Answer:
(-16, 17)
Step-by-step explanation:
The range of the function will be (-16, 17)
The range of function f(x) = 3x + 2 overthe interval -6 < x < 5 is (-13,14)
What is Range?The difference between the highest and lowest values.
The given function is f(x) = 3x + 2
f(x) equal tp three times of x plus two.
The given interval is minus six less than x less than five.
-6 < x < 5
Which means the x values are -5, -4, -3, -2, -1, 0, 1, 2,3,4
Plus in the function
f(-5)=-15+2=-13
f(-4)=-10
f(-3)=-9+2=-7
f(-2)=-6+2=-4
f(-1)=-3+2=-1
f(0)=0+2=2
f(1)=3+2=5
f(2)=6+2=8
f(3)=9+2=11
f(4)=12+2=14
Hence the range of function f(x) = 3x + 2 overthe interval -6 < x < 5 is (-13,14)
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Arrange 3/5,5/8,5/6 and 7/4 in ascending order
It’s already in ascending order.
3/5= .6
5/8= .625
5/6= .833
7/4= 1.75
Work out how many more skirts were sold on Friday than on Thursday ?
Answer:
15 more were sold on friday then thursday
Step-by-step explanation:
If f:X is 3x + b and ff(2) = 12, find the value of b
Answer:
[tex]b =6[/tex]
Step-by-step explanation:
Given
[tex]f(x) =3x + b[/tex]
[tex]f(2) = 12[/tex]
Required
Find b
[tex]f(2) = 12[/tex] implies that:
[tex]12 = 3 * 2 + b[/tex]
[tex]12 = 6 + b[/tex]
Collect like terms
[tex]b = 12 - 6[/tex]
[tex]b =6[/tex]
The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sample of 20 cables is selected and tested. Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population. Assume the variable is normally distributed.
Answer:
The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds.
This means that [tex]\mu = 2000, \sigma = 100[/tex]
A sample of 20 cables is selected and tested.
This means that [tex]n = 20, s = \frac{100}{\sqrt{20}} = 22.361[/tex]
Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population.
This is the 100 - 95 = 5th percentile, which is X when Z has a p-value of 0.05, so X when Z = -1.645. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.645 = \frac{X - 2000}{22.361}[/tex]
[tex]X - 2000 = -1.645*22.361[/tex]
[tex]X = 1963.2[/tex]
The sample mean that will cut off the upper 95% of all samples of size 20 taken from the population is of 1963.2 pounds.
Reggie and Jay go for a walk every morning. Reggie walks 2 14 miles. Jay walks 138 miles less than Reggie. What is the total distance they walk every morning?
Answer:
They walked a total distance of 290 miles every morning.
Step-by-step explanation:
First, we have to subtract 214 and 138.
= Jay walks 76 miles.
Next, we have add 214 and 76.
= 290 mi.
The cost of producing x units of a particular commodity is 2 C(x) = x' +6x +45 shillings, and the production level t hours into a particular production run is x(1)=0.312 +0.04 units. At what rate is cost changing with respect to time after 5 hours?
Complete question is;
The cost of producing x units of a particular commodity is C(x) = ⅔x² + 6x + 45 shillings and the production level t hours into a particular production run is x(t) = 0.3t² + 0.04t. At what rate is cost changing with respect to time after 5 hours?
Answer:
dC/dt = 49.45
Step-by-step explanation:
Since C(x) = ⅔x² + 6x + 45
And x(t) = 0.3t² + 0.04t
This means that;
C(x) = C(x(t))
The rate at what cost is changing with respect to time is given as;
dC/dt
Thus, from chain rule;
dC/dt = (dC/dx) × (dx/dt)
dC/dx = (4/3)x + 6
dx/dt = 0.6t + 0.04
Now, when t = 5, then;
x(5) = 0.3(5)² + 0.04(5)
x = 7.7
Thus;
dC/dx = (4/3)x + 6 = (4/3)(7.7) + 6 = 16.267
At 5 hours,
dx/dt = 0.6(5) + 0.04 = 3.04
Thus;
dC/dt = 16.267 × 3.04
dC/dt = 49.45
PLS HELP
If f(x) = x2 -1, what is the equation for f–1(x)?
We have a function,
[tex]f(x)=x^2-1[/tex]
and we are asked to find its inverse function.
An inverse function essentially gets you the original value that was dropped into a function.
For example,
If I put 5 into [tex]f(x)[/tex] I will get 24. Now If I take 24 and put it into the inverse function I have to get number 5 back.
The way to determine the inverse function swap the x and the [tex]f(x)[/tex], then solve for [tex]f(x)[/tex],
[tex]x=f(x)^2-1[/tex]
[tex]f(x)^2=x+1[/tex]
[tex]f(x)=\pm\sqrt{x+1}[/tex]
Of course the notation demands that the obtained function be called,
[tex]f^{-1}(x)=\pm\sqrt{x+1}[/tex]
Hope this helps :)
Analyze the diagram below and complete the instructions that follow. Find a, b, and c.
Answer:
The correct answer is the letter C.
Step-by-step explanation:
We can use the following trigonometric identity:
[tex]cos(60)=\frac{6}{b}[/tex] (1)
[tex]cos(45)=\frac{c}{b}[/tex] (2)
Solving each equation by b and equaling we have:
[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]
[tex]\frac{6}{cos(60)}=\frac{c}{cos(45)}[/tex]
Let's recall that:
[tex]cos(45)=\frac{1}{\sqrt{2}}[/tex]
[tex]cos(60)=\frac{1}{2}[/tex]
Then we have:
[tex]c=\frac{cos(45)*6}{cos(60)}[/tex]
[tex]c=\frac{2*6}{\sqrt{2}}[/tex]
[tex]c=\frac{12}{\sqrt{2}}[/tex]
[tex]c=6\sqrt{2}[/tex]
Using equation (1) we can find b.
[tex]cos(60)=\frac{6}{b}[/tex]
[tex]b=12[/tex]
Finally, we can find a using the next equation:
[tex]tan(60)=\frac{a}{6}[/tex]
[tex]a=6*tan(60)[/tex]
[tex]a=6\sqrt{3}[/tex]
Therefore, the correct answer is the letter C.
I hope it helps you!
Erica’s family is moving away from California. They decided to have a moving sale and sell each item for 70% off the price they originally paid for it. The sofa had an original price of $799, and the love seat had an original price of $549. What is the total cost of both items after the discount?
Find the sale price by multiplying the original price by 70% then add the two prices together to get the total.
799 x 0.70 = 559.30
549 x 0.70 = 384.30
Total: 559.30 + 384.30 = $943.60
Does the point (0, 0) satisfy the equation y = 9x?
Answer:
yes it does
Step-by-step explanation:
because the equation y=9x does not have a y-intercept (all slopes come in the form y=mx+b -- it can be written differently though) and since there is no 'b' that means the y-intercept is 0. So whenever there is no y-intercept, the slope starts at 0.
PLEASE HELP ASAP, Thank you
9514 1404 393
Answer:
2.244
Step-by-step explanation:
Your answer looks like it may have a transcription error.
The period is reasonably computed as the difference of the x-values of the given points:
period = 4.114 -1.870 = 2.244 . . . seconds
What are vertices of the conic 16x² - 25y² = 400 ?
Answer:
(-5, 0) and (5, 0)
Step-by-step explanation:
This equation fits the form for a hyperbola with x-intercepts. The standard form for such an equation is
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]
To get the equation in the question into this standard form, divide each term by 400.
[tex]\frac{16x^2}{400}-\frac{25y^2}{400}=\frac{400}{400}\\\frac{x^2}{25}-\frac{y^2}{16}=1[/tex]
To find the x-intercepts, make y = 0.
[tex]\frac{x^2}{25}=1\\x^2=25\\x=\pm 5[/tex]
The vertices are located at the points (-5, 0) and (5, 0).
Note: There are no y-intercepts; making x = 0 produces no real solutions for y.
At Dorcas's Hair Salon there are three hair stylists. 27% of the hair cuts are done by Martin, 30% are done by Jennifer, and 43% are done by Dorcas. Martin finds that when he does hair cuts, 6% of the customers are not satisfied. Jennifer finds that when she does hair cuts, 7% of the customers are not satisfied. Dorcas finds that when she does hair cuts, 3% of the customers are not satisfied. Suppose that a customer leaving the salon is selected at random. If the customer is not satisfied, what is the probability that their hair was done by Dorcas
Answer:
Dorcas's Hair Salon
If the customer is not satisfied, the probability that their hair was done by Dorcas is:
= 18.75%
Step-by-step explanation:
Number of hair stylists = 3
Martin Jennifer Dorcas Total
Percentage of haircuts
done 27% 30% 43% 100%
Percentage of dissatisfied
customers 6% 7% 3%
Proportion of dissatisfied
customers 37.5% (6/16) 43.75% (7/16) 18.75% (3/16)
If the customer is not satisfied, the probability that their hair was done by Dorcas
= 18.75%
write any five sentences of fraction?
Step-by-step explanation:
Fractions represent equal parts of a whole or a collection.
Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.
a fraction has 2 parts
The number on the top of the line is called the numerator. It tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator. It shows the total divisible number of equal parts the whole into or the total number of equal parts which are there in a collection.
There are different types of fraction
unit fractionimproper fractionproper fractionmixed fractionThe scatterplot shows the selling prices of homes and the square feet of living space.
A graph titled home value has square feet (thousands) on the x-axis, and price (hundred thousand dollars) on the y-axis. Points are at (1.2, 1), (1.5, 1.1), (2, 1.5), (2.5, 2). An orange point is at (3.8, 3.9).
Complete the statements based on the information provided.
The scatterplot including only the blue data points shows
✔ a strong positive
correlation. Including the orange data point at (3.8, 3.9) in the correlation would
✔ strengthen
and
✔ increase
the value of
Answer:
✔ a strong positive
✔ strengthen
✔ increase
ED2021
Answer:
- a strong positive
- strengthen
- increase
What is the vertex of the graph of this function
y= -(x+2) (x+4)
Answer:
y=-(x+2)(x+4)
y=-(x^2+4x+2x+8)
y=-(x^2+6x+8)
y=-(x^2+4x+2x+8)
Y=-x(x+4)+2(x+4)
y=-(x+2)(X+4)
So vertex is (2,4)
compute (-12)+(-8)+30
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-12 + (-8) + 30}\\\\\large\textsf{= -12 - 8 + 30}\\\\\large\textsf{-12 - 8 = \bf -20}\\\\\large\textsf{= -20 + 30}\\\\\large\textsf{= \bf 10}\\\\\\\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{10}}}}\huge\checkmark\\\\\\\\\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A box plot is shown
O
2
4
6
8
10
12
Determine the five-statistical summary of the data. Drag the correct number to each variable in the summary.
14
16
18
20
22 24 26
28
30
Minimum:
Maximum:
Median:
First Quartile:
Third Quartile:
1
2
3
4
11
5
12
6
ما تا ته
13
14
8
21
15
22
16
10
23
17
24
18
25
19
26
20
27
28
29
30
Please answer fast
Answer:
Minimum = 8
Maximum = 28
Median = 22
First Quartile = 12
Third Quartile = 26
Step-by-step explanation:
✔️Minimum value = the value at the beginning of the whisker from your left = 8
✔️Maximum value = the value at the end of the whisker to your right = 28
✔️Median = the value at the vertical line that divides the box into two = 22
✔️First Quartile = the value at the beginning of the edge of the box = 12
✔️Third Quartile = the value at end of the edge of the box = 26
How to find the inverse of this matrix
[tex]\left[\begin{array}{ccc}1&0\\0&3\\\end{array}\right][/tex]
Answer:
Here we have the matrix:
[tex]M = \left[\begin{array}{ccc}1&0\\0&3\end{array}\right][/tex]
And we want to find its inverse.
The inverse of a 2x2 matrix A is:
(1/det(A))*adj(A)
where det(A) is the determinant of the matrix.
Such that for a matrix:
[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right][/tex]
The determinant is:
det(A) = a₁₁*a₂₂ - a₁₂*a₂₁
in the case of our matrix M, the determinant is:
det(M) = 1*3 - 0*0 = 3
and adj(A) is a transposition along the diagonal, and for the other elements, we just change its sign.
Then for our matrix A we would have:
[tex]adj(A) = \left[\begin{array}{ccc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex]
Then for our matrix M, we have:
[tex]adj(M) = \left[\begin{array}{ccc}3&-0\\-0&1\end{array}\right][/tex]
Then the inverse of the matrix M is:
[tex]M^{-1} = \frac{1}{det(M)} *adj(M) = \frac{1}{3}\left[\begin{array}{ccc}3&0\\0&1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1/3\end{array}\right][/tex]
which polygon will NOT tessellate a plane?
Answer:
pentagons
Step-by-step explanation:
In fact, there are pentagons which do not tessellate the plane. The house pentagon has two right angles. Because those two angles sum to 180° they can fit along a line, and the other three angles sum to 360° (= 540° - 180°) and fit around a vertex.
Answer:
The Regular Pentagon.
Explanation
I got a 100 % on the quiz
I need help guys thanks so much
I think its A) (f+g)(z)=|2x+4|-2
Step-by-step explanation:
The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 60 cars per month. The cars cost $70 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%.
Required:
a. Determine the economic order quantity and total annual cost under the assumption that no backorders are permitted.
b. Using a $45 per-unit per-year backorder cost, determine the minimum cost inventory policy and total annual cost for the model racing cars.
c. What is the maximum number of days a customer would have to wait for a backorder under the policy in part (b)? Assume that the Hobby Shop is open for business 300 days per year.
d. Would you recommend a no-backorder or a backorder inventory policy for this product? Explain.
Answer:
Step-by-step explanation:
A) Demand per month= 40 cars
Annual Demand (D)= 12*40 = 480
Fixed Cost per order (K)= 15
Holding Cost= 20% of cost= 60 *0.2 = 12
a. Economic Order Quantity=
Q^{*}={\sqrt {{\frac {2DK}{h}}}}
= √(2*480*15)/12
=34.64 ~ 35
Total Cost =P*D+K(D/EOQ)+h(EOQ/2) P= Cost per unit
= 60*480+ 15(480/35) + 12(35/2)
= 28800+ 205.71+ 210
=$29215.71
B). Backorder Cost (b)= $45
Qbo= Q* × √( b+h/ h)
= 35*√(12+45/ 45)
= 35* 1.12
=39.28 ~ 39
Shortage (S)= Qbo * (K/K+b)
= 39* (15/15+45)
= 39* 0.25
= 9.75
Total Cost Minimum=( bS2/ 2Qbo) + P (Qbo- S)2/2Qbo + K(D/Qbo)
=45* 9.752 / 2* 392 + 60 (39-9.75)2/ 2* 392 + 15 ( 480/39)
= 1.40+ 21.9.+ 184.61
=$207.91
C)Length of backorder days (d) = Demand ÷ amount of working days
d = 480 ÷ 300
d = 1.6
Calculate the backorders as the maximum number of backorders divided by the demand per day
s/d = 9.75/1.6 = 6.09 days (answer)
D) Calculate the difference in total between not using backorder:
$207.85 + $207.85 - 207.91 = $207.79
The saving in using backorder is $207.79.
Therefore I would recommend using a backorder
The lengths of two sides of the right triangle ABC shown in the illustration given
b= 8ft and c= 17ft
Answer:
15ft
Step-by-step explanation:
By Pythagorean theorem
[tex] {a}^{2} + {b}^{2} = {c}^{2}\\ {a}^{2} + {8}^{2} = {17}^{2} \\ {a}^{2} + 64 = 289 \\ {a}^{2} = 289 - 64 \\ {a}^{2} = 225 \\ \sqrt{ {a}^{2} } = \sqrt{225} \\ a = 15ft \\ [/tex]
The price of an item has been reduced by 70%. The original price was $30. What is the price of the item now?
Answer:
$9
Step-by-step explanation:
30*(100%-70%)=9
Answer:
9
Step-by-step explanation:
Take the original price
Multiply by the discount percent
30 *70%
30 *.70
21
The discount is 21 percent
Subtract this from the original amount
30-21
9
find the slope of the line
Answer:
from one point to another, it increases by 1 and right by 2
1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Pick two points on the line
(0,1) and (2,2)
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (2-1)/(2-0)
= 1/2
the question is in the photo. it is asking for 2 answers
9514 1404 393
Answer:
2nd force: 99.91 lbresultant: 213.97 lbStep-by-step explanation:
In the parallelogram shown, angle B is the supplement of angle DAB:
∠B = 180° -77°37' = 102°23'
Angle ACB is the difference of angles 77°37' and 27°8', so is 50°29'.
Now, we know the angles and one side of triangle ABC. We can use the law of sines to solve for the other two sides.
BC/sin(A) = AB/sin(C)
AD = BC = AB·sin(A)/sin(C) = (169 lb)sin(27°8')/sin(50°29') ≈ 99.91 lb
AC = AB·sin(B)/sin(C) = (169 lb)sin(102°23')/sin(50°29') ≈ 213.97 lb
PLEASE HELP THIS IS DUE ASAP (answer in decimal!!!!)
Enter the equation of the line in slope-intercept form. Slope is -1/2, and (-9,4) is on the line. The equation of the line is y=
Answer:
[tex]y=\displaystyle-\frac{1}{2}x-\displaystyle\frac{1}{2}[/tex]
Step-by-step explanation:
Hi there!
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)
1) Plug in the slope (m)
We're given that the slope is [tex]\displaystyle-\frac{1}{2}[/tex]. In [tex]y=mx+b[/tex], replace m with [tex]\displaystyle-\frac{1}{2}[/tex]:
[tex]y=\displaystyle-\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\displaystyle-\frac{1}{2}x+b[/tex]
We're given the point (-9,4). Plug this point into the equation as [tex](x,y)[/tex] and solve for b:
[tex]4=\displaystyle-\frac{1}{2}(-9)+b\\\\4=\displaystyle\frac{9}{2}+b[/tex]
Subtract [tex]\displaystyle\frac{9}{2}[/tex] from both sides to isolate b:
[tex]4-\displaystyle\frac{9}{2}=\displaystyle\frac{9}{2}+b- \displaystyle\frac{9}{2}\\\\\displaystyle-\frac{1}{2} = b[/tex]
Therefore, the y-intercept is [tex]\displaystyle-\frac{1}{2}[/tex]. Plug this back into [tex]y=\displaystyle-\frac{1}{2}x+b[/tex] as b:
[tex]y=\displaystyle-\frac{1}{2}x+(\displaystyle-\frac{1}{2})\\\\y=\displaystyle-\frac{1}{2}x-\displaystyle\frac{1}{2}[/tex]
I hope this helps!
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after each of the following.
after 2s : cm2/s
after 5s : cm2/s
after 6s : cm2/s
9514 1404 393
Answer:
2s: 45,239 cm²/s5s: 113,097 cm²/s6s: 135,717 cm²/sStep-by-step explanation:
The radius is a function of time:
r(t) = 60t . . . . . radius in cm; time in s
Then the area of the circle is ...
A = πr² = π(60t)² = 3600πt²
The rate of change of area is the derivative of this:
A' = 2·3600πt = 7200πt
The rates of change of interest are ...
after 2s: 45,239 cm²/s
after 5s: 113,097 cm²/s
after 6s: 135,717 cm²/s
The distribution of widgets from a production line is known to be approximately normal with mean 2.7 inches and standard deviation 0.25 inches. About 95% of the distribution lies between what two values?
A. 2.45 inches and 3.2 inches
B. 2.45 inches and 2.95 inches
C. 2.2 inches and 3.2 inches
D. 1.95 inches and 3.45 inches
Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.
To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81
The formula for calculating the z-score is expressed as;
[tex]z=\frac{x-\overline x}{s}[/tex] where:
[tex]\overline x[/tex] is the mean
s is the standard deviation
z is the z-scores
Given the following
[tex]\overline x[/tex]=2.7 in
s = 0.25
if z = -2.81
[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]
Similarly:
[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]
Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.
Learn more on normal distribution here: https://brainly.com/question/23418254
