HELPPPP PLSSSSSss!!!!!!!

Answer:

d

Step-by-step explanation:

using the cosine ratio in the right triangle

cos B = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{10}[/tex] , then

B = [tex]cos^{-1}[/tex] ( [tex]\frac{2}{10}[/tex] ) ≈ 78.46° ( to 2 dec. places )

Using the sample space and probability concepts, we have that:

A) All the possibilities for the sample space are: {{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.

B) The probability is: 7/8.

C) The probability is: 1/2.

D) The probability is: 1/4.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The sample space is the set that contains all possible outcomes, hence in this problem, considering G for girl and B for boy, it is given by:

{{G,G,G}, {G,G,B}, {G,B,G}, {G,B,B}, {B,G,G}, {B,G,B}, {B,B,G}, {B,B,B}}.

For item B, 7 outcomes have at most two boys, hence the probability is 7/8.

For item C, 4 outcomes have at least two girls, hence the probability is 4/8 = 1/2.

For item D, 2 outcomes have all the babies with the same sex, hence the probability is 2/8 = 1/4.

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The given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

A vector space can be defined as a space (set) which comprises vectors, whose elements can be added under the associative and commutative operation, and can be multiplied by scalars under the associative and distributive operation.

This ultimately implies that, a vector space must be comprised of at least one element, which is generally regarded as its zero vector and the smallest possible vector space.

For every element {u, v and w} in vector (V), and element {a and b} in vector (F), this 8th axiom must be satisfied in order to have a vector space:

(k + m)u = ku + mu

Note: The above axiom (k + m)u = ku + mu is generally referred to as the "distributivity of scalar multiplication with respect to field addition."

Given the following vector:

k(x, y, z) = {k²x, k²y, k²z}

If x₁ · x₂ ≥ 0, then, (kx₁) · (kx₁) = k²x₁y₁ ≥ 0 [Closed in scalar multiplication].

If x₁ · x₂ ≥ 0, x₂ · y₂ ≥ 0, then (x₁ + x₂) · (y₁ + y₂):

x₁y₁ + x₂y₂ + x₁y₂ + x₂y₁ < 0

x₁y₁ + x₂y₂ < -(x₁y₂ + x₂y₁) [Not closed in vector addition].

In conclusion, we can infer and logically deduce that the given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

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Complete Question:

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail.

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = {k²x, k²y, k²z}.

Answer:

3550

Step-by-step explanation:

C.P=Rs 1250

S.P=8(12)(50)

Rs4800

P=S.P-C. P

=Rs4800-Rs1250

= Rs3550

From the given inverse function, we have

[tex]f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12[/tex]

By definition of inverse function,

[tex]f\left(f^{-1}(x)\right) = x[/tex]

so that

[tex]f\left(2x-\dfrac12\right) = x[/tex]

[tex]a\left(2x-\dfrac12\right) + \dfrac b2 = x[/tex]

[tex]2ax - \dfrac a2 + \dfrac b2 = x[/tex]

[tex]\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}[/tex]

[tex]\implies \boxed{a=\dfrac12}[/tex]

[tex]\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}[/tex]

Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of [tex]a^{2}[/tex] + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

[tex]3x^{2}[/tex] - 2 = -5x
[tex]3x^{2}[/tex] + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.

Katrina would pay less amount of interest on the nonsubsidized student loan

The total interest paid on the nonsubsidized loan is $3,860.80

What is monthly compounding?

Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.

In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.

In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:

FV=PV*(1+r/n)^(n*t)

FV=balance after 2 years=unknown

PV=loan amount

r=annual interest rate

n=number of times interest is compounded annually=12

t=number of years before repayments commence=2

Non-subsidized loan:

FV=$29,000*(1+2.5%/12)^(12*2)

FV=$30,485.28

Subsidized loan:

FV=$29,000*(1+4.5%/12)^(12*2)

FV=$31,725.71

Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly  payments would occur at the end of each month:

PV=PMT*(1-(1+r)^-N/r

PV=balance of loan after 2 years

PMT=monthly payment=unknown

r=monthly interest rate=annual interest rate/12

N=number of monthly payments in 6 years=12*6=72

Non-subsidized loan:

$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)

PMT=$456.40

total monthly payments=$456.40*72

total monthly payments=$32,860.80

Interest= total monthly payments-loan

interest=$32,860.80-$29,000

interest=$3,860.80

Subsidized loan:

$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)

PMT=$503.61

total monthly payments=$503.61 *72

total monthly payments=$36,259.92

Interest= total monthly payments-loan

interest=$36,259.92 -$29,000

interest=$7,259.92

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Answer:

71

Step-by-step explanation:

Evaluate for x=12

(8)(12)−25

(8)(12)−25

=71

Answer:

71

Step-by-step explanation:

To evaluate [tex]8x - 25[/tex] when [tex]x = 12[/tex], we have to replace x with 12 in the expression:

[tex]8x - 25[/tex]

⇒ [tex]8(12) -25[/tex]

⇒ [tex]96 - 25[/tex]

⇒ [tex]\bf 71[/tex]

Answer:

a) A = 3, B = 8.

b) C = 2, D = 25

Step-by-step explanation:

See the image below.

Answer:

40 liters of 30% solution.

20 liters of 60% solution.

Step-by-step explanation:

Let x = amount of 30% solution.

Let y = amount of 60% solution.

Equation of amounts of solutions.

x + y = 60

Equation of amounts of alcohol in the solutions.

0.3x + 0.6y = 0.4 × 60

x = 60 - y

0.3(60 - y) + 0.6y = 24

18 - 0.3y + 0.6y = 24

0.3y = 6

y = 20

x + y = 60

x + 20 = 60

x = 40

Answer:

40 liters of 30% solution.

20 liters of 60% solution.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 7 is an equation.

We have,

Let 30% solution = m

Let 60% solution = n

Now,

A scientist needs 60 liters of a 40% solution of alcohol.

He has a 30% solution and a 60% solution available.

This means,

m + n = 60 _____(1)

30% of m + 60% of n = 40% of 60

0.30m + 0.60n = 0.40 x 60

0.30m + 0.60n = 24 ____(2)

From (1) and (2) we get,

m + n = 60

m = 60 - n _____(3)

Putting (3) in (2) we get,

0.30m + 0.60n = 24

0.30(60 - n) + 0.60n = 24

18 - 0.30n + 0.60n = 24

18 + 0.30n = 24

0.30n = 24 - 18

0.30n = 6

n = 6/0.30

n = 20

Putting n = 20 in (3) we get,

m = 60 - 20

m = 40

Now,

The number of liters of the 30% solution is 40.

The number of liters of the 60% solution is 20.

Thus,

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

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Answer:

[tex]h = \bf 28.3 \space\ m[/tex]

Step-by-step explanation:

• We are given:

○ Volume = 36 m³,

○ Circumference = 4 m

• Let's find the radius of the cylinder first:

[tex]\mathrm{Circumference} = 2 \pi r[/tex]

Solving for [tex]r[/tex] :

⇒ [tex]4 = 2 \pi r[/tex]

⇒ [tex]r = \frac{4}{2\pi}[/tex]

⇒ [tex]r = \bf \frac{2}{\pi}[/tex]

• Now we can calculate the height using the formula for volume of a cylinder:

[tex]\mathrm{Volume} = \boxed{\pi r^2 h}[/tex]

Solving for [tex]h[/tex] :

⇒ [tex]36 = \pi \cdot (\frac{2}{\pi}) ^2 \cdot h[/tex]

⇒ [tex]h = \frac{36 \pi^2}{4 \pi}[/tex]

⇒ [tex]h = 9 \pi[/tex]

⇒ [tex]h = \bf 28.3 \space\ m[/tex]

Answer:

9π m ≈ 28.27m

Step-by-step explanation:

The volume of a right cylinder is given by the formula

πr²h where r is the radius of the base of the cylinder(which is a circle), h is the height of the cylinder

Circumference of base of cylinder is given by the formula 2πr

Given,

2πr = 4m

r = 2/π m

Volume given as 36 m³

So πr²h = 36
π (2/π)² h = 36

π x 4/π² h = 36

(4/π) h = 36

h = 36π/4 = 9π ≈ 28.27m

a. Line AB and line BC are not congruent because their distance of separation are not equal

b. Line AC and line BD are not congruent because their distance of separation are not equal

From the number line drawn, we have the following deductions;

Line AB = -5 to -2 = 3

Line BC = -2 to 0 = 2

Line AC = -5 to 0 = 5

Line AD = -5 to 5 = 10

Line BD = -2 to 5 = 7

We can see that;

a. Line AB and line BC are not congruent because their distance of separation are not equal

b. Line AC and line BD are not congruent because their distance of separation are not equal

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At the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].

Here, the initial population is [tex]P=1.23\times 10[/tex] and the growth rate is [tex]r=6.7\%[/tex].

So the population after [tex]t=4[/tex] years will be:

[tex]A=P(1+\frac{r}{100})^t\\\Longrightarrow A=1.23\times 10\times(1+\frac{6.7}{100})^4\\\Longrightarrow A=1.23\times 10\times(1.067)^4[/tex]

Therefore, at the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].

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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:

B

Step-by-step explanation:

The area of the triangle is half the base time the height.  The height is y sub 1.  The length is the distance between the x values.

Answer:

an angle bisector

Step-by-step explanation:

This is showing the construction of the bisector of ∠LNM

Answer:

The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.

'25' above sigma is the upper bound.

In general it means adding 42 from 1 to 25 times.

so 42(25).

Answer:

C. 42(25)

Step-by-step explanation:

Took the unit test review and this was the correct option choice.

Goodluck on your unit test, I am sure that you will do good :)

Answer:

option B is the answer of given question

Answer:

D. 93.5

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

The lower arc is twice 52

c = 1/2( 104  +83)

c = 1/2 ( 187)

c =93.5

Answer:

vertex : (-5/2, -53/4)

solutions: (-(5-sqrt53)/2, 0) (-(5+sqrt53)/2, 0)

Step-by-step explanation:

1.The vertex of the function is (-5/2, -53/4).

2.We have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

To find the vertex and solutions of the function y = x^2 + 5x - 7, we can use the formula for the vertex and the quadratic formula for finding solutions.

1. Vertex:

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:

x = -b / (2a)

y = f(x) = ax^2 + bx + c

Given: a = 1, b = 5, c = -7

x = -5 / (2 * 1) = -5 / 2

Now, substitute the value of x into the equation to find y:

y = (-5/2)^2 + 5 * (-5/2) - 7

y = 25/4 - 25/2 - 7

y = 25/4 - 50/4 - 7

y = (25 - 50 - 28) / 4

y = -53 / 4

So, the vertex of the function is (-5/2, -53/4).

2. Solutions (or roots or x-intercepts):

To find the solutions (x-intercepts) of the function, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Given: a = 1, b = 5, c = -7

x = (-5 ± √(5^2 - 4 * 1 * -7)) / 2 * 1

x = (-5 ± √(25 + 28)) / 2

x = (-5 ± √53) / 2

Now, we have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

So, the solutions of the function are approximately x ≈ 0.73 and x ≈ -5.73.

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According to the direct inspection, we conclude that the best approximation of the two solutions to the system of quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)

Herein we have two parabolae, that is, polynomials of the form a · x² + b · x + c, that pass through each other twice according to the image attached to this question. We need to estimate the location of the points by visual inspection on the Cartesian plane.

According to the direct inspection, we conclude that the best approximation of the two solutions, that is, the point where the two parabolae intercepts each other, to the system of two quadratic equations are (x₁, y₁) = (- 1, 0) and (x₂, y₂) = (1, 2.5). (Correct choice: C)

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The value of the rate of change of the function is 14a + 7h

The rate of change of function is also known as the slope expressed according to the equation shown below;

f'(x) = f(a+h)-f(a)/h

Given the function below expressed as:

f(x) =1 + 7x^2

Determine the function f(a)

To determine the function, simply replace x with 'a" to have:

f(a) =1 + 7a^2

Determine the function f(a+h)

f(a+h) = 1 + 7(a+h)^2

f(a + h) = 1 + 7(a^2+2ah+h^2)

f(a + h) = 1 + 7a^2 + 14ah + 7h^2

To determine the rate of change

f'(x) = f(a+h)-f(a)/h

f'(x) = 1 + 7a^2 + 14ah + 7h^2 - 1 - 7a^2/h
f'(x) =  + 14ah + 7h^2/h

f'(x) = 14a + 7h

Hence the value of the rate of change of the function is 14a + 7h

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The amount that Karsten's estate should pay his younger daughter each month over 20 years so that the accumulated present value will be equal to $50,000 is $358.22.

The monthly payments out of the present value of $50,000 can be computed using an online finance calculator.

The periodic payment represents the equal amount that can be paid to the daughter monthly so that it equals the PV of $50,000 of the estate share.

N (# of periods) = 240

I/Y (Interest per year) = 6%

PV (Present Value) = $50,000

FV (Future Value) = $0

Results:

Monthly Payment = $358.22

Sum of all periodic payments = $85,971.73 ($358.22 x 2400

Total Interest = $35,971.73

Thus, Karsten's younger daughter can be paid $358.22 to equal the accumulated present value of $50,000.

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Considering the given linear function, we have that:

A linear function is modeled by:

y = mx + b

In which:

His payment for x copies bought is:

y = 120x + 2400.

Hence:

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Answer: [tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]

Step-by-step explanation:

Given the requirement of function form

Point-slope form: y - y₁ = m (x - x₁)

Given information

Slope (m) = -6/5

Y-intercept (x₁, y₁) = 2 = (0, 2)

Substitute values into the required form

y - y₁ = m (x - x₁)

y - (2) = (-6/5) (x - 0)

[tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Using the combination formula, it is found that 436,270,780 different selections are possible.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 7 numbers are taken from a set of 61, hence the number of different selections is given by:

C(61,7) = 61!/(7! x 54!) = 436,270,780

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The mistake each student made and what each student needs to do to fix their mistake is;

x² - 6x + 8 = 0

x = - b ± √b² - 4ac / 2a

where,

x = - b ± √b² - 4ac / 2a

= -(-6) ± √(-6)² - 4(1)(8) / 2(1)

= 6 ± √36 - 32 / 2

= 6 ± √4 / 2

= 6 ± 2 / 2

x = 6/2 + 2/2 or 6/2 - 2/2

= 3 + 1 or 3 - 1

x = 4 or 2

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The equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60

From the question, we are to determine the equation that will give the number of boxes, x, that Joe needs to buy

From the given information,

Joe needs 60 donuts to feed his construction crew

Also,

There are 12 donuts per box

This means he needs to buy 60/12 boxes of donut

Since the number of boxes Joe needs to buy is x

∴ 60/12 = x

60 = 12x

12x = 60

Hence, the equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60

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Answer:

Step-by-step explanation:

85!/82! = 85*84*83 = 592620

n choose 0 is always equals 1

n P n also always equals 1