Answer:
x = 5
Step-by-step explanation:
You want the length of x in the figure showing similar triangles.
ProportionThe bottom edge of the triangle is 2/3 of the left edge.
The similar triangles have the same ratio of side lengths. That means x is 2/3 of (3+4.5):
(2/3)(7.5) = 5
The length x is 5 units.
If 12 subtracted from 7 time a number is equal to five times the sum of the number and 2,find the number.
Answer:
7-12=x
5(x+2)
7-12=-5
5(-5+2)
5(-3)
-15Step-by-step explanation:
a home with a swimming pool recently sold in the area for 250,000 another home in the same area that does not have a swimming pool but is similar in all other respects sold recently for 230,000 what can you assume from this information.a. All swimming pools cost $20.000b. The aproximate value of pool in that area is $20.000c. No home without a pool in that area will sell for more than $230.000d. Homes without a pool will sell faster in that area than homes with a pool
The correct answer is option b.The approximate value of pool in that area is $20.000c.
What is approximate value?A value that is similar to another value but not exactly equal to it is referred to as an approximation number. When the outcomes of the numerical calculations are unknown, the approximation is applied. They are typically used when greater place value decimal numbers emerge as a result.
Approximate value of a pool in the area = Value of home with a swimming pool in the area - Value of home without a swimming pool in the same area.
Value of home with a swimming pool in the area = $250,000
Value of home without a swimming pool in the same area = $230,000.
The approximate value of pool in the area = 250000 - 230000 = 20000.
Hence, the correct answer is option b. The approximate value of pool in that area is $20.000c.
Learn more about approximate value here:
https://brainly.com/question/2140926
#SPJ4
complete the following program to implement the user interface of the preceding exercise. for simplicity, only the units cm, m, and in are supported.
This program implements a user interface that can convert between the units centimeters (cm), meters (m), and inches (in) using the conversion formulas outlined.
#include <iostream>
using namespace std;
int main()
{
// Declare variables
double value;
char fromUnit;
char toUnit;
// Get input
cout << "Enter a value and the units you wish to convert from and to (cm, m, in): ";
cin >> value >> fromUnit >> toUnit;
// Convert the value
if (fromUnit == 'm' && toUnit == 'cm') {
value *= 100;
} else if (fromUnit == 'cm' && toUnit == 'm') {
value /= 100;
} else if (fromUnit == 'in' && toUnit == 'm') {
value /= 100 * 2.54;
} else if (fromUnit == 'm' && toUnit == 'in') {
value *= 100 * 2.54;
}
// Output the result
cout << "Result: " << value << toUnit << endl;
return 0;
}
The formula used in this program is the conversion between the units centimeters (cm), meters (m), and inches (in). The conversion formula used is as follows:
1 meter (m) = 100 centimeters (cm)
1 inch (in) = 2.54 centimeters (cm)
Therefore, if we are converting from centimeters (cm) to meters (m), the conversion formula is to divide the value by 100. If we are converting from meters (m) to centimeters (cm), the conversion formula is to multiply the value by 100. For the conversion from inches (in) to meters (m), the conversion formula is to divide the value by 100 and multiply it by 2.54. For the conversion from meters (m) to inches (in), the conversion formula is to multiply the value by 100 and divide it by 2.54.
For example, if we want to convert 5 meters (m) to centimeters (cm), we use the formula 5 * 100 = 500 centimeters (cm).
This program implements a user interface that can convert between the units centimeters (cm), meters (m), and inches (in) using the conversion formulas outlined above.
Learn more about conversion formula here:
https://brainly.com/question/29634168
#SPJ4
Simplify the following union and or intersection. [2,3] ∪ (3,∞)
The union of the set elements is [2, ∞)
How to determine the union or the intersectionFrom the question, we have the following parameters that can be used in our computation:
[2,3] ∪ (3,∞)
The above is a union set
The definition of the union set is that we write out all the elements in the set
Using the above as a guide, we have the following:
[2,3] ∪ (3,∞) = [2, ∞)
Read more about sets at
https://brainly.com/question/24713052
#SPJ1
han types the letters a, s, d, f, and then repeats them over and over what is the fith letter diego will type
The fith letter Diego will type is the letter a
How to determine the fith letter diego will typeFrom the question, we have the following parameters that can be used in our computation:
Letters: a, s, d and f
When the letters are repeated, we have
a s d f a s d f a s d f a s d f a s d f......
using the above as a guide, we have the following:
Fifth letter = a
Hence. the fifth letter is a
Read more about sequence at
https://brainly.com/question/7882626
#SPJ1
name each type of special quadrilateral that can meet the given condition. four right angles. make sketches to support your anwers
The name special quadrilateral that have four right angles. are Square , Rhombus , Rectangle have 4 right angle.
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
Square - The properties of square is it have 4 side and all side are equal and make 90 degree angle on all 4 side. that's why it has 4 right angle.
Rhombus - The properties of rhombus is it have 4 side and all side are equal and there diagonal cut each other at 90 degree that's why it has 4 right angle
Rectangle- The properties of square is it have 4 side and parallel sides are equal and make 90 degree angle on all 4 side.that's why it has 4 right angle.
Know more about quadrilateral with right angle click here ;https://brainly.com/question/29018314
#SPJ4
A credit sale of $2700 is made on July 15, terms 2/10, n/30, on which a return of $300 is granted on July 18. What amount is received as payment in full on July 24?
Answer:
$2,450
Step-by-step explanation:
2/10, n/30 = discounts of 2%
Credit sale = $2,700
Sale return = $200
Net Receivable =$ 2,700 - $ 200 = $2,500
Discount = 2,500 x %2 = 50
Payment Receipt = $2,500 - $50 = $2,450
please give brainliest
Using the diagram below, write a. in terms of Au b. in terms of AB and B A 2. Add the following vectors using the Triangle Law. a. 9 N on a heading of (S2"W) and 11 N on a heading of (N31*W). b. 7 m/s on a bearing of 30 and 2 m/s from a bearing of 343". (HINT: a vector "on" a bearing extends "out" from the origin and a vector "from" a bearing is directed in "toward" the origin) 3. Add the following vectors using the Component law a. 9 m/s (N30°E) and 2 m/s [N 80'E). b. 3 N in a direction 15" south of west and 4 N in a direction 12 east of south. 4. A plane is heading on a bearing of 200 with an airspeed of 400 km/h when it is blown off course by a wind of 100 km/h from the northeast Determine the resultant ground velocity of the plane. в M 0 18 Feb 血
Answer:
a. Au = 9cos(30) + 11cos(31)
b. AB = 9sin(30) + 11sin(31) and B = -9sin(30) + 11sin(31)
3. a. 9cos(30) + 2cos(80)
b. 3cos(15) + 4cos(12)
4. The ground velocity of the plane would be 349.4 km/h on a bearing of 225°.
A wildlife biologist captured and released 34 trouts from two different lakes and measured them to the nearest inch. She captured 17 of the fish from Fralest Lake and 17 of the fish from Lake Reverwalk. She then calculated the following statistical information.
Based on these samples, what generalization can be made?
A. At least half of the trout in Lake Reverwalk measure between 12 and 18 inches.
B. At least half of the trout in both lakes measure between 12 and 18 inches.
C. Not enough information is provided to draw any of these conclusions.
D. At least half of the trout in Fralest Lake measure between 12 and 18 inches.
The requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
Interquartile range (IQR), The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
In the given question we have 3 IQR data sets that jointly vary from 10 to 17 by this we can conclude that, at least half of the trout in both lakes measure between 12 and 18 inches.
Thus, the requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ1
Find the volume of the figure. Express the answer in terms of pi and then round to the nearest whole number.
Answer:
5025π m³
Step-by-step explanation:
the figure consists of two figures;
a cone and phere
volume of a cone=1/3πr²h
volume of hemisphere=2/3πr³
1/3×π×15×15×37=2775π
2/3×π×15×15×15=2250π
sum up the volumes
2775π+2250π
=5025π m³
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 5.7 meters and c = 9.6 meters, what is b? If necessary, round to the nearest tenth.
Answer:
[tex]b[/tex] ≈ [tex]7.7[/tex]
Step-by-step explanation:
We need to use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
In this case we have a and c. So let's plug those into the equation:
[tex](5.7)^2+b^2=(9.6)^2[/tex]
Solve:
[tex]32.49+b^2=92.16[/tex]
Round to the nearest tenth:
[tex]32.5+b^2=92.2[/tex]
Subtract 32.5
[tex]b^2=59.7[/tex]
Find 'b'
[tex]b=\sqrt{59.7}[/tex]
[tex]b[/tex] ≈ [tex]7.7[/tex]
I hope this helped you!
Be safe and have great day! (:
50
Question 10
A diagram has circles such that the area represents the populations of various
countries in the world. The circle for United States has a radius of 4.2 cm and the circle
for India has a radius of 8.7 cm. If 4% of the world's population is in United States, what
percentage of the world's population is in India? Round to the nearest percent.
Answer: 17%
Step-by-step explanation:
So, the formula to get the area of a circle is [tex]\pi r^{2}[/tex].
USA: [tex]4.2^{2} \pi[/tex] = 55.42cm
India: [tex]8.7^2\pi[/tex] = 237.79cm
From this, we can divide India by USA:
237.79 / 55.42 = 4.291
Then, with that we can multiply our 4% by 4.291:
4 * 4.291 = 17.16400
Rounded to the nearest percent is 17%
use the midpoint rule with the given value of n to approximate the integral. round the answer to four decimal places. integral 48 0 sin Vx dx, n=4
By using the midpoint rule, the value of n to approximate the integral is 9.24.
The integral of a function is a measure of the total area under the curve of the function over a given interval. The Midpoint Rule is a method used to approximate the value of an integral by dividing the interval into smaller subintervals, finding the midpoint of each subinterval, and using the height of the function at the midpoint to estimate the area of the subinterval.
In this specific problem, we are asked to approximate the integral of the function f(x) = sin root x from x = 0 to x = 48, using the Midpoint Rule with n = 4 subintervals. To do this, we divide the interval [0,48] into 4 equal subintervals of width
=> (48-0)/4 = 12.
The midpoint of each subinterval is calculated as follows:
1st subinterval: (0 + 12)/2 = 6
2nd subinterval: (12 + 24)/2 = 18
3rd subinterval: (24 + 36)/2 = 30
4th subinterval: (36 + 48)/2 = 42
Next, we find the height of the function f(x) = sin root x at each of these midpoints.
1st subinterval: sin root 6 = 0.77
2nd subinterval: sin root 18 = 0.97
3rd subinterval: sin root 30 = 0.87
4th subinterval: sin root 42 = 0.71
Finally, we multiply each height by the width of the subinterval to find the estimated area of each subinterval, and add up these areas to obtain the final estimate of the integral:
(0.77 * 12) + (0.97 * 12) + (0.87 * 12) + (0.71 * 12) = 9.24
So, our final estimate of the integral of f(x) = sin root x from x = 0 to x = 48 using the Midpoint Rule with n = 4 is 9.24. Rounding to 4 decimal places, our answer is 9.2400.
Complete Question:
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.
∫0 to 48 sin √x dx, n=4
To know more about integral here.
https://brainly.com/question/18125359
#SPJ4
Replace * with a digit so that the value of x is a whole number. Find all possibilities.
3x-694-10*
I need help with this please!
Answer:
d<0Step-by-step explanation:
3+d<3-d
3+d<3-dcancel equal terms
3+d<3-dcancel equal termsd<-d
3+d<3-dcancel equal termsd<-dMove the variable to the left
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0divide both sides
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0divide both sidesd<0
College level
Attached photo.
The value of b form the logarithmic equation [tex]log_b}3=0.7925[/tex] is 3.9998688.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
Given that, [tex]log_b}25=2.3219[/tex] and [tex]log_b}3=0.7925[/tex].
Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
We know that, logₐN=x is written exponential form as aˣ=N
Here, [tex]b^{2.3219}=25[/tex]
b=4.00006709
[tex]b^{0.7925}=3[/tex]
b=3.9998688
Therefore, the value of b is 3.9998688.
To learn more about the logarithmic equation visit:
https://brainly.com/question/14406101.
#SPJ1
Riley, Nathan, and Jeremy had a challenge to see who could
bike the farthest in one day. Riley biked 15 miles, Nathan biked
3 times as many miles as Jeremy and Jeremy biked 3 times as
many miles as Riley. How many miles did Nathan bike?
Nathan biked a total of 135 miles.
What is miles?Miles unit of distance between 2.1 map of the link of a johnny the tomb my list divided for the letting word thousand and the world to 1.609 kilometers my life report unit measurement is a united states uk kannada some other countries.
To solve this problem, we need to use the given information to find the amount of miles that Jeremy biked. Since Jeremy biked 3 times as many miles as Riley, we know that Jeremy biked 15 x 3 = 45 miles.
Since Nathan biked 3 times as many miles as Jeremy, we know that Nathan biked 45 x 3 = 135 miles. Therefore, Nathan biked a total of 135 miles.
To know more about miles click-
https://brainly.com/question/25631156
#SPJ1
What is the equation of a line with slope 1/4 which passes through the point (0,7)?
Answer:
y - 7 = 1/4 ( x - 0 )
y -7 = 1/4 x
y = 1/4 x + 7
prime factorization of 756
The solution is, prime factorization of 756 = 3*2*3*2*3*7
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
756
we know,
756 = 6*6*21
=3*2*3*2*3*7
as, we know, 2,3,7 all are prime.
so, prime factorization of 756 = 3*2*3*2*3*7
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ1
Question 1(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.
Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the length, in inches, of fish in a pond.
11 19 9 15
7 13 15 28
Determine if the data contains any outliers. If so, list the outliers.
There is an outlier at 28.
There is an outlier at 7.
There are outliers at 7 and 28.
There are no outliers.
Question 3(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 12.
The IQR is the best measure of variability, and it equals 12.
The range is the best measure of variability, and it equals 3.
Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5.
Question 6(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 1, 2, 3, 5, and 6. There are four dots above 7.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are outliers present.
Question 7(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of center for the data, and what is its value?
The median is the best measure of center, and it equals 6.5.
The mean is the best measure of center, and it equals 7.
The median is the best measure of center, and it equals 7.
The mean is the best measure of center, and it equals 6.5.
The median of 20 is the most accurate to use since the data is skewed.
Option C is the correct answer.
What is a histogram?A histogram is a representation of the distribution of data with intervals.
We have,
The data given shows a histogram that is skewed to the right.
Now,
Since the data is skewed.
The median is a better measure of the center of data than the mean.
Now,
Arrange the data in order:
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
Median = middle value.
Median = 20
Thus,
The median of 20 is the most accurate to use since the data is skewed.
Learn more about histograms here:
https://brainly.com/question/16819077
#SPJ1
Answer:
your question is a bit confusing...
Step-by-step explanation:
Rewrite 5^(2 .)5^(4) using a single exponent
Use the method for solving Bernoulli equations to solve the following differential equation. dy dx **=6x?y? Ignoring lost solutions, if any, the general solution is y= (Type an expression using x as the variable.)
The Bernoulli equation for this particular differential equation is [tex]dy/dx = 6x(y-1)[/tex] the final solution is [tex]y = x^3 + 1[/tex].
The Bernoulli equation for this particular differential equation is [tex]dy/dx = 6x(y-1)[/tex]. To solve the equation, we first use the substitution u = y – 1. This substitution simplifies the equation to [tex]dy/dx = 6xu[/tex], which is a first-order linear equation with constant coefficients. Now we can use the method for solving Bernoulli equations to find the solution.
We first find the integrating factor, which is [tex]I(x) = exp(∫6xdx)= exp(3x^2)[/tex]. Then we multiply both sides of the equation by I(x) to get [tex]I(x)dy/dx = 6xI(x)u[/tex]. We can now integrate both sides with respect to x and get the general solution of [tex]y = u + 1 = (1/I(x))∫6xI(x)dx + 1[/tex]. After calculating the integral, the final solution is [tex]y = x^3 + 1[/tex].
Learn more about Bernoulli equation here:
https://brainly.com/question/6047214
#SPJ4
Suppose that So, S1, S2,... is a sequence of subsets of N. Which one of the following sets is guaranteed to be different from all sets in the sequence? (a) S = {n | n & Sn²} (b) S = {n | n² & Sn²} (c) S = {n²| n & Sn²} (d) S = {n² | n² & Sn} (e) S = {n² | n & Sn} Explain why your chosen set is guaranteed not to be in the sequence So, S1, S2, ...
Suppose that So, S1, S2,... is a sequence of subsets of N the following sets is guaranteed to be different from all sets in the sequence is S = {n² | n² & Sn}.
Subsets are a part of the mathematical concept of sets. A set is anything that is wrapped in curly braces, such as "a,b,c,d." If set A is a collection of even integers and set B is composed of the numbers 2, 4, and 6, then set A is the superset of set B and set B is said to be a subset of set A. Review Sets Subset and Superset for further details.
Set A is referred to as a subset of Set B if each element of Set A is also present in Set B. In other words, Set B includes Set A.
As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.
Learn more about Subsets:
https://brainly.com/question/30379171
#SPJ4
Find the point slope form of a line with Slope: 6/7 that passes through (-5,4)
The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 6/7. Then the equation is given as,
y = (6/7)x + c
The equation passes through (-5, 4). Then we have
4 = (6/7) (-5) + c
4 = -30/7 + c
c = 58 / 7
Then the equation is given as,
y = (6/7)x + 58/7
7y = 6x + 58
The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.
More about the linear equation link is given below.
https://brainly.com/question/11897796
#SPJ1
Which two integers is /80
[tex] \sqrt{80} [/tex]
between? (A) 9 and 10 B) 7 and 8 8 and 9 D 11 and 12
Find the exact value of cos N in simplest radical form.
the simplest radical form of the exact value of cos A will be 7/8.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given a right-angle triangle that has a base of 14 height of √60 and a hypotenuse of 16.
From the general formula of cosine in a right-angle triangle:
Cos α = base/ hypotaneuse
In our case,
base = 14 and
hypotenuse = 16
Thus,
Cos A = 14/16
A = 0.5053 radians
Therefore, the simplest radical form of the exact value of cos A will be 7/8.
Learn more about right-angle triangles here:
https://brainly.com/question/3770177
#SPJ1
Complete question:
Out of 10,551 passing attempts, Drew Brees
completed 7,142
What is the completion percentage for
Drew Brees? Show or explain how you got
your answer.
Answer: 67.69%
Step-by-step explanation:
To calculate the completion percentage,
Divide the completed passes by the total passing attempts.
> 7142/10551
Then, multiply that answer by 100 to get the percentage.
> 67.69%
Use the cross products property to solve the proportion.9/10=d/6.4
Using the cross product property, the value of d is 5.76.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s
Given proportional relation is,
9 / 10=d / 6.4
Doing the cross multiplication,
9 × 6.4 = 10 × d
57.6 = 10d
d = 57.6 / 10
d = 5.76
Hence the solution of the proportion is d = 5.76.
Learn more about Proportions here :
https://brainly.com/question/26974513
#SPJ1
Rehan proved by mathematical induction that for all the positive integers,
is divisible by 3. Can you find an integer counterexample to show that this statement is not true? Explain.
A counterexample that shows that all the integers are not divisible by 3 is given as follows:
2.
How to obtain the counterexample?The statement for this problem is given as follows:
"All the positive integers are divisible by 3".
The statement is false, as only numbers whose sum of the digits is a multiple of 3 are divisible by 3, hence for example, the number 2 is not divisible by 3.
The counterexample is the statement that proves that a conjecture(another statement) is false, hence the number 2 is the counterexample showing that not all positive statements are divisible by 3.
More can be learned about conterexamples at brainly.com/question/3637836
#SPJ1
CAN SOMEONE HELP WITH THIS?✨
The population of the town is 2564 people after 4 years.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and x is the time period.
Given:
The initial population of the town is 1652 people.
And the town's population is tripling every 10 years.
Let y₀ be the initial population, r be the growth rate and t be the time.
So,
y = y₀(e[tex])^{rt}[/tex]
Substituting the values to the function,
y = 1652(e[tex])^{rt}[/tex]
In 10 years,
3y₀= y₀(e[tex])^{rt}[/tex]
r = log(3)/10
Now, the population of town after 4 years is,
y = 1652(e[tex])^{{ln(3)/10} \cdot {t}}[/tex]
y = 2563.64
y ≈ 2564 people.
Therefore, the population is y ≈ 2564, people.
To learn more about exponential growth;
https://brainly.com/question/12490064
#SPJ1