Answer:
In your question, the constant of proportionality already jump out at us which is to get y, we have to multiply x by 5/9. Therefore the constant of proportionality is y=5/9x.
It is known that a particular laboratory task takes the average person 2.5 seconds (the variance is not known). A researcher was interested in whether older people are slower (take longer) on this task. The researcher tested 30 randomly selected 80-year-olds. Their mean time was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude?
Complete Question
It is known that a particular laboratory task takes the average person 2.5 seconds (the variance is not known). A researcher was interested in whether older people are slower (take longer) on this task. The researcher tested 30 randomly selected 80-year-olds. Their mean time was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude? (Use the .05 significance level and use the five steps of hypothesis testing.)
Answer:
The researchers conclusion is
There is no sufficient evidence to show that older people are slower at the laboratory task
Step-by-step explanation:
From the question we are told that
The mean time is [tex]\mu = 2.5 \ seconds[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = 2.7 \ seconds[/tex]
The standard deviation is [tex]\sigma = 1.4 \ seconds[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 2.5[/tex]
The alternative hypothesis is [tex]H_a : \mu > 2.5[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{2.7 - 3 }{ \frac{1.4}{\sqrt{30} } }[/tex]
=> [tex]z =0.78[/tex]
From the z table the area under the normal curve to the right corresponding to [tex]z =0.78[/tex] is
[tex]p-value = P(Z > 0.78) = 0.2177[/tex]
From the value obtained we see that the p-value > [tex]\alpha[/tex]
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the older people are slower at the laboratory task
Which is defined using the undefined terms point and line? angle circle parallel lines ray
Answer:
D. Ray
Step-by-step explanation:
I just finished the quiz!
Point and line segment are used to define a ray.
RayA ray is a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.
A line extends infinitely in either direction but has no width and is one dimensional. A point is a 0-dimensional mathematical object with a location.
Point and line segment are used to define a ray.
Find out more on ray at: https://brainly.com/question/10404182
which ones are arithmetic or geometric ?
Marcus spent 3.25$ to wash his car. If one querter operates the car wash 60 seconds hiw long did it take him to wash his car.
10 min or 13 min. or 16 min ir 32.5 min
Answer:
answer=answer
Step-by-step explanation:
Y E S
I love simple math.
3.25$ to wash the car.
60 seconds: 1 quarter
how many quarters is 3.25?
4 quarters per dollar. so it'd be 13 quarters, then do 13*60=how many seconds u got. 780 seconds. I think you can do 780/60
HINT: hey, psst, it's 13 minutes. : D
HEY DOn'T teLL tHeM tHe ANSWER. :V
How to solve the triangle given one angle and 2 sides. I want help solving the problem not just an answer, thanks.
A. Use the law of cosines:
29² = 34² + c ² - 2•34•c cos(30.3°)
Use a calculator to solve for c ; notice this equation is quadratic, you get two possible solutions, c ≈ 5.973 ≈ 6 or c ≈ 52.738 ≈ 53.
Then use the law of sines to solve for the two possibles measures of angle C :
sin(30.3°)/29 = sin(C )/c
sin(C ) = c sin(30.3°)/29
sin(C ) ≈ 0.1039 or sin(C ) ≈ 0.9175
C ≈ 6.0° or C ≈ 66.6°
The interior angles of any triangle sum to 180°, so the remaining angle has measure either
B = 180° - 30.3° - C
B ≈ 143.7° or B ≈ 83.1°
So to recap,
B ≈ 143.7°, C ≈ 6.0°, c ≈ 6
and
B ≈ 83.1°, C ≈ 66.6°, c ≈ 53
Is (10,8) a solution of y =1/2x+3
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
1/2=.5 and .5x10=5, 5+3=8 so that proves it is correct.
f(x)=−3x 2 −6x+1 Find f(8)
Answer:
-239
Step-by-step explanation:
-3(8) 2-6(8)+1
-192-48+1
-240+1
=-239
Answer:
-239
Step-by-step explanation:
A:
Using this figure,
B' is the
of B.
reflection
prelmage
dilation
Image
Answer:
reflection
Step-by-step explanation:
The correct answer would actually be image... if you need to choose more than one option it could additionally be one of the other options but without a figure it's impossible to tell.
The advertising sticker on Allen's
new car says it gets 36 miles per
gallon on the highway. The graph
represents the actual relationship
between the number of miles Allen
drove on the highway and the
gallons of gasoline his new car used.
How does the advertised gas
consumption rate compare to the
actual rate?
Answer:
Step-by-step explanation:
The rate in this case is slope of the line. The formula of a slope is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
(10, 325)
(4, 130)
m = [tex]\frac{325-130}{10-4}[/tex] = [tex]\frac{195}{6}[/tex] = 32.5 miles per gallon
The actual rate is less (better) than advertising.
Solve the inequality 2x²+x-3<0
Answer:
[tex]-\frac{3}{2} <x<1[/tex]
Step-by-step explanation:
[tex]2x^{2} +3x-2x-3<0[/tex]
[tex]x(2x+3)-(2x+3)<0\\(2x+3)(x-1)<0\\When 2x+3=0 or x-1=0 \\x= -\frac{3}{2},1[/tex]
[tex]x<-\frac{3}{2} \\-\frac{3}{2} <x<1\\x<1[/tex]
answer asap..........
Answer:
Quadrant I: (⅓, 2⅓)
Quadrant II: (-1⅓, 3⅓)
Quadrant III: (-3, -10) (-3⅓, -1⅓)
Quadrant IV: (9, -1)
Step-by-step explanation:
If it is (+, +), it is in quadrant I.
If it is (-, +), it is in quadrant II.
If it is (-, -), it is in quadrant III.
If it is (+, -), it is in quadrant IV.
Two complex numbers have a product of 30 and positive integers as real parts. Write all possible combinations of such numbers.
Answer:
[tex][(1+i\sqrt{29}), (1-i\sqrt{29})][/tex], [tex][(1+i\sqrt{26}), (1-i\sqrt{26})][/tex], [tex][(1+i\sqrt{21}), (1-i\sqrt{21})][/tex],
[tex][(1+i\sqrt{14}), (1-i\sqrt{14})][/tex], and [tex][(1+i\sqrt{5}), (1-i\sqrt{5})][/tex].
Step-by-step explanation:
Given that two complex numbers have a product of 30 and the real part of the complex numbers are positive integers.
Let one complex number is [tex]a+ib[/tex] where [tex]a[/tex] is a positive integer and [tex]b[/tex] is a real number.
As the product of two complex numbers is a purely real number, so the other complex number must be the conjugate of the first complex number.
So, another complex number [tex]= a-ib[/tex]
As a product of both the numbers = 30
[tex]\Rightarrow (a+ib)(a-ib)=30 \\\\\Rightarroe a^2 - (ib)^2=30 \\\\\Rightarrow a^2 - (i^2b^2)=30 \\\\Rightarrow a^2 - (-1\times b^2)= 30[/tex] [as i^2=-1]
[tex]\Rightarrow a^2+b^2= 30 \\\\\Rightarrow b^2 = 30-a^2 \\\\[/tex]
[tex]\Rightarrow b=\pm \sqrt {30-a^2} \cdots(i)[/tex]
Now, as a is a positive integer, so by taking possible values of a, we can determine the values of b from the equation (i).
For [tex]a=1[/tex]
[tex]b=\pm \sqrt {30-1^2}=\pm \sqrt {29}[/tex]
The positive sign is for the one number and the negative sign is for the conjugate number (another number).
So, the 1st combination is [tex][(1+i\sqrt{29}), (1-i\sqrt{29})][/tex]
Similarly,
For [tex]a=2[/tex]
[tex]b=\pm \sqrt {30-2^2}=\pm \sqrt {26}[/tex]
So, the 2nd combination is [tex][(1+i\sqrt{26}), (1-i\sqrt{26})][/tex]
For [tex]a=3[/tex]
[tex]b=\pm \sqrt {30-3^2}=\pm \sqrt {21}[/tex]
So, the 3rd combination is [tex][(1+i\sqrt{21}), (1-i\sqrt{21})][/tex]
For [tex]a=4[/tex]
[tex]b=\pm \sqrt {30-4^2}=\pm \sqrt {14}[/tex]
So, the 4th combination is [tex][(1+i\sqrt{14}), (1-i\sqrt{14})][/tex]
For [tex]a=5[/tex]
[tex]b=\pm \sqrt {30-5^2}=\pm \sqrt {5}[/tex]
So, the 5th combination is [tex][(1+i\sqrt{5}), (1-i\sqrt{5})][/tex]
The higher integral value of [tex]a[/tex] is not possible for any real [tex]b[/tex].
Hence, the possible combinations of required numbers are
[tex][(1+i\sqrt{29}), (1-i\sqrt{29})][/tex], [tex][(1+i\sqrt{26}), (1-i\sqrt{26})][/tex], [tex][(1+i\sqrt{21}), (1-i\sqrt{21})][/tex],
[tex][(1+i\sqrt{14}), (1-i\sqrt{14})][/tex], and [tex][(1+i\sqrt{5}), (1-i\sqrt{5})][/tex].
how do you solve 4x+10=3x+37
Answer:
x = 27
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Equality PropertiesStep-by-step explanation:
Step 1: Define equation
4x + 10 = 3x + 37
Step 2: Solve for x
Subtract 3x on both sides: x + 10 = 37Subtract 10 on both sides: x = 27Step 3: Check
Plug in x to verify it's a solution.
Substitute: 4(27) + 10 = 3(27) + 37Multiply: 108 + 10 = 81 + 37Add: 118 = 118And we have our final answer!
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
Playing a game of roulette, where the wheel consists of slots numbered
00,0,1,2,...,48
To play the game, a metal ball is spun around the wheel and is allowed to fall
into one of the numbered slots.
Identify the sample space.
A). the sample space is (00,0)
B). the sample space is (00).
C). the sample space is (1,2,...,48)
D). the sample space is (00,0,1,2,...,48)
Answer:
D
Step-by-step explanation:
is _____. hjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj
Answer:
o.6
Step-by-step explanation:
I think sorry if wrong
Is the graph increasing, decreasing, or constant where -3
Probability gender of one child
Answer:
about 50% of a girl and 50% of a boy
Step-by-step explanation:
I hope this helps
Write an equation in slope-intercept form of the line shown.
Answer:
[tex] y = 2x - 5 [/tex]
Step-by-step explanation:
Find the slope using the points, (1, -3) and (3, 1):
[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 -(-3)}{3 - 1} = \frac{4}{2} = 2 [/tex]
m = 2
Find the y-intercept (b) by substituting x = 1, y = -3, and m = 2 in [tex] y = mx + b [/tex]
[tex] -3 = (2)(1) + b [/tex]
[tex] -3 = 2 + b [/tex]
Subtract 2 from both sides
[tex] -3 - 2 = 2 + b - 2 [/tex]
[tex] -5 = b [/tex]
[tex] b = -5 [/tex]
Plug in the value of m and b into the slope-intercept form equation, [tex] y = mx + b [/tex].
Thus:
[tex] y = 2x +(-5) [/tex]
✅[tex] y = 2x - 5 [/tex]
Please answer see the image
Answer:
39 km²Step-by-step explanation:
surface area of a square pyramid
= Area of base + 1/2 base perimeter * slant height
= (3 x 3) + (1/2 x (3*4) x 5)
= 9 + 30
= 39 km²
Solve six and two sixths times one and one half.
Answer:
9.5
Step-by-step explanation:
As Sally was shopping for a turkey tree for Thanksgiving, she looked at 48 trees. Of those, she found that 7/8 of them were too small. How many of the trees were too small?
Answer:
42 treesStep-by-step explanation:
48/1 x 7/8 = 6/1 x 7/1 (Simplify 48 and 8 because they have the common factor of 8)=42/1= 42Answer:
Forty-two (42) of the trees were too small.
Step-by-step explanation:
Find 7/8 of 48.
[tex]\frac{7}{8}[/tex] = 0.875
Multiply the quotient (0.875) by 48 to find [tex]\frac{7}{8}[/tex] of 48.
0.875 × 48 = 42
Two pools are being filled with water. To start, the first pool had 728 liters of water and the second pool was en pty. Water is being added to the first pool at a rate of 23 liters per minute. Water is being added to the second pool at a rate of 37 liters per minute. Let x be the number of minutes water has been added. Write an equation to show when the two pools would have the same amount of water. You do NOT need to solve this.
Answer:
52 minutes
Step-by-step explanation:
Equation:
[tex]728+23x=0+37x\\728+23x=37x\\728=14x\\x=52[/tex]
So 52 minutes.
Hope this helps plz hit the crown :D
(GIVING BRAINLIEST TO WHO HELPS ME!!)
What causes lightning?
A) Build up of electric charges in the clouds
B) Flow of electric charges among clouds
C) Light energy created in the clouds
D) Reflection of light by the clouds
Answer:
B
C and D are already out of the picture since we know lightning is not just light.
Answer:
Build up of electric charges in the clouds (A)
Step-by-step explanation:
A minor league baseball park has 6800 seats. Box seats cost $19, grandstand seats cost $9, and bleacher seats cost $4. When all seats are sold, the revenue is $61200. If the number of bleacher seats is 2 times the number of box seats, how many seats of each type are there?Box seats:_______ Grandstand seats:_______ Bleacher seats:______
Answer:
Step-by-step explanation:
Let us represent
The number of Box seats = x
The number of grandstand seats = y
The number of bleacher seats cost = z
A minor league baseball park has 6800 seats.
Hence,
x + y + z = 6800
Box seats cost $19, grandstand seats cost $9, and bleacher seats cost $4. When all seats are sold, the revenue is $61200.
Hence:
$19 × x + $9 × y + $4 × z = $61200
19x + 9y + 4 z = 61200
If the number of bleacher seats is 2 times the number of box seats
z = 2x
Hence we substitute
x + y + z = 6800
x + y + 2x = 6800
3x + y = 6800.... Equation 3
y = 6800 - 3x
For Equation 2, substituting 2x for z
19x + 9y + 4z = 61200
19x + 9y + 4(2x) = 61200
19x + 9y + 8x = 61200
27x + 9y = 61200...... Equation 4
Combining Equation 3 and 4
3x + y = 6800.... Equation 3
27x + 9y = 61200...... Equation 4
Note that:
y = 6800 - 3x
We substitute the above in Equation 4
27x + 9(6800 - 3x) = 61200
27x + 61200 - 27x = 61200
Box seats:_______ Grandstand seats:_______ Bleacher seats:______
PLEASE HELP ME FIRST ANSWER GETS BRAINLIST
Answer:
2 its given that cd bisects ab at e so that means e is midpoint of ab
3. vertically opposite angles
4.By SAS congruence
6.
Circumference is the same as the area of a circle.
a. True
b. False
Answer:
TRUE
Step-by-step explanation:
i just know it :>
A wolf population is growing exponentially. In 2011, 129 wolves were counted. By 2013, the population had reached 236 wolves. Write the equation representing the population N of wolves over time t. Write your answer in the form a(b)^t. Round your b value to 3 decimal places.
Answer:
129 [tex](1.3526)^{t}[/tex]
Step-by-step explanation:
Assuming N = [tex]ab^t[/tex]
t = number of years after 2011
N = number of wolves
When t = 0 , N = 129
129 = [tex]ab^0[/tex]
a = 129
N = 129[tex]b^{t}[/tex]
When t = 2 , N = 236
therefore 236 = 129 [tex]b^{2}[/tex]
[tex]b^{2}[/tex] = [tex]\frac{236}{129}[/tex]
therefore; b = 1.3526
Answer expressed in the form of a(b)^t.
129 [tex](1.3526)^{t}[/tex]
(GIVING BRAINLIEST ON THIS ONE!!)
Solve six and two sixths times one and one half.
A) eight and six twelfths
B) nine and six twelfths
C) ten and two twelfths
Answer:
B
Step-by-step explanation:
6 2/6 x 1 1/2
(6 x 6) + 2 = 38/6
(1 x 2) + 1 = 3/2
38/6 x 3/2 = 114/12.
114 ÷ 12 = 9 6/12
9 6/12 = 9 3/6 = 9 1/2.
B
Answer:
the answer is b) nine and six twelfths
Step-by-step explanation:
hoped that helped
5x-6y=-4
-6x+6y=-6
solve using elimination
HELP.
Answer:
x=10 y=9
Step-by-step explanation:
I only have 2 more including this pls help
Answer:
"Some irrational numbers are whole numbers" False
"All rational numbers are integers" False
"All integers are whole numbers" False
"No integers are irrational numbers" True
Step-by-step explanation:
I'm 100% sure of this