Answer:
38.2 miles
Step-by-step explanation:
343.8 miles divided by 9 gallons equals 32.2 miles per gallon.
Jackson bought 3 pounds of candies for $9.75. What was the price of these candies in cents per pound?
Answer:
325 cents per pound
Step-by-step explanation:
Answer:
325 cents per pound
Step-by-step explanation:
Officer Brimberry wrote 32 tickets for traffic violations last week, but only 28 tickets this week. What is the percent decrease
12.5 percent is the percent decrease.
Please help me out :)
Answer:
10d² + 8
Step-by-step explanation:
Given
(11 + 4d²) - (3 - 6d²) ← distribute parenthesis, second by - 1
= 11 + 4d² - 3 + 6d² ← collect like terms
= (4d² + 6d²) + (11 - 3)
= 10d² + 8
The ages of trees in a forest are normally distributed with a mean of 25 years and a standard deviation of 5 years. Using the empirical rule, approximately what percent of the trees are between 20 and 30 years old?
32%
68%
95%
99.7%
Answer:
68%
Step-by-step explanation:
The mean is 25 and the standard deviation is 5. So 20 is one standard deviation below the mean and 30 is one standard deviation above the mean.
According to the Empirical Rule, 68% of the normal curve is between ±1 standard deviations. So the answer is 68%.
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: The population mean is μ=25 and standard deviation is σ=5.
[tex]Z=\frac{X-\mu}{\sigma}=\frac{X-25}{5}[/tex]
We need to find the percent of the trees that are between 20 and 30 years old.
[tex]P(20<X<30)[/tex]
Subtract 25 from each side.
[tex]P(20-25<X-25<30-25)[/tex]
[tex]P(-5<X-25<5)[/tex]
Divide each side by 5.
[tex]P(-1<\frac{X-25}{5}<1)[/tex]
[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)[/tex]
Using standard normal table we get
[tex]P(-1<Z<1)=0.84134-0.15866=0.68268\approx 0.68=68\%[/tex]
68% of the trees are between 20 and 30 years old.
Therefore the correct option is 2.
Which function has the same range as
Answer: Second Option
[tex]g(x)=-\frac{5}{7}(\frac{3}{5})^{-x}[/tex]
Step-by-step explanation:
The function [tex]g(x)=(\frac{3}{5})^x[/tex] is an exponential function.
Functions of this type have a range that goes from (0, ∞)
When multiplying the function by a negative coefficient [tex]-\frac{5}{7}[/tex], now all the values of g(x) will be negative and the range of [tex]g(x)=-\frac{5}{7}(\frac{3}{5})^x[/tex] will be: (-∞, 0)
Then we must search among the options a function with range (-∞, 0)
Since the exponential functions of the form [tex](a) ^ x[/tex], where [tex]a>0[/tex] always have range (0, ∞) Then the correct option will be the one with a negative coefficient.
The correct option is the second option
The function [tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex]same range of [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex].
How to determine the range of another function based on transformationsIn this question we must determine a second function whose range is equal to the range of the first one. In geometry, a rigid transformation is a transformation experimented by a function such that euclidean distance is conserved. The range is the set of values of [tex]h(x)[/tex] associated to the function.
If we apply a reflection around the y-axis, then the range is conserved but relationship between the range and the domain is changed in rigid manner. The reflection around the y-axis follows the following formula:
[tex]h(x) = f(-x)[/tex] (1)
If we know that [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex], then the resulting function is:
[tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex]
The function [tex]h(x) = -\frac{5}{7}\cdot \left(\frac{3}{5} \right)^{-x}[/tex] has the same range of [tex]f(x) = - \frac{5}{7}\cdot \left(\frac{3}{5} \right)^{x}[/tex]. [tex]\blacksquare[/tex]
To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/5245372
For which value(s) of the constant k is the circle x² + (y − k)² = 16 tangent to the line y = 3?
Answer:
Step-by-step explanation:Let us find points of intersection of line
3
x
+
4
y
−
k
=
0
and circle
x
2
+
y
2
=
16
. We can do this by putting value of
y
from first equation i.e.
y
=
k
−
3
x
4
and we get
x
2
+
(
k
−
3
x
)
2
16
=
16
or
16
x
2
+
k
2
+
9
x
2
−
6
k
x
=
256
i.e.
25
x
2
−
6
k
x
+
k
2
−
256
=
0
This would give two values of
x
and corresponding two values of
y
i.e. two points. But tangent cuts the circle in only at one point. This will be so when discriminant is zero i.e.
(
−
6
k
)
2
−
4
⋅
25
⋅
(
k
2
−
256
)
=
0
or
−
64
k
2
+
25600
=
0
or
k
=
±
20
graph{(x^2+y^2-16)(3x+4y-20)(3x+4y+20)=0 [-10, 10, -5, 5]}
Answer:
-1, 7
Step-by-step explanation:
Equation of the circle:
x² + (y − k)² = 16
When the circle intersects y = 3:
x² + (3 − k)² = 16
x² + 9 − 6k + k² = 16
x² = 7 + 6k − k²
x = ±√(7 + 6k − k²)
For the circle to be tangent to the line, it can only intersect at one point. If x has only one value, then:
√(7 + 6k − k²) = -√(7 + 6k − k²)
2√(7 + 6k − k²) = 0
7 + 6k − k² = 0
k² − 6k − 7 = 0
(k − 7) (k + 1) = 0
k = -1, 7
The two values of k are -1 and 7.
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $13 monthly fee and charges an additional $0.17 for each minute of calls. The second plan has a $23 monthly fee and charges an additional $0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
To find the number of minutes at which the costs of the two plans will be equal, we set up an equation and solve for x. The costs will be equal after 250 minutes of calls.
Explanation:To find the number of minutes of calls at which the costs of the two plans will be equal, we can set up an equation. Let's denote the number of minutes as x. For the first plan, the total cost is given by:
Total Cost = $13 + $0.17x.
For the second plan, the total cost is given by:
Total Cost = $23 + $0.13x.
Setting these two equations equal to each other, we have:
$13 + $0.17x = $23 + $0.13x.
Simplifying this equation, we get:
$0.17x - $0.13x = $23 - $13.
$0.04x = $10.
Dividing both sides by $0.04, we get:
x = $10/$0.04 = 250 minutes.
Therefore, the costs of the two plans will be equal after 250 minutes of calls.
Learn more about Costs of phone plans here:https://brainly.com/question/3931843
#SPJ2
Which solid has a greater volume?
A. Figure A has a greater volume
B. Figure B has a greater volume
C. They are equal
D. It cannot be determined
Answer:
C
Step-by-step explanation:
The volume of a cone is given by [tex]V=\frac{1}{3}\pi r^2h[/tex]
The volume of a cylinder is given by [tex]V=\pi r^2 h[/tex]
Where h is the height and r is the radius
The first figure is a cone with height 6 and radius 5, we can put it into the formula and find the volume:
[tex]\frac{1}{3}\pi r^2 h\\\frac{1}{3}\pi (5)^2 (6)\\=157.08[/tex]
The second figure is a cylinder with height 50 and radius 1, we can put it into the formula and find the volume:
[tex]\pi r^2 h\\\pi (1)^2 (50)\\=157.08[/tex]
We can see that they are equal. So answer choice C is right.
A family of four went to an amusement park for their vacation. They started the vacation with $382. They spent a total of $150 the first three days. If they divided the remainder of the money evenly, how much did each person have to spend?
Answer: $58.00
Step-by-step explanation:
Which situation involves descriptive statistics?
A. An employer surveys a dozen employees to estimate how many employees would work on a certain holiday.
B. A recent poll shows that the president’s approval rating is at an all-time low of 40%.
C. A bowler’s scorecard shows he threw a strike on one fifth of his throws that night.
D. The sample indicates that about 5% of the cargo is damaged.
(c)A bowler’s scorecard shows he threw a strike on one-fifth of his throws that night. Descriptive statistics describe an event that happens over time, for example, a batting average would be a descriptive statistic or a win/loss ratio.
Choose the system of equations which matches the following graph:
A) x − 2y = 8
2x + 4y = 12
B) x − 2y = 8
2x − 4y = 12
C) x + 2y = 8
2x + 4y = 12
D)x + 2y = 8
2x − 4y = 12
I believe the answer is C.
Answer:
Option C.
Step-by-step explanation:
From the graph we can find the points (2,3) for first straight line (blue) and (2,2) for second straight line (red). These points Andre satisfied by option C.
x+2y=8
2+2×3=8
8=8.
Again, 2x+4y=12
2×2+4×2=12
12=12
The correct answer is Option C.
x + 2y = 8
2x + 4y = 12
How to find the equation of a line?In its simplest format in algebra, the definition of an equation exists as a mathematical statement that indicates that two mathematical expressions exist equal. For instance, 3x + 5 = 14 exists an equation, in which 3x + 5 and 14 exist two expressions separated by an 'equal' sign.
Equation of line in Two point form
When we know any two points on a line lets say [tex](a_1,b_1)[/tex] and [tex](a_2,b_2)[/tex], we can write its equation as:
[tex]y-b_1=m(x-a_1)[/tex]
where
[tex]m=\dfrac{b_2-a_2}{b_1-a_1}[/tex]
Here we have points of red line:( from graph) (0,3) and (6,0)
Equation of line: y-3=m(x-0)
m=0-3/6-0=-1/2
Equation:2y-6=-1(x)
2y+x=6
Now from graph, we can see that the blue line is parallel to red line, therefore their slopes are same
The equation of blue line is as follows
y=mx+c
Point on blue line :(0,4)
4=(-1/2)*(0)+c
c=4
The equation is x+2y=8.
Therefore, it matches with option C.
x + 2y = 8
2x + 4y = 12
To know more about equations refer to:
https://brainly.com/question/14323743
#SPJ2
The number of customers at a new taco truck triples every day for a week. The function f(x) = 3^x represents the number of customers on day x. On what day was there 243 customers? Write an equation you need to solve it
Answer:
Day 5
Step-by-step explanation:
There are 2 ways to solve this, one using exponents and the other using logs. The equation regardless of how you solve it looks like this:
[tex]y=3^x[/tex]
where y is the number of customers on day x. Filling in the number of customers we were given:
[tex]243=3^x[/tex]
There's a rule in exponents that says if the bases on both sides of the equals sign are like, then their exponents are equal to each other. So if we can rewrite 243 in terms of a base of 3, then we're good. I went to my calculator and started raising 3 to increasing powers of x: 3 to the first is 3; 3 squared is 9; 3 cubed is 27; 3 to the fourth is 81; 3 to the fifth is 243! That means that
[tex]3^5=3^x[/tex]
Since the bases are like, then x = 5.
Using logs to solve it:
Take the log of both sides:
[tex]log(243)=log(3)^x[/tex]
There's a law of logs that says when you take the log of a number with an exponent, you can bring down the exponent in front like this:
[tex]log(243)=xlog(3)[/tex]
Now to solve for x, divide both sides by log(3):
[tex]\frac{log(243)}{log(3)}=x[/tex]
You can do that on your calculator and get that x = 5.
Whichever way is easier for you to understand OR whichever way your teacher is teaching according to where you are in your log unit, do it that way! You can see that both give the same answer, the methods to get there vary.
A regular pentagon with a perimeter of 18 centimeters is dilated by a scale factor of 3 2 32 to create a new pentagon. What is the perimeter of the new pentagon?
Answer:
The perimeter of the new pentagon is [tex]27\ cm[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
so
To find the perimeter of the new pentagon, multiply the perimeter of the original pentagon by the scale factor
Let
z ----> the scale factor
[tex]z=3/2=1.5[/tex]
The perimeter of the new pentagon is equal to
[tex](18)*1.5=27\ cm[/tex]
True or false? in order to inscribe a circle in a triangle, the circle's center must be placed at the incenter of the triangle.
Answer:
The given statement is true.
Step-by-step explanation:
In order to inscribe a circle in a triangle, the circle's center must be placed at the incenter of the triangle.
This statement is true.
The INCENTER is the center of the circle that is inscribed in the triangle. Like the centroid, the incenter is always inside the triangle.
Answer:
true
Step-by-step explanation:
Given the equation, 3/(y - 5) = 15/(y + 4) what is the value of y?
To solve the equation 3/(y - 5) = 15/(y + 4) for the value of y, cross multiply to eliminate the fractions. Then collect the y terms on one side and the constant terms on the other side. Finally, divide both sides by the coefficient of y to find the value of y.
Explanation:To solve the equation 3/(y - 5) = 15/(y + 4) for the value of y, we first cross multiply to eliminate the fractions.
This gives us 3(y + 4) = 15(y - 5). Expanding this equation, we have 3y + 12 = 15y - 75.
Next, we collect the y terms on one side and the constant terms on the other side. Simplifying the equation, we get 12 + 75 = 15y - 3y.
Combining like terms, we have 87 = 12y. Finally, we divide both sides of the equation by 12 to solve for y.
Therefore, the value of y is 7.25.
Learn more about Solving Equations here:https://brainly.com/question/14410653
#SPJ12
Steel rods are manufactured with a mean length of 25 cm. because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.07 cm. if an order comes in for 10,000 steel rods, how many rods should the plant manager manufacture if the order states that all rods must be between 24.85 cm and 25.15 cm? (round your final answer (number of rods) up to the nearest integer.) the manager should manufacture _______ rods to satisfy the requirements of the order.
Answer:
700 im not sure
Step-by-step explanation:
Prove the identity. (steps needed to prove the identify aka= sin = 1/cscx)
its like a puzzle and im confused
sec(-x)-sin(-x)tan(-x)=cosx
Answer:
Step-by-step explanation:
sec(-x) − sin(-x) tan(-x)
So the first step is often to write everything in terms of sine, cosine, or tangent. So let's rewrite using sec x = 1 / cos x:
1/cos(-x) − sin(-x) tan(-x)
Now we need to deal with those -x angles. For that, we use reflection identities:
sin(-x) = -sin x
cos(-x) = cos x
tan(-x) = -tan x
Therefore:
1/cos(x) − sin(x) tan(x)
Now let's rewrite tan(x) as sin(x) / cos(x):
1/cos(x) − sin²(x)/cos(x)
Factoring:
(1 − sin²(x)) / cos(x)
Using Pythagorean identity: sin²(x) + cos²(x) = 1. So 1 − sin²(x) = cos²(x).
cos²(x) / cos(x)
And finally, we divide.
cos(x)
The function v(t) 1350(1.017)t represents the value v(t), in dollars, of a comic book t years after its purchase. the yearly rate of appreciation of the comic book is
Answer:
The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%
Step-by-step explanation:
we have
[tex]v(t)=1,350(1.017)^{x}[/tex]
This is a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
In this problem
a=$1,350
b=1.017
Remember that
b=1+r
so
1+r=1.017
r=1.017-1=0.017
therefore
The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%
Answer:
The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%
Step-by-step explanation:
we have
This is a exponential function of the form where
a is the initial value
b is the base
In this problem
a=$1,350
b=1.017
Remember that
b=1+r
so
1+r=1.017
r=1.017-1=0.017
therefore
The yearly rate of appreciation of the comic book is r=0.017 or r=1.7%
What is the surface area of a sphere with a radius of 16 units?
Answer:
D. 1024 π units²
Step-by-step explanation:
We have sphere, with a radius of 16 units.
The surface area of a sphere is given by the following formula:
Surface Area of a sphere = 4 π r²
We already know r, which is 16. So,
SA = 4 * π * 16² = 256 * 4 * π = 1024 π units²
That's enough for our answer, which matches answer D from the list.
If we want to have an actual number.... we would have to multiply 1024 by π.
SA = 1024 * π = 3217 units²
Answer:
option D
1024π units²
Step-by-step explanation:
Given in the question that radius of a sphere = 16 unit
Formula to use to calculate the surface area of the sphere
4 π r²here r is the radius of the sphere
4 π (16)²
4 π (256)
1024π units²
Surface area of a sphere with radius 16 units = 1024π units²
A chess club with 40 members is electing a new president. Amy received 38 votes. What percentage of the club members voted for Amy?
Answer:
95%
Step-by-step explanation:
Assuming each person can only vote once, just divide the amount of people that voted divided by the number of members. 38/40 gives a decimal of 0.95, and to find the percentage, just simply times it by 100.
Please help!!!! ASAP giving brainiest
KL= 6
ST=1.5
TU=4
The two figures shown are similar using the information given find the length of segment JK
Answer:
[tex]JK=2.25\ units[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
so
[tex]\frac{JK}{ST}=\frac{KL}{TU}[/tex]
substitute the given value and solve for JK
[tex]\frac{JK}{1.5}=\frac{6}{4}[/tex]
[tex]JK=(1.5)\frac{6}{4}[/tex]
[tex]JK=2.25\ units[/tex]
Katie studies math for 3 5 of an hour for every 1 4 of an hour she studies social studies. What is Katie's unit rate of the time she spends studying math to the time she spends studying social studies?
I don't really understand the 3 5. Are you talking about 3.5? Same with the 1 4 are you talking about 1.4 or 14 or what? I'll be willing to help if you could help me with that! :)
Which of the quadratic functions listed is written in vertex form?
Answer:
A is the best answer.
Step-by-step explanation:
A is. It can be written as y [ or v] = -2(x + 3)^2 + 7 which is the pure form of a vertex equation.
C doesn't work since that is a linear function. Nothing is squared.
D doesn't work. That is just the way an ordinary quadratic is written. (Standard form).
B doesn't work. The quadratic is written in factored form.
ANSWER
[tex]y - 7= - 2 {(x + 3)}^{2} [/tex]
EXPLANATION
The vertex form of a quadratic function is given by:
[tex]y = a {(x - h)}^{2} + k[/tex]
From the given options, the first choice is
[tex]y - 7= - 2 {(x + 3)}^{2} [/tex]
[tex]y=- 2 {(x + 3)}^{2} + 7[/tex]
where a=-2, h=-3, and k=7.
Therefore the vertex is (-3,7)
Hence the first choice is the correct option.
What is the measure of ∠DAB? Enter your answer in the box.
Answer:
91 degrees.
Step-by-step explanation:
This is a parallelogram (a quadrilateral with 2 pairs of parallel sides).
The 2 interior adjacent angles add up to 180 degrees in a parallelogram so
m < DAB = 180 - 89 = 91 degrees.
Answer: The measure of ∠DAB is 91°.
Step-by-step explanation:
Since we have given that
AB = CD
AD = BC
So, ABCD is a parallelogram.
m∠D=89°
and we know that
∠A and ∠D are adjacent angles.
So, their sum would be supplementary.
Now, it becomes,
[tex]89^\circ+\angle A=180^\circ\\\\\angle DAB=180^\circ-89^\circ\\\\\angle DAB=91^\circ[/tex]
Hence, the measure of ∠DAB is 91°.
Please answer this correctly
Answer:
914
I think it's the only answer
Hello There!
The answers are 916 and 914
HAVE A GREAT REST OF YOUR DAY!
find the volume of each figure. Round your answer to the nearest hundredth, if necessary.
Formula for volume of cone:
V = [tex]\pi r^{2} \frac{h}{3}[/tex]
r = 6 km
h = 12 km
V = [tex]\pi 6^{2} \frac{12}{3}[/tex]
V = [tex]\pi 36*4[/tex]
V = [tex]\pi 144[/tex]
V = 452.389 km^3 <----------------------Using the calculators pi button
V = 452.16 km^3 <-------------------------Using 3.14 for pi
Hope this helped!
~Just a girl in love with Shawn Mendes
the perimeter of pentagon A is 15 in. Its area is 30 in^2. The perimeter of pentagon B is 25 in. What is the area of pentagon B assuming that these pentagons are similar
Answer:
The area of pentagon B is [tex]83\frac{1}{3}\ in^{2}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z-----> the scale factor
x----> perimeter pentagon B
y----> perimeter pentagon A
[tex]z=\frac{x}{y}[/tex]
substitute the values
[tex]z=\frac{25}{15}[/tex]
Simplify
[tex]z=\frac{5}{3}[/tex] ----> scale factor
step 2
Find the area of pentagon B
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z-----> the scale factor
x----> area pentagon B
y----> area pentagon A
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{5}{3}[/tex]
[tex]y=30\ in^{2}[/tex]
substitute and solve for x
[tex](\frac{5}{3})^{2}=\frac{x}{30}[/tex]
[tex](\frac{25}{9})=\frac{x}{30}[/tex]
[tex]x=30*(\frac{25}{9})=83.33\ in^{2}[/tex]
convert to mixed number
[tex]83.33=83\frac{1}{3}\ in^{2}[/tex]
To find the area of pentagon B, we can use the fact that similar polygons have their corresponding sides proportional.
Explanation:To find the area of pentagon B, we can use the fact that similar polygons have their corresponding sides proportional. If the perimeter of pentagon A is 15 in and the perimeter of pentagon B is 25 in, we can set up the proportion:
perimeter of pentagon B / perimeter of pentagon A = corresponding side lengths of pentagon B / corresponding side lengths of pentagon A
To find the corresponding side lengths of pentagon B, we can multiply the corresponding side lengths of pentagon A by the ratio of the perimeters:
corresponding side lengths of pentagon B = corresponding side lengths of pentagon A * (perimeter of pentagon B / perimeter of pentagon A)
Once we have the corresponding side lengths of pentagon B, we can use the formula for the area of a regular pentagon: Area = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * s^2, where s is the length of a side. Calculate the area of pentagon B using the corresponding side lengths.
Please help me out please
Answer:
(500π)÷3
Step-by-step explanation:
area=4πr^2 , volume=4(πr^3)÷3
area=100π ,so r=5
Answer:
[tex]\frac{500\pi }{3}[/tex] ft³
Step-by-step explanation:
The surface area of a sphere = 4πr², hence
4πr² = 100π ( divide both sides by 4π )
r² = 25 ( take the square root of both sides )
r = [tex]\sqrt{25}[/tex] = 5, hence
V = [tex]\frac{4}{3}[/tex]πr³
= [tex]\frac{4}{3}[/tex]π × 5³
= [tex]\frac{4}{3}[/tex]π × 125 = [tex]\frac{500\pi }{3}[/tex] ft³
Given eight different sizes hats and three people, in how many ways can the three people be given a hat
24
Explanation:
8×3=24
Find the find the missing value to the nearest hundredth tan __=65
Find the missing value to the nearest hundredth
Cos __ =2/5
Answer:
Part 27) Option D. 89.12°
Part 28) Option B. 66.42°
Step-by-step explanation:
Part 27)
we have
tan(x)=65
so
using a calculator
x=arctan(65)=89.12°
Part 28)
we have
cos(x)=2/5
so
using a calculator
x=arccos(2/5)=66.42°
Answer:
Option D. 89.12°
Option B. 66.42°
Step-by-step explanation:
tan(x)=65
x=arctan(65)=89.12°
Part 28)
cos(x)=2/5
x=arccos(2/5)=66.42°