Solve for x in the equation x squared minus 8 x + 41 = 0.
x = negative 4 plus-or-minus StartRoot 37 EndRoot i
x = –4 ± 5i
x = 4 plus-or-minus StartRoot 37 EndRoot i
x = 4 ± 5i

Answer:

2.5 minutes or 150 seconds

Step-by-step explanation:

Time = Distance / speed

300/2 = 150.

150 seconds, or 2 and a half minutes

Answer:

Step-by-step explanation:

The function that will have the domain [tex](\infty, \infty)[/tex] and a range of [tex](-3, \infty)[/tex] is the

function in option d.) [tex]f(x) = e^x - 3[/tex]

Answer:

6 combinations

Step-by-step explanation:

Pants options: Navy Blue, Khaki

Shirt options: Red, white, blue

Possible combinations:

Navy Blue with:       Khaki with:

Red                           Red

White                        White

Blue                           Blue

There are 6 outfit possibilities

Hope this helps and let me know if you have any questions about my answer :)

[tex]\frac{1}{6}[/tex] of the original pan represents each serving

Solution:

Given that,

Mrs.Rome has 2/3 of a pan of lasagna left after dinner

She wants to divide the leftover lasagna into 4 equal servings

2/3 is divided into 4 equal servings

Therefore,

[tex]1\ equal\ serving = \frac{\frac{2}{3}}{4}\\\\1\ equal\ serving = \frac{2}{12} = \frac{1}{6}[/tex]

Thus [tex]\frac{1}{6}[/tex] of the original pan represents each serving

[tex]\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{45}{4}\\\\\frac{\text{Distance of tamar}}{\text{Distance of melkon}} = \frac{4}{45}[/tex]

Solution:

Given that,

Tamar travels 8/9 miles to the grocery store

Melkon travels 10 miles to the grocery store

Therefore,

[tex]Tamar = \frac{8}{9}\ miles\\\\Melkon = 10\ miles[/tex]

[tex]\text{ Distance of melkon : Distance of tamar } = 10 : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } = \frac{10 \times 9}{1 \times 9} : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } = \frac{90}{9} : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } =90 : 8\\\\In\ fraction\ form\\\\\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{90}{8}\\\\In\ simplest\ form\\\\\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{45}{4}[/tex]

[tex]\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : 10\\\\\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : \frac{10 \times 9}{1 \times 9}\\\\\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : \frac{90}{9}\\\\\text{ Distance of tamar : Distance of melkon } = 8 : 90\\\\In\ fraction\ form\\\\\frac{\text{Distance of tamar}}{\text{distance of melkon}} = \frac{8}{90}\\\\\frac{\text{Distance of tamar}}{\text{distance of melkon}} = \frac{4}{45}[/tex]

Thus the required are found

Answer:

Step-by-step explanation:

Final answer:

The remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7 is found using the remainder theorem, which gives us a result of 163.

Explanation:

To find the remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7, we can use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by a linear divisor of the form x - r, the remainder is f(r). Here, our linear divisor is x + 7, which we can rewrite as x - (-7). So, we substitute x = -7 into the polynomial to get the remainder.

Substituting x = -7 into the function gives us:
f(-7) = 4(-7)² + 5(-7) + 2 = 4(49) - 35 + 2 = 196 - 35 + 2 = 163.

Therefore, the remainder when f(x) is divided by x + 7 is 163.

The approximate mean age is [tex]\(45.15\)[/tex] years, and the approximate standard deviation for age is [tex]\(9.22\)[/tex] years, both rounded to two decimal places.

To approximate the mean and standard deviation for the age groups provided, we can calculate the weighted average based on the midpoint of each age group and use the formula for the standard deviation of a weighted dataset.

First, calculate the midpoints of the age groups:

- For 25-34 years: midpoint = (25 + 34) / 2 = 29.5

- For 35-44 years: midpoint = (35 + 44) / 2 = 39.5

- For 45-54 years: midpoint = (45 + 54) / 2 = 49.5

- For 55-64 years: midpoint = (55 + 64) / 2 = 59.5

Next, calculate the weighted mean using the formula:

[tex]\[ \text{Weighted Mean} = \frac{\sum (\text{Midpoint} \times \text{Number of People})}{\sum \text{Number of People}} \][/tex]

[tex]\[ \text{Weighted Mean} = \frac{(29.5 \times 22.1) + (39.5 \times 31.5) + (49.5 \times 37.7) + (59.5 \times 25.3)}{22.1 + 31.5 + 37.7 + 25.3} \][/tex]

[tex]\[ \text{Weighted Mean} \approx \frac{651.45 + 1244.25 + 1867.35 + 1503.35}{116.6} \][/tex]

[tex]\[ \text{Weighted Mean} \approx \frac{5266.4}{116.6} \][/tex]

[tex]\[ \text{Weighted Mean} \approx 45.15 \text{ years (approx)} \][/tex]

Now, calculate the standard deviation using the formula:

[tex]\[ \text{Weighted SD} = \sqrt{\frac{\sum (\text{Number of People} \times (\text{Midpoint} - \text{Weighted Mean})^2)}{\sum \text{Number of People}}} \][/tex]

[tex]\[ \text{Weighted SD} = \sqrt{\frac{(22.1 \times (29.5 - 45.15)^2) + (31.5 \times (39.5 - 45.15)^2) + (37.7 \times (49.5 - 45.15)^2) + (25.3 \times (59.5 - 45.15)^2)}{116.6}} \][/tex]

[tex]\[ \text{Weighted SD} \approx \sqrt{\frac{9919.575}{116.6}} \][/tex]

[tex]\[ \text{Weighted SD} \approx \sqrt{85.004} \][/tex]

[tex]\[ \text{Weighted SD} \approx 9.22 \text{ years (approx)} \][/tex]

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Good evening,

Answer:

Step-by-step explanation:

Two angles are supplementary if the sum of their measures is equal to 180°

then the measurement of an angle that is supplementary to an angle that measures 80° is :

180 - 80 = 100°

Answer:

5.5 pounds of seeds

Step-by-step explanation:

22 pounds seeds = 4-acre field

(x) pounds seeds = 1-acre(per acre)

x= 22/4

 = 5.5 pounds of seeds

Answer: The height/width has to be less than 9 for the area to be less than 36

Step-by-step explanation:

Pennant's are triangle.

Triangle area = bh(1/2)

the base is 8in

(8 * h)/2 = 36

*2

8 * h = 72

/8

h = 9

The height/width has to be less than 9

Answer:

The area of trapezoid PQRS is 125 square units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

If trapezoid PQRS with parallel sides PQ and RS is divided into four triangles by its diagonals PR and QS , intersecting at X, then the area of triangle PSX is equal to that of triangle QRX, and the product of the areas of triangle PSX and triangle QRX is equal to that of triangle PQX and triangle RSX

Let

A_1 ----> the area of triangle PSX

A_2----> the area of triangle QRX

A_3 ---> the area of triangle PQX

A_4 ---> the area of triangle RSX

[tex]A_1*A_2=A_3*A_4[/tex]

[tex]A_1=A_2[/tex]

so

[tex]A_1^2=A_3*A_4[/tex]

we have

[tex]A_3=20\ units^2\\A_4=45\ units^2[/tex]

substitute

[tex]A_1^2=(20)(45)\\A_1^2=900\\A_1=30\ units^2[/tex]

The area of trapezoid is equal to

[tex]A=A_1+A_2+A_3+A_4[/tex]

substitute

[tex]A=30+30+20+45=125\ units^2[/tex]

Final answer:

The area of trapezoid PQRS is found by adding the areas of triangle PQX (20 square units) and triangle RSX (45 square units) together, which equals 65 square units.

Explanation:

The area of trapezoid PQRS can be found by summing up the areas of triangle PQX and triangle RSX. Since diagonals PR and QS intersect at point X, both triangles share the same height, which is the perpendicular distance from point X to the bases PQ and RS. Thus, the area of trapezoid PQRS is simply the sum of the areas of the two triangles.

To calculate the area of trapezoid PQRS, we add the area of triangle PQX, which is given as 20, to the area of triangle RSX, which is given as 45. Therefore, the area of trapezoid PQRS is:

Area of trapezoid PQRS = Area of triangle PQX + Area of triangle RSX = 20 + 45 = 65

So, the area of trapezoid PQRS is 65 square units.

Answer:

1) a = 3189 b = 5

2) a = 53 b = -5

Step-by-step explanation:

Answer:

[tex]\frac{1}{90}[/tex]

Step-by-step explanation:

Before calculating the scale we require the dimensions to be in the same units.

Using the conversion

1 yard = 3 ft and

1 foot = 12 inches, then

5 yards = 5 × 3 × 12 = 180 inches

The scale is then

2 in : 180 in ← divide both quantities by 2

= 1 : 90

= [tex]\frac{1}{90}[/tex]

The scale of the drawing given is 1/90

Using the following conversion :

This means that ;

Then ;

Relating the expression :

2 inches = 180 inches

divide both sides by 2

1 inch : 90 inches

Hence, the scale is 1 /90

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Answer:

a. 1/10

b. 4/10

c. 20

Step-by-step explanation:

There are 10 equal sections.

a. 1 section is labeled "Large Prize", so the probability of winning a large prize is 1/10.

b. 1 section is labeled "Large Prize" and 3 sections are labeled "Small Prize", so there's 4 prize section.  Therefore, the probability of winning a prize is 4/10.

c. Each person has a 4/10 chance of winning a prize.  So if there are 50 people, we would expect 4/10 × 50 = 20 people to win a prize.

Answer:

look at picture shown please

Step-by-step explanation:

We have,

[tex]\dfrac{x+16}{3}=3x[/tex]

To find, the value of x in the given equation = ?

∴ [tex]\dfrac{x+16}{3}=3x[/tex]

By crossmultiplication, we get

3(3x) = x + 16

⇒ 9x = x + 16

⇒  9x - x = 16

⇒  8x = 16

⇒  x = [tex]\dfrac{16}{8}[/tex]

⇒  x = 2

∴ The value of x = 2

Thus, the required value of x is equal to 2.

Answer:

       _

-0.416       or for rounded     0.417

Step-by-step explanation:

when you multiply  -1/4 and 5/3 you will get a repeating decimal so what you will do is ether round it or put a line on top of the 6 showing that the number six never ends so when you round it you should round the thousandths plae making it -0.417

Answer y = 0.15x + 100

Step-by-step explanation:

Answer:

p=17

The drawing will help

Answer: p = 16

Step-by-step explanation: To solve for p in this equation, our first step is to simplify the left by distributing the 5 through both terms inside the parentheses.

When we do that,

we get 5 times 9 which is 45 and 5 times p which is 5p.

So we have 45 + 5p = 125.

Our next step is to isolate the p term by subtracting 45 from both sides of the equation. On the left side of the equation, 45 - 45 cancels and we're left with 5p.

On the right side of the equation, 125 - 45 simplifies to 80.

So we have 5p = 80.

We want to solve our equation for p so we want to get p by itself on the left side of the equation. Since p is being multiplied by 5, we need to divide both sides of the equation by 5. On the left side of the equation.notice that the 5 and 5 cancel each other out so we're just left with p and on the right side, 80 divided by 5 is 16 so we have p = 16.

Answer:

bunches up in the middle and tapers off symmetrically at either end

Step-by-step explanation:

By definition a normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Because the data towards the mean is more frequent in occurrence, the graph peaks at the center. The data occurs less frequently at the tail ends of the distribution, thus the shape of the distribution is a bell shape that peaks at the center and tapers off towards the tails.  The key characteristic is that the distribution of data is perfectly symmetrical.

This is why the answer is:

The data depicted in a histogram show approximately a normal distribution if the distribution bunches up in the middle and tapers off symmetrically at either end.

Approximately 3 bottles are needed to buy to completely fill the 6 glasses you need

Solution:

Given that,

A small bottle of Dr.Pepper holds 31.2 cm^3 of the delicious drink

Therefore,

[tex]Volume\ of\ small\ bottle\ of\ Dr.pepper = 31.2\ cm^3[/tex]

For a New Years Eve party, you need enough juice to fill 6 cone- shaped glasses that have a 4 cm diameter and a 3 cm height

Find the volume of cone

[tex]V = \frac{\pi r^2h}{3}[/tex]

Where, r is the radius and h is the height

Diameter = 4 cm

Radius = 4/2 = 2 cm

Height = 3 cm

Therefore,

[tex]V = \frac{3.14 \times 2^2 \times 3}{3}\\\\V = \frac{3.14 \times 12}{3}\\\\V = \frac{37.68}{3}\\\\V = 12.56[/tex]

Thus, for 6 cone shaped glasses:

Volume of 6 cone shaped galsses = 12.56 x 6 = 75.36 [tex]cm^3[/tex]

How many full bottles of Dr. Pepper do you need to buy to completely fill the 6 glasses you need?​

[tex]\text{Number of Dr.pepper bottles } = \frac{\text{Volume of 6 cone shaped galsses}}{\text{Volume of small bottle of dr pepper}}\\\\\text{Number of Dr.pepper bottles } = \frac{75.36}{31.2}\\\\\text{Number of Dr.pepper bottles } = 2.4153[/tex]

Thus approximately 3 bottles are needed to buy to completely fill the 6 glasses you need

Final answer:

To fill 6 cone-shaped glasses for a New Year's Eve party, you would need to buy 3 full bottles of Dr. Pepper. The volume of each glass is calculated using the formula for the volume of a cone, and then this volume is multiplied by 6 to find the total volume required for all glasses. The number of bottles needed is found by dividing this total volume by the volume of one bottle of Dr. Pepper.

Explanation:

To determine how many full bottles of Dr. Pepper you need to buy to fill 6 cone-shaped glasses with a 4cm diameter and a 3cm height, we need to calculate the volume of one glass and then multiply it by 6 to get the total volume required. The formula to calculate the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cone.

First, we find the radius of the glass by dividing the diameter by two, which yields 2cm. Plugging the values into the formula, we get:

V = (1/3)π(2^2)(3) = (1/3)π(4)(3) = 4π cm^3

Since π is approximately 3.14, we can simplify this to:

V = 4(3.14) cm^3 = 12.56 cm^3 per glass.

Now, multiplying the volume of one glass by 6 gives us the total volume needed:

Total volume = 12.56 cm^3/glass × 6 glasses = 75.36 cm^3.

To find out how many bottles of Dr. Pepper are needed, we divide the total volume by the volume of one bottle:

Number of bottles = 75.36 cm^3 / 31.2 cm^3/bottle ≈ 2.415 bottles.

Since you cannot buy a fraction of a bottle, you would need to purchase 3 full bottles of Dr. Pepper to ensure you have enough to fill all 6 glasses.

Answer:

The answer you have is Correct!

A number line can be defined as a horizontal line that can be extended and have numbers on it. The distance between -2/3 and 4/3 on a number line is 3 units.

A number line can be defined as a horizontal line that can be extended in any direction indefinitely and has all the integers over it. As one walks from left to right on the number line, the numbers grow, and as one proceeds from right to left, the numbers decrease.

The distance between the two can be found by deducting -2/3  from 4/3. Therefore, the distance between the two can be written as,

[tex]\rm Distance = \dfrac{4}{3}-(- \dfrac{2}{3}) = \dfrac{4}{3}+\dfrac{2}{3} = \dfrac{4+2}{3} = \dfrac{6}{3} = 2[/tex]

Thus, the distance between -2/3 and 4/3 on a number line is 3 units.

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Answer:

5/2 or 2 1/2

Step-by-step explanation:

Answer:

1, 2, 3

Step-by-step explanation:

The range includes only the y-axis. On this graph, the line only passes by the 1,2, and 3 on the y-axis.

Answer:

10/25 or 2/5

Step-by-step explanation:

since only 10 have sport as all the other students don't

Answer:

  they have the same value (0)

Step-by-step explanation:

Cosine is an even function, meaning that cos(x) = cos(-x). When x=90°, we have ...

  cos(90°) = cos(-90°)

Both values happen to be zero.

The relationship between cos(90°) and cos(-90°) is that they both equal 0.

The relationship between cos(90°) and cos(-90°) can be explained using the unit circle. In the unit circle, the cosine function represents the x-coordinate of the point on the circle corresponding to the given angle.

For cos(90°), the x-coordinate is 0, which means the cosine value is 0.

For cos(-90°), the x-coordinate is also 0, so the cosine value is also 0. Therefore, cos(90°) = cos(-90°) = 0.

The question cannot be fully answered as provided since only two dimensions of the ice block are given. To determine the amount of reflective material, all three dimensions (length, width, height) of the block are needed to calculate the total surface area. Without the third dimension, the exact surface area cannot be calculated.

The question asks how much reflective material would be needed to cover a block of ice with given dimensions completely for an ice carving competition. Since only two dimensions are provided, let's assume the block has a third dimension making it a rectangular prism. To find the surface area of the block (which is the amount of reflective material needed), we calculate the area of each face and sum them up. A rectangular prism has six faces: the front and back, the top and bottom, and the two sides. If we denote the dimensions of the block as length (l), width (w), and height (h), the areas of the respective faces are:

Assuming the dimensions provided are the length and height (l = 3 ft and h = 4 ft), and an unknown width (w), we cannot calculate the exact surface area without the third dimension. Ideally, the width would be provided to complete the calculation.

Answer:

a 90° clockwise rotation about the origin

a 180° rotation about the origin

a 90° counterclockwise rotation about the origin

Step-by-step explanation:

Transformations are done on a Cartesian Plane, which is the grid with four quadrants. (See picture) Each quadrant is 90°, so two quadrants is 180°.

When you rotate counterclockwise it is like in the picture. When you want to rotate clockwise, it's the other way.

When we rotate 180°, it does not matter if it is counterclockwise or clockwise because the result is the same (both move two quadrants).

We can imagine an example to help us solve the problem. Let's say we are rotating an object starting in first quadrant. (Upper right quadrant).

Find out which quadrant the object ends up with each instruction:

FROM THE PICTURE:

"a 90° counterclockwise rotation about the origin (Q2) and then a 180° rotation about the origin"

End: Quadrant 4

"a reflection across the x-axis (Q4) and then a reflection across the y-axis"

End: Quadrant 3

"a 90° clockwise rotation about the origin (Q4) and then a rotation 180° about the origin"

End: Quadrant 2

FROM YOUR LIST:

"a 90° counterclockwise rotation about the origin " Quadrant 2

"a 180° rotation about the origin " Quadrant 3

"a 90° clockwise rotation about the origin" Quadrant 4

Match each ending quadrant from your list with the same ending quadrant from the picture.

The order that you should put your list into the boxes is:

a 90° clockwise rotation about the origin

a 180° rotation about the origin

a 90° counterclockwise rotation about the origin