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Snezhnost [94]
2 years ago
11

Rebecca went swimming yesterday. After a while she had covered one fifth of her intended distance. After swimming six more lengt

hs of the pool, she had covered one quarter of her intended distance. How many lengths of the pool did she intend to complete?
A. 40
B. 72
C. 80
D. 100
E. 120
Mathematics
1 answer:
alukav5142 [94]2 years ago
4 0

Answer:

Option E.

Step-by-step explanation:

Let the intended length of Rebecca's swimming is = x units

and we assume the length of the pool = l units

Now it is given in the question that " She covers one fifth of her intended distance "

That means distance covered = \frac{x}{5}

" After swimming six more lengths of the pool she had covered one quarter of her intended distance"

So \frac{x}{5}+6(l)=\frac{x}{4}

6l=\frac{x}{4}-\frac{x}{5}

6l=\frac{x}{20}

x = 20×(6l)

x = 120l

Therefore, Rebecca has to complete 120 lengths of the pool.

Option E is the answer.

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Answer: Last option.

Step-by-step explanation:

Observe the base of the pyramid, which is a regular hexagon. You can see that there is a right triangle.

The area of the triangle can be calculated with this formula:

A_t=\frac{bh}{2}

Where "b" is the base and "h" is the height.

You can say that the apothem is the height of the right triangle, then, you need to find the base applying the Pythagorean Theorem:

(2x)^2=(x\sqrt{3})^2+b^2\\\\b=\sqrt{(2x)^2-(x\sqrt{3})^2} \\\\b=\sqrt{4x^2-3x^2}\\\\b=\sqrt{x^2}\\\\b=x

Then, the area of the triangle is:

 A_t=\frac{x(x\sqrt{3})}{2}=\frac{x^2\sqrt{3})}{2}

Since the base of the pyramid is a regular hexagon, then you can multiply by 12 the area of the right triangle calculated above, in order to find the area of the hexagon. Then you get:

A_h=12(\frac{x^2\sqrt{3})}{2})=6x^2\sqrt{3}\ units^2

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2 years ago
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The hypotenuse of a 45°-45°-90° triangle measures 10 StartRoot 5 EndRoot in. A right triangle is shown. The hypotenuse has a len
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Answer:

5\sqrt{10}\ units

5 StartRoot 10 EndRoot

Step-by-step explanation:

we know that

The legs of a 45°-45°-90° triangle are congruent

Let

x ---->  the length of one leg of the triangle

Applying the Pythagorean Theorem

c^2=a^2+b^2

where

c is the hypotenuse

a and b are the legs

we have

c=10\sqrt{5}\ units

a=b=x\ units

substitute

(10\sqrt{5})^2=x^2+x^2

500=2x^2\\x^2=250\\x=\sqrt{250}\ units

Simplify

x=5\sqrt{10}\ units

5 StartRoot 10 EndRoot

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2 years ago
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fgiga [73]
Let's start first by writing down the given:
σ = 100
sample mean = 450
sample size = 25

These information, plus the fact that we know that the population is approximately normally distributed, would tell us that we can use the normal distribution curve in analyzing the problem.

A confidence interval of the mean is just a range statistically estimated to contain the population mean. For a 90% confidence interval, we would look at the Z-table and see where 90% of the data falls. We'll notice that it will fall within 1.645 standard deviations of the mean.

Next, we look for the standard error of the mean. This will have a formula
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The standard error would just therefore be equal to
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Lastly, we just get the product of the standard error and 1.645 and add it to 450 for the maximum value and subtract it to 450 for the minimum value.
450-20(1.645)=417.1
450+20(1.645)=482.9

ANSWER: 417.1<μ<482.9

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2 years ago
Compare the area of the bases. If a base has a greater area, it will take up more space on the shelf. Base area of Box 1: 3x2 Ba
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Answer:

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Step-by-step explanation:

A graph shows that 3x^2 > (4x^2 -x) only between x=0 and x=1. Thus, Box 2 has a larger base area for all other values of x.

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If AD and BD are bisectors of CAB and CBA respectively. Find the sum of angles x and y.
olchik [2.2K]
The picture in the attached figure

step 1
we know that
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Therefore,
x = ∠CAB/2 -----> equation 1
y = ∠CBA/2 -----> equation 2

step 2
In triangle ABC,
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∠CAB + ∠CBA + 110° = 180°
∠CAB + ∠CBA = 180° - 110°
∠CAB + ∠CBA = 70° ------> divide by 2 both sides
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