he graph shows the relationship between the number of hours that michelle has been driving and the distance that she has left to travel to get to her destination. which statement is true?

the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.

In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.

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The largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

An initial-value problem is a type of boundary-value problem in mathematics, particularly in the field of differential equations.

The given initial-value problem is a separable differential equation, which can be written as:

dy/dt = -2(t + 1)y²

Integrating both sides, we get:

(1/y) = t² + 2t  + C

where C is the constant of integration.

Since we have an initial condition, we can use it to find the value of C:

y(0) = -1/15
C = -1/15

Solving for C, we get:

C = -1/15

So, the solution to the differential equation is:

(1/y) = t² + 2t -1/15

y = 1 / (t² + 2t -1/15)

The solution is defined for all t ≠ -1, since y = 0 is not defined. So, the largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

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Answer:

Option (4)

Step-by-step explanation:

Given sequence is,

-3 + 6 + 15 + 24 + ........+ 132

Difference in 1st and 2nd term = 6 - (-3)

                                                   = 9

Difference in 2nd and 3rd term = 15 - 6

                                                    = 9

There is a common difference of 9 in each successive term.

Therefore, it's an arithmetic sequence.

Let the nth term of this sequence is (a + bn).

For the first term → n = 0,

a = -3

For second term → n = 1

-3 + b(1) = 6

b = 6 + 3

b = 9

Therefore, nth term of the sequence will be,

\(T_n\) = -3 + 9n

For nth term = 132

-3 + 9n = 132

9n = 135

n = \(\frac{135}{9}\)

n = 15

Sum of 15 terms can be represented by the expression;

\(\sum_{n=0}^{15}(-3+9n)\)

Option (4) is the answer.

The probability of being a senior is the total number of seniors divided by the total number of students.

The probability of a student walking given that they are seniors can be calculated using Bayes' theorem. Bayes' theorem is a formula that relates conditional probabilities to their inverses. The formula is: P(A|B) = P(B|A) P(A) / P(B)where P(A|B) is the probability of event A given that event B has occurred. In this case, A is "walking" and B is "senior." P(B|A) is the probability of being a senior given that the student is walking, P(A) is the probability of walking, and P(B) is the probability of being a senior. We can also represent the above formula in the form of a tree diagram, where P(walk | senior) is one branch of the tree.

The probability of being a senior is represented by the root of the tree, while the probability of walking is represented by a branch from the root. The probability of walking given that the student is a senior is calculated by dividing the probability of a senior walking by the probability of being a senior. The probability of walking can be calculated by adding up the probabilities of walking for each grade level and dividing by the total number of students.

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The degree of polynomial 3x^4-0x^3+0x^5 is 4

Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).

Therefore, inx^3+3x+5, the degree of the polynomial is 3 as the highest power in its terms is 3. (power and exponent are same thing);

Given in the question;

Polynomial= 3x^4-0x^3+0x^5

The highest degree from observation is of 3x that is equal to 4

Hence, the correct degree will be 4

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Answer:

15% off of $60.00 would be $51.00

Step-by-step explanation:

(15 x 15) / 100 = 9

60-9=51

        </3 PureBeauty

For given circle, Area of shaded region is 52π cm².

What exactly is a circle?

A circle is a kind of ellipse with zero eccentricity and two foci that are coincident. A circle is also known as the locus of points drawn at equal distances from the center. The radius of a circle is the distance from its center to its outside line. The diameter of a circle is the line that divides it into two equal sections and is equal to twice the radius.

The equation for a circle in the plane is:

(x-h)^²+ (y-k)² = r²

When the coordinate points are (x, y)

(h, k) is the coordinate of a circle's center.

where r is the circumference of a circle.

where circle area = πr²

Circle circumference=2πr

Now,

Radius of biggest circle = 8cm

radius of unshaded circle= 4cm and

radius of smaller shaded circle= 2cm

Then,

Area of shaded region= Area of biggest circle - area of white circle + area of smaller shaded circle

=π*8² - π*4² + π*2²

=64π-16π+4π

=52π cm²

hence,

           Area of shaded region is 52π cm².

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The equation for curvature is given by κ = |r' × r''|/|r'|3 where r' = dr/dt and r'' = d2r/dt2. the curvature of r(t) at the point (7,1,1), r(t)=<7t,t2,t3> is √14/√490.

The equation for curvature is given by κ = |r' × r''|/|r'|3 where r' = dr/dt and r'' = d2r/dt2.

We are given the point (7,1,1) which is the same as t=1.

Therefore, we can substitute t=1 into the function r(t) to obtain r(1) =<7,1,1>.

From this, we can calculate the derivatives r' and r'' of the function r(t) at the point (7,1,1).

r' = <7,2,3>

r'' = <0,2,6>

Then, we can calculate the curvature κ using the equation κ = |r' × r''|/|r'|3.

κ = |<7,2,3> × <0,2,6>|/|<7,2,3>|3

= |<0,-14,18>|/|<7,2,3>|3

= √14/√490

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A) 6 because 12 divided by 2 is 6

B) 9 because 45 divided by 5 is 9

C) 23 because 207 divided by 9 is 23

The value of given expression is \(10^7\) which can be said as 10 raised to the power 7.

We have to find the value of \(10^5*\frac{10^4}{10^2}\)

It is a question of exponents and powers.

Exponents (Power)

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. It is placed as a superscript over a number. In other words, it indicates that the base is raised to a certain power.

For example, the mass of Earth is 5,97,219,00,00,00,00,00,00,00,00,000 kg. This cannot be read in simple words. Thus, to pronounce these types of numbers we make use of exponents.

Hence, the weight of earth will be written as \(5.97219 * 10^{24}\).

We know that:-

\(x^a*x^b = x^{a+b}\) and,

\(x^a/x^b = x^{a-b}\)

Hence, we can write,

\(\frac{10^4}{10^2} = 10^{4-2} = 10^2\)

Now,

\(10^5*10^2=10^{(5+2)}=10^7\)

Hence, the answer is \(10^7\).

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Answer:

11

Step-by-step explanation:

217 = 19x + 8

209 = 19x

x = 209/19

x = 11

Answer:

x = 3

Step-by-step explanation:

4 ( x - 7 ) = -6x + 12

→ Expand brackets

4x - 28 = -6x + 12

→ Add 6x to both sides

10x - 28 = 12

→ Add 28 to both sides

10x = 30

→ Divide both sides by 10

x = 3

The statement "x ∈ {x}" is true. The statement "{x} ⊆ {x}" is true. The statement "{x} ∈ {x}" is false. The statement "{x} ∈ {{x}}" is true.

a) The statement is true because an element x can be a member of a set that contains only itself. In this case, the set {x} contains the element x.

b) The statement is true because every element in {x} is also in {x}. Since both sets are identical, {x} is a subset of itself.

c) The statement is false because a set cannot be an element of itself. In this case, {x} is a set, and it cannot be an element of the same set.

d) The statement is true because the set {{x}} contains the set {x} as its only element. Therefore, {x} is an element of the set {{x}}.

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Direct labor efficiency variance = $6,100 F.

Given that

Standard labor-hours per unit of output     8.5 hours

Standard labor rate                                     $12.30 per hour

Standard labor hours allowed                          6,800 hours (800 units *                                         8.5 hours allowed)

The following data pertain to operations concerning the product for the last month:

Actual hours worked  6,300 hours

Actual total labor cost  $74,970

Actual output                  800 units

We can determine the labor efficiency variance using the following equation:

1. Direct labor efficiency variance = (Standard hours allowed - Actual labor hours) * Standard rate

2. Direct labor efficiency variance = (6,800 hours - 6,300 hours) * $12.20

3. Direct labor efficiency variance = $6,100 F

The variance is favorable as the actual labor hours used are less than the standard hours allowed.

Hence the answer is Direct labor efficiency variance = $6,100 F.

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Answer:

8 is the answer

Step-by-step explanation:

the equation is r = C/2*3.14

2*3.14=6.28

Because your C is 50  you do 50/6.28 and when you do that you get 7.962 (rounded) and then we round for the whole # so 8.

Given-

Annual interest rate = 5%

By using the rule of 72,

Rate x Time = 72

Rate = 5%

t = ?

So,

5 x t = 72

5t = 72

Isolate t by dividing both sides by 5 :-

→ 5t/5 = 72/5

→ t = 14.4 years

Hence, it will take 14.4 years for the deposit to double at 5% annual rate.

✍️ By Benjemin ☺️

The price of the article tomorrow will be #4.95.

If an article cost #5 yesterday and has risen by 10% today, it will now cost #5.50. To calculate the price tomorrow, we need to consider that the price will fall by 10%.

To do this, we can first calculate what 10% of #5.50 is, which is #0.55. This means that the price will fall by #0.55 tomorrow, bringing the price down to #4.95.

Therefore, the price of the article tomorrow will be #4.95. This calculation highlights the importance of understanding the impact of percentage changes on prices and how they can impact the overall cost. It also demonstrates the need for individuals to be aware of such changes when making financial decisions.

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Answer:

3

Step-by-step explanation:

The slope of the given line is \(\frac{2}{3}\).

If a line passes through two points (x₁, y₁) and (x₂, y₂) respectively, then slope of the line is \(m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Here, the given line passes through points (0, 6) and (-9, 0).

Therefore, the slope of this line is (m)

\(= \frac{0 - 6}{-9 - 0}\\= \frac{6}{9} \\= \frac{2}{3}\)

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Finally ahmod will have 4 nickels and 10 dimes.

Ahmod has two times as many dimes as nickels.

They have a combined value of 100 cents.

Group all coins in sets by grouping each nickel with 2 dimes.

Each set, containing 1 nickel and 2 dimes, is worth 5 + 2*10 = 25 cents.

You will have 100/25 = 4 such groups

As we have 4 such groups at last ahmod will have 4 nickels and 10 dimes.

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The value 2.75 goes in the first box, since it's the first term.

The expression \(0.69*a_{n-1}\) goes in the second box. The second line says "to get the nth term, we multiply the previous term by 0.69"

The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

No

Step-by-step explanation:

x + 1 is not a factor of the polynomial because the remainder is 2 and not 0

Im sorry but theres no picture or nothing I can work with!

Let a function f be analytic everywhere in a domain D. Prove that if f(z) is real-valued for all z in D, then f(z) must be constant throughout D. Suppose a function f(z) is analytic and real-valued throughout a domain D. Assume that there are two different points in D, say w and z, so that f(z) ≠ f(w). Therefore, we have a closed path consisting of the line segment from z to w and the line segment from w to z. Now let γ be any closed path in D that encloses the path from z to w.  Since f(z) ≠ f(w), f(z) - f(w) ≠ 0, so f(z) - f(w) / z - w ≠ 0. This makes the function 1 / (f(z) - f(w)) analytic throughout D. Thus, by Cauchy's theorem, $\oint_{\gamma } \frac{1}{f(z)-f(w)}dz = 0$.where gamma is a function.

frac stands for fraction. This leads to $\int_{w}^{z} \{1}/{f(z)-f(w)}dz + \int_{z}^{w} \{1}/{f(z)-f(w)}dz = 0$. But by substituting f(w) = f(z) and reversing the direction of integration in the second integral, we get, $\int_{w}^{z} \frac{1}{f(z)-f(w)}dz - \int_{w}^{z} \frac{1}{f(w)-f(z)}dz = 0$ . This results in the integral$\int_{w}^{z} \frac{f'(w)}{f(z)-f(w)}dz - \int_{w}^{z} \frac{f'(z)}{f(w)-f(z)}dz = 0$. Now it is time to simplify and evaluate each of the integrals. The first integral has value $\ln|f(z)-f(w)|$ and the second integral has value $\ln|f(z)-f(w)|$. Therefore, $f'(z)/f(z)-f(w) = f'(w)/(f(w)-f(z))$. This equation, however, is not possible unless $f(z) = f(w)$. Hence, we conclude that the function f(z) is constant throughout D.

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Given:

x - 2y = 11

2x + y = 19

To solve using elimination method, we have:

• Step 1:

Multiply equation 1 by 2, then multiply equation 2 by 1.

x - 2y = 11 ....................x2

2x + y = 19...................x1

2x - 4y = 22

2x + y = 19

• Step 2:

Now, subtract both equations:

• Divide both sides by -5:

Replace y with -3/5 in any of the equations to find x.

Let's take equation 2:

Multiply through by 5 to eliminate the fraction:

Add 3 to both sides:

Divide both sides by 10:

ANSWER:

Answer: $42 (b)

Step-by-step explanation:

So we know that: A salesperson at a furniture store earns a 3% commission on all sales.

The salesperson earn commission on a $1400 sale =3% of $1400

To convert percent to fraction we divide it by 100

=3\100 x 400

=3 x 14

= $42

Have a good day

The frequency of small-angle oscillations is given by\(f = (g/L)^(1/2) * (1/2π)^(1/2) * (M/L)^(-1/4).\)

The frequency of small-angle oscillations can be expressed in terms of the variables M (mass), L (length of the rod) and g (acceleration due to gravity). The expression is derived from the formula for the period of a pendulum, which is given by the equation T = 2π\((L/g)^(1/2)\). The frequency is the inverse of the period, so the expression for the frequency of small-angle oscillations is

f = \((g/L)^(1/2) * (1/2π)^(1/2) * (M/L)^(-1/4)\).

This expression demonstrates that the frequency of oscillations increases with increasing critical angle, as long as the mass is not changed. Additionally, the frequency decreases with increasing mass, as the mass of the rod slows down the oscillations. The frequency also increases with decreasing length, as a shorter pendulum swings faster due to the decreased time it takes for it to complete one oscillation.

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Answer:

  36.5 square units

Step-by-step explanation:

There are a number of ways to compute the area of a polygon from the coordinates of its vertices. There are algebraic formulas, geometric methods involving decomposing the figure, and an interesting method described by Pick's theorem.

__

The figure can be enclosed by a rectangle that is 7 units high by 9 units wide. The actual figure is obtained by removing the triangular corners of this rectangle. The areas of those are given by the triangle area formula ...

  A = 1/2bh

Working clockwise from lower left, the triangle base (horizontal) and height (vertical) dimensions are 5×6, 7×1, 2×6, 4×1. That means the area of the triangles is ...

  A = 1/2(5×6 +7×1 +2×6 +4×1) = 1/2(30 +7 +12 +4) = 1/2(53) = 26.5

The area of the bounding rectangle is ...

  A = bh = 9×7 = 63

So, the area of the figure is the difference ...

  A = 63 -26.5 = 36.5 . . . square units

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The other methods of finding the area have been added as attachments.