eamonn has just taken a statistics exam, and he wants to calculate a confidence interval to represent the exam scores in his class. the test mean was 75, with a standard deviation of 5. there are 30 students in the class. the 90% confidence interval for the class is:

Two triangles are similar if the ratio of their corresponding side equal'

Triangle

Because

Corresponding sides are

Therefore,

Triangle

Pam is a nurse that earns $93 in 6 hrs .The equation that can represents how much she get paid per hour can be computed below

The equation that passes through (-12, 15 with a slope of -1 in point slope form is y - 15 = - 1(x + 12)

Linear equation can be represented in different form such as point slope form, slope intercept form  and standard form.

Therefore, let's represent the line that passes through (-12, 15) with a slope of -1 in point slope form.

Hence,

y - y₁ = m(x - x₁)

where

Therefore,

m = slope = -1

using (-12, 15)

Hence,

y - 15 = - 1(x - (-12))

Therefore,

y - 15 = - 1(x + 12)

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The average acceleration of the golf ball as it was dropped from the second story window is 9.8m/s².

Given in the question is:

Since the ball started from rest

Initial velocity; u= 0m/s

Final velocity; v = 14.7 m/s

Time taken for the golf ball to hit the sidewalk; t = 1.5 s

Average Acceleration; g =?

To determine the average acceleration of the golf ball, we use the First Equation of Motion:

v = u + at

The Equation will be :

v = u + gt

Plug the all values in above equation:

14.7m/s = 0 + g x 1.5 s

g =  14.7 / 1.5

g = 9.8m/[tex]s^2[/tex]

Therefore, the average acceleration of the golf ball as it was dropped from the second story window is 9.8m/s².

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Answer:

2[tex]\sqrt{23}[/tex]

Step-by-step explanation:

The distance between the points (-4, -7) and (-8, -13) is 2√13 units as per the concept of distance between the two points.

To determine the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is as follows:

[tex]Distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]

Given the two points (-4, -7) and (-8, -13), we can assign the coordinates as follows:

x1 = -4, y1 = -7 (coordinates of the first point)

x2 = -8, y2 = -13 (coordinates of the second point)

Now, we substitute these values into the distance formula:

[tex]Distance = \sqrt{(-8 - (-4))^2 + (-13 - (-7))^2)}\\\\= \sqrt{((-8 + 4)^2 + (-13 + 7)^2}\\= \sqrt{((-4)^2 + (-6)^2)}[/tex]

= √(16 + 36)

= √52

= 2√13

Therefore, the distance between the points (-4, -7) and (-8, -13) is 2√13 units.

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Answer:

3/4 or 0.75

Step-by-step explanation:

The student that has the greatest percent error is Ebony.

The percentage error will be calculated as:

= Change in value / Initial values × 100

From the table, we can see that Ebony had the greater difference in values. This will be illustrated as:

= (Measured length - Actual length) / Actual length × 100

= (2.1 - 1.6)/1.6 × 100

= 0.5 / 1.6 × 100

= 31.25%

Ebony had the higher percentage error.

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Answer:

x = –1/3 and y = 11/3

or can be written as (–1/3, 11/3)

Solve the system of equations:

1x + 2y = 7

y = –2x + 3

Substitute y = –2x + 3 for y in the first equation:

1x + 2y = 7

1x + 2(–2x + 3) = 7

Substract 6 from both sides:

–3x + 6 = 7

–3x + 6 – 6 = 7 – 6

–3x = 1

Divide:

–3x/–3 = 1/–3

x = –1/3

Substitute –1/3 for x in the second equation:

y = –2x + 3

y = –2(–1/3) + 3

y = 11/3

Solution:

x = –1/3 and y = 11/3

or can be written as (–1/3, 11/3)

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Equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to x -55 =4.2.

As given in the question,

Given equation :

|x – 55| = 4.2

To determine the maximum and minimum speed in miles per hour from the given equation we have,

x-55 = 4.2 or x-55 =-4.2

Add 55 both the side of the equation,

x-55 +55 =4.2+55  or x-55+55 = -4.2 +55

x =59.2 or x = 50.8

Maximum speed is 59.2 determine by equation x-55 = 4.2

Minimum speed is 50.8 determine by equation x-55 = -4.2

Therefore, equation which is used to determine the maximum safe driving speed from the given equation |x – 55| = 4.2 is equal to

x -55 =4.2.

The complete question is:

On the freeway, it is unsafe to drive too slowly or too quickly. The safest driving speeds on the freeway near Allan’s town were scientifically determined to be between the minimum and maximum speeds (in miles per hour) according to the equation |x – 55| = 4.2. Which equation can be used to determine the maximum safe driving speed?

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Given:

Amount Marty spent per day = $3

Number of days = 14

Remaining amount = $68

Since the amount left depends on the number

Answer:

plan b

Step-by-step explanation:

unless your making 120 calls or more plan B is better

24-18=6

6/0.05

=120

Answer:

SAS Congruence Rule

A triangle is said to be congruent to each other if two sides and the included angle of one triangle is equal to the sides and included angle of the other triangle.

Answer: SAS (side side angle postulate.)

Step-by-step explanation:

can be used to prove triangles congruent.

sides and the corresponding angle of the other, then the triangles are congruent.

3 × 90 thus equals 280 degrees.

The figure moves onto the following quadrant of the graph with each 90 degree rotation. In order to shift Figure I to the location of Figure J, you must move the three figure quadrants in a clockwise direction. 3 × 90 thus equals 280 degrees. Only one transformation is needed.

Which transformation corresponds to turning a figure 90 degrees counterclockwise?

The coordinate transformation (x, y) (y, x) is equivalent to a rotation of the origin 90 degrees counterclockwise. The coordinate transformation (x, y) (x, y) is comparable to a 180 degree counterclockwise rotation of the origin.

Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x and y, making y negative.

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Answer: [tex]f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]

Step-by-step explanation:

[tex]f(x)=-9x-10 \implies x=-9f^{-1}(x)-10\\\\x+10=-9f^{-1}(x)\\\\f^{-1}(x)=-\frac{1}{9}(x+10)[/tex]

Answer:

2

Step-by-step explanation:

1.9541 lets only worry about 1.95 because it rounds to this rounding up because its five will be 2

Answer:4 sodas

Step-by-step explanation:

1.75 x 2 = 3.5

10- 3.5 = 6.5

6.5 Divided by 1.50 =  4.33333333

(Round that to 4 and he will be left with cents)

There are 54% of the participants are female.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage

Given:
There are 104 males and 121 females

participating in a marathon.

So, the total number of participants are,

104 + 121 = 225.

There are 225 total number of participants.

So, the percent of the female are,

[tex]\frac{121}{225} (100) = 53.78[/tex]

Therefore, the percent of the participants of female are 54%.

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(1) The graph is attached with the answer below.

(2)The equation of the line is y = x + 3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

The points are ( 3, 0 ) and ( 0, 3). The slope of the line will be calculated as:-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 3 - 0 ) ( 0 - 3 )

Slope = 1

Calculate the y-intercept,

y = mx + c

3 = 0 + c

c = 3

The equation of the line will be:-

y = x + 3

Therefore, the graph is attached with the answer below the equation of the line is y = x + 3.

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The equations that represent proportional relationships are:

A. 2x/12 = 3x/18

C. 4/6 = 10/15

E. 5/5 = 11/11

To determine if an equation represents a proportional relationship, ensure each side of the equation gives the same value when simplified. If they do not have the same value, then the equation does not represent a proportional relationship.

A. 2x/12 = x/6

3x/18 = x/6

Therefore, 2x/12 = 3x/18 represents a proportional relationship.

B. 3/6 = 1/2

6/3 = 2

Therefore, 3/6 = 6/3 does not represent a proportional relationship.

C. 4/6 = 2/3

10/15 = 2/3

Therefore, 4/6 = 10/15 represents a proportional relationship.

D. 4x/18 = 2x/9

x/18 = x/18

Therefore, 4x/18 = x/18 does not represent a proportional relationship.

E. 5/5 = 1

11/11 = 1

Therefore, 5/5 = 11/11 represents a proportional relationship.

F. 8/15 = 8/15

4/30 = 2/15

Therefore, 8/15/2/15 does not represent a proportional relationship.

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Answer:

[tex]m[/tex]perpendicular = 6

Step-by-step explanation:

Hope this helps! :))

Explanation

we have a secant and a tangent

To solve the question, we will apply the intersecting secant and tangent theorem

So, for the question

we have

Therefore, the value of PB is 12

Proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)

Given,

sin(x) + sin(3x) = 4 sin(x) cos²(x)

We have to prove the above given identity:

So,

sin(x) + sin(3x)

sin(x) + sin(2x + x)

By using the identity sin (A + B) we get,

sin(x) + sin (2x) cos(x) + cos (2x) sin(x)

Now use the identities:

sin 2x and cos 2x

We get,

sin(x) + 2sin(x) cos(x) cos(x) + (2cos²(x) - 1) sin(x)

Then,

sin(x) + 2sin(x) cos²(x) + 2sin(x) cos²(x) - sin(x)

We get,

4 sin(x) cos²(x)

Hence proved the identity sin(x) + sin(3x) = 4sin(x) cos²(x)

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The original equation is:

5 x^2 + (10 x^2 + 10) = 3 x^2 - 5

The first step the person did was:

15 x^2 + 10 = 3 x^2 - 5

so in this first step the person used the associative property of addition by associating 5 x^2 with 10 x^2 and combining them to give 15 x^2.

Please check if there is an option that states such among your options.

The area of a pool from the given situation is 816 ft².

Given that, the dimensions of plot is 50 ft and 40 ft.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Here, area of a plot = Length × Width

= 50 × 40

= 2000 ft²

Area of a pool = Area of a plot - Area of a grass

= 2000 - 1184

= 816 ft²

Therefore, the area of a pool from the given situation is 816 ft².

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We can conclude that (B) the data from Germany has a negative correlation because the slope of the regression equation is negative.

So, according to the given image, we can easily say that Germany has a negative correlation.

We can observe that the slope of the regression equation is negative.

Therefore, we can conclude that (B) the data from Germany has a negative correlation because the slope of the regression equation is negative.

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The negative sign means that temperature decreases of fell.

Deteremine the change in temperature for 5 hours.

So temperatute fell 4 degrees. Option C is correct.

The property demonstrated by:

a(b+c)=(a.b)+(a.c)

Is the Distributive property

Here we have the next expression:

a*(b + c) = (a*b) + (a*c)

So we have the product between a and the sum of b and c, is equal to the sum between the products of a and b, and a and c, so we "distributed" the product.

This property is called the "Distributive property".

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Answer:

3.44571

Step by step explanation:

3.44570830811

8 is the number next to the place value of hundred-thousandth, so we round it up to 1 and add it to 0

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Answer: f(7) = 52

Step-by-step explanation:

x = 7, so you would substitute x for 7

f(7) = 6(7) + 10

f(7) = 42 + 10

f(7) = 52

Hope this helps!