Scientists want to estimate the mean weight of mice after they have been fed a

special diet. From previous studies, it is known that the weight is normally

distributed with standard deviation 4 grams. How many mice must be weighed so

that a 95% confidence interval will have margin of error of 0.4 grams?

Write only an integer as your answer.

Answer:

∠ BCA = 25°

Step-by-step explanation:

the inscribed angle BCA is half the measure of the central angle BOA , so

∠ BCA = \(\frac{1}{2}\) × 50° = 25°

SOLUTION

To solve this question, we will apply the formula

Applying we have

Hence the answer is 125 : 1, the first option

The area of the quadrilateral is 48 in² and the perimeter of the quadrilateral is 34 inches.

The area of a rectangle is defined as the product of the length and width.

Area of the quadrilateral = 2 × area of triangle + area of a rectangle

Area of the quadrilateral = 2 × height × base + length × width

Area of the quadrilateral = 2 × 1/4 ft × 4 in + 8 in × 1/4 ft

Area of the quadrilateral = 2 × 1/4 × 12 in × 4 in + 8 in × 1/4 × 12 in

Area of the quadrilateral = 24 in² +  24 in²

Area of the quadrilateral = 48 in²

The perimeter of the quadrilateral = 5 + 8 + 5 + 16

The perimeter of the quadrilateral = 34 inches

Hence, the area of the quadrilateral is 48 in² and the perimeter of the quadrilateral is 34 inches.

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Answer:

89.75%

Step-by-step explanation:

Add up all the days, and you'll get 8.975 divided this by 10 and you get .8975 Proceed to multiply this by 100 to get a percentage and the answer 89.75% is received.

At 1.03 miles Debbie is far from reaching her goal.

Given that, Debbie’s goal is to run 10 miles each week.

While adding decimals, we need to remember some rules that would be helpful and make the addition easier.

Now, 1 3/4 can be written as 1.75 and 7/8 = 0.875

Total distance Debbie’s run from Monday to Friday = 2.25+2+1.75+0.875+2.1

=8.975

So, the remaining distance = 10-8.975= 1.025

≈1.03 miles

Therefore, at 1.03 miles Debbie is far from reaching her goal.

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Answer:

10^35=6

Step-by-step explanation:

All you need to remember is the picture above and you could do it.

Answer:

The slope is undefined.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-7-1)/(-4-(-4))

m=-8/(-4+4)

m=-8/0

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The largest angle of the triangle is ∠C = 66°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Now , the measure of ∠A = measure of ∠B = x

And , the measure of ∠C = measure of ∠A + 9°

Substituting the values in the equation , we get

x + x + ( x + 9 ) = 180

On simplifying the equation , we get

3x + 9 = 180

Subtracting 9 on both sides of the equation , we get

3x = 171

Divide by 3 on both sides of the equation , we get

x = 57°

So , the measure of ∠A = 57°

Now , the measure of ∠C = 57 + 9 = 66°

Hence , the measure of ∠C of triangle is 66°

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Answer:

$20.7

Step-by-step explanation:

The simplified solution of the linear equation is determined as -18v - 5t = 4.

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

The given equation is a linear equation;

6(-3v+1)=5(2+t)

The solution to the given linear equation is calculated as follows;

6(-3v + 1) = 5(2 + t)

open the brackets by multiplying with the coefficients

-18v + 6 = 10 + 5t

collect similar terms together

-18v - 5t = 10 - 6

-18v - 5t = 4

Thus, the simplified solution of the linear equation is determined as -18v - 5t = 4.

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Rule

The scale factor would be 4

The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

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Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

We have,

To determine the maximum number of miles Chenelle can travel without exceeding her spending limit of $300, we need to subtract the flat rate from her budget and divide the remaining amount by the cost per mile.

So,

Subtract the flat rate from Chenelle's budget:

Budget after subtracting the flat rate.

= $300 - $19.95

= $280.05

Divide the remaining budget by the cost per mile to find the maximum number of miles:

Maximum miles = Budget after subtracting the flat rate / Cost per mile

= $280.05 / $1.75

Using division.

Maximum miles = 160.028571

Therefore,

Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

To find the equation of a line passing through two points, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.

Given points:

Point 1: (1, 0)

Point 2: (3, 6)

Step 1: Calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates:

m = (6 - 0) / (3 - 1)

m = 6 / 2

m = 3

Step 2: Substitute one of the given points and the slope into the equation y = mx + b to find the y-intercept (b).

Using Point 1 (1, 0):

0 = 3(1) + b

0 = 3 + b

b = -3

Step 3: Write the equation of the line using the slope (m) and the y-intercept (b):

y = 3x - 3

Therefore, the equation of the line that passes through the points (1, 0) and (3, 6) is y = 3x - 3.

This equation represents a line with a slope of 3, indicating that for every increase of 1 unit in the x-coordinate, the y-coordinate increases by 3 units. The y-intercept of -3 means that the line crosses the y-axis at the point (0, -3). By substituting any x-value into the equation, we can determine the corresponding y-value on the line.

Hence, the equation of the line passing through (1, 0) and (3, 6) is y = 3x - 3.

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\(w=\sqrt{6},\sqrt{-6}\)

What is modulus ?

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the output is always favourable. The equation is y = |x|.

Given:

\(w|w|=6\\w(-w)=6\)  

or

\(w(w)=6\)

solving both one by one,

\(w(-w)=6\\-w^{2} =6\\w=\sqrt{-6}\)

and,

\(w(w)=6\\w^{2} =6\\w=\sqrt{6}\)

\(w=\sqrt{6},\sqrt{-6}\)

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Answer: B: 20

Step-by-step explanation: We can take 40% as a fraction to make it 4/10, simplifying gives 2/5. 2/5 of 50 is 20!

Hope this Helps!

For the value the functions F(x)=G(x) is here no solution.

In mathematics, function is an expression that defines a relationship between one independent variable and another dependent variable.

Given that F(x)= abs(3x+2)-6 =| 3x+2|-6

                 G(x)= 3x-5

for F(x)=G(x)

  |3x+2|-6=3x-5

  3x+2-6=3x-5

    3x-4=3x-5

Hence no solution.

The graph is given below.

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For the value the functions F(x)=G(x) is here no solution.

In mathematics, function is an expression that defines a relationship between one independent variable and another dependent variable.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

This means that a function f will map an object x to exactly one other object f if the object x is present in the set of inputs (referred to as the domain) (x) among the range of potential outcomes (called the codomain).

Given that F(x)= abs(3x+2)-6 =| 3x+2|-6

                G(x)= 3x-5

for F(x)=G(x)

 |3x+2|-6=3x-5

 3x+2-6=3x-5

   3x-4=3x-5

Hence no solution.

The graph is given below.

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How to solve cubic polynomials?

The easiest way is

Answer:

.......................

b (-3,-4)

Answer:

37

Step-by-step explanation:

Answer:

Height in w week = 12 + 2w

Step-by-step explanation:

Given:

Height of plant = 12 cm

Rate of plant growth = 2 cm per week

Find:

Equation

Computation:

Height in w week = Height of plant + (Rate of plant growth)(Number of week)

Height in w week = 12 + (2)(w)

Height in w week = 12 + 2w

The sequence of transformations involved is B) translation by 2 units to the right and followed by a B) reflection across the y-axis.

The sequence of transformations involved:

From all the information given, it is discovered that the sequence of transformations involved in transforming ABC to A'B'C' is translation and reflection.

Thus, from the graph it is clear that the sequence of transformations involved is B) translation by 2 units to the right and followed by a B) reflection across the y-axis.

Complete question is;

ABC goes through a sequence of transformations to form A’B’C’. The sequence of transformations involved is a:

A) rotation 180 degrees counterclockwise about the origin

B) translation 2 units to the right

C) translation 4 units to the left

D) reflection across the line y=x

followed by a:

A) reflection across the x-axis

B) reflection across the y-axis

C) rotation 90 degrees clockwise about the origin

D) translation 4 units to the right

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The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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The required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.

Given that,
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.

Number of days =  1       2     3      4      5       6            Total = 6
                              1.72  1.8    1.86 1.88  1.74   1.86                  

The average of the values is the ratio of the total sum of values to the number of values.

Since the mean of the heights of the tides,
= sum of heights / number of heights observation
=  (1.7 + 1.8 + 1.86 + 1.88 + 1.74 + 1.86)/6
= 10.86/6
= 1.81 meters

Thus, the required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.

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Answer:

  35.98

Step-by-step explanation:

Fill in the numbers and do the arithmetic.

  y = a + bx . . . . . . a=4.95, b=0.29, x=107

  y = 4.95 + 0.29(107) = 35.98

The predicted price is 35.98.

The length of the diagonal of the box is approximately 31 units.

Diagonal, d, = √(length² + width² + height²)

Given:

RV=29

RS = 21

RT= 24

Thus:

length of the box = ST = ?

Use Pythagorean Theorem to find ST:

ST = √(RT² - RS²)

Substitute

ST = √(24² - 21²)

ST = 12

Height of the box = SV = ?

Use Pythagorean Theorem to find SV:

SV = √(RV² - RS²)

Substitute

SV = √(29² - 21²)

SV = 20

Find the diagonal of the box, RU:

RU = √(ST² + RS² + SV²)

Substitute

RU = √(12² + 21² + 20²)

RU = 31 units.

Therefore, the length of the diagonal of the box is approximately 31 units.

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Answer:

D. 135 I think

The true statements are:

A circle is a closed, two-dimensional shape where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the middle.

To identify the true statements, we can first rewrite the given equation of the circle in standard form:

x² - 2x + y² = 8

Completing the square, we get:

(x - 1)² + y² = 9

Now we can identify the true statements:

Therefore, the true statements are:

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