ΔLMN ≅ ΔRST, ∠L = 49º, ∠M = 10x, ∠S = 70º, and ∠T = 4y + 9

Step-by-step explanation:

x current age of the father

y current age of the son

first equation (x-4)+(y-4)=27 so x=27+4+4-y=35-y

second equation (y+5) : (x+5)= 2:7

so (y+5)*7=(x+5)*2

let's replace x we found at the first equation with the one at second equation

(y+5)*7=(35-y+5)*2

7y+35=(40-y)*2

7y+35=80-2y

7y+2y=80-35

9y=45

y=5

x=35-y=35-5=30

Answer: 20

Step-by-step explanation:

30-60-90 triangles are special: Their side lengths fall in a ratio of 1:2:[tex]\sqrt{3}[/tex], in order of Shortleg : hypotenuse : longleg

Since we know the short leg is 10, the hypotenuse must be double, or 20.

The time taken by population of bacteria to be doubled whose normal growth is six fold in 10 hours is equal to 3.87 hours.

Let us consider 'n' is the time taken by the bacteria populations.

And P(n) represents the population of the bacteria in time 'n'

Using exponential growth function we know,

P(n) = K e^(a× n)

Where K and 'a' are the constants.

From the given condition we have :

P(10 ) = 6 P(0)

⇒ K e^ (10a) = 6k e^(0 × a )

⇒ e^(10a) = 6

⇒ 10a = log 6

⇒ a = ( log 6 ) / 10

Now required time when population is double :

P(n ) = 2P(0)

⇒  K e^ (n × a) = 2k e^(0 × a )

⇒ e^ [ n ×( log 6 ) / 10 ] = 2

⇒ n ×( log 6 ) / 10 = log 2

⇒ n = ( 10 × log 2 ) / log 6

⇒ n =  ( 10 × 0.3010 ) / 0.7782

⇒ n = 3.8679 hours

⇒ n = 3.87 hours

Therefore, the population of the bacteria will take 3.87 hours to get double.

The above question is incomplete , the complete question is:

A bacteria population increases sixfold in 10 hours. Assuming normal growth, how long did it take for their population to double?

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variety of statistics for 1057 inernet users are  = (0.9180, 0.8998)  solve by given question .

population proportion is the share of a population that belongs to a particular category. Confidence intervals are used to estimate population proportions.

Let p be the population proportion of respondents who say the Internet has been a good thing for them personally.

=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]

where z* = Critical value p = Sample proportion,n = sample size.

As per given , we have

n= 1057 By z-table , Critical value for 95% confidence interval : z*= 1.96

Then, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. will be :

=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]

=0.9+-1.96[tex]\sqrt{.9*(1-.9)/1057}[/tex]

=0.9180, .8998

Hence, the required 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally = (=0.918, .881)

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It says that raise school is 1. 7 miles from his house the student walks 17 miles in a 5-day school week

If the school is 1.7 miles from the student's house, then the round trip distance between the house and school is 2 times 1.7 miles, or 3.4 miles per day.

A mile is defined as the unit of length, which is exactly equal to 5280 feet, or 1760 yards, and standardized as exactly 1609.344 meters by the International agreement in 1959. It is the largest unit that is commonly used to measure the distance between places that are far from each other.

To find out how many miles the student walks in a 5-day school week, we can multiply the daily distance by the number of school days in a week:

3.4 miles/day x 5 days/week = 17 miles/week

Therefore, the student walks 17 miles in a 5-day school week

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The possible values of the number of quarters are at least 14 and more.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

1 dime = $0.10

1 quarter = $0.25

Number of dimes = x

Number of quarters = y

Now,

He has at most 25 coins worth at least $4.60 combined.

This means

we can write two inequalities.

x + y ≤ 25 ____(1)

0.10x + 0.25y ≥ 4.60 _____(2)

Now,

From (1) and (2).

x ≤ 25 - y

Substituting in (2).

0.10x + 0.25y = 4.60

0.10 (25 - y) + 0.25y ≥ 4.60

2.5 - 0.10y + 0.25y ≥ 4.60

2.5 + 0.15y ≥ 4.60

0.15y ≥ 4.60 - 2.5

0.15y ≥ 2.1

y ≥ 2.1/0.15

y ≥ 14

This means,

y is at least 14.

Thus,

The possible values of the number of quarters are at least 14 and more.

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Answer: Since triangle QRS and triangle TUV are both triangles, we can use the fact that the sum of the interior angles in a triangle is 180 degrees.

In triangle QRS, the measure of angle Q is 117 degrees and the measure of angle R is 180 - 117 = 63 degrees. The measure of angle S is 180 - 63 = 117 degrees, since the angles in a triangle add up to 180 degrees.

In triangle TUV, the measure of angle T is 180 - 30 = 150 degrees and the measure of angle U is 30 degrees. The measure of angle V is 180 - 150 = 30 degrees, since the angles in a triangle add up to 180 degrees.

The measures of LQ and LS can be found using the fact that the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

The measure of LQ is equal to the sum of the measures of angles R and T:

LQ = 63 + 150 = 213 degrees

The measure of LS is equal to the sum of the measures of angles Q and U:

LS = 117 + 30 = 147 degrees

So the measure of LQ is 213 degrees and the measure of LS is 147 degrees.

Step-by-step explanation:

The value of x that makes the shape a parallelogram is 2/3

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are kite, square, rectangle, parallelogram and so on.

A parallelogram is a quadrilateral with two pairs of parallel sides. Each parallel sides are equal. Also, the diagonals of a parallelogram bisect each other.

From the diagram, the diagonals bisect each other in other to be a parallelogram, hence:

6x = 3x + 2

3x = 2

x = 2/3

The value of x is 2/3

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a) Using the information provided, the sales forecast in retail dollars for the new "Bongo Bumpers" toy in Canada for its first year of launch is $6,259,500.

b) If Spin Master had an issue with the distribution and was only able to achieve 70 percent distribution, the sales forecast will be $4,381,650.

A sales forecast is a projected future sales revenue based on estimated sales units and selling price under some predicted market situations.

The sales forecast is usually broken down into various periods, for example, a week, a month, or a year.

The purposes of a sales forecast are to:

The unit selling price per Bongo Bumpers toy = $25

The population of Canadian males aged 5 - 9 years = 963,000

The percentage of Canadian boys who would see the advertised toy = 65%

The estimated percentage of Canadian boys who would ask their parents to purchase the toy = 80%

The estimated percentage of Canadian parents who would buy the toy as requested by their male children = 50%

Estimated sales units for the toys = 250,380 (963,000 x 0.65 x 0.8 x 0.5)

Sales forecast for the Bongo Bumpers toys = $6,259,500 ($25 x 250,380)

With 70% distribution, the Sales Forecast = $4,381,650 ($6,259,500 x 70%)

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The level of measurements that the data we collect is weights in pounds is Ratio level.

The Ratio level of measurement: At this level of measurement, observations can have a value of zero as well as equal intervals. Although the characteristics are similar to those of interval level measurement, the zero in the scale distinguishes this sort of measurement from others. In the ratio level of measurement, the divisions between the points on the scale have an equivalent distance between them. We may confidently assert that 20 pounds are twice as heavy as 10 pounds. Ratio variables also have a meaningful zero-point.

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The completed statements with regards to the projectile motion of the football are presented as follows;

This graph is a nonlinear function

The hang time of the football is 3 seconds

The football reaches its maximum height when t = 1.5 seconds

The maximum height is about 11 meters

For t between t = 0 and t = 1.5, the height is increasing

The motion of a projectile is one that involves an object thrown into the air or into space, which is acted upon by only gravitational force.

The graph in the question, showing the scale on the x-axis obtained from a similar question on the internet, indicates that we get;

The x-intercept of the graph are; (0, 0), and (3, 0)

Therefore;

The time the football is in the air, which is the hang time of the football can be obtained from the difference between the x-values of the x-intercept as follows;

Hang time = 3 - 0 = 3

The graph indicates that the coordinates of the maximum height is (1.5, 11). Therefore;

The height at t = 0 is 0 meters, and the height at t = 1.5 seconds is 11 meters, therefore; the height is increasing between t = 0 and t = 1.5 seconds

For t between t = 0 and t = 1.5, the height is increasing

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Answer:

Nonlinear

3

1.5

11

increasing

Step-by-step explanation:

The necessary equation is [tex]L= 52+2D[/tex], and the necessary overall length is [tex]114 miles[/tex].

Given: A road is being extended by construction workers. The road already had a length of miles, and the crew is continuously extending it by miles. Let the number of days the crew has worked and the distance of the entire road (in miles) be represented by D and L respectively. Create a corresponding equation L to D.

According to the inquiry,

The road's initial length is 52 miles.

The daily length of roadways that a crew adds is 2 miles.

This number represents the number of days the crew worked.

The total length of the road that the crew built is represented by L.

A given condition-based equation can be written as [tex]L= 52+2D[/tex].

Now, the crew's total length of the road after 31 days of construction is calculated.

[tex]L= 52+2*31\\L=52+62\\L=114 miles[/tex]

As a result, the needed equation and the total length is [tex]L= 52+2D[/tex]  and 114 miles respectively.

The complete question is:-

A construction crew is lengthening a road. The road started with a length of 52 miles, and the crew is adding 2 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D . Then use this equation to find the total length of the road after the crew has worked 31 days.

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If Lin walks at a speed of 2. 5 miles per hour. Andre walks at a speed of 3 miles per hour. It will take 4 hours until Lin and Andre meet on the path.

Lin and Andre are walking toward each other on a 22-mile trail, so they will meet when the sum of the distances they have walked is equal to 22 miles. Let's call the time they walk until they meet "t".

During this time, Lin will have walked a distance of 2.5t miles, and Andre will have walked a distance of 3t miles. The sum of these distances is equal to 22 miles, so we can set up the equation:

2.5t + 3t = 22

Combining like terms, we get:

5.5t = 22

Dividing both sides by 5.5, we get:

t = 4

So it will take Lin and Andre 4 hours to meet on the path.

Note that we could have also solved this problem by using the formula:

time = distance / speed

For Lin, the time to cover the 22-mile distance would be:

time = distance / speed = 22 / 2.5 = 8.8 hours

For Andre, the time to cover the 22-mile distance would be:

time = distance / speed = 22 / 3 = 7.33 hours

Since they are walking towards each other, we can add their times to get the time it takes for them to meet:

time = 8.8 + 7.33 = 16.13 hours

However, we can see that this answer is not correct, as it is greater than the time it would take for either of them to cover the entire distance. This is because the time it takes for them to meet is less than the sum of their individual travel times, due to them moving towards each other.

So we go back to our original equation and solve for "t" to get the correct answer of 4 hours.

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Answer:

5)1/12

6) 25%

Step-by-step explanation:

5)The odds of Mr Douglas eating two slices of cheese pizza can be calculated by doing 3/(5 + 1 +3) = 1/3

the second slice's odds can be calculated by doing 2/(5+1+2) = 1/4

Multiply these to get the odds of two being eaten

1/4 times 1/3 is 1/12.

6) the odds of her selecting a red pen the first time is 50%. to do it again would be another 50% chance. 50% times 50% is 25%.

Answer:

NOT

Step-by-step explanation:

There are no pairs of congruent sides.

If Benjamin invests $400 in a savings account that earns 5% interest each year, the expression that shows the correct balance is  A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

The principal amount = $400

interest rate = 5%

The equation of the simple interest

A = P (1+ rt)

Where A is the final amount

P is the principal amount

r is the interest rate

t is the time period

The final amount after one year

= 400( 1 + 0.05×1)

= 400(1 + 0.05)

The final amount after two year

= 400(1 + 0.05)(1 + 0.05)

The final amount after three year

= 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

Therefore, the balance amount after three years is A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

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Answer: none of these

Step-by-step explanation:

87 and 1/2% should be written as 87.5%

Answer:

A semicircle can be drawn by first drawing a diameter of a circle, which is a line segment connecting two points on the circumference that passes through the center of the circle. Then, the semicircle can be constructed by drawing an arc that is half of the circumference of the circle and connecting the ends of the arc to the endpoints of the diameter.

A quarter circle can be drawn in a similar way, but instead of drawing an arc that is half of the circumference, you would draw an arc that is a quarter of the circumference. To do this, you would need to find the central angle that subtends the arc and divide it by 4. The quarter circle can then be constructed by drawing an arc with this central angle and connecting the ends of the arc to the endpoints of a radius of the circle, rather than the diameter.

In both cases, you can use a compass or a protractor to accurately draw the arcs.

The scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:

k = zy/ab.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The figures for this problem are given as follows:

Hence the scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:

k = zy/ab.

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12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.

The second smallest number that has 1,2,3,4 and 5 in them is 12354. This number is made up of the digits 1, 2, 3, 4, and 5 in that order. It is the second smallest number because the smallest number that contains these digits is 12345.

To form this number, we start by arranging the digits in descending order, from the largest to the smallest, 5, 4, 3, 2 and 1. We then combine the digits together to form 12354.

12354 is the second smallest number because it contains all the digits 1, 2, 3, 4 and 5 in that order. This number can be used in different ways, such as counting, addition, subtraction, multiplication and division. For example, 12354 divided by 4 equals 3088.75.

The number 12354 can also be used in other ways, such as to represent a date or time. For example, the number 12354 can represent the date 12/3/54, which is December 3, 1954.

In conclusion, 12354 is the second smallest number that contains the digits 1, 2, 3, 4 and 5 in that order. It can be used in a variety of ways, such as counting, addition, subtraction, multiplication and division, as well as to represent dates and times.

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The exponential function that best models the number of game systems sold, in million, x years since 2015 is given as follows:

y = 30.5(0.7)^x.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which:

Considering the graph, the parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 30.5(0.7)^x.

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When ever the area is calculated the units will have a degree of two.

The area is defined as the space covered by any two-dimensional body. The unit if the area is calculated as square units. The square units come because the area is calculated by the two parameters of length.

The area of the rectangle is calculated by the multiplication of the two lengths like length and width.

Similarly, the area of the circle is calculated by taking the square of the radius of the circle it means that the length here is also multiplied by two times.

Therefore, the area is calculated in an square units.

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The required measure of angle m∠Q is 42 degrees, as of the given condition.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°

Here,
In a triangle, the sum of the angles is always equal to 180 degrees. Therefore, for triangle OPQ,

m∠O + m∠P + m∠Q = 180°

Using the given information,

m∠O = (6x - 14)°

m∠P = (2x + 16)°

m∠Q = (2x + 8)°

(6x - 14)° + (2x + 16)° + (2x + 8)° = 180°

10x + 10 = 180°

10x = 170

x = 17

Substituting the value of x back into the expression for m∠Q,

m∠Q = (2x + 8)°

m∠Q = (2 * 17 + 8)°

m∠Q = 42°

So the value of m∠Q is 42 degrees.

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Answer:

29.22

Step-by-step explanation:

answer:

if you multiply the 2 sides of the ratio by a number it will give you an equivalent ratio

5:8 = 10:16 multiplying by 2

5:8 = 15:24 multiplying by 3

5:8 = 20:32 multiplying by 4

5:8 = 25:40 multiplying by 5

5:8 = 30:48 multiplying by 6

5:8 = 35:56 multiplying by 7

and so on ...

Based on the information, it can be inferred that the original recipe contained 0.9 cups of banana.

To calculate the original amount of banana contained in the smoothie recipe we must perform the following mathematical operation:

We know that the final recipe has 1.4 cups of banana and that to make it have a more intense banana flavor they added 1/2 cups of banana, that is, 0.5 cups.

According to the above, we must subtract the amount that was added to the final amount to find how much the recipe has as shown below:

1.4 drinks - 0.5 drinks = 0.9 drinks

According to the above, the original recipe would have 0.9 cups of banana.

Note: This question is incomplete. Here is the complete information:

To make a strawberry banana smoothie, a recipe calls for 1.75L cups of strawberries and some bananas. To make the recipe taste more like banana, 1/2 C cup more banana was added to the blender. The smoothie now has 1.4 cups of bananas. How many cups of bananas were in the original recipe?

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Answer:

[tex]10[/tex] four point questions and [tex]30[/tex] two point questions

Step-by-step explanation:

Let's say [tex]f =[/tex] [tex]\text{number of four point questions}[/tex] and[tex]t = \text{number of two point questions}[/tex]. The total number of questions is [tex]40[/tex], therefore [tex]t + f = 40[/tex]. We know the test is worth [tex]100[/tex] points so we can write [tex]2t + 4f = 100[/tex]. We have a system of equations: [tex]t + f = 40 \text{ and } 2t + 4f = 100[/tex]. We can rewrite [tex]t[/tex] as [tex]t = 40 - f[/tex]. We rewrite this in the equation [tex]2t + 4f = 100[/tex]. Since [tex]t = 40 - f[/tex], we have [tex]2 \cdot (40 - f) + 4f = 100[/tex]. Distributing & simplifying gives

[tex]2 \cdot (40 - f) + 4f = 100\\(80 - 2f) + 4f = 100,\\\text{Remove parentheses} 80 - 2f + 4f = 100,\\80 + (-2f) + 4f = 100\\80 + 2f = 100,\\\text{Subtract 80 from both sides} 2f = 20,\\\text{Divide 2 by both sides} f = 10.\\[/tex]

Since we determined [tex]t = 40 - f[/tex] and [tex]f = 10[/tex], subtracting [tex]10[/tex] from [tex]40[/tex] will give [tex]t = 30[/tex].

Therefore, there are [tex]10[/tex] four point questions and [tex]30[/tex] two point questions.

Hope that helps!

Answer:

See below.  The answer is 8.8 feet, but none of the options offers this value.

Step-by-step explanation:

I get 8.8 feet.

2^2 + x^2 = 9^2

4 + x^2 = 81

x^2 = 77

x = 8.77496 to be exact.

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Answer:

27%

Step-by-step explanation:

a percent is a part of 100

so if we get the denominator to 100, the numerator is the percent of the equation

54/200

in order to get 200 to 100, we have to divide by 2.

however we have to divide the numerator aswell as if we don't, we simply just half the equation.

54/2 = 27

200/2 = 100

27/100 is the new equation. referring back to the first statement, i made, the numerator would be the percent of the equation that is a part of 100

27%.

54/200 is equal to 27/100. all we did was divide both the numerator and denominator by 2.