The 90% confidence interval that estimates the proportion of 8th graders that are involved in an after-school activity is (0.80853,0.93147).
The confidence interval for a population proportion for a given sample is given by the formula:
[tex](p-Z\sqrt{\frac{p(1-p}{n} } , p+Z\sqrt{\frac{p(1-p}{n} })[/tex],
where p is the population proportion, Z is the Z-score value for the confidence interval, and n is the sample size.
In the question, we are given a random sample of 81 8th graders at a large suburban middle school. This implies that the sample size, n = 81. Also, we are told that they indicated 87% of them were involved with some type of after-school activity. This implies that the population proportion, p = 87% = 0.87.
We are asked to find the 90% confidence interval that estimates the proportion of them that are involved in an after-school activity.
Z-score (Z) corresponding to a 90% confidence interval is 1.645.
Thus, we can find the confidence interval as follows:
(0.87 - 1.645√{(0.87(1 - 0.87))/81},0.87 + 1.645√{(0.87(1 - 0.87))/81})
= (0.87 - 0.061469,0.87 + 0.061469)
= (0.80853,0.93147).
Thus, the 90% confidence interval that estimates the proportion of 8th graders that are involved in an after-school activity is (0.80853,0.93147).
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Belinda is thinking about buying a car for $18,500. The table below shows the projected value of two different cars for three years:
Number of years
1
2
3
Car 1 (value in dollars) 17,390 16,346.60 15,365.80
Car 2 (value in dollars) 17,500 16,500 15,500
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)
Part C: Belinda wants to purchase a car that would have the greatest value in nine years. Will there be any significant difference in the value of either car after nine years?
Explain your answer, and show the value of each car after nine years. (4 points)
There is a significant value in the difference in the value of the car after nine years
The type of function (linear or exponential)?The table of values is given as:
Years 1 2 3
Car 1 17,390 16,346.60 15,365.80
Car 2 17,500 16,500 15,500
The values of car 1 have a common ratio of 0.94; this is calculated by dividing the terms of the function
The common ratio implies that the function of car 1 is a geometric function.
The values of car 2 have a common difference of -1000.
The common difference implies that the function of car 2 is a linear function.
The function of each car typeCar 1
In (a), we have:
Common ratio, r = 0.94
The initial value is given as:
a = 18,500
So, the function of car 1 is
f(x) = 18500 * 0.94^x
Car 2
In (a), we have:
Common difference, d = -1000
The initial value is given as:
a = 18,500
So, the function of car 2 is
f(x) = 18500 - 1000x
The car with the greatest value after 9 yearsThis means that
x = 9
So, we have:
Car 1
f(9) = 18500 * 0.94^9
f(9) = 10600
Car 2
f(9) = 18500 - 1000 *9
f(9) = 9500
10600 is greater than 9500
Hence, there is a significant value in the difference in the value of the car after nine years
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Solve the problems. Write the complete proof.
ONLY HAVE TO PROVE HOW BD IS PERPENDICULAR TO AC!
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. An isosceles triangle is one with two equal-length sides.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.
In ΔBAD and ΔBDC,
m∠ADB = m∠CDB {Given}
BD = BD {Common side in two triangles}
AD ≅ DC {Given}
Using the ASA postulate the two triangles are congruent. Therefore,
m∠BAD= m∠BCD.........equation 1
m∠ABD= m∠CBD
In ΔADC, AD ≅ DC {Given}, therefore, the triangle is an isosceles triangle. Thus,
m∠DAE = m∠DCE.......equation 2
Adding two of the equation 1 and 2,
m∠BAD + m∠DAE = m∠DCE + m∠BCD
∠BAC = ∠BCA
Since in ΔABC, ∠BAC = ∠BCA therefore, the triangle is an isosceles triangle, thus, AB = BC,
BE is the common side between ΔAEB and ΔCEB
Also, m∠ABD= m∠CBD
Therefore, ΔAEB ≅ ΔCEB
Now as ΔAEB ≅ ΔCEB, therefore, AE=EC,
Thus, BE is the median of the isosceles triangle ABC, and for an isosceles triangle, the median opposite to the non-common sides is the perpendicular bisector to the opposite side.
Hence, BD⊥AC.
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Someone please help me out with this one. If LM=XY, then LM-GH=
LM=XY, then LM-GH= XY - GH and this illustrates the subtraction property of equality.
How to illustrate the information?It should be noted that the subtraction property of equality simply implies that when the same number is subtracted form both sides, then the two sides will still remain equal.
In this case, when LM=XY, then LM-GH= XY - GH. This illustrates the subtraction property.
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Isla is dividing 3x3 + x2 – 12x – 4 by x + 2 using a division table.
Quotient
Divisor
3x2
– 5x
– 2
x
3x3
–5x2
–2x
+ 2
6x2
A
B
What are the missing values in the table?
The value of A and B are -10x and -4 respectively.
Division involves gathering a number of expressions into smaller forms.
The quotient is represented by the expression
Quotient= Dividend /Divisor
We have the value of the Dividend from the division table given in the question
Dividend of the Operation= A
Divisor of the Operation=2
Quotient of the Operation= -5x
As we know Quotient= Dividend /Divisor
So, -5x= A/2
multiplying 2 on both sides
⇒(-5x)2= A/2*2
⇒ A= -10x
Similarly, We have the value of the Dividend from the division table given in the question
Dividend of the Operation= B
Divisor of the Operation=2
Quotient of the Operation = -2
As we know Quotient= Dividend /Divisor
So, -2= B/2
multiplying 2 on both sides
⇒(-2)2= AB2*2
⇒ B= -4
Therefore the value of A and B are -10x and -4 respectively.
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RATING BRAINLIEST Which of the following demonstrates the Distributive Property?
4(2a + 3) = 8a + 3
4(2a + 3) = 2a + 12
4(2a + 3) = 6a + 7
4(2a + 3) = 8a + 12
Answer:
D: 4(2a+3)=8a+3
Step-by-step explanation:
4x2a = 8a and 4x3 = 12
Answer:
just saying this so other can get brainliest
Step-by-step explanation:
d
The shapes below are similar. Find the length x. Will mark brainliest!!!!!!
The value of x is 8 mm.
What are Similar Figures ?Similar Figures are the figures in which all the sides of one figure are in same ratio with the other side.
Two figures are given which are similar to each other .
When two figures are in ratio a:b then Area will be in ratio a² : b²
Area of figure 1 = 22 sq.mm
Area of figure 2 = 352 sq.mm
A1 :A2 = 22 /352
a² : b² = 1 / 16
a:b = 1/4
Therefore the bigger figure is 4 times the small figure .
The 4mm side will be 16 mm in the larger figure
The difference will be the value of x
x = 24 -16 = 8 mm
Therefore the value of x is 8 mm.
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Answer:
x = 8
Step-by-step explanation:
Similar shapes are dilations of each other using a scale factor.
As the area of both figures has been given, the scale factor that maps the green figure to the yellow figure can be calculated:
[tex]\implies \textsf{Scale factor (area)} = \dfrac{\textsf{area of yellow figure}}{\textsf{area of green figure}} = \sf \dfrac{352}{22} = 16[/tex]
Area is measured in square units. Therefore, to find the scale factor for length, square root the scale factor for area:
[tex]\begin{aligned}\implies \textsf{Scale factor (length)} & = \sf \sqrt{\textsf{Scale factor for area}} \\ & =\sf \sqrt{16}\\ & = \sf 4 \end{aligned}[/tex]
Use the found scale factor for length to find the perimeter of the yellow figure:
[tex]\begin{aligned} \sf \implies \textsf{Perimeter (yellow fig)} & = \sf \textsf{perimeter (green fig)} \times scale\:factor \\ & = \sf 26 \times 4 \\ & = \sf 104\: mm \end{aligned}[/tex]
Find the missing horizontal lengths of the yellow figure by using the corresponding length of the green figure:
⇒ 4 mm × 4 = 16 mm
⇒ 24 mm - 16 mm = 8 mm
Let the height of the yellow figure be y.
⇒ 24 + 8 + 16 + y + x + (y - x) = perimeter
⇒ 48 + 2y = 104
⇒ 2y = 56
⇒ y = 28 mm
Divide the yellow figure into two rectangles (see attachment).
Area of left rectangle = y × 8 = 28 × 8 = 224 mm²Area of right rectangle = 16x mm²To find x, sum the areas of the rectangles and equate to 352:
⇒ 224 + 16x = total area
⇒ 224 + 16x = 352
⇒ 16x = 128
⇒ x = 8
PLS HELP ME ASAP FIRST CORECT ANSWER GETS BRAINLEIST
Answer:
The area of the shape is 68 cm².
Step-by-step explanation:
We have to calculate the areas of the rectangle and triangle separately, and then add them together.
• Area of rectangle = length × breadth
= 30 cm × 2 cm
= 60 cm²
• Area of triangle = [tex]\frac{1}{2}[/tex] × base × perpendicular height
= [tex]\frac{1}{2}[/tex] × 2 cm × 8 cm
= 8 cm²
Adding the areas together = 60 cm² + 8 cm²
= 68 cm²
Multiply a Polynomial by a Monomial
In the following exercises, multiply.
236. (8b − 1)b
Answer:
The given expression is (8b − 1)b.We have to multiply the given expression.Distribute the expression then simplify to determine the answer.(8b − 1)b = 8b*b - 1*b
= 8b2 - b
Step-by-step explanation:
Hence the expression (8b − 1)b=8b2 - b.
If nicolai earns an 8 percent after tax rate of return, 9,500 today would be worth how much to nicolai in five years?
Nicolai would get worth of 13958.62 in five years for an 8% rate of return.
What is the rate of return?The net gain or loss of an investment over a given period stated as a percentage of the investment's starting cost is known as a rate of return (RoR).
Any type of investment instrument, including real estate, bonds, equities, and fine art, can be subject to a rate of return.
You determine the percentage change from the start of the period to the end when computing the rate of return.
Initial amount=9500
Rate of return=8%
Amount after 5 years=[tex]9500*(1+\frac{8}{100}) ^{5}[/tex]
[tex]=9500*(\frac{108}{100} )^{5}[/tex]
[tex]\\=13958.62[/tex]
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In the formula V = s²h, if s is doubled and
h tripled, then V multiplied by
This shows that if s is doubled and h tripled, then V multiplied by 12
Volume of a cuboidGiven the formula below expressed as:
V = s²h
If s is doubled and h tripled, the new volume will ne:
V1 = (2s)² * 3h
V2 = 4s² * 3h
V2 = 12s²h
V2 = 12V
This shows that if s is doubled and h tripled, then V multiplied by 12
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Complete the number pattern
An airline estimates that 90% of people booked on their flights actually show up. If the airline books 78 people on a flight for which the maximum number is 76, what is the probability that the number of people who show up will exceed the capacity of the plane
The probability that the number of people who show up will exceed the capacity of the plane is 0.002607722
What is the required probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The probability that x people show up follows a binomial distribution,
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]
Here, n represents the number of booked people and p represents the probability that a person shows up.
Then, the probability that x people show up is:
[tex]P(x)=\frac{78!}{x!(78-x)!}*0.90^{x}*(1-0.90)^{78-x}[/tex]
So, the probability that the number of people who show up will exceed the capacity of the plane is:
P(x>76) = P(77) + P(78)
Where P(77) and P(78) are calculated as follows:
[tex]P(77)=\frac{78!}{77!(78-77)!}* 0.90^{77}* (1-0.90)^{78-77} \\ =78*0.00029969*0.10\\ =0.0023375[/tex]
[tex]P(78)=\frac{78!}{78!(78-78)!}* 0.90^{78}* (1-0.90)^{78-78} \\ =1*0.00026972*1\\ =0.00026972[/tex]
Finally, P(x>76) is:
[tex]P(x > 76) = 0.0023375 + 0.00026972\\=0.002607722[/tex]
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Please help with this!!!!
Answer:
1)
Let the number of guests = x
∴ Pin hall total charge = 500 + 15x
Bloom place total charge = 350 + 18x
2)
The charges are equal.
∴ 500 + 15x = 350 + 18x
⇒ 150 = 3x
⇒ 50 = x
∴ x = 50
This means that the charges for both halls will be equal when there are 50 guests.
I need the answers can u help me please
Answer:
`1) 2.5cm, 2)1.25inches 3)2.25inches 4)1.25inches
Step-by-step explanation:
1) This is a centimeter rule, one small line represents 0.1cm and 1 long line represent 1cm, the line in between two long lines represent 0.5 cm
As you can see from A to B, is 2 cm + 0.5cm = 2.5cm.
2)This is found on the other side of rulers, inches.
1 small line represent 0.25 inches, line in between 2 long lines is 0.5 inches.
From S to T, is 1 inch + 0.25 inches = 1.25inches
3)Similar to Question 2.
Length of Pencil= 2 inches + 0.25 inches = 2.25 inches
4)This is a more detailed inch rule.
But length of heart shape = 1 inch + 0.25 inches = 1.25 inches
can someone please help mee (20 points will give brainliest!!!)
Answer:
Step-by-step explanation:
The is a factor of -3 which makes a vertical stretch on the y-axis of the original f(x) equation making a new g(x) equation.
g(x) = a * f(b(x-h)) + k
a - vertical stretch/shrink y-axis
b - horizontal stretch/shirink x-axis
h - horizontal shift right/left
k - vertical shift up/down.
Desmos
Analyzing Exponential Decay Graphs
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through (2, one-ninth), (1, one-third), (0, 1), and (negative 1, 3).
Analyze the graph of the exponential decay function.
The initial value is
.
The base, or rate of change, is
.
The domain is
Considering the given exponential function, we have that:
The initial value is of 1.The base is of [tex]\frac{1}{3}[/tex].The domain is of all real values.What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value, that is, the value of y when x = 0.b is the rate of change.When x = 0, y = 1, hence the initial value is of 1. When x changes by 1, y changes by 1/3, hence the base is of 1/3. Exponential functions have no restrictions, hence the domain is of all real values.
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Answer:
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through (2, one-ninth), (1, one-third), (0, 1), and (negative 1, 3).
Analyze the graph of the exponential decay function.
The initial value is
✔ 1
The base, or rate of change, is
✔ 1/3
The domain is
✔ all real numbers
Step-by-step explanation:
(05.02)The area of the parallelogram below is ___ square meters
Numerical Answers Expected!
Answer for Blank
Step-by-step explanation:
the area of a parallelogram is
baseline × height
which is in our case
9 × 7 = 63 m²
Answer:
ayo give the other guy brainilest
Step-by-step explanation:
Question 4 of 10; can someone help me.
pls help asap.............
The First graph does not have an initial Value
The second graph's solution is (3, -4)
What is Quadratic graph?A quadratic graph is a pictorial representation of quadratic functions.
It shows the relationship between a variable on the x-axis and a variable on the y-axis.
Analysis:
The First graph did not either start from the x or y-axis so it does not have an initial value.
The second graph each mark is 0.5 on both axes so the point of intersection of the two graphs is the solution of the graphs which the x- value is 3 and the y-value is -4.
Therefore (3, -4) is the solution of the graph.
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I need help please!!!
Based on the number of coins in the jar, the probability that Nina would not pick a penny or dime is a. 0.36.
The cost of the entire trip to the Cross family should they use the two cars is c. $107.07.
What is the probability to Nina?This can be found as:
= Number of quarters, and nickels) / (Number of quarters, nickels, dimes, and pennies)
= (13 + 18) / (13 + 25 + 18 + 30)
= 0.36
What is the cost of gasoline to the Cross family?= Cost of gas to first car + Cost of gas to second car
= (450/18 x 2.49) + (450 / 25 x 2.49)
= 62.25 + 44.82
= $107.07
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For the data in the table, tell whether y varies directly with x . If it does, write an equation for the direct variation.
x y
2 -6.6
3 -9.9
4 -13.2
5 -16.5
yes; y = x – 3.3
no
yes;
yes; y = –3.3x
Answer:
yes , y = - 3.3x
Step-by-step explanation:
if y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation , then
k = [tex]\frac{y}{x}[/tex]
checking k for each ordered pair in the table
[tex]\frac{-6.6}{2}[/tex] = - 3.3
[tex]\frac{-9.9}{3}[/tex] = - 3.3
[tex]\frac{-13.2}{4}[/tex] = - 3.3
[tex]\frac{-16.5}{5}[/tex] = - 3.3
thus k = - 3.3
so y varies directly with x and the equation of direct variation is
y = - 3.3x
what are the rates of the cyclists?
Answer:
24 km/h and 17 km/h
Step-by-step explanation:
We know that when two cyclists are traveling together, they will meet in the same time as if one cyclist with the combined speed of the two cyclists travelled the whole length. We don't know the speeds of the cyclists, so let's assign the one with the slower speed "x", and the one with the faster speed "x+7" the combined speeds is "2x+7"
Since the speed = distance / time, we can plug in the values
2x+7=205/5
2x+7=41
2x=34
x=17
We substitute x into the equation for the speed of the cyclists
Cyclist 1's speed: x, so their speed is 17 km/h
Cyclist 2's speed: x+7, so their speed is 17 + 7, or 24 km/h
Given: Triangle ADE~
Triangle CBF, ED bisects Angle ADC and F B bisects Angle ABC.
Prove: DF BE is a parallelogram.
Answer:
See proof below
Step-by-step explanation:
Given [tex]\triangle ADE \cong \triangle CBD[/tex]
Then, [tex]\angle AED \cong \angle CFB[/tex] because corresponding parts of congruent triangles are congruent.
Since [tex]\angle AED \text{ and } \angle DEB \text{ form a linear pair}[/tex], by the linear pair postulate, [tex]\angle AED \text{ and } \angle DEB \text{ are supplementary}[/tex].
Similarly, [tex]\angle CFB \text{ and } \angle BFD \text{ form a linear pair}[/tex], so by the linear pair postulate, [tex]\angle CFB \text{ and } \angle BFD \text{ are supplementary}[/tex].
By the Congruent supplements theorem, since [tex]\angle AED \text{ and } \angle DEB \text{ are supplementary}[/tex], [tex]\angle CFB \text{ and } \angle BFD \text{ are supplementary}[/tex], and [tex]\angle AED \cong \angle CFB[/tex] , then [tex]\angle DEB \cong \angle BFD[/tex]. (note, this is one pair of opposite angles inside quadrilateral DFBE)
Recalling that [tex]\overline {ED} \text{ bisects } \angle ADC, \text{ and } \overline {FB} \text{ bisects } \angle ABC[/tex], then, [tex]\angle ADE \cong \angle CDE[/tex], and [tex]\angle CBF \cong \angle FBA[/tex] by definition of angle bisector.
Note that [tex]\angle ADE \cong \angle CBF[/tex] because corresponding parts of congruent triangles are congruent.
Also, note that [tex]\angle EDF \cong \angle EDC[/tex] and [tex]\angle FBA \cong \angle FBE[/tex] because B, E, A are colinear, and D, F, C are colinear.
So, by the transitive property of angle congruence, [tex]\angle EDF \cong \angle FBE[/tex] (This is the other pair of opposite angles inside quadrilateral DFBE)
So, since both pairs of opposite angles are congruent, quadrilateral DFBE is a parallelogram, by a theorem about quadrilateral properties (your book may or may not have a name for it. It may just have a number).
G
E
H
LF
Each isosceles triangle had the same vertex angle as triangle EJF. The sum of the
vertex angles equals 180°. (2 points, one for the correct equation, one for the correct
solution.)
Let x = the number of isosceles triangles.
Fill in the equation with your answer from Q12 and solve for x.
- x = 180
The value of x in the triangle will be 30°
How to calculate the value?Let the base angles be x. The vertex angle will be:
= 2(x + x) = 4x
Since the sum of the angles in a triangle is 180°, therefore, 4x + x + x = 180°
6x = 180°
x = 180°/6
x = 30°
Therefore, the angles are 30°, 30°, and 120°. This makes up 180°.
Complete question:
In an isosceles triangle, the vertex angle is twice the sum of the base angles. Fund the angles of the triangle.
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What is the range of f?
Answer: [tex][-3,7][/tex]
Step-by-step explanation:
The range of a function is the set of y-values.
write a quadratic function F whose zeros are 12 and 1
Answer:
[tex]f(x) = (x-12)(x-1)[/tex]
Step-by-step explanation:
So when you have a quadratic equation it can usually be expressed as: [tex]a(x-b)(x-c)[/tex] where b and x are the roots of the equation. Since it's just asking for a function whose zeroes are 12 and 1, I'm assuming it doesn't care about the stretch/compression (value of a determines that), so I'll just assume a=1. if 12 and 1 are zeroes, that means it makes one of the factors equal to 0 because is x-b = 0 then no matter the value of x-c the value of y is 0 because 0 * (x-c) will be 0. So the equation becomes [tex]f(x) = (x-12)(x-1)[/tex] plugging in 12 or 1 as x will make one of the factors 0 thus making f(x) equal to 0
500 soldiers in a fort had enough food for 30 days if 125 more soldiers joined them then for how many days will the food last
Answer:
500+125=625625÷30=21 daysVERBAL
3. Explain how to interpret the initial value in a word problem that uses a linear function.
Answer:
The initial value in the word problem is the output value when input value is set to zero.
Step-by-step explanation:
In the question, it is given that a problem uses a linear function.It is required to explain how to interpret the initial value in a word problem.In order to find the initial value in a world problem, find the output value when input value is set to zero.If the initial value is marked as b for a linear function f(x), find it as follow,b = f (x=0)Find the decay factor from the equation y = 453(0.87)^4
The decay factor of the equation given in the task content is; 0.87.
What is the decay factor from the equation?According to the task content; the equation given is; y = 453(0.87)^4.
By comparison with exponential decay functions, it follows that the decay factor from the equation given is; 0.87 which insinuates that the factor of change after each decay is 0.87.
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what is the area of a polygone with vertices (-3,4) (2,4) (4,2) (2,-3) and (-3,-3)
By summing the areas of minor rectangles and triangles, the area of the irregular polygon whose vertices are (- 3, 4), (2, 4), (4, 2), (2, - 3) and (- 3, - 3) is equal to 42 square units.
How to determine the area of a irregular polygon
In this problem we have to determine the area of a irregular polygon, whose calculation is defined as a sum of the areas of triangles and rectangles. To determine the combination of squares and triangles, we need first to plot the vertices and construct the figure on a Cartesian plane.
The area of the irregular figure is:
A = (5) · (7) + 0.5 · 2² + 0.5 · (2) · (5)
A = 35 + 2 + 5
A = 42
By summing the areas of minor rectangles and triangles, the area of the irregular polygon whose vertices are (- 3, 4), (2, 4), (4, 2), (2, - 3) and (- 3, - 3) is equal to 42 square units.
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