Suppose the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points. It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students. Find what scores should be assigned A’s and B’s.

The solutions of the quadratic equation x³+ 16x -3x² = 48 are 3, –4i, 4i

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation.

We are given the quadratic equation as;

x³+ 16x -3x² = 48

Subtract 48 from both sides;

x³+ 16x -3x² - 48= 48 -48

x³+ 16x -3x² - 48= 0

Factor left side of equation.

(x - 3)( x² + 16) = 0

Therefore, the roots are 3, –4i, 4i

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X = 1

X + 6 = 7

     -6   -6

X = 1

Self check : 1 + 6 = 7

The value of the x in the given equation is 1.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, If X + 6 = 7, then X is equal to

Solving the equation, we get,

x + 6 = 7

Subtracting 6 from both side, we get,

x + 6 - 6 = 7 - 6

x = 1

Hence, The value of the x in the given equation is 1.

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Answer:

b)  7

Step-by-step explanation:

Given equation:

[tex](\sin x + \csc x)^2+(\cos x + \sec x)^2=k+\tan^2 x + \cot^2 x[/tex]

Expand the left side of the equation:

[tex]\implies \sin^2x+2 \sin x \csc x + \csc^2x + \cos^2 x + 2 \cos x \sec x + \sec^2 x[/tex]

Simplify:

[tex]\implies \sin^2x+2 \sin x \cdot \dfrac{1}{\sin x} + \csc^2x + \cos^2 x + 2 \cos x \cdot \dfrac{1}{\cos x} + \sec^2 x[/tex]

[tex]\implies \sin^2x+2 + \csc^2x + \cos^2 x + 2 + \sec^2 x[/tex]

[tex]\implies \sec^2 x+\csc^2x+ \sin^2x + \cos^2 x +4[/tex]

Use the identity:   sin²x + cos²x = 1

[tex]\implies \sec^2 x+ \csc^2x+1+4[/tex]

[tex]\implies \sec^2 x+ \csc^2x+5[/tex]

Use the identities:  sec²x = tan²x + 1  and  csc²x = cot²x + 1

[tex]\implies \tan^2x +1 +\cot^2x +1 +5[/tex]

[tex]\implies 7+\tan^2x + \cot^2x[/tex]

Therefore:

[tex](\sin x + \csc x)^2+(\cos x + \sec x)^2=7+\tan^2 x + \cot^2 x[/tex]

[tex] \huge{ \bold{Answer -: }}[/tex]

Option b is correct

[tex] \large \bf{given}[/tex]

[tex] \large{ \sf{ \: (sin \: x \: + cosec \: x) {}^{2} + (cos \: x + sec \: x) {}^{2} }}[/tex]

[tex]\large{ \sf{ = k + { \tan^{2} x + \cot^{2} x}}}[/tex]

[tex] \large{ \sf{\implies \: sin {}^{2} x + cosec {}^{2} x + 2 + {cos}^{2} x + {sec}^{2} x + 2}}[/tex]

[tex]\large{ \sf{ = k + {tan}^{2} x + {cot}^{2} x}}[/tex]

[tex]\large{ \sf{ \implies \: 1 + {cosec}^{2} x - {cot}^{2} x + {sec}^{2} x - {tan}^{2} x + 4 = k}}[/tex]

[tex]\large{ \sf{ \pink{ \implies \: 1 + 1 + 1 + 4 = k \implies \: k = 7}}}[/tex]

[tex] \therefore \: k \: = 7[/tex]

Answer:

Hi, the answer to your question is ×=20

X = 20

when we solve the given equation,

9/12 = 15/x

hence,

X = 15*12/9

X = 20

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Answer:

There are 12 nickels, 9 quarters, and 15 dimes.

I hope this turns out useful for you!

Step-by-step explanation:

Reading the problem repeatedly, I found that the nickels were the value that I could change to find out the values of the other coins and to find the answer. I started with the number of nickels as 20, calculating 20 x 5 (5 as the value of the nickel) = 100 ($1.00). Then, I subtracted three from 20 since the number of quarters was 3 less and got 17. 17 x 25 = a value far too big when we were going to add dimes as well, so 8 lowered the number of nickels a reasonable amount and tried again, following the directions in the problem. It took a bit, but I found a value that worked.

Nickel = $0.05

Quarter = $0.25

Dime = $0.10

My work (though I converted a bit using my sense of money)

12 x 5 = $0.60

12 - 3 = 9

9 x 25 = $2.25

9 + 6 = 15

15 x 10 = $1.50

$0.60 + $2.25 + $1.50 = $4.35

Step-by-step explanation:

At x=0, we have a zero and it bounces off so one of our answers must include

x^2.

Our other zeroes have multiplicities of 1, so our anly reasonable answer is A

a) The expression that represents the boiling temperature (in degree celsius) of platinum is of: y = 4x + 199.

b) The boiling temperature of platinum is of 3827 ºC.

The boiling temperature of the platinum is the output of a function, hence it is represented by the variable y.

The boiling temperature of zinc is the input variable of the function, hence it is represented by variable x.

The boiling temperature of platinum is 199 more than four times the boiling temperature of zinc, hence the expression is given as follows:

y = 4x + 199.

Since the boiling temperature of zing is of 907ºC, the boiling temperature of platinum is obtained as follows:

y = 4(907) + 199 = 3827 ºC.

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Using ratios we know that the number of guides on Sunday was 6.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

So, we know that the proportion of tourists to guides was the same on both days of the weekend.

On Saturday, the ratio was:

120:18

120/18

20/3

Ratio: 20:3

So, a number of guides on Sunday will be:

40:x

40/20 = x/3

20x = 40*3

x = 2*3

x = 6

Therefore, using ratios we know that the number of guides on Sunday was 6.

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Complete question:
The City Sights tour company had the same ratio of tourists to guides on both days this weekend. On Saturday, there were 120 tourists and 18 guides. On Sunday, there were 40 tourists. Find  number of guides on sunday.

Part a:  f(x) = -|x+ 2| - 1, is the modulus function.

part b: f(x) = 2x² - 5, the graph for each function is plotted along with the points.

For the given equation of the polynomial.

Part a: f(x) = -|x+ 2| - 1, is the modulus function.

Put the values for x and find y.

For x = -3, y = 0

For x = -2, y = 1

For x = 0, y = -1

For x = 3, y = -4

Thus, the graph for the obtained points are plotted.

part b: f(x) = 2x² - 5

Put the values for x and find y.

For x = -1.581, y = 0

For x = 1.581, y = 1

For x = 0, y = -5

Thus, the graph for the obtained points are plotted.

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To prove the given statement we can take into account the matrix produced by the tuples (1,2,0), (1,0,1) and (1,0,1). The three vectors are linearly independent if the matrix's where determinant is nonzero.

det ( -1 2 0

        -1 0 1

         1  0 1 )   = 4

Now that P2 has a dimension of 3, those three vectors serve as the foundation for P2 by definition.

Therefore, the polynomial forms the basis of P.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.

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Answer: 62 rows

992 divided by 16 is 62, so there are 62 rows.

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Answer:

992÷16=62

Step-by-step explanation:

I hope I helped you

From the diagram,  the values of  <CAB=60⁰, <ACB=90⁰, <ABC=30⁰,BC=15, DA=32 and BA= 32

You should know that an angle is the intersection of two or more straight lines.

Considering the two tringles

ΔACD≡ΔABC

lines DC=BC

<ACD=<ACB=90⁰

Line DA=AB

This implies that 5x+12=8x

Collecting like terms

8x-5x=12

3x=12

Therefore x=4

This means that 5*4+12=32

This implies that BA=AD=32

In triangle ABC;

<ACB=90⁰

<ADC=<ABC=30⁰

This means that

<BAC=90-30=60

Therefore <CAB=60⁰, <ACB=90⁰, <ABC=30⁰,BC=15, DA=32 and BA= 32 respectively

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All of the statements that correctly describe line ST include the following;

A. Perpendicular bisector of PQ.

C. Median of ΔPQR.

D. Altitude of ΔPQR.

In Mathematics, an isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles and two (2) side lengths that have the same measure or are equal in magnitude.

In every isosceles triangle such as triangle PQR (ΔPQR), both the median and altitude are the same and they will lie on the same line segment when drawn from the top to the base in accordance with the Isosceles Triangle Theorem.

In conclusion, we can logically deduce that the vertex that runs from point T to point S is a perpendicular bisector that bisects line PQ into two (2) equal halves.

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The line segment's unit of measure is 75.6 inches.

What is the conversion factor?

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.

Here, we have

Given

12in/1ft

We have to convert this into inches.

So, we apply here conversion factor and we get

= 6.3ft × 12in ÷1ft

= 75.6 inches

Hence, the line segment's unit of measure is 75.6 inches.

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After 23.1 years the population of Texas will reach 32 million.

In this question, we have been given the population P (in millions) of Texas from 2001 through 2014 can be approximated by the exponential function P = 20.913 e^(0.0184t),

where t represents the year, with t = 1 corresponding to 2001.

We need to find the time period t when the population reach 32 million.

For P = 32, we need to find t.

Substitute P = 32 in given exponential function.

32 = 20.913 e^(0.0184t)

32/20.913 = e^(0.0184t)

1.53 = e^(0.0184t)

ln(1.53) = 0.0184 * t

t = 0.4253/0.0184

t = 23.11 years

Therefore, after 23.1 years the population will reach 32 million.

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The complete question is:

The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P = 20.913e0.0184 t, where t represents the year, with t = 1 corresponding to 2001. According to this model, when will the population reach 32 million? (Source: U.S. Census Bureau)

The pilot is 231 mi from his destination at the time he notices the error.

What is the law of cosines?

The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.

Here, we have

This line is 300 mi long and makes an angle of 40° from the horizontal (based on N50°E bearing).

From point A draw a horizontal line to point C. This line=(35/60)*250=145.8 mi.

Draw a line connecting point C to point B. You now have a triangle with sides AB = 300 mi and AC = 145.8 mi and their included angle of 40.

Using the Law of cosines to find CB:

(CB)² = (AB)²+(AC)² -2*AB*AC*cos 40°

(CB)² = (300)²+(145.8)²-2*300*145.8*cos 40°

(CB)²  = 90000+21257 - 46928 = 64329

CB =√64329 = 253 mi

Hence, the pilot is 231 mi from his destination at the time he notices the error.

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There is a Rotation of 180 degrees

What is Co-ordinate Geometry?

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

We are given that point A is (4, 5) this means that the point lies in the First Quarter of the Co-ordinate System

and the transformed point lies in the Third Quarter of the Co-ordinate System

So, it can be very well said that there is a Rotation of 180 degrees

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With the given coordinates (-3, 1) and (0, 4), the slope is 1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)

Here,

1) (-3, 1) and (0, 4)

Δy=(4-1)=3 and Δx=(0(-3))=3

So, m= Δy/Δx =3/3 =1

2) (-6, 27) and (2, 3)

Δy=(3-27)=24 and Δx=(2-(-6))=8

So, m= Δy/Δx =24/8 =3

3) (5, 27) and (0, -8)

Δy=(-8-27)=-35 and Δx=(0-5)=-5

So, m= Δy/Δx =(-35)/(-5) =7

4) (1, 0) and (-7, -24)

Δy=(-24-0)=-24 and Δx=(-7-1)=-8

So, m= Δy/Δx =(-24)/(-8) =3

5) (-3, 20) and (-5, 32)

Δy=(32-20)=12 and Δx=(-5-(-3))=-2

So, m= Δy/Δx =12/(-2) =-6

6) (5, -4) and (0, -9)

Δy=(-9-(-4))=-5 and Δx=(0-5)=-5

So, m= Δy/Δx =(-5)/(-5) =1

7) (-8, -2) and (-1, -4.5)

Δy=(-4.5-(-2))=-2.5 and Δx=(-1-(-8))=7

So, m= Δy/Δx = -2.5/7

8) (-7, -2) and (6, 11)

Δy=(11-(-2))=13 and Δx=(6-(-7))=13

So, m= Δy/Δx =13/13 =1

9) (-2, -6.5) and (4, -8)

Δy=(-8-(-6.5))= -1.5 and Δx=(4-(-2))=6

So, m= Δy/Δx = -1.5/6 = -1/4

Therefore, slope of a line with the coordinates (-7, -2) and (6, 11) is 1.

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If a sample consists of 600 test scores, 516 of them would be at or below the 86th percentile. If a sample consists of 600 test scores, 228 of them would be at or above the 62th percentile.

A percentile is a score that compares a specific score to the scores of the other members of a group. It displays the proportion of other scores that a given score outperformed. For instance, if you have a test score of 75 and are placed in the 85th percentile, it signifies that your score is greater than those of 85% of other test takers.

Given that,

In general, 70 % of the values in a data set lie at or below the 70th percentile.

20 % of the values in a data set lie at or above the 20th percentile.

Generally percentile defines the percentage of a data set that is below or at a value that is being considered.

Hence the percentage of the values of a data set that lies below or at the 16th percentile is  16%

Also  the values of a data set that lies below or at the 24th percentile is  24%

Given a sample of 600 test scores , the number of test scores that will be at or below the 86th percentile is 86% of  600 which is mathematically represented as:

K = [tex]\frac{86}{100}[/tex] × 600

K = 516 test scores

Given a sample of 600 test scores , the number number of test scores that will be above  the 62 th percentile is (100 - 62 = 38 )% of  600 which is mathematically represented as:

a = [tex]\frac{38}{100}[/tex] × 600

a = 228 test scores.

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The function that is parallel to the graph of y = -4x + 4 is y = -4x - 9

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

y=-4x+4

To start with, we need to express the equation properly

So, we have the following representation

y = -4x + 4

Also, from the question;

We have the following points

The point is given as

Point = (-1, -5) i.e.  (x, y) = (-1, -5)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -4

This means that the slope is -4

The slopes of parallel lines have the same values

This means that the slope of the other line is -4

The equation of the line is then calculated as

y = m(x - x₁) + y₁

Where

m = -4

(x₁, y₁) = (-1, -5)

So, we have

y = -4(x + 1) - 5

Open the brackets

y = -4x - 4 - 5

Evaluate the like terms

y = -4x - 9

Hence, the line has an equation of y = -4x - 9

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Step-by-step explanation:

function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose

function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose

The range of the five numbers 0 , 10 , a , b and c is a + b + c < 13

According to the question,

Statement (1) Its given that a + b + c < 13

Since, a, b and c are positive integers So,  a,b,c > 0

Now, note that the maximum value that any one of a, b, c can take is 10

Range will always be = 10 - 0 = 10

Statement (2)  a < b < c < 13

There are multiple values of a, b, and c that can be possible.

eg; a = 1, b = 5, c = 12

=> Range = 12 - 0 = 12

or, a = 1, b = 2, c = 3

=> Range = 10 - 0 = 10

which can't possible

Therefore , Statement (1) is correct about range

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The minimum sample size required is 108.

What is the standard deviation?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.

To find the minimum sample size required, we can use the formula for the margin of error for a confidence interval for a mean:

margin of error = (z*s) / (√n)

where z is the z-score corresponding to the desired confidence level (in this case, z = 1.28 for an 80% confidence interval), s is the standard deviation of the population, and n is the sample size.

We are given that the margin of error should be no more than 0.06 and that the standard deviation is 0.9. We can solve for n by rearranging the formula and substituting in the given values:

n = [(zs) / margin of error]²

= [(1.280.9) / 0.06]²

= approximately 107.5

Since the sample size must be an integer, we must round up to the next integer, which is 108.

Hence, the minimum sample size required is 108.

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Answer:

12.56 km

Step-by-step explanation:

The circumference of a circle is given by

[tex]c = 2\pi \: r[/tex]

let's find the radius

the area of a circle is given by

[tex]a = \pi \: {r}^{2} [/tex]

12.56 = 3.14 r²

r² = 12.56/3.14

r² = 4

r = √4

r = 2

let's find the circumference

C = 2πr

C = 2 × 3.14 × 2

C = 12.56 km

I hope this helps

The domain of the function are all real numbers between -1 and 0. {x∈R|-1≤x≤0}

What is a function ?

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

See if any vertical lines that were drawn touch the curve more than once by carefully examining the graph. The graph does not represent a function if there is any such line. The graph does reflect a function if no vertical line can cross the curve more than once.

The domain of function are set of values of x for which the function covers.

For the given function, from the graph the function starts from x =-1 and ends at x = 0.

So, the domain of the function are all real numbers between -1 and 0.

{x∈R|-1≤x≤0}

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A linear function would best fit the data because as x increases, the y values change by an approximate constant. The rate of change of this function is approximately 8950 people a year.

To classify a function as linear or exponential, we have to check whether the differences or the quotients between consecutive terms are constant, as follows:

The differences for the consecutive terms in the table are given as follows:

The ratios for the table are given as follows:

The differences have less variation then the ratios, then a linear function best models this data, with an slope of approximately (8995 + 8905 + 8941)/3 = 8947, which is the mean of these differences.

(rounded to 8950).

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Answer:Above $297 we need to add 34%. Thus the result :

297 X 34/100 =100,98

Result = 297 + 100,98 = 397,98

Step-by-step explanation:Good luck

In linear equation, 16.27 is the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).

Describe a linear equation using an example.

An equation in which there is only one variable is known as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.

                    A linear equation in one variable would be 9x + 78 = 18, for instance.

l² = r² + h²

l² =  3² + 16²

l² =   9 + 256

     =   265

l =  √265

l = 16.27

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Answer:

12

Step-by-step explanation:

pythagoras thereom

a^2 +b^2=c^2

13^2-5^2=144

144 square root = 12

Answer:

12

Step-by-step explanation:

13^2 - 5^2 = 144

square root of 144 = 12