Express the area of the entire rectangle.

Answer:

c > 9

Step-by-step explanation:

[tex]\frac{2c}{3} +1 > 7[/tex]

To solve this, first subtract 1 from both sides

[tex]\frac{2c}{3} +1 > 7\\\frac{2c}{3} > 6[/tex]

multiply both sides by 3

2c > 18

divide both sides by 2

c > 9

Hope this helps! :)

Answer:

c > 9

Step-by-step explanation:

Step-by-step explanation:

any polynomial is factored by terms of its zeros (the terms of the x- values creating a 0-y-value as result).

y = (x - a)(x - b)(x - c)...

means that for x = a or b or c or ..., y = 0

and (x - a), (x - b), (x - c), ... are all the factors of the y-expression

so,

2x + 1 = 0

2x = -1

x = -1/2

so, for x = -1/2 our term (2x + 1) = 0.

if now the whole expression is 0 for x = -1/2, then (2x + 1) is a factor :

6×(-1/2)³ + 13×(-1/2)² + 17×(-1/2) + 6 =

= -6×1/8 + 13×1/4 - 17×/1/2 + 6 =

= -6/8 + 13/4 - 17/2 + 6 = -3/4 + 13/4 - 17/2 + 6 =

= 10/4 - 17/2 + 6 = 5/2 - 17/2 + 6 = -12/2 + 6 =

= -6 + 6 = 0

that is why (2x + 1) is indeed a factor of

6x³ + 13x² + 17x + 6

Answer:

[tex] \sqrt{ \frac{243}{867} } = \sqrt{ \frac{81}{289} } = \frac{9}{17} [/tex]

Thus, the value of c f · dr. f(x, y) = xi yj c: r(t) = (5t 2)i tj, 0 ≤ t ≤ 1 is found as 2c using the  vector function.

To evaluate c f · dr, we first need to find the vector function of f evaluated along the path r.

Using the given function f(x, y) = xi yj and the path r(t) = (5t^2)i + tj, we can substitute for x and y to get:

f(r(t)) = (5t^2)i * (t)j = 5t^3i + 5tj

Next, we need to find the differential of the path dr, which is:
dr = (10t)i + j dt

Now we can evaluate the dot product of c f and dr:
c f · dr = ∫c f · dr = ∫(c)(5t^3i + 5tj) · (10t)i + j dt, where c is a constant
= ∫(50c t^4) dt + ∫(5c t) dt
= 10c/5 t^5 + 5c/2 t^2 + C

Evaluating this from 0 to 1, we get:
c f · dr = 10c/5(1)^5 + 5c/2(1)^2 - 10c/5(0)^5 - 5c/2(0)^2
= 2c + 0
= 2c

Therefore, the value of c f · dr is 2c.

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the aardvark runs $10\sqrt{3} + 30$ meters.Since the circles have the same center, we can connect points $B$ and $C$ to the center of the circles to form radii of length $10$ and $20$ meters.
We can also draw a line segment connecting points $A$ and $K$ to form a straight line that intersects the two radii at points $D$ and $E$, respectively.

Using the Pythagorean theorem, we can find the length of $DE$ as follows:

$DE = \sqrt{AE^2 - AD^2}$

where $AE = 20$ meters and $AD = 10$ meters. Thus,

$DE = \sqrt{20^2 - 10^2} = 10\sqrt{3}$ meters.

We know that the aardvark runs along the path from $A$ to $D$, along the radius of the smaller circle, then along the path from $D$ to $E$, along the segment connecting the two radii, and finally along the path from $E$ to $K$, along the radius of the larger circle. Therefore, the total distance the aardvark runs is:

$AD + DE + EK = 10 + 10\sqrt{3} + 20 = 10\sqrt{3} + 30$ meters.

Thus, the aardvark runs $10\sqrt{3} + 30$ meters.
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The graph of the function f(x) = |-x - 10| + 5 in the context of the situation is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The function f(x) = |-x - 10| + 5

Where

Using the above as a guide, we have the following:

We plot the minutes on the x-axis and the distance on the y-axis

The graph of the function is added as an attachment

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Complete question

Kalani met her friend at a park for a morning run. The function f(x) = |-x - 10| + 5 models their run distance from Kalani's apartment, in miles, x minutes after they started running. Graph the function in the context of the situation.

Answer:

(-11.667, -9.333)

Step-by-step explanation:

were you looking for the intersection? that's what i just found. have a great day and thx for your inquiry.

The area of the sidewalk around the circular flower bed can be found by subtracting the area of the flower bed from the area of the larger circle formed by the outer edge of the sidewalk.

To calculate the area of the sidewalk, we first need to find the radius of the flower bed. We know that the diameter of the flower bed is 22m, so the radius is half of that or 11m.

Next, we need to find the radius of the larger circle formed by the outer edge of the sidewalk. This can be done by adding the width of the sidewalk on both sides of the flower bed, which is 3m x 2 = 6m, to the diameter of the flower bed.

Therefore, the diameter of the larger circle is 22m + 6m = 28m, and the radius is half of that or 14m.

Using the formula for the area of a circle (A = πr²), the area of the flower bed is 3.14 x 11² = 380.26m², and the area of the larger circle is 3.14 x 14² = 615.44m².

Finally, we can find the area of the sidewalk by subtracting the area of the flower bed from the area of the larger circle:

Area of sidewalk = 615.44m² - 380.26m² = 235.18m².

Therefore, the area of the sidewalk around the circular flower bed is 235.18 square meters.

In summary, to find the area of the sidewalk around a circular flower bed with a diameter of 22m and a width of 3m, we first need to calculate the radius of the flower bed and the larger circle formed by the outer edge of the sidewalk. Then, we can use the formula for the area of a circle to find the areas of both circles and subtract the area of the flower bed from the area of the larger circle to get the area of the sidewalk.

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Dan will need 360g of plain flour, 3 eggs, and 900ml of milk to make 12 pancakes.

To make 12 pancakes, Dan will need 360g of plain flour, 3 eggs, and 900ml of milk.

We can use proportions to figure out how much of each ingredient Dan will need. If 240g of plain flour, 2 eggs, and 600ml of milk are enough to make 8 pancakes, then we can set up the following ratios:

Plain flour: 240g/8 pancakes = x/12 pancakes

Eggs: 2/8 pancakes = y/12 pancakes

Milk: 600ml/8 pancakes = z/12 pancakes

Solving for x, y, and z in each of these ratios, we get x = 360g of plain flour, y = 3 eggs, and z = 900ml of milk. Therefore, Dan will need 360g of plain flour, 3 eggs, and 900ml of milk to make 12 pancakes.

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The two unit vectors orthogonal to the given vector v = (15, 8) are (-0.882, 0.471) and (0.471, -0.882).

Let v = (v1, v2) be a vector in R2. To show that (v2, -v1) is orthogonal to v, we need to prove that their dot product is equal to zero.

The dot product of v and (v2, -v1) is:

(v1, v2) • (v2, -v1) = v1*v2 + v2*(-v1) = v1*v2 - v1*v2 = 0

Since their dot product is zero, (v2, -v1) is orthogonal to v.

Now, let's use this fact to find two unit vectors orthogonal to the given vector v = (15, 8). The orthogonal vector to v is (8, -15). We need to find its magnitude and then divide each component by the magnitude to get the unit vectors.

Magnitude of (8, -15) = √(8^2 + (-15)^2) = √(64 + 225) = √289 = 17

Now, divide each component of (8, -15) by its magnitude:

Unit vector 1 (smaller first component) = (-15/17, 8/17) ≈ (-0.882, 0.471)
Unit vector 2 (larger first component) = (8/17, -15/17) ≈ (0.471, -0.882)

So the two unit vectors orthogonal to the given vector v = (15, 8) are approximately (-0.882, 0.471) and (0.471, -0.882).

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The notation p(z < a) represents the probability that a standard normal random variable is less than a. This can be found using a standard normal distribution table or a calculator that provides a normal distribution function.

The probability that a standard normal random variable is less than a can also be expressed as P(Z < a), where Z is a standard normal random variable.

The probability that a standard normal random variable is greater than a can be found using the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring. Therefore, P(Z > a) = 1 - P(Z < a).

The probability that a standard normal random variable is equal to a is zero, as the standard normal distribution is continuous and has an infinite number of possible values.

The probability that a standard normal random variable is not equal to a can be found using the complement rule again. P(Z ≠ a) = 1 - P(Z = a), where P(Z = a) = 0 (as mentioned above). Therefore, P(Z ≠ a) = 1.

Let's break down each part of your question and provide an explanation for each term:

a. The notation p(z < a) refers to the probability that a standard normal random variable (Z) is less than a certain value (a). In a standard normal distribution (with a mean of 0 and standard deviation of 1), this represents the area under the curve to the left of the value 'a'. To find this probability, you can refer to a standard normal table or use a calculator with a normal distribution function.

b. The probability that a standard normal random variable is greater than a (p(z > a)) can be calculated by subtracting the probability that the variable is less than a from 1 (since the total probability is always 1): p(z > a) = 1 - p(z < a).

c. In a continuous probability distribution like the standard normal distribution, the probability that a standard normal random variable is equal to a specific value (p(z = a)) is always 0. This is because there are an infinite number of possible values, and the probability associated with each individual value is negligible.

d. The probability that a standard normal random variable is not equal to a (p(z ≠ a)) is essentially the complement of the probability that it is equal to a. Since p(z = a) is 0 in a continuous distribution, the probability that the variable is not equal to a is 1: p(z ≠ a) = 1.

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Krystal should choose Plan 1 as it will save her $180 over the course of a year.

Plan 1 costs $134.97 every 3 months, which means it costs Krystal $134.97/3 = $44.99 per month.

If Krystal plans to stay with one service plan for 1 year (12 months), then she would pay 12 * $44.99 = $539.88 for Plan 1.

To compare this to Plan 2, we need to know the cost of Plan 2. Let's say Plan 2 costs $59.99 per month. Then for one year, Krystal would pay 12 * $59.99 = $719.88 for Plan 2.

Comparing the two plans, Krystal should choose Plan 1 as it will save her $719.88 - $539.88 = $180 over the course of a year.

Note that the exact amount Krystal would save depends on the cost of Plan 2, which was not given in the problem. But the method for comparing the two plans is the same regardless of the actual cost of Plan 2.

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Answer:

True

Right angles measure 90° . So each vertical angle = 90° and hence they are equal

Step-by-step explanation:

The probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

The symbol "∩" represents the intersection of two events.

For example, "a ∩ d" means the event where both "a" and "d" occur together.

The symbol "~" means "not" or "complement." So, "~ (a ∩ d)" means the event where "a ∩ d" does NOT occur, or in other words, where "a" OR "d" does not occur.

Now, onto the question.

We are given that p(a ∩ d) = 2/5, which means that the probability of both events "a" and "d" occurring together is 2/5.

We want to find the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur.

To find this probability, we need to use some basic probability rules.

One of these rules is that the probability of an event happening (let's call it "E") is equal to 1 minus the probability of the complement of that event not happening (~E).

In other words, p(E) = 1 - p(~E).

So, if we apply this rule to the event "~ (a ∩ d)", we get:
p(~ (a ∩ d)) = 1 - p(a ∩ d)

Now we can substitute in the value we were given for p(a ∩ d):
p(~ (a ∩ d)) = 1 - 2/5

Simplifying this gives:
p(~ (a ∩ d)) = 3/5

Therefore, the probability of the event "~ (a ∩ d)", or the probability that either "a" OR "d" does not occur, is 3/5.

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The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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The solutions are explained below.

the value of x is : x = 58.63 m

Here, we have,

Given that,

Jeremy and Leslie are each flying their own drones in a flat field with their drones hovering between the two of them.

Height of Jeremy's drone = 30 m

Height of Leslie's drone = x m

h / 70 = sin 53°

h = 70 × sin 53°

h = 57.34

Therefore, Leslie's drone is higher than Jeremy's drone.

Difference of height = 57.34 - 30 = 27.34 m

27.34 / x = tan25°

x = 58.63 m

Hence, the value of x is : x = 58.63 m

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The correlation coefficient between daily ice cream sales and maximum daily temperature is a measure of the strength and direction of the linear relationship between these two variables.

To calculate the correlation coefficient, we need a sample of paired data that includes daily ice cream sales and the corresponding maximum daily temperature.

We can use a statistical software or a calculator to calculate the correlation coefficient. In this case, the correlation coefficient between maximum daily temperature and daily ice cream sales is 0.934, which indicates a strong positive linear relationship between these two variables.

This means that as the maximum daily temperature increases, the daily ice cream sales also tend to increase. Conversely, as the maximum daily temperature decreases, the daily ice cream sales tend to decrease as well.

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The possible values for a, b, and c are a = 0, b = -10, and c = 3.

We have the following information:

||v|| = √(a^2 + b^2 + c^2) = √109

⟨v, u2⟩ = a⟨u1, u2⟩ + b⟨u2, u2⟩ + c⟨u3, u2⟩ = -10

⟨v, u3⟩ = a⟨u1, u3⟩ + b⟨u2, u3⟩ + c⟨u3, u3⟩ = 3

Since {u1, u2, u3} is an orthonormal basis, we have ⟨ui, uj⟩ = 0 if i ≠ j, and ⟨ui, ui⟩ = 1 for all i.

Using these properties, we can substitute the values into the equations:

-10 = b⟨u2, u2⟩

-10 = b(1)

b = -10

3 = c⟨u3, u3⟩

3 = c(1)

c = 3

Substituting the values of b and c into the norm equation, we get:

√(a^2 + (-10)^2 + 3^2) = √109

a^2 + 109 = 109

a^2 = 0

a = 0

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Answer:

If 38% of students said they liked the sports offered at the school, 62% of students said they did not like the sports offered at the school.

.62s = 217, so s = 350 students

After considering all the given data we reach the conclusion that the initial cost is evaluated as $250, depending on the rate of change is $150 per hour, a perfect expression to support the demand is y = 150x + 250 here y is the total cost and x is the number of hours and for the duration of 9 hours for the completion of the will the individual has to pay $1450.

Proceeding to the sub questions
a. The initial cost is $250.
b. The rate of change is $150 per hour.
c. The equation is y = 150x + 250 where y is the total cost and x is the number of hours.
d. The explanation for the evaluation of the payment that needs to be made for the completion of the will in the duration of 9 hours
Here,
The initial cost is $250.
The rate of change is $150 per hour.
To find out how much the individual has to pay if it takes 9 hours to complete the will, the individual has to apply  the equation
y = 150x + 250
Here,
x =  the number of hours.
Placing in x = 9 into the equation
y = 150(9) + 250
= 1350 + 250
= $1450.
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Y is proportional to square of (X-7), when Y = 2 , X = 12 .

to make an equation we need to remove proportionality and so we multiply Y with an variable.

Let that variable be 'p'.

So according to the question,

Yp = (X-7)² (from this we will find p)

putting all the known values

2p= (12-7)²

2p = 5 * 5

p = 25/2

Now, using the same equation we will find Y , when X= 17.

Y * 25/2 = ( 17- 7)²

Y * 25/2 = 10 * 10

Y = 100 * 2 / 25

Y = 8

Step-by-step explanation:

y=(x-7)^2k....... equation 1

2=(12-7)^2xk

where k is constant

2=(5)^2k

2=(5x5)k

2=25k

*Divide both sides by coefficient of k*

2/25=25/25k

k=2/25

y=(17-7)^2 x2/25..... equation 2

y=(10)^2x2/25

y=(10x10) x2/25

y=100x2/25

y=200/25

y=8

Assuming that cancellations are independent events, we can use the binomial distribution to find the probability that exactly 3 of the scheduled flights take place.

Let X be the number of flights that take place out of 3 scheduled flights. Then, X follows a binomial distribution with n=3 and p=0.81. The probability mass function of X is given by:

P(X=k) = (3 choose k) * (0.81)^k * (0.19)^(3-k)

where (3 choose k) is the binomial coefficient "3 choose k".

To find the probability that all 3 flights take place, we need to compute P(X=3):

P(X=3) = (3 choose 3) * (0.81)^3 * (0.19)^(0) = (1)(0.81)^3(1) = 0.531441

Therefore, the probability that all 3 scheduled flights will take place is approximately 0.531.

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Answer:

B

Step-by-step explanation:

it should be B

Let's denote the time it takes for the slower pipe to fill the tank on its own as $x$ hours. Then, the faster pipe takes $x-3$ hours to fill the tank on its own. We can use the formula for the rate of work to set up an equation: $r_1 + r_2 = \frac{1}{2}$, where $r_1$ and $r_2$ are the rates of work for each pipe.

We can express the rate of work in terms of the time it takes for each pipe to fill the tank on its own: $r_1 = \frac{1}{x}$ and $r_2 = \frac{1}{x-3}$. Substituting these expressions into the equation above and solving for $x$, we obtain $x=2$. Therefore, the slower pipe takes 2 hours to fill the tank on its own, and the faster pipe takes $2-3=-1$ hour, which doesn't make physical sense. This means there is an error in the problem statement.

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Benchmark fractions are used to compare the relative sizes of fractions.

These fractions are typically halves, thirds, fourths, fifths, sixths, eighths, tenths, or twelfths, which are easy to compare because they are common fractions with simple denominators. To use a benchmark fraction to determine who tiled a greater portion of a floor, you first need to convert the fractions to have a common denominator that is equal to the benchmark fraction. For example, if you are comparing 1/3 and 2/5, you can use 6 as the common denominator because both 3 and 5 divide into 6 evenly. You would then convert 1/3 to 2/6 and 2/5 to 2.4. You can then compare the fractions using the benchmark fraction that is closest to the resulting fractions. In this case, you could use 1/2 as the benchmark fraction because it is between 2/6 and 2/4. You can see that 2/4 is closer to 1/2, which means that 2/5 is the greater fraction. Therefore, the person who tiled 2/5 of the floor tiled the greater portion of the floor.

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To stretch a spring from its natural length to 0.6 feet beyond its natural length, a work of 0.36 foot-pounds is required.

The work done in stretching a spring is equal to the area under the force-extension graph. Since the force required to hold the spring stretched 0.2 feet beyond its natural length is 1 pound, we can assume that the force required to stretch the spring from its natural length to 0.6 feet beyond its natural length is directly proportional to the extension. Therefore, the force required to stretch the spring 0.4 feet beyond its natural length is 2 pounds.

To calculate the work done in stretching the spring from 0.2 feet beyond its natural length to 0.6 feet beyond its natural length, we can use the formula for work:

Work = Force x Distance

Since the force required to stretch the spring 0.4 feet beyond its natural length is 2 pounds, and the distance over which the force is applied is 0.4 feet, the work done is:

Work = 2 x 0.4 = 0.8 foot-pounds

Therefore, the work done in stretching the spring from its natural length to 0.6 feet beyond its natural length is:

0.8 - 0.2 = 0.6 foot-pounds.

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The method to convert a vector from component form to linear form to trigonometric form is shown below.

Given that;

To convert a vector from component form to linear form to trigonometric form.

Let a linear form of expression is,

⇒ x + iy

Now, We can change it into trigonometric form as;

Plug x = r cos θ, y = r sin θ

And, θ = tan ⁻¹ (y/x)

Hence, We get;

⇒ x + iy

⇒ r cos θ + i r sin θ

⇒ r (cos θ + i sin θ)

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Fr the solution of Linear equations, the dollars earned by barney and betty are equal to $1.471428571 and $2.428571428 respectively.

We have barney and betty break into a parking meter. Amount of money from dimes and quarters = $3.90

Let the number of dimes and quarters collected by Barney and betty be x and y respectively. According to seniror,

x = y + 5 --(1)

Also, from unit conversion, 1 quarters

= 0.25 dollar and 1 dimes are worth the same as 0.1 dollar. So,

(number of dimes × value of 1 dimes in dollars ) + (number of quaters × value of 1 quaters in dollars )

=> 0.1 x + 0.25 y = $3.90

Multiple both sides by 100, we result

10x + 25 y = 390 --(2)

Now, we have two linear equations and we have to solve these for determining the values of x and y

Using Substitution method, Substitute value of x from equation(1) to equation(2),

=> 10( y + 5) + 25y = 390

=> 10y + 50 + 25y = 390

=> 35y = 340

=>[tex] y = \frac{ 340}{35}[/tex]

= 9.71428571429

from equation (1), x = 9.71428571429 + 5

= 14.7142857143.

So, money get by barney= 9.71428571429 × 0.25 = $2.428571428

and for betty = 14.71 × 0.1 = $1.471428571

Hence, required values are 2.428571428 dollars and 1.471428571 dollars.

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Complete question:

Barney and Betty break into a parking meter with $3.90 in dimes and quarters in it (legal disclaimer: don't do this), and agree that Barney will get all the dimes, and Betty will get all the quarters. (Barney isn't terribly bright.) barney ends up with five more coins than betty. how much money did each get?. oo