Option (b) is correct as mean of top five scorers on soccer team is 8 from given bar graph.
What is mean in statistics?In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
Mean = (Sum of values)/(Total observations)
Using above formula, we get
Calculating mean for given bar graph,
\(=\frac{4+6+10+9+11}{5}\\=\frac{40}{5}\\=8\)
So, mean score of five players comes out to be 8.
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Write 3 1/2 cups as a multiplication expression using the unit, 1 cup, as a factor.
I ABSOLUTELY NEED HELP BY TOMORROW!!! I AM GIVING 100 POINTS
3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.
How to Write 3 1/2 cups as a multiplication expression using the unit, 1 cup, as a factor.To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:
3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup
Since there are 1 cup in each term, we can rewrite it as:
3 cups + (1/2) cup
Now, we can express each term as a multiplication expression:
3 cups = 3 * 1 cup = 3
(1/2) cup = (1/2) * 1 cup = 1/2
Putting it all together, the multiplication expression is:
3 * 1 cup + (1/2) * 1 cup = 3 + 1/2
Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.
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1000^4=10^X FIND VALUE OF X
Step-by-step explanation:
\(( {1000)}^{4} = {10}^{x} \\ ({10}^{3})^{4} = {10}^{x} \\ {10}^{12} = {10}^{x} \\ therefore \: x = 12 \\ \\ hope \: it \: will \: help\)
Given that NO ML and ML JK, which postulate or theorem can be used to show that all 3 center triangles in the
Antigua and Barbuda flag are similar?
A. ASA similarity theorem
B. SSS similarity theorem
C. SAS similarity theorem
D. AA similarity postulate
Answer:
A
Step-by-step explanation:
Source:
Trust me bro
The theorem used to prove the three triangles are similar is the ASA similarity theorem. The correct option is A.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and the side included between the angles of the second triangle.
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Choose the equation that represents the solutions of 0 = 0.25x² - 8x. 0.25± √(0.25)² - (4)(1)(-8) 2(1) O O X = X = X = X = -0.25± √√(0.25)² – (4)(1)(-8) 2(1) 8± √(-8)²-(4)(0.25) (0) 2(0.25) -8± √(-8)²-(4)(0.25)(0) 2(0.25)
The given equations represent the solutions of 0 = 0.25x² - 8x
What is an equation?An equation is a mathematical statement that shows the equality of two expressions, typically separated by an equal sign. Equations are used to solve problems and model real-world situations in many fields, including physics, engineering, and finance.
Redirecting to answer:
The equation 0 = 0.25x² - 8x can be rewritten as:
0.25x² - 8x = 0
Factoring out x gives:
x(0.25x - 8) = 0
So the solutions are x = 0 and 0.25x - 8 = 0, which gives x = 32.
Therefore, none of the given equations represent the solutions of 0 = 0.25x² - 8x
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What is the perimeter of each of the figures?
Answer:
x=16
Step-by-step explanation:
(x-8)+2x+2x=4(x+2)
x-8+4x=4x+8
x=16
Answer:
x=16
Step-by-step explanation:
perimeter of triangle=a+b+c =perimeter of Square =L²
2x+2x+x-8=4(x+2)
5x-8=4x+8
C.L.T
5x-4x=8+8
x=16
27 x 26 x 28 x 34 x 45
27 x 26 x 28 x 34 x 45 = 30,073,680
Answer:
30,073,680
Step-by-step explanation:
Use calculator.
xA radioactive isotope is decaying at a rate of 20% every hour. Currently there are 15 grams of the substance.
Questions:
A. Write an equation that will represent the number of grams present after n hours
B. How much will be left after 24 hours (one day)? (Round to the nearest hundredth)
C. After how many hours will there be approximately one gram left?
B. After 24 hours, approximately 2.49 grams will be left.
C. After approximately 18.13 hours, there will be approximately one gram left.
A. To represent the number of grams present after n hours, we can use the equation:
N(n) = 15 × (1 - 0.2)^n
Where:
N(n) is the number of grams present after n hours,
15 is the initial amount of the substance in grams,
0.2 represents the decay rate of 20% per hour, and
^n represents the exponentiation operation.
B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:
N(24) = 15 × (1 - 0.2)^24
Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.
C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:
1 = 15 × (1 - 0.2)^n
To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:
log(0.8)(1/15) = n
Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.
Therefore, the answers are:
B. After 24 hours, approximately 2.49 grams will be left.
C. After approximately 18.13 hours, there will be approximately one gram left.
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Given the two functions, which statement is true? f(x) = 3x, g(x) = 3x + 5 Question 12 options: g(x) is translated up 5 units compared to f(x) g(x) is translated left 5 units compared to f(x) g(x) is translated down 5 units compared to f(x) g(x) is translated right 5 units compared to f(x)
The correct statement is: g(x) is translated up 5 units compared to f(x).
The correct answer is A.
To determine the translation between the two functions, we can observe that the only difference between them is the constant term.In f(x) = 3x, there is no constant term, so the graph of f(x) passes through the origin (0, 0).In g(x) = 3x + 5, there is a constant term of 5 added to the function. This means that the graph of g(x) is shifted vertically upward by 5 units compared to the graph of f(x).Therefore, g(x) is translated up 5 units compared to f(x).The correct answer is A.
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Convert f ( x ) = 48 ( 1.02 ) x to the form f ( x ) = a e k x . Round k to 4 decimal places.
The exponential function can be rewritten as:
f(x) = 48*e^(0.0198*x)
How to transform the function?Here we start with the exponential function:
f(x) = 48*(1.02)^x
And we want to write this in the general form:
f(x) =a*e^(kx)
Notice that we can write the second form as:
f(x) = a*[e^k]^x
So, comparing this with the given exponential, we will get:
a = 48
e^k = 1.02
Apply the natural logarithm in both sides:
ln(e^k) = ln(1.02)
k*ln(e) = ln(1.02)
k = ln(1.02) = 0.0198
Then the exponential function is:
f(x) = 48*e^(0.0198*x)
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A pound of rice has a mixture of two types of rice, each costing $10 and $30, if the average cost per is $24, what is the ratio of the different types of rice?
Answer:
3:7
Step-by-step explanation:
Let x = pounds of the $10 rice in the mixture
Let y = pounds of the $30 rice in the mixture
Total cost of the $10 rice = 10x
Total cost of the $30 rice = 30y
(10x + 30y) / (x + y) = 24
Solve this equation for y/x:
10x + 30y = 24(x + y)
10x + 30y = 24x + 24y
30y - 24y = 24x - 10x
6y = 14x
y/x = 6/14 simplify the fraction
y/x = 3/7
So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.
Is (49,13),(61,36),(10,27),(76,52),(23,52) a function
Answer:
No
Step-by-step explanation:
To determine whether the given set of ordered pairs {(49,13),(61,36),(10,27),(76,52),(23,52)} represents a function, check if each x-value is associated with a unique y-value.
Check the x-values in the set: 49, 61, 10, 76, and 23. There are no repeated x-values. Still need to check if each x-value has a unique corresponding y-value.
Check the y-values: 13, 36, 27, 52, and 52. There is one repeated y-value, 52, for the pairs (76, 52) and (23, 52).
Conclusion: the y-value 52 is associated with 2 different x-values, therefore the given set of ordered pairs does not represent a function.
One of the legs of a right triangle measures 4 cm and the other leg measures 4 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
4\(\sqrt{2\\\) or 5.7
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + 4^2 = c^2
16 + 16 = c^2
32 = c^2
4\(\sqrt{2\\\) or 5.7
the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes
The standard deviation of the response time is 1.53 minutes.
What is the standard deviation of the response time?To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.
Z-score = z = (x - μ) / σ
For the lower bound of 10 minutes:
z = (10 - 13) / σ
For the upper bound of 16 minutes:
z = (16 - 13) / σ
As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.
Using z-scores, we set up equations:
(10 - 13) / σ = -1.96
(16 - 13) / σ = 1.96
Solving the first equation:
-3 / σ = -1.96
σ = -3 / -1.96
Solving the second equation:
3 / σ = 1.96
σ = 3 / 1.96
Dividing both sides by 1.96:
-3 / 1.96 = σ
1.53 = σ
Full question:
The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.
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The expression below was simplified using two properties of operations. 3(10n +2+14n)
Answer:
Associative property, then distributive property
Step-by-step explanation:
What is the third step in sketching the graph of a rational function
Answer:
use test numbers to find where the function is a positive and where it is negative. sketch the function's graph, plotting additional points as guides as negative. choose test numbers to t the left and right of each of these places, and find the value of the function at each test number.
Which fraction shows the reciprocal of the whole number 15? Group of answer choices 15/1 10/15 5/15
Step-by-step explanation:
10/15 and 5/15 aren't correct. Both aren't equal to a whole number. Irrational numbers.
15/1 is correct. The denominator is over 1, which makes the numerator equal to a whole number, 15.
y=-0.024x^2+0.0791x+4.873
The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol
The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.
The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.
The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.
The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.
The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.
To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.
Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.
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- Draw A' the symmetric of A with respect to point O
- Draw A' the symmetric of A with respect to (d)
Answer:
how am i supposed to answer this? draw a line lol
Step-by-step explanation:
Use a calculator to find the value of the acute 0 to the nearest degree
Tan0=7.7336
In degree mode, the answer is around 83. You use the inverse tangent button on the calculator to get rid of the tangent and find what theta is (make sure your calculator is in degree mode)
Need the correct answers for this. Can you help me?
The length of PQ is 3√5 and its slope is -2
The length of SR is 3√5 and its slope is -2
The length of SP is 5√2 and its slope is -7
The length of RQ is 5√2 and its slope is -1
So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.
Understanding QuadrilateralTo find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:
D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
and the slope formula:
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
1. Length PQ:
Using the distance formula, the length PQ can be calculated as follows:
PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
= √((3 - 0)² + (-4 - 2)²)
= √(3² + (-6)²)
= √(9 + 36)
= √45
= 3√5
2. Length SR:
Using the distance formula, the length SR can be calculated as follows:
SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
= √((1 - (-2))² + (-5 - 1)²)
= √((1 + 2)² + (-6)²)
= √(3² + 36)
= √(9 + 36)
= √45
= 3√5
3. Length SP:
Using the distance formula, the length SP can be calculated as follows:
SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
= √((1 - 0)² + (-5 - 2)²)
= √(1² + (-7)²)
= √(1 + 49)
= √50
= 5√2
4. Length RQ:
Using the distance formula, the length RQ can be calculated as follows:
RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)
= √((-2 - 3)² + (1 - (-4))²)
= √((-2 - 3)² + (1 + 4)²)
= √((-5)² + 5²)
= √(25 + 25)
= √50
= 5√2
Now, let's calculate the slopes of the sides:
1. Slope PQ:
The slope of PQ can be calculated using the slope formula:
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= (-4 - 2) / (3 - 0)
= -6 / 3
= -2
2. Slope SR:
The slope of SR can be calculated using the slope formula:
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= (-5 - 1) / (1 - (-2))
= -6 / 3
= -2
3. Slope SP:
The slope of SP can be calculated using the slope formula:
m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= (-5 - 2) / (1 - 0)
= -7 / 1
= -7
4. Slope RQ:
The slope of RQ can be calculated using the slope formula:
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)
= (1 - (-4)) / (-2 - 3)
= 5 / (-5)
= -1
Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:
Length PQ: 3√5
Length SR: 3√5
Length SP: 5√2
Length RQ: 5√2
Slope PQ: -2
Slope SR: -2
Slope SP: -7
Slope RQ: -1
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write an algebraic expression for y multipied by z
Answer:
y(z)
Step-by-step explanation:
sorry that was my opinion
6. Sue purchased a car for $18,000 three years ago. If the car depreciates at a rate of 20% per year, the value of the car now is
By writing and evaluating an exponential equation, we can see that the value of the car now is $9,216.
What is the value of the car now?
We know that the initial value of the car is $18.000, and the value depreciates at a rate of 20% per year.
If we define x as the number of years since the car was bought, we can write the value equation as:
V(x) = $18,000*(1 - 20%/100%)^x
V(x) = $18,000*(1 - 0.2)^x
V(x) = $18,000*(0.8)^x
The value of the car after 3 years is what we get if we evaluate the exponential equation in x = 3.
V(3) = $18,000*(0.8)^3
V(3) = $9,216
That is the value of the car now.
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What is the standard form for 80000 + 200+ 2
Answer:
80202
Step-by-step explanation:
Simply add according to number value:
200 - 2 goes into hundreds place
2 - 2 goes into ones place
80000 - 8 goes into ten-thousands place
FIND THE VALUE OF X PLEASE HELP ME
Answer:
x = 18
Step-by-step explanation:
4(18) = 72
2(18) - 10 = 26
4(18) + 10 = 82
72 + 26 + 82 = 180
A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix had a mean of 217.222 days and a standard deviation of 1.2019 days. At the 0.025 significance level, decide if the sample data support the claim that shelf life has increased. State your decision in terms of the null hypothesis.
Answer:
The calculated value t = 3.050 < 3.8325 at 0.0025 level of significance
The null hypothesis is accepted
The sample data support the claim that shelf life has increased.
Step-by-step explanation:
Step(i):-
Given that the Mean of the Population = 216days
Given that sample size n=9
Given that mean of sample x⁻ = 217.222 days
Given that the Standard deviation of the sample (S) = 1.2019days
Step(ii):-
Null hypothesis:-H₀:The sample data support the claim that shelf life has increased.
Alternative Hypothesis:H₁: The sample data support the claim that shelf life has decreased
Test statistic
\(t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }\)
\(t = \frac{217.222-216}{\frac{1.2019}{\sqrt{9 } } }\)
t = 3.050
Degrees of freedom γ = n-1 = 9-1 =8
t₀.₀₂₅ = 3.8325
Final answer:-
The calculated value t = 3.050 < 3.8325 at 0.0025 level of significance
The null hypothesis is accepted
The sample data support the claim that shelf life has increased.
a rectangle measures 5 feet by 10 feet. what is the perimeter in yards
Answer:
10 yards
Step-by-step explanation:
10 + 10 + 5 + 5 = 30 feet
30 feet = 10 yards
At the office supply store, a ream of paper costs $5.89 and a cartridge of ink costs $38.40. Delilah needs to buy 8 reams of paper and 6 cartridges of ink for her office. She needs to know how much money to bring, so estimate the cost of these supplies.
Answer:
Step-by-step explanation:
Delilah needs to buy 8 reams of paper which cost $5.89 each, $5.89 x 8 = $47.12
Delilah needs to buy 6 cartridges of ink which cost $38.40 each, $38.40 x 6 = $230.4
We then add $230.4 and $47.12
$230.4 + $47.12 = $277.52.
Delilah needs to bring $277.52 to cover the cost of her supplies.
Last month the amount on Jaden's bank account statement went from $200 to $150.
What was the percent change?
Answer:
That is a 25% change.
Step-by-step explanation:
What equation is graphed?
10
8
6
SK
-10-8-8/ 2 4 6 8 10
-8
-10
16
9
=1
=1
po
first off, let's take a peek at the picture above
hmmm the hyperbola is opening sideways, that means it has a horizontal traverse axis, it also means that the positive fraction will be the one with the "x" variable in it.
now, the length of the horizontal traverse axis is 4 units, from vertex to vertex, that means the "a" component of the hyperbola is half that or 2 units, and 2² = 4, with a center at the origin.
\(\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(x- 0)^2}{ 2^2}-\cfrac{(y- 0)^2}{ (\sqrt{3})^2}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{4}-\cfrac{y^2}{3}=1 \end{array}}\)
True or False: A square is a specific type of parallelogram?