Answer:
(3x^2 - 1)(3x^2 + 1)(9x^4 + 1).
Step-by-step explanation:
Using the identity for the difference of 2 squares;
a^2 - b^2 = (a - b)(a + b)
we put a^2 = 81x^8 and b^2 = 1 giving
a = 9x^4 and b = 1, so:
81x^8 − 1 = (9x^4 - 1)(9x^4 + 1)
Applying the difference of 2 squares to 9x^4 - 1:
= (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).
Answer:
The answer is (3x^2 - 1)(3x^2 + 1)(9x^4 + 1).
Step-by-step explanation:
What is the value of x in this proportion?
27=−5x+3
x=−20 1/2
x=−19
x=−16
x=−14 1/2
Answer:
x = -24/5
none of the options listed
Step-by-step explanation:
27=−5x+3
the choices all have x listed as a positive number, so we need to fix the question by moving 5x to the other side of the = and changing its sign.
27 +5x= 3
then move the 27
5x= 3 -27
then subtract
5x = -24
then divide both sides by 5
x = -24/5
Factor completely 3x(x 2) 4(x 2). (x 2)(3x 4) (x 2)(12x) (x 2)(7x) Prime.
The complete factor of the expression [tex]\rm 3x (x +2) + 4 (x +2)[/tex] is [tex]\rm(x+2)(3x + 4)[/tex]. Then the correct option is A.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The expression is [tex]\rm 3x (x +2) + 4 (x +2)[/tex].
To solve the expression properly we have to take common (x+2). Then we have
[tex]\rm 3x (x +2) + 4 (x +2)\\\\(x+2)(3x + 4)[/tex]
The correct factor is (x + 2)(3x + 4).
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Answer:
Yup A
Step-by-step explanation:
Find the circumference and area of the circle. Use 3.14 for . Round to the nearest hundredth if necessary.
3 m
The diameter of the pizza is 10 inches what is the conference of the pizza use 3.14 for pie
Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. Choose the correct option based on the problem information.
A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160. Use the P-value method of testing hypotheses. Choose the correct P-value and conclusion based on the null hypothesis.
A. P-value < 0.005. Fail to reject H0.
B. 0.01 < P-value < 0.025. Reject H0.
C. P-value < 0.005. Reject H0.
D. P-value = 0.05. Reject H0.
Answer:
C
explanation:
if The P-Value is low reject H0
The correct P-value and conclusion based on the null hypothesis. The correct option is C. P-value < 0.005. Reject H₀.
In this problem, we will use the P-value method to test a claim about the mean score of job applicants in a programming test. The claim is whether the sample of 25 job applicants from a large university comes from a population with a mean score greater than 160, given that the population is normally distributed. We'll use a significance level of 0.05 to make our decision. We'll set up the null and alternative hypotheses, calculate the test statistic, and find the P-value to draw a conclusion about the claim.
Let's begin by defining the null and alternative hypotheses:
- Null Hypothesis (H₀): The mean score of job applicants from the university is not greater than 160. H₀: μ ≤ 160.
- Alternative Hypothesis (H₁): The mean score of job applicants from the university is greater than 160. H₁: μ > 160.
Here, μ represents the true population mean score.
Next, we'll calculate the test statistic. Since the population standard deviation (σ) is not known, we'll use the sample's standard deviation (s) and perform a one-sample t-test. The formula for the t-test is:
t = (x' - μ₀) / (s/√n)
Where:
x' is the sample mean,
μ₀ is the hypothesized population mean under the null hypothesis (μ₀ = 160 in this case),
s is the sample standard deviation, and
n is the sample size.
Substituting the given values:
x' = 183 (sample mean)
μ₀ = 160 (hypothesized population mean under H0)
s = 12 (sample standard deviation)
n = 25 (sample size)
t = (183 - 160) / (12/√25)
= 23 / 2.4
≈ 9.583
Now, we need to find the P-value corresponding to this test statistic. Since this is a one-tailed test (claiming that the mean is greater than 160), we look for the area under the t-distribution curve to the right of t = 9.583.
By consulting a t-table or using statistical software, we find that the P-value is significantly less than 0.001. The exact P-value is not provided in the answer options, but it's crucial to note that it is well below 0.005.
Now, we compare the P-value to the significance level (α = 0.05). Since the P-value < α, we reject the null hypothesis (H₀). The data provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.
The correct option is C. P-value < 0.005. Reject H₀. The statistical analysis indicates that there is strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.
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7. Matthew drove 350 miles on 10 gallons of gasoline. How many miles per gallon does
his car get?
Answer:
35
Step-by-step explanation:
350miles/10=10gallons/10
=35miles=1gallon
The local y charges a yearly of $35 plus for each time you use the pool if you can spend no more than $170 each year for the y how many times can you use the pool
Answer:
Answer is 4
Step-by-step explanation:
35 times table
35 x 5= 175 too large
35X4= 140
Classify the angles in the figure by choosing the correct term from the choices below.
supplementary
complementary
vertical
none of these
Answer: none of these
Step-by-step explanation:
They are not supplementary because 101+77 = 178 and not 180.
They are not complementary because 101+77 = 178 and not 90.
They are not vertical because there are no intersecting lines and the two angle measures are not equal.
Therefore, none of these are true.
identify the triangle please hurry
First off, no sides have the same length as the others, so it cannot be an equilateral or an isoceles triangle, as it would required at least 2 sides to have the same length.
So, we're left with scalene triangle options.
There is an angle that is an obtuse angle (as it is more than 90 degrees and less than 180 degrees), so this is a scalene obtuse triangle.
Write an equation of the line described: the x-axis
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Assume:
+There are 365 days a year
+No spoilage issues
+Pi= 3.14
Answer: Assume π = 3.14(rounded upto two decimal point)
Case I. 1 year = 365 days
2 years = 730 days
3 years = 1095 days
And .14 years = 51 days 2 hours 24 minutes
So, 3.14 years = 1146 days 2 hours 24 minuts.
Now, suppose you born in a leap-year.
Case II. 1 year = 366 days
2 years = 732 days
3 years = 1098 days
and .14 years = 51 days 5 hours 45 minutes 36 seconds
Then, 3.14 years = 1149 days 5 hours 45 minuts 36 seconds
So, yes, it is possible to be exactly π years old. At exactly 1146 days 2 hours 24 minutes or 1149 days 5 hours 45 minutes 36 seconds (in case of a leap-year born), we could have celebrate at our π years birthday.
Step-by-step explanation:
need help please. math question.
Answer:
I think it's C
Step-by-step explanation:
360°-232° = 128°
Once a week Mrs. Baker makes sugar cookies.
The first week she makes the recipe, she uses
the 2 full cups of sugar called for. Each week
after that, she reduces the amount of sugar
by one third. How much sugar does she use
for cookies over 8 weeks? (Hint: The common
ratio is not 1/3.)
By getting the exponential decay that models the situation, we will see that after 8 weeks she uses 0.12 cups.
How much sugar does she use each week?
We know that the first week, she uses 2 cups of sugar, and each week she uses removes one-third of what she used the previous week.
Then the second week she uses:
S₂ = 2 cups - (1/3)*(2 cups) = 2 cups*(1 - 1/3) = 2 cups*(2/3)
The third week she uses:
S₃ = 2 cups*(2/3) - (1/3)*2 cups*(2/3) = 2 cups*(2/3)^2
You already can see the pattern, at week x, she will use:
Sₓ = (2 cups)*(2/3)^(x - 1)
This is an exponential decay.
To get how much sugar does she uses after 8 weeks, we just replace x by 8 in the above equation:
S₈ = (2 units)*(2/3)^(8 - 1) = 0.12 cups of sugar.
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Solve , 6x + 5 = 2y
(Hint : Use ax + by + c = 0 )
Answer:
soln;
given equation is 6x + 5 = 2y
or, 6x -2y + 5 = 0
comparing with ax + by + c = 0
a = 6, b = -2, c = 5
Pablo is mailing packages. Each small package costs him $2.20 to send. Each large package costs him $3.70. How much will it cost him to send 1small package and 5 large packages?
Answer:
$20.70
Step-by-step explanation:
5 × $3.70 = $18.50 + $2.20 =
$20.70
Every year, Alice's family runs the sand castle contest during the Fun in the Sun beach festival. Alice's job is to deliver empty buckets to the teams. This year, Alice hands out the same number of buckets to each of the 15 teams in the contest. Each team gets 8 buckets.
Use an equation to find the total number of buckets Alice delivers.
Answer:
120 buckets
Step-by-step explanation:
If there are 15 teams and each team gets the same number of buckets (8 buckets as mentioned in the problem), then you can multiply 15 by 8 to get 120.
15 teams * 8 buckets = 120 total buckets
Which number is not a rational number?
-4 4/11
The term solution is related to the word solve what do you think a solution might be
Answer:
something attained by mental effort and especially by computation
is called a solution, When you solve you get the solution meaning you have to tryed and never given up , to gain the solution.
6 gardeners can plant 18 trees in 30 minutes. How many gardeners would it take to plant 45 trees in 45 minutes
It would take 10 gardeners to plant 45 trees in 45 minutes.
Rule of ThreeIt's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.
The question gives:
6 gardeners can plant 18 trees in 30 minutes.
? gardeners can plant 45 trees in 45 minutes.
6 gardeners can plant [tex]\frac{18\; tree}{30\; min}=\frac{3}{5}[/tex] trees/min. You can calculate the second rate from [tex]\frac{45\; tree}{45\; min}=\frac{1}{1}=1[/tex] tree/min.
Write the previous text information in form of proportion.
6 gardeners ----------- 3/5 trees/min
x gardeners ----------- 1 tree/min
Then, applying cross multiplication:
[tex]\frac{3x}{5}=6\\ \\ 3x=30\\ \\ x=10[/tex]
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Why can you not do negative numbers to the power of 1. 5?.
Answer:
Lets say we have (-1)^(1.5)
Step-by-step explanation:
(-1)^(1.5) = (-1)^(3/2)
= (√(-1))^3 which has no solution in the real number field, as √(-1) does not exist.
In the complex number field √(-1) = i, and (-1)^(1.5) = i^3 = -i.
Manuel is driving 60 miles per hour on a state road with a 65 mph speed limit. He sees a fallen tree up ahead and must come to a quick, complete stop.
a. What is his approximate reaction distance?
b. What is his approximate braking distance?
c. About how many feet does the car travel from the time he switches pedals until the car has completely stopped?
a) The approximate reaction distance is 66 feet.
b) The approximate braking distance is 802.304 feet.
c) The total distance is 868.304 feet.
How to analyzing reaction time in a braking event
The average reaction time ([tex]t_{R}[/tex]) is 0.75 seconds. Manuel drives at constant velocity in the first 0.75 seconds, then he decelerates the vehicle.
a) The reaction distance ([tex]x_{R}[/tex]), in meters, is found by the following expression:
[tex]x_{R} = v_{o}\cdot t_{R}[/tex] (1)
Where [tex]v_{o}[/tex] is the initial velocity, in feet per hour.
If we know that [tex]v_{o} = 60\,\frac{mi}{h}[/tex] ([tex]v_{o} = 88\,\frac{ft}{s}[/tex]) and [tex]t_{R} = 0.75\,s[/tex], then the approximate reaction distance is:
[tex]x_{R} = (88)\cdot (0.75)[/tex]
[tex]x_{R} = 66\,ft[/tex]
The approximate reaction distance is 66 feet. [tex]\blacksquare[/tex]
b) A normal braking has magnitudes of about 0.15 times the value of gravitational acceleration ([tex]g = 32.174\,\frac{ft}{s^{2}}[/tex]). The approximate braking distance ([tex]d[/tex]), in feet, is found by the following kinematic formula:
[tex]d = \frac{v^{2}-v_{o}^{2}}{2\cdot a}[/tex] (2)
Where:
[tex]a[/tex] - Deceleration rate, in feet per square second.[tex]v[/tex] - Final velocity, in feet per second.If we know that [tex]v_{o} = 88\,\frac{ft}{s}[/tex] and [tex]v_{o} = 0\,\frac{ft}{s}[/tex], then the approximate braking distance is:
[tex]d = \frac{\left(0\,\frac{ft}{s}\right)^{2}-\left(88\,\frac{ft}{s} \right)^{2}}{2\cdot \left(0.15\right)\cdot \left(-32.174\,\frac{ft}{s^{2}} \right)}[/tex]
[tex]d = 802.304\,ft[/tex]
The approximate braking distance is 802.304 feet. [tex]\blacksquare[/tex]
c) The total distance is the sum of distances found in a) and b). Then, the total distance is 868.304 feet. [tex]\blacksquare[/tex]
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What is the positive solution to the equation 5x2+2=47
Answer:
X=3, or X=-3 But the positive answer is X=3
Step-by-step explanation:
Rewrite the equation 5x^2+2=47
Subtract 2 from each side -----> 5x^2+2-2=47-2
Simplify ---------> 5x^2=45
divide each side by 5 -----> 5x^2/5=45/5
Simplify x^2=9
Divide each side by using square root method --> Sqrt(9) - sqrt(9)
Now simplify to get X=3, or X=-3
The cash price of a laptop is $4799. It cab be boughton hire purchase by making a deposit of $540 and 12 monthly installment of $374. 98 each calculate the total hire purchase price of the laptop
Answer:
#29983873 is the best answer
Simply the expression by combining like terms.
9x+8+3x+4=
1 quart = ? pints=?cups
[tex]\Huge\green{\tt{✏Answer✏}}[/tex]
1 us liquid quart =
2 us liquid pints[tex]\Huge\blue{\tt{✏Explanation✏}}[/tex]
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Consider the equation and the graph
Answer:
-33/16
I'm pretty sure it is c sorry if not may be -39/16
Need help please answer
in Indiana the sales tax rate is 7% of the total cost. what is the amount of sales tax on a purchase of 47$
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 47}}{\left( \cfrac{7}{100} \right)47}\implies 3.29[/tex]
Find the discriminant of 5x2 – 3x + 2 = 0 =
Answer: -31
Step-by-step explanation:
5x³- 3x + 2 = 0
a = 5, b = -3, c = 2
(-3)² -4 × 5 × 2
-31
11 = - 5x - 2 help
11= -5x-2
[tex]11 = -5x-2\\5x = -2-11\\5x =-13\\x = -13/5[/tex]
Answer: x = -13/5
Ok done. Thank to me :>
