Answer:
Y = 0.4925X - 22.26 ;
(-12.413, 13.398) ;
Yes, there is
Step-by-step explanation:
X = IQ Score ; Y = musical aptitude
The regression equation from the table given using the slope and intercept coefficient :
Y = 0.4925X - 22.26
0.4925 = slope ; Intercept = - 22.26
The 95% confidence interval of the slope :
Confidence interval = b ± Tcritical*SE
Tcritical at 95%, df = n - 2 = (20 - 2) = 18
Tcritical = 2.1009
b = slope Coefficient = 0.4925
S.E = 6.143
Hence, we have :
Confidence interval = 0.4925 ± (2.1009 * 6.143)
Confidence interval = 0.4925 ± 12.9058287
Lower boundary = 0.4925 - 12.9058287 = - 12.413
Upper boundary = 0.4925 + 12.9058287 = 13.398
(-12.413, 13.398)
There is a significant relationship between IQ score and musical aptitude because, 0 is within the confidence interval obtained.
Which expression is equivalent to 3/56x^7y^5 , if x ≠0 and y≠0
Answer:
[tex]2x^2y\sqrt[3]{7xy^2}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt[3]{56x^7y^5}[/tex]
Required
Solve
Expand
[tex]\sqrt[3]{8*7*x^6*x*y^3*y^2}[/tex]
Rewrite as:
[tex]\sqrt[3]{8*x^6*y^3*7*x*y^2}[/tex]
Split
[tex]\sqrt[3]{8*x^6*y^3} *\sqrt[3]{7*x*y^2}[/tex]
Express 8 as 2^3
[tex]\sqrt[3]{2^3*x^6*y^3} *\sqrt[3]{7*x*y^2}[/tex]
Apply law of indices
[tex]2^{(3/3)}*x^{(6/3)}*y^{(3/3)} *\sqrt[3]{7*x*y^2}[/tex]
[tex]2*x^2*y *\sqrt[3]{7*x*y^2}[/tex]
[tex]2x^2y *\sqrt[3]{7xy^2}[/tex]
[tex]2x^2y\sqrt[3]{7xy^2}[/tex]
What is the value of x?
O A. x=15
O B. x=10
O C. x=20
D. x=5
When purchasing a new Cell Phone Plan you are given two pay options (Both included
unlimited text):
With Plan A, you can pay 23 cents per minute. This can be represented by the equation
C= 0.23m
With Plan B, you can pay 19 cents per minute plus a flat fee of $9.00. This can be
represented by the equation c = 0.19m + 9.00
Complete the following steps to determine how many minutes you would need to use for
Plan B to be less expensive than Plan A
Answer:
225 and greater
Step-by-step explanation:
900/4 or 900 cents/ 4 cents equals 225 on calculator
We use 225 minutes for Plan B to be less expensive than plan A.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
For plan A,
We can pay 23 cents per minute.
This can be represented by the equation,
C= 0.23m
For plan B,
We can pay 19 cents per minute plus a flat fee of $9.00.
This can be represented by the equation,
C = 0.19m + 9.00
Now, To find the minutes for plan B is less expensive than plan B
We can write an inequality that represent,
Plan A < Plan B
0.23m < 0.19m + 9
0.23m - 0.19m < 9
0.04m < 9
Divide 0.04 both side,
m < 225
Thus, We use 225 minutes for Plan B to be less expensive than plan A.
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Megan is reading a book about the tallest tree in the world, the redwood tree. One of the trees she reads about grew 300 feet tall over 150 years. If the tree grew at a steady rate, how many inches did it grow each year?
Answer:
24 inches per year
Step-by-step explanation:
Given that the growth of the red wood tree is about :
300 feet tall in over 150 years ;
Given a steady growth ;
The growth per year is given by :
Height / number of years
300 fts / 150 years
= 2 feets per year
1 Feet = 12 inches
2 feets per year = 24 inches per year
In 2009, a diabetic express company charged $38.85 for a vial of type A insulin and $30.34 for a vial of type B insulin. If a total of $1695.71 was collected for 50 vials of insulin, how many vials of each type were sold?
The number of vials of type A insulin sold were ___ and the number of vials of type B insulin sold were ____
Answer:
The number of vials of type A insulin sold were _21__ and the number of vials of type B insulin sold were __29__.
Step-by-step explanation:
Let a = number of type A vials.
Let b = number of type B vials.
38.85a + 30.34b = 1695.71
a + b = 50
38.85a + 30.34b = 1695.71
(+) -38.85a - 38.85b = -1942.50
---------------------------------------------------
-8.51b = -246.79
b = 29
a + b = 50
a + 29 = 50
a = 21
Answer: The number of vials of type A insulin sold were _21__ and the number of vials of type B insulin sold were __29__.
Please help meeeeeeeeee I’ll award brainliest
Answer:
should be also 63 and 70 move them up
Step-by-step explanation:
interior angles are angles that are the same
sometimes you have to divide the diamter by 2 to get the radius.
true
false
it is true
tbh am not sure
What is h(−8) for h(x)=1/4x^2+7x?
Answer:
h(-8) = -40
Step-by-step explanation:
Find h(-8) by plugging in -8 as x:
h(x) = 1/4x² + 7x
h(-8) = 1/4(-8)² + 7(-8)
Simplify:
h(-8) = 1/4(64) - 56
h(-8) = 16 - 56
h(-8) = -40
So, the answer is h(-8) = -40
The value of h(-8) is -40.
What is quadratic equation?Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Given:
h(x)=1/4x²+7x
h(-8)= 1/4* 64+7*(-8)
= 16-56
= -40
Hence, h(-8)=-40.
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I need help with #5. Please help. I have to show all work so please explain
Answer:
d = 13
Step-by-step explanation:
Use distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d=\sqrt{(5-0)^2+(5-(-7))^2}\\d=\sqrt{5^2+12^2}\\d=\sqrt{25+144}\\d=\sqrt{169}\\d=13[/tex]
Conceptual Set 1. A different researcher takes a sample of recently widowed spouses to measure how many times they leave the house. She wants to see if her sample is different from the population mean, which she knows to be 23.00. Which type of t-test should she use
Answer:
One sample t-test
Explanation:
The one sample t-test , also called single sample t test is a type of t test that measures the difference between a population mean and a hypothesized value,in this case the sample mean of widowed spouses that leave the house. The sample mean/hypothesized value is called the test value while the population mean is called the test variable. The one sample t test can only compare one sample mean to another given mean and not the mean of two samples or more.
Question Help
In a study of cell phone usage and brain hemisphen dominance, an Internet survey was e-mailed to 6957 subjects randomly selected from an online group involved with ears. There were 1319 surveys returned Use a 0.01
significance level to test the claim that the return rate is less than 20% Use the P-value method and use the normal distnbution as an approximation to the binomial distrbution
Identify the null hypothesis and alternative hypothesis
Answer:
The null hypothesis is [tex]H_0: p \geq 0.2[/tex]
The alternative hypothesis is [tex]H_1: p < 0.2[/tex]
The p-value of the test is of 0.0154 > 0.01, which means that at the 0.01 significance level, there is not significant evidence that the return rate is less than 20%.
Step-by-step explanation:
Test the claim that the return rate is less than 20%.
At the null hypothesis, we test if the return rate is of at least 20%, that is:
[tex]H_0: p \geq 0.2[/tex]
At the alternative hypothesis, we test if the return rate is less than 20%, that is:
[tex]H_1: p < 0.2[/tex]
Normal distribution as an approximation to the binomial distribution to find the Z-score.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
0.2 is tested at the null hypothesis. Sample of 6957.
This means that [tex]p = 0.2, n = 6957[/tex]. So
[tex]\mu = E(X) = np = 6957*0.2 = 1391.4[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{6957*0.2*0.8} = 33.36[/tex]
1319 surveys returned
This means that, due to continuity correction, [tex]X = 1319 + 0.5 = 1319.5[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1319.5 - 1391.4}{33.36}[/tex]
[tex]Z = -2.16[/tex]
P-value of the test:
The p-value of the test is the probability of 1319 or less people returning the survey, which is the p-value of Z = -2.16.
Looking at the z-table, Z = -2.16 has a p-value of 0.0154.
The p-value of the test is of 0.0154 > 0.01, which means that at the 0.01 significance level, there is not significant evidence that the return rate is less than 20%.
please help
with this !!!
Exercise 1.3
1. There are 10,785 English books, 8,973 Hindi books and 4,766 books on other languages in a library.
books are there in all in the library?
[tex]10.785 \times 8.973 \times 4.766[/tex]
Answer:
There are 24,524 books total.
Step-by-step explanation:
If you are asking for the total then you would just add 10785 and 8973 and 4766.
[tex]10785 + 8973+4766= 24524[/tex]
A local running group collected data on the number of miles its group members run each week, x, and their average mile time, y. The results are shown in the table below. Weekly Mileage, x 10 25 12 10 15 20 22 25 20 24 Avg. Mile Time, y 9.3 8.75 8.2 5.5 6.3 8.5 6.7 6.35 5.45 6.25 Calculate the correlation coefficient using technology and interpret what it represents. The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, the average mile time decreases. The correlation coefficient of the data is 0.87, which means as the weekly mileage increases, the average mile time increases. The correlation coefficient of the data is 0.87, which means as the weekly mileage increases, it has no affect on the average mile time. The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.
Answer:
The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.Step-by-step explanation:
The correlation coefficient of a data set describes how closely related two variables are. Correlation coefficients close to positive 1 show a strong positive correlation, while correlation coefficients close to negative 1 show a strong negative correlation. When a correlation coefficient is close to 0, it shows no correlation between the data.
For the given data set, calculate the correlation coefficient using technology.
This r-value is closer to 0 then it is to -1. Thus, the correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.
Answer:
The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.Step-by-step explanation:
The correlation coefficient of a data set describes how closely related two variables are. Correlation coefficients close to positive 1 show a strong positive correlation, while correlation coefficients close to negative 1 show a strong negative correlation. When a correlation coefficient is close to 0, it shows no correlation between the data.
For the given data set, calculate the correlation coefficient using technology.
This r-value is closer to 0 then it is to -1. Thus, the correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.
Use the given values to complete to each table.
PLEASE HELP.
Answer:
1. 10,12,14
2. 10,16,20
3. 3,23,61
Step-by-step explanation:
for example 2(3+r)
r would be 2 but it gave you that on the chart in the highlighted area
u replace it and it becomes 2(3+2)
distribute 2 and 3 and it becomes 6 then distribute 2 and 2 which becomes 4 then you add 6+4 which gives u 10 which is the first answer.
is the point (2,5) a solution to the equation y=3x-5?
Answer and Step-by-step explanation:
To figure out, we plug in the x-value into the equation and see if it is equal to the y-value.
y = 3(2) - 5
y = 6 - 5
y = 1
5 ≠ 1
The point (2, 5) is not a solution.
#teamtrees #PAW (Plant And Water)
We need to find the numerator and denominator of the quotient.
Answer:
[tex] \dfrac{(x - 2)^2}{(x - 1)^2} [/tex]
Step-by-step explanation:
[tex] \dfrac{x^2 + x - 6}{x^2 - 6x + 5} \div \dfrac{x^2 + 2x - 3}{x^2 - 7x + 10} = [/tex]
[tex] = \dfrac{x^2 + x - 6}{x^2 - 6x + 5} \times \dfrac{x^2 - 7x + 10}{x^2 + 2x - 3} [/tex]
[tex] = \dfrac{(x + 3)(x - 2)}{(x - 1)(x - 5)} \times \dfrac{(x - 5)(x - 2)}{(x - 1)(x + 3)} [/tex]
[tex] = \dfrac{(x + 3)(x - 2)(x - 5)(x - 2)}{(x - 1)(x - 5)(x - 1)(x + 3)} [/tex]
[tex] = \dfrac{(x - 2)(x - 2)}{(x - 1)(x - 1)} [/tex]
[tex] = \dfrac{(x - 2)^2}{(x - 1)^2} [/tex]
1. What term means "per hundred"?
A base B. percent
C. percentage
D.rate
2. Which of the following is correct?
A. 33% = 0.33 B. 33% = 03.3
C.33% = 33
D. 33% = 3.03
3. 45% of the grade 5 pupils are girls. Express 45% as decimals.
A. 0.045 B. 0.45
C. 4.5
D. 45.0
4. In the statement 35% of 600 = 210. Which is the percentage?
A. 35%
B. 600
C.210
D. none
5. Which does not belong?
A. 21%
B. 21/100 C. 21:100 D. 21
6. Which element of percent represent part of the whole?
A. base B. percent C. percentage D.rate
7. In a survey on the choice of pizza, 900 out of 1500 people preferred brand A to B.
What percent preferred A? What is the missing element?
A. base B. percent
C. percentage D. rate
8. What is the missing element in the problem, "A big theater has 1400 seats. During a
concert, it is 95% full. How many seats were taken?"
A. base B. percent
C. percentage
D. rate
9. Which element of percent represents the whole?
A. base B. percent
C. percentage D.rate
10. How many is 75% of a class?
A. 1/3 B. 1/2 C.3/4 D. 5/6
Answer:
1. B
2. B
3. B
4. A
5. D
6. A
7. C
8. D
9. A
10. C
Complete the conversion. Enter your answer in the box. 40 cm = m
Work out the equation of the line which passes through the point (-1,2)
and is parallel to the line y = x + 4.
Answer:
m = 1 (since the gradient of parallel lines is the same)
Then substitute point (-1;2)
C = 3
y = x+3
2. What is the equation of a line that has a slope of 3 and a y-intercept of
-2?
y=-3x + 2
y = 3x + 2
y = 3x - 2
3x - 2y = 6
Answer:
y=3x-2
Step-by-step explanation:
y = mx + b
m = slope
b=yint
y=3(slope)x+ -2(y int)
Translate and solve: 46 less than y is at least -184
Translate: y - 46 > -184
Possible answer: y > - 138
Solution:
y - 46 > -184
= y > - 184 + 46
= y > - 138
#CarryOnLearning
The Possible answer of the given statement could be as y > - 138.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true.
Such values are called solution to that equation or inequality.
A Set of such values is called solution set to the considered equation or inequality.
Given information; 46 less than y is at least -184
To Translate: y - 46 > -184
WE can solve it as;
y - 46 > -184
y > - 184 + 46
y > - 138
Therefore, The Possible answer of the given statement could be as y > - 138.
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Which of the following expressions is equivalent to 12x - 3 + 2x + 13?
Select all that apply.
A. 10x + 16
B. 14x + 16
C. 17x + 13
D. 2(7x+5)
E. 14x + 10
Answer:
D and E
Step-by-step explanation:
The simplified expression is 14x + 10.
The correct option is E (14x + 10), which matches the simplified form of the original expression.
To simplify the expression 12x - 3 + 2x + 13, we can combine like terms. Like terms are terms that have the same variable(s) raised to the same exponent(s).
First, we combine the x terms, which are 12x and 2x. Their sum is 14x.
Next, we combine the constant terms, which are -3 and 13. Their sum is 10.
Therefore, the simplified expression is 14x + 10.
Among the given options, the expression 14x + 10 is the correct one.
Option A (10x + 16) is not equivalent to the original expression because it does not combine the x terms correctly.
Option B (14x + 16) is not equivalent to the original expression because it does not account for the constant term correctly.
Option C (17x + 13) is not equivalent to the original expression because it combines the x terms incorrectly and does not account for the constant term correctly.
Option D (2(7x+5)) is not equivalent to the original expression because it is a different expression altogether, factoring out the common factor of 2 from the terms.
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If (3y-9)^2+7=43, then what is(are the values of y?
Answer:
y = 1 and y = 5
Step-by-step explanation:
[tex]( 3 y -9)^2 + 7 = 43\\\\((3y)^2 + (-9)^2 + 2(3y)(-9)) = 43 - 7\\\\(9y^2 + 81 -54y) = 36\\\\9y^2 -54y + 81 -36 = 0\\\\9y^2 -54y + 45 = 0\\\\9(y^2 -6y + 5) = 0\\\\y^2 - 6y + 5 = 0\\\\y^2 - 5y - y + 5 = 0\\\\y(y - 5) -1(y - 5 ) = 0 \\\\( y - 1 )( y - 5) = 0\\\\y = 1 \ , \ y = 5[/tex]
The values of y in the equation (3y-9)^2+7 = 43 are 1 and 5
How to solve for y?The equation is given as:
(3y-9)^2+7 = 43
Subtract 7 from both sides of the equation
(3y - 9)^2 = 36
Take the square root of both sides
3y - 9 = ±6
Add 9 to both sides
3y = 9 ± 6
Divide through by 3
y = 3 ± 2
Expand
y = (3 - 2 or 3 + 2)
Evaluate
y = 1 or 5
Hence, the values of y are 1 and 5
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Calculating area of rectangle
Your measurments Another student's measurements
Length (cm) 20.70 20.74
Width (cm) 10.44 10.46
Area (cm2)
Required:
Why might two students have different calculated areas when measuring the same rectangle?
Answer:
[tex]Area = 216.108cm^2[/tex] --- You
[tex]Area = 216.940cm^2[/tex] --- Another student
Reason: Because there is a variation in the given dimensions
Step-by-step explanation:
Given
Your measurement
[tex]Length = 20.70cm; Width =10.44cm[/tex]
Another students'
[tex]Length = 20.74cm; Width =10.46cm[/tex]
Solving (a): The area
Area is calculated as:
[tex]Area = Length * Width[/tex]
For you
[tex]Area = 20.70cm * 10.44cm[/tex]
[tex]Area = 216.108cm^2[/tex]
For the other student
[tex]Area = 20.74cm * 10.46cm[/tex]
[tex]Area = 216.940cm^2[/tex]
Solving (b): Reason for the variation in the areas
The given measurements are estimates of the dimensions of the rectangle.
Since there is a variation in the estimates, there will be some level of variation in the calculated area.
The volume of a cylinder can be expressed as V=πr2h, where r is the radius, and h is the height of the cylinder. Which expression represents the volume of this cylinder?
h= 2x+7 r=x-3
Answer:
The answer is V= ([tex]\pi[/tex]) ([tex]x-3^{2}[/tex]) (2x+7).
Step-by-step explanation:
To find the volume of the cylinder, plug in the information given in the question into the formula for the volume of a cylinder, which is V = [tex]\pi[/tex] [tex]r^{2}[/tex] h.
Express secΦ in terms of tanΦ
Answer:
[tex]\sec\theta=\sqrt{1+\tan^2\theta}[/tex]
Step-by-step explanation:
The trigonometric identity is :
[tex]\sec^2\theta-\tan^2\theta=1\\\\or\\\\\sec^2\theta=1+\tan^2\theta[/tex]
We need to express secθ in terms of tanθ.
The above equation becomes,
[tex]\sec\theta=\sqrt{1+\tan^2\theta}[/tex]
Hence, this is the required solution.
Question 22
Find the volume.
Answer:
D
Step-by-step explanation:
area times height dived by 3
note that the radius is 8
Answer:
D. [tex]\frac{512}{3}\pi[/tex] ≈ 535.9 m³
Step-by-step explanation:
Formula = πr²* h/3
Volume = π * 64 * 8/3
Volume = π * 512/3 = 535.89 ≈ 535.9
Answer = D. [tex]\frac{512}{3}\pi[/tex] ≈ 535.9m³
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
I need help asp please!!
Answer:
337.5 g
Step-by-step explanation:
mass=volume x density=112.5 x 3=337.5
Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
Let n represent the interger l, the three consective intergers are represented by
[tex]n[/tex]
[tex]n + 2[/tex]
[tex]n + 4[/tex]
The second one represent
[tex](n + 2) {}^{2} + 76 =( n + 4) {}^{2} [/tex]
Simplify both sides
[tex]n {}^{2} + 4n + 4 + 76 = {n}^{2} + 8n + 16[/tex]
[tex] {n}^{2} + 4n + 4 = {n}^{2} + 8n - 60[/tex]
[tex]4n + 4 = 8n - 60[/tex]
[tex]4n + 64= 8n[/tex]
[tex]64= 4n[/tex]
[tex]n = 16[/tex]
The intergers are 16,18,20