7) Complete the blanks in this bank statement.
Date
25/03/20
28/03/20
29/03/20
Income Outgoings Balance
£453
£1200
£957

A) The system of equations that you can use to find the number of five-dollar bills and ten-dollar bills are;

x + y = 125

5x + 10y = 990  

B) The number of five-dollar bills are 52 and ten-dollar bills are 73.

The parameters are that the total number of five and ten-dollar bills equals 125 dollars.

Let x denote the number of five dollar bills and let y denote the number of ten dollars bills. Thus;

Total number of bills is;

x + y = 125      --- (1)  

The total value of all bills is $990  

Thus, we have;

5x + 10y = 990  

Divided by 5 into both sides  to get;

x + 2y = 198  ----- (2)

Now solve (1) and (2) for x and y values

Subtract eq (1) from eq (2) to get;

x + 2y - x - y = 198 - 125

y = 73

Substitute y = 73 in (1)

x + 73 = 125

x = 52

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The calculator short hand notations are;

a) -4E3

b) -3E4

c) 3E4

d) 4E3

We have to note that the calculator short hand notation has to do with the manner in which the calculator would show an exponential function when we are solving the mathematical problem using the calculator.

It is common to see that the calculator would display the letter E to stand in for the mathematical figure * 10^n. The letter that is depicted by n would then be written at the right hand side of the letter E.

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Answer:

5:38 am

Step-by-step explanation:

Since the train arrived at it's final destination at 12:28 pm and it took two hours to get there. Subtract two hours from the final destination time and it's 10:28 am. Then it took 4 hours and 50 minutes to arrive to Wildgrove, so subtract four hours of the time when the train arrived. It is now 6:28 am. Subtract fifty minutes from that and you would get 5:38 am.

p.s. There are time calculators online if you need an answer if this is kinda hard to understand

A fraction can be converted to a decimal number by dividing the numerator—the piece at the top of the fraction—by the denominator, which can be done with a calculator. A decimal number that represents the value of the fraction is the answer.

The geometry and location of the primary source of radiation directly affect the ratio of flux between direct and reflected radiation, known as the "reflection fraction."

Flip is the mathematical term for reflection. An image of the shape reflected in a mirror. A line, called the line of reflection, is where an image will reflect. When one figure "reflect[s]" another, that phrase is used.

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Elizabeth would travel a distance of [tex]11\frac{2}{5}[/tex] miles.

The distance between Elizabeth's house and Carson's house = Sum of (the distance between Elizabeth's house and the Library + the distance between the library and Millo's house + the distance between Millo's House and Carson's House). That is:

Total Miles = [tex]6\frac{1}{2}[/tex] + [tex]2\frac{2}{5}[/tex] + [tex]2\frac{1}{2}[/tex]

To calculate the total miles, we need to transform the mixed numbers into fractions. We can do that as:

[tex]6\frac{1}{2}[/tex] = [(6 × 2) + (1)]/2 = 13/2

[tex]2\frac{2}{5}[/tex] = [(2 × 5) + (2)]/5 = 12/5

[tex]2\frac{1}{2}[/tex] = [(2 × 2) + (1)]/2 = 5/2

So, the distance from Elizabeth's house to Carson's House has 57/5 miles, and it is calculated as:

13/2 + 12/5 + 5/2 = 57/5

Then, convert 57/5 into a mixed number, and we get:

57/5 = [tex]11\frac{2}{5}[/tex]

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Answer:

3x (1 - 3)

Explanation in detail:

= 3x - 9x²

= 3x (1 - 3x) (1 - 3x)

Answer: x = -7

Step-by-step explanation: Subtract 23 from both sides. 4x + 23 - 23 = x + 2 - 23, than simplify and subtract x from both sides

The given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.

(1) 0.4 is a rational number because it can be written as 4/10 which is a fraction with a denominator that is not zero.

(2) 0.21 is a rational number because it can be written as 21/100 which is a fraction with a denominator that is not zero.

(3) 0.14 is a rational number because it can be written as 14/100 which is a fraction with a denominator that is not zero.

(4) 0.124 is a rational number because it can be written as 124/1000 which is a fraction with a denominator that is not zero.

(5) -1.124 is a rational number because it can be written as -1124/1000 which is a fraction with a denominator that is not zero.

(6) 19.45 is a rational number because it can be written as 1945/100 which is a fraction with a denominator that is not zero.

(7) -2.35 is a rational number because it can be written as -235/100 which is a fraction with a denominator that is not zero.

In conclusion, all the given recurring decimals are rational numbers as they can all be written as fractions with a denominator that is not zero.

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The member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

What is Equation of a straight line ?

The equation of a straight line as follows : y = mx+c where m is slope of a straight line and c is y-intercept.

Given that the equation of the line of best fit is given by

Let x represents the amount of time in minutes.

Let y represents the temperature in degrees Fahrenheit.

From the equation of line of best fit, it is obvious that the temperature that a person can tolerate is 173 degrees Fahrenheit at 0 minutes.

Because the y - intercept represents the temperature when the x - value is zero.

So,  the member can tolerate a temperature of 173° Fahrenheit for 0 minutes.

Therefore, The member can tolerate a temperature of 173° Fahrenheit for 0 minutes

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In a scenario when X is replaced with (x-3) then it means that the value of x will be reduced by 3 units.

This is referred to as the process which involves the replacement of a word , number or phrase with another when performing different types of operations.

During an arithmetic operation and X is replaced with (x-3), then it means that the value of X will be reduced by 3 units and an example is given below:

Let's assume X is 5 and we substitute it with (x-3) will therefore become (5-3) = 2. This depicts that there has been a reduction by 3 units thereby making it the correct choice.

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The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.

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The number of students who do not buy lunch is 624 students - 420 students = 204 students.

The circle graph represents the proportion of students who buy lunch and those who don't. To find the number of students who don't buy lunch, we need to subtract the number of students who buy lunch from the total number of students.

Since 255° represents the proportion of students who buy lunch, we can use this to find the number of students who buy lunch. To do this, we divide the number of degrees by 360° and multiply by the total number of students, 624:

(255° / 360°) x 624 students = 420 students

Therefore, the number of students who do not buy lunch is 624 students - 420 students = 204 students.

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The length of the diagonals of the rhombus is 3.5cm.

A rhombus's diagonals are always perpendicular to one another and always the same length. It contains four right angles, hence an acute angle of 840 is an obtuse angle. We are aware that in a rhombus, the diagonal is the hypotenuse of a right triangle, and the other two sides make up each half of the side.

Consequently, we can use the Pythagorean theorem to determine the diagonal's length:

c = √(a² + b²)

where an is the rhombus's half-length side and b is the other half, and c is the length of the diagonal. So we have:

a = (5cm) / 2 = 2.5cm

b = (5cm) / 2 = 2.5cm

c = √(2.5² + 2.5²) = √(6.25 + 6.25) = √12.5 = 3.5cm

Therefore, the length of the diagonals of the rhombus is 3.5cm.

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The diagonal V2 of the square will be √2 feet.

What are squares?

A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.

The most important properties of a square are listed below:

Area of square=(side)²

Perimeter of square=4*side

Now,

as side=1 foot

By applying Pythagorean theorem,

Diagonal²=side²+side²

therefore,

V2²=1²+1²

=2

V2= √2 feet

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It has a diameter of about 60,000 light-years (18,400 parsecs).

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Answer:

7 hours

Step-by-step explanation:

So you know in the second to third row of boxes how a hour and a half later the car loses 3 gallons of gas let's says another hour and a half goes by and the car has 1 gallon of gas left so each 30 minutes the car lost gas so now that we have that 1 gallon of gas left 30 minutes went by and now we are out gas

The length of GH is about 7.3 units. The solution has been obtained by using the formula of distance between two points.

What is distance between two points?

The distance between two points in a plane is the length of the line segment separating the two points. Typically, the equation

[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]  is used to calculate the distance between two points. One can use this formula to get the separation between any two points on an x-y plane or coordinate plane.

We are given two points as G(-9,-4) and H(-2,-6)

Using the distance formula,

[tex]d=\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]

[tex]d=\sqrt{(-2 +9)^{2} + (-6 +4)^{2} }[/tex]

[tex]d=\sqrt{(7)^{2} + (-2)^{2} }[/tex]

[tex]d=\sqrt{49 + 4 }[/tex]

[tex]d=\sqrt{53 }[/tex]

d = 7.3 units

Hence, the length of GH is about 7.3 units.

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She left the 1/6 yards pipes.

Now, According to the question:

Rose bought a length of 4/6 copper pipe.

She used 1/2 yard to repair a water line in her house.

To find how much pipe does she have left?

Pipes available = 4/6 yards

Pipes used = 1/2 yards

Pipes left = total pipes bought - she doesn't suit that way

Pipes left = Total pipes available - pipes used

= 4/6 yards - 1/2 Yards

= 4-3/6

= 1/6 yards

Pipes left = 1/6 yards

Hence,  She left the 1/6 yards pipes.

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The given question is incomplete, complete question is:

Rose bought a length of 4/6 copper pipe. She used 1/2 yard to repair a water line in her house. How much pipe does she have left? Solve this problem any way.

Answer: I believe the answer is 12

The simplify of given equation 11k/ (55k^2+ 22k) is 1/(5k+2).

Given,

[tex]\frac{11x}{55^{2}+22k }[/tex]  We have to simplify in rational expression

The common factor is 11. So, we have to pick the common factor from the equation.

= [tex]\frac{11x}{55^{2}+22k }[/tex]

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

Therefore the simplification of given equation is 1/(5k+2).

Reasonable expressions resemble fractions with variable denominators (and often numerators too). An example of a rational expression is x 2 x + 3 dfracx2x+3 x+3x2 start fraction, x, squared, divided by, x, plus, 3, end fraction.

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Answer: you can solve for x using the Pythagorean theorem:

Step-by-step explanation. let's say your questing in sides are 12 and 40 what is x. you have side x, y, and h. y=12 h=40. now you solve using the Pythagorean theorem x2 + y2 = h2. (The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent).)

The balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.

Let t be the number of seconds since the balloons took off, and Hp(t) and Hg(t) be the altitude of the purple and gold balloons respectively at time t.

We know that:

Hp(t) = 0 + 2.5t (the purple balloon starts at sea level and climbs at a rate of 2.5 m/s)

Hg(t) = 1515 + 222t (the gold balloon starts 1515 m above sea level and climbs at a rate of 2*22 m/s)

We want to find the time t when the balloons are at the same altitude, so we can set Hp(t) = Hg(t) and solve for t:

0 + 2.5t = 1515 + 222t

2.5t = 1515 + 222t

2.5t - 222t = 1515

0.5t = 1515 - 1515

t = 0

So the balloons were never at the same altitude because the gold balloon was already 1515 meters above the purple balloon at the start.

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a. The length of x is 4 cm.

b. The area of the shaded face in the triangle prism is 36 cm².

The net of the triangular prism shows that the shaded face is a rectangle.

The side labelled x is the same as the side of the triangular face with a side of 4 cm, when the net of the triangular prism is folded.

Therefore:

a. Length of x = 4 cm

b. Area of shaded face = area of rectangle = length × width

= 9 × 4

= 36 cm²

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Answer:

30 ft

Step-by-step explanation:

h/(40 + 8) = 5/8

h = 30

The correct option is Option C - 85.274.94.

The face value of the 10-year term insurance policy on a 25-year-old Female given that the annual premium for the insurance policy of $384.59 is 85,274. 94.

Given:

Annual premium for the insurance policy = $384. 59

According to the chart at the conclusion of the answer, the amount paid per $1,000 of coverage for a female 25 year old for a 10 year policy is 4.51.

Face value = (1,000 x Annual premium) / Amount paid for 25 year old female for 10 year policy)

Face value = (1000 x 384.59) /4.51

Face Value = 384590 / 4.51

Face Value = 85274.94

Therefore the face value is 85274.94.

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The table is given by the image shown at the end of the answer.

Answer:

28

Step-by-step explanation:

AB and TB are perpendicular because the tangent and radius are perpendicular. So you have a right triangle. Triangle ABT is a right triangle.

Also, TB is a radius of the circle, but so is TC. They are the same length.

Use Pythagorean Theorem to solve this problem.

AB^2 + TB^2 = AT^2

see image.

Using exponents rule the missing term in the equation 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____ is found to be 7^(-29).

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The given expression is - 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____

Let the missing term be x.

Then the equation is -

7^(-147) × 7^(98) = 7^(18) × 7^(-38) × x

Since, the base of the exponents is same, so apply the operations on the powers of the base.

The exponent rule is - a^(b) × a^(c) = a^(b + c)

Write the equation according to the rule -

7^(-147 + 98) = 7^(18 - 38) × x

Now perform the arithmetic operation of addition and subtraction -

7^(-147 + 98) = 7^(18 - 38) × x

7^(-49) = 7^(-20) × x

The exponent rule is - a^(b) / a^(c) = a^(b - c)

Write the equation according to the rule -

x = [7^(-49)] / [7^(-20)]

x = 7^[-49 - (-20)]

x = 7^(-49 + 20)

x = 7^(-29)

Therefore, the missing term is x = 7^(-29).

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Select the correct answer from the drop-down menu. Find the missing term. 7^(-147) × 7^(98) = 7^(18) × 7^(-38) ×____

The way that algebra can help in the creation of a histogram is that it helps organize and analyze the data in the histogram.

Algebra can be used to determine the range of values in the data set, and to create bins or intervals for the histogram. Algebra can be used to calculate the frequency of data points in each bin. This is important for creating the histogram, as it will determine the height of each bar.

Algebra can also be used to calculate the mean, median, mode, and standard deviation of the data set, which can provide a summary of the distribution of the data.

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Full question is:

Creating a historgram algebra. How does algebra help in creating a histogram ?

The value of x in the figure is 20

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or [tex]\dfrac{a}{b}[/tex]

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).

Suppose that we've got a = 6, and b= 4, then:

[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]

Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.

Given;

Ratio of first line segment = 4.4/6.3

Ratio of other line segment= 14.08/x

Now, to find the value of x

4.4/6.3 = 14.08/x

4.4x= 14.08x6.3

x=14.08x6.3/4.4

x=20.16

Therefore, according to ratio x will be equal to 20

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The ascending order of the given data is-

80g < 12254g < 0. 845kg <  1. 2kg.

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