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This prism has a right triangle for a base. What is the volume of the prism?

The gorilla has a heart rate that is four times faster than the chimpanzee's when they are resting.

Expression in math is a combination of numbers, variables, operations and/or symbols that represent a value, quantity or an equation. It can either be a single term, or several terms connected by mathematical operations such as addition, subtraction, multiplication and division. Expressions are typically used in equations, formulas and problems to help solve them.

To calculate the heart rate of the gorilla, we use the power function given: H(m) = 240m. Substituting in m = 200, we get H(200) = 240(200) = 48,000 beats per minute.

To calculate the heart rate of the chimpanzee, we use the same power function: H(m) = 240m. Substituting in m = 50, we get H(50) = 240(50) = 12,000 beats per minute.

Therefore, the gorilla has a heart rate that is four times faster than the chimpanzees when they are resting.

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Answer:

slope of 3/4 = line C

undefined slope = line A

Step-by-step explanation:

remember that slope is [tex]\frac{rise}{run}[/tex]. Pick any two points on the graph and count up and over to find the rise/run.

OR

use the slope formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] to plug the two points into and find the slope.

- vertical lines are always undefined.

- horizontal lines have a slope of 0

Answer:

area=36.5

Step-by-step explanation:

8×4=32

8-5=3 for the base of the triangle

7-4=3 for the height of the triangle

3×3=9

9÷2=4.5

4.5+32=36.5

area=36.5

The total number of different dinner special combinations offered by Lewis' Restaurant is 28 different dinner special combinations.

Lewis' Restaurant offers a dinner special that consists of a main dish, a vegetable, a salad, and a roll.

There are 4 main dishes, 7 vegetables, 1 salad, and 1 type of roll to choose from.

To determine the total number of different dinner special combinations that Lewis' offers, you have to multiply the number of options available for each course.

To find the total number of different dinner special combinations offered by Lewis' Restaurant, you have to use the multiplication rule.

The multiplication rule states that if an event can occur in 'a' different ways and another independent event can occur in 'b' different ways,

then the two events can occur in 'a x b' different ways.

Therefore, the total number of different dinner special combinations offered by Lewis' Restaurant can be calculated as follows:

4 main dishes × 7 vegetables × 1 salad × 1 type of roll= 28 different dinner special combinations

Note that we multiply the number of options for each course because the courses are independent.

This means that the choice of the main dish does not affect the choice of the vegetable, salad, or roll, and vice versa. Therefore, we can multiply the number of options for each course to determine the total number of different dinner special combinations that Lewis' Restaurant offers.

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Step-by-step explanation:

2 pictures are attached

sin waves are used in many medical devices like to measure heart beats

The expression or equation that correctly represents the situation given is y = 2x.

Based on the table, for each package of cashews 2 cans of peanuts are required. Here are some examples:

Based on this relationship and assuming y represents the cans of peanuts and x represents the packages of cashews a possible equation to represent this situation would be y = 2x.

Note: This question is incomplete; below I attach the missing information:

Write an equation to represent this relationship:

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The probability of getting 0 toppings when ordering a hamburger with a choice of up to 6 toppings is 0.0154, rounded to four decimal places.

The total number of ways to choose 6 toppings out of a possible 6 is given by the combination formula:

[tex]$${ \choose 6} = \frac{6!}{6!(6-6)!} = 1$$[/tex]

This is the total number of possible outcomes.

To get 0 toppings, we need to choose 0 toppings out of 6. The number of ways to do this is:

[tex]{6_{0} =[/tex] [tex]\frac{6!}{0!(6-0)!} = 1$$[/tex]

So the probability of getting 0 toppings is:

[tex]$$P(\text{0 toppings}) =[/tex]  [tex]\frac{number of ways to get 0 toppings}{total number of possible outcomes} $$[/tex] [tex]\frac{1}{1} = 1$$[/tex]

However, this is assuming that the cashier chooses the toppings randomly and without replacement. If the cashier has some bias or preference towards certain toppings, this probability may be different.

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Answer: 37.5

Step-by-step explanation:

Probability that exactly four workers carpool to work is 0.214990847, or approximately 21.5%.

We must apply the binomial distribution formula to resolve this issue. The number of successes in a certain number of independent trials that all have the same chance of success are described by the binomial distribution, which is a type of probability distribution. In this scenario, the number of successes is the number of workers who carpool, and the probability of success is 0.1.

The binomial distribution's formula is:

[tex]P(X=k) = to (n pick k) * p*k*1-p (n-k)[/tex]

Where n is the total number of trials (in this case, 8), p is the success probability (0.1), and (n choose k) is the binomial coefficient, which is equal to [tex]n! / (k! * (n-k)![/tex] and P(X=k) is the probability of obtaining exactly k successes.

This formula can be used to determine the likelihood that four employees will carpool to work:

[tex]P(X=4) = (8 pick 4) * 0.14 * 0.94 * 0.214 = 0.214990847.[/tex]

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Answer:

Hope this is what you were looking for :)

Step-by-step explanation:

tan = opposite/adjacent

IF YOU DONT NEED TO FIND THE VALUES OF THE SIDES:

tan A =  [tex]\frac{x}{11}[/tex]

tan B = [tex]\frac{11}{x}[/tex]

Replace the x for whatever the value of BC is or if it doesn't have a value, you can just leave it as x.

IF YOU DO NEED TO FIND THE VALUES OF THE SIDES:

tan 45 = 1

tan 45 =  [tex]\frac{BC}{11}[/tex]

(11) tan 45 = BC

BC = 11

tan 45 = [tex]\frac{11}{AC}[/tex]

AC = [tex]\frac{11}{tan 45}[/tex]

AC = 11

This can also be done without using tangent from taking a look at special right triangles.

In 45-45-90 triangles, the two legs are the same size while the hypotenuse is equal to one of the legs multiplied by [tex]\sqrt{2}[/tex]. In doing this, we can find that both legs are 11 and the hypotenuse is [tex]11\sqrt{2}[/tex].

The sequence follows a pattern of adding 7 to the previous term, and its formula is 7n - 3. The sum of the first 100 terms of the sequence is 35,350, which was found using the formula for the sum of an arithmetic series.

The next term in the sequence can be found by adding 7 to the previous term, so the next term is 25.

To find a formula for the nth term of the sequence, we can observe that each term is 7 more than a multiple of 7. In other words, the nth term is given by the formula 7n - 3.

To find the sum of the first 100 terms of the sequence, we can use the formula for the sum of an arithmetic series:

S = (n/2)(a1 + an)

where S is the sum of the first n terms, a1 is the first term, and an is the nth term. Substituting n = 100, a1 = 4, and an = 703, we get:

S = (100/2)(4 + 703) = 35,350

Therefore, the sum of the first 100 terms of the sequence is 35,350.

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The probability that the number of phone calls between 2:00 pm and 2:10 pm is exactly 25 is 1/110,592,893.

To calculate this probability, use the Poisson distribution formula: P(x) = (e^-λ * λ^x) / x!, where λ = 3 x 10 = 30. Therefore, P(25) = (e^-30 * 30^25) / 25! = 1/110,592,893.

The probability that the number of phone calls between 2:00 pm and 2:10 pm is more than 25 is the sum of probabilities of all calls more than 25. That is, the probability is 1 - (e^-30 * (30^0 + 30^1 + 30^2 + ... + 30^25)) / (0! + 1! + 2! + ... + 25!).

By using the same Poisson distribution formula, the probability is 1 - 0.99988822 = 0.00011178.

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We can see here that the figures that have the same area are: A. Figures I and II.

Area is a measure of the size of a two-dimensional surface or shape. It refers to the amount of space inside the boundaries of a flat object, such as a rectangle, triangle, or circle. Area is typically measured in square units, such as square meters, square feet, or square centimeters.

The area of Figure I which is a rectangle is = l × b = 2cm × 5.8cm = 11.6cm².

The area of Figure II which is a parallelogram is = b × h = 4cm × 2.9cm = 11.6cm².

Thus, Figures I and II have the same area.

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The percentage change in the visit of total number of customers in the second week as compare to first week is equal to 16.67%.

Total number of customers visited the store in the first week = 360

Total number of customers visited the store in the second week = 300

Percentage Change = (|First week - second week / First week) x 100%

Substitute the value of the number of customers in different weeks in the formula we get,

Percentage Change

= (|300 - 360| / 360) x 100

= (60 / 360) x 100

=( 100 / 6 )

= 16.66666%

= 16.67%

Therefore, the percentage change in the number of customers that visited the store from the first week to the second week is a decrease of 16.67%.

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The above question is incomplete, the complete question is:

Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store.

What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?

Answer:

The answer to your problem is, [tex]16cm^{2}[/tex]

Step-by-step explanation:

Sophie has a small cube shaped box.

Volume of the box is [tex]64cm^{3}[/tex]

We have to find the area of one face of the box.

Let one side of the box is x

Then volume = [tex]x^{3}[/tex] = 64

x³ = 4³

= 4

Now area of one face of the cube = x²

then area = 4² = 16 cm²

Thus the answer to your problem is, [tex]16cm^{2}[/tex]

Answer:2

Step-by-step explanation:

1+1=2

The equation of the circle is with the diameter given is x² + y² = 9.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

We can quickly determine the circle's centre and radius thanks to this form. We must first square the x and y terms before rearranging the components in order to transform a circular equation into standard form.

The endpoints of the diameter is (-3,0) and (3,0).

Now, using the section formula the coordinates of radius are:

((-3+3)/2, (0+0)/2) = (0,0

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

Substituting the values:

(x - 0)² + (y - 0)² = 3²

Hence, the equation of the circle is x² + y² = 9.

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Answer:

10 + 2x

also,

2x + 10

Step-by-step explanation:

"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)

"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.

"product" means multiplying. So the "product of 2 and a number" is 2x.

So to translate this word phrase into an algebraic expression, you get:

10 + 2x

but also 2x + 10 is the same thing.

To estimate the number of new subscribers in Charlottesville and Albemarle County, we'll use the given joint probability density function (pdf) f(x,y).

Here's a step-by-step explanation:
1. Identify the random variables: In this case, X represents the number of new subscribers (in thousands) in Charlottesville, and Y represents the number of new subscribers (in thousands) in Albemarle County outside of Charlottesville.
2. Understand the joint probability density function (pdf): The function f(x,y) describes the probability of having a specific number of new subscribers in both areas. The joint pdf is used to find the probability of a particular combination of X and Y values.
3. Determine the desired outcome: In this case, you want to estimate the number of new subscribers in both Charlottesville (X) and Albemarle County (Y) next year.
4. Calculate the probabilities: To find the probability of a specific combination of X and Y values, you'll need to evaluate the joint pdf f(x,y) at those values.
5. Analyze the results: Based on the probabilities you've calculated using the joint pdf, you can make informed estimates about the number of new subscribers in both areas next year.
By following these steps and using the joint probability density function f(x,y), you can estimate the number of new subscribers for F XYZ finity Cable in Charlottesville and Albemarle County next year.

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Answer:

14/24, 21/36, 28/48, 35/60, 42/72, 49/84, 56/96 are equivalent fractions of 7/12.

10/12, 15/18, 20/24, 25/30. are equivalent fractions of 5/6

Step-by-step explanation:

25 gallons of water will be dumped on Mr. Henderson's head.

To solve the problem, we first need to find the total amount of water dumped on Mr. Henderson's head by all the students. Since each student dumps a 5-quart bucket of water, we can find the total amount by multiplying the number of students by the amount of water per student:

Total amount of water = 20 students x 5 quarts/student = 100 quarts

Next, we convert the total amount of water from quarts to gallons since the problem asks for the answer in gallons. Since 1 gallon equals 4 quarts, we can divide the total amount of water by 4 to get the answer in gallons:

Total amount of water = 100 quarts ÷ 4 quarts/gallon = 25 gallons.

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Answer:

153

Step-by-step explanation:

The relationship in the row is below

4³ +2³ +1³ =64 + 8 +1 = 72

1³ + 2³ +6³= 1 + 8 + 216

3³ + 1³ + 5³ = 27 +1 +125 = 153

All numbers below the first level are raised to power 3 and added together

The probability that it rains at least one day this weekend is [tex]$\frac{a}{b}$[/tex],  so the value of a+b is given as 107.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

Let x be the probability that it rains on Sunday given that it doesn't rain on Saturday then we have,

3/5x + 2/5(2x) = 3/10

7/5x = 3/10

x = 3/14.

Therefore, the probability that it doesn't rain on either day is,

[tex]$\left(1-\dfrac{3}{14}\right)\left(\dfrac{3}{5}\right)=\dfrac{33}{70}$[/tex]

Therefore, the probability that rains on at least one of the days is

[tex]$1-\dfrac{33}{70}=\dfrac{37}{70}$[/tex],

so adding up the 2 numbers, we have,

37 + 70 = 107.

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Complete question;

There is a 40% chance of rain on Saturday and a 30% chance of rain on Sunday. However, it is twice as likely to rain on Sunday if it rains on Saturday than if it does not rain on Saturday. The probability that it rains at least one day this weekend is [tex]$\frac{a}{b}$[/tex], where a and b are relatively prime positive integers. Find a+b.

The inequality representing the number of players on the court is given by 0 ≤ x ≤ 5.

Let us consider variable 'x' represents the number of players in the basketball team.

As we know,

Number of players is always greater than or equal to zero.

As number of players in the basketball team cannot be negative players.

As per condition,

Number of players in the basketball team = At most 5 players.

This implies,

Number of players in the basketball team is less than or equal to 5

The inequality that best describes the number of players on the basketball court is written as,

⇒ 0 ≤ number of players ≤ 5

⇒ 0 ≤ x ≤ 5

Therefore, the inequality used to represents the number of players in the basketball court is equal to 0 ≤ x ≤ 5.

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"The speed of a randomly selected car on a highway" and "the percent change in the price of a share of IBM stock in a month" are examples of continuous random variables. Options A and C are the correct answers.

Continuous random variables are those that can take on any value within a given range, as opposed to discrete random variables, which can only take on certain values.The speed of a randomly selected car on a highway and the percent change in the price of a share of IBM stock in a month are examples of continuous random variables.

These variables have a range of values and can take on any value within that range.The number of claims on a medical insurance policy on a given year, the number of customers that enter a particular store on a randomly selected day, and the time that elapses between two customer service calls are examples of discrete random variables. These variables can only take on certain values, such as whole numbers or specific times.

Thus option A and option C are the correct answers.

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Answer:

For problem a: 0,4 0,5 0,6

For Problem B: 1,0 2,0 3,0

Step-by-step explanation:

Graph each equation on a graph Figure out either solid or dotted line. Then depending on <=,<,>,>= is whre you shade on your graph. The spot where both lines meet when shaded is your solution area and you pick any spot on that. You can check your answer by plugging in ordered pairs for your X,Y values in the system.

Method 1: Graphing

Graphing is best when the both equations are shown in slope-intercept form. For example:

[tex]y=\frac{1}{2} x+2\\y=-\frac{1}{2} x+4[/tex]

[tex](2,3)[/tex]

You can easily graph this system of equations and find the intersecting point. The graph is displayed below. This may not always be the case, however and you may get complicated fractions in your answer. In this case, substitution or elimination may be better.

Method 2: Substitution

Substitution is a good method to solve a system of equations when one of the equations can be rearranged to isolate one variable, or the equation already solves for a variable. This isolated expression can then be substituted into the other equation(s) to create a new equation(s) with only one variable.

For example, consider the system of equations:

[tex]y=x-2\\2x-5y=1[/tex]

Since y is much easier to substitute, we can choose y to substitute into the other equation:

[tex]2x-5(x-2)=1[/tex]

We can then simplify the equation:

[tex]2x-5x+10=1\\-3x=-9\\x=3[/tex]

Then you can substitute x into the original equation:

[tex]y=3-2\\y=1[/tex]

Solution: [tex](3,1)[/tex]

Substitution can be a useful method when the system involves two or three variables and one equation can be easily rearranged to isolate a variable. However, it can become more difficult or time-consuming when the system involves more variables or when the equations are not solving for a variable or can be easily solved. In these cases, other methods such as elimination is more efficient.

Method 3: Elimination

Elimination is a good method to solve a system of equations when the equations can be added or subtracted in a way that eliminates one of the variables.

For example, consider the system of equations:

[tex]x+y=90\\x-y=18[/tex]

We can cancel out the variable y and add the other numerals and variables:

[tex]2x=108[/tex]

This simplifies to:

[tex]x=54[/tex]

We can then solve for y:

[tex]54+y=90\\y=36[/tex]

Solution: [tex](54, 36)[/tex]

Once we have the value of x, we can substitute it back into one of the original equations to solve for y.

Although elimination is slightly more complicated, it is the most efficient method out of all of the three methods I have shown here.

Hope this helped you :)

(This took like 30 minutes ;-;)

Equation:

89.50=2.35c+5.50d

If theres 22 dogs and cats in total you can plug in number less than 22 for c(# of cats) and d(# of dogs).

So we try pats numbers 8 cats and 14 dogs so

89.50=2.35(8)+5.50(14)

89.50=18.8+77

89.50=95.8

So pats numbers were wrong so we try different numbers

So i started pluging in numbers from under 22 so i got c is 10 and d is 12 lets try it with the equation

89.50=2.35(10)+5.50(12)

89.50=23.5+66

89.50=89.50 so it works the answer to how many number of dogs and cats is 12 dogs and 10 cats

Answer:

Step-by-step explanation:

We can use the standard normal distribution to solve this problem by standardizing the score.

z = (x - mu) / sigma

Where:

x = 70 (score we are interested in)

mu = 60 (mean score)

sigma = 7 (standard deviation)

z = (70 - 60) / 7 = 1.43

Using a standard normal distribution table or calculator, we can find the probability that z is greater than 1.43. The probability is approximately 0.0764.

Therefore, the probability that a randomly selected student scored more than 70 on the exam is 0.0764 (or about 7.64%).

Factor  72 + 32 in the form of a ( b + c)  with A having gcf is 72 + 32 is 8(9 + 4).

To factor 72 + 32, we first need to find the greatest common factor (GCF) of 72 and 32.

The prime factorization of 72 is 2³ x 3², and the prime factorization of 32 is 2⁵.

The common factors of 72 and 32 are 1, 2, 4, 8, and 16. The greatest common factor is 8, since it is the largest factor that they both share.

So, we can write 72 + 32 as:

72 + 32 = 8 x (9 + 4)

Therefore, the factored form of 72 + 32 is 8(9 + 4).

To factor 72 + 32, we need to find the greatest common factor (GCF) of 72 and 32, which is 8. We can then use this GCF to write 72 + 32 in factored form as 8(9 + 4). This expression can also be simplified as 8(13), which equals 104. This means that 72 + 32 can be written as the product of 8 and 13, where 8 is the GCF of 72 and 32, and 13 is the sum of the quotients of 72 and 32 when divided by 8. Factoring expressions is an important skill in algebra and is used in many areas of mathematics and science.

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