ALGEBRAIC EXPRESSIONS AND EQUATIONS Evaluating a quadratic expression: Integers Evaluate the expression when b=5. b^(2)-7b+1

Step-by-step explanation:

when 2 shapes are similar, then that means (among few other things) that both have the same angles at their vertexes.

by looking at the relative sizes of the sides, we can map which vertex of one correlates to which vertex (and angle) in the other.

D -> X

C -> Y

G -> U

F -> V

E -> W

so, the angle W = angle E = 136°.

The given statement " let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 will be denoted by P(X=8)" is true. Because In probability theory, P(X=8) denotes the probability that the random variable X takes on the value 8.

Probability is a measure of the likelihood or chance that a certain event or outcome will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

In this case, X represents the number of male births between 1:00am and 3:00am at a hospital in Orange County. So, P(X=8) represents the probability that exactly 8 male births occur during that time period.

To know more about probability here

https://brainly.com/question/11234923

#SPJ4

--The given question is incomplete, the complete question is

"True or false let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 is denoted by P(X=8)"--

The number of people we would expect to be found within an area of 1400 m by 1.3 km is approximately 25.

The mass of the cube for the object that has the side lengths of 56 cm is 0.043904 g.

1. To find the number of people in an area of 1400 m by 1.3 km, we need to first convert the measurements to the same unit. Since the population density is given in people/km2, we will convert the measurements to kilometers.
1400 m = 1.4 km
Now we can multiply the two measurements to find the area:
1.4 km x 1.3 km = 1.82 km2
Next, we can use the population density to find the number of people in this area:
14 people/km2 x 1.82 km2 = 25.48 people
Therefore, we would expect to find approximately 25 people in an area of 1400 m by 1.3 km.

2. To find the mass of the cube, we first need to find the volume. Since the side lengths are given in centimeters, we will convert them to meters:
56 cm = 0.56 m
Now we can find the volume of the cube by multiplying the side lengths:
0.56 m x 0.56 m x 0.56 m = 0.175616 m3
Next, we can use the density to find the mass of the cube:
0.25 g/m3 x 0.175616 m3 = 0.043904 g
Therefore, the mass of the cube is 0.043904 g.

Learn more about population density here: https://brainly.com/question/29121577.

#SPJ11

\( \frac{-9 y-81}{y+9} \) simplifies to -9.

To simplify the given expression, \( \frac{-9 y-81}{y+9} \), we need to factor out the common factor of -9 from the numerator.

Factor out the common factor of -9 from the numerator.
\( \frac{-9(y+9)}{y+9} \)

Simplify the expression by canceling out the common factor of (y+9) from the numerator and denominator.
\( \frac{-9 \cancel{(y+9)}}{\cancel{y+9}} \)

The final simplified expression is -9.
\( -9 \)

\( \frac{-9 y-81}{y+9} \) simplifies to -9.

It is important to check for any restrictions on the variable y. In this case, y cannot be equal to -9, as it would make the denominator of the original expression equal to 0 and the expression would be undefined. Therefore, the simplified expression is valid for all values of y except -9.

Learn more about factor

brainly.com/question/14067703

#SPJ11

a. The radius of the circle O is 8 cm. 

c. The circle has an area of 213.66 square centimeters. 

e. AB's arc length equals 60 degrees 

f. ACE has arc measure of 240 degree. 

g. the arc length is 8.38 cm

h. area of the sector AOB is 33.51 cm²

a. The radius of the circle is solved using the properties of a regular hexagon

The radius is 8 cm since the base of one of the equilateral triangles is the radius.

b. Area of circle O

= 3.142 * 8^2

= 213.66 squared cm

e. measure of arc AB

The center angle that creates the intercepted arc is what is known as the arc measure, which is measured in degrees.

= 60 degrees

f. measure of arc ACE

= arc AB + arc BC + arc CD + arc DE

= 60 + 60 + 60 + 60

= 240 degrees

g. length of arc AB

= 60/360 * 2 * 3.142 * 8

= 8.38 cm

h. area of the sector AOB

= 60/360 * 3.142 * 8²

= 33.51 cm²

Learn more about  length of arc at:

https://brainly.com/question/8020286

#SPJ1

This is the equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10.

The equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10 can be found using the X=P+TD vector equation. In this equation, X represents the point on the line, P represents the point through which the line passes, T represents a scalar parameter, and D represents the direction vector of the line.

To find the direction vector of the line, we can use the normal vector of the plane, which is given by the coefficients of the x, y, and z terms in the equation of the plane. The normal vector of the plane is (2,-1,3).

Since the line is orthogonal to the plane, the direction vector of the line will be parallel to the normal vector of the plane. Therefore, the direction vector of the line is also (2,-1,3).

Now, we can plug in the values of P and D into the X=P+TD equation to find the equation of the line:

X = (2,1,-1) + T(2,-1,3)

X = (2+2T, 1-T, -1+3T)

The equation of the line in parametric form is:

x = 2+2T
y = 1-T
z = -1+3T

This is the equation of the line passing through the point P (2,1,-1) and orthogonal to the plane 2x-y+3z=10.

Learn more about Vectors

brainly.com/question/24256726

#SPJ11

The height of the trapezoid is 2.84ft.

What is area ?

In mathematics, area is the measure of the amount of space inside a two-dimensional shape or surface. It is usually expressed in square units, such as square inches, square meters, or square feet.

The formula for the area of a trapezoid is:

A = (1/2)h(b1 + b2)

where A is the area, h is the height, b1 and b2 are the lengths of the two parallel bases.

We can rearrange this formula to solve for the height:

h = 2A / (b1 + b2)

We are given that the area of the trapezoid is 25.5ft. However, we also need to know the  of the two parallel bases in order to find the height.

Assuming that you have a diagram or other information that provides the lengths of the two bases, you can plug in the values for A, b1, and b2 and solve for h using the formula above.

For example, if we assume that the trapezoid has bases of length 4ft and 7ft, we can plug these values into the formula to get:

h = 2(25.5) / (4 + 7) = 2.84ft

Therefore, the height of the trapezoid is 2.84ft.

To learn more about Area from given link.

https://brainly.com/question/27683633

#SPJ1

The factorization of the polynomial is (x-10)² (x² + 13x + 42).

To factor the given polynomial, we can use the fact that it has a zero at 10 with multiplicity 2. This means that (x-10)² is a factor of the polynomial. We can divide the polynomial by (x-10)² using long division to find the other factor.

To know more about long division click on below link:

https://brainly.com/question/28824872#

#SPJ11

Radians and degrees are two units of measurement for angles. Each one has its own pros and cons, and the choice between the two largely depends on the situation and personal preference.

Radians:
Pros:
- Radians are the natural unit of measurement for angles in mathematics and physics. They are closely related to the concept of a circle, and many formulas and equations involving angles are simpler when using radians.
- Radians are unitless, which can make calculations easier and more intuitive.
Cons:
- Radians are not as familiar to most people as degrees, and can be harder to visualize and understand.
- Radians can be more difficult to work with when measuring small angles, since they use fractions or decimals instead of whole numbers.

Degrees:
Pros:
- Degrees are the most commonly used unit of measurement for angles, and are more familiar to most people.
- Degrees are easier to work with when measuring small angles, since they use whole numbers instead of fractions or decimals.
Cons:
- Degrees are not the natural unit of measurement for angles, and many formulas and equations involving angles are more complicated when using degrees.
- Degrees require the use of a special symbol (°) and are not unitless, which can make calculations more difficult and less intuitive.

Overall, the choice between radians and degrees deends on the situation and personal preference. Radians are generally more natural and simpler to work with in mathematics and physics, but degrees are more familiar and easier to visualize.

To learn more about radians and degrees from the given link

https://brainly.com/question/30396383

#SPJ11

Yes, there is sufficient evidence to conclude that display at point of purchase helps in increasing the sales of the product. This is because the mean difference in sales after display (300) is greater than the standard deviation (314.8), which indicates that there is a significant difference between the two groups.

To further support this conclusion, we can use a 99% confidence interval (CI) for the true difference. The formula for a 99% CI is:

CI = mean difference ± (t-value)(SD/sqrt(n))

Where n is the sample size, t-value is the critical value for a 99% CI, and SD is the standard deviation. For a sample size of 11 and a 99% CI, the t-value is 3.106. Plugging in the values, we get:

CI = 300 ± (3.106)(314.8/sqrt(11))

CI = 300 ± 294.6

CI = (5.4, 594.6)

Since the 99% CI does not include 0, we can conclude that there is sufficient evidence to support the claim that display at point of purchase helps in increasing the sales of the product. In other words, we can be 99% confident that the true difference in sales between after display and before display is between 5.4 and 594.6, which supports the claim that display at point of purchase helps in increasing sales.

True difference in sales lies between -162 and 662

Yes, there is sufficient evidence to conclude that display at point of purchase helps in increasing the sales of the product. The mean of the differences in sales between after display and before display was found to be 300 with a standard deviation of 314.8. This indicates that, on average, the display helped to increase sales by 300.

Furthermore, with a 99% confidence interval, the true difference in sales lies between -162 and 662, which is statistically significant. Therefore, the display at point of purchase has a statistically significant effect on sales and should be implemented.

Learn more about standard deviation

brainly.com/question/16555520

#SPJ11

The probability of selling exactly 4 houses in one day is 0.0548, or about 5.48%.

To find the probability of selling exactly 4 houses in one day, use the Poisson distribution formula:

P(X = x) = (λ^x)(e^-λ) / x!

Where:

λ = the average number of events (in this case, the average number of houses sold)

x = the number of events we want to find the probability of (in this case, 4 houses)

e = the base of the natural logarithm (approximately 2.71828)

So, plugging in the values: P(X = 4) = (1.6^4)(e^-1.6) / 4! = (6.5536)(0.2019) / 24 = 0.0548

Therefore, since the data is Poisson distributed, selling exactly 4 houses in one day has a probability of 0.0548, or about 5.48%.

Learn more about Poisson distribution here: https://brainly.com/question/9123296.

#SPJ11

The responses which represents the area of the rectangle are 23 ⅝ and 198/8

The correct answer choice is option A and B

Area of a rectangle = Length × Width

Length = 5 ¼ metros

Width = 4 ½ metros

Area of a rectangle = Length × Width

= 5 ¼ metros × 4 ½ metros

= 21/4 × 9/2

= (21 × 9) / (4 × 2)

= 189 / 8 square metros

= 23 5/8 square metros

Hence, the area of the rectangle is given by 189 / 8 square metros or 23 5/8 square metros.

Read more on area of rectangle:

https://brainly.com/question/25292087

#SPJ1

Answer:

2.4.1. To calculate how many litres of fuel are needed to travel 400km, we need to use the given fuel consumption rate of 8L/100km:

Fuel consumed for 400km = (8/100) x 400 = 32 litres

Therefore, 32 litres of fuel are needed to travel 400km.

2.4.2. To calculate how far you can travel with 50L of fuel, we can rearrange the formula from part 2.4.1 to solve for distance:

distance = (fuel consumed / fuel consumption rate) x 100

Plugging in the values we have:

distance = (50 / 8) x 100 = 625 km

Therefore, with 50 litres of fuel, you can travel 625 km.

The given functions f(x) = x² + 4x – 5 and g(x) = x - 1 are to be evaluated.
(f+g)(9). The addition of two functions is denoted by (f+g)(x) = f(x) + g(x). Now, we need to find the value of (f+g)(9). Substituting the values in the formula, we get:
(f+g)(x) = f(x) + g(x)f(x) = x² + 4x – 5g(x) = x - 1
(f+g)(9) = f(9) + g(9) = (9)² + 4(9) – 5 + (9) - 1= 81 + 36 – 5 + 9 - 1= 120
Therefore, (f+g)(9) = 120.

The subtraction of two functions is denoted by (f-g)(x) = f(x) - g(x). Now, we need to find the value of (f-9)(9). Substituting the values in the formula, we get:(f-g)(x) = f(x) - g(x)f(x) = x² + 4x – 5g(x) = x - 1(f-9)(9) = f(9) - g(9) = (9)² + 4(9) – 5 - (9) + 1= 81 + 36 – 5 - 9 + 1= 104
Therefore, (f-9)(9) = 104.3. (fog)(9)The composition of two functions is denoted by (fog)(x) = f(g(x)). Now, we need to find the value of (fog)(9).
Substituting the values in the formula, we get:
(fog)(x) = f(g(x))
f(x) = x² + 4x – 5
g(x) = x - 1
(fog)(9) = f(g(9)) = f(9 - 1) = f(8)= 8² + 4(8) – 5= 64 + 32 – 5= 91
Therefore, (fog)(9) = 91.4. g(x) = x - 1
Now, we need to evaluate g(9). Substituting x = 9 in the formula, we get:
g(x) = x - 1
g(9) = 9 - 1= 8
Therefore, g(9) = 8.

To know more about functions refer here:

https://brainly.com/question/28193995

#SPJ11

The measure of the central angle defined by the arc in radians can be found using the formula:

θ = s/r

where θ is the central angle in radians, s is the arc length, and r is the radius.

Plugging in the given values:

θ = (23π)/(23)

θ = π

Therefore, the correct answer is e. None of these are correct, as the measure of the central angle in radians is π.

The farmer knows that the 5 camp division is an easier practical solution than the 9 camp division because it does not require dealing with fractions or decimals.

Both fractions and decimals are just two ways to represent numbers. Fractions are written in the form of p/q, where q≠0, while in decimals, the whole number part and fractional part are connected through a decimal point.

To understand why the 5 camp division is an easier practical solution than the 9 camp division, we need to consider the common factors of 8,085 and the numbers 9 and 15.

The prime factorization of 8,085 is:

8,085 = 3 x 3 x 3 x 5 x 5 x 6

The prime factorization of 9 is:

9 = 3 x 3

The prime factorization of 15 is:

15 = 3 x 5

From the prime factorizations, we can see that 9 has a common factor of 3 with 8,085, while 15 has two common factors of 3 and 5 with 8,085. This means that dividing 8,085 into 9 or 15 camps of equal size would require dealing with fractions or decimals, which can be impractical in a farming context.

On the other hand, the prime factorization of 5 is:

5 = 5

Since 5 is a prime number, it does not have any common factors with 8,085. This means that dividing 8,085 into 5 camps of equal size would not require dealing with fractions or decimals. The farmer can simply divide the grazing land into 5 equal parts, each with an area of 1,617 hectares, without needing to perform any division calculations or deal with any fractions or decimals.

Therefore, the farmer knows that the 5 camp division is an easier practical solution than the 9 camp division because it does not require dealing with fractions or decimals.

To learn more about fractions and decimals visit:

https://brainly.com/question/1190151

#SPJ1

If √x  = 150, then the value of x will be 22,500.

If √x = 150, then we can find the value of x by squaring both sides of the equation:

(√x)² = (150)²

Simplifying the left side of the equation:

x = (150)²

x = 150 x 150

x = 22,500

Therefore, the value of x for the given root function is determined as 22,500.

Learn more about root functions here: https://brainly.com/question/29111434

#SPJ1

The complete question is below:

If √x  = 150, find the value of x

Answer: 7/2 + 7b

Step-by-step explanation:

When applying the distributive property, you want to start by identifying which value you are distributing. That value in this case will be 7/8.

7/8 is going to be multiplied with 4, then multiplied with 8b, and you will then find the sum of those to products:

( (7/8) * 4 ) + ( (7/8) * (8b) )

The first product simplified will be 7/2.

The second product simplified will be 7b.

The sum of those two products is: 7/2 + 7b.

Hope this helps.

The answers are explained in the solution below.

Multiplication is an operation that represents the basic idea of repeated addition of the same number.

Given are some operation based on multiplication,

1) 26 x 3/4 = 78/4

2) 9 x 7/10 = 63/10

3) 2/5 x 32 = 64/5

4) 1/8 x 400 = 400/8 = 50

5) 15 x 4/5 = 60/5 = 12

6) 3/11 x 66 = 198/66 = 18

7) 45 x 3/8 = 135/8

8) 3/10 x 12 = 36/10 = 18/5

9) 55 x 2/5 = 110/5 = 22

10) 5/6 x 40 = 200/6 = 100/3

11) 7/9 x 54 = 378/54 = 7

12) 600 x 5/12 = 3000/12

= 250

13) 2/3 x 21 = 42/3 = 14

14) 500 x 3/5 = 1500/5 = 300

15) 72 x 5/8 = 360/8 = 45

16) 2/9 x 35 = 70/9

Learn more about multiplications, click;

https://brainly.com/question/5992872

#SPJ1

Answer: It is not possible to use only translations and dilations to map one circle to another unless the two circles are identical in size and shape.

A translation is a transformation that moves an object without changing its size, shape, or orientation. It involves moving every point on the object the same distance in the same direction. Since a circle is defined by all the points that are equidistant from its center, a translation will simply move the entire circle in the same direction, but will not change its size or shape.

A dilation is a transformation that changes the size of an object, but not its shape or orientation. It involves multiplying the distance of every point on the object from a fixed center point by a scale factor. While a dilation can change the size of a circle, it will also change the distance between points on the circle, and thus change its shape.

Therefore, if the two circles are not identical in size and shape, it would be necessary to use other transformations, such as rotations or reflections, to map one circle to the other.

Step-by-step explanation:

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

simply because the perimeter means to go along every side the shape has.

I don't see any answer options. you did not provide any. I can only give you the approach of how to solve this.

so, that means for us

2(6x + 5) + 2×3x = 100

12x + 10 + 6x = 100

18x = 90

x = 90/18 = 5

Answer:

2.51

Step-by-step explanation:

Layla goes out to lunch. The bill, before tax and tip, was $16.90. A sales tax of 6% was added on. Layla tipped 14% on the amount after the sales tax was added. How much tip did she leave? Round to the nearest cent.

Find the amount after sales tax was added:

Find the amount after sales tax was added:

bill

+

sales tax

=

bill+sales tax=

100

%

+

6

%

100%+6%

=

=

106

%

106%

amount after tax

=

amount after tax=

106

%

of

bill

106% of bill

=

=

1.06

×

$

16.90

1.06×$16.90

106% = 1.06

=

=

$

17.914

$17.914

Click to see alternative method

Find the tip:

Find the tip:

tip

=

tip=

14

%

of

amount after tax

14% of amount after tax

=

=

0.14

×

$

17.914

0.14×$17.914

14% = 0.14

=

=

$

2.50796

$2.50796

≈

≈

$

2.51

$2.51

Round to the nearest cent

Layla left a $2.51 tip.

Layla left a $2.51 tip.

The person had died approximately 5 hours and 10 minutes before the coroner's examination.

Using the formula, t=−10 log10(T-R/95.6-R), we can calculate the elapsed time since death.

Given that T = 83.5°F, R = 75°F and t is the elapsed time since death in hours, we can calculate the elapsed time.

t = -10 log10(83.5-75/95.6-75)

t = -10 log10(8.5/20.6)

t = -10 * 0.517 = -5.17 hours

Therefore, the person had died approximately 5 hours and 10 minutes before the coroner's examination.

Learn more about elapsed time

brainly.com/question/29775096

#SPJ11

The answer of  lines intersect at the point is (1, 2, -1)

To determine whether the lines L1(t) = ⟨3 − t, 8 − 3t, 1 − t⟩ and L2(s) = ⟨−1 − 2s, 3 + s, s⟩ intersect, we need to find a value of t and s that make the x, y, and z components of both lines equal.

First, let's set the x components of both lines equal to each other:

3 − t = −1 − 2s

Next, let's set the y components of both lines equal to each other:

8 − 3t = 3 + s

Finally, let's set the z components of both lines equal to each other:

1 − t = s

Now we can solve for t and s. From the first equation, we get:

t = 4 + 2s

Substituting this value of t into the second equation, we get:

8 − 3(4 + 2s) = 3 + s

Simplifying this equation gives us:

-4 − 6s = 3 + s

Solving for s gives us:

s = -1

Substituting this value of s back into the first equation gives us:

t = 4 + 2(-1) = 2

So the lines intersect at t = 2 and s = -1. To find the point of intersection, we can substitute these values back into either line equation. Substituting into L1(t) gives us:

L1(2) = ⟨3 − 2, 8 − 3(2), 1 − 2⟩ = ⟨1, 2, -1⟩

Therefore, the lines intersect at the point (1, 2, -1).

To know more about intersect lines refer here:

https://brainly.com/question/11297403#

#SPJ11

If Cindy bought 7/8 yards of ribbon, then the length of Ribbon that Jacob bought is 7/10 yard.

The length of ribbon which Cindy bought is = 7/8 yard;

Jacob bought 4/5 the length as Cindy,

Which means that he bought, (4/5) × (7/8) yards of ribbon,

On multiplying these two fractions,

We get,

⇒ (4/5) × (7/8) = (4×7)/(5×8) = 28/40;

On simplifying this fraction, we divide both the numerator and denominator by their greatest common factor, which is 4,

We get,

⇒ 28/40 = 7/10,

Therefore, Jacob bought 7/10 yard of ribbon.

Learn more about Length here

https://brainly.com/question/15102009

#SPJ4

the unlock code is: 54-575-26-12-7.5-36.

How to determine?

To find the area of each polygon, we need to use the formula for the area of each respective shape.

Assuming the polygons are rectangles, triangles, and trapezoids, we can find their areas as follows:

The area of the rectangle with length 9 ft and width 6 ft is A = length × width = 9 ft × 6 ft = 54 ft².

The area of the triangle with base 10 cm and height 115 cm is A = (1/2) × base × height = (1/2) × 10 cm × 115 cm = 575 cm².

The area of the trapezoid with bases 5 m and 8 m, and height 4 m is A = (1/2) × (base1 + base2) × height = (1/2) × (5 m + 8 m) × 4 m = 26 m².

The area of the triangle with base 3 cm and height 8 cm is A = (1/2) × base × height = (1/2) × 3 cm × 8 cm = 12 cm².

The area of the rectangle with length 1.5 m and width 5 m is A = length × width = 1.5 m × 5 m = 7.5 m².

The area of the trapezoid with bases 6 ft and 3 ft, and height 4 m is A = (1/2) × (base1 + base2) × height = (1/2) × (6 ft + 3 ft) × 4 m = 9 ft × 4 m = 36 ft².

Therefore, the unlock code is: 54-575-26-12-7.5-36.

Note that the areas are listed from left to right based on the order of the shapes in the original question. Also, the areas are separated by hyphens as requested.

To know more about polygon visit:

https://brainly.com/question/24464711

#SPJ1

The solution is, the initial amount that you invested is $1200.

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

here, we have,

Let the initial amount that you invested be $ x.

We are told that the new balance after investing $500 is $1760.

Thus, the balance you had before the deposit $500 us;

$1760 - $500 = $1260

So, when the amount invested was $x, the balance was $1260.

Since this money earned 5% interest on the amount you initially

Thus;

$1260 = initial deposit + (5% of inital deposit)

Thus;

x + (5% * x) = 1260

x + (0.05x) = 1260

1.05x = 1260

x = 1260/1.05

x = $1200

Hence, The solution is, the initial amount that you invested is $1200.

To learn more on interest click:

brainly.com/question/29335425

#SPJ1