\(\qquad\qquad\huge\underline{{\sf Answer}}\)
\( \textbf{Since it's a right angled Triangle we can } \\ \textbf{ use Pythagoras theorem } \)
\( \sf{Cos (29°) = \dfrac{b}{c}} \)\( \sf{Cos (29°) = \dfrac{b}{260}} \)\( \sf{b= 260\cdot Cos (29°) } \)\( \sf{b= 260\cdot 0.875 } \)[ \( \textsf{Cos(29°)= 0.875} \) ]
\( \sf{b= 227.5 in }\)\( \textsf{I hope you understood the procedure} \)
Select the correct answer. Which equation matches the function shown in the graph? A waveform on a coordinate plane starts from the y-axis at 1 unit and passes through (pi, minus 1), (2 pi, 1), and (3 pi, minus 1) and intercepts the x-axis at pi by 2, 3 pi by 2, 5 pi by 2, and 7 pi by 2.
The correct equation that matches the given graph is y = cos(x) + 1.
To determine the equation that matches the given graph, we can observe the key features and points provided.
The waveform starts from the y-axis at 1 unit: This suggests that the function has a vertical shift of 1 unit upwards.
The waveform passes through (π, -1), (2π, 1), and (3π, -1): This indicates that the function oscillates between the values of -1 and 1 as x increases.
The waveform intercepts the x-axis at π/2, 3π/2, 5π/2, and 7π/2: This suggests that the function has zeros or x-intercepts at these values.
Based on these observations, the function can be represented as a cosine function.
The cosine function with a vertical shift of 1, oscillating between -1 and 1, and having zeros at π/2, 3π/2, 5π/2, and 7π/2 is:
y = cos(x) + 1
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Which statement about residual plots is NOT true?
A. The vertical axis shows residuals.
B. If there is an obvious pattern, the model is probably reasonable.
C. The x-axis appears in the middle of the graph.
D. The sum of the residuals is 0.
Answer:
A is the correct answer
Step-by-step explanation:
The not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.
What is a residual plot?A residual plot shows the difference between the observed response and the fitted response values.
Given that, Which statement about residual plots is not true
In the given options,
If there is an obvious pattern, the model is probably reasonable, this option is not correct because, The pattern in the residual plot suggests that predictions based on the linear regression line will result in greater error as we move from left to right through the range of the explanatory variable.
So, it is not needed if there is an obvious pattern, then the model is probably reasonable,
Hence, the not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.
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pls help look on the images
You graph >7 with an open dot to the right.
The inequalities ≤ and ≥ would have a closed dot on the number line.
a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".
s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".
t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".
What are inequality signsInequality signs are mathematical symbols used to indicate that one quantity is greater than, less than, or equal to another quantity. These inequality signs includes:
Less than: <Greater than: >Less than or equal to: ≤Greater than or equal to: ≥These symbols are used in mathematical expressions and equations to compare values and express relationships between them.
Therefore, with a good understanding of inequality signs we conclude that:
On a graph, > 7 is with an open dot to the right.
Only the inequalities ≤ and ≥ would have a closed dot on the number line.
a > 3 is matched to the statement; "you must be older than 13 to play in the basketball league".
s < 3.5 is matched to the statement; "To use one stamp, your domestic letter must be under 3.5 ounces".
t ≥ 48 is matched to the statement; "You must be at least 48 inches tall to ride on the rollercoaster".
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Given f(x)=1−5x2 and g(x)=2x−1, show that f∘g is not equal to g∘f
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The value V of an item t years after it is purchased is given below.V = 9000exp(-0.6301t), 0 ≤ t ≤ 10Part b only-456.21 wrong-129.40 wrong
Answer:
• V'(4)=-456.10
,• V'(6)=-129.35
Explanation:
Given the function V which is defined as follows:
\(V=9000e^{-0.6301t},0\leq t\leq10\)First, find the derivative of V with respect to time.
\(\begin{gathered} \frac{dV}{dt}=9000\frac{d}{dt}(e^{-0.6301t}) \\ \text{ The derivative of }e^{kt}=ke^{kt} \\ V^{\prime}(t)=9000(-0.6301)e^{-0.6301t} \end{gathered}\)I. When t=4
\(\begin{gathered} V^{\prime}(t)=9000(-0.6301)e^{-0.6301t} \\ V^{\prime}(4)=9000(-0.6301)e^{-0.6301\times4} \\ =-456.10 \end{gathered}\)The rate of change when t=4 is -456.10 (correct to 2 decimal places).
II. When t=6
\(\begin{gathered} V^{\prime}(t)=9000(-0.6301)e^{-0.6301t} \\ V^{\prime}(4)=9000(-0.6301)e^{-0.6301\times6} \\ =-129.35 \end{gathered}\)The rate of change when t=6 is -129.35 (correct to 2 decimal places).
The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 41, 43, 49.5, 56, and 58 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
Which value does 50% of the data lie above, and what is it called?
58, the median
56, the upper quartile
43, the lower quartile
49.5, the median
The 50% of the data lies above is 49.5. it is called the median.
What is the upper quartile?
Assume that Q₃ represents the upper quartile, which is the median of the data set's upper half. In contrast, Q₁ represents the median and lower quartile of the lower half of the data set. The median is Q₂. Consider a data set that contains n items. The quartiles are then provided by:
Q₁ = [(n+1)/4]
Q₂ = [(n+1)/2]
Q₃ = [3(n+1)/4]
this item
The 50% of the data is median.
The formula of median is
(n+1)/2 th term
The given data is 41, 43, 49.5, 56, and 58.
The number of items is n = 5.
The median of the data is (5+1)/2 the term = 3rd term.
The third term of the data is 49.5.
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A spinner with sections labeled 1-8 has an equal chance of landing on each numbe. Find each probability.
P(even number)
Each of the equal sides of an isosceles triangle is 5 times the third side. The perimeter of the triangle is 121 inches. Find the sides of the triangle.
Answer: The small side is 11, and the other two are 55, 55,
Step-by-step explanation:
So the perimeter adds up to 121 inches.
we know that two of the sides are 5x the 3rd side while being congruent.
11 times 5=55. 55 times 2=110. 110+11=121
Answer:
The third side is 11 inches
the 2 equal sides are 55 inches each side.
Step-by-step explanation:
X + 2(5x) = 121
x + 10x = 121
11x = 121
x = 121/11
x = 11
What is 74% of 95? Can you help me understand
We need to calculate the 74% of 95. To do that, we need to remember that 74% = 74/100
Then:
74% of 95 = 74/100*95 = 703/10 = 70.3
A rodent species has a population of 25,000 and is decreasing in size at a factor of per year
due to the increase in snake population.
a. Write an exponential model that will estimate the rodent's population.
b. Describe the meaning of "a" and "b" in the context.
c. Copy the table and complete.
X Y
0
1
2
3
4
5
bookmarks
d. Using the model in part A, how many estimated population after 10 years. Write your
answer in whole number.
The exponential model for the rodent's population is 25,000\((0.08)^{x}\), where x is the number of years and 0.8 is the rate of decrease in population size per year.
What is an exponent?An exponent is a mathematical notation that indicates how many times a number has been multiplied by itself. It is commonly shown as a superscript next to the basic number, such as \(4^{2}\), which equals 4 x 4 = 16.
a. The exponential model for the rodent's population is Y = 25,000\((0.08)^{x}\), where x is the number of years.
b. The "a" in the exponential model is 25,000, which is the starting population of the rodent species. The "b" is 0.8, which is the rate of decrease in population size per year.
c.
X Y
0 25000
1 20000
2 16000
3 12800
4 10240
5 8192
d. After 10 years, the estimated population of the rodents is 2048. This is because the population decreases by a factor of 0.8 each year, so the population after 10 years is 25000\((0.8)^{10}\) = 2048.
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graph the line passing through (−4,−1) whose slope is m=-4/5
Answer:
\(y=-\frac{4}{5}x-\frac{21}{5}\)
Step-by-step explanation:
The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):
\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)
To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting m = -4/5, x = -4, and y = -1, we can solve for b:
-1 = (-4/5)(-4) + b
-1 = 3.2 + b
b = -4.2
Therefore, the equation of the line is:
y = (-4/5)x - 4.2
To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:
y = (-4/5)x - 4.2
y = (-4/5)(0) - 4.2
y = -4.2
So the y-intercept is (0,-4.2).
Using this point and the given point (-4,-1), we can draw a straight line passing through both points.
Here is a rough sketch of the graph:
|
|
| *
| /
| /
| /
-----*--------
|
|
|
|
|
The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.
Please Help Im stuck
Answer: The last one is the right one
Step-by-step explanation:
So first solve for n
1/2n+3<5
1/2n<2, multiple by 2 on both sides to remove fraction
n<4
the circle will be at 4, and since n<4, n is less than 4, so your line must also be less that 4.
35/-7
Is the expression
undefined? If not, find the quotient.
9514 1404 393
Answer:
-5
Step-by-step explanation:
The quotient is the opposite of 35/7 = 5, so is -5.
__
Division is only undefined when the denominator is 0. Clearly, -7 is not zero, so this expression is "defined."
35/-7 = -(35/7) = -5
Please help. Any unnecessary answers will be reported.
You are in a competition that involves building card towers. The quickest person to reach 100 stories wins the competition. After reaching 5 stories of cards as shown in the picture below, you needed to use 40 cards.
How many cards will be necessary to build , in a similar way, a tower with 100 stories? Make sure you include work.
The 10,100 cards will be necessary to build a 100-story card tower.
To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:
Triangular number = (n * (n + 1)) / 2
In this case, n represents the number of stories in the tower (100). Plug in the value for n:
Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050
Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:
Total cards = 5,050 * 2
Total cards = 10,100
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A rain gutter is made from sheets of
aluminum that are 24 inches wide by
turning up the edges to form right
angles. Determine the depth of the
gutter that will maximize its cross-
sectional area and allow the greatest
amount of water to flow. What is the
maximum cross-sectional area?
Flat sheet 24 inches wide
1 Write a quadratic function for the Area in terms of x: A(x) =
2 The cross-sectional area is maximized when the depth of the gutter is
3 The maximum cross-sectional area is square inches.
1. The quadratic function for the Area in terms of x: A(x) = 24x.
2. The cross-sectional area is maximized when the depth of the gutter is 0.
3. The maximum cross-sectional area is square inches 0.
To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.
1. Write a quadratic function for the area in terms of x:
The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.
2. The cross-sectional area is maximized when the depth of the gutter is:
To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.
3. The maximum cross-sectional area is square inches:
Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.
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Bryan invests $6500 in two different accounts. The first account paid 11 %, the second account paid 7 % in interest. At the end of the first year he had earned $519 in interest. How much was in each account?
$ at 11 %
$ at 7 %
Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.
The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).
According to the problem, the total interest earned after one year is $519. So we can set up the equation:
0.11x + 0.07(6500 - x) = 519
Simplifying the equation:
0.11x + 455 - 0.07x = 519
0.04x + 455 = 519
0.04x = 64
x = 64 / 0.04
x = 1600
Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).
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the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone
Answer:
Step-by-step explanation:
V = 3.9V
I = 0.12A
Ohm's Law, V = IR
Rearranging Ohm's Law, R = V/I
R = 3.9/0.12 = 32.5Ω
what is the y value of 9x+5y=8
Helpppp please.........
Answer:
C, 12 and 24
Step-by-step explanation:
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6
Factors of 24
List of positive integer factors of 24 that divides 12 without a remainder.
1, 2, 3, 4, 6, 8, 12
Determine whether a triangle can be formed with the given side lengths. If the side lengths
can form a triangle, determine if they will form an isosceles triangle, equilateral triangle, or
neither.
2 mi, 4 mi, 9 mi
Answer:
it can't form isosceles triangle cause any two sides of the triangle are not equal ,it can't form equalateral triangle cause 3 sides of the triangle are not equal and neither right angle triangle so triangle can't be formed
Mackenzie investigated the relationship between the number of hours studying and the test score for some of the students in her class. She constructed the scatterplot below.Which statement is correct based on the scatterplot?
Answer: there is a relationship between study hours and test score. as the hours of studying increase, the test scores increase.
Answer:
C) There is a relationship between study hours and test score. As the hours of studying increase, the test scores increase.
Step-by-step explanation:
In the scatter plot, I can see that when the hours increase, so does the test scores. Thus, the answer is C
Chet has $1200 invested in a bank account modeled by the function P(n) = 1200(1.002)
Answer:
Answer: 3) R(n) = 1200(1.002)n - 100n
Step-by-step explanation:
After n months, which function represents Chet’s net worth, R(n)?
(1) R(n) = 1200(1.002)n + 100n
(2) R(n) = 1200(1.002)12n + 100n
(3) R(n) = 1200(1.002)n - 100n
(4) R(n) = 1200(1.002)12n - 100n
Answer: 3) R(n) = 1200(1.002)n - 100n
Net worth is the amount of his savings minus his debt,
Everything in the problem is in terms of months, so there is no need to multiply the exponent by 12, which would convert n years into months.
Using log evaluate 3^x=10
Answer:
x ≈ 2.09590327429
Step-by-step explanation:
You want the solution to 3^x = 10 using logarithms.
LogsTaking logarithms of both sides of the given equation, we have ...
x·log(3) = log(10)
Dividing by the coefficient of x gives ...
x = log(10)/log(3)
x ≈ 2.09590327429
__
Additional comment
If the logarithm to the base 10 is used, then this becomes ...
x = 1/log₁₀(3)
The meaning of "log( )" varies with the context. In high-school algebra, it usually means "log₁₀( )". In other contexts, it may mean "ln( )", the natural logarithm.
For the purpose here, it doesn't matter what base the logarithms have, as long as log(10) and log(3) are to the same base.
<95141404393>
The approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
To evaluate the equation 3^x = 10 using logarithms, we can take the logarithm of both sides of the equation. The most commonly used logarithm is the base 10 logarithm, also known as the common logarithm (log).
Taking the log of both sides, we get:
log(3^x) = log(10)
Now, we can apply the logarithmic property that states log(a^b) = b * log(a). Applying this property to the left side of the equation:
x * log(3) = log(10)
Next, we can divide both sides of the equation by log(3) to isolate the variable x:
x = log(10) / log(3)
Using a calculator, we can evaluate the right side of the equation:
x ≈ 1.46497
Therefore, the approximate value of x that satisfies the equation 3^x = 10 is approximately 1.46497.
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How would you use 180(n-2)/n
The ordered pair (2, 10) is a point on a direct variation equation. Write the direct variation equation.
Answer:
Y=KX so its 10=K2
Step-by-step explanation:
Plug in the Number OR K=y/x
Mai got a prepaid debit card with 30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 23 cents per yard. If after that purchase there was 27.01 left on the card, how many yards of ribbon did Mai buy?
Answer:
The answer I got was 13.
Step-by-step explanation:
I first did 30-27.01 to get 2.99.
I then divided 2.99 by 0.23 or 2.99/0.23 to get 13.
Hope this helped any!
5a. find the value of a.
The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;
5 a. The value of a is 3.5
b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel
What is a logarithmic function?A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential function
The function is f(x) = a·log₃(x - 4),
x > 4 and a > 0
The coordinates of a point on the graph of the function, f is A(13, 7)
5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows
f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²
7 = a·log₃3²
7 = 2·a·log₃3 = 2·a·1 = 2·a
2·a = 7
a = 7 ÷ 2 = 3.5
a = 3.5
5 b. The coordinates of the x-intercept of the graph = (5, 0)
The equation of the function is;
f(x) = 3.5·log₃(x - 4)
A third point on the graph is given when f(x) = 14 as follows;
f(x) = 14 = 3.5·log₃(x - 4)
log₃(x - 4) = 14 ÷ 3.5 = 4
3⁴ = x - 4
x = 3⁴ + 4 = 85
Which gives the point, (85, 14)
Similarly, we have the point (31, 10.5), (7, 3.5)
Please find attached the graph of f(x) created with MS Excel
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Solve each system by elimination.
3) 3x + 4y = 12
-3x - y = 6
4) -5x – 6y = 5
-6x + 6y = 6
5) 7x - 4y = 19
10x - 2y = 16
6) 10x - 9y=-13
5x – 3y =-11
Answer:
3) x = -4 and y = 6
4) x = -1 and y = 0
5) x = 1 and y = -3
6) x = -4 and y = -3
Step-by-step explanation:
3) Add the equations:
(3x + 4y = 12) + (-3x - y = 6) (eliminate the x)
= 3y = 18
y = 18/3
y = 6
3x + 4(6) = 12
3x = 12 - 24
x = -12/3 = 4
4) Add the equations:
(-5x - 6y = 5) + (-6x + 6y = 6)
-11x = 11
x = -1
-5(-1) -6y = 5
-6y = 5 - 5
y = 0
5) 7x -4y = 19
10x - 2y = 16
Multiply the second equation by -2 to eliminate the y and add both equations.
-2(10x -2y = 16) =
(-20x + 4y = -32) + (7x - 4y = 19)
-13x = -13
x = 1
7(1) - 4y = 19
-4y = 19-7
y = 12/-4
y = 3
6) multiply the second equation by -2 to eliminate the x and then add the equations.
-2(5x - 3y = - 11) =
(-10x + 6y = 22) + (10x - 9y = - 13)
= -3y = 9
y = - 3
10x - 9(-3) = - 13
10x = -13 - 27
x = -40/10
x = -4
The height of a right triangular prism is 1 5/6 inches each side of the triangular base measures 10 inches and the height of the bases eight2 over 3 inches the triangular prism is place to top of cube whose side measures 10 inches so that one of the triangular prisms bases lies completely on one side of the cube what is the surface area of the solid formed
The surface area of the solid formed is approximately, 598.3 in².
What is the Surface Area of a Right Triangular Prism?Surface area of the solid is the area covered by the solid all round.
The given parameters are:
Height of the prism (L) = 1 5/6 = 1.83 in.Side of base (s1) = 10 in.Side of base (s2) = 10 in.Side of base (s3) = 8 2/3 = 8.67 in.base (b) = 10Height (h) = 8.67 in.a = 10 in.Surface area of the solid formed = 5(10×10) + (0.5×10×8.67) + 3(10×1.83) = 598.3 in²
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Select all solutions to M•M•M=729
The solution to the equation given by M * M * M = 729 is 9
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Given the equation:
M.M.M = 729
This gives:
M * M * M = 729
M³ = 729
Taking the cube root of both sides:
∛M³ = ∛729
M = 9
The solution to the equation is 9
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