which graph of y= 3/4x-3​

Answer:

Step 3

Step-by-step explanation:

The building and the person on it are illustrations of elevation and depression

The height of the building is 76.9 feet

To calculate the building height, we make use of the attached illustration

Considering the triangle DCB in the figure, we have:

tan(B) = DC/BD

Substitute known values

tan(28.3) = DC/(DA + 100)

Cross multiply

(DA + 100) * tan(28.3) = DC

Divide both sides by tan(28.3)

DA + 100 = DC/tan(28.3)

Subtract 100 from both sides

DA = -100 + DC/tan(28.3)

Considering the triangle DCA in the figure, we have:

tan(A) = DC/DA

Substitute known values

tan(33.5) = DC/DA

Make DA the subject

DA = DC/tan(33.5)

Substitute DA = DC/tan(33.5) in DA = -100 + DC/tan(28.3)

DC/tan(33.5) = -100 + DC/tan(28.3)

Evaluate the tangent ratios

0.56DC = -100 + 1.86DC

Collect like terms

-1.86DC + 0.56DC = -100

Evaluate

-1.3DC = -100

Divide both sides by -1.3

DC = 76.9 feet

Hence, the height of the building is 76.9 feet

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Answer:

the area of the rectangle is 35.25 square meters.

Step-by-step explanation:

To find the area of a rectangle, we multiply the length by the width.

First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:

4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4

7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6

Now we can multiply the length and width:

Area = (18/4) * (47/6)

Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)

Area = (9 * 47) / (2 * 6)

Area = 423/12

Area = 35.25

Therefore, the area of the rectangle is 35.25 square meters.

Answer:

Step-by-step explanation:

Using the formula for calculating the compound interest

A = P(1+r)^t

P is the principal = $3500

r is the rate = 4% = 0.04

T is the time = 8 years

Substitute

A = 3500(1+0.04)^8

A = 3500(1.04)^8

A = 3500(1.3686)

A = 4,789.99

Hence the resulting balance is $4,789.99

Answer:80 students

Step-by-step explanation:

80% of 100 is 80. :)

Answer:

a)

b)-4

Step-by-step explanation:

a) f(13) = 13-7=

b) f(3)= 3-7= -4

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

For n=10

For n=100

Answer: 2.70481

The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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Answer:

It will take 12 years using simple interest

Step-by-step explanation:

2,500 x 1.7% = 42.5

42.5 x 12 + 510

2500 +510 +3010

The exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

An exponential function is represented as:

\(y = b^x\)

The base is 3.

So, we have:

\(y = 3^x\)

It is stretched vertically by 2/3.

So, we have:

\(y = \frac23(3)^x\)

When reflected over the y-axis, we have:

\(y = \frac23(3)^{-x}\)

An asymptote of y = 2, makes the function becomes

\(y = \frac23(3)^{-x} + 2\)

Lastly, it passes through the point (0, 3.5).

So, we have:

\(y = \frac23(3)^{-x+h} + 2\)

This gives

\(3.5 = \frac23(3)^{-0+h} + 2\)

\(3.5 = \frac23(3)^{h} + 2\)

Subtract 2 from both sides

\(1.5 = \frac23(3)^{h}\)

Multiply by 3/2

\(2.25 = (3)^{h}\)

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in \(y = \frac23(3)^{-x+h} + 2\)

\(y = \frac23(3)^{-x+0.74} + 2\)

Hence, the exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

210 cm²

Step-by-step explanation:

Area of the surface having dimensions 6 cm × 11 cm

\(A_1\) = 11 × 6 = 66 cm²

Area of the surface having dimensions 3 cm × 6 cm

\(A_2\) = 3 × 6 = 18 cm²

Area of the surface having dimensions 7 cm × 6 cm

\(A_3\) = 7 × 6 = 42 cm²

Area of the surface having dimensions 5 cm × 6 cm

\(A_4\) = 5 × 6 = 30 cm²

Area of the trapezoidal surface on the top = \(\frac{1}{2}(b_1+b_2)h\)

\(A_5\) = \(\frac{1}{2}(11+7)3\)

    = 27 cm²

Area of the trapezoidal base \(A_6\) = Area of the surface on the top = 27 cm²

Total surface area = \(A_1+A_2+A_3+A_4+A_5+A_6=66+18+42+30+27 + 27\)

                                               = 210 cm²

Therefore, total surface area of the trapezoidal prism = 210 cm²

After the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

Before the 2:30 stop, the bus let off 15 people and let on 9 people. The total change in the number of people at that stop is -15 (let off) + 9 (let on) = -6.

Therefore, there are 6 fewer people on the bus after the 2:30 stop compared to before that stop.

Ten minutes later, the bus makes another stop and lets off 4 more people. This additional change needs to be considered.

Since the previous calculation only accounted for the changes up until the 2:30 stop, we need to adjust the total change by including the subsequent stop.

Adding the change of -4 (let off) to the previous total change of -6, we get a new total change of -10.

Therefore, after the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

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Answer:

C

Step-by-step explanation:

I suppose you have learned that for the sides of a triangle to work, it has to be a + b > c, the 4 is the a, the 8 is the b, the 12 is the c.

So: 4 + 8 > 12; however this is not true, they are equal so the triangle wont be a triangle, it would be lines that never connect.

Answer:

The answer is:-

(2x+1)(4-7)

Answer: 52

Step-by-step explanation:

    To find the range of a data set, we subtract the smallest value from the largest value.

54 - 2 = 52

Step-by-step explanation:

Just re-arrange it as so:

-3x + 12 y = 24      add 3x to both sides of the equation

12 y =  3x + 24       divide both sides by 12

   y =  1/4 x + 2    Done.

Answer:

The null and alternative hypothesis for this study are:

\(H_0: \mu=18500\\\\H_a:\mu< 18500\)

The null hypothesis is rejected (P-value=0.004).

There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

Then, the null and alternative hypothesis are:

\(H_0: \mu=18500\\\\H_a:\mu< 18500\)

The significance level is 0.05.

The sample has a size n=150.

The sample mean is M=18200.

The standard deviation of the population is known and has a value of σ=1400.

We can calculate the standard error as:

\(\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1400}{\sqrt{150}}=114.31\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{M-\mu}{\sigma_M}=\dfrac{18200-18500}{114.31}=\dfrac{-300}{114.31}=-2.624\)

This test is a left-tailed test, so the P-value for this test is calculated as:

\(P-value=P(z<-2.624)=0.004\)

As the P-value (0.004) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is  less than $18,500 per term.

The equation representing the total cost is 15x + 750 and the total cost of restringing 32 lacrosse sticks would be $1230.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Let, The number of lacrosse sticks be 'x' and the total cost is C(x).

Therefore, The equation representing the context is,

C(x) = 25x + 750.

The total cost of restringing 32 lacrosse sticks would be,

C(32) = 15×32 + 750.

C(32) = 480 + 750.

C(32) = 1230.

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Answer:

1 hour and 50 minutes

Step-by-step explanation:

Time Connie takes to clean the house: 210 minutes

Time takes for both of them at the same time: 100 minutes.
210 - 100 = 110 minutes

Therefore, Alvaro takes one hour and 50 minutes to clean the house by himself.

Answer:Alvaro can clean the house alone in approximately 3.89 hours.

Step-by-step explanation:

If Connie can clean her house in 3.5 hours, then her rate of work is 1/3.5 of the house per hour. Together, Connie and Alvaro can clean the house in 1 hour and 40 minutes, or 1.67 hours.

To find how long it would take Alvaro to clean the house alone, we can use the formula:

combined rate of work = sum of individual rates of work

So, (1/3.5 + 1/a) * 5/3 = 1, where "a" is the time it takes Alvaro to clean the house alone.

Simplifying the equation, we get 1/a = 9/35, which means that Alvaro can clean the house alone in approximately 3.89 hours (or 3 hours and 53 minutes).

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Given Dr. Sparrow's design, his study is best able to overcome the issue of causality, as well as the issue of some potential third variables.

By using a multivariate design, Dr. Sparrow is able to examine the relationships between multiple variables simultaneously, which can help to identify the potential influence of each variable on the outcome of interest (marital satisfaction in this case). This can help to establish a causal link between the variables if one is present, as it allows for the examination of multiple variables at the same time, rather than just two variables as in a simple bivariate design.

Additionally, by controlling for other potential confounding variables, Dr. Sparrow is able to account for the potential influence of these variables on the relationship between income and marital satisfaction, which helps to establish a more robust understanding of the potential causal link between these two variables.

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Answer:

The standard error of the proportion is 0.0367.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the standard error is \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question:

\(p = 0.16, n = 100\)

So

\(s = \sqrt{\frac{0.16*0.84}{100}} = 0.0367\)

The standard error of the proportion is 0.0367.