Find the distance between the points ( 4, 7) and (-1,2

Answer:

89.6 miles

Step-by-step explanation:

[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{56}[/tex]

5x = 448

x=89.6

Step-by-step explanation:

if 8km=5

x =56km

5x=8×56

5x=448

x=89.6 miles

Answer:

Hope this helps!

500 kwh

$105 - $30 = $75

$75 / $0.15 = 500

Answer:

$105-$30 service fee, this leaves only the electricity used. $75. now to find how many kilowatt hours used you divide $75/.15=500 answer 500 kilowatt hours.

Step-by-step explanation:

see above

9514 1404 393

Answer:

  (11, 3)

Step-by-step explanation:

That point is ...

  P = a + (1/6)(b -a) = (5a +b)/6

  P = (5(14, -1) +(-4, 23))/6 = (70-4, -5+23)/6 = (11, 3)

The point of interest is (11, 3).

Answer:

The coordinates of the point that is 1/6 of the way from a to b is thus (11, 3)

Step-by-step explanation:

Let's look first at the x coordinates of the two given points:  14 and -4.  From 14 to -4 is a decrease of 18.  Similarly, from y = -1 to y = 23 is an increase of 24.

Starting at a(14, -1) and adding 1/6 of the change in x, which is -18, we get the new x-coordinate 14 + (1/6)(-18), or 14 - 3, or 11.  Similarly, adding 1/6 of the increase in y of 24 yields -1 + 4, or 3.

The coordinates of the point that is 1/6 of the way from a to b is thus (11, 3)

Answer:

The choose (A)

y=(x-1)²-2

Answer:

[tex]{ \tt{2x + 4y = 8 - - - (a)}} \\ { \tt{x = 3y - 6 - - - (b)}} [/tex]

Substitute for x in equation (a) :

[tex]{ \tt{2(3y - 6) + 4y = 8}} \\ { \tt{6y - 12 + 4y = 8}} \\ { \tt{10y = 20}} \\ y = 2[/tex]

Substitute for y in equation (b) :

[tex]{ \tt{x = (3 \times 2) - 6}} \\ x = 0[/tex]

2x+4y =8

x=3y-6 ——> x–3y=–6

x–3y = – 6 ] ×(–2) ——> –2x +6y=12

2x+4y=8

–2x+6y =12

__o_o____

0+10y=20 —> 10y= 20 —> y= 20/10 —> y= 2

2x+4y=8 —> 2x + 4(2) = 8 —> 2x + 8=8 —> 2x = 0 —> x=0

(x,y) —> (0,2)

Answer:

Place value of 1 = 1 × 10 = 10

Step-by-step explanation:

In 382619,

Place of 1 = Tens

Place value of 1 = 1 × 10 = 10

Answer:

A. 8x = amount of broccoli needed

B. 4 people; 32÷8=4

Step-by-step explanation:

A. the variable (x) represents the amount of people.

B. 32 ounces divided by 8 ounces is enough for four people.

Answer:

(0.3049 ; 0.3751)

Step-by-step explanation:

The confidence interval for proportion can be obtained using the relation :

Phat ± Zcritical * [√phat(1-phat) / n]

phat = x / n

Sample size, n = 700

x = 238

phat = 238/700 = 0.34

Zcritical at 95% = 1.96

C.I = 0.34 ± 1.96 * [√0.34(1-0.34) / 700]

C.I = 0.34 ± 1.96 * 0.0179045

C. I = 0.34 ± 0.0350928

Lower boundary = 0.34 - 0.0350928 = 0.3049

Upper boundary = 0.34 + 0.0350928 = 0.37509

(0.3049 ; 0.3751)

Answer:

Use suitable identity to find the product (3-2x)(3+2x).Find the remainder when x³+ 3x²+3x+1 is divided by x+1.On a plane surface we can find straight lines.8√15 + 2√3The decimal form of 36 100(a-b)³ = a ³- ........ 3 + 3ab²-b³In the Cartesian plane the horizontal line is called .........The coefficient of x² in 2-x²+ x³ is -1.√225 is an irrational number.The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).

Answer:

0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%

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 46% of politicians are lawyers.

This means that [tex]p = 0.46[/tex]

Sample of size 662

This means that [tex]n = 662[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.46[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{662}} = 0.0194[/tex]

What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?

p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So

X = 0.5

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.5 - 0.46}{0.0194}[/tex]

[tex]Z = 2.06[/tex]

[tex]Z = 2.06[/tex] has a p-value of 0.9803

X = 0.42

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

[tex]Z = \frac{0.42 - 0.46}{0.0194}[/tex]

[tex]Z = -2.06[/tex]

[tex]Z = -2.06[/tex] has a p-value of 0.0197

0.9803 - 0.0197 = 0.9606

0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%

Answer:

7.5 ft³/min

Step-by-step explanation:

Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.

Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²

So, V = Ah = 2h = 2(10 - x)

The rate of change of volume is thus

dV/dt = d[2(10 - x)]/dt = -2dx/dt

Since dV/dt = 15 ft³/min,

dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min

Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt

= -dx/dt

= -(-7.5 ft³/min)

= 7.5 ft³/min

And the height at this point when x = 8 inches = 8 in × 1 ft/12 in  = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft

[tex]\rightarrow\sf {5a}^{2} + {b(a}^{2} + 5) + {b}^{2} [/tex]

[tex]\rightarrow\sf {5a}^{2} + {b(a }^{2} + 5) + {b}^{2} \\ = \sf {5a}^{2} + {ba}^{2} + b \times 5 + {b}^{2} \\ = \large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]

[tex]\rightarrow\large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]

[tex]\color{red}{==========================}[/tex]

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ

Answer:

The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 62, standard deviation of 8.

What is the approximate percentage of trees planted between 38 and 86?

38 = 62 - 3*8

86 = 62 + 3*8

So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Step-by-step explanation:

You look for the common factor of both of them which in this case is 5, therefore it's

5(x+7)..just divide 5 in 5x and in 35

Answer:

12x^3 is equivalent to

12x*12x*12x which if we multiply is

1728x

we divide by 4x

1728x divided by 4x=432x

Hope This Helps!!!

Answer:

3x^2

Step-by-step explanation:

when u divide 12x^3/4x....u divide 12/4=3 along with the x also..tat is x^3/x=x^2

Answer:

See attachment for graph

The height of the arch is: 120 m

The width to the nearest meter, at the base of the arch is 22 m

Step-by-step explanation:

Given

[tex]h = -0.06d^2 + 120[/tex]

Solving (a): The graph

See attachment for graph

Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.

Solving (b): The height

The curve of [tex]h = -0.06d^2 + 120[/tex] opens downward. So, the maximum point on the vertical axis represents the height of the arch,

Hence:

[tex]height = 120[/tex]

Solving (c): The width

The curve touches the horizontal axis at two different points.

[tex]x_1 = -11[/tex]

[tex]x_2 = 11[/tex]

The absolute difference of both points represents the width.

So:

[tex]Width = |x_2 - x_1|[/tex]

[tex]Width = |11 - -11|[/tex]

[tex]Width = |11 +11|[/tex]

[tex]Width = |22|[/tex]

Hence:

[tex]Width = 22[/tex]

Answer:

f(x) = 2(3) + 5

= 6 + 5 = 11

y = 11

x = 3

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.

Answer:

i put in 3 to make 23436 because 36 is divisible by 6

First simplify all polynomials and rewrite them in descending exponent order.

1. [tex]-x^2+2x[/tex]

2. [tex]x^3-4x^2[/tex]

3. [tex]-2x^2+2x+3[/tex]

Now observe the terms with highest exponents in each expression, in particularly focus on their exponent value,

[tex]-x^2[/tex] with value of 2

[tex]x^3[/tex] with value of 3

[tex]-2x^2[/tex] with value of 2

The value is also known as order of polynomial and it is a way to classify polynomials.

Every order creates a family of polynomials determined by the order (which is always greater than -1)

A polynomial such as (1) and (3) have an orders of 2, which is often called quadratic order and thus the polynomials (1), (3) are classified in the same family of quadratic polynomials, these are polynomials with order of 2.

Polynomial (2) however has an order of 3, which is called cubic order. This polynomial (2) is classified in the family of cubic polynomials.

There are of course many other families, in fact, infinitely many of them because you have order 0, 1, 2, 3, and so on there are precisely [tex]\aleph_0+1[/tex] read as "aleph 0 + 1" (the number of natural numbers + 1 (because 0 is not a natural number)) of polynomial families.

The first few have these fancy names, for example:

order 0 => constant polynomial

order 1 => linear polynomial

order 2 => quadratic polynomial

order 3 => cubic polynomial

order 4 => quartic polynomial

and so on.

Hope this helps!

Answer:

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex] --- set builder

[tex][-21,\infty)[/tex] --- interval notation

Step-by-step explanation:

Given

[tex]-3a - 15 \le -2a + 6[/tex]

Required

Solve

Collect like terms

[tex]-3a + 2a \le 15 + 6[/tex]

[tex]-a \le 21[/tex]

Divide by -1

[tex]a \ge - 21[/tex]

Rewrite as:

[tex]-21 \le a[/tex]

Using set builder

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex]

Using interval notation, we have:

[tex][-21,\infty)[/tex]

Answer:

yes it is

Step-by-step explanation:

Answer:

0.0032

Step-by-step explanation:

We need to compute [tex]e^{0.4}[/tex] by the help of third-degree Taylor polynomial that is expanded around at x = 0.

Given :

[tex]e^{0.4}[/tex] < e < 3

Therefore, the Taylor's Error Bound formula is given by :

[tex]$|\text{Error}| \leq \frac{M}{(N+1)!} |x-a|^{N+1}$[/tex]   , where [tex]$M=|F^{N+1}(x)|$[/tex]

         [tex]$\leq \frac{3}{(3+1)!} |-0.4|^4$[/tex]

         [tex]$\leq \frac{3}{24} \times (0.4)^4$[/tex]

         [tex]$\leq 0.0032$[/tex]

Therefore, |Error| ≤ 0.0032

Answer:

157,476 people

Step-by-step explanation:

the formula :

P(x) = 86700. (1+ 0.089)^r

for r = 7

=> P(x) = 86700 × (1+ 0.089)^7

= 86700 × (1.089)^7

= 86700 × 1.8163

= 157,476 people

Answer: adults = 79

children = 158

student = 46

Step-by-step explanation:

Let a = adults

Let c = children

Let s = student

From the information given,

a + c + s = 283 ....... i

c/a = 2, c = 2a ....... ii

5c + 7s + 12a = 2060 ...... iii

Put the value of c = 2a into equation i

a + c + s = 283

a + 2a + s = 283

3a + s = 283

s = 283 - 3a

Note that c = 2a

From equation iii

5c + 7s + 12a = 2060

5(2a) + 7(283 - 3a) + 12a = 2060

10a + 1981 - 21a + 12a = 2060

10a + 12a - 21a = 2060 - 1981

a = 79

Note c = 2a

c = 2 × 79 = 158

Since a + c + s = 283

79 + 158 + s = 283

s = 283 - 237

s = 46

adults = 79

children = 158

student = 46

A parallelogram is also a rhombus if the diagonal is a bisector of an angle enclosed by the two adjacent sides of a parallelogram.

In our case it means,

[tex]5x+25=12x+11[/tex]

[tex]7x=14\implies x=\boxed{2}[/tex]

Hope this helps.

In order for the parallelogram to be a rhombus, ,For the parallelogram to be a rhombus, x must be equal to 2.

To determine the value of x that would make the parallelogram a rhombus, we need to compare the lengths of its opposite sides. In a rhombus, all four sides are equal in length. So, we can equate the lengths of the opposite sides of the parallelogram and solve for x.

Given that one side has a length of (5x + 25) and the opposite side has a length of (12x + 11), we can set up the following equation: 5x + 25 = 12x + 11

To solve for x, we can start by isolating the x term on one side of the equation. We can do this by subtracting 5x from both sides: 25 = 12x - 5x + 11 Simplifying the equation further: 25 = 7x + 11 Next, we can isolate the x term by subtracting 11 from both sides: 25 - 11 = 7x 14 = 7x Finally, we can solve for x by dividing both sides by 7: 14/7 = x x = 2 Therefore, for the parallelogram to be a rhombus, x must be equal to 2.

To know more about parallelogram here

https://brainly.com/question/970600

#SPJ2

Answer:

36281629273781646181993836619946527189119292937467482919198$7473828191927364732818919283838292927383883829118661552621718919191019284746617171819001187373765252728

Step-by-step explanation:

173899918377+28910873638282

Answer:

[tex]-x^{2}[/tex]

Step-by-step explanation:

It simple really its just a reflection over the x-axis making it a negative towards the parent function

Answer:

The answer is -x²

Step-by-step explanation:

Hope this helps :)