The slope of diagonal AB is ___ , and it’s equation is ___.

Answer:

The first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Step-by-step explanation:

Given that two mechanics worked on a car, and the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours, and together they charged a total of $ 1125, to determine what was the rate charged per hour by each mechanic if the sum of the two rates was $ 140 per hour, the following calculation must be performed:

1125/15 = X

75 = X

80 x 10 + 60 x 5 = 800 + 300 = 1100

85 x 10 + 55 x 5 = 850 + 275 = 1125

Therefore, the first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Answer:

11/12 cups

Step-by-step explanation:

2/3+1/4 = ( 2x4 + 3x1 )/( 3x4 ) = ( 8+3 )/12 = 11/12

Answer:

4

3

0

Step-by-step explanation:

f(x) = y = -1/2 × sqrt(x+3)

2y = -sqrt(x+3)

4y² = x + 3

x = 4y² - 3

now renaming this, so that the normal symbols and names are used for this function definition, so that the input variable is called "x" :

f-1(x) = 4x² - 3

basically, just by itself, this function would be defined for all possible real values of x.

but because it is the inverse of the original function, which generates only values of y<=0, then for the inverse function that same range applies for its input variable x

x<=0

9514 1404 393

Answer:

  29.4 m/s

Step-by-step explanation:

Speed is proportional to time, so we have ...

  speed / time = s/3 = 49/5

  s = 3/5(49) = 29.4

The speed of the object is 29.4 m/s after 3 seconds.

Answer:

51

Step-by-step explanation:

(-3)^4-5(5)+6(5)÷(-3)(2)

81-25+30÷-6

81-25-5

81-30

51

(Remember order of operations-PEMDAS)

Answer:

7.5 dm

Step-by-step explanation:

Plus mo baka tama ako

Answer:

(5) we have multiple the powers

Answer:

The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is 68%.

The probability that a randomly selected infant has a birth weight between 110 and 130 is 38%.

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.

Mean of 120 ounces and a standard deviation of 20 ounces.

This means that [tex]\mu = 120, \sigma = 20[/tex]

The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is

p-value of Z when X = 140 subtracted by the p-value of Z when X = 100.

X = 140

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

[tex]Z = \frac{140 - 120}{20}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84

X = 100

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

[tex]Z = \frac{100 - 120}{20}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.16

0.84 - 0.16 = 0.68

The probability that a randomly selected infant has a birth weight between 100 ounces and 140 ounces is 68%.

The probability that a randomly selected infant has a birth weight between 110 and 130

This is the p-value of Z when X = 130 subtracted by the p-value of Z when X = 110.

X = 130

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

[tex]Z = \frac{130 - 120}{20}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.69

X = 110

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

[tex]Z = \frac{110 - 120}{20}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.31

0.69 - 0.31 = 0.38 = 38%.

The probability that a randomly selected infant has a birth weight between 110 and 130 is 38%.

Answer:

should be (5y-2)y = 72

Step-by-step explanation:

since the product of the two is 72, it's true that xy = 72. and it is also true that x is equal to five times y minus 2, so you can rewrite x as 5y-2. plug that in for x in the first equation, and you're set. hope this helps :)

9514 1404 393

Answer:

  6

Step-by-step explanation:

Work backward.

If he has 24 after adding 6, he had 18 before that addition.

If he had 18 after tripling his collection, he had 18/3 = 6 cards to start with.

__

Note that this is the same process you would use if you started with an equation.

  3c +6 = 24 . . . . where c is the number of cards Johnny started with

  3c = 24 -6 = 18 . . . . . subtract 6 from the final number

  c = 18/3 = 6 . . . . . . . . divide the tripled value by 3 to see the original value

Johnny started with 6 cards.

Answer:

less than or equal to -26

Answer:

9+c < 15

OR

c < 6

Step-by-step explanation:

"the sum of 9 and c" means: 9+c

"is less than or equal to 15" means: < 15

If you need to simplify it, then subtract 9 from both sides, and you get

c < 6

Answer:

8 suits

Step-by-step explanation:

Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then

30 ÷ 3.75 = 8

Then 8 suits can be made from 30 m of cloth

Step-by-step explanation:

3x-2x=5+10 [taking variables on one side and constant on other]

x=15

soln:

3x-5= 2x+10

3x -5+5=2x+10+5 [ adding 5 on both side]

3x=2x+15

3x-2x=2x+15-2x [subtracting 2x on both side]

x=15

Ans=15

Answer:

[tex]x = 15[/tex]

Step-by-step explanation:

[tex]3x - 5 = 10 + 2x[/tex]

[tex]3x - 2x = 10 + 5[/tex]

[tex]1x = 15[/tex]

[tex]x = 15[/tex]

Answer:

12

Step-by-step explanation:

10 - 1/2 x = 12-4/3x

60 - 3x = 72-2x

-12 = - x

Answer:

Hence the correct option is 3rd option. 40

Step-by-step explanation:

If two figures are similar, then the ratio of the corresponding sides is proportional.

[tex]\frac{15}{30} =\frac{20}{n} \\\\n=\frac{30 \times 20}{15} \\\\n= 40.[/tex]

Answer:

Step-by-step explanation:

[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]

= -5x² + 25xy + xy - 5y²

= 5x(-x + 5y) - y(-x +5y)

= (-x + 5y)(5x - y)

Answer:

a = 0.0040 m/s², v = 14.4 m/s.

Step-by-step explanation:

Given that,

The distance between Kathmandu and Khanikhola, d = 26 km = 26000 m

Time, t = 1 hour = 3600 seconds

Let a is the acceleration of the bus. Using second equation of motion,

[tex]d=ut+\dfrac{1}{2}at^2[/tex]

Where

u is the initial speed of the bus, u = 0

So,

[tex]d=\dfrac{1}{2}at^2\\\\a=\dfrac{2d}{t^2}\\\\a=\dfrac{2\times 26000}{(3600)^2}\\\\a=0.0040\ m/s^2[/tex]

Now using first equation of motion.

Final velocity, v = u +at

So,

v = 0+0.0040(3600)

v = 14.4 m/s

Hence, this is the required solution.

Answer:

[tex]P(X = 0) = 0.03125[/tex]

[tex]P(X = 1) = 0.15625[/tex]

[tex]P(X = 2) = 0.3125[/tex]

[tex]P(X = 3) = 0.3125[/tex]

[tex]P(X = 4) = 0.15625[/tex]

[tex]P(X = 5) = 0.03125[/tex]

Step-by-step explanation:

For each toss, there are only two possible outcomes. Either it is tails, or it is not. The probability of a toss resulting in tails is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

5 tosses:

This means that [tex]n = 5[/tex]

Probability distribution:

Probability of each outcome, so:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]

[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]

[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]

[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]

[tex]P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625[/tex]

[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]

Answer:

[tex]\log_{10}(147) = 2.1673[/tex]

Step-by-step explanation:

Given

[tex]\log_{10} 3 = 0.4771[/tex]

[tex]\log_{10} 5 = 0.6990[/tex]

[tex]\log_{10} 7= 0.8451[/tex]

[tex]\log_{10} 11 = 1.0414[/tex]

Required

Evaluate [tex]\log_{10}(147)[/tex]

Expand

[tex]\log_{10}(147) = \log_{10}(49 * 3)[/tex]

Further expand

[tex]\log_{10}(147) = \log_{10}(7 * 7 * 3)[/tex]

Apply product rule of logarithm

[tex]\log_{10}(147) = \log_{10}(7) + \log_{10}(7) + \log_{10}(3)[/tex]

Substitute values for log(7) and log(3)

[tex]\log_{10}(147) = 0.8451 + 0.8451 + 0.4771[/tex]

[tex]\log_{10}(147) = 2.1673[/tex]

Answer:

0.7246 radians

Step-by-step explanation:

According to the Question,

Given that, a rectangle box has length 12 inches, width 15 inches, and a height of 17 inches

d = √{ (12)² +(15)² }  = √(144+225) = √369inches

 Tan∅ = 17/√369

Taking the [tex]Tan^{-1}[/tex] , we have

∅ = [tex]Tan^{-1}[/tex](17/√369) ≈ 0.7246 radians

Answer:

5/11.... you put the 5 which is yellow over the others which is 12 but remember she removed 1 so it would be equal to 11

Answer:

ok so if she takes a red apple out that means

2 red

5 yellow

4 green

11 in total

so 5/11

The answer is D

Hope This Helps!!!

Answer:

g(x) is obtained by shift the function f(x) down 7 units by subtracting 7 units from f(x).

Step-by-step explanation:

We are given that

[tex]g(x)=f(x)-7[/tex]

We have to identify  the transformation that occurs to create the graph of g(x).

To identify  the transformation that occurs to create the graph of g(x)

We will subtract the 7 from f(x).

Let f(x) be any function

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

It means g(x) obtained by  shift the function f(x) down  k units by subtracting k units from f(x).

Therefore, g(x) is obtained by shift the function f(x) down 7 units by subtracting 7 units from f(x).

Answer:

χ² = 4.80

Pvalue = 0.1874

Step-by-step explanation:

Given :

Category Observed (Expected)

A 25 (20)

B 35(40)

C 50(60)

D 90(80)

The Chisquare statistic (χ²) is given by :

χ² = Σ(observed - Expected)² / Expected

χ² = (25-20)²/20 + (35-40)/40 + (50-60)²/60 + (90-80)²/80

χ² = 1.25 + 0.625 + 1.67 + 1.25

χ² = 4.795

χ² = 4.80 (2 decimal places)

Using the Chisquare Pvalue calculator :

df = n - 1 = 4 - 1 = 3

Pvalue = 0.1874

Answer:

Domain= {x:x £|R}

|R=any real number

(a) The region Y₁ < 1/2 and Y₂ > 1/4 corresponds to the rectangle,

{(y₁, y₂) : 0 ≤ y₁ < 1/2 and 1/4 < y₂ ≤ 1}

Integrate the joint density over this region:

[tex]P\left(Y_1<\dfrac12,Y_2>\dfrac14\right) = \displaystyle\int_0^{\frac12}\int_{\frac14}^1 (y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac{21}{64}}[/tex]

(b) The line Y₁ + Y₂ = 1 cuts the support in half into a triangular region,

{(y₁, y₂) : 0 ≤ y₁ < 1 and 0 < y₂ ≤ 1 - y₁}

Integrate to get the probability:

[tex]P(Y_1+Y_2\le1) = \displaystyle\int_0^1\int_0^{1-y_1}(y_1+y_2)\,\mathrm dy_2\,\mathrm dy_1 = \boxed{\dfrac13}[/tex]

Y₁ and Y₂ are not independent because

P(Y₁ = y₁, Y₂ = y₂) ≠ P(Y₁ = y₁) P(Y₂ = y₂)

To see this, compute the marginal densities of Y₁ and Y₂.

[tex]P(Y_1=y_1) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_2 = \begin{cases}\frac{2y_1+1}2&\text{if }0\le y_1\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]P(Y_2=y_2) = \displaystyle\int_0^1 f(y_1,y_2)\,\mathrm dy_1 = \begin{cases}\frac{2y_2+1}2&\text{if }0\le y_2\le1\\0&\text{otherwise}\end{cases}[/tex]

[tex]\implies P(Y_1=y_1)P(Y_2=y_2) = \begin{cases}\frac{(2y_1+1)(2y_2_1)}4&\text{if }0\le y_1\le1,0\ley_2\le1\\0&\text{otherwise}\end{cases}[/tex]

but this clearly does not match the joint density.

Answer:   6.1% decrease

Note: It appears that your teacher doesn't want you to type in the percent sign, as that's already covered for you.

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

Explanation:

The salary decreased by 51500-48355 = 3145

Divide this over the initial salary to get 3145/51500 = 0.0611 which is approximate.

This converts to the percentage 6.11% and that rounds to 6.1%

----------------

As an alternative, you can use the formula method below

A = old value = 51500

B = new value = 48355

C = percent change when going from A to B

C = [ (B-A)/A ] * 100%

C = [ (48355-51500)/51500 ] * 100%

C = (-3145/51500)*100%

C = -0.0611*100%

C = -6.11%

C = -6.1%

The negative C value indicates a percent decrease.

Answer:

x2 - 4x - 5 factored form is (x - 5)(x + 1)

Answer:

(x − 5)(x + 1)

Step-by-step explanation:

The answer above is correct.