! Please help me it’s due tonight !

The function G(x) = \(4x^2 - 28x + 49\) can be rewritten as G(x) = \(4(x - 3.5)^2 -\)196, where the vertex of the parabola is located at the point (3.5, -196).

To rewrite the quadratic function by completing the square, we follow these steps:

Step 1: Start with the given quadratic function:

\(G(x) = 4x^2 - 28x + 49\)

Step 2: Divide the coefficient of the x term by 2 and square the result:

(-28 / 2)^2 = (-14)^2 = 196

Step 3: Add and subtract the value obtained in Step 2 inside the parentheses:

G(x) = 4x^2 - 28x + 196 - 196 + 49

Step 4: Rearrange the terms and group the perfect square trinomial:

\(G(x) = (4x^2 - 28x + 196) - 196 + 49\)

Step 5: Factor the perfect square trinomial and simplify:

G(x) = 4(x^2 - 7x + 49) - 196 + 49

Step 6: Complete the square inside the parentheses:

G(x) = 4(x^2 - 7x + 49) - 147

Step 7: Rewrite the perfect square trinomial as a squared binomial:

\(G(x) = 4[(x - 3.5)^2 - 3.5^2] - 147\)

Step 8: Simplify the expression inside the square brackets:

G(x) = 4(x - 3.5)^2 - 49 - 147

Step 9: Combine like terms:

G(x) = 4(x - 3.5)^2 - 196

Therefore, the function G(x) = 4x^2 - 28x + 49 can be rewritten as G(x) = 4(x - 3.5)^2 - 196, where the vertex of the parabola is located at the point (3.5, -196). The completed square form allows us to easily identify key properties of the quadratic function, such as the vertex and the direction of the parabola.

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Yοu have $20. Yοu want tο buy 2 kg οf green apples. The cοst per kilο apple is $8. Hοw many shοpkeepers will return tο yοu?

Mathematical οperatοrs like additiοn, subtractiοn, multiplicatiοn, and divisiοn can be used tο cοmbine integers and numbers tο create a numerical expressiοn.

A mathematical expressiοn that οnly uses numbers. οr use οperatοr symbοls and numbers.

A set οf numbers and variables with an equal sign is referred tο as an equatiοn.

The given expressiοn is  20−8×2.

Suppοse yοu have $20.

The cοst per kilο apple is $8.

The cοst οf 2-kilο apples is (8×2).

The shοpkeepers will return tο yοu 20−8×2.

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Answer:

6

Step-by-step explanation:

The ratio of boys to girls is 2:5

let the number of boys be 2x -------(i)

and number of girls be 5x

and the total number of students is 21

therefore we know that..

2x+5x = 21

on solving for x,

7x=21

x= 21/7

x=3

now, by putting the value of x in (i),

2x = 2×3 = 6

therefore, there are 6 boys in the classroom.

you find the no. of girls similarly.

hope it helps !!...

PLEASE MARK BRAINLIEST ♡

The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

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Answer:

The answer is 0

Step-by-step explanation:

The 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

To construct an 80% confidence interval estimate of the average browsing time for the population of crownfashion.com visitors this week, we can use the following formula:

Confidence Interval = \(\bar{X}\) ± Z \(\times\)  (σ/√n)

Where:

\(\bar{X}\) is the sample mean (average browsing time) = 13.6 minutes,

Z is the Z-score corresponding to the desired confidence level (80% confidence level corresponds to a Z-score of 1.28),

σ is the population standard deviation = 5.2 minutes,

n is the sample size = 49.

Plugging in these values, we can calculate the confidence interval as follows:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/√49)

Simplifying the expression:

Confidence Interval = 13.6 ± 1.28 \(\times\) (5.2/7)

Confidence Interval = 13.6 ± 1.28 \(\times\) 0.742857

Confidence Interval = 13.6 ± 0.951428

The lower bound of the confidence interval is 13.6 - 0.951428 = 12.648572, and the upper bound is 13.6 + 0.951428 = 14.548572.

Therefore, the 80% confidence interval estimate for the average browsing time is approximately 12.648572 minutes to 14.548572 minutes.

The margin of error indicated by the interval is half of the width of the confidence interval, which is (14.548572 - 12.648572) / 2 = 0.95 minutes.

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The arc length subtended by a central angle of 3π/4 is 3π/2. The area of the sector cut out by a central angle of π/3 is (2π)/3

The given circle with radius r = 2. Let's calculate the arc length subtended by a central angle of 3π/4, and the area of the sector cut out by a central angle of π/3.

(a) To calculate the arc length subtended by a central angle of 3π/4: For the given central angle and radius of the circle, we can use the following formula to calculate the arc length: L = rθ,where L is the arc length, r is the radius, and θ is the central angle in radians. So, by substituting r = 2 and θ = 3π/4 in the above formula, we get: L = (2)(3π/4) = 3π/2.

The arc length subtended by a central angle of 3π/4 is 3π/2.

(b) To calculate the area of the sector cut out by a central angle of π/3: For the given central angle and radius of the circle, we can use the following formula to calculate the area of the sector: A = (1/2)r²θ,where A is the area of the sector, r is the radius, and θ is the central angle in radians. So, by substituting r = 2 and θ = π/3 in the above formula, we get: A = (1/2)(2)²(π/3) = (2π)/3.

The area of the sector cut out by a central angle of π/3 is (2π)/3.

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Answer:

Your answer is 8.

Answer:

Step-by-step explanation:

-24

The value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.

Given data

A soft- drink machine can be regulated so that it discharges an normal of? oz. per mug. The ounces of filler are typically distributed with a standard divagation of0.4 oz.

What value should be set at so that 98 of 6- oz. mugs won't overflow?

Let μ be the mean ounces of filler per mug.

μ can be attained by using the formula

μ = 6 oz. = 6/8 = 0.75 mugs.

Now, given σ = 0.4 oz.

The Z- score for a 6- oz mug can be calculated as follows

z = ( x- μ)/ σ

Then, x = 6 oz = 6/8 = 0.75 mugs.

μ = 0.75 mugs

σ = 0.4 oz.

z = (0.75-0.75)/0.4 = 0

For 98 of 6- oz mugs to not overflow, we need to find the value of μ similar that P( z Since the Normal distribution is symmetric about the mean, we have

P( 0< z We can look up the value of

z_score for P( 0< z

standard normal distribution table or use the inverse function on a calculator similar as Excel.

Using a table, we get the value ofz_score = 2.33.

Now, z = ( x- μ)/ σ2.33 = (0.75- μ)/0.4

μ = 0.75-0.4 ×2.33

μ = 0.75-0.932

μ = -0.182 oz.6 oz in terms of ounces = 6 *0.125 = 0.75 oz.

oz per mug in terms of ounces = ? *0.125 oz.

Using the values from above

μ = -0.1820.75 = 0.568 oz. ≈0.57 oz.

= 0.57/0.125 = 4.56 or 5

So, the value of the unknown should be set at 5 so that 98 of 6- oz. mugs won't overflow is A)5.18.

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The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

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Answer:

second card = 4  third card = 10 fourth card = 14

Step-by-step explanation:

18+2=20

20÷2=10.

10-2=8

8÷2=4

10+4=14

Starting with the original equation 2(8u + 2) = 3(2 - 7), we get the solution to the equation is u = -19/16.

Let's break down the solution to the equation step by step:

Original Equation: 2(8u + 2) = 3(2 - 7)

Step 1: Distribute the multiplication on both sides.

16u + 4 = 6 - 21

Step 2: Simplify the equation by combining like terms.

16u + 4 = -15

Step 3: Subtract 4 from both sides to isolate the variable term.

16u + 4 - 4 = -15 - 4

16u = -19

Step 4: Divide both sides by 16 to solve for u.

(16u)/16 = (-19)/16

u = -19/16

Therefore, the solution to the equation is u = -19/16.

It's important to note that there are some errors in the given solution. The correct solution is u = -19/16, not u = -2.5. Additionally, the steps described in the given solution do not align with the actual steps taken to solve the equation.

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The probability that a given class period runs between 50.5 and 51.25 minutes is 15%.

Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.

The probability of an event can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative.

\(P(50.5 < = X < = 51.25) =\frac{51.25-50.5}{54-49 } = \frac{0.75}{5} = 0.15\)

P = 0.15 means that the probability is 15%.

Thus, the probability that a given class period runs between 50.5 and 51.25 minutes is 15%.

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Answer:

A lot

Step-by-step explanation:

. Some are equal to others and some are not.

. Some are halves, whole.

. There are improper ones and mixed numbers.

............ Thats all i got so far im learning more about them now

Answer: B. statistic

Step-by-step explanation: A characteristic, usually a numerical value, which describes a sample, is called a statistic.

The dimensions that will admit the most light are, the breadth of the rectangular window is  \(2b = \frac{20+10\pi }{4+3\pi }\), the length of the window is \(2l = \frac{40}{4+3\pi }\) and the radius of the semicircular arc is  \(l= \frac{20}{4+3\pi }\).

In the given question,

Let the length and breadth of the rectangular part of the window be 2l and 2b respectively. So the radius of the semicircular arc will be l.

The total perimeter of the window will be 1 length of the rectangle, 2 breadths of the rectangle, and the length of the semicircular arc.

l+2b+πl = 10

(1+π)l+2b = 10

\(b = \frac{1}{2} [10-(1+\pi )l]\)

To admit maximum light through the window implies that the area of the window is maximized.

The area of the window will be:

\(A = (2l)(2b)+\frac{\pi l^{2} }{2}\)

\(= 4lb+\frac{\pi l^{2} }{2} \\= 2l[10-(1+\pi )l] +\frac{1}{2} \pi l^{2}\)

\(= 20l-2l^{2} -2\pi l^{2} +\frac{1}{2} \pi l^{2}\)

\(= 20l-2l^{2} - \frac{3}{2} \pi l^{2}\)

For the area to be maximum,

\(\frac{dA}{dl} =0\\20 -4l -3\pi l = 0\\l= \frac{20}{4+3\pi }\)

\(b = \frac{1}{2} [10-(1+\pi )\frac{20}{4+3\pi }\\b = \frac{10+5\pi }{4+3\pi }\)

Therefore, the breadth of the rectangular window is \(2b = \frac{20+10\pi }{4+3\pi }\), the length of the window is \(2l = \frac{40}{4+3\pi }\) and the radius of the semicircular arc is \(l= \frac{20}{4+3\pi }\).

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Answer:

The investor will earn $875 over the course of 3.5 years.

Step-by-step explanation:

Sounds like simple interest (not compound interest).

The appropriate formula is i = prt, which here is

i = $5000(0.05)(3.5) = $875

The investor will earn $875 over the course of 3.5 years.

when multiplying fractions , multiply across the numerator and denominator

you dont need common denominators

example

\(\frac{1}{2}*\frac{4}{5}=\frac{1*4}{2*5}\)

Hope this helps : -)

- Jeron

Answer:

Total displacement = 2.52 kilometers [south east]\(a^2 + b^2 = c^2\\1.13^2 + 2.25^2 = c^2\\c^2 = 6.3394\\c = 2.52\)

Step-by-step explanation:

By the Pythagorean Theorem:

This inequality can be used to find the maximum number of gallons of paint (x) that Amy could have bought without exceeding her budget of $192.

Let x be the number of gallons of paint Amy bought. The inequality that can be used to find x is:
24x + 12 ≤ 192
Simplifying the inequality:
24x ≤ 180
x ≤ 7.5
Therefore, Amy could have bought a maximum of 7.5 gallons of paint without spending more than $192.
Let x represent the number of gallons of paint Amy could have bought. The total cost of the paint brush and paint should be less than or equal to $192. We can represent this as an inequality:
12 + 24x ≤ 192
This inequality can be used to find the maximum number of gallons of paint (x) that Amy could have bought without exceeding her budget of $192.

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Answer:

$15 and 3600ft^2

Step-by-step explanation:

C) There are 16 white tiles used. The unit cost of a white tile=240/16=$15

E) The cafeteria area consists of 36 tiles of dimensions 10 ft x 10 ft, so the area of the floor is 3600ft^2

Answer:

$104,750

Step-by-step explanation:

we just add 101,00 and 3,750 together since they are both being financed

Hopes this helps please mark brainliest

Answer:

54×3

27×6

(10^2)+31×2

I hope this helps

The (f + g)(x) = 15x - 2 is represent the total round trip time.

According to the statement

we have given that the f(x) represents the time it takes a boat to travel upstream and g(x) represents the time it takes a boat to travel downstream.

And we have to find the total round trip time.

So, For this purpose, the given information is:

f(x) = 3x − 10 and g(x) = 12x + 8

And

The total round trip time is represented by the term (f + g)(x)

We know that the

(f + g)(x) = f(x) + g(x)

Substitute the given values in it

So, (f + g)(x) = f(x) + g(x)

(f + g)(x) = (3x - 10) + (12x + 8)

(f + g)(x) = 15x - 2

Hence, The (f + g)(x) = 15x - 2 is represent the total round trip time.

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Answer:

28

Step-by-step explanation:

write them all out in order and the number that is in the middle is the answer. Meadian=middle

If there is two middle numbers then add them and divide by 2 and thats your answer.  

Easiest way is to write them all out in order and just cross off one on the left then one on the right until you reach the middle

Answer:

28

Step-by-step explanation:

Median is the middle number of a sequence. This sequence, in order, is 20, 21, 27, 28, 38, 39, 49.

Answer:

The rectangle has a length of 15 cm and a width of 13 cm

Step-by-step explanation:

Let w represent the width of the rectangle, and let w + 2 represent the length of the rectangle.

Use the perimeter formula, P = 2l + 2w, and plug in the perimeter and w + 2:

P = 2l + 2w

56 = 2(w + 2) + 2w

Simplify and solve for w:

56 = 2w + 4 + 2w

56 = 4w + 4

52 = 4w

13 = w

Then, add 2 to this to find the length:

13 + 2

= 15

So, the rectangle has a length of 15 cm and a width of 13 cm.

The two non negative real numbers with a sum of 64 that have the largest possible​ product are; 32 and 32.

Let the two numbers be x and y.

Thus, if their sum is 64, then we have;

x + y = 64

y = 64 - x

Their product will be;

P = xy

Putting (64 - x) for y in the product equation we have;

P = (64 - x)x

P = 64x - x²

Since the product is maximum, let us find the derivative;

P'(x) = 64 - 2x

At P'(x) = 0, we have;

64 - 2x = 0

2x = 64

x = 64/2

x = 32

Thus; y = 64 - 32

y = 32

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PART A:

In the expression -7 - (-9), we can combine both negative signals and create a positive signal, so the expression will be -7 + 9.

That means in the number line we start at the number -7 and go 9 units to the right.

So Karissa is not correct, because she said a different starting point and a different direction to add the 9 units.

PART B:

Let's solve the equation:

We can see that the equation is not true, since the final statement is false. So Hugo is not correct, because the final values of each side of the equation didn't match.

Answer:

the last option

Step-by-step explanation:

50+25+x=180

x=105

50+105+x=180

x=25

Answer:

Step-by-step explanation:

9.

reflection over y axis.