Answers
Answer:
x = 0.39 or
x = -1.72
Step-by-step explanation:
The quadrateic formula is:
[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]
eq: 3x² + 4x - 2
which is of the form ax² + bx + c = 0
where a = 3, b = 4 and c = -2
sub in quadratic formuls,
[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]
Related Questions
A group of adults were asked how many children they have in their families. The bar graph below shows the number of adults who indicated each number of children. 4+ 3.5+ 3- 2.5 2- 1.5- 1 0.5- 0 1 2 Number of Children How many adults were questioned? m St 4 5 What percentage of the adults questioned had 2 children? Round answer to 1 decimal place. %
Answers
Answer:
Step-by-step explanation:
To determine the percentage of adults who had 2 children, we need to first find the total number of adults questioned.
Looking at the bar graph, we can see that the bar representing 2 children has a height of 2.5. This means that 2.5 adults indicated having 2 children.
Let's assume the total number of adults questioned is "m". According to the bar graph, the sum of the heights of all the bars represents the total number of adults questioned.
From the bar graph, we can see the following:
The bar representing 4+ children has a height of 4.
The bar representing 3- children has a height of 3.5.
The bar representing 2- children has a height of 2.5.
The bar representing 1- children has a height of 1.5.
The bar representing 1 child has a height of 1.
The bar representing 0.5- children has a height of 0.5.
The bar representing 0 children has a height of 0.
To find the total number of adults questioned (m), we sum up the heights of all the bars:
m = 4 + 3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5 + 0
m = 18
Therefore, the total number of adults questioned is 18.
To find the percentage of adults who had 2 children, we divide the number of adults with 2 children (2.5) by the total number of adults questioned (18) and multiply by 100:
Percentage = (2.5 / 18) * 100
Percentage ≈ 13.9 (rounded to 1 decimal place)
Therefore, approximately 13.9% of the adults questioned had 2 children.
JLK is similar to PQR find the value of X
Answers
Answer:
30
Step-by-step explanation:
22/33=20/x
cross multiply
22x=33x20
22x=660
x=660/22
x=30
which expression represents the product of x^3+2x-1 and x^4-x^3+3
Answers
Answer:
(x^3+2x-1) * (x^4-x^3+3)
Step-by-step explanation:
To simplify this expression, we can multiply each term in the first expression by each term in the second expression and combine like terms:
(x^3)(x^4) + (x^3)(-x^3) + (x^3)(3) + (2x)(x^4) + (2x)(-x^3) + (2x)(3) + (-1)(x^4) + (-1)(-x^3) + (-1)*(3)
Simplifying further:
x^7 - x^6 + 3x^3 + 2x^5 - 2x^4 + 6x - x^4 + x^3 - 3
Combining like terms:
x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3
Therefore, the expression representing the product of (x^3+2x-1) and (x^4-x^3+3) is x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3.
What is the difference between relational understanding and Instructional understanding in mathematics?
Answers
Relational understanding in mathematics involves a deep comprehension of concepts and connections. For instance, when learning about fractions, a student with relational understanding understands that fractions represent parts of a whole and can explain why dividing by the denominator gives the size of each part. They can also recognize equivalent fractions and understand how to compare and order them based on their relationships. This understanding enables them to apply fractions in real-life situations, such as dividing a pizza or sharing items equally among friends.
Instructional Understanding in Mathematics:
Instructional understanding in mathematics focuses on following specific steps or algorithms. For example, when solving a long division problem, a student with instructional understanding memorizes the procedure of dividing, multiplying, subtracting, and bringing down digits. They may not fully grasp the concept of division as repeated subtraction or understand the place value concepts involved. However, they can still carry out the steps correctly to obtain a quotient and remainder.
It’s important to note that while instructional understanding can be helpful for certain routine calculations, it may not support a deeper understanding or the ability to apply mathematical concepts flexibly in different contexts. Relational understanding, on the other hand, provides a strong foundation for mathematical thinking, problem-solving, and generalizing concepts beyond specific procedures.
Use the marginal tax rate chart to answer the question. Tax Bracket Marginal Tax Rate $0–$10,275 10% $10,276–$41,175 12% $41,176–$89,075 22% $89,076–$170,050 24% $170,051–$215,950 32% $215,951–$539,900 35% > $539,901 37% Determine the effective tax rate for a taxable income of $175,000. Round the final answer to the nearest hundredth.
Answers
Answer:
the effective tax rate for a taxable income of $175,000 is approximately 21.02%.
Step-by-step explanation:
Let's break down the income into the corresponding tax brackets:
The first $10,275 is taxed at a rate of 10%.
Tax on this portion: $10,275 * 0.10 = $1,027.50
The income between $10,276 and $41,175 is taxed at a rate of 12%.
Tax on this portion: ($41,175 - $10,276) * 0.12 = $3,710.88
The income between $41,176 and $89,075 is taxed at a rate of 22%.
Tax on this portion: ($89,075 - $41,176) * 0.22 = $10,656.98
The income between $89,076 and $170,050 is taxed at a rate of 24%.
Tax on this portion: ($170,050 - $89,076) * 0.24 = $19,862.88
The income between $170,051 and $175,000 is taxed at a rate of 32%.
Tax on this portion: ($175,000 - $170,051) * 0.32 = $1,577.44
Now, sum up all the taxes paid:
$1,027.50 + $3,710.88 + $10,656.98 + $19,862.88 + $1,577.44 = $36,836.68
The effective tax rate is calculated by dividing the total tax paid by the taxable income:
Effective tax rate = Total tax paid / Taxable income
Effective tax rate = $36,836.68 / $175,000 = 0.21024 (rounded to the nearest hundredth)
Please help me with this question
Answers
Answer:
try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is
2. Sandra's house is located at the point (2,2). The school is located at the point (7, 10). Each
unit on the graph represents 1 mi. How far is the school from Sandra's house? Remember to
show your work.
Plot and label your points on the coordinate plane (1 point)
Use the Pythagorean Theorem to calculate the diagonal distance between the two
points, express your answer as a radical and as a decimal rounded to nearest
hundredths.
Answers
Answer:
Step-by-step explanation:
Here is a unit circle with point P at (1, 0) Find the coordinates of P after the circle rotates the given amount counter clockwise around its center
1. 1/3 of a full rotation: ?
2 1/2 of a full rotation: ?
3. 2/3 of a full rotation: ?
Answers
1. 1/3 of a full rotation: The coordinates of point P after rotating 1/3 of a full rotation counterclockwise are approximately (0.5, 0.866).
2. 1/2 of a full rotation: The coordinates of point P after rotating 1/2 of a full rotation counterclockwise are (-1, 0).
3. 2/3 of a full rotation: The coordinates of point P after rotating 2/3 of a full rotation counterclockwise are approximately (-0.5, -0.866).
1/3 of a full rotation:
To find the coordinates of point P after rotating 1/3 of a full rotation counter clockwise, we need to determine the angle of rotation.
A full rotation around the unit circle is 360 degrees or 2π radians.
Since 1/3 of a full rotation is (1/3) [tex]\times[/tex] 360 degrees or (1/3) [tex]\times[/tex] 2π radians, we have:
Angle of rotation = (1/3) [tex]\times[/tex] 2π radians
Now, let's use the properties of the unit circle to find the new coordinates.
At the initial position, point P is located at (1, 0).
Rotating counterclockwise by an angle of (1/3) [tex]\times[/tex] 2π radians, we move along the circumference of the unit circle.
The new coordinates of point P after the rotation will be (cos(angle), sin(angle)).
Substituting the angle of rotation into the cosine and sine functions, we get:
New coordinates of P = (cos((1/3) [tex]\times[/tex] 2π), sin((1/3) [tex]\times[/tex] 2π))
Calculating the values:
cos((1/3) [tex]\times[/tex] 2π) ≈ 0.5
sin((1/3) [tex]\times[/tex] 2π) ≈ 0.866
Therefore, the coordinates of point P after rotating 1/3 of a full rotation counterclockwise are approximately (0.5, 0.866).
1/2 of a full rotation:
Following a similar process, when rotating 1/2 of a full rotation counterclockwise, we have an angle of (1/2) [tex]\times[/tex] 2π radians.
New coordinates of P = (cos((1/2) [tex]\times[/tex] 2π), sin((1/2) [tex]\times[/tex] 2π))
Calculating the values:
cos((1/2) [tex]\times[/tex] 2π) = cos(π) = -1
sin((1/2) [tex]\times[/tex] 2π) = sin(π) = 0
Therefore, the coordinates of point P after rotating 1/2 of a full rotation counterclockwise are (-1, 0).
2/3 of a full rotation:
For a rotation of 2/3 of a full rotation counterclockwise, the angle is (2/3) [tex]\times[/tex] 2π radians.
New coordinates of P = (cos((2/3) [tex]\times[/tex] 2π), sin((2/3) [tex]\times[/tex] 2π))
Calculating the values:
cos((2/3) [tex]\times[/tex] 2π) ≈ -0.5
sin((2/3) [tex]\times[/tex] 2π) ≈ -0.866
Therefore, the coordinates of point P after rotating 2/3 of a full rotation counterclockwise are approximately (-0.5, -0.866).
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Divisores pares de 100
Answers
Answer:
2, 4, 10, 20, 50, and 100.
Step-by-step explanation:
a) 9-12/2
b) 27-13/²2
Answers
a) Option a) 9 - 1/2 is equal to 17/2.
b) Option b) 27 - 2/3 is equal to 79/3.
a) The expression 9 - 1/2 can be simplified by finding a common denominator for the terms. The common denominator for 9 and 1/2 is 2.
Multiplying 9 by 2/2, we get:
9 * (2/2) = 18/2
So, the expression 9 - 1/2 can be simplified to:
18/2 - 1/2 = 17/2
Therefore, option a) 9 - 1/2 is equal to 17/2.
b) The expression 27 - 2/3 can be simplified in a similar manner by finding a common denominator for the terms. The common denominator for 27 and 2/3 is 3.
Multiplying 27 by 3/3, we get:
27 * (3/3) = 81/3
So, the expression 27 - 2/3 can be simplified to:
81/3 - 2/3 = 79/3
Therefore, option b) 27 - 2/3 is equal to 79/3.
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Q.14 In the figure given below, let the lines 1, and 1, be parallel and t is transversal. Find
the value of x.
Answers
Answer:
The consecutive interior angles are supplementary, so we have:
3x + 20 + 2x = 180
5x + 20 = 180
5x = 160, so x = 32
What is the answer? As the last one is incorrect
Answers
The best measure of center of the data is (a) mean; because the data are close together
How to determine the best measure of center of the dataFrom the question, we have the dataset of 10 values
In the given dataset, we can see that there are no outliers present in the dataset
By definition, outliers are extreme values.
Since there are no outliers, it means that the mean is the best measure of center
This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean
From the list of options, we have the mean value to be 42.536
Hence, the true statement is (a)
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¿Cuál es el costo de un plátano si el racimo de 22 plátanos cuesta $23.10?
Answers
The cost of a single unit is given as follows:
$1.05.
El costo de un plátano es el seguiente:
$1.05.
How to obtain the cost of a single unit?The cost of a single unit is obtained applying the proportions in the context of the problem.
The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:
23.1/22 = $1.05.
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at the movie theatre, child admission is $5.20 and adult admission is $9.60 on sunday, 131 tickets were sold for a total sales of $1020.00 how many adult tickets were sold that day
Answers
Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.
Definition of System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown with which when replacing, they must give the solution proposed in both equations.
Amount of adult tickets soldIn this case, a system of linear equations must be proposed taking into account that:
"a" is the amount of adult tickets sold."c" is the amount of children tickets sold.You know:
At the movie theatre, child admission is $5.20 and adult admission is $9.60 On sunday, 131 tickets were sold for a total sales of $1020.00So, the system of equations to be solved is
a + c= 131
9.60a + 5.20c= 1020
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable c from the first equation:
c= 131 -a
Substituting the expression in the second equation:
9.60a + 5.20×(131 -a)= 1020
Solving:
9.60a + 5.20×131 -5.20a= 1020
9.60a + 681.2 -5.20a= 1020
9.60a -5.20a= 1020 - 681.2
4.4a= 338.8
a= 338.8÷ 4.4
a= 77
In summary, 77 adult tickets were sold that day.
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The slope of the tangent line to the curve y= 3/x
at the point 5, 3/5 is-
The equation of this tangent line can be written in the form y = mx + b
where:
m is:
b is:
Answers
The tangent line at that point is:
y = (-3/25)*x + 6/5
so m = -3/25, and b = 6/5
How to find the slope of the tangent line?To find the slope at that point, we need to evaluate the derivative at that point.
y = 3/x
The derivative is:
y' = -3/x²
When x = 5, we have:
y' = -3/5² = -3/25
So that is the slope, m.
Now let's find the line.
The line must pass trhough the point (5, 3/5), then:
3/5 = (-3/25)*5 + b
3/5 = -3/5 + b
3/5 + 3/5 = b
6/5 = b
The equation of the line is:
y = (-3/25)*x + 6/5
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Given the sequence 9/8, 3/4, 1/2,...,8/81 is the geometric sequence. Find the common ratio and the number of all terms of this sequence.
Answers
Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.
As we know that,
Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.
So, r= (n+1)th term / nth term
where r ⇒ common ratio
(n+1)th term⇒ succeeding term
nth term⇒ preceding term
According to the given question, r = (9/8) / (3/4)
r = (2/3)
We also know,
Any term of a G.P. [nth term] can be obtained by the formula:
Tₙ= a[tex]r^{n-1}[/tex]
where, Tₙ= nth term
a= first term of G.P.
r=common ratio
Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.
Tₙ= a[tex]r^{n-1}[/tex]
⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])
⇒ (64/729)= ([tex]2/3^{n-1}[/tex])
⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])
⇒ n-1 = 6
⇒ n = 7
∴ The total number of terms in G.P. is 7.
Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.
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The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.
Explanation:The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.
So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.
To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.
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On a line graph, time is usually represented on the vertical axis.
O True
O False
--
Answers
A hose fills a hot tub at a rate of 2.82
gallons per minute. How many hours will it take to fill a 303
-gallon
hot tub?
Answers
Answer:
Step-by-step explanation:
60 minutes per hour
2.82gal *60mins = 169.2gal per hour.
303 gallons / 169.2 gph = about 1.7907 hours
it is my first time taking my baby to the cinemas in Junes 2023, and the cinemas have sales because there are tons of kids' movies to be seen. For adults the ticket costs 70$ and for children it costs 30$, which tickets sell like 1000$ a day leading to 31000 a month. Calculate the number of tickets that were sold for adults and children in a day. A+C=1000 70+30=31000.
A+C=1000
70+30=31000
if we wanted to extend this discussion beypnd what has been shared so far, what additional question could we ask?
Answers
Step-by-step explanation:
If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:
"What is the ratio of adult tickets to children's tickets sold in a day?"
This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.
A store employee notices that rowboats that cost his store 79$ are being sold for 175$. What percentage is the mark up?
Answers
Answer:
Step-by-step explanation:
Step 1. Determine the dollar amount of the markup
175 - 79 = 96
Step 2: Divide the markup Amount by the Cost
96/79 = 1.215
Step 3: Multiply by 100 and add the % sign
1.215 x 100 = 121.5%
anna rolled a pair of number cubes what is the probability of getting even number on both sides PLSSS HELP ME
Answers
It is best to draw a table of outcomes and list all the possible outcomes when you roll a pair of numbered cubes. As follows:
1 2 3 4 5 6
1 ( 1 , 1 ) ( 1 , 2 ) ( 1 , 3 ) ( 1 , 4 ) ( 1 , 5 ) ( 1 , 6 )
2 ( 2 , 1 ) ( 2, 2 ) ( 2 , 3 ) ( 2 , 4 ) ( 2 , 5 ) ( 2 , 6 )
3 ( 3 , 1 ) ( 3 , 2 ) ( 3 , 3 ) ( 3 , 4 ) ( 3 , 5 ) ( 3 , 6 )
4 ( 4 , 1 ) ( 4 , 2 ) ( 4 , 3 ) ( 4 , 4 ) ( 4 , 5 ) ( 4 , 6 )
5 ( 5 , 1 ) ( 5 , 2 ) ( 5 , 3 ) ( 5 , 4 ) ( 5 , 5 ) ( 5 , 6 )
6 ( 6 , 1 ) ( 6 , 2 ) ( 6 , 3 ) ( 6 , 4 ) ( 6 , 5 ) ( 6 , 6 )
- Each cube has 6 faces, Hence, 6 numbers for each are expressed as row and column for first and second cube respectively.
- Now locate and highlight all the even pairs shown in bold.
- The total number of even pairs outcomes are = 9.
- The total possibilities are = 36.
- The probability of getting even pairs as favorable outcome can be expressed as:
P ( Even pairs ) = Favorable outcomes / Total outcomes
P ( Even pairs ) = 9 / 36
P ( Even pairs ) = 1 / 4.
- So the probability of getting an even pair when a pair of number cubes are rolled is 1/4
If she wants to get an even number on both sides, the possible outcomes are (2,2), (2,4), (2,6), (4,2), (4,4), (4,6), (6,2), (6,4), and (6,6).
So there are 9 possible outcomes that result in an even number on both sides.
Therefore, the probability of getting an even number on both sides is 9/36, which can be simplified to 1/4 or 25%.
⦁ The construction of copying is started below. The next step is to set the width of the compass to the length of . How does this step ensure that the new angle will be congruent to the original angle?
Answers
Answer:
i believe by creating radii of equal lengths.
Step-by-step explanation:
it gives a path to create an angle congruent to angle APB. The angle APB would have the same radii (BP and AP) and the same width as the congruent angle that would be created.
Wish you good luck.
HELP THIS QUESTION IS HARD
Answers
Answer:
a)
[tex] \frac{1}{( - 7)^{4} } [/tex]
Answer:
[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]
Step-by-step explanation:
The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.
According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.
Thus, the negative exponent rule is given as:
[tex]b^-^n=\frac{1}{b^n}[/tex]
Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]
The hip width x of adult females is normally distributed with a mean of 37.6 cm and a standard deviation of 4.36 cm. The maximum width of an aircraft seat that will accommodate 98% of all adult women is about: (Give your answer to one decimal places if necessary.)
Answers
Answer:
Step-by-step explanation:
To find the maximum width of an aircraft seat that will accommodate 98% of all adult women, we need to determine the corresponding z-score for the 98th percentile of the normal distribution.
First, we find the z-score corresponding to the 98th percentile using a standard normal distribution table or calculator. The z-score for the 98th percentile is approximately 2.05.
Next, we use the z-score formula to find the corresponding value in the original distribution:
z = (x - μ) / σ
Solving for x (the maximum width of the aircraft seat):
x = z * σ + μ
Substituting the values given:
x = 2.05 * 4.36 + 37.6
x ≈ 45.98
Therefore, the maximum width of an aircraft seat that will accommodate 98% of all adult women is approximately 46 cm (rounded to one decimal place).
The base of a rectangular prism is a square whose sides each measure 9 inches. The height of the rectangular prism is 11 inches, find it’s volume?
Answers
Answer:
99
Step-by-step explanation:
since the height is 9 and the base is 11 we use the formula BH=V
substitute 9x11 and get 99
Find the area of the region bounded by the graphs of f(x) = x^3 + x^2 - 6x and g(x) = 2x - x^2
Answers
The area of the region bounded by the graphs of [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex] is 69 1/3 square units.
To find the area of the region bounded by the graphs of the functions [tex]f(x) = x^3 + x^2 - 6x[/tex] and [tex]g(x) = 2x - x^2[/tex], we need to determine the points of intersection and evaluate the definite integral.
First, let's find the points of intersection by setting f(x) equal to g(x):
[tex]x^3 + x^2 - 6x = 2x - x^2[/tex]
Rearranging the equation, we get:
[tex]x^3 + 2x^2 - 8x = 0[/tex]
Factoring out an x, we have:
[tex]x(x^2 + 2x - 8) = 0[/tex]
Using the quadratic formula, we find the solutions for [tex]x^2 + 2x - 8 = 0[/tex] to be x = -4 and x = 2. Therefore, the points of intersection are (-4, -16) and (2, 4).
To calculate the area, we integrate the difference of the two functions within the bounds of -4 to 2:
Area = ∫[from -4 to 2] (f(x) - g(x)) dx
Evaluating the definite integral, we have:
Area = ∫[-4 to 2] [(x^3 + x^2 - 6x) - (2x - x^2)] dx
= ∫[-4 to 2] (x^3 + 2x^2 - 8x) dx
Integrating each term and evaluating the integral, we find:
Area = [1/4x^4 + 2/3x^3 - 4x^2] from -4 to 2
= [(1/4)(2)^4 + (2/3)(2)^3 - 4(2)^2] - [(1/4)(-4)^4 + (2/3)(-4)^3 - 4(-4)^2]
= [4/4 + 16/3 - 16] - [16/4 + (-128/3) - 64]
= 1/3 + 128/3 - 16 + 4 - 128/3 + 64
= 1/3 + 4 + 64
= 69 1/3
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1) (20) The temperature on a mountain forms a linear relationship with
the altitude at any given point of the mountain.
The temperature at 4800 feet is 79 degrees while the temperature at
6400 feet is 67 degrees.
=Find a linear model T(x) = mx + b Where x is the altitude.
a) Find the linear model. Show work!
b) What are the units of m, the slope of the line? Hint: Look at the units
of the x values and y values.
c) Find T(5800)
Answers
By analyzing the temperature-altitude relationship on a mountain, we can establish a linear model that describes how temperature changes with varying altitudes.
Step-by-step explanation:
a) Knowing the altitude and temperature data, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are two points on the line.
Using the altitude and temperature values provided:
(x1, y1) = (4800, 79) and (x2, y2) = (6400, 67),
we can calculate the slope:
m = (67 - 79) / (6400 - 4800)
= -12 / 1600
= -0.0075.
Now, to find the y-intercept (b), we can substitute one of the points (4800, 79) into the equation:
79 = (-0.0075)(4800) + b.
Solving for b, we have:
b = 79 + 0.0075(4800)
= 79 + 36
= 115.
Therefore, the linear model is T(x) = -0.0075x + 115.
b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.
c) To find T(5800), we can substitute x = 5800 into the linear model:
T(5800) = -0.0075(5800) + 115
= -43.5 + 115
= 71.5.
Answers:
a) T(x) = -0.0075x + 115.
b) The units of the slope (m) can be determined by looking at the units of the y values (temperature) and x values (altitude). In this case, the units of temperature are degrees, and the units of altitude are feet. Therefore, the units of the slope (m) are degrees per foot.
c) 71.5 degrees.
In a sample of 5,000 students , the mean GPA is 2.80 and the standard deviation is 0.35. Assume the distribution to be normal.
How many students score below 2.60?
Answers
In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.
To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.
First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.
Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.
To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.
Since the number of students must be a whole number, we round down to 1428 students.
Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.
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Which of the segments below is a secant?
A. XY
B. UZ
C. XO
Answers
Jane just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Jane works out that's 62 hats for each hospital. Does that sound about right?
Answers
Answer:
31
Step-by-step explanation:
you add the hats to get the total number of hats then divide the answer by
No, it is much too high. Then the correct option is B.
What is an equation?An equation is a statement of equality between two expressions consisting of variables and/or numbers.
Given the question above, we need to find if the hats is to high or low.
Calculating the total numbers of hats made, we have
[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]
If Edna wants to split 62 hats evenly between two hospital, then each hospital will get
[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]
Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available
Hence, the correct option is B.
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Missing informationEdna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?
A. Yes
B. No, it is much too high
C. No, it is much too low