The approximate difference in years for Calvin and Makayla is that B. Makayla invests her money 2 years longer.
Calculations and Parameters:Given:
Interest rate= 5%Deposit of Calvin= $400Final amount after c years= $658.80We use the compound interest formula,
[tex]A= P(1 + r/t)^t[/tex]
[tex]658.8/400= (1205/1200)^1^2^c[/tex]
c= 10 years approx.
For Makayla,
Amount deposited= $300Interest rate= 6%Final amount= $613.4m= ?We use the same formula:
[tex]A= P(1 + r/t)^t\\[/tex]
[tex]613.4/300= (1206/1200)^1^2^m[/tex]
m= 12 years approx.
Hence, the difference in the years would be:
12-10
= 2 years.
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Answer:
Makayla invests her money 2 years longer
Step-by-step explanation:
b on edge
4. At which point does the function y = -x² + 6x - 5 reach its maximum value?
Answer:
(3,4)
Step-by-step explanation:
Hello!
To find the maximum value, we can find the vertex of the graph.
Since the coefficient of x² is negative, the graph opens downwards, meaning that the vertex would be the highest point.
To solve for the vertex, we can convert it to vertex form.
Converty = -x² + 6x - 5y = -1(x² - 6x) - 5y = -1(x² - 6x + 9) - 5 + 9y = -1(x - 3)² + 4The vertex is (3,4)
Please someone help me with this
Answer:
Option c
Step-by-step explanation:
Since tangent = op/adj, in this case the tan37 would be x/1000.
Then, set it up as an algebra problem.
tan37 = x/1000
Multiply both sides by 1000, so 1000tan37=x
that simplifies to x = 753.6
Triangle ABC is rotated 180 degrees about the origin. Describe the relationship between the corresponding angles of triangle ABC and its image
The corresponding angles of triangle ABC and its image are congruent
How to determine the relationship?The transformation rule is given as:
A rotation of 180 degrees about the origin
The rotation transformation is a rigid transformation.
This means that it does not alter the side lengths and the angle measure of the shape being rotated
Hence. the corresponding angles of triangle ABC and its image are congruent
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A telephone company charges a $0.25
connection fee, then $0.10 per minute for
long distance calls. Which statement is
true regarding this situation?
The value of a dependent variable is dependent on the value of an independent variable. The correct option is C.
What are independent and dependent variables?Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.
If a variable is taking its values independently of any visible direct cause, then that variable is called independent variable.The variables who take their values based on some other variables' values are called dependent variables.The complete question is:
A telephone company charges a $0.25 connection fee, then $0.10 per minute for long distance calls. Which statement is true regarding this situation?
A. The rate of change is $0.25 and minutes are the independent variable.
B. The rate of change is $0.25 and minutes are the dependent variable.
C. The rate of change is $0.10 per minute and minutes are the independent variable
D. The rate of change is $0.10 per minute and minute are the dependent variable.
The cost of making a call is the sum of the cost of connection fee which is one time fee and cost $0.25, and the cost charged for a minute which depends on the number of minute for which the call is been established. Therefore, the total cost can be written for a x minute call is,
Total Cost = $0.25 + $0.10(x)
Since the total cost is dependent on x, therefore, x which is the minute is the independent variable. The rate of change is $0.10 per minute and minutes are the independent variable.
Hence, the correct option is C.
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nth term of this quadratic sequence -1,2,7,14,23
Since we know it's quadratic, the n-th term will follow the pattern
[tex]x_n = an^2 + bn + c[/tex]
for some unknown coefficients a, b, and c.
Given that [tex]x_1=-1[/tex], [tex]x_2=2[/tex], and [tex]x_3=7[/tex], we have the following conditions on these coefficients:
[tex]\begin{cases} a + b + c = -1 \\ 4a + 2b + c = 2 \\ 9a + 3b + c = 7 \end{cases}[/tex]
Solve this system to get a = 1, b = 0, and c = -2. Then
[tex]\boxed{x_n = n^2 - 2}[/tex]
To solve the system, use elimination.
[tex](4a + 2b + c) - (a + b + c) = 2 - (-1) \implies 3a + b = 3[/tex]
[tex](9a + 3b + c) - (a + b + c) = 7 - (-1) \implies 8a + 2b = 8 \implies 4a + b = 4[/tex]
[tex](4a + b) - (3a + b) = 4 - 3 \implies a = 1 \implies b = 0 \implies c = -2[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
H
Step-by-step explanation:
every "|" is equal to 0.1
so you count 5 points which will get you to H which is 0.5
In ΔOPQ, o = 500 cm, p = 600 cm and q=380 cm. Find the measure of ∠P to the nearest 10th of a degree.
The measure of ∠P to the nearest 10th of a degree is 84.8°
Law of CosinesFrom the question, we are to determine the measure of ∠P
From the law of cosines, we can write that
[tex]cos \ P=\frac{o^{2}+q^{2}-p^{2} }{2oq}[/tex]
From the given information,
o = 500 cm
p = 600 cm
q = 380 cm
Putting the parameters into the formula, we get
[tex]cos \ P=\frac{500^{2}+380^{2}-600^{2} }{2\times 500 \times 380}[/tex]
[tex]cos \ P =\frac{34400}{380000}[/tex]
[tex]cos \ P =0.0905[/tex]
P = cos⁻¹(0.0905)
P = 84.8076
P ≅ 84.8°
Hence, the measure of ∠P to the nearest 10th of a degree is 84.8°
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1.How many more pupils go to school by tricycle than bicycle?
A.4
B.5
C.3
D.2
2.what is the total number of pupils in grade 6 Simplicity?
A.33
B.28
C.29
D.30
3.what fraction of the pupil in grade 6 Simplicity walk to school?
A.8/33
B.12/33
C.10/33
D.3/33
4.what percentage of the pupil goes to school by walking?
A.24%
B.33%
C.9%
D.36%
Solve for for x:
3x - 2 > 5x + 10
a. X> 6
b. x < 6
c. x < -6
d. X > -6
Answer:
[tex]x < -6[/tex]
Step-by-step explanation:
[tex]~~~~~~3x-2 > 5x+10\\\\\implies 5x+10 < 3x-2\\\\\implies 5x < 3x-2-10\\\\\implies 5x < 3x-12\\\\\implies 5x-3x < -12\\\\\implies 2x < -12\\\\\implies x < -\dfrac{12}2\\\\\implies x < -6[/tex]
What key features do the functions f(x) = 3x and g of x equals the square root of the x minus 3 end root have in common?
Both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.
Both f(x) and g(x) include domain values of [–3, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
Both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions have a y-intercept in common.
Both f(x) and g(x) include domain values of [–3, ∞) and range values of (–∞, ∞), and both functions increase over the interval (–3, 0).
The key features are (a) both f(x) and g(x) include domain values of [3, ∞) and range values of (0, ∞), and both functions are positive for the entire domain.
How to determine the key featuresThe functions are given as:
f(x) = 3x
[tex]g(x) = \sqrt{x -3}[/tex]
Next, we enter the above equations in a graphing calculator.
From the graphing calculator, we have:
The domain of g(x) is [3,∞) and its range is [0,∞)The domain of f(x) is (-∞,∞) and its range is (0,∞)Both functions have positive values for their domainsBy comparing the above highlights, the true statement between functions g(x) and f(x) is option (a)
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The table below shows some inputs and outputs of the invertible function fff with domain all real numbers.
xxx 141414 -6−6minus, 6 -1−1minus, 1 101010 -10−10minus, 10 333
f(x)f(x)f, left parenthesis, x, right parenthesis 777 -10−10minus, 10 -15−15minus, 15 141414 -4−4minus, 4 -9−9minus, 9
Find the following values:
f^{-1}(f^{-1}(7))=f
−1
(f
−1
(7))=f, start superscript, minus, 1, end superscript, left parenthesis, f, start superscript, minus, 1, end superscript, left parenthesis, 7, right parenthesis, right parenthesis, equals
7
f^{-1}(-4)=f
−1
(−4)=f, start superscript, minus, 1, end superscript, left parenthesis, minus, 4, right parenthesis, equals
(thats for the people who copied and pasted it off Khan Academy.)
PS: I DONT KNOW IF IT IS CORRECT!!!!! please, someone check it.
The value of f⁻¹(f⁻¹(7)) is 10
How to determine the value of the expression?The expression is given as:
f⁻¹(f⁻¹(7))
We start by solving the inner expression f⁻¹(7).
The above means that we determine the x value when y = 7.
So, we have:
f⁻¹(7) = 14
Substitute f⁻¹(7) = 14 in f⁻¹(f⁻¹(7))
f⁻¹(14)
Next, we determine the x value when y = 14
f⁻¹(14) = 10
Hence, the value of f⁻¹(f⁻¹(7)) is 10
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Answer:
20
10
Step-by-step explanation:
Indigo needs to order some new supplies for the restaurant where she works. The restaurant needs at least 430 knives. There are currently 269 knives. If each set on sale contains 18 knives, what is the minimum number of sets of knives Indigo should buy? (Help please)
Inequalities help us to compare two unequal expressions. The minimum number of sets of knives Indigo should buy is 8.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
Let the number of sets of knives indigo should buy be represented by x.
Given Indigo needs to order some new supplies for the restaurant where she works and the restaurant needs at least 430 knives. Also, There are currently 269 knives. Now, If each set on sale contains 18 knives the inequality that can represent the minimum number of sets of knives Indigo should buy is,
269+18x≥430
18x≥430-289
18x≥141
x≥7.833
x≥8
Hence, the minimum number of sets of knives Indigo should buy is 8.
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g(x)=-2x-5
what is g(-3)
a.1
b.6
c.-11
d.-6
Answer:
a. 1
Step-by-step explanation:
The question requires us to find the value of the function g(x) when x is -3.
g(x)= -2x -5
This means that for the function of g, when the input value is x, the output value is -2x -5.
For g(-3), x takes on the value of -3. We can thus evaluate the value of g(-3) by replacing x by -3 in the expression -2x -5.
g(-3)
= -2(-3) -5
= 6 -5
= 1
Therefore, a is the correct option.
Additional:
Here is another question on functions which you might wish to check out.
https://brainly.com/question/20922457It's giving me an error whenever I type the question, so might as well just do this.
Answer:
Here is the answer...hope it helps:)
To play a board game, a player spins the pointer of a spinner with four equal sections numbered 1–4, and then flips a fair coin. Use a tree diagram to represent the sample space. What is the probability of spinning either a 3 or a 4 AND flipping a head?
Answer:
2/8
Step-by-step explanation:
there is the 4 sections of a spinner and 2 sides on the coin when you lay it out that leaves 2 opportunities to spin a 3 or a 4 and flipping heads
Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line. 5x + 15< 60
The solution to the given inequality is x < 9
What are inequality
Inequality are expressions not separated by an equal sign, Given the inequality
5x + 15< 60
Subtract 15 from both sides
5x < 60 - 15
5x < 45
Divide both sides by 5
5x/5 < 45/5
x < 9
The number line that describes the solution is attached
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Fill in the missing number in this sequence:
{ } 216, 36, 6, 1
Answer:
1296
Step-by-step explanation:
times each number by 6
example: 1x6=6 6x6=36 36x6=216 216x6=1296
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to fill in the missing number in the sequence
[tex]\star~\mathrm{(~~),216,36,6,1}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Take a look at the common ratio.Since every number is divided by 6, we need to multiply 216 times the common ratio, 6:
[tex]\star~\mathrm{216\times6}[/tex]
Simplify!
[tex]\star~\mathrm{1296}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
Hi, I'm in 7th grade and I'm about to fail Mathematics. Please help me...
x+7=5
Answer:
x=-2
Step-by-step explanation:
x+7=5
To find x, we subtract 7 from both sides, to get x+7-7=5-7
x=5-7
x=-2
Hope this helped!
Answer:
x = -2
Step-by-step explanation:
in order to find x u need to subtract 7 from 5 to get -2. therefore your answer is -2
If you roll a dice four times, what is the chance that you roll a 2?
Answer:
about 51.77%
Step-by-step explanation:
The probability you will roll a 2 is the complement of the probability you will not roll a 2.
__
p(no 2)A die has 6 faces, one of which is labeled with 2. The probability of rolling a 2 on any given roll is 1/6, so is 1-1/6 = 5/6 that a 2 will not be rolled. Sequential rolls of the die are presumed to be independent, so the probability of 4 rolls not showing a 2 at any time is ...
p(no 2) = (5/6)^4 = 625/1296
p(2)The probability that at least one 2 will show up on at least one roll is the complement of this value:
p(some 2) = 1 -625/1296 = 671/1296 ≈ 0.517747
The chance you will roll at least one 2 is about 51.77%.
Tanya and tim clean the house in 3 hours their 3 children at the same 6 hours
how long would it take to clean the whole house if they did it together?
It will take them exactly 4hours 48 minutes.
what is rate?Rate is a measure of a given quantity against a known or standard quantity.
Analysis:
If Tanya and Tim cleaned the house in 3 hours. Then either of them would clean the house in 2 x 3 = 6 hours.
If their 3 children cleaned the house in 6 hours, then each child would clean the house in = 3 x 6 = 18 hours
Total time for cleaning the house = 18 hours + 6 hours = 24 hours
If the five people were to do it at once then time taken to clean the house = 24/5 = 4.8 hours = 4 hours 48 minutes
In conclusion, the time for 5 people to clean the house is 4 hours 48 minutes
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im wondering what is 4.3 x 2.9
Answer:
[tex]\frac{1247}{100}[/tex], or 12.47
Step-by-step explanation:
I looked this up on my scientific calculator. I hope this helps! :)
When Vince does 14 push-ups and 12 sit-ups, it takes a total of 52 seconds. In comparison, he needs 48 seconds to do 12 push-ups and 12 sit-ups. How long does it take Vince to do each kind of exercise?
Answer:
it takes 2 seconds to do one situp
it takes 2 seconds to do one pushup
to do 14 pushups, it takes 28 seconds.
to do 12 situps it takes 24 seconds
to do 12 pushups, it takes 24 seconds
BRAINLIEST PLEASE!
hope this helps :)
Step-by-step explanation:
14x + 12y = 52
12x + 12y = 48
^^^ this is an inequality that we can make.
x stands for pushups
y stands for situps
if we subtract the second equation from the first, we get
2x = 4
x = 2
now we can place x in one of the equations to solve for y
12(2)+12y=48
24 + 12y = 48
12y = 24
y = 2
A caterer charges the same price for each wrap orderd.each bottle of water is also the same price. The cost of buying 50 wraps and 60 water bottles is $445. The cost of buying 60 wraps and 40 water bottles is $470 what is the price?
Answer:it’s in the explanation
Step-by-step explanation:
a. Each wrap costs $2.00, and each bottle of water costs $6.50.
b. Each wrap costs $4.70, and each bottle of water costs $4.70.
c.Each wrap costs $5.30, and each bottle of water costs $3.00.
d. Each wrap costs $6.50, and each bottle of water costs $2.00.
Answer:
The wraps are $6.50 and the water bottles are $2
Step-by-step explanation:
What is the time in 24 hour clock for 03:50 pm?
a.0350 hrs
b.1350 hrs
c.1550 hrs
d.1650 hrs
Answer:
Option C
Step-by-step explanation:
Any evening time on a 24 hour clock will be that hour add 12 :
3:50 pm =
3:50 + 12:00 = 15:50
Option C must be the answer
Hope this helped and brainliest please
Answer:
c.1550 hrs
Step-by-step explanation:
It Is military time to it stays going for 12:00 to 13:00 14:00 15:00 and so on
Hope This Helped
There are 4 quarters, 5 nickels and 3 dimes in a jar. One coin is randomly drawn,
replaced and then another coin is drawn.
What is the probability of getting a quarter then a nickel?
5/36
9/12
9/144
1/5
Answer:
[tex]\displaystyle\frac{5}{36}[/tex]
Step-by-step explanation:
Probability is used to find how likely an outcome is to happen. Probability can be expressed as a fraction with the total outcomes as the denominator and the number of successful outcomes (what you want to happen) as the numerator.
Sample Size
The sample size is the number of possible outcomes. In this case, the sample size will be the total number of coins. To find the sample size we need to add together all of the coins.
4 + 5 + 3 = 12This means that the sample size is 12. For this type of probability, the sample size will serve as the denominator for each probability.
Replacement
In the question, it is stated that coins are replaced. This means that the sample size will not change at any point. So, the denominator will be the same for every probability.
Creating Probability Fractions
We are looking for the probability of getting a quarter and nickel, so we need to find the fractions that represent both situations.
First, let's find the quarter. As stated in the first paragraph, the number of successful outcomes is the numerator. There are 4 quarters, so 4 is the number of successful outcomes. Therefore, 4 will be the numerator. Then, 12 will be the denominator because 12 is the sample size.
[tex]\displaystyle\frac{4}{12}[/tex]Next, we need to find the probability of a nickel. Since there are 5 nickels, there are 5 successful outcomes. Then, the sample size is still 12 because there is replacement.
[tex]\displaystyle\frac{5}{12}[/tex]Complex Probability
Now we have the probability of both a quarter and nickel alone. However, this question asks about the probability of both, so this is an example of complex probability. To find complex probability, you have to multiply each probability together.
[tex]\displaystyle\frac{4}{12} *\frac{5}{12}=\frac{20}{144}[/tex]To reach the final answer we have to simplify the answer.
[tex]\displaystyle\frac{20}{144} =\frac{5}{36}[/tex]This means that the probability of pulling a quarter and then a nickel is 5/36.
24 is 12% of what number?
Answer:
200
Step-by-step explanation:
(24 x 100) / 12
Answer = 200
To solve this problem you multiply 24 by 100 and then divide the total by 12 as follows: (24 x 100) / 12
How to find x for −x/8 < 1.5
Answer:
x>-12
Step-by-step explanation:
We want to the equation so that x is the only thing on the left-hand side.
-x/8 < 1.5 (multiply both sides by 8)
-x < 12
Now, whenever you multiply or divide by a negative when dealing with an inequality, you have to switch the sign.
x > -12.
The diagram shows a convex polygon.
What is the sum of the interior angle measures of this polygon?
°
Answer:
1080
Step-by-step explanation:
PLEASE HELP ME I'M GIVING 20PTS AND MARKING BRAINLIEST!!!!
If sinθ=1/3, what are the values of cosθ and tanθ?
Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:
[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex][tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]What is the trigonometric identity using in this problem?The identity that relates the sine squared and the cosine squared of the angle, as follows:
[tex]\sin^{2}{\theta} + \cos^{2}{\theta} = 1[/tex]
In this problem, we have that the sine is given by:
[tex]\sin{\theta} = \frac{1}{3}[/tex]
Hence, applying the identity, the cosine is given as follows:
[tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex]
[tex]\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2[/tex]
[tex]\cos^2{\theta} = 1 - \frac{1}{9}[/tex]
[tex]\cos^2{\theta} = \frac{8}{9}[/tex]
[tex]\cos{\theta} = \pm \sqrt{\frac{8}{9}}[/tex]
[tex]\cos{\theta} = \pm \frac{2\sqrt{2}}{3}[/tex]
The tangent is given by the sine divided by the cosine, hence:
[tex]\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}[/tex]
[tex]\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]
[tex]\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\tan{\theta} = \pm \frac{\sqrt{2}}{4}[/tex]
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Students in a math class recorded the number of text messages they received the previous day. how many students received at least 10 messages?
Answer:
14 students
Step-by-step explanation:
You didn't include a graph, so I looked up the question to find the graph you are likely talking about.
If this graph does not match, ignore my answer (although the question is exactly the same so I'm guessing it might be the same)
{even if different , conceptually, here is what you do: }
Receiving at least 10 messages includes those who receive 10 messages.
Each X represents 1 student. So, 3 students received exactly 10 messages.
3 (who received 10)
2 (who received 15)
4 (who received 20)
5 (who received 25)
+________
14 students
14 students received ≥ 10 messages
(≥ means greater than or equal to,
< is less than (less < more)
> is greater than (more > less)
the line under includes the value _ (same or more ≥ than this value ; same or less ≤ than this value)
hope this helps you !!