A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 7 centimeters by 3 and three-fifths centimeters by 2 and two-fifths centimeters.

What is the surface area of the prism?

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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Answer:

14

Step-by-step explanation:

line from center to chord bisect chord

so x = 14

The solution of the inequality, log₂ 2m > log₂ (m + 5) is {m | m > 5 / 2}.

An inequality is an expression that have <, >, ≤ and ≥ . Therefore, let's solve the logarithmic inequality for the variable m.

Hence,

log₂ 2m > log₂ (m + 5)

Therefore, let's divide both sides by log₂.

Hence,

2m > m + 5

subtract m from both sides of the inequality

2m > m + 5

2m - m > m - m + 5

2m > 5

divide both sides by 2

2m / 2 > 5 / 2

Therefore,

m > 5 / 2

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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 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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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 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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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 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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The accrued value of Staci's investment in the account in the year 2029 is $26933.59

The statements in the question can be sumarrized as

The formula to calculate amount on investment is

Amount = P * (1 + r)ⁿ

Where

When the values are substituted in the amount equation, we have

Amount = 14500 * (1 + 3.5%)¹⁸

Evaluate

Amount = 26933.59

Hence, the amount after the investment is $26933.59

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Answer:

3. radius = 9.4

4. radius = 22.6

5. diameter = 13.3

Step-by-step explanation:

The diameter of a circle = 2 * radius

For problem 3 and 4,  you need to multiply the given radius by 2 to get the diameter.

For problem 5, you need to divide the diameter by 2 to get the radius.

Jordan's account balance at the end of the month would be $143.85.

What is the basic arithmetic operations?

The four basic mathematical operations are Addition, subtraction, multiplication, and division.

To determine Jordan's account balance at the end of the month, we need to add up the deposits and withdrawals to the initial balance.

Initial balance: $92.66

Deposits: $7.72 + $70.42 + $107.46 = $185.60 (sum of positive amounts)

Withdrawals: -$84.26 + (-$50.15) = -$134.41 (sum of negative amounts)

To calculate the account balance at the end of the month, we can add the deposits and withdrawals to the initial balance:

Account balance at the end of the month = Initial balance + Deposits - Withdrawals

= $92.66 + $185.60 - $134.41

= $143.85

Hence, Jordan's account balance at the end of the month would be $143.85.

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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).

Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200 is 4.62%.

Using the formula r = ln(A/P) / t, the interest rate, r, can be determined using an online finance calculator as follows:

Total P+I (A) = $4,200.00

Principal (P) = $2,200.00

Compound (n) = Compounding Continuously

Time (t in years) = 14 years

R = 4.619% per year

The calculation steps are as follows:

Solving for rate r as a decimal

r = ln(A/P) / t

r = ln(4,200.00/2,200.00) / 14

r = 0.0461877

Then convert r to R as a percentage:

R = r * 100

R = 0.0461877 * 100

R = 4.62%/year

Thus, the interest rate required to get a total amount of $4,200.00 from compound interest on a principal of $2,200.00 compounded continuously over 14 years is 4.62% per year.

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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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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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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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Using interval notation, the domain of f.g and f+g is [1/4, ∞).

Given, f(x)= 1/ (5x² + 3) and [tex]g(x) = \sqrt{4x-1}[/tex]

To find f.g, we substitute g(x) into f(x) and simplify:

f.g(x) = f(g(x))

[tex]=f(\sqrt{4x-1})[/tex]

[tex]=\frac{1}{5(\sqrt{4x-1})^2 +3}[/tex]

= 1/(5(4x-1)+3)

= 1 / (20x - 2)

To find f+g, we add the functions f(x) and g(x):

f+g(x) = f(x) + g(x)

= [tex]\frac{1}{5x^2+3}+\sqrt{4x-1}[/tex]

The domain of f.g and f+g is the intersection of the domains of f(x) and g(x).

The domain of f(x) is all real numbers except for the values of x that make the denominator zero, i.e., 5x² + 3 = 0. This equation has no real solutions, so the domain of f(x) is all real numbers.

The domain of g(x) is the set of all real numbers that make the argument of the square root non-negative, i.e., 4x - 1 ≥ 0. Solving this inequality, we get x ≥ 1/4.

Therefore, the domain of f.g and f+g is x ≥ 1/4.

Using interval notation, the domain of f.g and f+g is [1/4, ∞).

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Answer:5.25cm

Step-by-step explanation:

1)look back at your question

2)look after the 6th word

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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The Ferris Wheel can carry 2100 passengers on a total of 35 rides.

According to the question,

Number of cars in the Ferry Wheel = 15

Number of passengers in each car = 4

∴ Number of passengers in 15 cars = 15×4 = 60

So, the number of passengers on the Ferry Wheel = 60

Now,

The number of passengers the Ferry Wheel carries in one ride = 60

∴ The number of passengers in 35 rides = 60×35 = 2100.

Hence the Ferris Wheel can carry 2100 passengers on a total of 35 rides.

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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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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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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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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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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:

B

Step-by-step explanation:

Lateral surface contains B,C and D (because A and E are bases)

A (lateral surface area) = 70 + 70 + 56 = 196 cm^2