Exponents are a mathematical notation used to represent repeated multiplication and are a fundamental tool in various fields. The values of [tex]16^2[/tex] and [tex]12^2[/tex] are [tex]16^2[/tex] = 16 x 16 = 256, [tex]12^2[/tex] = 12 x 12 = 144
To rewrite each exponent as a single number, we can evaluate them using multiplication. For example, [tex]16^2[/tex] can be rewritten as 16 x 16, which equals 256. Similarly, [tex]12^2[/tex] can be rewritten as 12 x 12, which equals 144.
The exponent is a small number written above the base, which indicates the number of times the base should be multiplied by itself.
For example, the exponent 3 written above the base 2 means that we should multiply 2 by itself three times: 2 x 2 x 2 = 8. So, [tex]2^3[/tex] is equal to 8.
So, the values of [tex]16^2[/tex] and [tex]12^2[/tex] are:
[tex]16^2[/tex] = 16 x 16 = 256
[tex]12^2[/tex] = 12 x 12 = 144
By evaluating the exponents as single numbers, we can simplify the expressions they appear in and make them easier to work with.
They are used to represent large and small numbers in a compact form, and they simplify calculations by allowing us to perform repeated multiplication more efficiently.
To learn more about exponent please click on below link
https://brainly.com/question/219134
#SPJ1
i need help please Belle is hanging streamers for her brother's surprise birthday party. She secures two streamers of different lengths at the peak of the ceiling. The center of the floor is directly underneath the ceiling peak. The distance along the floor from the center of the room to where the first streamer is attached is 6 feet. The second streamer is attached to the floor further from the center of the floor than the first streamer.
we don't have enough information to determine the exact lengths of the streamers or the distance from the center of the floor to where the second streamer is attached.
Sure, I'd be happy to help! Based on the information you provided, we know that Belle is hanging two streamers of different lengths at the peak of the ceiling for her brother's surprise birthday party. The center of the floor is directly underneath the ceiling peak.
We also know that the distance along the floor from the center of the room to where the first streamer is attached is 6 feet.
Since the second streamer is attached to the floor further from the center of the floor than the first streamer, we can infer that the second streamer is longer than the first streamer.
I hope this helps! Let me know if you have any other questions.
To learn more about : lengths
https://brainly.com/question/28322552
#SPJ11
A home has a rectangular kitchen. if listed as ordered pairs, the corners of the kitchen are (8, 4), (−3, 4), (8, −8), and (−3, −8). what is the area of the kitchen in square feet? 20 ft2 46 ft2 132 ft2 144 ft2
The area of the kitchen in square feet is 132[tex]ft^{2}[/tex]
To find the area of the rectangular kitchen, we need to multiply the length by the width.
The length of the kitchen can be found by subtracting the x-coordinates of the two points on the same vertical side. So, the length is 8 - (-3) = 11 feet.
The width of the kitchen can be found by subtracting the y-coordinates of the two points on the same horizontal side. So, the width is 4 - (-8) = 12 feet.
Therefore, the area of the kitchen is:
Area = Length x Width = 11 ft x 12 ft = 132 square feet
So the answer is 132[tex]ft^{2}[/tex].
To learn more about area:
https://brainly.com/question/27683633
#SPJ4
lx-4l=1
Please help its for school!
Answer:
3 and 5
Step-by-step explanation:
|x-4| = 1 is the same as x-4 = 1 and -x+4 = 1
x-4=1
x = 5
-x+4 = 1
-x = -3
x = 3
adam, benin, chiang, deshawn, esther, and fiona have internet accounts. some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. each of them has the same number of internet friends. in how many different ways can this happen? (2012amc10a problem 23 or 2012amc12a problem 19)
Option A, For the aptitude puzzle, the number of ways each of people has the same number of internet friends is 60.
We want to count the number of ways that the 6 people can be internet friends with each other given that each person has the same number of internet friends and no one has an internet friend outside of the group.
Let k be the number of internet friends each person has. Since each person knows 5 other people in the group, we have 6k = 5 * 6, which means that k=5.
Thus, each person has 5 internet friends. We can choose these 5 friends in 5 to choose 5 times 4 choose 5 times 3 choose 5 times 2 choose 5 times 1 choose 5 = 1 × 0 × 0 × 0 × 0 = 0 ways since we can't choose 5 friends from fewer than 5 people.
Therefore, the answer is (A) 60.
Learn more about the aptitude puzzle at
https://brainly.com/question/2753472
#SPJ4
The question is -
Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen?
a. 60
b. 170
c. 290
d. 320
e. 660
helpp i need the surface area , hard to see the numbers but they are 18 and 15
Answer:
Step-by-step explanation:
Easy...
a=.5bh
so, .5*18*15= 135 in^2.
It looks like it has about four triangular sides, so just multiply that number four times.
135*4= 540
add the base
a=lw
=15*15
=225
540+225= 765 in^2
Let's hope. A better photo next time would definitely help....;)
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
Based on both the mean and median values, we can conclude that Wide Awake typically sells more coffee per hour than Coffee Ground.
What are the mean and median?
The mean and median are two measures of central tendency that can be used to describe a set of data. The median is the middle value in the data set when the values are arranged in order from lowest to highest. If there are an even number of values, the median is the average of the two middle values.
To determine which coffee shop typically sells the most amount of coffee per hour, we need to compare the measures of center (mean and median) of the data for each shop.
Calculating the mean of each dataset, we get:
Mean of Coffee Ground = (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5) / 12 = 6.5/2 = 5.42 gallons
Mean of Wide Awake = (2.5+10+4+18+4+3+6+5+2.5) / 9 = 56 / 9 = 6.22 gallons
Calculating the median of each dataset, we get:
Median of Coffee Ground = 4.25 gallons
Median of Wide Awake = 4.5 gallons
Comparing the measures of the center, we see that the mean value of coffee sold per hour at Coffee Ground is approximately 5.42 gallons, while the mean value of coffee sold per hour at Wide Awake is approximately 6.22 gallons.
Therefore, on average, Wide Awake sells more coffee per hour than Coffee Ground.
However, we also see that the median value of coffee sold per hour at Wide Awake is 4.5 gallons, while the median value of coffee sold per hour at Coffee Ground is 4.25 gallons.
This suggests that the middle value of coffee sold per hour is higher for Wide Awake than for Coffee Ground.
Therefore, based on both the mean and median values, we can conclude that Wide Awake typically sells more coffee per hour than Coffee Ground.
To learn more about the mean and median visit:
https://brainly.com/question/14532771
#SPJ1
would it be appropriate to construct a 95% confidence interval with the information in 1(b) through 1(d)? explain why in one sentence.
If a simple random of size n is drawn from a population, then the 95% confidence-interval about "μ", if the sample size "n" is 23 is (101.68 , 110.32).
The population from which a simple random of size "n" is drawn is normally distributed,
We have to construct "95% confidence-interval" when n = 23,
So, c = 0.95, n = 23,
⇒ degree of freedom(df) = 23 - 1 = 22,
from t-distribution table, the critical-value corresponding to c = 0.95 and df = 22 is t = 2.074,
the lower bound is = x' - (t×s)/√n = 106 - (2.074×10)/√23 = 101.68,
the upper bound is = x' + (t×s)/√n = 106 + (2.074×10)/√23 = 110.32,
Therefore, the required 95% confidence interval is (101.68 , 110.32).
Learn more about Confidence Interval here
https://brainly.com/question/28013993
#SPJ4
The given question is incomplete, the complete question is
A simple random of size n is drawn from a population that is normally distributed, the sample mean (x') is found to be 106, and the sample standard deviation is 10. Construct a 95% confidence interval about "μ", if the sample size "n" is 23.
Which of these actions will cause the expression's value to increase?
1/3A-B^2
Keeping AAAA constant and increasing BBBB
(Choice B) Keeping AAAA constant and decreasing BBBB
B
Keeping AAAA constant and decreasing BBBB
(Choice C) Increasing AAAA and keeping BBBB constant
C
Increasing A and keeping B constant
(Choice D) Decreasing A and keeping B constant
To increase the value of the expression 1/3A-B^2, increasing A and keeping B constant will cause the expression's value to increase.
This is because the expression has a linear term of A and a quadratic term of B^2. Increasing A will result in a larger linear term, which will increase the value of the expression. None of the other options will necessarily increase the value of the expression. Keeping AAAA constant and decreasing BBBB or decreasing A and keeping B constant will both cause the value of the expression to decrease while keeping AAAA constant and increasing BBBB will only increase the quadratic term of the expression and may or may not result in an overall increase depending on the values of A and B.
Find out more about expression
brainly.com/question/11883643
#SPJ1
|x+7| all posbilities
The possible values of |x + 7| are:
-(x + 7), if x < -7
0, if x = -7
(x + 7), if x > -7
What is the inequality equation?
The expression |x + 7| represents the absolute value of x + 7. An inequality equation involving absolute value can be written as:
|x + 7| < a
where "a" is a positive constant. This inequality means that the distance between x + 7 and 0 on the number line is less than "a". In other words, x can be any value within "a" units of -7.
The possible values of |x + 7| depend on the value of x.
If x is negative, then |x + 7| will be equal to -(x + 7), which is negative.
If x is zero or positive, then |x + 7| will be equal to (x + 7), which is non-negative.
Therefore, the possible values of |x + 7| are:
-(x + 7), if x < -7
0, if x = -7
(x + 7), if x > -7
To know more about inequality equations visit :
https://brainly.com/question/30238989
#SPJ1
when examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal compression from a vertical compression?
A horizontal compression is identified by a factor inside the function, affecting the input variable, while a vertical compression is identified by a factor outside the function, affecting the output variable.
When examining the formula of a function that is the result of multiple transformations, a horizontal compression can be identified by a factor that appears inside the function, affecting the input variable (typically x). For example, if the original function is f(x) and the horizontal compression is by a factor of 2, the function would be written as f(x/2), indicating that the input values are being compressed horizontally.
On the other hand, vertical compression can be identified by a factor that appears outside the function, affecting the output variable (typically y). For example, if the original function is f(x) and the vertical compression is by a factor of 1/2, the function would be written as (1/2)f(x), indicating that the output values are being compressed vertically.
Learn more about horizontal and vertical compression at
https://brainly.com/question/28968436
#SPJ4
Sam bought 2 cups of corn and 4 tacos for $19. Albert bought bought 3 cups of corn and 2
tacos for $14.5
How much are the tacos?
O $3.50
O $2.75
O $2.50
O $3.00
Let's represent the cost of a cup of corn as 'c' and the cost of a taco as 't'.
From the first statement, we know that:
2c + 4t = 19 (equation 1)
From the second statement, we know that:
3c + 2t = 14.5 (equation 2)
We can solve this system of equations using elimination or substitution. Here, we'll use substitution.
Rearranging equation 2, we get:
3c = 14.5 - 2t
Dividing both sides by 3, we get:
c = 4.83 - 0.67t
Now we can substitute this expression for 'c' into equation 1:
2(4.83 - 0.67t) + 4t = 19
Simplifying, we get:
9.66 - 0.34t = 19
Subtracting 9.66 from both sides, we get:
-0.34t = 9.34
Dividing both sides by -0.34, we get:
t = -27.47 ≈ $-2.75
Since a negative price for a taco doesn't make sense, we made an error somewhere. Checking our calculations, we can see that we made a mistake in the expression for 'c'. It should be:
c = (14.5 - 2t)/3
Substituting this expression for 'c' into equation 1:
2[(14.5 - 2t)/3] + 4t = 19
Multiplying both sides by 3:
2(14.5 - 2t) + 12t = 57
Expanding and simplifying:
29 - 4t + 12t = 57
8t = 28
t = 3.5
Therefore, the tacos cost $3.50.
a researcher wants to estimate the mean grade point average of all current college students in the united states. she has developed a procedure to standardize scores from colleges using something other than a scale between 0 and 4. how many grade point averages must be obtained so that the sample mean is within 0.1 of the population mean? assume that a 90% confidence level is desired. also assume that a pilot study showed that the population standard deviation is 0.88.1
A sample size of at least 109 GPAs to estimate the population mean with a 90% confidence level
Confidence level = 90%
Standard deviation = 0.88
Mean = 0.1
Calculating the sample size -
[tex]n = [(zα/2σ) / E]^2[/tex]
The crucial value for a confidence level of 90%, denoted by z/2, may be determined using a typical normal distribution table or calculator, where n is the required sample size. The value of z/2 at a 90% degree of confidence is around 1.645. The problem statement specifies that the population standard deviation at 0.88 and that E is the most significant error of the sample mean from the population mean at 0.1.
Therefore, substituting the values -
[tex]n = [(1.645 x 0.88) / 0.1]^2[/tex]
n = 108.25
Read more about a population mean on:
https://brainly.com/question/28103278
#SPJ4
Use the graph to answer the question. Graph of polygon ABCD with vertices at negative 1 comma negative 1, 1 comma negative 5, 5 comma negative 5, 3 comma negative 1. A second polygon A prime B prime C prime D prime with vertices at 4 comma negative 1, 6 comma negative 5, 10 comma negative 5, 8 comma negative 1. Determine the translation used to create the image. 5 units to the right 1 unit to the right 5 units to the left 1 unit to the left
The polygon is translated five units to the right.
Define translation?A translation does not alter the appearance of a shape; it merely shifts it up, down, or from side to side. A metamorphosis serves as an example of translation. A transformation is a method for changing a shape's size or placement. At each location, the shape is translated in the same direction by the same amount.
The polygon ABCD's vertices are provided to us as A (-1, -1); B (1, -5); C (5, -5) and D (3, -1)
Also, the vertices of second polygon A'B'C'D' are given as A' (4, -1); B' (6, -5); C' (10, -5) and D' (8, -1).
It is evident that neither polygon's y coordinates have changed.
A 5 increment is made to the x-coordinates.
The translation rule in use is therefore (x, y) → (x + 5, y)
As a result, the polygon is translated 5 units to the right.
To know more about translation, visit:
brainly.com/question/1046778
#SPJ1
The complete question is:
Graph of polygon ABCD with vertices at negative 1 comma negative 1, 1 comma negative 5, 5 comma negative 5, 3 comma negative 1.
A second polygon A' B' C' D' with vertices at 4 comma negative 1, 6 comma negative 5, 10 comma negative 5, 8 comma negative 1.
Determine the translation used to create the image.
1. 5 units to the right
2. 1 unit to the right
3. 5 units to the left
4. 1 unit to the left
a three digit number is not an odd number, does not contain 6, and one of the digits appear more than once. how many possible three digit numbers are there?
The total number of possible three-digit numbers is not odd, does not contain 6, and has at least one repeated digit is 13,221,888.
To find the number of possible three-digit numbers we need to use the systematic approach method
Step 1:
we have to find the number of three-digit numbers that are not odd. Number of possible choices for the units digit (0, 2, 4, or 8)= 4
Number of possible choices for tens and hundreds of digits (0-9 excluding 6 = 9
the total number of three-digit numbers that are not odd is,
= 4 x 9 x 9
= 324.
Step 2:
Count the number of three-digit numbers that do not contain 6.
Number of possible choices for each digit (0-5, 7, 8, or 9) = 8
the total number of three-digit numbers that do not contain 6 is,
= 8 x 8 x 8
= 512.
Step 3:
Count the number of three-digit numbers that do not have distinct digits. The number of possible choices for the repeated digit and 9 choices for the other digit = 9
the total number of three-digit numbers that have a repeated digit is
= 9 x 9 = 81.
Step 4:
Find the intersection of the sets of numbers counted in Steps 1-3.
To do this, we multiply the number of choices in each set:
= 324 x 512 x 81
= 13,221,888.
Therefore, 13,221,888 possible three-digit numbers are not odd, do not contain 6, and have at least one repeated digit.
To learn more about the systematic approach method:
https://brainly.com/question/27959993
#SPJ4
Is it a function yes or no
Answer:
Step-by-step explanation:
im assuming your saying number 3 which is yes
SUPER EASY!!!!!
What is degree of (4by+2b-by)?
I will make you brainliest if you can explain!!!
Answer: The degree of (4by+2b-by) is 2, as it is a quadratic expression with the highest exponent of the variable being 2.
Step-by-step explanation: The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent of the variable is 2, which appears in the term 4by. Therefore, the degree of (4by+2b-by) is 2.
carly got a model train set for her birthday, and it came with 200 assorted pieces of train track. she randomly picks some pieces of track out of the box. so far, she has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks. based on the data, what is the probability that the next piece of track carly picks will be straight?
The probability that the next piece of track Carly picks will be straight is 8/24 or 1/3
From the given information, Carly has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.
The total number of pieces of the track she has picked is 8 + 7 + 4 + 5 = 24
The probability that the next piece of track Carly picks will be straight is calculated as follows:
Probability = Number of straight tracks/Total number of tracks= 8/24= 1/3T
Therefore, the probability that the next piece of track Carly picks will be straight is 1/3.
Know more about Probability here :
https://brainly.com/question/24756209
#SPJ11
Answer: 1/3
Step-by-step explanation: i did this question and got it right
Find the surface area of a rectangular prism with dimensions of 6m by 4 m by 15
Answer: 348 square meters
Step-by-step explanation:
To find the surface area of a rectangular prism, we need to calculate the area of each of the six faces and add them together. A rectangular prism has three pairs of opposite faces: the length (l) and width (w), the length (l) and height (h), and the width (w) and height (h).
Given dimensions: length (l) = 6m, width (w) = 4m, and height (h) = 15m
Area of the length and width faces (lw): 6m * 4m = 24m²
Since there are two opposite faces, the total area of these faces is 2 * 24m² = 48m².
Area of the length and height faces (lh): 6m * 15m = 90m²
Since there are two opposite faces, the total area of these faces is 2 * 90m² = 180m².
Area of the width and height faces (wh): 4m * 15m = 60m²
Since there are two opposite faces, the total area of these faces is 2 * 60m² = 120m².
Now, add the areas of all the faces together:
Surface area = 48m² (lw faces) + 180m² (lh faces) + 120m² (wh faces) = 348m²
The surface area of the rectangular prism is 348 square meters.
Answer:
the surface area of the rectangular prism is 348 square meters.
Step-by-step explanation:
The surface area of a rectangular prism can be found using the formula:Surface Area = 2lw + 2lh + 2whwhere l, w, and h are the length, width, and height of the prism.In this case, the dimensions of the rectangular prism are:l = 6m
w = 4m
h = 15m
Substituting these values into the formula, we get:
Surface Area = 2(6m)(4m) + 2(6m)(15m) + 2(4m)(15m)
Surface Area = 48m^2 + 180m^2 + 120m^2
Surface Area = 348m^2
will give brainilest
Answer:
[tex]3 \: {cm}^{2} [/tex]
Step-by-step explanation:
Given:
h (height) = 1,5 cm
b (base) = 4 cm
Find: A (area) - ?
[tex]a = \frac{1}{2} \times b \times h[/tex]
[tex]a = \frac{1}{2} \times 4 \times 1.5 = 3 \: {cm}^{2} [/tex]
which statement is true about effect size? group of answer choices when the effect size is small, detecting it is easier and can be done with a smaller sample the effect size is the extent to which the null or statistical hypothesis is false there is one type of effect size measure used in research studies
The true statement about effect size is: The effect size is the extent to which the null or statistical hypothesis is false. Effect size is a measure used in research studies to quantify the magnitude of the difference between groups or the strength of an association between variables.
It helps determine the practical significance of the research findings, as opposed to the statistical significance.
When the effect size is small, detecting it is not necessarily easier, and a larger sample size may be required to achieve adequate statistical power. A larger effect size, on the other hand, might be easier to detect and might require a smaller sample size.
There is not just one type of effect size measure used in research studies. There are various measures of effect size, such as Cohen's d, Pearson's correlation coefficient (r), and odds ratio (OR), among others. Each type of effect size is suitable for different research designs and data types.
Choosing the appropriate effect size measure depends on the research question, the design of the study, and the type of data being analyzed.
for more questions on hypothesis
https://brainly.com/question/15980493
#SPJ11
Find the perimeter of the figure (use 3.14 as pi if u can)
The perimeter of a shape is the measurement around its edge and it is 101.36 in.
How is boundary determined?We must sum up the lengths of the quadrilateral four sides to determine its perimeter. Since there are two of each side measurement, it is easy to accomplish this by simply adding the length and width and multiplying the result by two.
Perimeter of given shape = 18 + 27 +27 + perimeter of the arc
the perimeter of the arc = Perimeter of the semicircle = [tex]\pi r[/tex]
Therefore the perimeter of the shape = 72 + 3.14 * 9 = 101.36 in.
Learn more about perimeter here:
https://brainly.com/question/6465134
#SPJ1
Please help! I need to find the perimeter, Predicted perimeter , Predicted area and Area.
The perimeter of the rectangle is 38 feet, the predicted perimeter is 26 feet, the area of the rectangle is 30 square feet, and the predicted area is also 30 square feet.
What is the formula of perimeter and area of Rectangle ?
The formulas for the perimeter and area of a rectangle are:
Perimeter = 2(length + width)
Area = length x width
In these formulas, "length" refers to the longer side of the rectangle, and "width" refers to the shorter side of the rectangle. The perimeter is the total length of the sides of the rectangle, and the area is the amount of space inside the rectangle.
To find the perimeter of the rectangle, we simply add up the lengths of all four sides:
Perimeter = 10 feet + 3 feet + 6 feet + 6 feet + 4 feet + 9 feet
Perimeter = 38 feet
To predict the perimeter, we could use the formula for the perimeter of a rectangle, which is:
Predicted Perimeter = 2(length + width)
We can find the length and width of the rectangle by finding the longest and shortest sides:
Length = 10 feet
Width = 3 feet
Therefore, the predicted perimeter would be:
Predicted Perimeter = 2(10 feet + 3 feet)
Predicted Perimeter = 26 feet
To find the area of the rectangle, we multiply the length by the width:
Area = 10 feet × 3 feet
Area = 30 square feet
To predict the area, we could use the formula for the area of a rectangle, which is:
Predicted Area = length × width
Using the same values for length and width as before, the predicted area would be:
Predicted Area = 10 feet × 3 feet
Predicted Area = 30 square feet
Therefore, the perimeter of the rectangle is 38 feet, the predicted perimeter is 26 feet, the area of the rectangle is 30 square feet, and the predicted area is also 30 square feet.
Learn more about Area and perimeter of Rectangle here
https://brainly.com/question/26669169
#SPJ1
what is the leading coefficient of this polynomial -4x^3+9
The leading coefficient of the polynomial -4x^3+9 is -4.
Identifying the leading coefficient of the polynomialThe leading coefficient of a polynomial is the coefficient of the term with the highest degree.
In this polynomial, -4x^3+9, the term with the highest degree is -4x^3, and the coefficient of this term is -4.
Therefore, the leading coefficient of the polynomial is -4.
The degree of a polynomial is the highest exponent of the variable in any of its terms. In this polynomial, the variable is x and the highest exponent is 3. So, the degree of this polynomial is 3.
Read more about polynomial at
https://brainly.com/question/7693326
#SPJ1
A charity is hosting a benefit dinner. They are asking 100 per table plus 40 per person. Nathaniel is purchasing tickets for his friends and does not wnat to spend more than 250
10t + 4p ≤ 25 inequality shows the maximum number of tables and people Nathaniel can invite while staying within his budget.
What is inequality?
In mathematics, an inequality is a statement that two values or expressions are not equal, but rather that one is greater than or less than the other. An inequality is denoted by the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
Let the number of tables Nathaniel buys be represented by t, and the number of people he invites be represented by p.
Then, the total cost can be expressed as:
Cost = 100t + 40p
Since Nathaniel does not want to spend more than 250, we can set up the inequality:
100t + 40p ≤ 250
We can simplify this inequality by dividing both sides by 10:
10t + 4p ≤ 25
This inequality shows the maximum number of tables and people Nathaniel can invite while staying within his budget.
To learn more about inequality, visit the link:
https://brainly.com/question/24372553
#SPJ1
Dave throws a ball upward with an initial velocity of 32 ft/s. The ball initially leaves his hand 5 ft. above the ground and eventually falls back to the ground.
The ball is in the air for a total of 2 seconds.
To find the total time that the ball is in the airWe can use the fact that the time it takes for the ball to reach its maximum height is half of the total time the ball is in the air.
The initial vertical velocity of the ball is 32 ft/s and the acceleration due to gravity is -32 ft/s^2 (since it acts in the opposite direction to the initial velocity). We can use the kinematic equation:
y = y0 + v0*t + (1/2)at^2
Where
y is the vertical position of the bally0 is the initial vertical positionv0 is the initial vertical velocitya is the acceleration due to gravityt is the timeWhen the ball reaches its maximum height, its vertical velocity becomes 0. Therefore, we can use the equation:
v = v0 + at
To find the time it takes for the ball to reach its maximum height, since the vertical velocity at that point is 0.
v = v0 + at
0 = 32 - 32t
t = 1 second
So it takes 1 second for the ball to reach its maximum height. At this point, the vertical velocity of the ball is 0, so we can use the equation:
y = y0 + v0*t + (1/2)at^2
to find the maximum height:
y = 5 + 32(1) + (1/2)(-32)(1)^2
y = 21 feet
Now we can use the fact that the time it takes for the ball to fall back to the ground is the same as the time it took to reach its maximum height. Therefore, the total time the ball is in the air is:
2*1 second = 2 seconds
So the ball is in the air for a total of 2 seconds.
Learn more about maximum height here : brainly.com/question/3358424
#SPJ1
What is the surface
area of a pyramid
with a square base
with sides of 10
inches and a length of
15 inches?
To find the surface area of a pyramid with a square base, we need to find the area of the square base and the area of each triangular face, then add them together.
The area of the square base is the square of the length of one of its sides. In this case, the side length is 10 inches, so the area of the base is:
[tex] \rm A_{base} = 10^2 = 100 \text{ square inches}[/tex]
To find the area of each triangular face, we need to find the height of the pyramid. The height of the pyramid is the perpendicular distance from the apex (the top of the pyramid) to the base. To find the height, we can use the Pythagorean theorem, since we know the length of the slant height (15 inches) and half the length of the base (5 inches):
[tex] \rm{h = \sqrt{15^2 - 5^2} = \sqrt{200} = 10\sqrt{2} \text{ inches}}[/tex]
Now we can find the area of each triangular face using the formula:
[tex] \rm{A_{face} = \frac{1}{2} \times \text{base} \times \text{height}}[/tex]
where the base is the side length of the square base, and the height is the height of the pyramid. In this case, we have:
[tex] \rm{A_{face} = \frac{1}{2} \times (10 \text{ inches}) \times (10\sqrt{2} \text{ inches}) = 50\sqrt{2} \text{ square inches}}[/tex]
Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the four triangular faces:
[tex] \rm{A_{total} = A_{base} + 4A_{face} = 100\text{ square inches} + 4(50\sqrt{2} \text{ square inches}) \approx 314.16 \text{ square inches}}[/tex]
Therefore, the surface area of the pyramid is approximately 314.16 square inches.
I am equivalent to 3/8 and the product of my numerator and denominator is 216.What am I
The fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.
To find the fraction equivalent to 3/8 with a numerator and denominator product of 216, follow these steps:
Set up an equation for the product of the numerator and denominator:
x × y = 216.
Since the fraction is equivalent to 3/8, you can write another equation: x / y = 3/8.
Solve for x in terms of y in the second equation:
x = (3/8) × y.
Substitute this expression for x in the first equation:
(3/8) × y × y = 216.
Solve for y: [tex]y^2 = (8/3) × 216.[/tex]
Simplify the equation: y^2 = 576.
Find the square root of both sides: y = 24.
Now, find x using the equation x = (3/8) × y:
x = (3/8) × 24.
Simplify the expression:
x = 9.
So, the fraction equivalent to 3/8 with a numerator and denominator product of 216 is 9/24.
for such more question on fraction
https://brainly.com/question/1622425
#SPJ11
The equation of a curve is y=e^(0.5x +3) a) Where does the curve cross the y-axis? The curve passes through the point (-2, k). b) Calculate the value of k. The curve passes through the point (h, 100). c) Calculate the value of h.
which are the first five trems of a geometric in which the second tem is 6 and the forufh trem is 54?
The first five terms are 2, 6, 18, 54, 162.
What are numbers?A number is a fundamental building block of mathematics.
Numbers are used for indexing, counting, measuring, and a variety of other tasks.
According to their characteristics, there are various sorts of numbers, including natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc.
The resultant number can be calculated by using the fundamental arithmetic operations for integers.
Tally marks were formerly used before numbers.
Numbers are a crucial aspect of our daily lives, from the number of rounds we run around the race track to the number of hours we sleep at night, and much more.
According to our question-
a series where each subsequent term is obtained by multiplying the preceding one by a shared ratio.
The order is provided by:
a, ar, ar2, aar3, aar4, aar5,...
What is the nth term provided by-
a_n = ar^(n-1)
Second term = 6
a_2 = ar^(2-1)
6 = ar^1
6 = ar
Hence, The first five terms are 2, 6, 18, 54, 162.
learn more about numbers click here:
brainly.com/question/17200227
#SPJ1
the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]
What is geometric sequence?Assume that "a" is the first letter of the geometric sequence and "r" is the common ratio.
According to the problem statement, the second term is 6. Therefore, we have:
[tex]ar = 6 .....(1)[/tex]
Similarly, the fourth term is 54, which gives us:
[tex]ar^3 = 54 .....(2)[/tex]
We must first determine the values of "a" and "r" in the geometric sequence. The two equations mentioned above can be solved simultaneously to achieve this.
The result of dividing equation [tex](2)[/tex] by equation [tex](1)[/tex] is
[tex]r^2 = 9[/tex]
When we square the two sides, we obtain:
r = ±3
Now, using equation (1), we can find the value of "a" as follows:
[tex]ar = 6[/tex]
Substituting r = 3, we get:
[tex]3a = 6[/tex]
[tex]a = 2[/tex]
Substituting [tex]r = -3[/tex], we get:
[tex]-3a = 6[/tex]
[tex]a = -2[/tex]
Therefore, the first term of the geometric sequence is either [tex]2[/tex] or [tex]-2[/tex] , and the common ratio is 3 or -3.
If the first term is 2 and the common ratio is 3, then the first five terms of the geometric sequence are: [tex]2, 6, 18, 54, 162[/tex]
The first five terms of the geometric sequence are as follows, if the common ratio is three and the first term is two:
[tex]-2, 6, -18, 54, -162[/tex]
So, the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]
Learn more about geometric here:
https://brainly.com/question/13008517
#SPJ1
Factor the polynomial Complete the table (8a - 8l)
9a) Factorization from 8d. 9b) Factorization from 8h 9c) Factorization from 8l
PLEASE HELP 30 POINTS
The factorization for 8i is 3x(5x+1)(x-2), which can also be checked by multiplying the factors and verifying that the result is equal to the original polynomial.
Polynomial GCF Factored with GCF Factored TrinomiaL Final
9x^4 + 3x^3 -1222 1 NA NA
2x^2 + 3x - 9 1 NA (2x-3)(x+3) (2x-3)(x+3)
15x^3 - 27x^2 - 6x 3x 3x(5x^2 - 9x - 2) not factorable 3x(5x+1)(x-2)
9a) Factorization from 8d: not factorable
9b) Factorization from 8h: (2x-3)(x+3)
9c) Factorization from 8i: 3x(5x+1)(x-2)
Note: The table shows the factoring process for each polynomial. In question 9, we just need to check the final factorization for each of the polynomials in question 8. The factorization for 8d is not factorable, so there is nothing to check. The factorization for 8h is (2x-3)(x+3), which can be checked by multiplying the factors and verifying that the result is equal to the original polynomial.
Find out more about factorization
at brainly.com/question/16613599
#SPJ1