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Using the normal distribution, it is found that the percentages are given as follows:

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The prorportion of students who receive an A is one subtracted by the p-value of Z = 1.8.

Looking at the z-table, Z = 1.8 has a p-value of 0.9641.

1 - 0.9641 = 0.0359.

3.59% of the grades will be A.

For B, it is the p-value of Z = 1.8 subtracted by the p-value of Z = 1.1, hence:

0.9641 - 0.8643 = 0.0998.

9.98% of the grades will be B.

For C, it is the p-value of Z = 1.1 subtracted by the p-value of Z = -1.2, hence:

0.8643 - 0.1151 = 0.7492.

74.92% of the grades will be C.

For D, it is the p-value of Z = -1.2 subtracted by the p-value of Z = -1.9, hence:

0.1151 - 0.0287 = 0.0864.

8.64% of the grades will be D.

For F, it is the p-value of Z = -1.9, hence 2.87% of the grades will be F.

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The equation that can be used to find the cost of each binder n in dollars is 861=7n.

Given that the cost of 7 binders is $8.61.

We are required to form an equation that represents the total cost of each binder n in dollars.

Equation is like a relationship between all the variables that are expressed in equal to form.It may be linear equation or may be more types.

Suppose the cost of 1 binder is n dollar.

We know that the total cost is basically the product of price of 1 unit and number of quantities of units.

Total cost=Price of 1 unit* number of units

8.61=n*7

8.61=7n

Hence the equation that can be used to find the cost of each binder n in dollars is 861=7n.

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Answer:

yes

Step-by-step explanation:

25x² - 40xy + 16y² can be factored as

(5x - 4y)² ← a perfect square

Answer:

5/12

Step-by-step explanation:

a foot =12 inches

fraction of 5 inches=5/12

Answer:

1. Plane N

2. Points P, Q, R

3. Plane CRW …

4. Points K and H

5. Line a

Answer:

Simplified: 4X^3

Step-by-step explanation:

Simplify the expression.

Step-by-step explanation:

important of festival in nepali languages for class seven

Answer:

b

Step-by-step explanation:

Answer: c) {1,245; 1,224; 1,203; 1,182; …}

Step-by-step explanation:

Concept:

For this question, we just go by eliminating each answer until we get the correct one

Given information

Common difference = -21 (decreasing sequence)

Answer Choice: a) {873, 894, 915, 936, …}

894 - 873 = 21

915 - 895 = 21

936 - 915 = 21

Since the common difference is 21, not -21

[tex]\large\boxed{FALSE}[/tex]

Answer Choice: b) {32, 20, 8, -4, …}

20 - 32 = -12

8 - 20 = -12

-4 - 8 = -12

Since the common difference is -8, not -21

[tex]\large\boxed{FALSE}[/tex]

Answer Choice: c) {1,245; 1,224; 1,203; 1,182; …}

1224 - 1245 = -21

1203 - 1224 = -21

1182 - 1203 = -21

Since the common difference is -21

[tex]\Huge\boxed{TRUE}[/tex]

Answer Choice: d) {1,563; 1,587; 1,611; 1,635; …}

1587 - 1563 = 24

1611 - 1587 = 24

1635 - 1611 = 24

Since the common difference is 24, not -21

[tex]\large\boxed{FALSE}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: 3

Step-by-step explanation:

Substituting into vertex form, the equation is

[tex]y=a(x+2)^2 +2[/tex]

Substituting in the coordinates (-3, 5),

[tex]5=a(-3+2)^2 +2\\\\5=a+2\\\\a=3[/tex]

Step-by-step explanation:

21) f(x)=1/x-6. g(x)=7/x+6

f(g(x))=f(7/x+6)=1÷7/x+6 - 6=x+6/7 - 6

g(f(x))=g(1/x-6)=7÷1/x-6 - 6 =7(x-6) - 6

simplify forward

25)f(x)=|x| g(x)=5x+1

f(g(x))=f(5x+1)=|5x+1|=5x+1=g(x)

g(f(x))=g(|x|)=5|x|+1=5x+1=g(x)

[tex]given \: that \: its \: linear \\ m = \frac{15 - 3}{3 - 0} = \frac{12}{3} = 4 [/tex]

[tex]b = y(0) = 3 \\ y = 4x + 3 \: [/tex]

Answer:

D) y = 4x + 3

Step-by-step explanation:

   [tex]\sf \boxed{\bf y = mx +b}[/tex]

Here, m is the slope and b is y intercept.

At y intercept, x = 0

         From the table, y intercept  = 3

Choose any two points from the table to find the slope.

(0 ,3)  & (3,15)

[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

           [tex]\sf =\dfrac{15-3}{3-0}\\\\=\dfrac{12}{3}\\\\=4[/tex]

m = 4 ; b = 3

 Equation of line:

                 y = 4x  + 3

Answer:

Step-by-step explanation:

y - 4 = 5/4(x - 8)

y - 4 = 5/4x - 10

y = 5/4x - 6

Step-by-step explanation:

sin(90-A) = sin90cosA-sinAcos90

= cosA*1-0*sinA

= cos90

hence proved

Step-by-step explanation:

sin(90-A)=cosA

sin(90-A)=sin(90-A)

90-A=90-A

-A+A=90-90

=0

Check the picture below.

notice, the dividend and divisor must be in descending order, and when one of the variables is "missing", is really not missing, it simply has a coefficient of 0.

Here is the solution process:

                     3 x² -  2 x  -   6                      

x² + 0x + 2 | 3 x⁴ -  2 x³ +  0  x² -     x -   4

                    3  x⁴ + 0 x³ +  6  x²                

                             - 2 x³  -  6  x² -      x -   4

                             - 2 x³  + 0  x² -   4 x        

                                        -  6  x² +  3 x  -  4

                                        -  6  x²  + 0 x  -  12

                                                        3 x  + 8

Long division:

Therefore, the correct option is "A".

Answer: [tex]48\pi[/tex]

Step-by-step explanation:

[tex](2 \times 24)\pi=48\pi[/tex]

Answer:

$20

Step-by-step explanation:

$5.00 = 10miles

$0.25(40) = 40 miles

Remaining miles: 100 - (10 + 40) = 50

0.10(50) = 50 miles

5.00 + 0.25(40) + 0.10(50)

5.00 + 10.00 + 5.00

$20.00 for 100 miles

Answer:

-25

Step-by-step explanation:

[tex] \dfrac{(20 - 5^2)(16 + 2^2)}{-2^3 + (3 \times 2^2)} = [/tex]

First, do all exponents.

[tex] = \dfrac{(20 - 25)(16 + 4)}{-8 + (3 \times 4)} [/tex]

Now do each operation in parentheses.

[tex] = \dfrac{(-5)(20)}{-8 + 12} [/tex]

Multiply in the numerator. Add in the denominator.

[tex] = \dfrac{-100}{4} [/tex]

Divide the numerator by the denominator.

[tex] = -25 [/tex]

Answer:

-25

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

Given expression:

[tex]\sf \dfrac{(20-5^2)(16+2^2)}{-2^3+(3 \times 2^2)}[/tex]

As the given expression is a fraction, carry out the operations in the numerator and denominator first before finally dividing them.

Following PEMDAS, carry out the calculations inside the parentheses first, then carry out the rest of the calculations following the order of operations:

Parentheses

Calculate the exponents inside the parentheses:

[tex]\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(3 \times 4)}[/tex]

Multiply:

[tex]\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(12)}[/tex]

Add and subtract:

[tex]\implies \sf \dfrac{(-5)(20)}{-2^3+(12)}[/tex]

Exponents

Calculate the exponent:

[tex]\implies \sf \dfrac{(-5)(20)}{-8+(12)}[/tex]

Multiply and Divide

Multiply:

[tex]\implies \sf \dfrac{-100}{-8+(12)}[/tex]

Add and Subtract

Add:

[tex]\implies \sf \dfrac{-100}{4}[/tex]

Finally, divide the numerator by the denominator:

[tex]\implies \sf -25[/tex]

Answer:

C

Step-by-step explanation:

the answer is c

Answer: well one is

Bc its the smallest besides zero, but zero is neither odd or even

Step-by-step explanation:

Answer:

Length = 30ft, Width = 5ft

Step-by-step explanation:

Let x be the width.

Area of Rectangle = Length * Width

Given from the information in the question,

Length = 6x ft

Width = x ft

Substitute the values into the formula:

6x * x = 150

[tex]6x^{2}[/tex] = 150

[tex]x^{2} =\frac{150}{6}[/tex]

[tex]x^{2} =25[/tex]

[tex]x=\sqrt{25}[/tex]

x = 5 ft.

Therefore,

Length = 6 * 5 = 30ft

Width = 5 ft.

The identity of  sin²Ф + cos²Ф  = 1 is verified below

Trigonometry ratio can be evaluated by following the laid down rules with the the use of table and calculator

Given that tan Ф =  1/√5

Where Tan Ф = Opposite / adjacent

We can calculate the hypotenuse by using Pythagoras theorem

Hyp² = 1² + (√5)²

Hyp² = 1 + 5

Hyp = √6

sin Ф = opp / hyp

sin Ф = 1/√6

sin²Ф = 1/6

cos Ф = adj / hyp

cosФ = √5 / √6

cos²Ф = 5/6

sin²Ф + cos²Ф =  1/6 + 5/6

sin²Ф + cos²Ф  = 6/6

sin²Ф + cos²Ф  = 1

Therefore, the identity of  sin²Ф + cos²Ф  = 1 is verified.

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a) The polynomial f(x) in expanded form is f(x) = x³ + 10 · x² - 20 · x - 24.

b) The rational function g(x) in factored form is g(x) = [(x - 6) · (x + 3)] / (x - 2). there is no slant asymptotes.

c) There is one evitable discontinuity at x = - 1, and one definitive discontinuity at x = 2, where there is a vertical asymptote.

a) In the first part of this question we need to determine the equation of a polynomial in expanded form, derived from its factor form defined below:

f(x) = Π (x - rₐ), for a ∈ {1, 2, 3, 4, ..., n}         (1)

Where rₐ is the a-th root of the polynomial.

If we know that r₁ = 6, r₂ = - 1 and r₃ = - 3, then the polynomial in factor form is:

f(x) = (x - 6) · (x + 1) · (x + 3)

f(x) = (x - 6) · (x² + 4 · x + 4)

f(x) = (x - 6) · x² + (x - 6) · (4 · x) + (x - 6) · 4

f(x) = x³ - 6 · x² + 4 · x² - 24 · x + 4 · x - 24

f(x) = x³ + 10 · x² - 20 · x - 24

The polynomial f(x) in expanded form is f(x) = x³ + 10 · x² - 20 · x - 24.

b) The rational function is introduced below:

g(x) = (x³ + 10 · x² - 20 · x - 24) / (x² - x - 2)

g(x) = [(x - 6) · (x + 1) · (x + 3)] / [(x - 2) · (x + 1)]

g(x) = [(x - 6) · (x + 3)] / (x - 2)

The slope of the slant asymptote is:

m = lim [g(x) / x] for x → ± ∞

m = [(x - 6) · (x + 3)] / [x · (x - 2)]

m = 1

And the intercept of the slant asymptote is:

n = lim [g(x) - m · x] for x → ± ∞

n = Non-existent

Hence, there is no slant asymptotes.

c) There is vertical asymptote at a x-point if the denominator is equal to zero. There is one evitable discontinuity at x = - 1, and one definitive discontinuity at x = 2, where there is a vertical asymptote.

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See below for the distance between the points and the lines

Question 2

The line and the points are given as:

x = y

P = (4, -2)

Rewrite the equation as:

y = x

The slope of the above equation is

m = 1

The slope of a line perpendicular to it is

m = -1

A linear equation is represented as:

y = mx + b

Substitute m = -1

y = -x + b

Substitute (4, -2) in y = -x + b

-2 = -4 + b

Solve for b

b = 2

Substitute b = 2 in y = -x + b

y = -x + 2

So, we have:

x = y and y = -x + 2

Substitute x for y

x = -x + 2

Solve for x

x = 1

Substitute x = 1 in y = x

y = 1

So, we have the following points

(1, 1) and (4, -2)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(1 - 4)² + (1 + 2)²

Evaluate

d = 3√2

Hence, the distance between x = y and P = (4, -2) is 3√2 units

Question 3

The line and the points are given as:

y = 2x + 1

Q = (2, 10)

The slope of the above equation is

m = 2

The slope of a line perpendicular to it is

m = -1/2

A linear equation is represented as:

y = mx + b

Substitute m = -1/2

y = -1/2x + b

Substitute (2, 10) in y = -1/2x + b

10 = -1/2 * 2 + b

Solve for b

b = 11

Substitute b = 11 in y = -1/2x + b

y = -1/2x + 11

So, we have:

y = 2x + 1 and y = -1/2x + 11

Substitute 2x + 1 for y

2x + 1 = -1/2x + 11

Solve for x

x = 4

Substitute x = 4 in y = 2x + 1

y = 9

So, we have the following points

(4, 9) and (2, 10)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(4 - 2)² + (9 - 10)²

Evaluate

d = √5

Hence, the distance between the line and the point is √5 units

Question 4

The line and the points are given as:

y = -x + 3

R = (-5, 0)

The slope of the above equation is

m = -1

The slope of a line perpendicular to it is

m = 1

A linear equation is represented as:

y = mx + b

Substitute m = 1

y = x + b

Substitute (-5, 0) in y = x + b

0 = 5 + b

Solve for b

b = -5

Substitute b = 5 in y = x + b

y = x + 5

So, we have:

y = x + 5 and y = -x + 3

Substitute x + 5 for y

x + 5 = -x + 3

Solve for x

x = -1

Substitute x = -1 in y = x + 3

y = 2

So, we have the following points

(-1, 2) and (-5, 0)

The distance between the above points is

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(-1 + 5)² + (2 - 0)²

Evaluate

d = 2√5

Hence, the distance between the line and the point is 2√5 units

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The point estimate of difference of the sample his will be -20.

Based on the information given, the. following can be depicted:

n1 = 13

x1 = 141

s1 = 13

n2 = 9

x2 = 161

s2 = 12

The point estimate of difference will be:

= 141 - 161

= -20

The margin of error to be used in constructing the confidence interval will be calculated by multiplying the standard error which is 5.467 and the critical value. This will be:

= 5.467 × 2.528

= 13.822

The margin of error is 13.822.

The confidence interval will now be:

= (-20 + 13.822) and (-20 - 13.822)

= -6.178 and -33.822

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Using the cosine double angle formula,

[tex]\cos 2\theta=2\cos^2 \theta-1=\frac{12}{13}\\\\2\cos^{2} \theta=\frac{25}{13}\\\\\cos^{2} \theta=\frac{25}{26}\\\\\boxed{\cos \theta=\frac{5}{\sqrt{26}}}[/tex]

(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)

Using the Pythagorean identity,

[tex]\sin^2 \theta+\cos^2 \theta=1\\\\\sin^2 \theta+\frac{25}{26}=1\\\\sin^2 \theta=\frac{1}{26}\\\\\boxed{\sin \theta=\frac{1}{\sqrt{26}}}[/tex]

(Note I took the positive case since [tex]\theta[/tex] terminates in the first quadrant)

Step-by-step explanation:

a)

z = (140 - 118)/16 = 22/16 = 11/8 = 1.375 ≈ 1.38

in the z-table this gives us the p-value : 0.91621

that is the probability of values 140 and below.

for above 140 we need to calculate the value of the other side of the bell-curve :

1 - 0.91621 = 0.08379

b)

z = (90 - 118)/16 = -28/16 = -7/4 = -1.75

in the z-table this gives us the p-value : 0.04006

that is the probability of values of 90 and below.

The value of the probability is 0.30

Using the table of values, we have:

P(x <= -3) = P(x = -5) + P(x = -3)

From the table of values, we have:

P(x = -5) = 0.17

P(x = -3) = 0.13

Substitute the known values in the above equation

P(x <= -3) = 0.17 + 0.13

Evaluate the sum

P(x <= -3) = 0.30

Hence, the value of the probability is 0.30

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[tex]f(x) = \sqrt[3]{11x} \\ y = \sqrt[3]{11x} \\ x = \sqrt[3]{11y} \\ x {}^{3} = 11y \\ y = \frac{x {}^{3} }{11} [/tex]

[tex]f(x) = \frac{x}{7} + 10 \\ y = \frac{x}{7} + 10 \\ x = \frac{y}{7} + 10 \\ x - 10 = \frac{y}{7} \\ y = \frac{x - 10}{7} [/tex]

[tex]f(x) = \frac{7}{x} - 2 \\ y = \frac{7}{x} - 2 \\ x = \frac{7}{y} + 2 \\ x - 2 = \frac{7}{y} \\ y = \frac{7}{x - 2} [/tex]

[tex]f(x) = 9x - 6 \\ y = 9x - 6 \\ x = 9y - 6 \\ x + 6 = 9y \\ y = \frac{x + 6}{9} = g(x)[/tex]

The solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)

From the question, we are to determine the solution to the given system of equations

The given system of equation is

y = 2/3 x + 3     ----------- (1)

x= -2                 ----------- (2)

The value of x has been given in the second equation of the system of equations.

Now, we will determine the value of y

From the second equation, we have that

x = -2

Substitute the value of x into the first equation,

y = 2/3 x + 3

y = 2/3 (-2) + 3

y = -4/3  + 3

y = 5/3

Hence, the solution to the given system of equations is x = -2, y = 5/3. That is (-2, 5/3)

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Answer:

-181 - 79x

Step-by-step explanation:

I am not sure your comment fits the given problem.

I get the following approach and solution :

T(1 + 4x) = 1×a + 4x×b = 2 + 2x

a = 2 + 2x - 4xb

T(4 + 15x) = 4×a + 15x×b = -3 + 3x

4×(2 + 2x - 4xb) + 15xb = -3 + 3x

8 + 8x - 16xb + 15xb = -3 + 3x

11 + 5x - xb = 0

11 + 5x = xb

b = (11 + 5x)/x

a = 2 + 2x - 4x(11 + 5x)/x = 2 + 2x - 44 - 20x = -42 - 18x

T(3 - 5x) = 3×a - 5xb = 3(-42 - 18x) - 5x(11 + 5x)/x =

= -126 - 54x - 55 - 25x = -181 - 79x

control :

T(1 + 4x) = a + 4xb = -42 - 18x + 44 + 20x = 2 + 2x

T(4 + 15x) = 4a + 15xb = -168 - 72x + 165 + 75x = -3 + 3x