The enrollment of a community college last
year was 4500 students. It increased by 5%
this year. What is the enrollment this year at
the community college?

Answer:

option (4)

Step-by-step explanation:

y = - 2x +7 → (1)

y = 4x - 5 → (2)

substitute y = 4x - 5 into (1)

4x - 5 = - 2x + 7 ( add 2x to both sides )

6x - 5 = 7 ( add 5 to both sides )

6x = 12 ( divide both sides by 6 )

x = 2

substitute x = 2 into either of the 2 equations and solve for y

substituting into (2)

y = 4(2) - 5 = 8 - 5 = 3

solution is (2, 3 )

\(\red{\boxed{ \green{\sf Option \: 4: (2 \: , 3)}}}\)

\( \\ \)

\( \sf First, \: we \: have \: to \: understand \: that: \\ \sf If \: \red{y} = \orange{a} \: and \: \red{y} = \blue{b}, \: then \: \orange{a} = \blue{b}.\)

\( \\ \)

\(\sf Let \: \orange{-2x+7} \: be \: \orange{a} \: and \: \blue{4x-5 \\ } \: be \: \blue{b}.\)

\(\star \: \sf Solve \: the \: equation \: \orange{a} = \blue{b}. \: \star\)

\( \\ \)

\( \sf \orange{a} = \blue{b} \\ \Longleftrightarrow \sf \orange{ - 2x + 7} = \blue{4x - 5} \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Subtract \: 4x \: from \: both \: sides. \diamond \\ \\ \Longleftrightarrow \sf - 6x + 7 = - 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Subtract \: 7 \: from \: both \: sides. \diamond \\ \\ \Longleftrightarrow \sf - 6x = - 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \diamond \: \sf Divide \: both \: sides \: by \: -6. \: \diamond \\ \\ \Longleftrightarrow \sf x = \dfrac{ - 12}{ - 6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \Longleftrightarrow \boxed{\sf \purple{x = 2}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

\( \\ \)

\(\star \: \sf Remplace \: \purple{x} \: with \: \purple{2} \: in \: one \: of \: the \: given \: equations. \: \star\)

\( \\ \)

\( \sf \red{y }= - 2 \purple{x} + 7 \\ \implies \sf \red{y} = - 2 \purple{(2)} + 7 \: \: \: \: \: \: \\ \\ \implies \boxed{\sf \red{y= 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

\( \\ \)

Therefore, the point which is a solution to the system of equations is (2 , 3). This corresponds to option 4.

Answer:

x= 4, -7

Step-by-step explanation:

x^2+3x-28

x^2 multipled by -28 = -28

Which two numbers add up to 3 and multiply to -28?

-4 and 7

-4 + 7 = 3

-4 x 7 = -28

so

(x−4)(x+7)=0

4-4=0

-7+7=0

The value of x is -3 for the given equation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 4 *3 + 4*x = 0

Simplify the equation using PEMDAS

=> 4*3 + 4*x = 0

=> 12 + 4x = 0

=> 4x = -12

=> x = -3

Therefore, the simplified value of the Given equation is x = -3.

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Answer:

I think it's D

Step-by-step explanation:

Answer:  I think its D

Step-by-step explanation:

Rigid transformation moves a shape without changing the size of the shape.

See attachment for the diagram that shows the position of D'

Answer:

\( \frac{y - 18}{x - 1} = \frac{23 - 18}{1.5 - 1} = \frac{5}{0.5} = 10 \\ y - 18 = 10(x - 1) = 10x - 10 \\ y = 10x + 18 - 10 = 10x + 8 \\ \boxed{f(x) = 10x + 8}\)

hope this helps.

Answer: r>13

Step-by-step explanation:

The sign is less than so r +8 has to be 20 or less.

Recall that the domain of a function is the set of numbers to which the function is defined. That is, if you replace the value of the independant variable (normally represented as x), then the function will give another number as a result.

In this case, we are given the function 400+13x. Since x is the independant variable, to determine the domain we must think on what possible values the variable x can take. Since in this case x represents the number of products made, it is impossible that it takes negative values, since in real life you can't produce negative amounts of products.

So far, we know that x should be greater or equal to zero. Once again, in this context, it doesn't make sense that, for example, x=7.8, since this would mean that 7.8 number of products were made. Since x represents the number of products made, it can only take values as x=0,x=1, x=2, x=3 and so on.

This set receives the name of whole numbers.

According to the table the independent variable remains constant for change in the dependent variable.

There are dependent and independent variables in statistical modelling, experimental sciences, and mathematical modelling.

Dependent variables get their name from the fact that during an experiment, their values are assessed under the assumption or obligation that they rely on the dependent variable as a result of a rule or law. Independent variables are ones that are not seen as being reliant on any other factors in the context of the experiment in question.

In this respect, frequent independent variables include things like space, density, mass, rate of fluid flow, and a particular value among some observed phenomena of interest. Every time, the variability of the dependent variable—also known as the regressor in a statistical context—is being examined. any element in an experiment .

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The probability that the time between consecutive customers is less than 15 seconds is approximately 0.29 or 29.02% (rounded to two decimal places).

To calculate the probability that the time between consecutive customers is less than 15 seconds using the Exponential distribution with a mean of 0.73 minutes, first convert 15 seconds into minutes.

15 seconds = 15/60 = 0.25 minutes

Next, use the Exponential distribution formula:

P(X ≤ x) = 1 - e^(-λx)

Here, λ is the rate parameter and is equal to 1/mean, which in this case is:

λ = 1/0.73 ≈ 1.37

Now, plug in the values into the formula:

P(X ≤ 0.25) = 1 - e^(-1.37 × 0.25) ≈ 1 - e^(-0.3425)

P(X ≤ 0.25) ≈ 1 - 0.7098 ≈ 0.2902

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Answer:

Table M does not represent a linear function, however table N does.

Step-by-step explanation:

In table M, y does not have a constant rate of change in relation to x

(in table M, the x value of -3 is repeated and the y value is not constant with the x value of -3)

In table N, the y value has a constant rate of change of 6 corresponding to each x value.

Answer:

y=(-1/2)(x)-8

Step-by-step explanation:

Since they give the slope and y intercept, you can literally plug it into the equation:

y=mx+b

where m is slope and b is y interecept.

Therefore, we get

y=(-1/2)(x)-8

The translation is as shown in the figure in option B

Translation transformation is a type of geometric transformation that moves every point of a figure the same distance and direction. This transformation does not change the size, shape, or orientation of the figure, but only its position in space.

The transformation required ahs the rule defined as

Applying the rule arrives the image in option B

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The lines which are perpendicular to 3x + 6y = 5 are; Choice B and C; y = 2x - 1 and y - 4 = 2(x + 7).

From the task content, it follows that the given equation is; 3x+ 6y = 5.

By rewriting the equation in slope intercept form; it follows that; y = (-1/2)x +5/6. Hence, the slope of the line is; -1/2.

From line geometry, it follows that two lines are perpendicular if; m1 × m2 = -1.

Therefore, a line perpendicular to the given line will have a slope of 2.

From the given option, the lines which are perpendicular to 3x + 6y = 5 upon conversion to the Slope-intercept form are; Choice B and C.

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Answer:

Step-by-step explanation:

20.29 :)

Answer:

45 degrees/360 degrees=1/8

So the area would be 1/8 *100=100/8=25/2

Step-by-step explanation:

Answer:

El precio de las manzanas = 27 pesos

El precio de las naranjas = 54 pesos

El precio de las bananas = 19 pesos

Step-by-step explanation:

Los parámetros dados son;

El monto total gastado = 100 pesos

Sea el precio de las naranjas = x

Sea el precio de las manzanas = y

Sea el precio de los plátanos = z

La cantidad pagada por las naranjas = 2 · y = x

La cantidad pagada por los plátanos = y - 8 = z

Por lo tanto, tenemos;

La cantidad total gastada = La cantidad pagada por las naranjas + La cantidad pagada por las bananas + La cantidad pagada por las manzanas

∴ El monto total gastado = 100 pesos = 2 · y + y - 8 + y

100 = 4 · años - 8

4 · y = 100 + 8 = 108

y = 108/4 = 27

y = 27

De

z = y - 8 tenemos;

z = 27 - 8 = 19

De 2 · y = x, tenemos;

2 × 27 = x

x = 54

Por lo tanto;

El precio de las naranjas = 54 pesos

El precio de las manzanas = 27 pesos

El precio de los plátanos = 19 pesos.

Answer:

\(y=\dfrac{1}{8}x^2\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}\)

Given that the vertex of the parabola is (0, 0):

Substitute the values of h and k into the formula:

\(y=a(x-0)^2+0\)

\(y=ax^2\)

Given that the parabola passes through the point (12, 18), substitute this into the equation and solve for a:

\(18=a(12)^2\)

\(18=144a\)

\(a=\dfrac{18}{144}\)

\(a=\dfrac{1}{8}\)

Therefore, the equation of the parabola in vertex form is:

\(y=\dfrac{1}{8}x^2\)

Answer:

1m=100cm

Step-by-step explanation:

do it correctly, sooo ya

Therefore, we conclude that there is evidence to support the claim that the return rate is less than 20%. Hence, option D03 Hp02 OLM is the correct answer.

According to the given problem, an internet survey was e-mailed to 6960 subjects randomly selected from an online group involved with cars. The return rate of the survey was 1305.Use the Pusle method and use the romal distribution as an approximation to the binomial distribution to test the claim that the return rate is less than 20% at 0.01 significance level. We are to set the null and alternative hypotheses. The null hypothesis is the claim that we are testing against. The alternative hypothesis is what we conclude when we reject the null hypothesis.We can state the null hypothesis as;H0: p >= 0.20The alternative hypothesis is;Ha: p < 0.20Where p is the population proportion.Now, we calculate the test statistic using the Pusle method, which is given by;P = (1305/6960) = 0.18804q = 1 - p = 0.81196n = 6960The standard deviation can be calculated using the formula;σ = sqrt (n * p * q)σ = sqrt (6960 * 0.18804 * 0.81196)σ = 23.43Now, we calculate the z-score using the formula;z = (x - μ) / σz = (0.20 - 0.18804) / 0.00349z = 3.43Finally, we can calculate the p-value using the z-score table or calculator.The critical value of z at the 0.01 significance level is 2.33. Since our calculated z-score (3.43) is greater than the critical value (2.33), we reject the null hypothesis.Therefore, we conclude that there is evidence to support the claim that the return rate is less than 20%. Hence, option D03 Hp02 OLM is the correct answer.

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The given statement "The median of a quantitative data set is always one of the individual data values" is false.

When a given data set is arranged in ascending order the observation which at the between of the data is the median of that data set. It is a value in the set whose left and right both have the same number of observations.

The given statement is not true, this is because the median is the mid-value of any data set.

Hence, the given statement "The median of a quantitative data set is always one of the individual data values" is false.

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The significance level of 0.01 indicates that we want to use a 1% level of significance to evaluate the evidence against the null hypothesis.

The null and alternative hypotheses for testing the claim that the majority of college students' cell phone bills are paid by their parents can be stated as follows:

Null hypothesis (H0): The majority of college students' cell phone bills are not paid by their parents.

Alternative hypothesis (Ha): The majority of college students' cell phone bills are paid by their parents.

In this scenario, the null hypothesis assumes that the proportion of college students whose parents pay their cell phone bills is less than 50% (not a majority), while the alternative hypothesis suggests that the proportion is greater than or equal to 50% (a majority). The significance level of 0.01 indicates that we want to use a 1% level of significance to evaluate the evidence against the null hypothesis.

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Answer:

the third one

Step-by-step explanation:

-5 is the least out of all of them and 6 is the greatest so then you can put the numbers in between

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

Option A is the correct answer.

For an experiment involving 2 Levels of factor A and 3 levels of factor B with a sample of n = 5 in each treatment condition, we need to calculate the value for df within treatments.

The formula to calculate df within treatments is given by, df within treatments = (A - 1) (B - 1) (n - 1)Where, A = Levels of factor AB = Levels of factor Bn = Sample size= 2 levels of factor A= 3 levels of factor B= 5 in each treatment conditionNow, df within treatments = (A - 1) (B - 1) (n - 1)= (2 - 1) (3 - 1) (5 - 1)= 1 × 2 × 4= 8Hence, the value of df within treatments is 8.

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The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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Answer:  -8

The ordered pair solution is ( -8, 8 )

=====================================================

To get that answer, we plug in y = 8 and solve for x.

6x+2y = -32

6x+2(8) = -32

6x+16 = -32

6x = -32-16

6x = -48

x = -48/6

x = -8

So that's how we end up with ( -8, 8 ). This point is on the line 6x+2y = -32.

"y" will represent the total cost per month

"x" will represent the number of movies watched in one month

There are two streaming plans:

Plan A

Has a monthly fee of $16 plus $2 per movie watched.

→ So if he watches no movies in a month, he will pay $16 and for each movie watched he will pay an extra $2

You can represent the monthly cost of plan A as follows:

Plan B

Has a monthly fee of $12 plus $3 for every movie watched.

The monthly cost of the plan can be expressed as follows:

For both equations the y-interceot represents the monthly fee of the plan and the slope of the line is the cost per movie.

To determine the number of movies (x) that would make both plans cost the same for one month using a graph, you have to draw both lines and determine the point where they intercept. The x-coordinate of said point will be the number of movies that make both plans cost the same.

To draw the lines you have to determine at least two points of the line.

The easiest point will be the y-intercept, for the second point, choose any value of x, replace it in the formula and calculate the corresponding value of y. Then plot both points and draw the line.

For plan A

y-intercept, x=0

The coordinates are (0,16)

Second point, for example, for x= 2 movies

The coordinates are (2,20)

For plan B

y-intercept, x=0

The coordinates are (0,12)

Second point, for example, for x=3

The coordinates are (3,21)

The red line represents the cost with respect to the number of movies for plan A

The purple line represents the cost with respect to the number of movies for plan B

Where both lines intercept indicates the point when both plans cost the same. Said point is (4,24), which means that when you watch x=4 movies both plans will cost $24 that month.