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amm1812
3 years ago
8

Used books cost $2.25 each. Which expression represents the total number of books that can be purchased for $10?

Mathematics
2 answers:
azamat3 years ago
6 0
The equation is this,10=2.25x then you solve for "x".

Ber [7]3 years ago
5 0

you can buy 5 books and have a $1 left over I think Hope this a helps! :D


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311, 305,299,...Find the 32nd term.
adell [148]

Answer:

503

Step-by-step explanation:

4 0
2 years ago
What is 1675 divided by 25 with remainder?
attashe74 [19]

Answer:

975

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Se tiene un lote baldío de forma triangular bardeado. La barda de enfrente tiene una medida de 4 m,las otras dos bardas no es po
dybincka [34]

Answer:

a) La medida de la barda que está enfrente del ángulo 64° es de, aproximadamente, 6.4292m. b) El triángulo en cuestión <em>no es un triángulo rectángulo</em>, es decir, ninguno de sus ángulos internos es <em>recto </em>(90 grados sexagesimales). En estos casos, no se puede aplicar el Teorema de Pitágoras o la simple utilización de las razones trigonométricas; se aplican, en cambio, leyes para la resolución de triángulos oblicuángulos (o triángulos no rectángulos).

Step-by-step explanation:

Este problema no se puede resolver "aplicando sólo las razones trigonométricas o el teorema de Pitágoras" porque es sólo aplicable a <em>triángulos rectos</em>, es decir, uno de los ángulos del triángulo es recto o igual a <em>90</em> grados sexagesimales. Los dos restantes triángulos suman 90 grados sexagesimales, o se dice, son <em>complementarios</em>.

La resolución de triángulos que no son rectos (conocida en algunos textos como solución de problemas de triángulos oblicuángulos) pueden resolverse usando, la <em>ley de los senos (o teorema del seno)</em>, <em>ley de los cosenos</em> y <em>la ley de las tangentes</em>. El caso propuesto en la pregunta se ajusta a la <em>ley de los senos</em>:

\\ \frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)} = \frac{c}{\sin(\gamma)}

Es decir, la razón entre el lado de un triángulo y el seno del ángulo que tiene frente a él es igual para todos los lados y ángulos del triángulo.

El triángulo de la pregunta no tiene un ángulo recto

La suma de los ángulos internos de un triángulo es de 180 grados sexagesimales:

\\ \alpha + \beta + \gamma = 180^{\circ}

En la pregunta tenemos que la suma de los dos ángulos propuestos es:

\\ 34^{\circ} + 64^{\circ} + \gamma = 180^{\circ}

\\ 98^{\circ} + \gamma = 180^{\circ}

Restando 98 grados sexagesimales a cada lado de la igualdad:

\\ 98^{\circ} - 98^{\circ} + \gamma = 180^{\circ} - 98^{\circ}

\\ 0 + \gamma = 180^{\circ} - 98^{\circ}

\\ \gamma = 82^{\circ}

Con lo que se deduce que no hay ningún ángulo recto en el triángulo propuesto y no se podría usar el Teorema de Pitágoras o simples razones trigonométricas para resolverlo.

Resolución del lado del triángulo

De la pregunta tenemos:

  • La barda de enfrente tiene una medida de 4m. El ángulo que está enfrente de esta barda (barda frontal) es de 34°.
  • No se sabe el valor del lado que está enfrente del ángulo de 64°, pero se puede calcular usando la Ley de los senos.

Digamos que:

\\ a = 4m, \alpha = 34^{\circ}

\\ b = x, \beta = 64^{\circ}

Entonces, aplicando la <em>Ley de los senos</em>:

\\ \frac{a}{\sin(\alpha)} = \frac{b}{\sin(\beta)}

Multiplicando a cada lado de la igualdad por \\ \sin(\beta)

\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = \frac{b}{\sin(\beta)}*\sin(\beta)

\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b*\frac{\sin(\beta)}{\sin(\beta)}

\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b*1

\\ \frac{a}{\sin(\alpha)}*\sin(\beta) = b

Sustituyendo cada valor en la expresión anterior:

\\ b = \frac{a}{\sin(\alpha)}*\sin(\beta)

\\ b = \frac{4m}{\sin(34^{\circ})}*\sin(64^{\circ})

\\ b = 4m*\frac{0.8988}{0.5592}

\\ b = 6.4292m

En palabras, la medida de la barda que está enfrente del ángulo 64° es de, aproximadamente, 6.4292m.

El lado <em>c</em> puede obtenerse de manera similar considerando que \\ \gamma = 82^{\circ}.

6 0
2 years ago
House of Mohammed sells packaged lunches, where their finance department has established a
blagie [28]

The revenue function is a quadratic equation and the graph of the function

has the shape of a parabola that is concave downwards.

The correct responses are;

  • (a) <u>R = -x² + 82·x</u>
  • (b) <u>$1,645</u>
  • (c) The graph of <em>R</em> has a maximum because the <u>leading coefficient </u>of the quadratic function for <em>R</em> is negative.
  • (d)  <u>R = -1·(x - 41)² + 1,681</u>
  • (e) <u>41</u>
  • (f) <u>$1,681</u>

Reasons:

The given function that gives the weekly revenue is; R = x·(82 - x)

Where;

R = The revenue in dollars

x = The number of lunches

(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;

R = x·(82 - x) = 82·x - x²

Which gives;

  • <u>R = -x² + 82·x </u>

<em>Where, the constant term, c = 0</em>

(b) When 35 launches are sold, we have;

x = 35

Which by plugging in the value of x = 35, gives;

R = 35 × (82 - 35) = 1,645

  • The revenue when 35 lunches are sold, <em>R</em> = <u>$1,645</u>

(c) The given function for <em>R</em> is R = x·(82 - x) = -x² + 82·x

Given that the leading coefficient is negative, the shape of graph of the

function <em>R</em> is concave downward, and therefore, the graph has only a

maximum point.

(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;

(h, k) = The vertex of the equation

a = The leading coefficient

The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;

R = x·(82 - x) = -x² + 82·x

At the vertex, of the equation; f(x) = a·x² + b·x + c,  we have;

\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}

Therefore, for the revenue function, the x-value of the vertex, is; \displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}

The revenue at the vertex is; R_{max} = 41×(82 - 41) = 1,681

Which gives;

(h, k) = (41, 1,681)

a = -1 (The coefficient of x² in -x² + 82·x)

  • The revenue equation in the form, a·(x - h)² + k is; <u>R = -1·(x - 41)² + 1,681</u>

(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41

Therefore;

  • The number of lunches that must be sold for the maximum revenue to be achieved is<u> 41 lunches</u>

(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681

  • <u>The maximum revenue of the company is $1,681</u>

Learn more about the quadratic function here:

brainly.com/question/2814100

6 0
2 years ago
If we reject the null hypothesis, does this mean that we have proved it to be false beyond all doubt? Explain your answer.a. Yes
crimeas [40]

Answer:

Yes, the test was conducted with a risk of a type I error.

Step-by-step explanation:

If we reject the null hypothesis, does this mean that we have proved it to be false beyond all doubt? Explain your answer.

Yes, for a null hypothesis to be rejected, it has being proven beyond all doubt that the null hypothesis will not work. the normal distribution has being used for the probability calculation.

if the null hypothesis is rejected and the alternative hypothesis is accepted, a type I error as occur.

In general terms:

‘a hypothesis has been rejected when it should have been accepted’. When this occurs, it is called a type I error.

5 0
2 years ago
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