how many quarter-pound patties can be made from an 8-pound package of ground meat

Approximately 11.21% of the racers did not complete the marathon.

To find the percentage of racers who did not complete the marathon, we need to calculate the ratio of the number of racers who did not complete (gave up or were disqualified) to the total number of racers who started the marathon.

The number of racers who did not complete the marathon is the sum of those who gave up and those who were disqualified, which is 29 + 8 = 37.

So, the percentage of racers who did not complete the marathon is given by:

(37 / 330) * 100

Calculating this expression:

(37 / 330) * 100 ≈ 11.21%

Therefore, approximately 11.21% of the racers did not complete the marathon.

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Answer:

The number that goes in the green box would be -3y^2

Step-by-step explanation:

There are no like term with the same variable y with an exponent of 2.

-Hope this helped

The given expression is,

→ -3y² - 3y + 4y + 100

Simplifying the given expression,

→ -3y² - 3y + 4y + 100

→ -3y² + (-3y + 4y) + 100

→ -3y² + y + 100

Hence, answer is -3y² + y + 100.

Answer:

Erm

Step-by-step explanation:

14.14

Answer:

C. Gregory's graph is incorrect because it shows 2 inches of growth for each week, when it should show 0.75 inches of growth each week

Step-by-step explanation:

Given that the plant grows 1.5 inches (y) every 2 weeks (x), it means that:

Rate of change = y/x = 1.5/2 = 0.75 inches per week

The graph he should create should have a rate of change of 0.75. that is, it should show 0.75 inches growth for every week.

The graph shown above has a rate of change of 2 inches per week.

Thus, the graph is incorrect. It should be showing 0.75 inches of growth per week instead of 2 inches.

Answer: $34

Step-by-step explanation:

After 11 years,188.76 more money would Lincoln have in his account than Robert

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Lincoln invested $440 in an account paying an interest rate of 7 ​% compounded continuously.

Robert invested $440 in an account paying an interest rate of 5 ​ %.

We need to find how much more money would Lincoln have in his account than Robert in 11 years.

\(A=Pe^{rt}\)

For Lincoln:

P=440,

r=7%=0.07

t=11

A=440e⁰⁰⁷ˣ¹¹

A=440e⁰⁷⁷

A=949.96

For  Robert,

P=440,

r=5%=0.05

A=440e⁰⁰⁵ˣ¹¹

A=440e⁰⁵⁵

A=761.2

Now find the difference of Albert and Robert money

949.96-761.2

188.76

Hence, After 11 years,188.76 more money would Lincoln have in his account than Robert

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The rules AAS, ASA, SSS and SAS are congruence rule of triangle  and the each rules has been explained

The rules AAS, ASA, SSS and SAS are congruence rule of triangle

SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent

SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to  the two sides and one included angles between the sides of the other triangle, then both triangles are congruent

ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent

AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent

Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle

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Answer:

----------------------

Use the formula for simple interest:

where:

Substituting the given values into the formula, we get:

Therefore, the rate of interest per year is 8%.

The line integral of the scalar function f(x,y,z)=2x2 8z over the curve c(t)=(et,t2,t),0≤t≤7 is (2/3) (e² + 1)³/².

The line integral of a scalar function f over a curve C parameterized by r(t) is given by the formula:

∫C f ds = ∫ₐᵇ f(r(t)) |r'(t)| dt

where r(t) = x(t) i + y(t) j + z(t) k is the parameterization of the curve C, and |r'(t)| is the magnitude of the derivative of r(t) with respect to t.

In this case, the curve C is given by:

r(t) = et i + t² j + t k, 0 ≤ t ≤ 7

So, we have:

x(t) = et, y(t) = t², z(t) = t

And the derivative of r(t) is:

r'(t) = e i + 2t j + k

So, |r'(t)| = √(e² + 4t² + 1)

Now, we can compute the line integral as follows:

∫C f ds = ∫₀⁷ f(r(t)) |r'(t)| dt

= ∫₀⁷ (2(et)² + 8t) √(e² + 4t² + 1) dt

= 2e² ∫0₀⁷ t √(e² + 4t² + 1) dt + 8 ∫₀⁷ t √(e² + 4t² + 1) dt

We can evaluate these integrals using a trigonometric substitution. Let e tanh(u) = 2t, then dt = e sech²(u) du, and we get:

∫₀⁷ t √(e² + 4t² + 1) dt = (1/4e²) ∫₀∞ (e² + 1)¹/² sech³(u) du

= (1/4e²) B(1/2, 3/2) (e²/4) = (1/3) (e² + 1³/²) / (2e²)

where B is the beta function.

Similarly, we can evaluate the other integral and get:

∫C f ds = (2/3) (e² + 1)³/²

Therefore, the line integral of f over C is (2/3) (e² + 1)³/².

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9514 1404 393

Answer:

  a.  f(x) = (4x +5)(x -3)

  b.  x-intercepts: {-1.25, +3}

  c.  f(x) goes to +infinity as x goes to ±infinity

  d. plot the x-intercepts, the vertex, and a few other points; draw a smooth curve through them

Step-by-step explanation:

a. Here, you're looking for factors of (4)(-15) = -60 that have a sum of -7. Those factors will be -12 and +5, so we can factor the function as ...

  f(x) = (4x -12)(4x +5)/4

  f(x) = (x -3)(4x +5)

__

b. The x-intercepts are the values of x that make the factors zero:

  x -3 = 0   ⇒   x = 3 . . . . (add 3)

  4x +5 = 0   ⇒   x = -5/4 . . . . (add -5, divide by 4)

__

c. As with all even-degree polynomials with positive leading coefficients, the end behavior of f(x) matches that of |x|:

  as x → ∞, f(x) → ∞

  as x → -∞, f(x) → ∞

__

d. The vertex of the function will be located halfway between the x-intercepts, at x = (3-5/4)/2 = (7/4)/2 = 7/8. The value of f(x) there is ...

  f(7/8) = (4(7/8) +5)(7/8 -3) = -289/16 = -18.0625

Since the leading coefficient is 4, the normal x^2 function behavior is stretched vertically by a factor of 4. So, additional points would be

  x = 7/8 ±1, f(x) = -18.0625 +4·1 = -14.0625

  x = 7/8 ±2, f(x) = -18.0625 +4·2^2 = -2.0625

The answers of part B locate two points on the graph, and help find the vertex. The answer of part C confirms the graph as opening upward.

__

Additional comment

I find a graphing calculator to be very helpful finding the roots and making the graph.

Answer:

1. 12.5%

2. 26%

3. 51

4. 16

Step-by-step explanation:

3/24=0.125 -> 12.5%

65/250=0.26 -> 26%

300*0.17=51

0.4*40=16

10 mph more unusual.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a larger range, a low standard deviation suggests that the values tend to be near to the mean (also known as the anticipated value) of the collection.

The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical literature and equations to indicate standard deviation. Standard deviation may be written as SD.

EXPLANATION : The speed recordings follow an approximately normal distribution the mean of

100 readings was 2384 mph. with a standard deviation of 3.56mph

The speed limit read 20 mph

We have to find the number of standard deviations from the mean that the car going

under the speed hmit would be

Let the car going under the speed 20mph bey standard deviations away from mean

That is.

20 — 23.84 +y(3.56)

20—2384 —1.078651685

So the car going under the speed limit would be less than or equal to 107865 standard

A car traveling 34 mph

The number of standard deviations from the mean that the car is going at 34mph is given by

That is the car going at 34mph is 2.8539 standard deviations above the mean

A car traveling at 10mph

The number of standard deviations from the mean that the car going at 10mph is given by.

y= 2.8539

That is. the car going at 10mph is 3.8876 standard deviations

We know from the empirical nile that 99.7% of the observations he with in ±3 standard

deviations from the mean for a normally distributed data

But the speed of 10mph is not within these limits, where as 34 mph is within these limits

So the car is  travelling t 10mph is more unusual

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a) The minimum value of the function f(x) = xcos(x) in the range 0 ≤ x ≤ 5 is approximately -4.92, and it occurs at x ≈ 3.38.

b) The maximum value of the function f(x) = xcos(x) in the range 0 ≤ x ≤ 5 is approximately 4.92, and it occurs at x ≈ 1.57 and x ≈ 4.71.

To find the minimum and maximum values of the function f(x) = xcos(x) in the specified range, we need to evaluate the function at critical points and endpoints.

a) To find the minimum, we look for the critical points where the derivative of f(x) is equal to zero. Taking the derivative of f(x) with respect to x, we get f'(x) = cos(x) - xsin(x). Solving cos(x) - xsin(x) = 0 is not straightforward, but we can use numerical methods or a graphing calculator to find that the minimum value of f(x) in the range 0 ≤ x ≤ 5 is approximately -4.92, and it occurs at x ≈ 3.38.

b) To find the maximum, we also look for critical points and evaluate f(x) at the endpoints of the range. The critical points are the same as in part a, and we can find that f(0) ≈ 0, f(5) ≈ 4.92, and f(1.57) ≈ f(4.71) ≈ 4.92. Thus, the maximum value of f(x) in the range 0 ≤ x ≤ 5 is approximately 4.92, and it occurs at x ≈ 1.57 and x ≈ 4.71.

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The statement "When using the chi-square goodness of fit test, the smaller the value of the chi-square test statistic, the more likely we are to reject the null hypothesis." is false.

When using the chi-square goodness of fit test, the larger the value of the chi-square test statistic, the more likely we are to reject the null hypothesis.

A small chi-square value indicates that the observed data fits the expected distribution well, which supports the null hypothesis.

A large chi-square value on the other hand indicates a poor fit between the observed data and the expected distribution, which suggests that the null hypothesis is not true and we should reject it.

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Answer:

91. The probability that Caroline will be ready before Andrew is 0.25 (Option B). Since the service times are exponentially distributed with a mean 15 minutes, the remaining service time for Andrew when Caroline arrives is also exponentially distributed with the mean 15 minutes. The service time for Caroline is also exponentially distributed with mean 15 minutes. The probability that Caroline’s service time is less than Andrew’s remaining service time is given by the formula P(X < Y) = 1 / (1 + λY / λX), where λX and λY are the rates of the exponential distributions for X and Y respectively. Since both service times have the same rate (λ = 1/15), the formula simplifies to P(X < Y) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Andrew is 0.25.

92. The probability that Caroline will be ready before Bob is 0.35 (Option A). Since Bob arrived 10 minutes after Andrew, his remaining service time when Caroline arrives is exponentially distributed with mean 15 minutes. Using the same formula as above, we get P(X < Y) = 1 / (1 + λY / λX) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Bob is 0.35.

Answer:

275%

Step-by-step explanation:

Given that,

Initial weight of the puppy = 600 grams

Final weight of the puppy = 2250 gram

We need to find the percent increase in the puppy's weight.

Increase in weight = 2250 gram - 600 grams

= 1650 grams

The percentage of increase in weight,

\(\%=\dfrac{1650}{600}\times 100\\\\=275\%\)

So, the required increase in puppy's weight is equal to 275%.

Answer:

B. At its lowest point, the wire is 24 feet above the ground

Step-by-step explanation:

The p-value is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.

The p-value can be calculated by using a one-proportion z-test. The null hypothesis would be that the percentage has stayed the same from last year, and the alternative hypothesis is that the percentage has decreased.

The formula for the z-score is (x-p)/√(p(1-p)/n), where x is the observed proportion (39/260), p is the expected proportion (0.20), and n is the sample size (260). The p-value is then calculated using the z-score and the cumulative distribution function.

Therefore p-value, in this case, is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.

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The density of the rectangular prism, you need to divide its mass by its volume.

1. Mass of the prism = 6.161 grams

2. Length of the prism = 1.669 cm

3. Width of the prism = 1.845 cm

4. Height of the prism = 6.907 cm

The volume of a rectangular prism is calculated by multiplying its length, width, and height:

Volume = Length * Width * Height

Volume = 1.669 cm * 1.845 cm * 6.907 cm

Volume ≈ 21.325

Now, divide the mass by the volume to obtain the density:

Density = Mass / Volume

Density = 6.161  / 21.325

Density ≈ 0.289 (rounded to three decimal places)

For the second part of your question, we need to calculate the percent abundance of zinc in the sample with the given densities.

1. Density of the sample = 7.801

2. Density of pure copper = 8.96

3. Density of pure zinc = 7.13

Since the densities are given in different units, we need to convert them to the same unit. We'll convert the density of the sample from g/mL to g/cm^3:

Density of the sample = 7.801 g/mL * (1 mL / 1 cm)

Density of the sample ≈ 7.801

Now, we can calculate the percent abundance of zinc using the densities:Percent abundance of zinc = (Density of sample - Density of copper) / (Density of zinc - Density of copper) * 100

Percent abundance of zinc = (7.801 - 8.96 ) / (7.13  - 8.96 ) * 100

Percent abundance of zinc ≈ -11.48%

The negative value indicates that the sample contains a higher Percentage of copper compared to zinc.

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Answer:

4x^2 + 9x + 23

Step-by-step explanation:

just factor the last equation and combine them all.

Answer:

y(t) = 494 (1.03)^t

y(10) = 663,89

Step-by-step explanation:

An increase in population by 3% each year means that at the end of each year, the population is 1.03 times what it was at the start of the year

This increase in population continues for t years

Exponential growth model that represents the population y (in thousands) t years after the beginning of the decade is

y(t) = 494 (1.03)^t

Where,

y = population

t = number of years

Find y when t = 10

y(t) = 494 (1.03)^t

y(10) = 494 (1.03)^10

= 494 ( 1.3439)

= 663.8866

Approximately y(10) = 663.89

This means that after 10 years from when the population was 494,000, it increased to 663,89.

The amount owed in 20 years is $712.08.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

Compound interest is when you receive interest on both your interest income and your savings.

Given:

P= $325

R= 4%

n= total years = 20 year

So, A = P \((1+ r)^n\)

A = 325 \((1+ 4/100)^{20\)

A = 325  \((1+ 0.04)^{20\)

A = 325 x 2.191

A = 712.08

Hence, the amount is $712.08

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Part 1:

To determine whether a function is linear or exponential, we need to check whether the rate of change is constant or not.

In the case of Car A, we can see that the value of the car is decreasing by a constant amount every year. Therefore, the function is linear.

Similarly, in the case of Car B, we can see that the value of the car is decreasing by a constant amount every year. Therefore, the function is linear.

Part 2:

a) The function for Car A can be written as V(t) = -2500t + 50000, where t is the number of years and V(t) is the value of the car in dollars.

The constant rate of decrease in the value of the car is $2500 per year. The initial value of the car is $50000.

b) The function for Car B can be written as V(t) = -1000t + 48500, where t is the number of years and V(t) is the value of the car in dollars.

The constant rate of decrease in the value of the car is $1000 per year. The initial value of the car is $48500.

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Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the information

lee charges= $3 per basket

and $2.5 for each pound.

ley y be the total cost

and x be the number of pounds,

the expression for the total cost is given as

a. Write an equation for this situation.

y=mx+b

b. What is the independent variable?

the independent variable is b

c. Explain the independent variable

the independent variable is the fixed cost which is the amount of $3 per basket that lee charges for each pound of fruit he picks

d. What is the b? b=$3

e. Explain the b

the $3 is the amount that lee charges regardless of the number of pounds he picks

Answer:

21 x 2 − 10x − 75

Step-by-step explanation:

Cant solve for x can only simplify^

Answer:

-15x+21x(squared)-75

Step-by-step explanation:

(3x+5) (7x-15)

3x(7x-15) 5(7x-15)

21x (squared) -45x+35x-75

-15x+21x(squared)-75

Answer:

Point A, C and D

Point B

Step-by-step explanation:

\({hope it helps\)