Frame three equations with solution x=-5

Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.

Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter

Time taken by Peter = 2PM - 10AM

= 4 hrs

Speed of Peter = 84 km/h

Distance travelled by Peter = speed × time

= 84 × 4

= 336 km

So, the distance between Town A and Town B  = distance travelled by Peter = 336 km.

Now, we will calculate time taken by William.

Speed of William = 70 km / hr

Distance travelled by William = distance between Town A and town B = 336 km

Time taken by William = distance / speed

= 336 / 70 hr

= 4.8 hr

This can b converted into hrs and minutes

4.8 hr = 4 hr + 0.8 × 60

= 4 hr 48 mins

Time William took off = 10 AM - 1hr 25 mins

= 8:35 AM

Now, we will calculate the time William would reach town B.

Time = 8:35 + 4hr 48 mins

= 1:23 PM

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The choice that shows a set of data that could be represented by the box plot below is (B)1,3,6,8,10,12,13,13,16,18,19

In the box plot, a left whisker extends from 1 to 6, therefore, the least value is 1.

The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. Therefore:

The lower quartile is 6

The median is 12

The upper quartile is 16

The right whisker extends from 16 to 19, therefore the highest value is 19.

The set of data that satisfies these conditions where the numbers in bold are the 5- number summary is

1,3,6,8,10,12,13,13,16,18,19The correct option is B.

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Which data set could be represented by the box plot shown below? A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 6. The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated. Choose 1 answer: Choose 1 answer: (Choice A) A 1,3,6,8,10,12,13,13,16,18,201,3,6,8,10,12,13,13,16,18,201, comma, 3, comma, 6, comma, 8, comma, 10, comma, 12, comma, 13, comma, 13, comma, 16, comma, 18, comma, 20 (Choice B) B 1,3,6,8,10,12,13,13,16,18,191,3,6,8,10,12,13,13,16,18,191, comma, 3, comma, 6, comma, 8, comma, 10, comma, 12, comma, 13, comma, 13, comma, 16, comma, 18, comma, 19 (Choice C) C 1,3,6,8,10,11,13,13,18,18,191,3,6,8,10,11,13,13,18,18,191, comma, 3, comma, 6, comma, 8, comma, 10, comma, 11, comma, 13, comma, 13, comma, 18, comma, 18, comma, 19 (Choice D) D 1,3,6,8,10,11,13,13,16,18,191,3,6,8,10,11,13,13,16,18,19

The simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

The given expression is simplified as follows;

The given expression is written as;

ab³/a⁴b  +  (c²)³

To simplify the expression given above, we will divide the fraction with the common factor as follows;

From the numerator; ab³, we will factor out "ab"

From denominator; a⁴b, we will factor out "ab"

The resulting expression becomes;

ab³/a⁴b  +  (c²)³

= b²/a³  +  c⁶

Note: for the power of c, we simplify by multiplying 2 and 3 = 6

Thus, the simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

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The binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

Given: Roll an 8-sided die 10 times and to find the probability of getting exactly 3 sevens in those 10 rolls.

Formula: The probability of getting exactly "k" successes in "n" trials of an event with a probability "p" of success in a single trial is given by the binomial probability formula:

P(k successes in n trials) = \(C(n , k) * p^k * (1 - p)^{(n - k)}\)

where:

Step1

Calculate the probability of rolling a seven on an 8-sided die (p).

Since there is 1 "success" outcome (rolling a seven) out of 8 possible outcomes (8-sided die),

p = 1/8.

Step 2

Plug the values into the binomial probability formula for getting exactly 3 sevens in 10 rolls:

P(3 sevens in 10 rolls) = \(C(10, 3) * (1/8)^3 * (1 - 1/8)^{(10 - 3)}\)

On subtracting gives:

=C(10,  3) * (1/8)^3 * (7/8)^{7}

Plugging the value of C(10,3) = 120 in the above equation:

= 120 * (1/8)^3 * (7/8)^{7}

Step 3:

Calculate the final answer using the formula:

P(3 sevens in 10 rolls) = 120 * (1/512) * (343/512)

≈ 0.0142

Therefore, the binomial probability of getting exactly 3 sevens in 10 rolls of an 8-sided die is approximately 0.0142 or 1.42%.

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Answer:

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

Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

Answer: A

Step-by-step explanation:

The polynomial has roots at \(x=-4, -2, 4\).

So, the equation should have factors of \((x+4), (x-2), (x-4)\).

This eliminates everything except for A.

Answer:

\( \frac{5}{9} \times \frac{6}{7} \\ = \frac{5 \times 6}{9 \times 7} \\ = \frac{30}{63} \\ thank \: you\)

Answer: Is 10/21

I hope it helps if it does mark me Brainliest Pls

Answer:

Yes, the conditions for inference are met

Step-by-step explanation:

Conditions for inference:

To build a confidence interval for a population proportion, the sample must have at least 10 successes and 10 failures.

In this question:

50 cars, 11 have damage and 50 - 11 = 39 do not.

Since both the number of sucesses and of failures is above 10, conditions for inference are met.

Answer:

Step-by-step explanation:

Divide 360 by the number of sides in a regular polygon to find θ

θ = 360/5 = 72°

Use law of cosines to find the radius of the circle which equals the common length sides of the isosceles triangle

12² = R² + R² - 2•R•Rcos72

12² = 2R² - 2R²cos72

12² =  2R²(1 - cos72)

R² = 12² / 2(1 - cos72)

R² = 104.1993788...

R = 10.2078...

The height of the isosceles triangle is

h = Rcos(θ/2) = 10.2078cos(72/2) = 8.258291...

The shaded area is the area of the circle minus the area of the pentagon.

A = π(104.1993) - 5(½(12)(8.258291))

A = 327.35200... - 247.74874...

A = 79.6032575...

A = 79.60 units²

The Area of the shaded region is A = 79.60 units²

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle that separates them by two.

Given:

length= 12

So, Divide 360 by the number of sides in a regular polygon

θ = 360/5

θ = 72°

Use law of cosines

12² = R² + R² - 2 x R x Rcos72

12² = 2R² - 2R² cos72

12² =  2R²(1 - cos72)

R² = 12² / 2(1 - cos72)

R² = 104.1993788...

R = 10.2078...

Thus, the height of the isosceles triangle is

h = R cos(θ/2)

   = 10.2078cos(72/2)

   = 8.258291...

and, the shaded area is

A = π(104.1993) - 5(½)(12)(8.258291))

A = 327.35200 - 247.74874

A = 79.6032575

A = 79.60 units²

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Answer:

Step-by-step explanation:

i belive it is correct.

The gardner is correct Because the total distance traveled by the roller is greater than the length of the bowling green.

A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

For the gardener to be correct,

8×Perimeter of the roller = Length of the bowling green

Therefore,

Let use first find the perimeter of the roller

Where:

Substitute these values into equation 1

For 8 full rotation,

Comparing the distance for 8 revolution of the roller with the length of the bowling green,

Therefore, the gardner is correct

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To completely solve the problem, Karim should convert the product back into standard decimal notation.

We cannot directly apply the product of powers property because the binomial is not raised to a power itself.

(1) To convert a number from scientific notation to standard decimal notation, we multiply the coefficient (0.0258) by 10 raised to the power of the exponent (-8).

0.0258 × \(10^{-8\)  = 0.0258 × 0.00000001

                         = 0.000000000000258

(2) The product of powers property states that when you raise a term with an exponent to another exponent, you can simplify it by multiplying the exponents.

In the expression \((3z + y)^3\), we have a binomial term (3z + y) raised to the power of 3. This is not a situation where we can directly apply the product of powers property because the binomial is not raised to a power itself.

To simplify the expression, we need to expand it using the binomial theorem or by applying the concept of binomial expansion.

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Haz un diagrama representando el rectángulo para visualizar la situación:

Observa que el rectángulo tiene dos lados que miden (x+4) y dos lados que miden (3x-2y). Por otro lado, el perímetro del rectángulo es igual a la suma de las longitudes de sus cuatro lados. Por lo tanto, el perímetro de este rectángulo está dado por la siguiente expresión:

Simplifica la expresión anterior sumando términos semejantes:

Por lo tanto, el perímetro del rectángulo, es:

Answer:

$405,44

Step-by-step explanation:

First of all we have to find how much the tv cost after 15% of discount.

we can use this proportion

15 : 100 = x : 499.99

x = (15*499.99)/100 = $74.9985

then we have to subtract the initial value to the value of the discount

499.99-74.9985 = $424,9915

thanks to the card we can apply another 10%

10 : 100 = x : 424,9915

x = (424,9915 *10)/100 = $42,49915

424,9915-42,49915 = $382,49235

now we have to apply taxes

6:100 = x : 382,49235

x = $22,949541

382,49235 + 22,949541 = $405,441891

that can be rewrite as $405,44

If we want to write an equation to solve this problem we can use this

499.99 - (499.99 * 15/100) - 1/10[499.99-(499.99*15/100)] + 6/100{1/10[499.99-(499.99*15/100) = x

Answer:

90

Step-by-step explanation:

i think

Answer:

A = 1168.67 cm²

Step-by-step explanation:

\(A=2\pi rh+2\pi r^{2}\)           Use this equation to find the surface area

\(A=2\pi (6)(25)+2\pi (6)^{2}\)  Multiply    

\(A=2\pi (150)+2\pi (36)\)     Multiply

A = 942.48 + 226.19     Add

A = 1168.67 cm²

Answer:

1169.14cm2

Step-by-step explanation:

The surface area is that area which you can feel. Now there are two circles one at the top and one at the bottom.

These areas are expressed as;

π×r2 { remember area of a circle}.

Therefore for the two areas we have twice the area of once since they are the same. Hence we have:

2×π×r2.

Secondly, there is still another area we haven't talked about yet. It's the area you feel at the side and this area curls into a circular fashion.

Now let's assume the two circles are the top and bottom are knocked off , we would have a shape that looks like a rectangle.

Now area of a rectangle is the multiplication of both sides. In this case the side would be the height,h and the circumference of the circle since the rectangle forms into a circle when she try to join both edges together.

Hence the area of this Shape would be;

2πr{circumference} × h=2πrh

Hence the total surface area would be;

2πr2 + 2πrh.

Substituting the giving values we have;

Note: to obtain raduis,r ; we divide the diameter by 2.

2 × 22/7 × 6^2 + 2 × 22/7 × 6× 25

2×22/7(36+150)

44/7(186)= 8184/7

=1169.1429cm2

=1169.14cm2{ to 2 decimal place}

Answer:

0.63

Step-by-step explanation:

Given that:

\(C \ = \ Californians \ (registered \ voters) \ preferrin g \ life \ in \ prison \ without \ parole \ over \ the \ death \\ penalty \ for \ a \ person \ convicted \ of \ first \ degree \ murder.\)P(C) = 0.48

L = Latino Californians

P(L) = 0.364

∴

P(C/L) = 0.63

The probability of getting exactly 9 of them major in STEM is 0.139 or 13.9%.

The probability of getting at most 11 of them major in STEM is approximately 0.898 or 89.8%.

The probability of getting at least 11 of them major in STEM is approximately 0.318 or 31.8%.

a. Exactly 9 of them major in STEM.

In this case, the probability of success (a student majoring in STEM) is 0.27, and the number of trials is 35. The probability of exactly 9 students majoring in STEM is then given by the formula:

P(X = 9) = (35 choose 9) x (0.27)⁹ x (0.73)²⁶

where (35 choose 9) is the number of ways to choose 9 students out of 35, and (0.27)⁹ x (0.73)²⁶ is the probability of 9 successes and 26 failures. Evaluating this expression gives a probability of approximately 0.139 or 13.9%.

b. At most 11 of them major in STEM.

To calculate the probability that at most 11 students out of 35 major in STEM, we can use the cumulative binomial probability distribution. This distribution calculates the probability of at most X successes, where X is any number from 0 to the total number of trials.

The probability of at most 11 students majoring in STEM can be calculated as follows:

P(X <= 11) = P(X = 0) + P(X = 1) + ... + P(X = 11) = 0.898 or 89.8%.

c. At least 11 of them major in STEM.

The probability of less than 11 students majoring in STEM can be calculated using the cumulative binomial probability distribution, as in part (b). Specifically:

P(X < 11) = P(X = 0) + P(X = 1) + ... + P(X = 10)

Subtracting this probability from 1 gives the probability of at least 11 students majoring in STEM:

P(X >= 11) = 1 - P(X < 11) = 31.8%

Again, we can use the binomial distribution formula from part (a), or a binomial probability calculator or statistical software package to calculate this probability.

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Answer:

because there is an exact square number such as:4,9

Answer:

✓2=1.41421

✓5=2.23607

✓8=2.82842

✓11=3.31662

✓14=3.74166

Step-by-step explanation:

Therefore the numbers are increasing by three so they cant be perfect square

Answer:

The interest earned is $421.2.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

\(E = P*I*t\)

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

In this question:

\(P = 2880, I = 0.045, t = 3 + \frac{1}{4} = 3.25\)

So

\(E = P*I*t\)

\(E = 2880*0.045*3.25\)

\(E = 421.2\)

The interest earned is $421.2.

Answer:

2x^2 +3x -2

18

12

-22

-46

Step-by-step explanation:

Answer:

19 skins

Step-by-step explanation:

Total surface area of the cone = πr(r+l)

r is the radius = 10ft/2 = 5ft

l is the slant height

l^2 = 12^2 + 5^2

l^2 = 144+25

l^2 = 169

l = 13ft

Get the surface area

TSA = 3.14(5)(5+13)

TSA = 15.7*18

TSA = 282.6 ft^2

If each skin covers 15 sq. feet

Number of skin needed = 282.6 /15

Number of skin needed = 18.84

Number of skin needed is approximately 19 skins

Answer:

Chris = $68, Pablo = $24, Debra = $17

Step-by-step explanation:

C + P + D = 109

C = 4D

P = D + 7

4D + D + D + 7 = $109

6D + 7 = $109

Subtract 7 from both sides...

6D = 102

Divide both sides by 6...

D = $17

and Debra has 17 dollars which means...

C = 4(17)

C = $68

Chris has $68

P = 17 + 7

P = $24

and Pablo has $24!

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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Answer:

the 2nd to last one................

To solve the expression 1 - (1 + 0.04/12)^(-12x10), you can follow these steps: Step 1: Simplify the exponent. In this case, -12x10 simplifies to -120.

Step 2: Evaluate the term within the parentheses first. 0.04/12 simplifies to 0.0033333 (approximately).

Step 3: Add 1 to 0.0033333 to get 1.0033333.

Step 4: Raise 1.0033333 to the power of -120.

Step 5: Calculate the value inside the parentheses using a calculator or software. The result is approximately 0.742657.

Step 6: Subtract the value obtained in Step 5 from 1.

1 - 0.742657 = 0.257343 (approximately).

Hence, the value of the expression 1 - (1 + 0.04/12)^(-12x10) is approximately 0.257343.

It's important to follow the order of operations (PEMDAS/BODMAS) when solving mathematical expressions. In this case, the exponent is evaluated first, followed by addition and subtraction. Utilizing a calculator or software that supports exponentiation and parentheses can help simplify complex expressions and obtain accurate results efficiently.

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The total number of boxes is the sum of all boxes each day

The total number of boxes he filled in the five days is \(23 \frac 18\)

The box each day is given as:

So, the total number of boxes is:

\(Total = 4\frac 78 + 5\frac 34 + 4\frac 72 + 4\frac 38 + \frac 58\)

Add the fractions

\(Total = 23 \frac 18\)

Hence, the total number of boxes he filled in the five days is \(23 \frac 18\)

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Answer: B i think

Step-by-step explanation:

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.