Answer:
An exponential function is written in the form of f(x) = a (b)x. When we want to find an initial value of 500, it means that when x = 0, then y must equal 500. So, you plug in 0 to x in the exponential function, which leaves you with f(0) = a. Then, since f(0) = 500, that means a = 500
Hope this will help! =)
Step-by-step explanation:
Lia has a dog and a cat the pets weigh 16 pounds The dog weighs 3 times as much as the cat
Answer:
The weight of the dog is 12 pounds and the weight of the cat is 4 pounds.
Step-by-step explanation:
Let d represent the weight of the dog. Let c represent the weight of the cat.
Let's make a system of equations.
d+c=16
d=3c
We can use subsitution.
3c+c=16
4c=16
c=4
We can subsitute back into one of the two equations to find the weight of the dog.
d=3c
d=3(4)
d=12
The weight of the dog is 12 pounds and the weight of the cat is 4 pounds.
When you cough,the radius of your trachea (windpipe) decreases,affecting the speed S of the air in the trachea. If r0 is the normal radius of the trachea, the relationship between the speed S of the air and the radius r of the trachea during a cough is given by a function of the form
S(r) = (r0 - r) ar^2
where a is positive constant. Find the radius r for which the speed of the air is greatest.
Answer: 2r(0)/3.
Step-by-step explanation:
So, we are given one Important data or o or parameter in the question above and that is the function of the form which is given below(that is);
S(r) = (r0 - r) ar^2 -----------------------------(1).
We will now have to differentiate S(r) with respect to r, so, check below for the differentiation:
dS/dr = 2ar (r0 - r ) + ar^2 (-1 ) ---------;(2).
dS/dr = 2ar(r0) - 2ar^2 - ar^2.
dS/dr = - 3ar^2 + 2ar(r0) ------------------(3).
Note that dS/dr = 0.
Hence, - 3ar^2 + 2ar(r0) = 0.
Making ra the subject of the formula we have;
ra[ - 3r + 2r(0) ] = 0. -------------------------(4).
Hence, r = 0 and r = 2r(0) / 3.
If we take the second derivative of S(r) too, we will have;
d^2S/dr = -6ar + 2ar(0). -------------------(5).
+ 2ar(0) > 0 for r = 0; and r = 2r(0)/3 which is the greatest.
Answer:
[tex]r =\frac{2r_{0}}{3}[/tex]
Step-by-step explanation:
We need to take the derivative of S(r) and equal to zero to maximize the function. In this conditions we will find the radius r for which the speed of the air is greatest.
Let's take the derivative:
[tex]\frac{dS}{dr}=a(2r(r_{0}-r)+r^{2}(-1))[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-2r^{2}-r^{2})[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-3r^{2})[/tex]
[tex]\frac{dS}{dr}=ar(2r_{0}-3r)[/tex]
Let's equal it to zero, to maximize S.
[tex]0=ar(2r_{0}-3r)[/tex]
We will have two solutions:
[tex]r = 0[/tex]
[tex]r =\frac{2r_{0}}{3}[/tex]
Therefore the value of r for which the speed of the air is greatest is [tex]r =\frac{2r_{0}}{3}[/tex].
I hope it helps you!
Needs help with this
Answer:
m<1 = 50°
m<2 = 130°
m<3 = 50°
m<4 = 130°
m<5 = 50°
m<6 = 130°
m<7 = 50°
m<8 = 130°
Step-by-step explanation:
Angle 4 & Angle 2 are congruent angles because they are diagonal from each other, this lets us set m<4 = m<2.
Then solve for x.
2x-10 = x+60
x-10 = 60
x = 70
Use x to find m<4 or m<2 (doesn't matter which b/c they are equal).
m<2 = (70)+60
m<2 = 130°
Angles 2, 4, 6 & 8 are congruent, so they will all have be 130°.
Angles 1 & 2 create a straight line (180°).
Find m<1 by subtracting 130° from 180°.
180-130 = 50
Angles 1, 3, 5 & 7 are also congruent, so they will all have be 50°.
Volume of a sphere in terms of π with a radius of 2
Answer:
33.51
Step-by-step explanation:
You need to use the equation [tex]\frac{4}{3} \pi r[/tex]³.
Hope this helps.
Answer:10.7π
Step-by-step explanation:
radius=r=2
volume of sphere=4/3 x π x r x r x r
Volume of sphere=4/3xπx2x2x2
Volume of sphere=(4xπx2x2x2) ➗ 3
Volume of sphere=32π ➗ 3
Volume of sphere=10.7π
please answer this correctly I have to finish this today as soon as possible
Estimate the measure of this angle within 10°.
The length of a rectangle is 3 feet less than 4 times the width. The perimeter is 34 feet
A.equation ?
B width ?
C.length?
A.Equation
Step-by-step explanation:
A. Equation 30 plus 4
Whats is the 6+8-16
Answer:
-2
Step-by-step explanation:
6+8 equals 14. 14-16 equals -2
Answer: The importance of learning is that it helps the individual to acquire the necessary skills through learning and knowledge so that he can achieve his set goals. An important fact about learning is that it is a means to improve knowledge and gain skills that will help in reaching specific goals
Step-by-step explanation:
The importance of learning is that it helps the individual to acquire the necessary skills through learning and knowledge so that he can achieve his set goals. An important fact about learning is that it is a means to improve knowledge and gain skills that will help in reaching specific goals
A paper describes a study of the use of MRI (Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was to determine if MRI exams do a better job than mammograms of determining if women who have recently been diagnosed with cancer In one breast have cancer in the other breast. The study participants were 980 women who had been diagnosed with cancer in one breast and for whom a mammogram did not detect cancer in the other breast.
These women had an MRI exam of the other breast, and 131 of those exams indicated possible cancer. After undergoing biopsies, it was determined that 40 of the 131 did in fact have cancer in the other breast, whereas 91 did not. The women were all followed for one year, and two of the women for whom the MRI exam did not indicate cancer in the other breast were subsequently diagnosed with cancer that the MRI did not detect.
Suppose that for women recently diagnosed with cancer In only one breast, the MRI is used to decide between the two "hypotheses.
H0: woman has cancer in the other breast
Ha: woman does not have cancer In the other breast
(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.)
A) One possible error would be deciding that a woman who does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?
B) There Is a second type of error that is possible In this setting. Describe this error.
A Type II error would be coming to the conclusion that the woman_______cancer in the other breast when in fact she_______cancer in the other breast.
Answer:
Step-by-step explanation:
A type I error occurs when the null hypothesis is rejected in favor of the alternative hypothesis when the null hypothesis is actually true.
A type II error occurs when the researcher fails to reject the null hypothesis when the null is false.
H0: woman has cancer in the other breast
Ha: woman does not have cancer In the other breast
A) One possible error would be deciding that a woman who does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?
This error is a type I error as the patient does have cancer which should warrant failing to reject the null but the null was rejected in favour of the alternative.
A Type II error would be coming to the conclusion that the woman does have cancer in the other breast when in fact she does not have cancer in the other breast.
This is a second type of error that can occur and it is a type II error: failing to reject the null when not true.
Drag graph to show a graph of each equation in the table
Answer:
see below
Step-by-step explanation:
The equations you have are in "slope-intercept form." The slope of the line is the coefficient of x. The y-intercept is the added constant.
Both the slopes and intercepts take on the values ±2 and ±1/2. This requires that you understand what each value looks like on the graph.
A slope of 2 will have a rise of 2 units for each run of 1 unit to the right. A graph with a slope of 2 will have a relatively steep line going upward to the right. (A slope of -2 will be a steep line going downward to the right.)
Similarly, a slope of 1/2 will have a rise of 1 unit for each two units to the right. A line with this slope will go up to the right with a less-steep rise. There is only one graph in the group with a slope of 1/2. Of course, a line with a slope of -1/2 will have a shallow angle down to the right.
__
The y-intercept is where the line crosses the y-axis (the dark vertical line in the middle of the graph, labeled y). The y-intercepts at ±1/2 are somewhat difficult to determine for the steep lines. (A careful look is needed.) However, the y-intercepts of ±2 are easily seen for the shallow lines.
The various graphs are sorted in the attachment.
A calzone is divided into 24 equal pieces. Sophie and Glenn each ate one-fourth
of the calzone on Saturday. The next day, Glenn ate one-sixth
of the calzone that was leftover. How many of the pieces of the original calzone remain? Explain your reasoning.
Answer:
10 pieces
Step-by-step explanation:
Total no. of pieces of calzone = 24
No of pieces of calzone eaten by sophie = 1/4 of Total no. of pieces of calzone = 1/4 of 24 = (1/4)*24= 6 pieces.
No of pieces of calzone eaten by Glenn = 1/4 of Total no. of pieces of calzone = 1/4 of 24 = (1/4)*24= 6 pieces.
Total no of pieces eaten by both of them on saturday = 12.
No of pieces of calzone left = 24-12 = 12
_______________________________________________
No of pieces of calzone eaten by Glenn on next day = 1/6 of Total no. of pieces of calzone left= 1/6 of 12 = (1/6)*12= 2 pieces
No of pieces of calzone left now after Glenn ate 2 of them = 12-2 = 10.
Thus 10 pieces of original calzone are left .
Suppose a 3x6 coefficient matrix for a system has three pivot columns. Is the system consistent? Why or why not? Choose the correct answer below. A. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have seven columns, could have a row of the form [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system could be inconsistent. B. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have seven columns, must have a row of the form [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system is inconsistent. C. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have seven columns and will not have a row of the form [Start 1 By 7 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 6st Column 0 7st Column 1 EndMatrix ], so the system is consiste
Answer:
Check the explanation
Step-by-step explanation:
All the 5 rows of the coefficient matrix (since it is of order 5×8) will have a pivot position. The augmented matrix obtained by adding a last column of constant terms to the 8 columns of the coefficient matrix will have nine columns and will not have a row of the form [0 0 0 0 0 0 0 0 1]. So the system is consistent.
Unlike most packaged food products, alcohol beverage container labels are not required to show calorie or nutrient content. An article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories. The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88. Does this data suggest that the true average estimated calorie content in the population sampled exceeds the actual content
Answer:
We conclude that the true average estimated calorie content in the population sampled exceeds the actual content.
Step-by-step explanation:
We are given that an article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories.
The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88.
Let [tex]\mu[/tex] = true average estimated calorie content in the population sampled.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 153 calories {means that the true average estimated calorie content in the population sampled does not exceeds the actual content}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 153 calories {means that the true average estimated calorie content in the population sampled exceeds the actual content}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean estimated calorie level = 193 calories
s = sample standard deviation = 88
n = sample of individuals = 58
So, the test statistics = [tex]\frac{193-153}{\frac{88}{\sqrt{58} } }[/tex] ~ [tex]t_5_7[/tex]
= 3.462
The value of t test statistics is 3.462.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical value of 1.6725 at 57 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 3.462 > 1.6725, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the true average estimated calorie content in the population sampled exceeds the actual content.
What is the area of a circle with a radius of 2.1cm? Use 3.14 for π.
Answer: I got's you lol
A≈13.85cm²
And the radius is 2.1
Step-by-step explanation:
Hope this helps let me know :)
Answer:
A= 13.8474
Step-by-step explanation:
The formula for the area of a circle is A= πr^2 (pi times r, or radius, squared).
So if you insert the values into the formula you have....
A= 3.14(2.1 cm)^2
You can use a calculator from there to get....
A= 13.8474
Which unit would be best for measuring the thickness of a coin?
kilometer
()) centimeter
meter
)) milli
Answer:
Since 1 mm = . 03937 inches, mm would seem to be the units appropriate for defining the thickness of a coin measuring 2 units.
Step-by-step explanation:
30 points!
The soccer team knows that if they score at least 8 goals, they will win the game. Which of the following inequalities shows the number of goals the team needs to win.
g ≥ 8 goals
g < 8 goals
g > 8 goals
g ≤ 8 goals
Answer:
g≥8
Step-by-step explanation:
They need at least 8 goals
g≥8
Answer:
g ≥ 8 goals
Step-by-step explanation:
Atleast 8 means greater than or equal to 8
A vendor at a street fair sells popcorn in cones, all of height 9 inches. The
sharing-size cone has 3 times the radius of the skinny-size cone. About how
many times more popcorn does the sharing cone hold than the skinny cone?
Answer:
The sharing cone holds about 9 times more popcorn than the skinny cone.
Step-by-step explanation:
The volume of a cone is given by the following formula:
[tex]V = \frac{\pi r^{2}h}{3}[/tex]
In which r is the radius and h is the height.
Two cones:
Both have the same height.
The sharing-size cone has 3 times the radius of the skinny-size cone.
Skinny:
radius r, height h. So
[tex]V_{sk} = \frac{\pi r^{2}h}{3}[/tex]
Sharing size:
radius 3r, height h. So
[tex]V_{sh} = \frac{\pi (3r)^{2}h}{3} = \frac{9\pi r^{2}h}{3} = 3\pi r^{2}h[/tex]
About how many times more popcorn does the sharing cone hold than the skinny cone?
[tex]r = \frac{V_{sh}}{V_{sk}} = \frac{3\pi r^{2}h}{\frac{\pi r^{2}h}{3}} = \frac{3*3\pi r^{2}h}{\pi r^{2}h} = 9[/tex]
The sharing cone holds about 9 times more popcorn than the skinny cone.
The Empire State Building weighs about 7.3×108pounds. The One World Trade Center building weighs about 88,200,000 pounds. What is the total weight, in pounds, of these two buildings? Expressing your answer in scientific notation in the form a×10b, what are the values of a and b?
Answer:
[tex]8.182X10^8 $pounds[/tex]
a=8.182 and b=8
Step-by-step explanation:
Weight of the Empire State Building =[tex]7.3X 10^8[/tex] pounds.
Weight of the One World Trade Center building= 88,200,000 pounds.
=[tex]8.82 X 10^7[/tex]
The addition of the two:
[tex]=7.3X 10^8+8.82 X 10^7\\$To make it easier to add, express both as powers of 8\\=7.3X 10^8+0.882 X 10^8\\=(7.3+0.882)X10^8\\=8.182X10^8 $ pounds[/tex]
Comparing with the form: [tex]aX10^b[/tex]
a=8.182 and b=8
change 5 out of 19 to a percentage
Answer:
26.3%
Step-by-step explanation:
5 is divided by 19
That answer is then multiplied by 100.
You may round your answer to the nearest whole number.
Solve for x .
18 ÷ x = -2
x =
Answer:
x = -9
Step-by-step explanation:
18 ÷ x = -2
18/x = -2/1
Cross multiplying, we get
-2x = 18
x = 18/-2
x = -9
hope it helps!
Anyone know the answer?
Answer:11 25/64 In^3
Step-by-step explanation:
Length =2 1/4
Volume of cube=L x L x L
Volume=2 1/4 x 2 1/4 x 2 1/4
Volume=9/4 x 9/4 x 9/4
Volume=(9x9x9) ➗ (4x4x4)
Volume=729 ➗ 64
Volume=11 25/64
Write an equation in slope-intercept form for the line that passes through (4,-4) and parallel to 3 +4x=2y-9
Answer:
y=-2x-12
Step-by-step explanation:
Make the equation into slope intercept form
-2y=-4x-12
divide by -2
y=2x+6
since the line is parallel the slope is the same
y=2x+b
plug in (4,-4)
-4=8+b
b=-12
y=-2x-12
*ill give you BRAINLIST * (have to get it right ) Write the equation of the line with the given slope and y-intercept.
slope = 1
y-intercept = - 3/7
Answer:
Y=x-3/4
Step-by-step explanation:
slope intercept form
(slope=x)(1x=x)
What is the value of a in the equation below? 2a + 3 = 4a + 5
Please show work :)
Solve (3x+7)=4x for x
Answer:
x=7
Step-by-step explanation:
(3x+7)=4x
Subtract 3x from each side
(3x+7) -3x=4x-3x
7 = x
Three cube-shaped boxes are stacked one above the other. The volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters. What is the height of the stacked boxes in meters?
A.
19
B.
29
C.
30
D.
31
Answer:
D. 31
Step-by-step explanation:
The edge dimension of a cube is the cube root of the volume. For the two boxes that are 1331 m³, the height is ...
∛(1331 m³) = 11 m
For the box that is 729 m³, the height is ...
∛(729 m³) = 9 m
Then the total height of the stack of boxes is ...
11 m + 11 m + 9 m = 31 m
Answer:
31
Step-by-step explanation:
I took the test on Edmentum, have a good day hope it helps :)
Round 38 to the nearest ten. Enter your answer in the box below.
Answer:
40
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Here are the rules;
• If the number undergoing the rounding is followed by 5, 6, 7, 8, or 9, round the number up
• If the number undergoing the rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Example: 32 and 38 rounded to the nearest ten is 30 and 40 respectively.
Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.
Suppose it takes about 0.5 seconds to hear the echo. How far away is the canyon wall, in feet?
feet
Now let's generalize that result. Suppose it takes n seconds to hear the echo. How far away is the canyon wall, in terms of n?
Answer:
The sound takes time to go to a point and reflect back to your position.
It means the sound went twice a distance.
=> Suppose it takes about 0.5 seconds to hear the echo, the canyon wall would be [750 x (0.5/3600)]/2 = 0.052 miles
=> Suppose it takes about n seconds to hear the echo, the canyon wall would be [750 x (n/3600)]/2 miles
Hope this helps!
:)
The distance the canyon wall is away is 33000 feet.
The distance the canyon is away in terms of n is 66000n feet.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Speed = 750 miles per hour
Time = 0.5 seconds
Distance = Speed x Time
Now,
1 mile = 5280 feet
750 miles = 3960000 feet
1 hour = 60 seconds
So,
Speed = (3960000/60) feet per second
Distance = 66000 x 0.5 feet = 33000 feet
This means,
The canyon wall is 33000 feet away.
Now,
For n seconds,
The canyon wall is 66000n feet away.
Thus,
The canyon wall is 33000 feet away.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
Element X decays radioactively with a half-life of 14 minutes if there are 680 grams of element X how long to the nearest 10th of a minute would it take the element to decay 17 grams
Answer:
It would take 74.5 minutes for the element to decay 17 grams.
Step-by-step explanation:
The amount of element X after t minutes is given by the follwoing equation:
[tex]X(t) = X(0)e^{rt}[/tex]
In which X(0) is the initial amount of the substance and r is the decay rate.
Half life of 14 minutes.
This means that [tex]X(14) = 0.5X(0)[/tex]
So
[tex]X(t) = X(0)e^{rt}[/tex]
[tex]0.5X(0) = X(0)e^{14r}[/tex]
[tex]e^{14r} = 0.5[/tex]
[tex]\ln{e^{14r}} = \ln{0.5}[/tex]
[tex]14r = \ln{0.5}[/tex]
[tex]r = \frac{\ln{0.5}}{14}[/tex]
[tex]r = -0.0495[/tex]
So
[tex]X(t) = X(0)e^{-0.0495t}[/tex]
There are 680 grams of element X
This means that [tex]X(0) = 680[/tex]
[tex]X(t) = X(0)e^{-0.0495t}[/tex]
[tex]X(t) = 680e^{-0.0495t}[/tex]
How long would it take the element to decay 17 grams
This is t for which X(t) = 17. So
[tex]X(t) = 680e^{-0.0495t}[/tex]
[tex]17 = 680e^{-0.0495t}[/tex]
[tex]e^{-0.0495t} = \frac{17}{680}[/tex]
[tex]e^{-0.0495t} = 0.025[/tex]
[tex]\ln{e^{-0.0495t}} = \ln{0.025}[/tex]
[tex]-0.0495t = \ln{0.025}[/tex]
[tex]0.0495t = -\ln{0.025}[/tex]
[tex]t = -\frac{\ln{0.025}}{0.0495}[/tex]
[tex]t = 74.5[/tex]
It would take 74.5 minutes for the element to decay 17 grams.
PLEASE HELP!!! WILL MARK AS BRAINLIEST!!!
A colony of 300 bacteria doubles in size every 22 minutes can be represented by the exponential function y=300(2)x. If you want to know how many bacteria will be present about 66 minutes, what should you plug in for x?
Answer:
[tex] y = 300 (2)^x[/tex]
Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:
[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]
So then we need to replace the value of x =3 and we got:
[tex] y= 300 (2)^3 = 2400[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] y = 300 (2)^x[/tex]
Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:
[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]
So then we need to replace the value of x =3 and we got:
[tex] y= 300 (2)^3 = 2400[/tex]
What is the difference between the two temperatures -13°C and 10°C
Answer:
23
Step-by-step explanation:
