The graph below illustrates the decay of a radioactive substance over t days.

Use the graph to estimate the average decay rate from t = 5 to t = 15 Note: Your answer will be negative.

The equation of the straight line, in point-slope form, is  

          [tex]y +3 = \frac{1}{4} ( x + 4)[/tex]

we have , the required line is perpendicular to the given line.

Also let us take any two coordinates of the given line , like  (-1 , 1 ) and  

( 0 , -3) . So the slope (m₁) of given line = [tex]\frac{y2 -y1}{x2 - x1 }[/tex]

                                      m₁ = -4

as the required line is perpendicular to the given line so , we know

for two perpendicular lines

                                   m₁  m₂ =  -1

therefore ,                 m₂ = 1/4

Now the required line passes through (-4,-3)

and the equation of straight line in point slope form is given by

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

here m = 1/4

y₁ = -3

x₁  = -4

therefore the required equation  in point-slope form is

         y + 3 = 1/4 ( x +4 )

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Marcus is accurate. Jeremy is wrong because he overlooked the negative sign in the equation's initial addend. Since -25 has a greater absolute value than 3, it is obvious that the sum should be negative.

Marcus is correct; the solution is -22.

The simplified expression is given as:

= -(5²)+ 3

= -(25) + 3

= - 22

The right response is this. Marcus saw the bracket or parentheses symbol when he condensed his sentence. This has major significance.

Jeremy scored 28. He squared -5 without noting that it was in a bracket or parenthesis, therefore his response is incorrect.

Consequently, Jeremy calculated this.

= -(5²) + 3

= 25 + 3

= 28

Jeremy gave a false response. He made a computation but failed to see the bracket.

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Complete Question

Marcus and Jeremy both evaluated the expression −(5²) + 3. Marcus said the answer was −22. Jeremy said the answer was 28. Who is correct? Explain the error in the other student’s work.

Bridgette gives 1/10 cans of food to each dog.

According to the question,

We have the following information:

Bridgette has 9 dogs. Every day, she feeds them a total of 9/10 of a can of food, where each dog is fed the same amount of food.

Now, we have the following expression:

9 dogs = 9/10 can

Now, we can easily find the cans given to each dog using division. We will divide the total number of cans of food by the number of dogs.

1 dog = 9/(10*9) cans

1 dog = 1/10 cans of food

Hence, Bridgette gives 1/10 cans of food to each dog.

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P(The aircraft is discoverd and has no locator) = P(discovered)  x P(no locator/discoved =0.28)

The information is based on the disappearance of the of the light aircraft in the flight in the in a certain country . 70% of the aircraft that disapear while in the flight were discovered . The probability that there is an emergency locator        

in the aircraft given that it is discovered is 60% and the probability that the aircraft that has not discovered have an emergenncy locator is 90%.

a) To determine probiblity it wount be discoverd

Calculation

P(the aircraft is discovered and has a locator) = P(discovered) X P(locator/discovered)

The probability of the flight discovered and has locator is obatained as given below:

P(The aircraft is discoverd and has no locator) = P(discovered)  x P(no locator/discovered)

The probability of the flight not discovered and has a locator is obatained below.

P(The aircraft is not discovered and has a locator) = P(not discovered) x P (locator  | not discorverd)    = 1-0

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The total interest that Magdalena's parents would have to pay to repay the loan is  $864.50

The interest that Magdalena's parents will pay per year is:

= Value of loan x Simple interest rate per year

= 2, 600 x 7%

= $182

To find the total interest paid, this amount should then be multiplied by the number of years it would take Magdalena's parents to repay the loan. 4 years and 9 months in years is:

= 4 + 9/12 months in a year

= 4 + 3 / 4

= 4 + 0.75

= 4.75 years

The total interest is:

= 4.75 x 182

= $864.50

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The solution for g(7) in the piecewise function g(x) = (x + 1)(x - 5) is 16

From the question, we have the equation that can be used in our computation to be a piecewise function

This piecewise function is represented as g(x)

Also from the question, we have the following function that we are to compute

g(7)

This means that the value of x is 7, and we calculate g(x) when x = 7

To do this, we make use of an equation in the piecewise function, where the domain occupies x = 7

This domain is x c (2, oo)

And the function is

g(x) = (x + 1)(x - 5)

Substitute the known values in the above equation, so, we have the following representation

g(7) = (x + 1)(x - 5)

So, we have the following equation

g(7) = (7 + 1)(7 - 5)

There is no constant to add or subtract to both sides of the equation

Also, there is no factor to multiply or divide from both sides of the equation

So, we have the following representation

g(7) = (7 + 1)(7 - 5)

Solving further, we have

g(7) = 16

Hence, the solution is 16

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Answer:

the correct she answer should be 5

Step-by-step explanation:

The solution set for the given inequality is  {.......-4, -3, -2, -1, 0, 1, 2, 3}, so the for x=5 the inequality is false. Therefore, the correct answer is option B.

The given inequality is 5x+6≤2x+15.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Here, the inequality can be solved as follows

5x+6≤2x+15

Subtract 6 on both the sides of the inequality, we get

5x+6-6≤2x+15-6

5x≤2x+9

Subtract 2x on both the sides of the inequality, we get

5x-2x≤2x+9-2x

3x≤9

Divide 3 on both the sides of the inequality, we get

x≤3

Here, solution set is {.......-4, -3, -2, -1, 0, 1, 2, 3}

So, the for x=5 the inequality is false.

Therefore, the correct answer is option B.

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Answer: [tex]f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x[/tex].

[tex]x=(2y+1)^2\\\\\pm \sqrt{x}=2y+1\\\\-1 \pm \sqrt{x}=2y\\\\y=-\frac{1}{2} \pm \frac{\sqrt{x}}{2}[/tex]

Since the domain of the original function is the same as the range of the inverse, the rate of [tex]f^{-1}(x)[/tex] is [tex]f^{-1}(x) \geq -1/2[/tex]. This means we consider the positive case.

[tex]\therefore f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]

Answer:

Step-by-step explanation:

um ok so

Answer:

x=0

Step-by-step explanation:

the rest of this is so i can reach twenty characters.

Answer: 2176 cm^2 i think

Step-by-step explanation:

Answer:

60 cm

Step-by-step explanation:

we can use the Pythagorean theorem:

a^2 = b^2 + c^2 where a is the hypothenuse

so 68^2 = 32^2 + c^2

rearrange: 68^2 - 32^2 = c^2

so 4624 - 1024 = c^2

= 3600

square root of 3600 = 60

missing side = 60 cm

Given function:

y = |x − 3| + 1

Table:

x     y  

1     3

2    2

3    1

4    2

5    3

Here the vertex is (3,1).

Graph is in the image uploaded.

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False, As the sample size is increased, the standard deviation of a sampling distribution of the sample's mean drops.

The term "standard error" also refers to the sample mean's standard deviation. The high dimensionality theorem establishes that as sample size increases, the sample mean's sampling distribution becomes more or less normal.

Using the formula below, the sample mean's standard deviation is determined.

σ ÷ √n

where n is the sample size and would be the population standard deviation.

As the denominator, or n, increases, the standard variance of the sample average would also decrease, as shown by the aforementioned calculation.

It follows that the standard deviation of a sample's average decreases as the sample size grows.

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The value of x which makes the given expression 1/2(3x+4) = 1/2x true is -2

We have to simplify the given expression to find the value of x

1/2(3x + 4) = 1/2x

Cancel 1/2 from both sides

⇒ 3x + 4 = x

⇒ 2x = -4

⇒ x = -2

Hence, the value of x is -2 which makes the given expression true.

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Answer:

A=-3,b=1,C=19

Step-by-step explanation:

y-7=3(x+4)

we will just simplify the bracket like this

y-7=3x+12

y=3x+12+7

y=3x+19

y-3x=19

A=-3,b=1,C=19

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Answer:

  AD = 32

Step-by-step explanation:

You want the length of side AD of square ABCD, when CD = (x+15) and angle ABC is (6x-12)°.

The value of x can be found by recognizing that the measure of any angle in a square is 90°.

  (6x -12)° = 90°

  6x = 102 . . . . . . . . divide by °, add 12

  x = 17

The sides of a square are congruent, so ...

  AD = CD = (x +15) = 17 +15 = 32

The length of AD is 32 units.

Answer:

1) ∠5 and ∠6 are supplementary angles not vertical angles this statement is false.

2) ∠2 and ∠7 are alternally interior angles yeah that statement is true.

3) ∠2 and ∠4 are supplementary angles no they are not complementary, because sum of those two angles i.e. ∠2+∠4 =180.

so this statement is false

Step-by-step explanation:

Step-by-step explanation:

here ∠2+∠5=180°; ∠1+∠6=180; ∠4+∠7=180°; and for ∠3+∠7=180°;

here ∠6+∠8=180°; ∠1+∠3=180°; ∠2+∠4=180°; ∠5+∠7=180; here the

∠1=∠4; ∠2=∠3; ∠5=∠8; ∠6=∠7 (opposite angles are equal)

[tex]{\sf{ \frac{10}{50} = \frac{y}{125} \\ →50y = 10 \times 125 \\→ y = 25}}[/tex]

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Answer:

f(4) = - 27

Step-by-step explanation:

substitute x = 4 into f(x) , that is

f(4) = - 2(4)² + 5 = - 2(16) + 5 = - 32 + 5 = - 27

Answer:

69

Step-by-step explanation:

Replace x with 4

-2(4)^2 +5

-8^2+5

64+5

69

Each bag got 2 pieces of gums and 4 pieces of candies.

Given, that

Ana is making treat bags to give to her 10 students.

She puts x number of gum and 4 pieces of candy in each bag.

She had used a total of 60 pieces.

Now, as she puts 4 pieces of candy in each bag and she prepare total 10 bags.

So, She used total 4×10 = 40 candies

Now, if she used 60 pieces out of which 40 pieces are of candies

Then, 60 - 40 = 20 pieces

20 pieces will be of gums.

So, she puts total 20 pieces of gums in 10 bags

Hence, in each bag she puts 20/10 pieces of gums i.e. 2 pieces of gums

So, each bag got 2 pieces of gums 4 pieces of candies.

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Michael drinks 33.5 fl oz more fluid ounces than Lydia.

Given in question,

30 ml = 1 fl oz

  1 ml = 1/30 fl oz

1 bottle = 335 milliliters

No. of bottles of water Michael drank = 6

                                                              = 6 * 335 milliliters

                                                              = 2010 milliliters

                                                              = 2010/30 fl oz

                                                              = 67 fl oz

No. of bottles of water Lydia drank = 3

                                                           = 3 * 335 milliliters

                                                           = 1005 milliliters

                                                           = 1005/30 fl oz

                                                           = 33.5 fl oz

Therefore, 67 - 33.5 = 33.5

Hence, Michael drinks 33.5 fl oz more fluid ounces than Lydia.

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Answer:

144 cm²

Step-by-step explanation:

1.) Find the area of all of the faces

10*4=40 (Top Face)

4*8=32 (Bottom Face)

6*8*0.5=24 (One Triangle)

6*8*.5=24 (Other Triangle)

6*4=24 (Back Face)

2.) Add them all together to get the surface area

40+32+24+24+24= 144

***Don't forget the cm². Some teachers are really annoying about this

A- the area of the plot as a function of x. is 6 x^2 +10x-5

B- the perimeter of the plot as a function of x is 10x+8

A rectangle plot of land has a width of 3x+5 feet,

and a length of 2x-1 feet.

A) the area of the plot as a function of x is given by

A= length * width

  = ( 2x-1) * ( 3x+5)

  =6 x^2 +10x-5

B) the perimeter of the plot as a function of x

P = 2( l+ W)

  = 2 (( 2x-1) +( 3x+5))

  = 2( 5x +4)

  = 10x +8

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Phil lives in a state where his tax rate does not change when his income changes. This is an example of a proportional or flat tax.

Tax is defined as the official way individuals contribute to their state revenue through the compulsory deduction of some amount of money from their monthly income.

There are two types of tax which include the following:

Proportional or flat tax: This is defined as the type of tax that is being paid by individuals from different class in the society whereby all are expected to pay tax with the same rate irrespective of the income.

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Answer:

y = [tex]\frac{7}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{7}{2}[/tex] x + 6 ← is in slope- intercept form

with slope m = [tex]\frac{7}{2}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{7}{2}[/tex] x + c ← is the partial equation of line h

to find c substitute (- 2, - 3 ) into the partial equation

- 3 = - 7 + c ⇒ c = - 3 + 7 = 4

y = [tex]\frac{7}{2}[/tex] x + 4 ← equation of line h

Each person need to pay $ 80.88345.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Bill without tax = 105.73

Tax = 6%

So, bill amount after tax = 105. 73 + 105. 73 x 6/100

                                        = 105.73 + 6.3438

                                        = $112.0738

Addition of 20% tip = 112.0738 + 211.46 = $323.5338.

If the amount is divided among 4 people, each will pay

= 323.5338/4

= $ 80.88345

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On solving the system of equations by substitution method , the solution is x = 0 , y = 1 and x = 4 , y = 9    .

In the question ,

it is given that

the system of equation is

y = x² - 2x + 1

y = 2x + 1

by using substitution method ,

Substituting y = 2x + 1 in y = x² - 2x + 1

we get

2x [tex]+[/tex] 1 [tex]=[/tex] x² - 2x [tex]+[/tex] 1

x² - 2x [tex]+[/tex] 1 - 2x - 1 [tex]=[/tex] 0

x² - 4x = 0

x(x-4) = 0

So , x=0      or    x = 4

for x=0 , y = 2x+1 = 1

for x = 4, y = 2(4) + 1 = 9

Therefore, the solution for the system of equations is x=0 , y=1 and x=4 , y=9    .

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Answer:

see explanation

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] x - 5 < 11 ( multiply through by 3 to clear the fraction )

2x - 15 < 33 ← equivalent inequality

to solve add 15 to both sides

2x < 48 ( divide both sides by 2 )

x < 24

The sum of all angles in a triangle sum up to 180.

∠1 = x+37

∠2=x+67

∠3=90° (right triangle)

∠1+∠2+∠3 = 180°

(x+37)+(x+67)+90=180

2x+104+90=180

2x+194=180

2x=-14

x=-7

An angle can't be negative, but when plugged in it works!!

∠1 = -7+37=30

∠2=-7+67=60

30+60+90=180

Hope it helps!