Step-by-step explanation:
Area of a square = s x s
(4x-7)x(4x-7)
Open brackets
4x(4x-7)-7(4x-7)
16x^2-28-28x+49
16x^2-28x+21
The linear equation Y = a + bX is often used to express cost formulas. In this equation:_________
a) the b term represents variable cost per unit of activity.
b) the a term represents variable cost in total.
c) the X term represents total cost.
d) the Y term represents total fixed cost.
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 5?
Answer:
1/5
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
probability that the ticket drawn has a number which is a multiple of 5 =
Number of tickets that are a multiple of 5 / total number of tickets
Multiple of 5 = 5, 10, 15, 20
there would be 4 tickets that would be a multiple of 5
= 4/20
To transform to the simplest form. divide both the numerator and the denominator by 4
= 1/5
(x+a)(x-a) = x² -25 then what is the value of a ?
Answer:
The value of A is 5
......
[tex]\huge{\boxed{\boxed { ⎆ Answer :- }}} \ [/tex]
[tex](x + a)(x - a) = {x}^{2} - 25[/tex]
Use, the algebraic identity ↦
[tex](a + b)(a - b) = {a}^{2} - {b}^{2} [/tex]
So,
[tex](x + a)(x - a) = {x}^{2} - 25 \\ \\ ⟹ \sqrt{25} = 5[/tex]
↦So, the value of a is 5.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
What is the longest side of a right angled triangle called?
Answer:
The hypotenuse
Estimate the student's walking pace, in steps per minute, at 3:20 p.m. by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)
This question is incomplete, the complete question is;
A student bought a smart-watch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded (t) minutes after 3:00 pm on the first day she wore the watch.
t (min) 0 10 20 30 40
Steps 3,288 4,659 5,522 6,686 7,128
a) Find the slopes of the secant lines corresponding to the given intervals of t.
1) [ 0, 40 ]
11) [ 10, 20 ]
111) [ 20, 30 ]
b) Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)
Answer:
a)
1) for [ 0, 40 ], slope is 96
11) for [ 10, 20 ], slope is 86.3
111) for [ 20, 30 ], slope is 116.4
b) the student's walking pace is 101 per min
Step-by-step explanation:
Given the data in the question;
t (min) 0 10 20 30 40
Steps 3,288 4,659 5,522 6,686 7,128
SLOPE OF SECANT LINES
1) [ 0, 40 ]
slope = ( 7,128 - 3,288 ) / ( 40 - 0
= 3840 / 40 = 96
Hence slope is 96
11) [ 10, 20 ]
slope = ( 5,522 - 4,659 ) / ( 20 - 10 )
= 863 / 10 = 86.3
Hence slope is 86.3
111) [ 20, 30 ]
slope = ( 6,686 - 5,522 ) / ( 30 - 20 )
= 1164 / 10 = 116.4
Hence slope is 116.4
b)
Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part .
Since this is recorded after 3:00 pm
{ 3:20 - 3:00 = 20 }
so t = 20 min
so by average;
we have ( [ 10, 20 ] + [ 20, 30 ] ) /2
⇒ ( 86.3 + 116.4 ) / 2
= 202.7 /2
= 101.35 ≈ 101
Therefore, the student's walking pace is 101 per minutes
The diagram shows that `/_A cong /_D` and `bar(AB) cong bar(DE)`. Which other statement do you need to prove triangle congruency through the SAS criterion?
A. /_C cong /_F
B. bar(BC) cong bar (EF)
C. /_B cong /_E
D. bar(AC) cong bar(DF)
Answer:
Option D
Step-by-step explanation:
In the given triangles ΔABC and ΔDEF,
∠A ≅ ∠D
AB ≅ DE
By SAS property of congruence of two triangles,
Two sides and the included angle of one triangles should be congruent to corresponding two sides and the included angle of the other triangle.
Therefore, AC ≅ FD will be the desired property to prove the given triangles congruent.
Option D will be the correct option.
Answer:
Step-by-step explanation:
Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches greater than the box he originally planned to build?
Answer:
The new volume is 3n^2+2n inches greater.
Step-by-step explanation:
Volume of a cube = s^3 where s is side of cube
Original volume = n^3
Volume of a Rectangular Prism = LBH
New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n
DIfference = New- original = 3n^2+2n
In 2013, the Public Religion Research Institute conducted a survey of 1,033 adults, 18 years of age or older, in the continental United States. One of the questions on their survey was as follows:
Answer:
Probability[Number of people from church] = 0.26 (Approx.)
Step-by-step explanation:
Given:
Total number of adult in survey = 1,033
Missing information:
Number of people from church = 269
Find:
Probability[Number of people from church]
Computation:
Probability of an event = Number of favourable outcomes / Number of total outcomes
Probability[Number of people from church] = Number of people from church / Total number of adult in survey
Probability[Number of people from church] = 269 / 1,033
Probability[Number of people from church] = 0.2604
Probability[Number of people from church] = 0.26 (Approx.)
The salaries of 235 nurses were recorded and analyzed. The analyst later found that the highest salary was incorrectly recorded as 10 times the actual amount. After the error was corrected, the report showed that the corrected value was still higher than any other salary. Which sample statistic must have changed after the correction was made?
The sample statistic that must have changed after the correction was made is mean. Because mean is based on all the observation in the data. So changing any value in the data will impact mean.
Changing the highest salary in the data will have no impact on median because median lies at the center of data.
Changing the highest salary in the data will have no impact on mode because mode is the most frequently occurring value in the data.
Changing the highest salary in the data will have no impact on minimum because minimum is the smallest value in the data.
Hence the only statistic which will change is mean.
Answer: A-Mean
Step-by-step explanation:
A.) Mean
B.) Median
C.) Mode
D.) Minimum
Which critical thinking issue is most relevant to the following situation:
A research journal reports that there are on average 2.773829473 TVs in homes of Endor college educators as opposed to 2.682390934 TVs in homes of Endor bank tellers.
perceived lack of anonnymity
loaded or leading question
nonresponse bias or missing data
voluntary response bias
assumed accuracy from overly precise numbers
self-interest study
9514 1404 393
Answer:
assumed accuracy from overly precise numbers
Step-by-step explanation:
Except when counting large sums of money or considering definitions, most real-world numbers are not accurate beyond about 6 significant figures. When considering survey or sample results, the accuracy can be considerably less than that, often not even good to 3 significant figures. (Margin of error is usually some number of percentage points greater than 1.)
Expressing the given ratios to 10 significant figures substantially misstates their accuracy. (10^-9 television is less than 1 day's accumulated dust).
Which answers describe the shape below? Check all that apply.
A. Trapezoid
B. Parallelogram
C. Rhombus
D. Rectangle
E. Quadrilateral
F. Square
Answer:
B, C, and E
Step-by-step explanation:
If a+bi, where b is not equal to 0, is a complex zero of a polynomial with real coefficients, then so is its _____ , a-bi.
a.) linear factorization
b.) irreducible factor
c.) reducible factor
d.) complex factor
e.) fundamental theorem
f.) conjugate
Hello,
answer f: conjugate
if all coefficients are real and a+ib a zero, its conjgate a-ib is also a zero.
which of the following sets represents the tangeof the function shown? {(-3,4),(5,11),(9,-1),(10,13)}
Explanation:
The range is the set of y outputs of a relation. So we just list the y coordinates of the points shown.
We could sort the values to get {-1, 4, 11, 13}, but order doesn't matter in a set. So this step is optional.
I’ll give brainliest
Answer:
A
Step-by-step explanation:
From f(x) to k(x), the graphed parabola is stretched and wider.
Answer: Choice B) Vertically compressed by a factor of 8.
Explanation:
Consider a point like (8,64) which is on f(x).
If we plug in x = 8 into k(x), then we would get k(8) = 8. The old output y = 64 is now y = 8. This is an example of a vertical compression of 8. It's 8 times smaller in the vertical direction compared to what it used to be. This is because the k(x) outputs are 1/8 those of the f(x) outputs.
Effectively we have k(x) = (1/8)*f(x).
Another example would be x = 16 leading to y = 256 on f(x). For k(x), we have x = 16 lead to y = 32
Refer to the graph below.
Does anyone know the awnser please
Answer:
please which level is this
and also is it core maths or elective math
Use the formula for the volume of a cube given by
V = s3
where s is the length of one of the sides. This formula yields the volume in cubic units.
Suppose a certain sugar cube has a side that measures 5/9 inches per side. What is the volume of this sugar cube (in in3)? Round the result to three decimal places.
Answer:
The volume of the cube is 0.171 cubic inches.
Step-by-step explanation:
The volume of a cube given by :
[tex]V=s^3[/tex]
Where
s is the length of one of the sides.
We need to find the volume of the sugar cube if its side is 5/9 inches per side.
So,
[tex]V=(\dfrac{5}{9})^3\\\\V=0.171\ inches^3[/tex]
So, the volume of the cube is 0.171 cubic inches.
fill in the blink
Given ,Simplify ,BC=EF ,Multiplication Property of Equality ,Substitution Property of Equality AC=DF DE+EF=DF Reflexive Property of Equality Transitive Property of Equality ,Segment Addition Postulate, Division Property of Equality ,Addition Property of Equality, Distributive Property, Subtraction Property of Equality
Answer:
see below
Step-by-step explanation:
[tex] \displaystyle AB = DE[/tex]
[given]
[tex] \displaystyle \boxed{BC = EF}[/tex]
[given]
[tex] \displaystyle AB + BC = AC[/tex]
[segment addition Postulate]
[tex] \displaystyle \boxed{DE+ EF=DF}[/tex]
[segment addition Postulate]
[tex] \rm\displaystyle DE+ BC = AC \: \: \text{and} \: \: DE+ BC = DF[/tex]
[Substitution Property of Equality]
[tex] \displaystyle \boxed{AE= DE}[/tex]
[Proven]
3. The size of a red blood cell is 0.000007 m and the size of a plant
cell is 0.0000127 m. Compare these two.
Given:
Size of a red blood cell = 0.000007 m
Size of a plant cell = 0.0000127 m
To find:
The comparison of these two values.
Solution:
We have,
Size of a red blood cell = 0.000007 m
Size of a plant cell = 0.0000127 m
Clearly, [tex]0.0000127>0.000007[/tex]. Now, the difference between these two values is:
[tex]0.0000127-0.000007=0.0000057[/tex]
Therefore, the size of a plant cell is 0.0000057 m more than the size of a red blood cell.
Will give brainliest answer please give explanation
If this block dropped into 23.0mL of water, what will the new volume be?
In a survey, 24 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $2. Construct a confidence interval at a 98% confidence level.
Answer:
The 98% confidence interval for the mean amount spent on their child's last birthday gift is between $40.98 and $43.02.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 24 - 1 = 23
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 23 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.5
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.5\frac{2}{\sqrt{24}} = 1.02[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.02 = $40.98.
The upper end of the interval is the sample mean added to M. So it is 42 + 1.02 = $43.02.
The 98% confidence interval for the mean amount spent on their child's last birthday gift is between $40.98 and $43.02.
Why can you use cross products to solve the proportion StartFraction 18 over 5 EndFraction = StartFraction x over 100 EndFraction for x?
Answer:
45
Step-by-step explanation:
PLEASE HELP ME BE CORRECT PLEASE
TELL ME WHERE to PUT EACH POINT
Answer:
Point A:
(3, -5)
Point B:
(6, -2)
Point C:
(5, -7)
Step-by-step explanation:
Background:
Moving to the right means adding to the x.
Moving to the left means subtracting from the x.
Moving up means adding to the y.
Moving down means subtracting from the y.
So take each point and add 3 to the x, and subtract 4 from they y.
Point B:
(3, 2) → (6, -2)
Point A:
(0, -1) → (3, -5)
Point C:
(2, -3) → (5, -7)
use dimensional analysis $3,000 to convert US Cash allowance into Peruvian currency.
Answer:
200000
Step-by-step explanation:
29563487
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean of 1262 and a standard deviation of 118. Determine the 26th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Answer:
a) 1186
b) Between 1031 and 1493.
c) 160
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 1262 and a standard deviation of 118.
This means that [tex]\mu = 1262, \sigma = 118[/tex]
a) Determine the 26th percentile for the number of chocolate chips in a bag.
This is X when Z has a p-value of 0.26, so X when Z = -0.643.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.643 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.643*118[/tex]
[tex]X = 1186[/tex]
(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.
Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a p-value of 0.025, so X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -1.96*118[/tex]
[tex]X = 1031[/tex]
97.5th percentile:
X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 1.96*118[/tex]
[tex]X = 1493[/tex]
Between 1031 and 1493.
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Difference between the 75th percentile and the 25th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.675*118[/tex]
[tex]X = 1182[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 0.675*118[/tex]
[tex]X = 1342[/tex]
IQR:
1342 - 1182 = 160
Can someone help me please..
The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 509 MPa with a standard deviation of 17 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 509 MPa
Answer:
0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 509 MPa with a standard deviation of 17 MPa.
This means that [tex]\mu = 509, \sigma = 17[/tex]
What is the probability that a randomly chosen sample of glass will break at less than 509 MPa?
This is the p-value of Z when X = 509. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{509 - 509}{17}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5
0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa
Find the value of x. Round to the nearest tenth. Chords and Arcs
9514 1404 393
Answer:
4.1
Step-by-step explanation:
x is the short leg of a right triangle with hypotenuse 8.8 cm and longer leg 7.8 cm. Its measure is found using the Pythagorean theorem:
x^2 +7.8^2 = 8.8^2
x^2 = 77.44 -60.84 = 16.60
x = √16.6
x ≈ 4.1
The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer. What is the probability that the sample mean would differ from the true mean by less than 1.1 dollars if a sample of 38 5-gallon pails is randomly selected
Answer:
0.5587 = 55.87% probability that the sample mean would differ from the true mean by less than 1.1 dollars.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The cost of 5 gallons of ice cream has a variance of 64 with a mean of 34 dollars during the summer.
This means that [tex]\sigma = \sqrt{64} = 8, \mu = 34[/tex]
Sample of 38
This means that [tex]n = 38, s = \frac{8}{\sqrt{38}}[/tex]
What is the probability that the sample mean would differ from the true mean by less than 1.1 dollars ?
P-value of Z when X = 34 + 1.1 = 35.1 subtracted by the p-value of Z when X = 34 - 1.1 = 32.9. So
X = 35.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35.1 - 34}{\frac{8}{\sqrt{38}}}[/tex]
[tex]Z = 0.77[/tex]
[tex]Z = 0.77[/tex] has a p-value of 0.77935
X = 32.9
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{32.9 - 34}{\frac{8}{\sqrt{38}}}[/tex]
[tex]Z = -0.77[/tex]
[tex]Z = -0.77[/tex] has a p-value of 0.22065
0.77935 - 0.22065 = 0.5587
0.5587 = 55.87% probability that the sample mean would differ from the true mean by less than 1.1 dollars.
A regression was run to determine whether there is a relationship between hours of tv watched per day(x) and number of sit-ups a person can do (y). The results of the regression are given below. Use this to predict the number of sit-ups a person who watches 11 hours of tv can do
Y=ax+b
A=-1.341
B=32.234
R=-0.896
Answer:
17
Step-by-step explanation:
Given the regression model :
Y=ax+b
x = Hours of TV watched per day
y= number of sit-ups a person can do
A=-1.341
B=32.234
Y = - 1.341x + 32.234
Predict Y, when x = 11
Y = - 1.341(11) + 32.234
Y = −14.751 + 32.234
Y = 17.483
Hence, the person Cann do approximately 17 sit-ups
In the accompanying diagram of isosceles triangle ABC, overline AB cong overline BC , BAC =X , and m angle ABC=3x+70
Answer:
x = 22
Step-by-step explanation:
In order to solve this, we need to understand that in an isosceles triangle the two angles that are located at its base are equal to each other.
base - (the side that is not one of the two sides that are equivalent to each other)
Knowing this we can see that ∠ACB will equal ∠BAC, therefore ∠ACB will be equal to x°. Since the sum of all inner angles of a triangle is equal to 180°, we can make the following equation...
x° + x° + (3x + 70)° = 180°
2x° + 3x° + 70° = 180°
5x° = 180° - 70°
5x° = 110°
x° = 110° / 5
x° = 22°
x = 22
Therefore, x = 22.