Answer:
\( 2 \frac{2}{3} \)
Step-by-step explanation:
\( - 2 \frac{1}{3} - ( - 5) = - \frac{(6 + 1)}{3} + 5 \\ \\ = - \frac{7}{3} + 5 \\ \\ = - \frac{7}{3} + \frac{15}{3} \\ \\ = \frac{ - 7 + 15}{3} \\ \\ = \frac{8}{3} \\ \\ = 2 \frac{2}{3} \)
I need help with this question
if you purchesd a $49.00 gift and you use a 20% off coupon how much do you spend
Answer:
$39.20
Step-by-step explanation:
$49 * (1-.2) = $39.20
Write the equation of the line that passes through (−2, 6) and (2, 14) in slope-intercept form.
y = 2x − 2
y = 2x + 10
y = 0.5x + 7
y = 0.5x − 4
Answer:
y = 2x + 10
Step-by-step explanation:
(-2,6) and (2,14)
Slope = (14-6)/2- - 2)
= 8/4 = 2
b = 6 - (2)(-2)
= 6 + 4 = 10
if the sum of a number and 6 is multiplied by 5, the result is the same as 7 times the number increased by 16. find the number?
Let:
x = number we want to find
the sum of a number and 6 is multiplied by 5:
(x + 6)*5
the result is the same as 7 times the number increased by 16. So:
(x + 6)*5 = 7x + 16
Let's solve for x:
Use distributive property on the left hand side:
5x + 30 = 7x + 16
Subtract 5x from both sides:
5x + 30 - 5x = 7x + 16 - 5x
30 = 2x + 16
Subtract 16 from both sides:
30 - 16 = 2x + 16 - 16
14 = 2x
Divide both sides by 2:
14/2 = 2x/2
7 = x
Exponential equation please help!!!
Answer:
809.6
Step-by-step explanation:
880*(1-8%)
What is the sign of the third term of the expansion of (x - y)n for n = 3, 4, and 5?
Cⁿ₁ is always positive, then the second term has negative sign.
What does binomial expansion mean?
Theorem that states that any power of a binomial (a + b) can be expanded as a specific sum of products (aibj), such as (a + b)2 = a2 + 2ab + b2.
The i-th term of the binomial expansion \((x- y)^{n}\)
Ti = nCi - 1 . (x)ⁿ+¹⁺i . (-y)i - 1
For any n, when i=2,
T₂ = nC₂₋₁ . xⁿ⁺¹⁻² . (-y)²⁻¹ = -Cⁿ₁ xⁿ⁻¹ . y
Given that is consistently positive, the second term has a negative sign.
Cn1 is consistently positive, and the second term is always negative.
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The length of a rectangle is 3 units more than the width. The area of the rectangle is 54 units. What is the width, in units, of the rectangle?
please hurry
Answer:
The width is 6 and the length is 9.
Step-by-step explanation:
Factors of 54: (1, 54), (2, 2), (3, 18), and (6, 9)
6 and 9 would work because 6+3=9
If S is a non-empty subset of R^n such that any linear combination of vectors in S is again a vector in S, then S is a subspace of R^n
Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.
Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;
The condition for being a subspace of Rⁿ
Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.
Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.
Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ
From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.
Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.
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In a class of students, the following data table summarizes how many students play
an instrument or a sport. What is the probability that a student chosen randomly
from the class plays a sport?
Plays a sport
Does not play a sport
Plays an instrument Does not play an instrument
3
8
10
9
Answer:
3 OR 8 hope this helps!
Step-by-step explanation:
Please help urgent
Answer:
x < 50
Step-by-step explanation:
No more means that it cannot equal 50. Therefore we can remove the 1st two options.
We now have the 3rd option and 4th option to choose from.
The 4th option is incorrect because the inequality is saying that a number is greater than 50.
∴ x < 50 is our answer.
the base of a triangle is 6 meters longer than the height of the triangle. if the area of the triangle is 80 square meters, what are the base and height of the triangle?
The length of the base of the triangle is 16 m and the height of the triangle is 10 m
What is Triangle ?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Use the equation area = 1/2 * base * height to determine a triangle's surface area.
The basic Properties of a triangle :
Three sides and three angles make up a triangle.A triangle's total angles are always 180 degrees.A triangle's outside angles are always a sum of 360 degrees.The total of the parallel interior and exterior angles is additional.Any two sides of a triangle can be added together to have a length larger than the third side. Similar to this, any two triangle sides have length differences between them that are smaller than the length of the third side.Always, the shortest side faces the smallest internal angle. Similar to this, the biggest internal angle is always opposite the longest side.The length of the base = b m
The height of the triangle = b - 6 m
The area of the triangle = 80 m²
Therefore,
(1/2)*b*(b-6) = 80
⇒ b² - 6b = 160
⇒ b² - 6b - 160 = 0
⇒b² - 16b + 10b - 160 = 0
⇒b(b-16) + 10(b- 16) = 0
⇒(b-16)(b =10) =0
The value of b = 16 and b = -10
The value of b is 16 as -10 is negetive and cannot be the length of the triangle.
The height of the triangle = b-6 = 10 m
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Using the Quine-McClusky method, find a minimal expression for vwxyz + vwxyz + vwxyz + vwxyz + vwxyz + vwxyz.
The minimal expression is: vwxy + vwxz + vxyz.
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.
The Quine-McCluskey method is a way to find the minimal expression for a Boolean function. We can use this method to simplify the expression vwxyz + vwxyz + vwxyz + vwxyz + vwxyz + vwxyz.
Step 1: Write out the minterms
We can write out the minterms for the given expression:
vwxyz
vwxyz
vwxyz
vwxyz
vwxyz
vwxyz
Step 2: Group the minterms
We can group the minterms based on the number of 1's in their binary representation. We start with groups of minterms with 0 or 1 1's, and keep combining until we cannot combine any more.
Group 0: (none)
Group 1: 00001, 00010, 00100, 01000, 10000
Group 2: (none)
Group 3: (none)
Group 4: (none)
Step 3: Generate the prime implicants
We can generate the prime implicants by finding all the groups of minterms that differ by only one variable. We can circle the pairs of minterms that differ by only one variable to make it easier to see.
Group 0: (none)
Group 1: 00001, 00010, 00100, 01000, 10000
Group 2: (none)
Group 3: (none)
Group 4: (none)
Prime implicants:
0000_
00_01
0_010
_1000
1_000_
Step 4: Generate the essential prime implicants
The essential prime implicants are the ones that cover at least one minterm that no other prime implicant covers. In this case, all the minterms are covered by multiple prime implicants, so we cannot choose any essential prime implicants.
Step 5: Generate the minimal expression
We can generate the minimal expression by choosing a subset of the prime implicants that covers all the minterms. We can use a table to help us choose the minimal set of prime implicants.
Prime implicant Covered minterms
0000_ 3, 4, 5, 6
00_01 1, 2, 5, 6
0_010 1, 2, 4, 6
_1000 1, 3, 4, 6
1_000_ 0, 2, 3, 5
We can see that all the minterms are covered by the combination of prime implicants 0000_, 00_01, and _1000.
Therefore, the minimal expression is: vwxy + vwxz + vxyz.
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Write a sequence with five terms with a third term is six
Answer:
2, 4, 6, 8, 10
Step-by-step explanation:
This is a sequence that answers the question. Hope it helped
If JKLM is a trapezoid, which statements must be true? Check all that apply.
A. JK=~KL
B. J is congruent to M.
DC. JK is parallel to LM.
I D. J is congruent to K.
E. KL is parallel to JM.
OF Jis supplementary to K.
JKLM is a trapezoid. Statements A and E are correct.
What is the definition of geometry?It is concerned with the geometry, region, and density of various 2D and 3D shapes. There are two parallel sides and two non-parallel sides to a trapezoid.
These are the actual statements:
(a) J is supplementary to K
(e) KL is parallel to JM
Hence, statements A and E are correct.
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1. In triangle DEF, EG bisects
2. Solve for x.
3. Find the value of x.
Please show all work.
The value of x in the triangle is 3.
In the given triangle we have to find the value of x.
Let us form a proportional equation to find value of x.
12.5+x+2/12.5 = 15+2x/15
14.5+x/12.5 = 15+2x/15
15(14.5+x)=12.5(15+2x)
15×14.5 + 15x=12.5×15 +12.5×2x
217.5+15x=187.5+25x
217.5-187.5=25x-15x
30=10x
Divide both sides by 10:
x=3
Hence, the value of x in the triangle is 3.
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for students who earned a score of 20 or lower on the quiz, the cumulative frequency is and the relative cumulative frequency is . a.) 16; 32% b.) 9; 18% c.) 38; 76% d.) 29; 58%
The cumulative frequency and relative cumulative frequency for students who earned a score of 20 or lower on the quiz is 29; 58%. (option d)
Cumulative frequency refers to the running total of frequencies, or the sum of frequencies up to a certain point. In this case, the cumulative frequency is the number of students who scored 20 or lower on the quiz.
Relative cumulative frequency, on the other hand, expresses the cumulative frequency as a percentage of the total number of students in the sample. To find the relative cumulative frequency, we divide the cumulative frequency by the total number of students and multiply by 100.
Therefore, for students who scored 20 or lower on the quiz, the cumulative frequency is 29 and the relative cumulative frequency is 58% (29/50 * 100).
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Answer: 38, 76%
Step-by-step explanation:
Recall that for cumulative frequency we add up all the values that fall above or below a given bin of data. So, if we want all scores less than 20 it should be the first four bins with a total of:
8 plus 8 plus 13 plus 9 equals 38
To get the relative frequency we take the total in the bins for scores of 20 and lower divided by the total of all bins:
38 over 50 equals 0.76 equals 76 percent sign
Angle Measures and Segment Lengths - Find the value of y - WILL GIVE BRAINLIEST!
Answer:
4.3 cm
Step-by-step explanation:
By the theorem of intersecting secants outside of a circle.
\(3 \times (y + 3) = 2 \times (2 + 6 + 3) \\ 3(y + 3) = 2 \times 11 \\ 3y + 9 = 22 \\ 3y = 22 - 9 \\ 3y = 13 \\ y = \frac{13}{3} \\ y = 4.3 \: cm\)
find the surface area generated by rotating the given curve about the y-axis x=e^t-t
To find the surface area generated by rotating the curve \($x=e^t-t$\) about the y-axis, we can use the formula for the surface area of revolution:
\($S = 2\pi \int_{a}^{b} f(x) \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx$\)
In this case, we need to express the curve in terms of y. Let's solve for t in terms of x:
\($x = e^t - t$\)
To isolate t, we take the natural logarithm of both sides:
\($\ln(x+t) = t$\)
Now, differentiate both sides with respect to x using the chain rule:
\($\frac{1}{x+t} \frac{d}{dx}(x+t) = \frac{d}{dx} t$\)
\($\frac{1}{x+t} = \frac{dt}{dx}$\)
Now, we can substitute this expression for \($\frac{dt}{dx}$\) in the surface area formula:
\($S = 2\pi \int_{a}^{b} f(x) \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx$\)
\($S = 2\pi \int_{a}^{b} (e^t - t) \sqrt{1 + \left(\frac{1}{x+t}\right)^2} dx$\)
\($S = 2\pi \int_{a}^{b} (e^t - t) \sqrt{1 + \frac{1}{(x+t)^2}} dx$\)
Since we want to rotate about the y-axis, we need to express the integral in terms of y. We know that \($x = e^t - t$\), so we can rewrite the integral as:
\($S = 2\pi \int_{c}^{d} (x(y) - \ln(x(y))) \sqrt{1 + \frac{1}{(x(y)+\ln(x(y)))^2}} \left(\frac{dx}{dy}\right) dy$\)
We can now evaluate the integral to find the surface area. The limits of integration, \($c$\) and \($d$\), depend on the range of y-values that correspond to the curve \($x=e^t-t$.\)
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when performing the steps of checking the abcs during the survey of the victim, the two most vital body systems are checked. which systems are those? (choose two.)
The two most vital body systems that are checked when performing the steps of checking the ABCs are the Circulatory and Respiratory Systems.
Blood veins in the circulatory system are responsible for moving blood away from and back toward the heart. Arteries carry blood out from the heart while veins carry it back. Oxygen, nutrients, and hormones are delivered to cells by the circulatory system, which also eliminates wastes like carbon dioxide.
The respiratory system refers to the network of tissues and organs in your body that facilitates breathing. It includes your lungs, blood vessels, and airways. The lungs' moving muscles are a part of the respiratory system. Together, these elements circulate oxygen throughout the body and remove waste gases like carbon dioxide.
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use your equation from part b to predict the highway MPG for a car that gets 68 MPG in the city.part b equation:\(y = \frac{7x}{9} + \frac{125}{9} \)
ok
\(\begin{gathered} \text{ y = }\frac{7(68)}{9}\text{ + }\frac{125}{9} \\ \\ \text{ y = }\frac{476}{9}\text{ + }\frac{125}{9} \\ \\ \text{ y = }\frac{601}{9} \\ \\ \text{ y = 66.8 } \end{gathered}\)MPG = 66.8
Una caja negra contiene una esfera blanca y tres guindas, otra caja gris contiene cuatro esferas blancas y cuatro esferas guindas. Se selecciona una caja al azar y se elige una esfera. Si la esfera resultante es guinda, calcule la probabilidad de que provenga de la caja negra. *
la probabilidad es de un 29.16666667% que sea de la caja negra
Patrick is excited to attend his son’s soccer game tomorrow
evening, but he also needs to ensure his daughter arrives at her
coding class on time. Patrick is debating whether taking the train
or his
Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.
On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.
If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.
Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.
Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.
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A line intersects the points (4, 3) and (11, -4). What is the slope of the line in simplest form? m = [?]
Answer: M=1
Step-by-step explanation:
hope this help!
THIS IS DIE RIGHT NOW PLEASE HELP ASAP
Answer:
answer
d
Step-by-step explanation:
have a good day
Answer:
ITS C
Step-by-step explanation:
250-35=215
no one can be seated above that number due to 35 people already being in there!!
AAA I HOPE THIS HELPED GOOD LUCK!!
Which of the following is not a requirement for testing means? Randomization Nearly Normal Condition 10% Condition Success/Failure Condition
Among the given options, the "Success/Failure Condition" is not a requirement for testing means. The other three options—Randomization, Nearly Normal Condition, and 10% Condition—are necessary conditions to be considered when conducting hypothesis tests on means.
Randomization: Randomization is essential to ensure that the samples being compared are representative of the population and to minimize bias. Random assignment of individuals to treatment groups helps control for confounding variables and increases the validity of the statistical analysis.
Nearly Normal Condition: The Nearly Normal Condition assumes that the data follows a roughly normal distribution within each group being compared. This condition is important because many statistical tests, such as t-tests, rely on the assumption of normality to provide accurate results.
10% Condition: The 10% Condition is relevant when sampling from a finite population. It states that the sample size should be no more than 10% of the population size to ensure that the sampling process does not significantly affect the population distribution.
Success/Failure Condition: The Success/Failure Condition is not directly related to testing means. It is typically associated with tests involving proportions, where the condition specifies that both the number of successes and the number of failures should be at least 10 in each sample or category being compared.
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Consider a sample of tissue cells infected in a laboratory treatment. For 225 tissues, the standard deviation for the number of cells infected was 80 and the mean was 350. What is the standard error
Thus, standard error for this sample of tissue cells infected in a laboratory treatment is 5.33.
The standard error (SE) is a measure of how much the sample mean deviates from the population mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.
In this case, the sample size is 225, the standard deviation is 80, and the mean is 350. Therefore, the standard error can be calculated as follows:
SE = 80 / √(225)
SE = 80 / 15
SE = 5.33
The standard error for this sample of tissue cells infected in a laboratory treatment is 5.33. This means that the sample mean of 350 is likely to be within 5.33 units of the population mean.
The smaller the standard error, the more precise the estimate of the population mean. In this case, the standard error is relatively small compared to the standard deviation, which suggests that the sample mean is a relatively accurate estimate of the population mean.
However, it is important to note that the standard error only provides information about the precision of the estimate, not its accuracy. Other factors, such as sampling bias or measurement error, could still affect the accuracy of the estimate.
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How do you solve an equation with x and y in one?
There are infinitely many solutions to an equation with two variables.
We know that an equation is a mathematical statement that contains equal symbol between two mathematical expressions.
In this question need to solve an equation with x and y in one equation.
Consider an equation with two variables: 5x + y = 8
If we solve given equation for x then it would be,
5x + y = 8
5x + y - y = 8 - y
5x/5 = (8 - y)/5
x = (8 - y)/5
for any arbitrary real value value of y we can find the value of x.
This means there are infinitely many solutions.
If we solve given equation for y then it would be,
5x + y = 8
5x + y - 5x = 8 - 5x
y = 8 - 5x
for any arbitrary real value value of x we can find the value of y.
Therefore, an equation with two variables has infinitely many solutions.
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consider a die where the probability of rolling 1, 2, 3, 4, 5, and 6 are in the ratio 1:2:3:4:5:6. what is the probability that when this die is rolled twice, the sum
The probability that when the die is rolled twice, the sum is 7 is 0.233.
The probability of rolling each number on the die can be expressed as follows:
P(1) = 1/6, P(2) = 2/6, P(3) = 3/6, P(4) = 4/6, P(5) = 5/6, P(6) = 6/6
To find the probability of rolling a sum of 7 when the die is rolled twice, we can use the concept of the convolution of probability distributions.
We can calculate the probability of obtaining each possible sum by multiplying the probabilities of the individual outcomes that add up to that sum, and then summing these products over all possible combinations of the outcomes. The possible sums that can be obtained when rolling the die twice are 2, 3, 4, ..., 11, 12.
For example, the probability of obtaining a sum of 7 is:
P(1 and 6) + P(2 and 5) + P(3 and 4) + P(4 and 3) + P(5 and 2) + P(6 and 1)
= (1/6)×(6/6) + (2/6)×(5/6) + (3/6)×(4/6) + (4/6)×(3/6) + (5/6)×(2/6) + (6/6)×(1/6)
= 0.233. Therefore, the probability of rolling a sum of 7 when the die is rolled twice is 0.233.
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Help. (i have to write 20 letters.)
If I fully understand the question right, it would be choice B. The coefficient or the variable would be either for the other terms.
WILL GIVE BRAINLIEST , pls helppp .
When firefighters are trying to put out a fire, the rate at which they can spray water on the fire depends on the water pressure. You can find the flow rate f in gallons per minute using the equation, f = 120p, where p is the nozzle pressure in pounds per square inch.
What would the flow rate be if the pressure was 16 Ibs/in square?
MUST SHOW WORK
(A) 2.13
(B) 1,920
(C) 43.8
(D) 960
Answer:
B
Step-by-step explanation:
f=120p
f=120(16)
f= 1920