If (x+1) is the factor of polynomial p(x) = ax²+x+1, then find a.

Answer: [tex]\dfrac{1}{56}[/tex]

Step-by-step explanation:

Total horses = 6

Number of ways to choose top 3 finishers in order = 3! = 6

Number ways to select 3 horses out of 8 in order = [tex]^8P_3[/tex]  [By permutations]

[tex]=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336[/tex]

Now, the probability that the gambler will win his bet =

[tex]\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}[/tex]

[tex]=\dfrac{6}{336}\\\\=\dfrac{1}{56}[/tex]

Hence, the required probability =  [tex]\dfrac{1}{56}[/tex]

Answer:

[tex]\boxed{\sf A. \ 0.34}[/tex]

Step-by-step explanation:

The first triangle is a right triangle and it has one acute angle of 70 degrees.

We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.

The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.

The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.

[tex]\sf \frac{3.4}{10} =0.34[/tex]

Answer:

[tex]x= \frac{5^{14}+3}{2}[/tex]

Step-by-step explanation:

The correct steps to solve the equation are:

[tex]14=log_5(2x-5)[/tex]

[tex]5^{14}=5^{log_5(2x-3)}[/tex]

Because [tex]a^{log_am}=m[/tex]

So, solving we get:

[tex]5^{14}=2x-3[/tex]

Sum 3 on every side:

[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]

Dividing by 2 into both sides:

[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]

So, the answer is  [tex]x= \frac{5^{14}+3}{2}[/tex]

Answer: Step 2

Step-by-step explanation:

This is correct according to Edge 2021

Answer:

63%

225 buyers

Step-by-step explanation:

To find the percent take the number that liked it over the total

376/600

Change to decimal form

.62666666

Change to percent by multiplying by 100

62.66666666%

The nearest percent is 63%

37.5 % would but it then multiply by the number of shoppers

37.5 % ( 600)

Change to decimal form

.375 * 600

225

Answer:

13

Step-by-step explanation:

We need to write our answer in exponential form. Ask yourself the question, "What times itself 3 times will give you 2197?" Your answer is [tex]13^{3}[/tex]. This will go inside of your cube root. You now have [tex]\sqrt[3]{13^{3} }[/tex]. Since there's a power of 3 and a cube root, those cancel each other out, and your answer is 13.

Answer:

[tex]\boxed{13}[/tex]

Step-by-step explanation:

=> [tex]\sqrt[3]{2197}[/tex]

Factorizing 2197 gives 13 * 13 * 13

=> [tex]\sqrt[3]{13*13*13}[/tex]

=> [tex]\sqrt[3]{13^3}[/tex]

We know that [tex]\sqrt[3]{} = ^{1/3}[/tex]

=> [tex]13^{3 * 1/3}[/tex]

=> [tex]13^1[/tex]

=> 13

Answer:

x=5

Step-by-step explanation:

2 − x = −3

Subtract 2 from each side

2-2 − x = −3-2

-x = -5

Multiply by -1

x = 5

Answer:

x=60

Step-by-step explanation:

This is an equilateral triangle which means all the sides are equal.

If all the sides are equal then all the angles are equal

180/3 = 60

x=60

Answer:

x= 60°

Step-by-step explanation:

We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°

Answer:

15 J

Step-by-step explanation:

There is a total of 100 J of energy being used which is then converted into sound energy, thermal energy, and friction. This means the total amount must equal 100 J.

1. Set up the equation

80 + x + 5 = 100

2. Simplify

x + 85 = 100

3. Solve for x by subtracting 85 from both sides

x = 15

Answer:

The correct answer is 15J which is B.

Answer:

True

Step-by-step explanation:

Answer: B. Perpindicular Bisector.

Step-by-step explanation:

BD is a perpindicular bisector because it splits CE into 2 equal segments via a right angle.

Answer:

midsegement

Step-by-step explanation:

Answer:

-7/3x + 3

Step-by-step explanation:

Answer:

(9x-7)/3x or (3-7/3x)

Step-by-step explanation:

Divide each term of numerator by denominator.

-28x^5/12x^6 +36x^6/12x^6

-7/3x +3

Answer: 1unit.

Step-by-step explanation:

Area of the rectangle

A = length × width

Since the area = 20 and the width is x and the length is x + 1.

We now substitute for the values in the above formula and solve for x

20 = x × x + 1

20 = x( x + 1 ), we now open

20 = x² + x , then re arrange.

x² + x - 20 = 0, this is a quadratic equation.we solve for x using quadratic means

Here, I am going to solve using factorization by grouping

x² + x - 20 = 0

x² + 5x - 4x - 20 = 0

x( x + 5 ) - 4( x + 5 ) = 0

( x + 5 )( x - 4 ). = 0

Therefore, the solution for x will be

x = -5 or 4, but x can not be -5 ( negative), so x = 4.

Now the difference between width and the length can easily be calculated from the above,

Width = 4 (x) , and length = 5 (4 + 1),

Now difference will be

5 - 4 = 1unit.

Answer:

All real numbers except for 5.

Step-by-step explanation:

[tex]f(x)=\frac{x}{x-5}[/tex]

The domain of rational functions is determined by the denominator. The denominator cannot equal zero since if they do, the function will be undefined.

Thus, we need to find the zero(s) of the denominator to determine the domain.

[tex]x-5=0[/tex]

[tex]x=5[/tex]

Therefore, the domain of the rational function is all real numbers except for 5.

In set builder notation, this is:

[tex]\{x|x\in \mathbb{R}, x\neq 5\}[/tex]

The complete question is;

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Answer:

A) P (x < 10) = 0.6700

B) P (x > 5 ) = 0.9406

C) P (8.0000 < x < 15.0000) = 0.6332

Step-by-step explanation:

A) we are given;

Mean;μ = 8.9 minutes

Standard deviation;σ = 2.5 minutes

Normal random variable;x = 10

So to find;P(x < 10) we will use the Z-score formula;

z = (x - μ)/σ

z = (10 - 8.9)/2.5 = 0.44

From z-distribution table and Z-score calculator as attached, we have;

P (x < 10) = P (z < 0.44) = 0.6700

B) similarly;

z = (x - μ)/σ =

z = (5 - 8.9)/2.5

z = -1.56

From z-distribution table and Z-score calculator as attached, we have;

P (x > 5 ) = P (z > -1.56) = 0.9406

C)between 8 and 15 minutes

For 8 minutes;

z = (8 - 8.9)/2.5 = -0.36

For 15 minutes;

z = (15 - 8.9)/2.5 = 2.44

From z-distribution table and Z-score calculator as attached, we have;

P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332

Answer:  without trying each calculation individually,  6750 4-digit numbers are not divisible by 4

Step-by-step explanation:  From 1000 to 9999 there are 9000 4-digit numbers 9999 - 999 = 9000.

Eliminate all the odd numbers 9000/2 = 4500

Eliminate the even numbers divisible by 2 but not by 4. 4500/2 = 2250

9000 - 2250 = 6750.

Answer:

1.9375.

Step-by-step explanation:

To solve this, we must use PEMDAS.

The first things we take care of are parentheses and exponents.

Since there are no parentheses, we do exponents.

4^-1+8^-1÷1/2/3^3​

= [tex]\frac{1}{4} +\frac{1}{8} / 1/ 2/ 27[/tex]

= 1/4 + (1/8) / 1 * (27 / 2)

= 1/4 + (27 / 8) / 2

= 1/4 + (27 / 8) * (1 / 2)

= 1/4 + (27 / 16)

= 4 / 16 + 27 / 16

= 31 / 16

= 1.9375.

Hope this helps!

Answer:

Step-by-step explanation:

From the given question, it can be concluded that Jessica and Kayla's planes took off an hour earlier than that of Lauren and at least two hours earlier than that of Maria. This implies that Maria's plane took off last among them.

Since each person's flight last 8 hours and Maria's plane lands at 4:45 pm, then Jessica and Kayla's planes land simultaneously at least at 2:45 pm. And that of Lauren lands exactly at 3:45 pm.

The correct answer is 24.5 m. You're given four different values but if you notice closely, not all the units match. Before you can add the values together, you need to get the same units. Because cm (centimeters) is the only one that's out of place, it will be easier to change it to m (meters). I think of centimeters as a century (same prefix) which equals 100. Therefore, to convert 300 cm to m, we will divide 300 by 100 to get 3. After that, add all the values together (6m+3m+3.5m+12m) to get a grand total of 24.5 m. I hope this helps!

The tape required to apply on the edge of the tape is 21.8m.

Perimeter is the sum of the length of the outer edges of a two-dimensional object.

A quadrilateral is a two-dimensional shape that is a polygon of four sides, one of the opposite sides of a quadrilateral is parallel.

Dan needs to apply tape on the edges of the stage, the tape required will be calculated by determining the perimeter of the stage.

The stage is in the shape of a quadrilateral.

The sides of the quadrilateral are as follows:

Side 1 = 6m

Side 2 = 300cm

Side 3 = 3.5m

Side 4 = 12m

300 cm will be converted into m

100 cm = 1m

300 cm = 0.3 m

The perimeter = Side 1 + Side 2 + Side 3+ Side 4

Perimeter = 6 + 0.3 +3.5 + 12

Perimeter = 21.8 m

The perimeter of the stage is 21.8m.

To know more about Perimeter

https://brainly.com/question/6465134

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Answer:

Angle BCA = 70

Angle CAB = 20

Step-by-step explanation:

Not sure what angle you meant, so I'll give you all of them <3

Angle BCA = 70 degrees, because If two angles form a line, they add up to 180.  (110+x=180, x = 70)

Angle CAB = 20 degrees, because there are 180 degrees in a triangle, so 90+70+x=180, x = 20

Hope it helps <3

Answer:

BCA = 70

CAB = 20

ABC=90

Step-by-step explanation:

ABC is 120 because the square indicates that

BCA = 70 because angles on a straight line add up to 180.

110+x=180

x=180-110

=70

Angle CAB = 20 degrees, because angles in a triangle add up to 180

90+70+x=180

x = 180-(90+70)

=180-160

=20

Please mark as brainliest

Answer:

[tex]\huge\boxed{x=\sqrt{21}}[/tex]

Step-by-step explanation:

ΔABD and ΔBCD are similar (AAA).

Therefore the corresponding sides are in proportion:

[tex]\dfrac{BD}{CD}=\dfrac{AD}{BD}[/tex]

Substitute

[tex]BD=x;\ CD=3;\ AD=7[/tex]

[tex]\dfrac{x}{3}=\dfrac{7}{x}[/tex]              cross multiply

[tex](x)(x)=(3)(7)\\\\x^2=21\to x=\sqrt{21}[/tex]

Answer:

Ok, we have a system of equations:

6*x + 3*y = 6*x*y

2*x + 4*y = 5*x*y

First, we want to isolate one of the variables,

As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:

(6*x + 3*y)/(2*x + 4*y) = 6/5

now we isolate one off the variables:

6*x + 3*y = (6/5)*(2*x + 4*y) =  (12/5)*x + (24/5)*y

x*(6 - 12/5) = y*(24/5  - 3)

x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y

Now we can replace it in the first equation:

6*x + 3*y = 6*x*y

6*(0.5*y) + 3*y = 6*(0.5*y)*y

3*y + 3*y = 3*y^2

3*y^2 - 6*y = 0

Now we can find the solutions of that quadratic equation as:

[tex]y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}[/tex]

So we have two solutions

y = 0

y = 2.

Suppose that we select the solution y = 0

Then, using one of the equations we can find the value of x:

2*x + 4*0 = 5*x*0

2*x = 0

x = 0

(0, 0) is a solution

if we select the other solution, y = 2.

2*x + 4*2 = 5*x*2

2*x + 8 = 10*x

8 = (10 - 2)*x = 8x

x = 1.

(1, 2) is other solution

Answer:

the amount of money Ian invested is P =  £2,500

Step-by-step explanation:

The standard formula for compound interest is given as;

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

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case, Given that;

A = £2652.25

t = 2 years

n = 1 (semiannually)

r = 3% = 0.03

substituting the given values into equation 1;

[tex]P = \frac{A}{(1+r/n)^{nt}} ...........1\\P = \frac{2652.25}{(1+0.03)^{2}} \\P = \frac{2652.25}{(1.03)^{2}} \\[/tex]

P =  £2,500

the amount of money Ian invested is P =  £2,500

Answer:

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Step-by-step explanation:

Using the fundamental theorem of calculus

Taking the derivative of the integral gives back the function

Since the lower limit is a constant when we take the derivative it is zero

d/dx [tex]\int\limits^x_4 {g(t)} \, dt = g(x)[/tex]

g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))

Replacing t with x

g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))

Answer:

vol = 96

Step-by-step explanation:

Area of a triangle = 1/2 * b * h

b = 4

h = 6

A = 0.5 * 4 * 6

A = 12

length = 8

vol = Area * length

vol = 12 * 8

vol = 96

Answer:

(104 + 16 sqrt 13)

Step-by-step explanation:

i did this on my school, it was correct

Answer:

$153

Step-by-step explanation:

Since she claimed two exemptions, Grace Kelly income's tax will only be $153, and $1847 being the yearly take home.

Effective tax rate is set at 7.65%

Answer:

A. The variance is the positive square root of the standard deviation. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Step-by-step explanation:

As we know that

The standard deviation is the square root of the variance and on the other side the variance is the square of the standard deviation

In mathematically

[tex]\sigma = \sqrt{variance}[/tex]

And,

[tex]variance = \sigma^2[/tex]

Moreover, the standard deviation and the variance could never by negative neither the squared deviation is negative. All three are always positive

Hence, the correct option is a.

Answer:

B. The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Answer:

When Ø = 300°, Ø = 60 degrees.

When Ø = 225°, Ø = 45 degrees.

When Ø = 480°, Ø = 60 degrees.

When Ø = -210°, Ø = 30 degrees.

Step-by-step explanation:

Reference angles are in Quadrant I (0° to 90°).

1. Find 300° (Quadrant IV) on the unit circle. Since it's in Quadrant IV, you use 360 - 300 = 60° to get your answer.

2. Find 225° (Quadrant III) on the unit circle. Since it's in Quadrant III, you use 225 - 180 = 45° to get your answer.

3. The angle 480° is not on the unit circle. To find its corresponding angle between 0° and 360°, use 480 - 360 = 120°. Then, find 120° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 120 = 60° to get your answer.

4. The angle -210° is not on the unit circle. To find its corresponding angle between 0° and 360°, use -210 + 360 = 150°. Then, find 150° (Quadrant II) on the unit circle. Since it's in Quadrant II, you use 180 - 150 = 30° to get your answer.

Answer:

52 dimes and 54 nickels

Step-by-step explanation: 52 dimes is $5.20 and 54 nickels is $2.70

Total coins 106 total $7.90