Mathematics High School

## Answers

**Answer 1**

Answer: The answer is D. Since all values have the same denominator, simply arrange them by least to greatest by referring to the numerator.

**Answer 2**

**Answer:**

**Step-by-step explanation: since there are 9s on all of the bottom it would be 1/9 ,4/9, 5/9, 8/9**

## Related Questions

A wire carries a current. If both the wire diameter and the electron drift speed are doubled, the electron current increases by a factor of A. 2 B. 4 C. 6 D. 8 E. Some other value.

### Answers

If both the wire diameter and the **electron drift speed **are doubled, the electron current increases by a factor of D. 8.

Electrons move about randomly in a **conductor, **but when an electric field is applied it applies a force on them and this random motion turns into a small flow in one direction, and the velocity of this flow is called drift velocity. Note that electrons don't move nearly even close to the speed of light but they are more like a very long line of markers joined together(because of the repulsion of the same charges the next electron moves when the first moves and it goes so on till the last one, making a line somewhat), and when the first electron will move, all of them will move in that direction and its effect will be at the speed of light at another position while electrons move at speeds of millimetres per second

1. The wire's cross-sectional area is proportional to the square of its **diameter.** So, if the diameter doubles, the area quadruples (increases by a factor of 4).

2. The current (I) is given by I = nqAv, where n is the number of charge carriers, q is the charge of each carrier, A is the cross-sectional area, and v is the electron drift speed.

3. If the electron drift speed (v) is doubled and area (A) is **quadrupled**, then the current increases by a factor of 2 * 4 = 8.

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8 divided by 2^3 -16 divided by two

### Answers

The result of the **expression **given will be -7.

**What exactly are expressions?**

In mathematics, an expression is a combination of numbers, **variables**, and operators (such as addition, subtraction, multiplication, and division) that can be evaluated to obtain a value. Expressions can be simple or complex, and can include constants, variables, functions, and **mathematical operations**. Examples of expressions include:

5 + 2

2x - 3y

(a + b) / c

√(x² + y²)

sin(θ) + cos(θ)

Now,

We need to use the **order **of operations to evaluate this expression:

8 ÷ 2³ - 16 ÷ 2

First, we need to evaluate the exponents: 2³ = 8

8 ÷ 8 - 16 ÷ 2

Next, we need to evaluate the division from left to right:

1 - 8

Finally, we need to evaluate the subtraction:

-7

Therefore, the **result **of 8 divided by 2³ -16 divided by 2 is -7.

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Right Question:- What is the resultant of expression 8 divided by 2^3 -16 divided by two.

Please Help, I will give brainliest.

### Answers

**Step-by-step explanation:**

|x-1| + |x-2| = - 3 has no answer ...both quantities on the L are positive and cannot add to a negative

|x-1| + |x-2| = 3 Has answers **x = 0 or 3 **

For x a negative :

-x +1 + -x +2 = 3

-2x +3 = 3

-2x = 0

x = 0

For x a positive

x-1 + x-2 = 3

2x -3 = 3

2x = 6

x = 3

URGENT!! If the probability of getting heads from a coin is 1/2, what is the probability that if you flip the coin ten times it will be heads.

### Answers

**Answer:**

Based on the calculations we just did, you expect that if you toss a coin 10 times, it will land on heads 50% of the time.

**Answer:**

The probability of getting heads from a coin is 1/2. If you flip the coin ten times, the probability that it will be heads every time is (1/2)^10 = 1/1024.

However, if you are asking for the probability of getting at least one head in ten flips, then you can use the complement rule to find the probability of getting no heads and subtract it from 1. The probability of getting no heads in ten flips is (1/2)^10 = 1/1024, so the probability of getting at least one head is 1 - 1/1024 = 1023/1024, which is approximately 0.999.

a rectangular screen has a width of 2x 8. the length is 4x 1. what is the area of the entire screen?

### Answers

The area of the entire **screen **is [tex]8x^2 + 34x + 8[/tex] square units.

To find the **area **of the entire screen, you need to multiply its width by its length.

Width = 2x + 8

Length = 4x + 1

Area = Width × Length

Area = (2x + 8) × (4x + 1)

Now, we'll use the distributive property to **multiply **these expressions:

Area = 2x * 4x + 2x * 1 + 8 * 4x + 8 * 1

Area = 8x^2 + 2x + 32x + 8

Now, we'll **combine **the like terms:

[tex]Area = 8x^2 + 34x + 8[/tex]

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Find the angle 0 in the given right triangle where a =5 and b =12. (Round your answer to the one decimal place.)

### Answers

**Answer:**

**Step-by-step explanation:**

Find the sin - ratio of the opposite side to the hypotenuse.

a/b = 5/12 = .41666

The ratio of .41666 is corresponds to an angle of 24.6

Five people who were convicted of speeding were ordered by the court to attend a workshop. A special device put into their cars kept records of their speeds for two weeks before and after the workshop. The maximum speeds for each person during the two weeks before and two weeks after are given below. In Parts A and B, we will do a t-test for dependent means to determine if we should conclude that people change their speeds after the workshop. We will do a two-tailed test with significance level.05 Participant Before After Difference Difference-M (Difference -(After-Before) M)^2 1 65 582 62 65 3 60 564 70 665 68 60 SUM 0 Part A. By hand, use the five steps of hypothesis testing and see if the data support your hypothesis. - Restate the question as a research hypothesis and a null hypothesis about the populations. - Determinethe characteristics of the comparison distribution.- Determine the cutoff sample score (or critical value) on the comparison distribution at which the null hypothesis should be rejected- Determine your sample's score on the comparison distribution- Decide whether to reject the null hypothesis

### Answers

Reject the null** hypothesis **

**How to find comparison distribution?**

The comparison distribution is a **t-distribution** with four degrees of freedom (df = n-1 = 5-1 = 4). Our significance level is .05, and we will be conducting a two-tailed test.

Using a t-table with four degrees of freedom and a significance level of .05, the critical values for a two-tailed test are ±2.776.

t = (Mdiff - 0) / (SDdiff / sqrt(n))

Where Mdiff is the **mean difference** in speeds before and after the workshop, SDdiff is the standard deviation of the differences, and n is the number of pairs of scores.

Mdiff = 65 - 582 + 60 - 564 + 70 - 665 + 68 - 60 + 62 = -199

SDdiff = sqrt([(-65+582)^2 + (-60+564)^2 + (-70+665)^2 + (-68+60)^2 + (-62+65)^2] / (n-1)) = 29.17

n = 5

t = (-199 - 0) / (29.17 / sqrt(5)) = -4.02

The calculated t-statistic (-4.02) is less than the critical value (-2.776) at a significance level of .05, and it falls in the rejection region of the t-distribution. Therefore, we can reject the **null hypothesis** and conclude that the workshop has a significant effect on the speeds of the five convicted speeders.

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1) Name the independent variable. Y= 12x + 25 *

10 points

### Answers

The **independent variable** is "x". In the equation Y = 12x + 25, x is the independent variable.

An independent variable is a variable that is changed or controlled in a **scientific experiment** or statistical analysis to see its effect on the dependent variable. In this case, Y is the **dependent variable**, which means it is affected by changes in the independent variable x. The equation is a linear equation in slope-intercept form, where 12 is the slope or rate of change, and 25 is the **y-intercept** or the value of Y when x equals zero. The equation can be used to determine the value of Y for any given value of x.

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The volume of a sphere is 2,240 cubic yards. What will be the new volume if the dimensions are multiplied by 1/4?

### Answers

The new volume of the sphere after multiplying its dimensions by 1/4 is 140 cubic yards, which is 1/16 of the original **volume**.

The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. If the dimensions of the sphere are multiplied by 1/4, the new **radius **will be 1/4 of the original radius. Therefore, the new volume can be found by:

V' = (4/3)π(1/4r)³

= (4/3)π(1/64)r³

= (1/16)(4/3)πr³

= (1/16)V

where V is the original volume.

So, the new volume will be 1/16 of the original volume:

V' = (1/16)(2,240 cubic yards)

= 140 cubic yards

Therefore, the new volume will be 140 **cubic yards**.

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How to find the value of a numerical or algebraic expression?

### Answers

The value of a **numerical** or **algebraic expression** can be determined by substitution, i.e. replacing the variables with their numerical values and performing the necessary operations. For example, if you are asked to find the value of the expression 3x + 5, where x = 4, you would substitute the value of x in the expression to get 3(4) + 5 = 17. This is the **value of the expression**.

To solve more complicated expressions, it may be necessary to use **algebraic manipulation **and the use of the order of operations to calculate the expression. For example, if the expression is 2(x + 7) + 3x, you would need to use the order of operations to solve this expression. You would first add 7 and x (2x + 7) and then multiply that result by 2 (2(2x + 7)) and add 3x to it (2(2x + 7) + 3x). Substituting x = 4, the expression would become 2(2(4) + 7) + 3(4) = 32 + 12 = 44. This is the value of the expression.

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Two of the early bandleaders who are credited for expanding small jazz groups into large band configurations were Paul Whiteman and Fletcher Henderson. True or False

### Answers

True. Paul Whiteman and Fletcher Henderson were both important figures in the development of **jazz music** in the early 20th century.

Paul Whiteman was a **violinist** and bandleader who became known as the "King of Jazz" for his popularization of jazz music to a wider audience through his large dance bands and **radio broadcasts**. Fletcher Henderson, on the other hand, was a pianist, arranger, and **bandleader** who is considered one of the most important early jazz arrangers, and was instrumental in the development of the big band format, which became the dominant form of jazz in the 1930s and 1940s. Both Whiteman and Henderson were influential in expanding the role of jazz in American popular music and in paving the way for the big band era.

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Find the area, and round your final answer to rhe nearest tenth of a square foot.

### Answers

The **area** of the **shape** is 59.1 ft² ( nearest tenth)

What is area of shape?

The **area** of shape is the space enclosed within the perimeter or the boundary of a given shape. The shape consist of a parallelogram and a rectangle.

For us to get the **area** of the **shape** , we calculate the **area** of parallelogram and add it to the area of the rectangle.

**Area** of parallelogram = b×h

height of the parallelogram is calculated as;

sin60 = h/4

√3/2 = h/4

4√3 = 2h

h = 4√3/2 = 2√3 ft

**Area** = 5.5 × 2√3

= 11√3 ft² = 19.1ft²

**Area** of rectangle = l×w

width of the rectangle is calculated as;

cos60 = w/4

1/2 = w/4

2w = 4

w = 4/2 = 2

Area = 2 × 20 = 40ft²

**Area** of the **shape** = 40+ 19.1

= 59.1ft²

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7(y + 2) = 84

what does y = ?

### Answers

**Answer:**

y= 10

**Step-by-step explanation:**

hope this helps !

or an ideal 2-winding transformer, an impedance z2 connected across winding 2 (secondary) is referred to winding 1 (primary) by multiplying z2 by

### Answers

For an ideal 2-winding** transformer**, an impedance z2 connected across winding 2 (secondary) is referred to winding 1 (primary) by multiplying z2 by the square of the turns ratio of the transformer. This is because the voltage at each winding is directly **proportional** to the number of turns in the winding.

A transformer is an **electrical **device that transforms electrical energy from one circuit to another by means of magnetic coupling without a direct electrical connection.

It changes the AC** voltage **level of an electric power supply to another voltage level in order to suit the demands of a load circuit.

The turns **ratio** of a transformer is given by the ratio of the number of turns in the primary winding to the number of turns in the secondary winding. It is represented by k. The ratio of the primary **winding **voltage to the secondary winding voltage is k, which is the turns ratio of a transformer.

The ratio of the primary current to the** secondary current **is inversely proportional to the turns ratio, which is k in this case. Because the number of turns on each winding is proportional to the voltage induced in it, the voltage in each winding is proportional to the number of turns in it.

When an AC voltage is applied to the primary winding of a transformer, a corresponding AC voltage is induced in the secondary winding. Because the windings are **inductively **coupled, the voltage in the secondary winding is proportional to the voltage in the primary winding.

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Suppose you have intercepted a ciphertext message and when you determine the frequencies of letters in this message, you find the frequencies are similar to the frequency of letters in English text. Which type of cipher do you suspect was used?

### Answers

The **type of cipher** that is suspected to have been used is a substitution cipher.

If the **frequency of letters **in the ciphertext message is similar to the frequency of letters in English text, then it indicates that the encryption was likely a substitution cipher, where each letter in the original message is replaced with another letter or symbol.

This is because substitution ciphers maintain the frequency distribution of letters in the plaintext, making it a relatively weak form of encryption that can be broken with frequency analysis.

On the other hand, **ciphers **such as transposition and stream ciphers do not preserve the frequency distribution of letters, so if the frequencies of letters in the ciphertext message were different than that of English text, then it could be indicative of one of these other types of ciphers.

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find the volume 10km 7km 6km

### Answers

**Answer:**

420km^3

**Step-by-step explanation:**

10×7×6=420km^3

a product's demand in each period follows a normal distribution with mean of 60 and standard deviation of 10. the order-up-to level is 200 and the lead time is 2 periods. what is the expected on-order inventory? (round to the nearest integer)

### Answers

The expected** on-order inventory **is approximately 80 units (rounded to the nearest integer).

1. **Determine **the average demand during the lead time:

Since the mean** demand** per period is 60 and the lead time is 2 periods, the average demand during the lead time is

60 × 2 = 120 units.

2. Determine the standard deviation of the demand during the lead time:

As the demand follows a normal distribution with a standard deviation of 10 per period, the standard deviation during

the lead time (2 periods) is** calculated** as sqrt(2) × 10 ≈ 14.14 units.

3. Calculate the expected on-order inventory:

**Subtract** the average demand during the lead time from the order-up-to level. In this case, it's 200 (order-up-to level) -

120 (average demand during lead time) = 80 units.

So, the expected on-order inventory is **approximately **80 units (rounded to the nearest integer).

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Find the FACTORS FOR: 6.25

### Answers

**Answer: Factors are used with whole numbers, not decimals.**

1 pound. Of apples for 2. 15or 3 pounds of apples for 5. 76 which one has the better deal

### Answers

The cost per p**ound** is less in the first one. Hence **price** -wise, the first deal is better.

The **pound** or pound-mass is the unit of mass used in common British, Imperial and American measurement systems. Various definitions are used; the most common today is the international pound, legally defined as 0.45359237 kilograms, divided into 16 pound ounces. The international standard symbol for the avoirdupois pound is lb; another symbol is lbm.

The kilogram is a unit of mass in the International System of Units (SI) with the unit symbol kg. It is a unit of measurement widely used in science, engineering, and business around the world and is often abbreviated colloquially as **kilogram**. It means "kilogram".

kilograms are defined in terms of seconds and meters, both based on fundamental physical constants. This allows properly equipped metrology laboratories to calibrate mass-measuring instruments, such as Kibble balances, as the primary standard for determining exact masses in kilograms.

Given that:

1 pound of apples = 2.15

3 **Pound** of apple = 5.76.

From this we can say that the 3 pound of apple is a better deal than the first one.

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A net of a rectangular prism with dimensions 4 and one-half centimeters by 3 centimeters by 8 and one-half centimeters.

What is the surface area of the prism?

### Answers

The **surface area **of the **rectangular prism** is 138 square centimeters.

What is rectangular prism?

A rectangular prism is a three-dimensional solid form with six rectangular sides that is used in **geometry**. The term "rectangular parallelepiped" is another name for it. The **length**, breadth, and height of a rectangular prism are all **perpendicular** to one another. The total of a rectangular prism's six rectangular sides makes up its surface area.

The surface area of the net of a rectangular prism can be determined by individual areas of the shape.

Thus,

Area of each top/bottom face = (4.5 cm) x (3 cm) = 13.5 sq. cm.

Area of each front/back face = (4.5 cm) x (8.5 cm) = 38.25 sq. cm

Area of each left/right face = (3 cm) x (8.5 cm) = 25.5 sq. cm

Total surface area is:

Surface area = (2 x 13.5) + (2 x 38.25) + (2 x 25.5) = 138 sq. cm

Hence, the surface area of the rectangular prism is 138 square centimeters.

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find the minimum value of n that guarantees an error of no more than 1/30,000 in approximating J4 3 1/x dx, by the trapezoidal rule with n equal subintervals.n =

### Answers

To find the **minimum **value of n that guarantees an error of no more than 1/30,000 in approximating J4 3 1/x dx, by the **trapezoidal** rule with n equal subintervals, we need to use the formula for the error of the trapezoidal rule. This formula is given by:

Error = -(h^3)/(12*n^2)*f''(c),

where c is any point within the interval [a,b], h is the length of each subinterval, and n is the number of subintervals.

We can rearrange this formula to get n = sqrt((-12*Error)/(h^3*f''(c))).

Substituting the given values, we get n = sqrt((-12*(1/30000))/(4^3*(12))),

Therefore, n = 7.07.

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harry has $2.25 in nickels, dimes, and quarters. if he had twice as many nickels, half as many dimes, and the same number of quarters, he would have $2.50. if he has 27 coins altogether, then how many of each does he have?

### Answers

**Answer:**

**Step-by-step explanation:**

Then you will subtract:

The answer is $25:00

Compute the standard deviation of the random variable with the given discrete probability distribution. x P(x) 5 0.4 15 0.25 20 0.15 35 0.2 a. 15.75b. 18.75c. 123.2 d. 11.1

### Answers

The answer is the **standard deviation** of the random variable with the given discrete** **probability distribution is approximately 11.1 (Option d).

To compute the standard deviation of the random variable with the given discrete **probability distribution**, follow these steps:

Computing the mean (μ) of the random variable,

Mean (μ) = Σ[x * P(x)]

μ = (5 * 0.4) + (15 * 0.25) + (20 * 0.15) + (35 * 0.2)

μ = 2 + 3.75 + 3 + 7

μ = 15.75

Computing the **variance** (σ²) of the random variable,

Variance (σ²) = Σ[(x - μ)² * P(x)]

σ² = [(5 - 15.75)² * 0.4] + [(15 - 15.75)² * 0.25] + [(20 - 15.75)² * 0.15] + [(35 - 15.75)² * 0.2]

σ² = (10.75² * 0.4) + (-0.75² * 0.25) + (4.25² * 0.15) + (19.25² * 0.2)

σ² = 46.00625 + 0.140625 + 2.70625 + 74.30625

σ² = 123.159375

Computing the **standard deviation** (σ) of the random variable,

Standard deviation (σ) = √(Variance)

σ = √(123.159375)

σ ≈ 11.1

Therefore, the standard deviation of the random variable with the given discrete probability distribution is approximately 11.1 (Option d).

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URGENTT!! Will give brainiest if right

The scatterplot shows the heights and arm spans of 12 girls on a basketball

team. The line of best fit for the scatterplot is y = x+ 2. What is the predicted

arm span for a girl who is 66 inches tall?

A. 67 inches

B. 64 inches

C.69 inches

D. 68 inches

### Answers

**Answer:**

d

**Step-by-step explanation:**

the answer is d 68 inches because when you look at the height in the x axis you find 66 and then you go up to where the predicted line and it follows to the y axis at 68

HELP DUE TONIGHT!!! HELPP, THANKSSS

### Answers

**Answer:**

[tex]a^{5}[/tex]

**Step-by-step explanation:**

A three-heap with n elements can be stored in an array A, where A[0] contains the root of the tree.

a) Draw the three-heap that results from inserting 5, 2, 8, 3, 6, 4, 9, 7, 1 in that order into an initially empty three-heap. You do not need to show the array representation of the heap. You are only required to show the final tree, although if you draw intermediate trees.

b) Assuming that elements are placed in the array starting at location A[0], give expressions to calculate the left, middle, and right children of the element stored in A[i]: Left child: Middle child: Right child:

c) Draw the array representation of your heap from part b.

d) Removing Arbitrary Items From Heaps One way to remove an object from a binary min heap is to decrease its priority value by 1 and then call deleteMin. An alternative is to remove it from the heap, thus creating a hole, and then repair the heap.

e) Write pseudocode for an algorithm that performs the remove operation using the alternative approach described above. Your pseudocode should implement the method call remove (int index), where index is the index into the heap array for the object to be removed. Your pseudocode can call the following methods described in lecture: insert, deleteMin, percolateUp, and percolateDown. Like in lecture, you may assume that objects are just priority integers (no other data).

f) What is the worst case complexity of the algorithm you wrote in part (a)?

### Answers

The remove algorithm starts by replacing the element to be removed with the last element in the three-heap, which takes constant time. The percolateDown operation to restore the **heap** order has a worst-case complexity of O(log n), since it may need to swap the element with its children several times to find the correct position

The three-heap that results from inserting 5, 2, 8, 3, 6, 4, 9, 7, 1 in that order into an initially empty three-heap is as follows:

1

/ | \

2 3 4

/ | \ / | \ / \

5 6 7 8 9 - - -

b) Assuming that **elements** are placed in the array starting at location A[0], the expressions to calculate the left, middle, and right children of the element stored in A[i] are:

Left child: A[3i - 2]

Middle child: A[3i - 1]

Right child: A[3i]

c) The array representation of the heap is:

1 2 3 4 5 6 7 8 9

[ 1 2 3 4 5 6 7 8 9 ]

d) **Pseudocode** for an algorithm that performs the remove operation using the alternative approach described above:

remove(int index):

A[index] = A[n-1]

n = n - 1

percolateDown(index)

percolateUp(index)

e) The worst case **complexity** of the remove algorithm is O(log n), where n is the number of elements in the heap.

Therefore, the remove **algorithm** starts by replacing the element to be removed with the last element in the heap, which takes constant time. The percolateDown operation to restore the heap order has a worst-case complexity of O(log n), since it may need to swap the element with its children several times to find the correct position. Similarly, the percolateUp operation to maintain the heap order after the removal also has a worst-case complexity of O(log n), since it may need to swap the element with its parent several times. Hence, the total worst-case complexity of the remove operation is O(log n).

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The total time, measured in units of 100 hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable X that has the density function below. Use the theorem below to evaluate the mean of the random variable Y = 51X2 + 40X, where Y is equal to the number of kilowatt hours expended annually Theorem: The expected value of the sum or difference of two or more functions of a random variable X is the sum or difference of the expected values of the functions, as given by the formula below 0, elsewhere

### Answers

**Answer:**

The mean of the random variable Y is (17/2) kilowatt hours.

**Step-by-step explanation:**

To find the expected value of Y, we can use the formula provided in the theorem:

E(Y) = E(51X^2 + 40X)

Using linearity of expectation, we can break this down into two separate expected values:

E(Y) = 51E(X^2) + 40E(X)

The given probability density function is, f(x) = (1/4)x, 0 ≤ x ≤ 2.

The expected value of a continuous **random variable** is calculated using the formula shown below, where E(x) is the expected value of x, and f(x) is the probability density function of x.

E(x) = ∫xf(x)dx

The expected value of the random variable X can be calculated as follows:

E(X) = ∫0² (1/4)x dx = (1/8) [x²]₀² = 1

E(X²) = ∫0² (1/4)x² dx = (1/12) [x³]₀² = (1/6)

Now we can substitute these values into our original equation:

E(Y) = E(51X² + 40X) = 51E(X²) + 40E(X) = 51(1/6) + 40(1) = (17/2) kilowatt hours.

Therefore, the** mean of the random variable** Y is (17/2) kilowatt hours.

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A. Write a part-to-part ratio that compares the number of squares to triangles.

B. Use ratio language to describe this ratio relationship.

### Answers

if there are 6 **squares** and 9 **triangles**, the ratio of squares to triangles would be 6:9 or simplified as 2:3. This means that for every 2 squares, there are 3 triangles.

A part-to-part ratio that compares the number of squares to triangles could be:

Number of squares : Number of triangles

We can use ratio **language** to describe this ratio relationship as "the ratio of the number of squares to the number of **triangles**." This means that we are comparing the quantity of squares to the quantity of triangles, and expressing this comparison in the form of a ratio. For example, if there are 6 squares and 9 triangles, the **ratio** of **squares** to triangles would be 6:9 or simplified as 2:3. This means that for every 2 squares, there are 3 triangles.

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URGENT!! if you roll a dice 50 times, and the probability to get 5 is 1/6 times, what is the probability that every single dice roll is a 5?

### Answers

**Answer: 1.237193076x10^-39 or 0.000000000000000000000000000000000000001237193076**

**Step-by-step explanation: **

**our favorable or desired outcome of getting 5 when dice is rolled 50 times is 1. **

**Number of possible outcomes is 6^50 which is 8.082812775 x 10^38**

**so now to get probability of getting 5 50 times is **

**P (probability)= Fav.Outcomes / TotalOutcomes**

**P= 1 / 8.082812775 x 10^38P= 1.237193076x10^-39**

**Hence, probability of getting 5 50 times is 1.237193076x10^-39 OR 0.000000000000000000000000000000000000001237193076**

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**Answer:**

The probability of getting a 5 on a single roll of a fair six-sided die is 1/6. To find the probability of rolling a 5 on all 50 rolls, we need to multiply the probability of rolling a 5 on each roll together. This is known as the multiplication rule of probability.

The probability of rolling a 5 on the first roll is 1/6. The probability of rolling a 5 on the second roll, assuming that the first roll was also a 5, is also 1/6. Similarly, the probability of rolling a 5 on the third roll, assuming that the first two rolls were also 5s, is also 1/6. We can continue this pattern for all 50 rolls.

Using the multiplication rule of probability, we can find the probability of rolling a 5 on all 50 rolls by multiplying the probabilities of rolling a 5 on each individual roll together:

(1/6) * (1/6) * (1/6) * ... * (1/6)

This can be simplified using exponentiation:

(1/6)^50

Evaluating this expression gives us approximately:

8.8817842 × 10^-40

This means that the probability of rolling a 5 on all 50 rolls is incredibly small - less than one in a trillion trillion trillion trillion trillion.

13. Find the volume of a cone whose diameter is 10' and altitude 8' to the nearest tenth

of a cu. ft.

### Answers

**Step-by-step explanation:**

r, radius = 1/2 diameter = 5 feet

volume of a cone = 1/3 pi r^2 h = 1/3 pi (5^2)(8) = **209.4 ft^3 **