15 points, Complete the statement based on the following information.

The solution of the inequality m + 1/4 < -[tex]1\frac{2}{5}[/tex] is  m < [tex]-1\frac {13}{20}[/tex].

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

We have the inequality expression,

m + 1/4 < -[tex]1\frac{2}{5}[/tex]

Simplifying,

m + 1/4 < -7/5

Subtracting 1/4,

m < -7/5 - 1/4

m < (-28-5)/20

m < -33/20

m < [tex]-1\frac {13}{20}[/tex]

Therefore, the solution is m < [tex]-1\frac {13}{20}[/tex].

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Answer:

95 m would be the answer.

The distance that the cyclist would ride in 8 seconds is; 97.6 yards

The general form of the equation of a line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

Now, from the function table, we are given the coordinates;

(2, 24.4), (3, 36.6), (5, 61), (6, 73.2)

Now, we can find the slope from the formula;

m = (y₂ - y₁)/(x₂ - x₁)

m = (36.6 - 24.4)/(3 - 2)

m = 12.2

At x = 0, we have;

12.2 = (24.4 - y)/(2 - 0)

2(12.2) = 24.4 - y

y = 24.4 - 24.4

y = 0

Thus, the equation is; y = 12.2x

Thus, at 8 seconds, we have;

y = 12.2(8)

y = 97.6 yards

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Answer:

x = -2

Step-by-step explanation:

Combine like terms

0 = 2x + 4

-4 = 2x

-2 = x

The width of the cooling tower at the base of the structure as calculated from the data is 40 meters.

The equation which is given is ,

x²/400 -(y-90)²/1600=1

To calculate the width,

Cooling tower width =2√400

=2×20

=40 meters

Therefore the width is 40 meters.

A cooling tower is a type of heat removal device which uses water to remove waste heat from a process and discharge it into the atmosphere.

Similarly, an industrial cooling tower works by removing heat from water by evaporating little percentage of the water that is recirculated through the unit. When warm water and cooler air mingle, the latent heat of vaporization is released, causing the water to cool.

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The width of the cooling tower at the base of the structure is 16 meters.

x = 16 meters

x^2/400 - (y - 110)^2/2304 = 1

x^2/400 = (y - 110)^2/2304 + 1

400x^2 = 2304(y - 110)^2 + 2304

400x^2 = 2304y^2 - 514240y + 2574304

x^2 = 514240y/400 - 2574304/400 = 514.6y - 6435.76

x = √(514.6y - 6435.76)

For y = 0, x = 16 meters

Therefore, the width of the cooling tower at the base of the structure is 16 meters (rounded to the nearest whole number).The width of the cooling tower at the base of the structure is 16 meters.

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Let E be the region enclosed by the paraboloids z = x² + y² and z = 2 – x² - y² , then ∫∫∫(√x² + y²)dV is equals to the [tex]∫^{\pi}₀∫^{1} ₀∫^{2 - {r}^{2}} ᵣ₂ r² dz dr dθ ,[/tex].

We have two equations of paraboloids are z = x² + y² and z = 2 – x² - y² . Let E be the region enclosed by the (1) and (2). We have to determine the value of volume integral ∫∫∫(√x² + y²)dV in polar form. Now, change the Cartesian co-ordinates (i.e., x and y) into polar coordinates ( i.e., r and θ ). In polar coordinates, x = r cosθ ; y = r sinθ then, x² + y² = (r cosθ)² + (r sinθ)²

= r²cos²θ + r²sin²θ = r²(sin²θ + cos²θ)

= r² or √x² + y² = √r² = r

Plugging the value in curve equation,

z = x² + y² = r² and z = 2 – x² - y² = 2 - r²

i.e., z varies from r² to 2 - r²

and θ varies from 0 to π ( see in graph) and r varied from 0 to 1. Also, dxdy = r dr dθ. So, the triple integral or volume integral in polar coordinates is

[tex]∫^{\pi}₀∫^{1} ₀∫^{2 - {r}^{2}} ᵣ₂ r² dz dr dθ ,[/tex]

Hence, we get the required expression in polar coordinates.

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The total number of children in Ms. Mayer's class is 32.

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by:

Percentage = (value / total value) * 100%

Let Total number of student = X

Therefore;

25% of X = 8

(25/100)X = 8

Therefore;

X = 8 / (25/100)

X = 800/25

X = 32

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If the length of one side of a square is increased by 20%, then the perimeter will increase by 40%.

To solve this, consider a square with side lengths. The perimeter of this square is 4s. If we increase the side length by 20%, the new side length is 1.2s. The perimeter of the new square is 4(1.2s) = 4.8s. The increase in the perimeter is 4.8s - 4s = 0.8s, or 80% of the original perimeter. Since the original perimeter was 4s, this is an increase of 80% of the original perimeter or 40% of the original side length.

Therefore, the correct answer is d) 40%.

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If the length of one side of a square is increased by 20%, then the perimeter will increase by 20%.

Therefore the answer is c) 20%.

Let length of the one side of a square be a. Then the new length after 20% is

a + 0.20a = 1.20a

Perimeter of a square is the sum of length of all four sides. Thus initial perimeter of the square is

a + a + a + a = 4a

New perimeter of the square with side 1.2a is thus calculated by

4×1.2a = 4.8a

Percentage increase in perimeter can be calculated by

(4.8a - 4a)/ 4a × 100, that is

[tex]=\ \frac{4.8a\ -\ 4a}{4a}\ 100[/tex]

= 0.8a/4a × 100

= 20%

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Answer:

YES ITS A DIRECT VARIATION

Step-by-step explanation:

explanation in the picture

I think the answer is D (Day) ...........

Median is not a measure of variability of a data set.

A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.

The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets can also be made up of a group of files or documents.

The information supplied in a public open data repository is measured in the open data discipline using data sets. Over one million data sets are collected through the European portal.

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The algebraic representation of the reflection in the image is the one in option A.

(x, y) → (-x, y)

Here we have an image with two moons, such that one is the reflection of the other.

Notice that the reflection is across the vertical axis (it is the y-axis). So the y-values don't change after the reflection, only the x-values change.

So we will have a change of sign on the x-value, then the reflection must be written as:

(x, y) → (-x, y)

In this way we can conclude that the correct option is A.

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Answer:

Step-by-step explanation:

1/4 + 4/9 + n= total amount of time spent on all of the instruments.

1/4 + 4/9=

9/36 + 16/36= 25/36 (time on piano and trombone)

36/36- 25/36= 11/36- total time spent on violin

The relationship between y and x can be equation as y = k/x, where k is a constant that does not change.

The equation y varies inversely as x means that as the value of x increases, the value of y decreases, and vice versa. To solve for y, we can use the general equation y = k/x, where k is a constant. This equation states that the value of y is directly proportional to the reciprocal of x.

1. Start by understanding that when two variables are inversely proportional, they follow the equation

y = k/x.

2. The constant, k, is a number that will remain the same throughout the equation.

3. For example, if y varies inversely as x, and

y = 2 when x = 4, then k = 8.

4. Therefore, the equation

y = k/x becomes y = 8/x.

5. To solve for y when x = 5, substitute x = 5 into the equation and solve: y = 8/5

= 1.6.

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Answer:

180-142 is angle a

There is a 7.4% probability that the first marble will be green and the second will be red.

To calculate the probability, you will need to use the following formula:

P(A and B) = P(A) x P(B).

In this case, P(A) is the probability of picking a green marble on the first pick and P(B) is the probability of picking a red marble on the second pick. Using this formula,

we get P(A and B) = 333/999 x 222/998 = 0.074,

which is the probability of picking a green marble on the first pick and a red marble on the second pick.

So, there is a 7.4% chance of this happening.

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Answer:

B

Step-by-step explanation:

The probability that both the two tossed coins will come down heads (or tails) is 1/2 x 1/2 or 1/4.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

To calculate the probability of two independent events happening at the same time, you multiply their individual probabilities.

In this case, the two events are the two coin tosses coming up heads (or tails).

The probability of the first coin coming up heads (or tails) is 1/2, and the probability of the second coin coming up heads (or tails) is also 1/2, so the probability of both of them coming up heads (or tails) is (1/2) x (1/2) = 1/4.

Hence, the correct answer would be an option (B).

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Answer:

She has ridden 25 miles this week

Step-by-step explanation:

She rode 4 miles on monday to start off the week. Then she rode 4 times the amount he did on Monday, so multiply 4x4. Then he rode 5 more miles so add 5 and receive the answer of 25 miles.

Equation:

1. Write Equation: 4+(4x4)+5=

2. Solve for parenthesis: 4+16+5=

3. Solve: 4+16+5=25

-Hope this helped & Happy New Years

Answer:

y = -4x + 1

Step-by-step explanation:

We find the equation of a line passing through two given points using the generalized slope-intercept which is

y = mx + b

m is the slope(gradient) of the line and b is the y-intercept i.e. the y-value where it crosses the y-axis. This is nothing but the value of y when x  0

Start by finding the slope first

Slope, m = (y2-y1)/(x2-x1)  

Taking(x1, y1) as (-1, 5) and (x2, y2) as (2, -7)

we get

y2 - y1 = -7 -5 = -12

x2 - x1 = 2 - (-1) = 1 2 + 1 = 3

m = -12/3 = -4

Equation would be
y = -4x + b

To find b, choose a known value for x and its corresponding y value and solve for b

Let's take (-1, 5)

Subbing this into the equation gives

5 = (-4)(-1) + b

5 = 4 + b

or b = 1

So the equation of the line in slope-intercept form is

y = -4x + 1

The expression y³x⁵ in terms of u and v is [tex]e^{3u} e^{5v}[/tex]

The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x.  The equation being [tex]e^{\ln x}=x[/tex]

Given here, the polynomial expression y³x⁵ where [tex]{\ln x}=u[/tex] and  [tex]{\ln y}=v[/tex]   thus, [tex]e^{v} =y[/tex] and [tex]e^{u} =x[/tex]

∴ , y³x⁵=[tex]e^{3u}e^{5v}[/tex]

Hence, The expression y³x⁵ in terms of u and v is [tex]e^{3u} e^{5v}[/tex]

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Answer:

r≈11 m or 1/2πr2   /=fraction

Step-by-step explanation:

too many fractions to put but yeah have fun with answer though i'm 1 hour late

The radius of the semicircle given in the given figure is 10in.

A semicircle is a half circle created by splitting a circle into two equal parts. It is created when a line pierces the circle's center and touches its two ends. The diameter of the circle is the name given to this line.

In the given figure, A semicircle is drawn on the base of the rectangle.

Since the Area of the rectangle is 200 inches square and the height of the rectangle is 10 inches.

Thus, the Base of the semicircle  = 200/10 = 20in.

Since the Base of the rectangle is equal to the diameter of the semicircle that is 10.

Therefore, the semicircle's radius in the provided illustration is 10 inches.

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Complete question:

Answer:

x=7

Step-by-step explanation:

2x-0.4=1+1.8x

Subtract 1.8x from both sides

0.2x-0.4=1

Add 0.4 to both sides of the equation

0.2x=1.4

Divide both sides by 0.2

x=7

The length of truck is equal to 6.325 feet.

In Mathematics, there are two (2) main types of percentage change and these include the following:

Mathematically, percentage increase can be calculated by using this formula:

Percentage increase = [Final value - Initial value]/Initial value × 100

Based on the information provided above, we have the following parameters about the car and truck;

Length of car = 5.5 feet.

Percentage increase in length of truck = 15%.

Now, we can calculate the length of the truck by using this mathematical expression;

Length of truck = 115/100 × 5.5

Length of truck = 1.15 × 5.5

Length of truck = 6.325 feet.

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There are existing infinite solutions for the given equation 12s + 1 = 3 ( 4s + 1) - 2.

Solving the equation,

12s + 1 = 3 ( 4s + 1) - 2

 12s + 1 = 12s + 3 -2

 12s + 1 equals to (=) 12s + 1

Bringing constant to one side of the equation and variables to the other side of the equation so that equation could be solved

+ 12s - 12s   =   +  1 -  1

        0        =      0

This shows that the given equation has infinite solutions because after solving it gives a solution where both sides are equal.

"

Complete question:

How many solutions exist for the given equation 2s + 1 = 3 ( 4s + 1) - 2?

"

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Answer:

-9

-4

1

|-2|

|-3|

|-5|

|-6|

Step-by-step explanation:

| |

This symbol means whatever number inside of it turns to positive

Answer:

-9

-4

1

|-2|

|-3|

|-5|

|-6|

Secant line is the name given to any line that intersects a circle at two or more points. This line is called "secant" because it comes from the Latin word secare, which means to cut.

In mathematics, the secant line is used as a tool for finding the length of an arc, area of a sector, and other geometric measurements. The secant line is also used in calculus to calculate derivatives and integrals of functions.

The secant line is formed by two points on a circle’s circumference, and its slope is determined by those points. Its slope is calculated by the difference between the two points divided by the product of the radius of the circle and the angle made by the two points.

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The answer is (a) exactly three. The probability of selecting exactly three adults out of a sample of 20 who have been told that they have hypertension is calculated using the Binomial Distribution. The probability can be calculated using the formula:

The probability of selecting at least three adults out of a sample of 20 who have been told that they have hypertension is calculated using the Cumulative Binomial Distribution. The probability can be calculated using the formula:

The probability of selecting at most five adults out of a sample of 20 who have been told that they have hypertension is calculated using the formula:

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The value of given expression -[tex]a^{2}[/tex] - 2bc - | c |  is 9 .

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given expression,

-[tex]a^{2}[/tex] - 2bc - | c |

Given values are a = -3 ,  b = -5 , c =2 .

By substituting given values we get,

= -(-3*-3) - 2 * (-5)(2) - |2|

= -9 - (-20) - 2

= 20-11

= 9

Hence , The value of given expression is 9 .

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The value of given expression - - 2bc - | c |  is 9 .

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

In mathematics, a variable is a symbol, usually a letter, that represents a value or a set of values. Variables are used to represent unknown or changing values in mathematical expressions and equations.

Given expression,

- - 2bc - | c |

Given values are a = -3 ,  b = -5 , c =2 .

By substituting given values we get,

= -(-3*-3) - 2 * (-5)(2) - |2|

= -9 - (-20) - 2

= 20-11

= 9

Hence , The value of given expression is 9 .

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Answer:

£ 15347.06

Step-by-step explanation:

 First find 19.5% of 19064.67.

        Decreased amount = percentage of decrease * total amount

                                          = 19.5% * 19064.67

                                          = 0.195 * 19064.67

                                         = £ 3717.61

Amount after decrease = 19064.67 - 3717.61

                                       = £ 15347.06

Answer:

[tex]f(-1)=-11\\f(0)=16\\f(2)=22[/tex]

Step-by-step explanation:

[tex]\displaystyle f(-1)=3(-1)-8=-3-8=-11\\f(0)=3(0)+16=16\\f(2)=3(2)+16=6+16=22[/tex]