Answer: Per 1/2 an hour it is changes by 5 so the constanT rate would be: 5 inches per 1/2 an hour
Need help with this math problem
Answer:
[tex]f(x)=-5x-3[/tex].
Step-by-step explanation:
From the given machine diagram it is clear that:
[tex]f(x)=-8[/tex] at [tex]x=1[/tex]
[tex]f(x)=-13[/tex] at [tex]x=2[/tex]
[tex]f(x)=-18[/tex] at [tex]x=3[/tex]
It is clear that the value of f(x) decreasing by 5 when the value of x is increasing by 1.
Since the function changing at a constant rate, therefore it represents a linear function.
If a linear function passing through two points, then the equation of line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The given linear function passes through (1,-8) and (2,-13), therefore the linear equation is
[tex]y-(-8)=\dfrac{-13-(-8)}{2-1}(x-1)[/tex]
[tex]y+8=\dfrac{-5}{1}(x-1)[/tex]
[tex]y+8=-5(x-1)[/tex]
[tex]y=-5x+5-8[/tex]
[tex]y=-5x-3[/tex]
So, the required function is [tex]f(x)=-5x-3[/tex].
A line with a slope of -7 passes through the points (10,v) (9,4) What is the value of V?
Answer:
-3
Step-by-step explanation:
An increase in x-value from 9 to 10 is an increase of 1 unit. The slope of -7 tells you that the corresponding change in y will by -7 units:
v = 4 -7 = -3
The value of v is -3.
_____
Alternate solutions
You can see this easily on a graph, or you can use the equation of the line. We have a point and a slope, so the point-slope form is useful.
y = m(x -h) +k
y = -7(x -9) +4
For x=10, the value of y is ...
v = -7(10 -9) +4 = -7 +4
v = -3
A movie membership costs $10 a month plus an additional $5 for each movie purchased. If you have only budgeted to spend a maximum of $25 this month, how many movies can you purchase?
Answer:
3
Step-by-step explanation:
25-10/3=3
Answer:
3 movies
Step-by-step explanation:
You can pay for 3 movies because
5*3=15 and you have to pay for the membership which is 10 so
10+15=25
Classify this triangle.
Acute scalene triangle
Obtuse isosceles triangle
Right isosceles triangle
Right scalene triangle
Answer: right isosceles
Step-by-step explanation:
the angle at the bottom is right therefore you need to figure out the lengths of the sides to conclude if it is isosceles or scalene. because two of the sides are the same length and the other is not it is isosceles
which of the following is an expression for”doubling a number n and dividing by 3”?
Answer:
2n/3
Step-by-step explanation:
hope this helps!! moo
What is the measure of angle A?
Answer:
A = 19.47
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin A = 2/6
Take the inverse sin of each side
sin ^-1 ( sin A) = sin ^-1 (2/6)
A =19.47122063
To the nearest hundredth
A = 19.47
Water is leaking out of an inverted conical tank at a rate of 8200.08200.0 cm3/min cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 11.0 m11.0 m and the the diameter at the top is 4.5 m4.5 m. If the water level is rising at a rate of 16.0 cm/min16.0 cm/min when the height of the water is 3.0 m3.0 m, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Answer: cm3/min
Answer:
I' = 197,474.47 cm^3/min
the rate at which water is being pumped into the tank in cubic centimeters per minute is 197,474.47 cm^3/min
Step-by-step explanation:
Given;
Tank radius r = d/2 = 4.5/2 = 2.25 m = 225 cm
height = 11 m
Change in height dh/dt = 16 cm/min
The volume of a conical tank is;
V = (1/3)πr^2 h .....1
The ratio of radius to height for the cone is
r/h = 2.25/11
r = 2.25/11 × h
Substituting into equation 1.
V = (1/3 × (2.25/11)^2)πh^3
the change in volume in tank is
dV/dt = dV/dh . dh/dt
dV/dt = ((2.25/11)^2)πh^2 . dh/dt ....2
And change in volume dV/dt is the aggregate rate at which water is pumped into the tank.
dV/dt = inlet - outlet rate
Let I' represent the rate of water inlet and O' represent the rate of water outlet.
dV/dt = I' - O'
Water outlet O' is given as 8200 cm^3/min
dV/dt = I' - 8200
Substituting into equation 2;
I' - 8200 = ((2.25/11)^2)πh^2 . dh/dt
I' = ((2.25/11)^2)πh^2 . dh/dt + 8200
h = 3.0 m = 300 cm (water height)
Substituting the given values;
I' = ((2.25/11)^2)×π×300^2 × 16 + 8200
I' = 197,474.47 cm^3/min
the rate at which water is being pumped into the tank in cubic centimeters per minute is 197,474.47 cm^3/min
6
An ordinary fair dice is thrown once.
(a) On the probability scale mark with a cross (X) the probability ti
the dice lands on an even number.
1
2
(b) Write down the probability that the dice lands on a number les
than 3.
Answer:
(a) 1/2(b) 1/3Step-by-step explanation:
(a) 3 of the 6 numbers on the die are even, so the probability that one of them will show is 3/6 = 1/2.
__
(b) 2 of the 6 numbers on the die are less than 3, so the probability that one of them will show is 2/6 = 1/3.
Graph the circle (x-3)^2+(y-7)^2=4
Please help ASAP! Will give BRAINLIEST! Please read the questionTHEN answer correctly! No guessing.
Answer:D
Step-by-step explanation:
(4/5)^0
4^0/5^0=1/1=1
A music professor offers his 40 students the option of coming to an additional rehearsal session the week before their juries (musical final exams.) In order to decide whether these extra sessions actually help students, he keeps track of who attends them and compares their jury scores to those of students who did not schedule extra sessions. This study is a(n): A) matched pairs design. B) randomized block design. C) nonrandomized experiment. D) observational study. E) completely randomized experiment.
Answer:
D. Observational Study
Explanation:
An observational study is one in which all the participants are subjected to a common treatment and then compared to people who did not receive the same treatment. This is the case with the students who where subjected to the same treatment; an additional rehearsal session. They are then observed by the professor and compared to those who did not participate in the experiment.
This is also an example of a cohort observational study. A cohort observational study is one in which all the participants have a common uniting factor. They are made to undergo a treatment and then compared to those who did not receive the treatment. This type of study is subject to bias because a positive or negative result might be because of other factors not related to the study.
Find two numbers for which the sum is 101 and the difference is 47
Answer:
74 and 27
Step-by-step explanation:
let x and y be the numbers
x + y =101........eqn 1
x - y = 47.......eqn 2
solve simultaneously
from equation 2, make x the subject
x= 47 + y........eqn 3
put eqn 3 into eqn 1
(47+y) + y = 101
47 + 2y = 101
2y= 101 - 47
2y=54
y= 54/2
y= 27
put y=27 into eqn 3
x = 47 + 27
x = 74
Two terms of an arithmetic sequence are a12=70 and a30=124. Write an explicit rule for the nth term.
Answer:
Tn = 34-3nStep-by-step explanation:
The formula for calculating the nth term of an arithmetic sequence is given as;
Tn = [tex]a+(n-1)d[/tex]
a is the first term
n is the number of terms
d is the common difference
If two terms of an arithmetic sequence are a12=70 and a30=124 then;
T12 = a+(12-1)d = 70
T12 = a+11d = 70...(1)
T30 = a+(30-1)d = 124
T30 = a+29d = 124...(2)
Solving equation 1 and 2 simultaneously to get a and d;
Taking the difference of both equation we have;
29d - 11d = 124-70
18d = 54
d = 54/18
d = 3
Substituting d=3 into equation 1 to get the value of 'a' we have;
a+11(3) = 70
a+33=70
a = 70-33
a = 37
To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3
Tn = 37+(n-1)3
Tn = 37+3n-3
Tn = 34-3n
This gives the required nth term
Brittany Monroe is a legal secretary. Her biweekly salary is $1,650.00 what is her annual salary?
Answer:
$42,900 a year
Step-by-step explanation:
so there are 26 bi-weeks in a year. (fun fact)
you take $1,650 and multiply that biweekly to get her annual salary.
1650*26=42,900
how many tenths are in 4600
Answer:
4600 tenths as a Fraction
Since 4600 tenths is 4600 over ten, 4600 tenths as a Fraction is 4600/10.
4600 tenths as a Decimal
If you divide 4600 by ten you get 4600 tenths as a decimal which is 460.00.
4600 tenths as a Percent
To get 4600 tenths as a Percent, you multiply the decimal with 100 to get the answer of 46000 percent.
4600 tenths of a dollar
First we divide a dollar into ten parts where each part is 10 cents. Then we multiply 10 cents with 4600 and get 46000 cents or 460 dollars and 0 cents.
Step-by-step explanation:
Hope this helped!
Stay safe!!!
Answer:
Step-by-step explanation:
To answer this, multiply 4600 by 10: 46000. There are 46000 tenths in 4600.
Help ASAP giving BRAINLIEST! Am i correct?
Answer:
You are correct
Step-by-step explanation:
x - 8 < 23
Add 8 to both sides
x - 8 + 8 < 23 + 8
Simplify
x < 31
Yes, you are correct.
256 divided by -16 with steps.
Answer:
256÷-16=16
Step-by-step explanation:
The complete expression is 256 divided by -16 is -16
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
256 divided by -16 = what
When represented as an equation, we have
Result = 256 divided by -16
Make the result the subject of the formula
So, we have
Result = 256/-16
Rewrite as
Result = -256/16
Evaluate the quotient
Result = -16
Hence, the number is -16
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Sara goes on a slingshot ride in an amusement park. She is strapped into a spherical ball that has a radius of centimeters. What is the volume of air in the spherical ball? Use this formula: , where r is the sphere’s radius.
A.
B.
C.
D.
Answer:
A. 4×π×3²×[tex]10^{6}[/tex]
Step-by-step explanation:
r = 3×10² = 3×100 = 300
[tex]\frac{4}{3}[/tex]×π×300³=
[tex]\frac{4}{3}[/tex]×π×27,000,000=
[tex]\frac{108,000,000}{3}[/tex]×π=
36,000,000π
Answers solved:
A. 36,000,000π
B. 108,000,000π
C. 3,600,000π
D. 32,400,000π
The solution is Option A.
The volume of the air in the spherical ball is given by the equation
V = 4π ( 3 )² ( 10 )⁶ cm³
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the volume of the sphere be represented as V
Now , the radius of the spherical ball be r
The value of r = 3 ( 10 )² cm
So , the volume of the spherical ball = ( 4/3 ) πr³
Substituting the values in the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x [ 3 ( 10 )² ]³
On simplifying the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x ( 3 )³ ( 10 )⁶
Volume of the spherical ball V = 4 x π x ( 3 )² ( 10 )⁶
Therefore , the value of V is 4π ( 3 )² ( 10 )⁶
Hence , the volume of the spherical ball is 4π ( 3 )² ( 10 )⁶
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Equations
What is the solution of the system of linear equations?
-3x + 4y = -18
2x - y = 7
(-2,-3)
(-2,3)
(2, -3)
(2, 3)
Answer:
Step-by-step explanation:
-3x + 4y = -18
8x - 4y = 28
5x = 10
x = 2
4 - y = 7
-y = 3
y = -3
(2, -3)
The solution of the system of linear equations given is (2,-3), the correct option is C.
What is System of Linear Equation?The system of linear equation is set of equations which have a common solution.
The equations are
-3x+4y = -18
2x-y =7
The linear equations can be solved using substitution method
y = 2x -7 from equation 2 will be substituted in equation 1
-3x +4 ( 2x -7) = -18
-3x +8x -28 = -18
5x = 10
x = 2
y = 2 * 2 -7 = -3
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What is the number of possible permutations of 5 objects taken 2 at a time? A. 10 B. 20 C. 60 D. 120
Answer:
B. 20
Step-by-step explanation:
5P2 is equal to 20 using the permutation formula.
There are five families that each have one child. Each of them hires Riley as a babysitter. Because the children she babysits are different ages, Riley charges each family a different amount. To visualize her earnings, Riley recorded and plotted her pay from each job. Using the scatterplot, calculate her average rate of pay.
Answer:
Average Rate of Pay = $ 5.23 /hr
Step-by-step explanation:
We have a data in form of Hours of Baby Sitting and Amount of Pay. Since the Amount of pay depends upon the Hours of Baby Sitting. Thus, we take y = Amount of Pay, while x = Hours of Baby Sitting. So, the data becomes:
x (Hours) = 12 13 16 17 20
y ($) = 54 56 65 64 100
The statistical data calculated is:
∑x = 78, ∑x² = 1258, ∑y = 339, ∑xy = 5504, n = no. of data points = 5
Now, we use linear regression model to fit a straight line to this data.
y = a + bx --------- eqn (1)
where,
b = [ n∑xy - ∑x.∑y]/[n∑x² -(∑x)²]
b = [ (5)(5504) - (78)(339)]/[(5)(1258) - (78)²]
b = 5.23
and,
a = (∑xy - b∑x²)/∑x
a = [5504 - (5.23)(1258)]/78
a = -13.83
Therefore, eqn (1) becomes:
y = -13.83 + 5.23x
The graph plot of this straight line fit is provided in the attachments.
Now, we derivate the equation with respect to x, to get the average rate of pay:
Average Rate of Pay = dy/dx = d/dx(-13.83 + 5.23x)
Average Rate of Pay = $ 5.23 /hr
Determine if the set of vectors shown to the right is a basis for IR3 If the set of vectors is not a basis, determine whether it is linearly independent and whether the set 311-4 spans R 12 Which of the following describe the set?
A. The set is a basis for R3
B. The set is linearly independent.
C The set spans R3
D. None of the above
Answer:
The problem is clearly solved in the attachment
Apply the distributive property to factor out the greatest common factor of all three terms. Explanation: 9-12x+6y what is the answer??
Answer: [tex]3(3-4x+2y)[/tex]
Step-by-step explanation:
[tex]9-12x+6y[/tex]
[tex]3(3-4x+2y)[/tex]
Which value has an absolute deviation of 5 from the mean of this data set?
26, 12, 35, 28, 14
A 28
B. 35
C. 26
D. 14
Answer: 28
Step-by-step explanation: see prev. explanation
The absolute deviation of 5 from the mean of this data set is 28.
What is absolute deviation?
Absolute deviation is "the distance between each data point to the mean".
According to the question,
The data set is 26, 12, 35, 28, 14
Average of the data set = [tex]\frac{sum of the data value }{Total number of observation}[/tex]
= [tex]\frac{26+12+35+28+14}{5}[/tex]
= [tex]\frac{115}{5}[/tex]
= 23.
Thus, the average of the data set is 23.
In order to find absolute deviation of 5 subtract each data point from the mean.
26 - 23 = |3| = 3
12 - 23 = |-11| = 11
35 - 23 = |12| = 12
28 - 23 = |5| = 5
14 - 23 = |-9| = 9.
Hence, the absolute deviation of 5 is from the mean of the data set is 28.
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A number pattern starts with 10 and follows the rule "multiply by 3." What is true
about all of the numbers in this pattern?
what is the best college to go to?
Answer:
The the best college to go to is the one where you feel comfortable.
Step-by-step explanation:
It is so important to understand the sence of what is actually "the best" college to go to.
You can look at that from a viriety of perspectives, and it is debatable to just go for the college which holds the highest rank on some site.
There are a lot of factors to consider, and what is generally considered the best college does not necassarilly the right one for you.
Ask your loved ones for advice and if you can take a look at yourvtop thee collages.
The the best college to go to is the one where you feel comfortable.
Which figure below has point symmetry
Answer:
Figure D
Step-by-step explanation:
Point Symmetry is when every part has a matching part: the same distance from the central point. but in the opposite direction. Hope this helps! :)
help plz now quick if right brain list
Answer:
c= 5 yards.
Step-by-step explanation:
4*1.5=6
30/6= 5
A fraction that is equivalent to 6/-5?
Answer:
12/-10
Step-by-step explanation:
Any multiple of a fraction is the equivalent of the original fraction, the only difference is that it wont be fully simplified. If we multiply the original fraction (6/-5) by 2, both the numerator and denominator, you will get 12/-10.
Answer:
12/-10
Step-by-step explanation:
6/-5
6×2= 12
-5×2=-10
12/-10
Two samples each of size 20 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 43.5 and standard deviation of 4.1 while the second sample has a mean of 40.1 and standard deviation of 3.2. A researcher would like to test if there is a difference between the population means at the 0.05 significance level. What can the researcher conclude?
Answer:
[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]
The degrees of freedom are
[tex]df=20+20-2=38[/tex]
And the p value is given by:
[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Step-by-step explanation:
When we have two independent samples from two normal distributions with equal variances we are assuming that
[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]
And the statistic is given by this formula:
[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]
Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:
[tex]S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]
The system of hypothesis on this case are:
Null hypothesis: [tex]\mu_1 = \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]
We have the following data given:
[tex]n_1 =20[/tex] represent the sample size for group 1
[tex]n_2 =20[/tex] represent the sample size for group 2
[tex]\bar X_1 =43.5[/tex] represent the sample mean for the group 1
[tex]\bar X_2 =40.1[/tex] represent the sample mean for the group 2
[tex]s_1=4.1[/tex] represent the sample standard deviation for group 1
[tex]s_2=3.2[/tex] represent the sample standard deviation for group 2
First we can begin finding the pooled variance:
[tex]\S^2_p =\frac{(20-1)(4.1)^2 +(20 -1)(3.2)^2}{20 +20 -2}=13.525[/tex]
And the deviation would be just the square root of the variance:
[tex]S_p=3.678[/tex]
The statistic is givne by:
[tex]t=\frac{(43.5 -40.1)-(0)}{3.678\sqrt{\frac{1}{20}+\frac{1}{20}}}=2.923[/tex]
The degrees of freedom are
[tex]df=20+20-2=38[/tex]
And the p value is given by:
[tex]p_v =2*P(t_{38}>2.923) =0.0058[/tex]
Since the p value for this cae is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true means for this case are significantly different
Using the t-distribution, as we have the standard deviation for the sample, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.
What are the hypothesis tested?At the null hypothesis, it is tested if there is no difference, that is:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, it is tested if there is a difference, that is:
[tex]H_a: \mu_1 - \mu_2 \neq 0[/tex]
What is the mean and the standard error of the distribution of differences?For each sample, we have that they are given by
[tex]\mu_1 = 43.5, s_1 = \frac{4.1}{\sqrt{20}} = 0.9168[/tex]
[tex]\mu_2 = 40.2, s_2 = \frac{3.2}{\sqrt{20}} = 0.7155[/tex]
Hence, for the distribution of differences, the mean and the standard error are given by:
[tex]\overline{x} = \mu_1 - \mu_2 = 43.5 - 40.2 = 3.3[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.9168^2 + 0.7155^2} = 1.163[/tex]
What is the test statistic?It is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{3.3 - 0}{1.163}[/tex]
[tex]t = 2.84[/tex]
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 20 + 20 - 2 = 38 df, the critical value is of [tex]|z^{\ast}| = 2.0244[/tex].
Since the absolute value of the test statistic is greater than the critical value, it is found that the researcher can conclude that there is a difference between the population means at the 0.05 significance level.
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