Answer:
0.5
Step-by-step explanation:
The slope m of a linear equation y = mx + b that goes through point (-9,6) and point (-3, 9) would have the following formula
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 6}{-3 - (-9)} = \frac{3}{6}= \frac{1}{2}[/tex] or 0.5
Where [tex](x_1,y_1), (x_2, y_2)[/tex] are the coordinates of the 2 points that this line goes through
what is the midpoint of a line segment with the endpoints (8, -3) and (-5, -9)?
A (2.5, -7)
B (1.5, -6)
C (-7, 2.5)
D (-6, 1.5)
Answer:
The answer to your question is B. (1.5, -6)
Step-by-step explanation:
Data
A (8, -3)
B (-5, -9)
Formula
Xm = [tex]\frac{x1 + x2}{2}[/tex]
Ym = [tex]\frac{y1 + y2}{2}[/tex]
Substitution
x1 = 8 x2 = -5
Xm = [tex]\frac{8 - 5}{2} = \frac{3}{2}[/tex]
y1 = -3 y2 = -9
Ym = [tex]\frac{-3 - 9}{2} = \frac{-12}{2} = -6[/tex]
Midpoint = (3/2, -6) = (1.5, -6)
A broker takes 2% as commission for the sale of property of value up to rupees 3,00,000. If the sale price is more than this, the broker changes 1.5% for the remaining amount. If a property was sold for rupees 4,50,000.What was the broker's commission.
Answer:
The broker's commission was rupees 8,250
Step-by-step explanation:
Selling price of property = rupees 450,000
The sale price is higher than rupees 300,000
Commission for rupees 300,000 = 2% × rupees 300,000 = rupees 6,000
Remaining amount = rupees 450,000 - rupees 300,000 = rupees 150,000
Commission for the remaining amount = 1.5% × rupees 150,000 = 0.015 × rupees 150,000 = rupees 2,250
Total commission = rupees 6,000 + rupees 2,250 = rupees 8,250
What was the importance of the massacre of 270 Indians by U.S. military forces at Sand Creek, Colorado, in 1864?
Answer:
That the government did not defend the rights of the Indians.
Step-by-step explanation:
Sand Creek, Colorado was the place where hundreds of Cheyenes and Arapahoes were massacred by the Colorado Territory militia, which terrorized indigenous peoples to abandon their lands.
A binomial event has n = 50 trials. The probability of success for each trial is 0.60. Let x be the number of successes of the event during the 50 trials. What are μx and σx?
30 and 3.4641
30 and 5.4772
20 and 3.4641
20 and 5.4772
50 and 3.4641
Answer:
A. 30 and 3.4641
Step-by-step explanation:
The solution is Option A.
The value of the standard deviation is given by μx = 30 and σx = 3.4641
What is Standard Error?The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The standard error of the mean is used when referring to a statistic that is the sample mean. The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.
The standard error S = √ [ ( 1 - p ) p / n ]
where p = population proportion
n = sample size
Given data ,
Let the number of trials n = 50
Let the probability of success be represented as p = 0.60
Now , let the standard deviation be σ
S = √ [ ( 1 - p ) p / n ]
Substituting the values in the equation , we get
S = √ ( 0.60 ) ( 0.40 ) / 50
S = √ 0.24/50
S = √0.0048
S = 0.0692820
So , the value of σ = 0.0692820
Therefore , the value of σx = 0.0692820 x 50 = 3.4641
Now , the value of μx = 0.60 x 50 = 30
Hence , the value of μx and σx are 30 and 3.4641 respectively
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Fred’s company is planning a new logo. The diagrams show two similar versions of the planned logo.
A) calculate the lengths of the sides marked a and b.
B) the smaller of the two versions of the logo costs £4.48 to paint with gold paint. Calculate the cost of the logo with the same gold paint.
Answer:
a=7.2*1.5=10.8 cm
b=6.3/1.5=4.2 cm
[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]
Step-by-step explanation:
Proportional Geometric Shapes
A) We are given two similar shapes of a logo. They are to be proportional. We only need to find the proportion ratio of two of them to find the rest of the lengths.
The upper sides have 7.5 cm and 5 cm respectively. This gives us the ratio
[tex]\displaystyle r=\frac{7.5}{5}=1.5[/tex]
Which means all the measures of the smaller logo are 1.5 smaller than those of the larger. This means
b=6.3/1.5=4.2 cm
a=7.2*1.5=10.8 cm
B) To paint the logos, we need to cover its surface, so the ratio of the surface is 1.5*1.5=2.25
This means the cost to paint the larger logo is
[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]
Answer:
A) a = 10.8, b = 4.2
B) £10.08
Step-by-step explanation:
A) 7.5/5 = 1.5
a = 7.2 x 1.5 = 10.8
5/7.5 = 2/3
b = 6.3 x 2/3 = 4.2
B) 1.5 x 1.5 = 2.25
£4.48 x 2.25 = £10.08
A school marching band will raise one dollar for each granola bar and five dollars for each pie they sell. Yesterday, they raise $260 by selling 80 bars and pies. How many of each did they sell?
Answer: 35 granola bars and 45 pies were sold.
Step-by-step explanation:
Let x represent the number of granola bar that was sold.
Let y represent the number of pie that was sold.
A school marching band will raise one dollar for each granola bar and five dollars for each pie they sell. Yesterday, they raise $260 by selling 80 bars and pies.
This means that
x + 5y = 260 - - - - - - - - - -1
Since they sold a total of 80 bars and pies, it means that
x + y = 80
Substituting x = 80 - y into equation 1, it becomes
80 - y + 5y = 260
- y + 5y = 260 - 80
4y = 180
y = 180/4 = 45
x = 80 - y = 80 - 45
x = 35
I like math because I get it done fast. And I get A's. And I made myself and my parents do it. I make my parents do it and myself. Thats why I love math
Answer:
proud of you keep ya head up
Step-by-step explanation:
the area of a circle is less than 64 π. which of the following can be the circumference of the circle? (select one or more answer choices)
a. 12 π
b. 16 π
c. 24 π
d. 32 π
Answer:
d. 32 π
Step-by-step explanation:
As given
Area of circle = 64 π
Area of circumference = 1/2*(Area of circle)
Area of circumference = 1/2*(64π)
Area of circumference = 0.5*64π
Area of circumference = 32π
A circle is a curve sketched out by a point moving in a plane. The correct option is A, 12π unit.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that the area of the circle is less than 64π. Therefor, the area of the circle can be written as,
Area of the circle < 64π units²
πR² < 64π
R < 8 units
Now, the circumference of the circle should be less than the circumference of the circle having radius of 8 units. Therefore, we can write,
Circumference of the circle with radius R < Circumference of the circle with radius of 8 units
2πR < 2 × π × 8 units
2πR < 16π units
Therefore, from the above inequality the circumference of the circle should be less than 16π unit. Since the only feasible option is 12π.
Hence, the correct option is A, 12π unit.
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In the test of gender selection technique, results consisted of 281 baby girls and 291 baby boys. Based on this result, what is the probability of a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?
-The probability that a girl will be born using this technique is approximately______
Does this technique appear effective in improving the likelihood of having a baby girl?
Answer:
The probability for a girl to be born is 0.4913. This technique doesnt appear to improve the likelihood of having a baby girl.
Step-by-step explanation:
Since the number of babies selected for this technique, using the law of big numbers, we conclude that the proportion of babies that are girls in the selection is approximately equal than the probability for a girl to be selected. Thus, the probability that a girl will be born using the technique is 281/(281+291) = 0.4913.
Since in general girls are slightly more likely to be born than boys, then we can conclude that the technique doesnt have an effect in improving the likelihood of having a baby girl, but the opposite.
I wish to determine the correlation between the height (in inches) and weight (in pounds) of 21-year-old males. To do this, I measure the height and weight of two 21-year-old men. The measured values are Height and weight of male 1: 70, 169 Height and weight of male 2: 69,164 The correlation r computed from the measurements on these males is Question 2 options: 1.0 -1.0 near 0 because the heights and weights of the men are similar.
Answer:
[tex]r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1[/tex]
So then the we have perfect linear association. Because the heights and weights of the men are similar.
Step-by-step explanation:
Let X represent the Height and Y the weigth
We have the follwoing dataset:
X: 70, 69
Y: 169, 164
n=2
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
For our case we have this:
n=2 [tex] \sum x = 139, \sum y = 333, \sum xy = 23146, \sum x^2 =9661, \sum y^2 =55457[/tex]
And if we replace in the formula we got:
[tex]r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1[/tex]
So then the we have perfect linear association. Because the heights and weights of the men are similar.
P(x)=2x^4-x^3+2x^2-6. What is the remainder when P(x) is divided by (x-2)?
Answer: 26
Step-by-step explanation: From the remainder theorem ,
If P (x) = 2x⁴ ⁻ x³ + 2x² ⁻ 6. is divided by ( x - 2 ).
It means that if P(x) is divided by (x - 2 ) and leaves a Remainder, it implies that x - 2 is not a factor of P(x) , but if it leaves no remainder, it means x-2 is a factor of P(x).
Therefore , to find the remainder, find the zero of x - 2, and substitutes for the value in P(x) to know the remainder
x - 2 = 0
x = 2
Now put this in P(x)
P(x) = 2(2)⁴ - (2)³ + 2(2)² - 6
= 2(16) -8 + 2(4) -6
= 32 -8 +8 -6
=26
Therefore the remainder when P(x) is divided by x -2
=26
Note: Since the division of P(x) by x - 2 leaves a remainder, it means that
x - 2 ≠ a factor of P(x)
(1) 4m+5=3m-5/2 (2) -2+7(x+2)=5(2x-2)+4 Show work for every step.
Answer:
m = -3x = 6Step-by-step explanation:
1)
[tex]4m+5=\dfrac{3m-5}{2} \quad\text{given}\\\\2(4m+5)=\dfrac{2(3m-5)}{2} \quad\text{multiply by 2}\\\\8m+10=3m-5 \quad\text{use the distributive property}\\\\(8m+10)-(3m+10)=(3m-5)-(3m+10) \quad\text{subtract $3m+10$}\\\\5m=-15 \quad\text{collect terms}\\\\\dfrac{5m}{5}=\dfrac{-15}{5} \quad\text{divide by 5}\\\\m=-3 \quad\text{simplify}[/tex]
____
2)
[tex]-2+7(x+2)=5(2x-2)+4 \quad\text{given}\\\\-2+7x+14=10x-10+4 \quad\text{use the distributive property}\\\\7x+12=10x-6 \quad\text{collect terms}\\\\(7x+12)-(7x-6)=(10x-6)-(7x-6) \quad\text{subtract $7x-6$}\\\\18=3x \quad\text{collect terms}\\\\\dfrac{18}{3}=\dfrac{3x}{3} \quad\text{divide by 3}\\\\6=x \quad\text{simplify}[/tex]
In Missy's sports card collection,3/4 of the cards are baseball cards. In franks collection 8/12 are baseball cards. Frank says they have the same fraction of baseball cards. Is he correct?
Frank is incorrect because both fractions are not same.
Step-by-step explanation:
We have to compare both fractions in their simplest forms to compare them
Given
Baseball cards in Missy's Collection: [tex]\frac{3}{4}[/tex]
Baseball cards in Frank's Collection: [tex]\frac{8}{12}[/tex]
Converting the fraction in simplest form will give us:
[tex]\frac{2}{3}[/tex]
Both the fractions are not same as one is 3/4 and one is 2/3.
Hence,
Frank is incorrect
Keywords: Fractions, decimals
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The amount of simple interest earned I, on an investment over a fixed amount of time ????, is jointly proportional to the principle invested P, and the interest rate ????. A principle investment of $1500.00 with an interest rate of 5% earned $375.00 in simple interest. Find the amount of simple interest earned if the principle is $2300.00 and the interest rate is 8%?
Answer:$920
Step-by-step explanation:
Since the variation is joint, I=KPr where k is the constant of proportionality.
Plugging in the values of I=$375, P=$1500 and r=5% in the equation I=KPr, the value of k can be calculated. Hence, the formula connecting the three quantities (I,P and r) can be generated.
375 = K (1500×5)
Making k the subject of change,
K = 375/(1500×5)
K=1/20
Formula connecting the three quantities :I =Pr/20
when P=$2300, r=8%,
I = (2300×8)/20
I = $920
Identify the sample chosen for the study.
The number of times 13 out of 22 students on your floor order take-out in a week.
All students who order take-out in a week. The 13 students on your floor. The 22 students on your floor.
Answer:
The 13 students on floor
Step-by-step explanation:
The sample is a portion of population selected to view the aspects of population as whole population is difficult to follow. Here, the sample is 13 students on the floor because it is selected from 22 students on the floor.
The population consists of 22 students on floor and 13 out of 20 is the sample because it is a portion of population.
If 9\geq4x+19≥4x+19, is greater than or equal to, 4, x, plus, 1, which inequality represents the possible range of values of 12x+312x+312, x, plus, 3?
Answer:
[tex]12x+3\leq 27[/tex]
Step-by-step explanation:
It is given that
[tex]9\geq4x+1[/tex]
We need to find the possible range of values of 12x+3.
Subtract -1 from both sides.
[tex]9-1\geq 4x[/tex]
[tex]8\geq 4x[/tex]
Multiply both sides by 3.
[tex]24\geq 12x[/tex]
Add 3 on both sides.
[tex]24+3\geq 12x+3[/tex]
[tex]27\geq 12x+3[/tex]
It can be rewritten as
[tex]12x+3\leq 27[/tex]
Therefore, 12x+3 must be less than or equal to 27.
A trains leaves Cincinnati at 2:00 pm.A second train leaves the same station in the same direction at 4:00 pm.The second train travels 24 mph faster than the first.If the second train overtakes the first at 7:00 pm, what is the speed of each train?
Answer:
Speed of first train = 36 mph
Speed of second train = 60 mph
Step-by-step explanation:
Given:
First train leaves Cincinnati at 2:00 PM
Second train leaves same station at 4:00 PM
Speed of second train is 24 mph faster than first train.
The second train overtakes the first at 7:00 PM
To find the speeds of each train.
Solution:
First train:
Let speed of first train be = [tex]x\ mph[/tex]
Time of travel between 2:00 PM to 7:00 PM = [tex]7-2=5\ h[/tex]
Distance traveled by 1st train in 5 hours in miles = [tex]Speed\times time = x\times 5 = 5x[/tex]
Second train:
Then, speed of second train will be = [tex](x+24)\ mph[/tex]
Time of travel between 4:00 PM to 7:00 PM =[tex]7-4 = 3\ h[/tex]
Distance traveled by second train in 3 hours in miles = [tex]Speed\times time = (x+24)\times 3=3x+72[/tex]
At 7:00 PM both trains meet as the second train overtakes the first. This means the distance traveled by both the trains is same at 7:00 PM as they both leave from same stations.
Thus, we have:
[tex]5x=3x+72[/tex]
Solving for [tex]x[/tex]
Subtracting both sides by [tex]3x[/tex]
[tex]5x-3x=3x-3x+72[/tex]
[tex]2x=72[/tex]
Dividing both sides by 2.
[tex]\frac{2x}{2}=\frac{72}{2}[/tex]
∴ [tex]x=36[/tex]
Speed of first train = 36 mph
Speed of second train = [tex]36+24=[/tex] 60 mph
Final answer:
The speed of the first train is 36 mph and the speed of the second train, which is 24 mph faster, is 60 mph. This was determined by setting up an equation based on the equal distances covered by both trains when the second overtakes the first.
Explanation:
The question involves solving a rate, time, and distance problem typically found in algebra or kinematics. To find the speeds of the two trains, we can set up an equation based on the fact that the distance covered by both trains is the same at the point where the second train overtakes the first. Let's define the speed of the first train as s (in mph). Therefore, the speed of the second train will be s + 24 mph. Since the first train leaves at 2:00 pm and is overtaken at 7:00 pm, it travels for 5 hours. The second train, leaving two hours later at 4:00 pm, travels for 3 hours.
The distance covered by each train can be expressed as their speed multiplied by the time traveled. For the first train, it's s 5 hours, and for the second train, it's (s + 24) 3 hours. Setting these two distances equal gives us:
s 5 = (s + 24) imes 3
Solving for s gives:
s imes 5 = 3s + 72
5s - 3s = 72
2s = 72
s = 36
So, the speed of the first train is 36 mph, and the speed of the second train is 60 mph (36 + 24).
Trevor stores his baseball cards in a book with nine pages each page holds nine cards seven of his cards won't fit in the book how many cards does he have
Answer:
88
Step-by-step explanation:
9 pages
Each holds 9
He has 7 more
81+7=88
Megan spent two out of five of her money on a doll and half of the remainder on a musical box she spent eight dollars more on the doll than on a musical box how much money did she have left
Answer:
Megan has left with $24.
Step-by-step explanation:
Let the total money she has be 'y'.
Given:
Megan spent two out of five of her money on a doll.
So we can say that;
Money spent on doll = [tex]\frac{2}{5}y[/tex]
Also Given:
half of the remainder on a musical box.
Money spent on musical box = [tex](y-\frac{2}{5}y)\frac{1}2[/tex]
Now we will make the denominator common using LCM we get;
Money spent on musical box =[tex](\frac{5y}{5}-\frac{2y}{5})\times\frac{1}2}=(\frac{5y-2y}{5})\times \frac{1}{2}=\frac{3y}{10}[/tex]
Now Given:
she spent eight dollars more on the doll than on a musical box.
[tex]\frac{2y}{5} = \frac{3y}{10}+8[/tex]
Combining like terms we get;
[tex]\frac{2y}{5}-\frac{3y}{10}=8[/tex]
Now we will make the denominator common using LCM we get;
[tex]\frac{2y\times2}{5\times2}-\frac{3y}{10}=8\\\\\frac{4y}{10}-\frac{3y}{10}=8\\\\\frac{4y-3y}{10}=8\\\\y=8\times10\\\\y=\$80[/tex]
Money spent on doll = [tex]\frac{2}{5}y=\frac{2}{5}\times 80 = \$32[/tex]
she spent eight dollars more on the doll than on a musical box.
So we can say that;
Money spent on musical box = Money spent on doll -8 = [tex]32-8 = \$24[/tex]
Now to find the remaining money left we will subtract Money spent on doll and Money spent on musical box from total money she had.
framing in equation form we get;
remaining money left = [tex]80-32-24= \$24[/tex]
Hence Megan has left with $24.
Mrs. King gets a 15% discount on merchandise bought in the store where she works. Last week she bought several items that totaled $57.25 before the discount. How much did she have to pay using her discount? Round off the amount to the nearest cent.
Answer:
48.6625 before rounding, I'm sure the instruction told you where it preferred you to round.
Step-by-step explanation:
1. Convert percent value to a decimal.
The way to do this is by moving the period at 15.00 two places to the left.
2. Now that you have the decimal .15, multiply it by Mrs. King's subtotal (57.25).
you should get 8.5875.
3. Subtract the discount amnt. (8.5875) from the subtotal (57.25).
You should get 48.6625.
In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a standard deviation of 34.4. A random sample of 64 students is drawn form this population.(A) Identifying the mean and standard error of the sample mean score ¯X (x bar).(B) What is the distribution of ¯ X? and Why?(C) Find the probability that the sample mean score ¯X(x bar) is at least 285.
Answer:
a) [tex] \mu_{\bar x} =\mu = 276.1[/tex]
[tex]\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3[/tex]
b) From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)[/tex]
c) [tex]P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)[/tex]
[tex]P(Z\geq2.070)=1-P(Z<2.070)=1-0.981=0.019[/tex]
Step-by-step explanation:
Let X the random variable the represent the scores for the test analyzed. We know that:
[tex] \mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4[/tex]
And we select a sample size of 64.
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Part a
For this case the mean and standard error for the sample mean would be given by:
[tex] \mu_{\bar x} =\mu = 276.1[/tex]
[tex]\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3[/tex]
Part b
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)[/tex]
Part c
For this case we want this probability:
[tex] P(\bar X \geq 285)[/tex]
And we can use the z score defined as:
[tex] z=\frac{\bar x -\mu}{\sigma_{\bar x}}[/tex]
And using this we got:
[tex]P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)[/tex]
And using a calculator, excel or the normal standard table we have that:
[tex]P(Z\geq2.070)=1-P(Z<2.070)=1-0.981=0.019[/tex]
Last week, Ray worked 46 hours. He incorrectly calculated he earned $45 of additional pay. What was Ray's error when he miscalculated his overtime pay? Explain your answer.
Answer: +$45
Step-by-step explanation: if his actual pay for the week was $100 then from the question he incorrectly calculated it as {$100 + $45} = $145 which is $45 above his actual pay.
Error = measured value - actual
value.
= $145 -$100 =$45.
NOTE: since the value he assumed{$145} is greater than his actual pay{$100}, we have to include a positive sign to the error{$45}.
Therefore, Error = +$45.
Ray's error was incorrectly calculating his additional pay as $45 instead of the correct amount of $90. To find the correct overtime pay, we need to determine how many hours Ray worked in excess of his regular hours and the rate at which he receives overtime pay.
Explanation:The error Ray made when calculating his overtime pay was incorrectly calculating the additional pay. To find the correct overtime pay, we need to determine how many hours Ray worked in excess of his regular hours and the rate at which he receives overtime pay. Let's assume that Ray receives time-and-a-half for overtime work.
First, we need to find Ray's regular hours. If we assume his regular hours are 40 hours per week, we can subtract this from the total hours worked to find the overtime hours: 46 hours - 40 hours = 6 hours of overtime. Next, we need to calculate the overtime pay rate. If Ray gets paid $10 per hour for regular work, we'll calculate the overtime rate by multiplying his regular pay rate by 1.5: $10/hour x 1.5 = $15/hour. Finally, we can calculate Ray's actual overtime pay by multiplying the overtime hours by the overtime pay rate: 6 hours x $15/hour = $90.
Therefore, Ray's error was incorrectly calculating his additional pay as $45 instead of the correct amount of $90.
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Company A offers a $35,000 annual salary plus a 6% commission of his total sales. Company B offers a flat annual salary of $36,000.How much would you need to have in total sales to earn the same amount in each job?
Answer: you need to have in total sales of $16667 to earn the same amount in each job
Step-by-step explanation:
Let x represent the amount that you need to have in total sales in order to earn the same amount in each job.
Company A offers a $35,000 annual salary plus a 6% commission of his total sales. This means that the total amount earned with company A when x sales is made yearly would be
35000 + 0.06x
Company B offers a flat annual salary of $36,000. This means that the total amount earned with company B yearly would be
36000
To earn the same amount with both jobs,
35000 + 0.06x = 36000
0.06x = 36000 - 35000
0.06x = 1000
x = 1000/0.06 = $16667
Cluster sampling is _____. A. a probability sampling methodB. a nonprobability sampling methodC. the same as convenience samplingD. None of these answers are correct
Answer:
A.
Step-by-step explanation:
Probability sampling means that each unit in population has an equal chance or probability of selection in a sample.
Cluster sampling is a probability sampling method because population is divided into clusters at random and no personal judgement is involved. Thus, each cluster has equal probability of selecting and sampling is done as random. Hence, cluster sampling is a probability sampling method.
Cluster sampling is a probability sampling method. Here option A is correct.
It involves dividing the population into clusters or groups based on certain characteristics, such as geographical location or other relevant attributes. Then, a random sample of clusters is chosen, and all individuals within those selected clusters become part of the sample.
This method is considered probabilistic because each cluster has a known probability of being selected, and thus each individual within the chosen clusters has a chance of being included in the sample. This makes it possible to estimate population parameters and make statistical inferences.
Cluster sampling differs from other probability sampling methods, such as simple random sampling, in that it involves a multi-stage process.
It is particularly useful when it's impractical or too costly to gather a complete list of all individuals in the population, making it a valuable tool in various fields of research, including public health, sociology, and economics. Here option A is correct.
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Simplify the expression.
(9x + 1/2)+(4x − 8 1/2)
PLZ RESPOND QUICK THIS IS FOR A MIDTERM AND THEY ARE SO ANNOYING!!!
Answer:
The simplified expression is:
⇒ [tex]13x-8[/tex]
Step-by-step explanation:
Given expression:
[tex](9x + \frac{1}{2})+(4x-8\frac{1}{2})[/tex]
To simplify the given expression.
Solution:
In order to simplify, we will combine the like terms by removing the parenthesis.
We have:
⇒ [tex]9x + \frac{1}{2}+4x-8\frac{1}{2}[/tex]
Combining like terms.
⇒ [tex]9x+4x+\frac{1}{2}-8\frac{1}{2}[/tex]
⇒ [tex]13x+\frac{1}{2}-8\frac{1}{2}[/tex]
In order to combine fractions, we will combine the whole number and the fraction separately.
⇒ [tex]13x-8+(\frac{1}{2}-\frac{1}{2})[/tex]
⇒ [tex]13x-8+0[/tex]
Thus, the simplified expression is:
⇒ [tex]13x-8[/tex]
In a set of normally distributed test scores that have a mean of 100 and standard deviation of 15, it would be correct to conclude that approximately 68 percent of the scores would fall between _____ and _____.
Answer:
It would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 100
Standard Deviation, σ = 15
We are given that the distribution is a bell shaped distribution that is a normal distribution.
Empirical rule
Also known as 68-95-99.7 rule.It states that almost all data lies within three standard deviation of mean for a normal distribution.About 68% of data lies within one standard deviation of mean.About 95% of data lies within two standard deviation of mean.About 99.7% of data lies within three standard deviation of mean.Thus, approximately 68% of data will lie within one standard deviation of mean.
[tex]\mu - \sigma = 100-15 = 85\\\mu + \sigma = 100 + 15 = 115[/tex]
Thus, it would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.
68 percent of the scores would fall between 85 and 115.
Empirical ruleEmpirical rule states that for a normal distribution, about 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviation from the mean.
Given that mean(μ) = 100 and standard deviation (σ) = 15
68 percent of the scores would fall between μ ± σ = 100 ± 15 = 85, 115
68 percent of the scores would fall between 85 and 115.
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Warning! No identities used in the lesson may be submitted. Create your own using the columns below. See what happens when different binomials or trinomials are combined. Square one factor from column A and add it to one factor from column B to develop your own identity. Column A (x - y) (x + y) (y + x) (y - x) Column B (x2 + 2xy + y2) (x2 - 2xy + y2) (ax + b) (cy + d)
The question is asking to create a new mathematical identity by combining binomials and trinomials from two different columns. An example of such identity could be 2x2 + 2y2. We also used the appendix to solve a quadratic equation by completing the square.
Explanation:This question is asking you to combine binomials and trinomials from column A and column B to create a new mathematical identity. An example of creating such an identity could be squaring the binomial (x - y) from column A and adding it to the trinomial (x2 + 2xy + y2) from column B.
So, if we square (x - y), we get x2 - 2xy + y2. Adding that to x2 + 2xy + y2 from column B, we get 2x2 + 2y2, which is the new identity.
Also, using the appendix to solve an equation of the form ax² + bx + c = 0, we rearrange terms and complete the square to find x. Using the example of x² +0.0211x -0.0211 = 0, the factors of 0.0211 are easy to determine. After rearranging terms, the equation becomes (x +0.01055)² - 0.0211 = 0. Finally, to solve for x, you would add 0.0211 to both sides and then take a square root.
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help fast pleaese Given a pyramid l = w = 9.0 mm and V = 324.0 cubic mm , find h in mm.
(Enter a numerical answer)
Answer: h = 12mm
Step-by-step explanation:
The volume of a pyramid is given as :
V = [tex]\frac{1}{3}[/tex] lwh
Therefore:
324 = [tex]\frac{1}{3}[/tex] lwh
324 x 3 = 9 x 9 x h
Therefore:
h = 972/81
h = 12mm
If z varies jointly with x and y, x = 2 and y = 2, z = 7. Find z when x = 4 and y = 8.
Answer:
56
Step-by-step explanation:
z varies jointly with x and y:
z = kxy
When x = 2 and y = 2, z = 7.
7 = k(2)(2)
k = 7/4
z = 7/4 xy
When x = 4 and y = 8:
z = 7/4 (4)(8)
z = 56
Chris types at an average speed of 35 words per minute. He has already typed 1,500 words of his final paper. The paper has to be more than 3,250 words. Which of the following inequalities could be used to solve for x, the number of minutes it will take Chris to type his paper?
Answer:
1750 + 35x ≥ 3250
Step-by-step explanation:
Average speed = 35 words
He has already typed 1500 words on his final paper
The paper must be more than 3250 words.
To find at least how many more words he has to type, we will subtract 1500 from 3250
3250 - 1500 = 1750 words
The equation will be 35x ≥ 1750
x is the number of minutes
The equation could be
1750 + 35x ≥ 3250