At 6 AM, the temperature in New Crampton, California was 64℉. By 4 PM, the temperature had risen to 76℉. What was the change in temperature over the 10-hour period?

Answer:

X= -7/5 - 7y/5 - 2z/5

X= 5/9 - 7y/9 - 2z/9

X= -1 + 7y^5z/2

Y= -1 - 5x/7 - 2z/7

Y= 5/7 - 9x/7 - 2z/7

Y= (square root symbol is the line--->) ^5 |4802z^4(x+1)/7z

Z= -7/2 - 5x/2 - 7y/2

Z= 5/2 - 9x/2 - 7y/2

Z= 2/7y^5 + 2x/7y^5

Step-by-step explanation:

I hope this makes sense.

if its solve then we can do it like above

Answer:

28

Step-by-step explanation:

[tex]4(3)^{2}+2(-5)-(-2)=36-10+2= 28[/tex]

Hope this helps

Answer:

[tex]3^{x-6}[/tex]

I cannot make out from the answer choices which correspond to this, the formatting is all gone but this is the answer. Choose the correct option from the original question which has formatting.

See graph for visual proof

Step-by-step explanation:

Translation of a graph on the x-axis by a units means moving the graph left or right by a units

When you translate a function f(x) by a units to the right, the translated function becomes f(x - a)

Original function is f(x) = 3ˣ
When you translate the graph by 6 units to the right, the translated graph is [tex]g(x) = f(x-6) = 3^{x-6}[/tex]

The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.

It should be noted that from the information, tje sophomore class is making blakets for the local animal shelter and the cost to make the blakets can be modeled by 0.2x² + 7.2x + 78.

Therefore, the number of blankets the sophomore class can make if they have $663 to spend on supplies will be illustrated as:

C = 0.2x² + 7.2x + 78.

0.2x² + 7.2x + 78 = 663

0.2x² + 7.2x = 663 - 78

0.2x² + 7.2x - 585 = 0

Using almighty formula, it should be noted that x will be 69.

The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.

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Using the z-distribution, it is found that since the test statistic is less than the critical value, there is not enough evidence that the manufacturer needs to recalibrate the machines.

At the null hypothesis, it is tested if the machine is calibrated correctly, that is, the mean is of 4 cm, hence:

[tex]H_0: \mu = 4[/tex]

At the alternative hypothesis, it is tested if the machine is not calibrated correctly, that is, the mean is different of 4 cm, hence:

[tex]H_1: \mu \neq 4[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

For this problem, the parameters are given as follows:

[tex]\overline{x} = 3.97, \mu = 4, \sigma = 0.14, n = 81[/tex]

Hence the test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{3.97 - 4}{\frac{0.14}{\sqrt{81}}}[/tex]

z = -1.93.

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance value of 0.01, hence, using a z-distribution calculator, the critical value is given by:

|z| = 2.575 -> z < -2.575 or z > 2.575.

Hence:

Since the test statistic is less than the critical value, there is not enough evidence that the manufacturer needs to recalibrate the machines.

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Answer:

A

Step-by-step explanation:

Answer: A. 18

Step-by-step explanation:

Let the smallest number be x

Hence,

x+(x+2)+(x+4)+(x+6)=60

x+x+2+x+4+x+6=60

4x+12=60

4x+12-12=60-12

4x=48

Divide both parts of the equation by 4:

x=12

x+6=

12+6=

18

Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.

To determine if the ball will ever reach a hgeight of 30 ft, we need to determine the maximum height of the ball.

Using the equation of motion, v² = u² - 2gh where

So, making h subject of the formula, we have

h = (v² - u²)/-2g

Substituting the values of the variables into the equation, we have

h = (v² - u²)/-2g

h = ((0 ft/s)² - (40 ft/s)²)/-(2 × 32 ft/s²)

h = (0 ft²/s² - 1600 ft²/s²)/-(64 ft/s²)

h = - 1600 ft²/s²/-64 ft/s²

h = 25 ft

Since the ball is released from a height of 3 ft, its maximum height above the ground is H = 3 ft + h

= 3f + 25 ft

= 28 ft

So, we see that H = 28 ft < 30 ft.

Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.

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According to the given statement;

a sloth go 600 units in 90 minutes

A fraction is used to denote a piece or component of a whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

According to the given values;

A sloth may move in one hour = 250÷5/8.

let us simplify 250÷5/8 first.

Division sign can be convert into multiplication sign and flip the right side fraction 5/8 to 8/5.

250×8/5

Dividing 250 by 5, we get

= 50 × 8

Multiplying 50 and 8,  we get

= 400.

So, we could say, a sloth may move in one hour = 400 units.

We need to find distance covered in 90 minutes.

Let us convert 90 minutes into hours.

60 minute = 1 hour.

1 minute = 1/60 th of an hour.

and 90 minutes = 90 * 1/60 = 90/60 = 9/6 = 1.5 hours.

a Sloth may move in one hour = 400 units.

Therefore, in 1.5 hours Sloth can move = 1.5 × 400 = 600 units.

So, a sloth go 600 units in 90 minutes

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Answer:

Step-by-step explanation:

Because in your previous question the scale factor was 1:30 you would simply multiple 5 by 30 to get 150 inches

Answer:

The total cost of the laptop including tax will be $952.43.

Step-by-step explanation:

885.98 x 7.5%= $66.45

885.98 + 66.45= $952.43

Hope this helps!

The average value of function can be calculated using the formula →

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex] and to find average rate of change of function can be calculated using → f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex].

We have a function (say f(x)).

We have to find the average value of a function and the average rate of change of function.

A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.

According to the question -

PART - A → Finding the Average value of a function.

The average (or the mean) value of f (x) on [a, b] is defined by -

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]

PART - B → Finding the Average Rate of Change of a function.

The average rate of change of function f(x) is found out as follows -

f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex]

Hence, to find the average value of function -

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]

and to find average rate of change of function -

f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex].

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The Slope is [tex]\frac{4}{-5}[/tex].

    m = change in y/change in x = Δy/Δx

        = (y2 – y1)/(x2 – x1)

    Where “m” is the slope of a line.

As a result, using the formula above, we can quickly determine the slope of a line connecting two points.

Given points are (-5,6),(-10,10)​.

⇒ m = Δy / Δx

    = [tex]\frac{10 - 6}{-10 - (-5)}[/tex]

   = [tex]\frac{4}{-5}[/tex]

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Answer:you need to show the options at the bottom

Step-by-step explanation:

The company which has the absolute advantage when it comes to producing phones is: a. Gonzalez and Bros. Inc.

A comparative advantage can be defined as the ability of a business firm or country to produce goods and services at a lower opportunity cost than their rivals (competitors) or trade partners.

An absolute advantage can be defined as a measure of the ability of an individual or a business firm (manufacturer) to perform a specific economic activity such as the production of goods and services, more efficiently than another individual or business firm.

In this scenario, we can reasonably infer and logically deduce that the company which has the absolute advantage when it comes to producing phones is Gonzalez and Bros. Inc because it can produce 300 phones in comparison with the G company Inc.

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Using the weighted mean, it is found that Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.

The complete problem is given as follows:

"Trent earns scores of 62, 86, and 80 on three chapter tests for a certain class.

His homework grade is 68 and his grade for a class project is 64.

The overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the course grade; the project accounts for 20% of the course grade and the final exam accounts for 20% of the course grade.

What range of scores can Trent earn on the final exam to pass the course if he needs a "C" or better?

A "C" or better requires an overall course score of 70 or better, and 100 is the highest score that can be earned on the final exam."

The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.

For this problem, we have that:

Hence his weighted mean is given by:

76 x 0.5 + 68 x 0.1 + 64 x 0.2 + 0.2x = 57.6 + 0.2x.

For a grade C, he needs a score of at least 70, hence:

57.6 + 0.2x ≥ 70.

0.2x ≥ 12.4

x ≥ 12.4/0.2

x ≥ 62.

Hence Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.

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Answer:

[tex]\frac{1}{2}[/tex] hour later

Step-by-step explanation:

Since Mr.A has already traveled 25 miles there are 53 miles left to person B's house. In half an hour, Mr. A will have traveled 25 miles, while person b will have traveled 28. 25 + 28 = 53.

The coordinates of G after it is reflected over the x-axis are (4, -3)

The graph represents the given parameter

On the graph, we have the following point

G = (4, 3)

The rule of reflection across the x-axis is

(x, y) = (x, -y)

This means that

G' = (x, -y)

So, we have

G' = (4, -3)

Hence, the coordinates of G after it is reflected over the x-axis are (4, -3)

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The square picture whose area is 9 square is 3 inch long.

Square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of rectangle.

Area of Square is the total number of unit squares forming a square is referred to as the square's area. In other terms, it is described as the area that the square occupies.

It is given that,

The area of a square = 9 square inches

We need to find,

The side length of the given square

Also, we know that,

Area of square = [tex]a^{2}[/tex]

Putting values in the formula

We get,

9 =      [tex]a^{2}[/tex]

a = [tex]\sqrt{9}[/tex]

a = 3 inch

Hence, the side length of the given square picture whose area is 9 square inches is 3 inch

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The slope of the line for which the line passes through the points (6, -5) and (-6, -5) is zero .

We have given two points  (6, -5) and (-6, -5) .

Using slope formula , we get

            m = - 5 - (-5) / - 6 - 6

            m = - 5 + 5 / -12

             m = 0 / 12

             m = 0

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Answer:

a = 1

b = 5

Step-by-step explanation:

a + 2b = 11

(a - b = -4) × 2

2a - 2b = -8

------------------------

a + 2b = 11

2a - 2b = -8

-------------------

3a = 3

÷3   ÷3

-----------

a = 1

----------------------------------------------------------------------------------------------------------

a - b = -4

1 - b = -4

-1         -1

---------------

-b = -5

÷-1   ÷-1

-------------

b = 5

I hope this helps!

Answer:

Step-by-step explanation:

You want to use rounding and approximation to compute the hourly wage of a person working 40 hours per week and making $71,600 per year. You also want a reasonableness check compared to the actual answer.

Rounding the $71,600 salary to the nearest $10,000, it becomes $70,000. Considering 50 weeks per year and 40 hours per week, the number of hours in a year is approximated by 40×50 = 2000. Then the hourly wage is approximately ...

  $70,000/(2000 h) = $35/h . . . . estimated wage

If we assume exactly 52 weeks in a year, there are 40×52 = 2080 working hours in a year. That means the hourly wage is actually ...

  $71,600/(2080 h) ≈ $34.42 . . . . actual hourly wage

The difference of the estimate from the actual value is ...

  $34.42 -35.00 = -$0.58

That is the actual value is between 1% and 2% lower than the estimate, a quite reasonable error. (Often anything within 10% is a reasonable estimate.)

__

Additional comment

Often, when doing estimates, you want to estimate the error in your estimating process. Here, there are two contributors.

Rounding 71,600 down to 70,000 reduces the value by a factor of 700/716, or 175/179. That means the error will be about 4 parts in 180 (an estimate), or 1 part in 45, about 2.2% (low).

Rounding 52 weeks per year down to 50 increases the value by a factor of 52/50 = 1.04, causing the estimated value to be about 4% high. These two errors are in opposite directions, so the net effect is an estimated error of about 4% -2.2% = 1.8% (high).

The error estimate has errors of its own, but this gets you in the ballpark of approximate error in the estimated value.

A year of 365 days is 52 weeks plus one day, so can be 2088 working hours. Using this value for hours reduces the hourly wage to about $34.29.

Answer: 1. 7:10

2. 10 blue cans

15 yellow cans.

3. 4 cans of blue paint.

5 cans of yellow paint.

4. 2 blue cans and 3 yellow cans.

Step-by-step explanation:

1. 14 blue paint cans/20 yellow paint cans=

14/20=

7/10 ==> 7:10

2. 4+6 blue cans=10 blue cans

6+9 yellow cans=15 yellow cans.

3. 14-10=4 cans of blue paint.

20-15=5 cans of yellow paint.

4. 10 blue cans/15 yellow cans=

10/15=

2/3 ==> 2:3 ==> 2 blue cans and 3 yellow cans.

Answer:

Step-by-step explanation:

Answer: 1. 7:10

2. 10 blue cans

15 yellow cans.

3. 4 cans of blue paint.

5 cans of yellow paint.

4. 2 blue cans and 3 yellow cans.

Step-by-step explanation:

1. 14 blue paint cans/20 yellow paint cans=

14/20=

7/10 ==> 7:10

2. 4+6 blue cans=10 blue cans

6+9 yellow cans=15 yellow cans.

3. 14-10=4 cans of blue paint.

20-15=5 cans of yellow paint.

4. 10 blue cans/15 yellow cans=

10/15=

2/3 ==> 2:3 ==> 2 blue cans and 3 yellow cans.

The dimensions of the photograph are the length= 14 in  and the width= 5 in.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).

The area of a rectangle is given by the multiplication between the base and the height.

The question gives:

Thenm

A= b * h

70 = (9 +w) * w

70= 9w +w²

w²+9w-70=0

[tex]w_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \left(-70\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-9\pm \:19}{2\cdot \:1}[/tex]

Thus,  [tex]w_{1}=\frac{-9-\:19}{2\cdot \:1}=\frac{-28}{2}=-14[/tex] and [tex]w_{2}=\frac{-9+\:19}{2\cdot \:1}=\frac{10}{2}=5[/tex]

The dimensions should have positive values, then w=5.

If w=5, the length will be 5+9 = 14. With these dimensions, the area will be 14 * 5 = 70.

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Answer: 24

Step-by-step explanation: 6 x 4 = 24
24 - 8 = 16

The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)

From the question, we are to solve the given system of linear equations

The given system of linear equation is

x + 2y -  z = 2       ----------- (1)

2x - 7y + 5z = 3    ----------- (2)

-4x + y + 2z = 4    ----------- (3)

From equations (1) and (2), eliminate z

5 × ( x + 2y -  z = 2      

1 × ( 2x - 7y + 5z = 3

---------------------------------------  

5x + 10y -5z = 10

2x -7y + 5z = 3

Add the resulting equations

7x + 3y = 13 ----------- (4)

From equations (2) and (3), eliminate z

2 × ( 2x - 7y + 5z = 3    

5 × ( -4x + y + 2z = 4  

-----------------------------------

4x - 14y + 10z = 6

-20x + 5y + 10z = 20

Subtract the resulting equations

24x - 19y = -14 ---------- (5)

Now, solve equations (4) and (5) simultaneously

7x + 3y = 13

24x - 19y = -14

Eliminate y
19 × ( 7x + 3y = 13

3 × ( 24x - 19y = -14

---------------------------------

133x + 57y = 247

72x - 57y = -42

Add the resulting equations

205x = 205

x = 205/205

x = 1

Substitute the value of x into equation (4)

7x + 3y = 13

7(1) + 3y = 13

7 + 3y = 13

3y = 13 - 7

3y = 6

c = 6/3

y = 2

Substitute the values of x and y into equation (1)

x + 2y -  z = 2

1 + 2(2) - z = 2

1 + 4 - z = 2

1 + 4 - 2 = z

3 = z

z =3

The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)

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The number 1/2 is a rational number and the number 9/3 is an integer rational number.

They are referred to as rational numbers if the value of a numerical expression terminates, in which case they are a rational number, and as irrational numbers if the value of the expression does not terminate.

The numbers are given below.

1/2 and 9/3

The fraction numbers are converted into decimal numbers. Then we have

1/2 = 0.5

9/3 = 3

The number 1/2 is a rational number and the number 9/3 is an integer rational number.

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