!!!!!!!
Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.​

Answer: this is just the first one

y = -3.5x + 2

subtract the 7x from both sides to get 2y = -7x + 4

divide by 2 to get rid of the 2 so you get y = -3.5 + 2

For the third the mistake was adding 3.

You're meant to subtract the 10x from both sides to get -3y = -10x + 6

Divide everything by -3 to get y = 3.3 - 2

The figure that is shaded here has the quadrant and the sector as the two parts that it has.

The area of the shaded is given as (πr²) / 4 - bh/2

We have ACD as the sector of the circle.

such that we can see that the arc of AC is the quadrant of the circle nad it has the line at point o.

We would solve the area of the shaded as:

the area of a circle / 4 - the area of the triangle

this is mathematically written as

πr²/4 - 1/2bh

where

b = base

h = height

r = radius

This is the area of the shaded

An isosceles traingle would be formed when < A = < C = x

AO is equal to radius of the circle equal to the height CO

mathematically,

< A = < C = x

180 - 90 = 90 / 2

x = 45 degrees

We have to find the area of the sector

This is

= ∅/360 * πr²  

= (45 / 360) * (πr²)

= (πr²) / 4

From the calculation we have here, we would see that

the area of the shaded is  area of sector - area of the right angle triangle

= (πr²) / 4 - bh/2

When we go on to compare the sides we would then find out that they are equal. Therefore the shaded quadrant equals to the shaded sector.

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The probability that all four defective bulbs will be obtained by the same person is 0.1140   .

In the question ;

it is given that

the total number of light bulbs in the box = 24 bulbs

total number of bulbs available for first person = 24 bulbs

number of defective bulbs = 4

So, the number of ways the first person can select 4 defective bulbs out of 10 selection = C(10,4)

total number of ways that first person can select 4 defective bulbs out of 24 bulbs  = C(24,4)

So , the Probability that all four defective bulbs obtained by first person = C(10,4)/C(24,4) . .......(i)

Since 10 bulbs have been selected

So, total number of bulbs available for second person = 14 bulbs

number of defective bulbs = 4

So, the number of ways the first person can select 4 defective bulbs out of 14 remaining bulbs = C(14,4)

total number of ways that first person can select 4 defective bulbs out of 24 bulbs  = C(24,4)

So , the Probability that all four defective bulbs obtained by second person = C(14,4)/C(24,4) . .....(ii)

Probability that all four of the defective bulbs will be obtained by the same person

= P(four defective bulbs obtained by first person) + P(four defective bulbs by second person)

Substituting the probabilities from (i) and (ii) , we get

= C(10,4)/C(24,4) + C(14,4)/C(24,4)

= (210/10626 )+(1001/10626) ...as C(10,4)=210 ,C(24,4)=10626, C(14,4)=1001

= 1211/10626

= 0.1139657

≈ 0.1140

Therefore , the probability that all four defective bulbs will be obtained by the same person is 0.1140   .

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The result of the subtraction are-

The subtraction formula:

Minuend - Subtrahend = Difference

Part 1:

   46,329

-   33, 108

_______

   13,221

_________

Part 2:

  8,695

-   702

_______

  7, 993

_________

Part 3:

 700,989

-     7,989

_______

 693,000

_________

Part 4:

   55

-   49

_______

   06

_________

Thus, the result of the given subtractions are found.

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Answer:

2.1

Step-by-step explanation:

Use a calculator then put in 4.2 (4 1/5)% then put 50

Example: 4.2%50 = 2.1

The median of the cans collected by the tuck shop will be 77.

In statistics and probability theory, the median is the number that separates the upper and lower half of a population, a probability distribution, or a sample of data.

The middle score in the group is called the median. You follow these steps to determine the median:

Put the results in numerical order.

Subtract 2 from the final score.

If your total scores are odd, round them up to the next whole number to determine where the median falls. If your total scores are even, find the number that is in the middle and add it to the one that is higher up to get the median.

Total cans collected = 20

Dividing 20 by 2 we get 10, which is even.

To calculate the total of the two scores (76 + 78 = 154) add the score in the tenth position of the given data set to the number in the next position. Dividing 154 by 2, we get 77.

Therefore, 77 is the median in this instance.

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Here is the completed table:

number of spring rolls        number of people

6                                                 3

30                                               15

40                                                20

28                                                  14

The first step is to determine the number of people that one spring roll would serve.

Number of people that one spring roll would serve = 3 / 6 = 1/2

Number of people that s spring rolls would serve = number of people that 1 spring roll would serve x s

Number of people that 30 spring rolls would serve = 1/2 x 30 = 15

Number of people that 40 spring rolls would serve = 1/2 x 40 = 20

Number of people that 28 spring rolls would serve = 1/2 x 28 = 14

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Answer:

[tex]8x + 4h + 3[/tex]

Step-by-step explanation:

[tex]f(x)=4x^2 + 3x-5 \\ \\ f(x+h)=4(x+h)^2+3(x+h)-5 \\ \\ =4(x^2+2xh+h^2)+3x+3h+5 \\ \\ =4x^2+8xh+4h^2+3x+3h+5 \\ \\ f(x+h)-f(x)=(4x^2+8xh+4h^2+3x+3h+5)-(4x^2+3x+5) \\ \\ =8xh+4h^2+3h \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{8xh+4h^2+3h}{h}=8x+4h+3[/tex]

Answer:

When multiplying whole numbers by 10, simply add a 0 to the end of the number

When dividing by 10 remove a 0 from the end of the number.

Step-by-step explanation:

Multiplication:

10 x 2 = 20

10 x 6970 = 69750

Division

20 / 10 = 2

6970 / 10 = 697

Hope this helps! :)

Answer:

Step-by-step explanation:

There are three different possibilities for our first decision, each corresponding to which container we choose. So, if we choose container A, with 1/3 probability, we have a 6/10=3/5 probability of drawing green, which means we have a (1/3)(3/5)=1/5 of picking Container A and then picking a green ball. Similarly for container B the probability is (1/3)(4/10)=2/15, and the same for container C. So, the total probability is (1/5)+(2/15)+(2/15) = 7/15.

well, let's check how much is 30% of £158.80

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 158.80}}{\left( \cfrac{30}{100} \right)158.80}\implies 47.64~\hfill \underset{ticket~price}{\stackrel{158.8~~ - ~~47.64}{\text{\LARGE \pounds 111.16}}}[/tex]

Answer:

148.4

Step-by-step explanation:

4.40x8.40x4=148.4

The graph of the absolute value function is an inverted "V" such that the vertex is at (-4, -5) and opens downwards.

We call a modular function the function f(x) = |x|, in which its domain is given by the real numbers and its range is the positive real numbers. This is because, for every negative value on the y-axis, the modular function will make |-y| = -(-y) = y

Therefore, to plot the graph of a modular function, it is enough to adopt some values ​​for x and apply them to the function f(x) = | x |, in order to obtain their respective values ​​in y.

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When we simplify ³√(-64x⁶y⁹), the result obtained is written as -4x²y³

To simplify ³√(-64x⁶y⁹), do the following:

³√(-64x⁶y⁹)

Simplifying individual term, we have

³√(-64) = -4

³√(x⁶) = x²

³√(y⁹) = y³

Combining the individual simplification, we have

³√(-64x⁶y⁹) = -4 × x² × y³

³√(-64x⁶y⁹) = -4x²y³

Thus, from the above illustration, we can conclude that simplifying ³√(-64x⁶y⁹) results in -4x²y³

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The correct option is Option(c) An observational study where religious affiliation is an independent variable.

Therefore, it is an observational study where religious affiliation is an independent variable.

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The complete question is: "According to a study published in the journal Social Psychological and Personality Science, people with religious affiliations live longer, on average, than those without religious affiliations. The study analyzed more than 1,000 obituaries and accounted for other variables like sex and marital status.

What type of study is this, and what is the explanatory variable?

A. A manipulative experiment where religious affiliation is an independent variable

B. A manipulative experiment where lifespan is an independent variable

C. An observational study where religious affiliation is an independent variable

D. An observational study where lifespan is an independent variable."

As per the direct variation formula, it take  11 hours : 6 minutes : 36 seconds to earn $25,000 for the restaurant.

Direct variation:

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

Direct variation equation: y = kx

Given,

A local fast food restaurant takes in $9000 in a 4 hours period. Write a direct variation equation for the relationship income and number of hours.

Here we need to estimate how many hours it would take the restaurant to earn $25,000.

a) Let us consider income (I) directly varies to number of hours (h) where k is the constant of variation.

I = kh   ⇒  Direct variation equation

Solve for k:

9,000 = (k)(4)

k = 9,000/4

k = 2,250

b) When income (I) = 25,000, find the number of hours:

I = kh

25,000 = (2,250) (h)

h = 25,000/2,250

h = 11.11

It will take approximately 11 hours : 6 minutes : 36 seconds for the restaurant to earn $25,000.

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The number of smaller squares that can fit inside a larger square with a side length of 31 units is A. 961 smaller squares if the larger square is a plane.

A side length is one part of the length of an object.

Determining the number of smaller squares in a larger square depends on if the square is an enclosure or a plane.

If the square object is an enclosure, then it has three dimensions, length, width, and height, which are squared.  In that case, the number of smaller squares will be 29,791.

But if the square object is a plane with two dimensions, the number of smaller squares is 961.

Side length = 31 units

Area of a square plane = 961 unit² (31 x 31)

Volume of a square enclosure = 29,791 unit³ (31 x 31 x 31)

Thus, the number of smaller squares depends on the dimensions of the larger square.

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Answer:

Step-by-step explanation:

Answer:

The percent of decrease in the price of the scooter is 30.6%.

Step-by-step explanation:

In order to calculate the percent of decrease, you have to divide the difference between the two numbers by the original number and multiply the result for 100:

% decrease=((10.75-15.50)/15.50)*100

% decrease=-0.306*100

% decrease= -30.6%

According to this, the answer is that the percent of decrease in the price of the scooter is 30.6%.

The formula for y in terms of x is y = 8/x^3 and x is 1/2 when y = 64

The variation statement is given as

y is inversely proportional to the cube of x

This means that

y = k/x^3

Where k represents the constant of variation

Using the points on the table, we have

(x, y) = (1, 8)

This gives

8 = k/1^3

Evaluate

k = 8

So, we have

y = 8/x^3

Here, we have

y = 64 and y = 8/x^3

This gives

8/x^3 = 64

So, we have

x^3 = 1/8

Take the cube roots

x = 1/2

Hence, the value of x is 1/2

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To know how much each chocolate bar costs, knowing that ten chocolate bars cost 3 pesos, we only have to divide the total cost of the 10 chocolate bars by the total number of chocolate bars.

So that:

Tenth that; the cost of each bar is 0.3 pesos.

Answer:

y = -x(x - 1).

Step-by-step explanation:

y = a(x - b)(x - c) where a is a constant and b and c are the x-intercepts.

y = a(x - 0)( x - 1)

y =   ax(x - 1).

When x = 2, y = -2 so:

-2 = a(2) (2 - 1)

2a = -2

a = -1.

So the equation is y = -x(x - 1).

Answer:

[tex]y=-x^2+x[/tex]

Step-by-step explanation:

Intercept form of a quadratic equation:

[tex]y=a(x-p)(x-q)[/tex]

where:

Given:

Substitute the given values into the formula and solve for a:

[tex]\begin{aligned}y&=a(x-p)(x-q)\\\\\implies -2&=a(2-0)(2-1)\\-2&=a(2)(1)\\-2&=2a\\\dfrac{2a}{2}&=\dfrac{-2}{2}\\\implies a&=-1\end{aligned}[/tex]

Substitute the given x-intercepts and the found value of a into the formula:

[tex]y=-1(x-0)(x-1)[/tex]

Expand to standard form:

[tex]\implies y=-1(x)(x-1)[/tex]

[tex]\implies y=-x(x-1)[/tex]

[tex]\implies y=-x^2+x[/tex]

Answer:

Not sure what you are looking for

Step-by-step explanation:

Acceleration = change in velocity / change in time

                     = (60 - 65) / 1 s =  - 5 m/s^2

Test of a horizontal line.Suppose f is a function.F does not have an inverse if any horizontal line crosses the graph of f more than once.F does have an inverse if no horizontal line crosses the graph of f more than once

How do you calculate f's inverse?

f= {(1,2),(2,3),(3,5),(4,7)}

Dom(gof)=dom(f)={1,3,4}.

(gof)(1)=g{f(1)}=g(2)=3,

(gof)(3)=g{f(3)}=g(5)=1

(gof)(4)=g{f(4)}=g(1)

∴gof={(1,3),(3,1),(4,3)}.

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Answer: y= -2x+5

Step-by-step explanation:

Answer:   [A]:  " 78 °  " .

_______

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

So, given m∠F & m∠G are supplementary angles:
 and given m∠F = (4x + 22) and:  m∠G = (6x + 18) ;

 Find m∠F ; which equals (4x + 22).

_______
So, add the 2 (two) supplementary angles;

set them as "equal to 180" ;

solve for x ;

then: plug that x  value into:
     (4x + 22) ; which is the m∠F ;

_______
 4x + 22 + 6x + 18 = 180 ;  

On the 'right-hand side of the equation" ;

 "combine the like terms" :
    + 4x + 6x = + 10x ;

    + 22 + 18 = 40 ;

Then rewrite the equation:
   10x + 40 = 180 ;

_______
Now:
Method 1):
 Subtract 40 from Each Side of the equation:
   10x + 40 − 40 = 180 − 40 ;
     to get:  10x = 140 ;  

  Now:  Divide Each Side of the equation by 10 ;  to isolate x on one side of the equation; & to solve for x ;
     10x / 10 = 140 / 10 ; to get:  " x = 14 " ;

Method 2):
  When we have:  10x + 40 = 180 ;

    Divide the entire equation (i.e. Each Side of the equation) by 10 ;

   to get rid of the "zeros" :

        (10x + 40) / 10 = (180)/10 ;

    to get:
    (10x/10) + (40/10) = (180/10);

     →  x  + 4 = 18 ;

     Subtract 4 from Each Side of the equation;  to isolate x on one side of the equation; & to solve for x ;
         x  + 4 − 4 = 18 − 4  ;
     to get:  x = 14 .
_______
 Now, find m∠F = 4x + 22  ;  
   Plug in 14 for x ; to solve:
                  m∠F = 4(14) +22 ;

                           =   56 + 22 ;

                  m∠F =  78°

        which corresponds to:
Answer choice:  [A]:  78°  .
_______
Hope this is helpful to you!

 Wishing you well!
_______

Answer:

A

Step-by-step explanation:

Angles that are supplementary add to 180°.

[tex]4x+22+6x+18=180 \\ \\ 10x+40=180 \\ \\ 10x=140 \\ \\ x=14 \\ \\ \therefore m\angle F=78^{\circ}[/tex]

I am not in this grade but I think it is A

Step-by-step explanation:

if right please mark brainiest

Answer: -2

Step-by-step explanation:

Answer: -2

Step-by-step explanation: