The equation 8x - 4y = -4 have y as the subject to be equal to 2x + 1 expresses in terms of x.
How to evaluate for yTo solve for y in the equation 8x - 4y = -4, we must make y the subject and it should be positive as follows;
8x - 4y = -4
add 4y to both sides
8x - 4y + 4y= -4 + 4y
8x = - 4 + 4y
also to make y the subject;
- 4 + 4y = 8x
add 4 to both sides
- 4 + 4 + 4y = 8x + 4
4y = 8x + 4
factorize the right hand side
4y = 4(2x + 1)
divide through by the coefficient of y
4y/4 = [4(2x + 1)]/4
y = 2x + 1
Hence, the equation 8x - 4y = -4 has y = 2x + 1
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chegg suppose 60% of all college professors like tennis, 65% like bridge, and 50% like chess; 45% like any given pair of recreations. (a) should you be suspicious if told 20% like all three recreations?
If you are told 20% of people prefer all three forms of recreation is 60 when 60% of all college professors enjoy tennis, 65% enjoy bridge.
Given that,
Assume that 60% of all college professors enjoy tennis, 65% enjoy bridge, 50% enjoy chess, and 45% enjoy any certain pair of recreational activities.
We have to find if you are told 20% of people prefer all three forms of recreation, should you be suspicious.
We know that,
Let the total professors be =100
n(tennis) = 60
n( bridege) = 65
n( chess)= 50
n( T U B) = 45, n(BU C) = 45, n(T UC)=45
n( T UBUC)= n(T) + n(B) + n(C) - n( T U B) - n( BU C) - n(TUC) + n(T∩B∩C)
100 = 60 + 65 + 50 - 45-45-45 +n(T∩B∩C)
n(T∩B∩C)=60
Therefore, If you are told 20% of people prefer all three forms of recreation is 60 when 60% of all college professors enjoy tennis, 65% enjoy bridge.
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If a line has a slope of 8 and includes the points (9, u) and (10, –1). What is the value of u?
The value of u that completes the ordered pairs is -9
How to calculate the value of u?From the question, the points are given as
(9, u) and (10, -1)
Slope = 8
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (9, u) and (10, -1)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (9, u) and (10, -1)
Substitute the known values in the above equation
So, we have the following equation
8 = (u + 1)/(9 - 10)
Evaluate
u + 1 = -8
So, we have
u = -9
Hence, the value of u is -9
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what is the estimate of 26% of 78
26% of 78
= 26*(1/100)*78
=(26/100)*78
=0.26*78 = 20.28
so, the required answer is 20.28.
what is percentage?
answer: The quantity of something represented as if it were a portion of a sum total of 100; a portion or share of a whole.
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The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations? (a) n 15 t 1.66 a 0.05 o Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
The null hypothesis must be rejected as there is enough evidence that the diameter differs from 0.5 inches.
Given values are
The population mean is 0.5 inches
The Null hypothesis is : H₀ : μ = 0.5 inches
The Alternative hypothesis is given by Hₐ : μ ≠ 0.5 inches
Now let us consider the parameter given:
sample size is n = 15
test statistics is t = 1.66
The level of significance : α = 0.05
The degree of freedom: df = n-1 = 15 -1 =14
Calculating the critical value : [tex]t_\frac{\alpha}{2} ,df[/tex] = 2.145
We are using the critical value of [tex]t_\frac{\alpha}{2}[/tex] as the test is one-tailed .
Comparing the value of t and [tex]t_\frac{\alpha}{2}[/tex] we can see that : [tex]t < t_\frac{\alpha}{2}[/tex]
Hence the null hypothesis can be rejected.
Given that the value of t does not fall within the range covered by (i.e., the range from -2.145 to the bottom of the normal distribution curve), we are unable to reject the null hypothesis.
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Elsa is a software saleswoman. Her monthly salary is $1500 plus an additional $70 for every copy of History is Fun she sells.
Let S represent her total salary this month (in dollars), and let N represent the number of copies of History is Fun she sells. Write an equation relating S to N, and then graph your equation using the axes below.
Answer:
Step-by-step explanation:
rawr u fel me
A pterodactyl could fly 75 miles in 3 hours. At this rate, how far could a pterodactyl travel in 5 hours?
A pterodactyl could fly 75 miles in 3 hours. At this rate, how far could a pterodactyl travel in 5 hours?
Answer:
125 miles
Step-by-step explanation:
75/3 to find the distance in 1 hour=25
25x5=125
Answer:
125 miles
Step-by-step explanation:
75/3 to find the distance in 1 hour=25
25x5=125
the mean score of 888 players in a basketball game was 14.514.514, point, 5 points. if the highest individual score is removed, the mean score of the remaining 777 players becomes 121212 points. what was the highest score?
The highest score is 12794706708
What is mean ?
The average of a set of data is referred to as the mean in statistics and arithmetic. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The basic arithmetic mean involves adding the numbers together and dividing the result by the number of observations.
At first (remaining + top player) /888 = 14514514
So remaining + top = 12888888432
Now after removing top
Remaining/777 = 121212
Remaining = 94181724
So top = 12888888432 - 94181724
= 12794706708
12794706708 is the score of the top player
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4. A room is 10 ft by 12 ft. How many square yards are in the room?
The area of the room is 120 ft² (area = length x width).
The room is 10 ft by 12 ft
The area of the room = 120 sq ft
1 yard= 3 feet
1 square yard=9 sq feet
The area of the room = 120 sq ft or 120/9=13.33 sq yards
Answer: 13.33 sq yards
a researcher studies language development by selecting a sample of two-year-old children and giving them a language skill test. each year for the next two years, the children are brought back and tested again. the researcher plans to compare the children's scores at age two, age three, and age four. this study is an example of a(n) .
The given study is an example of longitudinal developmental design.
Longitudinal developmental research design analyzes progress by observing or measuring a group of people over time. As a consequence, it assesses changes in behavior according to age over time by examining one group of participants of about the same age.
The same people's behavior is examined over time using longitudinal research designs. For instance, using our example of examining the relationship between intellect and aging, a scientist would carry out a longitudinal study to see whether 20-year-olds lose IQ as they get older.
Hence we get the required answer.
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Benjamin invested $20,000 in an account paying an interest rate of 7&5/8 % compounded monthly. Kehlani invested $20,000 in an account paying an interest rate of 7&3/4 compounded quarterly. After 10 years, how much more money would Kehlani have in her account than Benjamin, to the nearest dollar?
If Benjamin invested $20,000 in an account paying an interest rate of 7&5/8 % compounded monthly. The amount of money that Kehlani have in her account than Benjamin is: $322.83.
How to find the compounded amount?Using this formula to find the compounded amount
A = P(1+r/n)^nt
Where
A = Amount
r =Interest rate.
n =Number of years
P =Principal
Benjamin
P = $20,000
r = 7 5/8% = 7.625% = 0.07625
n = 12 months
t = 10 years
Hence,
A = 20,000 (1+0.07625/12)^12× 10
A = 20,000 (1+0.006354)^120
A = 20,000 (1.006354)^120
A = $42,768.42
Kehlani
P = $20,000
r = 7 3/4% = 7.75= 0.0775
n = 4 months
t = 10 years
Hence,
A = 20,000 (1+0.0775/4)^4× 10
A = 20,000 (1+0.019375)^40
A = 20,000 (1.019375)^40
A = $43,091.25
Difference:
Difference = $43,091.25 - $42,768.42
Difference = $322.83
Therefore the amount of money is $322.83.
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Answer:322
Step-by-step explanation:
when 40 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution.
Answer:
5
Step-by-step explanation:
Let x be that number.
(x^2) - 40 = 3x
x^2 - 40 = 3x
x*2-3x-40=0
(x-5)(x+8)=0
x=5
Convert y-8.25=(x-3) into slope intercept form
Answer:
y = x + 5.25
Step-by-step explanation:
y - 8.25 = (x - 3)
y - 8.25 = x - 3
y = x + 5.25
Could you please give me brainliest for this? Thank you!
Answer:
y = x + 5.25
Step-by-step explanation:
y - 8.25 = x - 3 Add 8.25 to both sides of the equation
y = x + 5.25
please helpppp!!! !!
The graph shows a scatter plot for a set of data. Scatter plot with x-axis labeled year and y-axis labeled megawatts. The 18 points plotted are 1982 and 76.2, 1983 and 50.6, 1984 and 46.4, 1985 and 35.5, 1986 and 31.1, 1987 and 26.1, 1988 and 21, 1989 and 15.6, 1990 and 14.9, 1991 and 13.8, 1992 and 13, 1993 and 13, 1994 and 10, 1995 and 10, 1996 and 7, 1997 and 6.9, 1998 and 6.6, and 1999 and 6.
What type of correlation exists? Is the model linear or non-linear?
The graph shows a negative correlation, and it is a linear model.
The graph shows a positive correlation, and it is a linear model.
The graph shows a negative correlation, and it is a non-linear model.
The graph shows a positive correlation, and it is a non-linear model.
The graph shows a negative correlation, and it is a non-linear model.
What is positive and negative correlation?
When two variables behave in unison, rising or falling in lockstep with one another, there is a positive correlation. When two variables move in opposition to one another—that is, when one rises, the other falls—this is known as a negative correlation.
As given data from the graph, y values goes decrease with increasing x values.
So, we can conclude that the graph shows a negative correlation.
And, the given data in the graph are not linear.
Hence, the graph shows a negative correlation, and it is a non-linear model.
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Answer:
The graph shows a negative correlation, and it is a non-linear model.
Step-by-step explanation:
y-x=2x-2/3x linear or nonlinear explain
Answer:
it is linear
Step-by-step explanation:
if you add x on both sides, you can get rid of the -x on the left side, and you are left with a linear equation in slope intercept form
y=7/3x
Select ALL the correct answers.
The graph shows a linear relationship.
Select all the true statements.
A right triangle with its hypotenuse along the line from (4,2) to (8,4) has legs measuring 4 units and 2 units.
A right triangle with its hypotenuse along the line from (2,1) to (4,2) has legs measuring 3 units and 1 unit.
A right triangle with its hypotenuse along the line from (2,1) to (4,2) has legs measuring 2 units and 1 unit.
A right triangle with its hypotenuse along the line from (2,1) to (6,3) has legs measuring 4 units and 1 unit.
A right triangle with its hypotenuse along the line from (4,2) to (8,4) has legs measuring 4 units and 3 units.
The true statements regarding the linear function are given as follows:
A right triangle with its hypotenuse along the line from (4,2) to (8,4) has legs measuring 4 units and 2 units.A right triangle with its hypotenuse along the line from (2,1) to (4,2) has legs measuring 2 units and 1 unit.What is correct regarding the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, representing the value of y when the function crosses the y-axis.In this problem, the function crosses the y-axis at the origin, hence the intercept is given as follows:
b = 0.
When x increases by one, y increases by 2, hence the slope is of:
m = 2.
Considering the slope, it means that the ratio of the legs of the right triangle with it's hypotenuse along the line is of 2.
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What is the smallest value or
lower extreme?
A. 304
B. 100
C. 400
Answer:
B. 100
Step-by-step explanation:
The lower extreme is the number in line with the left most dot.
5/8 = 8/x
A.5
B.64
C.0.2
D.12.8
Answer: It's 64
Hope this helps!
consider carrying out m tests of hypotheses based on independent samples, each at significance level (exactly) 0.01. (a) what is the probability of committing at least one type i error when m
The probability of committing when at least one type I error at a significance level (exactly) 0.01 at m = 11 is equivalent to 0.1047.
Given that:
The hypotheses are based on independent samples with each at a 0.01 level of significance.
We know that:
P (at least one type I error is committed) = 1 - [P (No error - type I error is committed)]^m
P (at least one type I error is committed) = 1 - [(1 - 0.01)]^11
P (at least one type I error is committed) = 1 - [0.99]^11
P (at least one type I error is committed) = 1 - 0.8953
P (at least one type I error is committed) = 0.1047
So, the probability of committing when at least one type I error is equivalent to 0.1047.
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A researcher wishes to calculate the height of patients suffering from a heart disease. From patient records, the mean was computed to be 156cm, with a standard deviation of 5cm. Further investigation reveals that the scale was misaligned, and that all readings are 2cm too large, for example, a patient whose height is really 180cm was measured as 182 cm. Furthermore, the researcher would like to work with statistics based on meters (1 meter= 100 centimeters). What would be the revised values for the mean and standard deviation of the patients’ height?
The revised values of the mean and standard deviation are respectively; 154 cm and 5 cm
What is the mean and standard deviation?Let us assume that the number of Patients is denoted as P. We are given;
Mean = 156 cm
We know that mean here is gotten from the formula;
Mean = Total height/number of patients
Thus;
Total Height = 156P cm
We are told that each height was measured 2 cm more. Thus;
Total height reduction = 2P cm
Thus;
Actual Total Height = 156P - 2P = 154P cm
Mean = 154P/P = 154 cm
Therefore, as each reading and mean both have shifted by 2 then Standard deviation will remain same as 5cm
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PLEASE HURY IM TIMED!!!!!!!
pick true or false.
Inequality True False
6.1<6.1
−2≤−2
5.6≥5.6
-4 > 4
Answer:
Step-by-step explanation:
false true true false
Answer:
false true true and false
Step-by-step explanation:
Priya and Han each wrote an equation of a line with slope 1/2 that passes through the point (1,2) Priya's equation is y-2=1/3(x-1) and Han's equation is 3y - x = 5. Do you agree with either of them?
Explain or show your reasoning
Both Priya's equation and Han's equation are wrong . So , I don't agree with either of them
Slope-intercept form of equation of line is y =mx + b
where m is a slope of line
b is y-intercept
According to the question,
Slope of line is given as 1/2
m = 1/2
Putting the value of m in equation of line
y = 1/2 x + b --------(1)
It is given that line(1) passes through (1,2)
so, x = 1 and y = 2
Substituing the value of x and y in equation (1)
2 = 1/2 +b
Multiplying by 2 both sides
4 = 1 + 2b
=> 2b = 3
=> b = 3/2
substituting the value of b
Equation of line is y = 1/2 x + 3/2
=> 2y = x + 3
Therefore, Both Priya's equation and Han's equation are wrong
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In an all boys school, the heights of the student body are normally distributed with a mean of 68 inches and a standard deviation of 4. 5 inches. Using the empirical rule, what percentage of the boys are between 54. 5 and 81. 5 inches tall?.
According to the empirical law of statistics, 99.7% of the males are between 54.5" and 81.5" tall.
What is empirical rule?The 68-95-99.7 rule, also known as the empirical rule, indicates where most of the values in a normal distribution are distributed: The majority of values—about 68%—fall within the range of the mean. The average value is within two standard deviations for about 95% of the data. Almost all values, 99.7% of them, fall within a 3 standard deviation range.
Here,
mean=68 inch
standard deviation=4.5 inch
The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.
68−4.5=63.5
68+4.5=72.5
The range of numbers is 63.5 to 72.5
The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.
68−2⋅4.5=59
68+2⋅4.5=77
The range of numbers is 59 to 77
Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.
68−3⋅4.5=54.5
68+3⋅4.5=81.5
The range of numbers is 54.5 to 81.5
99.7% of the boys are between 54. 5 and 81. 5 inches tall using the empirical rule of statistics.
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A class has 20 women and 16 men. In how many ways can you (a) put all the students in a row? (b) put 7 of the students in a row? (c) put all the students in a row if all the women are on the left and all the men are on the right?
Part a: All the students in a row = 36!.
Part b: 7 of the students in a row; 36 x 35 x 34 x 33 x 32 x 31 x 30.
Part c: women on the left = 20! x 16!
Explain the term combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the orientation of the selection is irrelevant. You can choose the component of combos in any order. Permutations and combinations can be jumbled up.For the stated question-
The class contains-
20 women16 menTotal students = 36Part a: all the students in a row.
Number of ways = 36!
Part b: 7 of the students in a row.
Number of ways = 36 x 35 x 34 x 33 x 32 x 31 x 30
Part c: All the students in a row if all the women are on the left and all the men are on the right.
women on the left = 20! x 16!
Thus, the number of ways in which all the students in a row if all the women are on the left and all the men are on the right is; 20! x 16!.
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Hello can someone help me with this question please
The exponential equation that models the population of the bacteria is:
y = 5*(7)^x
How to write the exponential equation?The general exponential equation is of the form:
y = A*(b)^x
Where A is the initial value, b is the base, and x is the variable.
Initially, Zach counted 5 bacteria, then:
A = 5
And we know that after one hour, Zach saw 35 bacteria, then we can write the equation:
35 = 5*(b)^1
35 = 5*b
35/5 =b
7 = b
Then the exponential equation is:
y = 5*(7)^x
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battery lifetime is normally distributed for large samples. the mean lifetime is 500 days and the standard deviation is 61 days. approximately what percent of batteries have lifetimes more than 561 days ?
15.87 % percent of batteries have lifetimes more than 561 days.
Given:
battery lifetime is normally distributed for large samples. the mean lifetime is 500 days and the standard deviation is 61 days.
μ = 500
σ = 61
we know that
z = X - μ / σ
z score :
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
Given X = 561 days
substitute
z = 561 - 500 / 61
= 61 / 61
z = 1
At z = 1 p value is 0.8413
1 - 0.8413 = 0.1587
= 0.1587 * 100 %
= 15.87 %
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Pentagon PQRST is a scale drawing of pentagon ABCDE.
In the scale drawing of the 2 pentagons the value of x is 3
How to find the value of xTo find the value of x in the pentagon, the scale factor is first determined
The scale factor is solved for as follows
AB * r = PQ
in the figure AB = 5 and PQ =2.5
5r = 2.5
r = 2.5 / 5
r = 0.5
Using the scale factor r = 0.5
6 * r = x
6 * 0.5 = x
3 = x
x = 3
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What is the result when the number 8 is decreased by 25%?
Answer:
6
Step-by-step explanation:
8 * (1.0 - .25) = 6
Answer: 6
Step-by-step explanation: 8 - 4 is equivalent to 8 - 50%, cut 4 in half which gives 2, 2 is 25% of 8, so 8 - 2 = 6
You roll two dice, one red and one green. Losing combinations are doubles (both dice showing the same number) and outcomes in which the green die shows an odd number and the red die shows an even number. The other combinations are winning ones. E is the event that you roll a winning combination.
The likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.
Here,
If the first die is red and the second one is green, then the sample space S is the following:
S=
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2, 1), (2,2), (2,3), (2,4), (2,5), (2,6), (3, 1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5, 1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)
Hence n(S)=36.
Let's list the losing combinations:
E={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 1),
(2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6,5)}
n(E)=15
There are 36 total possiblities.
Out of which, winning probability is 21.
=21/36
=7/12
Given that the winning combination is 21 and the total combination is 36, the chance of rolling a winning combination is 7/12.
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HELP!!! My question is "determine whether each ratio is equivalent to 1/2 3/9 or 5/7. Thee ratios are : 2/6,3/6,5/10,10/14,50/100,20/28,1/3,8/24. please show how to do the work with the answer!!
Answers:
Ratios equivalent to 1/2 are...
3/65/1050/100Ratios equivalent to 3/9 are...
2/61/38/24Ratios equivalent to 5/7 are...
10/1420/28===============================================
Explanation:
Let's see if 2/6 is equivalent to 1/2. For now, let's assume they are equal fractions. If so, then,
2/6 = 1/2
2*2 = 6*1 ... cross multiplying
4 = 6
The last equation is of course false, which then causes a domino effect to make the first equation false as well. This means 2/6 is not equivalent to 1/2.
You can use a calculator to find that
2/6 = 0.3333 approximately1/2 = 0.5 exactlyWhich is another way to see how the fractions aren't the same.
----------------
Let's check to see if 2/6 is equivalent to 3/9.
2/6 = 3/9
2*9 = 6*3 ... cross multiplying
18 = 18
We get the same thing on both sides, which means the third equation is true. By extension, the first equation is true as well. We have shown that 2/6 and 3/9 are equivalent.
Take note how both of those fractions reduce to 1/3, which is another way to see how they are equivalent.
Yet another way is to use a calculator to find that
2/6 = 0.3333...3/9 = 0.3333...Both approximate decimal values involve '3's going on forever.
Apply any of the methods discussed to check the other values, so you can properly sort each ratio mentioned. Let me know if you have any questions.