Great Escape bought a vintage bicycle for $3,000. They marked it up 43.3% to sell in their store. Then, they ran a sale for 30% off. What was the discount price of the bicycle?

The interest accrued in the first four years is $1.69 and a half years is $0.21.

What is interest rate?

The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given:

Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college.

The rate is 4.3%.

We have to find the interest accrued in the first four-and-a-half years.

First to find the interest for first four years.

p = $9.800,  r  = 4.3% = 0.043,  t = 4

⇒ I = P x r x t

   I = 9.800 x 0.043 x 4

   I = 1.6856

   I = $1.69

Now to find the interest for a half years.

p = $9.800 ,  r = 4.3% = 0.043,  t = 1/2

I = p x r x t

I = 9.800 x 0.043 x 1/2

I = 0.2107

I = $0.21

Hence, the interest accrued in the first four years is $1.69 and a half years is $0.21.

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9 pounds of the $50 coffee should be used

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

let's let p = the pounds of coffee we need.

50p + 80(20) = 6(p+ 20)

The total price of the $50 coffee is going to be the pounds x price per pound. The total amount of coffee is the number of pounds of each added together.

From the equation above 50p + 80(20) = 60(p+ 20)

expanding the brackets and collecting like terms

50p + 1600 = 6p + 120

50p - 6p = 1200 - 1600

44p= 400

p= 9

Therefore, 9 pounds of  $50 coffee should be used

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Answer:

1. 15cm,

2. 22.5ft

3. 24in

4. 24.2m

5. 8.9m

Step-by-step explanation:

1. √(9²+12²) = 15cm

2. √(8²+21²) = 22.47 ft = 22.5ft

3. 7²+x²=25²

x =√(25²-7²) = 24 in

4. √(15²+19²) =24.2 m

5. √(4²+8²) = 8.9m

all the answers related to the pythogorus theorem.

a²+b²=c²

in which a and b are the legs of the right angled triangle where c is the hypotenuse.

note: be careful abt the units.

To determine if the mean reduction in blood pressure is different between the two groups, you can use a statistical test such as a two-sample t-test. This test compares the means of two groups and determines whether the difference between the means is statistically significant.

To conduct the t-test, you will need the following information:

Once you have this information, you can use a statistical software or calculator to perform the t-test and determine the p-value. The p-value is a measure of the probability that the difference between the means is due to chance.

If the p-value is less than the level of significance (5% in this case), then the difference between the means is statistically significant and you can conclude that there is a significant difference in the mean reduction in blood pressure between the two groups.

If the p-value is greater than the level of significance, then the difference between the means is not statistically significant and you cannot conclude that there is a difference in the mean reduction in blood pressure between the two groups.

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The probability of selecting a white rabbit on the second draw, given that the first rabbit selected was a black rabbit is 3/5.

P(B∩W) = 1/4  getting a black and a white rabbit

P(B) = 5/12  getting a black rabbit

 P(W/B)

= P(B∩W) / P(B)

= (1/4) / (5/12)

= 12/20

= 3/5

Therefore, the conditional probability is 3/5.

Conditional probability is the chance of an event A occurring when another event B in relation to A has previously occurred. P(A|B) represents it. As seen in the picture above, S represents sample space, and A and B represent events.

The potential of an event or outcome occurring based on the existence of a preceding event or outcome is known as conditional probability. It is computed by multiplying the preceding event's probability by the renewed probability of the next, or conditional, occurrence.

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Answer:

Positive, two-tailed

Step-by-step explanation:

Answer:

½

pa brainliest po thanks

Answer:

Step-by-step explanation:

6 small rectangles, 3 are shaded and three are not, so half,

your answer is 1/2 (one half)

After doing the equation the original price of the tie is $20.

What do you mean by algebraic expression?

An algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression can be a combination of variables and constants. Anything that is prepended to a variable and multiplied by it is a coefficient.

It is given that Duke bought the shirt and tie at half off rate.

Cost of shirt = $24

Total money paid by Duke = $22

Let cost of tie be x

According to question:

[tex]24\times \frac{1}{2}+ x\times \frac{1}{2}=22[/tex]

12 + [tex]x\times \frac{1}{2}[/tex] = 22

[tex]x\times \frac{1}{2}[/tex] = 22 - 12

x = 10 × 2

x = 20

Therefore , cost of tie is $20.

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Observing the nature of the provided equation and the degree of the polynomial , The answer is Cubic.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The highest degree of a polynomial's monomials (individual terms) with non-zero coefficients is referred to as the polynomial's degree in mathematics.

Expression : [tex]8x^{3}-1[/tex]

Degree of polynomial =3

The expression is a Cubic Expression.

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Observing the nature of the provided equation and the degree of the polynomial , The answer is Cubic.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The highest degree of a polynomial's monomials (individual terms) with non-zero coefficients is referred to as the polynomial's degree in mathematics.

Expression : 8x³ - 1

Degree of polynomial =3

The expression is a Cubic Expression.

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Step-by-step explanation:

for question 1, the change in y is the highest value takeaway the lowest value.

change in y = 10 - 1 = 9

change in x = 6 - (-3) = 9

9/9 = 1

therefore m = 1, this works for all the questions

By using trigonometry, it can be calculated that -

cos B = 0.555

What is Trigonometry?

Trigonometry is a branch of mathematics that studies the relationships between angles and sides of triangles. It is used to solve problems involving lengths and angles of triangles, as well as circles and other shapes. Trigonometry is used in physics, engineering, and astronomy, and it has applications in the fields of navigation, surveying, and seismology. Trigonometry is based on the study of ratios and inverse functions, and it can be used to calculate the area of a triangle and its angles.

There are six trigonometrical functions. They are

[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]

Trigonometry is a very important tool in mathematics.

Here, trigonometry will be used

sin A = 0.555 cos A = 0.832

A + B = 90

B = 90 - A

cos B = cos(90 - A) = sin A = 0.555

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The number of country A forces in country B decreased to approximately 34,000 in 2014 from a high of about 10,000 in 2008. X represents the number of years after January 2007, this means that the amount of funding was approximately $10.5 billion in the year 2.135 years after January 2007, or approximately September 2009.

Generally, To find the year in which the amount of funding was approximately $10.5 billion, we need to solve the equation:

f(x) = 10.5

Substituting the given function for f(x), we get:

-1.384x^{2} + 5.253x + 5.517 = 10.5

We can solve this quadratic equation by using the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

where a = -1.384, b = 5.253, and c = 5.517.

Substituting these values into the formula, we get:

[tex]x = \frac{5.253 \pm \sqrt{5.253^2 - 4(-1.384)(5.517)}}{2(-1.384)}[/tex]

Simplifying this expression gives us:

[tex]x = \frac{5.253 \pm \sqrt{27.747029}}{-2.768}[/tex]

Since x represents the number of years after January 2007, we are only interested in the positive solution. Therefore, we can ignore the negative solution.

[tex]x = \frac{5.253 + \sqrt{27.747029}}{-2.768}[/tex]

Simplifying this expression further gives us:

x = 2.135

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40 miles will he have after 85 minutes of driving .

Given :

austin is driving to san francisco, suppose that the distance to his destination in miles is a linear function of total driving time. has 67 miles to his destination after 49 minutes of driving . He has 47.5 miles to his destination after 75 minutes of driving .

slope = y2  - y1  / x2 - x1

m = 47.5 - 67 / 75 - 49

= -19.5 / 26

= -3/4

= -0.75

Use the point slope y - y1 = m(x - x1)

y - 67 = -.75 ( x - 49 )

y - 67 = -.75x + 36.75

y = -.75x + 36.75 + 67

y = -.75x + 103.75

x = 85

y = -.75(85) + 103.75

y = -63.75 + 103.75

y = 40 miles  

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Full question :

austin is driving to san francisco, suppose that the distance to his destnation in miles is a linear function of total driving time  has 67 miles to his destination after 49 minutes of driving . He has 47.5 miles to his destination after 75 minutes of driving . How many miles will he have after 85 minutes of driving ?

Answer:

yes

Step-by-step explanation:

By using probability, it can be calculated that-

Probability that the next chew Gianna removes from the bag will be cherry chew = 42.86%

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here, number of times an experiment is performed = 49

A pineapple chew was selected 25 times.

A cherry chew was selected 21 times.

A lime chew was selected 3 times.

Probability that the next chew Gianna removes from the bag will be cherry chew = [tex]\frac{21}{49} = \frac{3}{7}[/tex]

         = [tex]\frac{3}{7} \times 100[/tex]

         = 42.86%

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Answer:m

Step-by-step explanation:

1. The required amount y after t years is as shown below:

When t=1,  y=74550

When t= 5, y = 88750

When t= 10, y = 106500

When t= 15, y = 124250

When t= 20, y = 142000

2. The required amount y after t years is as shown below:

When t=1, y = 73840

When t= 5, y = 86382.35607  

When t= 10, y = 105097.3442

When t= 15, y = 127866.988

When t= 20, y = 155569.743

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

1. x = 71000

  r =  3550

Use the below formula to find amount y after t years

y = x+( rt )

When t=1,   y= 71000 + ( 3550 * 1) = 74550

Similarly,  

When t= 5, y = 88750

When t= 10, y = 106500

When t= 15, y = 124250

When t= 20, y = 142000

2.  4% = 0.04

Use the below formula to find amount y after t years

y = x *( 1 + r )^ t

=> y = 71000*( 1.04)^t

When t=1,   y= 71000 * ( 1.04)^1 = 73840

Similarly,  

When t= 5, y = 86382.35607  

When t= 10, y = 105097.3442

When t= 15, y = 127866.988

When t= 20, y = 155569.743

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The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.

The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.

The given statement for the problem is, " 20 divided by 1 plus 4".

It can be written in the form of expression as follows,

The sign of plus is given as '+'.

And, for divide it is '÷'.

Now, 20 divided by 1 plus 4 can be written as,

20 ÷ 1 + 4

Which is evaluated  by BODMAS to give,

20 + 4 = 24.

Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.

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c. A greater proportion of adolescent girls with anorexia nervosa live in the South than live in the other regions when compared to the general US population.

Null Hypothesis, [tex]H_{0}[/tex] : All proportions are the same  

Alternative Hypothesis, [tex]H_{1}[/tex]: At least two of the proportions are not the same

The alternative and null are both population-based assertions. The reason for this is that the purpose of hypothesis testing is to draw conclusions about a population from a sample.

The null and alternative hypotheses are two competing claims that researchers weigh the evidence for and against using a statistical test:

Null hypothesis: There’s no effect on the population.

Alternative hypothesis: There’s an effect on the population.

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Answer:

Step-by-step explanation:

a) 1012⁵ can be written as:

1012⁵ = 15¹² + 05¹¹ + 1*5¹º

= 5¹² + 5¹º

= 3125 + 625

= 3750

(b) 101⁵ can be written as:

101⁵ = 15⁴ + 05³ + 1*5²

= 5⁴ + 5²

= 625 + 25

= 650

(c) 1.1⁵ can be written as:

1.1⁵ = 15¹ + 15º

= 5¹ + 5º

= 25 + 5

= 30

(d) 10.21⁵ can be written as:

10.21⁵ = 15² + 05¹ + 25º + 15⁻¹

= 5² + 2*5º + 5⁻¹

= 25 + 10 + 0.2

= 35.2

(e) 210⁵ can be written as:

210⁵ = 25⁴ + 15²

= 2*625 + 25

= 1250 + 25

= 1275

Answer: 12

Step-by-step explanation:

Since we are given what v and w are, we can directly plug them in to solve the expression.

w²+1v        [plug in v and w]

(3)²+1(3)     [exponent]

9+1(3)        [multiply]

9+3            [add]

12

The expression is equal to 12.

The two equations that equal Willie's number are given as follows:

Jennie's number is unknown, hence we use the variable x to refer to her number.

Robbie picked a number that is nine more than four times Jennie's number, hence:

y = 9 + 4x.

(using y to refer to Robbie's number).

Willie picked a number that is two less than three times Robbie's number, hence:

n = 3y - 2.

(using n to refer to Willie's number).

Considering the expression for y, the second expression that describes Willie's number is given as follows:

n = 3(9 + 4x) - 2

n = 12x + 25.

The problems asks foir the two expressions that equals Willie's number.

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The value of y(0.4) is 1.04384484247985 using  Runge-Kutta method of fourth order .

What is  Runge-Kutta method of fourth order ?

The RK4 method, also known as the fourth-order Runge-Kutta method, is the Runge Kutta technique most frequently employed to get the answer to a differential equation. For a given point x, the Runge-Kutta technique returns an approximation of the value of y. The Runge Kutta RK4 method can only be used to solve first order ODEs.

The step size is h = 0.1

f(x,y) = (x²+y²)/10

Step 1:

x₁ = 0 + 0.1 = 0.1

k₁ =f(0,1) = 0.1

k₂ = f(1/20, 1.005) = 0.1012525

k₃ = f(1/20, 1.005062625) =0.101265088017189

k₄ = f(1/10, 1.01012650880172) = 0.103035556378395

y₁ = 1+ (1/10)/6 +(0.1 + 2⋅0.1012525 + 2⋅0.101265088017189 + 0.103035556378395) = 1.01013451220688

Step 2:

x₂ = x₁ + h = 1/5

k₁ =f(1/10,1.01013451220688)=0.103037173275143

k₂ = f(3/20,1.01528637087064) = 0.105330641487567

k₃ = f(3/20, 1.01540104428126) = 0.105353928072747

k₄ = f(1/5, 1.02066990501415) = 0.10817670550016

y₂ =1.01013451220688 + (1/10)/6 +(0.103037173275143 + 2⋅0.105330641487567 + 2⋅0.105353928072747 + 0.10817670550016) = 1.02067756250514

Step 3:

x₃ = x₂ + h = 3/10

k₁ =f(1/5, 1.02067756250514)=0.108178268660144

k₂ = f(1/4,1.02608647593815)=0.111535345610318

k₃ = f(1/4, 1.02625432978566)=0.111569794940382

k₄ = f(3/10, 1.03183454199918)=0.115468252206266

y₃ =1.02067756250514 + (1/10)/6 (0.108178268660144 + 2⋅0.111535345610318 + 2⋅0.111569794940382 + 0.115468252206266) = 1.03184184253794

Step 4:

x₄ = x₃ + h = 2/5

k₁ =f(3/10, 1.03184184253794) = 0.115469758801209

k₂ = f(7/20,1.037615330478)=0.119914557404297

k₃ = f(7/20, 1.03783757040816)=0.119960682255071

k₄ = f(2/5, 1.04383791076345)=0.1249597583947

y₄ = 1.03184184253794 + (1/10)/6 (0.115469758801209 + 2⋅0.119914557404297 + 2⋅0.119960682255071 + 0.1249597583947) = 1.04384484247985

y(0.4) ≈ 1.04384484247985

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The empirical rule describes a statistical distribution of data within three standard deviations of the mean on a normal distribution.

According to the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, practically all observed data for a normal distribution will lie within three standard deviations (denoted by σ ) of the mean or average (denoted by μ ).

In specifically, the empirical rule predicts that 68 percent of observations will fall within the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.

An approximate test for a distribution's "normality" is the empirical rule. The distribution may not be normal and may be skewed or follow another distribution if a large number of data points are outside the three standard deviation bounds.

The given question is incomplete so I have given the answer in general according to my knowledge.

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Answer:

The answer is (x + 10)

Step-by-step explanation:

(9x + 6) - (8x - 4)

9x + 6 - 8x + 4

Rearrange it

9x - 8x + 6 + 4

Combine like terms

x + 10

Thus, The answer is (x + 10)

Using the two column proof, we have been able to prove that;

ΔPQR ≅ ΔTSR by AAS Congruency Postulate

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Thus, the two column proof required is as follows;

Statement 1: PR ≅ TR

Reason 1: Given

Statement 2: ∠PQR ≅ ∠TSR

Reason 2: Given

Statement 3: ∠PRQ ≅ ∠TRS

Reason 3: Opposite angles

Statement 4: ΔPQR ≅ ΔTSR

Reason 4: AAS Congruency postulate

AAS congruency postulate is one of the 5 major triangle congruency postulates that is defined as Angle-Angle-Side. This tells us that two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

We can also say that Opposite angles are defined as the angles that are directly opposite each other where two lines cross. The intersection point in this regards is called the vertex, which is the point where the lines connect to form the angle. Opposite angles are also referred to as vertical angles

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The correct statements regarding the transformations to the volumes are given as follows:

1. A cone's radius increases x 3: -> The cone's volume will increase x 9.

2. A cone's height increases x 3: -> The cone's volume will increase x 3

3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.

4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.

The volume of a cone of radius r and height h is given as follows:

V = πr²h/3.

Then the scale factors are considered as follows:

The volume of an sphere of radius r is given as follows:

V = 4πr³/3.

Then when the radius is multiplied by 3, the volume is multiplied by 27, as 3³ = 27, and the radius is cubed in the equation.

The volume of a cylinder of radius r and height h is given as follows:

V = πr²h.

Then if the radius is multiplied by 6, the volume is multiplied by 36, as the variable r is squared in the equation for the volume.

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In the case where a=78, b=716, c=0.8, and d=14, the simplest form of a mixed number is -117/640.

The smallest equivalent fraction of the number is the form that is the simplest. How to find the most basic form: In the numerator and denominator, look for shared factors. Examine the fraction to see if one of the numbers is a prime number.

The term "reduced form" refers to the fraction's simplest form. As an illustration, the simplest form of a fraction with a common component of 1 is 34 However, while 2/4 can be further condensed and expressed as 12, it is not the most basic form.

When the top and bottom of a fraction cannot be any smaller while remaining whole numbers, it is said to be in its simplest form.

b a + c d

b= -7/16

a= 7/8

c= 08.(4/5)

d= 1/4

It can therefore be calculated as follows.

-7/16×7/8 + 4/5×1/4

-49/128 + 1/5

-246+128/640

= -117/640

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first you add 117 to the x value and add 40 to the y value then divide by the opposite reciprocal and then you do it again to get the answer and whatever the answer is you divide by 157

We get 3y= √(x+2) after vertically stretches by 3 and translated 2 unit left.

If a function is multiplied by a positive value that greater than 1, the graph of function is called vertically stretched graph. Here vertically stretches means the factor 3>1 and we need to multiply the y value by 3.

Translation of a graph means move the graph from one position to another position without changing its size, shape or orientation. Here, the graph is translated 2 units left so we need to add 2 with the x value.

We are given a graph, y= √X

Hence, after transformation the graph became 3y= √(x+2)

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