80% of a number is x. What is 100% of the number? Assume x > 0.

Answer:

1. B) R = (p-q)/F

2. B) No, p does not represent the pressure in the outlet; it is the pressure in the inlet.

Step-by-step explanation:

Formula for the blood flow rate

\(F=\dfrac{p-q}{R}\)

where:

To solve the formula for vascular resistance, rearrange the given equation to make R the subject.

Multiply both sides of the equation by R:

\(\implies F\cdot R=\dfrac{p-q}{R} \cdot R\)

\(\implies FR=p-q\)

Divide both sides by F:

\(\implies \dfrac{FR}{F}=\dfrac{p-q}{F}\)

\(\implies R=\dfrac{p-q}{F}\)

Therefore, the formula for vascular resistance is:

\(R=\dfrac{p-q}{F}\)

To solve the formula for the pressure in the outlet, rearrange the given equation to make q the subject.

Multiply both sides of the equation by R:

\(\implies F\cdot R=\dfrac{p-q}{R} \cdot R\)

\(\implies FR=p-q\)

Add q to both sides of the equation:

\(\implies FR+q=p-q+q\)

\(\implies FR+q=p\)

Subtract FR from both sides of the equation:

\(\implies FR+q-FR=p-FR\)

\(\implies q=p-FR\)

Therefore, Dyana is incorrect as p does not represent the pressure in the outlet; it is the pressure in the inlet.

Answer:

(1 +a + b)(1 - a -b)

Step-by-step explanation:

1 - 2ab - (a² +b²) = 1 - 2ab - a² - b²

                           = 1 - (2ab + a² + b²)

                           = 1 - (a + b)²

                           = 1² - (a +b)²    

Identity: x² - y² = (x + y)(x - y)

                          = (1 + (a+b))(1- [a +b] )

                          = (1 +a + b)(1 - a -b)

Hyperkalemia is what is more likely to occur due to the results of the conditions.

This is used to refer to the condition where there is too much of potassium in the blood of a person.

The side effects is that the person would feel tiredness, weakness and he would feel abnormal heart beat.

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The minimum number of strands Kris needs to completely wrap the porch railing is 7.

One side of the square porch = 12 feet length

Length of the railing wrapped by one strand = 70 inches

To determine the minimum number of strands Kris needs to completely wrap the porch railing, we can follow these steps:

Calculate the perimeter of the square porch, which is the sum of the four sides:

Perimeter = 4 x 12 feet = 48 feet = 576 inches

Determine the length of the railing that needs to be wrapped around the square porch:

Length of railing = 3 x 12 feet = 36 feet = 432 inches

Divide the length of the railing by the length that can be wrapped by one strand:

Number of strands = Length of railing / Length wrapped by one strand

= 432 inches / 70 inches

= 6 with a remainder of 12 inches

Since Kris needs to have a whole number of strands, he will need to round up to the nearest whole number. Therefore, Kris needs at least 7 strands to completely wrap the porch railing.

Hence, the minimum number of strands Kris needs to completely wrap the porch railing is 7.

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Answer:

0.15

Step-by-step explanation:

Using trigonometry :

Tanθ = opposite / Adjacent

Opposite = distance between earth and sun = 238,900

Adjacent = distance between earth and moon = 93,000,000

Tanx = 238900 / 93000000

Tanx = 0.0025688

x = tan^-1 (0.0025688)

= 0.1471820°

Answer:

0.15

Step-by-step explanation:

Took the test.

a0 is the regression term that describes the constant or intercept in the linear regression equation.

In a simple linear regression model, the equation takes the form of y = a0 + a1x + e1, where y is the dependent variable (or response variable), x is the independent variable (or predictor variable), a0 is the intercept or constant term, a1 is the coefficient of the independent variable, and e1 is the error term.

The intercept term, a0, represents the value of the dependent variable when the independent variable is zero. For example, in a linear regression model that predicts salary based on years of experience, the intercept would represent the starting salary for someone with zero years of experience. The intercept is an important component of the regression equation because it allows us to make predictions for values of x that are outside the range of our observed data.

The coefficient, a1, represents the change in the dependent variable for each one-unit increase in the independent variable. In the salary example, the coefficient would represent the average increase in salary for each additional year of experience.

Both the intercept and coefficient are estimated from the data using methods such as least squares regression. Once these values are estimated, we can use them to make predictions for new values of x.

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Answer:

See the screenshot! :)

Step-by-step explanation:

we have a exponential function of the form

y=a(\(b^x\))

where

y ---> is the population of bacteria

x ---> the number of hours

a is the initial value or y-intercept

b is the base of the exponential function

r is the rate of change

b=(1+r)

we have

a=700 bacteria

r=5%=5/100=0.05

so

b=1+0.05=1.05

substitute

y=700(\(1.05^x\))

For x=20 hours

substitute in the equation and solve for y

y=700(1.05)^20= 1,857 bacteria

Hope this helped! :)

The probability mass function of X( -3, -1, 1 ,3)  is P(X) 1/8 3/8 3/8 1/8.

A fair coin is flipped 3 times and the random variable X is defined as follows:

   X = 3 times the number of heads - 2 times the number of tails

To find the probability mass function of X, we can list all the possible outcomes and calculate their probabilities.

The Possible outcomes are as shown:

   3 heads (X = 3)

   2 heads, 1 tail (X = 1)

   1 head, 2 tails (X = -1)

   3 tails (X = -3)

And the Probabilities are:

   P(X = 3) = 1/8

   P(X = 1) = 3/8

   P(X = -1) = 3/8

   P(X = -3) = 1/8

Therefore, the probability mass function of X is:

X( -3, -1, 1 ,3)  is  P(X) 1/8 3/8 3/8 1/8

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Answer:

See Explanation

Step-by-step explanation:

Given

\(d_1 =6in\) --- the first diagonal

\(Area = (20in^2,25in^2)\)

The question is incomplete, as the image of the kite and what is required are not given

However, a possible question could be to calculate the length of the other diagonal

Calculating the length of the other diagonal, we have:

\(Area = 0.5 * d_1 * d_2\)

Make d2 the subject

\(d_2 = \frac{Area }{0.5 * d_1}\)

Multiply by 2/2

\(d_2 = \frac{2 * Area }{2* 0.5 * d_1}\)

\(d_2 = \frac{2 * Area }{1 * d_1}\)

\(d_2 = \frac{2 * Area }{d_1}\)

When Area = 20, we have:

\(d_2 = \frac{2 * 20}{6}\)

\(d_2 = \frac{40}{6}\)

\(d_2 = 6.67\)

When Area = 25, we have:

\(d_2 = \frac{2 * 25}{6}\)

\(d_2 = \frac{50}{6}\)

\(d_2 = 8.33\)

So:

\(d_2 = (6.67,8.33)\)

This means that the length of the other diagonal is between 6.67in and 8.33in

The least-squares regression line given (predicted offspring = 1.4146 + 0.4399 * cone index) represents the best linear fit to the data collected by the researchers, using the method of least squares.

The relationship between the availability of food and the number of offspring produced by an animal species was examined through a 16-year study on red squirrels. The focus was on red squirrels' consumption of seeds from pinecones, a food source that sometimes experiences significant abundance.

The collected data—reflecting the pinecone abundance index and the average number of offspring per female—was used to calculate a least-squares regression line. The resulting formula, "predicted offspring = 1.4146 + 0.4399 (cone index)," indicates a positive correlation between the availability of pinecones and the average number of offspring per female squirrel.

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In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. the 90% confidence interval for the levels of lead is between (0.4958, 0.7422).

p is 26/42=0.6190

rootp(1-p)/n=root0.6190(1-0.6190)/42=0.0749

satisfies that above this and under the standard normal density there is an area of 0.05. In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. the 90% confidence interval for the true population proportion of water specimens that contain detectable levels of lead is between (0.4958, 0.7422).

Density is the number of things—which could be people, animals, plants, or objects—in a certain area. To calculate density, you divide the number of objects by the measurement of the area. The population density of a country is the number of people in that country divided by the area in square kilometers or miles.

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Answer:

6^-9

Step-by-step explanation:

(6 ^10 × 6 ^− 4 ) (6 ^− 5 × 6 ^2 )  (6 ^10 × 6 ^− 4 ) (6 ^− 5 × 6 ^2 )as a single term of the form 6 ^n.

hope this helped <3

When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.

Therefore, when the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.

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Answer:

x = 4

x = 10

Step-by-step explanation:

x^2 -14x + 40 = 0 ----> factor form

(x - 10)(x - 4) = 0 ---> separate equations

x - 10 = 0 ---> add 10 on both sides

x = 10

x - 4 = 0 ---> add 4 on both sides

x = 4

Answer:

small x= 4

large x= 10

Step-by-step explanation:

hello there!

x^2-14x+40=0

x^2-(10+4)x+40=0

x^2-10x-4x+40=0

pick out the common one!

x(x-10)-4(x-10)=0

(x-10)(x-4)=0

now;

x-10=0

x=10(which is large x)

again:

x-4=0

x=4( which is small x)

hope it helps.. thank u!

To find the probability of getting 10 or more successes in a binomial experiment with p = 0.63 and n = 11 trials, we can use the cumulative probability function.

P(X ≥ 10) = 1 - P(X < 10)

Using a binomial probability formula, we can calculate the probability of getting exactly k successes:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where C(n, k) represents the binomial coefficient.

Let's calculate the probability for each value from 0 to 9 and subtract it from 1 to get the probability of 10 or more successes:

P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)

P(X < 10) = Σ[C(11, k) * p^k * (1 - p)^(11 - k)] for k = 0 to 9

Using this formula, we can calculate the probability:

P(X < 10) ≈ 0.121

Therefore, the probability of getting 10 or more successes in the binomial experiment is:

P(X ≥ 10) ≈ 1 - P(X < 10) ≈ 1 - 0.121 ≈ 0.879

Rounding to three decimal places, the probability is approximately 0.879.

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The length of the shadow is changing rate at 2.69 \(\frac{ft}{sec}\).

What do you mean by length?

The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, the length and width of a rectangle define its dimensions.

According to data in the given question,

We have the given information:

The height of the person is 7 ft.

The person is walking away from the post at a rate of 5ft/sec.

The height of the lamppost is 20ft.

Let the person's distance from the bottom of the light post be x ft.

And his shadow's length is y ft.

Form the similar triangles,

\(\frac{x+y}{20}=\frac{y}{7}\\\)

7(x+y) = 20y

7x+7y = 20y

20y-7y = 7x

13y = 7x

y = \(\frac{7}{13}x\)

Now, we will differentiating wrt t,

\(\frac{dy}{dt}=\frac{7}{13}\frac{dx}{dt}................(1)\)

We know that,

\(\frac{dx}{dt}=5\frac{ft}{sec}\)

Putting the value of  \(\frac{dx}{dt}\)  in equation (1),

\(\frac{dy}{dt}=\frac{7}{13}.5=\frac{35}{13}=2.69\frac{ft}{sec}\)

Therefore, the length of the shadow is changing rate at 2.69 \(\frac{ft}{sec}\).

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The solution to the equation is - 6  

The mathematical statements which are formed by numbers and variables are known as equations. To solve an equation we can add or subtract the same integer from both sides.

Similarly, we can multiply or divide by the same integer on both sides. Here adding or subtracting, multiplying, or dividing doesn't change the condition of the equation.

Here we have

15 (negative 42 x + 40) = 15 (negative 8 x + 244)  

This can rewrite as follows

=> 15 (-42x + 40) = 15 (-8x + 244)

Divide by 15 into both sides

=> 15 (-42x + 40)/15 = 15 (-8x + 244)/15  

=>  (- 42x + 40) = ( -8x + 244)  

Add 8x on both sides

=>  - 42x + 40 + 8x =  -8x + 244 + 8x

=>  - 34x + 40 = 244

Subtract 40 from both sides

=> - 34x + 40 - 40 = 244 - 40

=> - 34x = 204

Divide by - 34 on both sides

=> - 34x/-34 = 204/-34

=>  x = - 6

Hence,

The solution to the equation is - 6  

Substitute x = - 6 in 15 (-42x + 40) = 15 (-8x + 244)  

=>  (-42(-6) + 40) =  (-8(-6) + 244)  

=>  252 + 40 = 292  [ Which is true ]

Hence, It is verified that x = -6

Hence,

The solution to the equation is - 6  

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The Method of Undetermined Coefficients is a technique used to find a particular solution to a homogeneous linear differential equation.

yp(x) = 3e 8x + c1e 4x + c2e 11x

We are attempting to find a particular solution, yp(x), to the given equation using the Method of Undetermined Coefficients. This method is used when we have a homogeneous linear differential equation with constant coefficients. The first step is to identify the complementary function, which is found by solving the homogeneous part of the equation (in this case, y'' + 17y = 0). The particular solution is then found by making an educated guess for the form of the solution and adjusting the constants of the solution until the equation is satisfied. In this example, we guessed that the particular solution is a linear combination of three exponentials: 3e 8x + c1e 4x + c2e 11x. We then adjusted the constants c1 and c2 until the equation was satisfied.

y'' + 17y = 3e 8x

y'' + 17y - 3e 8x = 0

Homogeneous equation: y'' + 17y = 0

Characteristic equation: r2 + 17 = 0

r = ± 4i

Complementary function: yc(x) = c1e 4x + c2e -4x

Particular solution: yp(x) = 3e 8x + c1e 4x + c2e 11x

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Step-by-step explanation:

\( {x}^{2} - 2x + 7x - 14\)

\( {x}^{2} + 5x - 14\)

Answer:

x² + 5x - 14

Step-by-step explanation:

Given

(x + 7)(x - 2)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x - 2) + 7(x - 2) ← distribute both parenthesis

= x² - 2x + 7x - 14 ← collect like terms

= x² + 5x - 14

Answer:

Mean:45

Mode:20

Median:45

Answer:

 A. -114

Step-by-step explanation:

Got it right.

The diameter of the larger candle is approximately 15.5 inches.

We can assume that the volume of wax used in both candles is equal since they are made of the same material.

The volume of a cylinder (which is what a candle looks like) is given by:

V = \(\pi r^2h\)

where r is the radius of the candle and h is the height (or length) of the candle.

Let's assume that the height of both candles is the same, so we can ignore the h term.

For the small candle, the radius is half the diameter, which is 5/2 = 2.5 inches:

\(V_{small}\) = \(\pi (2.5)^2(6)\) = 47.1239 cubic inches

For the large candle, we don't know the radius but we know that the volume of wax is 4 times as much as the small candle:

\(V_{large }\)= \(4V_{small}\)= \(4(\pi (2.5)^2(6))\) = \(\pi r^2(24)\)

Simplifying this equation, we get:

\(r^2\) = \(\frac{(4(2.5)^2(6))}{\pi }\) = 60

Taking the square root of both sides, we get:

r ≈ 7.75 inches

So the diameter of the larger candle is:

2r ≈ 15.5 inches

Therefore, the diameter of the larger candle is approximately 15.5 inches.

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Answer:

I don't know

Step-by-step explanation:

Use the app and search it instead of waiting.

Given the following Quadratic equation:

You can use the Quadratic formula to solve it:

In this case, you need to add "3x" to both sides of the equation:

You can identify that:

Substituting values into the formula and evaluating, you get:

Answer

Complex roots:

Answer:

the last one

Step-by-step explanation:

because it's true

Answer:

b=6.92820323

Step-by-step explanation:

To find b, you would do the opposite from ^2 which is the square root. So the square root of 48. That is 6.92820323

Answer:

b ≈ 6.928 or 4√3

Step-by-step explanation:

b² = 48. To find b, we need to square root both sides (we are doing the opposite of squaring):

b = √48 = 4√3 or ≈ 6.928

Hope this helps!

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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The values of P. and E. for each of the following signal are

(a) P = ∞, E = ∞

(b) P = ∞, E = ∞

(c) P = 2π, E = finite

(d) P = 1, E = 1

(e) P = ∞, E = ∞

(f) P = 2π, E = finite

To determine the values of P (period) and E (energy) for each of the given signals, let's analyze them one by one:

(a) xi(t) = e^u(1)

For this signal, the exponential term e^u(1) represents a unit step function, which is 1 for t ≥ 1 and 0 for t < 1. Since the signal is exponential and has a step function, it does not have a period (P = ∞). The energy (E) of this signal is also infinite since it is not bounded.

(b) x2(t) = e^(2+7/4)

Similar to the previous signal, this is an exponential function, but without any time dependency. It does not oscillate and thus does not have a period (P = ∞). The energy (E) is also infinite since it is unbounded.

(c) X3(t) = cos(t)

This signal is a cosine function with a period of 2π, as the cosine function repeats every 2π. Therefore, the period (P) is 2π. The energy (E) is finite since the signal is bounded.

(d) xi[n] = δ[n]

This signal represents the discrete-time unit impulse function, also known as the Kronecker delta. The impulse function has a period of 1, as it repeats every integer. Therefore, the period (P) is 1. The energy (E) of the impulse function is 1, since its amplitude is 1 at a single point and 0 elsewhere.

(e) x2[n] = e^((π/2)n+1/8)

Similar to the first continuous-time exponential signal, this is a discrete-time exponential function. Since the exponent contains π/2 as a coefficient, the signal oscillates and does not have a finite period (P = ∞). The energy (E) is infinite since it is unbounded.

(f) x3[n] = cos(n)

This signal is a discrete-time cosine function. Similar to the continuous-time case, the cosine function has a period of 2π in discrete-time as well. Therefore, the period (P) is 2π. The energy (E) is finite since the signal is bounded.

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$5,800

ok bye I'm really not sure

Joseph's monthly housing budget, according to the rule of housing, is D. $7,250, which represents approximately 25% of his annual salary of $29,000.

The rule of housing suggests that an individual's monthly housing budget should be approximately 25% to 30% of their monthly income. To determine Joseph's monthly housing budget, we need to calculate 25% to 30% of his annual salary and convert it to a monthly amount.

25% of $29,000 = $7,250

30% of $29,000 = $8,700

Therefore, Joseph's monthly housing budget should fall within the range of $7,250 to $8,700.

Among the options given, the closest match to this range is option D. $7,250. This amount represents approximately 25% of Joseph's annual salary and aligns with the rule of housing.

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