Please show working out. 25 points.

Answer: 3.2t − 2.4

Step-by-step explanation:

Add −3.6 and 1.2

Then, add −1.9t and 5.1t

3.2t − 2.4

Using the substitution to solve the following system of equations, 4x+2y=36

y=2x-2 we get value of x as 5 and y is equal to 8.

There are two methods for solving simultaneous linear equations: graphical methods and algebraic methods. The algebraic technique includes the substitution method as one of its categories.

We have two equations as,

4x+2y=36

y=2x-2

Substituting the value of y = 2x - 2 in the equation 1 we get,

4x + 2(2x - 2) = 36

4x + 4x - 4 = 36

8x = 36 + 4

8x = 40

x = 5

And y = 2 x 5 - 2 = 8

Therefore, the value of x is 5 and y is 8.

The algebraic approach for solving simultaneous linear equations is the substitution method. The value of one variable from one equation is substituted in the second equation, as the name implies. In this manner, a pair of linear equations is reduced into a single linear equation with only one variable, which can then be solved quickly. Before beginning to solve linear equations using the substitution approach, learn about the algebraic and graphical methods.

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The factored expression of 20 + 16 is 4 (5 + 4).

Factoring is the process of representing a given number or algebraic statement as the sum of its components.

A relevant strategy is used, depending on the situation, to identify the components.

Locating GCD (Greatest Common Divisor)

It is possible to factor an equation where every term has GCD 0 by eliminating GCD as a common component.

Employing Identity

The given expression is:

20 + 16

20 can be written as 4(5).

16 can be written as 4(4).

20 + 16 = 4(5) + 4(4)

Taking the common term out we have:

20 + 16 = 4 (5 + 4)

Hence, the factored expression of 20 + 16 is 4 (5 + 4).

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We can write the values of the function g(- 2) = 1/2 and

g(2) = 128.

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is the exponential function as -

f(x) = 8(1/4)ˣ

If the function f(x) is reflected across the {y} - axis, then the new function g(x) will be -

g(x) = f(-x)

So, we can write -

g(x) = 8(1/4)⁻ ˣ

Now, we can write -

g(- 2) = f(2) = 1/2

g(2) = f(-2) = 128

Therefore, we can write the values of the function g(- 2) = 1/2 and

g(2) = 128.

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The sum of squares formula is in statistics, one tool for assessing a dataset's dispersion is the sum of squares.

The term "sum of squares" refers to the total of the supplied integers' squares. It is the product of the squares of a dataset's variation. To do this, we must calculate the data's average and then square and add each data point's deviation from the mean. In algebra, the (a + b)2 identity is used to calculate the sum of the square of two numbers.

A formula can be used to determine the sum of the squares of the first n natural numbers. The mathematical induction concept can be used to get the formula. These fundamental arithmetic operations, which are necessary for algebra and statistics, are performed. The sum of squares of given numbers can be determined using a variety of methods.

Sum of squares = a2 + b2 = (a + b)2 - 2ab

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Reasonable prediction for the number of times he will get a completely striped sock is 15 times.

Random numbers are used to construct probability samples from a population and make statistical inferences from a survey, and also to decide which treatment should be applied to the various physical units in an experiment.

Daniel is selecting a sock from his drawer at random.

If Daniel does this 60 times.

To determine the reasonable prediction for the number of times he will get a completely striped sock.

Now,

There are 8 socks in total, including 2 stripped socks.

So, the probability of picking a stripped socks at random is 2/8 = 1/4

60 times × 1/4 = 15 × 4 times × 1/4

                       = 15 times

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Answer:

[tex]9x^{2} +14x+1[/tex]

Step-by-step explanation:

We need to add these two polynomials together.

The simple way to do this is by adding like terms.

[tex]9x^{2}[/tex] stays the same as there is only one term.

However, we add the integer and the x term together.

So our final answer would be:

[tex]9x^{2} +14x+1[/tex]

The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we can see in the picture, we have given a function:

We have a function:

g(x) = 4log(x) + 4

To find x-intercept plug g(x) = 0

0 = 4logx + 4

x = 0.1

(0.1, 0)

The vertical asymptote:

x = 0

The range of a function:

(-∞, ∞)

Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

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The size is a 1/4-20 drill hole is 5.1mm

Many factors contribute to tap failure or breakage, but one fundamental and obvious factor is often overlooked. The problem is that this factor cannot be calculated accurately using traditional tap/drill charts.

There have been many changes since the tapping/drilling chart was first developed - programmable machines, rigid tapping, synchronous tapping, better tool holders, special tapping fluids, higher quality taps, etc.

Most importantly, the drill bits used to make the holes to cut have improved. Enhanced drill bit geometries, new chip flute geometries, coolant holes, improved HSS and carbide grades, and coatings such as TiN and TiCN greatly improve hole quality and size.

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The probability that at most three bottles will be sold on a randomly selected day is about is 0.569

The probability of an event is a number that indicates how likely the event is to occur.

Given that, the number x of bottles of garden plant fungicide sold by a garden center each day was recorded, we need to find the probability that at most three bottles will be sold on a randomly selected day is about,

The possible values of x is 0, 1, 2, 3, 4, 5, 6 and 7

The probability that at most three bottles will be sold on the randomly selected day will be =

P(x≤3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

= 0.135 + 0.141 + 0.150 + 0.143

= 0.569

Hence, the probability that at most three bottles will be sold on a randomly selected day is about is 0.569

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Answer:

The perimeter of the new space used for the playground is 108 feet.

The perimeter of the space used for the new playground is 150 feet.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

The current space is rectangular and has a length of 24 feet and a width of 26 feet.

and, the new space is 36 feet long.

let the width of new space is x.

Since, the two space are similar then the scale factor will be

= 36/24 = 1.5

So, the width of new space = 1.5 x 26 = 39 feet

Thus, the Perimeter of new space

= 2(l +w)

= 2 (36+ 39)

= 150 feet

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Therefore , the solution of the given problem of linear equation comes out to be Emily used 8.1 pints of blue paint to paint her bedroom walls.

A straightforward regression curve is created using the equation y=mx+b. The y-intercept is m, and the slope is B. The previous line is usually referred to as a "math equation mixing numerous variables," even though y / y represent independent components. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations.

Here,

If 4/5 of the total paint used is white paint, then 1/5 of the total paint used is blue paint. We can use this information to find the amount of blue paint Emily used.

Let x be the total amount of paint used in pints. Then:

4/5 x = 8.1 (the amount of white paint used)

1/5 x = ?

To solve for the amount of blue paint, we can multiply both sides of the equation by 5:

1/5 x = ?

1/5 x * 5 = ? * 5

x = 40.5

So Emily used a total of 40.5 pints of paint. To find the amount of blue paint, we can multiply the total amount of paint by the fraction that represents the amount of blue paint:

1/5 * 40.5 = 8.1

Therefore, Emily used 8.1 pints of blue paint to paint her bedroom walls.

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With 95% confidence that the true population mean weight of the sardine cans is between 7.813 oz and 7.887 oz.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

In this scenario, we have a cannery that claims their sardine cans have a net weight of 8 oz. We want to test this claim by taking a simple random sample of 30 cans and measuring their weights

From our sample of 30 cans, we calculated a sample mean of 7.85 oz and a standard deviation of 0.1 oz. The sample mean is an estimate of the population mean, and the standard deviation tells us how much the weights in our sample vary from the mean.

To determine the cutoff values for the middle 95% of the mean weights in this distribution based on the sample data, we can use the t-distribution with n-1 degrees of freedom. The degrees of freedom in this case are 29, which is one less than the sample size.

Using a t-distribution table or calculator, we can find the t-value for a 95% confidence level with 29 degrees of freedom, which is approximately 2.045. We can use this t-value to calculate the margin of error for the sample mean as:

margin of error = t-value * (standard deviation / square root of sample size)

= 2.045 * (0.1 / √(30))

= 0.037

The margin of error tells us how much the sample mean is likely to vary from the true population mean. To find the cutoff values for the middle 95% of the mean weights, we add and subtract the margin of error from the sample mean as follows:

lower cutoff value = sample mean - margin of error

= 7.85 - 0.037

= 7.813

upper cutoff value = sample mean + margin of error

= 7.85 + 0.037

= 7.887

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13×4=52

Ok Multiplacation is a simple Math formula everyone can do so you have to do this:

13+13+13+13=52

Now do this:

13×4=52

Answer is 52

Answer: 3.1 kg

Step-by-step explanation:

Total amount sold of apples and pears = 6.6 kg

Of that 6.6 kg, 3.5 kg is the weight of the apples.

Subtract the weight of the apples from the total weight of the apples and pears.

6.6 kg (total weight) - 3.5 kg (weight of apples) = 3.1 kg (weight of pears)

The difference between relative frequency and cumulative relative frequency is that relative frequency is the ratio of the frequency of a particular value in a dataset to the total number of values, expressed as a percentage. Cumulative relative frequency is the sum of all relative frequencies up to a certain point in the data set.

For example, if a data set has 8 values and 4 are the same, the relative frequency would be 50%. Cumulative relative frequency would be 50% at this point since it is the sum of all relative frequencies up to this point in the data set. If there were another 4 of the same values after this point, the relative frequency would remain at 50%, but the cumulative relative frequency would increase to 100% since it includes all previous relative frequencies.

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The study described is a retrospective study.

A retrospective study, also known as a historical study, involves the collection and analysis of data from past events or behaviors. In this case, the study involves collecting and analyzing data on the different types of shoe designs by the designer Calvin Klein over the years from 1987 to 2014. The data has already been collected in the past, and the researcher is analyzing it to draw conclusions or make inferences about the shoe designs.

In contrast, a cross-sectional study involves the collection of data from a population at a specific point in time, while a prospective study (also known as a longitudinal study) involves the collection of data over a period of time to observe changes or trends in a population. An experiment involves the manipulation of one or more variables to observe their effect on a dependent variable, with the aim of establishing cause-and-effect relationships.

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Percent difference is a measure of the relative difference between two values, expressed as a percentage.

It is determined as follows:

% difference = |(Value 1 - Value 2) / (Average of Values 1 and 2)| x 100%

where:

Assume that the value of a quantity in 2019 is 100 and that the same amount in 2020 is 120. The percentage difference between these two values is determined as follows:

Percent difference = |(100 - 120) / ((100 + 120) / 2)| x 100%

= |(-20) / (220 / 2)| x 100%

= 9.09%

This signifies that the quantity's value increased by 9.09% between 2019 and 2020. If the percentage difference is negative, it signifies that the quantity's value has fallen by that proportion.

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Ivan ran a total distance of 550 meters during football practice.

To calculate the total distance Ivan ran, we need to add up the distances he covered in each direction:

To find the total distance, we can add up the absolute values of each distance, since distance is a scalar quantity and is always positive:

Total distance = |300 m| + |(200 m)| + |50 m|

= 300 m + 200 m + 50 m

= 550 m

So Ivan ran a total distance of 550 meters during football practice.

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The height of the​ heater is 5 feet.

The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs.

Given:

The length of one side of the base is 12 feet.

The slant height is 13 feet.

Using Pythagorean theorem we get

H² = slant height² - 1/2 base diagonal²

H² = 13² - 12²

H² = 169- 144

H² = 25

H= 5 feet

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Answer: The population three years ago was 156250.

Step-by-step explanation:

Let 3 years ago, the population of a city = P

Rate of growth (R) = 8% p.a.

Present population (P) = 1,96,830.

Therefore,

[tex]A=P(1+R100)n[/tex]

P = A÷(1 + 8/100)³

196830 ÷ (1+2/25)³

=156250.

3 years ago, the population of the city = 156250.

Forming linear equations, the cost of a t-shirt and a notebook will be $1 and $6 respectively.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Another term for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There are three more constants in addition to the constant C: the variables x and y, the coefficients A and B, and the variables.

Now,

Given that

club A sold 2 t-shirts and 3 notebooks, and made $20.

Club B sold 2 t-shirts and 1 notebook, for a total of $8.

Let x and y be the cost of t-shirt and notebook respectively

then 2x+3y=20--->1

and 2x+y=8 --->2  will be the equations formed.

Now subtracting 2 from 1

we get 2x-2x+3y-y=20-8

2y=12

y=6

then  2x+6=8

x=1

Hence,

           the cost of a t-shirt and a notebook will be $1 and $6 respectively.

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The solution is, sin∅ = 12/13 & theta is placed on the second quadrant.

that means  the answer is C.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

Let's solve the equation for theta

cos∅=5/13

so, we get,

∅ ≈ 112.6

This means angle theta is placed on the second quadrant.

We use Pythagorean's Theorem to find the other leg to find the sine function.

13² = 5² + x²

so, we get,

x = 12

It's important to know that the sine function is equivalent to the ratio between the opposite leg and the hypothenuse, and it has to be positive because sine functions are positive when the angle is on the second quadrant.

sin∅ = 12/13

Hence, the answer is C.

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Answer:

5

Step-by-step explanation:

The volume occupied by the lower square part of the shed is 4800 cubic ft.

A measurement of three-dimensional space is volume. Several imperial or US customary units, as well as SI-derived units (such the cubic metre and litre), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up. In other words, the volume is the amount of fluid (liquid or gas) that the container may hold.

The volume of the lower part of the shed is given as:

V = (l)(w)(h)

where, l is the length = 20 ft.

w is the width = 20 ft

h is the height = 12 ft

Substituting the value we have:

V = (20)(20)(12)

V = 4800 cubic ft.

Hence, the volume occupied by the lower square part of the shed is 4800 cubic ft.

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The size of the state of Colima is 519,100 square metres.

Confusion results from the fact that 1 metre squared and 1 metre by 1 metre squared are the same. Yet, square metres and metres squared are fundamentally different in all other situations, therefore it is important to use care when referring to either one.

First, it is necessary to convert square kilometres into square metres.

100 hectómeters cuadrados make up one kilómetro cuadrado.

Hence, the state of Colima is as follows in square metres:

519,100 hectómetros cuadrados (5,191 kilómetros cuadrados x 100 hectómetros cuadrados/kilómetro cuadrado)

Hence, the size of the state of Colima is 519,100 square metres.

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Answer:

a = √c²-b²

Step-by-step explanation:

Sup bro,

The correct answer is a = √c²-b²

Answer:

3%

Step-by-step explanation:

We know

In a shipment of 700 motors, 21 are defective.

Based on the shipment, what is the probability that a motor is defective?

We take

21 divided by 700, times 100 = 3%

So, the probability is 3%.

Answer:

Option B

Step-by-step explanation:

Let:

w = number of withdrawals

C = Monthly cost

For Bella:

$3 = Fixed monthly charge

$1.50 × w = Amount charged for every withdrawal she makes

∴Linear equation describing her monthly cost:

C = 3 + 1.5w

For Justin:

$0 = Fixed monthly charge

$2 × w = Amount charged for every withdrawal he makes

∴Linear equation describing his monthly cost:

C = 2w

∴System of equations:

      C = 3 + 1.5w

      C = 2w

∴Option B