solve the inequality 7/2 ≥ b + 9/5. Then graph the solution

mass (m) = 5.4g

Volume (V) = 2 cm^3

To find the density (p), we have to apply the next formula:

p= m/v

Replacing:

p´= 5.4/2 = 2.7 g/cm^3

Answer:

left handed = 7 ; right handed = 12

Step-by-step explanation:

r = right handed

l = left handed

r + l = 19

r = l + 5

If we use substitution method we have:

l +5 + l = 19

2 l = 14

l = 7

r = 7 + 5 = 12

Answers:

The system of equations is

\(\begin{cases}y = x-5\\x+y = 19\end{cases}\)

where x and y is the number of right-handed and left-handed people respectively.

The system solves to (x,y) = (12,7)

Interpretation:

There are  12   right-handed people and  7   left-handed people in the class.

=========================================================

Explanation:

x = number of right-handed people

y = number of left-handed people

x and y are positive whole numbers.

There are 5 more right-handed people compared to left-handed people, so we can say x = y+5 which is the same as y = x-5. So you could go for either equation. Let's go for the one where y is isolated.

The second equation to form is x+y = 19 because there are 19 people in the class, and you can only be one or the other (left-handed or right-handed but not both). I'm not considering the possibility anyone is ambidextrous though of course that may happen in a realistic setting.

The two equations then form the system

\(\begin{cases}y = x-5\\x+y = 19\end{cases}\)

There are a number of ways we can solve this system. Substitution is possibly the quickest way.

x+y = 19

x+(x-5) = 19 ... replace y with x-5; due to the first equation

2x-5 = 19

2x = 19+5

2x = 24

x = 24/2

x = 12 .... this is the number of right-handed people

y = x-5

y = 12-5

y = 7 .... this is the number of left-handed people

The slope of the line shown in the graph is __2/3__

and the y-intercept of the line is __6___

The general linear equation is written as follows:

y = ax + b

Where a is the slope and b is the y-intercept.

On the graph we can see that the y-intercept is y = 6, then we can write the line as:

y = ax + 6

The line also passes through the point (-9, 0), replacing these values in the line we will get:

0 = a*-9 + 6

9a = 6

a = 6/9

a = 2/3

That is the slope.

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Answer:

We can see the two triangles ABC and EDC are similar and their sides are proportional.

4 to 8, 6 to 12, 5 to 10

You could say,

1. ABC ~ EDC -- SSS criterion

2. ∠A = ∠E -- CPCTC

3. AB || ED -- Alternate Interior Angles Converse

Answer:

Moving 4 to the right on the x axis

Answer:

x = 12

Step-by-step explanation:

From the similar figures given in the picture,

(Figure A ~ Figure B)

Corresponding sides of the figures will be proportional.

By this property of the similarity,

\(\frac{x}{10}= \frac{30}{25}\)

x = \(\frac{300}{25}\)

x = 12

The simple interest using I = prt if Oliver borrowed $1,500 to purchase a riding lawn mowerat the rate of f 12% for 6 monthsis

The concept that will be used is the concpt of simple interest and thei can be calculates using the simple interst formular which is

I = [(prt)/100]

where p = principal =  $1,500

     I = intereste rate

     t=time

Then this can be expressed as

I= (prt)/100

I =  ($1,500* 6/12 * 12 )/100

=  $90

In conclusion the simple interest is now  $90 which is the second option that is given.

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Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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The 95% confidence interval for the population mean is approximately (4.01, 13.99).

To construct a 95% confidence interval for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / √n)

the sample: 8, 9, 8, 3, 6, 20

Calculate the sample mean:

Sample mean = (8 + 9 + 8 + 3 + 6 + 20) / 6 = 54 / 6 = 9

Calculate the deviations from the mean for each data point:

(8 - 9)^2 = 1

(9 - 9)^2 = 0

(8 - 9)^2 = 1

(3 - 9)^2 = 36

(6 - 9)^2 = 9

(20 - 9)^2 = 121

Calculate the sum of the squared deviations:

1 + 0 + 1 + 36 + 9 + 121 = 168

Calculate the variance:

Variance = sum of squared deviations / (n - 1) = 168 / (6 - 1) = 168 / 5 = 33.6

Calculate the standard deviation:

Standard deviation = √(variance) = √(33.6) ≈ 5.8

Calculate the critical value for a 95% confidence interval.

Since the sample size is small (n < 30) and the population standard deviation is unknown, we use the t-distribution and degrees of freedom (df = n - 1 = 6 - 1 = 5) to find the critical value.

Using a t-table or a statistical software, the critical value for a 95% confidence interval with 5 degrees of freedom is approximately 2.571.

Calculate the confidence interval:

Confidence Interval = sample mean ± (critical value) * (standard deviation / √n)

Confidence Interval = 9 ± 2.571 * (5.8 / √6) ≈ 9 ± 4.99

Therefore, the 95% confidence interval for the population mean is approximately (4.01, 13.99).

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Answer:

I believe the answer to your question would be 30.

Step-by-step explanation:

you know how functions work ?

the variable (or variables) in the findings expression is a placeholder for actual values.

when we have an actual value, we put that into the place of the variable and then simply calculate.

x = 5

therefore, the functional calculation is

y = 3×5 - 7 = 15 - 7 = 8

keep in mind the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

therefore, we need to calculate "3×5" before we deal with the "- 7" part.

Answer:

Step-by-step explanation:

y=8

The fraction that represents the part of the whole cake each child receives is 4/25

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

Five children divide 4/5 of a cake equally

The fraction that represents the part of the whole cake each child receives is calculated as

Fraction = 4/5 divided by 5

Mathematically, this can be represented as

Fraction = (4/5)/5

When the fraction is then evaluated, we have the solution to be

Fraction = 4/25

Hence, the solution is 4/25

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Answer:

I have graphed and attached it in the explanation.

Step-by-step explanation:

y–2=4(x+8)

y - 2 = 4x + 32

y = 4x + 34

The distance from point A to point C and the bearing from point A to point C is 229.5 miles.

Given that:

AB = 370 miles

angle A = 24 degrees

BC = 240 miles

angle B = 37 degrees 

To determine the distance from point A to C, we can use the cosine law since we are given two angles and two sides of a regular triangle. 

The angle opposite side AC is angle B which is equal to 37 degrees. 

(AC)^2 =(AB)^2 + (BC)^2 - 2(AB)(BC)cos(B)

Now we have to solve for AC:

(AC)^2 =(370)^2 + (240)^2 - 2(370)(240)cos(37) 

AC = 229.48 miles.

Hence the answer is, the distance from point A to point C and the bearing from point A to point C is 229.5 miles. 

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The null hypothesis is that the mean speed of the cable Internet connection is equal to or less than three Megabits per second (H0: μ ≤ 3). The alternative hypothesis is that the mean speed is greater than three Megabits per second (Ha: μ > 3).

Based on the terms provided and the context of the question, we can establish the null and alternative hypotheses as follows:

1. Null Hypothesis (H0): The mean speed (µ) of your cable Internet connection is equal to 3 Megabits per second. Mathematically, this is expressed as H0: µ = 3.

2. Alternative Hypothesis (H1): The mean speed (µ) of your cable Internet connection is greater than 3 Megabits per second. Mathematically, this is expressed as H1: µ > 3.

The alternative hypothesis is that the mean speed is greater than three Megabits per second (Ha: μ > 3).

To summarize, your null hypothesis (H0) states that the mean speed of your Internet connection is 3 Megabits per second, while your alternative hypothesis (H1) states that the mean speed is greater than 3 Megabits per second.

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The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

To solve the quadratic equation 3x^2 - 9x - 12 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 3, b = -9, and c = -12. Substituting these values into the quadratic formula, we have:

x = (-(-9) ± √((-9)^2 - 4 * 3 * (-12))) / (2 * 3)

= (9 ± √(81 + 144)) / 6

= (9 ± √(225)) / 6

= (9 ± 15) / 6.

We have two possible solutions:

For the positive root:

x = (9 + 15) / 6

= 24 / 6

= 4.

For the negative root:

x = (9 - 15) / 6

= -6 / 6

= -1.

The solutions to the equation 3x^2 - 9x - 12 = 0 are x = 4 and x = -1.

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So the maximum number of edges in an undirected graph with 100 vertices is 4950.

In an undirected graph, each edge connects two vertices, and as such, it is counted twice, once for each vertex it connects. Therefore, the total number of edges in the graph is the sum of the degrees of all vertices, divided by 2.

In a complete graph with n vertices, every vertex is connected to every other vertex, except itself, and so the degree of each vertex is n-1 (it is connected to n-1 other vertices). Therefore, the total number of edges in the graph is:

n * (n-1) / 2

Substituting n = 100, we get:

100 * 99 / 2 = 4950

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Answer:

Correct graph is B.

Answer:-3.5

Step-by-step explanation:

zeros of  y = 2x^2 - x - 21 means in there y=0,

so, and one of them (for example x1=3)

\(2x^{2} -x-21=0\\\)

with Vieta theorem,

x1+x2=-p=x/2

x1*x2=q=-21/2

3*x2=-21/2

x2=-7/2

x2=-3.5

Answer: The value of the other zero for the eq y=2x²-x-21 is -5/2.

Step-by-step explanation:

For a quadratic equation, we can find the sum of the zeros by dividing the coefficient of the linear term by the coefficient of the quadratic term (with the opposite sign).

In the given equation,

coefficient of the quadratic term = 2

coefficient of linear term = -1

∴ Sum of zeros= (-(-1))/2 = 1/2

Since one of the zeros is 3

∴ THE OTHER ZERO = Sum of zeros - Known zero = 1/2 - 3 = -5/2

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The measure of angle ZCBD is 90°. Therefore, the correct option is J. 90.

To find the measure of angle ZCBD, we need to examine the given information.

From the figure, we know that angle CDE is 155°.

Since the opposite angles of a rectangle are congruent, angle BCD is also 155°.

In a rectangle, the sum of the interior angles at a vertex is always 90°.

Therefore, angle CBD is 90°.

Hence, the measure of angle ZCBD is 90°.

Therefore, the correct option is J. 90.

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Answer:

here you go

Step-by-step explanation:

Answer:

P = \(\frac{40}{V}\)

Step-by-step explanation:

given P is inversely proportional to V then the equation relating them is

P = \(\frac{k}{V}\)

to find k use the condition when V = 8 , P = 5 , then

5 = \(\frac{k}{8}\) ( multiply both sides by 8 to clear the fraction )

40 = k

P = \(\frac{40}{V}\) ← equation of proportion

Answer:

P = 40/V.

Step-by-step explanation:

P = k/V where k is a constant

Substituting the given values:

5 = k/8

k = 5*8 = 40.

So the formula is:

P = 40/V

Answer:

C

Vertex at (-4 , 18)

Step-by-step explanation:

The vertex's x-coordinate is -4

To find the y-coordinate plug -4 into any of the equations but I recommend using the third one because it'll be the fastest route.

-2 (-4 + 4)^2 + 18

-2(0)^2 + 18

= 18

Vertex at (-4, 18)

a.

- The independent value is $3.75.

- The dependent value is $1.25 because it depends on the kilometer ride.

- Let us set x for each kilometer.

- Let us set F for the toral fare

Then, we can write the next equation that relates the fare to the distance.

b.

If we want to find the total cost for a 21-km ride. Then, we need to set x=21 on the equation.

Hence,

Hence, a 21-km ride has a total cost of $30.

Answer:

D.) 42

Step-by-step explanation:

7 multiplied by 6 is 42, and since the function rule is to multiply by 6, we multiply the input, 7, by 6, to get the output, 42.

Answer:

the answer is D.42

Step-by-step explanation:

have a nice day.

The gravitational potential energy of the vacationers will decrease as they approach the end of the pier.

As the vacationers approach the end of the pier, their gravitational potential energy will decrease.

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It depends on the height of the object and the acceleration due to gravity.

In this scenario, as the vacationers walk out on the horizontal pier, their height above the ground remains constant. Since the height does not change, the gravitational potential energy also remains constant.

However, as they approach the end of the pier, their distance from the center of the Earth decreases. As a result, the gravitational potential energy decreases because it is directly proportional to the distance from the center of the Earth.

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Answer:

you are correct

Step-by-step explanation:

since this was a random sampling, there can be no source of bias.

Answer:

60

Step-by-step explanation:

140 = 80 + z

z = 60

Answer:

60°

Step-by-step explanation:

The whole angle is 140° and one side is 80°. Now, you just have to subtract 140 and 80 to get 60. I hope this helps!

Different letter arrangements that can be obtained from the letters of the word statistically, using all the letters= 6,48,64,800

Given,

Total number of arrangements obtained = 6,48,64,800

Given words = STATISTICALLY

Total word count = 13

Here we have repeated alphabets as -

"S"s = 2

"T"s = 3

"A"s = 2

"I"s = 2

"L" = 2

Total permutations we have here = 13! / 2!2!2!2!3!

= 6,22,70,20,800 / 96

= 6,48,64,800

A permutation of a set in mathematics is, broadly speaking, the rearranging of its components if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

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