The solutions to the given problems involve setting up and solving proportions, as well as understanding and applying ratios.
Explanation:1. To solve for the variable n in the proportion n : 1/2 as 6 : 1, we set up the equation n/0.5 = 6/1.
By cross-multiplying, we get n = 3.
2. To find the variable b in the proportion 1/4 is to 1 1/4 as 2 is to b, we write it as 1/4 : 5/4 = 2/b.
Cross-multiplying gives us b = 10.
3. To find out how many total students are there given the ratio of girls to boys is 3 to 2 and there are 15 girls, we use the ratio to find the number of boys 15 girls * (2 boys/3 girls) = 10 boys.
Adding the number of girls to the number of boys (15 + 10) gives us a total of 25 students, which is option (C).
4. For the field trip with 12 adults and 14 students, the ratio of the number of adults to the total number of people is 12/(12+14) = 12/26, which simplifies to 6/13, giving us option (A).
5. If 2d = 5c, the statement that is not true is D) 2/d = c/5, because when dividing both sides by the respective variables, it should be d/2 = c/5.
Final answer:
1. n = 3
2. b = 10
3. Option C: 25
4. Option A: 6 to 13
5. Option D: 2/d = c/5.
Explanation:
To solve for the variable n in the proportion n : 1/2 = 6 : 1,
you cross-multiply to get n * 1 = 6 * (1/2), which simplifies to n = 3.
Therefore, n=3.
To find the value of b in the proportion 1/4 : 1 1/4 = 2 : b,
we cross-multiply again, which gives us (1/4) * b = 2 * (5/4), after simplifying this, we get b = 10/1.
Therefore, b=10.
For the ratio of girls to boys, which is 3 to 2, if there are 15 girls, then for every 3 girls, there are 2 boys.
So, 15 girls represent 5 groups of 3 (because 15/3=5).
If there are 5 groups, then there must be 5 * 2 = 10 boys.
Therefore, adding the girls and boys gives us 15 + 10 = 25 total students, selecting Answer C) 25.
To determine the ratio of the number of adults to the total number of people on the field trip, we have 12 adults and 14 students, therefore the total number of people is 12 + 14 = 26.
The ratio of adults to the total number of people is 12:26, which simplifies to 6:13 after dividing both numbers by 2.
So, Answer A) 6 to 13 is correct.
If 2d = 5c, then dividing both sides by 2c gives us d/c = 5/2 or 2.5.
We can also divide by 2d to get c/d = 2/5.
The incorrect statement would be D) 2/d = c/5, as this doesn't match the original equation when cross-multiplied.
Select the correct answer from each drop-down menu. ∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is units. The length of side BC is units. The length of side AC is units. ∠ABC ≈ °.
Answer:
√50
√65
√145
105 °
Step-by-step explanation:
Given the coordinates
A(-3, 6)
B(2, 1)
C(9, 5)
To find the length of AB ,AC and BC, we will use distance formula
√((x2-x1)² + (y2-y1)²)AB:
√(2+3)² + (1-6)²
√5²+5²
√50
BC:
√(9-2)² + (5-1)²
√7² + 4²
√49+16
√65
AC:
√(9+3)² + (5-6)²
√12²+1²
√145
To find ∠ABC
cos(B) = c² + a² − b² / 2ca
= 65 + 50 - 145 / 2(√65)(√50)
cosB = -0.26311
B = cos^-1(-0.26311)
= 105 °
Answer:
√50
√65
√145
105 °
Step-by-step explanation:
The monthly payment for a home loan is given by a function f(p,r,n)f(p,r,n) where pp is the principal (the initial size of the loan), rr the interest rate, and nn the length of the loan in months. interest rates are expressed as a decimal: a % interest rate is denoted by r=0.06r=0.06. if p=400000,r=0.06p=400000,r=0.06, and n=192n=192(a 16-year loan), then the monthly payment is f(400000,0.06,192)=1195f(400000,0.06,192)=1195. furthermore, with these values we have
a) The monthly payment increases by approximately $6.60 for a $1000 increase in the principal. b) The monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08. c) The monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.
To solve these problems, we'll use the partial derivatives of the monthly payment function with respect to the principal P, interest rate r, and the length of the loan in months N.
Given values:
- Principal P = 450,000
- Interest rate r = 0.075
- Loan term N = 312 (26 years)
- Monthly payment [tex]\( f(450000, 0.075, 312) = 1962 \)[/tex]
Partial derivatives:
- [tex]\(\frac{\partial f}{\partial P} = 0.0066 \)[/tex]
- [tex]\(\frac{\partial f}{\partial r} = 7849 \)[/tex]
- [tex]\(\frac{\partial f}{\partial N} = -1.3672 \)[/tex]
a) The change in monthly payment per 1000 increase in loan principal
The partial derivative [tex]\(\frac{\partial f}{\partial P}\)[/tex] tells us the rate of change of the monthly payment with respect to the principal. To find the change in the monthly payment for a $1000 increase in the principal:
[tex]\[\Delta f \approx \frac{\partial f}{\partial P} \cdot \Delta P\][/tex]
Here, [tex]\(\Delta P = 1000\):[/tex]
[tex]\[\Delta f \approx 0.0066 \cdot 1000 = 6.6\][/tex]
So, the monthly payment increases by approximately $6.60 for a $1000 increase in the principal.
b) The change in monthly payment if the interest rate changes from [tex]\( r = 0.075 \) to \( r = 0.08 \)[/tex]
The partial derivative [tex]\(\frac{\partial f}{\partial r}\)[/tex] tells us the rate of change of the monthly payment with respect to the interest rate. To find the change in the monthly payment for a change in the interest rate from 0.075 to 0.08, we calculate the difference in the rates:
[tex]\[\Delta r = 0.08 - 0.075 = 0.005\][/tex]
Then, using the partial derivative:
[tex]\[\Delta f \approx \frac{\partial f}{\partial r} \cdot \Delta r\][/tex]
[tex]\[\Delta f \approx 7849 \cdot 0.005 = 39.245\][/tex]
So, the monthly payment increases by approximately $39.25 for an increase in the interest rate from 0.075 to 0.08.
c) The change in monthly payment if the length of the loan changes from 26 to 24 years
The partial derivative [tex]\(\frac{\partial f}{\partial N}\)[/tex] tells us the rate of change of the monthly payment with respect to the length of the loan in months. To find the change in the monthly payment for a change in the loan term from 26 years (312 months) to 24 years (288 months), we calculate the difference in months:
[tex]\[\Delta N = 288 - 312 = -24\][/tex]
Then, using the partial derivative:
[tex]\[\Delta f \approx \frac{\partial f}{\partial N} \cdot \Delta N\][/tex]
[tex]\[\Delta f \approx -1.3672 \cdot (-24) = 32.8128\][/tex]
So, the monthly payment increases by approximately $32.81 for a decrease in the loan term from 26 years to 24 years.
The complete question is
The monthly payment for a home loan is given by a function f(P, r, N) where P is the principal (the initial size of the loan), r the interest rate, and N is the length of the loan in months. Interest rates are expressed as a decimal: A% interest rate is denoted by r = 0.075. If P = 450000, r = 0.075 and N = 312 (a 26-year loan), then the monthly payment is f(450000, 0.075, 312) = 1962. Furthermore, with these values we have
[tex]\frac{\partial f}{\partial P}=0.0066, \quad \frac{\partial f}{\partial r}=7849, \quad \frac{\partial f}{\partial N}=-1.3672[/tex]
Estimate
a) The change in monthly payment per 1000 increase in loan principal.
b) The change in monthly payment if the interest rate changes from r = 0.075 to r = 0.08
c) The change in monthly payment if the length of the loan changes from 26 to 24 years.
The function f shown in the graph is an even function. The graph has been hidden for x ≥ 0. Complete the following sentences.
Answer:
1. f is increasing over the interval 0 < x < 2.
2. f(2) = 3
3. f is decreasing over the interval 2 < x < 5.
Answer
increasing
3
decreasing
Step-by-step explanation:
There are two pizzas. Conor ate 1?4 of a pizza, Brandon 2?8, Tyler 3?4, and Audrey 4?8. Who ate the most of the two pizzas?
Answer:
Tyler ate most of the pizza.
Step-by-step explanation:
To make this much easier, we can convert this until it has a common denominator.
For these fractions, that common denominator is 8.
1/4 has to be multiplied by 2 to get 2/8.
2/8 doesn't need to be multiplied by anything to get to 2/8.
3/4 has the be multiplied by two to get 6/8.
Finally, 4/8 doesn't need to be multiplied by anything to get 4/8.
With 6/8 obviously being the biggest number here, we can conclude that Tyler ate the most of the two pizzas.
The scale on a map is 1: 25 000. How many kilometers on the ground is represented by 9 cm on the map?X
1 cm : 25000 cm
Convert 25000cm to km = 1cm : 0.25 km9cm = 9 x 0.25 km9cm = 2.25 kmOn a map with a scale of 1:25,000, 9 cm represents 225,000 km on the ground.
Explanation:To find how many kilometers on the ground is represented by 9 cm on the map, we can use the scale given. The scale is 1:25,000, which means that 1 cm on the map represents 25,000 cm on the ground. Since we want to find the number of kilometers, we need to convert the units. 1 km is equal to 100,000 cm. So we can set up the proportion: 1 cm (on the map) / 25,000 cm (on the ground) = 9 cm (on the map) / x km (on the ground). Cross multiplying, we get 1 * x km = 25,000 * 9 cm. Solving for x, we find that x = 225,000 km.
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the library is 5miles from the post office how many is the yards is the library from the post office
1 mile =1760 yd so 5 miles to the library=8800 yd yards hope this helps
A single die is rolled twice. the 36 equally-likely outcomes are shown to the right. find the probability of getting two numbers whose sum is 7
Answer:
1/6
Step-by-step explanation:
When a die is rolled twice the possible outcomes are:
Here the first value represents the first outcome and the second value represents the second outcome.
S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3),(2,4), (2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6), ( 4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)}
Total outcomes = n(S) = 36
Let A be the event that the sum of both outcomes is 7.
A = {(1, 6) , (2,5), (3,4) , (4,3), (5,2), (6,1)}
n(A) = 6
So, P(A) = n(A)/n(S)
= 6/36
= 1/6
In this scenario, there are 36 potential outcomes when rolling a die twice. Six of these outcomes would lead to a sum of 7. Therefore, the probability of rolling two numbers whose sum is 7 is 1/6.
Explanation:When rolling a single six-sided die twice, the sample space consists of 36 outcomes (since each roll can result in one of six possible outcomes, so 6 outcomes for the first roll times 6 outcomes for the second roll gives 36 total). Now, we need to find the probabilities that would result in a sum of 7. These are: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1. These are 6 possible outcomes. Hence, the probability of getting the two numbers whose sum is 7 is 6 out of 36, or 1/6 when simplified.
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Could you please help me?
Answer:
x = 31
Step-by-step explanation:
AC=BD
3x+7 = 131-x
Subtract 7 from both sides
3x = 124-x
Add x to 3x
4x = 124
Divide by 4
x = 31
Check:
3(31)+7 = 131 - 31
Mulitply 3 times 31 / subtract 131 and 31
93+7 = 100
Add 93 to 7
100 = 100
how would you solve 200 x 30/100? Please give instructions in how you did so.
Answer:
Well first you multiple 200 by 30 which equals 6,000 and then divide it by 100 which then leads you to the answer of 60. Hope I helped. :)
Step-by-step explanation:
Tom is the deli manager at a grocery store. He needs to schedule employees to staff the deli department at least 260260260 person-hours per week. Tom has one part-time employee who works 202020 hours per week. Each full-time employee works 404040 hours per week. Write an inequality to determine nnn, the number of full-time employees Tom must schedule, so that his employees will work at least 260260260 person-hours per week.
Answer:
6
Step-by-step explanation:
260=20+40n
subtract 20
240=40n
divide by 40
n=6
What is the surface area of this cylinder?
A) 6.4 m2.
B) 25.1 m2.
C) 37.7 m2.
D) 62.8 m2.
Answer:
it is c
Step-by-step explanation:
a thermometer read -17° f at 1:00 am. by 2:30 am the temperature has dropped 9.1 degree f. what was the temperature at 2:30 am?
Answer:
The temperature was -26.1° f at 2:30 am.
Step-by-step explanation:
* In this type of problems, we must think about
- What is the meaning of wards;
above and below or
raised and dropped or
increased and decreased
- For above , raised , increase
we will add the value of them to the initial value
- For below , dropped , decreased
we will subtract the value of them from the initial value
* In our problem:
- The reading of thermometer is -17° f at 1:00 am.
- The temperature has dropped 9.1° f when the time was 2:30 am.
* Lets use the explanation above
- We will subtract 9.1 from -17
∴ -17 - 9.1 = -26.1° f
* The temperature was -26.1° f at 2:30 am.
Final answer:
To find the temperature at 2:30 am, you subtract the temperature drop of 9.1°F from the initial temperature of -17°F, resulting in a new temperature of -26.1°F.
Explanation:
If a thermometer read -17°F at 1:00 am and by 2:30 am the temperature has dropped by 9.1 degrees Fahrenheit, we calculate the new temperature by simply subtracting the temperature drop from the initial temperature. Subtracting a negative change from the current temperature results in an even lower temperature because you are going further down the scale.
Here's the calculation:
Initial temperature at 1:00 am: -17°F
Temperature drop by 2:30 am: 9.1°F
New temperature at 2:30 am: -17°F - 9.1°F = -26.1°F
Solve for w
-4w+(2/5)=-(7/2)w-(3/2)
Answer:
-(19/5) or -3.8
Step-by-step explanation:
In this case we put the like terms together as follows
-4w+(7/2)w=(-3/2)-(2/5) note the change of signs when the equal sign. + changes to - and -changes to +.
Therefore -(1/2)w=-(19/10)
dividing both of the equal sign by -(1/2) gives:
w=-(19/10)/-(1/2)
w=-(19/5) or -3.8
Ken drinks 2/7 of a carton of milk each day. How much milk does he drink in 3 days. Be sure to show your work or explain your reasoning
Answer:
6/7 of a carton
Step-by-step explanation:
Option 1:
add: 2/7+2/7+2/7 = 6/7
Option 2:
multiply 2/7 * 3/1 = 6/7
The milk he drinks in 3 days should be 6 by 7.
Given information:Ken drinks 2/7 of a carton of milk each day.
Calculation of milk:Here we have to add [tex]2 \div 7[/tex] three times so it gives [tex]6 \div 7[/tex]
Now the milk should be
[tex]= 2\div 7 \times 3\div 1 \\\\= 6\div 7[/tex]
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Find the length of '' c '' using the pythagorean theorem. A triangle has a height of 5, and length of 12
Answer: 13
Step-by-step explanation:
[tex]5^{2} + 12^{2} = c^{2} \\25 +144= c^{2} \\\sqrt169= \sqrt c^{2} \\13=c[/tex]
lines DE and AB intersect at point C. What is the value of x? A) 12 B) 25 C) 38 D) 52
Answer:
B
Step-by-step explanation:
∠ACE and ∠ECB form a straight angle whose sum = 180°, hence
2x + 2 + 5x + 3 = 180
7x + 5 = 180 ( subtract 5 from both sides )
7x = 175 ( divide both sides by 7 )
x = 25 → C
The value of x if lines DE and AB intersect is 25
How to determine the value of xTo calculate the value of x, we make use of the following supplementary angle formula.
So, we have:
2x + 2 + 5x + 3 = 180
Collect like terms
2x + 5x+ 2 + 3 = 180
Evaluate the like terms
7x + 5 = 180
Subtract 5 from both sides
7x = 175
Divide both sides by 7
x = 25
Hence, the value of x is 25
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Rolling a Red and Yellow Dice
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
A red die and a yellow die are rolled. The outcome "3 on the red die and 4 on the yellow die" can be represented by the ordered pair (3,4). What is the probability that the sum of the die is lucky number 7?
1/2
5/6
1/9
1/6
Answer:
1/6
Step-by-step explanation:
The total number of possible outcomes are:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6) = 36
The possible outcomes with sum 7 from the sample space are:
(1,6)(2,5)(3,4)(4,3)(5,2)(6,1) = 6
The probability with the sum 7 is: [tex]\frac{Desired Outcomes}{Possible Outcomes} = \frac{6}{36}[/tex]
=> [tex]\frac{1}{6}[/tex]
Hence the last option is correct.
(50 Points & Brainliest)
A group of students plotted the number of hours they spent cycling and the number of hours they spent playing football in a week.
Which statement best describes the relationship between the number of hours spent cycling and the number of hours spent playing football?
A) Fewer hours cycled, fewer hours spent playing football
B) Greater hours cycled, greater hours spent playing football
C) Fewer hours cycled, greater hours spent playing football
D) There is no relationship between hours spent cycling and hours spent playing football.
Answer:
Answer: There is no relationship between hours spent cycling and hours spent playing football. I did flvs and I got this question correct.
Step-by-step explanation:
Answer:
D) There is no relationship between hours spent cycling and hours spent playing football.
Step-by-step explanation:
As we can see that the scatter plot dots are distributed very randomly and we cannot form any relation between both conditions. Rather to easily compare both conditions we need two plots with respect to time. So, we can compare the hours spent in cycling and hours spent in playing football.
So, the correct answer would be - There is no relationship between hours spent cycling and hours spent playing football.
Plz help me
When graphed, which function has a horizontal asymptote at 4?
A.f(x)=2x-4
B.f(x)=2(3^x)+4
C.f(x)=-3x+4
D.f(x)=3(2^x)-4
Answer:
It is B.
Step-by-step explanation:
f(x) = 2(3^x) + 4
As x approaches negative infinity 2(3^x) approaches zero and f(x) approaches 4.
Answer:
B.[tex]f(x)=2(3^x)+4[/tex]
Step-by-step explanation:
We have to find that which graph has horizontal asymptote at 4
We know that to find the horizontal asymptote , we simply evaluate the limit of the function as it approaches to infinity or it approaches to negative infinity.
A.[tex]f(x)=2x-4[/tex]
[tex]\lim_{x\rightarrow \infty}(2x-4)=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(2x-4)=-\infty[/tex]
Limit of function does not exits, so function have not horizontal asymptote.
B.[tex]f(x)=2(3^x)+4[/tex]
[tex]\lim_{x\rightarrow \infty}(2(3^x)+4)=\infty[/tex]
[tex]3^{\infty}=\infty [/tex]
[tex]\lim_{x\rightarrow -\infty}(2(3^x)+4)=4[/tex]
Because [tex]3^{-\infty}=0[/tex]
Hence, function have horizontal asymptote at 4.
C.[tex]f(x)=-3x+4[/tex]
[tex]\lim_{x\rightarrow \infty}(-3x+4)=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(-3x+4)=-\infty[/tex]
Hence, function have not horizontal asymptote.
D.[tex]f(x)=3(2^x)-4[/tex]
[tex]\lim_{x\rightarrow \infty}(3(2^x)-4)=\infty[/tex]
Because [tex]2^{\infty}=\infty[/tex]
[tex]\lim_{x\rightarrow -\infty}(3(2^x)-4)=-4[/tex]
[tex]2^{-\infty}=0[/tex]
Hence, function have horizontal asymptote at -4.
Therefore, option B is true.
The cost of three tickets to a movie is at least $20. Select an inequality that represents the cost x (in dollars) of each ticket. Then solve the inequality. Write your solution in decimal form rounded to the nearest cent.
Answer:
[tex]x\geq \$6.67[/tex]
Step-by-step explanation:
Let
x------> the cost of each ticket
we know that
[tex]3x\geq 20[/tex] ----> inequality that represent the situation
solve for x
Divide by 3 both sides
[tex]x\geq 20/3[/tex]
[tex]x\geq \$6.67[/tex]
The cost of each movie ticket, represented by x, can be determined by solving the inequality 3x ≥ 20 which gives the result x ≥ $6.67.
Explanation:The subject problem can be formulated as an inequality problem based on the given information. The cost of three tickets is at least $20. Therefore, we can express it as 3x ≥ 20, with x representing the cost of each ticket.
To solve for x, we would simply divide each side of the inequality by 3. Thus we get x ≥ 20/3.
Converted into decimal form and rounded to the nearest cent, this gives us that x ≥ $6.67. Hence, by solving this inequality, we established that the cost of each movie ticket is at least $6.67.
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Fiona ran 6 laps around a track each lap was 500 meters how far did Fiona run? Circle all that apply
A. 30 kilometers
B. 3 kilometers
C. 3,000 meters
D. 300 meters
the answer to this question is d
A cylinder has a height of 10 cm and a radius of 4 cm. A cone has a height of 5 cm and a radius of 4 cm. How does the volume of the cylinder compare to the volume of the cone? A) It is 2 times larger. B) It is 3 times larger. C) It is 6 times larger. D) It is 9 times larger.
A grocery store has 12 cartons of yogurt for sale, of which 3 are raspberry what is the probability that a randomly selected carton of yogurt will be raspberry?
a) 1/2,
b) 1/4,
c) 1/3
d) 4/5
Answer:
Your answer would be 1/4
Step-by-step explanation:
The probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of sample
Given that a grocery store has 12 cartons of yoghurt for sale, of which 3 are raspberry.
The probability that a randomly selected carton of yogurt will be,
Probability = Number of favourable outcomes / Number of sample
Probability = 3 / 12
Probability = 1 / 4
Therefore, the probability that a randomly selected carton of yoghurt will be raspberry is 1/4. The correct option is b.
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Which of the following is not a commonly used practice? Choose the correct answer below. A. If the original population is normally distributed, then for any sample size n, the sample means will be normally distributed. B. If the distribution of the sample means is normally distributed, and ngreater than30, then the population distribution is normally distributed. C. The distribution of sample means gets closer to a normal distribution as the sample size n gets larger. D. If the original population is not normally distributed and ngreater than30, the distribution of the sample means can be approximated reasonably well by a normal distribution.
Answer:
. B. If the distribution of the sample means is normally distributed, and greater than30, then the population distribution is normally distributed
Using the Central Limit Theorem, it is found that the statement which does not represent a commonly used practice is:
B. If the distribution of the sample means is normally distributed, and n greater than 30, then the population distribution is normally distributed.
The Central Limit Theorem establishes that, for a normally distributed random variable X, the sampling distribution of the sample means with size n can be approximated to a normal distribution. For a skewed variable, the Central Limit Theorem can also be applied, as long as n greater than 30.From this, we have that no matter the distribution, for samples of at least 30, the distribution of the sample means is normal. If the underlying distribution is normal, the sample size is not important.However, we cannot infer anything about the population given the distribution of the sample means, thus, statement B is false.A similar problem is given at https://brainly.com/question/4086221
Find the circumference of a cercle with the radious of 5.5 in. Use 3.14 for n round the nerest tenth
Answer:
34.54 in
Step-by-step explanation:
c = 2π r
c = 2 (3.14)(5.5)
c = 34.54 in
3x − 2y = 6
3x + 10y = −12
Find the common x and y.
x = 1
y = -3/2
Solution: (1, -3/2)
//Hope it helps.
Answer:
(x, y) = (1, -1.5)
Step-by-step explanation:
Subtract the first equation from the second to eliminate the x-variable.
(3x +10y) -(3x -2y) = (-12) -(6)
12y = -18
y = -18/12 = -1.5
Substituting into the second equation, you get ...
3x +10(-1.5) = -12
3x -15 = -12 . . . . . . .simplify
3x = 3 . . . . . . . . . . . add 15
x = 1 . . . . . . . . . . . . . divide by 3
The values of x and y that satisfy both equations are (x, y) = (1, -1.5).
rewrite the following equation in exponential form. log^5 25=2
logb(x) = y is equivalent to b^y =x
y = 2
b = 5
x = 25
Substitute the values to get 5^2 = 25
At a school 141 students play at least one sport. This is 30% of students at that school. How many students are at the school
Answer:
There are 470 students at the school.
Step-by-step explanation:
141 / x = 3 / 10 since 3/10 is equal to 30% you're looking for a denominator that corresponds equally to 141 and when simplified, 141 / x equals 3 / 10.
Use algebra to solve: 141 * 10 = 3x → 1410 = 3x → 470 = x.
Final answer:
There are 470 students at the school.
Explanation:
In the given question, we are dealing with a basic percentage problem. We are told that 141 students, which is 30% of all students at the school, are playing at least one sport. To find the total number of students in the school, we need to solve for the whole when a part and its percentage are known.
Let x represent the total number of students at the school. According to the question:
30% of x = 141 students
We can set up the equation:
0.30 * x = 141
To find x, we'll divide both sides of the equation by 0.30:
x = 141 / 0.30
Performing the division gives us:
x = 470
Therefore, there are 470 students at the school.
Rewrite the expression 5(10+12) using the disruptive of multiplication over addition
Answer:
5·10 + 5·12
Step-by-step explanation:
The distributive property of multiplication over addition says the factor outside parentheses can be applied to each of the terms inside parentheses:
5(10 + 12) = 5·10 + 5·12
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Of course, this can be simplified further if you like, to 50+60 = 110. But we already knew the value of the expression is 5·22 = 110.
Lawrence's father gave him 200 baseball cards. Each week, Lawrence purchase 25 baseball cards to add to his collection. Which inequality can be used to find w, the number of weeks after starting his collection when Lawrence will have more than 750 baseball cards in his collection?
Answer:
it would take 22 weeks to get 750 baceball cards
Step-by-step explanation:
sence you already have 200 and you get 100 every 4 weeks, then thats 20 weeks to get to 700, then add 2 more weeks to get 750