Answer:
0.33
Step-by-step explanation:
The specific number (females prefer cycling = 0.15) and the fitting total. There are 2 possibilities for that total :
all females
all people preferring cycling
the way it was phrased I would say the reference is all females.
the conditional relative frequency is then
0.15 / 0.46 = 0.326=0.33(rounded)
Hence the conditional relative frequency that a female prefers running is 0.33
I need help
What is 15% off of 10$
Answer: $8.50
hope this helps :)
im not the nest at math but im pretty sure that is what is is.
Step-by-step explanation:
Solve 5(4m + 1) − 2m = −13.
Answer:
Step-by-step explanation
5(4m+1)-2m=-13
20m+5-2m=-13
20m-2m=-13-5
18m=-18
m=-1
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{5(4m+1)-2m=-13 } \end{gathered}$}[/tex]
Apply the multiplicative law of distribution.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{20m+5-2m=-13 } \end{gathered}$}[/tex]
Combine as terms.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m+5=-13 } \end{gathered}$}[/tex]
Rearrange the unknown terms to the left side of the equation.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m=-13-5 } \end{gathered}$}[/tex]
Calculate the sum or difference.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{18m=-18 } \end{gathered}$}[/tex]
Divide both sides of the equation by the coefficient of the variable.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{m=-\frac{18}{18} } \end{gathered}$}[/tex]
Solve for the common factor.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{m=-1 \iff } \end{gathered}$}\boxed{\boxed{\bf{Answer}}}[/tex]
Simplify four fourths over nine
The simplification of four fourths over nine written as 4/4 ÷ 9 is given by 1/9
How to simplify fraction?Fraction refers to a number which consists of a numerator and a denominator.
A numerator is the upper or top value of a fraction while a denominator is the lower or bottom value of a fraction.
Given: four fourths over nine
= 4/4 ÷ 9
= 1 ÷ 9
= 1/9
Or alternatively
4/4 ÷ 9
multiply by the reciprocal of 9= 4/4 × 1/9
= (4 × 1) / (4 × 9)
= 4/36
= 1/9
In conclusion, the fraction four fourths over nine is simplified as 1/9
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what 93 by the power of 7
The value of the expression ''93 to the power of 7'' will be;
⇒ 60,170,087,060,757
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is,
''93 to the power of 7''
Now,
Solve the expression as;
93 to the power of 7 = 93⁷
= 93 × 93 × 93 × 93 × 93 × 93 × 93
= 60,170,087,060,757
Thus, The value of the expression ''93 to the power of 7'' will be;
⇒ 60,170,087,060,757
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AB bisects LDAC and
m/DAB = 37°. What is
m/DAC?
The value of the angle m∠DAC is 74° as AB bisects ∠DAC .
We know from the properties of angles that the angle bisector will bisect the angle into two equal parts.
∠DAC is bisected by the straight line AB. This forms two angles ∠DAB and ∠BAC .
∠DAC =∠DAB + ∠BAC
now, ∠DAB = ∠BAC
given that ∠DAB = 37
Hence m∠BAC = 37
now,
∠DAC = ∠DAB + ∠BAC
m∠DAC = 37° + 37°
m∠DAC = 74°
A line that divides an angle into two equal angles is known as an angle bisector in geometry. A device that splits an object or form into two equal halves is referred to as a "bisector." A ray that divides a given angle into two identical segments of the same length is called an angle bisector.
Therefore the value of m∠DAC is 74° .
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Graph the polygon with the given vertices and its image after a reflection in the given line.
J(2, 4), K(-4,-2), L( − 1, 0); y = 1
The coordinates of the image after reflection over line y = 1 is
preimage Image
J(2, 4 J' (2. -2)
K(-4,-2) K' (-4. 4)
L( − 1, 0) L' (-1, 2)
How to fine the coordinates of the reflected imageReflection is one of the movements in transformation that involve creation of mirror image
The reflection to be done is over line y = 1
Transformation rule for reflection over line y at origin (0, 0)) is
(x, y) → (x, -y)
However, reflection over line y = 1 which is (0, 1) is done as follows
J(2, 4) ⇒ (2, 4 - 1) ⇒ (2, 3) ⇒ (2, 1 - 3) → J' (2, -2)
from 4 to 1 = 4 - 1 = 3 units
reflecting 3 units over y = 1
1 - 3 = -2
J' (2, -2)
K(-4,-2) ⇒ (-4, -2 - 1) ⇒ (-4, -3) ⇒ (-4, 1 - -3) ⇒ K' (-4, 4)
from -2 to 1 = -2 - 1 = -3 units
reflecting -3 units over y = 1
1 - -3 = 4
K' (-4, 4)
L (-1, 0) ⇒ (-1, 0 - 1) ⇒ (-1, -1) ⇒ (-1, 1 - - 1) ⇒ L' (-1, 2')
from 0 to 1 = 0 - 1 = -1 unit
reflecting -1 unit over y = 1
1 - -1 = 2
L' (-1, 2)
see graph for more information
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Give Triangle QRS ~= Triangle TUV, QS = 3v + 2 and TV = 7v - 6, find the length of QS and TV
1) Since these triangles are congruent, then we can write out the following for congruent triangles have congruent sides:
[tex]\begin{gathered} QS=TV \\ 3v+2=7v-6 \\ 3v-7v=-6-2 \\ -4v=-8 \\ 4v=8 \\ \frac{4v}{4}=\frac{8}{4} \\ v=2 \end{gathered}[/tex]2) Still based on that principle, we can plug v=2 into any of those formulas to get the measure of QS and TV. So let's pick the simpler one:
[tex]\begin{gathered} QS=3v+2 \\ QS=3(2)+2 \\ QS=6+2 \\ QS=8 \\ --- \\ TV=7(2)-6 \\ TV=14-6 \\ TV=8 \end{gathered}[/tex]As we can see these segments are congruent.
Use inverse matrix to solve the linear system. Solve #19
19)
The given system of equations is,
[tex]\begin{gathered} 4x-3y=11 \\ 5x-2y=12 \end{gathered}[/tex]The above system of equations can be written in matrix form as,
[tex]\begin{bmatrix}{4} & {-3} & {} \\ {5} & {-2} & {} \\ {} & {} & \end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{11} & {} & \\ {12} & {} & \\ {} & {} & \end{bmatrix}\text{ -----(1)}[/tex]Here,
[tex]A=\begin{bmatrix}{4} & {-3} & {} \\ {5} & {-2} & {} \\ {} & {} & \end{bmatrix},\text{ X=}\begin{bmatrix}{x} & {} & {} \\ {y} & & {} \\ {} & {} & \end{bmatrix}\text{ },\text{ B=}\begin{bmatrix}{11} & {} & \\ {12} & {} & \\ {} & {} & \end{bmatrix}[/tex]Therefore, equation (1) can be written as,
[tex]AX=B[/tex]Therefore,
[tex]X=A^{-1}B\text{ -------(2)}[/tex]Now, we need to calculate the inverse of A.
(Note:
Let a 2x2 matrix P is of the form given below.
[tex]P=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {} \\ {} & {} & {}\end{bmatrix}[/tex]The inverse of the matrix P is,
[tex]\begin{gathered} P^{-1}=\frac{1}{|P|}\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & {} \\ {} & {} & {}\end{bmatrix} \\ =\frac{1}{ad-bc}\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex])
Similar to the inverse matrix of 2x2 matrix P, the inverse matrix of A can be written as,
[tex]\begin{gathered} A^{-1}=\frac{1}{4\times(-2)-(-3)\times5}\begin{bmatrix}{-2} & {3} & {} \\ {-5} & {4} & {} \\ {} & {} & {}\end{bmatrix} \\ =\frac{1}{-8+15}\begin{bmatrix}{-2} & {3} & {} \\ {-5} & {4} & {} \\ {} & {} & {}\end{bmatrix} \\ =\frac{1}{7}\begin{bmatrix}{-2} & {3} & {} \\ {-5} & {4} & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-2}{7}} & {\frac{3}{7}} & {} \\ {\frac{-5}{7}} & {\frac{4}{7}} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Now, put the values in equation (2) to find the solution to the system of equations.
[tex]\begin{gathered} X=A^{-1^{}}B \\ \begin{bmatrix}{x} & {} & {} \\ {y} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{\frac{-2}{7}} & {\frac{3}{7}} & {} \\ {\frac{-5}{7}} & {\frac{4}{7}} & {} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{11} & {} & \\ {12} & {} & \\ {} & {} & \end{bmatrix} \\ =\begin{bmatrix}{\frac{-2}{7}\times11+\frac{3}{7}\times12} & {} & {} \\ {\frac{-5}{7}\times11+\frac{4}{7}\times12} & & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-22}{7}+\frac{36}{7}} & {} & {} \\ {\frac{-55}{7}+\frac{48}{7}} & & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{-22+36}{7}} & {} & {} \\ {\frac{-55+48}{7}} & & {} \\ {} & {} & {}\end{bmatrix} \\ =\begin{bmatrix}{\frac{14}{7}} & {} & {} \\ {\frac{-7}{7}} & & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{x} & {} & {} \\ {y} & & {} \\ {} & {} & \end{bmatrix}=\begin{bmatrix}{2} & {} & {} \\ {-1} & & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Therefore, the solution to the system of equations using inverse matrix is x=2 and y=-1.
For the function g(x)=32/x+3, find (g^-1o g) (5)
The value of the composite function is found as 68/5.
What is meant as the inverse of the function?An inverse function is one that reverses the action of another function. A function g seems to be the inverse of a function f if and only if y=f(x) and x=g (y).The function is given as;
g(x) = 32/(x+3)
Write the function as 'y'
y = 32/(x+3)
Replace the value of x with y.
x = 32/(y+3)
Solve for y.
x(y + 3) = 32
xy = 32 - 3x
y = (32 - 3x)/x
Thus, g⁻¹ (x) = (32 - 3x)/x is the inverse of the function.
Now, find the value composite function; (g⁻¹ o g) (5).
(g⁻¹ o g) (5) = (32 - 3x)/x . 32/(x+3)
Put x = 5
(g⁻¹ o g) (5) = (32 - 15)/5 . 32/(5+3)
(g⁻¹ o g) (5) = 17×4/5
(g⁻¹ o g) (5) = 68/5
Thus, the value of the composite function is found as 68/5.
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Which equation is most likely used to determine the acceleration from a velocity vs. time graph?
a = t over delta v.
m = StartFraction v subscript 1 - v subscript 2 Over x subscript 2 minus x subscript 1 EndFraction.
a =
m = StartFraction x subscript 2 minus x subscript 1 Over v subscript 1 - v subscript 2 EndFraction.
An equation which is most likely used to determine the acceleration from a velocity vs. time graph is: B. m = (y₂ - y₁) / (x₂ - x₁).
What is a velocity vs. time graph?A velocity vs. time graph can be defined as a type of graph that is used to graphically represent the rate of change of velocity of an object with respect to time.
In Mathematics, the velocity of a physical object is plotted on the horizontal axis (y-coordinate) time is while plotted on the vertical axis (x-coordinate) of a velocity vs. time graph.
Mathematically, the acceleration of a physical object on a velocity vs. time graph can be calculated by determining the rate of change (slope) as modeled by this formula:
Acceleration, m = change in velocity/change in time
Acceleration, m = (y₂ - y₁) / (x₂ - x₁).
Where:
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Complete Question:
Which equation is most likely used to determine the acceleration from a velocity vs. time graph?
answer choices
A. a = t/delta v
B. m = (y₂ - y₁) / (x₂ - x₁)
C. a = delta v/t
D. m = (x₂ - x₁) / (y₂ - y₁)
Answer:
B. m = StartFraction v subscript 1 - v subscript 2 Over x subscript 2 minus x subscript 1 EndFraction.
Step-by-step explanation:
Got 100% on the test. Y'all have a good day! :D
Factor completely.
48-24x + 3x²
Answer:
3(4−x)²
Step-by-step explanation:
Answer:
3(4-x)^2
Step-by-step explanation:
factor
Which of the following equations does the graph below represent?
Answer:
The answer is -3x + 6y = 36
Step-by-step explanation:
PLEASE HELP ITS URGENT
Solve for the roots in simplest form using the quadratic formula:
x²-16x = -100
Answer:
[tex] \rm x = 8 \pm 6i [/tex]
Step-by-step explanation:
Given equation: x² - 16x = -100
x² - 16x + 100 = 0
By comparing given equation with standard quadratic equation i.e. ax² + bx + c = 0 we get:
a = 1
b = -16
c = 100
Quadratic formula:
[tex] \boxed{ \rm x = \dfrac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} } [/tex]
Now, substituting the values in the quadratic formula:
[tex] \rm \implies x = \dfrac{ - ( - 16) \pm \sqrt{ {( - 16)}^{2} - 4(1)( 100) } }{2(1)} \\ \\ \rm \implies x = \dfrac{ 16 \pm \sqrt{ 256 - 400} }{2} \\ \\ \rm \implies x = \dfrac{ 16 \pm \sqrt{-144 } }{2} \\ \\ \rm \implies x = \dfrac{ 16 \pm 12i }{2} \\ \\ \rm \implies x = 8 \pm 6i [/tex]
Answer:
x has no real solutions.
x = 8 + 6i, x = 8 - 6i
Step-by-step explanation:
First, move the all the terms to one side of the equation.
x^2 - 16x + 100 = -100 + 100
x^2 - 16x + 100 = 0
Then, based on our knowledge of the standard form of a quadratic equation: ax^2 + by + c = 0, we can plug the coefficients in front of the variables into the formula, which looks like [tex]x=\frac{-b+or-\sqrt{b^2-4ac} }{2a}[/tex].
Our a here is 1,
The b is -16,
The c is 100.
plugging it in:
[tex]\frac{-(-16)+or-\sqrt{(-16)^2-4*1*100} }{2*1}[/tex]
simplifies down to:
16/2 + or - (√(256 - 400))/2
= 8 + or - √(-36)
Here, we have a negative square root, meaning there will be no roots for this equation in the real number system.
If you include imaginary/complex numbers, this equation will have roots.
x = 8 + or - √(-36)
x = 8 + or - 6√(-1)
x = 8 + or - 6i
so the final answer:
x = 8 + 6i, x = 8 - 6i
In a circle with radius 0.9, an angle intercepts an arc of length 3.6. Find the angle inradians to the nearest tenth.
SOLUTION
Given the question on the question tab;
[tex]\begin{gathered} radius\text{ r=0.9} \\ angle\text{ }\theta=? \\ Length\text{ of arc=3.6} \end{gathered}[/tex][tex]\begin{gathered} Length\text{ of arc =}\theta r \\ 3.6=0.9\theta \\ \theta=\frac{3.6}{0.9} \\ \theta=4.0 \end{gathered}[/tex]
The angle is 4.0
what is the converted fraction of 110/17
Answer:
6 8/17
Step-by-step explanation:
17 x 6 is 102 so that can go into 110
Then you do 110-102 to find how many are left over 110-102= 8 so there are 8 left over so that goes into the numerator so the answer is 6 8/17 The denominator stays the same unless you can simply but in this case you can’t.
Which scatterplot shows the weakest negative linear correlation?
On a graph, points are grouped closely together and increase.
On a graph, points are grouped closely together in a line and increase.
On a graph, points are grouped closely together and decrease.
On a graph, points are grouped closely together in a line and decrease.
The scatterplot shows the weakest negative linear correlation is On a graph points are grouped closely together and increase. Option A.
The scatterplot showing the weakest negative linear correlation is the following scatterplot. The dots are scattered along the decreasing trend line. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that an increase in one variable tends to increase the other variable.
A negative correlation means that as one variable increases the other tends to decrease. Plotted points indicate correlations between variables if any. The scatterplot above is an example of a weak negative correlation. In this graph, y values decrease as x values increase, but the pattern does not resemble a straight line.
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nearest thousandth in 67directions: use a calculator to approximate each to the nearest thousandth subject: 2.2C evaluating common and natural logarithms
EXPLANATION
Given the expression:
ln 67:
Solving the operation with a calculator gives us the following result:
ln 67 = 4.204692619...
Thus, rounding to the nearest thousandth will give us:
= 4.205
So, answer to point 1) is D) 4.205
The graph shows the function f(x). Which equation represents f(x). F(x)=-3 square root x. F(x) = -3 square root x - 1. F(x) = 3 square root -x - 1. F(x) = 3 square root - x
The graph given is has the cubic function as the parent function.
The cubic function is shown below:
1. What is the x intercept of the graph y=x-32. What is the y intercept of the graph y=x-33. What is the x intercept of the graph y=4x+24. What is the y intercept of the graph y=4x+2
1. The x-intercept of a function is the point where the line crosses the x-axis. At this point, the y-coordinate is equal to zero.
You can identify the point from the graph or calculate the coordinates by replacing the equation of the linear function with y=0 and determine the corresponding value of x.
-Looking at the graph, the red line, that corresponds to the equation y=x-3, crosses the x-axis at point (3,0)
-Replacing the equation of the function by y=0:
[tex]\begin{gathered} y=x-3 \\ 0=x-3 \\ 0+3=x-3+3 \\ 3=x \end{gathered}[/tex]The x-intercept has coordinates at (3,0)
2. The y-coordinate is the point where the red line crosses the y-axis. At this point, the x-coordinate is equal to zero.
You can identify this point directly from the graph, or calculate it by replacing the equation of the line with x=0 and calculate the corresponding value of y.
-Looking at the graph, the red line crosses the y-axis at the point (0,-3)
-Replace the equation with x=0
[tex]\begin{gathered} y=x-3 \\ y=0-3 \\ y=-3 \end{gathered}[/tex]The y-intercept is (0,-3)
3. The equation y=4x+2 is represented in the graph by the blue line
As before, you have to identify the point where the line crosses the x-axis.
-From the graph:
-Replace the equation with y=0 and calculate the corresponding value of x:
[tex]\begin{gathered} y=4x+2 \\ 0=4x+2 \\ 0-2=4x+2-2 \\ -2=4x \\ -\frac{2}{4}=\frac{4x}{4} \\ -\frac{1}{2}=x \end{gathered}[/tex]The x-intercept is (-1/2,0)
4. The y-intercept is the point where the blue line crosses the y-axis.
-You can identify it from the graph:
-Or replace the equation with x=0 and determine the corresponding value of y
[tex]\begin{gathered} y=4x+2 \\ y=4\cdot0+2 \\ y=2 \end{gathered}[/tex]The coordinates of the y-intercept are (0,2)
help please which one is it
The function B has a greater rate of change.
What is rate of change?
How quickly something changes over time is referred to as its rate of change, or ROC. Therefore, rather than the size of each change individually, it is the rate—or the acceleration or deceleration of changes. In finance, rate of change is employed to comprehend price returns and spot trend momentum.
First to find the rate of change for function A.
Rate of change = [tex]\frac{0-5}{2.5-1.5} = \frac{-5}{1}=-5[/tex]
Function A has rate of change is -5.
Now consider, the second equation
y = -4.5x + 15
Since, the slope is rate of change for the equation.
So, function B has rate of change of -4.5
Now compare the rate of change for both the functions A and B
-5 < -4.5
Therefore, function B have greater rate of change.
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Which of the following equations have odd products? Select all that apply.
A.4x3=?
B.6x8=?
C.3x7=?
D.3x9=?
E.1x9=?
c, d, and e. this is because c equals 21, d equals 27, and e equals 9
1. What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.(a) Show your work.(b) is the product of 3x-4 and 5x² - 2x + 6 equal to the product of 4 - 3x and 5x² - 2x + 6? Explain
SOLUTIONS
(a) What is the product of 3x - 4 and 5x² - 2x + 6? Write your answer in standard form.
[tex](3x-4)(5x^2-2x+6)[/tex][tex]\begin{gathered} 3x(5x^2-2x+6)-4(5x^2-2x+6) \\ 15x^3-6x^2+18x-20x^2+8x-24 \\ collect\text{ like terms} \end{gathered}[/tex][tex]15x^3-26x^2+26x-24[/tex]The product is
[tex]15x^3-26x^2+26x-24[/tex][tex](4-3x)(5x^2-2x+6)[/tex]The product will be
[tex]\begin{gathered} 4(5x^2-2x+6)-3x(5x^2-2x+6) \\ 20x^2-8x+24-15x^3+6x^2-18x \\ -15x^3+26x^2-26x+24 \end{gathered}[/tex]The product of 4 - 3x and 5x² - 2x + 6 will be equal to the -1 multiply be the product of 3x - 4 and 5x² - 2x + 6, thus the two product are same
Checking
[tex]\begin{gathered} -1(-15x^3+26x^2-26x+24) \\ 15x^3-26x^2+26x-24 \end{gathered}[/tex]Hence the two answer are the same.
The rectangular floor of a classroom is 36 feet in length and 22 feet in width. a scale drawing of the floor has a length of 18 inches. what is the perimeter, in inches, of the floor in the scale drawing?
The perimeter of the floor in the scale drawing is 58 inches.
Define Perimeter of the rectangle.The whole distance that the sides or limits of a rectangle cover is known as its perimeter. Since a rectangle has four sides, its perimeter will be equal to the sum of those four sides. Given that the perimeter is a linear measurement, the rectangle's perimeter will be expressed in meters, centimeters, inches, feet, etc.
The letter "p" stands for the perimeter, which is equal to twice the width plus twice the length of the rectangle.
Given, the length of rectangular classroom is 36 feet
and the width is 22 feet.
The scale drawing has a length of 18 inches.
Here we can see that two different units are used.
So, we need to convert feet to inches.
1 foot = 12 inches
Now we will convert the length in inches,
36 feet = 36*12 inches
= 432 inches
Now we will convert the width in inches,
22 feet = 22*12
= 264 inches
Now, we will calculate by how many times the length has been scaled down:
[tex]\frac{432}{18} = 24[/tex]
So, the length has been scaled down to 24 times.
Now, we will scale down the width 24 times:
[tex]\frac{264}{24} = 11[/tex]
So, the width of the scale drawing is 11 inches.
Now, we will find the perimeter of the scale drawing:
Perimeter = 2(scale down length + scale down width)
= 2(18+11)
=2*29
=58 inches
Therefore, the perimeter of the scale down drawing is 58 inches.
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Page 5.26, Problem 3: A baseball team had 80 players show up last year and this year had 96 players show up for tryouts. Find increase in players from last year to this year. Your answer.
In order to determne the increse in the number of players, estimate the percentage increase. Proceed as follow:
First, calculate the difference in the number of player:
96 - 80 = 16
next, determine what is the associated percentage of such difference:
(16/80)(100) = 20%
Hence, the percentage increase was of 20%
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
Use the expression x^2 + 10x − 13 to answer the following questions.Part A: What numeric expression should be added in order to complete the square for the given expression?Part B: What expression is equivalent to the given expression after completing the square?Select two answers: one for Part A and one for Part B.
Given the expression below
[tex]x^2+10x-13=0[/tex]The general form of a quadratic equation is
[tex]ax^2+bx+c=0[/tex]Using the completing the square method,
[tex]\begin{gathered} x^2+10x-13=0 \\ x^2+10x=13 \end{gathered}[/tex]Where b =10 from the given equation
[tex]\begin{gathered} \text{Addding (}\frac{b}{2})^2\text{ to both sides} \\ ie\text{ (}\frac{10}{2})^2=5^2=25 \\ \text{Add 25 to both sides} \end{gathered}[/tex][tex]x^2+10x+25=13+25[/tex]For part A, the numerical value to be added is 25
Hence, for part A, the answer is 25-25
By completing the square
[tex]\begin{gathered} x^2+10x+25=13+25 \\ (x+5)^2=38 \\ (x+5)^2-38=0 \end{gathered}[/tex]Hence, for part B, the answer is (x+5)²-38
What is the value of -175-15- (-204)?
O-394
O-14
O 14
O 29
The value of -175-15- (-204) is 14
Mathematical operations, Addition, and Subtraction:We learn to add and subtract two or more integers or any other mathematical values using the two basic arithmetic operations of addition and subtraction. The plus sign (+) stands for addition, whereas the negative sign (-) stands for subtraction (minus sign). The opposite of addition is subtraction and vice versa.
The following are rules for addition and subtraction:
=> [tex]+ \times + = +[/tex]
=> [tex]- \times - = +[/tex]
=> [tex]+ \times - = -[/tex]
=> [tex]- \times + = -[/tex]
Here we have
-175-15- (-204)
=> - 175 - 15 + 204
=> - 190 + 204
=> 14
Therefore,
The value of -175-15- (-204) is 14
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what is the sum of the first five terms in this series?(picture of problem below)
Provided information:
We know the first 4th terms of the series:
[tex]6,-\frac{6}{3},\frac{6}{9},-\frac{6}{27}[/tex]We can express this series in summation notation as:
[tex]\sum_{i\mathop{=}1}^n\frac{6}{(-3)^{i-1}}[/tex]Therefore, the 5th term of the series is:
[tex]\frac{6}{(-3)^{5-1}}=\frac{6}{(-3)^4}=\frac{6}{81}[/tex]Now, we have to add the first five terms:
[tex]6+(-\frac{6}{3})+\frac{6}{9}+(-\frac{6}{27})+\frac{6}{81}[/tex]The next step is to convert all fractions to have the same denominator, so:
[tex]\begin{gathered} 1st:6*\frac{81}{81}=\frac{486}{81} \\ 2nd:-\frac{6}{3}*\frac{27}{27}=-\frac{162}{81} \\ 3rd:\frac{6}{9}*\frac{9}{9}=\frac{54}{81} \\ 4th:-\frac{6}{27}*\frac{3}{3}=-\frac{18}{81} \end{gathered}[/tex]Now, they have the same denominator, it remains the same and we just need to add the numerators:
[tex]\frac{486-162+54-18+6}{81}=\frac{366}{81}[/tex]And now, let's simplify the fraction by dividing the numerator and denominator by 3:
[tex]\frac{\frac{366}{3}}{\frac{81}{3}}=\frac{122}{27}[/tex]The answer is A. 122/27
Which expressions are equivalent to the one below? Check all that apply.log(103)A.3 • log 10B.1C.3 • 10D.3
We are given log ( 10^3)
We can use one of the properties of logs
log u^n = n log u
Rewriting log ( 10^3) using this property
log ( 10^3) = 3 log 10
log has an implied base of 10
log 10 = 1
3 log 10 = 3 *1 =3
The two correct choices are
A. 3 * log 10
D. 3
I’ve got 6 graphing questions today that I need help with please
For a given simultaneous equation,
The point at which both the lines intersect gives us the solution.
Thus,
the point A gives the solution of the system of equation.
Answer is A.