Answer:
2k+16
Step-by-step explanation:
Kevin: k
Ben: 8 years older than k, k+8
Hannah: 2 times Ben's age, 2(k+8)=2k+16
The admission fee at an amusement park is $2.25 for children and $5.60 for adults. On a certain day, 269 people entered the park, and the admission fees collected totaled 1091 dollars. How many children and how many adults were admitted?
Vanilla rent increased by 5%. The increase was $82. What was the original amount of Pavati's rent?
What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
58.85°
Step-by-step explanation:
You want to know the measure of the angle in the right triangle that has hypotenuse 29 and adjacent side 15.
CosineThe cosine function relates angles and sides by ...
Cos = Adjacent/Hypotenuse
cos(x) = 15/29
The inverse function is used to find the angle value:
x = arccos(15/29) ≈ 58.85°
The value of x is about 58.85°.
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David is trying to pick out an outfit for the first day of school. He can choose from 8 pairs of pants, 8 t-shirts, 4 sweaters or hoodies, and 3 pairs of shoes. How many different outfits does David have to choose from?
The number of the different outfits do David have to choose is 768.
Here we will use the concept of Combinations,
Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
Different outfits do Damian have to choose, will be;
⇒ 8C₁×4C₁×8C₁×3C₁
⇒ 8×4×8×3
⇒ 768
Hence, the number of the different outfits do David have to select is 768.
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Use a half-angle identity to find the exact value of tan5π/12
The required exact value of tan(5π/12) is (2 + √3) / 3.
We can use the half-angle identity for a tangent:
tan(x/2) = [1 - cos(x)] / sin(x)
to find the exact value of tan(5π/12), since 5π/12 is a half-angle of 5π/6.
First, we find the values of sin(5π/6) and cos(5π/6) using the unit circle:
sin(5π/6) = sin(π - π/6) = sin(π/6) = 1/2
cos(5π/6) = cos(π - π/6) = -cos(π/6) = -√3/2
Now we can use the half-angle identity for a tangent with x=5π/6:
tan(5π/12) = tan[(5π/6)/2] = [1 - cos(5π/6)] / sin(5π/6)
= [1 - (-√3/2)] / (1/2)
= (2 + √3) / 3
Therefore, the exact value of tan(5π/12) is (2 + √3) / 3.
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The endpoints of WX are W(-5,-1) and X(2,6).
What is the length of WX?
A. 7
B. 14
C. 4√2
D. 7/2
find the area of the figure (hint don’t forget units!)
5.2 ft 3 ft 2.4
Answer:
A = 11.4 ft²
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between the bases
here h = 3 , b₁ = 2.4 , b₂ = 5.2 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (2.4 + 5.2) = 1.5 × 7.6 = 11.4 ft²
A country recently had a GDP of $1000 billion. Its consumption expenditures were $650 billion, its government spent $250 billion, and it had domestic investment of $150 billion. What was the value of this country’s net capital outflow?
The value of this country's net capital outflow is $200 billion.
We have,
The formula for net capital outflow (NCO) is:
NCO = Domestic Investment - Foreign Investment
Since the problem only gives us information about domestic investment, we need to use another formula to calculate foreign investment.
The formula for national saving (S) is:
S = GDP - Consumption Expenditures - Government Spending
We can rearrange this formula to solve for foreign investment:
Foreign Investment = GDP - Consumption Expenditures - Government Spending - Domestic Investment
Substituting the given values, we get:
Foreign Investment = $1000 billion - $650 billion - $250 billion - $150 billion
Foreign Investment = $1000 billion - $1050 billion
Foreign Investment = -$50 billion
The negative sign indicates that there is a net capital inflow (i.e., foreign investment is greater than domestic investment).
Therefore, the value of this country's net capital outflow is:
NCO = Domestic Investment - Foreign Investment
NCO = $150 billion - (-$50 billion)
NCO = $150 billion + $50 billion
NCO = $200 billion
Thus,
The value of this country's net capital outflow is $200 billion.
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After running a 100 meter dash, Jane turns left 40 degrees and walks 60 meter. True or false: she is closer now to her starting position than when she crossed the finish line. What about if Jane turns left 90 degrees or 120 degrees?
False. When Jane turns left 40 degrees and walks 60 meters, she is farther away from her starting position than when she crossed the finish line.
If Jane turns left 90 degrees or 120 degrees, then she will also be farther away from her starting position than when she crossed the finish line. Turning left 90 degrees or 120 degrees will take her in a different direction, and thus she will be farther away from her starting position than when she crossed the finish line.
Therefore, the given statement is false.
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The list represents the ages of students in a gymnastics class. 10, 10, 11, 12, 12, 13, 13, 14, 14, 15 If another student of age 15 joins the class, how is the mean affected? The mean will remain the same at 13. The mean will remain the same at about 12.4. The mean will increase to about 12.6. The mean will decrease to about 11.
The required mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.
The original mean is the sum of the ages divided by the number of students:
Mean = (10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15) / 10
Mean = 124 / 10
Mean = 12.4
If another student of age 15 joins the class, the new sum of the ages is:
Sum = 10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 15
Sum = 139
The new mean is the new sum of ages divided by the new number of students:
New mean = Sum / (Number of students + 1)
New mean = 139 / 11
New mean = 12.63636... or about 12.6 (rounded to one decimal place)
Therefore, the mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.
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Find the area of the composite figure.
2 ft
F
4.5 ft
K
6.5 ft
1 ft
1 ft
Answer:
The area is 13 feet squared.
Step-by-step explanation:
To find the area, first separate the composite figure into two shapes: a rectangle and a triangle.
Find the area of each shape separately, and then add the areas together.
First, the rectangle:
length= 4.5 feet
width = 2 feet
[tex]2*4.5=9 ft^{2}[/tex]
The area of the rectangle is 9 feet squared.
Next, the triangle:
The base is 2 feet + 1 foot + 1 foot = 4 feet
The height is 6.5 feet - 4.5 feet = 2 feet
The formula to find the area of a triangle is [tex]\frac{h*b}{2}[/tex] (height times base over two)
[tex]\frac{2*4}{2}=4ft^{2}[/tex]
the area of the triangle is 4 feet squared.
Add the two areas together to find the total area of the composite figure:
[tex]9ft^{2} +4ft^{2}=13ft^{2}[/tex]
The area is 13 feet squared.
A boat heading out to sea starts out at Point A, at a horizontal distance of 1035 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 8°. At some later time, the crew measures the angle of elevation from point B to be 5°. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Note that given the angle of elevation, the distance from pont A to Point B is approximately 627.6ft.
See the attached image.
As shown in the attached figure:
L = AO Tan 8°
L = 1035 * Tan 8°
L = 1035 * 0.14054083470239144683811769343281
L = 1035 * 0.14054083470239144683811769343281
L = 145.46 Feet
BO = L/Tan 5°
BO = 145.459763917 / 0.08748866352592400522201866943496
BO = 1662.61270952
BO = 1662.6 Feet
Since AB = BO-AO
AB = 1662.6-1035
AB = 627.6 Ft.
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Please help !!!!!!!!!!!!!!!!
length LD = 6 units
length DF = 9 units
length HF = 6 units
length LH = 9 units
length L'D' = 2 units
length D'F' = 3 units
length H'F' = 2 units
length L'H' = 3 units
What is dilation?Dilation is the scaling of an object, where it gets bigger or smaller.
Scale factor = new dimension/old dimension
length LD = 15-9 = 6units
length DF = 6-(-3) = 9units
length HF = 15-9 = 6 units
length LH = 6-(-3) = 9 units
Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.
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Determine the value of y, if x is 3.
y = x² + 11
Answer:
20
Step-by-step explanation:
just a substitute 3 in x so 3x3=9
11+9=20
if f(x)=x³-1 and g(x)=x²
find (gof) ( x) and (fog) (x)
Answer:
(x²)³ - 1 = x^6 - 1
Step-by-step explanation:
To find (gof)(x), we first need to evaluate g(x), which is x², and then use the result as input to f(x), giving us f(g(x)).
So, we have:
g(x) = x²
f(g(x)) = f(x²) = (x²)³ - 1 = x^6 - 1
Therefore, (gof)(x) = g(f(x)) = (f(x))² = (x³ - 1)² = x^6 - 2x^3 + 1.
To find (fog)(x), we first need to evaluate f(x), which is x³ - 1, and then use the result as input to g(x), giving us g(f(x)).
So, we have:
f(x) = x³ - 1
g(f(x)) = g(x³ - 1) = (x³ - 1)² = x^6 - 2x^3 + 1
Therefore, (fog)(x) = f(g(x)) = (x²)³ - 1 = x^6 - 1.
A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Find P (4) and Find P (More than 2)
Probability of answering exactly 4 questions correctly = 0.206
P (More than 2) = 0.475
How to solve for the probability1.
ind P(4): Probability of answering exactly 4 questions correctly.
P(X=4) = (10C4) * (0.25^4) * (0.75^6)
10C4 = 10! / (4! * (10-4)!) = 210
P(X=4) = 210 * (0.25^4) * (0.75^6)
= 0.206
2. P(More than 2):P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056
P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187
P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282
Now, calculate P(X>2):
P(X>2)
= 1 - (P(X=0) + P(X=1) + P(X=2))
= 1 - (0.056 + 0.187 + 0.282)
= 1 - 0.525
= 0.475
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Let u = -2i+9j, v = 2i- j, and w= -4i. Find 3u - (2v-w).
3u - (2v-w) =
(Type your answer in terms of i and j.)
The value of 3u - (2v-w) is -6i + 25j.
We have,
u = -2i+9j, v = 2i- j, and w= -4i.
Now, 3u - (2v - w)
= 3(-2i + 9j) - [ 2(2i - j) - (-4i)]
= -6i + 27j - [4i - 2j + 4i]
= -6i + 27j - 4i - 2j + 4i
= -6i + 25j
Thus, the value of 3u - (2v-w) is -6i + 25j.
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Ayuda por favor es para mañana, fracciones equivalentes. Doy coronita
These fractions are equivalent fractions by algebraic property:
Case 1: YES
Case 2: NO
Case 3: YES
Case 4: NO
Case 5: YES
Case 6: YES
Case 7: NO
Case 8: YES
Case 9: YES
Case 10: YES
Case 11: NO
Case 12: YES
Case 13: NO
Case 14: YES
Case 15: YES
Case 16: YES
Case 17: NO
Case 18: YES
How to determine if two fractions are equivalent
In this question we must check 18 cases of equivalent fractions, two fractions are equivalent if the following algebraic property is met:
a / b = (a · c) / (b · c), where a, b, c are integers and c is nonzero.
Now we proceed to determine if each pair is equivalent:
Case 1
2 / 3 = (2 · 2) / (3 · 2)
2 / 3 = 4 / 6 (YES)
Case 2
2 / 6 = (2 · 3) / (6 · 3)
2 / 6 = 6 / 18 (NO)
Case 3
9 / 9 = (9 · 4) / (9 · 4) = 36 / 36 (YES)
Case 4
3 / 11 = (3 · 3) / (11 · 3) = 9 / 33 (NO)
Case 5
7 / 8 = (7 · 2) / (8 · 2) = 14 / 16 (YES)
Case 6
4 / 6 = (4 · 5) / (6 · 5) = 20 / 30 (YES)
Case 7
5 / 6 = (5 · 2) / (6 · 2) = 10 / 12 (NO)
Case 8
2 / 7 = (2 · 4) / (7 · 4) = 8 / 28 (YES)
Case 9
6 / 12 = (6 · 2) / (12 · 2) = 12 / 24 (YES)
Case 10
4 / 9 = (4 · 5) / (9 · 5) = 20 / 45 (YES)
Case 11
9 / 10 = (9 · 3) / (10 · 3) = 27 / 30 (NO)
Case 12
1 / 5 = (1 · 5) / (5 · 5) = 5 / 25 (YES)
Case 13
12 / 12 = (12 · 3) / (12 · 3) = 36 / 36 (NO)
Case 14
8 / 11 = (8 · 4) / (11 · 4) = 32 / 44 (YES)
Case 15
5 / 5 = (5 · 4) / (5 · 4) = 20 / 20 (YES)
Case 16
6 / 9 = (6 · 4) / (9 · 4) = 24 / 36 (YES)
Case 17
3 / 7 = (3 · 8) / (7 · 8) = 24 / 56 (NO)
Case 18
10 / 12 = (10 · 4) / (12 · 4) = 40 / 48 (YES)
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How many times greater is the
value of the 4 in 2,849 than the
value of the 4 in 3,824?
Answer:
The value of the 4 in 2,849 is 4 x 100 = 400, while the value of the 4 in 3,824 is 4 x 10 = 40. Therefore, the value of the 4 in 2,849 is 400/40 = 10 times greater than the value of the 4 in 3,824.
Step-by-step explanation:
i need help with this prblem
Answer:
y = x + 2
Step-by-step explanation:
y = mx + b
Point (0, 2) shows that the y-intercept is 2, so b = 2.
y = mx + 2
Now we find the slope using the 2 points, (0, 2) and (2, 4).
m = (4 - 2)/(2 - 0) = 1
y = x + 2
what is this pls help
Select the correct answer. Determine which statement is true about the zeros of the function graphed below. An upward parabola f on a coordinate plane vertex at (1, 4) and intercepts the y-axis at 5 units. A. Function f has one real solution and one complex solution. B. Function f has exactly one real solution and no complex solutions. C. Function f has exactly two real solutions. D. Function f has exactly two complex solutions.
The correct option is D, the equation has two complex solutions.
Which is the correct statement about the quadratic equation?Here we can see that we have the graph of a quadratic equation.
It opens upwards, and we can see that it has a vertex at (1, 4), which intercepts the y-axis at y = 5.
Now, we say that the solutions of a quadratic are the values of x such that the function becomes zero.
Particualrly, in this graph we can see that the graph never intercepts the x-axis, that means that this equation has no real roots.
Then the correct option is:
"Function f has exactly two complex solutions."
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Which relation is a function?
The only graph that represents a function is: Graph D
How to identify a function?A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
From the graphs, we can see that:
Graph A has 2 outputs at x = -2
Graph B has 2 outputs at x = 0
Graph C has two outputs at x = -1
Graph D has a unique output for every input and as such it is a function
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Answers for these test question
The missing lengths and angles in the geometric systems are listed below:
Case 8: x = 60
Case 9: x = 48
Case 10: x = 5.535
Case 11: x = 5.665
Case 12: x = 9.103
Case 13: θ = 60°
Case 14: θ = 23.025°
How to find missing lengths and angles in triangles
In this problem we find two cases of geometric systems formed by triangles:
Systems of two similar triangles with a common unknown side.A triangle with an unknown side or an unknown angle.First case is analyzed by means of proportionality ratios and second case done by trigonometric functions:
Case 8
100 / x = x / 36
x² = 3600
x = 60
Case 9
x / 36 = 64 / x
x² = 36 · 64
x = 48
Case 10
x = 17 · sin 19°
x = 5.535
Case 11
x = 11 · cos 59°
x = 5.665
Case 12
x = 13 · tan 35°
x = 9.103
Case 13
cos θ = 7 / 14
cos θ = 1 / 2
θ = 60°
Case 14
tan θ = 17 / 40
θ = 23.025°
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If Ton spend $76.25 on food for a party. And he is having 4 friends over what average amount of money he will spent for food per person?
Answer: He would be spending $15.25 for each person including himself
Step-by-step explanation:
step 1. you need to find out how many people are getting food
step 2. divide that number (5) by how much the total cost is ($76.25) to get 15.25
If m/8 = 133°, find m/1.
Answer:
1064
Step-by-step explanation:
If m/8 = 133°, find m/1.
m/1 = m (Any number, except zero, divided by itself is 1)
m : 8 = 133 : 1
m = 8 * 133 : 1
m = 1064
----------------------
check
1064 : 8 = 133 : 1
133 = 133
the answer is good
Solve the following for θ, in radians, where 0≤θ<2π.
−sin2(θ)−4sin(θ)+4=0
Select all that apply:
1.1
2.52
0.98
0.69
1.43
2.17
Answer:0.98
2.17 are correct
Step-by-step explanation:
-u^2 - 4u + 4 = 0
Multiplying both sides by -1, we get:
u^2 + 4u - 4 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 4, and c = -4. Substituting these values, we get:
u = (-4 ± sqrt(4^2 - 4(1)(-4))) / 2(1)
u = (-4 ± sqrt(32)) / 2
u = (-4 ± 4sqrt(2)) / 2
u = -2 ± 2sqrt(2)
Therefore, either:
For a population growing at 3% a year, what is the yearly growth factor?
7.35 km = _______ mm
Answer: 7.35 km = 7350000 mm
Step-by-step explanation:
Multiply km by 1000000
7.35 * 1000000 = 7350000 mm
How do l do this? Help please
By expanding and simplifying the algebraic expression (y + 7)(y - 5), we have the result y² + 2y - 35
How to expand and simplify algebraic expression in bracketsTo expand an algebraic expression in brackets, we need to use the distributive property to make is easy for simplification, thus we expand and simplify the expression as follows:
(y + 7)(y - 5) = y(y - 5) + 7(y - 5) {distributive property}
(y + 7)(y - 5) = y² - 5y + 7y - 35
by simplification, we have;
(y + 7)(y - 5) = y² + 2y - 35
Therefore, the expansion and simplification of the algebraic expression (y + 7)(y - 5), gives the result y² + 2y - 35.
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