Answer:
8. $114
10. 60 stamps
Step-by-step explanation:
8.
Let Dylan have d, Mike have m, and Jeremy have j
3 of them have 171, so we can write:
1. [tex]d + m + j = 171[/tex]
Mike has twice as Dylan, so we can write:
2. m = 2d
Jeremy had three times as Mike, so:
3. j = 3m
We can write equation 3 as m = j/3
Also, if we put this into equation 2, we have:
j/3=2d
d=j/6
Now we have d and m in terms of j. We put it into equation 1 and solve for j:
[tex]\frac{j}{6} + \frac{j}{3} + j = 171\\\frac{3j+6j+18j}{18}=171\\\frac{27j}{18}=171\\27j=18*171\\27j=3078\\j=\frac{3078}{27}\\j=114[/tex]
Jaime has $114
10.
amount of stamps Maddy has is m and amount Simon has is s
Maddy had twice as many stamps as Simon:
m = 2s
Also
After Maddy sold 60 stamps, Sinom had twice as many stamps as Maddy:
s+60=2(m-60)
We put the first equation in the second and solve for s:
s+60=2(m-60)
s+60=2(2s-60)
s+60=4s-120
180=3s
s=60
THus, m = 2(60) = 120
So maddy had 120 - 60 = 60 more stamps than Simon
What do exponential functions model in the real world? How does the
standard equation form of the exponential equation change in each
situation?
Exponential functions model growth patterns such as population growth under ideal conditions, while the logistic model accounts for resource limits. The standard exponential equation is Y=abˣ, while logistic growth has a more complex form that includes the carrying capacity.
Exponential functions model various real-world phenomena in which growth occurs at a rate proportional to the current amount. For example, in natural populations, exponential growth is observed when resources are abundant and organisms can reproduce without constraints.
The standard form of an exponential function is Y = abx, where 'a' is the initial amount, 'b' is the growth factor, and 'x' represents time or another independent variable. In the context of population growth, 'a' would be the initial population size, 'b' is the growth rate per time period, and 'x' is the time elapsed.
Logistic growth is another pattern that is observed when resources become limited. It starts off similar to exponential growth but eventually slows down as the population reaches the carrying capacity of the environment.
Environmental conditions represented by the exponential growth model imply unlimited resources and space, whereas the logistic growth model includes the effects of limiting factors such as space, food, and other resources.
Find the radius of the circle whose equation is (x² - 10x + 25) + (y² - 16y + 64) = 16. 4 8 16
Answer:
Radius of circle is 4
Step-by-step explanation:
The standard equation of circle is
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center and r is the radius.
We are given:
(x² - 10x + 25) + (y² - 16y + 64) = 16
we know that a^2-2ab+b^2 =(a-b)^2
Using the above formula and converting the given equation into standard form, we get:
(x-5)^2+(y-8)^2=(4)^2
So, radius of circle is 4.
which of the following equations of a line perpendicular to the line y=-1/3x+1 , passing through the point (2,7)?
Answer:
y=3x+1 (slope-intercept form)
-3x+y=1 (standard form)
3x-y=-1 (another version of standard form)
y-7=3(x-2) (point-slope form)
Step-by-step explanation:
y=mx+b is slope intercept form where m is slope and b is y-intercept.
The slope of perpendicular lines are opposite reciprocals.
The opposite reciprocal of -1/3 is 3.
So we are looking for a line of the form y=3x+b going through (2,7)
y=3x+b with (x,y)=(2,7)
7=3(2)+b
7=6+b
7-6=b
1=b
b=1
So the equation is y=3x+1.
Now you can also put it in standard form:
Subtract 3x on both sides:
-3x+y=1
You can also multiply both sides by -1:
3x-y=-1
ax+by=c is standard form.
We can also use point slope form.
y-y1=m(x-x1) where (x1,y1) is a point contained by our line and m is the slope.
We have m=3 and (x1,y1)=(2,7)
y-7=3(x-2)
if two cylinders are similar and the ratio between the lengths of the radii is 3:4 what is the ratio of their surface area
Answer:
that the linear scale factor is 4:3 which can be written as 4/3
the volume scale factor will be:
(4/3)^3
D. 64:27
Step-by-step explanation:
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If segment AD = 3 cm, what is the smallest diameter of wrapper that will fit the candy bar?
a.3
b.4
c.5
d.6
Answer:
6
Step-by-step explanation:
Because AD and BC Are congruent so when you add them that would equal the diameter of the rapper.
Option D is correct. The smallest diameter of wrapper that will fit the candy bar is 6
According to the attached figure - the cross-sectional view of candy bar ABC. If a cylindrical container is created from the cross-section, then the diameter of the cylindrical container formed from the cross-section will be the side AC.
From the figure, AD = DC and AC = AD + DC
Given the segment AD = 3cm
AC = AD + AD (Since AD = DC)
AC = 2AD
AC = 2(3)
AC = 6
This shows that the smallest diameter of wrapper that will fit the candy bar is 6. Option D is correct
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Determine if the ordered pair (6, 4) is a solution to the inequality
[tex]y < \frac{3}{4}x - 3[/tex]
A.No, because (6, 4) is above the line
B.Yes, because (6, 4) is below the line
C.Yes, because (6, 4) is on the line
D.No, because (6, 4) is on the line
Answer:
A
Step-by-step explanation:
all we need to do is to plug the point (6,4) in the inequality and see if it satisfies it :
pay attention that here we have x=6 y=4
4<[tex]\frac{3}{4} (6) - 3[/tex]
we simplify we get :
4<4.5-3
4<1.5 which is incorrect so (6,4) is not a solution. moreover
notice that 4 is > than 1.5 so the point lies above the line
thus the answer is : A
you can also solve this problem by graphing the line [tex]y= [/tex][tex]\frac{3}{4} x-3[/tex] and plotting the point (6,4) and hence you will notice that the point is above the line
Answer:
A. No, because (6, 4) is above the lineStep-by-step explanation:
[tex]y<\dfrac{3}{4}x-3\\\\\text{Put the coordinates of the point and check the inequality:}\\\\(6,\ 4)\to x=6,\ y=4\\\\4<\dfrac{3}{4}\cdot6-3\\\\4<\dfrac{18}{4}-3\\\\4<4.5-3\\\\4<1.5\qquad\bold{FALSE}\\\\\text{Therefore your answer is NO, because (6, 4) is above the line.}[/tex]
[tex]\text{Other mathod:}\\\\\text{Show this inequality in the coordinate system.}\\\\\text{Draw the dotted line}\ y=\dfrac{3}{4}x-3.\\\\for\ x=0\to y=\dfrac{3}{4}(0)-3=0-3=-3\to(0,\ -3)\\\\for\ x=4\to y=\dfrac{3}{4}(4)-3=3-3=0\to(4,\ 0)\\\\\text{shaded region below the line}\\\\\text{Mark point (6, 4) and check if it lies in the shaded region.}[/tex]
Find the interquartile range for each set of data.
Set 1: 21, 5, 14, 10, 8, 17, 2
Answer:
12.
Step-by-step explanation:
First arrange in ascending order:
2 5 8 10 14 17 21
The median is 10.
the lower quartile is the middle number of 2 5 and 8 which is 5.
Similarly the upper quartile is 17.
IQR = 17 - 5 = 12.
Answer:
12
Step-by-step explanation:
Slade draws triangle PQR. He then constructs a perpendicular bisector from vertex P that intersects side QR at point T. What can Slade conclude, based on his drawing? QT = RT TP = RQ PQ = PR PT = PQ
Answer:
QT = RT
Step-by-step explanation:
When drawing triangle PQR the perpendicular bisector cuts the triangle in half, which results in two sides that are congruent. This makes QT and RT congruent.
Based on the triangle QPR option C) PQ = PR and A) QT = RT
A) QT = RT B) TP = RQC) PQ = PR D) PT = PQWhat is congruent triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In QPR
∠Q = ∠R (∵ PT is a bisector)
∴QT = RT (∵ PT is a bisector of QR)
PT is a common between PQT and RQT
∴PQ = PR ( by congruent part of congruent triangle)
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What is the area of a trapezoid with bases of 15.8 yd and 21.8 yd and a height of 11.7 yd?
439.92 yd2
219.96 yd2
127.53 yd2
92.43 yd2
Add the bases together, divide that by 2 then multiply by the height.
15.8 + 21.8 = 37.6
37.6/2 = 18.8
18.8 x 11.7 = 219.96 yd^2
Answer:
B) 219.96 yd2
Step-by-step explanation:
The formula for finding the area of a trapezoid is:
(a + b) /2*h
Now you would plug in the numbers
(15.8 + 21.8) /2*11.7
Now solve this in order of operations
(15.8 + 21.8) /2*11.7
37.6/2*11.7
18.8*11.7
219.96
solve the equation, 3x^2+5x+2=0 using the quadratic formula
Given a quadratic equation [tex]ax^2+bx+c=0[/tex], the two solution (if they exist) are given by the formula
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In your case, the coefficients are
[tex]a=3,\quad b=5,\quad c=2[/tex]
So the quadratic formula becomes
[tex]x_{1,2}=\dfrac{-5\pm\sqrt{25-24}}{6} = \dfrac{-5\pm 1}{6}[/tex]
So, the two solutions are
[tex]x_1 = \dfrac{-5+1}{6}=-\dfrac{4}{6}=-\dfrac{2}{3}[/tex]
[tex]x_2 = \dfrac{-5-1}{6}=-\dfrac{6}{6}=-1[/tex]
solve this inequality-3(2x-5)<5(2-x)
[tex]
-3(2x-5)<5(2-x) \\
-6x+15<10-5x \\
-x<-5 \\
\boxed{x>5}
[/tex]
Hope this helps.
r3t40
A line passes through (9,-9) and (10,-5).
a. Write an equation for the line in point-slope form.
b. Rewrite the equation in standard form using integers.
y-9 = 46% + 9); -4x + y = 45
y + 9 = 4(x + 9); -4% + y = -45
Y + 9 = 4(-9); -4x + y = -45
y - 9 = 40%-9); -4% + y = 45
[tex]\bf (\stackrel{x_1}{9}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-9)}{10-9}\implies \cfrac{-5+9}{1}\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-9)=4(x-9)\implies y+9=4(x-9) \\\\\\ y+9=4x-36\implies y=4x-45\implies \stackrel{\textit{standard form}}{-4x+y=-45}[/tex]
just a quick note
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
now, however the inappropriate choices here, do have it with a negative "x".
Answer:
y + 9 = 4(x - 9); -4x + y = -45
Step-by-step explanation:
According to the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, so put the coordinates into their correct positions, depending on the signs. In the equation, there is a 9 in it [-(-9) = 9], according to the formula. By the way, this is its y-coordinate. The x-coordinate is 9, which is normal, according to the formula (see part of above answer in parentheses). So now, this is how your work will look:
y + 9 = 4x - 36 [Point-Slope Form]↷
- 9 - 9
----------------
y = 4x - 45 [Slope-Intercept Form]↷
-4x -4x
------------
-4x + y = -45 [Standard Form]
Here we are at this second equation.
I am joyous to assist you anytime.
Find measure of angle that is complementary to a 28•angle (•=degree)
14•
28•
62•
152•
WHAT IS A COMPLEMENTARY ANGLE?
Complementary comes from the word complement. When two angles sum a total of 90°, they 'complement' each other. A complementary angle is a combination of two angles whose sum is equal to 90°.
BACK TO THE QUESTION
The question is asking what the measure of the other angle is. The given angle is 28°.
HOW TO FIND YOUR ANSWER
When you're given the measure of one of the angles, it's easy to find the other. All you have to do is subtract the measure of the angle from 90°.
In this question, you are given that the angle is 28°. That means you have to subtract 28 from 90.
[tex]90\°-28\°=62\°[/tex]
a. 14° ✘
b. 28° ✘
c. 62° ✓
d. 152° ✘
The answer to your question is 62°, also known as choice c.
Question 11 (5 points)
The digestive system ends at the
Ocolon
Olarge intestine
Oanus
O small intestine
Answer:
C. anus
Step-by-step explanation:
The digestive system ends at the anus.
Therefore, it does not end in the colon, large intestine, or small intestine.
The digestive system starts when you take in food and ends in the anus.
8. Factor 12y2 + 5y - 2 completely.
A. (6y - 1)(2y + 2)
B. (4y - 2)(3y + 1)
C. (4y - 1)(3y + 2)
D. (4y + 1)(3y - 2)
Answer:
C. (4y -1)(3y+2)
Step-by-step explanation:
12 y^2 + 5 y - 2
12 y^2 + (-3+8) y - 2
12 y^2 - 3y + 8y - 2
3y(4y-1)+2(4y-1)
(4y-1)(3y+2)
What is the sum of the rational expressions below? 3x/x+9 + x/x-4
Answer:
[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]
Step-by-step explanation:
The sum of two rational expressions is done in the following way:
[tex]\frac{a}{b}+\frac{c}{d} = \frac{a*d + c*b}{b*d}[/tex]
In this case we have the following rational expressions
[tex]\frac{3x}{x+9} + \frac{x}{x-4}[/tex]
So:
[tex]a=3x\\d=(x+9)\\c=x\\d=(x-4)[/tex]
Therefore
[tex]\frac{3x}{x+9} + \frac{x}{x-4}=\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)}[/tex]
simplifying we obtain:
[tex]\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)}=\frac{3x^2-12x+x^2+9x}{(x+9)(x-4)}\\\\\frac{3x^2-12x+x^2+9x}{(x+9)(x-4)}=\frac{4x^2-3x}{(x+9)(x-4)}[/tex]
Answer:
[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]
Step-by-step explanation:
We are given the following expression and we are to find the sum of this rational expression below:
[tex] \frac { 3 x } { x + 9 } + \frac { x } { x - 4 } [/tex]
Taking LCM of it to get:
[tex]\frac{3x}{x+9} =\frac{3x(x-4)}{(x+9)(x-4)}[/tex]
[tex]\frac{x}{x-4} =\frac{x(x+9)}{(x-4)(x+9)}[/tex]
[tex]\frac{3x(x-4)}{(x+9)(x-4)}+\frac{x(x+9)}{(x-4)(x+9)}[/tex]
[tex]\frac{3x(x-4)+x(x-9)}{(x+9)(x-4)}[/tex]
[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]
i need help asap thank you marking brainliest
Answer:
[tex]a_{20} = 12+3(20-1)[/tex]
Step-by-step explanation:
What is the number pie
You meant pi, pi is a irrational number, but they use 3.14 for approximation, so that is your answer.
Hope this helped!
Nate
[tex]\pi-\bold{pi}\\\\\pi\ \text{it's the ratio of a circle's circumference to its diameter}\\\\\pi=\dfrac{\text{circumference of a circle}}{\text{circle diameter}}\\\\\pi\ \text{it's irrarional number}\\\\\pi=3.14159265358979323846264338327...\\\\\text{Approximation of}\ \pi:\\\\\pi\approx3.14\\\\\pi\approx\dfrac{22}{7}\\\\\pi\approx\dfrac{355}{113}[/tex]
The number pi occurs when calculating the surface area or volume of the rotational solids.
Cylinder:
[tex]S.A.=2\pi r^2+2\pi rH\\\\V=\pi r^2H[/tex]
Cone:
[tex]S.A.=\pi r^2+\pi rl\\\\V=\dfrac{1}{3}\pi r^2H[/tex]
Sphere:
[tex]S.A.=4\pi R^2\\\\V=\dfrac{4}{3}\pi R^3[/tex]
The number pi occurs when calculating the area and the circumference of a circle.
[tex]C=\pi d=2\pi r\\\\A=\pi r^2[/tex]
It is also used to convert angle measure in degrees to radians.
[tex]x^o=\dfrac{x\pi}{180}\ rad[/tex]
From a window, the angle of elevation of the top of a flagpole is 25°, and the angle of depression of the base of the
flagpole is 12°.How high is the flagpole if the window is in a building at a distance of 185 feet from the flagpole?
Answer:
125.59 feet
Step-by-step explanation:
(see attached)
Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $60 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1375 . How long did each mechanic work?
Answer:
Mechanic A worked for 5 hours and Mechanic B worked for 15 hours
I hope my answer and explanation helped!
okay to get started you need to make a system of equations:
x= number of hours worked by mechanic A
y= number of hours worked by mechanic B
x + y= 20
95x + 60y= 1375
substitute in an equation:
x + y= 20
y= 20- x
95x + 60(20-x)=1375
Solve for x
95x + 1200 - 60x=1375
35x =175
x= 5
plug in x to solve for y
x + y= 20
5 + y= 20
y=15
Check work
then you're done :D
You are one of 34 people entering a contest. What is the probability that your name will be drawn first?
Answer:
1/34 or 2.94%
Step-by-step explanation:
There is only one paper that has your name on it out of 34 papers. So there is a 1 out of 34 chance your name is drawn.
You have write this as a fraction 1/34 or as a percentage 2.94%
Final answer:
The probability that your name will be drawn first in a contest with 34 entrants is 1 in 34, based on the principle of equally likely outcomes in a random selection process.
Explanation:
The probability of any one person being chosen first in a random draw from a group of 34 people is based on the principle that each person has an equal chance of being selected. To determine this probability, we use the concept of equally likely outcomes, which suggests that each person has 1 chance in the total number of people competing. Therefore, the probability that your name will be drawn first from a group of 34 people is 1 in 34.
What is the equation of the following line written in general form? (The y-intercept is 7.)
Answer:
3x - y + 7 = 0Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Put the given y-intercept b = 7 and the coordinates of the point (-2, 1) to the equation:
[tex]1=-2m+7[/tex] subtract 7 from both sides
[tex]-6=-2m[/tex] divide both sides by (-2)
[tex]3=m\to m=3[/tex]
We have the equation:
[tex]y=3x+7[/tex]
Convert it to the general form [tex]Ax+By+C=0[/tex]:
[tex]y=3x+7[/tex] subtract 3x and 7 from both sides
[tex]-3x+y-7=0[/tex] change the signs
[tex]3x-y+7=0[/tex]
There are 20 squid and 36 eels in a fish tank. What is the ratio of squids to eels? What is the rate of squids to eels? What about the simplified ratio and unit rate?
Answer:
Ratio: 20:36
Rate: 20 squids per 36 eels
Simplified ratio:
[tex] = \frac{20}{36 } = \frac{10}{18} = \frac{5}{9} [/tex]
Unit ratio:
20/36 squids per eel (dividing by 36)
Please mark Brainliest if this helps!
Answer:
Step-by-step explanation:
Number of squid in the tank = [tex]20[/tex]
Number of eels in the tank = [tex]36[/tex]
Rate of squids to eels will be obtained by creating a fraction of number of squids over number of eels
Rate of squid to eels = [tex]\frac{20}{36}[/tex]
also ratio of squid to eels will be written as [tex]20:36[/tex]
Simplified ratio = [tex]\frac{20}{36} = \frac{5}{9} = 5:9[/tex]
Unit rate will be defined as number of squid per eels
Unit rate = [tex]\frac{20}{36} = 0.55[/tex]
An angle with its vertex at the center of a circle intercepts an 80° arc of that circle.
What is the measure of the angle?
let's recall that, arc's angle measures come from the central angle they're in.
if this intercepted arc is 80°, and is intercepted by an angle stemming from the center, namely a central angle, then the angle is also 80°. Check the picture below.
If angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is 80°.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that angle with its vertex at the center of a circle intercepts an 80° arc of that circle
We have to find the measure of the angle.
When an angle is formed at the center of a circle, it intercepts an arc of the circle that is equal in measure to the angle.
Since the given angle intercepts an 80° arc of the circle, we know that its measure is also 80°. so the measure of the angle is 80°.
Hence, if angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is 80°.
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Which describes the difference between the two sequences?
First Sequence: 5, 10, 20, 40..
Second Sequence: 8, 15, 22, 29, ...
The first sequence is geometric because there is a common ratio of 2. The second sequence is arithmetic because there
is a common difference of 7.
The first sequence is geometric because there is a common difference of 2.
The second sequence is arithmetic because there is a common ratio of 7
The first sequence is geometric because there is a common difference of 7. The second sequence is arithmetic because
there is a common ratio of 2.
The first sequence is arithmetic because there is a common difference of 2. The second sequence is geometric because
there is a common ratio of 7.
NEEDD THE ANSWER ASAP IMA MARK BRAINLIS! 1st one answer
Answer:
its a)the first sequence is geometric bc of the common ratio of 2. the second sequence is arithmetic bc of the common difference of 7.
Option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.
What is a number pattern?Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.
For the given situation,
First sequence: 5, 10, 20, 40..
Second sequence: 8, 15, 22, 29, ...
Now consider the first sequence: 5, 10, 20, 40..
Here, when we divide the second number by first number, we get the common ratio as 2.
⇒ [tex]\frac{10}{5}=2[/tex]
⇒ [tex]\frac{20}{10}=2[/tex]
⇒ [tex]\frac{40}{20}=2[/tex]
Thus the first sequence follows a geometric progression with common ratio 2.
Now consider the second sequence: 8, 15, 22, 29, ...
Here, when we subtract the first term is subtracted from the second term, the common difference is 7.
⇒ [tex]15-8=7[/tex]
⇒ [tex]22-18=7[/tex]
⇒ [tex]29-22=7[/tex]
Hence we can conclude that option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.
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Last year, your team bought 11 baseball caps for $55. This year, the cost per cap is the same. Write a
proportion that gives the cost c of buying 15 baseball caps.
To find the cost of buying 15 baseball caps, we set up a proportion using the information about the cost per cap from last year. The cost of buying 15 caps is $75.
Explanation:To write a proportion that gives the cost of buying 15 baseball caps, we can use the fact that the cost per cap is the same as last year. Let c represent the cost of buying 15 caps. We can set up the proportion as follows:
11 caps / $55 = 15 caps / c
To solve for c, we can cross-multiply and solve for the unknown variable:
11c = 15 * $55
c = (15 * $55) / 11 = $75
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To find the cost of buying 15 baseball caps, set up a proportion of 11 caps for $55 and 15 caps for (c). Solve for (c) by cross multiplying and dividing by 11. The cost of buying 15 baseball caps would be $75.
Explanation:To write a proportion that gives the cost (c) of buying 15 baseball caps, we can set up the ratio of the number of caps to the cost of the caps in two scenarios: 11 caps for $55 and 15 caps for (c). Since the cost per cap is the same in both scenarios, the proportion would be:
11/55 = 15/(c)
To solve for (c), we can cross multiply:
11 * c = 15 * 55
Dividing both sides of the equation by 11, we find:
c = 15 * 55 / 11 = 75
Therefore, the cost of buying 15 baseball caps would be $75.
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If a Canada goose completes a $2400$-mile migration in exactly $13$ days and $8$ hours, then what was her average speed for the whole trip in miles per hour?
Enter your answer as a fraction or as a decimal, without units.
Answer:
Her average speed = 7.5 miles/hour
Explanation:
First, since the required speed unit is miles/hour, we need to make sure that all units given are in miles (for distance) and hour (for time)
We are given that:
Distance covered = 2400 miles
Times taken = 13 days and 8 hours
We know that 1 day has 24 hours
Therefore:
13 days = 13 x 24 = 312 hours
Time taken = 13 days and 8 hours = 312 + 8 = 320 hours
Now, average speed is calculated as the total distance divided by the total time
This means that:
[tex]Average Speed=\frac{Total Distance}{Total Time} = \frac{2400}{320}=7.5[/tex] miles/hour
Hope this helps :)
To find the average speed, convert the total migration time of 13 days and 8 hours to hours, which is 320 hours. Then divide the total distance, 2400 miles, by the total time to get an average speed of 7.5 miles per hour.
Explanation:To calculate the average speed of the Canada goose on its $2400$-mile migration completed in $13$ days and $8$ hours, we must first convert the total time into hours. There are $24$ hours in a day, so $13$ days is equal to $13 \times 24 = 312$ hours. Adding the additional $8$ hours, we have a total travel time of $320$ hours. The average speed is then calculated by dividing the total distance by the total time.
The average speed of the goose is:
Divide the total distance of $2400$ miles by the total time of $320$ hours.Calculate $2400 \div 320$ to find the average speed in miles per hour.The average speed is $\frac{2400}{320} = 7.5$ miles per hour.
ASAP PLS: #11-8: At a local restaurant, the waiter earn a 7% commission on any dessert they sell. The average customer bill is $42, of which 10% is dessert. How much commission is earned on an average sale?
Which quadratic equation is equivalent to (x^2-1)^2-11(x^2-1)+24=0
Answer:
The correct answer is first option
u² - 11u + 24 = 0
When u = (x² - 1)
Step-by-step explanation:
It is given that,
(x² - 1)² - (x² - 1) + 24 = 0
To find the correct answer
Substitute u = x² - 1
The equation becomes,
u² - 11u + 24 = 0 Where u = (x² - 1)
Therefore the correct answer is first option
u² - 11u + 24 = 0
When u = (x² - 1)
Answer:
u² - 11u + 24 = 0 is equivalent to (x²-1)² - 11(x²-1) + 24 = 0
Step-by-step explanation:
(x²-1)² - 11(x²-1) + 24 = 0
Evaluate each equation by substituting the value of u to match the equation above.
1) u² - 11u + 24 = 0 where u = (x² - 1)
(x²-1)² - 11(x²-1) + 24 = 0
This equation matches (x²-1)² - 11(x²-1) + 24 = 0
2) (u²)² - 11(u²) + 24 where u = (x² - 1)
[(x²-1)²]² - 11(x²-1)² + 24
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
3) u² + 1 - 11u +24 = 0 where u = (x² - 1)
(x² - 1)² + 1 - 11(x²-1) + 24 = 0
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
4) (u² - 1)² - 11(u² - 1) + 24 where u = (x² - 1)
[(x²-1)²-1]² - 11(u² - 1)² + 24
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
Therefore, the first quadratic equation is equivalent to (x²-1)² - 11(x²-1) + 24 =0.
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The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:
A scientist measures the angle x and the distance y between the Sun and the moon. Using complete sentences, explain how the scientist can
use only these two measurements to calculate the distance between the Earth and the moon.
Answer:
The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x
Step-by-step explanation:
Let
EM -----> the distance between the Earth and the Moon.
y -----> the distance between the Sun and the Moon.
we know that
In the right triangle of the figure
The sine of angle x is equal to divide the opposite side to angle x (distance between the Earth and the Moon.) by the hypotenuse ( distance between the Sun and the Moon)
so
sin(x)=EM/y
Solve for EM
EM=(y)sin(x)
therefore
The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x