Ticket to the zoo cot $25 for adult and $10 for children. The total ticket ale one day were $47,750. The number of children, c, who viited the zoo wa 270 more than 6 time the number of adult, a, who viited. Write and olve a ytem of equation to find the total number of viitor to the zoo that day

Answer:

2

Step-by-step explanation:

pick two points that the line crosses through and write down the coordinates

eg. (3,3) and (2,1)

change in y/change in x

3-1/3-2

2/1

2

hope that helps :)

Answer:

2

Step-by-step explanation:

Since M is the centroid of triangle ΔGHI, so KI = 10

The centroid of a triangle is the point at which the three medians of the triangle intersect.

In triangle ΔGHI, M is the centroid of the triangle. If HI = 20, we need to find KI. We proceed as follows.

We know that M is the centroid of the triangle and is the center point where the three medians of the triangle intersect.

Now, GK is a median which passes through HI at K.

Since GK is a median, this implies that HK = KI.

Also, HK + KI = HI

So, since HK = KI, we have that

HK + KI = HI

KI + KI = HI

2KI = HI

KI = HI/2

Given that HI = 20, substituting this into the equation, we have that

KI = HI/2

= 20/2

= 10

So, KI = 10

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find overtime hours:

52-40 = 12

Multiply regular hours by rate:

40 x 16.50 = 660

Multiply rate by 1.5 x overtime hours:

16.50 x 1.5 x 12 = 297

Total = 660 + 297 = 957

Total = $957

Answer:(a) "95% confidence" means that if we were to repeat this study many times, we would expect the true proportion of members who would quit to be within the calculated interval for 95% of those studies. In other words, we can be 95% confident that the true proportion of members who would quit falls within the interval.

(b) The interval is [0.18, 0.075]. This means that we are 95% confident that the true proportion of members who would quit if the fee was raised to $50 falls between 0.18 and 0.075.

(c) No, the owner cannot be confident that the fee increase will be worthwhile because the interval from part (b) includes 20%. If the true proportion of members who would quit is 20%, then the fee increase would not be worthwhile. Since the interval includes 20%, we cannot be confident that the true proportion is less than 20%.

(d) One of the conditions for calculating the confidence interval is that the sample size is large enough and that the number of successes and failures in the sample are both at least 10. This is necessary because the interval calculation relies on the normal distribution, which is only valid when the sample size is large enough and the number of successes and failures are both at least 10. If this condition is not met, then the interval calculation may not be accurate or valid.

Step-by-step explanation:

So, the sum of the series as a function of x is: f(x) = 9x / (1 - 9x).

To determine the values of x for which the series converges, we need to find the values of x that satisfy the convergence criteria for the given series.

The series \((9x)^n, n = 1\), will converge if the absolute value of (9x) is less than 1.

|9x| < 1

To find the values of x that satisfy this inequality, we can solve it as follows:

-1 < 9x < 1

Divide all terms by 9 (since 9 is positive):

-1/9 < x < 1/9

Therefore, the series converges for x values in the interval (-1/9, 1/9).

The sum of the series as a function of x, denoted as f(x), can be found using the formula for the sum of a geometric series:

f(x) = a / (1 - r)

where a is the first term and r is the common ratio. In this case, the first term is \((9x)^1 = 9x\), and the common ratio is \((9x)^n / (9x) = (9x)^{(n-1)\).

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Answer:

i think it is A sorry if I am worng

Answer:

21 is the correct answer

Step-by-step explanation:

Answer:

equal to rolling an odd number

Step-by-step explanation:

fair number cube is your average 6 side die

even numbers = 2,4,6

odd numbers = 1,3,5

total sides=6

even number probability = 3/6

odd number probability = 3/6

Answer:

$187.50

Step-by-step explanation:

Set up an equation

250 m/$x = 1 m/$0.75

Cross multiply

250 miles × $0.75 = 1x

$187.50 = x

Answer:

square root of (2+10)²+(-5+3)²

square root of 144+4

square root of 148

The set of natural numbers is closed under addition and multiplication.

The set of natural numbers is closed under the operations of addition and multiplication. This means that when you add or multiply two natural numbers, the result will always be a natural number.

For addition:

If a and b are natural numbers, then a + b is also a natural number.

For multiplication:

If a and b are natural numbers, then a * b is also a natural number.

It's important to note that the set of natural numbers does not include the operation of subtraction, as subtracting one natural number from another may result in a non-natural (negative) number, which is not part of the set. Similarly, division is not closed under the set of natural numbers, as dividing one natural number by another may result in a non-natural (fractional) number.

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Answer:

\(f(x) = 144\)

Step-by-step explanation:

This problem deals with a function. All this question is asking is to plug in -4 every time an x appears.

So, let's do that:

\(f(-4) = 10(-4)^{2} + 3(-4) - 4\)

\(f(-4) = 10(16) - 12 - 4\)

\(f(-4) = 160 - 16\)

\(f(-4) = 144\)

The required width of the river is 70 meter

Trigonometric function are sine, cosine, tangent,etc. here we will use tangent function to find the width of the river.

We have given,

distance(d) that she walk along the river = 100m

The angle from her bascline to the tree = 35°

Let we consider width of the river is y,

We know that,

tanθ = y/d

y=dtanθ = (100)tan(35°)= 100×0.7 = 70m

Thus, the width of the river is 70 meter.

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Complete question:

A surveyor measures the distance across a straight river by the following method (Fig. above). Starting directly across from a tree on the opposite bank, she walks  d=100m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is θ=35.0 . How wide is the river?

The OLSE for β₁ in the simple regression model is B₁ = (n∑[x₁y₁] - B∑[x₁]) / ∑[x₁²]. It is unbiased, meaning its expected value is equal to the true coefficient β₁.

To find the ordinary least squares estimator (OLSE) for the regression coefficients in the simple regression model, we need to minimize the sum of squared residuals. The OLSE for the coefficient β₁ is obtained by differentiating the sum of squared residuals with respect to β₁ and setting it equal to zero. Let's go through the steps:

Step 1: Model Assumptions

MLR.1: Linearity: The relationship between the response variable (y₁) and the predictor variable (x₁) is linear.

MLR.2: Independence: The observations are independent of each other.

MLR.3: Homoscedasticity: The variance of the errors (ε) is constant for all values of x₁.

MLR.4: No perfect multicollinearity: There is no perfect linear relationship between the predictor variable (x₁) and other predictor variables.

Step 2: Define the sum of squared residuals (SSR)

SSR = ∑[y₁ - (Bo + B₁x₁)]²

Step 3: Minimize SSR

To find the OLSE for β₁, we differentiate SSR with respect to β₁ and set it equal to zero:

∂SSR/∂B₁ = -2∑[y₁ - (Bo + B₁x₁)]x₁ = 0

Step 4: Solve for B₁

Expanding the equation: -2∑[y₁x₁ - Box₁ - B₁x₁²] = 0

Rearranging and dividing by -2: ∑[y₁x₁] - ∑[Box₁] - ∑[B₁x₁²] = 0

Since it is a simple regression model, we have: n∑[x₁y₁] - B∑[x₁] - B₁∑[x₁²] = 0

Simplifying the notation: n∑[x₁y₁] - B∑[x₁] - B₁∑[x₁²] = 0

Step 5: Solve for B₁

Rearranging the equation, we get: B₁∑[x₁²] = n∑[x₁y₁] - B∑[x₁]

Dividing both sides by ∑[x₁²], we obtain: B₁ = (n∑[x₁y₁] - B∑[x₁]) / ∑[x₁²]

Step 6: Show that the OLSE B₁ is unbiased

To demonstrate that B₁ is unbiased, we need to show that its expected value is equal to the true coefficient β₁.

E(B₁) = E((n∑[x₁y₁] - B∑[x₁]) / ∑[x₁²])

Since expectation is a linear operator, we can split it up:

E(B₁) = (nE(∑[x₁y₁]) - BE(∑[x₁])) / E(∑[x₁²])

Now, by the law of iterated expectations:

E(B₁) = (n∑[xE(y₁|x)]) - B∑[xE(x₁)]) / ∑[xE(x₁²)]

Since E(y₁|x) = Bo + B₁x₁, and E(x₁) = x₁, we have:

E(B₁) = (n∑[x(Bo + B₁x₁)] - B∑[x(x₁)]) / ∑[x(x₁²)]

Expanding the sums:

E(B₁) = (nBo∑[x] + nB₁∑[x₁²] - B∑[x(x₁)]) / ∑[x(x₁²)]

Since Bo, B₁, and x₁ are constants, they can be taken out of the sums:

E(B₁) = Bo(n∑[x]) + B₁(n∑[x₁²]) - B(∑[x(x₁)]) / ∑[x(x₁²)]

The terms Bo(n∑[x]) and B₁(n∑[x₁²]) can be written as:

Bo(n∑[x]) = nBo(∑[x]) = n∑[x]Bo

B₁(n∑[x₁²]) = nB₁(∑[x₁²]) = n∑[x₁²]B₁

Substituting back into the equation:

E(B₁) = n∑[x]Bo + n∑[x₁²]B₁ - B(∑[x(x₁)]) / ∑[x(x₁²)]

Now, recall that the true model is given by: y₁ = Bo + B₁x₁ + ε₁

Taking expectations: E(y₁) = E(Bo + B₁x₁ + ε₁)

Since E(ε₁) = 0: E(y₁) = Bo + B₁x₁

Comparing this with the definition of E(B₁), we see that:

E(B₁) = B₁

Therefore, the OLSE B₁ is unbiased, as its expected value is equal to the true coefficient β₁.

Note: In the above derivation, I assumed that the error term ε₁ follows the properties of MLR.1 through MLR.4, namely, it has a mean of zero, constant variance, and is normally distributed. These assumptions are necessary for the unbiasedness property of the OLSE.

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Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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Answer: 21.45$

Step-by-step explanation: I can’t explain how i got it but i hope this helped!

Answer:

$43.55

Step-by-step explanation:

I took 65 and found 33% by making 33% .33 and did 65*33, then subtracted what I got from the total of 65, 65-21.45 which is $43.55.

Radical Equations

Step 1

To demonstrate how to solve a radical equation, let's use the following equation as an example:

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Answer:

The answer is A

Step-by-step explanation:

I took the test.

1. Since triangle ABC and DEF are congruent, the value of x is -3

2. length AB = 24

length DE = 24

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE

therefore;

12- 4x = 15-3x

collect like terms

12 -15 = -3x +4x

x = -3

therefore the value of x is -3 and

AB = 12 - 4x

AB = 12 -4( -3)

AB = 12 +12 = 24

DE = 15-3x

= 15-3(-3)

= 15 + 9

= 24

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Answer:

um the first one possible I'm not that go at math

Answer:

y = -7

Step-by-step explanation:

put the -10 to the other side, to get rid of it, you +10 to -17 to get -7

so Y=-7

Hope this helps :)

The value of x in the diagram is 100 degrees

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

The figure

On the figure, we can see that:

The angle x and 100 degrees are alternate angles

Alternate angles have equal values

So, we have

x = 100

Hence, the value is 100 degree

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Answer:

Step-by-step explanation:

Draw a figure!

160/L = sin 40°

L = 160/sin 40°

The distance of Jamal's house to the park is 12 miles.

The distance from Loretta's house to a park is 43 miles.

Her friend Jamal lives along this same highway between Loretta's house and the park.

The distance from Loretta's house to Jamal's house is 31 miles.

The situations forms a straight line segment.

Therefore,

Loretta's house distance to the park = 43 miles

Lorretta's house distance to Jamal's house = 31 miles

Therefore,

distance of Jamal's' house to the park =  43 - 31

distance of Jamal's' house to the park = 12 miles

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Answer:

Step-by-step explanation:

1. isolate the variable   subtract both sides by 8                   (12x+8-8<116-8)  

2. Divide both sides by twelve                                               (12x/12<116-8/12)                                            

3. Simplify                                                                                 (x<108/12)      

=12x+8−8<116−8

=12x<108

\( \frac{12x}{12} < \frac{108}{12} \)

x<9

Answer:

A

Step-by-step explanation:

Answer:

A) The slope is 2/3 and y intercept is -2

Step-by-step explanation:

Took it on edge

Answer:

Hello! The Answer is not proportional. Hope this helps!

Step-by-step explanation:

It has been shown that if A is a symmetric matrix with eigenvalues λ1, λ2, . . . , λn, then the singular values of A are |λ1|, |λ2|, . . . ,|λn|.

To show that the singular values of a symmetric matrix A are |λ1|, |λ2|, . . . ,|λn|, we first need to recall that the singular values of A are the positive square roots of the eigenvalues of \(A^T A\) (where \(A^T\) denotes the transpose of A).

Now, since A is symmetric, we know that \(A^T = A\), which means that \(A^T A = A^2\).

So the eigenvalues of \(A^T A\) are the squares of the eigenvalues of A.

That is, if λ1, λ2, . . . , λn are the eigenvalues of A, then λ1², λ2², . . . , λn² are the eigenvalues of \(A^T A\).

But we also know that the eigenvalues of a symmetric matrix are real, so λ1, λ2, . . . , λn are real numbers.

And since the singular values of A are the positive square roots of the eigenvalues of \(A^T A\), it follows that the singular values of A are |λ1|, |λ2|, . . . ,|λn|. This completes the proof.

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