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10 days ago

Jess will plant up to 27 acres on her farm with wheat and corn. More than 5 acres will be planted with wheat. Let w represent th

e number of acres of wheat and c represent the number of acres of corn. Identify two inequalities that represent this situation

Mathematics

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Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-

tester [12383]

To achieve a positive profit p(x)>0, we start with:
$-100 x^{2} +350x-150 \ \textgreater \ 0$

Next, we solve for x:
$-2 x^{2} +7x-3 \ \textgreater \ 0$

The parameters are:
a = -2
b = 7
c = -3

We will apply the quadratic formula:
$x_{1} = \frac{-b+ \sqrt{ b^{2}-4ac } }{2a} \\ \\ x_{2} = \frac{-b- \sqrt{ b^{2}-4ac } }{2a} \\ \\ x_{1} = \frac{-7+ \sqrt{ 49-24 } }{-4} = \frac{-7+5 }{-4} = \frac{-2 }{-4} = \frac{1}{2} \\ \\ x_{2} = \frac{-7- \sqrt{ 49-24 } }{-4} = \frac{-7-5 }{-4} = \frac{-12 }{-4} = 3$

This yields two results—one a fraction, the other a whole number. We focus on the whole number since the muffins sold must be a complete unit. Thus we conclude:
x>3

5 0

3 months ago

Read 2 more answers

Concur Technologies Inc is a large expense-management company located in Redmond Washington. The wall street Journal asked Concu

Zina [12379]

Answer:

Let's explore this step-by-step:

Greetings!

Here are the variables

X: daily cost of hotel rooms

Y: expenses for entertainment

Refer to the second attachment for the scatter plot.

The population regression equation can be expressed as E(Yi)= α + βXi

To find the y-intercept and the slope of the regression line, apply the following formulas:

a= Y[bar]-bX[bar] $b= \frac{sum XY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }$

In this scenario, n= 9; ∑X= 945; ∑X²= 103325; ∑Y= 1134; ∑Y²= 148804; ∑XY= 123307

Calculating X[bar]= ∑X/n= 945/9= 105

Calculating Y[bar]= ∑Y/n= 1134/9= 126

Thus, it follows that a= 126 - 1.03*105= 17.49 $b= \frac{123307-\frac{945*1134}{9} }{103325-\frac{(945)^2}{9} }= 1.03$

The regression equation is then given by ^Y= 17.49 + 1.03Xi

Slope interpretation: For each unit increase in the daily hotel rate, the expected average spending on entertainment rises by $1.03.

Given that the room rate in Chicago is $128 (X), we can predict the entertainment expenditure (Y) using the estimated regression line:

^Y= 17.49 + 1.03Xi= 17.49 + 1.03*128= 149.33

The anticipated spending on entertainment for Chicago is $149.33

I trust this will assist you!

6 0

2 months ago

Which function, g or h, is the inverse function for function ƒ? the function h because the graphs of ƒ and h are symmetrical abo

AnnZ [12381]

A function and its inverse, when graphed, exhibit symmetry about the line y = x. Without viewing your graphs, I can't specify if g or h is the inverse. Identify the function that reflects f over the diagonal line y = x, which passes through the origin.

4 0

3 months ago

For the angles α and β in the figures, find cos(α + β)?

Inessa [12570]

Let h units denote the hypotenuse of the smaller triangle. From the Pythagorean Theorem, we derive specific relationships involving the smaller triangle with dimensions

$\cos (\alpha)=\frac{4}{2\sqrt{5} }=\frac{2}{\sqrt{5} }$ along with the shorter leg of the second triangle denoted as s units. Furthermore, we apply the double angle property and substitute values to arrive at the final calculation.

3 0

2 months ago

Read 2 more answers

XY= 2x +1, YZ= 6x, and XZ=81

tester [12383]

x = 27 + 3 √ 129/ 4, 27 − 3 √ 129/ 4

Please note: the entire equation mentioned is divided by 4, not only the last term.

x approximates to 15.26836251, − 1.76836251

That concludes my response. I hope this is helpful. You will still need to work on finding y and z, which can be quite challenging:)

8 0

2 months ago