David signed up to provide snacks for his daughter and her school group's camping trip. He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days. He also wanted to buy some boxes of fruit snacks, which were $4 each. He just needed to decide how many to buy, and then figure the total cost.

Select the expression that will help him to determine the total cost.

We can write the integration domain as

[tex]D = \left\{(x,y) \mid -1 \le y \le 1 \text{ and } 2y-2 \le x \le -y+1\right\}[/tex]

so that the integral is

[tex]\displaystyle \iint_D -\sin(y+x) \, dA = \int_{-1}^1 \int_{2y-2}^{-y+1} -\sin(y+x) \, dx \, dy[/tex]

Compute the integral with respect to [tex]x[/tex].

[tex]\displaystyle \int_{2y-2}^{-y+1} -\sin(y+x) \, dx = \cos(y+x)\bigg|_{x=2y-2}^{x=-y+1} \\\\ ~~~~~~~~ = \cos(y+(2y-2)) - \cos(y+(-y+1)) \\\\ ~~~~~~~~ = \cos(3y-2) - \cos(1)[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_{-1}^1 (\cos(3y-2) - \cos(1)) \, dy = \left(\frac13 \sin(3y-2) - \cos(1) y\right) \bigg|_{y=-1}^{y=1} \\\\ ~~~~~~~~ = \left(\frac13 \sin(3-2) - \cos(1)\right) - \left(\frac13 \sin(-3-2) + \cos(1)\right) \\\\ ~~~~~~~~ = \boxed{\frac13 \sin(1) - 2 \cos(1) + \frac13 \sin(5)}[/tex]

Answer:

z = [tex]\sqrt{30}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

z² = 3 × (3 + 7) = 3 × 10 = 30 ( take square root of both sides )

z = [tex]\sqrt{30}[/tex]

Answer:

4x + 3 just take away rhe values

Answer:

To know the final result we have to make 30% of 56 dollars and add the result to the 56 dollars to know the original price.

Operations:

30% de 56 = (30x56)/100= 16,8 dollars.

56+16,8= 72,8 dollars (final result)

A pair of shoes is reduced by 30% down to a price of £56 then the original price of the pair of shoes was £80.

To find the original price of a pair of shoes using a mathematical approach. We are given that the shoes were reduced by 30% and their final price is £56. We will use algebraic equations to determine the original price of the shoes.

Let's denote the original price of the shoes as "P". Since the shoes were reduced by 30%, we can express this reduction as a decimal, which is 0.30 (30% = 30/100 = 0.30).

The amount of reduction is then given by 0.30 multiplied by the original price, which is 0.30P.

The final price of the shoes after the reduction is £56. We can set up an equation to represent this:

P - 0.30P = 56

Now, let's simplify the equation:

0.70P = 56

Next, we need to isolate "P" on one side of the equation. To do this, we divide both sides by 0.70:

[tex]\[ \frac{{0.70P}}{{0.70}} = \frac{{56}}{{0.70}} \][/tex]

This simplifies to:[tex]\[ P = \frac{{56}}{{0.70}} \][/tex]

Now, let's calculate the value of "P":

[tex]\[ P = \frac{{56}}{{0.70}} = 80 \][/tex]

So, the original price of the pair of shoes was £80.

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The area below the mean compares to the area above the mean in a normal distribution as the areas are always equal regardless of the mean. Option A This is further explained below.

Generally, The normal distribution, also known as the Gaussian distribution, is a kind of probability distribution that is symmetric around the mean. This means that it demonstrates that data that are closer to the mean are more likely to occur than data that are farther away from the mean. When represented graphically, the normal distribution takes the shape of a "bell curve."

In conclusion, In a normal distribution, the area below the mean is compared to the area above the mean since the areas are always equal regardless of the mean. This is true even if the mean is different.

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Complete Question

How does the area below the mean compare to the area above the mean in a normal distribution?

A. the areas are always equal regardless of the mean

B. the areas are sometimes equal depending upon the standard deviation of the distribution

C. the area above the mean is larger since the values are larger as you move above the mean

D. the areas are sometimes equal depending upon the value of the mean

Answer: 7 1/16  and 1 9/16

Step-by-step explanation:  1 3/8 x 1.5 is 1 3/8 x 1 5/10  11/8 x 15/10 which is 165/80. We divide it by 5/5 to get 33/16. This as a mixed number is 2 1/16.  We add 5 to get 7 1/16.

5/8 divided by 0.4 is 5/8 divided by 2/5. We divide this by first finding the reciprocal of 2/5 which is 5/2. 5/8 x 5/2 = 25/16. This as a mixed number is 1 9/16.

In matrix form, the system is given by

[tex]\begin{bmatrix} -1 & 1 & -1 \\ 2 & -1 & 1 \\ 3 & 2 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} -20 \\ 29 \\ 29 \end{bmatrix}[/tex]

I'll use G-J elimination. Consider the augmented matrix

[tex]\left[ \begin{array}{ccc|c} -1 & 1 & -1 & -20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right][/tex]

• Multiply through row 1 by -1.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 2 & -1 & 1 & 29 \\ 3 & 2 & 1 & 29 \end{array} \right][/tex]

• Eliminate the entries in the first column of the second and third rows. Combine -2 (row 1) with row 2, and -3 (row 1) with row 3.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 5 & -2 & -31 \end{array} \right][/tex]

• Eliminate the entry in the second column of the third row. Combine -5 (row 2) with row 3.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 3 & 24 \end{array} \right][/tex]

• Multiply row 3 by 1/3.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]

• Eliminate the entry in the third column of the second row. Combine row 2 with row 3.

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]

• Eliminate the entries in the second and third columns of the first row. Combine row 1 with row 2 and -1 (row 3).

[tex]\left[ \begin{array}{ccc|c} 1 & 0 & 0 & 9 \\ 0 & 1 & 0 & -3 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]

Then the solution to the system is

[tex]\boxed{x=9, y=-3, z=8}[/tex]

If you want to use G elimination and substitution, you'd stop at the step with the augmented matrix

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 1 & 20 \\ 0 & 1 & -1 & -11 \\ 0 & 0 & 1 & 8 \end{array} \right][/tex]

The third row tells us that [tex]z=8[/tex]. Then in the second row,

[tex]y-z = -11 \implies y=-11 + 8 = -3[/tex]

and in the first row,

[tex]x-y+z=20 \implies x=20 + (-3) - 8 = 9[/tex]

The height of the container be so as to minimize cost will be 1.20. inches.

The volume of the box will be:

= 2x × 3x × h

= 6x²h

Volume = 6x²h

12 = 6x²h

h = 2x²

The cost function will be:

C = 2.60(2)(6x²) + 4.30(12x)h

C = 31.2x² + 51.6xh

Taking the derivative

62.4x + 51.6h

h = 1.20

Therefore, the height of the container be so as to minimize cost will be 1.20 inches.

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Put the equation in standard linear form.

[tex]x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}[/tex]

Find the integrating factor.

[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5[/tex]

Multiply both sides by [tex]\mu[/tex].

[tex](t+5) x'(t) + x(t) = 5(t+5)e^{5t}[/tex]

Now the left side the derivative of a product,

[tex]\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}[/tex]

Integrate both sides.

[tex](t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt[/tex]

On the right side, integrate by parts.

[tex](t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C[/tex]

Solve for [tex]x(t)[/tex].

[tex]\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}[/tex]

Answer: 16

Step-by-step explanation:

1.5x = 24

24/1.5 = 16 students.

Given the width and length of Teresa's new desktop computer, the length of the diagonal of the desktop screen is approximately 22.8 inches.

If a diagonal line cuts through a rectangle, it forms two equal right triangles. the side lengths of this triangle can be easily determined using Pythagoras theorem. Pythagoras theorem is expressed as;

c² = a² + b²

Where c is the hypotenuse or diagonal, a is base length and b is perpendicular height.

Given the data in the question;

We substitute into the equation above.

c² = a² + b²

c² = (18in)² + (14in)²

c² = 324in² + 196in²

c² = 520in²

c = √( 520in² )

c = 22.8in

Given the width and length of Teresa's new desktop computer, the length of the diagonal of the desktop screen is approximately 22.8 inches.

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Answer:

7/18

Step-by-step explanation:

P(sophomore girl) is 7 out of a total 30.

P(girl) is 18 out of 30.

(7/30) / (18/30) = 7/18

If you just look at the girls column you can see this immediately. A given is that we're looking for a girl (18 girls), then what is the chance that it's a sophomore. That is 7 out of 18.

Answer:

The answer would be 7 over 18 in fraction form fill in 7 then 18

Step-by-step explanation:

7/18

Answer:

The original number is 72.

Step-by-step explanation:

Let the number by

[A][B]

The reverse number is

[B][A]

Original number:

A = B + 5

[A][B] - 2[B][A] = [A][B]/4

10A + B - 20B - 2A = (10A + B)/4

8A - 19B = (10A + B)/4

32A - 76B = 10A + B

22A - 77B = 0

22(B + 5) - 77B = 0

22B + 110 - 77B = 0

-55B = -110

B = 2

A = B + 5 = 2 + 5 = 7

The original number is 72.

The reverse is 27.

Let's check.

"the tens digit of a 2 digit number is 5 greater than the units digit"

7 is 5 greater than 2,so 72 looks good so far.

"if you subtract twice the reverse number the result is one fourth the original"

The reverse number is 27. Twice 27 is 2 × 27 = 54.

Subtract 54 from 72: 72 - 54 = 18

18 is 1/4 of 72. It works.

Answer: the original number is 72

Considering the definition of probability, 12 of the 48 students surveyed were in favor of the new dress code.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

Then, the probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.

P(A)=number of favorable events÷ number of total events

In this case, you know:

Replacing in the definition of probability:

P(A)=225 students÷ 900 students

Solving:

P(A)= 0.25

Expressed as a percentage:

P(A)= 25%

In this case, you know:

Replacing in the definition of probability:

0.25=students in favor of the new dress code÷ 48 students

Solving:

students in favor of the new dress code= 0.25×48 students

students in favor of the new dress code= 12 students

Finally, 12 of the 48 students surveyed were in favor of the new dress code.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Combining the above inequalities, we get :

[tex]\qquad❖ \: \sf \:0.2 < 0.8 < 0.801 < 0.9[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

There are 5 ways to find if two triangles are congruent.

SSS- {Side Side Side Congruence.}

This law of congruence states that if we have two triangles, each with the same measures on each 3 sides it deems the triangles congruent.

SAS- {Side Angle Side Congruence.}

This law of congruence states that if we have two triangles, with 2 equal sides and one angle which is common among them; the triangles are congruent.

ASA- {Angle Side Angle Congruence.}

This law of congruence states that if we have two triangles, with 2 congruent angle measures and 1 congruent side; the triangles are indeed congruent.

AAS- {Angle Angle Side Congruence.}

You may be wondering how this law of congruence differs from the previous one. ASA refers to any two angles and the included side, whereas AAS refers to the two corresponding angles and the non-included side.

HL- {Hypotenuse Leg Congruence.}

This law of congruence states that if we have two triangles, with a common (congruent) leg and hypotenuse; the triangles are congruent.

I really hoped this helped, if it didn't leave a comment I am always open to feedback. If it did let me know, brainiest is always appreciated!

Hope you have a great rest of your day.

Answer:

Step-by-step explanation:

for completeness, here is the answer again:

1 Given is correct

2 Definition of right angle is correct

3 should be sum of interior angles in a triangle

4 is substitution

5 subtracting 90degree from left and right hand side

6 is definition of complementary angles

Answer: 60

Step-by-step explanation:

Almost everything in this picture is irrelevant to finding the measure of x.

x = 180 - 90 - 30 = 60

The following statements are considered to be propositions:

Deductive reasoning can be defined as a type of logical reasoning that typically involves drawing conclusions based on a given set of rules and conditions or from one or more premises (factual statements) that are assumed to be generally (universally) true.

A proposition can be defined as a type of statement (assertion) that is typically used to express an opinion or a judgement, with either a true or false answer.

This ultimately implies that, a proposition refers to a type of statement (assertion) that is either a true or false.

In this context, we can infer and logically deduce that the following statements are considered to be propositions:

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The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let [tex]$&\overline{A B} \cong \overline{D E} \\[/tex] and [tex]$&\overline{A C} \cong \overline{D F}[/tex]

Angle between [tex]$\overline{A B}$[/tex] and [tex]$\overline{A C}$[/tex] exists [tex]$\angle A$[/tex].

Angle between [tex]$\overline{D E}$[/tex] and [tex]$\overline{D F}$[/tex] exists [tex]$\angle D$[/tex].

Therefore, [tex]$\triangle A B C \cong \triangle D E F$[/tex] by SAS, if [tex]$\angle A \cong \angle D$$[/tex].

Given:

[tex]$&\overline{A B} \cong \overline{D E} \\[/tex] and

[tex]$&\overline{A C} \cong \overline{D F}[/tex]

According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let [tex]$&\overline{A B} \cong \overline{D E} \\[/tex] and [tex]$&\overline{A C} \cong \overline{D F}[/tex]

Angle between [tex]$\overline{A B}$[/tex] and [tex]$\overline{A C}$[/tex] exists [tex]$\angle A$[/tex].

Angle between [tex]$\overline{D E}$[/tex] and [tex]$\overline{D F}$[/tex] exists [tex]$\angle D$[/tex].

Therefore, [tex]$\triangle A B C \cong \triangle D E F$[/tex] by SAS, if [tex]$\angle A \cong \angle D$$[/tex].

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Answer:

We lend 100% - 9.2% and this will equal 90.8%, then we will make this percentage of 42,600 which will give us 38,680 and we will add the 42,600 and this will give us a total of 81,460 copies.

The value of c such that the function f is a probability density function is 2

The density function is given as:

f(x) = cxe^(−x^2) if x ≥ 0

f(x) = 0 if x < 0.

We start by integrating the function f(x)

∫f(x) = 1

This gives

∫ cxe^(−x^2) = 1

Next, we integrate the function using a graphing calculator.

From the graphing calculator, we have:

c/2 * (0 + 1) = 1

Evaluate the sum

c/2 * 1 = 1

Evaluate the product

c/2 = 1

Multiply both sides of the equation by 2

c = 2

Hence, the value of c such that the function f is a probability density function is 2

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The sum of normally distributed random variables is also a normally distributed random variable.

Given [tex]n[/tex] random variables with [tex]X_i\sim\mathrm{Normal}(\mu_i,\sigma_i^2)[/tex], their sum is

[tex]\displaystyle\sum_{i=1}^n X_i \sim \mathrm{Normal}\left(\sum_{i=1}^n \mu_i, \sum_{i=1}^n \sigma_i^2\right)[/tex]

i.e. normally distributed with mean and variance equal to the sums of the means and variances of the [tex]X_i[/tex].

In this case, each of [tex]X_1,X_2,X_3[/tex] are normally distributed with [tex]\mu=4[/tex] and [tex]\sigma^2[/tex] = ... I'm not sure what you meant for the variance, so I'll keep it symbolic. Then

[tex]V = X_1+X_2+X_3 \sim \mathrm{Normal}(12, 3\sigma^2)[/tex]

Answer:

Most you can do is factor out the x and turn it into   x (3x + 7)

roots would be x = 0 and x = -7/3

Answer:  x(3x+7)

Step-by-step explanation:

You would factor the x out of both of your values and put on the outside of the parenthesis. And you put the two numbers that you have left inside of the parenthesis. And that is as far down as this function can be factored.

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:

A

Step-by-step explanation:

given the points

(0, 0 ) , (2, 4 ) , (4, 8 )

note that the y- coordinate is twice the value of the x- coordinate , so

y = 2x

0.1 or 10%

The numbers between 1 and 50 that end in 6 are as follows:

6, 16, 26, 36, 46

There are therefore 5 numbers between 1 and 50 that end in 6.

This means there are 5 out of 50, or 5/50.

5/50 is 0.1 as a decimal, or 10% in percentage form.

Answer:

  (f•g)(x) = 4x² -7x -11

Step-by-step explanation:

The product of the two functions is the product of their respective definitions.

(f•g)(x) = f(x)•g(x) = (x+1)•(4x -11)

  = x(4x -11) +1(4x -11) . . . . . use the distributive property

  = 4x² -11x +4x -11 . . . . . . . and again

(f•g)(x) = 4x² -7x -11 . . . . . collect terms

The volume of the rectangular prism aquarium = 17 1/16 ft.

Volume of a rectangular prism = (l)(w)(h), where:

The aquarium is a rectangular prism. Its dimensions are given as:

Length (l) = 3 1/4 ft

Width (w) = 3 ft

Height (h) = 1 3/4 ft

Substitute

Volume of the rectangular prism aquarium = (3 1/4)(3)(1 3/4)

Volume of the rectangular prism aquarium = (13/4)(3)(7/4)

Volume of the rectangular prism aquarium = (13 × 3 × 7)/(4 × 4)

Volume of the rectangular prism aquarium = (273)/(16)

Volume of the rectangular prism aquarium = 17 1/16 ft.

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Considering the definition of combination, if no meal is repeated, 210 different meal arrangements are possible.

Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.

To calculate the number of combinations, the following formula is applied:

[tex]C=\frac{m!}{n!(m-n)!}[/tex]

The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.

Joseph is planning dinners for the next 4 nights. There are 10 meals to choose from and no meal is repeated.

So, you know that:

Replacing in the definition of combination:

[tex]C=\frac{10!}{4!(10-4)!}[/tex]

Solving:

[tex]C=\frac{10!}{4!6!}[/tex]

[tex]C=\frac{3,628,800}{24x720}[/tex]

[tex]C=\frac{3,628,800}{17,280}[/tex]

C= 210

Finally, if no meal is repeated, 210 different meal arrangements are possible.

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