What is the slope of this graph?

A. -4

B. 1/4

C. -1/4

D. 4​

Answer:

\(7.5\:\text{square units}\)

Step-by-step explanation:

The area of a trapezoid is given by the average of the bases multiplied by the height.

What we're given:

The average of the bases 1 and 4 is equal to \(\frac{4+1}{2}=\frac{5}{2}=2.5\)

Therefore, the area of the trapezoid is \(2.5\cdot 3=\boxed{7.5\:\text{square units}}\)

Answer:

30 units²

Step-by-step explanation:

this ones kinda tricky but basically you need to dilate it all by 2 (to make the figure twice as big)

technically, it would be 7.5 units bc but bc of the dilation it'd be 30

Answer:

The expected rate of return is $442.5

Step-by-step explanation:

The expected rate of return is given by the following formula;

\(E[R] = \displaystyle\sum_{i=1}^n R_i \times P_i\)

Where;

E[R] = The expected return

\(R_i\) = The return received in the instance i

\(P_i\) = The probability for obtaining the return, \(R_i\), in the instance i

n = The number of instances for the calculation

Therefore, we have;

The expected rate of return E[R] = 0.3 × 200 + 0.5×415 + 0.2 × 875 = $442.5

Answer the answer is D 12.6%

Step-by-step explanation:

Based on the given information, we have the mean concentration of sodium in the drinking water of a water system in Connecticut as 26.4 mg/l and the standard deviation as 6 mg/l.

The water department selects a simple random sample of 32 water specimens over the course of a year. To answer the question using the distributions tool, we need to set the mean and standard deviation parameters on the tool to the expected mean and standard error for the distribution of sample mean concentrations.

The expected mean for the distribution of sample mean concentrations is the same as the mean concentration of sodium in the drinking water, which is 26.4 mg/l.

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The water department in Connecticut is monitoring the concentration of sodium in their drinking water. By calculating the mean and standard error for the distribution of sample means, they can determine the probability of the mean concentration exceeding the notification level of 28 mg/l. If this probability is low, the water department will notify the public and recommend necessary actions.

In this scenario, the water department in Connecticut wants to monitor the concentration of sodium in their drinking water. They have set a notification level of 28 mg/l, meaning that if the mean concentration of sodium across a sample of 32 water specimens exceeds this level, they will notify the public.

To analyze this situation, we can use the distribution of sample means. The mean concentration of sodium in the drinking water of the water system is given as 26.4 mg/l, with a standard deviation of 6 mg/l.

To find the expected mean and standard error for the distribution of sample means, we can use the following formulas:

Expected mean of sample means = population mean

                                                        = 26.4 mg/l
Standard error of sample means = population standard deviation / square root of sample size

Using the given values, the standard error of sample means can be calculated as follows:
Standard error of sample means = 6 mg/l / square root of 32

                                                      ≈ 1.06 mg/l

Now, we can use a distributions tool to find the probability that the mean concentration of sodium in the sample of 32 water specimens exceeds 28 mg/l. We will set the mean parameter on the tool to 26.4 mg/l and the standard deviation parameter to 1.06 mg/l.

By entering these values into the distributions tool, we can find the probability of obtaining a mean concentration greater than 28 mg/l. If this probability is less than a certain threshold (e.g., 0.05), it indicates that the mean concentration exceeding 28 mg/l is unlikely to occur by chance alone. In such cases, the water department would notify the public and recommend that individuals on sodium-restricted diets inform their physicians of the sodium content in their drinking water.

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Answer: D

Step-by-step explanation:

\(f(3)=5(-3)-1=-16\\\\\\g(3)=2(-3)^{2}+1=19\\\\(f\times g)(3)=-16 \times 19=\boxed{-304}\)

Answer:

B

Step-by-step explanation:

10x - 2y = 4 ( subtract 10x from both sides )

- 2y = 4 - 10x ( divide through by - 2 )

y = - 2 + 5x → (1)

3x - 6y = 12 → (2)

substitute y = - 2 + 5x  into (2)

3x - 6(- 2 + 5x) = 12 ← distribute parenthesis on left side and simplify

3x + 12 - 30x = 12

- 27x + 12 = 12 ( subtract 12 from both sides )

- 27x = 0 ⇒ x = 0

substitute x = 0 into (1)

y = - 2 + 5(0) = - 2 + 0 = - 2

solution is (0, - 2 )

Answer:

$2.85

Step-by-step explanation:

Answer:

$22.23

Step-by-step explanation:

7.8 x 2.85 = 22.23 :D

The period for the following graph is 90 degrees. So correct option is C.

In mathematics, a period is a specific type of repetition in a function or a sequence. A period is the smallest positive value of a constant T for which a function or a sequence f(x + T) = f(x) for all x.

Periods are used to describe the behavior of functions and sequences that exhibit a repeating pattern. The length of the period determines the frequency of the pattern, and it is often used to describe the periodicity of functions in various applications, such as signal processing, harmonic analysis, and Fourier series.

For example, the sine function sin(x) is periodic with a period of 2π. This means that sin(x + 2π) = sin(x) for all x. Similarly, the cosine function cos(x) is also periodic with a period of 2π. Other common examples of periodic functions include the tangent function, cotangent function, and exponential function.

In addition to their applications in mathematics, periods also have practical applications in fields such as physics, engineering, and computer science, where they are used to model periodic phenomena such as waves and oscillations.

Overall, periods are an important concept in mathematics and are used to describe the repeating patterns that are found in many mathematical functions and sequences.

The period for the following graph is 90 degrees.

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Answer:

Step-by-step explanation:

80        40

___________

 100        50

Answer:

7-x=-7+x

14-x=x

14=2x

x=7

Step-by-step explanation:

Answer:

7 - x =-7 +x

x  = 7

Step-by-step explanation:

7-7 =-7 +7

0 = 0

x = 239

y = 146

Step-by-step explanation:

Let two numbers be x and y

x + y = 385. ------------equation (1)

x - y = 93. ------------equation (2)

from (1) and (2)

x = 239 and y = 146

Answer:

\(12z^{2} -10z -12\)

Step-by-step explanation:

Let the number be z

2 more than 3 times z ==> 3z + 2

6 less than 4 times z ==> 4z - 6

Product of the above two is
\((3z + 2) (4z - 6) \\= (3z)(4z) + (3z)(-6) + (4z)(2) + (2)(-6)\\= 12z^{2} -18z + 8z - 12\\= 12z^{2} -10z -12\)

V' makes an angle of -/2 (or -90 degrees) with the positive x-axis. Let's divide this problem into two components: the size of the vector difference and the angle formed by V' with the positive x-axis.

(a) Graphical Solution:

To determine the magnitude of the vector difference V - V₂ - V₁ graphically, we can use vector addition and subtraction.

Draw vector V₁ with a magnitude of 12 units starting from the origin.

Draw vector V₂ with a magnitude of 15 units starting from the end point of V₁.

Draw vector V starting from the origin and ending at the end point of V₂.

Draw the negative vector V' (opposite direction to V) starting from the end point of V₂.

Draw the negative vector V₁ (opposite direction to V₁) starting from the end point of V'.

Draw the vector difference V - V₂ - V₁, which is the vector from the origin to the end point of V₁.

Measure the magnitude of the vector difference V - V₂ - V₁ using a ruler or measuring tool on the graph. The measured magnitude will give us the graphical solution for the magnitude of the vector difference.

(b) Algebraic Solution:

To determine the magnitude of the vector difference V - V₂ - V₁ algebraically, we can subtract the vectors component-wise and then calculate the magnitude.

V = (a, b) = (0, -18.69)

V₁ = (12, 0)

V₂ = (-15, 0)

V - V₂ - V₁ = (0, -18.69) - (-15, 0) - (12, 0)

= (0 - (-15) - 12, -18.69 - 0 - 0)

= (15 - 12, -18.69)

= (3, -18.69)

To find the magnitude of the vector (3, -18.69), we can use the magnitude formula:

|V - V₂ - V₁| = √(3^2 + (-18.69)^2)

= √(9 + 349.4761)

= √358.4761

≈ 18.944

Therefore, the algebraic solution for the magnitude of the vector difference V - V₂ - V₁ is approximately 18.944 units.

Now let's determine the angle that V' makes with the positive x-axis.

The angle θ can be calculated using the inverse tangent (arctan) function:

θ = arctan(b/a)

= arctan(-18.69/0)

= arctan(-∞)

= -π/2 (or -90 degrees)

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Answer:

x = 2, y = -3

Explanation:

Given the simultaneous equation

7x+4y=2

9x-4y=30​

Add both equations

7x + 9x = 2 + 30

16x = 32

x = 32/16

x = 2

Substitute x = 2 into equation 1

From 1;

7x + 4y = 2

7(2) + 4y = 2

14 + 4y = 2

4y = 2-14

4y = -12

y = -12/4

y = -3

Hence the solution to the equation is (2, -3)

Answer:

{a, b, c, d, e, f, g}

Step-by-step explanation:

B intersection C = (e) because that is the only variable they both share

Now A intersection (e) is just all different variables together.

So now we have 2 (e's) but they can just be written as one.

Answer:

863.5 ft³

Step-by-step explanation:

Given that :

Diameter, d = 10 ft

Height, h = 11 feets

Radius of tank, r = d/ 2 = 10ft / 2 = 5 ft

The volume of a cylinder is calculated using the relation :

Volume = πr²h

Volume = 3.14 * 5^2 * 11

Volume = 3.14 * 25 * 11

Volume = 863.5ft³

The given linear system can be represented as a matrix equation:

A * X = B

where `A` is the coefficient matrix, `X` is the variable matrix, and `B` is the constant matrix.

The augmented matrix for the system is:

[-6 1 4 -2 | 1]

Using Gaussian elimination or row reduction, we can transform the augmented matrix to its row-echelon form:

[1 -1/6 -2/3 1/3 | -1/6]

[0 1 2/3 -1/3 | 1/6]

[0 0 0 0 | 0 ]

This row-echelon form implies that the system has a dependent variable since the third row consists of all zeros. In other words, there are infinitely many solutions to the system. The dependent variable, denoted as `x3`, can be expressed in terms of free parameters `s1` and `s2`.

Therefore, the set of solutions to the given linear system is:

x1 = -1/6 + (2/3)s1 - (1/3)s2

x2 = 1/6 - (2/3)s1 + (1/3)s2

x3 = s1

x4 = s2

where `s1` and `s2` are arbitrary real numbers that serve as parameters. These equations represent the general form of the solution, accounting for the infinite possible solutions.

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Answer:

Approximately 10 died every minute with a remainder of 12

Step-by-step explanation:

I divided 60 seconds by 612 because 60 seconds is one minute and i got 10 remainder 12

Answer:

8x40=320

Step-by-step explanation:

According to the given question we can infer that here are 320 books in the bookcase.

If Trey has a bookcase with 8 shelves, and each shelf has 40 books, the total number of books in the bookcase can be calculated by multiplying the number of shelves by the number of books per shelf.

Total number of books = Number of shelves × Number of books per shelf

Total number of books = 8 shelves × 40 books per shelf

Calculating the multiplication:

Total number of books = 320 books

Therefore, there are 320 books in the bookcase.

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Using confidence interval concepts, it is found that the interval estimate of the true population proportion is of (0.35, 0.51).

It is given by the sample proportion plus/minus the margin of error.

Considering the margin of error is half the range, we have that:

M = (0.48 - 0.32)/0.5 = 0.08.

Then, considering the sample proportion is of 0.43, we have that the bounds of the interval are given as follows:

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Answer:

A. -4

B. -3.5

C. 6.5

D. -2

Step-by-step explanation:

The “less” indicates it is negative.

The “more” indicates it is positive.

Answer: is B  

Find the factors of c that add up to b.

Question: Given that BE bisects ∠CEA, which statements must be true? Select THREE options.

(See attachment below for the figure)

m∠CEA = 90°

m∠CEF = m∠CEA + m∠BEF

m∠CEB = 2(m∠CEA)

∠CEF is a straight angle.

∠AEF is a right angle.

Answer:

m∠CEA = 90°

∠CEF is a straight angle.

∠AEF is a right angle

Step-by-step explanation:

Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.

Angle on a straight line = 180°. Therefore, m<CEA + m<AEF = m<CEF. Each right angle measures 90°.

Thus, the three statements that must be TRUE are:

m∠CEA = 90°

∠CEF is a straight angle.

∠AEF is a right angle

The correct statements from the given diagram is m∠CEA = 90°, m∠CEF = m∠CEA + m∠BEF and m∠CEB = 2(m∠CEA)

From the given diagram, we have the following information

∠CEF is a straight angle.

∠AEF is a right angle.

Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.

Since the angle on a straight line is 180 degrees, hence;

<CEA + m<AEF = m<CEF

Hence, the three statements that must be TRUE are m∠CEA = 90°, ∠CEF is a straight angle and ∠AEF is a right angle

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Answer:

Step-by-step explanation:

The temperature when the plane reaches an altitude of 5000 ft will be 47.2 F.

Temperature Drop per 1000 ft      :       1.6 F

Temperature Drop for 5000 ft       :       1.6 x (5000/1000)

      :       1.6 x 5 = 8.0

Temperature at 5000 ft                   :      55.2 – 8  = 47.2 F

#1234

The temperature when the plane reaches an altitude of 5000 feet will be 47.2 Fahrenheit.

In the given case, there is a drop of 1.6 Fahrenheit in temperature for every thousand feet that an airplane climbs into the sky.

The temperature on the ground is 55.2 Fahrenheit.

Temperature Drop per 1000 feet = 1.6 Fahrenheit

Temperature Drop for 5000 feet = 1.6 x (5000/1000)

                                                       = 1.6 x 5

                                                       = 8.0 Fahrenheit

To get the temperature when the plane reaches an altitude of 5000 feet,

The temperature at 5000 feet = 55.2 – 8 = 47.2 Fahrenheit

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Answer:

\(\huge\boxed{\sf Add}\)

Step-by-step explanation:

To get the total number of atoms in a compound, we should add the subscripts to get the total number.

For example:

\(\sf C_6H_{12}O_6\) (Glucose)

Add the subscripts of the compound:

=> 6 + 12 + 6 = 24

Hence, Glucose has 24 atoms in its compound.

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

Add

Step-by-step explanation:

In the following question, among the conditions given, With digit combinations, there are 16,807 different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed.

To solve this problem, we can use the fundamental counting principle or multiplication rule. It states that if there are m ways to do one thing, and n ways to do another thing, then there are m*n ways to do both things. Therefore, to find the number of different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed, we can multiply the number of choices at each position. Since repetition is allowed, each of the five positions has 7 possible digits (0, 1, 2, 3, 4, 5, or 6). Thus, the total number of possible 5-digit sequences is:7 × 7 × 7 × 7 × 7 = 7^5 = 16,807Therefore, there are 16,807 different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed.

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There are 16,807 different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed.

To find out the number of different 5-digit sequences that can be formed using the digits 0, 1,...,6 if repetition of digits is allowed, we can use the fundamental principle of counting or multiplication principle.The fundamental principle of counting states that if there are n different ways of performing the first task, and for each of these n ways of performing the first task there are m different ways of performing the second task, then the total number of different ways of performing both tasks is n x m.

To apply this principle to this problem, we can consider each digit in the 5-digit sequence as a task. The first task is to choose a digit from 0, 1,...,6, which can be done in 7 ways since there are 7 digits to choose from. Similarly, for each of the first 5 digits, there are 7 ways to choose a digit from 0, 1,...,6, so the total number of different 5-digit sequences that can be formed with repetition of digits allowed is 7 x 7 x 7 x 7 x 7 = 7^5 = 16,807.

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A chord is a line segment joining two points on a circumference. If two different chords share one of their extremes then they form an angle known as an inscribed angle. The other extremes of these chords form an arc that is known as the intercepted arc of the inscribed angle. For example, in the picture you'll notice that chords AD and DB form the angle ADB and its intercepted arc is arcAB. The measure of an inscribed angle is half the aperture of its intercepted arc so we get:

Angle ACB also has arcAB as its intercepted arc. This means that we also have:

So angles ACB and ADB are congruent since they have the same measure. So as you can see, if two inscribed angles have the same intercepted arc they are congruent.

Angles CAD and CBD also share the same intercepted arc, arcCD. This means that this angles are also congruent.

ADB and CAD are not congruent because their intercepted arcs (arcAB and arcDC) are not the same. The same happens with BCA and CBA since their intercepted arcs are arcAB and arcBC.

The last pair of angles that we must analyze is the one composed by DEA and CEB. These two angles are formed at the intersection between two line segments. At this type of intersections four angles are formed with consecutive angles being supplementary and opposite angles being congruent. DEA and CEB are opposite angles since they share their vertex but not their sides. Therefore DEA and CEB are congruent.

Then the correct options are A, C and D.

Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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Answer: Im pretty sure its C

Step-by-step explanation:

The solution for the given equation is C) \(x=\frac{-1+-\sqrt{33} }{4}\)

What does a quadratic function mean?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other words, a "polynomial function of degree 2" is a quadratic function.

The formula for the solution of a quadratic equation \(ax^{2} +bx+c=0\) is

\(x=\frac{-b+-\sqrt[2]{b^{2}-4ac } }{2a}\).

So, the solution for the equation \(2x^{2} +x-4=0\) is

\(x=\frac{-1+-\sqrt[2]{1^{2}-4*2*(-4) } }{2*2}\\x=\frac{-1+-\sqrt[2]{1+32 } }{4}\\x=\frac{-1+-\sqrt{33} }{4}\)

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