The null and alternate hypotheses are
H0 : u = 0.44 vs Ha: u > 0.44
Null hypothesis: 44% of readers own a personal computer.
Alternate Hypothesis : greater than 44% of readers own a personal computer.
This is one tailed test and the critical region for this one tailed test for the significance level 0.1 is Z > ±1.28
The given values are
p1= 0.54 , p2= 0.44 ; q2= 1-p2= 0.56
Using z test
Z = p1-p2/√p2(1-p2)/n
Z= 0.54-0.44/ √0.44*0.56/200
z= =0.1/ 0.03509
z= 2.849
Since the calculated value of Z= 2.849 is greater than Z= 1.28 reject the null hypothesis therefore there is sufficient evidence to support the executive's claim.
Null hypothesis is rejected
There is sufficient evidence to support the executive's claim at 0.10 significance level.
https://brainly.com/question/2642983
Hallar el noveno término de la progresión aritmética 8, 13, 18,…
Answer:18
Step-by-step explanation:
Write the expression as a single trigonometric function.
cos 5x cos 6x- sin 5x sin 6x
Answer:
[tex]\cos(11x)[/tex]
Step-by-step explanation:
Given
[tex]\cos 5x\ \cos 6x- \sin\ 5x \sin 6x[/tex]
Required
Express as a single function
In trigonometry, we have:
[tex]\cos(A + B) = \cos A\cos B - \sin A \sin B[/tex]
By comparison, we have
[tex]\cos(5x + 6x) = \cos 5x\cos 6x - \sin 5x \sin 6x[/tex]
[tex]\cos(11x) = \cos 5x\cos 6x - \sin 5x \sin 6x[/tex]
do the two trapezoids in the figure appear to be similar? why or why not?
Answer:
The answer is D cuz two if the corresponding angles are congruent.
!!!!PLEASE HELP!!!!
What is the following quotient?
2
√13+ /11
O 13-2./11
13+ 11
6
13+ V11
12
√13 - 1
(D)
Step-by-step explanation:
Multiply and divide the fraction by the conjugate:
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}×\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]
[tex]= \dfrac{2(\sqrt{13} - \sqrt{11})}{(\sqrt{13})^2 - (\sqrt{11})^2}[/tex]
[tex]=\dfrac{2(\sqrt{13} - \sqrt{11})}{2}[/tex]
[tex]=\sqrt{13} - \sqrt{11}[/tex]
find the area of the triangle
Answer:
75.03
Step-by-step explanation:
14×11×sin(77)
= 75.02649499..
≈ 75.03 (rounded to nearest hundredth)
Answered by GAUTHMATH
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the _____. a. coefficient of determination b. correlation coefficient c. confidence interval estimate d. standard error of the estimate
Answer:
coefficient of determination
Step-by-step explanation:
The Coefficient of determination, R² which is the squared value of the correlation Coefficient is used to give Tha proportion of variation in the predicted / dependent variable that can be explained by the regression line. The coefficient of determination ranges from 0 to 1. Once the proportion of explained variation is obtained, the proportion of unexplained variation is ( 1 - proportion of explained variation).
State and prove the converse of the pythagorean theorem using a two-column proof
Answer:
Step-by-step explanation:
I'm from the UK and I'm not familiar with a two column proof, but the following proves the converse.
Draw 2 right angled triangles with the 2 legs = a and b in each case and the longest side = c in one triangle and f in the other.
By Pythagoras a^2 + b^2 = c^2 (Given)
Also in the other triangle a^2 + b^2 = f^2, if it is right-angled.
Therefore a^2 = f^2 and a = f.
So the 2 triangles are congruent by SSS.
So m < C in one triangle = m < F ( the angles opposite the hypotenuse)
Therefore the second triangle is right angled .
This completes the proof.
Question 3
A bottle of apple juice has 25 ounces. Find the number of quarts of apple juice in a case of 24 bottles. Give the answer as a decimal.
Answer:
The number of quarts of apple juice in a case of 24 bottles is 18.75.
Step-by-step explanation:
This question is solved by proportions, using rules of three.
Amount of ounces:
1 bottle - 25 ounces
24 bottles - x ounces
Applying cross multiplication:
[tex]x = 25*24 = 600[/tex]
600 ounces to quarts:
Each ounce has 0.03125 quarts.
1 ounce - 0.03125 quarts
600 ounces - x quarts:
[tex]x = 600*0.03125 = 18.75[/tex]
The number of quarts of apple juice in a case of 24 bottles is 18.75.
5. Does the infinite geometric series S = 25 + 20 + 16 + ... converge or diverge? Explain.
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Answer:
converges
Step-by-step explanation:
The common ratio is 20/25 = 16/20 = 4/5. The magnitude of this is less than 1, so the series converges.
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4 kg, the acceleration of the object is 13 m/s^2. When the same force acts upon another object, its acceleration is 2 m/s^2. What is the mass of this object?
Answer:
26 kg
Step-by-step explanation:
varies inversely :
y = k/x
acceleration = k/mass
13 = k/4
k= 52
---------------------
2 = k/mass
2 = 52/mass
mass = 26 kg
30 is what percent of 44?
Answer:
68.18
Step-by-step explanation:
→ Set up an equation
[tex]\frac{44x}{100} =30[/tex]
→ Times both sides by 100
44x = 3000
→ Divide both sides by 44
68.18
AB is tangent to the circle at B. M∠A = 27 and mBC=114 (The figure is not drawn to scale.)
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Answer:
a. x = 60
b. y = 93
Step-by-step explanation:
The relevant relations are ...
external angle A is half the difference of intercepted arcs BC and BDinscribed angle y° is half the measure of intercepted arc CDthe sum of arcs of a circle is 360°__
Using these relations, we have ...
A = (BC -x°)/2
x° = BC -2A = 114° -2(27°)
x° = 60°
__
y° = CD/2 = (360° -BC -BD)/2 = (360° -114° -60°)/2
y° = 93°
Find the circumference. Use 3.14. r = 4 cm C = [?] cm
Answer:
24.12
Explanation --
Circumference = Pi x D (d --> diameter)
Diameter = 2r (r --> radius)
4+4 (4[2]) = 8
3.14 times 8 (8 is the diameter we just found out, while 3.14 is pi) -->
25.12
Hope this helps!!
Answer: c=πd
we need 'd'
hence,
d=2r
d=2(4cm)
d=8cm
now,
c=3.14×8cm
c=25.12cm
Starting with a fresh bar of soap, you weigh the bar each day after you take a shower. Then you find the regression line for predicting weight from number of days elapsed. The slope of this line will be:__________.
Answer:
The slope will be negative
Step-by-step explanation:
The slope of the regression line tells us about the relationship or behavior of the dependent and independent variables. In the scenario above, where the weight is being compared with the number of days elapsed. What is expected of the weight and quantity of a bar soap each time it is used for a shower is that it will decrease in weight. Therefore, as the number of days increases, and hence, number of showers rise, the weight of soap will decrease. Hence, we'll obtain a negative slope, one in which the increase in a variable leads to decrease in the other.
Find the equation of the line passing through the point (-1,2)
and the points of intersections of the line 2x - 3y + 11 = 0 and
5x + y + 3 = 0
Answer:
[tex]y=-5x-3[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
To solve for the equation of the line, we would need to:
Find the point of intersection between the two given linesUse the point of intersection and the given point (-1,2) to solve for the slope of the lineUse a point and the slope in [tex]y=mx+b[/tex] to solve for the y-interceptPlug the slope and the y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation1) Find the point of intersection between the two given lines
[tex]2x - 3y + 11 = 0[/tex]
[tex]5x + y + 3 = 0[/tex]
Isolate y in the second equation:
[tex]y=-5x-3[/tex]
Plug y into the first equation:
[tex]2x - 3(-5x-3) + 11 = 0\\2x +15x+9 + 11 = 0\\17x+20 = 0\\17x =-20\\\\x=\displaystyle-\frac{20}{17}[/tex]
Plug x into the second equation to solve for y:
[tex]5x + y + 3 = 0\\\\5(\displaystyle-\frac{20}{17}) + y + 3 = 0\\\\\displaystyle-\frac{100}{17} + y + 3 = 0[/tex]
Isolate y:
[tex]y = -3+\displaystyle\frac{100}{17}\\y = \frac{49}{17}[/tex]
Therefore, the point of intersection between the two given lines is [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex].
2) Determine the slope (m)
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the two points [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex] and (-1,2):
[tex]m=\displaystyle \frac{\displaystyle\frac{49}{17}-2}{\displaystyle-\frac{20}{17}-(-1)}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{20}{17}+1}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{3}{17} }\\\\\\m=-5[/tex]
Therefore, the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-5x+b[/tex]
Plug in the point (-1,2) and solve for b:
[tex]2=-5(-1)+b\\2=5+b\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=-5x+b[/tex]:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
I hope this helps!
Another name for the standardized score from a normally distributed variable is the _____.
A. standard score
B. z-score
C. t-score
D. normal score
Answer:
the answer is b). z- score.
Answer:
b
Step-by-step explanation:
Which expressions are equivalent to -6(b+2)+8
Choose all answers that apply:
A. -6b+2+8
B. -6b-4
C. None of the above
Answer:
B. -6b-4
Step-by-step explanation:
-6(b+2)+8
Distribute
-6b-12+8
Combine like terms
-6b-4
The stemplot below represents the number of bite-size snacks grabbed by 37 students in an activity for a statistics class.
A stemplot titled Number of snacks has values 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 21, 22, 23, 25, 25, 28, 32, 38, 42, 45.
Which of the following statements best describes the distribution?
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 15 to 45. There are no outliers.
The distribution of the number of snacks grabbed is symmetric with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
The distribution of the number of snacks grabbed is skewed left with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
Answer:
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
Step-by-step explanation:
First, we can see if the graph is symmetric. A symmetric graph is even on both sides of the center. As there are a lot more students that grabbed a small number of snacks, and the data is not even around the center (which is somewhere around 20 or 30 snacks). This means that the graph is not symmetric, making the second answer incorrect.
Next, we can check if the graph is skewed right or left. If the left of the graph represents a smaller amount of snacks and the right of it represents a higher number of snacks, we can see that most of the data is on the left of the graph. There are a few values to the right, but the overwhelming amount of data is on the left, making the distribution skewed to the right. This keeps the first and last answers possible
Moreover, we can find the center of the distribution. This is generally equal to the median, which is 18, so the center is around 18
After that, we can see what the values vary from. The lowest tens value is 1, and the lowest ones value in that is 2, making the lowest value 12. Similarly, the highest tens value is 4, and the highest ones value there is 5, making the range 12 to 45. This leaves the last answer, but we can check the outliers to make sure.
With the data, we can calculate the first quartile to be 15, the third quartile to be 21.5, and the interquartile range to be 21.5-15 = 6.75 . If a number is less than Q₁ - 1.5 * IQR or greater than Q₃ + 1.5 * IQR, it is a potential outlier. Applying that here, the lower bound for non-outliers is 15 - 6.5 * 1.5 = 5.25, and the upper bound if 21 + 6.5 * 1.5 = 30.75. No values are less than 5.25, but there are four values greater than 30.75 in 32, 38, 42, and 45. There are possible outliers at 38, 42, and 45, matching up with the last answer.
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.
A) A = 100 + te^2
B) A = 100 + e^2t
C) A = 100e^2t
D) A = 100 + 2e^t
Answer:
D)
Step-by-step explanation: Im not so sure ok i sorry if Im wrong
Write the point-slope form of an equation of the line through the points (-4, 7) and (5,-3).
0
A. Y+4= -1; (1 – 7)
B.Y-5 = = 10 (x+3)
OC. y +3 = = 10 (2+5)
D. y - 7= -5° (x+4)
Answer:
Step-by-step explanation:
There are two possible equations, but neither matches the the choices you listed. The choices seem to have several typographical errors.
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 =(-10/9)(x + 4).
How to estimate the point-slope form of an equation of the line through the points (-4, 7) and (5,-3)?Slope
[tex]$= \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
= (-3 - 7) / (5 - (-4))
= -10/9
The point-slope equation for the line of slope -(10/9) that passes through the point (5, -3).
y + 3 = (-10/9)(x - 5)
Point slope equation for the line of slope -(10/9) that passes through the point (-4, 7)
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 = (-10/9)(x + 4).
Therefore, the correct answer is y - 7 = (-10/9)(x + 4).
To learn more about the equation of a line refer to:
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Mariah owed her grandfather 52.25 but was recently able to pay him back $1.50. How much does Mariah currently
owe her grandfather?
Answer:
52.25 - 1.50 = 50.75
Step-by-step explanation:
I'd recommend using a calculator or pencil and paper
53.25
- 1.50
--------
50.75
When a 0.42 tax was added to the price of a ticket, the total bill come to $7.03. Describe the above situation as a linear equation.
Answer:
P = 7.03 - 0.42T
Step-by-step explanation:
Let the price of a ticket be P.
Let the ticket be T.
A linear equation can be defined as an algebraic equation that's typically written for two (2) independent variables, in which each of them has an exponent of one (1) and they make a straight line when plotted on a graph.
Given the following data;
Tax = 0.42
Total bill = $7.03
Translating the word problem into an algebraic expression, we have;
0.42T + P = 7.03
P = 7.03 - 0.42T
Kara ate 2 7/9 of the raisins she packed. Which box shows the decimal equivalent of the amount of raisins she ate? Box A: 2.777 etc Box B: 2.79 Box C: 2.999 etc.
Answer: Box A, 2.777
=======================================================
Explanation:
When using a calculator or long division, you should find that
7/9 = 0.7777...
where the 7s go on forever
So we can say that 7/9 = 0.777 approximately. You could argue that the last '7' would round up to an '8' and we could say 7/9 = 0.778; however, I'll stick to the first value so that it matches with the answer.
Since 7/9 = 0.777, this means 2 & 7/9 = 2 + 7/9 = 2 + 0.777 = 2.777 which is box A.
Answer:
A
Step-by-step explanation:
3/4 pound of Colby cheese costs $1.69. Find the unit price per pound. (3/4 pound=12)
Answer:
2.25
Step-by-step explanation:
We can write a ratio to solve
1.69 x
------ = ---------------
3/4 lb 1 lb
Using cross products
1.69 * 1 = 3/4 *x
1.69 = 3/4 x
Multiply by 4/3
1.69 * 4/3 = x
x=2.25333
Rounding to the nearest cent
Suppose that the distribution of snake lengths in a certain park is not assumed to be symmetric. According to Chebyshev's Theorem, at least what percentage of snake lengths are within k =2.9 standard deviations of the mean?
According to Chebyshev,
P(|X - µ| ≤ 2.9σ) ≥ 1 - 1/2.9² ≈ 0.8811
HELP PLEASE AND BE CORRECT
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Answer:
see attached
Step-by-step explanation:
Each point moves to 3 times its original distance from P.
A is 2 up and 1 left of P, so A' will be 6 up and 3 left of P.
B is 1 down and 2 left of P, so B' will be 3 down and 6 left of P.
C is 2 right of P, so C' will be 6 right of P.
(Urgent)!
Fill in the blank with the correct response.
Find x
x = _____________
Answer:
4
similar right triangles
[tex]\frac{8}{x} = \frac{x}{2}[/tex]
[tex]x^{2} = 16\\x=4[/tex]
Step-by-step explanation:
Which statement is true about the value of Start Absolute Value negative 5 End Absolute Value?
Statements? At least look for one that says it is equivalent to positive 5.
The answer to this math problem need help
Step-by-step explanation:
you know that you can copy and paste and give the answer
Which polynomial is prime?
a. x³+3x²+2x+6
b. x³+3x²-2x-6
c. 10x²-4x+3x+6
d. 10x²-10x+6x-6
