We would expect the spinners to land on the same number approximately 2 times in 10 spins.
Based on the given probabilities, we know that the probability of the red spinner and blue spinner landing on the same number is 21%, and the probability of them landing on different numbers is 79%. We can use this information to calculate the expected number of times the spinners would land on the same number in 10 spins.
If we assume that the probability of the spinners landing on the same number is constant across all 10 spins, then we can model the number of times they land on the same number as a binomial distribution with n=10 (number of trials) and p=0.21 (probability of success).
Using the formula for expected value of a binomial distribution, we can calculate the expected number of times the spinners would land on the same number in 10 spins as:
E(X) = np = 100.21 = 2.1
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Complete question is:
The outcome of spinning 2 spinners 100 times is shown as.
Events Actual outcomes Probability
P(red spinner = blue spinner) 21 21%
P(not red spinner = blue spinner) 79 79%
How many times would you expect these spinners to land on the same number in 10 spins?
Two buses leave a station at the same time and travel in opposite directions. One bus travels 8 mih slower than the other. If the two buses are 432 miles apart after 3 hours, what is the rate of each bus?
The rate of each bus which leave a station at the same time are 76 mi/h and 68 mi/h respectively.
Given that,
Two buses leave a station at the same time and travel in opposite directions.
Let x be the distance travelled by the the first bus in 3 hours.
Then the distance travelled by the other bus in 3 hours = 432 - x
Rate of first bus = x/3 miles per hour
Rate of second bus = (432 - x) / 3 miles per hour
One bus travels 8 mi/h slower than the other bus.
x/3 - (432 - x) / 3 = 8
(x - 432 + x) / 3 = 8
2x - 432 = 24
2x = 456
x = 228
Rate of one bus = 228/3 = 76 mi/h
Rate of second bus = (432 - 228)/3 = 68 mi/h
Hence the rate of each bus are 76 mi/h and 68 mi/h respectively.
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How many lines are shown in the drawing
The given images shows us that we have a total of two lines
How to identify the lines?In mathematics, a point is referred to as the particular location on a plane. A point is identified by a dot. It has no length, shape or size.
A line is straight, without any type of thickness and it is the shortest distance that exists between 2 points. It has only length. It is without width.
A line segment has two end points. The difference that a line segment has with a line is that a line is extensive while the line segment has two end points.
Ray is defined as a line that has only one endpoint. The other end of the line just goes on. It has one start point and one end point.
From the attached image, it is vert clear that we have two lines which are the horizontal line and the line that divides it.
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Find the exact volume of a cylinder with radius 4 ft. and height 10 ft.
Select the correct answer.
Which of these statements defines the term resources?
O A. materials that help you achieve your goals
OB. all the goods and services provided to people
OC. the government's ability to deal with economic problems
Reset
Next
The statements that defines the term resources is A. materials that help you achieve your goals.
What is resources?Resource can be described as all the materials available that is available in individual environment and can be seen as one that is technologically accessible.
It should be noted that resources do help us to achieve most of our goals and can be seen as one that is economically feasible as welll as culturally sustainable and they serves as things that can help us and thjat can satisfy our needs and wants which is needed on daily basis.
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Jason is taking a multiple choice test with a total of 20 points available. Each question is worth exactly 1 point. What would be Jason's test score (out of o) if he got 9 questions wrong? What would be his score if he got a questions wrong?
Score with 9 questions wrong:
Score with x questions wrong:
The test score for Jason will be 55% for answering 11 questions right.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Jason is taking a multiple-choice test with a total of 20 points available. Each question is worth exactly 1 point.
The test score will be calculated as,
[tex]\text{Test score} =\dfrac{\text{Total questions - wrong answers}}{\text{Total questions}} \times100[/tex]
[tex]\text{Test Score}=\huge \text[\dfrac{(20-9)}{20}\huge \text] \times100[/tex]
[tex]\text{Test Score}=0.55\times100[/tex]
[tex]\text{Test Score}=0.55\%[/tex]
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2. Tell if the number shown is written in scientific notation. If it is, write correct, if incorrect
explain why and correct the mistake.
A. 0.5045 x 10
B. 2.804 x 10"
C. 12.04 x 10
The number shown is not written in scientific notation because the 10 do not raise to power of any number, and exponential on the second value do not represent a particular power.
What is Scientific notation?Scientific notation can be described as the way of writing very large as well as very small numbers.
It should be noted that the number is written in scientific notation which is been done as a result of the number falling between 1 and 10 and then this number is been multiplied by a power of 10 instance of this is 6.5 ✕ 10^8, then we can see that none of the given values have the sa,me expresion with this example.
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use a unit 2 multiplayer to convert 5.4 square meters to square centameters
To convert 5.4 square meters to square centimeters is 54,000 cm²
How to convert convert 5.4 square meters to square centimeters?To convert 5.4 square meters (m²) to square centimeters (cm²),
We need to multiply it by 10,000 (since 1 meter = 100 centimeters).
5.4 m² = 5.4 x 10,000 cm² = 54,000 cm²
Therefore, 5.4 square meters is equal to 54,000 square centimeters.
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Mia and Lia are competing in a race. 50 people are in the race and medals are given 1st, 2nd, and 3rd place. What is the likelihood that Mia and Lia place in 1st or 2nd?
The likelihood that Mia and Lia place in 1st or 2nd is unlikely
What is the likelihood that Mia and Lia place in 1st or 2nd?From the question, we have the following parameters that can be used in our computation:
People = 50
Positions = 1st, 2nd, and 3rd place
The probabilities are
P(1st) = 1/50
P(2nd) = 1/49
Using the above as a guide, we have the following:
P = 1/50 * 1/49
Evaluate
P = 0.00040816326
This value is less than 50%
So, the likelihood is unlikely or less likely
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PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
V = (1/2)(4/3)π(6.5^3) = 575.17 cubic inches
V = (1/2)(4/3)(3.14)(6.5^3) =
574.88 cubic inches
The correct answer is 574.9 cubic inches.
A cone has an apex. True False
Answer:
True, a cone has an apex which is the point where the sides of the cone meet to form a tip.
(HURRY PLEASE!!) First, a graph of f(x) = -x + 3 is drawn. Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3. Which will be true of these three graphs? A. Their slopes will be the same as the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x). B. Their slopes will be the same as the slope of f(x), and their x-intercepts will be different from the x-intercept of f(x). C. Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x). D. Their slopes will be different from the slope of f(x), and their x-intercepts will be different from the x-intercept of f(x).
The true statement about the graphs:
Their slopes will be different from the slope of f(x), and their x-intercepts will be the same as the x-intercept of f(x).
The correct answer is an option (C)
First we draw a graph of function f(x) = -x + 3.
Find the graph in attached figure.
the x-intercept of f(x) is:
0 = -x + 3
i.e., x-intercept = (3, 0)
Then, three graphs of k(-x + 3) are drawn, for k = -1, -2, -3.
Let g(x) = -1(-x + 3)
The x-intercept of g(x) would be,
0 = -1(-x + 3)
i.e., x-intercept = (3, 0)
Let h(x) = -2(-x + 3)
The x-intercept of h(x) would be,
0 = -2(-x + 3)
2x = 6
i.e., x-intercept = (3, 0)
Let t(x) = -3(-x + 3)
The x-intercept of t(x) would be,
0 = -3(-x + 3)
3x = 9
i.e., x-intercept = (3, 0)
the graph of functions g(x), h(x) and t(x) is shown below.
We can observe that the x-intercept is same for all graphs but the slopes are different.
Therefore, the correct answer is an option (C)
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. Find the exact circumference in terms of pi of the circles. (5 points each)
Step-by-step explanation:
The hypotenuse of each of these right triangles can be found using Pythagorean theorem....the hypotenuse is also the DIAMETER of the circle
diamter * pi = circumference
First one:
Hypot^2 = 13^2 + 13^2
hypot ^2 = 338
hypot = diameter = sqrt (338)
circumference = diamter * pi = sqrt 338 pi ft ( or 13 sqrt(2) pi ft )
The second one is the same with slightly different numbers...you try it ...
Answer:[tex]\sqrt{338}\pi[/tex], [tex]25\pi[/tex]
Step-by-step explanation:
I will start with the second one, since it will be easier. Because this is a right triangle, you can use the given side lengths of the triangle to find the hypotenuse, which is also equal to the diameter of the triangle. Since the pythagorean theorem states that a^2(the shorter leg, squared) + b^2 (the longer leg, squared) = c^2 (the hypotenuse, squared) we can turn it into an equation like this:
[tex]7^{2\ }+\ 24^{2}\ =\ c^{2}[/tex]
(lets use x in place of c in the next few equations, for algebraic simplicity)
Simplify
[tex]49+\ 576\ =x^{2}[/tex]
[tex]625=x^{2}[/tex]
Get the square roots
[tex]\sqrt{625}=\sqrt{x^{2}}[/tex]
[tex]x=25[/tex]
Since x is equal to the hypotenuse, we know that the hypotenuse is also 25. This means the diameter of the second circle is 25, and we can now find the circumference. The EXACT circumference of the second circle is 25π, but a simplified version can be created by calculating it as if it were an equation. This comes out to around 78.5398163397, which would trail for infinity. which is why to get an exact measurement of the diameter, the most simplified exact version is displayed by multiplying the diameter by the pi symbol, because it is impossible to fit an infinite number in a finite space.
Now for the first circle, which I am now realising is no more difficult than the last one. We can do the same thing in this case, using pythagorean theorem, because there are two dash lines marking two of the lines on the circle to be equal to one another, we know that the two marked lines are equal to 13, despite not appearing to be.
We can use the same equation as we did before, but slightly modified.
[tex]13^{2}+13^{2}=x^{2}[/tex]
Simplify:
[tex]169+169=x^{2}[/tex]
[tex]338=x^{2}[/tex]
Now we can take the square roots of both sides of the equation.
[tex]\sqrt{338}=\sqrt{x^{2}}[/tex]
This is where we come to a bit of a pause. Because the square root of 338 is an irrational constant number, we have to use the unsimplified square root in our answer for the circumference, otherwise, our answer would not be exact.
The diameter of our circle is [tex]\sqrt{338}[/tex], which means that we can use an equation like this to find the circumference:
[tex]\sqrt{338}\pi[/tex]
But since we cannot simplify this any further without it not being exact, we must leave it as is.
I need help to solve this...
Answer:
2.38888
Step-by-step explanation:
That's what is says hope this helps
How much more total interest will you earn when interest is calculated on the new yearly amount, rather than the original principal? (Compare the last row of the tables). In the next section, we will get to “see” the larger snowball, called compound interest.
The rate of interest with the given amount and compound interest is 5 percent.
Given that,
After 1 year: compound interest = $30 and total amount=$630.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Here, principal = 630-30=600
630=600(1+r/100)¹
630/600 = 1+r/100
1.05=1+r/100
1.05-1=r/100
0.05=r/100
r=5%
Therefore, the rate of interest with the given amount and compound interest is 5 percent.
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Answer this please for LARGE REWARD
Answer:
19.5625
Step-by-step explanation:
[tex]\frac{2(12) + 4(15) + 16 +18 + 2(20) + 22 +3(25) +2(29)}{16}[/tex] = [tex]\frac{313}{16}[/tex] = 19.5625
We add up all the numbers that are represented on the graph and then divide that by 16 because there are 16 numbers.
Helping in the name of Jesus.
What is the measure of EACH interior angle of a
regular 16-sided polygon?
The measure of each interior angle of a regular 16-sided polygon is 157.5 degrees
How to determine the valueTo determine the value of the interior angle, we need to note that;
The formula for calculating the sum of the interior angles of a polygon is expressed with the expression;
(n -2)180
Such that the variable n in the expression represents the number of sides of the polygon
From the information given, we have that;
(16- 2)180
expand the bracket
14(180)
multiply the values
2520 degrees
Then, we have;
16x = 2520
Make 'x' the subject
x= 157. 5 degrees
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Coordinate Proof!
Given: Isosceles ∆ABC; M is the midpoint of AC-.
Prove: area ∆ABM = area ∆CBM
Proof
AM = √(x₂ − x₁)² + (y₂-y₁)²
= √(4-0)² + (0-0)²
= √4² = _
BM = √(x2-x₁)² + (1₂-y₁)²
= √(4-4)² + (6-0)2
= √6² = _
AM- ≅ CM- ____
AM = CM ____
CM = 4. Subst.
area ∆ABM
A = 1/2 bh
= 1/2 ___
= ___
area ∆CBM
A = 1/2 bh
= 1/2 ___
= ___
Therefore: Area ∆ABM = area ∆CBM by ___
The completed calculation with regards to the area of the congruent triangles can be presented as follows;
The distance formula indicates;
AM = √((x₂ - x₁)² + (y₂ - y₁)²)
Therefore, we get;
AM = √((4 - 0)² + (0 - 0)²) = √(4²)
AM = √(4²) = 4
BM = √((x₂ - x₁)² + (y₂ - y₁)²)
BM = √((4 - 4)² + (6 - 0)²) = √(6²)
BM = √(6²) = 6
AM ≅ CM Definition of the midpoint of AC
AM = CM Definition of congruent segments
CM = 4 Substitution property
Area ΔABM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Area ΔCBM
A = (1/2)·b·h
= (1/2) × 4 × 6
= 12
Therefore Area ΔABM = area ΔCBM by congruence
What are congruent triangles?Triangles are congruent if they have the same size and shape.
The details of the reasons for the calculation steps and values are presented as follows;
Definition of midpoint of a segment
The midpoint of a line segment is the point that divides the segment into two parts of the same length
Definition of congruence?
Congruence refers to the existence of compatibility or harmony between objects, which in geometry indicates that the two geometric figures have the same measurement
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Triangle ABC
A
B
C
and triangle DEF
D
E
F
are similar. What is the measure of side DF
D
F
?
Answer:
19cm
Step-by-step explanation:
I think it's 19cm as sides BC on the green triangle measure 15cm, and EF is 25cm on the blue triangle. It also mentions that they are similar, meaning that ∆ DEF is just a translated and enlarged version of ∆ ABC
25 - 15 = 10cm
9 + 10 = 19cm
Hope this helped :)
Consider the sequence {3, 12, 21, 30, 39, 48, 57} What is a5
The value of the term a5 is 39
Calculating the value of a5From the question, we have the following parameters that can be used in our computation:
{3, 12, 21, 30, 39, 48, 57}
The expression a5 means the 5th term of the sequence
In {3, 12, 21, 30, 39, 48, 57} , the fifth eterm is 39
Hence, a5 = 39
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Question 1(Multiple Choice Worth 2 points) (Theoretical Probability MC) When rolling a 6-sided die twice, determine P(sum of 4). 1. 3/36 2. 5/36 3 8/36 4. 2/6
Answer:
5/36
Step-by-step explanation:
hope this helps
what is this?? i will give extra points
↬ x² - 6x -5
Substituting x = 3:-
⟶ x² - 6x -5
⟶ (3)² - 6(3) -5
⟶ 9 - 6 × 3 - 5
⟶ 9 - 18 - 5
⟶ 9 - 23
⟶ -14
Answer:
[tex] \gg{ \underline{ \large \: \boxed { \bf {- 14}}}}[/tex]
Step-by-step explanation:
[tex] \large \: \sf { \underline{Given}}[/tex]
[tex] \sf \: x {}^{2} - 6x - 5[/tex][tex] \sf \: x = 3[/tex][tex] \large \sf \underline{Solution }[/tex]
[tex] \large \: \displaystyle \sf {x}^{2} - 6x - 5[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \large \bf \blue{ \underline{putting \: the \: value \: of \: x}}[/tex]
[tex]\large \: \displaystyle \sf \: {3}^{2} - 6(3) - 5 [/tex]
[tex]\large \: \displaystyle \sf \: = \: 9 - 18 - 5[/tex]
[tex]\large \: \displaystyle \sf \: = \: - 9 - 5[/tex]
[tex]\large \: \displaystyle \bf \red{= - 14}[/tex]
What term refers to the basic characteristics of a population segment such as gender age and income?
The term that refers to the basic characteristics of a population segment such as gender, age, and income is demographics.
We have,
Demographics refers to statistical data that describes a population and its characteristics, such as age, gender, income, education level, marital status, and other relevant factors.
Demographic information is commonly used by businesses and organizations to analyze consumer behavior, market trends, and patterns in the population.
By understanding the demographics of a particular population segment, businesses can tailor their products and services to better meet the needs and preferences of their target audience.
Demographic information is also used by government agencies and policymakers to allocate resources, plan for future development, and assess the needs of the population.
Thus,
The term that refers to the basic characteristics of a population segment such as gender, age, and income is demographics.
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A researcher is interested in how client expectations of success before therapy relate to satisfaction with the sessions afterward. Ratings (on a 1-10 scale) for 10 participants are presented in the table below. This dataset will be used for Questions 1-4. Compute the Pearson r correlation coefficient for these data. Note: Show your work on a separate sheet of paper. You will be asked to upload a scan/picture of your work at the end of the test.
Client Expectations (x) Satisfaction (y)
1 3
1 1
2 3
3 7
3 9
4 5
6 8
6 7
7 10
7 7
Questions:
1.) What is the value of the Pearson correlation coefficient (r)? Please round your answer to 3 decimal places.
2.) What would the critical value (rcrit) be for a 2-tailed test with a .05 alpha level using the Client Expectation-Satisfaction dataset shown in Question 1? (Express your answer to 3 decimal places)
3.) Based on the correlation you calculated in Question 1 and the critical value you identified in Question 2, was the correlation statistically significant (i.e., would you reject the null hypothesis)?
1. Using the formula for Pearson correlation coefficient, we have:
x y xy x^2 y^2
1 3 3 1 9
1 1 1 1 1
2 3 6 4 9
3 7 21 9 49
3 9 27 9 81
4 5 20 16 25
6 8 48 36 64
6 7 42 36 49
7 10 70 49 100
7 7 49 49 49
n = 10
sum(x) = 40, sum(y) = 53, sum(xy) = 286, sum(x^2) = 214, sum(y^2) = 506
r = [n(sum(xy)) - sum(x)sum(y)] / sqrt{ [n(sum(x^2)) - sum(x)^2][n(sum(y^2)) - sum(y)^2] }
r = [10(286) - (40)(53)] / sqrt{ [10(214) - (40)^2][10(506) - (53)^2] }
r = 0.832 (rounded to 3 decimal places)
2. The critical value (rcrit) for a 2-tailed test with a 0.05 alpha level and 8 degrees of freedom is 0.632 (using a t-distribution table or calculator).
3. The calculated correlation coefficient (r = 0.832) is greater than the critical value (rcrit = 0.632), which means that the correlation is statistically significant. We would reject the null hypothesis and conclude that there is a significant positive correlation between client expectations and satisfaction with therapy sessions.
5. Which graph represents 4x - 2y = 8?
Answer:
A
Step-by-step explanation:
4x - 2y = 8
x - int y = 0
4x = 8
x = 2
(2, 0)
y-int, x = 0
-2y = 8
y = -4
Problems 2 and 3 refer to the following drawing.
2. The side AC corresponds to side AE of the other triangle.
3. The length of side BC is 15.
What are similar triangles?Two or more triangles are said to be similar if on comparing their properties, there exist some common relations. Some of the common relations are; measure of internal angles, scale factor etc.
From the diagram given, we have;
2. Given that the triangles are similar, thus:
The side AC corresponds to side AE of the other triangle.
3. On comparing the corresponding length of the triangles, we have;
15/ 25 = 9/ BC
15BC = 9 x 25
= 225
BC = 225/ 15
= 15
The length of side BC is 15.
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What are the values of the trigonometric ratios for this triangle?
Drag the answers into the boxes.
The values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.
From the given right triangle hypotenuse= 17 units and legs of triangle are 15 units and 8 units.
We know that, sinθ = Opposite/Hypotenuse
sinθ = 8/17
We know that, cosθ = Adjacent/Hypotenuse
cosθ = 15/17
We know that, tanθ = Opposite/Adjacent
tanθ = 8/15
Therefore, the values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.
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QUESTION 5 - 1 POINT
Rebecca invests $700 into an account with a 2.9% interest rate that is compounded semiannually.
How much money will she have in this account if she keeps it for 5 years?
Round your answer to the nearest dollar.
Provide your answer below:
Answer:
$814 she kept for 5 years if she don't spend it
Step-by-step explanation:
Can a rectangle be a parallelogram
Options
A. Sometimes
B. Always
C. Never
Answer:
B always because a rectangle has two sets of parallel sides
Hope this helps
What is the probability that the total team time in the
400-meter freestyle relay is less than 215 seconds?
O 0.056
O 0.1665
O 0.8335
0.944
The probability that the total team time in the 400-meter freestyle relay is less than 215 seconds is: 0.8345
How to find the probability from z-score?From the table given the mean and standard deviation, we can say that:
Total time spent = 54.2 + 57 + 55.3 + 53.7
Total time spent = 220.2 secs
The total standard deviation is:
2.8 + 3 + 2.4 + 2.5 = 10.7 secs
Formula for z-score here is:
z = (x' - μ)/(σ/√n)
where:
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
Thus:
z = (220.2 - 215)/(10.7/√4)
z = 0.972
From online p-value from z-score calculator, we have:
p(x < 0.972) = 0.8345
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Answer: b
Step-by-step explanation: cause i just did it
Rewrite the logarithmic equation below as an equivalent exponential equation.
log3(N) = x
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_3(N)=x\implies 3^x=N[/tex]