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Answer:

To determine which points lie in the solution set of the system of inequalities x-y>-4, 2x-y<5, and 2y + x>1, we can graph the inequalities on a coordinate plane and look for the region that satisfies all three inequalities.

To graph the inequality x-y>-4, we can first graph the line x-y=-4 by plotting the points on the line:

x y

0 -4

-4 0

Then, we can shade the region above the line, since all points above the line will satisfy the inequality x-y>-4:

 |

-4 |    x

  |   /

  |  /  

  | /  

  |/    

-8 +------

   -4   0

To graph the inequality 2x-y<5, we can first graph the line 2x-y=5 by plotting the points on the line:

x y

0 5

2.5 0

Then, we can shade the region below the line, since all points below the line will satisfy the inequality 2x-y<5:

 |

5 |     x

  |   / |

  |  /  |

  | /   |

  |/    |

 0 +----|--

   0  2.5

To graph the inequality 2y + x>1, we can first graph the line 2y + x = 1 by plotting the points on the line:

x y

0 0.5

1 0

Then, we can shade the region above the line, since all points above the line will satisfy the inequality 2y + x>1:

 |

2 |     x

  |     |

 1|-----

  |   /  

  |  /

  | /  

  |/    

 0 +------

   0   1

The solution set of the system of inequalities is the region that satisfies all three inequalities, which is the shaded region in the graph below:

 |

5 |      

  |      

  |    x

 2|     |      

  |     |    

  |     |      

  |    /|    

  |   / |    

 0+------+------

   -4  0  2.5

So the points that lie in the solution set are:

(-2,3), (-1,3), (2,-2)

Therefore, the correct answers are:

(-2,3), (-1,3), and (2,-2)

Answer: 15.

Step-by-step explanation: If one-third of the students are girls, then two-thirds of the students are boys:

number of boys = (2/3) * 30 = 20

Three-quarters of the boys play basketball, so the number of boys in the class who play basketball is:

number of boys who play basketball = (3/4) * 20 = 15

Therefore, the number of boys in the class who play basketball is 15.

a) 'The IQR is a better measure of spread for movies than it is for basketball games' best describes how to measure the spread of the data

According to the information provided, the box plots for movies and basketball games indicate that both have the same range of attendance data, with a minimum of 60 and a maximum of 150. However, when comparing the interquartile ranges (IQRs) of the two box plots, it can be seen that the IQR for movies is smaller than the IQR for basketball games.

The IQR represents the middle 50% of the data, and the smaller IQR for movies suggests that the attendance data for movies is more closely clustered around the median than the attendance data for basketball games. Therefore, the IQR is a better measure of spread for movies than it is for basketball games, as it gives a more accurate representation of the variability of the data for movies.

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The radian measure of the central angle which intercepts the arc is 6.2 radians.

We can use the formula relating the arc length to the angle and radius of the circle:

arc length = radius x central angle in radians

Plugging in the given values, we get:

148.8 = 24 x central angle in radians

Solving for the central angle, we have:

central angle in radians = 148.8/24

central angle in radians = 6.2 radians

Therefore, the radian measure of the central angle which intercepts the arc is 6.2 radians.

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The cost of the case of air fresheners is $33.25.

Let the cost of the case of air fresheners be represented by the variable a.

Then, the cost of 5 buckets is 5 times $2.89, or 5 x 2.89 = $14.45.

The cost of 10 brushes is 10 times $7.91, or 10 x 7.91 = $79.10.

The cost of 48 towels is 48 times $0.36, or 48 x 0.36 = $17.28.

The total cost of the purchases, including the case of air fresheners, is $144.08.

Therefore, we can write the equation:

14.45 + 79.10 + 17.28 + a = 144.08

Simplifying the left side of the equation, we get:

110.83 + a = 144.08

Subtracting 110.83 from both sides of the equation, we get:

a = 33.25

Therefore, the cost of the case of air fresheners is $33.25.

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Thus, the correct order of the numbers from least to greatest: 6% < 1/2 < 0.6 < 6/5

In an ascending list, the item that is smallest, first, or oldest will be at the top:

Given number-

1\2, 0.6,6%,6\5

convert all numbers in its fraction form:

1\2 = 0.5

0.6 = 0.6

6% = 0.06

6\5 = 1.2

Order  from least to greatest: 0.06, 0.5, 0.6 1.2

Or,

Thus, the correct order of the numbers from least to greatest 6% < 1/2 < 0.6 < 6/5

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Answer:

Each student will have passed 17 tests; It will take 3 weeks.

Step-by-step explanation:

The explanation is in the picture.

Answer: A and D as for angle 24 deg, we are using the sin=opp/hyp and for angle 66 we are using cos=adj/hyp.

To find angle 66, you just subtract all 180 by the angles we know. 180-24-90.

Answer: 7.5

Step-by-step explanation: 2 x 7.5 = 15

Answer:

p=30 s=30 k=90 x=0

Step-by-step explanation:

000000000000

The IQR for both runs is 8 minutes.

If there are outliers or extreme values ​​in the data set, we summarize the typical value using the median instead of the mean. When there are outliers in a data set, the variation is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.

 Based on the given box pairs, we can make the following comparisons:

The average wait time at Thrill Tower is about 5 minutes shorter than the average wait time at River Rapids. That's because the centerline of Thrill Tower is  about 5 units below the centerline of River Rapids.  The IQR (interquartile range) for both times is not  directly in the box. However, we can estimate this by finding the distance between the first quartile (Q1) and the third quartile (Q3) of each run. From the box plot of Thrill Tower, we can see that Q1 is around 6 and Q3 is around 14. Therefore, the IQR for Thrill Tower is:

 Thrill Tower IQR = Q3 - Q1 = 14 - 6 = 8 minutes

From the box plot for River Rapids, we can see that Q1 is about 8 and Q3 is about 16. Therefore, the IQR for River Rapids is:

 River Rapids IQR = Q3 - Q1 = 16 - 8 = 8 minutes

Therefore, the IQR for both runs is 8 minutes.

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Answer: HERE IS THE ANSWER BELOW :)

The surface area of the pyramid is 532m²

A pyramid is a 3D polyhedron with the base of a polygon along with three or more triangle-shaped faces that meet at a point above the base. It is made by connecting each vertex of the base to a common tip or apex giving it its typical shape.

The general formula for the lateral surface area of a regular pyramid is L.S.A.=1/2pl

where

Given that The pyramid is a rectangular,

Therefore the surface area is

L.S.A.=1/2(14*4) *19

Surface area = 28*19 = 532m²

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It seems like the answer could be $6,500, but I prefer to wait for a professional tbh☹.

The average rate of change of the function f(x) on the interval 1 ≤ x ≤ 8 is given as follows:

5.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

The parameters for the function are given as follows:

Hence the average rate of change for the function is given as follows:

r = (25 - (-10))/(8 - 1) = 35/7 = 5.

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Answer:

20/8 or 20:8

Step-by-step explanation:

Ok, so we start off with a smaller square with one side being 8.

We then have to go from one side being 8 to one side being 20.

So, the ratio has to be a number larger than 1 to go from smaller to larger, so we can use the ratio of 20/8 (or 2.5).

Check:

2.5x8=20

The resultant value of x for the given quadratic equation 9x² − 16 = 0 is x = ±4/3.

Any equation in algebra that can be written in standard form where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.  

An algebraic equation of the second degree in x is a quadratic equation.

The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

So, we have the quadratic equation:

9x² − 16 = 0

Now, solve as follows:

a = 9

b = 0

c = -16

Now,

c = -0 ± √0² - 4-9(-16)/2*9

x = ±4/3

Therefore, the resultant value of x for the given quadratic equation 9x² − 16 = 0 is x = ±4/3.

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Answer:

35.00 - (0.85x) = remaining amount

Step-by-step explanation:

To find out how much money she has left, we need to subtract this amount from her starting amount of $35.00:

35.00 - 0.85x

Therefore, the expression that shows how much money Pam has left after buying (x) peaches is:

35.00 - 0.85x

From the attached picture, it is proven that the diagonals of rectangle MNOP are congruent.

To show that the diagonals of rectangle MNOP bisect each other, we need to show that they intersect at their midpoint. Let's label the diagonals as AC and BD, where AC is the diagonal that goes from vertex M to vertex O, and BD is the diagonal that goes from vertex N to vertex P.

First, let's find the midpoint of AC. The midpoint of a line segment is the point that is exactly halfway between the two endpoints. The endpoints of AC are M and O, so we can find the midpoint by averaging their x-coordinates and y-coordinates:

midpoint of AC = ((Mx + Ox)/2, (My + Oy)/2)

Similarly, we can find the midpoint of BD:

midpoint of BD = ((Nx + Px)/2, (Ny + Py)/2)

Now we need to show that these midpoints are the same point. That is, we need to show that:

((Mx + Ox)/2, (My + Oy)/2) = ((Nx + Px)/2, (Ny + Py)/2)

To do this, we can set the x-coordinates equal to each other and the y-coordinates equal to each other:

(Mx + Ox)/2 = (Nx + Px)/2

(My + Oy)/2 = (Ny + Py)/2

Now we can solve for the values of x and y. First, we'll solve for x:

Mx + Ox = Nx + Px

2Mx + 2Ox = 2Nx + 2Px

Mx + Ox - Nx - Px = 0

(Mx - Nx) + (Ox - Px) = 0

Similarly, we can solve for y:

My + Oy = Ny + Py

2My + 2Oy = 2Ny + 2Py

My + Oy - Ny - Py = 0

(My - Ny) + (Oy - Py) = 0

Now we can see that the x-coordinate and y-coordinate of the midpoint of AC are equal to the x-coordinate and y-coordinate of the midpoint of BD, respectively. Therefore, the diagonals of rectangle MNOP bisect each other.

To show that the diagonals are congruent, we can use the Pythagorean theorem. Let's label the length of AC as a and the length of BD as b. Then we have:

a^2 = OM^2 + ON^2 (by the Pythagorean theorem in triangle OMN)

b^2 = PN^2 + PO^2 (by the Pythagorean theorem in triangle PON)

But we know that OM = ON and PO = PN, since MNOP is a rectangle. Therefore, we can simplify these expressions:

a^2 = 2OM^2

b^2 = 2PO^2

Since OM = PO (they are opposite sides of a rectangle), we can substitute to get:

a^2 = 2OM^2 = 2PO^2 = b^2

Therefore, a = b, and the diagonals of rectangle MNOP are congruent.

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The solution to the given problem of volume comes out to be the pyramid is 10 cm tall.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are the symbols for cubic measures.

Here,

The formula: gives the volume of a pyramid.

=> V = base_area * height * (1/3)

The area of the base (base_area) of a pyramid whose base is a rectangle with dimensions of 7.5 cm in length and 2 cm in width can be computed as follows:

base_area equals length * width,

=> 7.5 cm * 2 cm =15 cm².

Additionally, we are informed that the pyramid's (V) volume is 50 cm3.

=> (1/3) * 15 * height = 50

=> height =  (3 * V)/base_area.

When V and base_area's values are entered, we obtain:

=> height = (15/15) / (3*50) = 10 cm

Consequently, the pyramid is 10 cm tall.

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The accumulated amount 54675 ([tex]2.7^{t}\\[/tex]) in dollars of an account with an initial deposit of $7,500 and earns 3. 4% compound interest semi-annually.

A compound interest is calculated by the formula,

[tex]A = P [ 1 + ( r/n )]^{nt}[/tex]

where, A is the accumulated amount at the end of the period ,

P is the initial amount of deposit,

r is the rate of interest earned on the initial deposit in the period

t is the time periods elapsed

and n is the number of times interest is applied per time period

Here the account has an initial deposit , P = $7500 and earns 3.4% rate of interest, say r, compounded semi- annually, that is n= 2 ( as rate of interest is applied twice a year or twice per time period) in time period, say t.

Therefore by the formula of compound interest we get,

Accumulated amount, A = [tex]7500[ 1 + 3.4/2]^{2t}[/tex]

⇒ A = [tex]7500[ 1 + 1.7]^{2t}[/tex] in dollars

⇒ A = [tex]7500(2.7)^{2t}[/tex] in dollars

⇒ A = 7500 (2.7)² ([tex]2.7^{t}[/tex] ) in dollars

⇒ A = 54675 ([tex]2.7^{t}\\[/tex]) in dollars

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The expanded form of (2x² + 5y)⁵ using the binomial theorem is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.

Given the expression in the question:

(2x² + 5y)⁵

To expand (2x² + 5y)⁵ using the binomial theorem, we need to apply the following formula:

(a + b)ⁿ = C(n, 0)aⁿ b⁰ + C(n, 1)a⁽ⁿ⁻¹⁾ b¹ + C(n, 2)a⁽ⁿ⁻²⁾ b² + ... + C(n, r)[tex]a^{(n-r)}[/tex] [tex]b^r[/tex] + ... + C(n, n)a⁰ bⁿ

Where C(n, r) is the binomial coefficient, which represents the number of ways to choose r items from a set of n distinct items.

(2x² + 5y)⁵

Here: a = 2x² and b = 5y, so we have:

Plug into the above formula

(2x² + 5y)⁵ = C(5, 0)(2x²)⁵ (5y)⁰ + C(5, 1)(2x²)⁴ (5y)¹ + C(5, 2)(2x²)³ (5y)² + C(5, 3)(2x²)² (5y)³ + C(5, 4)(2x²)¹ (5y)⁴ + C(5, 5)(2x²)⁰ (5y)⁵

Simplifying each term using the binomial coefficient formula C(n, r) = n! / (r! (n-r)!):

(2x² + 5y)⁵ = 1(32x¹⁰)1(1) + 5(16x⁸)1(5y)¹ + 10(8x⁶)2(25y²) + 10(4x⁴)3(125y³) + 5(2x²)4(625y⁴) + 1(1)5(3125y⁵)

Simplifying the coefficients and the exponents of x and y:

(2x² + 5y)⁵ = 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵

Therefore, the expanded form is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.

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Answer: Exact Form:

1/16

Decimal Form:

0.0625

Step-by-step explanation:

Answer:

x = - [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

14 = [tex]\frac{8}{3}[/tex] (x + 6) ← multiply both sides by 3 to clear the fraction

42 = 8(x + 6) ← distribute parenthesis

42 = 8x + 48 ( subtract 48 from both sides )

- 6 = 8x ( divide both sides by 8 )

[tex]\frac{-6}{8}[/tex] = x , that is

x = - [tex]\frac{3}{4}[/tex]

We reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100, with a type I error rate of 10% and a p-value of 0.0068 indicating a low probability of obtaining the observed sample mean if the null hypothesis were true.

To test if the true average temperature of COVID patients exceeds 100, we can use a one-sample z-test.

The null and alternative hypotheses are

Null hypothesis: The true average temperature of COVID patients is less than or equal to 100.

Alternative hypothesis: The true average temperature of COVID patients exceeds 100.

We can calculate the test statistic as

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the hypothesized population mean (100 in this case), σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get

z = (101.2 - 100) / (6 / sqrt(56))

z = 2.47

We can find that the p-value is 0.0068. This means that if the true average temperature of COVID patients is actually 100, there is only a 0.68% chance of getting a sample mean of 101.2 or higher.

Since the alpha level is 10%, and the p-value is less than 10%, we reject the null hypothesis and conclude that the true average temperature of COVID patients exceeds 100.

The type of error that could have occurred is a type I error, which is rejecting the null hypothesis when it is actually true. The probability of a type I error is equal to the chosen alpha level, which is 10% in this case.

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For a hypothesis testing, [tex]H_0 : µ = µ_0[/tex] ; [tex]H_1 : µ > µ_0.[/tex] the calculated P-value for test statistic value are following a) 0.9906 ; b) 0.9370 ; c) 0.9773; d) 0.9678 ; e) 0.4404.

We are testing the null hypothesis versus alternative hypothesis. Both are defined as [tex]H_0 : µ = µ_0[/tex]

[tex]H_1 : µ > µ_0.[/tex].

We have to calculate the P-value for the following observed values test statistic one by one.

a)z = 2.35

The P -value is calculated for as follows P ( z > Zo) = 1 - P( z≤ z0)

= 1 - P( z≤ 2.35)

Now, using the normal distribution table, the value of P( z≤ 2.35) is equals to 0.009387. So, P( z> 2.35) = 1 - 0.009387

= 0.990613

b) z₀ = 1.53

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.53)

Now, using the normal distribution table , the value of P( z≤ 1.53) is equals to 0.063008. So, P( z> 1.53) = 1 - 0.063008

=0.936992

c) z₀ = 2.00

The P-value is calculated for as follows, P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 2.00)

Now, using the normal distribution table , the value of P( z≤ 2.00) is equals to 0.02275. So, P( z> 2.00) = 1 - 0.02275

=0.97725

d) z₀ = 1.85

The P-value is calculated for as follows P ( z > z₀) = 1 - P( z≤ z₀)

= 1 - P( z≤ 1.85)

Now, using the normal distribution table , the value of P( z≤ 1.85 ) is equals to 0.032157. So, P( z> 1.85) = 1 - 0.032157

=0.967843

e) z₀ = -0. 15

The P-value is calculated for as follows P ( z > -z₀) = P( z ≤ z₀)

= P( z≤ 0.15 )

Now, using the normal distribution table , the value of P( z≤ 0.15) is equals to 0.440382. So, P( z > - 0.15) = 0.44038. Hence the required P-value is 0.44038.

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Answer:5

Step-by-step explanation: you divide 15 by 3 which gives you 5

A measure of relative fit for a simple regression line is called the r² or coefficient of determination.

A regression line, or line of best fit, is a straight line used to model the relationship between two variables in a data set. It is drawn through the data points to minimize the distance between the line and the points, representing the best fit. The line's equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope represents the rate of change of y with respect to x, and the y-intercept represents the value of y when x is equal to 0. The line is often used to predict the dependent variable based on the independent variable, and the accuracy of the predictions depends on how well the line fits the data.

The coefficient of determination, also known as r², is a statistical measure used to determine the relative fit of a simple regression line. This measure represents the proportion of variance in the dependent variable that can be predicted by the independent variable. The calculation involves squaring the correlation coefficient (r) between the two variables. The resulting value of r² ranges from 0 to 1, where 0 indicates that the independent variable has no explanatory power over the dependent variable, while 1 implies that the independent variable explains all the variability in the dependent variable.

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Answer:

$51,500 in her savings account.

Step-by-step explanation:

If Pamela has $50,000 in a savings account with an interest rate of 3% per year and the interest is not compounded, then in 1 year she will earn an interest of $50,000 * 0.03 = $1,500.

So, after 1 year, Pamela will have a total of $50,000 + $1,500 = $51,500 in her savings account.

The conclusion that red is the preferred color of shirt among 7th grade students based on a survey of 6 random students in an art class is not necessarily valid due to the small sample size, sampling bias, and lack of generalizability.

The sample size of six pupils is tiny and may not be typical of the overall seventh-grade population. It's probable that the six students in the art class have different preferences or biases than the other seventh-grade students.

Also, the sample of six pupils is drawn at random from an art class rather than from the total 7th grade population. Students who are interested in art may have different preferences than students who are not. This can add bias into the sample.

Finally, the language of the survey question is critical. If the survey question specifically asks about the most chosen color of shirt among 7th grade kids in general, the conclusion that red is the most preferred color of shirt follows.

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