The value of the stamp collection in terms of b is; 45b + 43 cents
How to solve algebra word problems?
We are given;
If there are x 3-cent stamps, then there are 4x number 10-cent stamps
So the number of 2-cent stamps is 1 less than 3 cent stamps and that will be x - 1, 2 cent stamps
Number of 2 cents stamps = b
Thus; x - 1 = b
x = b + 1
The value of the stamp collection is as follows;
x number of 3 cents stamps = 3(b + 1) = 3b + 3 cents
4x number of 10 cents stamps = 10(4(b + 1)) = 10(4b + 4) = 40b + 40
The value of the 2 cents stamp = 2b cents
Total value is;
2b + 40b + 40 + 3b + 3 = (45b + 43) cents
Complete Question is;
I have 4 times as many 10-cent stamps as 3-cent stamps. I have one less 2-cent stamp than 3 cent stamp. If I have b2-cent stamps, what is the value of my stamp collection in terms of b ?
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I also dont know how to solve this one either. Please help! I just want to know how to solve it so i can do it on my own
Answer:
[tex]z=5[/tex]
Step-by-step explanation:
[tex]-\frac{3}{z}+\frac{7}{4z}=\frac{5}{z-25}\\\\\implies-\frac{12}{4z}+\frac{7}{4z}=\frac{5}{z-25}\\\\\implies-\frac{5}{4z}=\frac{5}{z-25}\\\\\implies125-5z=20z\\\\\implies25z=125\\\\\implies z=5[/tex]
Have a nice day, also mark brainliest please!
I need the volume of that figure
Answer:
708π in³ = 2224.25 in.³
Step-by-step explanation:
The composite solid is made up of a cone, a cylinder, and a half sphere.
Recall the volume formulas:
cone: πr²h/3
cylinder: πr²h
sphere: 4πr³/3
half sphere: (1/2) × 4πr³/3
We need to find teh heoght of the cone. The slant height is 10 in. The radius is 6 in. We can use the Pythaogorean theorem to find the height of the cone.
h = √(10² - 6²) = 8
total volume = π(6 in.)²(8 in.)/3 + π(6 in.)²(13 in.) + (1/2) × 4π(6 in.)³/3
total volume = π(96 in.³ + 468 in.³ + 144 in.³)
total volume = 708π in³ = 2224.25 in.³
A.
B.
10. Multiple choice. Determine the area of one face of a cube with a
side length of 14 cm.
A. 196 cm² B. 196 cm³ C. 14 cm²
D. 2744 cm³
Answer:
196cm²
Step-by-step explanation:
14*14=196
area = length of one side * the length of the other side
2x − 4y = 40,
−x + 2y = −20
Find x and y intercept
Answer:
The x and y intercept are (20,0)
Step-by-step explanation:
2x-4y=40—eqn1
-x+2y=-20—eqn2
Make x the subject of eqn2
-x=-20-2y
x=20+2y
plug this into eqn 1
2(20+2y)+4y=40
40+4y+4y=40
8y=40-40
y=0
plug y=0 into eqn2
-x+2(0)=-20
-x=-20
x=20
In sunlight, a vertical stick 6 ft tall casts a shadow 2 ft long. At the same time a nearby tree casts a shadow 14 ft long. How tall is the tree? Round to the nearest tenth.
Answer:
42.0 ft
Step-by-step explanation:
let t be the height of the tree.
At the same time ,the measure of something
and its shadow are proportional .
Then
[tex]\frac{2}{6} =\frac{14}{t}[/tex]
Then
2t = 6 × 14
Then
2t = 84
Then
t = 84/2
Then
t = 42
Therefore the tree is 42 ft tall
A Venn diagram is shown below: What are the elements of (A n B) ‘ ?
The elements of (A n B)' are ( 3, 4 , 5 ,6). Option A
How to determine the setThe elements of this set (A n B) explains the common elements of both sets without repetition
Set A = 3, 4
Set B = 5, 6
A n B = 1, 2
(A n B)' = Is the elements both A and B in common but is not found in the universal set
(A n B)' = ( 3, 4 , 5 ,6)
Thus, the elements of (A n B)' are ( 3, 4 , 5 ,6). Option A
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Fill in the gaps below:
Answer:
anticlockwise; reflection about x = 0; reflection about y = x - 1
Step-by-step explanation:
To get from A to A', we have to rotate anticlockwise. This rotation would take us around the coordinate plane from the first quadrant to the fourth quadrant to the third quadrant to the second quadrant. Clockwise about (0, -1) would not bring us to A'. To get from A' to A'', we to reflect across the line x = 0. As you can see in the image, the two triangles mirror each other across a vertical line in the center of them, and this vertical line would be x = 0 because both triangles are at least 1 unit away from it (they are equidistant from this line)
A single transformation that could map A onto A'' would be a reflection about y = x - 1. Both triangles happen to meet at this point so you might be able to visualize it. However, we can also test some points to see if this works. First, we can test the right-most point of A (which is the top-most point of A''). This point on A is (6, 0). If this point was reflected across y = x - 1, y would become 6 - 1 or 5, and since y = x - 1 is the same as x = y + 1, x would become 0 + 1 or 1. Indeed, the equivalent point on A'' is (1, 5).
need help ASAPP and show your work ( will rate 5 starts )
The cosine model is y = - 7 + 10 · cos (π · x/30 - π).
The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).
How to find sinusoidal functions from a given graph
Sinusoidal functions are periodic trascendent expressions which involves trigonometric functions. There are two kinds of sinusoidal functions:
[tex]y = A \cdot \cos (B\cdot x + C) + D[/tex] (1)
[tex]y = A\cdot \sin (B\cdot x + C) + D[/tex] (2)
Where:
A - AmplitudeB - Angular frecuencyC - Angular phaseD - MidpointFirst, we find the amplitude and the midpoint:
A = [3 - (- 17)]/2
A = 10
D = [3 + (- 17)]/2
D = - 7
Now we find the angular phase and the angular frequency for each model:
Cosine model (x, y) = (0, - 17), (x, y) = (30, 3)
- 17 = 10 · cos C - 7 (3)
3 = 10 · cos (30 · B + C) - 7 (4)
By (3):
- 10 = 10 · cos C
cos C = - 1
C = acos(- 1)
C = - π
And by (4):
3 = 10 · cos (30 · B - π) - 7
10 = 10 · cos (30 · B - π)
cos (30 · B - π) = 1
30 · B - π = acos 1
30 · B - π = 0
30 · B = π
B = π/30
The cosine model is y = - 7 + 10 · cos (π · x/30 - π).
Sine model
Obtain the sine model by using trigonometric expressions:
cos θ = sin (θ + π/2) (5)
By (5):
y = - 7 + 10 · sin (π · x/30 - π + π/2)
y = - 7 + 10 · sin (π · x/30 - π/2)
The sine model is y = - 7 + 10 · sin (π · x/30 - π/2).
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A motorbike is priced at $945.50 Johnson has $ 5000.
How many motorbikes could he buy?
The number of motorbikes is 5
How to determine the number of motorbikes?The given parameters are:
Motorbike = $945.50
Johnson = $5000.
The number of motorbikes is calculated as:
n = Johnson/Motorbike
So, we have:
n = 5000/945.5
Evaluate
n = 5.29
Remove the decimal
n = 5
Hence, the number of motorbikes is 5
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if sin x =
[tex] - \frac{ \sqrt{3} }{2} [/tex]
and cos x >0 find the value of x. pls an pls answer i will mark him or her brainlest. pls
Step-by-step explanation:
sin^-1√-3/2=300°
cos300°=0.5
A population of a particular yeast cell develops with a constant relative growth rate of 0.4425 per hour. The initial population consists of 3.1 million cells. Find the population size (in millions of cells) after 3 hours. (Round your answer to one decimal place.)
The exponential function is often used to model the growth or decay of a population
The population size of the yeast cell after 3 hours is 6.24 million
The given parameters are:
a = 3.1M --- initial number of cells
r = 0.4425 per hour --- rate
The nth term of an exponential function is:
f(n) = a(1+r)^n-1
After 3 hours; n = 3
So, we have:
f(3) = a(1+r)^3-1
Substitute values for a and r
f(3) = 3.1 (1+0.4425)^3-1
f(3) = 3.1 ( 1.4425)^2
f(3) = 6.24
Hence, the population size of the yeast cell after 3 hours is 6.24 million.
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HELPPPP PLEASEEE ASAPP!! The population of a small farming community is declining at a rate of
7% per year. The decline can be expressed by the exponential
equation P=C (1-0.07), where P is the population after t years and
C is the current population. If the population was 8500 in 2004, when
will the population be less than 6000?
Answer:
365/8500*7=0.30058823529411-0.07/100*7=0.9951
does anyone know how to do these??
Answer:
b)
c=140°
a= 40°
b=40°
c)
p= 60°
q= 60°
r= 120°
d)
a= 65 °
b= 65°
c= 65°
d= 115°
e=65°
Step-by-step explanation:
Hope it helps
A country specializes in agricultural production—in particular, pineapples and coconuts. last year, its economy was operating efficiently at point a. to capitalize on its favorable climate for growing these fruits, the country decides to build some islands near its coast to use for growing pineapples and coconuts. which ppc represents the change that results from this decision?
The country will achieve a blue PPC.
What is Production Possibilities Curve (PPC)?
The Production Possibilities Curve (PPC) Sometimes called the production possibilities frontier (PPF) is a model used to show the tradeoffs associated with allocating resources between the production of two goods. The PPC can be used to illustrate the concepts of scarcity, opportunity cost, efficiency, inefficiency, economic growth, and contractions.
Due to the increase in resources of the country, the production capacity for both pineapple & coconut will increase as a result country's PPC will shift rightward/forward. And the country will achieve blue PPC.
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A cab company calculates cab fares using the expression 1.50d + 3, where d is the distance traveled in miles. If a passenger has to pay a $21 fare for a ride, which number from the set {9, 12, 15, 18} is the value of d?
Answer:
12
Step-by-step explanation:
⇒ 21 - 3 = 18 = 1.5a
⇒ a = 12
You were painting a room in your house. Unfortunately, you lost the lid to the 5 gallon bucket of paint, but you only used half of the paint. You want to save the paint, so you plan on transferring it to a new container. The new container is shaped like a rectangular prism. If there are originally 1,155 cubic inches of paint in the 5 gallon bucket, is your container big enough to fit the paint that is left over? Remember that half the paint is left in the bucket.
Answer:
bro wuts da answer am so lost yo
Answer: It's my understanding that the answer would be the last one - No, the container is not large enough.....new container is 960 cubic inches. I saw this answer marked on another website but not how to find the answer.
Step-by-step explanation:
find the distance between (0,3) and (0,-6)
Answer:
the answer should be 9
Step-by-step explanation:
,look at a graph count from 0,-6 up to 0,3 . the distance between them is 9
Answer: 9
Step-by-step explanation:
let the two points P (0,3) and Q(0,-6)
We need to find distance PQ
PQ=[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
here
x1=x coordinate of P=0
y1=y coordinate of P=3
x2=x coordinate of Q=0
y2=y coordinate of Q=-6
Putting values
[tex]PQ=\sqrt{(0-0)^2+(-6-3)^2}\\[/tex][tex]PQ=\sqrt{(0)^2+(-9)^2} \\PQ=\sqrt{81} \\PQ=9[/tex]
If you anwser the question i give you brainly
The proportional relationship graph that shows the situation is: Graph C.
What is a Proportional Relationship?A proportional relationship is defined as y = kx, where k is the constant of proportionality between x and y, and k = y/x.
Given the equation, M = 3n,
k = 3.
Thus, the graph that has a constant of proportionality (k) of 3, will correspond to the situation.
In graph C, using a point, (400, 1,200), we have:
k = 1,200/400
k = 3
Therefore, the graph that corresponds to the situation is: C.
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Can someone solve this? please
Answer:
Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)]h
Where, l is the lower limit of the modal class
f₁ is the frequency of the modal class
f₀ is the frequency preceding the modal class
f₂ is the frequency succeeding the modal class
h is the class size
From the table,
Maximum frequency = 41
This frequency lies in the class 10000 - 15000
l = 10000
h = 5000
f₁ = 41
f₀ = 26
f₂ = 16
Now, f₁ - f₀ = 41 - 26 = 15
2f₁ - f₀ - f₂ = 2(41) - 26 - 16
= 82 - 42
= 40
[(f₁ - f₀)/(2f₁ - f₀ - f₂)] = 15/40
= 3/8
Now, mode = 10000 + (3/8)(5000)
= 10000 + (15000/8)
= 10000 + 1875
= 11875
Therefore, the modal income is 11875.Combine the radicals 4√7+3√28.
O 10√7
O
4√7
0 -2√7
10√14
Answer:
10sqrt(7)
Step-by-step explanation:
[tex]4 \sqrt{7} + 3 \sqrt{28} \\ \\ 4 \sqrt{7} + 3(2 \sqrt{7} ) \\ \\ 4 \sqrt{7} + 6 \sqrt{7} = 10 \sqrt{7} [/tex]
Use the quadratic formula to find both solutions to the quadratic equation
given below.
The solution of the equation are [tex]x = \frac{7 + \sqrt{61}}{6}[/tex] and [tex]x = \frac{7 - \sqrt{61}}{6}[/tex]
How to determine the solution?The equation is given as:
3x^2 - 7x- 1 = 0
The quadratic equation is represented as:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
So, we have:
[tex]x = \frac{7 \pm \sqrt{(-7)^2 - 4 *3 *-1}}{2*3}[/tex]
Evaluate the expression
[tex]x = \frac{7 \pm \sqrt{61}}{6}[/tex]
Expand
[tex]x = \frac{7 + \sqrt{61}}{6}[/tex] and [tex]x = \frac{7 - \sqrt{61}}{6}[/tex]
Hence, the solution of the equation are [tex]x = \frac{7 + \sqrt{61}}{6}[/tex] and [tex]x = \frac{7 - \sqrt{61}}{6}[/tex]
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10 divided by 34352 rounded to the nearest tenth
Answer: 0
Step-by-step explanation:
Answer:
34352.0
Step-by-step explanation:
What type of function is shown in the data in the table below?
Answer:
the function is quadratic because it have (2) turning points which is a sign of the ax² in rhe quadratic equation (ax²+bx+c)
Sir yesuba withdrew a sumof money from the bank he gave 3/8 of it to his son and 1/4 to his daughter if he had gh600 left, how much did he take form the bank
Sir Yesuba took Rs 1600 from the bank.
Concept : Addition and subtraction from an unknown quantity which can be calculated easily using variables.
Given: The Amount given to son = 3/8x
The Amount given to daughter = 1/4x
Money left = Rs 600
Let the amount taken by him be equal to Rs x.
The Amount given to son = 3/8x
The Amount given to daughter = 1/4x
x - (3/8x + x/4) = 600
x- x/8 = 600
7x/8=600
x= Rs1600
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help me please, you gonna be my hero
The rate of change of the relationship is 6/5
Rate of change of a lineThe rate of change of a line is also known as the slope of the line. The formula for calculating the slope of a line is expressed as:
Slope =y2-y1/x2-x1
Given the coordinate points (-3,-2) and (2, 4). On substituting;
Slope = 4-(-2)/2-(-3)
Slope =4+2/2+3
Slope = 6/5
Hence the rate of change of the relationship is 6/5
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Gareth buys two oranges. He pays with a £1 coin and gets 52p change. Work out the cost of one orange.
Answer:
24p
Step-by-step explanation:
£1 - £0.52 = £0.48 ← cost of 2 oranges
cost of 1 orange = £0.48 ÷ 2 = £0.24
Can someone please explain what an outlier is? it keeps popping up in all of my math questions and it is really confusing me...
Answer:
An outlier is something that is out of place compared to the rest of the group. For example, If you had the numbers 3,4,5,4,3,4, and 19, 19 would be the outlier.
Step-by-step explanation:
An outlier is a number that's far away from the rest of your data.
For example, if we look at the numbers 3, 2, 4, 5, 27, and 1, you can likely consider 27 to be an outlier because it's so far away from the rest of the data.
The specific definition of how far something has to be from the rest of the data to be an outlier depends entirely on the situation, but in general: if a number obviously sticks out from the rest, it's probably an outlier.
Last years freshman class at big state university totaled 5,305 students of those 1258 received a merit scholarship to help offset tuition costs their freshman year.the amount received was n(3456, 478) if the full cost was 4250 what percentage of students receive a merit scholarship did not receive enough to cover full tuition
Using the normal distribution, it is found that 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for the amounts are given as follows:
[tex]\mu = 3456, \sigma = 478[/tex]
The proportion is the p-value of Z when X = 4250, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4250 - 3456}{478}[/tex]
Z = 1.66
Z = 1.66 has a p-value of 0.9515.
Hence 95.15% of students receive a merit scholarship did not receive enough to cover full tuition.
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A sphere has a surface area of 16pi cm³. Find the volume giving your answer in form. Anyone know how to do this question?
Answer:
Your answer should be around 10.7π cm³
Step-by-step explanation:
The surface area formula for a sphere is SA = 4πr^2. The volume formula for a sphere is V=4/3πr^3. Use the given SA to find the value of V.16π=4πr^2 Divide by 4π on both sides. 4 = r^2. r=2 Plug in 2 for r in the equation V=4/3πr^3. Your answer should be around 10.7π cm³
Simplify by looking for like terms: 3a – a + 4b – 2b.
Answer:
2a+2b
Step-by-step explanation:
3a - a = 2a
4b - 2b = 2b
Answer:
2a+2b
Step-by-step explanation:
3a – a + 4b – 2b
Combine like terms
3a-a =2a
4b-2b =2b
3a – a + 4b – 2b. = 2a+2b