Answer
the answer for this question is 31/99
x = 0.3131313...
100x = 31.31313...
99x = 31
x = 31/99
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
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
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:
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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The polynomial p(x)=x^3-7x-6 has a non-factor of (x+1) rewrite p(x) as a product of linear factors.
Answer:
Using synthetic division suffices to answer your question:
Step-by-step explanation:
Synthetic division is the process by one reduces a large polynomial in your case [tex]x^3-7x-6[/tex] by a binomial in your case [tex](x+1)[/tex].
To do so one does the following:
[tex]\begin{array}{cccccc}-1|& 1&0&-7&-6\\ & &-1&1&6 \\& 1&-1&-6&0 \end{array}[/tex]
Since we divided by a linear binomial it reduces the power by one which produces the following quadratic:
[tex](x^2-x-6)[/tex]
Which can be factored in the following, and I will provide the complete factorization as well:
[tex]p(x)=(x+1)(x-3)(x+2)[/tex]
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 :)
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.
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.
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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Audrey grabs a meal with her two co-workers. If everyone paid an equal amount of $8.50 then how much would the total be
Answer:
$25.50
Step-by-step explanation:
There three people- Audrey and two co-workers
Each pay $8.50
Then the total is:
$8.50*3 = $25.50Scientists 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.
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.
Simplify the following algebraic expression:
10xy - 5ab - 15yx + 9ba
Answer:
- 5xy + 4ab
Step-by-step explanation:
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.
(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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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.
Identify the numbers sets to which the number 0 belongs
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)
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>
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
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.
Mr. John borrows $10,000 to remodel his kitchen; he borrows the money for 5 years, and has to pay a simple interest rate of 4.5% per year.
A) Since there are 12 months in the year, how many total months does Mr. John have to pay back this loan?
B) What will be the amount of Mr. john's monthly payment to the bank?
Answer:
A) 60
B)450
Step-by-step explanation:
A) you multiply 5x12
B)10,000(the whole) divided by 100(the 4.5% comes from 100%)is 100.Now instead of trying to divide the missing number,(you cant cause its not there) you instead multiply.You multiply 4.5% by the hundred that you got earlier.
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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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!
Solve the proportion
5 is correct
5/6 = 15/18
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.
URGENT!!!
Graph: -4x+2y=8
Answer:
Step-by-step explanation:
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
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
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