Based on the box-and-whisker plot shown below, match each term with the correct value. PLEASE ANSWER QUICKLY!!!

Based On The Box-and-whisker Plot Shown Below, Match Each Term With The Correct Value. PLEASE ANSWER

Answers

Answer 1

The value of the median is 18. The range of this plot is 6. The 25th percentile is 17 and the 75th percentile is 20. The interquartile range is 3.

We are given a box-and-whisker plot and we have to find the correct value of the median, range, 25th percentile, 75th percentile, and inter-quartile range with the help of this box-and-whisker plot.

We find the median with the help of the box. The line which splits the box into two halves is the median for the given data. Therefore, the median will be 18. To find the range, we subtract the minimum value from the maximum value. The minimum value is 15 and the maximum value is 21. Therefore, the range will be (21 - 15) = 6.

From the plot, we can see that the 25th percentile is 17, Q1, and the 75th percentile is 20, Q3. Now, we have to find the interquartile range. To find the interquartile range, we subtract Q1 from Q3. Therefore, our interquartile range will be (20 -17) = 3.

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Related Questions

Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 2x2 and the planes z = 0,2= 2 and y = 4.

Answers

Using the triple integral to find the volume of the solid bounded by the parabolic cylinder is 32/15 cubic units.

The given solid is bounded by the parabolic cylinder y = 2x², the plane z = 0, the plane z = 2, and the plane y = 4.

To find the volume of the solid using a triple integral, we can set up the integral as follows:

∫∫∫E dV

where E is the region of integration in three dimensions.

Region E can be described as:

0 ≤ z ≤ 2

0 ≤ y ≤ 4

0 ≤ x ≤ √(y/2)

Therefore, the triple integral can be written as:

∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz

Evaluating the integral gives us the volume of the solid:

V = ∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz = 32/15

Hence, the volume of the solid is 32/15 cubic units.

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the gender and age of acme painting company's employees are shown below. age gender 23 female 23 male 24 female 26 female 27 male 28 male 30 male 31 female 33 male 33 female 33 female 34 male 36 male 37 male 38 female 40 female 42 male 44 female if the ceo is selecting one employee at random, what is the chance he will select a male or someone in their 40s? 1/3 1/2 1/18 11/18

Answers

The probability to select a male or someone in their 40's for a ceo position is company is equals to the 1/18. So, the option(c) is right answer for the problem.

We have a data of employees' information. It contains gender and age of employees in acme painting company. Randomly one employee is selected. We have to determine chance or probability that a ceo select a male or someone in their 40's. Sample size, n= 18

Probability is defined as chances of occurrence of an event. It is calculated by dividing the favourable response to the possible total outcomes.

Total possible outcomes= 18

number of male in her 40's age = 1

So, probability that select a male or someone in their 40's = 1/18

Hence, required probability is 1/18.

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Complete question:

the above figure completes the question.

the gender and age of acme painting company's employees are shown below. age gender 23 female 23 male 24 female 26 female 27 male 28 male 30 male 31 female 33 male 33 female 33 female 34 male 36 male 37 male 38 female 40 female 42 male 44 female if the ceo is selecting one employee at random, what is the chance he will select a male or someone in their 40s?

a)1/3

b)1/2

c) 1/18

d) 11/18

2) You buy a brand new Audi R8 for $148,700 before taxes. If the car depreciates at a rate of 8%, how much will it be worth in 5 years?

Answers

To solve this problem, we will use the formula for exponential decay as follows: V = P * e^(-rt) where V is the value after t years, P is the initial value, r is the annual interest rate as a decimal, and t is the time in years.

What is Depreciation: Depreciation is dependent on a number of estimates.The method in which companies determine the depreciation value of their assets is different from one another. Some companies may use a straight line method of depreciation and another may count the depreciation according to asset's production value. What is exponential decay: An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time .Given that a brand new Audi R8 is purchased for $148,700 before taxes, and the car depreciates at a rate of 8%, we can find how much it will be worth in 5 years. Using the formula for exponential decay, we have V = P * e^(-rt) where     P = $148,700r = 0.08t = 5. Therefore,V = $148,700 * e^(-0.08 * 5), V = $148,700 * e^(-0.4)V ≈ $82,429.61. Therefore, the car will be worth approximately $82,429.61 in 5 years.

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Pls help i really need help on this

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Where the function f(x) = x² + 2x - 3 is given, note that the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4. See the attached graph.

What is the explanation for the above response?



To find the minimum and maximum points of the function f(x), we can complete the square:

f(x) = x^2 + 2x - 3

= (x + 1)^2 - 4

We can see that the function is in the vertex form f(x) = a(x - h)^2 + k, where the vertex is (-1, -4).

Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the vertex is the minimum point. Therefore, the minimum value of the function f(x) is -4.

To find the x-intercepts, we can set f(x) = 0:

(x + 1)^2 - 4 = 0

(x + 1)^2 = 4

Taking the square root of both sides, we get:

x + 1 = ±2

x = -1 ± 2

Therefore, the x-intercepts of the function f(x) are x = -3 and x = 1.

In summary, the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4, which occurs at the vertex (-1, -4).

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A college entrance exam had a mean of 80 with a standard deviation of 12 find the actual test score that coincides with a z-score of -1.25

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The actual test score that coincides with a z-score of -1.25 is 65 when A college entrance exam had a mean of 80 with a standard deviation of 12 and a z-score of -1.25.

The formula to calculate the actual test score from a z-score is given as,

X = μ + Zσ,

where:

X = the actual or raw test score

μ = the mean

Z = z-score

σ = standard deviation.

Given data:

μ = 80

Z = -1.25

σ =  12

Substuting the values of μ, Z, and σ in the formula, we get;

X = μ + Zσ,

X = 80 + (-1.25)(12)

X = 80 + (-15)

X = 65.

Therefore, the actual test score that coincides with a z-score of -1.25 is 65.

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En una serie de razones geométricas iguales,los antecedentes son 2, 3 y 5. si el producto de los consecuentes es 810. halle la suma del mayor y menor consecuente.

Answers

As per the given geometric sequence, the sum of the greater and lesser consequents is 51.

We are given that the antecedents (which are just the first three terms) of a geometric sequence are 2, 3, and 5. Let's call the common ratio of this sequence r. Using the definition of a geometric sequence, we can write the terms of this sequence as 2, 2r, 2r² (since the first term is 2 and the common ratio is r), 3, 3r, 3r², 5, 5r, 5r².

Next, we are told that the product of the consequents (which are just the terms after the first three) is 810. To find the product of the consequents, we just multiply all the terms after the first three together. So we have:

(2r³) * (3r²) * (5r) = 30r⁶

We know that this product is equal to 810, so we can set up the equation:

30*r⁶ = 810

Solving for r, we get:

r⁶ = 27

r = 3 (since 3⁶ = 729)

Now that we know the common ratio is 3, we can find the terms of the sequence by multiplying each antecedent by 3. So the terms of the sequence are:

2, 6, 18, 3, 9, 27, 5, 15, 45

The greater and lesser consequents are 45 and 6, respectively. So the sum of the greater and lesser consequents is:

45 + 6 = 51

Therefore, the answer to the problem is 51.

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Complete Question:

In a series of equal geometric ratios, the antecedents are 2, 3, and 5. If the product of the consequents is 810, find the sum of the greater and lesser consequents.

What is the radius if you are given the diameter of 36 m?

Answers

Answer:

Radius = 18 m

Step-by-step explanation:

Given:

Diameter = 36 m

To find:

Radius

Explanation:

We know that,

Radius = Diameter/2 = 36/2 = 18 m

Final Answer:

18 m

Find an equation in slope-intercept form for the line passing through each pair of points: (4, 7), (1, 4)

Answers

To find the equation of the line passing through (4, 7) and (1, 4) in slope-intercept form (y = mx + b), we need to first find the slope (m) of the line using the two points. The slope formula is:

m = (y2 - y1)/(x2 - x1)

Plugging in the coordinates of the two points, we get:

m = (4 - 7)/(1 - 4) = -3/-3 = 1

So the slope of the line is 1.

Now we can use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

We can choose either of the two points to plug in for (x1, y1). Let's use (4, 7):

y - 7 = 1(x - 4)

Simplifying this equation, we get:

y - 7 = x - 4

y = x + 3

Therefore, the equation of the line passing through (4, 7) and (1, 4) in slope-intercept form is y = x + 3.

Suppose F(x, y) = (2y, - sin(y)) and C is the circle of radius 8 centered at the origin oriented counterclockwise. (a) Find a vector parametric equation rt) for the circle C that starts at the point (8, 0) and travels around the circle once counterclockwise for 0 ≤ t ≤ 2pi.

Answers

The vector parametric equation for the circle C is r(t) = <8cos(t), 8sin(t)> for 0 ≤ t ≤ 2π.

To find a vector parametric equation r(t) for the circle C with radius 8, centered at the origin, starting at the point (8, 0)

and traveling counterclockwise for 0 ≤ t ≤ 2π, follow these steps:

Write down the equation for the circle centered at the origin with radius 8:

x² + y² = 64.

Parametrize the circle using trigonometric functions.

Since we are starting at (8, 0) and going counter clockwise,

we can use x = 8cos(t) and y = 8sin(t).

Write the parametric equation in vector form:

r(t) = <8cos(t), 8sin(t)>.

So the vector parametric equation for the circle C is r(t) = <8cos(t), 8sin(t)> for 0 ≤ t ≤ 2π.

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Federico enjoys catching pokemons in university campus. One day, while trying to catch charmander, he found the best spot next to a


perfectly circular pond. He was 43 feet from the bank and 75 feet from the point of tangency. Determine the radius of the pond using the


given information. Round to the nearest integer,

Answers

The radius of the pond is 32 feet, under the condition  that 43 feet from the bank and 75 feet from the point of tangency.

Let us consider that  the center of the circle O, the point of tangency T, and Federico's position P.
We can utilize these two points to form a line. The point of tangency is the place where Federico is closest to the pond. The radius of the pond is considered perpendicular to this line and passes through the point of tangency.

Firstly, we have to  the distance between Federico's position P and covers passes through points T and B (the bank). This distance is equivalent to the given  radius of the circle. We have to apply the formula for the distance between a point and a line to find this distance.

Let us assume this distance as  d.
d = (|BT x BP|) / |BT|

Here
|BT| = line segment length of  BT,
|BP| = line segment length of  BP,
BT x BP = vectors cross product of  BT and BP.

Here we evaluate  |BT| applying the Pythagorean theorem
|BT|² = 75²+ r²

Here,
r = radius concerning the circle.
Then,

|BP|² = 43² + r²
Staging these values into our formula for d:
d = (|BT x BP|) / |BT|
 = (|BT| × |BP|) / |BT|
 = |BP|
 = √(43² + r²)

We want to solve for r, so we can square both sides:

d² = 43² + r²

r² = d² - 43²

r = √(d² - 43²)

Placing in d = 75,

r = √(75² - 43²)
≈ 32 feet
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(Linear Systems: Applications). Find a polynomial p(2) of degree three such that
7(-2)=3,P(-1)=3,7(1)=-9,8(2)=-33.

Answers

Therefore, the polynomial p(x) that satisfies the given conditions is:

p(x) = ax^3 + bx^2 + cx + d
p(x) = x^3 - 2x^2 + 3x + 23

So, p(2) = 1(2)^3 - 2(2)^2 + 3(2) + 23 = 9.

To find a polynomial p(2) of degree three, we need four pieces of information. We can use the given values to set up a system of linear equations:

-7a + 2b - 4c + d = 3
-a - b + c - d = 3
7a + b + c + d = -9
8a + 4b + 2c + d = -33

We can solve this system using any method of linear algebra. One way is to use row reduction:

[ -7  2 -4  1 |  3 ]
[ -1 -1  1 -1 |  3 ]
[  7  1  1  1 | -9 ]
[  8  4  2  1 | -33 ]

R2 + R1 -> R1:
[ -8  1 -3  0 |  6 ]
[ -1 -1  1 -1 |  3 ]
[  7  1  1  1 | -9 ]
[  8  4  2  1 | -33 ]

R3 - 7R1 -> R1, R4 - 8R1 -> R1:
[ -8  1 -3  0 |  6 ]
[  0 -7  8 -1 | 51 ]
[  0 -4  4  1 |-51 ]
[  0  4 26  1 |-81 ]

R4 + R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0 -4  4  1 |-51 ]
[  0  4 26  1 |-81 ]

R3 + (4/3)R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0 50  4 |-11 ]
[  0  4 26  1 |-81 ]

R4 - (4/3)R2 -> R2, R3 - (5/6)R2 -> R2:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0  8  4 |-34 ]
[  0  0  8  1 |-103 ]

R4 - R3 -> R3:
[ -8  1 -3  0 |  6 ]
[  0 -3 34  0 | 30 ]
[  0  0  8  4 |-34 ]
[  0  0  0 -3 |-69 ]

Now we can back-substitute to find the coefficients of the polynomial:

d = -69/(-3) = 23
c = (-34 - 4d)/8 = 3
b = (30 - 34c + 3d)/(-3) = -2
a = (6 + 3b - 3c + d)/(-8) = 1

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Abby makes wants to make a gallon of punch. She uses 2 quarts of orange juice 1 cup of lemon juice and 2 1/2 pints of pineapple juice. How many cups of water should you add to make 1 gallon?

Answers

Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

To answer your question about how many cups of water Abby should add to make 1 gallon of punch, let's first convert all the given measurements to cups. One gallon is equivalent to 16 cups.

1. Orange juice: Abby uses 2 quarts of orange juice. Since there are 4 cups in a quart, she uses 2 x 4 = 8 cups of orange juice.


2. Lemon juice: Abby uses 1 cup of lemon juice.


3. Pineapple juice: Abby uses 2 1/2 pints of pineapple juice. There are 2 cups in a pint, so she uses (2 1/2) x 2 = 5 cups of pineapple juice.

Now, let's add up the cups of orange juice, lemon juice, and pineapple juice: 8 + 1 + 5 = 14 cups. Since Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

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The area of a rectangle is 42 square meters. The length is 7 meters. What is the width?
35 meters
14 meters
15 meters
6 meters

Answers

Answer: 6

Step-by-step explanation:42/7=6

ln(n^3 8) -ln(6n^3 13n) determine that the sequence diverges

Answers

Since ln(1/6) is a finite value, the sequence does not diverge. It converges to ln(1/6) as n approaches infinity.

To determine if the sequence diverges, we need to take the limit of the expression as n approaches infinity.

Using the logarithmic identity ln(a/b) = ln(a) - ln(b), we can simplify the expression as follows:

[tex]ln(n^3 8) - ln(6n^3 13n) = ln(n^3) + ln(8) - ln(6n^3) - ln(13n)[/tex]

= [tex]ln(n^3) - ln(6n^3) + ln(8) - ln(13n)[/tex]

= [tex]ln(n^3/6n^3) + ln(8/13n)[/tex]

=[tex]ln(1/6) + ln(8/13n)[/tex]

As n approaches infinity, ln(8/13n) approaches 0, so the limit of the expression is:

lim n→∞ [ln(1/6) + ln(8/13n)]

= ln(1/6)

Since ln(1/6) is a finite value, the sequence does not diverge. It converges to ln(1/6) as n approaches infinity.

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find the perimeter of the equilateral triangle whose area is 16root3/4

Answers

The perimeter of the equilateral triangle whose area is 16root3/4 is 15.9[tex]\sqrt{3/4} cm[/tex]

What is an equilateral triangle?

You should understand that a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted

An equilateral triangle is a special case of an isosceles triangle in which all three sides have the same length

Let the sides of the triangle be a

a + a + a = 16root3/4

3a = 16[tex]\sqrt{3/4}[/tex]

a = 5.3[tex]\sqrt{3/4}[/tex]

Therefore the perimeter of the equilateral triangle is

5.3[tex]\sqrt{3/4} + 5.3\sqrt{3/4} +5.3\sqrt{3/4}[/tex]

Therefore, the  perimeter is 15.9[tex]\sqrt{3/4} cm[/tex]

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Ana tiene que tomar un jarabe por 20 días, el doctor le ha recetado 3 frascos de 20ml cada uno, tiene que tomar el jarabe de tal manera que cada día que pasa toma 5ml menos que el día anterior

Answers

Ana will take 100 ml on the first day and 5 ml less each day for 20 days, requiring a total of 1050 ml; the prescribed amount of 960 ml is not enough, resulting in a shortage of 90 ml, which will last for 18 days.

Ana will take the syrup for 20 days, and on each day, she will take 5 ml less than the previous day. To calculate the total amount of syrup Ana will need for the 20 days, we can use the formula for the sum of an arithmetic series,

S = (n/2) x (a₁ + aₙ), In this case, n = 20, a1 = 100 ml, and an = 100 ml - (19 x 5 ml) = 5 ml. Plugging in the values, we get,

S = (20/2) x (100 ml + 5 ml) = 1050 ml

So Ana will need a total of 1050 ml of syrup for the 20 days. The doctor prescribed 3 bottles of 320 ml each, which is a total of 960 ml. This is not enough to cover the full 20 days of treatment, as Ana will need 1050 ml. Therefore, there is a shortage of 90 ml of syrup. To calculate how many days Ana will lack syrup for, we need to divide the shortage by the daily reduction in dose,

90 ml/5 ml per day = 18 days

So Ana will have enough syrup for the first 2 days, but she will lack syrup for the next 18 days.

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Complete question - Ana has to take a syrup for 20 days, the doctor has prescribed 3 bottles of 320 ml each, she has to take the syrup in such a way that each day that passes she takes 5 ml less than the day before. If you start taking a 100 ml dose, how many ml will you take on the last day? Was the amount of syrup prescribed by the doctor enough? How much syrup is left over or lacking? if he lacked syrup, for how many days would he lack?

Here is a list of ingredients for making 16 flapjacks.
Ingredients for 16 flapjacks
120 g butter
140 g brown sugar
250 g oats
2 tablespoons syrup
jenny wants to make 24 flapjacks.
work out how much of each of the ingredients she needs.

butter
brown sugar
oats
syrup tablespoons â

Answers

Jenny needs 180g of butter, 210g of brown sugar, 375g of oats, and 3 tablespoons of syrup to make 24 flapjacks.

To make 24 flapjacks, Jenny needs to increase the amount of each ingredient proportionally.

To calculate the required amounts, we can use ratios. If 16 flapjacks require 120g of butter, then 24 flapjacks require:

Butter: (24/16) x 120g = 180g

Brown sugar: (24/16) x 140g = 210g

Oats: (24/16) x 250g = 375g

Syrup: (24/16) x 2 tablespoons = 3 tablespoons

Therefore, Jenny needs 180g of butter, 210g of brown sugar, 375g of oats, and 3 tablespoons of syrup to make 24 flapjacks.

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Heights for 16-year-old boys are normally distributed with a mean of 68. 3 in. And a standard


deviation of 2. 9 in.


Find the z-score associated with the 96th percentile.


Find the height of a 16-year-old boy in the 96th percentile.


State your answer to the nearest inch

Answers

The height of a 16-year-old boy in the 96th percentile is approximately 73 inches. Rounded to the nearest inch, the answer is 73 inches.

Find out the height of a boy in the  96th percentile?

To find the z-score associated with the 96th percentile, we need to find the z-score such that the area to the right of it under the standard normal distribution is 0.96. Using a standard normal distribution table or calculator, we find that the z-score is approximately 1.75.

Next, we can use the z-score formula to find the height of a 16-year-old boy in the 96th percentile:

z = (x - μ) / σ

where z is the z-score, x is the height we want to find, μ is the mean height, and σ is the standard deviation.

Plugging in the values we have:

1.75 = (x - 68.3) / 2.9

Multiplying both sides by 2.9, we get:

x - 68.3 = 5.075

Adding 68.3 to both sides, we get:

x = 73.375

So the height of a 16-year-old boy in the 96th percentile is approximately 73 inches. Rounded to the nearest inch, the answer is 73 inches.

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Make sure to include your null and alternative hypothesis, your test statistic, your p-value, decision, and conclusion in the context in your response. A poll conducted by the General Social Survey asked a random sample of 1325 adults in the United States how much confidence they had in banks and other financial institutions. A total of 149 adults said they had a great deal of confidence. An economist claims that less than 15% of US adults have great confidence in banks. Use a= 0. 05 can you conclude that the economist's claim is true?Use a=0. 01 can you conclude that the economist's claim is true?

Answers

At both the 5% and 1% significance levels, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.

Null Hypothesis: The proportion of US adults who have great confidence in banks is 15% or higher.

Alternative Hypothesis: The proportion of US adults who have great confidence in banks is less than 15%.

We can use a one-tailed z-test to test the economist's claim.

The test statistic is

z = (P - p) / √(p * (1-p) / n)

where P is the sample proportion, p is the hypothesized proportion, and n is the sample size.

Using the sample data, we have

P = 149/1325 = 0.1121

p = 0.15

n = 1325

The test statistic is

z = (0.1121 - 0.15) / √(0.15 × (1-0.15) / 1325) = -3.196

Using a significance level of α = 0.05, the critical value for a one-tailed test is -1.645. Since our test statistic is less than the critical value, we reject the null hypothesis.

The p-value for this test is P(Z < -3.196) = 0.0007. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

At the 5% significance level, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.

Using a significance level of α = 0.01, the critical value for a one-tailed test is -2.33. Since our test statistic is less than the critical value, we reject the null hypothesis.

The p-value for this test is P(Z < -3.196) = 0.0007. Since the p-value is less than the significance level of 0.01, we reject the null hypothesis.

At the 1% significance level, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.

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Answer Immeditely Please

Answers

Answer:

6

Step-by-step explanation:

Plss someone answer this math question

Answers

The value of the reflex angle in this figure is 273 degrees

What is a reflex angle?

A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.

In this given figure, there's acute angle and an obtuse angle, therefore a reflex angle must be present.

To find the reflex angle in the figure, we have to trace the green part of the figure which will give us;

180° + 93°

i.e the sum of angle on a straight line with an obtuse angle

Reflex angle = 180 + 93 = 273°

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What is amplitude in Trig.

Answers

Answer:

It the distance from mid line to top of wave.

Step-by-step explanation:

Answer:

Height of a wave (from mid line to max.

Step-by-step explanation:

There are 5 red candies and 1 blue candy shown in the bag. What is the least number of red and blue candies that can be added to the bag to create a ratio of 3 to 2 for the number of red candies to the number of blue candies? Key: = red R B = blue​

Answers

Let's say we add 'x' red candies and 'y' blue candies to the bag to create the desired ratio of 3 to 2:

Then, the total number of red candies in the bag will be 5 + x, and the total number of blue candies will be 1 + y.

According to the problem, the ratio of red candies to blue candies should be 3 to 2:

(5 + x) / (1 + y) = 3/2

Cross-multiplying this equation, we get:

2(5 + x) = 3(1 + y)

Simplifying this equation, we get:

10 + 2x = 3 + 3y

2x - 3y = -7

We want to find the least number of red and blue candies that can be added to the bag to satisfy this equation.

One way to do this is to try different values of x and y that satisfy the equation until we find the smallest possible values that work.

For example, we can start by setting x = 1 and y = 2:

2(5 + 1) = 3(1 + 2)

12 = 9

This doesn't work, so let's try another set of values, x = 4 and y = 5:

2(5 + 4) = 3(1 + 5)

18 = 18

This set of values works, so we have found the least number of red and blue candies that can be added to the bag to create a ratio of 3 to 2 for the number of red candies to the number of blue candies:

We need to add 4 red candies and 5 blue candies to the bag to create a ratio of 3 to 2 for the number of red candies to the number of blue candies.

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If the arch were 32 inches wide but 44 inches tall high, how could you modify your function W to model the new arch

Answers

This new function W(x) = 22 - (11/8) * (x - 16)² will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall.

To modify the function W to model the new arch with dimensions of 32 inches wide and 44 inches tall, we need to adjust the formula to reflect the new proportions.

Currently, the function W is defined as:

W(x) = h/2 - h/(2a) * (x - a)²

Where h is the height of the arch and a is half of the width of the arch.

To modify the function for the new arch, we need to adjust the value of a to reflect the new width of 32 inches. Since a is half the width, we have:

a = 32/2 = 16

We also need to adjust the value of h to reflect the new height of 44 inches. Therefore, the new function for the arch would be:

W(x) = 44/2 - 44/(2*16) * (x - 16)²

Simplifying this expression, we get:

W(x) = 22 - (11/8) * (x - 16)²

This new function will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall. The parabolic shape of the function will remain the same, but the specific coefficients in the function have been adjusted to reflect the new proportions of the arch.

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Jose has scored 347 points on his math tests so far this semester. To get an A for the semester, he must score at least 403 points. Part 1 out of 2 Enter an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. Let n represent the number of points Jose needs to score on the remaining tests.

Answers

If Joe already scored 347 points in math-test, then to get a grade"A" he must score at least 56 marks, which is represented in inequality as n ≥ 56.

Jose has already scored 347 points on his math-tests so far, and he needs to score at least 403 points to get an A for the semester.

Let "minimum-points" he must score on the "remaining-tests" be denoted by "n". We can write an inequality to represent minimum-points as:

⇒ 347 + n ≥ 403,

⇒ n ≥ 403 - 347,

⇒ n ≥ 56.

Therefore, Jose must score at least 56 points on the remaining tests in order to get an A for the semester.

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The given question is incomplete, the complete question is

Jose has scored 347 points on his math tests so far this semester. To get an A for the semester, he must score at least 403 points. Write an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. Let "n" represent the number of points Jose needs to score on the remaining tests.

suppose x is a random variable with mean mu and standard deviation sigma. If a large number of trials are observed, at least what percentage of these values is expected to lie between mu minus 2 sigma and mu plus 2 sigma?

Answers

At least 95% of the observed values are expected to lie between mu minus 2 sigma and mu plus 2 sigma.

This is because of the empirical rule, also known as the 68-95-99.7 rule, which states that in a normal distribution, approximately 68% of the observations will fall within one standard deviation of the mean, about 95% of the observations will fall within two standard deviations of the mean, and around 99.7% of the observations will fall within three standard deviations of the mean.

In this case, we are given that x has mean mu and standard deviation sigma. Therefore, about 95% of the values of x are expected to lie between mu minus 2 sigma and mu plus 2 sigma, as this interval covers two standard deviations on either side of the mean.

Mathematically, we can express this as:

P(mu - 2sigma < x < mu + 2sigma) ≈ 0.95

where P is the probability that x falls within the interval mu - 2sigma to mu + 2sigma.

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In ΔLMN, m = 2. 1 inches, n = 8. 2 inches and ∠L=85°. Find the length of l, to the nearest 10th of an inch

Answers

The length of l is approximately 6.1 inches to the nearest tenth of an inch.

To find the length of l, we can use the Law of Cosines which states that:

                     c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the side opposite angle C, and a and b are the other two sides.

In this case, we want to find the length of l, which is opposite the given angle ∠L. So we can label l as side c, and label m and n as sides a and b, respectively. Then we can plug in the values we know and solve for l:

                      l^2 = m^2 + n^2 - 2mn*cos(L)

l^2 = (2.1)^2 + (8.2)^2 - 2(2.1)(8.2)*cos(85°)

l^2 = 4.41 + 67.24 - 34.212

l^2 = 37.438

l = sqrt(37.438)

l ≈ 6.118

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Given the measure of an acute angle in a right triangle, we can tell the ratios of the lengths of the triangle's sides relative to that acute angle.

Here are the approximate ratios for angle measures

55

°

55°55, degree,

65

°

65°65, degree, and

75

°

75°75, degree.

Angle

55

°

55°55, degree

65

°

65°65, degree

75

°

75°75, degree

adjacent leg length

hypotenuse length

hypotenuse length

adjacent leg length



start fraction, start text, a, d, j, a, c, e, n, t, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, h, y, p, o, t, e, n, u, s, e, space, l, e, n, g, t, h, end text, end fraction

0.57

0.570, point, 57

0.42

0.420, point, 42

0.26

0.260, point, 26

opposite leg length

hypotenuse length

hypotenuse length

opposite leg length



start fraction, start text, o, p, p, o, s, i, t, e, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, h, y, p, o, t, e, n, u, s, e, space, l, e, n, g, t, h, end text, end fraction

0.82

0.820, point, 82

0.91

0.910, point, 91

0.97

0.970, point, 97

opposite leg length

adjacent leg length

adjacent leg length

opposite leg length



start fraction, start text, o, p, p, o, s, i, t, e, space, l, e, g, space, l, e, n, g, t, h, end text, divided by, start text, a, d, j, a, c, e, n, t, space, l, e, g, space, l, e, n, g, t, h, end text, end fraction

1.43

1.431, point, 43

2.14

2.142, point, 14

3.73

3.733, point, 73

Use the table to approximate

m



L

m∠Lm, angle, L in the triangle below.


3.2

3.2

11.9

11.9

L

L

K

K

J

J

Choose 1 answer:

Answers

The angle measure of L in the triangle is approximately 75°.

Based on the given table, we can see that the ratio of the opposite leg length to the adjacent leg length for an angle measure of 75° is approximately 3.73. Looking at the triangle in the question, we can see that the side opposite to angle L is the hypotenuse and the adjacent leg is LK.

Therefore, the ratio of the opposite leg length to the adjacent leg length for angle L is equal to the ratio of the hypotenuse length to the length of segment LK.

From the figure, we can see that the length of segment LK is approximately 3.2 units. Therefore, the length of the hypotenuse is approximately 3.73 times the length of segment LK, or:

hypotenuse length ≈ 3.73 × 3.2 ≈ 11.9

Therefore, the angle measure of L is approximately 75°.

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Assume the annual rate of change in the national debt of a country​ (in billions of dollars per​ year) can be modeled by the function
D'(t)=858.29+819.48t-184.32t^2+12.12t^3
where t is the number of years since 1995. By how much did the debt increase between 1996 and 2003 ​?

Answers

The debt increased between 1996 and 2003. Then the national debt increased by approximately $4,903.73 billion between 1996 and 2003.

To find how much the debt increased between 1996 and 2003, we need to find the value of the function D'(t) for t=7 (since 2003 is 7 years after 1996).

D'(t)=858.29+819.48t-184.32t^2+12.12t^3

D'(7)=858.29+819.48(7)-184.32(7^2)+12.12(7^3)
D'(7)=858.29+5,736.36-8,132.32+3,458.68
D'(7)=1,921.01

Therefore, the annual rate of change in the national debt in 2003 was $1,921.01 billion per year.

To find how much the debt increased between 1996 and 2003, we need to integrate the function D'(t) from t=1 to t=7:

∫(D'(t))dt = ∫(858.29+819.48t-184.32t^2+12.12t^3)dt
= 858.29t + 409.74t^2 - 61.44t^3 + 3.03t^4 + C

where C is the constant of integration.

Evaluating this expression at t=7 and t=1 and taking the difference, we get:

(858.29(7) + 409.74(7)^2 - 61.44(7)^3 + 3.03(7)^4 + C) - (858.29(1) + 409.74(1)^2 - 61.44(1)^3 + 3.03(1)^4 + C)
= 6,111.09 - 1,207.36 = 4,903.73

Therefore, the national debt increased by approximately $4,903.73 billion between 1996 and 2003.

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slove log2(x-6)+log2(x+6)=6

Answers

Answer: x = 10

Step-by-step explanation: To solve this equation, you can use the logarithmic property that states loga(b) + loga(c) = loga(bc). So, you can rewrite the left side of the equation as log2((x-6)(x+6)). Then, you can use the property that states loga(b) = c is equivalent to a^c = b to solve for x.

So, you have log2((x-6)(x+6)) = 6, which is equivalent to 2^6 = (x-6)(x+6). Simplifying the left side gives you 64, and expanding the right side gives you x^2 - 36 = 64. Solving for x gives you x = ±√100, which is x = ±10. However, since the original equation includes logarithms.

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