Make a scatter plot of the data below.
Speed (mph)
Stopping distance (ft)
10
12.5
20
36.0
30
69.5
40
114.0
50
169.5
60
249.0
70
325.5

Use the quadratic regression feature of a graphing calculator to find a quadratic model. Round to the nearest hundredths place.
a.
y = 0.06 x squared + 0.31 x + 4
b.
y = negative 4.03 x squared + 0.32 x + 8.19
c.
y = 0.06 x squared minus 0.31 x minus 4
d.
y = 4.03 x squared minus 0.32 x minus 8.19

The numeric value of the exponential expression in this problem is given by the following option:

A. 2^12.

The exponential expression for this problem is defined as follows:

8^x/2^y.

8 is the third power of 2, hence:

8 = 2^3.

When a term is elevated to two of it's powers, the powers are multiplied, hence:

(2^3)^x = 2^(3x).

Meaning that the exponential expression is then written as follows:

8^x/2^y = 2^(3x)/2^y.

When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:

2^(3x)/2^y = 2^(3x - y).

As stated in the problem, the numeric value of the expression 3x - y is given as follows:

3x - y = 12.

Hence the entire expression is simplified as follows:

2^(3x - y) = 2^12.

Meaning that the correct option is given by option A.

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Answer:A. 2^12.

Step-by-step explanation:i did it and got it right

Answer:

x=18°

hope it helps.......

Answer:

x=15 degrees

hope it helps you

Answer is ADEF

Given that, two right tringle = R + ΔHEL , R +ΔPME

Hypotenuse equal , A set of corresponding right angles are equal.{HL};

LL=LE

So ∠E(M tringle HEL)∠LM (M tringle PME)

∠H=∠P 90°

∠L=∠E                        ⇒AAS

HE PM or LE =EM

∠E = ∠M

EL = ME                      ⇒ASA

∠L = ∠E

HF = PM

∠E = ∠M                       ⇒SAS

EL = ME

Hence choose A.D.E.F

{Determination of congruence of right tringle }

explanation of  Determination of congruence of right tringle

A plane figure bounded by three finite line segments to form a closed figure is known as a triangle. A right-angled triangle is a special case of the triangle. In a right-angled triangle, one of the interior angles measures 90°. Two right triangles are said to be congruent if they are of the same shape and size. In other words, two right triangles are said to be conger

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Answer: Q1 10 Q216 Q3 8

Step-by-step explanation:

BECAUSE I THIK THAT IS THE ANSWER

Answer:

b.× = 14 16

Step-by-step explanation:

#stay safe

hope it helps

Answer:

let marked price = x

on 10% discount, price= x-10%of x

=x-(10x/100)

=x-(x/10)

=9x/10

on further 10% discount, total discount = 10% of 9x/10

=10/100 * 9x/10

= 9x/100

= 9%of x

hence, the single discount given on marked price is 9%

Step-by-step explanation:

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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By rewriting the weights in decimal form and applying them to the correspondent percentages, we will see that the final grade is 92.8%.

The final grade will be given by:

G = a₁*x₁ + a₂*x₂ + ...

Where the values "a" are the weights, and the values "x" are the averages of Jeorge.

We know that the weights are:

Then we can write the weights in decimal form:

a₁ = 0.3

a₂ = 0.1

a₃ = 0.4

a₄ = 0.2

And the scores are:

So the final math grade will be:

G = 0.3*92 + 0.1*98 + 0.4*91 + 0.2*95 = 92.8%

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Answer:

the answer is 92.8%

Step-by-step explanation:

The translation form of each shape is given as follows:

a) X to Z: (x, y) -> (x + 5, y + 2).

b) Z to X: (x, y) -> (x - 5, y - 2).

The four translation rules are defined as follows:

For the composition of translations, we add the coordinates, hence:

Hence the rule from X to Z is given as follows:

(x, y) -> (x + 5, y + 2).

From Z to X, we have the inverse rule, hence:

(x, y) -> (x - 5, y - 2).

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Answer:

2.98

Step-by-step explanation:

First find 3% of 16.05 which is 0.48.

Then add 0.48 to 16.05 which is 16.53.

Then multiply .18 by 16.53 which gets you 2.98

Hope it helps

Answer:

To find the amount of the sales tax, we need to multiply the bill amount by the tax rate of 3% or 0.03:

Sales tax = 0.03 x $16.05 = $0.48

To find the total amount of the bill after the sales tax was added, we need to add the bill amount to the sales tax:

Total bill = $16.05 + $0.48 = $16.53

To find the amount of the tip, we need to calculate 18% of the total bill after the sales tax was added:

Tip = 0.18 x $16.53 = $2.98

Rounding to the nearest cent, Penelope left a tip of $2.98.

Step-by-step explanation:

Answer: 15cm

Step-by-step explanation: If the length of the model on the top is 6 cm, then the length of the model on the bottom must be 15 cm

Answer:

0.05

Step-by-step explana

There are 1820 different orders possible for selecting any 4 toppings out of a list of 16 toppings.

To calculate the number of different orders possible for selecting any 4 toppings out of a list of 16 toppings,

we can use the combination formula:

nCr = n! / r!(n-r)!

where n is the total number of items, r is the number of items to be selected, and ! represents the factorial operation.

Substituting the given values, we get:

16C4 = 16! / 4!(16-4)!

16C4 = (16 × 15 × 14 × 13) / (4 × 3 × 2 × 1)

16C4 = 1820

Therefore, there are 1820 different orders possible.

Option D. 1,820 is the correct option.

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Answer:

#C

Step-by-step explanation:

I am almost 95% positive it's C because if you look at the Isosceles shaped diagram.

The measure of angle A to the nearest degree is 30°

The triangle is right angled, so we would apply trigonometry ratio SOHCAHTOA

Angle = A

opposite = side opposite angle A = 8 feet

hypotenuse = longest side = 16 ft

adjacent = base = ?

Now, since we know the opposie and hypotenuse, we would use sin ratio (SOH):

Take inverse of sine:

The measure of angle A to the nearest degree is 30°

Interest earned on first investment in year 1 is $6,183.13

Interest earned on second  investment in year 1 is $6,167.68

Annual yield on first investment is 6.18%

Annual yield on second investment is 6.17%

What is daily compounding?

Daily compounding means that the interest on the investment is computed on daily basis, 365 days a year.

In a bid to determine the total interest earned in one year on the investment whose interest is compounded daily, we can make use of the future value below to determine its worth after 1 year, from which the initial investment can be deducted to determine the interest in year 1.

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

PV=initial investment=$100,000

r=rate of return=6%

n=365 days a year

t=1 year

FV=$100,000*(1+6%/365)^(365*1)

FV=$106,183.13

Interest=$106,183.13 -$100,000

interest=$6,183.13

Annual yield=effective annual interest

EAR=(1+6%/365)^(365)-1

EAR=6.18%

What is monthly compounding?

It means interest is compounded or computed every month, 12 months a year

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

PV=initial investment=$100,000

r=rate of return=6%

n=12 months a year

t=1 year

FV=$100,000*(1+6%/12)^(12*1)

FV=$ 106,167.78  

Interest=$ 106,167.78  -$100,000

interest=$6,167.68

Annual yield=effective annual interest

EAR=(1+6%/12)^(12)-1

EAR=6.17%

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Solution

0-12 years 13-19 years Total

Knee 14 9 23

Ankle 13 3 16

Quadricep 6 9 15

Shin 9 6 15

________________________________________

Total 42 27 69

Now we can calculate the chi square statistic given by:

The expected values for this case are:

0-12 years 13-19 years Total

Knee 14 9 23

Ankle 9.74 6.26 16

Quadricep 9.13 5.87 15

Shin 9.13 5.87 15

________________________________________

Total 42 27 69

Then the statistic is given by:

Solving we got:

The degrees of freedom are given by:

df = (2-1)*(4-1)= 3

And the p value is given by:

p = P(X > 5.53) = 0.137

Since the p value is higher than 0.05 we can conclude that we fail to reject the null hypothesis of independence

So then the correct answer is:

yes

The book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.

Current year book value

Land and buildings $707,150

Machinery, equipment, and internal-use software $671,793

Office furniture and equipment $106,073

Other fixed assets related to leases $855,652

Less Accumulated depreciation and amortization ($898,081)

Book value $1,442,587

Preceding year book value

Land and buildings $410,147

Machinery, equipment, and internal-use software  $530,363

Office furniture and equipment $91,930

Other fixed assets related to leases $643,507

Less Accumulated depreciation and amortization  ($749,579)

Book value $926,368

Therefore the book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.

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A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.

To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.

Let's calculate the sum of the digits in 1234:

1 + 2 + 3 + 4 = 10

The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.

To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.

The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.

1234 + 2 = 1236

we obtain the number 1236, which is divisible by 3.

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Answer:

9 in.

Step-by-step explanation:

Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.

As such, the ratio of the sides would give the same results.

Hence,

4/6 = 10/(6 + x)

cross multiplying

4(6 + x) = 60

Dividing both sides by 4

6 + x = 15

collecting like terms

x = 15 - 6

= 9

The Total Cost of Item is $1.06p.

The cost of item ( before tax) that Arthur wants to purchase = p dollars

Sales tax rate = 6%

6% as a decimal is :

6% = 0.06

Now we will use the decimal form of the tax to write an expression for just the cost of the sales tax.

cost of 6% sales tax for $p item = $ 0.06p

Now, we will write an expression for the total cost as a sum.

Total cost =  Cost of item + Sales tax on item

                = $p + $ 0.06p

                = $1.06p

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I don't know what your looking for, so be more specific, but I'm assuming your solving for x, so that's would be

x = -1

Answer:

We can simply solve all of these by simplifying them :)

1 . 13 - 4x = 1 - x =

x = 4

2 .  7a - 3 = 3 + 6a =

a = 6

3 . 5 + 2x = -2x + 6 =

x = 1/4

4 . -11 + x = 7x - 5 =

x = -1

The amount of the  interest revenue that  Princess will record in 2022 on this lease is:$413,553.82.

First step

Lease value payments after first payment:

Lease value payments=  $5,588,516- $716,000

Lease value payments= $4,872,516

Second step

Lease value payments after second payment:

Lease value payments=$4,872,516+ ($4,872,516×9%) - $716,000

Lease value payments=$4,872,516+$438,526.44-$716,000

Lease value payments=$4,595,042.44

Third step

2022 Interest revenue=$4,643,787.6×9%

2022 Interest revenue=$413,553.8196

2022 Interest revenue=$413,553.82 (Approximately)

Therefore the amount of the  interest revenue that  Princess will record in 2022 on this lease is:$413,553.82.

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Based on the given coordinate grid, and the increment for each grid line, the coordinates of point A is ( fraction negative 1 and 1 over 4, fraction 3 over 4) or (-1¹/₄, ³/₄).

The x-value of point A is said to be 5 grid lines to the left of y-axis. This means that the x value will be negative.

The increments are 1/4 so the x-value is:
= -1/4 x 5

= -1¹/₄

The y-value is given by the 3 grid lines above the x-axis which means that this value is positive:

= 1/4 x 3

= 3 /4

The coordinates of A are:

(-1¹/₄, ³/₄)

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Answer:

34 is the missing number

Step-by-step explanation:

hope this helps:))

Answer:

3(x+13)

Step-by-step explanation:

use the distributive property to multiply -3 by

3x -5

12x -9x + 15 + 24

then

combine 12x and -9x to get 3

add 15 + 24 to get 39

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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