Answer:
centre = (13,0)
radius = 8
Step-by-step explanation:
The standard equation of the circle is
(x-x0)^2 + (y-y0)^2 = r^2 ...............(1)
where
(x0,y0) is the centre,
r is the radius.
For
(x-13)^2 + y^2 = 64 ..............(2)
we rewrite (2)
(x-13)^2 + (y-0)^2 = 8^2 ...............(3)
and compare (3) with (1)
to identify
x0 = 13, y0 = 0, and r = 8
Therefore
centre = (13,0)
radius = 8
Write the equation in slope intercept form for the line that passes through the point (0,-3) with slope -1/2.
Answer:
y = -1/2x - 3
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Determine known variables
Slope = -1/2 (m = -1/2)
y-intercept - (0, -3), so b = -3
Step 2: Write in known variables
y = -1/2x - 3
Answer:
y = -1/2 - 3
Step-by-step explanation:
Well slope intercept is y = ax + b
ax is the slope which is given,
b is the y intercept which is -3 because the point (0,-3)
doesn’t have a x coordinate meaning if the line goes through that point it touches the y intercept at -3.
Thus,
the equation in slope-intercept is y = -1/2 - 3.
Hope this helps :)
Em uma prova de conhecimentos gerais, Fernando errou 3/8 do total de 72 questões. Quantas são as questões que Fernando ACERTOU?
Vamos lá.....
Duas maneiras praticas:
1 - Multiplicar a fraçao pelo total, vai informar quanto a fracao representa (o que é questionado na questao)
2 - Regra de 3.
1:
72 × (3/8)
216/8
27
Ele acertou 27 questoes
(pergunta mais que interessante: qntas questoes havia na prova??? 72)
Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Second-degree, with zeros of −7 and 6, and goes to −∞ as x→−∞.
Answer:
Step-by-step explanation:
Hello, because of the end behaviour it means that the leading coefficient is negative so we can construct such polynomial function as below.
[tex]\large \boxed{\sf \bf \ \ -(x+7)(x-6) \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The polynomial function will be f ( x ) = - x² - x + 42
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax²+ bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Given data ,
The polynomial function is of second degree with zeros of -7 and 6
So , x = -7 and x = 6
Let the function be f ( x ) where f ( x ) = ( x + 7 ) ( x - 6 )
Now , as x tends to infinity , the negative makes no such difference on the zeros of the function f ( x ) ,
And , f ( x ) = - ( x + 7 ) ( x - 6 )
Therefore , to find the polynomial function , f ( x ) = - ( x + 7 ) ( x - 6 )
f ( x ) = - [ x² - 6 x + 7 x - 42 ]
= - [ x² + x - 42 ]
= - x ² - x + 42
Hence , the polynomial function f ( x ) = - x ² - x + 42
To learn more about polynomial function click :
https://brainly.com/question/25097844
#SPJ2
What is the value of 3X to the 2nd power
Answer:
9 x^2
Step-by-step explanation:
( 3x) ^2
We are multiplying 3x * 3x
9 x^2
Find the total area of the prism.
Answer:
A=1,728
Step-by-step explanation:
To find the area of a prism, you must find the area of one side, then multiply it by so it would be Width*Hight*Depth, W*H*D.
The width is 12, the hight is 12, and the depth is 12 so you can write
A=12*12*12
Multiply 12 by 12
A=144*12
Multiply 12 by 144 to get your final total area
A=1,728
Hope this helps, feel free to ask follow-up questions if confused.
Have a good day! :)
Researchers recorded that a certain bacteria population declined from 800,000 to 500,000 in 6 hours after the administration of medication. At this rate of decay, how many bacteria would there have been at 24 hours? Round to the nearest whole number
Answer:
We can assume that the decline in the population is an exponential decay.
An exponential decay can be written as:
P(t) = A*b^t
Where A is the initial population, b is the base and t is the variable, in this case, number of hours.
We know that: A = 800,000.
P(t) = 800,000*b^t
And we know that after 6 hours, the popuation was 500,000:
p(6h) = 500,000 = 800,000*b^6
then we have that:
b^6 = 500,000/800,000 = 5/8
b = (5/8)^(1/6) = 0.925
Then our equation is:
P(t) = 800,000*0.925^t
Now, the population after 24 hours will be:
P(24) = 800,000*0.925^24 = 123,166
Answer:
122,070 bacteria.
Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt
Substitute the values in the formula.
500,000=800,000ek⋅6
Solve for k. Divide each side by 800,000.
58=e6k
Take the natural log of each side.
ln58=lne6k
Use the power property.
ln58=6klne
Simplify.
ln58=6k
Divide each side by 6.
ln586=k
Approximate the answer.
k≈−0.078
We use this rate of growth to predict the number of bacteria there will be in 24 hours.
AA0ktA=?=800,000=ln586=24hours=A0ekt
Substitute in the values.
A=800,000eln586⋅24
Evaluate.
A≈122,070.31
At this rate of decay, researchers can expect 122,070 bacteria.
Shawna spent half of her weekly allowance playing arcade games. To earn more money her parents let her clean the windows in the house for $4.37. What is her weekly allowance if she ended with $11.18?
Answer:
$13.62
Step-by-step explanation:
By working backward we can see that before she cleaned the windows she had $6.81.
We know that she spent half her allowance on the arcade and the $6.81 she had before cleaning the windows is the other half.
So, if you multiply by 2 you get that here weekly allowance is $13.62.
Answer:
$13.62
Step-by-step explanation:there
PLEASE HELP ?
A: 111.6 square centimeters
B: 323 square centimeters
C: 7.75 square centimeters
Answer:
B. 323 square centimeters
Step-by-step explanation:
multiply the inches by the conversion number
50 x 6.45 = 322.5
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
[tex]1 \ inch^2 = 6.45 \ cm^2[/tex]
Multiplying both sides by 50
[tex]1 * 50 \ inch^2 = 6.45 * 50 \ cm^2\\[/tex]
[tex]50 \ inch^2 = 323 \ cm^2[/tex]
You have $9000 with which to build a rectangular enclosure with fencing. The fencing material costs $30 per meter. You also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. The material for the partitions costs $25 per meter. What is the maximum area you can achieve for the enclosure
Answer:i explained it
Step-by-step explanation:
The total cost of the fence will be 30(2L + 2W) + 2*25 W <= 9000
60L + 110W <= 9000
60 L <= 9000 - 110W
L <= 150 - 11/6 W
For a given width, the maximum area will correspond to the maximum length, so we can just go ahead and say L = 150 - 11/6 W
A = LW = (150 - 11/6 W) W
A = 150 W - 11/6 W2
A' = 150 - 11/3 W = 0
150 = 11/3 W
W = 450/11
I need some help, see the picture for the question. Solve for V
Answer:
the answer is A) h=3V/(Pi*r^2)
Step-by-step explanation:
This question is asking to solve for h, the equation is allready solved for V.
to solve for h means to get h by itself on one side of the equation.
1) V=(1/3)*pi*r^2*h. Divide 1/3*pi*r^2 to the other side of the equation
2) V/(1/3)*pi*r^2=h. 1/3 on the bottom denominator means we can multiply the reciprocal to the bottom and the top and get an equivalent answer. In short, move the 3 from the 1/3 onto the top.
3) (3*V)/(pi*r^2)=h. Simplify.
4) 3V/(Pi*r^2)=h.
Four times a number added to 3 times a larger number is 31. Seven subtracted from the larger number is equal to twice the smaller number. Let x represent the smaller number and y represent the larger number. Which equations represent this situation? y = negative four-thirds x + 31. y = 2 x + 7. y = negative four-thirds x + StartFraction 31 Over 3 EndFraction. Y = 2 x + 7. y = negative four-thirds x + 31. y = negative 2 x + 7. y = negative four-thirds x + StartFraction 31 Over 3 EndFraction. Y = negative 2 x + 7.
Answer:
y = negative four-thirds x + StartFraction 31 Over 3 EndFraction
y = 2 x + 7
Step-by-step explanation:
Let x represent the smaller number and y represent the larger number.
Part 1Four times a number added to 3 times a larger number is 31.
It is translated as:
4x + 3y = 31Then, solving for y:
4x + 3y=31 ⇒ 3y= -4x+31 ⇒ y= (-4x+31)/3 = - 4/3x + 31/3⇒ y= - 4/3x + 31/3
Correct answer choice for this equation:
y = negative four-thirds x + StartFraction 31 Over 3 EndFraction
Part 2Seven subtracted from the larger number is equal to twice the smaller number.
It is translated as:
y-7= 2xThen, solving for y:
y-7= 2x ⇒ y= 2x+ 7Correct answer choice for this equation:
y = 2 x + 7
Answer:
It's A.
Step-by-step explanation:
I just got it correct on my unit test review.
Linda earned $13,500 in 3 months. What is her annual salary?
Answer:
$54,000
Step-by-step explanation:
Assuming that her salary does not change. Note that annual means "a year", which would mean 12 months.
First, find how much Linda makes per month. Divide the total earned in 3 months with 3 months:
13,500/3 = 4,500
Next, multiply 4,500 (the amount made per month) with 12 to get your annual salary:
4,500 x 12 = 54,000
Linda makes $54,000 annually.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.
Answer:
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
Step-by-step explanation:
The amount of Carbon-14 after t years is given by the following equation:
[tex]A(t) = A(0)e^{-rt}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.
This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]
How many years will it take for carbon–14 to decay to 10 percent of its original amount?
This is t for which:
[tex]A(t) = 0.1A(0)[/tex]
So
[tex]A(t) = A(0)e^{-rt}[/tex]
[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]
[tex]e^{-0.000124t} = 0.1[/tex]
[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]
[tex]-0.000124t = \ln{0.1}[/tex]
[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]
[tex]t = 18569.2[/tex]
It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount
The formula for the volume of a right circular cylinder is
V = 72h. If r = 26 and h = 5b + 3, what is the
volume of the cylinder in terms of b?
Answer:
20b^3+12b^2
Step-by-step explanation:
v=(2b)^2 (5b+3) = 4b^2 (5b+3) = 20b3+12b^2
Find the Slope of the line
-4
1
1/4
4
Answer:
Hey there!
The slope is rise over run, or 1/-4.
This gives us the slope, which is -1/4.
Hope this helps :)
Answer:
1/4
Step-by-step explanation:
( i mean i think it is - 1/4 but that isn't an answer choice- )
Slope (m) =
ΔY overΔX= -1 over 4 = -0.25
subtract x^1 and x^2 also y^1 and y^2
and put the answer of y' s over the answer of x 's
divide and you got your answer!
Problem 2
In the above diagram, circles O and O' are tangent at X, and PQ is tangent to both circles. Given that
OX= 3 and O'X = 8. find PQ.
Answer:
√96
Step-by-step explanation:
PQ is tangent to both lines, so PQ is perpendicular to PO and QO'.
The radius of the smaller circle is 3, and the radius of the larger circle is 8.
If we draw a line from O to O', and another line from point O to line QO' that is parallel to PQ, we get a right triangle where OO' is the hypotenuse, the short leg is 8−3=5, and the long leg is the same length as PQ.
Using Pythagorean theorem:
x² + 5² = 11²
x = √96
The Buzz Tool Company issued 1,000 shares of common stock. If the total value of this was $50,000,what's the par value of each share.
Answer:
$50.
Step-by-step explanation:
The formula for the stocks is...
Par value of preferred stock = (Number of issued shares) * (par value per share)
So, we can say that...
Par value per share = par value of preferred stock / number of issued shares.
The par value of the Buzz Tool Company is $50,000. There are 1,000 issued shares. So, each stock would be $50,000 / 1,000 = $50 / 1 = $50.
Hope this helps!
Answer: par value is $50.00
Step-by-step explanation:
$50,000.00 ÷ 1,000
= $50.00
Combine like terms to create an equivalent expression. -3.6-1.9t+1.2+5.1t−3.6−1.9t+1.2+5.1t
Question
Combine like terms to create an equivalent expression.
-3.6-1.9t+1.2+5.1t
Answer:
3.2t - 2.4
Step-by-step explanation:
Given;
-3.6 - 1.9t + 1.2 + 5.1t
Combining like terms means bringing terms that have "t" together and separately, those that don't have "t" together. i.e
=> − 1.9t + 5.1t - 3.6 + 1.2
=> 3.2t - 2.4
Therefore, the equivalent expression is;
3.2t - 2.4
Answer:
3.2t - 2.4
Step-by-step explanation:
right on khan
Identify the conclusion in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. There is not sufficient evidence to warrant rejection of the claim.
b. There is sufficient evidence to warrant rejection of the claim.
c. There is sufficient evidence to support the claim.
d. There is not sufficient evidence to support the claim.
Answer:
C
Step-by-step explanation:
Firstly, we set up the null and alternative hypothesis as follows;
The null hypothesis is;
H0: μ ≥ 12
The alternative hypothesis is;
Ha : μ < 12
Next step is to calculate the test statistic z
Mathematically;
z = (x - μ )/ σ /√n
= (11.58 - 12) /1.93/√(80
Test statistic z = -1.92
Now we proceed to find the probability value that is equal to the value of the test statistic. We can find this by using the standard normal table or NORMSTD function on excel
P(z < -1.92) = 0.0274
P-value = 0.0274
alpha = 0.05
From the above, we can see that
P-value < alpha
And because of this, we are going to reject the null hypothesis and therefore accept the alternative.
We then conclude that there is sufficient evidence to conclude that "The average battery life (between charges) of this model of tablet is at least 12 hours."
A car dealership earns a portion of its profit on the accessories sold with a car. The dealer sold a Toyota Camry loaded with accessories for $24,000. The total cost of the car was 8 times as much as the accessories. How much did the accessories cost? Cost of Accessories
Answer:
y = 2666.67
Step-by-step explanation:
Well to solve this we can make a system of equations.
x = cost of car alone
y = cost of accesories,
[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]
So now we plug in 8y for x in x + y = 24000.
(8y) + y = 24000
9y = 24000
Divide both sides by 9
y = 2666.666666
or 2666.67 rounded to the nearest hundredth.
Now that we have y we can plug that in for y in x=8y.
x = 8(2.666.67)
x = 21,333.33 rounded to the nearest hundredth.
Thus,
accessories "y" cost around 2666.67.
Hope this helps :)
One kind of candy (jelly) sells for $5 a pound and another (chocolate) for $10 a pound. How many pounds of each should be used to make a mixture of 10 pounds of candy (both kinds) that sells for a total $80 (i.e. $8/pound)?
Answer:
chocolate: 6 poundsjelly: 4 poundsStep-by-step explanation:
Let x represent the number of pounds of chocolate in the mix. Then the total price of 10 pounds of mix is ...
10x +5(10 -x) = 80
5x +50 = 80
5x = 30
x = 6 . . . . . . . . pounds of chocolate
10 -x = 4 . . . . . pounds of jelly candy
6 pounds of chocolate and 4 pounds of jelly should be used to make the mixture.
Please help. I’ll mark you as brainliest if correct!
Answer:
x +0y+0z = 400
-x +y+0z = 150
-8x +0y +z = 250
Step-by-step explanation:
The last column is the solution
The rest of the columns are the coefficients of the variables
x +0y+0z = 400
-x +y+0z = 150
-8x +0y +z = 250
is the midsegment of ABC. If is 30 centimeters long, how long is ?
A.
25 centimeters
B.
20 centimeters
C.
15 centimeters
D.
10 centimeters
Answer:
C. 15 centimeters
Step-by-step explanation:
The Triangle Midsegment Theorem
segment LM = 1/2 of AC
LM = 1/2 * 30
LM = 15 cm
Assume a significance level of alpha equals 0.05 and use the given information to complete parts (a) and (b) below. Original claim: More than 47% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0433.
Required:
a. State a conclusion about the null hypothesis.
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Answer:
Step-by-step explanation:
a. A conclusion with regards to the null hypothesis is this:
Since the p value observed which is 0.0433 is less than the alpha level of significant 0.05, we can reject the null hypothesis.
b. A final conclusion that addresses the original claim is this:
Since we rejected the null hypothesis, it means it means there was enough statistical evidence to support the claim that more than 47% of adults would erase all of their personal information online if they could.
6th grade math help me, please :))
Answer:
D
Step-by-step explanation:
100/5=20
20*7=140
Find the measure of a.
Answer:
a = 37
Step-by-step explanation:
the sum of any triangle angles is 180
then 62 + 81 + a = 180
a = 37
.. ..
Answer:
a = 37 degrees
Step-by-step explanation:
81+62 = 143
We know that all angles of a triangle = 180 degrees
180-143= 37 degrees
a = 37 degrees
Consider the following estimated regression equation based on 10 observations y 29.1270 5906x, 4980x2 011
a. Develop a point estimate of the mean value of y when x 1 = 180 and x 2-310 (to 3 decimals).
b. Develop a point estimate for an individual value of y when x 1 180 and x 2-310 (to 3 decimals)
Answer:
no tiene mas informaion?
Step-by-step explanation:
For a certain type of tree the diameter D (in feet) depends on the tree's age t (in years) according to the logistic growth model. Find the diameter of a 21-year-old tree. Please give the answer to three decimal places.
Answer:
[tex]D(21) = 1.612\ ft[/tex]
Step-by-step explanation:
The question has missing details;
[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex]
Given that t = 21
Solve for Diameter, D
To do this, we simply substitute 21 for t in the above function
[tex]D(t) = \frac{5.4}{1+2.9e^{-0.01t}}[/tex] becomes
[tex]D(21) = \frac{5.4}{1+2.9e^{-0.01 * 21}}[/tex]
[tex]D(21) = \frac{5.4}{1+2.9e^{-0.21 }}[/tex]
Solve for [tex]e^{-0.21}[/tex]
[tex]D(21) = \frac{5.4}{1+2.9* 0.81058424597}[/tex]
Simplify the denominator
[tex]D(21) = \frac{5.4}{1+2.35069431331}[/tex]
[tex]D(21) = \frac{5.4}{3.35069431331}[/tex]
[tex]D(21) = 1.61160628069[/tex]
[tex]D(21) = 1.612\ ft[/tex] (Approximated)
Hence, the diameter of the 21 year old tree is 1.612 feet
Please help. I’ll mark you as brainliest if correct
Answer:
1,-1,3,4
1,6,-2,-4
-4,6,-6,6
Step-by-step explanation:
I believe you just put in the values into the box. Watch the video to see how they did it to make sure it looks like how I did it.
An article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines. The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively. Does it appear the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg? Carry out an appropriate test of hypotheses at significance level .05 based on calculating a P-value.
Answer:
We conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.
Step-by-step explanation:
We are given that an article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines.
The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas, for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively.
Let = true average weight loss for the vegan diet.
[tex]\mu_2[/tex] = true average weight loss for the control diet.
So, Null Hypothesis, : 1 kg {means that the true average weight loss for the vegan diet exceeds that for the control diet by less than or equal to 1 kg}
Alternate Hypothesis, : > 1 kg {means that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\barX_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, = sample mean weight loss for the vegan diet = 6 kg
= sample mean weight loss for the control diet = 3.8 kg
= sample standard deviation weight loss for the vegan diet = 3.2 kg
= sample standard deviation weight loss for the control diet = 2.4 kg
[tex]n_1[/tex] = sample of vegan diet women = 33
[tex]n_2[/tex] = sample of control diet women = 33
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(33-1)\times 3.2^{2}+(33-1)\times 2.4^{2} }{33+33-2} }[/tex] = 2.83
So, the test statistics = [tex]\frac{(6-3.8)-(1)}{2.83 \times \sqrt{\frac{1}{33}+\frac{1}{33} } }[/tex] ~ [tex]t_6_4[/tex]
= 1.722
The value of t-test statistics is 1.722.
Also, the P-value of the test statistics is given by;
P-value = P([tex]t_6_4[/tex] > 1.722) = 0.0461 or 4.61%
Since the P-value of our test statistics is less than the level of significance as 0.0461 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.