Select the correct answer,
Which function defines (f + g)(x)?
(3.8)242
(2.6)241
g(x)
(f 4 g)(x) = (2.6) 2+1
(f + g)(z) = (1.8)
(f 4 g)(x)
D. (f 4 g)(z) = (28)***
A.
B.
C.
(1.8)2247242

The inequality which represents the possible number of hours , x, the salesperson works this week is 20x + 800 ≥ 1400 where x ≥ 30,

using equation formation steps.

What is an equation ?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation.

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

In given que,

minimum earning = $1400

The possible number of hours = x

No. of cars sold = 8

Price earned by sold cars = $800

Price earned per hour =$20

Price earned for x hours = $20x

So, the total amount = 20x + 800

The equation become 20x + 800 ≥ 1400

Solving inequality que,

20x >= 600

x ≥ 30

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The equation that represents the total amount is y = 50(4+x).

The mathematical statement that shows two mathematical terms have equal values is known as an equation. An equation simply states that two things are equal.

Equations contain both constant terms and algebraic terms which are combined by operations like Adding and subtraction etc.

Here we have

An electrician charges a callout fee of $ 200 and $ 50 per hour

Given that the total amount charged is y for x hours

As we know the electrician charges $ 50 per hour

=> The charge per x hours = 50x

And callout fee = $ 200

The equation that represents the above situation is

=> y = 200 + 50x

=> y = 50(4+x)

Therefore,

The equation that represents the total amount is y = 50(4+x)

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The perimeter of triangle XYZ is 48 units

What is the perimeter of a triangle?

The total of a triangle's sides equals the triangle's perimeter. The space encircled by a triangle's three sides is known as its area.

Here, we have

In The triangle XYZ

A is the midpoint of XY

B is the midpoint of YZ

AB = 1/2 XZ

AB = 5 units

Substitute the value of XZ in AB

5 = 1/2 × XZ

XZ = 10 units

B is the midpoint of YZ

C is the midpoint of XZ

BC =  1/2 XY

XY = 24 units

BC = 1/2 × 24 = 12 units

A is the midpoint of XY

C is the midpoint of XZ

AC = 1/2 YZ

AC = 7

7 = 1/2 YZ

YZ = 14

The perimeter of a triangle = the sum of the lengths of its sides

Perimeter ΔXYZ = XY + YZ + ZX

Perimeter ΔXYZ = 24 + 14 + 10

Hence, the perimeter of triangle XYZ is 48 units

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The given p-series 1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex]) is divergent as the value of is equal to 3/4 ⇒p < 1.

As given in the question,

Given p-series is equal to :

1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex])

As value of 1³ = 1 and fourth root of 1³ is equal to 1.

We can substitute 1 = (1 /fourth root of 1³) which is equal to

= (1/ [tex]\sqrt[4]{1^{3} }[/tex] ) + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex])

Apply nth formula we get,

= [tex]\sum\limits^\infty_0 {\frac{1}{\sqrt[4]{n^{3} } } }[/tex]

⇒ p = 3/4

And 3/4 < 1

⇒ p < 1

⇒P-series is divergent.

Therefore, as the value of p =3/4<1 the given series  1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex]) is divergent.

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The number of sections that are most likely on each color on the spinner are

From the question, we have the following parameters that can be used in our computation:

Number of times the spinner is spun = 50 times

The outcomes are

Number of sections = 10

The section of each color is then calculated as

Color = Color outcomes/Number of times * Number of sections

Using the above as a guide, we have the following:

Red = 19/50 * 10 = 3.8

Green = 11/50 * 10 = 2.2

Black = 4/50 * 10 = 0.8

Orange = 16/50 * 10 = 3.2

Approximate

Red = 4

Green = 2

Black = 1

Orange = 3

The above represents the possible sections

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The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).

What is dilation?

A dilation is a function f from a metric space M into itself that, for any points x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real number. Such a dilatation is a resemblance of the space in Euclidean space.

Here, we have

Given

The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin.

We have to find the image after dilation.

The coordinates of an image (-10,-6), dilating the coordinate by 1/2 means reducing the image by multiplying each coordinate by the factor of 1/2.

Image = (1/2(-10), 1/2(-6))

Image = (-5,-3)

Hence, the image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).

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The balance of the loan (not made any payments yet) of the bank

be after one year charges 3.8% interest each year is; $7785

There are mainly two types of interest. One which works only on principal(or say initial) amount, and one which works on amount plus interest to be paid till date.

For 1 year case, if interest is applied annually, both interests are same since there is no interest before first year.

For 1 year, interest with R% rate for principal amount P is just R% of P which is; (P/100) * R

We are given that R = 3.8% each year

Since P = $7500, thus, interest for 1 year is 3.8% of $7500 is;

I = 7500/100 * 3.8

I = $285

Thus, total payable amount = Principal amount + interest

Total amount = $7500 + $285 = $7785

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2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).

Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.

Given

Polynomial

(2x³ + 4x² − 5x)(x³ + 2x - 1)

Multiplying by distributive method,

2x³(x³ + 2x - 1) + 4x²(x³ + 2x - 1) - 5x(x³ + 2x -1)

2x⁶ + 4x⁴ - 2x³ + 4x⁵ + 2x³ - 4x² - 5x⁴ + 10x² - 5x

Adding polynomials with same powers

2x⁶ + 4x⁵ + 4x⁴ - 5x⁴ - 2x³ + 2x³ - 4x² + 10x² - 5x

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).

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The solution is Option A.

The values of x that makes the inequality equation x² + 5x > 6 is -6 < x < 1

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

x² + 5x > 6   be equation (1)

Now , on simplifying the equation , we get

Subtracting 6 on both sides of the equation , we get

x² + 5x - 6 > 0

On factorizing the equation , we get

x² + 6x - x - 6 > 0

Taking the common terms in the equation , we get

x ( x + 6 ) - 1 ( x + 6 ) > 0

( x - 1 ) ( x + 6 ) > 0

So , the values of x are

x + 6 > 0

Subtracting 6 on both sides of the equation , we get

x > -6  

And ,

x - 1 < 0

Adding 1 on both sides of the equation , we get

x < 1

So , the inequality equation is true when x < 1 and when x > -6

Hence , the inequality equation is -6 < x < 1

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Answer: The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of -0.993 indicates a very strong negative relationship, which means that as one variable increases, the other variable decreases. This suggests that you can be quite confident that your predicted value will be reasonably close to the actual value.

Answer: 2.795

Step-by-step explanation:

[tex]cos 56= \frac{x}{5}[/tex]

Answer:

[tex]\boxed{1.1914285714285713}[/tex]

Step-by-step explanation:

Jill earned a total of 9 + 6/7 = <<9+6/7=9.857142857142857>>9.857142857142857 points.

Alice earned a total of 8 + 2/3 = <<8+2/3=8.666666666666666>>8.666666666666666 points.

Therefore, Jill earned 9.857142857142857 - 8.666666666666666 = <<9.857142857142857-8.666666666666666=1.1914285714285713>>1.1914285714285713 more points than Alice. Answer: \boxed{1.1914285714285713}.

Alice earned approximately 1.19 points more than Jill.

To find the difference between the number of points earned by Jill and the number of points earned by Alice, we need to first convert both amounts to a common denominator.

Since the denominators of the fractions representing the number of points earned by Jill and Alice are different, we will need to find a common denominator. To do this, we can find the least common multiple (LCM) of 7 and 3, which is 21.

We can then rewrite the fraction representing the number of points earned by Jill as 9 + 6/7 = (9 * 3 + 6)/21 = 27/21 + 6/21 = 33/21, and the fraction representing the number of points earned by Alice as 8 + 2/3 = (8 * 7 + 2)/21 = 56/21 + 2/21 = 58/21.

To find the difference between the number of points earned by Jill and the number of points earned by Alice, we can subtract the number of points earned by Alice from the number of points earned by Jill:

33/21 - 58/21

We can simplify this expression by combining like terms:

(33 - 58)/21 = -25/21

This represents a difference of -25/21 points, or approximately -1.19 points. Since a negative difference represents a smaller quantity, this means that Alice earned approximately 1.19 points more than Jill.

The pair of Linear angles are 51° and 129°.

When two lines intersect at a point then they will form two linear angles. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.

In other words, if the sum of two adjacent angles is 180° then the pair of angles are said to be Linear Angles.

Here we have

Two angles form linear angles

Let x and y be the two angles

=> x + y = 180 ------ (1)  [ since both are linear angles ]  

Given that the sum of one angle plus 27 is equal to two times the sum of the other angle

=> x + 27 = 2y

=> x = (2y - 27) ---- (2)

Substitute (2) in (1)

=> 2y - 27 + y = 180

=> 3y = 153

=> y = 153/3

=> y =  51  

Now substitute y = 51 in (1)

=> x + 51 = 180

=> x = 180 - 51

=> x = 129

The pair of Linear angles are 51° and 129°.

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The null hypothesis cannot be rejected.

Given that,

A study is done to determine the average cost difference between utilizing two different statistical tools to analyze data. 15 data sets are used to do this. Each program performs an analysis on each, and the cost of the analysis is noted.

To test if cost is same, we test mean difference of scores =0

H0: d=0

H0: d != 0

z0 = 0-(-05467) / 0.039976

= 1.367

z score for alpha = .05 is 1.96

Since, z0 < z score, we cannot reject the null hypotheses

Therefore, the null hypothesis cannot be rejected.

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The list that shows his scores from greatest to least is B. Week 2, 1, 3, 4

From the information, Julian tracks his progress on his reading quizzes over a period of four weeks. The list is given below:

Week 1 = 17

Week 2 = 20

Week 3 = 10

Week 4 = 9

It should be noted that we want to arrange from greatest to lowest. This will be 20, 17, 10 and 9. Therefore, the correct option is B

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The value of y when X value is -1 would be = -5

The substitution equation method is the method of solving equation whereby a value is being simplified and substituted into the second equation to obtain the next unknown value.

From the given equation:

(x-2)²/16 - (y-4)²/9 = 1

Take X = -1 and substitute X for -1 into the given equation,

(-1-2)²/16 - (y-4)²/9 = 1

9/16 - (y-4)²/9 = 1

(y-4)²/9 = 9/16- 1

(y-4)²/9 = -7/16

Cross multiply

(y -4)² = 9(-7)/16

y²+16 = -63/16

16(y²+16) = -63

16y²+256 = -63

16y² = -319

y² = -319/16

y² = -20

y= -√20

y = -4.5

y = -5

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For the function f(x)=4x²-3x-16 then value of f(-2) is 6.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=4x²-3x-16.

f of x equal to four times of x square minus three times of x minus sixteen.

We need to find the value of f(-2).

We need to replace the value of x with -2.

f(-2)=4(-2)²-3(-2)-16.

=4(4)+6-16

=16+6-16

=6

Hence, the value of f(-2) is 6 for the function f(x)=4x²-3x-16.

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Susie is correct as it is not a right triangle

        Square of the hypotenuse side = 289

        Squares of the other two sides = 12 * 12 = 144

                                                             =9 * 9 = 81

        Sum of the squares of the other two sides = 144 + 81

                                                                               = 225

        So, here 225 ≠ 289

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Thee value of the function f(2) is 70

A function can be defined as an expression, law or rule that stands to explain the comparison between two variables.

These are namely;

From the information given, we have the function as;

f(x)=(3x-1)(2x+10)

To determine the value of the function when x = 2, we have to substitute the value of x as

Now, substitute the value into the function, we have;

f(2) = (3(2) - 1 )(2(2) + 10)

expand the bracket

f(2) = (6 -1)(4 + 10)

Add or subtract the values

f(2) = (5)(14)

Multiply the values, we have

f(2) = 70

Hence, the value is 70

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The slope of a line that is perpendicular to a line whose equation is; 3y = -4x + 2 is; 3 / 4.

As evident in the task content is; the given equation is; 3y = -4x + 2.

To determine the slope of the given line; the equation can be expressed in slope-intercept form by dividing through by; 3.

y = -4/3x + 2/3

On this note, by comparison with the slope-intercept form of a linear equation; the slope, m is; -4/3.

Therefore, since the product of the slopes of perpendicular lines equal; -1;

The slope of the required line which is perpendicular to the given line can be determined as follows;

Slope of perpendicular; m = -1 ÷ (-4/3)

= -1 × 3 / -4

= -3 / -4

= 3/4.

On this note, the slope of the line perpendicular to the given line is; 3 / 4.

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Answer:5 cm

Step-by-step explanation:

Answer: w=2.5cm

Step-by-step explanation:

when solving for a right triangle, you need to to the length multiplied by the width and then divided by two. You then get (6*5)/2=30/2=15.

When solving for a rectangle, it’s the same, but without dividing by two. But you need them to be equal, and you already have the measure six.
So 5/2=2.5 therefore w=2.5cm.

The cost per pound of organic peaches is $4.27.

What is cost?

A cost is the value of money that has been expended in the production or delivery of a good or service and is therefore no longer available for use in accounting, retail, research, or accounting. In business, the cost may be one of acquisition, in which case the cost is the sum of the money used to acquire it.

Given:

Mia went to the store and bought 3 3/4 pounds of organic peaches for $16.

First to convert improper fraction into a fraction.

[tex]3\frac{3}{4} = \frac{4*3 + 3}{4} = \frac{15}{4}[/tex]

So Mia bought 15/4 pounds.

⇒ The cost per pound is,

[tex]\frac{16}{(\frac{15}{4} )} = 16*\frac{4}{15} = \frac{64}{15} = 4.27[/tex]

Hence, the cost per pound of organic peaches is $4.27.

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Because the slope of the supplied line is -4, the needed slope of a line perpendicular to y=-4x-7 is 1/4.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope of a line is its steepness as it goes from LEFT to RIGHT. Slope is the ratio of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always constant (it never changes) no matter what 2 locations on the line you select. The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b.

Here,

y=mx+c

m=-4

slope of a line perpendicular to y=-4x-7,

m1=1/4

The required slope of a line perpendicular to y=-4x-7 will be 1/4 as the slope of given line is -4.

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Answer:

17

Step-by-step explanation:

The value of x from the angles between given parallel line is 17.

Consecutive angles lie along the transversal, both angles will always be on one side of the transversal, and they'll either both be inside the parallel lines or outside the parallel lines (interior or exterior angles, respectively). Consecutive angles are always supplementary if the transversal crosses parallel lines.

From the given figure, we have two angles 2x+5 and 8x+5.

As we know, sum of consecutive angles is 180°

Now, 2x+5+8x+5=180

10x+10=180

10x=170

x=17

So, 2x+5=39° and 8x+5=141°

Therefore, the value of x from the angles between given parallel line is 17.

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The values of the probability in both scenarios are 0

First two dice show aces, and the next three do not

From the question, we have the following parameters that can be used in our computation:

Experiment = rolling of dice

The outcome of an ace is not in the sample space of rolling a die

This means that the probability is 0.

Two of the five dice show aces, and the other three do not

Here, we have

Experiment = rolling of dice

The outcome of an ace is not in the sample space of rolling a die

This means that the probability is 0.

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the number of defective balls produced in a lot of 500 balls is 26 when 7 defective balls are produced in a lot of 275, and 14 defective balls are produced in a lot of 375

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

calculation

let y be the number of defective basket balls

x be the total number of basketball produced

let y1 = 12 , x2 = 200

y2 = 19 , x2 = 350

since its given that no. of defective basketballs produced is related by a linear equation to the total no. of produced we have

y  = mx +c

m = 19 - 12 / 350 - 200 = 7/150

y = 7x/150 + c

put x = 200 , y = 12

12 - 7 * 200/ 150 = c

c = 8/3

y = 7x /150 + 8 /3 ...........1

no. of defective balls produced in a lot of 500 balls

y (500) = 7*500/150 + 8/3

= 70/3 + 8 /3 = 78/3 = 26

the number of defective balls produced in a lot of 500 balls is 26 when 7 defective balls are produced in a lot of 275, and 14 defective balls are produced in a lot of 375

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For binary class classification, assumptions are necessary in a way:

Given that

From Boyer Naive classifier,

We evaluate (ai | vj) is given below

(ai | vj) = n(e) + m(p) / n + m

Here,

m = equivalent sample size

n(e) = number of training examples

for which v = vj and a = ai

n(i) = number of training example for which v = vj

P = a prior estimate for P(ai | vj)

Here, we calculate that

P(SUV | yes), P(Red | yes), P(Domestic | yes)

P(SUV | no), P(Red | no), P(Domestic | no)

We evaluating this value like

yes:

RED :                             SUV:                            DOMESTIC:

n = 5                              n = 5                             n = 5

n(c) = 3                          n(c) = 1                           n(c) = 2

P = 0.5                          P = 0.5                           P = 0.5

m = 3                              m = 3                            m = 3

Therefore, with the above calculation we can justify that the simplifying assumptions are necessary in a binary class classification.

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Answer:

a) 1 degree above

b) 4 degrees below

c) 12 degrees above

d) 7 degrees above

Step-by-step explanation:

Answer:

5[tex]\sqrt{3}[/tex]i

Step-by-step explanation:

[tex]\sqrt{-5(5)(3)}[/tex]  You can pull out a 5 and you are left with [tex]\sqrt{-1}[/tex] and [tex]\sqrt{3}[/tex].

The [tex]\sqrt{-1}[/tex] = 1

5[tex]\sqrt{3}[/tex] i

Answer: [tex]5\sqrt{3} i[/tex]

Step-by-step explanation:

The square root of -75 is not a real number, because it is not possible to find a real number that when squared results in a negative number.

In mathematics, the square root of a number is defined as the number that, when multiplied by itself, equals the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. Similarly, the square root of 9 is 3, because 3 x 3 = 9.

However, it is not possible to find a real number that, when squared, results in a negative number. This is because any real number multiplied by itself is always positive, regardless of whether the original number was positive or negative. For example, the square of -2 is 4, because    (-2) × (-2) = 4, which is a positive number.

Double however, complex numbers are used to represent numbers that have a non-zero imaginary component, such as the square root of -1. Complex numbers are written in the form a + bi, where a and b are real numbers and i represents the imaginary unit.

Therefore, the square root of -75 can be written in simplified form as  [tex]5\sqrt{3} i[/tex], where [tex]i[/tex] is the imaginary unit. This represents a complex number with a real component of 0 and an imaginary component of [tex]5\sqrt{3}[/tex].

The best option which describes the p-value is 0.02 < p-value < 0.025.

We know that for the p-value method,

Z = (Sample Mean - Population Mean) / (standard deviation/sqrt (number of selections))

The average GPA for all the college students in the United States as of 2006 = 3.11 (Sample Mean)

The average GPA of randomly selected students at Texas A&M

= 3.27 (Population Mean)

Number of students randomly selected = 47

Standard deviation of them = 0.54

Therefore, Z = (3.27-3.11)/ (0.54/ sqrt(47)) = 2.031

Hence, by right tailed test,

p = 0.024

which implies, 0.02 < p-value < 0.025.

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