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3 years ago

About 99.7% of sixth-grade students will have

Mathematics

2 answers:

attashe74 [19]3 years ago

6 0

Answer:

51.1

64.9

Step-by-step explanation:

Evgesh-ka [11]3 years ago

5 0

Answer: About 99.7% of sixth-grade students will have

heights between 51.1 inches and 64.9 inches.

Step-by-step explanation:

According to the empirical rule, 99.7% of data falls within the three standard deviations from the mean.

Given : Mean: $\mu=58\text{ inches}$

Standard deviation:= $\sigma=2.3\text{ inches}$

Then, the 99.7% of sixth-grade students will have heights between

$\mu-3\sigma$ inches and $\mu+3\sigma$ inches

i.e. $58-3(2.3)$ inches and $58+3(2.3)$ inches

i.e. 51.1 inches and 64.9 inches.

You might be interested in

Transform the Cartesian (rectangular) equation to a polar equation: x = -9. The selected answer is incorrect.

nika2105 [10]

Answer:

Solution : Option C

Step-by-step explanation:

We have the equations r² = x² + y², x = r cos(θ), and y = r sin(θ) that can be used to solve this problem. In this case we only need the second two equations ( x = r cos(θ), and y = r sin(θ) ) as we don't need to apply the concept of circles etc here.

Given : x = - 9,

( Substitute r cos(θ) for x )

r cos(θ) = - 9,

r = - 9 / cos(θ)

( Remember that sec is the reciprocal of cos(θ). Substitute sec for 1 / cos(θ) )

r = - 9 sec(θ)

Therefore the third option is the correct solution.

6 0

3 years ago

The height of a triangle is half the length of its base. The area of the triangle is 12.25cm. Find the height

pentagon [3]

Answer: The height of the triangle is: " 3.5 cm " .
_______________________________________________________

Note: The formula/equation for the area, "A" , of a triangle is:

A = (1/2) * b * h ; or write as: A = (b * h) / 2 ;
_________________________________________________
in which: "A = area of the triangle" ;
"b = base length" ;
"h = "[perpendicular] height" ;
_________________________________________________
Given: h = (b/2) ;
A = 12.25 cm²
{Note: Let us assume that the given area was "12.25 cm² " .}.
_________________________________________________
We are to find the height, "h" ;

The formula for the Area, "A", is: A = (b * h) / 2 ;

Let us rearrange the formula ;
to isolate the "h" (height) on one side of the equation;

→ Multiply EACH side of the equation by "2" ; to eliminate the "fraction" ;

2*A = [ (b * h) / 2 ] * 2 ;

to get: " 2A = b * h " ;

↔ " b * h = 2A " ;

Divide EACH SIDE of the equation by "b" ; to isolate "h" on one side of the equation:

 → (b * h) / b = (2A) / b ;

to get:

 → h = 2A / b ;

Since "h = b/2" ; subtitute "b/2" for "h" ;

Plug in: "12.25 cm² " for "A" ;

→ b/2 = 2A/b ; → Note: " 2A/b = [2* (12.25 cm²) ] / b " ;

Note: " 2* (12.25 cm²) = 24.5 cm² ;

Rewrite as:

→ b/2 = (24.5 cm²) / b ;
_____________________________________
Cross-multiply: b*b = (24.5 cm²) *2 ;

to get: b² = 49 cm² ;

Take the "positive square root" of each side of the equation" ;
to isolate "b" on one side of the equation ; & to solve for "b" ;

→ +√(b²) = +√(49 cm²) ;

→ b = 7 cm ;

Now, we want to solve for "h" (the height) :
_________________________________________________________
→ h = b / 2 = 7 cm / 2 = 3.5 cm ;
_________________________________________________________
Answer: The height of the triangle is: " 3.5 cm " .
_________________________________________________________

6 0

3 years ago

use the information provided to write the standard form equation of each hyperbola vertices:(4,14), (4,-10) foci: (4,15), (4,-11

Evgen [1.6K]

So... if you notice the picture below, based on the given vertices, is a hyperbola with a vertical traverse axis

meaning for the equation, the fraction with the "y" variable is the positive fraction, thus $\bf \cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1$

so... what' the point h,k for the center? well, just take a peek at the graph, the center is half-way between both vertices, that's h,k

what's the "a" component or the traverse axis... well, is the distance from one vertex to the center, notice the picture, notice how many units from either vertex to the center, that's "a"

now.. what's "b"? well, "b" comes from the conjugate axis, or the other runnning over the x-axis hmm the smaller one in this case.... well, we dunno what "b" is

however, we know the distance from either focus, to the center of the hyperbola, and that distance "c", is $\bf c=\sqrt{a^2+b^2}$

notice the picture, notice the distance from either focus to the center, that's the distance "c", thus $\bf c=\sqrt{a^2+b^2}\implies c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b$

that'd be "b"

bearing in mind that $\bf \cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1
\qquad 
\begin{cases}
center= ({{ h}},{{ k}})\\\\ b=\sqrt{c^2-a^2}
\end{cases}$

8 0

3 years ago

Can you share a strategy For multiplying?

Nadusha1986 [10]

Answer:

Step-by-step explanation:

It's like the same thing for adding. For example if you have 3 x 4. You can add 3 four times or you can add 4 three times. Like this.

3 + 3 + 3 + 3 = 12 because you know 3 + 3 =6 and 6 + 6 equals 12.

4 + 4 + 4 = 12 because you know 4 + 4 = 8 and 8 + 4 equals 12.

I hope this helped. I am sorry if I didn't do much of help. Have a wonderful day.

8 0

3 years ago

Unit of Measurement, a punk/disco band, played a benefit concert for New Year's Eve. They started at 7:00 p.m. on New Year's Eve

Maksim231197 [3]

810
count the number of hours they played which should be 13 hrs and 30 mins,
then since every hour is 60 mins multiply 60 by 13 and then add 30

6 0

3 years ago