The p-value is higher than 0.05, so we are unable to rule out the null hypothesis. There is little proof to back up the director's claim.
Hypothesis:
H₀ : μ = 3000
H₁ : μ > 3000
The t-test should be employed when the population mean and standard deviation are unknown. Since the sample size is high, we can infer that the sample mean's sampling distribution is normal.
The following information is provided:
s = 450
x = 3200
n = 14
Therefore, test statistics will be:
t = (x - μ) / (s / √n) = (3200 - 3000) / (250 / √14) = 1.66
The test in this instance is right-tailed, and its degree of freedom is df=n-1=14-1=13.
0.0601 is the p-value.
We are unable to reject the null hypothesis since the p-value is higher than 0.05. The director's allegation is not supported by a lot of evidence.
Since p =.0601, the director's assertion cannot be supported by the available data.
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Question 10 of 10
Which of the following is the solution to | x | +5 ≤1?
OA. No solution
OB. xs-4
C. All values are solutions *
OD. xs-4 and x ≥ −6
The solution of | x | +5 ≤ 1 is option C, All values are solutions
We need to find the solution of | x | +5 ≤ 1
Upon removing the modulus function, the term presnet within it can be either negative or positive
considering it as postive
| x | +5 ≤ 1
x + 5 ≤ 1
x ≤ 1 - 5
x ≤ -4
considering it as negative
| x | +5 ≤ 1
-x + 5 ≤ 1
-x ≤ 1 - 5
-x ≤ -4
x ≥ -4
Therefore, the solution of | x | +5 ≤ 1 is All values are solutions
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Write2 1/4 as an improper fraction in its simplest form
Answer:
9/4
Step-by-step explanation:
An estimated 3 out of every 25 men are left-handed.What percent of men are left-handed?
help me please
Answer:
12% of men are left handed.
Step-by-step explanation:
Percent of men who are left handed =
325×100=3×4=12 3 25 × 100 = 3 × 4 = .
12%
I hope this helps!
Gassama buys some bags of buttons
there are 20 buttons or 21 buttons or 22 buttons or 23 buttons in each bag
the table gives some information about the number of buttons in each bag
the total number of buttons is 280
work out the value of X
20 buttons = frequency x
21 buttons = frequency 5
22 buttons = frequency 3
23 buttons = frequency 3
The number of 20 button bags are 2.
Given that, Gassama buys some bags of buttons there are 20 buttons or 21 buttons or 22 buttons or 23 buttons in each bag.
What is frequency?Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.
Here,
Number of 20 buttons = 20×x=20x
Number of 21 buttons = 21×5=105
Number of 22 buttons = 22×3=66
Number of 23 buttons = 23×3=69
Total = 20x+105+66+69
20x+105+66+69=280
⇒ 20x+240=280
⇒ 20x=40
⇒ x=2
Therefore, the number of 20 button bags are 2.
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Can you find the measure of the indicated angle and type the correct code? Please remember to type in ALL CAPS with no spaces,
From the figure
A. alternate interior angles: 1
B. same side exterior: 4
C. vertical: 4 and 3
D. same side interior: 3
E. obtuse angle: 1
F. adjacent angle pairs: 1 and 2
G. alternate exterior: 2
H. corresponding: 4
I. complimentary:
What are parallel lines?parallel lines refer too lines that would never meet. When there is a pair of parallel lines with a transversal line like in the figure some angle theorems come into play
some of the are used in the in the problem and definition of some them include
adjacent angles refer to angles that are next to each other, such angles are being demarcated by a line to the other angle. in the figure angle 1 and 2 alternate angles
Obtuse angles refers to angles that are more than 90 degrees but less than 90 degrees
vertical angles are angles opposite to each other, formed when two lines meet
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Can someone help me on this question? I think it’s the 2nd choice but I’m not sure
Answer:
5√3
Step-by-step explanation:
There are two triangles shown in the image.
First one is a 45°-45°-90° right triangle with side lengths represented with a-a-a√2 respectively to the angle measures.
The second triangle is 30°-60°-90° special right triangle with side lengths represented with b-b√3-2b respectively to the angle measures.
In first triangle hypotenuse (the side length represented with a√2) is given as 10√2 so a = 10.
This is also the measure of hypotenuse for the second triangle which is represented with 2b, so b = 5 in this case.
x is the side length that sees angle measure 60° which we said is represented with b√3, we said b = 5 so the value of x = 5√3 the answer is the first option.
Mr.Hollis determines that he gives away 800each month if he gives away 16 of his budget then how much is his overall budget
The overall budget the Mr Hollis has is $12800.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Mr.Hollis determines that he gives away 800 each month and the fraction is 1/6 of his budget.
The value of the overall budget will be illustrated as x.
Therefore 1/16 × x = 800
x / 16 = 800
x = 16 × 800
x = 12800
Hollis has $12800 as budget.
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Calculate S16 for the arithmetic sequence defined by (an) = {5/8-5/16n}
65/
2
65/
8
-65/
8
-65/
2
The sum of the first 16 terms of the defined arithmetic sequence is given as follows:
-520/16.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, being called common difference d.
The nth term of an arithmetic sequence is given by the equation presented as follows, called general equation:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the arithmetic sequence.
The sum of the first n terms is given by the equation presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
The sequence in this problem is defined as follows:
[tex]a_n = \frac{5}{8} - \frac{5}{16}n[/tex]
The first term is of:
[tex]a_1 = \frac{5}{8} - \frac{5}{16} = \frac{5}{16}[/tex]
Hence the 16th term of the sequence is of:
[tex]a_{16} = \frac{5}{8} - \frac{5}{16}(16) = \frac{5}{8} - 5 = -\frac{35}{8}[/tex]
Hence the sum of the first 16 terms of the arithmetic sequence is defined as follows:
[tex]S_{16} = 8\left(\frac{5}{16} - \frac{35}{8}\right) = 8 \times \left(-\frac{65}{16}\right) = -\frac{520}{16}[/tex]
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Taub has a smart phone data plan that costs $20 per month that includes 8 GB of
data, but will charge an extra $10 per GB over the included amount. How much
would Taub have to pay in a month where she used 3 GB over the limit? How much
would Taub have to pay In a month where she used went over by T GB? (the equation)
Answer:
10t + 20
Step-by-step explanation:
solve for x 4{x+1 1/3]=9 2/3
The solution for the expression is X =87/ 48 or 1.812
To solve for x in the equation we follow the step below:
Step 1: Open the bracket by multiply 4
= 4x +4x/3 = 9 2/3
= 4x + 4x /3 = 29/3
Step 2: Evaluate for X
= [tex]\frac{12x + 4x}{3}[/tex] = [tex]\frac{29}{3}[/tex]
= [tex]\frac{16x}{3}[/tex] =[tex]\frac{29}{3}[/tex]
Step 3: Cross multiply
: 3 (16x) = 3(29)
48x = 87
Step 3: Divide both sides by 48
=[tex]\frac{48x}{48}[/tex] =[tex]\frac{87}{48}[/tex]
x = [tex]\frac{87}{48}[/tex] = 1.812
Therefore, the solution for the expression is X =87/ 48 or 1.812
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when looking at the results of a 99% confidence interval, we can predict what the results of the two-sided significance test will be:
0.01 is the results of the two-sided significance test in confidence interval,
What is alpha in statistics?
A test statistic's statistical significance is determined by its alpha value. The researcher selects it. In a statistical test, the probability of a Type I error is represented by alpha. Considering that alpha is a probability, its range is 0 to 1.confidence level = 1 - alpha
so alpha = 1 - confidence level = 1 - 0.99 = 0.01
In statistics, alpha is the number that evaluates the test statistic to see if it is significant or not. In other words, alpha is the allowable type 1 error margin. The significance level, or alpha, is the antithesis of the confidence level. Confusion level + significance level = 1.
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What is the equation of the line that passes through the points (-7.
-5) and (2, 3)? Write your answer in slope-intercept form.
Show your work here
The equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9
The first point = (-7, -5)
The second point = (2, 3)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line m = (3- (-5) / (2 - (-7))
= (3 + 5) / (2 + 7)
= 8 / 9
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
The point = (2,3)
Substitute the values in the equation
y - 3 = (8/9)(x - 2)
y - 3 = (8/9)x - 16/9
y = (8/9)x - 16/9 + 3
y = (8/9)x - 11/9
Hence, the equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9
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Select the correct answer.
What is the domain of function f?
D
Step-by-step explanation:
The domain is the X-values in your function
as you can see, the X values continue to increase as the lines continue, infinitely
Mr. Young is replacing the fencing around his rabbit pens and garden. The table shows the dimensions of the different areas.
Item
Length
(ft)
Width
(ft)
Rabbit Pen 3.5 4.5
Garden 12 10
How many feet of fencing will he need to replace two rabbit pens and his garden? The perimeter of a rectangle is 2ℓ+2w
2
ℓ
+
2
w
, where ℓ is the length and w is the width.
__ ft
Total fenced need to replaced is 60 feet
What is Perimeter of rectangle?The Perimeter of rectangle is two times the sum length and width.
i.e., Perimeter of rectangle= 2( l+ w)
Given:
Rabbit Pen: Length= 3.5, width= 4.5
Garden: length= 12, width = 10
So, Perimeter of Rabbit Pen = 2( 3.5 + 4.5)
= 2( 8)
= 16 feet
Now, Perimeter of Garden = 2 (12 + 10)
= 2( 22)
= 44 feet.
Total fenced need to replaces= 16 +44 = 60 feet
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Answer:
Step-by-step explanation:
76
Solve this equation:
11x^2=-8
Answer:
See below
Step-by-step explanation:
11x^2 = - 8
x^2 = - 8/11
x = + - i sqrt (8/11) or - .727 i or .727 i
a bank wishes to estimate the mean credit card balance owed by its customers. the population standard deviation is estimated to be $300. if a 98% confidence interval is used and an margin of error of $75 is desired, how many customers should be sampled?
Using a 98% confidence interval, the total number of customers that should be sampled is 87.
What exactly is sample size?The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.
Given,
Standard deviation σ=300
Confidence level: 0.98
Maximum allowable error: ε=75
The critical value is calculated using the standard normal table at the level of significance (0.02)
The critical value in this case is 2.326.
Sample size is calculated by,
n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²
n=((2.326)²×(300)²)/(75)²
n=86.564≈87
Therefore, the required sample size is 87.
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How do i graph this? 4x - 2y > 12
Step-by-step explanation:
X-intercept is where the line crosses the x-axis or where y = 0
So, put y = 0 in the given equation
4x + 2(0) = 12
4x = 12
x = 12/4
x = 3
Jodie wanted to match Mandy's obstacle course record of 74.6 seconds. She had already spent fifty and one fourth seconds on wall climbing and 10.56 seconds on the ropes. How much time did she have left to match the record?
60.81 seconds
64.04 seconds
10.60 seconds
13.79 seconds
Jodie has left 13.79 seconds to match the record.
What is a linear equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Here, we have
Jodie aimed to beat Mandy's 74.6-second mark on the obstacle course. She had already spent 10.56 seconds on the ropes and fifty-and-a-fourth seconds ascending the wall. To match the record, we must determine how much time she had remaining.
Jodie's total time for climbing the wall is fifty and one fourth seconds=50.25 seconds
The total time on ropes is 10.56 seconds
The total time she spent is 50.25+10.56=60.81
Left time = Record Time-Spent time
= 74.6-60.81 = 13.79
Hence, Jodie has left 13.79 seconds to match the record.
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Question 11-(3 marks available)
Find the total surface area of this triangular prism.
13 cm
5 cm
12 cm
9 cm
20 cm
Answer: 1080 [tex]cm^{2}[/tex]
Determine the values of b1, b2, and b3, the sides of the triangular base. Also determine the value of h, the height of the triangular base and l, the length of the prism (the length between the bases).
The sides of the triangular base are:
b1 = 13 in.
b2 = 14 in.
b3 = 15 in.
The triangular base is a right triangle, and so the height is one of our sides. We will use
h = 12 in.
The length of the prism is
l = 20 in.
total surface area = bh + (b1+b2+b3)*l
bh = 12*20 = 240 [tex]cm^{2}[/tex]
l * (b1+b2+b3) = 20*(13 + 14+ 15) = 840 [tex]cm^{2}[/tex]
TSA = bh + l * (b1 + b2 + b3) = 240 + 840 = 1080 [tex]cm^{2}[/tex]
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Find the missing exponent. 2 =32
Answer:
5
Step-by-step explanation:
The only way I know how to go about this is to multiply 2 until it becomes 32
2x2=4
4x2=8
8x2=16
16x2=32
Now just count how many 2 I used and I used 5 so the missing exponent is 5
Hopes this helps please mark brainliest
2x+2y=-22
5x +6y = -63
Answer:
Step-by-step explanation:
Find an equation to represent x or y
2x + 2y = -22
-2y
2x = -22 - 2y
Divide by 2
x = -11 -y
Plug in the found equation
5 (-11 - y) +6y = - 63
- 55 -5y + 6y = - 63
-55 + y = - 63
+55
y = - 8
Plug in the y to find x
2x + 2(- 8) = - 22
2x - 16 = - 22
+ 16
2x = - 6
Divide by 2
x = - 3
The length of segment AE is 5 centimeters. a. what is the length of segment CD? b. what is the length of segment AB? c. Name a segment that had the same length ...
a) The length of segment CD is; CD = 10 cm
b) The length of segment AB is; AB = 5 cm
c) Another segment with same length as segment AB is;
Segment AC
What is the length of the line segment?From the attached image, we see that Segment AE is a radius of the circle with center of A.
Now, any segment with origin from the center of the Circle that goes on to hit the circumference of the circle, is also a radius, and would be equal in length to segment AE.
a) Segment CD divides the circle into 2 equal parts and as such it will be the diameter of the circle.
Diameter = 2 × radius.
Diameter; CD = 2 × AE
CD = 2 × 5
CD = 10 cm
b) AB is a radius as defined earlier and as such; AB = AE
Thus; AB = 5 cm
c) The other segments that are also radius of the circle and have the same length as segment AB are;
Segment AC
Segment AD
Segment AG
Segment FA
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What are the coordinates of the vertices after a rotation 90 counterclockwise around the origin.
Answer:When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
Step-by-step explanation: trust me
Kareem cannot decide which of two washing machines to buy. The selling price of each is 600$. The first is marked down by 50%. The second is marked down by 30% with an additional 20% off. Find the sale price of each washing machine. Use pencil and paper. Explain why should buy the first washing machine rather than the second if the machines are the same except for the selling price.
The selling price of the first washing machine is $300
The selling price of the second washing machine is $336
The first washing machine appear to have more savings in cost
How to determine the selling prices of the two machinesThe question is a percentage problem
The first is marked down by 50%
= 50 percent
= 50 / 100
= 0.5
marked down factor = 1 - 0.5 = 0.5
selling price of the first machine = 600 * 0.5 = 300
Similarly the second selling washing machine has mark down of 30%
30% = 0.3
marked down factor = 1 - 0.3 = 0.7
selling price of the second washing machine at first mark down
= 600 * 0.7 = 420
second mark down
20% = 0.2
marked down factor = 1 - 0.2 = 0.8
selling price of the second washing machine at second mark down
= 420 * 0.8 = 336
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Find a1 if d = -2 and a21 = 18.
The answer is either 58 or 60
For the given values of the arithmetic sequence d = -2 , a₂₁ = 18,then the value of a₁ = 58.
As given in the question,
Given values of the arithmetic sequence :
Common difference 'd' = -2
Twenty first term a₂₁ = 18
Formula for the nth term of arithmetic sequence with common difference 'd' and first term a₁ is given by:
aₙ = a₁ + (n -1) d
Substitute the value n =21 , a₂₁ =18 and d = -2 in the above equation we get,
⇒a₂₁ = a₁ + (21 -1)(-2)
⇒18 = a₁ + 20(-2)
⇒ a₁ = 18 +40
⇒a₁ = 58
Therefore, for the given values of the arithmetic sequence d = -2 ,
a₂₁ = 18,then the value of a₁ = 58.
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Find the range for the measure of the third side of a
triangle given the measures of two sides.
8, 13
By using properties of triangle, it can be inferred that
The value of c lies between 5 and 21 and also 5 and 21 are not included
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles. The sum of the interior angles of a triangle is 180°
Let a = 8, b = 13 and let the third side be c
We know sum of two sides of a triangle is always greater than the third side
a < b + c
8 < 13 + c
c > 8 - 13
c > -5, which is obvious
b < c + a
13 < c + 8
c > 13 - 8
c > 5
c < a + b
c < 8 + 13
c < 21
5 < c < 21
The value of c lies between 5 and 21 and also 5 and 21 are not included
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6) In Jim’s school, there are 3 girls for every 2 boys. There are 800 students in total. Using this information, how many students are girls?
A. 260
B. 320
C. 480
D. 390
Answer:
C) 480
Step-by-step explanation:
Ratio:
[tex]\sf \dfrac{3}{5}*800 = 3 * 160[/tex]
= 480
Can anyone write the equation of the graph?
The equation of the absolute function graph given in the diagram is: y = |x - 3| + 5.
How to Find the Equation of the Graph of an Absolute Value Function?y = a|x – h| + k is the equation, in vertex form, that represents the absolute value function where:
The vertex of the graph of the absolute value function = (h, k) The graph opens up or opens down depends on the value of a.The vertex of the graph is (3, 5). This implies that:
(h, k) = (3, 5)
Substitute h = 3 and k = 5 into the equation in vertex form, y = a|x – h| + k:
y = a|x – h| + k
y = a|x - 3| + 5
To find the value of a, substitute a point on the graph, (5, 7), into the y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 - 5 = 2a [subtraction property]
2 = 2a
a = 1 [division property of equality]
Substitute a = 1 into the equation y = a|x - 3| + 5:
y = |x - 3| + 5
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How can you earn a high credit score?
A. After ten years of never making any payments or having loans.
B. After you have made your first credit card payment.
C. When you turn thirty years old.
D. Over time by paying off your loans and making payments on time.
Answer:
The correct answer is D because Option A won't work neither will option B because a long credit history will help ur credit score, C isn't right either
a manufacturing machine has a 5% defect rate. if 7 items are chosen at random, what is the probability that at least one will have a defect?
The probability of selecting at least one defective item at random is 0.3017.
The probability of an event occurring at least once will be calculated as the complement of the probability of the event never occurring. You can use exponents to multiply the number of events that occurred when calculating this amount.
Defect rate = P(defect) = 0.05
Probability is defined as the required outcome divided by the total number of possible outcomes.
P( at least 1 is defective) = 1 - P(none is defective)
P(not defective) = 1 - P(defective) = 1 - 0.05 = 0.95
P(none is defective) = P(non defective)^7
P(none defective) = 0.95× 0.95 × 0.95 × 0.95 × 0.95× 0.95× 0.95=0.6983
P(at least one is defective) = 1 - 0.6983 = 0.3017
Therefore, probability of at least one defective item is 0.3017.
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