A fair dice and unbaised coin are tossed once.what is the probability of obtaining 3 and a tail​

The area of the rhombus is 50\(\sqrt{3}\) .

Given:

In a rhombus, all the side lengths are $10,$ and one of the angles is equal to $120^\circ.

If angle = 120 the its half is 60 which forms a right angled triangle.

sin 60 = Height / 10

\(\sqrt{3}\)/2 *10 = height

height = 5\(\sqrt{3}\).

Area of rhombus = base * height

= 10*5\(\sqrt{3}\)

= 50\(\sqrt{3}\) .

Therefore the area of the rhombus is 50\(\sqrt{3}\) .

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Answer:

TAKEN FROM GOOGLE

Step-by-step explanation:

The reciprocal of a number is the number that the initial number can be multiplied by to get the product 1. Therefore, the reciprocal of .8 is 1.25, since those two factors when multiplied together created a product of 1, or 1.000. The easiest way to find a reciprocal is to write the initial number as a fraction ( in this case, 8/10) and then "flip it" (making it 10/8) and simplifying. (10/8 = 1 and 1/4, or 1.25)

Answer:

\(Total = 23\frac{1}{4}\) cups

Step-by-step explanation:

Incomplete question.

See attachment for line plot

Required

Total cups drank in 10 days

The number of x at the top of each dataset represent the frequency (i.e. number of cups) drank on that day.

To get the total, we simply multiply this frequency by the accompanying dataset.

So, we have:

\(Total = 2 * 1\frac{1}{2} + 1 * 1\frac{3}{4} + 2 * 2 + 2 * 2\frac{3}{4} + 3 * 3\)

Express fractions as improper fraction

\(Total = 2 * \frac{3}{2} + 1 * \frac{7}{4} + 2 * 2 + 2 * \frac{11}{4} + 3 * 3\)

Evaluate each product

\(Total = 3 + \frac{7}{4} + 4 + \frac{11}{2} + 9\)

Take LCM

\(Total = \frac{12+ 7+16+22+36}{4}\)

\(Total = \frac{93}{4}\)

\(Total = 23\frac{1}{4}\)

Based on the provided question, it seems like you are asking about the most efficient evaluation method, either by hand or using a computer. To determine which method is the most suitable, you need to consider the complexity of the evaluation process and the number of alternatives.

Using a computer is generally faster and more accurate when dealing with large datasets or complex calculations. On the other hand, evaluating by hand may be more suitable for smaller datasets or simpler calculations. It can provide a more hands-on approach, allowing for a deeper understanding of the evaluation process. However, this method is generally more time-consuming and prone to human error.

To select the most appropriate evaluation method, consider the complexity of the task and the available resources. If the evaluation involves a large amount of data or complex calculations, using a computer would likely be the most efficient choice. However, if the task is relatively simple or involves a smaller dataset, evaluating by hand may suffice. In conclusion, the choice between evaluating by hand or using a computer depends on the complexity of the task and the available resources. Consider these factors to determine the most suitable method.

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\(y=\frac{6}{5} x+1\)

Slope-intercept form is a common way to express a linear function.

Solving For Slope-Intercept

In the question, we are given standard form. In order to find slope-intercept, we need to solve for y. This means we need to use the properties of equality to isolate y from the other values.

First, add 6x to both sides.

Then, divide both sides by 6.

This gives us the final slope-intercept form of the given equation.

Interpreting the Equation

Slope-intercept form is written in the format of y = mx + b. In this equation, m is the slope and b is the y-intercept. Our equation is \(y=\frac{6}{5} x+1\). So, 6/5 is the slope. This means that the rate of change of the graph is 6 units per 5 units. Additionally, the y-intercept is 1. So, the graph crosses the y-axis at y = 1.

Answer:

4x^4−x^3+2x^2+x+7

_______________

              x

Step-by-step explanation:

4x^3-x^2+2x+7÷x+1

The two lines are parallel because both have equal slope.

What area parallel lines?

If two lines do not cross one another anywhere on the plane, they are considered to be parallel. All parallel lines are spaced equally apart from one another.

Numerous forms have parallel lines running along their edges. In the rectangle below, the single and double arrow lines, as well as their junction points, are parallel to one another. Additionally, it is possible to create both horizontal and vertical shapes.

Given : line 1  : y=5x+1

          line 2 :  2y-10x+3=0

                       2y = 10x - 3

We know that, parallel lines always have equal slope.

The slope can be found by using formula :

     coefficient of y / coefficient of x

So, here, line 1 has slope = 2/10 = 1/5

and, line 2 has slope = 1/5

So, both have same slopes hence, both are parallel lines.

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Answer:

2 nickels and 21 dimes

Step-by-step explanation:

0.05N + 0.1D = 2.2

N + D = 23

Let's use the substitution method. Solve the second equation for N.

N = 23 - D

Now where you see N in the first equation substitute N with 23 - D.

0.05(23 - D) + 0.1D = 2.2

1.15 - 0.05D + 0.1D = 2.2

0.05D = 1.05

D = 1.05/0.05

D = 21

Now substitute 21 for D in the second original equation and solve for N.

N + 21 = 23

N = 2

Answer: 2 nickels and 21 dimes

The height of the ramp is x = 0.95 when the elevation angle of the ramp is 5.22 degrees.

An angle is still a shape in Trigonometry made composed of straight rays, referring to as a angle's sides, that come together at a center point referred as the angle's summit. An angle that occurs in the sector where it rays are placed can be created by using two rays. Another angle is produced when two planes collide. Dihedral angles are the term coined to them. In planar geometry, an angle is the form of two rays but rather lines that share a termination. The English word "angle" derives from the Latin language "angulus," which means "horn." The vertex, also known as the angle's sides, is where the two rays' common terminals meet.

given

The short leg of a right triangle is the elevation, and the ramp is its hypotenuse.

The sine is equal to the angle formed by the ramp and the ground, which is opposite over the hypotenuse.

The hypotenuse, or where the ramp should be, is

sine=5/x

5.22 = 5 /x

= 5/5.22

The height of the ramp is x = 0.95 when the elevation angle of the ramp is 5.22 degrees.

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The constant of proportionality is 20.

What is constant of proportionality?

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.

Given,

the recipe uses 5 cups of strawberries per 1/4 cup of sugar.

And let constant of proportionality is k.

that is

5 α 1/4

5 = k1/4

k = 5(4)

k = 20

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Answer:

the value of x is 1......

as we know B is the midpoint....

then,

5x-7=3x-5

5x-3x=-5+7

2x=2

x=2/2

x=1

Answer:

X=3-(y/2)=8

Step-by-step explanation:

suppose the numbers is X

3 less than half the product of a number is 8

X= 3- (y/2)=8

\(\boxed{\sf a_n=\dfrac{a_{n-1}}{10}\times 4,n\gt 1}\)

Lets verify

\(\\ \sf\longmapsto a_2=\dfrac{a_1}{10}\times 4\)

\(\\ \sf\longmapsto a_2=\dfrac{500}{10}\times 4=50(4)=200\)

And

\(\\ \sf\longmapsto a_3=\dfrac{a_2}{10}\times 4\)

\(\\ \sf\longmapsto a_3=\dfrac{200}{10}\times 4=20(4)=80\)

And

\(\\ \sf\longmapsto a_4=\dfrac{a_3}{10}\times 4\)

\(\\ \sf\longmapsto a_4=\dfrac{80}{10}\times 4=8(4)=32\)

Hence verified

Lets predict next term

\(\\ \sf\longmapsto a_5=\dfrac{a_4}{10}\times 4\)

\(\\ \sf\longmapsto a_5=\dfrac{32}{10}\times 4=3.2\times 4=12.8\)

Answer:

81

Step-by-step explanation:

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Answer:

A) 15 and 16

Step-by-step explanation:

The square root of 250 is 15.8, so it falls between:

15 and 16

Answer:

the answer is b or the second blank

Step-by-step explanation:

The expression is simplified to give -r/24 - 8

An algebraic expression can be described as an expression that is made up of terms, coefficients, variables, factors and constants.

These expressions are also known to consist of certain arithmetic operations, which includes;

From the information given, we have that;

Substitute the values

-1/8(r) - 5 - 1/6r - (-6/8r + 3)

expand the bracket

-1/8r - 5 - 1/6r + 6/8r - 3

collect like terms

-3r - 4r + 6r /24 -8

-r/24 - 8

Hence, the value is -r/24 - 8

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The missing measurements are m ∠U = 69.34°, m ∠W = 20.66° and UW = 8.5.

Given that a right triangle UVW, we need to find the missing measurements,

Here, UW is the hypotenuse.

Using the Pythagoras theorem,

UW² = VU² + VW²

UW = √3²+8²

UW = √9+64

UW = √73

UW = 8.5

Using the Sine law,

So,

Sin W / VU = Sin V / UW

Sin W / 3 = Sin 90° / 8.5

Sin W = 3 / 8.5

Sin W = 0.3529

W = Sin⁻¹(0.3529)

W = 20.66

m ∠W = 20.66°

Since we know that the sum of the acute angles of the right triangles is 90°.

So, m ∠U = 90° - 20.66°

m ∠U = 69.34°

Hence the missing measurements are m ∠U = 69.34°, m ∠W = 20.66° and UW = 8.5.

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Answer: look at the explanation

Step-by-step explanation:

It goes down by 40%

For the given standard deviation the minimum value we would assign is 22.the maximum value we would assign is 88.

To calculate the minimum and maximum values based on the given information, we need to consider the standard deviation and the respective interest rates for the 3-year and 10-year periods.

Given:

S = 26.32 (Initial value)

E = 55 (Expected value)

t = 3 (Years)

Standard deviation = 60% (of the expected value)

3-year interest rate = 2.4%

10-year interest rate = 3.1%

To find the minimum value, we will calculate the value at the end of the 3-year period using the lowest possible growth rate.

Minimum value calculation:

Minimum value = E - (Standard deviation * E) = 55 - (0.6 * 55) = 55 - 33 = 22

Therefore, the minimum value we would assign is 22.

To find the maximum value, we will calculate the value at the end of the 10-year period using the highest possible growth rate.

Maximum value calculation:

Maximum value = E + (Standard deviation * E) = 55 + (0.6 * 55) = 55 + 33 = 88

Therefore, the maximum value we would assign is 88.

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14. The value of 15 - 3.2 + 2(0.5) is 12.8

15. The value of -3/4 + (3/4 - 4/5) is - 4/5.

16. The value of -2(2 3/4) + (-2)(-1/4) is -5.

17. The value of -2(4.6 - 3.5) is -2.2

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator

The value of 15 - 3.2 + 2(0.5) is:

= 15 - 3.2 + 1

= 12.8

The value of -3/4 + (3/4 - 4/5) is:

= -3/4 + 4 - 4/5

= - 4/5.

1The value of -2(2 3/4) + (-2)(-1/4) is:

= -5 1/2 + 1/2

= -5.

The value of -2(4.6 - 3.5) is:

= -2(1.1)

= -2.2

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Answer:

(b - 1) (5b - 6)

Step-by-step explanation:

The height of the cliff is approximately 269 feet.

We will be using the tangent function to find the height of the cliff.
Draw a right triangle with the rowboat at one corner, the cliff's base as the adjacent side, and the cliff's height as the opposite side.

The angle of elevation (73.8 degrees) is between the rowboat and the cliff's base.
We are given the adjacent side (75 feet) and we need to find the opposite side (height of the cliff).

To do this, we will use the tangent function:
tan(angle) = opposite side / adjacent side
Plug in the given values:
tan(73.8) = height / 75
Solve for the height:
height = tan(73.8) * 75
Calculate the value:
height ≈ 269.4 feet
Round the height to the nearest foot:
height ≈ 269 feet.

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The values of x and y in parallelogram PQRS are x = 3 and y = 7.

In a parallelogram, opposite sides are equal in length. Based on this property, we can set up equations using the given information to solve for the values of x and y.

Given:

PT = y

TR = 4x + 1

QT = 2y

TS = 4x + 14

Since opposite sides of a parallelogram are equal, we can set up the following equations:

PT = QS (opposite sides)

TR = SR (opposite sides)

Substituting the given values into these equations, we get:

y = 4x + 14 (equation 1)

2y = 4x + 1 (equation 2)

We now have a system of equations (equation 1 and equation 2) that we can solve to find the values of x and y.

To solve the system, we can use the method of substitution. From equation 2, we can express y in terms of x:

y = (4x + 1)/2

Substituting this expression for y into equation 1, we have:

(4x + 1)/2 = 4x + 14

Now, we can solve for x:

4x + 1 = 8x + 28

-4x = 27

x = -27/4

However, upon closer inspection, we realize that the values of x and y must be positive since they represent lengths. Therefore, we discard the negative value for x.

Let's solve for y using the positive value of x:

y = (4(3) + 1)/2

y = (12 + 1)/2

y = 13/2

Since we need whole numbers, let's convert y to a whole number by multiplying both the numerator and denominator by 2:

y = (13/2) * (2/2)

y = 26/4

y = 13/2

Therefore, the values of x and y in parallelogram PQRS are x = 3 and y = 7.

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Answer:

the answer is 1

Step-by-step explanation:

x2 equal to 1 by 28 and xby 2root7 equal to 1by 28 so are neglected

The probability is= 1/665,280 in fraction in simplest form.

The idea of probability describes the possibility of an event happening.

We frequently have to make forecasts about the future in real life.

We may or may not be aware of the outcome of an event.

When this happens, we declare that there is a chance the event will take place.

In summary, probability has a wide range of fantastic applications in entertainment, business, and this recently expanding branch of artificial intelligence.

The probability formula can be used to determine the likelihood of an event by only dividing the favorable number of possibilities by the entire number of p-ossible outcomes.

According to our question-

P(n, r) = n! / (n - r)!

P(12, 7) = 12! / (12 - 7)!

12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

5! = 5 × 4 × 3 × 2 × 1

1/665,280

Hence,  The probability is= 1/665,280 in fraction in simplest form.

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Neither Z10 ⊕ Z12 ⊕ Z6 is isomorphic to Z60 ⊕ Z6 ⊕ Z2 nor Z15 ⊕ Z4 ⊕ Z12.

To determine whether two groups are isomorphic, we need to compare their structures. In this case, we will compare the structures of the groups Z10 ⊕ Z12 ⊕ Z6 and Z60 ⊕ Z6 ⊕ Z2, as well as Z10 ⊕ Z12 ⊕ Z6 and Z15 ⊕ Z4 ⊕ Z12.

Z10 ⊕ Z12 ⊕ Z6 and Z60 ⊕ Z6 ⊕ Z2:

Let's break down each group to understand their structures.

Z10 ⊕ Z12 ⊕ Z6:

The group Z10 represents integers modulo 10 under addition.

The group Z12 represents integers modulo 12 under addition.

The group Z6 represents integers modulo 6 under addition.

Z60 ⊕ Z6 ⊕ Z2:

The group Z60 represents integers modulo 60 under addition.

The group Z6 represents integers modulo 6 under addition.

The group Z2 represents integers modulo 2 under addition.

Comparing the structures, we can see that the two groups have different orders for their cyclic components. In the first group (Z10 ⊕ Z12 ⊕ Z6), the orders are 10, 12, and 6, respectively. In the second group (Z60 ⊕ Z6 ⊕ Z2), the orders are 60, 6, and 2, respectively. Since the orders differ, the groups are not isomorphic.

Z10 ⊕ Z12 ⊕ Z6 and Z15 ⊕ Z4 ⊕ Z12:

Let's break down each group to understand their structures.

Z10 ⊕ Z12 ⊕ Z6:

The group Z10 represents integers modulo 10 under addition.

The group Z12 represents integers modulo 12 under addition.

The group Z6 represents integers modulo 6 under addition.

Z15 ⊕ Z4 ⊕ Z12:

The group Z15 represents integers modulo 15 under addition.

The group Z4 represents integers modulo 4 under addition.

The group Z12 represents integers modulo 12 under addition.

Comparing the structures, we can see that the two groups have different orders for their cyclic components. In the first group (Z10 ⊕ Z12 ⊕ Z6), the orders are 10, 12, and 6, respectively. In the second group (Z15 ⊕ Z4 ⊕ Z12), the orders are 15, 4, and 12, respectively. Since the orders differ, the groups are not isomorphic.

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Answer:

The graph will shift 6 unit  left   and 3 units    left

Step-by-step explanation:

\(g(x) = \sqrt{x+6+3}\)