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3 years ago

The isosceles triangle is a scale drawing of a flag.

Mathematics

1 answer:

Zolol [24]3 years ago

6 0

Answer:

Scale factor = $\frac{1}{2}$

Step-by-step explanation:

Perimeter of the actual flag = 22 in.

Perimeter of the scale drawing of the flag = 11 in.

Since, perimeter of a triangle = Sum of all three sides of the given triangle

Therefore, scale factor of the drawing

= $\frac{\text{Measure of the side of drawing}}{\text{Measure of the side of actual}}$ = $\frac{\text{Perimeter of drawing}}{\text{Perimeter of actual}}$

= $\frac{11}{22}$

= $\frac{1}{2}$

Therefore, scale factor of the drawing will be $\frac{1}{2}$ .

Each side of the scaled triangle will be half of the actual triangle.

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The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 7 feet, represented by a ve

xenn [34]

First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.

If we need the vertex to be at $x=4$ , the equation will contain a $(x-4)^2$ term.

If we start with $y=-(x-4)^2$ we have a parabola, concave down, with vertex at $x=4$ and a maximum of 0.

So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be $(4, 7)$

We have

$y = -(x-4)+7$

Now we only have to fix the fact that this parabola doesn't land at $(8,0)$ , because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want

$y = a(x-4)^2+7$

such that:

$a$
when we plug $x=8$ , we have $y=0$

Plugging these values gets us

$0 = a(8-4)^2+7 \iff 16a+7=0 \iff a = -\dfrac{7}{16}$

As you can see in the attached figure, the parabola we get satisfies all the requests.

3 0

3 years ago

David made a scale drawing of a mural he is going to paint. He used a scale of 1 cm=4ft. If the actual mural will be 16 feet lon

VikaD [51]

Answer:

4 cm

Step-by-step explanation:

we know that

The scale drawing is

$\frac{1}{4}\ \frac{cm}{ft}$

That means ----> 1 cm in the drawing represent 4 ft in the mural

To find out the dimensions in the drawing, multiply the actual dimension by the scale drawing factor

$(16\ ft)(\frac{1}{4}\ \frac{cm}{ft})=4\ cm$

3 0

3 years ago

Please Help.(picture below) 30 points

Sveta_85 [38]

Answer = B = 376 degrees - 3x

8 0

3 years ago

Read 2 more answers

In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older

Viktor [21]

Answer:

$p_v =P(t_{(63)}>2.5)=0.0075$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean age is significantly higher than 45 years at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=45$ represent the mean height for the sample

$s=16$ represent the sample standard deviation for the sample

$n=64$ sample size

$\mu_o =40$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean age is higher than 40 years, the system of hypothesis would be:

Null hypothesis: $\mu \leq 40$

Alternative hypothesis: $\mu > 40$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{45-40}{\frac{16}{\sqrt{64}}}=2.5$