You and a friend both would like a salad and a small drink. Between the two of you, you have $8.00. A salad costs $2.49 and a small drink is $.99. Can either of you have a second salad or drink? no, you cannot yes, 1 drink yes, 1 salad yes, 1 of each

Answer:

[tex]\sqrt{30}\times \sqrt{10}=10\sqrt{3\times}[/tex]

Step-by-step explanation:

We want to find the product:

[tex]\sqrt{30}\times \sqrt{10}[/tex].

We can rewrite the first term [tex]\sqrt{3\times 10}\times \sqrt{10}[/tex].

[tex]\sqrt{3}\times \sqrt{10}\times \sqrt{10}[/tex]

Recall that;

[tex]\sqrt{a}\times \sqrt{a}=a[/tex]

This implies that;

[tex]\sqrt{3} \times \sqrt{10}\times \sqrt{10}=10\sqrt{3}[/tex]

The required final product of the given radical is 2√3 × 5 = 10√3.

The product of √30 and √10 can be found by multiplying the values inside the square roots.

√30 = √(6 × 5) = √6 × √5

√10 = √(2 × 5) = √2 × √5

So, the product becomes (√6 × √5) × (√2 × √5).

Using the commutative property of multiplication, we can rearrange the terms:

(√6 × √2) × (√5 × √5).

Simplifying further:

√(6 × 2) × √(5 × 5) = √12 × √25.

√12 is equal to 2√3, and √25 is equal to 5.

Therefore, the final product is 2√3 × 5 = 10√3.

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Answer:

20.7 years

Step-by-step explanation:

Use the "compound amount, compounding continuously" formula:

A = Pe^(r · t)  

Here,

A = $2,500 = $1,450e^(0.06 · t)

Divide both sides by $1,450:  1.724 = e^(0.06 · t)

Taking the natural log of both sides, we obtain:

ln 1.724 = (0.06 · t).

Finally, we divide both sides by 0.06, obtaining:

ln 1.724

------------ = t = 20.7

   0.06

The Investment will reach a value of $2.500 in approximately 20.7 years.

Answer:

Years = natural log (total / principal) / rate

Years = natural log (2,500 / 1,450) / .06

Years = natural log (1.724137931) / .06

Years = 0.54472717542 / .06

Years = 9.078786257

Years = 9.1 (rounded)

Step-by-step explanation:

Answer:

y = 1/2x^2 - 2x + 1

Step-by-step explanation:

The equation of the parabola in vertex form is y = 1/2 (x - 2)^2 - 1. By finding the vertex at (2,-1) we plug in the point into the formula y = a(x-h)^2 + k. To convert it to standard form like the equations listed, multiply through the distributive property to clear the parenthesis.

y = 1/2 (x-2)(x-2) - 1

y = 1/2 (x^2 - 4x + 4) - 1

y = 1/2x^2 - 2x + 2 - 1

y = 1/2x^2 - 2x + 1

Answer:

A D F

Step-by-step explanation:

Area of rectangle: 80*45=3600

Area of semi-circle: ((60/2)^2)/2*pi=1413

Total area of grass=3600-1413=2187

Answer with explanation:

Coordinates of A, B, C, and D are  (-8, 1), (-2, 4), (-3, -1), and (-6, 5).

Plotting the points on two dimensional plane

1. You will find that, the four points, A , B , C and D do not lie on the dame Line.

[tex]\text{Slope of AB}=\frac{4-1}{-2+8}=\frac{3}{6}=\frac{1}{2}\\\\\text{Slope of CB}=\frac{4+1}{-2+3}=\frac{5}{1}=5\\\\\text{Slope of CD}=\frac{5+1}{-6+3}=\frac{6}{-3}=-2\\\\\text{Slope of AD}=\frac{5-1}{-6+8}=\frac{4}{2}=2\\\\\text{Slope of BD}=\frac{5-4}{-6+2}=\frac{1}{-4}=\frac{-1}{4}\\\\\text{Slope of AC}=\frac{-1-1}{-3+8}=\frac{-2}{5}[/tex]

→→None of the two lines are Parallel nor they are perpendicular,because neither product of slopes of two lines is equal to ,-1, nor the slope of two lines are equal.

It means they are Intersecting Lines .

Option D:⇒ And are intersecting lines but are not perpendicular.

Answer:

line AB and line CD are perpendicular lines

Step-by-step explanation:

Answer:

if this is geometry nation, the answer is c, 4671 sq cm

Step-by-step explanation:

Final answer:

The surface area of the triangular prism container needed to enclose the rolled document with a diameter of 10 cm and a length of 85 cm is 1695 cm².

Explanation:

To find the surface area of a triangular prism container, we need to consider the three rectangular faces and two triangular faces of the prism. The rectangular faces have the same dimensions as the rolled document, which is 10 cm in diameter and 85 cm in length. So, the area of each rectangular face is 10 cm x 85 cm = 850 cm².

For the triangular faces, we need to calculate the base and height. The base of the triangle is the same as the diameter of the rolled document, which is 10 cm. The height of the triangle can be found using the Pythagorean theorem, where the hypotenuse is the length of the rolled document (85 cm) and the base is half the diameter (5 cm). The height is then calculated as √(85 cm)² - (5 cm)² = 84.5 cm.

The area of each triangular face is 1/2 x base x height = 1/2 x 10 cm x 84.5 cm = 422.5 cm². Since there are two triangular faces, the total area of the triangular faces is 2 x 422.5 cm² = 845 cm².

Finally, to find the surface area of the triangular prism container, we add the areas of the rectangular faces and triangular faces: 850 cm² + 845 cm² = 1695 cm².

Answer:

y = |x| + 7

Step-by-step explanation:

Use desmos.com to see it in action

The answer is Y=|x| +7

The two sides are parallel on the top and bottom

It has two pairs of parallel opposite sides.  It has two pairs of equal opposite angles.  It has two pairs of equal and parallel opposite sides.  Its diagonals bisect each other.

Answer:

(-5)f(x)= -10x^2.

Step-by-step explanation:

If f(x) = 2x^2

We need to find (-5)f(x) = (-5) (2x^2) = -10(x^2) = -10x^2.

To solve this problem you just need to multiply (-5) by "2" which is the factor that multiplies the term "x^2"

Bill needs to sell more than 45 candy bars to reach his fundraising goal of $100, after factoring in his insurance cost.

Bill is trying to raise a minimum of $100 for soccer. If each candy bar is priced at $2 and he has an insurance cost of $10, we can start calculating how much product he needs to sell to reach his goal.

Firstly, we subtract the insurance cost from the total he needs to raise. This is because the insurance cost is a fixed cost that he needs to cover regardless of the number of candy bars sold. Hence, $100 - $10 = $90.

Now, the remaining $90 needs to be covered by selling candy bars. As each candy bar costs $2, we divide $90 by $2 to find out how many candy bars he needs to sell. Therefore, $90 ÷ $2 = 45 candy bars.

This shows that Bill needs to sell more than 45 candy bars to reach his goal, taking into account his initial fixed insurance cost.

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A straight line is 180°. So you can do:

(15x - 4) + (5x - 8) = 180  Simplify

20x - 12 = 180

20x = 192    Find the value of x

x = 9.6

m∠ABD = 15x - 4      Plug in x = 9.6

m∠ABD = 15(9.6) - 4 = 144 - 4 = 140°

m∠DBC = 5x - 8   Plug in 9.6

m∠DBC = 5(9.6) - 8 = 48 - 8 = 40°

Final answer:

To find the unknown angle, use the trig identity sin(90° - x) = cos x, ensure the calculator is in radian mode, and check if the answer is reasonable.

Explanation:

To find the unknown angle measure in the given problem, we need to use the trigonometric identity sin(90° - x) = cos x. This identity is useful when dealing with right-angled triangles and can help in finding missing angles when other angles or sides are known.

First, we need to identify the known values within the problem and the given equation. Assuming we are looking for value 'a', we then solve the equation by substituting the appropriate known values into it. After that, we need to ensure that our calculator is set to radian mode, as the instructions suggest that angle measurements should be in radians.

After obtaining the numerical solution, it is important to check if the answer is reasonable and makes sense within the context of the problem.

Explanation:

It is the same reason that the distance by road is not the same as the distance "as the crow flies." The two vectors are often not aligned so that the magnitudes both add to directly to the distance from the origin (or the tail of the first vector).

For example, suppose you walk two segments of 1 mile each. If you walk east in both cases, you end up 2 miles east of where you started. (The sum of the vectors is the sum of their magnitudes.)

If you walk east 1 mile and north 1 mile, you end up about 1.4 miles from where you started, not 2 miles. The second "vector" did not add directly to the distance from your starting point.

If you walk east 1 mile, then west 1 mile, you end up exactly where you started. The sum of the vectors is zero, but the sum of their magnitudes is still 2 miles.

The sum of magnitudes of vectors and magnitude of sum of two vectors are not equal due to the directionality property of vectors. The sum of vectors is calculated through the parallelogram rule, accounting both magnitude and direction. It uses the principles of geometry and trigonometry depending on the vectors' alignment.

The reason that the sum of the magnitudes of two vectors and the magnitude of the sum of two vectors is not equal lies in basic properties of vectors, specifically, the directionality of vectors. When you add two vectors, you are applying the parallelogram rule, which considers both the magnitude and direction of the vectors. Because the sum of vectors results in a resultant vector based on their geometrical arrangement, the magnitude of the resultant vector is not simply a sum of original magnitudes but a composition governed by rules of geometry and trigonometry.

To put it simply, if two vectors are aligned in the same or opposite direction, the magnitude of their sum or difference will be the sum or difference of their magnitudes. But if the vectors are at an angle (neither parallel nor anti-parallel), the magnitude of the sum will be less than the sum of the individual magnitudes, due to the Pythagorean theorem applied in the parallelogram rule.

For example, If you have vectors A and B and they happen to make a right angle (perpendicular), the magnitude of the sum (Resultant vector) will be √(A²+B²), not  A + B. The sum of the magnitudes would be aligned along one line while the magnitude of the sum would be along the hypotenuse of the right triangle formed by vectors, hence the difference.

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Divide total parking spaces by number of levels.

87 / 3 = 29

There are 29 parking spaces on each level.

To find out how many parking spaces are on each level of a garage with 87 total spaces and 3 levels, divide the total number of parking spaces (87) by the number of levels (3) to get 29 parking spaces per level.

If a parking garage has a total of 87 parking spaces and there are 3 levels in the garage with an equal number of parking spaces on each level, to find out how many parking spaces are on each level, we need to divide the total number of parking spaces by the number of levels.

Here is the step-by-step calculation:

Therefore, there are 29 parking spaces on each level in the garage.

A=259.8 cm^2 is the correct answer

A) 3/20 would be the answer

Answer:

Option b is correct (8,13).

Step-by-step explanation:

7x - 4y = 4

10x - 6y =2

it can be represented in matrix form as[tex]\left[\begin{array}{cc}7&-4\\10&-6\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}4\\2\end{array}\right][/tex]

A= [tex]\left[\begin{array}{cc}7&-4\\10&-6\end{array}\right] [/tex]

X= [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex]

B= [tex] \left[\begin{array}{c}4\\2\end{array}\right][/tex]

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (7*-6) - (-4*10)

                                    = (-42)-(-40)

                                    = (-42) + 40 = -2

so, |A| = -2

Adj A=  [tex]\left[\begin{array}{cc}-6&4\\-10&7\end{array}\right] [/tex]

A⁻¹ =  [tex]\left[\begin{array}{cc}-6&4\\-10&7\end{array}\right] [/tex]/ -2

A⁻¹ =  [tex]\left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right] [/tex]

X= A⁻¹ B

X=  [tex]\left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right] *\left[\begin{array}{c}4\\2\end{array}\right][/tex]

X= [tex]\left[\begin{array}{c}(3*4) + (-2*2)\\(5*4) + (-7/2*2)\end{array}\right][/tex]

X= [tex]\left[\begin{array}{c}12-4\\20-7\end{array}\right][/tex]

X= [tex]\left[\begin{array}{c}8\\13\end{array}\right][/tex]

x= 8, y= 13

solution set= (8,13).

Option b is correct.

You must know that % is a number out of 100.

Therefore given 91/100 trusted DNA surveying, we know as a percentage this is 91% from the equation below:

(91/100)*100=91

We can conclude that 1%=1 person.

Although the difference is only 1 (91-90=1), the actual proportion of people who trust DNA testing is larger than the 90% by 1%.

Testing the hypothesis, it is found that since the p-value of the test is of 0.37 > 0.01, there is not enough evidence to conclude that the actual proportion of people who trust DNA testing larger than 90%.

At the null hypothesis, we test if the proportion is of 90%, that is:

[tex]H_0: p = 0.9[/tex]

At the alternative hypothesis, it is tested if the proportion is larger than 90%, that is:

[tex]H_1: p > 0.9[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are: [tex]n = 100, \overline{p} = \frac{91}{100} = 0.91, p = 0.9[/tex]

Hence, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.91 - 0.9}{\sqrt{\frac{0.9(0.1)}{100}}}[/tex]

[tex]z = 0.33[/tex]

The p-value of the test is the probability of finding a sample proportion above 0.91, which is 1 subtracted by the p-value of z = 0.33.

Looking at the z-table, z = 0.33 has a p-value of 0.63.

1 - 0.63 = 0.37.

Since the p-value of the test is of 0.37 > 0.01, there is not enough evidence to conclude that the actual proportion of people who trust DNA testing larger than 90%.

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Answer:

C

Step-by-step explanation:

First we find the z-score.

z = (x - μ) / σ

z = (520 - 500) / 60

z = 0.33

Using a calculator or z-score table:

P(z < 0.33) = 0.6293

The probability is approximately 63%.  Answer C

Answer:

63%

Step-by-step explanation:

63%

Answer:

5 5/7 units

Step-by-step explanation:

Length = x

Width = 3/4 x

Perimeter = 20 units

2( x + 3/4 x) = 20

x + 3/4 x = 10

7/4 x = 10

x = 40/7 = 5 5/7 units

The width of the rectangle with a perimeter of 20 units and a width that is 3/4 of its length is 6 units.

The student's question relates to the perimeter of a rectangle that's been given as 20 units and the width as 3/4 of the length. To find the width, we first need to set up an equation based on the formulas for a rectangle's perimeter and the information provided.

The perimeter of a rectangle is given by the formula 2(length + width), or more simply 2L + 2W. Because the question states that the width (W) is 3/4 times the length (L), or W = 0.75L, this can be substituted into our initial formula. Our formula therefore becomes 2L + 2(0.75L) = 20, which simplifies to 2.5L = 20. If you divide both sides of this equation by 2.5, you find L = 8.

Having found the length, you can now find the width by using the relationship given in the question: W = 0.75L. Substituting 8 for L, we find W = 6 units.

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Answer:

= 14

Step-by-step explanation:

Given a right angled triangle with hypotenuse length c =18.6 and ∠B = 43°.

We can use the trigonometric forms of a right angled triangle,

That is;

Cos 43 = Adjacent/Hypotenuse

That is;

Cos 43 = BC/AC = a/c

Therefore;

Cos 43 = a/18.6

a = 18.6 × cos 43

   = 13.603

   = 14

Therefore, BC or a is 14 (to the nearest whole number)

Answer:

He should buy the 4 x 10 rug because it has the larger area.

Step-by-step explanation:

To find the area of a rectangle or square, you multiply length by width (A=l x w). 5x7=35 and 4x10=40, so 4 x 10 has the bigger area.

Answer:

75 miles

Step-by-step explanation:

Let x mph be the cyclist A rate, then x+3 mph is the cyclist B rate.

1. In 1 hour they both traveled x+x+3=2x+3 miles. In 5 hours they traveled

[tex]5(2x+3)=10x+15\ miles.[/tex]

2. Cyclist A spent [tex]\frac{31.8}{x}[/tex] hours to travel 31.8 miles. If the cyclist from B had started moving 30 minutes (1/2 hour) later than the cyclist A, then he spent [tex]\frac{31.8}{x}-\frac{1}{2}[/tex] hours to travel the rest of the distance. In total they both traveled the whole distance 10x+15 miles, thus

[tex]31.8+\left(\dfrac{31.8}{x}-\dfrac{1}{2}\right)\cdot (x+3)=10x+15[/tex]

Solve this equation. Multiply it by 2x:

[tex]63.6x+(63.6-x)(x+3)=2x(10x+15)\\ \\63.6x+63.6x+190.8-x^2-3x=20x^2+30x\\ \\-x^2+124.2x+190.8-20x^2-30x=0\\ \\-21x^2+94.2x+190.8=0\\ \\210x^2-942x-1908=0\\ \\35x^2-157x-318=0\\ \\D=(-157)^2-4\cdot 35\cdot (-318)=69169\\ \\x_{1,2}=\dfrac{-(-157)\pm\sqrt{69169}}{2\cdot 35}=\dfrac{157\pm263}{70}=-\dfrac{106}{70},\ 6[/tex]

The rate cannot be negative, thus, x=6 mph.

Hence, the distance between cities A and B is

[tex]10\cdot 6+15=60+15=75\ miles.[/tex]

Answer:

The simplified expression is d = (5√2) L

Step-by-step explanation:

* Lets explain the problem

- A walking path is shaped like a rectangle

- The width of the rectangle is 7 times its length L

∵ The length of the rectangle is L

∵ The width is 7 times the length

∴ The width of the rectangle is 7L

- The distance between the opposite corners represented by the

  diagonal of the rectangle

- The length , the width and the diagonal formed a right triangle

- Its hypotenuse is the diagonal of the rectangle

- Its two legs are the length and the width of the rectangle

* Now we have right triangle use the Pythagoras Theorem to find

 the hypotenuse

∵ The length , the width and the diagonal of the rectangle are the

   sides of a right triangle

∵ The diagonal is the hypotenuse (h) of the triangle

∵ hypotenuse = √[L² + W²]

∵ The length = L and the width = 7L

∴ h = √[(L)² + (7L)²] = √[L² + 49L²] = √[50L²]

∵ √50 = 5√2

∵ √(L²) = L

∴ h = 5√2 L

∵ The diagonal of the rectangle is the distance between the

   opposite corners

∴ The distance between the opposite corners is (5√2) L

* The simplified expression is d = (5√2) L, where L is the length

  of the rectangle

To find the distance between opposite corners of the walking path, which is shaped like a rectangle, we need to determine the length of the diagonal.
Given that the width is 7 times the length (l), we can represent the width of the rectangle as \(7l\).
Let's denote the length of the rectangle by \(l\) and the width by \(w\). According to the information, \(w = 7l\).
Now, to find the length of the diagonal, we use the Pythagorean theorem, which states that for a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
For our rectangle, the diagonal forms the hypotenuse, and the length and width are the other two sides of the right-angled triangle. Thus, if we denote the diagonal by \(d\), the Pythagorean theorem gives us:
\(d^2 = l^2 + w^2\)
Substituting the expression for the width:
\(d^2 = l^2 + (7l)^2\)
\(d^2 = l^2 + 49l^2\)
\(d^2 = 50l^2\)
To find \(d\), we take the square root of both sides:
\(d = \sqrt{50l^2}\)
Since \(50\) can be broken down into \(25 \times 2\) and \(25\) is a perfect square, we can simplify the square root as follows:
\(d = \sqrt{25 \times 2 \times l^2}\)
\(d = \sqrt{25} \times \sqrt{2} \times \sqrt{l^2}\)
\(d = 5l \times \sqrt{2}\)
So the simplified expression for the distance between opposite corners of the walking path is:
\(d = 5l\sqrt{2}\)

Answer:

16w^4

Step-by-step explanation:

(2w)^4 is just 2w mulitplied by itself 4 times. we can do this step by step and multiply the 2 by itself 4 times first:

2 x 2 x 2 x 2 or 2^4 = 16

next we can multiply w by itself 4 times:

w x w x w x w or w^4 = w^4

our answer would be 16w^4

you can also multiply it without breaking it down like this:

2w x 2w x 2w x 2w = 16w^4

The simplification of an expression [tex](2w)^{4}[/tex] without parentheses is [tex]16w^{4}[/tex].

Given:

Find:

Solution:

The given expression is [tex](2w)^{4}[/tex].

This means that 2w has to be multiplied itself by 4.

So, 2*2*2*2 = 16

and w*w*w*w = [tex]w^{4}[/tex]

So, the expression [tex](2w)^{4}[/tex] = [tex]16w^{4}[/tex]

Therefore, The simplification of the expression [tex](2w)^{4}[/tex] is [tex]16w^{4}[/tex]

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11.99 + d= 14.98

To get this answer you must come up with a simple equation at first. The total cost of the meal is $14.48 and without the drink it is $11.98.To calculate the drink price you must perform the equation, 14.48-11.98=d. Yet, that is still not in the array of choices. So, you have to add 11.98 on both sides. This will cancel out the 11.98 on the left side and give you 14.48=11.98+d and using the reflexive property you will get 11.98+d=14.48.

11.98+d=14.4 this equation can be used to find the cost of the drink.

In algebra, a number is always equal to itself according to the reflexive property of equality. The equality's reflexive quality. Assuming that an is a number, a = a.

Given

The total cost of the meal is $14.48 and without the drink it is $11.98.To calculate the drink price you must perform the equation, 14.48-11.98=d. Yet, that is still not in the array of choices. So, you have to add 11.98 on both sides. This will cancel out the 11.98 on the left side and give you 14.48=11.98+d and using the reflexive property you will get 11.98+d=14.48.

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Answer:

Angle B is 45°

Step-by-step explanation:

Since a and b are both of length 20, this is an isosceles right triangle, and the angle opposite side b must be 45°.

The Angle B is 45°

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Given

Since a and b are both of length 20, this is an isosceles right triangle, and the angle opposite side b must be 45°.

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Make because it’s statistical and his question is more specific

In the given question, Mark is correct.

A statistical question is one that can be answered by collecting data from several sources.

The question Elsie asked is a yes/no question, you can't answer the question in terms of data/numbers, but the question mark asked has to be answered in terms of data/numbers, hence it is a statistical question.

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For this case we have that by definition, the gravity of the earth is given by:

[tex]g = 9.807 \frac {m} {s ^ 2}[/tex]

On the other hand, Newton's second law states:

[tex]F = M * g[/tex]

Where:

F: It's the force

M: It's the mass

g: Acceleration of gravity

[tex]F = 200 * 9.807\\F = 1961.4 \ N[/tex]

Answer:

Option A

Answer: D. Matthew paid the correct amount for his purchases.

Step-by-step explanation:

($16.99 x 4) + $35.89 = $103.85 --cost of purchases

8.25% of $103.85 = $8.57 --sales tax

$103.85 + $8.57 = $112.42 --total cost

Answer:

D

Step-by-step explanation: