Answer:
y = 2(x - 3)² + 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, 5), thus
y = a(x - 3)² + 5
To find a substitute (1, 13) into the equation
13 = a(1 - 3)² + 5 ( subtract 5 from both sides )
8 = 4a ( divide both sides by 4 )
a = 2, then
y = 2(x - 3)² + 5 ← equation of parabola in vertex form
5. If W(-10, 4), X(-3,-1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your
answer.
Answer:
an isosceles right triangle
Step-by-step explanation:
The square of the length of a side can be found from the distance formula:
d^2 = (x2-x1)^2 +(y2-y1)^2
The square of the length of WX is ...
WX^2 = (-3-(-10))^2 +(-1-4)^2 = 49+25 = 74
The square of the length of XY is ...
XY^2 = (-5-(-3))^2 +(11-(-1))^2 = 4 +144 = 148
The square of the length of YW is ...
YW^2 = (-10-(-5))^2 +(4 -11)^2 = 25 +49 = 74
The sum of the squares of the short sides is equal to the square of the long side, so this is a right triangle. The squares of the short sides are equal, so this is an isosceles right triangle.
A local mattress manufacturer wants to know if its manufacturing process is in or out of control and has hired you, a statistics expert in the field, to analyze its process. Specifically, the business has run 20 random samples of size 5 over the past month and has determined the mean of each sample.
a. Determine the estimate of the mean when the process is in control.
b. Assuming the process standard deviation is .50 and the mean of the process is the estimate calculated in part a, determine the Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process.
c. Explain the results to the vice-president of the mattress manufacturer focusing on whether, based on the results, the process is in or out of control.
Sample no. Mean of Sample
1 95.72
2 95.44
3 95.40
4 95.50
5 95.56
6 95.72
7 95.60
8 95.24
9 95.46
10 95.44
11 95.80
12 95.20
13 94.82
14 95.78
15 95.18
16 95.32
17 95.08
18 95.22
19 95.04
20 95.
Answer:
Answer to question a = 95.4
Answer to question b = UCL = 96.07
LCL = 94.73
Answer to question c = Process is still in control
Step-by-step explanation:
a. The computation of estimate mean is as shown below:-
= 95.4
b. The computation of Upper Control Limit (UCL) and the Lower Control Limit (LCL) for the manufacturing process is shown below:-
= 95.4 + 0.67082
= 96.07
= 95.4 - 0.67082
= 94.73
c. The explanation is shown below:-
From the above calculation we can see that the sample lies between LCL AND UCL that is (94.73 ,96.07) ,
The Process is still in control
Brian needs to paint a logo using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle?
Answer:
7.5 cm²
Step-by-step explanation:
Dimensions of the large ∆:
[tex] base (b) = 3cm, height (h) = 9cm [/tex]
[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]
Dimensions of the small ∆:
[tex] base (b) = 2cm, height (h) = 6cm [/tex]
[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]
Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²
Patios can be made by mixing cubic meters of ash, stone, and wood chips in the ratio 5:7:3. How much stone is needed to make 45 cubic meters of patio?
Answer:
21 m^3
Step-by-step explanation:
5 + 7 + 3 = 15
The ratio of stone to the total is
7:15
If the total needed is 45 m^3, then we multiply both parts of the ratio by 3.
7 * 3 : 15 * 3
21:45
Answer: 21 m^3
coordinates of England
Answer:
52.3555 north
1.1745 west
Find the number of pieces of floor tiles each measuring 26cm long and 10cm wide needed to lay a floor measuring 260m long and 15m wide
Answer:
150,000
Step-by-step explanation:
1 m = 100 cm
260 m = 260 * 100 cm = 26000 cm
15 m = 15 * 100 cm = 1500 cm
area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2
area of 1 tile = 26 cm + 10 cm = 260 cm^2
number of tiles needed = 39,000,000/260 = 150,000
Answer: 150,000 tiles
The following shape is based only on squares, semicircles, and quarter circles. Find the area of the shaded part.
Answer:
this? hope it helps ........
Answer:
The answer is area=32pi-64 and the perimeter is 8pi
Step-by-step explanation:
What is the solution of 3(x + 4) = -12 ? Group of answer choices 3 0 8 -8
Answer:
Step-by-step explanation:
3(x + 4) = -12
3x+12 = -12
3x= -12-12
3x= -24
x = -24/3
x= -8
Answer:
x = -8
Step-by-step explanation:
3(x+4) = -12
3*x + 3*4 = -12
3x + 12 = -12
3x = -12 - 12
3x = -24
x = -24/3
x = -8
Check:
3(-8+4) = -12
3*-4 = -12
a wolf population of 850 wolves is increasing by 7% each year. Find the wolf population after 7 years
Answer:
1,267 wolvesStep-by-step explanation:
Initial population of wolf = 850 wolves
If the wolves increases by 7% each year, yearly increment will be 7% of 850
= 7/100 * 850
= 7*8.5
= 59.5 wolves.
This shows that the wolves increases by 59.5 each year.
After 7 years, increment will be equivalent to 59.5 * 7 = 416.5
The wolf population after 7 years = Initial population + Increment after 7 years
= 850 + 416.5
= 1266.5
≈ 1267 wolves
Hence the population of the wolves after 7 years is approximately 1,267 wolves
Solve this system of equations:
3x - 2y = -8
y=3/2x - 2
PLEASE WRITE THE STEPS
Hey there! I'm happy to help!
We see that y is equal to 3/2x-2. We can replace the y in the first equation with 3/2x-2 because they are equal and we can solve for x.
3x-2(3/2x-2)=-8
We use the distributive property to undo the parentheses.
3x-3x+4=-8
We combine like terms.
4=-8
We see that since there is no x anymore, there cannot be a solution. We have no x value to solve for the y value either, so there is no solution to this system of equations.
Have a wonderful day! :D
-4-(-1) answer the question
Answer:
-3
Step-by-step explanation:
Since you are subtracting a negative, it turns positive so it will be.
-4+1
-3
Answer:
-3
Step-by-step explanation:
-4-(-1) = -4 + 1 = -3
Select the correct answer.
Answer:
B
Step-by-step explanation:
With limits, the first thing one should always try is direct substitution. Therefore, let's try that.
[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) \\= (\frac{(1)^2+1}{(1)+1}+(1)^2+3) \\=\frac{2}{2}+1+3\\ =1+4=5[/tex]
Therefore:
[tex]\lim_{x \to 1} (\frac{x^2+1}{x+1}+x^2+3) =5[/tex]
Which of the following is a correct interpretation of the expression -4 - (-7)?
Answer:
D
Step-by-step explanation:
So we have the expression:
[tex]-4-(-7)[/tex]
First, simplify. Two negatives make a positive. Therefore, the -(-7) turns into +7:
[tex]-4-(-7)\\=-4+7[/tex]
When adding on the number line, we move to the right.
Therefore, the correct interpretation is the value 7 digits to the right of -4.
D is the correct answer.
Answer:
D. the number that is 7 to the right of -4 on the number line
Step-by-step explanation:
interpret -4 - (-7)
= -4 +7
therefore
the number that is 7 to the right of -4 on the number line
so its D.
Solve systems of equations 15 points NOT CLICKBAIT!!! -6y+11y= -36 -4y+7x= -24
Answer:
x = -264/35
y = -36/5
Step-by-step explanation:
-6y + 11y = -36
-4y + 7x = -24
Solve for y in the first equation.
-6y + 11y = -36
Combine like terms.
5y = -36
Divide both sides by 5.
y = -36/5
Plug y as -36/5 in the second equation and solve for x.
-4(-36/5) + 7x = -24
Expand brackets.
144/5 + 7x = -24
Subtract 144/5 from both sides.
7x = -264/5
Divide both sides by 7.
x = -264/35
Answer: -264/35
Step-by-step explanation:
i did my work on a calculator
f(x)=3x+5 and g(x)=4x2-2 h(x)=x2-3x+1 Find f(x)+g(x)-h(x).
Answer:
f(x)+g(x)-h(x) = 3x² + 6x + 2Step-by-step explanation:
f(x) = 3x + 5
g(x) = 4x² - 2
h(x) = x² - 3x + 1
f(x)+g(x)-h(x) means subtract h(x) from the sum of f(x) and h(x)
f(x)+g(x)-h(x) = 3x + 5 +( 4x² - 2) - (x² - 3x + 1)
Remove the brackets
That's
f(x)+g(x)-h(x) = 3x + 5 + 4x² - 2 - x² + 3x - 1
Group like terms
We have
f(x)+g(x)-h(x) = 4x² - x² + 3x + 3x + 5 - 2 - 1
Simplify
We have the final answer as
f(x)+g(x)-h(x) = 3x² + 6x + 2Hope this helps you
Hope this helps you
work out angle pqr please if you know it i willl give brainliest to fastest person
Answer:
∠PQR = 67.36° (Approx)
Step-by-step explanation:
Given:
PRQ is a right triangle
∠R = 90°
PQ = 13 cm
QR = 5 cm
PR = 12 cm
Find:
∠PQR = ?
Computation:
Using trigonometry application.
SinФ = 12 / 13
SinФ = 0.92
Sin 67.36° = 0.92
So,
∠PQR = 67.36° (Approx)
You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.
Answer:
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Solution Set : { x = 123, y = 246, z = 11 }
Step-by-step explanation:
Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,
x + y + z = 380,
And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.
5x + 3y + 10z = 1460
The silly string tickets were sold for twice as much as the car wash tickets.
y = 2x
Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.
System of Equations :
[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,
[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three
And we can continue, canceling the leading co - efficient in each row until this matrix remains,
[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]
x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold
Time spent using e-mail per session is normally distributed with a mean = to 8 minutes and standard deviation = 2minutes. If a random samples of 36 sessions were selected, the computed sample standard deviation would be
a. 0.25
b. 0.3333
c. 0.42
d. 0.48
Answer:
The correct option is (b) 0.3333.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].
The standard error is given as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]
Compute the standard deviation of the sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]
Thus, the standard deviation of the sample mean is 0.3333.
Simplify to create an equivalent expression. 4(-15-3p)-4(-p+5)
Answer:
- 8p - 80
Step-by-step explanation:
Given
4(- 15 - 3p) - 4(- p + 5) ← distribute both parenthesis
= - 60 - 12p + 4p - 20 ← collect like terms
= - 8p - 80
Answer:
-8p -80
Step-by-step explanation:
4(-15-3p)-4(-p+5)
Distribute
-60 -12p +4p -20
Combine like terms
-60-20 -8p +4p
-80-8p
-8p -80
If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal distribution. 1- What percentage of a cucumber give the crop amount between 778 and 834 kg? 2- What the probability of cucumber give the crop exceed 900 kg ?
Answer:
a
The percentage is
[tex]P(x_1 < X < x_2 ) = 51.1 \%[/tex]
b
The probability is [tex]P(Z > 2.5 ) = 0.0062097[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 800[/tex]
The variance is [tex]var(x) = 1600 \ kg[/tex]
The range consider is [tex]x_1 = 778 \ kg \ x_2 = 834 \ kg[/tex]
The value consider in second question is [tex]x = 900 \ kg[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{var (x)}[/tex]
substituting value
[tex]\sigma = \sqrt{1600}[/tex]
[tex]\sigma = 40[/tex]
The percentage of a cucumber give the crop amount between 778 and 834 kg is mathematically represented as
[tex]P(x_1 < X < x_2 ) = P( \frac{x_1 - \mu }{\sigma} < \frac{X - \mu }{ \sigma } < \frac{x_2 - \mu }{\sigma } )[/tex]
Generally [tex]\frac{X - \mu }{ \sigma } = Z (standardized \ value \ of \ X)[/tex]
So
[tex]P(x_1 < X < x_2 ) = P( \frac{778 - 800 }{40} < Z< \frac{834 - 800 }{40 } )[/tex]
[tex]P(x_1 < X < x_2 ) = P(z_2 < 0.85) - P(z_1 < -0.55)[/tex]
From the z-table the value for [tex]P(z_1 < 0.85) = 0.80234[/tex]
and [tex]P(z_1 < -0.55) = 0.29116[/tex]
So
[tex]P(x_1 < X < x_2 ) = 0.80234 - 0.29116[/tex]
[tex]P(x_1 < X < x_2 ) = 0.51118[/tex]
The percentage is
[tex]P(x_1 < X < x_2 ) = 51.1 \%[/tex]
The probability of cucumber give the crop exceed 900 kg is mathematically represented as
[tex]P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x - \mu }{\sigma } )[/tex]
substituting values
[tex]P(X > x ) = P( \frac{X - \mu }{\sigma } >\frac{900 - 800 }{40 } )[/tex]
[tex]P(X > x ) = P(Z >2.5 )[/tex]
From the z-table the value for [tex]P(Z > 2.5 ) = 0.0062097[/tex]
Solve 5(2x + 4) = 15. Round to the nearest thousandth.
[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]
Answer:
[tex]\huge\boxed{x=-0.5}[/tex]
Step-by-step explanation:
[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]
A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?
Answer:
8.8 pounds
Step-by-step explanation:
Given the following :
Combined weight loss which occurred within a week = 28 kg
Number of days in a week = 7 days
1 kilogram (kg) = 2.2 pounds
Combined weight loss in pounds that occurs within a week:
Weight loss in kg × 2.2
28kg * 2.2 = 61.6 pounds
Assume weight loss occurred at a constant rate :
Weight lost by the group per day :
(Total weight loss / number of days in a week)
(61.6 pounds / 7)
= 8.8 pounds daily
Answer:
88
Step-by-step explanation:
Found the answer and I am doing the quiz rn lel
Write "six and thirty-four thousandths" as a decimal
Answer:
6.034
Step-by-step explanation:
6 is a whole number.
.034 because it is 34 thousandths, not 34 hundredths.
Find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area. z -2.13 0 A normal curve is over a horizontal z-axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.13 and 0. The area under the curve between negative 2.13 and 0 is shaded. The area of the shaded region is nothing.(Round to four decimal places as needed.)
Answer:
The area of the shaded region under the standard normal curve is 0.4834.
Step-by-step explanation:
A random variable X is said to have a normal distribution with mean, µ and variance σ².
Then [tex]Z=\frac{X-\mu}{\sigma}[/tex], is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z [tex]\sim[/tex] N (0, 1).
The distribution of these z-variates is known as the standard normal distribution.
Compute the area under the curve between -2.13 and 0 as follows:
[tex]P(-2.13<Z<0)=P(Z<0)-P(Z<-2.13)[/tex]
[tex]=0.50-0.01659\\=0.48341\\\approx 0.4834[/tex]
Thus, the area of the shaded region under the standard normal curve is 0.4834.
Using the normal distribution, it is found that the area of the shaded region is of 0.4833.
In a normal distribution, our test statistic is the z-score, which measures how many standard deviations a measure is from the mean. Each z-score has an associated p-value, which is given at the z-table, and represents the percentile of a measure or or the z-score, which is the area to the left under the normal curve.The area between two z-scores is the subtraction of their p-values.In this problem, we want the area between Z = -2.13 and Z = 0.
Z = 0 has a p-value of 0.5.Z = -2.13 has a p-value of 0.0166.0.5 - 0.0166 = 0.4833
The area of the shaded region is of 0.4833.
A similar problem is given at https://brainly.com/question/22940416
Jullian measures the distance he drives to work each day using the odometer on his car, which measures distance in miles, accurate to the nearest tenth of a mile. Using that measurement, he claims that the exact distance he drives to work is 11.7 miles. Use complete sentences to explain why jullian is incorrect
Answer:
Kindly check explanation
Step-by-step explanation: Jullian's claim that the distance she drives to work is exactly 11.7miles is incorrect because, in other to record or get the exact result of a certain calculation such as Jullian's Distance, the value of the distance obtained will not be approximated or rounded. In this scenario, Distance was to the nearest tenth of a mile, thereby altering the true outcome of the calculation.
The word exact means that what is stated is very precise and does not fall below or above in any respect. However, a number whose accuracy is to the nearest tenth of a mile, violates this assertion.
Help Quick Please. Will give brainliest.
Answer:
72[tex]\sqrt{3}[/tex] units²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = ST = a = 12 and h = RS
To calculate RS use the tangent ratio in the right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex] , thus
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )
RS = 12[tex]\sqrt{3}[/tex]
Thus
A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²
Which is the solution to the inequality?
2 3/5 <b-8/15
Answer:
3 2/15 <b
Step-by-step explanation:
2 3/5 <b-8/15
Add 8/ 15 to each side
2 3/5 + 8/ 15 <b-8/15 + 8/15
2 3/5 + 8 /15 <b
Get a common denominator
2 3/5 *3/3 + 8/15
2 9/15 + 8/15 < b
2 17/15 < b
2 + 15/15 + 2 /15 < b
3 2/15 <b
Answer:
B > 3 2/15
Step-by-step explanation:
Plot A shows the number of hours ten girls watched television over a one-week period. Plot B shows the number of
hours ten boys watched television over the same period of time.
Which statement correctly compares the measures of center in the two sets of data?
Both the mean and median are greater for Plot A than for Plot B.
* Both the mean and median are greater for Plot B than for Plot A.
Plot A has a greater median than Plot B, but Plot B has a greater mean.
Plot B has a greater median than Plot A, but Plot A has a greater mean.
(It’s not B on edg2020 btw)
Answer: Hello I have your Answer
It's A
Step-by-step explanation:
Your welcome
Jilk Inc.'s contribution margin ratio is 62% and its fixed monthly expenses are $45,000. Assuming that the fixed monthly expenses do not change, what is the best estimate of the company's net operating income in a month when sales are $132,000?
Answer: $ 36,840.
Step-by-step explanation:
contribution margin=62% =0.62
fixed monthly expenses = $45,000
Sales = $132,000
We assume that the fixed monthly expenses do not change.
Then, company's net operating income = (contribution margin×Sales )-fixed monthly expenses
=$( (0.62×132000)-45000 )
= $ (81840-45000)
= $ 36,840
Hence, the best estimate of the company's net operating income in a month when sales are $132,000 is $ 36,840.
A patient with diabetes self-injected 5 units of regular insulin and 15 units of NPH insulin at 0800. When should the nurse assess this patient for signs of hypoglycemia?
Answer:
Hypoglycemia would sign at 1,000
Step-by-step explanation:
We know that a short-acting insulin (Regular insulin) work at last for 2 to 3 hours
Also intermediate acting insulin (NPH) insulin crests in 4 to 10 hours.
So, nurse assess this patient for signs of hypoglycemia 1000 to 1600
