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3 years ago

What is the constant in the algebraic expression to represent the patter below??

Mathematics

1 answer:

Hitman42 [59]3 years ago

8 0

Answer:

The constant in the algebraic expression to represent the pattern below is 4.

Step-by-step explanation:

Imortant Tip:

An Arithmetic sequence has a constant difference 'd' which can be determined by computing the differences of all the adjacent terms

Given the pattern

$15,11,7,3,-1,...$

computing the differences of all the adjacent terms

$11-15=-4,\:\quad \:7-11=-4,\:\quad \:3-7=-4,\:\quad \:-1-3=-4$

The difference between all the adjacent terms of the pattern is the same which is

$d=-4$

Hence, the given pattern represents the Arithmetic sequence.

Therefore, the constant in the algebraic expression to represent the pattern below is 4.

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find the surface areas of the larger cone and the smaller cone in terms of pi. compare the surface areas using a percent. (the m

serious [3.7K]

ANSWER :

Surface area of larger cone : 24π units^2

Surface area of smaller cone : 6π units^2

The surface area of the smaller cone is 25% of that of the larger cone.

EXPLANATION :

From the given problem,

AB = 3 is the radius of the larger cone and the slanted height is BC = 5

DE = 1.5 is the radius of the smaller cone and the slanted height is EC = 2.5

Recall the surface area of the cone :

$A=\pi r^2+\pi rL$

where r = radius and L = slanted height.

For the larger cone, r = 3 and L = 5

$\begin{gathered} A=\pi(3)^2+\pi(3)(5) \\ A=24\pi \end{gathered}$

For the smaller cone, r = 1.5 and L = 2.5

$\begin{gathered} A=\pi(1.5)^2+\pi(1.5)(2.5) \\ A=6\pi \end{gathered}$

Comparing the surface areas :

The area of the smaller cone compared to the larger cone is :

$\begin{gathered} \frac{smaller}{larger}\times100=\frac{6\pi}{24\pi}\times100 \\ \\ =25\% \end{gathered}$

3 0

1 year ago

Suppose 40% of the students in a university are baseball players. If a sample of 781 students is selected, what is the probabili

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Answer:

$P(p>0.43) = 0.0436$

Step-by-step explanation:

Given

$p = 40\%$ -- proportion of baseball players

$n = 781$ --- selected sample

Required

Determine P(p>43%)

First, calculate the z score using:

$Z = \frac{\^{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

This gives:

$Z = \frac{48\%-40\%}{\sqrt{\frac{40\% *(1 - 40\%)}{781}}}$

Convert % to decimal

$Z = \frac{0.43-0.40}{\sqrt{\frac{0.40 *(1 - 0.40)}{781}}}$

$Z = \frac{0.43-0.40}{\sqrt{\frac{0.40 *0.60}{781}}}$

$Z = \frac{0.43-0.40}{\sqrt{\frac{0.24}{781}}}$

$Z = \frac{0.03}{\sqrt{0.00030729833}}$

$Z = \frac{0.03}{0.01752992669}$

$Z = 1.71$

So:

$P(p>0.43) = P(Z>1.71)$

$P(p>0.43) = 1 - P(Z$

$P(p>0.43) = 1 - 0.9564$

$P(p>0.43) = 0.0436$

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3 years ago

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3 years ago

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Why is the information in the diagram enough to

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Because both triangles appear to be isosceles!!!!!!???!!!!

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3 years ago

What is the midpoint of (0,0.55) and (-3,6)

Contact [7]

Answer:

(-1.5, 3.275)

Step-by-step explanation:

midpoint = ( x1+X2/2 , y1+y2/2)

=(0+(-3)/2, 0.55+6/2)

=( -3/2, 6.55/2)

=( -1.5, 3.275)

8 0

3 years ago