Hayley bought a bike that was on sale with a 15% discount from the original price of $142. If there is a 6% sales tax to include after the discount, how much did Hayley pay for the bike?

Answer:

8 cm

Step-by-step explanation:

x:y= 2:5

x/y = 2/5

5x = 2y

y is the longer side

5x=2(20)

x=8 cm

The length of the shorter side is 8 cm.

What is rectangle?

A rectangle more generally than any quadrilateral whose axes of symmetry pass through each pair of opposite sides.This definition includes both right-angled rectangles and rectangles. Each has an axis of symmetry that is parallel and equidistant from a pair of opposite sides and a second that is a perpendicular bisector of those sides, but in the case of a crossed rectangle the first axis is not the axis of symmetry of either side. . that it divides.

Quadrilaterals that have two axes of symmetry, each passing through a pair of opposite sides, belong to the larger class of quadrilaterals that have at least one axis of symmetry through a pair of opposite sides. These quadrilaterals consist of isosceles trapezoids and crossed isosceles trapezoids (crossed quadrilaterals with the same arrangement of vertices as an isosceles trapezoid).

Given, sides of a rectangle are in ratio 2:5.

Let length of a rectangle be 5x cm and breadth of a rectangle be 2x cm.

We know length of a rectangle is longer than breadth.

So, length of the rectangle is 20 cm.

According to question,

[tex]5x = 20 \\ x = \frac{20}{5} \\ x = 4[/tex]

So, length of the rectangle (5×4) = 40 cm and breadth of the rectangle (2×4) = 8 cm.

Breath is shorter side of rectangle.

Therefore,The length of the shorter side is 8 cm.

Rectangle related one more question:

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Answer:

y = 4x + 21

Step-by-step explanation:

Hello!

Point-slope form is y - y1 = m(x - x1)

y1 is the y point

x1 is the x point

m is the slope

Put in what you know

y - -3 = 4(x - -6)

Subtracting a negative is the same as adding

y + 3 = 4(x + 6)

Distribute the 4

y + 3 = 4x + 24

Subtract 3 from both sides

y = 4x + 21

The answer is y = 4x + 21

Hope this helps!

Answer:

In the error term.

Step-by-step explanation:

A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).

Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.

Answer:

APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

yes E

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

Answer:

B. More

Step-by-step explanation:

This is according to the law of large numbers

An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.

Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.

An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed

Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.

Learn more about probability here:

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Answer:

$3,717

Step-by-step explanation:

Hello, in 1 year there are 12 months.

Let's note I the Initial amount.

So, after 1 month we will get the following, because we compute the interest amount for one month only.

I * ( 1 + 6% * (1/12) )

And the next month, we will have interest of the amount available from previous month so it gives

[tex]I * ( 1+6\% * \dfrac{1}{12} ) * ( 1+6\% * \dfrac{1}{12} ) \\\\=I*(1+\dfrac{6}{12*100})^2\\\\=I*(1+\dfrac{1}{200})^2\\\\=I*(1.005)^2[/tex]

... and after n months ...

[tex]I*(1.005)^n[/tex]

8 years is 8*12 = 96 months. so we are looking for I such that

[tex]I*(1.005)^{96}=6000\\\\<=> I =\dfrac{6000}{1.005^{96}}\\\\=\boxed{3717.14345....}[/tex]

Thank you.

Answer:

Step-by-step explanation:

Given x = 5, y = 3/4 and z = -1/7, 2=we are to calculate [tex]\frac{xz}{y}[/tex]. Substituting the value of x, y and z into the expression will give;

[tex]= \frac{xz}{y}\\\\ \frac{5(-1/7)}{3/4} \\= \frac{-5/7}{3/4}\\\\= \frac{-5}{7} * \frac{4}{3}\\ \\ = \dfrac{-20}{21}\\[/tex]

Hence the value of the expression is -20/21

[tex]\text{Solve the systems of equations:}\\\\2y+7x=-5\\5y-7x=12\\\\\text{Solve by adding and subtracting}\\\\7y=7\\\\\text{Divide}\\\\y=1\\\\\text{To find x, plug 1 into y in one of the equations and solve:}\\\\2(1)+7x=-5\\\\2+7x=-5\\\\\text{Subtract 2 from both sides}\\\\7x=-7\\\\\text{Divide by 7}\\\\x=-1\\\\\boxed{y=1\,\,and\,\,x=-1}[/tex]

Answer:

[tex]a = 6m/s^2[/tex]

Step-by-step explanation:

Given

When mass = 4kg; Acceleration = 15m/s²

Required

Determine the acceleration when mass = 10kg, provided force is constant;

Represent mass with m and acceleration with a

The question says there's an inverse variation between acceleration and mass; This is represented as thus;

[tex]a\ \alpha\ \frac{1}{m}[/tex]

Convert variation to equality

[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)

Make F the subject of formula;

[tex]F = ma[/tex]

When mass = 4kg; Acceleration = 15m/s²

[tex]F = 4 * 15[/tex]

[tex]F = 60N[/tex]

When mass = 10kg; Substitute 60 for Force

[tex]F = ma[/tex]

[tex]60 = 10 * a[/tex]

[tex]60 = 10a[/tex]

Divide both sides by 10

[tex]\frac{60}{10} = \frac{10a}{10}[/tex]

[tex]a = 6m/s^2[/tex]

Hence, the acceleration is [tex]a = 6m/s^2[/tex]

Answer:

C.

Step-by-step explanation:

[tex]\frac{7x}{3y}+\frac{12x}{9y}[/tex]

We can reduce the second term:

[tex]\frac{7x}{3y} +\frac{4x}{3y}[/tex]

Since they now have a common denominator, we can add them:

[tex]=\frac{7x+4x}{3y}=11x/3y[/tex]

The answer is C.

So, yes, you're answer was correct!

Answer:

[tex] \sqrt{4 {}^{2} + ( - 4) {}^{2} } [/tex]

[tex] \sqrt{32} [/tex]

and the angle

[tex] \tan( \alpha ) = - 4 \div 4 = - 1[/tex]

and since the sin component is -ve, we have our angle on 4th quadrant, which equals 315 degrees

Options:

Determine two pairs of polar coordinates for the point (-4, 4) with 0° ≤ θ < 360°. (5 points)

Group of answer choices

(4  , 135°), (-4  , 315°)

(4  , 45°), (-4  , 225°)

(4  , 315°), (-4  , 135°)

(4  , 225°), (-4  , 45°)

Step-by-step explanation:

The guy asking forgot to provide the options you can comment the awnswe in the comments just do it before brainly turns off comments to try and prevent people from learning

Answer:

(1+y^2) /2y

Step-by-step explanation:

arithmetic mean is the average of x and y

(x+y)/2

Using the equation

xy = 1

and solving for x

x = 1/y

Replacing x in the first equation

(1/y + y) /2

Multiply by y/y

(1/y + y) /2 * y/y

(1/y + y)*y /2y

(1+y^2) /2y

Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.

The value of the y-intercept is 9.

Step-by-step explanation:

Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]

[tex]=\dfrac{8}{2}=4[/tex]

So, the slope of the line that passes through (2, 12) and (4, 20) is 4.

To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).

[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]

By comparison,  c= 9

Hence, the value of the y-intercept is 9.

Answer:

$215,892.50

Step-by-step explanation:

This is a problem of compound interest.

In compound interest Amount A for principal p charged at interest r% per annum is given by

A = p(1+r/100)^n

where n is the time period in years.

_____________________________

given

p = $100,000

r = 8%

t = 10 years

A= 100,000( 1+ 8/100)^10

A= 100,000( 1.08)^10

A = $215,892.50

So , you need to pay $215,892.50 in total to debt cleared of debt.

Answer:

17,720 ft

Step-by-step explanation:

5.4 km * (1 mile)/(1.609 km) * (5280 ft)/(1 mile) = 17,720 ft

Answer:

=Vlookup'B13' A11' 7'false

Press enter.

Step-by-step explanation:

Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:

=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.

where true is approximate match and false is exact match.

Answer:=VLOOKUP(J2,A2:G23,2,FALSE)

Step-by-step explanation:

a. In cell J3, begin to enter a formula using the VLOOKUP function.

b. Use the Project ID (cell J2) as the lookup value.

c. Use the Projects table (range A2:G23) as the table_array.

d. Use the Project Name column (column 2) as the col_index_num.

e. Specify an exact match (FALSE) for the range_lookup.

Answer:

The exact distance is [tex]\sqrt{109}[/tex] miles.

The distance is approximately 10.4 miles.

Step-by-step explanation:

It is given that a rectangular city is 3 miles long and 10 miles wide. So,

Length = 3 miles

Width = 10 miles

We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.

Using Pythagoras theorem, the length of diagonal is

[tex]d=\sqrt{l^2+w^2}[/tex]

where, l is length and w is width.

Substitute l=3 and w=10.

[tex]d=\sqrt{(3)^2+(10)^2}[/tex]

[tex]d=\sqrt{9+100}[/tex]

[tex]d=\sqrt{109}[/tex]

The exact distance is [tex]\sqrt{109}[/tex] miles.

Now,

[tex]d=\sqrt{109}[/tex]

[tex]d=10.4403065[/tex]

[tex]d\approx 10.4[/tex]

The distance is approximately 10.4 miles.

Answer:

1/4 miles

Step-by-step explanation:

Hey there!

Well starting at Campbell and going to Morristown it is 1/4 miles.

Going from Campbell to Clarksville it is 2/4 miles.

So to find the difference we’ll subtract.

2/4 - 1/4

= 1/4 miles

Hope this helps :)

Answer:

El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.

Step-by-step explanation:

Sea [tex]c[/tex] el coste máximo que puede asumir el comensal, medido en pesos, el cual es representada por la siguiente suma:

[tex]c = c_{o} + c_{i} + c_{ii}[/tex]

Donde:

[tex]c_{o}[/tex] - Coste del consumo, medido en pesos.

[tex]c_{i}[/tex] - Coste del impuesto en el condado, medido en pesos.

[tex]c_{ii}[/tex] - Coste de la propina, medido en pesos.

Ahora, los costes por impuesto y por propina se determinan en función del coste de consumo:

Coste del impuesto en el condado

[tex]c_{i} = r_{i}\cdot c_{o}[/tex]

Donde [tex]r_{i}[/tex] es la razón entre el coste del impuesto en el condado y el coste del consumo, adimensional.

Coste de la propina

[tex]c_{ii} = r_{ii}\cdot (c_{o}+c_{i})[/tex]

[tex]c_{ii} = r_{ii}\cdot (c_{o}+r_{i}\cdot c_{o})[/tex]

[tex]c_{ii} = r_{ii}\cdot (1 + r_{i})\cdot c_{o}[/tex]

Donde [tex]r_{ii}[/tex] es la razón entre el coste de la propina y la suma de los costes de consumo y del impuesto del condado, adimensional.

Entonces, la suma completa queda representada por:

[tex]c = c_{o} + r_{i}\cdot c_{o}+r_{ii}\cdot (1+r_{i})\cdot c_{o}[/tex]

[tex]c = [1+r_{i}+r_{ii}\cdot (1+r_{i})]\cdot c_{o}[/tex]

A continuación, se despeja el coste de consumo (valor máximo de los platos):

[tex]c_{o} = \frac{c}{1 +r_{i}+r_{ii}\cdot (1+r_{i})}[/tex]

Si [tex]c = \$\,25[/tex], [tex]r_{i} = 0.07[/tex] y [tex]r_{ii} = 0.15[/tex], entonces:

[tex]c_{o} = \frac{\$\,25}{1+0.07+0.15\cdot (1+0.07)}[/tex]

[tex]c_{o} = \$\,20.32[/tex]

El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.

Answer:

B) 5

Step-by-step explanation:

Proportions:

8 ⇒ 10

20 ⇒ 5x

5x = 20*10/8

5x = 25

x = 25/5

x = 5

Answer: C

Step-by-step explanation:

Since this is an isosceles triangle as indicated by the markers on QP and PR, we know that QS and SR are equivalent.

To find the value of n, we set QS and SR equal to each other.

6n+3=4n+11                     [combine like terms]

2n=8                                 [divide both sides by 2]

n=4

Now that we know n=4, we know that A is incorrect. What we can do is use the value of n to solve for QS, SR, and QR.

QS

6(4)+3=13

Since the length of QS is 13, we know B is incorrect.

SR

4(4)+11=27

Since SR is 27, C is a correct answer.

QR

13+27=40

Since QR is 40, the only correct answer is C.

Answer:

There has been no significant change in the number of students in each major between the last school year and this school year.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: There has been no change in the number of students.

Hₐ: There has been a significant change in the number of students.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

Here,

[tex]O_{i}[/tex] = Observed frequencies

[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.

The chi-square test statistic value is, 1.662.

The degrees of freedom is:

df = 4 - 1 = 4 - 1 = 3

Compute the p-value as follows:

[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]

*Use a Chi-square table.

The  p-value is 0.645.

The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.

Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.

Answer:

x = 450

510/170 = 3

x/150 = 3

x = 450

Answer:

X=450 is the answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the question we use the following conversion

1 feet per second = 1.09728 kilometers per hour

Therefore 11 ,000 feet per second is

[tex]11000 \times 1.09728[/tex]

We have the final answer as

Hope this helps you

Answer:

t >± 1.895

t= 0.1705

Step-by-step explanation:

The null and alternative hypotheses are

H0: μd=0 Ha: μd>0

Significance level is set at ∝= 0.05

The critical region for  t  df=7       t >± 1.895

The test statistic under H0 is

t = d/ sd/ √n

Which has t distribution with n-1 degrees of freedom

Employee        After  Before         d = after - before        d²

1                          6         5               1                                  1

2                         6          2               4                               16

3                         7          1                6                               36

4                         7           3              4                               16

5                         4          3              1                                 1

6                         3          6              -3                               9

7                         5          3              2                               4

8                          6        7               -1                                1      

∑                                                    14                              84    

d`= ∑d/n= 14/8= 1.75

sd²= 1/8( 84- 14²/8) = 1/8 ( 84 - 24.5) = 59.5

sd= 7.7136

t= 3/ 7.7136/ √8

t= 0.1705

Since the calculated value of t= 0.1705 < ± 1.895  therefore reject the null hypothesis at 5 % significance level . On the basis of this we cannot conclude that the number of absences has declined.

Answer:

3x+19

Step-by-step explanation:

Let x be the unknown number

triple means 3 times

sum means add

3x+19

Answer:

2 servings of salad and 1 serving of soup

Step-by-step explanation:

In the given scenario the aim is to minimise the fat content of the food combination.

Fat content of soup is 3mg while fat content of salad is 2 mg.

Using Soup as 0 and Salad as 2 will not give the required vitamin content

The logical step will be to keep servings of soup to the minimum.

Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1

1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.

This will not work because amount of vitamin B complex is not up to 10 mg

2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat

This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.

Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving