A. Illustrates whether the two ratios are equal or not using cross the
products. Write your answer on the attached activity sheets.
8
4
12 4
1.
2.
106
155
B. Find the value of N in each of the following proportions.
18
21
3.
In
n 28
12
n
4.
16
64
Answers
The evaluation of the ratios using the product of the factors of the numerator and denominator and cross multiplication and values of n in the proportions in the question are;
A. 1. The ratios \(\dfrac{8}{10}\) and \(\dfrac{4}{6}\) are not equal
2. The ratios \(\dfrac{12}{15}\) and \(\dfrac{4}{5}\) are equal
B. 3. n = 24
4. n = 48
What is a ratio?A ratio indicates the number of times a quantity is contained in another quantity.
The possible ratios in the question, obtained from a similar question are presented as follows;
A. 1. \(\dfrac{8}{10}\), \(\dfrac{4}{6}\)
The expression of the numerator and denominators of the fractions as a product of their factors, we get;
\(\dfrac{8}{10} = \dfrac{4 \times 2}{5 \times 2}\)
\(\dfrac{4 \times 2}{5 \times 2} = \dfrac{4}{5}\)
Similarly, the fraction \(\dfrac{4}{6}\) can be expressed as the product of the factors of the numerator and denominator as follows;
\(\dfrac{4}{6} = \dfrac{2 \times 2}{3 \times 2} = \dfrac{2}{3}\)
\(\dfrac{4}{5} \neq \dfrac{2}{3}\), therefore, the ratios \(\dfrac{8}{10}\) and \(\dfrac{4}{5}\) are not equal
The cross multiplication of the numerators and denominators of the fractions also indicates;
8 × 6 = 24
4 × 10 = 40
Therefore; 8 × 6 ≠ 4 × 10, and the ratios are not equal
2. The ratios are; \(\dfrac{12}{15}\), \(\dfrac{4}{5}\)
Expressing the ratios as a product of the factors of the numerator and denominator, we get;
\(\dfrac{12}{15} = \dfrac{4 \times 3}{5 \times 3} = \dfrac{4}{5}\)
\(\dfrac{4}{5}\) = \(\dfrac{4}{5}\), therefore, the ratios are equal
Using cross multiplication, we get;
12 × 5 = 60
15 × 4 = 60
12 × 5 = 15 × 4, therefore, the ratios, \(\dfrac{12}{16}\) and \(\dfrac{4}{5}\) are equal
B. The specified proportions in the question are presented as follows;
3. \(\dfrac{18}{n} =\dfrac{21}{28}\)
Cross multiplying the proportions, we get;
18 × 28 = 21 × n
n = 18 × 28 ÷ 21 = 24
The value of n is 24
4. The proportions are;
\(\dfrac{12}{16}\) = \(\dfrac{n}{64}\)
Cross multiplying, we get;
12 × 64 = 16 × n
Therefore; n = 12 × 64 ÷ 16 = 48
n = 48
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Related Questions
4.
Triangle DEF is shown below.
E
19-6 m
I
10-4 m
13-2 m
D
It has sides of length 10.4metres, 13.2metres and 19.6metres.
Calculate the size of angle EDF.
Answers
Answer:
111.75 degrees
Step-by-step explanation:
EDF = cos^-1((b²+c²-a²)/2bc)
EDF = cos^-1((10.4²+19.6²-13.2²)/2(10.4)(19.6))
EDF = 111.75 degrees
Suppose we draw a single card from a deck of 52 fair playing cards. what is the probability of drawing an ace or a two?
Answers
The probability of getting an Ace is 1/13.
Probability of an event = number of favorable outcomes for the event/number of all possible products.
First, let's calculate the number of all possible outcomes. Randomly picking the cards could result in each of the 52 being selected. So, there are 52 possible outcomes.
But if you want an Ace in your desired event, you have four options—ace of Spades, Ace of Clubs, Ace of Hearts, and Ace of Diamonds. Therefore, the number of favorable outcomes for Aces = 4.
Therefore,
The probability of getting an Ace with a deck of 52 cards = 4/52 = 1/13.
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factorise fully the following expression (am-an+bm-bn)
Answers
Step-by-step explanation:
am-an+bm-bn
m(a+b)-n(a+b)
(m-n)(a-b)
Answer:
\( \small \sf \: ( m - n ) ( a + b )\)
Step-by-step explanation:
( am - an + bm - bn)
Do the grouping= ( am - an ) + ( bm - bn )
Factor out a in the first and b in the second group= a ( m - n ) + b ( m - n )
factor out common term m - n by using distributive property= ( m - n ) ( a + b )
use the organizer to determine whether the conclusion is valid. step 1: read the situation. Marcus wants to predict the next student council president. He polls every fourth person from each grade level as they exit the cafeteria. In his poll, 65% chose Sophia. So, Marcus predicts Sophia will win the election. Step 2: Determine the type of the sample taken.
Answers
Answer: representative sample
x-y=4 et xy=21 calculer x^3-y^3
Answers
Answer:
316 or -316.
Step-by-step explanation:
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
= 4(x^2 + y^2 + 21)
x - y = 4
xy = 21
Substitute x = 4 + y in the last equation
(4 + y) y = 21
y^2 + 4y - 21 = 0
(y + 7)(y - 3) = 0
y = 3, -7.
So, x = 7, - 3.
So, x and y are 7 and 3 or -7 and -3.
But x^2 + y^2 = 9 + 49 = 58 whichever is true,
So, x^3 - y^3
= 4(x^2 + y^2 + 21)
= 4 (58 + 21)
= 316,
If x = -3 and y = -7 , then the answer is
-316.
You would like to give your daughter $50,000 towards her college education 15 years from now. How much money must you set aside today for this purpose if you can earn 9 percent on your investments?
Answers
To give your daughter $50,000 towards her college education in 15 years, you must set aside approximately $14,803.42 today.
To calculate the amount of money you need to set aside today, we can use the concept of future value of a lump sum. The future value is the amount of money an investment will grow to in the future, given a certain interest rate and time period.
In this case, we want to determine the present value (the amount you need to set aside today) to achieve a future value of $50,000 in 15 years, assuming an annual interest rate of 9 percent. The formula to calculate present value is:
Present Value = \(Future Value / (1 + Interest Rate)^T^i^m^e\)
Plugging in the values, we have:
Present Value = \($50,000 / (1 + 0.09)^1^5\)
Present Value ≈ $14,803.42
Therefore, you would need to set aside approximately $14,803.42 today in order to accumulate $50,000 for your daughter's college education in 15 years, assuming an annual interest rate of 9 percent.
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Please help I will mark as brainliest!!
Answers
Answer:
117°
Step-by-step explanation:
x= 180-101+38= 117°
Use the inequality to help you complete the statements.
w > 4
The w in the inequality is the
The 4 in the inequality is the
Answers
The inequality w > 4 can be used to complete the following statements: The w in the inequality is the variable or unknown value being compared with the number 4. It represents an unknown quantity that is greater than 4.
The 4 in the inequality is the constant or known value that the variable w is being compared to. It is a number that is less than w.
Inequalities use mathematical symbols to compare two values and express their relationship.
In this case, the inequality w > 4 uses the symbol ">" which means "greater than." The inequality indicates that w is larger than 4, so any value of w that is greater than 4 will make the inequality true.
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What is the solution set for |x+3|=5?
S=-9 and 5=8
S=-2 and S=2
S=-8 and 5= 2
S= 2 and 5=8
o
Answers
Answer:
x = -8 and x = 2
Step-by-step explanation:
The given equation resolves into two:
x + 3 = 5-(x +3) = 5The solution to the first can be found by subtracting 3:
x = 2
The solution to the second can be found by multiplying by -1, then subtracting 3.
x +3 = -5
x = -8
The solution set is {-8, 2}.
PLEASE ANSWER
Micaela is searching for the best spot to plant her tomato plants. The east side of her house gets 6 hours and 45 minutes of sunlight each day. The west side receives 7 hours and 15 minutes of sunlight on a daily basis. How much less sunlight does the east side receive?
Keep in mind that there are 60 minutes in 1 hour.
Answers
Answer:
420 + 15 = 435
360 + 45 = 405
435 - 405 = 30.
30 minutes less sunlight
Step-by-step explanation:
Answer:
The east side gets 30 minutes less sunlight.
Step-by-step explanation:
To find the answer we have to subtract 6 hours 45 minutes from 7 hours 15 minutes. As we see that 15 is less than 45, we turn 7 hours 15 minutes to 6 hours 75 minutes, and now we can subtract. 6 hours 75 minutes - 6 hours 45 minutes = 30 minutes. Now, we see that the answer is 30 minutes less sunlight.
2 Points
Chelsea saw an advertisement for a loan that offered 6 months, same as
cash. If she takes the loan, which of these scenarios is most likely to occur?
O
A. Chelsea won't be charged interest for the first 6 months of the
loan, but she will have to make payments for the first 6 months.
O
B. Chelsea will be charged interest for the first 6 months of the loan,
and she will also have to make payments for the first 6 months.
O
C. Chelsea will be charged interest for the first 6 months of the loan,
but she won't have to make payments for the first 6 months.
D. Chelsea won't be charged interest for the first 6 months of the
loan, nor will she have to make payments for the first 6 months.
Answers
Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)
A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.
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Toasty Hands is a manufacturer of battery-powered heated gloves. Its top of the line model currently sells for $279, and it expects sales of 440,000 pairs in the next year. Its estimate of the demand for gloves suggests that if it cuts the price to $239 it could sell 540,000 pairs. What is the absolute value of the elasticity coefficient for Toasty Hands' gloves? Round your answer to two decimals. 1st attempt
Answers
The absolute value of the elasticity coefficient for Toasty Hands' gloves is 394,265.23.
The elasticity coefficient is calculated as follows:
Elasticity coefficient = (Change in demand)/(Change in price) * (Original price)/(Original demand)
In this case, the change in demand is 540,000 - 440,000 = 100,000 pairs. The change in price is 239 - 279 = -40. The original price is $279, and the original demand is 440,000 pairs.
Plugging these values into the formula, we get:
Elasticity coefficient = (100,000)/(-40) * (279)/(440,000) = -394,265.23
The absolute value of the elasticity coefficient is 394,265.23. This means that the demand for Toasty Hands' gloves is elastic, meaning that a small change in price will lead to a large change in demand.
Here is a more detailed explanation of the calculation:
The change in demand is calculated by subtracting the original demand from the new demand. In this case, the new demand is 540,000 pairs, and the original demand is 440,000 pairs. So the change in demand is 540,000 - 440,000 = 100,000 pairs.
The change in price is calculated by subtracting the original price from the new price. In this case, the new price is $239, and the original price is $279. So the change in price is 239 - 279 = -40.
The original price is $279, and the original demand is 440,000 pairs.
Plugging these values into the formula, we get the elasticity coefficient of -394,265.23.
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The graph shows a system consisting of a linear equation and a quadratic equation.
What is the solution to the system?
need it kinda asap
Answers
The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown.
Quadratic and linear equationQuadratic equation are equation that has a leading degree of 2 while a linear equation has a leading degree of 1.
From the given graph, the curve shown has a two solutions which is the point where the curve intersect the x-axis.
For the graph shows a system consisting of a linear equation and a quadratic equation, the solution will be the points where the line intersects the parabola.
The point where the line intersect the parabola are at (1, 8) and (4, 5) which gives the solution to the graph shown
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A computer processes tasks in the order they are received. Each task takes an Exponential amount of time with the average of 2 minutes. Compute the probability that a package of 5 tasks is processed in less than 8 minutes.
Answers
The probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.
Let X denote the time required to process a package of five tasks. X is an exponentially distributed random variable with mean 2 minutes.
The probability of X being less than 8 minutes is given by:
P(X ≤ 8) = 1 - P(X > 8)
= \(1 - (1 - e^{(-8/2)}^{5}\)
= 0.963
Therefore, the probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.
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if a 90onfidence interval for the difference of means 1 – 2 contains all positive values, what can we conclude about the relationship between 1 and 2 at the 90onfidence level?
Answers
At the 90% confidence level, we can conclude that mean 1 is significantly greater than mean 2.
A confidence interval for the difference of means (mean 1 - mean 2) containing all positive values implies that mean 1 is consistently higher than mean 2.
In this scenario, the lower limit of the confidence interval is above zero, indicating that there is a 90% probability that the true difference between the means falls within this interval. Therefore, at the 90% confidence level, we can conclude that there is a significant difference between the two means, and mean 1 is greater than mean 2.
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Integrate the following functions: 6e* dx e²x + C 6xe* + C e* +6+C 6e* +C
Answers
The integral of the given functions is computed. The integral of 6e^x is 6e^x + C, the integral of e^2x is (1/2)e^2x + C, the integral of 6xe^x is 6xe^x - 6e^x + C, and the integral of e^x + 6 is e^x + 6x + C.
To find the integral of a function, we use the rules of integration. In the first case, the integral of 6e^x is obtained by applying the power rule of integration, resulting in 6e^x + C, where C represents the constant of integration. Similarly, for e^2x, we use the power rule and multiply the result by (1/2) to account for the coefficient, resulting in (1/2)e^2x + C.
The integral of 6xe^x requires the use of integration by parts, where we consider 6x as the first function and e^x as the second function. Applying the integration by parts formula, we obtain 6xe^x - 6e^x + C. Lastly, the integral of e^x + 6 is simply e^x plus the integral of a constant, which results in e^x + 6x + C.
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For the vectors u = ⟨2, 9⟩, v = ⟨4, –8⟩, and w = ⟨–12, 4⟩, what is u + v + w? ⟨6, 1⟩ ⟨6, 5⟩ ⟨-6, 5⟩ ⟨-6, 21⟩
Answers
Answer:
< - 6, 5 >
Step-by-step explanation:
Add the corresponding components of each vector, that is
u + v + w
= < 2, 9 > + < 4, - 8 > + < - 12, 4 >
= > 2 + 4 - 12, 9 - 8 + 4 >
= < - 6, 5 >
Answer: C) < - 6, 5 >
Step-by-step explanation: :)
which point on the number line represtens 5 1/8
Answers
Answer:
5.125
Step-by-step explanation:
5 1/8 =(5*8+1)÷(8)
= 41/8
=.125
My teacher asked us what the square root of 144 is
Answers
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Because
I no longer need this to be answered
Answers
Answer:
oh ok hope you got the answer
Step-by-step explanation:
After three years, the value of a new car decreased from $25,000 to
$14,000. What was the percent decrease in the value of the car?
Answers
Answer:
56% decreaseStep-by-step explanation:
In this problem we are required to find the percentage decrease in the value of a car that originally cost $25,000
if the present value is now $14,000
we can solve for the percentage decrease by presentment the original cost of the car by the original cost and multiplying by 100
i.e = (14,000/25,000)*100
= (14/25)*100
= 0.56*100
= 56%
Hence the value of the car has decreased by 56%
solve for the area and perimeter of the swan show all work and include equations?
Answers
Answer:
Step-by-step explanation:
where is the swan?
A radioactive compound with mass 320 grams decays at a rate of 27% per hour. Which equation represents how many grams of the compound will remain after 7 hours?
Answers
Answer:
320 grams ÷ 27% = 8.3 grams
Step-by-step explanation:
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The slope of the line below is -0.5. Enter the equation for the line in point-
slope form.
(1, 1)
Answers
The equation for the line in point-(1, 1) is y = -0.5x + 0.5.
Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.
Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.
To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.
Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5
Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.
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Solve x2 + 6x = -6. If exact roots cannot be found, state the consecutive
integers between which the roots are located.
Answers
x²+6x＝-6 ‖+6
x²+6x+6＝0
x1＝-(6/2)+√((6/2)²-6)＝ -3+√(3) or ≈ -1.267
x2＝-(6/2)+√((6/2)²-6)＝ -3-√(3) or ≈ -4.732
The roots of the quadratic equation, x² + 6x = - 6 are between - 2 and - 1,
and 1 and 2.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, x² + 6x = - 6.
We know in ax² + bx + c = 0, x = ± √(b² - ac)/2a.
∴ x² + 6x + 6 = 0.
x = ± √(36 - 24)/2×1.
x = ± √(12)/2.
x = ± (2√3)/2.
x = ± √3.
We know √3 is between 1 and 2 and - √3 is between - 2 and - 1.
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please hurry!!
An office manager orders one calculator or one calendar for each of the office's 80 employees. Each calculator costs $10, and each calendar costs $15. The entire order totaled $1,000.
Write the system of equations that models this scenario.
Answers
The system of equations that models this scenario is:
x + y = 80
10x + 15y = 1000
Let's define the variables:
Let x represent the number of calculators ordered.
Let y represent the number of calendars ordered.
We can set up a system of equations based on the given information:
Equation 1: The total number of items ordered is 80.
x + y = 80
Equation 2: The total cost of the order is $1,000.
10x + 15y = 1000
These equations represent the number of items and the total cost of the order, respectively. Equation 1 states that the sum of the number of calculators (x) and the number of calendars (y) is equal to 80, which represents the total number of employees in the office. Equation 2 states that the total cost of the order, calculated by multiplying the cost of each calculator by the number of calculators (10x) and adding it to the cost of each calendar multiplied by the number of calendars (15y), is equal to $1,000.
Therefore, the system of equations that models this scenario is:
x + y = 80
10x + 15y = 1000
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The radius of a circle is 6 inches. What is the area of a sector bounded by a central angle measuring 120°
Answers
Knowing that a circle has a radius of 6 inches, the area of a sector with a central angle of 120º is 12π square inches.
The area of a sector can be found using the formula:
Area of sector = (Central angle/360°) × π × r²
Where "central angle" is the angle of the sector in degrees and "r" is the radius of the circle.
In this case, the central angle is 120° and the radius is 6 inches. Plugging these values into the formula, we get:
Area of sector = (120°/360°) × π × 6²
Area of sector = (1/3) × π × 36
Area of sector = 12π square inches
Therefore, the area of the sector bounded by a central angle measuring 120° in a circle with a radius of 6 inches is 12π square inches.
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45+5/6=50 steps please
Answers
Answer:
f
Step-by-step explanation:
from what i know you do division first so when you do that you get
.83 repeasted add theat to 46 and you ger 45.83 with the three repeated
Answer:
To write 45 as a fraction with a common denominator, multiply by 6/6.
45⋅6/6+5/6=50
Combine 45 and 6/6.
(45⋅6)/6+5/6=50
Combine the numerators over the common denominator.
(45(6+5))/6=50
Simplify the numerator.
275/6=50
Step-by-step explanation:
Need Help here Please!
Answers
Answer:
Step-by-step explanation:
To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:
a) To find the value of \(\sf 3(x - y) \\\):
\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)
b) To find the value of \(\sf 6x - 6y \\\):
\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)
c) To find the value of \(\sf y - x \\\):
\(\sf y - x = - (x - y) = -4 \\\)
Therefore:
a) The value of \(\sf 3(x - y) \\\) is 12.
b) The value of \(\sf 6x - 6y \\\) is 24.
c) The value of \(\sf y - x \\\) is -4.
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Consider an investment held over five years with a return of 10% in the first year, 3% in the second year, -5% in the third year, 1% in the fourth year, and 2% in the third year. What is the geometric mean return on the investment?
Answers
The geometric mean return on the investment over the five-year period is approximately 1.9591%.
To calculate the geometric mean return on the investment over the five-year period, we need to find the average return compounded annually.
The formula for the geometric mean return is:
Geometric Mean Return = \([(1 + r_1) * (1 + r_2) * (1 + r_3) * (1 + r_4) * (1 + r_5)]^{1/n} - 1\)
Where r₁, r₂, r₃, r₄, r₅ are the returns for each year, and n is the number of years.
Using the given returns:
r₁ = 10% = 0.10
r₂ = 3% = 0.03
r₃ = -5% = -0.05
r₄ = 1% = 0.01
r₅ = 2% = 0.02
n = 5 (since we have data for five years)
Plugging in the values, we have:
Geometric Mean Return = \([(1 + 0.10) * (1 + 0.03) * (1 - 0.05) * (1 + 0.01) * (1 + 0.02)]^{1/5} - 1\)
\([(1.10) * (1.03) * (0.95) * (1.01) * (1.02)]^{1/5} - 1\)
\([1.192569]^{1/5} - 1\)
\((1.192569)^{0.2} - 1\)
1.019591 - 1 = 0.019591
Therefore, the geometric mean return on the investment over the five-year period is approximately 0.019591, or 1.9591%.
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