Suppose √x + √y = 10 and y(9) = 49. Find y'(9) by implicit differentiation.

The answer is A)The list of favorable outcomes are 1) 1-1, 1-2 ; 2) 2-1, 2-2 ; 3) 3-1, 3-2 ; 4) 4-1, 4-2 ; 5) 5-1, 5-2 ; B) There's 50% chance of probability of being odd.

A) If the sample space of tossing a coin and picking a number between 1 and 5, inclusive then there are 5 set of probabilities as an outcome:

1) 1-1, 1-2 ;

2) 2-1, 2-2 ;

3) 3-1, 3-2 ;

4) 4-1, 4-2 ;

5) 5-1, 5-2

B) And in the case of getting odd numbers as an probability outcome, there are  50% chance of it being odd.                

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The probability of having no defectives in a sample of size 3 from a lot of 24 items with 5 known defectives is 0.0403 or approximately 4%.

The probability of having no defectives in a sample of size 3 from a lot of 24 items with 5 known defectives can be calculated using the binomial probability formula. The formula is given by:

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

where:

n = sample size (3)

k = number of successful trials (0)

p = probability of success (probability of an item being non-defective)

Since there are 24 items in the lot and 5 of them are known to be defective, the probability of success (p) is equal to 19/24.

Plugging in the values, we get:

P(X=0) = (3 choose 0) * (19/24) ^0 * (5/24) ^3

= 1 * 1 * (5/24) ^3

= (5/24) ^3

= 0.0403

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Step-by-step explanation:

2.5:10 = 1/4

1.4:1.8 = 7/10

0.04: 0.3 = 2/50

1/5: 4/5 = 1/5

3/4: 1/2 = 3/2

6.2:5 2/5 = 12/5

Angle - 51 degrees represent a counterclockwise rotation of 51 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

If 39 degrees represents a clockwise rotation of 39 degrees.

Then we can conclude that the clockwise is taken as positive and counterclockwise is taken as negative.

Angle - 51 degrees represent a counterclockwise rotation of 51 degrees.

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Answer:18

Step-by-step explanation:

Answer:18

Step-by-step explanation:

Answer:

Step-y-step explanation: я хз

The volume of a sphere with radius 10 units was found to be approximately 42 cubic units.

The volume of a sphere can be calculated using the formula:

V = (4/3) * π * r^3

Where, r is the radius of the sphere. In this case, the radius is 10 units, so we can plug in the values and calculate the volume:

V = (4/3) * π * 10^3 = 4184 cubic units

So, the approximate volume of the sphere with a radius of 10 units is 4184 cubic units.

Rounding off to the nearest whole cubic unit, 4184 cubic units becomes 42 cubic units.

Volume of a sphere is the amount of space inside a sphere.

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Los dos números dados en el conjunto de preguntas anterior son 32 y 160. Para resolver este problema, se puede establecer una ecuación con variables.

Sea x el número más pequeño, entonces el número más grande sería 5x. La suma de ambos es 192, por lo que

Al resolver esta ecuación simple, se obtiene que x = 32, y por lo tanto, 5x = 160. Estos son los dos números que cumplen con los requisitos dados en la pregunta.

En matemáticas, la sumatoria es la suma de una secuencia de cualquier tipo de números, llamados sumandos o sumandos; el resultado es su suma o total.

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The ordered pair that lies on the inverse of the function is (25, 0)

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

g(x)=−(x−3)^3−2.

Set x = 0

So, we have the following representation

g(0) =−(0−3)^3−2.

Evaluate the expression

This gives

g(0) = 25.

So, the ordered pair of teh inverse is (25, 0)

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Answer: -3,4

Step-by-step explanation:

A linear equation giving the value v of the equipment during the 5 years it will be in use is v = 955 - 191t

A linear equation models a linear relationship between two variables, where the rate of change between the two variables is constant. In this case, we can model the value of the equipment as it depreciates over time using a linear equation.

Since the value of the equipment decreases linearly over time, we can write an equation in the form:

v = a - bt

where v is the value of the equipment in year t, a is the initial value of the equipment, and b is the constant rate of depreciation.

Since the initial value of the equipment is $955, we can set a equal to 955. To find the constant rate of depreciation, we need to find the change in value over the 5 years it will be in use and divide by the number of years. Assuming after 5 years the value is 0,

constant rate of depreciation = 955/ 5

= 191

So, with a = 955 and b = $191 per year, the linear equation that models the value of the equipment over time is:

v = 955 - 191t

This equation gives the value of the equipment in year t based on the initial value and the constant rate of depreciation.

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The function is the relation between number of cars and toll collected in the toll booth. So the correct option is that the reasonable domain is a set of natural numbers.

While considering a function regarding to mathematical domain, for f(x) = 3.25x, x can be any values between -∞ to +∞. For every x value, we could calculate f(x).

But here, we are dealing with number of cars. So it can have only values as a natural number. A negative integer, fraction or decimal cannot represent x. So it will be a set of natural numbers.

So the domain here is the set of natural numbers.

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A regular solid shape is defined as a three-dimensional object that has all its faces congruent and all its vertices congruent. In other words, all faces have the same shape and size and all vertices have the same angle measures.

Among the options provided, only the cube is a regular solid shape. A cube is a three-dimensional object that has six equal square faces. Each face is a square and each vertex has the same angle measure. The edges of a cube are congruent and the shape is highly symmetrical.

The cylinder is not a regular solid shape because it has two congruent circular faces and one curved surface, which is not congruent to the other two faces. The vertices of a cylinder also have different angle measures.

The cuboid is not a regular solid shape because it has six rectangular faces, and the shape is not highly symmetrical. The vertices of a cuboid also have different angle measures.

In conclusion, a regular solid shape must have congruent faces and congruent vertices, and only a cube satisfies these conditions. It is important to note that not all regular shapes are regular solid shapes, for example, a sphere is a regular shape, but it is not a regular solid shape because it has no faces, vertices or edges.

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Answer:

Step-by-step explanation:

-2.67

The field is full of 18 horses and 15 geese.

Let's assume that there are x horses and y geese in the field. The number of heads can be represented as x + y = 33. The number of feet can be represented as 4x + 2y = 102.

We can use substitution to solve for one variable in terms of the other. From the first equation, we can solve for y in terms of x:

y = 33 - x

Substituting this expression for y into the second equation, we get:

4x + 2(33 - x) = 102

Expanding and simplifying the expression, we get:

4x + 66 - 2x = 102

Solving for x, we get:

2x = 36

And x = 18

So there are 18 horses in the field. Substituting this value for x into the expression for y, we get:

y = 33 - x = 33 - 18 = 15

So there are 15 geese in the field. Thus, the field is full of 18 horses and 15 geese.

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The area of the shaded region is 84.82 cm².

The area of the shaded region is calculated by subtracting the area of the sector from the area of the entire circle.

Since the angle of the sector is 90 degrees, we can conclude that the entire circle is divided into four.

Area of the shaded region = πr² - 1/4(πr²) = 3/4πr²

where;

The area of the shaded region is calculated as;

A = 3/4πr²

A = 3/4 x π ( 6 cm )²

A = 84.82 cm²

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Answer:

x= 19

Step-by-step explanation:

6x+4+4x-14= 180

10x-10= 180

10x= 190

x= 19

The value of x is 13.85.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

(7x + 1)° and (6x - 1)° makes a straight angle.

This means,

(7x + 1) + (6x - 1) = 180

7x + 1 + 6x - 1 = 180

13x = 180

x = 180/13

x = 13.85

Thus,

x is 13.85°

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Answer:

17

Step-by-step explanation:

To solve this problem, we need to use the distance between two points formula. It states that the distance is [tex]\sqrt{(x_{1} - x_{2} ) ^{2} + (y_{1} - y_{2})^{2} }[/tex]. Here, [tex]x_{1} = 1, x_{2} = 9, y_{1} = 0, y_{2} = 15[/tex]. Plugging these values in gets us [tex]\sqrt{64 + 225}[/tex] which equals [tex]\sqrt{289}[/tex] = 17 .

Answer:

44.44%

Step-by-step explanation:

Error percent can be found by this formula

Estimation/Actual number x 100/1

= 2/4.5 x 100/1

= 200/4.5 = 2000/45

= 400/9

= 44.44 %

1601000 students were awarded a bachelor’s degree in 2009.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

First, notice that the table is in thousands, remember that.

Now, we need to go to the part of the row of the table where we have "Bachelor".

There we can see that in 2009, a marginal total of 1,601 thousands got that degree.

Then we can conclude that in 2009, a total of:

1,601×100 = 1,601,000 students got a bachelor's degree.

Hence, 1601000 students were awarded a bachelor’s degree in 2009.

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Answer:

C. 1,601,000

Step-by-step explanation:

This is the correct answer.

Answer:

1.106209714987%

Step-by-step explanation:

Negative values detected. All input values threated as percentages (e.g. an input of 0.1 is threated as 0.1%, -10 is threated as -10%).

The amount invested in the 3% interest account is $11,342.11, and the amount invested in the 1.1% interest account is $10,000 - $11,342.11 = $-342.11.

What is the interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

Let's call the amount invested in the 3% interest account x. Then, the amount invested in the 1.1% interest account is $10,000 - x.

The interest earned in the 3% interest account is 0.03x, and the interest earned in the 1.1% interest account is 0.011($10,000 - x).

The total interest earned is equal to the sum of the interest earned in each account:

0.03x + 0.011($10,000 - x) = $215.04

Expanding and solving for x:

0.03x + 0.011 * $10,000 - 0.011x = $215.04

0.019x = $215.04 + 0.011 * $10,000 - 0.011 * $10,000

0.019x = $215.04

x = $215.04 / 0.019

x = $11,342.11

Hence, the amount invested in the 3% interest account is $11,342.11, and the amount invested in the 1.1% interest account is $10,000 - $11,342.11 = $-342.11.

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Answer:

Step-by-step explanation:

[tex]2123.72 = 4 \times 3.14 \times {r}^{2} [/tex]

[tex]2123.72 = 12.57 {r}^{2} [/tex]

[tex] \frac{12.57 {r}^{2} }{12.57} = \frac{2123.72}{12.57} [/tex]

[tex] {r}^{2} = 168.95[/tex]

[tex]r = 13.0[/tex]

[tex] \frac{4}{3}\pi {r}^{3} [/tex]

[tex] \frac{4}{3} \times 3.14 \times {13}^{3} = 9202.77 {m}^{3} [/tex]

By the definition of vertically opposite angle, the value of measure of ∠5 is, 100°.

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

In the figure,

⇒ m ∠7 = 100°

Now, By the figure we have;

Both the angles 7 and angle 5 are vertically opposite angle.

And, We know that the vertically opposite angles are equal to each other.

Hence, We get;

⇒ m ∠7 = m ∠5

⇒ 100° = m ∠5

⇒ m ∠5 = 100°

Thus, We get;

⇒ m ∠5 = 100°

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Answer:

BK=AK: no

BK=DK:yes

CK=AK:yes

CK=DK:no

Step-by-step explanation:

for the first and last, it is not needed because a rectangle is a parallelogram, for example, but its diagonals are not congruent. The diagonals intersect each other at both of their midpoints, on the other hand, so therefore the second and third must be true. Does this make sense?

Answer:

$14087.49

Step-by-step explanation:

APR=8%,

monthly interest rate (r)=8%/12=0.08/12

Monthly payment, A=$250

After 4 years, n=4*12 = 48 months,

the balance P is therefore

P= A((1+r)^n-1)/i

=250((1+0.08/12)^48-1)/(0.08/12)

=14087.49

Based on the information provided, if a block weighs w kg, then it is expected for 8 blocks to weigh 8w kg.

The weight can be defined as the mass contained in an object or body, this is often expressed using units such as grams, pounds, kilograms, or tons.

Considering w = the weight of a single block, the best expression to show the weight of 8 blocks is 8wkg. This letter can be replaced by the value of the weight if known, for example, 8 x 25 kg.

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Step-by-step explanation:

To calculate the potential energy of the ball at its highest point, we first need to find the gravitational potential energy of the ball. Gravitational potential energy is given by the equation:

PE = mgh

where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2 on the surface of the earth), and h is the height of the ball above the ground.

At its highest point, the height of the ball is 80 m, so the gravitational potential energy can be calculated as:

PE = m * g * h = m * 9.8 * 80

where m is the mass of the ball.

Since the ball was thrown at an angle of 30 degrees with the horizontal, its initial velocity can be broken down into horizontal and vertical components:

v0x = v0 * cos(30) = 10 * cos(30) = 10 * sqrt(3)/2 m/s

v0y = v0 * sin(30) = 10 * sin(30) = 10/2 m/s

The potential energy of the ball at its highest point can be found by adding the initial kinetic energy of the ball to its gravitational potential energy. The kinetic energy of the ball can be calculated as:

KE = 1/2 * m * v0y^2

where m is the mass of the ball and v0y is the vertical component of its initial velocity.

The total potential energy of the ball at its highest point is given by:

PE = KE + mgh = 1/2 * m * v0y^2 + m * g * h

Substituting in the given values, we find:

PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80

Note: The mass of the ball (m) is not given, so the answer is given in terms of m.

Answer:

Step-by-step explanation:

PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80

Answer: Let's assume that there are "m" jokes written by male authors and "f" jokes written by female authors, such that m + f = total number of jokes in the magazine.

If a joke by a man is told first, there are (m - 1)! ways to arrange the remaining m - 1 jokes written by male authors and f! ways to arrange the jokes written by the female author. The total number of ways the jokes can be delivered is (m - 1)! * f!.

So, the answer is (m - 1)! * f! ways to deliver the jokes if a joke by a man is told first.

Step-by-step explanation: