Tom observes 240 birds. He notices that 12 of them have blue tail feathers. The next day he spots 40 birds with blue tail feathers. How many birds did he view in total that day?

The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645

In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:

x²

When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -

x² = 3 -

When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x

x² = 3 - 4x

Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0

Where:

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)

x= {- 4 ± √ (16 + 12)} / 2

x= {- 4± √ 28} / 2

x= (- 4 ± 5.29 ) / 2

x1= (- 4 + 5.29 ) / 2

x1= (1,29) / 2

x1= 0.645

x2= (- 4 - 5.29 ) / 2

x2= (9.29) / 2

x2= -4.645

We can check the values, replacing them into the equation:

(x1)² = 3 - 4(x1)

(0.645)² = 3 - 4*(0.645)

0.42 = 0.42

(x2)² = 3 - 4(x2)

(-4.645)² = 3 - 4*(-4.645)

21.58 = 21.58

It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:

ax²+ bx + c = 0

Learn more about quadratic equation at: brainly.com/question/25841119 and brainly.com/question/7784687

#SPJ4

Answer:

-625

Step-by-step explanation:

Here we are basically multiplying each term by -5. So if you want two more terms, you would go like this...

5 × -5 = -25

-25 × -5 = 125

125 × -5 = -625

-625 × -5 = 3125

and so on!!!

Hope it helps and mark it as Brainliest if possible!!! Good Luck!!!

Answer:

d = 48

Step-by-step explanation:

The probability of observing a value less than 0.83, denoted as P(z < 0.83), can be found using the standard normal distribution table. The value obtained from the table represents the area under the standard normal curve to the left of the given value. For P(z < 0.83), the probability is approximately  0.7967 or 79.67%. (X.XX) (rounded to two decimal places).

The probability of observing a value less than 0.83, we need to compute the area under the standard normal distribution curve to the left of 0.83. This can be done using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can look up the probability associated with a z-score of 0.83. The table will give us the area to the left of 0.83, which is the probability of observing a value less than 0.83.

Looking up the value in the table, we find that the probability of observing a value less than 0.83 is 0.7967.

Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution to compute the probability of observing a value less than 0.83. The CDF of the standard normal distribution gives us the probability that a standard normal random variable is less than or equal to a given value.

Using a calculator, we find that the probability of observing a value less than 0.83 is approximately 0.7967.

Therefore, the probability of observing a value less than 0.83 is approximately 0.7967 or 79.67%.

To know more about probability , refer here :

https://brainly.com/question/30034780#

#SPJ11

Answer:

1: 544

2: 2,355.52

3:28, 288

Answer:

The correct answer is C.) h(x) = -4(x − 2)(x + 2).

The zeros of the function h are -2 and 2.

Step-by-step explanation:

yw;)

Answer:

The incorrect statement is decreasing from (-∞, -1)

Step-by-step explanation:

Intercepts are where it touches the axis

The x intercepts are -2 and 1

Increasing is where it goes up

We are increasing from (-∞, -1) and (1,∞)

Decreasing is where it goes down

We are decreasing from ( -1,1)

The incorrect statement is decreasing from (-∞, -1)

Step 1: Let's recall what is SAS:

"SAS" means "Side, Angle, Side"

Step 2: Let's use The Law of Cosines to calculate the unknown side of the triangles given:

Formula of The Law of Cosines is:

In the triangle ABC, we have:

b = 15, c = 21 and angle A is 75 degrees

Step 3: Substitute the values given in the formula

Step 4: Let's use The Law of Sines to find the smaller of the other two angles

Step 5: Find the last angle, recalling that the interior angles of a triangle add up to 180 degrees

Now, we have the sides and the angles of triangle ABC:

Sides = 15,21, 22.43

Angles = 75, 64.74, 40.26

Answer:

30.24%

Step-by-step explanation:

Each time you lose x%, you end up with 1 - 0.01x.

For example, if you lose 10% of an amount, you end up with 1 - 0.01(10), or 0.9 times the original amount.

Let's say you started with x.

You lost 10%. Now you have 0.9x.

Then you lost 20% of the remaining amount. Now you have 0.8(0.9x).

Then you lost 30% of the remaining amount. Now you have 0.7(0.8)(0.9x).

Finally you lost 40% of the remaining amount. Now you have 0.6(0.7)(0.8)(0.9x).

The final amount you have is

0.6(0.7)(0.8)(0.9x) = 0.3024x = 30.24% of x

Answer: 30.24%

The bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

What are scientific notations?

Scientific notations are a way of representing either a very small or a very large number in the powers of 10. Scientific notations comprise digits from 1 to 9 with powers of 10.

Calculation of the amount by which a bacterial cell is smaller than the amoeba cell

Given the length of amoeba cell in scientific notations is 3.5 × 10^(- 4)

The length of a bacterial cell in scientific notations is 5 × 10^(- 6)

To obtain how small the bacterial cell is from the amoeba cell, we need to divide both the lengths i.e.

= 3.5 × 10^(- 4) / 5 × 10^(- 6)

= 0.7 × 10^(2)

= 7 × 10^(1)

Hence, the bacterial cell is about 7 × 10^(1) times smaller than the amoeba cell in scientific notations.

To learn more about the scientific notations, visit here:

https://brainly.com/question/10401258

#SPJ4

Answer:

24 yards of ribbon

Step-by-step explanation:

1. figure out how much she spent

if the card started with $15 on it, and there's $10.44 left, that means she spent $4.56

2. divide

divide 4.56 (money spent) by .19 (cost per yard) to get your answer

24

24 yards of ribbon

Step-by-step explanation:

$ 3.15 each pendents .......

If a sample of 8 scores has a mean of 10 and after removing one score, the mean of the remaining scores is 11, the score that was removed is 7.

The mean of the original sample is 10. This means that the sum of the scores in the sample is 8 multiplied by 10, which equals 80. After one score is removed, the mean of the remaining scores is 11. Since there are now 7 scores remaining in the sample, the sum of those scores is 7 multiplied by 11, which equals 77.

To find the score that was removed, we need to calculate the difference between the sum of the original sample and the sum of the remaining scores. The difference is 80 minus 77, which equals 3. Therefore, the score that was removed from the sample is 3.

Learn more about sum here: https://brainly.com/question/17208326

#SPJ11

Answer:

100 miles per hour

Step-by-step explanation:

Step 1:

200 ÷ 2 = 100

Answer:

100 MPH

Hope This Helps :)

Therefore, the standard deviation of the data set is approximately 4.14.

The standard deviation is calculated by taking the square root of the variance, which is the sum of the squared deviations divided by the sample size minus 1.

So, first we need to calculate the variance:

variance = sum of squared deviations / (sample size - 1)

variance = 103 / (7 - 1)

variance = 17.17

Now we can find the standard deviation:

standard deviation = √(variance)

standard deviation = √(17.17)

standard deviation = 4.14 (rounded to two decimal places)

To know more about data set,

https://brainly.com/question/22210584

#SPJ11

Answer:

it would be answer B

if m right

Answer:

Below

Step-by-step explanation:

The plane's distance is the hypotenuse of a right triangle with legs of

(50 -20)mi = 30 miles     and     30500 - 18000 = 12500 ft

                             for consistent units  12500ft/5280ft/mile = 2.36742 miles

Now just use Pythagorean theorem

Hypotenuse^2 = leg1^2 + leg2^2

               h^2    = 30^2 + 2.36742^2

                   h = ~ miles 30.093 miles  ( note that the vertical descent distance does not matter much)

    (this is 158 892 feet)

Answer:

1 7/8 can be written as 8*1+7/8=15/8=1.875

Step-by-step explanation:

The number of races that were 10-kilometer long is 102.

An athlete ran a total of 1,500 kilometers in a race before retiring. The athlete completed 32 races that were at least 15 kilometers in length. The rest were 10-kilometer races. We need to find out the number of races that were 10-kilometer long.

Let the number of races that were 10-kilometers long be denoted by the variable "x". An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equal sign. We can write the equation as given below.

32×15 + 10x = 1,500

480 + 10x = 1,500

10x = 1,500 - 480

10x = 1,020

x = 1,020/10

x = 102

Hence, the number of races that were 10-kilometer long is 102.

To learn more about numbers, visit :

https://brainly.com/question/17429689

#SPJ4

Answer:

h = 5 units

Step-by-step explanation:

Step 1: Plug in known variables into formula

A = 1/2bh

30 = 1/2(12)h

Step 2: Multiply both sides by 2 (To get rid of fraction)

60 = 12h

Step 3: Divide both sides by 12

h = 5

Answer: 5 units

Step-by-step explanation:

30 devided by 12 then multiply that by 2

The answer of the given question based on the expression is equivalent expression to log Subscript 12 Baseline StartFraction x Superscript 4 Baseline StartRoot x cubed minus 2 EndRoot Over (x + 1) Superscript 5 Baseline EndFraction are given below,

In mathematics, expression is  combination of numbers, symbols, and operators that represents  value or quantity. Expressions can be the simple or the complex, and they can involve of one or more variables.

We can simplify given expression using following logarithmic rules:

log_a(b^c) = c*log_a(b)

log_a(b/c) = log_a(b) - log_a(c)

log_a(b * c) = log_a(b) + log_a(c)

Using these rules, we can simplify the given expression as follows:

log_12(x⁴ * (x³ - 2)⁽¹/²⁾ / (x + 1)⁵)

= log_12(x⁴) + log_12((x³ - 2)⁽¹/²⁾) - log_12((x + 1)⁵)

= 4*log_12(x) + (1/2)log_12(x³ - 2) - 5log_12(x + 1)

Therefore, the equivalent expression is:

4*log Subscript 12 Baseline x + StartFraction 1 Over 2 EndFraction log Subscript 12 Baseline x cubed minus 2 minus 5 log Subscript 12 Baseline x + 1.

To know more about Logarithmic rule visit:

https://brainly.com/question/30287525

#SPJ1

Answer:

As per Provided Information

Height of cone h is 3.25 cm

Diameter of cone is 2.2 cm

Radius = 2.2/2

Radius = 1.1 cm

We have been asked to determine the volume of the cone .

Using Formulae

\( \boxed{\bf \:Volume_{(Cone)} = \cfrac{1}{3} \pi {r}^{2}h}\)

Substituting the given value and let's solve it

\(\sf\longrightarrow \: Volume_{(Cone)} = \cfrac{1}{3} \times 3.14 \times {1.1}^{2} \times 3.25 \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = \cfrac{1}{3} \times 3.14 \times 1.21 \times 3.25 \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = \cfrac{1}{3} \times 3.14 \times 3.9325 \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = \cfrac{1}{3} \times 12.34805 \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = \cfrac{12.34805}{3} \\ \\ \\ \sf\longrightarrow \: Volume_{(Cone)} = 4.11 {cm}^{3} \)

Therefore,

Answer:

Length * Height * Width, or V = L * H * W. Ex: V = 5 in.

Answer:

28

Step-by-step explanation:

We are given the area of a base and the width of the prism.

Volume = area of base * width

Volume = 8/3 * 21/2 = 28

There are 56,046 different three-course meals that can be ordered at Pizza House.To calculate the total number of different three-course meal combinations, we need to use the counting principle.

The counting principle states that if there are A ways to do one thing and B ways to do another, then there are A x B ways to do both.
In this case, we have:
- 22 ways to choose a salad
- 77 ways to choose a pizza
- 33 ways to choose a dessert

Applying the counting principle, we can calculate the total number of different three-course meals by multiplying the number of choices for each course:
22 (salads) x 77 (pizzas) x 33 (desserts) = 56,046 different three-course meals.
So, there are 56,046 different three-course meals.

To know more about  counting principle click here

brainly.com/question/10275154

#SPJ11

The general solution of the given differential equation is y(t) = \(c_1 e^{2t} + c_2 e^{-t} -2t^2 + 6t -5\)

We first solve the associated homogeneous equation y'' − y' − 2y = −8t + 4t² to find the general solution of the given differential equation y'' − y' − 2y = 0.

The characteristic equation is r² - r - 2 = 0, which factors as (r - 2)(r + 1) = 0. Therefore, the roots are r = 2 and r = -1.

The general solution of the associated homogeneous equation is y_h(t) = \(c_1 e^{2t} + c_2 e^{-t}\), where c_1 and c_2 are constants.

To find a particular solution of the given non-homogeneous equation, we use the method of undetermined coefficients. Since the right-hand side of the equation is a polynomial of degree 2, we assume a particular solution of the form y_p(t) = At² + Bt + C. Substituting this into the differential equation, we get:

2A - 2A t - 2At² - B - 2Bt - 2C = -8t + 4t²

2A -B -2C - (2A + 2B)t -2At²= -8t + 4t²

Equating coefficients of like terms, we get:

2A -B -2C = 0

- (2A + 2B) = -8

-2A = 4

Therefore, A = -2, B = 6, and C = -5. Thus, a particular solution of the given non-homogeneous equation is y_p(t) = -2t² + 6t -5.

The general solution of the given differential equation is the sum of the general solution of the associated homogeneous equation and a particular solution of the non-homogeneous equation. Therefore, the general solution is:

y(t) = y_h(t) + y_p(t)

= \(c_1 e^{2t} + c_2 e^{-t} -2t^2 + 6t -5\)

where c_1 and c_2 are constants.

Learn more about Differential equation here

https://brainly.com/question/31230406

#SPJ4

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

Learn more about spirometry and its significance in assessing lung function:

https://brainly.com/question/18155241

#SPJ11

A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

Learn more about Congruent polygons here:

https://brainly.com/question/2096633

#SPJ1

Answer:

X=2

Step-by-step explanation:

Khan academy

The probability of light being not red will be 0.018.

What is probability?

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.

Given data:

Pedro drives the same route to work and only he faces one traffic light on his route.

Chances of light being red = 55%

Therefore,

The probability of light being red p = 0.55

So, the probability that light is not red

 q = 1 - 0.55

 q = 0.45

Now, if we calculate the probability of light being not red for all 5 days from Monday to Friday

      \(q'=q^5\\\\q'=(0.45)^5\\\\q'=0.018\)

Hence, we can conclude that the probability of light being not red will be 0.018.

To learn more about probability in mathematics, visit:

https://brainly.com/question/24756209

#SPJ4