Which histogram represents the data?

In order to raise money for holiday gifts for your family, you are planning on starting a dog walking and car wash business. You

kramer

Answer:

Part 1) see the explanation

Part 2) see the explanation

Part 3) see the explanation

Part 4) The graph in the attached figure

Part 5) see the explanation

Step-by-step explanation:

Part 1) Assign a variable to represent the number of hours that you will spend dog walking in November. Write an expression to represent the amount of money you need to earn while dog walking

Let

x ----> the number of hours spent dog walking in November

so

$12x=600$

solve for x

$x=50\ hours$

Part 2) Assign a variable to represent the number of hours that you will spend washing cars in November. Write an expression to represent the amount of money you need to earn while washing cars.

Let

y ----> the number of hours spent washing cars in November

so

$18y=600$

solve for y

$y=33.33\ hours$

Part 3) Write an algebraic model using inequalities that represents the total amount of money earned by dog walking and washing cars during the month of November.

Let

x ----> the number of hours spent dog walking in November

y ----> the number of hours spent washing cars in November

we know that

You need to earn at least $600 during the month of November

The word "at least" means " greater than or equal to"

so

$12x+18y\geq 600$

Part 4) Graph the algebraic model in the first quadrant only.

we have

$12x+18y\geq 600$

using a graphing tool

The solution is the shaded area

see the attached figure N 1

Part 5) Use the graph and algebraic model to answer the following:

a) Why does the graph exist only in the first quadrant?

Because the number of hours cannot be a negative number

b) Are you able to earn exactly $600? Use the solutions of the system to find possible combinations of outcomes that equal exactly $600. Where do all of the combinations occur in the graph?

Yes its possible to earn exactly $600. All the combinations of outcomes that equal exactly $600 occur in the solid line 12x+18y=600

c) Is it possible to earn more than $600? Use the solutions of the system to find possible combinations of outcomes that are greater than $600. Where do all of the combinations occur in the graph?

Yes its possible to earn more than $600. All the combinations of outcomes that are greater than $600 occur above the solid line 12x+18y=600

d) If you work for 10 hours walking dogs and 10 hours washing cars, will you have earned enough money for the holiday gifts?

we have the ordered pair (10,10)

substitute in the inequality

$12(10)+18(10)\geq 600$

$300\geq 600$ ----> is not true

therefore

You must not have earned enough money for holiday gifts.

e) Where does 10 hours walking dogs and 10 hours washing cars fall on the graph? Is this location representative of the solution to the algebraic model?

The ordered pair (10,10) fall below the solid line 12x+18y=600

This location is not representative of the solution to the algebraic model, because the solution of the model is above the solid line

f) How would the algebraic model be different if you needed to earn more than $600? Adjust your algebraic model to show that you must earn more than $600. Would the graph of the model be different from the original? Would you include the line in the solution?

we know that

$12x+18y=600$ ----> represent a linear equation that show the possible combinations of outcomes that equal exactly $600.

The solution is the set of ordered pairs belong to the solid line

$12x+18y\geq 600$ ----> represent a inequality that show the possible combinations of outcomes that are greater than or equal to $600. The solid line is included in this solution

The solution is the shaded area above the solid line (The solid line is included in the shaded area)

g) In complete sentences, explain the difference between a solid line and a dashed line when graphing an inequality. When graphing the two algebraic models, how did you determine which type of line to use?

we know that

When the inequality is of the form ≥ or ≤ we have a solid line

When the inequality is of the form > or < we have a dashed line

The difference is that in the solid line the line is included in the solution and in the dashed line the line is not include in the solution

h) How did you determine which part of the graph of the inequality to shade? What does the shaded area tell you? What does the area that is not shaded tell you?

we know that

when you have an inequality of the form

y> ax+b or y≥ax+b

The shaded area is above the line

when you have an inequality of the form

y< ax+b or y≤ax+b

The shaded area is below the line

The shaded area is the solution set of the inequality (ordered pairs that satisfy the inequality)

The area that is not shaded are the ordered pairs that are not solutions of the inequality (ordered pairs that satisfy the inequality)

5 0

3 years ago

Andre wrote the inequality to plan his time. Describe what 3x + 10 ≤ 30 represent in this inequality.

Neporo4naja [7]

Step-by-step explanation:

7 0

3 years ago

Find the y-intercept of the following equation. Simplify your answer.

jarptica [38.1K]

The y intercept is going to be 10x

4 0

3 years ago

Read 2 more answers

7] A recent poll discovered that only 24.5% of Americans are getting the recommended amount of exercise per week. Briscoe Middle

Evgesh-ka [11]

Answer:

your TRASH NOOB LOSER

Step-by-step explanation:

so todya eat hesde

In a handful of other worlds”particularly conservative Catholic ones”the essay did quite well. But those were the worlds that hardly needed it. For people of that persuasion, the omnipresent assault on Pius XII drives them toward the worst possibilities for their communities: a dread that rampant anti-Catholicism is shortly to unleash itself upon themhunger to flee to small fellowships of the saved and away from the corruption of the public square, an embracing of a self-image as victims, and a belief that a dark cloud rests over the sum of modern times. “Even a Jewish writer”and a rabbi, too”sees the slander for what it is,” they say. And thereby they confirm, for those whom the essay only angered, that David Dalin let himself be used as a Jew to advance a sectarian Catholic agenda (mine, presumably, although my friends have had the courtesy not to say that to my face). And so the whole coil curls up around itself once more, and we get no forwarder. Perhaps a book that collected the best reviews would help. However large it personally looms, the part played by David and me was small. The attempt to sift through the endless stream of books about Pius XII in recent years was actually carried out by indefatigable reviewers in dozens of magazines and journals, responding to the texts one by one.The controversy also motivated additional research, and new material now seems to arrive every week. As far as I can tell, all this recent information tells in favor of Pius XII. A recently discovered 1923 letter to the Vatican from Eugenio Pacelli, then nuncio to Germany, for instance, denounces Hitler’s putsch and warns against his anti-Semitism and anti-Catholicism. A document from April 1933, just months after Hitler obtained power, reveals how Pacelli (then secretary of state) ordered the new German nuncio, Cesare Orsenigo, to protest Nazi actions. Meanwhile, newly examined diplomatic documents show that in 1937 Cardinal Pacelli warned A. W. Klieforth, the American consul to Berlin, that Hitler was “an untrustworthy scoundrel and fundamentally wicked person,” to quote Klieforth, who also wrote that Pacelli “did not believe Hitler capable of moderation, and . . . fully supported the German bishops in their anti-Nazi stand.” This was matched with the discovery of Pacelli’s anti-Nazi report, written the following year for President Roosevelt and filed with Ambassador Joseph Kennedy, which declared that the Church regarded compromise with the Third Reich as “out of the question.”Archives from American espionage agencies have recently confirmed Pius XII’s active involvement in plots to overthrow Hitler. A pair of newly found letters, written in 1940 on the letterhead of the Vatican’s Secretariat of State, give Pius XII’s orders that financial assistance be sent to Campagna for the explicit purpose of assisting interned Jews suffering from Mussolini’s racial policies. And the Israeli government has finally released Adolf Eichmann’s diaries, portions of which confirm the Vatican’s obstruction of the Nazis’ roundup of Rome’s Jews. There’s more, a regular flow of new material. Intercepts of Nazi communications released from the United States’ National Archives include such passages as “Vatican has apparently for a long time been assisting many Jews to escape,” in a Nazi dispatch from Rome to Berlin on October 26, 1943, ten days after the Germany’s Roman roundup. New oral testimony from such Catholic rescuers as Monsignor John Patrick Carroll-Abbing, Sister Mathilda Spielmann, Father Giacomo Martegani, and Don Aldo Brunacci insists that Pius XII gave them explicit orders and direct assistance to help persecuted Jews in Italy. The posthumous publication this year of Harold Tittmann’s memoir, Inside the Vatican of Pius XII , is particularly interesting, for in it the American diplomat reveals, for the first time, that Pius XII’s wartime conduct drew upon advice from the German resistance.

7 0

3 years ago

Find the derivative.

krek1111 [17]

Answer:

$\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Expanding/Factoring

Calculus

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \frac{\sqrt{x}}{e^x}$

Step 2: Differentiate

Derivative Rule [Quotient Rule]: $\displaystyle f'(x) = \frac{(\sqrt{x})'e^x - \sqrt{x}(e^x)'}{(e^x)^2}$
Basic Power Rule: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}(e^x)'}{(e^x)^2}$
Exponential Differentiation: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{(e^x)^2}$
Simplify: $\displaystyle f'(x) = \frac{\frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x}{e^{2x}}$
Rewrite: $\displaystyle f'(x) = \bigg( \frac{e^x}{2\sqrt{x}} - \sqrt{x}e^x \bigg) e^{-2x}$
Factor: $\displaystyle f'(x) = \bigg( \frac{1}{2\sqrt{x}} - \sqrt{x} \bigg)e^\big{-x}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

7 0

3 years ago