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3 years ago

Leilani hung a triangular pennant for her favorite baseball team in her room as shown below.

Mathematics

1 answer:

ololo11 [35]3 years ago

3 0

Answer:

Step-by-step explanation:

recall the area of a triangle is Area = 1/2* Base* height

then we know the height, and the area solve for the base

I'll do the algebra symbolically so you can see how

A = 1/2 *B * H ( start here)

2A/H = B ( move to here )

Now plug in what you know on the left side

2*82.65/17.4 = base

9.5 = base :)

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I need some help on this question. Segment LM is the midsegment of trapezoid ABCD. AB=48, and DC=88. What is LM? I am not sure h

agasfer [191]

AB=48, DC=88

48+88=136
136÷2=68

Answer: LM=68
Remember that the length of the mid segment in a trapezoid is half the sum of the base lengths.

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4 years ago

Identify the type of pair of angles labeled as 1 and 2 in the figure.

myrzilka [38]

Hey!!

1 and 2 are vertical angles.

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3 years ago

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Multiply 3xyz ^ 2 / 6y ^ 4 by 2y / x z ^ 4

Marat540 [252]

$\dfrac{3xyz^2}{6y^4}=\dfrac{3}{6}\cdot\dfrac{xyz^2}{y^4}=\dfrac{1}{2}\cdot\dfrac{xz}{y^3}=\dfrac{xz}{2y^3}\\\\\\\dfrac{3xyz^2}{6y^4}\cdot\dfrac{2y}{xz^4}=\dfrac{xz^2}{2y^3}\cdot\dfrac{2y}{xz^4}=\dfrac{2}{2}\cdot\dfrac{xyz^2}{xy^3z^4}=1\cdot\dfrac{1}{y^2z^2}=\dfrac{1}{y^2z^2}$

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3 years ago

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Can someone please help me solve this?

mezya [45]

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3 years ago

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I will give lots of points please help

aalyn [17]

Answer:

a) 81π in³

b) 27 in³

c) divide the volume of the slice of cake by the volume of the whole cake

d) 10.6%

e) see explanation

Step-by-step explanation:

The cake can be modeled as a cylinder with:

diameter = 9 in
height = 4 in

$\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in$

$\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

$\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}$

$\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}$

If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.

$\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}$

The volume of each slice of cake is 27 in³.

The volume of the whole cake is 81π in³.

To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:

$\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}$

Probability is approximately 10.6% (see above for calculation)

If the four slices of cake are cut and passed out before anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, until the marble is found. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.

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2 years ago