please help! with algebra I question

Answer/ Step-by-step explanation:

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Proportional relationships are relationships between two variables where their ratios are equivalent.

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Lets take a look at example one attached image:

The constant of proportionality is the value of y when x = 1 in a proportional relationship.

On which line does y = 1/2 when x = 1?

Only line C has a y- value less than 1 when x = 1, but how can we be sure that the constant of proportionality is exactly 1/2?

If the constant of proportionality of a proportional relationship is 1/2 then:

y = 1/2x (like rise over run (slope), rise up 1 unit, and run right 2 units)

We can try the point (2, 1), and plug in the values into the equation, where x = 2, y = 1.

(1) = 1/2(2)

1 = 1

Line C has a constant proportionality of 1/2 between x and y.

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Example 2, 3, and 4 is a worked out example on khan academy (attached images)

The calculated value of the amplitude of the function is 3

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

y = 3sin[2(θ - 90)] + 2

A sinusoidal function is represented as

f(x) = Asin(B(x + C)) + D

Where

Amplitude = A

using the above as a guide, we have the following:

Amplitude = A = 3

Hence, the amplitude of the function is 3

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Question

What is the amplitude?

y = 3sin[2(θ - 90)] + 2

The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).

We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.

To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.

Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.

To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.

This is the equation of the line in standard form.

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The proportional sides/corresponding sides of the triangles are ST/XY = RT/YZ = SR/XZ.

The value of a and b are 5 and 20 respectively.

Corresponding sides refers to a pair of matching sides that are in the same spot in two different shapes.

ST/XY = RT/YZ = SR/XZ

ST/XY = 3/15

= 1/5

RT/YZ = 4 ÷ 1/5

= 4 × 5/1

YZ, b = 20

Hypotenuse² = opposite² + adjacent²

5² = 3² + 4²

25 = 9 + 16

25 = 25

Therefore,

SR = a = 5

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Answer:

4,200

Step-by-step explanation:

70s = b

70(60) = b

4200 = b

Helping in the name of Jesus.

Dot plots are graphical displays of data that use dots to represent the frequency or count of a specific value in a data set. The ages of five children in each of two families are represented in the dot plots above.

Both dot plots have a similar range of ages, but family A has a higher median age and a smaller spread of ages than family B.

For family A, the median age is 10 years old because the middle dot in the plot is located at 10. Family A has a small range of ages because all the dots are concentrated in the 8-12 age range.

In contrast, family B has a wider range of ages, from 6 to 15 years old, and a larger spread because the dots are scattered across the plot.

The median age for family B is approximately 11 years old.

In conclusion, dot plots are useful for comparing data sets and analyzing their characteristics such as median age and spread.

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Therefore, the package with 40 hooks is the better buy in terms of cost efficiency.

To determine which package is the better buy, we need to compare the cost per hook for each package.

For the package of 25 hooks costing $9.95, we divide the total cost by the number of hooks:

Cost per hook = $9.95 / 25 = $0.398

Rounding to the nearest cent, the cost per hook is $0.40.

For the package of 40 hooks costing $13.99, we divide the total cost by the number of hooks:

Cost per hook = $13.99 / 40 = $0.3498

Rounding to the nearest cent, the cost per hook is $0.35.

Comparing the two costs per hook, we can see that the package with 40 hooks for $13.99 offers a better deal, as the cost per hook is lower at $0.35.

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The compensation equation for the employee may be stated as follows:

A equation is a mathematical statement that claims the equivalence of two expressions. Equations are used in mathematics, science, engineering, and many other professions to express connections between variables and to solve problems.

If s denotes income, x denotes years of experience, and d denotes years of education.

The employee's remuneration is computed as the basic wage of $35,000 + $2,000 for each year of experience plus $3,000 for each year of study. In deciding an employee's wage, this equation considers both their experience and education.

Therefore, [tex]\text{S}=35000+2000\text{x}+3000\text{D}[/tex] is the compensation equation for the employee.

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Answer:

  A, D

Step-by-step explanation:

You want to identify the tables that represent inverse functions.

For every ordered pair (x, y) of a function, there is an ordered pair (y, x) of its inverse function.

The first table shown has an ordered pair (x, y) = (4, -14). That means its inverse function must have the ordered pair (-14, 4). The two tables with that characteristic are shown in the attachment.

<95141404393>

Indianapolis: Ratio as decimal: 0.006939, Owners per 100: 0.7

New York: Ratio as decimal: 0.049018, Owners per 100: 4.9

Cairo: Ratio as decimal: 0.000554, Owners per 100: 0.1

Beijing: Ratio as decimal: 0.045336, Owners per 100: 4.5

Tokyo: Ratio as decimal: 0.064198, Owners per 100: 6.4

To calculate the ratio as a decimal and the owners per 100 for each city, we need to divide the number of owners by the total population and perform some additional calculations.

Let's calculate the ratio as a decimal for each city:

For Indianapolis:

Number of Owners: 6,245

Total Population: 0.90 million

Ratio as decimal: 6,245 / 0.90 million

= 6,245 / 900,000

= 0.006939

For New York:

Number of Owners: 911,216

Total Population: 18.6 million

Ratio as decimal: 911,216 / 18.6 million

= 911,216 / 18,600,000

= 0.049018

For Cairo:

Number of Owners: 10,598

Total Population: 19.1 million

Ratio as decimal: 10,598 / 19.1 million

= 10,598 / 19,100,000

= 0.000554

For Beijing:

Number of Owners: 959,611

Total Population: 21.2 million

Ratio as decimal: 959,611 / 21.2 million

= 959,611 / 21,200,000

= 0.045336

For Tokyo:

Number of Owners: 1,700,510

Total Population: 26.5 million

Ratio as decimal: 1,700,510 / 26.5 million

= 1,700,510 / 26,500,000

= 0.064198

Now, let's calculate the owners per 100 for each city by multiplying the ratio as a decimal by 100:

Owners per 100 for Indianapolis: 0.006939 * 100 = 0.6939

Owners per 100 for New York: 0.049018 * 100 = 4.9018

Owners per 100 for Cairo: 0.000554 * 100 = 0.0554

Owners per 100 for Beijing: 0.045336 * 100 = 4.5336

Owners per 100 for Tokyo: 0.064198 * 100 = 6.4198

Therefore, rounding the ratio as a decimal to 6 places, and the owners per 100 to one decimal, we have:

Indianapolis: Ratio as decimal: 0.006939, Owners per 100: 0.7

New York: Ratio as decimal: 0.049018, Owners per 100: 4.9

Cairo: Ratio as decimal: 0.000554, Owners per 100: 0.1

Beijing: Ratio as decimal: 0.045336, Owners per 100: 4.5

Tokyo: Ratio as decimal: 0.064198, Owners per 100: 6.4

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Answer:

A ∩ B = {7, 8}

Step-by-step explanation:

A = {1, 2, 5, 7, 8}

B = {6, 7, 8, 9}

A ∩ B = set of elements in both A and B

A ∩ B = {7, 8}

Answer:

(x-2)^2 + (y+3)^2 = 5.1^2

Step-by-step explanation:

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where h and k are the x and y values of the center of the circle respectively and r stands for the radius.

The center is given to us, at (2, -3) so we can plug that in:

(x-(2))^2 + (y- (-3))^2 = r^2

Simplify:

(x-2)^2 + (y+3)^2 = r^2

We can also solve for the radius by getting another point given to us: (3,2).

Using the pythagorean theorem, we can find how far the two points are away from each other:

a^2 + b^2 = c^2

1^2 + 5^2 = c^2
1 + 25 = c^2

26 = c^2

c ~ 5.1

Plug the radius we solved for in for r:
(x-2)^2 + (y+3)^2 = 5.1^2

Julio will be 30 years old when his father is twice his age.

To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.

Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.

For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.

Setting up an equation to solve for x:

x + 30 = 2x

Simplifying the equation, we subtract x from both sides:

30 = x

Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.

Therefore, Julio will be 30 years old when his father is twice his age.

Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?

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Si un hombre camina a una velocidad promedio de 4 2/5 km por hora, podemos calcular la distancia que puede recorrer en 2 2/3 horas.

Primero, convertimos la velocidad promedio a una fracción impropia. 4 2/5 se puede expresar como 22/5. Por lo tanto, la velocidad es de 22/5 km por hora.

Luego, multiplicamos la velocidad por el tiempo para obtener la distancia. En este caso, la multiplicación sería (22/5) * (8/3) = 176/15 km.

Entoncs, el hombre puede llegar a una distancia de 176/15 km en 2 2/3 horas.

En resumen, el resultado es 176/15 km.

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If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.

To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.

First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:

9 feet = 9 * 12 = 108 inches

0 1/2 inch = 0.5 inch

Total height = 108 + 0.5 = 108.5 inches

Next, we divide the total height by the number of risers (14) to find the height of each riser:

Height of each riser = Total height / Number of risers

Height of each riser = 108.5 inches / 14

Using a calculator, we can compute:

Height of each riser ≈ 7.75 inches

Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.

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[tex]\underline{\underline{\purple{\huge\sf || ꪖꪀᦓ᭙ꫀ᥅}}}[/tex]

The given polynomial is:

p(t) = -t²(3 - 5t)(t² + t + 4)

To find the degree of the polynomial, we need to determine the highest power of t in the expression. This is given by:

degree = 2 + 1 + 2 = 5

So the degree of the polynomial is 5.

The leading term of the polynomial is the term with the highest power of t. This is given by:

leading term = -t² * 5t² = -5t^4

So the leading term of the polynomial is -5t^4.

The leading coefficient of the polynomial is the coefficient of the leading term. This is given by:

leading coefficient = -5

So the leading coefficient of the polynomial is -5.

The constant term of the polynomial is the term that does not contain any powers of t. This is given by:

constant term = -t²(3)(4) = -12t²

So the constant term of the polynomial is -12t^2.

To find the end behavior of the polynomial, we need to determine what happens to the value of the polynomial as t approaches positive or negative infinity. Since the degree of the polynomial is odd, we know that the end behavior will be opposite for t approaching positive or negative infinity. We can use the leading term to determine the end behavior:

- as t approaches positive infinity, the leading term approaches negative infinity, so the end behavior is p(t) → -∞ as t → ∞

- as t approaches negative infinity, the leading term approaches positive infinity, so the end behavior is p(t) → ∞ as t → -∞

So the end behavior of the polynomial is:

- p(t) → -∞ as t → ∞

- p(t) → ∞ as t → -∞

The radius of the semicircle protractor is approximately 4.693 cm.

Given,Perimeter of a semicircle protractor = 14.8 cm.

To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.

Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =[tex](1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693[/tex] cm.

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Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

Para calcular la población de bacterias al cabo de 4 horas, primero necesitamos determinar cuántos intervalos de 20 minutos hay en 4 horas.

4 horas son equivalentes a 240 minutos. Dividiendo 240 minutos entre 20 minutos por intervalo, obtenemos 12 intervalos.

Dado que la población de bacterias aumenta un 25% cada 20 minutos, podemos aplicar este crecimiento a cada intervalo de 20 minutos.

Para cada intervalo de 20 minutos, la población de bacterias aumentará en un 25%.

Por lo tanto, podemos calcular la población de bacterias al final de los 12 intervalos de la siguiente manera:

Población final = Población inicial * (1 + tasa de crecimiento)^número de intervalos

Población inicial = 32,200 bacterias

Tasa de crecimiento = 25% = 0.25

Número de intervalos = 12

Población final = 32,200 * (1 + 0.25)^12

Realizando los cálculos, obtenemos la población final de bacterias al cabo de 4 horas.

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a) The triangles in this problem are congruent.

b) The reason is the SAS congruence theorem.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The equal sides for this problem are given as follows:

Hypotenuses and PS.

As angle P is bisected, we have <1 = <2, which are the angles between the equal sides, hence the SAS theorem holds true for this problem.

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Answer:

Gender and passing the test appear to be ________, as the probability of each event occurring does not depend on the other. Both males and females pass or fail the test with similar likelihoods. To confirm this independence, you could perform a chi-square goodness-of-fit test comparing observed frequencies to expected frequencies under the null hypothesis of independence between gender and test outcome. If the calculated p-value from the test exceeds your chosen significance level, you can conclude that there is sufficient evidence to reject the null hypothesis, indicating that gender and passing the test are dependent.

The correct answer is a set S is T-finite if every nonempty subset X of the power set P(S) has a maximal element u, meaning there is no other element v in X such that u is a subset of v.

On the other hand, if a set S does not satisfy the condition of being T-finite, it is referred to as T-infinite.The notation "T" in this context represents Tarski, referring to the mathematician Alfred Tarski, who contributed to the study of set theory and lattice theory.In set theory, Tarski introduced the concept of T-finiteness to define a notion of finiteness for sets based on their subsets. A set S is considered T-finite if every nonempty subset X of the power set P(S) (the set of all subsets of S) has a maximal element u. This means that for any subset X, there exists an element u in X such that there is no other element v in X that properly contains u.

For example, consider the set S = {1, 2, 3}. The power set P(S) includes subsets such as {}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}. According to Tarski's T-finiteness, for any nonempty subset X from P(S), there should exist a maximal element. In this case, each nonempty subset has a maximal element because every subset has a largest element that cannot be properly contained within any other subset.

On the other hand, if a set S does not satisfy the condition of T-finiteness, it is considered T-infinite. This means that there exists a nonempty subset X of P(S) for which there is no maximal element. In other words, there are subsets within the power set that do not have a largest element.

Tarski's T-finiteness provides an alternative way to define finiteness based on the behavior of subsets within a set. It is a concept used in the study of set theory and has connections to other areas of mathematics, such as lattice theory.

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To calculate the interest earned in each case, we can use the formula for compound interest:

A = P(1 + r/n)^(nt) - P

where:

A is the final amount (including principal and interest)

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given:

P = $21,000

r = 4% = 0.04

(a) If interest is compounded semiannually, n = 2 (twice a year), and t = 2 years. Plugging these values into the formula, we get:

A = 21000(1 + 0.04/2)^(2*2) - 21000

Calculate A to find the final amount and subtract the principal to get the interest earned.

(b) If interest is compounded quarterly, n = 4 (four times a year), and t = 2 years. Plugging these values into the formula, we get:

A = 21000(1 + 0.04/4)^(4*2) - 21000

Calculate A to find the final amount and subtract the principal to get the interest earned.

(c) To find the difference in interest earned when compounded quarterly, subtract the interest earned in part (a) from the interest earned in part (b).

By calculating the interest earned and the difference in interest, we can determine the specific amounts.

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We can express the number 98 in exponential form as 10 raised to the power of 2. This means that by multiplying the base, which is 10, by itself twice, we obtain the value of 98.

To express 98 in exponential form, we need to determine the base and exponent that can represent the number 98.

Exponential form represents a number as a base raised to an exponent. Let's find the base and exponent for 98:

We can express 98 as 10 raised to a certain power since the base 10 is commonly used in exponential notation.

To find the exponent, we need to determine how many times we can divide 98 by 10 until we reach 1. This will give us the power to which 10 needs to be raised.

98 ÷ 10 = 9.8

Since 9.8 is still greater than 1, we need to continue dividing by 10.

9.8 ÷ 10 = 0.98

Now, we have reached a value less than 1, so we stop dividing.

From these calculations, we can see that 98 can be expressed as 10 raised to the power of 1 plus the number of times we divided by 10:

98 =[tex]10^1[/tex] + 2

Therefore, we can write 98 in exponential form as:

98 = [tex]10^3[/tex]

In summary, 98 can be expressed in exponential form as 10^2. The base is 10, and the exponent is 2, indicating that we multiply 10 by itself two times to obtain 98.

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In 5 years from 2020, the two colleges will have the same enrollment and At that time, both colleges will have an enrollment of 21,200 students.

To determine when the two colleges will have the same enrollment, we can set up an equation based on the given information.

Let's assume "x" represents the number of years from 2020.

For College A, the projected enrollment can be expressed as:

Enrollment_A = 18,700 + 500x

For College B, the projected enrollment can be expressed as:

Enrollment_B = 26,200 - 1000x

To find when the two enrollments will be equal, we set Enrollment_A equal to Enrollment_B and solve for "x":

18,700 + 500x = 26,200 - 1000x

Combining like terms:

1500x = 7,500

Dividing both sides by 1500:

x = 5

Therefore, in 5 years from 2020, the two colleges will have the same enrollment.

To find the enrollment at that time, we substitute "x = 5" into either of the enrollment equations. Let's use Enrollment_A:

Enrollment_A = 18,700 + 500(5)

Enrollment_A = 18,700 + 2500

Enrollment_A = 21,200

At that time, both colleges will have an enrollment of 21,200 students.

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The set intersection X' ∩ Y' is expressed as; {e, 24}

We are given the sets as;

U = {a, b, c, d, e, f, 19, 20, 21, 22, 23, 24}

X = {a, b, c, 20, 21, 22}

Y = {b, d, f, 19, 21, 23}

Union of the sets A and B , denoted A ∪ B , is the defined as the set of all objects that are a member of A , or B , or both. The union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4} . Intersection of the sets A and B , denoted A ∩ B , is the set of all objects that are members of both A and B

Thus:

X' ∩ Y' is as follows;

X' = {d, e, 19, 23, 24}

Y' = {a, c, e, 20, 22, 24}

X' ∩ Y' = {e, 24}

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The option that is not true about polynomial functions is:

Option D. The deg (f ^ 3) = 3m​

For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:

Option A: deg(f + g) = max(m, n)

This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.

Option B: deg(f * g) <= m + n

This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.

Option C: If g is a factor of f, then deg(f) <= m

This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.

D. The deg(f ^ 3) = 3m

This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.

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The value of x is 1.08

A logarithm is the power to which a number must be raised in order to get some other number.

For example log 100 = 2 . This means that the base 10 logarithm of 100 is 2 and we can also say that 10² = 100

Similarly, solving the equation;

log3(x+25) -log(x - 1) = 3

using law of logarithm

log( 3(x+25)/x-1) = log 1000

therefore;

3x + 75= 1000x -1000

1075 = 1000x -3x

1075= 997x

x = 1075/997

x = 1.08

Therefore the value of x is 1.08

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Answer: D

Step-by-step explanation:

To solve this question, we need to change the equation to standard form.

[tex]x^2=-13x-4[/tex]                              [add both sides by 13x and 4]

[tex]x^2+13x+4=0[/tex]                           [use quadratic equation]

[tex]\frac{-13+\sqrt{13^2-4(4)}}{2} , \frac{-13-\sqrt{13^2-4(4)}}{2}[/tex]       [simplify]

[tex]\frac{-13+\sqrt{13^2-16}}{2} , \frac{-13-\sqrt{13^2-16}}{2}[/tex]

[tex]\frac{-13+\sqrt{169-16}}{2} , \frac{-13-\sqrt{169-16}}{2}[/tex]

[tex]\frac{-13+\sqrt{153}}{2} , \frac{-13-\sqrt{153}}{2}[/tex]

Therefore, the answer is D.