How to find the answers?​

Answer:

Math = 97

English = 66

Step-by-step explanation:

Let the score of the Math test be x, and the score of the English text be y

Then we have the two equations

[tex]x+y = 163\\x-y = 31[/tex]

To solve for x and y there are multiple ways, one of the easy ways is just to add the two equations together because that would cancel out the y:

[tex]x + x + y -y = 163 +31\\2x = 194\\x = 97\\[/tex]

Then using the  x, we can find y by doing

[tex]x+y = 163\\97 + y = 163\\(97 + y) - 97 = (163) - 97\\y = 66[/tex]

Therefore, we have a math score of 97, and an English score of 66.

By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.

Herein we should present a statement that represents a real life situation and solve that statement. Here is an example:

In accordance with the Coulomb's law, electric force is inversely proportional to the square of the distance between the two electrically charged particles. If you know that electric force is 20 N when the two particles are 10 cm apart, what is the electric force if the distance is doubled.

Based on the statement, we have the following relationship:

F ∝ 1/r²

Where:

From such relation, we can determine the resulting force by the following equation:

F/20 = 10²/20²

F = 20 × 10²/20²

F = 5 N

By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.

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cos^-1(x) represents the inverse of cos(x).

Formula  [tex]\text { area }=1 / 2 \times \text { base } \times \text { height }=1 / 2 \times 2 \pi r \times r=\pi r^{2}[/tex]  for the circumference of a circle.

Archimedes stated in his Proposition that the area of a circle is equal to the area of a triangle with a base equal to the circumference and a height equal to the radius: (1/2)(r · 2πr) = πr2. Archimedes arrived at his approximation of the circumference of the circle by increasing the number of sides of the hexagon. Archimedes claimed that the area of any circle is equal to the area of a right triangle, where the radius of the circle is represented by one side and the circumference by the other.

Archimedes demonstrated using a similar method that the area of a circle of diameter D is equal to the area of a right-angled triangle with one side equal to the radius and the other to the circumference of the circle on the right angle.

Formula for the circumference of a circle:

A circle's area is equal to pi times the radius squared (A = r2). Discover how to apply this formula to determine a circle's area given its diameter.

The circumference is diameter x pi, or 2 x radius x pi.

[tex]\text { area }=1 / 2 \times \text { base } \times \text { height }=1 / 2 \times 2 \pi r \times r=\pi r^{2}[/tex].

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Account balance at the end of day is 195.

A word problem is a type of mathematics exercise where the majority of the problem's context is supplied in spoken language as opposed to mathematical notation.

now according to question

initial balance in account on march 16 =80

deposit in account on the same day = 50

overdraft fee charged by bank=25

several transactions amount deposited in bank=90

total amount deposited /available in bank account.

=80+50+90

=220

total amount deducted from account

=25

account balance at the end of day

=220-25

=195

hence answer is 195

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Answer:

75%

Step-by-step explanation:

Answer:

1800(5/6)^t

Step-by-step explanation:

I don't see any answer choices, but this would be another form if it is listed. The negative exponent means that you get the reciprocal of the fraction (in this case 1.2). This turns 1.2 into (1/1.2), which is equivalent to 5/6.

Answer:

No

Step-by-step explanation:

So to determine whether this is a function, we first need to know what a function is. A function is defined as for each input, there is only 1 output.

This output doesn't have to be unique and other inputs can output this output, but it only matters that each input outputs only one output.

So let's look at what you provided and specifically these two points:

(3, 5)

(3, -3)

This input 3, outputs 5 and -3, which is not a function since this input outputted 2 different outputs. One thing to note is had you provided the two points: (3, 5), (3, 5) instead then it would still be a function because the input outputted the same output of 5 both times.

By using Binomial Distribution the probability that exactly 6 workers take the bus to work is 0.001.

When every experiment shares the probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution.

The likelihood of observing a specific percentage of successful occurrences in a specific number of trials is determined by the binomial distribution.

The formula for binomial distribution is-

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

'p' is the probability of success,

(1-p) is probability of failure,

'n' is the number of workers,

'k' is number of given workers.

According to the question,

Calculate the probability of success as;

[tex]p=\frac{15}{100}=0.15[/tex]

The, the probability of the failure becomes;

[tex](1-p)=1-0.15=0.85[/tex]

Put above two value in formula of binomial theorem to get the value.

[tex]{ }^{10} C_{6}(0.15)^{6}(0.85)^{4}=0.001[/tex]

Therefore, the probability that exactly 6 workers take the bus to work is 0.001.

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Answer:

[tex]\huge\boxed{\sf x = -2.5}[/tex]

Step-by-step explanation:

4x + 2 = -8

Subtract 2 to both sides

4x = -8 - 2

4x = -10

Divide 4 to both sides

x = -10/4

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

4x + 2 = - 8

Subtract 2 from both sides,

Subtract 2 from - 8 = - 10,

Divide both sides by 4,

____________________

The values of x and y that are solutions to the simultaneous equations are; x = -11 and y = -4

We are given the simultaneous equations;

4x - 6y = -20   -----(eq 1)

-2x + 4y = 6     -----(eq 2)

Multiply equation 2 by 2 and eq 1 by 1 to get;

-4x + 8y = 12     -----(eq 3)

Add eq 3 to eq 1 to get;

2y = -8

y = -4

Thus;

4x - 6(-4) = -20

4x + 24 = - 20

4x = -20 - 24

4x = -44

x = -44/4

x = -11

Thus, the values of x and y that are solutions to the simultaneous equations are; x = -11 and y = -4

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The answers are:

Given that:

The perimeter of vegetable plot:

= 4m + 3.5m + 4m + 2m + (3.5 + 2m)

= 19m

Area of vegetable plot:

(1.3 x 5.5) + ( (4 - 1.3) x 3.5)

rounding up to one decimal place = 67.6m²

To know the numbers of meter fence that one can buy, the equation will be:

(perimeter of vegetable plot + the left plot)  - gates.

(19m + (6.5 + 4 + (6.5 - 2) ) )m  - (2.5ft x 2)

= 19m + 15m - 1.5424m

=32.476

=32.5m

Therefore, the answers are:

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The average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].

In the question, we are asked for the average increase in the number of flowers pollinated per day between days 4 and 10, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].

To find the average increase in the number of flowers pollinated per day between days 4 and 10, we use the formula {f(10) - f(4)}/{10 - 4}.

First, we find the value of the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex], for f(10) and f(4).

[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(10) = (3)^{\frac{10}{2} }\\\Rightarrow f(10) = 3^5 = 243[/tex]

[tex]f(x) = (3)^{\frac{x}{2} }\\\Rightarrow f(4) = (3)^{\frac{4}{2} }\\\Rightarrow f(10) = 3^2 = 9[/tex]

Thus, the average increase

= {f(10) - f(4)}/{10 - 4},

= (243 - 9)/(10 - 4),

= 234/6

= 39.

Thus, the average increase in the number of flowers pollinated per day between days 4 and 10 is 39, given that the number of pollinated flowers as a function of time in days can be represented by the function [tex]f(x) = (3)^{\frac{x}{2} }[/tex].

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For complete question, refer to the attachment.

The probability of on- time arrival in class given that the subject is biology is 82.4%.

Given the following table relating to subject on tie assignment submission and on time arrival in class.

Subject              On time submission                    On time arrival

Physics                    89.7%                                             82.3%

Maths                       88.2%                                            88.7%

Chemistry                89.4%                                             83.1%

Biology                     90.1%                                              82.4%

Total                         88.5%                                             84.7%

We have to find the probability of on time arrival in class given that the subject is biology.

We have been given the corresponding percentages and percentages in itself shows some quantity. Percentage is the ratio of total favourable outcome to total outcome.

From the table the probability of on time arrival in class given that the subject is biology is 82.4%

Hence the probability of on- time arrival in class given that the subject is biology is 82.4%.

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Question is incomplete as it should includes the following table:

Subject              On time submission                    On time arrival

Physics                    89.7%                                             82.3%

Maths                       88.2%                                            88.7%

Chemistry                89.4%                                             83.1%

Biology                     90.1%                                              82.4%

Total                         88.5%                                             84.7%

Answer:

82.4%.

Step-by-step explanation:

The measure of ∠6 is 54 degrees.

When parallel lines are cut by a transversal, angle relationship are formed. Therefore,

∠6 = 5x + 9 (vertically opposite angles)

∠6 = ∠2

Hence,

∠2 + 13x + 9 = 180

5x + 9  + 13x + 9 = 180

18x = 162

x = 162 / 18

x = 9

Hence,

∠6 = 5(9) + 9  54°

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Answer: 3n+3

Step-by-step explanation:

Adding 1 to an odd number results in an even number.

Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit

From the question, we are to determine if the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks

In the graph, we have a scatterplot.

The line drawn is the line of best fit

Hence,

Yes, the line can be used to make reasonable predictions of the number of cheese pizzas that would be sold in the upcoming weeks. This is because the line is the line of best fit.

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Answer:

y = -3x - 28

Step-by-step explanation:

y = mx + b is the slope-intercept of a line.  To write an equation in this form.  I need to find the slope (m) and the y-intercept (b).  Yay!  They gave us the slope (m).  It is -3.  Now we just need to figure out the y.  We can do that by plugging in the slope (-3) and using the x (-8) and the y (-4) that they gave us from the point to solve for b.

y = mx + b

-4 = -3(-8) + b  Multiple -3(-8) Remember a negative times a negative is a positive.

-4 = 24 + b  Now subtract 24 from both side of the equation

-28 = b  Now we can write the equation

y = mx + b

y = -3x + (-28) or y = -3x -28.  Adding a negative is the same as subtracting a positive.

The number of angles that are alternate exterior with angle 5 is one, which is angle 11.

Alternate exterior angles are formed on the outside of the two parallel lines that are intersected by a transversal, each being located on the opposite side of the transversal.

The alternate exterior angle pairs are two angles that are supplementary. This means they add up to give a sum of 180 degrees.

Considering transversal s and parallel lines t and u, the angle that is an alternate angle to angle 5 is angle 11.

Angle 11 is the only angle that is alternate exterior angles with angle 5. therefore, we can conclude that, the number of angles that are alternate exterior with angle 5 is just 1, which is angle 11.

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Answer:

$142.5

Step-by-step explanation:

225-60=165

165/2=82.5

82.5+60=142.5

The statement which identifies Melissa’s error and the correct answer is; Melissa added incorrectly. The correct answer is 4.5°F

New temperature = Initial temperature + (Change in temperature per × Number of hours)

= -20.5°F + (5°F × 5)

= -20.5°F + (25°F)

= 4.5°F

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Answer:

C

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

x + (22 - 13) = 53

x + 9 = 53

x = 44

Answer:

44

Step-by-step explanation:

x+(22-13)=53

x+22-13=53

x+9=53

x=44

Use the rules of exponents to simplify the expression.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{g^{5}h^{4} }{g^{2}h^{3} } \end{gathered}$}[/tex]

To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.

Subtract 2 from 5.

Subtract 3 from 4.

For any term t, t¹ =t.

Therefore, the correct option is "B".

m<1 =163 degrees

163,17,163,17 (all in degrees)

163,17,163,17  (all in degrees)

I have reproduced and attached a diagram (in figure 1) of the problem.

For ease of understanding, I have attached a second diagram which is labelled.

On line a

17+<CBE=180 (Linear Pair Postulate)

m<2=<CBE=180-17=163 degrees

<ABG=<CBE=163 degrees (Vertically Opposite Angles)

<ABE=<GBC= 17 degrees(Vertically Opposite Angles)

On line b

m<1=<DEB=<ABG=163 degrees (Corresponding Angles)

<BEF=<GBC= 17 degrees (Corresponding Angles)

<HEF=<DEB=163 degrees  (Vertically Opposite Angles)

<DEH=<BEF=17 degrees (Vertically Opposite Angles)

Therefore:

m<1 =163 degrees

Clockwise from top left, the angles formed with line a are: 163 degrees, 17 degrees, m<2=163 degrees and 17 degrees.

Clockwise from top left, the angles formed with line b are: m<1=163 degrees, 17 degrees, 163 degrees, and 17 degrees.

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One linear equation y=x ......(i)

And quadratic equation y=x^2 .....(ii)

(1)Solving them

y=x=x^2

x-x^2=0

x(x-1)=0

If x=0 then y=0

if x=1 then y=1

(x,y)=(0,0),(1,1)

(2) graphically [refer in attachemet]

What is linear equation ?

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Option 2) the first set of data has values that are closer to the mean because the standard deviation is lower is correct

If two samples have the same mean, then it means that the two values in the two samples are centered around the same value. However, this does not mean that the data values in the samples vary equally around this center and thus the standard deviations may also differ.

It depends what the standard deviations are. The standard deviation is a measure of how close the results are to the mean, a low standard deviation means that the measurements are accurate, so close to the mean. A high standard deviation means that the measurements are more spread out.

We need to find that if two sets of data both have a mean of 76. however, the first set has a standard deviation of 1.4 and the second set has a standard deviation of 5.7. what must be true about the two sets

The first set of data has values that are closer to the mean because the standard deviation is lower because in first set standard deviation is 1.4 and in second set standard deviation is 5.7

The one with smaller standard deviation are least spead from the mean

Hence the first set of data has values that are closer to the mean because the standard deviation is lower.

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Answer:

FP is 70 degrees 35 times 2 so PD is 180 half a turn minus 70 = 110 degrees

Step-by-step explanation:

Answer:

a = 1500     b = .97

Step-by-step explanation:

1500 ( .97)^x       = bone density after n years

                              3% loss leave 97% each year   (.97 in decimal)

The piecewise function is

f(x) = 2, 0 < x ≤ 1/2

f(x) = 2 + 0.7x, x > 1/2

From the question, we have:

Fares = $2.00 ⇒ up to (and including) 1/2 miles

Fares = $0.70 increment ⇒ greater than 1/2 miles

Let x represent the number of miles, and f(x) the fares.

So, we have:

f(x) = 2, 0 < x ≤ 1/2

f(x) = 2 + 0.7x, x > 1/2

The above represents the piecewise function

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