Write a polynomial function that meets the stated condition.

The zeros are -2/3 and , and the constant term of the polynomial is -10.

The probability that the resulting integer is divisible by 8 is 1/6

According to the question,

Nancy Rolled a six-sided die twice to generate two-digit integers

Total number of outcome by rolling a die = {1 , 2 , 3 , 4 ,5 ,6 }

If you roll twice then total number of outcomes becomes = 6 × 6

=> 36

We have to find  the probability that the resulting integer is divisible by 8

Number of two - digit integer divisible by 8 = 16 , 24 , 32 , 48 , 56 , 64

that is 6  

So, Probability = Number of favorable outcomes / total number of outcomes

=> 6 / 36

=> 1/6 is required probability

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On solving the given question, by the equation, A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer .A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

J can ride his bike 8 mph faster than A can ride. It takes A 3 hours longer than J to ride 48 miles. How fast can J ride?

Let r = rate that J rides, in miles per hour.

Then rate that A rides is (r – 8).

distance = rate * time

time = distance/rate

Time taken by J to ride 48 miles = 48/r.

Time taken by A to ride 48 miles = 48/(r – 8).

But A's time is 3 hours more than J's time.

48/(r – 8) = 3 + 48/r

Solve that for r.

48/(r – 8) = 3r/r + 48/r

48/(r – 8) = (3r + 48)/r

Multiply both sides by (r – 8)r.

[tex]48(r) = (3r + 48)(r - 8)\\ 48r = 3r2 -24r + 48r -384\\ 0 = 3r2 - 24r -384\\ 0 = r2 -8r - 128\\ 0 = (r -16)(r + 8)[/tex]

So r = 16 mph or r = –8 mph.

J riding 48 mi at 16 mph takes 3 hours.

A riding 48 mi at 8 mph takes 6 hours, which indeed is 3 hours longer.

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Answer:

a = [tex]\frac{b-4}{-2y}[/tex]

Step-by-step explanation:

ay + 4 = 3ay - b  Subtract 4 from both sides

ay = 3ay -b - 4  Subtract 3ay from both sides

ay - 3ay = b - 4  Factor out the a

a (y -3y)  = b =4  Combine like terms

a(-2y) = b - 4  Divide both sides by -2y

a = [tex]\frac{b-4}{-2y}[/tex]

The general solution of the given differential equation is y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2) and the largest interval is (-infinity, -2) U (-1, infinity).

The general solution of the mentioned differential equation will be calculated as follows -

Firstly rewriting the differential equation in standard form:

(x+1) dy/dx + (x+2)y = 2x[tex] {e}^{(xy)} [/tex]

Calculating the integrating factor to make the LHS as a total derivative:

As known, formula for integrating factor is:

mu = [tex] {e}^{(integral of (x+2)/(x+1) dx)} [/tex]

= [tex] {e}^{(ln(x+1) + ln(x+2))} [/tex]

= (x+1)(x+2)

Now multiplying both sides of the equation by the integrating factor:

(x+1)(x+2) × (x+1) dy/dx + (x+1)(x+2) × (x+2)y = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)

LHS will be a total derivative. Rearrange the equation for the same -

d/dx((x+1)(x+2)y) = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)

Integrating both sides of the equation:

(x+1)(x+2)y = integral of 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2) dx

= 2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C

Now find the equation for y:

y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2)

Equation for y is the general solution of the differential equation where constant C is the arbitrary constant of integration.

The general solution is not defined at the position x=-1 and x=-2. Hence, the largest interval over which the general solution is defined is (-infinity, -2) U (-1, infinity).

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Answer: A

Step-by-step explanation:

For II,  when the numerator is expanded, it contains terms of ab and a^2 which makes it a quadratic function, not an algebraic function.

For III, tricky one. The a can be cancelled out in the numerator and denominator and the resulting fraction is (b-3)/3. However, this can be further simplified to 1/3b - 1, which makes it not an algebraic fraction anymore.

This is an example of Systematic sampling.

Here we are drawing out every fifth invoice from the file available. Hence here we create an order where every fifth item is selected.

Hence this is called systematic sampling.

This is a type of probability sampling. In this method, samples are selected by the researcher at regular intervals.

This type of sampling is most suitable when we want to conduct a sampling method similar to simple random sampling but the list of population is unknown to us. However, this can also be used when the list of the same is available to us.

Another important condition is the order os the population, i.e ow it is spread must be random and not in some particular order or sample. Else the reult obtained will lose its credibility.

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Answer: a>6

Step-by-step explanation:

-3+21a-2a>111

Collect like terms on the left side

19a-3>111

Add 3 to both sides to solve for a terms

19a-3+3>111+3

19a>114

Divide both sides by 19

19a/19>114/19

a>6

[tex]-3+21a-2a > 111[/tex]

Simplify:

[tex]19a-3 > 111[/tex]

Add 3 to both sides:

[tex]19a-3+3 > 111+3[/tex]

[tex]19a > 114[/tex]

Divide both sides by 19:

[tex]\dfrac{19a}{19} > \dfrac{144}{19}[/tex]

[tex]\fbox{a} > \fbox{6}[/tex]

[tex]a > 6[/tex] on a graph:

Hence, the three side length of two triangles are same so they are congurent.  

What is the congurency?

Two shapes are congruent if they are the same (shape and size)- in other words, if the lengths of the sides and the angles are the same.

It is often useful to know when two triangles are congruent.

Here given coordinates of the triangle [tex]FGH[/tex] and triangle [tex]JKL[/tex] are

[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex].

So, the distance formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between [tex]FG[/tex]  is

[tex]d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]

Distance between [tex]GH[/tex]  is

[tex]d=\sqrt{(-9-(-2))^2+(10-(-7))^2}\\\\d=\sqrt{(-9+2)^2+(10+7)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]

Distance between [tex]HF[/tex]  is

[tex]d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]

Distance between [tex]JK[/tex]  is

[tex]d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]

Distance between [tex]KL[/tex]  is

[tex]d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]

Distance between [tex]LJ[/tex]  is

[tex]d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]

Since, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]

Hence, the three side length of two triangles are same so they are congurent.  

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Answer:just solve it

Step-by-step explanation:

it is super easy

The value of x is x ≤ 9 for which y ≤ -5(x - 18) - 2 when y = 43.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is y ≤ -5(x - 18) - 2.

Now the values of x when y = 43 is,

43 ≤ - 5(x - 18) - 2.

43 ≤ - 5x + 90 - 2.

43 - 88 ≤ - 5x.

- 45 ≤ - 5x.

5x ≤ 45.

x ≤ 9.

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(a) {2, 3, 4, 5, 6, 7, 8}

(b) {2, 4, 5, 9, 11, 12, 14}

(c) No next largest 7-subset; this is the last one in lexicographic order.

(d) {2, 4, 5, 6, 11, 12, 13}

(e) No next largest 7-subset; this is the last one in lexicographic order.

If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.

For instance, if A represents the set of natural numbers and B represents the set of all whole numbers, then B is a subset of A since the set of whole numbers contains all natural numbers. This is how we may comprehend it: Natural numbers 1, 2, 3, and so on make up the set A. B = A collection of whole numbers, such as "0, 1, 2, 3,..."

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Answer:

4

Step-by-step explanation:

Given expression:

[tex]\left(2-\log_{\sqrt{2}}10\right)\left(2-\log_{\sqrt{5}}10\right)[/tex]

[tex]\textsf{Apply the radical rule}: \quad \sqrt{a}=a^{\frac{1}{2}}[/tex]

[tex]\implies \left(2-\log_{2^{\frac{1}{2}}}10\right)\left(2-\log_{5^{\frac{1}{2}}}10\right)[/tex]

[tex]\textsf{Apply the log rule}: \quad \log _{a^n}(x)=\frac{1}{n}\log _a\left(x\right),\:\quad \:a > 0[/tex]

[tex]\implies \left(2-\dfrac{1}{\frac{1}{2}}\log_{2}10\right)\left(2-\dfrac{1}{\frac{1}{2}}\log_{5}10\right)[/tex]

[tex]\implies \left(2-2 \log_{2}10\right)\left(2-2\log_{5}10\right)[/tex]

Rewrite 10 as 2 · 5 and 10 as 5 · 2:

[tex]\implies \left(2-2 \log_{2}(2 \cdot 5)\right)\left(2-2\log_{5}(5 \cdot 2)\right)[/tex]

[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \left(2-(2 \log_{2}2+2\log_2 5)\right)\left(2-(2\log_{5}5 +2\log_52)\right)[/tex]

[tex]\implies \left(2-2 \log_{2}2-2\log_2 5\right)\left(2-2\log_{5}5 -2\log_52\right)[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies \left(2-2(1)-2\log_2 5\right)\left(2-2(1) -2\log_52\right)[/tex]

[tex]\implies \left(2-2-2\log_2 5\right)\left(2-2 -2\log_52\right)[/tex]

[tex]\implies \left(-2\log_2 5\right)\left(-2\log_52\right)[/tex]

Multiply:

[tex]\implies 4 \cdot \log_2 5 \cdot \log_52[/tex]

[tex]\textsf{Apply the log rule}: \quad \log _{a}(x) \cdot \log_{x}(a)=1[/tex]

[tex]\implies 4 \cdot 1[/tex]

[tex]\implies 4[/tex]

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. the expression.343 ^ { 4 / 3 } is 7,625

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 = 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.The expression 343^ {4/3} can be broken down into 343 to the power of 4 divided by 3. Before we evaluate the expression, we must understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 can be calculated using the formula 343 x 343 x 343 x 343. This results in 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.

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Answer:

120m/s

Step-by-step explanation:

v-? (speed)

s-5400m(travel)

t-45s(time)

v=s/t

v=5400/45

v=120m/s

2,092.1 is the population of the town after 5 years, and P(t)=2500*(1-0.035)^t is the exponential function.

In mathematics, exponential decay defines the process of diminishing an amount by a consistent percentage rate over a period of time.

It can be stated by the formula y=a(1-b)x wherein y is the total form and is the initial money, b is the decay factor, and x is the quantity of time that has passed.

So, we got:

r = 3.5%/100% = 0.035

We have our exponential function:

P(t) = 2500*(1 - 0.035)^t

The number after 5 years is provided by substituting t = 5, we will get:

P(5) =  2500*(1 - 0.035)^5 = 2,092.1

Therefore, 2,092.1 is the population of the town after 5 years, and P(t) = 2500*(1 - 0.035)^t is the exponential function.

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Correct question:
The population of the town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential decay function to find the population of the town after 5 years

The value of the x in g(h(x)) = 4 is 4 if the g⁻¹(4) = 2 and at x = 4 h(x) = 2 option (C) is correct.

The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The relation is,

g (h (x)) = 4

Now, Substitute x = 4;

LHS;

g (h (x)) = g (h (4))

            = g (2)

           = 4

Thus, The correct value of x when g(h(x)) = 4 is,

⇒ x = 4

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The equation of line passes through the points (14, 10) and (0, 2) will be;

⇒ y = 4/7x + 2

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (14, 10) and (0, 2)

Now,

Since, The equation of line passes through the points (14, 10) and (0, 2)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 10) / (0 - 14)

m = - 8 / - 14

m = 4/7

Thus, The equation of line with slope 4/7 is,

⇒ y - 10 = 4/7 (x - 14)

⇒ y - 10 = 4/7 (x - 14)

⇒ y = 4/7x - 8 + 10

⇒ y = 4/7x + 2

Therefore, The equation of line passes through the points (14, 10) and

(0, 2) will be;

⇒ y = 4/7x + 2

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Answer:

1.1 hectares

Step-by-step explanation:

6.93/6.3 = 1.1

He can plant 1.1 hectares of land.

In geometry, the distance formula is a formula used to calculate the distance between two points in a plane. It is derived from the Pythagorean Theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance formula is an equation used to calculate the distance between two points in a plane. It is derived from the Pythagorean Theorem which defines the relationship between the three sides of a right triangle. To calculate the distance between two points, (x1, y1) and (x2, y2), the formula is:

d = √((x2-x1)^2 + (y2-y1)^2).

This means that the distance between the two points is equal to the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates. To find the answer, you must first subtract the two x-coordinates (x2-x1) and then square the result. Then you must subtract the two y-coordinates (y2-y1) and square the result. Finally, add the two squared results together and take the square root of the sum to get the distance between the two points.

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(a) Area to the left of 24 is 0.6683.

(b) Area to the left of 17 is 0.284.

(c) Area to the right of 19 is 0.5028.

(d) Area to the right of 25 is 0.1019.

(e) Area between 17 and 30 is 0.0884.

We have given that a variable is normally distributed with mean 21 and standard deviation 7.

(a) We have to find area to the left of 24.

We will use z-formula

i.e Z = (X - μ) / σ

where X is the row score, μ is mean and σ is standard deviation.

Substituting the values we get,

Z = (24 - 21)/ 7

  = 3/7

Z = 0.4285

The p-value for 0.4285 is 0.6683.

Therefore area to the left of 24 is 0.6683.

(b) Now to find area to the left of 17,

Z =(17 - 21)/7

   = - 4/7

Z = -0.5714

The p-value for -0.5714 is  0.284.

The area to the left of 17 is 0.284

(c) To find the area of the the right of 19,

Z = (19 - 21)/ 7

   = -2/7

Z = -0.007

P-value for -0.007 is 0.4972

Area of the right of 19 is , 1 - 0.4972 = 0.5028

(d) The area of the right of 25 is,

Z = (25 - 24)/7

  = 1/7

Z = 0.1428

The p-value for 0.128 is 0.8981.

Area right of 25 is 1 - 0.8981 = 0.1019.

(e) To find area between 17 and 30 first we will find area of 17 and 30 individually.

We know area of 17 is 0.284.

Now area of 30,

Z = (30 - 24)/7

  = 6/7

Z = 0.8571.

P-value for 0.8571 is 0.1956.

Area between 17 and 30 is,

0.284-0.1956 = 0.0884.

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Answer: 24 cups of sugar

Step-by-step explanation: you multiple the orginal amount neede for one batch by 8

8*3=24

Considering the definition of perpendicular line, the equation of the perpendicular line is y= 1/5x - 13/5.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= -5x +1.

In this case, the line has a slope of  -5. If you multiply the slopes of two perpendicular lines, you get –1, you get:

(-5)× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-5)

slope perpendicular line= 1/5

So, the perpendicular line has a form of: y= 1/5x + b

The line passes through the point (2, -1). Replacing in the expression for perpendicular line:

-1= 1/5× 2 + b

-1= 2/5 + b

-1- 2/5= b

-13/5= b

Finally, the perpendicular line is y= 1/5x - 13/5.

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Answer:

48/7

Step-by-step explanation:

8/7/6

= 8 × 1/7/6

= 8× 6/7

48/7

The smallest unit of matter is an atom. The fundamental building block of an element is an atom, which is made up of protons, neutrons, and electrons. This statement is true.

An atom is made up of a nucleus and one or more electrons that are bound to the nucleus. The nucleus is made up of one or more protons, a significant number of neutrons, and other particles. Only the most common form of hydrogen lacks neutrons.

An atom, which is the smallest part of a material, retains all of its properties. A molecule is made up of protons, neutrons, and electrons, which are the building components of matter. Protons and neutrons, which are the only particles in an atom that contribute to its atomic mass, are found in the nucleus of each atom. These early 20th-century discoveries of particles that  a nuclide itself and chemical components are explained by contemporary atomic theory.

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The angle of elevation is 72.5° and the height at which the ladder will elevate on the building is 19.06 ft.

Here we have to find the angle of elevation of the ladder and the height the ladder will reach on the building if the ladder is leaned against a building.

Data given:

length of the ladder = 20 ft

the base of the ladder = 6ft

we have to find the angle of elevation.

cos Ф = base/ hypotenuse

= 6/20

Ф = [tex]cos^{-1}[/tex] ( 6/20)Ф

    = 72.5°

Now we have to find how high the ladder reaches on the building when leaned against a building.

sin(72.5°) = x/ 20

x = 0.953 ×20

x = 19.06 ft

Therefore the angle of elevation is 72.5° and the ladder will elevate to 19.06.

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No, The side lengths does not make a right triangle.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sides of the triangle are;

⇒ 20, 20 and √800

Now,

Since, The sides of the triangle are;

⇒ 20, 20 and √800

Hence, We can apply the Pythagoras theorem as;

⇒ (√800) ² = √ 20² + 20²

⇒ 800 ≠ √800

Thus, The side lengths does not make a right triangle.

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We might write [tex]y=x+\frac{1}{5} x[/tex] if the entire amount of money is y and the first week's deposit is x.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

When are given an x and y equation that is [tex]y=x+\frac{1}{5} x[/tex] , and the further discussion can be defined as follows:

We must now imagine a condition that can be represented by the above equation.

Let's calculate the place money in piggy bank over two weeks in a row.

In the first week, I deposit a [tex]\frac{1}{5}[/tex]  of a particular amount of money, and the next week, I deposit a quarter of such previous week's investment.

We must now determine the entire amount of money that I have deposited.

We might write [tex]y=x+\frac{1}{5} x[/tex] if the entire amount of money is y and the first week's deposit is x.

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The logarithmic form of e^a = 95/73 is  [tex]loge_{\frac{95}{73} }[/tex] = a

natural logarithm can be referred to as the power to which the base ‘e’ that has to be raised to obtain a number called its log number. Here e is the exponential function. It was initially discovered in the 17th century by John Napier, who discovered and conceptualized the theory of logarithms. Before looking into the key difference between ln and log, let’s understand the definition of log and ln.

if e^a = 95/73

means that the natural logarithm of 95/73 is the number a

so that we have

a =  [tex]loge_{\frac{95}{73} }[/tex]

In conclusion the logarithmic form of the expression is a =  [tex]loge_{\frac{95}{73} }[/tex]

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the first statement is false, and the 2nd statement is true.

the sign > indicates it is greater than the next value and the sign < indicates it is less than the next value.

In mathematics the above signs are used to compare two mathematical expressions.

7<5 cannot be possible as positive 7 is always greater than positive 5

in the next positive 3 is greater than positive 1 so it is true.

hence, 7<5 is false and 3>1 is true.

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Answer:

x = pm - pn

Step-by-step explanation:

m = n + [tex]\frac{x}{p}[/tex]  Subtract n from both sides

m - n = n - n + [tex]\frac{x}{p}[/tex]

m-n = [tex]\frac{x}{p}[/tex]   Multiply both sides by p

p(m - n) = ([tex]\frac{p}{1}[/tex]) [tex]\frac{x}{p}[/tex]          [tex]\frac{p}{1}[/tex] means the same as p

pm - pn = x             Distribute the p

x = pm - pn