The temperature dropped 2 F every hour for 7 hours. What was the total number of
degrees the temperature changed in the 7 hours?

The solution to the expression 3(7 + x) is 21 + 3x

From the question, we have the following parameters that can be used in our computation:

3(7+x)

Rewrite the expression properly

So, we have the following representation

3(7 + x)

Open the bracket using the Distributive Property

So, we have the following representation

3(7 + x) = 3 * 7 + 3 * x

Evaluate the products on both sides of the equation

3(7 + x) = 21 + 3x

Hence, the solution is 21 + 3x

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Answer:

x = 1, y = 2

Step-by-step explanation:

Solve the following system:

{2 y + 3 x = 7 | (equation 1)

4 y - 3 x = 5 | (equation 2)

Add equation 1 to equation 2:

{3 x + 2 y = 7 | (equation 1)

0 x + 6 y = 12 | (equation 2)

Divide equation 2 by 6:

{3 x + 2 y = 7 | (equation 1)

0 x + y = 2 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{3 x + 0 y = 3 | (equation 1)

0 x + y = 2 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 1 | (equation 1)

0 x + y = 2 | (equation 2)

Collect results:

Answer: {x = 1, y = 2

Answer:

\(r = \sqrt{ {(6 - 2)}^{2} + {(1 - ( - 3))}^{2} } \)

\(r = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} \)

So the equation of the circle is

\( {(x - 2)}^{2} + {(y + 3)}^{2} = 32\)

For this problem, we are given a circle, its radius, and an arc of 120º. We need to calculate the length of the arc.

We need to use the following expression:

Where theta is the angle. We have:

The length of the arc is approximately 16.755 cm.

Answer:

The first one!

Step-by-step explanation:

Answer:

D. 18 1/8

Step-by-step explanation:

The three 1/3’s add up to 1. The 7 and 9 add up to 16. Add the 1 to that and you get 17. Then change the 1/2 to 4/8 and add that to the 5/8. You then get 1 and 1/8. Then you add that to the 17.

The given statement "a parallelogram has exactly 1 pair of parallel sides. " is false because a parallelogram has two pairs of parallel sides.

This is one of the defining characteristics of a parallelogram. Opposite sides of a parallelogram are parallel and congruent, meaning they have the same length. The parallel sides are formed by the pairs of opposite sides that do not intersect. This property gives the parallelogram its unique shape and symmetry. If a quadrilateral has only one pair of parallel sides, it would not be classified as a parallelogram.

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The factored form and the vertex form of the given quadratic equation is given by :

Standard quadratic equation is  : ay²+ by + c

Factored form of the quadratic equation is : A ( y - p )( y - q ).

Vertex form of the quadratic equation is : A ( y - h )² + k .

As given in the question,

Let us consider the standard quadratic equation be :

ay²+ by + c

Example : 3x² + 15x  + 18

Factored form is :

= 3 (x² + 5x + 6 )

= 3 ( x² + 2x + 3x + 6 )

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

Standard factored form is :  A ( y - p )( y - q )

Let ( h ,k ) be the vertex of the quadratic equation ,

Vertex form is given by : A ( y - h )² + k

Therefore, the factored and the vertex form of the given quadratic equation is equal to

Standard quadratic equation is  : ay²+ by + c

Factored form of the quadratic equation is : A ( y - p )( y - q ).

Vertex form of the quadratic equation is : A ( y - h )² + k .

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Answer:

480,496 liters

Step-by-step explanation:

To calculate the amount of water needed to produce the beef consumed by one person in a more developed country per year, we need to first determine the amount of beef consumed per year and then multiply it by the water required to produce a given amount of beef.

The average person in a more developed country consumes 85 grams of beef per day. To find the annual consumption, we multiply this value by the number of days in a year:

Annual beef consumption = Daily beef consumption * Number of days in a year

Annual beef consumption = 85 grams/day * 365 days/year

Annual beef consumption = 31,025 grams/year

Now, we need to convert the beef consumption from grams to liters of water. It takes 1,750 liters of water to produce 113 grams of beef:

Water required per gram of beef = 1,750 liters / 113 grams

To calculate the total water needed per year, we multiply the water required per gram of beef by the annual beef consumption:

Water needed per year = Water required per gram of beef * Annual beef consumption

Water needed per year = (1,750 liters / 113 grams) * 31,025 grams/year

Calculating this value:

Water needed per year ≈ 480,496 liters/year

To calculate the sample size required to detect a true mean speed of 94 meters per second with a power of at least 0.85, we need to know the significance level and the standard deviation of the population.

Assuming a 5% significance level (alpha = 0.05) and a standard deviation of 10 meters per second, we can use the following formula:

n = (Z_beta + Z_alpha/2)^2 * σ^2 / d^2

where:

Z_beta is the Z-score for the desired power (0.85) from the standard normal distribution, which is approximately 1.04.

Z_alpha/2 is the Z-score for the desired significance level (0.05/2 = 0.025) from the standard normal distribution, which is approximately 1.96.

σ is the standard deviation of the population, which is 10 meters per second.

d is the difference between the true mean speed and the hypothesized mean speed, which is 100 - 94 = 6 meters per second.

Substituting these values into the formula, we get:

n = (1.04 + 1.96)^2 * 10^2 / 6^2

≈ 49.56

Therefore, a sample size of at least 50 would be required to detect a true mean speed as low as 94 meters per second with a power of at least 0.85, assuming a 5% significance level and a standard deviation of 10 meters per second.

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Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Answer:

B. (x-5)²+(y+1)² = 49

Step-by-step explanation:

An equation of a circle with center (h, k) and radius r is

\( \large \boxed{ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} }\)

We have all given information we need. Our h is 5 - Our k is -1 and our radius is 7

Substitute these values in

\( \large{ {(x - 5)}^{2} + {(y - ( - 1))}^{2} = {7}^{2} } \\ \large{ {(x - 5)}^{2} + {(y + 1)}^{2} = {7}^{2} } \\ \large{ {(x - 5)}^{2} + {(y + 1)}^{2} = 49 }\)

So the answer is B choice.

Answer:

2

Step-by-step explanation:

Given:

Point P is the incenter of triangle HKM.

To find:

The measure of JP.

Solution:

In triangle MNP, using Pythagoras theorem, we  get

\(Hypotenuse^2=base^2+Perpendicular^2\)

\((MP)^2=(MN)^2+(NP)^2\)

\((25)^2=(24)^2+(NP)^2\)

\(625=576+(NP)^2\)

\(625-576=(NP)^2\)

\(49=(NP)^2\)

Taking square root on both sides, we get

\(\pm \sqrt{49}=NP\)

\(\pm 7=NP\)

Side cannot be negative. So,

\(NP=7\)

Point P is the incenter of triangle HKM.

\(JP=NP\)       [Incenter is equidistant from each side of triangle]

\(JP=7\)

Therefore, the value of JP is 7 units.

As there is a positive correlation between the variables, the correlation will be larger than 0 and less than 1. The correct option is 0< correlation <1.

Given that,

Linear association is measured via correlation. A trend line drawn through the scatter will indicate a relationship between an explanatory variable X and a response Y that is positive and growing but has some curvature

To find : The correlation

From the provided information,

The two variables are positively related.

The correlation coefficient takes a value from -1 to 1.

Since, the correlation between the variables is positive, therefore, the correlation will be greater than 0.

Thus, the correct option is 0<correlation<1.

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Given:

The table of values of a linear function.

To find:

The equation of linear function in slope intercept form.

Solution:

The slope intercept form of a linear function is:

\(y=mx+b\)

Where, m is the slope and b is the y-intercept.

If a linear function passes through two point, then the equation of the linear function is:

\(y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\)

Consider any two points from the given table. Let the two points are (-6,12) and (-5,14). So, the equation of the linear function is:

\(y-12=\dfrac{14-12}{-5-(-6)}(x-(-6))\)

\(y-12=\dfrac{2}{-5+6}(x+6)\)

\(y-12=\dfrac{2}{1}(x+6)\)

\(y-12=2x+12\)

Adding 12 on both sides, we get

\(y-12+12=2x+12+12\)

\(y=2x+24\)

Therefore, the slope intercept form for the given linear function is \(y=2x+24\).

Answer: Rectangualr prism

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It will fold into a rectangular prism. Four out of the six shapes there in the cutout are rectangular, while the other two are squares. Since four of them are rectangular, we can infer, or discover, that the shape that the cutout will be folded into is a rectangular prism.

Answer:

A. 18

Step-by-step explanation:

10% of 60 is 6 therefore 30% of 60 would be 18

Answer:

h = (S - 2nr) / 2nr

Step-by-step explanation:

S = 2nr + 2nrh

2nrh = S - 2nr

h = (S - 2nr) / 2nr

Answer:

There is a possibility of births and deaths. This also, informs us of a larger population.

Step-by-step explanation:

This is because there are 333% more rabbits without a tag than with one. This giving us the possibility shown above!

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Answer:  560 total rabbits

Step-by-step explanation:

Your assumptions are great but you can also add the assumption that the ratio of the rabbits caught on Monday is the same ratio of the rabbits caught on Tuesday.

\(\text{Tuesday:}\quad \dfrac{15\ tags}{70\ rabbits}=\dfrac{3\ tags}{14\ rabbits}\ \leftarrow simplified\)

Assumption:

3/14 of the total rabbits on the farm = 120 tagged on Monday

Let r represent the total rabbits on the farm

then (3/14)r = 120

                r = 120(14/3)

                r = 560

Answer:

D) m<1 = 50 m<7 = 130

Step-by-step explanation:

Lets set up the equation!

We know m<4 is 4x-30 and the m<5 is 2x + 50 due to alternate interior angles they are congruent so we can forge an equation, all we do is set them equal to each other!

4x-30 = 2x+50

Add 30 to both sides

4x = 2x +80

Subtract 2x from both sides.

2x = 80

Divide both sides by 2

x = 40

Now that we know x we can just plug it into the expression of m<4 to find m<1

4x-30

4(40)-30

80 - 30

50

m<4 = 50

Because m<1 and m<4 are vertical angles they are congruent!

m<1 = 50

We also know m<4 and m<5 are congruent so m<5 = 50 as well.

Because <7 is supplementary to <5 we know that the sum of both angles amount to 180.

x represents m<7

50 + x = 180

Now we solve by subtraction 50 from both sides

x = 130

m<7 = 130

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Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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Given:

The data values are:

21, 32, 17, 24, 15, 30, 28 and 26.

To find:

The first quartile, third quartile, and interquartile range.

Solution:

We have,

21, 32, 17, 24, 15, 30, 28, 26

Arrange the data values in ascending order.

15, 17, 21, 24, 26, 28, 30, 32

Divide the data set in two equal parts.

(15, 17, 21, 24), (26, 28, 30, 32)

Divide each parenthesis in two equal parts.

(15, 17), (21, 24), (26, 28), (30, 32)

Now, the first quartile is:

\(Q_1=\dfrac{17+21}{2}\)

\(Q_1=\dfrac{38}{2}\)

\(Q_1=19\)

The third quartile is:

\(Q_3=\dfrac{28+30}{2}\)

\(Q_3=\dfrac{58}{2}\)

\(Q_3=29\)

The interquartile range is:

\(IQR=Q_3-Q_1\)

\(IQR=29-19\)

\(IQR=10\)

Therefore, the first quartile is 19, third quartile is 29 and the interquartile range is 10.

Answer:

18/7 or 2 4/7

Answer:

Exact form: 18/7

decimal form: 2.571428

mixed number form 2 4/7

The slope is 2, which equals the distance travelled each hour. The total distance hiked at the start of the second day is represented by the y-intercept, which is 4, which is also the y-value. intercept's

We locate the rise/run before calculating the slope. Since the line increases by 2 between each point, the rise is 2. It travels over 1 between the points, hence the run is 1. The slope is now 2/1, or 2.

Given that it is rise/run, this gives us miles/hours, which indicates the number of miles she treks per hour.

The line's crossing of the y-axis is known as the y-intercept. At four, this is.

The fact that the y-value at this time is 4 and the x-value at this point is 0 tells us that she has trekked 4 miles in the 0 hours since the start of the second day, which is the distance she has covered so far.

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Answer:

Step-by-step explanation:

Step one:

Given data

amount of money earned per hour= $6.25

amount of money made in tips= $8.5

if x represents the number of hours worked and

y represents the total amount earned

The linear function for the total is expressed as

y=mx+c

Step two:

Hence for the situation given the expression for the total is

y=6.25x+8.5

Say Kayla worked for 2 hours

that is x=2, the total she would have earned is

y=6.25(2)+8.5

y=12.5+8.5

y=21

For a 2 hour work, Kayla will make $21

Answer:

Option D, 4

Step-by-step explanation:

2 pizzas x 6 slices per pizza = 12 slices of pizza

12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend

Option D, 4, is your answer

Answer:

Not enough data is provided but I will try my best.

Step-by-step explanation:

If the couple is desiring to save money for their baby's education then and they can opt to following options:

I think they must first lower their fixed expenses which includes their rental expenses per year, branded clothing cost per year, use of luxury items, etc. This will help them save more than what they are desiring to plan for their baby's future. This will help them own a small house which will substantially lower their expenses because rentals are usually 10-20% of household Income. Luxury expenses can be lowered if the by 80% by simply opting local brands. Furthermore, if they use bicycle then the cost of traveling which is 4-10% can also be significantly lowered. Modern research shows that owning a car is expensive than using Uber a year. I think using local transport will be very beneficial. Eating quality products is recommended but they must be cooked at home because the street food is very expensive and increases the cost of living. All these measures will help them in buying a house that will help them keep their expenses under control. Average saving by using these measures would be $25k which means they can own a house costing them $100-150k within 4 to 6 years.

I recommend them funding Educational Savings Account when their baby is studying in 3rd standard because public high school education is free for all the US residents. The University degrees that are the most expensive in the world cost around $230-$331k which means that if the couple starts saving $2000 a month, 10 years before the child enters the university then according to Florida 529 planning, after deducting for college studies they can save up to $272k which is more than enough.

Furthermore the amount deposited in the account is tax deductible and have to be paid aggregated when the money is withdrawn. So it also has a tax advantage.

The result of dividing (x⁴-6x²-27) by (x+2) using synthetic division is x³ - 2x² - 10x + 20.

Synthetic division is a method used to divide a polynomial by a linear binomial (in this case, (x+2)). It involves writing the polynomial in standard form and performing a simplified long division process.

To perform synthetic division, we first set up the synthetic division table:

-2 | 1  0  -6  0  -27

Next, we bring down the leading coefficient (1) to the bottom row of the table. Then, we multiply the divisor (-2) by the value in the bottom row (1) and write the result (2) in the next column. We add this result to the next coefficient in the original polynomial (0) to get the next value in the bottom row (2).

-2 | 1  0  -6  0  -27

     -2    4   -16

___________________

    1   -2   -2  -16  -43

The bottom row of the table represents the coefficients of the quotient polynomial, reading from left to right. Therefore, the quotient polynomial is x³ - 2x² - 2x - 16. The remainder, -43, is written outside the division symbol.

Thus, the result of dividing (x⁴-6x²-27) by (x+2) using synthetic division is x³ - 2x² - 2x - 16 with a remainder of -43.

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Answer:

The number of nickels and quarters in the bank are 87 and 56, respectively.

Step-by-step explanation:

Let's denote the number of nickels in the bank as "n" and the number of quarters as "q". Then we can set up a system of two equations based on the given information:

n + q = 143 (equation 1, representing the total number of coins)

0.05n + 0.25q = 18.35 (equation 2, representing the total value of the coins)

To solve this system, we can use substitution or elimination method. Let's use elimination method here:

Multiplying equation 1 by 0.05, we get:

0.05n + 0.05q = 7.15 (equation 3, obtained by multiplying equation 1 by 0.05)

Subtracting equation 3 from equation 2, we get:

0.2q = 11.2

Dividing both sides by 0.2, we get:

q = 56

Substituting this value of q into equation 1, we get:

n + 56 = 143

n = 87

Therefore, there are 87 nickels and 56 quarters in the bank.

Hopefully this helped you! If not, I'm sorry! If you need more help, ask me! :]