We have that the ways 5-person committee such that exactly 2 local business owners are represented is mathematically given as
N=5940
What is Probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
The Probability that 2 local business owners are represented on the committee is given by finding the ways they can be seated amongst the 5
Generally, 2 local business owners are represented is mathematically given as
N=11C3 x 9C2
Therefore
N=165 x 36
N=5940
Therefore the way 5-person committee such that exactly 2 local business owners are represented is mathematically given as
N=5940
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For the function y= -2+5 sim {pi/12(x-2)}, what is the minimum value
The function has a local minima at ( 20 , -7 )
What is a Function ?Function is a mathematical statement formed when two algebraic expression are equated by an equal sign.
The expression given is
y = -2 +5sin ( (π/12) (x-2))
the minima of the given expression will be when
the sine term = -1
as the lowest value sin can have is -1
y = -2 +5 * (-1)
y = -7
The sin ( (π/12) (x-2)) = -1
(π/12) (x-2) = 3π /2
On solving this
x = 20
Therefore the function has a local minima at ( 20 , -7 )
It can also be confirmed form the graph attached with the answer.
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Graphing a exponential decay function
The process of Graphing a exponential decay function is shown in detail below.
There are two types of exponential equations: exponential decay and exponential growth. The fundamental shape of an exponential function and its corresponding graphs must be understood in order to fully comprehend the distinctions between exponential growth and decay. The fundamental distinction between the two is that in an exponential decay connection, the output values rise quickly as the input value rises, but in an exponential growth relationship, the output rises noticeably faster as the input value rises. Furthermore, neither of the two functions is linear, hence their rate of change is not constant. What distinguishes one equation from the other when they both have the same precise form, y = abx?
The value of the constant "b" is the fundamental factor in deciding whether the exponential function is one of growth or decay:
If function y = ab^x and b > 1then the function is an exponential growth function.If the function y = ab^x and 0<b<1 then the function is an exponential decay function. As noted before, "b" can never be exactly 1.In this way we can graph a exponential decay function
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what are the coordinates of this point help plssssssssssssssss
Answer:
(-2, -4)
Step-by-step explanation:
Use the (x,y) thing:
x = -2
y = -4
therefore, (-2, -4)
*Will give 30pts*Consider function f. f(x)=2x^2.What is the value of (f•f)(x)?
Answer:
[tex]\textbf {B}[/tex]
Step-by-step explanation:
f(x) = 2x²
f [f(x)]
f [2x²] = 2(2x²)²
f[f(x)] = 2(4x⁴)
f[f(x)] = 8x⁴
Find the area of the following triangle. Round your answers to the nearest hundredth. b = 0.923 km, c = 0.387 km, A = 43.333°
O 0.26 km²
O 0.358 km²
O 0.06 km²
O 0.12km ²
In a test of the effectiveness of garlic for lowering cholesterol, 50 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before-after) in their levels of LDL cholesterol (in mg/dL) have a mean of3.1 and a standard deviation of 16.6. Construct a 99% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol? Click here to view a t distribution table.LOADING... Click here to view page 1 of the standard normal distribution table.LOADING... Click here to view page 2 of the standard normal distribution table.LOADING... What is the confidence interval estimate of the population mean ?
The confidence interval estimates that the confidence interval limits contain 0., suggesting that the garlic treatment did not affect the LDL cholesterol levels.
A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95 percent confidence level is the most common, but other levels, like 90 percent or 99 percent, are occasionally used when computing a confidence interval.
Given in a test of effectiveness of garlic for lowering cholesterol, 50 subjects were treated with garlic in a processed tablet form.Both before and after the therapy, cholesterol levels were assessed.
LDL cholesterol variations had a mean of 4.4 and a standard deviation of 19.4 (in mg/dL). The best point estimate is 4.4.
We have to find 95% confidence interval estimate of the population mean
So,
x-bar = 4.4
ME = 1.96 = 5.27
H: no difference
Ha: is a difference
We fail to reject H since 0 is in the CI.
Hence the confidence interval estimates that the confidence interval limits contain 0., suggesting that the garlic treatment did not affect the LDL cholesterol levels.
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A sample of 40 11th graders were asked to select a favorite pattern out of 6
choices. The following display shows what their favorite color patterns were.
The counts have been recorded in the accompanying table according to
pattern and the number of students who selected that pattern. What is the
missing value in the table?
NEN
OA. 12
OB. 10
O C. 11
D. 13
Color Pattern
Blue on gray
Green
Pink polka dots
Purple
Red and orange
stripes
Yellow
Frequency
6
7
8
7
3
The missing value in the table is 12 , Option A is the correct answer.
What is a Graph ?A graph is a mathematical representation of the data available , It makes the study of the data over a wide period easier.
It is given in the question that there are 40 students and the frequency they select for each pattern is mentioned as number , which can be seen in the image attached with the answer.
It has been asked to determine the missing value in the frequency table corresponding to the pink Polka dots
The other number in the frequency table is 4, 6 ,8 ,7, 3
Total students are 40
Therefore the value corresponding to the pink polka dot is given by
40 - ( 4+6+7+8 +3)
= 12
Therefore The missing value in the table is 12 , Option A is the correct answer.
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Suppose y varies Inversely with x, and y = -1 when x = 3. What Inverse variation equation relates x and y?
The product of variables in inverse proportion is constant, so the equation is [tex]\boxed{xy=-3}[/tex]
Helppppppoppppoppppppppppppppp
This is my last question on my homework. pls help
Answer:
740
Step-by-step explanation:
$415-$230=$185
$185×0.25=740 max miles
Is it true that: If f"(c) > 0, then the slope of
the tangent line to the graph of the function at
x = c is positive.
Answer:
yes
Step-by-step explanation:
the FIRST derivative of a function tells us the slope of a tangent line to the curve at any point. if is positive, then the curve must be increasing. If is negative, then the curve must be decreasing.
the SECOND derivative gives us the slope of the slope function (in other words how fast the slope of the original function changes, and if it is accelerating up - positive - or if it is avengers down - negative).
so, the first derivative would be fully sufficient to get the answer of if the slope of the function at that point is positive or negative.
but because it is only a "if" condition and not a "if and only if" condition, the statement is still true.
there are enough cases, where the slope is positive, but the second derivative is not > 0 (usually = 0).
but if even the second derivative is positive, then, yes, the slope of the original function must be positive too.
Figure ABCD is a rhombus. Find the value of x.
58°
x = [ ? ]°
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 32°[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Diagonals of a Rhombus bisect each other at 90°
[tex]\qquad \tt \rightarrow \: x + 58 + 90 = 180[/tex]
[ Sum of interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \: x + 148 = 180[/tex]
[tex]\qquad \tt \rightarrow \: x = 180 - 148[/tex]
[tex]\qquad \tt \rightarrow \: x = 32 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The diagonals of the rhombus intersect at right angle. Then the value of x will be 32°.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. In a rhombus, opposite sides are parallel and equal.
Figure ABCD is a rhombus.
Its diagonals intersect at right angle.
Let the another angle be x. Then we have
x + 58° + 90° = 180°
x + 148° = 180°
x = 32°
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The blue dot is at what value on the number line -3 -1
Answer:
It's +2
Step-by-step explanation:
As the positive occurs on the right side of the negatives in the number line so if we keep extending on the right side so we get +2
(
Given that a = 7 cm and b = 8 cm,
work out the area of the triangle.
Give your answer rounded to 1 DP.
a
cm²
b
The diagram is not drawn accurately.
Answer:
28cm²
Step-by-step explanation:
The area of a triangle is given as:
= 1/2 × b × h
= 1/2 × 7 × 8
= 28cm²
A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/25 for red, 1/20 for green, 1/15 for purple, and 1/10 for black. What is the probability of pulling a green or red card, written as a reduced fraction?
Probability helps us to know the chances of an event occurring. The probability of pulling a green or red card is 9 / 100.
What is Probability?Probability helps us to know the chances of an event occurring.
P = [tex]\dfrac{Desired \ outcomes}{Posiible \ outcomes}[/tex]
The probabilities of different color cards being pulled are 1/25 for red, 1/20 for green, 1/15 for purple, and 1/10 for black Therefore, the probability of pulling a green or red card is,
Probability = 1/20 + 1/25
= (5 + 4) /100
= 9 / 100
Hence, the probability of pulling a green or red card is 9 / 100.
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Work out (4 x 3)² ÷ 6
An expression is defined as a set of numbers, variables, and mathematical operations. The solution of (4 x 3)² ÷ 6 is 24.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The solution of the expression (4 x 3)² ÷ 6 is,
(4 x 3)² ÷ 6
= (12)² ÷ 6
= 144 ÷ 6
= 24
Hence, the solution of (4 x 3)² ÷ 6 is 24.
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At the city museum child admission is $6.10 and adult admission is $9.20. On Wednesday, 144 tickets were sold for a total sales of 1083.00. How many adult tickets were sold that day
Henry knows that the circumstance of a circle is 18pi inches. What is the area of the circle?
a. 36pi in²
b. 81pi in²
c. 162pi in²
d. 324pi in²
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option B, 81}\pi\textsf{ in}^2[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Circumference = 18}\pi[/tex]
Find: [tex]\textsf{The area of the circle}[/tex]
Solution: We need to first determine the radius using the circumference formula and once we get the radius then we can plug in the value into the area formula and get our final answer.
Determine the radius
[tex]c = 2 \pi * r[/tex][tex]18\pi = 2 \pi * r[/tex][tex]\frac{18\pi}{2\pi} = \frac{2 \pi}{2\pi} * r[/tex][tex]\frac{18\pi}{2\pi} = r[/tex][tex]9 = r[/tex]Determine the area
[tex]A = \pi * r^2[/tex][tex]A = \pi * (9)^2[/tex][tex]A = \pi * (9 * 9)[/tex][tex]A = 81\pi[/tex]Therefore, the correct answer would be option B, 81π in2.
The surface area of a square pyramid is 189 square inches. The side length of the base is 7. What is the value of the height?
The value of the height of the prism is 8.68 inches
Surface of a square pyramidThe surface area is the sum of the area of the faces.
The formula for calculating the surface area of the pyramid is;
TSA = [tex]a^2+2a\sqrt{\frac{a^2}{4} + h^2}[/tex]
where
a is the side length. = 7in
h is the height
Substitute
[tex]189=7^2+2(7)\sqrt{\frac{7^2}{2} + h^2} \\189=49+14\sqrt{\frac{49}{2} + h^2}\\140=14\sqrt{\frac{49}{2} + h^2}\\10=\sqrt{\frac{49}{2} + h^2}\\[/tex]
Square both sides to have
100 = 49/2 + h²
h² = 100 - 49/2
h² = 151/2
h² = 75.5
h = 8.68in
Hence the value of the height of the prism is 8.68 inches
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Jordan wrote the expression 850p to represent the following scenario.
The cost of renting a bowling alley for a party is $850. The price per person depends on how many people attend the party. Write an expression for the price per person if p people attend.
Explain why Jordan's expression is incorrect. Provide the correct expression that represents the scenario.
Using proportions, the expression for the price per person is:
[tex]P = \frac{850}{p}[/tex]
Jordan's expression is wrong because the price per person is inverse proportional to the number of people in the party, not direct proportional.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The cost of renting a bowling alley for a party is $850, hence the cost per person is given by:
[tex]P = \frac{850}{p}[/tex]
Jordan's expression is wrong because the price per person is inverse proportional(that is, the amount is divided by p) to the number of people in the party, not direct proportional.
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(6-^8)^4 please helpppp
[tex](6^-^8)^4[/tex]
[tex]=6^-^2^4[/tex]
[tex]=\frac{1}{6^2^4}[/tex]
There are two boxes of cereal in the shape of rectangular prisms on a shelf. The
dimensions of each box of cereal are listed below.
. Box B has a height of 25 centimeters, a length of 19 centimeters,
and a width of 6 centimeters.
• Box A has a height of 25 centimeters, a length of 20 centimeters,
and a width of 9 centimeters.
What is the difference in volume, in cubic centimeters, between the two boxes of cereal?
A 1,650
B 3,900
C 4,500
D 7,350
Answer:
1650 Cubic Centimeters
Step-by-step explanation:
To get the volume of the cereal boxes, you must multiply their 3 dimensions together.
Box A:
25×20=500
500×9=4500
Box B:
25×19=475
475×6=2850
Now, to find the difference of these volumes, you want to subtract the smaller volume from the larger volume.
4500-2850=1650
The answer is 1650 cubic centimeters.
Pls help! Answer the question in the pic. I will give five stars, thanks, and brainliest!
*20 POINTS*
The table shows the population of a small town over time. The function P = 10,550(1.1)x models the population x years after the year 2000.
A 2-column table with 5 rows. The first column is labeled years after 2000, x with entries 0, 3, 4, 7, 10. The second column is labeled population, P with entries 10,5000; 14,000; 15,500; 20,500; 27,000.
For which year would this model most likely be sufficient to make a prediction of the population?
1950
2005
2025
2050
Answer:
B: 2005
Step-by-step explanation:
Worked on edge 2022
To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of a second point by going up 3 and over.
then draw a line through the points.
Thus, for drawing the graph for y = 3/4x + 7.
For drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
For this case, the equation given to us is:
y=3/4x+7
Any equation of the form y=mx+c where m and c are constants and x and y are variables is the equation of a straight line.
For a straight line to be characterized, only two points are sufficient.
For x = 0, the y-coordinate would be such that it would satisfy the equation
y=3/4x+7
Putting x = 0, we get:
y=3/4(0)+7
y=7
Thus, the y-coordinate of the point on this line whose x-coordinate is 0 is 7. Thus, (0,7) is one of the point coordinates on the considered line.
Putting x = 3, we get:
y=3/4(3)+7
y=9.25
Thus, the y-coordinate of the point on this line whose x-coordinate is 0 is 9.25. Thus, (0,9.25) is another of the point's coordinates on the considered line.
Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.
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When you raise (almost) anything to the power zero, you get 1.
Answer:
z^0= 1
(2v+2)^0 = 1
3^0 = 1
0^0= 0
Step-by-step explanation:
When you raise (almost) anything to the power zero, you get 1 and when you raise 0 to any number except 0 is 0
Graph the following pair of quadratic functions and describe any similarities/differences observed in the graphs.
f(x) = 8x² +2
h(x) = -8x²-2
a. fopens upward with a y-intercept at (2, 0); h opens downward with a y-intercept at (-2, 0)
b. f opens downward with a y-intercept at (0, -2); h opens upward with a y-intercept at (0, 2)
c. fopens downward with a y-intercept a(0, 2); h opens upward with a y-intercept at (0, -2)
d. fopens upward with a y-intercept at (0, 2); h opens downward with a y-intercept at (0, -2).
The f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2) , Option D is the right answer.
What is a Function ?A function is a law that defines relation between two variables.
The function given in the question is
f(x) = 8x² +2
h(x) = -8x²-2
The graph is plotted and the similarities or differences are studied ,
It can be seen from the graph that
f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2).
Therefore Option D is the right answer.
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What is the equation of the line that passes through the points (5,3) and (9,-13)?
The equation of the line that passes through the given points is y= -4x+23.
Linear FunctionA line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
From the stardard form equation:
For point (5,3) : 3=5a+b ( equation 1)For point (9,-13) : -13=9a+b (equation 2)Solving the system for equations 1 and 2.
3=5a+b
-13=9a+b * (-1)
3=5a+b
13=-9a-b * (-1)
16= -4a
4= -a
a= -4
If a= -4 from equation 1, you have
3= 5 * (-4)+b
3= -20+b
b=23
Therefore, the line equation is y= -4x+23.
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Find X and QT. The shape is a Rhombus
Answer:
See below ~
Step-by-step explanation:
Sides of a rhombus are equal.
⇒ QT = TS
⇒ x² - 4x - 10 = 6x + 14
⇒ x² - 10x - 24 = 0
⇒ x² + 2x - 12x - 24 = 0
⇒ x (x + 2) - 12 (x + 2) = 0
⇒ (x + 2)(x - 12) = 0
⇒ x = -2 or x = 12
Substitute both values and see which gives a positive value for QT :
When x = -2 :
QT = (-2)² - 4(-2) - 10QT = 4 + 8 - 10QT = 2When x = 12 :
QT = (12)² - 4(12) - 10QT = 144 - 48 - 10QT = 86The 2 possible answers are :
x = -2, QT = 2x = 12, QT = 86yo
24
yx
SECTION B
(a) Identity element;
(b) Inverse of 3 and -5 under *
Range y
[30 marks]
Answer all the questions in this section. All questions carry equal marks.
1. A binary operation is defined on the set of real numbers, R, by x + y = x + y + 10.
Find the:
X
x
Inverse
Answer:
Sike
Step-by-step explanation:
That's the wrong number only 123
