16. Peter works part time for 3 hours every day and Cindy works part time for 2 hours every day.

a. If both of them get $4.50 an hour, write an inequality to compare Peter’s and Cindy’s earnings.

b. What should Cindy’s per-hour income be so that she earns at least $14 a day? Write an inequality and an explanation of how to solve it.

Answer:

The volume of the rectangular swimming pool is [tex]384.75\ m^{3}[/tex]  or  [tex]384\frac{3}{4}\ m^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular swimming pool is equal to

[tex]V=LWH[/tex]

we have

[tex]L=19\ m[/tex]

[tex]W=13\frac{1}{2}\ m=\frac{13*2+1}{2}=\frac{27}{2}\ m[/tex]

[tex]H=1\frac{1}{2}\ m=\frac{1*2+1}{2}=\frac{3}{2}\ m[/tex]

substitute

[tex]V=(19)(\frac{27}{2})(\frac{3}{2})[/tex]

[tex]V=\frac{1,539}{4}=384.75\ m^{3}[/tex]

Convert to mixed number

[tex]384.75=384\frac{3}{4}\ m^{3}[/tex]

Answer: Option A

[tex]tan(60\°) = \sqrt{3}[/tex]

Step-by-step explanation:

We know the sides and z. So since it is a straight triangle we use the Pythagorean theorem to pull the length of the x side.

[tex]z ^ 2 = x ^ 2 + y ^ 2\\\\x^2 = z^2 - y^2\\\\x=\sqrt{z^2 - y^2}\\\\x=\sqrt{2^2 - 1^2}\\\\x=\sqrt{4 - 1}\\\\x=\sqrt{3}[/tex]

By definition, the tangent of an angle is:

[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]

In this case:

[tex]adjacent = y=1\\\\opposite=x =\sqrt{3}\\\\\theta=60\°[/tex]

Then:

[tex]tan(60\°) = \frac{\sqrt{3}}{1}[/tex]

[tex]tan(60\°) = \sqrt{3}[/tex]

The answer is:

The correct option is:

A. [tex]\sqrt{3}[/tex]

Since we already know the hypothenuse and the opposite side of the triangle (y), we can calculate the value of "x" using the Pythagorean Theorem.

We have that:

[tex]Hypothenuse^{2}=Adjacent^{2}+Opposite^{2}[/tex]

We know that:

[tex]Hypothenuse=z=2\\Adjacent=x=1[/tex]

So, substituting and calculating we have:

[tex]2^{2}=1^{2}+Opposite^{2}[/tex]

[tex]4-1=Opposite^{2}[/tex]

[tex]Opposite^{2}=3\\Opposite=\sqrt{3}[/tex]

Then,using the following trigonometric relation:

[tex]Tan(\alpha)=\frac{Opposite}{Adjacent}\\\\Tan(60\°)=Tan(\frac{Opposite}{Adjacent})=Tan(\frac{\sqrt{3} }{1})^=\sqrt{3[/tex]

We have that the correct option is:

A. [tex]\sqrt{3}[/tex]

Have a nice day!

Answer:

[tex]x = 16.6\ cm[/tex]

Step-by-step explanation:

To answer this question use the secant line theorem.

If two secant segments are drawn towards a circle from an outer point, then the product of the length of the secant segment y and the length of its outer secant segment is equal to the product of the length of the other secant segment and its external secant segment.

This is:

[tex](12+6)*6 = (5+x)*5[/tex]

Now we solve the equation for the variable x

[tex]18*6 = 5*5+x*5[/tex]

[tex]108 = 25+5x[/tex]

[tex]5x = 108-25[/tex]

[tex]5x = 83[/tex]

[tex]x = \frac{83}{5}[/tex]

[tex]x = 16.6\ cm[/tex]

Answer:

16.6

Step-by-step explanation:

got it right online

Answer:

1.5 < x < 4

Step-by-step explanation:

Let x be the pH of lemon juice

As it is said that the pH is less than it will be denoted by

x<4

Similarly it is also given that lemon juice's pH is greater than 1.5

x>1.5

So,

both inequalities will be combined.

1.5 < x < 4

It is read as x is greater than 1.5 and less than 4 ..

So option 2 is correct ..

Final answer:

The correct compound inequality to represent the normal pH range of lemon juice is 1.5 < x < 4, where x is the pH value. It indicates that the pH of lemon juice is greater than 1.5 but less than 4.

Explanation:

The pH scale measures how acidic or basic a substance is. To model the normal range of pH values for lemon juice, which is said to have a pH of less than 4 and greater than 1.5, we must use a compound inequality. A compound inequality that accurately represents this scenario is 1.5 < x < 4, where x stands for the pH value of lemon juice. It is important to use the less than symbol (<) and not the less than or equal to symbol (≤) because a pH of exactly 1.5 or 4 is not included in the "normal" range as stated.

Coordinates are the group of a number used to indicate the position of a point in a graph or at a scale.the coordinate of Cristian's house are (11,0)

Given-

Jayda's house is located at (1, 5).

A fast-food restaurant is located at (9, 1).

Fast-food restaurant partitions the way from Jayda's house to Cristian's house by a ratio of 4:1

Coordinates are the group of a number used to indicate the position of a point in a graph or at a scale.

Let the coordinate of jadya's be A (1,5))

Let the coordinate of Cristian's be B ([tex]x_2,y_2[/tex])

Let the coordinate of fast food restaurant be R (9,1)

The ratio is 4:1. Thus m is 4 and n is 1.

The coordinate of the point B is,

[tex]x_R=\dfrac{nx_1+mx_2}{m+n}[/tex]

[tex]9=\dfrac{1\times1+4\times x_2}{1+4}[/tex]

[tex]9=\dfrac{1+4 x_2}{5}[/tex]

[tex]4 x_2=9\times 5-1[/tex]

[tex]x_2=\dfrac{44}{4} =11[/tex]

Find the other point of Critian's house,

[tex]y_R=\dfrac{ny_1+my_2}{m+n}[/tex]

[tex]1=\dfrac{1\times5+4\times y_2}{1+4}[/tex]

[tex]1=\dfrac{5+4 y_1}{5}[/tex]

[tex]4y_1=5-5[/tex]

[tex]y_1=0[/tex]

Thus the coordinate of Cristian's house are (11,0).

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Answer:

Step-by-step explanation:

The values at two points that differ by 1 year differ by $125, so the slope is $125 per year.

The graph shows the total cost of membership, which includes the initiation fee (y-intercept) and yearly membership dues (increase per year). The slope represents the increase per year: the yearly membership dues.

The slope of a line is determined by the change in the y-axis divided by the change in the x-axis. In this case without specific graphical data, it is conjectured that the slope may represent the yearly membership cost increase or decrease over time. A positive slope shows an increase, while a negative slope shows a decrease.

The question seems to be asking about the slope of a line related to the cost of a membership at a nature preserve. However, the provided reference information does not connect directly to this question, but outlines concepts of slope in economics and business scenarios rather than the nature preserve context. In general, the slope of a line is calculated by the change in the y-axis divided by the change in the x-axis. In this context, without a graph, one can conjecture that the slope may represent the yearly membership cost increase or decrease over time. A positive slope indicates an increase, whereas a negative slope indicates a decrease.

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Answer: Radical conjugate.

Step-by-step explanation:

By definition  [tex]a+\sqrt{b}[/tex] and [tex]a-\sqrt{b}[/tex] are called "Conjugate radicals".

Therefore, by this definition, you can know the following:

1) [tex]a+\sqrt{b}[/tex] is the conjugate of [tex]a-\sqrt{b}[/tex]

2) [tex]a-\sqrt{b}[/tex] is the conjugate of [tex]a+\sqrt{b}[/tex].

Then, since you know that [tex]3+\sqrt{11}[/tex] is a root of a polynomial function, therefore you can conclude that the name given to the other root [tex]3-\sqrt{11}[/tex] of the same function is the following:

"Radical conjugate".

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf f(x)=\cfrac{20}{4+3e^{-0.2x}}\implies f(3)=\cfrac{20}{4+3e^{-0.2(\stackrel{\downarrow }{3})}}\implies f(3)=\cfrac{20}{4+3e^{-0.6}} \\\\\\ f(3)=\cfrac{20}{4+3\frac{1}{e^{0.6}}}\implies f(3)=\cfrac{20}{4+3\frac{1}{e^{\frac{3}{5}}}}\implies f(3)=\cfrac{20}{4+3\frac{1}{\sqrt[5]{e^3}}} \\\\\\ f(3)=\cfrac{20}{4+\frac{3}{\sqrt[5]{e^3}}}\implies f(3)\approx\cfrac{20}{4+5.6464}\implies f(3)\approx 3.5421[/tex]

you could also just use plug in 0.6 as the exponent for "e", Euler's constant, in your calculator, and that works the same.

Answer:

The lines are parallel.

Step-by-step explanation:

They are parallel if their slopes are the same.

Slope of Line A =  rise / run = (7-5) / (0 - -3) = 2/3.

Slope of Line B = (4-2) / 9-6) = 2/3.

Therefore they are parallel.

The lines passing through points (-3,5) and (0,7) and through points (6,2) and (9,4) are parallel to each other. The equation of a line perpendicular to y=-4x that passes through the point (2,6) is y=1/4x+5.5.

To determine whether the lines are parallel, perpendicular, or neither, we first need to calculate the slope of both lines. The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line. It's given by the formula m = (y2 - y1) / (x2 - x1).

For line A passing through points (-3,5) and (0,7), the slope (m1) is (7-5) / (0 - (-3)) = 2/3. For line B passing through points (6,2) and (9,4), the slope (m2) is (4-2) / (9-6) = 2/3. Since m1 = m2, Line A and Line B are parallel.

To write an equation of a line in slope-intercept form that is perpendicular to the line y = -4x and passes through the point (2,6), we first note that the slope of lines that are perpendicular to each other multiply to -1. Since the slope of the given line is -4, the slope of the line perpendicular to it would be 1/4. Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we substitute for m and a point on the line (2,6) to solve for b: 6 = 1/4*2 + b. Solving for b gives b = 5.5. So the equation of the line is y = 1/4x + 5.5.

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Answer:

Iris can make 2 hats in an hour.

Step-by-step explanation:

3 hats in one and a half hours is 1 hat per half hour. 2 hats would take two half hours, which is one whole hour.

She can make 2 hats.

Since she can make 3 hats in 1.5 hours, divide 1.5 by 3 to find the unit amount of hats she can make.

1.5/3=.5

.5 of an hour is 30 mins.

Now, multiply 30 mins by 2 to find the amount of time it would take to make 2 hats.

30*2=60 or 1 hour.

She can make 2 hats in an hour.

Hope this helps!

Answer:

We'll be making 35 liters of 19% glucose.

How much of a 15% solution and a 35% solution do we mix in order to get 35 liters of a 19% glucose solution?

X = liters of 15% and Y = liters of 35%

(.15 X + .35 Y) / 35 = .19

The number of Y liters will equal (35 -X) so the equation becomes

(.15 X + .35 *(35-X) ) / 35 = .19

(.15X + 12.25 -.35X) / 35 = .19

(-.20 X / 35) + (12.25 / 35) = .19

(-.20 X / 35) + .35 = .19

(-.20 X / 35) = -.16

-.20X = -5.6

X = 28 liters of 15% and

Y = 7 liters of 35% glucose

Answer is "c" 28 liters

Answer: Option a

They are equal and parallel

Step-by-step explanation:

If a and b have the same direction then necessarily a and b are parallel.

We know that they also have the same magnitude.

Two vectors are equal if they have the same magnitude and direction.

Then we can say that a and b are equal and we can also say that they are parallel.

Therefore the correct option is the option a

The x-coordinate of the solution to the system of linear equations is 0.

To find the x-coordinate of the solution to the given system of linear equations, we need to analyze the data points provided for both Equation 1 and Equation 2.

Similarly, examining the data points for Equation 2, we notice that as x increases by 4, y increases by 1. This implies a constant rate of change and suggests that Equation 2 also follows a linear pattern. We can express Equation 2 in the slope-intercept form:

y = (1/4)x + b.

To find the x-coordinate of the solution to the system, we need to set the two equations equal to each other and solve for x.

Equating the two equations, we have:

-x + b = (1/4)x + b

By simplifying the equation, we can eliminate the b term:

-x = (1/4)x

Next, we can multiply both sides of the equation by 4 to eliminate the fraction:

-4x = x

Bringing all the x terms to one side, we get:

-4x - x = 0

Combining like terms, we have:

-5x = 0

Finally, we divide both sides of the equation by -5 to solve for x:

x = 0

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Answer:

The answer is B.

Step-by-step explanation:

Simply you change 6 3/4 into decimal form which is 6.75 then you divide it by the amount which is 3/4= .75

divide 6.75 by .75 equals 9

i hope this helps

Answer:

b.  quantitative, continuous

Step-by-step explanation:

Since here Dog = 0.07

Cat = 0.1

Snake = 0.12, and so on.

It is a numeric form So, it is quantitative data. And we can't count them(it include numbers between two natural number) so it is Continuous Variable.

The variable which is in numeric form is called Quantitative Variable. Example: Weight, Marks, etc.

And, the variable which we can't count is known as Qualitative Variable. Example: Smoking, Non- Smoking, etc.

Further Quantitative Variable can be divided into two parts:

The variable which we can count is known as the Discrete variable. It includes the natural numbers only. Example: Number of apples, Number of senior citizens in a particular area, etc.

The variable which we can't count is known as Continuous Variable. Example: Height, Weight, etc.

Answer:

Option B [tex]HI=5\sqrt{2}\ units[/tex]

Step-by-step explanation:

Applying the Pythagoras Theorem

[tex]HI^{2}=(y2-y1)^{2}+(x2-x1)^{2}[/tex]

substitute the given values

[tex]HI^{2}=(2+3)^{2}+(3+2)^{2}[/tex]

[tex]HI^{2}=(5)^{2}+(5)^{2}[/tex]

[tex]HI^{2}=50[/tex]

[tex]HI=5\sqrt{2}\ units[/tex]

Answer:

B

Step-by-step explanation:

8 days ago is -8 and the time was 24 minutes

9 days ago is -9 and the time was 18 minutes.

The time 2 days ago was halfway in between.

Add the two times together and divide by 2:

24 + 18 = 42 / 2 = 21 minutes

The coordinate is at (-2,21)

Answer:

The coordinate would be (-1, -1)

Step-by-step explanation:

Answer:

24 m

Step-by-step explanation:

The last un-labeled side of the figure is 6 - 4 = 2 m

Simply add all the sides (including the one not labeled) to get the perimeter

4+6+6+2+2+4 = 24 m

Answer:

24m

Step-by-step explanation:

6 + 6 + 2 + 2 + 4 + 4 =24

Answer:

Your answer is 17%

Step-by-step explanation:

Divide the total number of seniors by the total number of students and turn it into a percentage.

5/30= 0.16666= 17%

Answer:

14%

Step-by-step explanation:

Answer: x = 19.42, y = 18.47, z = 18°

Step-by-step explanation:

This is assumed to be a 90° triangle so you can use Soh Cah Toa to answer the questions. You must use a calculator for the last step.

[tex]cos\theta=\dfrac{adjacent}{hypotenuse}\implies cos72^o=\dfrac{6}{x}\implies x=\dfrac{6}{cos72^o}\implies x=19.42\\\\\\tan\theta=\dfrac{opposite}{adjacent}\implies tan72^o=\dfrac{y}{6}\implies y=6\ tan72^o}\implies y=18.47\\\\[/tex]

Use Triangle Sum Theorem to find the angle measure of z:

90° + 72° + z = 180°

   162°     + z = 180°

                  z = 18°

Answer:

1.83×[tex]10^{-9}[/tex]

Step-by-step explanation:

The exponent on the base of ten is -9 for both.  The easiest way to do this when that is the case is to factor it out:

[tex]10^{-9}(6.33-4.5)[/tex]

and then perform the subtraction to give you

1.83×[tex]10^{-9}[/tex]

The multiplicative inverse of a number is the reciprocal of the number.

For a whole number this would be making it a fraction with 1 as the numerator.

The  multiplicative inverse of 5 is 1/5

Multiplicative inverse means that the numerator and denominator switch places. Remember that all non fraction numbers can be turned into a fraction by making the denominator 1 like so...

[tex]\frac{5}{1}[/tex]

Now you can take the multiplicative inverse of 5/1 to get...

[tex]\frac{1}{5}[/tex]

^^^That is equal to 0.2

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

r=0.8

Step-by-step explanation:

We know that a geometric series has the following look: (see picture attached).

Comparing both series, we can clearly see that r=0.8

The value of r in a geometric series can be positive, negative, or zero.

The value of r in a geometric series can be positive, negative, or zero. When r is positive, it means the population is increasing in size. When r is negative, it means the population is decreasing in size. And when r is zero, it means the population size is unchanging, which is known as zero population growth.

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Answer:

140 coins total

Step-by-step explanation:

Straightforward, this reads "7 is 5% of how many?".  Algebraically, the word "is" means an equals sign, and the word "of" means you multiply.  Of course, the 5% needs to be in decimal form.  Taking the sentence above, algebraically it is:  7 = .05x.  Divide by .05 on both sides to get x = 140

Answer: There are 30 gallons of anti freeze of  first brand and 120 gallons of anti freeze of second brand.

Step-by-step explanation:

Since we have given that

Percentage of anti freeze in first brand = 35%

Percentage of anti freeze in second brand = 85%

Percentage of anti freeze in mixture = 75%

Total number of gallons of mixture = 150 gallons

We will use " Mixture and Allegation":

 First brand         Second brand

      35%                      85%

                      75%

------------------------------------------------------------------

85%-75%         :            75%-35%

    10                :               40

     1                 :                 4

So, Number of gallons of anti freeze in first brand is given by

[tex]\dfrac{1}{5}\times 150\\\\=30\ gallons[/tex]

Number of gallons of anti freeze in second brand is given by

[tex]\dfrac{4}{5}\times 150\\\\=40\times 3\\\\=120\ gallons[/tex]

Hence, there are 30 gallons of anti freeze of  first brand and 120 gallons of anti freeze of second brand.

Answer:

  8 cm

Step-by-step explanation:

See the diagram below.

The triangle formed by the radius, half the chord length, and the distance (d) from the center to the water is a right triangle with hypotenuse 20 cm and one leg length 16 cm. Then the other leg (d) can be found using the Pythagorean theorem:

  d^2 + 16^2 = 20^2

  d = √(400 -256) = 12

The depth of the water is the difference between this distance and the radius, so is ...

  20 cm - 12 cm = 8 cm

The maximum depth of the water in the pipe is 8 cm.

Answer:

8 cm

Step-by-step explanation:

Answer:

DE and BC

Step-by-step explanation:

Because the pieces of the two sides of the triangle would be proportional the line in the middle that has specified points will be parallel to the bottom line that was specified points. and because neither f or g were specified to be proportional they are irrelevant.

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HAVE A GREAT DAY

Answer:

If there's no limits on the shape of the triangle, the length of the third side shall be between (excluding the endpoints)

Step-by-step explanation:

Let the length of the third side be [tex]x[/tex] kilometers. The length of each side shall be positive. In other words, [tex]x > 0[/tex].

Consider the triangle inequality theorem. The sum of any two ends shall be greater than the third end. For this triangle, the lengths of the three sides are:

By the triangle inequality theorem,

[tex]\left\{\begin{aligned}& 20 + 35 > x\\ & 20 + x > 35\\ & 35 + x > 25\end{aligned}\right.[/tex].

Rewrite and simplify each inequality:

[tex]\left\{\begin{aligned}& x < 55\\ & x > 15\\ & x > -15\end{aligned}\right.[/tex]

[tex]x[/tex] shall satisfy all three inequalities. As a result, the range of [tex]x[/tex] shall be the intersection of the solution sets of all three inequalities.

Refer to the sketch attached. On the sketch, the intersection is the region where the three colored lines are above each other. That's represents the interval

[tex]15 < x < 55[/tex].

In other words, the length of the third side is supposed to be between 15 kilometers and 55 kilometers.

Answer:

the answer is 15<x<55

Step-by-step explanation:

For this case we have that there are a total of 14 male students and a total of 16 female students. Thus, there is a total of 30 students distributed in the four categories.

On the other hand, we have a total of 8 Junior students.

Then, the probability of selecting a student Junior is [tex]\frac {8} {30} * 100 = 26.67[/tex]

Rounding off we have 27%

Answer:

27%

The probability that the student is junior to the nearest whole percent is 27%

Probability is defined as the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

The total outcome will be the total number of students (both male and female)

Total outcome = 4+6+2+2+3+4+6+3

Total outcome = 30

Since we are to find the probability that the student is a junior.

Total Juniors = 2 + 6 = 8

Expected outcome = 8

Probability that the student is junior = 8/30

Express as a percentage:

[tex]Pr(Juniors)=\dfrac{8}{30} \times 100\%\\ Pr(Juniors)=\dfrac{800}{30}\\ Pr(Juniors)=26.66\%\\[/tex]

Hence the probability that the student is a junior is 27%.

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