Work out the value of
a) (√7)²
b) (4√2)²

The pattern doing the coin flip would be: H-T-H-T-H-T-H-T-H-T

The term that refers to 5 heads/5 tails is the "middle" term in the binomial expansion of (a + b)n and there are 252 different ways to get 5 heads and 5 tails in 10 coin flips

The probability of having at least 5 boys is 0.2265625

An egg cell produced by the dog would be expected to have 39 chromosomes. A heart cell of the dog would be a somatic cell and have a diploid number of chromosomes, which is 78.

The probability of having three normal girls for the carrier Albino couple is (0.5)^3, or 12.5%.

The probability of an offspring having the genotype AA Bb cc Dd ee is (1/2) * (1/2) * (1/4) * (1/2) * (1/2), or 1/64.

If everyone in the class were to bias their results to 5 heads/5 tails, you would expect to see a pattern of alternating heads and tails. Specifically, the pattern would be: H-T-H-T-H-T-H-T-H-T, where H represents a head and T represents a tail.

The coefficient for the middle term can be calculated using the binomial formula:

C(n, k) = n! / (k! * (n - k)!)

C(10, 5) = 10! / (5! * (10 - 5)!) = 252

Assuming that the probability of having a boy or a girl is equal, the probability of having 10 boys in a row is (0.5)^10 = 0.0009765625, or about 0.1%.

The probability of having at least 5 boys out of 7 children is a bit more complicated to calculate directly, so we can use the complement rule. The probability of having less than 5 boys is the sum of the probabilities of having 0, 1, 2, 3, or 4 boys:

P(0 boys) = (0.5)^7 = 0.0078125

P(1 boy) = 7 * (0.5)^7 = 0.0546875

P(2 boys) = 21 * (0.5)^7 = 0.1640625

P(3 boys) = 35 * (0.5)^7 = 0.2734375

P(4 boys) = 35 * (0.5)^7 = 0.2734375

So the probability of having less than 5 boys is:

P(< 5 boys) = 0.0078125 + 0.0546875 + 0.1640625 + 0.2734375 + 0.2734375 = 1 - P(≥ 5 boys)

Therefore, the probability of having at least 5 boys is:

P(≥ 5 boys) = 1 - P(< 5 boys) = 1 - 0.7734375 = 0.2265625

A diploid cell has two sets of chromosomes, so an egg cell produced by the dog would be haploid and have half the number of chromosomes as a diploid cell. Therefore, an egg cell produced by the dog would be expected to have 39 chromosomes.

A heart cell of the dog would be a somatic cell and have a diploid number of chromosomes, which is 78.

In Albinism, since both parents are normal and the daughter is albino, the parents must both be carriers of the albinism gene. The probability of their normal son being a carrier is 50%, as he could inherit the gene from either parent.

The probability of having a normal girl for each child is 50%, since the parents are both normal. Therefore, the probability of having three normal girls is (0.5)^3, or 12.5%.

In genetics, the Law of Independent Assortment is carried out during meiosis I, when homologous chromosomes line up and segregate independently into daughter cells.

In the given cross, each parent is heterozygous for all five genes, so the probability of an offspring being homozygous recessive for any one gene is 1/4. The probability of an offspring being homozygous recessive for all five genes is (1/4)^5, or 1/1024.

The probability of an offspring having the genotype AA Bb cc Dd ee is (1/2) * (1/2) * (1/4) * (1/2) * (1/2), or 1/64.

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Answer:

Line 3

Step-by-step explanation:

The problem's lines are:

Line 1. 5(x - 5) = 15

Line 2. 5x - 25 = 15

Line 3. 5x - 25 = 15 - 25

Line 4. 5x = -10

Line 5. 5x/5 = -10/5

Line 6. x = -2

The first error is in Line 3, where 25 was subtracted from just the right side, and where 25 should have been added to both sides instead.

Answer:980

Step-by-step explanation:If they traveled 140 kilometre in 2 hours, then you do 2 times 7 is 14 and that's how long you are driving, so you do 140 times 7 to see how many kilometres they traveled.

The markdown dollars on each handbag sold would be $76.80.

To calculate the markdown dollars on each handbag sold, we need to find 40% of the initial retail price.

Step 1: Calculate the discount amount:

Discount = 40% of $128.00

Discount = 0.40 * $128.00

        = $51.20

Step 2: Subtract the discount amount from the initial retail price:

Markdown dollars = $128.00 - $51.20

               = $76.80

Therefore, the markdown dollars on each handbag sold would be $76.80.

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Answer:

-49

Step-by-step explanation:

rule of thumb: whenever you have two negatives, they equal a positive! when you have one negative and one positive, it is a negative!

comment or message me if you are still confused or have a question!

Pitas Pizza Parlor can make 420 different pizzas using the given options for crusts, sauces, meat toppings, and vegetable toppings.

To determine the number of different pizzas that Pitas Pizza Parlor can make, we need to multiply the number of options for each category: crusts, sauces, meat toppings, and vegetable toppings.

Crusts: There are 3 crust options.

Sauces: There are 2 sauce options.

Meat toppings: There are 7 meat options.

Vegetable toppings: There are 10 vegetable options.

To calculate the total number of different pizza combinations, we multiply the number of options in each category:

Total combinations = (Number of crust options) x (Number of sauce options) x (Number of meat options) x (Number of vegetable options)

Total combinations = \(3 * 2 * 7 * 10 = 420\)

Total combinations = 420.

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Answer: 3.9b−2.6

Step-by-step explanation: Hope this helps

Answer:

1.3b

Step-by-step explanation:

The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.

Sorry, this explanation isn't the best. Hope it helped! :)

(C) 1 mile/0.62 km conversion factor would be most useful in converting miles per gallon to kilometers per liter.

Therefore, (C) 1 mile/0.62 km conversion factor would be most useful in converting miles per gallon to kilometers per liter.

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The complete question is given below:
Which of the following conversion factors would be most useful in converting miles per gallon to kilometers per liter?

A) 1 gallon/4 quarts

B) 1 liter/1000 ml

C) 1 mile/0.62 km

D) 1 000 m/1 km

Step-by-step explanation:

Given

mZEFH = (5x + 1)'

mZHFG = 62°

mZEFG = (18x + 11)',

The addition property of the angle is true

mZEFG = mZEFH + mZHFG

(18x + 11) = (5x + 1)'+  62

18x+11 = 5x + 63

collect like terms

18x - 5x = 63-11

13x = 52

divide both sides by 13

13x/13 = 52/13

x = 4

Since angle mZEFH = (5x + 1)' and x = 4, we will substitute x = 4 into the function;

mZEFH = 5(4) + 1

mZEFH = 20 + 1

mZEFH = 21°

Similarly for mZEFG = (18x + 11)'

mZEFG = 18(4) + 11

mZEFG =72+11

mZEFG = 83°

Answer:

5/16

Step-by-step explanation:

Fraction of claim is 5/8

But you actually eat 1/2

Fraction of large pizza actually eaten 5/16

Hopefully this is correct and it can help you!

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

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The amount of material needed for the entire kite is 48 square inches

The given parameters:

KI =6 inches

ET = 8 inches

KT=10 inches

Area of ΔKIT = 17 square inches

Start by calculating the area of the bottom triangle using:

A = 0.5 * Base * Height

This gives

A = 0.5 * 10 * 6

Evaluate

A = 30

The amount of material is

A = 30 + 17

A = 47

Hence, 48 square inches of material is used for the entire kite,  quadrilateral KITE

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The permutation combination of license plate is 35152000.

Numbers can be 10 digits (0, 1, 2, …, 9) and 26 letters (A, B, C, ..., Z).

Repetition is allowed, leaving 26 next choices for each letter used and 10 next choices for each digit used.

Therefore, according to the multiplication principle, the total number of different letter permutations.

26× 26 × 26 = 17576

and the total number of digit permutation: 10 × 10 × 10 = 1000

now,  they can be in any order:

⁶C₃ = 6!/(6−3)!3!

We have to consider 20 different combinations of positions.

So the total number of different license plates possible by the multiplication principle is

17576 × 1000 × 20 = 351520000

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The system has a unique solution x₁​= -1/6, x₂​= 0, x₃​= 1/3. The correct option is A.

The system of equations:

3x₁+6x₂+3x₃​=−18

6x₁+3x₂−3x₃​=0

3x₁+18x₂−6x₃3​=18

To find all the solutions to the system of equations, we need to use the Gauss-Jordan elimination algorithm.

The augmented matrix for the given system is:

[3 6 3 -18 6 0 3 -6 1 | 18]

We use -3R₁ + 6R₂ - 2R₃ to eliminate the elements in the 3rd column. This step reduces the augmented matrix to:

[3 6 3 -18 6 0 0 0 -1 | 15]

We perform the following row operations:

R₃→-R₃ to change the sign of the 1st element in the 3rd row.

R₃→3R₃ to make the leading coefficient of the 3rd row equal to 3.

R₁→R₁ - R₃R₂→R₂ + 2R₃ to eliminate the elements in the 1st and 3rd rows.

This step reduces the augmented matrix to:

[3 6 0 -3 6 3 0 0 1 | -3]

We perform the following row operations:

R₂→R2/6 to make the leading coefficient of the 2nd row equal to 1.

R₁→R₁ - 2R₂R₃→R₃ + 3R₂ to eliminate the elements in the 2nd row.

This step reduces the augmented matrix to:

[3 0 0 -9 0 1 0 0 1 | -5]

We perform the following row operations:

R₁→R1/3 to make the leading coefficient of the 1st row equal to 1.

R₂→R₂ + 9R₁ to eliminate the elements in the 1st row.

This step reduces the augmented matrix to:

[1 0 0 -3 0 1 0 0 1 | -5/3]

The above matrix is in the row-echelon form.

Now, we convert the matrix into the reduced row-echelon form by performing the following row operations:

R₁→R₁ + 3R₂ to eliminate the elements in the 4th column.

R₂→R₂ - R₃ to make the element in the 3rd column equal to zero.

R₃→R₃ - R₂ to make the element in the 2nd column equal to zero.

[1 0 0 0 0 -2 0 1 0 | -1/3]

This matrix is in the reduced row-echelon form. We can write the system of equations in the matrix form as:

X = [x₁, x₂, x₃] and B = [-1/3]

The solution is: X = [-1/6, 0, 1/3]

Thus, the system has a unique solution x₁​= -1/6, x₂​= 0, x₃​= 1/3.

Therefore, the correct option is A. The system has a unique solution x1​= -1/6, x2​= 0, x3​= 1/3.

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Answer:

-2

Step-by-step explanation:

-5  -4  -3  -2  -1  0  1  2 3  4  5

The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

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Answer:

\(a \approx 30.00^\)

Step-by-step explanation:

Main concepts:

Concept 1: Angle of elevation

Concept 2: Right Triangle trigonometry

Concept 1: Angle of elevation

An angle of elevation is the angle measured between two rays, starting from straight-ahead, to another ray pointing upward.

If she stands 40m from the base of the tower, and the tower is 23.09m tall, then the diagram can be drawn as attached.

Concept 2: Right Triangle trigonometry

The three basic trigonometric functions are Sine, Cosine, and Tangent.  Each of these functions, when applied to an angle, gives the ratio of two sides of a right triangle that contains that angle:

\(sin(\theta)=\dfrac{opposite~side}{hypotenuse}\)

\(cos(\theta)=\dfrac{adjacent~side}{hypotenuse}\)

\(tan(\theta)=\dfrac{opposite~side}{adjacent~side}\)

These relationships are often memorized with SoaCahToa, where, the S, C, or T, represent the Sine, Cosine, and Tangent, functions, and the "o", "a", or "h", represent the opposite side, the adjacent side, or the hypotenuse (the side across from the right angle).

Picking up from the diagram, we're trying to find the angle "a", and we know two sides of a right triangle, so we need to identify which trigonometric function uses the two given sides, relative to angle "a".

For angle "a", the 40m distance to the tower is the adjacent side of the triangle (touching both the right angle, and the angle "a"), and the 23.09m tower height is the opposite side (touching the right angle, but not touching the angle "a").

Given that the known sides are "opposite" and "adjacent", we'll need to use the Tangent function:

\(\tan(\theta)=\dfrac{opposite}{adjacent}\)

substituting known values...

\(\tan(a^o)=\dfrac{(23.09~m)}{(40~m)}\)

simplifying units...

\(\tan(a^o)=\dfrac{23.09}{40}\)

applying arctan to both sides to undo the tangent function, and evaluating ...

\(\arctan ( ~tan(a^o)~)=\arctan \left (\dfrac{23.09}{40} \right)\)

\(a^o=\arctan \left (\dfrac{23.09}{40} \right)\)

\(a^o=29.99569...^o\)

Rounding to the nearest hundredth...

\(a^o \approx 30.00^o\)

Noting that the problem says that the angle of elevation is "a degrees", so "a" is just a number (without degrees).

\(a \approx 30.00^\)

The measure of angle EBF is 40 degrees

The complete question is added at the end of this solution

From the question, we have the following parameters that can be used in our computation:

EBF = 6x + 4

CBF = 7x - 2

Also from the question, we understand that the measures of angle EBF and the measure of angle CBF are congruent

This can be represented mathematically as follows

EBF = CBF

Substitute the known values in the above equation, so, we have the following representation

6x + 4 = 7x - 2

Multiply through by 1

6x + 4 = 7x - 2

Collect the like terms

7x - 6x = 4 + 2

Evaluate the like terms

x = 6

Recall that

EBF = 6x + 4

Substitute the known values in the above equation, so, we have the following representation

EBF = 6 x 6 + 4

Evaluate

EBF = 40

Hence, the measure is 40 degrees

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Complete question

If the measures of angle EBF and the measure of angle CBF are congruent and EBF = 6x+4 and CBF = 7x-2 find EBF

If on the following Tuesday, Terry fills out scale again and receives a score of 28 , then Terry's scores on the Self-Monitoring Scale do not appear to be Reliable .

The Terry's scores on the Self-Monitoring Scale do not appear to be reliable, because there is a significant difference between his score on Friday and his score on the following Tuesday.

The Reliability is defined as the consistency of measurement over time or across different conditions.

In this case, if Terry's scores on the Self-Monitoring Scale were reliable, we would expect them to be consistent or stable over time.

However, his score on Tuesday is significantly lower than his score on Friday suggests that there may be some inconsistency in his responses .

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Answer: The value of x is 20.

Algebraic function :

Given function is,  

We have to find the value of x when

The value of x is 20.

Step-by-step explanation: hope this helps

Answer:

A, C, and E

Step-by-step explanation:

if 16 watermelons cost 48, then 1 watermelon costs 3$ meaning A C and E apply to that.

Answer: is it an A.P or G.P

Answer:25%

Step-by-step explanation:60*0.25=15

Answer:

The answer is A I am pretty sure. Please tell me if I got it wrong.

Step-by-step explanation:

Answer:

The image of the point (1, -2) under a dilation of 3 is (3, -6).

Step-by-step explanation:

Correct statement is:

What are the coordinates of the image of the point (1, -2) under a dilation of 3 with the origin.

From Linear Algebra we get that dilation of a point with respect to another point is represented by:

\(\vec P' = \vec R + r\cdot (\vec P-\vec R)\) (Eq. 1)

Where:

\(\vec R\) - Reference point with respect to origin, dimensionless.

\(\vec P\) - Original point with respect to origin, dimensionless.

\(r\) - Dilation factor, dimensionless.

If we know that \(\vec R = (0,0)\), \(\vec P = (1, -2)\) and \(r = 3\), then the coordinates of the image of the original point is:

\(\vec P' = (0,0) +3\cdot [(1,-2)-(0,0)]\)

\(\vec P' = (0,0) + 3\cdot (1,-2)\)

\(\vec P' = (3,-6)\)

The image of the point (1, -2) under a dilation of 3 is (3, -6).

Below the climber's elevation = all values below 1,600 feet.

The answer is x < 1,600

Where x represents all possible values of locations below the climber's elevation.

In approximately 11.41% of years, the rainfall will be between 50 and 70 centimeters in that town.

To solve this problem, we need to find the percentage of years where the rainfall is between 50 and 70 centimeters. We can do this by standardizing the rainfall values and using a standard normal distribution table.

First, we need to standardize the rainfall values of 50 and 70 centimeters using the formula

z = (x - μ) / σ

where

z is the standardized value

x is the rainfall value

μ is the mean

σ is the standard deviation

For x = 50

z = (50 - 95) / 28

z = -1.607

For x = 70

z = (70 - 95) / 28

z = -0.893

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two standardized values. This represents the percentage of years where the rainfall is between 50 and 70 centimeters.

Using a standard normal distribution table, we can find that the area under the curve between z = -1.607 and z = -0.893 is 0.1141. This means that approximately 11.41% of years will have rainfall between 50 and 70 centimeters in this town.

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Answer: 9

Step-by-step explanation:

I am assuming that the grid units equal 1 inch.

We have to solve for x. For the width,

60 = 20/3 x

To divide by a fraction is to multiply by its reciprocal.

x = 60 * 3/20 = 180/20 = 9