Having a hard time with this one.

Answer:

[tex]g(x)=(x-8)^2-64[/tex]

Step-by-step explanation:

The given function is;

[tex]g(x)=-16x+x^2[/tex]

This is the same as;

[tex]g(x)=x^2-16x[/tex]

Add and subtract the square of half the coefficient of x.

[tex]g(x)=x^2-16x+(-8)^2-(-8)^2[/tex]

Observe that the first three terms is a perfect square trinomial.

[tex]g(x)=(x-8)^2-64[/tex]

The vertex form is [tex]g(x)=(x-8)^2-64[/tex]

The vertex (8,-64)

Answer:

Is [tex]10^{6}[/tex] times greater

Step-by-step explanation:

Find the quotient of the two numbers

[tex]\frac{8*10^{5}}{8*10^{-1}}= \frac{8*10^{5}*10^{1} }{8}}=10^{6}[/tex]

therefore

Is [tex]10^{6}[/tex] times greater

[tex]8 \times 10^{5}[/tex] is 1,000,000 times as great as  [tex]8 \times 10^{-1}[/tex]

To determine how many times greater 8 x 105 is compared to 8 x 10-1, we can use the properties of exponents.

First, let's write each term in standard form:

[tex]8 \times 10^{5}[/tex]  = 800,000

[tex]8 \times 10^{-1}[/tex] = 0.8

Next, find the ratio of these two numbers:

Ratio = ([tex]8 \times 10^{5}[/tex] ) ÷ ([tex]8 \times 10^{-1}[/tex])

Using the division of exponents rule:

[tex]10^{5}[/tex] / [tex]10^{-1}[/tex]

= [tex]10^{5-(-1)}[/tex]

= [tex]10^{6}[/tex]

So, the ratio is 106, which is: 1,000,000.

Therefore, [tex]8 \times 10^{5}[/tex] is 1,000,000 times as great as [tex]8 \times 10^{-1}[/tex]

Question:

How many times is [tex]8 \times 10^{5}[/tex] greater than [tex]8 \times 10^{-1}[/tex]?

Answer:

[tex]82,8m^2 = S.A[/tex]

Step-by-step explanation:

Area of a Rectangle: [tex]hb\:or\:wb = A[/tex]

Area of a Triangle: [tex]\frac{1}{2}hb; \frac{1}{2}bh, or\: \frac{hb}{2} = A[/tex]

Need to know

- Two small triangles

- Two big triangles

12m² = Rectangle

26,4m² EACH = Big Triangles

9m² EACH = Small Triangles

[tex]2[9] + 2[26,4] + 12 = 18 + 52,8 + 12 = 82,8[/tex]

So, the surface area of the rectangular pyramid is 82,8m².

* The answer is not 85,31 because this rectangular pyramid has two slant heights. If we ONLY had 9 as ONE SLANT HEIGHT, then the answer would have been 85,31, otherwise it is incorrect.

I am joyous to assist you anytime.

Their speeds are 45 mi/hr and 49 mi/hr

Answer:

The speed of the faster car is 68 miles/hr and speed of slower car is 40 miles/hr.

Step-by-step explanation:

Let the speed of the slower car be x

Now we are given that The speed of the faster car was 12 mph less than twice the speed of the other one.

So, Speed of faster car = 2x-12

Now we are given that In 6 hours the faster car got to San Diego, and by that time the slower one still was 168 miles away from the destination.

So, faster car completes the journey in 6 hours

Distance = [tex]Speed \times Time[/tex]

So, Distance traveled by faster car = [tex](2x-12)\times 6[/tex]

Distance traveled by slower car in 6 hours = [tex]Speed \times Time=6x[/tex]

Since we are given that when faster car completes the journey at that time slower car was 168 miles away from the destination .

A.T.Q

[tex](2x-12)\times 6-6x=168[/tex]

[tex]12x-72-6x=168[/tex]

[tex]6x-72=168[/tex]

[tex]6x=240[/tex]

[tex]x=\frac{240}{6}[/tex]

[tex]x=40[/tex]

So, speed of slower car is 40 miles/hr.

Speed of faster car = 2x-12 =2(40)-12=80-12=68 miles/hr.

Hence the speed of the faster car is 68 miles/hr and speed of slower car is 40 miles/hr.

Answer:

104

Step-by-step explanation:

Answer:

104

Step-by-step explanatio

Answer:

in the graph

Step-by-step explanation:

the function g(t)= sin t is a periodic function with amplitude a0= 1 and period T0=2[tex]\pi[/tex]

For our case, the 5 that multiplies g (t) increases the amplitude so that a = 5 * 1 = 5 and  the 3 that multiplies the variable increases the period being T = 2[tex]\pi[/tex]*1/3 = 2[tex]\pi[/tex]/3

Answer:

The answer is B.

Answer:

Step-by-step explanation:

If DMKT → FCBN, then

m∠D = m∠F, m∠M = m∠C, m∠K = m∠B and m∠T = m∠N

m∠K = 79° therefore m∠B = 79°.

Kyle) y= x Larry) 4y= x^2

The algebraic expression to represent the number of dogs Larry walked compared with Kyle is 2x +4 .

An algebraic expression can be defined as a mathematical statement which includes , variables , constant and mathematical operators.

It is given in the question that

Larry was able to walk 4 more than twice as many dogs as his friend Kyle  have.

Let number of dogs Kyle has = x

and Let Larry walks y miles.

According to the  given data

y = 2x + 4

Therefore , the algebraic expression to represent the number of dogs Larry walked compared with Kyle is 2x +4 .

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Incorrect

1000g=1kg

Therefore we would need 100 beads with a mass of 10g to estimate a total mass of 1kg or 1000g

So the estimate of 10beads at 10g each is only about 100g or 0.1kg or 1/10kg

Answer:

An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle. The interior or internal bisector of an angle is the line, half-line, or line segment that divides an angle of less than 180° into two equal angles.

Step-by-step explanation:

Answer:

The set of all points in a plane that are equidistant from the two sides of a given angle.

Step-by-step explanation:

Answer:

The answer to your question is: D it has 3

Hope this helps!!!!

    - Aaliyah

Step-by-step explanation:

A data set has outliers if the data lie out side the interval

The interquartile range of a data set is

For option A, the required interval is [5.5, 25.5]. Since all the data lie in this interval, therefore this data set has no outliers.

For option B, the required interval is [-5, 19]. Since all the data lie in this interval, therefore this data set has no outliers.

For option C, the required interval is [-2.5, 17.5]. Since all the data lie in this interval, therefore this data set has no outliers.

For option D,

3, 6, 7, 7, 8, 8, 9, 9, 9, 10

(3, 6), 7, (7, 8),( 8, 9), 9,( 9, 10)

3 lies out side the interval [4,12]. It means this data set has an outlier, i.e,.

Therefore correct option is D.

Answer:

D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

To find the correct one plug in 4 into x and if you get 3, that's the correct one.

A. y(4) = -4^2 + 4*4 + 4 = -16 + 16 + 4 = 4 X

B. y(4) = -4^2 + 8 * 4 - 13 = -16 + 32 - 13 = 3

Answer:

The correct answer is option B.

x = 10 and y = 46

Step-by-step explanation:

From the figure we can see a trapezium.

To find the value of x

We can write,

2x - 13 = x - 3

2x - x = 13 - 3

x = 10

To find the value of y

from the figure we can write,

3y - 4 + y = 180

4y = 180 + 4

4y = 184

y = 184/4 = 46

Therefore the correct answer is option B

x = 10 and y = 46

Answer:

Obtuse isosceles

Step-by-step explanation:

Two sides are the same length, so we know this is an isosceles triangle.

To determine if it's acute, right, or obtuse, we can compare it to a right triangle using Pythagorean Theorem:

c² = a² + b²

c² = 3² + 3²

c² = 18

c = √18

So if this were a right triangle, c would be √18, which is somewhere between 4 and 5.

Since the long side is greater than √18, we know this must be an obtuse triangle.

So this is an obtuse isosceles.

Answer:

[tex]\boxed{\text{14 in}^{2}}[/tex]

Step-by-step explanation:

The scale factor (C) is the ratio of corresponding parts of the two cylinders.  

The ratio of the areas is the square of the scale factor.  

[tex]\dfrac{A_{1}}{ A_{2}} = C^{2}\\ \\\dfrac{224}{ A_{2}} = \left (\dfrac{1}{\frac{1}{4}} \right )^{2}\\\\\dfrac{224}{ A_{2}}= 16\\A_{2} = \dfrac{224}{16\\\\}[/tex]

A₂ = 14 in²  

The surface area of the new cylinder will be [tex]\boxed{\textbf{14 in}^{2}}[/tex].  

Answer:

7 years

Step-by-step explanation:

A = P (1 + r)^(n)

where A is the final amount, P is the initial amount, r is the interest rate, and n is the number of times of compounding.

Compounded quarterly means compounded 4 times per year.  So the effective interest rate per compounding is:

r = 0.07 / 4

r = 0.0175

Given that A = 8000 and P = 5000:

8000 = 5000 (1 + 0.0175)^n

1.6 = 1.0175^n

log 1.6 = n log 1.0175

n = (log 1.6) / (log 1.0175)

n ≈ 27.1

Rounding up to the nearest whole number, it takes 28 compoundings.  Since there's 4 compoundings per year:

t = 28 / 4

t = 7

It takes 7 years.

I believe that the answer is A.

There are 26 letters in the alphabet, and 10 numbers to choose from: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

To find the answer, I used 26 • 10 • 10, which ends up being 2,600.

The reason I did this is because you can choose any 1 of the 26 letter, followed by any 1 of the 10 numbers, followed by any 1 of the 10 numbers again.

Answer:

0.953081279

Step-by-step explanation:

we have been given the following data set;

x; 4, 5, 8, 9, 13

y; 2, 9, 10, 12, 23

We are required to determine the r value of the data set.The r-value is the correlation coefficient that is used to measure the degree of association between two variables. It gives us information on the strength and direction of the association.

We can easily compute r in Ms. Excel;

We first enter the data into any two adjacent columns of an excel workbook.

Then we proceed to type;

=CORREL

into any blank cell. This is an in-built function that computes the correlation coefficient. Ms. Excel returns a value of  0.953081279

as the r value

Answer:

The value of r is 0.953.

Step-by-step explanation:

The correlation coefficient i.e. r is calculated by the formula,

[tex]r=\dfrac{n\sum{xy}-(\sum x)(\sum y)}{\sqrt{(n\sum x^2-(\sum x)^2)(n\sum y^2-(\sum y)^2)}}[/tex]

where n=5 is the sample size.

We create a table of required values,

         x        y          x²          y²           xy

        4        2         16           4             8  

        5        9         25         81            45

        8        10        64         100         80

        9        12         81         144         108

        13       23       169        529        299

∑      39      56        355       858        540

Substitute the values in the formula,

[tex]r=\dfrac{5\times 540-(39)\cdot (56)}{\sqrt{(5\times 355-(39)^2)(5\times 858-(56)^2)}}[/tex]

[tex]r=\dfrac{2700-2184}{\sqrt{(254)(1154)}}[/tex]

[tex]r=\dfrac{516}{\sqrt{293116}}[/tex]

[tex]r=\dfrac{516}{541.4018}[/tex]

[tex]r=0.9530[/tex]

Therefore, the value of r is 0.953.

Answer:

27

Step-by-step explanation:

135 divided by 5 (divide both sides by 5)

Answer:

y=27

Step-by-step explanation:

First you have to leave y by itself. So since the y is with a constant (5) then that means that you have to bring 5 to both sides and divide it by 135.

5y=135, y=135/5=27

Step-by-step explanation:

"Is" means equals.  "Less than" means subtracted from.

28 = k - 12

Add 12 to both sides to solve for k:

k = 40

The equation representing the statement '28 is 12 less than K' is 28 = K - 12. By adding 12 to both sides of the equation and simplifying, we find that K = 40.

To represent the statement '28 is 12 less than K' with an equation, you write: 28 = K - 12. To solve for K, you would add 12 to both sides of the equation.

Step 1: Add 12 to each side of the equation to isolate K.

28 + 12 = K - 12 + 12

Step 2: Simplify each side.

40 = K

Therefore, the value of K is 40.

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A) The probability of selecting a hockey card, keeping it out, and then selecting another hockey car is 1/9

B) The probability of selecting a hockey card, keeping it out, and then selecting a football card is 1/4

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

A box has 3 hockey and 6 football cards.

So, the probability of selecting a hockey card, keeping it out, and then selecting another hockey card

= 3/9 x 2/8

= 6/72

= 1/9

and,  the probability of selecting a hockey card, keeping it out, and then selecting a football card

= 3/9 x 6/8

= 18/72

=1/4

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Final answer:

The probability of selecting a hockey card, keeping it out, and then another hockey card is 1/12, whereas the probability of selecting a hockey card and then a football card is 1/4.

Explanation:

The probability of selecting a hockey card, keeping it out, and then selecting another hockey card from a box containing 3 hockey and 6 football cards is calculated as follows. First, the probability of picking one hockey card (Event A) would be 3 out of the total of 9 cards, or 3/9. Then, since the card isn't replaced, there are now 2 hockey cards left out of 8 total cards. So, the probability of picking another hockey card (Event B) after the first pick would be 2/8.

The probability of both events A and B occurring is found by multiplying the two probabilities together:

P(A and B) = P(A)  imes P(B) = (3/9)  imes (2/8) = 1/12.

For selecting a hockey card and then a football card, the initial probability of picking a hockey card remains 3/9. After a hockey card has been picked and kept out, there are still 6 football cards left out of 8 total cards. The probability of now picking a football card would be 6/8.

The probability of picking a hockey card first and then a football card is therefore:

P(Hockey and then Football) = P(Hockey)  imes P(Football) = (3/9)  imes (6/8) = 1/4.

Answer:

y=x+6

Step-by-step explanation:

If you need to find a standard linear equation from two points, you have to first find the slope, then find the y intercept.

To find the slope, you should do the change in y over the change in x.

that would be:

(4-9)/(-2-3)

(-5)/(-5)

the slope is 1

plug that in along with values of x and y taken from known point (3,9) to the standard equation of a linear relationship:

y=mx+b

m=1

y=9

x=3

b=?

9=(1)(3)+b

9=3+b

b=6

The equation of the line would be y=x+6

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Answer:

dfgedrgdrg32453245

Step-by-step explanation:4334534

rdgsdrg334523

45234453242

4

23

423

423

42

423

42

423

53465

Answer:

R= q+c over 5y

Step-by-step explanation: Good luck sweetie!!

Answer:

#3) 72; #4) 40,320; #5) 90.

Step-by-step explanation:

#3) The number of possible choices are found by multiplying the choices of flavors and the choices of toppings:

6*12=72.

#4) The ordering of 8 cards is a permutation, given by 8!=40,320.

#5) This is a permutation of 10 objects taken 2 at a time:

P(10,2) = 10!/(10-2)!=10!/8!=90.

P.S I had the same question once.

The number of choices which are possible for a single serving of frozen yogurt with one topping from a yogurt shop is 72.

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.

The number of possible ways to arrange is the n!. Here, n is the number of objects.

Let n is the total choices of selecting  6 different flavors of frozen yogurt and 12 different toppings. Thus,

n=6 x 12

n=72

These choice is equal to the possible choices for a single serving of frozen yogurt with one topping.

Thus, the number of choices which are possible for a single serving of frozen yogurt with one topping from a yogurt shop is 72.

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Answer:

It will take 4.858 years before the CD worth 8228.24

Step-by-step explanation:

* Lets revise the compound interest

- The formula for compound interest, including principal sum, is:

  A = P (1 + r/n)^(nt)

- Where:

• A = the future value of the investment/loan, including interest

• P = the principal investment amount (the initial deposit or loan amount)

• r = the annual interest rate (decimal)

• n = the number of times that interest is compounded per unit t

• t = the time the money is invested or borrowed for

- To find the time you can use the formula

  t = ln(A/P) / n[ln(1 + r/n)]

* Lets solve the problem

∵ P = $5600

∵ A = 8228.24

∵ r = 8/100 = 0.08

∵ n = 4

- Substitute all of these values in the equation of t

∴ t = ln(8228.24/5600) / 4[ln(1 + 0.08/4)] = 4.858 years

* It will take 4.858 years before the CD worth 8228.24

$1313.70 is the answer after a 51% markup

Final answer:

The selling price of a dining room set with a 51% markup on the selling price, and an actual cost of $870, is calculated to be $1775.51.

Explanation:

To determine the selling price of a dining room set with a 51% markup on the selling price based on the actual cost of $870, we first need to recognize the markup is on the selling price and not on the cost. Let the selling price be represented by the variable S. The markup can be represented by S multiplied by 51% (or 0.51), so we have:

Actual Cost + Markup = Selling Price

$870 + (0.51 × S) = S

To solve for S, we need to isolate it on one side of the equation:

$870 = S - (0.51 × S)

$870 = S(1 - 0.51)

$870 = S(0.49)

Now we divide both sides by 0.49 to solve for S:

S = $870 / 0.49

S = $1775.51

Therefore, the selling price of the dining room set at Macy's is $1775.51.

For this case we must find the value of the variable "x" of the following expression:

[tex]4(10^{5x})=200[/tex]

We divide both sides of the equation by 4:

[tex]10 ^ {5x} = \frac {200} {4}\\10 ^ {5x} = 50[/tex]

We find ln on both sides of the equation to remove the exponent variable:

[tex]ln (10^{5x}) = ln (50)\\5x * ln (10) = ln (50)[/tex]

We divide both sides of the equation between 5 * ln (10):[tex]x = \frac {ln (50)} {5 * ln (10)}[/tex]

In decimal form we have:

[tex]x = 0.33979400[/tex]

ANswer:

[tex]x = 0.33979400[/tex]

For this case we have by definition of properties of powers that:

To multiply powers of the same base, the same base is placed and the exponents are added. Also:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Now, applying the above properties, we can rewrite the given expression as:

[tex]3 ^ {-3-5} = 3 ^ {- 8} = \frac {1} {3 ^ 8}[/tex]

ANswer:

[tex]\frac {1} {3 ^ 8}[/tex]

Answer:

[tex]\frac{x^2}{400}+\frac{y^2}{625}=1[/tex]

Step-by-step explanation:

The equation of an ellipse that has its center at the origin is given by the formula:

[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]

The given ellipse is 50 units high.

This means that length of the major axis is 50.

[tex]2a=50[/tex]

[tex]2\implies a=25[/tex]

The ellipse is 40 units wide.

[tex]2b=40[/tex]

[tex]\implies b=20[/tex]

We substitute these values into the formula to get:

[tex]\frac{x^2}{20^2}+\frac{y^2}{25^2}=1[/tex]

[tex]\frac{x^2}{400}+\frac{y^2}{625}=1[/tex]

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For this case, we must simplify the following expression:

[tex]\frac {(x + 8)} {4} - \frac {(x + 5)} {4}[/tex]

They are fractions with the same denominator, they can be subtracted in the traditional way. We must bear in mind that the law of the signs of multiplication states:

[tex]- * + = -[/tex]

So:

[tex]\frac {(x + 8)} {4} - \frac {(x + 5)} {4} = \frac {x + 8-x-5} {4} = \frac {x-x + 8- 5} {4} = \frac {3} {4}[/tex]

ANswer:

Option C