Sarah has a collection of nickels, dimes, and quarters worth $28.75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?
nickels:
dimes:
quarters:

Answer: -1 and -9

Step-by-step explanation:

(- 1) + (-9) = -10

(-1) * (-9) = +9

hope this helps!

Answer:

B) Ground speed: 639 mph; direction 161°

Step-by-step explanation:

165° = 75° South of East = S15°E, therefore;

The component of the speed of the airplane are;

650 × cos(75°) East or x-direction in vector form:\($650 \times \cos \left(75^{\circ}\right) \mathrm{i}$\)

650 × sin(75°) South or negative y-direction in vector form: \($-650 \times \sin \left(75^{\circ}\right) \mathrm{j}$\)

The speed of the airplane is \($650 \times \cos \left(75^{\circ}\right) \mathrm{i}-650 \times \sin \left(75^{\circ}\right) \mathrm{j}$\)  

The speed of the wind in vector form is 25i + 25·√3 j

The combined speed of the airplane and the wind is found as follows;

Combined: \($\left(650 \times \cos \left(75^{\circ}\right)+25\right)\left[\dot{i}+\left(25 \cdot \sqrt{3}-650 \times \sin \left(75^{\circ}\right)\right) \mathrm{j}\right.$\), which gives;

The resultant speed of the airplane, \($\left.R=\sqrt{(} 193.23^{2}+(-584.55)^{2}\right)=615.66$\)

The resultant speed of the airplane, \($\mathrm{R}=615.66 \mathrm{mph}$\)

The direction =\($\arctan ((-584.55) /(193.23))=-71.7^{\circ}$\)

The bearing \($=90^{\circ}+71.7^{\circ}=162^{\circ}$\)

Therefore, the closest option is option B, ground speed: 639 mph; direction 161°

Learn more about speed refer:

The intervals of each behavior of the function are given as follows:

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When calculating the volume of the tree, the first step is to assume that each horizontal cross-section of the tree is circular. The circumference of the tree at different heights above the ground is provided in the table below.Height (in)020406080100120Circumference (in)31282117128 2The formula for the circumference of a circle is given by:C = 2πrWhere C is the circumference and r is the radius of the circle.

We can rearrange the formula to find the radius of the circle:r = C/2πUsing this formula, we can find the radius of the tree at each height above the ground. The results are shown below:Height (in)020406080100120Circumference (in)31282117128 2Radius (in)4.97.910.713.516.319.0Using the radius of each horizontal cross-section of the tree, we can find the volume of the tree using the following formula:Volume of a cylinder = πr²hWhere r is the radius of the circular cross-section, h is the height of the cylinder (which is equal to the distance between the two adjacent heights in the table), and π is a constant equal to approximately 3.14159.The volume of the tree at each height above the ground can be calculated using this formula and the results are shown in the table below:Height (in)020406080100120Circumference (in)31282117128 2Radius (in)4.97.910.713.516.319.0Volume (in³)0.0085.016.523.431.339.5Finally, we can estimate the volume of the entire tree by adding up the volumes at each height. This gives:Volume of tree = 0.008 + 5.016 + 16.523 + 23.431 + 31.339 + 39.5= 116.8 in³Therefore, the estimated volume of the tree is 116.8 cubic inches.

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Answer: C.

Step-by-step explanation:Parallel lines never touch so they cant be intersecting.

Answer:

En este problema se trata de una función exponencial, donde la cantidad de microbios en el recipiente se duplica cada minuto.

Si x representa el número de minutos transcurridos y y la cantidad de microbios en el recipiente, entonces se puede expresar la función exponencial como:

y = a * (2)^x

Donde "a" es la cantidad inicial de microbios en el recipiente, en este caso a = 1.

Después de 30 minutos, la cantidad de microbios en el recipiente es:

2^30 = 1,073,741,824

Esto significa que si se coloca un solo microbio en el recipiente, se tardará 30 minutos en llenarlo.

Si se colocan 2 microbios en el recipiente, entonces la cantidad inicial de la función exponencial es a = 2, y se busca el valor de x tal que:

2 * (2)^x = 1,073,741,824

Dividiendo ambos lados por 2, se tiene:

(2)^x = 536,870,912

Tomando logaritmos base 2 en ambos lados, se tiene:

x = log2(536,870,912) = 29

Por lo tanto, si se colocan 2 microbios en el recipiente, se tardará 29 minutos en llenarlo.

Step-by-step explanation:

Dirk will make 70 pars or better.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.

Out of 90 holes, Dirk made par or better on 42 holes.

At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.

Then, Out of 150 holes, Dirk will make par or better on -

(42/90 x 150) holes

(42/90 x 150)

70

Therefore, Dirk will make 70 pars or better.

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The solution of the system of equations by using substitution method is x = 1 and y = 3

The substitution method is a method for solving systems of equations. It involves solving for one variable in one of the equations and then substituting that value into the other equation to find the value of the other variable.

We have the equations 4x + 4y = 16 and y = x+2

Substitute y = x +2 into  4x + 4y = 16:

4x + 4y = 16

4x + 4(x +2) = 16

Clear the parenthesis:

4x + 4x + 8 = 16

8x + 8 = 16

8x = 16-8

8x = 8

x = 8/8

x = 1

put x = 1 into  y = x+2:

y = x+2

y = 1 + 2

y = 3

Therefore, the solution of the system of equations is x = 1 and y = 3

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Answer:

d. Keep the base the same and then subtract the exponents.

Step-by-step explanation:

To simplify the expression, keep the base the same and then subtract the exponents, the correct option is D.

An expression is a mathematical statement which consists of variables, constants and mathematical operators.

The expression is

\(\rm \dfrac{3^{-6}}{3^{-4}}\)

According to the exponent rule

\(\rm m^a/m^b = m ^{a-b}\)

3⁻⁶⁻⁽⁻⁴⁾

3⁻²

1/9

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Answer:

Width = 4 in

Length = 8 in

Step-by-step explanation:

Given:

Area of a rectangle = 32 in²

Find:

Length and width

Computation:

Assume;

Width = x

Length = x + 4

Area of a rectangle = lb

32 = (x+4)(x)

x² + 4x = 32

x² + 4x - 32 = 0

x² + 8x - 4x - 32 = 0

x(x+8) - 4(x+8) = 0

(x-4)(x+8)

x = 4 , x = -8

So,

Width = x = 4 in

Length = x + 4 = 4 + 4 = 8 in

Answer:

D. 8

Step-by-step explanation:

set up a proportion

3/20 = x/50

to get from 20 to 50 you have to multiply by 2.5

so multiply the top number (3) by 2.5 to find x

this comes out to 7.5 which you then round up to 8

Answer:

D

Step-by-step explanation:

Answer:

14,621 lbs.

Step-by-step explanation:

It says at the beginning of the question that the school district collected 14,621 lbs. of recycling. The part where it says that the school district collected 3,943 lbs. of recycling more than last year is un-needed information.

After 50 years, she gets the amount $5000 in her bank account.

According to the statement

we have given that the Lina placed $1000 in a bank account with an annual compound interest rate of 8%.

And we have to find that the How long will it take until she has $5000 in the account.

So, For this purpose, we know that the

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.

The principal amount = 1000

And 8% of P.A. = 8/100*1000

8% of P.A. = 80.

So, According to this after 1 year the amount become

1080.

it means the equation become after t years.

Amount(t) = 1000 + 80t

And the amount is 5000 which is given then

5000 = 1000 + 80t

4000 = 80t

t = 50.

So, After 50 years, she gets the amount $5000 in her bank account.

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Answer:

bgyr5y53bygtr3

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

go backwords y+x = 2

y=1

x=1

Simply count the number of red marbles in each sample and divide by the total number of marbles in the sample (16). Then, take the average of those proportions to estimate the proportion of red marbles in the jar as a whole

Based on the information provided, the best conclusion we can make is an estimate of the proportion of red marbles in the jar. We can use the four random samples of 16 marbles to calculate the proportion of red marbles in each sample, and then take the average of those proportions to estimate the overall proportion of red marbles in the jar.

It's important to note that this estimate may not be perfectly accurate, since the samples are small and may not perfectly represent the entire jar. However, it's a useful way to get an idea of how many red marbles are in the jar without having to count all of them.

To calculate the proportion of red marbles in each sample

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The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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Answer:

x = 15

Step-by-step explanation:

Step 1: Write out equation

1/4x - 7/4 = 2

Step 2: Add 7/4 to both sides

1/4x = 15/4

Step 3: Divide both sides by 1/4

x = 15

Answer:

Hey, kevinlopez1225, your answer is Number one!

Astradele

Answer:

Either a tangent line or a line parallel to the axis of symmetry will do.

A standard high school parabola has a vertical or horizontal axis of symmetry, so a line of the form  x=k  or  y=k  is the easiest way

hope it helps you

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

To find the Z-score corresponding to a particular value in a normal distribution, we use the formula:

Z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Part 1 of 2: For the oldest senator of age 85:

Z = (x - μ) / σ = (85 - 56.5) / 12.5 ≈ 2.28

Rounding to two decimal places, the Z-score corresponding to the oldest senator of age 85 is 2.28.

Part 2 of 2: For the youngest senator of age 39:

Z = (x - μ) / σ = (39 - 56.5) / 12.5 ≈ -1.4

Rounding to two decimal places, the Z-score corresponding to the youngest senator of age 39 is -1.40.

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The number of ways that 4 books can be arranged on a shelf are= 24. That is option 2.

To calculate the number of ways 4 books can be arranged is the find the permutation.

That is ,

4! = 4×3×2×1

4! = 24

Therefore, the number of ways that 4 books can be arranged on a shelf are= 24

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Answer:

\(Area = 4x^2 - 14x + 10\)

Step-by-step explanation:

See Attachment for Complete Question

Given

\(Width = 5mi\) --- For the forest

\(Length = 2mi\) -- --- For the forest

Required

Determine the area of the habitat

Since the distance between the animal's habitat is x mi on both sides;

The length and width of the habitat is:

\(Width = 5 - (x + x)\)

\(Width = 5 - 2x\)

\(Height = 2 - (x +x)\)

\(Height = 2 - 2x\)

The area is then calculated as follows;

\(Area = Width * Height\)

\(Area = (5 - 2x) * (2 - 2x)\)

Expand

\(Area = 5(2 - 2x) -2x(2 - 2x)\)

Open Brackets

\(Area = 10 - 10x - 4x + 4x^2\)

\(Area = 10 - 14x + 4x^2\)

Reorder

\(Area = 4x^2 - 14x + 10\)

Hence; the required polynomial for the habitat area is:

\(Area = 4x^2 - 14x + 10\)

The sample standar deviation formula is given by

where

In our case, the mean is 79 and there are 12 elements (n=12). By substituting the values into the formula, we have

This is equal to,

then, the sample standar deviation is equal to 2.52

Answer:

Can you use the angle bisecto

Step-by-step explanation:

Answer:

yes , we can use the angle bisector theorem to solve for RU

Step-by-step explanation:

The distribution of the sample is approximately normal with a mean of 0. 15 and a standard deviation of 0. 03852.

One can utilize the Central Limit Theorem (CLT) for proportions to detail the dispersion of the sample proportion. Explained by the CLT, if the size of the sample is sufficiently significant enough, then the distribution with respect to the sample proportion will be mostly indistinguishable from a typical distribution.

np ≥ 10

n(1-p) ≥ 10

Given that both conditions are fulfilled, we can essentially posit that the said sample proportion distribution  is almost normal. In light of this knowledge, it would be pertinent to ascertain the mean (μ) and standard deviation (σ) of the sample proportion distribution.

Mean = p = 0.15

Standard deviation:

= √ ( ( 0.15 x ( 1 - 0. 15 ) ) / 86 )

= 0.03852

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The measure of the angles formed between parallel lines and their transversals indicates;

9. m∠3 = 97°, m∠5 = 97°, m∠10 = 97°, m∠7 = 83°

Parallel lines are lines that  maintain the are equidistant from each other and have the same slope on the coordinate plane.

The angles formed between the parallel lines and their transversal are;

1. Alternate exterior angles; (c) ∠9 and ∠16
2. Supplementary angles (e);  ∠15 & ∠11

3. Alternate interior angles (a); ∠10 & ∠15

4. Vertical angles (d); ∠12 & ∠15

5. Corresponding angles (b); ∠9 & ∠11

6. None (f); ∠9 & ∠15

7. Supplementary angles (e); ∠13 & ∠14

8. Alternate interior angles; ∠14 & ∠11

9. The alternate interior angles theorem indicates that we get;

(a + 28) = 2·a

Therefore; 2·a - a = 28

2·a - a = a, therefore;

a = 28

∠MNP = (a + 28)° = (28 + 28)° = 56°

10. The alternate interior angles theorem indicates that we get;

5·y° = (2·y + 78)°

Therefore;

5·y - 2·y = 78

3·y = 78

y = 78/3 = 26

The measure of the angle WXZ, m∠WXZ = 5·y°

Therefore; m∠WXZ = 5 × 26 = 130

m∠WXZ = 130°

9. ∠2 ≅ ∠3 (Vertical angles theorem)

m∠2 = m∠3

Therefore; m∠3 = m∠2 = 97°

m∠5 + m∠6 = 180° (Linear pair angles theorem)

m∠5 + 83° = 180°

m∠5 = 180° - 83° = 97°

∠10 and ∠2 are corresponding angles, therefore;

m∠10 = m∠2 = 97°

∠7 and ∠6 are vertical angles, therefore;

m∠7 = m∠6 = 83°

∠9 and ∠3 are same side interior angles, therefore;

m∠9 + m∠3 = 180°

m∠9 = 180° - m∠3

m∠9 = 180° - 97° = 83°
∠8 and ∠6 are linear pair angles, therefore; m∠8 = 180° - 83° = 97°

∠16 and ∠6 are same side exterior angles, therefore;

m∠16 + m∠6 = 180°

m∠16 = 180° - 83° = 97°

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Answer:

2=-12.2/(-6.1

-2=16/(-8)

-3= -2 2/5/4/5

3= 3 3/7 / 1 1/7

Step-by-step explanation:

Answer:

$18.28

Step-by-step explanation:

To complete this problem is a straightforward answer:

First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!

Answer: The answer is 0.1111111111111

Step-by-step explanation: