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ExtremeBDS [4]
3 years ago
14

How do you solve 7a- 17=4a+1

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
5 0

Answer:

a = 6

Explanation:

7a − 17 = 4a + 1

Subtract 4a from both sides

7a − 17 − 4a = 4a + 1 − 4a

3a − 17 = 1

Add 17 to both sides

3a − 17 + 17 = 1 + 17

3a = 18

Divide both sides by 3

3a / 3 = 18 / 3

a = 6

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What would be the maximum value for f(x) = −5x2 + 9
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Well, looking at the expression, it has a -5 on the leading term, that means is not just a quadratic, but is a parabolic graph and because the coefficient of the leading term is negative, is upside-down, or opening downwards.

because it opens downwards, it looks like an arc, comes from the bottom up up up gets to a "maximum" or U-turn (vertex), then goes back down down down.  So, where's the vertex anyway?

\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lccclll}
f(x) = &{{ -5}}x^2&{{ +0}}x&{{ +9}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad 
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad  {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
\\\\\\
\left( -\cfrac{0}{2(-5)}~~,~~9-\cfrac{0}{4(-5)} \right)\implies (0~~,~~9)

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3 years ago
How Would You multiply This To get The Volume
weqwewe [10]
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7 0
3 years ago
Read 2 more answers
A gift shop sells 140 wind chimes per month at $90 each. The owners estimate that for each $5 increase in price, they will sell
guapka [62]

Answer: $95

Step-by-step explanation:

Te new price will be 90 + 5x, if the price increases "x" times

The number of wind chimes sold per month will become 140 - 7x

\begin{aligned}&\text {Revenue, } \mathrm{R}(\mathrm{x})=(90+5 \mathrm{x})(140-7 \mathrm{x}) \\&R^{\prime}(x)=5(140-7 x)-7(90+5 x) \\&R^{\prime}(x)=700-35 x-630-35 x \\&R^{\prime}(x)=70-70 x=0 \\&70 x=70 \\&x=1\end{aligned}

Therefore, if the price becomes (90 + 5(1)) = $95 per wind chime, then the revenue will be maximum

6 0
3 years ago
Lyle shot three times as many baskets as cliff, while kyle shot 12 more baskets than cliff. if lyle and kyle shot the same numbe
olga_2 [115]
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5 0
4 years ago
Each item produced by a certain manufacturer is independently of acceptable quality with probability 0.95. Approximate the proba
Diano4ka-milaya [45]

Answer:

The probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.

Step-by-step explanation:

Let <em>X</em> = number of items with unacceptable quality.

The probability of an item being unacceptable is, P (X) = <em>p</em> = 0.05.

The sample of items selected is of size, <em>n</em> = 150.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 150 and <em>p</em> = 0.05.

According to the Central limit theorem, if a sample of large size (<em>n</em> > 30) is selected from an unknown population then the sampling distribution of sample mean can be approximated by the Normal distribution.

The mean of this sampling distribution is: \mu_{\hat p}= p=0.05

The standard deviation of this sampling distribution is: \sigma_{\hat p}=\sqrt{\frac{ p(1-p)}{n}}=\sqrt{\frac{0.05(1-.0.05)}{150} }=0.0178

If 10 of the 150 items produced are unacceptable then the probability of this event is:

\hat p=\frac{10}{150}=0.067

Compute the value of P(\hat p\leq 0.067) as follows:

P(\hat p\leq 0.067)=P(\frac{\hat p-\mu_{p}}{\sigma_{p}} \leq\frac{0.067-0.05}{0.0178})=P(Z\leq 0.96)=0.8315

*Use a <em>z</em>-table for the probability.

Thus, the probability that at most 10 of the next 150 items produced are unacceptable is 0.8315.

5 0
3 years ago
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