4.)Write an inequality.
Seven more than the quotient of a
number b and 15 is greater than 6

The maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

To find the maximum value of z = 4x + y subject to the given constraints, we can use linear programming.

Graph the constraints:

First, we will graph the constraints to visualize the feasible region.

The constraint x + y ≤ 50 represents the region below the line x + y = 50:

The constraint 3x + y ≤ 90 represents the region below the line 3x + y = 90:

The feasible region is the shaded region that satisfies both constraints:

Identify the corner points of the feasible region:

The feasible region has four corner points: (0, 0), (0, 50), (30, 20), and (45, 0).

Evaluate z at each corner point:

z(0, 0) = 4(0) + 0 = 0

z(0, 50) = 4(0) + 50 = 50

z(30, 20) = 4(30) + 20 = 140

z(45, 0) = 4(45) + 0 = 180

Compare the values of z at the corner points:

The largest value of z is 180, which occurs at the corner point (45, 0).

Therefore, the maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

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the correct answer is a reflection across the x-axis.

How to solve questions?

Based on the given image, the type of transformation shown is a reflection across the x-axis.

A reflection is a transformation that flips a figure over a line of reflection, in this case, the x-axis. The resulting image is a mirror image of the original figure, with corresponding points on either side of the line of reflection equidistant from it.

In the given image, polygon ABCD is the preimage, and polygon A'B'C'D' is the resulting image. We can see that the two polygons are mirror images of each other across the x-axis. For example, point A in the preimage is reflected across the x-axis to point A' in the resulting image, which is directly below point A. Similarly, point B in the preimage is reflected to point B', point C to C', and point D to D'.

A 90° clockwise rotation would result in a different orientation of the polygon, where point A would move to the position of point B, point B to C, point C to D, and point D to A. A horizontal or vertical translation would result in a shift of the polygon in the respective direction, which is not the case here.

Therefore, the correct answer is a reflection across the x-axis.

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ANSWER:

368

EXPLANATION:

youre given:

l=14

w=5

h=5

just plug those into the given formula,

2×(14×5)+2×(14×6)+2×(5×6)

(you should do it yourself to check my math...)

Answer:

189.1034.

Step-by-step explanation:

The result of the expression is approximately 189.1035.

To calculate the expression 192 - 84 ÷ (71 + 16) x 3, follow the order of operations, which is commonly remembered by the acronym PEMDAS:

Parentheses: Perform the operation within the parentheses first.

71 + 16 = 87

Division: Perform the division.

84 ÷ 87 ≈ 0.9655 (rounded to four decimal places)

Multiplication: Perform the multiplication.

0.9655 * 3 ≈ 2.8965 (rounded to four decimal places)

Subtraction: Finally, perform the subtraction.

192 - 2.8965 ≈ 189.1035 (rounded to four decimal places)

The result of the expression is approximately 189.1035.

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Answer:

Step-by-step explanation: 462 Divided by 24 = 19.25$

Proof: 19.25 x 24 = 462

Answer: 19.25$

Answer: 480 in²

Step-by-step explanation:

    To calculate the surface area, we will find the area of each side and add it together.

Area of the rectangular sides can be found with A = LW:

    A = LW

    A = (12 in)(10 in)

    A = 120 in²

    A = LW

    A = (12 in)(10 in)

    A = 120 in²

    A = LW

    A = (12 in)(12 in)

    A = 144 in²

All the rectangular sides added together:

    120 in² + 120 in² + 144 in² = 384 in²

    Now, we will find the triangle sides. The formula for a triangle is [tex]A=\frac{BH}{2}[/tex], but since we have two congruent triangles I will not be dividing by 2.

    A = BH

    A = (12 in)(8 in)

    A = 96 in²

Lastly, I will add them both together:

384 in² + 96 in² = 480 in²

Answer:

- 2/1

Step-by-step explanation:

if u look at the graph/line it's going up by 2 then across 1

G. y = 37/24x

Direct variation means that the number of inches of rain (y) is directly proportional to the number of hours (x). In this case, 37 inches of rain fell in a 24-hour period. To find the constant of proportionality, divide the total inches of rain by the total hours:

k = 37 inches / 24 hours

Now, we can write the equation of direct variation:

y = kx

Substitute the value of k:

y = (37/24)x

The surface area is approximately 41.7 square units.

The rectangle has dimensions 18 units by 6 units, so its area is:

A(rectangle) = l x h = 18 x 6 = 108 square units

The semicircle has a radius of 5 units, so its area is half that of a full circle:

A(semicircle)

= 1/2 x π x r²

= 1/2 x π x 5²

= 1/2 x 25π

= 12.5π

To find the total surface area, we need to add the areas of the rectangle and the semicircle. However, since the semicircle is attached to the top of the rectangle, we need to subtract the area of the portion of the circle that overlaps with the rectangle. This overlapping area is equal to the width of the rectangle (18 units) times half the circumference of the circle (1/2 x π x r), or:

A(overlap)

= w x 1/2 x π x r

= 18 x 1/2 x π x 5

= 45π

Therefore, the total surface area is:

Surface area = A(rectangle) + A(semicircle) - A(overlap) = 108 + 12.5π - 45π ≈ 41.7 square units

Rounding to the nearest tenth, the surface area is approximately 41.7 square units.

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Answer:

5x - 9 and 3x + 9 are two mathematical expressions. The first expression, 5x - 9, represents a value obtained by multiplying 5 by x and then subtracting 9. The second expression, 3x + 9, represents a value obtained by multiplying 3 by x and then adding 9. Both expressions can be simplified further or used in various mathematical operations depending on the context of the problem or equation in which they are being used.

Answer:-45 and -3

Step-by-step explanation:

Volume First Cylinder: 50.24 in³

Volume Second Cylinder: 127.5625 inch³

Volume Third Cylinder: 904.32 inch³

Volume First Cylinder:

= πr²h

= 3.14(2)² (4)

= 3.14 x 16

= 50.24 in³

Volume Second Cylinder:

= πr²h

= 3.14(2.5)² (6.5)

=3.14 (6.25)(6.5)

= 127.5625 inch³

Volume Third Cylinder:

= πr²h

= 3.14(6)² (8)

=3.14 (36)(8)

= 904.32 inch³

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Answer:

See the below process

Step-by-step explanation:

let the Unknown value be x.

Now

[tex] \frac{17}{24} + x = \frac{ - 5}{12} [/tex]

[tex]x = \frac{ - 5}{12} - \frac{17}{24}[/tex]

Taking LCM

[tex]x = \frac{ - 10 - 17}{24} [/tex]

[tex]x = \frac{ - 27}{24} \\ = \frac{8}{9} [/tex]

we should add 8/9 to 17/24 to get -5/12

I hope it helped you

Please Mark me the brainliest

Answer:

100 Minutes

Step-by-step explanation:

Step 1: Break it down-

3¢ can be expressed as 0.3

Step 2: Add monthly charge-

Since there is a 10$ monthly charge: 40-10=30

Step 3: Subtract-

Now divide: 30 ÷ 0.3

Step 4: Final Answer-

Hence the amount of minutes per month= 100

An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.

The power-reducing formulas state that:

sin^2(x) = (1 - cos(2x))/2

cos^2(x) = (1 + cos(2x))/2

Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:

18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]

Expanding the right-hand side of the equation, we get:

18[(1 - cos^2(2x))/4]

Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:

18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8

Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.

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The probability that the friend is at least 22 minutes late is 0.266

Uniform density function for a friend = x minutes late

The Friend is at least 21 minutes late

Based on the above information, the probability that the friend is at least 21 minutes late is

= (Total minutes - minimum minutes)/Total minutes

=30-22/30

=8/30

=0.266

Based on the above formula we can easily find out the probability for the friend who is at least 22 minutes late

Hence, the probability that the friend is at least 22 minutes late is 0.266

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U is located in the plane or vector that A's columns span.

A mathematical concept with both magnitude and direction is a vector. It is frequently used to symbolise forces like the gravitational pull of an object or the electrical forces that exist between charged particles. It can be expressed mathematically as a line segment with two ends, a direction, and a magnitude.

Part 1

To calculate the resulting vector, vector operations including addition, subtraction, multiplication, and division can be used. The individual x, y, and z components of a vector—which stand for its magnitude and direction—can also be determined.

Part 2

Why the answer in Part 1 is correct?

Part 1's answer I gave was A. Yes, writing u as a linear combination of the columns of A after multiplying A by the vector [4, 20, 8]. This is so because the vector [4, 20, 8] may be expressed as a linear combination of the columns of A since it is a solution to the system of linear equations generated by the augmented matrix [A|u]. U is thus in the plane that is covered by the columns of A.

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Answer:

Step-by-step explanation:

6x + 15 = x - 10

5x + 15 = -10

5x = -25

x = -5

92 grams of recycled plastic were used to make Chanasia's bucket

Chanasia buys a plastic bucket

The bucket weighs 460 grams

The label on the bucket says it was made with 20% recycled plastic

The number of grams of recycled plastic that was used to make the bucket can be calculated as follows

= 460/100

= 4.6

= 4.6 × 20

= 92

Hence 92 grams of recycled plastic was used to make the bucket

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The probability that all four people regularly use seat belts is approximately 0.656 or 65.6%.

To find the probability that all four people regularly use seat belts, we need to use the multiplication rule of probability which states that the probability of two or more independent events occurring together is the product of their individual probabilities.

The probability that the first person uses a seat belt is 0.901, and assuming that the events of seat belt use by different people are independent, the probability that the second person also uses a seat belt is 0.901.

The probability that the third person uses a seat belt is also 0.901, and the probability that the fourth person uses a seat belt is also 0.901.

Therefore, the probability that all four people regularly use seat belts is:

P(all four use seat belts) = P(person 1 uses seat belt) x P(person 2 uses seat belt) x P(person 3 uses seat belt) x P(person 4 uses seat belt)

P(all four use seat belts) = 0.901 x 0.901 x 0.901 x 0.901

P(all four use seat belts) = 0.656

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The function has a local maximum at x = 1 and a local minimum at x = 1/5, as shown in the graph, and the absolute maximum and minimum occur at x = 0 and x = (3/5), respectively.

Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.

A function is an association between inputs and outputs that yields one unique outcome for each input. Every function has a domain and a codomain, often known as a scope. Functions are commonly represented with the letter f. (x). As input, an x is used. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four fundamental types of functions available.

To obtain the absolute maximum and lowest values of the function  over the interval −1 ≤ x ≤ 1, we must examine the critical points and the interval endpoints.

We first take the derivative of f(x) and set it to zero to determine the critical points:

The function is then assessed at these pivotal points and the interval's endpoints:

As we can see from the information above, f(x) has a maximum value of 4 and occurs at the values x = 0 and x = 1. The absolute minimum value of f(x) is approximately 2.65 for x = (3/5).

We can corroborate these findings by charting the graph of f(x) across the 1 x 1 interval: graph of f(x) = x5 x3 + 4

According to the graph, the function has a local maximum at x = 1 and a local minimum at x = 1/5, but the absolute maximum and lowest are, respectively, x = 0 and x = (3/5).

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Answer:

88

Step-by-step explanation:

y=2cm h=7cm

CSA=22/7×4×7

the sevens get crossed out and then 22/1 ×4=88.

Answer: It is 1.24x smaller.

Step-by-step explanation:

1.2(106)= 127.2

1.47(107)= 157.3

157.3/127.2 = 1.24x smaller

The required equation of the parabola is y² = 24x for focus (6,0) and directrix x= -6 .

The focus and directrix of the required parabola are as,

Focus (6, 0)

and, Directrix x = - 6

Since the focus of the parabola lies on the x- axis, the x- axis is said to be the axis of the parabola.

Therefore, the equation of the parabola is either of the form,

y² = 4ax

or, y2 = - 4ax

depending on which axis the parabola is in, that is whether negative or positive axis.

It is also seen that the directrix, x = - 6 which implies it is to the left of the y- axis while the focus is (6, 0) which implies it is to the right of the y-axis.

Hence, the parabola is of the form y² = 4ax.

Since, a = 6

Thus, the equation of the parabola is y² = 4(6)x

⇒ y² = 24x

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We can expect 4 of the next 20 pastries served to be bran muffins based on the given data.

What is meant by the term data?

Data refers to a collection of facts, statistics, measurements, or observations that are gathered and analyzed to gain insights or information about a particular topic or subject. Data can be both quantitative (numerical) and qualitative (descriptive) in nature, and it can be obtained from various sources, such as surveys, experiments, sensors, or records. The processing and interpretation of data can lead to new discoveries, trends, or predictions in various fields, including science, business, and technology.

According to the given information

The proportion of bran muffins out of the total pastries served can be calculated by dividing the number of bran muffins by the total number of pastries:

The proportion of bran muffins = 2 / (1 + 3 + 2 + 2 + 2) = 2 / 10 = 0.2

This means that 20% of the pastries served are bran muffins. To find out how many of the next 20 pastries served should be expected to be bran muffins, we can multiply 20% by 20:

The number of expected bran muffins = 0.2 * 20 = 4

Therefore, we can expect 4 of the next 20 pastries served to be bran muffins based on the given data.

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The missing step in the two column proof is

Statement              Reason

Δ DAC ≅ ΔBCA    ASA congruence theorem

The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).

The angle side angle theorem states uses the side two parameters which includes:

The parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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The equivalenet expression is 54[tex]n^{-11}[/tex]

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.

Starting with:

([tex]6n^-5[/tex])([tex]3n^-3[/tex])²

We can simplify as follows:

([tex]6n^-5[/tex])([tex]9n^-6[/tex])

Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.

Therefore:

6 x 9 = 54

[tex]n^-5 * n^-6 = n^-11[/tex]

So the simplified expression is:

[tex]54n^-11[/tex]

Therefore, the expression [tex](6n^-5)(3n^-3)^2[/tex] is equivalent to [tex]54n^-11.[/tex]

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The expression that is equal to (6n-5)(3n-3) option D, 54n11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:

(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)

                 = 18n² - 18n - 15n + 15

                 = 18n² - 33n + 15

Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.

So, the answer is option D, 54n11.

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Step-by-step explanation:

sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.

because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).

the confidence interval limits are

mean ± Z×sd/sqrt(n)

mean = mean value of the sample.

sd = standard deviation (either of - preferred - the entire population or of the sample)

n = number of data points (here 14).

Z = Z value of the standard normal distributing table for 99% (2.576).

here a little table for different confidence intervals :

Confidence Interval Z

80% 1.282

85% 1.440

90% 1.645

95% 1.960

99% 2.576

99.5% 2.807

99.9% 3.291

mean value = sum of all data points divided by the number of data points :

mean = 66.74/14 = 4.767142857...

sd = sqrt(sum((data point difference to mean)²)/n)

let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).

sd = 0.069941667...

the confidence interval limits are then

4.767142857... ± 2.576×0.069941667.../sqrt(14) =

= 4.767142857... ± 0.048152387...

upper limit = 4.815295244 ... ≈ 4.82

lower limit = 4.71899047 ... ≈ 4.72

that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.

in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.