Sadie has x quarters and y dimes. She has at most 22 coins worth no less than $3.60 combined. Solve this system of inequalities graphically and determine one possible solution.

John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Let's start by setting up the equations to solve for this problem.

Let x be the amount of money John had initially.

Then, Mary had (384 - x) initially.

After John gave Php 36 to Mary, John had (x - 36) left and Mary had (384 - x + 36) = (420 - x).

We are told that Mary had three times as much money as John after this transaction, so we can write:

3(x - 36) = 420 - x

Simplifying this equation gives:

3x - 108 = 420 - x

4x = 528

x = 132

Therefore, John initially had Php 132 and Mary initially had Php 252 (384 - 132).

Answer: Mary had Php 252 at first.

Learn more about initially  from

https://brainly.com/question/31041139

#SPJ11

The standard normal curve is symmetric about 0.

what is normal curve?

The normal curve, also known as the Gaussian distribution or bell curve, is a type of probability distribution that is commonly used in statistics and probability theory. It is a continuous probability distribution that is characterized by its symmetric bell-shaped curve.

The normal curve is defined by two parameters: the mean (μ) and the standard deviation (σ). The mean represents the center of the curve, while the standard deviation controls the spread or variability of the curve.

To find the area under the standard normal curve that lies to the right of 1.34, we can use the fact that the total area under the curve is 1 and the standard normal curve is symmetric about 0. Therefore, the area under the curve that lies to the left of -1.34 is the same as the area under the curve that lies to the right of 1.34.

Thus, the area under the standard normal curve that lies to the right of 1.34 is also 0.0901227.

The property of the standard normal curve that allowed us to answer part is B. The standard normal curve is symmetric about 0.

To learn more about standard normal curve from the given link

https://brainly.com/question/4079902

#SPJ1

The property of the standard normal curve is -

Option B: The standard normal curve is symmetric about 0.

What is normal curve?

The probability density function for a continuous random variable in a system defines the Normal Distribution or Normal Curve.

It is given that the region under the standard normal curve that lies to the left of,-1.34 has area 0.0901227.

Using the property of the standard normal curve that it is symmetric about 0, we know that the area to the right of 1.34 is equal to the area to the left of -1.34.

So, the area under the standard normal curve that lies to the right of 1.34 is also 0.0901227.

Therefore, the standard normal curve is symmetric about 0.

To learn more about Normal Curve from the given link

https://brainly.com/question/27271372

#SPJ1

is there any option choices to go along with the question?

Answer:

80 dollar

Step-by-step explanation:

76=95%

x=100%

x gives as 80 dollar

Answer: \(\theta = 120^\circ\) and \(\tan(\theta) = -\sqrt{3}.\)

Step-by-step explanation:

a. We are given that \(\cos(\theta) = -\frac12.\) Taking the inverse cosine tells us that the measure of \(\theta\) is either 120 or 240 degrees, but because \(\sin(\theta) > 0,\) we know that \(0^\circ < \theta < 180^\circ\). Therefore, \(\theta = 120^\circ\).

b. So we know that \(\tan(\theta) = \tan(120^\circ)\), and evaluating this yields \(\tan(\theta) = -\sqrt{3}.\)

Answer:

\(\textsf{a)} \quad \theta=120^{\circ}, \quad \theta=\dfrac{2}{3}\pi\;\text{(rad)}\)

\(\textsf{b)} \quad \tan \theta=-\sqrt{3}\)

Step-by-step explanation:

Cosine is negative in quadrants II and III, and sine is positive in quadrants I and II. Therefore, given cos θ = -1/2 and sin θ > 0, then angle θ is in quadrant II.

Using the Pythagorean identity, we can find the value of sin θ:

\(\begin{aligned}\sin^2 \theta+\cos^2\theta&=1\\\sin^2 \theta &= 1 - \cos^2 \theta\\\sin^2 \theta &= 1 - \left(-\dfrac{1}{2}\right)^2\\\sin^2 \theta &= \dfrac{3}{4}\\\sin\theta&=\sqrt{\dfrac{3}{4}}\\\sin \theta& = \dfrac{\sqrt{3}}{2}\end{aligned}\)

Since angle θ is in quadrant II, we know that it is between 90° and 180°.

In the unit circle, cosine is the x-coordinate of a point on the circle and sine is the y-coordinate of that point.

Therefore, according to the unit circle, the only angle in quadrant II that has a cosine of -1/2 and a sine of √3/2 is 120°.

Therefore, θ = 120°.

To convert degrees to radians multiply the angle in degrees by π/180°.

\(\implies \theta=120^{\circ}\cdot \dfrac{\pi}{180^{\circ}}=\dfrac{2}{3}\pi\)

Therefore, angle θ is 120° or 2π/3 radians.

The tangent trigonometric ratio identity is:

\(\tan \theta = \dfrac{\sin \theta}{\cos \theta}\)

To find the value of tan θ, substitute the values found in part (a) into the identity:

\(\begin{aligned}\implies \tan \theta &=\dfrac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}\\\\ &=\dfrac{\sqrt{3}}{-1}\\\\&=-\sqrt{3}\end{aligned}\)

Therefore, tan θ is -√3.

The probability that the number chosen at random is a member of A ∩ B is equal to 1/15.

The completed Venn diagram is on attached picture.

Venn diagrams are commonly used in mathematics, statistics, and logic to illustrate relationships between sets of data. It consists of circles that overlap to show the similarities and differences between the sets like in the case of students data.

A ∩ B is read as A intersection B, which implies the set of all datas found in both set A and set B without repeating any data.

Given that set A = {9, 15, 17, 19} and B = {5, 15, 25}

so;

A ∩ B = {15}

All possible outcome = {all odd numbers less than 30} = 15

probability that the number chosen at random is a member of A ∩ B = 1/15

Therefore, from the completed Venn diagram, the probability that the number chosen at random is a member of A ∩ B is equal to 1/15.

Read more about venn here:https://brainly.com/question/24713052

#SPJ1

If you want to buy fewer than 25 shirts, then prefer Shirts By Sam shop. If you want to buy more than 25 shirts, then prefer Might T Shirt shop.

What is an equation?

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Given that:

Shirts By Sam

The cost of 10 shirts is $127.5

The cost of 15 shirts is $168.75.

Assume the equation that represents total cost is y = ax+b

Putting x= 10 and y=127.5 in y = ax+b:

127.5 = 10a+b.....(i)

Putting x= 15 and y=168.75 in y = ax+b:

168.75 = 15a+b.....(ii)

Use elimination method to solve equation (i) and (ii).

Subtract equation (i) from (ii)

15a+b = 168.75

10a+b = 127.5

____________

5a = 41.25

a = 8.25

Putting a=8.25 in equation (i)

127.5 = 10×8.25+b

b = 40

The equation is y = 8.25x+40.

Might T Shirt

The cost of 8 shirts is $137

The cost of 12 shirts is $163

Assume the equation that represents total cost is y = ax+b

Putting x= 8 and y=137 in y = ax+b:

137 = 8a+b.....(iii)

Putting x= 12 and y=163 in y = ax+b:

163 = 12a+b.....(iv)

Use elimination method to solve equations (iii) and (iv).

Subtract equation (iv) from (iii)

 8a+b = 137

12a+b = 163

____________

4a = 26

a = 6.5

Putting a=6.5 in equation (iii)

137= 8×6.5+b

b = 85

The equation is y =6.5x+85.

The solution of the system of equations:

y = 8.25x+40 .....(vi)

y =6.5x+85   ......(vii)

Use substitution method to solve equations (vi) and (vii).

Subtract equations:

8.25x+40 - 6.5x-85=0

1.75x - 45 =0

x = 45/1.75

x = 25.71

Putting x = 26 in equations (vi) and (vii)

y = 8.25×26+40 = 254.5

y = 6.5×26+85 = 254

Putting x = 24 in equations (vi) and (vii)

y = 8.25×24+40 = 238

y = 6.5×24+85 = 241

Thus if you buy more than 25 shirts, then prefer Might T Shirt shop.

if you buy fewer than 25 shirts, then prefer  Shirts By Sam.

To learn more about the system of equations, click on the below link:

https://brainly.com/question/17245324

#SPJ1

Answer:

\(a^-^7\)

Step-by-step explanation:

\(\frac{a^{-13}}{a^{-6}}\)

\(\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\)

\(=a^{-13-\left(-6\right)}\)

\(\mathrm{Apply\:rule}\:-\left(-a\right)=a\)

\(=a^{-13+6}\)

\(\mathrm{Add/Subtract\:the\:numbers:}\:-13+6=-7\)

\(=a^{-7}\)

Answer \(=a^{-7}\)

~Learn with Lenvy~

Answer: 58.33%

Step-by-step explanation:

So, Liz flipped the coin a total of 60 times

Let this be the denominator.

Probability of coin landing up: 35/60

Probability of coin landing down: 24/60

We need the probability of the coin landing up.

So, convert 35/60 into a percentage

To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1003560 × 100100= (35 × 10060) × 1100 = 58.33/100

So, the probability is 58.33%

Answer:

3*r = 3

Step-by-step explanation:

\(\dfrac{24}{r}=3\\\\24 = r*3\\\\\dfrac{24}{3}=r\\\\6 = r\)6 is a solution.

\(3*r=3\\\r =\dfrac{3}{3}\\\\r = 1\\\)

6 is not a solution.

\(7r = 42\\\\r =\dfrac{42}{7}\\\\r = 6\)

6 is a solution

Answer:

My best answer is A

Step-by-step explanation:

if you plug in 6 for r, it doesn't work for A.

B is hard to see so can't tell

C works with r=6, so it's not C

and D works as well, so it's not D

hi, I'm no bot just in case...

the grapgh of the line shows y intercept of -9 and rate of change by 4

SoThe equation of the lline will be: \(y=4x-9\)

Answer:

C. Fertility= Nutrients * Moisture / Pollutant

Step-by-step explanation:

F=NM/P

F= Fertility of the soil

N= Amount of nutrients in the soil

M= Amount of moisture in the soil

P= Amount of pollutant in the soil

F=NM/P

Fertility of the soil

= Amount of nutrients in the soil * Amount of moisture in the soil / Amount of pollutant in the soil

Fertility= Nutrients * Moisture / Pollutant

Option C is the correct answer

Answer:

c - 8 + b

Step-by-step explanation:

c - ( 8 - b ) = c - 8 + b

Answer;

b+c-8

Step-by-step explanation:

8=0 infinity

Answer: S and T.

Step-by-step explanation:

I watched a video on how to do this just to answer, so it might not be right LOL. But since the angles are the same if you draw them from each other they both show the angles are equal which means the lines are parallel.

Answer:

y=71

x=109

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

The sequence are:

a, 2a, 4a, 8a, 16a.....

the total value of the first three terms is 63

That is,

a + 2a + 4a = 63

7a = 63

a = 63/7

a = 9

work out the total value of the first four terms

First four terms are: a, 2a, 4a, 8a

Where,

First term, a = 9

Second term, 2a = 2*9 = 18

Third term, 4a = 4*9 = 36

Fourth term, 8a = 8*9 = 72

The total value of the first four terms = 9 + 18 + 36 + 72

= 135

The total value of the first four terms = 135

It is possible that there could be an interaction between the nitrogen and phosphorus variables in their effect on crop yield. This means that the effect of one variable on crop yield may depend on the level of the other variable.

For example, if there is already an adequate amount of phosphorus in the soil, adding more nitrogen may not have a significant impact on crop yield. However, if there is a deficiency of phosphorus, adding nitrogen may have a greater impact on increasing crop yield. Therefore, it would be important to examine the data and analyze the relationship between crop yield and the two fertilizer variables to determine if there is indeed an interaction effect present.


When examining the response variable Y (crop yield in bushels per acre) and its relationship with the predictor variables nitrogen and phosphorus applied per acre, it's important to consider whether there might be an interaction between these two fertilizer variables. An interaction would imply that the effect of one predictor variable (e.g., nitrogen) on crop yield depends on the level of the other predictor variable (e.g., phosphorus).

Step-by-step explanation:

1. Identify the variables:
  - Response variable (Y): Crop yield in bushels per acre
  - Predictor variables: Nitrogen and phosphorus applied per acre

2. Analyze the relationship between crop yield and the fertilizer variables:
  - It's reasonable to expect that applying nitrogen or phosphorus individually could have a positive effect on crop yield, as these nutrients are essential for plant growth.
  - However, plants often require a specific balance of nutrients for optimal growth. This means that the effect of nitrogen on crop yield might depend on the level of phosphorus, and vice versa.

3. Determine if an interaction is present:
  - If applying both nitrogen and phosphorus simultaneously results in a higher (or lower) crop yield than expected based on their individual effects, this would indicate an interaction between the two fertilizer variables.

In conclusion, it is possible that an interaction between nitrogen and phosphorus applied per acre exists when predicting crop yield. To confirm this, you would need to conduct a statistical analysis of relevant data.

The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

To learn more about : circulation

https://brainly.com/question/30619471

#SPJ11

Question is not very clear, however answers will reflect numbers seen(with some assumptions since some questions are not entirely complete)

Answer and explanation:

1. If a rectangle has an area of 35 meters and width of 78 meters, what is the length

Given that area of rectangle is length *width

Let's call length x

We have the equation

78*x=35

78x=35/78

x= 0.449

Therefore length =0.449 meters

2. Greg wants to divide a 712 yard long ribbon into pieces of 14 yard long each.

How many pieces can he make?

Let's assume the ribbon is a square then it's area is 712*712= 506944

To find number of 14 yard long pieces from the 712 yard long ribbon, we first find area for 14 yard long ribbons= 14*14= 196

number of 14 yard long pieces from the 712 yard long ribbon= 506944/196

= 2586.449 pieces

3. Olivia has 23 minutes an hour to write thank you notes. It takes her 12 minutes of an hour per thank you note. How many can she write?

Since it takes Olivia 12 minutes to write thank you notes but she has 23 minutes to write one, in one hour(1 hour =60minutes) she would be able to write

60 minutes /12 minutes = 5 thank you notes instead of

60 minutes /23 minutes= 2.609 or 2 thank you notes

4. Jim has 14 cups of nuts. How much of the recipe can he make?

If recipe requires 7 cups of nuts for instance, Jim would be able to make 14/7 = 2 of the recipe

Answer:

SAS = SAS

Step-by-step explanation:

I hope this helps you out!

Answer:

SAS

Step-by-step explanation:

I think, been a while since I did this but you have side angle side so I'm pretty sure not 100 percent

Answer:

Step-by-step explanation:

rectangle and triangle is here

area of triangle = 1/2 * 5 * 12 = 30

area of rectangle = 1 * 12 = 12

total is 12 + 30 = 42

The gallons of gas that Aubrey would need to travel 111.54 miles is 7.8 gallons.

In Mathematics, a direct proportion simply refers to a mathematical equation which is typically used to represent the equality of two (2) ratios.

By applying direct proportion to the given information, we have the following mathematical equation:

15 gallons of gasoline = 214.5 miles

X gallons of gasoline = 111.54 miles

By cross-multiplying, we have the following:

214.5x = 15 × 111.54

x = 1,673.1/214.5

x = 7.8 gallons of gasoline.

Read more on direct proportion here: https://brainly.com/question/29672991

#SPJ1

The probability of a selected sample is 0.0001.

What is a normal distribution?

It is also known as Gaussian distribution. It shows the data near the more. This appears as bell curve in graphical form. It is a bell shaped frequency distribution curve of a continuous random variable.

Given that,

μ= 10 pounds

σ=2 pounds

n=16

Sampling distribution of mean is

μₓ⁻ =μ=10

Standard error of mean is

σₓ⁻ =σ/√n

=2/√16

=0.5

p(μₓ⁻ >12.5)

=1-p((x⁻-μₓ⁻/σₓ⁻ )≤ ((12.5-10)/0.5)

=1-p(z≤5)

using standard normal table,

=1-0.9999

=0.0001

The probability of a selected sample is 0.0001.

To know more about normal distribution, visit:

https://brainly.com/question/15103234

#SPJ4

Answer:

(x-13)^2+(y+16)^2=12.56

Step-by-step explanation:

Answer:

14%

Step-by-step explanation:

To find the percentage change of any two amounts you just need this formula: (new - old) ÷ old

New price = $2.45

Old price = $2.15

2.45 = 2.15 = 0.3

0.3 ÷ 2.15 = 0.139534883721

This would make the percentage increase = %13.9534883721

But the question wants it rounded to the near tenth, so it's %14

Answer:

13.9535% increase, so yeah, like, 14%

Step-by-step explanation:

Answer:

The two angles coterminal with π/10 are 21π/10 and -19π/10

Step-by-step explanation:

To find a two angles that are coterminal with π/10, we add and subtract 360°(that is 2π) from π/10.

So, the first angle coterminal with π/10 is

A = π/10 + 2π

taking the L.C.M which is 10, we have

A = (π + 20π)/10

A = 21π/10

The second angle coterminal with π/10 is

B = π/10 - 2π

taking the L.C.M which is 10, we have

B = (π - 20π)/10

B = -19π/10

So the two angles coterminal with π/10 are 21π/10 and -19π/10

Answer:

12.56 in.

Step-by-step explanation:

A=Pi*R to the 2nd power

A=3.14*2 to the 2nd power

A=3.14*4

A=12.56

Let me know if im wrong

Area of the circle is 12.56 square units which has radius 2 inches.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that radius of a circle is 2 inches.

We need to find the area of circle.

Radius= 2 inches.

π=3.14

We know that area of circle=πr²

Area of circle=3.142×2²

=3.142×4

=12.56 square inches.

Hence, area of the circle is 12.56 square units which has radius 2 inches.

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ2

Using the probability multiplication we know that the defect probability of the final product will be 7.5%.

Simply put, the probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

The higher the likelihood, the more likely it is that the event will take place.

So, the probability formula is:

P(E) = Favourable events/Total events

So, in the given situation, the number of components integrated:

500

Defect probability of each component:

0.015%

Then, the defect probability of the final product:

= 500 * 0.015

= 7.5%

Therefore, using the probability multiplication we know that the defect probability of the final product will be 7.5%.

Know more about probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

260 hours

Step-by-step explanation:

first take out the 20 fixed cost that doesn't change no matter how long he gardens from 800

divide the remainder which is 780 by 3 which is the amount he gets paid for every hour he gardens. He would have to work 260 hours for the bike if he only takes one yard job

Answer:

x = 7

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 24² = 25²

x² + 576 = 625 ( subtract 576 from both sides )

x² = 49 ( take square root of both sides )

x = \(\sqrt{49}\) = 7

Hey ! there

Answer:

Step-by-step explanation:

In this question we are provided with a right angle triangle having hypotenuse 25 cm , base 24 cm and perpendicular x . And we are asked to find the length of x .

For finding the length of x we'll use Pythagorean Theorem . Pythagorean Theorem states that sum of square of perpendicular and base is equal to the square of hypotenuse in right angle triangle that is ,

\( \: \qquad \: \qquad \: \underline{\boxed{ \frak{H {}^{2} = P {}^{2} + B {}^{2} }}}\)

Where ,

SOLUTION : -

Here in the triangle ,

Applying Pythagorean Theorem :

\( \quad \longmapsto \qquad \: (25) {}^{2} = (x ){}^{2} + (24) {}^{2} \)

On squaring 24 and 24 we get ,

\( \quad \longmapsto \qquad \:625 = (x) {}^{2} + 476\)

Subtracting 576 on both sides :

\( \quad \longmapsto \qquad \:625 - 576 = (x) {}^{2} + \cancel{ 576} - \cancel{576}\)

We get ,

\( \quad \longmapsto \qquad \:49 = (x) {}^{2} \)

Applying square root on both sides :

\( \quad \longmapsto \qquad \: \sqrt{49} = \sqrt{(x) {}^{2} } \)

We get ,

\( \quad \longmapsto \qquad \: \blue{ \underline{\boxed{\frak{7 \: cm = x}}}} \quad \bigstar\)

Verifying : -

We are verifying our answer by substituting all the values of hypotenuse , perpendicular and base in Pythagorean Theorem . So ,

Therefore, our answer is correct .