There are 40 students in Mrs. Rusczyk's first grade class. if there are three times as many students with blond hair as with blue eyes, 3 students with blond hair and blue eyes, and 15 students with neither blond hair nor blue eyes, how many students have blue eyes?

The perimeter becomes double when each side is twice as long as the original.

According to the statement

we have given that the perimeter of a rectangle is 24 inches. and we have to find that the what effect does this enlargement have on the perimeter.

So, For this purpose, we know that the

A rectangle is a parallelogram all of whose angles are right angles especially : one with adjacent sides of unequal length.

The formula to find the perimeter of rectangle is 2(L + B)

And we the length is goes to increased by double then the perimeter will also goes to double.

Because perimeter is directly proportional to the length and breadth of rectangle.

So, The perimeter becomes double when each side is twice as long as the original.

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Using equivalent angles, the solutions are given as follows:

a) [tex]x = \frac{15\pi}{23}[/tex].

b) [tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex].

c) [tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.

Hence:

[tex]\pi - \frac{8\pi}{23} = \frac{23\pi}{23} - \frac{8\pi}{23} = \frac{15\pi}{23}[/tex]

Hence [tex]x = \frac{15\pi}{23}[/tex].

For item b, if two angles are complementary, the sine of one is the cosine of the other.

Complementary angles add to 90º = 0.5pi, hence:

[tex]x + \frac{11\pi}{31} = \frac{\pi}{2}[/tex]

[tex]x = \frac{31\pi}{62} - \frac{22\pi}{62}[/tex]

[tex]x = \frac{9\pi}{62}[/tex]

The equivalent angle on the second quadrant is:

[tex]\pi - \frac{9\pi}{62} = \frac{62\pi}{62} - \frac{9\pi}{62} = \frac{53\pi}{62}[/tex]

Hence the solutions are:

[tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex]

For item c, the angles are also complementary, hence:

[tex]x + \frac{\pi}{8} = \frac{\pi}{2}[/tex]

[tex]x = \frac{4\pi}{8} - \frac{\pi}{8}[/tex]

[tex]x = \frac{3\pi}{8}[/tex]

The tangent is also positive on the third quadrant, hence the equivalent angle is:

[tex]x = \pi + \frac{3\pi}{8} = \frac{8\pi}{8} + \frac{3\pi}{8} = \frac{11\pi}{8}[/tex]

Hence the solutions are:

[tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]

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See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

Transverse axis

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

The vertices

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

The co-vertices

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola

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The linear equations are y - 25 = 0.89(x - 20) and y  = 0.89x + 7.2

The complete question is added as an attachment

The two points from the graph are (20, 25) and (38, 41)

The slope of the line is calculated using

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (41 - 25)/(38 - 20)

Evaluate

m =0.89

This is calculated as:

y - y1 = m(x - x1)

Substitute the known values in the above equation

y - 25 = 0.89 * (x - 20)

Evaluate

y - 25 = 0.89(x - 20)

We have:

y - 25 = 0.89(x - 20)

Expand

y - 25 = 0.89x - 17.8

Add 25 to both sides

y  = 0.89x + 7.2

Hence, the linear equations are y - 25 = 0.89(x - 20) and y  = 0.89x + 7.2

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Answer:

[tex]3x^2[/tex]

Step-by-step explanation:

First main thing to know is the product and quotient rule of exponents.

Product Rule:

  [tex]x^a*x^b = x^{a+b}[/tex]

  And if this doesn't make sense, you can think of the exponent like this:

  [tex]x^a*x^b = (x*x*x*x...\text{ a amount of times}) * (x * x * x \text{ b amount of times})[/tex]

  and since multiplication is commutative, we can just combine all these x's, and since the total amount on the left is "a", and the right is "b", the total combined x's should be a+b, which can be expressed as:
   [tex]x*x*x... \text{ a+b amount of times}[/tex]

   which can be expressed as an exponent (x^(a+b))

Quotient Rule:

   [tex]\frac{x^a}{x^b} = x^{a-b}[/tex]

  You can use similar reasoning for this, since if you write it out you get

   [tex]\frac{x*x*x...\text{ a amount of times}}{x*x*x\text{ b amount of times}}[/tex]

  and since you have an x in the numerator and the denominator, you can simply cancel the x's out. In doing this you want to remove the denominator, so you cancel out "b" x's. So there will be (a-b) x's left in the numerator, and a 1 in the denominator, so it's just x^(a-b)

Ok so now let's apply these to solve your question

[tex]\frac{(15x^{-4})*x^{15}}{(5x^4)*x^5}\\[/tex]

So let's combine the exponents in the numerator and denominator using the product rule

[tex]\frac{15x^{11}}{5x^9}\\[/tex]

Now we can divide the 15 by 5, and divide the x^11 by the x^9 using the quotient rule

[tex]3x^2[/tex]

Answer: TRS is congruent to CSE

Step-by-step explanation:

You can find congruent angles by locating the ones with the same number of lines. You want to start with the angles in the order of TRS.

Angle T has 1 line, so is congruent to C, which also has 1 line.

Angle R has 2 lines, so is congruent to S, which also has 2 lines.

Angle S has 3 lines, so is congruent to E, which also has 3 lines.

You want to keep these in the same order, so TRS, in the order of 1-2-3 lines, is congruent to CSE, also in the order of 1-2-3 lines (aka congruency markings).

The length of the trip at a distance of 300 miles and the given times are

The distance is given as:

d = 300

The formula is represented as:

d = r * t

Make t the subject

t = d/r

Substitute 300 for d

t = 300/r

When r = 50 mph,

t = 300/50

Evaluate

t = 60

When r= 70 mph, we have

t = 300/70

Evaluate

t = 30/7

When r = x, we have

t = 300/x

When r = x + 10, we have

t = 300/x + 10

When r = x - 5, we have

t = 300/x - 5

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Complete question

A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of:

Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.

Answer:

30calories

Step-by-step explanation:

Answer:

30 calories per ounce

Step-by-step explanation:

The answer given by rachelwang2022 is correct.

I am just adding to the explanation

Since there are 150 calories in a 5-ounce container, you can determine the number of calories per ounce by simply dividing 150 by 5.

150/5 = 30 calories per ounce

Answer:

d = [tex]\sqrt{65}[/tex]

Step-by-step explanation:

The distance between two points is found by

d = [tex]\sqrt{( x2-x1)^2 + ( y2-y1)^2}[/tex] where (x1,y1) and (x2,y2) are the two points

d = [tex]\sqrt{(-2 - -1)^2+(-6 - -14)^2 }[/tex]

d =[tex]\sqrt{( -2+1)^2 + (-6+14)^2}\\[/tex]

d = [tex]\sqrt{(-1)^2 +( 8)^2 }[/tex]

d = [tex]\sqrt{1+64}[/tex]

d = [tex]\sqrt{65}[/tex]

Answer:

Step-by-step explanation:

add both the equations then you will get

3x^3-x^2+2

but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x

so the equation will be

3x^3-x^2+0x+2

The value of the probability P(A and B) is 0.20

The given parameters about the probability are

P(A or B) = 0.9

P(A) = 0.5

P(B) = 0.6

To calculate the probability P(A and B), we use the following formula

P(A and B) = P(A) + P(B) - P(A or B)

Substitute the known values in the above equation

P(A and B) = 0.5 + 0.6 - 0.9

Evaluate the expression

P(A and B) = 0.2

Hence, the value of the probability P(A and B) is 0.20

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Answer:

Răspuns: 88=>rezultatul

Explicație pas cu pas:

a+2b =18/×3

b+3c=17/×2

3a+6b =54 ^

2b+6c=34 | +

3a+(6b+2b)+6c=54+34

3a+8b+6c=88

Step-by-step explanation:

Answer:

shift left 3

Step-by-step explanation:

(x+3)²

x = -3

therefore translation by (-3,0)

The negative number shows it move to the left

Answer:

X-intercepts:

[tex] (\frac{3}{7} ,0)[/tex]

Y-intercepts:(0,3)

Step-by-step explanation:

Hello!

given expression

[tex]y = - 7x + 3[/tex]

x-intercept is the point on the graph where y=0

solve

[tex] - 7x + 3 = 0 \\ - 7x = - 3 \\ x = \frac{3}{7} [/tex]

Thus, x-intercept

[tex]( \frac{3}{7} ,0)[/tex]

y-intercept is the point on the graph where x=0

solve

[tex]y = - 7(0) + 3 \\ y = 0 + 3 \\ y = 3[/tex]

Thus, y-intercept (0,3)

Hope it helps!

If (-1, -1) is an extremum of [tex]f[/tex], then both partial derivatives vanish at this point.

Compute the gradients and evaluate them at the given point.

[tex]\nabla f = \left\langle y - \dfrac1{x^2}, x - \dfrac1{y^2}\right\rangle \implies \nabla f (-1,-1) = \langle-2,-2\rangle \neq \langle0,0,\rangle[/tex]

[tex]\nabla f = \langle 2x+2,0\rangle \implies \nabla f(-1,-1) = \langle0,0\rangle[/tex]

[tex]\nabla f = \langle y, x-2y\rangle \implies \nabla f(-1,1) = \langle-1,1\rangle \neq\langle0,0\rangle[/tex]

[tex]\nabla f = \left\langle y + \frac1{x^2}, x + \frac1{y^2}\right\rangle \implies \nabla f(-1,1) = \langle0,0\rangle[/tex]

The first and third functions drop out.

The second function depends only on [tex]x[/tex]. Compute the second derivative and evaluate it at the critical point [tex]x=-1[/tex].

[tex]f(x,y) = x^2+2x \implies f'(x) = 2x + 2 \implies f''(x) = 2 > 0[/tex]

This indicates a minimum when [tex]x=-1[/tex]. In fact, since this function is independent of [tex]y[/tex], every point with this [tex]x[/tex] coordinate is a minimum. However,

[tex]x^2 + 2x = (x + 1)^2 - 1 \ge -1[/tex]

for all [tex]x[/tex], so (-1, 1) and all the other points [tex](-1,y)[/tex] are actually global minima.

For the fourth function, check the sign of the Hessian determinant at (-1, 1).

[tex]H(x,y) = \begin{bmatrix} f_{xx} & f_{xy} \\ f_{yx} & f_{yy} \end{bmatrix} = \begin{bmatrix} -2/x^3 & 1 \\ 1 & -2/y^3 \end{bmatrix} \implies \det H(-1,-1) = 3 > 0[/tex]

The second derivative with respect to [tex]x[/tex] is -2/(-1) = 2 > 0, so (-1, -1) is indeed a local minimum.

The correct choice is the fourth function.

Answer:

thanks for your support of the personal information on the direction of economics class

The amount add to the borrower's monthly payment is $313.33.

Given that lender requires PMI that is 0.8% of the loan amount of $470,000.

A loan's PMI, or personal mortgage insurance, is a type of mortgage insurance used by lenders when making traditional loans such as home loans. A PMI helps cover the loss to the lender (bank) if the borrower stops making monthly mortgage payments on their home loan. Therefore, the PMI can be described as a kind of risk mitigation tool for the bank when the borrower defaults on their EMIs (monthly mortgage payments). So, PMI for a borrower is an additional cost or payment for the borrower on top of his monthly payments i.e. EMI.

Thus, the additional amount of dollars that the borrower has to pay for the PMI on his loan along with his monthly mortgage payments

= Principal Loan amount × (PMI/12)

= $470,000 × (0.8%/12)

= $470,000 × (0.008/12)

= $470,000 × 0.0006666667

=$313.333349

Hence, the additional monthly payment for PMI where lender requires PMI that is 0.8% of the loan amount of $470,000 is $313.33.

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Using proportions and the markup concept, it is found that the cost to store is of $12.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The markup price of 80% means that the selling price is of 180% = 1.8 of the cost to store of x. The selling price is of $21.60, hence:

1.8x = 21.60

x = 21.60/1.8

x = $12.

The cost to store is of $12.

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The number of specimens should be tested is 1352.

According to the statement

we have to given that the in testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. and we have to find the number specimen should be tested.

so,

Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.

For an uniform distribution of bounds a and b, the standard deviation is given by:

σ = [tex]\sqrt{\frac{(b-a^{2})}{12} }[/tex]

and put the values a= 50 and b= 700 then the

standard deviation is 187.64

And here the critical value become 1.6 then

We want the sample for a margin of error of 10, thus, we have to solve for n with the help of value of m is 100.

Then n is 1352.

So,  The number of specimens should be tested is 1352.

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The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

The quadratic expression in its standard form is;

ax² + bx + c

Given the expression in the question;

x² - 2x + ------

Compared with the standard for a quadratic expression

Let the missing value be represented by "c"

x² - 2x + c

Now, to find the value of c, we divide the coefficient of x by 2 and then square the result.

Note that, coefficient of x is b

c = ( b/2 )²

We substitute

c = ( -2/2 )²

c = ( -1 )²

c = 1

The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

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Answer:

0.85

Step-by-step explanation:

1 - 15% = 1 - 0.15 = 0.85

[tex] y = (0.85)^\frac{t}{12} [/tex]

Answer: 0.85

Answer:370 play football and 20 play hockey

Step-by-step explanation: because 400 - 130 equals 370 for football

then hockey 150-130 equals 20

Then the total students are 420

150+400-130 equals 420

Answer:

49°

Step-by-step explanation:

The circumference of a circle measures 360 degrees, so arc XW is 98°.

So, angle XWY is 49°.

Using the z-distribution, the margin of error for the 95% confidence interval used to estimate the population proportion is 0.0683 = 6.83%.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

For this problem, the parameters are given as follows:

[tex]n = 198, \pi = \frac{80}{198} = 0.404[/tex]

Hence the margin of error is:

[tex]M = 1.96\sqrt{\frac{0.404(0.596)}{198}} = 0.0683[/tex]

The margin of error for the 95% confidence interval used to estimate the population proportion is 0.0683 = 6.83%.

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Answer:

Step-by-step explanation:

I am going to be honest here. I know the answer is 22 but I cant really explain it you kinda just have to trust I'm right.

Answer:

  |-3| = 3 and -|-4| = -4

Step-by-step explanation:

The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.

|-3| = 3 (true) and -|-4| = -4 (true)   ⇒ this statement is true

|-3| = 3 (true) and |-4| = -4 (false)   ⇒ this statement is false

-|3| = 3 (false) and |4| = 4 (true)   ⇒ this statement is false

|-3| = 3 (true) and -|4| = 4 (false)   ⇒ this statement is false

__

Additional comment

A compound "and" statement is only true if all of the parts of it are true.

Answer: [tex]4x^3 -29x^2 +10x-21[/tex]

Step-by-step explanation:

[tex](4x^2 -x+3)(x-7)\\\\=4x^3 -28x^2 -x^2 +7x+3x-21\\\\=4x^3 -29x^2 +10x-21[/tex]