Answer:
The Inequality representing the number of hours she want to babysit to make a profit is [tex]5+3x>26[/tex].
Katie should babysit for more than 7 hours in order to make profit.
Step-by-step explanation:
Given:
Money spent on advertising = $26
Initial fee = $5
Hourly charge = $3
We need to find the number of hours she want to babysit to make a profit.
Solution:
Let the number of hours be 'x'.
Now we can say that;
The sum of Initial fee and Hourly charge multiplied by number of hours should be greater than Money spent on advertising .
framing in equation form we get;
[tex]5+3x>26[/tex]
Hence The Inequality representing the number of hours she want to babysit to make a profit is [tex]5+3x>26[/tex].
On Solving the above Inequality we get;
Now Using Subtraction property of Inequality we will subtract both side by 5 we get;
[tex]5+3x-5>26-5\\\\3x>21[/tex]
Now Using Division Property of Inequality we will divide both side by 3 we get;
[tex]\frac{3x}{3}>\frac{21}{3}\\\\x>7[/tex]
Hence Katie should babysit for more than 7 hours in order to make profit.
Interpretation:
when x=7
Amount earned will be = [tex]5+3x=5+3\times7 =5+21=\$26[/tex]
Profit earned will be = Amount earned - Money spent on advertising = 26 -26 =0
when x= 8
Amount earned will be = [tex]5+3x=5+3\times8 =5+24=\$29[/tex]
Profit earned will be = Amount earned - Money spent on advertising = 29 -26 =$3
Hence at 7 hours of babysitting profit will be 0 and at 8 hours of babysitting profit will be $3.
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.
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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Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice.
Answer:
22 yards
Step-by-step explanation:
Use a (+) sign for yards gained and a (-) sign for yards lost.
Geno gained 4 yards 3 times: (+4) × 3.
Geno lost 1 yard twice: (-1) × 2.
Geno gained 6 yards twice: (+6) × 2.
Net change
in field position
=
(4 × 3) + (-1 × 2) + (6 × 2)
=
12 − 2 + 12
=
10 + 12
=
22.
Geno gained 22 yards.
The net change in the position of Geno if In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice, is 22 yards.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice,
Calculate the net change in position as shown below,
The net change = Total gained - Total lost,
Total gained = 4 × 3 + 6 × 2
Total gained = 12 + 12
Total gained = 24
Total lost = 1 × 2
Total lost = 2
The net change = 24 - 2
The net change = 22
Thus, the net change in the Geno position is 22 yards.
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The complete question is:
Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice. Find the net change in the position of Geno.
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
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.
Find the distance between the pair of points given on the graph
Answer: distance = 5
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = 1
x1 = - 2
y2 = 0
y1 = - 4
Therefore,
Distance = √(1 - - 2)² + (0 - - 4)²
Distance = √3² + 4² = √9 + 16 = √25
Distance = 5
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
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.
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]
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
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
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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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]
For a project on Egypt, Nick is building a paper model of a square based pyramid. The square base measures 8 inches by 8 inches. The slant height is 10 inches. Which measurement BEST describes the amount of construction paper needed to make this pyramid? (round to nearest whole number)
Answer:
Step-by-step explanation:
The square base measures 8 inches by 8 inches. The slant height is 10 inches.
The formula for determining the area of the square base of the pyramid is l^2. Therefore,
Area of the base = 8^2 = 64 inches^2
The formula for determining the perimeter of the square base is
4l. It becomes
4 × 8 = 32 inches
The amount of construction paper needed to make this pyramid is the total surface area of the pyramid. Therefore,
Total surface area = (1/2 × 32 × 10) + 64
= 160 + 64 = 224 inches^2
Nick will need approximately 224 square inches of construction paper for his square based pyramid project with a base measuring 8 inches by 8 inches and a slant height of 10 inches.
Explanation:To find the amount of construction paper needed for Nick's square based pyramid project, we need to calculate the surface area of the pyramid. The surface area of a pyramid includes the area of the base plus the area of the four triangular sides.
The area of the base (Abase) is the side length squared:
Abase = side × side = 8 inches × 8 inches = 64 square inches.
The area of one triangular side (Atriangular side) is given by the formula:
Atriangular side = 1/2 × base × slant height.
For Nick's project, the base of a triangular side is equal to the side of the square, so:
Atriangular side = 1/2 × 8 inches × 10 inches = 40 square inches.
Since there are four identical triangular sides:
Total area of triangular sides = 4 × 40 square inches = 160 square inches.
Adding the base and triangular sides areas together gives us the total construction paper needed:
Total construction paper needed = Abase + Total area of triangular sides = 64 square inches + 160 square inches = 224 square inches.
Therefore, Nick will need approximately 224 square inches of construction paper for his project. To get the nearest whole number, we round 224 to 224.
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
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
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.
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
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
x2 - 2x - 24 = 0
Solve for X
Answer:
x = 6 or x = -4
Step-by-step explanation:
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x - 6 =0 or x + 4 = 0
x = 6 or x = -4
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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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
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.
how to solve (-2/5x)(2/6y)=
Answer:
-2yx/15?
Step-by-step explanation:
The recommended angle for a wheel chair ramp is 5 degrees. If the rise of the ramp to go up the steps is 2 feet, find the horizantal run length that the ramp must start. (Round to one decimal place)
wheel chair ramp
Answer:
22.9 feet
Step-by-step explanation:
You are using Tangent because you have the opposite and adjacent sides
Tan 5 = 2/x
x Tan 5= 2
x= 2/Tan5
= 22.860
To find the horizontal run length of a wheelchair ramp with a 5-degree angle and a 2-foot rise, use the tangent function of trigonometry. Plug the given values into the tangent formula, rearrange to solve for 'Run', and calculate to get a run length of approximately 22.8 feet.
Explanation:The question is referring to the use of trigonometry to solve real-life problems. Here, we are going to use the tangent of the angle, which is defined as the ratio of the opposite side (the rise) to the adjacent side (the run). In this case, we know that the angle is 5 degrees and the rise is 2 feet.
In mathematical terms, this can be written as:
Tan(ρ) = Rise/Run
Substituting the values into the equation, we get:
Tan(5°) = 2/Run
Solving for Run, we get:
Run = 2/Tan(5°)
You can find this value using a calculator, rounding to the nearest tenth, to get the run as approximately 22.8 feet.
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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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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
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In May, the school store sells 80 erasers. In June, the store sells only 16 erasers. What is the percent of change in erasers sold from May to June?A) 80% B) 20% C) 64% D) 80%
Answer: 80%
Step-by-step explanation:
Since we have given that
Number of erasers sold in May = 80
Number of erasers sold in June = 16
Decrement in 1 month gap is given by
16-80=-64
So, Percentage of change in erasers sold from May to June is given by
[tex]\frac{-64}{80}[/tex] × 100
= -80% (Decreased 80%)
Answer:
80%
Step-by-step explanation:
I took a test with this question on it
To receive a grade of A on 80 question test 90% of the questions must be answered correctly what is the maximum number of questions that can't be missed to still receive an A
Answer:
Step-by-step explanation:
Total number of questions in the test is 80.
To receive a grade of A on the 80 question test, 90% of the questions must be answered correctly. It means that the number if questions that must be answered correctly would be
90/100 × 80 = 0.9 × 80 = 72.
Therefore, the maximum number of questions that can't be missed to still receive an A is 72