The amount of water lost from a leaking faucet every hour is represented by the graph below. Interpret the slope of the function in terms of the problem.

A. 5 mL of water are lost every hour
B. 2.5 mL of water are lost every hour
C. 2 mL of water are lost every hour
D. 10 mL of water are lost every hour

Answer:

Choice B:

2M + 4S = 100    

M + S = 41  

Step-by-step explanation:

2M                 [multiple choice questions were worth 2 points each]

4S                   [short answer questions were worth 4 points each]

= 100               [worth a total of 100 points.]

2M + 4S = 100    

M + S = 41     [There were 41 questions]

The simplified expression of 3y + 6x - 2x - 2y is y + 4x.

An algebraic expression is an expression which is made up of variables and constants, along with algebraic operations like addition and subtraction.

To simplify an expression means to write an equivalent expression which contains no similar terms or rewriting the same algebraic expression with no like terms.

Therefore, let's simplify the expression with no like terms as follows;

3y + 6x - 2x - 2y

combine like terms

3y - 2y + 6x - 2x

Therefore, the simplified expression is y + 4x

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Answer:

D

Step-by-step explanation:

if you move the preimage on the image you can see that the two figures are equals

Answer: y = 5x

Step-by-step explanation:

The chances that the revenue on the first show will exceed $800 when mean revenue is $336.25 and standard deviation is $38.16 is essentially zero. i.e. 0

A normal distribution is a type of continuous probability distribution in which the majority of data points cluster in the middle of the range, while the remainder taper off symmetrically toward either extreme. The mean of the distribution is also known as the middle of the range.

The normal distribution is primarily used to calculate the likelihood of an observation in a distribution falling above or below a given value.

Given,

Mean, [tex]\mu[/tex] = 336.25

variance, [tex]\sigma^2[/tex]= 1456

then,

standard deviation, [tex]\sigma = \sqrt{1456}[/tex] = 38.16

To determine the chances that the revenue on the first show will exceed 800 is1:

[tex]1-p(z=\frac{x-\mu}{\sigma})\\\\=1-p(z=\frac{800-336.25}{38.16})\\\\=1-p(z=\frac{436.75}{38.16})\\\\=1-p(z=12.15)\\\\=1-1=0[/tex]

Hence, there is no chance that the revenue will exceed $800 on the first show.

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In this case, the critical region will be in the right tail.

To answer this question, you need to conduct a hypothesis test to determine whether the mean amount of paint in 1-gallon cans from this manufacturer is significantly different from 1 gallon. The null hypothesis for this test is that the mean amount of paint in 1-gallon cans from this manufacturer is equal to 1 gallon, and the alternative hypothesis is that it is greater than 1 gallon.

To determine the critical region(s) for this test, you need to decide on the significance level, which is given as 0.05. This means that you will reject the null hypothesis if the test statistic falls in the critical region with a probability of less than 0.05.

In this case, since the alternative hypothesis is that the mean amount of paint in 1-gallon cans is greater than 1 gallon, the critical region will be in the right tail. This means that you will reject the null hypothesis if the test statistic falls in the right tail with a probability of less than 0.05.

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Answer:

x = [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

- 4x + 3 = 2(x - 1) ← distribute parenthesis by 2

- 4x + 3 = 2x - 2 ( subtract 2x from both sides )

- 6x + 3 = - 2 ( subtract 3 from both sides )

- 6x = - 5 ( divide both sides by - 6 )

x = [tex]\frac{-5}{-6}[/tex] = [tex]\frac{5}{6}[/tex]

Answer:

The inequality x + y > 15 would not be valid in this system. This inequality states that the total number of hours that you and your friend drive together is greater than 15 hours, but we know that the trip will take no more than 15 hours to complete. Therefore, this inequality is not valid.

The other inequalities in the system are:

x < 8, because you want to drive less than 8 hours

y > 10, because your friend agrees to drive at least 10 hours

x + y <= 15, because the trip will take no more than 15 hours to complete.

These inequalities are all valid and can be used to determine the possible number of hours that you and your friend will drive on your road trip.

The answers are n= -8/3 or 3

Changes made= n2 was replaced by n^2 and making the equation 3n²-n-24=0

Factoring 3n²-n-24

   The first term is,  3n² its coefficient is  3 .

   The middle term is,  -n  its coefficient is  -1 .

   The last term, "the constant", is  -24

Step 1: Multiply the coefficient of the first term by the constant   3 • -24 = -72

Step 2: Find two factors of  -72  whose sum equals the coefficient of the middle term, which is   -1 .

      -72    +    1    =    -71

     -36    +    2    =    -34

     -24    +    3    =    -21

     -18    +    4    =    -14

     -12    +    6    =    -6

     -9    +    8    =    -1

Step 3: Rewriting the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  8

                    3n2 - 9n + 8n - 24

Step 4: Adding up the first 2 terms, pulling out like factors :

                   3n • (n-3)

             Adding up the last 2 terms, pulling out common factors :

                   8 • (n-3)

Step 5: Adding up the four terms of step 4 :

                   (3n+8)  •  (n-3)

            Which is the desired factorization

The equation at the end of second equation:

(n - 3) • (3n + 8)  = 0

           Add  3  to both sides of the equation :

                         n = 3

           Subtract 8  from both sides of the equation :

                            3n = -8

            Divide both sides of the equation by 3:

                     n = -8/3 = -2.667

The answers are n= -8/3 or 3

Changes made= n2 was replaced by n^2 and making the equation 3n²-n-24=0

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Answer:

Five

Step-by-step explanation:

There are 9 two-digit numbers with a units digit of 7:

17, 27, 37, 47, 57, 67, 77, 87, 97

Of these, 4 are composite numbers:

27 = 3³

57 = 3×19

77 = 7×11

87 = 3×29

The remaining 5 are prime numbers:

17, 37, 47, 67, 97

After solving the equation, the value obtained for x will be equal to 1.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

4 times x plus one-half equals one-half times x plus 4.

Let's write it in mathematical form,

4x + 1/2 = 1/2x + 4

Now, solve the equation for x,

4x - 1/2x = 4 - 1/2

(8x - x)/2 = (8 - 1)/2

7x/2 = 7/2

x = (7 × 2)/(2 × 7)

x = 14/14

x = 1

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first 2;

a) 7(2) + 8 = 22 > 16, 7(4) + 8 = 36>32

36 - 22 = 14/2 = 7

32 - 16 = 16/2 = 8

7<8

the table has a greater rate of change

y intercept

equation; 8

table; 0

8> 0

the equation has a greater y intercept

Answer:

x=310°

x is a reflex angle

Step-by-step explanation:

x+50°=360°

x=360-50

x=310

X ia a reflex angle beacuse it is more than 180° but less then a 360°

Answer:

Step-by-step explanation:

a) The amount of their account on July 1 can be found by calculating the balance of the account at the end of the first six months and then adding the second $2,000 deposit:

balance at end of first 6 months = $2,000 * (1 + 0.06/2)^2 = $2,060.60

total balance on July 1 = $2,060.60 + $2,000 = $4,060.60

b) The balance of the account one year later on January 1 can be found by calculating the balance at the end of the second six months and adding it to the balance at the end of the first six months:

balance at end of second 6 months = $2,060.60 * (1 + 0.06/2)^2 = $2,123.36

total balance on January 1 = $2,123.36 + $2,060.60 = $4,183.96

c) The compound interest can be found by subtracting the initial deposit from the balance one year later:

compound interest = $4,183.96 - $2,000 = $2,183.96

The shirt that Brian can iron in a minute is 5/81 shirts.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In this case, when we have a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

Here, Brian irons 2/9 of his shirt in 3 3/5 minutes and it was stated that he irons at a constant speed

Therefore, to calculate the shirt he iron in a minute will go thus:

Here, set up a proportion (shirt ironed/minutes = shirt ironed/minutes). This will be illustrated as:

= 2/9 ÷ 3 3/5

= 2/9 ÷ 18/5

= 2/9 × 5/18

= 10 / 162

= 5 /81

The Fraction that illustrates the information is 5/81.

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Complete question

Brian irons 2/9 of his shirt in 3 3/5 minutes. If Brian irons at a constant speed how much of his shirt does he iron in a minute

Answer:

Step-by-step explanation:

x² = 16² + 30²

x² = 256 + 900

x² = 1156

x = √1156

x = 34 cm

34 + 16 + 30 =

80 cm

Answer:

Step-by-step explanation:

first of all find the value of 'x'

In a right angle triangle, x= underroot of (16 square+30square)cm [from Pythagorastheorem]

. Therefore, x=34

Now perimeter of the given triangle is = (16+30+34)cm =80cm

Answer:

x = 98

Step-by-step explanation:

Solve for x:

(x - 14)/7 = 12

Multiply both sides of (x - 14)/7 = 12 by 7:

(7 (x - 14))/7 = 7×12

(7 (x - 14))/7 = 7/7×(x - 14) = x - 14:

x - 14 = 7×12

7×12 = 84:

x - 14 = 84

Add 14 to both sides:

x + (14 - 14) = 14 + 84

14 - 14 = 0:

x = 84 + 14

84 + 14 = 98:

Answer:  x = 98

The distance travelled by car in 90 minutes will be 1.5x miles. The correct option is B.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that If a car travels at an average speed of x miles per hour. The distance travelled by car in 90 minutes will be calculated as,

x miles ⇒ 1 hours

x miles ⇒ 60 minutes

1 minute ⇒ x / 60 miles

90 minutes ⇒ ( 90x) / 60

90 minues ⇒ 1.5x miles

The missing options are given below.

A. 1.5x miles

B. 3x miles

C. 2x miles

D. 4x miles

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Answer:

The pattern is that each number in the sequence is the previous number minus 1.5. For example, -5.5 is -4 minus 1.5, -7 is -5.5 minus 1.5, and so on.

Answer:

-1.5

Step-by-step explanation:

You take two of the variables in the pattern and subtract them with the second one being the minuend, and the first being the subtrahend.

For example we will use -4 and -5.5

(-5.5) - (-4) = -1.5

There is a negative sign present so it indicates subtraction towards the pattern.

Hence, the pattern change rate is -1.5

Answer:

17/200 or [tex]\frac{17}{200}[/tex]

Step-by-step explanation:

The length of BC is approximately 5.72 miles and the length of AC is approximately 12.67 miles.

Let's represent the length of the side opposite angle A "BC" and the length of the side adjacent to angle A "AC". We can then use the sine function to find BC:

sin(A) = BC / AC

Substituting the given values, we get:

sin(24°) = BC / 14

We can use a calculator or look up the value of sin(24°) to get:

sin(24°) ≈ 0.406

Solving for BC, we get:

BC = 14 * sin(24°) ≈ 5.72

To find AC, we can use the cosine function:

cos(A) = AC / AC

Substituting the given values, we get:

cos(24°) = AC / 14

We can use a calculator or look up the value of cos(24°) to get:

cos(24°) ≈ 0.913

Solving for AC, we get:

AC = 14 x cos(24°) ≈ 12.67

Thus, BC is about 5.72 miles long while AC is about 12.67 miles in length.

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Answer:

x < -3

Step-by-step explanation:

15 < -5x

15/-5 > -5x/-5

-3 > x

Move the variable to the left and flip the inequality

x < -3

Answer:

Below

Step-by-step explanation:

See image:

The rate of interest in one account whose investment is $2300 will be 3.21%.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Aniyah puts $2300 in one record and $1400 in a record paying 4 % higher interest. Toward the finish of one year, she had procured $130 in interest.

Let 'x' be the interest. Then the equation is given as,

(2300 × x × 1)/100 + (1400 × 4 × 1) / 100 = 130

Simplify the equation, then we have

23x + 56 = 130

23x = 74

x = 3.21%

The pace of revenue in one record whose speculation is $2300 will be 3.21%.

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a) The table of the discrete function is given as follows:

Basketballs - Spending

0 - $0

1 - $15

2 - $30

3 - $45

4 - $60

5 - $75

6 - $90

7 - $105.

b) With the spending of $105, the number of basketballs purchased was of 7.

Discrete and continuous functions depends on the values assumed by the input values of the function, as follows:

In this problem, we have that the number of basketballs purchased is a countable amount, assuming only integers, hence it is a discrete function.

The proportional relationship means that each basketball costs $15, and hence the table is constructed considering it.

Hence the number of basketballs purchased with a cost of $105 is given as follows:

105/15 = 7 basketballs.

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Area del triangulo = base por altura/2

A = b*h/2    

A = 22,5cm²

Base = 5cm

a = b*h/2

22,5cm² = 5cm /h

22,5cm²/5cm = h

4,5cm = h

What is Area del?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

La altura del triangulo es de 4,5cm

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The solution is y = -2x + 2

The equation of line that passes through the point P ( -2 , 6 ) and is perpendicular to the line x - 2y = 7 is given by y = -2x + 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Let the point be P = P ( -2 , 6 )

The line is perpendicular to the line x - 2y = 7

So , the product of the slopes of the lines will be -1

And , m₁ x m₂ = -1

Now , the slope of the line x - 2y = 7 is calculated as

x - 2y = 7

Adding 2y on both sides of the equation , we get

2y + 7 = x

Subtracting 7 on both sides of the equation , we get

2y = x - 7

Divide by 2 on both sides of the equation , we get

y = x/2 - 7/2

The equation is of the form y = mx + b where m is the slope and b is the y-intercept

So , the slope of the line m₁ = 1/2

Now , since the lines are perpendicular

the product of the slopes of the line will be -1

And , m₁ x m₂ = -1

Substituting the values in the equation , we get

1/2 x m₂ = -1

Multiply by 2 on both sides of the equation , we get

m₂ = -2

Therefore , the slope of the line A is -2

Now , the equation of line A is given by the formula

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 6 = -2 ( x - ( - 2 ) )

y - 6 = -2 ( x + 2 )

y - 6 = -2x - 4

Adding 6 on both sides of the equation , we get

y = -2x + 2

Hence , the equation of line is y = -2x + 2 where slope of the line is -2 and the y intercept is 2

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Develop a 90% confidence interval for the population portion is = ( 0.594 , 0.546 )

Develop a 95% confidence interval for this population proportion is =

( 0.599 , 0.54 )

We are given the following in the question:

Sample size, n = 1007 adults

Number of respondent that  they will be able to afford health insurance in the future, x = 574

Point estimate of the population proportion

P = x/n

P = 574/1007

P = 0.57

Develop 90% Confidence Interval,

P + [tex]z_{critical}[/tex] * [tex]\sqrt{\frac{P(1-P)}{n} }[/tex]

[tex]z_{critical}[/tex] at a_0.10 = ± 1.64

Putting values, we get,

= 0.57 ± 1.64 * [tex]\sqrt{\frac{0.57(1-0.57)}{1007} }[/tex]

= 0.57 ± 1.64 * [tex]\sqrt{\frac{0.2451}{1007} }[/tex]

= 0.57 ± 1.64 * [tex]\sqrt{0.00024}[/tex]

= 0.57 ± 1.64 * 0.015

= 0.57 ± 0.024

= 0.57 + 0.024     , 0.57 - 0.024

= ( 0.594 , 0.546 )

Confidence interval 95% Confidence Interval,

P + [tex]z_{critical}[/tex] * [tex]\sqrt{\frac{P(1-P)}{n} }[/tex]

[tex]z_{critical}[/tex] at a_0.05 = ± 1.96

Putting values, we get,

= 0.57 ± 1.96 * [tex]\sqrt{\frac{0.57(1-0.57)}{1007} }[/tex]

= 0.57 ± 1.96 * [tex]\sqrt{\frac{0.2451}{1007} }[/tex]

= 0.57 ± 1.96 * [tex]\sqrt{0.00024}[/tex]

= 0.57 ± 1.96 * 0.015

= 0.57 ± 0.0294

= 0.57 + 0.0294     , 0.57 - 0.0294

= ( 0.599 , 0.54 )

Therefore,

Develop a 90% confidence interval for the population portion is = ( 0.594 , 0.546 )

Develop a 95% confidence interval for this population proportion is =

( 0.599 , 0.54 )

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Answer:  A= 52cm  B= 94mm  C= 9m  D= 17cm

Step-by-step explanation:

A) You first need to find the missing sides by doing

11-9= 2

and 15-9= 6

you then add it all together

6+2+9+9+15+11=52cm

B) You first need to find the missing sides by doing

25-18=7

and 22-6= 16

you then add it all together

25+22+18+16+7+6=94mm

C) You first need to find the missing sides by doing

0.5+1=1.5 then 2.5-1.5=1

and 1.2+0.8=2 then 2-0.5=1.5

you then add the numbers all together

1+1.5+0.8+1+0.5+0.5+1.2+2.5=9m

D) You first need to find the missing sides by doing

2.5+1= 3.5 then 3.5-2=1.5

and 1.5+2.5=4 then 5-4=1

you then add all the numbers together

2.5+2.5+1.5+1+5+2+1+1.5=17cm