Answer:
C.
Step-by-step explanation:
As seen below, the equation of a circle is (x - h)^2 + (y - k)2 = r^2.
In this case, h = the x-value of the center of the circle, which is -2, and k = the y-value of the center of the circle, which is 3. The radius r is 4.
(x - (-2))^2 + (y - (3))^2 = (4)^2
(x + 2)^2 + (y - 3)^2 = 16
This corresponds to answer choice C.
Hope this helps!
solve each question by graphing. round to the nearest tenth
2x^2 + 5 = 11x
Answer: x=5 and 1/2
Step-by-step explanation:
You have to go to a graph and put it simply it, makes it a lot easier, hope this helps!
Steps to solve:
2x^2 + 5 = 11x
~Subtract 11x to both sides
2x^2 - 11x + 5 = 0
~Factor
(2x - 1)(x - 5) = 0
~Solve each factor
2x - 1 = 0
2x = 1
x = 1/2
x - 5 = 0
x = 5
Best of Luck!
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer: m=0.5 or m=1/2
Step-by-step explanation:
To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Since we are given the coordinate points, we can directly plug them in.
[tex]m=\frac{0.25-0}{0.5-0} =\frac{0.25}{0.5} =0.5[/tex]
The following values of (x) and f(y) are given. Find the best value of (dy/dx) at
(x=6) using center difference method?
x
F(y)
5
3.2188
5.5
3.4096
6.5
3.7436
7
3.8918
7.5
4.0298
3.7436
4.1588
Answer:
dy/dx at x=6 is 0.334
Step-by-step explanation:
The center difference method requires that the values of the function are given in equal intervals which is the case, and allows one to find the value for x = 6 using those of the function for x = 5.5 and for x = 6.5 as follows:
[tex]\frac{dy}{dx} =\frac{3.7436-3.4096}{6.5-5.5} =0.334[/tex]
The mean and standard deviation of a random sample of n measurements are equal to 34.5 and 3.4, respectively.A. Find a 95 % confidence interval for μ if n=49.B. Find a 95% confidence interval for μ if n=196.C. Find the widths of the confidence intervals found in parts a and b.D. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?1. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4.2. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2.3. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the on confidence interval by a factor of 4.4. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval.5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Answer:
a. The 95% confidence interval for the mean is (33.52, 35.48).
b. The 95% confidence interval for the mean is (34.02, 34.98).
c. n=49 ⇒ Width = 1.95
n=196 ⇒ Width = 0.96
Note: it should be a factor of 2 between the widths, but the different degrees of freedom affects the critical value for each interval, as the sample size is different. It the population standard deviation had been used, the factor would have been exactly 2.
d. 5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.
Step-by-step explanation:
a. We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=34.5.
The sample size is N=49.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{49}}=\dfrac{3.4}{7}=0.486[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=49-1=48[/tex]
The t-value for a 95% confidence interval and 48 degrees of freedom is t=2.011.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.011 \cdot 0.486=0.98[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 34.5-0.98=33.52\\\\UL=M+t \cdot s_M = 34.5+0.98=35.48[/tex]
The 95% confidence interval for the mean is (33.52, 35.48).
b. We have to calculate a 95% confidence interval for the mean.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{196}}=\dfrac{3.4}{14}=0.243[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=196-1=195[/tex]
The t-value for a 95% confidence interval and 195 degrees of freedom is t=1.972.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=1.972 \cdot 0.243=0.48[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 34.5-0.48=34.02\\\\UL=M+t \cdot s_M = 34.5+0.48=34.98[/tex]
The 95% confidence interval for the mean is (34.02, 34.98).
c. The width of the intervals is:
[tex]n=49\rightarrow UL-LL=33.52-35.48=1.95\\\\n=196\rightarrow UL-LL=34.02-34.98=0.96[/tex]
d. The width of the intervals is decreased by a factor of √4=2 when the sample size is quadrupled, while the others factors are fixed.
Eruptions of the Old Faithful geyser have duration times with a mean of 245.0 sec and a standard deviation of 36.4 sec (based on sample data). One eruption had a duration time of 110 sec.Eruptions of the Old Faithful geyser have duration times with a mean of 245.0 sec and a standard deviation of 36.4 sec (based on sample data). One eruption had a duration time of 110 sec.
a. What is the difference between a duration time of 110 sec and the mean? Answer
135
b. How many standard deviations is that (the difference found in part (a))? Answer
c. Convert the duration time of 110 sec to a z score. Answer
d. If we consider "usual" duration times to be those that convert to z scores between -2 and 2, is a duration time of 110 sec usual or unusual?
Answer:
a) 135 seconds
b) 3.71 standard deviations below the mean
c) Z = -3.71
d) Unusual
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 245, \sigma = 36.4[/tex]
a. What is the difference between a duration time of 110 sec and the mean?
Duration of 110 seconds.
Mean of 245
245 - 110 = 135 seconds
b. How many standard deviations is that (the difference found in part (a))?
This is |Z|
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 245}{36.4}[/tex]
[tex]Z = -3.71[/tex]
[tex]|Z| = 3.71[/tex]
3.71 standard deviations below the mean
c. Convert the duration time of 110 sec to a z score
From b, Z = -3.71
d. If we consider "usual" duration times to be those that convert to z scores between -2 and 2, is a duration time of 110 sec usual or unusual?
Z is not in the interval of -2 and 2, so a duration time of 110 sec is unusual
Find the length of ST to the nearest meter.
Answer:
42 m
Step-by-step explanation:
First, find <S
<S = 180 - (41+113) [ sum of angles in a triangle)
<S = 180 - 154 = 26°
Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C
Let a = RT = 28m
A = <S = 26°
b = ST
B = <R = 41°
Thus, we have:
28/sin(26°) = b/sin(41°)
Cross multiply
28*sin(41°) = b*sin(26°)
28*0.6561 = b*0.4384
18.3708 = b*0.4384
Divide both sides by 0.4384 to make b the subject of formula
18.3708/0.4384 = b
41.9041971 = b
b ≈ 42m (rounded to nearest meter)
Length of ST to nearest meter = 42 meters
The number of rooms in hotel G is 10 less than twice the number of rooms in hotel H .The total number of rooms in both hotels is 425 .Find the number of rooms in each of the hotels.
Answer:
No of rooms in Hotel G = 280
No of rooms in Hotel H = 145
Step-by-step explanation:
I solved the question using Elimination Method.
Which best compares the volumes of the two cylinders? Geometry
Answer:
The correct answer would be C
Step-by-step explanation:
please mark brainliest
The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.
Which best compares the volumes of the two cylinders?From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.
Read more on cylinders;
https://brainly.com/question/9554871
#SPJ2
Answer the following True or False:
If the p-value is 0.13 and the level of significance , a , is 0.05 in a hypothesis test for a mean, then we
accept the null hypothesis.
O false
O true
Answer:
false.
I think .???
a null hypothesis doesn't matter regardless
A transformation of ΔSTV results in ΔUTV. 2 triangles are connected at their base. Both triangles have identical side lengths and angle measures. Which transformation maps the pre-image to the image? dilation reflection rotation translation
Answer:
the answer is reflection
Step-by-step explanation:
i took edg
The transformation maps the pre- image to image by reflection.
What is reflection?A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.
Given:
A transformation of ΔSTV results in ΔUTV.
As, both the triangles are connected to the base and having identical side length and angle measure.
So, here the transformation is refection.
Learn more about transformation here:
https://brainly.com/question/11709244
#SPJ2
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is: Temperature = 110 ‑ 2(Latitude). How does the estimated temperature change when latitude is increased by one?
Answer:
Decreases by 2 degrees
Step-by-step explanation:
The expression that describes temperature as a function of latitude is:
[tex]T=110-2(Latitude)[/tex]
This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.
write down 3 numbers that have a range of 5 and a mode of 8
Answer:
8, 8, 13
Step-by-step explanation:
The three numbers 8, 8, 13 have a range of 5.
13 - 8 = 5
The mode is 8, the repeated number.
Answer:
need pls
Step-by-step explanation:
What statement is true? Use the number line to help
Answer:
-2 is greater than -2 1/2
Step-by-step explanation:
All the other questions are false and only answer a is correct because -2 is closer to 0 than -2 1/2.
Answer:
-2 is greater than -2.5Step-by-step explanation:
B is wrong. This is because when you look on the number like you can see that the option for 1.5 is greater than one is false. This is because 1.5 is ahead of the 1 on the number line.
C is wrong. This is because the number 1 is greater than -1.5. The number one is ahead of the number -1.5.
D is wrong. D is wrong because when a smaller number is negative then it is bigger than a larger number that is negative. So -1.5 is smaller than -0.5.
So the answer is A. -2 is greater than -2.5. It can be proved because of the rule written that a smaller number is negative then it is bigger than a larger number that is negative. So -2.5 is smaller than -2. And the reciprocal is true. -2 is larger than -2.5.
Hope this helped,
Kavitha
A. No, because it fails the vertical line test.
B. Yes, because it passes the vertical line test.
C. Yes, because it passes the horizontal line test.
D. No, because it is not a straight line.
Answer:
B. Yes, because it passes the vertical line test.
Step-by-step explanation:
The is a function. It has a one to one correspondence
It will pass the vertical line test
drag the tiles to the correct boxes to complete the pears. Match the values based on parallelogram ABCD, shown in the figure.
length of BC
value of y
m
value of x
56–>
4–>
44–>
2–>
Answer:
[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]
Step-by-step explanation:
In parallelogram ABCD, BC=AD
Given:
BC=(6-x) units
AD =(x+2) units
Therefore:
6-x=x+2
x+x=6-2
2x=4
x=2
BC=(6-x) units
=(6-2) units
BC=4 units
The opposite angles of a parallelogram are equal. Therefore:
[tex]m\angle BCD=m\angle BAD\\12^\circ+y^\circ=100^\circ-y^\circ\\y^\circ+y^\circ=100^\circ-12^\circ\\2y^\circ=88^\circ\\y=44^\circ[/tex]
[tex]m\angle DAB=100^\circ-y^\circ\\=100^\circ-44^\circ\\m\angle DAB=56^\circ[/tex]
Therefore, the match is:
[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]
Answer:
Step-by-step explanation:
plato i guess
Perform the indicated operation and simplify the result.
Answer:
7/ (3a-1)
Step-by-step explanation:
3a^2 -13a +4 28+7a
------------------ * --------------------
9a^2 -6a+1 a^2 -16
Factor
(3a-1)(a-4) 7(4+a)
------------------ * --------------------
(3a-1) (3a-1) (a-4)(a+4)
Cancel like terms
1 7
------------------ * --------------------
(3a-1) 1
Leaving
7/ (3a-1)
A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below.
Before: 74, 83, 75, 88, 84, 63, 93, 84, 91, 77
After: 73, 77, 70, 77, 74, 67, 95, 83, 84, 75
Required:
a. Is there evidence to suggest the logic course improves abstract reasoning?
b. Construct a 95% confidence interval for the mean difference between the before and after scores.
Answer:
don't know
Step-by-step explanation:
sorry buddy
if you make $2710.00 a month and must spend 89% of that on recurring and variable expenses, how much money can you potentially save in one year?
Answer:
$3577.20
Step-by-step explanation:
You can save 11% of your income each month, so in 12 months, you can save ...
12×0.11×$2710 = $3577.20
Recall the equation that modeled the volume of the raised flower bed, y, in terms of the width of the box, y = x3 + 11x2 − 312x. Now, open the graphing tool and graph the equation. Remember, this equation represents the volume of a flower box, so neither the width nor the volume can be negative. Using the pointer, determine the x-intercept where the width is positive and the volume will change to positive as x increases.
Answer:
x = 17.349
Step-by-step explanation:
The right-most x-intercept is 17.349, where the curve continues upward to the right.
What is 15 x minus 3 y = 0 written in slope-intercept form?
Answer:
y= 5x
Step-by-step explanation:
15x - 3y =0
3y= 15x
y= 5x - slope- intercept form
Answer:
a
Step-by-step explanation:
y=5x
7. Look at the figure below.
Which theorem can be used to show that triangles QSN and LEJ are congruent?
A. HL
B. ASA
C. SAS
D. SSA
I'm pretty sure that ' HL ' stands for "hypotenuse and leg". That's the one.
-- We see the little boxes in the lower left corners, so we know that these are right triangles, and we can use the rules we know about for right triangles.
-- The hypotenuses of both triangles are marked with the same length.
-- The base legs of both triangles are marked with the same length.
-- So we have (the hypotenuse and one leg of one right triangle) equal to (the hypotenuse and corresponding leg of another right triangle). That's exactly the description of the HL conguence theorem, so we know that these two triangles are congruent.
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer:
m = 0.5
Step-by-step explanation:
m = (y2 - y1) / (x2 - x1)
= (0.25 - 0) / (0.5 - 0)
= 0.25/0.5
= 0.5
Find the area of the regular polygon. Round your answer to the nearest hundredth.
(4 , 3.3)
The area is about __
square units.
Answer:
total area = 39.6 square units
Step-by-step explanation:
determine the inside angle
360 / 5 = 72°
half of the triangle = 36°
given:
adj = 3.3
Ф = 36°
length of the opp of a small triangle is = adj. tan Ф
opp = 3.3 * tan 36 = 2.4
area of a triangle = 1/2 b * h x 2 tringles
area =( 1/2 * 2.4 * 3.3 ) * 2
area = 7.92 multiplied by 5 equal shapes
total area = 7.92 * 5
total area = 39.6 square units
hope this helps
If the volume of a full sphere is 4/3x πr^3 what is the volume of a half sphere, also called a hemisphere?
Answer:
Rebekah, the height of a hemisphere is its radius. The volume of a sphere is 4/3 π r3. So the volume of a hemisphere is half of that: V = (2 / 3) π r3.
Answer:
V = (2 / 3) π r3.
Step-by-step explanation:
1/2 x 4/3 x π r3 = 2/3π r3
Line segment ON is perpendicular to line segment ML. What is the length of segment NP?
Answer:
not sure if it's 26 or76
Answer:
its 2
Step-by-step explanation:
Plz solve this question, it's very urgent.
i think it is ur required ans..
Help pls urgent!!!!!!!!!!
Answer:
d
Step-by-step explanation:
Please answer this correctly
There are 6 total cards. There is one 5 and one 7
You have a 1/6 probability of picking each number.
The probability of picking the 5 then the 7 would be 1/6 x 1/6 = 1/36
A population of monkeys' tail lengths is normally distributed with a mean of 25 cm with a standard deviation of 8 cm. I am preparing to take a sample of size 256 from this population, and record the tail length of each monkey in my sample. What is the probability that the mean of my sample will be between 24 and 25 cm?
Answer:
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
Step-by-step explanation:
Step(i):-
Given mean of the Population 'μ'= 25c.m
Given standard deviation of the Population 'σ' = 8c.m
Given sample size 'n' = 256
Let X₁ = 24
[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]
Let X₂ = 25
[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]
Step(ii):-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)
= P( Z≤0) - P(Z≤-2)
= 0.5 + A(0) - (0.5- A(-2))
= A(0) + A(2) ( ∵A(-2) =A(2)
= 0.000+ 0.4772
= 0.4772
Final answer:-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
An arhaeologist, exploring the pyramids
of Africa, discovers a mummy. He finds
that it contains 53 % of original amount
of C-14. Find age of the mummy.
Answer:
5249 years
Step-by-step explanation:
Half-Life of Carbon-14 is approximately 5730 years.
When we want to determine the age of a fossil using carbon dating, we use the formula:
[tex]t=\dfrac{\ln(N/N_0)}{-0.693} \cdot t_{1/2}[/tex]
Where:
[tex]t_{1/2}[/tex] is the half-life of the isotope carbon 14, t = age of the fossil (or the date of death) and ln() is the natural logarithm functionIn this case:
N(t)=100
[tex]N_o=53\\t_{1/2}\approx 5730$ years[/tex]
Therefore, the age of the mummy
[tex]t=\dfrac{\ln(53/100)}{-0.693} \cdot 5730\\=5249.43$ years\\t \approx 5249$ years[/tex]
Answer:
the answer is 6349 :)
Step-by-step explanation:
Someone put the correct answer in the comments so I figured I would put it here so you wouldn't miss it :) (It is correct I have tested it)