suppose an isosceles triangle abc has a=pi/6 and b=c=5. what is the length of a^2?

Final answer:

After making her online payments totaling $792.01, Kwei-Twang Kuo will have a balance of $24.82 in her checking account.

Explanation:

First, we'll calculate the total payments Kwei-Twang Kuo needs to make by adding up all of her expenses:

Store charge account: $160

Charitable donation: $40

Rent: $550

Cable bill: $42.01

Adding these amounts together gives us a total of $792.01 for the payments.

Let's calculate the balance of her checking account after she transfers $800 and makes the payments:

Begin with checking account balance: $16.83

Transfer into checking account: +$800.00

New balance before payments: $816.83

Total payments to be made: -$792.01

Final checking account balance: $24.82

Therefore, after Kwei-Twang Kuo makes her online payments, she will have a balance of $24.82 in her checking account.

we know that

in the right triangle MNR

[tex]Sin(N\°)=Cos(R\°)[/tex]

[tex]Sin(56\°)=Cos(34\°)[/tex]

Because

[tex]N+R=90\°[/tex]

[tex]56\°+34\°=90\°[/tex] --------> by complementary angles

so

sin ∠MQP=[tex]Sin(56\°)[/tex]

therefore

the answer is the option

D. Cos R and Sin N

Final answer:

The number of possible batting orders a coach can make with 13 players for 9 positions is found by calculating [tex]^{13}P_9[/tex], which equals 518,918,400. Thus, the correct answer is C. 259,459,200.

Explanation:

To determine how many possible batting orders a baseball coach can make with 13 players to fill 9 positions, we use the concept of permutations since the order in which the players are arranged matters. The formula for permutations of n items taken r at a time is [tex]^{n}P_r[/tex] = n! / (n - r)!, where the exclamation point indicates a factorial. In this case, we have 13 players and want to find out the number of ways to arrange 9 of them, so we calculate-

[tex]^{13}P_9[/tex]= 13! / (13 - 9)!.

We can simplify this by calculating the factorials: 13! = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 and 4! = 4 × 3 × 2 × 1, so [tex]^{13}P_9[/tex] = 13! / 4!.

Instead of multiplying out both factorials completely, we can cancel out the common terms: (13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (4 × 3 × 2 × 1) = (13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5) / 1.

Calculating the above gives us 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 = 518,918,400 ways to arrange the batting order. Therefore, the correct answer to how many possible batting orders can be made is C. 259,459,200.

Answer:

b

Step-by-step explanation:

sisters age = x

martins age = x-6

equation: x +(x-6) <=22

2x -6 <=22

2x<=28

x<= 28/2

x<= 14

                 The number is:

                          1260

We know that the number of ways of arranging n items is calculated by the method of permutation.

If n letters are to be arranged such that there are [tex]r_1,r_2[/tex] items each of the same type.

Then, the number of ways of arranging is:

                   [tex]\dfrac{n!}{r_1!\times r_2!}[/tex]

We are asked to find the number of ways of arranging the letters of "Balloon"

There are a total of 7 words such that 'l' occurs two times and 'o' occurs two times.

Hence, the number of ways of arranging them are:

     [tex]=\dfrac{7!}{2!\times 2!}\\\\=\dfrac{7\times 6\times 5\times 4\times 3\times 2!}{2!\times 2}\\\\=1260\ ways[/tex]

By observing the given options we can conclude that equation

C. (0.5⋅0.5) + (0.5⋅0.3) + (0.5⋅0.2) = 0.5⋅(0.5 + 0.3 + 0.2) correctly applies the distributive property.

The other two properties are commutative property and associative property.

We know the distributive property for four terms states,

a(b ± c± d ± e)  = ab ± ac ± ad ± ae.

∴ From observing the given options we can conclude that

0.5⋅(0.5 +0.3 + 0.2) = (0.5⋅0.5) + (0.5⋅0.3 )+ (0.5⋅0.2).

Or

(0.5⋅0.5) + (0.5⋅0.3) + (0.5⋅0.2 ) = 0.5⋅(0.5 + 0.3 + 0.2).

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Shakira bowls about 8 games.

Two or more expressions with an equal sign are defined as an equation.

Let Shakira bowl x games.

Since Shakira has to pay $4.75 for each game, she would pay $4.75x for x games.

Shakira also paid $3 to rent shoes, therefore, the total money Shakira spent is:

4.75x + 3

Given that, the total spent is $42, therefore,

4.75x + 3 = 42

4.75x = 42 - 3

4.75x = 39

x = 39/4.75

x ≈ 8

Hence, Shakira bowls about 8 games.

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Answer:

[tex]4\ cases[/tex]

Step-by-step explanation:

Step 1

Divide the total cartons of juice that the company produces in [tex]21[/tex] days by the total days

so

[tex]\frac{8,064}{21}\frac{cartons}{days}=384\frac{cartons}{day}[/tex]

Step 2

Divide the total cartons of juice that the company produces in one day by the total coffee shops

so

[tex]\frac{384}{16}\frac{cartons}{coffee-shop}=24\frac{cartons}{coffee-shop}[/tex]

Step 3

Divide the total cartons of juice that the company delivered per day to each coffee shop by six (number of cartons per case)

so

[tex]\frac{24}{6}=4\ cases[/tex]

For this case we have the following expression:

[tex]b ^ 5b ^ 4[/tex]

We must consider the following property of the exponents.

Rewriting the given expression we have:

[tex]b ^ 5b ^ 4 = b ^ {(5 + 4)}\\b ^ 5b ^ 4 = b ^ 9[/tex]

Answer:

the correct simplification of the expression is:

[tex]b ^ 5b ^ 4 = b ^ 9[/tex]

Answer

It is 2 scoops

Step-by-step explanation:

3⁄8 x 1⁄4 = 3⁄32 quart

3⁄4 ÷ 3⁄32 = 8 scoops

The sampling distribution of the proportion follows the normal distribution when the values np and nq are greater than or equal to 5.

For the sampling distribution of the proportion to follow a normal distribution, the values np and nq must both be greater than or equal to 5.

For example, if you are performing a hypothesis test of a single population proportion, the conditions np >= 5 and nq >= 5 must be met to approximate the binomial distribution by the normal distribution.

Remember that np represents the number of successes in the sample and nq represents the number of failures in the sample.

Laura needs 35/9 cups (approximately 3.89 cups) of liquid ingredients for 8 people.


To find how many cups of liquid ingredients Laura needs for 8 people, follow these steps:

Therefore, Laura needs 35/9 cups (approximately 3.89 cups) of liquid ingredients for 8 people.

Solution:

The points at which Raquel Darts hit the coordinate grid having center at the origin are  (–5, 0), (1, –3), (4, 5), (–8, –6), (0, 2), and (9, 6).

As we can see that not all points are collinear.

As line of best fit is the the line which passes through some points , may be not through the single point, or all the points.

Plotting all the options on coordinate grid i.e on a scatter plot and then determining , the  line of best fit of the darts is

y= 0.6 x + 0.6 →→Option (A), the reason being it passes through a point (9,6).

The speed at which the distance is covered by the two vehicles is the sum of their speeds:

... (truck speed) + 1.5×(truck speed) = 2.5×(truck speed)

The time required to cover the distance is inversely proportional to speed, so is

... (2.5 hours)/2.5 = 1.0 hours

It takes 1.0 hours for the vehicles to meet.

_____

The speed of the truck is (145 mi)/(2.5 h) = 58 mi/h

The speed of the car is 1.5 × 58 mi/h = 87 mi/h.

The speed at which they move toward each other is

... 58 mi/h + 87 mi/h = 145 mi/h

So, the time it takes to cover 145 miles is

... (145 mi)/(145 mi/h) = 1.0 h

Answer:

(A) Similar triangles

Step-by-step explanation:

It is given that AB is parallel to DE, therefore ∠CAB=∠DEC=65°(Alternate angles),

Then from ΔACB and ΔDCE, we have

∠CAB=∠DEC=65°(Alternate angles)

and ∠ACB=∠DCE=50°(Vertically opposite angles)

Thus, by AA similarity, ΔACB is similar to ΔDCE.

Hence, option A that is similar triangles is correct.

Let us plug-in the values of x to know

> x = 0

f(0) = 3(0) + 1 = 1

g(0) = 3^0 + 1 = 2

> x = 1

f(1) = 3(1) + 1 = 4

g(1) = 3^1 + 1 = 4

> x = 2

f(2) = 3(2) + 1 = 7

g(2) = 3^2 + 1 = 10

> x = 3

f(3) = 3(3) + 1 = 10

g(2) = 3^3 + 1 = 28

Therefore the only answer is:

1

Answer:

The interpretation of the slope is that for each $1000 you spend, your revenue increases by $900.

Step-by-step explanation:

We have that:

The revenue y is a function of the advertising expediture x, and the relationship is given by the following function:

y = -48.3 + 9x.

However, since y is in thousands and x in hundreds, i am going to rewrite

y = -48.3 + 0.9x

This means that if you spend no money in advertising, you lose -48.3 thousands of dollars. However, for each $1000 you spend, your revenue increases by $900.

So the interpretation of the slope is that for each $1000 you spend, your revenue increases by $900.