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3 years ago

If a+ b + c= -6 and x +y = 5, what is 9y +9x - 10a-10c -10b ?

Mathematics

2 answers:

Lisa [10]3 years ago

5 0

Answer:

9y +9x - 10a-10c -10b = 105

Step-by-step explanation:

Given

a+b+c = -6 and x+y = 5

We have to find 9y +9x - 10a-10c -10b

Rearranging the terms

9x+9y-10a-10b-10c

Simplifying will give us:

= 9 (x+y) - 10(a+b+c)

Putting the values of x+y and a+b+c

= 9(5) -10(-6)

=45+60

=105

Therefore,

9y +9x - 10a-10c -10b = 105 ..

Gre4nikov [31]3 years ago

3 0

Answer:

9y + 9x - 10a - 10c - 10b = 105

Step-by-step explanation:

It is given that, a+ b + c = - 6 and x + y = 5

<u>To find the value of given expression</u>

Let the expression be 9y +9x - 10a-10c -10b

9y +9x - 10a -10c -10b = 9(y + x) - 10(a + c + b )

= 9(x + y) - 10(a + b + c)

= 9 * (5) - 10 * (-6)

= 45 + 60

= 105

Therefore 9y + 9x - 10a - 10c - 10b = 105

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3 years ago

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The height of the sail on a boat is 7 feet less than 3 times the length of its base. If the The area of the sail is 68 square fe

Dima020 [189]

Step-by-step explanation:

It is given that,

The height of the sail on a boat is 7 feet less than 3 times the length of its base.

Let the length of the base is x.

ATQ,

Height = (3x-7)

Area of the sail is 68 square feet.

Formula for area is given by :

$A=lb\\\\68=x(3x-7)\\\\3x^2-7x=68\\\\3x^2-7x-68=0$

x = 8 feet and x = -3.73 feet

So, length is 8 feet

Height is 3(8)-7 = 17 feet.

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2 years ago

PLEASE HELP!! will give brainliest

frutty [35]

A:
Table 1:
f(x) = 8x
X= cups so
ounces =
8* # of cups
Table 2:
f(x) =16x
X= pints so
ounces =
16*# of pints
Table 3:
f(x)= 32x
X= quarts so
ounces=
32*# of quarts
Note: another way instead of f(x)=kx is y=kx
B:
Depending on the slope we can easily find which is the steepest slope by easily comparing the slopes and seeing which is greater.
T1: 8
T2: 16
T3: 32
So, looking at our slopes, table 3 has the greatest slope because it has the greater slope out of the other two.
C:
The phrase, "rate of change" is another way to say the slope. To list again,
T1: 8
T2: 16
T3: 32
The table with the smallest slope would be table 1 since it is less than the other two tables.

I hope that helps, if you need any more assistance or you have any questions, please feel free to ask!!

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3 years ago

Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yi

aalyn [17]

Answer:

a) $t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

$df=12+15-2=25$

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) $(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309$

$(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691$

Step-by-step explanation:

Notation and hypothesis

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}}+\frac{1}{n_2}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

Part a

The system of hypothesis on this case are:

Null hypothesis: $\mu_2 \leq \mu_1$

Alternative hypothesis: $\mu_2 > \mu_1$

Or equivalently:

Null hypothesis: $\mu_2 - \mu_1 \leq 0$

Alternative hypothesis: $\mu_2 -\mu_1 > 0$

Our notation on this case :

$n_1 =12$ represent the sample size for group 1

$n_2 =15$ represent the sample size for group 2

$\bar X_1 =85$ represent the sample mean for the group 1

$\bar X_2 =91$ represent the sample mean for the group 2

$s_1=3$ represent the sample standard deviation for group 1

$s_2=2$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$\S^2_p =\frac{(12-1)(3)^2 +(15 -1)(2)^2}{12 +15 -2}=6.2$

And the deviation would be just the square root of the variance:

$S_p=2.490$

Calculate the statistic

And now we can calculate the statistic:

$t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

Now we can calculate the degrees of freedom given by:

$df=12+15-2=25$

Calculate the p value

And now we can calculate the p value using the altenative hypothesis:

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

Conclusion

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

Part b

For this case the confidence interval is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} S_p \sqrt{\frac{1}{n_1} +\frac{1}{n_2}}$

For the 99% of confidence we have $\alpha=1-0.99 = 0.01$ and $\alpha/2 =0.005$ and the critical value with 25 degrees of freedom on the t distribution is $t_{\alpha/2}= 2.79$