Answer:
4
Step-by-step explanation:
10 - 6 = 4
1. Find the length of a.
Answer:
Step-by-step explanation:
[tex]\dfrac{ 1 }{ 2 } \times 12\times 15\times \sin ( 110 )[/tex]
==> 84.57
Use the graph to write the explicit rule of the arithmetic sequence.
Question 19 options:
A)
ƒ(n) = 9 + 2(n – 1)
B)
ƒ(n) = 5 + 3(n – 1)
C)
ƒ(n) = –3 + 2(n – 1)
D)
ƒ(n) = 3 + 2(n – 1)
Answer: D
Step-by-step explanation:
The first term is 3 and the common difference is 2.
Substituting into the explicit formula for an arithmetic sequence gives D as the correct answer.
Five hats and three shirts cost $176. Three hats and five shirts cost $208. What is the cost of one hat?
The cost of one hat is __ dollars.
Let hats be x
Let shirts be y
We can set up a system of equations to figure out the cost of one hat.
5x+3y = 176 and 3x+5y = 208
Since we are finding the cost of the hats, we will need to isolate x from the equation. We can first get rid of y. One way we can do that is by multiplying the first equation with 5 and the second one with -3, effectively making y add up to 0 when we solve for x.
5(5x+3y = 176) --> 25x+15y = 880
-3(3x+5y = 208) --> -9x-15y = -624
We can now add the 2 equations together and solve for x.
25x+15y = 880
-9x-15y = -624
+>>>>>>>>>>>>>>>
16x = 256
x = 16
So the the cost of one hat is 16 dollars.
Answer:
$16
Step-by-step explanation:
Define the variables:
Let x = cost of one hatLet y = cost of one shirtCreate two equations using the defined variables and the given information.
Equation 1
Five hats and three shirts cost $176.
⇒ 5x + 3y = 176
Equation 2
Three hats and five shirts cost $208.
⇒ 3x + 5y = 208
Rewrite Equation 2 to make y the subject:
[tex]\implies \sf 3x+5y-3x=208-3x[/tex]
[tex]\implies \sf 5y=208-3x[/tex]
[tex]\implies \sf \dfrac{5y}{5}=\dfrac{208-3x}{5}[/tex]
[tex]\implies \sf y=\dfrac{208-3x}{5}[/tex]
Substitute the found expression for y into Equation 1 and solve for x:
[tex]\implies \sf 5x+3\left(\dfrac{208-3x}{5} \right)=176[/tex]
[tex]\implies \sf 5x+\dfrac{624-9x}{5}=176[/tex]
[tex]\implies \sf 5x+124.8-1.8x=176[/tex]
[tex]\implies \sf 3.2x+124.8=176[/tex]
[tex]\implies \sf 3.2x+124.8-124.8=176-124.8[/tex]
[tex]\implies \sf 3.2x=51.2[/tex]
[tex]\implies \sf \dfrac{3.2x}{3.2}=\dfrac{51.2}{3.2}[/tex]
[tex]\implies \sf x=16[/tex]
Therefore, the cost of one hat is 16 dollars.
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Algebra 3, in the excercise size the graphs to determine the functions domain and range, x and y intercepts if any, and the functions values indicated below the graphs
Answer:
Read explanation
Step-by-step explanation:
I answered another one of your questions just like this in detail so I'll keep this one shorter.
Domain: (-∞, 0]
Range: (-3,∞)
x-intercept: Approximately -3.75
y=intercept: -3
please help 14 points ASAP
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median: Upper quartile:
Maximum:
Interquartile range:
The desired measures for the data-set is given by:
Minimum: 48Lower quartile: 54.Median: 63.5.Upper quartile: 74.Maximum: 80.IQR: 20How to find the five number summary and interquartile range of the data-set?The five number summary is composed by the measures explained below, except the IQR.
The minimum value is the smallest value from the data-set, as the maximum value is the greatest value of the data-set.The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference of the third quartile and the first quartile.In this problem, we have that:
The minimum value is the smallest value, of 48.The maximum value is the smallest value, of 80.The data-set has even cardinality, hence the median is the mean of the middle elements, which are 63 and 64, hence the median is of 63.5.The first quartile is the median of the five elements of the first half, hence it is of 54.The third quartile is the median of the five elements of the second half, hence it is of 74.The IQR is the difference between the quartiles, hence 74 - 54 = 20.More can be learned about five number summaries at brainly.com/question/17110151
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You start at (-4, 0). You move left 1 unit and down 5 units. Where do you end?
Answer: (-5, -5)
Step-by-step explanation:
(-4, 0)
Here, -4 is our x value and 0 is our y value
The x value moves horizontal (left and right) while the y value moves vertical (up and down)
If we move 1 unit left, we change x by -1 so, -4 -1 = -5
If we move 5 units down, we change y by -5 so, 0 -5 = -5
Therefore,
our new endpoint is: (-5, -5)
1
2. Rotate Rectangle ABCD 90° counterclockwise.
Then, translate it along the vector (3,4).
A
D
B
C
-4 -2
4
2
АУ
O
-2.
-4
2
4
X
A'(
B'(
C'(
D'(
A"(
B"(
C"(
D"(
)
)
)
)
HELP ME PLS
Rotating 90 degrees counterclockwise: [tex](x,y) \longrightarrow (-y,x)[/tex]
[tex]A(-4,4) \longrightarrow A'(-4, -4)\\\\B(-3, 4) \longrightarrow B'(-4, -3)\\\\C(-3, 1) \longrightarrow C'(-1, -3)\\\\D(-4, 1) \longrightarrow D'(-1, -4)[/tex]
Translate along [tex]\langle 3, 4 \rangle[/tex]: [tex](x,y) \longrightarrow (x+3, y+4)[/tex]
[tex]A'(-4, -4) \longrightarrow A''(-1, 0)\\\\B'(-4, -3) \longrightarrow B''(-1, 1)\\\\C'(-1, -3) \longrightarrow C''(2, 1)\\\\D'(-1, -4) \longrightarrow D''(2, 0)[/tex]
Pls help I’ll brainlest
Asap
Answer:
C. slope
Greetings !
The symbol for slope is "m". Slope can be calculated by taking any two locations along a line and calculating the ratio of the RISE to the RUN (the ratio of the difference between vertical positions of the locations to the difference between horizontal positions of the locations).
Answer: slope.
Step-by-step explanation:
PLEASE HELP IM STUCK
Answer:
y= 2x + 10
Step-by-step explanation:
The variable depends on the $2 so, the green box should be 2
I need help here’s a picture can somone explain what I need to do??
Answer:
176 square feet
Step-by-step explanation:
add the areas of the rectangle and triangle
rectangle area is
16 times 8 which is
128
rectangle area is
1/2 times 12 times 8 which is
48
then add them
128 plus 48 is
176 square feet
Do the data in the table represent a direct variation or inverse variation? Write an equation to model the data in the table?
x 2 4 8 12
y 4 2 1 2/3
Based on the given data; the table represent an inverse variation and the equation that model the data in the table is y = 8/x
VariationDirect variationy = k × x
4 = k × 2
4 = 2k
k = 4/2
k = 2
when y = 2 and x = 4
y = k × x
= 2 × 4
y = 8
Indirect variationy = k/x
4 = k / 2
8 = k
when y = 2 and x = 4
y = k/x
2 = k/4
2 × 4 = k
k = 8
So,
y = k/x
y = 8/x
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Which of the following fractions has the largest value 11/20 10/21 9/19 8/17 or 6/13
Answer:
11/20
Step-by-step explanation:
You could turn them all into equivalent fractions, but the common denominator would be 1,763,580. Yuck.
Look at the relationship for the numerators to the denominators. The only numerator that is more than half of its denominator is 11/20. Half of 20 would be 10 and 11 has a larger value than 10, so as a decimal, it would be more than .5. All of the other numerators are less than half, so that they have to less than .5.
If you changed all of the numbers to decimals, you would see that 11/20 has the largest value.
Geometry: complete this proof (ASAP!!!!! It’s urgent)
Answer:
1. Given.
2. Alternate Interior Angles Theorem.
3. m<2 + m<7 = 180 by definition of supplementary angles. By definition of congruent angles, m<2 = m<4 and m<5 = m<7, therefore m<4 + m<5 = 180 by substitution property of equality. By definition of supplementary angles, <4 is supplementary to <5.
4. Converse of Consecutive Angles Theorem.
Use the given data set to complete parts (a) through (c) below. (Use α=0.05.)
1. The value of the linear correlation coefficient r is given as 0.8159. The correct option is a. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables
2. The scatterplot reveals a distinct pattern that is not a straight-line pattern.
What is the linear correlation coefficient?This is the data that we get when we try to get the existing relationship that is in existence between the variables that are used in a regression equation.
The value of r was calculated using a statistical tool online. The graph showed us it was not a straight line. The value of the r = 0.8159
The results of the test is in the attachment
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Janice walks 2 kilometers every morning. how many meters does janice walk each day? a) 0.20 meters b) 20 meters c) 200 meters d) 2,000 meters
Answer: 2000 meters
Step-by-step explanation: A kilometer means 1,000 meters a kilo means 1000. So, 2 x1000 = 2000 meters.
Given that log 2 = 0.3010 and log 3 = 0.4771 , how can we find log 6 ?
Step-by-step explanation:
log 6 = log (2×3) = log 2 + log 3 = 0.3010+0.4771
=0.7781
Answer:
[tex]\sf \log_{10}6=0.7781[/tex]
Step-by-step explanation:
Given:
[tex]\sf \log_{10} 2 = 0.3010[/tex]
[tex]\sf \log_{10} 3 = 0.4771[/tex]
To find log₁₀ 6, first rewrite 6 as 3 · 2:
[tex]\sf \implies \log_{10}6=\log_{10}(3 \cdot 2)[/tex]
[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \sf \log_{10}(3 \cdot 2)=\log_{10}3+\log_{10}2[/tex]
Substituting the given values for log₁₀ 3 and log₁₀ 2:
[tex]\begin{aligned} \sf \implies \log_{10}3+\log_{10}2 & = \sf 0.4771+0.3010\\ & = \sf 0.7781 \end{aligned}[/tex]
Therefore:
[tex]\sf \log_{10}6=0.7781[/tex]
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In quadrilateral qrst, angle r s t measures (5x 15)°. angle tqr measures (4x 3)°. circle p is inscribed with quadrilateral q r s t. what is the measure of angle rst?
The measure of the angle rst is [tex]105^{o}[/tex].
What is the inscribed quadrilateral theorem?According to the theorem, a quadrilateral can be inscribed by a circle if and only if its opposing angles are supplementary. A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.
The sum opposite angles of a quadrilateral is 180 degrees.
We can see that the angles rst and angle tqr are opposite angles of quadrilateral qrst, hence supplementary angles.
Therefore,
<RST + <TQR = 180
5x+15 + 4x+ 3 = 180
9x + 18 = 180
9x = 180 - 18
9x = 162
x = 162/9
x = 18
Since <RST = 5x+15
<RST = 5(18) + 15
<RST = 90 + 15
<RST = 105degrees
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What would cause an Inequality sign in an equation to flip?
a.) When dividing both sides by a negative.
b.) When adding a negative to both sides.
c.) When multiplying a fraction by both sides.
d.) When subtracting a negative to both sides.
Answer:
When dividing both sides by a negative.
Step-by-step explanation:
When dividing OR multiplying both sides by a negative, we need to flip the inequality signs.
Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centered at a=1. Write the Taylor series in summation notation
Answer:
[tex]e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...[/tex]
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
Step-by-step explanation:
Taylor series expansions of f(x) at the point x = a
[tex]\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...[/tex]
This expansion is valid only if [tex]\text{f}\:^{(n)}(a)[/tex] exists and is finite for all [tex]n \in \mathbb{N}[/tex], and for values of x for which the infinite series converges.
[tex]\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1[/tex]
[tex]\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]
[tex]\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4[/tex]
[tex]\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4[/tex]
[tex]\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4[/tex]
Substituting the values in the series expansion gives:
[tex]e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...[/tex]
Factoring out e⁴:
[tex]e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right][/tex]
Taylor Series summation notation:
[tex]\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n[/tex]
Therefore:
[tex]\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n[/tex]
Find the total surface area. A. 78 B. 98 C. 69 D. 92
The total surface area of the figure is 92 m².
How to find the surface area of a figure?The surface area of a figure is the sum of the whole sides of the figure.
Therefore,
surface area = 4 × 4 + 4 × 4 + 6 × 4 + 2 × 4 + 1 / 2 (2 + 6)3.5 + 1 / 2 (2 + 6)3.5
Hence,
surface area = 16 + 16 + 24 + 8 + 14 + 14
Therefore,
surface area = 32 + 24 + 8 + 28
surface area = 56 + 8 + 28
surface area = 92 m²
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A sampling method is _________ when the individuals selected for one sample are used to determine the individuals in the second sample.
Answer:
someone please help me check my page
someone please help me check my pageStep-by-step explanation:
pleasee mwa mwa mwa help me
Answer: About (-2.414, 0) and (0.414, 0)
Step-by-step explanation:
Let us graph the equation given and see what the x-intercepts are. These are points where the line intercepts the x-axis. See attached.
This means our x-intercepts are at about (-2.414, 0) and (0.414, 0).
These are also equal to [tex]-1-\sqrt{2}[/tex] and [tex]-1+\sqrt{2}[/tex]
Answer:
[tex]x = \bold{0.414} \textrm{ and } x= \bold{-2.414}[/tex]
Step-by-step explanation:
See attached graph for a visual
The x-intercepts of a graph are where the graph crosses the x-axis ie where the value of y = 0 The equation of the graph is y=-x^{2}-2x+1
Setting y = 0 and solving for the resultant equation will provide the x-intercepts
[tex]0=-x^{2}-2x+1or-x^{2}-2x+1=0[/tex]
Reversing the signs gives us
[tex]x^{2}+2x-1=0[/tex]
This is a quadratic equation of the form [tex]ax^{2}+bx+c=0[/tex] with a = 1, b = 2 and c=-1
For an equation of this form the roots of the equation ie the values of x which satisfy the equation are given by
[tex]\frac{-b\pm\sqrt{{b^{2}-4ac}}}{2a}[/tex]
Substituting we get the two roots as
[tex]x=\frac{-2\pm\sqrt{{2^{2}-4(1)(-1}}}{2}=\frac{-2\pm\sqrt{{4-(-4)}}}{2}x=\frac{-2\pm\sqrt{8}}{2}8 = 4(2)\sqrt{8}=\sqrt{4}\sqrt{2} = 2\sqrt{2}[/tex]
So the two roots are
[tex]x=\frac{-2\pm2\sqrt{2}}{2}[/tex]
Dividing by 2 we get the two roots(x-intercepts) as
[tex]x=-1\pm\sqrt{2}\\\\x_{1}=-1+\sqrt{2} =-1+1.414=\bold{0.414}[/tex]
[tex]x_{2}=-1-\sqrt{2}=-1-1.414=\boldsymbol{-2.414}[/tex]
general term for -13, -11, -9, -7
The general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.
Arithmetic progression-13, -11, -9, -7
First term, a = -13Second term = -11Common difference, d = Second term - first term
= -11 - (-13)
= -11 + 13
= 2
Therefore,
Tn = a + (n - 1)d
Where,
n = number of termsTn = a + (n - 1)d
= -13 + (n - 1)2
= -13 - 2n - 2
Tn = -15 - 2n
So therefore, the general term for the arithmetic sequence; -13, -11, -9, -7 is Tn = -15 - 2n.
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The river is 602 feet wide at Big Bend Corner. A boy is in the shallow
water, 135 feet from the shore. How far is the boy from the other side of
the river?
we conclude that the distance to the other side is 467 feet.
How far is the boy from the other side of the river?
We know that the width of the river is 602ft. This means that the distance from shore to shore is 602 feet.
If the boy is at a distance of 135 from the shore, then the distance to the other side is given by the difference:
d = 602ft - 135ft = 467ft
Then, we conclude that the distance to the other side is 467 feet.
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The equation for least regression line to this data set is ŷ = 76. 82x 88. 56. what is the predicted value (in dollars) for maintenance expenses when a truck is 7 years old?
The predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.
In this question,
The equation for least regression line to this data set is
y' = 76.82x + 88.56 ------- (1)
Number of years, x = 7
The general form of equation for least regression line is
y' = a + bx
where y is the dependent variable, x is the independent variable, a is the intercept of regression line and b is the slope of regression line.
The predicted value (in dollars) for maintenance expenses when a truck is 7 years old can be calculated as
y' = 76.82x + 88.56
Substitute the value of x in the above equation, we get
y' = 76.82(7) + 88.56
y' = 537.74 + 88.56
y' = 626.3
Hence we can conclude that the predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.
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what is the digit of 7 in 906point7
According to the Coase theorem, negative externalities can be internalized if Select one: a. the government takes action to solve the problem. b. property rights are assigned to the party who is being damaged. c. property rights are assigned to either party. d. property rights are assigned to the party who is doing the damage.
Answer:
B. Property right are assigned to the party who is being
PLEASE HELP IMMEDIATELY
Use the function f(x) to answer the questions:
f(x) = 5x2 + 2x − 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
For the given function f(x) = 5x² + 2x - 3,
Part A: The x-intercepts of the graph f(x) are: (-1, 0) and (3/5, 0).
Part B: The vertex of the graph of f(X) is going to be a minimum and its coordinates are (-0.2, -3.2).
Part C: The values obtained in the part A and Part B are used for graphing the given function. Since the vertex is minimum, the parabola opens upwards.
How to calculate x-intercepts of a function?The x-intercepts of a function or equation are obtained at y = 0.
Then, on substituting y = 0 in the function gives the x-coordinate i.e., the x-intercept.
How to calculate the coordinates of the vertex of a function?To calculate the x coordinate of vertex(h, k), use the formula mentioned below:
h = -b/2a
When the function is in the form of ax² + bx + c.
Then, to calculate the y-coordinate of the vertex, substitute obtained h value in the place of x in the function.
Thus, the required coordinates of the vertex are obtained as (h, k).
Calculation:It is given that,
f(x) = 5x² + 2x - 3
Part A: Finding the x-intercepts:
Substituting y = 0 i.e., f(x) = 0;
⇒ 5x² + 2x - 3 = 0
On simplifying/factorizing,
⇒ 5x² + 5x - 3x - 3 = 0
⇒ 5x(x + 1) - 3(x +1) = 0
⇒ (5x - 3)(x + 1) =0
∴ x = 3/5 or x = -1
Thus, the x-intercepts are (3/5, 0) and (-1, 0).
Part B: Finding the vertex of the given function:
We have h = -b/2a
From the given function 5x² + 2x - 3; a = 5, b = 2 and c = -3
So, h = -2/2(5) = -1/5 = -0.2
Then, on substituting h = x = -0.2 in the function we get
k = 5(-0.2)² + 2(-0.2) - 3
k = -3.2
Thus, the coordinates of the vertex are (h, k) = (-0.2, -3.2).
Since a > 0 i.e., 5 > 0, the vertex of the graph is going to be minimum and the graph of f(x) opens upwards.
Part C: Steps to graph f(X):
Step 1: Plot the x-intercepts in the coordinate plane
Step 2: Plot the vertex of the function
Step 3: draw a curve line passing through them, opening towards up.
Thus, the graph of the given function is plotted as shown below.
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A population of n = 10 scores has = 50 and = 5. what is the population variance? 5
The value of the Population Variance is 100.
According to the statement
we have given that the A population of N = 10 scores has μ = 50 and σ = 5. And we have to find the population variance.
So, For this purpose,
we know that the population variance can be defined as the average of the distances from each data point in a particular population to the mean squared, and it indicates how data points are spread out in the population.
Population variance = mean /(standard deviation/number of samples)
Population variance = μ / (σ /N )
Substitute the values in it and then
Population variance = 50 / (5 /10 )
Population variance = 50 / (0.5 )
Population variance = 100.
So, The value of the Population Variance is 100.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
A population of N = 10 scores has μ = 50 and σ = 5. What is the population variance?
a. 10
b. the square root of 5
c. the square root of 50
d. 25
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What is the solution for x in the equation?
10x − 4.5 + 3x = 12x − 1.1
x =
Answer: x= 3.4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x = 3.4
Step-by-step explanation:
[tex]10x - 4.5 + 3x = 12x -1.1 \\ 13x - 4.5 = 12x - 1.1 \\ 13x - 12x - 4.5 = 12x - 12x - 1.1 \\ x - 4.5 = - 1.1 \\ x - 4.5 + 4.5 = - 1.1 + 4.5 \\ x = 3.4[/tex]
