[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$6629\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]A=6629\left(1+\frac{0.1}{1}\right)^{1\cdot 4} \implies A \approx 9705.52~\hfill \underset{earned~interest}{\stackrel{9705.52~~ - ~~6629}{\approx\text{\LARGE 3076.52 }}}[/tex]
find the growth or decay rate: y=2.5(0.72)^x
Answer: decay
Step-by-step explanation: decay is when the input is less than 1 and greater than 0. 0.75 falls in between these numbers
the tell-tale factor is the value inside the parenthesis, if that's less than 1 is Decay, if more than 1 is Growth
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2.5\\ r=rate\to \text{\LARGE 28\%}\to \frac{28}{100}\dotfill &0.28\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=2.5(1 - 0.28)^{x} \implies A = 2.5(0.72)^x\hspace{5em}y= 2.5(0.72)^x[/tex]
rohit studies 5⅖ hrs daily. He devotes 1¼ hrs of his time for English abd 1½ hrs for Mathematics. How much time does he devote for other subjects
Answer:3 1/2 hours
Step-by-step explanation: 5 2/5 - 1 1/4 -1 1/2= 3 1/2
STATISTICS The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the individual scores are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one deviation of the mean have IQ scores that are 15 points higher or lower than the mean.
An absolute value equation that can be used to find the maximum and minimum scores within one standard deviation of the mean is |x - 20.9| = 5.3.
The minimum score that is within one standard deviation of the mean is equal to 15.6.
What is an absolute value function?In Mathematics, an absolute value function can be defined as a type of function that consist of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0).
Mathematically, an absolute value function can be represented by this mathematical expression:
|x| = x, x ≥ 0.|x| = x, x < 0.Since the standard deviation is 5.3 and the mean is 20.9, an absolute value equation for the scores that is within one standard deviation of the mean is given by:
|x - 20.9| = 5.3.
x - 20.9 = ±5.3
Evaluating the absolute value function, the maximum score is given by:
x - 20.9 = 5.3
x = 20.9 + 5.3
x = 26.2.
Evaluating the absolute value function, the minimum score is given by:
x - 20.9 = -5.3
x = 20.9 - 5.3
x = 15.6.
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Complete Question:
The most familiar statistical measure is the arithmetic mean, or average. A second important statistical measure is the standard deviation, which is a measure of how far the data are from the mean. For example, the mean score on the Wechsler IQ test is 100 and the standard deviation is 15. This means that people within one standard deviation of the mean have IQ scores that are 15 points higher or lower than the mean. One year, the mean mathematics score on the ACT test was 20.9 with a standard deviation of 5.3. Write an absolute value equation to find the maximum and minimum scores within one standard deviation of the mean. Use your equation to find the minimum score that is within one standard deviation of the mean
for each pair of points, find the slope of the line that passes through both points. If you get stuck, try plotting the points on graph paper and drawing the line thoruhg them wiht a ruler
The slope of points (1,3) and (4,5) will be 2/3.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise and the run of the line.
Given that the line is passing through points (1,3) and (4,5). The slope of the line will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 5 - 3 ) / ( 4 - 1)
Slope = 2 / 3
Therefore, the slope of points (1,3) and (4,5) will be 2/3.
The complete question is given below.
Find the slope of the line that passes through both points (11,3) and (4,5).
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What is the angle of elevation of the sun when a 47-ft mast casts a 14 ft
shadow?
O
The angle of elevation is
(Simplify your answer. Type an integer. Round to the nearest degree.)
***
The sun's angle of elevation when a 47-foot mast casts a 14-foot shadow 73.4127
What is the angle of elevation ?At the foot of the mast, place the 90 degree (right) angle of a right triangle. When the sun hits the mast, it casts a 47-foot shadow. Consider the mask's height to be on the "opposite side" of the elevation angle, and this shadow to be on the "adjacent side."
The "tangent" trig function includes the following variables:
Tan = (opposite side) (elevation angle) (adjacent side).
In this case, tan (angle of elevation) equals opposing side / adj opposing side.
is used for
radians, or tan (angle of elevation)
= 47/14 = 3.3571
3.3571 is equal to 73.4127 degree.
The angle of elevation of the sun when a 47-ft mast casts a 14 ft
shadow 73.4127 degree
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which choice does not determine the sampling distribution? the population size the population variance the population mean the sample size
The population size does not determine the sampling distribution.
In the give question we have to find which choice does not determine the sampling distribution.
We firstly learn more about sampling distribution
A sampling distribution is a probability distribution of a statistic that is derived from a bigger sample size of individuals chosen at random from a given population. The sampling distribution of a particular population is the distribution of frequencies of a variety of potential outcomes for a population statistic.
So, the population size does not determine the sampling distribution.
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Please help
What equation is represented by the values in this table
Answer:
y=2x-2
Step-by-step explanation:
use y2-y1/x2-x1 to find slope
4-2/3-2
2/1
2 is the slope
A and B are the only possible answers so far
Now to find y intercept
We know it can’t be +2 because at 2 x is equal to 2 so -2 is the only option
Hopes this helps please mark brainliest
each of 14 mothers-to-be received 3d ultrasound scans, which showed that 7 of them will give birth to girls. assuming that simultaneous births do not happen (i.e., babies are born one after another), what is the probability that the first two babies that are born happen to be boys? g
Probability that first two babies born are boys is 0.23
Number of Mothers to be received ultrasound = 14
Number of mother giving birth to girl = 7
Number of mother giving birth to boy = 14 - 7 = 7
P(giving birth to girl) = P(G) = 7 / 14 = 0.5
P(giving birth to boy) = P(B) = 7 / 14 = 0.5
Probability that the first two babies that are born happen to be boys =
favorable outcome / total outcome
here, favorable outcome = ⁷C₂
Total outcome = ¹⁴C₂
Required probability = ⁷C₂ / ¹⁴C₂
= (7×6 / 2×1) / (14×13 / 2×1)
= 7×6/14×13
= 42 / 182
=0.23
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On a math quiz, Tatiana earns 5 points for each question she answers correctly. She wrote this
equation to find how many points she earns (p) based on how many questions she answers
correctly (g):
p = 5q
Identify the dependent and independent variables.
Points earned (p)
Questions correct (g)
Dependent variable Independent variable
Answer:
For points earned (p), the button should be on the left, and for questions correct (q), its on the right.
Step-by-step explanation:
me not know how to speak English!
In the given equation p = 5q, p is the dependent variable and g is the independent variable.
Given that Tatiana earns 5 points for each question she answers.
So, the equation is p = 5q
The above equation explains that for every question she answers, she earns 5 points. That means answering questions which is "q" is an independent variable as it is not depending on any other factor.
The points earned which is "p", is completely depending on answering questions, so the "p" which is points earned is a dependent variable.
From the above explanation, we can conclude that p is dependent variable and q is independent variable.
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What are the coordinates of the point on the directed line segment from (-9, -10)
to (1,5) that partitions the segment into a ratio of 2 to 3?
The coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)
The end points of the line segment = (-9, -10) and (1, 5)
The partition ratio = 2 : 3
According to the partition rule
The x coordinate of the point = [tex]x_1+\frac{A(x_2-x_1)}{A+B}[/tex]
A = 2
B = 3
Substitute the values in the equation
The x coordinate of the point = -9 + [2(1--9) / 2+3]
= -9 + [2×10 / 5]
= -9 + [20/5]
= -9 + 4
= -5
Similarly,
The y coordinate of the point = [tex]y_1+\frac{A(y_2-y_1)}{A+B}[/tex]
= -10+[2(5--10)/2+3]
= -10+[2×15/5]
= -10+[30/5]
= -10 + 6
= -4
Hence, the coordinates of the point on the directed line segment from (-9, -10) to (1,5) that partitions the segment into a ratio of 2 to 3 is (-5,-4)
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Really need help!
Graph the equation y =x²
+ 4x - 5 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots
of the equation x² + 4x − 5 = 0.
Answer:
See picture below
Step-by-step explanation:
Use Desmos the free calcualtor.
If a interior angle of regular polygon equal 174. 5 how many ide doe a polygon have
Answer:
Each interior angle of a regular polygon is 174°
To find The number of sides of the polygon.
We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the number of sides of the polygon)
Now, the sum of an interior angle and an exterior angle of a regular polygon is always equal to 180°.
So, the exterior angle of the given regular polygon :
= (Sum of an interior angle and an exterior angle) - (An interior angle)
= 180° - 174°
= 6°
Let, the number of sides of the regular polygon = n
Now, the value of an exterior angle of a regular polygon = (360° / Number of sides)
So, the exterior angle of the given regular polygon :
= (360°/n)
By, comparing the two values of an exterior angle of the given regular polygon, we get :
360/n = 6
n × 6 = 360
n = 360/6
n = 60
Number of sides of the regular polygon = n = 60
(This will be considered the final result.)
Hence, the number of sides of the regular polygon is 60.
(
−
8
x
2
−
5
x
+
8
)
−
(
−
6
x
2
+
3
x
−
3
)
(−8x
2
−5x+8)−(−6x
2
+3x−3)
The simplified expression representing (−8x²−5x+8)−(−6x²+3x−3) is given as follows:
14x² - 8x + 11.
How to simplify the expression?The expression for this problem is presented as follows:
(−8x²−5x+8) − (−6x²+3x−3).
The first step towards simplifying the expression is removing the negative signal from the expression, inverting the signal of each term inside the second parenthesis, hence:
(−8x²−5x+8) − (−6x²+3x−3) = 8x² - 5x + 8 + 6x² - 3x + 3.
(the first parenthesis can be removed with no changes as there is not any signal in front of it).
Then the like terms, which are the terms with the same variable and same exponent, are added, adding the coefficients and keeping the variables and exponents, as follows:
8x² and 6x²: 8x² + 6x² = 14x².-5x and -3x: -5x - 3x = -8x.8 and 3: 8 + 3 = 11.The simplified expression is obtained by these three additions of the like terms above, hence:
14x² - 8x + 11.
Missing InformationThe problem is incomplete, and it asks for us to simplify the given expression.
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What is x in the equation 2x+6=8
X= 1
First you subtract 6 from both sides to get
2x=2
Then you divide by 2 to get 1
x=1
8x1 4* 28 × +8 help me
Answer:
8x1 4* 28 × +8 = 28x + 12
8x^1 + 4 times 28 + 8
Add common Factors which are 8x and 28x added they equals 36x and 4 and 8 which equals 12 so now we got 28x + 12 and that is the answer
PLEASE GIVE BRAINLIEST THANK YOU!!!
Question 4 (3 points)
Use a graphing calculuator, like desmos, to graph the function, then use the graph to determine the number of turning points, global
maximums and minimums, and local maximums and minimums that are not global.
h(x) = x²(x − 3)(x + 2) (x - 2)
-
Turning Points: 4
Local Maximum(2):
Local Minimum(s):
Blank 1: 4
Blank 2:
Blank 3:
From the graph the turning points are 4 i.e. (-1.467,17.765), (0,0), (1.251,6.665), (2.616,-7.472), global maximum is (-1.467,17.765), global minimum is (2.616,-7.472), local maximum is (0,0) and local maximum is (1.251,6.665).
In the given function, we have to graph the function, then use the graph to determine the number of turning points, global maximums and minimums, and local maximums and minimums that are not global.
The given function is h(x) = x^2(x − 3)(x + 2) (x - 2).
The graph of the given function is below:
As we know that
A local minimum or maximum is represented by each turning point. A turning point may occasionally be the peak or trough of the entire graph. In these situations, we argue that a global maximum or global minimum marks the turning moment.
The output at the greatest or lowest point of the function is referred to as a global maximum or global minimum.
So the terning point of the given function is 4 i.e. (-1.467,17.765), (0,0), (1.251,6.665), (2.616,-7.472).
Global Maximum = (-1.467,17.765)
Global Minimum = (2.616,-7.472)
Local Maximum = (0,0)
Local Maximum = (1.251,6.665)
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Change the following problem to an addition problem.
-5-4
Answer:-9
Step-by-step explanation:
-(5+4)
-(9)
100 PIONTS, FOR ANSWERING 10 Q'S
1. A zoo is keeping track of the weight of a baby elephant. The table shows the weight for the first, second, third, and fourth weeks. Which graph could represent the data shown in the table?
Week Weight
1 138
2 159
3 175
4 185
2. The table shows the amount of money made by a summer blockbuster in each of the first four weeks of its theater release. Which graph could represent the data shown in the table?
A two column table is shown. The first column is titled 'Week' and contains the values 1, 2, 3, and 4 from top to botom. The second column is titled 'Money in dollars' and contains the values 19,600,000, 7,800,000, 3,100,000, and 1,300,000 from top to bottom. (1 point)
3. In the diagram below, what is the relationship between the number of rectangles and the perimeter of the figure they form?
4. The table shows the relationship between the number of players on a team and the minutes each player gets to play.
Players Minutes
7 35
8 30
9 25
10 20
Is the relationship a function that is increasing or decreasing? Is the relationship a function that is linear or nonlinear? (1 point)
increasing; linear
increasing; nonlinear
decreasing; linear
decreasing; nonlinear
5. The ordered pairs left parenthesis 1 comma 1 right parenthesis, left parenthesis 2 comma 16 right parenthesis, left parenthesis 3 comma 81 right parenthesis, left parenthesis 4 comma 256 right parenthesis, and left parenthesis 5 comma 625 right parenthesis represent a function. What is a rule that represents this function? (1 point)
y equals 4 superscript x baseline
y equals 4 x
y equals x superscript 4 baseline
y equals x plus 4
6. Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase. Write a function rule for the cost of n sodas. How much would 10 sodas cost? (1 point)
C(n) = 0.5n – 0.75; $4.25
C(n) = 0.75n – 0.5; $7.00
C(n) = 0.5n – 0.5; $4.50
C(n) = 0.75n; $7.50
7. Identify the mapping diagram that represents the relation and determine whether the relation is a function.
{(–2, –4), (–1, –4), (3, –4), (6, –4)} (1 point)
8. Identify the mapping diagram that represents the relation and determine whether the relation is a function.
left-brace left-parenthesis negative 8 comma negative 6 right-parenthesis comma left-parenthesis negative 5 comma 2 right-parenthesis comma left-parenthesis negative 8 comma 1 right-parenthesis comma left-parenthesis 7 comma 3 right-parenthesis right-brace (1 point)
A relation is shown.The numbers negative 6, 1, 2, and 3 are shown in one oval. The numbers negative 8, negative 5, and 7 are shown in another oval. An arrow points from the negative 6 to the negative 8. An arrow points from the 1 to the negative 8. An arrow points from the 2 to the negative 5. And an arrow points from the 3 to the 7. Text at the bottom of the image reads The relation is not a function.
A mapping diagram is shown with two ovals.
The first oval contains the numbers negative 8, negative 5, and 7. The second oval contains the numbers negative 6, 1, 2, and 3.
Arrows point from negative 8 in the first oval to both negative 6 and 1 in the second oval.
An arrow points from negative 5 in the first oval to 2 in the second oval.
An arrow points from 7 in the first oval to 3 in the second oval.
Below the mapping diagram, text reads: The relation is a function.
9. The function b(n) = 12n represents the number of baseballs b(n) that are needed for n games. How many baseballs are needed for 15 games? (1 point)
27 baseballs
150 baseballs
180 baseballs
200 baseballs
10. Tell whether the sequence is arithmetic. If it is, what is the common difference?
2, 7, 13, 20, . . . (1 point)
yes; 5
yes; 6
yes; 2
no
The cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00
Soda is on sale for $0.75 a can, and you have a coupon for $0.50 off your total purchase
Let n-----> the number of sodas
C(n) -----> the total cost
we know that
The total cost is equal to the number of sodas multiplied by the cost of one soda minus $0.50 of the coupon
so
C(n) = 0.75n – 0.5
For n=10 sodas
substitute the value of n in the equation
C(10) = 0.75(10) – 0.5
7.5 - 0.5
= 7
Therefore, the cost of 10 sodas will be C(n) = 0.75n – 0.5; $7.00
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The diagram shows a circular disc with radius 6cm in the centre of the disk there is a circular hole with radius 0.5cm
The area of the shaded portion of the circular disc is 112.255 cm².
What is the area of the shaded portion?A circle is a bounded object in which points from its center to its circumference is equidistant.
The area of the shaded portion is the difference between the area of the circular disc and the area of the circular hole.
Area of a circle = πr²
Where :
π = pi = 3.14
R = radius
Area of the circular disc = 3.14 x 6²
Area of the circular disc = 3.14 x 36
Area of the circular disc = 113.04 cm²
Area of the circular hole = 3.14 x 0.5²
Area of the circular hole = 3.14 x 0.25
Area of the circular hole = 0.785 cm²
Area of the shaded portion = area of the circular disc - area of the circular hole
Area of the shaded portion = 113.04 cm² - 0.785 cm²
Area of the shaded portion = 112.255 cm²
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Find the nth term of this quadratic sequence
2, 8, 18, 32, 50
Answer:
it is 20
Step-by-step explanation:
use the formula
hope i helped
3. What linear equation models the relationship between the values in each table?
a)
P
t
0
11
1 2 3
16
21
26
b)
C
r
1
-2.1
2
-0.6
3
0.9
4
2.4
The linear equations that can satisfy the values given in tabular form are
t = 5d +11 c = [tex]\frac{2}{3}[/tex] r + 2.4How to form line equation using values given in tabular form?
A line equation is of the form y = mx + b where x and y are the coordinate values, m is the slope of the line and b is the y intercept.
Follow these steps to find the line equation:
Write the standard form of the line equation according to the variables given.Find the value of slope m by the formula [tex]m = \frac{y - y'}{x - x'}[/tex] where (x, y) and (x',y') are the given values.Find the value of y-intercept by substituting value of y,x and m in standard form.According to the given data:
Table I)
Standard form: t = md + b
Slope: m = [tex]\frac{16 - 11}{1 - 0}[/tex] = 5
y-intercept: t = 5d + b
Substituting (d, t) = (1, 16) as given in the table
16 = 5x(1) + b
∴ b = 11
Hence linear equation in terms of d and t is t = 5d +11
Similarly, for Table II)
Standard form: c = mr + b
Slope: m = [tex]\frac{2 - 1}{-0.6 + 2.1}[/tex] = [tex]\frac{2}{3}[/tex]
y-intercept: c = (2/3)r + b
Substituting (r, c) = (-2.1, 1) as given in the table
1 = 2/3 x (-2.1) + b
∴ b = 2.4
Hence linear equation in terms of r and c is c = [tex]\frac{2}{3}[/tex] r + 2.4
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Greg mow and rakes lawn to earn extra money He makes 45 for every lawn he mows and an extra 15 for raking his goal is to earn at least 250 per week
The inequality is 45m + 14 n ≥ 250.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
He makes 45 for every lawn he mows
and an extra 15 for raking
His goal earning= at least 250 per week
let the number of lawn he mow is m and the number of lawn rakes is n.
Then the inequality is
45m + 14 n ≥ 250
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Graph the function f(x)=-2 \log _{4}(x+8) on the axes below. You must plot the asymptote and any two points with integer coordinates.
Answer:
Asymptote: x= -8
Two points: (-7,0) and (-6,-1)
Step-by-step explanation:
1. Convert log form to exponential form.
y = -2log_4(x+8)
-y/2=log_4(x+8)
4^(-y/2)=x+8
x=4^(-y/2)-8
Note: from here, you can choose to find the inverse of the graph, solve f(x)^-1, and then revert the x and y coordinates to find the f(x) (but I won't be going over that because the question is not asking for the inverse).
2. Make a table by plugging in points.
At this point, all you need to do is to plug in y-values into the equation: x=4^(-y/2)-8
If we plug in y as 0, we get x as -7, and plug in y as -1, we get x as -6, so (-7,0) and (-6,-1) will be your two points.
3. Find the asymptote
An asymptote is a line in which the log function will approach infinitely close to, but never touch. Same deal, we can try to plug in more numbers into our graph -- y as 1 and we will get x as -15/2 (-7.5); y as 3 and we will get x as -63/8 (-7.875); y as 5 and we will get x as-255/32 (-7.96875). At this point, it's pretty clear that our graph is approaching -8. Hence, x= -8
We use vertical asymptote (x=) when graphing log and we use horizontal asymptote (y=) when graphing exponential.
The vertical asymptote is x = -8.
One point on the graph is (-7, 0).
Another point on the graph is (-6, -1).
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To graph the function [tex]f(x) =-2 \log _{4}(x+8),[/tex]
we need to first find the vertical asymptote, which is the value of x that makes the argument of the logarithm equal to zero.
x + 8 = 0
x = -8
So the vertical asymptote is x = -8.
Next, we can choose two integer values of x and find their corresponding values of f(x).
Let's choose x = -7 and x = -6.
When x = -7:
[tex]f(-7) = -2 \log _{4}(-7+8) = -2 \log _{4}(1) = 0[/tex]
So one point on the graph is (-7, 0).
When x = -6:
[tex]f(-6) = -2 \log _{4}(-6+8) = -2 \log _{4}(2) = -2(1/2) = -1[/tex]
So another point on the graph is (-6, -1).
Now we can plot the points and draw the vertical asymptote at x = -8.
Thus,
The vertical asymptote is x = -8.
One point on the graph is (-7, 0).
Another point on the graph is (-6, -1).
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Amadou and his children went into a grocery store and he bought $9 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought 4 times as many apples as bananas. By following the steps below, determine the number of apples, x, and the number of bananas, y, that Amadou bought.
Determine THREE ways to have 4 times as many apples as bananas.
There are 3 other ways so please try to answer them!
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The number of apples is 8.
The number of bananas is 2.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total cost = $9
Cost of one apple = $1
Cost of one banana = $0.50
The number of bananas = x
The number of apples:
y = 4x
Now,
1y + 0.50x = 9
4x + 0.50x = 9
4.50x = 9
x = 9/4.50
x = 2
Now,
y = 4 x 2 = 8
Thus,
The number of apples 8.
The number of bananas is 2.
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Between which two integers does the square root of 92 lie?
The square root of 92 lies between 9 and 10.
According to the question,
We have the following information:
Square root of 92
Now, we have to find the two integers between which its square root lie.
So, we will first find the perfect squares of positive integers to get an idea where the square root of 92 lies.
Perfect squares are given below:
1 = 1
2 = 4
3 = 9
4 = 16
5 = 25
6 = 36
7 = 49
8 = 64
9 = 81
10 = 100
Now, the square of 10 is greater than 92 and square of 9 is less than 92. So, it will lie between these two integers.
Hence, the square root of 92 lies between 9 and 10.
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The question is in the picture please help
The perimeter of the shaded region is 135 in.
Given, a triangle ABC in which K, L & M are the mid-points of the sides AB, BC, AC.
Also, the perimeter of the triangle ABC is 108 in.
Now, using the mid-point theorem, we get
KL = 1/2(AC)
LM = 1/2(AB)
KM = 1/2(BC)
Now, the perimeter of the shaded region is,
Perimeter of 3 small triangles + Perimeter of triangle KLM
Perimeter of 3 small triangles = (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4)
Perimeter of triangle KLM = AB/2 + BC/2 + AC/2
Perimeter of the shaded region = (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/4 + BC/4 + AC/4) + (AB/2 + BC/2 + AC/2)
Perimeter of the shaded region = 5/4(AB + BC + AC)
As, we know that AB + BC + AC = 108 in
Perimeter of the shaded region = 5/4×108
Perimeter of the shaded region = 135 in
Hence, the perimeter of the shaded region is 135 in.
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write a linear function f with the given values. f(-10) = 4, f (8) = -5 Can someone please help me with this question
Answer: y=-0.5x-1
Step-by-step explanation:
y=mx+b
Convert the given values f(-10) = 4, f (8) = -5 to coordinates (-10,4) (8,-5)
Hence we use the formula for finding the slope m:
[tex]\displaystyle\\\boxed{m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-1\ \ \ \ \ x_2=8\ \ \ \ \ \ y_1=4\ \ \ \ \ y_2=-5\\\\m=\frac{-5-4}{8-(-10)}\\\\m=\frac{-9}{8+10} \\\\m=\frac{-9}{18} \\\\m=-0.5\\\\Thus, y=-0.5x+b\ \ \ \ (1)\\\\[/tex]
We substitute the value of (-10,4) into equation (1):
[tex]4=-0.5(-10)+b\\\\4=5+b\\\\-1=b\\\\Thus, b=-1[/tex]
Hence, y=-0.5x-1
a wheat farmer is investigating the effectiveness of a treatment for controlling a pest. a random sample of 500 plants shows that 47 of them are infected by the pest. what does this sample indicate about the claim that 20% of the plants are infected?
The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.
This given test is a test for single sample proportion
The test hypothesis are:
[tex]H_{o} :p=0.20[/tex], null hypothesis
[tex]H_{1} :p\neq 0.20[/tex], alternative hypothesis
The test statistic fallows a standard normal distribution and is given by:
[tex]Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }[/tex]
p=0.20
X=47 plants
Sample size, n=500
x, is the sample mean:
x=X/n=47/500
x=0.094
So, test statistic is calculated as:
[tex]Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }[/tex]
Z=-5.93
From the z-table, the p-value associated with Z=-5.93 is approximately 0
The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level
In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim
So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.
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what is 6,000 lb/day = ____ t/wk?
Answer: 21 tons/wk
Step-by-step explanation:
6000 lb/day = 3 tons/day
3 t/day * 7 = 21 t/wk
in a survey of 1000 adult americans, 44.5% indicated that they were somewhat interested or very interested in having web access in their cars. suppose that the marketing manager of a car manufacturer claims that the 44.5% is based only on a sample and that 44.5% is close to half, so there is no reason to believe that the proportion of all adult americans who want car web access is less than 0.50. is the marketing manager correct in his claim? provide statistical evidence to support your answer. for purposes of this exercise, assume that the sample can be considered as representative of adult americans. test the relevant hypotheses using
Answer: No, the marketing manager was not correct in his claim.
We are given that in a survey of 1005 adult Americans, 46.6% indicated that they were somewhat interested or very interested in having web access in their cars.
Suppose that the marketing manager of a car manufacturer claims that the 46.6% is based only on a sample and that 46.6% is close to half, so there is no reason to believe that the proportion of all adult Americans who want car web access is less than 0.50.
Let p = population proportion of all adult Americans who want car web access.
SO, Null Hypothesis, : p 50% {means that the proportion of all adult Americans who want car web access is more than or equal to 0.50}
Alternate Hypothesis, : p < 50% {means that the proportion of all adult Americans who want car web access is less than 0.50}
The test statistics that will be used here are One-sample z-proportion statistics;
T.S. = ~ N(0,1)
where = sample proportion of Americans who indicated that they were somewhat interested or very interested in having web access in their cars = 46.6%
n = sample of Americans = 1005
So, test statistics =
= -2.161
Since in the question we are not given the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives the critical value of -1.6449 for the left-tailed test. Since our test statistics are less than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Step-by-step explanation: