adding and subtracting mixed numbers
1/4 + 1/2​

The distance covered by a scout is 24.96 meters.

The given information is that a scout steps off a distance of 48 steps and each step is 52 cm.

We need to calculate the distance in meters.

Therefore, to find the solution to the given question, we will first calculate the total distance the scout covered.

Step 1:

Calculation

The distance covered by scout = Number of steps × Length of each step

Distance covered = 48 × 52 cm

Distance covered = 2,496 cm

Step 2:

Conversion

The obtained value is in centimeters, and we need to convert it into meters as per the question.

1 meter = 100 cm

Therefore,

distance in meters = Distance in cm / 100distance in meters

                               = 2,496 cm / 100distance in meters

                               = 24.96 meters

Therefore, the distance covered by a scout is 24.96 meters.

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Answer:

Step-by-step explanation:

5z=75

5z/5=75/5

z=15

Answer:

2y=8

Step-by-step explanation:

your goal is to get y by itself

so you divide by 2 on both sides.

8 divided by 2 is 4.

y=4

A graph of the resulting image after the given triangle is rotated 90° counterclockwise about the origin is shown in the image below.

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle ABC, the coordinates of the vertices of the image are as follows:

(x, y)                               →            (-y, x)

Ordered pair A  = (-5, 7) → Ordered pair A' = (-(7), -5) = (-7, -5).

Ordered pair B  = (-8, 3) → Ordered pair B' = (-(3), -8) = (-3, -8).

Ordered pair C  = (-2, 6) → Ordered pair C' = (-(6), -2) = (-6, -2).

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(a) To calculate the probability of the first miss occurring after 12 attempts, we need to consider the scenario in which the shooter makes the first 11 shots and then misses the 12th shot. The probability of making a free throw is given as p = 0.9.

The probability of making a shot is 0.9, so the probability of missing a shot is 1 - 0.9 = 0.1. Therefore, the probability of making 11 shots in a row is (0.9)^11.

The probability of missing the 12th shot is 0.1. Since these events are independent, we can multiply the probabilities together. Therefore, the probability of making the first 11 shots and missing the 12th shot is (0.9)^11 * 0.1.

Therefore, the probability of having the first miss after 12 attempts is (0.9)^11 * 0.1.

(b) To calculate the probability that the third miss occurs on the 30th attempt, we need to consider the scenario in which the shooter makes the first 29 shots and then misses the 30th shot.

The probability of making a shot is 0.9, so the probability of missing a shot is 1 - 0.9 = 0.1. Therefore, the probability of making 29 shots in a row is (0.9)^29.

The probability of missing the 30th shot is 0.1. Since these events are independent, we can multiply the probabilities together. Therefore, the probability of making the first 29 shots and missing the 30th shot is (0.9)^29 * 0.1.

However, we also need to consider that the shooter must miss the first two shots before reaching the 30th attempt. The probability of missing two shots in a row is (0.1)^2.

Therefore, the probability that the third miss occurs on the 30th attempt is (0.9)^29 * 0.1 * (0.1)^2.

Note that these calculations assume that each shot is independent of the others and that the shooter's probability of making a shot remains constant throughout the attempts.

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Answer:

1 hour

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

So to do this problem, first find the area of the figure before you apply the scale factor, and then multiply that by 49. The reason you multiply it by 49 and not 7 is because you're multiplying both the length and the width of the figure by 7, so you have 7 * 7 = 49.

The area of the figure to start is 10 (you can find this by simply counting the blocks).

Then, 10 * 49 = C. 490 units squared.

hope that makes sense!

Answer:

x = 18

∠A = 83

Step-by-step explanation:

Since you have a line intersecting two parallel lines, the angles formed from the intersection will be equal to 180.  This means that you can add up the two angle measures and set them equal to 180.

(6x - 35) + (3x + 53) = 180

6x - 35 + 3x + 53 = 180

9x + 18 = 180

(9x + 18) - 18 = 180 - 18

9x = 162

x = 18

Now to solve for ∠A, plug in the x-value and solve.

∠A = 6x - 35

∠A = 6(18) - 35

∠A = 118 - 35

∠A = 83

Answer:

1 I don't know if those are questions but try if they are try the first one a

Answer:

(a)  a = 10 m s⁻²

(b)  s = 1500 m

(c)  a = 2 m s⁻²

(d)  s = 4400 m or 3600 m (see below for explanation)

Step-by-step explanation:

\(\boxed{\begin{minipage}{9 cm}\underline{The Constant Acceleration Equations (SUVAT)}\\\\s = displacement in m (meters)\\u = initial velocity in m s$^{-1}$ (meters per second)\\v = final velocity in m s$^{-1}$ (meters per second)\\a = acceleration in m s$^{-2}$ (meters per second per second)\\t = time in s (seconds)\\\\When using SUVAT, assume the object is modeled\\ as a particle and that acceleration is constant.\end{minipage}}\)

Given:

\(\begin{aligned}\textsf{Using }\:\:v & = u+at\\\\\sf \implies 200 & = \sf 100+10a\\\sf 200-100 & = \sf 10a\\\sf 10a & = \sf 100\\ \sf a & = \sf 100 \div 10\\\sf a & = \sf 10 \:\: m\:s^{-2}\end{aligned}\)

Given:

\(\begin{aligned}\textsf{Using }\:\: s & = \dfrac{1}{2}(u+v)t\\\\\implies s & = \sf \dfrac{1}{2}(100+200)(10)\\& = \sf 5(300)\\& = \sf 1500 \:\: m\end{aligned}\)

Given:

\(\begin{aligned}\textsf{Using }\:\:v & = u+at\\\\\sf \implies 240& = \sf 200+20a\\\sf 240-200 & = \sf 20a\\\sf 20a & = \sf 40\\ \sf a & = \sf 40\div 20\\\sf a & = \sf 2\:\: m\:s^{-2}\end{aligned}\)

It is not clear from the question if the distance the plane travels is:

Therefore, I have calculated both.

Distance the plane travels in the next 20 seconds

(i.e. from 10 to 30 seconds)

Given:

\(\begin{aligned}\textsf{Using }\:\: s & = \dfrac{1}{2}(u+v)t\\\\\implies s & = \sf \dfrac{1}{2}(200+240)(20)\\& = \sf 10(440)\\& = \sf 4400\:\: m\end{aligned}\)

Distance the plane travels in the first 20 seconds

This is the sum of the distance the plane travels in the first 10 seconds (from part b) and the distance the plane travels in the next 10 seconds (so between 10 and 20 seconds).

Given:

\(\begin{aligned}\textsf{Using }\:\: s & = ut+\dfrac{1}{2}at^2\\\\\implies s & = \sf (200)(10)+ \dfrac{1}{2}(2)(10)^2\\& = \sf 2000+100\\& = \sf 2100\:\: m\end{aligned}\)

Therefore, the distance the plane travels in the first 20 seconds of its journey is:

= 1500 m + 2100 m = 3600 m

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Using a system of equations, the quantity of Type A coffee that Trey's Coffee Shop blended with Type B coffee was 78 pounds.

A system of equations or simultaneous equations is two or more equations solved concurrently, simultaneously, or at the same time.

Unit Cost Per Pound:

Type A coffee = $5.80

Type B coffee = $4.25

The total quantity of pounds of the blend = 142 pounds

The total cost of 142 pounds = $724.40

Let the number of Type A coffee = x

Let the number of Type B coffee = y

x + y = 142 ... Equation 1

5.8x + 4.25y = 724.40 ... Equation 2

Multiply Equation 1 by 4.25:

4.25x + 4.25y = 603.5 ... Equation 3

Subtract Equation 3 from Equation 2:

5.8x + 4.25y = 724.40

-

4.25x + 4.25y = 603.5

1.55x = 120.9

x = 78

Substitute x = 78 in either equation:

x + y = 142

78 + y = 142

y = 64

Thus, 78 pounds of Type A coffee was used for the mixture.

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Answer:

11

Step-by-step explanation:

Answer:11

Step-by-step explanation:

because you have to create the equation and solve

Given the following question:

Point A = (7, 4) = (x1, y1)

Point B = (3, 6) = (x2, y2)

To find the slope use rise over run:

m = -0.5

We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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\(\sqrt[4]{567x^9 y^{11}} ~~ \begin{cases} 567=3\cdot 3\cdot 3\cdot 3\cdot 7\\ \qquad ~~ ~ 3^4\cdot 7\\ x^9=x^{4+4+1}\\ \qquad ~x^4\cdot x^4\cdot x\\ y^{11}=y^{4+4+3}\\ \qquad ~~ y^4\cdot y^4\cdot y^3 \end{cases}\implies \sqrt[4]{3^4\cdot 7 \cdot x^4\cdot x^4\cdot x\cdot y^4\cdot y^4\cdot y^3}\)

\(\left( 3^4\cdot 7 \cdot x^4\cdot x^4\cdot x\cdot y^4\cdot y^4\cdot y^3\right)^{\frac{1}{4}}\implies 3^{\frac{4}{4}}\cdot 7^{\frac{1}{4}}\cdot x^{\frac{4}{4}}\cdot x^{\frac{4}{4}}\cdot x^{\frac{1}{4}}\cdot y^{\frac{4}{4}}\cdot y^{\frac{4}{4}}\cdot y^{\frac{3}{4}}\)

\(3\cdot 7^{\frac{1}{4}}\cdot x\cdot x\cdot x^{\frac{1}{4}}\cdot y\cdot y\cdot y^{\frac{3}{4}}\implies 3x^2y^2\cdot 7^{\frac{1}{4}}x^{\frac{1}{4}} y^{\frac{3}{4}} \implies 3x^2y^2(7xy^3)^{\frac{1}{4}} \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x^2y^2\sqrt[4]{7xy^3} \end{array}}~\hfill\)

The value of x in the solution set of the inequality is -4.

Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.

We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).

9(2x+1) < 9x - 18

2x+1 < x - 2

2x < x - 3

x < -3

This means that x can be any value less than -3 (but not equal to -3 since the sign is < and not ≤) . Hence, the answer is -4.

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Answer:

-4

Step-by-step explanation:
taking  test

Answer:

3x(to the 2nd) + 19x-40

Step-by-step explanation:

Answer:

3x^2+19x-40

Step-by-step explanation:

distribute the parenthesis

so 3x*x and 3x*8

which gives you

3x^2+24x

distribute the -5

-5*x and -5*8

which gives you

-5x-40

now put thos together

3x^2+24x-5x-40

combine like terms

3x^2+19x-40

Answer:

42

Step-by-step explanation:

You get 42 by looking at the denominators 7 and 21. You times by 3 to get from 7 to 21, so you times 14 by 3 to get n, which is 42.

Answer:

42

Step-by-step explanation:

On the bottom 7 was multiplied by 3 so you would do the same to 14.

The amount made by Caroline is $593.75 and 200 + 0.25x when she made $1574 and $x in sales respectively.

The total amount will be given by the formula using percentage -

Total amount = Base salary + 25% × her total sales

Keep the value in equation when she made $1575

Total amount = 200 + 25% × 1575

Total amount = 200 + 393.75

Total amount = $593.75

Keep the value in equation when she made $x

Total amount = 200 + 25% × x

Total amount = 200 + 0.25x

Hence, the earned amount is $593.75 and 200 + 0.25x.

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The complete question is -

Caroline works in a department store selling clothing. She makes a guaranteed salary of $200 per week, but is paid a commision on top of her base salary equal to 25% ofher total sales for the week. How much would Caroline make in a week in which she made $1575 in sales? How much would Caroline make in a week if she made x dollars in sales?

Answer:

v3+2v2−21v+21/v+6

Step-by-step explanation:

There are no solutions to this equation

Answer:

-31 feet

Step-by-step explanation:

so, -25 is the start point.

he goes anither -13 feet, so hes at -38.

he rises 7 feet, so hes at -31 feet.

Answer:

x= -16

Step-by-step explanation:

distribute -2

-2 * 2x =-4x

-2 * 5 = -10

-4x - 10 -3 = -3 (x-1)

distribute -3

-3 * x = -3x

-3 * -1 = 3

-4x - 10 -3 = -3x + 3

combine like terms

-4x -13 = -3x + 3

-4x + 3x = -x

3 + 13 = 16

-x = 16

divide by -1

x = -16

Answer:

x = -16

Step-by-step explanation:

-2(2x + 5) - 3 = -3(x - 1)

-4x - 10 - 3 = -3x + 3

-4x - 13 = -3x + 3

-x = 16

x = -16   <--- This is the answer

Hope this helps!

Answer:

b

Step-by-step explanation:

I got it right on the quiz

Answer:

It is 53

Step-by-step explanation:

I dont know

Answer:

1

Step-by-step explanation:

Answer:

\(-35\)

Step-by-step explanation:

Finding the remainder using the Remainder Theorem

\(f(-2) = 5(-2)^3 -4(-2) -3 \\ f(-2) = 5(-8) -4(-2) -3 \\ f(-2) = -40 +8 -3 \\ f(-2) = -35\)

Please refer to my answer from this question to know more about the Remainder Theorem.

You may be wondering why did I make \(a = -2\) and not \(a = 2\). Notice that the Theorem states when we divide \(P(x)\) by \(x -a\) the remainder is \(P(a)\). In this case we are dividing by \(x \red{+} 2\) in which we can rewrite it as \(x -(\blue{-2})\).

The probability that on exactly one of these three occasions the voter approves of the mayor's work is given as follows:

0.189 = 18.9%.

The mass probability formula, giving the probability of x successes, is of:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are given by:

The values of these parameters in the context of this problem are given as follows:

n = 3, p = 0.7.

Then the probability of exactly one success is calculated as follows:

P(X = 1) = 3!/(1!2!) x 0.7 x (0.3)² = 0.189 = 18.9%.

The proportion of voters that approve the mayor's work is of 70%.

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Answer:

use a calculator

Step-by-step explanation:

Answer:

It would be B.

Please let me know if I'm incorrect!