A bag of baby carrots and a container of hummus dip contain a total of 650 calories. For a snack, Rosarita ate of the bag of carrots and of the container of hummus. Her snack contained a total of 260 calories. If x represents the total number of calories in the bag of carrots and y represents the total number of calories in the container of hummus, what is one of the equations for this scenario? X+y=650 x+y=260

Answer:

Part 1) The slopes are negative reciprocals of one another.

Part 2) There is no relationship.

Step-by-step explanation:

Part 1)

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

Part 2)

The y-intercept is the value of y when the value of x is equal to zero

Two linear functions that are perpendicular, could have the same y-intercept (the y-intercept would be the point of intersection between both lines)

so

There is no relationship

To find the value of b in the exponential function, we can use the given data points for the years 2010 and 2012. By substituting the values into the equations, we can solve for b.

To find the value of b in the exponential function, we can use the given data points for the years 2010 and 2012. Let's start by setting up two equations:

p(0) = ab0 = a = 425

p(2) = ab2 = 612

From the first equation, we know that a = 425. Substituting this value into the second equation:

425b2 = 612

Divide both sides of the equation by 425:

b2 = 612/425

Take the square root of both sides:

b = √(612/425)

Simplifying the expression gives us the value of b.

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Answer:

[tex]\displaystyle -11 = x[/tex]

Step-by-step explanation:

3x + 15 = x - 7

- 3x + 7 - 3x + 7

____________

[tex]\displaystyle \frac{22}{-2} = \frac{-2x}{-2} \\ \\ -11 = x[/tex]

I am joyous to assist you anytime.

Answer: C. 225

Step-by-step explanation:

To get the total population (x), we will take the 40% of the total population and equate to 90

40%× x = 90

40/100 × x = 90

40x/100= 90

Cross multiplying,

40x = 100 × 90.

x = 9000/40

x =225 C

Answer:

9.6.

Step-by-step explanation:

Because DE || AC:

x/12 = 8/10

10x = 96

x = 9.6.

Answer:

36

Step-by-step explanation:

Pretty simple

Multiply the numbers of different type of wood by the different type of length by the different type of width which is 4x3x3 = 36

4 wood type A B C D

3 length type L1 L2 L3

3 width type 1 2 3

So for wood A we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)

for wood B we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)

for wood C we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3)

for wood D we have, (L1, 1) (L1,2)(L1,3)(L2,1)(L2,2)(L2,3)(L3,1)(L3,2)(L3,3) if we count the combinations together we will arrive at 36

Answer:

The Inequality modelling the equation is [tex]425\leq x\leq 523[/tex].

The cafeteria typically serve lunch for students between 425 to 523.

Step-by-step explanation:

Given:

Each students pays for lunch = $2.75

Cafeteria brings between $1168.75 and $1438.25.

We need to find the number of students cafeteria typically serve.

Solution:

Let the number of student served be 'x'.

Now we can say that;

Total money make is equal to Each students pays for lunch multiplied by number of students served.

But total money made is in the form of range so we can say that;

[tex]1168.75\leq 2.75x\leq 1438.25[/tex]

Now Dividing all sides by 2.75 we get;

[tex]\frac{1168.75}{2.75}\leq \frac{2.75x}{2.75}\leq \frac{1438.25}{2.75}\\\\425\leq x\leq 523[/tex]

Hence the Inequality modelling the equation is [tex]425\leq x\leq 523[/tex].

Hence we can say that, The cafeteria typically serve students between 425 to 523.

Answer: It will take the largest pipe 5.5 hours to fill the swimming pool alone.

It will take the smallest pipe 16.5 hrs to fill the swimming pool alone.

It will take the other pipe 11 hours to fill the pool alone.

Step-by-step explanation: let time needed to fill the swimming pool by the largest pipe be x ... eq (1)

Let time needed to fill the swimming pool by the smallest pipe be 3x ... eq(2)

Let time needed to fill the swimming pool by the other pipe be 2x ...eq(3)

The job to be done (to fill a swimming pool) be 3/x +3/3x+3/2x=1 ... eq(4)

Multiply 6x on both sides you will get:

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

18+6+9=6x

33=6x

33/6=x

X=5.5hours

Substitute x=5.5 into EQ 2 and 3

3x=3×5.5=16.5hours

2x=2×5.5=11hours

Check: substitute the value of x into eq3/5.5+3/16.5+3/11

0.545+0.182+0.273=0.9997=1

Answer: c. The mean is much larger than the median

Step-by-step explanation:

A dataset is skewed to the right when the peak of the dataset is located in the left( left of the mean), and it has a long right tail. It is also call positive skewed distribution. One of the characteristics of right skewed dataset is that the mean of the dataset is always greater/larger than the median and mode.

Therefore, for the case above if the mean is much larger than the median, it indicates that the dataset is skewed to the right.

A dataset is skewed to the right when the mean is much larger than the median. Therefore, the correct answer is option c.

When a dataset is skewed to the right, it means that the distribution of data is not symmetric, and it is stretched out more towards the higher values (right side) than the lower values (left side). This can be due to the presence of outliers or a natural characteristic of the data.

Now, let's look at why option "c" indicates right skewness:

c. The mean is much larger than the median.

The mean is the arithmetic average of all the values in the dataset, while the median is the middle value when the data is arranged in order. When a dataset is positively skewed (skewed to the right), it means that there are some significantly larger values in the right tail of the distribution that pull the mean to the right (towards higher values).

In this situation:

The mean gets pulled toward the larger values because the larger values have a greater impact on the mean due to their magnitude.

The median remains closer to the bulk of the data because it is not affected by extreme values as much as the mean.

So, when the mean is much larger than the median, it is an indication that there are significant outliers or a longer right tail in the dataset, which is a characteristic of a right-skewed distribution.

Therefore, the correct answer is option c.

Learn more about Skewed to the right here:

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Answer:

y=4x

Step-by-step explanation:

Given : x represent the number of television show episodes that are taped in each seasons

To Find : write an expression for the number of episodes taped in 4 seasons

Solution:

Let number of episodes taped in 4 seasons be y

Number of the episodes taped in 1 season = x

So, number of episodes taped in 4 seasons :

y= 4x

Hence the required expression for the numder of episodes taped in 4 seasons :y= 4x

Answer:

Honestly, if you think about it, the answer is right in front of you!

Step-by-step explanation:

The y- intercept is 3, and the x-intercept is 1. This means that the curve should have coordinate plots of (0,3) and (1,0).

The other information is not really needed if you know the x-and-y-intercepts!

There is only 1 curve that has the included intercepts, and that is the curve on option A)'s graph.

I hope this helps and wasn't too confusing!

- sincerelynini

Answer:

the rise of the center of the rail will be given by =[tex]\sqrt{hypotenuse^{2}\hspace{0.15cm} -\hspace{0.15cm} base^{2} }[/tex]

= [tex]\sqrt{1500.065^{2} \hspace{0.15cm} -\hspace{0.15cm}1500^{2} }[/tex] m = 13.964 m

Step-by-step explanation:

i) the normal length of the railroad is 3 km = 3000 m.

ii) on a hot day day the railroad rail expands by 13cm  = 0.13m

iii) the center of the railroad is at 1500 m which is half of the total length.

iv) the expansion of the railroad in either half of the road is 0.065m which is half of the total expansion.

v) each half of the railroad can be represented by a right angled triangle whose base will be = 1500 m and hypotenuse will be = 1500.065 m .

vi) the rise of the center of the rail will be given by =[tex]\sqrt{hypotenuse^{2}\hspace{0.15cm} -\hspace{0.15cm} base^{2} }[/tex]

= [tex]\sqrt{1500.065^{2} \hspace{0.15cm} -\hspace{0.15cm}1500^{2} }[/tex] m = 13.964 m

The center of the rail would rise about 16.06 meters above the ground.

To find out how much the center of the rail rises above the ground due to expansion:

we can consider that the rail expands uniformly along its length.

If it expands by 13 cm over a length of 3 km, we can calculate the rise at the center using trigonometry, considering that the expansion causes the rail to form a very shallow arc.

The expansion forms a segment of a circle, where the rail length is the arc length, and the rise at the center is the height of the segment. We can use the formula for the height of a segment of a circle:

[tex]\[ h = r - \sqrt{r^2 - \left(\frac{l}{2}\right)^2} \][/tex]

Where:

h is the height of the segment (the rise at the center),

r  is the radius of the circle (which we can approximate as the radius of the Earth, as the rail is very long compared to its curvature),

l is the arc length of the segment (the expansion of the rail).

Given that the Earth's radius is approximately 6371 km, we need to convert all lengths to meters:

[tex]\[ r = 6371 \times 1000 \text{ meters} \][/tex]

[tex]\[ l = 3 \times 1000 \times 100 \text{ meters} \][/tex]

[tex]\[ h = 6371 \times 1000 - \sqrt{(6371 \times 1000)^2 - \left(\frac{3 \times 1000 \times 100}{2}\right)^2} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{(6371000)^2 - (150000)^2} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{40641464900000 - 22500000000} \][/tex]

[tex]\[ h \approx 6371000 - \sqrt{40641442400000} \][/tex]

[tex]\[ h \approx 6371000 - 6370983.94 \][/tex]

[tex]\[ h \approx 16.06 \text{ meters} \][/tex]

Answer:

The Subtraction equation use to find the age of his oldest relative is [tex]x-79=5[/tex].

Step-by-step explanation:

Given:

Age of youngest  relative = 5 years

We need to write a subtraction equation that could be used to find the age of his oldest relative.

Solution:

Let the age of the oldest relative be 'x'.

Now given:

Age of youngest  relative is 79 years less than the age of his oldest relative.

So we can say that;

Age of oldest relative minus 79 is equal to Age of the youngest relative.

framing in equation form we get;

[tex]x-79=5[/tex]

Hence the Subtraction equation use to find the age of his oldest relative is [tex]x-79=5[/tex].

Final answer:

The subtraction equation to find the age of Curry's oldest relative, based on the given information, is x - 5 = 79. Solving this equation reveals that the oldest relative is 84 years old.

Explanation:

The question involves setting up a subtraction equation to find the age of Curry's oldest relative, given that the youngest relative is 5 years old and this is 79 years less than the age of the oldest relative. We can represent the age of the oldest relative as x. The equation is based on the information that the difference in age between the oldest and youngest relatives is 79 years. Therefore, the equation can be set up as x - 5 = 79.

To solve for x, which represents the age of the oldest relative, you would add 5 to both sides of the equation to isolate x on one side. This results in x = 84. So, the oldest relative is 84 years old.

Yes, it is possible to get three different values for the same statistic when sampling from a set population due to sampling variation.

Yes, it is possible to get three different values for the same statistic when sampling from a set population.

For example, let's consider a population of students' test scores. If three different samples are taken from this population, each sample may have different scores, resulting in different values for the same statistic such as the mean.

This variability in sample statistics is due to sampling variation, which is a natural occurrence when selecting different samples from the same population.

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Final answer:

A person can talk for at most 19 minutes on a long-distance call without exceeding a $2 limit, accounting for the initial charge and the cost of additional minutes.

Explanation:

To find out at most how many minutes a person can talk on a phone without exceeding $2, considering the initial charge is 40 cents for the first three minutes, and 10 cents for each additional minute, we need to calculate the total cost based on the number of minutes.

The problem can be broken down as follows:

The cost for the first 3 minutes is 40 cents.

After the initial 3 minutes, each additional minute costs 10 cents.

We have a budget of $2 (or 200 cents) to not exceed.

First, subtract the initial 40 cents from the total budget:

200 cents - 40 cents = 160 cents

With 160 cents left and each additional minute costing 10 cents:

160 cents[tex]\(\div\)[/tex] 10 cents = 16 additional minutes

Therefore, adding the initial 3 minutes:

3 + 16 = 19 minutes

A person can talk for at most 19 minutes without exceeding a $2 limit.

Answer:

  1.685·10^-1 inches

Step-by-step explanation:

To find the total thickness, multiply the thickness of each sheet by the number of sheets and add the values for the different kinds of sheets:

  (15)(4.3·10^-3) +(20)(5.2·10^-3) = (64.5 +104.0)·10^-3 = 168.5·10^-3

  = 1.685·10^-1 . . . inches

Option A:

Hence, x ÷ 4 > x – 12 is true for x = 20.

Solution:

To find which is the suitable inequality is true for the value x = 20.

Option A: x ÷ 4 > x – 12

⇒ [tex]\frac{x}{4}>x-12[/tex]

Multiply 4 on both sides of the inequality,

⇒ x > 4x – 48

Subtract 4x on both sides of the inequality,

⇒ –3x > – 48

⇒ 3x > 48

Divide 3 on both sides,

⇒ x > 16

If x = 20, then 20 > 16 is true.

Option B: 2x < x +22

Subtract x on both sides of the inequality,

⇒ x < 22

If x = 20, then 20 < 22 is false.

Option C: x + 30 > 3x

Subtract x on both sides of the inequality,

⇒ 30 > 2x

Divide by 2 on both sides of the inequality,

⇒ 15 > x

If x = 20, then 15 > 20 is false.

Option D: x – 5 < 2x – 35

Subtract x on both sides of the inequality,

⇒ – 5 < x – 35

Add 35 on both sides of the inequality,

⇒ 30 < x

If x = 20, then 30 < 20 is false.

Hence, x ÷ 4 > x – 12 is true for x = 20.

Answer:

J < T - 5

Step-by-step explanation:

T =  The number of juice boxes Thomas had

J =  The number of juice boxes Thomas gave to his sisters

Thomas had 12 juice boxes

T = 12

He gave some to his sisters he now has more than 5 left.

T - J > 5

-J > 5 - T

J < -5 + T

J < T - 5

To determine the number of juice boxes Thomas gave to his sisters, the inequality 12 - j > 5 is used, which simplifies to j < 7, indicating that he gave away fewer than 7 juice boxes.

To find j, the number of juice boxes Thomas gave to his sisters, we start with the total number he had initially, which is 12. We know that he gave away some juice boxes and still has more than 5 left. If we let j represent the number of juice boxes given to his sisters, then 12 - j > 5 would be the inequality that can be used to determine j.

Since Thomas has more than 5 left, but we don't know the exact number, we use the inequality to represent the situation. Therefore, if we solve the inequality, subtracting 5 from both sides, we get j < 7. This means that Thomas gave away fewer than 7 juice boxes to his sisters because he had more than 5 remaining.

Answer: the number of single-crust cherry pies that was sold is 16

the number of double-crust apple pies that was sold is 20

Step-by-step explanation:

Let x represent the number of single-crust cherry pies that was sold.

Let y represent the number of double-crust apple pies that was sold.

The total number of pies sold on a busy Friday was 36. This means that

x + y = 36

Grandma's Bakery sells single-crust apple pie for $6.99 and double-crust cherry pie for $10.99. If the amount collected for all the pies that day was $331.64, it means that

6.99x + 10.99y = 331.64 - - - - - - - - -1

Substituting x = 36 - y into equation 1, it becomes

6.99(36 - y) + 10.99y = 331.64

251.64 - 6.99y + 10.99y = 331.64

- 6.99y + 10.99y = 331.64 - 251.64

4y = 80

y = 80/4 = 20

x = 36 - y = x = 36 - 20

x = 16

Answer:

The diameters of circles that could fit completely inside circle O are 25, 36, 42, 48 and 54.

Step-by-step explanation:

The actual diameter of the circle:

[tex]\pi r^{2} = 16 x \\2\pi r = x\\\\16(2\pi r)=16x\\\\32\pi r= \pi r^{2} \\\\\frac{32\pi r}{\pi r} = \frac{\pi r^{2} \\}{\pi r} \\\\r = 32[/tex]

Since the radius is equal to 32 units, the diameter is equal to 64 units.

Therefore, the diameters of circles that could fit completely inside circle O must be smaller than or equal to 64.

Answer:

Hallie ride 62 miles on bicycle.

Step-by-step explanation:

Given:

Let the number of miles Samantha rode be 'x'.

Hallie rode her bicycle 7 miles less than 3 times the number of miles Samantha rode.

It means that number of miles Hallie ride is equal to 3 multiplied by number of miles Samantha rode and then subtracting by 7.

framing in equation form we get;

number of miles Hallie ride = [tex]3x-7[/tex]

But Given:

number of miles Samantha rode =23 miles.

Now by substituting the value of [tex]x=23[/tex] in above equation we get;

number of miles Hallie ride = [tex]3x-7 = 3\times23-7 = 69-7 = 62 \ miles[/tex]

Hence Hallie ride 62 miles on bicycle.

Answer: E) 1/5

Step-by-step explanation:

The probability of any member being selected for each of the 3 posts is 1/10 that is they have equal probabilities of being selected for any of the posts.

The probability that harry would be selected for;

Secretary Ps= 1/10

Treasurer Pt = 1/10

So the probability of being selected for either secretary or treasurer is

P = Ps + Pt

P = 1/10 + 1/10

P = 2/10

P = 1/5

Note: ignore the sequence of selection

Answer:

A

Step-by-step explanation:

p = 25 + 5s

s = amount of shoes sold

Rich sold 7 shoes. Plug in 7 for s

p = 25 + 5(7)

p = 25 + 35

p = 60

Answer: the correct answer is a. $60

Step-by-step explanation:

Using the formula that states Rich's weekly salary

P= 25 + 5s , where p is the salary and s the number of pairs sold, then

P= $25 + $5*7

P=$25 + $ 35

P= $ 60

Answer:

2 fancy shirts and 5 plain shirts

Step-by-step explanation:

28x + 15x = 131

28(2) + 15(5) = 131

56 + 72 = 131

(there are no other equation i could find)

Answer:

1 3 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x represent the number of miles with either company A or company B.

Company A charges ​$70.50 and 18 cents per mile. Converting 18 cents to dollars, it becomes

18/100 = $0.18

Total cost of x miles with company A would be

0.18x + 70.50

Company B charges $30.50 and 11 cents per mile. Converting 11 cents to dollars, it becomes

11/100 = $0.11

Total cost of x miles with company B would be

0.11x + 30.50

For the amount that company A charges more than company B, it becomes

0.18x + 70.50 - 0.11x + 30.50

0.18x - 0.11x + 70.5 - 30.5

0.07x + 40

Company A charges 0.07x + 40 more than company B

The student uses Census sampling, a technique where every individual in a chosen population is surveyed. This method is reasonable for small populations, but can be impractical for larger groups.

The sampling technique used by the community college student in his statistics class is called Census sampling. This is because the student is collecting data from every individual in the total population of his statistics class. In other words, the student is not selecting a random or specific subset of the class; he is including everyone in his study. This can be useful for small populations, like a single class, as it provides data from all members, but it can be time-consuming and impractical for larger groups or populations.

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Answer:

So such system with fewer equations than unknowns can never have a unique solution.

Step-by-step explanation:

Linear equations are equations which contain variable with degree 1.

The variables can be 1 or 2 or any other number

say there are n varaibles

Then to solve this we must have n independent equations.

If number of equations are less than number of variables we can have parametric solutions only with infinite points lying on it.

There is no chance for this to have a unique solution.

For unique solutions, there must be equal number of equations with the variables and the determinant formed by the coefficients should not be 0.

So such system with fewer equations than unknowns can never have a unique solution.