Answer: the correct option is D
Step-by-step explanation:
Note: the chapter summary can be found in chapter 22 of the Pearson Education,Inc. (PDF format).
In the chapter, a single slit aperture diffraction and a circle aperture diffraction was discussed.
A circle aperture diffraction occurs when light pass through a tiny hole or aperture to produce a circular disc image. This disc is called Airy's disc.
To calculate the aperture diameter,d we can use the formula below;
d= m× λ/ sin θ. ------------------------------------------------------------------------------(1).
The single slit aperture diffraction is when light pass through a single slit to produce. The wavelength, λ is greater than the width of the aperture.
There are a total of 32 staff members working in the aquarium 5/8 of the staff are security guards. How many security guards are there in the aquarium
Answer:
Step-by-step explanation:
Total staff is 32
Security guards = 5/8 of 32
= 5/8 × 32
= 5 × 4
= 20 security guards
There were total 20 security guards.
What is fraction?Fractions are used to represent smaller pieces of a whole.
Given that, There are a total of 32 staff members working in the aquarium, 5/8 of the staff are security guards.
Total staff is 32
Security guards = 5/8 of 32
= 5/8 × 32
= 5 × 4
= 20
Hence, there were 20 security guards.
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In a computer catalogue, a computer monitor is listed as being 19 inches. This distance is the diagonal across the screen. If the height is 10 inches, what is the width to the nearest inch?
Answer:
[tex]3\sqrt{29}[/tex] or approximately 16.16
Step-by-step explanation:
The diagonal (hypotenuse) mesures 19 inches.
The height of the computer monitor is 10 inches.
Use the Pythagorean theorem:
a and b are the triangle's legs
h is the hypotenuse
[tex]a^{2} + b^{2} = c^{2}\\ \\a^{2} + 10^{2} = 19^{2}\\ \\361 - 100 = a^{2}\\ \\a = \sqrt{261} \\\\a = 3\sqrt{29}[/tex]
How do you solve for 2-9|-8b+8|=-70?
Answer:
The solution for the given equation is 0 and 2.
Step-by-step explanation:
Given equation:
[tex]2-9|-8b+8|=-70[/tex]
To solve for [tex]b[/tex].
Solution:
In order to solve the given equation, we will first isolate the absolute value expression:
Step 1: Isolating the absolute value expression
[tex]2-9|-8b+8|=-70[/tex]
Subtracting both sides by 2.
[tex]2-2-9|-8b+8|=-70-2[/tex]
[tex]-9|-8b+8|=-72[/tex]
Dividing both sides by -9.
[tex]\frac{-9|-8b+8|}{-9}=\frac{-72}{-9}[/tex]
[tex]|-8b+8|=8[/tex]
Step 2: Set the value of the absolute value expression to positive and negative.
[tex]-8b+8=8[/tex] and [tex]-8b+8=-8[/tex]
Step 3: Solve for the unknown.
Solving for [tex]b[/tex].
Subtracting both sides by 8.
[tex]-8b+8-8=8-8[/tex] and [tex]-8b+8-8=-8-8[/tex]
[tex]-8b=0[/tex] and [tex]-8b=-16[/tex]
Dividing both sides by -8.
[tex]\frac{-8b}{-8}=\frac{0}{-8}[/tex] and [tex]\frac{-8b}{-8}=\frac{-16}{-8}[/tex]
[tex]b=0[/tex] and [tex]b=2[/tex] (Answer)
Thus, the solution for the given equation is 0 and 2.
Perform the indicated operation. 5/8-[1/2-(-1/4)]
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]
Solution:
Given that, we have to perform the indicated operation
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})][/tex]
We can use BODMAS rule to perform the operation
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right
So, in the given expression, we have to solve for brackets first
Solve the innermost bracket
[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}][/tex]
Now solve the bracket again
[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}] = \frac{5}{8}-[\frac{4+2}{8}] = \frac{5}{8}-[\frac{6}{8}][/tex]
Now remove the parenthesis
[tex]\rightarrow \frac{5}{8} - \frac{6}{8}[/tex]
Now perform subtraction operation
[tex]\rightarrow \frac{5}{8} - \frac{6}{8} = \frac{5-6}{8} = \frac{-1}{8}[/tex]
Thus we got,
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]
Thus the indicated operation is performed
The combined height of one oak tree and one pine tree is 21 meters. The height of 4 oak trees stacked on top of each other is 24 meters taller than one pine tree. How tall is the oak tree and the pine tree
Answer:
Height of an oak tree= 9 meters
Height of a pine tree = 12 meters
Step-by-step explanation:
Given:
The combined height of 1 oak tree and 1 pine tree = 21 meters
Height of 4 oak trees = 24 meters more than 1 pine tree
To find the height of 1 pine tree and height of one oak tree.
Solution:
Let the height of one oak tree be = [tex]x[/tex] meters.
Let height of one pine tree = [tex]y[/tex] meters.
Combined height can be given as :
[tex]x+y=21[/tex]-------------[1]
Height of 4 oak trees = 24 meters more than 1 pine tree
The above statement can be given as :
[tex]4x=24+y[/tex]------------[2]
Rearranging equation [2] by subtracting both sides by [tex]y[/tex].
[tex]4x-y=24+y-y[/tex]
[tex]4x-y=24[/tex]-------------[2]
Adding rearranged equation [2] to [1].
[tex]x+y=21[/tex]
[tex]4x-y=24[/tex]
+--------------------
[tex]5x\ = 45[/tex]
Dividing both sides by 5.
[tex]\frac{5x}{5}=\frac{45}{5}[/tex]
∴ [tex]x=9[/tex]
Plugging in [tex]x=9[/tex] in equation [1]
[tex]9+y=21[/tex]
Subtracting both sides by 9.
[tex]9-9+y=21-9\\\therefore y=12[/tex]
Height of an oak tree= 9 meters
Height of a pine tree = 12 meters
Test scores were recorded for students in a statistics class. The scores for the first test had a standard deviation of 3.8 points. The scores from the second test had a standard deviation of 4.8 points. Choose the correct statement below.
1. The average test grade rose by 1 point
2. The scores of the second test were closer together than the first
3. The higher standard deviation of the second test indicates higher average scores on the second test than on the first
4. None of the above are true
Answer:
Step-by-step explanation:
The higher standard deviation of any data represents diversified data or data having more scattered value . Average value may be same for two samples of data having different standard deviation . So option one is incorrect. 3 rd option is also incorrect.
The scores of the second test were more widespread than the first , because its standard deviation is more for second test. option 2 is in- correct .
none is correct.
None of the supplied statements are true. The standard deviation is a measure of dispersion from an average, showing the spread of test scores, not average scores or proximity of scores. Therefore, a higher standard deviation means scores were more dispersed, not closer together.
Explanation:The correct statement is None of the above are true. The standard deviation is a measure of dispersion from an average. It reflects the variability or spread in a set of data. It does not provide information about the actual scores, their averages, or whether one test's scores were generally higher or lower than another's.
In this case, a standard deviation of 3.8 for the first test and 4.8 for the second test indicates that the test scores were more spread out around the mean on the second test compared to the first. It does not point to an increase in the average test grade. Furthermore, a higher standard deviation does not mean that the test scores were closer together; actually, it's the opposite – a higher standard deviation indicates that scores were more widely dispersed.
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how to solve (-2/5x)(2/6y)=
Answer:
-2yx/15?
Step-by-step explanation:
The popcorn stand sells only soft drinks and popcorn, and only one size of each. In fact, the same cup is used for both products this is part of the stand's "sales pitch. "A soft drink cost $2.00 and a popcorn cost $4.00. On a certain day, 120 cups were used and $330.00 was collected. How many soft drinks and how many popcorns were sold on that day? Use a system of equations approach to find your answer. Show all work.
Answer:
On that day 75 soft drinks and 45 popcorn were sold.
Step-by-step explanation:
Given:
Let the number of soft drinks be 'x'.
Let the number of popcorn be 'y'.
Number of cups sold = 120
Now we know that;
Number of cups sold is equal to sum of the number of soft drinks and the the number of popcorn.
framing in equation form we get;
[tex]x+y=120 \ \ \ \ equation \ 1[/tex]
Also Given:
Cost of Soft drink = $2 .00
Cost of popcorn = $4.00
Total amount collected = $330.00
Now we know that;
Total amount collected is equal to sum of the number of soft drinks multiplied by Cost of Soft drink and the number of popcorn multiplied Cost of popcorn.
framing in equation form we get;
[tex]2x+4y = 330 \ \ \ \ eqaution \ 2[/tex]
Hence The System of equation to determine the number of softdrinks and cups sold is [tex]\left \{ {{x+y=120} \atop {2x+4y=330}} \right.[/tex].
Now to find the number of each type of cups sold we will solve the above equations.
First we will multiply equation 1 with 2 we get;
[tex]2(x+y)=120\times2\\\\2x+2y =240 \ \ \ \ equation \ 3[/tex]
Now we will subtract equation 3 from equation 2 we get;
[tex]2x+4y-(2x+2y)=330-240\\\\2x+4y-2x-2y=90\\\\2y = 90[/tex]
Now Dividing both side by 2 we get;
[tex]\frac{2y}{2}= \frac{90}{2}\\\\y=45[/tex]
Now we will substitute the value of 'y' in equation 1 we get;
[tex]x+y=120\\\\x+45 =120\\\\x=120-45 = 75[/tex]
Hence On that day 75 soft drinks and 45 popcorn were sold.
Match the following. 1 . congruent circles the set of all points in a plane that are at a given distance from a given point in the plane 2 . circle two or more circles that lie in the same plane and have the same center 3 . concentric circles circles that have equal radii 4 . diameter a chord of a circle that contains the center of the circle 5 . radius a segment joining the center of a circle to a point of the circle
Answer:
1 is concentric circles
2 is concentric circles, they have same center
3 is congruent circles, they have equal radii
4 is correct
5 is correct
Step-by-step explanation:
Congruent circles are circles of the same size while concentric circles are circles that have same center but different radii. Diameter is the line passing through the center of a circle joining two points on the circumference while radius is the joining the center of the circle to any point on the circumference.
Choose which statement is true.
Question 3 options:
The product of (2x−5)(x^2+3x−1)is 2x^3+11x^2+13x+5 because the following are like term pairs: 6x^2+5x^2 and −2x+15x
The product of (2x−5)(x^2+3x−1)is 2x^3−11x^2−17x+5 because the following are like term pairs: −6x^2−5x^2 and −2x−15x
The product of (2x−5)(x^2+3x−1)is 2x^3+11x^2−13x+5 because the following are like term pairs: 6x^2+5x^2 and 2x−15x
The product of (2x−5)(x^2+3x−1)is 2x^3+x^2−17x+5 because the following are like term pairs: 6x^2−5x^2 and −2x−15x
The correct statement is,
⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
To find the correct statement about the expression.
Now, We have;
The expression is,
⇒ (2x - 5) (x² + 3x - 1)
Hence, We can simplify as;
⇒ (2x - 5) (x² + 3x - 1)
⇒ (2x³ + 6x² - 2x - 5x² - 15x + 5
⇒ 2x³ + x² - 17x + 5
Thus., The correct statement is,
⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.
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w is less than or equal to – 2 and greater than or equal to - 8
Use w only once in your inequality.
Answer:
-8 ≤w ≤-2
Step-by-step explanation:
The inequality -8 ≤ w ≤ -2 combines the given conditions into a single expression stating that the variable 'w' can take any value between -8 and -2 inclusive.
Explanation:In mathematics, when a single variable needs to satisfy multiple inequalities, we can write it in a combined form. Your conditions state that 'w' is less than or equal to -2, and 'w' is also greater than or equal to -8. This can be combined into a single inequality as follows: -8 ≤ w ≤ -2. This inequality indicates that the variable 'w' can take any value from -8 to -2, inclusive.
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Josie took a long multiple choice test. The ratio of the questions she got incorrect to the number of problems she got correct was 4:9. If there were 65 questions on the test, how many did Josie get incorrect
Answer:20 incorrect questions
Step-by-step explanation: using the ratio formula
Add up the correct n incorrect
4+9= 13 is the total ratio
Incorrect answer ratio is 4
So to know the number of incorrect answer is
4/13* number of questions on the test
4/13* 65= 20 incorrect answer
The length of Martin's driveway, rounded to the nearest foot, is 121 ft. What is the minimum possible length of the driveway? A 121.0 ft B 120.5 ft C 120.9 ft D 120.3 ft
Answer:
B. 120.5 ft
Step-by-step explanation:
Given:
Length of Martins drive way = 121 ft
We need to find the minimum possible length of the driveway
Solution:
Now we know that ;
When a number is rounded to nearest whole number.
We can say that the number is in decimal format.
Also rounding techniques applies when the decimal number has digit 5 or more in ten's place after decimal then the number in increase by 1 as a whole number.
Here the number is rounded to nearest foot which is 121 ft.
So we an say that;
Number ranging from 120.50 to 120.99 can be made to 121 as nearest foot.
Hence the minimum possible length of the drive way could be 120.5 ft
Zacarías and paz together have $756.80 if Zacarías has $489.50, how much does Paz have? Write and solve an addition equation to find how much money belongs to Paz.
ANSWER: Paz have $267.30
STEP BY STEP EXPLANATION
Let be Z for Zacarías and P for Pax
Z+P= 756.80
Z= 489.50
P=756.8 - Z
P=756.80 - 489.50
P= 267.30
Tito receives a weekly salary of $350 at an appliance store. He also receives a 5% commission on a total dollar amount of all sales he makes. What must his total sales be in a week if he is to make a total of $675
Answer:his total sales be $6500 in a week if he is to make a total of $675
Step-by-step explanation:
The total amount of money that Tito receives as weekly salary at an appliance store is $350.
He also receives a 5% commission on a total dollar amount of all sales he makes.
Let x represent his total sales in a week.
The amount of commission that he receives would be
5/100 × x = 0.05x
if he is to make a total of $675 in a week, it means that
0.05x + 350 = 675
0.05x = 675 - 350 = 325
x = 325/0.05 = $6500
By setting up an equation to represent Tito's total earnings and solving for total sales, we find that Tito must make $6500 worth of sales to earn a total of $675 in a week.
Explanation:The subject of this question is Mathematics, specifically dealing with algebraic calculations to find the value of the variable. The variable in this case is the total sales Tito must make to earn a total of $675 in a week.
We know that Tito earns a fixed weekly salary of $350 and he also receives a 5% commission on his total sales. He wants to know how much he needs to sell to reach a total earning of $675.
To solve this, we set up an equation to represent the total earnings that Tito wishes to make: $350 (salary) + 0.05x (sales commissions) = $675.
Now we solve the equation for x (total sales). First, subtract $350 from both sides to get 0.05x = $675 - $350, which simplifies to 0.05x = $325.
Next, divide both sides of the equation by 0.05 to find x, so x = $325 / 0.05.
Therefore, Tito's total sales in a week must be $6500 for him to make a total of $675.
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Levi wants to order the fractions 1/3, 2/5, and 11/30 in descending order? How can you help him by using a common denominator? Explain and order the fractions in descending order.
Answer:
The correct order of fractions in descending order will be:
[tex]\frac{2}{5}, \frac{11}{30}, \frac{1}{3}[/tex]
Step-by-step explanation:
Given fraction:
[tex]\frac{1}{3}, \frac{2}{5}, \frac{11}{30}[/tex]
To arrange them in descending order.
Solution:
In order to arrange the fractions in descending order, we will have to find the least common denominators.
To find the least common denominator, we will find the least common multiple of the denominators 3,5, and 30.
Since 30 is a common multiple of all 3 numbers, so it will be the least common denominator.
So, we multiply the numerators and denominators with same numbers in order to make the denominators = 30.
So, we have:
[tex]\frac{1}{3}, \frac{2}{5}, \frac{11}{30}[/tex]
⇒ [tex]\frac{1\times 10}{3\times 10}, \frac{2\times 6}{5\times 6}, \frac{11\times 1}{30\times 1}[/tex]
⇒ [tex]\frac{10}{30}, \frac{12}{30}, \frac{11}{30}[/tex]
Now, we compare the numerators and arrange them accordingly.
[tex]\frac{12}{30} > \frac{11}{30} > \frac{10}{30}[/tex]
So, the correct order of fractions in descending order will be:
[tex]\frac{2}{5}, \frac{11}{30}, \frac{1}{3}[/tex]
what is 32% of 240 PLEASE I WILL GIVE BRAINLIEST
Answer:
76.8
Step-by-step explanation:
Four out of 12 pieces of fruit in the basket are apples.Select all the fractions below that are equivalent to the fraction of fruit that is apples. 3/6 1/3 2/6 1/4 1/6
Four out of twelve converts to the fraction
4/12
if both sides are divided by four, you can simplify this fraction to
1/3
therefore, a is correct
1/3 times two makes
2/6
therefore, c is correct
1/3 has no more multiples in this selection
The equivalent fraction are 1/3 and 2/6.
What is Fraction?The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.
How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned in the fraction's upper portion.
Given:
Four out of twelve converts to the fraction
= 4/12
Now, simplifying the fraction we get
= 4/12
= 1/3
Now, 3/6 = 1/2
2/6 = 1/3
Hence, the equivalent fraction are 1/3 and 2/6.
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A basketball hoop in your backyard casts a shadow 109 inches long. You are 5‘8" tall in cast a shadow 62 inches long. Find the height of the basketball hoop in inches round your answer to the nearest whole number
Step-by-step explanation:
Height of shadow of basketball hoop = 109 inches
Height of person = 5 foot 8 inches = 68 inches
Height of shadow of person = 62 inches
[tex]\frac{\texttt{Height of person}}{\texttt{Height shadow of person}}=\frac{68}{62}=\frac{34}{31}[/tex]
[tex]\frac{\texttt{Height of basketball hoop}}{\texttt{Height of shadow of basketball hoop}}=\frac{34}{31}\\\\\frac{\texttt{Height of basketball hoop}}{109}=\frac{34}{31}\\\\\texttt{Height of basketball hoop}=119.55inches=120inches[/tex]
Height of the basketball hoop = 120 inches
Two hunters started to walk towards each other simultaneously from two different locations in the forest. The distance between them was 21 miles. The first hunter walked at a rate of 4 mph, while the second one walked at a rate of 3 mph. The first hunter took a dog with him, who ran at an average rate of 5 mph. The dog started to run towards the second hunter, met him and ran back to the first hunter. The dog repeated this until the two hunters met each other. How many miles did the dog run?
Answer:
The dog ran 15 miles
Step-by-step explanation:
The combined speed of the 2 hunters is 7mph, therefore, they will met in 21/7 = 3 hours, becuse they are walking in opposite directions. In this 3 hours the dog kept running and thus it ran 3*5 = 15 miles. Note that the position of the dog is always between the position of both hunters, therefore when both hunters met each other, the dog will be alredy there.
Plan A is a flat rate of $50 per month unlimited data. Plan B is zero dollars per month but you pay five dollars per gigabyte of data used. If you average about 6 GB of data used per month, which option will be least expensive?
Answer:
B
Step-by-step explanation:
For Plan A ---> you pay $50 per month flat
For Plan B,
average usage = 6 GB
cost per GB = $5 per GB
average cost per month = $5 per GB x 6 GB = $30
comparing the cost per month between the 2, we can clearly see that for plan B, $30 a month is the least expensive option
Plan B would be the least expensive option for someone who uses about 6 GB of data per month, costing $30, compared to Plan A's flat rate of $50 per month. It is important to also consider other costs and usage patterns when selecting a phone data plan.
When finding the least expensive phone data plan between a flat rate plan and a pay-per-gigabyte plan, you need to calculate the total costs based on the average data usage. In this case, Plan A offers unlimited data for a flat rate of $50 per month, while Plan B charges $5 per gigabyte of data used, with no monthly base cost.
For an average use of 6 GB of data per month:
Plan A would cost $50 every month, regardless of how much data you use.
Plan B would be 6 GB x $5/GB = $30 per month.
Comparing the two plans, Plan B is the least expensive option for someone who uses about 6 GB of data each month, as it would cost $30 as opposed to the $50 charged by Plan A.
However, it's important to consider your personal usage patterns and other potential costs, such as monthly charges for other services, occasional charges for peripherals or repairs, and any relevant annual costs or major costs when choosing a plan that fits your budget effectively.
A solid right pyramid has a square base with an edge length of s units and a height of h units. A solid right pyramid with a square base has an edge length of s units and a height of h units. Which expression represents the volume of the pyramid?
Answer:
The required expression is [tex]V=\dfrac{s^2h}{3}[/tex] units³.
Step-by-step explanation:
Consider the provided information.
The Volume square base pyramid is: [tex]V=\dfrac{a^2h}{3}[/tex]
Where a is the edge length and h is the height of the pyramid.
It is given that length of the side is s units and height of the pyramid is h unit.
Substitute the respective values in the formula above
The Volume square base pyramid is:
[tex]V=\dfrac{s^2h}{3}[/tex]
Hence the required expression is [tex]V=\dfrac{s^2h}{3}[/tex] units³.
What is [tex]x^{4} (x^{4} )[/tex]?
I will thank, comment and mark as Brainliest!
Answer:
The answer is x^8
Step-by-step explanation:
x^4(x^4)
=x^4*x^4
=(x*x*x*x)*(x*x*x*x)
=x*x*x*x*x*x*x*x
=x8
You are asked to draw a triangle with side lengths of 8 inches and 10 inches. What is the longest whole number length that your third side can be? Group of answer choices 18 20 16 21
Answer:
Correct number : c = 16
Step-by-step explanation:
The triangle theorem states that each side of the triangle is smaller than the sum of the other two and larger than their difference. We denote the three sides of a triangle as a, b, and c.
Suppose that a = 8 and b = 10 and as we see b is greater than a , b > a
b - a < c < b + a => 10 - 8 < c < 10 + 8 => 2 < c < 18
from the offered answers we choose number 16
c = 16
God is with you!!!
Answer:
Step-by-step explanation:
if a,b,c are three sides of a triangle,then a<b+c,b<c+a,c<a+b
or in general we can say any side < sum of other two sides.
third side<8+10
or third side <18
Here third side=16
if you are asked smallest side then any side >difference of other two sides.
third side >10-8 or>2
A cell phone company charges a monthly fee plus $.25 for each text message. The monthly fee is $30 and you owe $59.50. How many text messages do you have?
Answer: you have 118 text messages.
Step-by-step explanation:
Let x represent the number of text messages that you have or sent.
A cell phone company charges a monthly fee plus $.25 for each text message. The monthly fee is $30. This means that the total cost of x sending x messages in a month would be
0.25x + 30
If you owe $59.50, then your total cost is $59.50
Therefore,
59.50 = 0.25x + 30
0.25x = 59.50 - 30
0.25x = 29.5
x = 29.5/0.25
x = 118
Tiva earns $48 of 6 hours of babysitting. Complete each statement if Tiva keeps earning her babysitting money at this rate. For 8.5 hours of babysitting Tiva will earn? If Tiva babysits for Hours, she will earn $35.
Answer:
67
Step-by-step explanation:
48=6
35=8.5
67
Answer:
A.)$68
B.)$32
Step-by-step explanation:
For 8.5 hours of babysitting, Tiva will earn $ 68
If Tiva babysits for 4 hours, she will earn $32.
Thirty-eight is [tex]\frac{2}{5}[/tex] of what number?
Answer:
The number is 95.
Step-by-step explanation:
Solution,
Let the number be 'x'.
So, [tex]\frac{2}{5}[/tex] of 'x' = [tex]\frac{2}{5}x[/tex]
Now according to question, [tex]\frac{2}{5}x[/tex] is equal to 38.
So we can frame it as;
[tex]\frac{2}{5}x=38[/tex]
Now we solve it;
For solving it we will multiply both side by '5' using multiplication property and get;
[tex]\frac{2}{5}x\times5=38\times5\\\\2x=38\times5[/tex]
Now using division property, we will divide both side by '2' and get;
[tex]\frac{2x}{2}=\frac{38\times5}{2}\\\\x=19\times5=95[/tex]
Hence The number is 95.
Solve |2x - 2| < 8
A) { x| x < -3 or x > 5}
B) { x|-5 < x < 3}
C) { x|-3 < x < 5}
Select the perfect square trinomial for each polynomial. (There are 2 correct answers)
Question 1 options:
x^2−10x−25
x^2−18x+81
x^2+2x+1
x^2+7x+49
Answer:
x^2−18x+81
x^2+2x+1
Step-by-step explanation:
we know that
A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself
so
[tex]a^2\pm2ab+b^2=(a\pm b)(a\pm b)=(a\pm b)^2[/tex]
Verify each case
case a) x^2−10x−25
we know that
[tex](x-5)^2=x^2-10x+25[/tex]
therefore
Is not a perfect square trinomial
case b) x^2−18x+81
we know that
[tex](x-9)^2=x^2-18x+81[/tex]
therefore
Is a perfect square trinomial
case c) x^2+2x+1
we know that
[tex](x+1)^2=x^2+2x+1[/tex]
therefore
Is a perfect square trinomial
case d) x^2+7x+49
we know that
[tex](x+3.5)^2=x^2+7x+12.25[/tex]
therefore
Is not a perfect square trinomial
How many different ways can a teacher select 3 students from a class of 15 students to each perform a different classroom task?
Answer: 455ways
Step-by-step explanation:
This can be done according to rule of combination because it talks about selection.
In order to select r object from a pool of n objects, it is represented as nCr = n!/(n-r)!r!
Therefore to select 3 students from a class of 15students, this will give us 15C3.
15C3 = 15!/(15-3)!3!
= 15!/12!3!
= 15×14×13×12!/12!×6
= 15×14×13/6
= 455ways
This selection can be done in 455ways
The question is an illustration of combination
There are 455 ways of selecting the students
The number of students is 15, and the students to select are 3.
So, the number of selections is:
[tex]*nC_r = \frac{n!}{(n -r)!r!}[/tex]
This gives
[tex]^nC_r = \frac{15!}{(15 -3)!3!}[/tex]
Evaluate
[tex]^nC_r = 455[/tex]
Hence, there are 455 ways of selecting the students
Read more about combination at:
https://brainly.com/question/1216161