As per the unitary method, the cost of 8 bottles is $6.48
Unitary Method:
Unitary method is the way of solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
Hawa buys 15 bottles of apple juice at the corner store for a total cost of $12.15.
Here we need to find the if each bottle costs the same amount, how much is 8 bottles of juice.
Let x be the cost of one bottle.
so, based on the unitary method we can written the situation as,
15 bottles = costs $12.15
Therefore, the cost of one bottle is.
x = 12.15/15
x = 0.81
So, the cost of 8 bottle is calculated by multiplying the cost of one bottle with 8,
Then we get,
=> 8 x 0.81
=> 6.48
Therefore, the cost of 8 bottles is $6.48
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The perimeter of this triangle is not more than 30 cm. 2n+3 cm, 2n+2 cm, n cm
a. Write an inequality to show this.
b. Solve the inequality.
c. What are the largest possible lengths of the sides?
The inequality to represent the perimeter of the triangle is given by (2n + 3) + (2n + 2) + n ≤ 30
The solution to the inequality is n ≤ 5 The largest possible lengths of the sides is 13 cmInequality to represent the perimeter of a trianglePerimeter of the triangle = not more than 30 cmSide a = (2n + 3)cmSide b = (2n + 2) cmSide c = n cmSide a + side b + side c ≤ perimeter of the triangle
(2n + 3) + (2n + 2) + n ≤ 30
open parenthesis2n + 3 + 2n + 2 + n ≤ 30
5n + 5 ≤ 30
substract 5 from both sides
5n ≤ 30 - 5
5n ≤ 25
divide both sides by 5n ≤ 25/5
n ≤ 5 cm
The largest possible lengths of the sides is:
Side a = (2n + 3)cm
= 2(5) + 3
= 10 + 3
= 13 cm
Side b = (2n + 2) cm
= 2(5) + 2
= 10 + 2
= 12 cm
Side c = n cm
= 5 cm
So therefore, the largest possible length of the triangle is 13 cm
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Determine the smallest integer value of x in the solution of the following inequality.
-4x - 1 ≤ 13
Answer:
-3.5
Step-by-step explanation:
-4x-1+1≤ 13+1
-4x/-4 ≤ 14/-4
x≤ -3.5
what is the sum of the exponents of the prime factors of the square root of the largestperfect square that divides 12! ?
8 is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!
We are asked the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!.
As, the largest perfect square that divides 12! is
2^10 * 3^4 *5^2 = 2073600.
Now, the square root of the number 2073600 is,
1440
Now, we have to find the prime factorization of 1440
1440 = 2×2×2×2×2×3×3×5
Now, in the prime factorization of 1440
the exponent of 2 is 5, exponent of 3 is 2 and the exponent of 5 is 1.
So, the sum of the exponents of the prime factors be 5+2+1 = 8
Hence, 8 is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!
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A sample of size 50 from a normal distribution has sample mean 5 and sample variance 20. Find 96% confidence intervals for the variance and standard deviation of the distribution.
The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.
A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.
n = 50 makes up the sample size.
Furthermore, the sample variance is s² = 20
The following is the formula for both the variance confidence interval:
σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]
Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.
The 90% confidence interval's lower bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)
= 32.54
The 90% confidence interval's upper bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)
= 96.86
Consequently, the confidence level for the distribution's variance is (96.86, 32.54).
Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).
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What are some ways we have learned to solve percent increase or percent decrease problems? How are these ways related to one another?
The different ways of solving percent increase or percent decrease problems has been described below
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
One way to solve the percentage increase or decrease problem is by multiplying the original number by the percentage given and then adding the result with the original number.
Another method is by multiplier method
Here, the original number is taken as 1 and the given percentage has to be converted to decimal and then 1 and the percentage obtained as decimal is added or subtracted. The result obtained has to be multiplied by the original number to get the required number after increase or decrease
For the first method
Suppose the number is n and it is increased by p%
Required result is
[tex]n + \frac{p}{100}\times n\\n( 1 + \frac{p}{100})[/tex]
For the second method
Suppose the number is n and it is increased by p%
Here n is taken as 1 and p% is converted to decimal
then 1 and p% in decimal form is added
we get (1 + 0._p)
Now the result is obtained is multiplied by n
Required result is
n(1 + 0._p)
[tex]n(1 + \frac{p}{100})[/tex]
In this way the two methods are related
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Como puedo Terminar la sucesion asta el decimo termino 3.8 +2.7
The addition of the decimals given as 3.8 and 2.7 will be 6.5.
What are decimals?Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.
In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:
= 3.8 + 2.7
= 6.5
Therefore, the value is 6.5.
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PLEASE HELP 69 POINTS
Triangle A has vertices (−2, 1), (1, 1), and (1, 0).
Which triangle is similar to triangle A?
Responses
Triangle Y with vertices (−4, 3), (2, 3), and (2, 2)
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)
Triangle X with vertices (−2, 2), (1, 2), and (1, 0)
Triangle Z with vertices (−4, −1), (2, −1), and (2, −2)
The triangle with vertices (−2, 1), (1, 1), and (1, 0) is similar to
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions.
Examining the vertices shows that; Triangle W with vertices (−4, 2), (2, 2), and (2, 0) is in proportion to the given vertices (−2, 1), (1, 1), and (1, 0)
The difference is a scale factor of 2
(−2, 1) * 2 = (−4, 2)
(1, 1) * 2 = (2, 2)
(1, 0) * 2 = (2, 0)
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7. The total cost of Mrs. Goodwin's donut purchase varies directly with the amount of donuts purchased. If
the total cost was $7.50 for 15 donuts, how many donuts can she purchase for $10.00?
The number of donuts that can be purchased for $10 is 20.
The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.
Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.
The price is directly proportional to the number of donuts purchased.
p ∝ n
We will remove the proportionality sign.
p = k*n
7.5 = k*15
k = 1/2
The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.
p = (1/2)n
10 = (1/2)n
n = 10*2
n = 20
Hence, the number of donuts that can be purchased for $10 is 20.
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Can someone help I don’t understand??
Answer:
What you need to do is match with one is a regular, irregular, and or not a polygon.
Each shape has a label like A is a triangle and so on
Put the Label of the shape where it belongs inside the chart
Answer:
If all the sides and interior angles of the polygons are equal, they are known as regular polygons.
C and E are regular polygons.
Irregular polygons are those types of polygons that do not have equal sides and equal angles.
A, B and F are irregular polygons.
3D shapes are irregular polygons.
D is an irregular polygon.
Step-by-step explanation:
A car originally is worth $3000. It is decreasing in value by 3% every year. How much is it worth in 3 years.
(Round to the nearest cent)
Answer: $2738.02
Step-by-step explanation:
1) (3000x0.97) = 2910 } Year 1
2) (2910x0.97) = 2822.7 } Year 2
3) (2822.7x0.97) = 2738.019 } Year 3
How do i solve this equation? 4x - 2y > 12
As per the given equation in form of inequality 4x - 2y > 12 gives the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.
As given in the question,
Given equation in inequality form is :
4x - 2y > 12
Simplify the given equation in intercept form we get,
2y < 4x -12
⇒ y < 2x -6
If we write this inequality in equation form we have,
y = 2x -6
slope of the line is 2
x -intercept is x = 3
y - intercept is y = -6
And in inequality form x > 3 and y < -6.
Therefore, for the given equation in form of inequality 4x - 2y > 12 gives the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.
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Given: AD
Prove: DE
A
D
BC and ZBCD ZADC
CE
C
Intro
B
Correct! Assemble the next
statement.
Angles Segments Triangles Statements Reasons
SAS
CPCTC
reflexive property
Statements
✓1. AD BC
✓ 2. ZDEA and CEB are
vertical angles
3. ZBCD
ZADC
vertical angles theorem
Reasons
1. given
2. def. of vertical angles
3. given
Triangle ADC and ΔBDC are congruent. then DE ≅ CE
What do you mean by congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same form and size.Given,
AD ≅ BC
∠BCD ≅ ∠ADC
In triangle ADC and ΔBDC
AD ≅ BC ( GIVEN )
∠BCD ≅ ∠ADC ( GIVEN )
DC = DC ( Common line)
so triangle ADC and ΔBDC are congruent.
then DE ≅ CE
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students and courses have ....... relationship: a. one to one b. one to many c. many to many d. none. mcq answer
The students and courses have one to many relationship.
A one to many relationship is such kind of relation which exist when a particular function is linked to many other functions. It means that many elements of the set A is related to a single element of the set B.
In this case, the course is only one but the students studying the course are more in number. The same course is studied by many student but in different manner but the course is same. This is why we conclude that the relationship between the students and the course is one to many.
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In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?
Answer:
27
Step-by-step explanation:
You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.
SetupLet t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...
t +(t +5) = 2t+5
The value of the number is ...
10t +(t+5) = 11t +5
The value is 3 times the sum of digits, so we have ...
11t +5 = 3(2t +5)
Solution11t +5 = 6t +15
5t = 10 . . . . . . . . . . subtract (6t+5)
t = 2
(t+5) = 7
The number is 27.
Solve for X please help
Answer:
17
Step-by-step explanation:
4x-10=58(alternate interior angles)
4x=68
x=17
find the median of the following: 14.8, 16.2, 4.8, 12.1, and 6.9. if needed, round your answer to the nearest tenth.
The mean will be the middle number or 12.1.
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "expected value."There are different ways of measuring the central tendency of a set of values. There are multiple ways to calculate the mean. Here are the two most popular ones:Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection.According to our question-
The median is the middle number in the data set when the data set is written from least to greatest.
least to greatest 4.8, 6.9, 12.1, 14.8, 16.2
Hence, The mean will be the middle number or 12.1.
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A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same
amount of time it flew 300 miles against the wind. Find the speed of the wind.
The speed of the wind is 50 mile per hour .
In the question ,
it is given that
the speed of the plane is [tex]=[/tex] 200 miles per hour .
let the speed of the wind is = "w"
So ,the speed of the plane with wind is [tex]=[/tex] 200 + w
and the speed of the plane against wind is [tex]=[/tex] 200 - w
we know that , distance [tex]=[/tex] speed × time
the plane flew "500 miles" with wind ,
which means ,
500 [tex]=[/tex] (200 + w) × t .....(1)
and the plane flew 300 miles against the wind ,
which means ,
300 [tex]=[/tex] (200 - w) × t ......(2)
adding both the equations ,
we get
800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)
800 = t × 400
t = 2
Substituting , t = 2 in 500 [tex]=[/tex] (200 + w) × t
we get
500 = (200 + w) × 2
500/2 = 200 + w
250 = 200 + w
w = 250 - 200
w = 50
Therefore , The speed of the wind is 50 mile per hour .
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a data analyst creates a scatterplot. the analyst wants to put a text label on the plot to call out specific data points. what function does the analyst use?
The analyst should use the alpha aesthetic. The alpha aesthetic makes some points on a plot more transparent than others to call out specific data points.
What is scatterplot?A set of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of correlation, if any, between the values of observed quantities or phenomena, scatter plots are crucial in statistics (called variables). In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.
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Solve for a side in right triangles
Really need help with this one!!
The value of side AC is AC = 3.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
The given triangle ΔABC is a right angled triangle.
So, to find the side AC we can use the cosine ratio,
[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]
AC ≈ 3.
Hence, the length of side AC is 3.
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Determine the next three terms in the following sequence:
2, 3, 5, 8, ____, ____, ____,...
a.
13, 19, 26
b.
12, 17, 23
c.
12, 16, 20
d.
13, 17, 23
Answer:
b. 12, 17, 23
Step-by-step explanation:
Look at the differences between the numbers.
Number Difference
2
3 1
5 2
8 3 The difference increase by 1 at each step. The next 3 increase would be:
4
5
6
The next three numbers are:
12 4
17 5
23 6
Answer:
b.
12, 17, 23
Step-by-step explanation:
avoiding an accident when driving can depend on reaction time. that time, measured from the moment a driver sees the danger until he/she gets his/her foot on the brake pedal, is normally distributed with a mean of 1.5 seconds and a standard deviation of 0.18 seconds. what is the interquartile range of the reaction times? report your answer to at least the nearest hundredth of a second (i.e. with at least two digits after the decimal point).
The interquartile range of the reaction times is 0.528 or 52.80%
A normal model is represented as (μ, σ). Therefore for (1.5, 0.18), the mean (μ) = 1.5 and the standard deviation (σ) = 0.18
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
The z score shows by how many standard deviations the raw score is above or below the mean. It is given as:
The interquartile range is x = 1.45 and x = 1.75
For x = 1.45
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Z=(1.45-1.5)/0.18
= -0.28
For x = 1.75
Z=(1.75-1.5)/0.18
= -1.39
From the normal distribution table,
P(1.45 < x < 1.75) = P(-0.28 < z < 1.39)
= P(z < 1.39) - P(z< - 0.28)
= 0.9177 - 0.3897
= 0.528
= 52.8%
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Can someone help me with this aleks question
For the given triangles ΔTRS and ΔQRP , the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
As given in the question,
Two triangles ΔTRS and ΔQRP,
It is given that :
Line segment SR ≅ Line segment PR
Line segment SP bisects Line segment TQ
⇒ line segment TR ≅ line segment RQ
∠TRS ≅ ∠PRQ ( by vertically opposite angle )
By Side angle side theorem we have ,
ΔTRS ≅ ΔPRQ
Therefore, for the given triangles ΔTRS and ΔQRP ,the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
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Add/Subtract Rational Numbers :
Add ; -1/2 + 2/3 (Simplify)
Evaluate ; -1/8 - (-5/6) (Simplify)
Which of these strategies would eliminate a variable in the system of equations?
2x + 8y = -3
3x + 6y = -4
A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.
B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.
C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations
Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.
Rewriting the equation -
2x + 8y = -3 : Equation 1
3x + 6y = -4 : Equation 2
Multiplying equation 1 with and equation 2 with -2.
6x + 24y = -9 : Equation 3
-6x - 12y = 24 : Equation 4
Adding the equation 3 and equation 4. This will eliminate the variable x.
12y = 15
y = 5/4
So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.
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Please help
The equation y = -8/3x + 40 represents an alternative speed slide the city of Geocove is thinking of constructing in their waterpark. The graph of this equation is shown. Suppose that a rider travels downward 8 feet on this slide. What is the value of their horizontal change?
6 feet
2.7 feet
8 feet
3 feet
The value of their horizontal change is 2.7 feet
How to determine the value of their horizontal change?The equation of the function is given as
y = -8/3x + 40
From the question, the distance travelled by the rider is given as
Distance = 8 feet downward
This means that
Horizontal change = slope
A linear equation is represented as
y = mx + c
Where
Slope = m
By comparing y = mx + c and y = -8/3x + 40, we have
Slope = m = 8/3
This gives
Horizontal change = 8/3
Evaluate
Horizontal change = 2.7
Hence, the horizontal change is 2.7 feet
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2x-84=108
x=?
please help
Answer:
X=
Step-by-step explanation:
Let's solve your equation step-by-step.
2x−84=108x
Step 1: Subtract 108x from both sides.
2x−84−108x=108x−108x
−106x−84=0
Step 2: Add 84 to both sides.
−106x−84+84=0+84
−106x=84
Step 3: Divide both sides by -106.
−106x
−106
=
84/−106x=−42/53
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y, the length of the room
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0How do we obtain the relevant equations that can be used for the problem?First and foremost, we can begin solving this equation by noting the formula for calculating the area of a rectangle. This formula is given as follows:
Area of a rectangle = Length × Width
Since the width of the room is 5 feet less than the length of the room, we will have the resulting equation as the area of the rectangle:
y( y - 5) = 750
When this equation is fully expressed, we will get the following equations:
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0Therefore, options, B, C, and E are correct.
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Simplify negative 1 and 2 over 3 minus 9 and 2 over 5.
11 and 1 over 15
negative 10 and 4 over 8
negative 16 over 15
negative 166 over 15
The simplified form of the given expression; negative 1 and 2 over 3 minus 9 and 2 over 5 as required is; -166/15 (negative 166 over 15).
What is the simplified form of the expression?It follows from the task content that the simplified form of the given expression is to be determined.
Since the given expression is; -1 ⅔ - 9 ⅖.
First, the mixed numbers as in the task content must be converted to fractions so that we have;
- 1 ⅔ = -5/3 and
9 ⅖ = 47/5
Therefore, the required evaluation is; -5/3 - 47/5
= -25/15 - 141/15
= (-25 - 141) / 15
= -166/15
Therefore, the required simplified form of the expression is; negative 166 over 15.
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
32 kg to 56 kg
Answer:
4/7
Step-by-step explanation:
32:56
32÷2=16
56÷2=28
16:28
16÷2=8
28÷2=14
8:14
8÷2=4
14÷2=7
4:7
32:56 ~ 32/56
=4/7
Justify each of the following manipulations to multiply two binomials by filling in the blanks with the associative property the commutative property or the distribution (3x+5)(2x+7)=2x(3x+5)+7(3x+5) helpppp!!
The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
In this question we have been given an expression.
We need to identify the property that is used to multiply two binomials.
(3x+5)(2x+7)=2x(3x+5)+7(3x+5)
Consider two binomials,
(3x+5)(2x+7)
= (2x+7)(3x+5) ...............(commutative property)
= 2x(3x+5)+7(3x+5) ................(distributive property)
Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
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