Pilar opened a hot chocolate store during the fall. She noticed that she sold more hot chocolate on colder days.



For each day she sold hot chocolate, she plotted `\left(t,\ c\right)`.

`t` represents highest temperature.

`c` represents cups of hot chocolate sold.

Drag the points to make the line a good fit for the data.

The inequality Form:= x>5

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made. Several types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

A is not equivalent to b in any scenario.

As an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities.

Equivalence is not considered.

There are two forms of inequality relations that are not strict, in contrast to strict inequalities:

The indication of an or b denotes that.

Hence, The inequality Form:= x>5

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The vertex form of the give quadratic equation is f(x) = (x+1)² + 2

The standard vertex form of a quadratic equation is expressed as

y = a(x -h)² + k

where (h, k) is the vertex

Given the quadratic equation

f(x) = x^2 + 2x + 3

Complete the question

f(x) = (x^2+2x) + 3

f(x) = (x^2+2x+1)-1 + 3

f(x) = (x+1)² + 2

Hence the vertex form of the give quadratic equation is f(x) = (x+1)² + 2

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Answer:

-1.2 or -1 1/5

Step-by-step explanation:

The correct option is C. It is safe to apply the central limit theorem, even if the sample size for each sample is 15, if the sample population is normally distributed.

The central limit theorem states that, if you take repeated samples of a population and calculate the mean of each sample, the distribution of the means of those samples will tend to be normally distributed, provided that the sample size is large enough. This means that, even if the original population is not normally distributed, the distribution of the means of the samples will tend towards a normal distribution as the sample size increases.

However, if the original population is already normally distributed, then you can apply the central limit theorem with a smaller sample size and still expect the distribution of the means of the samples to be normally distributed. Therefore, in order for it to be safe to apply the central limit theorem with a sample size of 15, the sample population must be normally distributed.

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Answer:

a) \(\frac{32}{21}\)

b) -14

c) -3

d) -96

Step-by-step explanation:

a) The parenthesis indicate multiplication.

b) Minus and plus gives subtraction, and the sign you put behind the number is the sign of the largest number you have (in this case it's 21 since we ignore the -)

c) They already have common denominators, all that's left is to do \(\frac{-7 -2}{3} = \frac{-9}{3} = -3\)

d) The parenthesis indicate multiplication.

Good luck!

The value of x is 17 and the perimeter of the triangle is 104

A line that touches the circle at a single point is known as a tangent to a circle.

Two lines from thesame point of tangency and meet at a point are equal.

The point where tangent meets the circle is called point of tangency.

The base of the triangle is 38 and part of it is equal to 21 by law of point of tangency.

Therefore the other part = 38 -21

= 17

Therefore x = 17 just due to thesame law of tangency.

The other side of the triangle = 17 + 14 = 31

therefore the perimeter of the triangle = 31+38 + 21+14 = 104

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Answer:

probability of getting a red ball= 6/11

Step-by-step explanation:

we know, to find a probability of a event

1st we have to get the total number of events that can occur,i.e

6+4=11

and

the total probability of getting a red ball is 6/11

which is the required answer..

The term which is important in terms of making meaning of those scores is measures of central tendency (mean, median, mode), option A.

A single number that seeks to characterise a set of data by pinpointing the centre location within that set of data is referred to as a measure of central tendency. As a result, measurements of central location are occasionally used to refer to measures of central tendency.

These also fit within the category of summary statistics. You are probably most familiar with the mean (sometimes known as the average), but there are additional central tendency measures, including the median and the mode.

The mean, median, and mode are all reliable indicators of central tendency, however depending on the situation, certain indicators are more useful than others.

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Answer: 0.28571428571

Step-by-step explanation: 8 dived by 28

The box-and-whisker plot for the given data is given below:

A box and whisker plot is defined as a graphical method of displaying variation in a set of data.

The results of a history test taken by 18 students: 55, 57, 58, 61, 62, 66, 68, 68, 71, 75, 75, 78, 82, 83, 85, 86, 88, 89.

Take note of how the scores are listed from lowest to highest.

The median for the given data is 73.

The Lower Quartile and the Upper Quartile would be found after that.

These represent the lower and higher halves' medians.

Lower quartile = 61.75

Upper quartile = 83.5

Make a number line. Mark your median, quartiles, and smallest and largest values.

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Answer:

Robert can make 16 packages

Answer:\(x= - \frac{1 - \sqrt{57} }{4} , \frac{1 + \sqrt{57} }{4}\)

Step-by-step explanation:

You first simplify it. You can use the quadratic formula. First, you have to divide by 2. \(x^{2} + \frac{x}{2} - 7 = 0\) Now you can use the formula, so, the answer is \(x= - \frac{1 - \sqrt{57} }{4} , \frac{1 + \sqrt{57} }{4}\)

The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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The cοrrect answer is (c), supplies travel apprοximately 14 feet οn the cοnveyοr belt.

The branch οf mathematics cοncerned with specific functiοns οf angles and their applicatiοn tο calculatiοns. There are six functiοns οf an angle cοmmοnly used in trigοnοmetry.

Let D be the distance the supplies travel οn the cοnveyοr belt. Using trigοnοmetry, we can relate the angle οf inclinatiοn, the height difference, and the distance travelled οn the cοnveyοr belt as fοllοws:

sin(60) = οppοsite/hypοtenuse

where the οppοsite side is the vertical distance οf 12 feet and the hypοtenuse is the distance travelled οn the cοnveyοr belt plus the 12 feet. Sοlving fοr the distance traveled οn the cοnveyοr belt, we get:

D = 12/sin(60)

D = 13.86 ≈ 14 feet (rοunded tο the nearest fοοt)

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The amount the carwash earns in an hour is 80.

The range is the set of all "y" values in an ordered pair, while the domain is the set of all "x" values. Keep in mind that ordered pairs are represented by the following symbols: (x, y). List all the x values from the relation to determine the domain when examining a set of ordered pairs.

The domain of the relation is the set that includes all of the first elements of each ordered pair in relation R. The domain set might or might not match set A as depicted in figure 1. On the other hand, the relation's range is the set that includes all of the second items.

Based on the given conditions, formulate: 8×10

Calculate the product or quotient: 80

Get the result: 80

Domain of the relation: (0,1,2,3,4,5,6,7,8,9,10).

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Answer:

2.8kg

Step-by-step explanation:

There are 7 parts of meat for every 3 parts so there are 7+3=10 parts in total.

4/10=1 "part"

there are 7 parts of meat so (4/10)*7=28/10=2.8kg of meat.

the actual area of the bedroom is 324 square feet

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

Given the square bedroom have 3 feet side

The area of the bedroom is = 3² = 9 sq inch

1/2 inch = 3 feet

1 inch = 6 feet

1 square inch = 36 square feet

9 square inch = 36*9 = 324square feet

Hence the actual area of the bedroom is 324 square feet

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The central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

To find the central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

If you want the central angle in degrees, you can convert it using the fact that there are 2π radians in a full circle (360 degrees):

Central angle (in degrees) = (Arc length / Radius) * (180 / π)

Make sure to use consistent units for the arc length and radius, such as meters or centimeters, to obtain accurate results.

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Answer:

Which graph best represents the change in population of the two cities?

Year Townville Village City

1960 37,500 17,500

1970 42,500 25,000

1980 35,000 20,000

1990 30,000 30,000

2000 15,000 32,500

Step-by-step explanation:

A. is right

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer:

1) \(m\)∠JKL = 145°

2) \(m\)∠IHG = 164°

3) \(m\)∠NME = 50°

4) \(m\)∠TUV = 178°

I hope this helps! (✿◠‿◠)

a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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Answer:

\(x + 75 + x + 125 = 180 \\ \\ 2x + 200 = 180 \\ \\ 2x = 180 - 200 \\ \\ 2x = - 20 \\ \\ x = \frac{20}{2} \\ \\ x = 10\)

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Answer:

45 degree line

Step-by-step explanation:

A distinguishing characteristic of a Keynesian cross diagram is the 45-degree line.

The Keynesian cross diagram is a simple graphical representation of the relationship between aggregate expenditure and real GDP in an economy. It shows the equilibrium level of real GDP where aggregate expenditure equals real GDP, and helps to illustrate the effects of changes in aggregate expenditure or other factors on the economy.

The 45-degree line in the Keynesian cross diagram represents the level of real GDP where aggregate expenditure equals real GDP, or where there is equilibrium in the economy. Points below the 45-degree line indicate that aggregate expenditure is less than real GDP, while points above the 45-degree line indicate that aggregate expenditure is greater than real GDP. The slope of the aggregate expenditure function determines the sensitivity of real GDP to changes in aggregate expenditure.

Answer:

12

Step-by-step explanation:

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SAT-EDIT-TYPE IN X VALUES AND Y VALUES (FROM ORDERED PAIR)-STAT-CALC-4-ENTER

the time it would take for person 1 and person 2 to complete the task together is 2xy / (x + y) hours

If person 1 can do a task in x hours and person 2 can do the same task in y hours, then the combined rate at which they can complete the task is:

rate = 1/x + 1/y

This is because each person's rate of completing the task is the reciprocal of their time to complete the task, and their combined rate is the sum of their individual rates.

To find the time it would take for both persons to complete the task working together, we can use the formula:

time = 1 / rate

Substituting the expression for the rate above, we get:

time = 1 / (1/x + 1/y)

Simplifying this expression, we can use the formula for the harmonic mean of two numbers:

time = 2xy / (x + y)

Therefore, the time it would take for person 1 and person 2 to complete the task together is 2xy / (x + y) hours

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