Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 13)(0,13) and (3, 832)(3,832).

The length of the one of the leg of the triangle is 12√2 in. Thus, option B is correct.

The longest side of a right triangle in geometry is called the hypotenuse. Moreover, it is the side that faces the right angle. The definition of hypotenuse is "length under" or "stretch under." Plato was said to have used it for the first time around 400 BC.

In many applications of geometry and trigonometry, the hypotenuse plays a significant role. The Pythagorean Theorem is the most widely known. Using the Pythagorean Theorem, a2 + b2 = c2, one can determine the length of the hypotenuse.

The Right angles triangle is also a isosceles angled triangle which means two of the angles are equal.

When two angles are equal the corresponding sides are equal too.

a = b

Given that the measure of the triangles' hypotenuse is 24 inches

c² = a² + b²

24² = a² + b²

576 = a² + b²

But the sides are equal i.e.

a = b

Giving us

576 = a² + a²

576 = 2a²

a² = 576/2

a² = 288

a = √288

a = 12√2

Thus, the length of the one of the leg of the triangle is 12√2 in. Thus, option B is correct.

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Answer:

Step-by-step explanation:

b e2020

Answer:

To calculate the number of yards of ribbon Christine bought, we need to determine how much money she spent on the ribbon. We know that the card had $20 on it initially and that $18.42 was left on the card after her purchase, so we can subtract the remaining balance from the original balance to find out how much she spent:

$20 - $18.42 = $1.58

We also know that the ribbon was 14 cents per yard, so we can divide the amount spent on the ribbon by the price per yard to find out how many yards Christine bought:

$1.58 / $0.14 = 11.285714285714286

So, Christine bought 11.285714285714286 yards of ribbon.

The correct statement is,

⇒ - 8/5 < 3/5

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The numbers are,

⇒ 3/5 and - 8/5

Now, By comparing, we get;

⇒ 3/5 and - 8/5

⇒ 3/5 > - 8/5

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First of all remember that all triangles are always equal to 180 degrees from that we can figure out that x is is 70 because 30+80+70=180. z would be 40 because it is parallel to 40 and therefore equal to it. y is 100 because 40+40+100=180. Recap:

x: 70

z: 40

y: 100

i. α = 56°

ii. adj =  4.1

iii. opp = 2.79

We have to recall that what makes the right angle triangle unique is the fact that one of the angles that we find in the triangle is 90 degrees. We have to recall that the sum of the angles that we have in a triangle is 180°.

Hence we have;

α = 180 - (90 + 34)

α = 56°

Then;

Cos 34 = adj/5

adj = 5 cos 34

= 4.1

Sin 34 = opp/5

opp = 5 * sin 34

= 2.79

These are the parts of the right angled triangle required.

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The ratio of the mystery novel to all novels from Addison's novel collection, is D. 4 to 11.

Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another. Two quantities are compared using division in a ratio. In this case, the dividend is referred to as the "antecedent" and the divisor as the "consequent."

The ratio of the mystery novels to all novels can therefore be found by first finding the total number of novels :

= 2 + 4 + 5

= 11 novels

The ratio would then be:

Number of mystery novels : Number of all novels

                  4                         :               11

Which is 4 to 11.

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Answer:

21/4 * 11/2=5.25*5.5

Step-by-step explanation:

21/4 * 11/2=5.25*5.5

= 28.875

At the end of 28years the neurosurgeon will have an amount of $115875.00

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

The amount earned or paid after compounded interest is given as A = P(1+r/100)^t

Where P is the principal saved

t is the time for saving

and r is the rate of interest

Here t = 28 years

P = 25,000

and r = 5.63% per annum

therefore A = P(1+r/100)^t

A = 25000(1+5.63/100)^28

A = 25000(1+0.0563)^28

A = 25000(1.0563)^28

A = 25000× 4.635

A= $115875.00

This means at the end of 28 years, the neurosurgeon will have a amount of $115875.00

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Answer:

7/9

Step-by-step explanation:

Simplify the following:

(2/3)/(6/7)

Multiply the numerator by the reciprocal of the denominator, (2/3)/(6/7) = 2/3×7/6:

(2×7)/(3×6)

2/6 = 2/(2×3) = 1/3:

7/(3×3)

3×3 = 9:

Answer:7/9

To evaluate x/y for x = 2/3 and y = 6/7, you need to substitute these values into the expression x/y and simplify the result.

x/y = (2/3) / (6/7)

To simplify the fraction, you can cross multiply the numerator and denominator by 7, which is the denominator of the second fraction:

(2/3) / (6/7) = (2/3) * (7/6) = (27) / (36) = 14/18

The fraction can be simplified further by dividing both the numerator and denominator by their greatest common divisor (GCD) which is 2:

14/18 = (14/2) / (18/2) = 7/9

So x/y = 7/9 when x = 2/3 and y = 6/7

It's important to note that the result is a fraction, if you want to express it as decimal you can divide 7 by 9 or use a calculator to get 0.7777 repeating.

To prove this statement, we will use the following definitions and properties:

A finite dimensional vector space is a vector space that has a finite number of basis vectors.

A basis for a vector space is a set of vectors that span the space, meaning that any vector in the space can be written as a linear combination of the basis vectors.

A linear combination of a set of vectors is an expression of the form a_1v_1 + a_2v_2 + ... + a_nv_n, where v_1, v_2, ..., v_n are the basis vectors and a_1, a_2, ..., a_n are scalars from the field.

A non-zero element of a finite dimensional vector space is a vector that is not equal to the zero vector, the additive identity of the space.

Now, let's assume that V is a finite dimensional vector space over a field F, and let B be a basis for V. We will show that every non-zero element of V can be expressed as a unique linear combination of the basis vectors in B.

Let v be a non-zero element of V. Since B spans V, there exists a set of scalars a_1, a_2, ..., a_n from the field F such that v = a_1v_1 + a_2v_2 + ... + a_nv_n, where v_1, v_2, ..., v_n are the basis vectors in B. This is a valid linear combination representation of v with respect to B.

To show that this linear combination representation of v is unique, let's assume that there exists another set of scalars b_1, b_2, ..., b_n from the field F such that v = b_1v_1 + b_2v_2 + ... + b_nv_n. Then, subtracting the second equation from the first one, we get:

0 = (a_1 - b_1)v_1 + (a_2 - b_2)v_2 + ... + (a_n - b_n)v_n.

Since B is a basis for V, the only way for the left-hand side of the equation to be the zero vector is for all the scalars in the linear combination to be equal, i.e. a_1 = b_1, a_2 = b_2, ..., a_n = b_n. Thus, v can be expressed as a unique linear combination of the basis vectors in B, which completes the proof.

Since there is a 0.45 chance of winning a prize at the carnival game, the likelihood that he will win one is 0.04 out of every five games.

Probability theory, a subfield of mathematics, analyzes the likelihood that an event will occur or a statement is true. The probability of an event occurring is a number between 0 and 1, where approximately 0 indicates how unlikely the event is and 1 indicates how certain it is. A probability is a quantitative expression of the likelihood that a particular event will occur. Probabilities can also be expressed as percentages between 0% and 100% or as percentages between 0 and 1. the ratio of the total number of outcomes to the number of events in a complete collection of equally likely outcomes that result in a certain occurrence.

given

= (0.45 )* 1*5 / 5

= 0.04

Since there is a 0.45 chance of winning a prize at the carnival game, the likelihood that he will win one is 0.04 out of every five games.

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The value of the evaluated iterated integral is 0.1202.

As per the given data the iterated integral is [tex]I & =\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex].

Here we have to evaluate the given iterated integral.

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval [a, b] is expressed as[tex]$\int_a^b f(x) d x$[/tex] = F(b) - F(a)

Here,

[tex]$\int=$[/tex] Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, [tex]$\int a b f(x) d x$[/tex] is read as the definite integral of f(x) with respect to d x from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]I & =\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex]

Integrate the given iterated integral.

We get:

[tex]& =\int_0^1 \cos \left(s^7\right)\left(\int_0^{s^6} d t\right) d s[/tex]

[tex]& =\int_0^1 \cos \left(s^7\right) \times[t]_0^{s^6} d s . \\[/tex]

[tex]& =\int_0^1 \cos \left(s^7\right) \times\left(s^6-0\right) d s . \\[/tex]

[tex]& =\int_0^1 s^6 \cos \left(s^7\right) d s[/tex]

Say [tex]s^7=t[/tex]                 when s = 0

[tex]\Rightarrow \frac{d t}{d s}=7 s^6 \quad$[/tex]                          t = 0  

[tex]\Rightarrow \frac{d t}{7}=s^6 d s[/tex]              when s = 1.....   t = 1

Replace the assumed terms.

Then we get:

[tex]$I=\int_0^1 \cos (t) \frac{d t}{7}$[/tex]

[tex]$=\frac{1}{7} \int_0^1 \cos (t) d t$[/tex]

[tex]$=\frac{1}{7}[\sin (t)]_0^1=\frac{1}{7}[\sin (1)-\sin (0)]$[/tex]

[tex]=\frac{\sin (1)}{7}$[/tex]

[tex]\int_0^1 \int_0^{s^6} \cos \left(s^7\right) d t d s[/tex] = 0.1202

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For the m/m/1 queuing model, the average number in the system is equals to the four. So, the correct answer is option (c).

This is the most widely used queuing system in analytics. M/M/1 is a good approximation for a large number of

mass service systems. The M/M/1 quening system assumes a Poisson arrival process. This assumption is a very good approximation for the process of arriving at real systems that satisfy the following rules,

We have, customer service is every 4 minutes. So, the Service rate μ = 1 customer/4 minutes = 0.25 customer/minute or 15 per hour.

Customers arrive individually at a rate of one customer every 5 minutes according to the distribution of poisons.

Number of customer service= 1

The arrival rate is 1/ (mean time between arrivals) . Here, the rate of arrival of customers/5 minutes is λ = 0.2 customers/min or 12 per hour. Therefore,

Utilization factor = (arival rate /service rate)100 = λ/μs

Utilization factor = (12/15) 100%

= (4/5)100 = 80%

Utilization factor = 80%

Average number in the system = λ/( μ - λ)

= (60/5)/[ (60/4)-(60/5)]

= 12/3 = 4

So, the average number in the system is 4.

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Complete question:

A queuing model that follows the m/m/1 assumptions. a customer can be served every 4 minutes. customers arrive independently at the rate of one customer every 5 minutes according to a poisson distribution. the average number in the system is

a) 7

b) 5

c) 4

d) 6

Answer: Synthetic division and synthetic substitution are both methods used to divide polynomials, but they are used for different types of polynomials and have different steps and procedures.

Synthetic division is a method used to divide a polynomial by a linear binomial of the form (x-c), where c is a constant. It is used to find the quotient and remainder of the division, and it involves a process of simplifying the polynomial using a specific set of steps.

Synthetic substitution, on the other hand, is a method used to divide a polynomial by a polynomial of higher degree. It is used to find the quotient and remainder of the division, and it involves replacing a variable in the polynomial with an expression and then simplifying.

In summary, Synthetic Division is used when dividing a polynomial by a linear binomial and Synthetic Substitution is used when dividing a polynomial by a polynomial of higher degree.

Step-by-step explanation:

Synthetic division is used for polynomial division by a linear factor, resulting in a quotient polynomial. Synthetic substitution, however, is used to find the value of a polynomial function at a given x-coordinate.

Synthetic division and synthetic substitution are both methods used in algebra to evaluate polynomials. However, they differ in their specific applications and the outcomes they provide.

Synthetic division is a method used to divide a polynomial by a linear factor of the form (x - c). It allows for quick and efficient division without the need for long division. The process involves setting up a synthetic division table and performing a series of calculations based on the coefficients of the polynomial. The result is a simplified quotient polynomial.

On the other hand, synthetic substitution is a technique used to evaluate a polynomial function at a specific value of x. It involves substituting the given value into the polynomial and using synthetic division to perform the calculations. The result obtained is the value of the polynomial at that particular x-coordinate.

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Todd's conclusion is therefore incorrect, not all linear relationships are proportional, they can be represented by a linear equation but they don't need to have a constant ratio between the two variables.

What is a linear relationship?

A linear relationship is a relationship between two variables in which the change in one variable is directly proportional to the change in the other variable. Linear relationships can be represented by a linear equation, which is an equation that can be written in the form of y = mx + b, where m and b are constants.

Proportional relationships also have a constant ratio between the two variables, but the relationship between the variables is not always linear. Proportionality can be represented by the equation y = kx, where k is a constant.

In general, it is not true that all linear relationships must be proportional. While it is true that a proportional relationship will always result in a linear graph, there are also many other types of linear relationships that do not fit this definition. For example, the equation y = 2x + 3 describes a linear relationship, but it is not proportional because the ratio between y and x is not constant.

Hence, Todd's conclusion is therefore incorrect, not all linear relationships are proportional, they can be represented by a linear equation but they don't need to have a constant ratio between the two variables.

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Answer: W = 7

Step-by-step explanation:

do PEMDAS and then follow the order of operations rule

The amount of ingredient that is needed to make just 2 portions are:

Generally, the term "portion" refers to how much food is served to you or how much you eat. Portion sizes can differ from meal to meal. For example, you might serve yourself two small pancakes in one portion at home, but at a restaurant, you might get a stack of four pancakes as one portion.

Data

Needed 2 portions

Recipe: 250 g oats, 1.4 litres milk, 90 g suga

Portion of Oat:

250/5 * 4 = 50 *2 = 100g oats

Portion of milk:

1.2/5 * 2 = 0.48l milk

Portion of sugar:

90/5 * 2 = 18*2 = 36g sugar

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Since the ordered pair (a, b) satisfies the inequality y > x + 3, a statement which is true include the following: C. b is greater than a.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) data points or elements that are commonly written in a fixed order within parentheses as (x, y).

This ultimately implies that, an ordered pair is typically used for representing the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

Based on the given ordered pair (x, y) which satisfies this inequality y > x + 3, this can be rewritten in terms of a and b as follows;

y > x + 3

b > a + 3

In this context, we can reasonably infer and logically deduce that b is greater than a i.e b > a.

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Complete Question:

The ordered pair (a, b) satisfies the inequality y>x+3. Which statement is true?

A.if you add 3 to b , it will equal a

B. a is greater than b

C. b is greater than a

D. If you subtract 3 from b, it will equal a

The the experimental probability of rolling the given result that a number more than 3 is D. 0.44

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The following observations can be gotten based on the information:

1 = 32

2 = 36

3 = 44

4 = 20

5 = 30

6 = 38

Therefore, probability = sum of observation (3,4 and 5) / total no of observation

= 20 + 30+ 38 / 200

= 88 / 200

= 0.44

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A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a number more than 3 a. 0.88 c. 0.56 b. 0.34 d. 0.44 Please select the best answer from the choices provided A B C D

Therefore the slope of the line passes through  (5, 9) and (3, -5) comes out to be 7.

By computing the ratio of the vertical to horizontal distance (rise over run) between two points, the slope—a numerical value that defines how steep a line is—is often calculated.a number that indicates how inclined a line is, is frequently determined by dividing the vertical distance (rise over run) between two places by the horizontal distance (run over rise).

The slope of line that passes through  (5, 9) and (3, -5)

Slope= gradient between the two points

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

Where y2= -5

Y1= 9

X2= 3

X1= 5

(-5-9)/(3-5)

-14/-2

7

Therefore the slope of the line passes through  (5, 9) and (3, -5) comes out to be 7.

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Answer: To find the X and Y components of the 15N weight of the birthday cake, we can use trigonometry. We know that the angle of inclination of the table is 23° above the horizontal.

We can use the tangent function to find the X component of the weight, which is the component that is parallel to the table.

X = 15N * tangent (23°)

We can use the sine function to find the Y component of the weight, which is the component that is perpendicular to the table.

Y = 15N * sine (23°)

By applying these formulas and plugging in the angle and weight we can find the respective X and Y components.

Step-by-step explanation:

The required distinct roots of the following equation using the quadratic formula is x = -3±√5i.

Any quadratic problem can be solved using the quadratic formula.

The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients.

After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

So, the quadratic formula:

x = -b±√b²-4ac/2a

Now, insert values and calculate for roots as follows:

x = -b±√b²-4ac/2a

x = -b±√b²-4*4(1)*14/2(1)

x = -b±√36/56/2

x = -b±√-20/2

Discriminant: b² - 4ac < 0

Now,

x = -6± 2√5i/2

x = -6/2 ± 2√5i/2

x = -3±√5i

Therefore, the required distinct roots of the following equation using the quadratic formula is x = -3±√5i.

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Answer:

a

Step-by-step explanation:

to find the zeroes let f(x) = 0 , that is

- 2(x - 5)(x + 6)(x + 7) = 0

equate each factor to zero and solve for x

obviously multiplying any value by - 2 will not give zero

so only consider the binomial factors

x + 7 = 0 ⇒ x = - 7

x + 6 = 0 ⇒ x = - 6

x - 5 = 0 ⇒ x = 5

The solution's f[x] means f(x)=0 when x is not in [−2,2]

The answer to [-2,2] is: f(x)dx=P(X∈dx)=2∗(2−|x|)dx4∗(12∗2∗2)=14(2−|x|)dx

Consequently, f(x)=14(2|x|) on [2,2]

and if not, f(x)=0

For [2,0], it is 14(2+x), while for [2,0], it is 14(2-x).

I discovered a formula for the uniform distribution U=X for (a,b), however, I don't believe this is right since the answer would then be X+24 without X being an absolute value. It also doesn't apply to other questions of a similar nature.

Please assist; there is a very strange exercise question in the textbook that we are unable to solve on our own. I have no idea how they obtained the 2(2|x|)dx4(12|2]).

Furthermore,  f(x) may indicate f(x)=0 when x is not in [2,2].

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The Full question would be:

Consider a point picked uniformly at random from the area inside the shape with the coordinates (-2,0), (0,2), (2,0), (0,-2).

Answer:

z + 4 × 9

Sorry if this is wrong.

Answer: The new value of the sum of N1,500 investment at a simple rate of 15% per annum for 2 years is N1950

Step-by-step explanation:

Simple interest is calculated by multiplying the principal amount, interest rate, and time.

The formula for simple interest is:

Simple Interest = (principal x rate x time) / 100

In this case, the principal amount is N1,500, the interest rate is 15% per annum and the time is 2 years.

So the simple interest earned on the investment is:

Simple Interest = (1500 x 15 x 2) / 100

Simple Interest = N450

To find the new value of the investment, we add the simple interest earned to the principal amount.

New value = Principal + Simple Interest

New Value = 1500 + 450

New Value = N1950

Explanation: Simple interest is calculated by multiplying the principal amount, interest rate, and time. By using this formula, the interest earned on the investment was N450. And by adding the interest to the principal amount, we can find the new value of the investment which is N1950.