Which of the following statements are mathematical statement?


P: Math is not hard.
Q: Bill Gates is the founder of Microsoft.


A. P only

B. Q only

C. P and Q

D. None

Answer:

  153 feet

Step-by-step explanation:

The change in elevation is the difference between his ending elevation and his starting elevation:

  -108 -(-261) = 153 . . . feet

Step-by-step explanation:

Diameter, D = 42 feet

Circumference = πD = π x 42 = 131.95 feet

Number of rotations per minute = 3

Total time = 5 minutes

Total rotations = 5 x 3 = 15

Distance traveled per rotation = 131.95 feet

Distance traveled in 15 rotations = 15 x 131.95 = 1978 feet

Option C is the correct answer.

Final answer:

To determine the gross earnings for 40 hours worked at a pay rate of $6.50 per hour, multiply the pay rate by hours. The gross earnings would be $260.00.

Explanation:

To calculate the gross earnings given the pay rate and hours worked, we use a simple multiplication. However, there is an additional consideration mentioned in Exercise 3.1, which states that the employee should receive 1.5 times the hourly rate for hours worked above 40 hours. Therefore, the calculation involves two steps if the number of hours exceeds 40.

Calculation:

In this particular case, the student only worked 40 hours at a pay rate of $6.50 per hour. Using the first formula, the gross earnings would be:
Gross Earnings = $6.50/hour × 40 hours = $260.00

Answer:

tm = tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] }

Xm = Xₐ = (v₀m)/k - ({m²g}/k²) ㏑(1+{kv₀/mg})

Step-by-step explanation:

Note, I substituted maximum time tm = tₐ and maximum height Xm = Xₐ

We will use linear ordinary differential equation (ODE) to solve this question.

Remember that Force F = ma in 2nd Newton law, where m is mass and a is acceleration

Acceleration a is also the rate of change in velocity per time. i.e a=dv/dt

Therefore F = m(dv/dt) = m (v₂-v₁)/t

There are two forces involved in this situation which are F₁ and F₂, where F₁ is the gravitational force and F₂ is the air resistance force.

Then, F = F₁ + F₂ = m (v₂-v₁)/t

F₁ + F₂ = -mg-kv = m (v₂-v₁)/t

Divide through by m to get

-g-(kv/m) = (v₂-v₁)/t

Let (v₂-v₁)/t be v¹

Therefore, -g-(kv/m) = v¹

-g = v¹ + (k/m)v --------------------------------------------------(i)

Equation (i) is a inhomogenous linear ordinary differential equation (ODE)

Therefore let A(t) = k/m and B(t) = -g --------------------------------(ia)

b = ∫Adt

Since A = k/m, then

b = ∫(k/m)dt

The integral will give us b = kt/m------------------------------------(ii)

The integrating factor will be eᵇ = e ⁽k/m⁾

The general solution of velocity at any given time is

v(t) = e⁻⁽b⁾ [ c + ∫Beᵇdt ] --------------------------------------(iiI)

substitute the values of b, eᵇ, and B into equation (iii)

v(t) = e⁻⁽kt/m⁾ [ c + ∫₋g e⁽kt/m⁾dt ]

Integrating and cancelling the bracket, we get

v(t) = ce⁻⁽kt/m⁾ + (e⁻⁽kt/m⁾ ∫₋g e⁽kt/m⁾dt ])

v(t) = ce⁻⁽kt/m⁾ - e⁻⁽kt/m⁾ ∫g e⁽kt/m⁾dt ]

v(t) = ce⁻⁽kt/m⁾ -mg/k -------------------------------------------------------(iv)

Note that at initial velocity v₀, time t is 0, therefore v₀ = v(t)

v₀ = V(t) = V(0)

substitute t = 0 in equation (iv)

v₀ = ce⁻⁽k0/m⁾ -mg/k

v₀ = c(1) -mg/k = c - mg/k

Therefore c = v₀ + mg/k  ------------------------------------------------(v)

Substitute equation (v) into (iv)

v(t) = [v₀ + mg/k] e⁻⁽kt/m⁾ - mg/k ----------------------------------------(vi)

Now at maximum height Xₐ, the time will be tₐ

Now change V(t) as V(tₐ) and equate it to 0 to get the maximum time tₐ.

v(t) = v(tₐ) = [v₀ + mg/k] e⁻⁽ktₐ/m⁾ - mg/k = 0

to find tₐ from the equation,

[v₀ + mg/k] e⁻⁽ktₐ/m⁾ = mg/k

e⁻⁽ktₐ/m⁾ = {mg/k] / [v₀ + mg/k]

-ktₐ/m = ㏑{ [mg/k] / [v₀ + mg/k] }

-ktₐ = m ㏑{ [mg/k] / [v₀ + mg/k] }

tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] }

Therefore tₐ = -m/k ㏑{ [mg/k] / [v₀ + mg/k] } ----------------------------------(A)

we can also write equ (A) as tₐ = m/k ㏑{ [mg/k] [v₀ + mg/k] } due to the negative sign coming together with the In sign.

Now to find the maximum height Xₐ, the equation must be written in terms of v and x.

This means dv/dt = v(dv/dx) ---------------------------------------(vii)

Remember equation (i) above  -g = v¹ + (k/m)v

Given that dv/dt = v¹

and -g-(kv/m) = v¹

Therefore subt v¹ into equ (vii) above to get

-g-(kv/m) = v(dv/dx)

Divide through by v to get

[-g-(kv/m)] / v = dv / dx -----------------------------------------------(viii)

Expand the LEFT hand size more to get

[-g-(kv/m)] / v = - (k/m) / [1 - { mg/k) / (mg/k + v) } ] ---------------------(ix)

Now substitute equ (ix) in equ (viii)

- (k/m) / [1 - { mg/k) / (mg/k + v) } ] = dv / dx

Cross-multify the equation to get

- (k/m) dx = [1 - { mg/k) / (mg/k + v) } ] dv --------------------------------(x)

Remember that at maximum height, t = 0, then x = 0

t = tₐ and X = Xₐ

Then integrate the left and right side of equation (x) from v₀ to 0 and 0 to Xₐ respectively to get:

-v₀ + (mg/k) ㏑v₀ = - {k/m} Xₐ

Divide through by - {k/m} to get

Xₐ = -v₀ + (mg/k) ㏑v₀ / (- {k/m})

Xₐ = {m/k}v₀ - {m²g}/k² ㏑(1+{kv₀/mg})

Therefore Xₐ = (v₀m)/k - ({m²g}/k²) ㏑(1+{kv₀/mg}) ---------------------------(B)

The question is about an object projected upwards under gravity and a certain resistance. The equations of motion will be non-linear due to the nature of the resistance. Solving these equations metaphorically or numerically will yield the maximum height and time taken to reach that height.

The subject matter here is mechanics which falls under Physics. Given that there is a body of constant mass m projected upwards with an initial velocity v0 and the medium being passed through provides a resistance of k|v|, the equations of motion under this resistance will be non-linear.

The question here pertains to the calculations related to an object moving upwards under a given resistance and gravity. To obtain the maximum height achieved by the body xm and the time taken to reach that tm, we employ the trick of non-dimensionalisation. First, we observe the units of all physical quantities and using this, we can introduce reduced physical quantities which are dimensionless.

Unfortunately, these non-linear equations don’t have a neat analytical solution, and methods of approximation or numerical techniques might be necessary to solve them for particular initial conditions.

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Answer:

The given statement describe inferential statistics.    

Step-by-step explanation:

Descriptive Statistic:

Inferential Statistic:

Given Scenario:

"Based on a sample of 170 truck drivers, there is evidence to indicate that, on average, independent truck drivers earn more than company-hired truck drivers."

Thus, this is an example of a inferential statistics as a sample was used to estimate the population.

Here,

Sample:

Sample of 170 truck drivers

Population:

All truck drivers.

With the help of a sample, we approximated the population, thus, this statement describe inferential statistics.

The statement is an example of inferential statistics, as it makes a general conclusion about a population (all truck drivers) based on a sample.

The statement "Based on a sample of 170 truck drivers, there is evidence to indicate that, on average, independent truck drivers earn more than company-hired truck drivers" describes the use of inferential statistics. This type of statistics is used when analysts want to make predictions or inferences about a population based on the data collected from a sample. In contrast, descriptive statistics are used simply to describe what the data show, such as calculating averages, medians, ranges, and so on. Since the statement indicates a broader conclusion about the earnings of independent versus company-hired truck drivers in general, based on a sample, it utilizes inferential statistics.

Answer:

3.25

Step-by-step explanation:

36:24 = 2:3

6x-6 = (2/3)3x+7

x=3.25

Answer:

11=x

Step-by-step explanation:

AB   AC

    =

ED   EC

36:24=6x−6:3x+7

108x+252=144x−144

396=36x

11=x

Answer:

81.85% of the workers spend between 50 and 110 commuting to work

Step-by-step explanation:

We can assume that the distribution is Normal (or approximately Normal) because we know that it is symmetric and mound-shaped.

We call X the time spend from one worker; X has distribution N(μ = 70, σ = 20). In order to make computations, we take W, the standarization of X, whose distribution is N(0,1)

[tex] W = \frac{X-μ}{σ} = \frac{X-70}{20} [/tex]

The values of the cummulative distribution function of the standard normal, which we denote [tex] \phi [/tex] , are tabulated. You can find those values in the attached file.

[tex]P(50 < X < 110) = P(\frac{50-70}{20} < \frac{X-70}{20} < \frac{110-70}{20}) = P(-1 < W < 2) = \\\phi(2) - \phi(-1)[/tex]

Using the symmetry of the Normal density function, we have that [tex] \phi(-1) = 1-\phi(1) [/tex] . Hece,

[tex]P(50 < X < 110) = \phi(2) - \phi(-1) = \phi(2) - (1-\phi(1)) = \phi(2) + \phi(1) - 1 = \\0.9772+0.8413-1 = 0.8185[/tex]

The probability for a worker to spend that time commuting is 0.8185. We conclude that 81.85% of the workers spend between 50 and 110 commuting to work.

Answer:

5 , 4.5, 13.5 and 40.5

Step-by-step explanation:

Since the numbers are in geometric progression, their form is essentially:

a, ar, ar^2 and ar^3

Where a and r are first term and common ratio respectively.

From the information given in the catalog:

Third term is greater than the first by 12 while fourth is greater than second by 36.

Let’s now translate this to mathematics.

ar^2 - a = 12

ar^3 - ar = 36

From 1, a(r^2 - 1) = 12 and 2:

ar(r^2 - 1) = 36

From 2 again r[a(r^2 -1] = 36

The expression inside square bracket looks exactly like equation 1 and equals 12.

Hence, 12r = 36 and r = 3

Substituting this in equation 1,

a( 9 - 1) = 12

8a = 12

a = 12/8 = 1.5

Thus, the numbers are 1.5, (1.5 * 3) , (1.5 * 9), (1.5 * 27) = 1.5 , 4.5, 13.5 and 40.5

Final Answer:

The four numbers forming the geometric progression are 1.5, 4.5, 13.5, and 40.5.

Explanation:

Let's start by defining what a geometric progression (GP) is. A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Let's denote the four numbers in the GP as a, ar, ar², and ar³, where:
- a is the first term,
- r is the common ratio.
We've been given two conditions:
1. The third term is greater than the first by 12, which gives us the equation:
  ar² = a + 12
2. The fourth term is greater than the second by 36, which leads us to:
  ar³ = ar + 36
We need to solve this system of equations to find the values of a and r.
Starting with the first equation:
ar² = a + 12
We can subtract 'a' from each side to get:
ar - a = 12
Factor out 'a' from the left side:
a(r² - 1) = 12
Now notice that r² - 1 is a difference of squares and can be factored to (r + 1)(r - 1):
a(r + 1)(r - 1) = 12
This equation tells us that the product of 'a' and (r + 1)(r - 1) is 12. For now, let's keep this equation aside and look at the second condition.
Proceeding with the second equation:
ar = ar + 36
Subtract 'ar' from each side:
ar³ - ar = 36
Factor out 'ar':
ar(r² - 1) = 36
Again, we recognize a difference of squares in the parentheses, so we factor it:
ar(r + 1)(r - 1) = 36
This equation relates 'ar', and (r + 1)(r - 1), and tells us the product is 36.
Now, because we have a similar term in both equations, (r + 1)(r - 1), we can set the products equal to each other to find a relationship between 'a' and 'ar':
From the first equation, we have a(r + 1)(r - 1) = 12,
From the second equation, we have ar(r + 1)(r - 1) = 36.
Dividing the second equation by the first one gives us:
ar(r + 1)(r - 1) / a(r + 1)(r - 1) = 36 / 12
ar / a = 36 / 12
r = 3
Now that we have the value of 'r', let's substitute it back into either of the original equations to find 'a'. Let's use the first equation:
a(r² - 1) = 12
a(3² - 1) = 12
a(9 - 1) = 12
a(8) = 12
a = 12 / 8
a = 3 / 2
a = 1.5
Now we have both 'a' and 'r', which allows us to determine the four numbers in the GP:
The first number, a, is 1.5.
The second number, ar, is 1.5 * 3 = 4.5.
The third number, ar², is 4.5 * 3 = 13.5.
The fourth number, ar², is 13.5 * 3 = 40.5.
So, the four numbers forming the geometric progression are 1.5, 4.5, 13.5, and 40.5.

The correct answer is: Option number 4 (Last Option)

Step-by-step explanation:

Given inequality is:

-6x > 42

In order to solve the inequality,

Dividing both sides by 6

[tex]-\frac{6x}{6} > \frac{42}{6}\\-x > 7[/tex]

Multiplying by -1

[tex]x<7[/tex]

As the solution is x<7, this means that the number 7 will not be included in the solution and all numbers less than 7 will be a part of the solution.

The number which is not included in the solution is marked by a shallow circle on the number line.

Hence,

The correct answer is: Option number 4 (Last Option)

Keywords: Number line, inequality

Learn more about inequality at:

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Answer:

The total number of buns Mrs Klein made = 400

Step-by-step explanation:

Question

Mrs Klein made fruit buns. She sold 3/5 of it in morning and 1/4 of the remaining in the afternoon. If she sold 200 more buns in the morning than afternoon, how many buns did she make?

Given:

Mrs Klein sold  [tex]\frac{3}{5}[/tex]  of the buns in the morning.

Mrs Klein sold [tex]\frac{1}{4}[/tex]  of the remaining buns in the evening.

She sold 200 more buns in the morning than afternoon.

To find the total number of buns she make.

Solution:

Let the total number of buns be  =  [tex]x[/tex]

Number of buns sold in the morning will be given as =  [tex]\frac{3}{5}x[/tex]

Number of buns remaining = [tex]x-\frac{3}{5}x[/tex]

Number of buns sold in the evening will be given as =  [tex]\frac{1}{4}(x-\frac{3}{5}x)[/tex]

Difference between the number of buns sold in morning and evening = 200

Thus, the equation to find [tex]x[/tex] can be given as:

[tex]\frac{3}{5}x-\frac{1}{4}(x-\frac{3}{5}x)=200[/tex]

Using distribution:

[tex]\frac{3}{5}x-\frac{1}{4}x+(\frac{1}{4}.\frac{3}{5}x)=200[/tex]

[tex]\frac{3}{5}x-\frac{1}{4}x+\frac{3}{20}x=200[/tex]

Multiplying each term with the least common multiple of the denominators to remove fractions.

The L.C.M. of 4, 5 and 20  = 20.

Multiplying each term with 20.

[tex]20\times \frac{3}{5}x-20\times\frac{1}{4}x+20\times\frac{3}{20}x=20\times 200[/tex]

[tex]12x-5x+3x=4000[/tex]

[tex]10x=400[/tex]

Dividing both sides by 10.

[tex]\frac{10x}{10}=\frac{4000}{10}[/tex]

∴ [tex]x=400[/tex]

Thus, total number of buns Mrs Klein made = 400

Answer:

The type of sample is Stratified sampling.

Step-by-step explanation:

Consider the provided information.

Types of sampling.

Here the population is divided into groups of males and females therefore it is stratified sampling.

Hence, the type of sample is Stratified sampling.

Answer:

It's A

Step-by-step explanation:

Trust Me

Answer:

the opportunity cost of producing each additional car REMAINS CONSTANT

Answer:

The youngest brother's age is 21 years.

Step-by-step explanation:

Given:

The ages of 3 brothers are consecutive integers.

If the oldest brothers age is decreased by twice the youngest brother age the result is -19

To find the age of the youngest brother.

Solution:

Let the age of youngest broth be = [tex]x[/tex]  years

The ages are consecutive integers.

So, age of the next older brother will be = [tex](x+1)[/tex] years

The age of the oldest brother will be = [tex](x+2)[/tex] years

The oldest brothers age is decreased by twice the youngest brother age.

The above statement can be represented as:

⇒ [tex](x+2)-2x[/tex]

Simplifying.

⇒ [tex]x-2x+2[/tex]

⇒[tex]-x+2[/tex]

The result for the above expression = -19.

So, we have:

[tex]-x+2=-19[/tex]

Subtracting both sides by 2.

[tex]-x+2-2=-19-2[/tex]

[tex]-x=-21[/tex]

Multiplying both sides by -1.

∴ [tex]x=21[/tex]

Thus, the youngest brother's age is 21 years

Answer:

36

Step-by-step explanation:

Given that

[tex]R_n = R_{n+1} +3[/tex] is given

First term is 15

This is an arithmetic series with a =15 and d =3

If n is the number of terms, then we have

Sum of n terms = 36 xn = 36n

But as per arithmetic progression rule

[tex]S_n = \frac{n}{2} [2a+(n-1)d]\\= \frac{n}{2} [30+(n-1)3]=36n[/tex]

[tex]72 = 30+3n-3\\n-=15[/tex]

When there are n terms we have middle term is the 8th term

Hence median is 8th term

=[tex]a_8 = 15+7(3) \\=36[/tex]

Answer:

11 different combinations

Step-by-step explanation:

A salesman packed 3 shirts and 5 ties.

With one shirt, he could wear all 5 ties = 5 combinations

With another shirt, he could wear 4 ties  = 4 combinations

With the third shirt, he could wear only 2 ties= 2 combinations

number of different combinations= [tex]5+4+2=11[/tex]

so answer is 11

Answer: the number of ducks in the field is 25

the number of pigs in the field is 9

Step-by-step explanation:

Let x represent the number of ducks in the field.

Let y represent the number of pigs in the field.

A duck has one head and a pig also has one head.

The number of ducks and pigs in a field totals 34. This means that

x + y = 34

The total number of legs among them is 86. Assuming each duck has exactly two legs and each pig has exactly four legs, it means that

2x + 4y = 86 - - - - - - - - - - -- - 1

Substituting x = 34 - y into equation 1, it becomes

2(34 - y) + 4y = 86

68 - 2y + 4y = 86

- 2y + 4y = 86 - 68

2y = 18

y = 18/2 = 9

Substituting y = 9 into x = 34 - y, it becomes

x = 34 - 9 = 25

To find the number of ducks and pigs in the field, we can set up a system of equations and solve them. Using the given information and the equations x + y = 34 and 2x + 4y = 86, we can find that there are 25 ducks and 9 pigs in the field.

To solve this problem, we can use a system of equations. Let x represent the number of ducks and y represent the number of pigs. From the given information, we can set up two equations:

x + y = 34  (equation 1)

2x + 4y = 86  (equation 2)

Now, we can solve the system of equations. We can start by multiplying equation 1 by 2 to eliminate the x variable:

2(x + y) = 2(34)

2x + 2y = 68

Next, we can subtract equation 2 from this new equation:

(2x + 2y) - (2x + 4y) = 68 - 86

-2y = -18

Dividing both sides of the equation by -2 gives us:

y = 9

Substituting this value back into equation 1:

x + 9 = 34

x = 34 - 9

x = 25

Therefore, there are 25 ducks and 9 pigs in the field.

Answer:

Area of a square = Length × Length

Area of a triangle = 1/2 base × height

Area of a rectangle = Length × breadth

Area of a parallelogram = base × height

Area of a trapezoid = 1/2 × sum of parallel sides × height

Area of circle = π × square of the radius

Area of ellipse = π × product of major and minor radii

Area of equilateral triangle = 1/2 base × height

Step-by-step explanation:

The area of a square is calculated by multiplying the length by itself.

The area of a triangle is calculated by multiplying half the base of the triangle by its height

The area of a rectangle is found by multiplying the length of the rectangle by its breadth

The area of a parallelogram is calculated by multiplying the base of the parallelogram by its height

The area of a trapezoid is found by multiplying half the sum of the two parallel sides by its height

The area of a circle is calculated by multiplying pi by the square of the radius of the circle

The area of an ellipse is found by multiplying pi by the product of the major and minor radii of the ellipse

The area of an equilateral triangle is calculated by multiplying half the base of the triangle by its height. The height is calculated using Pythagoras theorem

Answer:

Emil's back pack weigh now [tex]5\frac{1}{8}\ pounds[/tex].

Step-by-step explanation:

Given:

Total Weight of backpack = [tex]6\frac{3}{8}\ pounds[/tex]

[tex]6\frac{3}{8}\ pounds[/tex] can be Rewritten as [tex]\frac{51}{8}\ pounds[/tex]

Weight of backpack =  [tex]\frac{51}{8}\ pounds[/tex]

Weight of Book 1 = [tex]\frac{3}{4}\ pound[/tex]

Weight of Book 2 = [tex]\frac{1}{2}\ pound[/tex]

We need to find weight of back pack after removing books.

Solution:

Now we can say that;

weight of back pack after removing books can be calculated by Subtracting Weight of Book 1 and Weight of Book 2 from Total Weight of backpack.

framing in equation form we get;

weight of back pack after removing books = [tex]\frac{51}{8}-\frac{3}{4}-\frac{1}{2}[/tex]

Now to solve the equation we will first make the denominator common using LCM.

weight of back pack after removing books =[tex]\frac{51\times1}{8\times1}-\frac{3\times2}{4\times2}-\frac{1\times4}{2\times4}=\frac{51}{8}-\frac{6}{8}-\frac{4}{8}[/tex]

Now the denominators are common so we will solve the numerator.

weight of back pack after removing books = [tex]\frac{51-6-4}{8}=\frac{41}{8}\ pounds \ \ OR \ \ 5\frac{1}{8}\ pounds[/tex]

Hence Emil's back pack weigh now [tex]5\frac{1}{8}\ pounds[/tex].

Answer: the company's annual profit if the price of their product is $32 is $3041

Step-by-step explanation:

A company's annual profit, P, is given by P = −x²+ 195x − 2175, where x is the price of the company's product in dollars.

To determine the company's annual profit if the price of their product is $32, we would substitute x = 32 into the given equation. It becomes

P = −32²+ 195 × 32 − 2175

P = −1024 + 6240 − 2175

P = $3041

Answer:

as v tends to c( speed of light), the mass of the particle moves towards an infinite value

Step-by-step explanation:

The concept applied here is the theory of relativity.

what the theory entails is the measurements of events i.e things that happen, where and when they happen and to what large extend are events seperated in space and time. Albert Einstein was the first to published his findings on the theory of relativity.

When velocity of particle approaches to velocity of light . then, mass of particle approaches to infinite value.

In theory of relativity, the mass of a particle with velocity v is given as,

                      [tex]m=\frac{m_{0}}{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]

where [tex]m_{0}[/tex] is the mass of the particle at rest and c is the speed of light.

When velocity v tends to velocity of light c.

                     [tex]m=\frac{m_{0}}{\sqrt{1-\frac{c^{2} }{c^{2} } } }\\\\m=\frac{m_{0}}{\sqrt{1-1} } \\\\m=\frac{m_{0}}{ 0} =\infty[/tex]

Hence, when velocity of particle approaches to velocity of light . then, mass of particle approaches to infinite value.

Learn more about the speed of light here:

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ANSWER: True

EXPLANATION:

The statement is true. Any correctly constructed frequency distribution is valid. However, some choices for the categories or classes give more information about the shape of the distribution.

Answer:19+25+10+14+80 gives you 148

Step-by-step explanation:

Tommy earned approximately $68 altogether.

Given:

- Clothes: 19%

- Food: 25%

- Savings: 10%

- Other: 14%

To find out how much Tommy earned altogether, we need to detemine what percentage of his earnings $80 on entertainment represents.

First, we sum up these percentages to find out what portion of his earnings $80 represents:

Total percentage spent = Clothes + Food + Savings + Other

Total percentage spent = 19% + 25% + 10% + 14%

Total percentage spent = 68%

Now, we need to find out how much $80 represents as a percentage of his total earnings:

Percentage of earnings spent on entertainment = (Amount spent on entertainment / Total percentage spent) * 100%

Percentage of earnings spent on entertainment = (80 / 68) * 100%

Percentage of earnings spent on entertainment ≈ 117.65%

Now, to find out how much Tommy earned altogether, we need to determine the total amount represented by 100%, which is his total earnings. Since $80 represents approximately 117.65% of his earnings:

Total earnings = (Amount spent on entertainment / Percentage of earnings spent on entertainment) * 100%

Total earnings = (80 / 117.65%) * 100%

Total earnings ≈ $68

Therefore, Tommy earned approximately $68 altogether.

Answer: right-tailed

Step-by-step explanation:

By considering the given information , we have

Null hypothesis : [tex]H_0: p\leq0.6[/tex]

Alternative hypothesis : [tex]H_a: p>0.6[/tex]

The kind of test (whether  left-tailed, right-tailed, or​ two-tailed.) is based on alternative hypothesis.

Since the given alternative hypothesis([tex]H_a[/tex]) is right-tailed , so out test is a right-tailed test.

Hence, the correct answer is "right-tailed".

Answer:

a. [1,2]

[tex] m= \frac{9-0}{2-1}=9[/tex]

b. [1,3.5]

[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]

c. [1,5]

[tex] m =\frac{0-0}{5-1}=0[/tex]

d. [0,3.5]

[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]

So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.

a. [1,2]

[tex] m= \frac{9-0}{2-1}=9[/tex]

Step-by-step explanation:

Assuming that we have the figure attached for the function. For this case we just need to quantify the slope given by:

[tex] m = \frac{\Delta y}{\Delta x}[/tex]

For each interval and the greatest slope would be the interval on which the volume of the box is changing at the fastest average rate

a. [1,2]

[tex] m= \frac{9-0}{2-1}=9[/tex]

b. [1,3.5]

[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]

c. [1,5]

[tex] m =\frac{0-0}{5-1}=0[/tex]

d. [0,3.5]

[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]

So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.

a. [1,2]

[tex] m= \frac{9-0}{2-1}=9[/tex]

The correct answer is A. [1,2].

To determine over which interval the volume of the box changes at the fastest average rate, we need to find the average rate of change of the volume function ( V(x) ) over the given intervals and compare them.
The volume ( V(x) ) of the box is given by:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \][/tex]
We first need to express ( V(x) ) in a simplified form. Let's expand the expression:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \]\[ V(x) = (x + 1)(x^2 - 6x + 5) \]\[ V(x) = x(x^2 - 6x + 5) + 1(x^2 - 6x + 5) \]\[ V(x) = x^3 - 6x^2 + 5x + x^2 - 6x + 5 \]\[ V(x) = x^3 - 5x^2 - x + 5 \][/tex]
Now, we calculate the average rate of change over each interval. The average rate of change of ( V(x) ) over an interval ([a, b]) is given by:
[tex]\[ \text{Average Rate of Change} = \frac{V(b) - V(a)}{b - a} \][/tex]
We need to compute this for each interval provided.
1. Interval [1, 2]:
[tex]\[ V(1) = (1 + 1)(5 - 1)(1 - 1) = 0 \]\[ V(2) = (2 + 1)(5 - 2)(2 - 1) = 3 \times 3 \times 1 = 9 \]\[ \text{Average Rate of Change} = \frac{V(2) - V(1)}{2 - 1} = \frac{9 - 0}{2 - 1} = 9 \][/tex]
2. Interval [1, 3.5]:
[tex]\[ V(1) = 0 \]\[ V(3.5) = (3.5 + 1)(5 - 3.5)(3.5 - 1) = 4.5 \times 1.5 \times 2.5 = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(1)}{3.5 - 1} = \frac{16.875 - 0}{3.5 - 1} = \frac{16.875}{2.5} = 6.75 \][/tex]
3. Interval [1, 5]:
[tex]\[ V(1) = 0 \]\[ V(5) = (5 + 1)(5 - 5)(5 - 1) = 6 \times 0 \times 4 = 0 \]\[ \text{Average Rate of Change} = \frac{V(5) - V(1)}{5 - 1} = \frac{0 - 0}{5 - 1} = 0 \][/tex]
4. Interval [0, 3.5]:
[tex]\[ V(0) = (0 + 1)(5 - 0)(0 - 1) = 1 \times 5 \times -1 = -5 \]\[ V(3.5) = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(0)}{3.5 - 0} = \frac{16.875 - (-5)}{3.5 - 0} = \frac{16.875 + 5}{3.5} = \frac{21.875}{3.5} \approx 6.25 \][/tex]
Comparing these average rates of change:
[tex]\([1, 2]\): 9\\ \([1, 3.5]\): 6.75\\ \([1, 5]\): 0\\ \([0, 3.5]\): 6.25[/tex]
The interval where the volume of the box is changing at the fastest average rate is [tex]\([1, 2]\)[/tex], with an average rate of change of 9.
Therefore, the correct answer is: A.[tex]\([1, 2]\)[/tex].

Complete question :

DC=14

Explanation

consider triangle ADB

<BAD=54°

sin<BAD=opposite side/ hypotenuse

sin 54°=BD/BA

BD=BA sin 54°=20*0.8=16

consider triangle BDC

cos <BCD=adjacent side/hypotenuse

=DC/BC

cos 28°=DC/BC

DC=cos28°  *BC

=0.88*16=14.08

Step-by-step explanation:

√(m + n) = √m + √n

Square both sides:

m + n = m + 2√(mn) + n

Simplify:

0 = 2√(mn)

mn = 0

The equation is only true if either m or n (or both) is 0.

Final answer:

The square root of the sum of two numbers is not equal to the sum of the square roots of those numbers.

Explanation:

No, √m+n is not equal to √m + √n for all values of m and n. This is because of the nature of square roots and how they interact with addition. Taking the square root of a sum is not the same as the sum of the square roots. For example, for m = 4 and n = 9, √4 + √9 = 2 + 3 = 5, but √(4 + 9) = √13, which is not equal to 5. This example illustrates how the two expressions yield different results, emphasizing the importance of understanding the properties of square roots in mathematical operations.

Answer:let us compare the following pairs of power of 10,9×10^6 ÷3×10^12=3×10^-6

Step-by-step explanation:

Comparing pairs of power of 10 involve applying principle of indices.in what is known as the laws of indices

Law1 states that X^a ×X^b=X^(a+b) meaning that multiplication of indices results to addition of the indexes raise as exponenet of 10, similarly a division as in the answer above always lead to substraction of the indexes as seen in the example 9×10^6/3×10^12 will becomen9÷3×10^(6-12)=3×10^-6.

Answer:

  x = -2.4

Step-by-step explanation:

  f(x) = -1/4x -3

  x = -1/4x -3 . . . . .  the desired value of f(x)

  5/4x = -3 . . . . . . . add 1/4x

  x = -12/5 . . . . . . . multiply by 4/5, the inverse of 5/4

__

Check

  -1/4(-2.4) -3 = 0.6 -3 = -2.4 = x . . . . answer checks OK