Plz plz plz plz plz plz
Help ​

Answer:

Step-by-step explanation:

GH bisects ∠FGI.

So,  ∠HGI =∠FGH

6x - 17 = 5x - 8      {Add 17 to both sides}

        6x = 5x - 8 + 17

        6x = 5x + 9     {Subtract 5x form both sides}

  6x - 5x = 9

a) x = 9

b) ∠FGH  = 5* 9 - 8

               = 45 - 8

  ∠FGH  = 37

c) ∠HGI = 6*9 - 17

            = 54 - 17

   ∠HGI = 37

d) ∠FGI = ∠FGH + ∠HGI

            = 37 + 37

  ∠FGI = 74  

This means that the probability that a randomly selected high school student who took the math portion of the ACT has a score between 19 and 24 is approximately 0.3557 or 35.57%.

To determine the probability that a randomly selected high school student who took the math portion of the ACT has a score between 19 and 24, we need to use the normal distribution formula and standardise the scores:
Z = (X - μ) / σ
Where X is the score, μ is the mean, and σ is the standard deviation.
So, for X = 19:
Z = (19 - 21.1) / 5.3 = -0.39
And for X = 24:
Z = (24 - 21.1) / 5.3 = 0.55
Using a standard normal distribution table or a calculator, we can find the area under the curve between these two Z-scores:
P(-0.39 < Z < 0.55) = 0.3557
This means that the probability that a randomly selected high school student who took the math portion of the ACT has a score between 19 and 24 is approximately 0.3557 or 35.57%.

Learn more about probability here, https://brainly.com/question/25839839

#SPJ11

Answer:

y = - 3x + 24

Step-by-step explanation:

Step 1:

y = mx + b         Slope Intercept Form

Step 2:

- 3x - y = - 24         Equation

Step 3:

- 3x = y - 24       Add y on both sides

Step 4:

- 3x + 24 = y        Add 24 on both sides

Answer:

y = - 3x + 24

Hope This Helps :)        

Using Trigonometry formulae,

the length of the longest item that can be carried horizontally around the corner is 19.60 feet.

Let's try to draw it and try to solve with a diagram we're moving into a new apartment. We see that the right corner is 8 feet wide, but then that's right there is 6 feet wide and we're going to have some ladder or a long item required here .

Creating some angle θ and let b feet be the distance parallel to 8 feet and a be the distance parallel to 6 feet and then one portion we'll call d, other one portion e . So, the total length (L) = d + e

In this case, sinθ = b/e,

because that's the opposite over the hypotenuse, => e sinθ = b

and d cosθ = a

We know that e = b cosecθ and d = a secθ

so the length(L) = a secθ + b cosecθ In order to maximize length , we want to take the derivative with respect to θ we get,

dL/dθ = - b cotθ cosecθ + a secθ tanθ

now, dL/dθ = 0

=> - b cotθ cosecθ+ a secθ tanθ = 0

=>b cotθ cosecθ = a secθ tanθ

=>tan³θ = b/a

=> tanθ = (b/a )⁰·³³

plugging value of b= 6 and a = 8

tanθ = (6/8)⁰·³³

=> tanθ = 0.9085

so, θ = tan⁻¹(0.9085)

=> θ = 42.2550

plug the value of θ in e and d

we get , e = 6 cosec(42.2550) = 8.8 d = 8 sec(42.2550) = 10.80

then, L = d + e

=> L = 8.8 + 10.80 = 19.60

Hence, the required length is 19.60 feet .

To learn more about trigonometry, refer:

https://brainly.com/question/24349828

#SPJ4

Answer:

Step-by-step explanation:

c(g) = 5g + 60

g is the number of arcade games played

c(7) = 5*7 + 60

      = 35 + 60

c(7) = 95

Cost of playing the arcade games is $ 95

b) c(g) = $ 115

5g + 60 = 115

Subtract 60 from both sides

5g = 115 - 60

5g = 55

Divide both sides by 5

g = 55/5

g = 11

I can play 11 games

The c-chart monitors nonconformities. UCLc is calculated and rounded to two decimal places, while LCLc is rounded to two decimal places (0 for negative values). No significant variation indicates control.

The c-chart is a quality control tool used to monitor the count of nonconformities or defects in a process. By calculating the UCLc and LCLc, the control limits are established to identify whether the process is within acceptable limits.

In this case, the UCLc is determined by rounding the nonconformities to two decimal places, while the LCLc is set to 0 for any negative values. If the observed nonconformities fall within the control limits, it indicates that there is no significant variation in the incidents of incorrect information given out by the IRS telephone operators.

Therefore, the process is considered to be under control.

To know more about variation visit -

brainly.com/question/32685007

#SPJ11

Answer:

The unit prices will be within the range of $0.77 ≤x≤$0.78

Step-by-step explanation:

If a package 8-count AA batteries cost $6.16 and a package of same 20-count AA batteries cost $15.60, to calculate the unit price, the following steps must be carried out:

8 counts AA batteries = $6.16

A unit price (i.e 1 count) = x

Cross multiplying

8 × x = 6.16 × 1

x = 6.16/8

x = $0.77 for a unit price

Similarly, if 20-count AA batteries cost $15.60, then:

20 counta = $15.60

1 count = x

Cross multiplying

20 × x = $15.60 × 1

x = $15.60/20

x = $0.78 for a unit price

From above calculation, of can be seen that the unit price is almost similar but with a difference of $0.01 ($0.78-$0.77) which is insignificant. Based on this, we can conclude that a unit price of the battery is between the range

$0.77 ≤x≤$0.78

Answer:

The 8-count pack of AA batteries has a lower unit price of 0.77

per battery.

Step-by-step explanation:

The surface are of the figure that gives answers are:  Part A) is 178.98 in² and Part B) is  932 ft

Area Congruence Postulate: If two polygons (or plane figures) are congruent, then their areas are congruent. Area Addition Postulate: The surface area of a three-dimensional figure is the sum of the areas of all of its non-overlapping parts

Part 1) [surface area of a cone without base]=π*r*l

where r=3 in

l= slant height ----> 6 in

Surface area of a cone without base = π*3*6------> 56.52 in²

Surface area of a cylinder =π*r²+2*π*r*h------> only one base

r=3 in

h=5 in

Surface area of a cylinder =π*r²+2*π*r*h

Surface area of a cylinder =π*3²+2*π*3*5-----> 122.46 in²

[surface area of the composite figure]=56.52+122.46-----> 178.98 in²

In conclusion the answer for  Part A) is 178.98 in² and for

Part B)

Surface area of the composite figure

=12*16+2*12*7+2*16*7+5*12+5*16+13*16----> 932 ft²

Therefore, the answer for Part B is  932 ft

Learn more about surface area of a cone on https://brainly.com/question/23877107

#SPJ1

A testable prediction of what will happen under a specific set of conditions is known as a hypothesis.

A hypothesis is a tentative explanation or prediction about a phenomenon or relationship between variables, based on limited evidence or prior knowledge. It is often formulated as a statement that can be tested through research or experimentation.

A hypothesis typically includes an independent variable (the variable that is being manipulated or studied) and a dependent variable (the variable that is being measured or observed). The hypothesis also includes a prediction about how the independent variable will affect the dependent variable.

Visit here to learn more about hypothesis brainly.com/question/30899146

#SPJ11

Answer:

B. x=3

Step-by-step explanation:

3x+4y=12

9x-4y=24

Add 9x and 3x

Subtract -4y from 4y which will cancel out

Add 12 and 24

12x=36

divide both sides by 12

x=3

6.1). the rate of depreciation, r, is approximately 10.77%.

6.2.1). Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2).  Ncominkosi borrowed approximately R 377,510.83 from the bank.

6.1) Let's assume the original price of the laptop is P. According to the reducing balance method, the value of the laptop after 4 years can be calculated as P * (1 - r/100)^4. We are given that this value is 31% of the original price, so we can write the equation as P * (1 - r/100)^4 = 0.31P.

Simplifying the equation, we get (1 - r/100)^4 = 0.31. Taking the fourth root on both sides, we have 1 - r/100 = ∛0.31.

Solving for r, we find r/100 = 1 - ∛0.31. Multiplying both sides by 100, we get r = 100 - 100∛0.31.

Therefore, the rate of depreciation, r, is approximately 10.77%.

6.2.1) To determine the monthly installment amount, we can use the formula for calculating the monthly payment on a loan with compound interest. The formula is as follows:

\(P = \frac{r(PV)}{1-(1+r)^{-n}}\)

Where:

P = Monthly payment

PV = Loan principal amount

r = Monthly interest rate

n = Total number of monthly payments

Let's calculate the monthly installment amount for Ncominkosi's loan:

Loan amount = Total amount paid to the bank - Interest

Loan amount = R 596,458.10 - R 0 (No interest is deducted from the total paid amount since it is the total amount paid)

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 9.5% / 12 = 0.0079167 (rounded to 7 decimal places)

Number of monthly payments = 6 years * 12 months/year = 72 months

Using the formula mentioned above:

\(P = \frac{0.0079167(Loan Amount}{1-(1+0.0079167)^{-72}}\)

Substituting the values:

\(P = \frac{0.0079167(596458.10}{1-(1+0.0079167)^{-72}}\)

Calculating the value:

P≈R10,505.29

Therefore, Ncominkosi's monthly installment amount was approximately R 10,505.29.

6.2.2) To determine the amount of money Ncominkosi borrowed from the bank, we can subtract the interest from the total amount he paid to the bank.

Total amount paid to the bank: R 596,458.10

Since the total amount paid includes both the loan principal and the interest, and we need to find the loan principal amount, we can subtract the interest from the total amount.

Since the interest rate is compounded monthly, we can use the compound interest formula to calculate the interest:

\(A=P(1+r/n)(n*t)\)

Where:

A = Total amount paid

P = Loan principal amount

r = Annual interest rate

n = Number of compounding periods per year

t = Number of years

We can rearrange the formula to solve for the loan principal:

\(P=\frac{A}{(1+r/n)(n*t)}\)

Substituting the values:

Loan principal (P) = \(\frac{596458.10}{(1+0.095/12)(12*6)}\)

Calculating the value:

Loan principal (P) ≈ R 377,510.83

Therefore, Ncominkosi borrowed approximately R 377,510.83 from the bank.

Learn more about interest rate here:

https://brainly.com/question/14599912

#SPJ11

Answer:

10.3

Step-by-step explanation:

Pythagorean Theorem:

\(a^{2} + b^{2} = c^{2} \\\)

a and b being the sides and c being the hypotenuse.

\(3.9^{2} + b^{2} = 11^{2}\)

15.21 + \(b^{2}\) = 121

\(b^{2}\) = 121 - 15.21

\(b^{2}\) = 105.79

b = \(\sqrt{105.79}\)

b = 10.3

Hope that helped!!! k

Two crucial tasks inherent in the initial stage of group therapy are orientation and establishing group norms.Ambiguity and lack of a structured approach in groups often lead to confusion, inefficiency, and potential challenges.

Orientation involves providing essential information to group members about the purpose, goals, and guidelines of the therapy group.

It helps individuals understand what to expect, builds trust, and creates a sense of safety and predictability within the group. Orientation may include discussing confidentiality, group rules, expectations, and addressing any questions or concerns.

Establishing group norms involves collaboratively developing shared guidelines and expectations that govern the behavior and interactions within the group. This process allows group members to contribute to the creation of a supportive and respectful group climate. Group norms help set boundaries, encourage open communication, and foster a sense of cohesion among members.

Without clear structure and guidance, group members may struggle to understand their roles, goals, or the process of the group therapy. Ambiguity can hinder progress, create frustration, and impede meaningful communication.

Lack of structure may also result in difficulty managing conflicts, decision-making, or time management within the group. It can lead to unequal participation, power struggles, and a lack of accountability.

To address these issues, it is important for group therapy to provide a clear framework, establish ground rules, and facilitate structured activities or interventions that promote clarity, engagement, and progress. A structured approach helps create a supportive environment, enhances group dynamics, and maximizes the therapeutic benefits of the group process.

For more such questions on tasks

https://brainly.com/question/30157542

#SPJ8

The wrong with following piece of mRNA, TACCAGGATCACTTTGCCA is that it contains T and not U. So, option(D) is right choice here.

Messenger RNA (mRNA) is present in DNA. DNA uses four bases in its code, adenine (A), guanine (G), cytosine (C) and thymine (T). RNA also uses four bases. However, instead of using "T" as DNA, it uses uracil (U). So, if your DNA sequence is 3' T C G T T C A G T 5', the mRNA sequence would be 5' A G C A A G U C A 3'. A strand of DNA is a template strand that has a nucleotide sequence on it that is read by RNA polymerases. Rna polymerase reads the template strand and encodes the m-RNA using the base-pairing rule. According to the rule, adenine pairs with thymine and guanosine with cytosine. So if the template DNA reads TAC GTT ACG, RNA polymerase will read it as AUG CAA UGC. Since no thymine is present in RNA, it will code for U instead of T.

To learn more about mRNA, refer:

https://brainly.com/question/12388408

#SPJ4

Answer:

The graph of the function is positive on (negative infinity, –7)

Step-by-step explanation:

Reason: f(-8)= 840,000a

840,000a is a positive number

https://brainly.com/question/2811695

https://brainly.com/question/16753961

Answer: 6 weeks

Step-by-step explanation: 42 days in weeks would be 6 weeks

Answer:

∠ 5 = 36°

Step-by-step explanation:

∠ 1 and ∠ 5 are corresponding angles and are congruent , so

∠ 5 = ∠ 1 = 36°

Answer: NOT D have a good day!

Step-by-step explanation:

Answer:

C. 9%

Step-by-step explanation:

That's it

Answer: 12.5

Step-by-step explanation:

Answer:

if a line is parallel they have the same slope

so the slope is 5

Hope This Helps!!!

Answer: Option: >

Step-by-step explanation: To compare the fractions 34/40 and 5/8, we can convert them to a common denominator. The least common multiple of 40 and 8 is 40, so we can convert 5/8 to 25/40. Now we can compare the fractions:

34/40 is equivalent to 17/20

17/20 is greater than 25/40

Therefore, the correct answer is >.

C. The standard deviation is 0.1204. The 10% condition is met because it is very likely there are more than 150 bass in the lake.

The standard deviation of the sampling distribution can be calculated as follows:

σ = √(p(1-p) / n)

Where:

p = Proportion of bass (0.32)

n = Sample size (15)

Therefore, σ = √(0.32(1-0.32) / 15) = 0.1204

The 10% condition is met because it is very likely there are more than 150 bass in the lake. This is because 0.32 x 500 (the total number of fish in the lake) = 160, which is greater than 150.

Learn more about standard deviation here

https://brainly.com/question/13905583

#SPJ4

The value of P(1.41 < Z < 2.85)  is 0.0771.

Hence, the correct answer is d.

A normally distributed random variable with mean μ= 0 and standard deviation σ= 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Because the Standard Normal Distribution is a probability distribution, the area under the curve between two points indicates the likelihood that variables will take on a range of values.

The whole area under the curve is one, or one hundred percent.

The mean and variance of a normal distribution are governed by two factors.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

The probability that a standard normal random variable Z is between 1.41 and 2.85 can be found using a standard normal table with a standard normal cumulative distribution function.

The answer is approximate:

P(1.41 < Z < 2.85)

= P(Z < 2.85) - P(Z < 1.41)

= 0.9927 - 0.9185

= 0.0742

For more questions on Standard Normal Distribution

https://brainly.com/question/4079902

#SPJ4

Answer:

57.47

Step-by-step explanation:

59.89+89.86=149.75

149.75+27.39=177.14

177.14+5.67=182.81

182.81-73.91=108.9

108.9-51.43=57.47

57.47

59.89+89.86=149.75

149.75+27.39=177.14

177.14+5.67=182.81

182.81-73.91=108.9

108.9-51.43=57.47

Step-by-step explanation:

Turn the standard form equation into a slope-intercept form equation using algebra.

Slope-intercept form: \(y=mx+b\)

Key:

Subtract each side by 3x:

\(8y=-3x+5\)

Divide each side by 8:

\(y=-\frac{3}{8} x+\frac{5}{8}\)

-3/8 is in the position of m, the slope.

The slope is -3/8.

Answer:

2x + x2 - 3 = 0

Step-by-step explanation:

im not 100% sure if this is right but hope it helps :-)

The required equivalent equation in factored form is (x + 3)(x - 1) = 0.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,

We can solve for x by factoring the quadratic equation x² + 2x - 3 = 0.

To factor, we need to find two numbers that multiply to -3 and add up to 2. Those two numbers are 3 and -1, so we can write:

x² + 2x - 3 = (x + 3)(x - 1) = 0

This equation is equivalent to the original equation x² + 2x - 3 = 0.

Thus, the equivalent equation in factored form is (x + 3)(x - 1) = 0.

Learn more about Factors here:

https://brainly.com/question/24182713

#SPJ2

We want to find the value of x, which is the hypotenuse of the triangle on the image.

We will see that the value of x is 5.77 units.

On the figure we can see a right triangle, we want to find the value of x, which is the hypotenuse of this triangle.

To do so, we can use the trigonometric relation:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Where θ is an internal angle of the triangle, and the adjacent cathetus is the cathetus that forms the angle.

Here we can use θ = 30°, and the adjacent cathetus is the one that has a measure of 5 units,  then the value of x is given by the equation:

cos(30°) = 5/x

Solving that for x we will get:

x = 5/cos(30°) = 5.77

The hypotenuse measures 5.77 units.

Learn more about right triangles:

https://brainly.com/question/2217700

#SPJ1

The geometric solid suggested by a typical American house is:

d. Prism

A typical American house often has a rectangular base and parallel, congruent faces.

This shape is best represented by a rectangular prism.

The geometric solid suggested by a typical American house is a prism, specifically a rectangular prism.

A prism is a three-dimensional solid that has two congruent and parallel bases that are connected by a set of parallelograms.

A rectangular prism has two rectangular bases and rectangular faces that are perpendicular to the bases.

Most American houses are rectangular in shape and have a flat roof, which suggests that they are in the form of a rectangular prism.

The walls of the house form the rectangular faces of the prism, and the roof forms the top face of the prism.

The rectangular shape of the house provides a practical and functional design that allows for efficient use of interior space.

It is also an aesthetically pleasing design that has become a standard for American homes.

d. Prism.

For similar question on  geometric solid.

https://brainly.com/question/18979572

#SPJ11

The minimal point does not have x = 0.

(a) Kuhn-Tucker conditions for the minimal value of fThe Kuhn-Tucker conditions are a set of necessary conditions for a point x* to be a minimum of a constrained optimization problem subject to inequality constraints. These conditions provide a way to find the optimal values of x1, x2, ..., xn that maximize or minimize a function f subject to a set of constraints. Let's first write down the Lagrangian: L(x, y, λ1, λ2, λ3) = f(x, y) - λ1(x+y-1) - λ2(xy-3) - λ3x - λ4y Where λ1, λ2, λ3, and λ4 are the Kuhn-Tucker multipliers associated with the constraints. Taking partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4 and setting them equal to 0, we get the following set of equations: 4x - 2y - λ1 - λ2y - λ3 = 0 2y - 2x - λ1 - λ2x - λ4 = 0 x + y - 1 ≤ 0 xy - 3 ≤ 0 λ1 ≥ 0 λ2 ≥ 0 λ3 ≥ 0 λ4 ≥ 0 λ1(x + y - 1) = 0 λ2(xy - 3) = 0 From the complementary slackness condition, λ1(x + y - 1) = 0 and λ2(xy - 3) = 0. This implies that either λ1 = 0 or x + y - 1 = 0, and either λ2 = 0 or xy - 3 = 0. If λ1 > 0 and λ2 > 0, then x + y - 1 = 0 and xy - 3 = 0. If λ1 > 0 and λ2 = 0, then x + y - 1 = 0. If λ1 = 0 and λ2 > 0, then xy - 3 = 0. We now consider each case separately. Case 1: λ1 > 0 and λ2 > 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have the following possibilities: x + y - 1 = 0, xy - 3 ≤ 0 (i.e., xy = 3), λ1 > 0, λ2 > 0 x + y - 1 ≤ 0, xy - 3 = 0 (i.e., x = 3/y), λ1 > 0, λ2 > 0 x + y - 1 = 0, xy - 3 = 0 (i.e., x = y = √3), λ1 > 0, λ2 > 0 We can exclude the second case because it violates the constraint x, y ≥ 0. The first and third cases satisfy all the Kuhn-Tucker conditions, and we can check that they correspond to local minima of f subject to the constraints. For the first case, we have x = y = √3/2 and f(x, y) = -1/2. For the third case, we have x = y = √3 and f(x, y) = -2. Case 2: λ1 > 0 and λ2 = 0From λ1(x + y - 1) = 0, we have x + y - 1 = 0 (because λ1 > 0). From the first Kuhn-Tucker condition, we have 4x - 2y - λ1 = λ1y. Since λ1 > 0, we can solve for y to get y = (4x - λ1)/(2 + λ1). Substituting this into the constraint x + y - 1 = 0, we get x + (4x - λ1)/(2 + λ1) - 1 = 0. Solving for x, we get x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4. We can check that this satisfies all the Kuhn-Tucker conditions for λ1 > 0, and we can also check that it corresponds to a local minimum of f subject to the constraints. For this value of x, we have y = (4x - λ1)/(2 + λ1), and we can compute f(x, y) = -3/4 + (5λ1^2 + 4λ1 + 1)/(2(2 + λ1)^2). Case 3: λ1 = 0 and λ2 > 0From λ2(xy - 3) = 0, we have xy - 3 = 0 (because λ2 > 0). Substituting this into the constraint x + y - 1 ≥ 0, we get x + (3/x) - 1 ≥ 0. This implies that x^2 + (3 - x) - x ≥ 0, or equivalently, x^2 - x + 3 ≥ 0. The discriminant of this quadratic is negative, so it has no real roots. Therefore, there are no feasible solutions in this case. Case 4: λ1 = 0 and λ2 = 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have x + y - 1 ≤ 0 and xy - 3 ≤ 0. This implies that x, y > 0, and we can use the first and second Kuhn-Tucker conditions to get 4x - 2y = 0 2y - 2x = 0 x + y - 1 = 0 xy - 3 = 0 Solving these equations, we get x = y = √3 and f(x, y) = -2. (b) Show that the minimal point does not have x=0.To show that the minimal point does not have x=0, we need to find the optimal value of x that minimizes f subject to the constraints and show that x > 0. From the Kuhn-Tucker conditions, we know that the optimal value of x satisfies one of the following conditions: x = y = √3/2 (λ1 > 0, λ2 > 0) x = √3 (λ1 > 0, λ2 > 0) x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4 (λ1 > 0, λ2 = 0) If x = y = √3/2, then x > 0. If x = √3, then x > 0. If x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4, then x > 0 because λ1 ≥ 0.

To know more about constraints, visit:

https://brainly.com/question/17156848

#SPJ11