Answer:
is b
Step-by-step explanation:
In the triangle RST, RS = 65 and ST = 60. Which equation could be used to find the value of angle S?
A) tan(S) = 65/60
B) sin(S) = 65/60
C) sin(S) = 60/65
D) cos(S) = 60/65
Answer:cos(S) =
60
65
Step-by-step explanation:
Answer:
D.[tex]Cos S=\frac{60}{65}[/tex]
Step-by-step explanation:
We are given that in triangle RST, RS=65 and ST=60
We have to find the equation that could be used to find the value of angle S.
We know that
[tex]cos\theta=\frac{Base}{Hypotenuse}[/tex]
Base=ST=60 units
Hypotenuse=RS=65 units
[tex]\theta=S[/tex]
Substitute the values in the given formula
Then, we get
[tex]Cos S=\frac{60}{65}[/tex]
Hence, option D is true.
An engineering student is studying the effects of cryogenic treatments on a particular material. The treatment involves cooling the material with
specific applications of liquid nitrogen
The temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours, since the
treatment began
Answer:
option c
Step-by-step explanation:
The object reaches -200 degrees C at 15 hrs, coldest temperature it ever achieved
Answer:
The correct option is C.
Step-by-step explanation:
It is given that the temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours.
From the given graph it is clear that
1. The y-intercept is 40, so the initial temperature is 40 degree Celsius.
2.The vertex of the upward parabola is at (15,-200), so material's temperature reaches a minimum -200 degrees Celsius at 15 hours.
3. The material return to its initial temperature after 30 hours because the temperature is 40 degree Celsius at x=30.
Therefore the correct option is C.
Solve 2x2 + x − 4 = 0. x2 + x + = 0
Answer:
2x^2+x-4=0
x^2+\dfrac12x-2=0
x^2+\dfrac12x+\dfrac1{16}-\dfrac{33}{16}=0
\left(x+\dfrac14\right)^2=\dfrac{33}{16}
x+\dfrac14=\pm\dfrac{\sqrt{33}}4
x=\dfrac{-1\pm\sqrt{33}}4
Step-by-step explanation: lol tooooo much ∅∞
Answer:
1/2 and -2 are the first answers to the question
1/16 and 1/16 are the next answers
1/4 and 33/16 are the last ones
and for the multiple choice answer which is last is A
Step-by-step explanation:
In a kitchen there are three containers that can hold different quantities of water, as shown in the figure below:
*PIC*
How many liters of water can the three containers hold in all?
A) 3x
B) x + 3
C) 3x + 1
D) x^2 + x − 1
Answer:
A) 3x
Step-by-step explanation:
The total of all the volumes is ...
(x -1) + (x) + (x +1) = (1+1+1)x +(-1+1) = 3x+0 = 3x . . . . . matches choice A
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!
Answer:
B
Step-by-step explanation:
If we imagine this is on a clock, then point P is at the 9-o'clock position. When we rotate it 90 degrees clockwise, that's a quarter rotation, so P' will be at the 12-o'clock position. So the coordinates of P' will be (0, 5).
Find the length of a picture frame who’s width is 3 inches and whose proportions are the same 9 inch wide by 15 inch long
Answer:
5 inch
Step-by-step explanation:
The frames are proportional, so we can set the ratios equal:
width / height = width / height
3 / h = 9 / 15
9h = 45
h = 5
Given the proportionality between two pictures one with width 3 inches and another with dimensions 9 inches by 15 inches, we can set up a ratio and solve for the unknown length, yielding the length of the picture frame as 5 inches.
Explanation:The question is asking to find the length of a picture frame, given that its width is 3 inches and that it has the same proportions as a picture that is 9 inches wide and 15 inches long. The proportions can be used to set up a ratio, as follows:
3 inches (width of the new picture frame) divided by 9 inches (width of the existing picture) = x (unknown length of the new picture frame) divided by 15 inches (length of the existing picture).
To solve for x, cross-multiply: 3 inches * 15 inches = 9 inches * x.
Then, divide by 9 to solve for x: 45 inches/9 = 5 inches.
So, the length of the picture frame whose width is 3 inches would be 5 inches, if it shares the same proportions as the 9 inch wide by 15 inch long picture.
Learn more about Proportionality here:https://brainly.com/question/29153656
#SPJ11
What is the simplest form of 3sqrt x^2
Answer:
3|x|
Step-by-step explanation:
√(x^2) = |x|, the positive root. Multiplying this by 3, you get ...
3√(x²) = 3|x|
Please help need answer quick
Answer:
20 students
Step-by-step explanation:
The percentage of students scoring a B or A = 38 + 25 = 63%
We need to evaluate 63% of the 32 students who did the test
(63/100)*32 = 20.16
Therefore, approximately 20 students earned a B or higher
Answer:
20
Step-by-step explanation:
The percentage of students gaining an A or B = 38 + 25 = 63%
Calculate 63% of the 32 students
63% = [tex]\frac{63}{100}[/tex] = 0.63, hence
0.63 × 32 ≈ 20
This circle below is centered at the point (3 -4) and has a radius of length 3. What is its equation
Answer:
[tex](x-3)^2+(y+4)^2=9[/tex]
Step-by-step explanation:
The equation of a circle with center at (h,k) and radius r units is found using:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
The given circle is centered at the (3,-4) and has radius 3 units,
The equation of this circle is obtained by substituting the given values.
This gives us:
[tex](x-3)^2+(y--4)^2=3^2[/tex]
We simplify to get:
[tex](x-3)^2+(y+4)^2=9[/tex]
Answer:
(x-3)2+(y-4)2=9
Step-by-step explanation:
Evaluate the expression.
9! - 4!(5!)
Answer:
360,000
Step-by-step explanation:
The exclamation point is factorial:
9! = 9×8×7×6×5×4×3×2×1 = 362880
5! = 5×4×3×2×1 = 120
4! = 4×3×2×1 = 24
362880 - 120× 24 = 360000
A spinner has 4 equal sections. after 12 spins, the spinner landed on section a 4 times, section b 5 times, section c 2 times, and section d 1 time. what is the experimental probability of the spinner stopping on section a?
Answer:
The Experimental Probability of the spinner stopping on Section A is 1/3.
Step-by-step explanation:
Number of time spinner landed on section A = 4
Number of time spinner landed on section B = 5
Number of time spinner landed on section C = 2
Number of time spinner landed on section D = 1
Total Number of spins = 12
[tex]Probability=\frac{Number\:of\;Favorable\:outcome}{Number\:of\:total\;outcome}=\frac{4}{12}=\frac{1}{3}[/tex]
Therefore, The Experimental Probability of the spinner stopping on Section A is 1/3.
Given the function f(x) = 6x2 −13, what is f(-3)? A. -67 B. -4 C. 41 D. 311
Answer: C. 41
Step-by-step explanation:
The quadratic function is:
[tex]f(x) = 6x^2-13[/tex]
Then, to find [tex]f(-3)[/tex] you need to substitute the input value [tex]x=-3[/tex] into the quadratic function, to obtain the corresponding output value.
Then, when [tex]x=-3[/tex] the output value is:
[tex]f(x) = 6x^2-13[/tex]
[tex]f(-3) = 6(-3)^2-13[/tex]
[tex]f(-3) = 6(9)-13[/tex]
[tex]f(-3) = 41[/tex]
This matches with the option C.
Answer:
-4
Step-by-step explanation:
Please write f(x) as 6x^2 - 13; " ^ " indicates exponentiation.
With f(x) = 6x^2 - 13, we substitute -3 for x in both instances:
f(-3) =(-3)^2 - 13 = 9 - 13 = -4
Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.
y = 7.82x0.844
y = 6.81 e0.316x
y = 7.19 + 12.8 ln x
y = 4.40 + 5.00x
Answer:
i)
Find the attached
ii)
The mathematical model that best fits the data is;
y = 7.19 + 12.8 ln x
Step-by-step explanation:
i)
A scatter-plot can easily be constructed using applications such as Ms. Excel and Stat-Crunch.
In Ms. Excel we first enter the data in any two adjacent columns. Next, highlight the data, then click the insert ribbon and select the scatter-plot option.
Excel returns a scatter-plot chart as shown in the attachment below.
ii)
After obtaining the scatter-plot, we shall need to add a trend line in order to determine the mathematical model that best fits the data given.
Click anywhere inside the chart, then select the design tab under chart tools. Click on the Add Chart element in the upper left corner of the excel workbook and select more trend-line options. This feature will enable us to fit any trend-line to our data.
Select any trend line option ensuring you check the boxes; Display Equation on chart and Display R-squared value on chart.
Find the attached for the various trend-lines.
The mathematical model that best fits the data is;
y = 7.19 + 12.8 ln x
Since it has the largest R-squared value of 0.9905
[tex]\rm y = 7.19 + 12.8\ ln\ x[/tex], in this function, the scatter points follow this function. Then the correct option is C.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Construct a scatterplot and identify the mathematical model that best fits the data.
Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models.
Use a calculator or computer to obtain the regression equation of the model that best fits the data.
You may need to fit several models and compare the values of R2.
A. [tex]\rm y = 7.82x + 0.844[/tex], in this function, the scatter points do not follow this function.
B. [tex]\rm y = 6.81 e^{0.316x}[/tex], in this function, the scatter points do not follow this function.
C. [tex]\rm y = 7.19 + 12.8\ ln\ x[/tex], in this function, the scatter points follow this function. Because the best fits.
D. [tex]\rm y = 4.40 + 5.00x[/tex], in this function, the scatter points do not follow this function.
The graph is shown.
More about the function link is given below.
https://brainly.com/question/5245372
joshua brought 156 of his 678 legos to emily house.what percentage of legos did joshua bring
Answer:
23%
Step-by-step explanation:
156 / 678 * 100 = 23%
The correct answer is 23%
Final answer:
Joshua brought about 23% of his LEGOs to Emily's house, which is calculated by dividing 156 (the number of LEGOs he brought) by 678 (the total number he owns) and then multiplying by 100.
Explanation:
To find what percentage of LEGOs Joshua brought to Emily's house, you divide the number of LEGOs Joshua brought by the total number of LEGOs he owns and then multiply the result by 100.
The formula to find the percentage is:
(Number of items of interest ÷ Total number of items) × 100 = Percentage
So in this case, it would be:
(156 ÷ 678) × 100
First, you perform the division:
156 ÷ 678 = 0.23 (rounded to two decimal places)
Then multiply by 100 to find the percentage:
0.23 × 100 = 23%
Therefore, Joshua brought about 23% of his LEGOs to Emily's house.
Please help me with this
Answer:
ASA
Step-by-step explanation:
One pair of corresponding angles (in the bottom left/right) are already marked for us, and we're also given a pair of corresponding sides (the 8cm ones on the left and right). The two triangles have one more angle in common too - the one they're overlapping on the top corner. So, we have:
- Two pairs of congruent corresponding angles, and
- A pair of congruent corresponding sides between them,
which is enough information to call the triangles congruent by Angle-Side-Angle (ASA).
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 75 pounds. A total of 22 boxes of paper were shipped weighing 1350 pounds altogether. Determine the number of small boxes shipped and the number of large boxes shipped.
To determine the number of small boxes and large boxes shipped, we can set up a system of equations and solve for the variables. In this case, we have two equations based on the total weight and the total number of boxes. By using the elimination method, we can find that 10 small boxes and 12 large boxes were shipped.
Explanation:To solve this problem, we can set up a system of equations. Let's denote the number of small boxes as x and the number of large boxes as y. We can then write two equations based on the information given:
45x + 75y = 1350 (equation 1) (since the total weight is 1350 pounds)
x + y = 22 (equation 2) (since the total number of boxes is 22)
We can solve this system of equations by either substitution or elimination method. Let's use the elimination method. Multiply equation 2 by 45 to make the coefficients of x in both equations equal:
45x + 45y = 990 (equation 3)
Now, subtract equation 3 from equation 1:
45x + 75y - (45x + 45y) = 1350 - 990
30y = 360
y = 12
Substitute the value of y back into equation 2:
x + 12 = 22
x = 10
Therefore, the number of small boxes shipped is 10 and the number of large boxes shipped is 12.
Learn more about System of Equations here:https://brainly.com/question/21620502
#SPJ12
Pam shipped 10 small boxes and 12 large boxes of paper.
Let's denote:
- x : Number of small boxes of paper.
- y : Number of large boxes of paper.
1. Total number of boxes shipped:
x + y = 22
2. Total weight of the shipment:
[tex]\[ 45x + 75y = 1350 \][/tex]
Now, let's solve these equations step-by-step.
Solve for x + y = 22
From equation (1):
[tex]\[ x + y = 22 \]\[ y = 22 - x \][/tex]
Substitute y = 22 - x into equation (2)
Substitute y = 22 - x into equation (2):
[tex]\[ 45x + 75(22 - x) = 1350 \][/tex]
Expand and simplify:
[tex]\[ 45x + 1650 - 75x = 1350 \]\[ -30x + 1650 = 1350 \][/tex]
Solve for x
Subtract 1650 from both sides:
[tex]\[ -30x = 1350 - 1650 \]\[ -30x = -300 \][/tex]
Divide both sides by -30:
[tex]\[ x = \frac{-300}{-30} \]\[ x = 10 \][/tex]
Find y
Now that we have ( x = 10 ), substitute back into ( y = 22 - x ):
[tex]\[ y = 22 - 10 \]\[ y = 12 \][/tex]
- Number of small boxes: 10
- Number of large boxes: 12
Check the total weight:
[tex]\[ 45 \times 10 + 75 \times 12 = 450 + 900 = 1350 \text{ pounds} \][/tex]
This matches the given total weight of 1350 pounds, confirming that our solution is correct.
Assume that the wooden triangle shown is a right triangle.
a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram. Hint: (leg 1)2 + (leg 2)2 = (hypotenuse)2
b. Transform each side of the equation to determine if it is an identity.
Answer:
Part 1) [tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]
Part 2) The answer in the procedure
Step-by-step explanation:
Part 1)
we know that
Applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
we have
[tex]c=(10x+15y)[/tex]
[tex]a=(6x+9y)[/tex]
[tex]b=(8x+12y)[/tex]
substitute the values
[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}[/tex]
Part 2) Transform each side of the equation to determine if it is an identity
[tex](10x+15y)^{2}=(6x+9y)^{2}+(8x+12y)^{2}\\ \\100x^{2}+150xy+225y^{2}=36x^{2}+54xy+81y^{2}+64x^{2}+96xy+144y^{2}\\ \\100x^{2}+150xy+225y^{2}=100x^{2}+150xy+225y^{2}[/tex]
The left side is equal to the right side
therefore
Is an identity
Answer:
b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]
a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]
Step-by-step explanation:
b. [tex]\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2[/tex]
a. [tex]\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2[/tex]
The two expressions are identical on each side of the equivalence symbol, therefore they are an identity.
I am joyous to assist you anytime.
Which relationships would most likely be causal? Check all that apply.
a positive correlation between depth under water and pressure
a negative correlation between total distance run and the runner’s height
a positive correlation between a puppy’s age and weight
a negative correlation between temperature and snowboards sold
a positive correlation between the price of milk and the price of socks
The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur. The correct option is A, C, and D.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.
The relationships that would most likely be causal are:
A.) A positive correlation between depth under water and pressure.
This is a casual relationship since the water pressure increases with depth, and can be observed while swimming in a deep swimming pool.
C.) A positive correlation between a puppy’s age and weight.
This is a casual relationship because as the puppy grows, its weight as well as its size both increase.
E.) A negative correlation between temperature and snowboards sold
This is a casual relationship because as the temperature increases fewer people prefer going out snowboarding.
Hence, the correct option is A, C, and D.
Learn more about Correlation:
https://brainly.com/question/6563788
#SPJ2
Write the formula of the function y whose graph is show.
Answer:
im on the same question
What is the solution to the equation below?
Answer:
C x=6
Step-by-step explanation:
sqrt(x+3) = x-3
Square each side
(sqrt(x+3))^2 = (x-3)^2
x+3 = (x-3)^2
x+3 = (x-3)(x-3)
FOIL
x+3 = x^2 -3x-3x+9
Combine like terms
x+3 = x^2 -6x+9
Subtract x from each side
x-x+3 = x^2 -6x-x +9
3 = x^2 -7x +9
Subtract 3 from each side
3-3 = x^2 -7x +9-3
0 = x^2 -7x+6
Factor
0 = (x-6)(x-1)
Using the zero product property
x-6=0 x-1 =0
x=6 x=1
Since we squared we need to check for extraneous solutions
x=1
sqrt(1+3) = 1-3
sqrt(4) = -2
2=-2
False
Extraneous
x=6
sqrt(6+3) = 6-3
sqrt(9) = 3
3=3
True solutions
Answer: Option C.
Step-by-step explanation:
First, we need to square both sides of the equation:
[tex]\sqrt{x+3}=x-3\\\\(\sqrt{x+3})^2=(x-3)^2[/tex]
We know that:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
Then, applying this, we get:
[tex]x+3=x^2-2(x)(3)+3^2\\\\x+3=x^2-6x+9[/tex]
Now we need to subtract "x" and 3 from both sides of the equation:
[tex]x+3-(x)-(3)=x^2-6x+9-(x)-(3)\\\\0=x^2-6x+9-x-3[/tex]
Adding like terms:
[tex]0=x^2-7x+6[/tex]
Factor the quadratic equation. Find two numbers whose sum be -7 and whose product be 6. These numbers are: -1 and -6. Then:
[tex](x-1)(x-6)=0[/tex]
Then:
[tex]x_1=1\\x_2=6[/tex]
Checking the first solution is correct:
[tex]\sqrt{1+3}=1-3\\ 2=-2 \ (False)[/tex]
Checking the second solution is correct:
[tex]\sqrt{6+3}=6-3\\ 3=3 \ (True)[/tex]
Skee ball is a game played by rolling a wooden sphere up a ramp into a series of rings. The wooden ball has a surface area of about 531 square centimeters. What is the radius, in centimeters, of the ball? Round to the nearest tenth.
Answer:
Radius of the ball is approximately 6.5 cm to the nearest tenth
Explanation:
The ball has the shape of a sphere
Surface area of a sphere can be calculated using the following rule:
Surface area of sphere = 4πr² square units
In the given problem, we have:
Surface area of the ball = 531 cm²
Substitute with the area in the above equation and solve for the radius as follows:
[tex]531 = 4\pi r^2\\ r^2=\frac{531}{4\pi } = 42.255 \\ \\ r=\sqrt{42.255}=6.5004 cm[/tex] which is approximately 6.5 cm to the nearest tenth
Hope this helps :)
The slope of a speed-time graph indicates
Answer:
acceleration
Step-by-step explanation:
In a speed-time graph, the speed data is on the Y-axis and the time is represented on the X-axis.
A slope is the variation of Y-values over the variation of the X-values between to points.
So, the slope of a speed-time graph would be the variation of the speed over the variation of time.
Let's say your units are m/s for the speed and s for the time.
The slope units would then be calculated by dividing m/s by s... (m/s) / s....
That would give you m/s², which is an acceleration unit.
Over which interval are the exponential and linear function approximately the same? from 0.25 to 0.5 from 0.5 to 0.75 from 0.75 to 1.0 from 1.25 to 1.5
Answer:
the answer is C 0.75 to 1.0
Over the intervals 0.25 to 0.5, 0.5 to 0.75, and 0.75 to 1.0, the exponential and linear functions are approximately equal.
To determine over which interval the exponential and linear functions are approximately the same, we first need to define the functions. Let's denote the exponential function as [tex]\( f(x) = e^x \)[/tex] and the linear function as ( g(x) = mx + c ), where ( m ) is the slope and ( c ) is the y-intercept.
Given the intervals, we'll first need to calculate the values of the exponential function at the endpoints of each interval and then find the linear function that best approximates those values. We'll choose the linear function with the same value at the starting point of each interval and approximate the slope ( m ) based on the difference in the exponential function values at the endpoints of the interval.
Let's start with each interval:
1. Interval from 0.25 to 0.5:
- Endpoint 1:[tex]\( f(0.25) = e^{0.25} \approx 1.284 \)[/tex]
- Endpoint 2: [tex]\( f(0.5) = e^{0.5} \approx 1.649 \)[/tex]
- Approximating a linear function starting at ( f(0.25) ):
[tex]- \( m = \frac{f(0.5) - f(0.25)}{0.5 - 0.25} = \frac{1.649 - 1.284}{0.5 - 0.25} \approx 0.73 \)[/tex]
[tex]- \( c = f(0.25) \approx 1.284 \)[/tex]
- So, the linear function is [tex]\( g(x) \approx 0.73x + 1.284 \)[/tex]
2. Interval from 0.5 to 0.75:
- Endpoint 1:[tex]\( f(0.5) = e^{0.5} \approx 1.649 \)[/tex]
- Endpoint 2: [tex]\( f(0.75) = e^{0.75} \approx 2.117 \)[/tex]
- Approximating a linear function starting at ( f(0.5) ):
[tex]- \( m = \frac{f(0.75) - f(0.5)}{0.75 - 0.5} = \frac{2.117 - 1.649}{0.75 - 0.5} \approx 0.934 \)[/tex]
[tex]- \( c = f(0.5) \approx 1.649 \)[/tex]
- So, the linear function is [tex]\( g(x) \approx 0.934x + 1.649 \)[/tex]
3. Interval from 0.75 to 1.0:
- Endpoint 1: [tex]\( f(0.75) = e^{0.75} \approx 2.117 \)[/tex]
- Endpoint 2: [tex]\( f(1.0) = e^{1.0} \approx 2.718 \)[/tex]
- Approximating a linear function starting at ( f(0.75) ):
[tex]- \( m = \frac{f(1.0) - f(0.75)}{1.0 - 0.75} = \frac{2.718 - 2.117}{1.0 - 0.75} \approx 1.202 \)[/tex]
[tex]- \( c = f(0.75) \approx 2.117 \)[/tex]
- So, the linear function is [tex]\( g(x) \approx 1.202x + 2.117 \)[/tex]
4. Interval from 1.25 to 1.5:
- Endpoint 1:[tex]\( f(1.25) = e^{1.25} \approx 3.490 \)[/tex]
- Endpoint 2: [tex]\( f(1.5) = e^{1.5} \approx 4.482 \)[/tex]
- Approximating a linear function starting at ( f(1.25) ):
[tex]- \( m = \frac{f(1.5) - f(1.25)}{1.5 - 1.25} = \frac{4.482 - 3.490}{1.5 - 1.25} \approx 3.946 \)[/tex]
- [tex]\( c = f(1.25) \approx 3.490 \)[/tex]
- So, the linear function is[tex]\( g(x) \approx 3.946x + 3.490 \)[/tex]
Now, we can compare each linear approximation to the exponential function within its respective interval:
1. For the interval from 0.25 to 0.5, the linear function [tex]( g(x) \approx 0.73x + 1.284 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]
2. For the interval from 0.5 to 0.75, the linear function[tex]\( g(x) \approx 0.934x + 1.649 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]
3. For the interval from 0.75 to 1.0, the linear function [tex]\( g(x) \approx 1.202x + 2.117 \)[/tex] is approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]
4. For the interval from 1.25 to 1.5, the linear function [tex]\( g(x) \approx 3.946x + 3.490 \)[/tex] is not approximately equal to the exponential function [tex]\( f(x) = e^x \).[/tex]
So, the exponential and linear functions are approximately the same over the intervals from 0.25 to 0.5, 0.5 to 0.75, and 0.75 to 1.0.
Find the radian measure of an angle of 280
Formula for degree to radian:
degree ×[tex]\frac{\pi }{180}[/tex]
so...
[tex]280* \frac{\pi }{180}[/tex]
Exact answer:
[tex]\frac{14\pi }{9}[/tex]
Rounded answer:
4.89
Hope this helped!
The scatter plot shows the annual earnings and tenures of a few employees of Stan & Earl Corp.
The regression line for this data set has a slope close to m = (5.5,35,-50,-2.5) , and the correlation coefficient is close to (0.20,0.40,0.75,0.95) .
Based on this information, we can conclude that employees’ annual earnings are (strongly related, moderately related, weakly related, not related) to their tenure. Employee earnings (increase with, decrease with, are not affected by) tenure.
Answer:
i) 35
ii) 0.95
iii) employees’ annual earnings are strongly related to their tenure
iv) Employee earnings increase with tenure.
Step-by-step explanation:
i) The regression line for this data set has a slope close to m = 35
To find the slope of the regression line we need to find two points that lie on the line or that are very close to the line.
We have the following two points;
(1, 175) and (2.5, 225)
slope = (change in y) / (change in x)
= (225-175)/(2.5-1) = 33.33
This is close to 35.
ii) The correlation coefficient is close to 0.95
The coefficient of correlation is a measure of the degree of association between two variables. Correlation coefficient gives information on the strength and direction of a linear association.
The scatter-plot reveals that the annual earnings and tenures of the employees of Stan & Earl Corp are strongly positively associated hence the correlation coefficient is close to 0.95.
iii) Based on this information, we can conclude that employees’ annual earnings are strongly related to their tenure.
The correlation coefficient was found to be close to 0.95. A value greater than 0.7 shows a strong degree of association between two variables. Therefore, employees’ annual earnings are strongly related to their tenure
iv) Employee earnings increase with tenure.
The slope of the regression line of the data set was found to be close to 35. A positive slope implies that the response variable increases with increase in the explanatory variable.
Nevertheless, the correlation coefficient was also found to be positive which suggests a positive association between employee earnings and tenure.
Answer:
The regression line for this data set has a slope close to m = (35) , and the correlation coefficient is close to (0.95) .
Based on this information, we can conclude that employees’ annual earnings are (strongly related) to their tenure. Employee earnings (increase with) tenure.
Step-by-step explanation:
PLEASE HELP ME THANK YOU
Answer:
Midpoint Formula is (x1+x2/2, y1+y2/2)
(-3+4/2, -5+4/2)
Midpoint is (1/2, -1/2)
Step-by-step explanation:
what is slope and y-intercept of the two points (0,4) and (7,18)
Answer:
Answer: The slope is 2. The y-intercept is 4 which means point (0, 4).
Step-by-step explanation:
First, find the slope of the line that passes through those two points using the slope formula.
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
where the points are [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex]
[tex] slope = m = \dfrac{18 - 4}{7 - 0} = \dfrac{14}{7} = 2 [/tex]
The slope is 2.
One of the given points is (0, 4). Since the y-intercept lies on the y-axis, the x-coordinate of the y-intercept is 0. Point (0, 4) is the actual y-intercept.
Answer: The slope is 2. The y-intercept is 4, or point (0, 4).
To find the slope, use the S=(y2 - y1)/(x2 - x1) formula
S=(18-4)/(7-0)
S=14/7
S=2
After finding the slope, us the intercept formula to find the intercept
m is the slope
y-y1=m(x-x1)
y-4=2(x-0)
y=2x+4
163, 159, 155, 151.... What will the 23rd term in this sequence be?
the 23rd term would be 71. try using the website * m a t h w a y *and you can find answers like this.
hope i helped :)
Answer: Your answer is 71 and the other answerer is right m a t h w a y is really helpful with algebra and math questions.
For a class project, Jina made a model of the Empire State Building that was 23.7 centimeters tall. Her friend Caleb made a moel that was 23 3/5 centimeters tall. Whose model was taller? How much tall was it?
Answer:
jina by .1 cm
Step-by-step explanation:
3/5 = .6
caleb = 23.6
jina = 23.7
Jina's model of the Empire State Building was taller by 0.1 centimeter compared to Caleb's model.
Explanation:The question is comparing the heights of two models of the Empire State Building. Jina's model is 23.7 centimeters tall. Caleb's model is 23 3/5 centimeters tall, which in decimal form is equivalent to 23.6 centimeters tall. Therefore, Jina's model is taller. The height difference between Jina's model and Caleb's model is 23.7 - 23.6 = 0.1 centimeter. So, Jina's model is 0.1 centimeter taller than Caleb's model.
Learn more about Comparison of Heights here:https://brainly.com/question/31956811
#SPJ2
If f(-2)=16 which could be the equation for f(x)
A. f(x)=x-18
B.f(x)=20-2x
C. f(x)=3x+24
D.f(x)=8-4x
The answer is D
Let x = -2
f(-2) = 8 - 4(-2)
f(-2) = 8 + 8
f(-2) = 16
D is the answer.
If f(-2)=16 which could be the equation for f(x) f(x)=8-4x will yield f(-2)=16
What is function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
Given
Let x = -2
f(-2) = 8 - 4(-2)
f(-2) = 8 + 8
f(-2) = 16
therefore, f(x)=8-4x will yield f(-2)=16
To know more about functions refer to :
https://brainly.com/question/9418047
#SPJ2