What is -1 - 9
Solve for 2x-4y =20
X=4

Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).  Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

Abigail and Curtis Siebert have a $270,000 mortgage at an interest rate of 7% for a term of 20 years.

To calculate the monthly mortgage payment, we can use the formula for an amortizing mortgage:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1),

where M is the monthly mortgage payment, P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of monthly payments.

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is 7% divided by 12, which is approximately 0.5833%.

The total number of monthly payments is the term of the mortgage multiplied by 12. In this case, it's 20 years * 12 months, which equals 240 months.

Now, we can substitute the values into the formula:

M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).

Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

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Answer:

If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. Given : ABCD is a quadrilateral in which ∠A = ∠C and ∠B = ∠D. We know that the sum of the angles of a quadrilateral is 360o.

Step-by-step explanation:

hope that helps

Answer:

$428

Step-by-step explanation:

you can do 72*24= the 2 year period and then you get 1728

you then do 1728-1300 and you will get $428 more

a. P(Z = 1) = ∫G(s)f(s)ds is the distribution of Z.

b. X and Z are independent.

c. X and Y are not independent.

a) We have Z = I(S > 2T), where I is the indicator function. Then,

P(Z = 1) = P(S > 2T) = ∫∫(s > 2t) f(s) f(t) ds dt

Using the fact that S and T are independent, we get

∫∫(s > 2t) f(s) f(t) ds dt = ∫∫f(s)ds ∫∫f(t)I(s > 2t)dt ds

Letting G(s) = ∫f(t)I(s > 2t)dt, we get

P(Z = 1) = ∫G(s)f(s)ds

b) We have X = min(S,T) and Z = I(S > 2T). To check whether X and Z are independent, we compute their joint distribution:

P(X > x, Z = 1) = P(S > 2T, S > x, T > x) = ∫∫(s > 2t) f(s) f(t) ds dt ∫\(x^\infty\)f(u)du

= ∫\(x^\infty\)f(u)du ∫\((u/2)^x\) f(t) dt ∫\(t^\infty\) f(s) ds

= 1/2 ∫\(x^\infty\)f(u) ∫\(t^\infty\) f(s) ds dt

= 1/2 ∫\(x^\infty\)f(u) G(t) dt

= 1/2 ∫\(x^\infty\)f(u) ∫f(t)I(u > 2t)dt du

= ∫\(x/2^\infty\) f(u) ∫f(t)I(u > 2t)dt du

= P(X > x)P(Z = 1), using the fact that S and T are independent.

Therefore, X and Z are independent. Similarly, we can show that Y and Z are independent and (X, Y) and Z are independent.

c) X and Y are not independent, since the event {X > x} implies that both S and T are greater than x, which means that the event {Y > y} is more likely to occur for larger values of y.

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The calculated price per video game for store A is $1.79 per game

From the question, we have the following parameters that can be used in our computation:

The price per video game for store A is calculated as

Price per video game = Total price/Number of games

using the above as a guide, we have the following:

Price per video game = 8.95/5

Evaluate the quotient

So, we have

Price per video game = 1.79

Hence, the price per video game for store A is $1.79 per game

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Applying the intersecting secants theorem, the length of segment KL is approximately, 45.8.

According to the intersecting secants theorem, if two lines from a point outside a circle intersect the circle, then the product of the length of one line segment and its portion outside the circle is equal to the product of the length of the other line segment and its portion outside the circle.

Using the theorem, we have:

MN * MO = ML * MK

Substitute:

21 * 48 = 22 * KL

1,008 = 22KL

1,008/22 = KL

KL = 45.8 (nearest tenth)

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Answer:

Point Form:

(4,−12)(4,-12)

Equation Form:

x=4,y=−12

Answer:

Respuesta certificada por un experto

El doble de 0.25 es 0.50. El doble de 0.50 es 1.00.

Step-by-step explanation:

We will investigate the missing value under division operation.

The missing value will be represented as a variable ( x ). We can then write down the division of two numbers as follows:

We are to solve the above equation by manipulating the entire equation. We will try to isolate the vairable ( x ) on the left hand side of the " = " sign! To do that we will multiply the entire equation by the denominator value as follows:

Simplify the left hand side of the " = " sign as follows:

Therefore, the solution to the missing value is:

Answer:

We reject the Null and conclude that the mean costs of a meal at fast food restaurants in two different cities are different.

Step-by-step explanation:

Given :

City n x s

A 26 $4.05 $0.55

B 32 $5.15 $0.85

H0 : μ1 - μ2 = 0

H0 : μ1 - μ2 ≠ 0

n1 = 26 ; x1 = 4.05 ; s1 = 0.55

n2 = 32 ; x2 = 5.15 ; s2 = 0.85

Tstatistic :

(x1 - x2) / √(s1²/n1 + s2²/n2)

(4.05 - 5.15) / √(0.55²/26 + 0.85²/32)

-1.1 / 0.1849668

= - 5.947

Using the smaller n;

df = n - 1 ; 26 - 1 = 25

Pvalue = (-5.947, 24)

Pvalue = 0.000001

Since Pvalue < α ; We reject the Null and conclude that the mean costs of a meal at fast food restaurants in two different cities are different.

Answer:

\(\textsf{a)} \quad T_n=-n^2+n+20\)

\(\textsf{b)} \quad T_{12}=-112\)

\(\textsf{c)} \quad \sf 8th\;term\)

a)  Second difference is 2.

b)  First term is 10.

Step-by-step explanation:

The given number pattern is:

To determine the type of sequence, begin by calculating the first differences between consecutive terms:

\(20 \underset{-2}{\longrightarrow} 18 \underset{-4}{\longrightarrow} 14 \underset{-6}{\longrightarrow}8\)

As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):

\(-2 \underset{-2}{\longrightarrow} -4 \underset{-2}{\longrightarrow} -6\)

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

As the second difference is -2, the coefficient of the n² term is -1.

Now we need to compare -n² with the given sequence (where n is the position of the term in the sequence).

\(\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}\sf operation&+21&+22&+23&+24\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}\)

We can see that the algebraic operation that takes -n² to the terms of the sequence is to add (n + 20).

\(\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}+n&0&-2&-6&-12\\\cline{1-5}+20&20&18&14&8\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}\)

Therefore, the expression to find the the nth term of the given quadratic sequence is:

\(\boxed{T_n=-n^2+n+20}\)

To find the value of T₁₂, substitute n = 12 into the nth term equation:

\(\begin{aligned}T_{12}&=-(12)^2+(12)+20\\&=-144+12+20\\&=-132+20\\&=-112\end{aligned}\)

Therefore, the 12th term of the number pattern is -112.

To find the position of the term that has a value of -36, substitute Tₙ = -36 into the nth term equation and solve for n:

\(\begin{aligned}T_n&=-36\\-n^2+n+20&=-36\\-n^2+n+56&=0\\n^2-n-56&=0\\n^2-8n+7n-56&=0\\n(n-8)+7(n-8)&=0\\(n+7)(n-8)&=0\\\\\implies n&=-7\\\implies n&=8\end{aligned}\)

As the position of the term cannot be negative, the term that has a value of -36 is the 8th term.

\(\hrulefill\)

Given terms of a quadratic number pattern:

We know the first differences are negative, since the difference between the second and third terms is -7. Label the unknown differences as -a, -b and -c:

\(T_1 \underset{-a}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-b}{\longrightarrow}T_4 \underset{-c}{\longrightarrow} -14\)

From this we can create three equations:

\(T_1-a=1\)

\(-6-b=T_4\)

\(T_4-c=-14\)

The second differences are the same in a quadratic sequence. Let the second difference be x. (As we don't know the sign of the second difference, keep it as positive for now).

\(-a \underset{+x}{\longrightarrow} -7\underset{+x}{\longrightarrow} -b \underset{+x}{\longrightarrow}-c\)

From this we can create three equations:

\(-a+x=-7\)

\(-7+x=-b\)

\(-b+x=-c\)

Substitute the equation for -b into the equation for -c to create an equation for -c in terms of x:

\(-c=(-7+x)+x\)

\(-c=2x-7\)

Substitute the equations for -b and -c (in terms of x) into the second two equations created from the first differences to create two equations for T₄ in terms of x:

\(\begin{aligned}-6-b&=T_4\\-6-7+x&=T_4\\T_4&=x-13\end{aligned}\)

\(\begin{aligned}T_4-c&=-14\\T_4+2x-7&=-14\\T_4&=-2x-7\\\end{aligned}\)

Solve for x by equating the two equations for T₄:

\(\begin{aligned}T_4&=T_4\\x-13&=-2x-7\\3x&=6\\x&=2\end{aligned}\)

Therefore, the second difference is 2.

Substitute the found value of x into the equations for -a, -b and -c to find the first differences:

\(-a+2=-7 \implies -a=-9\)

\(-7+2=-b \implies -b=-5\)

\(-5+2=-c \implies -c=-3\)

Therefore, the first differences are:

\(T_1 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}T_4 \underset{-3}{\longrightarrow} -14\)

Finally, calculate the first term:

\(\begin{aligned}T_1-9&=1\\T_1&=1+9\\T_1&=10\end{aligned}\)

Therefore, the first term in the number pattern is 10.

\(10 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}-11 \underset{-3}{\longrightarrow} -14\)

Note: The equation for the nth term is:

\(\boxed{T_n=n^2-12n+21}\)

Answer:

4?

Step-by-step explanation:

Answer:

2n-(n+5)=3

Step-by-step explanation:

Answer:

(x+1)(x+5)(x-5)

Step-by-step explanation:

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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The length of the arc intercepted by a central angle of 3 radians in a circle of radius 76 is 228 and the length of the arc intercepted by a central angle of 2 radians in a circle of radius 15 is 30.

Explain:

The following formula determines the length of an arc that a circle's central angle intercepts:

Arc length is equal to (central angle / 2) 2r r r

where r denotes the circle's radius. We can determine the length of the two arcs using the following formula:

For the first circle, with a radius of 76 and a center angle of 3 radians:

Arc length = 3 x 76 = 228

Therefore, in a circle with a radius of 76, the length of the arc that is intercepted by a central angle of 3 radians is 228.

For the second circle, whose radius is 15, and whose center angle is 2 radians:

Arc length = 2 x 15 = 30

As a result, the length of the arc in a circle with a radius of 15 is 30 when it is intercepted by a central angle of 2 radians.

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Complete question is;

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:

Do the results support the manufacturer's claim?

Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed

Answer:

We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

Step-by-step explanation:

For the first sample, we have;

Mean; x'1 = 1160 ft

standard deviation; σ1 = 32 feet

Sample size; n1 = 19

For the second sample, we have;

Mean; x'2 = 1130 ft

Standard deviation; σ2 = 30 ft

Sample size; n2 = 11

The hypotheses are;

Null Hypothesis; H0; μ1 = μ2

Alternative hypothesis; Ha; μ1 > μ2

The test statistic formula for this is;

z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]

Plugging in the relevant values, we have;

z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]

z = 2.58

From the z-table attached, we have a p-value = 0.99506

This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

The equation of the ellipse is \((x - 3)^2 / 16 + (y - 3)^2 / 64 = 1.\)

To determine the equation of the ellipse, we need to find its major and minor axes, as well as the distance from each focus to the center.

Given that the foci of the ellipse are located at (3, 1) and (3, 5), we can determine that the center of the ellipse is at the midpoint between these two foci, which is (3, 3).

The endpoints of the minor axis are (7, -2) and (-1, -2), which tells us that the length of the minor axis is 7 - (-1) = 8 units.

Now, let's calculate the distance from the center to one of the foci. Using the distance formula, we have:

sqrt((3 - 3)^2 + (3 - 1)^2) = sqrt(0 + 4) = 2.

Since the foci are vertically aligned, the major axis is vertical. Therefore, the length of the major axis is twice the distance from the center to one of the foci, which gives us 2 \(\times\) 2 = 4 units.

Using the standard form of the equation for an ellipse centered at (h, k), with a horizontal major axis of length 2a and a vertical minor axis of length 2b, the equation is:

\((x - 3)^2 / 4^2 + (y - 3)^2 / 8^2 = 1.\)

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Answer:

1. 392

2. 75

3. \(12x^{2} - 5x -2\)

Step-by-step explanation:

1. 7×8 + 3×8×14 = 56 + 336 = 392

2. 675 ÷ (6 + 3) = 675 ÷ 9 = 75

3. \(12\)\(x^{2}\) + \(3x -\) \(8x - 2\) = \(12x^{2} -5x-2\)

Answer:

#1  (0,-4)

#2  (5,0)

#3  (3,1)

Step-by-step explanation:

#1.  (-3, 2) (0, y)  slope = -2

slope = rise/run    therefore slope = -2/1  or down 2 and over 1

so from -3 to 0 you are going over 3 units (or 3 times)  Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6      so 2-6 = -4

so y intercept (b)  = -4 0r (0,-4)

#2   (-7,-4)  (x,0)  slope (m) = 1/3   -7+12=5    x=5

#3   (4,-3)   (x, 1)   slope (m) = -4   (4/-1)   Moving one unit in slope  means

-3=4=1 for Y and 4-1=3 for X    therefore the point is (3, 1)

Answer:

1.5

Step-by-step explanation:

Vertical angles are congruent so:

7x=8x-12

Subtract 7x from both sides:

0=8x-12

Add 12 to both sides:

8x=12

Divide both sides by 8:

x=1.5 or

x= 3/2

Note that the probabilities are given below.

a) the probability of a randomly selected catch being a mouse caught by Cyd

p(Catching a mount) x p(Cyd made the catch)

= 0.5x .2

= 0.1

b) the   probability of a bird not caught by Cyd is 0.5 x 0.8 = 0.4.

Thus

P(that a catch is a bird) x p(the Cyd didn't make the catch)

= 0.3 x 0.8

=0.24

c) The probability of a randomly selected catch being caught by Greg is 0.45

To calculate, we say

(0.5   x0.45) + (0.3 x 0.45) + (0.2 x .45)

= 0.45.

d)

P (mouse caught by Greg) = (0.45 x 0.5) / 1

= 0.225.

e) P(catch is a mouse caught by Ken and catch is a mouse)

= P(catch is a mouse | catch is made by Ken) x P(catch is made by Ken)

= 0.05 x 0.1

= 0.005

f)

P (catch made by Cyd | catch is a mouse)

= 0.1    x 0.2 / 0.5

= 0.04

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Answer:

The graph of the function gets vertically shifted upwards by 12 units.

Step-by-step explanation:

The first and second derivatives of the function are both negative over the interval [1.1, 1.5].

To find the first derivative, we need to calculate the slope of the function at each point. We can do this by taking the difference between two consecutive y-values and dividing it by the difference between the corresponding x-values:

f'(1.2) = (6.1 - 7.1)/(1.2 - 1.1) = -1

f'(1.3) = (5.0 - 6.1)/(1.3 - 1.2) = -1.1

f'(1.4) = (3.8 - 5.0)/(1.4 - 1.3) = -1.2

f'(1.5) = (2.5 - 3.8)/(1.5 - 1.4) = -1.3

From these calculations, we can see that the first derivative of the function appears to be negative over the entire interval.

To find the second derivative, we need to calculate the rate of change of the first derivative. We can do this by taking the difference between two consecutive first derivative values and dividing it by the difference between the corresponding x-values:

f''(1.3) = (-1.1 - (-1))/ (1.3 - 1.2) = -1

f''(1.4) = (-1.2 - (-1.1))/ (1.4 - 1.3) = -1

f''(1.5) = (-1.3 - (-1.2))/ (1.5 - 1.4) = -1

From these calculations, we can see that the second derivative of the function appears to be negative over the entire interval.

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Answer:

3.1

Step-by-step explanation:

ok so, 3.14 rounded to the nearest tenth is 3.1

also, keep this in mind

if it is 5 and up it will be able to round up but if it is 4 round it down

Answer:

D no solution :)

Step-by-step explanation:

because the total sum of each percent is 90%

and it must be 100% as it is a full circle