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Question 3(Multiple Choice Worth 5 points)

(08.03 MC)


The two dot plots below compare the forearm lengths of two groups of schoolchildren:


Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length followed by inches in parentheses. There are markings from 11 to 14 on each line at intervals of one. For the top line there are 3 dots above the second mark, 4 dots above the third mark, and 3 dots above the fourth mark. For the bottom line there are 3 dots above the first mark, 5 dots above the second mark, and 2 dots above the third mark.


Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?


Group B, because three children in the group have the least forearm length of 11 inches

Group A, because three children in the group have the least forearm length of 11 inches

Group A, because seven children have a forearm length longer than 12 inches

Group B, because two children have a forearm length longer than 12 inches

Answer:

1/3

Step-by-step explanation:

That is the simplified version of the number of all the double-digit odd days (11,13,15,17,21,23,25,27,29), 10, over the total number of days in April, 30

10/30=1/3

Answer:

Step-by-step explanation:

the number of combinations of 4 people we can form from 6 is :

[tex]C^{4}_{6}=\frac{6!}{4!\left( 6-4\right) !} = 15[/tex]

Answer:

y = 1/5x + 3

Step-by-step explanation:

y = mx + b

m: slope = 1/5

b: y - intercept

(x, y): (-5, 2)

2 = 1/5(-5) + b

2 = -1 + b

add 1 to both sides to get b alone

2 + 1 = -1 + b + 1

3 = b

[tex]xy \\\\=\left(\log_{5\sqrt 5} ~125 \right)\left(\log_{2\sqrt 2} ~64 \right)\\\\=\left(\log_{5\sqrt 5} ~5^3 \right)\left(\log_{2\sqrt 2}~2^6 \right)\\\\=\left(3\log_{5\sqrt 5} ~5 \right)\left(6\log_{2\sqrt 2} ~2 \right)\\\\=\left( 18 \cdot \dfrac{\ln5}{\ln\left(5\sqrt 5\right)} \cdot \dfrac{\ln 2}{ \ln \left( 2 \sqrt 2 \right)}\right)\\\\[/tex]

[tex]=\left( 18 \cdot \dfrac{\ln5}{\ln\left(5^{\tfrac 32}\right)} \cdot \dfrac{\ln 2}{ \ln \left( 2^{\tfrac 32} \right)}\right)~~~~~~~~~~~;\left[\sqrt a = a^{\tfrac 12}~~ \right]\\\\=\left( 18 \cdot \dfrac{\ln5}{\tfrac 32\ln5^} \cdot \dfrac{\ln 2}{\tfrac 32 \ln 2 }\right)\\\\\\=18 \cdot \dfrac 23 \cdot \dfrac 23 \\\\=\dfrac{72}9\\\\=8[/tex]

Answer:

Driving Distance : 569 KM and 398 meters / 353.8 miles.

Straight Line Distance : 467 KM and 700 meters / 290.6 miles.

Travel time : 11 hours and 19 minutes.

Direction and bearing : South side, 159 degree.

Step-by-step explanation:

Answer:

7/32

Step-by-step explanation:

what's your question question question

Answer:

2.5 seconds.

Step-by-step explanation:

h(t) = -4t^2 + 20t

= -4(t^2 - 5t)

Convert to vertex form by completing the square:

h(t) = -4[(t - 2.5t)^2 - 6.25]

     = -4(t - 2.5)^2 + 25    <--------- vertex form

So the vertex is at the point (2.5, 25).

So the athlete reaches the maximum height ( of 25 feet), after 2.5 seconds.

Answer:

Area = 213.52 sq.ft

Step-by-step explanation:

[tex]A_{s} =\pi (18)^{2} -\pi (16)^{2} =324\pi -256\pi =68\pi[/tex]

[tex]\pi =3.14[/tex]

[tex]A_{s} =68(3.14)=213.52sq.ft[/tex]

Hope this helps

Answer:

  113.04 ft²

Step-by-step explanation:

The area of the ring can be found by multiplying its center-line length by its width.

__

The diameter of the circle that is the center-line of the ring is ...

  16 ft + 2 ft = 18 ft . . . . center-line diameter

The length of the center-line is then ...

  C = πd

  C = 3.14(18 ft) = 56.52 ft

And the area of the ring is ...

  A = LW = (56.52 ft)(2 ft) = 113.04 ft²

The shaded area is 113.04 square feet.

Answer:

between 4 and 5

Step-by-step explanation:

consider perfect cubes either side of 81 , that is

64 < 81 < 125 , then

[tex]\sqrt[3]{64}[/tex] < [tex]\sqrt[3]{81}[/tex] < [tex]\sqrt[3]{125}[/tex] , that is

4 < [tex]\sqrt[3]{81}[/tex] < 5

The height from the ground at which the ladder touched the building is 12feet.

A right-angled triangle is a type of triangle that has three sides and one of its  three angles as 90°.

Analysis:

The ladder length, height of the ladder from the ground, and the distance of the foot of the ladder from the foot of the building form a right angle triangle.

let x, be the distance from the foot of the building to the foot of the ladder.

x+7 = height of ladder from building to foot of  building.

length of ladder = 13 feet

using Pythagoras, we have

[tex](13)^{2}[/tex] = [tex]x^{2}[/tex] + [tex](x+7)^{2}[/tex]

169 = [tex]x^{2}[/tex] + [tex]x^{2}[/tex] + 7x + 7x + 49

169 = 2[tex]x^{2}[/tex] + 14x + 49

2[tex]x^{2}[/tex] + 14x = 169-49

2[tex]x^{2}[/tex] + 14x  = 120

divide through by 2

[tex]x^{2}[/tex] + 7x - 60 = 0

[tex]x^{2}[/tex] +12x -5x - 60 = 0

(x+12) -5(x+12) = 0

(x+12)(x-5) = 0

x = -12 or 5

Since measurement cannot be negative, therefore x = 5

Height the ladder touches the building is x+7 = 5+7 = 12 feet

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The sales they might anticipate if they raise the price to $40 a bottle is $1,500.

Using this formula

Anticipated sales=(Current selling price÷Increase in price)×Number of bottle sold

Let plug in the formula

Anticipated sales=($30÷$40)×2,000

Anticipated sales=$0.75×2,000

Anticipated sales=$1,500

Therefore the sales they might anticipate if they raise the price to $40 a bottle is $1,500.

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Answer:

3/4

Step-by-step explanation:

Subtract 3 2/4 from 2 3/4

- Multiply 3 and 4 to get 12.

- Add 12 and 2 to get 14.

- Reduce the fraction 14/4 to lowest terms by extracting and canceling out 2.

- Multiply 2 and 4 to get 8.

- Add 8 and 3 to get 11.

- Least common multiple of 2 and 4 is 4. Convert 7/2 and 11/4 to fractions with denominator of 4

- Since 14/4 and 11/4 have the same denominators, subtract both by subtracting their numerators

- Subtract 11 from 14 to get 3

Check the picture below.

the area of the triangle whose base is AC and height is BD, is the same area of the triangle whose base is AB and altitude is BC, namely

[tex]A=\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{6})\implies 18[/tex]

Answer:

From the diagram you can see that we have constructed a right triangle, with height A and base 15.Length of shadow = 15 feet.Height of flagpole = A.We know the angle of elevation is 40∘. Using this angle and the tangent ratio, we can find A.tan(40∘)=oppositeadjacent=A15∴tan(40∘)=A15Rearranging:A=15tan(40∘)By calculator:A=12.59 feet.  ( 2 d.p.)

Answer:

441 square feet.

Step-by-step explanation:

Area = length times width. Both length and width are 21 feet (3×7).

Answer:

D

Step-by-step explanation:

The interval notation for the graph :

This is not a valid conclusion because the data was not randomly collected from various classes in the school but from a particular class.

The collection of data for a research work should be done in such a way as to include a good number of the test subjects.

The sampling methods that can be used to gather better data include the following:

These methods will ensure that a good number of the test subjects are included in the research work in order to form a valid conclusion.

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Answer:

84cm

Step-by-step explanation:

Given that;

1cm = 7m

12cm = x

Cross Multiply

x = 12×7

x = 84m

Answer:

Hi! There are 3600 seconds in one hour.

Step-by-step explanation:

60 min. = one hour

60 seconds = one minute

:)

Answer:

y= x5

Step-by-step explanation:

y = 5 times the number of x.

Answer:

Mean = 1.8 in

Step-by-step explanation:

The Median is the middle value when all data values are placed in order of size.

Ordered data values:  0, 0, 0, 1, 1, 1, 2, 3, 4, 6

As there is an even number of data values, the middle value is the mean of the middle two data values.  Therefore, the Median = 1 in

The Mean is the sum of all data values divided by the total number of data values.

[tex]\implies \textsf{Mean}=\dfrac{0+0+0+1+1+1+2+3+4+6}{10}=1.8[/tex]

Therefore, the Mean = 1.8 in

The Median is a better measure of central tendency when the data includes outliers (data values that are far away from the majority), as it is not affected by those outliers.  As there does not appear to be any outliers in this data set, the mean can be used to best describe the center of the data.

Therefore, the Mean = 1.8 in

Answer:

[tex]f(2)=\frac{7}{4}[/tex]

Step-by-step explanation:

Step 1:  Input 2 for x and solve

[tex]f(x) = \frac{2x + 7 - x^2}{4}[/tex]

[tex]f(2) = \frac{2(2) + 7 - (2)^2}{4}[/tex]

[tex]f(2)=\frac{4+7-4}{4}[/tex]

[tex]f(2)=\frac{7}{4}[/tex]

Answer: [tex]f(2)=\frac{7}{4}[/tex]

Answer:

the top right (2) answer is probably what you'll want to go for, if this is incorrect then you have my deepest apologies

Step-by-step explanation:

Answer:X is equal to -4 twice

Step-by-step explanation:

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To solve the equation 2x² + 8x = x² - 16, we first simplify it by moving all the terms to one side:

2x² + 8x - x² + 16 = 0

Simplifying further, we get:

x² + 8x + 16 = 0

This is a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 8, and c = 16.

We can solve this equation by factoring it:

(x + 4)(x + 4) = 0

This gives us two solutions:

x + 4 = 0 or x + 4 = 0

x = -4 or x = -4

Therefore,

The solution to the equation 2x² + 8x = x² - 16 is x = -4.

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