115.2 pounds of type A coffee were used.
What is the solution of the equation?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
Let the number of pounds of type A coffee be x and the number of pounds of Type B coffee be y.
According to the question, the equations are,
5.50x + 4.40y = 762.30
x = 4y
So, the solution of the equation is obtained as follows:
5.50(4y) + 4.40y = 762.30
26.40y = 762.30
y = 762.30/26.40
y = 28.8 pounds
x = 4*28.8 = 115.2 pounds
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A company is reviewing a batch of 28 products to determine if any are defective. On average,3.2 of products are defective.
What is the probability that the company will find 2 or fewer defective products in this batch?
What is the probability that 4 or more defective products are found in this batch?
If the company finds 5 defective products in this batch, should the company stop production?
Using the Poisson distribution, it is found that:
There is a 0.3799 = 37.99% probability that the company will find 2 or fewer defective products in this batch.There is a 0.3975 = 39.75% probability that 4 or more defective products are found in this batch.Since [tex]P(X \geq 5) > 0.05[/tex], the company should not stop production it there are 5 defectives in a batch.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.In this problem, the mean is:
[tex]\mu = 3.2[/tex]
The probability that the company will find 2 or fewer defective products in this batch is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]
[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]
[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0408 + 0.1304 + 0.2087 = 0.3799[/tex]
There is a 0.3799 = 37.99% probability that the company will find 2 or fewer defective products in this batch.
The probability that 4 or more defective products are found in this batch is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]
[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]
[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]
[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0408 + 0.1304 + 0.2087 + 0.2226 = 0.6025
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6025 = 0.3975[/tex]
There is a 0.3975 = 39.75% probability that 4 or more defective products are found in this batch.
For 5 or more, the probability is:
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]
[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]
[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]
[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]
[tex]P(X = 4) = \frac{e^{-3.2}3.2^{4}}{(4)!} = 0.1781[/tex]
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0408 + 0.1304 + 0.2087 + 0.2226 + 0.1781 = 0.7806
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.7806 = 0.2194[/tex]
Since [tex]P(X \geq 5) > 0.05[/tex], the company should not stop production it there are 5 defectives in a batch.
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what is the pattern 324,256,196,144
The pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.
What is a sequence?A sequence is a set of things next to each other in a set order. It is also referred to as a series.
According to this question, the following sequence is given: 324, 256, 196, 144. A careful observation of these numbers shows that each is the square of even numbers.
18² = 324
16² = 256
14² = 196
12² = 144
Therefore, the pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.
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Intelligence test.
If you get it right ,you are a critical thinker.
You were in the garden, there are 34 people in the yard. You killed 30 .How many people are in the garden.
I
Answer: 5
Step-by-step explanation:
Because there are 35 when you add yourself so u subtract 30 to get 5
There would be 4 people left in the garden.
34 - 30 = 4.
Subtraction of NumbersSubtraction is a mathematical operation that involves taking away one number from another to find the difference between them. For the question, At first, there were 34 people in the garden and later 30 people were no longer alive in the garden, so the difference between 30 people and 34 people is 4.
Subtraction is the opposite of addition, and it is used to measure the distance between two values on the number line.
Subtraction is represented by minus Sign (-). For example, subtracting 5 from 10 gives you a difference of 5 (10 - 5 = 5).
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Points A, B and C make the triangle triangle ABC and are at the coordinates A(- 4, 3) , B(- 48, 17) and C(22, - 53) . Point D is the midpoint of BC and AD is a median of triangle ABC . What is the equation of the median in standard form?
PLEASE HELP ASAP
The equation of the median in standard form is; 9y - 38x = 179.
What is the equation of the media in standard form?It follows from the task content that the point D is the midpoint of segment BC; Hence, the coordinates of point D given the coordinates of B and C above are given as; D(-13, -35).
The equation of the median which is the line joining points A and D is therefore determined as follows;
Slope = (-35-3)/(-13-(-4)) = 38/9
38/9 = (y-3)/(x+4)
9y -27 = 38x + 152
9y - 38x = 179.
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( 13/7 ) ^2
[answer in fraction form]
Answer:
[tex]\frac{169}{49}[/tex]
Step-by-step explanation:
Square the top and bottom numbers in the fraction
13^2 = 169
7^2 = 49
169/49
On Monday, Cinthia studied for 3 1/2 hours. On Tuesday, she studies 2/3 of her study time on Monday. How many hours did Cinthia study on Tuesday?
Answer:
Cinthia studied 2/3 of her time on Tuesday
Construct a 96% confidence interval if a sampling distribution has a mean of 20, a standard deviation of 5, and a size of 100.
Using the t-distribution, the 96% confidence interval is given as follows:
(18.96, 21.04).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 96% confidence interval, with 100 - 1 = 99 df, is t = 2.0812.
The parameters are given as follows:
[tex]\overline{x} = 20, s = 5, n = 100[/tex]
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 20 - 2.0812\frac{5}{\sqrt{100}} = 18.96[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 20 + 2.0812\frac{5}{\sqrt{100}} = 21.04[/tex]
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At an Ice cream parlor, ice cream cones cost x dollars each and sundaes cost y dollars each. The total cost of 4 cones and 3 sundaes is more than $20. The total cost of 5 cones and 1 sundae is less than $16. Which system of inequalities models this situation?
The following data show the height, in inches, of 11 different plants in a garden:
9
4
10
9
5
2
22
10
3
3
5
After removing the outlier, what does the mean absolute deviation of this data set represent?
On average, the height of a plant varies 2.8 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 5 inches.
On average, the height of a plant varies 2.8 inches from the mean of 5 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.
What does the mean absolute deviation represent?An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.
Mean absolute deviation = (1/n) x ∑ l x - m(x) l
Mean without the outlier : (9 + 4 + 10 + 9 + 5+ 2 + 10 + 3 + 3+ 5) / 10 = 6
(1/10) x ∑ l (9 - 6) + (4 - 6) + (10 - 6) + (9 - 6) + (5 - 6) + (2 - 6) + (10 - 6) + (3 - 6) + (3 - 6) + ( 5 - 6) = 3.2
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On which intervals is the function increasing? Choose
all that apply.
The function is increasing on the intervals:
(-∞, 3] and [5, ∞)
Then the correct options are a and c.
On which intervals is the function increasing?
The function is increasing when, reading from left to right, we can see that the curve goes upwards.
By looking at the graph, we can see that the function increases between -∞ and 3, and also increases between 5 and ∞, then the correct options are a and c-
(-∞, 3] and [5, ∞)
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Calculate the distance between the points C = (0,-2) and L= (-4, 1) in the coordinate plane. Give an exact answer. (not a decimal approximation)
Answer: 5
Step-by-step explanation:
[tex]\sqrt{(-4-0)^2 + (1-(-2))^2}=5[/tex]
For f(x) = 4x+1 and g(x)=x²-5, find (f-g)(x).
Answer: -x² + 4x + 6
Given:
f(x) = 4x + 1
g(x) = x² - 5
Solve:
= (f - g)(x)
= f(x) - g(x)
= 4x + 1 - (x² - 5)
= 4x + 1 - x² + 5
= -x² + 4x + 6
Answer:
(f-g) (x) = 4x+1 - x² + 5 = -x² + 4x + 6
Step-by-step explanation:
Explanation can be given if needed in the comments (ㅅ´ ˘ `)
20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5)
20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5) = -115
Answer:
The simplified form of the above expressions solution is -115.
Step-by-step explanation:
Hello!20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5).. given expression [tex] - 100 + 10( - 3) + ( - 5)( - 6) - 15 \\ - 100 - 30 + ( - 5)( - 6) - 15 \\ - 100 - 30 + 30 - 15 \\ - 130 + 30 - 15 \\ - 100 - 15 \\ - 115[/tex]Andy is preparing the company's income statement. His first line item is the company's service revenue. What will he deduct from this line item to obtain the net income?
Andy needs to subtract _______ from the service revenue.
Fill in the blank
Andy needs to subtract cost from the service revenue.
What does Andy need to subtract?
Revenue is the total income earned before any deductions are made. Net income is the total revenue less total expenses or cost.
Net income = total revenue - cost
For example, if a company sold 100 loaves of bread for $100 dollars. The cost of making the bread is $50. The revenue is $100 and the net income is $50 (100 - 50).
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Results from a survey conducted in a certain grocery store showed that 3 out of 5 people preferred crispy-flakes cereal to crunchy-flakes cereal. Based on this survey, if a total of 2,500 customers bought one of these two cereals, how many most likely purchased crunchy-flakes cereal?
The number of people who how many most likely purchased crunchy-flakes cereal is 1000 customers.
How many most likely purchased crunchy-flakes cereal?
Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).
The first step is to determine the ratio of people who preferred crunchy-flakes cereal:
Ratio of people who preferred crunchy-flakes cereal : 5 - 3 = 2
Now, multiply the ratio of those who prefer crunchy-flakes cereal by the total number of customers: (2/5) x 2500 = 1000 customers.
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Using traditional methods, it takes 103 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 60 students and observed that they had a mean of 102 hours. Assume the variance is known to be 9. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.
The test statistic based on the probability illustrated is -2.57.
How to calculate the probability?The basic training is given as 103 hours. The variance is also given as 9.
The test statistic will be:
= (102 - 104/3/✓60)
= -1/(3/7.7)
= -2.57.
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solve this equation -1/2 ( -3y + 10)
Answer:
3/2y-5
Step-by-step explanation:
Find the axis of symmetry:
Picture is below.
Answer:
x = -3
Step-by-step explanation:
Axis of symmetry:Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.
From the graph, Vertex (-3, 4)
Axis of symmetry: x = -3
in ΔWXY, m∠W = (2x - 12)°, m∠X = (2x +17)°, and m∠Y = (9x - 7)°. Find m∠X.
Answer:
45°
Step-by-step explanation:
Angles in a triangle add to 180 degrees, so
2x - 12 + 2x + 17 + 9x - 7 = 18013x - 2 = 18013x = 182x = 14So, the measure of angle X is 2(14)+17=45°
Can you guys show me what process you would use for this? I mostly need the process
The value of the expression for the given values of the variables is 1/9
Evaluating an ExpressionFrom the question, we are to determine the value of the expression for the given values of the variables
The given expression is
[tex](\frac{4x^{3} -2y-2z^{3} }{4y^{2}-16x^{2} }) ^{2}[/tex]
From the given information,
x = 2
y = -5
z = 3
Putting the values of the variables into the expression
[tex](\frac{4(2)^{3} -2(-5)-2(3)^{3} }{4(-5)^{2}-16(2)^{2} }) ^{2}[/tex]
[tex](\frac{4(8) +10-2(27) }{4(25)-16(4) }) ^{2}[/tex]
[tex](\frac{32 +10-54 }{100-64 }) ^{2}[/tex]
[tex](\frac{-12 }{36 }) ^{2}[/tex]
[tex](\frac{-1 }{3 }) ^{2}[/tex]
[tex]= \frac{1}{9}[/tex]
Hence, the value of the expression for the given values of the variables is 1/9
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Please answer fast!
Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.
Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)
Answer:
x = 15 & y = 35
Step-by-step explanation:
[tex]y = x + 20[/tex]
[tex]x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15[/tex]
[tex]y = x + 20 = (15) + 20 = 35[/tex]
Craig decides to purchase a property that has been valued at $475,000. He has $80,000 available as a deposit and will require a mortgage for the remaining amount. The bank offers him a 25 year mortgage at 2% interest. Calculate the total interest he will pay over the life of the loan, assuming he makes monthly payments. Give your answer in dollars to the nearest ten dollars. Do not include commas or the dollar sign in your answer.
THE REAL ANSWER IS $107, 270
First, we note that Craig requires a mortgage on $475,000−$80,000=$395,000. To calculate the monthly repayments we must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk)(rk).
We have P0=$395,000,r=0.02,k=12,N=25, so substituting in the numbers into the formula gives
$395,000=d(1−(1+0.0212)−25⋅12)(0.0212),
that is,
$395,000=235.9301d⟹d=$1,674.22.
Therefore the total interest payable is
I=$1,674.22×25×12−$395,000=$107,266
which is $107,270 to the nearest $1
The total interest is $107,270
What is monthly payment formula?
The formula for monthly payment is:
[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]
We can find total interest as shown below:
Value of property = $475,000
Money available as a deposit = $80,000
P = 475,000-80,000
= 395000
t = 25 year
r = 2% = 0.02
n = 25*12 = 300
[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]
Putting the value of P, t, r, and n in the above formula
[tex]=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}[/tex]
after solving the above expression
M = $1674.22
Interest = M*n-P
Putting the value of P, n and M
= 1674.22*300-395000
= 502266-395000
= 107,266
Rounding to nearest ten dollar
= $107,270
Hence, the total interest is $107,270.
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Answer:
Step-by-step explanation:
find x and the length of each segment
s
13
T
6
U
2x-18
y
4x-29
Answer:
x = 15, UV = 12, SV = 31
Step-by-step explanation:
13 + 6 + (2x - 18) = 4x - 29
2x + 1 = 4x - 29
2x = 30
x = 15
UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12
SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31
Find all pairs of prime numbers (a,b) such that a^b✖️b^a+1 is prime
The pairs of prime numbers (a,b) between 1 and 10 inclusive such that a^b * b^a+1 is prime are
How to determine the pairs of numbers?The expression that is a prime number is given as:
a^b * b^a + 1
The boundary or range of numbers of a and b is not given.
So, we make use of numbers between 1 and 10
i.e. 1 ≤ a ≤ 10 and 1 ≤ b ≤ 10
Using the above range, we have the following program to determine the pairs of prime numbers (a, b).
for a in range(1,11):
for b in range(1,11):
num = (a* *b) * (b* *a) + 1
flg = False
if num > 1:
for i in ra nge(2, num):
if (num % i) == 0:
flg = True
break
if not flg:
print(str(a)+","+str(b))
The output of the above program is:
(1,1), (1,2), (1,4), (1,6), (1,10), (2,1), (2,2), (2,3), (2,4), (3,2), (4,1), (4,2), (4,4) and (4,6)
The above represent all pairs of prime numbers (a,b) such that a^b * b^a+1 is prime
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Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selections down to six mysteries and nine nonfiction books. If she randomly chooses three books from her selections, what’s the probability that they will all be nonfiction? Enter a fraction or round your answer to 4 decimal places, if necessary.
Please explain in detail
The probability that all 3 books would be nonfiction is 0.1846.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that all 3 books would be nonfiction = (number of non fiction books / total number of books) x (number of non fiction books - 1 / total number of books - 1) x (number of non fiction books - 2 / total number of books - 2)
9 /15 x 8/14 x 7/13 = 0.1846
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Question 1 of 10
What is the slope of the line that contains the points (-2, 5) and (6,-3)?
OA. 8
OB. 1
O C. -1
OD. -8
Answer:
slope is -1
Step-by-step explanation:
Slope of the line is changes in y over changes in x. It can also be referred as rise over run.
We can express mathematically as:
[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where m is slope.
Let (-2,5) be [tex]\displaystyle{(x_2,y_2)}[/tex] and (6,-3) be [tex]\displaystyle{(x_1,y_1)}[/tex]. Hence, apply the slope formula:
[tex]\displaystyle{m=\dfrac{5-(-3)}{-2-6}}\\\\\displaystyle{m=\dfrac{5+3}{-8}}\\\\\displaystyle{m=\dfrac{8}{-8}}\\\\\displaystyle{m=-1}[/tex]
Therefore, the slope is -1
A cellular network transmits its signals in a circular pattern. The tower is considered the origin, (0,0), of the signal and there is a house located on the edge of the circle at (2, 4). Which of the following coordinates could represent the location of another house that is also on the edge of the circle?
A.(1.3)
B.(-2,-4)
C.(3,3)
D.(4,4)
Answer:
B
Step-by-step explanation:
because at origin they are both positive and when it rotates about 270 both will change to negative
90°
Find mZR.
A. 30°
B. 60°
C. 120°
D. 180°
(2x)
to
P
90°
S
Answer:
120°
Step-by-step explanation:
Angles in a quadrilateral add to 360°, so
90+90+x+2x=360
180+3x=360
3x=180
x=60
So, angle R measures 120°.
find the slope of this line
Answer:
0
Step-by-step explanation:
On a graph, any line that is horizontal has a slope of zero. Try any points and and plug them into the slope formula equation
(Y2-Y1/X2-X1).
The answer will always be zero.
4/3*(1/2-6)=(4/3*1/2)-(4/3-6)
Answer:
The product would be: -22/3 = 16/3, if true or false: false the left side -7.3 does not equal to the right side 5.3 which means the given statement is false, if it is evaluated -22/3 = 16/3, if multiplied it would still be -22/3 = 16/3 (you never said how to solve it so here are ways)