, we need to multiply the number of outcomes for each individual event.
There are 12 cards labeled 1 through 12, so there are 12 possible outcomes for selecting a card. The spinner is divided into three equal-sized portions, so there are 3 possible outcomes for spinning the spinner. There are 2 possible outcomes for tossing a coin (heads or tails).
the total number of possible outcomes for the compound event:
12 (selecting a card) x 3 (spinning the spinner) x 2 (tossing a coin) = 72
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50 POINTS ASAP Polygon D has been dilated to create polygon D′.
Polygon D with top and bottom sides labeled 8 and left and right sides labeled 9.5. Polygon D prime with top and bottom sides labeled 9.6 and left and right sides labeled 11.4.
Determine the scale factor used to create the image.
Scale factor of 1.6
Scale factor of 1.2
Scale factor of 0.9
Scale factor of 0.8
Answer:
1.2
Step-by-step explanation:
based on your description the top sides are corresponding pairs, the bottom sides are corresponding sides, the left sides are corresponding sides, and the right sides are corresponding sides between the 2 polygons.
the dilation (scaling) is happening for all points on the polygon with the same scaling factor.
so, we only need to find the scaling factor f between one of these corresponding pairs.
8×f = 9.6
f = 9.6/8 = 1.2
Answer: The answer is 1.2
Step-by-step explanation:
Just trust me.
Sebastian is 12 34 years old. camden is 1 38 years older than sebastian and jane is 1 15 years older than camden. how old is jane?
Jane is 14 years old, if Sebastian is 12 34 years old. Camden is 1 38 years older than Sebastian and Jane is 1 15 years older than Camden.
To find out how old Jane is, we will first determine the ages of Sebastian and Camden, then add the additional years to find Jane's age.
Sebastian is 12 34 years old, but the correct age should be 12 years old (ignoring the typo).
Camden is 1 38 years older than Sebastian, which should be correctly written as 1 year older. So, Camden's age is 12 (Sebastian's age) + 1 = 13 years old.
Jane is 1 15 years older than Camden, which should be correctly written as 1 year older. Therefore, Jane's age is 13 (Camden's age) + 1 = 14 years old.
So, Jane is 14 years old.
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Be Precise The base of a triangle is 2 ft. The
height of the triangle is 15 in. What is the area
of the triangle in square inches?
Thus, the area of triangle for the given values of height and base is found as: 180 sq. in.
Explain about the conversion units:A number of steps are involved in the Unit of Conversion process, which involves multiplying or dividing by a numerical factor. There are numerous ways to measure things like weight, separation, and temperature.
Unit conversion is the process of changing the unit of measurement for a comparable quantity by multiplying or dividing by conversion factors.
Scientific notation is used to express the units, which are then translated into numerical values in accordance with the amounts.
Given data:
base of triangle b = 2 ft.Height h = 15 in.We know that,
1 foot = 12 in.
2 feet = 12*2 = 24 in.
Area of triangle = 1/2 * b * h
Area of triangle = 1/2 * 24 * 15
Area of triangle = 12* 15
Area of triangle = 180 sq. in
Thus, the area of triangle for the given values of height and base is found as: 180 sq. in.
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8 pound of peanuts cost 24 dollars. 6 pounds of walnuts cost half as much. Which is more expensive and by how much.
Answer:
Step-by-step explanation:
The cost of 1 pound of peanuts can be found by dividing the total cost of 8 pounds by 8:
Cost of 1 pound of peanuts = $24 / 8 pounds = $3 per pound
The cost of 1 pound of walnuts can be found by dividing the total cost of 6 pounds by 6 and then multiplying by 2 (since the cost of 6 pounds is half that of the peanuts for the same weight):
Cost of 1 pound of walnuts = ($24 / 6 pounds) x 2 = $8 per pound
Therefore, we see that walnuts are more expensive than peanuts by $5 per pound ($8 - $3).
In other words, 1 pound of walnuts costs $5 more than 1 pound of peanuts.
Find the number(s)
b
such that the average value of
f(x)=6x 2
−38x+40
on the interval
[0,b]
is equal to 16 . Select the correct method. Set
b
1
f(3)=16
and solve for
b
Set
f(b)=16
and solve for
b
Set
∫ 0
b
f(x)dx=16
and solve for
b
Set
b
1
∫ 0
b
f(x)dx=16
and solve for
b
b=
Use a comma to separate the answers as needed.
The value(s) of b that satisfies the given condition is/are 0.506 and 5.327.
How to find the average value of a given function over the interval?We can use the method of setting the integral of f(x) over [0,b] equal to 16 and solving for b.
[tex]\begin{equation}\int 0 b f(x) d x=16\end{equation}[/tex]
Substituting [tex]f(x) = 6x^2 - 38x + 40[/tex], we get:
[tex]\begin{equation}\int 0 b\left(6 x^{\wedge} 2-38 x+40\right) d x=16\end{equation}[/tex]
Integrating with respect to x, we get:
[tex][2x^3 - 19x^2 + 40x]0b = 16[/tex]
Substituting b and simplifying, we get:
[tex]2b^3 - 19b^2 + 40b - 16 = 0[/tex]
Using numerical methods or polynomial factorization, we can find that the solutions to this equation are approximately 0.506 and 5.327.
Therefore, the value(s) of b that satisfies the given condition is/are 0.506 and 5.327.
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Write the absolute value inequality in form |x-b| c that has the solution set x<-5 or x>7
The absolute value inequality in form |x-b| < c that has the solution set x<-5 or x>7 is |x-1| < 7
To write an absolute value inequality in the form |x-b| < c, we need to think about what this form means.
The expression |x-b| represents the distance between x and b on the number line. Therefore, |x-b| < c means that the distance between x and b is less than c.
Now, let's consider the given solution set: x < -5 or x > 7. We can see that the midpoint between -5 and 7 is 1, so we choose b = 1. Then, we need to determine c, which is the maximum distance between b and any of the solutions.
If we take x = -6 (which is less than -5), then |x-b| = |-6-1| = 7. Similarly, if we take x = 8 (which is greater than 7), then |x-b| = |8-1| = 7. Therefore, the maximum distance is 7.
Putting it all together, we get the absolute value inequality:
|x-1| < 7
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If the arc length of a circle with a radius of 5 cm is 18.5 cm, what is the area of the sector, to the nearest hundredth
i need it quick please
The area of the sector, to the nearest hundredth, is 45.87 cm^2.
The formula for the length of an arc of a circle is L = rθ, where L is the arc length, r is the radius, and θ is the angle in radians subtended by the arc.
We solve for θ by dividing both sides by r: θ = L/r.
In this case, r = 5 cm and L = 18.5 cm, so θ = 18.5/5 = 3.7 radians.
The formula for the area of a sector of a circle is A = (1/2)r^2θ.
Plugging in the values, we get A = (1/2)(5^2)(3.7) ≈ 45.87 cm^2.
Therefore, the area of the sector, to the nearest hundredth, is 45.87 cm^2.
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Solve the trigonometric equation in the interval [0, 2π). give the exact value, if possible; otherwise, round your answer to two decimal places. (enter your answers as a comma-separated list.) 2 cos2(x) + cos(2x) = 0 x =
To solve the trigonometric equation 2cos^2(x) + cos(2x) = 0 in the interval [0, 2π), we will first use the double angle formula for cos(2x) and then solve for x. Recall that cos(2x) = 2cos^2(x) - 1.
Substitute this into the equation: 2cos^2(x) + (2cos^2(x) - 1) = 0 Combine the terms: 4cos^2(x) - 1 = 0 Now, isolate cos^2(x): cos^2(x) = 1/4 Take the square root of both sides: cos(x) = ±√(1/4) = ±1/2 Now, find the values of x in the interval [0, 2π) that satisfy the equation: For cos(x) = 1/2: x = π/3, 5π/3 For cos(x) = -1/2: x = 2π/3, 4π/3 Combine the answers as a comma-separated list: x = π/3, 2π/3, 4π/3, 5π/3
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Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank.
Which statement about the savings plans is true?
Responses
Natalie uses a safer way to save money because she can protect her piggy bank.
Maria's way of saving money allows her to earn interest and make her money grow.
Maria will have less money because she must pay sales tax on her money.
Natalie's method of saving is better because Maria must pay interest on her money.
In a case whereby Natalie saves money in her piggy bank. Maria saves money in a savings account at a bank the statement about the savings plans that is true is B.Maria's way of saving money allows her to earn interest and make her money grow.
What is savings account ?An efficient approach to keep your money safe and earning interest is in a savings account. You can keep your savings in a liquid state with a savings account, which allows you to access your money anytime you need to, while also creating some breathing room between your savings and your daily spending requirements.
Because of their safety, liquidity, and potential for collecting interest, savings accounts are a suitable way to put money set aside for future use. These accounts are perfect for saving for short-term objectives like a trip or home repair or for your emergency fund.
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Select all ordered pairs that satisfy the function y=-4x+20
6,4
0,20
-4,20
10,-20
The ordered pairs that satisfy the function is B)(0,20) and D)(10,-20).
What is function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Here the given function is y=-4x+20.
Now put x=6 and y=4 then,
=> 4=-4(6)+20
=> 4 = -24+20
=> 4 ≠ -4.
Then the coordinate (6,4) dost not satisfy the function.
Put x=0 and y=20 then,
=> 20 = -4(0)+20
=> 20= 0+20
=> 20=20
Hence the coordinate (0,20) satisfy the function.
Now put x=-4 and y=20 then,
=> 20 = -4(-4)+20
=> 20 = 16+20
=> 20 ≠ 36
Hence the coordinate (-4,20) does not satisfy the function.
Now put x=10 and y=-20 then,
=> -20 = -4(10)+20
=> -20 = -40+20
=> -20=-20
Then the coordinate (10,-20) satisfy the function.
Hence the ordered pairs that satisfy the function is B)(0,20) and D)(10,-20).
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