Solving the system of equations, the number of children, parents, and Grandparents who were in attendance are 190, 140 and 70 respectively.
Let C, P and G denotes the number of children, parents and the grandparents in the function.
We get the system of equations,
C + P + G = 400 [equation 1]
P = 2G ⇒ G = P/2 [equation 2]
C = P + 50 [equation 3]
Substituting 2 and 3 in 1,
(P + 50) + P + (P/2) = 400
2P + P/2 = 350
5/2 P = 350
P = 140
C = P + 50 = 140 + 50 = 190
G = P/2 = 140/2 = 70
Hence the number of parents = 140, grandparents = 70 and children = 190.
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This graph represents the flight path of a model rocket launched in a park.
What do the key features of the curve represent in terms of the flight path of the rocket?
Chose from the drop-down to match each situation.
ill give brainlyest to the first to correctly answer this
The drop down menu is used to match each situation as below.
1. The rocket reached its maximum the x-value of the vertex
height in 5 s.
2. ground level the y-intercept
3. The rocket launcher was the y-value of the point containing
on the ground. the x-intercept on the right
4. The rocket was in the air 10 the x-intercept on the right
5. The maximum height of the the y-value of the vertex
rocket is 50 ft.
6. the time the rocket was the x-value of the point containing the
launched y-intercept
What is the key feature of the curveThe key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.
The vertex is the point the rocket had the maximum and height.
Generally, the curve traces a parabolic path
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Michel-Eugène Chevreul found that the greatest intensity came from placing ________colors next to each other.
tertirary
analogous
complementary
arbitrary
Michel-Eugène Chevreul found that the greatest intensity came from placing complementary colors next to each other. The Option C is correct.
Which colors create the greatest intensity?Chevreul made great contributions to the field of color theory as he made key findings was that placing complementary colors next to each other creates the greatest intensity.
These colors are opposite to each other on the color wheel such as red & green, blue & orange or yellow & purple. When these color are placed next to each other, these colors create a visual contrast that makes them appear brighter and more intense.
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Quadrilateral ABCD is inscribed in a circle such that:
Answer:
∠ C = 84°
Step-by-step explanation:
A quadrilateral inscribed in a circle is a cyclic quadrilateral.
the opposite angles sum to 180° , that is
∠ A + ∠ C = 180 , then
x² + 60 + 8x + 36 = 180
x² + 8x + 96 = 180 ( subtract 180 from both sides )
x² + 8x - 84 = 0 ← in standard form
(x + 14)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x + 14 = 0 ⇒ x = - 14
x - 6 = 0 ⇒ x = 6
x > 0 , then x = 6 , so
∠ C = 8x + 36 = 8(6) + 36 = 48 + 36 = 84°
which parent functions have a y-intercept at (0,0)? select all that apply
Answer: A,E or F.
Step-by-step explanation: That's the only ones that have X's and then x is 0
Anwer fast due tomorrow show work
Answer:45.3 miles/h
Step-by-step explanation
let 'x' be the speed of the car.
60 × 2/3 = 120/3 = 40
30 × 1/5 = 151/5
151/5 /40 = x / 60
151 / 200 = x / 60
=> x = (151×60) / 200
=> x = 45.3
2. The ramp above connects two vertical supports,
forming two similar triangles: AADE~ AABC. Side AC corresponds to which side in the other triangle?
Answer:
3. What is the length of side BC?
The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units
Side AC corresponds to which sideFor two triangles to be similar, the corresponding sides of the triangles must be in proportion
Having said that
The side AC corresponds to the side AC in the other triangle
What is the length of side BC?The length BC is calculated as
BC/9 = 25/15
Express as products
So, we have
BC = 9 * 25/15
Evaluate the products
BC = 15
Hence, the length of BC is 15 units
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Find the interest earned and the future value of an annuity with monthly payments of $200 for two years into an account that pays 6% interest per year compounded monthly.
The interest earned and the future value of an annuity with monthly payments of $200 for two years that pays 6% interest per year compounded monthly is $25.43 and $225.43
What is the interest earned?Principal,P = $200
Time, t = 6%
Number of periods, n = 12
Interest rate, r = 6%
= 6/100
= 0.06 rate per year,
FV = P(1 + r/n)^nt
FV = 200.00(1 + 0.06/12)^(12)(2)
FV = 200.00(1 + 0.005)^(24)
FV = $225.43
Therefore,
Principal = $200.00
Interest = $25.43
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In the figure below, the segments HI and HJ are tangent to the circle centered at O. Given that OI = 3.9 and OH= 6.5, find HJ.
H
6.5
9
O
HJ = 0
X
Based on the figure, we can see that triangles OHJ and OIX are similar because they share the same angle at O and HI and HJ are tangent to the circle. Thus, we can set up the following proportion:
OH / OI = HJ / (HJ + 9)
Substituting the given values:
6.5 / 3.9 = HJ / (HJ + 9)
Cross-multiplying:
6.5(HJ + 9) = 3.9HJ
Distributing:
6.5HJ + 58.5 = 3.9HJ
Simplifying:
2.6HJ = -58.5
HJ = -22.5
However, this answer doesn't make sense in the context of the problem. Since HJ represents a length, it cannot be negative. Therefore, we need to re-examine our work.
Looking back at our proportion, we can see that the ratio of OH to OI is greater than 1, which implies that HJ is greater than 9. This makes sense since HJ is a chord of the circle and thus must be longer than the radius.
Let's try the problem again, but this time we'll rearrange the proportion to solve for HJ:
HJ / (HJ + 9) = OI / OH
Substituting the given values:
HJ / (HJ + 9) = 3.9 / 6.5
Cross-multiplying:
6.5HJ = 3.9HJ + 35.1
Simplifying:
2.6HJ = 35.1
HJ = 13.5
Therefore, HJ is equal to 13.5.
(Scatterplots/Line of Best Fit) Jason designed an electronic system for a class
project. He recorded the temperature of the system over several minutes of
usage, shown in the table below. If the temperature is approximately 48 degrees,
how many minutes of usage did he record?
The most likely number of minutes of usage recorded by Jason is A . approximately 50.
How to find the minutes of usage ?We can see that initially, the temperature of the electronic system began to increase as the time increased. It then began to decrease from the 20 minute and ketp decreasing till the 40th minute.
Assuming that the temperature keeps decreasing, it would mean that at 50 minutes, the temperature would be more than the temperature at 40 minutes and so would most likely be 48 degrees.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
The second scatterplot does not suggest a linear relationship between x and y.
Answer appreciated! :D
Answer:
5/2
Step-by-step explanation:
Slope is rise over run, or how far it goes in the y direction over how far it goes in the x direction. In this case, y increases by a value of 5 at the same time x is increasing by a value of 2. This makes the slope 5/2, and it is positive since the values are increasing. If there is a problem your stuck on like this try graphing the points, desmos has a good graphing calculator :)
A cube has volume 3375 cubic inches. Determine the area of one face of the cube.
The area of one face of the cube that has a volume of 3375 cubic inches is: 225 square inches.
What is the Volume of a Cube?A cube has equal edge length, and therefore has faces with the same area. The formula for finding the volume of a cube is given as:
Volume of cube = s³, where s is the side length of the cube.
Also, to find the area of one face of a cube, we would use the formula below:
Area of one face of a cube = s².
Given the following:
Volume of a cube = 3375 cubic inches
Find s as shown below:
s = ∛3375
s = 15 inches.
Therefore, we have:
Area of one face of a cube = 15² = 225 square inches.
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Calculate the area of the square
The area of the given rectangle is 83.6cm²
How to find the area of the shape?We know that the area of a rectangle is equal to the product between the dimensions, here we can see that:
b = 11cm
h = 7.6cm
The formula for the area is:
A = b*h
Replacing the values we will get:
A = 11cm*7.6cm = 83.6cm²
that is the area.
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Use the binomial theorem to find specified term of the given power of binomial ( remember that r starts at 0 in the binomial theorem so finding say the second term means that r=1)
The fourth term in the expanded form of (x - 1)⁶ is -20x³.
What is the fourth term in the expanded form of (x - 1)⁶?The fourth term in the expanded form of (x - 1)⁶ using the binomial theorem is calculated as follows;
The expanded form of (x - 1)⁶ using the binomial theorem is;
(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1
(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1
To find the fourth term, we look for the fourth term from the left side to right side, which is -20x³.
Therefore, the fourth term in the expanded form of (x - 1)⁶ is -20x³.
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Danielle deposited $300.00 into a new savings account that earns interest compounded continuously. After 8 years, the balance in the account
was $907.00. What was the interest rate on the account?
O 13.8%
O 12.5%
O 14.5%
O 10.1%
A ribbon is lining the outside of a circular object. If the object has a radius of 7 cm, then how long should the ribbon be?
Answer:
Length= 43.98 cm
Step-by-step explanation:
Circumference=2πr
r=7cm
C=2π(7)
C=43.98 cm
circumference is equal to the length of ribbon along the outside of the circular object
MODELING REAL LIFE A hemisphere-shaped mole has a diameter of 5.7 millimeters and a surface area of about
51 square millimeters. The radius of the mole doubles. Estimate the new surface area of the mole. Round your
answer to the nearest whole number.
The new surface area is square millimeters.
The new surface area of the hemisphere-shaped mole would be = 102mm².
How to calculate the new surface area for the hemisphere-shaped mole?A hemisphere-shaped mole has a shape that has one surface that is curved and the other surface a flat circular base.
Since the surface area of one hemisphere has been given, the second hemisphere can be determined.
To calculate the new surface area of the hemisphere-shaped moles the following is carried out;
Radius of the initial mole = 5.7/2 = 2.85 mm
If 2.85mm radius = 51 mm²
2(2.85mm) radius = x
Make X the subject of formula;
X = 2×2.85 × 51/2.85
= 102 mm²
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given the expression (2^-3)(2^5)/2^7), select the three equivalent numerical expressions
The three equivalent numerical expressions are 1/32, 0.03125, 3.125 x 10^-2
How to simplify the numerical expressionsUsing the exponential rules, we can simplify the expressions as:
(2^-3)(2^5)/2^7)
= 2^(5-3)/2^7
= 2^2/2^7
= 1/2^(7-2)
= 1/2^5
= 1/32
Therefore, three equivalent numerical expressions for the given expression are: 1/32, 0.03125, 3.125 x 10^-2
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Given P( A) =0.12 P (B) = 0.12 P(A)=0.12, = 0.3 P(B)=0.3 and P(A ∪ B) = 0.334 P(A∪B)=0.334, find the value of P(A∩B), rounding to the nearest thousandth, if necessary.
The value of P(A∩B) rounding to the nearest thousandth, if necessary is: 0.086
How to solve probability problems?The parameters given are:
P(A) = 0.12
P(B) = 0.3
P(A ∪ B) = 0.334
We want to find the probability P(A∩B)
The P(A∪B) probability formula is given as:
P(A∪B) = P(A) + P(B) - P(A∩B)
where:
P(A) is Probability of event A happening
P(B) is Probability of event B happening
P(A∩B) is Probability of happening of both A and B.
Thus:
0.334 = 0.12 + 0.3 - P(A∩B)
P(A∩B) = 0.12 + 0.3 - 0.334
P(A∩B) = 0.086
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b. Allison went to the bakery and spent $3.75 for each cookie she bought and $1.50 for
a cup of lemonade. She spent a total of $24.00. What was the cost of each cookie?
Equation:
Answer:
PLEASE HELP ME! I will give brainliest answer! Please please!!
Answer:
12/2
Step-by-step explanation:
(x - h)^2 + (y - k)^2 = r^2
where (h,k) is the center of the circle and r is the radius.
Comparing this to the given equation, we see that the center of the circle is (-10,0) and the radius is sqrt(9) = 3.
The diameter of the circle is twice the radius, so:
diameter = 2(radius) = 2(3) = 6
Therefore, the diameter of the circle is 6.
We can write this in simplified, rationalized form as:
diameter = 6 = 6/1 = 12/2
Find (fog)(2).
f(x) = 3x + 2
g(x) = x²
(fog)(2)=
Answer:
(f·g)(2) = 14----------------------------
Find the composition of the functions f(x) and g(x), which is written as f(g(x)).
Given functions:
f(x) = 3x + 2,g(x) = x² .Find f(g(x)):
f(g(x)) = f(x²) = 3(x²) + 2Evaluate f(g(2)):
f(g(2)) = 3(2²) + 2 = 3(4) + 2 = 12 + 2 = 14So, (f·g)(2) = 14.
5- Solve the following expression and write the answers in the lowest term possible. [1
point]
a.
(m-8)²
m-4
n²-12m+32
2m
X
2m²-16m
m²-8m+161
The solutions to the expressions are (m-8)² = m² - 16m + 64 and 2m²-16m + m²-8m+161 = 3m²- 24m + 161
Solving the expressionsFrom the question, we have the following parameters that can be used in our computation:
(m-8)²
Expand
So, we have
m² - 16m + 64
Next, we have
2m²-16m + m²-8m+161
Evaluate the like terms
3m²- 24m + 161
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Solve for W.
w² + 7w = 0
Answer:
w=0,
w=-7
Step-by-step explanation:
Evelyn has 36 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 154 square meters. List each set of possible dimensions (length and width) of the field.
The possible dimensions (length and width) of the field which is rectangle are (26m, 5m) or (5m, 26m) and (28m, 4m) or (4m, 28m)
Let's assume the length of the rectangle be L and the width be W.
We know that we have three sides of the rectangle to fence, so the total length of the fence will be L+2W = 36m.
Also, we know the area of the rectangle = L×W = 154 sq.m
Using the two equations above, we can solve for L and W as follows:
L = 36 - 2W (from the first equation)
Substituting this value of L in the second equation:
(36 - 2W)W = 154
2W² - 18W + 77 = 0
We get two possible values of width: W = 5 or W = 4
For W = 5, L = 26
For W = 4, L = 28
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which statement about odd functions is correct?
Answer: C
Step-by-step explanation:
Think about y=[tex]x^{3}[/tex] This is an odd function because the highest exponent(degree) is odd
A. is wrong. Symmetry is where you can fold it and it would be the same. If i folded y=[tex]x^{3}[/tex] along the y- axis it would not be the same.
B is wrong. Transformations are where has it moved, which has nothing to do with odd functions in general
C. is correct. It is folded along y=x and flipped.
D. is wrong. If folded y=x it's in the same quadrant but it's not the same, its' reversed.
Find P U (Q n R).........................
Select an association attribute in each box to complete the sentence
Answer:
The pattern of association between time and distance is positive and linear.
write an equivilant fractions for 3 3/4 and 1 2/3 using a common denominator iready
The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.
To find a common denominator for 4 and 3, we can multiply them together to get 12.
So, we can convert 3 3/4 as:
3 3/4 = 12/4 + 3/4 = 15/4
Similarly, we can convert 1 2/3 as:
1 2/3 = 5/3
Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:
15/4 = 45/12 and 5/3 = 20/12
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If I have 100 tiles and 98 are letters and 2 are blank I randomly drawl 2 title the first is a consonant and the 2 nd is a vowel what is the probability that both events will occur
The probability that both events will occur is 23.76%.
Given that, you have 100 tiles and 98 are letters and 2 are blank you randomly drawl 2 title the first is a consonant and the 2nd is a vowel.
Consonants (A) = 56
Vowels (B) = 42
Blank = 2
Total letters = 100
Two letters are drawn with replacement.
P(A) = 56/100 = 0.56
P(B) = 42/ (100-1) = 0.424
P(A).P(B) = 0.56*0.424 = 0.2376
Hence, the probability that both events will occur is 23.76%.
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Complete question is attached.