If you look at these six numbers, you can see they range from 98 all the way to 642. Would the best interval to use for this group be 10 or 100?

the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,

In the given question,

Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.

From the problem, we know that:

The first mechanic worked for 20 hours, so he charged 20x dollars.

The second mechanic worked for 15 hours, so he charged 15y dollars.

Together, they charged a total of $2600, so we have:

20x + 15y = 2600

The sum of the two rates was $155 per hour, so we have:

x + y = 155

We can use these two equations to solve for x and y. First, we can rewrite the second equation as:

y = 155 - x

Then, we can substitute this expression for y into the first equation:

20x + 15(155 - x) = 2600

Simplifying and solving for x, we get:

20x + 2325 - 15x = 2600

5x = 275

x = 55

Now that we know x, we can use the second equation to find y:

y = 155 - x = 155 - 55 = 100

Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.

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Answer: 25/546 chance

Step-by-step explanation:

total is 15 chocolates.

Five are milk, so chance of getting milk is 1/3. second is dark, so 5/14 chance. Then white, so 5/13 chance

1/3*5/14*5/13=25/546

The decimal - 2. 97 is the solution to the subtraction problem of D.  - 6. 1  - ( - 3. 13 ).

When subtracting decimal numbers, the effective method is to align their decimal points and begin removing each corresponding digit from one another. You may extend any decimals with fewer digits by appending zeros on the right-hand side as required for parity.

= - 6. 1  - ( -3. 13 )

= - 6. 1  + 3. 13

= - 2. 97

The decimal 2.97 is the solution to the subtraction problem - 6. 61 - (- 3. 13).

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a) We are given that f(x) = x^3 - 10x^2 + 19x + 30 and x - 6 is a factor of f(x). Using long division or synthetic division, we can divide f(x) by x - 6 to get the other factor(s):

 6 │ x^3 - 10x^2 + 19x + 30

     x^3 - 6x^2

     -------------

          -4x^2 + 19x

          -(-4x^2 + 24x)

          ---------------

                     5x + 30

                     5x - 30

                     -------

                            0

Therefore, we can write:

f(x) = (x - 6)(x^2 - 4x + 5)

The quadratic factor x^2 - 4x + 5 cannot be factored further using real numbers.

b) We are given that f(x) = x^3 + 6x^2 + 5x - 12 and x + 4 is a factor of f(x). Using long division or synthetic division, we can divide f(x) by x + 4 to get the other factor(s):

-4 │ x^3 + 6x^2 + 5x - 12

     -x^3 - 4x^2

     --------------

              2x^2 + 5x

              2x^2 + 8x

              ------------

                     -3x - 12

                     -3x - 12

                     --------

                            0

Therefore, we can write:

f(x) = (x + 4)(x^2 + 2x - 3)

The quadratic factor x^2 + 2x - 3 can be factored further using the product-sum method:

x^2 + 2x - 3 = (x + 3)(x - 1)

Therefore, we have:

f(x) = (x + 4)(x + 3)(x - 1)

Answer:

x<=-2.75

Step-by-step explanation:

Answer:

option c) x=-6

Step-by-step explanation:

-15x = 90

= x = 90/-15

= x = (-6)

If local city government wants to display the ages of the city citizen, It would be better to organize the data using a histogram.

A histogram is a graph that shows the distribution of a set of continuous data. The ages of city citizens can be considered as continuous data, as there are many possible values for age within a certain range.

A dot plot, on the other hand, is a graph that shows the distribution of a set of discrete data. Discrete data are values that can only take on specific, isolated values, like shoe sizes or the number of siblings a person has.

A histogram would be more effective for displaying the distribution of the ages of city citizens because it can show the range of ages in a more continuous manner, and provide a more precise representation of the frequency of the different age groups.

A dot plot, on the other hand, would be less effective, as it could be difficult to represent every age value as a single dot, and the resulting graph may not provide a clear indication of the distribution of ages.

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The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. Expressions can be simple or complex and are used to represent mathematical relationships and operations.

To find -4 - 2 1/2 expression on the number line by drawing an arrow, we need to start at -4 and then move left by 2 1/2 units.

To do this, we can draw an arrow starting at -4 and then mark off 2 1/2 units to the left. One way to represent 2 1/2 units is to divide the space between -4 and -5 into two equal parts, and then mark off one of those parts.

The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

Here's an example of what the arrow would look like:

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Step-by-step explanation:

Compounding formula

FV = PV ( 1 + i )^n      FV = Future value (4000)       PV = present value

                      i = decimal interest per PERIOD = .09/365

                      n = periods = 2 1/4 yrs * 365 days/yr = 821.25 periods

4000 = PV ( 1 + .09/365)^821.25

Solve for PV = $ 3266.83

Answer:

We can calculate the slope by taking 2 points on the line. I took A(4,4) and B(-4,0), so we get m=1/2.

2. y-intercept is the point where a line crosses the y-axis which is (0,2)

3. We have f(x)=1/2x +b

By taking a particular point on the line,we get :

2=1/2(0)+b

==》 b=2

So the slope intercept form is

y=1/2x+2

A. Area of the rectangle, in standard form is: 14x² + 19x - 3

B. The degree of a polynomial is: 4. It has 4 terms (4x², 3y, -6x^4y, and 4.); C ALWAYS result in another polynomial.

A polynomial is a mathematical expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication of non-negative integer exponents.

Part A:

Area of the rectangle = (7x - 1)(2x + 3) = 7x(2x + 3) -1(2x + 3)

= 14x² + 21x - 2x - 3

Combine like terms:

Area of the rectangle = 14x² + 19x - 3 (standard form)

Part B: Given the expression, 4x² + 3y - 6x^4y + 4,

The degree of a polynomial is the highest exponent of its variable.

Therefore, the degree is 4.

It has 4 terms, which are: 4x², 3y, -6x^4y, and 4.

Part C: When two polynomials are subtracted, multiplied, or added, it will ALWAYS result in another polynomial.

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Answer: x<4/3

Step-by-step explanation: 17-5=12/9

Answer:

If point A (-4,-5) of the trapezoid is reflected across the y-axis, the x-coordinate will change sign while the y-coordinate remains the same. This gives us the point A' (4, -5).

Next, if we shift the point A' by -6 units in the x-direction and 7 units in the y-direction, we get the new point A":

A" = (4 - 6, -5 + 7) = (-2, 2)

Therefore, the coordinates of point A after it is reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction are (-2, 2).

Step-by-step explanation:

Answer:

(-2, 2)

Step-by-step explanation:

I did the test

Hope this helps :)

The value of the length of line segment AB, in feet, that corresponds to the width of the television is,

⇒ 12 feet

We have to given that;

A new curved projection system for a small media room states the optimal viewing angle is 74° (m/ACB = 74°) when you sit 10 feet from the center of the TV (length of CD = 10 ft). The depth of the curved screen is 2 feet (length of DE = 2 ft).

Now, We can formulate;

CE = 10 - 2 = 8 feet

∠ACD = 74/2 = 37°

Hence, We can formulate;

tan 37° = AE / CE

0.75 = AE / 8

AE = 0.75 × 8

AE = 6

Hence, The value of the length of line segment AB, in feet, that corresponds to the width of the television is,

⇒ AB = 6 x 2

⇒ AB = 12 feet

Thus, The value of the length of line segment AB, in feet, that corresponds to the width of the television is,

⇒ 12 feet

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The zeros of the quadratic profit function are explained as:

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

The quadratic function is given as:

f(x) = −x² + 50x − 264

The general form of expression of a quadratic function is:

f(x) = ax² + bx + c

The quadratic formula to find the zeros is:

x = [-b ± √(b² - 4ac)]/2a

Thus, we have the zeros as:

x = [-50 ± √((-50)² - 4(-1 * -264))]/2(-1)

x = 6 and x = 44

This represents number of monthly memberships where no profit is made.

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Answer:

(10, -10)

Step-by-step explanation:

This are the farest the graph can go unless you want (100,-100)

Change the values from negative to positive and positive to negative to get the most farest results

Answer: D

Step-by-step explanation:

I graphed so you can see.  Count how far each are away.

(5,8) is 12 away

(-7,-5) is 13 away

So you answer is D

Or

You can also think of it as, for, (5, 8)  only the x changed so you only moved in the x direction.  subtract the numbers 5-(-7)=12

For (-7,-5) you only moved in the y direction, so subtract those 8-(-5)=13

Answer:

i think its b sorry if  it's wrong

Step-by-step explanation:

Olivia could have used a combination of a rotation and a translation to move ABCDE onto A"B"C"D"E".

Angelica's transformed figure will not match A"B"C"D"E" because reflecting ABCDE over the y-axis will change the order of the letters in the figure.

No, Michael is not correct.

Translating ABCDE diagonally by 8 units up and 10 units right will move each point in ABCDE the same distance horizontally and vertically, which will change the shape of the figure.

In order to match A"B"C"D"E", the transformation must preserve the order of the letters and the angles between the segments.

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Step-by-step explanation:

we just need to find out how many percentage of the daily goal each day, so let's assume that $50 is 100% of the daily goal.

Answer:

[tex]6\sqrt{2}+3\sqrt{10}[/tex]

Step-by-step explanation:

Use the Distributive Property. Remember that you can multiply the numbers under a square root whether or not they're the same. But you can ONLY add square roots when the square root part is the same.

[tex]\sqrt{3}(2\sqrt{6}+\sqrt{30})\\= \sqrt{3}(2\sqrt{6})+\sqrt{3}(\sqrt{30})\\=2\sqrt{18}+\sqrt{90}[/tex]

Simplify each square root part:

[tex]2\sqrt{18}+\sqrt{90}\\=2(3\sqrt{2})+3\sqrt{10}\\=6\sqrt{2}+3\sqrt{10}[/tex]

Since the square root parts are different, you cannot simplify any further.

Answer:

No solution.

Step-by-step explanation:

To solve this problem, all you have to do is graph the lines and see where they intersect.

This is what you would do to solve a normal problem. However, these lines are parallel this means that the solution to these lines is no soultion

Answer:

Area = ½* height(a+b)

Where;

a=4units

b=8units

h=6units

Therefore Area= ½*6(4+8)

= ½*6*12

=36sq.un

Answer:

24sq²

Step-by-step explanation:

Area = ( b1 + b2) x h

          ---------------------

                     2

Area =   (8 + 4) x 6

          ---------------------

                     2

Area =     (12) x 6

          ---------------------

                     2

A = 72/2

A = 36

A = 1/2 * b * h

A = (1/2) * 4 * 6

A = (1/2) * 24

A = 12

36 - 12 = 24sq²

I hope this helps!

Alan and his mom will each have completed 10 rows after 3 hours.

An expression is a combination of numbers, variables, and/or operations (such as addition, subtraction, multiplication, division, exponents, and roots) that are grouped together to represent a value.

Let x be the number of hours it takes for Alan and his mom to have planted the same number of rows.

Alan will have planted 4 + 2x rows of carrots, and his mom will have planted 7 + x rows of tomatoes.

Setting these two expressions equal to each other gives:

4 + 2x = 7 + x

Solving for x, we get:

x = 3

Thus, after 3 hours, Alan will have planted:

4 + 2(3) = 10 rows of carrots

And his mom will have planted:

7 + (3) = 10 rows of tomatoes

Therefore, they will each have completed 10 rows of vegetables after 3 hours.

To graph these equations, we can plot them on a coordinate plane, where the x-axis represents the number of hours and the y-axis represents the number of rows planted.

Alan's equation is y = 2x + 4, and his mom's equation is y = x + 7.

The graph of these two equations intersect at the point (3, 10), which represents the moment when they have each planted 10 rows.

Therefore, Alan and his mom will each have completed 10 rows after 3 hours

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If we express the 9!  we have 9×8×7×6×5×4×3×2×1.

A factorial operation is described as  a mathematical formula represented by an exclamation mark. (!). This operation is carried out when a whole number is being multiplied by its successive smaller numbers until it gets to 1.

for Example

n! = n(n-1)(n-2)........(1)

From the question, it is are asked to evaluate 9!

9! = 9×8×7×6×5×4×3×2×1

Hence, when 9! is evaluated, we get 9×8×7×6×5×4×3×2×1.

#Probable complete question;

Use the factorial operation to evaluate 9!.

8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

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The probability that the team wins the debate is 0.6475

P(win) = P(win | S)P(S) + P(win | J)P(J) + P(win | R)P(R)

= (0.25)(0.2) + (0.6)(0.35) + (0.85)(0.45)

= 0.6475

Therefore, the probability that the team wins the debate is 0.6475.

In order to simulate the probability that a Sophomore is never selected to give the closing argument in the next 5 debates, we can use the following steps:

Create a table of random digits with enough rows and columns to simulate the 5 debates. Each row represents a debate and each column represents a team member.

Assign the digits 0, 1, and 2 to represent the events that a sophomore, junior, and senior gives the closing argument, respectively.

Starting from the first row and first column, read the digits from the table and determine which team member gives the closing argument for the first debate.

If a sophomore is selected, record a 0 for that debate. Otherwise, record a 1.

Repeat steps 3 and 4 for the remaining debates, filling in the table as you go.

Calculate the proportion of simulations where a Sophomore is never selected to give the closing argument in the next 5 debates.

Repeat steps 1-6 many times (e.g., 10,000 times) to get a more accurate estimate of the probability.

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