Mr. Macdonald Has 480 Animals On His Farm . 0.5 Of The Animals Arecows 1/8 Are Goats The Remainder Of (2024)

Answer:

50%

Step-by-step explanation:

50% = 0.5

$90000 times 0.5 = $45000

So, 50% of $90000 is equal to $45000

Answer: 50%

Hope this helps :)

Step-by-step explanation:

45,000 / 90,000 = .5 (50 out of 100)

45 * 2 = 90

Answer:

Second choice:

[tex]\mbox{\large y = \sqrt{wz}}[/tex]

Step-by-step explanation:

Consider the right triangle ABC

By the Pythagorean theorem,

AB² = BC² + AC²

BC = x, AC = (w + x) and AB = v

Plug in above values
(w + z)² = v² + x² (1)

In right triangle BCD,
BC² = BD² + CD²

Plugging in values we get
x² = w² + y² (2)

In right triangle ABD
AB² = BD² + AD²
v² = y² + z² (3)

Plug in values of x² from eq (2) and v² from eq 3 into equation (1) to get

(w + z)² = y² + z² +w² + y²

Left side (w + z)² = w² + 2wz + z²

==> w² + 2wz + z² = y² + z² +w² + y²

w² and z² cancel out since they are on both sides of the equation with same sign

=> 2wz = y²+y²

2wz = 2y²

Divide by 2:

wz = y²

Switch sides:

y² = wz

[tex]\mbox{\large y = \sqrt{wz}}[/tex]

•Mr Bradford lunged at his wedding ring as it fell into the WHIRLPOOL of the bathtub drain.

•Sarah's morher CALMED her screaming baby by giving her a teddy bear to hold.

Answer: whirlpool, calmed

Step-by-step explanation:

A vortex looks like a whirlpool

Since the baby is scream giving a teddy bear will probably calm it

Answer:

The damaged area of rubber will touch the ground 834 times. This can be determined by using the formula for circumference, which is 2πr where r is the radius. In this case, the radius is 0.67 meters, so the circumference of the wheel is 4.24 meters. Since the farmer drives 1.5 km, this would be equal to 1500 meters. Therefore, the damaged piece of rubber will touch the ground 1500 meters/4.24 meters = 834 times.

The given mixed fraction can be written in decimal form as 1.5.

What are mixed fractions?

These are just improper fractions written as a sum of whole number and a proper fraction. (improper fraction has the upper value(also called numerator) bigger or equal to denominator(the bottom value) and proper fraction has numerator value is less than that of the denominator)

The given mixed fraction is [tex]1\frac{1}{2}[/tex].

Now, the given mixed fraction can be written as 3/2

3/2 can be written in decimal number as 1.5.

Decimal number 1.5 is between 1 and 2.

Therefore, the given mixed fraction can be written in decimal form as 1.5.

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Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

Given equation is ,

3^x - 3^{x-2} = 24

we can write it as,

3^x - (3^x/3^2) = 24

take out 3^x as common,

3^x ( 1 - 1/3^2) = 24

simplify,

3^x (1 -1/9)=24

3^x (9-1/9)=24

3^x * 8/9 = 24

3^x = 24 * 9/8

3^x = 27

3^x = 3^3

on comparing,

x = 3

and we are done!

Answer:

x = 3

Step-by-step explanation:

Given equation:

[tex]3^x-3^{x-2}=24[/tex]

Rewrite the exponent of the first term as (x - 2 + 2):

[tex]3^{x-2+2}-3^{x-2}=24[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]3^{(x-2)+2}-3^{x-2}=24[/tex]

[tex]3^{x-2}\cdot 3^2-3^{x-2}=24[/tex]

[tex]\textsf{Factor out the common term $3^{x-2}$}:[/tex]

[tex]3^{x-2}(3^2-1)=24[/tex]

Simplify the brackets:

[tex]3^{x-2}\cdot 8=24[/tex]

Divide both sides by 8:

[tex]3^{x-2}=3[/tex]

Apply the exponent rule a = a¹ :

[tex]3^{x-2}=3^1[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]x-2=1[/tex]

Add 2 to both sides of the equation:

[tex]x=3[/tex]

The volume of the buoy is the sum of volume of hemisphere and volume of cone which is 0.504m³

What is volume of the buoy

To calculate the volume of the buoy, we need to find the volume of the hemisphere and the volume of the cone.

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

V = (2/3) * π * (r^3)

where "r" is the radius of the hemisphere.

So, the volume of a hemisphere with radius "r" is equal to (4/3) times π times the cube of the radius.

The base is 0.95 and the radius is half the length of the base.

radius = 0.95 / 2 = 0.475m

The volume of the hemisphere = 2/3 * 3.14 * 0.475³

volume of hemisphere = 0.224m³

The volume of the cone = 1/3 πr²h

The volume of the cone = 1/3 * 3.14 * 0.475² * 1.2

The volume of the cone = 0.28m³

The volume of buoy = volume of sphere + volume of cone

The volume of buoy = 0.224 + 0.28 = 0.504m³

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Answer:

3.) 3:7

Step-by-step explanation:

We know

Of the 300 television sets sold at an electronics store last month, 90 were flat-screen TVs.

300 - 90 = 210

So, we know the store sold 90 flat-screen TVs and 210 other TVs

What was the ratio of flat-screen TVs to other TVs sold last month?

The ratio is

90:210

3:7

So, the answer is 3.) 3:7

Answer:

3.) 3:7

Step-by-step explanation:

The unsimplified ratio would be 90:210 since flat-screen TVs are excluded, but if you simplify this you get 3:7.

90:210

9:21

3:7

The required radical form of the given expression [tex](x^2)^{4/3}[/tex] is ∛x⁸.

What are the radical expressions?

Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.

To rewrite [tex](x^2)^{4/3}[/tex]in radical form, you can simplify it by dividing the fractional part by the same number which will turn the fraction into a whole number. In this case, that number is 3.

So, you can simplify [tex](x^2)^{4/3}[/tex] as follows:

[tex](x^2)^{4/3}[/tex]

[tex]x^{2\times4/3}[/tex]

[tex]x^{8/3}[/tex]

[tex](x^8)^{1/3}[/tex]

∛x⁸

This is the radical form of [tex](x^2)^{4/3}[/tex].

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KN is 6 units long, AL is 6 units long, AR is 10 units long, and RG is 4 units long.

What is line segment?

A line segment is a section of a straight line that is bounded by two different end points and contains every point on the line between them. The Euclidean distance between the ends of a line segment determines its length. A line segment has endpoints, but a line can be extended forever on both ends. A line segment is a section of a line that links two places known as the line's endpoints. It is possible to measure the distance between two places. Because line segments have a fixed length, they may be used to create the sides of any polygon.

Here,

They are equal in ratio.

4/8=x/12

x=6 units

4/8=3/y

y=6 units

4/8=5/z

z=10 units

4/8=2/p

p=4 units

The length of line segment KN is 6 units, AL is 6 units, AR is 10 units and RG is 4 units.

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The term that best describes the analysis conducted by the researcher is; Observational Study

How to identify the system of research?

We are given the parameters as;

Number of all adult members of a tribe = 217

Average height of the adult members = 5.49 ft

Now, there are different methods of research analysis such as experiment

randomized trial

double blind study

observational study

Now, in this case we are only told what the researcher has observed from his analysis and an observational study is used to answer a research question based purely on what the researcher observes.

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Answer: a) 0.00000047 = 4.7*10 7square. b) 0.0000000738 = 73.8 * 10 9 square .

Step-by-step explanation:

Answer: [tex]4.7 x 10^{-7}[/tex]

Answer:

108

Step-by-step explanation:

480÷30= 6 [no. of groups in 30]

18×6= 108

Answer:

288

Step-by-step explanation:

To estimate the number of 7th graders attending the dance, we need to extrapolate the sample proportion to the total population.

The sample proportion of 7th graders who are going to the dance is 18/30 = 0.6.

So, the estimated number of 7th graders who will attend the dance is:

0.6 * 480 = 288.

No, there are no whole numbers with a cube root between 0 and 1. A cube root of a number is a value that, when multiplied by itself three times, gives the original number.

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. The cube root of a positive number is always positive. If a positive number is between 0 and 1, then its cube will be even smaller.

For example, the cube root of 8 is 2, and the cube root of 27 is 3. If we take the cube root of a number less than 1, such as 0.5, the result is less than 1. However, since we are talking about whole numbers, 0.5 is not a whole number and therefore not in the scope of the question.

Therefore, it can be concluded that there are no whole numbers with a cube root between 0 and 1 because any positive whole number raised to the power of 1/3 will result in a value greater than 1.

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Expression of given expression as simple fraction is ax/3y.

What is fraction ?

Fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given expression

(ax + ay)/xy² . x²y/(3x + 3y)

simplifying

(ax + ay)/y . x/(3x + 3y)

Factoring out common factors

a(x + y)/y . x/3(x + y)

Simplifying

= ax/3y

Hence, given expression as simple fraction is ax/3y.

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Kimi's weekly total savings would be $17.

Kimi's total earnings from her job in a week would be $9 × 1 = $9.

Her total allowance and earnings from her job would be $9 + $8 = $17.

Kimi earns $9 an hour at her job, and her allowance is $8 per week, so her total weekly income is $9 + $8 = $17.

Jordan earns $7 an hour, and his allowance is $16 per week, so his total weekly income is $7 + $16 = $23.

So, Kimi's weekly total savings would be $17.

Hence, the answer to the given problem is $17.

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--The given question is incomplete; the complete question is

"Komi and Jordan are each working during the summer to earn money in addition to their weekly allowance, and they are saving all their money. Kimi earns $9 an hour at her job, and her allowance is $8 per week; Jordan earns $7 an hour, and his allowance is $16 per week. If the number of hours worked in a week is one, what are Kimi’s weekly total savings?"--

The values in the parallelogram figure are as follows

angle B = 74 degrees

x = 4

angle BCA = 49 degrees

How to find angle B

Remembering that opposite angels of a parallelogram are equal will help us know that angel B is equal to angel D which is 74 degrees

The property that the two opposite sides of parallelogram is used to find x

4x = 16

x = 4

Applying alternate interior angles postulate, we can see that

angle BCA = angle DAC = 49 degrees

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The value of c is zero and a and b can be something else, because the vector are linearly independent.

A set of vectors is linearly independent if no vector can be expressed as a linear combination of the others (i.e., is in the span of the other vectors). A set of vectors is linearly independent if no vector can be expressed as a linear combination of those listed before it in the set.

Assume the following:

[tex]a\left[\begin{array}{ccc}2\\2\\0\end{array}\right] + b\left[\begin{array}{ccc}1\\-1\\1\end{array}\right] +c\left[\begin{array}{ccc}4\\2\\-2\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]

Determine if a=b=c=0

[tex]2a+b+4c =0 (1)\\ 2a-b+2c =0 (2)\\b-2c=0(3)\\[/tex]

Subtract (2) from (1)

[tex]b+c = 0\\b-2c=0[/tex]

Substitute (5) into (4), we get c=0.

So now what do I do with this fact? I'm tempted to say that only c=0, and a and b can be something else.

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Answer:

(-3,1)

Step-by-step explanation:

The value of x [tex]\frac{-9+3}{2}[/tex] = -3

The value of y [tex]\frac{4-2}{2}[/tex] = 1

Answer:

Mid point is (-3, 1)

Step-by-step explanation:

Let mid point be M

[tex] { \boxed{ \sf{m = ( \frac{x _{1} + x _{2} }{2}} , \: \frac{y _{1} + y _{2}}{2}) }} \\ \\ { \tt{m = ( \frac{ - 9 + 3}{2} , \: \frac{4 - 2}{2} )}} \\ \\ { \tt{m = ( \frac{ - 6}{2}, \: \frac{2}{2} ) }} \\ \\ { \tt{m = ( - 3, \: 1)}}[/tex]

The value of the expression is 94.9

How to determine the value

Algebraic expressions are expression with variables, terms, coefficients, factors and constants.

They are also made up of mathematical operations, such as;

AdditionSubtractionBracketParenthesesSubtraction, etc

From the information given, we have that;

8.3x + 7.5y

When x = 3 and y = 4

Substitute the values into the formula

8.3(3) + 7.5(4)

expand the bracket

24.9 + 60

Add the values

84. 9

Hence, the value is 84.9

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Answer:

Step-by-step explanation:

The formula for kinetic energy is:

KE = (1/2) * m * v^2

where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.

We are given the mass of the pick-up truck as 1500 kg and its velocity as 31.0 m/sec. We can plug these values into the formula to calculate its kinetic energy:

KE = (1/2) * m * v^2

= (1/2) * 1500 kg * (31.0 m/sec)^2

= (1/2) * 1500 kg * 961.0 m^2/sec^2

= 720750 J

Therefore, the kinetic energy of the pick-up truck is 720750 Joules.

r

Step-by-step explanation:

v

Answer:

Both models are exponential

A: $21,573.58

B: $21,589.58

Step-by-step explanation:

A

f(x) = 16,000[tex](1 + .03/4)^{4(10)}[/tex]

f(x) = (16000)[tex]1.0075^{40}[/tex]

f(x) = $21,573.58 Rounded to the nearest cent.

B

f(x) = 16000[tex](1+ .03/12)^{12(10)}[/tex]

f(x) = (16000)[tex]1.0025^{120}[/tex]

f(x) = $21,589.66 Rounded to the nearest cent

As a result, on a graph of dP/dt vs P, the curve would be concave down for P b/a and concave up for P > b/a. The curve would reach its maximum when P = b/a, with dP/dt equal to zero.

What is equation?

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

The equation dP/dt = aP² - bP represents the rate of change of the population P over time t.

When dP/dt is positive, the population is increasing. When dP/dt is negative, the population is decreasing.

To find when dP/dt is positive and negative, we need to find the critical points where dP/dt = 0.

Solving the equation dP/dt = aP² - bP = 0, we get:

aP² - bP = 0

aP(P - b/a) = 0

This equation has two solutions: P = 0 and P = b/a.

For P < b/a, dP/dt is negative (the population is decreasing). For P > b/a, dP/dt is positive (the population is increasing).

So, on a graph of dP/dt against P, the curve would be concave down for P < b/a and concave up for P > b/a. At P = b/a, the curve would have a maximum and dP/dt = 0.

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As per unitary method,

a) The length of the rope left after tying the parcel 260 cm

b) The initial length of the rope was 305cm.

The unitary method is a mathematical tool used to solve problems involving the partition of a whole into parts.

(a) To find the length of the rope left after tying the parcel, we subtract the length of the rope used to tie the parcel from the initial length of the rope. The length of the rope left is:

=> Initial length of the rope - Length of rope used to tie the parcel = Length of rope left

We are told that Ravi used 45cm of the rope to tie a parcel. Therefore, the length of rope left can be expressed as:

Initial length of the rope - 45 = Length of rope left

(b) To find the initial length of the rope, we add the length of the rope used to tie the parcel to the length of the rope left.

We know that the length of the rope left is divided into 4 pieces of 65cm each. Therefore, the total length of the rope left is

=> 4 x 65 = 260cm.

We can now use this information to find the initial length of the rope:

Length of rope left + Length of rope used to tie the parcel = Initial length of the rope

260 + 45 = 305cm

Complete Question:

Ravi had a rope. He used 45cm of the rope to tie a parcel. He then cut the remaining rope equally into 4 pieces. Each piece was 65cm long.

(a) Find the length of the rope left after tying the parcel.

(b) How long was the rope at first?

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The displacement x of the moving puck is; 0.43 meters

How to find the displacement?

The displacement is defined as the change in position of an object. It is also called a vector quantity and has a direction and magnitude

The parameters given here are;

The polar coordinate initial velocity vector; U = 2.35 m/s, -22°

Final velocity vector; V = 6.42 m/s, +50°

This suggests to us that Cartesian x axis is parallel to angle 0° and y axis is parallel to +90°.

Change of velocity component parallel to +90° = magnitude*sinθ,.

Thus, the change of that velocity

Δv = |V|sin(50) - |U|sin(-22)

Δv = 6.42sin(50) - 2.35sin(-22)

Δv = 4.9 - (-0.88)

Δv = +5.8 m/s

The equation for displacement is;

s = ut +1/2at^2

where acceleration time t = Δt = 0.215 s

initial velocity u = |U|sin(-22) = -0.88 m/s

acceleration parallel to u is a = Δv/Δt = +5.8/Δt

a = 5.8/t m/s^2

Thus;

s = -0.88t + ¹/₂* 5.8/t * t²

s = -0.88t +2.9t

s = 2.0t

s = 2.0 * 0.215

s = 0.43 m

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To sell 80% of a total of 1400 units, the salesman must sell 1120 units, and he must sell 520 units from his next shipment of 600 units.

To solve this problem, we need to find out how many units the salesman must sell in order to have sold 80% of the 1400 units in total (800 units from the first shipment and 600 units from the next shipment).

The 80% of the total number of units is calculated as:

0.8 * 1400 = 1120 units

To find out how many units from the next shipment the salesman must sell, we subtract the number of units from the first shipment (800 units) from the total number of units that need to be sold (1120 units), which results in:

1120 - 800 = 320 units

Finally, we subtract the number of units the salesman has already sold from the next shipment (600 units) from the number of units he still needs to sell (320 units), which results in:

320 - 600 = -280 units

However, since the number of units sold cannot be negative, we must instead calculate the number of units the salesman must sell from the next shipment, which is:

600 - 320 = 520 units.

Hence, the salesman must sell 520 units from his next shipment of 600 units.

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Answer:

Below

Step-by-step explanation:

4/ 9 z - 5/9 z + 2 - 3/9 z - 9

(4-5-3)/9 z +2 - 9

-4/9 z +2-9

-4/9 z - 7

Answer:

The equation "3(g + h) = 12" can be translated into a sentence as: "Three times the sum of g and h equals 12."

Hope this helps.

Answer: 3 times g plus h equals 12

Step-by-step explanation:

3 times g + h = 3(g+h)

equals 12 = =12

Hope this helps!

The exponential function for each set of points is y = 3 * 2ˣ,

What is the exponential function?

An exponential function is a Mathematical function in form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

The exponential function can be described as y = 3 * 2ˣ,

where,

x is the input value

and y is the output value.

This function says that for every increase in x by 1 unit, the value of y will be multiplied by 2, starting from an initial value of 3.

For example, when x = 0, y = 3 * 2⁰ = 3, and when x = 1, y = 3 * 2¹ = 12.

Hence, the exponential function for each set of points is y = 3 * 2ˣ,

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In light of this, Liam's earnings after six years will be roughly $47,139.92.

Profits from Liam's company have reached $43,200, and they are growing at a 1.2% annual rate.

We can use the compound interest calculation to calculate the number of profits after six years.

The formula is P = P0 *[tex](1 + r/100)^t[/tex], If t is the number of years, which is 6, P0 is the initial sum of $43,200, r is the yearly interest rate of 1.2%, and t is the number of years.

By substituting these values into the formula,

we can calculate the final amount as P = 43,200 * [tex](1 + 1.2/100)^6[/tex] = 43,200 * [tex]1.012^6[/tex] = 43,200 * 1.07711 = $47,139.92.

In light of this, Liam's profits after six years will be roughly $47,139.92.

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