Which expression helps you find the length x of a side of a rectangle that has a diagonal of 17 units and a width of 8 units?

Answer:

B) simple random

The sampling method described in the scenario is "simple random sampling." Option B

With basic random sampling, every unit in the population has an equal chance of being chosen, and there is no set pattern or grouping involved in the selection process.

In this instance, the hammers are put into boxes, and a random box is chosen for quality assurance inspection. It meets the criteria for simple random sampling because each box has an equal probability of being picked.

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Hi There!

Solution + Answer:

2 gallons of milk: 3.29 * 2 = $6.58

4 gallons of ice-cream: 3.59 * 4 = $14.36

5 pounds of strawberries: 0.72 * 5 = $3.60

Total price before tax: 6.58 + 14.36 + 3.60 = $24.54

Tax: 24.54 * 0.0375 = $0.92025

Total price after tax: 24.54 + 0.92025 = $25.46025

Round: 25.46025 = $25.46

Hope This Helps :)

According to the question,

2 gallons of milk,

= [tex]3.29\times 2[/tex]

= [tex]6.58[/tex] ($)

4 gallons of ice-cream,

= [tex]3.59\times 4[/tex]

= [tex]14.36[/tex] ($)

5 pounds of strawberries,

= [tex]0.72\times 5[/tex]

= [tex]3.60[/tex] ($)

Now,

The total price before tax will be:

= [tex]6.58+14.36+3.60[/tex]

= [tex]24.54[/tex] ($)

The tax will be:

= [tex]24.54\times 0.0375[/tex]

= [tex]0.92025[/tex] ($)

hence

The total price after tax will be:

= [tex]24.54+0.92025[/tex]

= [tex]25.46025[/tex]

or,

= [tex]25.46[/tex] ($)

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Answer:

x = 21.5

Step-by-step explanation:

In the given trapezoid, the angles are consecutive interior angles.

i.e, consider the parallel sides of a trapezoid as parallel lines and the common side as the transversal. So, it is parallel lines cut by a transversal make a pair of consecutive interior angles which are supplementary.

i.e,

(5x + 13)° + (3x - 5)° =180°

5x + 13 + 3x - 5 = 180

8x + 8 = 180

8x = 180 - 8 =172

x= 172/8 = 21.5

So, 5x + 13 = 5(21.5) + 13 = 120.5°

3x - 5 = 3(21.5) -5 = 59.5°

Answer:

[tex]x^4-5x^2-36=0[/tex]

Step-by-step explanation:

We need to find equation that has exactly two real and two non real solutions

2 real  and 2 non real solution means 4 solutions

x^3 equation has maximum of 3 solutions

So we ignore equation that has largest exponent x^3

We ignore options B  and D

Let check option A

[tex]x^4 - 36x^2=0[/tex]

factor the left hand side

Factor out x^2

[tex]x^2(x^2 - 36)=0[/tex]

WE set each factor =0  and solve for x

x^2 =0  so x=0

x^2 - 36 =0 so x= +-6

So solutions are x=0, x=6 , x=-6. Only 3 real solutions we got

LEts check with option C

[tex]x^4-5x^2-36=0[/tex]

Factor left hand side

[tex] (x^2-9)(x^2+4)=0[/tex]

set each factor =0  and solve for x

x^2 -9 =0  so x= -3, + 3

x^2 + 4 =0 , x^2 = -4, so x= +2i, -2i

So we got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

Answer:

C. x^4 - 5x^2 - 36 = 0

[tex]Use\ (a^n)^m=a^{(n)(m)}\\\\((-3)^2)^3=(3^2)^3=3^{(2)(3)}=3^6\\\\((-3)^2)^3=(-3)^{(2)(3)}=(-3)^6[/tex]

Two answers: A. (-3)^6 and B. (3)^6.

Answer:

A and B

Step-by-step explanation:

using the law of exponents

• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex], hence

[tex]((-3)^2)^{3}[/tex] = [tex](-3)^{6}[/tex] → A

note that (- 3)² = 9 = 3², hence

[tex](-3)^2)^{3}[/tex] = (3²)³ = [tex](3)^{6}[/tex] → B

Answer:  The required ratio in simplest form is 7 : 5 : 8.

Step-by-step explanation:  Given that in a fruit punch drink, the 3 ingredients are apple juice orange juice and cranberry juice. [tex]\frac{1}{4}[/tex] of the drink is apple juice and [tex]\frac{2}{5}[/tex] is orange juice.

We are to find  the ratio of cranberry juice to apple juice to orange juice in its simplest form.

Let x, y and z be the fractions of the cranberry juice, apple juice and orange juice in the fruit punch drink.

Then, according to the given information, we have

[tex]y=\dfrac{1}{4},~~z=\dfrac{2}{5}.[/tex]

Now,

[tex]x+y+z=1\\\\\\\Rightarrow x+\dfrac{1}{4}+\dfrac{2}{5}=1\\\\\\\Rightarrow x=1-\dfrac{1}{4}-\dfrac{2}{5}\\\\\\\Rightarrow x=\dfrac{20-5-8}{20}\\\\\\\Rightarrow x=\dfrac{7}{20}.[/tex]

Therefore, the ratio of cranberry juice to apple juice to orange juice is given by

[tex]x:y:z\\\\\\=\dfrac{7}{20}:\dfrac{1}{4}:\dfrac{2}{5}\\\\\\=\dfrac{7}{20}:\dfrac{5}{20}:\dfrac{8}{20}\\\\=7:5:8.[/tex]

Thus, the required ratio in simplest form is 7 : 5 : 8.

Answer:

b = 2

Step-by-step explanation:

Using the midpoint formula

(2, 1) = [ [tex]\frac{1}{2}[/tex](- 4 + 8), [tex]\frac{1}{2}[/tex](b + 0) ]

considering the y-coordinate, then

[tex]\frac{1}{2}[/tex] b = 1 ( multiply both sides by 2 )

⇒ b = 2

Answer:

i got 185.4 so basically 184.

412 times 5% equals 20.6

times that by 9 for 9 months then that gives you the answer.

Answer:

1. The population increases exponentially, therefore the number of members in the team will increase by the equation modeled by :

[tex]\text{Number of members = }a_0(1+\frac{Rate}{100})^{Time}\\\\\implies\text{Number of members = }412(1+\frac{5}{100})^9\\\\\implioes\text{Number of members after 9 months = }639[/tex]

2. Total cost of the toy is calculated by multiplying the initial cost and the amount of tax charged on the toy.

Here, 15.85 represents the initial cost of the toy

Hence, 1 + x represents the amount of tax charged on the toy.

3. Rate per year is given to be 12.5%

Now, to find monthly rate, divide the yearly rate by 12

[tex]\text{Monthly Rate = }\frac{12.5}{12}=1.04\%[/tex]

4. Rate per year is given to be 20%

Now, to find monthly rate, divide the yearly rate by 12

[tex]\text{Monthly Rate = }\frac{20}{12}\approx 1.7\%[/tex]

5. The value of a truck after t years is represented by the function f(t)=22,200(0.92)t .

Here, 2200 is the initial value of the truck.

Answer:

(no horizontal asymptotes found)

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

on a football feild there are 4,320 inches and on a basketball court there are 2,865 centemeters

Answer:

[tex]g(x)= 24(3)^{x-2}+6[/tex]

Step-by-step explanation:

f(x)=8(3)^x−2 +2

The graph of f(x) is stretched vertically by a factor of 3 to form the graph of g(x)

When f(x) is stretched vertically then we multiply f(x) by 3 to get g(x)

g(x) = 3f(x)

[tex]g(x)= 3(8(3)^{x-2}+2)[/tex]

Now we distribute 3 inside the parenthesis

[tex]g(x)= 24(3)^{x-2}+6[/tex]

This is our required g(x)

Answer:

3

Step-by-step explanation:

D. 3

the scale factor of △TOE to △CUP is 3

A scale factor is a number that's used as multiplier when scaling the size of the object. It can be used to scale objects in one, two, and three dimensions and as fractions, ratios, percentages, and decimals. When a scale factor is applied, the size of the object is increased or decreased according to the desired scale.

What does the scale factor stand for?

To scale measurement to the smaller measurement, to instance, when making the blueprint, simply divide the real measurement by a scale factor. The scale factors are commonly expressed as 1:n or 1/n, where n means the factor. For example, a scale factor is 1:8 or the real measurement is 32, divide 32 ÷ 8 = 4 to convert.

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Answer:

A polynomial needs to have either addition, subtraction or multiplication in the equation.

The 2nd, 3rd and 4th answers have subtraction and addition, so those are polynomials.

The first answer is a fraction, which is a division problem, therefore is not a polynomial.

Answer:

D. [tex]\frac{3}{7}[/tex]

Step-by-step explanation:

We have been given that the probability of an event is 3/10.  

To find the odds of the same event we will use formula:

[tex]\text{Odds of an event}=\frac{\text{Probability of the event}}{\text{1-Probability of the event}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{1-\frac{3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{1*10}{10}-\frac{3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{10-3}{10}}[/tex]

[tex]\text{Odds of the event}=\frac{\frac{3}{10}}{\frac{7}{10}}[/tex]

Dividing a fraction with another fraction is same as multiplying the 1st fraction by the reciprocal of second fraction.

[tex]\text{Odds of the event}=\frac{3}{10}\times \frac{10}{7}[/tex]

[tex]\text{Odds of the event}=\frac{3}{7}[/tex]

Therefore, the odds of the same event is [tex]\frac{3}{7}[/tex] and option D is the correct choice.

Answer:

Correct choice is D (1,0) and (-2,-1)

Step-by-step explanation:

Triangle DBC has vertices B(-3,1), C(3,3) and D(-1,-3). By the triangle midline theorem, the midline joining the midpoints of two sides is parallel to the third side. Thus, you have to find the coordinates of the midpoints of the sides DB and DC of the triangle DBC.

Let point E be the midpoint of the side BD, then point E has coordinates [tex]\left(\dfrac{x_B+x_D}{2},\dfrac{y_B+y_D}{2}\right).[/tex] If B(-3,1) and D(-1,-3), then

[tex]E\left(\dfrac{-3+(-1)}{2},\dfrac{1+(-3)}{2}\right)\Rightarrow E(-2,-1).[/tex]

Let point F be the midpoint of the side DC, then point F has coordinates [tex]\left(\dfrac{x_C+x_D}{2},\dfrac{y_C+y_D}{2}\right).[/tex] If C(3,3) and D(-1,-3), then

[tex]F\left(\dfrac{3+(-1)}{2},\dfrac{3+(-3)}{2}\right)\Rightarrow F(1,0).[/tex]

Answer:

D: (1,0) and (-2,-1)

Step-by-step explanation:

if you where to plot all the other answers and take a straight edge (ruler) and drew a line through them you would find this is the only proper answer. and i used geogebra

Answer:

TRUE

Step-by-step explanation:

Given that line segment JK and LM are parallel. From picture we see that LK is transversal line.

We know that corresponding angles formed by transversal line are congruent.

Hence ∠JKL = ∠ MLK ...(i)

Now consider triangles JKL and MLK

JK = LM  {Given}

∠JKL = ∠ MLK { Using (i) }

KL = KL  {common sides}

Hence by SAS property of congruency of triangles, ΔJKL and ΔMLK are congurent.

Hence given statement is TRUE.

The statement that if JK and LM are congruent and parallel, then angles JKL and MLK are congruent is false. Congruency of angles depends on more than just the congruency and parallelism of two lines.

In the field of geometry, just because two lines are congruent and parallel, this does not necessarily mean that the angles formed by the intersection of the lines with a third line are congruent. The statement 'If JK and LM are congruent and parallel, then JKL and MLK are congruent' is false. Congruency of angles JKL and MLK depends on the relationship between the two other sides of the angles, not solely the lines JK and LM. Therefore, for the angles to be congruent, additional conditions besides the congruency and parallelism of JK and LM must be satisfied.

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Answer:

Step-by-step explanation:

1) [tex](a^3)^{-2}  = a^{-6}\\[/tex]

2) [tex](a^{-1} * a^{-2} )^{-3} = (a^{-1 + (-2)})^{-3} }=a^{-9}[/tex]

3) [tex]((a^{2})^{-2})^{2}=(a^{-4})^{2}=(a^{-8})[/tex]

4) [tex](a*a)^{2} =  (a^{2})^{2}=a^{4}[/tex]

Since there are 55 candies in the bag, and there are 20% of blue candies, it would look like this:

55 x 0.20 = 11

Now that we have 11, you multiply it by the damage coating, so

11 x 0.10 = 1.1

Approximately 1 blue chocolate had a damaged candy coating from Kathleen's bag since 20% of the 55 chocolates were blue (resulting in 11 blue chocolates), and 10% of these were damaged (resulting in approximately 1 chocolate).

Kathleen has a bag with a total of 55 candy-coated chocolates. Since 20% of these chocolates are blue, we first need to compute the number of blue chocolates. 20% of 55 translates to 0.20 × 55, which gives us 11 blue chocolates.

Of these blue chocolates, 10% had a damaged candy coating. To find out how many are damaged, we calculate 10% of 11, which is 0.10 × 11. This calculation results in 1.1, which we round to approximately 1 since we cannot have a fraction of a chocolate. Therefore, about 1 of the blue chocolates had a damaged coating.

The correct answer to the question is B. 1

The given polynomial only has one exponent, so the degree of the polynomial is the number of the exponent.

The degree is 3.

Answer:

22662

Step-by-step explanation:

14000(1+3.5/100)^14

The population after 14 years is 22662.

It is given that,

Explanation:

The exponential growth model is:

[tex]P=P_0\left(1+r\right)^t[/tex]

Where, [tex]P[/tex] is population after [tex]t[/tex] years, [tex]P_0[/tex] is the initial population and [tex]r[/tex] is the growth rate.

Substituting [tex]P_0=14000,r=0.035,t=14[/tex] in the above equation.

[tex]P=14000\left(1+0.035\right)^{14}[/tex]

[tex]P=14000\left(1.035\right)^{14}[/tex]

[tex]P=22661.7233[/tex]

[tex]P\approx 22662[/tex]

Thus, the population after 14 years is 22662.

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Answer:

The cost of the 40 rulers is £8 .

Step-by-step explanation:

As given in the question

15 rulers cost £3

i.e

15 rulers = £3

Cost of the one ruler.

[tex]1\ ruler = \frac{3}{15}[/tex]

1 ruler cost =  £ 0.2

Now find out the cost for 40 rulers .

Cost for 40 rulers = 40 × 0.2

                              = £8

Therefore the cost of the 40 rulers is £8 .

The question involves finding the unit price of a ruler and then finding the cost of 40 rulers. The price for one ruler is £0.2, and hence, the price for 40 rulers would be £8.

This is a mathematics question about unit price and proportionality. First, we need to find the price of one ruler by dividing the total cost by the number of rulers. So, £3 divided by 15 rulers is £0.2 per ruler. To find out how much 40 rulers costs, we multiply the price of one ruler by the quantity we desire which is 40 rulers. So, £0.2 multiplied by 40 equals to £8.

Therefore, the cost of 40 rulers would be £8.

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Final answer:

A disadvantage of using credit is that it can be tempting to overspend.

Explanation:

A disadvantage of using credit is that it can be tempting to overspend.

When using credit, individuals can easily spend more than they can afford, leading to financial difficulties and debt. It is important to use credit responsibly and only borrow what can be comfortably repaid.

Answer:

see attached diagram

Step-by-step explanation:

A dilation with a scale factor of [tex]\dfrac{1}{3}[/tex] centered at the origin has a rule:

[tex](x,y)\mapsto\left(\dfrac{x}{3},\dfrac{y}{3}\right).[/tex]

Then the image of the triangle ABC is triangle DEF(see attached diagram) with coordinates

Answer:

The product of the 5^56 x 5^22 x 5^-96= 1/5^18.

Step-by-step explanation:

The problem represents the Laws of Exponents.  When you multiply using exponents, you keep the base and add the exponents.  In this case, the base is 5 and our exponents are 56 + 22 + -96.  We we add these three integers, we get a total of -18, which gives us a base of 5 and exponent of -18 or 5^-18.  We don't typically have negative exponents, so our next rule to follow is when you have negative exponents, you flip the base, or make it a fraction, and make the exponent positive.  This gives us a final answer of 1/5^18.  

The value of the product is 5^56 × 5^22 × 5^(-96) is 1/(5^18)

         While multiplying two exponents with the same base then we should add the powers to get the result.

            Example: x^a + x^b = x^(a+b)

              5^56 × 5^22 × 5^-96 = 5^(56+22+(-96))

                                                    = 5^(-18)

       A non-zero real number with negative power is written as

    1/ (non-zero number with the positive power of the same number).

     Example:  x^(-2) = 1/(x^2)

  So, we can write 5^(-18) as 1/5^(18).

   Hence,

       5^56 × 5^22 × 5^-96 = 1/5^(18).

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Answer:

Step-by-step explanation:

Problem One (left panel)

Question A

Question B

The rate of change = (56 - 52)/(3 - 1) = 4/2 = 2  miles / hour^2 (you have a slight acceleration.

Question C

The way I have done it the domain is n from 1 to 6

Question 2 (Right Panel)

Question A

The equation for the table is f(x) = 3x - 3 which was derived simply by putting all three points into y = ax + b and solving.

Part B

Answer: D

Step-by-step explanation:

log₂ (x - 4) = 4

        x - 4 = 2⁴

        x - 4 = 16

        x      = 20

Hello from MrBillDoesMath!

Answer:

10.2

Discussion:

Let the length of the missing side = "s" Applying the Pythagorean theorem to this right triangle gives:

4^2 + s^2 = 11^2    =>

16 + s^2 = 121        =>             ( 4*4 = 16, 11*11 = 121)

16 - 16  + s^2 = 121 - 16 =>     (subtract 16 from both sides)

s^2 = 105 =>

x = sqrt (105)

which is approximately 10.2

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

Answer:

The slope is 2

The slope represents  how much it costs per visit the pool.

We have a positive slope when lines go  from bottom left to top right

The y intercept is where we cross the y axis which is 4.

x is the  number of visits to the pool

y is the  total cost in dollars

f(x) = 2x+4

Step-by-step explanation:

To find the slope we take two point ( 0,4) and (1,6)

and use the formula

m = (y2-y1)/(x2-x1)

  = (6-4)/(1-0)

 m= 2/1

The slope is 2

It represents  how much it costs per visit the pool.

We have a positive slope when lines go  from bottom left to top right

The y intercept is where we cross the y axis which is 4.

x is the  number of visits to the pool

y is the  total cost in dollars

f(x) = mx+b  where m is the slope and b is the y intercept

f(x) = 2x+4

Answer:

the answer is D edge 2021

Step-by-step explanation:

Hello from MrBillDoesMath!

Answer:

Choice C    (6)

Discussion:

Since it is an isosceles trapezoid the length of the two legs (i.e.  AB = 5y-10 and CD = 2y+8) are equal.  In other words,

5y - 10 = 2 y + 8

Subtract 2y from each side:

5y - 2y - 10 = 8

Now add 10 to each side

5y - 2y - 10 + 10 = 8 + 10 =>

3y + 0 = 18 =>

3y = 18 =>

y = 6

Regards,  

MrB

To find the value of y in the isosceles trapezoid ABCD, set up an equation using the given measurements for AB, BC, and CD. Solve the equation to find the value of y.

To find the value of y in the isosceles trapezoid ABCD, we can set up an equation using the given measurements for AB, BC, and CD. Since AB and CD are the legs of the trapezoid, they should be equal. Therefore, we can set AB equal to CD and solve for y:

5y - 10 = 2y + 8

Subtract 2y from both sides:

3y - 10 = 8

Add 10 to both sides:

3y = 18

Divide both sides by 3:

y = 6

Therefore, the value of y is 6. Answer choice C) 6 is correct.

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