4.
The sum of two odd consecutive integers is 88. Find the integers.

The required equation of inequality is 4 ≤ b ≤ 6

Given ; Cups of iced tea = 120 cups

and the cups of iced coffee should not be less than 180 cups

Thus this is a question of inequality

Each batch of iced tea makes = 30 cups

thus the required equation is

[tex]\frac{120}{30}[/tex] and this is less than the number of batches which is represented by b

thus the equation would be [tex]\frac{120}{30}[/tex]  ≤ b

And it should be less than 180 cups of iced tea

thus the equation would be

b ≤ [tex]\frac{180}{30}[/tex]

Thus the required equation is :

[tex]\frac{120}{30}[/tex] ≤ b ≤ [tex]\frac{180}{30}[/tex]

On simplifying this we will get ;

4 ≤ b ≤ 6

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Answer:

I think b 1/3

Step-by-step explanation:

slope is rise over run

Answer:

1/2

Step-by-step explanation:

find 2 clear points A(2,0) B(8,3)

use the formula of the angular coefficient

[tex]c = \frac{y2 - y1}{x2 - x1} [/tex]

Answer:

d = 15

Step-by-step explanation:

(-5, 4), (4, -8)

(x₁, y₁)   (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4 - (-5))² + (-8 - 4)²

d = √(4 + 5)² + (-12)²

d = √(9)² + (-12)²

d = √81 + 144

d = √225

d = 15

I hope this helps!

The total middle school enrollment is 889 for the given city.

According to the question,

We have the following information:

Three middle schools in a city had enrollments of 296,315 and 278.

Now, the total middle school enrollment can be easily found by adding the enrollments in three middle schools of the city.

So, we have the following expression:

Total middle school enrollment = 296+315+278

(We already know that the digits are first added from the right hand side and then we move to the left hand side.)

Total middle school enrollment = 889

Hence, the total middle school enrollment is 889 for the given city.

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Answer:

a.  x = 1.75,  x = 4.25

b.  y = -7

c.  Maximum point at (3, 5).

d.  Domain:  (-∞, ∞)

e.  Range:  (-∞, 5]

f.  See attachment.

Step-by-step explanation:

Given function:

[tex]\text{f}(x)=-4|x-3|+5[/tex]

As per the question, use a graphing calculator to graph the given function.

The x-intercept(s) are the points at which the curve crosses the x-axis.

The y-intercept is the point at which the curve crosses the y-axis.

From inspection of the graph:

The domain of a function is the set of all possible input values (x-values).

The domain of the given function is unrestricted.

The range of a function is the set of all possible output values (y-values).

As the function has a maximum point at y = 5, the range is restricted.

Graph label the axes using a scale of 1 (see attachment).

Substitute x = 5 into the function to find the value of y at that point:

[tex]\begin{aligned}\implies \text{f}(5)&=-4|5-3|+5\\&=-4|2|+5\\&=-4(2)+5\\&=-8+5\\&=-3\end{aligned}[/tex]

The conversion of the measurement of 65 lb will be 29483.5 g.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

In this case, we need to convert 65 lb to g

It should be noted that we have to multiply the weight value by 453.5

Therefore, it should be noted that 65 lb will be:

= 65 x 453.5

= 29483.5 g.

Therefore, it should be noted that the conversion of the measurement of 65 lb will be 29483.5 g.

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Answer:

D: 3x9/5

Step-by-step explanation:

the formula for dividing fractions is skip flip multiply where we keep the first term the same and then flip the second to multiply

Hopes this helps please mark brainliest

In both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

What is  Obtuse triangle?

Triangle B = Obtuse triangle

Triangle C = Obtuse triangle

in both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

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Answer:

33.8ohms

Step-by-step explanation:

10A : 13ohm

26A : 33.8ohm

a) An equation relating the miles traveled to gallons of gas used is m = 14g.

b) With 3.7 gallons of gas, one can drive up to 51.8 miles.

An equation is a mathematical statement that makes two mathematical expressions equivalent or equal using the equation symbol (=).

Equations establish the equality of two or more values, variables, or numbers.

The total distance driven on one tank of gas = 168 miles

The quantity of gas used = 12 gallons

The number of miles per gallon of gas = 14 (168/12)

Let m = distance in miles

Let g = gallons of gas used

Equation: m = 14g

Solution:

Gallons of gas used = 3.7

m = 14g

= 14(3.7)

= 51.8 miles

Thus, based on the established equation, with 3.7 gallons of gas used, the driver can cover 51.8 miles.

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The solution to the equation 5x - 5 = 15 in the replacement set is x = 4

From the question, we have the following equation that can be used in our computation:

5x - 5 = 15

The replacement set is given as

{0,1, 2, 3, 4}

So, we replace the variables using the elements in the replacement set

When x = 0, we have

5(0) - 5 = 15

-5 = 15 -- false

When x = 1, we have

5(1) - 5 = 15

0 = 15 -- false

When x = 2, we have

5(2) - 5 = 15

5 = 15 -- false

When x = 3, we have

5(3) - 5 = 15

10 = 15 -- false

When x = 4, we have

5(4) - 5 = 15

15 = 15 -- true

Hence, the value of the equation is x = 4

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In the equation given 2[(4m * 3.5) / 400] = 171.5, m has a value of 2450.

Equations are mathematical statements containing two algebraic expressions on both sides of an equal to sign. This can be expressed as the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

We can find the value of m by applying changing the subject of formula

2[(4m * 3.5) / 400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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The equation used to determine height and time is y = 16x² + 96x + 10 and y = 17x + 5

What is Projectile Motion ?

A projectile is something that has only one force acting on it the entire time, which is gravity, with the exception of the beginning.There are numerous types of projectiles.A projectile is something that is launched from the position of rest.A projectile is also any object that is hurled vertically upward as long as air resistance has no effect. Additionally, a projectile is any object that is fired upward at an angle to a horizontal plane.

The height of projectile after t seconds is given,

h(t) = 1/2 gt² + v₀t + s₀

where,

v₀ ( initial velocity ) = 96 feet per second

s₀ ( initial height ) = 10 feet

g = 32 feet per second²

put the values,

h(t) = 1/2 (32)t² + 96 t + 10

h(t) = 16 t² + 96 t + 10

so, let h(t) = y and t = x

y = 16x² + 96x + 10

We know, Amy's bullet follows a linear path,

The linear equation is,

y = mx + b

where, slope (m) = 17 feet per second and,

y-intercept (b) = 5 feet

plug in the values in linear equation,

y = 17x + 5

Therefore, The equation used to determine height and time is y = 16x² + 96x + 10 and y = 17x + 5

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The completion of the trend analysis for sales with 2010 as the base year is as follows:

                               2013           2012           2011           2010

Sales               $ 158,000   $ 615,000   $ 280,000   $ 500,000

Trend Analysis       32%           123%           56%           100%

Trend analysis uses observed historical data to predict future developments and monitor performances about a particular topic.

Undertaking a trend analysis for sales, which is a technical analysis, involves setting a base year.  The sales figure for the base year is set to 100% and used to check changes during the review periods.

The other years' sales results, in percentages, are compared to the base year by dividing each year's sales by the base year.

2013 (D) = 32% ($158,000/$500,000 x 100)

2012 (C) 123% ($615,000/$500,000 x 100)

2011 (B) 56% ($280,000/$500,000 x 100)

2010 (A) = 100% ($500,000/$500,000 x 100)

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The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.

Given,

In the question:

To see the figure:

To select the values that makes the inequality  s ≤ 4 true.

Number table are given in figure.

To see the figure and analysis.

Now, According to the question;

To make the inequality s ≤ 4 true.

The selected value must be less than 4 {Properties of Inequality}

The values are sorted from small to large:

So, The answer is -4, -1, 1, 3, 3.9, 3.99, 3.999.

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The quantity that is needed for you to be able to use arcsine to calculate the percentage grade is D. The change in elevation along a section of road

A geographic location's elevation is its height above or below a set reference point, most typically a reference geoid, which is a mathematical model of the Earth's sea level as an equipotential gravitational surface.

Elevation is described as the height above the ground or other surface, as well as a location or position of elevation. A plane flying 36,000 feet above the ground is an illustration of elevation. A pope being elevated to the position of saint is an example of elevation.

When driving on mountain roads, road signs frequently reflect the route's steepness as a percentage grade, which represents the angle of elevation as the road increases. In this case, the correct option is D.

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Answer:

3/20

Step-by-step explanation:

3/5 : 4

3/5 x 1/4

3/20

An integral graph with graph spectrum is the utility graph.The utility graph's adjacency, incidence, and graph distance matrices are displayed in the aforementioned graphs.

These technologies enable users to mathematically represent their ideas, dynamically link several representations, form hypotheses, and finally create totally new concepts.

Use a graphing utility

See attached file

 The value  of X in the interval  [0, 2π) are

X1=0

X2=π/2-----1.5708

X3=π------- 3.1416

Values of X  (0,1.5708,3.1416)

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The distance between the line containing points (4, –1) and (4, 9) and point p (1,6) is of:

3 units.

The standard equation of a line is given by the rule presented as follows:

ax + by + c = 0.

The coordinates of the points which we want to find the distance from the line are given as follows:

(x0,y0).

Then the shortest distance is given by the equation presented as follows:

D = |a(x0) + b(y0) + c|/sqrt(a²+b²).

The two points of the line are given as follows:

(4, –1) and (4, 9).

Since the x-coordinate is constant, the line has a slope of infinite, meaning that it is a vertical line defined as follows:

x = 4.

x - 4 = 0.

The point p has these following coordinates:

p(1,6).

Hence the distance between the point and the line is:

D = |a(x0) + b(y0) + c|/sqrt(a²+b²).

D = |1(1) + 0(6) - 4|/sqrt(1² + 0²).

D = |-3|

D = 3 units.

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The Z distribution also referred to as the standard normal distribution is the distribution that we would have to use here.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.

By transforming the values of any normal distribution into z-scores, it is possible to standardize it. Z-scores indicate the number of standard deviations from the mean that each value falls within.

This is the z distribution given that the value of n is more than 30.

We have to make use of z when n which is the number of samples  is greater than 30.

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Using the t-distribution, it is found that:

a)

b)

The bounds of the confidence interval are given according to the rule presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are listed as follows:

The margin of error of the interval is:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

Then the interval can be interpreted as the sample mean plus/minus the margin of error.

For the confidence interval in this problem, using a calculator, the parameters are given as follows:

[tex]\mu = 1280.1111, s = 33.5799, n = 9[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 9 - 1 = 8 df, is t = 1.86.

Then the margin of error of the interval is:

M = 1.86 x 33.5799/sqrt(9) = 21.

Then the bounds of the interval are:

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For the given geometric sequence the seventh term is equal to 19/81 and the 12th term is equal to "-57" the value of the 15th term is 1539.

What is a geometric sequence?

One particular sort of sequence is a geometric sequence. It is a sequence in which each term, with the exception of the first, is multiplied by a fixed integer to obtain the following term. The common ratio must be multiplied by the current term in the geometric sequence to obtain the next term, and the common ratio must be divided by the current term to obtain the previous term.

Solution Explained:

We know, a7 = 19/81, a12 = -57

So, ar^7 = 19/81 and ar^12 = -57     (r= common ratio)

Since r< a15 < 0 [the sign alternate]

Ignoring the signs,
r^12 = r^7 X r^5
57 = 19/81 X r^5

(57 X 81)/19 = r^5

243 = r^5

r = the fifth ratio of 243 = 3

therefore, r = -3

So, a15 = a12 X r^3
            =  -57 X (-3)^3
            = 1539

Hence, the value of the 15th term is 1539.

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Simplification of the given expression 2cd³ (c - d +5) is given by

2c²d³ − 2cd⁴ + 10cd³.

As given in the question,

Given expression is equal to :

2cd³ (c - d +5)

Law of exponents for multiplication is given by:

mᵃ × mᵇ  =mᵃ⁺ᵇ

Simplification of the given expression by open the parenthesis we have,

= 2cd³ × c - 2cd³ × d + 2cd³ × 5

Apply law of exponents for multiplication we get,

= 2c¹⁺¹d³ -2cd³⁺¹ + (2×5)cd³

= 2c²d³ -2cd⁴ + 10cd³

Therefore, simplification of the given expression 2cd³ (c - d +5) is given by 2c²d³ − 2cd⁴ + 10cd³.

The complete question is:

Simplify : 2cd³ (c - d +5)

a. 2cd³− 2c²d⁴ + 10c²d³

b. 2c²d³ − 2cd⁴ + 10cd³

c. 2cd³ − 2cd³ + 10cd³

d.  2c²d³− 2c²d⁴ + 10cd²

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The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). For example -

y = 4x⁴ + 3x³ + 2x² + 6x + 7

We have the following polynomial -

y = 2x⁴ - 5x³ + x² - 2x + 4

Now -

at x = 0, y = 4

at x = 1, y = 0

at x = 2, y = 32 - 40 + 4 - 4 + 4 = - 4

Refer to the graph attached. The points (0, 4), (1, 0) and (2, - 4) are plotted.

Therefore, the graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

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Step-by-step explanation:

4t - 7 + 83 = 180

4t + 76 = 180

4t = 104

t = 26

The value of k in 10 × 10 = [tex]10^k[/tex] is k = 2

The equation is give

10 × 10 = [tex]10^k[/tex]

The equation is defined as the mathematical statement that represent the two algebraic expression with an equal sign. The equation will no contain the inequality signs like greater than, less than etc..

The power of a number is the base number is raised to the exponent

Here the equation is

10 × 10 = [tex]10^k[/tex]

10 is the base number and k is the exponent.

We know that,

10 × 10 = [tex]10^2[/tex]

The value of k = 2

Here 2 is the exponent of base number 10

Hence, The value of k in 10 × 10 = [tex]10^k[/tex] is k = 2

The complete question is:

What is the value of k in 10 × 10 = [tex]10^k[/tex] ?

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