Dracula has 48 pieces of candy. He gave ⅓ of his candy to his friend and 25% of his candy to his cousin. How many pieces of candy does Dracula have left?

Answer: 5/3

Step-by-step explanation:

Answer:

μd= 1 second

σd= square root (1.25) = √1.25 seconds= 1.1180 seconds

Step-by-step explanation:

Assume that their times are independent. Let DDD be the difference between their times in a random 100-meter dash (D=A-J)(D=A−J)left parenthesis, D, equals, A, minus, J, right parenthesis.

Find the standard deviation of DD

The mean difference is found out by subtracting the individual means.

The mean difference = μd= μA- μJ= 11.5- 10.5= 1 second

The difference standard deviation is given by the square root of sum of the individual variances divided by n. But here n1= n2= 1

σd = sqrt( σ1² / n1 + σ2 ²/ n2 )

First we calculate the variances.

Variance is the square of the standard deviation.

The variance of Andy =σA²= 1²= 1

The variance of Jim =σJ²= (0.5)²= 0.25

The standard deviation difference= σd= √σ²A+ σ²J/1= √1+ 0.25/1= √1.25/1 = √1.25 seconds = 1.1180 seconds

Answer:

$139

Step-by-step explanation:

to solve this you must put write the equations first

N + x = 97

N + 5x = 265

you can use elimination to find the answer

-4x = -168

x = 42

you must plug this in to find Ns amount

N + 42 = 97

N = 55

lastly you make the equation for a two hour job and then plug the values in

2x + N = ?

2(42) + 55 = ?

84 + 55 = ?

2 hours = 139

The annual interest rate is, 2%.

Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.

Given that;

John loaned $1,612 to his niece to buy a computer. 2 years later, she paid him back the $1,612 along with an interest of $64.48.

Now, Let the annual interest rate = x

Then, we can formulate;

Simple interest = PRT / 100

Substitute all the given values,

$64.48 = 1612 × R × 2 / 100

6448 = 3224 × R

R = 6448 / 3224

R = 2

Hence, The annual interest rate is, 2%.

Learn more about the multiplication visit:

https://brainly.com/question/10873737

#SPJ1

ANSWER:

C. Write each student's name on a slip of paper and put the slips in a bag. Randomly draw a slip of paper. The student whose name is on the paper wins.

D. Roll a number cube. If it lands on 1 or 3, Alina wins. If it lands on 2 or 4, Robert wins. If it lands on 5 or 6, Makayla wins.

STEP-BY-STEP EXPLANATION:

The ways in which a fair decision can be made about who goes to dinner, it must be taken into account that each one has the same possibilities and that all the scenarios are met.

Option A is not fair, for even numbers, there are 3 and for odd numbers there are 3, there are no chances for Makayla.

In option B, it is not taken into account that there are two events, and Robert has an advantage.

In option C, it is totally fair, everyone has the same chance.

Like option C, in option D the probabilities are the same in each case.

Therefore, the correct answers are:

C. Write each student's name on a slip of paper and put the slips in a bag. Randomly draw a slip of paper. The student whose name is on the paper wins.

D. Roll a number cube. If it lands on 1 or 3, Alina wins. If it lands on 2 or 4, Robert wins. If it lands on 5 or 6, Makayla wins.

Answer:

(a) - \(y=-2x+18\)

(b) - \(y=\frac{1}{2} x-\frac{9}{2}\)

Step-by-step explanation:

Given the equation of a line, which we'll call line 1, find the following.

(a) - The equation of a line, which we'll call line 2, that is parallel to line 1 and travels through the point (9,0)

(b) - The equation of a line, which we'll call line 3, that is perpendicular to line 1 and travels through the point (9,0)

Given:

\(3y+6x=-6\)

(1) - Write the equation of line 1 in slope-intercept form

\(\boxed{\left\begin{array}{ccc}\text{\underline{Slope-Intercept Form:}}\\y=mx+b\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ b \ \text{is the y-intercept of the line}\end{array}\right}\)

\(3y+6x=-6\\\\\Longrightarrow 3y=-6-6x\\\\\Longrightarrow y=-\frac{6}{3} -\frac{6}{3}x \\\\\therefore \boxed{y=-2x-2}\)

Thus, we can conclude the slope of line 1 is -2.

(2) - Answering part (a)

To find a line that is parallel to line 1, the slopes must be the same, -2. Use the point-slope form for a line to find the equation for line 2.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Point-Slope Form:}}\\y-y_1=m(x-x_1)\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ (x_1,y_1) \ \text{is a point the line passes through}\end{array}\right}\)

\(y-y_1=m(x-x_1); \ \text{Recall that} \ m=-2 \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=-2(x-9)\\\\\therefore \boxed{\boxed{ y=-2x+18}}\)

Thus, the equation for line 2 is found.

(2) - Answering part (b)

To find a line that is perpendicular to line 1, the slope of line 3 must be the opposite-reciprocal of line 1's. Once again, use the point-slope form of a line to find the equation of line 3.

\(y-y_1=m(x-x_1); \ \text{Recall that} \ m=\frac{1}{2} \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=\frac{1}{2}(x-9)\\\\\therefore \boxed{\boxed{ y=\frac{1}{2} x-\frac{9}{2} }}\)

Thus, the equation of line 3 is found.

Answer:

Sin A = 3/5

Cos A = 4/5

Step-by-step explanation:

To find trigonometric ratio, recall SOHCAHTOA.

Thus:

Reference angle = <A

Opposite side to <A = 6

Adjacent side = 8

Hypotenuse = AB = √(8² + 6²) = 10 (pythagorean theorem)

Therefore,

✔️Sin A = Opp/Hyp

Sin A = 6/10 = 3/5

✔️Cos A = Adj/Hyp

Cos A = 8/10 = 4/5

The triangle ∠ADC is a central angle, m∠ADC is 60 degrees, and m∠ABC is 30°.

The central angle is the angle that a circle's arc occupies in its centre. The arms of the central angle are formed by the radius vectors. In other terms, it is an angle whose vertex is the centre of a circle, with the two radii lines acting as its arms and intersecting the circle at two distinct places. These two points make an arc when they are coupled together. The angle that this arc at the circle's centre subtends is called the central angle.

Half of the central angle is the circumferential angle.

∠ABC is equal to 1/2 of ∠ABC.

∠ABC = \(\frac{1}{2}*60\)

∠ABC = 30°

Option b. 30° is the right response, so.

To learn more about the central angle, refer:-

https://brainly.com/question/15698342

#SPJ1

Answer:

1650

Step-by-step explanation:

1350+300=1650

Answer:

Step-by-step explanation:

One person makes 375$ and the other makes 975$

Kim's test scores indicate that he scored as well as or better than 72% of the test takers, and 28% of the test takers scored better than him. His grade equivalent of 12.1 indicates that he would perform adequately in a twelfth grade science class.

His percentile of 88 indicates that he scored as well as or better than 88% of the test takers. His raw score of 72 does not directly indicate the percentage of questions answered correctly, but it can be assumed that he answered a majority of the questions correctly to achieve his score.

Learn more about tests:

https://brainly.com/question/1265793

#SPJ4

It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

For more questions on relative velocity.

https://brainly.com/question/11418015

#SPJ8

The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.

To design a program in Raptor that prompts the user to enter a person's weight in pounds and height in inches, and then calculates and displays their body mass index (BMI), we can follow these steps:

Start by opening Raptor and creating a new program.

Add three input symbols to prompt the user for their weight, height, and a constant value for BMI. Label each input symbol accordingly.

Add three assignment statements to assign the input values to variables. We can use the labels we assigned to the input symbols as variable names to make the code more readable.

Add two calculation statements to calculate the person's BMI using the formula \(BMI = (weight in pounds * 703) / (height in inches)^2.\)Assign the result to the BMI variable.

Add three output symbols to display the person's weight, height, and BMI. We can concatenate strings with the variable values to make the output more informative.

Finally, save the program and run it to test it with different input values.

Here's what the program would look like:

Start

// Prompt the user for weight, height, and BMI

Input "Enter weight in pounds:", weight

Input "Enter height in inches:", height

Input "BMI:", bmi_constant

// Calculate BMI

Set weight_in_kg = weight / 2.205 // Convert weight to kilograms

Set height_in_m = height / 39.37 // Convert height to meters

\(Set bmi = weight_in_kg / (height_in_m ^ 2)\) // Calculate BMI

// Display results

Output "Weight: " + weight + " lbs"

Output "Height: " + height + " in"

Output "BMI: " + bmi

Stop

When the program is run, it will prompt the user to enter their weight, height, and a constant value for BMI. It will then calculate the person's BMI using the formula, convert the weight to kilograms and the height to meters, and display the results along with the original weight and height values. The program uses the conversion factors of 2.205 pounds per kilogram and 39.37 inches per meter to convert the input values to the correct units for the formula.

To know more about conversion factors click here:

brainly.com/question/30166433

#SPJ4

Answer: 1

Step-by-step explanation:

12-8=4

12-8=4

4 over 4 is 1

if it perpendicular then it's the opposite reciprocal

hope that help

Items that can be produced and sold in order to make a profit is

\(5\leq n\leq 38\)

Given :

The cost of producing n items is (950+63n). The items can be sold for (280-5n) per item

Cost price = \(950+63n\)

Selling price is 280-5n for one item

Selling price of 'n' items

\(n \cdot (280-5n)\\280n-5n^2\)

We know that ,  profit = selling price for n items  - cost price for n items

We make profit only when selling price - cost price >=0

Lets replace the expressions

\(280n-5n^2 - (950+63n)\geq 0\\280n-5n^2 - 950-63n\geq 0\\\\-5n^2+217n-950\geq 0\)

Solve the inequality for n

Apply the quadratic formula to solve for n

\(-5n^2+217n-950=0\\n=\frac{-217\pm \sqrt{217^2-4\left(-5\right)\left(-950\right)}}{2\left(-5\right)}\\n=\frac{-217\pm \:3\sqrt{3121}}{2\left(-5\right)}\\n=\frac{-217+3\sqrt{3121}}{2\left(-5\right)},\:n=\frac{-217-3\sqrt{3121}}{2\left(-5\right)}\\n=4.94022 ,\:n=38.45977\)

Now we check the inequality

lets pick a number before 4.9 , n=4

\(-5n^2+217n-950\:\geq 0\\-162\geq 0 false\\\\Pick, n=10\\-5\left(10\right)^2+217\left(10\right)-950\geq 0\\720\geq 0 true\\\\Pick, n=40\\-5\left(40\right)^2+217\left(40\right)-950\geq 0\\-270\geq 0 false\\\)

n=40 satisfies our inequality  

40 lies between n=4.9  and n=38

So, \(5\leq n\leq 38\) items can be produced and sold in order to make a profit

Learn more :  brainly.com/question/15697949

Based on the information in the image, it can be inferred that the sides of the box measure 5 cm each.

To find the measure of the sides of the box we must carry out the following mathematical procedure:

As we know the volume of a cube is the equivalent to the length of its sides raised to the cube (raised to the 3). In this case, to identify the value of the sides we must find the cube root of the volume and the result is the length of the sides.

So this cube has a volume of 125cm³, so its sides would be the cube root of 125.

\(\sqrt[3]{125} = 5\)

According to the above, the length of the sides is 5 taking into account that all the sides are equal.

Learn more about cubes in: https://brainly.com/question/30962206

#SPJ1

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

For more such questions on GCF

https://brainly.com/question/902408

#SPJ8

Answer:

Other leg: 25 cm

Hypotenuse: 25√2 cm

Step-by-step explanation:

Hi there!

We are given a 45°-45°-90° triangle, and one leg (a side that makes up the right triangle) measures 25 cm

We want to find the length of the other sides

First, let's find the length of the other leg

A 45°-45°90° triangle is actually an isosceles triangle, and if it was to be drawn, the base angles are 45 and 45 degrees

That means the legs of the right triangle are actually the legs in the isosceles triangle as well

So the other leg is also 25 cm

Now, let's find the length of the hypotenuse, which is the side OPPOSITE from the 90° angle

You can solve for the other side using Pythagorean Theorem if you wish, however, there is a shortcut to finding the hypotenuse

In a 45°-45°-90° triangle, if the length of the legs are a, then the hypotenuse is a√2 cm

So that means the length of the hypotenuse in this case is 25√2 cm

Hope this helps!

The length of pipes are 235 inch and 47 inch.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

length of pipe = 282 inch

as, One piece is five times the length of the other.

then the pipe is in 6 parts

So, length of each = 282/6 = 47 inch

and, then the length of pieces

=47 * 5

= 235 inches

Hence, the length of pipes are 235 inch and 47 inch.

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ1

Answer:

25%

Step-by-step explanation:

6+6+6+6 equals 24,

The sum of the sequence based on the function Sn = ( -1 )n + 1 will be -6.

The formula for finding the nth term in an arithmetic sequence given as:

= a + (n - 1)d

Here, Sn is given as ( -1 )n + 1. This is used to illustrate the sum in the sequence. Based on the function given, let's assume that n = 5. Therefore, the 5th term will be:

= (-1)n + 1

= (-1)5 + 1

= (-1)6

= -6

Here is the complete question:

Find the 5th term of a sequence given the function Sn = ( -1 )n + 1.

Learn more about sequence on:

brainly.com/question/6561461

#SPJ1

Answer: 16

Step-by-step explanation:

Range is the largest number in the set minus the smalllest number in the set pf numbers or data.

9-(-7)

9+7

16

Answer:

  {-7, -1, 0, 9}

Step-by-step explanation:

The range of a function is the set of second values of the ordered pairs of the function.

  range = {-7, -1, 0, 9}

_____

It is often convenient, but not essential, to list the elements of a set in order.

Answer:

Notice that:

Since all the corresponding proportions are different, we get that triangles UVW and FGH are not similar.

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ1

Answer:

a) 0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.

b) 0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.

c) 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 7.7 grams per mililiter.

This means that \(\mu = 65, \sigma = 7.7\)

a. What is the probability that the amount of collagen is greater than 60 grams per.

This is 1 subtracted by the pvalue of Z when X = 60. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{60 - 65}{7.7}\)

\(Z = -0.65\)

\(Z = -0.65\) has a pvalue of 0.2578

0.2578 = 25.78% probability that the amount of collagen is greater than 60 grams per mililiter.

b. What is the probability that the amount of collagen is less than 90 grams per.

This is the pvalue of Z when X = 90.

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{90 - 65}{7.7}\)

\(Z = 3.25\)

\(Z = 3.25\) has a pvalue of 0.9994

0.9994 = 99.94% the probability that the amount of collagen is less than 90 grams per mililiter.

c. What percentage of compounds formed from the extract of this plant fall within 1 standard deviation of the mean?

Between Z = 1 and Z = -1, so the proportion is the pvalue of Z = 1 subtracted by the pvalue of Z = -1

Z = 1 has a pvalue of 0.8413

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826*100% = 68.26% of compounds formed from the extract of this plant fall within 1 standard deviation of the mean

Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

Answer:

Step-by-step explanation:

The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.

To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.

So, the growth rate of the investment is:

1.035 - 1 = 0.035

0.035 * 100 = 3.5%

Therefore, the growth rate of the investment is 3.5%.

Model B is the most appropriate for the set (-2,3), (-1,-3), (0, -5), (1, -3), (2,3).

Learn more about Linear, Quadratic, & Exponential Models refer to :

https://brainly.com/question/29929981

#SPJ1