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3 years ago

What number is equivalent to 23/8

Mathematics

1 answer:

Bumek [7]3 years ago

5 0

23/8 = 46/16 = 92/32

Answer: 46/16, 92/32

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Find the perimeter of the triangle defined by the coordinates (7, 1), (-6, 1), and (10, 6). (Round to nearest tenth)

matrenka [14]

Answer:

$35.6\ units$

Step-by-step explanation:

we know that

The perimeter of triangle is equal to the sum of the length of the three sides

Let

$A(7, 1), B(-6, 1), C(10, 6)$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

$A(7, 1), B(-6, 1)$

substitute in the formula

$d=\sqrt{(1-1)^{2}+(-6-7)^{2}}$

$d=\sqrt{(0)^{2}+(-13)^{2}}$

$dAB=13\ units$

Find the distance BC

$B(-6, 1), C(10, 6)$

substitute in the formula

$d=\sqrt{(6-1)^{2}+(10+6)^{2}}$

$d=\sqrt{(5)^{2}+(16)^{2}}$

$dBC=16.8\ units$

Find the distance AC

$A(7, 1), C(10, 6)$

substitute in the formula

$d=\sqrt{(6-1)^{2}+(10-7)^{2}}$

$d=\sqrt{(5)^{2}+(3)^{2}}$

$dAC=5.8\ units$

Find the perimeter

$P=dAB+dBC+dAC$

$P=13+16.8+5.8=35.6\ units$

4 0

2 years ago

point b on the ground is 5 cm from point E at the entrance to Ollie's house. He is 1.8 m tall and is standing at Point D, below

enot [183]

Point B on the ground is 5 cm from point E at the entrance to Ollie's house.

Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

The complete question is as follows:

Ollie has installed security lights on the side of his house that is activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.

The objective of this information is:

To find angle CAB and;
Find the distance Ollie is from the entrance to his house when he first activates the sensor.

The diagrammatic representation of the information given is shown in the image attached below.

Using cosine rule to determine angle CAB, we have:

$\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}= \dfrac{CA}{Sin \hat {ABC}}}$

Here:

$\mathbf{\dfrac{AB}{Sin \hat {ACB}} = \dfrac{BC}{Sin \hat {CAB}}}$

$\mathbf{\dfrac{4.5}{Sin \hat {15^0}} = \dfrac{6}{Sin \hat {CAB}}}$

$\mathbf{Sin \hat {CAB} = \dfrac{Sin 15 \times 6}{4.5}}$

$\mathbf{Sin \hat {CAB} = \dfrac{0.2588 \times 6}{4.5}}$

$\mathbf{Sin \hat {CAB} = 0.3451}$

∠CAB = Sin⁻¹ (0.3451)

∠CAB = 20.19⁰

From the diagram attached;

assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;

Then, we can say:

∠CBD = ∠GBF

∠GBF = (CAB + ACB)

(because the exterior angles of a Δ is the sum of the two interior angles.

∠GBF = 15° + 20.19°

∠GBF = 35.19°

Using the trigonometric function for the tangent of an angle.

$\mathbf{Tan \theta = \dfrac{GF}{BF}}$

$\mathbf{Tan \ 35.19 = \dfrac{1.8 \ m }{BF}}$

$\mathbf{BF = \dfrac{1.8 \ m }{Tan \ 35.19}}$

$\mathbf{BF = \dfrac{1.8 \ m }{0.7052}}$

BF = 2.55 m

Finally, the distance of Ollie║FE║ from the entrance of his bouse is:

= 5 - 2.55 m

= 2.45 m

Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.

Learn more about exterior angles here:

8 0

2 years ago

Can someone please help me with the question in the image. i will mark as brainliest if correct

ExtremeBDS [4]

Answer: 15

Step-by-step explanation:

x:9 = 25:15

x = 25:15*9 = 15

5 0

2 years ago

find the probability exactly 3 successes in 6 trials of a binomial experiment in which the probability of success if 50%. round

Dennis_Churaev [7]

Answer:

Hence, the probability of exactly 3 successes in 6 trials of a binomial experiment round to the nearest tenth of a percent is:

31.2%

Step-by-step explanation:

The probability of getting exactly k successes in n trials is given by the probability mass function:

$P(k;n,p)=P(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}$

Where p denotes the probability of success.

We are given that the probability of success if 50%.

i.e. $p=\dfrac{1}{2}$

also form the question we have:

k=3 and n=6.

Hence the probability of exactly 3 successes in 6 trials is:

$P(3;6,\dfrac{1}{2})=P(X=3)={\binom {6}{3}}(\dfrac{1}{2})^{3}(1-\dfrac{1}{2})^{6-3}$

$P(3;6,\dfrac{1}{2})=P(X=3)={\binom {6}{3}}(\dfrac{1}{2})^{3}(\dfrac{1}{2})^{3}$

$P(3;6,\dfrac{1}{2})=P(X=3)={\binom {6}{3}}(\dfrac{1}{2})^{6$

$\binom {6}{3}=20$

Hence,

$P(3;6,\dfrac{1}{2})=P(X=3)=20\times (\dfrac{1}{2})^6=\dfrac{5}{16$

In percentage the probability will be:

$\dfrac{5}{16}\times 100=31.25\%=31.2\%$

8 0

3 years ago

Which expression represents the composition [g o f](x) for the functions below? f(x) = 3x – 2 g(x) = 1 + 2x 6x – 1 6x + 3 6x + 1

azamat

Answer:

It’s D

Step-by-step explanation:

I did it on EDG

3 0

2 years ago

Read 2 more answers