The length of a rectangle is four times its width. If the area of the rectangle is 100 ft?, find its perimeter

Answer:

4 : 24 or 1 : 6

Step-by-step explanation:

There are 4 bananas and 24 fruits so we just make that a ratio of 4 : 24.

We can then simplify that ratio to 1 : 6.

Answer:

the answer is 1:3

i did the test

Step-by-step explanation:

We kinda need the graph

Answer:

35

Step-by-step explanation:

First, we will define range.

The difference between the highest and lowest values in a data is called range. To find the range, first the highest and lowest values are found from data, then the lowest value is subtracted from the highest value.  

In the above data,

Highest Value=71  

Lowest Value=36  

Range=Highest value-lowest value  

=71-36  

=35  

The range in the number of fish across the 12 large aquariums is 35, calculated by subtracting the minimum number of fish, 36, from the maximum number, 71.

The question asks us to calculate the range in the number of fish across 12 large aquariums at a zoo. To find the range, we need to identify the largest and smallest numbers in the given data set and then subtract the smallest from the largest.

Here is the list of the numbers of fish in each aquarium: 37, 58, 62, 36, 42, 71, 56, 58, 69, 66, 47, 68.

First, we find the maximum and minimum values:

Maximum (the largest number of fish in an aquarium): 71

Minimum (the smallest number of fish in an aquarium): 36

Next, we calculate the range by subtracting the minimum value from the maximum value:

Range = Maximum - Minimum

Range = 71 - 36

Range = 35

Therefore, the range in the number of fish across the 12 aquariums is 35.

To find the distance from point P to line RQ, we first find the vectors for PQ and PR. Then we calculate the projection of PR onto PQ which gives us the vector from P to the point on line RQ nearest to P. The length of this vector gives us the shortest distance from point P to the line RQ. This explanation assumes we have coordinate data for points P, Q, and R.

The distance from point P to RQ can be found utilizing mathematical principles of geometry and vectors. Let's assume that we know the coordinates of points P, R, and Q. Having these information, we can follow these steps:

Remember, this is the process given that you know the coordinates of the points involved. If you only have a diagram, you might need to use tools like a ruler or a protractor to measure distances and angles.

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Answer: 22 feet.

Step-by-step explanation:

Note that there are two right triangles in the figure attached: ACD and BCD. Where "h" is the height of the chimeney  from John's eye level to the top of the chimney.

You need to use the trigonometric identity [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] for this exercise.

[tex]tan(45\°)=\frac{h}{x}[/tex]

Solve for h:

[tex]h=xtan(45\°)\\h=x[/tex]

[tex]tan(30\°)=\frac{h}{x+16}[/tex]

Substitute [tex]h=x[/tex] and solve for h:

[tex]tan(30\°)=\frac{h}{h+16}\\\\(h+16)(tan(30\°))=h\\\\0.577h+9.237=h\\\\9.237=h-0.577h\\\\9.237=0.423h\\\\h=\frac{9.237}{0.423}\\\\h=21.836ft[/tex]

Rounded to the nearest foot:

[tex]h=22ft[/tex]

Answer: 60 degrees

Step-by-step explanation:

the line is 180 degrees so minus 50 equals 130 minus 10 120 divide my 2 60

Answer:

[tex]\large\boxed{S.A.=368\ cm^2}[/tex]

Step-by-step explanation:

The formula of a surface area of a rectagular prism:

[tex]S.A.=2(lw+lh+wh)[/tex]

l - length

w - width

h - height

We have the dimensions 6cm × 14cm × 5cm. Substitute:

[tex]S.A.=2(6\cdot14+6\cdot5+14\cdot5)=2(84+30+70)=2(184)=368\ cm^2[/tex]

The surface area of the rectangular prism is 368 cm²

To calculate the surface area of the prism, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The surface area of the rectangular prism is 368 cm².

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Answer:

Option b (4,1)

Step-by-step explanation:

The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function [tex]f(x, y) = 8x + 8y[/tex]

The minimum points are found in the lower vertices of the region.

These vertices are found by equating the equations of the lines::

[tex]3x+2y=14\\-5x +5y=10[/tex]

-------------------

[tex]x = 2\\y = 4[/tex]

[tex]-8x + 3y = -29\\3x + 2y = 14[/tex]

---------------------

[tex]x = 4\\y = 1[/tex]

The lower vertices are:

(4, 1) (2, 4)

Now we substitute both points in the objective function to see which of them we get the lowest value of [tex]f(x, y)[/tex]

[tex]f(4, 1) = 8(4) +8(1) = 40\\f(2, 4) = 8(2) + 8(4) = 48[/tex]

Then the value that minimizes f(x, y) is (4,1).

Option b

AO is a line segment containing the radii of both circles, which are AK and OE, so AO = AK + OE = 9.

Extend AO to a point P on the line KE. Then we get two similar triangles APK and OPE. Let [tex]x[/tex] be the length of KE, [tex]y[/tex] the length of EP, and [tex]z[/tex] the length of OP.

By similarity, we have

[tex]\dfrac{OE}{AK}=\dfrac{EP}{KP}=\dfrac{OP}{AP}\iff\dfrac45=\dfrac y{y+x}=\dfrac z{z+9}[/tex]

OPE is a right triangle, so

[tex]OP^2=OE^2+EP^2\implies z=\sqrt{16+y^2}[/tex]

Now,

[tex]\dfrac45=\dfrac y{y+x}\implies 4(y+x)=5y\implies 4x=y[/tex]

and we also have

[tex]z=\sqrt{16+(4x)^2}=\sqrt{16+16x^2}=4\sqrt{1+x^2}[/tex]

Substituting this into the expression containing [tex]z[/tex] gives us an equation that we can solve for [tex]x[/tex]:

[tex]\dfrac45=\dfrac z{z+9}=\dfrac{4\sqrt{1+x^2}}{4\sqrt{1+x^2}+9}[/tex]

[tex]16\sqrt{1+x^2}+36=20\sqrt{1+x^2}[/tex]

[tex]9=\sqrt{1+x^2}[/tex]

[tex]\implies KE=x=\sqrt{80}=3\sqrt{10}[/tex]

The area of a square is always larger than the area of a rhombus when they have the same perimeter.

The areas of a square and a rhombus with the same perimeter are not equal. The square will always have a larger area than the rhombus.

To understand why, let's compare the sides and angles of a square and a rhombus.

Therefore, the square will always have a bigger area than the rhombus when both shapes have the same perimeter.

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Answer:

⅖  pizza

Step-by-step explanation:

Divide each pizza into five slices.

Then there will be 10 slices, and each person will get two slices.

Two slices = ⅖ pizza

Each person will receive ⅖ pizza.

Each of the five people will receive 2/5 of a pizza when two pizzas are shared equally amongst them.

The student asked how much pizza each person will receive if five people are sharing two pizzas equally. To answer this, we divide the total number of pizzas by the number of people. Since there are 2 pizzas and each pizza is usually considered to be 1 whole, when split among 5 people, each person will get 2/5 of a pizza.

Answer:

2.8 putts in average on any given green

Step-by-step explanation:

To calculate how many putts Madison will need on any given green, we need to calculate the weighted average of his putts.

We use a global sample of 100 puts and factor in the fact he had a one-putt performance 15% of the time, two-putts 20% of the time and so on.

So, the calculation goes like this:

[tex]\frac{1 * 15 + 2 * 20 + 3 * 35 + 4 * 30}{100}  = \frac{280}{100}  = 2.8[/tex]

So, he'll need an average of 2.8 putts in average on any given green.

Which makes sense since 65% of the time, he needs 3 putts or more on the green.

The expected number of putts Madison will need for any given green is 2.85. This is calculated by multiplying each possible outcome by its probability and then summing these values.

The subject of this question is the calculation of an expected value in the context of a game of golf. The expected value is a weighted average, taking into account the probability of each event. Expected value calculations are common in probability and statistics.

In Madison's case, the expected number of putts can be calculated with the following formula:

E(X) = Σ [x * P(X = x)], where x is the outcome (number of putts) and P(X = x) is the probability of that outcome.

Applying the probabilities and outcomes given: E(X) = 1(0.15) + 2(0.20) + 3(0.35) + 4(0.30) = 2.85

So, the expected value of the number of putts Madison will need for any given green is 2.85.

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Answer:

The length of the third side could be 9 ft

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

In this problem

Let

c-----> the length of the third side, in feet

Applying the Triangle Inequality Theorem

1) [tex]6+10>c[/tex] -------> [tex]c<16\ ft[/tex]

2) [tex]c+6>10[/tex] -----> [tex]c>4\ ft[/tex]

so

The length of the third side must be greater than 4 ft and less than 16 ft

Remember that

The scalene triangle has three different sides

therefore

The length of the third side could be 9 ft

Answer:

2.25 hours for the man and 1.83 hours for the woman.

Step-by-step explanation:

We first find the number of calories consumed by both the man and the woman.

The man's calories are:

750+400+225 = 1375

The woman's calories are:

370+400+0 = 770

The man burns 610 calories per hour.  This means to find the number of hours, we divide the number of calories by the rate burned per hour:

1375/610 = 2.25 hours

The woman burns 770 calories per hour.  This means to find the number of hours, we divide the number of calories by the rate burned per hour:

770/420 = 1.83 hours

A 190-pound man needs to shovel snow for approximately 2.25 hours, and a 130-pound woman needs to shovel for approximately 1.83 hours to burn off the calories from their Burger King meal.

The question involves calculating the time it takes for a 190-pound man and a 130-pound woman to burn off the calories consumed from a meal at Burger King through the physical activity of shoveling snow. The man consumed a total of 1375 Calories (750 Cal for BK Big Fish sandwich, 400 Cal for medium french fries, and 225 Cal for a large Coke). The woman consumed a total of 770 Calories (370 Cal for a basic hamburger, 400 Cal for medium french fries, and 0 Cal for a diet Coke).

To find out how long each person needs to shovel snow to burn off the lunch calories, we divide the total number of calories consumed by the rate at which they burn calories while shoveling snow.

For the man: 1375 Calories / 610 Cal/h = approximately 2.25 hours.

For the woman: 770 Calories / 420 Cal/h = approximately 1.83 hours.

Answer:

  [tex]v\sqrt[28]{v^{13}}[/tex]

Step-by-step explanation:

The exponent rules that apply are ...

[tex](a^b)(a^c)=a^{b+c}\\\\a^{\frac{b}{c}}=\sqrt[c]{a^b}[/tex]

Using these rules for your product, we have ...

[tex]v^{\frac{3}{4}}\times v^{\frac{5}{7}}=v^{\frac{3}{4}+\frac{5}{7}}\\\\=v^{\frac{41}{28}}=v\cdot v^{\frac{13}{28}}=v\sqrt[28]{v^{13}}[/tex]

let's not forget that a function and its inverse have a domain <-> range relationship, namely, if the original function has a point of say (3 , 7 ), then its inverse function will have a point of (7 , 3 ), the same pair just flipped sideways.

[tex]\bf (g\circ f^{-1})(x)\implies g(~~~f^{-1}(x)~~~) \\\\\\ (g\circ f^{-1})(2)\implies g(~~~f^{-1}(2)~~~) \\\\[-0.35em] ~\dotfill\\\\ \textit{so let's firstly find out what is }f^{-1}(2)[/tex]

we don't have an f⁻¹(x), darn!! but but but, we do have an f(x) on the left-hand-side graph, and it has a pair where y = 2, namely ([ ] , 2), so then, f⁻¹(x) will have the same pair but sideways, let's inspect f(x).

hmmmmmm when y = 2, x = 0, notice the y-intercept on the graph, ( 0, 2 ).

so then, that means that f⁻¹(x) has a pair sideways of that, namely ( 2, 0), or f⁻¹(2) = 0.

so then, g(  f⁻¹(2)  ), is really the same as looking for g(  0  ), well then, what is "y" when x = 0 on g(x)?  let's inspect the right-hand-side graph.

hmmmmmmmmmmm  notice, the point is at ( 0 , 2 ), namely when x = 0, y = 2.

[tex]\bf (g\circ f^{-1})(2)\implies g(~~~f^{-1}(2)~~~)\implies g(0)\implies 2[/tex]

Answer:6

Step-by-step explanation: 1,000 divided by 7 is 994 with a remainder of six. Which means the principal had six left

To determine the number of apples John picks on the 10th day, we use the formula for the nth term of an arithmetic sequence. Given the first day's pick at 150 apples and an increase of 100 apples each day, we find that John picks 1050 apples on the 10th day.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the preceding term.

In this case, the first term (the number of apples picked on the first day) is 150, and the common difference (the increase each day) is 100 apples.

To find the number of apples picked on the 10th day, we use the formula for the nth term of an arithmetic sequence, which is:

an = a1 + (n - 1) × d

Where an is the nth term, a1 is the first term, n is the term number, and d is the common difference. For the 10th day:

a10 = 150 + (10 - 1) × 100

a10 = 150 + 9 × 100

a10 = 150 + 900

a10 = 1050

Therefore, John picks 1050 apples on the 10th day.

Answer:

The total area of the side of the house in the drawing is [tex]1.4\ in^{2}[/tex]

Step-by-step explanation:

step 1

Convert the actual dimensions of the side view of a house to the dimensions of the drawing

The scale of the drawing is [tex]\frac{1}{20}\frac{in}{ft}[/tex]

so

[tex]20\ ft=20/20=1\ in[/tex]

[tex]24\ ft=24/20=1.2\ in[/tex]

[tex]8\ ft=8/20=0.4\ in[/tex]

The total area is equal to the area of rectangle plus the area of triangle

so

[tex]A=(1)(1.2)+\frac{1}{2}(1)(0.4)=1.4\ in^{2}[/tex]

Assuming the question is "at what rate did the chemist heat the solution," the answer is the chemist heated the solution at +4.5 degrees Celsius per minute.

75-21=54

54/12=4.5

Answer: 2830.40

Step-by-step explanation:

By using mathematical formulas for calculating compound interest and the total payment of an installment loan, and then subtracting the original loan principal, the total interest paid on the loan is identified as $9,830.40.

To solve this problem, use the formula for the compound interest on a loan: A = P(1 + r/n)^(nt), where:

Since Randy is not going to start paying off his loan until 10 months later, the money will compound for 20 years and 10 months. Convert 10 months into years we get 10/12 = 0.833 years. Therefore, t = 20 + 0.833 = 20.833 years.

The loan was compounded monthly which means n = 12 and the rate is r = 3.6/100 = 0.036. Now you can substitute these values into the formula.

Next, find the total amount paid over the entire period of the loan by using the formula for the total payment of an installment loan: M = P*r*(1 + r)^n / [(1 + r)^n – 1], where M is monthly payment.

Subtract the principal from the total payment to find the total interest paid. From the given options, it appears that the answer is B.) $9,830.40

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[tex] \frac{5 \: = \: number \: of \: favorable \: outcomes}{6 \: = \: number \: of \: possible \: outcomes} [/tex]

Since there are 6 possible outcomes, that will become the denominator. In addition, since we are trying to find the probability of rolling 5 numbers out of that 6, 5 would be the numerator.

So the answer is,

[tex] \frac{5}{6} [/tex]

The probability that the number is 2,6,3,4, or 1 is 5/6.

Probability is the ratio that shows the likelihood that an event will occur from a given set of events.

A cube has six sides. Each side has a unique number.

We have to find the probability of getting 2,6,3,4, or 1.

The total number of favorable events = 5

The sample space has 6 events.

Therefore, the probability is given by 5/6.

Therefore, we have found the probability that the number is 2,6,3,4, or 1 to be 5/6.

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Answer:

If the angle is in degrees, when taking the tangent, make sure your calculator is in Degree mode.

I hope this helps.

Answer:

Step-by-step explanation:

For f(x) = 4x + 3 and g(x) = 9x

(a) (f o g) (x)

= f (g (x))

= f (9x)

= 4(9x) +3

= 36x + 3

Its domain is any real number.

(b) (g o f) (x)

= g (f (x))

= g (4x + 3)

= 9 (4x + 3)

= 36x + 27

Again its domain is any real number.

(c) (f o f) (x)

= f (f (x))

= f (4x + 3)

= 4(4x + 3) + 3

= 16x + 12 + 3

= 16x + 15

Again its domain is any real number.

(d) (g o g) (x)

= g ( g (x))

= g (9x)

= 9(9x)

= 81x

Again its domain is any real number.

Answer:

solution given:

f(x) = 4x + 3

g(x) = 9x

answer:

a.fog(x)=f(9x)=4×9x+3=36x+3

domain=real number

b.gof (x)=g(4x+3)=9(4x+3)=36x+26

domain=real number

c.fof(x)=f(4x+3)=4(4x+3)+3=16x+12+3

=16x+15

domain: real number

d.

gog(x)=g(9x)=9×9x=81x

domain: real number.

Answer:

20

Step-by-step explanation:

You multiply the 80 and the 18 and then you add 82

Answer:

The analysis of your expresson is given in the images below.

Please see attached pictures.

Answer:

$386794

Step-by-step explanation:

To be able to find how much we get in 5 years, we need to base it off the initial salary value.

So in the first year we get.

$70,000

To get how much we get in the 2nd year we add the extra 5%.

2nd year salary = (1.05)70000

2nd year salary = 73500

Now we continue to do that until the 5th year

3rd year = (1.05)73500

3rd year = 77175

4th year = (1.05) + 77175

4th year = 81033.75

5th year = (1.05) + 81033.75

5th year = 85085.44

Now we add them all up to get the total.

70000 + 73500 + 77175 + 81033.75 + 85085.44 = $386794.19 or $386794

Reflection over x-axis, shift down 5 units.

Answer:

Option B is correct.

Step-by-step explanation:

Given Parent Function, f(x) = |x|

Transformed function, f(x) = - |x| + 5

In transformed function, f(x) = -|x|

Represent that parents function is first reflected ove x - axis.

then in transformed function, f(x) = -|x| + 5

represent that after reflection function is shifted 5 unit in upward direction.

Therefore, Option B is correct.

Answer:

x=-5

Step-by-step explanation:

Set up the rational expression with the same denominator over the entire equation.

2x-2/6=3x+3/6

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

2x−2=3x+3

Move all terms containing x to the left side of the equation.

−x−2=3

Move all terms not containing x to the right side of the equation.

-x=5

Multiply each term in x=−5 by −1

x=−5

Answer:

[tex]A=53.13\°[/tex]

Step-by-step explanation:

The figure shows a right triangle.

To calculate the measure of the angle A, you can use the inverse trigonometric function arctangent:

[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]

Identify the angle [tex]\alpha[/tex], the opposite side and the adjacent side:

[tex]\alpha=A\\opposite=4cm\\adjacent=3cm[/tex]

Substitute into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex].

The measure of the angle A is:

[tex]A=arctan(\frac{4}{3})\\\\A=53.130\°[/tex]

Rounded to the nerarest hundreth:

[tex]A=53.13\°[/tex]

The answer is m∠A = 53.13 °