Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2100. What was the rate charged per hour by each mechanic if the sum of 2 rates was $190 per hour?

Using it's concept, it is found that the probability that an ID code does not contain the letter I is given by:

A. 0.9246

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering that for each letter there are 26 possible outcomes and for each digit there are 10 possible outcomes, the total number of outcomes is given by:

T = 26 x 26 x 10 x 10 x 10 x 10 = 6,760,000.

Without the letter "l", the desired number is given by:

D = 25 x 25 x 10 x 10 x 10 x 10 = 6,250,000.

Hence, the probability is given by:

p = 6,250,000/6,760,000 = 0.9246.

Which means that option A is correct.

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

If we look at this spinner, we first need to find out how many letters there are in total.

There are 12 letters in total.

1.

For this question, they want us to find the probability of getting the letter 'R'.

We need to find how many letter 'R's there are.

There are 2 lettered 'R', out of the 12 letters.

So the probability of getting the letter 'R' is 2/12 which simplifies to 1/6.

2.

For this question, they want us to find the probability of getting the letter 'L'.

We need to find how many letter 'L's there are.

There are 3 lettered 'L's, out of the 12 letters.

So the probability of selecting the letter 'L' is 3/12 which simplifies to 1/4.

3.

For this question, they want us to find the probability of getting the letter 'B'.

We need to find how many letter 'B's there are.

There are 0 lettered 'B's, out of the 12 letters.

Therefore the probability of selecting the letter 'B' is impossible.

4.

For this question, they want us to find out which letter has the most likely chance of getting landed on.

In order to find this, we need to find one letter that is repeated a lot in this spinner, that way it is more likelier of getting that letter.

Let's look at each individual letter keeping the letters we've found so far to the side.

P(Z) = 4/12, which simplifies to 1/3.

P(S) = 1/12, which is already in simplest form.

P(F) = 2/12, which simplifies to 1/6.

Now let's compare all the probabilities for selecting each letter.

P(R) = 1/6

P(L) = 1/4

P(B) = impossible ← immediately eliminate this choice

P(Z) = 1/3

P(S) = 1/12

P(F) = 1/6

Now out of all of these probabilities, we can infer that the chances of getting the letter 'Z' is the most likeliest.

Answer:

x=3
y=12

Step-by-step explanation:

The scale factor is 1:4

we divide 12 by 4 to get 3

if we multiply 3 by 4 it is 12 so y=12

Answer:

Step-by-step explanation:

Time to complete each of jobs

Total time at job

If the work day lasts for 8 hours, then Lana has only 1/4 hr to travel between jobs and a lunch break.  

This time is not sufficient so she can't complete all the jobs.

Answer:

No (see explanation below)

Step-by-step explanation:

Approximate times to carry out each job:

For one Saturday, Lana needs to:

Therefore, the total time for the jobs is:

[tex]\begin{aligned}\sf Total\:time & = \sf 3\:small\:lawns+1\:large\:lawn+2\:tidy\:yards+1\:plant\:annuals\\\\& = \sf 3 \cdot \dfrac{1}{2}+\dfrac{3}{4}+2 \cdot 1 \frac{1}{2}+2\frac{1}{2}\\\\& = \sf 1 \frac{1}{2}+\dfrac{3}{4}+3+2\frac{1}{2}\\\\& =\sf 7 \frac{3}{4}\: hours\end{aligned}[/tex]

The likelihood of Lana being able to complete all the jobs in one day is dependent on how far she needs to travel between jobs and how long she wishes to break for lunch.  A typical working day is around 8 hours. Therefore, unless Lana wishes to work for a longer day, it is unlikely she will be able to complete all of the jobs in one day as there is only 15 minutes available for traveling and lunch, which is likely not enough.

Answer:

Formula for volume of cylinder;

V = π[tex]r^{2}[/tex]h

Where 'π' is pi(22/7 or 3.14), 'r' is the radius which is being squared, and 'h' represents the height.

Plug in your values given that;

8 in. = height

4 in. = radius

V = π[tex]r^{2}[/tex]h

V = 3.14(4^2) x 8

V = 3.14(16) x 8

V = 50.24 x 8

V = 401.92 cubic inches or [tex]401.92^{3}[/tex] inches is the volume.

Answer:

Yes it does!

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Answer:

183 cm^2

Step-by-step explanation:

the line through the shape line means that they are equivalent meaning the side that is empty not making the trapezoid would be 9 as well. moving the 3 over since it is right next to it. 3 times 9 equal 27cm^2. later we are gonna use this number to subtract

then make a different equation with 3+9 to the the full height of the trapezoid pretending it is not missing anything. 3+9=12

then use the formula to find the area of the trapezoid which is 1/2(h)(b1+b2)

add the 2 bases together to get 35. how did i get 35. 12+14=26 yes then include the 9 to get 35.

1/2(height=12)(35)=6(35)=210cm^2

then you used 210-27 to get 183cm^2

Answer:

B

Step-by-step explanation:

The 1st quartile is 135. The 3rd quartile is 195. To find the interquartile, you would subtract the 3rd quartile from the 1st quartile. 195-135=60. The interquartile range for the spring musical is 60

Answer:

N = 35

Step-by-step explanation:

The pattern in this sequence is x3, +2.

3 * 3 = 9

9 + 2 = 11

11 * 3 = 33

33 + 2 = N

N * 3 = 105

N = 33 + 2 = 105/3 = 35

Answer:

|x - 8| = 6

Step-by-step explanation:

   |x - b| = c

⇒ (x - b)² = c²

Given:

Substitute the values of x into (x - b)² = c²:

(2 - b)² = c²

(14 - b)² = c²

Equate and solve for b:

(2 - b)² = (14 - b)²

⇒ 4 - 4b + b² = 196 - 28b + b²

⇒ 4 - 4b = 196 - 28b

⇒ 24b = 192

⇒ b = 8

Substitute b = 8 into the equations to find c:

x = 2 ⇒ |2 - 8| = 6

x = 14 ⇒ |14 - 8| = 6

Therefore, c = 6

Final equation:  |x - 8| = 6

Answer:

Question 1

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, or a right triangle)

Given:

⇒ BC² + 8² = 10²

⇒ BC² = 36

⇒ BC = 6 cm

Question 2

Given:

⇒ MB = AB - AM = 8 - x

As ΔABC ~ ΔMBN

⇒ AB : AC = MB : MN

⇒ 8 : 10 = (8 - x) : MN

[tex]\sf \implies \dfrac{8}{10}=\dfrac{(8-x)}{MN}[/tex]

[tex]\sf \implies \dfrac45=\dfrac{(8-x)}{MN}[/tex]

[tex]\sf \implies MN=\dfrac54(8-x)[/tex]

Question 3

D = (6, 8)

As ΔBAD ~ ΔMAP

⇒ AB : AD : BD = AM : AP : MP

⇒ 8 : 6 : 10 = x : AP : MP

[tex]\sf \implies \dfrac{8}{6}=\dfrac{x}{AP}[/tex]

[tex]\sf \implies AP=\dfrac34x[/tex]

[tex]\sf \implies \dfrac{8}{10}=\dfrac{x}{MP}[/tex]

[tex]\sf \implies MP=\dfrac54x[/tex]

Question 4

Perimeter of MNCDP = MN + NC + CD + PD + MP

As ΔABC ~ ΔMBN

⇒ AB : BC : AC = MB : BN : MN

⇒ 8 : 6 = (8 - x) : BN

[tex]\sf \implies \dfrac86=\dfrac{(8-x)}{BN}[/tex]

[tex]\sf \implies BN=\dfrac34(8-x)[/tex]

NC = BC - BN

[tex]\sf \implies NC=6-\dfrac34(8-x)[/tex]

PD = 6 - AP

[tex]\sf \implies PD=6-\dfrac34x[/tex]

Perimeter of MNCDP = MN + NC + CD + PD + MP

[tex]\sf \implies perimeter=\dfrac54(8-x)+6-\dfrac34(8-x)+8+6-\dfrac34x+\dfrac54x[/tex]

[tex]\sf \implies perimeter=10-\dfrac54x+6-6+\dfrac34x+8+6-\dfrac34x+\dfrac54x[/tex]

[tex]\sf \implies perimeter=10+8+6=24[/tex]

Answer:

Step-by-step explanation:

[tex]A=P(1+\frac{r}{n})^{nt[/tex]

A = future value ($)

P = principal (orignal amount - $400)

R = rate (written as a decimal - 3%/100= 0.03)

N = compound (yearly - 1)

T = number of years (0, 5, 10, 15)

Now, substitute each number into the formula and record them in the table.

0 years:

[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*0}\\\\A=400(1+\frac{0.03}{1})^0 < ==any\ number\ raised\ to\ zero=1\\\\A=400(1)\\\\A=\$400[/tex]

5 years:

[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*5}\\\\A=400(1+\frac{0.03}{1})^{5}\\\\A=400(1+{0.03})^{5}\\\\A=400({2.03})^{5}\\\\A=400({1.1593})\\\\A=\$463.72 < ==round\ to\ the\ nearest\ dollar\\\\A=\$464[/tex]

10 years:

[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*10}\\\\A=400(1+\frac{0.03}{1})^{10}\\\\A=400(1+{0.03})^{10}\\\\A=400({1.03})^{10}\\\\A=400({1.3439})\\\\A=\$537.56 < ==round\ to\ the\ nearest\ dollar\\\\A=\$538[/tex]

15 years:

[tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*15}\\\\A=400(1+\frac{0.03}{1})^{15}\\\\A=400(1+{0.03})^{15}\\\\A=400({1.03})^{15}\\\\A=400({1.5579})\\\\A=623.16 < ==round\ to\ the\ nearest\ dollar\\\\A=\$623[/tex]

20 years:

 [tex]A=P(1+\frac{r}{n})^{nt}\\\\A=400(1+\frac{0.03}{1})^{1*20}\\\\A=400(1+\frac{0.03}{1})^{20}\\\\A=400(1+{0.03})^{20}\\\\A=400({1.03})^{20}\\\\A=400({1.8061})\\\\A=722.44 < ==round\ to\ the\ nearest\ dollar\\\\A=\$722[/tex]

Note that since we are rounding, answers may vary by a dollar or two.

Hope this helps!

The given expression [tex]\rm 12x^2-13x+3[/tex]equivalent to (3x - 1)(4x - 3) option second is correct.

A quadratic expression is a second-degree algebraic expression represented by the:

[tex]\rm f(x)=ax^2+bx+c[/tex] ........(1)

Where a, b, and c are the constants and  

We have the quadratic expression:

[tex]\rm f(x)=12x^2-13x+3[/tex]

[tex]\rm f(x)=12x^2-9x-4x+3[/tex]  (we can write -13x as a sum of -9x and -4x)

After taking common term, we get:

[tex]\rm f(x)=3x(4x-3)-(4x-3)[/tex]

[tex]\rm f(x)=(4x-3)(3x-1)[/tex]  or

[tex]\rm f(x)=(3x-1)(4x-3)[/tex]

Thus, the given expression [tex]\rm 12x^2-13x+3[/tex]  is equivalent to (3x - 1)(4x - 3).

Learn more about quadratic equations here:

brainly.com/question/2263981

Answer:

7918

Step-by-step explanation:

If you round Earth's diameter, I believe that it is 7,918 miles.

Now

Comparing to the standard equation, the parabola with a vertex at (-2,0) is given by:

y = (x + 2)²

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, we have that h = -2 and k = 0, and all the options have leading coefficient a = 1, hence the equation is:

y = (x + 2)²

More can be learned about the equation of a parabola at https://brainly.com/question/17987697

Answer:

Answer:

  9 cm²

Step-by-step explanation:

Sometimes these inscribed polygon problems respond nicely to a little geometrical thinking. The figure is symmetrical about the vertical line through the center of the square(s).

__

That line of symmetry divides the figure into halves that are twice as tall as wide. That same ratio applies to both the outer square and the inner (blue shaded) square.

In other words, a line from the center of the top segment through either bottom corner of the figure will pass through the corners of both squares. That line will have a slope of ±2, making it easy to find the coordinates of one of the lower corners of the shaded square.

__

Analytically, we can write the equation of the right circle shown in the attachment as ...

  x² +y² = 5²

and the equation of the line as ...

  y = 2x +5

__

Then the x-value of the lower left corner will be found where these intersect.

  x² +(2x +5)² = 25 . . . . . . substitute for y

  x² +4x² +20x +25 25 . . . . eliminate parentheses

  5x² +20x = 0 . . . . . . . . . . . . subtract 25

  5x(x +4) = 0 . . . . . . factor

  x = -4 or 0 . . . . . the x-coordinates of the points of intersection

The y-coordinate of the lower left point is ...

  y = 2(-4) +5 = -3

__

Since the top edge of the blue square has a y-coordinate of 0, this means the square is 3 cm on a side. Its area is ...

  A = s² = (3 cm)² = 9 cm² . . . . area of the blue shaded square

Answer:

A = 390

Step-by-step explanation:

l=14

w= 3

h= 9

A= 2 (wl+hl+hw) = 2 (3.14+9.14+9.3) = 390

Answer: 390in^2

Step-by-step explanation:

2(14 x 3) + 2(9 x 3) + 2(14 x 9)

84 + 54 + 252 = 390 in^2

It will take approximately 282.352 hours for one to go round the earth, this is equivalent to 11.764 days

Given Data

We know that the relationship between speed, distance and time is given as

Speed = Distance/Time

Hence,

Time = Distance/Speed

Substituting our given data into the expression we have

Time = 2.4x10^4/8.5x10

Time = 2.4x10^3/8.5

Time = 282.352 hours

Learn more about speed, distance and time here:

https://brainly.com/question/4931057

Answer:

42 ft²

Step-by-step explanation:

→ State the area of the formula of rectangle

Length × Width

→ Substitute in the numbers

14 × 3 = 42 ft²

Answer:

42 sq ft

Step-by-step explanation:

L*W=A
14*3=42

Answer: 1

Step-by-step explanation: the lowest number they divide into evenly is 1

Answer:

Hiroko removed common factors, which leads to smaller numbers, which can be easier to work with.

Step-by-step explanation:

However, this step is not entirely needed in the grand scheme of solving the problem. It simply uses smaller numbers to digest.

Do the opposite of PEMDAS when isolating the variable, d. Note the equal sign, what you do to one side of the equal sign, you do to the other.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)
Multiplication

Division

Addition

Subtraction.

First, subtract 490 from both sides of the equation:

10d + 490 (-490) = 2500 (-490)

10d = 2500 - 490

10d = 2010

Next, divide 10 from both sides of the equation:

(10d)/10 = (2010)/10

d = 2010/10

d = 201

201 is your value for d.

~

Answer:

[tex](x + 2) ^{2} = - 8[/tex]

Step-by-step explanation:

[tex] {x}^{2} + 4x + 8 = 0 \\ {x }^{2} + 4x = - 8 \\ {x}^{2} + 4x + 4 = - 8 + 4 \\ ( x + 2)^{2} = - 4[/tex]

Answer:

6.47

Step-by-step explanation:

1.99/1 lb= x/3.25lb

3 1/4=3.25

Cross multiply

X=(1.99)(3.25)=6.47

Answer:

73.81

Step-by-step explanation:

You know that the formula for circumeference is 2(pi)r.

2x3.14x11=69.08;

However, a part of the circle is cut off, leaving 3/4 of it.

3/4x69.08=51.81.

However, you add the 11+11 to it because of the slice.

22+51.81=73.81

Answer:

25 degrees

Step-by-step explanation:

complementary angles are 90 degrees

90-65=25 degrees

Answer:

55 degrees

Step-by-step explanation:

well, x is on the same line as 125, and a line is always a straight 180 degrees, so you subtract 180-125=55, and angle x and angle y are corrisponding angles, so y also equals 55 degrees.

hope that helps!

Answer:

T is not a function.

Step-by-step explanation:

The definition of a function is a relationship where only one x value has a specific y value. So if an x-value has more than one y value, it is not a function due to its rule. This can also be checked by using a graph, graphing the function, and checking if it fits the vertical line test.

We see all of them work except T, where 2 x values are stated that are the same but have different y values.

So T is not a function.

I hope this helped!

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Answer:

722.5792 cm²

Step-by-step explanation:

1 in ≈ 2.54 cm

Squaring both sides:

⇒ (1 in)² ≈ (2.54 cm)²

Apply exponent rule (ab)² = a²b²

⇒ (1)² in² ≈ (2.54)² cm²

⇒ 1 in² ≈ 6.4516 cm²

Therefore, to convert an area measured in inches squared to centimeters squared, multiply by 6.4516:

⇒ 112 in² ≈ (112 × 6.4516) cm²

               = 722.5792 cm²