The number of employees per department are normally distributed with a population standard deviation of 198 employees and an unknown population mean. If a random sample of 22 departments is taken and results in a sample mean of 1460 employees, find the error bound (EBM) of the confidence interval with a 80% confidence level.
Answer:
EBM = +-54.126
Step-by-step explanation:
In this question we have confidence interval to be 80%
The formula to solve this is in the attachment.
Bar X = 1460
Z-alpha/2 = 1.282
Sd = standard deviation = 198 employees
n = 22 departments
After we have inserted all values in to the formula we have:
1460 +-(1.282*198/√22)
= 1460+-(54.12604)
= (1405.87, 1514.126)
The error bounded mean EBM
= +-z-alpha/2 x (sd/√n)
= 1.282 x 198/√22
= 1.282 x 42.22
EBM = +-54.126
Please help me, I'm really confused. Given that a ∥ b and m∠6 is 1/8 of m∠4, find m∠4 and m∠6.
9514 1404 393
Explanation:
Finish the Given statement, make use of the relationships of angles and parallel lines, then finish the algebra.
__
2. m∠6 = (1/8)m∠4 . . . . Given
3. m∠6 + m∠4 = 180° . . . . 3. same-side interior angles are supplementary
4. m∠6 + 8·m∠6 = 180° . . . . 4. Substitution (from 2, above: 8·m∠6 = m∠4)
Here is the "algebra" that gets you to line 5:
4a. 9m∠6 = 180° . . . collect terms
4b. m∠6 = 20° . . . . . divide by 9
4c. m∠4 = 8·20° = 160° . . . use the same relation as in step 4
5. m∠6 = 20°, m∠4 = 160° . . . . Algebra
m∠6=1/8m∠4
m∠6+m∠4=180° S.S int. of parallel lines
m∠6+8·m∠4=180°
m∠6=20° m∠4=160°
Determine the number of real solutions of the following system of equations.
y = x^2 + 1
y=1
O 3
O 0
O 2
O 1
three consecutive terms in a geometric sequence are r ,r+4, and r+6 in that order. Determine the value of r.
9514 1404 393
Answer:
r = -8
Step-by-step explanation:
The terms of a geometric sequence have a common ratio, so we have ...
[tex]\dfrac{r+4}{r}=\dfrac{r+6}{r+4}\\\\1+\dfrac{4}{r}=1+\dfrac{2}{r+4}\\\\4(r+4)=2(r)\qquad\text{subtract 1, cross multiply}\\\\2r=-16\qquad\text{subtract $2r+16$}\\\\\boxed{r=-8}\qquad\text{divide by $2$}[/tex]
_____
Then the terms of the sequence are ...
-8, -4, -2, ...
and the common ratio is 1/2.
Answer: r = -8
Step-by-step explanation:
On the basis of a survey of 545 television viewers, a statistician has constructed a confidence interval and estimated that the proportion of people who watched the season premiere of Glee is between .16 and .24. What level of confidence did the statistician use in constructing this interval?
Answer:
0.98 also 98%
Step-by-step explanation:
In this question we have the Lower limit to be 0.16
We have the Upper limit to be 0.24
Such that (0.16+0.24)/2 = 0.40/2 = 0.20
Standard deviation= √(0.2x0.8/545) this gives 0.017134
Next we get margin of error
Margin of error = 0.24-0.20 = 0.04
Z multiplied by sd =0.04
Such that
Z = 0.04/0.017134 =2.33
On this z score, the Corresponding level of confidence is 0.98
Which is 98%
To paint, a House, a painting company charges a flat rate of $400 for supplies, plus 60$ for each hour of labor. Write an equation for this situation.
helppppp please I will give brainliest
Answer:
y = -1/2x
Step-by-step explanation:
The slope is negative and 1/2, and y-intercept is 0
Hhhhhheelllp ASAPpppppp
Answer:
c
Step-by-step explanation:
Write each of the following numbers as a power with an exponent to the base 2:16
Given:
The number is 16.
To find:
The given number as a power with an exponent to the base 2.
Solution:
First write the given number as the product of the prime factors.
The factor form of 16 is
[tex]16=2\times 2\times 2\times 2[/tex]
[tex]16=2^4[/tex]
Therefore, the given number 16 as a power with an exponent to the base 2 is [tex]2^4[/tex].
Answer:
2^4
Step-by-step explanation:
would would the slope and y intercept be
Taylor had 100 pieces of Lego in her collection, but she lost 15 pieces. What
percent did she lose?
Answer:
15%
Step-by-step explanation:
Percent is (usually) out of 100. So since the unit is already 100 you can just look at how much she did lose. (^-^)
There are 40 students in a class.
Each student walks to school or cycles to school or gets the bus to school
There are 22 girls in the class.
9 of the girls walk to school.
7 of the boys cycle to school.
6 of the 10 students who get the bus to school are boys.
Find the number of these students who walk to school.
Step-by-step explanation:
Total no. of students = 40
Total no. of girls = 22
Total no. of boys = 40 - 22 = 18
No. of girls walking to school = 9
No. of girls who cycle to school = 22 - 9
No. of boys who cycle to school = 7
No. of students who take the bus = 10
(6 boys and 4 girls)
No. of boys who walk to school = 18 - (7 + 6) = 5
Total no. of students who walk to school = 9 + 5 = 14
The number of students who walked to school was 14 students
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The equations will be ,
Let the total number of students in the class be A = 40 students
The number of girls in the class = 22 students
The number of boys in class = total number of students - number of girls
= 40 - 22
= 18 students
Now ,
The number of girls who walked to school = 9 students
The number of boys who cycled to school = 7
So , remaining boys = 18 - 7
= 11 students
The number of boys who take bus to school = 6 students
So , remaining boys = 11 - 6
= 5 students
Therefore , the remaining boys in the class walks to school = 5 students
So , the equation will be
And , the total number of students who walked to school =
number of boys in the class that walks to school + number of girls who walked to school
Total number of students who walked to school = 9 + 5
= 14 students
Hence , The number of students who walked to school was 14 students
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Charmaine runs 4 miles in 30 minutes. At the same rate how many minutes would she take to run 10 minutes
Answer:
It will take her 75 minutes To run 10 miles.
Step-by-step explanation:
I believe to run 10 miles (not minutes)
30/4= 7.5 minute per mile
7.5*10= 75 minutes
Answer:
10x0.133=1.33 so approximately 1.3 miles
Step-by-step explanation:
Charmaine runs 0.133 miles per minute
If you have a math equation with an addition symbol in the middle (such as -8 + 4), what are the rules for determining whether to add or subtract?
Answer:
-8+4=-4
Step-by-step explanation:
Rearrabge the equation to bcm 4-8
This will make it simpler to give us the answer as -4
If there are 7 girls and 8 boys on the school’s track team, what is the ratio of girls to boys? how would I answer in three different ways.
Answer:
7:8
7 to 8
7/8
Step-by-step explanation:
Answer:
49:56
7/8
.875
Step-by-step explanation:
Here's 3 different ways
trapezoid has parallel sides with length 10 cm. and 15 cm. Give the area of the trapezoid.
Answer:
150
Step-by-step explanation:
Length times width you learned about that in elementary school every one has.
Answer:
150
Step-by-step explanation:
Jordan and $35 for taking care of his neighbors lawn suppose the neighbor gave him a $15 tip which would be the total amount Jordan earned
Jordan made a total of $50 for maintaining his neighbor's yard.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
given, Jordan earned $35 for taking care of his neighbors lawn suppose the neighbor gave him a $15 tip.
Thus,
Total money Jordan earned = Salary + tip
Total money Jordan earned = 35 + 15
Total money Jordan earned = 50
therefore, the total amount Jordan earned is $50 for taking care of his neighbor's lawn.
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Ali has a collection of 177 snap-together building blocks. Ali has one fourth as many red blocks as blue blocks, half as many white blocks as black blocks, an equal number of black and blue blocks, and 34 miscellaneous blocks of other colors. How many red blocks does Ali have?
Help me plz!
Answer:
The number of red blocks Ali has is 13 red balls
Step-by-step explanation:
The given parameters are;
The number of snap-together building blocks Ali has = 177
The number of red blocks Ali has = 1/4 × The number of blue blocks Ali has
The number of white blocks Ali has = 1/2 × The number of black blocks Ali has
The number of black blocks Ali has = The number of blue blocks he has
The number of miscellaneous blocks Ali has = 34
Let x represent the number of blue blocks Ali has, therefore, we have;
The number of red blocks Ali has = 1/4 × x
The number of black blocks Ali has = The number of blue blocks = x
x = 1/2 × The number of white blocks Ali has
∴ The number of white blocks Ali has = 2·x
The number of known colored blocks Ali has = 177 - 34 = 143
Therefore, we have;
x + 1/4·x + x + 1/2·x = 143
11/4·x = 143
x = 143 × 4/11 = 52
Therefore, the number of blue blocks Ali has = x = 52 blue balls
The number of red blocks Ali has = 1/4 × The number of blue blocks Ali has = 1/4 × 52 = 13
The number of red blocks Ali has = 13 red balls.
6
Given the table below, tell the domain and range.
ON
x
y
0
-1
2
0
4.
1
6
Ok, this one is really easy your domain is all the x values and the range is all of the y values.
Thus, here is your answer...
Domain → { -2, -1, 0, 1 }
Range → { 0, 2, 4, 6 }
A hot air balloon is descending at a rate of 6.75 feet per second.
What is the change in the balloon's height after 3 1/3 seconds?
The hot air balloon descends 22.498 feet after 3.333 seconds.
How much does a hot air balloon's height decreases?
The situation indicates that the height decrease is directly proportional to time. The distance is equal to the product of speed (v), in feet per second, and time (t), in seconds.
s ∝ t
s = v · t (1)
If we know that v= 6.75 ft / s and t = 3.333 ft, then the change in the height of the hot air balloon is:
s = (6.75 ft / s) · (3.333 s)
s = 22.498 ft
The hot air balloon descends 22.498 feet after 3.333 seconds.
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Please solve: y = 2x + 5... X = 2
Answer:
2,9 or y=9
Step-by-step explanation:
So since x=2, plug it in the equation.
y=2(2)+5
y=9
In a coordinate, it would be 2,9
Answer: y = 9
Step-by-step explanation: Substitute the value of x, which is 2, into the equation. 2 multiplied by 2 equals 4, and 5 plus 4 equals 9, thus y equals 9
What expression can be used to add 7/10 + 13/20
Segment CD has point E located on it such that CE:ED = 3:5. If the endpoints are located at C(5, -6) and D(11,18) then what are the coordinates of E ?
Answer:
E(29/4,3)
Step-by-step explanation:
Given that,
Segment CD has point E located on it such that CE:ED = 3:5
The coordinates of C and D are (5, -6) and (11,18) respectively.
We need to find the coordinates of E. Let the coordinates are (x,y). Using section formula to find it as follows :
[tex](x,y)=(\dfrac{m_1x_2+m_2x_1}{m_1+m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2})\\\\(x,y)=(\dfrac{3(11)+5(5)}{3+5},\dfrac{3(18)+5(-6)}{3+5})\\\\=\dfrac{29}{4},3[/tex]
So, the coordinates of E are (29/4,3).
Which inequality shows the relationship between the plotted points on the
number line?
-8
0
A. -4<-8
B. -8<-4
C. -8>-4
O D. 4<-8
Answer: if yall need the answer for this then its C
Step-by-step explanation:
Please answer number 4 please!
I believe the answer is A.
Solve for h.
-18 + h = 28
Answer:
h=46
Step-by-step explanation:
Add 18 to both sides
Rachel worked 2.5 hours on Monday, 3.5 hours on Tuesday, 2 hours on Thursday, and 5 hours on Saturday. She is paid $10.66 per hour. How much money did Rachel earn that week?
Answer:
$138.58
Step-by-step explanation:
You would first set up an equation. You want to know how much money Rachel earned that week, so let's refer to that by using variable t for total money earned this week.
Next, we also know that Rachel is paid 10.66 per hour, so we'll be multiplying it by the number of hours she worked this week. This allows us to set our equation up as follows:
10.66(2.5+3.5+2+5) = t
You would now add like terms.
10.66(13) = t
You would now multiply 10.66 and 13(total number of hours worked this week).
This would get us 138.58, or the total numnber of money Rachel earned this week.
10. A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the
station every 6 minutes. Suppose it is 6:30 am right now. At what time will both trains leave the
station together?
Answer:
7:00
Step-by-step explanation:
(Giving brainliest!!)
How would the decimal point move to solve the equation 124 ÷ 101 = ________?
A) 1 place to the left
B) 1 place to the right
C) 2 places to the left
D) 2 places to the right
Answer:
1 place to the right
Step-by-step explanation:
hope it help
A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what proportion of cars are driving between 60 and 70 mi/hr? Round to the nearest thousandth) Group of answer choices
Answer:
Approximately [tex]0.157[/tex].
Step-by-step explanation:
Let [tex]X[/tex] denote the speed of a car. The question is asking for [tex]P(60 \le X \le 70)[/tex].
That probability is equal to [tex]P(X \le 70)- P(X \le 60)[/tex].
Find each of [tex]P(X \le 60)[/tex] and [tex]P(X \le 70)[/tex] using a [tex]Z[/tex]-table.
Calculate the [tex]Z[/tex] value for [tex]x = 70[/tex] and [tex]x = 60[/tex]:
At [tex]x = 70[/tex], [tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{60 - 55}{5} = 3[/tex].
At [tex]x = 60[/tex], [tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{70 - 55}{5} = 1[/tex].
In other words: [tex]P(X \le 70) = P(Z \le 3)[/tex] whereas [tex]P(X \le 60) = P(Z \le 1)[/tex].
Look up [tex]P(Z \le 3)[/tex] and [tex]P(Z \le 1)[/tex] on a [tex]Z[/tex]-table. The question is asking that the answer be rounded to the nearest thousandth. Therefore, keep at least more decimal places than that in intermediate values.
[tex]P(Z \le 3) \approx 0.9987[/tex] and [tex]P(Z \le 1) \approx 0.8413[/tex].
Therefore:
[tex]\begin{aligned}P(60 \le X \le 70) &= P(X \le 70)- P(X \le 60) \\ &= P(Z \le 3) - P(Z \le 1) \approx 0.157\end{aligned}[/tex].