The difference of two whole numbers is 2. If two times the square of the smaller number added to three times the square of the larger number equals 140, find the numbers.

Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

Answer:

there are 42

Step-by-step explanation:

because 12 + 30 = 42 hope this helps =)

Answer:

70 I guess is the correct answer

53)

median of

6, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 18

n=15

median= X(n+1 )/2

median = x8

median=10

answer

the median is the number in the middle of the data, in this case the 8th value or the number 10

C)10

54)

we are request for the third quartil

since we have 15 values we split this data into 4 datasets each with (n+1 )/2 numbers

6, 6, 6, 7

8, 9, 9, 10,

11, 12, 12, 13,

14, 15, 18

the third quartil can be solve as

then the answer is B)14

Answer:

AMEN

Step-by-step explanation:

.

Hence, there is a 0.68 percent probability that the fifth driver will be the one that police officer summons over while wearing a safety belt.

The word "probability" derives from the Latin word "propitiate," which means "credibility, probability," from the noun probabilism in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

Part A:

The likelihood that precisely 3 drivers are buckled up can be determined using the binomial probability formula:

P(X = 3) = (5 choose 3) × (0.68)³ × (0.32)²

Where (5 choose 3) = 10 is the number of ways to choose 3 drivers out of 5.

P(X = 3) = 10 × 0.68³ × 0.32²

P(X = 3) = 0.267

Consequently, there is a 0.267 percent chance that all 3 drivers are buckled up.

Part B:

The fifth driver will be pulled by by the police officer since 4 other drivers have already been stopped. We are looking for the likelihood that the motorist is wearing a safety belt.

Since 68% of drivers are safety belt wearers, there is a 0.68 percent chance that the following motorist will be as well.

Thus, there is a 0.68 percent chance that the next vehicle the police officer pulls over is driven by a person wearing a safety belt.

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Answer:

26 inches

Step-by-step explanation:

Tan = opp/adj = height/base

tan 21 = 10/base

base = 10/tan21

base = 26.050890646938015

Rounded

26 inches

Answer:

26 in. to nearest inch.

Step-by-step explanation:

tan 21 =  10 / L   where L is the length of the base.

L = 10 / tan 21

= 26.05 in.

Answer:  B:  3x + 4 = 3(x - 5)   (has no solution)

Step-by-step explanation:  (these have solutions)

C:        X+ 6 = 6x = 6/5

A:      x + 3 = 5(x+3) = −3

D:        5x + 2 = 4x - 3  =   −5

Answer:

b

Step-by-step explanation:

I had this question before

The scale used to measure the number of inches of a 300-foot-long football field is thousands so, option A is correct.

The relationship between the dimensions on a model and the equivalent dimensions on the real figure or object is represented by the ratio known as scale. It aids in transferring smaller-scale representations of real-world objects to paper.

We employ a scale to precisely express our dimensions when we depict an actual object on paper. A scale of 1:1, for instance, means that the size of 1 unit in the drawing corresponds to the size of 5 units in the real world. A scale of 1:5 is evident, for instance, if a giraffe that stands 150 inches tall in real life is depicted on the drawing as 30 inches tall.

Given:

300-foot-long football field,

300 comes in the range of 100 - 1000,

Thus, the scale would be thousands.

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Answer:

9.95h + 5  ≤ 125

Step-by-step explanation:

let 'h' = number of hats

Answer:

17 hours

Step-by-step explanation:

We first need to find the hourly rate:

156 / 12 = 13

Hourly Rate: $13

Now we can divide 221 by 13, this gives us 17.

That means that Frank will have to work 17 hours to make $221.

Hope this helps!

Answer:

\(\huge\boxed{\sf 252\ in.\²}\)

Step-by-step explanation:

TOP and BOTTOM:

Surface Area = 2 ( Length * Breadth)

SA = 2 ( 6 * 12 )

SA = 2 (72)

SA = 144 in. ²

FRONT and BACK:

SA = 2 ( Length * Breadth)

SA = 2 ( 3*12 )

SA = 2 (36)

SA = 72 in.²

SIDES:

SA = 2 ( Length * Breadth )

SA = 2 ( 3 * 6 )

SA = 2 (18)

SA = 36 in.²

Adding all to get the SA of rectangular prism:

= 144 + 72 + 36

= 252 in.²

\(\rule[225]{225}{2}\)

Hope this helped!

Answer: each base angle in an isosceles right triangle measures 45 degrees.

Step-by-step explanation:

In an isosceles right triangle, two sides have equal lengths, and one angle is a right angle (90 degrees).

Since it is an isosceles triangle, the two base angles (the angles opposite the equal sides) must be congruent, meaning they have the same measure.

To find the measure of each base angle, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let's denote the measure of each base angle as "x". Then, the sum of the three angles in the triangle can be expressed as:

x + x + 90 = 180

Simplifying the equation:

2x + 90 = 180

Subtracting 90 from both sides:

2x = 90

Dividing both sides by 2:

x = 45

\( cos(A) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc} \)

The cos A will be b/c

Cosine function in a triangle is the ratio of the adjacent side to that of the hypotenuse

The steps are as follow:

AB = c

BC = a

AC = b

Cos A = Adjacent side to A / Hypoteneous

Cos A = AC / AB

Cos A = b / c

Therefore the value of Cos A in given figure will be b / c

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Answer:

y=-3x+1

Step-by-step explanation:

Have a good one.

Answer

Step-by-step explanation:

Answer:

See the argument below

Step-by-step explanation:

I will give the argument in symbolic form, using rules of inference.

First, let's conclude c.

(1)⇒a  by simplification of conjunction

a⇒¬(¬a) by double negation

¬(¬a)∧(2)⇒¬(¬c) by Modus tollens

¬(¬c)⇒c by double negation

Now, the premise (5) is equivalent to ¬d∧¬h which is one of De Morgan's laws. From simplification, we conclude ¬h. We also concluded c before, then by adjunction, we conclude c∧¬h.

An alternative approach to De Morgan's law is the following:

By contradiction proof, assume h is true.

h⇒d∨h by addition

(5)∧(d∨h)⇒¬(d∨h)∧(d∨h), a contradiction. Hence we conclude ¬h.  

Answer:

1039.23 square inches

Step-by-step explanation:

                      a = 20 inches

    \(\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}\)

                                                   \(= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2\)

Answer:

54.91

Step-by-step explanation:

64.6/x=100/85

(64.6/x)*x=(100/85)*x

64.6=1.17*x  (divide both sides of the equation by 1.17 to get x)

54.91=x

x=54.91

now we have 85% of 64.6= 54.91

Answer:

76

We make the assumption that 85 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that 100% = 85

The range and domain of the graph shown is

domain -4 ≤ x < ∞

range ∞ ≤ x < 3

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The domain of a graph is every value in the graph, from left to right.

Examining the curve the extreme left has x coordinate value of -4 and the right end have an arrow which means the value continues. this is written as

-4 ≤ x < ∞

The graph's entire range, from lower to higher numbers, in the vertical line represents the range.

Examining the curve the lowest point the curve reached in y-coordinate have an arrow which means the value continues and the top end have the value of 3. this is written as

∞ ≤ x < 3

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Answer: f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Step-by-step explanation: Using the given recursive formula:

f(1) = 0

f(n) = f(n-1) + 2

We can find the values of f(n) for different values of n:

f(1) = 0

f(2) = f(1) + 2 = 0 + 2 = 2

f(3) = f(2) + 2 = 2 + 2 = 4

f(4) = f(3) + 2 = 4 + 2 = 6

f(5) = f(4) + 2 = 6 + 2 = 8

And so on.

We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:

f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

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Answer:

the answer is 3

Step-by-step explanation:

21 x 3 =7

hope it helps

Answer:

21/7

Step-by-step explanation:

Move 7 to next side with opposite process it is multiple after move it will be divided so 21x (21/7) it will be 7 although (21/7)equivalent to 1/3

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

\(\frac{20}{3}\)

Step-by-step explanation:

we have  : lines 2 x + 4 y = 0 and 2 x + y = 10

   Let ,

2 x + 4 y = 0............. (1)

2 x + y = 10...............(2)

solve these equations for x and y

Now subtract (2)  from (1) ,we get

3y=-10

⇒y = \(\frac{-10}{3}\)

Put the value of y in (1) , we get

2x+4(\(\frac{-10}{3}\)) = 0

⇒2x= \(\frac{40}{3}\)

⇒x=\(\frac{20}{3}\)

∴ Point  of intersection is \((\frac{20}{3},\frac{-10}{3} )\).

Hence,the x-coordinate of that point is \(\frac{20}{3}\).

The correct statements regarding the transformations are given as follows:

Examples of transformations are given as follows:

Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.

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so that's

$300,000

*30*4/100

$36,000

2

prob. = total probs./no of probs

=0.35+0.45/2

=0.575

sweetie please verify tou answer am not 100% sure but that how it should be done

please I need brainliest thanks

Answer:

20People

Step-by-step explanation:

Buying of a picture = $4

if the total revenue made after people bought it was $80

Total number of people who bought it

= $80/$4

=20People

Answer:

300/300 =1

Step-by-step explanation:

Given negative five and one third times negative four and fifteen hundredths, determine the product.

\(-5*\frac{1}{3} (-4)*\frac{15}{100}\)

Let's convert all expressions into fractions:

\(-5=-\frac{5}{1}\)

\(\frac{1}{3} (-4)=\frac{1}{3} *-\frac{4}{1} =-\frac{4}{3}\)

\(\frac{15}{100}\)

Now, multiply all the terms:

\(-\frac{5}{1} *-\frac{4}{3} *\frac{15}{100}\)

Multiply the upper part first (numerators):

\(-5*-4*15=300\)

Multiply the lower part (denominators):

\(1*3*100=300\)

Join the numerator and denominator into a fraction:

\(\frac{300}{300}=1\)

Another way to represent what we did is the following:

\(\frac{-5*-4*15}{1*3*100} =\frac{300}{300} =1\)