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2 years ago

The equation of a graph is 4x - 3y = 5. What is the x-intercept?

2 answers:

6 0

4x - 3y = 0

The x-intercept is the point on the graph where it crosses the x-axis.
But everywhere on the x-axis, y=0.
So, at the intercept ...

4x - 3(0) = 5

4x = 5

Divide each side by 4 : x = 5/4 or 1.25

user100 [1]2 years ago

4 0

X intercept is where y=0
so make y=0
4x-0=5
x=5/4

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A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 9% vinegar, and the second brand co

kobusy [5.1K]

So, the first brand has 9% vinegar, and say we use "x" amount of it, then, the amount of vinegar in "x" is 9% of x, or (9/100) * x, 0.09x.

the second brand has 14% of vinegar, and if we use say "y" amount of it, then the amount of vinegar in "y" is really just 14% of "y" or, (14/100) * y, 0.14y.

$\bf \begin{array}{lccclll}
&\stackrel{mL}{amount}&\stackrel{\%}{concentration}&\stackrel{amount}{concentration}\\
&------&------&------\\
\textit{first brand}&x&0.09&0.09x\\
\textit{second brand}&y&0.14&0.14y\\
------&------&------&------\\
mixture&230&0.13&29.9
\end{array}$

so, whatever "x" and "y" are, we know that x + y = 230.

and we also know that their concentration amounts will also add up, 0.09x + 0.14y = 29.9.

$\bf \begin{cases}
x+y=230\implies \boxed{y}=230-x\\
0.09x+0.14y=29.9\\
----------\\
0.09x+0.14\left(\boxed{230-x} \right)=29.9
\end{cases}
\\\\\\
0.09x+32.2-0.14x=29.9\implies -0.05x=-2.3\implies x=\cfrac{-2.3}{-0.05}
\\\\\\
x=46$

how many milliliters will it be for the second brand? well, y = 230 - x.

3 0

2 years ago

Most dermatologists recommend using sunscreens that have a Sun Protection Factor (SPF) of at least 30. One of the authors wanted

Basile [38]

Answer: We are 95% confident that the mean SPF level of sunscreen used by all Cal Poly students is between 29.0813 and 40.0187.

Step-by-step explanation:

Given : Significance level : $\alpha: 1-0.95=0.05$

Sample size : n= 52 , which is a large sample (n>30), so we use z-test.

By using z-value table,

Critical value: $z_{\alpha/2}=1.96$

Sample mean : $\overline{x}= 34.55$

Standard deviation : $\sigma= 20.12$

The confidence interval for population means is given by :-

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

i.e. $34.55\pm(1.96)\dfrac{ 20.12}{\sqrt{52}}$

$=34.55\pm5.46867829455\\\\\approx34.55\pm5.4687\\\\=(34.55-5.4687, 34.55+5.4687)=(29.0813,\ 40.0187)$

Now, the 95% confidence interval for the ppopulation mean = . (29.0813, 40.0187)

Hence, We are 95% confident that the mean SPF level of sunscreen used by all Cal Poly students is between 29.0813 and 40.0187.

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2 years ago

Ships A and B are 1,425 feet apart and detect a submarine below them. The angle of depression from ship A to the submarine is 59

andreyandreev [35.5K]

Answer: The distance from ship B to the submarine is 1270.68 feet and the distance from ship A to the submarine is 1084.18 feet.

Step-by-step explanation:

Since we have given that

Distance between Ships A and B = 1425 feet

Angle of depression from ship A to the submarine =59°

Angle of depression from ship B to the submarine = 47°

As shown in the figure below:

Remaining angle will be

$180\textdegree-(47\textdegree+59\textdegree)\\\\=180\textdegree-106\textdegree\\\\=74\textdegree$

So, we will use "Sine formula ":

$\frac{\sin 74\textdegree}{1425}=\frac{\sin 59\textdegree}{B}\\\\B=\frac{1425\times \sin 59\textdegree}{\sin 74\textdegree}\\\\B=1270.68\ feet$

Similarly,

$\frac{\sin 74\textdegree}{1425}=\frac{\sin 47\textdegree}{A}\\\\A=\frac{1425\times \sin 47\textdegree}{\sin 74\textdegree}\\\\A=1084.18\ feet$

Hence, the distance from ship B to the submarine is 1270.68 feet and the distance from ship A to the submarine is 1084.18 feet.

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2 years ago

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Find the least common denominator (LCD) of 5/8<br> and 1/4

Effectus [21]

Answer:

Step-by-step explanation:

1. 1/4 × 2/2 = 2/8 (denominator is 8)

2. 5/8 × 1 = 5/8 (denominator is 8)

Therefore, the common denominator is 8.

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2 years ago

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BabaBlast [244]

Answer:

Step-by-step explanation:

Negative numbers are less than zero.

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2 years ago