Question 6: What is the probability of drawing a king and then queen from a standard deck of playing cards?
(3 marks)

Answer: height = 1.16 ft

Step-by-step explanation:

14 inches = 1.17 feet

Height of the oven =

Height = volume / lw

H = 1.59 / 1.17*1.17

H = 1.16 feet

Answer:

a. 3.25 m

b.1.2 ft

Solution,

a. Let 'h' be the height of cylinder

Given,

Radius(r)=0.7 m

Volume(v)=5 m^3

Formula to find volume of cylinder

[tex]\pi {r}^{2} h[/tex]

where r= radius and h= height

so,

[tex] \frac{22}{7} \times 0.7 \times 0.7 \times h = 5 \\ or \: h = \frac{5 \times 7}{22 \times 0.7 \times 0.7} \\ or \: h = \frac{35}{22 \times 0.49} \\ or \: h = \frac{35}{10.78} \\ h = 3.25 \: m[/tex]

b.

[tex]volume = 1.59 = \frac{14}{12} \times \frac{14}{12} \times h \\ 1.59 = \frac{ {14}^{2} }{144} \times h \\ h = \frac{1.59 \times 144}{196} \\ h = 1.168 \: ft \\ h = 1.2 \: ft[/tex]

hope this helps...

Good luck on your assignment...

Answer:

2600

Step-by-step explanation:

the number of female : 5000*48%= 2400 female

males =5000-2400=2600 0r 52%

Answer:

I think it's 1/2 because it might be right

Answer:

See attached graph for the first part

Answer to second part: The end part of the graph show the slowest increase

Step-by-step explanation:

The attached picture represents the number of infected people, starting with a relatively small number at the origin of the horizontal axis (x=0, or time=0) then increasing abruptly in the center of the graph with steep slope. and then infection slowing down (although still slowly increasing) in the region highlighted in yellow to the right of the graph.

Answer:

The coordinates seem to be A(-2, -4), B(3, 4) and C (3, -4). The rule (2x, 2y) means that you multiply the coordinates of the points by 2 so you just have to plot the points A'(-4, -8), B'(6, 8), C'(6, -8) and then connect them.

Answer:

B. 5

Step-by-step explanation:

[tex] \tan(30 ) = x \div 5 \sqrt{3} = \tan(30) \times 5 \sqrt{3} = 5[/tex]

Answer:

36°

Step-by-step explanation:

Let m∠8 = x°

Therefore, m∠7 = 4x°

Since, ∠7 and ∠8 are linear angles.

Therefore,

m∠7 + m∠8= 180°

4x° + x° = 180°

5x° = 180°

x° = 180°/5

x° = 36°

x = 36

Hence,

m∠8 = 36°

Answer:

195 students voted for the blue and silver color combination.

Step-by-step explanation:

First, you have to convert 65% to a decimal ( You should get 0.65 ).

Next, you multiply 300 by the decimal ( 0.65 )

You should get 195, so that's how many people voted for the blue and silver color combination.

Answer:

195

Step-by-step explanation:

Answer:

The midpoint is (3,8)

Step-by-step explanation:

To find the x coordinate of the midpoint,  add the two coordinates together and divide by 2

( 4+2)/2 = 6/2 = 3

To find the y coordinate of the midpoint,  add the two coordinates together and divide by 2

( 7+9)/2 = 16/2 = 8

The midpoint is (3,8)

Answer:

Step-by-step explanation:

To get the value f x, we need to use SOH, CAH, TOA identity on ΔAEB but first we need to know any of the sides EB or AB.

From ΔBED, sum of the the angle in the triangle is 180° i.e ∠BED+∠EDB+∠EBD = 180°

65+55+∠EBD  = 180

∠EBD  = 180-120

∠EBD  = 60

Also ∠DBC = 90- ∠EBD

∠DBC = 90- 60

∠DBC = 30°

Applying sine rule on ΔBCD;

52/sin∠DBC = DB/sin115

52/sin30 = DB/sin115

DB = 52sin115/sin30

DB = 52sin115/0.5

DB = 104sin115

DB = 114.75 m

Also applying sine rule on ΔBED to get side BE;

BE/sin55 = 114.75/sin65

BEsin65 = 114.75sin55

BE =  114.75sin55/sin65

BE = 93.998/0.906

BE = 103.75m

Finally, applying the trigonometry identity SOH on  ΔABE

sinΔEAB = opp/hyp

sin70° = BE/AE

Since AE = x;

sin70° = 103.75/x

x = 103.75/sin70°

x = 110.41m

Hence, the value of x missing is approximately 110.41m

Answer: 15π m³

Step-by-step explanation:

Volume of a cone = 1/3πr²h

where,

r = radius = 3 meters

h = height = 5 meters

Volume = 1/3πr²h

Volume = 1/3 × π × 3² × 5

Volume = 1/3 × π × 9 × 5

Volume = 1/3 × π × 45

Volume = 45π/3

Volume = 15π m³

Answer:

Number of lawns mow in 49 hours = 31.5 lawns

Step-by-step explanation:

Given:

Number of lawns mow = 9

Time taken = 14 hours

Find:

Number of lawns mow in 49 hours

Computation:

Time taken for 1 lawn = 14 / 9

Number of lawns mow in 49 hours = 49 / Time taken for 1 lawn

Number of lawns mow in 49 hours = 49 / (14/9)

Number of lawns mow in 49 hours = 31.5 lawns

Answer:

B. [tex] 4\sqrt{7}[/tex]

Step-by-step explanation:

The right triangle altitude theorem states that the altitude of a right angled triangles formed on the hypotenuse is equal to the geometric mean of the 2 line segments it creates.

This can be represented as:

[tex] h = \sqrt{(xy)} [/tex]

Where,

h = the length of the altitude,

x and y are the lengths of the 2 segments formed.

Therefore, the length of the altitude = [tex] h = \sqrt{(14*8)} [/tex]

[tex] h = \sqrt{112} [/tex]

[tex] h = \sqrt{16}*\sqrt{7}[/tex]

[tex] h = 4\sqrt{7}[/tex]

Answer:

3x³ - 2x² + 1 = 0

Step-by-step explanation:

By definition, a quadratic equation cannot have an exponent higher than 2.

Answer:

3x³ - 2x² + 1 = 0

Step-by-step explanation:

Answer:

The correct answer is 260

Step-by-step explanation:

Also known as B

Answer:

260 so Answer B

Step-by-step explanation:

Answer:

I believe it is A; Its x- and y- coordinates are 2 times the correspopnding coordinated of the triangle RST.

Step-by-step explanation:

It just seems the most plausible. I am also taking the Quiz right now.

Answer:

Its A

Step-by-step explanation:

The Triangle is 2x bigger

Got it right on edg

Answer:

1) 2 (11) - 1/2

Step-by-step explanation:

Given the following:

A line “t” is parallel to 3y = 6x + 9

Equation of a line;

y = mx + c

Where the Coefficient of x, 'm' is the gradient or slope and c is the intercept.

From the equation;

3y = 6x + 9

Divide through by 3

y = 2x + 3

Comparing the line equation with the equation provided :

Coefficient of x = 2, therefore 2 = slope

Since line t is Parallel to y = 2x + 3

Then, slope of line 't' is the same as that of y:

Slope of line 't' = 2

(11) For perpendicular lines :

Slope of original line : 3y = 6x + 9

Divide through by 3

y = 2x + 3

Compare to line equation:

y = mx + c

m = gradient/ slope, c = intercept

Gradient of original line, m = 2

For a line 'r' perpendicular to y = 2x + 3

Gradient, m of line r equals to the negative reciprocal of the gradient of original line

Therefore, gradient of r equals :

-1/2

Hey there!

Let's think of this with a simpler example. Let's say one package is 4 pounds and one is 2 pounds. How many times heavier is the first than the second?Well, two, because the first package is double the weight of the second package! It's twice as heavy! And to get to that number, we divide four by two!

So, in our actual problem, we just divide 3.92 (bigger package) by 2.8 (smaller package).

3.92÷2.8=1.4

So, the first package is 1.4 times heavier than the first one!

Have a wonderful day!

Answer:

715

Step-by-step explanation:

The total milliliters of water is 715 if the birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division,and  multiplication by a conversion factor.

We have:

A birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

1/2 liters = 0.5 liters

We know,

1 lter = 1000 ml

0.5 liters = 0.5×1000 = 500 ml

Total water = 215 ml + 500 ml = 715 ml

Thus. the total milliliters of water is 715 if the birdbath contains 1\2 liters of water. A rainy day adds 215 milliliters.

Learn more about the unit conversion here:

brainly.com/question/14350438

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Answer:

a.) 7/20

b.) 0.375

c.) 1/15

Step-by-step explanation:

a. 0.35 is out of 1, so to find 0.35 in fraction form: 35/100.

Simplify that down by dividing both top-bottom by 5 and you get 7/20

b. 1/8th of anything is 0.125, so 0.125(3) = 0.375. Alternatively you can use a calc to calculate the decimal.

c. Find the area of the rectangular carpet: 60m. Then find the area of the square rug: 4m

Find the fraction: 4/60

Simplify by dividing top-bottom by 4 and you get 1/15

Answer:

6 + 6y + 6 = 12 + 6

Step-by-step explanation:

2(3) + 6y = 12

Multiply 2(3).

6 + 6y = 12

Subtract 6 on both sides, so y variable is isolated.

6 + 6y - 6 = 12 - 6

6y = 6

Divide by 6 on both sides.

6y/6 = 6/6

y = 1

Answer:  NO. He had an increase of 25%

Step-by-step explanation:

To find the percentage increase, use the following formula where New (this week) = 25 and Original (last week) = 20.

[tex]\% Change=\dfrac{\text{New - Original}}{\text{Original}}\\\\\\.\qquad \qquad =\dfrac{25-20}{20}\\\\\\.\qquad \qquad =\dfrac{5}{20}\\\\\\.\qquad \qquad =\dfrac{1}{4}\qquad \rightarrow \qquad =0.25[/tex]

Convert the decimal into percentage by moving the decimal point two places to the right.  0.25 = 25%

Evan spent 25% more time this week than last week.

It can also be stated that this week Evan did 125% of homework compared to last week.

If Even spent 125% more than last week, he would have spent 100% (20 hours) + 25% (4 hours) = 24 hours.

Answer:

About 157 meters

Step-by-step explanation:

The circumference of a circle is [tex]2\pi r[/tex]. In this case, this means that one loop around the roundabout would be a distance of:

[tex]2\cdot \pi \cdot 12.5\approx 78.5[/tex]

Multiplying this by 2, you get a distance of about 157 meters. Hope this helps!

Answer:

Solution,

1 round = circumference

[tex]2\pi \: r[/tex]

[tex] = 2 \times \frac{22}{7} \times 12.5[/tex]

[tex] = \frac{44}{7} \times 12.5[/tex]

Required distance covered:

[tex]2 \times \frac{44}{7} \times 12.5 \\ = \frac{88 \times 12.5}{7} \\ = 157.14 \: m[/tex]

hope this helps..

Good luck on your assignment...

Answer:

200=4hrs=10 of the machines

200=4hrs

300=xhrs

Cross multiply

200×xhrs = 300×4hrs

X=1200/200

X= 6 hours

Answer: angles EBA and HBI are congruent

Step-by-step explanation:

they are the congruent because they are verticle angles

Answer:

6n(n³ - 4n² + 3)

Step-by-step explanation:

Given

6[tex]n^{4}[/tex] - 24n³ + 18n ← factor out 6n from each term

= 6n(n³ - 4n² + 3) ← which may be factored further if required

6n(n³ - 4n² + 3)  is the factored form.

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given that,

⇒6n⁴ - 24n³ + 18n

factor out 6n from each term

⇒6n(n³ - 4n² + 3)

There are two factors 6n and (n³ - 4n² + 3) of given expression.

Learn more about expression here:

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Answer:

(-14,0)

Step-by-step explanation:

-x+2y=14 to find the x intercept means y=0

-x+0=14

x=-14

Answer:

  4733

Step-by-step explanation:

Please refer to the attached diagram.

Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.

Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.

We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...

  (12p)(12r) = -1

  r = -1/(144p)

The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:

  slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified

The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...

  tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))

__

Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...

  slope AB = ((slope AC) +2)/(1 -(slope AC)(2))

  [tex]6(p+r)=\dfrac{12p+2}{1-(12p)(2)}\\\\3(p+r)(1-24p)=6p+1\qquad\text{multiply by $1-24p$}\\\\3\left(p-\dfrac{1}{144p}\right)(1-24p)=6p+1\qquad\text{use the value for r}\\\\3(144p^2-1)(1-24p)=144p(6p+1)\qquad\text{multiply by 144p}\\\\ 3456 p^3+ 144 p^2+ 24 p+1 =0\qquad\text{put in standard form}\\\\144p^2(24p+1)+(24p+1)=0\qquad\text{factor by pairs}\\\\(144p^2+1)(24p+1)=0\qquad\text{finish factoring}\\\\p=-\dfrac{1}{24}\qquad\text{only real solution}\\\\r=\dfrac{-1}{144p}=\dfrac{1}{6}[/tex]

So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...

  d^2 = (6r^2 -6p^2)^2 +(r -p)^2

  d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216

Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...

  Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b

Then a+b = 125 +4608 = 4733.

_____

Comment on the solution

The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.

Answer: 2398.72

Step-by-step explanation:

Simply do 3100*0.95*0.95*0.95*0.95*0.95 ≈ 2398.72

Hope it helps <3

Answer:

$2398.72( I cannot use your dollar sign).

Step-by-step explanation:

If it decreases by 5% every year, then 3100*0.95=2945. Then 2945*0.95=2797.75. Then the 3rd year is 2797.75*0.95=2657.8625. Then 2,657.8625*0.95=2524.96938. Lastly, in the fifth year, it is 2524.96938*0.95=2398.72091. Then, I round off to the nearest penny(hundredths). The answer I get is $2398.72!