Two cyclists start at the same point and travel in opposite directions. One cyclist travels 5 faster than the other. If the two cyclists are 74 miles apart after 2 hours, what is the rate of each cyclist?

The statements that apply to the algebraic expression are

The complete question is added as an attachment

The statement is given as:

Twice the difference of a number and six

Represent the number with n.

So, the statement becomes

Twice the difference of a n and six

Twice means 2 *

So, we have

2 * difference of a n and six

Express difference as minus i.e. -

So, we have

2 * (n - 6)

Hence, the expression is written as 2(n - 6)

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Answer:

600

Step-by-step explanation:

250/1 times 6/ 100 times 40/1

Answer:

1,920 watts per circuit

Step-by-step explanation:

To find the load for 1 circuit (per circuit) we can divide 28,800 watts by 15 circuits

28800/15 = 1,920 watts per circuit

Answer:

x = 4

Step-by-step explanation:

Hello!

We can solve for x by expanding the parentheses and isolating x.

The value of x is 4.

The fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively. option D

9√4.000

= 4.000/9

= 0.444

Approximately,

= 0.4

Fraction

This is a ratio of two numbers, the numerator and the denominator, usually written one above the other and separated by a horizontal bar.

Decimal

This is a number expressed in the decimal system (base 10).

Therefore, the fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively.

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Answer:

120 four digit numbers can be created from the gives.

Step-by-step explanation:

Solution

You are given 5 digits in the givens.

1 3 5 7 9

Therefore

5 * 4 * 3 * 2 is the answer to your question. 4 and 3 and 2 determine that none of the digits can be repeated. That equals 120.

The expression, the  fifth term of the binomial expansion is y^4

Binomial expansion is a means of expanding expressions into terms

Given the expression (x+y)^4, according to the theorem, as the power of x is decreasing, the power of y will be increasing up till the power of the expression.

Expand (x+y)^4

(x+y)^4 = x^4y^0 + x^3y^1 + x^2y^2 + xy^3 + x^0y^4

Include the coefficients according to the Pascal triangle to have:

(x+y)^4 = x^4y^0 + 4x^3y^1 + 6x^2y^2 + 4xy^3 + x^0y^4

(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

From the expression, the  fifth term of the binomial expansion is y^4

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Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

It states that, for a normally distributed random variable:

Considering the mean of 110 and the standard deviation of 15, we have that:

These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

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if any number or variable is outside a parenthesis it will go to all the number rin the parenthesis.

in this case -y is outside the parenthesis so it will got to both the sides :

-y(-6y-3) = -6y x y - 3 x y

= -6y² -3y//

Without using general formula we will solve it in bit lengthy manner

For first half

Time=Distance/Speed

For second half

Time

So

Average speed

Option C

The answer is 412.3 km/h.

The formula to find average velocity is :

[tex]\boxed {V_{avg} = \frac{d_{1}+d_{2}}{t_{1}+t_{2}}}[/tex]

Let's find t₁ and t₂.

Now, let's substitute in the formula to get the answer.

The reverse number of the three-digit number is 732

Let the three-digit number be xyz.

So, the reverse is zyx

This means that

Number = 100x + 10y + z

Reverse = 100z + 10y + x

From the question, we have the following parameters:

y = x + 1

z = 1 + 2y

The sum is represented as:

100x + 10y + z + 100z + 10y + x = 10^3 - 31

100x + 10y + z + 100z + 10y + x = 969

Evaluate the like terms

101x + 101z + 20y = 969

Substitute y = x + 1

101x + 101z + 20(x + 1) = 969

101x + 101z + 20x + 20 = 969

Evaluate the like terms

101x + 101z + 20x = 949

121x + 101z = 949

Substitute y = x + 1 in z = 1 + 2y

z = 1 + 2(x + 1)

This gives

z = 2x + 3

So, we have:

121x + 101z = 949

121x + 101* (2x + 3) = 949

This gives

121x + 202x + 303 = 949

Evaluate the sum

323x = 646

Divide by 323

x = 2

Substitute x = 2 in z = 2x + 3 and y = x + 1

z = 2*2 + 3 = 7

y = 2 + 1 = 3

So, we have

x = 2

y = 3

z = 7

Recall that

Reverse = 100z + 10y + x

This gives

Reverse = 100*7 + 10*3 + 2

Evaluate

Reverse = 732

Hence, the reverse number of the three-digit number is 732

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The probability that the student plays football is 20/33.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that the student plays football = total number of students who play football / total number of students

The probability that the student plays football = 40/66 = 20/33

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Answer:

TS=QV

Step-by-step explanation:

To prove SAS congruence, you need to prove that two lines and the angle between them are all respectively equal.

In the diagrams we already have RS=WV and ∠RST=∠WVQ, so it follows that we need to prove that TS=QV.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

For triangles to be congruent by SAS congruency criteria, one angle and the two adjacent sides to the angle should be equal to corresponding angle and it's adjacent aides of another triangle.

And we have already been given the angle and one of the side. so the third side that need to be equal in both side to pe proved congruent are :

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

x  = 9, y = 13 , z = - 19

Step-by-step explanation:

3y + 4z = - 37 → (1)

2x + 4y - 3z = 127 → (2)

4y = 52 → (3)

divide both sides by 4 in (3)

y = 13

substitute y = 13 into (2) and solve for z

3(13) + 4z = - 37

39 + 4z = - 37 ( subtract 39 from both sides )

4z = - - 76 ( divide both sides by 4 )

z = - 19

substitute y = 13 and z = - 19 into (2) and solve for x

2x + 4(13) - 3(- 19) = 127

2x + 52 + 57 = 127

2x + 109 = 127 ( subtract 109 from both sides )

2x = 18 ( divide both sides by 2 )

x = 9

solution is x = 9, y = 13 , z = - 19

Answer:

13

Step-by-step explanation:

3x + 7

x = 2

3 × 2 + 7 = 6 + 7 = 13

Hi there.

3x+7

x=2 :

3(2)+7

6+7

13

That's it.

Answer: The guy wire  = 393.4 ft

Step-by-step explanation:

Given images:

Refer to the attachment below (I apologize for the bad writing on the computer)

Given information:

Height of the tower = 175 ft

Height of the wire = 15 ft from the top (Opposite)

Angle with the ground = 24°

Length of wire = Unknown (Hypotenuse)

Determine the trigonometric function:

The primary choice will be the Sine function because the angle is opposite to the height and the wire is the hypotenuse of the system.

Determine the equation:

sin θ = (Opposite) / (Hypotenuse)

sin (24°) = (175 - 15) / (Length)

Simplify value in parenthesis

sin (24°) = (160) / (Length)

Multiply the Length of wire on both sides

sin (24°) * (Length) = (160) / (Length) * (Length)

sin (24°) * (Length) = (160)

Divide sin (24°) on both sides

sin (24°) * (Length) / sin (24°) = (160) / sin (24°)

Length = 160 / sin (24°)

[tex]\Large\boxed{Length~=~393.4~ft}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

-1/3

5

Step-by-step explanation:

We need to complete

y = mx + b

with a slope, m, and with the y-intercept, b.

From the graph, we see that the line intersects the y-axis at y = 5, so the y-intercept, b, is 5.

We now have y = mx + 5.

Now we need the slope.

We pick two points that are easy to read, (0, 5) and (3, 4).

m = slope = rise/run

To go from (3, 4) to (0, 5), we go up vertically 1 unit. The rise is 1.

Then we go left horizontally 3 units. The run is -3.

m = slope = rise/run = 1/(-3) = -1/3

Now we have the slope, so we can finish.

y = -1/3 x + 5

Answer:

-1/3

5

Answer:

a=170

Step-by-step explanation:

(a+10)=180[because being a straight line]

or, a+10=180

or,a=180-10

a=170

Therefore,a=170

Using the relation between velocity, distance and time, it is found that the rate of the current is of 3.33 mph.

Velocity is distance divided by time, hence:

v = d/t

A small motorboat travels 12mph in still water. With the current, upstream, 46 miles are traveled in t hours, hence:

12 + r = 46/t

r = 46/t - 12

Downstream, the time is of t + 2 hours, hence:

12 - r = 46/(t + 2)

r = 12 - 46/(t + 2)

Hence, equaling the values for r:

46/t - 12 = 12 - 46/(t + 2)

46/t + 46/(t + 2) = 24

[tex]\frac{46t + 92 + 46t}{t(t + 2)} = 24[/tex]

92t + 92 = 24t² + 48t

24t² - 44t - 92 = 0

Using a quadratic equation calculator, the solution is t = 3. Hence the rate is found as follows:

r = 46/t - 12 = 46/3 - 12 = 3.33 mph.

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Answer:

C

Step-by-step explanation:

Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.

The correct option is:

b. Most of students' test scores are around the mean.

A large range indicates that there is a significant difference between the highest and lowest scores in the set.

On the other hand, a small standard deviation indicates that the data points (test scores) are clustered closely around the mean.

When the range is large but the standard deviation is small, it means that most of the students' test scores are relatively close to the mean, and there are no extreme values that are significantly far from the mean. In other words, the majority of students performed similarly on the test, with only a few outliers having scores much higher or much lower than the mean.

Option b accurately reflects this scenario, as it states that most of the students' test scores are around the mean, which aligns with the idea of a small standard deviation.

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Using translation concepts, the equation for function g is given by:

g(x) = 7x/3 + 1.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

Supposing that we have a function f(x), a horizontal compression by a factor of a is equivalent to finding f(ax).

In this problem, the function is:

f(x) = 7x + 1.

For the horizontal compression by a factor of 1/3, we have that:

g(x) = f(1/3x) = 7x/3 + 1.

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I'm tentatively changing my answer to say this kind of relies on practical knowledge of how stores tend to operate. If 20 coupons are given out, the store has sold all 500 shirts, arguably at a loss to the retailer. They have to have more shirts in stock to be sold at full price because, well, that's how they make money. It's more likely that such a store would carry more than just 500 shirts at the start of each day, so A is (probably) wrong.

Answer:

Option 3: -2

Step-by-step explanation:

The slope of the graph is negative, and the only option with a negative term for the slope is -2.

So the slope of the graph is -2.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

According to given figure,

Angle 11, Angle 20 and Angle 16 forms angles of a triangle,

so, by angle sum property of a triangle :

[tex]\qquad❖ \: \sf \: \angle11 + \angle20 + \angle16 = 180 \degree[/tex]

[tex]\qquad❖ \: \sf \: \angle11 +66 + 43 = 180 \degree[/tex]

[tex]\qquad❖ \: \sf \: \angle11 +109 = 180 \degree[/tex]

[tex]\qquad❖ \: \sf \: \angle11 = 180 \degree - 109[/tex]

[tex]\qquad❖ \: \sf \: \angle11 =71 \degree [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

Rhoda and Ming are both correct, but Ming's prediction is closer because the result is accurate to two decimal places.

Step-by-step explanation:

Answer:

15 $1 bills

10 $5 bills

10 $10 bills

Step-by-step explanation:

Let x = number of $1 bills

"There are five fewer $5-bills than $1-bills."

The number of $5 bills is x - 5

"There are half as many $10-bills as $5-bills."

The number of $10 bills is (x - 5)/2.

A $1 bill is worth $1.

x $1 bills are worth x × 1 = x dollars

A $5 bill is worth $5.

x - 5 $5 are worth 5(x - 5) dollars.

A $10 bill is worth $10.

(x - 5)/2 $10 bills are worth 10(x - 5)/2 = 5(x - 5) dollars.

Now we add the value of each type of bills and set it equal to $115.

x + 5(x - 5) + 5(x - 5) = 115

x + 10(x - 5) = 115

x + 10x - 50 = 115

11x = 165

x = 15

There are 15 $1 bills.

$5 bills: x - 5 = 10 - 5 = 10

There are 10 $5 bills

$10 bills: (x - 5)/2 = (15 - 5)/2 = 5

There are 5 $10 bills

Answer: 15 $1 bills; 10 $5 bills; 10 $10 bills

Check:

First, we check the total value of the bills.

15 $1 bills are worth $15

10 $5 bills are worth $50

10 $10 bills are worth $50

$15 + $50 + $50 = $115

The total does add up to $115.

Now we check the numbers of bills of each denomination.

The number of $1 is 15.

The number of $5 is 5 fewer that 15, so it is 10.

The number of $10 bills is half the number of $5 bills, so it is 5.

All the given information checks out in the answer. The answer is correct.

[tex]x[/tex] and [tex]3x+5[/tex] are being multiplied to form the expression, and are not being added or subtracted.

Here, x and (3x+5) are given in the form of multiplication, instead of being separated by addition or subtraction. This is why x and (3x+5) are factors of the expression x(3x + 5)² and not terms of the expression.

What are terms and factors in an expression?

Terms of an expression can be a variable, a signed number, or a constant multiplied by one or more variables. On the other hand, the factors are the items that have been multiplied by another items. Any integer, variable, phrase, or lengthier expression can be a factor.

For instance, the expression 2x(y - 5) has three components: 2, x, and (y-3). These three components are its factors, since when multiplied, they produce the same expression. The factors may or may not be comprised of more than one terms.

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The required answers are calculated by using the simple interest formula:

a. She needs to deposit $793.65 in the account each month

b. The total money she put into an account for a year is $285,714.29

c. The total interest she earns is $514,285.71

The formula for the simple interest is

A = P(1 + RT)

Where,

A - amount after T years

P - principal amount

R - the rate of interest

T - time (years)

It is given that,

A = 8,00,000

T = 30 years

R = 6% = 0.06

So,

a. Finding the amount needs to deposit in the account each month:

We have A = P(1 + RT)

⇒ P = A/(1 + RT)

On substituting,

P = 8,00,000/(1 + 0.06×30)

  = 8,00,000/2.8

  = $285,714.29(per year)

Thus, the amount needs to deposit in the account for each month

= P/T×12

= 285,714.29/30×12

= $793.65

b. Finding the total money that she put into account:

That is nothing but,

P = A/(1 + RT)

On substituting,

P = 8,00,000/(1 + 0.06×30)

  = 8,00,000/2.8

  = $285,714.29(per year)

c. FInding the total interest:

We have I = A - P

⇒ I = 8,00,000 - 285,714.29

∴ I = $514,285.71

Therefore, a. $793.65, b. $285,714.29, and c. $514,285.71

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width = 7

length = 10

Step-by-step explanation:

solve for the one letter that gets talked about the most

which is w or width

width = w

length = 3 + w

2 inch border means

width = w + 2

length = 3 + w + 2

area = length times width

area = ( 3 + w + 2 ) times (w + 2 )

108 = ( 3 + w + 2 ) times (w + 2 )

108 = ( w + 5 ) times (w + 2 )

( w + 5 ) times (w + 2 ) = 108

w^2 + 7w +10 = 108

w^2 + 7w - 98 = 0

going to make w = x

x^2+7x-98=0

(x-7)(x+14)

x = 7

x = -14

w=7

w= -14

cant have a negative measurement so w=7 is used

width = w

length = 3 + w

width = 7

length = 3 + 7 = 10