The answer is option B: 0.040. When Z is a standard normal random variable, it means that Z has a mean of 0 and a standard deviation of 1. Therefore, P(-1.75 < Z < -1.25) represents the area under the standard normal curve between -1.75 and -1.25 standard deviations from the mean.
Using a standard normal distribution table or calculator, we can find that the area under the curve between -1.75 and -1.25 is approximately 0.040. Hence, the answer is option B: 0.040.
To solve your question, we need to find the probability P(-1.75 ≤ Z ≤ -1.25) where Z is a standard normal random variable.
Step 1: Identify the given values
Z1 = -1.75
Z2 = -1.25
Step 2: Look up the Z-values in a standard normal table or use a calculator to find the corresponding probabilities
P(Z ≤ -1.75) = 0.0401
P(Z ≤ -1.25) = 0.211
Step 3: Use the properties of probabilities to find the required probability
P(-1.75 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -1.75)
P(-1.75 ≤ Z ≤ -1.25) = 0.211 - 0.0401
P(-1.75 ≤ Z ≤ -1.25) = 0.1709
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Although the technology was not specifically mentioned in the unit, there is no denying it has become such a huge part of our lives – including our fitness. What are some ways that increased technology use has negatively impacted personal fitness? What are some ways that it has helped personal fitness?
Answer: One way is video games. Video games help people escape from reality, which prevents people from going out and exercising. One way is treadmills, where you are able to increase your heart rate through cardio without straining the body.
Step-by-step explanation: a
2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
Answer:
The angles of the cyclic quadrilateral are
84 degrees96 degrees98 degrees80 degreesHow to find the measure of the anglesIn a cyclic quadrilateral the opposite angles are supplementary hence we have that
x - 4 + x + 8 = 180 degrees
gathering like terms
2x = 180 - 8 + 4
2x = 176
isolating x
x = 88 degrees
angles on each side
x- 4 = 88 - 4 = 84
x + 8 = 88 + 8 = 96
2x - 78 = 2(88) - 78 = 98
sum of the angles of a cyclic quadrilateral is 360
the fourth angle = 360 - 84 - 96 - 98
the fourth angle = 80 degrees
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Cos (90°-0) / sin (180°- 0) - sin^2 (-0)
The answer to the mathematical expression of Cos (90°-0) / sin (180°- 0) - sin^2 (-0) is:
= -1
How to calculate the expressionTo calculate the expression, we can begin by determining the values and subtracting or dividing as is the case. First, we begin by determining the values as follows:
Cos 90° = 0
Cos 0 = 1
Sin 180° = 0
Sin -0 = 0
Now we express the values as follows:
Cos (90°-0) / sin (180°- 0) - sin^2 (-0)
0 - 1/0 - 0
= -1
So, the answer obtained from resolving this expression is -1.
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1) A liquor store owner wants to re-order their store to put the more expensive wines near the front. The owner samples 40 bottles of red and 40 bottles of white wine to find out which is more expensive. The owner finds the average price of white is $19.33, while the average price of red is $20.87 (standard deviation of $2.88 for white and $3.05 for red).
1a) What is the point estimate of the population price difference between red and white wines?
1b) What is the margin of error for alpha=0.01?
1c) What is the confidence interval for the difference between the two population means? Use alpha=0.05.
Answer:
Bellow
Step-by-step explanation:
1a) The point estimate of the population price difference between red and white wines is given by:
$$\bar{x}_1 - \bar{x}_2 = 20.87 - 19.33 = 1.54$$
Therefore, the point estimate of the population price difference between red and white wines is $1.54.
1b) The margin of error for alpha=0.01 can be calculated using the following formula:
$$ME = z_{\alpha/2}\cdot\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$
where $z_{\alpha/2}$ is the critical value of the standard normal distribution for the given level of significance, $s_1$ and $s_2$ are the sample standard deviations, and $n_1$ and $n_2$ are the sample sizes for the two populations.
For alpha=0.01, the critical value of the standard normal distribution is $z_{\alpha/2}=2.58$. Substituting the given values, we get:
$$ME = 2.58\cdot\sqrt{\frac{2.88^2}{40} + \frac{3.05^2}{40}} \approx 1.01$$
Therefore, the margin of error for alpha=0.01 is approximately $1.01.
1c) The confidence interval for the difference between the two population means can be calculated using the following formula:
$$(\bar{x}_1 - \bar{x}_2) \pm z_{\alpha/2}\cdot\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$
For alpha=0.05, the critical value of the standard normal distribution is $z_{\alpha/2}=1.96$. Substituting the given values, we get:
$$(20.87 - 19.33) \pm 1.96\cdot\sqrt{\frac{2.88^2}{40} + \frac{3.05^2}{40}}$$
Simplifying this expression, we get:
$$(1.54) \pm 1.11$$
Therefore, the 95% confidence interval for the difference between the two population means is approximately $(0.43, 2.65)$.
what conditions/assumptions must be met in order for the two-sample test for means with independent samples to be appropriate?
If these conditions/assumptions are met, then the two-sample test for means with independent samples can be used to determine if there is a statistically significant difference between the means of two independent groups.
In order for the two-sample test for means with independent samples to be appropriate, the following conditions/assumptions must be met:
Independent samples: The samples for each group should be selected independently of each other.
Normality: The population distributions should be approximately normal, or the sample sizes should be large enough (n > 30) for the central limit theorem to apply.
Equal variances: The variances of the two populations should be approximately equal. This assumption is important for calculating the pooled variance estimate, which is used in the t-test formula.
Random sampling: The samples should be randomly selected from the populations of interest.
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expinential function alg 1 help
The missing part of the table is completed as shown below
x y
-1 1 / 6
0 1
3 216
What is an exponential function?Exponential function is a function of the form f(x) = a(b)^x
Considering the given problem,
the starting = a
the base = b
the exponents = x
Using the formula, y = 6^x the table is completed by substitution
for x = -1
y = 6^(-1) = 1/ 6
for x = 0
y = 6^(0) = 1
for x = 3
y = 6^(3) = 216
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Question: James and Samuel go to work at different parts of the town. James' house is located at the coordinates (3,4) and his job is at the coordinates (9,8). He decides to grab a snack before his job from the gas station which is at the coordinates (4,1). Samuel's house is located at the coordinates (10,2) and his job is at the coordinates (4,5). He decides to visit his mother before his job, whose house is at the coordinates (5,8). Whose journey to their job was longer, Samuel's or James'?
James had a longer commute to work than Samuel did.
We need to figure out how far each person went from their starting point to their destination in order to evaluate whose journey was longer. The formula for calculating the distance between two locations is as follows:
[tex]d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
For James:
Distance from his house to the gas station:
[tex]d_1 = \sqrt{((4 - 3)^2 + (1 - 4)^2)}\\ = \sqrt{(10)[/tex]
Distance from the gas station to his job:
[tex]d_2 = \sqrt{((9 - 4)^2 + (8 - 1)^2)}\\ = \sqrt{(90)}[/tex]
Total distance traveled:
[tex]d_1 + d_2 = \sqrt{(10)} + \sqrt{(90) }\\= 12.016[/tex]
For Samuel:
Distance from his house to his mother's house:
[tex]d_1 = \sqrt{((5 - 10)^2 + (8 - 2)^2)} \\= \sqrt{(74)[/tex]
Distance from his mother's house to his job:
[tex]d_2 = \sqrt{((4 - 5)^2 + (5 - 8)^2})\\ = \sqrt{(10)[/tex]
Total distance traveled:
[tex]d_1 + d_2 = \sqrt{(74)} + \sqrt{(10)} \\ =10.872[/tex]
Therefore, Samuel's journey to his job was shorter than James'
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Your gross annual pay is $19 163. Employment insurance premiums are deducted at a rate of 2. 25% and Canada Pension Plan premiums are 3. 75% based on total earnings. You pay income taxes at a rate of 17% on all amounts over $8131. What is your Net Pay for the year?
The Net Pay for the year for gross annual pay is $19 163. Employment insurance premiums are deducted at a rate of 2 with income taxes at a rate of 17% on all amounts over $8131 is $16,137.03.
To find the net pay for the year, we need to subtract the deductions from the gross pay and then subtract the income tax from the remaining amount.
First, we need to find the total amount deducted for EI and CPP premiums:
EI premium = 2.25% of $19,163 = $431.67
CPP premium = 3.75% of $19,163 = $720.86
Total deductions = $431.67 + $720.86 = $1,152.53
Next, we need to find the taxable income by subtracting the basic personal amount from the gross pay:
Taxable income = $19,163 - $8,131 = $11,032
Then, we need to calculate the income tax on the taxable income:
Income tax = 17% of ($11,032) = $1,873.44
Finally, we can calculate the net pay by subtracting the total deductions and income tax from the gross pay:
Net pay = $19,163 - $1,152.53 - $1,873.44 = $16,137.03
Therefore, the net pay for the year is $16,137.03.
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find the area of the parallelogram with vertices a(−4, 2), b(−2, 5), c(2, 3), and d(0, 0).
8 square unit to find the area of the parallelogram with vertices A(-4, 2), B(-2, 5), C(2, 3), and D(0, 0), follow these steps:
Step 1: Find the base and height vectors of the parallelogram. Let's use AB and AD as the base and height vectors, respectively.
AB = B - A = (-2 - (-4), 5 - 2) = (2, 3)
AD = D - A = (0 - (-4), 0 - 2) = (4, -2)
Step 2: Calculate the cross-product of the base and height vectors.
Cross product = AB_x * AD_y - AB_y * AD_x = (2 * -2) - (3 * 4) = -4 - 12 = -16
Step 3: Find the area by taking the absolute value of the cross product divided by 2.
Area = |Cross product| / 2 = |-16| / 2 = 8
The area of the parallelogram with vertices A(-4, 2), B(-2, 5), C(2, 3), and D(0, 0) is 8 square units.
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Eric owns and operates the Hot Ham food truck. The expression
3.25
�
+
2
ℎ
3.25b+2h3, point, 25, b, plus, 2, h gives the cost of
�
bb burgers and
ℎ
hh hot dogs.
What is the cost of
4
44 burgers and
6
66 hot dogs?
The cost of 4 burgers and 6 hot dogs is $25.
We are given that;
Expression= 3.25+2ℎ
Number of burgers=444
Number of hot dogs= 666
Now,
To find the cost of 4 burgers and 6 hot dogs, we need to substitute b = 4 and h = 6 in the expression 3.25b+2h. We get:
3.25(4)+2(6)
Using the order of operations, we first multiply 3.25 by 4 and 2 by 6. We get:
13+12
Then we add 13 and 12. We get:
25
Therefore, by the given expression the answer will be $25.
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What’s the answer? Please I need help
Answer: 21/29
Step-by-step explanation:
sin B = opposite side/hypotenuse
=21/29
Answer:
21/29
Step-by-step explanation:
sin B= opposite/hypotenuse
sin B = 21/29
REASONING
5. In problem #4, there is a relationship between the measure of the smaller are intercepted by the tangents and
the measure of the exterior angle.
(a) Determine the relationship. If you need to,
generate more examples using the same
diagram. Illustrate the relationship with at
least one pair.
(b) If mAB=x, prove the relationship you
found in (a).
The relationship of the angles is ∠P = 1/2(ACB - AB) and the measure of angle P is (180 - x) degrees
Determining the relationship of the anglesGiven that
Arc are intercepted by tangents and the exterior angle
The theorem of intersected tangents states that
The measure of the angle is the difference between the measures of the arc
So, the relationship of the angle is ∠P = 1/2(ACB - AB)
Proving the theorem in (a)Here, we have
AB = x
This means that
ACB = 360 - x
So, we have
∠P = 1/2(360 - x - x)
When evaluated, we have
∠P = 180 - x
Hence, the measure of angle P is 180 - x degrees
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What is the concept of asymptotic stability?
Asymptotic stability is a property of a dynamical system where the solutions of the system approach a particular equilibrium point as time goes to infinity, but they do not oscillate or move away from the equilibrium point. In other words, the solutions of the system converge to the equilibrium point as time goes to infinity.
Formally, a critical point x* of a dynamical system x' = f(x) is asymptotically stable if for any solution x(t) that starts sufficiently close to x*, there exists a positive constant ε such that ||x(t) - x*|| → 0 as t → ∞, where ||.|| denotes the Euclidean norm.
Intuitively, this means that if the initial condition of the system is perturbed slightly from the equilibrium point, then the solutions of the system will still converge to the equilibrium point as time goes to infinity. This is a desirable property for many systems, as it implies that the system will eventually settle down to a steady state.
The concept of asymptotic stability is often studied in the context of linear systems, where the stability of the equilibrium point is determined by the eigenvalues of the system matrix. For a linear system, the equilibrium point is asymptotically stable if all the eigenvalues have negative real part. In this case, the solutions of the system decay to zero exponentially as time goes to infinity.
Overall, asymptotic stability is an important concept in the study of dynamical systems, as it provides a way to analyze the long-term behavior of a system and predict its future state.
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How do you find the answer to this
(3+-/7)2
In radical
The solutions in radical form is
16 + 6√7 16 - 6√7How to solve in radical formThis is of the form
(3 ± √7)²
Then we have to write this in two cases such that
Case 1: (3 + √7)²
Case 2: (3 - √7)²
Solve the first case
(3 + √7)²
(3 + √7)(3 + √7)
= 3² + 2(3)(√7) + (√7)² =
9 + 6√7 + 7
= 16 + 6√7
Next we have to solve for case 2
(3 - √7)²
(3 - √7)(3 - √7)
= 3² - 2(3)(√7) + (√7)²
= 9 - 6√7 + 7
= 16 - 6√7
The values and solutions would be:
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(2 points) Important: With this multiple choice question, you only get one attempt (not the usual three)! To test whether there is a significant difference in mean household debt between Regina and Sasaktoon households, samples of 100 households in each city are collected. A test statistic z-score of 1.51 is calculated based on the collected sample data. We wish to perform the test at the 5% level of significance. What final conclusion could be drawn from this information? Select the best answer. At this level of significance, ? ? we cannot conclude that there is a significant difference between the two populations. we can conclude that household debt is the same in the two cities. Preview My Answers we can conclude that household debt is different in the two cities. You have attempted this probl we cannot make any conclusions, since the sample sizes are the same. You have 1 attempt remaining we can conclude that there is a significant difference between the two populations. we can conclude that household spending in Regina is higher.
Based on the information given, we can conclude that there is a significant difference between the two populations.
The calculated z-score of 1.51 is greater than the critical value of 1.96 (at the 5% level of significance), which indicates that the sample mean differences are unlikely to have occurred by chance. Therefore, we reject the null hypothesis and conclude that household debt is different in the two cities.
At this level of significance, we cannot conclude that there is a significant difference between the two populations.
Explanation:
To determine if there is a significant difference between the mean household debt of Regina and Saskatoon households at the 5% level of significance, we need to compare the calculated z-score of 1.51 to the critical z-score for a two-tailed test. For a 5% level of significance, the critical z-scores are -1.96 and 1.96. Since 1.51 is between -1.96 and 1.96, we cannot reject the null hypothesis, which means we cannot conclude that there is a significant difference between the two populations at the 5% level of significance.
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A: Plot point C so that its distance from the origin is 1. B: Plot point E 4/5 closer to the origin than C. What is its coordinate? DUE IN 10 MINUTES. HELP
A) A point C such that the distance from the origin can be plotted at (1, 0).
B) A point E which is at 4/5 closer to the origin than C can be plotted at (4/5, 0) = (0.8, 0)
A) Given a point O(0, 0).
A distance of 1 from the origin can be marked at 4 points :
(1, 0), (-1, 0), (0, 1) and (0, -1).
Using the distance formula, all the points from O is 1.
Let's take C as (1, 0).
B) Point E is at 4/5 closer to O than C.
Ratio of the distance between OE and EC is 4/5 : 1/5 = 4 : 1.
The section formula states that If a line with end points (x, y) and (x', y') is divided in the ratio m : n, then the divided point is,
P = [(mx' + nx)/(m + n) , (my' + ny)/ (m + n)]
Here (x, y) = (0, 0) and (x', y') = (1, 0)
m : n = 4 : 1
Using the section formula,
Coordinates of E = ((4 + 0)/ 5 , (0 + 0)/5) = (4/5, 0) = (0.8, 0).
If the distance between (0, 0) and (1, 0) is divided in to 5 segments, then the point E will be at 4th segment.
Hence the required coordinates are C(1, 0) and E(0.8, 0).
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PLEASE HELP I INCLUDED A WRITTEN VERSION OF MY PROBLEM I WROTE IT PLEASE HELP!!!
Factor.
x2−6x+9
Responses
(x−3)2
left parenthesis x minus 3 right parenthesis squared
(x−9)2
left parenthesis x minus 9 right parenthesis squared
(x+3)2
left parenthesis x plus 3 right parenthesis squared
(x+9)2
Answer:
A
Step-by-step explanation:
x^2-6x+9
to factorise this you need two numbers that times to make 9 and add to make -6
these two numbers are -3 and -3
putting it into brackets is
(x-3)(x-3)
this can also look like
(x-3)^2
so the answer is A
what line passes through (8,2) and is parallel to y= 1/2x +1
The equation of the line is y = 1/2x - 2
Calculating the equation of the lineFrom the question, we have the following parameters that can be used in our computation:
y= 1/2x +1
Point = (8, 2)
Parallel lines have equal slopes
This means that the slope of the line is 1/2
So, the eqiuation is calculated as
y = m(x - x1) + y1
substitute the known values in the above equation, so, we have the following representation
y = 1/2(x - 8) + 2
Evaluate
y = 1/2x - 2
Hence, the equation is y = 1/2x - 2
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The p-value is _____ or less if the chi-square statistic is 2.71 or more.
Without the degrees of freedom, we cannot provide a specific p-value. If the chi-square statistic is 2.71 or more, the p-value will be equal to or less than the value corresponding to 2.71 in the chi-square distribution table for the given degrees of freedom.
1. The chi-square statistic is a measure of the difference between observed and expected frequencies in a contingency table. When the observed frequencies are similar to the expected frequencies, the chi-square statistic is low. When they are different, the chi-square statistic is high.
2. The p-value is a probability that indicates how likely it is to observe a chi-square statistic as extreme as the one obtained, assuming the null hypothesis (i.e., no association between the variables) is true. A lower p-value means there is stronger evidence against the null hypothesis, suggesting an association between the variables.
3. To determine the p-value corresponding to a chi-square statistic of 2.71, you would look up the value in a chi-square distribution table or use statistical software. The p-value depends on the degrees of freedom, which is determined by the size of the contingency table.
Without the degrees of freedom, we cannot provide a specific p-value. However, if the chi-square statistic is 2.71 or more, the p-value will be equal to or less than the value corresponding to 2.71 in the chi-square distribution table for the given degrees of freedom.
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6( 3x + 12)] = 54 what is the value of x ?
The value of x based on the stated expression using mathematical operations is -1.
The calculation of x will be performed using mathematical operations in following format. Here are the steps -
Solve the parenthesis
18x + 72 = 54
Switch the position of number 72 from Left Hand Side to Right Hand Side
18x = 54 - 72
Performing subtraction on Right Hand Side of the equation
18x = -18
Rewrite the equation according to x
x = -18/18
Performing division on Right Hand Side of the equation
x = -1
Hence, the value of x is -1.
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Please help me with this homework only the answer
Answer: 9/8 is the slope
a rectangle has side lengths of 3 and 4 one of its verticles is at the point 1,2 which of the following could not be the coordinates of one of its other verticles? A -3,-1 B 1,-5 C 5,-1 D -2,6 E1,-1 helb, 15 points
The following which could not be the coordinates of one of its other vertices is (1, -5).
Given that,
Rectangle has side lengths of 3 and 4.
One of the vertices = (1, 2).
We have to find the other coordinates of the vertex.
The distance from the other vertex to this vertex needs to be either 3 or 4.
Find the distance using the distance formula.
A. (-3, -1) from (1, 2)
Distance = √(1 + 3)² + (2 + 1)² = √25 = 5
B. (1, -5) from (1, 2)
Distance = √(1 - 1)² + (2 - -5)² = √49 = 7
C. (5, -1) from (1, 2)
Distance = √(1 - 5)² + (2 - -1)² = √25 = 5
D. (-2, 6) from (1, 2)
Distance = √(1 - -2)² + (2 - 6)² = √25 = 5
Hence the coordinate which cannot be the other vertex is (1, -5).
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What parametric statistical method(s) a researcher can use to determine if the mean total cholesterol level of the population is the same for four groups of subjects (Group 1 = Diet Restriction; Group 2 = Exercise; Group 3 = Both Diet and Exercise; Group 4 = None).
a. Statistical Test is _____.
b. Null Hypothesis is _____.
c. Alternative Hypothesis is _____.
The alternative Hypothesis is that at least one of the mean total cholesterol levels is different from the others in the four groups of subjects.
A researcher can use an analysis of variance (ANOVA) parametric statistical method to determine if the mean total cholesterol level of the population is the same for four groups of subjects (Group 1 = Diet Restriction; Group 2 = Exercise; Group 3 = Both Diet and Exercise; Group 4 = None).
a. Statistical Test is ANOVA.
b. Null Hypothesis is that the mean total cholesterol level of the population is the same for all four groups.
c. Alternative Hypothesis is that the mean total cholesterol level of the population is different for at least one group.
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The Sweet Encounter is a touring International candy festival. The festival's most popular product is rainbow lollipops. At one stop of the tour, 17 out of every 53 products offered are rainbow lollipops. At that stop, the festival promoter took a sample of the products offered. He found that 27 of the 82 products offered in his sample were rainbow lollipops. For the festival promoter's sample, find and write with proper notation the sample proportion and population proportion of products offered that were rainbow lollipops. Write the proportions as decimals (not percentages) rounded to two decimal places
The sample proportion of rainbow lollipops in the festival promoter's sample is 0.33 (27/82), rounded to two decimal places. The population proportion of rainbow lollipops among all products offered at the stop of the tour is 0.32 (17/53), rounded to two decimal places.
The sample proportion and population proportion of rainbow lollipops in the given situation.
For the entire population (all products offered) at the stop, there were 17 rainbow lollipops out of every 53 products offered. To find the population proportion (P), we can use the formula:
P = Number of Rainbow Lollipops / Total Number of Products
P = 17 / 53
Now let's calculate the population proportion:
P ≈ 0.32 (rounded to two decimal places)
For the festival promoter's sample, he found that 27 of the 82 products offered were rainbow lollipops. To find the sample proportion (p'), we can use the formula:
p' = Number of Rainbow Lollipops in Sample / Total Number of Products in Sample
p' = 27 / 82
Now let's calculate the sample proportion:
p' ≈ 0.33 (rounded to two decimal places)
So, in proper notation, the population proportion (P) is approximately 0.32, and the sample proportion (p') is approximately 0.33.
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B
Problem Solving
HABITS
measure of
Be Precise Describe the rays of an angle that has a measure of 1/2 turn
The rays of the angle from the measure 1/2 turn is 180 degrees
Describing the rays of the angle from the measureFrom the question, we have the following parameters that can be used in our computation:
Angle measure = 1/2 turn
By definition, rays have two endpoints where they extend indefinitely on one of the endpoints
As a general rule, we have
a full turn = a full circle = 360°half a turn = 180°Substitute the known values in the above equation, so, we have the following representation
Angle measure = 1/2 * 360
Evaluate
Angle measure = 180
Hence, the angle measure is 180 degrees
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If a local car dealership sells new and used car the total number of cars currently at the dealership is 114.The dealership reported that they have 5 new cars for every 1 used car on the lot, how many total used cars are currently on the lot?
Using the given ratio we can see that there are 19 used cars.
How to find the number of used cars?We know that the dealership reported that they have 5 new cars for every 1 used car on the lot, so we need to use that ratio.
5/6 of the cars are new.
1/6 of the cars are used.
The total number is 114, then the number of used cars is:
(1/6)*114 = 19
There are 19 used cars.
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What is the value of y?
Y/ 1/5=20
Answer:
100
Step-by-step explanation:
To solve for y in the equation Y/1/5=20, we can multiply both sides of the equation by 1/5 to isolate y on one side of the equation. This gives us:
Y/1/5 * 1/5 = 20 * 1/5
Simplifying this expression gives us:
Y = 100
Therefore, the value of y is one hundred.
Answer:
Y = 4
Step-by-step explanation:
Now we have to,
→ Find the required value of Y.
The equation is,
→ Y/(1/5) = 20
Then the value of Y will be,
→ Y/(1/5) = 20
Simplifying the left hand side:
→ Y × (5/1) = 20
→ 5Y/1 = 20
→ 5Y = 20
Dividing 20 by the number 5:
→ Y = 20/5
→ [ Y = 4 ]
Hence, the value of Y is 4.
Deborah studies dolphins and wants to estimate the population in a certain region. She catches 60 dolphins, marks them, and releases them. At a later point, Deborah catches 330 dolphins and observes that 33 of them are marked. To the nearest whole number, what is the best estimate for the dolphin population?
The best estimate for the dolphin population in the region is 600 dolphins.
Estimated Population Size = (Number of dolphins captured) × (Number of dolphins recaptured) / (Number of marked dolphins recaptured)
In this case, the equation would be:
Estimated Population Size = (60) × (330) / (33)
This equation simplifies to:
Estimated Population Size = 600
Therefore, the best estimate for the dolphin population in the region is 600 dolphins.
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Suppose two cards are drawn randomly.
What is the probability of
drawing two green cards, if
the first card IS replaced
before the second draw?
Assume the first card
drawn is green.
[?]
Show your answer as a
fraction in lowest terms.
Enter the numerator.
The probability of drawing two green cards is 25/169
Calculating the probability of drawing two green cardsFrom the question, we have the following parameters that can be used in our computation:
Cards = 13
Green = 5
Selecting the first card we have
P(Green) = 5/13
The card is returned
So, we have the probablility of the second to be
P(Green) = 5/13
The probability of drawing two green cards is
P = 5/13 * 5/13
Evaluate
P = 25/169
Hence, the probability is 25/169
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This drawing shows two streets that cross each other. What kind of angle is formed where main street and oak stret
The solution is, the measure of angle 7 is, ∠7 = 145°.
Here, we have,
∠4 and ∠8 are corresponding angles
∠8 and ∠7 are supplementary angles
so, we get,
Then, ∠4 and ∠7 are supplementary angles.
This means that
∠4 + ∠7 = 180°
we, have,
35° + ∠7 = 180°
so, we get,
∠7 = 180° - 35°
or, ∠7 = 145°
Hence, The solution is, the measure of angle 7 is, ∠7 = 145°.
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complete question:
Oak Street and Elm Street run parallel to each other. When Main Street interest them, it forms interior angle 4, and measuring 35 degrees. What is the measure of angle 7 ?