Sally goes to the store and buys a camera for $65. The store is
running a discount of 10%. What is the price of the camera after the
discount?

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed. Therefore, the correct answer is 200%.

Speed is a measure of how quickly an object or person moves from one point to another. It is usually expressed in terms of distance traveled over time, for example, miles per hour or kilometers per hour.

To calculate this, we need to find the time taken for her to reach her home if her speed is doubled.

If her initial speed is 40 km/hr, then by doubling her speed, she will be travelling at a speed of 80 km/hr.

By travelling at this speed, she can reach her home in half an hour i.e. 30 minutes.

Therefore, the time taken to reach her destination by doubling her speed is 30 minutes.

The time taken to reach her destination while travelling at her initial speed is 2 hours.

To calculate the percentage increase in speed, we have to find the ratio of the time taken to reach her destination when the speed is doubled to the time taken to reach her destination when the speed is not doubled.

Therefore, the percentage increase in speed

= (30/120) x 100

= 25%.

Since she needs to double her speed to reach her home in half an hour, the percentage increase in speed required is 100%.

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed.

Therefore, the correct answer is 200%.

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Answer:

it is AB+bc to the nearest 100

Step-by-step explanation:

it is divided by 2

Answer:

A.  Complementary and Adjacent

B.  ∠KLM = 22°  and  ∠MLN = 68°

Step-by-step explanation:

Question A

As ∠KLN is a right angle, ∠KLN = 90°

⇒ ∠KLM + ∠MLN = 90°

When the sum of two angles is 90°, they are called complementary angles.

∠KLM and ∠MLN have a common side of ML and a common vertex (corner point) L.

When two angles have a common side and a common vertex but do not overlap in any way, the are called adjacent angles.

Question B

First find n:

∠KLM + ∠MLN = ∠KLN

⇒ 2n + (6n + 2) = 90

⇒ 2n + 6n + 2 = 90

Combine like terms:

⇒ 8n + 2 = 90

Subtract 2 from both sides:

⇒ 8n = 88

Divide both sides by 8:

⇒ n = 11

Now substitute the found value of n into the expressions for the two angles:

⇒ ∠KLM = 2(11) = 22°

⇒ ∠MLN = 6(11) + 2 = 68°

Answer: 1

Step-by-step explanation:

The length of side DE of the system of two similar triangles is equal to 8 units.

In this problem we find a geometric system formed by two similar triangles. Two triangles are similar if each triangle has congruent angles and sides that are not congruent though proportional. Thus, the system may be described well by this proportion formula:

AD / DE = AB / BC

If we know that AD = 10, AB = 25 and BC = 20, then the length of side DE is:

DE = (BC / AB) × AD

DE = (20 / 25) × 10

DE = (4 / 5) × 10

DE = 8

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The ratio is  15+\(r_2\) : \(12+r_1\).

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here surface area of the cylinder = \(2\pi rh+2\pi r^2\) square unit

=> A = \(2\pi r(h+r)\) square unit.

Now Height = 12 in , radius = r1 then,

=> \(A_1 = 2\pi r_1(12+r_1)\) -----> 1

Now Height = 15 in , radius = r2 then,

=>\(A_2=2\pi r_2(15+r_2)\)-------> 2

Now the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder then,

=>\(2\pi r_2(15+r_2) : 2\pi r_1(12+r_1)\)

=>\(15+r_2:12+r_1\)

Hence the ratio is \(15+r_2:12+r_1\).

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Answer:

25:16

Step-by-step explanation:

I took the

Answer:

Let x be the distance traveled by you to the north and y be the distance traveled by your friend to the west. Let d be the distance between you and your friend at time t. Then, we have:

d^2 = x^2 + y^2

Taking the derivative of both sides with respect to time, we get:

2d (dd/dt) = 2x(dx/dt) + 2y(dy/dt)

Simplifying this expression, we get:

dd/dt = (x(dx/dt) + y(dy/dt)) / d

Since you are driving north at a constant speed v and your friend is driving west at a constant speed w, we have:

dx/dt = v and dy/dt = -w

Substituting these values and simplifying, we get:

dd/dt = (v^2 + w^2)^0.5

Therefore, the speed of separation between you and your friend at time t is the square root of the sum of the squares of your speeds.

To find the second derivative of the distance between you and your friend, we take the derivative of dd/dt with respect to time:

d^2d/dt^2 = (v dv/dt + w dw/dt) / (v^2 + w^2)^0.5

Since v and w are constant, their derivatives with respect to time are zero, so the second derivative of the distance between you and your friend is zero.

Suppose you wait for an hour (i.e., t = 1 hour) before driving off to the north. Then, at time t > 1 hour, the distance between you and your friend is given by:

d = (vt)^2 + ((t-1)w)^2)^0.5

Taking the derivative of both sides with respect to time, we get:

dd/dt = 2v^2t / (2((vt)^2 + ((t-1)w)^2)^0.5)

Simplifying this expression, we get:

dd/dt = v / ((v^2 + ((t-1)w)^2)^0.5)

Therefore, the speed of separation between you and your friend at time t (greater than one hour) is given by v divided by the square root of the sum of the squares of your speed and your friend's speed.

The second derivative of the distance between you and your friend is given by:

d^2d/dt^2 = -vw(t-1) / ((v^2 + ((t-1)w)^2)^1.5)

Answer:

It could be 0, is the question multiple choice?

a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}\)

Answer:

B.

Step-by-step explanation:

it's B because if you put it as a mixed number it would be 21/2 ÷ 9/4 and then the rest is easy

Answer:

B

Step-by-step explanation:

4 2/3

The required value of h, representing the height of the three-dimensional rectangle, is 12.

The diagonal of a three-dimensional rectangle is defined by the equation d² = x² + y² + h². To solve for h, we can rearrange the equation as follows:

h² = d² - x² - y²

Given the values d = 13, x = 3, and y = 4, we can substitute them into the equation:

h² = 13² - 3² - 4²

h² = 169 - 9 - 16

h² = 144

Taking the square root of both sides, we find:

h = 12

Therefore, the value of h, representing the height of the three-dimensional rectangle, is 12.

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Answer:

y = -3

Step-by-step explanation:

-8=2y-2

+2   +2

-6=2y

-6/2   2y/2

-3= y

Answer: 16j^3+2

Step-by-step explanation:

Answer:

15.2

Step-by-step explanation:

Answer:

Area = 100x^2 + 80x + 16

Step-by-step explanation:

Since a square's sides all should be congruent, divide (40x+16) by 4 since a square has 4 sides.

Each side would be 10x+4 after the division.

Area is lengthxwidth so it would be (10x+4) x (10x+4)

Area is 100x^2 +40x+40x+16 = 100x^2 + 80x + 16

9514 1404 393

Answer:

Step-by-step explanation:

When looking for extremes, one must consider both the turning points and the ends of the interval. Here, there is a relative minimum at x=7, and a relative maximum at x=3. However, the values at the ends of the interval are more extreme than these.

The absolute minimum on the interval is 2 at x=0.

The absolute maximum on the interval is 10 at x=10.

Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.

What is frequency?

Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).

The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.

The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.

The experimental and theoretical probabilities do not match exactly. For example, the experimental  of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.

The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.

Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).

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Commplete Question:

A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:

Field Trip Number of times selected

A                8

B                16

C               9

D                12

E                5

Apply math models to analyze the data and answer the following questions:

What is the experimental probability of selecting each field trip?

What is the theoretical probability of selecting each field trip?

Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?

What is the relative frequency of selecting each field trip?

Based on the data, which field trip appears to be the most popular?

Answer:

The answer would be 536 cones.

Step-by-step explanation:

You have to subtract 164 from 700.

700-164=536.

The 90% confidence interval estimate of the difference between the two population means is (-0.144, 4.144).

The samples are independent and taken from the normal population. The population is unknown and the sample sizes are very small. The 'independent t-test statistic of a sampling distribution is used to construct the confidence interval estimate of the difference between the two population means. The true difference value of the population means lies inside the confidence interval with a 90% confidence level.

Sample 1:

Sample size, \(n_1=6\).

The sample mean is defined as \(\bar x_1= \frac{\sum x_i}{n_1}\)

Excel function for the sample mean:

Average \(=\frac{(10+7+13+7+9+8)}{6}\)

Average = 9

Thus, the sample mean is \(\bar x_1 = 9\)

The standard deviation of the sample is defined as

\(s_1=\sqrt \frac{\sum (x_i - \bar x_1)^2}{n_1 -1}\)

Excel function of the sample standard deviation:

Now, \(s_1=\sqrt{\frac{(10-9)^2+(7-9)^2+(13-9)^2+(7-9)^2+(9-9)^2+(8-9)^2}{6-1} }\)

\(=\sqrt{\frac{1+4+16+4+0+1}{6-1} }\)

\(=\sqrt{\frac{26}{5}\)

\(=\sqrt{5.2}\)

\(=2.28\)

This yields a sample standard deviation \(s_1\) = 2.28

Sample 2: (8, 7, 8, 4, 6, 9)

Sample size, \(n_2\) = 6

The sample mean is defined as

Mean \(= \frac{(8+7+8+4+6+9)}{6}\)

\(=7\)

So, \(\bar x_2 = 7\)

The standard deviation of the sample is defined as

\(s_2=\sqrt \frac{\sum (x_i - \bar x_2)^2}{n_2 -1}\)

Excel function of the sample standard deviation:

Now, \(s_2=\sqrt{\frac{(8-7)^2+(7-7)^2+(8-7)^2+(4-7)^2+(6-7)^2+(9-7)^2}{6-1} }\)

\(=\sqrt{\frac{1+0+1+9+1+4}{5} }\)

\(=\sqrt{\frac{16}{5}\)

\(=\sqrt{3.2}\)

\(=1.79\)

The sample standard deviation is \(s_2\) = 1.79

The 90% confidence interval for the difference between the population means is defined as:

\(\bar x_1 - \bar x_2 \pm t_{0.10/2} \times \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}\)

Level of significance, α =0.10

Degrees of freedom, \(df = n_1 + n_2 -2\)

= 6+6-2

= 10

Excel function for the confidence coefficient:

TINV(0.1, 10).

Then, P(T<-1.812) = \(\frac{0.1}{2}\)

Therefore, \(t_{0.10/2}\) = 1.812

Substituting values, the confidence interval is then:

\(\bar x_1 - \bar x_2 \pm t_{0.10/2} \times \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}\)

\(= 9-7\pm1.812\times\sqrt {\frac{2.28^2}{6} + \frac{1.79^2}{6}}\)

= \(2\pm2.144\)

= (-0.144, 4.144)

Therefore, the 90% confidence interval estimate of the difference between the two population means is (-0.144, 4.144).

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"Your question is incomplete, probably the complete question/missing part is:"

Consider the following data for two independent random samples taken from two normal populations.

What is the 90% confidence interval estimate of the difference between the two population means?

Answer:

100 miles

Step-by-step explanation:

20x5

Answer:

51

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Multiplication first, then division, and then addition.

(8*18)÷4+15 (Multiplication)

(144÷4)+15 (Division)

(36) + 15 (Addition)

   51

Hope that helps!

Answer:

51.

Step-by-step explanation:

When we use PEMDAS, we need to know what it stands for first. What it stands for will give us the steps necessary to complete and solve this problem.

PEMDAS stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

In this problem we do not have parenthesis or exponents, so we can go ahead and skip to multiplication. So:

8 x 18 ÷ 4 + 15

144 ÷ 4 + 15

Now we can go to doing division.

144 ÷ 4 + 15

36 + 15

Now we can do addition.

36 + 15

So, the answer is 51.

I hope that this helps.

Answer:

B. bisector of an angle.

The measure of other two angles in the given quadrilateral are 10° and 25°.

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices.

Given that, two angles of a quadrilateral measure 130° and 195°.

The other two angles are in a ratio of 2:5.

So, the other two angles are 2x and 5x

Now, 130°+195°+2x+5x=360°

325°+7x=360°

7x=360°-325°

7x=35°

x=5

So, 2x=10° and 5x=25°

Therefore, the measure of other two angles in the given quadrilateral are 10° and 25°.

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

The probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

Step-by-step explanation:

Let the random variable X represent the amount of gas in Sarah's car.

It is provided that \(X\sim Unif(1, 16)\).

The amount of gas in a car is a continuous variable.

So, the random variable X follows a continuous uniform distribution.

Then the probability density function of X is:

\(f_{X}(x)=\frac{1}{b-a};\ a<X<b\)

For a continuous probability distribution the probability at an exact point is 0.

So, to compute the probability that the amount of gas in Sarah's car is exactly 7 gallons use continuity correction on both sides:

P (X = 7) = P (7 - 0.5 < X < 7 + 0.5)

              = P (6.5 < X < 7.5)

              \(=\int\limits^{7.5}_{6.5} {\frac{1}{16-1}} \, dx \\\\=\frac{1}{15}\times |x|^{7.5}_{6.5}\\\\=\frac{1}{15}\times (7.5-6.5)\\\\=\frac{1}{15}\\\\=0.0666667\\\\\approx 0.067\)

Thus, the probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

Answer:

7(3e+5) alternative form 92.08392

Step-by-step explanation:

Answer:

a) 15yd

b)2.45ft

Step-by-step explanation:

P = perimeter, l=length and w = width of the rectangle

P = 2l+2w

a) 40 = 2l+2(5)

40 = 2l+10

30=2l

15=l

b) 18.4 = 2(6.75) + 2w

18.4 = 13.5+2w

4.9=2w

2.45=w

Let A be a diagonalizable matrix. If c₁ and c₂ are solution to system

x⃗' (t) = A x⃗ ( t )

the possible values of c₁ is 1 and c₂ is 2 .

So, the correct option is option(a) and (e).

We have given that A is 2 × 2 diagonalizable matrix and x⃗ (t) = ( 3eᵗ + eᶜ₁t , 3e²ᵗ + eᶜ₂ᵗ) is a solution of system, x⃗ '(t) = A x⃗(ᵗ) .

A Solution of system always satisfied the equation of system.

Now, Differenating x⃗ (t) wih respect to t we get, x⃗' (t)=( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ)

So, ( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ)= A ( 3eᵗ + eᶜ₁t , 3e²ᵗ + eᶜ₂ᵗ) where A is diagonalizable and A = [a 0 0 b].

Then, ( 3eᵗ + c₁ eᶜ₁t , 6e²ᵗ + c₂ eᶜ₂ᵗ) = ( 3aeᵗ + aeᶜ₁t , 3be²ᵗ + b eᶜ₂ᵗ)

equating the coefficients on both sides we get, 3eᵗ + c₁ eᶜ₁t = 3aeᵗ + aeᶜ₁t 6e²ᵗ + c₂ eᶜ₂ᵗ = 3be²ᵗ + b eᶜ₂ᵗ

after equating the corresponding equations , 3 = 3a and c₁ = a and 6 = 3b and c₂ = b after solving all we get a = 1 and b = 2 which implies c₁ = 1 and c₂ = 2. Hence, the possible values are c₁ = 1 and c₂ = 2.

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Complete question:

Let A be a diagonalizable matrix. If c₁ and c₂ are solution to system x⃗ (t) = A x⃗

then check all the possible values of c₁ and c₂ and below.

(a) c₁ = 1

(b) c₁ = 3

(c) c₁ = 2

d) c₂ = 1

(e)c₂ =2

(f) c₂ = 3

Answer:

64 Bottles

Step-by-step explanation:

that is the procedure above