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3 years ago

Leah flips a coin, and then she spins a spinner with 3 equal sections colored red, green, and blue. What is the probability that

Mathematics

1 answer:

svet-max [94.6K]3 years ago

8 0

Answer: 33.3%

Step-by-step explanation:

Since there are two sides to a coin, the probability is 1/2. Since there are 3 sections on the spinner, the probability would be 2/3. Since "and" means multiply in this scenario, your answer would be 2/6, which simplifies to 1/3, which, in percentage form to the nearest percent, is 33.3%.

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Show work please \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

4 0

2 years ago

For each point, identify the axis or quadrant where the point is located. Drag and drop the choices into the boxes to complete t

Radda [10]

Answer:

we need help with the same thing

Step-by-step explanation:

6 0

2 years ago

Could 10.3cm 4.4cm and 8.3 cm be the side lengths of a triangle yes or no

evablogger [386]

Answer:

Step-by-step explanation:

As you probably know, triangles have 3 sides. The longest side is called the hypotenuse. In this case, the hypotenuse is 10.3. Now, you might or might not know the pythagorean theorem, which states that the a² + b² =c ². 

In this case, we can say that 4.4 is a and 8.3 is b. Now if we square 4.4 and add it to 8.3 squared, we get 88.25. However, if you square 10.3, you get 106.09. Thus, the values cannot be this way. So, your answer is no.

3 0

3 years ago

Which exponential function goes through the points (1, 8) and (4, 64)?

Mama L [17]

An exponential function can be expressed as:

y=ab^x we have two points so we can solve

64/8=(ab^4)/(ab^1)

8=b^3

2=b, now we have:

y=a(2^x), using point (4,64)

64=a(2^4)

64=16a

4=a so

y=4(2^x)

6 0

3 years ago

Put this in order from least to greatest 80,850,000,000 805,000,000 8,850,500,805

Burka [1]

Answer

805,000,000
8,850,500,805
80,850,000,000

6 0

4 years ago

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