A parabola has a vertex at (0,0). The focus of the parabola is located on the positive x-axis. Which part of the graph will the directrix pass through?

Answer:

The answer is B. 40 meters on plato

Answer:

The total amount of money he earned was $160

Step-by-step explanation:

Bill worked 24 hours last week

He earns $ 8.25 per hour.

We have to use front-end estimation, we have to round to the first number all the values. So. Bill worked h = 20 hours and he earns 3 =$8 per hour.

Total amount (T) wil be the hours (h) multiplied by the earning (e)

T = h*e

T = (20 hours)(8 $/hours)

T = 160 $

After using front-end estimation, we can conclude that Bil earned $160.

labored 24 hours remaining week

He earns $ 8.25 in step per hour.

We should use the front-stop estimation, we have to round to the first number of all of the values. So. invoice worked h = 20 hours and he earns 3 =$eight according to an hour.

the entire amount (T) can be the hours (h) extended through the earning (e)

T = (20 hours)(eight $/hours)

T = 160 $

After using front-end estimation, we will conclude that Bil earned $one hundred sixty.

front-cease estimation is a particular way of rounding numbers to estimate sums and variations. to apply the front-end estimation, add or subtract the handiest of the numbers in the finest location cost. Then upload the decimals rounded to the closest 10th.

what are front-end estimation examples?

In the front-cease estimation, we replace the original quantity with quite a number it is close by but the handiest has one non-zero digit. as an example, 20, three hundred, -50, 1,000, eighty,000. Take the quantity 32; the selections to update it with are 30 or forty (they both have the handiest one non-0 digit).

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To determine the length of the curve, we find the derivative of the given vector function, compute its magnitude, and then compute the integral of the magnitude from 0 to 1. This involves calculus techniques.

To find the length of the curve, we have to compute the integral of the magnitude of the derivative on the interval from 0 to 1. First, we find the derivative of r(t) = 3 i + t^2 j + t^3 k which is r'(t) = 2t j + 3t^2 k. The magnitude of r'(t) is |r'(t)| = sqrt((0)^2 + (2t)^2 + (3t^2)^2) = sqrt(4t^2 + 9t^4). Thus the length of the curve is the integral of this magnitude from 0 to 1: ∫ from 0 to 1 of sqrt(4t^2 + 9t^4) dt. This integral can be evaluated using techniques from calculus.

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Answer:

Triangle 1 is rotated to result in triangle 2.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

GOT IT RIGHT

To evaluate a triple integral over a region of a sphere, we switch to spherical coordinates. We then express the integrand and the limits of the variables in terms of these new coordinates. Don't forget the Jacobian when changing variables.

The subject is a mathematical problem that requires evaluating a triple integral over a specific part of a ball in three-dimensional space. The function to integrate is f(x,y,z)=z*(x2+y2+z2)-3/2 and the region of integration is defined as the part of the sphere with radius 7 (x2+y2+z2<=49) in which z >= 3.5. Unfortunately, the solution to such a problem requires advanced mathematical skills and knowledge, such as spherical coordinates and integration techniques, which cannot be elaborated within the word limit here.

However, to solve such problems, you typically switch to spherical coordinates, where x=r*cos(theta)*sin(phi), y=r*sin(theta)*sin(phi), z=r*cos(phi). Then, you express your function and the limits of your variables r, theta, and phi in terms of these new coordinates. You need to consider the Jacobian determinant when changing variables. Eventually, you integrate over the specified region. The solution needs careful elaboration of every step due to the complexity of the integral.

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The value of P( a or b)= 0.47.

The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier occurrence by the increased likelihood of the later, or conditional, event.

Conditional probability is the likelihood that any event A will occur in the presence of another event B that is related to A. P(A|B) illustrates it.

Given:

p(a) = 0.65, p(b) = 0.58, and p(a and b)= 0.76

Now, using the formula

P(a∪b) = P(a) + P(b) - P(a∩b)

           = 0.65 + 0.58 - 0.76

           = 0.47

Hence, the value of P( a or b)= 0.47.

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Answer:Archer's speed is 60 mph.

Sassoon's speed is 40 mph.

Step-by-step explanation:

Let the distance that Sassoon travels is d miles.

Let his average speed be x mph.

The time of travel is from 1 p.m. to 4 p.m., which is 3 hours.

Therefore

3x = d                            (1)

The distance that Archer travels is (d + 300) miles.

The time of travel is from 9 a.m. to 4 p.m., which is 7 hours.

The average traveling speed is (x + 20) mph, therefore

7(x + 20) = d + 300    

That is,

7x + 140 = d + 300

7x = d + 160                  (2)

Subtract (1) from (2).

7x - 3x = d + 160 - d

4x = 160

x = 40 mph  (Sassoon's average speed)

x+20 = 60 mph (Archer's average speed)

From (1), obtain d = 120 mi

Answer:

Archer's speed is 60 mph.

Sassoon's speed is 40 mph.

By using distributive property, the answers are :(a)468, (b) 20430, (c) 735.

Distributive property is the mathematical property to solve expressions in the form of a(b + c), in which firstly bracket term is solve and then other terms are solved.

(a)

The given term is,

18(26),

According to distributive property, bracket changes in multiply.

Therefore, 18(26)⇒18×26=468.

(b)

The given term is,

6(3405),

According to distributive property, bracket changes in multiply.

Therefore, 6(3405)⇒6×3405=20430.

(c)

The given term is,

21(35),

According to distributive property, bracket changes in multiply.

Therefore, 21(35)⇒21×35=735.

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The multiplication [tex]20880 \times \dfrac{2}{5}[/tex] is [tex]\boxed{8352}.[/tex]

Further explanation:

Always use the PEDMAS rule to solve the grouping of multiplication, addition, subtraction and division.

Here, P is parenthesis, E is exponents, M is multiplication, D is division, A is addition and S is subtraction.

Given:

The expression is [tex]20880 \times \dfrac{2}{5}.[/tex]

Explanation:

The given expression is [tex]20880 \times \dfrac{2}{5}.[/tex]

Consider the expression [tex]20880 \times \dfrac{2}{5}[/tex] as A.

[tex]A = 20880 \times \dfrac{2}{5}[/tex]

Solve the above expression to obtain the simplest form.

[tex]\begin{aligned}A&= 20880 \times \frac{2}{5}\\&= \frac{{41760}}{5}\\&= 8352\\\end{aligned}[/tex]

Another way of solving the expression can be expressed as follows,

First divide 2 by 5.

[tex]\begin{aligned}b&= \frac{2}{5}\\&= 0.4\\\end{aligned}[/tex]

Now multiply 20880 to 0.4.

[tex]\begin{aligned}A&= 20880 \times 0.4\\&= 8352\\\end{aligned}[/tex]

The multiplication [tex]20880[/tex] times [tex]\dfrac{2}{5} \:{\text{is}\: \boxed{8352}.[/tex]

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: factor, factorization, 20880, 2/5, times, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.

Answer:

The correct option 4.

Step-by-step explanation:

The given equation is

[tex]2.75x+3.25y=215[/tex]          .... (1)

Let x is the number of pretzels sold and y is the number of popcorn bags sold.

Total sales is defined as

[tex]Sales=C_1x+C_2y[/tex]         ... (2)

From (1) and (2) it is clear that,

The cost of each pretzel is $2.75 or 275 cents. The cost of each popcorn bag is $3.25 or 325 cents ($1 = 100 cents). Total sales is $215.

[tex]325-275=50[/tex]

Pretzels cost is 50 cents less than popcorn bags. The variable x represents the number of pretzels sold and y represents the number of popcorn bags sold. The total sales was $215.

Therefore the correct option 4.

To evaluate the line integral, we need to parameterize the line segment and calculate the differential arc length. After simplifying the integrand, we can evaluate the line integral by integrating the simplified expression.

To evaluate the line integral ∫cx^4zds, where c is the line segment from (0,6,5) to (8,4,1), we need to parameterize the line segment c. Let's parameterize it with t, where t varies from 0 to 1. The parameterization of c is given by:

x(t) = 8t, y(t) = 6 - 2t, z(t) = 5 - 4t.

Next, we need to calculate ds, which is the differential arc length along the line. The differential arc length ds is given by:

ds = √(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt.

Substituting the parameterized values of x(t), y(t), and z(t) into the above equation, we get:

ds = √[(8)^2 + (-2)^2 + (-4)^2] dt = √84 dt.

Now, we can rewrite the line integral as:

∫cx^4zds = ∫(8t)^4(5 - 4t)√84 dt.

Next, we simplify the integrand:

(8t)^4(5 - 4t) = 4096t^4(5 - 4t).

Finally, we evaluate the line integral by integrating the simplified integrand over the interval [0, 1]:

∫(8t)^4(5 - 4t)√84 dt = √84 ∫4096t^4(5 - 4t) dt.

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To express 0.63¯¯¯¯ as a fraction, first set it up as x = 0.6363¯¯¯¯, then follow a process of subtraction, multiplication, and division to simplify it to 4063/9900.

To express 0.63¯¯¯¯ as a fraction in simplest form, we can set it up as x = 0.6363¯¯¯¯.

Combining these steps, we get:

99x = 3.606363¯¯¯¯¯¯¯¯ x = 3.606363¯¯¯¯ / 99 = 4063/9900 as the fraction in simplest form.

the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are 8 and [tex]\( 2\sqrt{7} \)[/tex], respectively.

The image depicts a right-angled triangle with a hypotenuse of length 10 and one leg of length 6, with the other leg labeled as [tex]\( a \)[/tex]. There is also a smaller right-angled triangle within it, sharing the leg of length 6 with the larger triangle, with the hypotenuse of the smaller triangle labeled as 8 and the other leg labeled as [tex]\( b \).[/tex]

To find the lengths of [tex]\( a \)[/tex] and [tex]\( b \)[/tex], we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse [tex](\( c \))[/tex] is equal to the sum of the squares of the lengths of the other two sides [tex](\( a \)[/tex] and [tex]\( b \)[/tex]): [tex]\( c^2 = a^2 + b^2 \).[/tex]

For the larger triangle:

[tex]\[ 10^2 = 6^2 + a^2 \][/tex]

For the smaller triangle:

[tex]\[ 8^2 = 6^2 + b^2 \][/tex]

We will solve these two equations to find [tex]\( a \)[/tex] and [tex]\( b \)[/tex]. Let's start with the calculations for [tex]\( a \)[/tex] and [tex]\( b \)[/tex] using the Pythagorean theorem.

Using the Pythagorean theorem for each triangle, we find:

For the larger triangle:

[tex]\[ a^2 = 10^2 - 6^2 \][/tex]

[tex]\[ a^2 = 100 - 36 \][/tex]

[tex]\[ a^2 = 64 \][/tex]

[tex]\[ a = 8 \][/tex]

For the smaller triangle:

[tex]\[ b^2 = 8^2 - 6^2 \][/tex]

[tex]\[ b^2 = 64 - 36 \][/tex]

[tex]\[ b^2 = 28 \][/tex]

[tex]\[ b = \sqrt{28} \][/tex]

[tex]\[ b = 2\sqrt{7} \][/tex]

So, the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are 8 and [tex]\( 2\sqrt{7} \)[/tex], respectively.

To find the number of miles Mr. Lee drove the moving truck, we can set up an equation using the given information and solve for 'm'. The equation is $250 + $0.40x = $314, where 'x' represents the number of miles driven. Simplifying the equation, we find that Mr. Lee drove a total of 160 miles in the moving truck.

To find the number of miles Mr. Lee drove the moving truck, we can set up an equation using the given information. The moving company charges $250 to rent the truck and $0.40 for each mile driven. Let's let 'm' represent the number of miles he drove. The total cost Mr. Lee paid, including the rental fee and the cost per mile, is $314. So, the equation can be written as:

$250 + $0.40x = $314

To solve for 'm', we can subtract $250 from both sides of the equation:

$0.40x = $314 - $250

$0.40x = $64

Finally, we can divide both sides of the equation by $0.40 to find the value of 'm':

x = $64 / $0.40

x = 160

Therefore, Mr. Lee drove a total of 160 miles in the moving truck.

3rd tree = x

1st tree = 3x+50

2nd tree = 2x+100

3x+50 = 2x+100

subtract 50 from each side

3x= 2x+50

subtract 2x from each side

x = 50

 so 3rd tree = 50 feet tall

 Answer is B

The system of inequalities are y > x and y > 4 option (C) y > x, y > 4 is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have a graph shown in the picture,

As we can see in the picture there two lines are shown which represent the inequality and the shaded region is the solution to the pair of the linear inequality.

y > x and

y > 4

Thus, the system of inequalities are y > x and y > 4 option (C) y > x, y > 4 is correct.

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The graph of the equation y = 1/3x - 4 is a straight line that contains the points (3, -3) and (0, 04)

The bottom left is the correct answer.

We have,

To graph this equation, we can start by finding the y-intercept, which is the point where the line crosses the y-axis.

In this equation,

The y-intercept is -4, so we plot the point (0, -4).

Next, we can find another point on the line by choosing a value for x and calculating the corresponding y-value.

Let's choose x = 3.

Plugging this value into the equation, we get:

y = (1/3)(3) - 4

y = 1 - 4

y = -3

So point (3, -3) lies on the line.

Now we can plot these two points (0, -4) and (3, -3) and draw a straight line passing through them.

Since the coefficient of x is positive (1/3), the line will have a positive slope, meaning it rises as we move from left to right.

Thus,

The graph of the equation y = 1/3x - 4 would look like a straight line that slants upward as you move from left to right, crossing the y-axis at -4.

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