6th grade math I mark as brainliest

The future value of the investment when interest is compounded continuously is; $3408.29

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given Data

P= $1500, r = 3.95%, t = 5 yr

To Calculate the number of periods: in this case we have 5*12= 60 months.

- The monthly interest rate, we have to divide the annual nominal rate by 12 (the number of periods in the year).

Then, we can calculate the future value as:

A = P (1 + r/n)^nt

A = 1500(1 + 3.95/365)(365)^(5)

P = 1500/ (1 + 0.00010137)^(5)

P = $3408.29

The future value when compounded monthly is $3408.29.

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Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

Answer:

The area of Alison's pizza would be 30 in.

Answer:

x=-2/5

Step-by-step explanation:

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Answer: MN = 15

Step-by-step explanation:

1x+5x+1x=21

1x=3 (Length of the Segment with 1)

5*3=15

A line segment is also a line but a line with finite length and fixed endpoints. The length of line segment MN is 15 units.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. A line segment is also a line but a line with finite length and fixed endpoints.

Given that the ratio of LM: MN: NO is equal to 1: 5: 1. Therefore,  we can write,

LM : MN : NO = 1:5:1

If the ratio is multiplied by x, which is the factor that brings the ratio to its original value,

LM : MN : NO = 1x : 5x : 1x

Therefore, The length of the sides LM, MN, and NO are 1x, 5x, and 1x, respectively.

Now, since the length of LO is 21 units, it is made by joining LM, MN, and NO. Therefore, we can write,

LO = LM + MN + NO

21 = 1x + 5x + 1x

21 = 7x

x = 21 /7

x = 3

Further, the length of line segment MN is,

MN = 5x

      = 5(3)

      = 15 units

Hence, the length of line segment MN is 15 units.

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Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

Answer: The sequence firmed here is the arithmetic progression or sequence

Step-by-step explanation:

The sequence firmed here is the arithmetic progression. The numbers are given as 2,4,6,8,10,12,14,16. Here the first term is 2 and the common difference is (6-4) = 2.

Let's check to confirm. Let's find the 5th term. This will be:

= a + (n - 1)d

= 2 + (5 - 1)2

= 2 + (4 × 2).

= 2 + 8

= 10

The fifty term is 10.

This is correct as shown with the figures given.

The multiples of 3,4,5 would also make up and arithmetic progression.

Answer:

27/64

Step-by-step explanation:

(7×16)+(5×64)64×16

=112+3201/024

=432/1024

Simplifying 432/1024, the answer is

=27/64

Step-by-step explanation:

40 :100        yellow to purple,  divide both sides by 20

2:5

Answer:

the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.

Step-by-step explanation:

Hope it helps.

Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

The intermediate step in the form (x+a)²=b as a result of completing the square for the given equations is (x+4)²=18.

The given quadratic equation is x²+4x-9=-4x-7.

Here, x²+4x-9+4x=-7

x²+8x=-7+9

x²+8x=2 ------(i)

Choose coefficient of x, that is 8.

Half of coefficient of x is 4.

Take square of 4, that is 4²=16

Add 16 to both the sides of the equation, we get

x²+8x+16=2+16

(x+4)²=18

Therefore, the intermediate step in the form (x+a)²=b as a result of completing the square for the given equations is (x+4)²=18.

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Answer:

they are positively correlated.

Step-by-step explanation:

We can calculate the individal expectations first. FIrst player will win if that player's roll is greater than the bank's roll. There are (6 possible rolls of player 1 * 6 possible rolls of bank =) 36 total possible rolls, out of which player 1 will win in 15 cases.

\(\therefore E(I_i) = 1\cdot \frac{15}{36} + 0 \cdot \frac{21}{36} = \frac{5}{12} \approx 0.4167\)

For the joint expectation, there are (6 possible rolls of player 1 * 6 possible rolls of player 2 * 6 possible rolls of bank =) 216 total possible rolls.

Cases where both players win: Expectation = $2.

If bank rolls 1, both players will win in 5*5 = 25 cases. P1 is one of {2,3,4,5,6}, P2 is one of {2,3,4,5,6}

If bank rolls 2, both players will win in 4*4 = 16 cases.

If bank rolls 3, both players will win in 3*3 = 9 cases.

If bank rolls 4, both players will win in 2*2 = 4 cases.

If bank rolls 5, both players will win in 1*1 = 1 cases.

If bank rolls 6, both players will win in 0*0 = 0 cases.

Total cases = 25+16+9+4+1+0 = 55 cases.

Cases where player 1 wins $1 and player 2 loses: Expectation = $1.

If bank rolls 1, player 1 will win and player 2 will lose in 5*1 = 5 cases. P1 is one of {2,3,4,5,6}, P2 is {1}

If bank rolls 2, player 1 will win and player 2 will lose in 4*2 = 8 cases.

If bank rolls 3, player 1 will win and player 2 will lose in 3*3 = 9 cases.

If bank rolls 4, player 1 will win and player 2 will lose in 2*4 = 8 cases.

If bank rolls 5, player 1 will win and player 2 will lose in 1*5 = 5 cases.

If bank rolls 6, player 1 will win and player 2 will lose in 0*6 = 0 cases.

Total cases = 5+8+9+8+5+0 = 35

Cases where player 2 wins $1 and player 1 loses: Expectation = $1.

This is the same as above with player 1 and 2 exchanged.

Total cases = 35

Cases where both players lose: Expectation = $0.

If bank rolls 1, both players will lose in 1*1 = 1 cases. P1 is {1}, P2 is {1}

If bank rolls 2, both players will lose in 2*2 = 4 cases.

If bank rolls 3, both players will lose in 3*3 = 9 cases.

If bank rolls 4, both players will lose in 4*4 = 16 cases.

If bank rolls 5, both players will lose in 5*5 = 25 cases.

If bank rolls 6, both players will lose in 6*6 = 36 cases.

Total cases = 1+4+9+16+25+36 = 91 cases.

Total of all cases (we expect this to be 216 as mentioned above) = 55+35+35+91=216

So, joint expectation is:

\(E(I_1I_2) = \frac{2\cdot 55 +1\cdot 35+1\cdot 35+0\cdot 91}{216} = \frac{180}{216}= \frac{5}{6} \approx 0.8333\)

So, the covariance is given by:

\(\texttt{Cov}(I_1I_2) =E(I_1I_2) -E(I_1)\cdot E(I_2)= \frac{5}{6}-\frac{5}{12}\cdot\frac{5}{12}=\frac{95}{144} \approx 0.6597\)

As this is greater than 0 and closer to 1, they are positively correlated.

The reason why this result is expected is because the same bank roll is being used for both players. So, it is very likely that both players will win if the bank roll is 1 or even 2. Also, it is very likely that both players will lose if the bank roll is 6, 5, or even 4. This shows positive correlation between the events.

The total cost for the family of four is $944

Cost denotes the amount of money that a company or a person spends on the creation or production or acquiring of goods or services.

Here the family needs the service if transportation.

The cost of adult is $280. Out of four members , two are under 3years. This means the total cost for adult is 2 × 280 = $560

The cost of under 3 is ⅔ of the cost of adult.

= ⅔ × 280= $192

The cost of the two under 3 = 2 × $192 = $384

therefore the total cost for the family is $560 +$384 = $944

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Answer:

<

Step-by-step explanation:

Answer:

She typed for 60 minutes (1 hour).

Step-by-step explanation:

Do 2,700 divided by 45 to get your answer.

2,700 ÷ 45 = 60

She typed for 60 minutes (1 hour).

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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Answer:

a) 0.00031

b)  0.0017

c)  0.31

d) 0.00018

Step-by-step explanation:

attached below is the detailed solution

Total number of 7-poker cards are 52P7 = 133784560

A) Determine the probabilities of Seven-card straight

probability of seven-card straight = 0.00031

B) Determine the probability of four cards of one rank and three of a different rank

P( four cards of one rank and three of different rank ) = 0.0017

C) Determine probability of three cards of one rank and two cards of each two different ranks

P( three cards one rank and two cards of two different ranks ) = 0.31

D) Determine probability of two cards of each of three different ranks and a card of a fourth rank

P ( two cards of each of three different ranks and a card of fourth rank ) =  0.00018

The 5th term of the arithmetic series is  1179/ 19.

The 10th term of the arithmetic series , S is 66.

Using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

66 = a + 9d

The sum of the first 20 terms of S is 1290.

Therefore,

Sₙ = n / 2 (2a + (n - 1)d)

1290 = 10(2a + 19d)

1290 = 20a + 190d

combine the equation

66 = a + 9d

1290 = 20a + 190d

Hence,

a = 66 - 9d

1290 = 20(66 - 9d) + 190d

1290 = 1320 - 180 + 190d

1290 - 1320 + 180 = 190d

190d = 150

d = 150 / 190

d = 15 / 19

Hence,

a = 66 - 9(15  /19)

a = 66 - 135 / 19

a = 1254 - 135/ 19

a = 1119 / 19

Hence, let's find the fifth term.

a₅ = a + 4d

a₅ = 1119 / 19 + 4(15 / 19)

a₅ = 1119 / 19 + 60 / 19

Therefore,

a₅ =  1179/ 19

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Answer:

The mode is 1

Step-by-step explanation:

Mode is the number that occurs the most in the following numbers the statment gives you.

The volume V of the solid obtained by rotating the region bounded by the curves \(y^2=2x\) and \(x=2y\) about the y-axis is 107.168

Given,

The curves are \(y^2=2x...i\) and \(x=2y....ii\)

We need to determine the volume V of the solid obtained by rotating the region bounded by the given curves about y-axis.

Volume of the region can be obtained by using washer method.i.e.

\(V=\int \pi [(f(y)_{outer})^2-(f(y)_{inner})^2]dy\)

From figure, we can observe that the inner curve i.e. \(f(y)_{inner}\) is \(y^2=2x = > x=\frac{y^2}{2}\)

and outer curve i.e. \(f(y)_{outer}\) is \(x=2y\).

To determine the boundaries of the integral, substitute eq.ii in eq.i, we get

\(y^2=2(2y)\\\\y^2=4y\\\\y^2-4y=0\\\\y(y-4)=0\\\\\)

y=0 and y=4

These are the limits of the integral

Now, substituting the equations for volume V,

\(V = \int\limits^4_0 \pi [ (2y)^2 - (\frac{y^2}{2} )^2] dy\\\\ V = \int\limits^4_0 \pi [ 4y^2 - (\frac{y^4}{4} )] dy\\\\V = \pi [ \frac{4}{3} y^3 -\frac{1}{20} y^5 ]\limits^4_0\\\\V=\pi[\frac{4}{3}(4)^3-\frac{1}{20}(4)^5]\\\\V=\pi[\frac{256}{3} - \frac{1024}{20}]\\\\V=\pi[85.33-51.2]\\\\V=\pi [34.13]\\\\V=107.168\)

Hence, the volume of the region bounded by the curve after rotating is 107.168

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The mean and standard deviation of X are 0.9 and 1.68 points.

Since Nikola gets 3 points for each ringer which he scores, then total points he gets from ringers could be determined by multiplying the number of ringers by 3.

So, X = R * 3 = 3R

Where:

R = numbers of ringers

X = total points Nikola gets from ringers

Given:

Mean : μR = 0.3

Standard deviation : σR = 0.56

Thus, multiplying by 3 will effects the mean as follows:

μX = 3 (μR)

= 3 (0.3)

= 0.9

And, multiplying by 3 also will effects the standard deviation as follows:

σX = 3 (σR)

≈ 3 (0.56)

≈ 1.68

Hence, the mean of X is 0.9 and and the standard deviation of X is 1.68.

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The solution set for 1<|x+3|<4 is:

x ∈ (-2, 2)

To solve this inequality, we first need to isolate the absolute value. This gives us:

|x+3| - 1 < 4 - 1

We can then remove the absolute value signs by considering two cases:

* Case 1: x + 3 > 0

In this case, we have:

x + 3 < 5

Solving for x, we get:

x < 2

* Case 2: x + 3 < 0

In this case, we have:

-(x + 3) < 5

Multiplying both sides by -1, we get:

x + 3 > -5

Solving for x, we get:

x > -8

Combining the solutions from both cases, we get:

x ∈ (-2, 2)

Answer:

ya ya ya ya ya ya ya ya

Step-by-step explanation:

The total quantity of meat is 5.5 pounds.

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, quantity of ground beef = 1.68 pounds, quantity of chicken = 2.8 pounds and quantity of turkey = 1.02 pounds.

Here, total = The quantity of ground beef + The quantity of chicken + The quantity of turkey

Total = 1.68+2.8+1.02

= 5.5 pounds

Therefore, the total quantity of meat is 5.5 pounds.

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Answer:

3 yards

Step-by-step explanation:

Divide inches by 36

\(108/36\\=3yards\)

Answer:

\(3 \: \: yards\)

Step-by-step explanation:

\(1 \: \: yard = 36\: \: inches \\ yard \: \: x = 108 \: \: inches\)

So,

\( 1 = 36 \\ x = 108 \\ \\ cross \: \: \: multiple \\ \\ 108 = 36x \\ \frac{108}{36} = \frac{36x}{36} \\ x = 3 \: \: yards\)

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Answer:

  x = 6

Step-by-step explanation:

Compare the given formula to the equations shown in the attachment. First of all, you see that all of the numbers are scaled by a factor of 4. Removing that gives ...

  \(r=\dfrac{6.6}{1+1.1\cos{\theta}}=\dfrac{1.1\cdot6}{1+1.1\cos{\theta}}\)

This matches the formula for the hyperbola with e=1.1 and d=6, for a directrix of x = 6.

Answer:

Step-by-step explanation:

Coordinates of the vertices of the triangle ABC are A(3, 4), B(-7, 2) and C(2, 1).

Rule for the dilation of the coordinates of the ends of a segment is,

(x, y) → k(x, y)

        → (kx, ky)

Where k = scale factor by which the segment is dilated

If the given triangle ABC is dilated by a scale factor = \(\frac{1}{3}\)

Coordinates of the vertices of the image triangle will be,

A(3, 4) → A'(1, \(\frac{4}{3}\)) Or A'(1, 1.3)

B(-7, 2) → \(B'(\frac{7}{3},\frac{2}{3})\) Or B'(2.3, 0.7)

C(2, 1) → \(C'(\frac{2}{3},\frac{1}{3})\) Or C'(0.7, 0.3)

Now we can plot these points on the given graph

answer/explanation:

hope this helps