Karen spent $7.80 on a pair of stockings. She spent 3/8
on a skirt and a blouse; after which, half of her money was left. The skirt cost 8 times as much as the blouse. How much did she spend on the skirt?​

Answer:

The expansion of (3x² - k/x)^9 can be found using the binomial theorem. The binomial theorem states that for any real numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:

(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1)b^1 + C(n, 2)a^(n-2)b^2 + ... + C(n, n-1)a^1b^(n-1) + C(n, n)a^0b^n

where C(n, k) = n! / (k! (n-k)!).

Using this formula, we can find the coefficient of the term in x^6 in the expansion of (3x² - k/x)^9. The term in x^6 will be of the form C(9, 3) (3x²)^3 (-k/x)^6. We can find the value of C(9, 3) as follows:

C(9, 3) = 9! / (3! (9 - 3)!) = 84.

So, the coefficient of the term in x^6 is 84 * (3^3) * (-k/x)^6 = 84 * 27 * (-k)^6.

Since we are told that this coefficient is 6048, we can set these two expressions equal to each other:

6048 = 84 * 27 * (-k)^6

Dividing both sides by 84 * 27, we get:

k^6 = -6048 / (84 * 27) = -1.

Taking the sixth root of both sides, we find:

k = -1^(1/6).

So the value of k is approximately -1.122462048309372981433.

Answer:

Step-by-step explanation:

No

Answer:

4.8 miles

Step-by-step explanation:

have a good day!

Answer:

4.8 Miles

Step-by-step explanation:

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

x<47/6

Step-by-step explanation:

-6x + 38 > -9

Subtract 38 from both sides;

-6x+38-38>-9-38

Simplify:

-6x>-47

Multiply both sides by (-1) ( reverse the inequality)

(-6x)(-1)<(-47)(-1)

Simplify;

6x<47

Divide both sides by 6

6x/6=47/6

Simplify;

x<47/6

Answered by NONE other than the ONE & ONLY #QUEEN herself aka #DRIPPQUEENMO!!!

HOPE THIS HELPED!!!

Answer:

(-2a+5)^6-5(-2a+5)

Step-by-step explanation:

plug f(a) into g(a) where there is an 'a'

Answer: The first 3 are functions. The last one is not a function

Step-by-step explanation: What you can do is the line test. If you draw a line through it, the line shouldn't touch the arrow twice. Like the last one, it touches the line twice, so it is not a function

Answer:

07.50086956521739% (round it)

Step-by-step explanation:

Find what percent 43.13 (Number A) is of 575 (Number B). To do this you divide Number A by Number B.

43.13 / 575 = 0.0750086956521739

Move the decimal point two places to the right.

007.50086956521739

Get rid of the zeros.

7.50086956521739

Answer:

07.5%

Step-by-step explanation:

\(2x - 7x + 2 + 1 - 2\)

\(2x - 7x + 3 - 2\)

\( - 5x + 1\)

Work Shown:

Complementary angles add to 90 degrees.

A+B = 90

(3x+18)+(2x+17) = 90

5x+35 = 90

5x = 90-35

5x = 55

x = 55/5

x = 11

Then we can determine each angle:

As a check: A+B = 51+39 = 90 to confirm the answer.

Answer:

Step-by-step explanation:

This is a very impossible question to solve because we are not given any idea what both sets are, or at least either of them is. And thus, even if we write down an inequality equation, I doesn't solve the question, it rather makes one ask more questions.

If the two numbers are, say, a and b, and the first set is x, while the second set is y then we have an inequality in the sense that

a + b = 12x

a + b = 29y

How to proceed with no idea what x or y is, is well, not possible

Answer:

113

Step-by-step explanation:

divide the volume with the length

Answer:

x = 12

Step-by-step explanation:

Reference angle = 45°

Opposite side length = x

Hypotenuse = 12√2

Thus, to find x, apply trigonometric ratio.

\( sin(45) = \frac{x}{12\sqrt{2}} \)

Multiply both sides by 12√2

\( sin(45)*{12\sqrt{2}} = x \)

\( \frac{1}{\sqrt{2}}*{12\sqrt{2}} = x \) (sin 45 = 1/√2)

\( \frac{1*12\sqrt{2}}{\sqrt{2}} = x \)

\( \frac{12\sqrt{2}}{\sqrt{2}} = x \)

12 = x

x = 12

The quadratic function that represents the given graph is:

y = ¹/₂(x − 4)² - 1

The general form of a quadratic equation in Vertex Form is expressed as:

y = a(x − h)² + k,

where

(h, k) is the vertex.

From the given graph, we can see that the coordinates of the vertex is (4, -1). Thus, we have:

y = a(x − 4)² - 1

Looking at the four given options from Option A to Option D, we can deduce that only given option that gives us the coordinates of the quadratic curve vertex is option D.

Thus, we can conclude that the quadratic function that truly represents the given parabolic graph curve is:

y = ¹/₂(x − 4)² - 1

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The equation will be 6x - 4= 8.

Solve the equation: 6x - 4 = 8 + 4 + 4.

6x = 12. 6 6. x = 2

Hopefully, that helps

Answer:

210 million

Step-by-step explanation:

The simplified expression is \(-4x^2 + 3x + 1\), which is a quadratic polynomial. Option D.

To simplify the expression \((8x^2 + 3x) - (12x^2 - 1)\), we can distribute the negative sign to each term within the parentheses:

\(8x^2 + 3x - 12x^2 + 1\)

Next, we can combine like terms by adding or subtracting coefficients of similar powers of x:

\((8x^2 - 12x^2) + 3x + 1\)

Simplifying further, we have:

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

The resulting polynomial \(-4x^2 + 3x + 1\) is a quadratic polynomial since it has a highest power of x^2 (the exponent of x is 2), which is\(-4x^2.\)Quadratic polynomials are polynomials of degree 2 and can be represented by a parabola when graphed.

In summary, the simplified expression \((8x^2 + 3x) - (12x^2 - 1)\) simplifies to \(-4x^2 + 3x + 1\) , which is a quadratic polynomial. So Option D is correct

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Note the complete question is

The pairs of prime numbers (p,q) such that  p^2-p=37q^2-q is (43, 7)

The expression is given as:

p^2 - p=37q^2 - q

The boundary or range of numbers of p and q is not given.

So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)

i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000

Using the above range, we have the following program to determine the pairs of prime numbers (p, q).

for a in range(2,1000000):

  for b in range(2,1000000):

      if ((a* *2) - a) == (37 * (b* *2) - b):

          print(str(a)+","+str(b))

The output of the above program is:

(43, 7)

The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q

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Triangle ADC also has a right angle at D, making it a right-angled triangle.

The exact value of x be 2.25.

The hypotenuse's square is equal to the sum of its two other side squares of a right-angled triangle, according to the Pythagoras theorem.

Triangle ADB exists even a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADB = BD = 4,

Height of Triangle ADB = AD = 3,

Hypotenuse of Triangle ADB = AB

Using the Pythagoras Theorem, we get,

\($\left[(A D)^2+(B D)^2\right]=(A B)^2$\)

substitute the values in the above equation, we get

or,\($(A B)^2=\left[(3)^2+(4)^2\right]$\)

simplifying the equation, we get

or, \($(A B)^2=[9+16]$\)

or, \($(A B)^2=25$\)

or, \($\sqrt{(A B)^2}=\sqrt{25}$\)

or, AB = 25

Triangle ADC is also a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADC = DC = x

Height of Triangle ADC = AD = 3,

And, Hypotenuse of Triangle ADC = AC

Using the Pythagoras Theorem, we get,

\(& {\left[(D C)^2+(A D)^2\right]=(A C)^2} \\\)

simplifying the equation, we get

\(& \text { or },(A C)^2=\left[(3)^2+(x)^2\right] \\\)

\(& \text { or },(A C)^2=\left[9+x^2\right]\)

Triangle ABC is also a right-angled triangle with right-angle at A. Therefore, Base of Triangle ABC = AC,

Height of Triangle ABC = AB = 5,

And, Hypotenuse of Triangle ABC =  BC = (4 + x)

Using the Pythagoras Theorem, we get,

\(& {\left[(A C)^2+(A B)^2\right]=(B C)^2} \\\)

\(& \text { or, }(B C)^2=\left[(A C)^2+(A B)^2\right] \\\)

substitute the values in the above equation, we get

\(& \text { or, }(4+x)^2=\left[\left(9+x^2\right)+(5)^2\right] \\\)

simplifying the equation, we get

\(& \text { or, }\left[4^2+(2 \times 4 \times x)+x^2\right]=\left[9+x^2+25\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[(9+25)+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[34+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]-\left[34+x^2\right]=0 \\\)

\(& \text { or, },(16-34)+8 x+\left(x^2-x^2\right)=0 \\\)

8x - 18 = 0

8x = 18

\(& \text { or, } x=\frac{18}{8} \\\)

\(& \text { or, } x=\frac{9 \times 2}{4 \times 2} \\\)

\(& \text { or, } x=\frac{9}{4} \\\)

Therefore, the value of x be 2.25.

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Given:

Conditional statement x is even, then x + 1 is odd.

Required:

What is the converse of the conditional statement?

Explanation:

The converse statement of a conditional statement "If p then q" is given by "If q then p".

Then, the converse statement of the given conditional statement will be :

If x is odd then x+1 is even.

Answer:

If x is odd then x+1 is even.

The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.

Let the cost price of rice is R and cost price of sugar is S.

Case 1 :  total cost of 5 kg rice and 6 kg sugar is Rs. 940.

5R + 6S = 940 ...(1)

Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.

The new cost price of rice = R + 20% of R = 1.2R

The new cost price of sugar = S - 10% of S = 0.9S

So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.

Thus,

4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)

From equations (1) and (2) we have,

(5R + 6S)/(4.8R + 2.7R) = 940/627

R/S = 8/9

Hence, if the price of rice is 8 then the price of sugar is 9.

It is clear that the price of sugar is more than that of rice.

The percent cost by which cost of rice is less than sugar is:

(9 - 8)/ 9 (100) = 11 1/9%.

Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

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Domain: \(x \in \mathbb{R}\)

Range: \(y \in \{ \mathbb{R} | y \geqslant 24 \}\)

Domain:

In finding the Domain of a function, the values for the input of the function should not make the output of the function undefined or complex. Because of this, we can think of the values for the input that make the output of the function undefined or complex so that we will not include them in our Domain. We can only make the output undefined if the input makes the denominator \(0\). In \(f(x)\), there's no value for \(x\) that makes the denominator \(0\) as it is constant, \(1\) (Note: All expressions implicitly have \(1\) as their denominator even though it's not written). We can only make the output of the function complex if the value of \(x\) makes the function take the \(n\text{th}\) root of a negative number where \(n \in \mathbb{E}\). There's no radical sign in \(f(x)\) so we shouldn't worry about the output of \(f(x)\) being complex. Because there's no value for the input, \(x\), that can make the output of \(f(x)\) undefined or complex, its Domain can be any number.

Domain: \(x \in \{\mathbb{R}\}\)

Range:

In finding the Range, it is actually the same logic as finding the Domain but first, we'll have to do a bit of rewriting for the given function.

Let \(y = f(x)\) so \(y = 24 +x^2\).

First, we need to make \(x\) the subject of the equation.

Making \(x\) the subject:

\(y = 24 +x^2 \\ y -24 = 24 +x^2 -24 \\ y -24 = x^2 \\ \pm \sqrt{y -24} = \sqrt{x^2} \\ x = \pm \sqrt{y -24}\).

In the Domain, we'll have to think of the value for the input, \(x\), that makes the output undefined or complex. In the Range, the same logic for the Domain, we'll have to think for the value of \(y\), that makes the \(x\) undefined or complex. That's why we made \(x\) in the equation the subject. In our rewritten equation, we can see that \(y -24\) is under the square root. Which means if \(y -24\) is negative, \(x\) will be complex. So we have to make \(y -24\) be greater than or equal to \(0\) (\(y -24 \geqslant 0\)) so that \(x\) won't be complex.

Solving for the inequality, \(y -24 \geqslant 0\)

\(y -24 \geqslant 0 \\ y -24 +24 \geqslant 0 +24 \\ y \geqslant 24\)

Range: \(y \in \{ \mathbb{R} | y \geqslant 24 \}\)

The distance between  Georgetown and clayton on the scale model  is 2 inches.

In math, the term scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.

The distance between Georgetown and clayton on a map with a scale of 1 inches: 14 miles can be found as follows;

They are actually 28 miles.

Therefore,

14 miles = 1 inches

28 miles = ?

cross multiply

distance between Georgetown and clayton on the scale model = 28 / 14

distance between Georgetown and clayton on the scale model = 2 inches

Therefore, the distance on the scale model is 2 inches.

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Answer:

Step-by-step explanation:

If the speed of a bus was decreased by 20% to 48 mph, how fast was the bus going originally?

48 mph = 80% (100%-20%=80%)

so

48 : 80 * 100 = 60mph

---------------------

check

60 - 20% = 48

the answer is good

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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The new triangle will be smaller than the old triangle if the scaling factor is less than 1, as its sides will be smaller.

A factor is a number that is multiplied by another to produce a result. A multiplication puzzle has a product as its answer. Consider a multiplication problem as the process of multiplying the factors to obtain the product.

A composite number is a number that is composed of more than two elements. The number one is neither a composite nor a prime. It just has one factor—itself.

Similarly, if the scale factor is less than 1, the sides of the new triangle will be smaller than those of the original triangle, making it smaller than the latter.

Factors are the figures that can divide an amount precisely. As a result, there is no residue after division. Factors are the sums of numbers that you multiply to produce another number. A factor is hence the divisor of another number.

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