(a) One patient did not receive the medication.
(b) One patient did not get either the medicine or the placebo.
(c) None of the patients took the drug or experienced migraines (or both).
(d) One patient who received a placebo experienced no migraines.
what is variable?A variable in algebra is an alphabet that is used to symbolize the unknowable integer. It stands in for the value. An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown.
from the question:
(a)
Logical expression: ∀x D(x)
Negation: ¬(∀x D(x))
Applying De Morgan's law: ∃x ¬D(x)
One patient did not receive the medication.
(b)
Logical expression: ∀x (D(x) ∨ P(x))
Negation: ¬(∀x (D(x) ∨ P(x)))
Applying De Morgan's law: ∃x ¬(D(x) ∨ P(x))
Applying De Morgan's law: ∃x (¬D(x) ∧ ¬P(x))
One patient did not get either the medicine or the placebo.
(c)
Logical expression: ∃x (D(x) ∧ M(x))
Negation: ¬∃x (D(x) ∧ M(x))
Applying De Morgan's law: ∀x ¬(D(x) ∧ M(x))
Applying De Morgan's law: ∀x (¬D(x) ∨ ¬M(x))
None of the patients took the drug or experienced migraines (or both)
(d)
Logical expression: ∀x (P(x) → M(x))
Using the conditional identity: ∀x (¬P(x) ∨ M(x))
Negation: ¬∀x (¬P(x) ∨ M(x))
Applying De Morgan's law: ∃x ¬(¬P(x) ∨ M(x))
Applying De Morgan's law: ∃x (P(x) ∧ ¬M(x))
One patient who received a placebo experienced no migraines.
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complete question;
In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates:
P(x): x was given the placebo
D(x): x was given the medication
M(x): x had migraines
Translate each statement into a logical expression. Then negate the expression by adding a negation operation to the beginning of the expression. Apply De Morgan's law until each negation operation applies directly to a predicate and then translate the logical expression back into English.
Sample question: Some patient was given the placebo and the medication.
∃x (P(x) ∧ D(x))
Negation: ¬∃x (P(x) ∧ D(x))
Applying De Morgan's law: ∀x (¬P(x) ∨ ¬D(x))
English: Every patient was either not given the placebo or not given the medication (or both).
(a)Every patient was given the medication.
(b)Every patient was given the medication or the placebo or both.
(c)There is a patient who took the medication and had migraines.
(d)Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p → q ≡ ¬p ∨ q.)
Given the linear function f(x) = −4x + 8, what is the value of x if f(x) = 24?
x = 104
x = −4
x = −8
x = −88
Answer:
The value of x = -4
Step-by-step explanation:
The given linear function is f(x) = -4x+8
We have to find the x corresponding to f(x) = 24
For our convenience, let f(x) = y
Then y = -4x + 8
This equation implies y in terms of x.
Isolating x to one side of the equation, we get,
x = (y - 8)/-4 = (8-y)/4
This equation gives x in terms of y.
So when f(x) = y = 24,
x = (8-24)/4
⇒ x = -4
What is an equation of the line that passes through the points ( 2 , 8 ) (2,8) and ( − 8 , − 7 ) (−8,−7)?
Therefore , the solution of the given problem of linear equation comes out to be y= (3/2)x + 5 .
Define linear equation.The equation y=mx+b is the basis of a linear regression model. B is the slope, and m is the y-intercept. The aforementioned sentence is repeatedly alluded to as a "math problem with two variables," despite the fact that y and y are distinct parts. In bivariate linear equations, there are only two variables. The application regions for linear equations have no definitive solutions.
Here,
We must first determine the slope of the line before using the point-slope form of the equation of a line to determine the equation of the line that goes through two points.
The angle of the line that connects the coordinates (2, 8) and (8, 7) is:
=> slope = (−7 − 8) / (−8 − 2)
=> slope = −15 / −10
=> slope = 3/2
When we express the equation of a line in the point-slope format, where (x1, y1) is one of the line's points and m is its slope, we get the following result:
=> y − y1 = m(x − x1)
By selecting the line's origin (2, 8) and substituting the slope m = 3/2, we obtain:
=> y − 8 = (3/2)(x − 2)
The equation y = mx + b is transformed into the slope-intercept form by condensing and reordering the variables.
=> y = (3/2)x + 5
Consequently, y = (3/2)x + 5 represents the equation of the line going through the points (2, 8) and (8, 7) respectively.
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Porter is visiting India and would like to purchase some local spices. He finds some spices that cost 320.38 rupees. If the current exchange rate is 1 dollar:73.6500 rupees, how much do the spices cost in U.S. dollars?
$0.04
$4.35
$22.99
$23,595.99
Answer: $4.35
Step-by-step explanation:
320.38 rupees / 73.6500 rupees = $4.35
two numbers sum 20 difference of 9
Answer: 14.5 and 5.5
Step-by-step explanation:
The issue is using whole numbers. 14+6=20, but 14-6=8. 15+5=20, but 15-5=10. If we use decimals, we can get in between the numbers a little to get 9. 14.5+5.5=20, but unlike 14+6, 14.5 gives 5 a tiny boost to push it to 14.5-5.5=9. Hope that helps!
Answer:
14.5
5.5
Step-by-step explanation:
14.5+5.5=20
14.5-5.5=9
Find an equation for the line that passes through the points (- 1, -6) and (3, 4)
Answer:
y=5/2x-7/2
Step-by-step explanation:
Which equation could be used to find the area of this circle in
square feet?
Answer:
22² · π
Step-by-step explanation:
The formula to find the area of the circle is
A = π · r²
r = 22
Looking at the options, the answer is 22² · π
Nine times the input minus seven is equal to the output. Which of the following equations describes this function?
7x-9=y
9y-7=x
9x-7=y
7y-9=x
An equation that describes this function include the following: C. 9x - 7 = y.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.
This ultimately implies that, an input value (x-value) represents the value on the x-axis of a cartesian coordinate while a output value (y-value) represents the value on the y-axis of a cartesian coordinate.
Based on the information provided, an equation that models the situation is given by;
9x - 7 = y.
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9. Zola solved a question on her math test that. asked her to find the volume of the sphere shown
below in terms of T. Explain Zola's error and solve for the correct answer.
d=11 in
v-(-X5.5¹)
V=((16.5)
V = 22π in³
if d=11 in then the volume of the sphere=697.19
[tex]V=\frac{4}{3} \pi d[/tex]
[tex]V=\frac{4}{3} *\frac{22}{7} *5.5^{3} =697.19[/tex]
The amount of room a spherical occupies inside is its volume. Because every point on the sphere's surface is equally spaced from its center, the sphere can be considered a three-dimensional round solid object. The fixed point and fixed distance, respectively, represent the sphere's center and radius. V = 4/3 r3, where r is the radius and V is the volume, is the formula for a sphere's volume. The radius of a sphere is equal to half its diameter. A circle and a sphere are both round, if you compare them. As the sphere is a three-dimensional object rather than a two-dimensional circle, we can estimate its volume and surface area.
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Sadie is planning to go paddleboarding this weekend, but wants to know the water temperature at the lake so she can wear the correct gear. The lake temperature is reported to be 10.5 °C today. After a few sunny days, it should be 1.5 °C warmer this weekend.
what will the water temperature be this weekend in F°?
Answer:
To convert from Celsius to Fahrenheit, we can use the formula F = (C × 1.8) + 32.
First, we need to convert 10.5 °C to Fahrenheit:
F = (10.5 × 1.8) + 32
F = 18.9 + 32
F = 50.9 °F
Then, we can add the 1.5 °C increase in temperature:
New C temperature = 10.5 + 1.5 = 12 °C
And convert that to Fahrenheit using the same formula:
F = (12 × 1.8) + 32
F = 21.6 + 32
F = 54.6 °F
Therefore, the water temperature this weekend in F° will be approximately 54.6 °F.
In the circle below, suppose m WXU = 152° and mXWV=71°. Find the following.
(a) mWXU =
(b) mXUV =
The value of angle mXUV is 76⁰.
The value of angle mXUV is 109⁰.
What is the value of angle mWXU ?
The measure of angle mWXU is calculated by applying the following circle theorem.
mWXU = ¹/₂ ( 152⁰ ) (angle at tangent is half the angle subtended by an arc )
mWXU = 76⁰
The value of angle mXUV is calculated as follows;
mXUV + mXWV = 180 (opposite angles of a cyclic quadrilateral)
mXWV + 71 = 180
mXWV = 180 - 71
mXWV = 109⁰
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According to the scale on a map, 1 inch on the map = 12 miles. How many miles are represented by 2.5 inches on the map?
Answer:
30 miles
Step-by-step explanation:
(12 miles/inch)(2.5 inches) = 30 miles
7) 83÷9 = That I put que pongo
3.Jason needs at least 260 eggs for a charity breakfast. He writes the inequality
12d+72 ≥ 260 to represent the number of dozens of eggs, d, that he needs to buy
since he already has 72 eggs. Which statement best explains whether d = 7 is a solution to
Jason's inequality?
A. d= 7 is a solution because 12 x 7 = 84 and 84 is greater than 72.
B. d= 7 is a solution because 12 x 7 + 72 = 156 and 156 is less than 260.
C. d= 7 is not a solution because 127 + 72 = 199 and 199 is less than 260.
D. d= 7 is not a solution because 12 x 7+72 = 156 and 156 is less than 260.
Answer:
The answer is D hope this helps:)
Step-by-step explanation:
Please I need help. I don’t understand this. It keeps saying I’m getting the answer wrong but I don’t know what I am doing wrong.
Step-by-step explanation:
This figure is made up of a cone and a semi sphere. Let's find the area of the cone
Volume of a cone
[tex] \frac{1}{3} \pi {r}^{2} h[/tex]
The height is 34 cm.
The radius is half the diameter of the sphere ,
this the radius is 14
[tex] \frac{1}{3} \pi( {14}^{2} )(34)[/tex]
Hint: Do not round mid calculations, only when you are done.
Volume of the semi sphere is
[tex] \frac{1}{2} ( \frac{4}{3} \pi {r}^{3} )[/tex]
The radius is 14
[tex] \frac{1}{2} ( \frac{4}{3} \pi(14) {}^{3} )[/tex]
Add both areas
[tex] \frac{1}{3} \pi( {14}^{2} )(34) + \frac{2}{3} \pi(14) {}^{3} [/tex]
Use 3.14 for pi
Which gives us
12719 to the nearest whole number
One angle of a right triangle measures 45°. What is the measure of the other acute angle?
Answer:
Below
Step-by-step explanation:
EVERY triangle's angles add up to 180 degrees
a RIGHT triangle has a 90 degree angle
this right triangle also has a 45 degree angle
let x° = third angle
90° + 45° + x° = 180°
x = 180 - 90 - 45 = 45 degrees
Find sin 8.
45
53
28
8
Answer:
A. 45/53
Step-by-step explanation:
.............
Answer:
A. 45/53
Step-by-step explanation:
sin ø is A.
have a nice day
12. A mosaic wall is divided into 100 equal
Name
sections. If 30 sections are reserved for
orange tiles and 40 sections are reserved
for blue tiles, what fraction of the mosaic
wall is left for other colors?
Answer:
There are 30 + 40 = 70 sections reserved for orange and blue tiles. This means there are 100 - 70 = 30 sections left for other colors.
To express the fraction of the mosaic wall left for other colors, we can write:
30 sections left / 100 total sections = 3/10
Therefore, the fraction of the mosaic wall left for other colors is 3/10.
Mathilde has 30 pints of green paint. She uses 3/5 of it to paint a landscape and 3/10 of it while painting a clover. She decides she that, for her next painting, she will need 16 pints or green paint. How much more green paint will she need to buy?
Answer: 13 pints
Step-by-step explanation:
she used 27 pints at first (9/10 of the 30)
so she has 3 pints left.
and 16-3 = 13 pints.
Solve for x given the info.
Ignore the pencil mark
Answer x is 7
Step-by-step explanation:
The three angles are 104degrees, (9x-25) and unknown
The pictures shows that the two sides are equal therefore the two opposite angles are equal
104 + (9x-25) +(9x-25) =180
RE write
104 +2(9x-25) =180
Subract 104 from both sides
2(9x-25) = 180-104
2(9x-25) = 76
Divide both sides by 2
9x - 25 = 38
Add 25 to both sides
9x = 63
Divide both sides by 9
X =7
The angle is 9x-25 = 38
A swimming pool is draining at a constant rate. The amount of water in gallons left in the pool after X minutes is represented by the expression shown.
25,000-30x
What does 30 represent in this context?
So, 30 reflects the amount of water that is being removed from the swimming pool per minute in gallons.
How variables figure out an equation?In the provided formula, 25,000 - 30x, x is the amount of time in minutes and 30 is the pace in gallons per minute at which the pool is draining.
The expression is a linear equation of the form y = mx + b, where x is the length of time that has passed and y is the amount of water that is still in the pool.
The slope (m) of the equation in this instance is -30, which means that the pool's water level is dropping at a rate of 30 gallons per minute.
The expression's value decreases as more time passes because the value of x rises. As a result of the water draining out of the pool at a constant rate of 30 gallons per minute, the pool's volume is dropping linearly over time.
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Question 1 of 24
In right -angled triangle, the base is 9 centimeters long and the height is 12 centimeters long. What is the measure of the hypotenuse of the triangle?
The measure of the hypotenuse of the triangle is 15 cm.
What is a hypotenuse?The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.
Given that, in a right-angled triangle, the base is 9 centimeters long and the height is 12 centimeters long. we need to find the measure of the hypotenuse of the triangle
Using the Pythagoras theorem,
9² + 12² = h²
h² = 81+144
h² = 225
h = 15
Hence, the measure of the hypotenuse of the triangle is 15 cm
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3(x+7) in distributive property then in expanded form
Answer:
Using the distributive property on 3(x+7), we get:
3(x+7) = 3x + 37
Simplifying the expression, we get:
3(x+7) = 3x + 21
Therefore, in expanded form, 3(x+7) is equal to 3x + 21.
On a standardized science test, the seniors at a high school have a mean score of 425 with a standard deviation of 80. What is the probability that a random sample of 50 seniors has a mean score of at most 415?
The probability that a random sample of 50 seniors has a mean score of at most 415 is given as follows:
0.1894 = 18.94%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters are given as follows:
[tex]\mu = 425, \sigma = 80, n = 50, s = \frac{80}{\sqrt{50}} = 11.31[/tex]
The probability that they scored at most 415 is the p-value of Z when X = 415, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (415 - 425)/11.31
Z = -0.88
Z = -0.88 has a p-value of 0.1894.
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9-65 Eric set up this ratio for two similar triangles:
x/12 = 5/9
He solved the problem and found x = 6.67. What was his mistake? What does x REALLY equal?
Eric made the wrong ratio of the sides of the triangle. As corresponding sides of both triangles are in proportion to each other. So, the proportion will be x/12=9/5. x equal to 21.6.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. If the corresponding sides and angles of two triangles are proportionate, then the triangles are similar. As a result, using another triangle, we may determine the dimensions of one triangle.
So, the right ratio of the sides of the triangle is x/12=9/5
12 * 9 / 5 =x
108/5 = x
21.6 = x
Therefore, x is equal to 21.6
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Jevonte mowed 6 lawns in 4 hours. What was his rate of mowing in lawns per hour?
Jevonte's rate of mowing is 1.5 lawns per hour.
How do rates work?A rate in mathematics is an indicator of how one quantity has changed in relation to another, usually given as a ratio or fraction. Rates are frequently used to explain the relationship between two quantities as they vary through time, space, or another variable. For instance, whereas interest rates track the evolution of money over time, speed tracks the change in distance per unit of time. Rates are used to describe and study numerous phenomena in several disciplines, including physics, economics, and finance.
Given that, Jevonte mowed 6 lawns in 4 hours.
Thus,
Rate of mowing = Number of lawns / Number of hours
Rate of mowing = 6 lawns / 4 hours
Rate of mowing = 1.5 lawns per hour
Hence, Jevonte's rate of mowing is 1.5 lawns per hour.
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The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder? Question 8 options: 350 m3 700 m3 437.5 m3 175 m3 70 m3
With a scaling ratio of 5:2, the larger cylinder's volume is (C) 70m³.
What is the scale factor?A scale factor is used when a shape is enlarged and each side is multiplied by the same quantity.
This number represents the scaling factor. Map scale factors are used to show distances between locations accurately.
The new shape created by scaling the original shape is twice as big when the scale factor is 2.
Thus, calculate the larger cylinder's volume as follows:
x/5 = 28/2
2x = 28*5
2x = 140
x = 70m³
Therefore, with a scaling ratio of 5:2, the larger cylinder's volume is (C) 70m³.
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Complete question:
The scale factor of two similar cylinders is 5:2. The volume of the smaller cylinder is 28 m3. What is the volume of the larger cylinder?
Question 8 options:
A. 700 m3
B. 350 m3
C. 70 m3
D, 437.5 m3
E. 175 m3
Answer: 70m^3
Step-by-step explanation:
I took the test
For a binomial probability distribution, let n = 6 and p = 0.2608. Determine the probability of five successes. (Use 4 decimal places.)
The probability of five successes where the number of trials is 6 and the probability of success is p = 0.2608, for the binomial probability distribution is; P(x = 5) = 0.00535
What is the binomial probability function?The binomial probability function can be expressed as follows;
Pₓ = [tex]\binom{n}{k}[/tex] × Pˣ × (1 - P)⁽ⁿ ⁻ ˣ⁾
Where;
P = The probability of success
x = The number of successes
n = The number of trials
The details from the question includes;
The type of probability distribution = Binomial probability distribution
The number of trials = 6
The probability of success = 0.2608
Therefore;
The probability of success, P = 0.2608
Number of trials, n = 6
The required number of successes, x = 5
Plugging in the above values in the binomial probability formula , we get;
P₅ = [tex]\binom{6}{5}[/tex] × 0.2608⁵ × (1 - 0.2608)⁽⁶ ⁻ ⁵⁾ = 6 × 0.2608⁵ × (1 - 0.2608)⁽⁶ ⁻ ⁵⁾ ≈ 0.0054
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Andrea and her friend were planning to paint Andrea’s aunt's fence this summer.The last time Andrea painted the fence alone the painting job took her 6 hours. Her friend had painted a similar fence or similar surface area in 4 hours. Which is the best estimate of the time it will take Andrew and her friend to paint the fence together?
The best estimate of the time it will take Andrea and her friend to paint the fence together is 2.4 hours.
What is work and time in mathematics?
In mathematics, work refers to the amount of effort or energy needed to complete a task or achieve a goal. Work is often measured in units such as joules or calories.
Time refers to the duration or amount of time it takes to complete a task or achieve a goal. Time is often measured in units such as seconds, minutes, hours, or days.
To estimate the time it will take Andrea and her friend to paint the fence together, we can use the formula:
Total Time = (Time for Person 1 x Time for Person 2) / (Time for Person 1 + Time for Person 2)
Using this formula, we can estimate the time it will take Andrea and her friend to paint the fence together as:
Total Time = (6 hours x 4 hours) / (6 hours + 4 hours) = 24/10 = 2.4 hours
Therefore, the best estimate of the time it will take Andrea and her friend to paint the fence together is 2.4 hours.
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50 points! Compare the triangles and determine whether they can be proven congruent, if possible, by SSS, SAS, ASA, AAS, or HL. Write your answer in the box.
Answer:
1. ASA
2.SSS
3. AAS
4. HL
5. it cannot be proven congruent (not satisfy any criteria)
6. ASA (the top angle of each triangle are congruent)
7. SAS
8. SSS
9. HL
10. AAS
11. it cannot be proven congruent (not satisfy any criteria)
12. SAS or AAS or ASA (the three angles of each triangle are congruent)
Step-by-step explanation:
In the picture attached, the triangles are shown. The criteria are:
SSS: side side side
SAS: side angle side
ASA: angle side angle
AAS: angle angle side
HL: hypotenuse-leg (only valid for right triangles)
Hello, can someone help me figure out the standard deviation of this chart?
Answer:
Below
Step-by-step explanation:
I think statistically that all of the scores will fall within 6 standard deviations ..... 3 above the mean and 3 below the mean
from 85 to 165 is 3 standard deviations
165 - 85 = 80 80 / 3 = 26.67 = standard deviation
Hmm.....not sure how they get the S.D. is 40 ....hope someone else can help us !
Standard bellcurve below.... score 125 does not seem to be in the 1 S.D. position of the curve....Kinda close I guess....
Maybe they are saying from 80 to 165 is TWO Standard deviations....THAT would equal 40.....what have your lessons been using?