Use the point-slope form from the previous question and fill-in the following table of values.

The point-slope equation went through the following 2 points: (0, -1) and (1, 2)

(0, -1)

(1, 2)

(2, )

(3, )

since the two triangles are congruent..

AB=ED

AC=FD(side opposite to the right angle)

FD=AC

•°•FD=13m

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:

$14.40

Step-by-step explanation:

my way of doing things:

15/100=0.15=1%of total amount

0.15 x 6=0.9= the 6% which is the tax

0.15 x 10 = 1.5=the coupon

Take the coupon amount $1.50 minus the tax amount $0.90 =$0.60. Because the coupon amount is greater than the tax the 60 cents gets taken away from the original 15 dollars leaving Mr. Longely only having to pay $14.40.

Answer:

Step-by-step explanation:

Number of attendees the first day = x.

Solve the following equation for x:

Answer:

8x-3

Step-by-step explanation:

Average of 2 numbers means add the two numbers and divide by 2

(y+z)/2 = 5x

Let z = 2x+3

(y+2x+3)/2 = 5x

Multiply each side by 2

y+2x+3 = 10x

Subtract 2x from each side

y+3 = 10x-2x

y+3 = 8x

Subtract 3

y = 8x-3

The other number is 8x-3

Answer:

26 cm

Step-by-step explanation:

P = 2a + 2b

a = side

b = base

Answer:

The area=base×height

=10×4

=40cm^2

perimeter=2(length+breadth)

I think to find the height Dc you use the pythagoras theorem of

Dc^2=de^2+ce^2

=√16+9

=5

therefore the perimeter will be

p=2(5+10)

=20cm

I hope this helps and sorry if it's wrong

Answer:

C. rotation 180º about the origin

Step-by-step explanation:

Given

Quadrilaterals GWVY and G'W'V'Y'

Required

Describe the transformation rule

Pick points Y and Y'

[tex]Y = (5,-4)[/tex]

[tex]Y' = (-5,4)[/tex]

The above obeys the following rule:

[tex](x,y) \to (-x,-y)[/tex]

When a point is rotated by 180 degrees, the rule is:

[tex](x,y) \to (-x,-y)[/tex]

Hence, (c) is correct

Answer:

The situation that represents this situation is:

[tex]t = \frac{60}{n}[/tex]

Step-by-step explanation:

The amount of time t needed to assemble the set is inversely  proportional to the number people n working.

This means that:

[tex]t = \frac{k}{n}[/tex]

In which k is the constant of proportionality.

Twelve people can assemble the set in 5 hours.

This means that for [tex]n = 12, t = 5[/tex]. We use this to find k.

[tex]t = \frac{k}{n}[/tex]

[tex]5 = \frac{k}{12}[/tex]

[tex]k = 12*5 = 60[/tex]

Write an equation to represent the situation.

[tex]t = \frac{60}{n}[/tex]

1,4,9,16,25,36,49,........

7th pattern =49.....

Answer:

1, 4, 9, 16, 25, 36, 49…................the 7 the pattern is 49

Answer:

0.9332

Step-by-step explanation:

We are given that

Mean diameter, [tex]\mu=73[/tex]

Variance, [tex]\sigma^2=4[/tex]

We have to find the probability that the diameter of a selected bearing is less than 76.

Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]

[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]

[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]

Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]P(x<76)=P(Z<1.5)[/tex]

[tex]P(x<76)=0.9332[/tex]

Hence, the probability that the diameter of a selected bearing is less than 76=0.9332

Answer:

i) 410 cm³

ii) 48 min

Step-by-step explanation:

we start with 250 cm³.

and then we fill in 20 cm³ per minute.

i)

after 30 minutes we have

250 + 8×20 = 250 + 160 = 410 cm³

ii)

how long (how many minutes) does it take to reach 1210 cm³ in the tank ?

well, first we subtract the start amount (250).

and then we see how often 20 cm³ will "fit" into the remainder. and then we know how many minutes the water has to run.

1210 - 250 = 960 cm³

so, the incoming water needs to reach 960 cm³ to have a total of 1210 cm³.

and

960 cm³ / (20 cm³ / min) = 960 cm³ min / 20 cm³ =

= 960 min / 20 = 48 min

Answer:

24

Step-by-step explanation:

The topic here is COMBINATORICS.

The parent topic is PERMUTATIONS & COMBINATORICS.

Permutation deals with arrangement in a definite order while, as stated in the question here, definite order in not needed in Combinatorics.

Now, the multiplication rule of counting, also known as the rule of product, talks about the multiplication of the figures that represent the different ways of doing something.

For example, in this question, the robot needs to attach 4 wires to a circuit board. If you know how Physics or Electricity works, you'll that truly this is a combination matter and not permutation.

Putting/Connecting the 4 wires together (in a square shaped circuit for instance), the arrangement RGBY is different from RGYB or RBGY.

So there will be more ways to connect or combine these wires, than if we were to follow a definite rule like: "Red and Green must always stay together".

So using the multiplication rule of counting to determine 4 choices for the Red wire, 3 choices for the Green wire, 2 choices for the Blue wire, and 1 choice for the yellow wire, we have:

R4 x G3 x B2 x Y1  =  4 x 3 x 2 x 1  =  4!  =  24

The term "4!" means "Four Factorial".

Answer:

the answer is D. infinitely many

The number of solutions there are to the system of equations is Infinitely many, the correct option is D.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

We are given that;

The two identical lines

Now,

We can find the equations of the two lines by using the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

For line 1, we have two points (0,2) and (1,0), so we can find the slope as:

m1 = (0 - 2) / (1 - 0) = -2

Using point-slope form, we can write the equation of line 1 as:

y - 2 = -2(x - 0)

y = -2x + 2

For line 2, we have two points (-1,4) and (2,-2), so we can find the slope as:

m2 = (-2 - 4) / (2 - (-1)) = -2

Using point-slope form, we can write the equation of line 2 as:

y - 4 = -2(x - (-1))

y = -2x + 2

We can see that the two lines have the same slope and the same y-intercept.

Therefore, by the given slope of the line the answer will be infinitely many.

Learn more about slope here:

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Hi there!

[tex]\large\boxed{a + b + c = 6}[/tex]

We can begin by using the point (0, 1).

At the graph's y-intercept, where x = 0, y = 1, so:

1 = a(0)² + b(0) + c

c = 1

We can now utilize the first point given (-3, 10):

10 = a(-3)² + b(-3) + 1

Simplify:

9 = 9a - 3b

Divide all terms by 3:

3 = 3a - b

Rearrange to solve for a variable:

b = 3a - 3

Now, use the other point:

15 = a(2)² + 2(3a - 3) + 1

14 = 4a + 6a - 6

Solve:

20 = 10a

2 = a

Plug this in to solve for b:

b = 3a - 3

b = 3(2) - 3 = 3

Add all solved variables together:

2 + 3 + 1 = 6

Answer:

13.5 %

Step-by-step explanation:

For a normal distribution, the Empirical Rule states that 68% of values lie between 1 standard deviation of the mean, 95% of values lie between 2 standard deviations of the mean, and 99.7% of values lie between 3 standard deviations of the mean. Here, we can see that 54.5 is 1 standard deviation away from the mean and 57 is 2 standard deviations away. This means that we want to find the difference between 1 and 2 standard deviations from the mean (in the positive direction)

To find the difference, we can simply find (percent of values 2 standard deviations of the mean) - (percent of values 1 standard deviation from the mean) = percent of values between 1 and 2 standard deviations from the mean

= 95-68 = 27 %

Finally, this gives us the percent of values between 1 and 2 standard deviations from the mean on both sides. We want to only find the positive aspect of this, as we don't care how many values are between 49.5 and 47 years old. Because normal distributions are symmetric, or equal on both sides of the mean, we can simply divide by 2 to eliminate the half we don't want, resulting in 27/2 = 13.5

The probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

Given that, average age managers = 52 years standard deviation = 2.5 years.

Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.

Considering the equation Z =  (X−μ)/σ

Where, X is the lower or higher value, as the case may be μ  is the average σ  is standard deviation

Now, z1= (54.5 - 52)/2.5

= 1

z2= (57 - 52)/2.5

= 2

Now, z2-z1= 2-1

= 1

P(54.5>Z<57)= 0.8413

Therefore, the probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.

Learn more about the standard deviation visit:

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Answer: C

Step-by-step explanation:

Answer:

probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)

=194/285 or 0.6807.

Step-by-step explanation:

The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.

The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.

Hence

|E'| = C(14,3)

= 14×13×12/3!.

Therefore probability P(E')

= |E'|/|S|

= (14×13×12)/(20×19×18)

= (14×13×2)/(20×19×3)

=(7×13)/(5×19×3)

= 91/285.

Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.

Answer:

-78

Step-by-step explanation:

Zinc group :

Mean, x1 = 3328

σ1 = 640

Sample size, n1 = 28

Placebo group :

Mean, x2 = 3406

σ2 = 851

Sample size, n2 = 31

The point estimate for the true difference between the population means is obtained as :

Mean difference between population :

x1 - x2 = 3328 - 3406 = - 78

Answer:

Hypotenuse = XY = 17 cm

Base = YZ = 15 cm

Perpendicular = XZ = 8 cm

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  (a) (-∞, -8), (-5, -2), (2, 5)

  (b) -8, -2, 5

  (c) negative

  (d) 6

Step-by-step explanation:

(a) The function is increasing on intervals where the graph slopes upward left-to-right. Those are (-∞, -8), (-5, -2), and (2, 5).

__

(b) The local maxima are at the right end of each interval on which the function is increasing: -8, -2, 5.

__

(c) The function opens downward (∩), so has a negative leading coefficient.

__

(d) There are three local maxima and two local minima (left end of an increasing interval), so a total o 5 turning points. The degree of the polynomial is at least one more than this: 6.

Answer:

g(1)=(1-1)*2 -2

= -2

g(2) = (2-1)*2 -2

= -1

g(3) = 1/2 (3) -2

= -1/2

Answer:

g(1) = -2

g(2) = -1

g(3) = -1/2 or -0.5

Step-by-step explanation:

you really need help for typing numbers into your calculator ? because there is nothing else to do here.

we get 3 values of x and need to calculate the functional values based on the given expressions by using each given value for x.

the only thing that requires a bare minimum of intelligence is to find the fitting expression.

so, for g(1) and g(2) we need to use the middle one, and for g(3) the third one. uhhhh, very difficult ...

typing it in here is way more effort than doing it directly on the calculator or really in the head.

so, g(1) = (1-1)² - 2 = -2

g(2) = (2-1)² - 2 = 1 - 2 = -1

g(3) = 1/2 ×3 - 2 = 3/2 - 2 = 3/2 - 4/2 = -1/2

uhhhh, come in, you could have done that too. and way faster.

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the ratio of the rectangle base to the triangle side length. Then the height of the small triangle above the rectangle will be x times the height of the equilateral triangle. Then the height of the rectangle is (1-x) times the height of the equilateral triangle. The rectangle's area will be ...

  A = bh

  A = (xL)(1-x)(L·√3/2) = (L²√3/2)(x)(1-x)

This graphs as parabola opening downward with x-intercepts at x=0 and x=1. The vertex is on the line of symmetry, halfway between these zeros, at x = 1/2.

The base of the rectangle is L/2.

The height of the rectangle is L√3/2.

_____

The general solution to this sort of problem is that one side of the rectangle is the midsegment of the triangle.

Answer:

The student's GPA is of 0.82.

Step-by-step explanation:

GPA:

To find the student's GPA, we find his weighed mean.

Grades:

7 hours worth 3(B)

6 hours worth 1(D)

20 hours worth 0(F). So

[tex]M = \frac{7*3 + 6*1 + 20*0}{7+6+20} = 0.82[/tex]

The student's GPA is of 0.82.

Answer:

xsqrt(2)

Step-by-step explanation:

sqrt(a) / sqrt(b) = sqrt(a/b)

sqrt(22x^6) / sqrt(11x^4)

sqrt(22x^6/11x^4)

sqrt(2x^2)

We know sqrt(ab) = sqrt(a) sqrt(b)

sqrt(x^2) sqrt(2)

xsqrt(2)

Answer:

A. 4

Step-by-step explanation:

The diagonals are also congruent to each other. Diagonals of a square bisect each other. This implies that:

MO bisects LN, thereby dividing LN into two equal segments, LG and GN.

Thus, LG = GN.

Since the length of LG = 4, therefore:

GN = 4

Answer:

Discrete

Discrete data represent items that can be counted; they take on possible values that can be listed out. The list of possible values may be fixed (also called finite); or it may go from 0, 1, 2, on to infinity (making it countably infinite).

Step 1: Find the area of the rectangle

A = base x height

A = 39 x 20

A = 780

Step 2: Find the area of the semi-circles

---Two semi-circles is the same as one whole circle, so I will be finding the area of one whole circle.

A = pi x r^2

A = pi x 10^2

A = 100pi = 314

Step 3: Find the area of the figure

Area = area of the rectangle - area of the semi-circles

A = 780 - 314

A = 466 cm^2

Hope this helps!

Answer:

466 cm^2

Step-by-step explanation:

This one is done basically the same as the other.

Rectangle = 20 x 39

Circle = (3.14) x 10^2

Rectangle = 780

Circle = 314

rectangle - circle

780 - 314 = 466

Answer:

1:3

Step-by-step explanation:

because you would get 1 of 3 flavours