Answer:
D
Step-by-step explanation:
The slope if before the x so in this case it's -3.
The y-intercept is at the end so it's -2.
Answer:
D. slope = -3 and y-intercept = -2
Step-by-step explanation:
Slope Intercept Form:
y - y₁ = m(x - x₁) (original version)y = mx + b (simplified version)The variables:
m ⇒ represents slopeb ⇒ represents the y-intercepty = -3x -2
m = -3b = -27.34 the gpas of all students enrolled at a large university have an approximate normal distribution with a mean of 3.02 and a standard deviation of .29. find the probability that the mean gpa of a random sample of 20 students selected from this university is
The probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher is 10.93%
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 normally distributed samples are solved using the z-score methods.
We know that, in a set with mean and standard deviation , the z-score of a measure X is given by:
Z = X - μ/σ
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 and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .
For a Skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
μ = 3.02 , σ = 0.29 , n = 20 and s = 0.29/√ 20 = 0.0648
Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
This is 1 subtracted by the p- value of Z when X = 3.10. So
By the Central Limit Theorem:
Z = X - μ / s
⇒ Z = 3.1 - 3.02/ 0.0648
⇒ Z = 1.23
The Z = 1.23 has a P- value of 0.8907
∴ 1 - 0.8907 = 0.1093
Now, for getting the percentage,
0.1093 × 100% = 10.93%
10.93% probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
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Does the equation y+x=45 2y+2x=6 have No solutions or infinite solutions
The equation, y + x = 45 and 2y + 2x = 6 has No Solution .
In the question ,
it is given that ,
the equations are y + x = 45 and 2y + 2x = 6 .
y = 45 - x
Substituting the value of y = 45 - x in the equation 2y + 2x = 6
we get ,
2(45 - x) + 2x = 6 ...by using associative property
Simplifying further ,
we get
90 - 2x + 2x = 6
90 = 6 .....because -2x+2x = 0
we know that 90 ≠ 6 ,
hence , the equations have No Solution .
Therefore , The equation, y + x = 45 and 2y + 2x = 6 has No Solution .
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SOME HELP FAST!! What is the slope of this line?
Answer:
-2/3
Step-by-step explanation:
70% of the class has a pet.
There are 30 kids in the class.
How many kids have a pet?
Answer: 21
Step-by-step explanation:
70x30/100
= 21
Hope this helps! :)
1. A revenue of $2000 is obtained from the sales of item A at $40 each and item B at $35 each. Write an
equation that shows the relationship between the numbers of items sold.
2. A revenue of $3000 is obtained from the sales of item A at $50 each and item B at $80 each. Write an equation that shows the relationship between the numbers of items sold.
Answer:
Step-by-step explanation:
Hi vengefull, :0 like that show on Netflix about revenge, huh :0 anyway, back to math.
the equation 1):
40*A+ 35*B=2000
the equation 2):
50*A + 80*B=3000
Points located on a function include: (3, 6), (-5, 7), (13, 1), and (7, 14). Which point cannot be included in the function?
A (14, 5)
B (5, 6)
C (7, 2)
D (8, 0)
The point cannot be included in the function is (7, 2). Therefore, option C is the correct answer.
The given coordinate points are (3, 6), (-5, 7), (13, 1), and (7, 14).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
A) (14, 5)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (14, 5) is included in the function.
It is a function as every input has a unique output.
B) (5, 6)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (5, 6) is included in the function.
It is a function as every input has a unique output.
C) (7, 2)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (7, 2) is not included in the function.
Since the element 7 corresponds to two different images i.e., 14 and 2.
D) (8, 0)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (8, 0) is included in the function.
It is a function as every input has a unique output.
The point cannot be included in the function is (7, 2). Therefore, option C is the correct answer.
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On a map with a scale 1: 100,000, the distance between two cities is 12 cm. What would be the distance between these two cities on a different map with a scale 1:300,000?
The distance between these two cities on a different map with a scale 1:300,000 is 4vm
How to calculate the distance?From the information, on the map with a scale 1: 100,000, the distance between two cities is 12 cm.
In this case, the distance between these two cities on a different map with a scale 1:300,000 will be:
= (100000 / 300000) × 12
= 1/3 × 12
= 4cm
The distance is 4cm.
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What is the equation of the line that passes through the point (-1,5) and has a slope of -3
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-1)}) \implies y -5= -3 (x +1) \\\\\\ y-5=-3x-3\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}[/tex]
complete the recursive formula of the arithmetic sequence calculator -5,-25,-45,-65
The recursive formula of the arithmetic sequence calculator -5, -25, -45, and -65 is an = -20n + 15
The arithmetic sequence is
-5,-25,-45,-65
The initial term = -5
The common difference = The second term - The first term
= -25 - (-5)
= -25 + 5
= -20
The nth term of the arithmetic sequence is
an = a+(n- 1)d
When an is the nth term
a is the initial term
d is the common difference
Substitute the values in the equation
an = -5 +(n-1)( -20)
Apply the distributive property
an = -5 -20n + 20
an = -20n + 15
Hence, the recursive formula of the arithmetic sequence calculator -5,-25,-45,-65 is an = -20n + 15
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x varies inversely as the square of y. If x= 6 when y = 2, then the value of x when y = 8 will be
Answer: 24
Step-by-step explanation:
You can use proportions to calculate this:
[tex]\frac{6}{2} =\frac{x}{8} \\\\2x=6*8\\\\2x=48\\\\x=\frac{48}{2} =24[/tex]
emma estimated the
first digit in the quotient of 2,183 ÷ 42 as 4. She adjusted the quotient to 3. What did she do wrong? Explain how Emma can avoid her mistake.
Quotient is 51.97 by dividing 2,183 by 42. A quotient is the amount that results from dividing two numbers.
How to divide a number ?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.
Multiply the first fraction by the reciprocal of the second to divide rational expressions. We factor everything and search for common factors after rewriting the division as multiplication of the first statement by the reciprocal of the second. Separate logical expressions.
The number 2183 is called the numerator or dividend, and the number 42 is called the denominator or divisor.
The quotient of 2183 and 42, the ratio of 2183 and 42, as well as the fraction of 2183 and 42 all mean (almost) the same:
2183 divided by 42, often written as 2183/42.
2183/42 = 51.97
The answer that is quotient is 51.97
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The mistake she done is that the acutal quotient is 51.97.
How to divide a number ?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.Multiply the first fraction by the reciprocal of the second to divide rational expressions. We factor everything and search for common factors after rewriting the division as multiplication of the first statement by the reciprocal of the second. Separate logical expressions.The number 2183 is called the numerator or dividend, and the number 42 is called the denominator or divisor.
The quotient of 2183 and 42, the ratio of 2183 and 42, as well as the fraction of 2183 and 42 all mean (almost) the same:
2183 divided by 42, often written as 2183/42.
2183/42 = 51.97
The answer that is quotient is 51.97
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100 Points Please help ASAP
Question 1(Multiple Choice Worth 1 points)
(04.07 LC)
Data were collected and showed an increase in ice cream sales as the weather gets warmer.
Which of the following best describes this situation?
Based on the data, this is an example of correlation and causation.
Based on the data, this is an example of correlation.
Based on the data, this is an example of causation.
Based on the data, this is not an example of causation or correlation.
Question 2(Multiple Choice Worth 1 points)
(04.07 MC)
Trey believes there is a correlation between the number of texts sent in class and GPA. He collected data and found that the line of best fit for the data can be modeled by the equation y = 3.9 − 0.3x.
Identify the slope and the type of association.
The slope is −3.9, which indicates a negative correlation.
The slope is 3.9, which indicates a positive correlation.
The slope is 0.3, which indicates a positive correlation.
The slope is −0.3, which indicates a negative correlation.
Question 3(Multiple Choice Worth 1 points)
(04.07 MC)
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
Question 4(Multiple Choice Worth 1 points)
(04.07 MC)
Based on the time recorded for 700 attendees at an amusement park, the average amount of time spent at the park was 7.25 hours with a margin of error of ±1.65 hours. If 3,000 people attended the park on a given day, what is the estimated range of total hours the attendees spent in the park?
8,375 to 16,800 total hours spent in the park
16,800 to 21,785 total hours spent in the park
16,800 to 26,700 total hours spent in the park
16,800 to 35,885 total hours spent in the park
Question 5(Multiple Choice Worth 1 points)
(04.07 MC)
Data regarding fuel efficiency of an airliner were collected. The graph shows the correlation between the distance traveled (in thousands of miles) and the altitude (in thousands of feet):
image of a scatter plot with Distance Traveled on the x axis and Altitude on the y axis with 2 comma 2, 3 comma 10, 5 comma 15, 10 comma 20, 15 comma 15, 18 comma 10, and 19 comma 2
Estimate the average rate of change from x = 15 to x = 19.
−3.25
4
−4
−0.31
Question 6(Multiple Choice Worth 1 points)
(04.07 MC)
An observational study determined that there is a strong correlation between sitting close to the television and poor eyesight. Can it be determined that sitting too close to the television causes poor eyesight? Explain.
Causation cannot be proven because everyone watches television.
Causation can be proven because it is well known that sitting close to the television causes poor eyesight.
Causation can be proven because an experiment was used to prove this hypothesis.
Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.
Question 7(Multiple Choice Worth 1 points)
(04.07 LC)
Aretha wanted to gather data about the cost of local bowling leagues in her area. She plotted the data and determined that the average bowling league costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 20.
Identify and interpret the y-intercept in this model.
The y-intercept is 20. This is the cost per month.
The y-intercept is 20. This is the cost of registration.
The y-intercept is 15. This is the cost of registration.
The y-intercept is 15. This is the cost per month.
Question 8(Multiple Choice Worth 1 points)
(04.07 MC)
Analyze the following statement:
Marcus notices that he runs faster in the mornings rather than the evenings.
Is the statement an example of correlation or causation?
Correlation, because time of day doesn't cause a person to run faster or slower
Causation, because Marcus has noticed this over several trials
No relationship, because time of day has nothing to do with how fast a person runs
There is not enough information to make a conclusion
Question 9(Multiple Choice Worth 1 points)
(04.07 MC)
A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$52,815
$53,700
$54,915
$56,300
Question 10(Multiple Choice Worth 1 points)
(04.07 MC)
The price of milk has been increasing over the last month. Audrey believes there is a positive correlation between the number of predicted storms and the price of milk.
Number of Storms Predicted Milk Price
1 $2.70
3 $2.89
4 $3.50
6 $3.88
7 $3.91
Use the table to determine the average rate of change from 3 to 6 storms.
3
0.98
1.21
0.33
Answer:
1.Based on the data, this is an example of correlation and causation.
2.The slope is −0.3, which indicates a negative correlation.
3.$5972.65
4.16,800 to 26,700 total hours spent in the park.
5. -3.25
6.Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.
7.The y-intercept is 20. This is the cost of registration.
8.Correlation, because time of day doesn't cause a person to run faster or slower
9.$53,700
10.0.33
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Comment if u need explanation of any answer
Noah is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Noah made a total of 11 shots altogether and scored a total of 29 points. Write a system of equations that could be used to determine the number of two point shots noah made and the number of three point shots he made. Define the variables that you use to write the system.
The system of equations is x + y = 11 and 2x + 3y = 29 and variables are x and y.
Let us assume the number of two point shots be x and the number of three point shots be y. Forming the equation now -
x + y = 11 : Equation 1
2x + 3y = 29 : Equation 2
Rewriting the equation 1 as per x.
x = 11 - y : Equation 3
Keep the value of x form equation 3 in equation 2
2(11 - y) + 3y = 29
Performing multiplication on Left Hand Side of the equation
22 - 2y + 3y = 29
y = 29 - 22
y = 7
Keep the value of y in equation 3.
x = 11 - 7
x = 4
So, the two point shots are 4 and three points shots are 7. The variables are x and y and system of equations are equation 1 and equation 2.
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APProximate the following numbers to The nereast thousand.
1• 6203
Answer:
the answer should be 6000
These tables represent a quadratic function with a vertex at (0, -1). What is
the average rate of change for the interval from x = 8 to x = 9?
OA. -82
OB. -17
C. -65
D. -2
x y
0
1
23456
125
-10
-17
-26
-37
Interval
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
Average rate
of change
-1
-3
-5
-7
-9
-11
3-2
1-2
3-2
1-2
3-2
Answer:
B
Step-by-step explanation:
We can notice that based on the given pattern, the average rate of change from [tex]x=n[/tex] to [tex]x=n+1[/tex], where [tex]n \in \mathbb{Z}[/tex], is [tex]-2n-1[/tex].
So, the average rate of change from [tex]x=8[/tex] to [tex]x=9[/tex] is [tex]-2(8)-1=-17[/tex].
The rate of change for the interval from x = 8 to x = 9 is -17.
What is Rate of change?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.
We know the standard form of quadratic function
y = a (x - b)² + c with vertex (b, c)
Since the vertex is (0, -1) then b= 0, c= -1.
Then, the quadratic equation is:
y= ax² - 1 passes through (1, 2), (2, -5),.....
So, the rate of change in interval (8, 9) is
= y(9)- y(8)/ (9-8)
= -9² -1 - 8² - 1/ 1
= -17.
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Need help!! Hurry!!!!!
A model train goes 8 inches in 2 seconds.
1. Calculate two unit rates for the model train and enter them in the table.
2. Explain the meaning of each of the numbers you found.
Answer:
16
Step-by-step explanation:
8 x 2 = 16 16 - 8 =2
Answer:
16......................
A sports ball has a diameter of 10 cm. Find the volume of the ball.
cm.3
Round your answer to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
take the radius which is 5 square it 5^2 and divide by 3 then round hope it helps
Answer: 8,33333333333333333
Step-by-step explanation: 5^2 =25 divided by 3 is 8,33333333333333333
what is the slope of this line a) 1/4 b) 4 c) -1/4 the 1 is not negitive the / is negitive d) -4
to get the slope of any straight line, we simply need two points off of it, so let's use those two in the picture below.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-8}{1 +1} \implies \cfrac{ -8 }{ 2 } \implies - 4[/tex]
based on the results of the simulation, is there convincing statistical evidence at the significance level of 0.05 that the event of audrey selling at least 7 of the 30 selected tickets is unlikely to have occurred by chance alone? responses yes, because the distribution of the trials in the simulation is skewed to the right. yes, because the distribution of the trials in the simulation is skewed to the right. yes, because the number in the histogram with the greatest frequency is 4, not 7. yes, because the number in the histogram with the greatest frequency is 4, not 7. yes, because 7 appears in the right tail of the distribution, indicating that it is more than 2 standard deviations away from the mean. yes, because 7 appears in the right tail of the distribution, indicating that it is more than 2 standard deviations away from the mean. no, because the simulation suggests that it is likely that audrey could sell anywhere from 0 to 11 of the selected tickets. no, because the simulation suggests that it is likely that audrey could sell anywhere from 0 to 11 of the selected tickets. no, because the simulation suggests that audrey selling at least 7 of 30 selected tickets would occur about 13.8% of the time.
No, there isn't any statistical proof because, according to the simulation, Audrey would sell at least 7 out of the 30 chosen tickets roughly 13.8% of the time.
What exactly is statistical proof?
A type of explanation known as statistical evidence is one that is based on information that has been gathered and then assessed using a mathematical model.
Based on the information provided, the students created the following simulation:
Choose 88 red chips and the rest 600 blue chips.
30 chips are chosen at random, with no replacements.
When choosing the 30 chips, keep track of and record the amount of red chips.
Therefore, we may say that there is no statistical proof that the occurrence happened by chance alone at = 0.05.
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Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
15x2
The given polynomial is a binomial and the degree is 2.
What are the various degrees of polynomial ?In a given expression if we have to know the degree of the polynomial we must look at the HIGHEST degree of the polynomial. This along with the table given below will help us identify the degree of the polynomial.
Degree 0 Constant Polynomial
Degree 1 Linear Polynomial
Degree 2 Quadratic Polynomial
Degree 3 Cubic Polynomial
Degree 4 Quartic Polynomial
The above mentions the various degrees of the polynomial , you may refer to it for future references .
The given expression is [tex]15x^2[/tex]
since the degree of the given polynomial is 2
the given is a binomial polynomial .
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What is the rectangular form of Theta = StartFraction 3 pi Over 4 EndFraction? x − y = 0 x − y = 1 x + y = 0 x + y = 1
The rectangular form of Theta = StartFraction 3 pi Over 4 EndFraction is x + y = 0.
What are polar coordinates?The polar coordinates system is a two-dimensional coordinate system in which each point is determined by distance from the point and an angle from the reference direction.
This is about converting polar coordinate to rectangular form.
Relationship between coordinates is:
x = r cosθ
y = r sinθ
then;
y/x = sinθ/cosθ
y/x = tanθ
We have θ = 5π/6, finding the value of tan:
tan 5π/6 = tan (π - π/6)
= - 1/√3
= - √3/3
Now Substitute tan with its value:
y/x = -√3/√3
√3y = -√3x
y + x = 0
x + y = 0
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Answer:
c on edge
Step-by-step explanation:
in september 2011, gallup surveyed 1,004 american adults and asked them whether they blamed barack obama a great deal, a moderate amount, not much, or not at all for u.s. economic problems. the results showed that 53% of respondents blamed barack obama a great deal or a moderate amount. using these data, we calculated a 99% confidence interval of (0.489, 0.571) for the proportion of all american adults who blame barack obama a great deal or a moderate amount. does the confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems?
The 99% confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems is (0.571, 0.489).
In the given question we have to find the confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems.
Gallup surveyed 1,004 american adults.
So n=1004
The results showed that 53% of respondents blamed barack obama a great deal or a moderate amount.
So p=53% = 0.53
The 99% confidence interval for the proportion of all american adults who blame barack obama a great deal or a moderate amount for u.s. economic problems is
CI=p±z× √{p(1−p)}/n
Now finding the value of z for 99% confidence interval.
The z critical value at 99% confidence interval is 2.575.
Now putting the value
CI=0.53±2.575× √{0.53(1−0.53)}/1004
CI=0.53±2.575× √(0.53*0.47)/1004
CI=0.53±2.575× √0.2491/1004
CI=0.53±2.575× √0.00025
CI=0.53±2.575× 0.0158
CI=0.53±0.0407
CI=(0.53+0.0407, 0.53−0.0407)
CI=(0.571, 0.489)
Hence, the 99% confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems is (0.571, 0.489).
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HELP ASAP PLEASE!!!!
and if you can pls tell the steps on how you get the answer
Given: (GH) is a midsegment of ∆DEF. Show all work.
a. Find the value of x and y.
b. What is the length of DF?
Applying the triangle midsegment theorem:
a. x = 17; y = 2
b. Length of DF = 20 units.
What is the Triangle Midsegment Theorem?The triangle midsegment theorem states that the midsegment of a triangle is always parallel to the third side, and has a length that is half the length of the third side of the triangle.
GH is said to be the midsegment of triangle DEF, therefore:
a. GH = 1/2(EF) [triangle midsegment theorem]
Substitute
x - 3 = 1/2(28)
2(x - 3) = 28
2x - 6 = 28
2x = 28 + 6
2x = 34
2x/2 = 34/2
x = 17
HF = x - 7
Plug in the value of x
HF = 17 - 7
HF = 10
HF = DH = 10
y + 8 = DH
y + 8 = 10
y = 10 - 8
y = 2
b. Length of DF = HF + DH
Length of DF = 10 + 10 = 20 units.
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Which of the following is true of prime numbers?
A.
A prime number may be an even number or an odd number.
B.
A prime number is always an even number.
C.
A prime number is always an odd number.
D.
A composite number may be an even number or an odd number.
Answer:
C
Step-by-step explanation:
Prime numbers are only divisible by themselves and 1 ....all even numbers are divisible by '2' , so all primes are odd numbers
Yesterday was the first playoff game for the Culver City Cyclones baseball team. The
stadium's manager predicted attendance at the game would be 5,600 fans. Unfortunately, the
threat of a storm caused many to stay home, and his prediction wound up being 28% higher
than the actual attendance. What was the actual attendance at the baseball game?
The actual attendance at the baseball game is 7168 fans
What is meant by percentage?A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. The abbreviations "pct," "pct," and occasionally "pc" are also used to represent percentage in addition to the symbol "%". A% has neither a recognized unit of measurement nor any dimensions. Take this as an example: There will be 50 men in the class if there are 100 students total and there are 50 men in the class. There are 250 male students overall, or 250 out of 500.
Given,
The actual attendance at the game=5600 fans
Also given that, the threat of a storm caused many to stay home, and his prediction wound up being 28% higher than the actual attendance.
Then,
28% of 5600
=5600×(28/100)
=1568
Total=5600+1568
Total=7168
Therefore, the actual attendance at the baseball game is 7168 fans.
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Answer:
4,375 fans
Step-by-step explanation:
percent error= amount of error/correct amount
1.28x=5600
1.28x/1.28= 5000/1.28
x=4375
Steven's birthday party will cost $168 if he invites 14 guests. If there are 59 guests, how much will Steven's birthday party cost? Solve using unit rates.
Calculated using unit rates, Steven's birthday party will cost him $ 708 if he were to invite 59 guests.
If the party will cost him $168 for him to invite 14 guests, then we will need to calculate the cost for each guest using unit rates.
if 14 guests = $168,
1 guest = 168/14 = $12
so it will cost him $12 per guest he invites
Knowing that each guest will cost him $12, then if Steven wants to invite 59 guests to his birthday party, he will be spending:
59 × $12 = $708
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Select the correct answer.
Which graph is the graph of f(x) = x³ - 10x² + 16x?
OA.
B.
-5
4
-3 -2
-3
-2
-3
-4
-5
2
-3
5
The graph of the cubic equation, f(x) = x³ - 10x² + 16x, is shown below
Graph of Cubic equationFrom the question, we are to determine graph of the given cubic equation.
The given cubic function is
f(x) = x³ - 10x² + 16x
To graph the equation, we will determine the value of f(x) for certain values of x
When x = 0
f(x) = x³ - 10x² + 16x
f(x) = (0)³ - 10(0)² + 16(0)
f(x) = 0
When x = 2
f(x) = x³ - 10x² + 16x
f(x) = (2)³ - 10(2)² + 16(2)
f(x) = 0
When x = 5
f(x) = x³ - 10x² + 16x
f(x) = (5)³ - 10(5)² + 16(5)
f(x) = -45
When x = 8
f(x) = x³ - 10x² + 16x
f(x) = (8)³ - 10(8)² + 16(8)
f(x) = 0
When x = 10
f(x) = x³ - 10x² + 16x
f(x) = (10)³ - 10(10)² + 16(10)
f(x) = 160
Using the determined points above, the graph of the cubic equation is shown below
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HELP!!!!!PLEASE!! ASAPPP
By calculating the percentage of earnings, we find out that Gary earns more money in one week as compared to Tara. Gary earns $900 and Tara earns $705 in one week. Therefore, the last option is correct.
It is given to us that -
Gary and Tara work as tutors at two different test prep companies
In a week, Gary earns 45% of the $2000 collected from the pupils
In the same week, Tara earns 20% of the $3,525 collected from the pupils
We have to find out who earns more money in a week.
We know that, in a week, Gary earns 45% of the $2000 collected from the pupils. This implies earning of Gary in a week
= 45% of 2000
= $900
Similarly, we know that, in the same week, Tara earns 20% of the $3,525 collected from the pupils. This implies earning of Tara in the same week
= 20% of 3,525
= $705
Thus, by calculating the percentage of earnings, we can see that Gary earns more money in one week. Gary earns $900 and Tara earns $705 in one week. Therefore, the last option is correct.
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