Bob wants to break the school record of scoring 30 points in his basketball game. He scored 13 points in the first half. How many two point baskets must Bob make in the second half to break the school record?

Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses.

The parameter of interest is the difference in population proportions of females and males who took advanced math courses. We can denote this parameter by p₁ - p₂, where p₁ is the population proportion of females who took advanced math courses, and p₂ is the population proportion of males who took advanced math courses.

To construct a confidence interval for the difference in population proportions, we need to check the following conditions,

The sample of high school students should be a simple random sample.

The sample of high school students should be independent of each other.

Both groups of females and males who took advanced math courses should have at least 10 successes and 10 failures.

The sample proportions of females and males who took advanced math courses can be calculated as follows,

p₁ = 53/150 = 0.353

p₂ = 89/275 = 0.324

The sample size of females and males can also be calculated as follows,

n₁ = 150

n₂ = 275

The standard error of the difference in sample proportions can be calculated as follows,

SE = √[(p₁(1 - p₁))/n₁ + (p₂(1 - p₂))/n₂]

= √[(0.353(1 - 0.353))/150 + (0.324(1 - 0.324))/275] ≈ 0.048

Using a t-distribution with (n₁ + n₂ - 2) degrees of freedom and a 98% confidence level, we can construct a confidence interval for the difference in population proportions as follows:

(p₁ - p₂) ± t*SE

where t is the t-score corresponding to a 98% confidence level and (n₁ + n₂ - 2) degrees of freedom. Using a t-table, we can find that t ≈ 2.33.

Substituting the values into the formula, we get,

(0.353 - 0.324) ± 2.33*0.048

0.029 ± 0.112

True difference in population proportions of females and males who took advanced math courses lies between 0.029 and 0.147.

Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain.

Yes, our interval from part A gives convincing evidence of a difference between the population proportions because it does not contain zero. The interval (0.029, 0.147) is entirely positive, which means that the proportion of females who took advanced math courses is higher than the proportion of males who took advanced math courses. Additionally, the interval does not contain the value of one, which means that the difference in population proportions is not due to chance. Therefore, we can conclude that there is a significant difference in the population proportions of females and males who took advanced math courses.

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Answer:

r=1

Step-by-step explanation:

The Pearson correlation coefficient is used to measure the strength of a linear association between two variables, where the value r = 1 means a perfect positive correlation and the value r = -1 means a perfect negataive correlation. So, for example, you could use this test to find out whether people's height and weight are correlated (they will be - the taller people are, the heavier they're likely to be).

To find the expected number of dog owners who brush their dog's teeth, we can multiply the total number of dog owners (639) by the percentage that brush their dog's teeth (18% or 0.18).

Expected number of dog owners who brush their dog's teeth = 639 x 0.18

= 115.02 (rounded to the nearest whole number)

So, we can expect about 115 dog owners out of 639 to brush their dog's teeth.

Therefore , the solution of the given problem of expressions comes out to be  the buddies need to gather to reach their objective is

9x² - 10xy - 1.

It is preferred to employ shifting numbers, which may also prove to be increasing, diminishing, or blocking, rather than random estimations. Only by exchanging tools, information, or answers to problems could they assist one another. The statement of truth equation may comprise the arguments, elements, or quantitative remarks for strategies like increased disagreement, production, and blending.

Here,

Part A:

=> Jasmine: 9x²

=> 6x² - 4 for Tyree

=> Ben: 4xy + 3

These three phrases added together represent the total amount of canned food collected:

=> 9x² + (6x² - 4) + (4xy + 3)

=> 15x² + 4xy - 1

As a result, the expression for how many cans of food the three buddies have so far amassed is 15x² + 4xy - 1.

Part B's collection objective is 24x² - 6xy - 2.

Collection total: 15x² + 4xy - 1

The distinction between these two phrases shows the quantity of cans the buddies still need to gather:

=> (24x² - 6xy - 2) - (15x² + 4xy - 1)

=> 9x² - 10xy - 1

As a result, the phrase for how many more cans the buddies need to gather to reach their objective is 9x² - 10xy - 1.

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a) The probability that a randomly selected student is taking a Math class or an English class is 0.82.

b) The probability that a randomly selected student is taking neither a math class nor an English class is 0.18.

Probability refers to the chance or likelihood that an expected success, event, or outcome occurs from many possible successes, events, or outcomes.

Probability is represented as a fractional value using decimals, fractions, or percentages.

The percentage of students taking a math class =79%

The percentage of students taking an English class = 70%

The percentage of students taking both classes = 67%

Let the event that a student is taking a math class = m

Let the event that a student is taking an English class = e

The probability of m is p(m) = 0.79

The probability of e is p(e) = 0.70

The probability of m and e is p(m and e) = 0.67

The probability that a randomly selected student is taking a math class or an English class = 0.82 (0.79 + 0.70 - 0.67)

The probability that a randomly selected student is taking neither a math class nor an English class = 0.18 (1 - 0.82)

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The surface area of the prism is 360in²

A prism is a solid shape that is bound on all its sides by plane faces.

The surface area of a prism is expressed as;

SA = 2B + ph

where h is the height of the prism and B is the base area , p is the perimeter of the base.

Base area = 1/2 × 5 × 12

= 5 × 6 = 30 in²

Perimeter of the base = 5+12+13

= 30 in²

height = 10 in

SA = 2 × 30+30× 10

= 60 + 300

= 360 in²

therefore the surface area of the prism is 360 in²

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Answer:

1/6

Step-by-step explanation:

Chances of getting 2 = 1/6

For the drug used to treat asthma in a clinical trial:

Part 1:

The test is right-tailed because the alternative hypothesis is that less than 9% of treated subjects experienced headaches.

Part 2:

The test statistic is z = 0.64, rounded to two decimal places (given in the calculator display).

Part 3:

The P-value is 0.7401, rounded to four decimal places (also given in the calculator display).

Part 4:

The null hypothesis is Upper H₀: p ≥ 0.09. We conclude that there is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

Part 5:

We fail to reject the null hypothesis because the P-value is greater than the significance level, α=0.01.

Part 6:

The final conclusion is: D, There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

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The area of each circle would be given below:

Circle A= 153.86 in²

Circle B = 314in²

Circle C = 615.44in²

Circle D = 452.16 in²

To calculate the area of a circle, the formula that should be used is given below such as follows:

Area of circle = πr²

For circle A;

radius = 7 in

area = 3.14×7×7 = 153.86 in²

For circle B;

radius = 3+7 = 10in

area = 3.14×10×10 = 314in²

For circle C;

radius = 10+4 = 14 in

area = 3.14×14×14

= 615.44in²

For circle D;

radius = 14-2 = 12in

radius = 3.14×12×12

= 452.16 in²

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Answer:

3 yards

Step-by-step explanation:

The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.

The percentage increase can be determined by finding the difference or the amount of increase in sales.

This difference is divided by the previous month's sales and multiplied by 100.

The total number of boxes of cookies Molly's Scout Troop sold last month = 148

The total number sold this month = 165

The increase = 17 (165 - 148)

Percentage increase = 11.5% (17 ÷ 148 x 100)

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Answer:

14

Step-by-step explanation:

line from center to chord bisect chord

so x = 14

From the discrete distribution given, the standard deviation is of 0.83 children.

The distribution is:

P(X=1) =0.5

P(X=2) =0.25

P(X=3) =0.25

The mean is 1.75.

The standard deviation is the square root of the sum of the difference squared between each value and the mean, multiplied by it's respective probability.

Hence:

The standard deviation is 0.83 children.

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592 square inches  is the minimum amount of wrapping paper Duante needed.

Duante will need a minimum of 592 square inches of wrapping paper.

Lets convert the dimensions to the same units.

Since there are 12 inches in a foot, the dimensions are:

Width = 1 foot = 12 inches

Length = 10 inches

Height = 8 inches

The rectangular box is known as a cube

The surface area of a b=cuboid is given by SA = 2lw + 2lh + 2wh

where l is length, w is width and and h is the height of the cuboid

Substituting the given values, we get:

SA = 2(10)(12) + 2(10)(8) + 2(12)(8)

= 240 + 160 + 192

= 592

Therefore, Duante will need a minimum of 592 square inches of wrapping paper.

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Answer:5.25cm

Step-by-step explanation:

1)look back at your question

2)look after the 6th word

The area, in square inches, of the label needed to cover the face of the box is 96 in².

Option A is correct.

We must first determine the length and breadth of the rectangle before multiplying them together to determine the area of the rectangular face.

The distance between the x-coordinates of two opposite points determines the length of the rectangle:

length equals 3 - (-5) = 8.

The distance between the y-coordinates of the same two opposite points determines the rectangle's width:

width = 8 + (-4) = 12

In conclusion, the rectangle's size is: 8 × 12 = 96 square inches is the area formula.

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well, let's find out how much she made on each week

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]

The volume of a cylinder whose diameter measures 32 feet and has a height of 10 feet is equal to: C. 8,038.4 ft³.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius = diameter/2 = 32/2 = 16 ft.

By substituting the parameters, we have:

Volume of cylinder, V = 3.14 × 16² × 10

Volume of cylinder, V = 8,038.4 cubic feet.

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Among the given options, V [tex]57^\circ[/tex]   is the closest estimate for the measure of the other acute angle.

To find the measure of the other acute angle, we can use the fact that the sum of the angles of a triangle is 180°. Let x be the measure of the other acute angle. Then we have:

[tex]x + 32.9^\circ + 90^\circ = 180^\circ[/tex]

Simplifying the equation, we get:

[tex]x = 180^\circ - 32.9^\circ - 90^\circ[/tex]

[tex]x = 57.1^\circ[/tex]

So the exact measure of the other acute angle is [tex]57.1^\circ.[/tex]

Therefore, Among the given options, V [tex]57.1^\circ.[/tex] is the closest estimate for the measure of the other acute angle.

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For the given vector v = 2i - 3j, the value of the vector magnitude ||2v|| is 2√13.

To find the norm, or magnitude, of a vector, we use the Pythagorean theorem in the following way:

||v|| = √(v₁² + v₂² + ... + vn²)

In this case, we have v = 2i - 3j, so:

||v|| = √((2)² + (-3)²)

= √(4 + 9)

= √13

So the norm of the vector v is √13.

To find ||2v||, we simply double the vector and then find its norm:

2v = 2(2i - 3j)

= 4i - 6j

||2v|| = √((4)² + (-6)²)

= √(16 + 36)

= √52

= 2√13

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James pays back approximately 82.33% of the total loan in interest over the 20-year period.

To calculate the percentage of the total loan that James pays back in interest, we need to determine how much of the monthly payments go towards interest and how much goes towards paying down the principal.

Using a loan calculator or a formula, we can determine that the monthly interest rate for James' loan is approximately 0.35% (4.25% annual rate divided by 12 months). The monthly payment of $915.00 is comprised of both principal and interest.

In the first month, the interest portion of the payment would be $531.25 and the remaining $383.75 would go towards the principal. As the loan is paid down over time, the interest portion of each payment decreases while the principal portion increases.

To calculate the total interest paid over the life of the loan, we can multiply the monthly interest by the number of months (20 years x 12 months/year = 240 months) and subtract the original principal amount of $150,000. This gives us a total interest paid of approximately $123,500.

To find the percentage of the total loan that this represents, we can divide the total interest paid by the original principal and multiply by 100:

$123,500 ÷ $150,000 x 100 ≈ 82.33%

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The expression without the absolute value symbol is:

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

Since, An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

|(x + 3) | if x > 5

This can be written as,

= |x + 3|

Now,

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

Thus,

The expression without the absolute value symbol is:

|x + 5| = x + 5, if x > 5

|x - 5| = 0, if x = 5

|x - 5| = 5 - x, if x < 5

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(11) The value of expression 3/y + 2y/4 when y = 4 is [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The value of expression 12/y + 3y/4 when y = 8 is [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) 2x/3 + 4 = 10 equation does x = 9.

Hence the correct option is (b).

(11) The given expression is,

3/y + 2y/4 = 3/y + y/2

Substituting the value of y = 4 we get,

3/4 + 4/2 = 3/4 + 2 = [tex]2\frac{3}{4}[/tex].

Hence the correct option is (b).

(12) The given expression is,

12/y + 3y/4

Substituting y = 8 in the given equation we get,

12/8 + (3*8)/4 = 3/2 + 6 = 1 + 1/2 + 6 = [tex]7\frac{1}{2}[/tex].

Hence the correct option is (c).

(13) Given the solution is x =9.

For first option: (2/3)*9 - 6 = 6 - 6 = 0

2x/3 - 6 = 12 does not satisfied by x = 9.

For second option: (2/3)*9 + 4 = 6 + 4 = 10

So, x = 9 satisfies 2x/3 + 4 = 10.

For third option: 3*9 - 12 = 27 - 12 = 15

So x = 9 does not satisfy 3x - 12 = 21.

For fourth option: 3*9 + 12 = 27 + 12 = 39

So x = 9 does not satisfy 3x + 12 = 19.

Hence the correct option is (b).

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The scale of Sarah's zoomed-in map is 1cm = 1000 cm or 1cm = 10 m. So the answer is (B) 1cm = 10 m.

To find the scale of Sarah's zoomed-in map, we can use the ratio of the width of the park on the map to its actual width.

Let's first convert the width of the park from meters to centimeters, since the width of the park on the map is given in centimeters.

15 m = 1500 cm

Next, we can set up a proportion:

0.5 cm / x = 1500 cm / (3x)

where x is the scale of the zoomed-in map.

Simplifying the proportion, we get:

0.5(3x) = 1500

1.5x = 1500

x = 1000

Therefore, the answer is (B) 1cm = 10 m.

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The area of the polygon is 33cm²

A polygon is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.

The area of a polygon is expressed as;

A = 1/2 × p × a

where p is the perimeter of the polygon and a is the apothem.A pentagon is a 5 sides polygon.

Therefore;

Perimeter = 5 × 4.4

= 22cm

apothem = 3cm

area = 1/2 × 22 × 3

= 11× 3

= 33 cm²

therefore the area of the Pentagon in is 33cm²

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The equation that models the given situation is: f(t) = 21e^(-0.000361)t

We can model this situation with an exponential decay function.

f(t) = Pe^(rt)

Where:

f(t) = amount of isotope

P = starting amount

r = growth rate

t = time

Let's assume that there is 1 mg of our isotope. Thus,in 1920 years, we will have 1/2 mg. Thus:

(1/2) = (1)e^(1920r)

Take the natural log of both sides to bring the exponent down and to cancel out the e

ln(1/2) = ln(e^(r(1920))

ln(1/2) = r(1920)

ln(1/2)/1920 = r

r = -0000361

Thus, we have:

f(t) = Pe^(-0.000361)t

Plug in 21 for P to get:

f(t) = 21e^(-0.000361)t

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If Diego's family spent a total of $130, on a night out, then the each ticket for the fair cost's $15.

In order to find the "total-cost" of the tickets, we subtract the cost of the family dinner from the total amount spent;

⇒ Total cost of tickets = Total amount spent - Cost of family dinner,

⇒ Total cost of tickets = $130 - $55,

⇒ Total cost of tickets = $75.

Next, we divide the total cost of the tickets by the number of tickets purchased to find the cost of each ticket:

So, Cost per ticket = (Total cost of tickets)/(Number of tickets),

⇒ Cost per ticket = $75/5,

⇒ Cost per ticket = $15,

Therefore, each ticket to the fair cost $15.

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