11) Factor the following polynomials: (5pts each) i) x^2 + 5x - 24 ii) 9x^2 - 12x+4 iii) 16x^2 -49

Answer:

$223,787

Step-by-step explanation:

r = 0.02

C = 191,000

t = 8

S = 191,000 (1 + 0.02)⁸

Follow order of operations (PEMDAS).

S = 191,000 (1.02)⁸

S = 191,000 (1.171659381)

S = 223,786.9

(We want to round to the nearest dollar, which is the ones place, so ignore all digits after the tenths place.)

Rounding, S = 223,787

Answer:

307 meters tall

Step-by-step explanation:

190.5 / 62 = x / 100

19050 / 62 = 307

If it is rounded up.

to lease a new car, you must make a dowm payment when you sign the lease, then pay $199 per month . six months after signing his lease, Mr Scott had paid $2,694. write and solve an equation to find the total amount he will have paid after 3 years.

Number of squares

when n =1, the number of squares =2,

when n = 2, the number of squares = 6,

when n= 3, the number of squares = 12,

From the list of the equations, the one that satisfies the relationship between the step number and the number of squares in the pattern = n^2 + n

The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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4 · n + 2 < -24

Hope this helps! Good luck! :)

Answer:

$31.00

Step-by-step explanation:

Given:

We need to find the LCM of 6 and 10:

Multiples of 6:  6, 12, 18, 24, 30

Multiples of 10: 10, 20, 30

Therefore, the LCM = 30

So the least number of notebooks and pencils the teacher can buy to have the same numbers of each is 30.

⇒ 30 ÷ 6 = 5 packages of notebooks

⇒ 30 ÷ 10 = 3 packages of pencils

5 packages of notebooks = 5 × $5.00 = $25.00

3 packages of pencils = 3 × $2.00 = $6.00

Therefore, the least amount of money the teacher can spend to have the same number of notebooks and pencils (30 each) is:

⇒  $25.00 + $6.00 = $31.00

The least amount of money the teacher can spend to have the same number of notebooks and pencils is $31.00.

To find the least amount of money the teacher can spend and have the same number of notebooks and pencils, we need to determine the least common multiple (LCM) of the quantities in the packages.

Notebooks come in packages of 6, and pencils come in packages of 10. The LCM of 6 and 10 is 30.

To achieve the same number of notebooks and pencils, the teacher could buy:

5 notebook packages (5 * 6 = 30 notebooks)

3 pencil packages (3 * 10 = 30 pencils)

Now, let's calculate the cost:

Cost of notebook packages = 5 * $5.00 = $25.00

Cost of pencil packages = 3 * $2.00 = $6.00

Total cost = $25.00 + $6.00 = $31.00

So, the least amount of money the teacher can spend to have the same number of notebooks and pencils is $31.00.

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Answer:

37.5

Step-by-step explanation:

Area= (Base1+base2)/2 *height

Base 1=b

Base 2=c

height=h

a=h(b+c)/2

h= line AB

Line AB has length \(\sqrt{4^2+3^2}=5\) using the distance formula

h=5

c= 10

b=5

a=5(10+5)/2=37.5

Answer:

infinit many solutions

Step-by-step explanation:

Y=2x-6.    Equation 1

2y=4x-12. Equation 2

2(2x-6)=4x-12 substitute y value of equation 1 into y value of equation 2

4x-12=4x-12. Infinite many solutions

y = a + bx Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance.

The estimated regression equation is the best estimate of the market weekly gross revenue given the amount spent on television advertising.

To develop an estimated regression equation with the amount of television advertising as the independent variable,

we need to perform a simple linear regression analysis. Using the given data, the equation will be in the form of y = a + bx, where y represents the market weekly gross revenue (100s) and x represents the television advertising (100s).

Step 1: Calculate the means of x (television advertising) and y (market weekly gross revenue).

Step 2: Calculate the covariance and variance of x.

Step 3: Find the regression coefficient b (slope) using the formula b = covariance(x,y) / variance(x).

Step 4: Calculate the regression constant a (intercept) using the formula a = mean(y) - b × mean(x).

After performing these calculations, we get the estimated regression equation:

y = -13.016 + 47.209x

Step 1: Calculate the correlation coefficient r and the coefficient of determination \(r^2\).

Step 2: Perform a t-test to determine the significance of the relationship. Compare the t-value obtained with the critical t-value at the 0.05 level of significance.

If the calculated t-value is greater than the critical t-value, we can conclude that there is a significant relationship between the amount spent on television advertising and weekly gross revenue. Based on the data and calculations, there is a significant relationship between the amount spent on television advertising and weekly gross revenue.

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The weighted average length of a nail from the carpenter's box whose distribution is give in image is: 3.5cm.

What is weighted average ?

Weighted average is a type of average that takes into account the relative importance or weight of each data point. In a weighted average, each data point is multiplied by a corresponding weight, which reflects its relative importance, and the products are then summed and divided by the sum of the weights.

To find the weighted average length of a nail, we need to multiply each nail length by its percent abundance, then add up all the products and divide by the total percent abundance.

Let's start by calculating the product of each nail length and its percent abundance:

Short nail: (2.5 cm) x (70.5%) = 1.7625 cm

Medium nail: (5.0 cm) x (19%) = 0.95 cm

Long nail: (7.5 cm) x (10.5%) = 0.7875 cm

Now, we add up all the products:

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

Finally, we divide by the total percent abundance:

70.5% + 19.0% + 10.5% = 100%

Therefore, the weighted average length of a nail from the carpenter's box is: 3.5 cm ÷ 100% = 3.5cm

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Answer:

1.8465

Step-by-step explanation:

Math is nice

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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The median would be 22:

Step-by-step explanation: The median is the number that is in the middle

Simply defined, the median is the number right in the middle of a set.

But before I get down to finding the median, I will order the numbers from least to greatest:

15, 17, 19, 20, 21, 22, 23

Now, the middle number is 20. So that's the median.

As for the range, it's the difference between the largest number and the smallest one:

Range = Greatest number - Smallest number

           = 23 - 15

           = 6

In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.

The weeks for which the team sold the same amount in percentages of candy bars are A. Weeks 1 and 2.

A percentage is a mathematical expression of the relationship between two numbers or variables.

It is also known as a ratio and is usually denoted as "%."

Week     Amount Sold

Week 1       32%

Week 2    eight twenty-fifths (8²⁰/₅₀)

Week 3 seventeen fifty-firsts (¹⁷/₅₁)

In percentage terms, the sales for each week are as follows:

Week 2    eight twenty-fifths (8²⁰/₅₀)

= 8²⁰/₅₀

= 160/500

= 32%

Week 3 seventeen fifty-firsts (¹⁷/₅₁)

= ¹⁷/₅₁

= 33%

Thus, the weeks for which the team sold the same amount in percentages of candy bars are A. Weeks 1 and 2.

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9514 1404 393

Answer:

  60°

Step-by-step explanation:

You recognize the ratio of the long side to the short side as 2 : 1, so you know this is the 1 : √3 : 2 "special" triangle that has angles 30°, 60°, 90°. The angle of interest is opposite the longer side, so is the 60° angle.

  x° = 60°

_____

In case you don't remember the "special" 30-60-90 and 45-45-90 right triangles, you can use the relevant trig function:

  Cos = Adjacent/Hypotenuse

  cos(x°) = 16/32 = 1/2

  x° = arccos(1/2)

  x° = 60°

a percentage of second lunch. 47% of students eat outside, so answer option A is true.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

based on the provided statement;

Taking the table,

the percentage of kids that have lunch outside is calculated or reported as follows:

% =( Number of students. Who eat outside.÷ Total no of students who had Second Lunch) × (100× T)

(21÷45)×(100÷T)

=46.66%

The percentage of Second-lunch. student who eat outside is 47%

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Answer:

y-1 over 3 (y -5)

Step-by-step explanation:

i think that s correct but the getting the app m a t h w a y for any further problems

Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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INFORMATION:

The next inequality is given

And we must subtract 12 from each side

STEP BY STEP EXPLANATION:

To solve the problem, we need to subtract 12 from each side of the given inequality

Finally, simplifying we obtain

ANSWER:

-2 < 0

Answer:

3/4

Step-by-step explanation:

hope this helps. I have to wrote this random think so it can be 20 characters hope this helps enjoy

The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.

Starting with the given inequality:

-3(x - 4) > 6(x - 1)

First, distribute -3 and 6 to the terms inside the parentheses:

-3x + 12 > 6x - 6

Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:

-3x - 6x > -6 - 12

-9x > -18

To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:

x < (-18) / (-9)

x < 2

Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

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The half-life of an element is 630 days and the time taken is 510.867 days

What is radioactive elements ?

Atoms that have unstable nuclei make up radioactive elements, and as they work to become stable, the unstable nuclei release atomic radiation. Radioactive atoms are converted into another chemical element through radiation emission, which can either make the element stable or radioactive enough to cause further decay.

The half life equation  is   P(t)  =  P (0) .  \((0.5)x^{\frac{t}{H} }\)

P(t) is the quantity at time t  (proportional to the radioactivity), P(0) the quantity at time zero, H the half life.

The units of t and H are the same.

So we know that when t = 880,  P(880) = P(0). 0.38

0.38 = 1 - 0.62     (decrease by 62% means we multiply original by 0.38).

\((0.5^{\frac{880}{H} } )\) = 0.38

Taking log on both sides we get

\(\frac{880}{H}\)log (0.5) = log (0.38)

\(\frac{880}{H}\) = \(\frac{log (0.38)}{log (0.5)}\)

\(\frac{H}{880} = \frac{log (0.5)}{log (0.38)}\)

H = 880 \(\frac{log (0.5)}{log (0.38)}\)

  = 880 * 0.71636

  = 630.3968

  ≅ 630 days

As for b, 100 mg to 57 mg.  P(t) = 57, P(0) = 100,   H = 630.  

57 = 100 (0.5)t/630  

(57/100) = (0.5)t/630

log (0.57) = t/630  log (0.5)

log (0.57)/log (0.5) = t/630

t = 630  log (0.57) / log (0.5)

 = 630*0.8109

 =  510.867 days

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Here is the final matching of multiplication expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173

81.4 x 32.1 ≈ 2,618

32.9 x 4.81 ≈ 158

46.7 x 31.7 ≈ 1,479

59.3 x 3.57 ≈ 212

Match each multiplication expression on the left with the best estimate of its product on the right:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9

81.4 x 32.1

32.9 x 4.81

46.7 x 31.7

59.3 x 3.57

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

Estimates for the remaining expressions:

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

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3/4, 6/8, 9/12, 12/16 , 15/20, 18/24, 21/28, 24/32 , 27/36, 30/40, 33/44, 36/48 , 39/52, 42/56, 45/60, 48/64 , 51/68, 54/72, 57/76, 60/80, ect..

I hope this is what you are looking for :)

verified and e-x/2 function is defined in the interval (-∞,+∞)

We need to verify, whether, (2y' + y = 0) , when y = e-x/2

From y = e−x/2 ,

we obtain,

→y′ = − (1/2)e−x/2

→2y′ + y = −2(1/2)e−x/2 + e−x/2

= −e−x/2 + e−x/2

= 0 →hence verified and e-x/2 function is defined in the interval (-∞,+∞)

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Answer:

\(y=-\frac{4}{5}x-\frac{21}{5}\)

Step-by-step explanation:

The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):

\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

     |

     |

     |     *

     |    /

     |   /

     |  /

-----*--------

     |

     |

     |

     |

     |

The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

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Answer:

= 130.435% difference

Answer:

The largest perfect square that is a factor of 1575 is 225.