There are 59 integer solutions
Such questions are best solved by writing cases and calculating the total number of cases. So beginning with
1) x = -3. The possible combinations are as follows:-
-3 2 13
-3 3 12
-3 4 11
-3 5 10
-3 6 9
-3 7 8
-3 8 7
-3 9 6
-3 10 5
-3 11 4
10 combinations
2) x = -2
-2 2 12
through
-2 11 3
10 combinations
3) x = -1
-1 2 11
through
-1 10 3
9 combinations
4) x = 0
0 2 10
through
0 9 3
8 combinations
as we can see from the pattern at x =1 we get 7 combinations, at x =2 we get 6 combinations, at x=3 we get 5 combinations and at x =4 we get 5 combinations.
Thus total number of combinations 4+5+6+7+8+9+10+10 = 59 integer solution.
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Mya has ballet lessons every sixth day and swimming lessons every fourth day. Today she has both lessons. In how many days will Mya have both lessons on the same day again?
Mya would have both lessons on the same day again on the 12th day.
In how many days would they have the classes on the same day again?In order to determine when they would have the both lessons on the same day, the common multiple of 6 and 4 has to be determined. A multiple of a number is the product of an integer and that number. A common multiple is the multiple that is common to two or more numbers.
Multiple of 6 = 6, 12, 28, 24, 30, 36,
Multiple of 4 = 4, 8, 12, 16, 20, 24, 28
Common multiple = 12
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Find the surface area of this composite solid.
Answer: C, 93m^2
Step-by-step explanation:
first step is to find the surface area of the base. it's 3x3, so that would be 9m^2. the sides of the rectangular prism are 5x3, so one side is 15m^2. there are 4, so 15x4=60m^2. now for the top, which is a triangular prism. each side has a height of 4 and a base of 3. the area of a triangle is 1/2bh, so 1/2(3)(4), which is 6. 4 of these makes 24 m^2. add up all of final numbers to get 9+60+24. this comes to 93m^2, or C.
Wayne made cookies. He used 4/5 of a cup of flour and 2/5 of a cup of sugar. How much more flour than sugar did Wayne use?
Write your answer as a fraction or as a whole or mixed number.
Answer:
Wayne used 2/5 more flour than sugar
Step-by-step explanation:
If you add 2/5 to 2/5 you get 4/5
The graph shows the amount of money that the journalism club raised for a scholarship fund over a 5-week period. If x represents the number of weeks, which function is the BEST fit for the information in this graph?
The line of best fit for the information in this graph is:
f(x) = 200x + 100.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (t,v) are given as follows:
(2, 500), (3, 700), (4, 900), (5, 110)
Hence, inserting these points into a calculator, the equation is given by:
f(x) = 200x + 100.
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Choose the best answer from the choices below: the perpendicular bisector of a chord ____.
The perpendicular bisector of a chord passes through the center of a circle.
What is a chord?In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. It is the longest possible segment within the circle.
The perpendicular bisector of a chord is a line that passes through the midpoint of the chord, creating two equal halves, and is perpendicular to the chord.
Notably, for any chord in a circle, its perpendicular bisector always intersects at the center of the circle, making it a significant geometric property.
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If a polynomial function, f(x), with rational coefficients has roots 3 and startroot 7 endroot, what must also be a root of f(x)?
The conjugate which is 3 - √7 is also a root of f(x).
What is the root of a polynomial function?The root of a polynomial function f(x) is the value of x for which f(x) = 0.
Now if a polynomial function has a root x = a + √b then the conjugate of x which is x' = a - √b is also a root of the function, f(x).
What must also be a root of f(x)?
Given that the polynomial function, f(x), with rational coefficients has roots
3 + √7, then by the above, the conjugate which is 3 - √7 is also a root of f(x).
So, 3 - √7 is also a root of f(x).
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-5/208 + 4/7 + -3/4. Please answer my question as soon as possible. Thanks!
Answer:
[tex] - 0.2026[/tex]
Step-by-step explanation:
I hope it is the right answer
Explain the conceptual and quantitative relationships between alpha risk and beta risk when testing hypotheses, and include the impact sample size plays in managing these risk levels
The conceptual and quantative relationship between Alpha risk and Beta risk is related to the probability of accepting Null hypothesis. They are also known as Type 1 and type 2 error.
Alpha Risk:
Alpha risk is the risk that in statistical test a null hypothesis will be rejected when it is actually true. This is also known as a type I error, or a false positive. The term risk refers to chance or likelihood of making an incorrect decission.
Beta risk:
Beta risk represents the probability that a false hypothesis in a statistical test is accepted as true. Beta risk contrast with alpha risk, which measures the probability that a null hypothesis is rejected when it is actually true.
Determining the type of risk in a quantitative relationship is primarily based on sample size. The Sample Size directly affect the Alpha and Beta risk. If Sample size is larger, the Alpha and Beta risk will lower, and if the sample size is lower the risk of Beta and Alpha increases.
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If z = 1+ i√3, what is z^5?
Answer:
.....................................
Find the horizontal asymptote of the function
A. none
B. x = 0
c.y=0
D.y = 1
Reset Selection
(x-1)(x-3)²(x+1)²
(x-2)(x+2)(x-1)(x+3)*
Horizontal asymptote y = 1.
What is meant by horizontal asymptote?A slant asymptote has a specific instance known as a horizontal asymptote. A "recipe" for locating a rational function's horizontal asymptote is as follows: Let deg D(x) and deg N(x) represent the degree of the denominator and the numerator, respectively. No horizontal asymptote exists.1) If the degree of the numerator is smaller than the degree of the denominator, the horizontal asymptote is y = 0. 2) The horizontal asymptote is y = c, where c is the ratio of the leading terms or their coefficients if the degree of the numerator and denominator are equal.The denominator of the function, n(x), can be used to find vertical asymptotes by solving the equation n(x) = 0 (note that this only works if the numerator, t(x), is not zero for the same x value). Find the function's asymptotes. The graph exhibits a vertical asymptote at x = 1.Find the horizontal asymptote of the function:
Horizontal asymptotes are the lines perpendicular to the y-axis and meet the curve at infinity.
Horizontal asymptote y = 1.
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Determine which of the following graphs does not represent a function.
Answer:
Graph b.
Step-by-step explanation:
B is not a function because it fails the vertical line test.
To be a function any vertical line drawn must pass through the graph at one point only. That is not true for graph B - a line can pass through 2 points on this graph.
Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x<110)? (The greater than sign is actually greater than or equal to)
A. 0.975
B. 0.025
C. 0.16
D. 0.84
Using the normal distribution, the probability that x is less than 110 is:
A. 0.975.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 98, \sigma = 6[/tex]
The probability is the p-value of Z when X = 110, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 98}{6}[/tex]
Z = 2
Z = 2 has a p-value of 0.975.
Hence option A is correct.
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How many solutions does the following equation have?
23y+50+27y=50y+5023y+50+27y=50y+50
The equation 23 · y + 50 + 27 · y = 50 · y + 50 has infinite solutions.
How to infer the number of solutions of a linear equation of the form f(y) = 0
In this question we have an equation in implicit form: 23 · y + 50 + 27 · y = 50 · y + 50, we need to transform its expression into explicit form by using algebra properties:
23 · y + 50 + 27 · y = 50 · y + 50 Given
50 · y + 50 = 50 · y + 50 Commutative, associative and distributive properties / Definition of addition
0 = 0 Compatibility with addition / Existence of additive inverse / Modulative property / Result
The equivalence indicates that the equation 23 · y + 50 + 27 · y = 50 · y + 50 has infinite solutions.
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Write an inequality
greater than (-3) but less than or equal to 3
meaning x
An inequality greater than (-3) but less than or equal to 3 is as follows:
- 3 < x ≤ 3
What is an inequality?An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.
An inequality have the following signs:
<>≤≥Therefore, an inequality greater than (-3) but less than or equal to 3 can be represented as follows:
Note the value we are comparing is x.
Hence,
- 3 < x ≤ 3
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808, 408, 208,108, 68 find out wrong number.
68 is the wrong number in the sequence 808, 408, 208,108, 68
What is Number system?A number system is defined as a system of writing to express numbers.
Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given sequence is 808, 408, 208,108, 68
Eight hundred eight, Four hundred and eight, two hundred and eight, one hundred eight and sixty eight.
808, 408, 208,108, 68
Let us find the difference between the consecutive numbers
400, 200, 100, 40
As we observe the first three terms having the common ratio where as 40 and 100 has different ratio.
Hence, 68 is the wrong number in the sequence 808, 408, 208,108, 68
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Choose the inverse of y=x²-10x.
Oy=±√√x-25-5
O y = ± √√x-25 +5
Oy=√x+25-5
Oy=+√√x+25 +5
Answer:
[tex]y = \sqrt{x+25} + 5[/tex]
Step-by-step explanation:
Swap x and y
x = y² – 10y
Add 25 to each side to complete the square
x + 25 = y² – 10y + 25
Factor
x + 25 = (y – 5)²
Take the square root of each side
[tex]\sqrt{x+25}[/tex] = y – 5
Add 5 to both sides
[tex]\sqrt{x+25}[/tex] + 5 = y
What is (-7624928) * 997 + 7624928 * (-3)
Answer:
-7624928000 is the right answer.
Step-by-step explanation:
(-7624928) × 997 + 7624928 × (-3)
= -7602053216 + (-22874784)
= -7624928000 Ans..
Hope its helpful :-)
If so, please mark me as brainlist :-)
Answer:
Step-by-step explanation:
=(-7624928) * 997 + 7624928 * (-3)
=-7602053216+(-22874784)
=-7624928000
Can someone help me this is Algebra 2 thank you
Answer:
Order of exponentiation can be swapped here, and the fractional power written as a root.
Step-by-step explanation:
The commutative property of multiplication and the rules of exponents apply.
Product of exponentsThe rule is ...
(a^b)^c = a^(bc)
ApplicationThe given expression can be rearranged to ...
[tex]\left(3^\frac{1}{5}\right)^2=3^{\frac{1}{5}\cdot2}=3^{2\cdot\frac{1}{5}}=\left(3^2\right)^\frac{1}{5}\\\\=9^\frac{1}{5}=\boxed{\sqrt[5]{9}}[/tex]
1.** Mr. Jokinen is complaining about his heavy backpack. He removed a few books which decreased the weight of his backpack by 20%, but it still weighs 20 pounds. How much did his backpack weigh before he removed the books?
Answer: 25 pounds
Step-by-step explanation: 100% - 20% = 80%
20 divided by 80% = 25
Simplify the expression. x≠0. (4x^2)^0
1
Step-by-step explanation:Anything raised to the power of zero is 1, other than zero itself.
However, as it is given that x is not equal to zero, the answer must be 1.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathsf{(4x^2)^0}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{(4x^2)^0}\\\\\mathsf{= (4 \timesx^2)^0}\\\\\mathsf{= 4(x \times x)^0}\\\\\mathsf{= (4x^2)^0}\\\\\mathsf{= 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should:}[/tex]
[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
In a school of 910 pupils, 3/7 are boys and 2/5 of the boys wear glasses. how many boys wear glasses?
The number of boys wear glasses are 156 boys.
In this question,
Total number of pupils in the school = 910
Ratio of boys = 3/7
Then, number of boys = 910 × 3/7
⇒ 130 × 3
⇒ 390
Ratio of boys wear glasses = 2/5
Then, number of boys wear glasses = 390 × 2/5
⇒ 78 × 2
⇒ 156
Hence we can conclude that the number of boys wear glasses are 156 boys.
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2 plus 0.5x if x is equal to 5
Answer: 4.5
Step-by-step explanation:
2 + 0.5x
x = 5
2 + 0.5 ( 5 )
2 + 2.5
2 + 2.5 = 4.5
Hope this helps!
The speed, s, of the current in a certain whirlpool is modeled by x = StartFraction 300 Over d EndFraction, where d is the distance from the center of the whirlpool. Which statement is true?
The real statement is that the closer you get to the center of the vortex, the closer the current speed approaches infinity. option C is correct.
Given the speed s of the flow in a given vortex is modeled by x=300/d, where d is the distance to the center of the vortex.
speed is defined as the rate of change of an object's position in any direction. Speed is measured as the ratio of distance traveled to time traveled.
As d approaches 0, you are approaching the center of the vortex.
[tex]\begin{aligned}S&=\lim_{d\rightarrow 0}\frac{300}{d}\\ &=\frac{300}{0}\\ &=\infty\end[/tex]
Thus, if the flow in a given vortex is modeled by x = 300/d, as one approaches the center of the vortex, the speed of the flow tends to infinity.
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Answer: C- As you move closer to the center of the whirlpool, the speed of the current approaches infinity.
Which of the following is equivalent to the quotient below?
√135/√3
A. 5√3
B. √45/3
C. 3√5
D. 3√15
The answer is C. 3√5.
√135/√3√45√3² × 53√5If the p-value is smaller than the level of significance, what conclusion should we reach?
If the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.
In this question,
A p-value is a probability, calculated after running a statistical test on data and it lies between 0 and 1. The p-value only tells you how likely the data you have observed is occurred under the null hypothesis.
One of the most commonly used p-value is 0.05. If the value is greater than 0.05, the null hypothesis is considered to be true. If the calculated p-value turns out to be less than 0.05, the null hypothesis is considered to be false, or nullified (hence the name null hypothesis).
A small p-value (< 0.05 in general) means that the observed results are unusual, assuming that they were due to chance only. Now, the smaller the p-value, the stronger the evidence that should reject the null hypothesis.
Hence we can conclude that if the p-value is smaller than the level of significance, then it indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null hypothesis is correct.
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In the right triangular prism below, BG Perpendicular FC
A right triangular prism is shown. Triangles A E D and B F G are the base triangles. A perpendicular bisector is drawn from point B to point G on side F C.
The volume of the prism is 900 cubic centimeters. The height of the prism is 15 centimeters and the height of the triangular base is 10 centimeters. What is the length of edge FC?
cm
The length of edge FC in the triangular prism is: 12 cm.
What is the Volume of a Right Triangular Prism?Volume of a right triangular prism = 1/2(Length of triangular base × height of triangular base × height of the prism).
Considering the image given showing a right triangular prism, we have the following:
Volume of triangular prism = 900 cubic centimeters
Length of triangular base = FC = ?
Height of triangular base = 10 centimeters
Height of the prism = 15 centimeters
Plugin the values
900 = 1/2(FC × 10 × 15)
900 = 1/2(FC × 150)
Multiply both sides by 2
2(900) = 2(1/2(FC × 150))
1,800 = FC × 150
Divide both sides by 150
1,800/150 = FC × 150/150
12 = FC
FC = 12 cm
The length of edge FC is: 12 cm.
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Answer: 12
Step-by-step explanation:
Need help look at attachment
3x 2y = 4 2x - y = 5 this system of equations has no solution. has one solution. is coincident.
Answer:
no solution
Step-by-step explanation: because if it has no variables that are the same it has no solution.
A sequence is defined by the recursive function f(n 1) = one-halff(n). if f(3) = 9 , what is f(1) ?
[tex]f(1)[/tex] is [tex]81.[/tex]
What is a recursive function?A recursive function generates a series of phrases by repeating or using its own prior term as input.Problems that can be split down into smaller, repeating problems are ideal for recursion to solve. It is particularly useful when working on issues with numerous potential solutions that are too complex to handle iteratively. Searching a file system is an effective illustration of this.A recursive formula is one that defines each term in a sequence by reference to the one before it.To find f(1):
f(n 1) = one-half(n).
f(3) = 9.
[tex]f(3) = 9If n = 1,f(2) = 9×3f(2) = 27If n = 0,f(1) = 27 ×3f(1) = 81[/tex]
A sequence is defined by the recursive function [tex]f(1)[/tex] is [tex]81.[/tex]
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Answer:
36
Step-by-step explanation:
Assuming I understand the question correctly
[tex]\text{one-halff(n)} = \frac{1}{2} f(n)[/tex]
We have the recursive relationship
[tex]f(n+1) = \frac{1}{2} f(n)[/tex]
[tex]f(3) = 9[/tex]
[tex]f(3) = \frac{1}{2} f(2)[/tex]
[tex]f(2) = \frac{1}{2} f(1)[/tex]
So
[tex]f(3) = \frac{1}{2} (\frac{1}{2} f(1) = \frac{1}{4} f(1) \\[/tex]
So [tex]f(1) = 4f(3) = 4(9) = 36[/tex]
Verifying
If f(1) = 36 then f(2) = (1/2)f(1) = (1/2)36 = 18
f(3) = (1/2) f(2) = (1/2)(18) = 9
graph: g(x)=5cos((\pi )/(2)x-(3\pi )/(2))-2
[tex]g(x)=5cos((\pi )/(2)x-(3\pi )/(2))-2[/tex]
generate by: Amplitude:5 Period:4
Phase shift:(3 to the right) Vertical shift:-2
x=3,g(x)= 3
x=4,g(x)= -2
x=5,g(x)= -5
x=6,g(x)= -2
x=7,g(x)= 3
the graph is like cos(x)
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