If m varies directly as p, and m=63 when p=9, find m when p is 5

Answer:

$900.10

Step-by-step explanation:

15 percent of 999.99 = $849.15

(999 x 15)/100 = $149.85

849.15 with 6 percent sales tax is 900.10

Answer: random events

Step-by-step explanation:

Based on the information given in the question, the scenario can be best explained by a random event.

Random event refers to the event that cannot be made exact and one whose outcome can't be predicted. An example is the sum of numbers that are gotten when two rolled dice are rolled.

From the experiment, one student had five heads in a row, while the other student's coin toss had no pattern depicts a random event.

Answer:

a variable expression

Step-by-step explanation:

because it consists unknown variable d

Answer:

The common denominator for 2 1/5 and 1 5/6 is 11.

Step-by-step explanation:

it is 5 if you do keep change flip so you flip 1⅚ to 1 6/5 to match the denominator and solve the problem and then change the plus to a minus also keep the 2 1/5 there.

Volume of a right cone with base radius r cm and height h cm :

V = 1/3 π r² h cm³

Surface area :

A = (π r² + π r √(h² + r²)) cm²

Volume of a sphere with radius r cm :

V = 4/3 π r³ cm³

Surface area :

A = 4 π r² cm²

Volume of a cuboid with dimensions r cm × r cm × h cm :

V = r² h cm³

Surface area :

A = 2 r² + 4 r h

a. If the cone and sphere have the same volume, then

1/3 π r² h = 4/3 π r³   ⇒   h = 4r

b. If the area of the cuboid is 98 cm², then

2 r² + 4 r h = 98   ⇒   r (r + 2 h) = 49

c. Since h = 4r, substituting this into the equation from (b) gives

r (r + 8 r) = 9 r² = 49   ⇒   r² = 49/9   ⇒   r = 7/3

d. With r = 7/3, we have

h = 4 × 7/3 = 28/3

and so the volume of the cuboid is

V = (7/3 cm)² (28/3 cm) = 1372/27 cm³

Give an example of a proportion that uses the numbers 2, 3, 4 and 6.

2:3 is the same as 4:6

Proportion says that two ratios (or fractions) are equal.

Based on the information provided, it is impossible to determine whether the store sold more sweaters than shirts during the sale. We do not know how many of each item was sold.
During the sale, the clothing store sold shirts for $15 each and sweaters for $25 each. To determine whether the store sold more sweaters than shirts, additional information such as the total number of items sold or the total revenue generated from each type of clothing is needed. Without this information, it is not possible to definitively say whether the store sold more sweaters or shirts during the sale. However, we can assume that the store made more profit from the sale of sweaters, as each sweater was sold at a higher price than each shirt. It is also possible that the store sold equal amounts of sweaters and shirts, but generated more revenue from the sale of sweaters. Ultimately, more information would be needed to make a definitive statement about which item sold more during the sale.

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The solution to this system of linear equations is  (7, 3).

What is equation?

In mathematics, an equation is a formula that expresses the equivalency of two expressions, by connecting them with the equals sign =

Main body:

x - 3y = -2

x = 3y - 2 ….. (1)

x + 3y = 16 …… (2)

Let us solve the system of linear equations using the substitution method.

Substituting x in equation (2)

3y - 2 + 3y = 16

6y = 16 + 2

6y = 18

Divide both sides by 6

y = 3

Substituting the value of y in equation (1)

x = 3 (3) - 2

x = 9 - 2

x = 7

Therefore, the solution is (7, 3).

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Answer: 5

Step-by-step explanation:

The combination formula helps to determine the number of non-negative solutions of equation

x₁ + x₂ + x₃ + x₄ + x₅ = 21 in different cases.

a) Total number of solutions for equation in case of x₁ ≥ 1, is equals to the 10626.

b) Total number of solutions for equation in case of xᵢ ≥ 2 for i = 1, 2, 3, 4, 5, is equals to the 1365.

c) Total number of solutions for equation in case of 0 ≤ x₁ ≤ 10 is equals to the 11649.

d) Total number of solutions for equation in case of 0 ≤ x₁ ≤ 3, 1 ≤ x₂ < 4, and x₃ ≥ 15, is equals to the 76.

We have an equation x₁ + x₂ + x₃ + x₄ + x₅ = 21, where xᵢ , i = 1, 2, 3, 4, 5 and we have to determine the number of solution of equation.

a) Solution of equation when x₁ ≥ 1

Let there are 5 boxes namely, x₁,x₂,x₃,x₄,x₅ in which 21 balls are placed distinguished. First ball is placed in box x₁. So, remained 20 balls are placed into 5 boxes with repititions. So, number of ways are C(n+r−1, r-1) = (n + r − 1)!/(r-1)!n! , where n = 20 , r = 5

C(n + r −1, r- 1) = C(20 + 5− 1 ,4)

= C(24,4) = 10626

b) Solution of equation for xᵢ ≥ 2 for i = 1,2,3,4,5.

Now, xᵢ ≥ 2 for i = 1,2,3,4,5, means first drop two balls into every box. Then, only 11 balls, remaining

n =11, r = 5

C(n+r−1, r-1) = (n+r−1)!/(r-1)!n!

= C(11 + 5−1, 4) = C(15, 4)

= 1365

c) Solution of equation for 0 ≤ x1 ≤ 10

when 21 balls dropped into five boxes x₁, x₂, x₃, x₄,x₅ then C(n+r−1, r-1) = (n+r−1)!/(r-1)!n! ; n= 21, r = 5

C(n + r −1, r - 1) = C(21+ 5− 1 ,4)

C(25, 4) = 12650

xi ≥ 11 , n=11, r = 5 then

C(n + r−1, r- 1 ) = C(11+4−1,4)

C(14,4) = 1001

C(25,4) − C(14,4) = 12650 − 1001 = 11649

d) Solution of equation for 0 ≤ x₁≤ 3, 1 ≤ x₂ < 4, and x₃≥ 15. For this condition solution is = { x1≥ 0, x2≥ 0, x3 ≥ 15} - { x₁≥3, x₃≥ 15} - { x₂≥4, x₃≥ 15} - { x₁=0, x₃ ≥ 15}

Now, first 15 balls are dropped into x3 and remaining 6 are droped into remaining boxes, { x₁ ≥ 0, x₂≥ 0, x₃≥ 15}, Then, n = 6, r = 5

C(n + r −1, r - 1) = C(6+ 5− 1 ,4)

C(10, 4) = 210

Also, { x₁ ≥3, x₃ ≥ 15}, represents 3 and 15 balls are dropped into x₁ and x₃ respectively. and remaining 3 balls will dropped into 5 boxes with repititions, n = 3, r = 5

C(n + r −1, r - 1) = C(3+ 5− 1 ,4)

C(7, 4) = 35 ways

{ x₂≥4, x₃≥ 15} , represents 4 and 15 balls are dropped into x₂ and x₃ respectively. and remaining 2 balls will dropped into 5 boxes with repititions, n= 2, r = 5

C(n + r −1, r - 1) = C(5+ 4− 1 ,4)

C(7, 3) = 15 ways

{ x₂ = 0, x₃ ≥ 15}, represents 0 and 15 balls are dropped into x₂ and x₃ respectively. and remaining 6 balls will dropped into 4 boxes with repititions, n= 6, r= 4

C(n + r −1, r - 1) = C(6+ 4− 1 ,3)

C(9, 3) = 84 ways

So, the number of solutions for this case = 210 - 35 - 15 - 84 = 76.

Hence there are 76 non-negative integer solutions.

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False. If E and F are independent events, then Pr(E|F) is not necessarily equal to Pr(E).

The probability of an event E given event F, denoted as Pr(E|F), represents the probability of event E occurring given that event F has already occurred. In the case of independent events, the occurrence of one event does not affect the probability of the other event occurring.

By definition, two events E and F are independent if and only if Pr(E ∩ F) = Pr(E) × Pr(F), where Pr(E ∩ F) represents the probability of both events E and F occurring.

Now, let's consider the statement that Pr(E|F) = Pr(E) when E and F are independent events. This implies that the probability of event E occurring given that event F has occurred is the same as the probability of event E occurring without any knowledge of event F.

However, this is not necessarily true. The conditional probability Pr(E|F) takes into account the occurrence of event F, which may affect the probability of event E. Even if events E and F are independent, the value of Pr(E|F) may differ from Pr(E) if the occurrence of event F provides additional information or changes the probability distribution of event E.

The statement "Pr(E|F) = Pr(E)" when E and F are independent events is false. While independence between events E and F ensures that the occurrence of one event does not affect the probability of the other event, it does not guarantee that the conditional probability Pr(E|F) will be equal to the unconditional probability Pr(E).

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Answer: B

Step-by-step explanation:

B) Copernicus rediscovered Aristarchus's heliocentric model. The event which took place during the Copernican revolution.

Answer: HELP

Step-by-step explanation:

HELP MEEEE

N(t) approaches 550.

The equation N(t) = 550 / (1 + 49e^(-0.7t)) models the number of people in a town who have heard a rumor after t days. The equation describes the growth of the number of people who have heard the rumor over time. The e^(-0.7t) term in the denominator represents the rate of decay or the slowing down of the spread of the rumor as t increases. As t increases without bound, the exponential term approaches 0, so the fraction approaches 550 / (1 + 49 * 0) = 550 / 1 = 550.

This means that as time goes on, the number of people who have heard the rumor will approach 550, the limit or maximum value of N(t). This value is not limited by any of the factors mentioned in the options (b) to (e).

The number of people who started the rumor is not given in the equation and cannot be determined from the information provided.

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Answer:

(2,5)

Step-by-step explanation:

-3+5=2 and 4+1=5

Answer:

x=61

2x+3 = 125

x-6 = 55

Step-by-step explanation:

The two angles shown form a straight line so they add to 180

2x+3 + x-6 = 180

Combine line terms

3x-3 =180

Add 3 to each side

3x-3+3 =180+3

3x=183

Divide each side by 3

3x/3 =183/3

x =61

The angle on the left is 2x+3

2x+3 = 2*61+3 = 122+3 = 125

The angle on the right is x-6 = 61-6 = 55

Answer:

RS = 18

Step-by-step

PR = x

RS = x+2

SQ = x+4

x+(x+2)+(x+4)=54

3x+6=54

3x=48

x=16

PR = 16

RS = 18

SQ = 20

The length of the middle segment RS is determined as 18.

Let's assume that the three consecutive even integers are x, x + 2, and x + 4

So, the length of PR (x) + the length of RS (x + 2) + the length of SQ (x + 4) equals the total length of PQ (54).

Mathematically, this can be represented as:

x + (x + 2) + (x + 4) = 54

Now, let's solve for x:

3x + 6 = 54

Subtract 6 from both sides:

73x = 48

Now, divide by 3:

x = 16

So, the first even integer (PR) is 16, the second even integer (RS) is 16 + 2 = 18, and the third even integer (SQ) is 16 + 4 = 20.

Thus, the length of the middle segment RS is 18.

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Answer:

Let S = price of sweater

Let P = price of pants

S + P = 89.47 because that was the total spent

S = P - 8.53   because the sweater is 8.53 less than pants

Substitute P-8.53 in place of S in the

1st equation and solve for P

P - 8.53 + P = 89.47

2P - 8.53 = 89.47     add 8.53 to both sides

2P = 89.47 + 8.53

2P = 98.00  divide both sides by 2

P = 98.00/2

P = $49.00

S = P - 8.53

S = 49.00-8.53

S = $40.47

A sweater costs $40.47 and the pants cost $49.00

Answer:

18.84

Step-by-step explanation:

Hope this helps :)

Answer:

18.84

The equation for circumference is 2πr which means that you times 2 by pi and then the radius which is 6 divided by 2 so 3. Then you get 6π which is 18.84

The equation of circle P include the following: D. x² + (y - 3)² = 4

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 3)² = 2²

x² + (y - 3)² = 4.

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Answer:

C. The amount of money that is raised

Step-by-step explanation:

in the equation, it is the amount of money that is raised because how much money is raised affects the amount of basketballs purchased.

In other words, if the amount of money is less, then there will be less basketballs purchased as a result. If the amount of money is more, then there will be more basketballs purchased as a result.

Answer:

C. the amount of money that is raised

Step-by-step explanation:

I always think of it like this:

independent: money they are raising

dependent: the amount of a certain item the money is being used on

Answer:

1)D 2)A 3)D 4)A 5)A

I hope this help but in question 6 you can report

Answer:

637/1000

Step-by-step explanation:

Hopes this helps

Answer: One

Step-by-step explanation:

Answer:
yes

Step-by-step explanation:

−8 ≤ 4(3)− 7

−8 ≤ 12-7

−8 ≤ 5 it works