Answer:
a) 7000
b) 20000
c) 300000
Rounding is the act of replacing a number with values that are an approximation.
can be used to create simpler, or more explicit answersBasic rounding rules:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 68 rounded to 1 significant figure would be 70.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 13 rounded to 1 significant fugue is 10.
3. Zero digits that come after a non zero digit are non significant. Example: 10000 only has 1 significant figure
Calculations:
A) 78 x 92 = 7176
to round to 1 sig fig we must make all digits after 7 insignificantwe must also take note of whether the 7 will remain the same or be rounded upthe digit that comes after is a 1, following the rules of rounding it will remain a 7The answer for A is 7000
B) 615 x 38 = 23370
all digits after 2 must be insignificant the digit that comes after is a 3, following the rules of rounding the 2 will remain a 2Answer for B is 20000
C) 423 x 764 = 323172
all digits after 3 must be insignificantthe digit that comes after is a 2, following the rules of rounding the 3 will remain a 3Answer for C is 300000
What is the value for x when solving the equation –x (–1) = 3x (–5) using algebra tiles? x = –1 x = 1 x = 2 x = 3
The value of x in the equation –x (–1) = 3x (–5) is x = 1
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
–x (–1) = 3x (–5)
Remove the bracket in the above equation
-x - 1 = 3x - 5
Collect the like terms in the above equation
3x + x = 5 - 1
Evaluate the like terms in the above equation
4x = 4
Divide both sides by 4 in the above equation
x = 1
Hence, the value of x in the equation –x (–1) = 3x (–5) is x = 1
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Answer:
-3, or D
Step-by-step explanation:
list all the 3-digit numbers that can be created by rearranging these number tiles
582
Answer:
see explanation
Step-by-step explanation:
3- digit numbers starting with 5 are
528 and 582
3- digit numbers starting with 2 are
258 and 285
3- digit numbers starting with 8 are
825 and 852
there are 6 possible 3- digit numbers
258 , 285 , 528 , 582 , 825 , 852
When measuring variables, it is often preferable to use a small sample size because:______.
When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.
What are variables?A variable is defined as any property, number, or amount that can be measured or counted. A variable is also known as a data item. Variables include age, business revenue and expenses, country of birth, capital expenditure, class grades, eye color, and vehicle type. A variable in research is essentially a person, place, object, or phenomenon that you are attempting to quantify in some way. The simplest way to comprehend the distinction between a dependent and independent variable is to consider what the words tell us about the variable in question. When measuring variables, small sample size is frequently preferred because the smaller the sample, the greater the likelihood of a misleading result.Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.
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Use a comparison test (either normal or limit) to determine whether the following series converges or diverges. Be sure to clearly identify what you are comparing too and if that converges or diverges.
By the comparison test, the series converges.
We have
[tex]\dfrac1{k\sqrt{k+2}} \le \dfrac1{k \sqrt k} = \dfrac1{k^{3/2}}[/tex]
so we can compare to a convergent [tex]p[/tex]-series,
[tex]\displaystyle \sum_{k=1}^\infty \frac1{k\sqrt{k+2}} \le \sum_{k=1}^\infty \frac1{k^{3/2}} < \infty[/tex]
By the comparison test, the series converges.
What are convergence series and diverging series?
If the infinite series converges to a real number it is called converging if not then it is called diverging series.
If the larger series is convergent the smaller series must also be convergent. Likewise, if the smaller series is divergent then the larger series must also be divergent.
For this series to be converging it must follow the following :
⇒ [tex]| \frac{t_{n+1} }{t_{n} } | \leq 1[/tex]
⇒Putting n = 1
[tex]| \frac{t_{2} }{t_{1} } | \leq 1[/tex]
[tex]\t_{2} t_{1}[/tex] [tex]t_{2}[/tex]= 1/4
[tex]t_{1}[/tex]=1/[tex]\sqrt{2}[/tex]
[tex]\frac{t_{2} }{{t_{1} }}[/tex] = 1/2[tex]\sqrt{2[/tex]
⇒ t₂/t₁≤1
⇒ Hence it converges
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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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Find the area of the shape
3.14 for pi
[tex]a = \frac{\pi.r {}^{2} }{4} = \frac{3.14 \times 10 {}^{2} }{4} = \frac{3.14 \times 100}{4} [/tex]
[tex]a = 78.5[/tex]
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!
If 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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If y = -9 when x = 3, find y when x = -6. when x = -5.
Answer:
When x is -6, y will be 18
When x is -5 y will be 15
Step-by-step explanation:
Create a proportion
y/x
-9/3 = x/-6 What do we need to multiply 3 by to get 6? -2, so we will multiply -9 by -2 to get 18
Some people like to solve by cross multiplying.
That would give us
(-9)(-6) = 3x
54 = 3x divide both sides by 3
18 = x
Set up the second problem as a proportion
-9/3 = x/-5 This is a little trickier. I am trying to think what I have to multiply 3 by to get -5. 3(-5/3) will give me -5, so I will multiply the top number that I know (-9) by (-5/3) to find my x.
(-9)(-5/3) = 45/3 or 15
If z = 1+ i√3, what is z^5?
Answer:
.....................................
Here are the steps Tyler took to solve the equation.
Please answer these two questions! Thank youuu
Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. Thus the steps taken by Tyler are correct if x = 22.
ii. Tyler made no mistake.
Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. The value of the alphabet in the expression would be determined by applying mathematical operations appropriately.
To solve the question given to Tyler, we have:
[tex]\sqrt{x + 3}[/tex] = -5
square both sides of the equation to have;
(x + 3) = [tex](-5)^{2}[/tex]
x + 3 = 25
collect like terms to get;
x = 25 - 3
= 22
x = 22
1. Thus the equation is true if x = 22.
2. Tyler did not make any mistake in solving for x.
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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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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
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:
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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(d) The perimeter of the figure below is equal to 150 cm.
X
x+6
x+5
x+1
x+8
X+4
What is the length of the longest side of the polygon?
Use mathematics to explain how you determined your answer.
Use words, symbols, or both in your explanation.
Based on the given perimeter of the polygon and the length of each side; the length of the longest side of the polygon is 29 cm
Perimeter of a polygonPerimeter = 150 cmPerimeter of the polygon = x + (x + 6) + (x + 5) + (x + 1) + (x + 8) + (x + 4)
150 = x + x + 6 + x + 5 + x + 1 + x + 8 + x + 4
150 = 6x + 24
150 - 24 = 6x
126 = 6x
x = 126/6
x = 21
The longest side of the polygon is (x + 8)
= 21 + 8
= 29 cm
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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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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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Armando used algebra tiles to represent the product 3 x (2 x minus 1). an algebra tile configuration. 3 tiles are in the factor 1 spot and are labeled x. 3 tiles are in the factor 2 spot: 2 are labeled x and 1 is labeled negative. 15 tiles are in the product spot: 2 are labeled x squared, 4 are labeled x, 1 is labeled negative x, and 4 are labeled negative. which is true regarding armando’s use of algebra tiles?
The correct powers of x are not displayed in several of the goods.
What is algebraic tiles?Algebra tiles are mathematical manipulatives that help pupils better comprehend algebraic thinking and its ideas. These tiles have shown to give beginning algebra pupils in elementary, middle, high, and college concrete models.
How do algebraic tiles function?Blocks called algebra tiles can be used to symbolize constant, linear, and quadratic terms. Small yellow squares stand in for constant blocks, green rectangles for linear blocks, blue squares for quadratic blocks, and red squares for negative sides for all other types of blocks.
Future:
The image shows,
3x(2x - 1) = 6x² - 3x
This should be the appropriate representation on the tile:
_____+x _____ +x _____ +x
+x _ +x² ______+x² ______+x²
|
+x__ +x² _____ +x² ______+x²
|
- __ -x ______ -x _______-x
+6x² - 3x
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rewrite in standard form (only)
5x+10y=30
8x +2y=12
-12x+3y=27
-24x-12y=60
Answer:
Below in bold.
Step-by-step explanation:
Standard form is Ax + By = C
where A, B and C are integers and A must be positive.
So the first 2 are already in standard form but the last 2 can be converted to standard form by multiplying each term by -1:
-12x+3y=27
= -1*-12x + -1*3y = -1*27
12x - 3y = -27 is the answer.
The last one is:
24x + 12y = -60.
When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the function representing the number of people, f(x), at the fair x hours after the gates open.
The function that represents the number of people at the fair after x hours is f(x) = 68 + 1.5x
What is the function that represent the number of people at the fair?
The function that represents the number of people at the fair is known as a linear function. A linear function is any function that graphs to a straight line. The dependent variable in the linear function increases by a constant number.
Linear functions can be represented by : y = mx + c
Where:
y = dependent variable c = constantf(x) = 68 + (1.5x)
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The height of a right rectangular prism is 3 units greater than the length of the base. the edge length of the square base is x units. which expression represents the volume of the prism, in cubic units?
The expression x³+3x² is a cubic unit representation of the prism's volume.
What is right rectangular prism?Having 6 faces, 12 edges, and 8 vertices, a right rectangular prism is a three-dimensional object. Angles between the base and sides are right angles in a right rectangular prism. Rectangles make up each of the six faces.
We have provided that to:
In a right rectangular prism, the height is three units more than the base's length.
The square base has edges that are x units long.
How much volume does a rectangular prism have?
Volume of the rectangular prism = width × length × height
V = W × L × H ....................(1)
We've indicated that the
bigger by three than the base's length, h
and the length of the base is x:
Hence,
H = X +3
Length of the base = X
Width = X
Adding the values l h and w to the formula (1) yields,
V = W × L × H
= X × X × (X+3)
= (X²) × (X+3)
= X³ + 3X³
Consequently, the phrase
X³ + 3X³
represents, in cubic units, the prism's volume.
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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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what is (b-2)x(b-7) multiplied
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \:(b - 2) \sdot(b - 7)[/tex]
[tex] \qquad❖ \: \sf \:(b \sdot b) + (b \sdot - 7) - (2 \sdot b) - (2 \sdot - 7)[/tex]
[tex] \qquad❖ \: \sf \: {b}^{2} - 7b - 2b + 14[/tex]
[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex] \sf \:(b - 2) \sdot(b - 7) = {b}^{2} - 9b + 14[/tex]
Answer:
b² - 9b + 14
Step-by-step explanation:
(b - 2) × (b - 7)
= b×b - 7b - 2b + 2×7 (Expand)
= b² - (7b + 2b) + 14 (gather like terms)
= b² - 9b + 14
Find, leave your answers in terms of pie,
a) the area of the shaded region,
b) the perimeter of the shaded region
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On a number line, the coordinates of P and Q are 8 and 48, respectively. The midpoint of PQ is B, the midpoint of BQ is C, and the midpoint of PC is D. What is the coordinate of D?
Answer:
23 is the answer
Myra is 555 years younger than her sister Talat. Myra wants to write an equation for her own age (m)(m)left parenthesis, m, right parenthesis given Talat's age (t)(t)left parenthesis, t, right parenthesis.
The equation that represents the Myra's age given Talat age is as follows:
t = m + 5
How to represent an equation?Myra is 5 years younger than her sister Talat
Myra age is represented by m while Talat age is represented by t.
Hence,
m = age of Myra
t = age of Talat
Myra is 5 years younger than Talat. This means Talat is 5 years older than Myra.
Therefore, the equation that represents the Myra's age given Talat age is as follows:
t = m + 5
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Answer:
[tex]m=t-5[/tex]Step-by-step explanation:
give me brainiest if I'm correct
Need help look at attachment
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
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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