A submarine is exploring the ocean floor and begins to ascend to the surface. The depth of the submarine in the water can be modeled by the function `d=500t-4,500` where t is the time (in minutes) since the submarine began to ascend

Step-by-step explanation:

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Answer:

the first one is wrong.

Step-by-step explanation:

Step-by-step explanation:

here, 4 days = 20 miles

so, 1 day = 5 miles

hence, x miles = 5x miles

Yoko pumped 48 gallons of water out of her pool over 8 minutes at a constant rate. The change in the amount of water in the pool each minute was 6 gallons.

To find the change in the amount of water in the pool each minute, we divide the total amount of water pumped (48 gallons) by the total time taken (8 minutes). This gives us the rate at which the water was being pumped out.

In this case, 48 gallons divided by 8 minutes equals 6 gallons per minute. This means that Yoko was pumping out 6 gallons of water from the pool every minute.

The constant rate indicates that the amount of water being pumped out remained the same throughout the entire 8-minute period. So, in the first minute, 6 gallons of water were pumped out, in the second minute another 6 gallons, and so on, until the entire 48 gallons were pumped out by the end of the 8-minute period.

Therefore, the change in the amount of water in the pool each minute was a consistent decrease of 6 gallons, resulting in a total of 48 gallons being pumped out over 8 minutes.

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Answer:

c

Step-by-step explanation:

a line of credit with a fixed total amount.

The closed line of the credit is the line of credit with the fixed total amount. Option c is the correct option.

On the bases of the requirement, a person or firm takes the open or closed line of credit.

Thus, the closed line of the credit is the line of credit with the fixed total amount. Option c is the correct option.

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Answer:

ok?

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

I will be using pythagorean triples for some, but you can use sqrt(a^2+b^2)=c^2

1. 12 13 5 x=5

2. 3 4 5 x=5

3. sqrt(14.7^2-11.9^2)=sqrt(74.48) or around 9 (root is irrational)

4. sqrt(15.4^2-6.3^2)=sqrt(197.47) or around 14 (same thing)

5. sqrt(15^2-11^2)=2*sqrt(26) or around 10

6. sqrt(4^2-sqrt(6)^2)=sqrt(16-6)=sqrt(10) or around 3

7. sqrt(12^2+9^2)= 15, so it is a right triangle

8. 9, 12, 15 divide by 3- 3, 4, 5 pythagorean triple - is a right triangle

9. 9, 12, 15-17>15, obtuse

10. sqrt(20.1^2+18^2)=20.4 - 20.1<20.4, acute

11. sqrt(4.8^2+28.6^2)=29, 29=29, right

Answer:

-8

Step-by-step explanation:

\(4^3*4^{-6}=4^5*4^{?}\\\\4^{3-6}=4^{5+?}\\\\4^{-3}=4^{5+?}\\\\\:so\\\\5+?=-3\\\\?=-3-5\\\\?=-8\)

Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Let us remember that in a 6-sided dice, the numbers it contains are (1,2,3,4,5,6), and of those 3 are odd, then we are going to substitute in the following formula of the simple probability of an event :

Probability of an event=Favorable Cases/Possible Cases

Probability of tossing an odd number with 6 sided number cube =3/6

Probability of tossing an odd number with 6 sided number cube =1/2

Finally we obtain that the probability of tossing an odd number with 6 sided number cube is 1/2.

Divide 6.3 meters of leather

between 14

Then

6.3 meters= 630 cm

Now divide

630/14 =

Find m,c,d (max common divisor), between 63 and 14. Its 7.

divide by 7, both numerator and denominator

90/2 = 45

Then answer is , each piece is 45 cm long

The solution to the given initial-value problem by using the Laplace transform  is \(y(t) = e^{(-t) }- cos(t) + t sin(t) - t cos(t).\)

To solve the initial-value problem using Laplace transform, we'll first take the Laplace transform of both sides of the differential equation and use the initial condition to find the Laplace transform of the solution.

Taking the Laplace transform of the given differential equation, we have:

\(L{[y']} + L{[y]} = L{[t sin t]}\)

Applying the linearity property of the Laplace transform and using the derivative property \(L{[y']} = sY(s) - y(0)\), where Y(s) represents the Laplace transform of y(t), we get:

\(sY(s) - y(0) + Y(s) = L{[t sin t]}\)

Since y(0) = 0 according to the initial condition, the equation simplifies to:

\(sY(s) + Y(s) = L{[t sin t]}\)

Using the table of Laplace transforms, we find that the Laplace transform of t sin t is:

\(L{(t sin t)} = 2 / (s^2 + 1)^2\)

Substituting this into the equation, we have:

\(sY(s) + Y(s) = 2 / (s^2 + 1)^2\)

Now, we can solve this equation for Y(s):

\(Y(s)(s + 1) = 2 / (s^2 + 1)^2\)

Dividing both sides by (s + 1), we get:

Y(s) = 2 / ((s + 1)(s^2 + 1)^2)

\(Y(s) = 2 / ((s + 1)(s^2 + 1)^2)\)

Now, we need to find the inverse Laplace transform of Y(s) to obtain the solution y(t).

Using partial fraction decomposition, we can express Y(s) as:

\(Y(s) = A / (s + 1) + (Bs + C) / (s^2 + 1) + (Ds + E) / (s^2 + 1)^2\)

Solving for the constants A, B, C, D, and E, we can rewrite Y(s) as:

\(Y(s) = 1 / (s + 1) - (s + 1) / (s^2 + 1) + (2s - 1) / (s^2 + 1)^2\)

Taking the inverse Laplace transform, we find that the solution y(t) is:

\(y(t) = e^{(-t)} - cos(t) + t sin(t) - t cos(t)\)

Therefore, the solution to the given initial-value problem by using the Laplace transform  is \(y(t) = e^{(-t) }- cos(t) + t sin(t) - t cos(t).\)

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A variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called dummy variable.

In this question,

A dummy variable is a numeric variable that represents categorical data, such as gender, race, political affiliation, etc. Each dummy variable represents one category of the explanatory variable and is coded with 1 if the case falls in that category and with 0 if not.

In dummy variables, we don't need to write out separate equation models for each subgroup because they enable us to use a single regression equation to represent multiple groups. It is an artificial variable created to represent an attribute with two or more distinct categories/levels.

A dummy variable can take values either 1 or 0. It can express either a binary variable or a categorical variables. The number of dummy variables we must create is equal to k - 1, where k is the number of different values that the categorical variable can take on.

Hence we can conclude that a variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called dummy variable.

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Answer:

A  $12.84

Step-by-step explanation:

Sweater was originally $48.00 before tax.  $48.00 x 7% tax rate (.07) = $3.36 in tax

So the sweater originally would've cost $48.00 + $3.36 = $51.36

The sale price was 25% off the $48.00.  $48.00 x 25% (.25) = $12.00

Then you subtract the $12.00 from the $48.00 to get the new price of $36.00

Now that's before tax, so $36.00 x 7% tax rate (.07) = $2.52 in tax

So the sweater would cost on sale $36.00 + $2.52 = $38.52

To figure out how much she would've saved you subtract the sale price & tax from the original price & tax $51.36 - $38.52 = $12.84

There are 12 players of right handed, according to the question.

What do you mean by percentage?

A percentage in mathematics is a number or ratio that is expressed as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, though the percent sign, "%," is most frequently used. A percentage has no dimensions and no standard measurement.

According to data in the given question,

We have given data:

A local little league has a total of 60 players of whom 20% are right-handed.

Let x be the total number of players that are right-handed.

The value of x can be found as follow:

x = 20% of 60

x = (20/100)60

x = 0.2(60)

x = 12

Therefore, the total number of players that are right-handed is 12, if the local little league has a total of 60 players of whom 20% are right-handed.

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The graph of ƒ has a point of inflection  is (D) -3.259, 0, and 1.603

To determine if a function has a point of inflection, we need to find the values of x where the second derivative changes sign from positive to negative or vice versa. The sign of the second derivative at a point determines the concavity of the function at that point. If the second derivative is positive, the function is concave up, and if it is negative, the function is concave down.

Since ƒ"(a)=x² cos(2a+22), we can see that the second derivative is positive for x²>0. So the function is concave up when x²>0, which means when x is in the interval (-∞,0)∪(0,∞).

Since the interval (-4,3) includes both negative and positive values of x, the graph of ƒ may have a point of inflection within this interval. To determine the exact points of inflection, we need to find the values of x where the second derivative equals zero or is undefined.

Therefore, the answer is (D) -3.259, 0, and 1.603.

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we know that the cos(θ) is -(3/5), however θ is in the II Quadrant, where the cosine is negative whilst the sine is positive, meaning the fraction is really (-3)/5, so

\(cos(\theta )=\cfrac{\stackrel{adjacent}{-3}}{\underset{hypotenuse}{5}}\qquad \qquad \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\)

\(\pm\sqrt{5^2-(-3)^2}=b\implies \pm\sqrt{25-9}=b\implies \pm 4=b\implies \stackrel{II~Quadrant}{+4=b} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}~\hfill\)

The actual price is 13.6% lower than the expected price.

CPI or Consumer Price Index is a measure of determining retail inflation in an economy, based on price variations in a fixed basket of goods and services, over overtime periods.

Let's suppose the expected price is x.

The percent relation of the actual price of a winter hat to the expected price is given by;

CPI = ( expected price ) : ( price in 1983 ) × 100

219  =  ( x  : 12.95 ) × 100

Divide both sides by 100.

x : 12.95 = 2.19

x =2.19 × 12.95

x = $28.36 ( expected price )

p = ( 24.50 × 100 ) / 28.36

p= 2450/28.36

p = 86.4 %

100 % - 86.4 % = 13.6 %

Hence, the actual price is 13.6% lower than the expected price.

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Answer:The answer is the first one, angle JLK

Step-by-step explanation:

The permutation combination is 120 for 3 different topping pizzas are available.

Permutation Combination:

A variety of ways to select objects from a set, usually forming a subset without replacement. The selection of this subset is called a permutation if the order of selection is a factor, and a combination if the order is not a factor. The French mathematicians Blaise Pascal and Pierre de Fermat, in the 17th century, used many chances in his game of combinatorics and probability by considering the ratio of the number of required subsets to the number of all possible subsets stimulated the development of the theory.

The concepts of permutations and combinations and their differences can be illustrated by examining all the different ways of selecting pairs of objects from five identifiable objects such as the letters A, B, C, D and E.

According to the Question:

Given that :

Number of different toppings = 10

Number of Pizzas = 03

therefore,

The permutation  combination are :

                = 10!/7! 3!

                = 15 × 8

                = 120.

Therefore, there are 120 different combinations of toppings.

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The equation that represents the data given (line r and s) is  y = (-19/5)x + 76/5.; y = 5y-8 respectively.

To get the equations of the lines represented by the given tables, we can use the point-slope form of the equation of a line...

y - y₁  = m ( x - x₁)

where

( x₁, y ₁) is a point on the line, and

m is the slope of the line.

For line r, we can use points (4 ,  8) and (9, -11) to find the slope ...

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

=

(-11 - 8) / (9 - 4) = - 19/5

Let's use the point (4, 8) to write the equation of line r  

y - 8 = (-19/ 5) ( x - 4)

Simplifying, ti becomes

y = (-19/5) x + 76/5

For line s, we can use the points (-2, - 18) and ( 1, -3) to find the slope  ..

m = (y₂ - y₁) / (x₂ - x₁) = (-3 - (-18)) / (1 - (-2) ) = 5

Let's use the point (-2, -18) to write the equation of line s

y - (-18) = 5(x - (-2))

Simplifying we have

y = 5x - 8

Therefore, the equation of line s is y = 5x - 8.

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The probability that a 3 will get any given times the dies is rolled is 0.17x

Total number of outcomes in one roll = 6

The favorable outcome = 3

The probability = Number of favorable outcomes / Total number of outcomes

Substitute the values in the equation

The probability of getting 3 in first roll= 1 / 6

Total number of times the die rolled = 11 times

The probability of getting 3 in all given times = (The probability of getting 3 in first roll )^ (Number of times the die rolled)

Consider the number of rolls as x

Substitute the values in the equation

The probability of getting 3 in all the given times = (1/6)^x

= 0.17x

Hence, the probability that a 3 will get any given times the dies is rolled is 0.17x

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Scatter plot Answ

Step-by-step explanation:

Answer:

Answer:

(a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ftsin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned.

Answer:

(a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ftsin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned

Answer: Y=30x+120

Step-by-step explanation

The x stands for each week, the m stands for the money being added or subtracted. That is why the m and x are being multiplied together in the equation. The b stands for how much the person, Mike, already has. Hope this helps

Answer:

\(a) 8y = 32.\\b)14-2y = 6.\)

\(the \: right \: expression \: for \\ 3 \: is \: less \: than \: y \: is \: less \: than \: 7 \: is \\ 3 < y < 7. \\ then \\ y \: can \: be \: any \: value \: form \: (4 \: to \: 6). \\ so \: if \: y = 4. \\ then \\ 8y = 8 \times 4= 32. \\ and \\ 14 - 2y = 14 - 2 \times 4 = 6.\)

The maximum and minimum value of the expressions are -

1 - 8y              Max [1] = 48              Min [1] = 32

2 - 14 - 2y           Max [2] = 6                  Min [2] = 2

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Given is that 3 is less than y is less then 7.

We can write the inequality -

3 < y < 7

Expression 1 : 8y

Maximum value of the expression = Max [1] = 48

Minimum value of the expression = Min [1] = 32

Expression 1 : 14 - 2y

Maximum value of the expression = Max [2] = 14 - 2 x 4 = 14 - 8 = 6

Minimum value of the expression = Min [2] = 14 - 2 x 6 = 14 - 12 = 2

Therefore, the maximum and minimum value of the expressions are -

1 - 8y              Max [1] = 48              Min [1] = 32

2 - 14 - 2y           Max [2] = 6                  Min [2] = 2

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There is no restrictions for x for f(x) =3✓x because you can take the cube root of any real numbers. Therefore, the domain is infinity she. dealing with the set of real numbers.

You can't take the square root of negative numbers. So, x values are restricted for f(x) = ✓x for real numbers and the domain is (0, infinity).

It should be noted that since x cannot take negative values in the question, the square root he undefined. Hence it is an imaginary value.

Also, You can't take the square root of negative numbers. So, x values are restricted for f(x) = ✓x for real numbers and the domain is (0, infinity).

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The output y[n] is given by y[n] = (4/2) x[n] + (5/2) x[n-1] y[n]. By substituting the given values, we get output sequence of {1, 3, -19, 231, ...}.

We can use the difference equation relating the input x and the output y to solve for y[n]. Substituting n with (n-1) in the given equation, we get:

y[n-1] = (4/2) x[n] + (5/2) x[n-1] y[n]

Substituting n-1 with n and solving for y[n], we get:

y[n] = (4/2) x[n-1] + (5/2) x[n-2] y[n-1]

Substituting the given values of x and y and simplifying, we get:

y[n] = 16 - 10y[n-1] + 5y[n-2]

Using the initial conditions y[0] = 1 and y[1] = 3, we can recursively compute the output y[n] for any value of n. For example,

y[2] = 16 - 10(3) + 5(1) = -19

y[3] = 16 - 10(-19) + 5(3) = 231

Thus, the output sequence is {1, 3, -19, 231, ...}.

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Answer:

127  Alternate Interior

Step-by-step explanation:

Due to the angles being inside the parallel lines it would be alternate interior, if it were outside the lines it would be exterior. And because of the alternate interior property its 127

Answer:

X= 4

Step-by-step explanation:

28 = 4(x+3)

7 = x+3

x = 4

x=4

All sides of a square are the same

28/4 is 7

x+3=7

x=4

Answer: 1.45litres

Step-by-step explanation:

250ml = 0.25litres

1.2+0.25= 1.45

ans is 1.45litres