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3 years ago

An artist designed a badge for a school club. Figure ABCD on the coordinate grid below shows the shape of the badge.

Mathematics

2 answers:

rjkz [21]3 years ago

6 0

Answer:

Option B is right.

Step-by-step explanation:

Given that an artist designed a badge for a school club.

ABCD is given in the picture.

AD = $\sqrt{(-7+8)^2 +(7-5)^2} \\=\sqrt{5}$

If JKLM is enlargement of ABCD, then scale factor would b the ratio of AD to JM

JM = $\sqrt{(5-2)^2+(4+2)^2} \\=\sqrt{45} \\3\sqrt{5}$

Scale factor = 3

AB = 3 hence JK = 9

DC = 1 and so ML = 3

ML is parallel to x axis with a distance of 3 units.

COordinates of L = (5+3, 4) = (8,4)

Option B is right

dedylja [7]3 years ago

3 0

Answer:

(8, 4)

Step-by-step explanation:

AD is enlarged to JM

AD² = 2² + 1² = 4 + 1 =5

AD = √5

then you plug in JM

JM² = 6² + 3² = 36 + 9 = 45

JM = √45 = 3 √5

so if 

JM=3 AD

then

ML= 3 DC

then you add

5+3=8

the coordinates for point L are (8, 4)

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Matt has 3 dark t-shirts and 6 white t-shirts. First, he will close his eyes to select a

valina [46]

Answer:

around 73-89%

Step-by-step explanation:

Hope this helps!

8 0

3 years ago

Due to a manufacturing error, two cans of regular soda were accidentally filled with diet soda and placed into a 18-pack. Suppos

crimeas [40]

Answer:

a) There is a 1.21% probability that both contain diet soda.

b) There is a 79.21% probability that both contain diet soda.

c) $P(X = 2)$ is unusual, $P(X = 0)$ is not unusual

d) There is a 19.58% probability that exactly one is diet and exactly one is regular.

Step-by-step explanation:

There are only two possible outcomes. Either the can has diet soda, or it hasn't. So we use the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

A number of sucesses $x$ is considered unusually low if $P(X \leq x) \leq 0.05$ and unusually high if $P(X \geq x) \geq 0.05$

In this problem, we have that:

Two cans are randomly chosen, so $n = 2$

Two out of 18 cans are filled with diet coke, so $\pi = \frac{2}{18} = 0.11$

a) Determine the probability that both contain diet soda. P(both diet soda)

That is P(X = 2).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 2) = C_{2,2}(0.11)^{2}(0.89)^{0} = 0.0121$

There is a 1.21% probability that both contain diet soda.

b)Determine the probability that both contain regular soda. P(both regular)

That is P(X = 0).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 0) = C_{2,0}(0.11)^{0}(0.89)^{2} = 0.7921$

There is a 79.21% probability that both contain diet soda.

c) Would this be unusual?

We have that $P(X = 2)$ is unusual, since $P(X \geq 2) = P(X = 2) = 0.0121 \leq 0.05$

For P(X = 0), it is not unusually high nor unusually low.

d) Determine the probability that exactly one is diet and exactly one is regular. P(one diet and one regular)

That is P(X = 1).

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{2,1}(0.11)^{1}(0.89)^{1} = 0.1958$

There is a 19.58% probability that exactly one is diet and exactly one is regular.

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=Factor%3A%20x%5E2-9" id="TexFormula1" title="Factor: x^2-9" alt="Factor: x^2-9" align="absmidd

Bezzdna [24]

Answer:

x²-9=x²-3²=(x+3)(x-3)

Step-by-step explanation:

use formula

a²-b²=(a+b)(a-b)

7 0

2 years ago

using the slope formula find the slope of the line through the points (0,0) and (3,9) use pencil and paper explain how you can u

maxonik [38]

Answer:

9/3

Step-by-step explanation:

you can't subtract from zero or you can't subtract a number from zero.

7 0

2 years ago

Read 2 more answers

Find the missing side length XI. round your answer to the nearest tenth.

lianna [129]

Answer: XI = 10.35 mm

Step-by-step explanation:

Considering the given triangle XIF, to determine XI, we would apply the sine rule. It is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

XI/SinF = XF/SinI = FI/SinX

The sum of the angles in a triangle is 180°. It means that

F + 63 + 52 = 180

F = 180 - (63 + 52)

F = 65°

Therefore

XI/Sin 65 = 9/Sin 52

Cross multiplying, it becomes

XISin52 = 9Sin65

0.788XI = 9 × 0.906

0.788XI = 8.154

XI = 8.154/0.788

XI = 10.35

7 0

3 years ago