Hamza found a pattern with some division expressions.

1. Calculate each quotient. (I already did this.)

2. Describe a pattern you see. (I can't find anything :)

Answer:

1) It's a slope

2) It's the x-intercept

3) It's the y- intercept

Answer:

5 - b

6 - a

7 - d

Step-by-step explanation:

5. When a number has an exponent for a fraction, it is asking for the root of the number.

[tex]b(x) = 6(\sqrt{16})[/tex]

[tex]b(x)=6*4[/tex]

[tex]b(x)=24[/tex]

6. Same thing as the previous problem.

[tex]k(x)=6(\sqrt[3]{27})[/tex]

[tex]k(x)=4(3)[/tex]

[tex]k(x)=12[/tex]

7. In the table of values, gives the value of f(x) and x when the other value is zero.

When x is zero, the other value is -4.

When f(x) is zero, the other value is 24.

The required number of flour cups does he need to make the muffins are 7.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

We have,

Ratio of 3.5 cups of flour for every 1.75 cups of sugar.

cups of flour/ cups of sugar = 3.5/1.75

= 2:1

So, for every two cups of flour, there is one cups of sugar.

The number of cups of flour for 3.5 cups of sugar.

= 2(3.5)

= 7 cups.

Thus, there are 7 cups of flour required.

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Lexi made more than 400 fluid ounces of punch.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this phrase can be replaced by any of the inequality symbols, such as greater than (>), less than (<), more than or equal to (≥), less than (≤), or not equal to (≠).

Given Lexi made fruit punch for her Fourth of July party and split it equally among 50 cups There were more than 8 fluid ounces of punch in each one.

let x be the total punch Lexi made,

linear inequality for the condition is,

x/50 > 8

multiply both sides by 50

(x/50)*50 > 8*50

x > 400

Hence she made more than 400 ounces of punch.

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An expression (in terms of d ) that represents your distance east of the stop sign (in meters) is (29 - d).

You are 29 meters west of a stop sign (-29 meters east of the stop sign) when you start walking due east.

let d represent the distance (in meters) you have walked east since you started walking.

You have to cover total 29 meters distance.

You covered d meters from the 29 meters distance.

Since you have to cover total 29 and you covered d meters. Now the remaining distance should be differnce between the 29 and d meters distance.

So the equation should be

= 29 - d

Now you have to cover only 29 - d meters distance.

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The value of 96.1% of 146 is 140.31

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the value of 96.1% of 146.

Convert 96.1% to the decimal value by dividing with 100

96.1/100=0.961

Now multiply 0.961 with the 146 to find the value.

0.961×146

140.306

Hence, the value of 96.1% of 146 is 140.31

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The following is the correct way to swap the values in these two variables is:

d) int temp = num2;

num2 = num1;

num1 = temp;

This is because in d), the value of num2 is stored in a temporary variable temp before swapping. Then, the value of num1 is assigned to num2 and the value of temp is assigned to num1. This way the values of num1 and num2 are successfully swapped. The other options have logical errors in the swapping process.

Swapping values of variables is a basic concept in computer programming and is not a mathematical concept. However, it is related to mathematics in that programming can be used to solve mathematical problems.

For example, in mathematics, we might want to swap two values in a list so that we can sort the list in a certain order. In this case, the ability to swap values in programming can be applied to solving a mathematical problem. But the concept of swapping values itself is not a mathematical concept.

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Answer:

x = 15º

Step-by-step explanation:

you see they are complementary angles in a straight line (180º), so:

6x - 5 + 6x + 5 = 180

12x = 180

x = 180 / 12

x = 15

And 6x - 5 is not equal 6x + 5 and will never be, I don't know where you got that from.

Katie and Erica each bowled for 5 hours, and they both ended up paying P = $35.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

If both Katie and Erica play for t hours, then  Katie pays a total of

$(15 + 4t), while Lisa pays a total of $(5+ 6t). If they both pay the same amount P, then

15 + 4t = P

5+ 6t= P

Solve for t :

15 + 4t = 5+ 6t

6t - 4t = 15-5 = 10

=> 2t=10

=> t=5

So Katie and Erica each bowled for 5 hours, and they both ended up paying P = $35.

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For any value of k and h = -18, the system will have infinitely many solutions.

Hence, option (b) is the correct choice.

A coefficient matrix in linear algebra is a matrix made up of the coefficients of the variables in a group of linear equations. In order to solve systems of linear equations, the matrix is employed.

The system will have infinitely many solutions when the determinant of the coefficient matrix is equal to 0.

The determinant can be calculated from the upper triangular matrix as the product of the diagonal elements, which is 0 * (-20) * (h + 18) = 0.

Therefore, the system will have infinitely many solutions when h + 18 = 0,

or h = -18.

This means the answer is (b) any value of k and h = -18.

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Answer:

x = 34°

Step-by-step explanation:

The angle x and 146° are complementary angles, meaning that they form a 180° angle when combined. This is known because they share a straight line.

Because they are complementary, the sum of the angles is 180°:

x + 146° = 180°

Now we have a one-step equation! Solve by subtracting 146 from both sides:

x = 34°

The following complex numbers are in cartesian form needs four decimal  places for accuracy.

-0.75e^j10° in Cartesian form is -0.75cos(10°) + i-0.75sin(10°) = -0.71 - 0.71i.

The values for cosine and sine should be evaluated to at least 4 decimal places for accuracy.

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If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard as a function of x is (150/x - 10)(x - 4).

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides.

x = width of the billboard designer

Total Area including margin = 150 ft^2

Height of the billboard = Area/width

Height of the billboard = 150/x

Before the height of the billboard = (150/x - 5 × 2)

Before the height of the billboard = (150/x - 10) ft

The width of the printed region billboard = (x - 2 × 2)

The width of the printed region billboard = (x - 4) ft

The area of the printed region of the billboard = The width of the printed region billboard × The height of the printed region billboard

The area of the printed region of the billboard = (150/x - 10)(x - 4)

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The complete question is:

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 150 ft^2 (including the margins).

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard.

Area as a function of x =

A polynomial of degree 3 with real coefficients can be written in the form f(x) = a(x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots of the polynomial. Since the given zeros are -4 and 2 + i, we can write the polynomial as follows: f(x) = a(x + 4)(x - (2 + i))(x - (2 - i)).

What is polynomial of degree?

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only the operations of addition, subtraction, and multiplication. The degree of a polynomial is defined as the highest power of the variable in the polynomial. For example, the polynomial 3x^2 + 2x + 1 has a degree of 2, since the highest power of x is 2. A polynomial of degree 0 is a constant, a polynomial of degree 1 is a linear function, a polynomial of degree 2 is a quadratic function, and so on.

A polynomial of degree 3 with real coefficients can be written in the form f(x) = a(x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots of the polynomial. Since the given zeros are -4 and 2 + i, we can write the polynomial as follows:

f(x) = a(x + 4)(x - (2 + i))(x - (2 - i))

The third root is the complex conjugate of the second root, and since the coefficients of the polynomial are real, the conjugate must also be included.

To determine the value of the coefficient a, we can use synthetic division or long division to divide (x + 4) into (x^3 + bx^2 + cx + d). To get the cubic polynomial:

x^3 + bx^2 + cx + d = (x + 4)(x - (2 + i))(x - (2 - i))

Expanding the right side of the equation, we get:

x^3 + bx^2 + cx + d = x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16

Comparing the coefficients of like terms on both sides of the equation, we get:

b = -4

c = 4 + 4i

d = -16

So the polynomial is:

f(x) = a(x + 4)(x - (2 + i))(x - (2 - i)) = a(x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16)

Since the coefficient a is arbitrary, we can set it to 1 for convenience:

f(x) = (x + 4)(x - (2 + i))(x - (2 - i))

= x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16

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We are 95% confident that the true population proportion is between 71.6% and 80.4%

The 95% confidence interval for the proportion of all U.S. grown people who would include those  on their list of 10 historic events can be constructed using the formula:

Where:

[tex]pi[/tex] = sample proportion (76%)

SE = standard error (square root of [tex]pi(1-pi)/n[/tex])

z = the critical value for a 95% confidence level (1.96)

n = sample size (2025)

Plugging in the values, we get:

[tex]SE =\sqrt{(0.76(1-0.76)/2025)} = 0.0240\\CI = 0.76 ± (1.96)(0.0240) = (0.716, 0.804)[/tex]

The 95% confidence interval can be interpreted as follows: If we repeated this study many times, 95% of the intervals constructed would contain the true population proportion of all U.S. grown persons who would include on their list of 10 historic events. Based on this sample, we are 95% confident that the true population proportion is between 71.6% and 80.4%.

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The length of side PT by using the ratio of similar triangles is 49/3 or 16 1/3. Option A is correct.

Triangles that are similar to one another in terms of shape but not necessarily size are called similar triangles. In simple words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are also equivalent.

In the event that two triangles are similar with sides P, Q, R and p, q, r, then the pair of their matching sides is also proportional.

From the given figure, using the ratios of similar triangles;

QP/QS = RP/RT

(12+28)/12 = (7 + x)/7

40/12 = (7 +x)/ 7

7(40/12) = 7 + x

70/3 = 7 + x

x = 49/3 o 16 1/3

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The required probability that a randomly selected bird is a parakeet given that it is green is 54.1%.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
From the table,
Total green birds = 37
Total green parakeets = 20

Now,
The probability that a randomly selected bird is a parakeet given that it is green,
= 20 / 37 = 54.1%

Thus, the required probability that a randomly selected bird is a parakeet given that it is green is 54.1%.

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The smallest number which has only 1s and 0s as its digits and is divisible by the given number a is "100...0" with a number of zeros equal to the number of digits in a.

To find the smallest number which has only 1s and 0s as its digits and is divisible by the given number a, we need to consider the divisibility rules of the number a. If the number a is divisible by 2, then the smallest number which has only 1s and 0s as its digits and is divisible by a is 100...0 (with a number of zeros equal to the number of digits in a).

If the number a is divisible by 5, then the smallest number which has only 1s and 0s as its digits and is divisible by a is 10...0 (with a number of zeros equal to the number of digits in a - 1).

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[tex]\texttt{speed} = {\dfrac{d}{t}[/tex]

distance = 30 km

t = 3 hr

[tex]\texttt{speed}=\dfrac{30}{3}[/tex]

[tex]\fbox{\texttt{speed} = 10 km/hr}[/tex]

For a given polynomial 45x+7, x will be -7/45.

What are polynomials?

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.

Based on the number of terms present in the expression, it is classified as

Monomial:-A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. A Examples of monomials are: 5x,3.

Binomial:-A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials.  Examples of binomials are:

– 5x+3, 6a^4 + 17x.

Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:

– 8a^4+2x+7, 4x^2 + 9x + 7.

Now,

Given polynomial is is in form of a linear equation i.e. 45x+7

To find value of x, put 45x+7=0

45=-7

x=-7/45

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It will take 27.8 hours for all beetles to embark onto the ark.

Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

There are 1/4 million beetles

250,000 beetles

they move side by side in pairs

250,000 /2 = 125,000 pairs form a line.

Length of each beetle 1 cm

space of 7cm between them

total distance = 8cm.

125,000 form a line

so total length = 125,000 * 8 = 1000,000 cm is the length of the line.

the length of the plank = 500 cm

so the distance covered = 1000,000+500 = 1000,500 meters

distance = 1000,500 cm

speed = 10 cm/s

Time = distance / speed

Time = 1000,500/10

Time = 100050 seconds

         = 100050/3600 hours

         = 27.8 hours

Hence, all 1/4 million species will take 27.8 hours to embark onto the ark.

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The cost of seed for one acre of land is $79.68

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.

The cost of 80,000 kernel bag of seed is $255.60

He will plant 25,000 kernels of corn per acre

Therefore the cost of one seed = 255/80,000

. This means the cost of seed corn per acre = 255/80,000 × 25000

= $79.68

Therefore the cost of seed for 1 acre is $79.68

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Answer:

below

Step-by-step explanation:

x = # of students in student body

.18 * x = 28

x = 28/.18 = ~ 156 students

Answer: 36 problems

Step-by-step explanation:

40% is nothing but 40/100, which is just 4/10. To start, multiply 60 by the fraction 4/10. Cancel out the 10 from the denominator of the fraction to get 4 x 6 = 24. Now, we just found the number of problems that the student solved, but we need to find how many problems still need to be solved. To do that, do 60 - 24 = 36. The student needs to solve 36 more problems.

I hope this helps!

Answer:

m<1 = 92°

m<2 = 24°

m<3 = 64°

m<4 = 35°

m<5 = 81°

Step-by-step explanation:

The coordinates of its P-intercept is -18.

The coordinate points give values of dependent and independent variables.

Coordinates on graphs, it is typically represented by a pair of numbers: the first number indicates the length along, while the second number indicates the length up or down. The point (12,5), for instance, is 12 units down and 5 units up.

The coordinates of its P-intercept is the value of the P intercept is the value of P(x) when t = 0.

The given function is as follows:

Given the function P(x) = -(x-1) (x+3) (x-6)

when x = 0

P(0) = -(0 - 1) (0 + 3) (0 - 6)

P(0) = -(-1) (3) (-6)

P(0) = -18

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Answer: 10 7/12 or if you don't want a mixed number 127/12

Step-by-step explanation: use 10 7/12 just realized it said used a mixed number so the answer is 10 7/12

Answer:

5

Step-by-step explanation: