Find the probability that at most 2 heads occured when 5 fair coins are tossed

Answer:

c=d-ab

Step-by-step explanation:

ab+c=d

move over to the other side

change sides change signs

c=d-ab

Answer:

c=d−ab

Subtract ab from both sides of the equation

Answer: 34.50

Step-by-step explanation: Since 3 bags cost 17.25 and Marco would buy 6, 3 times 2 is 6 so 17.25 times 2 is 34.50

Slope of AB = 2; Slope of DC = 2

Slope of AD = -1/2; Slope of BC = -1/2

Both pairs of opposite sides are parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.

A parallelogram is a quadrilateral that has two pairs of opposite sides that have the same lengths and are parallel to each other.

Since the opposite sides of a parallelogram are parallel, therefore, they have the same slope value.

Slope = change in y / change in x.

Find the slope of AB and DC. then AD and BC:

Slope of AB = (-2 - 2)/(-3 -(-1)) = -4/-2

Slope of AB = 2

Slope of DC = (-3 - 1)/(-1 - 1) = -4/-2

Slope of DC = 2

Slope of AD = (-3 -(-2))/(-1 -(-3)) = -1/2

Slope of AD = -1/2

Slope of BC = (2 - 1)/(-1 - 1) = 1/-2

Slope of BC = -1/2

Therefore, since AB and DC have the same slope, they are parallel, so also is AD and BC parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.

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Answer: 3.3%

Step-by-step explanation:

Principal not given.

SI = PRT/100

CI = P(1+R/100)^T -

SI + CI = 85470

[P×7×2]//100 + P [1+ (7/100)]^2 = 85470

on solving: P = 3,00,000

P = 300000 SI for 2 years = 42000

CI = Rs 43470

The difference= Rs 1470

as percentage to CI = [1470/ 43470] ×100

= 3.38%

The algebraic equation and the original price is:

original price - discount = sales price

x - 27 = 89

x = 116

An algebraic equation is made up of two expressions that are made up of variables or numbers that are connected by an arithmetic operation.  

A discount reduces the price of a good or service. In order to determine the price of a good after the discount has been applied, subtract the amount of the discount from the original price of the item.

original price - discount = sales price

x - 27 = 89

Combine similar terms: x = 89 + 27

Add similar terms together: x = 116

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Answer: G=62, I = 62, H =54

Step-by-step explanation:

3x+26=4x+14

x=12

G=36+26 = 62

180-62-62=54

Balance of Kevin after 1 quarter will be 1.0055(x)

Compound interest is interest that is calculated using both the starting amount and the interest that has accrued over time.

Interest is considered to be compounded quarterly if it is compounded four times each year.

If interest is compounded four times or quarterly each year, the formula for the amount at time t is as follows.

A = P( ( 1 + (r/4))⁴ⁿ

A = Accumulated amount

P= Principal amount

r = interest rate

n = time

Given that Kevin has x dollars in an account that pays 2.2% interest, compounds quarterly

∴ P = x

r = 2.2% = 2.2/100

To find balance after one quarter , i.e. time n = 1/4 year

⇒ Balance = accumulated amount  =$  x(1 + 2.2/400)¹  = $ 1.0055(x)

Therefore, Balance of Kevin after 1 quarter will be 1.0055(x)

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Hence proved that triangle   AB = 3(3) - 1 = 9 - 1 = 8.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

Given that,

AB + AC = AC

3y - 1 + 7y = 29

10y = 29 + 1 = 30

y = 30/10 = 3

Therefore, AB = 3(3) - 1 = 9 - 1 = 8.

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Answer: 3x^12

Step-by-step explanation:

66 / 22 = 3

We can add exponents when multiplying them.

-3 + 12 = 9

Answer:

8

Step-by-step explanation:

Billy started with 15 apples.

Lost 2, and another 5, In total 7 apples were taken.

" Lost " Indicates subtraction.

The equation would look like this: 15 - 7.

Subtract.

Hence, your answer should be 8.

Hopes this helps!

Have a good day :).

Answer: 8

Step-by-step explanation: 15 - 2 = 13 and 13 - 5 = 8.

Answer:

x = 5

Step-by-step explanation:

Comment

The three sides need to add up to 23 (the perimeter is given as 23)

Givens

The sides are

Solution

x + x + 3 + 2x = 23                   Combine

4x + 3 = 23                               Subtract 3 from both sides

4x + 3-3 = 23-3                         Combine

4x = 20                                      Divide  by 4

4x/4 = 20/4

x = 5

The three sides of a triangle is x, x+3 and 2x. If the perimeter is 23 feet. Find the value of x.

In this question we are given

We are asked to calculate the value of x.

To solve this problem first we have to form an equation.

Let us solve this question.

We know that the perimeter of a triangle is the sum of all three sides.

According To Question

x + x + 3 + 2x = 23

→ 2x + 3 + 2x = 23

→ 4x + 3 = 23

→ 4x = 23 - 3

→ 4x = 20

→ x = 20/4 = 5

x = 5

The value of x is 5.

[tex] \rule{70mm}{2pt}[/tex]

The equivalent expression for 10⁶ / 10⁴  will be equal to 10²

Given,

Exponents: 10⁶ and 10⁴

We have to find an equivalent expression for 10⁶ / 10⁴

Equivalent expression:

In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are plugged into the formula.

Here,

aˣ / aⁿ = x - n

So,

10⁶ / 10⁴ = 6 - 4 = 2

That is,

The equivalent expression for 10⁶ / 10⁴  will be equal to 10²

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Considering the concepts of the diameter and the radius of a circle, it is found that the correct statement is:

The ratio of the lengths of EF and AD is 2:1.

In the context of the circle given in this problem, we have that:

hence:

EF = 2AD, meaning that the ratio is of 2:1.

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Answer:

BC- AB < CA < AB + BC

Step-by-step explanation:

The sides opposite the larger angles are longer than the sides opposite smaller angles.

So, BC (opposite < A) is longer than AB (opposite < C) so,

BC > AB

The other side AC cannot be greater than AB + BC, otherwise the triangle would not exist, so,

AC < AB + BC

Also, CA > BC - AB  

The range for AC is

BC- AB < CA < AB + BC

Answer:

32

Step-by-step explanation:

this expression cannot be simplified because there are no like terms to combine with the numbers in the expression.

the number that goes in the ? is 32

Hello! So...

We are given the following to solve:

[tex]-9+8=?[/tex]

In order to solve this, we simply need to add.

[tex]-9+8=-1[/tex]

Hence, our solution is -1, and would be marked -1 on a number line. Graph is displayed below.

____________________________________

Hope this helps! If so, lmk! Thanks and good luck!

Answer:

[tex]\textsf{D)} \quad P(n)=0.024n^2-0.3n+4.3[/tex]

Step-by-step explanation:

From inspection of the graph, when the number of coils is 10, the length of the spring is between 0 cm and 20 cm.

Substitute n = 10 into the equation of each given answer option:

[tex]\begin{aligned}\textsf{Option A}: \quad P(10)&=10^2+4.3\\ & =100+4.3\\&=104.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option B}: \quad P(10)&=10^2-0.3(10)+4.3\\ & = 100-3+4.3\\&=97+4.3\\&=101.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option C}: \quad P(10)&=0.24(10^2)+4.3\\&=0.24(100)+4.3\\&=24+4.3\\&=28.3\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Option D}: \quad P(10)&=0.024(10^2)-0.3(10)+4.3\\ & = 0.024(100)-3+4.3\\&=2.4-3+4.3\\&=-0.6+4.3\\&=3.7\end{aligned}[/tex]

Therefore, as 0 < P(10) < 20, the only suitable equation is Option D:

[tex]\boxed{P(n)=0.024n^2-0.3n+4.3}[/tex]

Answer:

2³ * 3² * 5

Step-by-step explanation:

Prime factorize 360 and find how many times each number is repeated and write in index notation.

360 = 36 * 10

       = 6 * 6 * 2 * 5

       = 2 * 3 * 2 * 3 * 2 * 5

      = 2 * 2 * 2 *  3 * 3 * 5

      = 2³ * 3² * 5

The area of the parallelogram based on the given parameters is 0.0324 m²

Area of the parallelogram = Base × height

= 0.36 m × 0.09m

= 0.0324 m²

Total cost of Lilian's apple = Cost of each pound of apple × Weight of Lilian's apple

= $1.77 × 1.32 lb

= $2.3364

Ethan:

3.045 × 1.3

= 3.9585

Anica:

3.045 × 1.3

= 39.585

Ethan is more correct because he moved the decimal point 4 places to the left.

Total mass of the green rope = Length of the green rope × Mass of each meter of the rope

= 60.5 × 0.052

= 3.146 kg

0.102 × 7.3

= 0.7446

Therefore, the area of the parallelogram when calculated is 0.0324 m²

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Answer:

The answer is C

Step-by-step explanation:

The increase between the numbers in a arithmetic sequence is always the same, in this case the number always increased by 3.

Here is a another example

3, 5, 7, 9

The difference between the consecutive terms is always 2

Answer:

Step-by-step explanation:

Here, what they're really saying is to find  3 different ways to rearrange the letters A, B, and C. Then, put them together to give the angle a combination of "names"

(1 ABC

(2 BAC

(3 CAB

Hope this helps! :D

The amount of rye seed and bluegrass seed used in the mixture is 109.8 and 70.2 pounds respective.

In response to the given question;

Let's say the amount of rye seed is 'x.'

The cost of rye seed = $6.50 per pound

Let's say the amount of bluegrass seed is 'y.'

The cost of bluegrass seed = $3.50 per pound.

The total seeds are 180 pounds.

Thus,

x + y = 180

x = 180 - y .......eq 1.

The other equation for the total cost of $5.33 per pound is;

6.50x + 3.50y = 5.33×180

Put the value of x from eq 1.

6.50(180 - y) + 3.50y = 959.4

1170 - 6.50y + 3.50y = 959.4

3y = 210.6

y = 70.2

x = 180 - 70.2 = 109.8

Thus, the amount of rye seed and bluegrass seed used in the mixture is 109.8 and 70.2 pounds respectively.

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Answer: -4096

Step-by-step explanation: Use the geometric sequence formula to find the 10th term (image attached). So, the 10th term = 8(-2)^9

Note: the common ratio can be found by 2ndterm/1stterm

Answer:

a₁₀ = -4096

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence:

[tex]\boxed{a_n=ar^{n-1}}[/tex]

where:

Given terms of the geometric sequence:

To find the common ratio (r), divide consecutive terms:

[tex]\implies \dfrac{a_3}{a_2}=\dfrac{32}{-16}=-2[/tex]

Substitute the values of a and r into the formula to create an equation for the nth term of the sequence:

[tex]\implies a_n=8(-2)^{n-1}[/tex]

To find the 10th term of the sequence, substitute n = 10 into the equation:

[tex]\begin{aligned}\implies a_{10}&=8(-2)^{10-1}\\&=8(-2)^{9}\\&=8(-512)\\&=-4096\end{aligned}[/tex]

Therefore, the 10th term of the given geometric sequence is -4096.

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Answer:Your friend is incorrect

x=-2

Step-by-step explanation:

Add 6 to both sides

-6+2x=-10

+6          +6

2x=-4

Then divide each side

2x/2=-4/2

x=-2

1. The transformation is: A. rotation 90° clockwise about the origin.

2. Based on the alternate exterior angles theorem, the value of x is: 2.

3. x = 10

4. The slope of the given line is: A. 2

The slope of a line = change in y/change in x.

The theorem states that alternate exterior angles are congruent if they each lie on lines that are parallel to each other.

1. The transformation that took UVWX to U'V'W'X' is: A. rotation 90° clockwise about the origin.

2. 26x - 2 = 50 [based on the alternate exterior angles theorem]

Solve for x

26x = 50 + 2

26x = 52

x = 52/26

x = 2

The value of x is: D. 2.

3. 9x + 15 + 6x + 15 = 180 [based on the same-side interior angles theorem]

Solve for x

15x + 30 = 180

15x = 180 - 30

15x = 150

x = 150/15

x = 10

The value of x is: C. 10

4. Using two points on the line, (1, 1) and (-1, -3), we have:

Slope of the line = (-3 - 1)/(-1 - 1) = -4/-2

Slope of the line = 2

The slope is: A. 2

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Answer:

You need at least 101 cans of food in order to meet or surpass the goal.

Step-by-step explanation:

a.

135+89=224

224+c>=325

b.

224-224+x>=325-224

x>=101

You need at least 101 cans of food in order to meet or surpass the goal.

[tex]32^{\frac{1}{25}}\cdot 2^x ~~ = ~~8^{\frac{1}{4}}\implies (2^5)^{\frac{1}{25}}\cdot 2^x~~ = ~~(2^3)^{\frac{1}{4}}\implies 2^{\frac{5}{25}}\cdot 2^x~~ = ~~2^{\frac{3}{4}} \\\\\\ \stackrel{same~exponent}{\underset{same~base}{2^{\frac{5}{25}+x}~~ = ~~2^{\frac{3}{4}}}}\implies \cfrac{5}{25}+x~~ = ~~\cfrac{3}{4}\implies \cfrac{1}{5}+x~~ = ~~\cfrac{3}{4}[/tex]

[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( \cfrac{1}{5}+x \right)~~ = ~~20\left( \cfrac{3}{4} \right)}\implies 4+20x~~ = ~~15 \\\\\\ 20x=11\implies {\Large \begin{array}{llll} x=\cfrac{11}{20} \end{array}}[/tex]

A group of two or more inequalities in one or more variables is referred to as a system of inequalities. The system of inequalities graphed is y > x² - 4 and y < x² + 6.

A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are used.

A system of inequalities is one where the total number of inequalities is greater than or equal to the number of variables.

A system of inequalities may have,

The equation of the vertical parabola with y-intercept -4 is equal to

y = x² - 4.

The solution of the inequality is the shaded area above the dashed line.

The inequality must be y > x² - 4

2) The equation of the vertical parabola with y-intercept 6 is equal to y = x² + 6.

The solution of the inequality exists the shaded area below the dashed line. The inequality must be y < x² + 6

The system of inequalities graphed is

y > x² - 4

y < x² + 6

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The number of children and the number of adults that swam in the swimming pool that day are 69 and 366 respectively.

Given that:-

Total number of people that swam in the swimming pool = 435

Price for children = 1.25

Price for adults = 2

Total receipts = 818.25

We have to find the number of  children and the number of adults that swam in the swimming pool that day.

Let the number of children that swam that day be x and,

the number of adults that swam that day be y.

Hence, we can write,

1.25x + 2y = 818.25  ...(1)

x + y = 435 ... (2)

Solving the linear equation in two variable by elimination method

Multiplying (2) by 2 , we get

2x + 2y = 870 ... (3)

(3) - (1)

0.75x = 870 - 818.25

0.75x = 51.75

x = 51.75/0.75

x = 69

From (2), we can write,

69 + y = 435

y = 435 - 69

y= 366

Hence, the number of children and the number of adults that swam that day are 69 and 366 respectively.

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