Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.

The mass of a sheet of metal is directly related to its area and thickness. This means that the mass of a sheet of metal is proportional to the product of its area and its thickness. Mathematically, this can be expressed as the formula M = kAT, where M is the mass, k is a constant, A is the area and T is the thickness.In the given example of a sheet of metal with an area of 250 cm and a thickness of 1mm, we can calculate the mass of the sheet by substituting the given values into the formula: M = k(250)(1) = 200g. The constant k in this example is equal to 0.8 g/cm*mm.Therefore, the mass of the sheet of metal is 200g. This can also be expressed in other units, such as 0.2 kg or 0.002 tonnes.

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What is the mass of a sheet of metal with an area of 250cm and a thickness of 1mm?

Answer:

Square Plot

Step-by-step explanation:

Let us compare the Area of both plots

Rectangular Plot :  L X B = 45 x 25 = 1125 M^2
Square Plot : S X S = 35 x 35 = 1225 M^2

Area of Square Plot > Area of Rectangular Plot

Therefore he should prefer the Square Plot as it has more area.

Hope it helps.

The difference in the loudness of sound when the two teams score is about 14.77 decibels

Sound intensity is defined as the power carried by sound waves per unit area in a direction perpendicular to that area.

We can use the fact that the loudness of sound is measured in decibels (dB) and that the dB scale is logarithmic.

Let's assume that the loudness of the sound when the away team scores is x decibels. Then the loudness of the sound when the home team scores a touchdown is 30 times as great, which means it is 30x decibels.

The difference in loudness between the two scenarios is given by the difference in decibels:

difference in decibels = 10 log (30x/x) = 10 log 30 = 14.77

Therefore, the difference in the loudness of sound when the two teams score is about 14.77 decibels

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Answer:

900 cubic feet

Step-by-step explanation:

[tex] \frac{1}{2} (15 \times 12 \times 10) = \frac{1}{2} (1800) = 900[/tex]

Answer:

[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the area of a circle.}[/tex]

[tex]\textsf{First, we should identify the formula for the area of a circle.}[/tex]

[tex]\large\underline{\textsf{Formula:}}[/tex]

[tex]\mathtt{Area = \pi (radius)^{2}}[/tex]

[tex]\textsf{The radius is \underline{half} of the diameter.}[/tex]

[tex]\mathtt{\frac{17}{2} = 8.5ft.}[/tex]

[tex]\textsf{Let's begin solving for the area.}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{Area = \pi (8.5)^{2}}[/tex]

[tex]\mathtt{Area = 72.25 \pi}[/tex]

[tex]\boxed{\mathtt{Area \approx 227ft^{2}}}[/tex]

The cost per square inch of the apple pie is $ 0.16.

Given that,

The diameter of the pie = 10 in

The radius of the pie = 10/2

                             = 5 inches.

Area of the pie = [tex]\pi r^{2}[/tex]

                         =  3.14 × 5²

                         = 3.14 × 25

                          = 78.5 in²

The cost of the apple pie = $ 12.85.

Therefore, the cost per square inch of the pie = 12.85 ÷ 78.5

                                                                             = $ 0.16.

Hence, the cost per square inch of the apple pie is $ 0.16.

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Answer:

A. If the diameter is 6 cm, then the radius is half of that:

radius = 6 cm / 2 = 3 cm

B. The formula for the surface area of a cylinder is:

S.A. = 2πr^2 + 2πrh

C. Plugging in the values for r, h, and π:

S.A. = 2π(3 cm)^2 + 2π(3 cm)(12 cm)

S.A. = 2π(9 cm^2) + 2π(36 cm^2)

S.A. = 18π cm^2 + 72π cm^2

S.A. = 90π cm^2

Therefore, the surface area of the soup can is 90π square centimeters. This can be simplified to approximately 282.74 square centimeters by using the value 3.14 for π.

Therefore , the solution of the given problem of standard deviation comes out to be he average difference between the population mean and the sample mean is 6.

Variance is a measure of variation used in statistics. The average difference between the gathering and the mean is calculated using the photo of that figure. By comparing each number to the mean, it incorporates those data points into the calculations on their own, in contrast to many other legitimate measures of variable. Variations could result from deliberate errors, unrealistic expectations, or changing economic or commercial circumstances.

Here,

For a group of n = 4, the standard error of the mean (SEM) is as follows:

=> SEM = α/√(n)

=> 24/√(4) = 12

Therefore, for n = 4 scores drawn at random from the population, the average difference between the population mean and the sample mean is 12.

b. The SEM for a group of n = 9 is:

=> α/√(n) = 24/√(9)

=> 8; SEM = α

Therefore, for n = 9 scores drawn at random from the population, the average difference between the population mean and the sample mean is 8.

c. The SEM for a sample of 16 is as follows:

=> α / √(n) = 24 / √(16) = 6;

=>  SEM =α

Therefore, for n = 16 scores drawn at random from the population, the average difference between the population mean and the sample mean is 6.

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The total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" is also used. A percentage is a dimensionless number; it has no unit of measurement.

To calculate the total percentage increase in the investor's stock account, we first need to calculate the new values of the stocks in Company A and Company B after the increase.

The new value of the stock in Company A is:

[tex]4500 + (5 \times 4500) = $4725[/tex]

The new value of the stock in Company B is:

[tex]3900 + (11 \times 3900) = 4339[/tex]

The total value of the investor's stock account after the increase is:

$4725 + $4339 = $9064

To calculate the percentage increase in the investor's stock account, we need to find the difference between the new total value and the original total value, and then divide that difference by the original total value:

($9064 - $8400) / $8400 = 0.0795

We then multiply this decimal by 100 to get the percentage increase:

0.0795 x 100 = 7.95%

Therefore, the total percentage increase in the investor's stock account is 7.95% (rounded to the nearest tenth).

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Optiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 =x² + 2x - 4.

Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.

Tο substitute fοr y in the secοnd equatiοn, we can replace y with its equivalent expressiοn in terms οf x frοm the first equatiοn, which gives us:

x - 3 = x² + 2x - 4

This is option B.

Optiοn A is incοrrect because it substitutes y fοr its expressiοn in terms οf x in the wrοng equatiοn.

Optiοn C is incοrrect because it subtracts (x-3) instead οf adding it tο the secοnd equatiοn.

Optiοn D is incοrrect because it sets the expressiοn fοr y in the first equatiοn equal tο x² instead οf the expressiοn fοr y in the secοnd equatiοn.

Hence, οptiοn B. is cοrrect, the result οf substituting fοr y in the given equatiοns is x - 3 = x² + 2x - 4.

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Complete question:

What is result of substituting for y in the bottom equation?

y = x – 3,

y = x² + 2x – 4

A. y=(x-3)²+2(x-3)-4

B. x-3=x²+2x-4

C. y=x²+2x-4-(x-3)

D. (x-3)=x²

Answer:The quantity of grocer of price $1.40 is 45 pounds

The quantity of grocer of price 40 cents is 55 pounds

Step-by-step explanation:

Let The quantity of one grocer = x pound

Let The quantity of other grocer = y pound

The selling price of x grocer = 40 cents per pound

The selling price of y grocer = $ 1.40 per pound = 1.40 × 100 = 140 cents

Total quantity = 100 pounds

Total price of both grocer = 85 cents

According to question

x + y = 100                        .........A

And

40 × x + 140 y = 85 × 100

Or, 40 x + 140 y = 8500         ........B

Solving eq A and eq b

(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100

Or, (40 x - 40 x) + (140 y - 40 y) = 8500 - 4000

or, 0 + 100 y = 4500

∴  y =

i.e  y = 45 pounds

So, The quantity of grocer of price $1.40 = y = 45 pounds

Again

Put the vaue of y in eq A

x + y = 100

i.e x = 100 - y

or, x = 100 - 45

∴   x = 55 pounds

So, The quantity of grocer of price 40 cents = x = 55 pounds

Hence, The quantity of grocer of price $1.40 is 45 pounds

And The quantity of grocer of price 40 cents is 55 pounds  Answer

Answer:

P(0,2), Q(3,5), R(3,0)

Step-by-step explanation:

Answer:6 feet

Step-by-step explanation:

The formula for the area of a parallelogram is:

Area = base x height

We know that the area is 60 square feet and the height is 10 feet, so we can plug these values into the formula and solve for the base:

60 square feet = base x 10 feet

Dividing both sides by 10 feet gives:

6 feet = base

Answer:

y = - [tex]\frac{5}{2}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 4, 9) and (x₂, y₂ ) = (2, - 6) ← 2 ordered pairs from the table

m = [tex]\frac{-6-9}{2-(-4)}[/tex] = [tex]\frac{-15}{2+4}[/tex] = [tex]\frac{-15}{6}[/tex] = - [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at point (0, - 1 ), ordered pair from table, then

c = - 1

y = - [tex]\frac{5}{2}[/tex] x - 1 ← equation of line

Find CD:

Let,

[tex]r_1[/tex] be a radius of Circle A

[tex]r_2[/tex] be a radius of Circle B

Given:

[tex]r=4cm.[/tex]

Circumference: [tex]2\pi r[/tex]

[tex]2\pi r_1=30[/tex]

[tex]r_1=\dfrac{15}{\pi }[/tex]

[tex]CD=D_1+D_2[/tex]

[tex]=2r_1+2rx_2[/tex]

[tex]=2\times(\dfrac{15}{\pi })+2\times4[/tex]

[tex]CD=17.55cm.[/tex]

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Therefore , the solution of the given problem of area comes out to be

A = 16 is the equation that accurately depicts how to calculate the sector's area.

Its total size can be determined by figuring out how much space is required to completely cover the outside. The immediate surroundings are taken into consideration when calculating the surface of a trapezoidal shape. The total measurements of something are determined by its surface area. A cuboid's capacity for internal water is determined by the sum of the borders that link all of it's six rectangle edges.

Here,

The formula for calculating a circle's sector's area is:

=> A = (θ/360) x πr²

where A is the sector's area, is its central angle measurement, and r is the circle's radius.

Since the radius is 8 cm and the central angle is 90 degrees in this instance, we can reduce by plugging in these values:

=> A = (90/360) x π(8²)

=>  A = (1/4) x π(64)

=>  A = π(16)

=>  A = 16π

A = 16 is the equation that accurately depicts how to calculate the sector's area.

The answer will be given in radius squared units, in this case, cm2.

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Option D. The correct calculation of the area of the sector is      [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]

An area of the sector is the portion of the area of a circle that is enclosed by two radii and an arc. The area of a sector can be found using the formula:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Given, the radius is 8 cm and the central angle is 90° in this instance, put all these values:

[tex]A=(\frac{90}{360}) * \pi (8^{2} )[/tex]

or we can write down, [tex]A=(\frac{90}{360}) * (\pi 8^{2} )[/tex]

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If the screen door spring has a spring constant of 188 N/m, then the force it exert is 54.9 N .

The force exerted by the screen door spring can be calculated using Hooke's law,

The Hooke's Law states that the force exerted by a spring is directly proportional to its spring constant and the amount it is stretched.

The formula for "Hooke's-law" is ⇒ F = kx

Where F is = force exerted by spring, k is = spring constant, and x is = amount spring is stretched.

In this case , the spring constant(k) = 188 , the distance stretched(x) = 292m ;

Substituting the values,

We get,

⇒ F = (188 N/m)(0.292 m)

⇒ F = 54.896 N

⇒ F ≈ 54.9N

Therefore, The force exerted by the screen door spring is approximately 54.9 N.

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The cumulative distribution function gives us the probability that the random variable is less than or equal to a given value.

The cumulative distribution function (CDF) of a continuous random variable x is a function which gives the probability that the random variable x is less than or equal to a given value x. Mathematically it is expressed as:

[tex]F(x) = P(X ≤ x)[/tex]

The calculation of the cumulative distribution function is done by integrating the probability density function (PDF) from the lower limit to the given value x. Thus,

[tex]F(x) = ∫-∞ x f(u) du[/tex]

Where f(u) is the probability density function.

For example, if we have a continuous random variable x with probability density function f(x) = x2, then the cumulative distribution function [tex]F(x) = ∫-∞ x x2 du = 1/3x3 + c.[/tex]

Thus, It is a powerful tool for analysing the probability distribution of a continuous random variable.

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Complete question:

What is the cumulative distribution function for a continuous random variable x?

To fully describe a triangular prism, you would need to provide the dimensions of its triangular bases (e.g. base length and height), the length of the prism, and the length and width of the rectangular faces. Thus, option C is correct.

To find the volume of filler material required to surround the triangular prism, we need to first calculate the volume of the box and the volume of the triangular prism.

The volume of the box is given by:

[tex]8[/tex] inches ×  [tex]13[/tex] inches ×  [tex]16[/tex] inches =  [tex]1,664[/tex] cubic inches

The volume of the triangular prism is given by:

[tex](1/2) × 8[/tex] inches ×  [tex]13[/tex] inches ×  [tex]16[/tex] inches = [tex]832[/tex] cubic inches

To completely fill the box, we need to add filler material with a volume equal to the difference between the volume of the box and the volume of the triangular prism, which is:

 cubic inches— [tex]832[/tex] cubic inches   [tex]= 832[/tex] cubic inches

Therefore, the [tex]832[/tex]  Cubic inches.

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Answer:

Part A:

To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:

Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)

Simplifying the expression by combining like terms, we get:

Side 1 + Side 2 = 2x^2 + 1

Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.

Part B:

To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:

5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]

Simplifying the expression by distributing the negative sign, and then combining like terms, we get:

5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4

Simplifying further by combining like terms, we get:

5x^3 - 4x^2 + 11x - 4

Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.

Answer:

A) 5x^3 - 4x^2 + 3x - 4

Step-by-step explanation:

Answer:

A) 5x^3 - 4x^2 + 3x - 4

Step-by-step explanation:

Part A:

To find the total length of sides 1 and 2 of the triangle, we need to add the lengths of these sides:

Side 1 + Side 2 = (3x^2 - 4x - 1) + (-x^2 + 4x + 5)

Simplifying the expression by combining like terms, we get:

Side 1 + Side 2 = 2x^2 + 1

Therefore, the total length of sides 1 and 2 of the triangle is 2x^2 + 1.

Part B:

To find the length of the 3rd side of the triangle, we can subtract the sum of sides 1 and 2 from the perimeter of the triangle:

5x^3 - 2x^2 + 3x - 8 - [(3x^2 - 4x - 1) + (-x^2 + 4x + 5)]

Simplifying the expression by distributing the negative sign, and then combining like terms, we get:

5x^3 - 2x^2 + 3x - 8 - 2x^2 + 8x + 4

Simplifying further by combining like terms, we get:

5x^3 - 4x^2 + 11x - 4

Therefore, the length of the 3rd side of the triangle is 5x^3 - 4x^2 + 11x - 4.

Answer:

A) 5x^3 - 4x^2 + 3x - 4

You need to add 225mL of the 75% alcohol solution to obtain the desired 30% alcohol solution.

To find the amount of 75% alcohol solution needed to obtain a 30% alcohol solution, we must use the formula for dilution:

M1V1 = M2V2

Where M1 is the concentration of the initial solution, V1 is the volume of the initial solution, M2 is the desired concentration, and V2 is the desired volume.

In this case, M1 is 5%, V1 is 675mL, M2 is 30%, and V2 is unknown.

We can rearrange the equation to solve for V2, which is the volume of the 75% alcohol solution needed:

V2 = (M1V1) / M2

V2 = (5% x 675mL) / 30%

V2 = 225mL

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The probability that no one gets a hole on the sixth hole is given as follows:

0.9534 = 95.34%.

The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.

The mass probability formula is given as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

The holes are independent, hence the probability of no one getting a hole in the sixth hole is P(X = 0), thus:

P(X = 0) = (1 - 1/3709)^175

P(X = 0) = 0.9534 = 95.34%.

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The equation is -7x+y=0.

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, The equation is -7x+y=0.

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Answer:

He is now selling only one product and making less money because he is not selling other TVs.

Step-by-step explanation:

So if you read the paragraph, you get to the point where he says only making and selling the television model that makes the most money. If you think about it if they only sell one product, the other products they used to sell aren't being sold and they are making less money. I hope this helps!

Answer:

J. 56

Step-by-step explanation:

The picture in this question can be a little deceiving. Each rectangular glass pane is 3 by 10 inches. This means that the picture of the 4 panes overlapping, leaves the center square open. The open area has your inner edges. The question asks for the sum of the inner and outer edges.

Every pane is 10 inches long, so the out perimeter of the figure is 40 inches because the figure has four sides. The rectangles overlap, creating 3 by 3 inch square. 3 inches off either side of a pane leaves 4 inches as the length for the edge of the inner square. Therefore, the perimeter of the inner square is 16 inches.

Outer Perimeter + Inner Perimeter = 40 + 16 = 56 inches

The height, in meters, where the pumpkin lands on the hill is 4.9 meters.The equation for the height of the hill is y = 0.9x.

This equation can be rearranged to solve for x, giving x = y/0.9. The equation for the height of the pumpkin is y = -0.1x² + 4.9x. Substituting the x value from the previous equation into the equation for the height of the pumpkin gives y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying this equation gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill.

The equation for the height of the hill is y = 0.9x, which describes the incline of the hill. This equation can be rearranged to solve for x, giving x = y/0.9. This equation can then be used to substitute into the equation for the height of the pumpkin, which is y = -0.1x² + 4.9x. When the x value from the previous equation is substituted into the equation for the height of the pumpkin, the equation simplifies to y = -0.1(y/0.9)² + 4.9(y/0.9). Simplifying further gives y = 4.9, which is the height, in meters, where the pumpkin lands on the hill. This can be verified by substituting 4.9 for y in the equation for the height of the hill, which gives x = 4.9/0.9 = 5.4. This value can be substituted into the equation for the height of the pumpkin, which gives y = -0.1(5.4)² + 4.9(5.4) = 4.9, verifying the result.

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The magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale

Magnitude: The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. It is typically determined using a logarithmic scale called the Richter scale or other similar scales like the moment magnitude scale (MMS), surface wave magnitude (Ms), or body wave magnitude (Mb). The Richter scale is based on the amplitude of the largest seismic wave recorded on a seismographs, and each increase of one unit on the scale corresponds to a ten-fold increase in the amplitude of the seismic waves and a 32-fold increase in the amount of energy released.

Amplitude: The amplitude of an earthquake is the size of the seismic waves that are generated by the earthquake. It is measured in microns (millionths of a meter) and is recorded on a seismographs. The amplitude of seismic waves can vary greatly depending on the distance from the earthquake's epicenter and the geological structure of the surrounding area.

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake, and is typically determined using a logarithmic scale called the Richter scale.

The formula for calculating the magnitude of an earthquake based on its amplitude is:

Magnitude = log10 (Amplitude) - 3

where the amplitude is measured in microns.

Assuming the amplitude of the earthquake is 100,000 microns, we can calculate its magnitude as:

Magnitude = log10 (100,000) - 3

Magnitude = 5 - 3

Magnitude = 2

Therefore, the magnitude of the earthquake with an amplitude of 100,000 is 2 on the Richter scale.

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The value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2 is Option B: 11.8.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

To find the value of the expression 1.3(x + 2) - (y - 6) when x = 4 and y = 2, we substitute these values into the expression and simplify -

Substitute the values x = 4 and y = 2 into the expression -

1.3(x + 2) - (y - 6)

= 1.3(4 + 2) - (2 - 6)

Apply the addition and subtraction operation -

= 1.3(6) - (-4)

Apply the multiplication operation -

= 7.8 + 4

= 11.8

Therefore, the value of the expression is 11.8.

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Answer:

plot the point at 1

Step-by-step explanation: