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Firdavs [7]
3 years ago
10

Translate the given phrase into an algebraic expression and simplify if possible: the product of -13 and the difference of c

Mathematics
1 answer:
Musya8 [376]3 years ago
7 0

Answer:  -13c+13d

Step-by-step explanation:

For this exercise it is important to remember the following:

1. By definition, the "Product" is the result of a multiplication.

2. The "Difference" is defined as the result of a subtraction.

3. The Distributive property states that:

a(b+c)=ab+ac\\\\a(b-c)=ab-ac

Keeping the above on mind, you know that:

"The difference of c and d" can be represented with the following expression:

c-d

Therefore, "The product of -13 and the difference of c and d" can be represented with this expression:

-13(c-d)

Finally, you must apply the Distributive property in order to simplify the expression. You get:

=-13c+13d

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If a graph is said to be EVEN, what can you say about its symmetry?
stealth61 [152]

Answer:

A function is said to be an even function if its graph is symmetric with respect to the y-axis. For example, the function f graphed below is an even function. Verify this for yourself by dragging the point on the x-axis from right to left. Notice that the graph remains unchanged after a reflection across the y-axis!

4 0
3 years ago
Is there statistically significant evidence that the districts with smaller classes have higher average test​ scores? The t​-sta
Musya8 [376]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  95% confidence interval is [670.03  , 673.97 ]

The  test statistics is t = 7.7

The  p-value  is    p-value  =  0

The <u>p-value</u>  suggests that the null hypothesis is<u> rejected </u>with a high degree of confidence. Hence  <u>there is</u> statistically significant evidence that the districts with smaller classes have higher average test score  

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  408

    The sample mean is  \= y  =  672.0

   The standard deviation is  s = 20.3

Given that the confidence level  is 95% then the level of significance is  

   \alpha = (100 -95 )\% = 0.05

From the normal distribution table  the critical value of \frac{\alpha }{2} = \frac{0.05 }{2} is  

    Z_{\frac{\alpha }{2} } =  1.96

Generally  the margin of error is mathematically represented as  

     E  =  Z_{\frac{\alpha }{2} } *  \frac{s}{\sqrt{n} }

=>   E  =  1.96 *  \frac{20.3}{\sqrt{408} }

=>     E  =  1.970

Generally the 95% confidence interval is mathematically represented as

       \= y -E  < \mu <  \= y + E

=>     672.0 -1.970  < \mu < 672.0 +1.970

=>     670.03  < \mu < 673.97

=>     [670.03  , 673.97 ]

From the question we are told that

   Class size                                  small                                      large

  Avg.score(\= y)         \= y_1 = 683.7   \= y_2 =  676.0

   S_y                          S_{y_1} =20.2    S_{y_2} = 18.6

   sample size                             n_1 = 229        n_2 =  184

The  null hypothesis is  H_o :  \mu_1 - \mu_2 = 0

The alternative hypothesis is  H_a :  \mu_1 - \mu_2 > 0

Generally the standard error for the difference in mean is mathematically represented as

       SE =  \sqrt{\frac{S_{y_1}^2 }{n_1} +\frac{S_{y_2}^2 }{n_2}   }

=>     SE =  \sqrt{20.2^2 }{229} +\frac{18.6^2 }{184_2}   }

=>     SE =  1.913

Generally the test statistics is mathematically represented as

      t = \frac{\= y _1 - \= y_2 }{SE}

=>    t = \frac{683.7 - 676.0 }{1.913}

=>   t = 7.7

Generally the p-value is mathematically represented as

    p-value  =  P(t >  7.7 )

From the  z-table

        P(t >  7.7 ) =  0

So

   p-value  =  0

From the values we obtained and calculated we can see that p-value  <  \alpha

This mean that

The p-value  suggests that the null hypothesis is rejected with a high degree of confidence. Hence  there is statistically significant evidence that the districts with smaller classes have higher average test score  

4 0
3 years ago
Una heladeria dispone de 20 frutas distintas para elaborar sus malteadas. Si los clientes pueden elegir tres sabores para mezcla
Dahasolnce [82]

Answer:

Existen 6840 permitaciones de malteadas de tres sabores distintos que la heladería puede ofrecer.

Step-by-step explanation:

En este caso, el cliente que adquiere una malteada de tres sabores distintos sigue el siguiente procedimiento:

1) El primer sabor sale de cualquiera de las 20 frutas disponibles.

2) El segundo sabor es distinto al primer sabor, es decir, que sale de las 19 frutas restantes.

3) El tercer sabor es distinto al primer sabor y al segundo sabor, es decir, que sale de las 18 frutas restantes.

Puesto que existe una doble conjunción y que puede importar el orden según la preferencia del cliente, se habla matemáticamente de una permutación, definida como:

n\mathbb{P}k = \frac{n!}{(n-k)!} (1)

Donde:

n - Número de sabores disponibles, adimensional.

k - Número de sabores escogidos, adimensional.

Si tenemos que n = 20 y k = 3, entonces la cantidad de malteadas de tres sabores distintos es:

n\mathbb{P}k = \frac{20!}{(20-3)!}

n\mathbb{P}k = \frac{20!}{17!}

n\mathbb{P}k = 20\cdot 19\cdot 18

n\mathbb{P}k = 6840

Existen 6840 permitaciones de malteadas de tres sabores distintos que la heladería puede ofrecer.

5 0
3 years ago
I need help quickly please have clear explanation and answer written in brainly
Andrei [34K]

Answer:

ii

Step-by-step explanation:

i

4 0
2 years ago
Read 2 more answers
What is the slope of a line perpendicular to the line whose equation is x - y = 6. Fully simplify your answer.​
Marat540 [252]

Answer:

-1

Step-by-step explanation:

first put the equation in slop int form:

y= x-6

to find the slope of a line that is perpendicular take the negative reciprical of the slope

so the answer is

-x

3 0
2 years ago
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