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Sophie saves $11.25 when she buys the dress with a 15% discount.

To calculate the amount of money Sophie saves on the dress with a 15% discount, we need to find 15% of the original price and subtract that amount from the original price.

Original price of the dress: $75

Discount percentage: 15%

Calculate the discount amount

Discount amount = 15% of $75

Discount amount = (15/100) \(\times\) $75

Discount amount = $11.25

Calculate the final price after the discount

Final price = Original price - Discount amount

Final price = $75 - $11.25

Final price = $63.75

Calculate the amount saved

Amount saved = Original price - Final price

Amount saved = $75 - $63.75

Amount saved = $11.25

Therefore, Sophie saves $11.25 when she buys the dress with a 15% discount.

It's important to note that the discount amount may vary depending on the specific store policies and rounding methods used.

The above calculation assumes a straightforward 15% discount without any additional conditions or fees.

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Answer:

x= -2

Step-by-step explanation:

7x-3=4x-9

3x-3= -9

3x= -6

x= -2

Answer:

x=-2

Step-by-step explanation:

7x=4x-6

7x-4x=4x-6-4x

3x=-6

3x/3 = -6/3

x=-2

(a) The team can be chosen in (4 choose 0) * (5 choose 5) + (4 choose 1) * (5 choose 4) + (4 choose 2) * (5 choose 3) + (4 choose 3) * (5 choose 2) + (4 choose 4) * (5 choose 1) = 1 + 20 + 30 + 20 + 5 = 76 ways.

(b) The team can be chosen with just three women in (4 choose 2) * (5 choose 3) = 6 * 10 = 60 ways.

(c) The probability that the team includes just 3 women is given by the number of ways to choose a team with 3 women and 2 men (60 ways) divided by the total number of ways to choose a team (76 ways), so the probability is 60/76 ≈ 0.7895.

(d) The probability that the team includes at least three women is given by the number of ways to choose a team with at least three women (60 ways) divided by the total number of ways to choose a team (76 ways), so the probability is 60/76 ≈ 0.7895.

(e) The probability that the team includes more men than women is given by the number of ways to choose a team with more men than women (0 ways) divided by the total number of ways to choose a team (76 ways), so the probability is 0/76 = 0.

(a) The purpose of plotting a scatter diagram in regression analysis is to visually explore the relationship between two variables. It helps in determining whether there is a correlation between the variables, and if so, the nature and strength of the correlation.

(b) (i) A strong direct linear relationship between variables X and Y would be represented by a scatter diagram where the points are closely clustered along a straight line that rises from left to right.

(ii) A weak inverse linear relationship between variables X and Y would be represented by a scatter diagram where the points are loosely scattered along a line that slopes downwards from left to right.

(c) The linear regression equation of Y on X can be determined by fitting a line that best represents the relationship between the variables. This line can be obtained through methods such as the least squares regression.

(ii) To predict the value of Y for X = 3, we can substitute the value of X into the linear regression equation obtained in part (c).

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Horizontal asymptote y = 1.

Find the horizontal asymptote of the function:

Horizontal asymptotes are the lines perpendicular to the y-axis and meet the curve at infinity.

Horizontal asymptote y = 1.

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Answer:

1) Area = 12cm²

2) x = 5cm

Surface area : 69cm²

Step-by-step explanation:

Opposites sides in a rectangle would equal the same.

so Top/bottom = 20+20=40

Front/back = 15+15=30

40+30=70cm²

94-70=24cm² for left and right side 24÷2=12cm²

2) Those lines represents what side it is equal too which also means the same.

3cm, you know that base x height = surface area so surface area ÷ height = base

15/3=5cm

x=5cm

Formula : Base x Height = One surface area

Front/Back= 15+15=30

Top/bottom = 5x3 = 15+15=30

side/side = 3x3=9

30+30+9=69cm²

The fundamental theorem of arithmetic states that every natural number greater than 1 can be written as a product of primes. Using strong induction, we can prove this.

Let's proceed with the strong induction proof. We start by considering the base case, where m = 2. Since 2 is prime, it can be written as a product of primes itself.

Next, we assume that for all natural numbers k such that 2 ≤ k ≤ m, the statement holds true, i.e., k can be expressed as a product of primes. Now, we aim to prove that m+1 can also be expressed as a product of primes.

We know that m+1 is either prime itself or composite. If m+1 is prime, then it can be written as a product of a single prime, satisfying the theorem.

On the other hand, if m+1 is composite, it can be written as a product of two positive integers a and b, where 2 ≤ a ≤ b ≤ m. Since a and b are both less than or equal to m, we can apply the inductive hypothesis to express a and b as products of primes. Therefore, we can write m+1 as a product of primes by combining the prime factorizations of a and b.

By strong induction, we have shown that for any natural number m greater than 1, it can be expressed as a product of primes. This completes the proof of the fundamental theorem of arithmetic.

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Answer: a

Step-by-step explanation:

a) Hypothesis test:

Null hypothesis (H0): The percentage of graduate students looking for housing on campus is equal to 15%.

Alternative hypothesis (Ha): The percentage of graduate students looking for housing on campus is greater than 15%.

To test the hypothesis, we can use a one-sample proportion test. We will calculate the test statistic and compare it to the critical value or p-value to make a decision.

The observed proportion of graduate students looking for housing on campus is 78/433 = 0.1804.

Using a significance level (α) of 0.05, we will conduct the test and calculate the test statistic and p-value.

Plan:

Test statistic: z = (p - p) / sqrt(p(1-p)/n)

where p is the observed proportion, p is the hypothesized proportion (0.15), and n is the sample size (433).

Do:

Calculating the test statistic:

z = (0.1804 - 0.15) / sqrt(0.15 * 0.85 / 433)

z ≈ 2.07

Conclude:

Since the test statistic is 2.07, we compare it to the critical value or calculate the p-value.

The critical value for a one-sided test with a significance level of 0.05 is approximately 1.645. Since 2.07 > 1.645, the test statistic falls in the rejection region.

The p-value associated with the test statistic of 2.07 is less than 0.05. Therefore, we reject the null hypothesis.

Based on the survey data, there is evidence to suggest that the percentage of graduate students looking for housing on campus is greater than 15%. The housing office should consider increasing the amount of housing available to graduate students.

b) The p-value obtained in part a) represents the probability of obtaining a test statistic as extreme as the one observed (or more extreme), assuming the null hypothesis is true.

In this case, the p-value is less than 0.05, which suggests strong evidence against the null hypothesis. It indicates that the observed proportion of graduate students looking for housing on campus is significantly higher than the hypothesized proportion of 15%.

c) Including the 21 non-respondents would change the sample size and potentially affect the estimated proportion. If these additional respondents had similar characteristics to the 433 who responded, it is possible that the recommendation might still remain the same.

However, the exact impact depends on the responses of the non-respondents, so it is difficult to determine the precise effect without their data.

d) Type II error in this study would occur if the housing office fails to increase the amount of housing on campus when it is actually necessary (i.e., the percentage of graduate students looking for housing on campus is higher than 15%).

This means the null hypothesis would not be rejected when it should have been. A consequence of this type of error would be the unmet demand for housing, potentially causing dissatisfaction among graduate students and a shortage of available housing options.

e) Type I error in this study would occur if the housing office increases the amount of housing on campus when it is not necessary (i.e., the percentage of graduate students looking for housing on campus is not higher than 15%). This means the null hypothesis would be rejected incorrectly.

A consequence of this type of error would be allocating resources and efforts towards increasing housing capacity unnecessarily, which could result in wastage of resources and potentially impact other areas of the university's operations.

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Answer:

$200

Step-by-step explanation:

You can find a point where they are both equal (2,400)

and than divided y/x (400/2)=200

The correlation coefficients are expressed on a standard scale that always ranges from -1.00 up to +1.00.

Correlation does not mean equal causation. Just because two variables have a relationship does not necessarily mean that changes in one variable cause changes in the other. Correlations indicate that there is a relationship between variables, but this does not necessarily determine that one variable causes the other to change.

Correlations range from -1.00 to +1.00. The correlation coefficient (expressed as r ) shows the strength and direction of a relationship between two variables. The closer the r value is to +1 or -1, depending on how stronger the linear relationship between the two variables is.

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Answer:

3ab

Step-by-step explanation:

i hope you don't want to know how i did this :)

Therefore:

The area under the normal probability density function (p.d.f.) within 1.96 standard deviations of the mean on both sides is approximately 0.95.

In a normal distribution, the area under the p.d.f. curve represents probabilities. The area between the mean and 1.96 standard deviations to the left or right represents approximately 95% of the data. Since the normal distribution is symmetrical, we can split this area equally on both sides, resulting in approximately 0.475 (or 47.5%) on each side.

To calculate the total area, we add up the areas on both sides: 0.475 + 0.475 = 0.95. This means that 95% of the data falls within the range of 1.96 standard deviations from the mean. Consequently, the remaining 5% is distributed outside this range (2.5% to the left and 2.5% to the right). Therefore, the correct answer is A. 0.05, which corresponds to the area outside the range of 1.96 standard deviations from the mean.

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Answer:

10

Step-by-step explanation:

Answer:

f(x)=x^3 - 13x^2 + 40x + 17

Step-by-step explanation:

x-0=0    x-5=0       x-8=0

  x=0        x=5           x=8

y=x(x-5)(x-8)+b  ==> b is what's going to be used to find the equation so that

                                y=17 when x=0

17=0(0-5)(0-8)+b  ==> plugin 0 for x and 17 for y

17=0*(-5)*(-8)+b  ==> simplify

17=0+b  ==> anything multiplied by 0 is 0.

b=17  

Hence, the equation is:

y=x(x-5)(x-8)+17  ==> expand this equation

y=x*(x-5)(x-8) + 17

y=x*(x(x - 8) - 5(x - 8)) + 17  ==> distribute x-8 to x and -5

y=x*(x*x - 8x - 5x - (8)(-5)) + 17  ==> distribution property

y=x*(x^2 - 13x - (-40)) + 17   ==> simplify

y=x*(x^2 - 13x + 40) + 17  ==> subtracting a negative number is equivalent to

                                              adding a positive number

y=x^3 - 13x^2 + 40x + 17 ==> multiply x with x^2, 13x, and 40 using the

                                              distribution property.

Answer: f(x)=x^3 - 13x^2 + 40x + 17

Answer: Okay, lets explain.

Step-by-step explanation:Since 0, 5 & 8 are given as the zeros of the required 3rd degree polynomial f(x), therefore, one may take it as ; f(x) =k (x-0)(x-5)(x-8)

= k(x³−13x²+40) …. .. .(1) . Since f(10) = 17 (given), it implies 17 = k(1000 -1300 + 400) = 100 ==> k = 17/100 = 0.17 . Put this value of k in eq(1) and get the required polynomial.

Answer:

y=2/3x+1

Step-by-step explanation:

slope intercept form is y=mx+b.

slope is m, which is 2/3.

y-int is b, which is 1.

y=2/3x+1

Answer:

2.7384

Step-by-step explanation:

So you would do 0.652 x 4.2

so you first times .652 by .2 you get .1304

next you times .652 by 4 you get 2.608

add them together and you get 2.7384

If you are confused about where to put the point count the amount of number after the point and thats where you should place it. (Hope this makes sense)

example: we have .652 and .2 if you count all the numbers after the point yo get four and our answer is 1304 so you count from the end of the number until 4 thats how I got .1304

same with the other one 4 and .652 4 doesn't have a point so its 3 I got 2603 then count from the end of the number 3 times and you get 2.603

I really hope this makes sense if you have anymore question lmk  

Answer:

29.415984

Step-by-step explanation:

The tree has 11 vertices with degree 1.

To find the number of vertices with degree 1 in a tree with degree sequence (6,6,6,6,4,...), we can use the Handshaking Lemma. This lemma states that the sum of all vertex degrees in a graph is twice the number of edges. In a tree, the number of edges is one less than the number of vertices, so we can write:

6+6+6+6+4+...+2+2+1+1 = 2n-1

where n is the number of vertices. Simplifying this equation gives:

n = (6+6+6+6+4+...+2+2+1+1+1)/2 + 1

The term inside the parentheses is the sum of all vertex degrees, which we know from the degree sequence. Plugging in the values and simplifying, we get:

n = 18

So the tree has 18 vertices. Since we know that the rest of the vertex degrees are either 2 or 1, we can subtract the six vertices with degree 6 and the one vertex with degree 4 to get:

18 - 6 - 1 = 11

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Answer:

(x+2)(x+1)(4x+1)(4x-3)

Step-by-step explanation:

(4x² + 5x)² - 5(4x² +5x) - 6

= (4x² + 5x)² - 6(4x² +5x) + 1(4x² +5x) -6

= (4x² + 5x)(4x² +5x -6) +1 (4x² +5x -6)

= (4x²+5x-6)(4x²+5x+1)

= (4x² + 8x - 3x - 6)(4x² + 4x + x +1)

= (4x(x + 2) - 3(x + 2))(4x(x+1) +1(x+1))

= (x+2)(4x-3)(x+1)(4x+1)

Answer:

Let's assume that the price before adding the VAT is x.

We know that the VAT rate is 8%, which means that the VAT amount is 8% of x, or 0.08x.

The total price including VAT is the sum of the price before VAT and the VAT amount, so we can write:

Total price = price before VAT + VAT amount

or

2,700 = x + 0.08x

Simplifying this equation, we can combine like terms on the right-hand side to get:

2,700 = 1.08x

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 1.08:

x = 2,700 / 1.08

x = 2,500

Therefore, the price before VAT was added is 2,500.

Answer:

The value of z is 58    

Step-by-step explanation:

The mean is the average of a set of numbers.  Mean = (sum of the numbers)/(the number of numbers).

We are told that the mean of x+y+z is = 55.  

We can wriote this as:

 55 = (x+y+z)/3

We learn that x+y = 107.  So lets enter that number for x + y:

 55 = (x+y+z)/3

55 = ((x+y)+z)/3    

55 = ((107)+z)/3           [Substitution]

55 = (107+z)/3

165 = 107+z               [Multiply both sides by 3]

z = 58                       [Simplify]

CHECK:

Is the mean of x, y, and z 55?

55 = (x+y+z)/3  ?

55 = ((107)+z)/3 ?   [Since we know x+y = 107]

55 = ((107)+58)/3 ?  [Since z=58]

55 = (165)/3)  ?

55 = 55  YES  The value of z is 58    

We can see here that the smallest positive integer that can be expressed as the sum of two cubes in two different ways is 1729.

The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion.

Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. With integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division.

We see that the above answer is true because:

1^3 + 12^3 = 1729

9^3 + 10^3 = 1729

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Answer:

y=4/5x + 8

Step-by-step explanation:

The 8 is the y-intercept and the 4/5 is the slope when you do rise/run on the marked points.

Answer:

The retail value of one bag of one bag of a synthetic hair bundle is $47 and the retail value of a bag of natural hair bundle is $38

Step-by-step explanation:

The given information are;

The number of bags of synthetic hair bundles the owner buys = 700

The number of bags of natural hair bundles the owner buys = 400

The number of synthetic hair bundles the Forestville location receives = 300

The number of natural hair bundles the Forestville location receives = 250

The total retail value of the hair bundles the Forestville location receives = $23,600

The number of synthetic hair bundles the Largo location receives = 400

The number of natural hair bundles the Forestville location receives = 150

The total retail value of the hair bundles the Largo location receives = $24,500

Let the price of a bag of synthetic hair bundle = x

Let the price of a bag of natural hair bundle = y

∴ 300·x + 250·y = $23,600...(1)

400·x + 150·y = $24,500...(2)

Making y the subject of the formula in both equations gives;

For equation (1)

y = 23,600/250 - 300/250·x = 94.4 - 1.2·x

y = 94.4 - 1.2·x

For equation (2)

400·x + 150·y = 24,500

y = 24,500/150 - 400/150·x = 490/3 - 8/3·x

y = 490/3 - 8/3·x

Finding the common solution gives;

490/3 - 8/3·x = 94.4 - 1.2·x

490/3 - 94.4 = 8/3·x  - 1.2·x

1034/15 = 22/15·x

x = 1034/15/(22/15) = 47

x = 47

∴ The price of a bag of synthetic hair bundle = x = $47

The price of a bag of synthetic hair bundle = $47

y = 490/3 - 8/3·x = 490/3 - 8/3 × 47 = 38

y = 38

The price of a bag of natural hair bundle = y = $38

The price of a bag of natural hair bundle = $38.

Therefore, the retail value of one bag of one bag of a synthetic hair bundle is $47 and the retail value of a bag of natural hair bundle is $38.

Answer:

f(0)=-5

f(2)=3

f(-2)=-15

f(4)=11

f(-1)=-9

Step-by-step explanation:

Pretty simple once it clicks.You just need to substitute the x in f(x). So f(2) is just replacing the x in the equation. We would get 4*2-5. This would get us 8-5 which is 3. So rule of thumb, just substitute the x.

The partial derivatives are:

∂ z / ∂ x = − [ 5x⁴z⁶ ] / [ 6x⁵z⁵ + 6z⁵y⁴cos ( y⁴z⁶ )]

∂ z / ∂ y  = − [ 4y³z⁶ cos ( y⁴ z⁶ ) ] / [ 6x⁵z⁵ + 6z⁵y⁴cos ( y⁴z⁶ )]

We have,

f(x, y, z) = x⁵z⁶ + sin (y⁴z⁶) + 2 = 0

Now, partially differentiating we get

∂ z / ∂ x

= - [ ∂ F / ∂ x ] /  [ ∂ F / ∂ z  ]

= − [ 5x⁴z⁶ ] / [ 6x⁵z⁵ + 6z⁵y⁴cos ( y⁴z⁶ )]

and,

∂ z / ∂ y

= - [ ∂ F / ∂ y ] / [ ∂ F / ∂ z ]

= − [ 4y³z⁶ cos ( y⁴ z⁶ ) ] / [ 6x⁵z⁵ + 6z⁵y⁴cos ( y⁴z⁶ )]

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The measurements are;

a. 4 inches = No

b. 15 inches = Yes

c. 23 inches = Yes

d. 5 inches =  Yes

e. 25 inches = Yes

f. 10 inches = Yes

Jose in this problem draws a triangle, ABC.

We know the length of two sides of the triangle:

AB = 10 inches

BC = 15 inches

The length of the third side in a generic triangle can be calculated using the cosine theorem:  

\(\alpha = \sqrt{b^2 + c^2 - 2bc cos \alpha }\)

where;

Looking at the formula, we observe that:

- The maximum value for  is obtained for α = 180 degrees, so that cos α = -1 .

In this case, the length of the missing side  (AC, in this case) is

\(AC = \sqrt{10^2 + 15^2 - 2*10*15 *-1 }\)

AC = 25 inches

- The minimum value for α is obtained for 180 degrees , for which cos α= 1;

\(AC = \sqrt{10^2 + 15^2 - 2*15*10*1}\)

AC = 5 inches

Hence, the length must be between 5 and 25 inches.

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The complete question:

Jose draws ABC. AB has a length of 10 inches and BC has a length of 15 inches.

Determine whether each measurement could be the length of AC.

Choose Yes or No for each measurement.

a. 4 inches Yes : No

b. 15 inches Yes : No

c. 23 inches Yes : No

d. 5 inches Yes : No

e. 25 inches Yes : No

f. 10 inches Yes : No

Answer:

n = 2/3

Step-by-step explanation:

3n - 22 = -20

Add 22 to both sides

-20 + 22 = 2

3n = 2

Divide both sides by 3

2 / 3 = 2/3

n = 2/3

Let me know if I've done something wrong :)

Answer:

\(n = \frac{2}{3}\)

Step-by-step explanation:

I hope this helps!

Hello! My name is Chris and I’ll be helping you with this problem.

Date: 9/28/20 Time:  11:06 am CST

Answer:

-6.2

Explanation:

-2 (3.1) = -6.2

I hope this helped answer your question! Have a great rest of your day!

Furthermore,

Chris  

Answer:

\(m = \frac{ - 5 - 1}{2 - ( - 3)} = - \frac{6}{5} \)