f'(x) = 4f(x) and f(0) = 10

The graph of the inequality is attached below.

We are given an inequality. The inequality is linear in nature. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. The inequality is given below.

y < 2x - 3

We need to graph the inequality. The first step is to find out the corresponding equation of the straight line. The equation is found by replacing the greater-than or less-than sign with the equal-to sign. The equation is given below.

y = 2x - 3

We plot this equation on the graph with a dotted line. Now we shade the area that satisfies the given inequality. The graph is given below.

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Answer:

Step-by-step explanation:

Arithmetic Sequence

Answer:

  (a)  Arithmetic Sequence

Step-by-step explanation:

You want to know if the graph of a straight line represent an arithmetic, geometric, or neither sequence.

An arithmetic sequence is characterized by a common difference between terms that are 1 unit apart. A graph of an arithmetic sequence is points that lie on a straight line.

The graph shows an Arithmetic Sequence.

__

Additional comment

A graph of a geometric sequence would show points that lie on an exponential curve.

The value of x in the given triangle is x = 12  .

Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .

In the question ,

a triangular figure is given

in which , the measure of angle A is (6x - 19)°

the measure of angle B is [tex]=[/tex] 84°

the measure of angle C is [tex]=[/tex] (3x + 7)°

So , By Angle sum property ,

we get

∠A + ∠B + ∠C [tex]=[/tex] 180°

substituting the values of angle A, B and C ,

we get

(6x - 19)° [tex]+[/tex] 84° + (3x + 7)° [tex]=[/tex] 180°

6x - 19 [tex]+[/tex] 84 [tex]+[/tex] 3x + 7 [tex]=[/tex] 180

9x + 72 = 180

9x = 180 - 72

9x = 108

x = 108/9

x = 12

Therefore , the value of x is [tex]=[/tex] 12

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Sophie's favorite number is 83

We have that;

A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.

To get Sophie's favorite number, we need to assume the case as;

Let,

⇒10x + y = 10y + x + 45

   x + y = 11

   y = 11-x

⇒10x + 11 - x = 10(11 - x) + x + 45

  10x + 11 - x = 110 - 10x + x + 45

  9x + 11 = 155 - 9x

  18x + 11 = 155

  18x = 144

  x = 8

Therefore, y = 11 - 8

                  y = 3

Sum = x + y = 8 + 3 = 11

Hence, the given condition is satisfied.

Sophie's favorite number is 83.

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Answer:

P=(2.25 x 10^4)(1 + 0.051)(1 +0.051)

Step-by-step explanation:

The number of combinations of random samples of 5 students can be 792.

Given, 12 groups of students

We have to select random samples of 5 students,

Here we will use the combination formula,

Cₙ,ₓ = n! / x! (n - x)!

Here n=12 and x=5

Cₙ,ₓ = 12! / 5! (7!)

Cₙ,ₓ = 479,001,600 / (120) × (5040)

Cₙ,ₓ = 792

Therefore the possible ways of selecting the random samples of 5 students are 792.

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By using the concept of equation of line in slope intercept form, it can be obtained that

a)  x- intercept is 5

  This means, Priya has exhausted all her money by buying 5 comics

   y- intercept is 20

   This means, Priya had $20 before buying any comics

b) Slope = -4

   This means Priya's money has been decreasing by $4 after buying        one comics    

c)  Equation of line

     y = -4x + 20

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

x represents the number of comic books Priya buys at the store

y represents the amount of money (in dollars) Priya has after buying the comic books.

a)From the figure, it is clear that x- intercept is 5

  This means, Priya has exhausted all her money by buying 5 comics

   From the figure, it is clear that y- intercept is 20

   This means, Priya had $20 before buying any comics

b) The line passes through (5, 0) and (0, 20)

    Slope = [tex]\frac{20 - 0}{0 -5}[/tex] = -4

     This means Priya's money has been decreasing by $4 after buying

    one comics

c) Equation of line

   y - 0 = -4(x - 5)

   y = -4x + 20

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Complete Question

The figure has been attached-

The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram

The statement is  

"The median and altitude of an isosceles triangle can be same"

Draw an isosceles triangle ABC with BD = CD,

Draw a line segment AD perpendicular to the side BD

Here AD is the height of the triangle which is the altitude of the triangle

From the figure we can see that the length of BD = length of CD

Where D is the mid point of the line BD.

Therefore the line AD is the median of the triangle

Hence, The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram

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Answer: The sum of two prime numbers is always even (which is composite).

Hope this helped :)

The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289.

What is a sequence?

A sequence is a function from natural numbers to the set of real numbers. it maps the set of number numbers on the set of real numbers.

We are given a sequence 8, 5,2, -1,.....

Now the first term of the sequence is 8 and common difference is -3.

As the difference between 2 consecutive terms is same, the given sequence is arithmetic.

now substituting this in the standard equation

we get,

t(n) = a+ (n-1)d

t(n)= 8+(n-1)(-3)

t(n) = 8-3n+3

t(n) = 11-3n                           (1)

Now we have to find the 5th, 6th, 7th term of the sequence

We substitute n=5, n=6, n=6 in equation 1

We get

t(5) = 11-3(5)

t(5) = 11-15

t(5) = -4

And,

t(6) = 11-3(6)

t(6) = 11-18

t(6) = -7

And,

t(7) = 11-3(7)

t(7) = 11-21

t(7) = -10

Hence the next three terms are -4, -7, -10.

The equation is t(n) = 11-3n

The 100th term would be given as

t(100)  = 11-3(100)

t(100)  = 11-300

t(100) = -289

Hence, The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289

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The equation using the absolute value function is x+2y-8=0.

In the given graph, we have:

(h, k) ∈ (4, 2) and a = -1/2

In the general absolute value function, substitute these values:

Let's f(x) be y:

Therefore, the equation using the absolute value function is x+2y-8=0.

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The expression similar to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.

A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]

According to some of the laws of indices, we have;

[tex]\dfrac{1}{x^n} =x^{-n}[/tex]

[tex]x^m \cdot x^n = x^{m+n}[/tex]

[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]

The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]

Simplifying the above expression gives;

[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

Collecting terms with an index of a multiple of 3 gives;

[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]

[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

The expression that is equivalent to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.

A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

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Answer:

y+6 =-2(x-5)

Step-by-step explanation:

The question is asking for the equation of the line

The equation for point-slope form is always written as y-y₁=m(x-x₁)

y₁ and x₁ are the points given to you in this order (x₁, y₁)

so x₁=5 and y₁=-6

Now you plug in all the numbers you have into the point slope form

y- (-6)= -2(x-5)

When you subtract a negative (a double negative you get a positive)

y+6=-2(x-5)

Point-Slope form is usually the easiest form of a line to write since you do not need to solve for any intercepts or other points. You have y on one side of the equation, usually the left to make it easier to read, and x on the other, usually the right.You subtract the point that you are given from the y and the x. Multiply everything that is on the same side of the equation of the x by the slope (m).

Notes:

For y₁ and x₁, they could be any point on the line. For example, (1,2) is also on this line. So the equation would be

y-2=-2(x-1)

Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

As per the unitary method, the cost of 8 bottles is $6.48

Unitary Method:

Unitary method is the way of solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

Hawa buys 15 bottles of apple juice at the corner store for a total cost of $12.15.

Here we need to find the if each bottle costs the same amount, how much is 8 bottles of juice.

Let x be the cost of one bottle.

so, based on the unitary method we can written the situation as,

15 bottles = costs $12.15

Therefore, the cost of one bottle is.

x = 12.15/15

x = 0.81

So, the cost of 8 bottle is calculated by multiplying the cost of one bottle with 8,

Then we get,

=> 8 x 0.81

=> 6.48

Therefore, the cost of 8 bottles is $6.48

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The ordered pairs that are a solution to the given linear equation -5x + 3y > 12 are:

In order to determine which ordered pairs are true solutions based on the given linear equation, we would have to test each of the ordered pairs by substituting their values into the linear equation as follows;

For ordered pair (3, 9), we have:

-5x + 3y > 12

-5(3) + 3(9) > 12

-15 + 27 > 12

12 > 12 (False).

For ordered pair (-5, 5), we have:

-5x + 3y > 12

-5(-5) + 3(5) > 12

25 + 15 > 12

40 > 12 (True).

For ordered pair (3, -6), we have:

-5x + 3y > 12

-5(3) + 3(-6) > 12

-15 - 18 > 12

-33 > 12 (False).

For ordered pair (-2, -5), we have:

-5x + 3y > 12

-5(-2) + 3(-5) > 12

10 - 15 > 12

-5 > 12 (False).

For ordered pair (2, 8), we have:

-5x + 3y > 12

-5(2) + 3(8) > 12

-10 + 24 > 12

14 > 12 (True).

For ordered pair (-6, 0), we have:

-5x + 3y > 12

-5(-6) + 3(0) > 12

30 + 0 > 12

30-5 > 12 (True).

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The algebraic expression is C(5) =2.5 * 5 + 1.4 and the total cost is $13.9

From the question, the equation of the total sales amount is given as

Equation = 2.3q + 1.4

Where q represents the number of days

Rewrite as

Cost = 2.3q + 1.4

Express the equation as a cost function

So, we have the following representations

C(q) = 2.3q + 1.4

When the number of days is 5, we have

q = 5

Substitute the known values in the above equation So, we have the following equation

C(5) =2.5 * 5 + 1.4

Evaluate the products

C(5) = 12.5+ 1.4

Evaluate the sum

C(5) = 13.9

Hence, the total cost for the 5 days is $13.9

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Answer:

$72 / hr

Step-by-step explanation:

$36 / (1/2 hr ) =  $72 per hour

Answer; the  Negative of 12 is -12

Step-by-step explanation: first of all the reciprocal of 12 is 1 over 12. so that's not it. The absolute value of 12 is still 12 so that's not it. So the only thing that it can be is the Negative of 12 is -12  

Using the theories of statistical design, we got that both related sample t test and one-way within-subjects ANOVA is the appropriate statistical design for the study in which a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus.

Statistical design of experiments and the  response surface methodology has become a standard tool for the medium development. There are several applications reported in literature, such as the production of antibiotics, secondary metabolites, and enzymes.

Applications of statistical design of experiment shown in the Table 1 and several other studies use exclusively of the response surface method with quadratic polynomial models and the central composite design with on average 20–30 experiments. In most cases, the important components were identified by fractional factorial design or by the Plackett–Burman design with 10–15 experiments. Methods for narrowing  optimal variable range are only infrequently applied.

Hence, when a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus and wants to know if anxiety levels were higher in the fearful stimulus condition and if the same participants are observed in each group, then the appropriate statistical design is  that both related sample t test and one-way within-subjects ANOVA .

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The z-observed value for the test of average number of times that a typical american says a word that is considered to be profane is -0.41.

The formula for calculating the z-score is-

z = (x - μ)/s

in which,

n = sample size (= 15)

μ = mean (= 4)

σ = standard deviation (= 5.6)

s = σ/√n

s = 5.6/√15

s = 1.44

Put the value in z score;

z = (3.4 - 4)/1.44

z = -0.41

Because of how near to zero this test statistic is, we will not be able to rule out the null hypothesis. Seven.

There isn't enough proof to claim that there is a mean difference or that it exists in your circumstance.

Thus, they're basically arguing that we can't rule out the null hypothesis.

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Answer:

1368

Step-by-step explanation:

let 3rd game be x

151+183+x=1702

334+x=1702

x=1702-334

x=1368

The length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

According to the question,

We have the following information:

The first side of a triangle is 2 feet longer than the second. The third side is 5 feet shorter than twice the second. The perimeter is 49 feet.

Let's take the second side to be x feet.

So, we have the following sides:

First side = (x+2) feet

Third side = (2x-5) feet

Perimeter = 49

x+x+2+2x-5 = 49

4x-3 = 49

Adding 3 on both the sides:

4x = 49+3

4x = 52

Dividing by 4 on both the sides:

x = 52/4

x = 13 feet

First side = 2+13

First side = 15 feet

Third side = 2*13-5

Third side = 26-5

Third side = 21 feet

Hence, the length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Equation of a line:

y = 2x  - 3

y = 2 x 0 - 3 = -3

y = 2 - 3 = -1

y = 2 x 2 - 3 = 4 - 3 = 1

Table

x   0     1     2

y  -3    -1     1

The graph of the straight line is given below.

Thus,

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

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The radical form of each of the given expressions are;

1) 2^(2/3) =  ∛(2²)

2) 3^(1/3) = ∛3

3) 3^(3/2) = √3³

4) 2^(1/2) = √2

The radical form of the expression [tex]a^{\frac{x}{y} }[/tex] is; [tex]\sqrt[y]{a^{x} }[/tex]

Thus, we can solve each of the given expressions;

1) We are given the expression as 2^(2/3).

Thus;

x = 2 and y = 3 and we have; ∛(2²)

2) We are given the expression as 3^(1/3).

Thus, x = 1 and y = 3 and so we have;

∛3

3) We are given the expression as 3^(3/2). Thus;

x = 3 and y = 2 and so we now have; √3³

4) We are given the expression as 2^(1/2). Thus;

x = 1 and y = 2 and so we now have; √2

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The equation of line [L] would be y = (1/6)x + 9.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have a equation of line [k] is y + 2 = -6(x - 7). Line [L] includes the point (-6,8) and is perpendicular to line k.

We have the equation of line [K] as -

y + 2 = - 6(x - 7)

y = - 6(x - 7) - 2

y = - 6x + 42 - 2

y = - 6x + 40

Slope of line [L] will be -

m[L] = 1/6

Assume the equation to be -

y = (1/6)x + c

Line [L] includes the point (-6, 8), so we can write -

8 = (1/6) x (- 6) + c

8 + 1 = c

c = 9

So, the equation will be -

y = (1/6)x + 9

Therefore, the equation of line [L] would be y = (1/6)x + 9.

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There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

Given,

The equations;

The value of k = -50

We have to solve the given equations using k as -50 and find the true ones;

Lets check;

1.5 - (-50/5) = 11.5

1.5 - (-10) = 11.5

1.5 + 10 = 11.5

11.5 = 11.5

This equation is true.

(-2 x -50) + 78 = -22

100 + 78 = -22

178 ≠ -22

This equation is false

(-4 x -50) + 80 = -120

200 + 80 = -120

280 ≠ -120

This equation is false

(6 x -50) - 150 = -150

-300 - 150 = -150

-450 ≠ -150

This equation is false

(-50/10) - 3 = -8

-5 - 3 = -8

-8 = -8

This equation is true.

That is,

There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.

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The diagonal of the rectangle is 14.87 units.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area of rectangle = 110 square units

Length = 11 units

Area of a rectangle = Length x Wide.

110 square units = Length x Wide

110 = 11 x Wide

Wide = 110/11

Wide = 10

Now,

The diagonal of a rectangle.

Using the Pythagorean theorem we get,

Diagonal² = Wide² + Length²

Diagonal² = 10² + 11²

Diagonal² = 100 + 121

Diagonal² = 221

Diagonal = √221

Diagonal = 14.87 units.

Thus,

The diagonal of the rectangle is 14.87 units.

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