Answer:
You have a 25%, or 1/4 chance that you will choose a yellow paper clip.
Step-by-step explanation:
1) First, you want to find the total number of paper clips.
6 + 3 + 4 + 2 + 5 = 20 total paper clips
This is your denominator.
2) From the problem, we can understand that there are 5 yellow paper clips.
This is your numerator.
3) From the numerator and denominator we have from above, your fraction is 5/20.
4) This can be simplified into 1/4, which is 25%.
The probability of choosing a yellow paper clip is [tex]\frac{1}{4}[/tex].
What is probability?'Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.'
According to the given problem,
Number of yellow paper clips = 5
Total number of paper clips = 20
Probability = [tex]\frac{Number of favorable events}{Total number of events}[/tex]
= [tex]\frac{5}{20}[/tex]
= [tex]\frac{1}{4}[/tex]
Hence, we can conclude, the probability of choosing a yellow paper clip is [tex]\frac{1}{4}[/tex].
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Identify the numbers sets to which the number 0 belongs
Leigh bought a conical candle wax mold. The height of the mold is 18.9 inches and the radius of the inside of the top of the conical
mold is 2.1 inches. She fills the mold completely with candle wax so that it is level with the top of the conical mold.
Answer:
87.28 cubic inches
Step-by-step explanation:
Leigh wants to fill the conical candle wax mold completely with candle wax.
We have to calculate the volume of the cone by the formula :
[tex]V=\pi r^2\frac{h}{3}[/tex]
Here, V = volume
r = radius = 2.1 inches
h = height = 18.9 inches
By substituting these values given, into the formula
[tex]V=\pi (2.1)^2(\frac{18.9}{3})[/tex]
= (27.783)π
= 87.28 inch³
Conical mold can hold 87.28 inch³ candle wax.
The radius of a circle is 8 units. What is the diameter of the circle
Answer:
16
Step-by-step explanation:
The radius is half the size of the diameter.
8 * 2 = 16
Identify the term(s), coefficient(s), and constant(s) in the expression 7 + 3d2 + d4
Answer:
Step-by-step explanation:
Terms
7
3d²
d⁴
Constant : 7
Coefficient of 3d² = 3
Coefficient of d⁴ = 1
Final answer:
The expression 7 + 3d2 + d4 contains terms 7, 3d2, and d4, with coefficients 3 and 1 (implicit), and the constant 7. We identify each part according to algebraic principles and ensure to simplify and check our work.
Explanation:
The expression given is 7 + 3d2 + d4, which is a polynomial in d. The terms in this expression are 7, 3d2, and d4. Each part of a term can be classified as follows:
The coefficients are the numerical factors of the variables, which in this case are 3 for the term 3d2 and 1 for the term d4 (note: the coefficient is implicitly 1 here, since it's not written).
The constants are terms that do not contain variables, which here is only the number 7.
As a part of algebra, it's important to eliminate terms where possible to simplify the algebra and always check the answer to see if it is reasonable.
5. Solve: (2n – 5)^2= 81
Answer:
(n -7)(4n + 8) = 0
Step-by-step explanation:
(a -b)² = a² - 2ab + b²
(2n - 5)² = 81
(2n)² - 2*2n*5 + 5² = 81
4n² - 20n + 25 = 81
4n² - 20n + 25 - 81 = 0
4n² - 20n - 56 = 0
4n² - 28n + 8n - 8*7 = 0
4n*(n -7) + 8*(n - 7) = 0
(n -7)(4n + 8) = 0
Ali was asked to factorise x^2y^2 + 36 - 4x^2 - 9y^2.He tried some ways of grouping terms as shown below.
x^2y^2 + 36 - 4x ^2 - 9y^2=(x^2y^2 + 36) - (4x ^2 + 9y^2)
x^2y^2 + 36 - 4x^2 - 9y^2=( x^2y^2 + 36 - 4x^2) -9y^2
x^2y^2 + 36 - 4x^2 - 9y^2=x^2y^2 + (36 - 4x^2 - 9y^2)
As he could not carry out factorisation with the above groupings,he concluded that the expression could not be factorised.Do you agree with him? Why or why not?
Answer:
It can be factorised
Step-by-step explanation:
Given
x²y² + 36 - 4x² - 9y² ( rearranging )
x²y² - 4x² - 9y² + 36 ( factor first/second and third/fourth terms )
= x²(y² - 4) - 9(y² - 4) ← factor out (y² - 4) from each term
= (y² - 4)(x² - 9)
Both factors are a difference of squares and factor in general as
a² - b² = (a - b)(a + b)
Thus
y² - 4
= y² - 2² = (y - 2)(y + 2) , and
x² - 9
= x² - 3² = (x - 3)(x + 3)
Hence
x²y² + 36 - 4x² - 9y² = (y - 2)(y + 2)(x - 3)(x + 3)
A sector of a circle has a central angle of 80°. If the circle has a radius of 5.5 inches,what is the area of the sector? (pi = 3.14) *
Answer:
[tex] area = 21.11 ~in.^2 [/tex]
Step-by-step explanation:
Area of sector of circle with central angle measuring n degrees and radius r:
[tex] area = \dfrac{n}{360^\circ}\pi r^2 [/tex]
[tex] area = \dfrac{80^\circ}{360^\circ} \times 3.14 \times (5.5~in)^2 [/tex]
[tex] area = \dfrac{80^\circ}{360^\circ} \times 3.14 \times (5.5~in)^2 [/tex]
[tex] area = 21.11 ~in.^2 [/tex]
The area of the sector of the circle will be 21.12 inch².
How to estimate the area of the sector of the circle?The area of sector of circle central angle θ in degree and radius r will be represented as
A= (θ/360°)πr²
the sector has a central angle θ=80°
r=5.5 inches
substituting these values in above formula for the area of the sector of circle,
Area= A
= (θ/360°)πr²
= (80°/360°)π(5.5)²
=21.12 inch²
Therefore, the area of the sector will be 21.12 inch².
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Find the measure of b
Answer:
the answer is C: 90
Step-by-step explanation:
if its across from the number then its gonna be the same
Answer:
c: 90°
Step-by-step explanation: The lines are a reflection of each other, so the 90° angle is the same as B. :) sorry if my explanation is bad.
What is the simplified base for the function f(x) = 2RootIndex 3 StartRoot 27 EndRoot Superscript 2 x?
2
3
9
18
Answer:c
Step-by-step explanation:
How to round to the nearest degree
Answer:
to the nearest whole degree means that you look at the first decimal place. if it is less than 5, you keep the whole number and eliminate the decimal. if otherwise, the decimal is ≥5, you round up the whole number and eliminate the decimal.
Miko can type 70 words in one minute.At that rate,how many words can he type in 12 minutes?
Words typed in 1 minute = 70
Words typed in 12 minutes = 70 x 12 = 840 words
If Miko types at 70 words per minute, in 12 minutes he can type 840 words if he maintains the same speed throughout.
Simplify the following algebraic expression:
10xy - 5ab - 15yx + 9ba
Answer:
- 5xy + 4ab
Step-by-step explanation:
Rylee shopped at a clothing store, where she spent $36.50 plus 8% tax. Then, she spent $25 to refuel her car at the gas station. Finally, she bought groceries worth $23.50. At the grocery checkout, she handed over a coupon for a 20% discount on her purchase. what is her net change
Rylee's total spending was $39.42 for clothing (including tax), $25 for gas, and $18.80 for groceries (after applying a 20% discount). Summing these up, her total expenditure for all purchases was $83.22.
Explanation:This is a question involving basic arithmetic and percentage operations. In total, Rylee made three different purchases. She shopped for clothing costing $36.50 and paid 8% tax on it, which amounts to $36.50 * 0.08 = $2.92. Therefore, her total expenditure at the clothing store was $36.50 + $2.92 = $39.42. She then spent $25 to refuel her car.
Lastly, she bought groceries worth $23.50, but had a 20% discount coupon so she only paid 80% of the price, which is $23.50 * 0.80 = $18.80. If we add these expenditures together, we can find that Rylee's total spending was $39.42 (clothing) + $25 (gas) + $18.80 (groceries) = $83.22.
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Is y = 24x proportional
Answer:
yes
Step-by-step explanation:
A proportional relationship has the form
y = kx ← k is the constant of proportionality
y = 24x ← is in this form and is proportional with k = 24
Kelsey graphed the equation y = 3x + 1 as shown below. On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3). Which describes Kelsey’s error?
Answer: Kelsey graphed the slope as the y-intercept and the y- intercept as the slope.
Step-by-step explanation:
Answer: D on edg
Step-by-step explanation:
Kelsey graphed the slope as the y-intercept and the y- intercept as the slope.
A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch 75,000 fish. Due to population decreases, the number of fish the company was able to catch decreased by 8% each year. How many total fish did the company catch over the first 7 years, to the nearest whole number?
Answer:
The total amount of fishes caught is 414,519 fishes
Step-by-step explanation:
Here, given the percentage decrease in the population of fishes, we want to know the total amount of fishes caught by the company in the first 7 years.
First year, we have 75,000 fishes
Second year, we would have 75,000 - (8% of 75,000) = 75,000 - (0.08 × 75,000) = 75,000 - 6,000 = 69,000
Third year, we would have 69,000- (0.08 × 69,000) = 69,000 - 5520 = 63,480
Fourth year, we would have 63,480 - (0.08 × 63,480) = 58,401.6
Fifth year, we would have 58,401.6 - (0.08 × 58,401.6) = 58,401.6 - 4,672.18 = 53,729.472
Sixth year, we would have 53,729.472 - (0.08 × 53,729.472) = 53,729.472 - 4,298.3578 = 49,431.114
Seventh year, we would 49,431.114 - (0.08 × 49,431.114) = 45,476.625
The addition of all these values will give the total number of fishes caught = 75,000 + 69,000 + 63,480 + 58,401.6 + 53,729.472 + 49,431.114 + 45,476.625 = 414,518.8 = 414,519 fishes to the nearest whole number
Final answer:
Learn how to calculate the total fish caught by a fishing company over 7 years with decreasing catches.
Explanation:
A major fishing company caught 75,000 fish in the first year. Each year, the number of fish caught decreased by 8%. To find the total fish caught over 7 years:
Calculate the number of fish caught each year by multiplying the previous year's catch by (100% - 8%).
Add up the catches for 7 years.
Round the final total to the nearest whole number.
Therefore, the fishing company caught approximately X fish over the first 7 years.
A rectangle has a height of 4x ^ 3 width of x ^ 3 + 3x ^ 2 + 2x . Express the area of the entire rectangle .
Answer:
[tex]4x^6+12x^5+8x^4[/tex]
Step-by-step explanation:
To find the area of a triangle, you need to multiply the width by the height. In this case:
[tex](4x^3)(x^3+3x^2+2x)=\\4x^6+12x^5+8x^4[/tex]
Hope this helps!
How can you determine if a function is odd?
Answer:
Its easy !
Step-by-step explanation:
Test to determine if a function y=f(x) is even, odd or neither: Replace x with -x and compare the result to f(x). If f(-x) = f(x), the function is even. If f(-x) = - f(x), the function is odd.
Can someone please explain this?
Answer:
-pi
Step-by-step explanation:
as x equals zero, g(x) = -3.14 = -pi
Your answer would be the second option, -π.
This is because as x approaches 0, cos(x + π) approaches cos(π) = -1. On top, x + π as x approaches 0 will tend to π, so you end up with π/-1. This simplifies to -π.
I hope this helps! Let me know if you have any questions :)
Which word describes the slope of the line?
positive
negative
zero
undefined
Answer:
If it is horizontal then it is zero, if it is vertical then it is undefined
Step-by-step explanation:
horizontal= <------------->
^
vertical=| (up and down)
v
Answer:
undefined
Step-by-step explanation:
The length of a rectangle is 4 units more than the width. The area of the rectangle is 32 units ^2 What is the length, in units, of the rectangle?
Answer:
Length = 4 units
Step-by-step explanation:
Width = x units
Length = (x + 4) units
Area = 32 square units
length * width = 32
(x +4) *x = 32
x *x + 4 * x = 32
x² + 4x -32 = 0
Sum = 4
Product = -32
Factor = 8 , (-4)
x² + 4x -32 = 0
x² + 8x - 4x - 4 * 8 = 0
x(x + 8) - 4(x +8) = 0
(x + 8) (x - 4) = 0
(x + 8) is ignored because measurements will not have negative sign.
x-4 =0
x = 4
Width = 4 units
Length = x + 4 = 4 + 4 = 8 units
What is the probability of flipping a coin 75 times and getting tails 30 times or fewer? Round your answer to the nearest tenth.
A. 5.3%
B. 32.3%
C. 75.6
D. 99.7
HELP
Answer:
B
Step-by-step explanation:
Answer:
A. 5.3%
Step-by-step explanation:
36x^4/ 42x^7
Rational expressions
Show work along with it
PLEASE HELP! :)
Answer:
=6/7x^3
Step-by-step explanation:
36x^4/42x^7
(36/42)(x^4/x^7)
6/7(x^-3)
6(x^-3)/7
6/7x^3
Solve the proportion
5 is correct
5/6 = 15/18
(6x10^8) divided by (1.5 x 10^-4)?
Answer:
4 x 10^12
Step-by-step explanation:
I used a calculator.
(6x10^8) divided by (1.5 x 10^-4) is 4 x 10^12.
What is the division?Division is the action of separating something into parts or the process of being separated.
How to solve?
While dividing;
[tex]\frac{6(10^8)}{1.5(10^-4)} \\\frac{6(10^8)(10^4)}{1.5}\\ 4(10^{12})[/tex]
The answer will be 4 x 10^12.
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If f(x) = 6x – 4, what is f(x) when x = 8? 2 16 44 52
Answer:
44
Step-by-step explanation:
f(x) = 6x-4
Let x=8
f(8) = 6*8 -4
= 48 -4
=44
Answer:
44
Step-by-step explanation:
f(x) = 6x – 4
f(8) = 6(8) – 4
= 48 - 4
= 44
what is 1/6(12z-18)=2z-3
Answer:
Always true
All real numbers
Step-by-step explanation:
2z - 3 = 2z -3 Move all terms containing z to the left side of the equation.-3 = -3The given equation 1/6(12z-18)=2z-3 has no solution.
The given equation is 1/6(12z-18)=2z-3.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, 1/6(12z-18)=2z-3
12z/6 -18/6 =2z-3
2z-3=2z-3
Transpose 3 to other side of the equation, we get
2z=2z-3+3
2z = 2z
Transpose 2z to other side of the equation, we get
2z-2z=0
Therefore, the given equation has no solution.
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See below! Thanks Durtle!
Answer:
(6,7)
Step-by-step explanation:
The length of the new vector is [tex]\sqrt{85}[/tex], with side lengths 7 and 6. Therefore, the new coordinates are (6,7). Hope this helps!
9515 1404 393
Answer:
<6, 7>
Step-by-step explanation:
The sum of two vectors is found by summing their corresponding components.
a + b = <4, 1> + <2, 6> = <4+2, 1+6>
a + b = <6, 7>
Scientists researching amphibians put tags on 30 frogs in a wetland area. Later, the scientists captured 520 frogs, of which 12 had tags. To the nearest whole number, what is the best estimate for the frog population?
Final answer:
The best estimate for the frog population, calculated using the mark-recapture method where 30 frogs were initially tagged and later 12 tagged frogs were found in a sample of 520, is approximately 208 frogs.
Explanation:
The question involves estimating the total population of frogs in a wetland area based on a mark-recapture study. The calculation is based on a proportion set up by the initial number of tagged frogs to the total initial tagging, compared with the number of tagged frogs found in a later sample to the size of that sample. This is a classic example of a capture-recapture method used in ecology for estimating population sizes.
The initial number of tagged frogs is 30, and later, from a sample of 520 frogs, 12 are found to be tagged. To estimate the total population (N), we set up the proportion as follows:
30 tagged frogs / N total population = 12 tagged frogs / 520 sample size
Now we cross-multiply and solve for N:
30N = 12 × 520
N = (12 × 520) / 30
N = 6240 / 30
N = 208
Therefore, the best estimate for the total frog population is approximately 208 frogs, rounded to the nearest whole number.
use the given information to find the p-value. also use a0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail tor rejected the null hypothesis)
With H1 : p < 3/5; the test statistic is z = -1.68
A: 0.093 ; fail to reject the null hypothesis
B: 0.0465 ; fail to reject the null hypothesis
C: 0.0465 ; reject the null hypothesis
D: 0.09535 ; fail to reject the null hypothesis
With H1 : p > 0.383, the test statistic is z = 0.41
A: 0.6591 ; fail to reject the null hypothesis
B: 0.3409 ; fail to reject the null hypothesis
C: 0.3490 ; reject the null hypothesis
D: 0.6818 ; reject the null hypothesis
Answer:
(a) C: 0.0465 ; reject the null hypothesis
(b) B: 0.3409 ; fail to reject the null hypothesis
Step-by-step explanation:
Firstly, the decision rule based on P-value to reject the null hypothesis or fail to reject the null hypothesis is given by;
If the P-value of test statistics is less than the level of significance, then we have sufficient evidence to reject our null hypothesis.If the P-value of test statistics is more than the level of significance, then we have insufficient evidence to reject our null hypothesis due to which we fail to reject our null hypothesis.(a) Now, we are given alternate hypothesis, [tex]H_1[/tex] : p < 3/5
Also, z test statistics is -1.68. Since this is a left tailed test, so P-value is given by;
P-value = P(Z < -1.68) = 1 - P(Z [tex]\leq[/tex] 1.68)
= 1 - 0.95352 = 0.0465
Since, the P-value of test statistics is less than the level of significance as 0.0465 < 0.05, so we have sufficient evidence to reject our null hypothesis due to which we reject the null hypothesis.
(b) Now, we are given alternate hypothesis, [tex]H_1[/tex] : p > 0.383
Also, z test statistics is 0.41. Since this is a right tailed test, so P-value is given by;
P-value = P(Z > 0.41) = 1 - P(Z [tex]\leq[/tex] 0.41)
= 1 - 0.6591 = 0.3409
Since, the P-value of test statistics is more than the level of significance as 0.3409 > 0.05, so we have insufficient evidence to reject our null hypothesis due to which we fail to reject the null hypothesis.
To determine the null hypothesis's fate, compare the p-value to α = 0.05. For the first scenario, H1: p < 3/5 with the test statistic z = -1.68, the conclusion is unclear without the exact p-value. For the second scenario, H1: p > 0.383 with z = 0.41, we fail to reject the null hypothesis as the p-value (0.3409) is higher than α.
Explanation:The task is to compare the p-value to the significance level (alpha, α) to determine if the null hypothesis should be rejected or not. If the p-value is less than or equal to α, reject the null hypothesis; otherwise, fail to reject it. The significance level given is α0.05.
First Scenario:
For H1: p < 3/5, the test statistic z = -1.68. Comparing the test statistic to the critical value for α=0.05 (which is between -1.65 and -1.64), -1.68 falls to the left of -1.65. However, without the exact p-value provided, the answer cannot be definitively chosen from the options. Still, the general rule is that if the test statistic is more extreme than the critical value, the null hypothesis is rejected.
Second Scenario:
For H1: p > 0.383, the test statistic z = 0.41. The p-value corresponding to z = 0.41 on the upper tail of a standard normal distribution is approximately 0.3409 (since the p-value is the area to the right of z). Therefore, the p-value is greater than α0.05, meaning that we fail to reject the null hypothesis.