Find the probability of drawing a green card, not replacing it, and then drawing another green card.

Answer:

B. All squares are rectangles.

Step-by-step explanation:

B is the correct answer, because all the squares are rectangles have 4 sides.

The accurate statement is that all squares are rectangles.

The statement that is true among the options provided is All squares are rectangles. This is because squares have all the properties of a rectangle, which is a quadrilateral with four right angles, but with the additional property of having all four sides of equal length. Therefore, because a square fulfills all the criteria of a rectangle, we can conclude that all squares are indeed rectangles. On the other hand, not all rectangles are squares since rectangles do not require all sides to be equal, only that the opposite sides are equal. Similarly, not all quadrilaterals are rectangles because other quadrilaterals, like rhombuses or kites, do not have the necessary four right angles. Finally, while all rectangles are parallelograms (a quadrilateral with opposite sides that are equal and parallel), not all parallelograms have right angles and thus are not all rectangles.

To elaborate, a rectangle is defined as a parallelogram with right angles. When it comes to comparing areas, the area of a rectangle is calculated by multiplying its base by its height. And in the case of squares, since all sides are equal, it's just the side length squared. However, when you have two shapes with equal area -- for instance, a square and a rectangle -- the one with the longer perimeter would be the one with the less compact shape, which in most cases would be the rectangle unless it is also a square.

Answer:

b. 9/5

Step-by-step explanation:

Cotangent is the inverse of tangent.

tan θ = y/x

cot θ = x/y

cot θ = (-9)/(-5)

cot θ = 9/5

just to add to that great reply by @MathPhys above

[tex]\bf (\stackrel{adjacent}{-9},\stackrel{opposite}{-5})~\hfill cot(\theta )=\cfrac{\stackrel{adjacent}{-9}}{\stackrel{opposite}{-5}}\implies cot(\theta )=\cfrac{9}{5}[/tex]

bear in mind that, the value coordinate pairs we get is the (x,y) coordinates, and x = adjacent side of the triangle whilst y = opposite side of it.

Answer:

2/3

Step-by-step explanation:

These two figures are similar since they have the same shape but not the same size

Yellow figure is larger than the orange figure therefore, the yellow figure is a larger or a dilated version of the orange figure.

Scale factor = Small side

                       Large side

Scale factor = 10/15

Scale factor = 2/3

The scale factor of this dilation is 2/3. The orange figure is dilated 2/3 times to form the yellow figure.

!!

Answer:

It's 2/3

Step-by-step explanation:

Trust me

Answer:

765.

Step-by-step explanation:

Sum of n terms = a1 (r^n - 1) / (r - 1) where a1 = the first term and r = the common ratio.

Here r = 6/3 = 2 and  a1 = 3.

Sum of 8 terms = 3 * ( 2^8 - 1) / 2 -1)

= 3 * 255

= 765 (answer).

Answer:

[tex]\sqrt{28} \approx 5.3[/tex]

Step-by-step explanation:

The Pythagorean Theorem says if you have a right triangle, then relationship between the three sides is the sum of the square of each leg is the hypotenuse squared.

So [tex]a^2+b^2=c^2[/tex]

where a and b are legs and c is the hypotenuse.

Plug in your a,b, and c. In this case it is a,6, and 8.

This means we have

[tex]a^2+6^2=8^2[/tex]

Simplify where you can before we begin the solving (the moving around of things to other sides).

[tex]a^2+36=64[/tex]

Now time for the solving. We are first going to get [tex]a^2[/tex] by itself.

To do this, we just need to subtract 36 on both sides giving us:

[tex]a^2=64-36[/tex]

[tex]a^2=28[/tex]

Now to get rid of the square on a, just square root both sides:

[tex]a=\sqrt{28}[/tex].

Answer:

  12.9 m

Step-by-step explanation:

Let d represent the length of the diagonal. Then d-2 is the length and d-6 is the width. The Pythagorean theorem can be used to relate these measures, which are the legs and hypotenuse of a right triangle.

  d² = (d-2)² + (d-6)²

  d² = d² -4d +4 + d² -12d +36 . . . . eliminate parentheses

  0 = d² -16d +40 . . . . . . . . . . . . . . . subtract d², collect terms

  0 = d² -16d +64 -24 . . . . . . . . . . . rearrange the constant to make a square

  0 = (d -8)² -24 . . . . . . write in vertex form

  d -8 = √24 . . . . . . . . . add 24 and take the square root

  d = 8 + √24 . . . . . . . . the negative square root is extraneous in this problem

  d ≈ 12.9 . . . meters

The length of the diagonal is about 12.9 meters.

Answer:

x= 16±√-64 over 2

Step-by-step explanation:

x= -(-16)±√(-16)²-4×1×80 over 2×1

x= 16±√256-320 over 2

x= 16±√-64 over 2

can also be represented with all real numbers.

Answer:

The last option is correct for two independent events.

P(A and B) = P(A) P (B)

And P(B and A) = P(B) P(A) which is equal. And other three cases are false.

P(AB) = P(BA) is true.

If outcomes of an event doesn't affect the outcomes of other event, the the events are called independent events, i.e. they are independent to each other.

For two independent events,

P(AB) = P(A)P(B)

Also, P(BA) = P(B)P(A)

And,  P(A)P(B) = P(B)P(A)

Hence, we can say that P(AB) = P(BA)

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Answer:

(0.78,0)

Step-by-step explanation:

I would use the quadratic formula.

[tex]a=3[/tex]

[tex]b=-8[/tex]

[tex]c=5[/tex]

[tex]\text{ The quadratic formula is } x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\\\\\text{ Let's find } b^2-4ac \text{ first}\\(-8)^2-4(2)(5)\\64-8(5)\\64-40\\24\\\\\text{ Now let's find } -b\\-b=8\\\text{ And } 2a\\2(2)=4\\\\\text{ Let's plug in this information }\\x=\frac{8 \pm \sqrt{24}}{4}\\\\\text{ We are now going to simplify }\\x=\frac{8}{4} \pm \frac{\sqrt{24}}{4} \\x=2 \pm \frac{\sqrt{4 \cdot 6}}{4}\\x=2 \pm \frac{\sqrt{4} \sqrt{6}}{4} \\x=2 \pm \frac{2 \sqrt{6}}{4}\\[/tex]

[tex] x=2 \pm \frac{\sqrt{6}}{2}[/tex]

So let's put both of these into out calculator

2 + sqrt(6)/2                  and             2-sqrt(6)/2

One of them should be approximately 3.22 as the question suggests.

3.22                                                        0.78

So the other x-intercept is approximately (0.78,0)

Answer:

Answer B

Step-by-step explanation:

The triangle has side lengths that are dilated by 2x in the second triangle

Answer:

2

Step-by-step explanation:

A P E X

Answer:

Yes.

Step-by-step explanation:

To see if h is a factor of f, we can use the factor theorem.

h(x)=x-3 has a zero at x=3 because h(3)=3-3=0.

So we want to see if the zero of h is a zero of f.

Is x=3 a zero of f?

You can check using synthetic division or just plug in 3.

Let's do both.

If you use synthetic you are trying to see if you get a remainder of 0.

If you plug it in you are trying to see if you get 0 as the output when plugging your input 3.

Let's do synthetic first:

Since we are checking to see if x=3 is a zero, that will go on the outside:

3 |  1   -1  -1   -15

 |        3   6    15

- ------------------------

     1    2   5     0

So yep the remainder is 0 so the answer is yes.

Let's plug it in:

f(3)=3^3-3^2-3-15

f(3)=27-9-3-15

f(3)=18-3-15

f(3)=15-15

f(3)=0

The result is 0 so the answer is yes.

You pick your favorite way here.

Answer:

c

Step-by-step explanation:

It would be c because you would add subtract 30 - x which equals 30x then you would divided 5 / 6 which equals 0.12 then you would add y plus some number which equals 12y then you would add 12y+12=24y=24y / 2=12 thenyou have 30x,12y.

Answer:

D

Step-by-step explanation:

A might be right for the wrong linear equation type. It could be describing a y intercept slope line. So even if it is right, it is not the answer. Actually the answer to A should be y = (5/6)x - 13

The general formula for the answer you want is

Givens

y -y1 = m(x - x1)

x1 = 30

y1 = 12

m = 5/6

Solution

y - 12 = (5/6)(x - 30)

That makes the answer D

Answer:

B

Step-by-step explanation:

Answer:

Its B) 60°

Step-by-step explanation:

135°=75°+CAD

135°-75°=CAD

60°=CAD

Answer:

See below in bold.

Step-by-step explanation:

The ratio of oil to vinegar is 5 : 1. That means that 5/6 of the mixture is oil and 1/6 is vinegar.

So to make 57 oz of the polish,  57/ 6 = 9 1/2 oz is vinegar and 5/6 * 57 =

47 1/2 oz is olive oil.

i was a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

AC, CE, AB, and AS

I belive those are your answers

Answer:

chords: CE and AB; secant: CE; tangent:t; diameter AB; radii: AS and SB

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability of drawing a boy's name is found in:

number of boys/total number of students

Our ratio then is

16/16+18 which is

16/34 which reduces to

8/17

As a percentage, it would be about 47%

Total students = 16 + 18 = 34

16 boys

Probability of picking boy = 16/34

Which reduces to 8/17

By looking at the graph, we can visually determine that the value of y when point x = -2 is -4.

Answer:

-4

Step-by-step explanation:

The y value at x=-2 is -4 because when you go to -2 on the x-axis the function is below there.  You can only go straight up or straight down to determine the y-value that corresponds to x=-2 so we go down because the function is below the x-axis there.

We are going to go down until we get on the graph of the line.  Scroll over with eyeballs to see that the y there is -4 (use the y-axis).

So the ordered pair (-2,-4) is on our line and when x=-2, y=-4.

Another example:

y=0 when x=2

Another example:

y=2 when x=4

Another example:

y=-3 when x=-1

Answer:

Mean = 0.8

Standard Deviation = 0.8

P(x = 3) is unusual event

Step-by-step explanation:

Part A)

The probability distribution with correct formatting is shown in the table attached with:

We have to find the mean and standard deviation of this distribution. The mean of the probability distribution is calculated as summation of the products of "the variable with its respective probability".

[tex]u = \sum x P(x)[/tex]

So, for the given distribution:

Mean = 0(0.4096) + 1(0.4096)+2(0.1536)+3(0.0256)+4(0.0016)

Mean = 0.8

Standard deviation is calculated by the following formula:

[tex]\sigma=\sqrt{\sum x^{2}P(x) - u^{2}}[/tex]

[tex]x^{2}P(x)=1.28[/tex]

Substituting the values, we get:

[tex]\sigma=\sqrt{1.28-(0.8)^{2}}\\\\ \sigma=0.8[/tex]

Part B)

Since the probability of 3 defective computers is less than 0.05, this is an unusual event.

So it would be unusual to have 3 defective computers in the batch.

Answer:

9

Step-by-step explanation:

Plug the numbers in

The result for each number when plugged in order is:

121

81

0

9

49

So 9 would be the answer

Answer:

9

Step-by-step explanation:

If (x-2)^2=49 then x could be 9.

(x-2)^2 = 49

x or 9 - 2 = 7

7^2 = 49

Answer:

B. H0: μd = 0 Ha: μd < 0

Step-by-step explanation:

Let μ1 and μ2 represent the number of correct answers during the timed condition and the unlimited time condition, respectively.

Let μd be the mean of the differences in the number of correct answers (timed − un timed) of all sixth graders.

The answer is B. H0: μd = 0 Ha: μd < 0

Here we have to check that the students will get few correct answers in the timed condition as compared to the unlimited time condition.

To know this, difference was calculated so we get the correct hypotheses as : H0: μd = 0 and Ha: μd < 0 .

Answer:

Also "H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0" is correct

Step-by-step explanation:

Answer:

  13 lb

Step-by-step explanation:

The horizontal component of the force is the magnitude of the force multiplied by the cosine of the angle with the horizontal.

  (16 lb)·cos(35°) ≈ 13.1 lb ≈ 13 lb

Answer:

b.13 lb

Step-by-step explanation:

We are given that  a boy pulls his sled with a rope .

The rope makes an angle with horizontal =[tex]35^{\circ}[/tex]

If a pull on the rope is needed to move the sled=16 pounds

We have to find the horizontal component of force

We know that horizontal component force=[tex]fcos\alpha[/tex]

Therefore, we have f=16 pound

Then, horizontal component of force=[tex]16cos 35^{\circ}[/tex]

Horizontal component of force=[tex]16\times 0.819=13.1lb[/tex]

Hence, horizontal component of force=13 lb

Answer:b.13 lb

Answer:

  see below

Step-by-step explanation:

The attached printable graph paper is a scale drawing. The 1 : 100 scale means each meter will be represented by 1 cm.

Answer:

x = 5.34

Step-by-step explanation:

The reference angle is 24 degrees.  I'm sure you are aware from the square at the other base angle that is a right triangle.  Right triangles have ratios by which we can determine missing side and angle measures.  The sin of a reference angle has a ratio that is side opposite/hypotenuse.  The cos of a reference angle has a ratio that is side adjacent/hypotenyse.  The tan of a reference angle has a ratio that is side opposite/side adjacent.

We need to decide which of these fits our needs according to the angle and sides we are given and need to find.  We have the reference angle as 24 degrees, we have the side adjacent to this angle as 12.  We are looking for x, which is the side opposite the reference angle.  Looking to what our definitions are for each ratio, the sides opposite and adjacent are defining the tan of the reference angle.  Setting up the ratio then looks like this:

[tex]tan(24)=\frac{x}{12}[/tex]

Multiply both sides by 12 to get

12 tan(24) = x

Do this on your calculator in DEGREE mode to get that

x = 5.342744224

Not sure what your teacher has you round to, but I usually have my students give me 2 decimal places

Answer:

[tex]\frac{2}{3}\text{ feet}[/tex]

Step-by-step explanation:

Let the equation that models the height of the tree after x years,

y = mx + c

Where, m is constant amount of increasing and c is any constant,

Given,

When x = 0, y = 4,

⇒ 4 = m(0) + c ⇒ c = 4,

Now, the height of plant after 4th year = m(4) + c = 4m + c

Also, the height of plant after 6th year = m(6) + c = 6m + c

According to the question,

6m + c is [tex]\frac{1}{5}[/tex] more than 4m + c,

[tex]6m+c=4m+c + \frac{1}{5}(4m+c)[/tex]

[tex]6m+c = \frac{6}{5}(4m+c)[/tex]

[tex]30m+5c=24m+6c[/tex]

[tex]6m=c[/tex]

By substituting the value of c

6m = 4

⇒ [tex]m=\frac{4}{6}=\frac{2}{3}[/tex]

Hence, 2/3 feet of height is increased each year.

Answer:

x=9

Step-by-step explanation:

I have answered ur question

Answer:

[tex]\large\boxed{y=\dfrac{3}{5}x-2}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of aline:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfraxc{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points:

(-5, -5)

y-intercept (0, -2) → b = -2

Calculate the slope:

[tex]m=\dfrac{-2-(-5)}{0-(-5)}=\dfrac{3}{5}[/tex]

Put the value of the slope and the y-intercept to the equation of a line:

[tex]y=\dfrac{3}{5}x-2[/tex]

Using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution

Let the quadratic equation given be of the form [tex]ax^2 + bx + c = 0[/tex], then

The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

There are two roots of a quadratic equations always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solution if roots are distinct, and have 1 solutions when both roots are same.

For this case, the given equation is:

[tex]x^2 - x = -1/4[/tex]

Converting this to the form [tex]ax^2 + bx + c = 0[/tex], we get:

[tex]x^2 - x + 1/4= 0\\or\\4x^2 -4x + 1 = 0[/tex]

Thus, we get:

a = 4, b = -4, c = 1

Putting these values in the expression for discriminant, we get:

[tex]D = b^2 - 4ac =(-4)^2 - 4(4)(1) = 16 - 16 = 0[/tex]

The discriminant is 0, so the considered quadratic equation is going to have both roots real and equal. Or in terms of distinct solutions, it is going to have one real solution (distinct).

Thus, using the discriminant to know about the nature of the solution of the quadratic equation x² -x = -1/4 tells us the fact as given by: Option c. one real solution

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Answer:

90 sq. ft.

Step-by-step explanation:

To find the "volume," you will need to multiply every the LxWxH.

Length = L

Width = W

Height = H

Then the answer is 90 sq. ft.

Answer:

Surface area = 126 square ft .

Step-by-step explanation:

Given : Rectangular cuboid .

To find : Find the total area of the solid figure.

Solution : We have given Rectangular cuboid .

Length = 3 ft .

Width = 5 ft .

Height = 6 ft .

Surface area = 2 ( l*w + w*h + l *h).

Plug the values

Surface area = 2 ( 3*5 + 5*6 + 3 *6).

Surface area = 2 (15 + 30 + 18).

Surface area = 2 ( 63).

Surface area = 126 square ft .

Therefore, Surface area = 126 square ft .

so the rainwater flows as R(x), and the decrease of the flow will be D(x), the new smaller pipe after the decrease will have water flowing at R(x) - D(x)

[tex]\bf \begin{cases} R(x)=-0.1x^3+1.4x^2-1.5x\\ D(x)=-0.04x^3+0.5x^2+x \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{R(x)}{(-0.1x^3+1.4x^2-1.5x)}-\stackrel{D(x)}{(-0.04x^3+0.5x^2+x)} \\\\\\ (-0.1x^3+1.4x^2-1.5x)+0.04x^3-0.5x^2-x \\\\\\ -0.1x^3+1.4x^2-1.5x+0.04x^3-0.5x^2-x \\\\\\ -0.10x^3+0.04x^3+1.4x^2-0.5x^2-1.5x-x\implies \stackrel{H(x)}{-0.6x^3+0.9x^2-1.6x}[/tex]

To find the rate of water flow through the smaller pipe, subtract the decrease function from the original rate function.

To find the rate at which rainwater flows through the smaller pipe, we need to subtract the decrease function from the original rate function. Let's call this new function H(x). So, H(x) = R(x) - D(x).

Substituting the given values, H(x) = (-0.1x^3 + 1.4x^2 - 1.5x) - (-0.04x^3 + 0.5x^2 + x). Simplifying, H(x) = -0.1x^3 + 1.4x^2 - 1.5x + 0.04x^3 - 0.5x^2 - x.

Combining like terms, H(x) = -0.06x^3 + 0.9x^2 - 2.5x.

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