A spice mixture is 25% thyme. How many grams of thyme must be added to 12g of the mixture to increase the thyme content to 40%?

Answer:

31

Step-by-step explanation:

2⋅5+5⋅3+2⋅3

10+15+6

31

Answer:

The answer is 35 children and 105 adults

Step-by-step explanation:

we don't know the number of kids or adults in the theater , so they are unknown.

x: adults

y: kids

we know that y=3x (1)

we also know that all the people in the theater are 140.

so we also know that x+y= 140 (2)

And now you need to take (1) and put it in (2):

y=3x

x+y= 140 x+3x=140 =} 4x=140=} x=140/4=} x=35 kids. so if we put on (1) the number of the kids we have the number of adults: y=3*35=}y=105 adults

I hope I helped !

The mean of the probability distribution of X is 0.9375.

Given that,

From the given

We have to find the probability distribution of X and mean of X.

Now, We know,

X --                               0         1          2        3        4

Probability of X--        1/2     1/4       1/8      1/16     1/16

The mean is average of the distribution

Statistics refers to deviation as the difference between the observed value of a data point and the expected value. The average deviation of a data point from the mean, median, or mode of the data collection is known as the mean deviation, sometimes known as the mean absolute deviation. 

μₓ=0×1/2+1×1/4+2×1/8+3×1/16+4×1/16

μₓ=1/4+1/4+3/16+1/4

μₓ=15/16

μₓ=0.9375

Therefore, The mean distribution of X is 0.9375.

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Answer:

F-1(x) = 4x2 - 3 x<0

The value of x in given triangle is 6.403

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angled triangle whose one angle is 90 degrees.

We find the value of x by using pythagoras theorem.

the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

4²+5²=x²

16+25=x²

41=x²

Take square root on both sides

x=√41=6.403

Hence the value of x in given triangle is 6.403

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The solution with a pH of 3.3 has a hydronium ion of 0.000501

The pH of a solution is a measure of hydrogen ion concentration, which in turn is a measure of its acidity. Pure water dissociates slightly into equal concentrations of hydrogen and hydroxyl (OH−) ions.

Applying the formula of pH which is given as

pH = -log[H₃O⁺]

But the fruit juice has a pH = 3.3

3.3 = -log[H₃O⁺]

This becomes 10⁻³.³

[H₃O⁺] = 0.000501

The concentration of hydronium ion is 0.000501

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Triangle ONM is congruent to Triangle CBA

∵∵∵∵∵∵∵∵∵∵∵∵.........................ω

Answer:

[tex]\textsf{center \quad $(x,y)=\left(\; \boxed{6,-2}\; \right)$}[/tex]

[tex]\textsf{radius \quad $r=\boxed{8}$}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Given equation:

[tex]x^2+y^2-12x+4y-24=0[/tex]

Move the constant to the right side of the equation and collect like variables on the left side of the equation:

[tex]\implies x^2-12x+y^2+4y=24[/tex]

Create perfect square trinomials for the both variables by adding the square of the half the coefficient of x and y to both sides:

[tex]\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2+y^2+4y+\left(\dfrac{4}{2}\right)^2=24+\left(\dfrac{-12}{2}\right)^2+\left(\dfrac{4}{2}\right)^2[/tex]

[tex]\implies x^2-12x+\left(-6\right)^2+y^2+4y+\left(2\right)^2=24+\left(-6\right)^2+\left(2\right)^2[/tex]

[tex]\implies x^2-12x+36+y^2+4y+4=24+36+4[/tex]

[tex]\implies x^2-12x+36+y^2+4y+4=64[/tex]

Factor the two perfect trinomials:

[tex]\implies (x-6)^2+(y+2)^2=64[/tex]

Therefore:

[tex]\textsf{center \quad $(x,y)=\left(\; \boxed{6,-2}\; \right)$}[/tex]

[tex]\textsf{radius \quad $r=\boxed{8}$}[/tex]

Answer:

Step-by-step explanation:

there are 6 numbers, but 3 and 6 take up double the space, so the probabilities are not 6 but 8

1/8 is your answer

Answer:

x = 4.5

Step-by-step explanation:

5(2x + 1) = 50  Distribute the 5

5(2x) + (5) (1) = 50

10x +5 = 50  Subtract 5 from both sides

10x = 45  Divide both sdies by 10

x = 4.5

For the given equation (x/4)+3= 1/5, the value of x which will make the given equation valid is lies between the numbers of ( -10 and -15).

As given in the question,

Given equation is equal to :

(x/4)+3= 1/5

Simplify the given equation (x/4)+3= 1/5 to get the value of x we have,

(x/4)+3= 1/5

Take least common multiple of 4 and 1 we get,

( x + 12) / 4 = 1/5

⇒5( x +12 )  =  4

⇒ 5x + 60 = 4

⇒ 5x = -56

⇒ x= -11.2

-11.2 lies between (-10 and -15).

Therefore, for the given equation (x/4)+3=1/5, the value of x which will make the given equation valid is lies between the numbers of

(-10 and -15).

The complete question is:

Consider the following equation:

(x/4)+3= 1/5

The value of x that will make the equation above valid lies between

which of the following numbers?

A) 10 and 15

B) -1 and -5

C) 1 and 5

D) -10 and -15

E) -5 and -10

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Answer: 260 calories

Step-by-step explanation:

    If one serving has 80 calories, we will multiply 80 by 3 1/4 to find the total number of calories in 3 1/4 servings.

80 calories * (3 1/4) servings = 260 calories

Answer:

3,4,5

Step-by-step explanation:

x+x+1+x+2

therefore ,

4(x+2)=17+3

4x+8=20

4x=20-8

4x=12

x=3

The area of the garden with a base of [tex]6\frac{1}{2}[/tex] feet and a height [tex]2\frac{5}{8}[/tex] feet is equal to 17.06 square feet.

What is a Parallelogram?

In the given question, it is said that the garden decided to be created by the Johnson family is in the shape of a parallelogram.

The base and height of the parallelogram are given as  [tex]6\frac{1}{2}[/tex] feet and [tex]2\frac{5}{8}[/tex] feet respectively.

[tex]\implies b=6\frac{1}{2} =\frac{13}{2}[/tex], and

[tex]h=2\frac{5}{8} =\frac{21}{8}[/tex]

The area of a parallelogram is calculated using the formula,

[tex]A=b \times h[/tex]

Substituting the values in the given formula, we get

[tex]A=\frac{13}{2} \times \frac{21}{8} \\\implies A=\frac{273}{16}\\ \implies A=17.06 ft^{2}[/tex]

Therefore, the required area of the garden is equal to 17.06 square feet.

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Answer:

Option 4

Step-by-step explanation:

In integer division or multiplication,

1) If a < 0  and b < 0 means a and b are both negative numbers.

Then a/b will be positive. But it is given that a/b < 0. So, it is wrong.

2) If a< 0 and b > 0 means a is negative & b is positive. So, a/b will be negative. But it is given a/b is positive. So, it is wrong.

3) a and b are positive (as a >0 and as b > 0), then a/b > 0  (a\b will be positive). So, it is wrong.

4) a is positive (as a>0) & b is negative (as b < 0), then a/b will be negative So, this is correct.

Answer:

900 meters long

Step-by-step explanation:

Toby is riding his bicycle at 15 m/s. If it takes him 60 seconds to get to the end of the street. What was the length of the street?

at 15 meters per second for 60 seconds:

= time * speed

60* 15= 900 meters traveled,

so the street is 900 meters long.

Check the picture below, so the parabola looks more or less like so, the "p" distance is negative, because the horizontal parabola is opening to the left-hand-side, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-2\\ k=5\\ p=-5 \end{cases}\implies 4(-5)( ~~ x-(-2) ~~ )=(y-5)^2 \implies -20(x+2)=(y-5)^2 \\\\\\ x+2=-\cfrac{1}{20}(y-5)^2\implies {\Large \begin{array}{llll} x=-\cfrac{1}{20}(y-5)^2-2 \end{array}}[/tex]

Answer:

The Board of Governors of the Federal Reserve System is responsible for the discount rate and reserve requirements, and the Federal Open Market Committee is responsible for open market operations.

Step-by-step explanation:

Answer:

Belle has 25 apples she shares them equally with her 5 friends, how many apples does each friend get? 25/5=5

Step-by-step explanation:

Answer

Infinite solutions

Step-by-step explanation:

try any example you want it keeps going on and on.

The correct system of equations is 5x-y=2,x-5y=10

In order to find the system of equations of the graph, we have to check the solution in the graph and then check for the system of equations that gives the same value.

Looking at the graph, the values of x and y at the point of intersection is the solution. Thus:

x =  0 and y = -2

Let's check the equations now:

5x+3y=-6, 3x+5y=-10

Solve for x and y using elimination

3 (5x+3y=-6)

5 (3x+5y=-10)

15x + 9y = -18

15x + 25y = -50

-6y = 32

y = -32/6 = -16/3 (This cannot be the system)

3x-5y=10, x-5y=-10

3x-5y = 10

x-5y = -10

2x = 20

x = 20/2 = 10  (This cannot be the system)

5x-y=2,x-5y=10

1(5x-y=2)

5(x-5y=10)

5x -y =2

5x-25y = 50

24y = -48

y = -48/24 = -2

put y = -2 into 5x -y =2:

5x -(-2) =2

5x + 2 = 2

5x = 0

x = 0

Therefore, 5x-y=2,x-5y=10 is the system of equations. The 3rd option is the answer. Move it to the box

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Answer:

EDC = 56 degrees

Step-by-step explanation:

triangle OED is isosceles : base angles are congruent

2 * EDC + 68 = 180

2 * EDC = 180 - 68

2 * EDC = 112

2/2 EDC = 112/2

EDC = 56 degrees

Step-by-step explanation:

Triangle DOE is isosceles. So OED and ODE has same angle.

Total angle for isosceles triangle is 180.

ODE + OED = 180 - 68 = 112

OED = ODE = 112 /2 = 56

Considering the given scatter plot, it is found that:

a. The line of best fit is: y = -0.245x + 5.59.

b. The correlation coefficient is: r = -0.57.

c. The interpretation of the correlation coefficient is of: There is a negative association between y and x.

d. The estimate of y when x = 12 is of: 2.65

A scatter plot is a set of points of a data-set, and these points are used to calculate both the correlation coefficient and the line of best fit.

For this problem, the points are given as follows:

(0,5), (1,7), (2, 6), (3, 4), (4, 3), (5,5), (6,4), (7,2), (8,5), (9,3), (10,4).

Inserting these points into a linear regression calculator, the line of best fit is given as follows:

y = -0.245x + 5.59.

Hence the estimate of y when x = 12 is obtained as follows:

y = -0.245(12) + 5.59 = 2.65.

Inserting these points into a correlation coefficient calculator, the correlation coefficient is given as follows:

r = -0.57.

The interpretation is that there is a negative association between y and x, which is neither strong neither weak, as the absolute value of the coefficient is close to the threshold of 0.6.

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The error in this answer is that : The sum of angle of triangle is 180°

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Since, we know that Angle sum property of triangle is

∠A + ∠B + ∠C = 180°

Now, let ∠A = 115, ∠B = 39 and ∠C = m∠1

Substituting the value, we get

115° + 39° + m∠1 = 180°

154° + m∠1 = 180°

m∠1 = 180 - 154

m∠1 = 26°

Thus, m∠1 = 26°

Hence, The error for finding m∠1 is that angle sum of the triangle is equal to 180° and not 360°

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The present age of Tom is 12 years old

Jan is five years older than Tom

The age of Tom = x

The age of Jan = x + 5

After 3 years

The age of Tom = x + 3

The age of Jan = x + 5 + 3

= x + 8

The Tom's age is 3/4 of Jan's age

Then the equation will be

x + 3 = 3/4(x + 8)

Apply distributive property

x + 3 = (3/4)x + 6

x - (3/4)x = 6 - 3

Subtract the terms

1/4 x = 3

Move 1/4 to the right hand side of the equation

x = 3 ÷ 1/4

x = 3 × 4

Multiply the terms

x = 12 years old

Hence, the present age of Tom is 12 years old

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Answer:

Step-by-step explanation:

What is the value of 3 + 5x when x=3?

3 + 5x =

3 + 5 × 3 =

3 + 15 =

18

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

The functions f(x) = (2x - 3) / 2 and g(x) = (2x + 3) / 2 are the inverse functions because the composite of the given functions equal to x that is fog = x and gof = x.

The conditions for two functions f and g to be inverses: f(g(x)) = x or g(f(x)) = x.

where, f(g(x)) and g(f(x)) is the composite function.

We are given:

f(x) = (2x - 3) / 2

g(x) = (2x + 3) / 2

Let us find the value of f(g(x)) and g(f(x)):

Substitute the value of x with g(x) in f(x), we will get:

f(g(x)) = (2 * g(x) - 3) /2 = (2 * ((2x + 3) / 2) - 3) /2 = (2x + 3 - 3) / 2 = 2x / 2 = x

So, f(g(x)) = x.

Substitute the value of x with f(x) in g(x), we will get:

g(f(x)) = (2 * f(x) + 3) /2 = (2 * ((2x - 3) / 2) + 3) /2 = (2x - 3 + 3) / 2 = 2x / 2 = x

So, g(f(x)) = x.

Thus, the functions f(x) = (2x - 3) / 2 and g(x) = (2x + 3) / 2 are the inverse functions because the composite of the given functions equal to x that is fog = x and gof = x.

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