Pulling a red card from a deck of cards, replacing it, and pulling another red card.

Answer:

\(\sqrt{20}\) or 4.47

Step-by-step explanation:

To find the distance between two points on a plane, you can use the distance formula: \(d=\sqrt{(y^{2}-y^{1})^2 + (x^{2}-x^{1})^2 }\)

Plug your values in to get the distance between the two points.

\(d=\sqrt{(y^{2}-y^{1})^2 + (x^{2}-x^{1})^2 }\)

\(d=\sqrt{(2-4)^2 + (7-3)^2 }\)

\(d=\sqrt{(-2)^2 + (4)^2 }\)

\(d=\sqrt{4 + 16 }\)

\(d=\sqrt{20}\) or 4.47

The length of u, to the nearest inch, is 1818 inches.

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In this case, we'll use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

Let's label the sides and angles of the triangle:

Side a = u (length of u)

Side b = t (820 inches)

Side c = v (length of v)

Angle A = m/U (132°)

Angle B = m2V (25°)

Angle C = 180° - A - B (as the sum of angles in a triangle is 180°)

Now, we can use the Law of Sines to set up the equation:

u/sin(A) = t/sin(B)

Plugging in the given values:

u/sin(132°) = 820/sin(25°)

To find the length of u, we'll solve this equation for u.

u = (820 \(\times\) sin(132°)) / sin(25°)

Using a calculator, we can evaluate the right side of the equation to get the approximate value of u:

u ≈ (820 \(\times\) 0.9397) / 0.4226

u ≈ 1817.54 inches

Rounding to the nearest inch, we have:

u ≈ 1818 inches

For similar question on Law of Sines.

https://brainly.com/question/30401249  

#SPJ8

We have the data set:

90, 79, 32, 94, 84, 14, 44

Ordering it:

14, 32, 44, 79, 84, 90, 94

The range is given by the highest value minus the lowest value:

Range: 94 - 14 = 80

The median is 79

First quartile: 32

Third quartile: 90

Answer: Last option

Answer:

  (b)  as marked

Step-by-step explanation:

Subtract r, multiply by u^2/(-k-y-r), and take the square root.

  \(\dfrac{m}{u^2}+r=-k-y\qquad\text{given}\\\\\dfrac{m}{u^2}=-k-y-r\qquad\text{subtract $r$}\\\\\dfrac{m}{-k-y-r}=u^2\qquad\text{multiply by $\dfrac{u^2}{-k-y-r}$}\\\\u=\pm\sqrt{\dfrac{m}{-k-y-r}}\qquad\text{take the square root}\)

Answer:

H0 : σ = 0.5

H0 : σ < 0.5

Step-by-step explanation:

From the scenario described above, the company wants to see conclusive evidence that the population standard deviation of sheath thickness is less than .05 mm ; THIS SIMPLY means ; REJECTION OF the NULL HYPOTHESIS. This is because once there is a significant or conclusive evidence in hypothesis testing, then we reject the null and support the claim of the alternative hypothesis.

Hence, the alternative hypothesis is ; population standard deviation of sheath Thickness is less than 0.5.

H1 : σ < 0.5 ;

Therefore, our null will be ;

H0 : σ = 0.5

Answer: We can first find the dot product of vec r with hat j and hat k:

vec r * hat j = (3 hat i - 2 hat j + 6 hat k) * (- hat j) = -2

vec r * hat k = (3 hat i - 2 hat j + 6 hat k) * hat k = 6

Substituting these values into the expression given, we get:

(vec r * hat j).(vec r * hat k) - 12 = (-2) * (6) - 12 = -24

Therefore, the value of (vec r * hat j).(vec r * hat k) - 12 is -24.

Step-by-step explanation:

The inequality that represents the number of each type of calculator she can buy will be 25x + 65y ≤ 800

Given that teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each.

Consider that x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators.

The inequality that represents the situation becomes as;

25x + 65y ≤ 800

Learn more about inequality ;

brainly.com/question/14164153

#SPJ1

Answer:

the 13 and one-third cups of flour he has. If each loaf requires 3 and four-fifths cups of flour, how many loaves can Josh bake?

3 loaves of bread

4 loaves of bread

50 loaves of bread

51 loaves of bread

Step-by-step explanation:

Answer:

t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32

Step-by-step explanation:

Solve for t:

16 t^2 - 23 t + 18 = 0

Divide both sides by 16:

t^2 - (23 t)/16 + 9/8 = 0

Subtract 9/8 from both sides:

t^2 - (23 t)/16 = -9/8

Add 529/1024 to both sides:

t^2 - (23 t)/16 + 529/1024 = -623/1024

Write the left hand side as a square:

(t - 23/32)^2 = -623/1024

Take the square root of both sides:

t - 23/32 = (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32

Add 23/32 to both sides:

t = 23/32 + (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32

Add 23/32 to both sides:

Answer: t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32

Answer:

B

Step-by-step explanation:

V = area of base * hight ; consider the base the triangle

V= (b*h of triangle /2 ) * h of figure

V= (6*8/2)*13 = 312 cm³

Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

No, there are x values which map to more than 1 y-value.

Given that Matthew examines the relation as shown in the below.

{(4, -11), (3,1), (0,1), (2,6), (3, -1)}

We need to check whether the relation is a function or not,

So, we know that,

A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.

If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.

Here we can see that the y values are repeated, so it is not a function.

Learn more about functions click;

https://brainly.com/question/31062578

#SPJ1

Answer:

Step-by-step explanation:

1). ∠1 and ∠2 are supplementary.

  m∠1 + m∠2 = 180°

2). ∠1 and ∠2 are complementary angles.

   m∠1 + m∠2 = 90°

3). If ∠1 and ∠2 are vertical angles,

   m∠1 = m∠2 = 64°

4). ∠Q and ∠R are complementary angles.

   m∠Q + m∠R = 90°

   If m∠R = 73°,

   m∠Q + 73° = 90°

   m∠Q = 90° - 73°= 17°

5). m∠AED = 135°

a). Since, ∠AED and ∠AEC are supplementary angles,

   m∠AED + m∠AEC = 180°

   m∠AED = 152°

   152° + m∠AEC = 180°

   m∠AEC = 180° - 152° = 28°

b). m∠CEB + m∠AEC = 180°

    28° + m∠CEB = 180°

    m∠CEB = 180° - 28° = 152°

c). m∠FEC = m∠FEA + m∠AEC

                 = 90° + 28°

                 = 118°          

Answer:

Step-by-step explanation:

A

Answer:

-5

Step-by-step explanation:

plz mark brainliest :)

Answer:

94.85 rounded to the nearest tenth is 94.9

...with 6 dice

15,625 / 46,656

33.49 %

31,031 / 46,656

66.51 %

Answer:

where is the graph

Step-by-step explanation:

In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.

The missing table is given below.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Shawn is collecting money from students at his school for a charity.

The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.

Since 30 is 1/3 of 90, we know the ratio is 1:3.

In order of blank boxes going from left to right then down

1, 9, 5, 75, 35

The complete table is attached below.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

#SPJ1

Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches

Answer:

120

Step-by-step explanation:

LCM of (2^3×3×5) and (3×5) is​

The LCM of the expression will be the product of all the factors that are in both expressions

(2^3×3×5) = 2 * 2 * 2 * 3 * 5

(3 * 5) = 3 * 5

since 3 * 5 is common to both factors, we will not have to repeat it twice to get our LCM again. Hence the LCM is expressed as;

LCM = 2 * 2 * 2 * 3 * 5

LCM  = 8 * 3 *5

LCM = 24 * 5

LCM = 120

Hence the required LCM is 120

Answer:

48

Step-by-step explanation:

2 x 8 = 16

4 x 8 = 32

8 x 8 = 64

6 x 8 = 48

2 div 16 = 8

4 div 32 = 8

8 div 64 = 8

6 div 48 = 8

The calculation of volume for the different kind of prisms are:

Rectangular Prism- 1 dm³

Tall triangular prism- 1 dm³

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

Rectangular prism: A rectangular prism that is not a cube can have dimensions of 0.5 dm x 0.5 dm x 4 dm.

This gives a volume of:

0.5 dm x 0.5 dm x 4 dm = 1 dm³

The rectangular prism has six faces, all of which are rectangles.

Tall triangular prism: A tall triangular prism can have a triangular base with sides of length 1 dm, 1 dm, and 2/√3 dm, and a height of 2√3/3 dm. This gives a volume of:

(1 dm x 1 dm x 2/√3 dm) x (2√3/3 dm) = 1 dm³

The tall triangular prism has five faces, one of which is a parallelogram and the other four are triangles.

To prove that each of these prisms has a volume of 1 dm³, we can use the formula for the volume of a prism, which is:

Volume = Base Area x Height

For each of the prisms above, we have calculated the base area and height such that their product equals 1 dm³.

Therefore, each prism has a volume of 1 dm³.

To know more about Volume check:

https://brainly.com/question/13338592

#SPJ9

Answer:

It's 12

Step-by-step explanation: yup

Answer:

12

Step-by-step explanation:

x/18=8/12

*Multiply both sides by 18

x=144/12

x=12

Answer:

Step-by-step explanation:

\(\frac{2}{5} : \frac{1}{15}\\\)

LCM of the denominator = LCM ( 5 , 15 ) = 15

∴ Now we have to multiply LCM by both the fractions , we get ,

\(\frac{2}{5}.15 : \frac{1}{15}.15\\ 6 : 1\)

Answer:

SAS

Step-by-step explanation:

statements:

reasons:

Answer:

someone has type A blood 40%

Step-by-step explanation:

The probability that a certain person has the A-type blood is 40%, or 0.4

Answer:

b

Step-by-step explanation:

The graph that represents the numbers of packages of mix A and mix B that can be produced is graph (b)

The representations are:

So, the system of inequalities is:

\(8x + 4y \le 120\)

\(6x + 6y \le 96\)

Next, we plot the graphs of the inequalities (see attachment)

Hence, the graph that represents the numbers of packages of mix A and mix B that can be produced is graph (b)

Read more about systems of inequalities at:

https://brainly.com/question/11234618

Answer:

∠R = 17°

∠Q = 100°

∠P = 63°

Step-by-step explanation:

In a triangle all the degrees added together should be 180°. Because we know this, we can add up every component and set it to 180 like this:

\(4x - 5 + 6x - 2 +x = 180\)

After combining like terms we get:

\(11x - 7 = 180\)

add 7 to both sides and then divide by 11 to get:

\(x = 17\)

Now that we know x we know ∠R = 17°.

In order to find the rest we plug in 17 for x into their given formulas. For ∠Q:

\(6(17) - 2 = 100\)

And for ∠P you can plug in to get the answer or do 180 - 100 - 17 (subtracting the other 2 angles):

180 - 100 - 17 = 63

or

\(4(17) - 5 = 63\)