The temperature at 5:00 a.m. was –6 °F. By 3:00 p.m., the temperature had risen to a high of 36 °F. If the temperature at 8:00 p.m. decreased from the high by latex of the change in temperature in Fahrenheit degrees from 5:00 a.m. to 3:00 p.m., what was the temperature at 8:00 p.m.?

Answer: Yes it does.

Step-by-step explanation:

Answer:

Samantha's age = 27 years

Step-by-step explanation:

As Samantha is one year less than twice her brother Jack’s age.

As the sum of their ages is 41.

Thus, the equation become

x+2x-1 = 41

3x-1 = 41

3x = 42

Dividing both sides by 3

x = 14

It indicates that Jack's age = 14 years

Therefore,

Samantha's age = 2x-1 = 2(14)-1 = 27 years

Answer:

There were 76 childrens and 14 adults.

Step-by-step explanation:

Since the group has a total of 90 children and adults, then the sum of the number of adults with the number of children must be equal to 90 as shown below:

children + adults = 90

Since the total cost for their tickets was 548 then the number of children multiplied by the price of their ticket summed by the number of adults multiplied by the price of their ticket must be equal to that. We have:

5*children + 12*adults = 548

With these two equations we have a system of equations shown below:

children + adults = 90

5*children + 12*adults = 548

In order to solve this we will multiply the first equation by -5, and sum both equations we have:

-5*children - 5*adults = -450

5*children + 12*adults = 548

7*adults = 98

adults = 98/7 = 14

children + 14 = 90

children = 90 - 14 = 76

There were 76 childrens and 14 adults.

Answer:

r is greater then 5

Step-by-step explanation:

if it's pointing from say 3 up to 10 the number is bigger then the answer

Answer:

1130

Step-by-step explanation:

twice as much would be 1180 and then take away 50 is 1130

Answer:

Subtract 5 from the number before.

Step-by-step explanation:

7-5=2, 2-5=-3, -3-5=-8, -8-5=-13

Lori will make more than Darryl, then the after 10 years Lori will have make $27.00 more in their account.

Darryl deposits into a savings = $1,500

Account that has a simple interest rate = 2.7%.

Lori deposits into a savings = $1,400

Account that has a simple interest rate = 3.8%.

Let us assume,

\(P_{1}\) = $1,500

\(r_{1}\) = 2.7%.

\(r_{1}\) =  2.7/100

\(r_{1}\) = 0.027

After 10 years = t = 10years

The formula to calculate simple interest is,

\(A_{1}\) = \(P_{1} (1+r_{1} t)\)           (Equation-1)

\(P_{1}\) = Principal amount

\(r_{1}\) = rate of interest ( in decimal )

t = time

First we calculate Darryl's deposit,

So we can substitute values in the equation-1,

\(A_{1}\) = 1,500(1 + 0.027×10)

\(A_{1}\) = 1,500 ( 1+0.27 )

\(A_{1}\) = 1,500 × 1.27

\(A_{1}\) = $1905

Now we will calculate Lori's deposit,

\(A_{2}\) = \(P_{2} (1+r_{2} t)\)                (Equation-2)

\(P_{2}\) = $1,400

\(r_{2}\) = 3.8%.

\(r_{2}\) =  3.8/100

\(r_{2}\) = 0.038

So we can substitute values in the equation-2,

\(A_{2}\) = 1,400 ( 1 + 0.038 × 10 )

\(A_{2}\) = 1,400 ( 1 + 0.38 )

\(A_{2}\) = 1,400 × 1.38

\(A_{2}\) = $1,932

Darryl will make money after 10 years = $1905

Lori will make money after 10 years = $1,932

Hence,

Lori will make more than Darryl,

Then the difference will be = 1,932 - 1,905 = $27

Therefore,

After 10 years Lori will have make $27.00 more in their account.

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y=2x+0 is the slope for this line

Answer:

k = 2

1x = 2y

x = 2y

The equilibrium quantity in this scenario is 625, and the consumer surplus at the equilibrium quantity is $39,062.50.

To find the equilibrium quantity, we need to set the demand and supply functions equal to each other and solve for x:

500 - 0.2x = 0.6x

Simplifying the equation:

500 = 0.8x

x = 625

Therefore, the equilibrium quantity is 625.

To find the consumer surplus at the equilibrium quantity, we first need to find the equilibrium price. We can do this by plugging in the equilibrium quantity into either the demand or supply function:

d(625) = 500 - 0.2(625) = 375

So the equilibrium price is 375.

Next, we need to find the area of the triangle between the demand curve, supply curve, and equilibrium price. To do this, we need to find the difference between the maximum price the consumer is willing to pay (500) and the equilibrium price (375), and then multiply that difference by the equilibrium quantity (625):

Consumer surplus = 0.5(500-375) x 625 = 39,062.5

Therefore, the consumer surplus at the equilibrium quantity is $39,062.50.

The equilibrium quantity in this scenario is 625, and the consumer surplus at the equilibrium quantity is $39,062.50.

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From probability P(A|B) = 0.74 , P(A) = 0.48 , and P(B) = 0.20. P(B|A) is 0.308.

To calculate the probability of the event B, given that the event A has already occurred, Bayes' theorem is used.

Bayes' theorem is a method of determining the probability of an event occurring based on prior knowledge of the conditions that could influence the event. It is a method of determining the probability of an event based on prior knowledge of the conditions that could influence the event.

P(A|B) = 0.74, P(A) = 0.48, and P(B) = 0.20.

We can calculate P(B|A) using the following formula:

P(B|A) = [P(A|B) * P(B)]/P(A)P(B|A)

P(B|A) = [0.74 * 0.20] / 0.48

P(B|A) = 0.3083 (rounded to three decimal places)

Therefore, P(B|A) = 0.308.

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Answer:

72

Step-by-step explanation:

just take off two zeros

Answer:

Step-by-step explanation:the answer isis currently 72

Answer: 400

Step-by-step explanation: cube root 8000 then that times itself

Answer:

45 and 50

Step-by-step explanation:

each large square is 5 minutes.

for 0 < t < 30, there are three columns of 15 minutes ( 3 x 5)

15 x 3 = 45

for 40 < t < 60 there is two columns of 25 minutes (5 x 5)

25 x 2 = 50

From the given histogram we have the values of the empty box are 45 and 50.

We have given that,

the incomplete histogram and table give some information about the waiting time in minutes, experienced by patients at a dental surgery.

We have to complete the given table.

A histogram is an approximate representation of the distribution of numerical data. The term was first introduced by Karl Pearson.

each large square is 5 minutes.

for 0 < t < 30, there are three columns of 15 minutes ( 3 x 5)

15 x 3 = 45

for 40 < t < 60 there is two columns of 25 minutes (5 x 5)

25 x 2 = 50

Therefore the values of the empty box are 45 and 50.

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Answer: 5.7 (rounded)

Step-by-step explanation: The formula to find the diagonal of a square is \(\sqrt{2\) * a, where a is a side length on the square. Since we are solving for half of a diagonal, we use this formula and divide our result by two. We start by multiplying root 2 by 8 and we get 11.31371, next we divide by two and we get 5.656855 which is 5.7 when rounded.

It is possible that someone else collecting a different sample from the same population and measuring the same variable would calculate the same sample statistic, but it is not guaranteed.

Statistical measures that are derived from samples of data rather than the complete population are called sample statistics. A population parameter, such the mean or standard deviation, is estimated using this method. Depending on the type of data and the research issue being examined, sample statistics can be estimated using a variety of formulae and techniques. For instance, to get the sample mean, multiply the sum of all the observations in the sample by the total number of observations. The sample standard deviation is calculated by taking the square root of the sum of the squared differences between each observation and the sample mean. In research studies and surveys, sample statistics are frequently utilized to draw conclusions about the population.

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The value of the limit is -4/3.

Using the Taylor series expansion for sin(2x) and simplifying, we get:

sin(2x) = 2x - (4/3)x^3 + (2/15)x^5 + O(x^7)

Substituting this into the expression sin(2x) - 2x, we get:

sin(2x) - 2x = - (4/3)x^3 + (2/15)x^5 + O(x^7)

Dividing by x^3, we get:

(sin(2x) - 2x)/x^3 = - (4/3) + (2/15)x^2 + O(x^4)

As x approaches 0, the dominant term in this expression is -4/3x^3, which goes to 0. Therefore, the limit of the expression as x approaches 0 is:

lim x → 0 (sin(2x) - 2x)/x^3 = -4/3

Therefore, the value of the limit is -4/3.

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The area of the Trapezium given in the question is 28ft²

The area of a trapezium is calculated using the relation :

Using the parameters given for our compuation:

height, h = 4

b1 = 9

b2 = 5

Inputting the parameters into our formula :

Area = 4/2(5 + 9)

Area = 2(14)

Area = 28ft²

Therefore, the area of the Trapezium is 28ft²

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Answer:.2 grams per year

Step-by-step explanation:you divide 6 by 30 and thats what you get:)

Answer:5

Step-by-step explanation:30/6=5

Answer:

D 17.43

Step-by-step explanation:

3.5 times 3.63 equals 12.67 and 2 1/3 times 2.04 equals 4.76.  When you add them together you get 17.43.

The exact change Rodney needs to take with him to the produce stand is 17.42 dollars.

A unitary method is a mathematical technique for obtaining the value of a single unit and then deriving the required units by multiplying it with the single unit.

The exact change Rodney needs to take with him to the produce stand is the price of 3.5 pounds of cherries which is (3.5×3.62) dollars = 12.67 dollars added to the price of 2.33 pounds of peaches which is (2.33×2.04) dollars = 4.75 dollars.

∴ The total amount is (12.67 + 4.75) dollars.

= 17.42 dollars.

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Answer:

Yes

Step-by-step explanation:

Each x-value corresponds with only one y-value.

Answer:

2(2x+5)

Step-by-step explanation:

Length of the rectangle=l= 3x

Breadth of the rectangle=b= 5

Perimeter= 2(l+b)

= 2(3x+5)

The probability that the defending champion wins the tournament in a single elimination format is approximately 65.17% or 0.6517.

To calculate the probability that the defending champion wins the tournament in a single elimination format, we need to consider all possible paths that lead to the champion winning three consecutive matches.

There are two possible scenarios:

1. The champion wins the first three matches.

2. The champion loses one match but wins the next three matches.

Let's calculate the probability for each scenario:

Scenario 1: The champion wins the first three matches.

Since the champion has a probability of 0.7 of winning each match, the probability of winning three consecutive matches is:

P(win) x P(win) x P(win) = 0.7 x 0.7 x 0.7 = 0.343

Scenario 2: The champion loses one match but wins the next three matches.

The champion can lose any of the first three matches with a probability of (1 - 0.7) = 0.3. After losing one match, the champion must win the remaining three matches.

Therefore, the probability of losing one match and winning the next three matches is:

P(lose) x P(win) x P(win) x P(win) = 0.3 x 0.7 x 0.7 x 0.7 = 0.1029

Now, we need to consider the number of ways these scenarios can occur. In Scenario 1, the champion can win the first three matches in only one way. In Scenario 2, the champion can lose any of the first three matches in three different ways (assuming each challenger is equally likely to win).

So, the total probability of the defending champion winning the tournament is:

Total Probability = (Probability of Scenario 1) + (Probability of Scenario 2)

Total Probability = (0.343 x 1) + (0.1029 x 3) = 0.343 + 0.3087 = 0.6517

Therefore, the likelihood of the defending champion emerging victorious in the single elimination tournament is roughly 0.6517, which can also be expressed as 65.17%.

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The time taken by both to mow the lawn is 36 minutes.

This is a question of time and work.

It is given that:-

Time taken by boy to mow the loan = 90 minutes.

Time taken by girl to mow the loan = 60 minutes.

We have to find the time taken by both of them together to mow the lawn.

LCM(60,90) = 180

Let the total work to be done to mow the lawn be 180 units.

Hence,

Efficiency of boy = 180/90 = 2 units

Efficiency of girl = 180/60 = 3 units

Total efficiency = 2 + 3 = 5 units.

Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.

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Answer:

$49950

Step-by-step explanation:

you do 45000(.11) which equals 4950. and then you add 4,950 to 45000, and then you get your answer

Yes, there is a continuous utility function that represents a rational preference relation when it is both continuous and monotone.

In a two-commodity framework, let's assume the two commodities are represented by X and Y. We can construct a diagram with the axes representing the quantities of X and Y. The indifference curves, which represent the bundles of X and Y that yield the same level of utility, can be plotted on this diagram.

Since the preference relation is continuous and monotone, we can draw the indifference curves as smooth, upward-sloping curves without any gaps or jumps. The upward slope reflects the monotonicity, indicating that more of either X or Y is preferred to less.

To represent this preference relation with a continuous utility function, we can assign utility levels to different bundles of X and Y. For example, we can assign a utility level of 1 to a specific bundle (X₁, Y₁), and higher utility levels to bundles that are preferred to (X₁, Y₁).

By assigning utility levels in a continuous manner across the diagram, we can construct a continuous utility function that represents the rational preference relation. This function will map each bundle of X and Y to a corresponding level of utility.

In conclusion, for a rational preference relation that is continuous and monotone in a two-commodity framework, there exists a continuous utility function that represents this preference relation. The utility function can be constructed by assigning utility levels to different bundles of commodities, and the resulting indifference curves on a diagram will be smooth, upward-sloping curves. This relationship between the utility function and the preference relation allows us to mathematically model and analyze the choices and preferences of individuals in economics.

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Answer:1493.1

Step-by-step explanation:

The rent of the apartment during the 8th year of living in the apartment is $1,605.13.

Given that, you rent an apartment that costs $900 per month during the first year, but the rent is set to go up 7.5% per year.

We need to find What would be the rent of the apartment during the 8th year of living in the apartment.

The formula to find the rent of the apartment during the 8th year of living in the apartment is Amount \(=P(1+\frac{r}{100} )^{n}\)

Where, P=principal, r=rate of interest and n=number of years.

Now, amount=\(=900(1+\frac{7.5}{100} )^{8}\)

\(=900(1.075)^{8}\)

=900×1.78347782556

=1,605.13

Therefore, the rent of the apartment during the 8th year of living in the apartment is $1,605.13.

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If the data values are as shown in the picture I have attached, then the following should help.

Answer: 226.56  m²

Step-by-step explanation:

  We need to find the area of three rectangles and two triangles.

    The triangles: 34.56 m²

A = \(\frac{B*H}{2}\)

-> Since they are both congruent, we will skip dividing by two

A = B * H

A = 7.2 * 4.8

A = 34.56 m²

   The rectangles: 192 m²

A = L * W

-> We have two that are congruent, and one that is not

A = 10 * 6 * (2, since there are two)

A = 120 m²

-

A = L * W

A = 7.2 * 10

A = 72 m²

-

72 m² + 120 m² = 192 m²

   Total surface area:

34.56 m² + 192 m² = 226.56  m²

3) The two triangles that are congruent are:

ΔRST ≅ ΔTMN

4) The two triangles that are congruent are:

ΔDEF ≅ ΔEDC

5) The value of the missing side x is: x = 13.9

6) The value of the missing side x is: x = 8.5

Some of the postulates to determine that two triangles are congruent are:

SAS

SSS

ASA

AAS

HL

3) The two triangles are congruent by SSS Congruency as they have three congruent sides. Thus:

ΔRST ≅ ΔTMN

4) The two triangles are congruent by SSS Congruency as they have three congruent sides. Thus:

ΔDEF ≅ ΔEDC

5) Using trigonometric ratios, we have:

10/x = cos 44

x = 10/cos 44

x = 13.9

6) Using trigonometric ratios, we have:

x/20 = tan 23

x = 20 * 23

x = 8.5

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So, the gradient of f at the point (1,2,2) is: ∇f(1,2,2) = (1/2) i + (1/4) j + (1/2) k where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

To find the gradient of the function f(x,y,z) at the point (1,2,2), we need to find the partial derivatives of f with respect to x, y, and z and evaluate them at the given point.

So, we have:

f(x,y,z) = (x^2 y^2 z^2)^(-1/2) ln(xyz)

∂f/∂x = (-1/2) (x^2 y^2 z^2)^(-3/2) (2xy^2 z^2) + (1/x) (x^2 y^2 z^2)^(-1/2)

= (-xy^2 z^2)/(x^2 y^2 z^2) + (1/x) (x^2 y^2 z^2)^(-1/2)

= -y^2 z^2/(x^2 y^2 z^2) + 1/xsqrt(x^2 y^2 z^2)

= -1/(xyz) + 1/x

∂f/∂y = (-1/2) (x^2 y^2 z^2)^(-3/2) (x^2 2yz^2) + (1/y) (x^2 y^2 z^2)^(-1/2)

= (-x^2 yz^2)/(x^2 y^2 z^2) + (1/y) (x^2 y^2 z^2)^(-1/2)

= -x^2/z^2 + 1/ysqrt(x^2 y^2 z^2)

= -x^2/(z^2 y) + 1/y

∂f/∂z = (-1/2) (x^2 y^2 z^2)^(-3/2) (x^2 y^2 2z) + (1/z) (x^2 y^2 z^2)^(-1/2)

= (-x^2 y^2 z)/(x^2 y^2 z^2) + (1/z) (x^2 y^2 z^2)^(-1/2)

= -x^2 y^2/(z^2 x^2 y^2) + 1/zsqrt(x^2 y^2 z^2)

= -x^2 y^2/(z^3) + 1/z

Now we can evaluate these partial derivatives at the point (1,2,2):

∂f/∂x (1,2,2) = -1/(122) + 1/1 = 1/2

∂f/∂y (1,2,2) = -1/(222) + 1/2 = 1/4

∂f/∂z (1,2,2) = -1/(122) + 1/2 = 1/2

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