In a class of pupils, 7 play the flute and
piano.
14 play the flute only.
10 play the piano only.
6 play neither instrument.
How many pupils are in the class?

The correct option is the first one, the graphs are:

I) This is an identity.

II) This is a reciprocal function.

III) This is an absolute value function.

IV) This is a square root.

First let's define general graphs for each of these functions.

Then the graphs are:

I) This is an identity.

II) This is a reciprocal function.

III) This is an absolute value function.

IV) This is a square root.

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We can use the given formula for the rate of change of the weight of the solid to estimate the amount of solid 1 second later.

If there is 6 grams of solid at time t, then f(t) = 6 g.

To estimate the amount of solid 1 second later, we can use the derivative formula:

f'(t) = −2f(t)(5+ f(t))

We want to estimate the value of f(t+1), which represents the weight of the solid 1 second later.

To do this, we can use Euler's method, which is an approximation method for solving differential equations.

Euler's method uses the formula:

f(t+1) ≈ f(t) + f'(t)Δt

where Δt is the time step (in minutes).

Since we want to estimate the amount of solid 1 second later, we can set Δt = 1 minute.

Plugging in the values for f(t) and f'(t), we get:

f(t+1) ≈ f(t) + f'(t)Δt

f(t+1) ≈ 6 - 2(6)(5+6)

f(t+1) ≈ -66

Therefore, the estimated weight of the solid 1 second later is -66 grams. However, this result does not make physical sense since weight cannot be negative.

It is possible that the given formula for f'(t) does not accurately describe the behavior of the solid, or that there was an error in the calculation.

or maybe im just bad at maths

Answer:

770,400

Step-by-step explanation:

770,400 seconds

The two different trinomials that have a greatest common factor of  \(5x^{2} y^{3}\) are:

a) \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\)

b) \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z\\\)

Let us verify,

a)  Consider the trinomial   \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\),

The Greatest Common Factor  of 35, 5, 15 is 5

The Greatest Common Factor  of  \(x^{2} ,x^{4} ,x^{3} =x^{2}\)

The Greatest Common Factor  of  \(y^{5} ,y^{9} ,y^{3} = y^{3}\)

There is no G.C.F for z because it is missing in the 3rd term.

So, the G.C.F  of the trinomial   \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\) =  \(5x^{2} y^{3}\)

b) Consider the trinomial   \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z\\\),

The Greatest Common Factor  of 25, 5, 10 is 5

The Greatest Common Factor  of \(x^{4} ,x^{7} ,x^{2} =x^{2}\)

The Greatest Common Factor  of \(y^{3} ,y^{8} ,y^{4} = y^{3}\)

There is no G.C.F for z because it is missing in the 2nd term.

So, the G.C.F of the trinomial  \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z = 5x^{2} y^{3}\)

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Answer:

1:72

Step-by-step explanation:

The scale of a drawing is the ratio of the length in the drawing to the real length.

Drawing length: 7 inches

Real length: 42 ft × 12 in. / ft = 504 in.

Scale:

7 in. to 504 in.

Divide both numbers by 7:

1 in. to 72 in.

Scale: 1:72

Answer:

70m-175=6m-12

70m-6m=175-12

64m=163

m=163/64

Answer:

6b - 2

Step-by-step explanation:

Product of b and 6 : b*6 = 6b

6b decreased by 2:       6b - 2

The test statistic (37.96) is greater than the critical value (11.345), we can reject the null hypothesis and conclude that there is a significant relationship between admission date and birthday.

The test statistic for this test is calculated by summing the squared differences between the observed and expected frequencies in each category, divided by the expected frequency in that category. This formula is:

X² = ∑(observed - expected)² / expected

The degrees of freedom for this test are equal to the number of categories minus one (4-1=3). Using a significance level of 0.01, the critical value for this test is 11.345.

To calculate the test statistic for this sample, we first need to calculate the expected frequencies. Each category should have an expected frequency of 196/4 = 49.

Category 1: expected frequency = 49, observed frequency = 12

Category 2: expected frequency = 49, observed frequency = 22

Category 3: expected frequency = 49, observed frequency = 65

Category 4: expected frequency = 49, observed frequency = 97

Using the formula above, we can calculate the test statistic:

X² = [(12-49)²/49] + [(22-49)²/49] + [(65-49)²/49] + [(97-49)²/49]

X² = 37.96

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Complete Question:

An article focuses on the existence of any relationship between the date of patient admission for treatment of alcoholism and the patient's birthday. Assuming a 365-day year (i.e., excluding leap year), in the absence of any relation, a patient's admission date is equally likely to be any one of the 365 possible days. The investigators established four different admission categories: (1) within 7 days of birthday, (2) between 8 and 30 days, inclusive, from the birthday, (3) between 31 and 90 days, inclusive, from the birthday, and (4) more than 90 days from the birthday. A sample of 196patients gave observed frequencies of 12, 22, 65, and 97 for categories 1, 2, 3, and 4, respectively. State and test the relevant hypotheses using a significance level of 0.01. Calculate the test statistic.

Answer:

The value of 4 is 400

Step-by-step explanation:

Answer:

hundred

Step-by-step explanation:

The solution of the inequality 15n>8n-21 is given by, n<-3.

Inequality is a relation between two or more mathematical expression or quantities via unequal signs i.e. greater, less, greater or equal, less or equal, not equal.

Given that the inequality is 15n<8n-21

Solving the inequality we have,

15n<8n-21

15n-8n<8n-21-8n, subtracting from both sides

7n<-21

n<-3, dividing 7 from both sides

So the solution of the given inequality is, n<-3.

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Answer:

Red Delicious: $1.30/lb

Honeycrisp: $2.55/lb

Red delicious is the better deal.

Step-by-step explanation:

Red Delicious:

($0.65)/(1/2 lb) = $1.30/lb

Honeycrisp:

($1.70)/(2/3 lb) = $2.55/lb

Red delicious is the better deal.

163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units

164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.

165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.

166. Missing side = 29 ft.

The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.

163. The distance between A(-5, 6) and B(5, -5):

AB = √[(5−(−5))² + (−5−6)²]

AB = √221

AB ≈ 14.9 units

164. Apply the Pythagorean theorem to find the diagonal:

Diagonal = √(15² + 15²) ≈ 21.2 ft.

165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:

c = √676 = 26 units.

166. Missing side = √(20² + 21²) = 29 ft.

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Answer:

you now if you wont to find the value you can type distance calculator and see the points

Step-by-step explanation:

Answer:

60 miles

Step-by-step explanation:

por que si es la verdad

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

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39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:

We can write a mixed fraction in a fraction:

6 1/2 = 13/2

8 1/2  = 33/2

7 3/4 = 31/4

8 1/12 = 97/12

8 5/12 = 101/12

Adding all the fractions:

\(=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}\)

\(=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}\)

\(=23+\dfrac{64}{4}\)

= 39 hours

Thus, 39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

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Answer: 3√3 , -3√3

Step-by-step explanation:

Answer:

+/-3 √3

Step-by-step explanation:

:p

Answer:

the answer is 16

Step-by-step explanation:

because if you do long divison

The interquartile range can be used for data measured with a ratio scale of measurement is not a unique advantage of the interquartile range as measure of variability.

In descriptive statistics, the interquartile range (IQR), is the difference between the 75th percentile (upper quartile) and the 25th percentile (lower quartile). In other words, the IQR is the third quartile minus the first quartile. The quartiles can be identified clearly through a line box diagram.

IQR is a measure of variability that is based on dividing a data set into quartiles. Quartiles divide an ordered data set into four equal parts. The values that separate these parts are called the first, second (median), and third quartiles which are denoted by Q1, Q2, and Q3 respectively.

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Answer:

(x+y)/xy or  (1/x + 1/y) portion of the leaves

Step-by-step explanation:

Let the total work done to rake the leaves be a for representation.

Thus,

given Maya takes x minutes to rake the leaves

thus,

work done by may in x minutes = a

dividing both side by x

work done by maya in x/x = 1 minutes = a/x

similarly

given Calra takes y minutes to rake the leaves

thus,

work done by may in y minutes = a

dividing both side by y

work done by maya in y/y = 1 minutes = a/y

__________________________________

Total work done by both in 1 minutes = a/x + a/y = a(1/x+1/y) = a(x+y)/xy

Thus, if a is the total work , then they do (x+y)/xy of a work in one minute.

Thus, (x+y)/xy portion of leaves do they rake in one minute if they work together.

Answer:

Question 1: The appropriate measures of center for this data set would be (1) Mean and (2) Median. There is no mode in this data set as there are no repeating values.

Question 2: To find the standard deviation, we first need to find the mean:

Mean = (513 + 490 + 496 + 380 + 490 + 513 + 503 + 513 + 500 + 492) / 10 = 494.0

Next, we find the difference between each data point and the mean:

(513 - 494.0), (490 - 494.0), (496 - 494.0), (380 - 494.0), (490 - 494.0), (513 - 494.0), (503 - 494.0), (513 - 494.0), (500 - 494.0), (492 - 494.0)

19, -4, 2, -114, -4, 19, 9, 19, 6, -2

Then we square each difference:

361, 16, 4, 12996, 16, 361, 81, 361, 36, 4

The sum of these squared differences is:

361 + 16 + 4 + 12996 + 16 + 361 + 81 + 361 + 36 + 4 = 14136

To find the variance, we divide the sum of squared differences by the number of data points minus one:

Variance = 14136 / 9 = 1570.7

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √1570.7 ≈ 39.6 (rounded to the tenths place)

Step-by-step explanation:

Answer:

sin3t*cos(s)*cos(t)+sin3t*sin(s)*sin(t).

Step-by-step explanation:

sin3t*cos(s-t);

1) cos(s-t)=cos(s)cost+sin(s)sint; then

2) sin3t*cos(s-t)=sin3t*cos(s)*cos(t)+sin3t*sin(s)*sin(t).

Answer: -88

Step-by-step explanation:

See if that's correct :)

Answer:

UNLOCK

UNLOCK

A normal number

Answer:The answer is ONE

Step-by-step explanation:

Answer:

1600

Step-by-step explanation:

\(\text{Number of terms}, ~n = 40\\\\\text{Sum of n odd integers} = n^2 = 40^2 = 1600\)

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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The cost per pound of the sausage and brisket are $3.75 and $4.5 respectively

Let

s = cost per sausage

b = cost per brisket

Therefore,

Lets combine the equation to find cost per pound of the sausage and brisket.

2s + 3b = 21

10s + 14b = 100.50

Multiply equation(i) by 5

10s + 15b = 105

10s + 14b = 100.50

subtract equation(ii) from the new equation

b = 4.5

2s + 3(4.5) = 21

2s  = 21 - 13.5

2s = 7.5

s = 7.5 / 2

s = 3.75

Therefore, the cost per pound of the sausage and brisket are $3.75 and $4.5 respectively.

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Step-by-step explanation:

1.

123445+(89-23765)=99769

2.

234.57+(5.23-2.678)=237.122

3

(21.54+ 80.27)-68.501=33.309

Answer:

a) \(\log_{9} 8 + \log_{9} 11 = \log_{9} 88\)

b) \(\log_{7} 11 - \log_{7} 3 = \log_{7} \frac{11}{3}\)

c) \(\log_{7}\frac{1}{81} = -4\cdot \log_{7} 3\)

Step-by-step explanation:

Now we proceed to solve each case by appropriate rules for logarithms.

a) The following property shall be used: \(\log_{c} a +\log_{c} b = \log_{c} a\cdot b\) (\(a = 8\), \(b = 11\), \(c = 9\))

\(\log_{9} 8 + \log_{9} 11 = \log_{9} 8\cdot 11\)

\(\log_{9} 8 + \log_{9} 11 = \log_{9} 88\)

b) The following property shall be used: \(\log_{c} a - \log_{c} b = \log_{c} \frac{a}{b}\) (\(a = 11\), \(b = 3\), \(c = 7\))

\(\log_{7} 11 - \log_{7} 3 = \log_{7} \frac{11}{3}\)

c) The following properties shall be used: \(\frac{1}{d} = d^{-1}\), \(\log_{c} a^{b}\)

\(\log_{7} \frac{1}{81} = \log_{7} 81^{-1}\)

\(-\log_{7} 81\)

\(-\log_{7} 3^{4}\)

\(\log_{7}\frac{1}{81} = -4\cdot \log_{7} 3\)