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3 years ago

10

Find the area of the triangle below.

1 answer:

svp [43]3 years ago

5 0

Answer:

(5/6)x²

Step-by-step explanation:

The area of a triangle is given by the formula

A = (1/2)bh

Here, the base is 5/3x, and the height is x. So, the area is ...

A = (1/2)(5/3x)(x) = (5/6)x²

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Help please. I need this answer and you don’t have to explain it

wariber [46]

Answer:

y=-5x+22

Step-by-step explanation:

4 0

2 years ago

A research company desires to know the mean consumption of meat per week among people over age 40. A sample of 610 people over a

Papessa [141]

Answer: $(3.0,\ 3.2)$

Step-by-step explanation:

Confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$ (1)

, where $\overline{x}$ = Sample mean

$z_{\alpha/2}$ = Critical z-value

$\sigma$ = Population standard deviation.

n= Sample size.

As per given , we have

n= 610

$\sigma=1.1$

$\overline{x}=3.1$

Significance level for 85% confidence : $\alpha=1-0.85=0.15$

By z-table critical two tailed z-value : $z_{\alpha/2}=z_{0.075}=1.44$

Put all values in (1) , we get

$3.1\pm 1.44\dfrac{1.1}{\sqrt{610}}$

$3.1\pm 1.44\dfrac{1.1}{24.698}$

$3.1\pm 0.064$

$=(3.1-0.064,\ 3.1+0.064)=(3.036,\ 3.164)\approx(3.0,\ 3.2)$

Hence, the 85% confidence interval for the mean consumption of meat among people over age 40. = $(3.0,\ 3.2)$

5 0

3 years ago

The distance d in miles that can be covered by a rabbit in X hours is given in the equation y = 30 x The distance covered by a b

AveGali [126]

Answer:

Rabbit is faster than bear.

Step-by-step explanation:

Speed of rabbit or bear is determined by their rate of change of their distances with time.

The distance covered by rabbit in $x$ hours is given as:

$y=30x$

The above equation is of the form $y=mx$ , where, $m$ is the rate of change of $y$ with $x$ .

Therefore, the rate of change of rabbit's distance with time is 30 mi/h.

Now, from the graph, the slope is given as the rise over run.

Rise is 50 miles and run is 2 miles.

So, rate of change of bear's distance with time is, $m_b=\frac{50}{2}=25\ mi/h$

Now, 30 is greater than 25. So, rabbit is faster than bear.

6 0

3 years ago

Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference

Bezzdna [24]

Since $a_1,a_2,a_3,\cdots$ are in arithmetic progression,

$a_2 = a_1 + 2$

$a_3 = a_2 + 2 = a_1 + 2\cdot2$

$a_4 = a_3+2 = a_1+3\cdot2$

$\cdots \implies a_n = a_1 + 2(n-1)$

and since $b_1,b_2,b_3,\cdots$ are in geometric progression,

$b_2 = 2b_1$

$b_3=2b_2 = 2^2 b_1$

$b_4=2b_3=2^3b_1$

$\cdots\implies b_n=2^{n-1}b_1$

Recall that

$\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n$

$\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2$

It follows that

$a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)$

so the left side is

$2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n$

Also recall that

$\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}$

so that the right side is

$b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)$

Solve for $c$ .

$2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}$

Now, the numerator increases more slowly than the denominator, since

$\dfrac{d}{dn}(2n(n-1)) = 4n - 2$

$\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2$

and for $n\ge5$ ,

$2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2$

This means we only need to check if the claim is true for any $n\in\{1,2,3,4\}$ .

$n=1$ doesn't work, since that makes $c=0$ .

If $n=2$ , then

$c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0$

If $n=3$ , then

$c = \dfrac{12}{2^3 - 6 - 1} = 12$

If $n=4$ , then

$c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N$

There is only one value for which the claim is true, $c=12$ .

3 0

2 years ago

Find the difference <br> (6ab+4a-3) - (2ab-4)

Y_Kistochka [10]

This would be 8(ab) sooo yaaaa

3 0

3 years ago

Read 2 more answers