2 (5y-4)>32
Solve the inequality for y.

Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

The service area of the cylinder is 42\(\pi\) square fts.

Two parallel bases joined by a curving surface make up the three-dimensional solid known as a cylinder.

Typically, the bases are shaped like circles. The height "h" of the cylinder stands for the perpendicular distance between the bases, while "r" stands for the cylinder's radius.

The uses of cylinder are-

Total surface area of the cylinder formula:

It is the sum of the base surface area and the lateral surface area;

Total area = base area + lateral area , or

Total area = 2 π r² + (2 π r) h , or

Total area = 2 π r (r + h)

Calculation for the total area of the cylinder;

Base diameter is 6 ft

Radius is 6/2 = 3 ft

Height is 4 ft

Total area = 2\(\pi\)3(3 + 4)

                 = 6\(\pi\)×7

                 = 42\(\pi\)

Therefore, the total surface area of the cylinder is 42\(\pi\) square fts.

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Answer:

No

Step-by-step explanation:

5(3+2) = 5(5) = 25

5.3 + 5.2 = 10.5

25 doesn't equal 10.5 therefore 5(3+2) isn't equivalent to 5.3 + 5.2

Answer:

1.a

2.c

3b

4.c

5.a or b

Step-by-step explanation:

The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

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The differential equation that has y=C1 sin(4x+C2) as its general solution is d) y''+ 16y=0.

To find the differential equation, we need to take the derivative of the general solution twice.

The first derivative of the general solution is:

y' = C1*4*cos(4x+C2)

The second derivative of the general solution is:

y'' = -C1*16*sin(4x+C2)

Substituting the general solution back into the second derivative gives us:

y'' = -16y

Rearranging the equation gives us the differential equation:

y''+ 16y=0

Therefore, the correct answer is d) y''+ 16y=0.

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Answer:

Its d

Step-by-step explanation:

because you square 10 and you get 100 and you have to multiply 6 with 100 which is 600 and then you multiply the 3.14 which gives you 1,884

PLEASE MARK AS BRAINLIEST

Evaluating the functions we will get:

a) f(36)  = 6

b) (g + f)(4)  = 9/4

c) (f × g)(0)  = NaN

Here we have the functions:

f (x) = √x and g(x) = 1/x.

We want to evaluate these functions in some values, to do so, just replace the variable x with the correspondent number.

We will get:

f(36) = √36 = 6

(g + f)(4) = g(4) + f(4) = 1/4 + √4  = 1/4 + 2 = 9/4

(f × g)(0) = f(0)*g(0) = √0/0 = NaN

The last operation is undefined, because we can't divide by zero.

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Answer:

1.2

Step-by-step explanation:

Divide then add.

Answer:

1.2

Step-by-step explanation:

-6/20 + 1.5 = 1.2

Hope this helps☺️

Answer:

19/23, 50/23

Step-by-step explanation:

We can take the first equation and isolate the x:

x + 5y = 3 ⇒ -5y ⇒

x = 3 - 5y.

Then we can substitute the x in the first equation by this:

3y + 2 = 4(3-5y) ⇒

3y + 2 = 12 - 20y ⇒ +20y

23y + 2 = 12 ⇒ -2

23y = 10 ⇒ ÷23

y = \(\frac{10}{23}\)

Then we can add the value of y into the equation equaling x we made:

x = 3 - 5(\(\frac{10}{23}\)) ⇒

x = 3 - \(\frac{50}{23}\) ⇒

x = \(\frac{19}{23}\)

Hope this helps! :)

The natural length of the spring is approximately 3.97 cm.

The natural length (in cm) of the spring can be found by the following steps:

Given that 2.4 J of work is needed to stretch a spring from 15 cm to 19 cm  and 4 J is needed to stretch it from 19 cm to 23 cm.

We know that the work done in stretching a spring is given by the formula;

W = ½ k (x₂² - x₁²)

Where,W = work done

k = spring constant

x₁ = initial length of spring

x₂ = final length of spring

Let the natural length of the spring be x₀.

Then,

2.4 = ½ k (19² - 15²)

Also,4 = ½ k (23² - 19²)

Expanding and solving for k gives:

k = 20

Next, using the value of k in any of the equations to solve for x₀,

x₀² - 15² = (2 × 2.4) ÷ 20

x₀² = 15² + (2 × 2.4) ÷ 20

x₀² = 15.72

x₀ = √15.72

x₀ ≈ 3.97

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It will take approximately 7.42 years for an initial amount of $25,000, compounded quarterly at 8% interest, to accumulate to $45,000. The effective rates for 12% compounded semi-annually, quarterly, and monthly are approximately 12.36%, 12.55%, and 12.68% respectively.

To find the number of years it takes for an amount to accumulate to a certain value, we can use the formula for compound interest:

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

Where:
A = the final amount
P = the initial principal amount
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years

For part (a), we are given:
P = $25,000
r = 8% (or 0.08 as a decimal)
n = 4 (compounded quarterly)
A = $45,000

We need to find t (the number of years). Rearranging the formula, we have:

t = (1/n) * log(A/P) / log(1 + r/n)

Substituting the given values:

t = (1/4) * log(45000/25000) / log(1 + 0.08/4)

Simplifying this equation gives us:

t ≈ 7.42 years

Therefore, it will take approximately 7.42 years for the initial amount of $25,000 to accumulate to $45,000 when compounded quarterly at an interest rate of 8%.

For part (b), we are given three different compounding periods: semi-annually, quarterly, and monthly. To find the effective rate for each, we can use the formula:

Effective Rate = (1 + r/n)^n - 1

For 12% compounded semi-annually, we have:
r = 12% (or 0.12 as a decimal)
n = 2 (compounded semi-annually)

Substituting the values into the formula gives us:

Effective Rate = (1 + 0.12/2)^2 - 1

Simplifying this equation gives us:

Effective Rate ≈ 12.36%

Therefore, the effective rate for 12% compounded semi-annually is approximately 12.36%.

For 12% compounded quarterly, we have:
r = 12% (or 0.12 as a decimal)
n = 4 (compounded quarterly)

Substituting the values into the formula gives us:

Effective Rate = (1 + 0.12/4)^4 - 1

Simplifying this equation gives us:

Effective Rate ≈ 12.55%

Therefore, the effective rate for 12% compounded quarterly is approximately 12.55%.

For 12% compounded monthly, we have:
r = 12% (or 0.12 as a decimal)
n = 12 (compounded monthly)

Substituting the values into the formula gives us:

Effective Rate = (1 + 0.12/12)^12 - 1

Simplifying this equation gives us:

Effective Rate ≈ 12.68%

Therefore, the effective rate for 12% compounded monthly is approximately 12.68%.

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Answer:

A

Step-by-step explanation:

the brigde means anything in between

Answer:

she can use 14.025 gigabytes

Answer:

Is there anything else to this question cause it's confusing and I would help you but if there is more information

Step-by-step explanation:

x=x

Step-by-step explanation:

finding by mathematical operation and distribution law over multiplication added with subtraction is the formula now it might be easy for you

Answer:

5 blue tiles on each row

Step-by-step explanation:

Given

\(Tiles = 80\)

\(Rows= 8\)

\(Color = \{White, Blue\}\)

\(White = Blue\)

See comment for original question

Required

The number of blue in each row

First, we calculate the number of tiles in each row.

\(Unit = \frac{Tiles}{Rows}\)

\(Unit = \frac{80}{8}\)

\(Unit = 10\)

The distribution of tiles on each row is:

\(White + Blue = Unit\ Tiles\)

\(White + Blue = 10\)

On each row, we have: \(White = Blue\)

So, the equation becomes

\(Blue + Blue = 10\)

\(2\ Blue = 10\)

Divide both sides by 2

\(Blue = 5\)

Answer:

7:4

Step-by-step explanation:

70 / 2 : 40 / 2

35:20

35 / 5 : 20 / 5

7:4

Answer:

isosceles but not equilateral

Answer:

It has two of its sides equal in length.

So the Answer is ISOSCELES BUT NOT EQUILATERAL

Answer:

The absolute value function that models the path of the ball is

\(f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |\)

The coordinates when the ball passes within 3 meters of the wall is \(\left (3, 12\tfrac{3}{4} \right )\)

Step-by-step explanation:

Given that the ball rolls without other external influences, we have;

(y - 0) = (x - 15)

The slope, m is give by the relation;

m = (y₂ - y₁)/(x₂ - x₁)

m = (15 - 0)/(0-20) = -3/4

The equation of the path of the ball in slope and intercept form is presented as follows;

y = m·x + c

15 = -3/4 ×0 + c = 15

c = 15

The absolute value function that models the path of the ball is then;

\(f(x) = \left | -\frac{3}{4}\cdot x + 15 \right |\)

The vale of the function when x = 3 is given by the relation

\(f(x) = \left | -\dfrac{3}{4}\times 3 + 15 \right | = \dfrac{51}{4}\)

Therefore, we have the coordinates as  \(\left (3, 12\tfrac{3}{4} \right )\).

the probability of rolling two integers that differ by 2 on the first two rolls is \($\frac{3}{36}$\), since there are 3 favorable outcomes out of 36 total possible outcomes

The probability of rolling integers that differ by 2 on the first two rolls is \(\frac{3}{36}\).

There are six possible outcomes on a standard 6-sided die - 1,2,3,4,5,6.

The possible outcomes that could produce two integers that differ by 2 are (1,3), (3,5), and (5,1).

Therefore, the probability of rolling two integers that differ by 2 on the first two rolls is \(\frac{3}{36}\), since there are 3 favorable outcomes out of 36 total possible outcomes. the probability of rolling two integers that differ by 2 on the first two rolls is \(\frac{3}{36}\) since there are 3 favorable outcomes out of 36 total possible outcomes

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Answer:

We have to use a little bit of casework to solve this problem because some numbers on the die have a positive difference of 2 when paired with either of two other numbers (for example, 3 with either 1 or 5) while other numbers will only have a positive difference of 2 when paired with one particular number (for example, 2 with 4).

If the first roll is a 1, 2, 5, or 6, there is only one second roll in each case that will satisfy the given condition, so there are 4 combinations of rolls that result in two integers with a positive difference of 2 in this case. If, however, the first roll is a 3 or a 4, in each case there will be two rolls that satisfy the given condition- 1 or 5 and 2 or 6, respectively. This gives us another 4 successful combinations for a total of 8.

Since there are 6 possible outcomes when a die is rolled, there are a total of \(6\cdot6=36\) possible combinations for two rolls, which means our probability is \($\dfrac{8}{36}=\boxed{\dfrac{2}{9}}.$\)

OR

We can also solve this problem by listing all the ways in which the two rolls have a positive difference of 2:

(6,4), (5,3), (4,2), (3,1), (4,6), (3,5), (2,4), (1,3).

So, we have 8 successful outcomes out of  possibilities, which produces a probability of \(\frac{8}{36}=\frac29\)

Answer:

3,999,960

Step-by-step explanation:

1)let me take an example, the sum of all the digits numbers can be formed using the 1,2 without repetition.

(12, 21 ) , The sum is 12+21= 33

2)Another one, the sum of all the digits numbers, can be formed using three digits 1,2,3, without repetition.

(123,231,321,213,312,132) Their sum is by adding and is 1332

For the above example, we can find the answer by using the formula.

(n-1)! x sum of the digits x ( 111111111….n times)

For example, 1)

n = 2, the sum of the digits 2+1= 3

(2–1)! x3 (11)

1x 3 x 11= 33

For example 2

n= 3 sums of the numbers 1+2+3 = 6

(3–1)! x 6( 111)

2x1x6x111

12x111= 1332

Both answers verified

For the given question

n= 5 , sum of the digits 1+2+3+4+5=15

(5–1)! x 15 x 11111

4! x 15 x 11111

4 x 3 x x2 x 15 x 11111

24 x 15 x 11111

360 x 11111= 3999960

Answer: 3999960

Using simultaneous equations, the investor invested $7,560 in the 2% term, if the total investment averaged 3.75% for the year.

Simultaneous equations are a system of equations solved concurrently.

The solutions to a system of equations are found at the same time.

The total investment in the portfolio = $42,000

Investment in a 2% term for one year = a

Investment in 4.5% mortgage for one year = b

The average earnings from the investment = 3.75%

a + b = 42,000... Equation 1

(0.02a + 0.045b) ÷ 2 = 0.0375

0.01a + 0.0225b = 0.0375... Equation 2

Multiply Equation 1 by 0.0225:

0.0225a + 0.0225b = 945 ... Equation 3

Subtract Equation 2 from Equation 3:

0.0225a + 0.0225b = 945

-

0.01a + 0.0225b = 0.0375

0.0125a = 944.9625

a = 7,560

= $7,560

b = 42,000 - 7,560

b = 34,440

= $34,440

Thus, the investor invested $7,560 in the 2% term and $34,440 in the mortgage.

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The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.

The "center" of circle is called as midpoint of diameter.

The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and

The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.

So, center of circle is (4,3),

The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:

⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.

⇒ distance = √((4 - 4)² + (9 - (-3))²)

⇒ √(144) = 12.

So, radius is 6.

The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,

Substituting the values

We get,

⇒ (x - 4)² + (y - 3)² = 6²,

⇒ (x - 4)² + (y - 3)² = 36,

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.

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Answer:

112° in the first quadrant

68° in the second quadrant

292° in the third quadrant

248° in the fourth quadrant

Step-by-step explanation:

To find an angle in each quadrant with a common reference angle with 112°, we need to first determine the reference angle.

The reference angle is the acute angle between the terminal side of the angle and the x-axis. To find the reference angle, we subtract the nearest multiple of 180° from the given angle, 112°, so that the result is between 0° and 180°:

Reference angle = 112° - 180° = -68°

Since the reference angle is negative, we can find the corresponding positive angle by adding 180°:

Reference angle = -68° + 180° = 112°

Now that we have the reference angle, we can find an angle in each quadrant with that reference angle as follows:

First quadrant: To find an angle in the first quadrant with a reference angle of 112°, we simply take the reference angle itself since it is already acute and positive:

θ = 112°

Second quadrant: To find an angle in the second quadrant with a reference angle of 112°, we subtract the reference angle from 180°:

θ = 180° - 112° = 68°

Third quadrant: To find an angle in the third quadrant with a reference angle of 112°, we add the reference angle to 180°:

θ = 180° + 112° = 292°

Fourth quadrant: To find an angle in the fourth quadrant with a reference angle of 112°, we subtract the reference angle from 360°:

θ = 360° - 112° = 248°

Therefore, the angles with a common reference angle of 112° in each quadrant, from 0°≤θ<360°, are:

112° in the first quadrant

68° in the second quadrant

292° in the third quadrant

248° in the fourth quadrant

The probability of winning the game is 0.5.

The problem requires us to find the probability of winning the game, which is 0.411. To approach this problem, we can use the formula for conditional probability which says that the probability of A given B is equal to the probability of A and B divided by the probability of B. This method allows us to define certain events like A, B, and C to find the probabilities of each event.

Event A represents both cards being of the same suit, and its probability is P(A) = 1/4 because there are four suits, and we need two cards of the same suit. Event B represents neither of the first two cards being the same suit, and its probability is P(B) = 3/4 * 2/3 = 1/2 since the first card can be any suit, but the second card must be a different suit. Event C represents the third card matching the suit of one of the first two cards. If both cards are of the same suit, any third card will match. Therefore, the probability of C given A is P(C|A) = 1. If the first two cards are not the same suit, there will be two suits left that can match one of the first two cards, making the probability of C given B as P(C|B) = 1/2.

Now, we can calculate the probability of winning by adding the probabilities of events A and B multiplied by the probability of event C given B. So, P(A) + P(B)P(C|B) = 1/4 + (1/2)(1/2) = 1/4 + 1/4 = 1/2. Therefore, the probability of winning the game is 0.5.

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Answer:

f = (N² - H)/6

Step-by-step explanation:

Step 1: Write equation

N² = 6f + H

Step 2: Solve for f

Answer:

C

Step-by-step explanation: