The guards change over between 10:16 pm and 10:25 pm which means the hallway is clear during that time. How many minutes do you have exactly to cross the yard without being noticed?

Answer:

either a ratio 8;7. or a percentage of 53% for picking the blue marble first i think and a 50/50 chance if you keep that blue marble out.

Step-by-step explanation:

Answer: [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

Given: Number of blue marbles = 8

Number of red marbles = 7

Total number of  marbles = 8+7=15

Now, the probability that she first pulls a blue marble is given by :-

[tex]P(B)=\frac{\text{blue marbles}}{\text{Total marbles}}\\\\=\frac{8}{15}[/tex]

Now, total marbles left in bag = 15-1=14

Now, the probability that she second pulls a red marble is given by :-

[tex]P(B)=\frac{\text{red marbles}}{\text{Total marbles left}}\\\\=\frac{7}{14}=\frac{1}{2}[/tex]

Thus, the probability that she first pulls a blue marble and then a red marble is given by :-

[tex]P(B)\timesP(R)=\frac{8}{15}\times\frac{1}{2}=\frac{4}{15}[/tex]

Answer:

Since, KLMN is a parallelogram, then by the property of parallelogram that opposite angles of a parallelogram is equal, therefore ∠N=∠L and ∠M=∠K.

Step-by-step explanation:

Answer:

It is followed by properties of parallelogram and the proof is explained in step-by-step solution.

Step-by-step explanation:  

Given a parallelogram KLMN

Parallelogram is a quadrilateral with parallel opposite sides.  

To Prove: ∠N≅∠L and ∠M≅∠K  

In Parallelogram KLMN the opposite sides are parallel therefore, the opposite angles are vertical angles. And the vertical angles are always equal and congruent. Hence,  

∠N≅∠L and ∠M≅∠K  

For any quadrilateral sum of all angles equal to 360°  

m∠K + m∠L + m∠M + m∠N = 360°  

Now given quadrilateral is parallelogram therefore opposite angles are equal. So, we can write m∠L = m∠N, m∠M = m∠K  

⇒ m∠K + m∠N + m∠K + m∠N = 360°  

2 m∠K + 2 m∠N = 360°  

m∠K + m∠N = 180°  

For the same parallelogram, because opposite sides are equal therefore use m∠K = m∠L, m∠N = m∠M using above equation, we get  

m∠L + m∠M = 180°  

Because m∠M = m∠K  

m∠K + m∠L = 180°  

Same Side Interior Angles Theorem states that if the two parallel lines intersect or cut by a transversal then the interior angles on the same side are supplementary that means their sum is equal to 180°  

Hence, by above theorem m∠K + m∠N = 180°  

& m∠K + m∠L = 180°  

By above two equations, we get  

m∠K + m∠N = m∠K + m∠L  

because m∠K = m∠M & ∠N = ∠L  

⇒ m∠L + m∠M = m∠K + m∠L  

Because opposite angles of a parallelogram are alternate angles therefore are equal. hence,  

m∠N = m∠L  

m∠M = m∠K  

Angle congruency postulate  

Opposite angles of parallelogram are vertical angles and the vertical angles are congruent as well as equal.  

∠N≅∠L and ∠M≅∠K  

Substitution Property of equality states that if one angle is equal to another angle the one can be substituted in the place of another that means if ∠M=∠K then we can substituted ∠K in place of ∠M  

Transitive property of congruence states that if if the two angles or segments or triangles are congruent to third then they are congruent to each other.  

Subtraction Property of Equality states that if if two sides of any equation are equal then subtraction of same value from both sides results in equality of equation.  

Parallel lines are those lines which do not intersect or cut each other at the end.  

Parallelogram is a quadrilateral have opposite sides equal and parallel.  

:

Answer:

15

Step-by-step explanation:

The fact angle G and F are equal means the triangle is isosceles triangle. And an isosceles triangle has two equal sides on the opposite sides of the equal angles. Which means x equals HF which is 15.  

Question

What is the value of x?

Answer:

Step-by-step explanation:

this is an isosceles triangle, 2 equal sides and 2 equal angles, so

FH = GH

15 = 15

Answer:

your answer is true.

Step-by-step explanation:

As 8 is in the hundredth place.

Answer:

The answer is True.

Step-by-step explanation:

9 is in the "ones place", 2 is in the "tens place, 8 is in the "hundreds place", and so on...

Answer:

y=6

Step-by-step explanation:

I took the test and got 100%

Answer:

I think the answer is neither. Hope this helps.

Step-by-step explanation:

A general proof for this would be that since Angle A + Angle F + Angle E = 180°, and each of these angles is congruent to some angle inside of Triangle CGH; that CGH would equal 180°.

Interior angles of triangles = 180°, which is common knowledge; unfortunately this isn't an answer choice - so we use the above proof.

F ~= C

A ~= H

E ~= G

So, Angles A and H are congruent would be the correct solution.

Answer:

-30

Step-by-step explanation:

-18x1 - 4x3 = -18-12= -30

Answer:

None

Step-by-step explanation:

The center of the ellipse is at  (2,  4)

The length of the x axis is  a=  (8-2) =6

The length of the y axis is b=(16-4) = 12

The formula for an ellipse is

(x-h) ^2       (y-k)^2

----------- + -------------- = 1^2

a^2              b^2

where (h,k) is the center

and a and b are the  lengths of the major and minor axes

(x-2) ^2       (y-4)^2

----------- + -------------- = 1

6^2              12^2

 none of your choices have b>a  and for the ellipse to be vertical b>a

Answer:

43680 different arrangements are possible.

Step-by-step explanation:

The total number of horses are :16

We have to find different arrangement of four horses

Since, we have to find arrangements means we will use permutation

So, the required arrangement will be:

[tex]^{16}P_4[/tex]

Now, using: [tex]^{n}P_r=\frac{n!}{(n-r)!}[/tex]

Here, n= 16 and r=4 on substituting the values we get:

[tex]^{16}P_4=\frac{16!}{(16-4)!}[/tex]

[tex]\Rightarrow \frac{16!}{12!}[/tex]

[tex]\Rightarrow \frac{16\cdot 15\cdot 14\cdot 13\cdot 12!}{12!}[/tex]

Cancel out the common term that is 12! we get:

[tex]16\cdot 15\cdot 14\cdot 13[/tex]

After simplification we get: 43680

Hence, 43680 different arrangements are possible.

Answer:

The equation of this line is y - 3 = 4/7(x - 7)

Step-by-step explanation:

To find this, start with the base form of point-slope form.

y - y1 = m(x - x1)

Now put the slope in for m and the two coordinates in for (x1, y1).

y - 3 = 4/7(x - 7)

In reference to the image below, the trigonometric ratio cos  [tex]\alpha[/tex]° is calculated by dividing the base by the hypotenuse, thus making part c) 15 ÷ 17 the correct option.

The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.

In the given question, the trigonometric ratio cos is given by dividing the base of the triangle to the hypotenuse.

In any question,

hypotenuse = side opposite of the right angle = 17

base  = side adjacent to the acute angled marked =  15

Thus giving the value of cos [tex]\alpha[/tex]° as 15 ÷ 17.

Learn more about trigonometric ratios here

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The complete question is given below:

A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as  [tex]\alpha[/tex] degrees.

What is the value of cos [tex]\alpha[/tex]°?

a. 8 ÷ 17

b. 17 ÷ 8

c. 15 ÷ 17

d. 8 ÷ 15

The figure of triangle is given below:

Answer:

[tex]\text{cos}(B)=\frac{c}{a}[/tex]

Step-by-step explanation:

We have been given a triangle. We are asked to find [tex]\text{cos}(B)[/tex].

We know that cosine relates adjacent side of a right triangle to its hypotenuse.

[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]

We can see that side AB is adjacent side and CB is hypotenuse of our given right triangle.

[tex]\text{cos}(B)=\frac{AB}{CB}[/tex]

[tex]\text{cos}(B)=\frac{c}{a}[/tex]

Therefore, our required value is [tex]\text{cos}(B)=\frac{c}{a}[/tex]

Answer:

4b^3 + 10b^2 - 32b + 15

___________________

             2(2b - 3)

Step-by-step explanation:

Take out the greatest common factor of (4b - 6) which is 2 and 3.

Answer:

heptagon

Step-by-step explanation:

This polygon has 7 sides

heptagon is a seven sided polygon

decagon is a ten sided polygon

dodecagon is a 12 sided polygon

hexagon is a six sided polygon

Answer:

(III), (VI),(VII), (I), (IV)

Step-by-step explanation:

Solving the system of equations one by one by elimination method

(I) 2x+y=10

   x-3y= -2   ( multiply by 2)

we have unique solution

x=4, y=2

(II) 2x+y=10    (multiply by -3)

 -6x-3y= -2

No solution.

(III) x+2y=5   (multiply by 2)

    2x+y=4

Unique solution

x=1, y=2

(IV) 5x+ y= 33

     x=18-4y ---> x+4y=18    (multiply by 5)

Unique solution

x=6, y=3

(V) Y=13 -2x   ----> 2x+y=13     ( multiply by 4)

   8x + 4y =52

No solution

(VI) x+ 3y =5

    6x-y=11    (multiply by 3)

Unique solution

x=2, y=1

(VII) Y=10 + x    ----> -x+y=10   (multiply by 2)

      2x + 3y =45

Unique solution

x=3 , y=13

Values of x in increasing order= (III), (VI),(VII), (I), (IV)

Answer:

[tex]\frac{7}{9}[/tex]

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]

step 1

Find the probability of selecting a literature book

we have

[tex]x=3[/tex]

[tex]y=3+4+2=9[/tex]

substitute

[tex]P=\frac{3}{9}[/tex]

step 2

Find the probability of selecting an algebra book

we have

[tex]x=4[/tex]

[tex]y=3+4+2=9[/tex]

substitute

[tex]P=\frac{4}{9}[/tex]

step 3

Find the probability of selecting a literature book or an algebra book

Adds the probability of selecting a literature book plus the probability of selecting an algebra book

[tex]P=\frac{3}{9}+\frac{4}{9}=\frac{7}{9}[/tex]

Answer:

Step-by-step explanation:

Is it mutually exclusive?

Answer:

Yes they can be

Answer:

C) [tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]

Step-by-step explanation:

[tex]f(x) = \frac{1}{x}  \ g(x) = x^2 + 2x -5[/tex]

To find (g-f)(x) , we need to calculate g(x) - f(x)

WE know f(x) = 1/x  and g(x) = x^2 + 2x -5

Plug in g(x) and f(x) and then subtract

[tex]g(x)-f(x)=x^2 + 2x -5- (\frac{1}{x})[/tex]

All are unlike terms so we cannot combine like terms

[tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]

In order to find (g - f)(x), you need to subtract f(x) from g(x). The correct subtraction results in the expression x^2+2x-5-1/x, corresponding with answer choice C.

The question asks you to calculate (g - f)(x) where f(x) = 1/x and g(x) = x^2 + 2x -5. This entails finding the difference between g(x) and f(x).

Firstly, write out g(x) and f(x):

Secondly, subtract f(x) from g(x):

g(x) - f(x) = (x^2 + 2x - 5) - (1/x)

This simplifies to: g(x) - f(x) = x^2 + 2x - 5 - 1/x

Therefore, the correct answer is C. x^2+2x-5-1/x

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Answer:

40 units²

Step-by-step explanation:

substitute the given values for s and h into the formula

SA = ( 2 × 2² ) + (4 × 2 × 4 ) = 8 + 32 = 40

Answer:

40 units²

Step-by-step explanation:

Given that the surface area for a rectangular prism with a square base is SA=2s2+4sh.

Where the values of the variables in the equation which are s and h are known, the area can be computed by the substitution of the known variables into the equation.

Hence where s = 2 and h = 4

SA = 2(2)² + 4(2)(4)

= 8 + 32

= 40 units²

Answer:

25 represents how much he makes per hour

Step-by-step explanation:

Answer:

65,550.

Step-by-step explanation:  

We have been given that the population of a town increased by 15% in 2016, and decreased by 5% in 2017.

Since an exponential is in form: [tex]a*b^x[/tex].  

For growth b=(1+r), where r in rate in decimal form.  

For decrease b=(1-r), where r in rate in decimal form.

[tex]15\text{ percent}=\frac{15}{100}=0.15[/tex]

Let us find the population increase in 2015.

[tex]\text{Population at the end of year 2016}= 60,000*(1+0.15)^1[/tex]  

[tex]\text{Population at the end of year 2016}= 60,000*(1.15)[/tex]  

[tex]\text{Population at the end of year 2016}= 69,000[/tex]

Therefore, the population at the end of year 2016 will be 69,000.

Now let us find population decrease of 5% in year 2017.

[tex]15\text{ percent}=\frac{5}{100}=0.05[/tex]

[tex]\text{Population at the end of year 2017}= 60,000*(1-0.05)^1[/tex]  

[tex]\text{Population at the end of year 2017}= 60,000*(0.95)[/tex]  

[tex]\text{Population at the end of year 2017}= 65,550[/tex]  

Therefore, the population at the end of year 2017 will be 65,550.

Answer:

C. (-3.6, 17)

Step-by-step explanation:

The relative maximum occurs at an x coordinate between -3 and -4. The relative maximum is between 15 and 20. The best approximation is

C. (-3.6, 17)

Answer:

c. (-3.6, 17)

Step-by-step explanation:

The relative maximum is the maximum in a region.  The maximum between -6 and  is found and x=-3.6 and the value is 17.  So x=-3.6 and y=17

Answer:

He earned 1800 reward points for 600 dollars

Step-by-step explanation:

Given the statement: Omar has a new credit card. He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points.

Unit rate are expressed as a quantity of 1, such as 3 feet per second or 4 miles per hour, they are called unit rates.

Earn  300 reward point for every 100 dollars.

⇒ unit rate per reward = [tex]\frac{100}{300}[/tex] dollars

we have to find how many dollars he earned for 1800 points.

[tex]Number of dollars = unit rate \times 1800[/tex]

                                 = [tex]\frac{100}{300} \times 1800 = 600[/tex]

Therefore, he earned 1800 reward points for 600 dollars

Answer:

$600 money Omar spends .

Step-by-step explanation:

As given

Omar has a new credit card.

He earns 300 reward points for every 100 dollars he spends.

i.e

300 reward points for every 100 dollars .

Let  us assume that the Omar earned 1800 reward points when he spends x money.

Than the equation becomes

[tex]x = \frac{1800\times 100}{300}[/tex]

[tex]x = \frac{1800}{3}[/tex]

x = $600

Therefore $600 money Omar spends .

Answer:

The machine uses 1575 meters of yarn per cardigan and uses 1500 meters per pullover.

Step-by-step explanation:

Let P be yarn needed by machine for each pullover and C be yarn needed by machine for each Cardigan.

We are told that the machine takes the same length of yarn to make 21 pullovers as to make 20 cardigans. We can represent this information as:

[tex]20C=21P...(1)[/tex]

The machine used a total of 457,500 meters of yarn to make 100 cardigans and 200 pullovers. We can represent this information as:

[tex]200P+100C=457,500...(2)[/tex]

Let us solve our system of equations using substitution method.

From equation (1) we will get,

[tex]C=\frac{21P}{20}[/tex]

Upon substituting this value in equation (2) we will get,

[tex]200P+100(\frac{21P}{20})=457,500[/tex]

[tex]200P+5*21P=457,500[/tex]

[tex]200P+105P=457,500[/tex]

[tex]305P=457,500[/tex]

[tex]P=\frac{457,500}{305}[/tex]

[tex]P=1500[/tex]

Therefore, the machine uses 1500 meters of yarn per pullover.

Upon substituting P=1500 in equation (1) we will get,

[tex]20C=21*1500[/tex]

[tex]20C=31,500[/tex]

[tex]C=\frac{31,500}{20}[/tex]

[tex]C=1575[/tex]

Therefore, machine uses 1575 meters of yarn per cardigan.

Answer:

1575 meters of yarn per cardigan

1500 meters per pullover

Step-by-step explanation:

Answer:

B.) 28%

Step-by-step explanation:

There are 50 total spins so far and 28% of them have been 4's. So that is the probability.