a) __m=10km 25m =___km

b) __m=__km__m=1.5 km

9514 1404 393

Answer:

  3x +y -13 = 0

Step-by-step explanation:

The perpendicular line will have the variable coefficients swapped and one of them negated. The new constant will be appropriate to the given point.

  3(x -4) +1(y -1) = -0

  3x +y -13 = 0

_____

Additional comment

The given equation is in "general form", so that is the form of the equation we have given as the answer. This form is convenient in that the general form equation for a line through the origin, ax+by=0, is easily translated to make it pass through a point (h, k): a(x -h) +b(y -k) = 0. Eliminating parentheses puts the equation back into general form.

Answer:

[tex]{ \tt{ {x}^{3} - 2 {x}^{2} + x - 2 }} \\ = { \tt{(x - 2)(x - i)(x + i)}}[/tex]

Answer:

A) 10%

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.

Sam's monthly bills are normally distributed with mean 2700 and standard deviation 230.9.

This means that [tex]\mu = 2700, \sigma = 230.9[/tex]

What is the probability that his expenses will exceed his income in the following month?

Expenses above 2*1500 = $3000, which is 1 subtracted by the p-value of Z when X = 3000.

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

[tex]Z = \frac{3000 - 2700}{230.9}[/tex]

[tex]Z = 1.3[/tex]

[tex]Z = 1.3[/tex] has a p-value of 0.9032.

1 - 0.9032 = 0.0968 that is, close to 10%, and thus the correct answer is given by option A.

9514 1404 393

Answer:

  a) $135.97

  b) $342,892.60

Step-by-step explanation:

a) The attached spreadsheet shows the use of the "payment" function for determining the amount of a payment that will give the desired future value. It shows the deposit needs to be $135.97 per month.

__

b) The interest earned is the difference between 420 payments and the account balance. The interest amount is $342,892.60.

Answer:

the answer is 40.27

Step-by-step explanation:

37.99 × 6%= 2.28

37.99+2.28= 40.27

Answer: -4/6 or -2/3

Step-by-step explanation:

First, you find a common denominator among the fractions, which would be 6.

Convert -1/2 to have 6 as its denominator.

-1/2* 3/3 = -3/6

And then subtract them.

-3/6 - 1/6 = -4/6

-4/6 simplified is -2/3

When you subtract a positive number from a negative number, you are adding their absolute values.

Answer:

see below

Step-by-step explanation:

10 + 15k

Factor out the greatest common factor 5

5( 2+3k)

Rewriting

5(3k+2)

Rami is correct if a=2 then his expression is 5(3k+2)

Kenneth

yk+6+8k+4

Add the terms together

k(y+8) + 10

If y =7 then Kenneth is correct otherwise he is incorrect

Answer:

[tex]f(x) = -4(x+7)(x+1)[/tex]

Step-by-step explanation:

Quadratic equation:

A quadratic equation, with roots(x-intercepts) at [tex]x_1[/tex] and [tex]x_2[/tex], and leading coefficient a, is given by:

[tex]f(x) = a(x - x_1)(x - x_2)[/tex]

Has x-intercepts of -7 and -1

So [tex]x_1 = -7, x_2 = -1[/tex]. Thus

[tex]f(x) = a(x - (-7))(x - (-1)) = a(x+7)(x+1)[/tex]

Passes through the point (-4,36).

This means that when [tex]x = -4, y = 36[/tex], and we use this to find the leading coefficient.

[tex]36 = a(-4+7)(-4+1)[/tex]

[tex]a(3)(-3) = 36[/tex]

[tex]-9a = 36[/tex]

[tex]a = -\frac{36}{9}[/tex]

[tex]a = -4[/tex]

So

[tex]f(x) = -4(x+7)(x+1)[/tex]

Answer: 20 ft × 12.5 ft

Step-by-step explanation:

Since 1 cm = 2.5 ft,

Therefore, 8 cm × 5 cm = 20 ft × 12.5 ft

Answer: -21

[tex]-3[5 - (-8 + 6)]\\=-3[5 - (-2)]\\=-3[5+2]\\=-3(7)\\=-21[/tex]

Answer:

-21

Step-by-step explanation:

-3[5 - (-8 + 6)]

Inner parentheses first

-3[5 - (-2)]

Then remaining parentheses

-3[5 +2]

-3(7)

Multiply

-21

Answer:

that's 4,188.8 if it's gonna be a 10cm sphere

Answer:

Total Distance : 1*60 +60=120

Total time taken = 1+ 60/30= 1+2=3

Hence average speed for the trip = 120/3= 40 kmph

Hence Answer is 40

Step-by-step explanation:

The average speed is 40 km/h.

The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:

Average Speed = Total distance covered ÷ Total time taken

Example:

sing the average speed formula, find the average speed of Sam, who covers the first 200 kilometers in 4 hours and the next 160 kilometers in another 4 hours.

Solution:

To find the average speed we need the total distance and the total time.

Total distance covered by Sam = 200Km + 160 km = 360 km

Total time taken by Sam = 4 hour + 4 hour = 8 hour

Average Speed = Total distance covered ÷ Total time taken

Average Speed = 360 ÷ 8 = 45km/hr

Given:

d1= 60 km

d2= 30

d3 = 60

Total Distance : 1*60 +60=120

Total time taken = 1+ 60/30= 1+2=3

Now,

average speed = total distance/ total time taken

= 120/3

= 40 kmph

Learn more about average speed here;

https://brainly.com/question/12322912

#SPJ2

Answer:  24.33

======================================================

Explanation:

The range is

range = max - min

range = 28.17 - 12.82

range = 15.35

This is the width of this particular uniform distribution.

Apply 75% to this value

75% of 15.35 = 0.75*15.35 = 11.5125

Then finally, add that to the min

12.82 + 11.5125 = 24.3325 which rounds to 24.33

We can see that 75% of the values are below 24.33 which makes it the 3rd quartile (Q3).

Answer:

V≈678.58cm³

Step-by-step explanation:

V=πr^2h/3=π·6^2·18/3≈678.58401cm³

Hope this helps! :D

Answer:

11

Step-by-step explanation:

Step 1:  Round [tex]11 \frac{7}{16}[/tex] to the nearest whole number

In order to round up, the fraction must be greater or equal to 1/2.  However, in our problem, it is less than half which means that we do not round up.  Therefore, the answer is 11.

Answer:  11

Answer:

40

Step-by-step explanation:

The shape has 6 sides a,b,c,d,e,f

The perimeter is the sum of the sides

P = a+b+c+d+e +f

4 of the sides add to 195  a+b+c+d = 195  Replace in the equation

P = 195 +e+f

We know that e and f are equal

P = 195+f+f

P = 195+2f

The perimeter is 275

275=195+2f

Subtract 195 from each side

275 -195 = 195+2f-195

80 = 2f

Divide by 2

80/2 = 2f/2

40 =f

The other 2 sides are 40 ft each

Q) 145+ (-15) + (-188) = ?

→ 145+ (-15) + (-188)

→ {145 - 15} - 188

→ 130 - 188

→ -58 is the solution.

Answer:

y=-4x-6

Step-by-step explanation:

It jwust is mwannn

Answer:

Step-by-step explanation:

Given functions are,

f(x) = x + 6

g(x) = 2x + 6

(f - g)(x) = (x + 6) - (2x + 6)

                   = -x

(f . g)(x) = f(x) × g(x)

            = (x + 6)(2x + 6)

            = 2x² + 6x + 12x + 36

            = 2x² + 18x + 36

(f + g)(x) = (x + 6) + (2x + 6)

             = 3x + 12

(f + g)(1) = 3(1) + 12

            = 15  

Answer:

Step-by-step explanation:

f(n) = 8 + 3(n) - 3

f(n) = 5 + 3n

f(1) = 5 + 3(1)

f(1) = 8

f(2) = 5 + 3(2)

f(2) = 5  + 6

f(2) = 11

f(3) = 5 + 3*3

f(3) = 14

f(4) = 5 + 3*4

f(4) = 17

Answer:

7

Step-by-step explanation:

2 x (3-1) + 3

Evaluate using PEMDAS

Parenthesis

Exponents

Math and Division ( left to right )

Addition and Subtraction ( left to right )

2 x (3-1) + 3

According to PEMDAS we do the operations inside of the parenthesis first

3 - 1 = 2

We now have: 2 x 2 + 3

Next we do exponents

There are no exponents so let's move on to multiplication and division

There is indeed multiplication so we do it

2 x 2 = 4

We now have: 4 + 3

Finally we do the addition

4 + 3 = 7

The answer is 7

Answer:

6400

Step-by-step explanation:

6428

4 is in the hundreds place

looking at the tens place = 2

Since it is less than 5

We leave the hundreds place alone

6400

Answer:

192

Step-by-step explanation:

x is the altitude of the right triangle. Thus, we would apply the geometric mean theorem to find the value of x. Thus, the formula is given as:

h = √(ab)

Where,

h = altitude = x

a = 144

b = 400 - 144 = 256

Plug in the given values into the formula

x = √(144*256)

x = √(36,864)

x = 192

Answer:

sin x° = opposite ÷ hypotenuse

Step-by-step explanation:

SOH - CAH - TOA

SOH: Sin(θ) = Opposite / Hypotenuse

CAH: Cos(θ) = Adjacent / Hypotenuse

TOA: Tan(θ) = Opposite / Adjacent

Answer:

last option

Step-by-step explanation:

Sin is opposite/negative

Given

e ˣʸ = sec(x ²)

take the derivative of both sides:

d/dx [e ˣʸ] = d/dx [sec(x ²)]

Use the chain rule:

e ˣʸ d/dx [xy] = sec(x ²) tan(x ²) d/dx [x ²]

Use the product rule on the left, and the power rule on the right:

e ˣʸ (x dy/dx + y) = sec(x ²) tan(x ²) (2x)

Solve for dy/dx :

e ˣʸ (x dy/dx + y) = 2x sec(x ²) tan(x ²)

x dy/dx + y = 2x e ⁻ˣʸ sec(x ²) tan(x ²)

x dy/dx = 2x e ⁻ˣʸ sec(x ²) tan(x ²) - y

dy/dx = 2e ⁻ˣʸ sec(x ²) tan(x ²) - y/x

Since e ˣʸ = sec(x ²), we simplify further to get

dy/dx = 2 tan(x ²) - y/x

Answer:

1.) Yes, because the x distribution is mound-shaped and symmetric and σ is unknown. ;

df = 24 ;

H0 : μ = 8.5

H1 : μ ≠ 8.5 ;

1.250 ;

At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

There is insufficient evidence at the 0.05 level to reject the null hypothesis.

Step-by-step explanation:

Given :

Sample size, n = 25

xbar = 9 ; Standard deviation, s = 2

α = 0.05 ;

The degree of freedom, df = n - 1 ; 25 - 1 = 24

The hypothesis (two tailed)

H0 : μ = 8.5

H1 : μ ≠ 8.5

The test statistic :

(xbar - μ) ÷ (s/√(n))

(9 - 8.5) ÷ (2/√(25))

0.5 / 0.4

Test statistic = 1.250

The Pvalue from Tscore ;

Pvalue(1.250, 24) = 0.2234

Pvalue > α ; We fail to reject H0 ;

Answer:

x = 5

Step-by-step explanation:

I'm taking all bases as b so not typing it

2/3 log 125 = log (125^2/3) = log 25

1/2 log 9 = log (9^1/2) = log 3

So we can rewrite the equation as,

log x = log 25 + log 3 - log 15

or, log x = log (25×3) - log 15

or, log x = log 75 - log 15

or, log x = log (75/15)

or, log x = log 5

or, x = 5

Answered by GAUTHMATH

Answer:

c

Step-by-step explanation:

product is the answer to a multiplication problem.