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03 Multiple Choice
Select all of the expressions that are equivalent to (9x+6)-(8x-4).
M. 2(x + 1)
P. 2x+6
R. 2x + 2
S. 2(x + 3)
T.
8x
OE
0/20

Answer:

Y=6x-12

Step-by-step explanation:

whenever the X is at zero the number across from it is the Y-intercept. and to find the slope just count how much they are increasing or decreasing by.

The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)

The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.

Here we have given the inequality (x² - 5)/ (x - 36) < 0

And we need to find the solution in inequality notation and in interval notation.

In order to find the inequality notation, we have to solve the given inequality, then we get.

(x² - 5)/ (x - 36) < 0

(x² - 5) < 0

x² < 5

x < √5

While we looking into the inequality we must know that the denominator must not be 0.

So, the interval notation can be written as,

=>  (-∞ . -√5]∪[√5,36)

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Sister's age will be equal to 12 and Kim's age is 24.

An equation is an expression that shows the relationship between two or more numbers and variables. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Consider that x is sister's age, Kim's age is twice that of her sister

Thus Kim's age = 2x

Kim’s age + Sister’s age = 36

The equation:

x + 2x = 36

Now solve the equation;

x + 2x = 36

3x = 36

 x = 36 / 3

 x = 12

Therefore, Kim's age = 2x = 2(12) = 24

Hence, Sister's age is 12 and Kim's age is 24.

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The equivalent expression for the given expression is 29/3.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given mixed fraction [tex]9\frac{2}{3}[/tex].

There are equivalent improper fractions for all mixed numbers. By multiplying the integer by the denominator and then adding the numerator, they are transformed. The numerator will not change.

Convert mixed fraction to improper fraction as follows

Improper fraction = [(Numerator × Denominator)+Numerator]/Denominator

[(9×3)+2]/3

=[27+2]/3

= 29/3

Therefore, the equivalent fraction for the given mixed fraction is 29/3.

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The value of y(0.4) is 1.04384484247985 using  Runge-Kutta method of fourth order .

What is  Runge-Kutta method of fourth order ?

The RK4 method, also known as the fourth-order Runge-Kutta method, is the Runge Kutta technique most frequently employed to get the answer to a differential equation. For a given point x, the Runge-Kutta technique returns an approximation of the value of y. The Runge Kutta RK4 method can only be used to solve first order ODEs.

The step size is h = 0.1

f(x,y) = (x²+y²)/10

Step 1:

x₁ = 0 + 0.1 = 0.1

k₁ =f(0,1) = 0.1

k₂ = f(1/20, 1.005) = 0.1012525

k₃ = f(1/20, 1.005062625) =0.101265088017189

k₄ = f(1/10, 1.01012650880172) = 0.103035556378395

y₁ = 1+ (1/10)/6 +(0.1 + 2⋅0.1012525 + 2⋅0.101265088017189 + 0.103035556378395) = 1.01013451220688

Step 2:

x₂ = x₁ + h = 1/5

k₁ =f(1/10,1.01013451220688)=0.103037173275143

k₂ = f(3/20,1.01528637087064) = 0.105330641487567

k₃ = f(3/20, 1.01540104428126) = 0.105353928072747

k₄ = f(1/5, 1.02066990501415) = 0.10817670550016

y₂ =1.01013451220688 + (1/10)/6 +(0.103037173275143 + 2⋅0.105330641487567 + 2⋅0.105353928072747 + 0.10817670550016) = 1.02067756250514

Step 3:

x₃ = x₂ + h = 3/10

k₁ =f(1/5, 1.02067756250514)=0.108178268660144

k₂ = f(1/4,1.02608647593815)=0.111535345610318

k₃ = f(1/4, 1.02625432978566)=0.111569794940382

k₄ = f(3/10, 1.03183454199918)=0.115468252206266

y₃ =1.02067756250514 + (1/10)/6 (0.108178268660144 + 2⋅0.111535345610318 + 2⋅0.111569794940382 + 0.115468252206266) = 1.03184184253794

Step 4:

x₄ = x₃ + h = 2/5

k₁ =f(3/10, 1.03184184253794) = 0.115469758801209

k₂ = f(7/20,1.037615330478)=0.119914557404297

k₃ = f(7/20, 1.03783757040816)=0.119960682255071

k₄ = f(2/5, 1.04383791076345)=0.1249597583947

y₄ = 1.03184184253794 + (1/10)/6 (0.115469758801209 + 2⋅0.119914557404297 + 2⋅0.119960682255071 + 0.1249597583947) = 1.04384484247985

y(0.4) ≈ 1.04384484247985

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To determine if the mean reduction in blood pressure is different between the two groups, you can use a statistical test such as a two-sample t-test. This test compares the means of two groups and determines whether the difference between the means is statistically significant.

To conduct the t-test, you will need the following information:

Once you have this information, you can use a statistical software or calculator to perform the t-test and determine the p-value. The p-value is a measure of the probability that the difference between the means is due to chance.

If the p-value is less than the level of significance (5% in this case), then the difference between the means is statistically significant and you can conclude that there is a significant difference in the mean reduction in blood pressure between the two groups.

If the p-value is greater than the level of significance, then the difference between the means is not statistically significant and you cannot conclude that there is a difference in the mean reduction in blood pressure between the two groups.

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the measure of ∠LPM is 90°

the measure of ∠PMN is 102°

the length of LN is 10 units.

Define Rhombus.

A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal.

For a Rhombus, LMNO

∠LON = 102°

NP = 5 units

By the properties of Rhombus, we know that

All sides of a rhombus are congruent (equal)

So, LM = MN = NO = OL

and

Opposite angles are equal and the opposite sides are parallel.

So, ∠LON = 102° = ∠LMN

Since Adjacent angles add up to 180°.

Therefore ∠L + ∠M = 180°

                 ∠M + ∠N = 180°

                 ∠N + ∠O = 180°

                 ∠O + ∠L = 180°

So, ∠N = 180° - ∠O = 180° - 102° =78°

      ∠L = 180° - ∠O = 180° - 102° =78°

      ∠M = 180° - ∠L = 180° - 78° =102°

Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.

So, ∠LPM = ∠NP0 = ∠MPN = ∠LPO =90°

Thus, the measure of ∠LPM is 90°

         the measure of ∠PMN is 102°

         the length of LN is 10 units.

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Answer:

Lpm= 90

PMN=51

LN= 10

Step-by-step explanation:

The distance between Wet Creek and Soggy will be 894.03 miles.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The distances between Dry Ravine, Wet Rivulet, and Saturated Waterway can be addressed by a triangle.

The distance between Dry Ravine and Wet Rivulet is 530 miles and the distance between Dry Gorge and Saturated Waterway is 721 miles.

The distance between Wet Creek and Soggy will be given as,

d² = 530² + 721²

d² = 280,900 + 518,400

d² = 799,300

d = 894.03 miles

The distance between Wet River and Soaked will be 894.03 miles.

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It has been (mathematically) proven that there is no polynomial time algorithm for any np-complete problem. the given statement is false.

In order to solve previously unsolvable issues, Leonid Khachiyan developed a polynomial-time method, in which the number of processing steps increases as a power of the number of variables rather than exponentially.

Determining whether NP-complete problems are tractable or intractable remains one of the most crucial concerns in theoretical computer science since it is unknown if any polynomial-time algorithms will ever be developed for them.

So, it is unknown if any polynomial-time algorithms will ever be developed for them.

By applying different constraints, a linear function is maximized or reduced in linear programming, a mathematical modelling approach. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

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As per the linear equation, the x-intercept of the graph of the equation will be (-8, 0).

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the information given in the question,

The given equation is,

y= -1/4 x + 2

Now, let's take y = 0 for x- intercept,

So, the equation will be,

0 = 1/4x + 2

1/4x = -2

x= -8

The x-intercept is (-8, 0).

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The question sees incomplete, your question may be:

Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?

The end behavior of the graph of the polynomial function:

As x approaches ∞, y approaches -∞

As x approaches -∞, y approaches ∞

What is an end behavior?

The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f.

Here, we have

f(x) = –x⁵ + 9x⁴ – 18x³

F(x) is a fifth-degree (odd function ) with a negative leading coefficient

If the exponent is odd and the leading coefficient is negative then the end behavior is

As x approaches ∞, y approaches -∞

As you go on the right, f(x) goes down

As x approaches -∞, y approaches ∞

As you go on the left, f(x) goes up.

Hence, the end behavior of the graph of the polynomial function: As x approaches ∞, y approaches -∞

As x approaches -∞, y approaches ∞

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c. A greater proportion of adolescent girls with anorexia nervosa live in the South than live in the other regions when compared to the general US population.

Null Hypothesis, [tex]H_{0}[/tex] : All proportions are the same  

Alternative Hypothesis, [tex]H_{1}[/tex]: At least two of the proportions are not the same

The alternative and null are both population-based assertions. The reason for this is that the purpose of hypothesis testing is to draw conclusions about a population from a sample.

The null and alternative hypotheses are two competing claims that researchers weigh the evidence for and against using a statistical test:

Null hypothesis: There’s no effect on the population.

Alternative hypothesis: There’s an effect on the population.

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The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.

Given that,

The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean,

In layman's words, the theorem asserts that regardless of the form of the initial population distribution, the sampling distribution of the mean tends to resemble a normal distribution as the sample size rises.

Statistics benefits from the Central Limit Theorem because it makes it safe to assume that the sampling distribution of the mean will be typically normal. As we will see in the next section, this means that we can benefit from statistical methods that presume a normal distribution.

The distribution of people's heights within a population is one illustration of how the central limit theorem is put to use. Even though the population's distribution of heights is not normal, when we sample this population, the distribution of the sample averages will be roughly normal.

Therefore,

The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.

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Answer:

-41.328

Step-by-step explanation:

Answer:

-41.328

Step-by-step explanation:

Addition multiplied by subtraction gets you subtraction. +-=-

so now, ()= multiplication

so now all you have to do is 17.22 times 2.4 which gets us 41.328

then, add the negative sign which gives you -41.328

yw :)

When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws variable has binomial distribution

The possibility that a value would take one of two independent values given a particular combination of factors or assumptions is summarised by the statistical distribution known as the binomial distribution.

The basic presumptions of the binomial distribution are:

As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.

The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.

The result is then multiplied by the sum of the number of attempts and the number of successes.

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Answer:

Step-by-step explanation:

a) 1012⁵ can be written as:

1012⁵ = 15¹² + 05¹¹ + 1*5¹º

= 5¹² + 5¹º

= 3125 + 625

= 3750

(b) 101⁵ can be written as:

101⁵ = 15⁴ + 05³ + 1*5²

= 5⁴ + 5²

= 625 + 25

= 650

(c) 1.1⁵ can be written as:

1.1⁵ = 15¹ + 15º

= 5¹ + 5º

= 25 + 5

= 30

(d) 10.21⁵ can be written as:

10.21⁵ = 15² + 05¹ + 25º + 15⁻¹

= 5² + 2*5º + 5⁻¹

= 25 + 10 + 0.2

= 35.2

(e) 210⁵ can be written as:

210⁵ = 25⁴ + 15²

= 2*625 + 25

= 1250 + 25

= 1275

Answer:

Hope this helps!

Answer:

0.1904

Step-by-step explanation:

4/7 ÷ 3 is = 0.1904

Answer: I hope this helps

Step-by-step explanation:

4/7 divided by 3

Dividing is equivalent to multiplying by the reciprocal
4/7 times 1/3 or 4/7•1/3

Multiply the fractions

And you get

4/21 or 0.190476

Variance  of customers who pay by card = 16

Mean number of customers = 20

Given that,

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with

P(A)=0.4,

P(B)=0.2,

and

P(C)=0.4

Because we are interested in whether or not a debit card was used, we can use the binomial distribution.

Let X= the number of customers who use a debit card.

Here, probability of customers who pay with debit card (or success) is

p=0.2

(a) Mean and variance of the number of customers who pay with a debit card:

The mean number of customers who pay with a debit card can be calculated as given below:

μ=np =100×0.2

=20

The variance of the number of customers who pay with a debit card can be calculated as given below:

σ²=np(1−p) =100×0.2(1−0.2)

=16

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Answer:

B, F

Step-by-step explanation:

[tex]2x^2(x-4)^2=0 \\ \\ \implies x^2=0, (x-4)^2=0 \\ \\ \implies x=0,4[/tex]

Answer:

9

Step-by-step explanation:

3.4^0 = 1

9^1 = 9

1 * 9 = 9

A 99% confidence interval for the true proportion of college students believing in ghosts is Option(c)  (0.4901, 0.6699)

According to the question,

A professor wanted to know what proportion of college students believe in ghosts.

For that he drawn a sample from the college.

Sample size : n = 200

Proportion of students that believed in ghosts in sample = 58%

=> p = 0.58

Proportion of students who does not believe in ghost : q = 1 - p

=> q = 0.42

We have to create a 99% confidence interval for a true proportion of college students believing in the ghosts

Formula of C.I = [tex]p \pm ( z_{\alpha} \sqrt{\frac{pq}{n}})[/tex]

Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size

C.I at 99% = 0.58 ± 2.576 √0.58×0.42/200

=> 0.58 ± 2.576 √0.001218

=>  0.58 ± 2.576 × 0.035

=> 0.58 ± 0.08958

C.I = ( 0.58 - 0.08958 , 0.58 + 0.08958)
=> C.I = (0.4901, 0.6699)

Hence, Option (c) is correct

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Answer:

41%

Step-by-step explanation:

So, the ordered pair which lies on the graph of the function y = -2x + 1 is (3,-5)

We will use the substitution method and check for all the ordered pair which are given

If the ordered pair lies on the graph, then it should satisfy the function.

So,

Given,

y = -2x+1

First check for (0,-2)

x=0, y=-2

Substitute the values,

y = -2x+1

-2=-2(0)+1

-2=1

It is false.

Next check for (2,-2)

x=2, y=-2

Substitute the values,

y = -2x+1

-2=-2(2)+1

-2=-3

It is false.

Next check for (3,-5)

x=3, y=-5

Substitute the values,

y = -2x+1

-5=-2(3)+1

-5=-5

It is true.

Next check for (5,2)

x=5, y=2

Substitute the values,

y = -2x+1

2=-2(5)+1

2=9

It is false.

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Answer:

See below and attached graph

Step-by-step explanation:

If you are using a graphing calculator it is a breeze. You write down the equation as it is and it should plot it, depending on what calculator you use.

If you are doing this manually here are the steps
We are given y - 2 = 3(x-2)

Expand the brackets on the right hand side
3(x - 2) = 3x - 6

So the original equation becomes
y - 2 = 3x - 6

Adding 2 to both sides
y - 2 + 2 = 3x -6 + 2

y = 3x - 4   [1]

This form of equation is known as a slope-intercept form of the line

We need two points to plot a line. This can be done by choosing a value for x, finding the y value which gives one point. Then repeat for another value of x to get y for that value giving another point. Draw a straight line through both points

Point 1
Let's choose x = 2 and plug this into the equation [1]
y = 3·2 - 4 = 6- 4 = 2.
So (2, 2) is one point on the graph

Point 2

Choose another value for x, say x = 4

y = 3·4 - 4

y = 12-4

y = 8

So (4, 8) is another point

Draw a line through these two points

A. Model is fitted using training dataset and E. Validation dataset is used to minimize model overfitting are true about machine learning algorithms

The process by which an AI system completes its task—generally, forecasting output values from provided input data—is known as a machine learning algorithm. Classification and regression are the two key operations of machine learning algorithms.

Simple linear regression, decision trees, logistic regression, the KNN algorithm, and other well-known supervised learning techniques are some examples.

Machine learning is crucial because it helps businesses identify trends in customer behaviour and operational patterns and facilitates the creation of new goods.

According to the question,

Option A and option E are correct about the machine learning algorithms

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According to Trigonometric Identity , tan(theta) = -5 / 13

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. The relationship between a triangle's side length and angle is expressed by a variety of specific trigonometric identities.

Sin, cos, and tan are the three fundamental trigonometric ratios. The reciprocals of sin, cos, and tan are represented by the three additional trigonometric ratios sec, cosec, and cot in trigonometry, respectively.

According to the given information

We know that

tan(theta) = 1/cot(theta)

                = 1 / -2.6

                = -1 / 2.6

                = -10 / 26

                = -5 / 13

According to Trigonometric Identity , tan(theta) = -5 / 13

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The interest accrued in the first four years is $1.69 and a half years is $0.21.

What is interest rate?

The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given:

Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college.

The rate is 4.3%.

We have to find the interest accrued in the first four-and-a-half years.

First to find the interest for first four years.

p = $9.800,  r  = 4.3% = 0.043,  t = 4

⇒ I = P x r x t

   I = 9.800 x 0.043 x 4

   I = 1.6856

   I = $1.69

Now to find the interest for a half years.

p = $9.800 ,  r = 4.3% = 0.043,  t = 1/2

I = p x r x t

I = 9.800 x 0.043 x 1/2

I = 0.2107

I = $0.21

Hence, the interest accrued in the first four years is $1.69 and a half years is $0.21.

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Answer:

  7.2 cm

Step-by-step explanation:

You want the value of C to the nearest tenth centimeter, given that 4^2 + 6^2 = C^2.

Simplifying gives ...

  4^2 + 6^2 = C^2

  16 +36 = C^2 = 52

  C = √52 ≈ 7.2

The length of the missing side is about 7.2 cm.

Step-by-step explanation:

for question 1, the change in y is the highest value takeaway the lowest value.

change in y = 10 - 1 = 9

change in x = 6 - (-3) = 9

9/9 = 1

therefore m = 1, this works for all the questions