Understanding the truth values and logic behind these statements is important to correctly determine their validity. The questions that are True are B and D, and the questions that are A, C, and E.
a. False. In a conditional statement, if the antecedent (the "if" part) is false, the truth value of the conditional statement depends on the truth value of the consequent (the "then" part). If the consequent is true, the conditional statement is true, but if the consequent is false, the conditional statement is false.
b. True. In a disjunction (logical OR), if at least one of the disjuncts is true, then the entire disjunction is true. It only takes one true statement for the disjunction to be true.
c. False. Similar to statement a, if the consequent of a conditional statement is false, the truth value of the conditional statement depends on the truth value of the antecedent. If the antecedent is true, the conditional statement is true, but if the antecedent is false, the conditional statement is false.
d. True. In a conjunction (logical AND), for the entire conjunction to be true, all conjuncts must be true. If one conjunct is true, it guarantees that the conjunction will be true.
e. False. In a conjunction (logical AND), if at least one conjunct is false, the entire conjunction is false. All conjuncts must be true for the conjunction to be true. If any conjunct is false, the conjunction will be false.
Therefore, it's important to understand the truth values and logic behind these statements to correctly determine their validity.
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Find the are of the polygon
Answer:
264 cm²
Step-by-step explanation:
You want the area of a polygon composed of a 12 cm square with triangles of height 5 cm attached to each side.
Square areaThe area of the square is the square of its side lenght:
A = s²
A = (12 cm)² = 144 cm²
Triangle areaThe area of the four triangles is ...
A = 4 × (1/2bh)
A = 4 × 1/2(12 cm)(5 cm) = 120 cm²
Total areaThe total area of the composite figure is ...
A = square area + triangle area
A = 144 cm² +120 cm² = 264 cm²
The area of the polygon is 264 cm².
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18. Find the value of x.
√3
60°
30°
X
a. x = 3
b. x = 3√3
c. x = √3
d. x = 9
Answer:
3
Step-by-step explanation:
the answer is 3, the working is in the image
The function f(x)=(x-4)(x-2) is shown.
-10-8- -6 -4
Mark this and return
10
0-
6
4
2
-4
-6
-8
-10-
6 8 40-X
What is the range of the function?
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
O all real numbers greater than or equal to -1
Save and Exit
Next
Submit
The statement that defines the function's range is option a) all real numbers greater than or equal to -1.
The given function is a quadratic function, which is a parabola that opens upwards. The graph of the function has its vertex at the point (3,-1), which is the minimum point of the parabola.
The range of the function is the set of all possible output values or y-values that the function can produce.
Since the parabola opens upwards and the minimum point is at y=-1/4, the range of the function f(x)=(x-4)(x-2) is all real numbers greater than or equal to -1.
Therefore, we can say that the range is all real numbers greater than or equal to -1.
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Correct Question
The function f(x) = (x − 4)(x − 2) is shown.What is the range of the function? a) all real numbers less than or equal to 3
b) all real numbers less than or equal to −1
c) all real numbers greater than or equal to 3
d) all real numbers greater than or equal to −1
There are 16 airplanes at the airport. Some are big, and 11 are small how many airplanes are big
Answer:
5 Big Airplanes
Step-by-step explanation:
16 airplanes IN TOTAL
11 airplanes ARE SMALL
so we simply subtract 11 from 16 to find how many airplanes are left besides the small ones.
16-11 = 5Cubes with Fractional Edge Lengths: Pt 2
If Lin and Noah use their small cubes to find the volume of the 1 1/2 inch cube, would they get the same value?
(Lin's edge length is 1/2 inch) (Noah's edge length is 1/4 inch)
Since these values are not equal, Lin and Noah would obtain different volume measurements when using their small cubes to find the volume of the 1 1/2 inch cube.
No, Lin and Noah would not get the same value for the volume of the 1 1/2 inch cube using their small cubes.
The volume of a cube is determined by multiplying the length of its edges three times. Lin's cube has an edge length of 1/2 inch, and Noah's cube has an edge length of 1/4 inch.
For Lin's cube, the volume would be (1/2) * (1/2) * (1/2) = 1/8 cubic inches.
For Noah's cube, the volume would be (1/4) * (1/4) * (1/4) = 1/64 cubic inches.
Lin's cube would yield a volume of 1/8 cubic inches, while Noah's cube would result in a volume of 1/64 cubic inches.
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Express each of the following as a rational number: -4/3 - 2 + 2/5 +1
Answer: -29/15.
Step-by-step explanation:
-4/3 - 2 + 2/5 + 1
= (-20/15) - (30/15) + (6/15) + (15/15) (finding a common denominator of 15)
= (-20 - 30 + 6 + 15) / 15
= -29/15
Simplify (3x+4)/(x+2)+(x^2+2x)/(2x+4).
The notation P(F E)means the probability of event ____ given event ___.
.
The notation P(F|E) means the probability of event F given event E.
In probability notation, P(F|E) represents the conditional probability of event F occurring given that event E has already occurred. It is read as "the probability of F given E." The vertical bar "|" indicates "given" or "conditional on." This notation allows us to calculate the probability of one event happening, taking into account the occurrence of another event. For example, P(F|E) would represent the probability of rain (event F) given that the weather forecast predicts a cloudy day (event E). The conditional probability allows us to analyze how events are related and make more accurate predictions or assessments based on the given information.
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pls help Which is a step in showing that n^3+2n is divisible by 3 is true by mathematical induction?
a.Show that the statement is true for n = 1
b.Prove that the statement is true when n = k.
c.Assume that the statement is true for the (k + 1) value.
d.Assume the statement is true for all the integers.
The step in showing that[tex]n^3+2n[/tex] is divisible by 3 by mathematical induction is: Prove that the statement is true when n = k. Option B
How to determine the step showing that n^3+2n is divisible by 3 is true by mathematical inductionThis step involves substituting k for n in the expression [tex]n^3+2n[/tex] and showing that the result is divisible by 3. In other words, we need to show that:
[tex]k^3 + 2k[/tex] is divisible by 3.
If we assume that the statement is true for n = k, then we can substitute k+1 for n in the expression [tex]n^3+2n[/tex] and simplify:
=[tex](k+1)^3 + 2(k+1) = k^3 + 3k^2 + 3k + 1 + 2k + 2[/tex]
= [tex]k^3 + 3k^2 + 5k + 3[/tex]
= [tex](k^3 + 2k) + (3k^2 + 3k)[/tex]
Since we assumed that the statement is true for n = k, we know that [tex]k^3 + 2k[/tex] is divisible by 3. Also, [tex]3k^2 + 3k[/tex] is divisible by 3 because it has a factor of 3. Therefore, the entire expression [tex](k+1)^3 + 2(k+1)[/tex]is also divisible by 3.
This completes the inductive step, and we can now conclude by mathematical induction that the statement [tex]n^3+2n[/tex] is divisible by 3 is true for all positive integers n.
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The original price of a book was $48. It is now 70% off. What is the sale price of the book?
Answer:
$14.40-------------
Original price is $48 and it is now 70% off, then the sale price is:
$48 - 70% of $48 = $48 - 0.7*$48 = 0.3*$48 = $14.40Therefore, the sale price of the book is $14.40.
a central angle of 2 radians off an arc of length 6 inches. find the area of the sector formed
[tex]\textit{arc's length}\\\\ s = r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =2\\ s=6 \end{cases}\implies 6=r2\implies \cfrac{6}{2}=r\implies 3=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=3\\ \theta =2 \end{cases}\implies A=\cfrac{(2)(3)^2}{2}\implies A=9~in^2[/tex]
now consider that the penetrance of the disease is 75%. what is the probability that individual ii-2 exhibits this disease given this penetrance?
The probability that individual ii-2 exhibits the disease given a 75% penetrance is 0.75 or 75%.
Penetrance refers to the probability of an individual expressing a particular trait or disease given their genetic makeup. In this case, the penetrance of the disease is 75%, which means that there is a 75% chance that an individual with the genetic mutation for the disease will actually exhibit the disease. Therefore, the probability that individual ii-2 exhibits the disease given this penetrance is also 0.75 or 75%.
1. Penetrance is the probability that an individual with a specific genotype will express the associated phenotype or disease.
2. In this case, the penetrance of the disease is 75%, which means there is a 75% chance that an individual with the disease-associated genotype will exhibit the disease.
3. Given this penetrance, the probability that individual ii-2 exhibits the disease is 0.75 or 75%.
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A corporate finance manager would like to test the claim that the average percent of a company's budget spent on overhead expenses is less than 25 percent. To test this claim at the 5% significance level, the corporate finance manager collects the following data on a sample of 40 companies and records the percent of their budget spent on overhead expenses. The following is the data from this study: Sample size = 40 companies Sample mean = 23 percent From past data, it is known that the population standard deviation is 4.44 percent. Identify the null and alternative hypothesis for this study by filting in the blanks with the correct symbolor > represent the correct hypothesis)
There is the not sufficient evidence that the average small business loan is different that the amount stated in the investment blog.
We have,
The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.
Here we have given that,
Claim: To check whether the average small business loan is different that the amount stated in the investment blog.
The hypothesis is,
H0: μ= 20 thousand dollars Versus H0: μ ≠ 20 thousand dollars
We have given that,
n= Number of observation = 25
x bar = sample mean =18.5
S= sample standard deviation =5
Here, population standard deviation is unknown, we use the one sample t test.
t - statistics = (x bar - μ) / (s / √n)
= (18.5 - 20) / (5 / √25)
= -1.342
we get,
the Test statistic is -1.342
Now we find the P-value
α = level of significance = 0.05
Degrees of freedom = n - 1 = 25 - 1 = 24
This is two tailed test as our interest is to show the population mean is equal or not equal to zero.
Now, we can find the P-value
P-value = 0.1922 Using EXCEL = TDIST( | t-statistics | = 1.342 , D.F=24, tail=2)
Hence, There is the not sufficient evidence that the average small business loan is different that the amount stated in the investment blog.
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complete question:
Complete the steps of a one-mean hypothesis test with Population SD unknown ritical Value Approach Complete the steps of a one-mean hypothesis test with Population SD unknown - Critical Value approach Question An investment blog states the average small business loan is 20 thousand dollars. A business loan broker would like to test the claim that the average small business loan is different than the amount stated in the investment blog. To test this claim at the 5% significance level, the business loan broker collects the following data on a sample of 25 small business loans and records the amount of the loan. The following is the data from this study: Sample size=25 small business loans Sample mean= 18.5 thousand dollars Sample standard deviation = 5 thousand dollars Identify the null and alternative hypothesis for this study by filling in the blanks with the correct symbol (=..<, or > to represent the correct hypothesis.) Provide your answer below: null hypothesis: 20 alternative hypothesis: 20
A Cube has a length of 65cm. find its surface area.
Answer:
25350 cm²
Step-by-step explanation:
A Cube has a length of 65cm. find its surface area.
a cube has 6 equal faces, having the side we find the area of one face and multiply by 6
65 × 65 × 6 =
4225 × 6 =
25350 cm²
Find the center and vertices if the ellipse x^2/49 +y^2/4=1
The center and vertices if the ellipse is,
Center = (0, 0)
Vertex = (±7, 0)
We have to given that;
Equation of Ellipse is,
⇒ x²/49 + y² / 4 = 1
Since, We know that;
For equation of ellipse,
x²/a² + y²/b² = 1
Center = (0, 0)
Vertex = (±a, 0); for a > 0
Here, Equation of Ellipse is,
⇒ x²/49 + y² / 4 = 1
Here, a² = 49
a = ± 7
And, b² = 4
b = ±2
Hence, a > b
So, We get;
Center = (0, 0)
Vertex = (±a, 0); for a > 0
Vertex = (±7, 0)
Thus, The center and vertices if the ellipse is,
Center = (0, 0)
Vertex = (±7, 0)
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A heater uses 3 units of electricity in 40 mins. How many units does it use in 2 hours?
In a die game, you roll a fair six-sided die. If you roll a 2, you win $25. If you roll anything else, you lose $5. What is the expected profit of one roll in this game?
Round your answer to the nearest cent.
Enter an expected loss as a negative number.
The expected profit of one roll in this game is $0.
To determine the expected profit of one roll in the die game, we need to calculate the weighted average of the possible outcomes.
The probability of rolling a 2 is 1/6 since there is one favorable outcome out of six possible outcomes. In this case, you win $25.
The probability of rolling any other number (1, 3, 4, 5, or 6) is 5/6 since there are five unfavorable outcomes out of six possible outcomes. In this case, you lose $5.
Now, we can calculate the expected profit:
Expected Profit = (Probability of Winning * Amount Won) + (Probability of Losing * Amount Lost)
= (1/6 * $25) + (5/6 * -$5)
= $4.17 - $4.17
= $0
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The volume of a rectangular pyramid is 765 units
3
3
. If the length of the rectangular base measures 9 units and the width of the rectangular base measures 15 units, find the height of the pyramid.
The height of the pyramid is equal to 17 units.
How to calculate the volume of a rectangular pyramid?In Mathematics and Geometry, the volume of a rectangular pyramid can be calculated by using the following formula:
Volume of a rectangular pyramid = 1/3 × L × W × H
Where:
L represents the length of a rectangular pyramid.W represents the width of a rectangular pyramid.H represents the height of a rectangular pyramid.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular pyramid, we have the following;
765 = 1/3 × 9 × 15 × H
Height, H = 765/45
Height, H = 17 units.
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There are 36 students in Mr. Chips first block math class. 1/9 of them made a level 5 on their EOG last year. 5/6 of them made a level 4 last year. The rest made a level 3. How many of Mr. Chips first black students made a level 3?
Answer:
2 students
Step-by-step explanation:
First, you have to find how many made a level 5, so we do 36•1/9=4. So, 4 students made a level five. That leaves us with 36-4=32 students left. Next, you find the students that made a level 4. 36•5/6=30 students made a level 4, so that leaves us with 32-30=2 students that got a level 3.
Find the value of x that makes lines u and v parallel.
The value of x in the parallel line is 11.
How to find angles in parallel lines?When parallel lines are cut with a transversal line, angle relationship are formed such as corresponding angles, alternate interior angles, alternate exterior angles, corresponding angles, vertically opposite angles etc.
Therefore, let's use the angle relationship to find the value of x .
Hence,
6x + 14 = 80(corresponding angles and vertically opposite angles)
6x + 14 = 80
subtract 14 from both sides of the equation
6x + 14 - 14 = 80 - 14
6x = 66
divide both sides of the equation by 6
x = 66 / 6
x = 11
Therefore,
x = 11
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Write as many mathematical expressions or equations as you can about the image. Include a fraction, a decimal number, or a percentage in each. FUNDRAISER OUR GOAL: $250,000 $250,000 $200,000 $150,000 $100,000 - $50,000 O
The mathematical expressions or equations about the image 44%, 0.44 and 11/25
Writing the mathematical expressions or equations about the imageFrom the question, we have the following parameters that can be used in our computation:
The fundraiser image (see attachment)
From the image, we have the following readings
Total amount to be raised = $250,000
Amount already raised = $110,000
When represented as a percentage, we have
percentage = 110,000/250,000 * 100%
Evaluate
percentage = 44%
As a fraction, we have
percentage = 44/100 = 11/25
As a decimal, we have
percentage = 0.44
Hence, the mathematical expressions about the image are 44%, 0.44 and 11/25
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Find the mean median and mode for 44, 4, 27, 5
Answer:
Mean: 20
Median: 16
Mode: No mode
Step-by-step explanation:
For the mean:
44 + 4 + 27 + 5 = 80
80/4 = 20
For the median:
5 + 27 = 32
32/2 = 16
For the mode:
None of the numbers are repeated.
g what assumption must be made regarding the population in order to make inferences about the average length of stay?
To make inferences about the average length of stay, an assumption must be made regarding the population's distribution. The assumption is that the population follows a normal distribution or is approximately normally distributed.
In order to make accurate inferences about the average length of stay, it is important to assume that the population from which the sample is drawn follows a normal distribution or is approximately normally distributed. The normal distribution assumption allows for the use of statistical techniques that rely on the properties of the normal distribution, such as calculating confidence intervals and conducting hypothesis tests.
When the population distribution is approximately normal, the Central Limit Theorem comes into play. According to this theorem, the sampling distribution of the sample means will be approximately normally distributed, regardless of the population distribution shape, as long as the sample size is sufficiently large. This allows for the use of inferential statistics to make inferences about the population parameter, such as the average length of stay.
Therefore, assuming a normal distribution or an approximately normal distribution within the population is crucial when making inferences about the average length of stay. It provides the foundation for applying statistical techniques and drawing meaningful conclusions based on the sample data.
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In the figure below, III h. Find the values of z and x.
(3x-31)-=-
HE
M
HE
#1
A
0
The measure of angle x and z are 45.7° and 74° respectively.
Given that, straight line l and h are parallel.
Here, in the given figure,
(3x-31)°+z°=180° (Adjacent angles)
z°=180°-(3x-31)°
From the given figure,
z°=74° (Corresponding angles are equal)
180°-(3x-31)°=74°
180°-74°=(3x-31)°
(3x-31)°=106°
3x=106+31
3x=137
x=137/3
x=45.7°
Therefore, the measure of angle x and z are 45.7° and 74° respectively.
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I need your help please
The mass of this rectangular object is equal to 232 grams.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular object = 5 × 4 × 2
Volume of rectangular object = 40 cubic centimeter.
Mass of rectangular object = density × volume
Mass of rectangular object = 5.8 × 40
Mass of rectangular object = 232 grams.
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runners do 5 hill sprints a day. at the end of the week, the coach shows them that their average time for sprinting improved each day of the week. what kind of feedback is this?
The feedback that the runners received from their coach is called positive feedback. Positive feedback is a type of feedback that reinforces the current behavior, making it more likely to continue or increase in frequency.
In this case, the runners' average time for sprinting improved each day, so the coach provided positive feedback to encourage them to continue with their training. Positive feedback can be a powerful motivator, as it provides a sense of accomplishment and encourages individuals to continue striving for improvement. In contrast, negative feedback involves pointing out areas for improvement or mistakes, and can be demotivating if not delivered constructively.
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4a^3 - a^2b - 36a + 9b
Answer:
[tex]4 {a}^{3} - {a}^{2} b - 36a + 9b[/tex]
[tex] = {a}^{2} (4a - b) - 9(4a - b)[/tex]
[tex] = ( {a}^{2} - 9)(4a - b)[/tex]
[tex] = (a + 3)(a - 3)(4a - b)[/tex]
IF YOU SOLVE THIS CORRECTLY WITH EXPLANATION U WILL GET BRAINILEST
(2y-3)(3y-2)
6y² - 13y + 6 is the product of 2y -3 and 3y - 2.
Expanding linear equations
Given the following linear expression
(2y-3)(3y-2)
We need to expand the expression to get a quadratic function as shown below:
(2y-3)(3y-2) = 2y(3y) - 2(2y) - 3(3y) -3(-2)
(2y-3)(3y-2) = 6y² - 4y - 9y + 6
(2y-3)(3y-2) = 6y² - 13y + 6
Hence the product of 2y - 3 and 3y - 2 is equivalent to 6y² - 13y + 6
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The angle of elevation from the bottom of the ski lift to the top of the mountain is 62°. If the vertical height of the mountain is 1,760 feet, what is the total distance traveled on the ski lift from the bottom to the top of the mountain?The angle of elevation from the bottom of the ski lift to the top of the mountain is 62°. If the vertical height of the mountain is 1,760 feet, what is the total distance traveled on the ski lift from the bottom to the top of the mountain?
Answer:
We can use trigonometry to solve this problem. Let's call the total distance traveled on the ski lift "d". We know that the angle of elevation from the bottom of the ski lift to the top of the mountain is 62°, which means the angle of depression from the top of the mountain to the bottom of the ski lift is also 62°.
Using trigonometry, we can write:
sin(62°) = 1,760 / d
To solve for "d", we can isolate it by multiplying both sides by "d" and then dividing both sides by sin(62°):
d = 1,760 / sin(62°)
Using a calculator, we get:
d ≈ 1,966.6 feet
Therefore, the total distance traveled on the ski lift from the bottom to the top of the mountain is approximately 1,966.6 feet.
O is the center of the regular nonagon below. Find its area. Round to the nearest
tenth if necessary.
The area of the regular polygon is equal to 117.99 square units
How to calculate for the area of the polygonArea of regular polygon = 1/2 × apothem × perimeter
perimeter = (s)side length of nonagon × (n)number of side
apothem = s/[2tan(180/n)]
6 = s/[2tan(180/9)]
s = 6 × 2tan20
s = 4.34
perimeter = 4.34 × 9 = 39.33
Area of nonagon = 1/2 × 6 × 39.33
Area of nonagon = 117.99
Therefore, the area of the regular polygon is equal to 117.99 square units
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