An item costs $430 before tax, and the sales tax is $8.60.
Find the sales tax rate. Write your answer as a percentage.

Answer:

44 square centimetres.

Explanation:

The shape consists of two rectangles and one triangle with the following dimensions:

• A rectangle (Rectangle 1) with dimensions of 4cm by 2cm.

• A rectangle (Rectangle 2) with dimensions 6cm by 4cm.

• A triangle with base 6cm and height of 4cm.

Thus, the area of the figure made will be:

The area of the figure is 44 square centimetres.

Answer: True

Step-by-step explanation:

If you look both triangles have the same angles, so that means that they are congruent.

Answer:

1.) y = -3/4x +2

2.) y = x - 4

3.) y = 2/3x - 4

4.) y = -1/2x + 5

5.) y = 8/3x +5

Step-by-step explanation:

1.)

Parallel means that the slopes will be the same.

So, m = -3/4

To find the equation, we must first use point-slope form.

[tex]y-y_{1} =m(x-x_{1} )[/tex]

y-(-1) = -3/4(x-4)

Now we clean this up and solve for y to get the answer in slope intercept form.

y+1= -3/4x + 3   =>    y = -3/4x +2

2.)

Perpendicular means that the slope is the negative reciprocal of the slope of the first line.

So, m = 1 as the negative reciprocal of -1 is +1.

Once again, we use point-slope form and the clean it up and solve for y to get the answer in slope-intercept form.

y - (-3) = 1(x-1)       =>   y + 3 = x-1    =>   y = x - 4

3.)

Similar to the previous one, but with slope m = 2/3 (negative reciprocal)

y - (-4) = 2/3 (x - 0)     =>   y + 4 = 2/3x     =>    y = 2/3x - 4

4.)

Similar to the previous one, but with slope m = -1/2 (negative reciprocal)

y - 4 = -1/2(x-2)    =>   y - 4 = -1/2x +1    =>   y = -1/2x + 5

5.)

Similar to the previous one, but with slope m = 8/3 (negative reciprocal)

y - (-3) = 8/3(x - (-3))   =>   y + 3 = 8/3x +8     => y = 8/3x +5

Answer

• a) 30.9

• b) 76

Explanation

Given

• Homework: 25%

• Project: 10% (each)

• Final exam: 45%

A student has:

Part A

• Homework: 86

• First project: 94

Part B

• Second project: 71

• Third project: 78

• Total grade: 80

Procedure

• a)

To know the student's grade at the point where he has an 86 homework average and 94 on the first project. We have to multiply the ponderation of each category times the grade to find the final grade (TG), meaning:

Simplifying:

• b)

Following the same procedure, now we have to multiply the ponderations of the new grades, as follows:

Next, as we are asked to find the calculations of the grade of the exam to get a final grade of 80, we have to consider the latter and the ponderation for the exam:

where x is the grade of the exam.

Solving for x:

The standard error for the sample mean exists

[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].

Let the value of mean be [tex]$P(\bar{X} < 0.95)$$[/tex]

Normal Distribution, [tex]$\mu=1, \sigma=0.1, n=12$[/tex]

[tex]$P(\bar{X} < 0.95)=$[/tex] Area to the left of 0.95

we convert this to standard normal using

[tex]$z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}$[/tex]

[tex]$z=\frac{0.95-(1)}{0.1 / \sqrt{12}} \approx-1.732051 \approx-1.73$[/tex]

[tex]$P(\bar{X}[/tex] < 0.95) = P(Z < -1.73) = 0.0418 (from z-table)

P(Z < -1.73); in a z-table having area to the left of z, locate -1.7 in the left most column. Move across the row to the right under column 0.03 and get value 0.0418.

[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex]

Therefore, the standard error for the sample mean exists

[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].

The complete question is;

What is the probability that the sample mean will be below 0.95 centimeters?

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken.

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According to the given data we have the following:

measure of three angels of a triangle are 43, 70, x

x?

The sum of the measures of the three angles of the triangle is 180

Therefore, to calculate the value of x we would have to make the following calculation:

43 + 70 + x = 180

113+ x=180

x=180-113

x=67

Therefore, the value of the angle of x would be 67

Given the initial value, w1, and the final value, w2, the percent decrease can be calculated as:

The initial value is 247 and the final one is 221, so:

So, the percent decrease is approximately 10.53%.

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

What variable expression should you subtract from both sides of the equation so that you are left with no variables on the right-hand side?

The variable expression is: subtract 5x from both sides so that you are left with no variables on the right-hand side

CONCLUSION:

The final answer is:

​

If a perpendicular b and b parallel to c, then the value of x = 8

Here b and c are parallel lines

The parallel lines are two lines in the same plane that are at equal distance from each other and that do not intersect at any point

Then a is perpendicular to b

The perpendicular lines are the line that forms the angle of 90 degrees for both angles

Therefore the given angles are 90 degrees

9x+18 = 90

9x = 90-18

9x = 72

x = 72/9

x = 8

Hence, If a perpendicular b and b parallel to c, then the value of x = 8

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The domain of the function of the equation cannot include zero because h(0) is not real.

A scale used to weigh objects is analogous to an equation. When the two pans are filled to the same level with anything, the scale will balance and the weights will be considered to be equal (such as grain).

The equation is given as  [tex]h(x) = \sqrt{2x^2+5x+3}[/tex]

The equation at x=0 given

h(0) = √(0+0-3)

or, h(0) = √(-3) which is an imaginary number

Therefore for the equation the value of x at 0 is undefined.

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The packing carton has a square bottom with measures 18in x 18in and has a volume of V=3ft³

The volume of cubic prims can be calculated by multiplying its width by its length and height:

So the formula to calculate the volume is

If we know the width, length, and volume we can determine the height. First, write the formula for h, that is, divide the volume by the width and height:

The units of the width and length are in inches and the volume is in cubic feet, to determine the height of the box, all units must be the same. To make the calculations easier I will pass the units from inches to feet.

The unit rate between inches and feet is the following:

To express 18 inches in feet you have to multiply them by 1/12

This means that the width and length of the box measure 1.5ft

Now we can determine the height of the box as follows:

w=l=1.5ft

V=3ft³

The height of the box is 3/4ft, if you multiply it by 12 you can express the measure in inches:

The box has a deph of 9 inches.

The relationship between the discriminant of a quadratic polynomial and the number of real roots is that the discriminant let us know the number and type of the solutions.

Basically for a quadratic polynomial ax²+ bx + c = 0,  the  b² - 4ac is the  discriminant.if the discriminant is greater than zero (b²- 4ac > 0), the graph intersects the abscissa twice which means it has two real solutions,  whereas if the discriminant is equal to zero ( b² - 4ac = 0), then the graph intersects once the abscissa which means it has a  single real solution and at last  if less than zero (b² - 4ac < 0), then the graph doesn't at all intersect the abscissa which, it has imaginary solutions.

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Answer:

B. [tex]4*10^6[/tex]

Step-by-step explanation:

All you have to do is divide the first value by the second value to find the ratio between the two numbers.

The equation would look like this:

[tex]\frac{9.2*10^8}{2.3*10^2}[/tex] or [tex]\frac{920000000}{230}[/tex]

Solving this gives you [tex]4 * 10^6[/tex], or 4000000.

You can also figure this out without a calculator. Simply subtract the smaller power from the larger power to get your exponent.

Since this problem has [tex]10^8[/tex] and [tex]10^2[/tex], subtract 2 from 8 to get 6. This will be the exponent in your answer, ruling out answers A and C.

Then, just estimate 9.2/2.3. You can do 9/2 to get 4.5, which is closer to 4. Therefore, D is ruled out, so the answer must be B.

Hope this helps :)

ANSWER

cos(bº) = 4/5

EXPLANATION

When a triangle is dilated, the resulting triangle is similar to the original triangle. Therefore, the interior angles of the dilated triangle are congruent to the interior angles of the original triangle. This means that cos(bº) is the same for both triangles.

Using the relationship between these three trigonometric ratios:

We can find the cosine:

In deductive thinking, you start with a given set of rules and conditions and determine what must be true as a consequence - True

In deductive thinking, conclusions are reached based on premises that are typically taken to be true. A conclusion is based on the concordance of several premises typically presumed to be true in this logical procedure. Top-down logic is another name for deductive thinking. It only makes use of data that is believed to be reliable. It excludes sentiments, feelings, and unsupported assumptions because it is challenging to assess the integrity of this data.

Making logical assumptions and basing a conclusion on them are the foundations of deductive thinking. It enables the individual to combine the information from two or more assertions to arrive at a sound conclusion. If something is presumptively true and a different object is connected to the first presumption, then the original truth must also apply to the second. Therefore, In deductive thinking, if you start with a given set of rules and conditions and determine what must be true as a consequence holds true.

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the given equation is

calculate f(-3) by putting x = -3

now, f(4)

now the final calculation

that is 70 -49 = 21

so the correct answer is 21

2f(-3) - f(4) =​ 21 .

x, x

1.7

Explanation

Step 1

we can see in the graph, that :

the solutions of the equation f(x)=0, are the values where y =0 , it is when the line crosses the x-axis, so the solution of the first blank is

x

Step 2

and, the solution of the inequality

is the set of values wich the graph is above the x-axis

Step 3

now, for the next question, let's check the points where the line crosses the x-axis, and the intervals where the lines is above the x-axis

we can see the solution of f(X)=0 are

Finally, check the interval where the graph is above the x-axis, it is from a to 7, in interval notation

I hope this helps you

Given:-

The mean of 40,50 and 90 is P. If the mean of 40,50,90 and P is Q.

To find:-

The value of Q.

So now the mean of 40,50 and 90 is P. so we get,

So the value of p is 60.

Also we have the mean of 40,50,90 and P is Q. so we get,

So the value of q is 60.

Answer:

B

Step-by-step explanation:

the full domain is

(-∞,-7[ ∪ ]-7,+∞)

This will be simplified with this law of indices

Going further, we can simplify to:

From the table :

Lin worked for 5 hours and earned 90$

LIn worked for 1 hour and earned 18$

Lin worked for 8 hour

so the earning is

Lin worked for 8 hours so the earning is 144$

If lin works for 3 hours then the earning is

So the answer for 3 hours is 54$.

If lin works for 21 hours then the earning is

so the answer for 21 hours is 378$.

We will have that the expression that represents the problem is:

So, at most he will be able to carry 40 crates with him.

1) All of these questions are about evaluating those functions for each input.

9) So, let's check them out evaluating each one.

10)

11)

12)

The dilated function g(x) will be g(x) = x(x + 4)(x + 2). The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2. The graph of the function g(x) is attached.

Scale factor is used to compare 2 quantities, indicating by how much one quantity is greater than the other. It is denoted by K. Mathematically-

K = a/b.

If a coordinate point (x, y) is dilated by a scale factor of [k], then the coordinate point after dilation will be - (kx, ky).

Given is the function -

f(x) = (x+4)(x+2)

[A] -

For dilating the given f(x) by [x] times -

g(x) = [tex]x[/tex] f(x)

g(x) = x(x + 4)(x + 2)

Therefore, the dilated function g(x) will be -

g(x) = x(x + 4)(x + 2)

[B] -

The graph of the function g(x) is attached with the answer.

[C] -

The points where the graph of g(x) touches or cuts the x - axis, will represent the zeroes of the function g(x) = x(x + 4)(x + 2). It can be seen that the points are -

x = 0

x = - 4

x = - 2

The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2.

Therefore,  the dilated function g(x) will be g(x) = x(x + 4)(x + 2). The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2. The graph of the function g(x) is attached.

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Let B be the number of cups of boiling water that we should mix with I cups of ice to get 3 cups of 110°F water.

Therefore, we can set the following equation:

Subtracting B from the first equation we get:

Substituting the above equation in the second one we get:

Simplifying the above result we get:

Subtracting 96 to the above equation we get:

Dividing the above equation by 188 we get:

Substituting B=1.24 at I=3-B we get:

Answer:

To get the antiderivative of the function, we will integrate F(x), as follows:

Now, to get the particular antiderivative, we evaluate the antiderivative for x = 1, and it must be equal to 11. This can be shown as:

Hence, the particular antiderivative is

a. Data values are 13.4, 16.3, 14.2 , 15.4 , 14.2 ,17.5

b. ∑x =  91

c. n = 6

Adding all numbers in the data and then dividing by the number of values is called mean. Median is defined as the middle value when a data set is in such a way that it goes from least to the greatest value. Whereas the number that occurs most often in a data set is mode. Sample size is represented by "n". Whereas, symbol Σ denotes the summation.

For the given mean,

The data values are 3.4, 16.3, 14.2 , 15.4 , 14.2 ,17.5

Summation, ∑x = 3.4+ 16.3+ 14.2 + 15.4 + 14.2 +17.5

                           = 91

n is the number of data that is 6.

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