Answer:
D. The mathematical work is correct.
Step-by-step explanation:
The student precisely squares both sides of the equation correct 2x + 11 = 12.5 by multiplying both sides by 2x + 11, resulting in (2x + 11)^2 = (12.5)^2. The student then isolates the variable x by subtracting 11^2 from both flanks of the equation and dividing both sides by 2. This results in x = -9.5. So, the student's solution and the mathematical result are correct.
Please help!
The area of parallelogram
ABCD is 24 square units.
Find x.
The value of x determined from the area of parallelogram is 6 units.
What is area of parallelogram?A parallelogram's area is the area that it occupies in a two-dimensional plane. A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposing sides. The space bounded by a parallelogram's four sides is known as its area. A parallelogram's area is determined by multiplying its length by its height.
Given that the area of the parallelogram is 24 square units.
The area of the parallelogram is given by the formula:
A = (b)(h)
Substitute the value of A = 24, and b = 8 as given in the figure:
24 = 8(h)
h = 3
The measure of the height is 3 units.
For the triangle, we can observe that it is a right-angled triangle and the angle given is 30 degrees.
Using trigonometric functions, we have:
sin 30 = h / x
Substitute the values:
0.5 = 3 / x
x = 6
Hence, the value of x determined from the area of parallelogram is 6 units.
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Find the mean of the values. Round to two decimal places.
79, 83, 54, 77, 98 61, 88
Answer:
77.14
Step-by-step explanation:
To find the mean(average) we add all the values and divide the sum by the number of values. Here, we are given 7 total values.
The sum of these values = 79 + 83 + 54 + 77 + 98 + 61 + 88 = 540
Because there are 7 total values we divide the sum by 7 to get the mean
So mean = 540 / 7 = 77.14 (rounded to two decimal places)
The digit in the ones place of 2^88 is 6. What is the digit in the ones place of 2^90?
The digit in the ones place of 2^90 is 4. The pattern of the digits in the ones place for powers of 2 follows a repeating cycle of 0, 2, 4, 6, 8, 0, 2, 4, 6, 8 and so on.
The digit in the ones place of 2^88 is 6 because the last digit of 2^88 is 6. The pattern of the digits in the ones place for powers of 2 is 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, etc. Therefore, the digit in the ones place of 2^90 is 4 since the pattern starts over again at 0 after 8.
The pattern of the digits in the ones place for powers of 2 follows a repeating cycle of 0, 2, 4, 6, 8, 0, 2, 4, 6, 8 and so on. This pattern is a result of the fact that 2^n is divisible by 10 for all integers n greater than or equal to 0. Since 10 is divisible by 10, the remainder of 2^n divided by 10 will always be the same for certain powers of 2. The remainder for 2^0 is 0, 2^2 is 4, 2^4 is 6, 2^6 is 8 and 2^8 is 0. This pattern then repeats with 2^10 being 2 and so on. Therefore, the digit in the ones place of 2^90 is 4, since the pattern starts over again at 0 after 8.
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subtracting 12 inverse operation that will undo the given operation
Answer:
+ 12
Step-by-step explanation:
Inverse means the opposite of the operation, and if the operation is subtraction the inverse would be addition. Add 12 to undo the -12.
special right triangle
The missing length of the triangle be 7.93725.
What is meant by Pythagorean Theorem?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, [tex]$c^2=a^2+b^2$$[/tex], are equal to the total of the squares on the legs.
Remember that in every right triangle, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the two legs side (the two sides that meet at a right angle).
With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares.
By using Pythagorean Theorem is:
[tex]$c^2=a^2+b^2$$[/tex]
where c exists the hypotenuse and a and b exists the sides.
[tex]$\sqrt{\left(12^2-9^2\right)}=7.93725$$[/tex]
Therefore, the correct answer is 7.93725.
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No recuerdo cómo hacer esto...
Para completar la piramide hay que ir sumando los polynomios que hay en cada bloque.
¿Como completar las piramides?Para construir las piramides, solo debes sumar los polinomios de los bloques inferiores para obtener los superiores.
La primer piramide tiene los valores en los dos bloques de la izquierda:
2r - 3s y 5s - r
Si los sumamos, obtendremos:
(2r - 3s) + (5s - r) = (2r - r) + (-3s + 5s) = r + 2s
Entonces eso es lo que colocamos en el bloque que esta justo arriba.
Si vemos el segundo y el tercero son:
5s - r y 7r - 6s
Sumandolos obtenemos:
5s - r + 7r - 6s = 6r - s
Y eso va en el bloque que esta justo arriba, y asi de a poco vamos completando la piramide.
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GEOMETRY HELP HELP
What triangle congruence theorem could you use to prove triangle ADE is congruent to triangle CBE?
SAS
ASA
SSS
HL
which of the following represent a positive correlation? select all answers that are correct. there may be more than one. group of answer choices if a car decreases speed, travel time to a destination increases. the more time you spend running on a treadmill, the more calories you will burn. as the number of trees cut down increases, the probability of erosion increases. as you drink more coffee, the number of hours you stay awake increases. the more one runs, the less likely one is to have cardiovascular problems.
The following represents a positive correlation
the more time you spend running on a treadmill, the more calories you will burn.as the number of trees cut down increases, the probability of erosion increases. as you drink more coffee, the number of hours you stay awake increases.What Is Positive Correlation?
Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. Theoretically, the same external forces can affect both of these separate variables because they travel in the same direction.
A positive correlation may not imply progress or advantage. Instead, it refers to any two or more variables that move in tandem, meaning that as one increases, the other does too.
the following represents a positive correlation
the more time you spend running on a treadmill, the more calories you will burn.as the number of trees cut down increases, the probability of erosion increases. as you drink more coffee, the number of hours you stay awake increases.Know more about Positive Correlation
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Which of the following is not true about continuous random variables? (Points : 5) The entire area under each of the curves equals 1.Some may be described by uniform distributions or exponential distributions.They can only be integer values.The area under each of the curves represents probabilities.They have an infinite set of values.
The statement "They can only be integer values" is not true about continuous random variables.
Continuous random variables can take any value within a certain range, not just integers. They are characterized by a probability density function (pdf) that describes the distribution of the variable over a range of values. The pdf is a continuous curve, not a set of discrete points.
The other statements about continuous random variables are true: the entire area under each of the curves does equal 1, some may be described by uniform distributions or exponential distributions, the area under each of the curves represents probabilities, and they have an infinite set of values.
Therefore, The statement "They can only be integer values" is not true about continuous random variables.
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Mr. Dharmendra Yadav has a rectangular mango farm having length 1.4 km and width 600 m. If he wishes to fence the farm with four rounds over the wall by sharp pointed fencing wire at the rate of Rs 50 per meter. find the total cost of fencing.
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form. Show your work.
0, 5, -5+sqrt8
The polynomial function is f(x) = x(x - 5)(x + 5)² - 8)
How to determine the polynomial from the zeros?From the question, we have the following parameters that can be used in our computation:
Zeros: x = 0, 5, -5 + √8
The polynomial can be repesented as
f(x) = product of (x - zeros)
using the above as a guide, we have the following:
f(x) = x(x - 5)(x - (-5 + √8))(x - (-5 - √8))
This can be expressed as
f(x) = x(x - 5)(x + 5)² - 8)
hence, the polynomial is f(x) = x(x - 5)(x + 5)² - 8)
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in a hypertensive study, nurses took the blood pressure readings of 250 participants. to determine the accuracy of their readings, they wanted to test the sensitivity of their instruments. if the number of true positives is 40, and the total number of participants with disease (true positives plus false negatives) is 55, the sensitivity of the instrument is . group of answer choices
The sensitivity of the instrument can be calculated as the ratio of true positives (40) to the total number of participants with disease (55) is 73%.
Sensitivity, also known as the true positive rate or recall, is a measure of the accuracy of a diagnostic test or medical screening tool in detecting positive cases. In medical research, sensitivity is an important aspect to evaluate the performance of a diagnostic test.
In a hypertensive study, if a participant has a blood pressure reading above a certain threshold, they are diagnosed as having hypertension (a positive case). Sensitivity is calculated as the proportion of true positive cases (those with hypertension and correctly diagnosed) to the total number of actual positive cases (those with hypertension, both correctly and incorrectly diagnosed).
The formula for sensitivity is:
sensitivity = true positive / (true positive + false negative)
In the example given, the number of true positives is 40 and the total number of participants with disease (true positives plus false negatives) is 55. So, the sensitivity of the instrument is:
sensitivity = 40 / 55 = 0.73 or 73%
This means that out of all the participants with hypertension, the instrument correctly diagnosed 73% of them.
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a tangent is drawn from a point at a distance of 17 cm of circle
From a position 17 cm from the circle's center, the tangent to it is 8 cm long.
What is the length of A tangent from A point distance 17 cm?Distance from a circle's center to any point along its perimeter is known as the radius of the circle. R or r are frequently used to indicate it.
Almost every formula involving circles makes use of this amount.
A circle's radius is used to determine both its surface area and circumference.
Give the circle's radius, r.
Given:
PQ=8cm
PO=17cm
OQ=r
Since the radius across the point of contact is perpendicular to any point on a line, it follows that any point on a line must be.
According to Pythagoras' Theorem, in OPQ, OP 2 = PQ 2 + OQ 2.
(17) ² = (8) ² +r ²
⇒ r= √289−64 = √225 =15cm
Consequently, the circle has a 15 cm radius.
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What method proves this two triangles congruent?
Write down the percentage multiplier to find 67% of an amount.
Answer:
To find 67% of an amount, we use the percentage multiplier of 0.67.
This is because 67% can be expressed as 67/100, and when we divide a number by 100, we are essentially moving the decimal point two places to the left. So, 67/100 can also be written as 0.67.
Therefore, the percentage multiplier to find 67% of an amount is 0.67.
the average complexity a(n) of linearsearch for a list of size n assuming the list elements are distinct and the search element is equally likely to be found in any position is
The average complexity of linear search for a list of size n is O(n).
The average complexity of linear search for a list of size n is calculated by taking the sum of the number of comparisons for each possible position of the search element, and then dividing it by the total number of possible positions.
For example, if we have a list of size n = 10, and the search element is equally likely to be found in any position, then the number of comparisons to find the element in each position is as follows:
Position 1: 1 comparison Position 2: 2 comparisons Position 3: 3 comparisons Position 4: 4 comparisons Position 5: 5 comparisons Position 6: 6 comparisons Position 7: 7 comparisons Position 8: 8 comparisons Position 9: 9 comparisons Position 10: 10 comparisons
Therefore, the average number of comparisons to find the search element in the list is (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10 = 5.5
This means that the average complexity of linear search for a list of size n is O(n).
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differentiate with respect to x: (x2 - 3x + 2)(x+2)
By the product rule of differentiation, the derivative of (x² - 3x + 2)(x + 2) with respect to x is: 2x² - 7x + 4.
d/dx [(x² - 3x + 2) (x + 2)]
= (x² - 3x + 2)'(x + 2) + (x² - 3x + 2) (x + 2)'
= (2x - 3) (x + 2) + (x² - 3x + 2) (1)
= 2x² - 7x + 4.
What is differentiation?Differentiation is a concept in calculus that involves finding the rate of change or the slope of a function at a particular point. It involves finding the derivative of a function, which is a measure of how the function changes as its input changes. The derivative of a function can be used to determine important features of the function, such as maximum or minimum points, as well as to study the behavior of the function over an interval.
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the digits {1,2,...,5} are randomly arranged in a row. how many ordered elements are in the sample space?
The digits {1,2,...,5} are randomly arranged in a row so total 5 ordered elements are in the sample space.
The digits {1,2,...,5} are randomly arranged in a row.
We have determine how many ordered elements are in the sample space.
The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.
So, we use the combination formula
[tex]^nC_{r} = \frac{n!}{r!(n-r)!}[/tex]
Total digits are 5. So,
Sample space = [tex]^5C_{1}[/tex]
Sample space = [tex]\frac{5!}{1!(5-1)!}[/tex]
Sample space = [tex]\frac{5!}{1!4!}[/tex]
Sample space = [tex]\frac{5\times 4!}{1\times 4!}[/tex]
Sample space = 5
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Select ALL the statements about the number 2^−3 that are true.
2^−3 is greater than 3^−2.
2^−3 multiplied by −1 equals 2^3.
2^−3 is less than 1. 2^−3 raised to the third power equals 1.
2^−3 is equal to −8.
ALL the statements about the number 2⁻³that are true are:
2⁻³ is equal to −82⁻³ multiplied by −1 equals 2³ 2⁻³ is < 1What is an inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way. It can be used most frequently by comparing the sizes of two numbers on a number line.
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another. Therefore, inequality comes from an imbalance.
The phenomena of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is known as inequality.
Inequalities can be shown in the speed limits on roads, the minimum age for watching particular movies, or even in how long it takes to walk to the park. Inequalities don't represent a precise sum.
First
2⁻³ = -8
So, 2⁻³ is equal to −8 is true
2⁻³ is greater than 3⁻²
No, as negative odd exponent will result in negative number while negative even exponent would result in positive number.
2⁻³ multiplied by −1 equals 2³
Yes, -8 × -1 = 8 = 2³
2⁻³ is less than 1
As negative odd exponent is there
2⁻³ raised to the third power equals 1, Nope.
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Solve this system of equations by graphing. First graph the equations, and then type the solution.
y=
7/2x –3
y=–3/2x +7
By graphing, the solution to the given system of equations is: (2, 4).
How to Solve a System of Equations by Graphing?To solve a system of equations by graphing:
Graph each equation on the same set of axes.Look for the point(s) at which the two graphs intersect.Check that the point(s) of intersection satisfy both equations.If there is only one point of intersection, it is the solution to the system. If there is no point of intersection, the system has no solution. If there are infinitely many points of intersection, the system has infinitely many solutions.The graph of y = 7/2x - 3 is the red line while that of y = –3/2x + 7 is the red line. They intersect at (2, 4).
Therefore, the solution of the system of equations is: .
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sammi wanted to create a dot plot based on this tally chart. a 2-column table with 4 rows. column 1 is labeled hours with entries 3, 4, 5, 6. column 2 is labeled tally with entries 4, 6, 3, 5. in which step, if any, did sammi make a mistake creating his dot plot?
Based on the information provided, it appears that Sammi did not make any mistakes in creating the tally chart. The information appears to be correctly recorded and organized.
To create a dot plot, Sammi would simply plot a dot above the appropriate number on the number line for each entry in the "hours" column and mark it the number of times specified in the corresponding entry in the "tally" column.
Dot Plot Mistake CheckThe answer was determined based on the information provided in the question, which was a 2-column table with 4 rows. The first column was labeled "hours" and had entries of 3, 4, 5, 6. The second column was labeled "tally" and had entries of 4, 6, 3, 5.
Given this information, it can be concluded that Sammi correctly recorded the hours and their respective tallies. Therefore, there is no mistake in the creation of the tally chart.
It is important to note that the question only asks about the creation of the tally chart and not the creation of the dot plot, so the answer is based solely on the information provided in the question and not any assumed knowledge or steps in creating a dot plot.
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Round 684 to the nearest hundred
Answer:
700
Step-by-step explanation:
A metal bar weights 8.15 ounces 93% of the bar is silver how many ounces of silver or silver are in the bar
There are 7.58 ounces of silver are in the bar.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We have to given that;
A metal bar weights 8.15 ounces.
And, 93% of the bar is silver.
Now, Let the amount of silver in the bar = x
So, We can formulate;
⇒ x = 93% of 8.15
⇒ x = 93/100 × 8.15
⇒ x = 7.58
Thus, the amount of silver in the bar = 7.58 ounces
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Evaluate this expression for x = 5: 6+ (10 -x2-20
Salut/Hello!
Answer:
Step-by-step explanation:
x = 5 : 6 + (10 - 2x - 20)
x= 0,8(3) + 10 - 2x - 20
2x + x = 0,8(3) + 10 - 20
3x = 0,8(3) + 10 - 20
3x = -10,8(3)
x = -3.6(1)
I hope it was helpful! :]
Of a group of patients having injuries, 28% visit both a physical therapist and a chiropractor and 8% visit neither. Say that the probability of visiting a physical ther apist exceeds the probability of visiting a chiropractor by 16%. What is the probability of a randomly selected person from this group visiting a physical therapist?
The probability of a randomly selected person from this group visiting a physical therapist is 0.68.
The probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible. Let A denote the event that the person visits a physical therapist, and let B denote the event that the person visits a chiropractor. Now, we need to use the laws of probability to arrive at each individual probability i.e. P(A) and P(B).
Given: P(A∩B)=0.28
(ii) P(AC∩BC)=0.08
(iii) P(A)−P(B)=0.16
Required: P(A)
By the laws of inclusion/exclusion,
P(A∪B)=P(A)+P(B)−P(A∩B)
Therefore,
P(A)+P(B)=P(A∩B)+P(A∪B)
By DeMorgan's Law,
P(AC∩BC)=1−P(A∪B)
Therefore,
P(A)+P(B)=0.28+1−0.08=1.2
By adding the equation,
P(A)−P(B)=0.16
we get
2P(A)=1.36
Therefore, P(A)=0.68
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For f(x)=2/√10-6
Evaluate f (-6) = ?
The value of the function when evaluated is 1/2
How to evaluate the functionFrom the question, we have the following parameters that can be used in our computation:
f(x)=2/√10-6
Express properly
So, we have the following representation
f(x)=2/√(10-x)
Substitute the known values in the above equation, so, we have the following representation
f(-6)=2/√10+6
Evaluate the like terms
f(-6)=2/√16
So, we have
f(-6) = 1/2
Hence, the function value is 1/2
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hugo is a veterinarian. he knows the following information about his 41 4141 patrons: 20 2020 patrons in total do not have a dog. 17 1717 patrons in total have a cat. 7 77 patrons have neither a dog nor a cat. can you help hugo organize the results into a two-way frequency table?
Attached is a two-way frequency table, to help Hugo organize the results.
A two-way frequency table is a table used to organize and display the relationship between two categorical variables. It is constructed by counting the number of occurrences of each combination of categories and presenting the results in a table format.
To create a two-way frequency table, follow these steps:1. Identify the categorical variables and list their possible categories.
cat, no cat, dog, no dog
2. Count the number of observations for each combination of categories.
cat = 17
no dog = 20
no cat no dog = 7
3. Organize the counts in a table with the categories of one variable as rows and the categories of the other variable as columns.
| dog | no dog | total
cat | | | 17 |
no cat | | 7 | |
total | | 20 | 41 |
4. Fill in the table with the counts of the observed combinations of categories.
cat but no dog = 20 - 7 = 13
both cat and dog = 17 -13 = 4
total no cat = 41 - 17 = 24
total dog = 41 - 20 = 21
dog but no cat = 24 - 7 = 17
| dog | no dog | total
cat | 4 | 13 | 17 |
no cat | 17 | 7 | 24 |
total | 21 | 20 | 41 |
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Select all of the following true statements if R = real numbers, I = integers, and T = {..., -5, -4, -3, -2}.
All the correct statements are,
⇒ ∅ ⊂ R
⇒ {... , - 5, - 4, - 3, - 2} ⊆ T
⇒ T ⊂ I
⇒ 0 ∈ I
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We know that;
For ∅ ⊂ R;
A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition.
Hence, We get;
⇒ ∅ ⊂ R
For 6 ∈ T;
Since T is the set of negative integers less than - 1.
Hence, 6 ∉ T
For {... , - 5, - 4, - 3, - 2} ⊆ T
The set on the left is exactly what is defined on the problem statement for T. (The bar below the subset symbol just means that the subset is not strict, therefore the set on the left can be equal to the set on the right. Without it, the statement would be false since a strict subset requires that the two sets should not be equal).
Hence, {... , - 5, - 4, - 3, - 2} ⊆ T
For T ⊂ I;
Clearly, T is the set of negative integers less than - 1.
Hence, It is subset of integers.
Hence, T ⊂ I
For 0 ∈ Z;
Zero is indeed an integer thus it is an element of Z.
Hence, 0 ∈ Z
For R ⊂ T
Since, T is the set of negative integers less than - 1.
So, Not all real numbers are some integers. Some real numbers do not meet this criteria.
Hence, R ⊄ T
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The complete question is shown in figure.
PLS HELPPP!!!!! A student is running a 5 km race he runs 1 km every three minutes select a function that describes his distance from the finish line after X minutes
Answer:
Step-by-step explanation:
multiply 5km by 3 minutes he would have run the 5km in 1 5 minutes
Pls helppppp I’m begging youuuuu
The amounts and the situations are matched as follows:
Amount spent on breakfast each day: 2B + J.Amount spend on granola bars each day: 2B.Amount spent on juice each day: J.Number of days Donovan buys breakfast: 7.How to model the situation?The situation is modeled by a system of equations, in which the variables are given as follows:
B: price of a granola bar.J: price of a glass of juice.The meaning of each variable is used to build the expressions for this problem.
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