A parent is buying two types of chocolate truffles for their family. The oldest child can eat twice as much as their younger siblings and prefers white chocolate (W), the younger three like dark chocolate (D) and the spouse likes white chocolate (W). Five white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 6 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $34.00, how much was each dark chocolate truffle

y'' - 6y' + 9y = 0

If y = C₁ exp(3x) + C₂ x exp(3x), then

y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))

y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))

Substituting these into the DE gives

(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))

… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))

… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))

= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))

… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))

… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)

= 0

so the provided solution does satisfy the DE.

Answer:

-25/4 = u

Step-by-step explanation:

-3u-17=(u+8)

Add 3u to each side

-3u+3u-17=(u+3u+8)

-17 = 4u +8

Subtract 8 from each side

-17-8 = 4u+8-8

-25 = 4u

Divide by 4

-25/4 = 4u/4

-25/4 = u

Given:

The set is:

[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]

To find:

The raster form of the given set.

Solution:

We know that, natural numbers are all positive integers.

Natural numbers: 1, 2, 3, 4,... .

The given set is:

[tex]\{x|x\text{ is a natural number less than }-2\}[/tex]

Here, x is a natural number and it is less than -2, which is not possible.

Since all natural numbers are greater than or equal to 1, therefore the given set has no element.

[tex]\{x|x\text{ is a natural number less than }-2=\phi[/tex]

Therefore, the roaster form of the given set is [tex]\phi[/tex] or [tex]\{\ \}[/tex].

Answer:

B

Step-by-step explanation:

Subtracting second equation from first, term by term , gives

(8x - 4x) + (3y - 3y) = (14 - 8) , that is

4x + 0 = 6, so

4x = 6 → B

Answer:

Please look at the picture

Step-by-step explanation:

Please look at the picture I have drawn it for you

Answer:

60

Step-by-step explanation:

10 x 6 = 60

Hope this helped! :)

Answer:

[tex]{ \tt{ = ( log_{x}16)( log_{2}x) }}[/tex]

Change base x to base 2:

[tex]{ \tt{ = (\frac{ log_{2}16}{ log_{2}x } )( log_{2}x)}} \\ \\ { \tt{ = log_{2}(16) }} \\ = { \tt{ log_{2}(2) }} {}^{4} \\ = { \tt{4 log_{2}(2) }} \\ = { \tt{4}}[/tex]

Answer:

[tex]A)\:x<12[/tex]

[tex]5(x+5)<85\\5x+25<85\\5x<85-25\\5x<60\\x<12[/tex]

OAmalOHopeO

Answer:

x < 12.................................

Answer:

y = 3

Step-by-step explanation:

6sin(30) = 3

Answer:

The p-value of the test is 0.242 > 0.05, which means that this information does not indicate a difference between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts.

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Women:

51 out of 222, so:

[tex]p_1 = \frac{51}{222} = 0.2297[/tex]

[tex]s_1 = \sqrt{\frac{0.2297*0.7703}{222}} = 0.0282[/tex]

Men:

49 out of 174, so:

[tex]p_2 = \frac{49}{174} = 0.2816[/tex]

[tex]s_2 = \sqrt{\frac{0.2816*0.7184}{174}} = 0.0341[/tex]

Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts?

Either way, so a two tailed test to see if the difference of proportions is different of 0.

At the null hypothesis, we test if it is not different of 0, so:

[tex]H_0: p_1 - p_2 = 0[/tex]

At the alternative hypothesis, we test if it is different of 0, so:

[tex]H_1: p_1 - p_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_1 - p_2 = 0.2297 - 0.2816 = -0.0519[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0282^2+0.0341^2} = 0.0442[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.0519 - 0}{0.0442}[/tex]

[tex]z = -1.17[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the differences being of at least 0.0519, either way, which is P(|z| > 1.17), that is, 2 multiplied by the p-value of z = -1.17.

Looking at the z-table, z = -1.17 has a p-value of 0.121.

0.121*2 = 0.242

The p-value of the test is 0.242 > 0.05, which means that this information does not indicate a difference between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts.

Answer:

Creo que es 36

Step-by-step explanation

:D

Answer:

36

Step-by-step explanation:

minus sign ironically makes it go to the right

because the function crosses the y axis at -13

It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of  transformation, we have to compare the two equations and look for changes.

In the equation y = x - 13, we subtract 13 from the value of x.

This means that the graph of y = x is shifted 13 units downwards,

since every point on the graph has 13 subtracted from its y-coordinate.

Hence,  It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.

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Answer:

The last one. 4.

Step-by-step explanation:

The square root of a positive or negative number can't be negative. so it's positive 4.

Answer: a = 25.67

Step-by-step explanation:

Answer:

Multiply the product of 16,544 x 7 by 10 as it id the same as multiplying 16,544 x 70.

Solution :

Given data:

Mean, μ = $87,500

Standard deviation, σ =  $26,000

Sample number, n = 63

a). The value of [tex]$\mu_{x}$[/tex] :

   [tex]$\mu_x=\mu$[/tex]

       = 87,500

b). The value of [tex]$\sigma_x$[/tex] :

    [tex]$\sigma_x = \frac{\sigma}{\sqrt n}$[/tex]

   [tex]$\sigma_x = \frac{26000}{\sqrt {63}}$[/tex]

        = 3275.69

c). The shape of the sampling distribution is that of a normal distribution (bell curve).

d). The value z-score for the value =80,000.

   [tex]$z-\text{score} =\frac{\overline x - \mu}{\sigma - \sqrt{n}}$[/tex]

  [tex]$z-\text{score} =\frac{80000-87500}{26000 - \sqrt{63}}$[/tex]

                = -2.2896

                ≈ -2.29

e). P(x > 80000) = P(z > -2.2896)

                           = 0.9890

9514 1404 393

Answer:

  (-13, 10)

Step-by-step explanation:

If M is the midpoint of segment DE, then ...

  D = 2M -E

  D = 2(-3, 4) -(7, -2) = (2(-3)-7, 2(4)+2) = (-13, 10)

The other end point is (-13, 10).

Answer:

32

Step-by-step explanation:

Answer:

x = 10

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

14x - (-5x + 6 - 3x - 4) = 4(5x) + 10

Step 2: Solve for x

Answer:

39-13=26

Step-by-step explanation:

plus(minus)=minus

9514 1404 393

Answer:

  split the number into equal pieces

Step-by-step explanation:

Assuming "splitting any number" means identifying parts that have the number as their sum, the maximum product of the parts will be found where the parts all have equal values.

We have to assume that the number being split is positive and all of the parts are positive.

If we divide number n into parts x and (n -x), their product is the quadratic function x(n -x). The graph of this function opens downward and has zeros at x=0 and x=n. The vertex (maximum product) is halfway between the zeros, at x = (0 + n)/2 = n/2.

Similarly, we can look at how to divide a (positive) number into 3 parts that have the largest product. Let's assume that one part is x. Then the other two parts will have a maximum product when they are equal. Their values will be (n-x)/2, and their product will be ((n -x)/2)^2. Then the product of the three numbers is ...

  p = x(x^2 -2nx +n^2)/4 = (x^3 -2nx^2 +xn^2)/4

This will be maximized where its derivative is zero:

  p' = (1/4)(3x^2 -4nx +n^2) = 0

  (3x -n)(x -n) = 0 . . . . . . . . . . . . . factor

  x = n/3  or  n

We know that x=n will give a minimum product (0), so the maximum product is obtained when x = n/3.

A similar development can prove by induction that the parts must all be equal.

Answer:hi

Step-by-step explanation:

Answer:

B) All real numbers except 0 and integer multiples of 8π∕5

Step-by-step explanation:

Cotangent function:

The cotangent function is given by:

[tex]y = \cot{ax} = \frac{\cos{ax}}{\sin{ax}}[/tex]

Domain:

All real values except those at which:

[tex]\sin{ax} = 0[/tex]

The sine is 0 for 0 and all integer multiples of [tex]\frac{1}{a}[/tex]

In this question:

[tex]a = \frac{5}{8}[/tex], so the values outside the domain are 0 and the integer multiples of [tex]\frac{8}{5}[/tex]. Then the correct answer is given by option b.

9514 1404 393

Answer:

Step-by-step explanation:

1. Input 3 for x and do the arithmetic.

  z(x) = x+1

  z(3) = 3+1 = 4 . . . . . the output is 4

__

2. The expression for n(x) has x in the denominator. The expression will be undefined when the denominator is zero, so x=0 cannot be used.

D

A

B

C

for more explanation please don't hesitate to just respond

Answer:

See Below.

Step-by-step explanation:

We are given the equation:

[tex]\displaystyle y^2 = 1 + \sin x[/tex]

And we want to prove that:

[tex]\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1[/tex]

Find the first derivative by taking the derivative of both sides with respect to x:

[tex]\displaystyle 2y \frac{dy}{dx} = \cos x[/tex]

Divide both sides by 2y:

Find the second derivative using the quotient rule:

[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}[/tex]

Substitute:

[tex]\displaystyle 2y\left(-\frac{2y^2\sin x+\cos ^2 x}{4y^3}\right) + 2\left(\frac{\cos x}{2y}\right)^2 +y^2 = 1[/tex]

Simplify:

[tex]\displaystyle \frac{-2y^2\sin x-\cos ^2x}{2y^2} + \frac{\cos ^2 x}{2y^2} + y^2 = 1[/tex]

Combine fractions:

[tex]\displaystyle \frac{\left(-2y^2\sin x -\cos^2 x\right)+\left(\cos ^2 x\right)}{2y^2} + y^2 = 1[/tex]

Simplify:

[tex]\displaystyle \frac{-2y^2\sin x }{2y^2} + y^2 = 1[/tex]

Cancel:

[tex]\displaystyle -\sin x + y^2 = 1[/tex]

Substitute:

[tex]-\sin x + \left( 1 + \sin x\right) =1[/tex]

Simplify. Hence:

[tex]1\stackrel{\checkmark}{=}1[/tex]

Q.E.D.

Answer:

(0,1) and (3,4)

Step-by-step explanation:

It's the points where they meets, judging the graph, it's x = 0, y = 1 and x = 3, y = 4

put them in the equation and you'll see the the values satisfies the equation

Answered by GAUTHMATH

Answer:

100 in²

Step-by-step explanation:

4 triangles, each of them has area = 10*5/2

so total area = (10*5/2)*4

= (10*5*2)

= 100 in²

Answered by GAUTHMATH

The lateral surface area of the pyramid is 100 in²

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.

4 triangles, each of them has an area = 10 x ( 5/2 )

So total area = (10 x 5/2) x 4

Total area = (10 x 5 x 2)

Total area = 100 in²

Therefore the lateral surface area of the pyramid is 100 in²

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Answer:

b

Step-by-step explanation:

2 * 3 to the -2 power. 3x-3=-9

2x-9=-18