A population of 228 student consist of 160 taster. Allele T and t are for taster. Calculate the frequency of the tasters​

Answer:

It's B

Step-by-step explanation:

Functions can be represented by tables and equations

The function represented by the table is f(x) = x + 1

From the table, we have the following ordered pairs

(x,y) = (-1,0) (0,1) (1,2) and (2,3)

Notice that the difference between the x and y values is 1.

So, we have:

y - x = 1

Add 1 to both sides

y = x + 1

Express as a function

f(x) = x + 1

Hence, the function represented by the table is f(x) = x + 1

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The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.

To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:

Given:

u = 4i - 6j

v = 5i + 4j

Step 1: Calculate the dot product of u and v.

The dot product of two vectors u and v is given by:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.

To calculate the dot product, we multiply the corresponding components of u and v and sum them:

u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4

Step 2: Calculate the magnitudes of vectors u and v.

The magnitude of a vector is given by:

|u| = √(u₁² + u₂²)

For vector u:

|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21

For vector v:

|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40

Step 3: Calculate the angle θ.

Using the dot product formula mentioned earlier, we have:

-4 = (7.21)(6.40)cosθ

Solving for cosθ:

cosθ = -4 / (7.21 * 6.40) ≈ -0.086

To find θ, we can take the inverse cosine (arccos) of cosθ:

θ ≈ arccos(-0.086) ≈ 1.66 radians

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To determine if it would be unusual to randomly select 12 people and find that fewer than 5 recognize the Yummy brand name, we can use the concept of standard deviation and z-scores.

First, we need to calculate the z-score, which measures how many standard deviations an observation is from the mean. The formula for calculating the z-score is:

z = (x - μ) / σ

where

z = (5 - 9.3) / 0.99

z = -4.394

Next, we can consult a standard normal distribution table or use statistical software to find the corresponding percentile associated with the z-score. This percentile represents the probability of randomly selecting a group of 12 people with fewer than 5 recognizing the Yummy brand name.

In this case, the z-score of -4.394 corresponds to an extremely low percentile, close to 0.

The exact probability can be determined using the z-score and the standard normal distribution table.

Since the probability is extremely low, it would be considered unusual to randomly select 12 people and find that fewer than 5 recognize the Yummy brand name.

However, it's important to note that the definition of "unusual" may vary depending on the specific criteria or threshold chosen.

In statistical terms, a common threshold for defining unusual events is a significance level of 5% (or 0.05). If the probability of observing the event is lower than the significance level, it is considered unusual.

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Answer:

217.703

Step-by-step explanation:

From the decimal you have tenths, hundredths then thousandths so you need to round to the 3rd decimal place. The 4th decimal place is greater than 5 so you would round the thousandths place up to 3.

Answer:

217.703

Step-by-step explanation:

The thousandth place is the third digit to the right of the decimal point. Since the number on the ten thousandth place is greater than 5, then the number on the thousandth place (which is 2) is rounded up to 3.

Answer:

I think 3 not sure don't angry if wrong

Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Answer:

  4 cm

Step-by-step explanation:

You want the length of the smaller of two similar pieces of cardboard when the larger has an area of 150 cm² and a length of 10 cm, while the smaller has an area of 24 cm².

The scale factor for lengths is the square root of the scale factor for areas. It will be ...

  √(24/150) = 0.4 . . . . . . = smaller / larger

The smaller cardboard has a length of ...

  0.4 × 10 cm = 4 cm

__

Additional comment

Sometimes folks like to write this as a proportion:

  \(\dfrac{\text{smaller length}}{\text{larger length}}=\sqrt{\dfrac{\text{smaller area}}{\text{larger area}}}\)

Solving this for "smaller length" gives the expressions we used above:

  smaller length = (larger length) × √(smaller area/larger area)

The is the average of a set of given numbers or data.

It can be found by adding all the numbers/data together and then dividing it by the number of items in the set. Which can also be represented by the equation;

So for our question we have the grades 62, 78, 59 and 89. All in all we have 4 grades.

In order for us to find the mean we must first add all our grades together, so we have;

Now that we have the total of the grades which is 288, we will now divide it by the number of grade there is (which is 4) in order to find the mean.

Therefore our MEAN is 72.

And now we can say that the average grade that Carl have in all 4 math test is 72.

Answer:

94 in

Step-by-step explanation:

Taking the base angles to be <H =84° and ∠I=84° and h = h = 94 inches then you can apply the sine rule which states mathematically that;

a/sin A = b/sin B =c/sin C

In this case ;

h/ sin 84° = i/ sin 84°

94/ sin 84° = i /sin 84°

i= 94 in

Reason

ΔGHI is an isosceles triangle where angles <H and < I = 84°  and if side h = 94 inches  then side i =94 inches  because  side h = side i.

Answer:

24 and 56

Step-by-step explanation:

8*3=24

7*8=56

Answer:

Wasim has enough money.

Step-by-step explanation:

1. find the area of the garden path:

600 cm x 120 cm = 72,000 sq. cm

2. find the area of each stone:

it is a square of 30 cm by 30 cm, so:

30 cm x 30 cm = 900 sq. cm

3. find how many stones can fit in the path:

72,000 / 900 = 80 stones

4. multiply that by the price of each stone:

80 stones x $2.50 = $200

Wasim's budget is $220 and the stones will only cost $200, so it is within the budget

With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

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To find the sum of the first 6 terms of the given sequence, we need to identify the pattern and use it to calculate the terms.

Looking at the sequence, we can observe that each term is obtained by adding the square root of the previous term to the previous term. Let's calculate the terms of the sequence:

First term: 100

Second term: 100 + √100 = 100 + 10 = 110

Third term: 110 + √110 ≈ 110 + 10.49 ≈ 120.49

Fourth term: 120.49 + √120.49 ≈ 120.49 + 10.97 ≈ 131.46

Fifth term: 131.46 + √131.46 ≈ 131.46 + 11.46 ≈ 142.92

Sixth term: 142.92 + √142.92 ≈ 142.92 + 11.95 ≈ 154.87

Now, let's calculate the sum of the first 6 terms:

Sum = 100 + 110 + 120.49 + 131.46 + 142.92 + 154.87 ≈ 759.74

Rounding to the nearest hundredth, the sum of the first 6 terms of the sequence is approximately 759.74.

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The total balance he will have in the accounts at the end of 2 years

is D. $870.88.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

The formula for simple interest is SI = (p×r×t)/100 and the formula for compound interest is A = P(1 + r/100)ⁿ.

∴ P + (p×r×t)/100 + P(1 + r/100)ⁿ is the total amount after 2 years.

= 450 + (450×4.5×2)/100 + 350(1 + 4.25/100)².

= 450 + 40.5 + 350(1.0425)².

= 490.5 + 380.38.

= $870.88.

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Answer:

Rita's down payment is $3000 and she borrowed $12000.

Step-by-step explanation:

The cost of the car is $15000.

Given that she paid 20% down and borrowed the remainder.

So, Rita's down payment= 20% of $15000

\(=\frac{20}{100}\times 15000\)

= $3000

As she borrowed the remainder cost, so,

the borrowed amount = 15000-3000

= $12000

Hence, Rita's down payment is $3000 and she borrowed $12000.

he number of ways the friends can choose seats without sitting next to each other is 7! - 4! = 5040

If there are 5 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 5 factorial (5!) which is equal to 5 × 4 × 3 × 2 × 1 = 120.

(b) If there are 7 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 7 factorial (7!) which is equal to 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

(c) If two friends are required to sit next to each other, we can treat them as a single entity. This reduces the problem to arranging four entities (three individual friends and one pair of friends) and three empty seats. The total number of ways the friends can choose seats is then 4 factorial (4!) which is equal to 4 × 3 × 2 × 1 = 24.

(d) If two friends are required to not sit next to each other, we can count the complement of the situation in part (c). There are 7 factorial (7!) total seating arrangements without any restrictions. From part (c), we found that there are 4 factorial (4!) seating arrangements where the two friends sit next to each other. - 24 = 5016.

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Answer:

y = -3/4x + 9

Step-by-step explanation:

first, find the slope by taking the difference of the y-values / difference of the x-values

(-3-12) / (16-(-4)) which equals -15/20 or -3/4

now use that value to represent the 'm' in the formula in order to find 'b'

y = mx + b

-3 = -3/4(16) + b

-3 = -12 + b

9 = b

y = -3/4x + 9

Answer: $26

Step-by-step explanation:

Given the following :

X(total dollar amount of customer's bill) = 50, 100, 75, 80, 90, 140, 150, 95, 125, 160, 165.

Y(total daily wages) = 36, 43, 38, 40, 42, 50, 60, 43, 46, 50, 55.

The regression equation is given as :

Y = 0.1770X + 25.94 ( using the online regression calculator)

Therefore, if the total amount of customer's bill equals 0, that is X = 0 (her minimum amount if she serves no customer)

Y = 0.1770(0) + 25.94

Y = 25.94

$25.94

Answer:

$26

Step-by-step explanation:

\(\frac{-5 + \sqrt{37} }{2}\)

Answer:

see explanation

Step-by-step explanation:

The area (A) of the rectangle = length × breadth, that is

A = BC × CA

   = (x + 3)(x + 2) ← expand using FOIL

    = x² + 5x + 6

Given that A = 9 , then

x² + 5x + 6 = 9 ( subtract 6 from both sides )

x² + 5x = 3 ← as required

QUESTION-:

The inequalities x < -5 and -X > -5 are the same.

True

False

ANSWER-:

FALSE

!! HOPE ITS HELP U !!

The maximum range is 20.

As, per the data the number of observations of each interval is:

1 to 5: 2 observations.

6 to 10: 5 observations.

11 to 15: 2 observations.

16 to 20: 6 observations.

21 to 25: 1 observations.

Here are two similarly high bins, hence the distribution can be said to be bimodal.

The maximum range is

= 25 - 5

= 21 - 1

= 20.

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Answer:

The distance between the two is 465 meters

Step-by-step explanation:

We first need to set up a triangle that shows the relative position and distances of the two friends

Please check attachment for this

To get this distance, which represents the hypotenuse of the triangle, we make use of Pythagoras’ theorem

Mathematically;

Pythagoras’ theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides

Thus;

D^2 = 256^2 + 388^2

D^2 = 216,080

D = √216,080

D = 464.84 which is approximately 465 m

The area of the region bounded by the graphs of the given equations is 0.

To find the area of the region bounded by the graphs of the given equations y = -2x - x^2 and y = -8, we need to determine the points of intersection between the two curves.

Setting the equations equal to each other:

-2x - x^2 = -8

Rearranging and simplifying the equation:

x^2 - 2x + 8 = 0

This quadratic equation does not have real solutions. Therefore, the two curves do not intersect, and there is no region bounded by them.

As a result, the area of the region bounded by the graphs of the given equations is 0.

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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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The transformation from the graph of f(x) = 4x²-5 to the graph of g(x) = f(x) +7 is a vertical translation 7 units down. This means that every point on the graph of f(x) is moved 7 units downwards to create the graph of g(x).

To identify the graphs of f and g, we can plot some points on each graph. For example, when x = 0, f(x) = -5 and  g(x) = 2. When x = 1, f(x) = -1 and g(x) = 6. We can see that the graph of g(x) is the same as the graph of f(x), but shifted do   wnwards  by 7 units.

To write an equation that represents g in terms of x, we can start with the equation for f(x) and add 7 to it. So:

g(x) = f(x) + 7
g(x) = 4x² - 5 + 7
g(x) = 4x² + 2

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As per given by the question,

There are given that the triangle in quadrant III.

Now,

From the quadrant III, there are given a triangle.

Then,

If we wiil rotate the triangle on counterclockwise or anticlockwise direction , then it will be matched with given triangle on fourth quadrant at angle of 90 degree.

Hence, the option A is correct.

The answer is "A" 90 Degrees

To say that two variables are negatively correlatted means that when one variable increases, the other variable decreases.

Negative correlation refers to a relationship between two variables where they tend to move in opposite directions. When one variable increases, the other variable tends to decrease, and vice versa. This negative relationship indicates an inverse association between the two variables.

Option A, "When one variable increases, the other decreases," accurately describes negative correlation. As one variable increases, the other variable decreases, reflecting the negative relationship between them.

Negative correlation does not imply that both variables change at the same rate (Option D). In negative correlation, the relationship is characterized by the opposite direction of change, not necessarily the same magnitude or rate of change.

Option B, "When variable increases, the other also," suggests a positive correlation, where both variables move in the same direction. This is not the case in negative correlation.

Option C, "When one variable decreases, the other also decreases," is a misinterpretation of negative correlation. In negative correlation, when one variable decreases, the other variable tends to increase, not decrease.

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