Answer:
(X, Y) = (3, 5)
AB = AC = 8
BC = 11.3
Step-by-step explanation:
The difference between sides AB and AC is zero:
AC -AB = 0
(6X -2Y) -(X +5) = 0
5X -2Y -5 = 0
The difference between the sum of sides and 27.3 is zero:
AC +AB +BC -27.3 = 0
(6X -2Y) +(X +5) +(Y +6.3) -27.3 = 0
7X -Y -16 = 0
__
To solve these, we can subtract the first equation from twice the second to eliminate Y.
2(7X -Y -16) -(5X -2Y -5) = 2(0) -(0)
9X -27 = 0 . . . . simplify
X -3 = 0 . . . . . . . divide by 9
X = 3
Substituting into the second equation gives ...
7(3) -Y -16 = 0
5 = Y . . . . . . . . . . add Y
The solution for X and Y is X = 3, Y = 5.
AB = AC = X+5 = 8
BC = Y +6.3 = 11.3
The side lengths are AB = AC = 8, and BC = 11.3.
A teaching hospital in South-West Part of Nigeria receives on the average 5 pregnant women with high blood pressure per week. What is the probability that on a particular week, the teaching hospital will receive:
1.) No high BP pregnant woman
Answer:
The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Step-by-step explanation:
We use the Exponential distribution,
Since we are given that on average, 5 pregnant women with high blood pressure come per week,
So, average = m = 5
Now, on average, 5 people come every week, so,
5 women per week,
so, we get 1 woman per (1/5)th week,
Hence, the mean is m = 1/5 for a woman arriving
and λ = 1/m = 5 = λ
we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,
P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,
Now,
P(X>1) = 1 - P(X<1),
Now, the probability density function is,
\(f(x) = \lambda e^{-\lambda x}\)
And the cumulative distribution function (CDF) is,
\(CDF = 1 - e^{-\lambda x}\)
Now, CDF gives the probability of an event occuring within a given time,
so, for 1 week, we have x = 1, and λ = 5, which gives,
P(X<1) = CDF,
so,
\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)
So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068
Find the value of Y.
The value of the side y is 3√3. Option C
How to determine the value of the sideIt is crucial to note the different types of trigonometric identities.
They are;
sinetangentcotangentsecantcosecantcosineFrom the diagram shown, we have that;
The angle θ = 60 degrees
The opposite side = y
The adjacent side = 3
Let's use the tangent identity
tan 60 = y/3
Find the value
√3 = y/3
cross multiply
y = 3√3
Hence, the value is 3√3
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Plz help! Will give Brainliest!!!
Does coordinate mmm or coordinate nnn represent a greater number?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
mmm
(Choice B)
B
nnn
Answer:
choice A m
Step-by-step explanation:
n= 1
m= 7
dgcjbknohhfg
If GMAT scores for applicants at Oxnard Graduate School of Business are N(500, 50), then the top 5 percent of the applicants would have a score of at least (choose the nearest integer):
find the measure of minor arc RV
The measure of the minor arc m∡rv = 111°
What is the explanation for the above response?Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c
Where a = ∡RV
b = ∡SU = 37°:
and c = ∠T (the angle between intersecting secants.
Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:
(a - 37) / 2 = 37
Multiplying both sides by 2 gives:
a - 37 = 74
Adding 37 to both sides gives:
a = 111
Therefore, a is equal to m∡rv = 111°.
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If I give my brother 5 dollars, then we will have the same amount of money. If instead he gives me 10 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?
We will have the same amount of money if I give my brother $5. If he instead offers me ten dollars, I'll have twice as much money as he has. Brother currently have $62.
Let y represent the amount of money you now have.
Let s denote the amount of money your sister now possesses.
If you give your sister $5, you will have $5 less (y - 5) and she will have $5 more (s + 5)
Because they are now equal:
y - 5 = s + 5
---> y = s + 10
Now, we will form another equation.
If your sister gives you 14 dollars, you will have 14 dollars more (y + 14) and she will have 14 dollars less (s - 14).
Because you now have twice as much money as she does:
y + 14 = 2(s - 14)
---> y = 2s - 28
y = 2s - 42
Putting the equations together:
s + 10 = 2s - 42
52 = s
Because s = 52,
we get y = 62.
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What is the slope of the line?
Answer:
-3
Step-by-step explanation:
First, let's remind ourselves the definition of a slope.
Slope = rise/run OR the height from one point to another/ the distance from one point to another.
First, let's find two points on this graph that are marked easily.
One point that can be found is (0, -3) and the other is (0, -1).
Let's apply our formula to these points!
<------- Starting from point (0, -3), we are RISING 3 points and RUNNING -1 points.
Rise 3
------- = ----------
Run -1
3/-1 = -3
The slope of the line is -3.
Answer:
-3.
Step-by-step explanation:
1) to choose two points on the given line on the graph. For example, A(-2;3) and B(-1;0);
2) to calculate the required slope according to the rule:
\(slope=\frac{Y_B-Y_A}{X_B-X_A};\)
3) the required slope:
slope=-3/1=-3.
What is the equation of the line that is parallel to the line y = 2x + 3 and
passes through the point (-2, 1)?
O A. y = 2x + 5
O B. y--3x+2
O C. y=-3x
O D. y = 2x-5
solve the system of equation — 3х + бу = 9
5х + 7y = -49
Answer:
y = 64/3
x = -119/3
Step-by-step explanation:
3х + 6у = 9 => 5*3x+5*6у = 9*5 => 15x+30у=45 (1)
5х + 7y = -49 => 3*5x + 3*7y = -49*3 => 15x+21y=-147 (2)
(1)-(2) => 9y = 192 => y = 64/3
x = -119/3
2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)
Answer:
16/45x-11/12
Step-by-step explanation:
Multiply across
2/15x-30/40-1/6+2/9x=
Get common denominators of like terms
6/45x+10/45x-9/12-2/12=
Combine like terms
16/45x-11/12
The simplified expression is: (16/45)x - (11/12)
To simplify the given expression, we'll follow the steps:
Step 1: Distribute the fractions through the parentheses.
Step 2: Simplify the expression by combining like terms.
Let's proceed with the simplification:
Step 1: Distribute the fractions through the parentheses:
2/5 * (1/3x - 15/8) - 1/3 * (1/2 - 2/3x)
Step 2: Simplify the expression:
To distribute 2/5 through (1/3x - 15/8):
2/5 * 1/3x = 2/15x
2/5 * (-15/8) = -15/20 = -3/4
So, the first part becomes: 2/15x - 3/4
To distribute -1/3 through (1/2 - 2/3x):
-1/3 * 1/2 = -1/6
-1/3 * (-2/3x) = 2/9x
So, the second part becomes: -1/6 + 2/9x
Now, the entire expression becomes:
2/15x - 3/4 - 1/6 + 2/9x
Step 3: Combine like terms:
To combine the terms with "x":
2/15x + 2/9x = (2/15 + 2/9)x
Now, find the common denominator for (2/15) and (2/9), which is 45:
(2/15 + 2/9) = (6/45 + 10/45) = 16/45
So, the combined x term becomes:
(16/45)x
Now, combine the constant terms:
-3/4 - 1/6 = (-18/24 - 4/24) = -22/24
To simplify -22/24, we can divide both numerator and denominator by their greatest common divisor (which is 2):
-22 ÷ 2 = -11
24 ÷ 2 = 12
So, the combined constant term becomes:
(-11/12)
Putting it all together, the simplified expression is:
(16/45)x - (11/12)
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Complete question is:
Simplify the given expression: 2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)
9+ 8 74 6 5 4 3 re -3 Enter the coordinates of a point in coordinate notation, such as ( - 3,2). If there is more than one intercept, enter a list of points, such as ( - 3, 2), (3, 2). If an intercept Does Not Exist, enter DNE. What are the coordinates of the x-intercept? What are the coordinates of the y-intercept? What type of symmetry does the graph have? x-axis y-axis origin none o
The x intercept is the point where the graph meets the x axis and the y intercept is the point where the graph meets the y axis.
Hence, from the graph, the coordinates of the x intercept is (0, 0).
The coordinates of the y intercept is (0, 0).
From the graph, it is clear that the graph is symmetric about the
36 apartments on 9 floors = apartments per floor
Answer:
4 apartments per floor
Answer: 4
Step-by-step explanation:
If there are 36 apartments in the building with 9 on each floor, you can find the answer by simply doing the equation 36/9=4.
Suppose a one year subscription to a magazine cost $12.99 and a three-year subscription cost $25.98 the cost and length of the subscription are related write an equation to a model the cost of a subscription for any period of time
Answer:
What are the choice man
Step-by-step explanation:
Target charges $4.40 for 8 sodas. Walmart charges $7.08 for 12 sodas. Which store has
the best unit price? How much cheaper is it?
Answer:
Target
Step-by-step explanation:
$4.40/8 is 0.55 and $7.08/12 is 0.59
Please help. Miguel had 2 bags containing number tiles as shown below. Without looking, Miguel selected one tile from each bag. What is the probability that Miguel selected two numbers less than 3?
The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.
The given tiles in bag-1 = {2, 4, 5, 8, 9}
Total number of tiles in bag-1 = 5
The number of tiles less than number 3 in the bag - 1 = 1
The probability of Miguel selecting a tile number less than 3 =
number of tiles less than 3 / total number of tiles = 1/3
The given tiles in bag-2 = {0, 1, 3, 6, 7}
Total number of tiles in bag-2 = 5
The number of tiles less than number 3 in the bag-2 = 2
The probability of Miguel selecting a tile number less than 3 =
number of tiles less than 3 / total number of tiles = 2/3
From the above analysis, we solved the problem.
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use elimination method to solve the following system of equations . VIEW ATTATCHED IMAGE .
Given the equation system:
\(\begin{cases}3x=4y \\ 4x-5y=2\end{cases}\)To solve this equation system using the elimination method, first, you have to express both equations using the standard form. This means you have to express the first equation to standard form, for this you have to equal the equation to zero:
\(\begin{gathered} 3x=4y \\ 3x-4y=4y-4y \\ 3x-4y=0 \end{gathered}\)Now you have to multiply both equations by a number so that the leading coefficients are the same.
The first coefficients of the s
Select all the correct answers. If the measure of angle is is , which statements are true? The measure of the reference angle is . The measure of the reference angle is . The measure of the reference angle is . cos(0)=-3/10
The measure of angle is θ cannot determine the statements that are true about its reference angle.
There are two issues with the given statement.
First, it does not specify the measure of angle θ.
Second, the statement cos(0)=-3/10 is not related to the reference angle of θ.
The reference angle of θ is the acute angle between the terminal side of θ and the x-axis.
It is always positive and its measure is between 0 and 90 degrees or between 0 and π/2 radians.
The measure of the reference angle of θ is denoted by θ'.
To determine the reference angle of θ, we need to know the quadrant in which θ lies.
The reference angle of θ in standard position is the acute angle between the terminal side of θ and the x-axis.
If θ is in the first quadrant, then θ' = θ.
If θ is in the second quadrant, then θ' = π - θ.
If θ is in the third quadrant, then θ' = θ - π.
If θ is in the fourth quadrant, then θ' = 2π - θ.
The measure of angle θ, we can determine its reference angle using the above rules.
The statement cos(0)=-3/10 is not related to the reference angle of θ.
It is the value of the cosine function at 0 radians or 0 degrees.
This value does not correspond to any angle that has a reference angle.
The measure of angle θ cannot determine the statements that are true about its reference angle.
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Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2. This system of equations models the scenario: 4x + 2y ≤ 16 x + y ≥ 4 Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set. (4 points) Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically. (3 points) Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points)
Part A: the system of inequalities has a definite solution to it.
Part B: Yes the point is a part of Solution Area
What is Linear Inequality?
In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
Solution:
The inequalities 4x + 2y ≤ 16
And x + y ≥ 4 is attached below please refer to it.
Part A: The graph of both inequalities intersects each other therefore the system of inequalities has a definite solution to it.
Part B: Yes point (2, 3) is included in the solution area, the following is the mathematical proof.
Using substitution 4*2 + 2*3 ≤ 16
8+6 ≤ 16
14 ≤ 16
And 2+3 ≥ 4
5 ≥ 4
Hence, the point is included in the solution area.
Part C:
Let’s assume a point 1,1 in the solution set so it implies that only the inequality 4x + 2y ≤ 16 is satisfied. Thus, not giving a feasible solution.
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If Jaime wants to find 60% of 320, which table should he use?
Answer:
in 3th table or 30percent
the projected value of an investment is modeled by the exponential function V(t)=30,000(1.125)^t ,where V(t) is the total value after t amount of years.what is the percent increase each year for the investment?
We have the following:
\(V(t)=30000\cdot(1.125)^t\)Now, to know the percentage we use the term that is elevated to time (t), that is,
\(1.125\)If 1 represents 100% then the percentage that increases would be
\(1.125-1=0.125\)Therefore, the percentage is 12.5%
Which of the following are perfect powers?
1
24
Answer:
Uhh, I guess 24? I don't understand this question
Question: Which of the following are perfect powers?
Answer:
The answers on Edge are 27, 81, and 100. These are perfect powers.
If a1 = 6 and an
-5an-1 + 4 then find the value of a4.
9514 1404 393
Answer:
a4 = -666
Step-by-step explanation:
Use the recursive definition repeatedly.
a1 = 6
a2 = -5(6) +4 = -26
a3 = -5(-26) +4 = 134
a4 = -5(134) +4 = -666
Help anyone? Who knows this 6th grade math
Answer:
√33 ≈ 5.7
Step-by-step explanation:
The length of the bottom diagonal is given by pythagoras, let's call it d:
\(d =\sqrt{5^2+2^2}\)
Then, the length of the diagonal through the box is also given by pythagoras as:
\(\sqrt{d^2 + 2^2}\)
In total, that is:
\(\sqrt{5^2 + 2^2 + 2^2} = \sqrt{33} \approx 5.7\)
You just found 13,406,190 pennies! How many dollars did you actually find? If each penny weighs 4 grams, how much did all that loot weigh in lbs?
Answer:
congrats you just found 118,222.36 pounds of pennies worth $134,061.9
you should buy a house or car with 59 tons of pennies
A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10 degrees to the horizontal. Calculate the length of the zip wire.
∘
to the horizontal. Calculate the length of the zip wire
The length of the zip wire, with a 10-degree angle to the horizontal and a distance of 25 meters between the posts, is approximately 25.35 meters.
To calculate the length of the zip wire, we can use trigonometry. Let's consider the triangle formed by the zip wire, where the horizontal distance between the two posts is 25 meters and the angle between the zip wire and the horizontal is 10 degrees.
Using trigonometric functions, we can determine the length of the zip wire. In this case, we'll use the sine function because we have the opposite side (the vertical distance) and we want to find the hypotenuse (the length of the zip wire).
The formula for sine is:
sin(angle) = opposite / hypotenuse
Rearranging the formula, we have:
hypotenuse = opposite / sin(angle)
In this case, the opposite side is the vertical distance, which is h.
So, the formula becomes:
hypotenuse = h / sin(angle)
To find h, we can use the formula for the length of the zip wire:
h = 25 * tan(angle)
Substituting this into the previous formula, we get:
hypotenuse = (25 * tan(angle)) / sin(angle)
Calculating the value, we have:
hypotenuse = (25 * tan(10°)) / sin(10°)
Using a calculator, we find:
tan(10°) ≈ 0.1763
sin(10°) ≈ 0.1736
Substituting these values, we can calculate the length of the zip wire:
hypotenuse ≈ (25 * 0.1763) / 0.1736 ≈ 25.35 meters
Therefore, the length of the zip wire is approximately 25.35 meters.
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Evaluate the expression 23^0-15^1+18^0+(43-12)
Answer:
18
Step-by-step explanation:
23^0 - 15^1 + 18^0 + (43 - 12) =
= 1 - 15 + 1 + 31
= -14 + 1 + 31
= -13 + 31
= 18
Given the circle below with secants JKL and NML, find the length of JK. Round to the nearest tenth if necessary.
Using the Intersecting secants theorem, the length of JK in the given diagram is 17
Intersecting secants theorem: Calculating the length of of JKFrom the question, we are to determine the length of JK in the given diagram.
The diagram shows a circle with intersecting secants.
From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".
Then,
We can write that
JK × KL = NM × ML
From the given diagram,
KL = 14
NM = 14
ML = 17
Substituting the values
JK × 14 = 14 × 17
JK = (14 × 17) / 14
JK = 17
Hence, the length of JK is 17
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can someone help me with my work so i can pass
The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.
Here, we have,
we know that,
The sum of the angles in a triangle add to 180
x+2x+6x = 180
Combine like terms
9x= 180
Divide by 9
9x/9 = 180/9
x = 20.
Hence, The measure of the angles are:: x = 20. so, angles are, 20°, 40°, 120°.
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complete question:
The sum of the angle measures in a triangle is 180°. The angles of a certain triangle measure x°, 2x°, and 6x°. Solve for x.
Imagine that two researchers, Bill and Ted, independently carry out clinical trials to test the same null hypothesis: H0: COX-2 selective inhibitors (used to treat arthritis) have no effect on the risk of cardiac arrest. They use the same population for their study, but Bill uses a sample size of 60 randomly selected subjects and Ted uses a sample size of 100 randomly selected subjects. Assuming all other aspects of their studies are the same, answer the following:
Required:
a. Whose study has the higher probability of a Type-II error?
b. Whose study has higher power?
c. Whose study has the higher probability of a Type-I error?
d. Should their alternative hypotheses be one-sided or two-sided? Explain
e. Suppose Bill’s analysis results in p-value = 0.03. What should be his conclusion?
Answer:
A) The 60-subject study will have the higher probability of a Type-II error.
B) 100-subject study will have higher power.
C) they will have the same probability of a Type-I error
D) Two tailed because either of the two results would be of interest
E) If p-value = 0.03, he should reject the null hypothesis if this p-value is less than the significance level. But if it's more than the significance level, he will fail to reject the null hypothesis.
Step-by-step explanation:
A) A type II error is an error that occurs when we accept the null hypothesis even though it is actually false.
Now, Smaller sample sizes usually would have a lesser chance of rejecting the null hypothesis even though it's false. Thus, the 60-subject study will have the higher probability of a Type-II error.
B) power = 1 - Pr(Type II error)
Since the 60-subject study has a higher probability of type II error it means it will have lesser power. Thus, 100-subject study will have higher power.
C) Type I error is when we incorrectly reject a true null hypothesis.
Pr(Type I error) = significance level
Now, since we are told that other aspects of their study are the same it means their significance levels are the same, it means they will have the same probability of a Type-I error
D) It should be two tailed because either of the two results would be of interest. It's either the drug was associated with more cardiac arrests or less potential treatment option.
E) If p-value = 0.03, he should reject the null hypothesis if this p-value is less than the significance level. But if it's more than the significance level, he will fail to reject the null hypothesis.
What does the circled portion represent in the confidence interval formula?
p±z.
O Sample proportion
O Margin of error
p(1-p)
n
Confidence interval
O Sample Size
The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.
In the confidence interval formula p ± z, the circled portion represents the Margin of Error.
The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.
It indicates the range within which the true population parameter is likely to fall based on the sample data.
The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.
The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.
The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.
It reflects the trade-off between the desired level of confidence and the width of the interval.
A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.
Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.
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