Answer:
=
15/4
(Decimal: 3.75)
Step-by-step explanation:
55) Lenny has $3.69 in pennies,
dimes, and quarters. The number
of pennies is three more than
the number of dimes. The number
of quarters is twice the number
of dimes. How many each coin does
he
have?
Answer:
For each coin he has 6 dimes, 12 quarters, and 9 pennies.
3x – y = -1 x – 2y = -12
The solution to the system of equation is (2, 7)
System of equationGiven the system of equation expressed as:
3x – y = -1 * 2
x – 2y = -12 * 1
________________
6x – 2y = -2
x – 2y = -12
Subtract to have;
6x-x = -2-(-12)
5x = 10
x = 2
Substitute x = 2 into 2 to have:
2 - 2y = -12
-2y = -14
y = 7
Hence the solution to the system of equation is (2, 7)
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A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: μ = 12 against H1: μ < 12, using a random sample of four specimens. (a) What is the type I error probability if the critical region is defined as x < 11.5 kilograms? (b) Find β for the case in which the true mean elongation is 11.25 kilograms. (c) Find β for the case in which the true mean is 11.5 kilograms.
The Type I error's computed value is 0.02275 and The Type II error has a computed value of 0.50 based on probability.
What is probability?
The potential or opportunity of an event happening is known as probability. The probability is equal to the variety of possible outcomes. the estimated number of outcomes that could occur.(a) Type I error probability if the critical region is defined as x < 11.5 kilograms
[tex]P(Type\ Error)=P\ xbar < 11.5\ when\ mu=12)\\\\[/tex]
[tex]=P(Z < \frac{11.5-12}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z < -2)\\\\=0.02275[/tex]
The Type I error's computed value is 0.02275.
Observe that there is a 2.275% likelihood of dismissing the null hypothesis if it is true based on the Type I error probability.
(b) β for the case in which the true mean elongation is 11.25 kilograms.
[tex]b= P(Type II Error)\\\\=P(xbar\geq 11.5\ when\ mu_1\ =11.25)[/tex]
[tex]=P(Z \geq \frac{11.5-12}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z \geq 1)\\\\= 1-P(Z < 1)\\\\=1-0.8413\\\\=0.1587[/tex]
The Type II error's computed value is 0.1587.
Observe that there is a 15.87% possibility of refusing to disprove the null hypothesis when it is untrue based on the Type II error probability.
(c) β for the case in which the true mean is 11.5 kilograms.
[tex]b= P(Type II Error)\\\\=P(xbar\geq 11.5\ when\ mu_1\ =11.25)[/tex]
[tex]=P(Z \geq \frac{11.5-11.5}{\frac{0.5}{\sqrt{4} } } )\\\\=P(Z \geq 0)\\\\= 1-P(Z < 0)\\\\=1-0.50\\\\=0.50[/tex]
The Type II error has a computed value of 0.50.
Observe that there is a 50% possibility of neglecting to disprove the null hypothesis when it is untrue based on the Type II error probability.
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Larry put $1,287 into a savings account 8 years ago. • The account earned 4% simple annual interest. • He made no additional deposits or withdrawals. Based on this information, what is the balance in dollars and cents in Larry's savings account at the end of these 8 years? Record your answer in the boxes below. Be sure to use the correct place value.
The balance in Larry's savings account at the end of these 8 years is 1698 dollars and 84 cents
What is the balance in dollars and cents in Larry's savings account at the end of these 8 yearsThe given parameters are
Principal, P = 1287
Rate, R= 4%
Time, T = 8
The balance in dollars and cents in Larry's savings account at the end of these 8 years
Balance = P * PRT
This gives
Balance = 1287 + 1287 * 4% * 8
Evaluate
Balance = 1698.84
Hence, the balance in Larry's savings account at the end of these 8 years is 1698 dollars and 84 cents
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K
Pedro has scores of 85, 84, 69, and 82 after four tests. What score must he make on his fifth test to have an average of 79 or greater?
The score that Pedro needs on his fifth test to get an average of at least 79 is
(Round to the nearest integer as needed.)
Answer: x > 75
Step-by-step explanation:
(85+84+69+82+x)/5 > 79
85+84+69+82+x > 395
x > 75
Please help, This is urgent 7th-grade math.
There was 2/3 of a pan of lasagna in the refrigerator. Bill and his friends ate half of what was left. Write a number sentence and draw a model to represent the problem. How much of the pan did they eat?
Explanations/Answers, please!
3x+4=2x+8 solve linear equation
Answer:
3x±4=2x±8
3x-2x=8-4
x=4
Step-by-step explanation:
Hope its helpful for you
hhhhhheeeeeeeeeeellllllllllllppppppppppp!!!!!!!!!!!!
Answer:7
Step-by-step explanation:
The probability mass function of X is f(x)= 1/6, x 1.2...,6 then find out the value
of mean and standard deviation.
For the given probability mass function of X, the mean is 3.5 and the standard deviation is 1.708.
A discrete random variable X's probability mass function (PMF) is a function over its sample space that estimates the likelihood that X will have a given value. f(x)=P[X=x]. The total of all potential values for a random variable X, weighted by their relative probabilities, is known as the mean (or expected value E[X]) of that variable. Mean(μ) = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6).Mean(μ) = (1+2+3+4+5+6)/6Mean(μ) = 21/6Mean(μ) = 3.5The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution represents its standard deviation. It is denoted by 'σ'. A random variable's variance (or Var[X]) is a measurement of the range of potential values. It is, by definition, the squared expectation of the distance between X and μ. It is denoted by 'σ²'. σ² = E[X²]−μ²σ² = [1²(1/6) + 2²(1/6) + 3²(1/6) + 4²(1/6) + 5²(1/6) + 6²(1/6)] - (3.5)²σ² = [(1² + 2²+ 3² + 4²+ 5²+ 6²)/6] - (3.5)²σ² = [(1 + 4 + 9 + 16 + 25 + 36)/6] - (3.5)²σ² = (91/6) - (3.5)²σ² = 15.167-12.25σ² = 2.917σ = √2.917Standard deviation (σ) = 1.708To learn more about variance, visit :
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can someone help me please
Answer:
A(-9/2, 0)B(1, 0)C(0, -9)Step-by-step explanation:
Given the quadratic equation y = 2x² +7x -9, you want the coordinates of the x- and y-intercepts.
X-interceptsThe values of x where y=0 can be found by factoring the equation.
y = (2x +9)(2x -2)/2 = (2x +9)(x -1)
The constants 9 and -2 in the binomial terms are factors of the product of leading and trailing coefficients (2)(-9) = -18. Those factors are chosen because their sum is 7, the middle coefficient.
The x-intercepts are the values of x that make these factors zero:
2x +9 = 0 ⇒ x = -9/2
x -1 = 0 ⇒ x = 1
Points A and B are ...
A(-9/2, 0)B(1, 0)Y-interceptThe y-value at point C is where x=0. It is the constant in the quadratic equation.
y = 2(0²) +7(0) -9 = -9
Point C is ...
C(0, -9)Which of the following is equivalent to the quantity three fifths end quantity to the power of 2 times x?
A - the quantity three fifths end quantity to the power of x
B - the quantity 6 over 10 end quantity to the power of x
C - the quantity 9 over 5 end quantity to the power of x
D - the quantity 9 over 25 end quantity to the power of x
Answer:
B is correct
Step-by-step explanation:
three fifths= 6/10= 0.6
since the quantity is to a power of (2×x)=2x
so B is correct
How many subsets are there in A={x:x is letters of the alphabet}
The number of subsets formed is 67,108,864.
What is defined as the subsets?Set 1 is said to be a subset of set 2 if all of its elements are present in it. A set is a clearly defined group of numbers, alphabets, items, or any other items.
If set 1 = A,B,C and set 2 = A,B,C,D,E,F, then set 1 is a subset of set 2 because all of the elements in set 1 are also present in set 2.A subset is a subset of a larger set (another set or the same set). To symbolize a set A as a subset of a larger set B, use the set notation: A ⊆ B.The number of subsets of an n-element set is 2ⁿ.
As a result, the formula for determining the number of subsets of the a set with 'n' components is 2ⁿ.
For the given question;
A={x:x is letters of the alphabet}
Thus, the n = 26 (total letter is English alphabet).
Total subsets = 2ⁿ
Total subsets = 2²⁶ = 67,108,864.
Therefore, the total number of subsets formed by the English alphabet are 2²⁶ = 67,108,864.
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Use the diagram to find the measures of the lengths of the
sides. The perimeter of the trapezoid on the right is 67
inches.
The length of all four sides of the Isoclesles Trapezium is 67 inches.
What is an area of a Trapezium?Area of a Trapezium is (1/2)(a+b)h.Where and b are the parallel sides of the trapezium and h is the distance between the two parallel side
We know that for a plane 2D figure perimeter is the sum of the lengths of all the sides.
Given an isosceles Trapezium with a perimeter of 67 inches,
As the sides are given in variables we can equate the sum of all the sides with the given perimeter and obtain the value of x.
∴ (x + 1.5x + 2.5x - 5 + x) = 67.
6x = 67 + 5.
6x = 72.
x = 12.
So, the measure of lengths of four sides are [ 12 + 1.5(12) + 2.5(12) - 5 + 12) which is ( 12 + 18 + 30 - 5 + 12 ) = 67 inches.
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A=bh;A=5,h=5
HELP ME
Answer:
b = 1
Step-by-step explanation:
5 = 5b
b = 1
Simplify: 2.4 × 10-4
The four is a exponent
Answer: 20
Step-by-step explanation:
Multiply 2.4*10-4
Calculate 24-4
the answer is (12x^10000)/5
6) Four pieces measuring 29.cm, 19.62cm, 32.49cm and 24.74cm are cut from a board that is 200cm long. Allowing 1cm for waste in cutting, what is the length of the remaining piece?
The Remaining length of the cardboard piece is 94.15 cm.
According to the statement
We have to find that the length of the remaining piece.
So, For this purpose, we know that the
Length is defined as the measurement or extent of something from end to end.
From the given information:
Four pieces measuring 29.cm, 19.62cm, 32.49cm and 24.74cm are cut from a board that is 200cm long.
Then
Total length of the four pieces become:
Four pieces length = 29+19.62+ 32.49 + 24.74
Four pieces length = 105.85 cm
Then the
Remaining length of the cardboard piece = total length - length of the four pieces.
Remaining length of the cardboard piece = 200 - 105.85
Remaining length of the cardboard piece = 94.15cm.
So, The Remaining length of the cardboard piece is 94.15 cm.
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4(x + 2)-2=6x-21-4+x)
Answer:
3.5 or [tex]\frac{7}2}[/tex]
Step-by-step explanation:
4(x+2)-2=6x-2(4+x)
4x + 8 - 2 = 6x - 8 + 2x
4x + 6 = 8x - 8
14 = 4x
x = 3.5 or [tex]\frac{7}2}[/tex]
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Argyle wants to make T-shirts for
students. Customink is willing to offer a
deal with the school that each shirt will
cost $5 plus a $50 fee for each shirt color.
Argyle wants to make a teal and a purple
shirt.
Answer:
55
Step-by-step explanation:
A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts moving the rabbit sees it and starts running away at a speed of 40 feet per second. What should the fox's speed be to catch up to the rabbit.
The speed of the fox should be 35/t + 40 to catch up to the rabbit.
What is speed?Speed is the ratio of distance and time.
Speed = Distance / Time
We have,
The distance between the rabbit and fox = 35 feets
The rabbit's speed = 40 feet per second
Let fox's speed = F
Let the time taken to catch up to the rabbit = t
Now,
Rabbit's distance from fox after time t will be:
= 35 + (40 × t)
= 35 + 40t
Fox's distance after time t:
= F × t
Fox and rabbit distance must be the same in order for the fox to catch up with the rabbit.
35+40t = Ft
Dividing both sides by t.
35/t + 40 = F
Therefore the fox's speed must be 35/t + 40 in order to catch up with the rabbit.
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number of gram in p gram?
Answer:
1 pound (lb) is equal to 453.59237 grams (g)
I NEED HELP PLEASE
f+3n=7n
Answer:
4n
Step-by-step explanation:
Please help!
Simplify:
Answer: Raise
5
to the power of
4
= 625
Answer:
[tex]5^{4} =625..[/tex]
Step-by-step explanation:
[tex]5^{4} = 625[/tex]
[tex]=625[/tex]
hopefully this helps you :)
What proportion of people surveyed would be willing to pay more than $6.75 for a sandwich?
The proportion of people surveyed would be willing to pay more than $6.75 for a sandwich is 94.4%.
What is termed as normal distribution?The normal distribution, also recognized as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.
Early statisticians started to notice the same shape recurring in different distributions and designated it the normal distribution. Normal distributions are distinguished by their symmetric bell shape. The mean and median are the same; they are both in the middle of the distribution.As, for the given value in the question;
The formula for finding the z-score is;
z = (x - μ)/s
where,
n = sample size ( = 528)
σ = standard deviation ( = 1.19)
μ = mean of the sample (= 6.56)
Put the values and fine z-score.
z = (x - μ)/s
z = (6.75 - 6.56)/1.19
z = 0.19/1.19
z = 0.159
For the probability; see the p-value from the positive z-score table.
p(z > 0.159) = 0.944
p(z > 0.159) = 94.4%
Thus, the probability that the people would be willing to pay more than $6.75 for a sandwich is calculated as 94.4%.
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The complete question is -
A sample of 528 people were asked how much they would be willing to pay for a sandwich. Their responses were approximately normal with a mean of $6.56 and a standard deviation of $ 1.19.
What proportion of people surveyed would be willing to pay more than $6.75 for a sandwich?
37+1/2-(x+1/4)=9(4x-7)+5
Find all points having a -coordinate of whose
distance from the point is .
The points which are a distance of 13 units from (12,5) are (0,0)and (24,0).
The distance between two point with co-ordinates ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) is calculated by the distance formula [tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
All points on the x-axis have their y-coordinates equal to 0. So let the point (a,0) be a point on the x-axis such that the distance from (12,5) to (a,0) is 13 units.
Let us substitute the values into the distance formula to calculate the values of a so that we can find the two points.
[tex]13=\sqrt{(12-a)^2+(5-0)^2}[/tex]
Squaring both sides we get:
[tex]or,13^2=144-24a+a^2+25\\or,169-144-25-24a+a^2\\or,a^2-24a=0\\or,a(a-24)=0[/tex]
Now either a=0 or (a-24)=0
Therefore either a=0 or a=24.
Therefore the two points (0,0) and (24,0) .
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33. How many 3-cup servings are in 4 cups? A. 2 B. 3 C. C. 4 D. 12
A cone has a volume of 9 pi in cubed and a diameter of 6 in . Wilson states that a cylinder
Answer:
ok then what's the correct answer?
Step-by-step explanation:
Find the perimeter of the rectangle.
X+1
2.5x - 4
Answer: 7x-6
Step-by-step explanation:
P=perimeter. L=length. W=width
P=2L+2W
P=2(x+1)+2(2.5x-4)
P=2x+2+5x-8
P=2x+5x+2-8
P=7x-6
find the domain of the following functions and simplify their expressions.
The domain of the function is (-∞,∞) and the simplified expression is x²-6x-40 .
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.
The given functions are
f(x)=6x+24
g(x)=x²-16
Now we have to find (g-f)(x) .
(g-f)(x)=x²-16-6x-24
or,(g-f)(x)=x²-6x-40
or,(g-f)(x)=x²-10x+4x-40
or,(g-f)(x)=x(x-10)+4(x-10)
or,(g-f)(x)=(x-10)(x+4)
So the domain of the function (g-f)(x) are the values for which the function exists. we can see that the function exists for all values of x.
Domain in set builder notation={x|x∈R}
Domain in interval notation=(-∞,∞)
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Question -: If ( 1 + tan θ ) ( 1+ ∅ ) = 2 , then what is ( θ + ∅ ) ?
a . 30⁰ b. 45⁰ c. 60⁰ d. 90⁰
Answer this question
Please Give Explanation
thanks
Correct choice is B.) 45°
The solution is in attachment ! do check it
Step-by-step explanation:
6.25 points
Find the GCF for the list.
10m4, 40m⁹
10m5
40m4
10m4
6.25 points
hey
list
