The Broad Street subway line express train stops at city hall every 9 minutes. The local train stops at the station every 12 minutes. If you arrived at the station just as both trains left, how long will you have to wait until they both arrive at the same time again?

Answer:

x = 200

Step-by-step explanation:

Given equation:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30[/tex]

Steps:

1. Substitute 15 as the value of y in the equation:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\Rightarrow \dfrac{1}{5}x-\dfrac{30}{3}=30\ \textsf{[ simplify ]}\\\\\Rightarrow \dfrac{1}{5}x-10=30[/tex]

2. Add 10 to both sides:

[tex]\sf \dfrac{1}{5}x-10+10=30+10\\\\\Rightarrow \dfrac{1}{5}x=40[/tex]

3. Multiply both sides by 5 to isolate x:

[tex]\sf 5\left(\dfrac{1}{5}\right)x=5(40)\\\\\Rightarrow x=200[/tex]

4. Check your work:

[tex]\sf \dfrac{1}{5}x-\dfrac{2}{3}y=30\ \textsf{[ substitute 200 for x, and 15 for y ]}\\\\\dfrac{1}{5}(200)-\dfrac{2}{3}(15)=30\ \textsf{[ multiply ]}\\\\\dfrac{200}{5}-\dfrac{30}{3}=30\ \textsf{[ divide ]}\\\\40-10=30\ \textsf{[ subtract ]}\\\\30=30\ \checkmark[/tex]

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Hey there!

[tex] \boxed{\bold{\green{ x = 200}}} [/tex]

[tex] \\ [/tex]

Given expression :

[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{y} = 30 } [/tex]

1) Substitue 15 for [tex] \sf{\orange{y}} [/tex] :

[tex] \sf{ \frac{1}{5} \green{x} - \frac{2}{3} \orange{ \times 15} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - \frac{30}{3} = 30 } \\ \\ \implies\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]

[tex] \\ [/tex]

2) Solve for x :

[tex]\sf{ \frac{1}{5} \green{x} - 10= 30 } [/tex]

⇢Add 10 to both sides of the equation :

[tex]\sf{ \frac{1}{5} \green{x} - 10 \: \bold{+ \: 10}= 30 \: \bold{+ \: 10 }} \\ \\ \implies \sf{\frac{1}{5} \green{x} \: = 40 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

⇢Multiply both sides of the equation by 5:

[tex] \Big( \dfrac{1}{5} \green{x}\Big) \: \bold{ \times \: 5}=40 \: \bold{ \times \: 5} \\ \\ \implies \sf{\dfrac{5}{5} \green{x} \: = 200} \\ \\ \implies \green{ \boxed{\sf{x = 200}}}[/tex]

[tex] \\ [/tex]

3) Let's check our answer by replacing [tex] \green{x} [/tex] with 200 and [tex] \orange{y} [/tex] with 15 :

[tex] \sf{\dfrac{1}{5}\overbrace{\green{\times \: 200}}^{\green{x}} - \dfrac{2}{3}\underbrace{\orange{\times \:15}}_{\orange{y}}= \dfrac{200}{5} - \dfrac{30}{30} = 40 - 10 = \boxed{ 30} } [/tex]

[tex] \\ \\ [/tex]

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The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth if  you have $1000 and need to buy 10 chairs worth $5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that you have $1000 and need to buy 10 chairs worth $5. Let x represent the money that can be spent on the booth, hence:

x + 10(5) ≤ 1000

The inequality x + 10(5) ≤ 1000 shows how much money you can spend on the booth, if you have $1000 and need to buy 10 chairs worth $5.

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The number of eggs sold on Tuesday is 2 complete circles, while the number of eggs sold on Wednesday is 2 complete circles and 1 quarter of the circle.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

Given on Monday the shop sold 18 eggs. Therefore, each quarter of the circle represents 3 eggs.

Hence, the number of eggs sold on Tuesday is 2 complete circles, while the number of eggs sold on Wednesday is 2 complete circles and 1 quarter of the circle.

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Answer:

2x^3 - 3x^2 + 7x - 3

Step-by-step explanation:

Area = length * width

= (2x - 1)(x^2 - x + 3)

= 2x(x^2 - x + 3) - 1(x^2 - x + 3)

= 2x^3 - 2x^2 + 6x - x^2 + x - 3

= 2x^3 - 3x^2 + 7x - 3

The area of the rectangle is 64.8 square .inch

A rectangle is a polygon with four sides , opposite sides are parallel and equal.

It is given that

A rectangle is divided into exactly 20 congruent squares

If they are lined up the Length is 36 inches

Therefore the length of each square or the side of the square = 36/20

= 1.8 inch

The area of the rectangle will be

20* Side of square * Side of square

=20*1.8*1.8

= 64.8 square inch

The area of the rectangle is 64.8 square .inch

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The shortest height of the box that will hold the map is 6 ft option (C) is correct.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have:

Dina is shipping a wall map to a collector. When the map is rolled up, it measures.

From the figure we can apply the Pythagoras theorem to find the length BA:

BA² = 3² + 3²

BA = √18

Again applying Pythagoras theorem:

The height

AD² = 7² - (√18)²

AD² = 31

AD = √31 ft = 5.56 ft ≈ 6 ft

Thus, the shortest height of the box that will hold the map is 6 ft option (C) is correct.

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Answer:

-1

Step-by-step explanation:

Let the points be (0, a) and (a, 0) (As it mentions the intercepts are equal)

==============================================================

Applying slope formula :

⇒ m = 0 - a / a - 0

⇒ m = -a/a

⇒ m = -1

Answer:

Step-by-step explanation:

let r be the radius of the circle.

→ We know that in circle , the length of an arc

and the corresponding central angle are proportional.

180 corresponds to πr

120 corresponds to 10π

Then

[tex]\frac{\uppi r}{180} =\frac{10\uppi }{120}[/tex]

[tex]\Longrightarrow r=\frac{180\times 10\pi }{120\pi } =\frac{180}{12} =15[/tex]

Answer:

the answer is in picture

Step-by-step explanation:

hope it will help you

Answer:

The arrows on the line segments mean that the lines are parallel.

⇒ EB ║ DC

Therefore, according to Triangle Proportionality Theorem, EB divides the two sides AD and AC proportionally.

Therefore:

[tex]\begin{aligned}\sf \dfrac{AE}{AD} & = \sf\dfrac{AB}{AC}\\\\ \implies \sf \dfrac{10}{10+8} & = \sf \dfrac{x}{10}\\\\ \sf \dfrac{10}{18} & = \sf \dfrac{x}{10}\\\\ \sf 10 \cdot 10 & = \sf 18x\\\\\sf 100 & = \sf 18x\\\\ \sf x & = \sf \dfrac{100}{18}\\\\ \sf x & = \sf 5.5555...\end{aligned}[/tex]

As x = 5.55555... round to 5.6 to the nearest tenth,
none of the choices are correct.

Let's see

Use Thales theorem

[tex]\\ \rm\Rrightarrow \dfrac{AE}{AD}=\dfrac{AB}{AC}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{10}{10+8}=\dfrac{x}{10}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{10}{18}=\dfrac{x}{10}[/tex]

[tex]\\ \rm\Rrightarrow 18x=100[/tex]

[tex]\\ \rm\Rrightarrow x=5.56[/tex]

NOTA

Answer:

6.5

Step-by-step explanation:

Median is always the middle number of the set of data, so lets re order the numbers least to greatest

1,2,4,5,6,7,8,8,9,12

Since there's an even amount there wont be an exact middle number, however we know its in-between 6 and 7. So we can do 6+7 = 13 and then 13/2 = 6.5 to get the middle number or median.

Answer:

30.34 degree

Step-by-step explanation:

Apply sine formula

[tex]\frac{sin\left(A\right)}{a}=\frac{sin\left(B\right)}{b}[/tex]

[tex]\frac{\sin \left(45^{\circ \:}\right)}{7}=\frac{\sin \left(b\right)}{5}[/tex]

->simplify

[tex]\frac{\sin \left(b\right)}{5}=\frac{\frac{\sqrt{2}}{2}}{7}[/tex]

you will get

[tex]\sin \left(b\right)=\frac{5\sqrt{2}}{14}[/tex]

which
sin b is about 0.50507

[tex]sin^{-1}\left(0.50507\right)[/tex]

->arc sine in degree mode

the answer is 30.34

If the standard deviation of an exam is 5, the z-score us 1.95 and the mean is 80, the actual test score is; 89.75

We are given;

Standard deviation; s = 5

z-score = 1.95

Mean = 80

Formula for z-score is;

z = (x' - μ)/σ

Thus;

1.95 = (x' - 80)/5

1.95 * 5 = (x' - 80)

9.75 = x' - 80

x' = 80 + 9.75

x' = 89.75

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By taking a quotient between the number of packages and the rate at which James works, we conclude that he will need 467 hours.

We know that James wraps at a rate of 8 packages in one hour. Then to get the time in which he can wrap a number N of packages, we need to take the quotient between N and 8.

In this case, N = 3,736.

Taking the quotient we get:

3,736/8 = 467

This means that in 467 hours he will wrap the 3,736 packages.

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Answer: x = log₃₇(12)

Step - by - step explanation:

1. Remove the variable from the exponent using logarithms

37^x=12

Take the common logarithm of both sides of the equation:

log₁₀(37^x)=log₁₀12)

Use the log rule:  log_a(x^y)=y*log_a(x) to move the exponent outside the logarithm:

x*log₁₀(37)=log₁₀(12)

2. Isolate the x-variable

x*log₁₀(37)=log₁₀(12)

Divide both sides of the equation log₁₀(37) by:

x = log₁₀(12) / log₁₀(37)

Use the formula  [tex]log_{b}(x)/log_{b}(a) = log_{a} (x)[/tex]

to combine the logarithms into one:

x=log₃₇(12)

Decimal form:

x=0.6881648129099501

Hope this helps!

Answer:

22 pages per hour.

Step-by-step explanation:

5.5/15 = 0.36666

0.36666 * 60 = 22

The proportion of sophomores that do not own a car is equal to 0.93.

Ratio is a mathematical expression that is used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

The proportion of sophomores that do not own a car is given by:

Therefore, proportion = 398/427 = 0.93.

The proportion of all students who are seniors who own cars is given by:

Therefore, proportion = 123/1192 = 0.10.

The proportion of non-car owners who are juniors is given by:

Therefore, proportion = 339/976 = 0.35.

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Complete Question:

At Central High School, there are 398 sophomores who do not own a car and 29 who do. There are 64 juniors who own a car and 339 who do not. There are 123 seniors who own a car, compared to 239 who do not. The above is a two-way table depicting this situation. Complete the following statements below by finding the ratio, then converting to a decimal. Round to the nearest hundredth.

The proportion of sophomores that do not own a car is?

The proportion of all students who are seniors who own cars is?

The proportion of non-car owners who are juniors is?

1. 20,000×10%=2,000

2. 20,000×14%=2,800

3. 20,000×5%=1,000

4. Business Marketing

5. 20,000×30%=6,000

The wrong conclusions that can be drawn from the circle graph are:

The Country section has the smallest area.

The Classical section is not included in the Circle Graph.

A circle graph is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees

In the circle graph, the country section has a percentage of 10% while the classical section has a percentage of 2%.

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Answer:

the answer is D  

Step-by-step explanation:

look at the table there are 5 music genres but there's only 4 on the circle graph.

The correct true statement is: b.  The swimmer comes back up 9 seconds after the timer was started.

Given:

h(t)=t^2−12t+27

Let velocity of the function= 0

h(t) = 2t - 12

0 = 2t - 12

2t = 12

Divide both side by 2t

t=12/2

t = 6secs

Substitution

h(6) = 6²-12(6)+27

h(6) = 36 - 72 + 27

h(6) = -36 + 27

h(6) = -9 feet

The correct statement is b.

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Using a calculator, it is found that the equation of linear regression that fits the data is given by:

C. y=-0.295x+20.667

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points are given as follows: (1, 20.71), (2, 19.69), (3, 19.61), (4, 19.64), (5, 19.26). Hence the equation is:

Doing this, the equation is:

y = -0.295x + 20.667.

Hence option C is correct.

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Answer:

Option A: Linear Regression

Step-by-step explanation:

The sale values do not increase in a quadratic or exponential function.

Answer:

132°

Step-by-step explanation:

We use the circle theorem which states that :

Opposite angles in a cyclic quadrilateral add up to 180 .

Now we know that angles ADC and ABC add up to 180. So :

We make an equation and solve for x :

x+(3x-12) = 180

4x-12 = 180

4x = 192

x = 48

Now we substitute the value of x into Angle B :

3(48) -12 =

144 - 12 = 132

Angle B = 132 °

Hope this helped and have a good day

Answer:

C. 1

Step-by-step explanation:

this is how you solve it

Answer:

see explanation

Step-by-step explanation:

the centroid is where the medians intersect.

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

(3)

GF = [tex]\frac{1}{2}[/tex] CG = [tex]\frac{1}{2}[/tex] × 14 = 7

CF = CG + GF = 14 + 7 = 21

(4)

GD = [tex]\frac{1}{3}[/tex]  AD = [tex]\frac{1}{3}[/tex] × 45 = 15

AG = 2 × GD = 2 × 15 = 30

(5)

GE = 2 × BG , that is

9x = 2(3x + 6) = 6x + 12 ( subtract 6x from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Answer:

Radius=4 units

Centre= (0,-10)

Step-by-step explanation:

Given equation of circle is x^2 +(y-10)^2=16

Comparing it with (x-h)^2 +(y-k)^2 = r^2 ,we get,

r=4

Since, centre of a circle=(h,k)=(0,-10)

Answer:

Center (0;10) Radius= 4. Make me brainliest? :(

Step-by-step explanation:

[tex](x + 0)^{2} + (y - 10)^{2} = 16 \\ center(0.10) \\ radius = \sqrt{16} = 4[/tex]

Answer:

Rational numbers is a ratio (i.e., P/Q and Q≠0)

Irrational numbers cannot be expressed as a fraction.

so a

Rational numbers can show a Fraction

Irrational numbers can not show a Fraction

Hope This Helped

Answer:

Rational numbers are any infinite number or ratio that goes on and on and represents such mathematical values, e.g five-over-twelve is a rational number because it is a fraction.

Irrational numbers are squares of a number or any number that does not include a comparison(e.g division, fraction, ratio, etcetera) of a value. For instance, the square root of 2 is an irrational number because it does not go on indefinitely.

The amount of money that Suzie will make over the four weeks is; $1856

Suzie will make a profit of:

The first week =  $300

The second week =  (300 * 30%) + 300 = $390

The third week = 390 * (1430%) = $507

The fourth week: 507 × (1430%) = $659.1

Thus, Sum of profit = $300 + $390 + $507 + $659.1

Sum of Profit = $1856.1 ≈ $1856

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