A bottler of drinking water fills plastic bottles with a mean volume of 993 milliliters (mL) and standard deviation of 7 mL. The fill volumes are normally distributed. What proportion of bottles have volumes between 988 mL and 991 mL?
Answers
Given data:
Mean: 993mL
Standard deviation: 7mL
Find p(988
1. Find the z-value corresponding to (x>988), use the next formula:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{988-993}{7}=-0.71 \end{gathered}[/tex]2. Find the z-value corresponding to (x<991):
[tex]z=\frac{991-993}{7}=-0.29[/tex]3. Use a z score table to find the corresponding values for the z-scores above:
For z=-0.71: 0.2389
For x=-0.29: 0.3859
4. Subtract the lower limit value (0.2389) from the upper limit value (0.3859):
[tex]0.3859-0.2389=0.147[/tex]5. Multiply by 100 to get the percentage:
[tex]0.147*100=14.7[/tex]Then, 14.7% of the bottles have volumes between 988mL and 991mL
Related Questions
1.BhEvaluate the formula V =3O 9.6 in.³O 288 in. 3332 in.O 96 in.3for B = 9 in.² and h = 32 in.
Answers
Given -
B = 9 in²
h = 32 in
To Find -
Evaluate the formula (V) =?
Step-by-Step Explanation -
As we are given
[tex]V\text{ = }\frac{Bh}{3}[/tex]Simply putting the values in the above formula:
[tex]V\text{ = }\frac{9\times32}{3}\text{ = 3}\times32\text{ = 96 in}^3[/tex]Final Answer -
Option D. 96 in³
simplify the expression 6w + 2/3 + 3w
Answers
we have
6w + 2/3 + 3w
step 1
Combine like terms
(6w+3w)+2/3
9w+2/3If a person travels at a speed of 33 m/s and travels 132 meters, how long does the trip take?
Answers
Answer: 4 seconds.
Step-by-step explanation: Simply divide 132 meters by 33 m/s. This gives you four. (as in the trip took four seconds.)
It is a uniform rectilinear movement which is one in which an object moves in a straight line, in one only direction, with a constant speed.
When we spoke of constant speed we mean that the movement retains the same speed, that is; that the object does not move faster, or slower and always at the same speed.
If a person travels at a speed of 33 m/s and travels 132 meters, how long does the trip take?We obtain the data according to the exercise.
Data:
V = 33 m/s
D = 132 m
t = ?
We have that the uniform motion formula is:
[tex]\large\displaystyle\text{$\begin{gathered}\sf V=\dfrac{d}{t}, \to where \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf V=Speed \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf D=distance \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf T=Time \end{gathered}$}[/tex]We solve for time, since that is what we are asked to calculate. And substitute data in the formula.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=\dfrac{d}{V} } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=\frac{132 \not{m}}{33 \ \frac{\not{m}}{s} } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{t=4 \ s} \end{gathered}$}}}[/tex]
I brought on the trip, a time of 4 seconds.The angle of elevation from ground level to the top of a water tower that is 280 ft away measures 27 degrees. What is the height of the tower?
Answers
We can draw
x represents the height of the water tower
we have a right triangle
we can use a trigonometric function
[tex]\tan (27)=\frac{x}{280}[/tex]we need to clear x
[tex]x=\tan (27)\cdot280=142.66\text{ ft}[/tex]The following data values represent a population. What is the variance of thepopulation? μ = 11. Use the information in the table to help you.X8101214(x-μ)²9119OA. 10B. 5O C. 11OD. 20
Answers
The variance is calculated given the formula:
[tex]\begin{gathered} Variance=\frac{\sum(x-\mu)^2}{N} \\ \\ \sum(x-\mu)^2=9+1+1+9 \\ \\ \sum(x-\mu)^2=20 \end{gathered}[/tex]The sample
Hi can you help me with this problem?Formulate a system of equations for the situation below and solve.The total number of passengers riding a certain city bus during the morning shift is 1300. If the child's fare is $0.50, the adult fare is $1.50, and the total revenue from the fares in the morning shift is $1550, how many children and how many adults rode the bus during the morning shift?children=adults=
Answers
Let "A" represent the number of adults that ride the bus and "C" represents the number of children that ride the bus.
On a certain morning shift 1300 people rode the bus, this means that the number of adults and the number of children add up to 1300. You can express the total number of passengers on that shift as follows:
[tex]A+C=1300[/tex]The child's fare is $0.50, so if C children ride the bus a total of 0.50C will be paid.
The adult's fee is $1.50, so if A adult rides the bus, the total earned will be 1.50A.
If you add both fares, you will determine the total fares for the shift, which was $1550
[tex]1.50A+\text{0}.50C=1550[/tex]Using both equations you have determined the number of adults and children that rode the bus:
-First, write the first expression for one of the variables, for example, write it for A:
[tex]\begin{gathered} A+C=1300 \\ A=1300-C \end{gathered}[/tex]-Second, replace the expression obtained in the second equation
[tex]\begin{gathered} 1.50A+0.50C=1550 \\ 1.50(1300-C)+0.50C=1550 \end{gathered}[/tex]Now you have to solve for C
→ Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 1.50\cdot1300-1.50\cdot C+0.50C=1550 \\ 1950-1.50C+0.50C=1550 \end{gathered}[/tex]→Simplify the like terms
[tex]\begin{gathered} 1950+(-1.50C+0.50C)=1550 \\ 1950+-C=1550 \\ 1950-C=1550 \end{gathered}[/tex]→Subtract 1950
[tex]\begin{gathered} 1950-1950-C=1550-1950 \\ -C=-400 \end{gathered}[/tex]→ Multiply both sides by -1 to invert the sign:
[tex]\begin{gathered} (-1)(-C)=(-1)(-400) \\ C=400 \end{gathered}[/tex]Finally, once you have determined the value of C, you can calculate the value of A as follows:
[tex]\begin{gathered} A=1300-C \\ A=1300-400 \\ A=900 \end{gathered}[/tex]So, 400 children and 900 adults rode the bus.
PART E.)In terms of the trigonometry ratios for triangle BCD, what is the length of line BD. Insert text on the triangle to show the length of line BD. When you’re done use the formula for the area of a triangle area equals 1/2 times base times height write an expression for the area of triangle ABC this when you do this base your answer on what u did in part E
Answers
Sine formula
[tex]\sin (angle)=\frac{\text{opposite side}}{hypotenuse}[/tex]Considering angle C from triangle BCD, the opposite side is side BD and the hypotenuse is side BC which length is a units. Then:
[tex]\begin{gathered} \sin (\angle C)=\frac{BD}{a} \\ \text{ Isolating BD} \\ \sin (\angle C)\cdot a=BD \end{gathered}[/tex]The area of a triangle is calculated as follows:
[tex]A=\frac{1}{2}\cdot\text{base}\cdot\text{height}[/tex]In triangle ABC the base is b units long and its height is segment BD, then the area of triangle ABC is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot BD \\ \text{ Substituting with the previous result:} \\ A=\frac{1}{2}\cdot b\cdot a\cdot\sin (\angle C) \end{gathered}[/tex]
Find the difference: (−1−5i)−(5−7i)
Answers
To determine the difference between complex number:
[tex](-1-5i)-(5-7i_{})[/tex]Step 1: Remove the bracket and find the difference
[tex]\begin{gathered} (-1-5i)-(5-7i_{}) \\ -1-5i-(5-7i_{}) \\ -1-5i-5+7i_{} \end{gathered}[/tex]Step2: Collect like terms
[tex]\begin{gathered} (-1-5i)-(5+7i_{}) \\ (-1-5i)-(5+7i_{} \\ -1-5-5i+7i \\ -6+2i \\ 2i-6 \end{gathered}[/tex]Hence the final answer is 2i - 6
10 + 8x + 2 = 4x + 36
Answers
we have
10 + 8x + 2 = 4x + 36
solve for x
step 1
Combine like terms left side
12+8x=4x+36
step 2
subtract 12 both sides
8x=4x+36-12
8x=4x+24
step 3
subtract 4x both sides
4x=24
step 4
Divide by 4 both sides
x=6
the answer is x=6Lin's mom bikes at a constant speed of 12 miles per hour. Lin walks at a constantspeed 1/3 of the speed her mom bikes. Sketch a graph of both of these relationships
Answers
ANSWER :
The graph is :
EXPLANATION :
From the problem we have the rates :
Lin's mom : 12 miles per hour
Lin : 1/3 of Lin's mom, that will be 12(1/3) = 4 miles per hour
Plot the points as (hour, miles).
(1, 12) and (1, 4)
Connect the points with the origin (0, 0)
That will be :
The black line represents Lin's mom and the orange line represents Lin.
1. choose one of the theorems about chords of a circle and state it using your own words2. create a problem that uses the theorem you explained3. explain how to solve the problem you just did
Answers
ANSWER:
We have the following:
1. A given chord in a circle is perpendicular to a radius through its center and is a distance less than the radius of the circle.
2. A circle with center C has a radius of 5 units. If a 6-unit chord AB is drawn at a distance D from the center of the circle, determine the value of D.
3.
Given:
Radius = 5 units
Length of chord = 6 units
A radius that meets the chord at center O divides it into two equal parts. Therefore:
AO = OB = 3 units
We can apply the Pythagorean theorem on the resulting triangle COB to determine the distance D, like this:
[tex]\begin{gathered} h^2=a^2+b^2 \\ \\ h=CB=R=5 \\ \\ a=OC=D \\ \\ b=OB=3 \\ \\ \text{ We replacing:} \\ \\ 5^2=D^2+3^2 \\ \\ 25=D^2+9 \\ \\ D^2=25-9 \\ \\ D=\sqrt{16} \\ \\ D=4 \end{gathered}[/tex]Therefore, the chord is at a distance of 4 units to the center of the circle.
2.) for the line represented by the given equation, find both the X intercept and the y-intercept. (Don’t simply look on the graphing calculator ). Make sure you indicate which answer is the x-intercept and which is the y-intercept . Then graph the line
Answers
Answer:
To find the y-intercept, we substitute x=0 in the given equation:
[tex]\begin{gathered} y=\frac{1}{2}\cdot0+3, \\ y=3. \end{gathered}[/tex]Therefore, the y-intercept has coordinates (0,3).
To find the x-intercept, we set y=0, and solve for x:
[tex]\begin{gathered} 0=\frac{1}{2}x+3, \\ 0-3=\frac{1}{2}x+3-3, \\ -3=\frac{1}{2}x, \\ 2\cdot(-3)=2\cdot(\frac{1}{2}x), \\ x=-6. \end{gathered}[/tex]Therefore, the x-intercept has coordinates (-6,0).
Finally, the graph of the given equation is:
identify two different types of optional deductions that an employer may subtract from a paycheck
Answers
Two possible deductibles can be the social care or the medical care
write an explicit formula for an nth term of the sequence 7, 35, 175,....
Answers
hello
to write an explicit formula, we have to determine what type of sequence is it
7, 35, 17
this is clearly a geometric progression with values of
first term = 7
common ratio = 5
the explicit formula of a geometric progression is given as
[tex]\begin{gathered} a_n=a\cdot r^{(n-1)}^{} \\ n=\text{nth term} \\ a=\text{first term} \\ r=\text{common ratio} \end{gathered}[/tex]now let's substitute the variables into the equation
[tex]\begin{gathered} a_n=a\cdot r^{(n-1)} \\ a_n=7\cdot5^{(n-1)} \\ a_n=35^{(n-1)} \end{gathered}[/tex]the equation above is the explicit formula for the sequence
Use the distributive property to write an equivalent expression. If you get stuck, consider drawing a diagram p( 4p + 9)
Answers
Given data:
The given expression is p( 4p + 9).
The given expression can be written as,
[tex]p(4p+9)=4p^2+9p[/tex]Thus, the simplification of the given expression is 4p^2 +9p.
Type the correct answer in each box. Use numerals instead of words.Sabrina is researching the growth of a population of horses on a ranch. She models the population of horses using the function below, where n is the number of years after she begins the research and b is an unknown base.
Answers
The initial number of horses is given by n=0.
Replacing on the equation:
[tex]\begin{gathered} w(0)=15\ast b^0 \\ w(0)=15\ast1 \\ w(0)=15 \end{gathered}[/tex]The initial number of horses is 15.
Now, if b= 1.35
We need to convert it to percentage:
b = 1.35 = 135%
Therefore, the growth is:
135%-100% = 35%
Then,
If b = 1.35, the annual percentage growth rate of the number of horses would be 35%.
please find the slopes and lengths then fill in the words that best describes the type of quadrilateral.
Answers
We can find the slopes using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]And the lengths using the following formulas:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Therefore:
[tex]m_{QR}=\frac{5-2}{-1-(-9)}=\frac{3}{8}[/tex][tex]m_{RS}=\frac{9-5}{1-(-1)}=\frac{4}{2}=2[/tex][tex]m_{ST}=\frac{6-3}{-7-1}=\frac{3}{8}[/tex][tex]m_{TQ}=\frac{6-2}{-7-(-9)}=\frac{4}{2}=2[/tex][tex]\begin{gathered} L_{QR}=\sqrt[]{(-1-(-9))^2+(5-2)^2} \\ L_{QR}=\sqrt[]{73} \end{gathered}[/tex][tex]\begin{gathered} L_{RS}=\sqrt[]{(1-(-1))^2+(9-5)^2} \\ L_{RS}=2\sqrt[]{5} \end{gathered}[/tex][tex]\begin{gathered} L_{ST}=\sqrt[]{(6-9)^2+(-7-1)^2} \\ L_{ST}=\sqrt[]{73} \end{gathered}[/tex][tex]\begin{gathered} L_{TQ}=\sqrt[]{(6-2)^2+(-7-(-9))^2}_{} \\ L_{TQ}=2\sqrt[]{5} \end{gathered}[/tex]Since:
[tex]\begin{gathered} m_{RS}=m_{TQ}\to m_{RS}\parallel m_{TQ} \\ m_{QR}=m_{ST}\to m_{QR}\parallel m_{ST} \end{gathered}[/tex]And:
[tex]\begin{gathered} L_{QR}=L_{ST} \\ L_{RS}=L_{QT} \end{gathered}[/tex]According to this, we can conclude it is a parallelogram
6) Raul received a score of 74 on a history test for which the class mean was 70 with a standard deviation of 3. He received a score of 70 on a biology test for which the class mean was 70 with standard deviation 7. On which test did he do better relative to the rest of the class?a)biology testb)history test c)the same
Answers
Solution:
The z score value is expressed as
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ where \\ x\text{ is the sample score} \\ \mu\text{ is the mean score} \\ \sigma\text{ is the standard deviation of the score} \end{gathered}[/tex]Given that
[tex]\begin{gathered} History: \\ x=74 \\ \mu=70 \\ \sigma=3 \\ Biology: \\ x=70 \\ \mu=70 \\ \sigma=7 \end{gathered}[/tex]To determine which test Raul did better,
step 1: Determine the z score value for the history test.
Thus,
[tex]\begin{gathered} z_{history}=\frac{74-70}{3}=1.333333333 \\ \end{gathered}[/tex]step 2: Determine the z score value for the biology test.
[tex]z_{biology}=\frac{70-70}{7}=0[/tex]step 3: Determine the probability that he did better in the history test.
Thus, from the normal distribution table,
[tex]Pr(history)=0.9088[/tex]step 4: Determine the probability that he did better in the biology test.
From the normal distribution table,
[tex]Pr(biology)=0.5[/tex]Since the probability that he did better in history is higher than the probability he did better in the biology test, this implies that he did better in the history test, relative to the rest of the class.
The correct option is B.
Simply the expression 11s(4)
Answers
44s
Explanation:[tex]\begin{gathered} \text{Given:} \\ 11s(4) \end{gathered}[/tex]To simplify the expression, we will expand the parenthesis:
[tex]\begin{gathered} 11s(4)\text{ = 11s }\times\text{ 4} \\ 11\text{ and 4 are numbers so we will multiply them together} \\ 11\text{ }\times\text{ 4 = 44} \end{gathered}[/tex][tex]\begin{gathered} 11s(4)\text{ = 11 }\times\text{ s }\times\text{ 4} \\ =\text{ 44 }\times\text{ s} \\ =\text{ 44s} \end{gathered}[/tex]Solve the inequality and graph the solution set on a real number line. Express the solution set in interval notation|x2 + 3x - 29 > 25The solution set is(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
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Given:
[tex]|x^2+3x-29|>25[/tex]Solve the following system of equations graphically on the set of axes below.y = -1/3x - 4 y = 2/3x + 2
Answers
Given:
[tex]\begin{gathered} y=-\frac{1}{3}x-4 \\ y=\frac{2}{3}x+2 \end{gathered}[/tex]Therefore, the system of solution is (-6,-2)
If angle AOB and angle BOC are complementary angles, and m angle AOB = x°, what is the measure of the supplement of angle BOC?
Answers
Complementary angles are angles whose sum is 90 degrees.
If angle AOB and angle BOC are complementary and angle AOB is x degrees, it means that angle BOC is (90 - x) degrees
Supplementary angles are angles whose sum is 180 degrees. If angle BOC is (90 - x) degrees, then the measure of its supplement would be
180 - (90 - x)
= 180 - 90 + x
= 90 + x
the measure of the supplement of angle BOC is (90 + x) degrees
- Your shipping staff of 15 employees must pack an order of 240 case today. In order for each person to do an equal share of the work How many cases does each staff member need to pack to the order?
Answers
Divide the 240 cases into the 15 employees:
Then, each staff member need to pack 16 cases.Jen L cut out the following figures on the solid lines and folded them on the third lines which figure formed a rectangle prism
Answers
A rectangular prism is a figure that has the following shape:
When the figure is unfolded the shape it has is the following:
Therefore, the right answer is the bottom right shape.
In the figure, BC||DE Angles_____1.CAF and EFA2.GAC and DFE3.CAF and EFH4.GAB and EFAare congruent______1.By the linear pair Theorem.2. because they are corresponding angles of parallel lines cut by transversal.3. by the vertical angles theorem.4. by the transitive property of congruence.GAC - CAFE because they are corresponding angles of parallel lines cut by a transversal.LAFE - HFD by the Vertical Angles Theorem.GAC - HFD by the_____1. Addition 2. Subtraction3. Substitution4. TransitiveProperty of Congruence.
Answers
CAF and EFH are congruent because they are corresponding angles of parallel lines cut by transversal.
Explanation:
BC is parallel to DE
Checking the options for angles that are congruent(the same):
1) CAF and EFA
Both angles are not corrsponding angles. They are not equal
2) GAC and DFE are not equal. DFE is a straight line.
3) CAF and EFH are corresponding angles. Hence the angles are congruent.
4) GAB and EFA are not equal. Hence, they are not congruent.
Hence, CAF and EFH are congruent because they are corresponding angles of parallel lines cut by transversal.
The profit P(x) obtained by manufacturing and selling x units of a certain product is given by P(x) = 60x - x2. Determine the number of units that must be produced and sold to maximize the profit. What is the maximum profit?
Answers
Answer:
The number of units that must be produced and sold to maximize the profit is 30 units
[tex]30\text{ units}[/tex]The maximum profit is;
[tex]\text{ \$900}[/tex]Explanation:
Given that the profit P(x) obtained by manufacturing and selling x units of a certain product is given by;
[tex]P(x)=60x-x^2[/tex]The maximum point is at;
[tex]P^{\prime}(x)=0[/tex]Differentiating P(x);
[tex]\begin{gathered} P^{\prime}(x)=60-2x=0 \\ 60-2x=0 \\ 2x=60 \\ x=\frac{60}{2} \\ x=30 \end{gathered}[/tex]The number of units that must be produced and sold to maximize the profit is 30 units
Substituting x into p(x);
[tex]\begin{gathered} P(30)=60(30)-30^2 \\ P(30)=900 \end{gathered}[/tex]The maximum profit is;
[tex]\text{ \$900}[/tex]5/3x+1/3x=13 1/3 + 8/3
Answers
Is this correct?
Now we will add the terms of the left side
[tex]\begin{gathered} \frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x \\ \frac{6}{3}x=13\frac{1}{3}+\frac{8}{3}x \end{gathered}[/tex]Now subtract 8/3 x from both sides
[tex]\frac{6}{3}x-\frac{8}{3}x=\frac{40}{3}+\frac{8}{3}x-\frac{8}{3}x[/tex][tex]-\frac{2}{3}x=\frac{40}{3}[/tex]Cancel the denominator 3 from both sides
-2x = 40
Divide two sides by -2
[tex]\frac{-2x}{-2}=\frac{40}{-2}[/tex]x = -20
Find the quotient and remainder using long division.x4 − 5x3 + x − 4 / x2 − 7x + 1
Answers
Given:
[tex]\frac{x^4-5x^3+x-4}{x^2-7x+1}[/tex]Required:
To find the quotient and remainder using long division.
Explanation:
Now
[tex]\begin{gathered} x^^2+2x+13 \\ ----------- \\ x^2-7x+1)x^4-5x^3+x-4 \\ \text{ }-x^4+7x^3-x^2 \\ --------------- \\ \text{ }+2x^3-x^2+x \\ \text{ }-2x^3+14x^2-2x \\ ---------------- \\ \text{ }+13x^2-x-4 \\ \text{ }-13x^2+91x-13 \\ ----------------- \\ \text{ }90x-17 \end{gathered}[/tex]Final Answer:
The quotient is
[tex]x^2+2x+13[/tex]The remainder is
[tex]90x-17[/tex]Find the value of X and each arc measurex =mGK=mHJ = mHGJ =mGKJ=
Answers
where:
[tex]\begin{gathered} m\angle GK=9x-22 \\ m\angle GH=61 \\ m\angle HJ=5x-7 \\ m\angle KJ=34 \\ so\colon \\ 9x-22+61+5x-7+34=360 \\ \end{gathered}[/tex]add like terms:
[tex]14x+66=360[/tex]Solve for x:
[tex]\begin{gathered} 14x=360-66 \\ 14x=294 \\ x=\frac{294}{14} \\ x=21 \end{gathered}[/tex]Hence:
[tex]\begin{gathered} m\angle GK=9x-22=9(21)-22=167 \\ m\angle HJ=5x-7=5(21)-7=98 \end{gathered}[/tex]Can you help me with this problem 5^3 x 5^1 then it says select one Add, Subtract, Multiply
Answers
Fractions and exponents
5^3 x 5^1
FIRST ADD 3+1 = 4
THEN MULTIPLY 4 times 5^4= 5x5x5x5= 625