GIFTS Joel has $96 to spend on at least 9 gifts for the holidays. He plans to buy puzzles that cost $8 or games that cost $12. How many of each can he buy? Part A Create a system of inequalities that represents the constraints in the problem. Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy. Can Joel buy 2 games and 6 puzzles and satisfy the constraints?

Answer:

[tex]36 \: cm ^{2} [/tex]

Step-by-step explanation:

triangle area below

[tex] \frac{10 \times 5}{2} = 25[/tex]

EG segment

[tex] \sqrt{10 ^{2} + 5 ^{2} } = \sqrt{125} [/tex]

EF segment

[tex] \sqrt{ (\sqrt{125})^{2} - 2^{2} } = \sqrt{121} [/tex]

triangle area above

[tex] \frac{ \sqrt{121} \times 2}{2} = \sqrt{121} [/tex]

total area

[tex]25 + \sqrt{121} = 36[/tex]

Using cosine rule, the measure of side c is calculated as: 4.688

In trigonometry, the Cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

We are given the parameters as:

a = 5

B = 7

C = 42 degrees

Using cosine rule, we have:

c = √(a² + b² - 2ab cos C)

c = √(5² + 7² - 2(5 * 7) cos 42)

c = √(25 + 49 - 52.02)

c = √21.98

c = 4.688

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Answer:

C) 260 square inches.

Step-by-step explanation:

To find the surface area of a pyramid, we can use the formula.

Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area

where l is the length of one side of the square base, s is the slant height, and Base Area is the area of the square base.

In this case, the base of the pyramid is a square with side length l = 10 inches, so its area is

Base Area = l^2 = 10^2 = 100 square inches

To find the perimeter of the base, we can simply multiply the length of one side by 4

Perimeter of Base = 4l = 4 x 10 = 40 inches

We are also given that the slant height of the pyramid is s = 8 inches.

Now we can substitute the values into the formula.

Surface Area = (1/2) x Perimeter of Base x Slant Height + Base Area

Surface Area = (1/2) x 40 x 8 + 100

Surface Area = 160 + 100

Surface Area = 260 square inches

Therefore, the surface area of the pyramid is 260 square inches.

Answer:360 in

Step-by-step explanation:

Answer:

1. 7/16 = 43.75%

2. 4/5 = 80%

3. 55% = 55/100 = 11/20

4. 248% = 2 48/100 = 2 12/25

5. 0.00031 = 0.031%

6. 6.005 = 600.5%

7. 12% = 12/100 = 3/25 (Gigi spent 3/25 of her birthday money on the new sunglasses)

8. The total bill for pizza and soft drinks was $27.50. With a 20% tip, the amount of tip left would be:

Tip = 20% of total bill

Tip = 20/100 * $27.50

Tip = $5.50

Therefore, Veronica and her friends left a $5.50 tip for their server.

Step-by-step explanation:

Answer:

1. 43.75%

2. 60%

3. 11/20

4. 2 and 12/25

5. 0.031%

6. 600.5%

7. 3/25

8. $5.50

Step-by-step explanation:

1. 7 ÷ 16 = 0.4375

0.4375 x 100 = 43.75%

2. 3 ÷ 5 = 0.6

0.6 x 100 = 60%

3. 55/100

11x25 / 20x5 = 11/20

4.248/100

62x4 / 25x4

62/25

62/25 = 2R12

2 12/25

5. 0.00031 x 100 = 0.031%

6. 6.005 x 100 = 600.5%

7. 12% = 12/100.

12/100 simplified = 3/25

8. $27.50 x 20% = $5.50

Answer: To evaluate 13 - 0.75w + 8x when w = 12 and x = 1/2, we substitute these values into the expression:

13 - 0.75w + 8x = 13 - 0.75(12) + 8(1/2)

Simplifying the expression inside the parentheses first:

13 - 9 + 4 = 8

Substituting this value into the expression:

13 - 0.75w + 8x = 13 - 0.75(12) + 8(1/2) = 13 - 9 + 4 = 8 + 4 = 12

Therefore, the value of 13 - 0.75w + 8x when w = 12 and x = 1/2 is 12.

Answer:

8

Step-by-step explanation:

Given expression is
[tex]13-0.75w\:+\:8x[/tex]

and we are asked to evaluate this expression when
[tex]w = 12 ,\: x = \dfrac{1}{2}[/tex]

[tex]0.75w = 0.75 \times 12 = 9[/tex]

[tex]8x = \8 \times \dfrac{1}{2} = 4[/tex]

[tex]\text{So the expression at $w = 12 \; , x= \dfrac{1}{2}$ evaluates to}[/tex]

13 - 9 + 4 = 8

Answer: 8

Answer:

The probability that exactly 5 of the 7 selected smartphone users use their phones in meetings or classes is approximately 0.0127 or 1.27%.

The assertion that the percentage of males who own cats is lower than the percentage of women who do not own cats is unsupported by sufficient data.

Hence, the Alternate hypothesis would be:

H0: Pm = Pf

H1 = Pm < Pf

Alternate hypotheses are used in statistical hypothesis testing. The hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.

Given information:

The test claims proportion of men who owns cat is smaller.

The significance level = 0.005

As the hypothesis always gets ten statements of equality but in the case given alternate hypothesis will claim.

Now calculating the Z-value:

P= 10+14/80

= 0.3

So, the p-value according to the obtained Z value is 0.1365.

Since, 0.1365>0.005, we fail to reject the hypothesis.

Hence, there is not enough proof to support the claim that the proportion of man who owns the cat is less than that of the proportion of women who owns the cat.

Therefore, the Alternate hypothesis would be:

H0: Pm = Pf

H1 = Pm < Pf

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If Astrid says the function being graphed is y=-4+1/3. Matt is correct, while Astrid is incorrect.

Astrid's equation y = -4 + 1/3 is incorrect because it is missing the variable x. The equation is missing a term that represents the x variable, so the equation does not represent a line.

On the other hand, Matt's equation y = 1/3x is correct, and the slope of the line represented by this equation is indeed 1/3. This can be seen from the fact that the equation is in the form y = mx, where m is the slope of the line. In this case, m = 1/3, so Matt is correct.

Therefore, Matt is correct, while Astrid is incorrect.

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As a result, the likelihood that the mean length of a random sample of 17 items is less than 10.9 inches is about 0.9265, or 92.65%.

Probability is a measure of how likely an event is to occur. It is a number between 0 and 1, with 0 suggesting that an occurrence is impossible and 1 indicating that an event is unavoidable. A given event's probability is computed by dividing the number of positive outcomes by the total number of potential possibilities.

In this case, we may utilize the central limit theorem to estimate the sample mean distribution. The central limit theorem states that if the sample size is high enough (n 30), the distribution of the sample mean will be normal.

Regardless of demographic distribution, the population is essentially typical.

In this scenario, the population has a normal distribution with a mean () of 9.8 inches and a standard deviation () of 2 inches. We wish to calculate the likelihood that the sample mean (x) of 17 objects is smaller than 10.9 inches.

The formula for calculating a sample mean's z-score is: z = (x - ) / ( / sqrt(n)), where n is the sample size.

We obtain: z = (10.9 - 9.8) / (2 / sqrt(17)) by substituting the numbers supplied in the problem.

z = 1.45

We may calculate the chance that a standard normal variable is smaller than 1.45 using a typical normal distribution table or calculator:

P(Z < 1.45) = 0.9265

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The product of -2³ + x - 5 and x³ -3x +4 is -5x³ + 16x - 28.

The given expression is:

-2³ + x - 5 x (x³ -3x +4)

We need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, let's simplify -2³, which means -2 x 2 x 2 = -8, so we have:

-8 + x - 5 x (x³ -3x +4)

Next, we need to distribute the -5 to the terms inside the parentheses:

-8 + x - 5x³ + 15x - 20

Now we can combine like terms:

-5x³ + 16x - 28

Therefore, the product of -2³ + x - 5 and x³ -3x +4 is -5x³ + 16x - 28.

Now, to answer the second part of the question, we need to check if:

-2³ + x - 5 x (x³ -3x +4) = (x³ -3x +4) * (-2³ + x - 5)

We can simplify both expressions first:

-8 + x - 5x³ + 15x - 20 = -8 + x - 5x³ + 15x - 20

We can see that both expressions are identical, which means that the product of -2³ + x - 5 and x³ -3x +4 is equal to the product of x³ -3x +4 and -2³ + x - 5, regardless of the order in which we multiply the factors.

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Answer:

∂z/∂x = 3x^2 + 6y

∂z/∂y = 6x - 3y^2

Now, we need to solve the system of equations:

3x^2 + 6y = 0

6x - 3y^2 = 0

From the first equation, we get:

y = -x^2/2

Substituting this into the second equation, we get:

6x - 3(-x^2/2)^2 = 0

Simplifying, we get:

6x - 3x^4/4 = 0

Multiplying by 4 and rearranging, we get:

3x^4 - 24x = 0

Factoring out 3x, we get:

3x(x^3 - 8) = 0

Therefore, the critical values of x are x = 0 and x = 2.

For x = 0, we have y = 0 (from y = -x^2/2). So, one critical point is (0, 0).

For x = 2, we have y = -2. So, the other critical point is (2, -2).

To find the critical values of the function, we need to evaluate the function at each critical point:

z(0, 0) = 0^3 + 6(0)(0) - 0^3 - 1 = -1

z(2, -2) = 2^3 + 6(2)(-2) - (-2)^3 - 1 = -13

Therefore, the critical values of the function are -1 and -13.

The cuboidal prism has a volume of 40.625 cubic centimeters

Multiplying the cuboidal prism's length, width, and height yields its volume. Assuming that the width b and height h are both 2.5 cm and the length l is 6.5 cm. The volume of the cuboidal prism is given by multiplying these dimensions:

V = l b h = 6.5cm x 2.5cm x 2.5cm

 = [tex]40.625cm^3.[/tex]

As a result, the cuboidal prism has a volume of 40.625 cubic centimeters. As a result, the prism can be utilized for a variety of purposes, including packaging, storage, and transportation, and it can accommodate 40.625 cubic centimeters of material inside its boundaries.

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The final amount after 5 years is $ 49521.98.  

Compound interest refers to the interest that is earned on the initial amount of money deposited or borrowed and also on the accumulated interest from previous periods.  

The formula for calculating compound interest is:

Where

Where:

A = Final amount

P = Principal amount

r = Annual interest rate

n = Number of times the interest is compounded per year

t = Time period

Here we have

The deposited amount, P= $200.00  

Rate of interest, r = 9% = 9/100 = 0.09%

Number of compounds per year, n = 1

Time period, t = 5 years

Using the formula,

A = 2000(1 + 0.09/1)⁽¹⁽⁵⁾⁾

A = 2000(1.09)⁵

A = 49521.98  

Therefore,

The final amount after 5 years is $ 49521.98.  

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Answer: 2x-6

Step-by-step explanation:

Answer:21>15+2x

Step-by-step explanation:

we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12).

HOW TO SOLVE THE QUESTION?

To create a two-way relative frequency table, we can use the following table:

       | English | Mathematics | Total

--------|---------|-------------|-------

Male    |   x     |     24      |   30

Female  |   y     |     11      |   20

--------|---------|-------------|-------

Total   |   35    |     35      |   50

Here, x and y represent the number of male and female students who preferred English, respectively.

To calculate the values for x and y, we can use the fact that there were 35 students who preferred mathematics, and 24 of them were male. Therefore, the number of females who preferred mathematics is 35 - 24 = 11. Since there are a total of 20 female students, the number of females who preferred English is 20 - 11 = 9. Similarly, the number of male students who preferred English is 30 - 24 = 6.

To calculate the relative frequencies, we can divide each cell by the total number of students (50). For example, the relative frequency of male students who preferred mathematics is 24/50 = 0.48.

The resulting two-way relative frequency table is as follows:

       | English | Mathematics | Total

--------|---------|-------------|-------

Male    |   0.12  |     0.48    |  0.60

Female  |   0.18  |     0.22    |  0.40

--------|---------|-------------|-------

Total   |   0.30  |     0.70    |  1.00

From this table, we can see that a larger proportion of male students preferred mathematics (0.48) compared to female students (0.22), while a larger proportion of female students preferred English (0.18) compared to male students (0.12). However, it would not be safe to assume that all females prefer English and all males prefer mathematics based on this data alone, as there may be individual variations and exceptions to this trend.

It's also important to note that the sample size is relatively small, with only 50 students surveyed, and may not be representative of the larger population. Further research with a larger and more diverse sample size would be needed to make more accurate conclusions about gender-based preferences in this population

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The percent increase in the amount of interest paid between a household with a 780 credit score and one with a 589 credit score is approximately 0.8%, which is closest to option B, 0.8% or 39.9%.

Finding the entire amount paid by each family and comparing the difference in total amount paid will allow us to determine the percentage rise in the amount of interest paid between a household with a credit score of 780 and one with a score of 589.

The overall cost for a FICO score of 780 is:

$12,650 for the principal balance and all installments plus (33 x $60) to get $14,930.

With a 589 FICO score, the total cost is:

Total payments plus principal balance equal $12,650 plus (40 x $60) = $15,050.

The two households' combined total outlays differ in the following ways:

$15,050 - $14,930 = $120

We multiply by 100 and divide the difference by the initial sum to determine the percent increase:

($120 / $14,930) x 100% = 0.802% ≈ 0.8%

In light of this, the difference in interest rates between a family with a 780 credit score and one with a 589 credit score is roughly 0.8%, which is closest to option B, 0.8% or 39.9%.

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Answer: To find the average of x, y, and z in terms of m, we first need to find expressions for x, y, and z in terms of m:

x = (m + 9)/2

y = (2m + 15)/2

z = (3m + 18)/3 = (m + 6)

To find the average of x, y, and z, we add them up and divide by the number of terms:

average = (x + y + z)/3

Substituting the expressions for x, y, and z, we get:

average = [(m + 9)/2 + (2m + 15)/2 + (m + 6)]/3

Simplifying the expression by combining like terms, we get:

average = (4m + 30)/6

Simplifying further by dividing both the numerator and denominator by 2, we get:

average = (2m + 15)/3

Therefore, the average of x, y, and z in terms of m is (2m + 15)/3.

Step-by-step explanation:

The mean οf the remaining claim is R6739.

The average οf a grοup οf variables is referred tο as the mean in mathematics and statistics. There are several methοds fοr calculating the mean, including simple arithmetic means (adding the numbers tοgether and dividing the result by the number οf οbservatiοns), geοmetric means, and harmοnic means.

Here We knοw that,

Mean = Sum οf amοunts οf claim  / Tοtal number οf claim

Accοrding tο the given,

Mean οf 50 claim οf insurance pοlicy = R 4500 then,

Sum οf amοunt οf 50 claim = 4500*50 = R 225000

Mean οf 15 οf these claim = R 2109 then,

Sum οf amοunt οf 15 claims = 2109*15 = R 31635

Mean οf 14 οther claim = R 3704 then

Sum οf 14 οther claim = 3704*14 = R 51856

Nοw remaining claim amοunt = 50-14-15 = 21

Sum οf 21 remaining claim = 225000-31635-51856 = R 141509

Now Mean = Sum of 21 amount of claim / Total number of claim

=> Mean = 141509/21 = R 6739

Hence the mean of remaining 21 sample is R 6739.

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2) They tοgether will take 10.9 hours οr 120/11

3) jοsh will take 21/11 hrs οr 1.9 hrs

4) Tοgether they will take 36/13 οr 2.8 hrs

The place values οf the digits in a decimal number are displayed οn the decimal place value chart. We knοw that a digit in a number represents a numerical value οr place value.

Decimal place value charts are used tο determine the prοper placement οf each digit in a decimal number.

A decimal number cοnsists οf a whοle number and a fractiοnal cοmpοnent, separated by the decimal pοint, a dοt.

Fοr instance, the decimal number 4.37 has twο parts: an actual number pοrtiοn οf 4 and a fractiοnal pοrtiοn οf 37.

Sοlutiοns tο the abοve prοblem

2) Tοm takes = 12 hrs

Huck takes= 10hrs

We can aply unitary methοd

tοgether they will take= 1/12+1/10=2/t

11t=120;

t=120/11 οr 10.9 hrs

3) Tοgether Kim and jοsh can clean the hοuse tοgether in = 3 hrs

Kim takes = 7hrs

Jοsh will take= 1/7+1/x=2/3

3x+21=14x

21=11x

x=21/11 οr 1.9 hrs

4) Jack makes baseball grοunds in= 2 hrs

Mike takes= 3 hrs

Chris takes= 4 hrs

Tοgether they will take= 1/2+1/3+1/4=3/x

13x=36

x=36/13 οr 2.8 hrs

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The value of r'(1) = 60 for the given function, using the chain rule.

By adding the derivatives of f(x) with regard to g(x) and g(x) with respect to the variable x, one may get the derivative of the composite function h(x) = f(g(x)). The chain rule of differentiation can be used to derive derivatives of composite functions. Now, let's go over what composite functions are. When a function is expressed in terms of another function, it is said to have a composite function. This suggests that a function can be changed into another function in a composite function.

Using the chain rule of derivatives we have:

r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)

Substituting the values we have:

r'(1) = f'(g(h(1))) * g'(h(1)) * h'(1)

r'(1) = f'(g(3)) * g'(3) * 3

r'(1) = f'(4) * 4 * 3

r'(1) = 5 * 4 * 3

r'(1) = 60

Hence, the value of r'(1) = 60 for the given function, using the chain rule.

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Answer:

Without knowing the number of pieces that the pizzas were cut into, it is not possible to determine the fraction of a whole pizza that is left.

Step-by-step explanation:

simple interest

1 year: [tex]3.6\% \cdot 150,000 = \dfrac{3.6}{100} \cdot 150,000 = 5,400[/tex]

5 years: [tex]5,400(5) = 27,000[/tex]

the maturation value:

[tex]150,000 + 27,000 = \$ 177,000[/tex]

Answer:

Step-by-step explanation:

We can start by writing the given equation in terms of polar form:

Re(z1,z2-bar) = modulus of z1 * modulus of z2

If we write z1 and z2 in polar form, we get:

z1 = r1(cosθ1 + i sinθ1)

z2 = r2(cosθ2 + i sinθ2)

Then, the conjugate of z2 is:

z2-bar = r2(cosθ2 - i sinθ2)

Using the formula for the real part of the product of two complex numbers, we get:

Re(z1,z2-bar) = Re(z1 * z2-bar)

Substituting the expressions for z1 and z2-bar, we get:

Re(z1,z2-bar) = Re(r1(cosθ1 + i sinθ1) * r2(cosθ2 - i sinθ2))

Simplifying the product, we get:

Re(z1,z2-bar) = Re(r1r2[(cosθ1 cosθ2 + sinθ1 sinθ2) + i(sinθ1 cosθ2 - cosθ1 sinθ2)])

The real part of this expression is:

Re(z1,z2-bar) = r1r2(cosθ1 cosθ2 + sinθ1 sinθ2)

Using the identity cos(θ1 - θ2) = cosθ1 cosθ2 + sinθ1 sinθ2, we can write:

Re(z1,z2-bar) = r1r2 cos(θ1 - θ2)

Now we can substitute this expression back into the original equation and get:

r1r2 cos(θ1 - θ2) = r1r2

Dividing both sides by r1r2, we get:

cos(θ1 - θ2) = 1

This equation is true if and only if θ1 - θ2 = 2πn for some integer n. In other words, θ1 = θ2 + 2πn, where n is an integer.

Therefore, we have proved that Re(z1,z2-bar) = modulus of z1 * modulus of z2 if and only if arg z1 = arg z2 + 2πn, where n is an integer.

The 24 parking spοt length is 68 yards.

The same feature is expressed in a different unit οf measurement thrοugh a unit cοnversiοn. Time can be stated in minutes rather than hοurs, and distance can be expressed in kilοmetres rather than miles, οr in feet rather than any οther unit οf length.

Here the given width of One parking spot is eight and one-half feet.

Now  we know that 1 feet = [tex]\frac{1}{3}[/tex] yard,

Then , [tex]8\frac{1}{2}[/tex] feet = [tex]\frac{17}{2}[/tex] feet = [tex]\frac{17}{2}\times\frac{1}{3}[/tex] = [tex]2\frac{5}{6}[/tex] yd.

Now Parking lot have 24 parking spot, Then,

=> Total length of parking lοt = 24 [tex]\times[/tex] [tex]2\frac{5}{6}[/tex] = [tex]24\times\frac{17}{6}[/tex] = 68 yard.

Hence The length of parking lοt is 68 yard.

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The angle x opposite to the side measuring 17 is approximately 20.68 degrees using trigonometry.

Let x stand for the side that is the shortest. The Pythagorean theorem yields the following result: x2 + 172 = 19.

When we simplify this equation, we obtain:

[tex]x^2 = 19^2 - 17^2[/tex]

[tex]x^2 = 36x = 6[/tex]

Hence, the shortest side is six inches long.

Using the inverse trigonometric function tangent, we can determine the angle opposite the side measuring 17. (tan).

tan = adjacent/opposite = x/17

By changing the value of x, we obtain:

[tex]tanθ = 6/17[/tex]

We may determine the angle whose tangent is 6/17 using a calculator or a trigonometric table.

[tex]θ = 20.68°[/tex]

As a result, the angle that is opposite the side that measures 17 is roughly 20.68 degrees.

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Answer:

They will need 6 vans to hold all 44 people.

Step-by-step explanation:

1 bus holds : 8

2 bus holds : 16

3 bus holds : 24

4 bus holds : 32

5 bus holds : 40

6 bus holds : 48 (4 extra seats)

Answer:

To find the total balance after three years, we can use the formula for continuous compounding:

A = Pe^(rt)

Where A is the total balance, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years.

In this case, P = $12,000, r = 0.0125 (1.25% expressed as a decimal), and t = 3. Plugging these values into the formula, we get:

A = $12,000 x e^(0.0125 x 3)

A = $12,000 x e^(0.0375)

A = $12,000 x 1.038163

A = $12,458.54

Therefore, the total balance after three years is $12,458.54.