This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeEnter a decimal rounded to the nearest hundredth.Enter

Answer:

check the attached files.

We have to use the simple interest formula

Where P = 13,000, r = 5% (0.05), t = 90 (0.25 years). Let's replace these values to find the interest

Because we have to add the total interest with the amount borrowed.

The given question is

Use the identity

Then replace the denominator by sec^2 (x)

Since sec is the reciprocal of cos, then

Replce sec^2(x) by 1/cos^2(x)

Since denominator of denominator will be a numerator

Use the value of tan

Replace tan by sin/cos

Reduce cos(x) up with cos(x) down

Use the identity

Replace 2 sin(x)cos(x) by sin(2x)

The answer is

2 sin(2x)

ANSWER

P(gold marble) = 1/12

EXPLANATION

In total, there are:

36 marbles in the bag, where only 3 are gold marbles.

The probability is:

In this case, the number of posible outcomes is 36, because there are 36 marbles in the bag. The number of times the event can happen is 3, because there are 3 gold marbles:

The two unit vectors orthogonal to both j-k and i+j  are [tex]\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }[/tex]

Let a bar = j- k  = < 0,1,-1>

b bar = i+j = <1,1,0>

the cross product a x b bar is orthogonal to both a and b bar

= i ( 0-(-1) ) -j ( 0-(-1) ) + r (0-1)

= i-j-k

A unit vector is a vector whose length is 1 unit

There the unit vector is :

[tex]\frac{i-j-k}{\sqrt{1^2+(-1)^2+(-1)^2} } = \frac{i-j-k}{\sqrt{3} }[/tex]

= [tex]\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }[/tex]

The second unit vector orthogonal to both a and b bar would be negative of the previous vector.

= [tex]-\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }[/tex]

Hence the two unit vectors orthogonal to both j-k and i+j are  [tex]\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }[/tex]

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ANSWER:

$104.37

STEP-BY-STEP EXPLANATION:

To calculate the total profit, we must add the amount he earned each day, multiplying the salary by the number of hours, like this:

Therefore, he earned in the last three days a total of $104.37

Given: Different statement

To Determine: Which of the statement would give a valid conclusion

Solution

Please note that the statement must be a true representation of the population

Answer:

150 blue marbles

Step-by-step explanation:

Hello!

If 1/2 of the marbles are yellow, and 1/8 of the marbles are red, then 3/8 of the marbles should be blue.

The percentages are as given:

To calculate the possible number of blue marbles out of the 400 marbles, we can find 37.5% of 400, as there is a 37.5% chance of getting blue for each turn.

Helen should expect to pick out 150 blue marbles.

Reflection rule over y - axis is given as

(x , y) ------------ (-x, y)

This implies that the y - axis will remain the same and the x - axis will be negated

Pre image ABC at point (2, -1)

The reflection over y - axis will be

ABC A'B'C' A''B''C'' A'''B'''C'''

(2, -1) -----------------(-2, -1) ----------------------(2, -1) -------------------(-2, -1)

ABC A'B'C' A''B''C'' A'''B'''C'''

(2, -4) (-2, -4) (2, -4) (-2, -4)

The area of the circle can be calculated with the following formula

First let's find the radius

The answer would be 200.96 square yards

Explanation

We are given the following equation:

We are required to determine the value of x.

This is achieved thus:

Hence, the answer is:

As given by the question

There are given that function

Now,

To find the value of r(a^2), put x = a^2 into the function

Then,

Hence, the function is shown below:

Answer:

$35,708.4

Explanation:

His net income will be the total that he earns less the taxes.

So, we need to calculate how much money does Rob pays for each tax.

Therefore, 6.2% of 4200 is equal to:

It means that Rob pays $260.4 each month for social security,

In the same way, 1.45% of 4200 is equal to:

16% of 4200 is equal to:

5.5% of 4200 is equal to:

Now, we can calculate the net income per month as:

$4200 - $260.4 - $60.9 - $672 - $231 = $2975.7

Finally, his annually net income will be the net income per month multiplied by 12 months:

$2975.7 x 12 = $35,708.4

So, the answer is $35,708.4

Answer:

The vertical shift is of 2 units up

Step-by-step explanation:

We have a function in the following format:

F(x) = a(x+b) + c

The vertical shift is given by c.

If c > 0, the shift is up.

If c < 0, the shift is down.

In this question:

F(x) = 9|x+1| + 2

So c = 2

The vertical shift is of 2 units up

The area is 25π square inches

Given a radius, r = 5 in.

The area of a circle is given by the formula:

Substituting the value of r, we have:

The area is 25π square inches

Solve;

Therefore, x = -1

Given the expression:

Let's simplify the expression.

To simplify the expression, we have:T

Solving further:

Apply the multiplication rule for exponents.

ANSWER:

Solution:

Given the expression below

Applying the combination formula below

The binomial coefficient will be

Hence, the answer is 56

Explanation:

Step 1

Given;

Required; To write the answer in exponential form

Step 2

Answer;

The total area of all four walls is 224 square meters.

According to the question,

We have the following information:

A square room has a floor area of 49 square meters.

So, we have:

Area of square = 49 square meters

Side*side = 49

Side = [tex]\sqrt{49}[/tex] m

Side of the square = 7 m

Now, the side of the floor will be the width of the wall.

So, we have the width of the wall = 7 m.

The height of the room is 8 meters.

It means that the height of the wall is 8 m.

Area of 1 rectangular wall = length*width

Area of wall = 8*7

Area of 1 wall = 56 square meters

Now, the are of 4 walls will be (4*56) square meters or 224 square meters.

Hence, the total are of all four walls is 224 square meters.

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Answer:

  B.  Distributive Property

Step-by-step explanation:

You want to know the reason in the proof that best supports the transition from 5. 99-3x = 12(x+2) to 6. 99-3x = 12x+24.

You will notice that in the transition from

  5. 99-3x = 12(x+2)

to

  6. 99-3x = 12x+24

the expression 12(x+2) has been replaced by the expression 12x+24.

The property of addition and multiplication that makes it true that ...

  12(x +2) = 12x +24

is the distributive property of multiplication over addition. That property tells you that parentheses can be eliminated by multiplying each of the terms inside by the factor outside.

the given series is 4 -16 64 -256

that is

4 x -4 = -16 = -4^2

-16 x -4 = 64 = 4^3

64 x -4 = -256 = -4^4

so we can say that is every time the number is multiplied with -4,

for a7, as 7 is an odd number so the negative sign will be there from the above observations

-4^7 = -16384

the recursive rule will be'

26÷ 2.40= 10.833333

Nearest cent means ,2 numbers after decimal point

Then it is 10.83

count 2 numbers to right ,and discard rest of 3333

Then answer is = 10.83

Answer:

Step-by-step explanation:

The y-value of Function A when x = - 2 is less than the y-value of Function B when x = - 2.

The function is given as,

It is asked to find the value of the expression,

This can be obtained by replacing 'x' by 7 in the given expression of the function,

Resolve the parenthesis,

Simplify the terms further,

Thus, the value of the expression f(7) is obtained as,

Given data:

The given figure is shown.

The area of the given figure is,

Thus, the area of the composite figure is 978 sq-inches.

Yesterday Ali had n Baseball cards.

Today he gave away 6 cards.

We are asked to write an expression for the number of cards Ali has left.

Ali had a total of n cards and he gave away 6 from them.

So, we have to simply subtract 6 cards from the total n cards.

Therefore, the expression is n - 6 represents the number of cards Ali has left.

Without dividing, we can tell that 30:6 has smaller quotient between 30:5 and 30:6.

According to the question,

We have the following two expressions:

30:5 and 30:6

Now, we can easily find which expression has a smaller quotient when the dividend is the same. We need to look at the divisor. If the dividend is the same then the quotient will be smaller for the one with the greater divisor.

In this case, 30:6 has a greater divisor than 30:5 (6 is larger than 5). So, it will have smaller quotient.

Now, we can prove this by dividing both the expressions.

30/6 = 5

(So, it has smaller quotient.)

30/5 = 6

Hence, 30:6 has smaller quotient than 30:5.

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Answer:

Step-by-step explanation:

I would recommend looking up the magic trig hexagon, it has all of these identities and more within it.

1 - this corresponds with C as sin^2(x)+cos^2(x)=1

1-cos^2(x) - this corresponds with A, using the identity from number 1, we can rewrite it in the form sin^2(x)=1-cos^2(x)

cot(x) - for this it is important to know that cotangent is the inverse of tangent. Since tan(x)=sin(x)/cos(x), cot=cos(x)/sin(x) which is B.

sec^2(x) - much like the cos and sin pythagorean identity, sec and tan are related. sec^2(x)=tan^2(x)+1 which is answer choice E.

tan(x) - this is sin(x)/cos(x), choice D.