Answer: 780
Step-by-step explanation:
Two times 2 is 4
4 + 89 = 93
93 +765 = 858
858 - 78 = 780
a variable is normally distributed with mean 21 and standard deviation 7. use your graphing calculator to find each of the following areas. write your answers in decimal form. round to the nearest thousandth as needed. a) find the area to the left of 24. b) find the area to the left of 17. c) find the area to the right of 19. d) find the area to the right of 25. e) find the area between 17 and 30.
(a) Area to the left of 24 is 0.6683.
(b) Area to the left of 17 is 0.284.
(c) Area to the right of 19 is 0.5028.
(d) Area to the right of 25 is 0.1019.
(e) Area between 17 and 30 is 0.0884.
We have given that a variable is normally distributed with mean 21 and standard deviation 7.
(a) We have to find area to the left of 24.
We will use z-formula
i.e Z = (X - μ) / σ
where X is the row score, μ is mean and σ is standard deviation.
Substituting the values we get,
Z = (24 - 21)/ 7
= 3/7
Z = 0.4285
The p-value for 0.4285 is 0.6683.
Therefore area to the left of 24 is 0.6683.
(b) Now to find area to the left of 17,
Z =(17 - 21)/7
= - 4/7
Z = -0.5714
The p-value for -0.5714 is 0.284.
The area to the left of 17 is 0.284
(c) To find the area of the the right of 19,
Z = (19 - 21)/ 7
= -2/7
Z = -0.007
P-value for -0.007 is 0.4972
Area of the right of 19 is , 1 - 0.4972 = 0.5028
(d) The area of the right of 25 is,
Z = (25 - 24)/7
= 1/7
Z = 0.1428
The p-value for 0.128 is 0.8981.
Area right of 25 is 1 - 0.8981 = 0.1019.
(e) To find area between 17 and 30 first we will find area of 17 and 30 individually.
We know area of 17 is 0.284.
Now area of 30,
Z = (30 - 24)/7
= 6/7
Z = 0.8571.
P-value for 0.8571 is 0.1956.
Area between 17 and 30 is,
0.284-0.1956 = 0.0884.
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2. the shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. about what percent of the products last between 9 and 15 days? about what percent of the products last between 12 and 15 days? about what percent of the products last 6 days or less? about what percent of the products last 15 or more days? 3. a line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a standard deviation of 4 minutes. what percentage of the people in line waited for more than 28 minutes? if 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes?
1) The percentage of the products last between 9 and 15 days is 68.26%.
2)The percent of the products last between 12 and 15 days is 34.13%.
3) The percentage of the people in line waited for more than 28 minutes 2.28%.
4) The percentage of the people wait for less than 16 minutes 15.87%
What is percent example?Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
What is the number whose 20% is 150?
20% of 150 is 30.
1) µ = 12
sd = 3
a) P(9<X<15)=P
(\frac{9-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})
9-12\sP(\s15\s12
= P(-1 < Z < 1)
= P(Z < 1) - P(Z < -1)
= 0.8413 - 0.1587
= 0.6826
= 68.26%
b) P(12<X<15)=P
(\frac{12-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})
12 - 12\sP(\s15\s12
= P(0 < Z < 1)
= P(Z < 1) - P(Z < 0)
= 0.8413 - 0.5
= 0.3413
= 34.13%
c) P(X6) = P(frac X-mu sigma frac 6 mu sigma)
=P(Z<\frac{6-12}{3})
= P(Z < -2)
= 0.0228
= 2.28%
d) P(X>15)=P(frac X–mu–sigma>frac X–mu–sigma)
=P(Z>\frac{15-12}{3})
= P(Z > 1)
= 1 - P(Z < 1)
= 1 - 0.8413
= 0.1587
= 15.87%
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Find two different sets of parametric equations for the rectangular equation. (Enter your answer in a list as [x = f(t), y = f(t)], [x = f(t), y = f(t)].) y = 6x - 1
The parametric equations of y = 6x -1 are [x = t, y = 6t - 1].
What are parametric equations?Parametric equations divide an equation into two or more equations, depending upon the variables in the original equation, both dependent and independent.
What does the variable t mean?In parametric equations we mostly use t as an independent variable and write all equations in terms of t.
To convert a rectangular equation in its parametric representation, the easiest way to do is to equate x with the variable t in the original equation. Now, our x is equal to t. Hence, the final answer is [x = t, y = 6t - 1].
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Marcus monthly salary is $1,500 plus 10% of sales. How much could Marcus earn per month with salary and 9% sales? Please explain your answer.
pls
If Marcus monthly salary is $1,500 plus 10% of sale, then he could earn 1500 + 0.09x per month with salary and 9% sales
Monthly salary of Marcus = $1500
The percentage incentives for sales = 10%
If the percentage of incentive for sales is 9 %
Consider the amount of sales is $x
Therefore the monthly salary of Marcus = Monthly salary of Marcus + (The amount of sales × 9/100)
Substitute the values in the equation
The monthly salary of Marcus = 1500 + (x×9/100)
Divide the numbers in the equation
= 1500 + (x × 0.09)
Multiply the numbers the numbers
= 1500 + 0.09x
Therefore, the monthly salary of Marcus will be 1500 + 0.09x
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Ava thinks of a number, v.
She squares her number and multiplies her result by 3.
Next, she divides this number by 4 and finally adds 9 to get an answer of
57,
Write an equation to describe this.
Answer:
Step-by-step explanation:i think she multiplyed 9x4 and got36. The next thing she did is added 3 i don’t know the rest for this
How do you write 145,000,000,000 in scientific notation?
The scientific notation is [tex]1.45*10^{11}[/tex]
Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We, therefore, employ scientific notations.
We need to move the decimal point 11 places to the left therefore the exponent for the 10s term will be positive:
[tex]145,000,000,000=145,000,000,000.0=1.45*10^{11}[/tex]
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the graph below shows the solution to which system of inequalities?
Answer: The correct answer is C
Step-by-step explanation: Let's find each equation without any inequalities first. We have a dotted line at y = 1, so we can already remove A and B. Now, a dotted line represents exclusivity and hence; it should not include the = sign.
which is the graph of y=2(x-3)^2 2
What is fg(x) given that f(x) equals x² + 7x and g(x) equals -2x² + 3x-5
Answer:
[tex] \huge{ \boxed{f(g(x)) = 4 {x}^{4} - 12 {x}^{3} + 15 {x}^{2} - 9x - 10 \\ }}[/tex]
Step-by-step explanation:
[tex]f(x) = {x}^{2} + 7x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ g(x) = - 2 {x}^{2} + 3x - 5[/tex]
To find f(g(x)), substitute g(x) into f(x). That is for every x found in f(x) replace it with g(x) and solve.
[tex]f(g(x)) = {( - 2 {x}^{2} + 3x - 5) }^{2} + 7( - {2x}^{2} + 3x - 5) \: \: \: \: \: \: \: \: \: \: \\ \\ = (4 x^4 - 12 x^3 + 29 x^2 - 30 x + 25) + (-14 x^2 + 21 x - 35) \\ = 4 {x}^{4} - 12 {x}^{3} + 29 {x}^{2} - 14 {x}^{2} - 30x + 21x + 25 - 35 \\ \\ = 4 {x}^{4} - 12 {x}^{3} + 15 {x}^{2} - 9x - 10[/tex]
We have the final answer as
[tex]f(g(x)) = 4 {x}^{4} - 12 {x}^{3} + 15 {x}^{2} - 9x - 10 \\ [/tex]
Find the domain and range.
The domain of the given function is (-∞, ∞), the rage of the function is (-∞, 1).
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The lowest to highest value of x-coordinate is the domain of the function.
The lowest to highest value of y-coordinate is the range of the function.
The highest point of the function is (2.5, 1).
The highest value of y-coordinate is 1.
Since the graph function can be expended to infinity, the lowest value of y-coordinate is -∞.
The range of the function is (-∞, 1).
Both ends of graph can be extended -∞ to ∞ for x-coordinate.
The domain of the function is (-∞, ∞).
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Triangle PQR is similar to triangle STU. Find the measure of side ST. Figures are not
drawn to scale.
Answer:
ST = 2.6
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{ST}{PQ}[/tex] = [tex]\frac{SU}{PR}[/tex] ( substitute values )
[tex]\frac{ST}{18}[/tex] = [tex]\frac{5.2}{36}[/tex] ( cross- multiply )
36 × ST = 18 × 5.2 = 93.6 ( divide both sides by 36 )
ST = 2.6
2. Using the equation y = 3x - 5, what would the output be for an input of 4?
a. 3
b. -3
c. -5
d. 7
i need help answering with steps
-40-2(3m+1/2) =7m-2
Answer:
Step-by-step explanation:
-Start by distributing the 2, -2(3m+1/2).
-Getting -6m-1, your equation should look like -40-6m-1=7m-2
-Combine -40 and -1 to get -41, and then add the -6m to the other side.
-The equation should look like -41=13m-2. Add the 2 to the -41 to get -39.
-Now, we have -39=13m. divide both sides by 13 to get m=-3.
Calculate the initial value for -12x - 10y = -50
The initial value for the equation, -12x - 10y = -50, is: 5.
How to Determine the Initial Value of a Linear Equation?The initial value of a linear equation is also known as the y-intercept of the equation. Th equation in slope-intercept form can be expressed as y = mx + b, where the initial value of the equation is represented as the value of b, while m is the slope.
Given the linear equation, -12x - 10y = -50, in standard form, to find the initial value, b, we have to rewrite the equation in slope-intercept form:
-12x - 10y = -50
Add 12x to both sides of the equations:
-10y = 12x - 50 [addition property of equality]
Divide both sides by -10
-10y/-10 = 12x/-10 - 50/-10 [division property of equality]
y = -6/5x + 5
Thus, the initial value of the y-intercept of the equation is: 5.
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Given: side AD congruent side DC and Angle ADB congruent angle CDB. Prove triangle ADE congruent triangle CDE!
ΔADE is congruent to ΔCDE if AD≅DC and ∠ADB≅CDB.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given that AD≅DC and ∠ADB≅CDB.
We need to prove that ΔADE≅ΔCDE
AB≅BC congruent sides.
AD≅DC congruent sides.
ΔABC≅ΔADC are similar triangles.
ΔABD≅ΔCBD are similar triangles.
ΔADE≅ΔCDE are congruent triangles and similar.
Hence, if triangles ∠ADB≅CDB and AD≅DC then ΔADE≅ΔCDE.
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Jack and Diane are jogging back and forth along a one-mile path. They started out at 9:00 A.M. from opposite ends of the path. They passed each other in 10 minutes when Diane has gone 1/3 mile. What time will they meet at the same end of the path? You have to assume they keep jogging at the same speeds.
Explain:
If they keep running at the same pace, they will eventually meet at the same end of the course after 30 minutes.
what is speed ?The rate at which distance and time change is what is meant by speed. It has the aspect of temporal and spatial distance. The basic unit of distance with the basic unit of time are combined to form the SI unit of speed. This means that the SI unit of speed is the metre per second.
The way that the issue is described is vague.
I believe what is being said here is that they continue to jog at the same speed.
Half a mile per ten minutes is Diane's speed.
2/3 miles per 10 minutes is Jack's speed.
The numerator and denominator (top and bottom of the ratio) must be multiplied by the factor between 10 minutes and an hour (60 minutes) in order to convert this to a standard miles per hour format.
60/10 = 6.
In order to convert the above speeds to miles per hour, we must multiply both speeds by 6.
Diane: (1/3 divided by 6)/hour equals 2 miles/hour
Jack: (4 miles per hour) = (2/3 x 6) / hour
Diane will complete one length in the time it takes Jack to complete a round trip (back) because he runs twice as fast as she does.
Running a mile at a speed of two miles per hour takes Diane 30 minutes.
Running 2 miles (back and forth) at a speed of 4 miles per hour will take Jack 30 minutes.
So after 30 minutes they will meet again at his starting point.
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Make X the
subject of m=n+x/p
Answer:
x = pm - pn
Step-by-step explanation:
m = n + [tex]\frac{x}{p}[/tex] Subtract n from both sides
m - n = n - n + [tex]\frac{x}{p}[/tex]
m-n = [tex]\frac{x}{p}[/tex] Multiply both sides by p
p(m - n) = ([tex]\frac{p}{1}[/tex]) [tex]\frac{x}{p}[/tex] [tex]\frac{p}{1}[/tex] means the same as p
pm - pn = x Distribute the p
x = pm - pn
4. Rudo buys a computer for $920. If this is 115% of what the store paid for
the same computer, how much did the store earn on the sale? Lesson 3-3
5. For each situation, select the percent to answer the question.
The amount that store earns is $120. By writing the equation for the given payment of the computer by Rudo, we get the required value.
How much did the store earn on the sale of a computer?It is given that, Rudo buys a computer for $920. This is 115% of what the store paid for the same computer.
So, consider the amount paid by the store for the same computer as 'x'.
Then, from the given information we can write that,
$920 = 115% of x
⇒ 920 = 0.15x
⇒ x = 920/0.15 = 800
So, the amount paid by the store for the same computer is $800
Thus, the amount earned by the store on the sale is $920 - $800 = $120.
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Write two expressions that are equivalent to -5/4x-3/4
Answer:
-10/8x-6/8
Step-by-step explanation:
Answer: -1.25x-0.75 or 1/4*(-5x-3)
Step-by-step explanation:
The first answer is converting the original expression into decimals (0.75 = 1/4). The second answer is factoring 1/4 out of the original expression (dividing each term by 1/4).
Assuming the cost of an associate leaving within 90 day is $3,000 what will be your facility's approximate cost of early turnover for this year?
The facility's approximate cost of early turnover for this year is $45000.
The cost of turnover is the cost associated with turning over one position. This calculation includes the cost of hiring for that position, training the new employee, any severance or bonus packages, and managing the role when it is not filled. Every company will experience some turnover.
Turnover cost refers to expense both tangible or intangible associated with replacing an employee. It is extremely high: it's estimated that losing an employee can cost a company 1.5-2 times the employee's salary.
Shift A has number of associated leaving the facility within 90 days is 8, per associated cost is $3000 and total cost is $24000.
Shift B has number of associated leaving the facility within 90 days is 5, per associated cost is $3000 and total cost is $15000.
Shift C has number of associated leaving the facility within 90 days is 2, per associated cost is $3000 and total cost is $6000.
Shift D has number of associated leaving the facility within 90 days is 0, per associated cost is $3000 and total cost is $30.
Therefore
Total cost = $24000 + $3000 + $6000
Total cost = $45000
Hence the facility's approximate cost of early turnover for this year is $45000.
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Find the value of x so that the ratios are equivalent.
x: 5/2 and 8:10
The value of x in the given ratio is 2.
What is ratio?The relationship in quantity, amount, or size between two or more things.
Given is a ratio, x:5/2 = 8:10
x/5/2= 8/10
2x/5 = 8/10
2x = 40/10
2x = 4
x = 2
Hence, The value of x in the given ratio is 2.
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given: \overline{ac} \perp \overline{bd} ac ⊥ bd and \angle a \cong \angle c.∠a≅∠c. prove: \triangle abd \cong \triangle cbd△abd≅△cbd.
It has been proved that △ABC is congruent to △CBD (△ABC ≅ △CBD) under the SAS condition.
What is the congruency of the triangle?In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Two triangles are said to be congruent if all the sides of a triangle are equal to all the corresponding sides of another triangle.
So, we have:
AC⊥BD and BD bisect AC
We have to prove:
△ABC ≅ △CBD
∠ADB = ∠CDB (Given: AC⊥BD)
BD = BD (Common side)
AD = CD (BD bisect AC)
So, △ABC ≅ △CBD under SAS condition.
Therefore, it has been proved that △ABC is congruent to △CBD (△ABC ≅ △CBD) under the SAS condition.
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Complete question:
Given: \overline{AC} \perp \overline{BD} AC ⊥ BD and \overline{BD} BD bisects \overline{AC}. AC. Prove \triangle ABD \cong \triangle CBD△ABD≅△CBD.
What is x/5 (fraction) = 40 looking for help
Answer: 200
Step-by-step explanation: first we will turn this into an equation
x/5=40, then we need to isolate the variable by multiplying both sides by 5.
x = 200
what is the equation of the function shown in the graph, given that the equation of the parent function is f(x)=(17)x?
The equation is shown in the graph as (C) g(x) = (1/7)^x - 4.
What are equations?A relationship between two terms on either side of an equal sign is described by a straightforward equation.
Additionally, addition, basic arithmetic, multiplication, and division are one or more of the four arithmetic calculations that simple equations undertake.
The system of equations can be expressed in three different ways: in point-slope form, standard form, and slope-intercept form.
So, the parent function is therefore known to be:
f(x) = (1/7)^x
Observe that the y-intercept results from evaluating this in zero:
f(0) = (1/7)^0 = 1
The graph's y-intercept is located at y = -3.
As a result, the function was translated downward by 4 units, bringing it to a point 4 units below the y-intercept of the parent function.
Thus, the graphed function is as follows:
g(x) = f(x) - 4
g(x) = (1/7)^x - 4
Therefore, the equation is shown in the graph as (C) g(x) = (1/7)^x - 4.
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Complete question:
What is the equation of the function shown in the graph, given that the equation of the parent function is f(x)=(1/7)^x ?
A. g(x)=(1/7)^x−3
B. g(x)=(1/7)^x−2
C. g(x)=(1/7)^x−4
D. g(x)=(1/7)^x+3
When a number is increased by 6, the answer is 13. Translate into linear equation but do not solve.
Answer:
n + 6 = 13
Step-by-step explanation:
let n be the number, then increasing by 6 means adding 6 to it , so
n + 6 = 13 ← linear equation
if a snowball melts so that its surface area decreases at a rate of 1cm2/min1cm2/min, find the rate at which the diameter decreases when the diameter is 10cm10cm.
The rate at which the diameter decreases is -0.16cm/min
Diameter:
In geometry, diameter refers the straight line that goes from one side to the other side of a circle, passing through the center.
Given,
Here we need to find if a snowball melts so that its surface area decreases at a rate of 1cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm. Finish solving the problem. Write an equation that relates the quantities.
Here we obtained the equation that relates the surface area S and the diameter D of a sphere given by
=> S = πD²
Now, we have differentiate the equation as,
=> dS/dt = d/dt (πD²)
=> dS/dt = π d/dt (D²)
=> dS/dt = 2πD dD/dt
Now, Solving for dD/dt, which is the unknown for this problem, we have
=> dD/dt = 1/2πD x dS/dt
Now, substituting the given values, the rate of change of the diameter when D=10 cm and dS/dt as (-1) is
=> dD/dt = 1/2 x π x 10 (-1)
=> dD/dt = -1/20π
=> dD/dt = -0.16cm/min
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More multiple choice math
Answer:
The System of inequalities shown is C.
the output voltage for an electric circuit is specified to be 130.asampleof40independentreadings on the voltage for this circuit gave a sample mean 128.6 and standard deviation 2.1.test the hypothesis that the average output voltage is 130against the alternative that it is lessthan 130.useatestwithlevel.05
Consequently, we deduce that the typical output voltage is under 130.
What is standard deviation ?In statistics, the standard deviation measures how widely distributed or how much a bunch of values can vary. While a big standard deviation shows that values are scattered throughout a wider range, a low standard deviation suggests that values are frequently close to the set's mean.
Here,
A defined output voltage of 130 is offered for an electrical circuit.
The voltage for this circuit was measured 40 times independently, with a sample mean of 128.6 and a standard deviation of 2.1.
Let's say the average output voltage.
Null Hypothesis, [tex]H_{0}[/tex]: = 130 denotes that the average output voltage is 130.
A Different Hypothesis, [tex]H_{A}[/tex] : < 130 ( it indicates that the average output voltage is below 130.)
One-sample t test statistics will be employed in this case because we are unsure about the population standard deviation;
T.S. = ~ [tex]\frac{X^{'}-u }{\frac{s}{\sqrt{n} } }[/tex]
In this case, sample mean output voltage equals 128.6
Sample standard deviation equals 2.1, or s.
n = 40 for the sample of independent readers.
Thus, test statistics equal.
So, test statistics = ~[tex]\frac{128.6-130 }{\frac{2.1}{\sqrt{40} } }[/tex]
= -4.216
Now, for a left-tailed test with a 0.05 level of significance, the t table provides a critical value of -1.685 at 39 degrees of freedom. We have enough data to reject our null hypothesis because it will fall in the rejection region because our test statistics are smaller than the crucial value of t, which is -4.216 -1.685.
Consequently, we deduce that the typical output voltage is under 130.
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A Blue spruce grows an average of 6 inches per year. A hemlock grows an average of 4 inches per year. If a blue spruce is 48 inches tall, and a Hemlock is 70 inches tall, when would you expect the trees to be the same height? What height will that be? Write and solve the system of equations for this problem.
In 12 years the two trees will be at the same height of 120 inches for the given condition of the equation.
What is an equation?
A mathematical statement called an equation demonstrates the equality of two mathematical expressions.
Based on the given condition of a question,
Let X be the required time duration, and then the equation will be
or, (48+6X)=(72+4X)
or, 48+6X=72+4X
or, 6X-4X=72-48
or, 2X=24
or, X=24/2
or, X=12 year
And height = 48 + 6*12 = 48 + 72 = 120 inches
Hence, In 12 years the two trees will be at the same height of 120 inches.
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Drag the tiles to the correct boxes to complete the pairs.
Match the one-to-one functions with their inverse functions.
f(x)=-17
f(x)=x-10
Inverse Function
f-¹(x) = 5x
ƒ-¹ (x) = ²
f-¹ (z) = x + 10
f-¹ (z) = 3(z+17)
f(x) = √2x
Function
f(x) = //
The inverse of a function is f^-1(x) = 3(x + 17)/2 and f^-1(x) = x + 10
What is function ?
An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.
Functions can be roughly categorized into four sorts. based on the element Numerous to one function, onto function, one to one and onto function, into function.
1.f(x) = 2x/3 - 17
Finding the inverse
y = f(x)
= 2x / 3 - 17
Exchange the variables, x for y and y for x
x = 2y / 3 - 17
Isolate the variable y
Adds 17 both sides
x + 17 = 2y / 3
Multiply by 3 both sides
3(x+17) = 2y
Divide by 2 both sides
y = 3(x + 17)/2
let f^-1(x) = y
f^-1(x) = 3(x + 17)/2
2. f(x) = x - 10
Finding the inverse
y = f(x)
= x - 10
Exchange the variables, x for y and y for x
x = y - 10
Isolate the variable y
Adds 10 both sides
y = x + 10
Multiply by 3 both sides
3(x+17) = 2y
let f^-1(x) = y
f^-1(x) = x + 10
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