A tea shop owner is mixing a blend of two teas, one of which costs $6.50 per pound, the other costing $4.00 per pound. The owner wants to have 20 pounds of a mixture that will sell for $5.50 per pound. How much of each type of teach should be used?

Answer:

21 girls.

Step-by-step explanation:

50% of 42 students are girls.

So 42/2 = 21.

Therefore 21 of the students are girls.

Hope I helped

The solution of the given equation (x + 5) - ( 2x - 3) = 6 is 2.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is;

(x + 5) - ( 2x - 3) = 6

To solve;

(x + 5) - ( 2x - 3) = 6

Distribute the negative;

(x + 5) - 2x + 3 = 6

we need to get the like terms together;

x - 2x + 5+ 3 = 6

-x + 8 = 6

Subtract 8 from both sides, we get;

-x = -2

x = 2

Hence, the solution of the given equation is 2.

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Answer:

4 inches

Step-by-step explanation:

Given information:

Let y = height of snow on the lawn

Let t = time in hours

⇒ y = 2 + 0.5t

To find how much snow is on the lawn after 4 hours of snowing, substitute t = 4 into the found equation and solve for y:

⇒ y = 2 + 0.5(4)

⇒ y = 2 + 2

⇒ y = 4 inches

Therefore, Amadou will have 4 inches of snow on his lawn after 4 hours of snow falling.

After 4 hours of continuous snowfall at a rate of 0.5 inches per hour, Amadou would have 4 inches of snow on his lawn. After t hours of snow falling at the same rate, he would have 2 + 0.5t inches of snow on his lawn.

After 4 hours of snow falling at a constant rate of 0.5 inches per hour, Amadou would have:

Snow accumulation = Initial snow + (Snowfall rate × Time)

Snow accumulation = 2 inches + (0.5 inches/hour × 4 hours)

Snow accumulation = 2 inches + 2 inches

Snow accumulation = 4 inches of snow.

After t hours of snow falling, the amount of snow on Amadou's lawn would be:

Snow accumulation = Initial snow + (Snowfall rate × Time)

Snow accumulation = 2 inches + (0.5 inches/hour × t hours)

Snow accumulation = 2 + 0.5t inches of snow.

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Answer:

9

Step-by-step explanation:

a^2+b^2=c^2

a^2+12^2=15^2

a^2=225-144

a=sqrt(81)

a=9

Answer:

The height of the water increases 2 inches per minute.

Step-by-step explanation:

the slope is always the ratio of

y coordinate change / x coordinate change

in our case, x is the time (minutes), and y is the water height (inches).

we see, the longer the pool get filled, the higher the water gets. logical, right ?

by checking the data points we see :

with every 2 minutes passing the water height increases by 4 inches.

so, the slope is +4/+2 = 2/1 = 2

and that ratio tells us now the increase of the water height with every fraction or multiple of the measured 2-minute interval.

every 2 minutes 4 inches more.

so, e.g. every 3×2 = 6 minutes we get 3×4 = 12 inches more.

and - every 1/2 × 2 = 1 minute more we get 1/2 × 4 = 2 inches more.

The correct answer is the fourth option.

Answer:

22-3d=x

Step-by-step explanation:

where d is the days that it melts and the amount of snow x is the snow that is left.

Answer:

14N+5

Step-by-step explanation:

Five years ago; Rose Nx

Amanda x

Now; Rose Nx+5

Amanda x+5=19

x=19-5=14years

Rose(NOW) =14N+5

Answer:

4

Step-by-step explanation:

We know that [tex]a = 4[/tex] and [tex]b = -1[/tex], as they are given in the problem. All we have to do is plug them into the equation and solve it.

[tex]5 - 2(a + 3b)/2\\ = 5 - 2(4 -3)/2\\= 5 - 1\\= 4[/tex]

The sign of the leading coefficient can be found using the graph of a polynomial function.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have given the graph of polynomial functions:

In the first graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → -∞

Degree of a function = 3

In the second graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → -∞

Degree of a function = 4

In the third graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → ∞

Degree of a function = 4

In the fourth graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → ∞

Degree of a function = 3

Thus, the sign of the leading coefficient can be found using the graph of a polynomial function.

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In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.

The missing table is given below.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Shawn is collecting money from students at his school for a charity.

The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.

Since 30 is 1/3 of 90, we know the ratio is 1:3.

In order of blank boxes going from left to right then down

1, 9, 5, 75, 35

The complete table is attached below.

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Answer:

X = ABC+ AB+ ABC

X = AB(C+1+C)

X = AB(2C+1)

Answer:

Morgan

Step-by-step explanation:

because the pythagoras theorem is

H

[tex] {h1}^{2} = {b}^{2} + {h2}^{2} [/tex]

where h1=hypotenuse

h2=height

b=base

Using the combination formula, it is found that there are 495 ways to choose a 4-topping sandwich.

The order in which the toppings are chosen is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

4 toppings are chosen from a set of 12, hence the number of ways is given by:

[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]

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The dimensions of the TV are 15 inches by  (√3)*15 inches, so the correct option is D.

We can think of this as a right triangle, where the hypotenuse measures 30 inches, and the angles of the triangle are 30°, 60° and 90°.

If we step on the 30° angle, the length will be the opposite cathetus, then we can use the trigonometric relation:

sin(θ) = (opposite cathetus)/(hypotenuse).

Replacing what we know:

sin(30°) = length/30 in

length = sin(30°)*30in = (1/2)*30 in = 15in

And the adjacent cathetus will be the width, then we can use:

cos(θ) = (adjacent cathetus)/(hypotenuse).

Replacing what we know:

cos(30°) = width/(30 in)

width = cos(30°)*30in = (√3/2)*30in = (√3)*15in

Then the dimensions of the TV are 15 inches by  (√3)*15 inches, so the correct option is D.

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The expected number of M&M's in the bag is 308

The parameters that complete the question are:

Number of blue pieces = 4

Total = 15

From the question, the number of blue pieces is:

Blue = 82

Let the total number of M&M be M.

So, we have:

Blue = Number of blue/Total * M

This gives

82 = 4/15 * M

Multiply both sides by 15/4

15/4 * 82 = M

Evaluate

M = 307.5

Approximate

M = 308

Hence, the expected number of M&M's in the bag is 308

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Answer:

Answer:

A,B,D

Step-by-step explanation:

The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

y = x³ - 5x + 2

The maximum is at dy/dx = 0, hence:

3x² - 5 = 0

x = -1.29 or x = 1.29

y = (-1.29)³ - 5(-1.29) + 2 = 6.3

The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29

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The value of cos(A+B) is 36/325.

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

cos(A)=−5/13

sin(B)=7/25

Now Using identity,

sin²A + cos² A= 1

sin A= √1 - cos² A

sin A = √1- 25/169

sin A= √144/169

sin A= 12/13

Again,

sin²B + cos² B= 1

cos B= √1 - sin² B

cos B = √1- 49/625

cos B= √576/625

cos B= -24/25

Now,

cos (A +B) = cos A cos B - sin A sin B.

= -5/13* (-24/25) - 12/13* 7/25

=  120/325 - 84/325

= 36/325

Hence, the value of cos (A + B) is 36/325.

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0.21094 is the probability that the surgery is successful on exactly 3 patients.

It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

According to the given question,

Let Y = The number of patients who respond yes: [tex]Y - Bin (n,p)[/tex]

Given , [tex]n = 4 , p = 0.75 , q = 1 - p = 0.25[/tex]

[tex]P (Y = 3) = \left(\begin{array}{ccc}4\\3\\\end{array}\right) (0.75)^{2}(0.25)^{4-3} \\ = 0.21094\\\\[/tex]

The probability that the surgery is successful on exactly 3 patients is 0.21094

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Answer:

Step-by-step explanation:

Comment

If you know this formula

tn = t1 + (n - 1)*d then you don't even have  to count how many odd numbers there are. If you don't know the formula, then you have to count how many odds there are between 1 and 25 inclusive. Just to save you the trouble, there are 13.

Givens

1 = t1

25 = tn

d = 2

Solution

25 = 1 + (n - 1)*2                 Subtract 1 from both sides?

25-1 = 1-1 + (n - 1)*2            Combine

24 = (n  -  1) * 2                   Divide by 2

24/2 = (n - 1)*2/2                

12 = n - 1                               Add 1 to both sides

12 + 1 = n - 1 + 1                     Combine

13 = n

Answer

So you have 13 cards that  will bring success.

The correct option is Option D: Yes, the graph passes the vertical line test.

The function is a relationship between two distinct sets X and set Y which can be many-one or one-one. here set X is called the domain and set Y is called the codomain.

The vertical line test states that

If we draw a straight vertical line( which is also parallel to the y-axis) and it touches the graph at only one point at all locations, then that relation is said to be a function and this relation will be also one-one.

So here in this function shown in the graph.

If we draw a vertical line parallel to the y-axis in this at any location then it crosses the graph only once. So, it passes vertical line test. And this graph is a function. Therefore option D is correct.

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Answer:

n = [tex]\frac{1}{36}[/tex]

Step-by-step explanation:

n × 18 = [tex]\frac{1}{2}[/tex]

To find the value of n we have to divide both sides by 18.

Let us solve it now.

18n = [tex]\frac{1}{2}[/tex]

[tex]\frac{18n}{18}[/tex] = [tex]\frac{1}{2}[/tex] ÷ 18

n =  [tex]\frac{1}{2}[/tex] ÷ 18

n = [tex]\frac{1}{2}[/tex] ÷ [tex]\frac{18}{1}[/tex]

n =  [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{18}[/tex]

n = [tex]\frac{1}{36}[/tex]

Answer: x=0

Step-by-step explanation:

[tex]x=4+(4x-4)\\\\x=4+4x-4\\\\x=4x\\\\3x=0\\\\\boxed{x=0}[/tex]

The solution to the equation x = 4 + (x + 4) is 0.

The correct option is "one real solution".

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Expanding the expression on the right-hand side, we have:

x = 4 + (4x - 4)

x = 4x

Subtracting 4x from both sides, we get:

x - 4x = 0

-3x = 0

Dividing both sides by -3, we get:

x = 0

Therefore, there is one solution to the equation x = 4 + (4x - 4) as the equation simplifies to 0.

So the correct answer is 0, "one real solution".

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The zeroes of the quadratic function f(x) = 6x² + 12x – 7 will be given below. Then the correct option is A.

The quadratic function is given as ax² + bx + c = f(x).

For finding the zeroes of the polynomial we have to find the roots of the polynomial , The value of f(x) = 0

The given function is f(x) = 6x² + 12x – 7

Then the zeroes of the quadratic function will be

[tex]roots = \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}\\\\[/tex]

Here a =6 , b = 12 ,c = -7

Therefore the zeroes are

[tex]\rm roots = \dfrac {-12 \pm \sqrt{12^2 -4 * 6 * (-7)}}{2 *6}\\\\[/tex]

[tex]\rm root_1 = -1 + \sqrt{\dfrac {13}{6}}\\\\\rm root_2 = -1 - \sqrt{\dfrac {13}{6}}[/tex]

Therefore the correct option is A.

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The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

Length of the arc of a circle:

s = 7.34 units

The measure of central angle:

θ = 81 degrees =  1.413 radians

s = rθ

r is the radius of the circle

7.34 = r(1.413)

r = 5.19 ≈ 5.2 units

Thus, the radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

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Answer:

The radius of the circle is 5.2 units if the length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°

Step-by-step explanation: