Partial credit
Leslie invests in a bank account that earns interest compounded quarterly. The expression 500(1.026) can be used to find the account balance in t years.
Part A
What was Leslie's initial investment?

Part B
What is the quarterly interest rate the account earns?

Answer:

a) 1/5 bucket = 1 gallon

b) 8.4 buckets = 1 barrel

c) 5376 fl oz per barrel

Step-by-step explanation:

a) From the given information, 1 bucket = 5 gallons. This means 1/5 of a bucket is 1 gallon.

b) From the given information, 8.4 buckets = 1 barrel. This seems to be in the form that the question is asking for. If the question was asking how many barrels were in a bucket the answer would be 1/8.4 barrels = 1 bucket.

c) From the previously determined conversion factors, we can take ounces to barrels by converting barrels down to gallons.

1/8.4 barrels = 1 bucket; 1/5 bucket = 1 gallon; 1 gallon = 128 fluid ounces

We need to set up a series of fractions that use these factors:

\(\frac{128 fl oz}{1 gallon}*\frac{1 gallon}{1/5 buckets}*\frac{1 bucket}{1/8.4 barrels}\)

These fractions can be simplified to \(\frac{128 fl oz}{1 gallon}*\frac{5 gallon}{1 bucket}*\frac{8.4 buckets}{1 barrel}\)

Multiply the fractions: 5376 fl oz per barrel

(Note that the units cancel out in the fractions so that only fluid ounces per barrel are left.)

Answer:

P(A|B) = 0.5

Step-by-step explanation:

A: set of prime numbers ={1,2,3}

B: set of divisors of 3 ={1,3}

P(A)=P(1)+P(2)+P(3)= 0.1+0.1+0.3 =0.5

P(B)=P(1)+P(3)=0.1+0.3=0.4

P(A|B) means: probability of A knowing that B

In other words we have to find the probability that a prime outcome occurs knowing that it is a divisor of 3

Its formula is given by:

P(A|B) = P(AintersectionB) /P(B)

A intersection B: outcome is prime and a divisor of 3 at the same time. (common elements between sets A and B)

A int B= {1,3}

P(AintB)= P(A)xP(B) = 0.5x0.4=0.2

Now back to the formula:

P(A|B) =P(AintB) / P(B)

=0.2/0.4=0.5

HOPE THIS HELPS :)

Answer:

A. down

Step-by-step explanation:

The parent graph is

f(x)=x

If this graph is transformed to obtain

g(x)=f(x)−4

The subtracttion means the graph will shift downward vertically

The graph of g(x) is obtained by shifting f(x) down by 4 unit.

Therefore the direction is down.

Mark this as brainliest please.

Step-by-step explanation:

volume of a cylinder is

ground area × height = pi×r²×h

r = 4

what we need to calculate is how high the water stands with one "serving" of 2m³.

that height is then added every minute (with the additional 2m³ during that minute).

so,

2 = pi×4²×h = pi×16×h

2/16 = 1/8 = pi×h

h = (1/8) / pi = 1/(8pi) = 0.039788736... m

that is rounded about 0.04 m or 4 cm.

therefore, the water rises by 0.04 m or 4 cm per minute

0.04m/min

a) The probability of not matching any of the six winning numbers is the probability that all six numbers chosen by the player are not among the six winning numbers. The probability of choosing a number that is not a winning number is 39/45 since there are 45 total numbers and only 6 are winning numbers. The probability of choosing six non-winning numbers is:

(39/45) x (38/44) x (37/43) x (36/42) x (35/41) x (34/40) = 0.4361

hence, the probability that none of the player's numbers match the six winning numbers is approximately 0.4361.

b) To determine if events E and E2 are independent, we need to check if the probability of both events occurring is equal to the product of their individual probabilities.

The probability of E, the event that the bit string chosen begins with 01, is 1/4. This is because there are four possible bit strings that begin with 01: 0100, 0101, 0110, and 0111, and there are 16 possible bit strings in total (2^4).

The probability of E2, the event that the bit string chosen ends with 10, is also 1/4. This is because there are four possible bit strings that end with 10: 0010, 0110, 1010, and 1110.

The probability of both E and E2 occurring is the probability of choosing a bit string that begins with 010 and ends with 10. There are two such bit strings: 0101 and 0100. Since there are 16 possible bit strings, the probability of both E and E2 occurring is 2/16 = 1/8.

To determine if E and E2 are independent, we need to check if the probability of both events occurring is equal to the product of their individual probabilities. That is, we need to check if:

P(E and E2) = P(E) x P(E2)

Substituting the probabilities we have calculated, we get:

1/8 = (1/4) x (1/4)

Since this equation is true, we can conclude that events E and E2 are independent.

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The graph is vertically stretched by a factor of 2 and translated 3 units right when it is transformed. Option A is correct.

Transformation of a function is shifting the function from its original place in the graph.

Types of transformation-

The given function is,

\(f(x) = x^3\)

This function is changed to the function,

\(g(x) = 2f(x -3),\)

Here the 3 units is substrate in the function. Thus, it is shiftet 3 units right. The number 2 is multiplied in the function which vertically stretched the graph by a factor of 2.

Thus, the graph is vertically stretched by a factor of 2 and translated 3 units right when it is transformed. Option A is correct.

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Answer:

1/8 I think

Step-by-step explanation:

The tank holds approximately 994,040 liters.

The volume of a right circular cylinder is given by the formula:

V = πr^2h

Where

The cylinder's diameter is specified as 13 m, hence the radius may be computed using the formula: r = d/2 = 13/2 = 6.5 m

The cylinder is described as having a 6 m length.

These values are substituted into the volume calculation to produce the following result:

V = π(6.5)^2(6)

V ≈ 994.04 cubic meters

Since 1 cubic meter equals 1000 liters, we can convert the volume to liters by multiplying by 1000.

V = 994.04 cubic meters x 1000 liters/cubic meter

V = 994,040 liters

Therefore, the tank holds approximately 994,040 liters.

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Answer:

6x − 20y

Step-by-step explanation:

−2[−3(x − 2y) + 4y] =

= −2[−3x + 6y + 4y]

= −2[−3x + 10y]

= 6x − 20y

Answer:

Step-by-step explanation:

Here you go mate

PEDMAS:

Parenthesis

Exponent

Multiplication

Addition

Subtraction

Step 1

−2[−3(x − 2y) + 4y]  Equation

Step 2

-2[-3(x -2y) + 4y]  simplify

(-2)(-3(x-2y))+(-2)(4y)

Step 3

(-2)(-3(x-2y))+(-2)(4y)   Add,Subtract And Remove parenthesis

6x-12y-8y

answer

6x-20y

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

a) The confidence level of 99% means that we are 99% sure that the interval contains the true population proportion.

b) The 99% confidence interval for the population proportion is given as follows: (0.3145, 0.4055). It means that we are 99% sure that the true population proportion is between 0.3145 and 0.4055.

c) The 95% confidence interval would be narrower, as it would have a lower critical value, thus the margin of error would also be lower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

The parameters for this problem are given as follows:

\(\pi = 0.36, n = 739\)

The lower bound of the interval is given as follows:

0.36 - 2.575 x sqrt(0.36 x 0.64/739) = 0.3145.

The upper bound of the interval is given as follows:

0.36 + 2.575 x sqrt(0.36 x 0.64/739) = 0.4055.

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Answer:

hi

Step-by-step explanation:

hi

To divide 30 into five parts such that the first and last parts are in the ratio of 2:3, we can follow these steps:

1. Determine the ratio between the first and last parts. In this case, it is 2:3.

2. Add the ratio values together to find the total number of parts: 2 + 3 = 5.

3. Divide the total value (30) by the total number of parts (5) to find the value of each part: 30 / 5 = 6.

4. Multiply the value of each part by the respective ratio values to obtain the individual parts:

- First part: 2 * 6 = 12

- Second part: 6

- Third part: 6

- Fourth part: 6

- Last part: 3 * 6 = 18

Therefore, the five parts of 30, with the first and last parts in the ratio of 2:3, are 12, 6, 6, 6, and 18.

The probability that the IQ is less than 128 is 0.91924

The given parameters about the distribution are

The z-score of the data value is calculated as

z = (x - μ)/σ

Substitute the given parameters in the above equation

z = (128 - 100)/20

Evaluate

z = 1.4

The probability that the IQ is less than 128 is then calculated as:

P(x < 128) = P(z < 1.4)

From the z table of probabilities, we have;

P(x < 128) = 0.91924

Hence, the probability is 0.91924

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Answer:

112.5$

Step-by-step explanation:

\(80 - 60 = 20 \\(20 \div 80)100 = 25\% \\ 75\% \times 150 = 112.5 \)

Answer: I cant see the picture right. So im sorry i could not help :(

Step-by-step explanation: IM SOOO SORRY D:

The measure of the inscribed angle G in the circle is 85 degree.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationhip between an an inscribed angle and intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

Since the circle equals 360 degrees, we can determine the intercepted arc DF.

Hence:

Arc DF = 360 - ( 70 + 120 )

Arc DF = 360 - 190

Arc DF = 170°

Now, plug the value into the above formula:

Inscribed angle = 1/2 × intercepted arc.

Inscribed angle G = 1/2 × 170°

Inscribed angle G = 85°

Therefore, angle G has a measure of 85 degree.

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Answer:

k= 2.5

Step-by-step explanation:

solve for k by simplifying both sides of the equation the isolatating the variable. hope this helps have a good night/day :) ❤

Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

\( \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 \)

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

Skipper's finance charge at the end of the billing period is given as follows:

$14.77.

The finance charge is obtained using simple interest, as there is a simple compounding per year for the debt, and the charge is the amount of interest accrued during the period of one month.

The amount of interest accrued after t years, using simple interest, is given as follows:

I(t) = Prt.

The parameters for the equation are given as follows:

Considering a period of one month = 1/12 of an year, the values of these parameters for this problem are given as follows:

P = 933, r = 0.19, t = 1/12.

Hence the finance charge for Skipper's purchase is calculated as follows:

I = 933 x 0.19 x 1/12 = $14.77.

(rounding to the nearest penny = nearest cent).

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Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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Answer:

y = - 3

Step-by-step explanation:

\(y = \frac{1}{4}x\)

y = 0.25 · x

y = 0.25 · - 12

y = - 3

Answer:

someone deleted ur ans from y question can you please write it again

thank you.

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Answer:

x  is 22

Step-by-step explanation:

because it is

Step-by-step explanation:

\(25 = 9x + 4 - 6x\)

\(25 - 4 = 9x - 6x \\ \)

\(21 = 3x\)

\( \frac{21}{3} = x\)

\(7 = x\)

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{x = 7}}}}}\)

Step-by-step explanation:

\( \star{ \tt{ \: 25 = 9x + 4 - 6x}}\)

\( \sf{Step \: 1 \: }\) : Collect like terms

Like terms are those which have same base

\( \longmapsto{ \sf{25 = 3x + 4}}\)

\( \tt{Step \: 2 \: }\) : Swap the sides of the equation

\( \longmapsto{ \sf{3x + 4 = 25}}\)

\( \tt{Step \: 3 \: }\) : Move 4 to right hand side and change it's sign

\( \longmapsto{ \sf{3x = 25 - 4}}\)

\( \tt{Step \: 4}\) : Subtract 4 from 25

\( \longmapsto{ \sf{3x = 21}}\)

\( \tt{Step \: 5}\) : Divide both sides by 3

\( \longmapsto{ \sf{ \frac{3x}{3} = \frac{21}{3}}} \)

\( \tt{Step \: 6}\) : Calculate

\( \longmapsto{ \sf{x = 7}}\)

The value of x is 7

Hope I helped!

Best regards! :D

~TheAnimeGirl

Answer:

0.006

Step-by-step explanation:

On the first draw, there are 52 cards, 4 of which are sevens.

On the second draw, there are 51 cards, 4 of which are nines.

The probability is:

(4/52) × (4/51)

= 4/663

≈ 0.006

Answer:

The Balina is faster than the Delfino.

Step-by-step explanation:

Divide the amount of miles covered by the amount of hours it took for each one.

For the Delfino:

57.5 / 5 = 11.5

For the Balina:

54 / 4.5 = 12

You're welcome T^T

Answer:

216

Step-by-step explanation:

Cube A volume

3*3*3=27

Cube B volume

6*6*6=216

Edge length of cube B=2(3)=6in

Volume:-

\(\\ \sf\longmapsto V=(6)^3\)

\(\\ \sf\longmapsto V=6(6)(6)\)

\(\\ \sf\longmapsto V=216in^3\)