The students in Class A and Class B were asked how many pets they each have. The dot plots below show the
results
Students in Class A
Number of Pets
Students in Class B

What is the difference between the ranges in the dot plot

The rate of change of temperature with time at a point in time is given by

the derivative of the function for the temperature of the soup.

The correct responses are;

Reasons:

a) From the data in the table, we have;

The approximate value of H'(5) is given by the average value of the rate of

change of the temperature with time between points, t = 3, and t = 8

Therefore;

[tex]\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}[/tex]

Which gives;

[tex]\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}[/tex]

Therefore, H'(5) = -2.6°C per minute

b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12

At t = 0, H(0) = 90 °C

At t = 12, H(12) = 58 °C

Therefore, there exist a temperature, of 60 °C between 90° C and 58 °C

c) The given derivative of C is, [tex]C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}[/tex]

At t = 3, we have;

[tex]The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1[/tex]

Therefore, we have;

y - 80 ≈ -3.1 × (x - 3)

The equation for the tangent is; y = -3.6 × (x - 3) + 80

y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8

The  value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8

d) Based on the the model above, the rate at which the temperature of the

soup is changing at t = 3 minutes is -3.6 degrees per minute.

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Answer:

[tex]3(3x-5)[/tex]

Step-by-step explanation:

First, you have to rewrite 9 as 3 * 3 and 15 as 3 * 5

Finally, you have to factor out the common term 3 to get [tex]3(3x-5)[/tex]

Hope this helps!

P.S next time list the answer choices it would help alot :)

Answer:2

Step-by-step explanation:

x+3=5

subtract 3 from both sides

x=5-3

x=2

Answer:

x=    2

Step-by-step explanation:

Answer:

Interest rate

Step-by-step explanation:

The amount owed is called the principal and the price of borrowing money is called interest. Some people spend a day's pay (or more) per week repaying the interest and principal owed on car loans, credit card bills, student loans, and other consumer debts.

[tex]\text{Given that,}~x^2 +y^2 = 125 ~ \text{and}~ xy =22\\\\(x+y)^2 = x^2 +y^2 +2xy = 125 +2(22) = 169[/tex]

[tex]\huge \bf༆ Answer ༄[/tex]

Here's the solution ~

[ by using formula ]

I hope it helps ~

Answer: D

Step-by-step explanation: less than or equal to 4. graph leads to negative

Answer:

9) 21

10) 70

11) 34

12) 31

13) 50

14) 31

15) 137

16) 101

Step-by-step explanation:

9)

20+40=60

60 + b =180 ( sum of the interior angles on a triangle is 180 )

b = 180 - 60

b = 120

39 + c + ? = 180 ( sum of the interior angles on a triangle is 180 ) c =120 ( vertically opposite angles are equal )

39 + 120 + ? = 180

159 + ? = 180

? = 180 - 159

? = 21

________________________________________________________________________________________

10)

60 + 65 + b = 180 ( sum of the interior angles on a triangle is 180 )

125 + b = 180

b = 180 - 125

b = 55

50 + b + c = 180 ( sum of the angels on a straight line is 180 )

50 + 55 + c = 180

105 + c = 180

c = 180 - 105

c = 75

35 + c + ? = 180

35 + 75 + ? = 180

110 + ? = 180

? = 180 - 110

? = 70

________________________________________________________________________________________

11)

84 + 36 + b = 180 ( sum of the interior angles on a triangle is 180 )

120 + b = 180

b = 180 - 120

b = 60

86 + b + ? = 180 ( sum of the interior angles on a triangle is 180 )

86 + 60 + ? = 180

146 + ? = 180

? = 180 - 146

? = 34

________________________________________________________________________________________

12)

35 + 23 + b = 180 ( sum of the interior angles on a triangle is 180 )

58 + b = 180

b = 180 - 58

b = 122

27 + c + ? = 180 ( sum of the interior angles on a triangle is 180 ) c =122 ( vertically opposite angles are equal )

27 + 122 + ? = 180

149 + ? = 180

? = 180 - 149

? =31

________________________________________________________________________________________

13)

115 + b = 180 ( sum of the angels on a straight line is 180 )

b = 180 - 115

b = 65

65 + 90 + c = 180 ( sum of the angels on a straight line is 180 )

155 + c = 180

c = 180 - 155

c = 25

155 + d = 180 ( sum of the angels on a straight line is 180 )

d = 180 - 155

d = 25

c + d + e = 180 ( sum of the interior angles on a triangle is 180 )

25 + 25 + e = 180

50 + e = 180

e = 180 - 50

e = 130

e + ? = 180 ( sum of the angels on a straight line is 180 )

130 + ? = 180

? = 180 - 130

? = 50

________________________________________________________________________________________

14)

35 + 20 + b = 180 ( sum of the interior angles on a triangle is 180 )

55 + b = 180

b = 180 - 55

b = 125

156 + c = 180 ( sum of the angels on a straight line is 180 )

c = 180 - 156

c = 24

c + e + ? = 180 ( sum of the interior angles on a triangle is 180 ) e= 125 ( vertically opposite angles are equal )

24 + 125 + ? = 180

149 + ? = 180

? = 180 - 149

? = 31

________________________________________________________________________________________

15)

b = 45 ( vertically opposite angles are equal )

b + 60 + c = 180 ( sum of the interior angles on a triangle is 180 )

45 + 60 + c = 180

105 + c = 180

c = 180 - 105

c = 75

68 + 75 + e = 180 ( sum of the angels on a straight line is 180 )

143 + e = 180

e = 180 - 143

e = 37

100 + 37 + j = 180 ( sum of the interior angles on a triangle is 180 )

137 + j = 180

j = 180 - 137

j = 43

j + ? = 180 ( sum of the angels on a straight line is 180 )

43 + ? = 180

? = 180 - 43

? = 137

________________________________________________________________________________________

16)

b = 75 ( vertically opposite angles are equal )

c = 45 ( vertically opposite angles are equal )

b + c + e = 180 ( sum of the interior angles on a triangle is 180 )

75 + 45 + e = 180

120 + e = 180

e = 180 - 120

e = 60

e + 79 + j = 180 ( sum of the angels on a straight line is 180 )

60 + 79 + j = 180

139 + j = 180

j = 180 - 139

j = 41

j + 60 + s = 180 ( sum of the interior angles on a triangle is 180 )

41 + 60 + s = 180

101 + s = 180

s = 180 - 101

s = 79

s + ? = 180 ( sum of the angels on a straight line is 180 )

79 + ? = 180

? = 180 - 79

? = 101

________________________________________________________________________________________

hope this helps☆☆☆

it took soooo long to do btw ⊙•⊙

27) 115=5(5a-2)

115= 25a-10

125=25a

a=5

28) -72=-x-6(x+5)

-72=-7x-30

-42=-7x

x=6

i did two of them. now i gtg so won't do the rest

First, look for the zeroes of the integrand in the interval [0, 6] :

x² - 6x + 8 = (x - 4) (x - 2) = 0   ⇒   x = 2   and   x = 4

Next, split up [0, 6] into sub-intervals starting at the zeroes we found. Then check the sign of x² - 6x + 8 for some test points in each sub-interval.

• For x in (0, 2), take x = 1. Then

x² - 6x + 8 = 1² - 6•1 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

• For x in (2, 4), take x = 3. Then

x² - 6x + 8 = 3² - 6•3 + 8 = -1 < 0

so x² - 6x + 8 < 0 over this sub-interval.

• For x in (4, 6), take x = 5. Then

x² - 6x + 8 = 5² - 6•5 + 8 = 3 > 0

so x² - 6x + 8 > 0 over this sub-interval.

Next, recall the definition of absolute value:

[tex]|x| = \begin{cases}x & \text{for }x \ge0 \\ -x & \text{for }x < 0\end{cases}[/tex]

Then from our previous analysis, this definition tells us that

[tex]|x^2 - 6x + 8| = \begin{cases}x^2 - 6x + 8 & \text{for }0<x<2 \text{ or } 4<x<6 \\ - (x^2-6x+8) & \text{for }2<x<4\end{cases}[/tex]

So, in the integral, we have

[tex]\displaystyle \int_0^6 |x^2-6x+8| \, dx = \left\{\int_0^2 - \int_2^4 + \int_4^6\right\} (x^2 - 6x + 8) \, dx[/tex]

Then

[tex]\displaystyle \int_0^2 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_0^2 = \frac{20}3 - 0 = \frac{20}3[/tex]

[tex]\displaystyle \int_2^4 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_2^4 = \frac{16}3 - \frac{20}3 = -\frac43[/tex]

[tex]\displaystyle \int_4^6 (x^2 - 6x + 8) \, dx = \left(\frac13 x^3 - 3x^2 + 8x\right) \bigg|_4^6 = 12 - \frac{16}3 = \frac{20}3[/tex]

and the overall integral would be

20/3 - (-4/3) + 20/3 = 44/3

Answer:

14 nickels is the answer

Step-by-step explanation:

Answer:

The coordinates of the focus are [tex](-3,0)[/tex]

Step-by-step explanation:

Since [tex]B^2-4AC=0^2-4(1)(0)=0[/tex], the conic section is a parabola.

Convert general form into standard form by completing the square:

[tex]x^2+6x-4y+5=0[/tex]

[tex]x^2+6x+5=4y[/tex]

[tex]x^2+6x+9=4y+4[/tex]

[tex](x+3)^2=4(y+1)[/tex]

Now that the equation is in the form of [tex](x-h)^2=4p(y-k)[/tex], we can see that [tex]h=-3[/tex] and [tex]k=-1[/tex] which tells us that the vertex is at [tex](-3,-1)[/tex]. To determine the coordinates of the focus, we need to solve the equation [tex]4p=4[/tex] and plug the value of [tex]p=1[/tex] into [tex](h,k+p)[/tex] to get [tex](-3,-1+1)[/tex] which is [tex](-3,0)[/tex].

In conclusion, the coordinates of the focus for the conic section are [tex](-3,0)[/tex].

The probability of getting an odd number on the first roll and less than 3 on the second roll is 1/6.

It is a branch of mathematics that deals with the occurrence of a random event.

The probability of getting an odd number on the first roll is 3/6

since there are three odd numbers (1, 3, 5) out of six possible outcomes (1, 2, 3, 4, 5, 6).

The probability of getting less than 3 on the second roll is 2/6, since there are two possible outcomes (1, 2) out of six.

To find the probability of both events happening, we multiply the probabilities:

P(odd on first roll and less than 3 on second roll) = P(odd on first roll) × P(less than 3 on second roll)

= (3/6)×  (2/6)

= 1/6

Therefore, the probability of getting an odd number on the first roll and less than 3 on the second roll is 1/6.

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Answer:

-2(x^2+1)

Step-by-step explanation:

1. Divide The Numbers:

-2x^2+2(-3/3)

-2x^2+2(-1)

2. Multiply The Numbers:

-2x^2+2(-1)

-2x^2-2

3. Common Factor:

a. Factor by grouping

-2x^2+2(-3/3)

-2x^2-2

b. Factor by Grouping

-2x^2-2

-2(x^2+1)

-2x^2+(2)(-3/3)

Solution: -2(x^2 + 1)

Answer:

229.6 square units

Step-by-step explanation:

19.9×16.8=334.32

19.9-4-4=11.9

16.8-4-4= 8.8

11.9×8.8= 104.72

334.32-104.72= 229.6 sq units

the answer is D newscast

Answer:

Step-by-step explanation:

1. In some zoos the are more elephants than giraffes, then this conjecture can be true sometimes, however, this can not always be true because some zoo could have more giraffes

2. This can be true unless that turtle ages, or another is found that is taken into captivi9ty and found to be older

3. While most American bison are usaually below 6 feet, that is no gureantee there is no occasaional taller American Bison.

I do not know if these meet your teacher's starndard, but I hope they do. Please thanks and rate!

Answer:

  1.  x^2 +2x -24 = 0

  2.  x^2 -7x +10 = 0

Step-by-step explanation:

If you look at the factored and expanded forms of a quadratic with solutions p and q, you see ...

  (x -p)(x -q) = x^2 -(p+q) +pq

The x-term coefficient is the opposite of the sum of solutions.

The constant is the product of solutions.

This knowledge lets you write down the standard form equation with no particular effort.

1.  x^2 +2x -24 = 0

2.  x^2 -7x +10 = 0

Answer:

I'm sorry what?

The total cost curve shows the cost of total shipment from the different

cities.

Reasons:

The given parameters are;

The number of shipment per = From 550,000 to 600,000 per year

The given table is presented as follows;

[tex]\begin{tabular}{|l|c|c|c|}Location&Annual Fixed Costs&Variable Cost \\Denver&\$5,000,000&\$4.65 \\Santa Fe&\$4,200,000&\$6.25\\Salt Lake City&\$3,500,000&\$7.25\end{array}\right][/tex]

a. Required:

The plot total cost curve for the locations on a single graph.

Solution:

b. Required:

The city that provides the lowest overall cost.

Solution:

The two cities with the lowest overall costs are Denver and Salt Lake City.

Area under the curve for Denver;

(7557500 + 7790000) ÷ 2 × 50,000 = 383687500000

Area under the curve for Salt Lake City

(7487500 + 7850000) ÷ 2 × 50,000 = 383437500000

Therefore;

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Answer:

$10.06

Step-by-step explanation:

Tax rate = 6% , convert into 0.06

10 × 0.06 = 0.6

10 + 0.6 = 10.06

Answer:

Step-by-step explanation:

Assuming the density is the same for both lollipops, we can calculate what volume is required to make the 2158.7kg the same density of the smaller lollipop.  

Small Lollipop

r = 2cm

V=4 /3πr^3

V = 33.51 cm^3

Mass is 50 g in 33.51 cm^3, so the density is:

50g/(33.51 cm^3) = 1.492 g/cm^3

We have 2158.7kg in the larger lollipop.  That is 2158700 grams.

Find the volume required to contain 2158700 grams with a density of 1.492 g/cm^3.  :

       (2158700 grams)/(1.492 g/cm^3) = 1446775 cm^3

V=4 /3πr^3

1446775 cm^3 = (4/3)*π*r^3

r = 70.12 cm

Therefore, -14x + 40x² is the answer.

Hoped this helped.

[tex]-BrainiacUser1357-[/tex]

The correct statement is The cost of natural gas is $0.83 per unit.

The equations representing her utility costs in July and December are known as simultaneous equations. These equations have to be solved jointly in order to determine the cost of electricity and natural gas.

Given the equation gotten by Karina: 116y = 96.28

Where y represent the cost of natural gas

In order to determine the value of y, divide both sides of the equation by 116

y = 96.28 / 116

y = $0.83

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Answer:

expected profit=$-3

Step-by-step explanation:

1 tail=-5

1 head=3

3/2=1.5

1.5*3=4.5

1.5*-5=-7.5

4.5-7.5=-3

$-3

Answer:

Total earning Kanica wants to make is at least $750

The commission she gets is 7.5 % Therefore to find the sales she should make we use :

(Total earnings * 100% )/ Commission

= (100 * 750) / 7.5

=75000/7.5

= $ 10,000

The minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells is $10,000.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Kanica wants to earn at least $750 this week in commission.

Let x be the minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells.

The value of x can be found as follows:

x = 750/(7.5%)

x = (750/7.5)x100

x = $10,000

Thus, the minimum amount she needs to sell in order to earn $750 if she earns a 7.5% commission on everything she sells is $10,000.

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Answer:

x+y=1

Step-by-step explanation:

The Linear Equation Standard Form is = ax+by=c.

Given y=-x+1, we will use Algebra to convert the equation from slope-intercept  form to standard form:

x+y=-x+x+1

We added x to both sides to cancel out and move the -x.

x+y=1 is the answer.