Answer:
(a) 1416
(b) 2 × 2 × 2 × 3 × 59
Step-by-step explanation:
The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357
The square numbers between 0 and 10 are 1, 4, 9 and in descending order 9,4.1so n = 941
m - n = 2357 - 941 = 1416
Unique prime factors of 1416 are 2,3,59
1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59
6.Find by suitable rearrangement
a)4x2984x250
b) 495+114+205
factor of 13965
The solutions by suitable arrangement are:
2984000814How to find the suitable arrangementa)4x2984x250
By suitable arrangement, we would arrange this as
(4 x 250) x 2984
= (1000 * 2984)
= 2,984,000
b. b) 495+114+205
By suitable arrangement we would have:
(495 + 205) + 114
= 814
c. The factors of 13965 are all of the numbers that can divide this number.
They are: 1, 3, 5, 7, 15, 19, 21, 35, 49, 57, 95, 105, 133, 147, 245, 285, 399, 665, 735, 931, 1995, 2793, 4655, and 13965
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If I went to bed at around 1:20 AM, and woke up at 8 AM, around how many hours of sleep did I get?
Answer:
you would get about 6:20 of sleep
you would have gotten at least 6 hours of sleep and 20 mins
Step-by-step explanation:
(a) sin x° = 0.8
Given that x is an obtuse angle, find x.
(b) cos 127° = -cos yo
Given that y is an acute angle, find y.
The value of x is 126.87° and the value of y is 53°.
What is an obtuse and an acute angle?An obtuse angle is an angle that is greater than 90° but lesser than 180° while an acute angle is an angle between 0-90°.
From the given information:
sin x° = 0.8
x = sin⁻¹ (0.8)
x = 53.13°
x + 53.1° = 180°
x = 180° -53.13°
x = 126.87°
If cos 127° = -cos y°,
-cos y = -0.6018
cos y = 0.6018
y = cos⁻¹ (0.6018)
y = 53°
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117 Mr. Turtle, Mrs. Squirrel and Ms. Pigeon work at the Magic Forest's post office. Mr. Turtle can
deliver a package from the Southern Glade to the Northern Glade in 3 days, while Ms. Pigeon can
deliver it in 30 minutes. How much time will the same job take Mrs. Squirrel, if the ratio of Mr.
Turtle's time to the Mrs. Squirrel's time is the same as the ratio of Mrs. Squirrel's time to Ms.
Pigeon's time?
The proportion shows that the time taken to do the same job by Mrs. Squirrel is 6 hours.
How to calculate the value?From the information given, the ratios are:
Turtle / Squirrel = Squirrel / Pigeon
3/x = x/(1/48)
x² = 1/16
x = 1/4
The number of days will be:
= 1/4 × 24
= 6 hours.
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A triangle has vertices as D(4,5), E(1,8) and F (1,2). Show that the height from D is also the median from D.
The x-coordinate of the altitude on EF is the same as the point D(4, 5) and by calculation, the height from D (1, 5) is also median from D (1, 5)
How can the height and median be calculated?The height from D is perpendicular to EF
The slope of EF = (8 - 2)/(1 - 1) = ∞
Therefore, the side EF is parallel to the y-axis.
Therefore, the coordinates of the point of intersection of the altitude from D and the line EF is (1, 5)
The median is the midpoint of the side EF
The coordinates of the midpoint is found as follows;
[tex] \mathbf{ \left(1 + \frac{1 - 1}{2}, \: 1 + \frac{8 - 2}{2}\right)} = (1 ,5)[/tex]
Therefore;
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What is the system of inequalities associated with the following graph?
A) {y>−2
{x+y≥1
B){y<−2
{x+y≥1
C){y<−2
{x+y<1
D){y< -2
{x+y> 1
Answer: C
Step-by-step explanation:
[tex]y=-2[/tex] is dotted and shaded below, so it represents [tex]y < -2[/tex].
Also, [tex]x+y=1[/tex] is shaded above, so it represents [tex]x+y < 1[/tex].
A triangle is translated by using the rule (x,y) →(x-4.y+1). Which describes how the figure is moved?
O four units left and one unit down
O four units left and one unit up
O one unit right and four units down
O one unit right and four units up
Answer:
Four units left and one unit up.
Step-by-step explanation
Adding -4 to each x-coordinate shifts the figure to the left 4 units.
Adding +1 to each y-coordinate shifts the figure up 1 unit.
The figure is moved ...
four units left and one unit up
Answer:
2nd option
Step-by-step explanation:
x-4 = 4 left
y+1 = 1 up
2nd option
In an interview of 45 students, 12 liked Mathematics and Science, 5 liked Mathematics and English, 25 liked Mathematics; 23 liked Science; 4 liked all three subjects; 15 liked English; 10 liked Science and English. How many students did not like any of the subjects?
Answer:
Step-by-step explanation:
plus 18 and subtract 4
Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?
SSS
AAS
SAS
HL
Answer: Option 2 or B. AAS
Step-by-step explanation: B. AAS
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When two angles and the non-included side of one triangle are congruent to other triangle the by AAS congruency they are congruent. Therefore, option B is the correct answer.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
AAS, two angles and one side of a triangle are equal to two angles and one side of another triangle then they are congruent.
Therefore, option B is the correct answer.
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Briefly explain how multiple regression enhances the two primary purposes of regression analysis.
The statistical goal of multiple regression analysis is to build a linear equation model that identifies the optimal weighted linear combination of independent variables in the study in order to optimally predict the reference variable.
Regression analysis is usually performed for one of two purposes. Predicting the value of the dependent variable of a person whose information about the explanatory variable is available, or estimating the effect of the explanatory variable on the dependent variable.
In multiple regression analysis, researchers can determine the strength of the relationship between the outcome (dependent variable) and multiple predictors, and the importance of each predictor in the relationship, often the effect of other predictors. It can be evaluated by statistically eliminating it.
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The amount of water in a leaky bucket is given by the linear function , where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.
The y-intercept = 127 and the slope = -10
How to determine the y-intercept and the slope?The function is given as:
y = 127 - 10x
A linear function is represented as:
y = c + mx
Where
c = the y-intercept
m = slope
This means that:
y-intercept = 127
slope = -10
The y-intercept implies that, the initial amount of water is 127 ounces and the slope implies that the water leaks by 10 ounces per minute
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Complete question
The amount of water in a leaky bucket is given by the linear function y = 127 - 10x, where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.
Solve the following linear system by elimination. Check your solution:
1. x + 5y =4
2. 4x + 12y = 8
Answer:
(- 1, 1 )
Step-by-step explanation:
x + 5y = 4 → (1)
4x + 12y = 8 → (2)
multiplying (1) by - 4 and adding to (2) will eliminate x
- 4x - 20y = - 16 → (3)
add (2) and (3) term by term to eliminate x
0 - 8y = - 8
- 8y = - 8 ( divide both sides by - 8 )
y = 1
substitute y = 1 into either of the 2 equations and solve for x
substituting into (1)
x + 5(1) = 4
x + 5 = 4 ( subtract 5 from both sides )
x = - 1
As a check
substitute these values into the left side of both equations and if equal to the right side then they are the solution.
- 1 + 5(1) = - 1 + 5 = 4 = right side
4(- 1) + 12(1) = - 4 + 12 = 8 = right side
(- 1, 1 ) is the solution to the system of equations
is 2x 2 times or 2x mean 2 x or 1x+1x or 0x+2?
Answer:
Generally x means times so the best and not dummest option is 2 times
2x and 2 x is the same the 2 x is spaced out a little
Step-by-step explanation:
Does dy/dx in a graph mean the value of f'(x), or the slope of f'(x) at the point?
What is the logarithmic form of 13² = 169?
The logarithmic form of 13² = 169 is ㏒₁₃ 169 = 2
How to determine the logarithmic formUsing the logarithmic rule , we have that
㏒ₙn = bⁿ
Given 13² = 169
It is important to note that it can be written either in the logarithmic form or in the index form.
In this case, we have written in the index form as .
㏒₁₃ 169 = 2
Thus, the logarithmic form of 13² = 169 is ㏒₁₃ 169 = 2
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Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
Substituting the equation y = 4x + 1 into the equation 2y = -x – 1 will produce the equation ________.
a.)
7x = -3
b.)
7x = 1
c.)
9x = -3
d.)
9x = 1
Answer:
C.
Step-by-step explanation:
This is substitution method in solving simulteanous equations.
given y = 4x + 1
we will substitute y into 2y = -x-1
[tex]2(4x + 1) = - x - 1 \\ 8x + 2 = - x - 1 \\ 8x + x + 2 = - 1 \\ 9x + 2 = - 1 \\ 9x = - 1 - 2 \\ 9x = - 3[/tex]
Therefore the answer is C.
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Substituting the equation given into another equation will produce another equation. But which one?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
[tex]\bf{2y=-x-1}[/tex] | substitute the required equation
[tex]\bf{2(4x+1)=-x-1}[/tex] | solve in terms of x
[tex]\bf{8x+2=-x-1}[/tex] | carry on solving
[tex]\bf{9x+2=-1}[/tex] | carry on solving
[tex]\bf{9x=-3[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=The\;third\;option}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta 1}}[/tex]
PLEASE HELP, kinda forgot how to do it
Answer:
20
Step-by-step explanation:
Rise over run
Answer:
m = 20
Step-by-step explanation:
What is the measure of the corresponding central angle for XY in radians?
Answer:
4 radians
Step-by-step explanation:
Arc Length (Radians) = rθ
Given Arc Length XY = 40cm and radius, r = 10cm,
we will substitute these 2 values into the formula to find θ.
(10)θ = 40
θ = 40 / 10
= 4 radians
Answer:
A
Step-by-step explanation:
the length of arc XY is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{0}{2\pi }[/tex] ( r is radius and Θ is central angle )
here arc = 40 and r = 10 , then
2π × 10 ×[tex]\frac{0}{2\pi }[/tex] = 40
20π × [tex]\frac{0}{2\pi }[/tex] = 40 ( cancel 20π and 2π by 2π )
10Θ = 40 ( divide both sides by 10 )
Θ = 4 radians
Write at least 1 full sentence explaining the steps you would take to evaluate an expression.
The step you would take to evaluate an expression is to follow the order of operation
What are expressions?Expressions are mathematical statements that involve variables, terms, coefficients and mathematical operators
How to determine the steps?Different expressions require different ways of solving
However, the general guide is that the order of operation must be followed
The order of operation is represented by the acronym BEDMAS
Which means
Bracket
Exponent
Division
Multiplication
Addition
Subtraction
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What else would need to be congruent to show that triangle ABC is congruent to DEF by AAS?
Answer:
B
Step-by-step explanation:
In order the angles <C and <F are shared, then <B and <E, then the side equaling 10. This together proves that this triangle is congruent because of AAS (angle,angle,side) a triangle congruency rule.
NEED HELP ASAP!!
This graph shows the total number of patients seen by a doctor over the course of a 5-day workweek.
What are the domain and range of this relationship??
Using the domain and range concepts, we have that:
The domain is: {0, 1, 2, 3, 4, 5}.The range is: {0, 12, 24, 36, 48, 60}.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input. In a graph, it is given by the values of x.The range of a function is the set that contains all the values of the output. In a graph, it is given by the values of y.Hence, considering the given graph:
The domain is: {0, 1, 2, 3, 4, 5}.The range is: {0, 12, 24, 36, 48, 60}.More can be learned about the domain and the range of a data-set at https://brainly.com/question/10891721
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Problem Set
Show instructions
Question 4 (1 point)
Given a triangle with sides of length 5 and 8, find the range of possible values for the third side. (Note: left
hand side of inequality in Blank 1 and right hand side in Blank 2)
Blank 1:
Blank 2:
____
Answer:
3 < x < 13
Step-by-step explanation:
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Let x be the length of the unknown side.
Therefore, x will either be the longest side or one of the shorter sides.
Therefore:
x < 5 + 8
⇒ x < 13
And:
8 < 5 + x
⇒ 3 < x
So the range of possible values of the third side is greater than 3 and less than 13: 3 < x < 13
For which value of b can the expression x2 + bx + 18 be factored?
An expression is defined as a set of numbers, variables, and mathematical operations. The value of b for which the expression x² + bx + 18 can be factored is 9.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of b for which the given expression x² + bx + 18 can be factored is 9. This will make the expression factored as (x+3) and (x+6).
Thus, the value of b for which the expression x² + bx + 18 can be factored is 9.
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PLEASE HELP!!
Triangle not drawn to scale
Given: m & B = 18°, b = 9, and c = 20. Find
m & Co to nearest whole number.
Answer:
43°
Step-by-step explanation:
Calculating for the measure of angle C using
sine rule[tex] \frac{sin18}{9} = \frac{sinc}{20} \\ sinc = \frac{sin18 \times 20}{9} \\ sinc = 0.6867 \\ c = \csc(0.6867) \\ c = 43.3869 \\ c = 43 \: degrees[/tex]
Can someone help me out on these geometry fill in the blanks questions? Just questions 2,3,4.. it’s urgent
The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy, or New York, New York:
High Low Q1 Q3 IQR Median Mean σ
Rome 21 1 1.5 7.5 6 4.5 6.5 6.6
New York 20 1 3.5 7.5 4 5 6.5 5.2
Which of the choices below best describes how to measure the center of these data?
Both centers are best described by the mean.
Both centers are best described by the median.
The Rome data center is best described by the mean. The New York data center is best described by the median.
The Rome data center is best described by the median. The New York data center is best described by the mean.
Choices for the measure of center that is best are: C. Rome data center is best described by the mean while that of New York data is best described by the median.
What are the Measures of Center?The measures of center include the mean and the median. Mean is best for a symmetrical data distribution while median is good for a skewed data distribution with an outlier.
The data for New work has an outlier, while that of Rome does not. Therefore, the best choices for the measure of center is: C. Rome data center is best described by the mean while that of New York data is best described by the median.
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an=−2+32(n−1)
What is the 21st term of the sequence?
Answer:
a₂₁ = 638
Step-by-step explanation:
substitute n = 21 into the explicit formula
a₂₁ = - 2 + 32(21 - 1) = - 2 + 32(20) = - 2 + 640 = 638
What is a disadvantage of debt consolidation?
OA. You can have payments that are lower.
B. You can spread payments over a longer time.
о C. You can have a lower interest rate.
о D. You can pay more money in the long term.
A disadvantage of debt consolidation is you can pay more money in the long term.
What is debt consolidation?
Debt consolidation is when a person takes out a new loan in order to pay off an existing loan. Debt consolidation increases the money you pay in the long term because you would still have to pay for the new debt incurred.
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Michell is making a sign for her sister's birthday. The sign says "HAPPY BIRTHDAY" in all capital letters. If each letter is 4/5 inches long estimate the length needed to spell out “HAPPY BIRTHDAY."
ps.also add 4/5 for the space between the two words..................... Thanks
Answer:
5/4 is the correct answer for this question