The measure of angle B, rounded to the nearest degree, is 37 degrees.
How to find the measure of angle B when tan(B) is equal to 3/4?In trigonometry, the tangent function (tan) relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle.
To find the measure of angle B, we use the inverse tangent function (arctan) with the given tangent value of 3/4:
B = arctan(3/4)
Using a calculator or a trigonometric table, we find that arctan(3/4) is approximately 36.87 degrees. Round the result to the nearest degree to obtain the final measure of angle B.
Therefore, the measure of angle B, rounded to the nearest degree, is 37 degrees.
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What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.
a cylinder has radius labeled 2.2 meters and height labeled 6.5 meters
99 square meters
105 square meters
117 square meters
120 square meters
The surface area of the cylinder, rounded to the nearest square meter, is: D. 120 square meters
What is the Surface Area of a Cylinder?The surface area of a cylinder can be calculated by using the formula expressed as:
SA = 2πr(h + r), where r is the radius and h is the height.
Given the following:
π = 3.14
radius (r) = 2.2 m
height of the cylinder (h) = 6.5 m
Plug in the values:
SA = 2 * 3.14 * 2.2 * (6.5 + 2.2)
SA ≈ 120 square meters (rounded to the nearest square meter)
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Suppose a population is known to be approximately normal and you are finding a 98% confidence interval with a sample size of 32. Identify the critical value you will use if you are using a
The critical value you will use for your 98% confidence interval with a sample size of 32 is 2.33.
When finding a 98% confidence interval for a normally distributed population with a sample size of 32, you will need to use a critical value from the standard normal (z) distribution.
To find the critical value, you can refer to a z-table or use a calculator with statistical functions. For a 98% confidence interval, you will need the z-score that corresponds to the middle 98% of the data, leaving 1% in each tail. This z-score is approximately 2.33.
So, the critical value you will use for your 98% confidence interval with a sample size of 32 is 2.33.
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- My family wants to start a food business. Every Sunday, the family prepares the best dishes. We need a loan to start our business as a family. We decided to get an SBA Loan and they offered a PPP (Paycheck Protection Program) loan option. The initial amount will be 20,000. This loan has an interest 4. 5% compounded quarterly. What will be the account balance after 10 years?
I’ll mark as BRANLIEST!!
35 POINTS!!
This loan has an interest 4. 5% compounded quarterly, account balance after 10 years:
The initial loan amount is $20,000, and it has an interest rate of 4.5% compounded quarterly. You would like to know the account balance after 10 years.
To calculate the account balance, we will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan
P = the initial loan amount ($20,000)
r = the annual interest rate (0.045)
n = the number of times the interest is compounded per year (4, since it is compounded quarterly)
t = the number of years (10)
Plugging in the values:
A = 20000(1 + 0.045/4)^(4*10)
A = 20000(1.01125)^40
A ≈ 30,708.94
The account balance after 10 years will be approximately $30,708.94.
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The table shows the number of beads used to make a necklace.
Ginger wants to make a smaller necklace using the same ratio of pink to white beads.
How many different necklaces could Ginger make?
How do you know?
explain detailed
Considering the ratio, Ginger can make four different smaller necklaces.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is given as follows:
a to b.
Which is also the division of the two amounts.
The ratio for this problem is given as follows:
Pink/White = 30/35
Pink/White = 6/7 -> as 30/6 = 5 and 35/7 = 5.
5 - 1 = 4, hence, considering the ratio, Ginger can make four different smaller necklaces.
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What is the measure of angle A? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠A=° Right triangle A B C, with right angle C B A. Side A B is three centimeters, side B C is four centimeters, and side C A is five centimeters.
The measure of angle A is given as follows:
m < A = 53.13º.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.Angle A is opposite to a side of length 4 cm, while the hypotenuse is of 5 cm, hence it's measure is obtained as follows:
sin(A) = 4/5
m < A = arcsin(4/5)
m < A = 53.13º.
Missing InformationWe have a right triangle, in which the side length opposite to angle A is BC = 4, while the hypotenuse is CA = 5.
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The average weight of Carl, Carla, Carmen, Clark, and Cathy is 107.6 lb. Cathy weighs 115 lb. What is the average weight of the other four? Show your work.
Answer:
Step-by-step explanation:
Let's start by finding the total weight of all five people:
Total weight = Average weight x Number of people
Total weight = 107.6 x 5
Total weight = 538
We know that Cathy weighs 115 lb, so we can subtract her weight from the total weight to find the total weight of the other four people:
Total weight of other four = Total weight - Cathy's weight
Total weight of other four = 538 - 115
Total weight of other four = 423
To find the average weight of the other four, we can divide the total weight of the other four by the number of people:
Average weight of other four = Total weight of other four / Number of people
Average weight of other four = 423 / 4
Average weight of other four = 105.75 lb
Therefore, the average weight of the other four is 105.75 lb.
Use the first three non-zero terms of a Maclaurin series to estimate the integral from 0 to 1 of the cosine of x squared, dx.
0. 905
0. 904
0. 806
1. 16
Using the first three non-zero terms of a Maclaurin series, the estimated value of the integral from 0 to 1 of the cosine of x squared, dx is 0.905
To estimate the integral from 0 to 1 of the cosine of x squared, dx using the first three non-zero terms of a Maclaurin series, we first need to find the Maclaurin series for cosine of x squared:
cos(x^2) = 1 - x^4/2! + x^8/4! - x^12/6! + ...
The first three non-zero terms are 1, -x^4/2!, and x^8/4!.
Now we can use these terms to estimate the integral from 0 to 1:
∫₀¹ cos(x²) dx ≈ ∫₀¹ [1 - x^4/2! + x^8/4!] dx
Integrating term by term, we get:
∫₀¹ [1 - x^4/2! + x^8/4!] dx ≈ [x - x^5/5! + x^9/9!] from 0 to 1
Plugging in 1 and 0, respectively, and simplifying, we get:
[x - x^5/5! + x^9/9!] evaluated at x=1 - [x - x^5/5! + x^9/9!] evaluated at x=0
= [1 - 1/120 + 1/6561] - [0 - 0 + 0]
≈ 0.905
Therefore, the estimated value of the integral from 0 to 1 of the cosine of x squared, dx using the first three non-zero terms of a Maclaurin series is 0.905.
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PLSSS HELPP
1a. Model the periodic motion of the horses using an
equation and a graph.
Horse Equation: Use function notation in degrees. Your
function will graph below.
1a. The period of the motion is the time it takes for the horse to complete one full cycle of motion, and it is given by:
T = 2π/ω.
See attached graph.
1b. The period of the motion is the time it takes for the carousel to complete one full cycle of motion, and it is also given by:
T = 2π/ω.
1a.
let's assume that the motion of the horse can be modeled by a simple harmonic motion. The equation for simple harmonic motion is:
y = A sin(ωt + φ)
where:
y is the displacement from the equilibrium position
A is the amplitude (maximum displacement)
ω is the angular frequency (2π times the frequency)
t is time
φ is the phase angle
Assuming that the horse's motion is in a vertical direction and that the highest point of its motion corresponds to y = 0, we can write the equation as:
y = A sin(ωt)
where A is the amplitude of the motion and ω is the angular frequency.
We can plot this function as a sine wave on a graph, where the horizontal axis represents time and the vertical axis represents displacement. The period of the motion is the time it takes for the horse to complete one full cycle of motion, and it is given by:
T = 2π/ω
To determine when Ivan will get his next opportunity to take a perfect shot, we need to know the period of the horse's motion. Without additional information, it's difficult to estimate the period accurately.
The graph of the carousel equation θ = A cos(ωt) can be labeled as follows:
1b.
The motion of the carousel can also be modeled as a simple harmonic motion, with the equation:
θ = A cos(ωt + φ)
where:
θ is the angular displacement from the equilibrium position
A is the amplitude (maximum angular displacement)
ω is the angular frequency (2π times the frequency)
t is time
φ is the phase angle
The period of the motion is the time it takes for the carousel to complete one full cycle of motion, and it is given by:
T = 2π/ω
To determine when Ivan will get his next opportunity to take a perfect shot, we need to know the period of the carousel's motion. Without additional information, it's difficult to estimate the period accurately.
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An amusement park charges $4. 25 for admission, plus $1. 50 for each ride ticket. Chase has $30 to spend on admission and ride tickets. What is the greatest number of ride tickets Chase can buy?
The greatest number of ride tickets Chase can buy is 17 and spend $30 for total cost of admission.
To solve this problem, we need to use algebraic equations. Let x be the number of ride tickets that Chase can buy. We know that the total amount of money Chase can spend on admission and ride tickets is $30, so we can write:
4.25 + 1.5x = 30
To solve for x, we can isolate the variable by subtracting 4.25 from both sides and then dividing by 1.5:
1.5x = 25.75
x = 17.17
Since Chase can't buy a fractional number of ride tickets, we need to round down to the nearest whole number. Therefore, Chase can buy a maximum of 17 ride tickets with his $30 budget.
To double-check our answer, we can calculate the total cost of admission and 17 ride tickets:
4.25 + 1.5(17) = 29.25
This is less than $30, so it is indeed possible for Chase to buy 17 ride tickets within his budget.
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Pentagon A'B'C'D'E'A
′
B
′
C
′
D
′
E
′
A, prime, B, prime, C, prime, D, prime, E, prime is the image of pentagon ABCDEABCDEA, B, C, D, E under a dilation with a scale factor of \dfrac{1}{2}
2
1
start fraction, 1, divided by, 2, end fraction.
The length of segment C'D' is given as follows:
C'D' = 2.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The length of segment CD is given as follows:
CD = 4. (4 vertical units of difference).
The scale factor is given as follows:
k = 1/2.
Hence the length of segment C'D' is given as follows:
C'D' = 1/2 x 4 = 2.
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Fill in the boxes 3(n+7) = (3)( ) + (3)( ) = +
the final result will be 3n + 21
what is ditribustion propety?
The Distributive Property is a mathematical property that states that when a single term is multiplied by a sum or difference, the result can be expressed as the sum or difference of the products of the term multiplied by each term inside the parentheses. It is often used to simplify expressions and equations in algebra. 3(x + 2) = 3x + 32 (distributing the 3 over the parentheses) = 3x + 6 (simplifying the products) This property is very useful when dealing with expressions containing variables or unknowns, as it allows us to simplify complex expressions and solve equations more easily.
using distribution propety
3(n + 7)
= (3)(n) + (3)(7)
= 3n + 21
Hence the final result will be 3n + 21
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City A and City B had two different temperatures on a particular day. On that day, four times the temperature of City A was 7° C more than three times the temperature of City B. The temperature of City A minus three times the temperature of City B was −5° C. The following system of equations models this scenario:
4x = 7 + 3y
x − 3y = −5
What was the temperature of City A and City B on that day?
The temperature of City A and City B on that day was 4°C and 3°C respectively.
How to solve an equation?Let x represent the temperature of city A and y represent the temperature of city B.
Four times the temperature of City A was 7° C more than three times the temperature of City B, hence:
4x = 3y + 7
4x - 3y = 7 (1)
The temperature of City A minus three times the temperature of City B was −5° C, hence:
x - 3y = -5 (2)
From both equations, solving simultaneously:
x = 4, y = 3.
The temperature of City A and City B on that day was 4°C and 3°C respectively.
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What is the ratio of hours spent at soccer practice to hours spent at a birthday party? choose 1 answer:
The ratio of hours spent at soccer practice to hours spent at a birthday party can be represented as 2 for every 3
To provide an accurate ratio, I would need the specific number of hours spent at both soccer practice and the birthday party.
Once you provide that information, you can create the ratio by putting the two numbers in the form 2 for every 3.
For example, if you spent 3 hours at soccer practice and 2 hours at a birthday party, the ratio would be 3:2. This means that for every 3 hours spent at soccer practice, you spent 2 hours at the birthday party.
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The table shows how many hours Sara spent at several activities one Saturday.
Activity "Hours
Soccer practice 2
Birthday party 3
Science project 1
What is the ratio of hours spent at soccer practice to hours spent at a birthday party?
Choose 1 answer:
1 for every 2
B
2 for every 1
2 for every 3
3 for every 2
12
Find the lowest common multiple (LCM) of 28, 42 and 63
Show your working clearly.
Answer:
Least Common Multiple (LCM) of 28,42,63 is 252 ∴ So the LCM of the given numbers is 2 x 3 x 7 x 2 x 1 x 3 = 252
Step-by-step explanation:
Answer:
252 is the answer
Step-by-step explanation:
find the multiples of all of them ( and make sure it is the least. )
28:
28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308
42:
42, 84, 126, 168, 210, 252, 294, 336
63:
63, 126, 189, 252, 315, 378
bolded + undurlined is the answer
you see that 252 is the answer
252 is the answer
Sara reduced the time it takes her to run a mile from 12 minutes to 8 minutes. Which is closest to Sara's
percent decrease in the time it takes her to run a mile?
A. 14%
B. 25%
C. 33%
D. 75%
The closest answer is C. 33%.
We can use the percent decrease formula to calculate Sara's percent decrease in the time it takes her to run a mile:
percent decrease = [(original value - new value) / original value] x 100%
In this case, Sara's original time was 12 minutes and her new time is 8 minutes, so we have:
percent decrease = [(12 - 8) / 12] x 100%
percent decrease = (4 / 12) x 100%
percent decrease = 0.33 x 100%
percent decrease = 33%
Therefore, the closest answer is C. 33%.
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The start of an arithmetic sequence is 29, 17, 21, 25, The rule for the sequence can be written in the form xn=cn+d, where c and d are numbers. a) By first calculating the values of c and d, work out the rule for the sequence. b) What is the value of x11?
Answer:
Step-by-step explanation:
The value of 2s in 43,290 is 2,000, while the value of 2s in 32,865 is 20.
B. 200 is 1/20 the value of 2,000.
This statement is correct, as 200 is 1/10 of 2,000, and there are two 0s in the value of 2s in 43,290 compared to one 0 in the value of 2s in 32,865.
Item 8
Find the measure of a central angle of a regular polygon with 7 sides. Round your answer to the nearest tenth of a degree, if necessary
The measure of a central angle of a regular polygon with 7 sides is approximately 51.4 degrees.
What is the central angle in a regular 7-sided polygon, rounded to the nearest tenth of a degree?For a regular polygon with 7 sides, we can substitute n = 7 into the formula:
central angle = 360 degrees / 7
central angle ≈ 51.4 degrees
A regular polygon is a polygon with equal sides and equal angles. The measure of each interior angle of a regular polygon with n sides is given by the formula:
interior angle = (n-2) x 180 degrees / n
For example, for a regular polygon with 7 sides:
interior angle = (7-2) x 180 degrees / 7
interior angle = 5 x 180 degrees / 7
interior angle ≈ 128.6 degrees
Since a central angle of a regular polygon is an angle formed by two consecutive radii from the center of the polygon, the measure of a central angle is equal to the measure of the exterior angle.
The measure of an exterior angle of a regular polygon with n sides is given by the formula:
exterior angle = 360 degrees / n
For a regular polygon with 7 sides, we can use the formula above to find the measure of each exterior angle:
exterior angle = 360 degrees / 7
exterior angle ≈ 51.4 degrees
Therefore, the measure of a central angle of a regular polygon with 7 sides is approximately 51.4 degrees, rounded to the nearest tenth of a degree as requested.
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help asspppp.............
The value of x and y in the right triangle are 11.31 units and 8 units respectively.
The tangential ratio of ∠P and ∠Q are 16 / 12 and 12 / 16 respectively.
How to find the side and angle of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios as follows:
tan 45 = opposite / adjacent
tan 45 = 8 / y
cross multiply
y = 8 / tan 45
y = 8 /1
y = 8 units
Therefore,
sin 45 = opposite / hypotenuse
sin 45 = 8 / x
cross multiply
x = 8 / sin 45
x = 11.313816999
x = 11.31 units
Let's find the tangent ratio of ∠p and ∠q.
Hence,
tan ∠P = 16 / 12
tan ∠Q = 12 / 16
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B. It will be a curve.
C. It will be a line.
D. There is no way to tell.
The given equation on a graph can be described best as C. It will be a line.
Why would this be a line ?The given equation is a linear equation because it has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation can be rewritten as:
y = 3x + 15 - 64
y = 3x - 49
Since it's a linear equation, it will represent a straight line on the graph that can be found by using the equation and some values of x, to find values of y and then plotting them.
In conclusion, the best answer is C. It will be a line.
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The full question is:
An equation is given to be 3x + 15 = 64
What will this be on a graph ?
A. It will be irregular
B. It will be a curve.
C. It will be a line.
D. There is no way to tell.
Calcula la longitud del puente que se quiere construir entre los puntos A y B, para lo cual se sabe que los ángulos ABO Y OAB miden 32" y 48° respectivamente y que la
distancia entre Ay O medida en línea recta es 120 m. (sugerencia, trace una linea vertical desde o hasta el segemto AB).
La longitude del Puente entre loss punts A y B es de aproximadamente 97.9 metros.
How to calculate the bridge length?Para calcular la longitud del puente entre los puntos A y B, podemos utilizar el teorema del seno en el triángulo OAB.
Primero,trazamos una línea vertical desde O hasta el segmento AB, creando un triángulo rectángulo OAD. La distancia entre A y O, medida en línea recta, es de 120 m.
Luego, utilizando el ángulo OAB, que mide 48 grados, y el ángulo ABO, que mide 32 minutos (o 32/60 grados), podemos encontrar el tercer ángulo del triángulo OAB aplicando la propiedad de que la suma de los ángulos de un triángulo es 180 grados.
El tercer ángulo del triángulo OAB será: 180 - 48 - (32/60) ≈ 101.467 grados.
Ahora, aplicamos el teorema del seno:
sen(OAB) / AO = sen(ABO) / BO
Despejando BO
BO = (AO * sen(ABO)) / sen(OAB)
Sustituyendo los valores conocidos:
BO = (120 * sen(48)) / sen(101.467) ≈ 120 * 0.7431 / 0.9933 ≈ 89.568 m
Por lo tanto, la longitud del puente que se quiere construir entre los puntos A y B es aproximadamente 89.568 metros.
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Gazza and Julia have each cut a rectangle out of paper. One side is 10 cm. The other side is n cm. (a) They write down expressions for the perimeter of the rectangle. Julia writes Gazza writes 2n+20 2(n + 10) Put a circle around the correct statement below.
Julia is correct and Gazza is wrong.
Gazza is correct and julia is wrong.
Both are correct.
Both are wrong.
The correct statement regarding the perimeter of the rectangle is given as follows:
Both are correct.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
The rectangle in this problem has:
Two sides of n cm.Two sides of 10 cm.Hence the perimeter is given as follows:
2 x 10 + 2 x n = 2 x (10 + n) = 20 + 2n = 2n + 20 cm.
Hence both are correct.
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A punch recipe requires 2 cups of cranberry juice to make 3 gallons of punch. Using the same recipe, what is the amount of cranberry juice needed for 1 gallon of punch?
Answer:
To make 3 gallons of punch, you need 2 cups of cranberry juice.
We can set up a proportion to find out how much cranberry juice is needed for 1 gallon of punch:
2 cups / 3 gallons = x cups / 1 gallon
To solve for x, we can cross-multiply:
2 cups * 1 gallon = 3 gallons * x cups
2 cups = 3x
x = 2/3 cup
Therefore, you would need 2/3 cup of cranberry juice to make 1 gallon of punch using this recipe.
Marcus charges 130$ per week to pet sit. Next week he is offering an 18% discount. What is the amount of the discount?
Answer:23.4
Step-by-step explanation: 18 divided by 130
The amount of the discount is $23.40.
The problem asks us to find the amount of the discount given a percentage discount on a known price. To do this, we use the formula for calculating a percentage of a number.
To calculate the discount amount, we need to find 18% of the original price, which is $130 per week.
We can start by calculating 18% of $130:
Discount = 0.18 * $130 = $23.40
Therefore, the amount of the discount is $23.40.
Select the correct answer.
What is the domain of the exponential function shown in the graph?
A. x ≥ -1
B.-∞ < x <∞
C. x< 0
D.x ≤ -1
Answer:
Step-by-step explanation:
cle Graphs MC)The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.circle graph titled San Francisco Residents' 9, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80
Do couples get engaged or not? If they are engaged, how long did they date before becoming engaged? A poll of 1000 couples conducted by Bruskin and Goldring Research for Korbel Champagne Cellars gave Time Never Engaged Number of Couples 200 the following information: Time Number of Couples Never Engaged 200 Less than 1 year 240 1 to 2 years 210 More than 2 years 350 What is the sample space in this problem?
The sample space in this problem is the total number of couples surveyed, which is 1000.
The sample space in probability refers to the set of all possible outcomes of an experiment. In this case, the experiment is the survey conducted by Bruskin and Goldring Research, and the possible outcomes are the different categories of time taken by couples before getting engaged.
The given information provides the number of couples in each category, which can be added to find the total number of couples surveyed:
Sample space = Number of couples never engaged + Number of couples engaged for less than 1 year + Number of couples engaged for 1 to 2 years + Number of couples engaged for more than 2 years
Sample space = 200 + 240 + 210 + 350
Sample space = 1000
Therefore, the sample space in this problem is 1000, which represents the total number of couples surveyed by the research firm.
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Which proportion is correct?4/10=3/61/2=7/81/2=3/64/10=7/8
Determine which proportion is correct, we will compare the cross products of each proportion. The correct proportion will have equal cross products. The correct proportion is 1/2 = 3/6.
1. 4/10 = 3/6
To check this proportion, we'll calculate the cross products:
(4 * 6) = (10 * 3)
24 = 30
Since 24 ≠ 30, this proportion is incorrect.
2. 1/2 = 7/8
To check this proportion, we'll calculate the cross products:
(1 * 8) = (2 * 7)
8 = 14
Since 8 ≠ 14, this proportion is incorrect.
3. 1/2 = 3/6
To check this proportion, we'll calculate the cross products:
(1 * 6) = (2 * 3)
6 = 6
Since 6 = 6, this proportion is correct.
4. 4/10 = 7/8
To check this proportion, we'll calculate the cross products:
(4 * 8) = (10 * 7)
32 = 70
Since 32 ≠ 70, this proportion is incorrect
So, the correct proportion is 1/2 = 3/6.
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A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with a = 19. 0 milligrams. Construct a 95% confidence interval for the
true mean cholesterol content,, of all such eggs.
We can say with 95% confidence that the true mean cholesterol content of all such eggs is between 223.99 milligrams and 232.01 milligrams.
To construct a 95% confidence interval for the true mean cholesterol content of all such eggs, we can use the following formula:
CI = X ± Zα/2 * σ/√n
where:
X = sample mean = 228 milligrams
Zα/2 = the critical value from the standard normal distribution corresponding to a 95% confidence level, which is 1.96
σ = population standard deviation = 19.0 milligrams
n = sample size = 82
Substituting the values into the formula, we get:
CI = 228 ± 1.96 * 19.0/√82
= 228 ± 4.01
= (223.99, 232.01)
Therefore, we can say with 95% confidence that the true mean cholesterol content of all such eggs is between 223.99 milligrams and 232.01 milligrams.
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Scores at a local high school on the Algebra 1 Midterm are extremely skewed left with a mean of 65 and a standard deviation of 8. A guidance counselor takes a random sample of 10 students and calculates the mean score, x¯¯¯.
(a) Calculate the mean and standard deviation of the sampling distribution of x¯¯¯
(b) Would it be appropriate to use a normal distribution to model the sampling distribution? Justify your answer
The mean of the sampling distribution is 65 and the standard deviation is 2.53. Yes, it would be appropriate to use a normal distribution to model the sampling distribution of x¯¯¯ due to the central limit theorem.
(a) To calculate the mean of the sampling distribution of x¯ ¯ ¯, we can use the formula:
μx¯ ¯ ¯ = μ = 65
This means that the mean of the sampling distribution of x¯ ¯ ¯ is equal to the population mean of 65.
To calculate the standard deviation of the sampling distribution of x¯ ¯ ¯, we can use the formula:
σx¯ ¯ ¯ = σ/√n = 8/√10 ≈ 2.53
This means that the standard deviation of the sampling distribution of x¯ ¯ ¯ is approximately 2.53.
(b) Yes, it would be appropriate to use a normal distribution to model the sampling distribution because of the Central Limit Theorem.
The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.
In this case, we have a sample size of 10, which is relatively small, but it is still large enough for us to assume that the sampling distribution of x¯ ¯ ¯ is approximately normal. Additionally, the population distribution is not too skewed, so this further supports the use of a normal distribution to model the sampling distribution.
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Consider the function f(x) = 1 – 5x², -3 ≤ x ≤ 2. The absolute maximum value is and this occurs at x equals The absolute minimum value is and this occurs at x equals
The absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.
To find the absolute maximum and minimum values of the function f(x) = 1 - 5x² on the interval [-3, 2], we first find the critical points of f(x) and then evaluate f(x) at the critical points and endpoints of the interval.
The derivative of f(x) is:
f'(x) = -10x
Setting f'(x) = 0, we get:
-10x = 0
which has only one critical point at x = 0.
Now, we evaluate f(x) at the critical point and endpoints of the interval:
f(-3) = 1 - 5(-3)² = -44
f(0) = 1 - 5(0)² = 1
f(2) = 1 - 5(2)² = -49
Therefore, the absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.
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HELP!! Which statements describe the end behavior of f(x)?f(x)?
Select two answers.
Answer:
As x approaches ∞, y approaches -∞
As x approaches -2.5, y approaches ∞
Step-by-step explanation: