Write the following comparison as a ratio reduced to lowest terms.

37 nickels to 23 dimes

The theater sold 82 children tickets and 60 adult tickets.

Step-by-step explanation:

No. of tickets sold = 142

Total sales = $890

Cost of one child ticket = $5

Cost of one adult ticket = $8

Let,

x be the number of children tickets

y be the number of adult tickets

According to given statement;

x+y=142    Eqn 1

5x+8y=890   Eqn 2

Multiplying Eqn 1 by 5

[tex]5(x+y=142)\\5x+5y=710\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](5x+8y)-(5x+5y)=890-710\\5x+8y-5x-5y=180\\3y=180[/tex]

Dividing both sides by 3

[tex]\frac{3y}{3}=\frac{180}{3}\\y=60[/tex]

Putting =60 in Eqn 1

[tex]x+60=142\\x=142-60\\x=82[/tex]

The theater sold 82 children tickets and 60 adult tickets.

Keywords: linear equations, subtraction

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Answer:

The positive real number is 26

Step-by-step explanation:

Let

x ----> the number

we know that

The algebraic expression that represent this problem is

[tex]x^{2} =15x+286[/tex]

so

[tex]x^{2}-15x-286=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-15x-286=0[/tex]

so

[tex]a=1\\b=-15\\c=-286[/tex]

substitute in the formula

[tex]x=\frac{-(-15)(+/-)\sqrt{-15^{2}-4(1)(-286)}} {2(1)}[/tex]

[tex]x=\frac{15(+/-)\sqrt{1,369}} {2}[/tex]

[tex]x=\frac{15(+/-)37}{2}[/tex]

[tex]x_1=\frac{15(+)37}{2}=26[/tex]

[tex]x_2=\frac{15(-)37}{2}=-11[/tex]  ---> the solution cannot be negative

therefore

The positive real number is 26

The value of the expression is : 61

Using the expression given :

Using the values of n and m given ;

Substituting our values into the expression ;

7 + 9(6)

7 + 54

= 61

Hence, the value of the expression is. 61

Complete Question :

Evaluate the expression n + 9m when m=6 and n=7

Answer:

C

Step-by-step explanation:

Final answer:

This answer clarifies the true statement about the division of 1.23 by 0.15, highlighting key misconceptions about the dividend, divisor, and quotient.

Explanation:

Which statement about 1.23 ÷ 0.15 is true?

The dividend should become 15. This statement is false as the dividend after the division remains 1.23.

The divisor is a whole number. This statement is false as 0.15 is not a whole number.

The quotient does not have a hundredths place. This statement is true as the quotient after dividing 1.23 by 0.15 is 8.2, which does not have a hundredths place.

Answer:

they are both correct

Step-by-step explanation:

If the radius is 4 feet like Clare says, the circumference would be 2(radius)(pi) which is 8pi.

If the diameter were 4 feet, circumference would be (diameter)(pi), which is 4pi.

Answer:

48.92

Step-by-step explanation:

A= (1/2)(b)(h)

A=(1/2)(1.56)(3.92)=3.0576

A=(3.0567)(16)=48.9216

A=48.92

The approximate area of Circle A can be found by understanding that the base of a sector is part of the circumference, and using the radius (height) value of 3.92 units in the area formula A = πr². Accounting for significant figures, the area of Circle A is approximately 48 units².

To find the approximate area of Circle A, we need to understand that the base of a sector, which is a part of the circumference of the circle, is close to the length of the arc for a small sector. By dissecting the circle into 16 congruent sectors, each sector represents 1/16 of the circle's full circumference. Since the base of one sector is given as 1.56 units, if we multiply this by 16, we would have the total circumference of the circle. However, the value provided for the 'height' is indeed the radius of the whole circle, which is 3.92 units. The area of a circle is calculated using the formula A = πr².

Using the radius (3.92 units), we can calculate the area:

A = π * (3.92 units)²

A = 3.1415927 * 15.3664 units²

A = 48.2544695988 units²

Considering the significant figures provided in the question, we should limit the calculated area of the circle to two significant figures, matching the least number of significant figures we were originally given, which were in the radius measurement. Therefore, the approximate area of Circle A is:

A = 48 units²

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Answer:

Option 2. [tex]x > 11[/tex]

Step-by-step explanation:

we have

[tex]72 < 7x-5[/tex]

Solve the inequality for x

Adds 5 both sides

[tex]72+5 < 7x-5+5[/tex]

[tex]77 < 7x[/tex]

Divide by 7 both sides

[tex]77/7 < 7x/7[/tex]

[tex]11 < x[/tex]

Rewrite

[tex]x > 11[/tex]

Answer:

Step-by-step explanation:

the unit rate of rainfall is [tex]\( \frac{1}{8} \)[/tex] inches per hour.

To find the unit rate of rainfall, which is the amount of rain per unit of time, we divide the total amount of rain by the total time.

Given:

Total amount of rain: 9 inches

Total time: 72 hours

Step 1: Divide the total amount of rain by the total time:

[tex]\[ \text{Unit rate} = \frac{\text{Total amount of rain}}{\text{Total time}} \][/tex]

[tex]\[ \text{Unit rate} = \frac{9 \text{ inches}}{72 \text{ hours}} \][/tex]

Step 2: Simplify the expression:

To simplify the unit rate, we divide 9 by 72.

[tex]\[ \text{Unit rate} = \frac{9}{72} \text{ inches per hour} \][/tex]

Step 3: Simplify the fraction:

[tex]\[ \text{Unit rate} = \frac{1}{8} \text{ inches per hour} \][/tex]

So, the unit rate of rainfall is [tex]\( \frac{1}{8} \)[/tex] inches per hour.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]f(x)=2(4^x)[/tex]

This is a exponential function of the form

[tex]f(x)=a(b^x)[/tex]

where

a is the initial value

b is the base

r is the rate

b=(1+r)

In this problem we have

[tex]a=2\\b=4\\r=b-1=4-1=3=300\%[/tex]

For x=0

[tex]f(0)=2(4^0)[/tex] -----> [tex]f(0)=2[/tex] ---> y-intercept or initial value

For x=1

[tex]f(1)=2(4^1)[/tex] -----> [tex]f(1)=8[/tex]

Identify the graph

using a graphing tool

The graph in the attached figure

Using probability and binomial distribution, we determined that the probability of exactly 5 out of 40 machines not working is approximately 0.18. The probability that all machines are working is around 0.024, and the probability that at least one machine is working is almost certain, approximately 1.

To address this problem, we will use the concepts of probability and the binomial distribution.

Calculating the Probabilities:

Let’s denote the probability of a single machine not working as p = 0.12. The probability of a single machine working is q = 1 - p = 0.88.

1. Probability that exactly 5 out of 40 machines are not working

We can use the binomial distribution formula:

P(X = 5) = C(40, 5) * p^5 * q^(40-5)

Where C(40, 5) is the number of combinations of 40 machines taken 5 at a time.

C(40, 5) = 40! / [5!(40-5)!] = 658,008

Therefore:

P(X = 5) = 658,008 * (0.12)^5 * (0.88)^35 ≈ 0.18 (using a calculator for binomial probability)

2. Probability that all 40 machines are working

This can be found by raising the probability of one machine working to the power of 40:

P(all working) = q^40 = 0.88^40 ≈ 0.024

3. Probability that at least one machine is working

The easiest way to calculate this is to find the complement of the probability that none are working and subtract it from 1:

P(none working) = p^40 = (0.12)^40 ≈ 9.0949 x 10^-38 (which is extremely close to 0)

P(at least one working) = 1 - P(none working) ≈ 1 - 0 = 1

Final answer: A company has 200 machines. Each machine has 12% probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is _0.18_ , the probability that all would be working is_0.024_, and the probability that at least one machine would be working is_1_.

Complete question:

A company has 200 machines. Each machine has 12% probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is ____ , the probability that all would be working is____, and the probability that at least one machine would be working is______

If you were to pick 40 machines randomly, the probability that 5 would not be working is 0.186 , the probability that all would be working is 0.011, and the probability that at least one machine would be working is 0.989.

This problem involves probability calculations for a company that has 200 machines, each with a 12% chance of not working. Let's break down the calculations step-by-step:

1. Probability that 5 out of 40 machines are not working:

This can be modeled using the binomial distribution. The binomial formula is:

[tex]P(X = k) = C(n, k) \times p^k \times (1-p)^{(n-k)[/tex]

where:

For our problem, it becomes:

P(X = 5) = C(40, 5) × (0.12)⁵ × (0.88)³⁵

= 0.186

2. Probability that all 40 machines are working:

This is calculated using the complement probability as follows:

P(All working) = (0.88)⁴⁰

≈ 0.011

3. Probability that at least one machine is working:

This can be calculated using the complement rule:

P(At least one working) = 1 - P(None working)

= 1 - (0.88)⁴⁰

≈ 0.989

Answer:

7 meters

Step-by-step explanation:

Assume that the length is l and the width is w. Therefore, l is equal to 7 times its width (7*w) minus 28, or l=7*w-28. As we know that w*l = area = 9555, we can plug our value for l in to limit our equation to 1 variable, resulting in w*(7*w-28) = 9555. Adding 28 to both sides to separate the 7w (because we want to solve for that), we get 9583=7w. Then, to solve for the width, we can divide both sides by 7 to get that 9583/7=1369=w. Plugging that back into the formula that w*l=area, we get that 1369*l=9583 -- dividing 1369 from both sides to separate l, we get that l=7.

To find the length of a rectangle where the area is 9555 square meters and the length is 28 meters less than 7 times its width, express the length in terms of the width, use the area to form a quadratic equation, solve for the width, and substitute it back to find the length.

To find the length of the rectangle when the area is 9555 square meters and the length is 28 meters less than 7 times its width, let's denote the width of the rectangle as w and the length as l. According to the problem, the length l can be expressed as l = 7w - 28. The area of a rectangle is the product of its length and width, which gives us the equation w × (7w - 28) = 9555.

To find the value of w, we need to solve the quadratic equation 7w2 - 28w - 9555 = 0. Factoring or using the quadratic formula leads to the width, and substituting this back into l = 7w - 28 gives us the length of the rectangle. In solving, ensure to discard the negative value of w as a width cannot be negative.

Once we calculate the width w, the length is found by multiplying it by 7 and then subtracting 28. This process will provide the final length of the rectangle.

Answer:  2b/3 (second answer choice)

======================================

Explanation:

The work shown on the screenshot basically shows plugging x = 2(a+c)/3 into the y(x) function and then simplifying. Step 5 isnt fully simplified, so let's combine like terms, factor, and then divide out a pair of (a-2c) terms to get the following:

y = (2ab+2bc-6bc)/(3(a-2c))

y = (2ab-4bc)/(3(a-2c))

y = (2b*a-2b*2c)/(3(a-2c))

y = 2b(a-2c)/(3(a-2c))

y = 2b/3

Answer:

The greatest number is A. 1.3 * 10⁵

Step-by-step explanation:

Let's find the greatest number:

Option A : 1.3 * 10⁵ = 1.3 * 100,000 = 130,000

Option B : 9.8 * 10² = 9.8 * 100 = 980

Option C : 9.6 * 10⁴ = 9.6 * 10,000 = 96,000

Option D : 4.6 * 10⁻⁵ = 4.6 * 0.00001 = 0.000046

130,000 > 96,000 > 980 > 0.000046

The greatest number is A. 1.3 * 10⁵

Answer:

m∠S=30°

m∠T=60°

m∠P=90°

Step-by-step explanation:

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

In the triangle STP

m∠S+m∠T+m∠P=180° ----> equation A

m∠T=2(m∠S) ----> equation B

m∠P=3(m∠S) ----> equation C

Solve the system of equations by substitution

Substitute equation B and equation C in equation A

m∠S+2(m∠S)+3(m∠S)=180°

Solve for m∠S

6m∠S=180°

m∠S=30°

Find m∠T

m∠T=2(m∠S)

m∠T=2(30°)=60°

Find m∠P

m∠P=3(m∠S)

m∠P=3(30°)=90°

Answer:

Step-by-step explanation:

Hello

Area triangle DCE :

10 x (8/2) / 2 = 10 x 4 / 2 = 20 cm^2

Area triangle ABE = Area triangle DCE

Area ABCD :

10 x 8 = 80 cm^2

Area triangle AED :

Area ABCD - 2 area DCE

= 80 - 2 x 20

= 80 - 40

= 40 cm^2

Answer:

[tex]x < 18[/tex]

Step-by-step explanation:

We are given the following information in the question:

"Citizens less than 18 years old are not allowed to vote"

We define a variable x such that x represents the age of citizens.

We have to write a relationship with the help of an inequality for the ages of citizens who are not allowed to vote.

Citizens less than 18 are not allowed to vote.

So x should be less than 18.

This can be written as:

[tex]x < 18[/tex]

is the required  inequality for the ages of citizens who are not allowed to vote.

Answer:

C) (x-2)(x+3)

Step-by-step explanation:

x^2+x-6=(x-2)(x+3)

Because (x-2)(x+3)=x^2-2x+3x-6=x^2+x-6.

Final answer:

The polynomial x² + x - 6 factors to (x + 3)(x - 2) by finding two numbers that multiply to -6 and add to 1.

Explanation:

To factor the polynomial x² + x - 6, one needs to find two numbers that multiply to -6 (the constant term) and add up to 1 (the coefficient of the middle term, x). These numbers are 3 and -2, because 3 × (-2) = -6, and 3 + (-2) = 1. Therefore, the factored form of the polynomial is (x + 3)(x - 2).

Answer:

t = 3.3 seconds

Step-by-step explanation:

From the formula of vertical motion of an object under gravity we can write the equation

[tex]H = ut + \frac{1}{2} gt^{2}[/tex] ....... (1)

Where u is the initial velocity (in feet per second) of throw of the object and t is time of travel in seconds and the value of g i.e. gravitational acceleration is 32 feet/sec².

Now, while a ball is thrown vertically upward with velocity 50 ft/sec from a height of 7 ft then the time of travel of the ball before reaching the ground, the equation (1) will be written as

[tex]- 7 = 50t - \frac{1}{2} \times 32 \times t^{2}[/tex]

As we have selected the upward direction as positive so, gravitational acceleration,g will be negative and as the displacement is downward by 7 feet, so it will be negative.

⇒ 16t² - 50t - 7 = 0 ........ (2)

Now, applying Sridhar Acharya formula,

[tex]t = \frac{-(-50) + \sqrt{(-50)^{2} - 4(16)(-7)}}{2(16)}[/tex] {Neglecting the negative root as t can not be negative}

⇒ t = 3.3 seconds {Rounded to the nearest tenth}

(Answer)

Answer:

No

Step-by-step explanation:

According to the property of the triangle ,

sum of any two sides should we greater then third side of the triangle.

Here, Measurement of three sides are given as 3,3,5 .

So, sum of the measurement of first two sides is 6.

And third side equals 10.

Clearly 6 is less than 10. So . it violates the property sum of any two sides should we greater then third side of the triangle.

Thus , Sides of a triangle can't be 3,3,10.

Answer:

Yes

Step-by-step explanation:

As long as there are three sides and it forms a triangle, the answer is yes.

Answer:

the value of x is 7cm.

Step-by-step explanation:

i looked it up on the Internet next u could try n do tht

Answer:

x=65 degrees

Step-by-step explanation:

in a triangle all angles will have to add up to 180 adding the two given you can find the third one.

Answer:

a) YES. Repeating decimal

b) YES. Repeating decimal

c) NO. Decimal neither terminates nor repeats

d) YES. Terminating decimal

Step-by-step explanation:

Any rational number can be written as a fraction, that is, a division of integers.

a) The number [tex]\overline{0.54}[/tex] has a repetitive period of 54. It can be expressed as a fraction because its decimal are repeating forever

b) The number 0.16666... (expressed as a repeating 6) can also be converted to a fraction because it's a repeating decimal

c) The number 0.5473... cannot be expressed as a fraction because the ellipsis (...) means the decimals continue with no limit and no pattern can be found (no repetitive decimal)

d) The number 0.378 can be easily expressed as a fraction because it has a finite number of decimals (no ellipsis) or a terminating decimal

The expression is equivalent to −78x − 198.

To simplify the expression −13(6x + 15) − 3, you can start by distributing the −13 across the terms inside the parentheses:

−13 * 6x = −78x

−13 * 15 = −195

So, the expression becomes:

−78x − 195 − 3

Next, combine the constant terms:

−195 − 3 = −198

The simplified expression is now:

−78x − 198

This expression is equivalent to the original expression −13(6x + 15) − 3. It cannot be further simplified as the terms are not like terms and cannot be combined further. So, the answer is −78x − 198.

The expression represents a linear equation where x is the variable. It can be used to find the value of the expression for specific values of x.

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Answer:

5 over 7 and 7 over 9

Step-by-step explanation:

Answer:

5 over 7 and 7 over 9 is the answer 0w0

Answer:

30

Step-by-step explanation:

to find how many Isabelle has, we multiply Anaele's number by 5. 18(5)=90. Isabelle has 90. Arlene has one third (1/3) of the number of Isabelle. So, we divide 90 by 3. 90/3=30. Arlene has 30 goldfish

Answer:

7k

Step-by-step explanation:

Note that - (- 8k) = + 8k

Given

- k - (- 8k)

= - k + 8k

= 7k

Answer:

the answer is 194

Step-by-step explanation:

Answer:

6r+24

Step-by-step explanation:

2(r+3)=2r+6

2(2r+9)=4r+18

(2r+6)+(4r+18)=6r+24

The value of z is zero

Step-by-step explanation:

The slope is the steepness of the line.

The formula for slope is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\Here\\(x_1,y_1)\ are\ the\ coordinates\ of\ first\ point\ on\ line\\(x_2,y_2)\ are\ the\ coordinates\ of\ second\ point\ on\ line[/tex]

Here

(x1,y1) = (1,z)

(x2,y2) = (2,8)

So,

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\8 = \frac{8-z}{2-1}\\8=\frac{8-z}{1}\\8-8 = -z\\z = 0[/tex]

The value of z is zero

Keywords: slope, Line

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Answer:

A. Therefore, the slope of the above equation is 7 and x-intercept is (-1,0)

B. The slope 7 and y-intercept (0,7)

C. The slope is 7 and (1,14) is the point.

D. Y-intercept = (0,7) and X-intercept = (-1,0).

E. (1,14) is the point and the y-intercept is (0,7).

F. Points (1,14) and (2,21) are the two points.

Step-by-step explanation:

Apolline charges a fixed initial fee and a constant fee for each hour for mowing work.

If we try to model the above conditions with a total cost for mowing as C for working for h hours then we will get  

C = a + bh ....... (1)

Where a is the initial fee and b is the rate of charge per hour of work.

Now, her fee for a 5-hour job is $42 and her fee for a 3-hour job is $28.

Hence, from equation (1),  

42 = a + 5b ........ (2) and

28 = a + 3b ......... (3)  

Now, solving equations (2) and (3) we get 2b = 42 - 28 = 14

⇒ b = 7 dollars per hour of work.

And from equation (3) we get, a = 28 - 3b = 7 dollars.

So, the equation (1) becomes C = 7 + 7h ....... (4)

A. Therefore, the slope of the above equation is 7 and x-intercept is (-1,0)

B. The slope 7 and y-intercept (0,7)

C. The slope is 7 and (1,14) is the point.

D. Y-intercept = (0,7) and X-intercept = (-1,0).

E. (1,14) is the point and the y-intercept is (0,7).

F. Points (1,14) and (2,21) are the two points. (Answer)

Answer:

in short response the answer is F

Step-by-step explanation:

the two points dont intercept