given that f(x)= 7x-1 and g(x) = 7-x^2, calculate

The truth table for the statement is

p     q     ~p    q ↔️ ~p   ~(q ↔️ ~p)

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

T     T     F     F        T

T     F     F     F        T

F     T     T     T        F

F     F     T     F        T

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

~(q↔️~p)

To construct the truth table, we make use of the following notations

p, q, ~p, (q↔️~p) and ~(q↔️~p)

The truth table for the statement ~(q ↔️ ~p) is then represented as follows:

p     q     ~p    q ↔️ ~p   ~(q ↔️ ~p)

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

T     T     F     F        T

T     F     F     F        T

F     T     T     T        F

F     F     T     F        T

The condition for ↔ is that it is true if both statements are true

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The original markup price that will lead to a markup on cost of 25 % would be $ 1. 68 per pound

To find the marked up price, first, find the amount that is a 25 % markup on cost to be :

= ( 100 pounds x 79 cents per pound ) x ( 1 + 25 %)

= 79 x 1. 25

= $ 98. 75

The 40 % sold would bring in:

= 40 % x 100 x 0. 79

= $ 31. 60

The amount left to be raised is:

= 98. 75 - 31. 60

= $ 67. 15

The markup price on the rest of the mushrooms is:

= 67.15 / ( 100 - 40 % - 20 %)

= $ 1. 68 per pound

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The fraction that correctly represents the ratio of 5 to 15 in it's simplest form is option C. 1/3.

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

The given ratio is 5 to 15.

Fraction in simplest form means that, the numerator and denominator cannot be factored by a common factor again.

In order to find the given ratio in simplest form, find the greatest common factor of both 5 and 15.

5 = 5

15 = 3 × 5

5 is the only common factor and so the greatest common factor of both 5 and 15.

5 / 15 = (5 × 1) / (5 × 3)

         = 1/3

Hence 1/3 is the simplest form of the ratio 5 to 15.

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Your question is incomplete. The correct question is as follows.

Chose the fraction that correctly represents the ratio 5 to 15 in simplest form.

A. 2/3

B. 10/30

C. 1/3

D. 1/5

The statement describes the solutions of this equation is

The Equation have two valid solution and No Extraneous solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

x/3 + (x-1)/ (x+ 4)= (x+3)/ (x+4)

Now, simplifying the above Expression

(x² + 4x + 3x - 3) / 3(x+4) = (x+3)/ (x+4)

(x² + 4x + 3x - 3) / 3 = (x+3)

x² + 7x -3 = 3(x+3)

x² + 7x -3 - 3x - 9 = 0

x² + 4x - 12 = 0

Solving the above Quadratic Equation

x² + 6x- 2x - 12 = 0

x(x+6)- 2(x+6)= 0

(x-2)(x+6)= 0

x= 2, -6.

So, the Equation have two valid solution and No Extraneous solution.

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Answer:

D

Step-by-step explanation: for p(x), the slope from 0 to 3 is 30, meaning if linear every time x increases by 3, the y value should as well, meaning that six as an x value to be linear should have been 90, but it was not.

For q(x), the slope from 0 to 3 is 90, and following the same thing from above, this means for every 3 units moved on the x, it should increase by 90 units on the y. This means 6 to be linear should have been 200 but instead was 380 making it also nonlinear

The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

g(x) = 4ˣ

The function is shifting up 2 and shifting right 5. Then the function is given as,

g(x) = 4⁽ˣ⁺⁵⁾ + 2

The function after reflecting over the x-axis is given as,

- g(x) = 4⁽ˣ⁺⁵⁾ + 2

g(x) = - 4⁽ˣ⁺⁵⁾ - 2

And then horizontally compressing by a factor of 5. Then the function is given as,

f(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2

The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.

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Answer:

C

Step-by-step explanation:

In this equation, you would need to do 32/5 to figure out how much each person will get. 32/5=6.4 feet

Hope this helps! Please give brainliest!

Answer:

To perform a t-test for the equality of two population means with unequal variances, we can use the Welch's t-test. In this test, the formula for the t-statistic is:

t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)

Where x1 and x2 are the sample means, s1^2 and s2^2 are the sample error variances, and n1 and n2 are the degrees of freedom for the two samples.

Plugging in the given values, we have:

t = (52.8 - 48.4) / sqrt(20.31/36 + 45.06/24) = 4.25

Next, we need to find the critical t-value from the t-distribution table with degrees of freedom equal to the smaller of n1 and n2, which is 24. With a 95% confidence level, the critical t-value is approximately 2.492.

Since our calculated t-statistic (4.25) is greater than the critical t-value (2.492), we reject the null hypothesis that the two population means are equal. This suggests that there is strong evidence that the mean yield of oats is different between the two experiments.

Step-by-step explanation:

The equation for the function is [tex]y=-0.15x+240[/tex].

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."

It is given that the amount of fuel filled up in Jon's semi truck is 240 gallons.

It is also given that for 1 mile the truck uses 0.15 gallons of fuel.

So, for "x" miles, the truck uses 0.15*x gallons of fuel.

So, the remaining fuel in the tank will be 240-0.15x.

Let the remaining fuel be "y".

This can be written as:

[tex]y=240-0.15x\\y=-0.15x+240[/tex].

Therefore the remaining fuel in the tank after Jon drives x miles will be a linear equation [tex]y=-0.15x+240[/tex]

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The quadratic equation y2 + 7y - 2 = 0 can be solved using the quadratic formula, which states that the solutions for x in the equation ax^2 + bx + c = 0 are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

We can apply the quadratic formula to this equation by letting a = 1, b = 7, and c = -2:

y = (-7 ± √(7^2 - 4 * 1 * -2)) / 2 * 1

y = (-7 ± √(49 + 8)) / 2

y = (-7 ± √57) / 2

So the solutions to the equation y2 + 7y - 2 = 0 are:

y = (-7 + √57) / 2

y = (-7 - √57) / 2

The solutions to the equation are y = (-7 + √57) / 2 and y = (-7 - √57) / 2.

Answer:

j1gru3hek3n

Step-by-step explanation:

bso2jw4usk8

Based on the information provided, we can prepare a cost of production report for the Roasting Department as follows: (see attached images)

A Cost of Production Report is a document that summarizes the total costs incurred by a company to manufacture a product or provide service during a specific period of time.

The report provides information on the direct materials, direct labor, and factory overhead costs that were involved in producing the item, as well as any other costs associated with the production process.

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Answer: 25 per child

Step-by-step explanation:

20 x 10 = 200

200/8 = 25

The ratio table is given below:-

Oranges      3         4       8     10     12  

Cost( in $)   3.75   5       10     12.5   15

Fractions are frequently used to describe ratios and proportions. A ratio is shown when a fraction is stated as a:b, whereas a proportion implies that two ratios are equal. a and b can be any two numbers in this situation. The ratio and proportion are two fundamental ideas that lay the groundwork for comprehending other concepts in mathematics and science.

We use the concept of ratio and proportion in our daily lives, such as in business when dealing with money or in cooking.

As a result, the ratio defines the relationship between two values, such as a:b when b is higher than zero. For example, the 2:4 ratio is expressed as 2:4 = 1:2. And in this instance, the comment is deemed proportionate.

Now,

As given no. of oranges = 8

Cost of 8 oranges = 10

cost of 1 orange=10/8=1.25 rs/orange

then

The table will be as follow

Oranges      3         4       8     10     12  

Cost( in $)   3.75   5       10     12.5   15

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Answer:

122.3°

Step-by-step explanation:

Vertical angles are congruent.  That means that they have the same measurement.

The set of numbers for which the statement that the square root of a number is greater than the square of the number is true, is equals to (0,1). So, right choice is option (a).

In mathematics, when we multiplying the number by itself, the result is called square of number. This is usually equivalent to raising a number to the power of 2. For example, square of 4 is 4² = 16. The square root of a number is that factor of a number which when multiplied by itself the original number. Square root of number is usually equivalent to raising a number to the power of 1/2. It is represented using the symbol '√'. Now, we have to check the options and determine where square root of a number is greater than the square of the number.

a) (0, 1), if we plug f(x) = √x , x∈(0,1) and g(x) = x² , x∈(0,1) on calculator then we get, the value of f(x) is greater than g(x), i.e, x = 1/2 , f(1/2) = 0.70 and g(1/2) = 0.25.

b) [0, 1], if we plug x = 0 then f(0) = 0 , g(0) = 0

that is f(x) is greater than and equal to g(x). But we have to consider only greater than not equal.

c) [1,∞), closed bracket again represents equality which is not consider. So, statement is false for it.

d) (1,∞), here number inbetween 1 and infinite but not for all reals it is true that square root of a number is greater than the square of the number, for example x = 2 , f(2) =1.414, g( 2) = 4 implies f(x)< g(x) for x = 2. So, the statement is false for it.

Hence, required option is option (a).

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Complete question :

The square root of a number is greater than the square of the number. For what set of numbers is this true?

a) (0, 1)

b) [0, 1]

c) [1, ∞ )

d) (1,∞)

Answer: To solve for the length of all sides, we need to set the perimeter equal to the sum of the lengths of the three sides:

30 cm = 3x + 2 + x + 4x - 6

30 cm = 8x + 2

Now we can solve for x:

30 cm = 8x + 2

28 cm = 8x

x = 28/8

x = 3.5

So each of the sides is 3.5 cm long, and the lengths of the three sides are:

3x + 2 = 3 * 3.5 + 2 = 11.5 cm

x = 3.5 cm

4x - 6 = 4 * 3.5 - 6 = 11.5 cm

Therefore, the lengths of the sides are 11.5 cm, 3.5 cm, and 11.5 cm.

Step-by-step explanation:

Answer:

(3x+2+4x-6)2=30

7x-4=30

7x=34

x=34/7

To find the side lengths of the rectangle;

3x+2=116/7. and. 4x-6=94/7

Answer: The  range of f(x) is [tex]f(x)\geq -2[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)+2=\frac{1}{6}|x-3|[/tex]

It can be written as

[tex]f(x)=\frac{1}{6}|x-3|-2[/tex]                ...(1)

The function is in the form of

[tex]g(x)=a|x-h|+k[/tex]               ...(2)

Where, a is scale factor and (h,k) is vertex of the graph.

On comparing (1) and (2), we get

[tex]a=\frac{1}{6}[/tex]

[tex]h=3[/tex]

[tex]k=-2[/tex]

The value of a is [tex]\frac{1}{6}[/tex] . So, the graph compressed vertically. The value of a is positive, therefore the graph of f(x) opens upward.

We know the absolute value is always greater than or equal to 0.

[tex]|x-3|\geq 0[/tex]

[tex]\frac{1}{6}|x-3|\geq \frac{1}{6}(0)[/tex]

[tex]\frac{1}{6}|x-3|\geq 0[/tex]

[tex]\frac{1}{6}|x-3|-2\geq 0-2[/tex]

[tex]f(x)\geq -2[/tex]

hope you've understood...

The order of the rectangular area from greatest to least is green sticker > yellow sticker > red sticker

The area of a rectangle is calculated by multiplying its length by its width. So if the length of a rectangle is l and the width is w, then its area A is given by the formula A = l x w.

To solve this problem, we can find the area of each sticker one after the other.

Area = length * width

1. red sticker = 2 * 1.5 = 3cm²

2. green sticker = 12 * 0.5 = 6cm²

3. yellow sticker = 3 * 1.25 = 3.75cm²

The order is green sticker > yellow sticker > red sticker

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The equations of the parabolas are y = x² - 6x - 7 and y = x² - 7

Parabola 1

Given that

The points (-1,0), (7, 0) and (3,-16)

The equation is represented as

y = ax² + bx + c

So, we have

a - b + c = 0

49a + 7b + c = 0

9a + 3b + c = -16

Make c the subject in a - b + c = 0

c = b - a

So, we have

49a + 7b + b - a = 0

9a + 3b + b - a = -16

48a + 8b = 0

8a + 4b = -16

Multiply 8a + 4b = -16 by 2

48a + 8b = 0

16a + 8b = -32

Subtract

32a = 32

So, we have

a = 1

Recall that 48a + 8b = 0

So, we have

48 + 8b = 0

This gives

8b = -48

Divide

b = -6

Also, we have

c = b - a

This gives

c = -6 - 1

c = -7

So, the equation is

y = x² - 6x - 7

Parabola 2

Given that

The points (-4,9), (-3, 2) and (0,-7) and (4,9)

The equation is represented as

y = ax² + bx + c

So, we have

16a - 4b + c = 9

9a - 3b + c = 2

c = -7

16a + 4b + c = 9

The equations become

16a - 4b = 16

9a - 3b = 9

16a + 4b = 16

Add (1) and (3)

32a = 32

So, we have

a = 1

Subtract (1) and (3)

-8b = 0

So, we have

b = 0

So, the equation is

y = x² - 7

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Using equations, they sold 165 tickets before both accounts had the same amount of money.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The variables that must be included in the equation are also known as the unknowns.

Given that, Jaelyn had $150 in the school account and sold tickets for the fundraiser at a cost of $8 per ticket.

and Erik had $480 in his school account and sold tickets for the fundraiser at a cost of $6 per ticket.

Let they sold x tickets and they have the amount in their account is y.

After sold tickets, Jaelyn accounts had the amount is

y = 150 + 8x

After sold tickets, Erik accounts had the amount is

y = 480 + 6x

the amount in their account is same, so we compare both equation to find x

150 + 8x = 480 + 6x

arranging like terms in same side

8x - 6x = 480 - 150

2x = 330

divide both sides by 2 we get,

x = 330/2

x = 165

So, they sold 165 tickets before both accounts had the same amount of money.

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If we select all possible samples of a certain size from this population, then, on average, the value of the sample variance is 36.

In Science, a population can be defined as a set of similar items or events that comprises every member of a group and from which a researcher, scientist, or experimenter, obtains or generates data for a statistical study.

In Statistics and science, a sample can be defined as a set of data that is collected from a population based on a well-defined sampling procedure.

In this context, we can reasonably infer and logically deduce that the sample variance on average would be equal to 36 because all possible samples of a certain size are selected from a population of 36 members.

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Answer:

6-oz bottle is a better deal

Step-by-step explanation:

To find which is a better value, find the unit rates for both types of bottles

The bottle with the lower unit rate is the better deal

6-ounce bottle costs $4.19
Unit rate = 4.19/6 oz = $0.70 per oz

14-ounce bottle costs $10.89
Unit rate = 10.89/14 = $0.78 per oz

Hence the 6-oz bottle is a better deal

To answer this question, we need to use some basic trigonometry. We know that Dirk's shadow is as tall as the town hall and that Dirk is 1.40m tall. So, if we can determine the angle of elevation of the spotlight, we can calculate the height of the town hall.

Let's call the angle of elevation "α" and the distance from the spotlight to the town hall "d". To determine α, we can use the tangent function.
tan α = opposite/adjacent = (d-5)/35 = (30/35) = 0.8571

The angle of elevation is arctan(0.8571) = 53.13°.

Now, we can use the sine function to calculate the height of the town hall:
sin α = opposite/hypotenuse = 1.4/d
d = 1.4/sin 53.13° = 16.2m

Therefore, the town hall is 16.2m tall.

Answer:

The solution is 23/500 or 0,046

Step-by-step explanation:

6 3/14÷250+5 2/7÷250

= 6 3/14×1/250+5 2/7×1/250

= (87/14×1/250)+(37/7×1/250)

= (87/3500)+(37/1750)

= 87+37(2)/3500

= 87+74/3500

= 161/3500

= 161÷7/3500÷7

= 23/500

= 0,046

Answer:

0.60

Step-by-step explanation:

sales tax=

\,\,\text{6\% of \color{blue}{bill}}

6% of bill

=

=

\,\,0.06\times\color{blue}{\$10}

0.06×$10

6% = 0.06

=

=

\,\,\color{green}{\$0.60}

$0.60

\text{The sales tax was \$0.60.}

The sales tax was $0.60.

Answer:

3w= 17.98-6.88

3w=11.1

w =3.7

Step-by-step explanation:

After subtracting divide both side by 3

Answer:

w = 3.70

Step-by-step explanation:

Given that,

6.88 + 3w= 17.98 ..........(1)

Now subtracting both sides by 6.88 in equation (1), We have

6.88 + 3w - 6.88 = 17.98 - 6.88

or, 3w + 0 = 11.1

or, 3w = 11.1

Again dividing both sides by 3 in the above equation, We have

[tex]\frac{3w}{3}=\frac{11.1}{3} = 3.70[/tex]

Hence the required answer is w = 3.70

On solving the provided question, we can say that the slope intercept equation is 12x + 3y = -3 and slope, m = -4

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

the slope intercept equation is

12x + 3y = -3

3y = -12x - 3

y = -4x - 1

also, y = mx + c

so, slope, m = -4

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Answer:

The percentage of students in Kiri's brother's class who think aliens exist is 11/25 = 44%.

Since the number of students in Kiri's class is not given, it's not possible to compare the percentage of students in Kiri's class who think aliens exist to the percentage in her brother's class. We need to know the number of students in Kiri's class and the number of students who believe in aliens in order to compare the percentages.

A rectangle's length is 4 inches greater than its breadth.. If the perimeter of the rectangle is 36. Area will be 77[tex]cm^{2}[/tex].

A quadrilateral with in all four of its angles being right angles is a rectangle. A quadrilateral with four right angles and four equal-length sides is called a square. As a result, a square is indeed a particular form of rectangle since it has rectangles with equal-length sides.As a result, a square is indeed a particular form of rectangle since it has rectangles with equal-length sides. Because a square is indeed a quadrilateral with in all four angles at right angles, every square is also a rectangle. To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.

Finding the Area , we obtain:

Let the rectangle's breadth be x cm.

Its length is then x+4 cm.

According to the problem,

2{x+x+4}=36

or, 2x+4=18

or, x=7.

So, breadth  is 7 cm and length is 11 cm.

So, the area  is 7×11=77 [tex]cm^{2}[/tex].

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