Two trains, each moving at 20 miles per hour towards each other, are initially 60 miles apart. A bee starts at the front of one train, flies to the other train, then back to the first train, and so on. If the bee always flies at 30 miles per hour, how far does the bee fly before the trains collide? Hint: For how long does the bee fly?

An apple pie requires 7 apples and an apple tart requires 4 apples

To set up this problem, we can let p represent the number of apples needed for one pie and t represents the number of apples needed for one tart.

We can then set up the following system of equations to represent the information given in the problem:

2p + 6t = 38

2p + 8t = 46

To solve this system, we can subtract the first equation from the second to eliminate the p terms:

2p + 8t - 2p - 6t = 46 - 38

2t = 8

t = 4

Substituting this value back into the first equation, we get:

2p + 6(4) = 38

2p = 14

p = 7

Thus, an apple pie requires 7 apples and an apple tart requires 4 apples.

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Therefore the value of x from the given equation comes out to be 13.5

A statement proving the equality of two mathematical expressions is known as an equation. The equal sign (=) is used to represent an equation between two mathematical expressions. Anything that contains the equal sign is an equation, to put it simply. Examples of equations include x=7, 2x+5=7, etc.

Here,

The equation given is 3(x+2)=7x-48

thus we find the value of x from the given equation

=> 3(x+2)=7x-48

=> 3x+6=7x-48

=> 7x-48-3x-6=0

=>  4x-54=0

=> 4x=54

=> x=54/4

=> x=13.5

Therefore the value of x from the given equation comes out to be 13.5

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Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the personal best time of Dean be = A

Now , the value of A = 3 hours 14 minutes 45 seconds

And ,

The time taken by Dean to complete 1 km = 9 minutes 30 seconds

Now , the total distance of the race lap = 20 km

So , the equation will be

Total time taken by Dean to complete 20 km race B = 20 x time taken by Dean to complete 1 km

Substituting the values in the equation , we get

Total time taken by Dean to complete 20 km race = 20 x 9 minutes 30 seconds

Total time taken by Dean to complete 20 km race = 20 x 9 minutes + 20 x 30 seconds

Total time taken by Dean to complete 20 km race = 180 minutes + 600 seconds

1 hour = 60 minutes

1 minute = 60 seconds

180 minutes = 3 hours

600 seconds = 10 minutes

So , the equation is

Total time taken by Dean to complete 20 km race B = 3 hours 10 minutes

So , the value of B < value of A

Therefore , the Dean will beat his personal best time and the race is completed in 3 hours 10 minutes

Hence , Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time

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Greta's current age is m + n years.

An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

In other words, algebraic expressions are combinations of variables, numbers, and at least one arithmetic operation

Therefore, let's convert the word's expression to an algebraic expression.

Greta was m years old n years ago. Her age now is as follows:

n years ago Greta was m years old. This simply means n years ago Greta was m years old. Her current age will be the sum of her current age and the number of years ago.

Therefore,

(m + n) years

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Answer:

It would be most appropriate to use the mode for categorical data, such as favorite ice cream flavor. This is because you can't use mean or median for flavors such as chocolate or vanilla, so mode would make the most sense there.

The scale factor of triangle PQR to triangle STU is 3/2

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

Taking a point of reference say PR and SU

PR = 8

SU = 12

let the scale factor be r such that

8 * r = 12

r = 12 / 8

r  = 3/2

checking with other sides

PR to UT

6 * 2/3 = 9 correct

QP to TS

10 * 3/2 = 15 correct

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The percent increase is 56%

The percent increase if the airline charges an additional $50 baggage fee with the new ticket price is 76%

The formula for determining percent increase is expressed as;

Percent increase = x₂ - x₁/x₁  × 100/ 1

Where;

Now, substitute the values, we have;

Percent increase = $320 - $210/$210  × 100/ 1

Find the difference

Percent increase = $110/$210  × 100/ 1

Percent increase = 0. 52  × 100/ 1

Multiply through

Percent increase = 52%

If there is an increase of $50

Percent increase = $370-210/210 × 100/ 1

= 160/210 × 100/ 1

= 76%

Hence, the values are 52% and 76% respectively,

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The cost from company A and company B will be the same at 40 square feet of countertop

Given that:

Company A will sell Mikayla a countertop according to the given

graph, which includes a $1, 000 installation fee.

Company B will sell a countertop according to the values given in the

table, which includes an $800 installation fee and a constant rate of change

With this information, you can make cost function for both Company A and Company B

Company A

A linear function is of the form y = mx + c

where c is the y-intercept (starting point) and m is the slope (rate)

c = 1000  (from the graph)

m = 1150-1000 / 10-0  (By using the 2 points on the graph: m = y2-y1/x2-x1)

m = 15

y = mx + c

y = 15x+1000

Company B

c = 800  (given)

m = 1100-1000 / 15-10  (From table)

m = 100/5 = 20

y = mx + c

y = 20x+800

Equate the two cost functions and solve for x:

20x+800 = 15x+1000

20x-15x = 1000-800

5x = 200

x = 200/5

x = 40 square feet

Therefore, at 40 square feet of countertop, the cost from each company will be the same

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Answer:

.05 yd

Step-by-step explanation:

5/91.44=.05468066

geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately  3.7973 × 10⁹ years old is the sample.

The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.

According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.

t1/2 of U₂₃₈ is 4.5 × 10⁹ years

moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles

moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles

Now, U₂₃₈ → Pb₂₀₆

As Pb₂₀₆ comes from U₂₃₈ hence,

moles of  U₂₃₈ decayed = moles of  Pb₂₀₆

                                        = (0.686 × 10⁻⁶ / 206) moles

Therefore, initial moles of U₂₃₈:

N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles

and N = (1 × 10⁻⁶ / 238) moles

Now, λ (decay constant) = 0.693 / (t1/2)

                                        = 0.693 / ( 4.5 × 10⁹ years)

So,

t = 2.303 / λ × log (N₀ / N)

t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]

t = 14.95 × 10⁹ × 0.254

t = 3.7973 × 10⁹ years.

Thus, the sample is: 3.7973 × 10⁹ years old.

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Answer:

Make the denominators equal by L.C.M

--> 8/20 + 5/20

--> 13/20

Answer:

the daily fee is 37 and the mileage charge is .24 per mile.

Step-by-step explanation:

256 = 450x + 4b

159 = 200x + 3b

Multiple the top equations by -3 all the way through the bottom equations by 4 all the way  through then add the equation together.

-768 = -1350x -12b

636 = 800x + 12b

-132 = -550x  Divide both sides by -550

.24 = x  This is the charge per mile.

Plug in .24 for x into either of the original 2 equations to solve for b which is the daily fee.

256 = 450(.24) = 4b

256 = 108 + 4b  Subtract 108 from both sides

148 = 4b  Divide both sides by 4

37 = b  This is the daily fee.

Answer: it is 8103.38

Step-by-step explanation:

The total of his sales for that week is $49,500.

Given :

Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135.

Let x be the total sales.

2135 = 2.5 % * 50000 + 3 % (x - 50000 )

= 2.5 * 50000 / 100 + 3/100 ( x - 50000 )

1235 = 2.5 * 500 + 0.03x - 0.03 * 50000

1235  = 1250 + 0.03x - 1500

0.03x = 1235 - 1250 + 1500

0.03x = -15 + 1500

0.03x = 1485

multiply by 100 on both sides

0.03x * 100 = 1485 * 100

3x = 148500

x = $49500

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Compared to the graph of y = x graph y = -x/3 is a negative slope

Compared to the graph of y = x graph y = -x/3 intersects the y axis at same point

Compared to the graph of y = x graph y = x - 2 is a parallel line

Compared to the graph of y = x graph y = x - 2 intersects the y axis at 2 units down

The two graphs compared are linear function graphs

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

y = x

slope = 1

c = 0

y = -x/3

slope = -1/3

c = 0

y = x - 2

slope = 1

equal slopes means the lines are parallel

c = -2 (down 2 units)

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Answer:

statements 2 and 3 are true

Step-by-step explanation:

using the rule of exponents

[tex]a^{0}[/tex] = 1

then

1 [tex]a^{0}[/tex]≠ a ← lie

2 [tex]x^{0}[/tex] = 1 ← true

3 [tex]5^{0}[/tex] = 1 ← true

The given statistic is said to be an "unbiased estimator". In this statistic, the mean is equal to the true value of the estimated parameter.

In a statistic, if the mean is equal to the estimated parameter, then that statistic is said to be an unbiased estimator. It is used to estimate a population parameter.

Consider a statistic.

"A statistic describes a portion of the target population".

"A parameter describes the whole population".

In a statistic, the mean of the sampling distribution is equal to the true value of the estimated parameter.

I.e., μ = E(x)

So, that statistic is said to be an unbiased estimator.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}[/tex]

[tex]A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}[/tex]

An equation of the parabola with focus (1, 6) and directrix y = 1 is: C. y = 1/10(x²) - 1/5(x) + 18/5

Mathematically, the standard equation of the directrix lines for any parabola is given by:

y = a(x - h)² + 2.

Where:

Since the directrix is horizontal, the axis of symmetry would be vertical. Therefore, the equation of this parabola would be modeled by this standard mathematical expression;

(x - h)² = 4p(y - k)

Where:

h = 1

In Mathematics, the focus for either a right or left parabola is modeled by this mathematical expression (h + p, k) while its directrix is modeled by this mathematical expression x = h - p;

k + p = 6

k - p = 1

Solving the set of linear equations simultaneously, we have:

2k = 7

k = 7/2

For the value of p, we have;

p = 6 - k

p = 6 - 7/2

p = 5/2

Substituting the given parameters into the formula, we have;

(x - 1)² = 4(5/2)(y - 7/2)

x² - 2x + 1 = 10(y - 7/2)

x² - 2x + 1 = 10y - 35

10y = x² - 2x + 1 + 35

10y = x² - 2x + 36

y = (x² - 2x + 36)/10

y = x²/10 - x/5 + 18/5

y = 1/10(x²) - 1/5(x) + 18/5

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Molly would need 43 feet of fencing to fence the triangular area.

What is Pythagorean theorem?

Pythagorean theorem states 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).

According to the given question:

We can see that the area is in the form of a right-angled triangle. Since only two sides of the triangle is given, we could utilize Pythagoras theorem to our advantage to find out the third side.

In Δ ABC

AB² (base) + AC² (perpendicular) = BC² (hypotenuse)

Substituting the values of AB as 10 feet and BC as 18 feet

AC²= BC²- AB ²

∴AC²= 224  

∴AC= 14.96 cm

Amount of fence required by molly would equal perimeter of the area.

⇒The perimeter of the area would equal AB+BC+AC

⇒Summing up the values of AB, AC and BC

Perimeter= 10+14.96+18= 42.96 feet which is about 43 feet

Hence, Molly would require 43 feet of fencing.

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Given that he is running on a treadmill at a pace of 7.2 miles per hour, the necessary expression will be y=7.2x.

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. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

Here,

Speed of him=7.2 miles/hour

Let y be the total distance and x be the number of hours,

speed=distance/time

7.2=y/x

y=7.2x

The required expression will be y=7.2x as he is running on a treadmill at a speed of 7. 2 miles per hour.

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The algebraic expression that can be represented by the statement is  43y + 16

From the question, we have the following statement that can be used in our computation:

16 more than the product of 43 and a number

Represent the variable with y

So, we have the following representation

16 more than the product of 43 and y

Express the product as an actual product

So, we have the following representation

16 more than  43y

more than as used here means addition

So, we have

43y + 16

Hence, the expression is (d) 43y + 16

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Answer: 43y + 16

Step-by-step explanation:

i did the test

Answer:

The first one is the answer