Answer:
Length is 28. Width is 8.
Step-by-step explanation:
The perimeter of a rectangle is given by the following formula:
[tex]P=2l+2w[/tex]
We know that the length is 4 inches less than 4 times the width. Therefore:
[tex]l=4w-4[/tex]
Substitute this for l. Let's also substitute 72 for P. Therefore:
[tex]72=2(4w-4)+2w[/tex]
Distribute:
[tex]72=8w-8+2w[/tex]
Combine like terms:
[tex]72=10w-8[/tex]
Add 8 to both sides:
[tex]80=10w[/tex]
Divide both sides by 10:
[tex]w=8[/tex]
Therefore, the width is 8.
The length is 4 less than 4 times the width. Thus: "
[tex]l=4(8)-4[/tex]
Multiply:
[tex]l=32-4[/tex]
Subtract:
[tex]l=28[/tex]
Therefore, the length is 28 and the width is 8.
And we're done!
Amber owns a plum orchard, and needs to harvest at least 2293 plums to cover the costs of running the orchard, but also wants to donate 280 plums to charity. If each tree bears an average of 83 plums, how many plum trees need to be in the orchard? Express your answer in interval notation.
Answer:
27 trees needs to be in the orchard.
Step-by-step explanation:
amber needs to harvest at least 2293 of plums to cover the cost of running the orchard.
but also wants to donate 280 plums.
each tree produces an average of 83 plums
find: how many plums of trees needed to be in the orchard?
number of trees required = total harvest / number of plums produced per tree
therefore,
number of trees required = 2293 / 83 ≅ 27 trees needs to be in the orchard.
so Amber can donate 280 plums to charity.
Solve the problem. A variable x has the possible observations shown below. Possible observations of x: -3 -1 0 1 1 2 4 4 5 Find the z-score corresponding to an observed value of x of 2.
Answer:
[tex]z = 0.228[/tex]
Step-by-step explanation:
Given
x: -3 -1 0 1 1 2 4 4 5
n = 9
Required
Determine the z-score x = 2
z score is calculated by
[tex]z = \frac{x - Mean}{SD}[/tex]
First, we need to calculate the mean
[tex]Mean = \frac{\sum x}{n}[/tex]
Mean = \frac{-3- 1 + 0 + 1 + 1 + 2 + 4 + 4 +5}{n}
[tex]Mean = \frac{13}{9}[/tex]
[tex]Mean = 1.44[/tex]
Next is to calculate the standard deviation
[tex]SD = \frac{\sum (x_i - Mean)^2}{n}[/tex]
[tex]SD =\sqrt{ \frac{(-3-1.44)^2+(-1-1.44)^2+(0-1.44)^2+(1-1.44)^2+(1-1.44)^2+(2-1.44)^2+(4-1.44)^2+(4-1.44)^2+(5-1.44)^2}{9}[/tex][tex]SD =\sqrt{ \frac{(-4.44)^2+(-2.44)^2+(-1.44)^2+(-0.44)^2+(-0.44)^2+(0.56)^2+(2.56)^2+(2.56)^2+(3.56)^2}{9}[/tex]
[tex]SD =\sqrt{ \frac{19.7136+5.9536+2.0736+0.1936+0.1936+0.3136+6.5536+6.5536+12.6736}{9}[/tex]
[tex]SD =\sqrt{ \frac{54.2224}{9}[/tex]
[tex]SD =\sqrt{6.02471111111}[/tex]
[tex]SD = 2.455[/tex]
Substitute these values in
[tex]z = \frac{x - Mean}{SD}[/tex]
Where x = 2
[tex]z = \frac{2 - 1.44}{2.455}[/tex]
[tex]z = \frac{0.56}{2.455}[/tex]
[tex]z = 0.228[/tex]
Hence, the z score of x = 2 is o.228
Noah buys 3 packages of pens. Each package has 4 blue pens and 2 black pens.
Which equation can be used to find p, the total number of pens?
3 x (4+2) =p
3 X 4 X 2 =p
3+ (4 x 2) =P
3 +4+2 =p
Answer:
A
Step-by-step explanation:
So he bought 3 packages of pens.
And each package has 4 blue and 2 black.
Thus, the equation that can be used to find the total number of pens p is:
[tex]3\times(4+2)=p[/tex]
The (4+2) represents the total number of pens in 1 package. And the 3 represents the total number in 3 packages.
Further notes:
The total number of pens would be 18.
Answer:
3 times (4+2)=p
Step-by-step explanation
this is the answer because it gives us that key word and the key word is each and total and when you solve it the answer would be 18 because always use the parentheses first then add 4+2 and that equals 6 and times 6 with the 3 and that gives 18
I hope this helps you have a wonderful day:)
The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 10 years. A random sample of 50 cars had an average age of 9.5 years. It is believed that the population standard deviation for the age of cars is 3.4 years. The Department of Transportation would like to set = 0.10. The critical value for this hypothesis test would be ________.
Answer:
0.1492
Step-by-step explanation:
Mean (m) = 9.5
Standard deviation (sd) = 3.4
Number of observations (n) = 50
Computing the test statistic :
X = 10
Z = (x - m) / standard error
Standard Error = sd/sqrt(n)
Z = (x - m) / (sd/sqrt(n))
Z = (10 - 9.5) / (3.4/sqrt(50))
Z = 0.5 / 0.4808326
Z = 1.0398 = 1.04
Using a P-value calculator, we can obtain the critical value with α = 0.10, hence, the critical value = 0.14917
= 0.1492
I need help with the following question, whichever one is right will get brainliest!
Given: m∠A + m∠B = 90° (Definition of Complementary Angles).
Given: m∠B = (5x + 8)°
A) m∠A = 180° + (5x + 8) is your answer choice:
Why it isn't the others:
B) m∠A = 90° - (5x + 8)
You are solving for complementary angles (90° in total when combined), so you subtract the measurement for B (5x + 8) to get A.
C) m∠A = 180° - 2(5x + 8)°
You double the complementary angle to solve for the supplementary. Essentially, just divide this answer by two to get the complementary angles.
D) m∠A = 82 - 5x
I was confused by this one, but essentially they just did one step of the isolating the variable, which was subtracting 8 from both sides. They did not finish isolating the variable however.
New heat lamps are reported to have the mean lifespan of 100 hours with a standard deviation of 15 hours. Before replacing their current lamp to the new heat lamps for the university, OSU decided to test whether the mean lifetime is equal to 100 or not by sampling 36 heat lamps. They turned them on and recorded the time, in hours, until each lamp failed. The sample provided a mean lifespan is 105.1 hours.
1) What set of hypotheses are correct for this problem?
SET 1 - H0: µ = 100 hours , Ha: µ < 100 hours
SET 2 - H0: µ = 100 hours , Ha: µ > 100 hours
SET 3 - H0: µ = 100 hours , Ha: µ ≠ 100 hours
A) SET 1.
B) SET 2.
C) SET 3.
2) If we assume the null hypothesis to be true, the average of the distribution of sample means, μ x ¯, from a sample size of 36 is:______.
a) 15.
b) 115.
c) 100.
d) 105.1. .
3) According to the Central Limit Theorem, the standard deviation of the distribution of the sample means is:______.
a) 115.
b) 15.
c) 6.
d) 2.5. .
4) What is the approximate probability of observing a sample mean of 105.1 or more from the distribution of sample means, again assuming that the null hypothesis is true?
a) 0.68.
b) 0.025.
c) 0.975.
d) 0.16.
Answer:
1
The correct option is C
2
The correct option is C
3
The correct option is A
4
The correct option is B
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 100[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
The sample size is [tex]n = 36[/tex]
The sample mean is [tex]\= x = 105.1[/tex]
Generally
The null hypothesis is [tex]H_o: \mu = 100 \ hours[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 100\ hours[/tex]
Given that the null hypothesis is true then the distribution of sample means [tex]\mu_{\= x }[/tex], from a sample size of 36 is mathematically represented as
[tex]\mu_{\= x } = \mu[/tex]
=> [tex]\mu_{\= x } = 100[/tex]
According to the Central Limit Theorem the test stated in the question is approximately normally distributed if the sample size is sufficiently large[tex](n > 30 )[/tex] so given that the sample size is large n = 36
Then the test is normally distributed and hence the standard deviation is 15
Generally the standard error of mean is mathematically represented as
[tex]\sigma_{\= x } = \frac{ \sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x } = \frac{15}{\sqrt{36} }[/tex]
=> [tex]\sigma_{\= x } = 2.5[/tex]
Generally the approximate probability of observing a sample mean of 105.1 or more is mathematically represented as
[tex]P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(\frac{\= X - \mu }{\sigma_{\= x }} <\frac{105.1 - 100}{2.5} )[/tex]
=> [tex]P( \= X \ge 105.1 ) =1 - P(\= X < 105.1) = 1- P(Z<2.04 )[/tex]
From the z-table (reference calculator dot net )
[tex]P(Z<2.04 ) = 0.97932[/tex]
So
[tex]P( \= X \ge 105.1 )= 1 - P(\= X < 105.1) = 1- 0.97932[/tex]
[tex]P( \= X \ge 105.1 ) =0.02[/tex]
112 equals 2 times the length minus 5
Answer:
l = 58.5
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
112 = 2l - 5
Step 2: Isolate term l by adding 5 on both sides
117 = 2l
Step 3: Isolate l by dividing both sides by 2
117/2 = l
Step 4: Evaluate
l = 58.5
Answer:
[tex]\Large \boxed{l = \frac{117}{2}}[/tex]
Step-by-step explanation:
Let the length be [tex]l[/tex].
[tex]112 = 2 l - 5[/tex]
Adding 5 to both sides.
[tex]112 +5= 2 l - 5+5[/tex]
[tex]117 = 2 l[/tex]
Dividing both sides by 2.
[tex]\displaystyle \frac{117}{2} = \frac{2 l}{2}[/tex]
[tex]\displaystyle \frac{117}{2} = l[/tex]
The table below shows the price in dollars for the number of roses indicated is the price proportional to the number of roses explain in 2 college sentence
Answer:
Price of roses is proportional to the number of roses.
Step-by-step explanation:
Let the price of roses are proportional to the number of roses.
Equation representing this phenomenon will be,
P = k(R) ⇒ k = [tex]\frac{P}{R}[/tex]
where 'P' = price of the roses
R = Number of roses
k = Proportionality constant
If we substitute the values of P and R and we get the same value of constant 'k', then the equation will be true.
For R = 3 and P = $9
k = [tex]\frac{9}{3}[/tex]
k = 3
For R = 6 and R = 18
k = [tex]\frac{18}{6}[/tex]
k = 3
K is same in both the conditions, therefore, Price of roses are proportional to the number of roses.
Simplify: 3(2x-y)-(5x+4y-2)
Please show steps
Answer:
6 x ^2 − 5 x y − 4 y ^2
Step-by-step explanation:
Expand
( 2 x + y ) (3 x − 4 y )
using the FOIL Method.
Apply the distributive property.
2 x ( 3 x − 4 y ) + y ( 3 x − 4 y )
Apply the distributive property.
2 x ( 3 x )+ 2 x (− 4 y ) + y ( 3x − 4 y )
Apply the distributive property.
2 x ( 3 x ) + 2 x( − 4 y ) + y ( 3 x) + y ( −4 y )
Simplify and combine like terms.
6 x ^2 − 5 x y − 4^ 2
Step-by-step explanation:
so it is 3×2=6 3×y=3y so here it 6-3 =3
5+4=9-2=7
so 7-3=4
What is an equation for "five more than the
product of 7 and a number t is 10?"
Answer:
Option (B) will be the correct option.
Step-by-step explanation:
Statement states "five more than the product of seven and a number t is 10."
Split this statement into parts.
1). Product of 7 and a number 't' = 7 × t
2). 5 more than the product of 7 and a number 't' = 7t + 5
3). Five more than the product of 7 and a number t is equal to 10 ⇒ 7t + 5 = 10
Therefore, Option (B) will be the correct option.
Money Eric returned from a trip to Las Vegas with
$300.00, which was 50% more money than he had at the
beginning of the trip. How much money did Eric have at
the beginning of his trip?
Answer:
$200
Step-by-step explanation:
money he has now is 150% of what he had in the beginning
300 = 1.5x
x = 200
if he had $200 in the beginning, you add half of that to itself (200 + 100 = 300)
What number is the opposite of 4? Enter your answer in the box below.
Answer:
-4
Step-by-step explanation:
The only difference between 4 and -4 is that 4 is positive and the other 4 is negative because of “-”.
Minstrel Manufacturing uses a job order costing system. During one month, Minstrel purchased $198,000 of raw materials on credit; issued materials to production of $195,000 of which $30,000 were indirect. Minstrel incurred a factory payroll of $150,000, of which $40,000 was indirect labor. Minstrel uses a predetermined overhead rate of 150% of direct labor cost. The total manufacturing costs added during the period is:
Answer:
$440,000
Step-by-step explanation:
Direct material:
= $195,000 - $30,000
= $165,000
Direct labor:
= $150,000 - $40,000
= $110,000
Manufacturing overhead:
150% of direct labor cost.
= $110,000 x 150 ÷ 100
= $16,500,000 ÷ 100
= $165,000
Total manufacturing costs:
= $165,000 + $110,000 + $165,000
= $275,000 + $165,000
= $440,000
The total manufacturing costs added during the period is: $440,000
Set up and solve an equation for the following business situation. Pitt's Pit Stop sold $15,934.50 worth of gasoline yesterday. Regular sold for $3.30 a gallon and premium sold for $3.45 a gallon. If the station sold 390 more gallons of regular than premium, answer the following questions. (a) How many gallons of each type of gasoline were sold?
Answer:
2,000
Step-by-step explanation:
it is the opposite of what it really was
What is the common ratio of the geometric sequence below?
Answer:
The answer is option BStep-by-step explanation:
Since it's a geometric sequence, to find the common ratio divide the previous term by the next term.
That's
[tex] \frac{48}{ - 96} = - \frac{1}{2} [/tex]And also
[tex] \frac{ - 24}{48} = - \frac{1}{2} [/tex][tex] \frac{12}{ - 24} = - \frac{ 1}{2} [/tex]Also
[tex] \frac{ - 6}{12} = - \frac{1}{2} [/tex]Since the common ratio is the same for any of the terms chosen the common ratio of the sequence is
[tex] - \frac{1}{2} [/tex]Hope this helps you
Answer:
B. -1/2
Step-by-step explanation:
The common ratio is the ratio between two numbers next to each other To find the common ratio, divide a term by the preceding term.
For example, if the term is 48, divide by -96.
48/-96 = -1/2
Another example, if the term is -24, divide by 48.
-24/48= -1/2
Let’s try one more example. If the term is 12, divide by -24
12/-24= -1/2
Therefore, the common ratio is 1/2 and the correct answer is B.
jane has 16 cards. ten of the cards look exactly the same and have number 1 on them. the other 6 cards look exactly the same and have the number 2 on them. jane is going to make a row contaning all 16 cards. how many different ways can she order the row?
Answer:
8008 ways.
Step-by-step explanation:
That is 16! / 10! 6!
= 16*15*14*13*12*11 / 6*5*4*3*2*1
= 16*15*14*13*11 / 6*5*2
= 16*14*13*11 / 2*2
= 4*14*13*11
= 8008.
is 7 to 4 the same as 4 to seven? explain why or why not.
Answer:
The answer is No
Step-by-step explanation:
7 to the fourth is 2401
4 to the seventh is 16384
23. Due to an increase in taxes on electronic devices, the price of a 46" LED flat TV screen has increased
to £845, which is 30% increase of the original price.
What was the original price of the TV prior to the increase?
Answer:
£591.5
Step-by-step explanation:
First find the price increase by multiplying the new price by 30 percent . Then subtract the answer from the new price.
The original price of the TV prior to the increase is £650 and this can be determined by using the unitary method.
Given :
The price of a 46" LED flat TV screen has increased to £845, which is 30% increase of the original price.
The following steps can be used in order to determine the original price of the TV prior to the increase:
Step 1 - The unitary method can be used in order to determine the original price of the TV prior to the increase.
Step 2 - According to the given data, the increased price of the TV is £845 which is 130%.
Step 3 - Now, let the original price of the TV be 'x'.
Step 4 - So, the value of 'x' is:
[tex]x = \dfrac{100}{130}\times 845[/tex]
Step 5 - Simplify the above expression.
[tex]x = \dfrac{8450}{13}[/tex]
[tex]x = 650[/tex]
So, the original price of the TV prior to the increase is £650.
For more information, refer to the link given below:
https://brainly.com/question/12116123
42 divided by 7 get a decimal answer
Answer:
6
Step-by-step explanation:
just put 6.00 bro it divides evenly
What is the coefficient of 9(14)P
Answer:
the answer is 126 because 9 times 14 is 126
If you translate this figure 4 units right and 2 units down, point Q' will be at what coordinate?
(0,3)
(-2,2)
(2,-2)
(0,0)
PLS HELP BEST ANSWER GETS BRAINLIEST\
A dog needs 4/3 liters of water for 2/5 of a day. How many liters of water does the dog need for an entire day? *
Answer:
A dog needs 4/3 liters of water 2/5 of a day, Therefore
he'll need 4/3 liters for 5/2 day or
4/3 * 5/2 = 20/6 = 10/3 liters or 3 and 1/3 liters per day
Step-by-step explanation:
Which of the following is in order from largest to smallest?
0.4, 151, 1-131
1-131, 0, 4, 151
1-131, 151, 4,0
151.4, 0.1-131
Answer: 151.4, 0.1-131
Step-by-step explanation:
Express 125 4 as a power with base 5
Answer:
125^-4
125=5²
125^-4=5^-12
A fruit bowl has 5 apples 7 oranges and 4 bananas. What is the ratio of apples to bananas?
Answer:
5 apples to 4 bananas
Step-by-step explanation:
Answer:
5:4
Step-by-step explanation:
A ratio divides the number with a colon. And since there are 5 apples to 4 bananas, the ratio of apples to bananas would be 5:4 (or another way to write it is 5 to 4)
Roll three fair 6-sided dice. What is the chance that they will all land on ace? What is the chance that they will not all land on ace? What is the chance that none of them will land on ace ?
Answer:
5% chance of ace and 15% of not landing ace
Step-by-step explanation:
lol trust me i play dice in school
a 3 yard roll of waxed paper costs $3.33. what is the price per foot?
Answer:
$.37 per foot
Step-by-step explanation:
1 yd = 3ft
3 yd = 3*3 = 9ft
Take the dollar amount and divide by the number of ft
3.33 / 9
$.37 per foot
Answer:
$0.37 per foot
Step-by-step explanation:
3 feet=1 yard 3 yards= 9 feet
First Way:
3.33 divided by 9 = 0.37
Second Way:
9x= 3.33
9x÷9. 3.33÷ 9
x= 0.37 per foot
In a recent survey, three out of every five students said they would prefer going to a water park for the class trip.
If 105 students were surveyed, how many can be expected to prefer the water park?
O A 21
OB. 35
O c. 63
O D. 70
E. 103
Answer:
the answer is d
Step-by-step explanation:
Just multiply and divide
What is probability?
the quality or state of being probable; the extent to which something is likely to happen or be the case
We have,
Surveyed student = 105
Students would prefer to going to a water park= 3/5
According to question
students who expected to prefer the water park
= 105 × 3/5
= 21×5×3/5
= 21×3
= 63
Hence, students who expected to prefer the water park is 63
To learn more about probability from here
https://brainly.in/question/20635873
#SPJ2
A stock price S is governed where z is a standardized Wiener process. Find the process that governs G(t)
This question is incomplete, the complete question is;
A stock price S is governed by dS = aSdt + bSdz
where z is a standardized Wiener process. Find the process that governs G(t) = S^1/2(t)
Answer:
G = S^1/2
Step-by-step explanation:
Solving the Equation
dS = aSdt + bSdz
First we Take S common from Right hand Side
dS = S(a dt + b dz)
Then we also take S Left Hand Side(LHS) from RHS
dS/S = a dt + b dz
So d = a dt + b dz
now we Take d Common from RHS
d = d(a t + b z)
So
d/d = a t + b z
1 = a t + b z
So, t = (1-b z) / a
Now substitute value of t in equation G(t) = S^1/2(t)
we have
G{(1- b z)/a} = S^1/2 {(1- b z)/a}
(1- b z)/a) from both sides cancels out each other
So we have G = S^1/2
Solve for the indicated variable in each math formula. 1.C=2(3.14)r for r 2.A=1/2bh for b 3.y=Mx+b for x 4.A=1/2(a+b)h for h 5.V(3.14)r(r)h for h
Answer:
See below
Step-by-step explanation:
1. C = 2(3.14) for r
r = C / 3.28
2. A = 1/2 b h for b
b = A2 / h
3. y = Mx + b for x
y - b = Mx
x = (y - b) / M
4. A = 1/2 (a + b) h for h
A = (1/2a + 1/2b)h
A = 1/2ah + 1/2bh
A = (a + b) h / 2
h = 2A / (a + b)
5. V = (3.14) r² h for h
h = V / (3.14 r²)