Answer:
[tex] {3}^{2} \div 48 - 6 \\ 9 \div 48 - 6 \\ = - 5.8125[/tex]
The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 509 MPa with a standard deviation of 17 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 509 MPa
Answer:
0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa
Step-by-step explanation:
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.
Mean of 509 MPa with a standard deviation of 17 MPa.
This means that [tex]\mu = 509, \sigma = 17[/tex]
What is the probability that a randomly chosen sample of glass will break at less than 509 MPa?
This is the p-value of Z when X = 509. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{509 - 509}{17}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5
0.5 = 50% probability that a randomly chosen sample of glass will break at less than 509 MPa
I need help with this word problem.
Answer:
$3.22 per square feet
Step-by-step explanation:
To solve, I usually set up an equation:
sq ft = 12 1/2 = 1
$ 40.21 x
Then, use cross multiplication.
(12 1/2)x=40.21
Divide both sides by 12 1/2 or 12.5
x = 3.2168
Round to the hundredths place [because we're dealing with money]
$3.22
I hope this helps!
Answer:
3.22 per sq ft
Step-by-step explanation:
Take the total cost and divide by the amount of tiles
40.21 / 12.5
3.2168 per sq ft
Rounding to the nearest cent
3.22 per sq ft
The yield in bushes per acre is related to the average temperature. The attached sample data was obtained in a recent study. The least-square regression equation for yield in bushes and the average temperature is
Region Temperature Yield (in bushes per acre)
1 4 3
2 8 7
3 10 8
4 12 10
5 9 8
6 6 4
Answer:
y = 0.9143x - 0.8
Step-by-step explanation:
Given the data :
Region Temperature Yield (in bushes per acre)
4 ______ 3
8 ______ 7
10 _____ 8
12 _____ 10
9 ______ 8
6 ______ 4
Using technology, the least square regression equation obtained by fitting the data is :
y = 0.9143x - 0.8
Where ;
y = predicted Bush yield, predicted variable
x = Average temperature, dependent variable
The slope Coefficient = 0.9143
The intercept = - 0.8
[tex](v+6)^{2}=2v^{2}+14v+12[/tex]
Answer:
v=-6 or 4
Step-by-step explanation:
Answer:
the answer would be 5
Step-by-step explanation:
have to do the question multiply add and divide to find your answer
angle P and angle Q are complementary. The measure of angle Q is 33.5°. What is the measure of angle P?
Answer:
56.5 degrees
Step-by-step explanation:
Because complementary angles are when their sum is 90, you get the equation:
P + Q = 90
Since Q is 33.5,
P + 33.5 = 90
Subtracting 33.5 from both sides,
P = 56.5
If you vertically stretch the linear parent function, f(x) = x, by a factor of 5, what is the equation of the new function?
9514 1404 393
Answer:
f(x) = 5x
Step-by-step explanation:
Vertical stretch is accomplished by multiplying the function value by the stretch factor. f(x) = x is stretched by a factor of 5 by multiplying it by 5:
f(x) = 5x
Answer:
f(x)=5xStep-by-step explanation:
hope it helps much
The degree of polynomial 8x^2y^2-5x^2y^2-x^3y is
Answer:
The degree is the highest number exponent....
that is hard to see in your question...
it does appear to be a 2?
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 70th percentile in mathematics. Explain the difference in these two scores.
Answer:
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class.
This means that in her statistics class, Marla got 70% of her test correct.
When Marla took the SAT exam, she scored at the 70th percentile in mathematics.
This means that on the SAT exam, graded on a curve, Marla scored better than 70% of the students.
Explain the difference in these two scores.
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Solve for X.
-6x + 14 < -28
AND 3x + 28 < 25
Answer:
1. -6x + 14 < -28
6x<42
x<7
2. 3x + 28 < 25
3x < -3
x<-1
Hope This Helps!!!
A few people gather together to play a game in which one needs to roll 3 six-sided dice. One person notices that the sum of the number of spots on three dice comes up as 11 (the event E1) more often than it does 12 (the event E2) even though it looks like it should be even. This person argues as follows: E1 occurs in just six ways:
{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}, and E2 occurs also in just six ways: {(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}.
Therefore E1 and E2 have the same probability P(E1) = P(E2). Why isn’t it?
Answer:
Yes, P(E1)=P(E2)
Step-by-step explanation:
We are given that
Number of dice=3
Total outcomes of 1 die=6
Therefore,
Total number of outcomes =[tex]6^3=216[/tex]
E1={{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}
E2={(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}
We have to show that E1 and E2 have the same probability P(E1) = P(E2).
Probability, [tex]P(E)=\frac{Favorable\;outcomes}{Total\;outcomes}[/tex]
Using the formula
[tex]P(E_1)=\frac{6}{216}[/tex]
[tex]P(E_1)=0.0278[/tex]
[tex]P(E_2)=\frac{6}{216}[/tex]
[tex]P(E_2)=0.0278[/tex]
Hence, P(E1)=P(E2)
Romans Food Market, located in Saratoga, New York, carries a variety of specialty foods from around the world. Two of the store's leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans, which are purchased from a distributor located in New York City. Because Romans purchases large quantities, the coffee beans may be purchased on an as-needed basis for a price 10% higher than the market price the distributor pays for the beans. The current market price is $0.47 per pound for Brazilian Natural and $0.62 per pound for Colombian Mild. The compositions of each coffee blend are as follows: Blend
Bean Regular DeCaf
Brazilian Natural 75% 40%
Columbian Mild 25% 60%
Romans sells the regular blend for $3.60 per pound and the Decaf blend for $4.40 per pound. Romans would like to place an order for the Brazilian and Columbian coffee beans that will enable the production of 1000 pounds of Romans Regular coffee and 500 pound of Romans DeCaf coffee. The production cost is $0.80 per pound for the Regular blend. Because of the extra steps required to produce DeCaf, the production cost for the DeCaf blend is $1.05 per pound. Packaging costs for both products are $0.25 per pound. Formulate a linear programming model that can be used to determine the pounds of Brazilian Natural and Columbian Mild that will maximize the total contribution to profit. What is the optimal solution and what is the contribution profit?
Answer:
z(max) = 2996.13 $
x₁ = 968 x₂ = 430 ( quantities of regular and Decaf coffee respectevely)
Total quantity of BN = 898 pounds
Total quantity of CM = 500 pounds
Step-by-step explanation:
Cost of the beans
Brazilian natural = Price market + 10 % = 0.47 + 0.047
BN Cost = 0.517 $/lb
Clombian Mild = Price market + 10 % = 0.62 + 0.062
CM Cost = 0.682 $/lb
Composition of the coffee blend
Regular coffee 0.75 BN + 0.25 CM
De Caf coffee 0.40 BN + 0.60 CM
PRICES
Regular Roman = 3.60 $
Decaf = 4.40 $
Production costs:
Regular Roman = 0.80 $/lb
Decaf = 1.05 $/lb
Packaging costs: 0.25 $/Lb both
Profit = Price - cost
Profit of regular coffee = 3.60 - 0.80 - 0.25 -Cost of bean
for regular coffee cost of BN + CM
BN is : 0.75*BN cost = 0.75*0.517 = 0.38775 and
CM is : 0.25*0.682 = 0.1705
Profit of regular coffee = 1.99175 $
Profit for Decaf coffee = 4.4 - 1.05 - 0.25 - ( 0.517*0.4 + 0.6*0.682)
Profit for Decaf coffee = 4.4 - 1.30 - 0.616
Profit for Decaf coffee = 2.484 $
Let´s call x₁ pounds of regular coffee and x₂ pounds of Decaf coffee then:
Objective Function is:
z = 1.99175*x₁ + 2.484*x₂ to maximize
Subject to:
Availability of beans for 1000 pounds of Regular coffee means:
750 pounds of BN + 250 pounds of CM
Availability of beans for 500 pounds of Decaf coffee means
200 pounds of BN + 300 pounds of CM
Then 750 + 200 = 900 pounds of BN
And 250 + 300 = 550 pounds of CM
Availability of beans for 1000 pounds of Decaf coffee correspond to
0.75 *x₁ + 0.40*x₂ ≤ 900
Availability of beans for 500 pounds of Regular coffee correspond to
0.25*x₁ + 0.60*x₂ ≤ 500
Then the model is:
z = 1.99175*x₁ + 2.484*x₂ to maximize
Subject to:
0.75 *x₁ + 0.40*x₂ ≤ 900
0.25*x₁ + 0.60*x₂ ≤ 500
General constraints x₁ ≥ 0 x₂ ≥ 0 both integers
After 6 iterations optimal solution ( maximum z) is
z(max) = 2996.13 $
x₁ = 968 x₂ = 430
x₁ and x₂ are quantities of Regular and Decaf coffee respectively, to find out quantities of Brazilian Natural and Colombian Mild
we proceed as follows
Regular coffee is : 0.75*968 = 726 pounds of BN
Decaf coffee is : 0.40*430 = 172 pounds of BN
Total quantity of BN = 898 pounds
Regular coffee is : 0.25*968 = 242 pounds of CM
Decaf coffee is : 0.6*430 = 258 pounds of CM
Total quantity of CM = 500 pounds
Matthew earns extra money by doing odd jobs for his neighbors. He charges a flat fee of $20 plus $7 per hour for each job. If he earned $90 for a job he did last week, how many hours did he work?
Answer:
10 hours
Step-by-step explanation:
ok so we know he is getting payed $20 + $7 every hour so what i would do is keep the multiply the 7 till you get 70 so thats 7x10=70 and 70+20=90 so he worked for 10 hours last week :) i hope this helps, i tried my best to explain it
I WILL MARK THE ANSWER AS BRAINLIEST BE CORRECT BEFORE YOU ANSWER PLEASE
LOOK AT THE PROBLEM
Answer:
yes I look this problem in this figure
Jane has earned a 91, 85, and 84 on her first three quizzes of the semester. If she hopes to have an A quiz average (90 or above), what is the lowest score Jane can make on her fourth and final quiz?
She cannot earn an A quiz average*****
100
97
95
Answer:
100
Step-by-step explanation:
CalculationLet mark to be scored in fourth =x
but since the total will be more or above we will have the sign
[tex] \geqslant [/tex]
[tex]91 + 85 + 84 + x \div 4 \geqslant 90[/tex]
[tex]260 + x \div 4 \geqslant 90[/tex]
L.c.m =4 ( cross multiplying)
260+xtex 90*4
260+xtex 360
x tex 360-260
x tex 100
The value of the lowest score Jane can make on her fourth and final quiz is, 100
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
Jane has earned a 91, 85, and 84 on her first three quizzes of the semester.
And, she hopes to have an A quiz average (90 or above).
Let us assume that;
her fourth and final quiz = x
Hence, We get;
(91 + 85 + 84 + x) / 4 = 90
260 + x = 360
x = 360 - 260
x = 100
Thus, the lowest score Jane can make on her fourth and final quiz is,
x = 100
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ2
Type the correct answer in each box.
Jessica has $24 and plans to spend it all at the grocery store. She wants to purchase bags of carrots and bagels. Bags of
carrots cost $2 each, and bagels cost $3 per bag. Let x represent the number of bags of carrots and y represent the
number of bags of bagels. Complete the equation in standard form that models this scenario.
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y=(
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Step-by-step explanation:
Jessica has $24 and plans to spend it all at the grocery store.Bags of carrots cost $2 each, and bagels cost $3 per bag.Let x represent the number of bags of carrots and y represent the number of bags of bagels.the cost for the 'x' bags of carrots = $2xand the cost for the 'y' bags of bagels = $3ySo, the equation would be,so the equation in standard form that models the given scenario is
2x + 3y = 24
2x + 3y = 24Find the slope of the line that passes through the two points. 4,4 & 4,9
HELPPPPPPP
Answer:
is 22
Step-by-step explanation:
Answer:
It doesn't have a slope?
Step-by-step explanation:
Knowing that the slope equation is y2-y1/x2-x1
9-4 5
----- = ------ = 0
4-4 0
this means that the slope is 0...
What is the area of triangle ABC? - OP 03 square units 0 7 square units o 11 square units 0 15 square units see pic
Answer:
7 sq unit
Step-by-step explanation:
Area of triagle ABC = Area of rectangle mnBp - Area of trangle AmC - Are of triangle CnB - Area of triangle ABp
Area of rectangle mnBp = 5x3 = 15 sq unit
Area of trangle AmC = 4x2 /2 = 4 sq unit
Are of triangle CnB = 5x1 /2 = 2.5 sq unit
Area of triangle ABp = 3x1 /2 = 1.5 sq unit
I believe you can work out thd answer from the above
The weights for newborn babies is approximately normally distributed with a mean of 5.4 pounds and a standard deviation of 1.8 pounds. Consider a group of 1500 newborn babies: 1. How many would you expect to weigh between 3 and 6 pounds
Answer:
You would expect 807 babies to weigh between 3 and 6 pounds.
Step-by-step explanation:
We are given that
Mean,[tex]\mu=5.4[/tex]pounds
Standard deviation,[tex]\sigma=1.8[/tex]pounds
n=1500
We have to find how many would you expect to weigh between 3 and 6 pounds.
The weights for newborn babies is approximately normally distributed.
Now,
[tex]P(3<x<6)=P(\frac{3-5.4}{1.8}<\frac{x-\mu}{\sigma}<\frac{6-5.4}{1.8})[/tex]
[tex]=P(-1.33<Z<0.33)[/tex]
[tex]P(3<x<6)=P(Z<0.33)-P(Z<-1.33)[/tex]
[tex]P(3<x<6)=0.62930-0.09176[/tex]
[tex]P(3<x<6)=0.538[/tex]
Number of newborn babies expect to weigh between 3 and 6 pounds
=[tex]1500\times 0.538=807[/tex]
Helppp and explain!!!!!!!!!!!!!
Answer:
6x -15
Step-by-step explanation:
plug in gx for x in fx. So you have 2(3x-9) + 3
Kamala marked the price of a cosmetic item as Rs 400. She offered her customers a discount of 20% and made a loss of Rs 30, what was the actual cost of the item to her?
Answer:
350
Step-by-step explanation:
400- 80 ( 20% discount)
=320+30(loss)
=350
find the measure of angle c of a triangle ABC, if m
Find m angle NML; m angle QML=115^ and m angle NMQ=28^
Answer:
We're provided - m ∠ QML = 115° , m ∠ NMQ = 28° and we're asked to find out m ∠ NML. Set up an equation and solve for m ∠ NML.[tex] \large{ \tt{❀ \: m \: \angle \: NML= m \: \angle \:QML + m \: \angle \: NMQ}}[/tex]
[tex] \large{ \tt{⤇m \: \angle \:NML= 115 \degree + 28 \degree }}[/tex]
[tex] \boxed{ \large{ \tt{⤇ \: m \: \angle \:NML = 143 \degree }}}[/tex]
Hence , Our final answer is 143° . Hope I helped! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
7/10th
There are 42 red marbles in the bag and each is equally likely to be chosen.
Work out how many marbles in total there must be.
Answer:
60 marbles in total
Step-by-step explanation:
Find how many marbles there are in total by dividing 42 by 0.7:
42/0.7
= 60
So, there are 60 marbles in total
PLEASE HELP
The function in the table is quadratic:
TRUE
FALSE
Answer:
False
Step-by-step explanation:
Each f(x) increases by 8 therefore this equation is a linear function. If you where to graph it would be a straight line
Hope this helped :)
Answer:
False
Step-by-step explanation:
The slope is the same between all pounts which means the function is linear.
Hope this helps!
3/8-1/4=?
Answer ……..
Step 1: Find the LCD (Least Common Denominator)
The LCD between 4 and 8 is 8. Therefore, if I change all of the fractions to have a denominator of 8, the problem is as such:
3/8 - 2/8 = ?
Step 2: Subtract
3/8 - 2/8 = 1/8
Hope this helps!
Answer:
[tex]\frac{1}{8}[/tex] (1/8)
Step-by-step explanation:
1. The LCD & basics8·1=8
4·2=8
LCD=8
If the denominator is multiplied, the numerator also has to be multipled by the same value.
2. Solving[tex]\frac{3}{8} -\frac{2}{8} =\frac{1}{8}[/tex][tex]\frac{1}{8}[/tex]
Hope this helped! Please mark brainliest :)
Sameer bought 8kg 500g mango and 5kg 250g apples and Anil bought 7kg 800g Guava and 4kg 625g Banana. Who bought more fruits? And by how much?.
Answer:
Below.
Step-by-step explanation:
Sameer:-
Number of mango's = total weight / weight of 1 mango
= 5 kg / 500g
= 5000/500
= 10.
Number of apples: = 5000/250 = 20.
Total number of fruit = 30.
Anil :-
Number of guava = total weight / weight of 1 guava
= 7 kg / 800g
= 7000/800
= 9.
Number of banana: = 4000/625 = 6.
Total number of fruit = 15.
Sameer bought the most fruit, 15 more than Anil.
Note: in Anil's case I rounded the values to the nearest whole number.
Jo invest 5000 at a rate of 2% per year compound interest.calculate the value of her investment at the end of 3years.
Answer:
If you need further explanation, comment on this
Solve this
4 X (10 - 3+2)
Answer:
36
Step-by-step explanation:
10-3=7+2=9
4×9=36
36 is the answer
A large on-demand, video streaming company is designing a large-scale survey to determine the mean amount of time corporate executives watch on-demand television. A small pilot survey of 10 executives indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. The estimate of the mean viewing time should be within 0.25 hour. The 95% level of confidence is to be used. How many executives should be surveyed? (Use z Distribution Table.)
How many executives should be surveyed? (Round the final answer to the next whole number.)
Answer:
554 executives should be surveyed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 3 hours.
This means that [tex]\sigma = 3[/tex]
The 95% level of confidence is to be used. How many executives should be surveyed?
n executives should be surveyed, and n is found with [tex]M = 0.25[/tex]. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.25 = 1.96\frac{3}{\sqrt{n}}[/tex]
[tex]0.25\sqrt{n} = 1.96*3[/tex]
[tex]\sqrt{n} = \frac{1.96*3}{0.25}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*3}{0.25})^2[/tex]
[tex]n = 553.2[/tex]
Rounding up:
554 executives should be surveyed.
Find the radius of a circle with a diameter whose endpoints are (-7,1) and (1,3).
Answer:
r = 4.1231055
Step-by-step explanation:
So to do this, you need to find the distance between the two points:
(-7,1) and (1,3).
To do this, the distance or diameter (d) is equal to:
d = sqrt ((x2-x1)^2 + (y2-y1)^2)
In this case:
d = sqrt( (1 - (-7))^2 + (3 - 1)^2 )
d = sqrt( 8^2 + 2^2)
d = sqrt( 64 + 4)
d = sqrt( 68 )
The radius is half of the diameter, so:
r = 1/2 * d
r = 1/2 * sqrt( 68 )
r~ 4.1231055
