4. If a set of data is normally distributed with a mean of 40 and standard
deviation of nine. Determine the percent of the data that is between 36 and 41.

9.18%
18.81%
21.38%
54.38%

Answer:

15 times

Step-by-step explanation:

50% of the time, 50% of 30=15

Answer: 15 times

Step-by-step explanation:

A coin has a 50/50 chance to get either heads or tails. 50% of the time it's heads, 50% is tails. So, if you tossed a coin 30 times, you would expect the coin to land on the tail 15 times because 30 / 2 = 15.

Answer:

Step-by-step explanation:

Brian could have more juice than Sonya in actual sense, This is because the representation used, that is the container has been calibrated to show tenth. This means that decimal values of juice in the container will not show explicit volume beyond tenth. Hence the volume will be rounded.

For instance, if the actual volume of juice Brian has Is 0.74 and that owned by Sonya is 0.69. In actual sense, 0.74 > 0.69 . However, if both pour their juice into the calibrated container, Brian's volume will be rounded to the nearest tenth as 0.7 and Sonya's (0.69) will also be rounded to 0.7.

But in actual sense, Brian has more Juice than Sonya.

Given:

An exponential equation passes through the points (0,4) and (2,9).

To find:

Exponential equation that passes through the given points.

Solution:

Let the required exponential function is:

[tex]y=ab^x[/tex]           ...(i)

The function passes through the points (0,4) and (2,9). It means the above equation must be true for these points.

[tex]4=ab^0[/tex]

[tex]4=a(1)[/tex]

[tex]4=a[/tex]

And,

[tex]9=ab^2[/tex]

Substituting [tex]a=4[/tex], we get

[tex]9=(4)b^2[/tex]

[tex]\dfrac{9}{4}=b^2[/tex]

[tex]\pm \sqrt{\dfrac{9}{4}}=b[/tex]

[tex]\pm \dfrac{3}{2}=b[/tex]

In an exponential function b>0. So, [tex]b=\dfrac{3}{2}[/tex].

Putting [tex]a=4,b=\dfrac{3}{2}[/tex] in (i), we get

[tex]y=4\left(\dfrac{3}{2}\right)^x[/tex]

Therefore, the required exponential function is [tex]y=4\left(\dfrac{3}{2}\right)^x[/tex].

Mass = density x volume

Mass = 178 x 25 = 4,450 grams

Answer:

(x+2)(x-8)

Step-by-step explanation:

Answer: 5 m

Step-by-step explanation:

Given

Length of 16 m fir tree is 12 m

length of the ash tree is 8 m

Suppose x is the length of the ash tree

angle [tex]c[/tex] made by fir and ash tree will be same as shown in figure

[tex]\Rightarrow \tan c=\dfrac{16}{12}=\dfrac{8}{x}\\\\\Rightarrow x=8\times \dfrac{12}{16}\\\\\Rightarrow x=5\ m[/tex]

Answer: I think the perimeter is 17ab4

Step-by-step explanation:

Answer:

x ≤ 10

Step-by-step explanation:

2x-6-5 ≤ 9

2x-11 ≤ 9

2x ≤ 20

x ≤ 10

Answer:

x=3, y= -6

Step-by-step explanation:

make 4+y= -x as equation (1) and make y=2x-10 as equation (2, then you must find a third equation either from equation (1)or (2). If you choose to find equation (3) from (2) it will be y=2x-10 , then substitute equation (3) from (1) because you can't choose (2) , then it will be 4+(2x-10)= -x

the answer will be x =2

substitute x from equation (3)

y=2x-10

y=2 (2)-10

y= -6

Answer:

3,672

Step-by-step explanation:

Given the sequence 6, 9, 12...

The sequence is an arithmetic sequence

first term a = 6

common difference d = 9 - 6 = 12 - 9 = 3

number of terms n = 48

Sn = n/2[2a+(n-1)d]

Substitute the given values

S48 = 48/2[2(6)+(48-1)(3)]

S48 = 24(12+(3*47))

S48 = 24(12+141)

S48 = 24(153)

S48 = 3,672

Hence the sum of the first 48terms is 3,672

Answer:

The value of cos 45° is equal to 1/√2

Answer:

Its 1/2

Step-by-step explanation:

I just took the test

Answer:

because the length is 4 feet more than the width

=> the length is x + 4 (feet)

because the base has an area of 21 square feet

=> x(x + 4) = 21

<=> x² + 4x = 21

Answer:

the length of the hypotenuse must be 10.

Step-by-step explanation:

This is a right triangle, so we can apply the Pythagorean Theorem.

6² + 8² = 10²   so the length of the hypotenuse must be 10.

Answer:

B. 40°

Step-by-step explanation:

AB // ED       ∠ABC = ∠EDF = 50°

AC // EF        ∠AGE = ∠CAB = 90 - ∠ABC = 90 - 50 = 40°

wer:

B 4

Step-by-step explanation:

Answer:

Isosceles and Right

Step-by-step explanation:

An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.

Answer:

Isosceles and right

Step-by-step explanation:

We have a picture of triangle and are asked to name it, look at definitions below :

Isosceles - Geometrical figure with three sides and three angles

Right - Triangle where one angle is a right angle (90°)

Scalene - Triangle where all three sides have different lengths

Acute - Triangle where all three sides are less than 90°

If we look at the triangle, we can tell that it has three sides and three angles, therefore isosceles must be in one of the answer choices. Crossing out the options scalene and acute / scalene and right.

Now we have two options and we need to determine whether this triangle is an acute triangle or is a right triangle.

To figure out so we can look at the angle in the bottom left, which when measures equals to 90°. Therefore making it a right triangle and crossing out the other option.

Our answer left is Isosceles and Right.

Interpreting as: circle 8.5 inches.

Assuming

"circle"

is a geometric object

circle | radius 8.5 inches

Equation:

(x - x_0)^2 + (y - y_0)^2 = 72.

(assuming center (x_0, y_0))

Properties:

diameter | 17 inches

area enclosed | 227 in^2 (square inches)

circumference | 53.4 inches

answer is D. 17/C

Answer:

359.19

Step-by-step explanation:

Using the formula V=(πr^2) * h/3 and plugging in the given values we get 359.19.

I estimated pi at about 3.14

Answer:

x = 2

Table:

0,0

3,9

-2,-6

4,12

Step-by-step explanation:

distribute

3(2x+1)=15

6x+3 = 15

subtract 3 from both sides

6x + 3 = 15

6x + 3 - 3 = 15 - 3

simplify

6x= 12

divide both sides by 6

answer= x=2

Answer:

Area of the unshaded sector = 113.4 sq units

Area of the shaded sector = 200.6 sq units

Step-by-step explanation:

First let us calculate the area of the circle

Area of the circle = πr²

radius r  = 10units

Area of the circle = π(10)²

Area of the circle = π(100)

Area of the circle = 3.14(100)

Area of the circle = 314 sq. units

Area of a sector = theta/360 * πr²

Area of the unshaded sector = 130/360 * 314

Area of the unshaded sector = 13/36 * 314

Area of the unshaded sector = 113.389 sq units

Area of the unshaded sector = 113.4 sq units

Area of the shaded sector = Area of circle - Area of the unshaded sector

Area of the shaded sector = 314 - 113.89

Area of the shaded sector = 200.6sq. units

Answer:

7/25

Step-by-step explanation:

Cos x=Adjacent/hypotenuse

Clad=21/75=7/25

Answer:

[tex]y=-\frac{1}{2} +3[/tex]

Step-by-step explanation:

Answer:

y = -1/2x + 3

Answer:

7/16

Step-by-step explanation:

Answer:

7/16

Step-by-step explanation:

Simplify

Answer:

10 miles

Step-by-step explanation:

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

6^2 + 8^2

36 + 64 = 100

square root = 10

Answer:

-5x-1/6=3/2

-5×1/6+1/6=3/2+1/6

-5×÷5×=10/6/-5x

x=-10/30