we know that
[tex]I=Prt[/tex]
where
I is the amount in interest
P is the investment
r is the interest rate
t is the time in years
Solve for t
[tex]t=I/(Pr)[/tex]
we have
[tex]I=\$1,400\\ P=\$27,000\\ r=4.2\%=0.042[/tex]
substitute
[tex]t=1,400/(27,000*0.042)=1.23\ years[/tex]
therefore
the answer is
[tex]1.23\ years[/tex]
Using the formula r=d/t, where d is the didtance in miles, r is the rate, and t is the time in hours,at which rate must you travel to cover 185 miles in 2.5 hours
The rate of speed would be 74 mph
Nick works two jobs to pay for college. He tutors for $15 per hour and also works as a bag boy for $8 per hour. Due to his class and study schedule, Nick is only able to work up to 20 hours per week but must earn at least $150 per week. If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?
A.) t + b greater than or equal to 20 15t + 8b = 150
B.) t + b less than or equal to 20 15t + 8b greater than or equal to 150
C.) t + b less than or equal to 20 15t + 8b less than or equal to 150
D.) None of the systems shown represent this scenario.
Answer:
Option B is the correct answer.
Step-by-step explanation:
Earning for tutoring per hour = 15$
Earning for bag boy per hour = 8$
We have Nick is only able to work up to 20 hours per week but must earn at least $150 per week and t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy.
Nick is only able to work up to 20 hours per week
t + b ≤ 20
But must earn at least $150 per week
15 t + 8 b ≥ 150
Option B is the correct answer.
A party host is making identical party bags for guests using 44 bottles of bubbles, 89 stickers, and 55 pencils. What is the greatest number of identical party bags the host can make with the least amount of items leftover? Describe the contents of each bag.
Answer: 11 party bags with 1 sticker leftover
Each bag contains 4 bubbles, 8 stickers, and 5 pencils.
Step-by-step explanation:
Find the GCF of 44 (bubbles), 89 (stickers), and 55 (pencils)
44: 2 x 2 x 11
89: prime so choose 88 with 1 leftover
88: 2 x 2 x 2 x 11
55: 5 x 11
GCF = 11
Disregard the GCF to see how many of that item should go in each bag.
Bubbles: 2 x 2
Stickers: 2 x 2 x 2
Pencils: 5
Joe rented a truck for ine day. There was a base fee of $15.99 and there was an additonal charge of 75 cents for each driven mile joe had to pay $183.24 when he returned the truck for how many miles did he drive the truck
if f(x)=2x and g(x)=1/x, what is the domain of (fg)(x)
Answer: all real #s except x=0
Step-by-step explanation:
Edge 2022
What is the justification for each step in the solution of the equation?
23x−13=2(x+2) Given
2x−1=6(x+2)
2x−1=6x+12 Distributive Property
2x=6x+13
−4x=13 Addition or Subtraction Property of Equality
x=−134
For this case we have the following equation:
[tex]\frac{2}{3}x-\frac{1}{3}= 2 (x + 2)\\[/tex]
If we multiply both sides of the equation by 3 we get:
[tex]2x-1 = 6 (x + 2)[/tex] ---> Multiplication Property of Equality
Applying the distributive property we have:
[tex]2x-1 = 6x + 12[/tex] ---> Distributive Property
Adding 1 on both sides of equality we have:
[tex]2x-1 + 1 = 6x + 12 + 1\\[/tex]
[tex]2x = 6x + 13[/tex] ---> Addition Property of Equality
Subtracting [tex]6x[/tex] on both sides we have:
[tex]-6x + 2x = 6x-6x + 13\\[/tex]
[tex]-4x = 13[/tex] ---> Subtraction Property of Equality
Finally, dividing by -4 on both sides we have:
[tex]\frac{-4x}{-4}= \frac{13}{-4}\\[/tex]
[tex]x = -\frac{13}{4}[/tex]---> Division Property of Equality
Graph x<2
please only answer if you know what your doing
This is the same concept as the previous question. The symbol (<) means it is a dashed line and shaded to the left.
Answer: B
a person who is entitled to social security benefits but is not receiving them would take his or her case to...
A: administrative court
B: Civil court
C: criminal on the state
D: It depends on the state
Answer:
A: administrative court.Step-by-step explanation:
An administrative court is specialize in administrative laws, its concern is mainly about public powers. Basically, the role of these type of courts is to ensure that officials are doing their job according to the law. Some of the issues that matters to an administrative courts are: taxation, dispensation of monetary benefits, environmental licenses, building inspection, child custody, immigration decisions, and more.
So, in this case we are talking about social security, someone is not receiving the benefits from it, so this means that a public institution is not working well, that's an administrative court jurisdiction, because it's in the public sector.
The estimated insurance loss from a hurricane was $18.218.2 billion. This was $12.412.4 billion more than the loss from a tsunami three years later. What was the estimated insurance loss from the tsunami?
Answer:
If you are asking about the difference between the two, the difference is $5,805.80
Step-by-step explanation:
As a farmer, one of your responsibilities is to plow the field to prepare it for planting. On day 1, you plowed of the field. On day 2, you plowed of the field. How much more of the field did you plow on day 1 than on day 2?
Answer:
1/2 more then day 2.
Step-by-step explanation:
The difference in the amount of field plowed on day 1 compared to day 2 is 1/4, assuming day 1 was ½ and day 2 was ¼ of the field.
Explanation:To calculate how much more of the field was plowed on day 1 than on day 2, we need to subtract the fractions that represent the part of the field plowed on each day. However, you did not specify the fractions, so I will assume you meant to say ½ of the field was plowed on day 1 and ¼ of the field on day 2. Thus, the difference can be calculated as follows:
Calculate the difference in fractions: ½ - ¼.Find a common denominator for the two fractions, which is 4 in this case.Convert both fractions to have the common denominator: ½ = 2/4 and ¼ remains the same.Subtract the numerators: 2 - 1 = 1.Write the result as a fraction with the common denominator: 1/4.Therefore, you plowed 1/4 more of the field on day 1 than you did on day 2.
A toy jeep is 12 1/2 inches long while an actual Jeep measures 18 3/4 ft long what is the value of the ratio length of a toy Jeep to the length of a actual Jeep
The length of toy jeep = [tex]12 \frac{1}{2}[/tex]
= [tex]\frac{25}{2}[/tex] inches
The length of actual Jeep = [tex]18 \frac{3}{4}[/tex] feet
We have to find the ratio length of a toy jeep to the length of actual jeep.
Firstly, we will make the dimensions of the both the given lengths same.
As 1 foot = 12 inches
[tex]18 \frac{3}{4}[/tex] feet = [tex]18 \frac{3}{4} \times 12[/tex] inches
=[tex]\frac{75 \times 12}{4}[/tex]
= 225 inches
So, the ratio length of toy jeep to actual jeep
= [tex]\frac{25}{2} \div 225[/tex]
= [tex]\frac{25}{2} \times \frac{1}{225}[/tex]
= [tex]\frac{1}{18}[/tex]
= 1:18
So, the ratio length of a toy Jeep to the length of a actual Jeep is 1:18.
Length of toy jeep = [tex]12\frac{1}{2}=\frac{25}{2}[/tex] inches
Length of actual jeep = [tex]18\frac{3}{4}=\frac{75}{4}[/tex] feet
Now to find the ratio between the two, we must convert both of them in same units. So, lets convert the actual jeep length in feet to inches.
1 feet = 12 inches.
So, [tex]\frac{75}{4}[/tex] feet = [tex]\frac{75}{4}\times12=225[/tex] inches
Ratio of length of toy jeep to actual jeep will be =
[tex]\frac{\frac{25}{2}}{225}[/tex]
[tex]\frac{25}{2\times225}[/tex]
[tex]\frac{25}{450}[/tex] = [tex]\frac{5}{90}[/tex]
ratio is : [tex]\frac{1}{18}[/tex] or 1:18
please try to answer quickly :) thanks
For the 1 and 2/5, go four little lines past the 1.
-1/2, go five little lines in between 0 and -1.
and for -2 1/10, go to -2 and then one little line towards the 3, so it is one little line to the left of -2.
In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =
The angles in the triangle ABC total 120 degrees, verifying it as a correct triangle. Given it is an isosceles triangle with AB and AC being the equal sides of length 6, and by applying the law of cosines, the length of side AC can be calculated.
Explanation:Given the angles of the triangle ABC as m
We can use the Law of Cosines to find the length of the side AC. The Law of Cosines states that c² = a² + b² - 2ab * cos(y). By substituting the given values into this formula, we find AC = sqrt[4² + 6² - 2*4*6*cos(50°)] which gives us the length of side AC.
Learn more about Triangle ABC here:https://brainly.com/question/29285631
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what the value of tge expression 30+(6÷3)+(3+4)
Remember to follow PEMDAS (Parenthesis, Exponents (and roots), Multiplication, Division, Addition, Subtraction)
First, solve the parenthesis
30 + (6/3) + (3 + 4)
30 + 2 + 7
Next, simplify. Combine like terms
30 + 2 + 7 = 39
39 is your answer
~Rise Above the Ordinary
Hello there!
Hint⇒⇒⇒⇒⇒⇒ You had to used PEMDAS.
P-Parenthesis
E-Exponents
M-Multiply
D-Divide
A-Add
S-Subtract
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓↓
[tex]30+(6/3)+(3+4)[/tex]
First you had to calculate with parenthesis first.
[tex](6/3)=2[/tex]
[tex]30+2+(3+4)[/tex]
Then you can calculate with parenthesis again.
[tex](3+4)=7[/tex]
[tex]30+2+7[/tex]
You had to add and subtract from left to right.
[tex]30+2+7=39[/tex]
[tex]=39[/tex]
Answer⇒⇒⇒⇒39
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
helpppppppp? please thank you
The x values are the same for both green dots, so you are looking at a simplified version of the distance formula.
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Since x1 = x2 = 5, the first set of brackets = (5 - 5) = 0
d = sqrt( y2 - y1)^2 )
d = y2 - y1
y2 = 5
y1 = - 1
d = 5 - - 1
d = 6 Answer
Sarah received a gift in a rectangular box with a volume of 240 in3. If the base of the box was 20 in2, how tall was the box? A) 2 inches B) 10 inches C) 12 inches D) 15 inches
Answer:
12 inches
Step-by-step explanation:
volume = length * width * height
volume = (length * width) * height
volume = (area of base) * height
height = volume/(area of base)
height = (240 in^3)/(20 in^2) = 12 in
Answer the box was 12 in bc 20x240divided by 4 =12
What steps would you take to construct an angle bisector? How many arcs would you make?
The steps are as follows:
1. Put the compass at one point on the vertex of the angle and draw an arc that intersects both sides of the angle.
2. Now, draw an arc from each of these points of intersection, in such a way that the arcs intersect in the interior of the angle. Keep the compass open in the same amount throughout this step.
3. Now, draw a ray/line from the vertex of the angle to the intersection point of the two arcs drawn during step 2.
How many arcs would you make? We will draw 3 arcs.
A bag of marbles contains 7 red, 5 blue, 4 red, and 2 yellow marbles. Jon selects a marble, replaces it, then selects another marble. What is the probability that Jon selects a red marble and then a yellow marble?
Question 2 options:
about 0.778 or 77.8%
0.5 or 50%
about 0.043 or 4.3%
0.25 or 25%
[tex]|\Omega|=18^2=324\\|A|=7\cdot2=14\\\\P(A)=\dfrac{14}{324}=\dfrac{7}{162}\approx0.043(=4.3\%)[/tex]
First, we find the total number of marbles.
We add up the red, blue, and yellow marbles:
The number of red marbles is 7 + 4 which equals to 11.
The number of blue marbles is 5.
The number of yellow marbles is 2.
To find the total number, we add these numbers together: 11 (red) + 5 (blue) + 2 (yellow) = 18. So, the total number of marbles is 18.
Second, we find the probability of each event - that is, picking a red marble and then a yellow marble.
Probability is the number of desired outcomes divided by the total number of possible outcomes.
The probability of picking a red marble, denoted as P(red) is the number of red marbles divided by the total number of marbles. So, P(red) = 11 / 18 which is about 0.611 or 61.1%.
The probability of picking a yellow marble, denoted as P(yellow) is the number of yellow marbles divided by the total number of marbles. So, P(yellow) = 2 / 18 which is about 0.111 or 11.1%.
Finally, we can find the answer to our question: What is the probability that Jon selects a red marble and then a yellow marble?
Because these are independent events (selecting a red marble does not affect the chance of selecting a yellow marble next), we can use the multiplication rule of probability to find the overall probability.
The multiplication rule states that the probability of two independent events both happening is the product of their individual probabilities. So the probability of picking a red marble and then a yellow marble, denoted as P(red and yellow), is P(red) * P(yellow).
P(red and yellow) = P(red) * P(yellow) = 0.611 * 0.111 which results in about 0.0679 or 6.8%.
So, the closest option is about 0.043 or 4.3% which seems to be incorrect as our calculated probability is different. There might be a mistake in the question or the provided options.
Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, t, for which the account will have less than or equal to $7,020.
Every year, Sam will have 103% of the amount from the previous year.
[tex]p\%=\dfrac{p}{100}\\\\103\%=\dfrac{103}{100}=1.03[/tex]
After the first year:
[tex]1.03\cdot\$4,500[/tex]
After the second year:
[tex]1.03\cdot1.03\cdot\$4,500=\$4,500(1.03)^2[/tex]
After the t-th year:
[tex]\$4,500(1.03)^t[/tex]
Therefore we have the inequality:
[tex]\$4,500(1.03)^t\leq\$7,020\ \ \ \ |\text{divide both sides by \$4,500}\\\\(1.03)^t\leq1.56\\\\(1.03)^{15}\approx15.56\\\\\text{therefore}\ t\leq15[/tex]
Answer: t ≤ 15.The question is in the attached. Thank yo
C Is your awnser! have a good day Pretty sure its C because theres only 1 line
You and your friend are having a race, but since you are faster than him, you decide to give him a head start. He starts 10m in front of the starting line while you start on the starting line. You run at 6 meters/second, while your friend runs at 5.5 meters/second. After how many seconds will you and your friend be same distance from the starting line? seconds months
Answer:
20 seconds
Step-by-step explanation:
Your friend starts 10 meters in front of the starting line.
You start from the starting line.
You run at 6 meters/ second.
Your friend runs at 5.5 meters/second.
You and your friend will be at the same distance from the starting line only when you are able to catch your friend.
The relative speed between you two is the difference in your speed and your friend's speed that is:
[tex]6-5.5=0.5m/s[/tex]
So to cover 10 meters of separation at the speed of 0.5 meter/second it will take:
[tex]t=\frac{10}{0.5}= \frac{100}{5}=20s[/tex]
So it will take 20 seconds for you and your friend to be at the same distance from the starting line.
Answer:
20 seconds is correct.
Step-by-step explanation:
PLZ help 20pts
Which graph represents the equation y=2/3x−2 ?
The slope-intercept form:
y = mx + b
m - slope
b - y-intercept
We have y = 2/3 x - 2
y-intercept = -2
Only the one graph has that y-intercept (look at the picture).
y = [tex]\frac{2}{3}x[/tex] - 2 means the line will intercept the y-axis at -2 and have a slope (rise over run) of 2 over 3.
Answer: C
△ABC is mapped to △A′B′C′ using the rule (x, y)→(−x, −y) followed by (x, y)→(x, −y) .
Which statement correctly describes the relationship between △ABC and △A′B′C′ ?
A. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.
B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
C. △ABC is not congruent to △A′B′C′ because the rules do not represent a sequence of rigid motions.
D. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a reflection, which is a sequence of rigid motions.
Answer:
B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
Step-by-step explanation:
I just took the test, good luck! Have a wonderful day! :)
Transformation involves changing the position of a shape.
The correct statement is: (b) △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
The transformation rule is given as:
[tex]\mathbf{(x,y) \to (-x,-y)}[/tex], then:
[tex]\mathbf{(x,y) \to (x,-y)}[/tex]
The first transformation [tex]\mathbf{(x,y) \to (-x,-y)}[/tex] is 180 degrees rotation across the originThe second transformation [tex]\mathbf{(x,y) \to (x,-y)}[/tex] is a reflection across the x-axisRotation and reflection are both rigid transformation.
Hence, the correct option is (b):
Read more about rotation and reflection at:
https://brainly.com/question/15577335
Lucia knows the fourth term in a sequence is 52 and the ninth term in the same sequence is 82. Complete the explanation of how she can find the common difference for the sequence. Then use the common difference to find the second term of the sequence
well, I really can't really understand the way you asked the question, But, If it helps I can give you the entire sequence all the way to 82.
The sequence is,
2, 12, 22, 32, 42, 52, 62, 72 , 82, ect...,
Which correctly describes the point of discontinuity of the function?
A real-valued univariate function f=f(x) has a jump discontinuity at a point [tex]x_0[/tex] in its domain provided that
[tex]\lim \limits_{x\to x_0^-}f(x)=A_1[/tex]
and
[tex]\lim \limits_{x\to x_0^+}f(x)=A_2[/tex]
both exist and that [tex]A_1\neq A_2.[/tex]
As you can see at x=-3,
[tex]\lim \limits_{x\to -3^-}f(x)=6,[/tex] [tex]\lim \limits_{x\to -3^+}f(x)=9[/tex] and [tex]6\neq 9.[/tex]
Therefore, there is a jump discontinuity at x=-3.
Answer: correct choice is A.
Five cats each ate 1/4 cup of cat food. How much food did the five cats eat?
Answer: Five cats ate 1 and a quarter of cat food.
Step-by-step explanation
Given:-
Cat food ate by one cat = 1/4 cup
Cat food ate by five cats =[tex]5\times \frac{1}{4} \text{ [Multiplying both sides with 5 ]}\\\\=\frac{5}{4}=\frac{4+1}{4}=\frac{4}{4}+\frac{1}{4}=1+\frac{1}{4}[/tex]=1 and 1/4 cup.
Therefore cat food ate by five cats = 1 and a quarter of cup.[ here a quarter =1/4]
What is the equation of the following graph in vertex form?
Courtesy of Texas Instruments (2 points)
y = (x - 3)2 - 1
y = (x + 3)2 - 1
y = (x - 4)2 - 2
y = (x - 4)2 + 8
For this case we have:
The equation in vertex form of the parabola is given by:
[tex]y = a (x-h) ^ 2 + k\\[/tex]
The vertex is (h, k) and is given by the highest or lowest point of the parabola, in this case it is observed that it is [tex](h, k) = (- 3, -1)\\[/tex]
Thus, the equation is given by:
[tex]y = a (x - (- 3)) ^ 2 + (- 1)\\\\y = a (x + 3) ^ 2-1\\[/tex]
We look for the value of a, substituting a point of the parabola in the equation in the form of vertex, we will take the point [tex](x, y) = (0,8)\\[/tex]
Substituting we have:
[tex]8 = a (0 - (- 3)) ^ 2 + (- 1)\\\\8 = a (0 + 3) ^ 2-1\\\\8 = a (3) ^ 2-1\\[/tex]
[tex]8 = 9a-1\\\\8 + 1 = 9a\\\\9 = 9a\\[/tex]
[tex]a = \frac{9}{9}\\\\a = 1\\[/tex]
Thus, the equation of the parabola is given by:
[tex]y = (x + 3) ^ 2-1\\[/tex]
Answer:
[tex]y = (x + 3) ^ 2-1[/tex]
Answer:
y = (x + 3)2 - 1
Step-by-step explanation:
Explain why a vertical line is said to have undefined slope or no slope.
Which of the following is equivalent to 17g – 2g?
A.) (17 – 2) + g
B.) (17 – 2)g²
C.) (17 – 2) + g²
D.) (17 – 2)g
Hey there!!
Given equation :
17g - 2g
Let;s first look at something which is common in both the terms.
Yes, the alphabet which is common is the ' g '.
Now, let's apply distributive property.
... 17g - 2g
... g ( 17 - 2 )
Hence, the appropriate answer would be ' D '.
Hope my answer helps!
What is the value of x in the equation 3(2x + 4) = –6? (4 points)
–3
1
12
19
3.
The steps below show the incomplete solution to find the value of x for the equation
5x –2x –3 = –2 + 15:
Step 1: 5x –2x –3 = –2 + 15
Step 2: 5x –2x –3 = 13
Step 3: 3x –3 = 13
Which of these is most likely the next step? (4 points)
3x = 16
3x = 10
3x = 39
3x = 3