The best-fit linear regression equation gives us the equation y = 0.0804x + 1.1794, where the slope is 0.0804 and the y-intercept is 1.1794.
The trendline equation will give us the equation for the linear regression line, which can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.
Once we have the trendline equation, we can use it to make predictions about future enrollment percentages based on the number of years after 1820.
The slope of the line tells us the rate at which the enrollment percentage is increasing or decreasing over time, and the y-intercept tells us the enrollment percentage when x is equal to zero (i.e., in 1820).
Here we have find that the best-fit linear regression equation gives us the equation
=> y = 0.0804x + 1.1794,
where the slope is 0.0804 and the y-intercept is 1.1794.
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Think about prime numbers and composite numbers.list all the digits that are the last digit of at least one prime number.
Answer:
1,3,5,7,9
Step-by-step explanation:
0 can't be, let's take 10 or 20 or 30 for example, not a prime number.
1 can be because let's take 11, 31 as example, they're prime numbers.
2, 4, 6, 8 can't be the answer because they have factors
The rest of off numbers, namely 3,5,7,9 can be. Let's take for example 23, 05, 67, 59
To the nearest ten dollars, what can Carlos expect the value of the computer to be 3 years after purchase
Carlos can expect the value of the computer to be $580 three years after purchase.
To model the value of the computer, we can use the formula:
y = abˣ
We know that the initial value of the computer is $1,350, so a = 1350.
We also know that one year after purchase, the value of the computer is $810, so we can use this to find the value of b:
810 = 1350b
b= 0.6
b = 0.6
So our exponential equation is:
y = 1350(0.6)ˣ
To find the value of the computer 3 years after purchase, we can substitute x = 3:
y = 1350(0.6)³
y = 583
Hence, Carlos can expect the value of the computer to be $580 three years after purchase.
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A model rocket is launched with an initial upward velocity of 60 m/s the rocket's height h meters after t seconds h=60t-5t^2 find values for which rockets height is 30 meters
The model rocket will have a height of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.
How to determine the time associated with the height of a rocket on air
In this problem we have the case of a model rocket being launched, the height of the rocket in time is described by the following quadratic equation:
h(t) = 60 · t - 5 · t²
Where:
h - Height, in meters.t - Time, in seconds.We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:
30 = 60 · t - 5 · t²
6 = 12 · t - t²
t² - 12 · t + 6 = 0
(t - 11.477) · (t - 0.523) = 0
t = 11.477 s. or t = 0.523 s.
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Find x. Simplify completely.
X
8
C
17
x = [?] √ [
Enter the number that belongs in the green box.
Enter
Answer:
17/x = x/8
x^2 = 136, so x = 2√34
Amanda’s new job has a 50% employer match on the first 4% of her salary contributed to her 401(k). How much was deposited in Amanda’s account if she makes $61,000 a year and she took advantage of the entire contribution match?
Answer:
$2,440 + $1,220 = $3,660
Step-by-step explanation:
If Amanda makes $61,000 a year, and she contributes 4% of her salary to her 401(k), that would be:
$61,000 x 0.04 = $2,440
Since her employer has a 50% match on the first 4% of her salary, they would contribute:
$2,440 x 0.5 = $1,220
Prove the following this:The number of left cosets of a subgroup is equal to the number of its right cosets?
To prove: The number of left cosets of a subgroup is equal to the number of its right cosets.
Proof: Let H be a subgroup of a group G. Let g be an element of G. Consider the map f: H→ gH defined by f(h) = gh for all h in H. We claim that f is a bijection from H to gH.
First, we show that f is injective. Suppose f(h1) = f(h2) for some h1, h2 in H. Then gh1 = gh2, which implies that h1 = h2, by left cancellation law. Therefore, f is injective.
Next, we show that f is surjective. Let gh be an element of gH. Then h is an element of G, since gH is a subset of G. Since H is a subgroup of G, it follows that gh is an element of gH. Therefore, f(h) = gh, which shows that f is surjective.
Hence, f is a bijection from H to gH. Therefore, the number of left cosets of H is equal to the number of right cosets of H.
Let f ( x ) = a x n − b x 2 + 14 c x m + d x 3 − 7 f(x)= cx m +dx 3 −7 ax n −bx 2 +14 f, left parenthesis, x, right parenthesis, equals, start fraction, a, x, start superscript, n, end superscript, minus, b, x, squared, plus, 14, divided by, c, x, start superscript, m, end superscript, plus, d, x, cubed, minus, 7, end fraction, where m mm and n nn are integers and a aa, b bb, c cc and d dd are unknown constants. Which of the following is a possible graph of y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis? Choose 1 answer:
The graph in option C is the one that best satisfies the function y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis
How to solveThe ultimate exponent of the equation, [tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.
If one between these values is odd, an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).
If both of these variables fit an even figure, the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).
The [tex]x^3[/tex] term, however, will sway the overall form between such high-powered terms.
Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive flight path and curves.
Solving the given problem:
f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]
At x= 0 on the y- axis
f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]
Thus, only option C satisfies this condition.
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what is 2x multiplied by 7 with the exponent of 4
The simplified expression of 2x multiplied by 7 with the exponent of 4 is 4,802x.
What is the simplification of the expression?
The expression is simplified by applying the rules of multiplication and exponent rules.
the expression = 2x(7⁴)
simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401
Multiply the resultant solution of 2,401 as follows;
= 2,401 x (2x)
= 4,802x
Thus, the simplified expression of 2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of multiplication.
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Andy saved $32 in June, $27 in July, and $38 in August. Then Andy spent $18 on school supplies and $47 on new clothes. How much money does
Andy have left?
Andy has $32 money left after spending $18 on school supplies and $47 on new clothes.
To find out how much money Andy has left, we need to start with the total amount of money he saved and then subtract the amount he spent on school supplies and new clothes.
The total amount Andy saved is:
$32 + $27 + $38 = $97
The amount Andy spent is:
$18 + $47 = $65
To find out how much money Andy has left, we can subtract the amount he spent from the amount he saved:
$97 - $65 = $32
So, after spending $18 on school supplies and $47 on new clothes, Andy is left with $32.
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Find the volume of the composite solid. Round your answer to the nearest hundredth.
To the nearest hundredth, the volume of composite solid, giving us 904.600 cubic metres.
specify the solid volume?How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many unit cubes are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.
For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:
V = l × w ×h
The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and two hemispheres. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.
Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.
V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.
We arrive at a total volume of 792 cubic meters by adding these volumes together.
To the nearest hundredth=904.600 cubic meters.
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Verify the given linear approximation at a = 0. Then use a graphing calculator or computer to determine the values of x for which the linear approximation is accurate to within 0.1. (Round your answers to three decimal places. Enter your answer using interval notation.)
sin−1(x) ≈ x
Therefore, the linear approximation sin⁻¹(x) ≈ x is accurate to within 0.1 when x is in the interval [-0.099, 0.099].
What is function?In mathematics, a function is a relationship between two sets, called the domain and range, such that for each element in the domain there is exactly one element in the range. In other words, a function assigns a unique output value to each input value. Functions are typically denoted using a rule or formula that describes how to calculate the output value based on the input value.
Here,
The linear approximation of sin⁻¹(x) at a = 0 is given by:
sin⁻¹(x) ≈ x
To verify this, we can take the derivative of sin⁻¹(x) and evaluate it at x = 0:
d/dx(sin⁻¹(x)) = 1/√(1-x²)
d/dx(sin⁻¹(x))|x=0 = 1
Since the derivative of sin⁻¹(x) evaluated at x = 0 is equal to 1, we can use the linear approximation sin⁻¹(x) ≈ x near x = 0.
To determine the values of x for which the linear approximation is accurate to within 0.1, we can use a graphing calculator or computer to plot the graphs of sin⁻¹(x) and x, and find the intervals where the difference between the two functions is less than or equal to 0.1.
Using a graphing calculator, we can plot the two functions and find the intervals where the difference is less than or equal to 0.1. The result is:
-0.099 ≤ x ≤ 0.099
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which fraction is the smallest? 3to4, 2/3, 10:12, 2to1
The smallest fraction is 8/12, which is equivalent to 2/3.
How to determine the smallest fractionTo compare fractions, it's best to convert them all to a common denominator.
3/4 is equivalent to 9/12
2/3 is equivalent to 8/12
10/12 is equivalent to 5/6
2/1 is equivalent to 24/12
So, the smallest fraction is 8/12, which is equivalent to 2/3.
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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.80 and the cost of a large greeting card is $3.85. How much would it cost to get 4 small greeting cards and 3 large greeting cards? How much would it cost to get
�
x small greeting cards and
�
y large greeting cards?
Answer: 18.75
Step-by-step explanation:
small greeting cards = 1.80
large greeting cards = 3.85
1.80 x 4 = 7.20
3.85 x 3 = 11.55
7.20 + 11.55 = 18.75
18. Triangle GHJ has GH = 13, GJ = 15, and
m/G = 74. What is the area of the triangle?
SEE EXAMPLE 4
Answer: 97.5
Step-by-step explanation:
Just do base times height divided by 2, which I'm assuming is 13x15 , that'd be 195. 195 divided by 2 is 97.5
All but 36 of the 120 state capitals have an interstate highway serving them. What percent of the capitals do not have interstates?
Therefore, 70% of state capitals do not have interstate highways serving them.
What is percent?Percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the numerical value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and changes in quantities.
Here,
If all but 36 of the 120 state capitals have an interstate highway serving them, then the number of capitals that do not have interstates is 120 - 36 = 84.
To find the percentage of capitals that do not have interstates, we need to divide the number of capitals without interstates by the total number of capitals and then multiply by 100:
84 / 120 x 100% = 70%
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The frequency table below shows a student’s quiz scores. One data value in the table is missing. If the mean of the data set is 2.2, what is the score for the missing data item? A. 0 B. 1 C. 2 D. 3
Answer:
B. 1
Step-by-step explanation:
Let's use the formula for finding the mean of a set of data:
mean = (sum of all data values) / (number of data values)
We know that the mean is 2.2, and we have all the other data values except for one. Let's call the missing value "x". The total number of data values is 10 (since there are 10 scores listed in the frequency table). So we can set up an equation:
2.2 = (sum of all 10 data values, including x) / 10
Multiplying both sides by 10, we get:
22 = sum of all 10 data values, including x
We can then subtract the sum of the known data values from both sides to find the missing value:
22 - (01 + 12 + 23 + 31 + 42 + 51) = x
22 - (0 + 2 + 6 + 3 + 8 + 5) = x
x = 22 - 24 = -2
However, a quiz score cannot be negative, so we made a mistake somewhere. Checking the frequency table, we see that there are no scores of 0 or 1, so the missing score must be 0 or 1. Let's try both possibilities:
If the missing score is 0:
2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 0*1) / 10
2.2 = 18 / 10
2.2 = 1.8
This is not true, so the missing score cannot be 0.
If the missing score is 1:
2.2 = (01 + 12 + 23 + 31 + 42 + 51 + 1*?) / 10
2.2 = (18 + ?) / 10
22 = 18 + ?
? = 4
So the missing score is 1, and the answer is B.
Answer:
Answer is B
Total scores/total frequency =mean
54/24=2,25
If you added a score of 1
55/25=2,2
Step-by-step explanation:
hope that helps you
18. The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
Answer:
64.14
Step-by-step explanation:
Reading the passage I see that you have to multiply then divide
The surface area of the larger solid is, 171.7 mm²
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The volumes of two similar solids are 857.5 mm³ and 540 mm³.
And, The surface area of the smaller solid is 108 mm².l
Now, Let us assume that;
The surface area of the larger solid is, x
Hence, We get;
857.5 / x = 540 / 108
Solve for x as;
857.5 x 108 = 540 x
92,718 = 540x
x = 171.7 mm²
Thus, The surface area of the larger solid is, 171.7 mm²
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
-7n + 5n^2 + 6 - 3n^2 - 11n + 30
Answer:
2 (n - 3) (n - 6)
Step-by-step explanation:
[tex]-7n+5n^2+6-3n^2-11n+30[/tex]
Group like terms and combine...
[tex]2n^2-18n+36[/tex]
Observe that all terms contain a factor of 2. Factor out a 2...
[tex]2(n^2-9n+18)[/tex]
The leading coefficient is 1. The shortcut applies. Find the factors of "c" (18)
18 = 1 * 1818 = 2 * 918 = 3 * 6Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").
Finish factoring the trinomial into two binomials:
[tex]2(n-3)(n-6)[/tex]
To verify that this is a valid factoring, distribute, and recombine terms:
[tex]2(n-3)(n-6)[/tex]
[tex]2(n^2-3n-6n+18)[/tex]
[tex]2(n^2-9n+18)[/tex]
True or False Deductive reasoning is when someone uses lots of data to make a conjecture.
Answer:
Step-by-step explanation:
One respondent said they watched 10 movies. This seems to be an
symmetrical
This graph is
skewed
to the
left
because the data is stacked on the left with a "tail" going to the right.
Most people watched
[ Select ]
movies
The graph seems to be a left symmetrical distribution and most people watched action movies
Calculating the skewness of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
From the graph, we have the following readings and observations
The movie with the highest frequency is Action moviesThe data is stacked on the right with a "tail" going to the left.Using the above as a guide, we have the following conclusions
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MODELING REAL LIFE About 5.2% of a population
contracted the flu last year. A test used to diagnose the
flu was 92% accurate for people who had the flu and
85% accurate for people who did not have it. Find and
interpret the ratio of true positives to false positives.
The ratio of true positives to false positives, given the accuracy of the test would be 239 : 711 .
Here. we have,
First, find the number of people who have the flu:
= 5. 2 % x 10, 000
= 520 people
Those who don't have it:
= 10, 000 - 520
= 9, 480 people
True positive :
= 92 % x 520
= 478 people
False negatives:
= 8 % x 520
= 42 people
False positives:
= 15 % x 9, 480
= 1, 422 people
The ratio of true positives to false positives is therefore:
478 : 1, 422
239 : 711
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Please answer this please you will not understand how much this means 30 points
The solutions to the equation over the interval [0°, 360°) are: x = 45°, 135°, 225°, 315°.
How to explain the equationWe can rewrite this equation as:
1 - sin² x = sin²x
Solving for sin x, we get:
sin x = ±✓(1/2)
Since sin x is positive in the first and second quadrants and negative in the third and fourth quadrants, we have:
sin x = ✓(1/2) = 1/✓(2) in the first and second quadrants, corresponding to x = 45° and 135°.
sin x = -✓(1/2) = -1/✓(2) in the third and fourth quadrants, corresponding to x = 225° and 315°.
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Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A(-7,-2)A(−7,−2), B(-3,1)B(−3,1), C(-3,4)C(−3,4), D(5,4)D(5,4), E(5,-6)E(5,−6), F(-3,-6)F(−3,−6), G(-3, -2)G(−3,−2)
The total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) has been found as 51 square units.
What is a Graph?A graph is described as a mathematical representation of a network and it describes the relationship between lines and points.
The first step is to divide the figure is into two rectangles and a triangle.
we notice that the points B, C, E, and F will form a rectangle with base BC and height of 7 units.
We also notice that the points A, D, and G form a rectangle with base AG and height 5 units.
we notice that points C, D, and E form a triangle with base CE and height 4 units.
we notice that the length of BC is 4 - 4 = 0, therefore the area of the rectangle with base BC is 0.
The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.
In conclusion, the total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 45 + 6 = 51 square units.
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A chef has 5 containers of rice. Each container has 2 cups of rice in it. If the chef uses cup of rice for a recipe, how many cups of rice do they have left?
Answer:10-x
Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.
Tickets of a program at college cost $3 for general admission or $2 with student ID. If 181 people paid to see a performance and $435 was collected, how many of each type of ticket were sold.
Can someone please help me with this problem? I'm struggling and the assignment is already late :(
soooooooooo what is x^2=-20
The value of x in the equation x² = -20 is x = 2i√5
Evaluating the equation for xFrom the question, we have the following parameters that can be used in our computation:
x² = -20
To start with, we take the square root of both sides of the equation
So, we have
√x² = √-20
When the square roots are evaluated, we have
x = √-20
Express -20 as 4 * -5
So, we have
x = √4 * -5
This gives
x = 2√-5
The expression √-5 is a complex number
So, we have
x = 2i√5
Hence, the value of x in x² = -20 is x = 2i√5
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if the volume of a rectangular prism is 26,214 m3 and it has a height of 17 m what is the value of b , the area of the base ? A. 13,062 m2 B. 13,062 m3 C.1,542 m2 D. 1,542 m3
Answer:
C
Step-by-step explanation:
The area of a rectangle is 2 dimensions so it would be measured in square meters.
a = lwh
26241 = lw(17) Divide both sides by 17
1542 = lw
The lw is he area of the base.
Helping in the name of Jesus.
PLEASE HELP
Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed.
C=0.90, x=13.7, s =3.0, n= 10
The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is (9.7, 14.7).
Here, we have,
1. Identify the given information:
- Confidence level (c) = 0.95
- Sample mean (x) = 12.2
- Sample standard deviation (s) = 3.0
- Sample size (n) = 8
2. Determine the degrees of freedom (df) for the t-distribution:
- df = n - 1 = 8 - 1 = 7
3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:
- You can use a t-table or an online calculator for this.
- The t-value for a 0.95 confidence level and 7 df is approximately 2.365.
4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):
- ME = t-value * (s / sqrt(n))
- ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5
5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):
- Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7
- Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7
So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).
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Ali had 3469 bags of maize each weighing 90 kg.Hesold 2654 of them. How many kg of maize was he left with?
The number of kg of maize was left with Ali is 73350 Kg.
Given that, Ali had 3469 bags of maize each weighing 90 kg.
Ali sold 2654 of them.
Number of bags left = 3469-2654
= 815
Number of Kg's of maize left = 815×90
= 73350 Kg
Therefore, the number of kg of maize was left with Ali is 73350 Kg.
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