Answer:
1.575
Step-by-step explanation:
Determine whether the given ordered pair is a solution of the system.
(1, -8)
y = 5x - 13
2x + 4y = - 30
Maths questions
X+1/x-6 times 7x/x+2
Answer:
7x^2+7x/x^2-4x-12
Step-by-step explanation:
Given the expression
X+1/x-6 times 7x/x+2
Rewrite
X+1/x-6 * 7x/x+2
= 7x(x+1)/(x-6)(x+2)
= 7x^2+7x/x^2+2x-6x-12
= 7x^2+7x/x^2-4x-12
Hence the product of both function is expressed as 7x^2+7x/x^2-4x-12
Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level. The null and alternative hypothesis would be: H 0 : μ = 2 H 0 : μ = 2 H 1 : μ > 2 H 1 : μ > 2 H 0 : p = 0.5 H 0 : p = 0.5 H 1 : p ≠ 0.5 H 1 : p ≠ 0.5 H 0 : p = 0.5 H 0 : p = 0.5 H 1 : p > 0.5 H 1 : p > 0.5 H 0 : μ = 2 H 0 : μ = 2 H 1 : μ < 2 H 1 : μ < 2 H 0 : p = 0.5 H 0 : p = 0.5 H 1 : p < 0.5 H 1 : p < 0.5 H 0 : μ = 2 H 0 : μ = 2 H 1 : μ ≠ 2 H 1 : μ ≠ 2 Based on a sample of 60 people, the sample mean GPA was 2.02 with a standard deviation of 0.06 The test statistic is (to 3 decimals) The critical value is (to 3 decimals) Based on this we fail to reject the null hypothesis reject the null hypothesis
Answer:
[tex]H_0: \, \mu = 2[/tex].
[tex]H_1:\, \mu > 2[/tex].
Test statistics: [tex]z \approx 2.582[/tex].
Critical value: [tex]z_{1 - 0.025} \approx 1.960[/tex].
Conclusion: reject the null hypothesis.
Step-by-step explanation:
The claim is that the mean [tex]\mu[/tex] is greater than [tex]2[/tex]. This claim should be reflected in the alternative hypothesis:
[tex]H_1:\, \mu > 2[/tex].
The corresponding null hypothesis would be:
[tex]H_0:\, \mu = 2[/tex].
In this setup, the null hypothesis [tex]H_0:\, \mu = 2[/tex] suggests that [tex]\mu_0 = 2[/tex] should be the true population mean of GPA.
However, the alternative hypothesis [tex]H_1:\, \mu > 2[/tex] does not agree; this hypothesis suggests that the real population mean should be greater than [tex]\mu_0= 2[/tex].
One way to test this pair of hypotheses is to sample the population. Assume that the population mean is indeed [tex]\mu_0 = 2[/tex] (i.e., the null hypothesis is true.) How likely would the sample (sample mean [tex]\overline{X} = 2.02[/tex] with sample standard deviation [tex]s = 0.06[/tex]) be observed in this hypothetical population?
Let [tex]\sigma[/tex] denote the population standard deviation.
Given the large sample size [tex]n = 60[/tex], the population standard deviation should be approximately equal to that of the sample:
[tex]\sigma \approx s = 0.06[/tex].
Also because of the large sample size, the central limit theorem implies that [tex]Z= \displaystyle \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}[/tex] should be close to a standard normal random variable. Use a [tex]Z[/tex]-test.
Given the observation of [tex]\overline{X} = 2.02[/tex] with sample standard deviation [tex]s = 0.06[/tex]:
[tex]\begin{aligned}z_\text{observed}&= \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}} \\ &\approx \frac{\overline{X} - \mu_0}{s / \sqrt{n}} = \frac{2.02 - 2}{0.06 / \sqrt{60}} \approx 2.582\end{aligned}[/tex].
Because the alternative hypothesis suggests that the population mean is greater than [tex]\mu_0 = 2[/tex], the null hypothesis should be rejected only if the sample mean is too big- not too small. Apply a one-sided right-tailed [tex]z[/tex]-test. The question requested a significant level of [tex]0.025[/tex]. Therefore, the critical value [tex]z_{1 - 0.025}[/tex] should ensure that [tex]P( Z > z_{1 - 0.025}) = 0.025[/tex].
Look up an inverse [tex]Z[/tex] table. The [tex]z_{1 - 0.025}[/tex] that meets this requirement is [tex]z_{1 - 0.025} \approx 1.960[/tex].
The [tex]z[/tex]-value observed from the sample is [tex]z_\text{observed}\approx 2.582[/tex], which is greater than the critical value. In other words, the deviation of the sample from the mean in the null hypothesis is sufficient large, such that the null hypothesis needs to be rejected at this [tex]0.025[/tex] confidence level in favor of the alternative hypothesis.
25 percent of ____ is 6
Answer:
24
Step-by-step explanation:
1/4 of x is 6 so you multiply 6 by 4
If 7x + 5y = 25 and 3x + 2y = 10, what is the value of x +y?
Answer:
Step-by-step explanation:
7x+5y=25
3x+2y=10
21x+15y=75
21x+6y=30
0x+11y=45
11y=45
y=45/11
y = 4.09
sub in 4.09 into equation 1
7x+5(4.09)=25
7x+20.45=25
7x=25-20.45
x=4.55/7
How many grams are in 1 Bag of suger
Answer:
One pound of granulated sugar converted to gram equals to 453.59 g. How many grams of granulated sugar are in 1 pound? The answer is: The change of 1 lb ( pound ) unit in a granulated sugar measure equals = into 453.59 g ( gram ) as per the equivalent measure and for the same granulated sugar type.
A car is sold for $18,000. After one year, the value of the car is $9,900. Write an exponential function y to determine the value of
the car after x years if the rate of decrease is the same each year.
y =
Estimate the value of the car after 6 years. Round the answer to the nearest dollar.
Answer:
temperature and kinctic energy are related
Fred can paint a 30-foot fence in 5 hours. Which of the following is true?
Answer:
lol
Step-by-step explanation:
A normal distribution has a mean of 10 and a standard deviation of 1. What is the probability of selecting a number that is at most 10
Answer:
15.87% probability of selecting a number that is at most 9
Step-by-step explanation:
Find the slope of the line given the pair of points.
(-9,5), (10, 4)
Answer:
-1/19
Step-by-step explanation:
What is 6 2/3 x 1 1/2
Answer:
6 2/3 x 1 1/2 is 10
Step-by-step explanation:
what is 5/ 16 expressed as a percentage
Answer:
31.25%Step-by-step explanation:
To express a number as a percent we will first divide the top number by the bottom number.
5/16 = 0.3125
A percent is expressed by moving the decimal two places to the left.
31.25%A case of bottled juice contains 30 bottles.Each case contained a total of 507 ounces of juice.Which equation represents the relationship between ounced of juice,y and number of bottles,x A.y=16.9x+30B.y=0.6x C.y=30x+16.9D.y=16.9x
Step-by-step explanation:
the answer is D (y=16.9)
I divided 507 and 30 and got the answer 16.9.
if you would've put any other answer it would've been wrong because the answer had the 30 in it after it was divided.(not sure if its 100% correct)
does it look like I play any sports?? if so what sports
Answer:
ayyyye i play soccer too lol
Step-by-step explanation:
Answer:
looks like you play softball or basketball
Step-by-step explanation:
2,5,9,12,7,10,6,3,6
a) find the mean of the above data
Answer:
Step-by-step explanation:
2,5,9,12,7,10,6,3,6
mean=(2+5+9+12+7+10+6+3+6)/9
=60/9
=6.67(approx)
You deposit $2000 in an account earning 3% interest compounded monthly.How much will you have in the account in 15 years?
f(x)=-2x^2+14/x^2-49 which statement describes the behavior of the graph of the function shown at the vertical asymptotes?
Answer:
Option 3 :
x → 7+, y → –[infinity]
Step-by-step explanation:
f(x) = (-2x² + 14)/(x² - 49)
x² - 49 = (x + 7)(x - 7)
Hence f(x) goes to infinity at x = - 7 or 7
x < - 7 = (-ve)(-ve) = + ve
=> x → –7–
Here, x² - 49 is + ve
-7 < x < 7 = (+ve)(-ve) = - ve
=> x → –7+ or x → 7– .
here, x² - 49 is - ve
x > 7 = (+ve)(+ve) = + ve
=> x → 7+
Here, x² - 49 is + ve
So (-2x² + 14) is - ve for all [ x → –7– , x → –7+ , x → 7– , x → 7+ ]
As,
-2(-7)² + 14 = -84 and -2(+7)² + 14 = -84
x → –7– = (-ve)/(+ve)
=> y → -[infinity].
x → –7+ or x → 7– = (-ve)/(-ve)
=> y → [infinity]
x → 7+ = (-ve)/(+ve)
=> y → -[infinity].
x → 7+, y → –[infinity]. is the correct option
The statement (C) as x approaches 7 from the left, y approaches -∞ describe the behavior of the graph of the function.
What is a function?It is defined as a spceial type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a rational function:
[tex]\rm f(x) =\dfrac{-2x^2+14}{x^2-49}[/tex]
x² - 49 cannot be zero:
x² - 49 ≠ 0
x ≠ 7, x ≠ -7
From the graph, as x approaches 7 from the left, y approaches -∞
Thus, the statement (C) as x approaches 7 from the left, y approaches -∞ describe the behavior of the graph of the function.
Learn more about the function here:
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What is the solution to the equation 23(y−6)=−(y+2)+1 2 3 ( y - 6 ) = - ( y + 2 ) + 1 ?
Answer:
Substitute the given value into the function and evaluate.
23 (y − 6) = −(y + 2) + 1 = y = 137/24
2 = y = 137/24
3 = y = 137/24
y − 6 = −(y + 2) + 1 = y = 5/2
Which steps show how to use the distributive property to evaluate 5. 58?
A. 5(58) = 5(50 + 8) = 5.50 – 5.8 = 250 – 40 = 210
B. 5(58) = 5(50 + 8) = 5.50 +8 = 250 + 8 = 258
C. 5(58) = 5(50 + 8) = 5.50 + 50 8 = 250 + 400 = 650
D. 5(58) = 5(50 + 8) = 5.50 +5.8 = 250 + 40 = 290
Answer:
D.
Step-by-step explanation:
You are splitting the equation up. (I don't really know how to explain it sorry)
The correct steps to evaluate 5 · 58 using the distributive property following are: 5(58) = 5(50 + 8) = 5 · 50 +5 · 8 = 250 + 40 = 290.
What is the distributive property of multiplication?The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.
The correct steps to evaluate 5 · 58 using the distributive property are:
Start with the expression 5 · 58.
Use the distributive property to rewrite the expression as 5(50 + 8).
Use the distributive property again to rewrite the expression as 5 · 50 + 5 · 8.
Calculate the value of each term in the resulting expression:
5 · 50 = 250 and 5 · 8 = 40.
Add the values of the two terms to get the final result:
250 + 40 = 290.
Therefore, the correct answer is D. 5(58) = 5(50 + 8) = 5 · 50 + 5 · 8 = 250 + 40 = 290.
To learn about the distributive property of multiplication here:
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How many milliliters of full-strength Sustacal are needed to prepare 240ml of half-strength sustacal?
The question is incomplete, the complete question is;
How many milliliters of full-strength Sustacal are needed to prepare 240 mL of half-strength Sustacal?
1. 120 mL
2. 240 mL
3. 360 mL
4. 480 mL
Answer:
120 mL
Step-by-step explanation:
From the question, we can see that the full strength solution is supposed to contain 240 ml of Sustacal .
If that is so, we can get a half strength solution by using only 120 ml of full strength solution and making up the remaining volume with water. This solution now has half the strength of a 240 ml full strength solution.
Consider the function f(x)=xln(x). Let Tn be the nth degree Taylor approximation of f(2) about x=1. Find: T1, T2, T3. find |R3| <= ?
Answer:
R3 <= 0.083
Step-by-step explanation:
f(x)=xlnx,
The derivatives are as follows:
f'(x)=1+lnx,
f"(x)=1/x,
f"'(x)=-1/x²
f^(4)(x)=2/x³
Simialrly;
f(1) = 0,
f'(1) = 1,
f"(1) = 1,
f"'(1) = -1,
f^(4)(1) = 2
As such;
T1 = f(1) + f'(1)(x-1)
T1 = 0+1(x-1)
T1 = x - 1
T2 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2
T2 = 0+1(x-1)+1(x-1)^2
T2 = x-1+(x²-2x+1)/2
T2 = x²/2 - 1/2
T3 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2+f"'(1)/6(x-1)^3
T3 = 0+1(x-1)+1/2(x-1)^2-1/6(x-1)^3
T3 = 1/6 (-x^3 + 6 x^2 - 3 x - 2)
Thus, T1(2) = 2 - 1
T1(2) = 1
T2 (2) = 2²/2 - 1/2
T2 (2) = 3/2
T2 (2) = 1.5
T3(2) = 1/6 (-2^3 + 6 *2^2 - 3 *2 - 2)
T3(2) = 4/3
T3(2) = 1.333
Since;
f(2) = 2 × ln(2)
f(2) = 2×0.693147 =
f(2) = 1.386294
Since;
f(2) >T3; it is significant to posit that T3 is an underestimate of f(2).
Then; we have, R3 <= | f^(4)(c)/(4!)(x-1)^4 |,
Since;
f^(4)(x)=2/x^3, we have, |f^(4)(c)| <= 2
Finally;
R3 <= |2/(4!)(2-1)^4|
R3 <= | 2 / 24× 1 |
R3 <= 1/12
R3 <= 0.083
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 19 feet more than the length of the shortest side. Find
the dimensions if the perimeter is 163 feet.
What is the length of the shortest side?
The length of the shortest side is
This is simple as the perimeter is given. All you have to do is make an expression and then equate it to the perimeter.
Side lengths:
Shortest Side: [tex]x[/tex]
1st side: [tex]2x[/tex] (Given that it's twice the length of the shortest of twice of [tex]x[/tex])
3rd side: [tex]x + 19[/tex] (Given that it's 19 more than the length of the shortest side or [tex]x[/tex])
Since the perimeter is just the addition of all the sides of the shape, the perimeter is going to be the addition of all the expression we made.
So the final expression is going to be: [tex]x + 2x + x + 19[/tex]
This is nothing but the perimeter so we can therefore equate it to [tex]163[/tex]
[tex]x + 2x + x + 19 = 163[/tex]
Now we solve the equation. Here it goes!:
[tex]4x + 19 = 163\\4x = 163 - 19\\4x = 144\\x = 144/4 = 36[/tex]
Therefore, [tex]x = 36[/tex]
So now we plug them into the previous expressions we made for the sides and you get:
Shortest side: [tex]36[/tex]
1st side: [tex]72[/tex]
3rd side: [tex]55[/tex]
And also, the length of the shortest side is [tex]36[/tex] as mentioned previously :D
Which ordered pairs are solutions to the equation 5x+12y=15?
10 POINTS.. ILL GIVE BRAINLIEST
Solve for x:
a) x = 18
b) x = 19
c) X = 20
d) x = 21
Answer:
D. x = 21
Step-by-step explanation:
So a straight line is equal to 180º and that's what we're trying to figure out here. Set both equations to equal 180, it should look like:
5x + 4x - 9 = 180
Now we just solve!
5x + 4x - 9 = 180
5x + 4x = 9x
9x - 9 = 180
+9 +9
------------------
9x = 189
Divide both sides by 9 to get x by itself.
189/9 = 21
x = 21
Alex is selling tickets to a school play. An adult ticket costs $6.50 and a student ticket costs $4.00. Alex sells x adult tickets and 12 student tickets. He made $243 selling tickets. How many adult tickets did he sell?
Answer:
30
Step-by-step explanation:
12x4=48
243-48=195
195/6.50= 30
hope that helps :)
In science class, Polly learned that trees help make the oxygen that people breathe. One tree makes about 250 pounds of oxygen each year. Polly wonders how much oxygen the trees on her street make. When she gets home, she counts 32 trees on her street. How many tons of oxygen do they make in a year?
Answer:
They make 4 approximately tons of oxygen each year.
Step-by-step explanation:
( 250lbs × 32 ) ÷ 2000 = 4t
250 pounds because each tree makes about 250 pounds of oxygen a year.
× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.
÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.
John spent $75 on a shopping trip for new clothes last week. He had expected to spend $100 on clothes. Complete the table.
A 6-column table with 1 row. Column 1 is labeled Approximate Value with entry 100 dollars. Column 2 is labeled Exact Value with entry 75 dollars. Column 3 is labeled Error with entry 25 dollars. Column 4 is labeled Absolute Error with entry 25 dollars. Column 5 is labeled Ratio with entry e. Column 6 is labeled Percent Error with entry f.
What is the ratio? e =
What is the percent error? f =
Answer:
I think it would be Column 2
Step-by-step explanation:
Answer:
What is the ratio? e = 25/75
What is the percent error? f = 33%
Step-by-step explanation:
Use the graph of y = sin x to find all values of x, 0 < x < 2pi, for which the following is true. (Enter your answers as a comma-separated list.)
sin x = 0
Answer:
if x = pi/2, then y =1.
if x = pi/4, then y = [tex]\frac{\sqrt{2 } }{2}[/tex]
if x = pi, then y = 0
Step-by-step explanation:
The required answer as a comma-separated lists are (0, 0), ([tex]\frac{\pi}{6}[/tex], 0.5), ( [tex]\frac{\pi}{4}[/tex], [tex]\frac{1}{\sqrt{2} }[/tex]), ( [tex]\pi[/tex], 0)
Given the equation of a sine graph expressed as:
[tex]y=sinx[/tex] for all values of x within the range 0 < x < 2π
We need to get the value of y for the values of x within the range as shown:
If x = 0;
y = sin0
y = 0
The required solution is (0, 0)
If x = 30;
y = sin30
y = 0.5
The required solution is ([tex]\frac{\pi}{6}[/tex], 0.5)
If x = [tex]\frac{\pi}{4}[/tex];
y = sin [tex]\frac{\pi}{4}[/tex]
y = [tex]\frac{1}{\sqrt{2} }[/tex]
The required solution is ( [tex]\frac{\pi}{4}[/tex], [tex]\frac{1}{\sqrt{2} }[/tex])
If x = [tex]\pi[/tex]
y = sin [tex]\pi[/tex]
y = 0
The required solution is at ( [tex]\pi[/tex], 0)
If x = [tex]2\pi[/tex]
y = sin[tex]2\pi[/tex]
y = 0
Hence the required answer as a comma-separated lists are (0, 0), ([tex]\frac{\pi}{6}[/tex], 0.5), ( [tex]\frac{\pi}{4}[/tex], [tex]\frac{1}{\sqrt{2} }[/tex]), ( [tex]\pi[/tex], 0)
Learn more here: https://brainly.com/question/2919352
PLEASE HELP ILL GIVE AS MANY POINTS AS YOU WANT!!!
And to some reason this was deleted???! Cause I didn’t mean to if I did
Answer:
1. Take the value of X and replace X with that value in the equation.
2. Now you solve Y.
I need help pleaseeeee
