During a week in January in Cleveland, Ohio, the daily high temperatures were -4 °F, -2 °F, -12 °F, 5 °F, 12 °F, 16 °F, and 20 °F. Which expression can be used to find the difference between the highest temperature of the week and the lowest temperature of the week?

True.

The normal distribution is a probability distribution that follows a bell-shaped curve. The curve is symmetric around the mean, with the majority of the data falling within one standard deviation from the mean. Probabilities for a given range of values can be calculated by finding the area under the curve for that range. This is because the area under the curve represents the probability of a random variable falling within that range. The properties of the normal distribution make it a useful tool for statistical analysis, as it can be used to model many natural phenomena and is often assumed in hypothesis testing and confidence interval calculations.
True, the normal distribution follows a bell-shaped curve, where probabilities are found by calculating the area under the curve. This distribution is symmetrical around its mean, with probabilities decreasing as values move away from the mean. To find the probabilities, we calculate the area under the curve using integration, which gives us the likelihood of a value occurring within a specific range. The total area under the curve is equal to 1, representing 100% probability. The normal distribution is useful for understanding real-world phenomena and predicting outcomes based on patterns of data.

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The limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

To use the ratio test, we take the limit of the absolute value of the ratio of the (k+1)th term to the kth term:

lim as k approaches infinity of |(6(k+1)^4)/(6k^4)|

Simplifying this expression, we get:

lim as k approaches infinity of |(k+1)^4/k^4|

Using L'Hopital's rule, we can evaluate this limit:

lim as k approaches infinity of |4(k+1)^3/4k^3|

lim as k approaches infinity of |(k+1)/k|^3

Since the limit is less than 1, by the ratio test, the series converges absolutely.

Alternatively, we can use the root test, which involves taking the kth root of the absolute value of the kth term:

lim as k approaches infinity of |(6k^4 k)^(1/k)|

Simplifying this expression, we get:

lim as k approaches infinity of |6^(1/k) * k^(4+1/k)|

The exponent 4+1/k approaches 4 as k approaches infinity, so we can ignore the 1/k term. Taking the limit of just the k^(4) term, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k)

Using the fact that lim as k approaches infinity of 6^(1/k) = 1 and lim as k approaches infinity of k^(4/k) = 1, we get:

lim as k approaches infinity of |6^(1/k) * k^4|^(1/k) = 1

Since the limit is less than 1, by the root test, the series converges absolutely.
To determine if the given series converges absolutely or diverges, we can use the Ratio Test. The series is given as:

Σ(6k^4 * k) for k = 1 to ∞

First, let's simplify the series:

Σ(6k^5) for k = 1 to ∞

For the Ratio Test, we need to compute the limit as k goes to infinity of the ratio of consecutive terms:

lim (k → ∞) (|a_(k+1)| / |a_k|)

For our series, a_k = 6(k+1)^5 and a_(k+1) = 6k^5. So we have:

lim (k → ∞) (|6(k+1)^5| / |6k^5|)

We can simplify by canceling the common factor of 6:

lim (k → ∞) ((k+1)^5 / k^5)

Now, let's take the limit:

lim (k → ∞) (1 + 1/k)^5 / 1 = 1^5 / 1 = 1

For the Ratio Test, if the limit is less than 1, the series converges absolutely; if it is equal to 1, the test is inconclusive; if it is greater than 1, the series diverges.

In this case, the limit is equal to 1, so the Ratio Test is inconclusive. Further tests would be required to determine if the series converges absolutely or diverges.

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The numerical length of GH = 20 units

FH is a line segment.

G is a point on the line segment.

Then G divides the line segment FH into two line segments FG and GH.

We are given the lengths of FH, FG and GH in terms of x.

That is,  FH=4x+8, FG=x and GH=5x

We need to find the numerical length of the line segment GH. We first need to find the x for this.

As G cuts the line segment FH into two parts, the length of the line segment FH is the sum of the lengths of the line segments FG and GH.

That is, FH = FG + GH

⇒ 4x+8 = x +5x

⇒ 4x+8 = 6x

⇒ 2x = 8

⇒ x = 4

So the numerical length of GH = 5x = 5 x 4 = 20 units

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Answer: Choice A) 44

==============================================

Work Shown:

cos(angle) = adjacent/hypotenuse

cos(X) = 13/18

X = arccos(13/18)

X = 43.7617 approximately

X = 44

Side note: The arccosine function is the same as inverse cosine as notated by \(\cos^{-1}\). Make sure your calculator is in degree mode.

Answer:

It is -2/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

first we need to calculate the area of isosceles triangle having sides 48cm, 48cm and 30cm

a = 48

b= 30

Area of isosceles triangle using only sides = ½[√(a^2 − b^2 /4) × b]

= 1/2*30√( 48² - 1/4×30²)

=1/2*30√ (2304 -225)

=684sq cm

cost required to make umbrella= 10*684*5

= 34200

To determine the local minimum and local maximum of the function A(x) = ∫₀ˣ f(t) dt on the interval (0, 6), we need to analyze the behavior of A(x) and its derivative.

Let's denote F(x) as the antiderivative of f(x), which means that F'(x) = f(x).

To find the local minimum and maximum, we need to look for points where the derivative of A(x) changes sign. In other words, we need to find the values of x where A'(x) = 0 or A'(x) is undefined.

Using the Fundamental Theorem of Calculus, we have:

A(x) = ∫₀ˣ f(t) dt = F(x) - F(0)

Taking the derivative of A(x) with respect to x, we get:

A'(x) = (F(x) - F(0))'

Since F(0) is a constant, its derivative is zero, and we are left with:

A'(x) = F'(x) = f(x)

Now, let's analyze the behavior of f(x) based on the given figure to determine the local minimum and maximum of A(x) on the interval (0, 6). Without the specific information about the shape of the graph, it is not possible to determine the exact values of x that correspond to local minimum or maximum points.

To find the local minimum, we need to locate a point where f(x) changes from decreasing to increasing. This point would correspond to x = x_min.

To find the local maximum, we need to locate a point where f(x) changes from increasing to decreasing. This point would correspond to x = x_max.

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Answer:

x = 2 , y = 1

Step-by-step explanation:

For the triangles to be congruent then the hypotenuse and leg must be congruent, that is

x = y + 1 → (1)

4y = x + 2 → (2)

Substitute x = y + 1 into (2)

4y = y + 1 + 2

4y = y + 3 ( subtract y from both sides )

3y = 3 ( divide both sides by 3 )

y = 1

Substitute y = 1 into (1)

x = y + 1 = 1 + 1 = 2

Answer:

C) 8^8

Step-by-step explanation:

4*2=8 so 8^8

Hope this helps!

Answer:

C

Step-by-step explanation:

We can use the rule [ (x^y)^z = x^yz ] to solve.

(8^4)^2

8^4*2

8^8

Best of Luck!

For the parabola \(y = 3x² - 4x - 2\):  The vertex is (2/3, -10/3).  The axis of symmetry is x = 2/3.  The minimum value is -10/3. The range is y ≥ -10/3.To identify the vertex, axis of symmetry.

we can use the vertex form of a parabola equation, which is y = a(x - h)² + k. First, we need to rewrite the given equation in vertex form. We can do this by completing the square.

1. Start by isolating the x terms: \(y = 3x² - 4x - 2.\)
2. Group the x terms together: \(y = (3x² - 4x) - 2.\)
3. Factor out the coefficient of x² from the first two terms: y = 3(x² - (4/3)x) - 2.

4. Take half of the coefficient of x, square it, and add it inside the parentheses. In this case, half of \(-(4/3) is -2/3,\) so we add (\(-2/3)² = 4/9: y = 3 (x² - (4/3)x + 4/9 - 4/9) - 2.\)

5. Simplify inside the parentheses: \(y = 3[(x - 2/3)² - 4/9] - 2.\)
6. Expand and simplify: \(y = 3(x - 2/3)² - 4/3 - 2.\)
7. Combine like terms: \(y = 3(x - 2/3)² - 10/3.\)

- The range is the set of all possible y-values. Since the parabola opens upwards and has a minimum value of -10/3, the range is y ≥ -10/3.

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Answer:

15

Step-by-step explanation:

140x(3/4)=105 went to sport club

105x(1/7)=15 went to sport club and art club

Answer:

It's a 1954 Arnolt Bristol Bolide

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

If X = 2 then you do 2+4 which equals 6

x + 4x and - 2 maybe i think its the answer

The value of x will be -45 by the multiplicative property for the given expression x/3=-15.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

The given expression is x/3=-15. The value of x will be calculated as below:-

x/3=-15.

x = -15 x 3

x = -45

Therefore, the value of x will be -45 by the multiplicative property.

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Answer:

1.  3³

2.  (-5)⁴

3.  3¹⁰

4.  4⁰

Step-by-step explanation:

When multiplying exponents with the same base, you add the exponents.  When dividing exponents with the same base, you subtract the exponents.  When raising a number with an exponent to another power, multiply the exponents.

1.  \(\frac{3^4*3^6}{3^2*3^5} =\frac{3^{10}}{3^7}=3^3\)

2.  \(\frac{(-5)^{12}}{(-5)^3*(-5)^5} =\frac{(-5)^{12}}{(-5)^8}=(-5)^4\)

3.  \((3^2)^5=3^{10}\)

4.  \(\frac{4^0*4^4}{4^1 * 4^3} =\frac{4^4}{4^4}=4^0\)

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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The distance from -4 to 1 is 5 units.

The correct number line and expression to find the distance from -4 to 1 are:

Number line: -4 -3 -2 -1 0 1

Expression: |-4 - 1|

To find the distance, we subtract the smaller number (-4) from the larger number (1) and take the absolute value:

|-4 - 1| = |-5| = 5

Therefore, the distance from -4 to 1 is 5 units.

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Answer:

y = 8x+6

Step-by-step explanation:

First find the slope since it is a linear function

m = (y2-y1)/(x2-x1)

    = (18-2)/(1 1/2 -  -1/2)

    =16 /  (1 1/2 +1/2)

    = 16/2

  = 8

The linear function is in the form

y = mx+b where m is the slope

y = 8x+b

Substitute the other point into the equation to determine b

10 = 8(1/2) +b

10 = 4+b

10-4 = b

6 = b

y = 8x+6

The third one

This graph is the only one that shows the correct slops with the correct y intercepts (-3 and 3)

Answer

∠A = 22.62 degrees

∠B = 67.38 degrees

The sum of ∠A and ∠B is 90°. ∠A and ∠B are complementary angles.

Step-by-step explanation:

∠A = 22.62 degrees

∠B = 67.38 degrees

The sum of ∠A and ∠B is 90°. ∠A and ∠B are complementary angles.

Which angles are complementary to each other?

What is the formula for Complementary angles?

Complementary angles formulae. To find the complement on an angle, say ' x ', when expressed of radians, use the formula below: Complement of x rad = π/2 - x. For example, The complementary angle of 1/3π radian = π/2 - 1/3π = π/6 rad. To find the complement of an angle, say ' y 'when expressed in degrees, use the formula below: Complement of y ° = 90° - y .

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Step-by-step explanation:

Given angle of elevation = angle ACB.

angle ACB + angle ABC + angle BAC = 180(sum of angles in a triangle)

angle ACB + 90 + 58 = 180

angle ACB = 180 - 90 - 58

=32

Answer:

? = 32 degrees

Step-by-step explanation:

since the angles inside a triangle has to add up to 180 degrees then we can use this equation to find the missing angle:

58° + 90° + ? = 180°

The number of likes for which each user is responsible during the year is given as follows:

111 likes per user.

The number of likes per user is obtained applying the proportions in the context of this problem.

A proportion is applied as the number of likes per user is given by the division of the number of likes by the number of users.

The parameters for this problem are given as follows:

Hence the number of likes per user is calculated as follows:

839000000/7560000 = 111 likes per user.

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Answer:

Step-by-step explanation:

\( {x}^{2} - 3x + 8\)

(Putting value of x = 4)

\( = {4}^{2} - 3 \times 4 + 8\)

= 16 - 12 + 8

= 24 - 12

= 12 (Ans)

Answer:

It is 12

Step-by-step explanation:

\(f(x) = {x}^{2} - 3x + 8\)

When x is 4, substitute x as 4:

\(f(4) = {(4)}^{2} - 3(4) + 8 \\f(4) = 16 - 12 + 8 \\ f(4)= 12\)

To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

1.The modular inverse of 1/7 (mod 8) is 7, as 7 * 7 ≡ 1 (mod 8). 2.The modular inverse of 1/14 (mod 15) is 14, as 14 * 14 ≡ 1 (mod 15). 3.The modular inverse of 1/6 (mod 7) does not exist because 6 and 7 are not coprime.

To find the modular inverse of 1/7 (mod 8), we need to find a number x such that (1/7) * x ≡ 1 (mod 8). In this case, x = 7 satisfies the equation since 7 * 7 ≡ 49 ≡ 1 (mod 8).

For the modular inverse of 1/14 (mod 15), we need to find a number x such that (1/14) * x ≡ 1 (mod 15). In this case, x = 14 satisfies the equation since 14 * 14 ≡ 196 ≡ 1 (mod 15).

However, in the case of 1/6 (mod 7), the modular inverse does not exist because 6 and 7 are not coprime. In modular arithmetic, a number has an inverse only if it is coprime with the modulus. Since 6 and 7 share a common factor of 2, they are not coprime, and thus, the modular inverse of 1/6 (mod 7) does not exist.

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Answer:

\(3^{1.5}\)

Step-by-step explanation:

\(3 = 3^1\)

\(\sqrt{3} = x^{0.5}\)

\(3*\sqrt{3} = 3^{1} * 3^{0.5} = 3^{1 + 0.5} = 3^{1.5}\)

Answer:

Infinite Solutions

Step-by-step explanation:

3(5x - 4) needs to be simplified

So we multiply 5x by 3

So 3 x 5x = 15x

Then we multiply -4 by 3

3 x -4 = - 12

Put those together we get 15x - 12

The same equation as the one on the right side

So since 15x - 12 = 15x - 12, the x variable can be any number

Also a little tip:

With Forms quizzes, you can hit control + U and find the answers in the code

Answer:

200 miles

Step-by-step explanation:

you travel 20 miles for 1 gallon, so 10*20=200miles

Answer:

200

Step-by-step explanation:

if you have to dive its 20 times 10 because 20 miles 10 dollars

Answer:

9/3

7/0

0/5

Step-by-step explanation:

9/3=6

7/0= 0

0/5=0

Ordered pair (0, 6) and  (2, 7)  satisfy both inequalities in the system and are solutions to the system.

To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.

When we plot the graph of inequality separately:

    2. y ≥ 2x + 3:

The overlapping shaded region represents the solution to the system of inequalities.

To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:

Ordered pair 1: (0, 6)

Ordered pair 2: (2, 7)

These two points satisfy both inequalities in the system and are solutions to the system.

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The correct question is given below -

Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.

y > x + 5

y ≥ 2x + 3