A bank teller had 125 Bills in $10 and $20 bills to start the day. If the total in her register was $1650, how many of each bill did the teller start off with ?

Answer: x = \(\sqrt{y^2 -1}\)

Step-by-step explanation:

Answer:

14 weeks

Step-by-step explanation:

so from what we know she already learned one appetizer recipe so she needs to learn 42 more so what we need to do since it's three every week we need to multiply three until we are able to get 42 so three times 14 gets 42 so that means that the answer would be 14

H(t) = -16t^2 +704t = -16(t^2 -44t)

Putting in vertex form: -16(t^2 -44t +484) + 704

h(t) = -16(t-22)^2 + 704

It takes 22 seconds to reach the maximum height, which is the vertex of the parabola at (22,704)

please mark me as the BRAINLIEST.....

Answer:

Step-by-step explanation:

Given function:

Maximum value is obtained at vertex. Using vertex formula to find the value of t at maximum height: x = -b/2a of a  quadratic formula ax² + bx + c

Answer:

C. To make predictions about the values of y for a given​ x-value (I THINK)

Answer:

Area= π(R^2-r^2)

Step-by-step explanation:

Although I can't find the attached file

Let the radius of the large circle be R

And the radius of the small circle be r

Area of large circle is

Area= πR^2

Area of small circle is

Area= πr^2

The difference is

Area= πR^2- πr^2

Area= π(R^2-r^2)

Shortest distance between start and end point is 55.9 miles

According to given statement,

Terry had to travel south 50 miles and then west 25 miles.

We are taking X as a start point and Z is end point.

In triangle XYZ, we are taking angle Y to be of 90 degrees, which qualifies the Triangle XYZ to qualify Pythagorean theorem [The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right angle triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.]

XY = 50 miles

YZ= 25 miles

XZ^2 = XY^2 + YZ ^2

XZ^2 = (50) ^2 + (25) ^2 = 3125

XZ = 55.9

Shortest distance between start and end point is 55.9 miles

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Approximately 95.44% of the time, the car will stop at a distance between 120 feet and 140 feet.

To calculate the percentage of the time the car stops at a distance between 120 feet and 140 feet, we need to find the probability within that range in the given normal distribution.

The Z-score formula can help us calculate the probability in a normal distribution:

Z = (X - μ) / σ

In this case, we want to calculate the probability between 120 feet and 140 feet, which means X = 120 and X = 140.

Calculating the Z-scores for these values:

Z1 = (120 - 130) / 5 = -2

Z2 = (140 - 130) / 5 = 2

Now, we can use a Z-table or a calculator to find the probabilities corresponding to these Z-scores. Since the normal distribution is symmetric, the probability between -2 and 2 is the same as the probability between 2 and -2.

Using a standard normal distribution table or calculator, the probability of a Z-score between -2 and 2 is approximately 0.9544.

Therefore, approximately 95.44% of the time, the car will stop at a distance between 120 feet and 140 feet.

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Answer:

I WOULD SAY ITS rotaiton UWU

Rotation is the transformation applied from brick A to brick B.

We need to find which transformation is applied from brick A to brick B.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, line, or geometric figure.

Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point.

Brick A rotated 90° to brick B.

Therefore, rotation is the transformation applied from brick A to brick B.

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Answer: \(y-1=\dfrac32(x+3)\)

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = \(\dfrac{d-b}{c-a}\)

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =\(\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}\)

Since parallel lines have equal slope . That means slope of the required line would be .

Equation of a line passing through (a,b) and has slope m is given by :_

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

\((y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)\)

Required equation: \(y-1=\dfrac32(x+3)\)

Answer: 19

Step-by-step explanation:

g(4) = 4² + 3

g(4) = 16 + 3

g(4) = 19

Answer:

A cone with a diameter of 18ft and a slant height of 30ft

Using Pythagorean theorem, the height is calculated by:

H = sqrt(18^2 - (30/2)^2) = 9.95

The surface area:

A = lateral surface area + base

A = pi x radius x slant height + pi x radius^2

A = pi x (30/2) x 18 + pi x (30/2)^2 = ~1555.1 (ft2)

The volume:

V = base x height x (1/3)

V = pi x radius^2 x height

V = pi x (30/2)^2 x 9.95 = 7033.2 (ft3)

Hope this helps!

:)

Answer:

she descended 436 feet

Step-by-step explanation:pls mark brainliest i really want to move up a ranking

Since the provided equation is inconsistent, it cannot intersect.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

we can see that the second set of equation,

4x+2y=12

20x+10y=30

4/20=2/10≠12/30

1/5=1/5≠2/5

The given equation is inconsistent so it does not intersect.

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a)

\( \frac{10}{x} h\)

b)

\( \frac{10}{x + 1} h\)

c) (i) shown^^

(ii)

\(x = 4\)

(iii)

\(2 \times \frac{1}{2} h\)

Measure of all angles must equal 180 degrees.

Therefore,
(4x+20) + (2x+34) + x = 180

6x + 54 + x = 180

7x + 54 = 180

7x = 126

x = 18

4(18)+20 = 92

Angle A = 92

2(18)+34 = 60
Angle C = 60 degrees

Unknown angle is 18 degrees because the "x" represents the third angle.

Answer:

y2 = m(x1 - x2)+ y1

Step-by-step explanation:

m = y2 - y1 / x1 - x2

m(x1 -x2) = y2 -y1

y2 = m(x1 - x2)+ y1

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1)

Multiply both sides by (x2 - x1)

m(x2 - x1) = y2 - y1

Add y1 to both sides

m(x2 - x1) + y1 = y2

y = m(x2 - x1) + y1

Answer:

x\(\leq\)28

Step-by-step explanation:

The point at 28 is solid, so it is included in the graph, so x=28,  The line extends in the negative direction, with an arrow, is given by x<28.  Taken together, x\(\leq\)28.

Answer:

1. 6

2. 3, 10

3. 7

4. 95%

5. 7.5

6. (I assume the chart is the same as the one above) 8

7. 8

8. 4

Step-by-step explanation:

Have a great summer :)

Answer:

Step-by-step explanation

to find median u ned to arrange the data from ascending to descending order

Data=3,3,4,5,6,7,9,10,10

Median=N+1/2   (N means no of data)

=9+1/2

=10/2

=5 th term

=6

Mode is 3 and 10 because they repeats maximum number of time.

range=largest value-smallest value

=10-3

=7

average =sum of data/no of data

=100+91+96+93/4

=380/4

=95

therefore average is 95.

The resulting dilated triangle is as attached and it has the coordinates; (2, 4), (4, -2) and (-6, -2).

When a triangle is dilated, it means that each vertex of the figure has it's coordinates multiplied by the scale factor of the dilation. Now, due to the fact that multiplication operation is involved, it means that the original triangle and the dilated triangle are not congruent, as their side lengths are different.

The vertices of the triangle are given as follows:

(1, 2), (2, -1) and (-3, -1).

The dilation has a scale factor of 2, meaning that each coordinate of the vertices will be multiplied by 2 and as such, the coordinates of the dilated triangle are given as follows:

(2, 4), (4, -2) and (-6, -2).

The new triangle is as attached

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Answer:

62%

Step-by-step explanation:

1040-110-145-139=646

646/1040=62%

The simplified trigonometric expression in this problem is defined as follows:

sin(3x)/sin²(x) = 3csc(x) - 4sin(x).

The trigonometric expression in this problem is defined as follows:

sin(3x)/sin²(x).

The equivalent expression for the sine of 3x is given as follows:

sin(3x) = 3sin(x) - 4 sin³(x).

Then the expression can be written as follows:

(3sin(x) - 4 sin³(x))/sin²(x)

The subtraction is in the numerator, hence the expression can be simplified as follows:

3sin(x)/sin²(x) - 4sin³(x)/sin²(x)

3/sin(x) - 4sin(x)

One divided by the sine is equivalent to the cossecant, hence:

3/sin(x) - 4sin(x) = 3csc(x) - 4sin(x).

Meaning that the first option among those given on the image at the end of the answer is correct.

The problem is given by the image shown at the end of the answer.

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Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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Answer:x − x^{2} − 1.

Step-by-step explanation:

.

The common ratio for infinite geometric series with first term -3/2 and sums twice the common ratio is -1/2.

First keep in mind the common ratio must -1 < r < 1 for geometric series converges.

Common ratio can be calculated using standard formula for infinite geometric series converges which is Sum = a/(1-r) with a as first term and r as common ratio. So,

Since sum is twice the common ratio, so the equation is

2r = a/(1-r)

we can substitute (1-r). So,

2r(1-r) = a

2r-2r^2 = -3/2

we can multiple all by two. So,

4r-4r^2 = -3

0 = 4r^2-4r-3

0 = (2r-3)(2r+1)

So the result is either r = 3/2 or r = -1/2. as previously mentioned above, r result only in -1 < r < 1. So, the result of r = 3/2 is rejected.

Thus, the common ratio is -1/2.

You question is incomplete, but most probably your full question was

An infinite geometric series has first term -3/2 and sums to twice the common ratio. Find the sum of all possible values for the common ratio.

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The set of free variables found in the expression (λx.λy.y (λz.x)) (λx.z) is { } (the empty set).

To find the set of free variables in the given lambda calculus expression, we need to identify all variables that are not bound by any lambda abstraction.

Starting from the innermost expression (λx.z), we see that x is bound by the lambda abstraction, so x is not a free variable. Moving outward to the next expression (λy.y (λz.x)), we see that y is also bound by the lambda abstraction, so y is not a free variable. Finally, we reach the outermost expression (λx.λy.y (λz.x)), where the only occurrence of x is bound by the lambda abstraction.

Since there are no variables in the expression that are not bound by any lambda abstraction, the set of free variables is { } (the empty set).

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The general solution of given DE (D²+2D+1) (D²+4)y=0  is     (C)..                 y=(C₁+C₂x) eˣ + C3cos2x+ C4sin2x.

The given differential equation, (D²+2D+1) (D²+4)y=0, can be factored as (D+1)²(D+2)²y=0. This equation represents a homogeneous linear differential equation of fourth order. The characteristic equation can be obtained by replacing D with λ in the equation (λ+1)²(λ+2)²=0, which yields two repeated roots at λ=-1 and two repeated roots at λ=-2.

To solve the homogeneous linear differential equation, we consider each root separately. For the repeated root λ=-1, the general solution is given by y=(C₁+C₂x)e⁻ˣ, where C₁ and C₂ are constants. This solution accounts for the two repeated roots at λ=-1.

For the repeated root λ=-2, the general solution is given by y=C₃cos(2x)+C₄sin(2x), where C₃ and C₄ are constants. This solution accounts for the two repeated roots at λ=-2.

In summary, the general solution of (D²+2D+1) (D²+4)y=0 is given by       y=(C₁+C₂x)eˣ + C₃cos(2x) + C₄sin(2x). This solution combines the exponential and trigonometric functions to encompass the different roots of the characteristic equation. The constants C₁, C₂, C₃, and C₄ are determined by the initial conditions or specific constraints of the problem at hand. SO option C is the solution.

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The probability of getting the numbers whose product is greater than 10 is 0.73.

Given that there are 10 numbers from which Krishanu and Shanunk choose numbers.

We are required to find the probability that the product of the numbers will be more than 10.

Probability is basically the likeliness of happening an event among all the events possiible.It cannot be negative.

Total outcomes possible=(1,1)(1,2)........(1,10),(2,1),(2,2)................(2,10),(3,1),(3,2).......(3,10),(4,1),(4,2)..........(4,10),(5,1),(5,2)..(5,10),(6,1),(6,2),.............(6,10),(7,1),(7,2),.......(7,10),(8,1),(8,2),...........(8,10),(9,1),(9,2),..............(9,10),(10,1),(10,2)............(10,10).

Combinations that gives the product greater than 10=(2,6),(2,7),(2,8),(2,9),(2,10),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(3,10),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8),(4,9),(4,10),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8),(5,9),(5,10),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8),(6,9),(6,10),(7,2),(7,3),(7,4),(7,5),(7,6),(7,7),(7,8),(7,9),(7,10),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7),(8,8),(8,9),(8,10),(9,2),(9,3),(9,4),(9,5),(9,6),(9,7),(9,8),(9,9),(9,10),(10,2),(10,3),(10,4),(10,5),(10,6),(10,7),(10,8),(10,9),(10,10),

Number of total combinations=10*10=100

Number of combinations that gives product greater than 10=73

Probability of getting the numbers whose product is greater than 10=73/100

=0.73

Hence the probability of getting the numbers whose product is greater than 10 is 0.73.

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The approximate length of the hypotenuse of triangle XYZ is approximately 8.94 units.

To find the approximate length of the hypotenuse of triangle XYZ, we can use the distance formula. The hypotenuse is the side opposite the right angle and connects points X and Z.

The distance formula states that the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is given by :

\(d = \sqrt{} ( x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2}\)

Applying this formula to points X(1, 5) and Z(-7, 1),

we can calculate the distance:

\(d = \sqrt{} ((-7 - 1)^{2} + (1 - 5)^{2} )\)

= \(\sqrt{} ((-8)^{2} + (-4)^{2} )\)

= √(64 + 16)

= √80

= 8.94

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