Write and solve the inequality.​Then, graph the solution.

Nine less than the product of a number n and 1/5
is no more than 97.

The length of the side x in the triangle is 82.1 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sun of angle in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using trigonometric ratios as follows

Hence,

tan 75 degrees = opposite / adjacent

opposite side = x

adjacent side = 22 units

Therefore,

tan 75° = x / 22

cross multiply

x = 22 tan 75

x = 22 × 3.73205080757

x = 82.1

Therefore,

x = 82.1

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If p represents the total profit in dollars and cents when the store buys any number of sweaters, s, then the  proportional equation for p in terms of s is, p = $21 x s

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Let's call the selling price of each sweater "sp".

The store buys 15 sweaters for $90, so each sweater must cost

=$90 / 15

= $6

The store sells each sweater for

= $405 / 15

= $27,

so sp = $27

The total profit is equal to the selling price minus the buying price, so the equation for the total profit, p, in terms of the number of sweaters sold, s, is:

p = sp x s - $6 x s

We can simplify this equation to:

p = ($27 - $6) x s

p = $21 x s

So, the proportional equation for the total profit in dollars and cents when the store buys any number of sweaters, s, is:

p = $21 x s

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Based on the data of increase in ice cream sales as the weather gets warmer the data is

A statistical measure known as correlation expresses how linearly connected two variables are (meaning they change together at a constant rate). It is frequently used to describe straightforward relationships without explicitly stating cause and effect.

In this case, the data shows a relationship between the weather (one variable) getting warmer and an increase in ice cream sales (another variable). However, just because two variables are correlated does not necessarily mean that one causes the other.

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The interest you can get from this account after two years is $382.49.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

Given:

P= $3000

R= 6%
T= 2 years

A = P[tex]e^{rt[/tex]

A = 3,000.00[tex](2.71828)^{(0.06)(2)[/tex]

A = $3,382.49

and, A = P + I

I (interest) = $3,382.49- $3000

I =  $382.49.

Hence, the interest is $382.49.

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The correct response is 503 acres. Around 503 acres with more than 190 bushels of maize per acre is what we would anticipate.

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.

Let X serve as the random variable representing the yield of corn. The issue reveals that the formula for the random variable X's distribution is as follows:

[tex]X[/tex]≅Nμ=185.2, σ=23.5

A sample of n=1200 acres is taken by a quality control inspector. The sample size is reflected by that.

The likelihood that the random variable X contains more than 190 bushels of maize per acre is also something we wish to calculate. Consequently, we seek to discover:

[tex]P(X > 190)[/tex]

Additionally, we may use the z score this calculation produces:

z=X-μ/σ

If we substitute the provided values, we get:

[tex]z=190-185.2/0.2042[/tex]

We desire the possibility that:

[tex]P(z > 0.2042)=1-P(z < 0.2042)=1-0.5809=0.4191[/tex]

And to determine how many, it would be necessary to assume that each acre would produce more than 190 bushels of maize. The faction obtained can be multiplied by the sample size.

[tex]r=1200*0.4191=502.92=503[/tex]acres

A 503acre crop with more than 190 bushels of maize per acre is what we would anticipate.

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Answer:

y= x/2 - 3 : linear

y= 6/x -2 : nonlinear

3x + y = 12: linear

y = x: linear

The order of the numbers from least to greatest is as follows:

7, 31/4,7¹⁹/₂₅,7.765,8.44

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.

Given here: The numbers containing fractions and decimal numbers.

To get a clarity on the magnitude of the numbers, let's convert every fraction to decimal numbers

Thus 7¹⁹/₂₅=7.76

31/4=7.75

Hence, The order of the numbers from least to greatest is as follows:

7, 31/4,7¹⁹/₂₅,7.765,8.44

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Option (a) is correct. There'll be No Solution to the given system of linear equations.

According to the solutions of linear equations, we know the following things,
1. If two intersecting lines are at one common point, the system has only one solution.
2. If two coincidental lines mean both equations give the same line, that means the system has infinitely many solutions.
3. If the lines are parallel to each other, the system will have no solution.

We can see lines are parallel but we can also find whether the given lines are parallel or not by simply finding their slope m.

For Line 1, we have the following data
[tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,2)$[/tex]

[tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)=(3,1)$[/tex]

For slope m of the line 1,
slope m₁ = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{3-0}=-\frac{1}{3}[/tex]

For Line 2, we have the following data

[tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,-1)$[/tex]

[tex]- $\left(x_2, y_2\right)=(3,-2)$[/tex]

For slope m of line 2,
slope m₂[tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-(-1)}{3-0-x_1}=-\frac{1}{3}$[/tex]

As the slope of both lines is equal, so lines are parallel to each other, and hence, if lines are parallel so there'll be no solution to the system.
Hence, option (a) is correct.

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Your question was incomplete, the most probably question you asked was:

How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points (0, 2) and (3, 1) and another line that passes through the points (0, -1) and (3, -2).
(a) No solution
(b) One solution at (−1, 0)
(c) One solution at (0, −1)
(d) Infinitely many solutions

The amount of the bottle that is filled with sand is; The whole bottle is full of sand

When talking about fraction word problems we are simply referring to fraction parameters being represented in the form of word problems.

The parameters given are;

Fraction with pink sand = 1/6

Fraction with red sand = 3/6

Fraction with white sand = 2/6

Thus;

Total sand = 1/6 + 2/6 + 3/6

= 6/6 = 1

Thus, the bottle will be full

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The population of the green sea turtle on the island in 2012 is 68 turtle

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristics.

To find the exponential decrease in a population which obtain it by using the formula;

P(t) = P(o) e^-kt

P(o) = 750

k = 0.2

t = 12

P (t) = 750 e ^ -0.2 ×12

p(t) = 750 e^ -2.4

p(t) = 750 × 0.09

p(t) = 68( approximately) turtle

Therefore in 2021 the population of turtle on the island is 68

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Answer:

B

Step-by-step explanation:

10*10*10 =1000

5*5 =25

2*2 =4

1000+25+4 =1029

The amounts of bacteria are given as follows:

The exponential function y = 8^x is graphed by the image presented at the end of the answer.

An exponential function is defined as follows:

y = ab^x.

In which:

The parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 8^x.

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The new volume of the cylinder is 39.94cm³

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.

The volume of a cylinder is expressed as V = πr²h

The volume of the original cylinder = 10cm³

The radius and height of the new cylinder = 4r and 4h

10 = 3.14 × r²h

V 2= 3.14 × 4r²4h

V2 = 3.14× 4( r²h)

10=3.14 × r²h

r²h = 10/3.14

r²h = 3.18

from

V2 = 3.14 × 4(r²h)

represent 3.18 by r²h in the equation

V2 = 3.14 × 4 ( 3.18)

V2 = 39.94cm³

therefore the volume of the new cylinder is 39.94 cm³

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The difference 120.45-116.9 is 3.55.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

The two decimal numbers,

120.45 and 116.9.

Applying subtraction operation,

the difference 120.45-116.9.

By adding on strategy,

116.9 is 3.55 left to the number 120.45 on the number line.

That means,

116.9 + 3.55 = 120.45.

Therefore, the difference is 3.55.

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The independent quantity is the number of days into the monitoring and the dependent quantity is the number of mole rats counted.

The independent quantity refers to a variable that is not influenced by any other factor and can be changed freely in an experiment or study.

In this case, the number of days into the monitoring is the independent quantity because it can be varied at the discretion of the zoo keeper.

The dependent quantity, on the other hand, is a variable that depends on the independent quantity and is affected by changes in it.

In this case, the number of mole rats counted is the dependent quantity because it is determined by the number of days into the monitoring. The zoo keeper counts a different number of mole rats based on how many days have passed, which is determined by the independent quantity.

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A zoo keeper thinks there is a problem with the Mole-Rat population at the zoo. He starts keeping track of the animals in the tunnels. 7 days into his monitoring he counts 120 mole rats, 13 days in he counts 108.

what information is provided?

Answer: $6000

Step-by-step explanation:

The initial value will be what the person deposits before the interest. Because Liam deposited $6000 the initial value would be $6000.

Hope this helps!

There are 3600 ways to seat 6 people at two round tables, with at least one person at each table.

In this scenario, we have 6 people to seat at 2 round tables, meaning each table must have at least 3 people.

We can start by finding the number of ways to seat 6 people at one table, then divide that by 2 to account for the two tables.

For one round table, there are 6! (6 factorial) ways to seat 6 people. This is because, for the first seat, there are 6 options. For the second seat, there are 5 options remaining; for the third seat, there are 4 options, and so on.

However, this number counts the same arrangement of people multiple times, as the arrangement can start with any person. So, to correct this, we divide 6! by 6, which gives us 720/6 = 120 ways to seat 6 people at one round table.

Now, since we have two tables, each table must have 120/2 = 60 arrangements. This means there are 60 x 60 = 3600 ways to seat 6 people at two round tables.

In conclusion, there are 3600 ways to seat 6 people at two round tables, with at least one person at each table.

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The correct options of the solution of the equation 2x+7y=-5 is (a) -6,1 and (c) 8,-3.

In mathematics, two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

In  order to determine whether an ordered pair is a solution, all we have to do is plug in the values of x and y and see if we end up with a true statement.

(a) for (-6, 1)

put the value of 1 for y and -6 for x:

2(-6)+7(1)=-5

-12+7=-5

-5=-5

Yes! Here we have a true statement. Therefore, this ordered pair is a solution.

(b) for (9, 2)

put the value of 2 for y and 9 for x:

2(9)+7(2)=-5

18+14=-5

32≠-5

Well, we can see that we have a false statement, because ≠ means "not equal to". Therefore, this ordered pair is not a solution.

(c) for (8, -3)

put the value of -3 for y and 8 for x:

2(8)+7(-3)=-5

16-21=-5

-5=-5

Yes! Here we have a true statement. Therefore, this ordered pair is a solution.

Let's try the last option.

(d) for (-5, -4)

put the value of -4 for y and -5 for x:

2(-5)+7(-4)=-5

-10-28=-5

-38≠-5

Well, we can see that we have a false statement, because ≠ means "not equal to". Therefore, this ordered pair is not a solution.

Hence, the correct options of the solution of the equation 2x+7y=-5 is (a) -6,1 and (c) 8,-3.

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A woman you know has five children among which all five  are boys. probability for a woman that she will have all five boy as a five children is  0.5.

The probability or the outcome  in which a women with five children have all the girls and none of them as boys is :-

0.5x0.5=0.25.

So for the  first child there is a a 50% chance that is will be of a male. And same for the  second child being male there will be equal probability that it can be boy so it  also will have a probability .

So the probability of having five females is  0.55=0.03125

Except the above define value all the other outcome or choices means that the women have a least one son in the five children  and the total probability of an event is 1.

.The theoretical probability is mainly reasoning bases which is behind probability. For example, if a coin is tossed then the theoretical probability or the outcome of getting a head will be ½.

Probability provides information about the happening of   something which might happen and might not depending upon the outcome demand happen. Meteorologists, also take the help of probability to predict whether the rain may happen or not for instance In epidemiology, also probability theory is used to understand  about various risk related to life an to demonstrate various relation .

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The total amount spent by Mrs. Rivera is given by the equation A = $ 2.25

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.

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 data ,

Let the total amount spent by Mrs. Rivera be represented as A

Now , the equation will be

The cost of one pound of banana = $ 0.45

The total amount of bananas = 5 pounds

So , the total amount of money for 5 pounds = 5 x cost of one pound of banana

Substituting the values in the equation , we get

The total amount of money for 5 pounds of banana A = 5 x 0.45

The total amount of money for 5 pounds of banana A = $ 2.25

Hence , the total amount is $ 2.25

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If  ∆AFD, m ∠F = 90° AD = 14, m ∠D = 30° .The  Area of ∆AFD is 49 square units.

To find the area of triangle AFD, we can use the formula for the area of a triangle given its base and height. In this case, the base is AD, and the height can be found by constructing an altitude from F to AD.

First, we will find the length of FD. Since m ∠D = 30°, we can use the trigonometric  function sine to find the length of FD. Using the sine formula:

FD = AD * sin(∠D) = 14 * sin(30°) = 14 * 1/2 = 7

Next, we will find the length of A.F. Since m ∠F = 90°, FD is the height of the triangle. So, the area of triangle AFD is given by:

Area = (AD * FD) / 2 = (14 * 7) / 2 = 49 square units

Therefore the area of ∆AFD is 49 square units.

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The measure of the supplementary angles is:

∠X = 117°

∠Y = 63°

Here we know that angles ∠X and ∠Y are supplementary angles. Remember that two angles are supplementary if their measures add up to 180°.

Here we know that the measures are:

∠X = 3n − 18

∠Y = 2n − 27

We can write:

∠X + ∠Y = 180°

(3n - 18) + (2n - 27) = 180

Then we can solve that for n.

3n + 2n - 18 - 27 = 180

5n = 180 + 45

n = 225/5 = 45

Then the measures of tha angles are:

∠X = 3n − 18 = 3*45 - 18 = 117°

∠Y = 2n − 27 = 2*45 - 27 = 63°

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The length and width of a rectangle are 36cm and 4.5cm

Finding the Width:

The formula to find the perimeter of the rectangle is:

P=2(l+w),

where P is the perimeter, l be the length, and w be the width.

Now substitute the given values to solve for w, since we need to find the width.

The given information is:

the length of a rectangle is six inches more than eight times the width so the equation becomes:

L=8w+6

P=120

w=8w

now plug the values in the above formula:

P=2(l+w),

120=2(8w+6)+8w

120=16w+12+8w

120=24w+12

24w=108

w=4.5

To find the length just substitute in the L.

L=8(4.5)+6

L=30+6

L=36

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The ratio of the area of a regular hexagon to the area of the smaller hexagon that uses its midpoints as vertices is 4:1. The common factor in this expression is 4

The closed polygonal shape of a regular hexagon has six equal sides and six equal angles. Any regular polygon has equal sides and angles on all sides. Regular pentagons, for instance, have 5 equal sides, and regular octagons have 8 equal sides. When these requirements are not met, polygons might resemble many other asymmetrical shapes. A regular hexagon is formed when six equilateral triangles are placed side by side. The regular hexagon's area then increases to six times that of the same triangle. In this post, let's learn about its features, the formula for area, and the perimeter.

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The spatial scale at which the data was collected is the distance from the shore of Lake Erie.

We can see that the data shows a gradual decline in snowfall totals with increasing distance from the shore of Lake Erie. The decline starts at around 425 cm at 0 km and decreases to 375 cm by 30 km. It then decreases more quickly over the next 20 km before declining relatively consistently out to 100 km, where the snowfall is 150 cm.

The graph shows the declining snowfall totals with increasing distance from the shore of Lake Erie, starting from 0 km and ending at 100 km. The data points are measured in increments of 10 km, with the total snowfall measured in cm.

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The expression which can be used to represent the given using the fewest possible terms is 2x + 2

The correct answer choice is option B.

(−5x − 12) + (14 + 7x)

open parenthesis

-5x - 12 + 14 + 7x

collect like terms

-5x + 7x - 12 + 14

2x + 2

In conclusion, 2x + 2 is the expression which represents the fewest possible terms of (−5x − 12) + (14 + 7x)

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Answer:

its C

Step-by-step explanation:

other guy wasn't reasonable and chose the actual shortest one possible instead of the one that made sense

Work is defined as the product of force and distance, and can be calculated using the equation W = F * d, where W is work, F is force, and d is distance.

When lifting the whole log, the force required is equal to the weight of the log, and the distance over which the force is applied is the distance from the ground to the height of the shoulder.

When lifting one end of the log, the force required is still equal to the weight of the log, but the distance over which the force is applied is reduced. This is because the lever arm (the distance from the axis of rotation, which is the shoulder joint, to the point where the force is applied, which is the end of the log) is reduced.

So the equation for work done in lifting the whole log would be  W = m * g * h, where m is the mass of the log, g is the acceleration due to gravity, and h is the height from the ground to the shoulder. The equation for work done in lifting one end of the log would be W = (m/2) * g * h', where h' is the reduced height.

It can be seen that the work done in lifting one end of the log is equal to half the work done in lifting the whole log, because the force applied is the same, but the distance over which it is applied is reduced.

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Answer:

Below

Step-by-step explanation:

Value will be original value * ( 1 + i)^n      i = decimal annual interest

                                                                      n = years

  Value = 300 ( 1 + .07)^10 = 590.15  (dollars ?)