One hundred voters were asked whether they supported a bill that had

Answer:

4,000 which is four thousand

Answer:

4000

Step-by-step explanation:

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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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:

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.

Answer:

I'm sorry what?

Answer:

60% of the people surveyed were satisfied with the car

Step-by-step explanation:

1140 satisfied people / 1900 total people = 0.60 = 60% satisfied people

Answer:

It is congruent to the angle F, as they are similar triangles.

Answer:

6[tex]\pi[/tex]

Step-by-step explanation:

The period of a sinusoidal function in the form a * cos (b (x + h)) + m is [tex]\frac{2\pi }{|b|}[/tex]. Therefore, we can see that "b" in g(x) is 1/3 and 1/3 substituted into [tex]\frac{2\pi }{|b|}[/tex] is 2[tex]\pi[/tex]/1/3 which is 6[tex]\pi[/tex].

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 ⊙•⊙

Answer:

Yes.

Step-by-step explanation:

Associative property of multiplication is:

(A×B)×C = A×(B×C).

It says that "The way of grouping of terms doesn't change the product."

So, given example (2×3)×4=2×(3×4) is an example of associative property of multiplication.

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

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].

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

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 :)

Explanation:

Refer to the y = mx+b form

The slopes are the only thing we focus on. For the equations y = 6x-1 and y = -6x-4, the slopes are 6 and -6 in that order.

The slopes are not equal, so the lines aren't parallel.

The slopes aren't opposite reciprocals of one another, so they aren't perpendicular either. An example of an opposite reciprocal pairing would be 6 and -1/6. Any pair of nonzero opposite reciprocal slopes always multiply to -1.

Therefore, the two lines are neither parallel nor perpendicular, they just intersect.

Step-by-step explanation:

How many ways are there to select 3 candidates from 8 equally qualified recent graduates for

openings in an accounting firm?

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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Therefore, -14x + 40x² is the answer.

Hoped this helped.

[tex]-BrainiacUser1357-[/tex]

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

[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 ~

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve ~

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:

  a) 49

  b) 84

  c) (B) -- always odd

Step-by-step explanation:

We observe that the number of square tiles is the square of the pattern number. The number of circular tiles is 1 more than the pattern number on each side of the square.

  square tiles = n²

  circular tiles = 4(n +1)

__

7² = 49 square tiles are needed for pattern number 7.

__

4(20+1) = 84 circular tiles are needed for pattern number 20.

__

The parity of the number of square tiles matches the parity of the pattern number. (The square of a number has the same parity as the number.) Since 4 is a factor in the number of circular tiles, its parity is always even. The parity of the total number of tiles will match the parity of the pattern number.

When the pattern number is odd, the total number of tiles will always be odd. (B)

Answer:

[tex]\huge\purple{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}[/tex]

6/2 ÷ 2/2 = 3/1

3 ÷ 1 = 3

Answer: 3

#CarryOnLearning

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:

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:

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.

Answer: 331,250

Step-by-step explanation: hope it helps