Justify each answer. 11. a. If y = civi + c2V2 + c3V3 and ci + c2 + c3 = 1, then y is a convex combination of V1, V2, and V3. b. If S is a nonempty set, then conv S contains some points that are not in S. c. If S and T are convex sets, then S UT is also convex. 12. a. A set is convex if x, y e S implies that the line segment ose between x and y is contained in S. b. If S and T are convex sets, then SnT is also convex. c. If S is a nonempty subset of RS and y e conv S, then there exist distinct points Vi...., Vo in S such that y is a convex combination of vi,

Answer:

the answer is -x/2 -1

if its not then beat me up for that- :^

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

Work Shown:

x = price before the discount

30% of x = 0.30x = amount saved

x - 0.30x = 0.70x = price after discount = 1659

0.70x = 1659

x = 1659/(0.70)

x = 2370

First we'll have to convert the percent into decimal.

We'll have to divide the value by 100.

\(\frac{30}{100}\)

\(\bold{=0.30}\)

Now, we can find the original price.

\(\large\boxed{\bold{Formula:OP= \frac{price}{1-Discount}}}\)

We have all the necessary values to find the original price.

Let's solve!

Substitute the values according to the formula.

\(OP=\frac{1659}{1-0.30}\)

OP= $2370

Therefore, the original price of the television set is $2370

Answer:

2040

Step-by-step explanation:

2000+ 20%=2400-15%=2040

pls mark brainiest

Answer:

Step-by-step explanation:

100%= Rs2000

1%=Rs 20

120%= Rs2400

Cost is 2400 Rs

100%= 2400

1%= 24

(100-15=85)

85%= 2040

With discount it is Rs2040

Then with an extra 15% VAT

100%= 2040

1%= 20.4

115%= 2346

I think the answer is Rs2346

Hypothesis testing is an important statistical tool that helps us make informed decisions based on data and evidence.

The hypothesis statement h: µ = 25 is an example of a null hypothesis. A null hypothesis is a statement that suggests there is no significant difference between two variables or that any difference is due to chance. It is often denoted as H0 and is used to compare against an alternative hypothesis, which suggests that there is a significant difference between two variables. In this case, the null hypothesis is that the population mean µ is equal to 25, and there is no significant difference between the sample mean and the population mean. If the null hypothesis is rejected, it means that there is enough evidence to suggest that the alternative hypothesis is true. However, if the null hypothesis cannot be rejected, it does not necessarily mean that it is true. It only suggests that there is not enough evidence to support the alternative hypothesis.

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Answer:

Step-by-step explanation:

\(y=2x+1\)

\(2y=4x-3\rightarrow y=2x-\frac{3}{2}\)

\(d=\frac{|1-(-\frac{3}{2} )|}{\sqrt{1+2^2} }\)

  \(=\frac{(\frac{5}{2} )}{\sqrt{5} }\)

  \(=\frac{5}{2\sqrt{5} }\)

  \(=\frac{5}{2\sqrt{5} }\times \frac{\sqrt{5}}{\sqrt{5} }\)      (this is to rationalize the denominator...tidies it up.)

  \(=\frac{5\sqrt{5} }{2\times5 }\)

  \(=\frac{\sqrt{5} }{2 }\)

There are 35 students that have only dogs

What is subset?

If every element of set A is also an element of set B, then set B is a superset of set A and set A is a subset of set B. A and B could be equal; if they are not, then A is a legitimate subset of B. Include refers to the property that one set is a subset of another.

Total students =350

Cats only student = 175

Having both pets student= 140

Students having dog= 350- 175 = 175

Dogs only student = 175 - 140 = 35

So, There are 35 students which have dog only.

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The slope of the tangent to the curve \(y = 6 + 5x^2 - 2x^3\) at the point where x = a is given by the derivative of the equation, which is obtained by differentiating the equation with respect to x.

To find the slope of the tangent to the curve \(y = 6 + 5x^2 - 2x^3\) at the point where x = a, we need to take the derivative of the equation with respect to x. Differentiating each term of the equation, we get:

dy/dx = \(d(6)/dx + d(5x^2)/dx - d(2x^3)/dx\)

The derivative of a constant (6) is zero, and for the other terms, we apply the power rule of differentiation. The power rule states that the derivative of \(x^n\) with respect to x is \(nx^{(n-1)\). Applying the power rule, we obtain:

dy/dx = \(0 + 2(5x) - 3(2x^2)\)

Simplifying this expression, we get:

dy/dx = \(10x - 6x^2\)

Now, to find the slope of the tangent at the point where x = a, we substitute a for x in the derivative:

m = \(10a - 6a^2\)

Therefore, the slope of the tangent to the curve \(y = 6 + 5x^2 - 2x^3\) at the point where x = a is given by the expression \(10a - 6a^2\).

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The approximately 99.38% of the data falls between the values 120 and 280.

To find the percentage of data that falls between the values 120 and 280, we need to find the standard scores (z-scores) that correspond to these values and use a standard normal table to find the proportion of data within this range.

First, we'll find the z-score for 120:

z = (120 - 200) / 40 = -2.5

Similarly, the z-score for 280 is:

z = (280 - 200) / 40 = 2.5

Now we can use a standard normal table to find the proportion of data between -2.5 and 2.5 standard deviations from the mean. This proportion is approximately 0.9938 or 99.38%.

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The solution to the linear function M(x) = 180 is of x = -5.

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

In this problem, the function is defined as follows:

M(x) = 120 - 12x.

M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.

The domain of the situation is given as follows:

x ≥ 0. {discrete}

As the number of tickets cannot assume negative neither decimal values.

The equation is:

M(x) = 180.

The solution is calculated as:

120 - 12x = 180

12x = -60

x = -60/12

x = -5.

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Answer:

Yes, the runners number of strides will fit evenly into the length of the race.

Step-by-step explanation:

The bridge is 138,435 feet. You would divide this to get 46,145 as a whole number.

Answer:

Step-by-step explanation:

You are dividing 138435 by 3.

The quotient would be 46145 with no remainder. So the answer would be yes.

A 2nd way to do this is to see if 183435 is a multiple of 3.

Hope this helps!

Have a great day!

Answer:

137/24

Step-by-step explanation:

6 - f ÷ 6/7                              f = 1/4

6 - 1/4 ÷ 6/7

= 6 - 7/24

= 137/24

So, the answer is  137/24

\(\stackrel{ {\Large \begin{array}{llll} \mathbb{PEMDAS} \end{array}} }{6-f\div \cfrac{6}{7}\implies 6-\cfrac{1}{4}\div \cfrac{6}{7}}\implies 6-\cfrac{1}{4}\cdot \cfrac{7}{6}\implies 6-\cfrac{7}{24} \\\\\\ \cfrac{144-7}{24}\implies \cfrac{137}{24}\implies 5\frac{17}{24}\)

Answer:

multiply both sides by three

Answer:

The overview of the specific problem is outlined in the following section of the explanation.

Step-by-step explanation:

So that the above is the right answer.

Answer:

No

Step-by-step explanation:

They are not the same size.

Answer:

No, they are not congruent.

Step-by-step explanation:

Congruency is defined as moving, rotating, etc. without changing its shape or size.

Answer:

C (9,-2)

Step-by-step explanation:

Move to the right 9 times and move down 2 times (or -2)

Hope this helps!

Answer:

the answer is C

Step-by-step explanation:

the x axis goes first then the y

Answer:

5x² + 5x + 9

Step-by-step explanation:

(3x + 4) + ((5x² - 1) + (2x + 6))

Remove parenthesis

3x + 4 + 5x² - 1 + 2x + 6

Group like terms

5x² + 3x + 2x + 4 - 1 + 6

Subtract 1 from 4

5x² + 3x + 2x + 3 + 6

Add 3 and 6

5x² + 3x + 2x + 9

Combine like terms

5x² + 5x + 9

Answer: 5x² + 5x + 9

Answer:

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

Step-by-step explanation:

x - 5(x - 1) = x - (2x - 3) ← distribute parenthesis and simplify both sides

x - 5x + 5 = x - 2x + 3

- 4x + 5 = - x + 3 ( add x to both sides )

- 3x + 5 = 3 ( subtract 5 from both sides )

- 3x = - 2 ( divide both sides by - 3 )

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

Answer:

wouldn't it be 17 meters?

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

Explanation:

Draw a right triangle. The horizontal leg is 8 meters. The hypotenuse is 9 meters. The vertical height is unknown, so we'll call it x.

Apply the pythagorean theorem to solve for x

\(a^2 + b^2 = c^2\\\\8^2 + x^2 = 9^2\\\\64 + x^2 = 81\\\\x^2 = 81-64\\\\x^2 = 17\\\\x = \sqrt{17}\\\\x \approx 4.1231056\\\\x \approx 4.12\\\\\)

The tree is approximately 4.12 meters tall

Check out the diagram below.

Based on the given information, there is convincing evidence of a difference in the proportions of households with and without school-aged children that would support starting the school year a week earlier.

Based on the 90% confidence interval given, which ranges from 0.03 to 0.36, there is convincing evidence of a difference in the true proportions of households that would support starting the school year a week earlier, between those with school-aged children and those without. This is because the interval does not include 0, which suggests that the difference is statistically significant. However, it's important to note that this conclusion is based on the specific confidence level of 90%. If a different confidence level was used, the interval could potentially contain 0, indicating that there may not be a significant difference. Therefore, it's important to consider the level of confidence when interpreting the results. Additionally, the fact that different sample sizes were used could potentially impact the validity of the results. It's generally preferred to have equal sample sizes in order to increase the accuracy of the comparison. However, in this case, the difference in sample sizes does not necessarily invalidate the results, but it should still be taken into consideration.

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Answer:

\(\huge\boxed{\sf 2}\)

Step-by-step explanation:

Since these triangles are similar, we'll use proportion to find the unknown side.

\(\sf \frac{25}{10} = \frac{5}{?}\)

Cross Multiply

\(\sf ? * 25 = 10*5\)

Divide 25 to both sides

\(\sf ? = 50/25\\\\? = 2\)

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

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Answer:

True

Step-by-step explanation:

-6X = 42

Divide each side by -6

-6x/-6 = 42/-6

x = -7

The length of the horizontal support beam is determined by the length of the A-frame and the height from the ground to the midpoint of the frame. This can be computed using the Pythagorean Theorem.

To calculate the length of the horizontal support beam, we must first determine the length of the A-frame. Let's call this length "L". Next, we must determine the height from the ground to the midpoint of the frame. Let's call this height "H". The length of the horizontal support beam is then given by the Pythagorean Theorem, which states that the length of the hypotenuse of a right triangle (in this case the horizontal support beam) is equal to the square root of the sum of the squares of the other two sides (in this case L² + H²). Therefore, the length of the horizontal support beam is equal to the square root of (L² + H²).

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Answer:

b. vertical shrink

Step-by-step explanation:

Answer:

l = (3x+5)

Step-by-step explanation:

Given that,

The area of a room, \(A=3x^2-x-10\)

The width of the room, \(b=(x-2)\)

We need to find the length of the room.

The area of the room is given by :

A = lb

\(l=\dfrac{A}{b}\\\\l=\dfrac{3x^2-x-10}{x-2}\\\\l=\dfrac{(x-2)(3x+5)}{x-2}\\\\l=(3x+5)\)

So, the length of the room is equal to (3x+5).

For exercise 1, the derivative of F(x) = 2x^3 - 3x^2 + 3/x^2 is f'(x) = 6x^2 - 6x + 6/x^3, obtained by applying the power rule. For exercise 2, the derivative of F(x) = (x^2 + 2x)(3x^2 - 4) is f'(x) = 12x^3 - 8x + 18x^2 - 8, obtained by expanding and differentiating each term separately using the power rule.

Exercise 1:

Given: F(x) = 2x^3 - 3x^2 + 3/x^2

To find the derivative f'(x), we first rewrite F(x) as a polynomial:

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

Applying the power rule to find f'(x), we differentiate each term separately:

For the first term, 2x^3, we apply the power rule:

f'(x) = 3 * 2x^(3-1) = 6x^2

For the second term, -3x^2, the power rule gives:

f'(x) = -2 * 3x^(2-1) = -6x

For the third term, 3x^(-2), we use the power rule and the chain rule:

f'(x) = -2 * 3x^(-2-1) * (-1/x^2) = 6/x^3

Combining these derivatives, we get the overall derivative:

f'(x) = 6x^2 - 6x + 6/x^3

Exercise 2:

Given: F(x) = (x^2 + 2x)(3x^2 - 4)

To find the derivative f'(x), we expand the expression first:

F(x) = 3x^4 - 4x^2 + 6x^3 - 8x

Applying the power rule to find f'(x), we differentiate each term separately:

For the first term, 3x^4, we apply the power rule:

f'(x) = 4 * 3x^(4-1) = 12x^3

For the second term, -4x^2, the power rule gives:

f'(x) = -2 * 4x^(2-1) = -8x

For the third term, 6x^3, we apply the power rule:

f'(x) = 3 * 6x^(3-1) = 18x^2

For the fourth term, -8x, the power rule gives:

f'(x) = -1 * 8x^(1-1) = -8

Combining these derivatives, we get the overall derivative:

f'(x) = 12x^3 - 8x + 18x^2 - 8

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Answer:55

Step-by-step explanation:

The purchase price in dollars of the television that has been marked up 25% of the retail price of $4,500 would be $5,625.

To find the purchase price of the television in dollars, follow these steps:

1. Determine the markup amount: 25% of the retail price ($4,500).
2. Subtract the markup amount from the retail price to find the purchase price.

Step 1: Calculate the markup amount:
25% of $4,500 = 0.25 × 4,500 = $1,125

Step 2: Subtract the markup amount from the retail price:
$4,500 (retail price) - $1,125 (markup) = $3,375

The purchase price of the television in dollars is $3,375.

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