Yesterday Ali had n Baseball cards. Today he gave away 6. Using n, Write an expression for the number of cards Ali has left

Answer:

The total volume of fluid ounces of water she have is;

Explanation:

Given that she has 4 containers that are 2 1/2 quarts each

Recall that to convert quarts to ounce;

Also, she has 3 containers that are 4.25 cups each;

To convert cups to ounces;

So;

The total volume of fluid ounces of water she have is;

substituting the values;

Therefore, the total volume of fluid ounces of water she have is;

Solution

We have the original function defined as:

And we want to obtain the new red line so then we need to check how many units down and right the function moves:

And we have 3 units to the right and 2 units down then the answer is:

Then the final answer is:

h(x) = -sqrt(x-3) -2

The given equation-

After three seconds, we evaluate for t = 3.

Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. To get the decimal of the form a.bcd, we will count the digits that are there after the decimal point; then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.

Given that Jason's Work:

0.105

Jason provided the work when asked to convert 0.105 to its simplest fraction form which could be;

0.105 = 105/1000

= 21/200

Hence, Jason provided the work when asked to convert 0.105 to its simplest fraction form which is; 21/200

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We can calculate the percent of change by means of the following formula:

Where x2 is the new value and x1 is the original value.

In this case, we go from 60 to 24, then the original value (x1) was 60 and the new value (x2) is 24, by replacing these values into the above equation, we get:

Then, the percent of change equals -60%

She landed on the number 25 on the hundred chart.

What is an 100 chart?

It consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows.

We are given that she was on 57th number

Then she moved down 3 rows

Each row contains 10 elements Hence we subtract 30 for 3 rows

57-30=27

Then also she took 2 steps back

Hence we again subtract 2 from 27

We get 27-2=25

Hence she is at 25th number

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Given two sides of a triangle, x, and z, such that

then the third side y must satisfy the following condition

x =13, and z = 17

Then, the third side y

lies in

17-13 < x < 17 +13

4 < x < 30

Hence the largest possible whole number of the third side is 29

The sampling distribution can be approximated to follow the normal distribution if the sample size is large, and the values of 'np' and 'n(1-p)' are much greater than 10.

Consider option A,

Consider option B,

Consider option C,

Consider option D,

It is observed that only the values in option D, give that 'np' and 'n(1-p)' are greater than 10. Therefore, option D will be the correct choice.

The general rule of P(A or B) is given by the formula

Given:

The number of girls =10 and the total number of students =30.

The percentage of the total amount of girls is

Hence the percentage of the total amount of girls is 33.33 %.

Explanation

We are required to determine the coterminal, quadrant and reference angle of 707°.

This can be achieved as:

Therefore, the reference angle can be gotten as:

Hence, the reference angle is 13°.

The angle lies in the fourth quadrant.

The cotermi

Answer:

Solving the expression gives;

Explanation:

Given the expression;

Applying the rule of BODMAS or PEMDAS;

multiplication comes first;

Then we can do the addition;

Therefore, solving the expression gives;

We have to graph this piecewise function.

It will be two horizontal lines that change when x = -1: to the left it will be y = 5, as x ≤ 1, and to the right, it will be y = -3.

We can see it graphed as:

b) The range is the set of values that f(x) takes for the domain for which it is defined.

We can see that f(x) only takes two values: y = -3 and y = 5, so the set {-3,5} is the range of f(x).

Answer:

a) Graph

b) Range = {-3, 5}

The areas and volumes are given as follows:

a) Area of the four sides to be painted: 2448 m².

b) Area to be covered with shingles: 1140 m².

c) Volume of concrete needed to pour a floor 16 cm deep: 174.72 m³.

d) Total surface area: 5878.4 m².

The sides painted are divided as follows:

Hence the total area to be painted is found as follows:

Total area = 2 x 26 x 18 + 2 x 42 x 18 = 2448 m².

(Area rectangle = base x height)

This part of the problem seems incomplete, however the answer is correct.

The volume is given by:

Volume = base area x height.

Hence:

Hence the volume is given by:

V = 26 x 42 x 0.16 = 174.72 m³.

The base is a rectangular prism of dimensions 26 m, 42 m and 18m, hence:

Surface area base = 2 x (26 x 42 + 26 x 18 + 42 x 18) = 4632 m².

The top is composed by:

Hence:

Surface area top = 2 x 13.6 x 42 + 2 x 0.5 x 26 x 4 = 1246.4 m².

Then the total surface area is:

Total surface area = 4632 + 1246.4 = 5878.4 m².

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The number of minutes when they would both paint the same strip of wood is 8 minutes.

The linear equation that represents the total strip of wood that is painted by Henry is: amount of strips already painted + (strips painted per minute x minute)

14 + (3½x m)

14 + 3½m

The linear equation that represents the total strip of wood that is painted by Sandy is: amount of strips already painted + (strips painted per minute x minute)

10 + (4 x m)

10 + 4m

When both people paint the same strip of wood, the two above equations would be equal.

10 + 4m  = 14 + 14 +3½m

4m - 3½m = 14 - 10

0.5m = 4

m = 4 / 0,5 = 8

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If a figure has a vertex, (x, y) and it is rotated 180 degrees counterclockwise, the corresponding vertex of the new image would have a coordinate of (- x, - y)

Looking at the given figure, we would compare the corresponding coordinates of a given vertex. Looking at vertex A,

For the original figure, the coordinate is (1, 3)

For the ratated figure, the coordinate of A' is (- 1, - 3)

This corresponds to what was we stated earlier

Thus, it was rotated 180 degrees in the counterclockwise direction

To solve for the equation of the line parallel :

For parallel line equation:

Slope-intercept form: y=mx+b, where m is the slope and b is the y-intercept

First let's find the slope of the line.

To find the slope using two points, divide the difference of the y-coordinates by the difference of the x-coordinates.

Slope= 5

The y-intercept is (0, b). The equation passes through the origin, so the y-intercept is 0.

Hence the

Postulates and Theorems of Parallel Lines

First, we need to know what type of angles are <3 and <7. Following the definition:

If two lines are crossed by another line, the angles in matching corners are called Corresponding Angles.

Angles 3 and 7 are corresponding angles and they are told to be congruent.

Now we apply the postulate that reads:

The Converse of the Corresponding Angles Postulate. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

The postulate that can be used to prove that the lines are parallel is The Converse of the Corresponding Angles Postulate

As per given by the question,

There are given that a graph.

Now,

1. The given graph is cosine graph.

2. The aplitute of the given graph is,

From the graph, it is lie between -2 to 2.

So,

The amplitude of the given graph is 2.

Now,

3. The equation of the midline is,

Now,

4.The period of the fumction is,

Now,

The equation of the function.

First the general form of cosine graph function is,

Then,

Now,

Where, D is vertical shift.

Hence, the equation of the function is,

Solution;

Given the results:

From the above data:

A) The low-end value is

B) The high end value is

C) Does this data set have outlier?

D) Outlier:

We are asked to find the area of the given circle.

Recall that the area of a circle is given by

Where π is a constant and r is the radius of the circle.

From the figure, we see that the diameter is 22 km

Recall that the radius is half of the diameter.

So, the radius of the circle is

So, the area of the circle is

Therefore, the area of the circle is 380.1 square km (rounded to the nearest tenth)

To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:

As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:

As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4

Our final answer will be x = -4

b)

Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph

As we can see it touches the graphic at y = 2, hence, f(0) = 2

To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:

As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:

As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4

Our final answer will be x = -4

b)

Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph

As we can see it touches the graphic at y = 2, hence, f(0) = 2

Explanation

Step 1

Domain:The domain of a function is the complete set of possible values of the independent variable, by the graph is it a continuous line, so the domain is

Step 2

Range:The range is the set of all second elements of ordered pairs (y-coordinates), by the graph is it a continuous line, so the range is

Step 3

x-intercept

it is when y= 0 , by the graph :

Step 4

y-intercept

it is when x= 0 m by the graph:

Step 5

rate of change

Let

P1(-2,0) P2(0,4)

rate of change:2

1) In this problem, we need to find the constant of proportionality assuming these triangles are similar. So let's divide each corresponding leg:

2) So, based on that constant of proportionality (k) we can find the missing leg.

Note that since the triangle on the top is larger than the one on the bottom, we can tell that x must be larger than 36.

Answer:

Step by step explanation:

We can solve this situation by the theorem of the angle formed outside of a circle by intersection:

*For two tangents:

Then, if m

[tex]\begin{gathered} 65=\frac{1}{2}((360-mXY)-mXY) \\ 65=\frac{1}{2}(360-\text{mXY-mXY)} \\ 65=\frac{1}{2}(360-2\text{mXY)} \\ 65=180-\text{mXY} \\ \text{mXY}=180-65 \\ \text{mXY}=115 \end{gathered}[/tex]

To find the slope of the line we have to use this equation:

Now we have to replace two coordiantes in the line, so I was able to see the coordinates: (0,40) and (20,50), sothe equation become:

and we simplify so:

So the slope is 1/2

Answer

Rs. 3125 is equivalent to 50 units of the foreign currency.

Step-by-step Explanation

The exchange rate of the foreign currency in Indian Rupee is Rs. 62.50

This means that

1 unit of that foreign currency = Rs. 62.50

Or better written as

Rs. 62.50 = 1 unit of the foreign currency

So, we are then told to find how much Rs. 3125 is in the foreign currency

Let Rs. 3125 be equal to x units of the foreign currency

Rs. 62.50 = 1 unit of the foreign currency

Rs. 3125 = x units of the foreign currency

A simple mathematics relation obtained by cross multiplying will give us the value of x

After cross multiplying

62.50 × x = 3125 × 1

62.50x = 3125

Divide both sides by 62.50

(62.50x/62.50) = (3125/62.50)

x = 50

Therefore, Rs. 3125 is equivalent to 50 units of the foreign currency.

Hope this Helps!!!

The completion of the statements about the number of students in Mr. Baker's class is as follows:

A prime number is a number divisible by itself and 1 only.

When a prime number is divided by another number except by itself and 1, there is always a remainder in the quotient.

Some examples of the prime numbers in Mr. Baker's class include 19, 23, 29, 31, or 37 students.

Thus, these numbers of students cannot be divided by another number without a remainder because they are prime numbers.

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1. The number of students in his class must be a --- number.

2. The quotient from the division of the students into equal-sized groups is .... because there must be a .....

ANSWER

EXPLANATION

The graphical solution to the given equation is obtained at the points where the two graphs of the two functions intersect each other on the coordinate plane.

To graph f(x), we simply draw a straight horizontal line at the point y = -5.

To graph g(x), we have to find coordinate points by substituting values of x into the function and obtaining values for g(x).

Let us find the value of g(x) when x = -3, -1, 1:

Now, we have three points to plot the graph with: (-3, -5), (-1, -9), (1, -5)

Let us now plot the graphs of the functions:

Therefore, the solutions to the equation f(x) = g(x) are:

The height of the mountain is 2936.39 feet.

Given,

In the question:

The angle of elevation to the top of the mountain is 25°.

To find the height of the mountain, we can draw triangles as in the image attached.

Now, According to the question:

Let's call the height of the mountain 'h', and the distance from the first point (25degrees) to the mountain 'x'.

Then, we can use the tangent relation of the angles:

tan(29) = h/x

tan(25) = h/(x+1000)

tan(25) is equal to 0.4663, and tan(29) is equal to 0.5543, so:

h/x = 0.5543 -> x = h/0.5543

using this value of x in the second equation:

h/(x+1000) = 0.6009

h/(h/0.5543 + 1000) = 0.4663

h = 0.4663 * (h/0.5543 + 1000)

h = 0.8412h + 466.3

0.1588h = 466.3

h = 466.3 / 0.1588 = 2936.39 feet

Hence, the height of the mountain is 2936.39 feet.

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