Lea wrote a number riddle. Her clues were:

9 is 10 times the value of the 9 in 329,513
2 is 110 the value of the 2 in 7,562
6 is 110 the value of the 6 in 4.68
Which number is an answer to Lea's riddle?

Answer:

The vector AB is represented by (11, 2).

Step-by-step explanation:

Given two points on the same plane, we can determine the vector \(\overrightarrow{AB}\) by this formula:

\(\overrightarrow{AB} = B(x,y) - A(x,y)\) (1)

Where:

\(A(x,y)\) - Coordinates of point A.

\(B(x, y)\) - Coordinates of point B.

If we know that \(A(x,y) = (3, 7)\) and \(B(x,y) = (14,9)\), then the vector AB is:

\(\overrightarrow {AB} = (14,9) - (3,7)\)

\(\overrightarrow{AB} = (11, 2)\)

The vector AB is represented by (11, 2).

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

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In order to determine which inequality represents a graph, you need to look at the inequality and identify if the equation is an open or closed interval. If it is an open interval, it will be represented by a dashed line on the graph. If it is a closed interval, it will be represented by a solid line on the graph.

1. Look at the inequality and identify if the equation is an open or closed interval.

2. If it is an open interval, it will be represented by a dashed line on the graph.

3. If it is a closed interval, it will be represented by a solid line on the graph.

4. Determine the starting and ending points of the inequality, and plot them on the graph.

5. Draw the line that connects the two points, either dashed or solid, depending on whether the interval is open or closed.

6. Shade the area of the graph that is represented by the inequality.

7. Label the graph with the inequality, the points, and the shading.

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Answer:

1

Step-by-step explanation:

\(y - 3 = \frac{1}{4} (x - 8) \\ y = \frac{1}{4} x - \frac{1}{4} \times 8 + 3 \\ \\ y = \frac{1}{4} x - 2 + 3 \\ \\ y = \frac{1}{4} x + 1 \\ equating \: it \: with \: y = mx + b \\ b = 1 \\ y - intercept = 1\)

Answer:

1

Step-by-step explanation:

i just took the test

Answer:

66

Step-by-step explanation:

2m = 11

m = 11/2

m = 5.5

m² - 1 = 29.25

m² + 1 = 31.25

The perimeter = 29.25+31.25+5.5 = 66

Answer:

6 yard = 5.49 meter

Step-by-step explanation: if im wrong im sorry :)

Answer:

D

Step-by-step explanation:

equally likely or unlikely because it is 50%

Answer:

It is D hope this helps bud :)

Step-by-step explanation:

Answer:

164 cubic units

Step-by-step explanation:

volume of a sphere = (4/3) x (n) x (r^3)

If volume = 4r^3

volume = 4 x (4)^3 = 164 cubic units

Answer:

E

Step-by-step explanation:

Answer:

7) (f+g) (x) = 4^x + 5x -5

8) (f-g) (x) = 4^x + x - 5

Step-by-step explanation:

7)  Find (f +g)(x)

(4^x + 3x + 2x - 5)

(4^x + 5x -5)

(f+g) (x) = 4^x + 5x -5

8) Find (f-g)(x)

(4^x + 3x - 2x - 5)

(4^x + x - 5)

(f-g) (x) = 4^x + x - 5

The values of sin(t), cos(t), and tan(t) for the terminal point P(x, y) = (4/5, 3/5) are

a) sin(t) = 3/5

b) cos(t) = 4/5

c) tan(t) = 3/4

We are given the point P(x, y) = (4/5, 3/5), and we want to find sin(t), cos(t), and tan(t) for some real number t. So we have to use trigonometry

Let's first find the values of x and y using the given point

x = 4/5

y = 3/5

Next, we can use the unit circle to find the values of sin(t), cos(t), and tan(t). Since the point (x, y) is on the unit circle, we know that

x = cos(t)

y = sin(t)

Using the values of x and y that we found earlier, we get

cos(t) = 4/5

sin(t) = 3/5

To find tan(t), we can use the identity

tan(t) = sin(t) / cos(t)

Substituting the values we found earlier, we get

tan(t) = (3/5) / (4/5) = 3/4

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The given question is incomplete, the complete question is:

The terminal point P(x, y) determined by a real number t is given  that (4/5, 3/5) . Find sin(t), cos(t), and tan(t).

Answer:

a. After 4 years, the amount in the account can be found by using the formula for simple interest:

A = P * (1 + r * t), where P is the initial deposit, r is the annual interest rate as a decimal, and t is the number of years.

Plugging in the values, we get:

A = $2,000 * (1 + 0.05 * 4) = $2,000 * 1.2 = $2,400

So after 4 years, there will be $2,400 in the account.

b. After 16 years, the amount in the account can be found using the same formula:

A = $2,000 * (1 + 0.05 * 16) = $2,000 * 1.8 = $3,600

So after 16 years, there will be $3,600 in the account.

c. To find the number of years it will take for the account to contain $2,500, we can use the formula:

t = (A - P) / (P * r), where A is the desired amount.

Plugging in the values, we get:

t = ($2,500 - $2,000) / ($2,000 * 0.05) = ($500) / ($100) = 5 years

So it will take 5 years for the account to contain $2,500.

d. To find the number of years it will take for the account to contain $3,000, we can use the same formula:

t = ($3,000 - $2,000) / ($2,000 * 0.05) = ($1,000) / ($100) = 10 years

So it will take 10 years for the account to contain $3,000.

Step-by-step explanation:

pls mark brainlist

Answer:

D

Step-by-step explanation:

The lines are on the same trnasversal and by parallel lines l and m.

The interval within which 95 percent of all possible sample estimates will fall by chance is defined as the sample mean +/- 1.96 standard errors.

C. The sample mean +/- 1.96 standard errors.

This is known as the confidence interval, and it is calculated by taking the sample mean and adding and subtracting 1.96 times the standard error of the sample.

This range provides a level of confidence that the true population parameter falls within this range, based on the sample data.

The Central Limit Theorem is a statistical concept that explains how sample means tend to follow a normal distribution, but it is not directly related to the calculation of confidence intervals.

The lower and upper confidence boundaries refer to the endpoints of the confidence interval.

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The interval within which 95 percent of all possible sample estimates will fall by chance. The correct answer is: C. The sample mean +/- 1.96 standard errors

The interval within which 95 percent of all possible sample estimates will fall by chance is defined as the "Upper and Lower Confidence Boundaries" or "Confidence Interval." This interval is calculated based on the sample mean and standard error, with the common formula being the sample mean +/- 1.96 standard errors for a 95% confidence interval.

This interval is often referred to as the 95% confidence interval. It is calculated by taking the sample mean and adding/subtracting 1.96 times the standard error. This range represents the boundary within which 95 percent of all possible sample estimates are expected to fall by chance.

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The time traveler explained that time travel was possible by utilizing a time machine that allowed him to manipulate the fabric of space-time.

"The Time Machine" by H.G. Wells, the Time Traveler explains that time travel is possible by using a device he invented called the Time Machine. He describes the concept of the fourth dimension, suggesting that time is like a spatial dimension that can be traversed.
The Time Traveller's experimental verification involves him actually using the Time Machine to travel into the future. He shares his experiences of traveling to the year 802,701 AD, where he encounters two different species: the Eloi and the Morlocks. He provides vivid descriptions of the future society and the physical changes that have occurred over time.
By sharing his personal experiences and observations from his journey, the Time Traveller provides experimental evidence for the possibility of time travel.

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Answer:

97

Step-by-step explanation:

exterior angle property of triangle

64+33 equals 97

in other ways

By Angle sum property of triangle, the measure of 3rd angle is 83 and

angle 1 and 3rd angle are supplementary

so,

180 - 83 = 97

Answer:

A. Claie runs 5 km in a half hour. In 2 1/2 hours she runs 25 km.

B. Malia runs 2.5 miles in a half hour, and 12.5 miles in 2 1/2 hours.

C. Claire runs farther. She runs approximately 15.5 miles while Malia runs 12.5 miles.

Answer:

Step-by-step explanation:

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The dew point of an air sample with a temperature of 30 degrees C and a mixing ratio of 17 g/kg is -26.61 degrees C.

Firstly, we will convert the mixing ratio to vapor pressure.

The mixing ratio is given in grams of water vapor per kilogram of dry air (g/kg).

To convert it to vapor pressure, use the formula:
Vapor pressure = (mixing ratio / (1000 + mixing ratio)) * Saturation vapor pressure

But, we also have to determine the saturation vapor pressure for the given temperature (30 degrees C) using a reference table or empirical formula.

An example of an empirical formula is the August-Roche-Magnus approximation:
Saturation vapor pressure = 6.1094 * exp(17.625 * temperature / (243.04 + temperature))

Plug the values into the formulas:

Saturation vapor pressure = 6.1094 * exp(17.625 * 30 / (243.04 + 30)) = 42.37 hPa

and

Vapor pressure = (17 / (1000 + 17)) * 42.37 = 0.708 hPa

Now, we will calculate the dew point temperature using the inverse of the August-Roche-Magnus approximation:

Dew point = (243.04 * ln(vapor pressure / 6.1094)) / (17.625 - ln(vapor pressure / 6.1094))

Plug the values into the formula:
Dew point = (257.14 * ln(0.708 / 6.1121)) / (18.678 - ln(0.708 / 6.1121)) ≈ -26.61 degrees C

The dew point of the air sample with a temperature of 30 degrees C and a mixing ratio of 17 g kg-1 is approximately -26.61 degrees C.

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The length of the shorter leg is 16 units which was found using the given data.

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.

Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.

We know that,

Area of triangle = 1/2(larger leg)(shorter leg)

                  400=1/2(larger leg)(shorter leg)   Equation(1)

larger leg = 2 + 3(shorter leg)

We need to substitute this in Equation(1)

400 = 1/2[2+3(shorter leg)](shorter leg)

800 = 2(shorter leg) + 3(shorter leg)²

3(shorter leg)² + 2(shorter leg) - 800 = 0

Solving this quadratic equation,

we get, shorter leg = - 16 or +16

Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.

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The range of possible values for c is from about 49.5 to 51.3 miles. Therefore, the error in the calculation of the distance between A and B is approximately 0.9 miles.

To find the distance between A and B, we can use the Pythagorean theorem:

c^2 = a^2 + b^2

where c is the distance between A and B, and a and b are the distances from the known point to A and to B, respectively.

In this case, we have:

a = 30 ± 1 miles

b = 40 ± 0.1 miles

So the range of possible values for a is from 29 to 31 miles, and the range of possible values for b is from 39.9 to 40.1 miles.

Using these ranges, we can calculate the range of possible values for c:

c^2 = (30 ± 1)^2 + (40 ± 0.1)^2

c^2 = 900 ± 60 + 1600 ± 8

c^2 = 2500 ± 68

Taking the square root of both sides, we get:

c = √(2500 ± 68)

So the range of possible values for c is from about 49.5 to 51.3 miles. Therefore, the error in the calculation of the distance between A and B is approximately 0.9 miles.

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The 87th term of the arithmetic sequence is -1020.

To find the 87th term of an arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence, which is:

a_n = a₁ + (n - 1)d

Where a₁ is the first term in the sequence, d is the common difference between terms, and n is the position of the term that we are trying to find.

In this case, the first term is 12, the common difference is -12, and we are trying to find the 87th term, so we can plug these values into the formula to find the 87th term:

a₈₇ = (12) + (87 - 1)(-12)

a₈₇ = (12) + (86)(-12)

a₈₇ = (12) - 1032

a₈₇ = -1020

So, the 87th term of the arithmetic sequence is -1020.

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We have the following expression

we have 2 terms, one of them is

and the other one is

We can note that (3v-2) is repeated on both terms, so we can factorize (3v-2) in both terms, which gives

so this equivalent to:

therefore, the answer is:

Answer: 4 science and 2 math books

Step-by-step explanation:

Let M and S stand for the numbers of math and science books.

We know that M+S = 6 books

and M*80 + S*50 = $360

Rearance the first: M = 6-S

Use this definition of M in the second equation:

(6-S)*80 + S*50 = $360

480-80S + 50S = 360

-30S = - 120

S = 4

Use S=4 in the first equation (M=6-S) to find the number of math books, 2.

Check to see if there number work:

4*($50)= $200

2*($80)= $320160

Total is $360. It works.

The cost of one rose bush is $10 and the cost of one pot of ivy is $10.

Let's assume the cost of one rose bush is represented by "R" and the cost of one pot of ivy is represented by "I".

According to the given information:

Jaidee spent $140 on 2 rose bushes and 12 pots of ivy:

2R + 12I = 140 ...(1)

Beth spent $120 on 6 rose bushes and 6 pots of ivy:

6R + 6I = 120 ...(2)

We now have a system of two equations with two variables. To solve this system, we can use either substitution or elimination method. Let's use the elimination method.

Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of "R" in both equations equal:

6R + 36I = 420 ...(3)

12R + 12I = 240 ...(4)

Now, subtract equation (4) from equation (3):

(6R + 36I) - (12R + 12I) = 420 - 240

-6R + 24I = 180 ...(5)

Now we have a new equation (5) that relates "R" and "I".

Let's solve equations (5) and (2) together:

-6R + 24I = 180 ...(5)

6R + 6I = 120 ...(2)

Add equation (5) and equation (2):

(6R - 6R) + (24I + 6I) = 180 + 120

30I = 300

Divide both sides of the equation by 30:

I = 10

Now substitute the value of "I" into equation (2) to find the value of "R":

6R + 6(10) = 120

6R + 60 = 120

6R = 120 - 60

6R = 60

Divide both sides of the equation by 6:

R = 10

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The probability that each of the balls will be; a) P( of the same color) = 0.08875. b) P ( of different color) = 0.247678

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

The Number of red balls = 5

The number of blue balls = 6

The number of green balls = 8

The Total number of balls = 5 + 6 + 8 = 19

Then with three balls selected at random, by using combination method ;

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

a) P( of the same color) = 5C3 + 6C3 + 8C3 / 19C3

=  86/969 = 0.08875

b) P ( of different color) = 5C1 X 6C1 X 8C1 /19C3

= 240/969 = 0.247678

Hence, The probability that each of the balls will be; a) P( of the same color) = 0.08875. b) P ( of different color) = 0.247678

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simple interest:  i = p * r * t; compound interest would be A=p(1+r/n)^(nt)

Here,   A = $500 (1.10)^2 = $605 (answer for "once per year."

Once per month:

A = $500 (1 + 0.10/12)^(12*2) = $610.20

Once per week:  Can y ou figure that out?  # of compounding periods is 12 per year in this problem.

Answer:

There are 15 calories in 1 fluid ounce.

Step-by-step explanation:

To find the answer, you can use a rule of three to find the number of calories in 1 fluid ounce given that there are 120 calories in 8 ounces:

8 ounces → 120 calories

1 ounce    →        x

x=(1*120)/8

x=15

According to this, the answer is that there are 15 calories in 1 fluid ounce.

Answer:

\(\displaystyle y' = - \frac{e^{x^2 + 7} \sqrt{\csc 5x} \Bigg[ \bigg[ 5 \cot (5x) - 4x \bigg] \sin (3x + 4) - 6 \cos (3x + 4) \Bigg] }{2}\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
\(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)

Derivative Property [Addition/Subtraction]:
\(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)

Derivative Rule [Basic Power Rule]:

Derivative Rule [Product Rule]:
\(\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)\)

Derivative Rule [Chain Rule]:
\(\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)

Step-by-step explanation:

Step 1: Define

Identify.

\(\displaystyle y = e^{x^2 + 7} \sin (3x + 4) \sqrt{\csc (5x)}\)

Step 2: Differentiate

∴ we have found the derivative of the function.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

To find the derivative of the function \(\displaystyle\sf\:y=e^{x^{2}+7}\sin(3x+4)\sqrt{\csc(5x)}}\) with respect to \(\displaystyle\sf x\), we'll use the chain rule and product rule.

Let's break down the function into its individual parts:

\(\displaystyle\sf u= e^{x^{2}+7}\)

\(\displaystyle\sf v= \sin(3x+4)\)

\(\displaystyle\sf w= \sqrt{\csc(5x)}}\)

Now, let's differentiate each part separately:

Using the chain rule, the derivative of \(\displaystyle\sf u= e^{x^{2}+7}\) is:

\(\displaystyle\sf \dfrac{du}{dx}= (2x)e^{x^{2}+7}\)

Using the chain rule, the derivative of \(\displaystyle\sf v= \sin(3x+4)\) is:

\(\displaystyle\sf \dfrac{dv}{dx}= 3\cos(3x+4)\)

To differentiate \(\displaystyle\sf w= \sqrt{\csc(5x)}}\), we can rewrite it as \(\displaystyle\sf w= (\csc(5x))^{1/2}\). Using the chain rule, the derivative of \(\displaystyle\sf w\) is:

\(\displaystyle\sf \dfrac{dw}{dx}= \dfrac{1}{2}(\csc(5x))^{-1/2}(-\cot(5x))(5)\)

Simplifying the derivative \(\displaystyle\sf \dfrac{dw}{dx}\):

\(\displaystyle\sf \dfrac{dw}{dx}= -\dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}\)

Now, using the product rule, the derivative of \(\displaystyle\sf y\) with respect to \(\displaystyle\sf x\) can be calculated as follows:

\(\displaystyle\sf \dfrac{dy}{dx}= \dfrac{du}{dx} \cdot v \cdot w + u \cdot \dfrac{dv}{dx} \cdot w + u \cdot v \cdot \dfrac{dw}{dx}\)

Substituting the values of \(\displaystyle\sf \dfrac{du}{dx}\), \(\displaystyle\sf \dfrac{dv}{dx}\), and \(\displaystyle\sf \dfrac{dw}{dx}\):

\(\displaystyle\sf \dfrac{dy}{dx}= \left((2x)e^{x^{2}+7}\right) \cdot \sin(3x+4) \cdot \sqrt{\csc(5x)} + e^{x^{2}+7} \cdot \left(3\cos(3x+4)\right) \cdot \sqrt{\csc(5x)} - e^{x^{2}+7} \cdot \sin(3x+4) \cdot \dfrac{5\cot(5x)}{2\sqrt{\csc(5x)}}\)

Simplifying further:

\(\displaystyle\sf \dfrac{dy}{dx}= \left(2xe^{x^{2}+7}\right) \sin(3x+4) \sqrt{\csc(5x)} + 3e^{x^{2}+7}\cos(3x+4) \sqrt{\csc(5x)} - \dfrac{5e^{x^{2}+7} \sin(3x+4) \cot(5x)}{2\sqrt{\csc(5x)}}\)

Therefore, the derivative of \(\displaystyle\sf y\) with respect to \(\displaystyle\sf x\) is:

\(\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 3e^{x^{2}+7}\sqrt{\csc(5x)}\cos(3x+4) - \dfrac{5e^{x^{2}+7}\sin(3x+4)\cot(5x)}{2\sqrt{\csc(5x)}}\)

Simplifying further, we have:

\(\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x \sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}\)

Therefore, the derivative of \(\displaystyle\sf y\) with respect to \(\displaystyle\sf x\) is:

\(\displaystyle\sf y' = -2e^{x^{2}+7}\csc(5x)[5\cot(5x)-4x]\sin(3x+4) - 6e^{x^{2}+7}\cos(3x+4)\sqrt{\csc(5x)}\)

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

1

Step-by-step explanation:

1/2x1x2

1

The valid and useful Internal Rate of Return (IRR) is 14.98%. The Internal Rate of Return (IRR) is a financial metric used to assess the profitability and viability of an investment project.

It represents the discount rate at which the present value of cash inflows equals the present value of cash outflows. In simpler terms, it is the rate of return that makes the net present value of an investment zero. In this case, there are two IRR values provided: -14.79% and 14.98%. The valid and useful IRR is the positive value, which is 14.98%. The negative value, -14.79%, is not considered valid because it implies a negative rate of return, which is not meaningful in this context.

The positive IRR of 14.98% indicates that the project is expected to generate a rate of return of 14.98%, which is higher than the required rate of return or the cost of capital. This suggests that the project is potentially profitable and should be considered for investment. The higher the IRR, the more attractive the project becomes.

It is important to note that the IRR should be interpreted in conjunction with other financial metrics and considerations, such as the project's cash flows, risk factors, and the organization's investment criteria. Additionally, sensitivity analysis and scenario testing should be conducted to assess the robustness and reliability of the IRR estimate.

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