how many integers from 1 through a

Answer:

The answer is 40 chocolates in the box in total

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Value of the expression in which each variable was swapped out with a number from its corresponding domain sinh⁡ (l5)

sinh (5)

=sinh(1.6094) =2.39990 rad

=sinh⁡(1.6094) =2.3

By doing the following, you may determine the numerical value of an algebraic expression: Replace each variable with the specified number. Then, enter your score in your team's table.

Value of the expression in which each variable was swapped out with a number from its corresponding domain. In the case of a number with only one digit, referring to the numerical value associated with a digit by its "value" is a convenient shorthand.

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Answer:

Step-by-step explanation:

Let take a look at the given function y = 4x - 1 whose point is located between (1,3) and (4,15) on the graph.

Here, the function of y is non-negative. Now, expressing y in terms of x in y = 4x- 1

4x = y + 1

[tex]x = \dfrac{y+1}{4}[/tex]

[tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

By integration, the required surface area in the revolve is:

[tex]S = \int^{15}_{ 3} 2 \pi g (y) \sqrt{1+g'(y^2) \ dy }[/tex]

where;

g(y) = [tex]x = \dfrac{1}{4}y + \dfrac{1}{4}[/tex]

∴

[tex]S = \int^{15}_{ 3} 2 \pi \Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}y + \dfrac{1}{4}\Big)'\Bigg)^2 \ dy }[/tex]

[tex]S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \sqrt{1+\Bigg(\Big( \dfrac{1}{4}\Big ) \Bigg)^2 \ dy } \\ \\ \\ S = \dfrac{1}{2} \pi \int^{15}_{ 3} (y+1) \dfrac{\sqrt{17}}{4} \ dy[/tex]

[tex]S = \dfrac{\sqrt{17}}{8} \pi \int^{15}_{ 3} (y+1) \ dy[/tex]

[tex]S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(y+1)^2)\Big|^{15}_{3} \\ \\ S = \dfrac{\sqrt{17} \pi}{8} (\dfrac{1}{2}(15+1)^2-\dfrac{1}{2}(3+1)^2 ) \\ \\ S = \dfrac{\sqrt{17} \pi}{8} *120 \\ \\\mathbf{ S = 15 \sqrt{17}x}[/tex]

Answer:

[tex]CI=189.5,194.5[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=40[/tex]

Mean [tex]\=x =192[/tex]

Standard deviation[tex]\sigma=8[/tex]

Significance Level [tex]\alpha=0.05[/tex]

From table

Critical Value of [tex]Z=1.96[/tex]

Generally the equation for momentum is mathematically given by

 [tex]CI =\=x \pm z_(a/2) \frac{\sigma}{\sqrt{n}}[/tex]

 [tex]CI =192 \pm 1.96 \frac{8}{\sqrt{40}}[/tex]

 [tex]CI=192 \pm 2.479[/tex]

 [tex]CI=189.5,194.5[/tex]

Answer:

12

Step-by-step explanation:

Answer:

[tex]x=\frac{5}{2} \\y=5[/tex]

( 5/2, 2 )

Step-by-step explanation:

Solve by substitution method:

[tex]2x+5=10\\\2x+3y=20[/tex]

Solve [tex]2x+5=10[/tex] for [tex]x[/tex]:

[tex]2x+5=10[/tex]

[tex]2x=10-5[/tex]

[tex]2x=5[/tex]

[tex]x=5/2[/tex]

Substitute [tex]5/2[/tex] for [tex]x[/tex] in [tex]2x+3y=20[/tex]:

[tex]2x+3y=20[/tex]

[tex]2(\frac{5}{2} )+3y=20[/tex]

[tex]3y+5=20[/tex]

[tex]3y=20-5[/tex]

[tex]3y=15[/tex]

[tex]y=15/3[/tex]

[tex]y=5[/tex]

∴ [tex]x=\frac{5}{2}[/tex] and [tex]y=5[/tex]

hope this helps....

Answer:

C

Step-by-step explanation:

x + 2 < -5

x < - 5 - 2

x < - 7

Answer:

{x| x R, x<-7}

Step-by-step explanation:

=> x+2<-5

=> x<-5-2

=> x<-7

Answer:

a) -0.94

b) 0.3472

c) -2.327, 2.327

Step-by-step explanation:

A claim is made that the proportion of 6-10 year-old children who play sports is not equal to 0.5.

At the null hypothesis, we test if the proportion is of 0.5, that is:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, we test if the proportion is different from 0.5, that is:

[tex]H_1: p \neq 0.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5*(1-0.5)} = 0.5[/tex]

A random sample of 551 children aged 6-10 showed that 48% of them play a sport.

This means that [tex]n = 551, X = 0.48[/tex]

(a) Calculate the value of the test statistic used in this test.

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.48 - 0.5}{\frac{0.5}{\sqrt{551}}}[/tex]

[tex]z = -0.94[/tex]

So the answer is -0.94.

(b) Use your calculator to find the P-value of this test.

The p-value of the test is the probability that the sample proportion differs from 0.5 by at least 0.02, which is P(|z| > 0.94), which is 2 multiplied by the p-value of Z = -0.94.

Looking at the z-table, z = -0.94 has a p-value of 0.1736.

2*0.1736 = 0.3472, so 0.3472 is the answer to option b.

(c) Use your calculator to find the critical value(s) used to test this claim at the 0.02 significance level.

Two-tailed test(test if the mean differs from a value), Z with a p-value of 0.02/2 = 0.01 or 1 - 0.01 = 0.99.

Looking at the z-table, this is z = -2.327 or z = 2.327.

Answer:

2.25 miles per hr

Answer:

2.25 miles per hour

Step-by-step explanation:

speed = distance / time

speed = [tex]\frac{3}{4} / \frac{1}{3}[/tex] (take the reciprocal of [tex]\frac{1}{3}[/tex])

= [tex]\frac{3}{4} * 3[/tex]

= [tex]\frac{9}{4}[/tex] = 2.25 miles per hour

Answer:

Step-by-step explanation:

[tex]f(x) = \frac{4}{x}\\\\f(a) = \frac{4}{a}\\\\f(a+h) = \frac{4}{a+h}\\\\\frac{f(a+h) - f(a)}{h} = \frac{\frac{4}{a+h} - \frac{4}{a}}{h}[/tex]

                [tex]=\frac{\frac{4(a)}{(a+h)a} - \frac{4(a+h)}{a(a+h)}}{h}\\\\=\frac{\frac{4a - 4a - 4h}{a(a+h)}}{h}\\\\=\frac{\frac{ - 4h}{a(a+h)}}{h}\\\\= \frac{-4h}{a(a+h) \times h}\\\\= -\frac{4}{a(a+h)}\\\\[/tex]

Answer:

The interval is [98,132]

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normal with mean 115 and standard deviation 25.

This means that [tex]\mu = 115, \sigma = 25[/tex]

Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.

Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = -0.675*25[/tex]

[tex]X = 98[/tex]

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 115}{25}[/tex]

[tex]X - 115 = 0.675*25[/tex]

[tex]X = 132[/tex]

The interval is [98,132]

Answer:

the total square footage = 194

1.88 x 194 = 364.72

Step-by-step explanation:

Area for triangle ends.

A = [tex]\frac{2.5 (8)}{2}[/tex]   (Times two, because there are two ends.)

Base of prism = 8 x 10 = 80

Sides of prism = 2(10 x 4.7 ) = 94  (What's the 2?  There's two of them)

Add all together : 10 + 10 + 80 + 94 = 194

1.88 x 194 = 364.72

Answer:

remember the chain rule:

h(x) = f(g(x))

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

or:

dh/dx = (df/dg)*(dg/dx)

we know that:

z = 4*e^x*ln(y)

where:

y = u*sin(v)

x = ln(u*cos(v))

We want to find:

dz/du

because y and x are functions of u, we can write this as:

dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)

where:

(dz/dx)  = 4*e^x*ln(y)

(dz/dy) = 4*e^x*(1/y)

(dx/du) = 1/(u*cos(v))*cos(v) = 1/u

(dy/du) = sin(v)

Replacing all of these we get:

dz/du = (4*e^x*ln(y))*( 1/u) + 4*e^x*(1/y)*sin(v)

          = 4*e^x*( ln(y)/u + sin(v)/y)

replacing x and y we get:

dz/du = 4*e^(ln (u cos v))*( ln(u sin v)/u + sin(v)/(u*sin(v))

dz/du = 4*(u*cos(v))*(ln(u*sin(v))/u + 1/u)

Now let's do the same for dz/dv

dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*(dy/dv)

where:

(dz/dx)  = 4*e^x*ln(y)

(dz/dy) = 4*e^x*(1/y)

(dx/dv) = 1/(cos(v))*-sin(v) = -tan(v)

(dy/dv) = u*cos(v)

then:

dz/dv = 4*e^x*[ -ln(y)*tan(v) + u*cos(v)/y]

replacing the values of x and y we get:

dz/dv = 4*e^(ln(u*cos(v)))*[ -ln(u*sin(v))*tan(v) + u*cos(v)/(u*sin(v))]

dz/dv = 4*(u*cos(v))*[ -ln(u*sin(v))*tan(v) + 1/tan(v)]

The first sum is a geometric series:

[tex]1+\dfrac15+\dfrac1{5^2}+\dfrac1{5^3}+\cdots+\dfrac1{5^n}+\cdots=\displaystyle\sum_{n=0}^\infty\frac1{5^n}[/tex]

Recall that for |x| < 1, we have

[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

Here we have |x| = |1/5| = 1/5 < 1, so the first sum converges to 1/(1 - 1/5) = 5/4.

The second sum is exponential:

[tex]1+5+\dfrac{5^2}{2!}+\dfrac{5^3}{3!}+\cdots+\dfrac{5^n}{n!}+\cdots=\displaystyle\sum_{n=0}^\infty \frac{5^n}{n!}[/tex]

Recall that

[tex]\exp(x)=\displaystyle\sum_{n=0}^\infty\frac{x^n}{n!}[/tex]

which converges everywhere, so the second sum converges to exp(5) or e⁵.

Answer:

x=[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Hi there!

We are given the following equation:

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

and we need to find the value of x

To do this, we need to isolate the value of x with a coefficient of 1 (1x) on one side. The value of x, or everything else is on the other side

So let's get rid of [tex]\frac{1}{10}[/tex] from the left side by adding [tex]\frac{1}{10}[/tex] to both sides (-[tex]\frac{1}{10}[/tex]+[tex]\frac{1}{10}[/tex]=0).

[tex]\frac{4x}{5}[/tex]-[tex]\frac{1}{10}[/tex]=[tex]\frac{3}{10}[/tex]

  +[tex]\frac{1}{10}[/tex]  +[tex]\frac{1}{10}[/tex]

___________

[tex]\frac{4x}{5}[/tex]=[tex]\frac{3}{10}[/tex]+[tex]\frac{1}{10}[/tex]

as the fractions on the right side both have the same denominator, we can add them together

[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]

Now we need to have the value of 1x. Currently we have [tex]\frac{4x}{5}[/tex].

In order to get x with a coefficient of 1, multiply both sides by the reciprocal of [tex]\frac{4}{5}[/tex], which is [tex]\frac{5}{4}[/tex]

[tex]\frac{5}{4}[/tex]×[tex]\frac{4x}{5}[/tex]=[tex]\frac{4}{10}[/tex]*[tex]\frac{5}{4}[/tex]

which simplifies down to

x=[tex]\frac{20}{40}[/tex]

Now reduce the fraction by dividing the numerator and denominator both by 20

x=[tex]\frac{1}{2}[/tex]

Hope this helps!  

Answer:

0.7994 = 79.94% probability that the proportion of persons with myopia will differ from the population proportion by less than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 42% of the population has myopia.

This means that [tex]p = 0.42[/tex]

Random sample of size 442 is selected

This means that [tex]n = 442[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.42[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.42*0.58}{442}} = 0.0235[/tex]

What is the probability that the proportion of persons with myopia will differ from the population proportion by less than 3%?

Proportion between 0.42 + 0.03 = 0.45 and 0.42 - 0.03 = 0.39, which is the p-value of Z when X = 0.45 subtracted by the p-value of Z when X = 0.39.

X = 0.45

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.45 - 0.42}{0.0235}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

X = 0.39

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.39 - 0.42}{0.0235}[/tex]

[tex]Z = -1.28[/tex]

[tex]Z = -1.28[/tex] has a p-value of 0.1003

0.8997 - 0.1003 = 0.7994

0.7994 = 79.94% probability that the proportion of persons with myopia will differ from the population proportion by less than 3%.

Step-by-step explanation:

Answer:

[tex]x<41[/tex]

Step-by-step explanation:

[tex](x)+(x+1)<83[/tex]

simplify both sides

[tex]2x+1<83[/tex]

subtract one from the both sides to isolate the variable

[tex]2x<82[/tex]

divide both sides by 2 to isolate the variable

[tex]x<41[/tex]

Answer:

-15 -3.45 -3.15 -3.0

Step-by-step explanation:

Answer:

You can go ahead with option D

Step-by-step explanation:

Answer:

15.9

Step-by-step explanation:

The distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

Two numbers on a number line:

-10.2 and 5.7

As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

Indicating the above numbers on a number line:

= 5.7 -(-10.5)

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 5.7 + 10.5

= 15.9

Thus, the distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.

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SOLUTION:

10•10= 100

Answer:

35

Step-by-step explanation:

3x7=35

There are 60 students and 13 teachers on a bus .what is the ratio of students to teachers.

Given :-

To Find :-

Answer :-

Taking the given expression,

→ 4x² - 8x + 4

→ 4x² - 4x -4x + 4

→ 4x ( x - 1 ) -4( x -1)

→ (4x - 4)(x-1)

Hence the required answer is (4x - 4)( x - 1) .

Answer:

x = 100 degree

Step-by-step explanation:

EF//GC => NF // OC

∠ANE=∠ONF     [Vertically opposite angles]

∠ONF=80

In Quadrilateral OCFN,

NF // OC

∠ ONF + x = 180     [Linear Pair]

=> 80 + x = 180

=> x = 180-80

=> x = 100

Answer:

x=100°

Step-by-step explanation:

corresponding angles

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

Answer:

[tex]\bar x = 3.545[/tex]

[tex]Median = 3.435[/tex]

Step-by-step explanation:

Given

[tex]x:3.89, 3.51, 3.97, 3.31, 3.21, 3.36, 3.67, 3.24, 3.27[/tex]

[tex]10th: 4.02[/tex]

Solving (a): The mean

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{3.89 +3.51 +3.97 +3.31 +3.21 +3.36 +3.67 +3.24 +3.27+4.02}{10}[/tex]

[tex]\bar x = \frac{35.45}{10}[/tex]

[tex]\bar x = 3.545[/tex]

Solving (b): The median

First, we sort the data; as follows:

[tex]3.21, 3.24, 3.27, 3.31, 3.36, 3.51, 3.67, 3.89, 3.97, 4.02[/tex]

[tex]n = 10[/tex]

So, the median position is:

[tex]Median = \frac{n + 1}{2}th[/tex]

[tex]Median = \frac{10 + 1}{2}th[/tex]

[tex]Median = \frac{11}{2}th[/tex]

[tex]Median = 5.5th[/tex]

This means that the median is the average of the 5th and 6th item

[tex]Median = \frac{3.36 + 3.51}{2}[/tex]

[tex]Median = \frac{6.87}{2}[/tex]

[tex]Median = 3.435[/tex]

Answer:

The measure of the smallest angle is 30º

Step-by-step explanation:

Let the angles be:

[tex]x \to[/tex] the first angle (the smallest)

[tex]y \to[/tex] the second angle

[tex]z \to[/tex] the third angle

So, we have:

[tex]y = 2x[/tex]

[tex]z=x + 60[/tex]

Required

Find x

The angles in a triangle is:

[tex]x + y +z = 180[/tex]

Substitute values for y and z

[tex]x + 2x +x + 60 = 180[/tex]

[tex]4x + 60 = 180[/tex]

Collect like terms

[tex]4x = 180-60[/tex]

[tex]4x = 120[/tex]

Divide by 4

[tex]x = 30[/tex]

Answer:

1. 3

2. D

3. KE

4. B

5. A

Step-by-step explanation:

those should be your answers

Answer:

1. 3

2. D

3. E and K

4. B

5. A

negative integers lie on the negative side of the number line(usually having a minus sign in front of them)

positive ones lie on the positive side( usually have no signs in front of them)