write the equation of the line parallel to y=6/5x+7/5 that passes through the point (-5,1). Type an equation using slope-intercept form or using the given point in point-slope form.

The statement " Parallel lines are never coplanar."  statement is always true.

Coplanar is a term that refers to any points, lines, curves, or surfaces that are situated in the same plane.

Two lines that are parallel and coplanar will never intersect one another.

As a result, when two lines are parallel, they are always coplanar.

Two or more lines in the same plane, on the other hand, are coplanar.

These lines are said to be parallel if they never meet at any point.

In three-dimensional space, two lines can be parallel or skew (neither parallel nor intersecting).

Parallel lines will always be equidistant from one another, no matter how long they stretch.

When a straight line intersects a pair of parallel lines, it creates some corresponding angles.

These corresponding angles are equal in magnitude, indicating that if one of them is 75 degrees, the other is also 75 degrees. So, parallel lines are never coplanar.

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Answer:

p : q : r = 1 : 8/3 : 3/2

Step-by-step explanation:

p/q = (3/4)/2 = 3/(4*2) = 3/8

=> q = (8/3)p

p/r = (1/3)/(1/2) = (1*2)/(3*1) = 2/3

=> r = (3/2)p

=> (p, q ,r) = (p, (8/3)p, (3/2)p)

=> p : q : r = 1 : 8/3 : 3/2

Hope this helps!

Both of the following statements are true about confidence intervals: Small samples produce large confidence intervals. Large samples produce small confidence intervals.

Confidence intervals are statistical estimations used in hypothesis testing. They are calculated from a random sample taken from a population, and they help to measure the accuracy and variability of the population parameter being tested.

The confidence interval is calculated by using a sample mean and a margin of error. In general, the larger the sample size, the smaller the margin of error and the narrower the confidence interval. The confidence interval is larger if the sample size is small, indicating that the sample mean is less likely to accurately represent the population parameter.

Small samples will produce larger confidence intervals because of greater uncertainty in the sample estimates. In contrast, larger samples will produce smaller confidence intervals because they provide more accurate estimates of the population parameter.

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The Laplace Transform Method can be used to solve all of these equations except for equation (e).

a.) Yes, the Laplace Transform Method can be used to solve this third-order linear differential equation with constant coefficients and a nonhomogeneous term.

b.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with constant coefficients.

c.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

d.) Yes, the Laplace Transform Method can be used to solve this second-order linear homogeneous differential equation with variable coefficients.

e.) No, the Laplace Transform Method cannot be used to solve this first-order nonlinear differential equation.

f.) Yes, the Laplace Transform Method can be used to solve this second-order linear differential equation with constant coefficients and a nonhomogeneous term.

g.) Yes, the Laplace Transform Method can be used to solve this first-order nonlinear differential equation.

h.) Yes, the Laplace Transform Method can be used to solve this first-order linear differential equation with constant coefficients and a nonhomogeneous term.

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The given statement "when a researcher rejects the null hypothesis, they are saying that the difference between two groups is statistically significant." is true.

The word hypothesis in statistics refers a formal statement, which gives the explanation about the relationship between the two or more variables

Here we have given the statement "when a researcher rejects the null hypothesis, they are saying that the difference between two groups is statistically significant." and we need to find whether the given statement is true or not.

While we looking into the given question, we know that in null hypothesis testing, then this criterion is called α (alpha) and is almost always set to . 05. Where as if there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, and then the null hypothesis is rejected. If this happens, then the result is said to be statistically significant .

Based on these concept the given statement is true.

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Answer:

greater

Step-by-step explanation:

The ratio of Kaido's age to Hiroshi's age to Saitama's age is 5:8:24.

Hiroshi is 6 years older than Kaido. Saitama is three times as old as Hiroshi. The sum of their three ages is 79.

Therefore, the ratio of Kaido's age to Hiroshi's age to Saitama's age can be calculated as follows:

Hence,

let

x = Kaido age

Hiroshi age = 6 + x

Saitama age = 3(6 + x) = 18 + 3x

Therefore,

x + 6 + x + 18 + 3x = 79

5x = 79 - 24

5x = 50

x = 50 / 5

x = 10

Therefore,

x = Kaido age = 10 years

Hiroshi age = 6 + x = 6 + 10 = 16 years

Saitama age = 3(6 + x) = 18 + 3x = 18 + 3(10) = 48 years

Hence, the ratio of there ages are as follows:

10:16:48

Let's divide through by 2

5:8:24

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Answer:

Basically it is an x and y axis type of equation. The 3 could be how many steps to the right and the 4 could be how many steps forward.

Step-by-step explanation:

Start from the center of the grid which is called the origin and jump 3 times to the left. Then, you move 4 steps forward and then you have your ordered pair

The store should order calculators 8.73 times per year and each order should have a size of 44.24 calculators to minimize costs.

We have,

Let's assume that the store orders the calculators 'n' times a year and each order has a size of 'Q' calculators.

Then, the total cost (TC) can be expressed as:

TC = Cost of ordering + Cost of holding inventory

Cost of order = Total number of orders x Cost per order

= n x (8 + 2.25Q)

Cost of holding inventory = Cost of holding one calculator x Total number of calculators held

= 2 x 800/Q x Q/2

= 800

Therefore, the total cost can be expressed as:

TC = n(8 + 2.25Q) + 800

To minimize the total cost, we need to find the values of 'n' and 'Q' that minimize TC.

To do that, we can take partial derivatives of TC with respect to 'n' and 'Q' and set them to zero:

∂TC/∂n = 8 + 2.25Q = 0

∂TC/∂Q = 2.25n - 800/Q^2 = 0

Solving these equations, we get:

Q = √(800/2.25n) = 16.97√n

n = (2.25Q^2)/800 = 0.025Q^2

We can substitute the expression for 'Q' in terms of 'n' in the equation for 'n' to get:

n = 0.025(16.97√n)² = 2.293n

Solving for 'n', we get:

n = 8.73

Substituting this value of 'n' in the equation for 'Q', we get:

Q = 16.97√n = 44.24

Therefore,

The store should order calculators 8.73 times per year and each order should have a size of 44.24 calculators to minimize costs.

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Maria must cut an additional $70 from her expenses each month in order to save enough money to buy a new TV that costs $420 in 6 months. By allocating this additional amount towards her savings goal, she will be able to reach her target within the desired timeframe. It's important for Maria to review her budget and identify areas where she can reduce expenses in order to make room for the additional savings. This could involve cutting back on discretionary spending, finding ways to save on daily expenses, or exploring opportunities to increase her income.

Maria must cut an additional $70 from her expenses each month.

To determine how much additional money Maria must cut from her expenses each month to afford a new TV that costs $420 in 6 months, we divide the total cost by the number of months.

Additional money per month = Total cost / Number of months

Additional money per month = $420 / 6

Additional money per month = $70

With careful planning and commitment to her budget, Maria can achieve her goal of purchasing a new TV without compromising her financial stability.

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Answer:

C

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

x² = 20 × (20 + 36) = 20 × 56 = 1120 ( take square root of both sides )

x = \(\sqrt{1120}\) = \(\sqrt{16(70)}\) = \(\sqrt{16}\) × \(\sqrt{70}\) = 4\(\sqrt{70}\)

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer: \(184,724.153\)

Step-by-step explanation:

Given

In 1990, there were 1200 cell phone subscriber in small town of stephenville

It is increasing by 75% per year after 1990

In year 1991 it is

\(\Rightarrow 1200+1200\times 0.75\\\Rightarrow 122(1.75)\)

In year 1992 it is

\(\Rightarrow 1200(1.75)+1200(1.75)\times 0.75\\\Rightarrow 1200(1.75)(1+0.75)\\\Rightarrow 1200(1.75)^2\)

So, it is increasing as \(1200(1.75)^x\)

where \(x=\)no of years spent

After 9 years, it is

\(\Rightarrow 1200(1.75)^9=184,724.153\)

The greatest positive integer that completely divides both of the numbers is known as the greatest common factor, or GCF. The GCF or HCF is composed of two or more non-zero integers.

In other words, the greatest common factor (GCF) among all the factors of the provided numbers is the case when there are two or more numbers. The Highest Common Factor of the Given Numbers is another name for it.

The approaches that are utilized to discover the GCF are listed below.

citing common elements:

Here, we list the common components of the given numbers and highlight those that are most frequently occurring.

main determinants:

In order to determine the highest common factors from both prime factor lists, we must write the given numbers as the product of prime numbers.

division strategy

Here, we must use the long division method to divide the greatest integer by the lowest number until the result is zero. The GCF of the given integers will make up the rest of the divisor when we reach the point where we have zero.

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Answer: Third answer option, \(\sqrt{3} *\sqrt{12}\)

Step-by-step explanation:

     Both 3 and 9 are not irrational numbers, so the first option is incorrect.

     The \(\sqrt{3}\) is irrational, but 0 is not, so the second option is also incorrect.

     The \(\sqrt{3}\) and \(\sqrt{12}\) are both irrational. Let us see if they result in a rational number when multiplied together;

                 \(\sqrt{3} *\sqrt{12} =\sqrt{3*12} =\sqrt{36} =6\)

      They do, so this answer option is correct.

Answer:

Small scooters = 6

Large scooters = 4

Step-by-step explanation:

Let S represents small scooter and L represents large scooter

The cost of a small scooter is £80

Mathematically,  the cost of S number of small scooters is

80S

The cost of a large scooter is £130

Mathematically,  the cost of L number of large scooters is

130L

The total amount spent on both scooters is £1000

Mathematically,

80S + 130L = 1000

So we have 2 unknowns and only 1 equation. Therefore, we have use trial and error method .

Trial and Error Method:

80S + 130L = 1000

80S = 1000 - 130L

S = (1000 - 130L)/80

Let’s suppose they bought 1 large scooter

S = (1000 - 130(1))/80

S = 10.875

Number of scooters cannot be in fraction so 1 doesn’t work

Let’s suppose they bought 2 large scooter s

S = (1000 - 130(2))/80

S = 9.25

Number of scooters cannot be in fraction so 2 doesn’t work

Let’s suppose they bought 3 large scooter s

S = (1000 - 130(3))/80

S = 7.625

Number of scooters cannot be in fraction so 3 doesn’t work

Let’s suppose they bought 4 large scooters

S = (1000 - 130(4))/80

S = 6

So that means they bought 6 small scooters and 4 large scooters.

Similarly, other combinations for scooters don’t work since they yield either fractional value or negative value which cannot be correct.

Therefore, the only possible combination of small and large scooters is

6 Small scooters

4 Large scooters

Verification:

80S + 130L = 1000

80(6) + 130(4) = 1000

480 + 520 = 1000

1000 = 1000 (satisfied)

Answer:

-182

Step-by-step explanation:

911 - 729 = 182. the difference in elevation is 182 feet but because they descended its a negative 182

Answer:

jawaban :178,000 itu jawabanya ya dah

Step-by-step explanation:

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Answer:

A.  0.055 dolars per ounce

B. 0.45 dolars per ounce

Best answer:

B

Answer:

12

Step-by-step explanation:

Answer:

A) spinning a number less than 3

B) spinning a 4 or 5

D) Spinning a number greater than 8

Step-by-step explanation:

You want to choose the ones where there are two outcomes.

A) spinning a number less than 3

B) spinning a 4 or 5

D) Spinning a number greater than 8

The correct answers are A, B and D

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.

Given that,  Total numbers on spinner = 10

We have to find the event that has theoretical probability of exactly 1/5.

A) Spinning a number less than 3

Number less than 3 = 1  and 2

Favourable cases = 2

Probability, P(E) = 2/10 = 1/5

It is true.

B) Spinning a 4 or 5

Favourable cases = 2

Probability, P(E) = 2/10 = 1/5

It is true.

D) Spinning a number greater than 8

Number greater than 8=9 and 10

Favourable cases=2

Probability, P(E) = 2/10 = 1/5

It is true.

Hence, Option A, B and D are true.

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Based on the common factors of 24 and 36, the possible numbers of friends to whom the cadburies and snikers can be equall distributed include 2, 3, 4, 6 and 12.

Common factors of two numbers are the numbers that can divide them equally without leaving a remainder.

Common factors are quotients obtained from the division of a number when there is no remainder.

The number of snikers distributed at Bishwant's birthday = 24

The number of cadburies distributed equally at Bishwant's birthday = 36

The common factors of 24 and 36 are 2, 3, 4, 6 and 12 because each of the five numbers can divide 24 and 36 without a remainder.

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It is feasible to distribute the Snickers and Cadbury chocolates evenly to the following numbers of friends: 1, 2, 3, 4, 6, and 12.

We must determine the 24 and 36 common factors.

The numbers 1, 2, 3, 4, 6, 8, 12, and 24 make up the number 24.

1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.

The total number of friends must be a common factor of both 24 and 36 in order to distribute the chocolates equitably. 1, 2, 3, 4, 6, and 12 are the common factors.

Therefore, It is feasible to distribute the Snickers and Cadbury chocolates evenly to the following numbers of friends: 1, 2, 3, 4, 6, and 12.

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Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

44664.59503

Step-by-step explanation:

Hello,

In this question, you're asked to find the radical of a number. However in mathematics, the radical of a number simply means "√" and not directly square root of that number, its could be the cube root "³√" or even the fourth root "⁴√".

In this case, we're asked to find the 3 radical of p/q which means 3√(p/q)

P = 2.78×10¹¹

Q = 3.12×10⁻³

p / q = 2.78×10¹¹ / 3.12×10⁻³

p / q = 8.91×10¹³

The 3 radical = 3√(8.91×10¹³)

3√(p/q) = 44664.59503

The expression for the cost, C (in dollars), of hiring a fancy-dress costume for h hours can be given as:

C = 20 + 2.5h

where the fixed cost of the non-refundable deposit is $20, and the variable cost per hour of hire is $2.50.

For example, if you wanted to hire a fancy-dress costume for 4 hours, the cost would be:

C = 20 + 2.5(4) = 20 + 10 = 30

So the cost of hiring the costume for 4 hours would be $30.