two integers whose product is 90 and whose sum is 21

Final answer:

The median is a more accurate indicator of the average student's SAT score at Groveland High School in a right-skewed distribution because it is not affected by outliers, unlike the mean.

Explanation:

The question addresses why the median is a more accurate indicator of the SAT score of the average student at Groveland High School rather than the mean when the data is strongly skewed to the right. This is because the median is the middle value that divides the number set into two equal halves, and it is not affected by outliers or extremely high scores that are present in a right-skewed distribution. In contrast, the mean is the average of all values and can be significantly influenced by outliers, leading to a value that may not accurately represent the 'central' tendency of the data. Thus, for a right-skewed data set, the median provides a better measure of center for what can be considered a typical score because it is not skewed by unusually high values.

Answer:

a.always

b.never

c.sometimes

Final answer:

The blank spaces in the statements regarding properties of parallelograms should be filled with 'always' for diagonals bisecting each other, 'always' for opposite sides having the same length, and 'sometimes' when referring to parallelograms being rectangles, as not all parallelograms have right angles.

Explanation:

The given question asks you to fill in the blanks with sometimes, always, or never to make each statement about a parallelogram true. Here are the completed statements with explanations:

To understand these properties, consider that a parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Additionally, the diagonals of a parallelogram bisect each other, which means they cut each other exactly in half at the point where they cross. This property is invariant under any affine transformation, so it holds true regardless of how the parallelogram is oriented or scaled.

To reduce the variable of natural differences in puppy growth rates, the investigators should block on dog breed. Breed significantly impacts growth rates compared to geographic location or gender.

In designing an experiment to test whether a new high-protein puppy food promotes faster weight gain than an existing formula, the strategy that would most effectively reduce variability due to natural differences in puppy growth rates would be option A- Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.

Puppy growth rates can vary significantly by breed, with larger breeds often growing faster than smaller ones. By blocking on breed, the researchers can ensure that any differences in weight gain are due to the food, not differences in breed-specific growth rates.

The other strategies - blocking or stratifying on geographic location, or stratifying on gender - would not be as effective, because these factors have less influence on a puppy's growth rate compared to its breed.

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So in 5 acres of land produces 21,000 pounds of strawberries.

Step-by-step explanation:

Step 1:

Last year, [tex]3\frac{1}{2}[/tex] acres i.e 3.5 acres produced 14,700 pounds of strawberries. So we need to determine how many strawberries were produced per acre.

To do this we divide the total number of strawberries produced by the number of acres it was produced in.

The number of strawberries produced per acre[tex]= \frac{14,700}{3.5} = 4,200[/tex] pounds.

Step 2:

To determine the number of strawberries in 5 acres of land, we multiply the number of strawberries per acre by the number of acres.

The number of strawberries produced in 5 acres[tex]= 5(4,200) = 21,000[/tex] pounds.

So in 5 acres of land produces 21,000 pounds of strawberries.

Answer:

Step-by-step explanation:

Relatively less golf and attend relatively more concerts whenever his leisure time becomes more scarce.

- This is called the marginal utility, that with every successive unit that utility decreases. With each passing hour while playing golf Joe is less inclined to play for an extra hour. When leisure time is less than 2 hrs he is equally likely to opt out of golf for concert.

Answer: 5.37.

Step-by-step explanation:8 percent markup which in this case is 8 cents per dollar and s in nice its 5 multiply 5 by 8 and that gives you the cents part.

The equation for the resale value of the stereo is V = V0 * e^(-kt), where V0 is the initial value, V is the resale value at time t, and k is the decay constant. Using the given resale value after 4 years, we can solve for k and substitute it back into the equation to find the resale value of the stereo as a function of time.

To find an equation giving the resale value of the stereo as a function of time, we can use the formula for exponential decay: V = V0 * e^(-kt). V0 represents the initial value, V represents the resale value at time t, and k is the decay constant. The given resale value after 4 years is $275, so we can substitute these values into the equation: 275 = 1300 * e^(-4k). To solve for k, divide both sides by 1300 and take the natural logarithm of both sides: ln(275/1300) = -4k. Calculate the logarithm and solve for k to get the decay constant. Finally, substitute the value of k into the equation to get the complete equation for the resale value of the stereo.

Answer: it would take 7 years more for Brianna's money to double than for Adam's money to double

Step-by-step explanation:

Considering Brianna's investment,

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = $480

r = 6.5% = 6.5/100 = 0.065

A = 2 × 480 = $960

Therefore,

960 = 1800 x 2.7183^(0.065 x t)

960/1800 = 2.7183^(0.065t)

2 = 2.7183^(0.065t)

Taking ln of both sides, it becomes

Ln 2 = 0.065tln2.7183

0.693 = 0.065t

t = 0.693/0.065

t = 10.66

Approximately 17 years

Considering Adam's investment, we would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 480

A = 960

r = 6.75% = 6.75/100 = 0.0675

n = 4 because it was compounded 4 times in a year.

Therefore,.

960 = 480(1 + 0.0675/4)^4 × t

960/480 = (1 + 0.016875)^4t

960/480 = (1.016875)^4t

Taking log of both sides, it becomes

Log 2 = 4t log 1.016875

0.301 = 0.0291t

t = 0.301/0.0291

t = 10.34

Approximately 10 years

To graph the polar equation, plot points based on r and θ values. To express the quotient of complex numbers in rectangular form, operate division, simplify, then convert. To convert a rectangular equation to polar form, substitute x and y with their polar form.

1. To graph the polar equation, you would plot points based on the r (magnitude/distance) and θ (angle) values from the origin (0,0). As you've not provided the specific polar equation, I cannot provide a full step-by-step explanation.

2. To divide complex numbers and express the quotient in rectangular form, you multiply the numerator and the denominator by the conjugate of the denominator, simplify, and convert the result into rectangular coordinates (x+iy) form. For example,

2(cos150° + isin150°) / 8(cos210° + isin210°)

After calculating the division, you end up with the cosine and sine of an angle in the numerator. Then, convert this to rectangular form. Unfortunately, as Brainly platform constraints, computational solutions cannot be provided through this medium.

3. To convert the rectangular equation (x+5)^2+y^2=25 in polar form, replace x = rcosθ and y = rsinθ in the equation. Then simplify the equation to get a polar equation.

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Answer:

[tex]\\3 percent of 900 = 27 \\900 + 27 = 927 \\ 927 * 36 = 33372[/tex]

Step-by-step explanation:

First you have to find out the 3% of 900 (is 27)

then you add 27 to 900

then you multiply it by 3 years (36 months)

and your result is 33372 :)

The rent over the three-year term of the new lease will be $33,372, calculated with a 3% increase annually.

Step 1:

Calculate the new monthly rent after the 3% increase.

The new monthly rent will be the current rent plus 3% of the current rent.

New monthly rent = $900 + 0.03 * $900 = $900 + $27 = $927.

Step 2:

Calculate the total rent over the three-year term.

Since there are 12 months in a year and the lease is for three years, multiply the new monthly rent by the number of months in three years.

Total rent over three years = $927/month * 12 months/year * 3 years = $33,372.

So, the rent over the three-year life of the new lease will be $33,372.

Answer:

Correct option is (B). 20%.

Step-by-step explanation:

The number of managers is, 1200.

The percentage of managers who identified work experience as an important characteristic to consider is, P (W) = 72%.

The percentage of managers who identified appropriate attire and behavior as an important characteristic to consider is, P (AB) = 55%.

Compute the number of managers who identified work experience as an important characteristic to consider as follows:

[tex]n(W)=1200\times P(W)\\=1200\times\frac{72}{100}\\=864[/tex]

Compute the number of managers who identified appropriate attire and behavior as an important characteristic to consider as follows:

[tex]n(AB)=1200\times P(AB)\\=1200\times\frac{55}{100}\\=660[/tex]

Compute approximately what percent greater is P (W) than P (AB) as follows:

[tex]P(W>AB)=\frac{n(W)-n(AB)}{1200}=\frac{864-660}{1200}=\frac{204}{1200}=0.17\approx0.20[/tex]

Thus, the number of managers surveyed who identified work experience as an important characteristic to consider was approximately 20% percent greater than the number who identified appropriate attire and behavior as an important characteristic to consider.

Correct option is (B).

The horizontal distance the plan has covered when it has flown 4,000 feet is 694 feet.

Step-by-step explanation:

Step 1:

For the given triangle, assume the opposite side has a length of x units, the hypotenuse of the triangle measures 4,000 feet. The given angle of the triangle is 10°.  To calculate the opposite side's length of the triangle, we use the sine of the given angle.

[tex]sin A = \frac{oppositeside}{hypotenuse}[/tex]

Step 2:

The length of the opposite side = x feet.

The length of the hypotenuse side = 4,500 feet.

[tex]sin A = \frac{oppositeside}{hypotenuse}, sin 10 = \frac{x}{4000}.[/tex]

[tex]x = sin10 (4000), sin 10 = 0.1736, x = 0.1736(4000) = 694.4 feet[/tex].

So the horizontal distance is 694.4 feet, rounding this off to the nearest foot, we get the horizontal distance as 694 feet.

Answer:

Period of 2π

Step-by-step explanation:

The graph of sine starts at zero on the y axis while that of cosine starts at the point 1 as sin 0=0 at t=0 and cos 0=1 at t=0. We say the cosine curve is a sine curve which is shifted to the left by [tex]\frac{\pi}{{2}}\[/tex]

​The basic sine and cosine functions have a period of 2π (in radians). The period is the time it takes to go through one complete cycle. It means that after every complete cycle, the graph repeats itself over and over again..  

Answer:

Check

Step-by-step explanation:

The high and low points repeat in a pattern.

The cycle repeats at equal time intervals.

The swinging motion is smooth, unabrupt.

Answer:

[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]

Step-by-step explanation:

The given functions are:

[tex]f(x) = {x}^{3} - 2 {x}^{2} + 12x - 6[/tex]

and

[tex]g(x) = 4 {x}^{2} - 6x + 4[/tex]

We want to find

[tex](f - g)(x)[/tex]

Recall that:

[tex](f - g)(x) = f(x) - g(x)[/tex]

This implies that:

[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - (4 {x}^{2} - 6x + 4)[/tex]

[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - 4 {x}^{2} + 6x - 4[/tex]

We combine similar terms to get:

[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]

Answer:

Solution given:

f(x)=x3−2x2+12x−6

g(x)=4x2−6x+4

now

(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4

=x³-6x²+18x-10

Answer:

$140

Step-by-step explanation:

If the Monthly Budget for Landscaping=$400

and the Percentage of Landscaping Budget Spent this Month=35%

The Amount Spent on Landscaping=35% of Total Landscaping Budget

=35 percent of $400

Recall that percentage is always over 100, therefore 35%=35/100

=[tex]\frac{35}{100}X400[/tex]

=$140

The homeowner spent $140 on landscaping this month.

Answer:

$260 was spent.

Step-by-step explanation:

The main problem is about proportion, specifically direct proportion.

$400 is the total budget, wich means is 100% of the budget.

They spent 35%, so we need to substract the amount of spent budget to total budget, in order to know how much was spent, we will call it remaining budget:

total budget=100%

spent budget=35%

remaining budget=total budget - spent budget

remaining budget= 100% - 35% = 65%

remaining budget= %65

As a result of the substraction we have the   percentage of remaining budget, 65%. The next step is to transform that percentage into an amount of money.   To do that we use the Mathematical Rule of Three.

The Rule of Three is a method to solve direct proportion problems, when we have three quantities related to each other. For this case %100 equals $400 and %65 equals to unknown, that's the cuantitie we want to know, that is, remaining budget, as shown below:

%100  -> $400

%65 -> x

On a general form it could be understood as a relation between a-b and c-x:

a -> b

c -> x

Next we will apply the following formula

[tex]x= \frac{c*b}{a} [\tex]

For this case:

[tex]x= \frac{65*400}{100}  [\tex]

[tex]x= $260[\tex]

The remaining budget is $260

Answer:

2,880 tons of sand

Step-by-step explanation:

In this question, we are asked to calculate the amount of tons of sand required to produce a certain amount of tarry materials if a certain amount of sand had produce an amount of tarry materials.

We work as follows:

First, we write the relation that 144,000 tons of sand produces 125,000 barrels of tarry material, then x of tons would produce 2,500 barrels of tarry materials

To find c, we cross multiply:

x * 125,000 = 2,500 * 144,000

x = (2,500 * 144,000)/125,000

x = 2,880

Answer: the diameter of the can is 2.8 inches

Step-by-step explanation:

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

From the information given,

height = 4.5 inches

Volume of can = 454 millilitres

1 cubic inch = 16.387 millilitres

Converting 454 millilitres to cubic inches, it becomes

454/16.387 = 27.7 cubic inches

Therefore

27.7 = 3.14 × r² × 4.5

27.7 = 14.13r²

r² = 27.7/14.13

r² = 1.96

r = √1.96

r = 1.4

Diameter = 2 × radius

Diameter = 2 × 1.4 = 2.8 inches

I believe the answer is B. Hope this helps!

Answer:

-4 2/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm going to assume that the problem is -23x -214 = 274

And in that case...

1. First isolate the x-value by adding 214 to both sides of the equation:

-23x = 488

2. Then, divide both sides by -23 to truly get x alone:

x = [tex]-\frac{488}{23}[/tex] or -21.22

Answer:

 x = -18

Add the opposite of the constant on the left:

 -2/3x = 21/4 +27/4 = 48/4 = 12

Multiply the equation by the inverse of the coefficient of x:

 x = (-3/2)(12) = -18

The solution is x = -18.

Step-by-step explanation:

Answer:

The constant of variation, k = 0.57

Step-by-step explanation:

We are given that z varies jointly as the second power of x (x²), and the third power of y (y³).

For a constant of variation, k, z can be written as

z = x²y³k.

We are also given

z = 31.5

x = 2

x = 2.4

31.5 = (2²)(2.4)³k

31.5 = 4×13.824k

31.5 = 55.296k

k = 31.5/55.296

= 0.57

Answer:

Her hourly rate is $14.

Step-by-step explanation:

Given:

Penelope goes to work after school for 4.5 hours on Mondays, Tuesdays, and Fridays.

She works 8 hours each on Wednesdays or Thursdays.

Now, to find her hourly rate.

So, total hours Penelope work on Mondays, Tuesdays, and Fridays:

[tex]4.5+4.5+4.5=13.5\ hours.[/tex]

And, total hours she work on Wednesdays and Thursdays:

[tex]8+8=16\ hours.[/tex]

Now, the total hours each week she work:

[tex]13.5+16=29.5\ hours.[/tex]

Total money she makes each week = $413.

Now, to get the hourly rate we divide the total hours each week she work by total money she makes each week:

[tex]413\div 29.5[/tex]

[tex]=\$14.[/tex]

Therefore, her hourly rate is $14.

Answer:

130°

Step-by-step explanation:

The diagram for the question is redrawn on the attached image. It was obtained online.

Basically, what the question is asking is for the angle between the new path of the beam and the old path if the beam continued without being reflected by the mirror.

The line of the old path of the beam of light is a straight line. And the sum of angles on straight line = 180°

25° + 25° + y° = 180°

y = 180° - 50° = 130°

Answer:

Step-by-step explanation:

Assuming there is a punitive removal of one point for an incorrect response.

Five undiscernable choices: 20% chance of guessing correctly -- Expectation: 0.20*(1) + 0.80*(-1) = -0.60

Four undiscernable choices: 25% chance of guessing correctly -- Expectation: 0.25*(1) + 0.75*(-1) = -0.50

I'll use 0.33 as an approzimation for 1/3

Three undiscernable choices: 33% chance of guessing correctly -- Expectation: 0.33*(1) + 0.67*(-1) = -0.33 <== The approximation is a little ugly.

Two undiscernable choices: 50% chance of guessing correctly -- Expectation: 0.50*(1) + 0.50*(-1) = 0.00

And thus we see that only if you can remove three is guessing neutral. There is no time when guessing is advantageous.

One Correct Answer: 100% chance of guessing correctly -- Expectation: 1.00*(1) + 0.00*(-1) = 1.00

The expected value of eliminating one answer and guessing among the remaining four possible answers is 1/16. The expected value of eliminating three answers and guessing between the remaining two possible answers is 3/8.

To find the expected value of eliminating one answer and guessing among the remaining four possible answers, we need to consider the probabilities associated with each outcome.

Since there are four possible answers remaining, the probability of guessing the correct answer is 1/4. The value of getting the correct answer is +1, and the value of getting it wrong is -1/4. Therefore, the expected value is:

Expected Value = (Probability of Correct Answer * Value of Correct Answer) + (Probability of Wrong Answer * Value of Wrong Answer)

Expected Value = (1/4 * 1) + (3/4 * (-1/4)) = 1/4 - 3/16 = 1/16.

So, the expected value of eliminating one answer and guessing among the remaining four possible answers is 1/16.

For eliminating three answers and guessing between the remaining two possible answers, the probabilities change.

Since there are now two possible answers remaining, the probability of guessing the correct answer is 1/2. The value of getting the correct answer is +1, and the value of getting it wrong is -1/4. Therefore, the expected value is:

Expected Value = (Probability of Correct Answer * Value of Correct Answer) + (Probability of Wrong Answer * Value of Wrong Answer)

Expected Value = (1/2 * 1) + (1/2 * (-1/4)) = 1/2 - 1/8 = 3/8.

So, the expected value of eliminating three answers and guessing between the remaining two possible answers is 3/8.

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Answer:

Option 1) A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.  

Step-by-step explanation:

We are given the following in the question:

95% confidence interval of mean body mass index (BMI) for girls between 13 and 19 years of age is:

[tex](19.5, 26.3)[/tex]

Lower limit = 19.5

Upper limit = 26.3

1. A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.

The given statement is false. This is not the right interpretation for confidence interval.

2. The margin of error is 3.4

The confidence interval can be found as

[tex]\text{sample mean}\pm \text{Margin of error}[/tex]

Let x be the sample mean and y be the margin of error, thus, we can write

[tex]x - y =19.5\\x + y = 26.3\\2x =45.8 \\x = 22.9\\y = 22.9 - 19.5\\y = 3.4[/tex]

Thus, the margin of error is 3.4

Thus, the given statement is true.

3. The value z in the margin of error is 1.96.

The statement is true.

The z-multiplier for a 95% confidence interval used is 1.96

4. A total of 95% of all SRS of size n contain the true mean body mass index

The given statement is true. It is the right interpretation of 95% confidence interval.

Among the provided statements, 'A total of 95% of all teenage girls have BMI between 19.5 and 26.3' is NOT accurate. A 95% confidence interval does not indicate that 95% of the data is in that range.

In this case, the statement that is NOT true about the confidence interval for estimating the mean body mass index (BMI) for girls between 13 and 19 years of age is: 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3.

A 95% confidence interval does not claim that 95% of the population data falls within this range. Instead, it asserts that if we were to take many samples and build a confidence interval from each sample, then about 95% of the confidence intervals would contain the true mean BMI (this is the meaning of statement 4).

Statement 2 is incorrect since the margin of error is not 34. It is calculated as (26.3 - 19.5)/2 = 3.4.

Statement 3 is correct as the value for 'z' in a 95% confidence interval is indeed 1.96. This is because 1.96 is the z-score that cuts off the top 2.5% and bottom 2.5% of data in a standard normal distribution, leaving 95% of the data in between.

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Answer: 360 mg of the medicine will be detected after 48 hours

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

P represents the initial dosage of the medicine.

A represents the final dosage of the medicine after t hours.

t represents the number of hours.

r represents the rate of decay

From the information given

P = 1000 mg

r = 40% = 40/100 = 0.4

The expression becomes

A = 1000(1 - 0.4)^t

A = 1000(0.6)^t

In 48 hours, t = 2

Therefore,

A = 1000(0.6)^2

A = 360

Final answer:

The child's shadow is lengthening at a rate of 6 m/min as they walk away from the street lamp.

Explanation:

The child's shadow lengthens as they walk away from the street lamp because the angle between the child and the light source increases. To find the rate at which the shadow lengthens, we can use similar triangles. The ratio of the length of the shadow to the height of the child remains constant. So, if the child's height increases by 1 meter, the shadow length increases by 6 meters. Therefore, the child's shadow is lengthening at a rate of 6 m/min.

The rate of lengthening of the child's shadow is 4 meters per minute.

Step 1: Defining the variables.

Let:

It is given that the child walks away from the light at a rate of 20 m/min. This is:

[tex]\frac{dx}{dt} = 20\ meters\ per\ min[/tex]

Step 2: Relating the variables using similar triangles.

The two triangles formed (one by the lamp post and its shadow, and the other by the child and the child's shadow) are similar. Therefore, the following proportion:

[tex]\frac{x+s}{h} = \frac{s}{y}[/tex]

Substituting the known values (h = 6 m and y = 1 m), we get:

[tex]\frac{x+s}{6} = \frac{s}{1}[/tex]

Step 3: Solving for s.

Cross-multiplying gives:

[tex]6s=x+s[/tex]

Rearranging terms:

[tex]5s=x[/tex]

So the length of the shadow, s, in terms of the child's distance from the lamp, x, is:

[tex]s = \frac{x}{5}[/tex]

Step 4: Differentiate with respect to time.

Differentiating both sides with respect to t:

[tex]\frac{ds}{dt} = \frac{1}{5}\frac{dx}{dt}[/tex]

Substituting the known rate of change [tex]\frac{dx}{dt} = 20\ meters\ per\ min[/tex]:

[tex]\frac{ds}{dt} = \frac{1}{5}*20 = 4\ meters\ per\ min[/tex]

Therefore, the child's shadow is lengthening at a rate of 4 meters per min.

Answer:

[tex]7+6a+5m(4+3a)=0[/tex]

Step-by-step explanation:

We want to simplify the expression

[tex](3 + 3 a ) + (1 + 5 m )(3 + 3 a ) + (1 + 5 m )=0[/tex]

Expanding the expression in the middle

[tex](3 + 3 a ) + 1 (3 + 3 a )+ 5 m (3 + 3 a ) + (1 + 5 m )=0[/tex]

Eliminating all brackets

[tex]3 + 3 a + 3 + 3 a + 15m + 15m a + 1 + 5 m =0[/tex]

Next, we collect our like terms

[tex]3+3+1+3a+3a+15m+5m+15ma=0[/tex]

When you collect like terms, ensure the number of terms are still the same

[tex]7+6a+20m+15ma=0[/tex]

This simplified gives us:

[tex]7+6a+5m(4+3a)=0[/tex]

I caculated it all and it is the same as Newton9022

Hope this helps.

Answer:

q = 29

Step-by-step explanation:

4(q -10) = 76