16. A car leaves a parking lot and travels directly north for
6 miles. It then turns and travels 8 miles east. How many
miles is the car from the parking lot?

Answer:

21.58 miles

Step-by-step explanation:

First let's find how many miles Alex walked.

It said "Alex walked five times as many miles as Sue" so lets multiply 3.38 with 5: 3.38 x 5 = 16.9

So, Alex walked 16.9 miles. Now we can find Dan's.

It said "Dan walked 4.68 miles more than Alex" so lets add 4.68 to 16.9: 16.9 + 4.68 = 21.58

So Dan walked 21.58 miles

Step-by-step explanation:

Volume = base area × height

= width × length × height

= (1/5×4/5) × 10/3 cm × cm × cm

= ...... cm³

I hope this helps you

Volume Of Rectangular prism is:

width. length. height

1/5.4/5.10/3

8/15

nearest 0,54

Answer:

3.7142

Step-by-step explanation:

Answer:

3 remainder 15

Step-by-step explanation:

your welcome

Answer:

50400 seconds

Step-by-step explanation:

60 seconds are in a minute and 60 minutes are in an hour. 60x14 is 840x60 is 50400

in order to figure out if we can pay the car, we need to know how much it costs.

Step-by-step explanation:

There needs to be more explanation for people to help you, maybe tou can send a picture so someone can help you.

Answer:

11325

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[a+l]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $l$ is the last term.\\\phantom{ww}$\bullet$ $n$ is the number of terms.\\\end{minipage}}\)

A positive integer is a whole number that is greater than zero.

Therefore:

Substitute the values into the formula to find the sum of the first 150 positive integers:

\(\implies S_{150}=\dfrac{1}{2}(150)\left[1+150\right]\)

\(\implies S_{150}=75 \cdot 151\)

\(\implies S_{150}=11325\)

Answer:

Platonic solids

Step-by-step explanation:

To solve this we must be knowing each and every concept related to geometry. Therefore, icosahedron and the dodecahedron represents geometry of molecule.

Molecular geometry in chemistry depicts a molecule's three-dimensional form as well as the relative location of its atomic nuclei.

Understanding a molecule's molecular geometry is critical since the spatial connection between atoms dictates its reactivity, color, bioactivity, state of matter, polarization, as well as other features. A molecule's form influences its physical and chemical properties, including its colour, sensitivity, and bioactivities. Icosahedron and the dodecahedron represents geometry of molecule.

Therefore, icosahedron and the dodecahedron represents geometry of molecule.

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Answer:

the speed of sound is 12 miles per minute

Step-by-step explanation:

To know the speed we have to divide the distance by the time because the speed of sound is constant and we have to use a formula of uniform rectilinear motion

Uniform rectilinear motion: When an object travels at a constant speed with zero acceleration it is known as uniform rectilinear motion

The distance it gives us is 1 mile and the time it gives us is 1/12 minute

v = speed

v = 1mi / (1/12 m)

v = 12 mi/m

in the result as we can see we have a whole number (12)

the speed of sound is 12 miles per minute

Answer:

72 olives will be left

Step-by-step explanation:

1140÷89= 12 with 72 left over

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

Answer:c  

placement(0.4)&(2.5)

Step-by-step explanation:

The equation the line is, C) y= 1/2x + 4

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (0,4) and, (2,5)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>x-2y+8=0

=>y=x/2+4

Hence, the required equation is,  C) y= 1/2x + 4

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Answer:

y=3, 0; 9x-3y=18, 3; line through (5, 7) and (5, – 8), undefined; the line through ( – 4, – 1) and (-1,–7), -2;

Step-by-step explanation:

y=3 is a horizontal line so the slope is 0

9x-3y=18 can be written as 3y=9x-18 or y=3x-6 so the slope is 3

the line through (5,7) and (5,-8) is a vertical line since the x value didnt change between the two points so the slope is undefined

we have to find the slope of the line through ( – 4, – 1) and (-1,–7). to do this use the formula (y_2-y_1)/(x_2-x_1)=(-7-(-1))/(-1-(-4))=(-7+1)/(-1+4)=-6/3=-2 so the slope is -2

Answer:

Step-by-step explanation:

Given system:

Divide the first equation by 2 and rearrange:

We got the same equation with the second one. It means we have two of the same lines overlapping.

This gives us infinitely many solutions.

The answers are a) FR = 365 N b) u = 70.8° d and c) (MR)O = 2364 N m (counterclockwise)

When an object is subject to several forces, the resultant force is the force that alone produces the same acceleration as all those forces.

Given is a figure, we need to find equivalent resultant force and couple moment at point O

Equivalent Resultant Force And Couple Moment At O.

+→ (FR)x = ΣFx; (FR)x = 600 cos 60° - 455(12 / 13)

= -120 N = 120 N ←

+ ↑ (FR)y = ΣFy; (FR)y = 455(5/13) - 600 sin 60° = -344.62 N = 344.62 N ↓

As indicated in Fig (attached)

a) FR = √F(R)x²+F(R)y²

= √2120² + 344.62² = 364.91 N = 365 N

And

b) θ = tan-1{(FR)y / (FR)x}

= tan-1 {344.62/120}

= 70.80°

Also,

c) a+(MR)O = ΣMO; (MR)O = 455(12/13)(2) + 600 cos 60° (0.75) + 600 sin 60° (2.5)

= 2364.04 N m

= 2364 N m (counterclockwise)

Hence, The answers are a) FR = 365 N b) u = 70.8° d and c) (MR)O = 2364 N m (counterclockwise)

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The volume of the cylinder would be 2120.6\(units^3.\)

To find the volume of a cylinder, you need to use the formula:

Volume = π x \(radius^2\) x height

Where π (pi) is a mathematical constant approximately equal to 3.14159, radius is the distance from the center of the cylinder to its edge, and height is the distance from one end of the cylinder to the other.

To apply this formula, you need to know the values of the radius and height of the cylinder. Once you have these values, simply substitute them into the formula and solve for the volume.

For example, if the radius of a cylinder is 5 units and the height is 27 units, the volume of the cylinder would be:

Volume = π x \(radius^2\)x height

Volume = 3.14159 x\(5^2\)x 27

Volume = 2120.6 \(units^3\)

Therefore, the volume of the cylinder would be 2120.6\(units^3.\)

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The net price of the saws that Black & Decker Manufacturing sold to True Value Hardware on a chain discount of 8/3/1 is $3,357.21.

A chain discount refers to a type of discount offered to customers, which is sequentially applied to the list price to arrive at the net price.

Chain discounts involve a series of trade discounts applied in sequence.

List price = $3,800

Chain discount = 8/3/1

First net price = $3,496 ($3,800 x 1 - 8%)

Second net price = $3,391.12 ($3,496 x 1 - 3%)

Third net price = $3,357.21 ($3,391.12 x 1 - 1%)

Thus, the net price based on a chain discount of 8/3/1 is $3,357.21.

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Answer:

15:20

Step-by-step explanation:

18:24 can be written \(\frac{18}{24}\)  if I simplify this by dividing the top and bottom by 6, I get \(\frac{3}{4}\)

I am looking for what other ration will reduce to \(\frac{3}{4}\)

\(\frac{15}{20}\)  Divide the top and bottom by 5 and you will get \(\frac{3}{4}\)

Answer:

a

Step-by-step explanation:

if im right, the answer would be in the question :) its asking for the probability of a senior who plays a sport, and the third sentence is "the probability that a student is a senior and plays a sport is 0.08". sorry if im wrong!

Answer: I think that the answer is 3/4 miles

Step-by-step explanation:

The function cannot exist for the values of x = 8, -3.

The domain of a function is the complete set of possible values of the independent variable.

Given is the function -

(x + 4)/(x² - 5x - 24)

We have the function -

(x + 4)/(x² - 5x - 24)

Let -

x² - 5x - 24 = 0

x + 3x - 8x - 24 = 0

x(x + 3) - 8(x + 3) = 0

(x - 8)(x + 3) = 0

x - 8 = 0     or     x + 3 = 0

x = 8   or   x = - 3

So, [x] cannot be equal to 8 and -3.

Therefore, the restrictions on the domain of the function is of the form -

x ≠ 8, -3.

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Answer:

A

Step-by-step explanation:

\( \Large{\boxed{\sf | \sf z| = \sf \sqrt{40} = 2\sqrt{10} }} \)

\( \\ \)

We are given a complex number in algebraic form, and we would like to find its modulus, |z|.

\( \\ \\ \)

\( \\ \\ \)

Let's recall that a complex number in algebraic form is written as \( \sf z = a + ib \) , where a is its real part and b is its imaginary part.

\( \\ \)

The modulus of said complex number is calculated as follows:

\( \sf | \sf z| = \sqrt{a^2 + b^2} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

Let's identify our values:

\( \sf z = -2 - 6i \Longleftrightarrow z = \underbrace{\sf -2}_{\sf a} + (\underbrace{\sf -6}_{\sf b})i \)

\( \\ \)

Now, substitute these values into our formula:

\( \sf | \sf z | = \sqrt{(-2)^2 + (-6)^2} = \sqrt{4 + 36} = \boxed{\sf \sqrt{40}} \)

\( \\ \)

While this may be optional, the result can be simplified by using the following property:

\(\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Product \: rule \: of \: square \: roots\text{:}}}} \\ \\ \sf{ \diamond \: \sqrt{ab} = \sqrt{a} \times \sqrt{b} } \\ \end{array}}\\\end{gathered} \end{gathered}}\)

\( \\ \)

\( \sf \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = \boxed{\boxed{\sf 2\sqrt{10}}} \)

\( \\ \)

\( \hrulefill \)

\( \\ \)

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Answer:

d) 1/12

Step-by-step explanation:

The constant of proportionality between the side length and the perimeter of the equilateral triangle would be = 3.

The constant of proportionality is defined as the constant value that exists between two variables that are in a direct proportional relationship to each other.

For example, the constant of proportionality (k) between the side lengths and the perimeter of the equilateral triangle= y/X= 15/5= 3 or 24/8 = 3 or 27/9 = 3 or 30/10=3.

Therefore, the constant of proportionality which is the constant value existing between the two variables= 3.

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Answer:

1st one is b.  2nd one is A

Step-by-step explanation:

i did the quiz

The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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The guests in the birthday party ate 33 cookies.

We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.

Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.

6 1/4 dozen = 25/4 dozen

3 1/2 dozen = 14/4 dozen

Now we can subtract the number of cookies that were left from the number of cookies that were made:

25/4 - 14/4 = 11/4 dozen

To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.

There are 12 cookies in one dozen, so:

11/4 x 12 = 33

Therefore, the guests ate 33 cookies.

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