Which linear function has the greatest initial value? Which has the greatest rate of change? Use the drop-down menus to show your answer.

Answer:

------------------------------------------------

Find the sum of the volumes of the two given cones.

Cone volume:

Cone 1, d = 4m, h = 8m:

Cone 2, r = 2m, h = 6 m:

Total volume:

Find the Sum, Difference, or Product

1. [tex]3x^2 + 4x -1 - 2x^2 -3x + 2 = x^2 + x + 1[/tex]

2. [tex]12x^5 - 3x^4 + 2x -5+8x^4-3x^3+4x+1 = 12x^5 +5x^4-3x^3+6x-4[/tex]

3. [tex]3x^3 - 2x^2 + 4x-8-5x^3-12x^2+3x+4 = -2x^3-14x^2+7x-4[/tex]

4. [tex]5x^6 - 2x^4 +9x^3+2x-4-7x^5+8x^4-2x+11 = 5x^6-7x^5+6x^4+9x^3+7[/tex]

5. [tex]x^3+3x^2-10x-24[/tex] (Multiply the first two factor, then multiply the product to the last factor)

6. [tex](7h+4)*(7h+4)= 49h^2+28h+28h+16 =49h^2+56h+16[/tex]

Factor the Sum or Difference of Cubes

Sum of Cubes Formula: [tex]a^3+b^3 = (a+b)(a^2-ab+b^2)\\[/tex]

Difference of Cubes Formula: [tex]a^3-b^3 = (a-b)(a^2+ab+b^2)\\[/tex]

Just apply it to the equations.

1. [tex]x^3 + 4^3 = (x+4) (x^2 - 4x+16)[/tex]

2. [tex]c^3 - 3^3 = (c-3) (c^2+3c+9)[/tex]

3. [tex](3d)^3 + 2^2 = (3d+2)((3d^)^2-(3d)(2)+4) = (3d+2)(9d^2-6d+4)[/tex]

4. [tex]5^3-(2b)^3= (5-2b)(5^2+(2b)(5)+(2b)^2) = (5-2b)(25+10b+4b^2)[/tex]

Factor the Polynomials Completely

Nt. I'm having a hard time with this one

1. [tex]x(x-6)(x+4)+24(x-1)[/tex]

2. [tex]2m^4 (m-4)(m-8)[/tex]

3. [tex](6v+7)(3v+2)[/tex]

4. [tex]4n^2(n^5-2)(n^5-6)[/tex]

5. [tex](9a^2-16b)(9a^2+16b)[/tex]

6. [tex](4z^2-25y)(4z^2+25y)[/tex]

(1) To multiply two powers with the same base, add their exponents.

(2) An  example of an expression you could simplify using the quotient of powers property is  xᵃ / xᵇ

(3) The answer of following exponents are  4¹¹ , 5¹¹ , 6⁸ and  7⁹

A number's exponent indicates how many times the number has been multiplied by itself.

In general, xⁿ denotes that x has been multiplied by itself n times.

According to the question,

(1) Assuming two exponent having same base be xᵃ and xᵇ

Multiplying both the number => xᵃ . xᵇ

To Multiplying two exponent having same base , we add the power

=> x⁽ᵃ ⁺ᵇ⁾

Hence , To multiply two powers with the same base, add their exponents

(2) Simplifying using the quotient of powers property

Let  xᵃ / xᵇ

Dividing exponent with same base , we subtract the powers

=> xᵃ⁻ᵇ

Simplifying the followings

3.  4².4⁹

=> 4⁽²⁺⁹⁾

=> 4¹¹

4. 5³.5⁸

=> 5 ⁽³⁺⁸⁾

=> 5¹¹

5. 6⁷.6

=> 6⁸

6. 7³.7⁴.7²

=> 7⁽³⁺⁴⁺²⁾

=> 7⁹

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The  answer is 7525381507

The combination is defined as “An arrangement of objects where the order in which the objects are selected does not matter.” And the formula is given by [tex]_n C_r=\frac{n !}{r ! (n-r) !}[/tex]        [tex]_n C_r[/tex]= number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Given here, select 8 cards out of a possible 52 thus using the formula we get

[tex]=\frac{52 !}{8 ! (52-8) !}[/tex]

[tex]=\frac{52 !}{8 ! (44) !}[/tex]

= 7525381507

Hence the answer is 7525381507

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[tex]P(B|A) = \frac{P(AandB)}{P(A)}[/tex]

Answer:

0.3324

Step-by-step explanation:

The volume of the cone is 144π units³.

The volume of a cone can be calculated as follows:

volume of a cone = 1 / 3 πr²h

where

Therefore, the height of the cone is 27 units and the radius of the cone is given as 4 units.

Let's find the volume using the formula,

r = 4 units

h = 27 units

Therefore,

volume of a cone = 1 / 3 πr²h

volume of a cone = 1 / 3 × π × 4² × 27

volume of a cone = 1 / 3 × π × 16 × 27

volume of a cone = 432 / 3 π

Therefore,

volume of a cone = 144π

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Answer:

(a) They paid $25-$15=$<<25-15=10>>10 to make each wreath.

(b) They collected $15114=$<<15114=1710>>1710.

(c) They made $1710-$10114=$<<1710-10114=180>>180.

(d) They sold $180/$15=<<180/15=12>>12 wreaths.

Step-by-step explanation:

Sure, here is a breakdown of the solution:

(a) The cross-country team paid $10 to make each wreath because they sold the wreaths for $25 and made $15 for each wreath they sold, so the cost to make each wreath was $25-$15=$10.

(b) They collected $1710 because they sold 114 wreaths and made $15 for each wreath they sold, so they collected a total of $15*114=$1710.

(c) They made $180 because they collected $1710 and it cost them $10 to make each wreath, and they sold 114 wreaths, so the total cost of making all the wreaths was $10*114=$1140. They made $180 because they collected $1710 and it cost them $1140 to make all the wreaths, so their profit was $1710-$1140=$180.

(d) They sold 12 wreaths because they made $180 and it cost them $15 to make each wreath, so they sold $180/$15=12 wreaths.

a) The standard error is of: 0.0167.

b) The test statistic is of: 2.99.

c) The p-value is of 0.0013, representing the probability of finding a sample proportion of at least 55%.

At the null hypothesis, it is tested if there is not enough evidence that a majority of the population supports the measure, hence:

[tex]H_0: p \leq 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that a majority of the population supports the measure, hence:

[tex]H_1: p > 0.5[/tex]

The equation that defines the test statistic is given as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

The values of these parameters in this problem are given as follows:

[tex]p = 0.5, n = 900, \overline{p} = 0.55[/tex]

Then the standard error is calculated as follows:

Standard error = square root (0.5 x 0.5/900) = 0.0167.

Then the test statistic is calculated as follows:

z = (0.55 - 0.5)/0.0167 = 2.99.

We have a right-tailed test, as we are testing if the mean is different of a value, hence the p-value represents the probability of finding a sample proportion of at least 0.55.

Using a z-distribution calculator, with z = 2.99, the p-value is of:

0.0013.

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The required expression that can be simplified without the conversion of terms is 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵. Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
In order to do, no needs to convert terms, so then expression with the same exponent of 10 is the required expression.
So,
= 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵
= 10.00 × 10⁻⁵
= 10⁻⁴

Thus, the required expression that can be simplified without the conversion of terms is 9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵. Option A is correct.

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Answer:

9.32 × 10 ⁻⁵ + 1.078 × 10⁻⁵

Step-by-step explanation:

Using the concept of ratio, the rate at which questions were answered correctly is 0.867 which is option B

Rate can be defined as comparing two or more ratio with a standard value.

The rate of correct answer can be calculated using the ratio between the number of correct answers to numbers of questions answered.

The rate is given as;

rate = 65 / 75

rate = 0.867

The rate of correct answers is 0.867

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As per the given inversion, the time independent Schrödinger equation in one dimension is [tex]\frac{-hx^{2}}{2m} \times\frac{d^{2}(x)}{dx^{2} } + U(x)f(x)=Ef(x)[/tex]

The term inversion in math refers a concept in discrete mathematics to measure how much a sequence is out of its natural order.

Here we have given that the potential energy function is given by the following: -a CO r I 2 -a 2 V(r)={ 0, s > a CO < 2}

And we need to find the eigenfunctions must be either even or odd under the same reflection operation.

While we looking into the given question, let us consider E is the total energy of the particle, and U (x) the potential energy function and ψ (x) the spatial part of the wavefunction.

Based on the the function can be written as,

=>  [tex]\frac{-hx^{2}}{2m} \times\frac{d^{2}(x)}{dx^{2} } + U(x)f(x)=Ef(x)[/tex]

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The scatter plot for provide data is shown above in figure. The slope-intercept form of the equation of the line that best fits the data is

y = - 0.3319 x + 312.16

Scatter charts are similar to line charts in that they use horizontal and vertical axes to represent points of data. However, they have a very specific purpose. The scatterplot shows how much one variable is influenced by another. The relationship between two variables is called their correlation. There are three types of correlation: positive, negative, and none (no correlation).

• Positive correlation: when one variable increases, the other also increases. ...

• Negative correlation: an increase in one variable causes a decrease in the other variable. ...

• No Correlation: nothing displayed

We have the following observations,

X Y

10 20

10 630

30 390

40 160

90 210

100 370

Now , we construct a scatter plot for the provide data. The constructed scatter plot is shown above. As we see in plot that there is no increase or decrease with increasing values of one variable .So, there is no correlation between two variables. Now, equation of the line that best fits the data, A best line of fit never connect all the points on the scatter plot. but it connects only a few points. There will have data points above and below the line. The equation of a line of best fit can be represented as y = mx+b y = m x + b , where m is the slope and b is the y-intercept.

here, y = - 0.3319 x + 312.16

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Answer:

= –4√5

Step-by-step explanation:

√−80

=√ –( 16 × 5

= √ –(4² × 5)

= –4√5

this is what I think I hope I helped

Answer:

21

Step-by-step explanation:

84x35=2940

2940x2=5880

84+21=105

35+21=56

105*56=5880

Answer:

0.99548

Step-by-step explanation:

P(not die)=100000-452/100000

Brad looks at a scatterplot that shows the correlation between the typical population's access to health insurance and the number of cars owned by each household in different parts of the country. A substantial positive association can be seen in the plot.

What are some examples of scatter plots?

The association between two sets of data is depicted by points on a scatter (XY) plot. Each dot in this illustration represents the weight and height of one individual. (The information is displayed as "Cartesian (x,y) Coordinates")

What is the purpose of a scatter plot?

Data points are plotted on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

                 The values of the columns selected on the X and Y axes determine where each row in the data table is represented by a marker, whose position.

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Option B) 17

A simple kind of data visualization known as a "dot plot" involves the representation of data points as dots on a graph with x and y axes. Sai has 17 albums in his collection altogether.

Given data;

6 = 0; 7 = 1 ; 8 = 2; 9 = 2; 10 = 4; 11 = 1; 12 = 2; 13 = 2; 14 = 1; 15 = 0; 16 = 2

[tex]= 1+2+2+4+1+2+2+1+2[/tex]

[tex]=17[/tex]

The total number of albums in Sai collection is 17

A basic style of data visualization called a dot plot, often referred to as a strip plot or dot chart, shows data points as dots on a graph with x and y axes. The purpose of these graphs is to visually portray particular data patterns or groups.

Each dot in the provided dot plot represents an album. As a result, the total number of dots in the dot plot equals the total number of albums in Sai's collection.

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From the graph that shows Jeremy's distance from home each hour , then he will be 500 miles from home after 10 hours .

In the question ,

a graph is given ,

we have to find the distance that Jeremy's car will travel after 10 hours.

from the graph we can see that the points in the graph form a straight line .

we can see that ,

in 1 hour Jeremy's car travels a distance of 50 miles .

So , in 10 hours Jeremy's car will travel = 10×50 miles .

= 500 miles .

So , Jeremy's car will be 500 miles away from home after 10 hours .

Therefore , the correct option is (a) 500 miles .

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Answer: Time: 2 hours and 15 minutes, Fraction: I don't know

Step-by-step explanation:

1 hour=1 hour

30+45=1 hour and 15 minutes

1 hour+1 hour+15 minutes=2 hours and 15 minutes

The pressure in the can become triple the original value. Option B is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
From the ideal gas equation, we know that,
pressure is directly proportional to the temperature,
So,
P₁ / P₂ = T₁ / T₂
Where,
P₁ and T₁ are the initial pressure and temperature,
P₂ and T₂ are the final pressure and temperature.

Substitute the values,
P₁ / P₂ = 300 / 900
P₂ = 3P₁

Thus, the pressure in the can become triple the original value. Option B is correct.

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(a) Probability that sample mean lies between 79 and 81 is 0.9946.

(b) It is 0.04% likely is it that the sample mean diameter exceeds 81 when n = 36.

We are given that the metal sheets of a particular type, its mean value and standard deviation are 85 GPA and 2.3 GPA, respectively.

Suppose the distribution is normal.

Let X = sample mean diameter

The z-score probability distribution for sample mean is given by;

                                Z  =  (X - μ) / (σ / √n)

where,

μ = population mean = 85 GPA

σ = standard deviation = 2.3 GPA

n = sample size = 25

(a) Probability that sample mean lies between 79 and 81 is given by

= P(79<X<81) = P(X<81) - P(X≤79)

P(X<81) = P {(X - μ) / (σ / √n) < (81 - 85) / (2.3 / √25) = P(Z < 2.78) = 0.9973

P(X<79) = P {(X - μ) / (σ / √n) < (79 - 85) / (2.3 / √25) = P(Z < 2.78) = 0.0027

The above probability is calculated by looking at the value of x = 2.78 in the z table which has an area of 0.9973.

Here, P(79 < X < 81) = 0.9973 - 0.0027 = 0.9946

(b) Probability that the sample mean diameter exceeds 81 when n = 36 is given by = P(X > 81)

P(X<81) = P {(X - μ) / (σ / √n) < (81 - 85) / (2.3 / √25) = P(Z < 3.33) = 0.0004

The above probability is calculated by looking at the value of x = 3.33 in the z table which has an area of 0.9996.

Therefore, probability that sample mean lies between 79 and 81 is 0.9946 and it is 0.04% likely is it that the sample mean diameter exceeds 81 when n = 36.

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Examples of a continuous function that is continuous at exactly one point are x=0,1,2,3,4.

In mathematics, a continuous function is one where a continuous variation of the argument results in a continuous variation of the function's value (i.e., a change without a leap). This indicates that there aren't any discontinuities or sudden changes in value. More specifically, a function is continuous if it is possible to guarantee that its value will not vary significantly even with arbitrarily tiny changes to its parameter.

We know that the modulus function,

f(x)=∣x∣ is continuous but not differentiable at x=0.

So,

f(x)=∣x∣+∣x−1∣+∣x−2∣+∣x−3∣+∣x−4∣ is continuous but not differentiable at x=0,1,2,3,4.

Hence, this is the answer.

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Regression analysis, regression, and immigration analyst analysis are the solutions.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the relationships between a dependent variable (often referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon), and one or more independent variables (often referred to as "predictors," "covariates," "explanatory variables," or "features").

In linear regression, the most typical type of regression analysis, the line (or a more complicated linear combination) that most closely matches the data in terms of a given mathematical criterion is found.

When using the ordinary least squares method, for instance, the specific line (or hyperplane) that minimizes the sum of squared differences between the genuine data and that line is computed (or hyperplane).

This enables the researcher to estimate the for precise mathematical reasons (see linear regression).

Hence, Regression analysis, regression, and immigration analyst analysis are the solutions.

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Its Taylor polynomial T3(x) for function f with the number an as the center is T 3(x)=(x 2 + 61 x 2 ). 3

Sums of terms with the pattern kxn—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5. Polynomials: An introduction In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered. A polynomial is a function that exclusively uses positive integer exponents or non-negative integer powers of a variable in an equation, such as a quadratic or cubic equation. A polynomial with an exponent of 1 is, for instance, 2x+5.

T 3 (x)=f(a) + 1!f ′ (a)(xa) + 2!f ′′(a)(xa) 2 plus 1 3!f ′′′(a)(x−a) 3=0plus 1!−1(x− 2π)+ 2!0(x− 2π) 2 plus 1 3!1​ (x− 2π) 3=−(x− 2π)+ 61\s(x− 2π) 3

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All different: Since there are 30 books and 5 shelves, the books can be placed in 30!/(5!*25!) ways, which is 5,852,114,406 ways.

A library is a collection of books, periodicals, audio and visual materials, and other educational and informational resources that are made available for public use. Libraries typically provide a range of services and resources, such as access to computers, books, reading materials, reference assistance, classes, and programs.

A. (a) All different: Since there are 30 books and 5 shelves, the books can be placed in 30!/(5!*25!) ways, which is 5,852,114,406 ways. This is because the number of ways to arrange 30 different books across 5 shelves is the same as the number of permutations of 30 objects taken 5 at a time.

B. (b) All identical: Since there are 5 shelves and 30 books, the books can be placed in 5^30 ways, which is 922,337,203,685,477,439,232,000 ways. This is because there are 5 choices for each book, so the total number of possible arrangements is 5^30.

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regression output from a model for predicting annual murders per million from percentage living in poverty based on a random sample of 20 metropolitan areas with Standard Error: 11.734

Regression Output:

R-squared: 0.674

Standard Error: 11.734

Intercept: -9.572

Poverty (%): 0.108

The interpretation of this output is that an increase of 1% in poverty is associated with an increase of 0.108 annual murders per million people. Additionally, this model explains 67.4% of the variance in annual murders per million people. The standard error of 11.734 indicates that the estimated regression line is likely to be 11.734 murders per million people away from the true population regression line.

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The following sequences are convergent an arithmetic sequence with d=-2/3.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where each successive number is obtained by adding a constant value to the previous number. This constant value is referred to as the common difference. Arithmetic sequences are especially useful in mathematics, as they can be used to model real-world phenomena such as population growth and the depreciation of assets. By finding the common difference, one can solve a variety of problems involving the sequence. For example, given two terms of an arithmetic sequence, one can find the sum of the sequence, the nth term, and the number of terms in the sequence.

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Answer:

The other answer is actually wrong.

The answers are: r=3/5 and r=-1/6

Step-by-step explanation:

Answer:

(-2,-7) , yes

(2,-1) , no

Step-by-step explanation:

the question says y is less than or equal to -2 . In the first order pair (-2,-7) , x= -2 & y = -7 in the number line -2 comes first than -7 it means -2 is grater than -7 so the answer is yes but in the second order pair (2,-1) the value of x is 2 and the value of y is = -1 thus -1 is grater than -2 however the question says y should be less or equal but not greater than -2 so the answer is yes for the first order pair and no for the second one

The range of the data set are

{10.2, 3.8, 21.9, 33.4, 31.8, 17.2} = 29.6

{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71} = 0.6

{6, 2, 14, 11, 28, 10, 19, 15, 11} = 26

The first data set is

{10.2, 3.8, 21.9, 33.4, 31.8, 17.2}

The range is the difference between the highest value and the smallest value

The highest value = 33.4

Lowest value = 3.8

The range = 33.4 - 3.8

= 29.6

The second data set is

{0.5, 0.65, 0.22, 0.11, 0.47, 0.55, 0.55, 0.71}

The highest value = 0.71

Lowest value = 0.11

The range = 0.71 - 0.11

= 0.6

The third data set is

{6, 2, 14, 11, 28, 10, 19, 15, 11}

Highest value = 28

Lowest value = 2

The range = 28 - 2

= 26

Therefore, the range of the each data set has been found

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Answer: A

Step-by-step explanation:

Our given equation is: y = -2x - 8

In order to have an equation with infinitely many solutions, it needs to be the same as the given equation.

Look at the answer choices:

A) y = -(2x + 8) = -2x - 8

This is the exact same equation, which means that any solutions for the given will also be solutions for this one. That means there will be infinitely many solutions.

B) y = -2(x - 8) = -2x + 16

We can tell this is definitely not the same as the given, so eliminate.

C) y = -2(x - 4) = -2x + 8

Again, this has a +8 instead of -8, so it's not the same and wrong.

D) y = -(-2x + 8) = 2x - 8

Here, we have positive 2 as the slope instead of -2, so it's not the same and wrong. Thus, the answer is A.