Answer:
27%
Step-by-step explanation:
6/10*45/100=270/1000 which is 27/100 which is 27%
Which statements are true about reflections? Check all that apply.
An image created by a reflextion will always be congruent to its pre-image.
An image and its pre-image are always the same distance from the line of reflection.
If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image.
The line of reflection is perpendicular to the line segments connecting corresponding vertices.
The line segments connecting corresponding vertices are all congruent to each other.
The line segments connecting corresponding vertices are all parallel to each other.
Point A' (2,3) is the image of A(3,-4)
under a translation.
Determine the translation.
Use non-negative numbers.
A translation by
units to the
right/left v
and
units
up/down
Answer:
up/down
Step-by-step explanation:
Darby states this generalization:
All odd numbers greater than 30 are divisible by 3.
Which number could be used to show that Darby's generalization is not correct?
A. 33
B .35
C. 39
D. 45
PLEASE HELP AS QUICKLY AS POSSIBLE THANK YOU :)
Answer:
35
Step-by-step explanation:
35 is not divisible by 3 as all the other numbers are
Answer: The number to show he is incorrect is 35 because 35 divided by 3 is 11.6666666667 which is not a whole number.
Step-by-step explanation:
A group of hikers buy 8 bags of trail mix. Each bag contains 3 1/2 cups of trail mix. The trail mix is shared evenly among 12 hikers. How many cups of trail mix will each hiker receive?
Each hiker will receive cups of trail mix.
Answer:
Each hiker will get 2 1/3 cups
Step-by-step explanation:
8 bags multiplied by 3.5
28 cups overall
The 28 cups is shared between 12 hikers
28/12=2 1/3 cups
Alexander threw a dart at this board a total of 40 times. Predict the number of times the dart will land on the number 3.
PLZ HURRY
Answer:
5% chance so 2 times
Step-by-step explanation:
Got chu:)
A researcher collected data on the hours of TV watched per day from a sample of five people of different ages. Here are the results:i Age TV Hrs 1 43 1 2 30 6 3 22 4 4 20 3 5 5 6 1. Calculate the least squares estimated regression equation using simple linear regression. 2. What is the independent variable in this study?a) {y}b) agec) tv hoursd) Ie) 53) Create an ANOVA table. Using α=.05.
Answer:
1. The least squares regression is y = -0.1015·x + 6.51
2. The independent variable is b) age
Please see attached table
Step-by-step explanation:
The least squares regression formula is given as follows;
[tex]\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y} \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}}[/tex]
We have;
[tex]\bar x[/tex] = 24
[tex]\bar y[/tex] = 4
[tex]\Sigma (x_i - \bar x) (y_i - \bar y)[/tex] = -79
[tex]\Sigma (x_i - \bar x)^2[/tex] = 778
[tex]\therefore \hat \beta =\dfrac{\sum_{i = 1}^{n}(x_{i} - \bar{x})\times \left (y_{i} - \bar{y} \right ) }{\sum_{i = 1}^{n}(x_{i} - \bar{x})^{2}} = \frac{-79}{778} = -0.1015[/tex]
The least squares regression is y = -0.1015·x + α
∴ α = y -0.1015·x = 6 - (-0.1015 × 5) = 6.51
The least squares regression is thus;
y = -0.1015·x + 6.51
2. The independent variable is the age b)
3. Steps to create an ANOVA table with α = 0.05
The overall mean = (43 + 30 + 22 + 20 + 5 + 1 + 6 + 4 + 3 + 6 )/10 = 14
There are 2 different treatment = [tex]df_{treat} = 2 - 1 = 1[/tex]
There are 10 different treatment measurement = [tex]df_{tot} = 10 - 1 = 9[/tex]
[tex]df_{res} = 9 - 1 = 8[/tex]
[tex]df_{treat} + df_{res} = df_{tot}[/tex]
The estimated effects are;
[tex]\hat A_1 = 24 - 14 = 10[/tex]
[tex]\hat A_2 = 4 - 14 = -10[/tex]
[tex]SS_{treat} = 10^2 \times 5 + (-10)^2 \times 5 =1000[/tex]
[tex]\sum_{i}\SS_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y)= [(1 - 4)^2 + (6 - 4)^2 + (4 - 4)^2 + (3 - 4)^2 + (6 - 4)^2] = 18[/tex]
[tex]\sum_{i} S S_{row}_i = \sum_{i}\sum_{j} (y_{ij} - \bar y) ^2= [(43 - 24)^2 + (30 - 24)^2 + (22 - 24)^2 + (20 - 24)^2 + (5 - 24)^2] = 778[/tex]
[tex]S S_{res} = \sum_{i} S S_{row}_i = 778 + 18 = 796[/tex]
[tex]SS_{tot}[/tex] = (43 - 14)² + (30 - 14)² + (22 - 14)² + (20 - 14)² + (5 - 14)² + (1 - 14)1² + (6 - 4 )² + (3 - 14)² + (6 - 14)² = 1796
[tex]MS_{treat} = \dfrac{SS_{treat} }{df_{treat} } = \dfrac{1000}{1} = 1000[/tex]
[tex]MS_{res} = \dfrac{SS_{res} }{df_{res} } = \dfrac{796}{8} = 99.5[/tex]
F- value is given by the relation;
[tex]F = \dfrac{MS_{treat} }{MS_{res} } = \frac{1000}{99.5} = 10.05[/tex]
We then look for the critical values at degrees of freedom 1 and 8 at α = 0.05 on the F-distribution tables 5.3177
Hence; [tex]F = 10.05 > F_{1,8}^{Krit}(5\%) = 5.3177[/tex], we reject the null hypothesis.
Stefan and his friends used four tables for all the dishes the guests brought to the party. The tables were 2 8/10 meters long, 2.48 meters long, 2 59/100 meters long, and 2.83 meters long. Enter each length as a decimal number in order from greatest to least.
Answer:
[tex]2.83,2.8,2.59,2.48[/tex]
Step-by-step explanation:
Given:
Numbers are [tex]\frac{28}{10}\,m,\,2.48\,m,\,\frac{259}{100}\,m,\,2.83 \,m[/tex]
To express: each length as a decimal number in order from greatest to least
Solution:
A number which consists of a whole number part and the fractional part separated by a decimal point is known as a decimal number.
[tex]\frac{28}{10}=2.8\\ 2.48=2.48\\\frac{259}{100}=2.59\\ 2.83=2.83[/tex]
Numbers arranged in order from greatest to least: [tex]2.83,2.8,2.59,2.48[/tex]
A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 31 ft/s. (a) At what rate is his distance from second base decreasing when he is halfway to first base? (Round your answer to one decimal place.) ft/s (b) At what rate is his distance from third base increasing at the same moment? (Round your answer to one decimal place.)
Answer:
Step-by-step explanation:
Given that :
the side of the square = 90ft
The speed of the runner = 31 ft/sec
By the time the runner is halfway to the first base; the distance covered by the runner in time(t) is (31 t) ft and the distance half the base = 90/2 = 45 ft
Thus; 31 t = 45
t = 45/31
From the second base ; the distance is given as:
P² = (90)² + (90 - 31t )²
P = [tex]\sqrt{(90)^2 + (90 - 31t )^2}[/tex]
By differentiation with time;
[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +(90-31t)^2} } *(0+ 2 (90-31t)(0-31))[/tex]
[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +(90-31t)^2} } * 2 (-31)(90-31t)[/tex]
At t = 45/31
[tex]\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +45^2} } * 2 (-31)(45)[/tex]
[tex]\dfrac{dP}{dt} =\dfrac{-35*45}{100.623}[/tex]
= - 13.86 ft/sec
Hence, we can conclude that as soon as the runner is halfway to the first base, the distance to the second base is therefore decreasing by 13.86 ft/sec
b) The distance from third base can be expressed by the relation:
q² = (31t)² + (90)²
[tex]q = \sqrt{(31t)^2+(90)^2}[/tex]
By differentiation with respect to time:
[tex]\dfrac{dq}{dt} = \dfrac{1}{2\sqrt{90^2 + (31)t^2} } *(0+31^2 + 2t)[/tex]
At t = 45/31
[tex]\dfrac{dq}{dt} = \dfrac{1}{2\sqrt{90^2 + 45^2} } *(0+31^2 + \frac{45}{31})[/tex]
[tex]= \dfrac{31*45}{100.623}[/tex]
[tex]= 13.86 \ ft/sec[/tex]
Thus, the rate at which the runner's distance is from the third base is increasing at the same moment of 13.86 ft/sec. So therefore; he is moving away from the third base at the same speed to the first base)
a) The distance from second base is decreasing when the batter is halfway to first base at a rate of 13.9 feet per second.
b) The distance from third base is increasing when the batter is halfway to first base at a rate of 13.9 feet per second.
a) As the batter runs towards the first base, both the distance from second base and the length of the line segment PQ decrease in time. The distance from the second base is determined by Pythagorean theorem:
[tex]QS^{2} = QP^{2}+PS^{2}[/tex] (1)
By differential calculus we derive an expression for the rate of change of the distance from second base ([tex]\dot QS[/tex]), in feet per second:
[tex]2\cdot QS \cdot \dot{QS} = 2\cdot QP\cdot \dot{QP} + 2\cdot PS\cdot \dot {PS}[/tex]
[tex]\dot{QS} = \frac{QP\cdot \dot QP + PS\cdot \dot{PS}}{QS}[/tex]
[tex]\dot {QS} = \frac{QP\cdot \dot {QP}+PS\cdot \dot {PS}}{\sqrt{QP^{2}+PS^{2}}}[/tex] (2)
If we know that [tex]QP = 0.5L[/tex], [tex]PS = L[/tex], [tex]L = 90\,ft[/tex], [tex]\dot {QP} = -31\,\frac{ft}{s}[/tex] and [tex]\dot {PS} = 0\,\frac{ft}{s}[/tex], then the rate of change of the distance from second base is:
[tex]\dot {QS} = \frac{(45\,ft)\cdot \left(-31\,\frac{ft}{s} \right)}{\sqrt{(45\,ft)^{2}+(90\,ft)^{2}}}[/tex]
[tex]\dot {QS} \approx -13.864\,\frac{ft}{s}[/tex]
The distance from second base is decreasing when the batter is halfway to first base at a rate of 13.9 feet per second.
b) As the batter runs towards the first base, both the distance from third base increases and the distance from home increase in time. The distance from the third base is determined by Pythagorean theorem:
[tex]QT^{2} = HT^{2}+QH^{2}[/tex] (3)
By differential calculus we derive an expression for the rate of change of the distance from third base ([tex]\dot QT[/tex]), in feet per second:
[tex]2\cdot QT\cdot \dot{QT} = 2\cdot HT\cdot \dot {HT} + 2\cdot QH\cdot \dot {QH}[/tex]
[tex]\dot {QT} = \frac{HT\cdot \dot {HT}+QH\cdot \dot {QH}}{QT}[/tex]
[tex]\dot {QT} = \frac{HT\cdot \dot {HT}+QH\cdot \dot {QH}}{\sqrt{HT^{2}+QH^{2}}}[/tex]
If we know that [tex]HT = 90\,ft[/tex], [tex]QH = 45\,ft[/tex], [tex]L = 90\,ft[/tex], [tex]\dot{HT} = 0\,\frac{ft}{s}[/tex] and [tex]\dot {QH} = 31\,\frac{ft}{s}[/tex], then the rate of change of the distance from third base is:
[tex]\dot{QT} = \frac{(45\,ft)\cdot \left(31\,\frac{ft}{s} \right)}{\sqrt{(90\,ft)^{2}+(45\,ft)^{2}}}[/tex]
[tex]\dot{QT} \approx 13.864\,\frac{ft}{s}[/tex]
The distance from third base is increasing when the batter is halfway to first base at a rate of 13.9 feet per second.
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If f(a) = 3a - a2, which of the following are not true statements?
Select all that apply.
f(4) = -4
f(3) = 0
f(-1) = 2
f(0) = 3
f(-5) = -40
Answer:
f(-1) = 2
f(0) = 3
Step-by-step explanation:
f(a) = 3a - a²
f(4)= 3*4-4²= -4 ⇒ correctf(3)= 3*3-3²= 0 ⇒ correctf(-1) = 3*(-1)-(-1)²=-3+1= -2 ⇒ incorrect f(0) = 3*0-0²= 0 ⇒ incorrect f(-5) = 3*(-5)-(-5)²= -15-25= -40 ⇒ correctAnswer:
The 3rd and the 4th statement are not the true statements.
Step-by-step explanation:
In the 3rd statement, if you put a=-1 into the equation f(a), it would be
=3x(-1) - (-1)2
=-3 - 1
=-4.
In the 4th statement, if you put a=0 into the equation f(a), it would be
=3x(0) - (0)2
=0 - 0
=0.
For the other statements, they show the correct results.
A motor oil retailer needs to fill 40 one quart bottles, and he has two tanks: one that contains 12 gallons of oil and one that contains 2 gallons of oil. Which will he need to fill the bottles?
Answer:12 gallons
Step-by-step explanation: It is enough to fill 40
The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
A motor oil retailer needs to fill 40 one-quart bottles.
We know that in 1 gallon, there are 4 quarts. Then the number of gallons in 40 quarts will be given as,
⇒ 40 / 4
⇒ 10 gallons
The number of gallons in 40 quarts will be 10 gallons. Then the one that contains 12 gallons of oil.
More about the Algebra link is given below.
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What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
Volume of fudge cubes = 1 ×1×1
= 1 inch³
The cylinder contains 12.6 fudge cubes
So,
Volume of cylinder = 12.6 inches³
Height of cylinder = 1 inch
Base area of cylinder = Volume / Height
= 12.6 / 1
= 12.6 inches²
Suppose f , g , h , and j are functions such that: f ( r ) represents the circumference (in cm) of a circle whose radius is r cm. g ( C ) represents the radius (in cm) of a circle whose circumference is C cm. h ( r ) represents the area (in cm2) of a circle whose radius is r cm. j ( A ) represents the radius (in cm) of a circle whose area is A cm2.
a. Use function notation to represent the area of a circle whose circumference is 133 cm.
b. Use function notation to represent the circumference of a circle whose area is 6.82 cm^2
Answer:
(a)h(g(133))
(b)f(j(6.82))
Step-by-step explanation:
(a)Area of a circle whose circumference is 133 cm.
Since g(C) represents the radius (in cm) of a circle whose circumference is C cm.
The radius of the circle whose circumference is 133 cm = g(133)h(r) represents the area [tex](in$ cm^2)[/tex] of a circle whose radius is r cm.
Area, h(r) =h(g(133))Therefore, the area of a circle whose circumference is 133 cm is:
h(g(133))
(b)Circumference of a circle whose area is [tex]6.82 cm^2[/tex]
j(A) represents the radius (in cm) of a circle whose area is A [tex]cm^2[/tex].
The radius of the circle of area [tex]6.82 cm^2[/tex] = j(6.82)f(r) represents the circumference (in cm) of a circle whose radius is r cm.
Therefore:
Circumference, f(r) = f(j(6.82))The circumference of a circle whose area is [tex]6.82 cm^2[/tex] =f(j(6.82))
Find the area of the triangle ABC given angle A = 45°, b = 8, and c = √2.
Answer:
a = 4
Step-by-step explanation:
[tex]A = \frac{b * c * sen 45}{2} \\\\A = 8 * \sqrt{2} * \frac{\sqrt{2} }{2} * \frac{1}{2} \\\\\\\\A = 4[/tex]
Answer:
4
Step-by-step explanation:
At the 0.05 level of significance, is there a difference in the variance of average graduation debt incurred by students for private universities and public colleges? Using the results of (a), which t test is appropriate for comparing mean debt at graduation incurred by students at private universities and public colleges? At the 0.05 level of significance, conduct the test selected in (b). Write a short summary of your findings.
Answer:
Step-by-step explanation:
2. Suppose you obtain a $3,000 T - note with a 3% annual rate, paid quarterly, with maturity in 5 years. How much interest will you earn?
Answer:
You will earn $483.55 in interest.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
$3,000 T - note with a 3% annual rate
This means that [tex]P = 3000, r = 0.03[/tex]
Paid quarterly
Quarterly is 4 times per year, so [tex]n = 4[/tex]
Maturity in 5 years.
This means that [tex]t = 5[/tex]
How much interest will you earn?
Interest is the final amount subtracted by the principal.
Final amount:
A(5).
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(5) = 3000(1 + \frac{0.03}{4})^{4*5}[/tex]
[tex]A(5) = 3483.55[/tex]
Interest:
$3,483.55 - $3,000 = $483.55
You will earn $483.55 in interest.
Find the average of each of the following.
(a) $357, $452, $589, $602, $775
I need help anybody knows how to do?
Answer:
555
Step-by-step explanation:
(357+452+589+602+775)/5
Step-by-step explanation:
I HAVE DONE AT HERE YOU HAVE ASK WHE\E *O PUT 120°
The angle measures associated with which set of ordered pairs share the same reference angle? (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction , negative one-half), (negative one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction) (one-half, Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half) (Negative one-half, negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction), (One-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction) (StartFraction StartRoot 3 EndRoot Over 2 EndFraction, one-half), (one-half, StartFraction StartRoot 3 EndRoot Over 2 EndFraction)
Answer:
[tex](C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)[/tex]
Step-by-step explanation:
The reference angle is the angle that the given angle makes with the x-axis.
For an ordered pair to share the same reference angle, the x and y coordinates must be the same or a factor of each other.
From the given options:
[tex](A)\left(-\dfrac{\sqrt{3} }{2} ,-\dfrac{1 }{2}\right)$ and \left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)\\\\(B)\left(\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(-\dfrac{\sqrt{3} }{2}, \dfrac{1 }{2}\right)\\\\(C)\left(-\dfrac{1 }{2},-\dfrac{\sqrt{3} }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)\\\\(D)\left(\dfrac{\sqrt{3} }{2},\dfrac{1 }{2} \right)$ and \left(\dfrac{1 }{2},\dfrac{\sqrt{3} }{2} \right)[/tex]
We observe that only the pair in option C has the same x and y coordinate with the second set of points being a negative factor of the first term. Therefore, they have the same reference angle.
Answer:
C
Step-by-step explanation:
An investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. The investigator gets a sample of 21 country owners and 20 city owners. The mean number of hours per week that city owners spend walking their dogs is 10.0. The standard deviation of hours spent walking the dog by city owners is 3.0. The mean number of hours country owners spent walking theirs dogs per week was 15.0. The standard deviation of the number of hours spent walking the dog by owners in the country was 4.0. Do dog owners in the country spend more time walking their dogs than do dog owners in the city?
Using an alpha level of .05 (t= 2.32), what is the conclusion you are entitled to draw as a result of this test?
Answer:
Yes, there is enough evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city (P-value=0.0000263).
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that dog owners in the country (sample 2) spend more time walking their dogs than do dog owners in the city (sample 1).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=20 has a mean of 10 and a standard deviation of 3.
The sample 2, of size n2=21 has a mean of 15 and a standard deviation of 4.
The difference between sample means is Md=-5.
[tex]M_d=M_1-M_2=10-15=-5[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{3^2}{20}+\dfrac{4^2}{21}}\\\\\\s_{M_d}=\sqrt{0.45+0.762}=\sqrt{1.212}=1.101[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-5-0}{1.101}=\dfrac{-5}{1.101}=-4.54[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=20+21-2=39[/tex]
This test is a left-tailed test, with 39 degrees of freedom and t=-4.54, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-4.54)=0.0000263[/tex]
As the P-value (0.0000263) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that dog owners in the country spend more time walking their dogs than do dog owners in the city.
Using the t-distribution, it is found that since the test statistic is t = 4.54 > 2.32, it can be concluded that dog owners in the country spend more time walking their dogs than do dog owners in the city.
At the null hypothesis, we test if dog owners in the country and in the city spend the same amount of time walking their dogs, that is:
[tex]H_0: \mu_{Co} - \mu_{Ci} = 0[/tex]
At the alternative hypothesis, we test if dog owners in the country spend more time, that is:
[tex]H_1: \mu_{Co} - \mu_{Ci} > 0[/tex]
The standard errors are:
[tex]s_{Co} = \frac{4}{\sqrt{21}} = 0.8729[/tex]
[tex]s_{Ci} = \frac{3}{\sqrt{20}} = 0.6708[/tex]
The distribution of the differences has:
[tex]\overline{x} = \mu_{Co} - \mu_{Ci} = 15 - 10 = 5[/tex]
[tex]s = \sqrt{s_{Co}^2 + s_{Ci}^2} = \sqrt{0.8729^2 + 0.6708^2} = 1.1009[/tex]
We have the standard deviation for the samples, hence, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu[/tex] is the value tested at the null hypothesis, for this problem [tex]\mu = 0[/tex], hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{5 - 0}{1.1009}[/tex]
[tex]t = 4.54[/tex]
Since the test statistic is t = 4.54 > 2.32, it can be concluded that dog owners in the country spend more time walking their dogs than do dog owners in the city.
A similar problem is given at https://brainly.com/question/17192140
The measure of angle 1 is (3x + 10) and the measure of
angle 4 is (4x - 15)
What is the measure of angle 7?
2 4
6 8
5 7
13
b
Answer:
95
Step-by-step explanation:
just did it on ed
Harriet spins this 6 colour spinner and flips a coin.
What is the probability of getting grey and tails?
Answer: 9%
Step-by-step explanation:
In probabilities; when two or more conditions must be met, the "and" operator is used. The probability of grey and tails is 1/12
From the attached spinner, we have:
[tex]Grey = 1[/tex]
[tex]n =6[/tex] --- partitions
So, the probability of landing on grey is:
[tex]P(Grey) = \frac{Grey}{n}[/tex]
This gives:
[tex]P(Grey) = \frac{1}{6}[/tex]
In a coin, we have:
[tex]Tail = 1[/tex]
[tex]n =2[/tex] --- faces
So, the probability of tail is:
[tex]P(Tail) = \frac{Tail}{n}[/tex]
[tex]P(Tail) = \frac{1}{2}[/tex]
The probability of grey and tail is:
[tex]Pr = P(Grey) \times P(Tail)[/tex]
[tex]Pr = \frac{1}{6} \times \frac{1}{2}[/tex]
[tex]Pr = \frac{1}{12}[/tex]
Hence, the probability of getting grey and tail is 1/12
Read more on probability at:
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Give the answer in a + bi form. (−7 + 6i) + (6 − 8i)
Answer:
-1 -2i
Step-by-step explanation:
(-7+6) + (6i-8i) = -1 -2i
Answer:
(-1 - 2i)
Step-by-step explanation:
You simply add them.
-7 + 6 = -1
6i + (-8i) = 6i - 8i = -2i
One cylinder has a volume that is 8 cm' less than a of the volume of a second cylinder. If the first cylinder's volume is 216
cm? what is the correct equation and value of x, the volume of the second cylinder?
x+8-216; x = 182 cm
-8-2167 - 196 cm
coll
+8-216-238cm
col
-8-216
-256 cm
Nacks and otum
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Corrected Question
One cylinder has a volume that is 8cm less than 7/8 of the volume of a second cylinder. If the first cylinder’s volume is 216cm³, what is the correct equation and value of x, the volume of the second cylinder?
Answer:
The equation is: [tex]216=\frac{7}{8}x-8[/tex]
Volume of the second cylinder= [tex]256cm^3[/tex]
Step-by-step explanation:
Volume of the first cylinder=[tex]216cm^3[/tex]
Let the volume of the second cylinder=x
7/8 of the volume of a second cylinder=[tex]\frac{7}{8}x[/tex]
8 less than 7/8 of the volume of a second cylinder=[tex]\frac{7}{8}x-8[/tex]
Therefore, the equation is:
[tex]216=\frac{7}{8}x-8[/tex]
Next, we solve for x
[tex]216=\frac{7}{8}x-8\\216+8=\frac{7}{8}x\\224=\frac{7}{8}x\\$Cross multiply\\7x=224*8\\Divide both sides by 7\\x=256cm^3[/tex]
The volume of the second cylinder is [tex]256cm^3[/tex]
Answer:
The answer is D
Step-by-step explanation:
Consider xdy = 3ydx.
(a) Apply Theorem 1 and show the equation has unique solution in xy-plane where x 6= 0
(b) Theorem 1 will be inconclusive about existence and uniqueness of solution where x = 0 (that is on y-axis). For points on the y-axis (i) Show there are infinitely many different solutions for xdy = 3ydx y(0) = 0. (ii) Show there is no solution for xdy = 3ydx y(0) = b b != 0.
Question:
Consider xdy = 3ydx.
(a) Apply Theorem 1 and show the equation has unique solution in xy-plane where x ≠ 0
(b) Theorem 1 will be inconclusive about existence and uniqueness of solution where x = 0 (that is on y-axis). For points on the y-axis (i) Show there are infinitely many different solutions for xdy = 3ydx y(0) = 0. (ii) Show there is no solution for xdy = 3ydx,
y(0) = b, b ≠0.
Theorem 1 is attached.
Answer:
Given:
xdy = 3ydx
a) Given theorem 1 :
dy/dx = f (x, y)
we have:
[tex] f(x, y) = \frac{3y}{x}[/tex]
[tex] \frac{d}{dy} f(x, y) = \frac{3}{x}[/tex]
[tex] \frac{d}{dy} [/tex] is at interior of all angles except at point x=0.
Therefore for x≠0
[tex] \frac{d}{dy} f(x, y) = \frac{3}{2}[/tex]
Thus, from theorem 1, there is a unique solution in the xy plane where x≠0
b) i) xdy = 3ydx y(0) = 0
We have:
[tex] \frac{dy}{y} = \frac{3}{x} dx [/tex]
Integrating, we have:
∫[tex] \frac{dy}{y}[/tex] =∫[tex] \frac{3}{x} dx [/tex]
ln y = 3lnx + lnC
y = Cx³
Hence, y(0)=0 is satisfied for all values of C
Thus, there are infinitely many solutions for xdy = 3ydx
ii) xdy = 3ydx
y(0) = b, b ≠ 0.
From our part (i) above, we already know that, y = Cx³
Let's now take initial value of y as b,
ie, y(0) = b
b = 0
From the question, b≠0.
Thus, it means it has no solution.
what is a proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
Each contestant in the Hunger Games must be trained to compete. Suppose that the time it takes to train a contestant has mean 5 days and standard deviation 4 days, independent of the time it takes other contestants to train. If the Hunger Games has 100 contestants to train, approx imate the probability that it will take less than 450 days to train all the contestants. Leave your answer in terms of the standard normal distribution phi(a).
Answer:
11.51% probability that it will take less than 450 days to train all the contestants.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sum of n variables, the mean is [tex]\mu*n[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
In this question:
[tex]n = 100, \mu = 100*5 = 500, s = 4\sqrt{100} = 40[/tex]
Approximate the probability that it will take less than 450 days to train all the contestants.
This is the pvalue of Z when X = 450.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{450 - 500}{40}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151
11.51% probability that it will take less than 450 days to train all the contestants.
In a research article, you find that r is reported to be 4.8. How would you interpret this finding?
a. The relationship is reported incorrectly
b. The relationship is strong
c. The relationship is moderate
d. The relationship is weak
Based on the information given, the correct option is A. The relationship is reported incorrectly.
It should be noted that in a research, the normal value or r can range between -1 to 1. This shows the linear relationship between the variables.
In this case, since r is reported to be 4.8, the relationship is reported incorrectly.
Learn more about regression on:
https://brainly.com/question/25987747
You would interpret this finding of r to be reported as 4.8 as (a) the relationship is reported incorrectly.
The variable r in regression represents correlation.
And in regression, correlation can only take values between -1 and 1 (inclusive)
Given that:
r = 4.8
4.8 is outside the range -1 to 1.
This means that, the value is either calculated incorrectly or reported incorrectly.
Hence, the true statement is (a)
Read more about regression and correlation at:
https://brainly.com/question/14585820
Jan is solving the equation shown below. Which of the following
represents the solution to Jan's equation?
Answer:
C. x = 27
Step-by-step explanation:
To solve we must undo what is being done to the variable. It is being modified in several ways in this equation so we must do the opposites of each step to both sides of the equation.
1. 1/3x + 9 = 7 + 11
2. 1/3x = 18 - 9
3. (1/3x) * 3 = 9 * 3
4. x = 27
Hope this helps! (Please consider giving brainliest)
India is the second most populous country in the world, with a population in 2008 of about 1.14 billion people. The population is growing by about 1.34% each year. If the population continues following this trend, during what year will the population reach 2 billion?
Answer:
India's population will reach 2 billion during the year of 2050.
Step-by-step explanation:
India's population in t years after 2008 is modeled by the following equation:
[tex]P(t) = P(0)(1+r)^{t}[/tex]
In which P(0) is the population in 2008 and r is the growth rate, as a decimal.
Population in 2008 of about 1.14 billion people. The population is growing by about 1.34% each year.
This means that [tex]P(0) = 1.14, r = 0.0134[/tex]. So
[tex]P(t) = P(0)(1+r)^{t}[/tex]
[tex]P(t) = 1.14(1+0.0134)^{t}[/tex]
[tex]P(t) = 1.14(1.0134)^{t}[/tex]
If the population continues following this trend, during what year will the population reach 2 billion?
t years after 2008.
t is found when P(t) = 2. So
[tex]P(t) = 1.14(1.0134)^{t}[/tex]
[tex]2 = 1.14(1.0134)^{t}[/tex]
[tex](1.0134)^{t} = \frac{2}{1.14}[/tex]
[tex]\log{(1.0134)^{t}} = \log{\frac{2}{1.14}}[/tex]
[tex]t\log{1.0134} = \log{\frac{2}{1.14}}[/tex]
[tex]t = \frac{\log{\frac{2}{1.14}}}{\log{1.0134}}[/tex]
[tex]t = 42.23[/tex]
2008 + 42 = 2050
India's population will reach 2 billion during the year of 2050.
What’s the correct answer for this?
Answer:
54
Step-by-step explanation:
Since diameter AB divides MN into two equal parts hence
MO = NO
NOW,
5x+34 = -2(1-7x)
5x+34 = -2+14x
34+2 = 14x-5x
36 = 9x
Dividing both sides by 9
x = 4
Now,
NO = -2(1-7(4))
NO = -2+56
NO = -2+56
NO = 54
What would the amplitude be? How do I find it? Should I add 1.25+6.75 then divide by 2 ?
Answer:
2.75
Step-by-step explanation:
The amplitude is half of the difference between the highest and lowest y-coordinates.
amplitude = 0.5|6.75 - 1.25| = 0.5(5.5) = 2.75
