Find the lateral area of the regular pyramid.

L. A. =

Answer:

 coefficient of x²  

Step-by-step explanation:

Co-efficient of x² says if the parabola is open upward or downward.

If the coefficient of x² is positive, the parabola is open upward.

If the coefficient of x² is negative, the parabola is open downward.

Roland made 16 sales this week, while Vickie made 8 more sales than Roland.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the number of sales Roland has.

Roland earns a base of $49 plus $15 per sale. HenceL

Total earning by Roland = 15x + 49

Vickie made 8 more sales than Roland. Vickie earns a base of $145 plus $6 per sale.

Total earning by Vickie = 6(x + 8) + 145 = 6x + 193

Roland and Vickie are salespeople who earned the same amount this week, Therefore:

15x + 49 = 6x + 193

9x = 144

x = 16

Roland made 16 sales this week.

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The correct answer is A) smaller than.

The statement refers to the concept of the Central Limit Theorem (CLT). According to the CLT, when random samples are drawn from a population, the distribution of sample means will tend to follow a normal distribution, regardless of the shape of the population distribution, given that the sample size is sufficiently large. This means that as the number of samples increases, the variability of the distribution of sample means will decrease.

In this case, drawing 1,000 samples of size 100 from a population and computing the mean of each sample implies that we have a large number of sample means. Due to the CLT, the distribution of these sample means will have less variability (smaller standard deviation) compared to the variability of the raw scores in any one sample. Thus, the variability of the distribution of sample means will tend to be smaller than the variability of the raw scores in any one sample.

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\((\stackrel{x_1}{30}~,~\stackrel{y_1}{450})\hspace{10em} \stackrel{slope}{m} ~=~ - 25 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{450}=\stackrel{m}{- 25}(x-\stackrel{x_1}{30}) \\\\\\ y-450=-25x+750\implies \boxed{y=-25x+1200} \\\\\\ \stackrel{\textit{if x = 20, what's "y"?}}{y=-25(20)+1200}\implies \boxed{y=200}\)

Answer:

30,246

Step-by-step explanation:

multiply the two numbers

Answer:

The correct answer is 1.75

Step-by-step explanation:

5 x 0.50 = 2.5

3 x 1.25 = 3.75

2 x 2.75 = 5.5

Then we want to add

2.5 + 3.75 + 5.5 = 11.75

Now, Subtract.

11.75 - 10.00 = 1.75

The total amount spent will be equal to $12, so the money added by Ralph will be equal to $2.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data given in the question,

The total money Ralph has is $10.

Price of each pencil = $0.50

Then, price of 5 pencil will be = 5 × 0.50 = $2.5

Price of each pen = $1.25

Then, the price of 3 pens will be = 3 × 1.25 = 3.75

Price of each notebook = $2.75

Then, the price of 2 notebooks will be = 2 × 2.75 = 5.5

Then, the total money spent by Ralph = 5.5 + 3.75 + 2.75 = 12

The money that he should have to add will be,

$12 - $10 = $2

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Let's solve the problem using the signed-rank test:

Step 1: The null hypothesis (H₀) is that the median waiting time is 20 minutes or less, and the alternative hypothesis (H₁) is that the median waiting time is more than 20 minutes.

Step 2: Calculate the differences between each observation and the hypothesized median of 20 minutes, and assign ranks to the absolute values of the differences:

Observation: 17 15 20 20 32 28 12 26 25 25 35 24

Difference: -3 -5 0 0 12 8 -8 6 5 5 15 4

Rank: 3 4 5 5 8 6 2 7 9 9 12 1

Step 3: Calculate the sum of positive ranks (W⁺) and the sum of negative ranks (W⁻):

W⁺ = 8 + 6 + 7 + 9 + 9 + 12 = 51

W⁻ = 3 + 4 + 5 + 5 + 8 + 2 = 27

Step 4: Determine the test statistic (T) as the smaller of W⁺ and W⁻:

T = min(W⁺, W⁻) = min(51, 27) = 27

Step 5: Find the critical value or calculate the p-value based on the significance level (0.05) and test statistic (T):

For a sample size of 12 and a significance level of 0.05, we can consult a signed-rank test table to find the critical value. In this case, the critical value is 8. Since T (27) is greater than the critical value (8), we reject the null hypothesis.

Step 6: Make a decision: We have sufficient evidence to conclude that the median waiting time for the patients is more than 20 minutes.

In summary, based on the signed-rank test, we reject the doctor's claim that the median waiting time for her patients is not more than 20 minutes before being admitted to the examination room.

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Answer:

100.48

Step-by-step explanation:

Multiply the radius by 2 to get the circumference. Then multiply by pie, 3.14

Answer:

100.48

Step-by-step explanation:

circumference=3.14 times 16 squared(which means you just do 16 times 16)

256 times 3.14 and you get 100.48

when the edges of the cube are doubled in length, the volume of the new cube is 8,000 cubic inches.

To find the volume of the new cube when the edges of the original cube are doubled in length, we'll first need to find the side length of the original cube using the surface area, and then calculate the volume of the new cube. Here are the steps:

1. The surface area of the original cube is given as 600 square inches. A cube has six faces, so we'll divide the surface area by 6 to find the area of one face: 600 / 6 = 100 square inches.

2. To find the side length of the original cube, we'll take the square root of the area of one face. In this case, the square root of 100 is 10 inches.

3. Now that we know the side length of the original cube (10 inches), we'll double it to find the side length of the new cube: 10 x 2 = 20 inches.

4. Finally, we'll calculate the volume of the new cube using the formula for the volume of a cube, \(V = (side)^3\). In this case, \(V = (20)^3 = 20 x 20 x 20 = 8,000 cubic inches\).

So, when the edges of the cube are doubled in length, the volume of the new cube is 8,000 cubic inches.

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Answer:

FP is 70 degrees 35 times 2 so PD is 180 half a turn minus 70 = 110 degrees

Step-by-step explanation:

The Answer of the given question based on the triangle is angle ∠α ≈ 56.4° degrees , angle ∠β ≈ 33.6° degrees , side C ≈ 14.4° units.

In a right triangle, the hypotenuse is the longest side and it is opposite the right angle. It is the side that is directly opposite the right angle and is always opposite the largest angle of the triangle. The hypotenuse is also the side that connects the two legs of the right triangle. The length of hypotenuse can be found using Pythagorean theorem.

From the problem statement, we know that angle ∠gamma = 90° degrees, which means that BC is the hypotenuse of the right triangle. We also know that side A = 12 and side B = 8.

Using Pythagorean Theorem, we can find length of  hypotenuse by:

c² = a² + b²

c² = 12² + 8²

c² = 144 + 64

c² = 208

c = √(208)

c ≈ 14.4

So the length of BC is approximately 14.4 units.

To find the altitude CA, we can use the formula for the area of a right triangle:

area = (1/2) * base * height

Since angle gamma = 90° degrees, the altitude CA is equal to the length of side A:

CA = A = 12 units.

Now we can use the trigonometric ratios to find the acute angles∠α and :

sin(α) = opposite/hypotenuse = CA/c

sin(α) = 12/14.4

α ≈ 56.4° degrees

Since α and gamma are complementary angles (they add up to 90° degrees), we can find β using the following formula:

β = 90 - α

β ≈ 33.6° degrees

Therefore, the unknown values for the given right triangle are:

angle ∠α ≈ 56.4° degrees

angle ∠β ≈ 33.6° degrees

side C ≈ 14.4° units.

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The group that would be the most stable based on size would be 10 people. So, the correct answer is c. 10 people.

A group is a set of people or objects that are deemed to be equivalent or share a common feature. Group members may collaborate and share knowledge to achieve a common goal. The group's performance is frequently greater than the sum of its members' individual efforts, and this is known as the group effect.

Group stability is defined as the ability of a group to remain together and keep working toward its objective over time. It is essential for a group to achieve its objectives and is typically linked to the group's size and objective. A stable group can withstand external pressures and is less susceptible to breaking up or being disbanded.

A group's size has a significant influence on its stability. Small groups are often more cohesive and productive than large groups. On the other hand, as a group's size grows, it becomes more challenging to sustain cohesion and productivity. A group of 10 people would be the most stable since it's not too large or too small. Thus, the correct option is c. 10 people.

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Answer:

B. product graph

Step-by-step explanation:

Hope it helps

CarryOnLearning

Answer:

The program in Python is as follows:

age = int(input("Age: "))

if age>=13 and age <=19:

   print("Teenager")

else:

   print("Not a teenager")

Step-by-step explanation:

This gets input for age

age = int(input("Age: "))

This checks if age is between 13 and 19 (inclusive)

if age>=13 and age <=19:

If yes, the age is teenage

   print("Teenager")

If otherwise, the age is not teenage

else:

   print("Not a teenager")

The probability that the mean GPA of a random sample of 20 students selected from this university  is 3.10 or higher is 10.93%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Problems of normally distributed samples are solved using the z-score methods.

We know that, in a set with mean and standard deviation , the z-score of a measure X is given by:

                              Z = X - μ/σ

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 p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard deviation .

For a Skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

μ = 3.02 , σ = 0.29 , n = 20 and s = 0.29/√ 20 = 0.0648

Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.

This is 1 subtracted by the p- value of Z when X = 3.10. So

By the Central Limit Theorem:

             Z = X - μ / s

       ⇒  Z = 3.1 - 3.02/ 0.0648

       ⇒ Z = 1.23

The Z = 1.23 has a P- value of 0.8907

∴ 1 - 0.8907 = 0.1093

Now, for  getting the percentage,

0.1093 × 100% = 10.93%

10.93% probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.

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The investment with the bigger return is investment B.

Simple interest rate is the interest that is paid only on the principal portion of a loan. This means that the debtor does not pays interest on the interest rate already accrued. This differs from compound interest where the debt holder pays interest on the principal and the interest rate already accrued

The formula for calculating future value:

FV = P (1 + r)^n

2000 x (1.06)^12 = $4024.39

Compound interest =  $4024.39 - $2000 =  $2024.39

Simple interest = principal x time x interest rate

2000 x 0.08 x 12 = $1920

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Answer:

as far as he wants. is he walking the diameter, to the store, across the field?

if it is across the field, then about 255 ft

Step-by-step explanation:

Bob will walk for 2512 feet.

The circumference of a circle is basically the perimeter of the circle.

Given that, the stadium has a diameter of 800 ft,

Bob will walk on the perimeter of the stadium, therefore,

circumference = π*diameter

= 800*3.14 = 2512

Hence, Bob will walk for 2512 feet.

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Answer:

Step-by-step explanation:

A bitmap is a digital image format that is made up of a grid of square colored dots called pixels.

Each pixel in the bitmap contains information about its color and position, which allows the computer to display the image on a screen or print it on paper. Bitmaps are commonly used for photographs, illustrations, and other complex images that require a high degree of detail and color accuracy.

However, because bitmaps store information for each individual pixel, they can be memory-intensive and may result in large file sizes. Additionally, resizing a bitmap can lead to a loss of quality, as the computer must either interpolate or discard pixels to adjust the image size.

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Answer:

Y=36

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

y/3 - 2 = 10

y/3=10+2

y/3=12

y=12×3

y=36

S + R represents the total trips done by these trucks.

Volume is defined as the amount of space occupied by an object that is bound by a boundary. It must be noted that the volume is a mathematical term that is only applicable to 3D (three-dimensional) objects or spaces. As such, the units commonly used for volume are cubic units, that is, m3, cm3, in3, etc.

Two dump trucks hauling rock to a construction site is given by the expression. xS + yR

S +R

Truck 1 can haul x cubic yards

Truck 2 can haul y cubic yards.

Truck 1 makes P trips to the construction site, while truck 2 makes R trips.

Hence the trips made by truck 1 and truck 2 should be the addition of the trips made by the trucks individually.

So the total trips is represented by S + R

Therefore, S + R represents the total trips done by these trucks.

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a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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The simplified form of (√y+√2)(√y - 7√2) is y - 5√2y - 14. Simplifying in mathematics refers to the process of reducing or transforming an expression, equation, or mathematical object into a more concise or manageable form without changing its essential meaning or value.

The goal of simplification is to make mathematical expressions easier to understand, manipulate, and work with.

In various mathematical contexts, simplifying involves applying mathematical rules, properties, and operations to eliminate redundancies, combine like terms, reduce fractions, factorize, cancel out common factors, or rewrite expressions using equivalent forms. By simplifying, we can often reveal underlying patterns, highlight important relationships, and facilitate further analysis or computation.

To simplify the given expression (√y+√2)(√y - 7√2), we can use the distributive property of multiplication over addition.

Expanding the expression, we multiply each term in the first parentheses by each term in the second parentheses:

(√y + √2)(√y - 7√2) = √y * √y + √y * (-7√2) + √2 * √y + √2 * (-7√2)

Simplifying each term, we have:

√y * √y = y

√y * (-7√2) = -7√2y

√2 * √y = √2y

√2 * (-7√2) = -14

Combining the terms, we get:

y - 7√2y + √2y - 14

Simplifying further, we can combine like terms:

y - 5√2y - 14

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Question:

Marshall models the data with the equation y = −1.5x + 121, where x represents the number of minutes spent watching television and y represents the number of minutes spent exercising.

A certain student watches television for an average of 38 minutes per night. Based on Marshall's model equation, how many minutes will that student spend exercising?

 Answer:

The student will exercise for 64 minutes

Step-by-step explanation:

Given

\(y = -1.5x + 121\)

x = minutes of TV

y = minutes on exercising

Required

Find y when x = 38

\(y = -1.5x + 121\)

Substitute 38 for x

\(y = -1.5 * 38 + 121\)

\(y = -57 + 121\)

\(y = 64\)

For the first expression: b - (d-c) = 5

For the second expression: b - (c-d) = 15

For the first expression, we are given the values of four variables:

a=4, b=3, c=-1, and d=-3.

We are asked to evaluate the expression b² - (d-c)² using these values.

To do this, we first need to substitute the given values into the expression:

b² - (d-c)² = 3² - (-3-(-1))²

Next, we need to simplify what's inside the parentheses:

-3 - (-1) = -3 + 1 = -2

So we can further simplify the expression to:

b² - (d-c)² = 3²  - (-2)²

Now we can evaluate the squared term:

(-2)²  = 4

So we have:

b²  - (d-c)²  = 3²  - 4

Finally, we evaluate the remaining expression:

3² - 4 = 9 - 4 = 5

Therefore, when a=4, b=3, c=-1, and d=-3,

The value of the expression b²  - (d-c)²  is 5.

For the second expression, we follow the same steps.

We are given the values of four variables: a=2, b=4, c=-3, and d=-4.

We are asked to evaluate the expression b²  - (c-d)²  using these values.

First, we substitute the given values into the expression:

b²  - (c-d)²  = 4²  - (-3-(-4))²

Next, we simplify what's inside the parentheses:

-3 - (-4) = -3 + 4 = 1

So we can further simplify the expression to:

b²  - (c-d)²  = 4² - 1²

Now we evaluate the squared term:

1²  = 1

So we have:

b²  - (c-d)²  = 4²  - 1

Finally, we evaluate the remaining expression:

4 - 1 = 16 - 1 = 15

Therefore, when a=2, b=4, c=-3, and d=-4,

The value of the expression b²  - (c-d)²  is 15.

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Answer:

\( - \frac{2}{9} \div 3 \frac{1}{4} \\ \\ \dashrightarrow \: - \frac{ 2}{9} \div \frac{13}{4} \\ \\ this \: can \: also \: \: be \: written \: as \: \\ \dashrightarrow \: - \frac{2}{9} \times \frac{4}{13} \\ \\ \dashrightarrow \: \boxed{ \: - \frac{8}{117} }\)

hope helpful! :)

Answer:

-8/117

Step-by-step explanation:

\(\frac{-2}{9} /3\frac{1}{4} \\\\\)

-first simplify 3 1/4

-simply multiply 4 by 3 and add 1. This is how you convert mixed fractions to whole fractions. Multipy denominator by whole number and add the numerator. The denominator stays the same so this will become

=13/4

- next because you're dividing two fractions, it is easier to take reciprocal of the denominator. You flip the fraction and change the sign. So instead of dividing by 13/4, you multiply by 4/13

- lets move the negative fraction (-2/9) to rigth hand side to make things easier to visualize. so our expressions right now will be:

=\(\frac{4}{13} *\frac{-2}{9}\)

-now multiply like normal

= -8/117

Answer:

Step-by-step explanation:

116