Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-4) = -11 B. g(0) = 2 C. g(7) = -1 D. g(-13) = 20

Answer:

According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have:

c^2 = a^2 + b^2

where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Substituting the given values, we get:

c^2 = 14^2 + 48^2

c^2 = 196 + 2304

c^2 = 2500

Taking the square root of both sides, we get:

c = 50

Therefore, the length of the hypotenuse is 50 units.

Answer) : B measure of angle CBD

Step-by-step explanation: BD is perpendicular to ADC now we know that there is no scale so all you have to do is measure the length and we gat that answer.

Simplifying this equation, we get: PQ ≈ 6.93 and QR ≈ 8.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides.

To find the lengths of PQ and QR in triangle RPQ, we can use the law of sines:

sin(R) / RP = sin(P) / PQ = sin(Q) / QR

We are given R = 30° and P = 60°, so we can find Q:

Q = 180° - R - P

Q = 180° - 30° - 60°

Q = 90°

Now we can use the law of sines:

sin(30°) / 4 = sin(60°) / PQ = sin(90°) / QR

Simplifying this equation, we get:

PQ = (4 * sin(60°)) / sin(30°) ≈ 6.93

QR = (4 * sin(90°)) / sin(30°) = 4 * 2 ≈ 8

Therefore, PQ ≈ 6.93 and QR ≈ 8.

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According to the information, we can infer that the correct sentences about the graph is A person with annual income of at least $50,000 is more likely to be 45 years old or above.

To find the correct sentence we have to analyze the information of the graph and read the options. Once we make this procedure, we can compare each sentence with the information of the graph to establish the correct one.

According to the information the correct option would be A person with annual income of at least $50,000 is more likely to be 45 years old or above (option C).

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We reject the null hypothesis since the p-value is less than the significance level of 0.05.

The null hypothesis in statistics is a claim that presupposes there is no statistically significant distinction among the two or even more variables be compared. The antithesis of the alternative hypothesis, it is frequently denoted as H0 (Ha). While conducting statistical studies, the null is often evaluated to see if there is sufficient proof against it or not. The default assumption is typically the null hypothesis, and it serves as a benchmark for comparison of the statistical analysis's findings. A statistically significant distinction between the variables under comparison is said to exist if the statistical analysis yields sufficient data to refute a null hypothesis.

given

To test the hypothesis, we can utilise a z-test. This is the test statistic:

[tex]z = (x - E) / σ[/tex]

where x is the observed percentage of patients whose conditions are getting better. x = 820 * 0.52 = 426.4 is the result. Therefore:

z = (426.4 - 393.6) / 0.026 = 1245.98

P(Z > z) = 1 - P(Z z) is the p-value for this one-tailed test, where Z is a normal standard variable. By using a typical table or calculator, we discover:

P(Z > 1245.98) < 0.0001

We reject the null hypothesis since the p-value is less than the significance level of 0.05.

We have enough data to draw the conclusion that the percentage of patients whose conditions are improving is more than 0.48.

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Answer: So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.

Step-by-step explanation:

Let O be the center of the circle, and let A and B be the points of tangency of the two tangents with the circle. Since OA and OB are radii of the circle, they have the same length of 8 centimeters.

Let C be the vertex of the angle formed by the two tangents. Since the tangents are perpendicular to the radii at the points of tangency, we have that angle AOC = angle BOC = 90 degrees.

Since the measure of the angle formed by the two tangents is 80 degrees, we have that angle AOB = 180 - 80 - 80 = 20 degrees.

Let D be the foot of the perpendicular from C to line AB. Then angle OCD = 90 - 20/2 = 80 degrees, so triangle OCD is an isosceles triangle. Therefore, we have that OD = OC = 8 centimeters.

Finally, since triangle OCD is a right triangle, we can use the Pythagorean theorem to find the length of CD. We have:

CD^2 = OD^2 - OC^2 = 8^2 - 8^2 = 0

Therefore, CD = 0 centimeters.

So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.

The P-value is between 0.025 and 0.05. and t = -1.85

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.

Therefore tests the hypotheses:

[tex]H_0[/tex] : μ = 25 versus Ha: μ < 25,

where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

The alternative hypothesis is:

[tex]H_1:\mu < 25[/tex]

The test statistic is given by:

[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }[/tex]

The parameters are:

the values of the parameters are:

x = 23.5 , [tex]\mu=25[/tex] , s = 4.8, n = 35

Plug all the values in above formula of t- statistic is:

[tex]t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }[/tex]

t = -1.85

Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

t = –1.85; the P-value is between 0.025 and 0.05.

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Answer:

7(-6) + 4(8) = -42 + 32 = -10, so (-6, 8) is the solution to this system of equations.

The answer is Yes.

Answer:sorryy if this is late but its 2

Step-by-step explanation:

The angle of elevation of the ladder is approximately 71.6 degrees.

To find the angle of elevation of the ladder, we can use trigonometry. The ladder forms a right triangle with the ground and the tree.

The base of the triangle is 4 feet, the height is 12 feet, and the hypotenuse is the length of the ladder.

Using the trigonometric function tangent (tan), we can write:

tan(angle) = opposite/adjacent

In this case, the opposite side is the height of the tree (12 feet) and the adjacent side is the base of the triangle (4 feet).

Therefore, we can calculate the angle of elevation as follows:

tan(angle) = 12/4

angle = arctan(12/4)

Using a calculator or a trigonometric table, we can find that arctan(12/4) is approximately 71.6 degrees.

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the answer is option C: The difference in overall gain is $293.90.

How to solve the question?

To calculate the difference in overall loss or gain, we need to calculate the current value of the investor's portfolio for both high and low prices and then compare the two values.

First, let's calculate the current value of the investor's holdings for stock A:

High price: 120 shares x $105.19 per share = $12,623.80

Low price: 120 shares x $103.25 per share = $12,390.00

Next, let's calculate the current value of the investor's holdings for stock B:

High price: 35 shares x $145.18 per share = $5,080.30

Low price: 35 shares x $43.28 per share = $1,514.80

Now we can calculate the total current value of the investor's portfolio:

High price: $12,623.80 + $5,080.30 = $17,704.10

Low price: $12,390.00 + $1,514.80 = $13,904.80

The difference between the two values is:

High price: $17,704.10 - ($120 x $90) - ($35 x $145) = $299.30

Low price: $13,904.80 - ($120 x $90) - ($35 x $145) = $293.90

Therefore, the answer is option C: The difference in overall gain is $293.90.

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Answer:

[tex] \frac{4}{3} \pi {r}^{3} = 1332[/tex]

[tex]r = \sqrt[3]{ \frac{1332}{ \frac{4}{3}\pi } } = 6.8[/tex]

The radius of this sphere is about 6.8 feet

If the function f(x) = x, the effect of f(x) - 8 is: is (D) The y intercept decreases.

The function f(x) = x is a linear function with a slope of 1, which means that for every increase of 1 in the x-value, the y-value also increases by 1.

If we subtract 8 from the function, we get:

f(x) - 8 = x - 8

This is still a linear function with a slope of 1, but it has been shifted downwards by 8 units.

Therefore, the effect of f(x) - 8 is that the y-intercept decreases by 8 (since the y-intercept of f(x) is 0 and the y-intercept of f(x) - 8 is -8), while the slope remains the same.

So the correct answer is (D) The y intercept decreases.

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Answer:

Step-by-step explanation:

72+65+68+68+73+45+68+71 = 530

530/8 because there are 8 numbers

mean: 66.25

for the median, you line the numbers up from small to big and find the center number. But since there are 2 of them (68 and 68) , add 68+68 and divide by 2 which is still 68!

45,65,68,68,68,71,72,73

the mode is 68 because it is the most occurring number.

ok yea

I Got U Bro! Answer:(x+5)2+(y+3)2=16

:D

Answer:

the value of x is 7

Step-by-step explanation:

First, find the half of the perimeter that is 36 divided by 2 which is 18

Next, write like this

18= l+w( length = width)

which means you have to get the sum of 18

so try sums of 18 randomly like

17 + 1

11 + 7

16+2 etc

but the thing is the value of x must be the same it must not be different so

11 + 7 will be suitable because

11 = 7 + 4

7 = 2 x 7 - 7 = 7

and to find the area which is l x b

11 x 7= 77sq. cm

please mark me the brainliest and a thanks too

Answer:

x=7

Step-by-step explanation:

7+4=11(2)=22

2(7)-7= 14-7= 7(2)=14

22+14=36

The height of the parallelogram is equal to the diameter of the circle. The base of the parallelogram is equal to half of the circumference of the circle. Therefore, the area of the circle (πr2) is equal to bh and the circumference of the circle is equal to 2b.

The height of the parallelogram is equal to the diameter of the circle. This can be seen because each of the eight sectors has the same area, so they are all the same size. If we place them next to each other in the shape of a parallelogram, we can see that the height of the parallelogram is equal to the diameter of the circle.

The base of the parallelogram is equal to half of the circumference of the circle. This is because the circumference of the circle is divided equally into eight sectors, and the base of the parallelogram is formed by placing two adjacent sectors together. Therefore, the base of the parallelogram is equal to the arc length of one sector plus the arc length of its adjacent sector. Each sector is 1/8th of the circle, so the arc length of one sector is 1/8th of the circumference. Adding the arc lengths of two adjacent sectors gives 1/4th of the circumference, which is half of the base of the parallelogram.

Therefore, the area of the circle (πr2) is equal to the area of the parallelogram (bh), where h is the diameter of the circle and b is half of the circumference of the circle. Additionally, the circumference of the circle is equal to the base of the parallelogram multiplied by 2.

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Answer:  1. To find the time when the management should deploy more cashiers, we need to find the time when the number of customers queueing is the highest. We can find the maximum value of y by taking the derivative of the equation and setting it equal to zero:

dy/dt = 3t^2 - 28t + 50 = 0

Solving for t, we get:

t = (28 ± sqrt(28^2 - 4350)) / (2*3) = 4.67 or 9.33

Since the time has to be between 0 and 8.5 hours, the maximum occurs at t = 4.67 hours. Therefore, the management should deploy more cashiers around 1:40 pm (9:00 am + 4.67 hours). At this time, the number of customers queueing is:

y = 4.67^3 - 14(4.67)^2 + 50(4.67) = 51.64

So, there will be approximately 52 customers queueing at that time.

2. To find the number of man-hours spent per day by shoppers queueing, we need to integrate the equation for y over the range 0 ≤ t ≤ 8.5:

∫(0 to 8.5) y dt = ∫(0 to 8.5) (t^3 - 14t^2 + 50t) dt

Evaluating the integral, we get:

= [(1/4)t^4 - (14/3)t^3 + 25t^2] from 0 to 8.5

= (1/4)(8.5)^4 - (14/3)(8.5)^3 + 25(8.5)^2

= 1907.81

Therefore, the total number of man-hours spent per day by shoppers queueing is approximately 1908.

Step-by-step explanation:

To determine when the shop should deploy more cashiers, we need to find the maximum point of the function y(t), which corresponds to the peak of the queue. The maximum point of a cubic function is found at its turning point, which is where its derivative equals zero. Therefore, we can find the turning point by taking the derivative of y(t) and setting it equal to zero:

y'(t) = 3t^2 - 28t + 50

0 = 3t^2 - 28t + 50

Using the quadratic formula, we get t = 4.47 or t = 3.19.

However, we need to make sure that the maximum point lies within the given range of 0 ≤ t ≤ 8.5. Since 3.19 is within this range and 4.47 is not, the maximum point occurs at t = 3.19 hours after the shop opens.

To find the number of customers queueing at that time, we simply plug in t = 3.19 into the original equation:

y(3.19) = (3.19)^3 - 14(3.19)^2 + 50(3.19) ≈ 30.8

Therefore, the management of the shop should deploy more cashiers at 12:11 pm (9 am + 3.19 hours) when there are approximately 30.8 customers queueing.

To determine the number of man-hours spent per day by shoppers queueing, we need to find the total area under the curve of y(t) from t = 0 to t = 8.5. This area represents the total number of customers queueing during the day.

Using integration, we get:

∫(t^3 - 14t^2 + 50t)dt = (t^4/4) - (14t^3/3) + (25t^2) + C

where C is the constant of integration.

Evaluating this expression at t = 8.5 and t = 0, and subtracting the latter from the former, we get:

(8.5^4/4) - (14(8.5)^3/3) + (25(8.5)^2) - (0^4/4) + (14(0)^3/3) - (25(0)^2) ≈ 2233.1

Therefore, the total number of man-hours spent per day by shoppers queueing is approximately 2233.1. Note that this assumes that each customer spends exactly one hour in the queue, which may not be realistic, but provides a rough estimate of the total time spent.

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The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.

An expression is a combination of numbers, symbols, and/or operators that represents a quantity, a value, or a computation. Expressions can include variables, which are letters that represent unknown values, and can be manipulated and evaluated using mathematical operations like addition, subtraction, multiplication, and division. Expressions can be simple or complex, and they are used in various areas of mathematics, including algebra, calculus, and geometry, as well as in many other fields such as physics, engineering, and economics.

The expression that represents the real-world situation is:

p - 8 + 5

Explanation:

Initially, there are p people on the bus. Then, 8 people get off, which is represented by the subtraction of 8 from p (p - 8). After that, 5 more people get on the bus, which is represented by adding 5 to p - 8, giving us the final expression: p - 8 + 5. This expression simplifies to p - 3, which represents the final number of people on the bus.

Therefore, The expression that represents the real-world situation is "p - 8 + 5". It simplifies to "p - 3" and represents the final number of people on the bus.

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Answer:

Step-by-step explanation:

The potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.

Degree of a polynomial is the highest power of the variable in that polynomial. For example, in a cubic polynomial, the variable [[tex]\bold{x}[/tex]] has the highest power of 3.

Given is the following function with degree of 2 as -

We will plot the graph and find the roots of this function. The number of x - intercepts [coordinates where the graph cuts the x axis] will give us the roots or zeroes of the polynomials. Refer to the graph attached, it shows that the graph intercepts the x - axis at three different coordinates which are → x = 1, x = -1.5, and x = 12. Hence, these three values of [x] are the potential roots of the function p(x) = x² - 9x² - 4x + 12.

Therefore, the potential roots of the function p(x) = x² - 9x² - 4x + 12 are x = 1, -1.5, and 12.

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The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.

To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x: 0 = x² - 9x - 12.

Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.

So, Final answer:

The potential roots of the given polynomial equation are +4 and -3. These roots are found by factoring the equation, setting each factor equal to zero and solving for x.

To find the potential roots of the polynomial equation p(x) = x² - 9x - 12, we can set the equation to zero and solve for x:

0 = x² - 9x - 12.

Next, we look for the factors of 12 which when multiplied would give you -12 and when subtracted would give you 9. There we have -4 and +3. Therefore the factors of the equation are (x - 4)(x + 3) = 0.

So, potential roots of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned). of the equation are x = 4 and x = -3 if we set each factor equal to zero and solve for x. This means that from the given options, the potential roots to the equation would be +4 and -3 (though -3 is not mentioned).

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The net value of the $10,000 bonus in a normal savings account after taxes and interest in five years will be $9,181.

Assuming an 8 percent nominal interest rate and a 30 percent tax bracket, the after-tax return on the normal savings account is 5.6 percent. Thus, after five years, the $10,000 bonus will grow to $14,693.

However, since Sarah is in the 30 percent tax bracket in every year, she will owe taxes on the interest income earned each year. This reduces the after-tax return to 3.92 percent. Therefore, in five years, the $10,000 bonus in the normal savings account will be worth $9,181 after taxes.

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Apply the fraction rule:

[tex]\text{a}\times\dfrac{\text{b}}{\text{c}} =\dfrac{\text{a}\times\text{b}}{\text{c}}[/tex]

Answer:

[tex]\longrightarrow\boxed{\bold{\frac{\text{fx}}{\text{g}}}}[/tex]

Answer:

5x - 9 and 3x + 9 are two mathematical expressions. The first expression, 5x - 9, represents a value obtained by multiplying 5 by x and then subtracting 9. The second expression, 3x + 9, represents a value obtained by multiplying 3 by x and then adding 9. Both expressions can be simplified further or used in various mathematical operations depending on the context of the problem or equation in which they are being used.

Answer:-45 and -3

Step-by-step explanation:

The height of the triangle is 6 inches and the base of the triangle is 30 inches.

Let's denote the height of the triangle as h inches. According to the given information, the base of the triangle is 6 inches more than 4 times the height, which can be expressed as 4h + 6 inches.

The formula for the area of a triangle is given by the formula A = (1/2) * base * height. Substituting the given values, we have:

90 = (1/2) * (4h + 6) * h

To solve for h, we can first multiply both sides of the equation by 2 to eliminate the fraction:

180 = (4h + 6) * h

Next, we can distribute the h on the right-hand side:

[tex]180 = 4h^2 + 6h[/tex]

Rearranging the equation to form a quadratic equation in standard form:

[tex]4h^2 + 6h - 180 = 0[/tex]

Now, we can solve this quadratic equation for h using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

[tex]x = (-b ± \sqrt{(b^2 - 4ac)) / (2a)}[/tex]

In our equation, a = 4, b = 6, and c = -180. Plugging in these values, we get:

[tex]h = (-6 ± \sqrt{(6^2 - 4 * 4 * -180)} ) / (2 * 4)[/tex]

Simplifying further:

[tex]h = (-6 ± \sqrt{(36 + 2880)} ) / 8h = (-6 ± \sqrt{(2916)} ) / 8[/tex]

h = (-6 ± 54) / 8

Now we can find the two possible values for h:

h1 = (-6 + 54) / 8 = 48 / 8 = 6

h2 = (-6 - 54) / 8 = -60 / 8 = -7.5

Since height cannot be negative in this context, we discard the solution h2 = -7.5.

So, the height of the triangle is 6 inches.

Now, we can use this value of h to find the base of the triangle:

Base = 4h + 6 = 4 * 6 + 6 = 24 + 6 = 30 inches.

So, the height of the triangle is 6 inches and the base of the triangle is 30 inches.

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1/(x-2)². The correct option is C

The quotient rule is a formula used in calculus to find the derivative of a function that is the quotient of two other functions. Specifically, it gives the formula for finding the derivative of a function of the form f(x) = g(x) / h(x), where g(x) and h(x) are both functions of x.

We can use the quotient rule to find the derivative of h(x):

h(x) = (x+2)/(x-2)

h'(x) = [ (x-2)(1) - (x+2)(1) ] / (x-2)^2 (apply quotient rule)

Simplifying the numerator, we get:

h'(x) = [ x-2 - x-2 ] / (x-2)^2

h'(x) = -4 / (x-2)^2

Therefore, the answer is (C) 1/(x-2)².

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Given:

[tex]\sqrt{z+5}+4\leq 13[/tex]

Move 4 to the right side:

[tex]\sqrt{z+5}\leq 9[/tex]

Simplify

[tex]z+5 \leq 81[/tex]

Move 5 to the right side:

[tex]z\leq 76[/tex]

Find singularity points

Find non-negative values for radicals:  [tex]z\geq -5[/tex]

Combine the intervals

[tex]z\leq 76 \ \text{and} \ z\geq -5[/tex]

Merge overlapping intervals

[tex]-5\leq z\leq 76[/tex]

Answer:

Step-by-step explanation:

Look at the points  (0,-3)  and  ( 3,0)

slope,  m = rise / run =   3 / 3 =  1  

Answer:

1

Step-by-step explanation:

y=x+3

Answer:

7.D

8.A

Step-by-step explanation:

For the function f(x) = √x+2+5:

(D) D= {x|x≥2}, R= {y|y≥5}

The domain is restricted to x values greater than or equal to 2 because the function contains the square root of x+2, which cannot be negative. The range starts at y = 5 because the lowest possible output of the function is √2+2+5 = 5.

(A) f(x)+∞o as x→ +∞o; f(x) +∞ as x――∞

As x approaches positive infinity, the output of the function approaches infinity as well. As x approaches negative infinity, the function is undefined since it involves taking the square root of negative numbers. However, the limit of the function as x approaches negative infinity from the right is positive infinity.

Answer: The rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.