A hospital director is told that 54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 120 patients found that 60 were insured. Find the value of the test statistic. Round your answer to two decimal places.

There are 20 questions which worth is 4 points, and 4 questions which worth is 5 points.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

There are 24 questions on a test. Each question is worth either 4 points or 5 points.

And, The total number of points is 100.

Let number of 4 points questions = x

And, Number of 5 points questions = y

Here, There are 24 questions on a test.

Hence, We get;

⇒ x + y = 24 .. (i)

Each question is worth either 4 points or 5 points. And, The total number of points is 100.

Hence, We get;

⇒ 4x + 5y = 100 .. (ii)

Multiply by 4 in (i) and subtract from (ii);

⇒ 4x + 5y - 4x - 4y = 100 - 96

⇒ y = 4

From (i);

⇒ x + y = 24

⇒ x + 4 = 24

⇒ x = 20

Thus, There are 20 questions which worth is 4 points, and 4 questions which worth is 5 points.

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Answer: x = $1.75

Step-by-step explanation:

Let's assume that the cost of each sparking plug is x dollars. Then, the cost of the fan belt is x + $1.75 since it costs $1.75 more than each sparking plug.

According to the problem, the total cost of four sparking plugs and a fan belt is $10.50. We can express this as an equation:

4x + (x + $1.75) = $10.50

Simplifying and solving for x, we get:

5x + $1.75 = $10.50

5x = $8.75

x = $1.75

Therefore, each sparking plug costs $1.75 and the fan belt costs $3.50 ($1.75 + $1.75).

Step-by-step explanation:

solution,

given,

Nikki spent 50% of her money for a shirt.

again she spent 25 % of her money.

here,

50% + 25% = 75%

100% - 75%= 25%

now,

25% = $7

multiplying both sides by 4

25% × 4 = $7 × 4

100% = $28

Her total money is $28

again, 75% of 28

= 75/100 × 28

28

so, she spent $ 28

The total amount of money spent by Nikki on the shirt and the gift given the amount she has left is $28.

The first step is to determine the fraction of the money she has left: 1 - (fraction of the money spent on shirt + fraction of the money spent on gifts)

1 - [1/2 + (1/2 x 1/2)]

= 1 - 3/4 = 1/4

Now, divide $7 by 1/4 : $7 x 4 = $28

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Y=10x-4

Slope: 10

Y intercept: -4

Answer:

Were my money?

Step-by-step explanation:





May I have brainliest please I'm trying to level up!

</3 PureBeauty

Answer:

1

Step-by-step explanation:

12 - 2 + 3 = 13

13 - 12 = 1

Answer:

-1

Step-by-step explanation:

she must walk down 1 flight of stairs

Step-by-step explanation:

Log(x²+8)=log 10+ log x

Log(x²+8)=log(10×x)

x²+8=10x

x² - 10x + 8=0

x is approximately to - 1 and - 8✅

The solutions to the given equation are x = -1 and x = 8.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

Using logarithmic properties, we can simplify the given equation:

logs(x² + 8) = 1 + log g(x)

logs(x² + 8) - log g(x) = 1

log[(x² + 8)/g(x)] = 1

(x² + 8)/g(x) = 10

x² + 8 = 10g(x)

Now we can solve for x by substituting the given answer options and solving for g(x):

For x = -2 and x = -4:

x = -2:

(-2)² + 8 = 12, which is not equal to 10 g(x) for any value of g(x).

So x = -2 is not a solution.

x = -4:

(-4)² + 8 = 24, which is also not equal to 10g(x) for any value of g(x).

So x = -4 is not a solution.

For x = -1 and x = 8:

x = -1:

(-1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = -1 is a solution.

x = 8:

(8)² + 8 = 72, which is equal to 10g(x) when g(x) = 7.2.

So x = 8 is a solution.

For x = 1 and x = -8:

x = 1:

(1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = 1 is a solution.

x = -8:

(-8)² + 8 = 56, which is not equal to 10g(x) for any value of g(x).

So x = -8 is not a solution.

Therefore,

The solutions to the given equation are x = -1 and x = 8.

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Answer:

Y=-4x 2

Step-by-step explanation:

Answer:

-2<=y<=-7

Step-by-step explanation:

Answer:

C) \(|-54.2| < |-58.6| < 5.745 \times 10^2\)

Step-by-step explanation:

\(|-54.2| = 54.2\)

\(|-58.6| =58.6\)

\(5.745 \times 10^2=574.5\)

< means "is less than"

Therefore,  54.2 < 58.6 < 574.5

Answer:

7.6

Step-by-step explanation:

19/5 = 3.8

So,

3.8 x the amount of gallons = the amount of litres

If we have 2 gallons, then,

3.8 x 2 = 7.6

Answer:

7.6

Step-by-step explanation:

Add it

The standard form based on the information given will be:

a) 2.35 x 10^-3 = 0.00235 (in standard form)

b) 2.35 x 10^3 = 2350 (in standard form)

It should be noted that in mathematics and computer science, a normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.

Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way

he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form.

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Answer:

D= f/4G-m3

Step-by-step explanation:

I believe this is it but I'm not quite sure.

you should ask a tutor as well.

The equation for D is;  \(D = \frac{f}{(4G - m^{3}) }\).

Here,

The given equation is, \(f = 4GD - m^{3} D\)

We have to find the equation for D.

What is Equation?

An equation is written as two expressions, connected by an equals sign.

Now,

The given equation is, \(f = 4GD - m^{3} D\)

Hence, the equation in form of D is,

\(f = 4GD - m^{3} D\\\\f = D ( 4G - m^{3} )\\\\D = \frac{f}{4G -m^{3} }\)

Hence, The equation for D is;  \(D = \frac{f}{(4G - m^{3}) }\).

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we know that

diameter of the base of a cylindrical can= 4 in----------> r=2 in

h=6.5 in

[surface area]=2*[pi*r²]+[2*pi*r*h]

then

[surface area]=2*[pi*2²]+[2*pi*2*6.5]=[ 25.13 ]+[ 81.68 ]=106.81 in²

the answer is 106.8 in²

Answer:

two sides have the same length which is less than the length of third side

Step-by-step explanation:

The sum of the lengths of the two sides is equal to the length of the third side.

Option D is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

In a triangle,

The side opposite to the equal angle are equal.

Now,

We have two 45 angles.

This means,

The sides opposite to the 45 angles will be congruent.

And,

The other angle is 90 degrees.

Which is a right triangle

Thus,

The sum of the lengths of the two sides is equal to the length of the third side.

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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:

Yes

Step-by-step explanation:

All you need to do is just divide 5,184 by 10.

5,184/10= 518.4

Therefore, the answer is yes.

Answer:

We conclude that the population mean is equal to 490.

Step-by-step explanation:

We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.

Let \(\mu\) = population mean.

So, Null Hypothesis, \(H_0\) : \(\mu\) = 490      {means that the population mean is equal to 490}

Alternate Hypothesis, \(H_A\) : \(\mu\neq\) 490     {means that the population mean is different from 490}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  \(\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }\)  ~ \(t_1_4\)

where, \(\bar X\) = sample mean = 495

            s = sample standard deviation = 9

             n = sample of observations = 15

So, the test statistics =   \(\frac{495-490}{\frac{9}{\sqrt{15} } }\)  ~ \(t_1_4\)

                                     =  2.152

The value of t-test statistics is 2.152.

Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 490.

Answer:

5

Step-by-step explanation:

Explanation

you can solve this by using the distance between 2 points formula

then

Step 1

Let

P1(0,0,0)

P2(6,4,8)

now , replace

I hope this helps you

Thus, for any vector x = (x1, x2, x3) in R3, we have: L(x) = Ax where A is the matrix given above.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used extensively in mathematics, science, engineering, and computer science to represent and manipulate linear equations, systems of equations, vectors, and other mathematical objects. Matrices can be added, subtracted, multiplied, inverted, and transformed in various ways to solve problems in algebra, calculus, statistics, and other fields. Matrices are also used in computer graphics, machine learning, and other areas of artificial intelligence to represent data, images, and other information. The size of a matrix is given by its number of rows and columns, and matrices can be classified as square (when they have the same number of rows and columns) or rectangular (when they have different numbers of rows and columns).

Here,

To find the matrix A that corresponds to the linear transformation L, we need to write L(e1), L(e2), and L(e3) as linear combinations of the standard basis vectors in R2.

L(e1) = (1+0, 0+0) = (1, 0)

L(e2) = (0+1, 1+0) = (1, 1)

L(e3) = (0+0, 1+0) = (0, 1)

So we can write:

L(x) = L(x1 e1 + x2 e2 + x3 e3)

= x1 L(e1) + x2 L(e2) + x3 L(e3)

Now we can assemble the coefficients of this linear combination into a matrix A:

A=  \(\left[\begin{array}{ccc}1&1&0\\0&1&1\end{array}\right]\)

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The rate of the first athlete is greater than the rate of the second athlete.

To determine if the rate of the first athlete is greater than, less than, or equal to the rate of the second athlete, we need to compare their average speeds.

The average speed of an athlete is calculated by dividing the distance traveled by the time taken.

For the first athlete who runs 3 miles in 24 minutes, the average speed can be calculated as:

Speed1 = Distance1 / Time1 = 3 miles / 24 minutes = 1/8 miles per minute.

For the second athlete who runs 4 miles in 33 minutes, the average speed can be calculated as:

Speed2 = Distance2 / Time2 = 4 miles / 33 minutes.

To make a comparison, we need to convert both rates to a common unit. Let's convert both rates to miles per minute:

Speed2 =\((4 miles / 33 minutes) * (24 minutes / 24 minutes)\) = (96 miles / 792 minutes) ≈ 0.1212 miles per minute.

Comparing the two rates, we see that Speed1 (1/8 miles per minute) is greater than Speed2 (0.1212 miles per minute). The rate of the first athlete is greater than the rate of the second athlete.

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Answer:

4x(6x + 11 ) -9 (6x + 99)

hope it is helpful to you

Answer:

1.785074354

Step-by-step explanation:

I don't know the ans want how many significant so I put all

Answer:

B. The power is the probability that the assembly process continues because the proportion of items that must be rejected has not increased.

Step-by-step explanation:

The probability is the percentage which determines the occurrence of an event. The probability measure is of power determines that the assembly process will continue because the proportion of the items that must be rejected is not increased.

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

Answer:

A. 36, -36

Step-by-step explanation:

y = x^2 - 12x - 5

steps to complete the square

add a 5 to both sides to move the constant

x^2 - 12x = 5

Then take -12, the coefficient of the variable and divide by 2 and square.

12/2 = 6, 6^2 = 36

Then add 36 to both sides.

x^2 - 12x + 36 = 5 + 36

Then subtract the 5 and 36 from both sides.

x^2 - 12x + 36 - 36 - 5

Answer:

Minh says that the rectangle on the left in Fig- ure 11.12 is larger than the one on the right, Sequoia says the rectangle on the right is larger than the one on the left. Explain why Minh and Sequoia can both be right. 25 Figure 11.12 Two rectangles. 24