Graph the solution to this inequality on the number line. 2/3z > 4/5

Answer:

C) ( 8,2) and (4,1)

The slope of the line

         \(m = \frac{1}{4}\)

Step-by-step explanation:

Explanation:-

Given that the set of points ( 8,2) and (4,1)

ThesSlope of the line

             \(m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }\)

             \(m = \frac{1-2 }{4-8 }= \frac{-1}{-4} = \frac{1}{4}\)

The slope of the line

         \(m = \frac{1}{4}\)

The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.

Given the following information from the table:

Likes running: 28

Does not like running: 46

Column totals: 74

Enjoys swimming: 62

Enjoys cycling: 90

Row totals: 110

The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:

Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)

From the table, the number of students who do not like running and enjoy swimming is given as 46.

Total number of students is given as 74.

Joint relative frequency = 46 / 74

Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.

Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.

In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.

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In total, the number of greetings will be 1159.

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

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Answer: 4

Step-by-step explanation:

(Can someone please answer my math question)

The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

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Answer:

Step-by-step explanation:

51,200 divided by 52. (52 weeks in a year.) 984.615385 is answer. So each week he gets paid $984.62. So then we multiply that by 3 since we are finding 40% of 3 weeks of pay. $984.62x3= $2953.86. Then we multiply that by 40%.. $2953.86x40%= Answer is $11181.54

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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Answer:

f(g(3) = 1

Step-by-step explanation:

f(g(3)

Step one: Plug in 3 for X

g(x)= 2x - 5  ->  g(3) = 2 * 3 - 5

Step two : Solve ( By Using PEMDAS)

g(3) = 6 -5

g(3) = 1

The total pounds of trash is 4500 pounds. Then the number of trips that will take for the Jones Company to remove all of the trash will be 9.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Each truck from Jones Expulsion Organization can pull 500 pounds of waste at a time. On Wednesday, the organization has tasks to eliminate 1,500 pounds of garbage from one site, 500 from another site, and 2,500 from a third site.

The total pounds of trash is given as,

⇒ 1500 + 500 + 2500

⇒ 4500 pounds

The number of trips will it take for the Jones Company to remove all of the trash will be given as,

⇒ 4500 / 500

⇒ 9

The total pounds of trash is 4500 pounds. Then the number of trips that will take for the Jones Company to remove all of the trash will be 9.

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Answer:   a-b = 3

Step-by-step explanation: if the a = 5 and the b = 2    a+b=7    ab=10

\( \sf \: a + b = 7 => a=7-b- - - - (1) \\ \sf \: ab = 10 - - - --(2)\)

Put equation 1 in 2:

\( \sf(7 - b) b= 10\)

\( \sf7b - {b}^{2} = 10\)

\( \sf { - b}^{2} + 7b - 10 \\ \sf {b}^{2} - 7b + 10\)

Factor the quadratic equation:

\( \tt {b}^{2} - 7b + 10 \\ \tt {b}^{2} - 5b - 2b + 10 \\ \tt \: b(b - 5) - 2(b - 5) \\ \tt \: (b - 5)(b - 2) \\ \tt \: b_{1} = a = 5 \: and \: b_{2} = 2\)

Therefore,

The length of the line segment AB is 5 units.

Unfortunately, you haven't provided any information about PQ such as its location or any other data to help solve the question.

Therefore, it's impossible to determine the length of PQ using the given options. However, here is an explanation of how to find the length of a line segment using the distance formula, which may help you in solving similar questions in the future.

The distance formula is used to find the distance between two points in a coordinate plane, such as the length of a line segment. The formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where d is the distance, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

To use the distance formula, you first need to find the coordinates of the two points that make up the line segment. Then, substitute these coordinates into the formula and simplify to find the distance.

For example, let's say you have two points: A(1, 2) and B(4, 6), and you want to find the length of the line segment AB. Using the distance formula:

d = √((4 - 1)² + (6 - 2)²)
d = √(3² + 4²)
d = √(9 + 16)
d = √25
d = 5

Remember, the distance formula can be applied to any two points in a coordinate plane to find the distance between them.

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Let's use the point-slope formula to find the equation

Replacing the point and the slope, we have.

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  confidence interval is  \(64.86<\mu<67\)

Step-by-step explanation:

From the question we are given the following data

   The following heights are

66, 65, 67, 62, 62, 65, 61, 70, 66, 66, 71, 63, 69, 65, 71, 66, 66, 69, 68, 62, 65, 67, 65, 71, 65, 70, 62, 62, 63, 64, 67, 67      

 The  sample size is n  =32

  The confidence level is \(k = 95\)% = 0.95

The mean is evaluated as

          \(\= x = 66+ 65+ 67+ 62+ 62+ 65+ 61+ 70+ 66+ 66+ 71+63+ 69+ 65+ 71+ 66+ 66+ 69+ 68+ 62+ 65+ 67,+\\65+ 71+ 65+ 70+ 62+ 62+ 63+ 64+ 67+ 67 / 32\)

=>   \(\= x = \frac{2108}{32}\)

=>     \(\= x = 65.875\)

The standard deviation is evaluated as

           \(\sigma = \sqrt{ v}\)

Now  

   \(v = ( 66-65.875 )^2+(65-65.875)^2+( 67-65.875)^2+ (62-65.875)^2+ (62-65.875)^2+ (65-65.875)^2+( 61-65.875)^2+ (70-65.875)^2+ (66-65.875)^2+ (66-65.875)^2+ (71+63-65.875)^2+ (69-65.875)^2+ (65-65.875)^2+ (71-65.875)^2+( 66-65.875)^2+ (66-65.875)^2+ (69-65.875)^2+ (68-65.875)^2+ (62-65.875)^2+ (65-65.875)^2+ (67-65.875)^2,+\\(65-65.875)^2+ (71-65.875)^2+ (65-65.875)^2+ (70-65.875)^2+( 62-65.875)^2+( 62-65.875)^2+ (63-65.875)^2+ (64-65.875)^2+ (67-65.875)^2+ (67-65.875)^2 / 32\)

=>\(v= 8.567329\)

=>   \(\sigma = \sqrt{8.567329}\)

=>   \(\sigma = 2.927\)

The level of significance is evaluated as

        \(\alpha = 1 - 0.95\)

        \(\alpha = 0.05\)

The degree of freedom is  evaluated as

    \(Df = n- 1 \equiv Df = 32 -1 = 31\)

The critical values for the level of significance is obtained from the z -table as

      \(t_c = t_{\alpha/2 } , Df = t _{0.05/2}, 31 =\pm 1.96\)

The confidence interval is evaluated as

       \(\mu = \= x \pm t_c * \frac{\sigma }{\sqrt{n} }\)

substituting values

        \(\mu =65.875 \pm 1.96* \frac{2.927}{\sqrt{32} }\)

       \(\mu =65.875 \pm 1.01415\)

=>    \(64.86<\mu<67\)

Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.

A graph can be described  as a pictorial representation or a diagram that represents data or values in an organized manner.

The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.

In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.

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Answer:

D

Step-by-step explanation:

it is a quadratic trinomial

A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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Answer: -24

Step-by-step explanation:

\(\frac{x}{3}=-8\\\frac{x}{3}(3)=-8(3)\\ x=-24\)

Answer:

\(\displaystyle 4\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

g(x) = 4x

Interval [1, 5]

Step 2: Find Change

Answer:

Step-by-step explan

21

The slope of AB is given by:(0 - (-1/2x - 5/2)) / (0 - x)= 1/2

Given that the slope of BC is -1/2. We need to find the slope of AB.

Slope of a line can be defined as the ratio of the change in y-coordinate to the change in x-coordinate between any two distinct points on the line.

Let us consider the coordinates of point B as (x, y)Coordinates of point C can be obtained by moving 3 units to the right from point B.

Therefore, coordinates of point C are (x+3, y+1).Since the slope of BC is -1/2, we can say that:(y+1 - y) / (x+3 - x) = -1/2y + 1 = -1/2(x + 3)y = -1/2x - 5/2Therefore, the coordinates of point B are (x, -1/2x - 5/2).

Point A lies on the x-axis. Therefore, its y-coordinate is zero. Therefore, the slope of AB is given by:(0 - (-1/2x - 5/2)) / (0 - x)= 1/2

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First do inside the parentheses:

4 + [8/1 + 6-12] . 10

Now work inside the brackets doing division first

4 + [8 + 6 -12]. 10

Still inside the brackets add an subtract from left to right:

4 + 2 . 10

Multiply:

4 + 20

Add to get final answer of 24

Answer:

4+[8 ÷(8-7) +6 -12] . 10

4+[8÷1+6-12].10

4+[8+6-12].10

4+[14-12].10

4+2×10

4+20

24

Answer: 6/32 or .1875

Step-by-step explanation:

There are 6 numbers between 2 and 33 that are either squares or cubes

Square 4,9,16,25

Cube 8,27

Therefore the probability of getting a squared or cubed number is 6/32 or 0.1875

Answer:

Brooke finished faster

Step-by-step explanation:

Brooke: 60m(1 hr)+55m=115m

Lamont: 125m

Answer:

Brooke

Step-by-step explanation:

I25 minutes is 2 hours and 5 minutes. Brooke finished faster.

Answer:

The answer is 1054ft³

Step-by-step explanation:

Volume of rectangular prism =1/3LWH

V=1/3×31/2×51/3×12

V=1054ft³

Answer:

Step-by-step explanation:

triangle ABC is an equilateral so all angles and sides are equal to each other

AB = 6

triangle DEF is an isosceles so two of its angles are equal to each other

a triangles angles add up to 180°

to find the measure of these angles we’ll write this equation:

x + x + 40 = 180

and solve for x

2x + 40 = 180

2x = 140

x = 70°

so mF is 70°

Answer:

8.3

Step-by-step explanation:use law of cosine

solve equation

substitute

simplify

The length of l to the nearest 10th of an inch is 8.3 inches in the given triangle.

A triangle is a two-dimensional closed shape with three straight sides and three angles. It is one of the most fundamental shapes in geometry, characterized by the three locations where the sides join, known as the vertices.

The sum of a triangle's internal angles always equals 180 degrees. Triangles are characterised as equilateral, isosceles, scalene, acute, right, or obtuse based on their sides and angles. Triangles are used extensively in mathematics, science, and engineering, including trigonometry, navigation, and architecture.

Given,

In LMN, m = 2.1 inches, n = 8.2 inches and L=85°,

So, the length of l is:

\(l^2= m^2+ n^2- 2mn cos angle L\\l= \sqrt{(2.1)^2+ (8.2)^2- 2*2.1*8.2 cos 85} \\l= \sqrt{4.41+ 67.24- 34.44 cos 85\\l= \sqrt{71.55- 3}\\ l- \sqrt{68.55} \\l=8.3 inches\)

Therefore, the length of l to the nearest 10th of an inch is 8.3 inches in the given triangle.

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Your question is incomplete, most probably the complete question is:

In triangle LMN, m = 2.1 inches, n = 8.2 inches and L=85°. Find the length of I, to the nearest 10th of an inch.

Answer:

salary increases by $ 10 every hour

Answer:

x = 1

Step-by-step explanation:

A right triangle is a triangle with a (90) degree angle. A box around one of the angles of a triangle indicates that this angle has a (90) degree measure. All of the triangles in the given picture are right triangles, as all of them contain a (90) degree angle. More than just being right triangles, the triangles in the diagram also have red arcs indicate that the angles are congruent. The base angles converse theorem states that in a triangle with two congruent angles, the sides opposite the congruent angles are also congruent, thus forming an isosceles triangle. Therefore, the given triangles are isosceles right triangles. One property of isosceles right triangles are that their sides follow the ratio:

\(a\ :\ a\ :\ a\sqrt{2}\)

Where the sides with a measurement of (a) are the ones opposite the congruent angles, and the side with a measure of (\(a\sqrt{2}\)) are the sides opposite the right angle. Apply this to the given triangle, refer to the attached diagram for further clarification about side namings,

\(BC*\sqrt{2}=AB\\\\BC=\frac{AB}{\sqrt{2}}\\\\BC=\frac{4}{\sqrt{2}}\)

\(BD*\sqrt{2}=BC\\\\BD=\frac{BD}{\sqrt{2}}\\\\BD=\frac{\frac{4}{\sqrt{2}}}{\sqrt{2}}\\\\BD = \frac{4}{\sqrt{2}*\sqrt{2}}\\\\BD=\frac{4}{2}=2\)

\(BE*\sqrt{2}=BD\\\\BE=\frac{BD}{\sqrt{2}}\\\\BE=\frac{2}{\sqrt{2}}\)

\(BF*\sqrt{2}=BE\\\\BF=\frac{BE}{\sqrt{2}}\\\\BF=\frac{\frac{2}{\sqrt{2}}}{\sqrt{2}}\\\\BF = \frac{2}{\sqrt{2}*\sqrt{2}}=\frac{2}{2}=1\)

\(BF = x = 1\)

Answer:

The zeros of the function are x = -3, x = 1, x = 3. The multiplicity of the zero x = 3 is 3.

Step-by-step explanation:

Answer:

0, 1, -1

Step-by-step explanation:

7x³ - 7x = 0

=> x(7x² - 7) = 0

=> 7x(x² - 1) = 0

=> x(x² - 1) = 0

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

=> x = 0 or x = -1 or x = 1