Answer: 12 toy airplanes for $33.36
Step-by-step explanation:
We will find the price of one plane (the unit price) by dividing the price by the number of planes bought for each case.
$33.36 / 12 = $2.78 per plane
$14.50 / 5 = $2.90 per plane
In relation to the price per plane, 12 toy airplanes for $33.36 is the better buy.
-6,-5,-4,-3,...rule
What is answer
Answer:
[tex]a_{n}[/tex] = n - 7
Step-by-step explanation:
There is a common difference between consecutive terms in the sequence
d = - 5 - (- 6) = - 4 - (- 5) = - 3 - (- 4) = 1
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 6 and d = 1 , then
[tex]a_{n}[/tex] = - 6 + 1 (n - 1) = - 6 + n - 1 = n - 7
Consider sample of 47 football games, where at of them were won by the bomo tam. Use a 0.01 significance level to test the claim that the probability that the home team wins is greater than one half. Identify the null and alternative hypothes for this test.
The null hypothesis for this test is that the probability that the home team wins is equal to or less than one half. The alternative hypothesis is that the probability that the home team wins is greater than one half.
1. Identify the null hypothesis (H0): The null hypothesis for this test is that the probability that the home team wins is equal to or less than one half (P ≤ 0.5).
2. Identify the alternative hypothesis (Ha): The alternative hypothesis is that the probability that the home team wins is greater than one half (P > 0.5).
3. Determine the significance level (α): The significance level, also known as the alpha level, is set at 0.01. This means that we are willing to accept a 1% chance of rejecting the null hypothesis when it is actually true.
4. Collect the sample data: In this case, we have a sample of 47 football games, where "at" of them were won by the home team (let's assume "at" to be a specific number).
5. Calculate the test statistic: To test the claim, we need to calculate the test statistic based on the sample data. Since we are comparing a proportion (probability), we can use the z-test. The test statistic formula is given by:
z = (p - P) / √(P * (1 - P) / n)
Where:
p is the proportion of games won by the home team in the sample,
P is the claimed probability that the home team wins (in this case, P = 0.5),
n is the sample size.
6. Determine the critical value: Since we have a one-tailed test (alternative hypothesis is directional), we need to find the critical value corresponding to the significance level of 0.01 in the standard normal distribution (z-distribution). Using a z-table or a statistical software, the critical value for a 0.01 significance level is approximately 2.33.
7. Compute the test statistic: Plug in the values from the sample data into the test statistic formula calculated in Step 5 to obtain the z-value.
8. Compare the test statistic with the critical value: If the test statistic is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
9. Make a decision: If the test statistic is greater than the critical value, we reject the null hypothesis, indicating that there is sufficient evidence to support the claim that the probability that the home team wins is greater than one half. If the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis, indicating that there is not enough evidence to support the claim.
10. Provide a conclusion: Based on the decision made in Step 9, state the conclusion in the context of the problem. For example, if we reject the null hypothesis, we can conclude that there is significant evidence to suggest that the home team has a greater than 50% chance of winning in these football games.
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find the coordinate vector of a =[ 2 3 4 5] with respect to the basis = [e22, e21, e12, e11 ] of m22.
The coordinate vector of vector a = [2, 3, 4, 5] with respect to the basis B = [e22, e21, e12, e11] of M22 is [3, 4, 5, 2].
To find the coordinate vector, we need to express vector a as a linear combination of the basis vectors. The given basis B represents the standard basis for a 2x2 matrix.
Let's break down the process step by step:
Start with the basis vectors: e22, e21, e12, e11.
Express vector a as a linear combination of the basis vectors:
a = 2 * e22 + 3 * e21 + 4 * e12 + 5 * e11
The coefficients in front of each basis vector represent the coordinates of a with respect to the basis B.
Therefore, the coordinate vector of a with respect to B is [2, 3, 4, 5].
However, it's important to note that the given basis B is not the standard basis for a 2x2 matrix. The standard basis for a 2x2 matrix consists of the following vectors: e11 = [1, 0, 0, 0], e12 = [0, 1, 0, 0], e21 = [0, 0, 1, 0], e22 = [0, 0, 0, 1].
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Find the Surface area of the following figure below
Answer:
495
Step-by-step explanation:
Base area = 11*11 = 121
Lateral area = (11*4)*17/2 = 11*2*17 = 374
121+374=495
Find the measure of each angles:
Answer:
10. 123º
13. 65º
Step-by-step explanation:
For number 10, a straight line is equal to 180º so all we have to do is subtract 57 (the number that we're given) from 180
For number 13, vertical angles are always congruent (the same) so we know that it's 65º
Please solve as soon as possible thank you I appreciate it!
John’s friend told him that he could earn $25 for handing out flyers at a local concert. John wants to calculate the hourly rate. If he works a total of 2 hours, the equation 2x=25 can be used to determine his hourly rate. What would John’s hourly rate be, in dollars?
A
$12.50
B
$23
C
$27
D
$50
Answer:
D
Step-by-step explanation:
Sandra needs a new bicycle tire. Her tire has a circumference of 26π inches. What is the radius of her tire?
Answer:
it should be by mult by 10 is 816.81
5. Write a function of the form f(x) = - + k with a vertical asymptote at x = -15 and a horizontal asymptote of y = -6.
A certain reality TV show lost a total of 9,000 viewers over the past 3 months. It lost the same number of
viewers each month.
The following equation describes this situation.
-9,000 = 3 = -3,000
What does -3,000 tell us?
Answer:
Step-by-step explanation:
- 3, 000 tells the number of views loss in each month.
I really need help please and thank you
Answer:
117 Degrees
Step-by-step explanation:
plz give brailiest, the 1 and 117 are the exact same angle
Can someone explain pls I don’t understand how to do it lol
Find the volume of the
rectangular prism.
3 cm
9 cm
7 cm
V = [?] cm3
Answer:
189cm^3
Step-by-step explanation:
First, we need to find the formula of "how to find the volume of any prism":
length * width *height
* = multiply
So that means we need to do:
7cm * 9cm * 3cm
= 189cm^3
^ = exponent
Hope this helped :)
Francesca makes and sells jewelry. She uses the equation p = "285 + 45n to model the situation, where p is the amount of profit she
makes and n is the number of necklaces she sells. What does the y-intercept
The y-intercept for the given equation p = 285+45n is 285.
What is Y intercept?The Y-intercept is the point where the graph intersects the y-axis.
Y-intercept formulaTo find the y-intercept of a function y = f(x), substitute x=0 and solve for y.
According to the given question
we have an equation p = 285+45n
where,
p is the amount of profit
and, n is the number of necklaces
Let, p = y and n = x
then the given equation becomes y=285+45x
substitute, x = 0 in equation y = 285+45x
⇒ y = 285
Hence, the y-intercept of the equation p=285+45n is 285.
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3(2w -4) equals what
Answer:
6W-12
Step-by-step explanation:
Answer:
6w-12
Step-by-step explanation:
distribute:
3(2w-4) = 6w-12
"Suppose X --> N(20,5)
(a) Find: (i) P(X> 18)
(ii) P(7 < X < 15)
(b) Find the value a such that P(20-a < X < 20+ a) = 0.99
(c) Find the value b such that P(20-b< X < 20+ b) = 0.95
a) i)P(X > 18)= 0.65542
ii)P(7 < X < 15)=0.154
b)The value of a using the standard normal table or a calculator is 12.875
c)the value of b using the standard normal table or a calculator is 9.8
a) Let X be the normal random variable with mean μ = 20 and standard deviation σ = 5. We have to find P(X > 18) and P(7 < X < 15).
(i) P(X > 18)
This can be calculated using the standard normal table or a calculator as follows:
z = (18 - μ)/σ
= (18 - 20)/5
= -0.4
P(X > 18) = P(Z > -0.4)
= 1 - P(Z ≤ -0.4).
Using the standard normal table or a calculator, P(Z ≤ -0.4) = 0.34458
Therefore, P(X > 18) = 1 - 0.34458 = 0.65542
(ii) P(7 < X < 15). This can be calculated using the standard normal table or a calculator as follows:
z₁ = (7 - μ)/σ
(7 - 20)/5 = -2.6z₂
(15 - μ)/σ = (15 - 20)/5
= -1
P(7 < X < 15) = P(-2.6 < Z < -1)
= P(Z < -1) - P(Z < -2.6)
Using the standard normal table or a calculator,
P(Z < -1) = 0.15866P(Z < -2.6) = 0.00466
Therefore, P(7 < X < 15) = 0.15866 - 0.00466 = 0.154
b) We have to find the value of a such that
P(20 - a < X < 20 + a) = 0.99.
This can be calculated as follows:
z₁ = (20 - a - μ)/σ
= (20 - a - 20)/5
= -a/5z₂ = (20 + a - μ)/σ
= (20 + a - 20)/5 = a/5
We need to find a such that
P(z₁ < Z < z₂) = 0.99
Using the standard normal table or a calculator,
P(Z < z₂) - P(Z < z₁) = 0.99P(Z < a/5) - P(Z < -a/5) = 0.99
This can be rewritten as
P(Z < a/5) - [1 - P(Z < a/5)] = 0.99P(Z < a/5) - P(Z < -a/5) = 0.995
From the standard normal table or a calculator,
P(Z < 2.575) = 0.995P(Z < -2.575) = 0.005
Therefore,
2.575 = a/5 or -2.575 = -a/5a = 12.875
Therefore, the value of a is 12.875.
c) We have to find the value of b such that P(20 - b < X < 20 + b) = 0.95.
This can be calculated as follows:
z₁ = (20 - b - μ)/σ
= (20 - b - 20)/5
= -b/5z₂
= (20 + b - μ)/σ
= (20 + b - 20)/5 = b/5
We need to find b such that
P(z₁ < Z < z₂) = 0.95
Using the standard normal table or a calculator,
P(Z < z₂) - P(Z < z₁) = 0.95P(Z < b/5) - P(Z < -b/5) = 0.95
This can be rewritten as
P(Z < b/5) - [1 - P(Z < b/5)] = 0.95P(Z < b/5) - P(Z < -b/5) = 0.975
From the standard normal table or a calculator,
P(Z < 1.96) = 0.975P(Z < -1.96) = 0.025
Therefore,1.96 = b/5 or -1.96 = -b/5b = 9.8
Therefore, the value of b is 9.8.
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Your reading teacher
has
20 students in his elos. If
he uses popnicle sticks to
randomly call on
students during class,
what is the probability
your name will
be
called
Answer:
5%
Step-by-step explanation:
20= 100%
1 x100 = 100
100/20= 5
x=-2
Identify what's the slope and what's the y-intercept
Answer:
There is no slope and no y-intercept.This is a line that is parallel to Y-axis
kam
A company's stock was selling at
$28 a share. A month later, it was
selling at $21 a share. What is the
percent loss?
[?]%
Answer:Im pretty sure it's 25% percent loss
Step-by-step explanation:
sorry if im wrong
Which situation CANNOT be represented by this equation? 6−7=29 6 x - 7 = 29 CLEAR CHECK Joel earns $7 $ 7 per hour to mow his aunt's lawn. If he spends $6 $ 6 on gas, how many hours, x , will he need to mow to have $29 $ 29 left? Joel mows his aunt's lawn for $6 $ 6 per hour. If he spends $7 $ 7 on gas, how many hours, x , will he need to spend mowing the lawn to have $29 $ 29 left? Joel takes 6 6 hours to mow his aunt's lawn. If he spends $7 $ 7 on gas, how much does he get paid per hour, x , to mow the lawn and still have $29 $ 29 left?
Answer:
Joel earns $7 per hour to mow his aunt's lawn. If he spends $6 on gas, how many hours, x , will he need to mow to have $ 29 left?
Step-by-step explanation:
The given equation is :
6x - 7 = 29
It is given that total hours be = x
Joel earns $7 per hour, so the total earning of Joel in x hours is = $ 7x
He spends $6 on gas, so = 7x - 6
He is left with $ 29 after spending on gas.
Therefore, the equation becomes :
7x - 6 = 29
Clearly, it can be seen that in this case, the given situation cannot be represented by the given equation, i.e. 6x - 7 = 29.
Pls help me plz either sdys
Answer:
44
Step-by-step explanation:
14x3.14 is 43.96 and that after being rounded to the nearest tenth becomes 44
Explain, using an example, why you need to multiply when converting from a larger unit to a smaller unit
Answer:
This is often called scaling in math, used in ratios, fraction, percent's etc.
Step-by-step explanation:
Answer:
You can use similar processes when converting from smaller to larger units. When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide. Here is an example..
Marie charges $8 for a dozen of her pineapple cupcakes. She sold 23 dozen at the street fair yesterday. How much money did
Marie collect?
A) $144
B) $164
C) $184
D) $194
Help please and I’ll I’ve BRAINLIEST
Answer:
c
Step-by-step explanation:
each dozen cost $8 so do the $8 times the 23 dozen she sold to get the answer
Answer:
C)$184
Step-by-step explanation:
8 times 23=$184
plz can i get brainliest:)
what's the answer !!
[tex] \sqrt{44 \times 2 \times 2 \times 11} [/tex]
Answer:
44
Step-by-step explanation:
[tex] \sqrt{44 \times 2 \times 2 \times 11} [/tex]
[tex] \sqrt{88 \times 2 \times 11} [/tex]
[tex] \sqrt{176 \times 11} [/tex]
[tex] \sqrt{1936}[/tex]
[tex] \sqrt{ {44}^{2} } [/tex]
Pull terms out from under the radical, assuming positive real numbers.
[tex]44[/tex]
Hope it is helpful.....Step-by-step explanation:
[tex] \sqrt{44 \times 2 \times 2 \times 11} \\ = \sqrt{11 \times 4 \times 4 \times 11} \\ = \sqrt{11 \times 11 \times 4 \times 4} \\ = 11 \times 4 \\ = 44[/tex]
What is the volume of a sphere with a radius of 6.3 cm, rounded to the nearest tenth of a cubic centimeter?
Answer:
1047.4 cm^3
Step-by-step explanation:
Answer:1047.4
Step-by-step explanation:
.
Jason wants to create a box with the same volume as the one shown below. He wants the length to be 4 inches. What would be the measurements of the width and height?
Answer:
Width-6
height-3
I determinded the width and the height by counting how many cubic blocks there are up and down.
Step-by-step explanation:
The measurements of the width and height can 3 inches each or 1 and 9 inches.
What is volume of cuboid?The volume of the cuboid is defined as the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height. The volume of a cuboid is equal to the product of length, width and height of a cuboid.
Given data as :
Jason wants to create a box with the same volume as the one shown
To determine measurements of width and height of box
Volume of given box (cuboid) = 6 × 2 × 3
Volume of given box = 36
length to be 4 inches.
length × width × height = 36
⇒ 4 w × h = 36
⇒ w × h = 9
Now multiplication factors of 9 as
9 = 1 × 9
9 = 3 × 3
So, width and height can 3 inches each or 1 and 9 inches.
Hence, the measurements of the width and height can 3 inches each or 1 and 9 inches.
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Find two negative consecutive integers such that the square of the first is five more than the second. Find the integers.
Answer:
the two consecutive negative integers are -2 and -1.
Step-by-step explanation:
Represent these negative integers by m and n.
Then (because the integers are consecutive) n = m + 1, and m^2 = n + 5.
Substituting m + 1 for n in the second equation, we get:
m^2 = m + 1 + 5, or
m^2 - m - 6 = 0
This factors into (m - 3)(m + 2) = 0. The only negative root is -2.
Thus, the two consecutive negative integers are -2 and -1.
Check: Is the square of the first five more than the second?
Is (-2)^2 = -1 + 5? YES
The integers aer -2 and -1.
Which pair of equations below is a result of constructing the altitude, h, in triangle ABC?
Answer:
the answer is A:
sinA=h/c
sinC=h/a
Step-by-step explanation:
edge 2020
The pair of equations is sinA=h/a cosC=h/a
What is trigonometry?
Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms.
When a altitude is drawn from the base of the triangle
we can write
sinA=height/ a where a, is the side length of AB
also,cos C=height/a where a, is the side length of AB
Therefore,The pair of equations is where a, is the side length of AB
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whats 10k - 90 = -10
Answer:
k = 8
Step-by-step explanation:
10*8 - 90 = -10
:/
Complete the equation
Three companies, A, B and C, make computer hard drives. The proportion of hard drives that fail within one year is 0.001 for company A, 0.002 for company B and 0.005 for company C. A computer manufacturer gets 50% of their hard drives from company A, 30% from company B and 20% from company C. The computer manufacturer installs one hard drive into each computer.
(a) What is the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year? [4 marks]
(b) I buy a computer that does experience a hard drive failure within one year. What is the probability that the hard drive was manufactured by company C? [4 marks]
(a) The probability of the chosen hard drive to fail within one year is 0.005.
(b) The probability that the hard drive was manufactured by company C is 3.95%.
(a) The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:
Probability of choosing hard drive from company A and failure within one year + Probability of choosing hard drive from company B and failure within one year + Probability of choosing hard drive from company C and failure within one year
P(A and F) = P(A) x P(F|A) = 0.5 x 0.001 = 0.0005
P(B and F) = P(B) x P(F|B) = 0.3 x 0.002 = 0.0006
P(C and F) = P(C) x P(F|C) = 0.2 x 0.005 = 0.0010
The probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is:
0.0005 + 0.0006 + 0.0010 = 0.0021 (or 0.21%)
(b) Let F be the event that the hard drive fails within one year and C be the event that the hard drive is manufactured by company C.
We want to calculate P(C|F), the probability that the hard drive was manufactured by company C, given that it failed within one year;
P(C|F) = P(C and F) / P(F) = [P(C) x P(F|C)] / [P(A) x P(F|A) + P(B) x P(F|B) + P(C) x P(F|C)]
P(C|F) = (0.2 x 0.005) / (0.5 x 0.001 + 0.3 x 0.002 + 0.2 x 0.005)
P(C|F) = 0.083 / 0.0021 = 0.0395 (or 3.95%)
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The probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.
(a) Let the random variable X denote the number of hard drives in the computer manufacturer's hard drives that fail within one year. The probability distribution of X can be found as follows:
[tex]P(X = 0) = 0.5(1 - 0.001) + 0.3(1 - 0.002) + 0.2(1 - 0.005) = 0.9957[/tex]
[tex]P(X = 1) = 0.5(0.001) + 0.3(0.002) + 0.2(0.005) = 0.0016[/tex]
Thus, the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year is 0.0016.
(b) Let the event H denote that the computer I buy experiences a hard drive failure within one year. Let the event Ci denote that the hard drive in my computer is manufactured by company
i. Then, using Bayes' theorem, we have:
[tex]P(C3 | H) = P(H | C3)P(C3) / P(H)[/tex]
We can find the values of the three probabilities in the above formula as follows:
P(H | C1) = 0.001
P(H | C2) = 0.002
P(H | C3) = 0.005
P(C1) = 0.5
P(C2) = 0.3
P(C3) = 0.2
[tex]P(H) = P(H | C1)P(C1) + P(H | C2)P(C2) + P(H | C3)P(C3)≈ 0.00135[/tex]
Thus, P(C3 | H) = 0.005(0.2) / 0.00135 ≈ 0.74
Therefore, the probability that the hard drive in my computer is manufactured by company C given that my computer experiences a hard drive failure within one year is approximately 0.74.
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