MATHEMATICS HIGH SCHOOL

Bella has sampled the heights of 30 students at Ridgemont High and obtained a mean of 64.2 inches. He constructs a 90% confidence interval, which turns out to be (61.0, 67.4). What is the ma A) 2.1 inches

B) 3.2 inches

C) 4.2 inches

D) 6.4 inches rgin of error?

Answers

Answer 1
Answer: The correct answer for the question that is being presented above is this one: "C) 4.2 inches." Bella has sampled the heights of 30 students at Ridgemont High and obtained a mean of 64.2 inches. He constructs a 90% confidence interval, which turns out to be (61.0, 67.4). The margin of error is C) 4.2 inches 
Answer 2
Answer:

Answer:b 3.2

Step-by-step explanation: I just did it

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Write the equation of the line that is parallel to the line whose equation is y = –4 and that passes through the point (1, 5).A. y=-5
B. y=-4
C. y=1
D. y=5

Answers

The equation of the line, y = -4, has a slope of 0. For lines to be parallel their slopes should be equal. Given the slope and a point, the equation of the line is generally expressed as,
                                y - y1 = m(x - x1)
Substituting gives the answer of,
                                   y - 5 = 0     ;    y = 5
The answer is letter D.

Jordan takes 50% of the cherries from a bowl. then Mei takes 50%of the remaining cherries. Finally Greg takes 50 %of the remaining cherries. There are 3 cherries left. How many cherries were in the bowl before Jordan arrived

Answers

Answer:

24

Step-by-step explanation:

Let total cherries in a bowl=x

Jordan takes cherries=50% of x=(50)/(100)x

Remaining cherries=x-(50)/(100)x=(50)/(100)x=(x)/(2)

Mei takes cherries=50% of (50x)/(100)=(x)/(4)

Now, remaining cherries=(x)/(2)-(x)/(4)=(x)/(4)

Greg takes cherries=50% of(x)/(4)=(x)/(8)

Now, remaining cherries=(x)/(4)-(x)/(8)=(x)/(8)

Now,remaining cherries in a bowl=3

We have to find total cherries in a bowl before Jordan arrived.

According to question

(x)/(8)=3

x=3* 8=24

Hence,  total cherries in a  bowl=24
So in the final smallest bowl when half are removed there are 3 so the total amount was double 3 which is 6 before greg removed some.
Mei had removed half of the cherries which left 6 cherries so the total amount before Mei removed half was 12.
Jordan took half of the cherries which left 12. If you follow the same logic you double 12 which makes....
Good luck, hope this helped you understand the question more, feel free to comment and ask for help :)

FIND MAGNITUDE AND DIRECTIONS OF TRANSLATIONS APPLIED ON A TRIANGLE. Question Linked below.

Answers

The three translations applied on the triangle, where the first element of each vector represents the magnitude of the translation, and the second element represents the direction of the translation.

To find the magnitude and direction of the translations applied on a triangle, we need to know the coordinates of the vertices of the original triangle and the coordinates of the vertices of the transformed triangle.

Let's say the coordinates of the original triangle are (x1, y1), (x2, y2), and (x3, y3), and the coordinates of the transformed triangle are (x1', y1'), (x2', y2'), and (x3', y3').

The magnitude of the translation can be found by calculating the distance between the corresponding vertices of the original and transformed triangles using the distance formula. For example, the magnitude of the translation from (x1, y1) to (x1', y1') is given by:

sqrt((x1' - x1)^2 + (y1' - y1)^2)

Similarly, we can find the magnitudes of the other two translations.

The direction of the translation can be found by calculating the angle between the line connecting the corresponding vertices of the original and transformed triangles and the x-axis. We can use the arctangent function to find this angle. For example, the direction of the translation from (x1, y1) to (x1', y1') is given by:

tan^-1((y1' - y1)/(x1' - x1))

Similarly, we can find the directions of the other two translations.

Once we have the magnitudes and directions of the translations, we can describe the transformation using vector notation. The vector of the translation is given by:

< magnitude1, direction1 >

< magnitude2, direction2 >

< magnitude3, direction3 >

This represents the three translations applied on the triangle, where the first element of each vector represents the magnitude of the translation, and the second element represents the direction of the translation.

Learn more about translations here

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What is the simplified base for the function f(x) = 2(3√27(2x)?2
3
9
18

Answers

Answer:

option C is correct i.e. 9

Step-by-step explanation:

We have given that : f(x)=2 \sqrt[3]{27^(2x)}

To find : The simplified base of the function f(x)  

Solution:

Now, we solve the equation  

f(x)=2 \sqrt[3]{27^(2x)}

f(x)=2(27^x)^{(2)/(3)}  

f(x)=2(3^(2x))  

f(x)=2((3^2)^(x))  

f(x)=2(9^(x))  

Therefore, the  simplified base of the function f(x) is 9

Answer:

Option C is correct

9 the simplified base for the given function f(x)

Step-by-step explanation:

Using exponent rules:

(x^m)^n = x^(mn)

\sqrt[n]{x^b} = x^{(b)/(n)}

Given the function:

f(x) = 2\sqrt[3]{27^(2x)}

We can write 27 as:

27 = 3 \cdot 3 \cdot 3 = 3^3

then;

f(x) = 2\sqrt[3]{(3^3)^(2x)}

Apply the exponent rules:

f(x) = 2\sqrt[3]{3^(6x)}

Apply the exponent rules:

f(x) =2 \cdot (3^(6x))^{(1)/(3)} = 2 \cdot 3^(2x)

⇒f(x) = 2 \cdot (3^2)^x = 2 \cdot 9^x

⇒f(x) =2 \cdot 9^x

On comparing with exponential function f(x) = ab^x where, b is base of the exponent function, then

b = 9

Therefore, the simplified base for the given function is, 9

The product of three and a squared number is twice the sum of the number and four

Answers

From the text of the task we can write the equation:


3 x^(2) =2(x+4)\n \n 3x^2=2x+8\n \n 3x^2-2x-8=0\n \n \Delta=(-2)^2-4.3.(-8)=4+96=100\n \n x=(2 \pm√(100))/(2.3)=(2 \pm10)/(6)\n \n x_1=(2-10)/(6)=-(8)/(6)=-(4)/(3)\n \n x_2=(2+10)/(2.3)=(12)/(6)=2
3x^2=2(x+4)\n 3x^2=2x+8\n 3x^2-2x-8=0\n 3x^2-6x+4x-8=0\n 3x(x-2)+4(x-2)=0\n (3x+4)(x-2)=0\n x=-(4)/(3) \vee x=2

Solve h = −16t2 + 36t + 4.

Answers

I can do each of the things I asked above.
So, let's change this into vertex form:
h=-16t^2+36t+4
h=(-16t^2+36t)+4
h=-16(t^2-2.25t)+4
h=-16(t^2-2.25t+1.27-1.27)+4
h=-16(t^2-2.25t+1.27)+20.32+4
h=-16(t-1.125)^2+24.32
The vertex is at (1.125,24.32)
Answers may vary due to rounding

Factored Form:
h = -16t^2 + 36t + 4
h = -4\left(4t^2-9t-1\right)

Quadratic Formula:
x = (-b +/- √(b^2-4(a)(c)))/(2a)
h = -16t^2 + 36t + 4
a = -16 b = 36 c = 4
h = (-(36) +/- √((36)^2-4(-16)(4)))/(2(-16))
h = (-36 +/- √(1552))/(-32)
h = ≈-0.11
h = ≈2.36
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