An image shows two right triangles A B C and D E F. Triangle A B C: Side A B is 3. Side B C is 5. Side C A is 4. Triangle D E F: Side D E is 6. Side E F is 10. Side F D is 8. Which statement about the two triangles is correct? ~ because You cannot tell if the triangles are similar because the angles are not given. is not similar to , because , while . is congruent to

1) Gathering the data

$4 granola

$2 raisins

25 pounds of raisin granola

2) Let's write a system of equations, based on that:

4g +2r = 80 This equation relates the prices

g + r = 25 This one relates to the weight

4g +2r = 80

g +r = 25 x( -4) To eliminate g

4g +2r = 80

-4g -4r = -100

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

-2r = -20 Divide both sides by -2

r= 10

3) So we must include a total of 10 pounds of raisin to make it cost a total of $80.

\((f+g)(x) = f(x) +g(x)\)

\((f+g)(x) = \left(\dfrac{x}{2}-3\right)+\left(3x^2+x-6\right)\)

\((f+g)(x) =3x^2 +\dfrac{3x}{2}-9\)

Answer:

C - 403

Step-by-step explanation:

Answer: 110.04

Step-by-step explanation: because it is what it is

The Jenny's net pay with given bonus and over time is $675.96. Therefore, option C is the correct answer.

Given that, Jenny worked 44 hours.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

4 hours were overtime - she is paid time and a half for that.

Her regular wage is $16/hour.

Money she is getting for overtime is 16+16/2

= $24

So, total money =40×16+4×24

= 640+96

= $736

With bonus =736+50

= $786

Her tax rate is 14 percent

So, tax =14% of 786

= 0.14×786

= 110.04

Now, net pay =786-110.04 =$675.96

The Jenny's net pay with given bonus and over time is $675.96. Therefore, option C is the correct answer.

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Answer:

The second one

Step-by-step explanation:

USE THE BUTTERFLY TECHINQUE

3/8 O 1/6

18 3/8 O 1/6 8

18 > 8

3/8 > 1/6

Answer:

B is correct

3/8> 1/6 = 3 · 3/8 · 3 > 1 · 4/6 · 4 = 9/24 > 4/24 = 9 > 4 = Yes

Answer:

a)

i) With an eight digit binary number, there are 2⁸, or 256 possible combinations.

ii) Each digit is set to 1 or 0 for exactly half of all combinations.  This means that half of all strings, or 256 / 2 = 128 strings end with a zero.

iii) 3/4, or 128 + 64 = 192 of the combinations have a 1 for either the second or fourth digit.  If you consider:

Half of all digits will have the second bit set to 1

Half of all digits will have the fourth bit set to 1

Half of those will overlap

Then that's half the digits, plus half the digits, minus half of half the digits. 1/2 + 1/2 - 1/4 = 3/4

iv) This is a duplicate of iii, so again, 192

b) If we're allowed to repeat the usage of the digits, then answer would be the number of values available to the power of the number of digits used.  We're allowed six distinct digits, so the total combination of 9 digit numbers would be 6⁹, or 10077696

c) In this case we can look at it simply as permutations of the set {"ABC", "D", "E", "F"}, which gives us 4! which equals 24

Answer:

The correct answer is

For addition, Caulleen used the words total, sum, altogether, and increase. But we could also have used the words combine, plus, more than, or even just the word "and". For subtraction, Caulleen used the words, fewer than, decrease, take away, and subtract. We also could have used less than, minus, and difference.

Step-by-step explanation:

hope this helps u!!!

The total amount the mechanic will need in retirement savings to meet their retirement income goa is (B) $950,000, the correct option is B

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

Annual gross wage=  $47,500

Percentage saved= 80%

Draw in 1 year=4%

Now,

To calculate the total amount the mechanic will need in retirement savings to meet their retirement income goal, we can follow these steps:

Determine the retirement income goal: The mechanic wants to live off 80% of their current annual gross wage, which is:

0.8 x $47,500 = $38,000 per year

Calculate the amount of savings needed to generate the retirement income: The mechanic wants to draw 4% of their savings in the first year, so the amount of savings needed to generate $38,000 per year is:

$38,000 / 0.04 = $950,000

Therefore, by the given interest rate answer will be $950,000.

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Answer:

Hello,

Step-by-step explanation:

\(\displaystyleV=2*\pi*\int\limits^4_2 {(\dfrac{1}{x}-\dfrac{1}{x^3} )*x } \, dx \\=2*\pi*\int\limits^4_2 {(1-\dfrac{1}{x^2} ) } \, dx \\=2*\pi* [x+\dfrac{1}{x}]^4_2\\\\\boxed{V=\dfrac{7\pi}{2}}\\\)

Sara's score is 10.5; Hamza's score is 2.5; Luna's score is 8. The inequality for Mario's score is M ≥ 23 - X - Y - K - Z.

c) Let H be Hamza's score. Then we have the equation H + 4.5 = 7. Solving for H, we get:

H = 7 - 4.5 = 2.5

Therefore, Hamza's score is 2.5.

d) Let L be Luna's score. Then we have the equation L - 4 = 4. Solving for L, we get:

L = 4 + 4 = 8

Therefore, Luna's score is 8.

e) Let M be Mario's score. Then we have the inequality:

X + Y + K + Z + M ≥ 23

We can rearrange this inequality as:

M ≥ 23 - X - Y - K - Z

This represents the minimum score that Mario needs to achieve in order for the sum of all scores to be at least 23. Since we don't know the values of X, Y, K, and Z, we can't determine a specific value for M.

However, we can graph this inequality on a coordinate plane to see the possible values of M that satisfy the inequality.

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\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

Answer:

hi

Step-by-step explanation:

hello

The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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Answer:

m<2=80° m<3= 100° m<4= 80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14= m<15=100° m<16=80°

Step-by-step explanation:

The Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent so <1 = <3. m<1 = 100° so m<3=100°. When the lines are parallel, the interior angles on the same side of the transversal are supplementary so

<1+<2=180°. We already know that <1 is 100° so to find <2, you need to subtract 100° from the 180° to get 80°, m<2=80°. <2=<4 according to the vertical angle theorm so m<4=80°. It's the same thing for all the others.

Answer:

y = 6x - 5

Step-by-step explanation:

Two points on the line are (0, -5) (this is the y-intercept) and (2, 7).

Starting at (0, -5), we move to the right to (2, 7).  In doing this we see that x increases by 2 (this is the 'run') and y increases by 12 (this is the 'rise').

The slope of this line is thus m = rise/run = 12/2, or m = 6.

As we have already found, the y-intecept is (0, -5).

The slope-intercept form is y = mx + b.  With m = 6 and b = -5, we have the equation

y = 6x - 5.  This is the "simplified slope-intercept form."

Answer: y=6x-5

Step-by-step explanation:

first, find the slope using the formula rise/run

count the squares on the y axis from point to point

and you get 6

count the squares on x axis and you get 1

so the slope is 6/1 or 6

the formula for slope intercept form is y=mx+b where b is the y intercept and m is the slope

to find the y intercept look at the graph to see where the line touches the y axis, and you will see it is at -5

therefore y=6x-5

Answer:

2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.

Step-by-step explanation:

do some math

Answer:

  x ≥ 5

Step-by-step explanation:

You want the domain of the equation y = √(x -5) -1.

The domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...

  x -5 ≥ 0

  x ≥ 5 . . . . . . the domain of this function

__

Additional comment

The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.

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Answer:

1/3 is the probability for the blue marbal

As the x-values go to negative infinity, the function’s values go to positive infinity.

The end behavior of a function f(x) is given by; lim x → ∞ (f(x))

In the given graph attached, we can see that when as x goes to negative infinity (to the left) the y-values go up (toward positive infinity) since y is pointing upwards.  

Thus, lim x → ∞ (f(x)) = ∞ and as such the correct option is As the x-values go to negative infinity, the function’s values go to positive infinity.

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Answer:

There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.

There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.Thus the expectation for winning is about $0.30 and losing very close to $1...the t total expectation is about -$0.70.

There are 23C6 ways to pick 6 numbers from 23; the probability of any particular one is just shy of 1/100000.Thus the expectation for winning is about $0.30 and losing very close to $1...the t total expectation is about -$0.70.You can calculate the exact number by using the exact probability of picking the winning number stated in the first line of this answer.

Step-by-step explanation:

I hope it's helpful

Interpretation: On average, we lose about 95 cents each time we play the game.

This is not a fair game because the expected value is not 0.

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

Explanation:

There is only one way to win the game which is to match all the numbers.

This is out of 376,740 different ways to select 6 items from a pool of 28. The steps on how to get this value are shown below

\(_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{28} C _{6} = \frac{28!}{6!*(28-6)!}\\\\_{28} C _{6} = \frac{28!}{6!*22!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23*22!}{6!*22!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23}{6!}\\\\_{28} C _{6} = \frac{28*27*26*25*24*23}{6*5*4*3*2*1}\\\\_{28} C _{6} = \frac{271,252,800}{720}\\\\_{28} C _{6} = 376,740\\\\\)

I used the nCr combination formula. n = 28 is the pool size and r = 6 is the sample size.

Therefore, the probability of winning is 1/376740 and the probability of losing is 1-1/(376740) = 376739/376740

Multiply the odds found by each corresponding net winnings

Win: (1/376740)*(20,000) = 0.05308700960874

Lose: (376739/376740)*(-1) = -0.99999734564951

Then add up those results

0.05308700960874 + (-0.99999734564951) = -0.94691033604078

Rounding to the nearest cent, we get -0.95

The expected value is -0.95

We expect to lose, on average, 95 cents every time we play the game. The game is considered not fair because the expected value is not 0. The game is in favor of the lotto company.

Answer:

C. F(x) = x^2 + 4

Step-by-step explanation:

Took the test

Solution :

Given :

2y''' + 15y'' + 24y' + 11y= 0

Let x = independent variable

\((a_0D^n + a_1D^{n-1}+a_2D^{n-2} + ....+ a_n) y) = Q(x)\)  is a differential equation.

If \(Q(x) \neq 0\)

It is non homogeneous then,

The general solution  = complementary solution + particular integral

If Q(x) = 0

It is called the homogeneous then the general solution =  complementary solution.

2y''' + 15y'' + 24y' + 11y= 0

\($(2D^3+15D^2+24D+11)y=0$\)

Auxiliary equation,

\($2m^3+15m^2+24m +11 = 0$\)

-1  | 2    15    24     11

    | 0   -2    - 13    -11  

      2    13    11       0

∴ \(2m^2+13m+11=0\)

The roots are

\($=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$\)

\($=\frac{-13\pm \sqrt{13^2-4(11)(2)}}{2(2)}$\)

\($=\frac{-13\pm9}{4}$\)

\($=-5.5, -1$\)

So, \(m_1, m_2, m_3 = -1, -1, -5.5\)

Then the general solution is :

\($= (c_1+c_2 x)e^{-x} + c_3 \ e^{-5.5x}$\)

Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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Answer:

(5, 2 )

Step-by-step explanation:

5x + 2y = 29 → (1)

x + 4y = 13 → (2)

multiplying (1) by - 2 and adding to (2) will eliminate y

- 10x - 4y = - 58 → (3)

add (2) and (3) term by term to eliminate y

- 9x + 0 = - 45

- 9x = - 45 ( divide both sides by - 9 )

x = 5

substitute x = 5 into either of the 2 equations and solve for y

substituting into (2)

5 + 4y = 13 ( subtract 5 from both sides )

4y = 8 ( divide both sides by 4 )

y = 2

solution is (5, 2 )

The primitive function for \(f(x) = 4e^{2x} + e^{-x}\) is given by it's indefinite integral.

To calculate it, recall:

\(\frac{d}{dx}e^{ax}=ae^{ax}\)

\(\int c f(x)dx = c\int f(x)dx\)

Let's begin

\(\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1} + c\\\)

\(F(x) = 2e^{2x}-e^{-x} +c\)

To find the costant, we just need to use the fact that \(F(0)=2\)

\(F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3\)

Therefore,

\(\boxed{F(x) = 2e^{2x} - e^{-x} -3 }\)

Step-by-step explanation:

answer: 3/4 or 0.75

=5 1/4 - 4 1/2

=21/4 - 9/2

= (21-9) / 4

=3/4  or 0.75

Answer:

Angle ABC and angle DEF are supplementary if and only if they add up to 180 degrees

The answer is C because of distribution.

Note that in the prompt above, the value of x is given as: 16°

To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.

As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 53°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(53°) = 180°
∠O = 180 - 106

∠O = 74°

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

74° + 90° + ∠OCB = 180°

∠OCB = 180° - 74° - 90°

∠OCB = 16°

Hence, the value of x is 16°.

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