R(-9,4) and S(2,-1); Find T

In this equation, the value of x in the ratio 4x-1/ 3x + 7 = 6/5 is 23.5.  In algebra, an equation is a mathematical statement .

A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. An equation is a mathematical statement that proves the equality of two mathematical expressions, according to the definition of an equation in algebra. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable.

given

4x-1/ 3x + 7 = 6/5

20x - 5 = 18x + 42

x = 23.5

In this equation, the value of x in the ratio 4x-1/ 3x + 7 = 6/5 is 23.5.

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Answer:

y=x-5000

Step-by-step explanation:

Given,

total sum of money mom has=x

money spent on grocery=Rs 3000

money spent on milk= Rs 2000

total money spent by mom=Rs 5000

Let the money left with the mom =y

then the algebric expression for the amount left with her is given by

y=x-5000

Remaining two data of Theo's observation is 9 and 11.

Mean is the average of all data value. Range is the difference between the highest and lowest value of a data set. Median implies the middle value of a data set. If the number of data is even than median is calculated from average of two middle value. If the number of data is odd, then the median is the middle of all data.

given, Kendra and Theo both collected data of bird observation.

Kendra data's summary are as following.

range = 6

median = 7

mean = 7

From the Theo's data

range = 6

median = 7

mean = 7.5

the question shows 6 data among the total 8 data of Theo's observation.

5,5,6,6,8,10 are 6 data of total 8 data.

let, the missing value are X and Y.

we know mean of a data list is calculated by adding all the value and divided the sum by total amount of data.

mean = 7.5 = (X + Y + 5+ 5+ 6+ 6+ 8+10) / 8

             X + Y + 40 = 60

                               X+Y = 20

we know range is the difference between the highest and the lowest number of a data set.

let, the highest number is X and lowest number is assumed 5.

As range is 6, range = X - 5

                          X- 5 = 6

                     X = 11

 highest number of data set = 11

now we get the other missing data from the equation, X + Y = 20

                                                          Y = 20 -11

                                                     Y = 9

now, the data set can be arranged as

5,5,6,6, 8,9, 10,11

we notice that the two middle value is 6 and 8.

median = (6+8) / 2 = 7

that is equal to given median by Theo.

hence, the determination is verified.

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Answer:

Emma scored 90% in her English exam, as 80 marks out of 80 is equivalent to 100%. Thus, 72 marks out of 80 is equivalent to 90%.

Answer:

The first value of a relation is an input value and the second value is the output value. A function is a specific type of relation in which each input value has one and only one output value.

An input is an independent value, and the output value is the dependent value, as it depends on the value of the input.

The resistance of 19.0m of the given copper pipe is 1.19 x [tex]10^{-6}[/tex] ohm.

The resistance of a pipe is given by the formula:

R = (p * L) / (A * n)

where R is the resistance, p is the resistivity of the material (in this case, copper), L is the length of the pipe, A is the cross-sectional area of the pipe, and n is the number of conductors (in this case, 1).

To find the cross-sectional area of the pipe, we first need to find the radius of the pipe. We can do this by taking the difference between the outside diameter and the inside diameter and dividing by 2:

r = (d_outside - d_inside) / 2

r = (5.00 cm - 3.00 cm) / 2

r = 1.00 cm

Now we can find the cross-sectional area of the pipe:

A = pi * [tex]r^2[/tex]

A = pi * [tex](1.00 cm)^2[/tex]

A = 3.14

Next, we can use the resistivity of copper, which is 1.68 x[tex]10^{-8}[/tex] ohm-cm. Now we have all the values required to find the resistance of the pipe:

R = (p * L) / (A * n)

R = (1.68 x [tex]10^{-8}[/tex] ohm-cm * 19.0 m) / (3.14 [tex]cm^2[/tex] * 1)

R = (1.68 x [tex]10^{-8}[/tex] ohm-cm * 19.0 m) / (3.14 [tex]cm^2[/tex])

R= 1.19 * [tex]10^{-6}[/tex] ohm

Therefore, the resistance of 19.0m of this pipe is 1.19 x [tex]10^{-6}[/tex] ohm.

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The bearing form the cliff to the island is 58.09 degrees

Information from the question

A puffin leaves a cliff and flies 33 km due east

and then 53 km due north

Work out the bearing form the cliff to the island = ?

The bearing form the cliff to the island is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The direction of movements describes a right triangle of

opposite = 53 km

adjacent = 33 km

The bearing is calculated using tan, TOA

let the angle be x

tan x = Opposite / Adjacent

tan x = 53 / 33

tan x = 1.60606

x = arc tan 1.60606

x = 58.09 degrees

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Therefore , the solution of the given problem of function comes out to be we cannot consider the fourth statement  as linear function.

Mathematicians frequently use the word "function" to refer to a connection that describes how two variables are connected to one another. There are two: a predictor variable, which is the function's output, and a variable, which can be any input of an equation.

Here,

Given:

A car loses value at a rate of 8.3% annually.

2.25 inches of snow were falling every hour.

A sunflower was expanding by 1.5 inches every week.

A set rate of $2.50 is charged by taxis for pickup, and an additional $3.75 is added for each subsequent mile.

thus,

From the following above expression we cannot consider the fourth statement

As if we write it in the formula it comes out to be linear equation not function.

Therefore , the solution of the given problem of function comes out to be we cannot consider the fourth statement  as linear function.

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We can conclude that we have sufficient data to reject the null hypothesis and that the mean breaking strength is different from 8000 at 5% of significance if we compare the p value and the significance threshold, for example, α = 0.05.

The information provided and notation

X = 7750 indicate the sample's mean breaking strength, which is 145.

n = 6 sample size μ o= 8000 reflect the sample standard deviation indicate the quantity we want to test, and

α = 0.05 denotes the level of significance for the hypothesis test.

The statistic (interesting variable) would be represented by t, and the test's p value would be represented by P u (variable of interest)

Name the prevailing and competing hypotheses.

It is a test with two tails.

We wish to determine whether or not the genuine mean is equal to 8000.

Null hypothesis μ = 8000.

Alternate hypothesis μ₀ ≠ 800

Determine the test statistic.

[tex]t = \frac{X-\mu}{\frac{s}{\sqrt{n} } }[/tex]

t-test: "enables the comparison of group means. One of the most widely used tests, it is used to assess whether the mean is (greater, lower, or not equal) to a given value ".

Determine the statistic.

We can substitute the following information in the above formula

[tex]t = \frac{7750-8000}{\frac{145}{\sqrt{6} } } = -4.22[/tex]

Give the test's appropriate conclusion -

To begin with, we must determine the degrees of freedom indicated by: df = n-1 = 6-1 = 5.

Given that the test has two possible outcomes, the p value is

Pv = 2 ×  P(t(5) < -4.22) = 0.0083.

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The area not covered by the white board is 192 cm².We can find by using area of rectangular formula.

A rectangle is a quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence it is also called quadrilateral. Since the opposite sides are equal and parallel in rectangle.

The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle.The formula for the Area of a Rectangle is A = l × b. The area of any rectangle is calculated once its length and width are known.

Now we find

A white rectangular board 28 cm long and 16 cm wide.

Substitute the respective values

Area of White Board = 28 *16

The area of white board is 448 cm²

Wooden board creates a border of 2 cm around it.

Wooden Board dimension = (28 + 2 + 2) cm long and (16 + 2 + 2) cm wide

Wooden Board dimension = 32 cm long and 20 cm wide.

The area of Wooden board = 32*20=640

The area not covered by the white board is

640 cm² - 448 cm² = 192 cm²

The area not covered by the white board is 192 cm².

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There will be a total of 3 batches of soup can Fabian make.

Explain how to calculate the total weight of ingredients needed for making a specific number of batches of a recipe.

To calculate the total weight of ingredients needed for making a specific number of batches of a recipe, you can multiply the weight of each ingredient per batch by the number of batches you want to make. This will give you the total weight of ingredients needed for the desired number of batches. For example, if a recipe requires 1 pound of flour per batch and you want to make 3 batches, the total weight of flour needed is 1 pound per batch * 3 batches = 3 pounds.

To find out how many batches of soup Fabian can make, we need to divide the total weight of tomatoes by the weight of tomatoes used per batch of soup.

Let x be the number of batches of soup Fabian can make. We know that:

10 pounds of tomatoes - 2.8 pounds of tomatoes = 7.2 pounds of tomatoes are available to make soup

The weight of tomatoes used per batch of soup is 2 2/5 pounds, we can write this as:

x * 2.4 = 7.2

To find the number of batches of soup Fabian can make, we can divide both sides by 2.4

x = 7.2/2.4

x = 3

So Fabian can make 3 batches of soup.

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the function f(x)=10^x and ploted below.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

function f(x)=10^x

Y = 0

Y greater than 0

(0,1)

Decreases toward 0

Hence, the function f(x)=10^x and plotted below.

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Answer: Let's say Trisha is currently T years old and Mina is currently M years old.

We know from the problem statement that Trisha is twice as old as Mina:

T = 2M

We also know that 10 years from now, Trisha will be 4 years older than Mina:

T + 10 = M + 4

We can substitute the first equation into the second equation:

2M + 10 = M + 4

We can then solve for M:

M = 6

So, Mina is currently 6 years old.

We can use the first equation to find Trisha's current age:

T = 2M = 2 * 6 = 12

Therefore, Trisha is currently 12 years old and Mina is currently 6 years old.

Step-by-step explanation:

Answer:

? = 1

Step-by-step explanation:

You are trying to mind the MEDIAN of the given expression.

The MEDIAN is the middle number of a set of given values.

1. Arrange the terms in ascending order.

= 0.1 , 0.4 , 1.6 , 2.5

2. The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

= (0.4 + 1.6)/2

Write as a fraction where (0.4 + 1.6) is the NUMERATOR & 2 is the DENOMINATOR. Include parentheses.

3. Remove parentheses.

= 0.4 + 1.6/2

Write as a fraction where 0.4 + 1.6 is the NUMERATOR & 2 is the DENOMINATOR.

4. Add 0.4 and 1.6.

= 2/2

5. Divide 2 by 2.

= 1

6. Convert the median 1 to decimal.

= 1

Answer:

Infinitely many solutions

A system of equations is solving for 2 or more lines. Solving it means finding the point where they intersect.

One solution means the lines only intersect once and have a different slope.

No solution means the lines never intersect and have the same slope but a different y-intercept.

Infinitely many solutions means the lines are always intersecting, meaning the lines have the same y-intercept and slope.

y= 2x - 2

y = 2x - 2

They have the same slope and y-intercept, so there are infinitely many solutions.

Answer: Its definitely 7.2 for the first two and 4.5 on the last one to the right

Step-by-step explanation: i did the quiz

Bank A will give better return for the money we invest. The solution has been obtained using the concept of compound interest.

What is compound interest?

The interest earned on savings that is computed using both the original principal and the interest accrued over time is known as compound interest.

It differs from simple interest in that simple interest does not take the principal into account when calculating the interest for the following month. In math, compound interest is typically represented by the letter C.I.

We have 2 different financial institutions which suit our investment needs.

1. Bank A offering an interest rate of 8.8% compounded quarterly.

2. Bank B offering an interest rate of 9.0% compounded annually.

In order to find that which bank will give better return of our money, we need to calculate the effective rate of interest for both the options.

1. 8.8% compounded quarterly

Effective interest= (1+(0.088/4))^4-1

= (1.022)^4-1

= 1.09094-1

= 0.09094

= 9.094%

2. 9.0% compounded annually

Effective interest= (1+(0.09/1))^1-1

= 1.09-1

= 0.09

= 9%

Hence, Bank A will give better return for the money we invest.

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They are known as the two types of first is null hypothesis and the second is alternative hypothesis. These two hypotheses bear opposite viewpoints.

H0: also known as null hypothesis: It is a statement about the population that either is taken to be true or is used to put forth an argument until it can be shown to be incorrect behind a reasonable doubt.

Ha: also known as the alternative hypothesis: It is a state about the population that is contradictory to H0 and what we conclude when we reject H0.

H0 every time has a symbol with an equal in it. It never has a symbol with an equal in it. The option of the symbol depends on the wording of the hypothesis test.

Yet, be aware that many researchers use = in the null hypothesis, even with > (greater) or < (less) as the symbol in the alternative hypothesis.

We can accept this practice because we only decide to reject or not reject the null hypothesis.

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The expression a² + b⁴ - 7a³ - a² + b⁴ - 7a³ is a binomial.

Degree of the binomial = 4.

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

The degree of a polynomial is the highest power of the variable in a polynomial expression.

Given expression

a² + b⁴ - 7a³ - a² + b⁴ - 7a³

Combining like terms

2b⁴ - 14a³

above expression has where a and b as variables with power 4 and 3 and coefficients 2 and 14 respectively combined with subtraction operation.

So, it is a polynomial with two terms which means it is a binomial and its degree is 4.

Hence, the expression a² + b⁴ - 7a³ - a² + b⁴ - 7a³ is a binomial with degree 4.

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If events R and S are independent, the probability of both occurring (P(R and S)) is the product of their individual probabilities which will give 3/32.

To calculate the probability that if events R and S are independent, both events occurring (P(R and S)) is the product of the individual probabilities of each event.

So, P(R and S) = P(R) x P(S) = (1/4) x (3/8) = 3/32

This is because when events are independent, the occurrence of one event does not affect the probability of the other event, so the probability of both events occurring is just the product of the individual probabilities of each event.

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Answer: It would take the ostrich 4 minutes

Step-by-step explanation:

The time taken by the Ostrich running at a rate of 50 miles in 60 minutes to cover a distance of 15 miles is 18 minutes.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given the data in the question;

An ostrich can run at a rate of 50 miles in 60 minutes.

First, we determine the speed of the ostrich.

Speed = Distance / time

Speed = 50 / 60

Speed = 5/6 miles per min

Now, time taken for the ostrich to run 15 miles will be;

Speed = Distance / time

Time = Distance ÷ Speed

Time = 15 ÷ 5/6

Time = 15 × 6/5

Time = 3 × 6

Time = 18 min

Therefore, the time taken by the Ostrich is 18 minutes.

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Y = 12.12 cm is determined by Pythagoras' Theorem, where the hypotenuse and one side of a right-angled triangle are specified as being 14 cm and 7 cm, respectively.

Triangles are shapes with three sides and three vertices, making them polygons. It is one of geometry's fundamental forms. A triangle containing vertices A, B, and C is known as a triangle ABC. In Euclidean geometry, a singular plane and triangle are discovered when the three points are not collinear. A polygon with three sides and three corners is called a triangle. The corners of the triangle are the points where the three sides meet one another end to end.

given

by Pythagoras theorem

c2 = a2 + b2

14*14 = y2 + 7*7

196 - 49 = y2

y2 = 147

y = [tex]\sqrt{147}[/tex]  = 12.12 cm

Y = 12.12 cm is determined by Pythagoras' Theorem, where the hypotenuse and one side of a right-angled triangle are specified as being 14 cm and 7 cm, respectively.

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The gradient of the line in the image will be -3.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is defined as the ratio of the rise of the line to the run of the line.

Given that the line in the image is passing through the points ( 0,3) and (1,0). the gradient or slope of the line will be calculated as:-

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 0 - 3 0 / 9 1 - 0 )

Slope = -3

Hence, the gradient will be -3.

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Answer:

150 miles

Step-by-step explanation:

Total miles by the two motorcycles

300 miles

The first motorcycle travel 65 miles per hour

The second motorcycle travel 85 miles per hour

Total miles the two motorcycles travels

65 mile + 85 miles

=150 miles

Long it will take for the two motorcycles to meet

= 300 miles + 150 miles

=150 miles.

Hence it will take 150 miles for the two motorcycles to meet.

When asked which of the following is true in this situation, "if a distribution has zero variants," the response is "D."

Due to the variance's definition, which is the same for both continuous and discrete random variables, all of the values must be equal to one another. For all possible values of X, the variance is determined by measuring the excess distance from the mean.

If any one of these individual values deviates from the mean, it follows that the variations must also deviate from zero because the integration will result in the difference squared being represented as a positive number.

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Answer:

Step-by-step explanation:

yes

no

no

ye

Answer:

Step-by-step explanation:

The number in consideration here is 45 and the integers that divide it evenly are known as the factors of 45. There are a total of six factors of the number 45: 1, 3, 5, 9, 15 and 45. The numbers that are multiplied in pairs to produce 45 are the factor pairs of 45.

The solution of the System of Equation is (5.71, 514.2) and this means that at that point the money they save are the same .

A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

A system of equations consists of two or more equations and looks for common answers. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."

The point provides a singular solution to the system of equations if the two lines cross at the same location. There are an endless number of solutions in the situation when the two lines meet, and there is none in the case where the two lines are parallel.

From the graph :

i)The stipper line have 2 points at (0,300) and (4,450)

ii)The other line having points (0,400) and (5,500)

The slope of the line (i) is

The slope in the line (ii) is

The equation of lie (i) is

y = 37.5x + c

putting (0,300) in the equation we get,

300 = 37.5*0 + c

⇒ c = 300

The equation is y = 37.5x + 300

And the 2nd line putting (0,400) in the equation (ii) we get,

y = 20x + c

400 = 20*0 + c

⇒ c = 400

The equation is y = 20x + 400

Solving the both equation we get

37.5x + 300 - 20x - 400 = 0

⇒ 17.5x = 100

⇒ x = 5.71 and y = 514.2

The solution of the system is (5.71, 514.2) and this means that at that point the money they save are the same .

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