In a right triangle, the length of the long leg is 2 inches more than the length of the short leg. The hypotenuse is 8 inches less than three times the length of the short leg. What is the length of each side of the triangle?

The original bill of the man can be calculated using the formula for discount, which is:

Discount = Original Price × Discount Rate

Given that the discount is Php 160 and the discount rate is 2%, we can rearrange the formula to solve for the original price:

Original Price = Discount ÷ Discount Rate

Original Price = Php 160 ÷ 2%

Original Price = Php 160 ÷ 0.02

Original Price = Php 8,000

Therefore, the original bill of the man was Php 8,000 before the 2% discount was applied.

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Answer: 8

Step-by-step explanation: (9-7)^3= 8

Answer: ? = 8

Step-by-step explanation: 2 x 2 x 2 = 8

P(event) represents the probability of an event occurring.

Probability is a branch of mathematics that deals with the study of random events or experiments. It is the measure of the likelihood or chance that a particular event will occur. Probability is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to happen.

An event is a set of outcomes of a random experiment, and the probability of an event is the measure of how likely it is to occur.

Here are some examples:

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Answer:

The original cost for 1 pound of coffee is $4.50, and Gabriel wants to buy 4 pounds, so the total cost without the coupon would be:

4 pounds x $4.50/pound = $18

With the coupon, Gabriel can subtract $2 from the final amount, so the total cost with the coupon would be:

$18 - $2 = $16

Therefore, Gabriel would have to pay $16 to buy 4 pounds of coffee with the coupon.

To write an expression for the cost to buy p pounds of coffee, we can use the formula:

cost = price per pound x number of pounds - coupon

If Gabriel buys at least one pound of coffee, then the expression would be:

cost = $4.50p - $2

So the cost to buy p pounds of coffee can be calculated by plugging in the desired value for p into this expression.

Answer:

The inequality that shows the range from -9 to 9, but only including the range from -4 to 3, can be written as:

-4 ≤ x ≤ 3

This inequality means that x can take on any value between -4 and 3, including -4 and 3 themselves, but it cannot be less than -4 or greater than 3. The inequality does not include the values between -9 and -4, or between 3 and 9.

Step-by-step explanation:

explanation of how to arrive at the inequality -4 ≤ x ≤ 3 to represent the range from -9 to 9, but only including the range from -4 to 3:

Start with the range from -9 to 9:

-9 ≤ x ≤ 9

Identify the portion of the range that we want to include:

-4 ≤ x ≤ 3

Replace the original range with the desired range:

-4 ≤ x ≤ 3 replaces -9 ≤ x ≤ 9

Check that the inequality is inclusive of the desired range but not of any values outside of that range:

-4 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Similarly, 3 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Any values less than -4 or greater than 3 are excluded from the range -4 ≤ x ≤ 3, as desired.

Therefore, the inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.

The inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.

The inequality that shows the range from -9 to 9, but only including the range from -4 to 3, can be written as:

-4 ≤ x ≤ 3

This inequality means that x can take on any value between -4 and 3, including -4 and 3 themselves, but it cannot be less than -4 or greater than 3. The inequality does not include the values between -9 and -4, or between 3 and 9.

explanation of how to arrive at the inequality -4 ≤ x ≤ 3 to represent the range from -9 to 9, but only including the range from -4 to 3:

Start with the range from -9 to 9:

-9 ≤ x ≤ 9

Identify the portion of the range that we want to include:

-4 ≤ x ≤ 3

Replace the original range with the desired range:

-4 ≤ x ≤ 3 replaces -9 ≤ x ≤ 9

Check that the inequality is inclusive of the desired range but not of any values outside of that range:

-4 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Similarly, 3 is included in the range -4 ≤ x ≤ 3, but is not included in the original range -9 ≤ x ≤ 9. Any values less than -4 or greater than 3 are excluded from the range -4 ≤ x ≤ 3, as desired.

Therefore, the inequality -4 ≤ x ≤ 3 represents the range from -9 to 9, but only including the range from -4 to 3.

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True. All real numbers satisfy the equation -4(6y+4)+19=12(-2y+5)-55.

The statement "If the equation is true for all real numbers enter 'All'" has been used to indicate that the given equation is true for all real numbers.

Given equation: -4(6y + 4) + 19 = 12(-2y + 5) - 55

Using distributive property, simplify both sides of the equation.

-24y - 16 + 19 = -24y + 60 - 55-24y + 3 = -24y + 5

By transposing -24y from the right-hand side of the equation to the left-hand side of the equation, we can simplify it as follows:

3 = 5

Since the above equation is always false for all real numbers, there is no solution. Therefore, we conclude that the given equation has no solution.

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The probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80% is 0.0107.

To find the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%, use the formula for the standard error of a proportion:

SE = √(p(1-p)/n)

Where p is the proportion of the population that is making an effort to conserve water or electricity, and n is the sample size.

In this case, p = 0.72 and n = 110. Plugging these values into the formula gives:

SE = √(0.72(1-0.72)/110) = 0.0347

Next, we need to find the z-score for the proportion of 0.80. The z-score is given by:

z = (P - p)/SE

Where P is the sample proportion and p is the population proportion. In this case, P = 0.80 and p = 0.72. Plugging these values into the formula gives:

z = (0.80 - 0.72)/0.0347 = 2.30

Finally, we can use the z-score to find the probability that the proportion of sampled residents who are making an effort to conserve water or electricity is greater than 80%. This is given by:

P(z > 2.30) = 1 - P(z < 2.30) = 1 - 0.9893 = 0.0107

Therefore, the probability is 0.0107 or 1.07%.

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Answer:

Step-by-step explanation:

big semicircle circumference=1/2*3.14*64

100.48cm

small semicircle circumference=1/2*3.14*16=25.12cm

total perimeter=125.6cm

The exact value of sec(sin-1(3/10)) is 1.049988251.

The exact value of sec(sin-1(3/10)) can be found using the following steps:

Step 1: Enter the value of sin-1(3/10) into a calculator to get the angle measure in radians. This will give you an angle measure of 0.304692654.

Step 2: Take the cosine of this angle measure using a calculator. This will give you a value of 0.952424403.

Step 3: The value of secant is the reciprocal of the value of cosine. So, to find the exact value of sec(sin-1(3/10)), take the reciprocal of 0.952424403. This will give you an exact value of 1.049988251.

Step 4: Simplify any radicals if necessary. In this case, there are no radicals to simplify.

Therefore, the exact value of sec(sin-1(3/10)) is 1.049988251.

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The price per can has been lowered by R2, making the standard can cost R7.

A mathematical assertion that establishes the equivalence of two expressions is known as an equation. It is made up of two sides, a left and a right side, separated by the equal sign (=). The equation, which is typically used to determine an unknown variable's value, requires that the values on both sides be equal. Exponents, logarithms, multiplication, division, addition, subtraction, and other mathematical operations can all be used in equations.

given

Let's say that the standard price per can is "x" Rand.

The revised price is (x-2) Rands if the price is decreased by R2.

The issue is that 14 cans are being offered for the customary price of 10 cans. Thus, we can construct the equation:

10x = 14(x-2) (x-2)

After finding x, we obtain:

10x = 14x - 28

-4x = -28

x = 7

The price per can has been lowered by R2, making the standard can cost R7.

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The numeric value of the composite function at x = 4 is given as follows:

|f(4) - 1|.

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

If g is the outer function, as is the case for this problem, we have that:

(g • f)(x) = g(f(x)).

At x = 4, the numeric value of the composite function is given as follows:

g(f(4)) = |f(4) - 1|.

The problem is incomplete, hence the composite function is given in general terms.

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Therefore , the solution of the given problem of fraction comes out to be -3 5/8 as a result.

Any combination of equal portions or fractions can be combined to represent a whole. In standard English, the quantity of a certain size is defined as a fraction. 8, 3/4. Wholes also include fractions. The ratio of numerator to ratio is a mathematical symbol for integers. All of these number fractions are simple fractions. There is a fraction inside of the fraction but rather remainder in a difficult fraction.

Here,

=> 9 1/4 = (4 x 9 + 1)/4 = 37/4

=> 12 7/8 = (8 x 12 + 7)/8 = 103/8

4 and 8 have the same shared factor, which is 8.

=> 37/4 - 103/8 = (2 x 37)/(2 x 4) (2 x 4) - 103/8

=> 74/8 - 103/8

=> -29/8

There is no simpler way to describe the outcome.

Since the outcome is already an incorrect fraction, we can change it back to a mixed integer as follows:

-29/8 = -3 5/8

9 1/4 - 12 7/8 Equals -3 5/8 as a result.

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The type of sampling used by the University of Iowa in their investigation of student drinking is C) Cluster sampling.

Cluster sampling is a method where the population is divided into groups, or clusters, and a random sample of these clusters is selected for the study. In the case of the University of Iowa's investigation, the population was the entire student body and the clusters were the different classrooms. By randomly selecting 10 classrooms and interviewing all the students in each of these groups, the University of Iowa was using cluster sampling.

Therefore, the correct answer is  C: cluster sampling.

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Simplified each expression of  (x²-25x-24)/(6x+2x²)*(5x²)/(8-x) is (-5x(x-24)(x-1))/(2(3+x)(x-8)).

To simplify the expression (x²-25x-24)/(6x+2x²)*(5x²)/(8-x), we need to factor the polynomials in the numerator and denominator and then cancel out any common factors.

First, let's factor the polynomials:

(x²-25x-24) = (x-24)(x-1)
(6x+2x²) = 2x(3+x)
(5x²) = 5x*x
(8-x) = -(x-8)

Now, let's plug these back into the expression and cancel out any common factors:

((x-24)(x-1))/(2x(3+x))*(5x*x)/(-(x-8))

= ((x-24)(x-1)*5x*x)/(2x(3+x)*-(x-8))

= ((x-24)(x-1)*5x)/(2(3+x)*-(x-8))

= (5x(x-24)(x-1))/(-2(3+x)(x-8))

Finally, let's simplify the expression by multiplying the constants:

= (-5x(x-24)(x-1))/(2(3+x)(x-8))

So the simplified expression is (-5x(x-24)(x-1))/(2(3+x)(x-8)).

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Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.

The formula that expresses the described relationship where A varies inversely as h is A = k/h, where k is the constant of proportionality.

In an inverse relationship, one variable increases as the other variable decreases. In this case, as h increases, A decreases, and as h decreases, A increases. The constant of proportionality, k, remains the same throughout the relationship.

To find the value of k, you can use the formula and plug in known values for A and h. For example, if A = 4 and h = 2, you can plug these values into the formula and solve for k:

4 = k/2

k = 8

Once you know the value of k, you can use the formula to find the value of A or h, given the value of the other variable. For example, if you know that h = 3 and k = 8, you can plug these values into the formula and solve for A:

A = 8/3

A = 2.67

Therefore, the formula that expresses the described relationship where A varies inversely as h is A = k/h.

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Answer:

1/4

Step-by-step explanation:

Fractions have two parts, the numerator and the denominator. The denominator is the bottom number and it tells us what unit of fraction we are working with (ie: it denotes fourths, halves, etc.)

Hope it helps! :D

Answer:

Step-by-step explanation: point form: (4,1)

x=4 , y=1

Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds.

The function f(x) = 8192(0.05)^x represents exponential decay, where the number of players is decreasing by a factor of 0.05 in each round. However, in this tournament, the number of players is decreasing by a factor of 0.5 (half the players) in each round. Therefore, the correct function should be f(x) = 8192(0.5)^x.

To find the number of players remaining in the tournament at the end of x rounds, simply plug in the value of x into the function and solve.

For example, if we want to find the number of players remaining at the end of 3 rounds, we would plug in x = 3 and solve:

f(3) = 8192(0.5)^3
f(3) = 8192(0.125)
f(3) = 1024

Therefore, there would be 1024 players remaining in the tournament at the end of 3 rounds. Similarly, you can plug in any value of x to find the number of players remaining at the end of x rounds.

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The equation log_x y = 4  can be written as y = x⁴ and the true, correct option is 1.

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number. that is, b raised to x = n, in which case one writes x = log base b n. Scientists embraced logarithms immediately because of a number of advantageous characteristics that made complicated, time-consuming computations simpler. In specifically, by searching up each number's logarithm in a special database, adding the logarithms together, and then rechecking the table to discover the number with that computed logarithm, scientists could find the product of two integers m and n.

Given that, log_x y = 4 .

Using the logarithmic rule we have:

log_x y = 4  

y = x⁴

Hence, the equation log_x y = 4  can be written as y = x⁴ and the correct option is 1.

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The surface area of the rectangular prism is 174 cm^2

Rectangular Prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangle such that all the pairs of the opposite faces are congruent.

To determine the surface area of Rectangular prism

SA = 2(LH + LW + WH)

Where W = Width = 2 cm

L = Length = 5 cm

H = Height = 11 cm

SA = 2[(5*11) + (5*2) + (11*2)]

SA = 2(55 + 10 + 22)

SA = 2(87)

SA = 2 * 87

SA = 174

Therefore, the surface area of rectangular prism is 174 cm^2

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Answer:

Step-by-step explanation:

Decreasing.

This is because the as you increase the X value and solve for Y, the Y value decreases.

For example:

[tex]x=1 \\y=2(\frac{1}{3} )^1\\y=\frac{2}{3} =0.667\\\\x=2\\y=2(\frac{1}{3} )^1\\y=\frac{2}{9}=0.222\\\\x=3\\y=2(\frac{1}{3} )^3\\y=\frac{2}{27}=0.074[/tex]

A(t) = $3,600(1.125)t is the function that displays the balance of the account after t years, rounded to four decimal places.

The definition of the word "invest" is to "expend money with the idea of attaining a profit or material consequence by putting it into financial plans, etc." A person is "vested" when they are "secured in their possession or allocated to a person," on the other hand. It can also imply outfitted with a vest, although that is unimportant just now.

A(t) = P(1 + r)t

where:

A(t) represents the balance of the account after t years.

P is the initial investment, $3,600, and r is the growth rate per year.

The number of years is t.

A(t) = $3,600(1 + 0.125)t

A(t) = $3,600(1.125)t

We can take the growth rate and subtract 1 to get the annual growth percentage, which we can then translate to a percentage as follows:

Percentage growth rate = (1.125 - 1) * 100% = 12.5%

So the account grows by approximately 12.5% per year.

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Based on the information, we can infer that the second plan is the best for the bicycle company because it will cost less and will earn more.

To identify the best alternative for the bicycle company, we must take into account the information on the cost of design and construction of the bicycles and the cost of labor and production.

In accordance with the above, we can infer that in alternative one the design and construction of the bicycle would be more expensive than alternative two. However, the production of each bicycle would be less.

Therefore, the best alternative would be option two because it requires less initial research and the product will cost more, so it would have a higher retail value, so the investment could be recovered much faster. .

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No, (8, 2) is not a solution to the inequality y ≥ 3x + 4 because when we substitute x = 8 and y = 2 into the inequality, we get a false statement. In other words, the point (8, 2) does not satisfy the inequality y ≥ 3x + 4, which means it is not a valid solution to the inequality.

To determine whether (8, 2) is a solution to the inequality y ≥ 3x + 4, we need to substitute the values of x and y into the inequality and check if the inequality holds true.

y ≥ 3x + 4

Substituting x = 8 and y = 2:

2 ≥ 3(8) + 4

2 ≥ 24 + 4

2 ≥ 28

The inequality is not true since 2 is not greater than or equal to 28.

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Answer:

$512.17

$286.48

$1,958.40

$1,628.85

$56.37

$324.24

$135.55

Note: These calculations were made assuming simple interest. If the interest is compounded, the final amounts will be slightly different.

Step-by-step explanation:

The scale factor used to produce Figure 2 from Figure 1 is given as follows:

7/3.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The side lengths are given as follows:

Hence the scale factor of the dilation is given as follows:

7/3.

(the scale factor is the division of the side length of the dilated figure by the equivalent side length of the original figure).

The problem asks for the scale factor used from figure 1 to figure 2.

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Answer:

C 7/3 because i got it right

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-3}{h}~~,~~\underset{6}{k})}\qquad \stackrel{radius}{\underset{5}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-3) ~~ )^2 ~~ + ~~ ( ~~ y-6 ~~ )^2~~ = ~~5^2\implies (x+3)^2+(y-6)=25[/tex]

Answer:

187

Step-by-step explanation:

how to do long division, you know how to start im assuming. then you then bring down and Divide, Multiply, Subtract, with the first number then bring the next number down and repeat that.

Answer:

187

Step-by-step explanation:

I personally just do multiplication whenever I can, but that's just me. Like for example I know 100 x 3 = 300 and 200 x 3 = 600. SO it has to be between 100 and 200.

150 x 3 = 450. So know it narrows it down to between 150 and 200.

175 x 3 = 525

180 x 3 = 540

185 x 3 = 555

190 x 3 =570

So now it's between 185 and 190.

Now I just need to do the following.

186 x 3 = 558

187 x 3 = 561

And there we have the answer.

Answer:

In believe it’s 68 but I might be wrong so if it is sorry

Step-by-step explanation:

The equation correctly represents the amount of money in her savings account in terms of the monthly growth rate is [tex]y = 2000(1 + 0.0033)^t[/tex]. Option D is the correct answer.

The interest earned on savings that is computed using both the original principle and the interest accrued over time is known as compound interest. It is said that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely computed on the principal sum.

Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

Given that, the function of the model of the account is:

[tex]y = 2000(1.04)^t[/tex]

The monthly interest rate is:

r = 4% / 12 = 0.00333

The model in terms of monthly interest rate can be written as:

[tex]y = 2000(1 + r)^{12t/12}[/tex]

Substituting the value of r:

[tex]y = 2000(1 + 0.0033)^t[/tex]

Hence, the equation correctly represents the amount of money in her savings account in terms of the monthly growth rate is [tex]y = 2000(1 + 0.0033)^t[/tex].

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